docs/tutorials/B_Model_Tutorial_4_Hidden_Markov_Models.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "70d24e61",
   "metadata": {},
   "source": [
    "## Hidden Markov Models\n",
    "\n",
    "author: Jacob Schreiber <br>\n",
    "contact: jmschreiber91@gmail.com\n",
    "\n",
    "Hidden Markov models (HMMs) are a probability distribution over sequences that are made up of two components: a set of probability distributions and a transition matrix (sometimes represented as a graph) describing how sequences can proceed through the model. HMMs are the flagship implementation in pomegranate and were the first algorithm originally implemented.\n",
    "\n",
    "HMMs are a form of structured prediction method that are popular for tagging all elements in a sequence with some \"hidden\" state. They can be thought of as extensions of Markov chains where, instead of the probability of the next observation being dependant on the current observation, the probability of the next hidden state is dependant on the current hidden state, and the next observation is derived from that hidden state. An example of this can be part of speech tagging, where the observations are words and the hidden states are parts of speech. Each word gets tagged with a part of speech, but dynamic programming is utilized to search through all potential word-tag combinations to identify the best set of tags across the entire sentence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d4ba80d9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n",
      "numpy      : 1.23.4\n",
      "scipy      : 1.9.3\n",
      "torch      : 1.13.0\n",
      "pomegranate: 1.0.0\n",
      "\n",
      "Compiler    : GCC 11.2.0\n",
      "OS          : Linux\n",
      "Release     : 4.15.0-208-generic\n",
      "Machine     : x86_64\n",
      "Processor   : x86_64\n",
      "CPU cores   : 8\n",
      "Architecture: 64bit\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "import seaborn; seaborn.set_style('whitegrid')\n",
    "\n",
    "import torch\n",
    "\n",
    "numpy.random.seed(0)\n",
    "numpy.set_printoptions(suppress=True)\n",
    "\n",
    "%load_ext watermark\n",
    "%watermark -m -n -p numpy,scipy,torch,pomegranate"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c06a7df3",
   "metadata": {},
   "source": [
    "### Identification of GC-rich regions of the genome\n",
    "\n",
    "Lets take the simplified example of CG island detection on a sequence of DNA. DNA is made up of the four canonical nucleotides, abbreviated 'A', 'C', 'G', and 'T'. We can say that regions of the genome that are enriched for nucleotides 'C' and 'G' are 'CG islands', which is a simplification of the real biological concept but sufficient for our example. The issue with identifying these regions is that they are not exclusively made up of the nucleotides 'C' and 'G', but have some 'A's and 'T's scatted amongst them. A simple model that looked for long stretches of C's and G's would not perform well, because it would miss most of the real regions.\n",
    "\n",
    "We can start off by building the model. Because HMMs involve the transition matrix, which is often represented using a graph over the hidden states, building them requires a few more steps that a simple distribution or the mixture model. Our simple model will be composed of two distributions. One distribution will be a uniform distribution across all four characters and one will have a preference for the nucleotides C and G, while still allowing the nucleotides A and T to be present."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3770cbc1",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pomegranate.distributions import Categorical\n",
    "\n",
    "d1 = Categorical([[0.25, 0.25, 0.25, 0.25]])\n",
    "d2 = Categorical([[0.10, 0.40, 0.40, 0.10]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5939f6a7",
   "metadata": {},
   "source": [
    "Now we can define the HMM and pass in states. Note that in pomegranate v1.0.0, HMMs are split into two implementations: `DenseHMM`, which has a dense transition matrix and so can use standard matrix multiplies in the backend, and `SparseHMM`, which has a sparse transition matrix and uses more complicated scatter-add operations. Also note that you no longer need to wrap the distributions in `Node` objects. You pass the distributions in directly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2b033a88",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pomegranate.hmm import DenseHMM\n",
    "\n",
    "model = DenseHMM()\n",
    "model.add_distributions([d1, d2])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99ab6ba2",
   "metadata": {},
   "source": [
    "Then we have to define the transition matrix, which is the probability of going from one hidden state to the next hidden state. In some cases, like this one, there are high self-loop probabilities, indicating that it's likely that one will stay in the same hidden state from one observation to the next in the sequence. Other cases have a lower probability of staying in the same state, like the part of speech tagger. A part of the transition matrix is the start probabilities, which is the probability of starting in each of the hidden states. Because we create these transitions one at a time, they are very amenable to sparse transition matrices, where it is impossible to transition from one hidden state to the next. Note that we are passing in distribution objects, not node objects as in the previous version, here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a3a45214",
   "metadata": {},
   "outputs": [],
   "source": [
    "model.add_edge(model.start, d1, 0.5)\n",
    "model.add_edge(model.start, d2, 0.5)\n",
    "model.add_edge(d1, d1, 0.9)\n",
    "model.add_edge(d1, d2, 0.1)\n",
    "model.add_edge(d2, d1, 0.1)\n",
    "model.add_edge(d2, d2, 0.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad8c3b70",
   "metadata": {},
   "source": [
    "Another big change is that we no longer need to bake the HMM once we're done!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "453e2e92",
   "metadata": {},
   "outputs": [],
   "source": [
    "#model.bake()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08cc2637",
   "metadata": {},
   "source": [
    "Now we can create a sequence to run through the model. Make sure that this sequence has been converted to a numeric representation of categories. This can be done either simply, as below, or using a preprocessing tool from some other package like scikit-learn. Also, make sure that your input sequence is 3D with the three dimensions corresponding to (batch_size, sequence length, dimensionality). Here, batch_size and dimensionality are both 1. The inclusion of batch size helps significantly when processing several sequences in parallel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a3f465b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 51, 1)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sequence = 'CGACTACTGACTACTCGCCGACGCGACTGCCGTCTATACTGCGCATACGGC'\n",
    "X = numpy.array([[[['A', 'C', 'G', 'T'].index(char)] for char in sequence]])\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66ee1c74",
   "metadata": {},
   "source": [
    "Now we can make predictions on some sequence. Let's create some sequence that has a CG enriched region in the middle and see whether we can identify it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "77aba624",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sequence: CGACTACTGACTACTCGCCGACGCGACTGCCGTCTATACTGCGCATACGGC\n",
      "hmm pred: 000000000000000111111111111111100000000000000001111\n"
     ]
    }
   ],
   "source": [
    "y_hat = model.predict(X)\n",
    "\n",
    "print(\"sequence: {}\".format(''.join(sequence)))\n",
    "print(\"hmm pred: {}\".format(''.join([str(y.item()) for y in y_hat[0]])))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66fb5e21",
   "metadata": {},
   "source": [
    "It looks like it successfully identified a CG island in the middle (the long stretch of 1's) and another shorter one at the end. More importantly, the model wasn't tricked into thinking that every CG or even pair of CGs was an island. It required many C's and G's to be part of a longer stretch to identify that region as an island. Naturally, the balance of the transition and emission probabilities will heavily influence what regions are detected.\n",
    "\n",
    "Let's say, though, that we want to get rid of that CG island prediction at the end because we don't believe that real islands can occur at the end of the sequence. We can take care of this by adding in an explicit end state that only the non-island hidden state can get to. We enforce that the model has to end in the end state, and if only the non-island state gets there, the sequence of hidden states must end in the non-island state. Here's how:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7ac4a61d",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = DenseHMM()\n",
    "model.add_distributions([d1, d2])\n",
    "model.add_edge(model.start, d1, 0.5)\n",
    "model.add_edge(model.start, d2, 0.5)\n",
    "model.add_edge(d1, d1, 0.89 )\n",
    "model.add_edge(d1, d2, 0.10 )\n",
    "model.add_edge(d1, model.end, 0.01)\n",
    "model.add_edge(d2, d1, 0.1 )\n",
    "model.add_edge(d2, d2, 0.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "533e21a1",
   "metadata": {},
   "source": [
    "Note that all we did was add a transition from n1 to model.end with some low probability. This probability doesn't have to be high if there's only a single transition there, because there's no other possible way of getting to the end state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e1a4e059",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sequence: CGACTACTGACTACTCGCCGACGCGACTGCCGTCTATACTGCGCATACGGC\n",
      "hmm pred: 000000000000000111111111111111100000000000000000000\n"
     ]
    }
   ],
   "source": [
    "y_hat = model.predict(X)\n",
    "\n",
    "print(\"sequence: {}\".format(''.join(sequence)))\n",
    "print(\"hmm pred: {}\".format(''.join([str(y.item()) for y in y_hat[0]])))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff42a49b",
   "metadata": {},
   "source": [
    "This seems far more reasonable. There is a single CG island surrounded by background sequence, and something at the end. If we knew that CG islands cannot occur at the end of sequences, we need only modify the underlying structure of the HMM in order to say that the sequence must end from the background state.\n",
    "\n",
    "In the same way that mixtures could provide probabilistic estimates of class assignments rather than only hard labels, hidden Markov models can do the same. These estimates are the posterior probabilities of belonging to each of the hidden states given the observation, but also given the rest of the sequence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d80b5c2e",
   "metadata": {},
   "outputs": [
    {
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SSy9tsb1CCCGcz5K86i4zaaCz5owoCtRV2vivyo59W/hnx4dsSUkJf/zxB7NmzWoUiFhYejrWrFlDSUkJN998c7PHsnUF3O+++453332X+fPn88MPP7Bw4UISExNbPO68efP48ssveeqpp1i/fv1pq/nW1NTwzjvv8Mwzz/DBBx+QnZ3N008/bX38nXfeYcWKFTzxxBN8+OGHlJWV8dNPP9nUXiGEEM7hbsmr0Bl7RhQF3jkXMv9sdVcd4O+o88aMgRu/AxuCg6NHj6IoCn369Glxv8OHDwPQu3dv6307duzg+uuvt/7/hRdeYMqUKa2eMzs7m/DwcMaNG4enpyfR0dEMGTKk2f0tvSkAMTEx3HXXXTz66KM8+uij1vvr6+uZP38+sbGxAMyaNYuFCxdaH1+yZAlz587l3HPPRVEU/vnPf7J+/fpW2yqEEMI5ymvqOVxQCUgw4gLaLoXcGstQha29Gifr378/K1euBOCcc86xOfHovPPOY8mSJZx11llMnDiRyZMnM2XKFDw8mn4JrF+/njfeeIMDBw5QUVGByWSitraWqqoqa2+Or6+vNRABiIyMpLCwEIDy8nLy8/NJTU21Pu7h4cHgwYNlqEYIITSyO7scgOggH8K6eWvcmhM6XzCi06k9FPVVre6qKApVVdX4+fm2KTBoxNPPpl4RgLi4OHQ6HQcPHuSss85qdr/4+HhA7SFJSUkBwMvLi7i4OLub16NHD7777jvWrFnDunXrmD9/Pm+//Tbvv/8+np6ejfY9duwYc+fOZebMmdx1110EBQWxefNm5s2bh9F4YpnpUwMZnU4ngYYQQrgxdyt2ZtH5ghFQgwIvGwZgFAWMOvCyPZBwhODgYCZMmMDSpUuZPXv2aXkjZWVlBAYGMn78eIKDg3nzzTd59dVX231eHx8fzjzzTM4880yuueYazj//fPbt28egQYMa7Zeeno7JZOLBBx9Er1fTir799lu7zhUQEEBERATbtm1j5MiRABiNRnbu3MnAgQPb/bMIIdrHbFY4VlLN3pxy9uaWsyennH055XQP8uHVa1IJ8PFs/SCiw0lvmNbrTkM00FmDkQ7gkUce4eqrr2bGjBn87W9/IykpCZPJxJo1a1i2bBnffvst/v7+PP7449xzzz3MnTuX2bNnEx8fT2VlJX/88QeANVhozWeffYbJZGLo0KH4+vryv//9Dx8fH6Kjo0/bNzY2FqPRyPvvv8/UqVPZvHkzH330kd0/43XXXcebb75JfHw8ffr04c0336SsrMzu4wgh2i+ruIofd+Vag499OeVU1p0+zLs3t5y/friVt68fgYehc85x6Mp2HnOvNWksJBjRSExMDJ999hmvv/46Tz/9NHl5eYSGhjJo0KBGSaJnn302y5Yt48033+SBBx6gtLSUbt26MXjwYF588UWbkldBnaGzaNEinnrqKcxmM4mJibz++uuEhISctu+AAQN46KGHePPNN3nhhRcYMWIE9957Lw888IBdP+ONN95Ifn6+tYflkksu4ayzzqKiosKu4wgh2ie7tJrz//MH5bXGRvd7GnQkRHSjf1QAiVEBhPt78/AX6fy2L59HvtjJ45cNbv8QtnAbNfUmDuSr77+D3WyYRqd0gEF+k8nEtm3bSElJwWBovNRxTU0Nhw8fpnfv3vj4+Nh1XDVnRE3IlD8453LVtW7P66EzaOlvRThOR7vOf/1wC1/tyKZPuD8XDulBYvcA+kcFEB/uj+cpvR/fpedw29LNKAr868IB3Dyx5Vl/ztTRrrO725ZZwmWvriG8mxcb551lfS925nW29djSMyKEEJ3Y2oMFfLUjG70OXr4mlUGtdM+fNziKf54/gCe+2c0T3+wmJtSPcwdFuai1wpmsyavRQW73BVwGBIUQopOqN5l55H87AZg1Oq7VQMTi5om9mTU6FkWBuz7ayo6sEie2UrjKTjdNXgUJRoQQotNasjaD/XkVhPp78fdzmq+4fCqdTsf8SwYxOTGCmnozNy3ZZF3lVXRc6ZbkVTfLFwEJRoQQolPKK6vhPz/tB+D+c5MI9vOy6/keBj2vXJNK/6gA8struXHxRspr6p3RVOEC9SYze3PUgmfuNpMGJBgRQohO6alv91BRa2RoryCuHBHTpmME+Hjy9g0jiQjwZm9uOXd8uBWjyezglgpX2J9bQZ3JTICPBzGhvlo35zSdJhjpAJOChAvI60AI2JhRxGdbj6HTwb8vHYxe3/ZkxZ7Bvrxz/Uh8PQ383jDlV/7OOh5LsbPBbpi8Cp0gGLGUMq+qar38u+j86urqAGQaoOiyjCYz/7cyHYCZI2MYGhPc7mMm9wripZkp6HSw9M+jvPXH4XYfU7jWzmPum7wKnWBqr8FgIDg4mLy8PAC76lgoikJtbS16vd4tI8XOxBXX2mw2k5+fj5+fX7MLAArR2S398yh7csoJ8vXkH+f2d9hxzxkUxbwLBvD417t56rs9XDw0mqigrlfLp6Paedx9k1ehEwQjAFFR6hx4S0BiK0VRqK+vx9PTU4IRJ3PVtdbr9cTGxsrvU3RJBRW1PP/DXgDuOzeJUH/7klZbc9OE3ny5/Tjbs0r5fV8+V45sWy6KcC2TWWFXtiUYkZ4Rp9HpdPTo0YPIyEjq623P9jaZTOzZs4e+fftKt76Tuepae3l52bxejxCdzTPf7aGsxsig6ECuGRXr8OPrdDomJ0WyPauU3/ZLMNJRHC6opKrOhK+ngd7h3bRuTpM6RTBiYTAY7PqgM5nURaJ8fHwkGHEyudZCONfWo8V8sikLgH9fOghDO5JWWzI5MZz//ryf1fsLMJkVp51HOI6l2NnA6EC3/X3JV0ghhOjgTGaFhxsqrU4f1ovhcaFOO9fQXsEE+HhQWl0vlVk7CEu+iLsmr4IEI0II0eF9vDGTtGOlBHh78OD5jktabYqHQc+EvuEA/L6vwKnnEo5hWZPGHYudWUgwIoQQHVi9ycxzDUmr95ydSESAt9PPOSkxAoDf9+c7/VwdzbGSar7acZz0Y6VU15m0bg6KopxYIM9Nk1ehk+WMCCFEV7M3p5yiyjoCfDy4bmycS85pCUa2ZZZQWl1PkK+nS87r7uqMZq55cz1HCtW6VzqdWjSuX2Q3+kZ2o19kAH27q9uBPq65ZlnF1ZTVGPEy6OkXGeCSc7aFBCNCCNGBbW/I20iJCcbD4JrO7p7BviRE+HMwv5K1Bwo4P7mHS87r7pZtOMqRwir8vAz4eBooqqwjq7iarOJqft3buBcpIcKfZbeMITLQubVaLL0iSVEBeHm472CIBCNCCNGBbc8sAWBIL9fmA0xKjOBgfiW/7cuXYASorDXy8i/qwoT/vGAA146Jo7CilgN5FezPq+DASf9yymo4mF/Ju2szuP885+b4dITkVZBgpENRFIU3/zjEh38e5cHz+3PeYHkDEKKr25GlfvMd2ivYpeedlBjB4jUZ/L4vH0VRunyhwXdWH6agoo64MD+uaqi/EtbNm7Bu3ozuE9Zo32/Ssrl96RY+2pjJ387sh4+n88odbDlaDMAgN628auG+fTaikeo6E3d9tI0nv9lDRmEVd3+8zTp3XAjRNVXWGtmXqy4Ln+KANWjsMaZ3GF4eeo6X1nAwv8Kl53Y3RZV1vPH7IQD+fk4Snq0Ml50zsDvRQT4UVdbx1Y5sp7XrQF45aw8WotPBxIYZUO5KgpEOIKu4iumvreWL7cfx0OvoHxVATb2Zue9tpqiyTuvmCSE0kn6sFLMCPYJ8nJ57cCpfLwOj4tV6Jr918Sm+C389QEWtWvn2IhuGrDwMeq5tSDZesjbDaasgWxY0PHtAd+LD/Z1yDkeRYMTNrTtYyCWvrGFXdhlh/l4svXk0H88dS1yYH8dKqvnrh1swmsx2H3fxmsOMeuInPtpw1AmtFkK4giV51dVDNBaTEi31RrruFN9jJdW8t/4IAPef1x+9jRVOZ46MxctDT9qxUrYcLXF4u/LLa/ls6zEAbpnUx+HHdzQJRtyUoigsWZvBtW//SVFlHYN7BvLFnRMY3SeMID9P3rxuBH5eBtYeLGTBt3vsOu6z3+9h/pe7yCuvZd7KdNYc6NrfaoToqLZnqkO1Q2K0yQewTPH983AhNfXa19TQwks/7aPOaGZMn1Am9bN9KCTU34tLh0YD8N66DIe36/31R6gzmkmJCWZEXIjDj+9oEoy4oVqjiQdW7OCRL3ZiMitcmhLNp38ZR89gX+s+id0DeOHKoQC8vfown23JavW4JrPCPz9P59VfDwIwoEcgJrPC7Uu3cKSwsk1tzSio5N9f7rKOWwshXGdbw0yaFI16RpK6B9A90JuaejMbM4o0aYOW9ueWs3yz+t57/3n97U7ivX5cPKAmtOaV1zisXdV1Jt5vCHBumdinQyQXSzDiZnLLapi5aD2fbMpCr4N5FwzgP1el4Ot1erb1eYN78NcpfQF46LM063zyptQaTfz1wy0s23AUvQ4WTEvm89vHkRITTGl1PTcv2UR5je0rHgPsySnjitfX8s6aw1z71p/klTnuj0kI0bKCilqOlVSj08FgF0/rtdDpdEzq11CNtQsO1Tz3w17MCpw7qDvDYu3vfRjcM4jhcSHUmxQ+/NNxQ+YrtmRRXFVPrxBfzh3U3WHHdSYJRtzIgbxyLn55NVuPlhDk68m7c0Zxy6SWo9p7zk5kav9Iao1m5r63iYKK2tP2qag1MmfxRr5Nz8HLoOfVa4Zx9ahYfDwNLJo9nO6B3uzPq+Duj7ZhMtuWSJWWVcrMRespqFATaPPKa7n1g83UGrtmV60QrmZZpC4hwnXVPJtiLQ3fxZJYtx4t5vudueh1cN85SW0+jqV3ZOmfR6kz2p//dyqzWeHt1Wri6k0TerusEF57dYxWdhEv/XyAvPJaErt344u/jrf+kbfEoNfx4lUp9A7353hpDXcs3UL9SQmthRW1XL1oPWsPFuLvZeDdOSMbFSiKDPRh0ewReHvo+XlPnnWNi5ZsPlLENW+up6SqnpSYYP53x3gCfTzYcrSER7/Y1aaf/du0bKY+v4qPN0pCrRC22JapTX2RU03oG45OB3tzy8kp7Rq9o4qi8PR3aq7e9GG96Ne97WXWzxsURWSAN/nltXyb3v5pvj/tzuVwQSWBPh5cOSKm3cdzFQlG3ITJrLC6YdGpJy5PJi7M9mlYQb6eLJo9HH8vA38eLuKJr3cDapb3jNfXkXaslFB/L5bNHcO4JuaaD40J5pkrhgDw2qqD/G/bsWbPtfZAAbPf3kB5rZFRvUP54ObRDI0J5r9Xp6LTqeWQl/55xJ4fnU82ZXLHh1s4lF/JvM/T2Xyk2K7nC9EVWSqvpmiUvGoR4u/FkIaAqKsM1fy+v4D1h4rw8tBz99mJ7TqWl4eea0bHAvDeOvveO5timc57zeg4/L07Tl1TCUbcRPqxUoqr6gnw9mhT8aJ+3QN44aoUAN5dm8F/ftrH9IVrOVRQSc9gXz69daz1DaMpl6b05LYzEgC4f/kO6xvdyX7dm8ecdzdSVWdiYr9wlswZRbeGF/sZSZH841y1q/LRL3ayycZktsVrDnP/8h2YFYgK9MFoVvjbsq2UVEn9FCGaoyiKdVpvS3/XrjK5YRbJb11gFV+zWeGZhl6R68bENZpY0FbXjI7F06Bj85HiFnP/WrMts4QNGUV4GnTc0DD801FIMOIm/mj4Ix7XN6zV6n3NOXdQFH87sx8A//lpPzllNfSN7Mby28aSENGt1ef/45wkzhrQkH/y/qZGCanfpWcz971N1BrNnDWgO29dP+K0pNrbJidwYXIP6k0Kty3d0mKXraIovPLLfuZ/qQ7r3DyhNz/cO4n4hvop93263WmFgITo6DKLqimpqsfLoKd/D+1XYrUMKa/eX2Bz3llH9VVaNjuPl9HN24PbGyYQtFdkgA8XNAyfv7s2o83HefMPtQrsxUOjiQpybRG89pJgxE1Ykr9syRNpyd1n9uOsAZGAWh7607+MpUeQbZG7viH/pF9kN3LLapn7/mZq6k38b9sx7vhwK/UmhQuH9OC1a4fh7XH67B6dTsczVwyhf1QA+eW1/OWDzU3WHlAUhae+3cNzP+wD4J6zEpl34QACfTx55ZpheBn0/LQ7z5qEJYRobFtDr8iA6MAm/xZdLSUmmAAfD0qr662JtZ1RvcnM8w15dXMn9SHU38thx7Yksn6x/TiFTUxEaE1mURXfpqk5JzdPcP8iZ6eSYMQNlNfUWxczskyTayu9XsfCWcP54KbRfDR3DCF2/rEE+Hjy1vUjCPL1ZFtmCTMXrefuj9VZNtOH9eK/M1Nb7Lnx9/Zg0Wz1+dszS3j4f+mNejjMZoV/rUy3ruPwrwsHcNdZ/awzhgb3DOL/LhoAwFPf7mHrUckfEeJU1nwRjab0nsrDoGd8gqUaa+edVfPxxkyOFFYR3s2Lmyb0duixU2OCSe4ZRJ3RzMebMu1+/uI1GZgVmNgvnIFuvkJvUyQYcQNrDxZiNCv0DvcnJtSv3cfz8tAzoV94m1eCjAvzZ+GsYRj0OrZllqAocO2YWJ69YggGG0odx4b58fLVqeh18MmmLD5oKJVsNCvct3wHS/88ik4HT01L5uaJp0fw146J48LkHhjNCn/9cCulVfbVPxGis7MEI0NdvDheS6xTfDtx3ohlCOWvU/o6PDlUp9NZe0c+WHfErmU+SqvrrTMRm3pP7QgkGHEDlnwRe0oJO9v4vuE8dulg/L0M3Do5gccuHWzzmgugvjE9cF5/AOZ/uYvVBwp4bl0J/9uejYdex39npjJzVGyTz9XpdCyYnkxsaEP+yHLJHxHCot5kJr1hxW73CkbU969tmSWUVne+LxDVdSbr6sQXDGl9Mby2uGhID0L9vTheWsNPu3Ntft6yDUeprDOR1D3ArT5H7CHBiBuwdGtObOcQjaNdMzqWHY+ey4Pn21/mGNQx1YuHRmM0K1y/eBMbj9fi5aFn0XXDubhhTYbmBPp48mpD/siPu3J5Z01GG38KITqXfbnl1NSbCfD2oLcdJQCcrVeIH30i/DGZFdZ2wvWu9ueVoyjqmjIR3bydcg4fTwNXj1Jrg9iayFpnNPNuw/vjzRN7d4jS702RYERjGQWVHC2qwtOgY2xCmNbNOY0twzLN0el0PDN9CAN7qOOXPh463rl+OFP721aeOLlXEPMutOSP7LauwyFEV7Yj68TiePb0VrqCtTR8Jxyq2ZOjrr/VPyrAqR/4s0bHYdDrWH+oiL05ra/59XXacXLKaogI8OaSlJa/5LmzNgUjS5cuZerUqSQnJzNt2jQ2bdrU4v5ffPEFl1xyCUOHDmXChAk89NBDFBdLYiKc+KMdHhfSoQrU2MrXy8A7N4xk7sTePHZGKGP72BdwXTc2jvMHR1FvUvjrh1s6ZfevEPaw5ou4QX2RU01uyBv5bW9+pxtatQQGSVHOnUodHezLOQPVL2xLWlnNV1EUFv2uzjq8YVy8W8ysaiu7P/2++eYbFixYwCOPPMKwYcP46KOPuOWWW/j666+Jjj49Ktu0aRMPPPAADz30EFOmTCE3N5dHH32Uf/3rX7z66qsO+SE6MncdonGkqCAfHjgviW3bttn9XJ1Ox9NXDGHn8TKOFlVx//LtvH7t8A7bFSlEe21zw+RVi9F9QvEy6DleWsPB/Ar6RmpfA8VR9p7UM+Js14+L59v0HD7bkkVNvYlAH08CfDwa/nlab7NLqtmdXYavp4FZo5vOweso7A5GFi9ezPTp05kxYwYA8+bNY/Xq1Sxbtoy///3vp+2/fft2evbsyXXXXQdATEwMV111FW+99VY7m97x1RnNrDuoBiOT21lfpDNT64+kMv21tXy/M5dlGzKt5ZOF6Eqq6ozsy1U/FNtSqdnZ/Lw8GNk7hDUHCvltX0GnCkb2WHtGnD9tdnTvUAb2CGRXdhmfbWl+eQ6LK0f0ItjPcTVPtGBXMFJXV8fOnTuZO3duo/vHjx/P1q1bm3xOamoqL774Ir/99huTJk2isLCQ77//nsmTJ9vdWJPJsSvCWo7n6OPaalNGEZV1JkL9vUiK9NesHa7Q3ms9qEcAf5val+d/3M//tmVx1Yiejmxep6H1a7qr0Oo678gsblg6wZtwf0+3/D1P7BuuBiN787hhbPu+NLjL67mwso6Cilp0OkgI93VJexbNHsave/MorzGe9K9eva01UtFw6+9l4OYJ8e1qkzOvs63HtCsYKS4uxmQyERbWeNw/PDyc/PymE5aGDRvGc889x913301dXR1Go5GpU6fyf//3f/acGoC0tDS7n6PlcVuzPE2NtAeF6dmxY7smbXC19lzraNR8ke2ZJWzZuhW9DNU0S6vXdFfj6uv87b5KAGK70aZhT1eINKt/p+sPFfDb+s0E+bQ/j0Hr13NanloRtbufgX270l123oFegBfQqDPG0PDvxIyevIy95DngfFpe5zZlTJ46Xq8oSrNj+AcOHODxxx/njjvuYMKECeTn5/PMM8/wyCOP8OSTT9p13uTkZAwGxyXomEwm0tLSHH5cWz2yZi0Al4zqR0pK5/6m74hrPdhkZt6qn6ipNxPYsx99I1tfb6er0fo13VVodZ3f2bMNKGfS4FhSUhJcdl57DFUUXt26moP5lTy3qYalN40i0NezTcdyl9fz1rUZQDHJsWGkpKRo1g5nceZ1thy7NXYFIyEhIRgMBgoKGs8hLywsJDy86UIrb7zxBsOGDePmm28GoH///vj6+jJr1izuvvtuIiMjbT6/wWBwygvSWcdtSWFFLTuzywCYnBjZZT442nOtDQYDg6OD2HSkmJ3Z5ST1cI9S2O5Ii9d0V+Tq67yjYUXX1NhQt/79vnX9SGa8vo5d2eXc9N5m3r9pdLtmC2r9et6XqxY7G9Aj0K2ve3tpeZ3tmtrr5eXFoEGDWLNmTaP7165dS2pqapPPqampQa9vfBrLD9vZpn7ZY/WBAhRFzcyODOxYqytqKblhLQ5LrQUhuorCiloyi6qBE38H7qp3uD/v3zSKIF9PthwtYe77m5pcNLOj2OvC5NWuyu46I3PmzGH58uUsX76cgwcP8uSTT5Kdnc3MmTMBeP7557n//vut+0+ZMoUff/yRDz/8kMzMTDZv3szjjz/OkCFD6N7dtuJXnZFlSq/MorGPpbZCZ14ZVIimWALwhAh/An3aNuzhSgN6BPLunJH4eRlYc6CQO5dtpd6O9VbchdmsWHtGnF1jpCuzu9/sggsuoLi4mIULF5KXl0diYiKLFi2iZ0815yE/P5/s7Gzr/tOmTaOyspKlS5fy9NNPExAQwJgxY/jHP/7huJ+ig1EU5cR6NBKM2MXyjXDn8TLqTeYWVxAWojPZ3hCAu2Oxs+akxobw1vUjuGHxRn7clcs/Pt3OC1emuF3l2JYcLaqiut6El4ee+LD2L2QqmtamQbxZs2Yxa9asJh976qmnTrtv9uzZzJ49uy2n6pT25JSTV16Lj6eeEfEhWjenQ+kd5k+AtwfltUb251Z0yKWyhWgLd1yp1xbjEsJ5bdYw/vL+ZlZuO46/twePXza4wxQutNQX6RfZDQ/58uM0cmU1YOkVGdMnrEOX79WCXq9jcE9L3kiJto0RwkUURWF7lvut1GurMwd054WrUtDpYOmfR3nq2z0dJmfQVWXguzoJRjRgyReZ1IlLwDvTkJiGYOSYJLGKriGruJqiyjo8DToG9OiYH4qXDI1mweXJALzx+yFe/fWAxi2yzd5cddajK8rAd2USjLhYdZ2JDRlFgOSLtNWQnsGA9IyIrsOyHs3AHoEdujd15qhY/tWwEvdzP+zj3TWHNW5R61xZBr4rk2DExdYfLqTOaCY6yIeECH+tm9MhDWlIYt2bU96hpws2kr8P6iq1bsUJHaQLvavoqPkiTbl5Yh/uOrMfAP/+ahfHS6o1blHzaupNZBSof5cDpGfEqSQYcbE/LEM0iREdJoHL3fQK8SXEz5N6k2L91tJhVeTDp3Pg1ZHw31TY/rG2gYDJCBvehOeT4P3LoThDu7YIK8u03iEdaCZNS+4+qx+DewZiVmDTkWKtm9OsA3kVmBUI8fMkIsC79SeINpNgxMV+lym97abT6axvymkddahGUWD7R2oQsvMz9b6KXPh8Liw+H3I0WCPi0G/wxkT45j61LQd/gYXj1ODE3PHqQ3QWRpOZtIb8qJQY9y52ZiudTsewWHUmoaXXxx3tOSl5Vb48OpcEIy50vKSaA3kV6HUwPqHp8vnCNkMbhmq2d8RKrCWZsHQGfP4XqC6G7slw049w5sPg6QdH18Ebk+Cbf6iPO1txBnx8Lbx3CeTtAt8QOOdxiJsA9ZVqcLLkYihy//H9zmh/XgXV9Sa6eXvQJ7zzrMeU0jDktM2Ng5G9OZbkVckXcTYJRlzo931qr8jQmGCC/Ny/gqI7S7b2jHSgYMRsVnsZFo6BAz+CwVsNQOb+CjGjYOLf4a8bYdDloJhhwyJ4eThsec85PRN1lfDzY/DKKNj9JegMMGou3LkFxt0J138JFzynBkhHVsNr4+DPRdJL4mKWnoMhvYI6VLGw1liCkfRjpW5bmXWPTOt1GQlGXOiP/TKl11EsSaz788qpqjNq3BobFOyHdy9QexnqKiBmNNy6Wg1ADCcFpkG9YMa7cN0XENEfqgrhizvh7bPg2GbHtEVRYMen8PII+OM5MNVC70lqey54FvxC1f30ehh1C9y2FuInQn0VfPsPWHIRFB1yTFtEq6yVVztB8urJ4sP8CfTxoNZottbycDdSY8R1JBhxEZNZYfUBS/KqDNG0V/dAH7oHemNW1NLwbktRYPWL8Np4dfjF0x/OfxbmfAcRic0/r89kNTg45wnwClADkTfPhDUvta89NWXw7kXw2c1QfhyC4+CqD9Tgp/vApp8T2lt9/ILn1PYfWaPmkqx/XXpJXGB7ZkOxs06SvGqh1+usAdZWNxyqKaqsI6+8FoDE7hKMOJsEIy6yPauE0up6Anw8Ot2bilYsSazunADH1g/gp0fV3oeEM+GO9TB6rtrr0BqDJ4z7K9y5CYZcBSjwy+NQdrzt7Vn3ijrk4ukHU/8Fd2yAARdDa8l5ll6S2xt6SYzV8N0DsPLWtrdFtCqvrIa9ueq386GdJHn1ZJahGnf8G97TkC8SE+pLN+82rZwi7CDBiIus3HoMgAl9w2V9AwcZ0lAWPs1dK7GajPDH8+r2xPvg2hUQHGv/cQKi4PI3IHYsmOpg9X/a1p7qYlj/mrp92Wsw6R/g6WPfMULi1V6SC58HnR52fAzZO9rWHtGqV389gMmsMCw2mB5Bvlo3x+HcOYnVOkTTXZJXXUE+FV3grT8O8d66IwBcltpT49Z0HkMa3sh2uGsS687Pofgw+IbChHta731oiU4HZzyobm9+F8qyW9y9SesWQm0ZRA6CAZe0vS16PYy8GQZPV/+/+oW2H0s0K7Ooig83HAXgvnOTNG6Nc1iGaQ7mV1BWU69tY05hCUakDLxrSDDiZMs2HOXxr3cDcN85iZw7KErjFnUeyQ09I4cLKimtdq83MszmE70iY24HbwdMyew9GWLGqEM+a/5j33OriuDP19XtMx6wbZioNRPuUW93roSCjrHOSEfy0s/7qTcpjO8bxrhOWgogvJs3vUJ8URT3mxknM2lcS4IRJ/pi+3H++blavOovk/twx5S+Greocwn19yImVO26Tne3oZq9X0P+bvAOVHMtHOHU3pHyHNufu/41tVek+2Dof7Fj2tN9ECSeDyiw5kXHHFMAcCCvnM+2ZAFw3zmds1fEwh2HasxmhX250jPiShKMOMnPu3O59+NtKArMGh3Lg+f1lwp+TnBi0Tw3CkYUBX5/Tt0eeTP4Bjvu2H3OUKcFG2tszx2pKjqRKzLZQb0iFhP/rt5u/whKsxx33C7uxR/3Y1bg7IHdSW2oVNpZuWMwklVcTVWdCS+DnvhwWUPMFSQYcYK1Bwu4bekWjGaFy1KieezSwRKIOIml3ohbreB78GfI3gYevjD2Dsceu1HvyGLbekfWL4S68oZekYsc256YkersGrMR1r7i2GN3UenHSvk6LRudDv5+TgvTvzuJk4MRxU0WaLTMpEmI7IanTDhwCbnKDrb1aDE3L9lEndHM2QO78+yMoZ2qaqK7sUzvdauekd8bckVGzAF/J4z195kCvUapvSOt1R2pKlLrgYAaxDiyV8Ri4r3q7eZ3obLA8cfvYp77YS8AlwyN7hJlyAf3DMKg15FfXsvx0hqtmwNI8qoWJBhxoN3ZZdyweCNVdSYm9A3n5atTJap2ssE9A9Hp4FhJNYUVtVo3B46shaNrweClllR3hpN7Rza9A+W5ze+77tWGXpFkSLrQOe3pMwWiU9XaI5bhINEmGzOKWLU3H4Nexz1ndf5eEQAfT4P1Q99d6o3skXwRl5NPSgc5lF/B7Lc3UFpdz7DYYBZdNxwfT4PWzer0Anw86dMwprvDHZJYLbkiKddAYLTzzpMwFXqNbLl3pKoI/nxD3XbUDJqm6HQnckc2vAk1bvB76IAUReHZ79RekStH9OpSuQruljciZeBdT4IRBzheUs21b/1JQUUtA3sEsnjOKPy8pGKfq1iHajI1/hA8tkXNF9EZYPzdzj3Xqb0jFXmn77PuFbVXJCrZ8bkip0q6EMKToLYUNr7t3HN1Ur/vL2BDRhFeHnrunNpP6+a4lDUYOVqiaTsAao0mDhdUArJarytJMOIAL/+yn+OlNfSJ8Oe9m0YR5Csr8rqSJYk17ViJtg2x1BVJnqGu5+JsCWdCzxHq8MipvSMn94pMfrB9BddsodefqDuyfiHUVzv3fJ2Moig8973aKzJ7TBzRwZ2v2mpLLMFI2rFSjBqv4HsgrwKTWSHI15Pugd6atqUrkWDEAbY2RPMPnNef8G7y4nU1SzCyPatUu2z83F2w5ytAdyKh09l0OjjjIXV749uNekd06xeqqwNHJUN/J+WKnCr5CgiKhcp8dU0eYbPvd+aQdqwUfy8Dt5+RoHVzXC4hohsB3h5U15vYl1uhaVtOHqKRWZCuI8FIO9XUm9ifp/7xWD4UhWsN7HEiGz+3TKMkVktJ9AEXQ4QLi1T1PRN6Dld7R9b+FwBDbSm6jYvUx894yPm9IhYGTxj/N3V7zUtgcrOquG7KZFZ47od9ANw4oTdhXfALjV6vY0jDQoBa543skZk0mpBgpJ12Z5dhMiuE+XsRFWjnomPCIXy9DPSLVMutb9ei3kjhQUhfoW5Pus+15z65d2TDW1CZT/dDn6Kz9IokXeDa9qReC/6RUJoJaZ+69twd1P+2HeNAXgVBvp7cPLGP1s3RzFA3WYVbysBrQ4KRdko/rhbHGdwzSLr0NGR5I9NkfYs1/wHFDP3OgR5DXX/+vmdB9DAwVqP75d9EHv5cvd+VvSIWnicVelv9orpGj2hWndHMiz+pvSK3Tk7o0vlm7jKjZm9DwTPpGXEtCUbaKb3hw29wT8m61lKyNW+kxLUnLs2CbcvU7Yku7hWxOKl3RL9tKQZTNUrUENf3iliMuBF8gqBgX0MejWjOx5syySyqJrybN9ePi9O6OZqyBCP78sqpqDVq0oaSqjrrUG9idwlGXEmCkXZKP64GI5YVZIU2rD0jx1ycxLr2ZTDXqyXRY0e77ryn6ne2WnisgXnSA67vFbHwCYRRc9XtP55X1+oRpzGazLzyy34A7pzat8uXA4gM9CE6yEfTFXwtQzQ9g30J8Om6vVRakGCkHWqNJuvKjoOiJRjRUlJUAF4GPSVV9WQWuWhaaUW+WgIdXJ8rciqdDqb+C4CK4AGQeJ627Rl9G3j6qWv0HPxF27a4qSNFVeSW1eLraWDmqBitm+MWUmKDAe2GaqQMvHYkGGmHfTkV1JsUgv086RXSteoCuBsvDz0DejSUlHbVUM2ulWoF1Ohh0Huya87Zkr5nYZr7BwfGPK1dr4iFfxgMv0Hdbm39nC7qcL5aWKt3uD/eHlKtGbRPYpXkVe1IMNIOaQ3lxwdHS/KqOxhy0lCNS2SsVm/7X6D9h79F90GYPLtp3QrVqFvU2yNroK5S27a4IUuVzz4RXafse2u0TmK1JK9KMOJ6Eoy0gyVfZLDki7gFaxKrK97IFEVdFA8gbrzzz9cRhfSGwF5gNkLWRq1b43YOWYKRLrQGTWuSewWh10FOWQ05Ll7BV1EUa8E1KQPvehKMtEP6MZlJ404sXbzpx0oxm52cNFl4ECrzwOCtDtOI0+l0EDdO3bYEbsLqUL76wddbekas/Lw8rLNYXN07klVcTUWtEU+DTnqrNCDBSBvVm8zsyVbHF2UmjXtIiPDH19NAZZ2JQwVOLil9ZI1622skeEqxu2ZJMNIsyzBN73A3GVZzE6kaJbFaklcTIrrhaZCPRleTK95G+3LLqTOZCfDxIDbUT+vmCMDDoLf2Uu1w9tRASzBi+bAVTbNcn6yNYKzTti1upKLWSF65Ws+itwzTNKJVEuveXJlJoyUJRtpo57GGyquSvOpWknsGAy74VmXNF5FgpEXhieAXps46Or5V69a4jYyGXpHwbl5duupqUyzTe3dklWBy9nDrSU7MpJFhdy1IMNJGaZIv4pbGJoQBsHLrMcpqnLRQW8lRde0VvQfEjHLOOTqLRnkja7Rtixs5VHBiWq9orF9kAH5e6nDrgXzXrOCrKAo7G97TpWdEGxKMtNGJYETyRdzJmf0j6RfZjbIaI++tzXDOSTIaPlSjU8FLPkxaZZltdHSdtu1wI9bkVQlGTmPQ66x5eDsyXTNNP/1YGYcKKvHy0DMsNsQl5xSNSTDSBkaTmd3ZJxbIE+5Dr9fx16l9AXhr9WHnrHEh+SL2iR2r3h5dD2aTtm1xE5K82jJrJVYXFTD8ZFMmAOcOiiLIT4bNtCDBSBscyK+g1mjG38tA7zD5ZuNuLhoSTZ8If0qq6nlvXYbjTyD1RewTlQxeAVBbBrnpWrfGLRyWYZoWpTYUP9vugp6RmnoT/9t2DIArR/Ry+vlE0yQYaYP0huTVQdFB6PWSvOpuDHodd1p6R/44TKUje0fKc6DoIKCD2DGOO25npjecuFYyxRdFUayl4BOknkWThlpX8K2gxmh26rm+35lDWY2RnsG+jEsId+q5RPMkGGmDdMkXcXsXD4kmPsyPoso6lv55xHEHtgzRRCWDj/z+bRbXMFQjwQgFFXWU1xrR6SA2TMoCNKVHkC/dA70xmRUOFTthqPUkn27KAmD68F4Y5MulZiQYaQOpvOr+PAx67pii9o4s+v0Q1XUOylWQIZq2sVyvI2vVUvpdmCV5tVeIryyQ1wJLvZEDRU6aFQdkFVex5mABADOGyxCNliQYsZPJrLDzuDpMI5VX3dtlqT2JCfWloMKBvSNSX6RtolPBwweqCqBgv9at0ZQkr9rGksS6z4nByIrNx1AUGJcQRowUr9SUBCN2OlxQQXW9CV9PA30i5M3EnXka9Nxxhto78sbvh6ipb2fvSGUh5O1StyUYsY+Ht1o6H+Bo1x6qOSwL5NnEsoLv/iLnVO41mxU+3azOopkhiauak2DETpb6IgOjA2V8sQOYNqwXPYN9yS+v5aMNR9t3MEudjIj+4C+JbnaLlbwROGm1XklebVFyzyB0OiioMnOsuNrhx19/qJCs4moCvD04b1APhx9f2EeCETulW8vAS75IR+Dloee2MxIAeO23g+3rHZEhmvaRRfMAmdZrqwAfT0bFqwXI3vj9kMOPb6ktcnFKNL5ekrujNQlG7CSVVzueGSN60SPIh9yyWj7dnNX2Ax1Zrd5K8mrbxIxSS+iXZqol9bsgo8nMkUIJRmx195n9APh4UxZHC6scdtzS6nq+Tc8B4MoRMQ47rmg7CUbsYDYr7DoulVc7Gm8Pw4nekV8PUNeWugU1pZCTpm5Lz0jbePlDj6Hq9pGuWRr+WEk19SYFLw890UG+WjfH7Y3qHUpKdy+MZoX//LTPYcf9cvtxao1mErt3Y2gveS93BxKM2CGjsJKKWiPeHnr6RUryakdy5YgYIgO8OV5aw/K29I5kbgDFDCG9ITDa8Q3sKrr4onnWBfLC/KVgoo2uHqwuXPf5tmPsyy13yDE/bRiiuXJEjKy67iYkGLFDekOvSP8egXgY5NJ1JD6eBm6drPaOvPrrAepNdvaOZMgQjUOcXG+kC7JUXpXkVdv1DfXk3EHdURR4/oe97T7e3pxytmeV4qHXcVlqTwe0UDiCfKLawVLsLFmKnXVIV4+KJbybN8dKqvl8yzH7nmz58IyXYKRdYscAOijcDxX5WrfG5SR5tW3uOasfOh18vzOX7Zkl7TqWpVfkzAGRhHfzdkDrhCNIMGIHa+XVaBlj7Ih8vQz8ZVIfAF759QBGW3tH6qrg+BZ1W/JF2sc3BCIHqttdsN7IoQK1+qoEI/bpF9mNyxt6MZ5rR+9IndHM51sti+JJ4qo7kWDERoqiyJo0ncCsMbGE+ntxtKiKlduO2/akrI1gNkJgTwiOc24DuwJ3n+JbnAGVBU45tAzTtN09ZyXiadDxx/4C1h0sbNMxftmTR2FlHREB3kxOjHBwC0V7SDBio8yiaspqjHgZ9CR2D9C6OaKN/Lw8uHF8PABf7bAxGLEkW8aNA0l2az93TGJVFDjwM7x3Gbw0FBaOhbJsh56ius7E8dIaQErBt0VMqB8zR8YCau+I0oY1jixDNNOG9ZS8Pzcjvw0bWeqLJEUF4OUhl60jGxarFlI6YmvdAlkcz7EswUhOujplWkvGWti6FF4bDx9Mg0O/qvdX5sGKm8HkuBVjMxrqiwT7eRLq7+Ww43Yld07ti4+nns1Hivl1b55dz80tq7E+Z8ZwGaJxN236VF26dClTp04lOTmZadOmsWnTphb3r6ur48UXX2TKlCkMHjyYs846i+XLl7epwVpJPy4r9XYWlmXbs4qrMJlb+XZlrFWHaUCCEUcJiILQPoACR//Upg1VRfDH8/CfIfC/2yFvJ3j6w+jbYPZK8OqmFrn77WmHnVKSV9svMtCH68fGA/Dc9/swt/b3e5LPthzDrMDwuBD6SmkGt+Nh7xO++eYbFixYwCOPPMKwYcP46KOPuOWWW/j666+Jjm66/sJdd91FYWEhTzzxBLGxsRQVFWE0Ou4bhytIvkjn0SPIF0+DjnqTQnZpNb1CWlit89gWMNaAXziE93NdIzu7uHFQdEgdqkk8x3XnLT4C616Fre9DfUPPWEAPGH0rDL8BfIPV+y76D3x2M/z+rNrWhCntPvWhfEledYRbJyew9M+j7Mou45v0bC4a0nrdH0VRTqotIoviuSO7e0YWL17M9OnTmTFjBgkJCcybN4+oqCiWLVvW5P6///47GzduZNGiRYwbN45evXoxZMgQhg0b1u7Gu0qj5FWZSdPhGfQ6YhoCkFZLTEu+iHNYepmOurASa9lxeGMibHhDDUS6J8Plb8BdO2DC3ScCEYAhM2DY9YACn90C5TntPv0hWa3XIUL8vbhlojor7oUf9tk0K27L0WIOFVTi62ngQhuCF+F6dvWM1NXVsXPnTubOndvo/vHjx7N169Ymn/PLL78wePBg3nrrLf73v//h5+fH1KlTueuuu/Dx8bGrsSZTO5eAb+Z4rR33WHE1xVX1eOh19Ivwc3g7ugJbr7WrxIT6cqigksMFFYzuHdLsfvoja9AB5thxKG7S9pa423VuVq/RGADl2BbMNeXg2ULvlIPoNr6NvqYUJawf5vOeht6TTwSYTV2vc55En7URXd4ulBU3Y571GegNDbvbf50PN/SMxIXKe4itmrvON4yLZcnawxwqqGT5pkxmNNPboSgKB/Ir+e/P+wG4IDkKXw+dXP9TOPN9w9Zj2hWMFBcXYzKZCAsLa3R/eHg4+flNFzDKzMxk8+bNeHt78+qrr1JcXMz8+fMpKSlhwYIF9pyetLQ0u/Z31HH/PKZmwPcKMLB7p3Pa0FU463doLz+z2iOycXcG/T2bmSZoNpGSsQ4DsKc6jOpt21zWvvZyl+vcLEUh2Sccr5oCDvz2MRXhqU49nc5UR/Kfb6MHDsVfTUlZMGzf3urzvAfez4DCWzFk/EHup/eRnXR9o8ftuc77c9UKznWFmWzb1v6elq6kqet8cT8flmyv57nvdhGvy8fToAaWJrPCnsJ6Nh6vYePxWnIqTnwYDguqZlsH+jt2NS3fN+zOGQFOq+WvKEqz9f0tjz333HMEBKhTYh988EH+9re/8cgjj9jVO5KcnIzB4Lilnk0mE2lpaa0e9+f8fUAJI/t2JyUl2WHn70psvdauMrwyg28P7KHWsxspKSlN73R8CwZTNYpPEEkTL7N+K3Zn7nadW6I7PBl2rqCfZx5Kc78DR50r7VP0dcUoAT2IP/cOMHja+MwUdEE18L9b6bHvPbqPuhx6T7L7OhdX1VFRpwYg544bJkvW26il69x/kInvD/9OTlktmyuC6B3ux4+781i1N5/iqnrrfl4GHWMTwrhqRC/OHRTl6h+hQ3Dm+4bl2K2xKxgJCQnBYDBQUNC4IFBhYSHh4eFNPiciIoLu3btbAxGAhIQEFEUhJyeH+Ph4m89vMBic8gbb2nF3ZauLMyX3Cnb7N3h356zfob3iGuo8HC2qbr49mesB0MWOw+DZsaZiust1blH8eNi5An3menB2Wze9BYBuxI0YvOwbHib1aji6Bt3W9zF8PhduXa0mNGP7dT5SVA1AdJAP3Xw71mvJHTR1nf0NBv52ZiL//DyNZ39ovKJvsJ8nU5MiOXtgdyYmRtDNu03fu7scLd837Epg9fLyYtCgQaxZ07hY0dq1a0lNbbqbddiwYeTl5VFZWWm97/Dhw+j1eqKi3D9KlcqrnVNc2IkE1maLJ1nri0gJeKewXNfMDWCsc955jm1Rp2frPRuSUtvg/GfUMvaVeWpCq9m+sfVDDZVXe0vlVYeaMaIXid3VLxZxYX7cPKE3H80dw6Z5Z/HCVSmcn9xDApEOwu7f0pw5c7j//vsZPHgwqampfPzxx2RnZzNz5kwAnn/+eXJzc3nmmWcAuOiii1i4cCEPPfQQf/vb3yguLubZZ59l+vTpdiewaiG3rJaCijoMeh0De0iNkc4iNlQNRsprjRRX1Z9ehMpslmJnzhaeBL6hUF0E2dshZmTjx421aiBxdB0c2wzxE2DMbfafZ6PaK8KgyyGge9va6uUHM96FRWfA4d/QrX4BAs+2+elSY8Q5PA16Vtw2juLKemJCfZtNFxDuz+5g5IILLqC4uJiFCxeSl5dHYmIiixYtomdPdRGj/Px8srNPlFH29/fnnXfe4fHHH2f69OkEBwdz/vnnc/fddzvsh3AmS+XVvhHd8PF0825vYTMfTwPdA73JLavlSGHl6cFI3i6oKVELYfUYokkbOz29Xu0d2fOVumheeF+1l+ToOji6Xg1ETLUn9t/zFfQcDjGjbD9HZSGkNRRYHDW35X1bE5EEF74AK29F9/vTdBsTAaTY9NTD1mm9UmzL0QJ8PAnwsTUHSLirNvVfzZo1i1mzZjX52FNPPXXafQkJCSxevLgtp9KcDNF0XnGh/uSW1XK0qIrU2FOm9x5rqCrca4QdyY7CbrFj1SBj1VPw48OnP+4fCbFj1MDw8O/w9b1wyyow2PjWtfU9NaDpkaL+Ltsr5WrI+APdtqX03voUTJ1tU76LtWdEhmmEaJIMprVAURS+TVd7eVJig7VtjHC42DA/NmQUNb1GTdEh9TYiybWN6mr6nKHeWqqhhvVVg4/Yseq/0D5qLZDKAnh5OOSkwaa3YfRfWj+22QQb31a3R811XNG6C55F2f0FXjV5mLK3QWzLPTVms3JSz4gEI0I0RYKRFqw+UMC+3Ar8vAxcMlSq9nU2cQ15I00HI4fV25DeLmxRFxQ1GK79DOoq1eCjWzPLuvuHw5kPqz0jvzwOAy9rPf9j77dQmqnmpQye5rg2e/mrBdP2fIXuwE+tBiPHS6upNZrxNOjoGezruHYI0YnI8rMteHu1+oF05YgYgnylq76zsSyYd7So8vQHixuCkVAJRpyu75kw8JLmAxGL4TdAdCrUljU9pHOqDYvU22HXgadjgwCl71kA6A7+1Oq+ll6R2FA/WbZeiGbIX0YzDuSVs2pvPjodzBkfr3VzhBPEhald5keLTukZURR1QTWQnhF3ojfAhc8DOtjxEWSsaX7f/L1w+DfQ6WHkTQ5vipJwprpxbIuaJNsC6xBNhCSvCtEcCUaa8fbqDADOHtDd+qElOhfLME1uWS019SfVjagqUr99A4TEadAy0ayew9UeEoCv/w6m+qb32/Cmept0AQTHOr4dgT2pCuiDDgUO/tLirpYaI5IvIkTzJBhpQlFlHZ9tyQLgpgnyzbizCvbzJMBHTZtq1DtiGaIJiHZ4975wgDMfBr8wyN8Nf75++uM1ZbC9YRXxUbc4rRllkQ25Igd+bHG/Q1JjRIhWSTDShA//PEKt0czgnoGM6h2qdXOEk+h0Omsl1kZJrEWSL+LW/ELhrPnq9qqnoOx448e3fwR1FRCeqCaaOkmpNRj5WS2S14zDBepqvRKMCNE8CUZOUWs0sWSdmi9w84Q+UtGvk4u1zqg5KYnV0jMSEu/6BgnbpMyCXqPUoOP7f564X1FOJK46cjpvEypDB6F4dYOqAsje1uQ+tUYTWcXqujRSY0SI5kkwcoqvtmeTX15L90BvLkjuoXVzhJPFhjaRxCrTet2fXq8ms+r0sPNzOPirev+hVVC4H7wCYOhMpzZB0Xue6Hk50PSsGnXtIwjw9iCim7dT2yNERybByEkURbFO571ubDxeHnJ5Orsmh2lkWm/H0GMIjGzICfnmH+paNpZekZSrwTug+ec6iNK3YVbN/qbzRg6dVHlVelmFaJ582p5k/aEidmWX4etpYNZoJ2TgC7djmVEjPSMd1NR5asn4wv3w7QNqoTM4EaQ4mZKg1hvh2CZ1FtYprKv1Sr6IEC2SYOQkb69WS4BPH96TYD+vVvYWnYGl8FlWcRUmswJ1VVCRoz4oPSPuzycIznlc3d68GFCgzxSISHTN+YN6QcQAUMxNTvGV5FUhbCPBSIPDBZX8vCcPgDnj5UOoq+gR5IunQUe9SeF4STUUZ6gPeAeBb0iLzxVuYsiVEDf+xP/buzqvvfo19I40kTdyWKb1CmETCUYaLF5zGEWBqf0jSZBKiV2GQa8jJuSkoRprvki8U2diCAfS6eCC58DTDyL6Q+K5rj1/37PV2wM/nTbF1xKMyHuKEC2TYAQora7n001qkbObpchZlxN7chKr5It0TN0Hwt+2wk0/qGXjXSl2LHh1g8p8yNluvbu0up6CijoA4qVnRIgWSTACfLQxk+p6E/2jAhibEKZ1c4SLNUpitQzTSL5IxxMQpeaQuJqHV5NTfC29IpEB3nTzlgXShWhJlw9GjGaF9xqKnN00obdMv+uCYq0L5lWeVPBMghFhB0veyP6TgxFJXhXCVl0+GFmXVUNOWS3h3by5JCVa6+YIDcSFNjFMIz0jwh6WvJGsDVBdDMBhywJ5UnlViFZ16WBEURS+2qfWl7hubBzeHi4eaxZuwVL4LKuwAqXkqHqn9IwIewTHqMmzitlaDdZS8KxPuCSvCtGaLh2MbD5awoHierw89FLkrAuLaegZCajLRWeuB4MXBEovmbBT38ZTfGVarxC269LByPc71eJWl6VEEybrRnRZPp4Gugd6E6vLVe8IjnX9jAzR8fU7McVXMZtOBCMyTCNEq7p0ivfFQ6I5cjyPv5/dT+umCI3FhfoTV9kQjMgQjWiL2LHg6Q8VuRzfu5GqOhOehhN1bIQQzevSPSNDegVx+4ggwqVXpMuLDfMjTqdW4JXkVdEmHt7QR53im7P5SwBGxIXKgptC2ED+SoRAnVFjHaaRnhHRVg15I90yVwFwRlKEdm0RogORYEQILD0jDcGI9IyItmoIRhJqdhFIJWckRWrcICE6BglGhMDSM9IwTCM9I6KtQuKoDOyDh87MRd32kthdpvUKYQsJRoQA4n2rCdBVA1Dt30vj1oiObIfPSAAuD9gtFZ2FsJEEI0IAQTXqQonZSihHyxWNWyM6shVlAwFIrt4IiryWhLCFBCNCALpidX2io0qkumCeEG1wpLCSL0riqVK88anJg9x0rZskRIcgwYgQYF0g74i5O0cKKzVujOioVu3Npw5PdvukqHfs/1HT9gjRUUgwIgRYF8g7onSXnhHRZqv2qknQlbFT1DsO/NTC3kIIi64djGT+Se/Nj0HZMa1bIrTW0DNyVIlUV+8Vwk419SbWHSoEIHrEReqdmX+CsVbDVgnRMXTpYES350tCj/+K7tcntW6K0FrRiWBEekZEW/x5uIiaejNRgT4k9BsEXt3AbITiDK2bJoTb69LBiDLwMgB0O1dAea62jRHaqauCCnXRxCNKd7KKqzCZZRaEsM9ve/MBmJwYgU6vh7AE9YHCAxq2SoiOoUsHI/QcQUXIIHSmOtj4ltatEVpp+OaqeAdSaQig3qRwvKRa2zaJDmfVPjVfxFoCPqxhAU4JRoRoVdcORoDcPleoG5vehnr5AOqSGvJFdKG9iQlRl3uXoRphj8yiKg7lV+Kh1zG+X7h6Z1hf9VaCESFa1eWDkZKoCShBMVBVCDs+1ro5QgsN+SKE9CY2TF3uXZJYhT0ss2iGxYUQ6OOp3mkJRgokGBGiNV0+GEFvQBk1V91e/5pUTOyKGnpGCO1NXGhDMFIktUaE7VY15Is0WqVXckaEsJkEI4CSMhu8AiB/Dxz8WevmCFdr1DPSMEwjPSMdTmZRFYUVrp9GW1NvYu1BdUrvGYknrdJr6RmpzIOaUpe3S4iORIIRAJ9AGDZb3V73qrZtEa7XVM+IBCMdSvqxUs58/jemv7YWo8ns0nNvzCiiut5EZIA3A3oEnHjAJxC6dVe3Cw+6tE1CdDQSjFiM/gvo9HDwF8jbrXVrhKuYTVByVN0O6U1cQ87I0aIqFBmy6xDMZoV/rUynzmQmo7CKH3e5dpr+qpOn9J66Sq81iVWCESFaIsGIRUg89L9Q3V6/UNOmCBcqzVILUxm8IDCamIaekYpaI8VV9Ro3Ttji082ZbMsssf5/yboMl57fkrx6RlLk6Q9a80b2u7BFQnQ8EoycbOxf1dvtH0NlgbZtEa5hGaIJjgO9AR9PA1GBPgCyYF4HUFxZx1Pf7gHgpgm9Meh1rD9UxN6ccpecP6u4ioP5lRj0OiZYpvSeTKb3CmETCUZOFjMaooeBqRY2vq11a4QrFJ3IF7GIPWmoRri3Z77fS3FVPYndu/Hg+f05Z6Cao/Gei3pHftunfmkZFhtMkK/n6TtIMCKETSQYOZlOB2PvULc3viULXHUFxSdm0lhIEmvHsC2zhI82qvk+j106GE+DnuvGxgPw2ZZjlFY7f5jtt32WKb1NDNHASVVYD0rZACFaIMHIqQZeCoE91el4acu1bo1wNuu03njrXbESjLg9k1nhXyvTUBSYltqT0X3CABjTJ5TE7t2orjexfHOWU9tQb1JYd6gIUJNXmxQSrybG11VAhax/JURzJBg5lcETRt2ibq9fKN9mOrviloZpJGfEXX345xHSj5UR4OPBQxcMsN6v0+msvSPvr8vA7MQFD3cV1FFVZyIiwJtB0YFN7+ThpeYjARRIEqsQzZFgpCnDbwBPP8hNh8O/ad0a4SyKAkUZ6vbJwzQNhc+kZ8Q9FVTU8uz3ewG475wkIgK8Gz1+eWpPAnw8yCis4vf9+U5rx7YcdRi3ySm9J5O8ESFaJcFIU3xDIGWWur1Opvl2WlWFUNcw6yIkznq3JWckr7yW6jqTFi0TLXjq2z2U1RgZFB3ItWPiTnvc39uDGcNjAHhv3RGntWNLTh1wSgn4pkgwIkSrJBhpzpjbAB3s/166VzsrS75IQDR4+lrvDvbzJMDHA5AZNe5mU0aRNRfkscsGY9A33SMxe6wapPy6N88pU7SPl1STVWZEr4OJfVsJRsKl8JkQrZFgpDlhCZB4nrotRdA6pybyRUDNO4izrt4reSPuwmgy86+V6QDMHBnDsNiQZvftHe7P5MQIFAU+WO/43pFVDbNoUmKCCfJrYkrvyaRnRIhWSTDSEss0323LoKpI27YIxys6fVqvRVxow4J50jPidN+l5/DZliwyWynBv2TdEfbklBPs58n95/Vv9bjXj1N7Rz7emOnw4TZLfZFmZ9GczBKMFB8Gk1T1FaIpHlo3wK3FT4CoIZCzQ53mO3qu1i0SjlScod6Gxp/2UGyYTO91hfRjpdz6wWbr/7sHejMiPpSRcSGMiA9lQI9ADHoduWU1vPjjPgDuP7c/of5erR57cmIksaF+HC2qYuW2Y1w9KtYhbS6vqWddwyq9kxObqLp6qoBo8PAFY7W6DpKlRLwQwkqCkZbodND/IjUYObYJkGCkU2mi4JlFfEMwciCvwpUt6nLWHlR7GAJ8PKipN5FbVsvXO7L5ekc2AN28PUiNDaaqzkRFrZGhMcHMHBlj07ENeh2zx8TxxDe7WbI2g5kjY1qe9WIDRVH45+fpVNaZ6O5vYFCPZqb0nkyvVwOQ3HR1qEaCESFOI8M0rYlOUW+zt2vaDOEETZSCt0htyEfYmllMndG1S9J3JRsOq8Off5vajx2PnMtHc8dw3zmJTE6MIMDbg4paI3/sL2DzkWJ0Onj80sHom0labcqMEb3w8dSzJ6ecjRnF7W7vsg2ZfLn9OAa9jr+NCrK9LZI3IkSLpGekNT2GqrcF+6CuErz8tW2PcIy6KqjIUbeb6BnpG9GNED9PiqvqSTtWyvC45pMlRduYzYo1QBjVOxRfLwNj+oQxpqGaqsmssCenjE0ZxWzLLGFU71CSewXZdY5gPy8uT+3Jsg2ZLFmXwajeoW1u767jZTz65U4A7jsnkf4BpbY/WYIR56kqgrLjEDlQ7YUSHVKbfnNLly5l6tSpJCcnM23aNDZt2mTT8zZv3szAgQO59NJL23JabQREQbcoUMyQk651a4SjWPJFfILA7/QPKL1ex8h49X7Lt3fhWPvyyimtrsfPy9BkBVODXseg6CCuHxfPi1eltDnnY/aYeAC+T88hp7SmTceoqDXy1w+3UGc0M7V/JDePj7fvAJZgRMoEOJaxFt46C14fDy/0hy/+Bnu/g/pqrVsm7GR3MPLNN9+wYMECbrvtNlauXMnw4cO55ZZbOH78eIvPKy8v54EHHmDs2LFtbqxmLL0j2ds0bYZwoOLT16Q5lWW9kw2HC13QoK7HEuQNjwvBw+C8b7QDowMZFR+K0azw4Yajdj9fURTmfZ7GoYJKegT58PyMoXYNFQEn9YxIrRGH2rwEihquaUUubFkCy66CZ/rAR7Ng24dQKX+/HYHd7wCLFy9m+vTpzJgxg4SEBObNm0dUVBTLli1r8XkPP/wwF110ESkpKW1tq3Ykb6TzaWFar8Xohi79TRnFmJy4xklX9WdDMDIqvu1DJ7a6rmGa74d/HrU7B+jjjZn8b5uaJ/Ly1amE2DCT5zSWpNXy41ArSdEOUVcJvz+rbp/3NFz7GYy8WV3otL4K9nwFK2+D5/rCO+fD9o+1ba9okV05I3V1dezcuZO5cxvPKhk/fjxbt25t9nkrVqzg6NGjPPvss7z22mttaylgMjm2VoDleK0et3syBkA5vhWzg9vQVdh8rV1EV3QIPWAOjkdppk2Jkf508/agvNZIelYxg3val6+gBXe7zs1RFIUNDSvejogLdnp7z+ofQWSAN3nltXy94xiXDI226Xl7csp55As1T+TvZ/cjNSYIk8lk/3X2DkLvF4auqhBTwQGISm7Tz9HVtHSddetfR1+ZhxISj3nY9WDwgt5nwLlPQ84OdHu/QbfvO3S5aXB0LRxdi6lblFqyQTTizPcNW49pVzBSXFyMyWQiLCys0f3h4eHk5ze9IFVGRgbPP/88S5cuxcOjffmyaWlp7Xp+W4/rWe3JEID8PWzf/CeKwbvF/UXznPU7tFffIzsIAo5WGCjctq3Z/RJDDGzJMbJyTTrGxI6TvOwu17k52RVG8itq8dADRUfYVmr/8Im9psR68vHOWp7+eifZWUcZEe2NoYWpvtVGM/f/VEit0UxqlBcjA0rZdsprxZ7rnOQdRbeqQo5s+ZniaPcOFt3NqdfZUF/B4D9eQA9kxF9NUdqu058UfD6MOh+vqhx67XyVkJw1lPzyXzKGdXNNozsgLd832hQdnDpXX1GUJufvm0wm/v73v3PnnXfSu3fz3eG2Sk5OxmAwtPs4FiaTibS0tNaPqygoa8PRVRUwNMoAPVMc1oauwuZr7SL6Neo4cszQScTEpzS731llh9iSs49j9X4dYojR3a5zc/ZvygIKSIkJYdTwVJecs2dCLT9mrCGnso5n1pYQF+bHTePjmZbaE1+vxtdKURTuW57G8XITUYHeLLpxfKNCa225zrqjQ6B4J/EBRuI6wGvJHTR3nXW/PoG+vgIloj+xF9xLrL6V30FcBLxzNqG5qwnu3wd8bKgP04U4833DcuzW2BWMhISEYDAYKCgoaHR/YWEh4eGnVyKsrKwkPT2d3bt389hjjwFgNptRFIWBAwfy9ttv25XQajAYnPIGa9Nxo1PgwE8YctMgdrTD29BVOOt3aBeTUa2ECRjCEqCF9ozuEw7sY2NGETqd3v7ERY24xXVuwcYjJQCM7hPqsnZGBfvx3V0TeXdtBh+sP8KRwioe/mIXL/60n2vHxHHd2HgiAtRez483HmWlJU/kmmFEBPo2eUy7rnN4PwD0RQdbfM2J0zW6zhX58OfrAOim/h8GTxtyeGJGQsQAdPm7Mez+HEbc6MTWdlxavm/YlcDq5eXFoEGDWLNmTaP7165dS2rq6d9uunXrxpdffsnKlSut/2bOnEnv3r1ZuXIlQ4cObV/rXckyo+b4Nk2bIRygLAvMRnWMObDl3IHknkH4ehoorqrnQL4kHjrKxoyG5NXeYa3s6ViRgT7cf15/1j10Jo9ePJCYUF+Kq+p5+ZcDjH/qF+5fvp3v0nOseSL3np1oneLdblJrxDFWvwD1lRA9DPpfaNtzdDpIvVbd3vqB89om2szuYZo5c+Zw//33M3jwYFJTU/n444/Jzs5m5syZADz//PPk5ubyzDPPoNfrSUxMbPT8sLAwvL29T7vf7fVIUW9lRk3HZ6kxEhwHrXTvennoGRYXzJoDhfx5uIjE7gHOb18nl11azdGiKvQ6GBYbrEkb/L09uGF8b2aPjef7nTm8+cchth4t4ZNNWXyyKQuASYkR3DbZgaXbw9SeEQoPgKKoH5DCPiWZsPEtdfvM/7PvGg65Cn56BI5thtxd0H2gc9oo2sTuqb0XXHABDz30EAsXLuTSSy9l06ZNLFq0iJ49ewKQn59Pdna2wxuqOUvPSN5utdCO6LiOrldvQ/vYtPuoeEu9ESl+5giW6zgoOogAH09N22LQ67gguQef3z6eFbeN5dxB3dHpoGewLy9e2YZ6Ii0J7Q3ooKYUqqT2RZv8/gyY6iB+IvSZYt9zu0VA4nnq9raljm+baJc2JbDOmjWLWbNmNfnYU0891eJz77zzTu688862nFZbwbHgGwLVxZC3C6Jdk3QnHKy2HNY3TC9PnmHTUywlxP88VNhssrawnSUYaU9pdmcYHhfKG7NDySuvwcfTQKCjAyVPXwiKgdKjau+Ivw0r/ooTCg7A1oYgYqqdvSIWqdeq9Ue2fwRnPgIebagZI5xCCvnbSqeTvJHOYMObUFOijt8PnmbTU1Jjg/Ey6Mkrr+VIYZVz29cFnMgXca9gxCIywMfxgYiFpfiZlIW336onQTGpvRttnUTQ92zo1h2qCmD/945tn2gXCUbsIXkjHVttBax7Rd2e9I9W80UsfDwNDI1RC57JUE37FFXWsS9XTQR2WGJoRyJJrG2Tkw7pK9Ttqf9q+3EMHjBUzW+URFb3IsGIPWSNmo5t09vqWH1oHxh8hV1PtXyLXy/r1LSLpVekX2S3RnU7uozwk5JYhc30q55UNwZNa3/12pSGWTX7f4TynPYdSziMBCP2sKxRk7sTTPWaNkXYqa4K1vxX3Z54n/oNyQ6je0sSqyNsdNN8EZexDNPIgnk28y/aiW7/d6AzwJR57T9gRCLEjFaHfLZ/1P7jCYeQYMQeIb3BO0jN5s7brXVrhD02L1bHiYPjYMiVdj99WFwIBr2OrOJqjpXI8uRttcHN80WczjJMU3QIzFISvlWKQs89b6vbKddAeF/HHPfkmiOKLILpDiQYsYdOBz2GqNuSN9Jx1FfDmpfU7Yl/B4P9yYndvD0YHK2WkN4ovSNtUlFrJP1YKdBF80VAnU1j8AJTLZRmat0a93f4NwIKt6EYvGDyA4477qDLwdMPCvdD5gbHHVe0mQQj9pK8kY5ny3tQkat+EAy9us2HGd1HHar5U/JG2mTzkWLMCsSE+hId3HR59U5PbzhR30byRlql/00tFaEMnwPBMY47sHcADLxM3d76vuOOK9pMghF7WeqLSM9Ix1BfA6tfVLcn3tuuugKjGr7N/yk9I21izReJd20JeLdjnVEjeSMtqilFl6X2WihjnVCbyjJUs/Nzdaad0JQEI/ay9IzkpKsLrgn3tu0DKM+GwJ6Q0nShPluNjA9Fp4ND+ZXkl0sVXnudKHYWonFLNCbTe21zbAsAtX49Wl1Dqk3ixqm9VHUVsOt/jj++sIsEI/YKTQCvbmCshoJ9WrdGtMRYC3809IpMuAc8vNt1uCA/T5Ia1qaxTFEVtqmpN7EtswRw/eJ4bkeCEdsc2wxAZXB/5xxfpzvxBUVqjmhOghF76fUQZUli3aZpU0Qrtn2ortDbLQpSZzvkkGMseSOHJG/EHtszS6gzmYkI8CY+zE/r5mjLEowUSDDSImcHI6DmkOn0cHStDJtpTIKRtrDUG5G8Efdlqoc/XlC3J9wNnj4OOax1nRrJG7GLtQR8fKis7WMJRkoz1Zle4nSKAlmbAKgMGeC88wT1hIQz1W1ZPE9TEoy0haxR4/62f6QuSOYfCcNvcNhhLVNS9+aWU1JV57DjdnZ/dvViZyfzDwefIECBosNat8Y9lWZBZR6K3oOqoH7OPZclkXXbh1L7RUMSjLSFZY2anDR58bojkxH+eE7dHn+Xulqqg0QEeJMQ4Y+iwKaMYocdtzMzmsxsOaJeKwlGUHMVJG+kZcfUXhEiB6EY2pfr1aqk89UV2cuz4eAvzj2XaJYEI20R3k8tmFNfKW8m7ijtUyjOAL9wGDHH4Ye3JGBKvRHb7Mouo7LORKCPhzUBuMuTYKRlDUM0Ss/hzj+XhzcMuUrdlpojmpFgpC30hhOLNUneiHsxm+D3Z9XtcXeCl7/DTzG64du9rFNjG8t1Ghkfil7fxfNFLCQYaVnDtF56DnPN+SxDNXu+gSr5u9aCBCNtJXkj7mnP11B0EHxDYeTNTjmFZagh/XgZFbVSa6Y1ki/SBOuCeRKMnMZktM5UVKJd0DMC6pfL8EQw10t5eI1IMNJWlrwR6RlxL0fWqLfJM8C7m1NOER3sS0yoLyazwuYjkjfSErNZOTGTRoKRE6RnpHn5u6G+CrwD1SFxV7F8wczb6bpzCisJRtrKukbNdjCbtW2LOMHSvdtrhFNPYylpvkHyRlp0IL+Ckqp6fD0NDO4ZpHVz3EdoQ89IVaEMC5yqIV+E6FS1BoirRA5Ub3N3ue6cwkqCkbaK6A8ePlBXDsUyPc8tmIyQs0PdjnbuWLPkjdjGMkQzLC4YT4O83Vh5d4OAhhLnRYe0bYu7scykcfIXitN0H6Te5kkwogV5d2grg8eJF+/xrdq2Rajyd4OxRu3etayM6iSj+6jByPbMUmrqZXp3czbI4njNs+SNFOzXth3uxpq86qJ8EQtLz0jBPjBKDSFXk2CkPSRvxL1YgsLoFLVsvxPFhvrRPdCbOpOZrUdLnHqujkpRlBMr9Uq+yOkkb+R0teWQt1vd7uninpGgXuAdBGYjFEqA6GoSjLSHNW9km6bNEA0s36iiU51+Kp1OZ603IkM1TTtUUElOWQ2eBh2pscFaN8f9SDByuuNbAQWCYiCgu2vPrdNBZEPp+VxJYnU1CUba4+Q1ahRF06YITuoZcU1tAkveyPc7c1Dc5Pe/5WgxpTXuMWz07poMAMYmhOPjadC2Me7IMlNEFmg7oWFxPJfVFzlVd0sSqwQjribBSHtEDACDF9SUqhU/hXaMtSfeQFzQMwJwYXIP/LwM7MouY9W+fJecsyU/7splxht/8tgfxZjN2gZHeeU1fLwpE4BbJzs3f6fDOrlnRBbMU1lm0rh6iMbCkjciSawuJ8FIe3h4nXjxSt6ItnLT1YJFfmEQHOuSU4b4ezFrtHquV385oGnviNms8MKP+wA4XGLk+125mrUF4J3VGdQZzaTGBjO2jySvNikkXh2OMFbDxre1bo170Cp51cIyKUGm97qcBCPtJXkj7uHkfBEXLlF/y8Q+eHno2XSk2DqNVQs/7s5ld3aZ9f///eWAZr0jpVX1fLD+CAB3nNEXnQt/Hx2K3gCT71e3V7+gJm92ZWXHofw46AwnhsBdzZIzUpYF1SXatKGLkmCkvU7OGxHacXG+iEVkoA9XjugFwKu/apOIqCgKL/2kZv9fOzoWPw8d+3Ir+DY9R5P2vLcug4paI/2jApjaP1KTNnQYQ69RC6BVFcL617RujbYsQzSRA52yppRNfEMgsKe6bZnVI1xCgpH2OnmNGjdJYuySrMGIa/JFTvaXSQkY9Dr+2F/AtswSl5//x1257Mouw9/LwN1n9eXCRD8AXvp5n8t7R6rqjLyzRi0CeNsZCbIwXmsMHjDln+r22pe7djVWrZNXLax5I5LE6koSjLRX5CDQe0B1EZRmat2arqmuEvL3qNsaBCMxoX5clqJ+m3rlF9f2jiiKwks/q70i14+LJ8TPi4v7+RPg46FJ78hHGzIprqonNtSPC5N7uPTcHdagadB9MNSWwZqXtG6NdizBiKsrr56qu5SF14IEI+3l6aPOqgGpxKqV7B2gmCGgBwRq8wF4+5QEdDr4aXcue3LKWn+Cg/y0O4+dx9VekZsnqrNW/L30zBkXB7i2d6TOaGbR72pp81snJ+Ah5d9to9fD1P9Tt/98A8q1GV7TlNl04v1Tq5k0FpFSFl4L8m7hCDGj1Nsf/k9NwhKuddySvKpd925CRDcuaOgJePVX19SNUHtF1Bk0142LJ9Tfy/rYnHHx1t6Rb9KzXdKez7dmkVNWQ2SAN9OH93TJOTuNxHOh1yh1Zs3vz2ndGtfL3wt1FeDVDSKStG3LyTNqZOjdZSQYcYTJD0BIbyg5Au9dBpUFWreoa9EwX+Rkd5yh1o34esdxDhdUOv18P+/OI/1YGX5eBm6Z2LiWR6CvJzdN6A3ASz/td3rviMms8NoqNQibO6kP3h5S5MwuOh2c2dA7svldKD6iaXNc7thJK/XqNX7thCeqQ++1pVB2TNu2dCESjDhCQHe47n9qFnbBXvhgmloITbiGtTaBtsHIwOhAzuwfiVmB11Y5N3fk5FyR68Y27hWxmDO+NwE+HuzPq+DrNOf2jnyTlk1GYRXBfp5cPco1dV46nd6ToM8Zar2c357WujWu5S7Jq6DWjwprqI4reSMuI8GIo4TEweyV4BeuTvP98Cqoq9K6VZ1fdQkUNQyL9NA2GAG4Y6raO/LZlmNkFTvv9//LnjzSjpXi62nglom9m9wnyNeTmyeoPSb//Xk/Jif1jiiKwsKGXpEbxsXj7+3hlPN0CVMfVm+3L4P8fdq2xZWyLMGIxvkiFt1lRo2rSTDiSBGJMPtzdeXHo+vg41lqmXLhPJZic8Fx4K99pc9hsSGMSwjDaFasyZyO1qhXZFwcYd28m933hvHxBDb0jnzjpN6RVXvz2Z2tDhfdMC7eKefoMnoNh/4XqQnZvz6hdWtco67yxIe+1jNpLCJljRpXk2DE0XoMgVmfgqcfHPwFVtwEJqPWreq83CRf5GR/naL2jny0MZO88hqHH//XvXnsyFJ7ReZObHndlyBfT25yYu+Ioii80lDs7doxcQT7nT5cJOw0ZR6gg10ru0YxxeztJ82Gi9a6NSopC+9yEow4Q+xomPmhuoje7i/hi7+C2ax1qzona76IG4w1NxibEMaw2GDqjGbe/uOwQ499crXV68a23CtiMWfCid4RR+eObDhcxOYjxXgZ9Nw8oenhImGn7gMheYa6/cvj2rbFFayL42m0Hk1TLD0jBfvAVK9tW7oICUacJWEKzHhXXWdh+zL47gGZJuYMx7eptxpO6z2VTqfjrw25Ix+sP0JxZZ3Djr1qbz7bG3pFbplk22q4gT6e1hokju4dseSKXDGiF5GBPg47bpd3xoPqjI79P8CRdVq3xrksM2ncZYgG1MU2vQLUZOKC/Vq3pkuQYMSZ+l8Il78O6GDDIvjlMa1b1LlUFkDpUUB3oiy/m5iSFMnAHoFU1plYvDbDIcdUFIX/NOSKXDsmlnAbekUsLLkjBxzYO5J+rJTf9uWj18GtkxIcckzRICwBUq9Vt395rHN/kdF6pd6m6HQnFs2T4mcuIcGIsw25Ei58Xt3+43lI/0zb9nQmljex8H7gE6htW06h0+m4oyF35N01hymvaX9X76p9+WzPLMHHU89cOz/8A308rbVIXvppn0N6RxY2TF++ZGg0sWF+7T6eOMWk+8HgDUfWqPlnnVF5bsMyGjq3yvsCTioLL0msriDBiCuMvAnG3KFup6/Qti2diRsmr57svMFR9Inwp6zGyH9/bl/hscYr88YREWB7r4jFDePjCfL15GB+JV/taHulYJNZ4Y3fDlrXvbmtodibcLCgnjDqFnW7s/aOWOqLRPQH7wBt23IqKQvvUhKMuErydPX20G+SEOUoblAGviUGvY47G3JH3vzjMDMXredQfoXdx8kqruLWDzazzdIrMtm2XJFTBfh4WmuS/OPTHTz93R4qau2b6XUgr5zpr61lwbd7UBS4elQMSVFu9iHSmUy4R80dOb4VSrO0bo3jWfNF3GiIxkIWzHMpCUZcpUcK+IZCXTlkbdS6NR2forh9zwjAZSk9+felg/DzMrAho4jzXvqD11YdxGhqfXZVTb2J//68nzOf/43vd+Zi0Ot46PwBRAa0PVH0xgm9OSMpgjqTmddWHWTqc6v4bEtWq702xob9L/jvarZllhDg7cEz04fw5OXJbW6LsIF/+IlpppZehM7EOpPGjZJXLSwzakqPQo3rFr/sqiQYcRW9QZ1hA513/NeVyo5DRa46WynKfT8QdTod142N54d7JjEpMYI6o5mnv9vDZQvXsPN400sGKIrCT7tyOefF33nhx33UGs2M6RPKt3dN5Pp2FhXz8/Jg8Q0jefO6EcSF+ZFXXsu9n2xn+utr2ZZZ0uRz9ueqvSFPf7eHOqOZM5Ii+OHeSVw5MgadTteu9ggbWBI7O1swYjaftFKvG/aM+IVCQEPdk7zd2ralC5BgxJUSzlRvD/ysbTs6A8ubWOQA8HL/5MleIX4smTOS52cMJcjXk/RjZVzyyhqe/X4PNfUm636HCyq58d2N3PzeJo4WVREV6MPLV6ey7JYxJHZ3zHCITqfj7IHd+eGeSdx/XhJ+Xga2Hi3hslfXcN+n28krUwu1GU1mFq46wIX/Xc32rFICfDx49oohLL5hJD2CfB3SFmEDazCyRdt2OFrhfqgtUwtEWnoh3I2UhXcZWUTClSw9I8e3QmWhW5Qv77Cs+SLuO0RzKp1Ox/ThvZiUGMGjX+zk67RsXv1VTQSdf8kg1h8q5M3fD1NnMuNp0HHzxD78dUpfp6314u1h4PYz+jJ9WC+e/m4Pn205xvLNWXybls0tk/rwyx610ivA1P6RPHl5MlFBUkvE5Sw5UdnbwGzSflVbR7EM0fRIAYObfhRFDoQDP0neiAu46SugkwqMVl/cebvg8CoYPF3rFnVcHSBfpDkRAd68OmsYF6fn8H//S+dQfiWz395gfXxSYgSPXjyQPhHdXNKe7oE+vHBlCteOiWP+FzvZnlXKfxpm7gT6ePDIxYOYNqynDMloJSIJPP2hrkKtCGqpf9HRudNKvc3pLjNqXEWGaVwtYap6e0DyRtrs5ORVd34ja8V5g6P46Z7JXDUiBoCewb68MXs4S+aMdFkgcrJhsSF8fvt4npsxlLgwP84bFMWP905m+vBeEohoSW84EXR3lrwRRYHMP9Vtd6q8eqqTF8zrjFOr3Yj0jLhawlRY9woc/Fl9ccubvP2KM6C6WF37x1ILoIMK8vPk6SuGcNdZ/Qjr5oW3h7Zd8Hq9jiuG9+KK4b00bYc4Rc9hcGS1GoxYKrN2VIoCP/wLctPVacsxY7RuUfMiktQk+ZoSNWk+qKfWLeq0pGfE1eLGgYcPlGdD/h6tW9MxWfJFug8Gj86xSmx0sK/mgYhwY51pRs3vz6pfyAAu+g8E9tC0OS3y8IawhqJ+MlTjVBKMuJqnL8SNV7dlVk3bdOB8ESHaxBKM5O6E+hpt29Ie61+DX59Qt89dAMNma9seW0hZeJeQYEQLfRum+B6UYKRNjnX8fBEh7BLUC/wjwGyEnDStW9M2W96H7x5Ut8/4J4y9Xdv22ErKwruEBCNasCSxHlkL9dXatqWjMZvUKY4gPSOi69DpOvZQTfpn8OXf1O2xf4XJ92vbHntIWXiXkGBECxH91cp+xho1IBG2KzygTnH09IPwJK1bI4TrdNRgZN8P8NktoJhh2PVwzuMdK3HfMqOmYK+sK+ZEEoxoQaeDvg29I1Ia3j6WKpRRQ9y3UJIQzmAZluxIwUjGavhktjq8NPgKuOjFjhWIAATHqXVeTHVQeFDr1nRabQpGli5dytSpU0lOTmbatGls2rSp2X1/+OEH5syZw5gxYxg2bBhXXXUVf/zxR5sb3GlY641I3ohdOkF9ESHaxFKJteigOrXd3R3bDB9epfYAJ54Pl7/eMavH6vUnCs1JWXinsTsY+eabb1iwYAG33XYbK1euZPjw4dxyyy0cP368yf03btzIuHHjWLRoEZ999hmjR4/mtttuY9euLj7+1mcKoIP83er8dWGbDlgGXgiH8AuFkN7qtiUod1e5u+CD6eqQau9JMONdMHhq3aq2s1RilbwRp7E7GFm8eDHTp09nxowZJCQkMG/ePKKioli2bFmT+8+bN49bbrmFIUOGEB8fz7333ktcXBy//NLFhyf8Qk98u5ehGtuY6k/MJIiWnhHRBXWEvBGzGT66Ru296TUSZi4Dzw6+ppGUhXc6uwbd6+rq2LlzJ3Pnzm10//jx49m61bZI3Ww2U1lZSXBwsD2nBsBkMrW+UxuO5+jj2krXZwr6Y5sx7/8JZcjVmrTBVRxyrXN2YjDWoHgHYA6OA41+b+5M69d0V6HVddZFp6JPX46StRmzu/6Oc9IwFB9G8fTDPPMj8PBt89+q27yew/tjAJTcne573dvBmdfZ1mPaFYwUFxdjMpkIC2u82mx4eDj5+fk2HeOdd96hurqa888/355TA5CW5pz59c46bmv8TTH0B8z7f2b71s1q2eFOrj3XusfeJUQD5QF92b99h+Ma1Qlp9Zrualx9nf0rA+gPGI+sZ8fWrW6ZDNp9/4f0AkpDhnBw7xHgSLuPqfXr2VBnIgXQlRxhx6a1mD38nH5Or8rjBOeswaO+HIOxEkN9wz9jJYb6CvTGKgzGSswefuwb+xx1fu2vZKvldW7TdIRTF81SFMWmhbS++uorXnnlFRYuXHhaQGOL5ORkDAbHfWCbTCbS0tIcflzbGzAIZfO/8KgtI6W7DqJTXN8GF2n3tc78E/3+DwDoNu5mUoamOLaBnYTmr+kuQrPrXJ+EsvYePGuLSekToRZDczP6HQ8DEDjsclJSUtp1LHd6PStrotBV5DAkyhN6pTj5ZAr6N25HZ8uSIXWlDCr+EWXcC20+nTOvs+XYrbErGAkJCcFgMFBQUNDo/sLCQsLDw1t87jfffMO8efN46aWXGDdunD2ntTIYDE55QTrruDacGHpPhj1fYTi0CmJGur4NLtama11VBJ/dDIoJBl+BPnWWW34jdCeavaa7GJdfZ0M3tQhXThqGnG0QGue6c9uitsK6Gq++39nqe5wDuMXruftAqMjBULAH4py8uN/BX9W1yzz9IeVq8A4En8CG26AT/y/NghU3od/xEZz5f+Df8udwa7S8znYlsHp5eTFo0CDWrFnT6P61a9eSmtr87IavvvqKBx98kOeff54zzjijTQ3ttKyl4TtxEmvxEXTf/gP/ojZMizOb4fNboewYhCbAxf+RQER0bdYk1i3atqMpGX+AuV6tzRHaR+vWOFakC9eo2bBIvU2dBRc+D2c9AhPugZE3QfIVkHgOxI6BwdPVmYXGGtj4lvPb5UR2z6aZM2cOy5cvZ/ny5Rw8eJAnn3yS7OxsZs6cCcDzzz/P/fefKPX71Vdf8cADD/DAAw8wdOhQ8vPzyc/Pp7y83HE/RUdmqTeStQFqyrRtizPUlsPSGeg3vU3iur/D/h/te/66V2D/92DwhiuXgHeAc9opREfhzjNqLHWT+p7Z+b40uGp6b/ER2Putuj3ylpb31elg3J3q9oY3O/TyInYHIxdccAEPPfQQCxcu5NJLL2XTpk0sWrSInj17ApCfn092drZ1/48//hij0ci///1vJkyYYP33xBNPOO6n6MhC4tVv/GYjHP5d69acrj0rhFp6NQr2ouj06M116D+ZBTs/t+35mRvg5/nq9vlPQVRy29siRGdhCUaOb1PXanInlsU/E87Uth3OYOkZydsJiuK882x8C1DUWlQRia3vP+BSCIqFqgLY8bHz2uVkbUpgnTVrFrNmzWrysaeeeqrR/99///22nKJr6XsmbDioDtUMuEjr1pywbiH8+DCMmAPnPa1WIrTH78/Cnq/A4IV59kpKf3iW0OO/wvIb1bHllpYPrypS9zMbYdA0GD6nfT+LEJ1FRH81l6CuHAr2Q2R/rVukKjoMRYdA76EWOutsIpJAp1frp5TnQGD7Z6+cpq4Ktrynbo/+i23PMXjAmFvh+3/C2lcg9Tr736vdQMdrcWdkGaqxfKtwB/u+V1/c5np1/PJ/t4PJaPvz93wDq55Uty96EWLGcHjYPzGnzlYXzPrir7D+taafqyiw8nYozVTHnS9+qfN1+QrRVnoD9BiqbrvTUI3l/avXKDW5srPx9IWIhrLw6cudc460T6GmRM256XeO7c8bdh14B0Hhftj/g3Pa5mQSjLiD+Img94TiDMcsxFRfDbu/UvM12iJ/Lyy/CVDUtukMsH2ZOqPFllUr8/fBZw2F8UbNhdRr1W2dAeXC/6hLiAN89yD89uzpXZ7rXoV934LBSy0j3Rnf2IRoD0v15uNulMR6oCEJ37IIaGc05jb19o/noabUscdWFDXvA2Dkzfat4+MdAMOvV7fXveLYdrmIBCPuwLubmhkN7Z9VYzLCsqvh41nwzvlQnmvf86uKYNlMtQs4bgJc+5maOKr3VHM9Pp7dch5JTalaCrquHOLGw7lPNn5cp1OXEJ8yT/3/r4/Dj/93IiDJ2gQ/PaJun7fgxDdAIcQJ7pbEaqo/kfPWGfNFLIZeDeFJ6lDN2pcde+yj6yA3Ta1Ya/kCZ4/Rt6pDZBl/uP/aRU2QYMRdWIdq2hmM/DwfDv2qbuemwTvnqmO5tjAZYfkcddw3OFYNQjy8YMDFcPVH4OGj9lgsm6mObZ7KbFZ7RAr3Q2BPmLGk6cWxdDqYfD+cu0D9/9qX4at71EDo0zlqnsjAy2DETW26BEJ0epZgJCe9fUnmjpK5Qf0C4hcGPVK0bo3zGDzUeh6g9uBW5Dnu2H++od4OuVJdu8xeQT3Vqb6g5o50MBKMuAtLMHL4dzDWte0Yacth7X/V7XMeV2fqFB9WA5Kc9Naf/8O/4NAqNTlu5rLGBXT6nQWzlquPHfpVXZHz1KnIqxbAvu/UoGXmUugW0fL5xt4Ol7wM6GDzYnhlJJQeVVcmveS/kiciRHOCY8EvXM3pyrXhb9vZrLNopnbI5Em79L9IDQbrq+C3ZxxzzNJjsPtLdXvU3Jb3bYllCHzn51CS2f52uVAnf9V0IFFD1DeXugq15oi9snfA/xpeiOPvVuee3/g9dB8MFbmw+AI4sq755295D/5sSCid9gZEDT59n94T4bqVaqLU0bXw/mVqbwaof0i/N/xhXvySWojHFsOugyveVrsXqwpOyhMJsu35QnRFOp17DdUc6MRTek+l08FZj6rbmxfb3vPcks2L1QrTceObfu+1VY8h6kwmxQR/vt7+drmQBCPuQq8/UY31izshz4Y1CSwqC9UcEWO1+mZwpro2BAFRcMPXEDsWakvV4GHf96c//8g6+OpedXvKPHVYpjkxo+D6L8A3VH0TXHIJHP5DrScCMOZ2GDrT9raD2rU4c5navXvpwk69Ro8QDmNJYtU6GKnIh+xt6nZCJ05ePVnvSep7rdkIvz7Z+v4tMdbC5nfV7fb0iliM+5t6u3mJ45NsnUiCEXcy+QG1eE3RIXjrTNjzdevPMRlh+Q1Q0jC8ccXbjbOwfYPVJNTE89SSwcuuhu0fnXi8JBM+vlbt7h14GUz6R+vnjE5Rgxz/SDUvZclFao9O/EQ4+zH7fmaLxHPgL7/BkBlte74QXY27lIW35Kh1T4aA7tq2xZUsX/rSPoWcdqx2u/NzqMxX8+z6O6DOVN+z1Fo0deUnapZ0ABKMuJOwBJj7q/qhXlehzkpZ9ZSaGNqcnx5R80w8/WHmh+Abcvo+Xn5w1QcwZKbafff5X9SCZnWV8NHV6vBIVDJcttD2PI3uA2HOt+ofEKhB1Ix31QQvIYTzRTf0jBTuh+oS7dphLQHfRXpFLKJT1IKMKPDzv9t+HEvi6ogbHfP+qdPB2DvU7fWv2VaOwQ1IMOJu/MNh9ufqNC1Qk0I/md10zZAdn56YU375a2qA0ByDJ1z2GoxpeJF+/xC8MUmN6P3C1WESL3/72hreV81LmfQPNZeknStGCiHs4B+mJqmDdlM5zeYTMwC7Qr7Iqab+S8132/8DZKxpff9TZW1Wa8UYvGDY9Y5rV/KVas912THYudJxx3UiCUbckcETzn8aLn1VfZHu+QreOqtxQbTj29QqpgAT/w4DL239uHo9nPvEie7FwgNq/ZCrPoDgmLa1NThG/YMMS2jb84UQbad1EmtuOlTmgaffiVpJXUlYgpqED2pZBXvXrNnQ0CsyeHrrsw/t4elzIv9k3cvOXUvHQSQYcWep16pDIQE9IH8PvDkFDvwElQVqnoexBvqefaKAmC10OjV4ueRldYG+y16DuLHO+xmEEM5jGarRKm/EMqU3fiJ4eGvTBq1Nul8tVJb554nVdm1RkQfpn6nbjkhcPdXIm9R2ZW+HjNWOP76DSTDi7nqNgLmroNdINTN66Qy1bkhpphpMTH/LvrLBFsOug79tkYRRIToyrXtGrPkiXXCIxiKwh7pQHai5I7aupLz5XXXiQK+RJ2ZGOZJfKKQ2LGjr6GqxTiDBSEdgmaJrWWSu8AB4dWtIWA3WunVCCK30GKKuHVWRA2XHXXvu2go4ul7d7or5Iicbfzf4BEP+btjxSev7m+ph0zvqtjN6RSzG3A7oYP/36grPbkyCkY7Cw1sdWrnweXXmyxWL3WfpcCGENrz8IbIhcd3VvSMZq9Vv9sFxkjPmGwwT7lG3f31SrR3SHEWB9BVQnq0mmQ68zHntCkuAPmeo24dWOe88DiDzMDsSnU5dzXHkzVq3RAjhLnoOU+v9HNvccsFCRzt40hCNLN2g9nD8+bq6pMWmd2DUX9Tt/L0n/hXsVVc1r20oRjZijrr+lzP1GqnWgrEUpnNTEowIIURH1nMYbFni+p6RrlQC3hZefnDGg/DlXfDTo/DTfLUqdlN0enVFcmcO0VhYVj7P3u78c7WDBCNCCNGRWZNYt6qLbDr7mzZAcQYUHVRrbPSe5PzzdRQp16oFJQv2qv83eEFYP4hIVKuihjfchiW4bvaRJRjJ260OH7nprCcJRoQQoiOLGKDmHlTmqYtdjr/L+ee09Ir0GgU+gc4/X0dh8IDrv1R7IcIS1HwaratSB/VSK3NXF6sBiZuu/SUJrEII0ZEZPE6sIrvqadfMqumqJeBtEdBdXWsrLEH7QATUfJ4OMFQjwYgQQnR0Q69WeynqK+GH/3PuuUz16npYIPkiHYUEI0IIIZxOr4cLngV0kL4cDv/hvHNlblBXhPULgx4pzjuPcBwJRoQQQrhEdIq68ivAt/c7b7VWy5TePlPUIEi4v6iGYCQ3HUxGbdvSDHklCSFEZzH1X+AbCnm7YMObjj++osD+H9XtrlwCvqMJ7aNW7TbWQKF7VmKVYEQIIToLv1A46xF1e9UCKM917PH/eA5ydqhTeiVfpOPQ6yFqiLrtpkM1EowIIURnkjobolOhtgx+esRxx01bDr88rm6f/4w6a0R0HG6eNyLBiBBCdCZ6A1zwvLq9fdmJxeza4+h6WHm7uj32r+ry9KJj6SE9I0IIIVyp13C1hwTg6/tsX9a+KYUHYdnVYKqF/hfB2f92TBuFa1l6RnLSwGzWti1NkGBECCE6o7MeBZ8gdRE9y3L19qoqgg+vhOoidehn2iK150V0POFJ4OGjDt8VH9a6NaeRYEQIIToj/3CY2lAA7ZfHoLLAvucb6+Dj2VB4AAJ7wdUfgZe/49spXMPgAd0HqdtuOFQjwYgQQnRWI26EqGSoKVVXkrWVosCXf4Mjq8ErAGZ9AgFRTmumcBE3TmKVYEQIITorvQEueE7d3vo+ZG227Xm/P6cmv+oMcOW7J75Ri47Njaf3SjAihBCdWewYde0agOU3wLcPwpb3IGsT1Facvv+OT+HXhim8Fz4Hfc9yWVOFk1mTWHeovV9uxA2WFBRCCOFUZ/8b9v8AJUfhz9caPxYSD5ED1X/dIuGHf6n3j/3rifLyonOIHKgWrKsqhLJjENRL6xZZSTAihBCdXbdIuG2tWso9bzfk7YTcXVCZB8UZ6r+935zYX6bwdk6ePhAxQJ1hlb1dghEhhBAuFhAFw2Y3vq+yQF3HJm835O5UbwOi4PLXZQpvZ9VjyIlgpP+FWrfGSoIRIYToqvzDofck9Z/oGnoMhW1L3S6JVRJYhRBCiK7COr13h7btOIUEI0IIIURX0X0woIPy41CRp3VrrCQYEUIIIboK724Q1lfddqPeEQlGhBBCiK7EOlSzTdNmnEyCESGEEKIrccOy8BKMCCGEEF3JyZVY3YQEI0IIIURX0qNhjZriDKgu1rQpFhKMCCGEEF2JbwgEx6rbOWnatqWBBCNCCCFEV+NmeSMSjAghhBBdjQQjQgghhNBUjxT11k1qjUgwIoQQQnQ1UQ1JrAX7oK5S27YgwYgQQgjR9QR0h25RgAK56Vq3RoIRIYQQoktqyBvRuUG9EQlGhBBCiK7IjZJYJRgRQgghuqKG4mc6N6g1IsGIEEII0RVZekbyd6Mz1WnaFAlGhBBCiK4oKAZ8Q9CZjfiWZ2jaFAlGhBBCiK5Ip7P2jviV7tO0KW0KRpYuXcrUqVNJTk5m2rRpbNq0qcX9N2zYwLRp00hOTubMM89k2bJlbWqsEEIIIRzIGozs17QZdgcj33zzDQsWLOC2225j5cqVDB8+nFtuuYXjx483uX9mZiZz585l+PDhrFy5kltvvZUnnniC77//vt2NF0IIIUQ7NBQ/8y09oGkz7A5GFi9ezPTp05kxYwYJCQnMmzePqKioZns7PvroI3r06MG8efNISEhgxowZTJs2jXfeeafdjRdCCCFEOzSUhfcrOwhmo2bN8LBn57q6Onbu3MncuXMb3T9+/Hi2bt3a5HO2bdvG+PHjG903ceJEVqxYQX19PZ6enjaf32Qy2dNcm4/n6OOK08m1dg25zq4h19k15Dq7QHAcei9/9HWV1OfugR6DHXp4W393dgUjxcXFmEwmwsLCGt0fHh5Ofn5+k88pKCggPDy80X1hYWEYjUaKi4uJjIy0+fxpac6ZC+2s44rTybV2DbnOriHX2TXkOjtXv8AkAgu2cDj9T8pztekdsSsYsdDpdI3+ryjKafe1tn9T97cmOTkZg8Fg13NaYjKZSEtLc/hxxenkWruGXGfXkOvsGnKdXcPUcyEZaz8lfvIsDF4+jj12w++wNXYFIyEhIRgMBgoKChrdX1hYeFrvh0VTvSZFRUV4eHgQHBxsz+kxGAxOeUE667jidHKtXUOus2vIdXYNuc5OFpFIYdyFxHj5aHad7Upg9fLyYtCgQaxZs6bR/WvXriU1NbXJ56SkpLB27dpG961evZrBgwfblS8ihBBCiM7J7tk0c+bMYfny5SxfvpyDBw/y5JNPkp2dzcyZMwF4/vnnuf/++637z5w5k+PHj7NgwQIOHjzI8uXLWbFiBTfeeKPjfgohhBBCdFh254xccMEFFBcXs3DhQvLy8khMTGTRokX07NkTgPz8fLKzs637x8TEsGjRIhYsWMDSpUuJjIxk3rx5nHvuuY77KYQQQgjRYbUpgXXWrFnMmjWryceeeuqp0+4bNWoUn3/+eVtOJYQQQohOTtamEUIIIYSmJBgRQgghhKYkGBFCCCGEpiQYEUIIIYSmJBgRQgghhKYkGBFCCCGEpiQYEUIIIYSmJBgRQgghhKYkGBFCCCGEptpUgdXVFEUB1KWIHclyPEcfV5xOrrVryHV2DbnOriHX2TWceZ0tx7R8jjdHp7S2hxuoq6sjLS1N62YIIYQQog2Sk5Px8vJq9vEOEYyYzWaMRiN6vR6dTqd1c4QQQghhA0VRMJvNeHh4oNc3nxnSIYIRIYQQQnReksAqhBBCCE1JMCKEEEIITUkwIoQQQghNSTAihBBCCE1JMCKEEEIITUkwIoQQQghNSTAihBBCCE1JMCKEEEIITXXpYGTp0qVMnTqV5ORkpk2bxqZNm7RuUoe2ceNGbr31ViZMmEBSUhI//fRTo8cVReHll19mwoQJDBkyhNmzZ7N//36NWttxvfHGG0yfPp3U1FTGjh3L7bffzqFDhxrtI9e6/T788EMuvvhihg0bxrBhw7jqqqv47bffrI/LNXaON954g6SkJJ544gnrfXKt2+/ll18mKSmp0b/x48dbH9f6GnfZYOSbb75hwYIF3HbbbaxcuZLhw4dzyy23cPz4ca2b1mFVVVWRlJTEww8/3OTjb775JosXL+bhhx9m+fLlhIeHM2fOHCoqKlzc0o5tw4YNzJo1i08++YTFixdjMpm46aabqKqqsu4j17r9oqKiuO+++1ixYgUrVqxgzJgx3HHHHdY3aLnGjrdjxw4+/vhjkpKSGt0v19ox+vXrx+rVq63/vvzyS+tjml9jpYu64oorlIcffrjRfeedd57y3HPPadSiziUxMVH58ccfrf83m83K+PHjlTfeeMN6X21trTJ8+HBl2bJlWjSx0ygsLFQSExOVDRs2KIoi19qZRo4cqXzyySdyjZ2goqJCOeecc5Q1a9Yo1157rfL4448riiKvZ0f573//q1xyySVNPuYO17hL9ozU1dWxc+dOJkyY0Oj+8ePHs3XrVo1a1bllZWWRn5/f6Jp7eXkxcuRIuebtVF5eDkBQUBAg19oZTCYTX3/9NVVVVaSmpso1doJ///vfTJ48mXHjxjW6X6614xw5coQJEyYwdepU7rnnHjIzMwH3uMYeLjmLmykuLsZkMhEWFtbo/vDwcPLz8zVqVedmua5NXXMZGms7RVFYsGABw4cPJzExEZBr7Uh79+5l5syZ1NbW4ufnx6uvvkrfvn3ZsmULINfYUb7++mt27drF8uXLT3tMXs+OMWTIEJ5++mni4+MpLCzktddeY+bMmXz11VducY27ZDBiodPpGv1fUZTT7hOO1dQ1F23373//m3379vHhhx+e9phc6/br3bs3K1eupKysjB9++IEHHniADz74wPq4XOP2y87O5oknnuCdd97B29u72f3kWrfP5MmTG/0/JSWFs88+m5UrVzJ06FBA22vcJYdpQkJCMBgMFBQUNLq/sLCQ8PBwjVrVuUVERADINXegxx57jF9++YUlS5YQFRVlvV+uteN4eXkRFxdHcnIyf//73+nfvz/vvfeeXGMH2rlzJ4WFhUybNo2BAwcycOBANmzYwPvvv8/AgQOt11OutWP5+fmRmJhIRkaGW7yeu2Qw4uXlxaBBg1izZk2j+9euXUtqaqpGrercevXqRURERKNrXldXx8aNG+Wa20lRFP7973/zww8/sGTJEmJiYho9LtfaeRRFoa6uTq6xA40ZM4Yvv/ySlStXWv8NHjyYiy++mJUrVxITEyPX2gnq6uo4ePAgERERbvF67rLDNHPmzOH+++9n8ODBpKam8vHHH5Odnc3MmTO1blqHVVlZydGjR63/z8rKYvfu3QQFBREdHc11113HG2+8QXx8PHFxcbzxxhv4+Phw0UUXadjqjmf+/Pl89dVXLFy4EH9/f+t4b0BAAD4+Puh0OrnWDvDCCy8wadIkoqKiqKys5JtvvmHDhg289dZbco0dqFu3btZ8Jws/Pz+Cg4Ot98u1br+nn36aKVOm0KNHD4qKinjttdeoqKjg8ssvd4vXc5cNRi644AKKi4tZuHAheXl5JCYmsmjRInr27Kl10zqs9PR0rrvuOuv/FyxYAMDll1/OU089xS233EJtbS3z58+ntLSUoUOH8s4779CtWzetmtwhLVu2DIDZs2c3un/BggVMmzYNQK61AxQUFHD//feTl5dHQEAASUlJvPXWW9ZCUXKNXUeudfvl5ORw7733UlJSQkhICCkpKXzyySfWzzytr7FOkSwgIYQQQmioS+aMCCGEEMJ9SDAihBBCCE1JMCKEEEIITUkwIoQQQghNSTAihBBCCE1JMCKEEEIITUkwIoQQQghNSTAihBBCCE1JMCKEEEIITUkwIoQQQghNSTAihBBCCE1JMCKEEEIITf0/IUtWCsOO16cAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(model.predict_proba(X)[0], label=['background', 'CG island'])\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53ce7fda",
   "metadata": {},
   "source": [
    "We can see here the transition from the first non-island region to the middle island region, with high probabilities in one column turning into high probabilities in the other column. The predict method is just taking the most likely element --- the maximum-a-posteriori estimate.\n",
    "\n",
    "In addition to using the forward-backward algorithm to just calculate posterior probabilities for each observation, we can count the number of transitions that are predicted to occur across each edge."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "cb57f555",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[28.9100,  2.4128],\n",
       "        [ 2.8955, 15.7806]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transitions = model.forward_backward(X)[0][0]\n",
    "transitions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0519180b",
   "metadata": {},
   "source": [
    "### Initializing Hidden Markov Models\n",
    "\n",
    "There are two ways to initialize an HMM using pomegranate. The first is to explicitly pass a list of distributions, a dense transition matrix, and optionally start and end probabilities. We can recreate the above model using this approach."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "6bd07c92",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = DenseHMM([d1, d2], edges=[[0.89, 0.1], [0.1, 0.9]], starts=[0.5, 0.5], ends=[0.01, 0.0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6adc4910",
   "metadata": {},
   "source": [
    "We can check that this initialization produces the same model by making the same plot of predicted probabilities across the sequence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "21036aaf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(model.predict_proba(X)[0], label=['background', 'CG island'])\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fef1d863",
   "metadata": {},
   "source": [
    "This also works when creating a `SparseHMM` object, though the edges must be a list of 3-ples rather than a matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "58e15480",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pomegranate.hmm import SparseHMM\n",
    "\n",
    "edges = [\n",
    "    [d1, d1, 0.89],\n",
    "    [d1, d2, 0.1],\n",
    "    [d2, d1, 0.1],\n",
    "    [d2, d2, 0.9]\n",
    "]\n",
    "\n",
    "model = SparseHMM([d1, d2], edges=edges, starts=[0.5, 0.5], ends=[0.01, 0.0])\n",
    "\n",
    "plt.plot(model.predict_proba(X)[0], label=['background', 'CG island'])\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45a110ac",
   "metadata": {},
   "source": [
    "The second way is to follow the procedure outlined above where you first create an uninitialized model with nothing passed into it and then you add the distributions and edges using the appropriate methods. Although this can be used for both `DenseHMM` and `SparseHMM` modls, this is likely most useful for `SparseHMM` models that are very sparse or when you're trying to procedurally generate an HMM based on external factors. Here is the same code as before that implements the HMM using this approach."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "63d27732",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = SparseHMM()\n",
    "model.add_distributions([d1, d2])\n",
    "model.add_edge(model.start, d1, 0.5)\n",
    "model.add_edge(model.start, d2, 0.5)\n",
    "model.add_edge(d1, d1, 0.89 )\n",
    "model.add_edge(d1, d2, 0.10 )\n",
    "model.add_edge(d1, model.end, 0.01)\n",
    "model.add_edge(d2, d1, 0.1 )\n",
    "model.add_edge(d2, d2, 0.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40c26d2c",
   "metadata": {},
   "source": [
    "Similar to other methods, we can create an HMM with uninitialized distributions. These distributions will be initialized using k-means clustering when provided with data. When using a `DenseHMM` we can also choose to not pass in edges and have them be initialized to uniform probabilities. When using a `SparseHMM` we must pass in edges because, otherwise, the model will not know which edges exist and which do not. Essentially, it would have to assume uniform probabilities as well, at which point the model would have a dense transition matrix but just operate inefficiently by treating it as a sparse matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "96e650df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Parameter containing:\n",
       " tensor([-0.6929,  0.2710]),\n",
       " Parameter containing:\n",
       " tensor([1.0994, 0.7262]),\n",
       " Parameter containing:\n",
       " tensor([ 0.4207, -1.0267]))"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from pomegranate.distributions import Normal\n",
    "\n",
    "X3 = torch.randn(100, 50, 2)\n",
    "\n",
    "model3 = DenseHMM([Normal(), Normal(), Normal()], verbose=True)\n",
    "model3._initialize(X3)\n",
    "model3.distributions[0].means, model3.distributions[1].means, model3.distributions[2].means"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d480be39",
   "metadata": {},
   "source": [
    "You can control how the k-means itself is initialized by passing in a value to `init`.\n",
    "\n",
    "However, you do not need to manually initialize your models. If you call the `fit` method or the `summarize` method, these distributions will be initialized if they have not yet been."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "c9481c5d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] Improvement: -23.134765625, Time: 0.007689s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "DenseHMM(\n",
       "  (start): Silent()\n",
       "  (end): Silent()\n",
       "  (distributions): ModuleList(\n",
       "    (0): Normal()\n",
       "    (1): Normal()\n",
       "    (2): Normal()\n",
       "  )\n",
       ")"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X3 = torch.randn(100, 50, 2)\n",
    "\n",
    "model3 = DenseHMM([Normal(), Normal(), Normal()], max_iter=5, verbose=True)\n",
    "model3.fit(X3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd93f0d6",
   "metadata": {},
   "source": [
    "#### Dense and Sparse HMMs\n",
    "\n",
    "Separately from whether the HMM is initialized by passing in the distributions and edges initially or building the model programmatically, the transition matrix can be represented using a sparse matrix or a dense matrix. Although a dense transition matrix allows fast matrix multiplications to be used for each algorithm, once there are enough zeroes a matrix multiply wastes a lot of computation handling them. \n",
    "\n",
    "Because the backend and strategy for initializing the model (i.e., passing in a dense transition matrix or a list of edges) differ, pomegranate v1.0.0 splits the implementation in two: `DenseHMM` and `SparseHMM`. Both have the same functionality and API and, given the same transition matrix, will yield the same result. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "c392872e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0.8016, 0.1984],\n",
       "        [0.6708, 0.3292],\n",
       "        [0.6163, 0.3837],\n",
       "        [0.4196, 0.5804],\n",
       "        [0.3092, 0.6908],\n",
       "        [0.2535, 0.7465],\n",
       "        [0.2361, 0.7639]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "edges = [[0.89, 0.1], [0.1, 0.9]]\n",
    "starts = [0.5, 0.5]\n",
    "ends = [0.01, 0.0]\n",
    "\n",
    "model1 = DenseHMM([d1, d2], edges=edges, starts=starts, ends=ends)\n",
    "model1.predict_proba(X)[0][12:19]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "212880ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0.8016, 0.1984],\n",
       "        [0.6708, 0.3292],\n",
       "        [0.6163, 0.3837],\n",
       "        [0.4196, 0.5804],\n",
       "        [0.3092, 0.6908],\n",
       "        [0.2535, 0.7465],\n",
       "        [0.2361, 0.7639]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "edges = [\n",
    "    [d1, d1, 0.89],\n",
    "    [d1, d2, 0.1],\n",
    "    [d2, d1, 0.1],\n",
    "    [d2, d2, 0.9]\n",
    "]\n",
    "\n",
    "model2 = SparseHMM([d1, d2], edges=edges, starts=starts, ends=ends)\n",
    "model2.predict_proba(X)[0][12:19]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "e46f5fb3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "102 ms ± 13.9 ms per loop (mean ± std. dev. of 5 runs, 10 loops each)\n",
      "177 ms ± 12.9 ms per loop (mean ± std. dev. of 5 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "X = numpy.random.choice(4, size=(1000, 500, 1))\n",
    "\n",
    "%timeit -n 10 -r 5 model1.predict_proba(X)\n",
    "%timeit -n 10 -r 5 model2.predict_proba(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7e1c416",
   "metadata": {},
   "source": [
    "Check out the benchmarks folder to see a more thorough comparison of the two, but it looks like even for a tiny model that the dense transition matrix is around twice as fast."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f42ef6a",
   "metadata": {},
   "source": [
    "### Fitting Hidden Markov Models\n",
    "\n",
    "Hidden Markov models are usually fit to unlabeled data using the Baum-Welch algorithm. This is a structured EM algorithm that accounts for transitions between distributions as well as the distribution parameters themselves. Essentially, one uses the forward-backward algorithm to infer the expected number of transitions across each edge and the expected probability of each observation aligning to each state and uses those estimates to update the underlying parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "7ffaad1d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] Improvement: 16405.125, Time: 0.09408s\n",
      "[2] Improvement: 420.75, Time: 0.0876s\n",
      "[3] Improvement: 207.25, Time: 0.09545s\n",
      "[4] Improvement: 116.125, Time: 0.107s\n",
      "[5] Improvement: 75.3125, Time: 0.09284s\n",
      "[6] Improvement: 47.6875, Time: 0.0797s\n",
      "[7] Improvement: 34.75, Time: 0.1045s\n",
      "[8] Improvement: 27.3125, Time: 0.08161s\n",
      "[9] Improvement: 16.0625, Time: 0.08903s\n",
      "[10] Improvement: 15.6875, Time: 0.1197s\n",
      "[11] Improvement: 9.1875, Time: 0.09623s\n",
      "[12] Improvement: 10.625, Time: 0.08911s\n",
      "[13] Improvement: 8.125, Time: 0.1064s\n",
      "[14] Improvement: 6.3125, Time: 0.07936s\n",
      "[15] Improvement: 2.3125, Time: 0.08887s\n",
      "[16] Improvement: 5.0625, Time: 0.108s\n",
      "[17] Improvement: 4.3125, Time: 0.08656s\n",
      "[18] Improvement: 3.1875, Time: 0.08103s\n",
      "[19] Improvement: 1.75, Time: 0.1282s\n",
      "[20] Improvement: 4.4375, Time: 0.09025s\n",
      "[21] Improvement: -1.6875, Time: 0.07991s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "DenseHMM(\n",
       "  (start): Silent()\n",
       "  (end): Silent()\n",
       "  (distributions): ModuleList(\n",
       "    (0): Categorical()\n",
       "    (1): Categorical()\n",
       "  )\n",
       ")"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d1 = Categorical([[0.25, 0.25, 0.25, 0.25]])\n",
    "d2 = Categorical([[0.10, 0.40, 0.40, 0.10]])\n",
    "\n",
    "edges = [[0.89, 0.1], [0.1, 0.9]]\n",
    "starts = [0.5, 0.5]\n",
    "ends = [0.01, 0.0]\n",
    "\n",
    "model = DenseHMM([d1, d2], edges=edges, starts=starts, ends=ends, verbose=True)\n",
    "model.fit(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5e96225",
   "metadata": {},
   "source": [
    "We can change the number of iterations by setting either the `max_iter` parameter or the `tol` parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "de6627ad",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] Improvement: 16405.125, Time: 0.1029s\n",
      "[2] Improvement: 420.75, Time: 0.1356s\n",
      "[3] Improvement: 207.25, Time: 0.1192s\n",
      "[4] Improvement: 116.125, Time: 0.08874s\n",
      "[5] Improvement: 75.3125, Time: 0.1781s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "DenseHMM(\n",
       "  (start): Silent()\n",
       "  (end): Silent()\n",
       "  (distributions): ModuleList(\n",
       "    (0): Categorical()\n",
       "    (1): Categorical()\n",
       "  )\n",
       ")"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d1 = Categorical([[0.25, 0.25, 0.25, 0.25]])\n",
    "d2 = Categorical([[0.10, 0.40, 0.40, 0.10]])\n",
    "\n",
    "edges = [[0.89, 0.1], [0.1, 0.9]]\n",
    "starts = [0.5, 0.5]\n",
    "ends = [0.01, 0.0]\n",
    "\n",
    "model = DenseHMM([d1, d2], edges=edges, starts=starts, ends=ends, max_iter=5, verbose=True)\n",
    "model.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "66c35bdf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] Improvement: 16405.125, Time: 0.1512s\n",
      "[2] Improvement: 420.75, Time: 0.1788s\n",
      "[3] Improvement: 207.25, Time: 0.1501s\n",
      "[4] Improvement: 116.125, Time: 0.127s\n",
      "[5] Improvement: 75.3125, Time: 0.08657s\n",
      "[6] Improvement: 47.6875, Time: 0.1011s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "DenseHMM(\n",
       "  (start): Silent()\n",
       "  (end): Silent()\n",
       "  (distributions): ModuleList(\n",
       "    (0): Categorical()\n",
       "    (1): Categorical()\n",
       "  )\n",
       ")"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d1 = Categorical([[0.25, 0.25, 0.25, 0.25]])\n",
    "d2 = Categorical([[0.10, 0.40, 0.40, 0.10]])\n",
    "\n",
    "edges = [[0.89, 0.1], [0.1, 0.9]]\n",
    "starts = [0.5, 0.5]\n",
    "ends = [0.01, 0.0]\n",
    "\n",
    "model = DenseHMM([d1, d2], edges=edges, starts=starts, ends=ends, tol=50, verbose=True)\n",
    "model.fit(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bef914f3",
   "metadata": {},
   "source": [
    "The same parameters and signature applies to `SparseHMM` models."
   ]
  }
 ],
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