{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Stochastic Gene Expression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "The expression level of a gene refers to how many biomolecules encoded by the gene are produced. If the gene encodes a functional protein, then we may like to know how many copies of this protein are produced. The biochemical processes involved in the production of biomolecules are stochastic, since at the molecular level each chemical reaction happens at a random time. Therefore, gene expression is stochastic in nature, and such stochasticity is significant for genes that are not highly expressed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as st\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Production and degradation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "We can study stochastic gene expression in the same way as for population growth. Imagine that we are interested in a gene that encodes a particular protein. The production and degradation of the protein is analogous to the birth and death of individuals in a population. For simplicity, let us assume that the protein is being produced at a constant rate, $k$. Unlike for population growth, this rate is not proportional to the number of existing members, since proteins do not self-reproduce (they are translated from mRNAs). On the other hand, the degradation rate will be proportional to the number of proteins, $N$, since each protein has the same probability of being degraded per unit time; let this degradation rate *per protein* be $\\gamma$. Therefore, in a short time interval $\\Delta t$, there will be about $k \\Delta t$ new proteins produced, and $N \\gamma \\Delta t$ proteins degraded. We may expect that, at equilibrium, the production and degradation will balance out, hence the equilibrium number of proteins will be $N_{eq} = k / \\gamma$. This is true only *on average*. As we have seen for population growth, the actual number will fluctuate with time. We would like to find out the range of such fluctuations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "To do that, let us simulate the stochastic processes. Denote the protein by $A$, then we can write down the reactions corresponding to the production and degradation of this protein:\n",
    "\\begin{align}\n",
    "\\emptyset &\\xrightarrow{k} A \\\\\n",
    "A & \\xrightarrow{\\gamma} \\emptyset\n",
    "\\end{align}\n",
    "The first reaction means the protein is being created from \"nothing\" at a constant rate $k$, and the second reaction means the protein is being removed at a per capita rate $\\gamma$. As before, we will simulate these reactions using the Gillespie algorithm. Recall that the main idea is to draw exponentially distributed random numbers as putative times of the next event. In this case, the waiting time for the production of another protein is exponentially distributed with mean $1/k$, and that for the degradation of an existing protein has mean $1/(N\\gamma)$. Which random number happens to be smaller determines which event actually happens in the simulation, i.e., whether the next event is production or degradation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "source": [
    "Here is a python class that simulates such a process, based on our [previous code](./birth-death.ipynb) for the birth-death process. You may notice that, besides changing variable names, we only had to change one line of the code (where `k_b` is no longer proportional to $N$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "class ProductionDegradation:\n",
    "    \"\"\"\n",
    "    simulate the production and degradation of a protein using Gillespie algorithm.\n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, production_rate, degradation_rate=1., N0=0):\n",
    "        \"\"\"\n",
    "        initialize the simulation.\n",
    "        inputs:\n",
    "        production_rate: float, overall production rate.\n",
    "        degradation_rate: float, degradation rate per protein.\n",
    "        N0: int, initial population size.\n",
    "        \"\"\"\n",
    "        self.production_rate = production_rate\n",
    "        self.degradation_rate = degradation_rate\n",
    "        self.num = N0    # current number of proteins\n",
    "        self.time = 0.    # time since beginning of simulation\n",
    "        self.num_hist = [N0]    # list to record history of protein numbers\n",
    "        self.time_hist = [0.]    # list to record time of all events\n",
    "    \n",
    "    def next_event(self):\n",
    "        \"\"\"\n",
    "        generate the waiting time and identity of the next event.\n",
    "        outputs:\n",
    "        tau: float, waiting time before next event.\n",
    "        event: int, 0 means production and 1 means degradation.\n",
    "        \"\"\"\n",
    "        k_b = self.production_rate    # overall production rate, NOT proportional to number of proteins\n",
    "        k_d = self.num * self.degradation_rate    # overall degradation rate\n",
    "        k_d = max(k_d, 1e-10)    # if k_d is zero (when N=0), replace by a small number to avoid division by 0\n",
    "        t_b = np.random.exponential(1/k_b)    # draw putative production time\n",
    "        t_d = np.random.exponential(1/k_d)    # draw putative degradation time\n",
    "        if t_b < t_d:    # production happens first\n",
    "            event = 0    # use 0 to label production\n",
    "            return t_b, event\n",
    "        else:    # degradation happens first\n",
    "            event = 1    # use 1 to label degradation\n",
    "            return t_d, event\n",
    "    \n",
    "    def run(self, T):\n",
    "        \"\"\"\n",
    "        run simulation until time T since the beginning.\n",
    "        inputs:\n",
    "        T: float, time since the beginning of the simulation.\n",
    "        \"\"\"\n",
    "        while self.time < T:\n",
    "            tau, event = self.next_event()    # draw next event\n",
    "            self.time += tau    # update time\n",
    "            if event == 0:    # production happens\n",
    "                self.num += 1    # increase number of proteins by 1\n",
    "            elif event == 1:    # degradation happens\n",
    "                self.num -= 1    # decrease number of proteins by 1\n",
    "            self.time_hist.append(self.time)    # record time of event\n",
    "            self.num_hist.append(self.num)    # record protein number after event"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "Let us test this class. We will start from $N_0 = 0$, i.e., with no protein initially. (Such an initial value was not possible for population growth, as it means the population is already extinct.) Let us aim for an equilibrium number of proteins $N_{eq} = 100$. We can always rescale time so that the degradation rate $\\gamma = 1$; then we need the production rate to be $k = N_{eq} \\gamma = 100$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "k = 100.    # production rate\n",
    "g = 1.    # degradation rate per protein\n",
    "N_eq = k / g    # expected equilibrium number"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "current time = 10.000858598390236, current protein number = 111\n"
     ]
    }
   ],
   "source": [
    "pd1 = ProductionDegradation(k, g, N0=0)\n",
    "pd1.run(10)\n",
    "print(f'current time = {pd1.time}, current protein number = {pd1.num}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "As for any stochastic simulation, if we rerun the simulation, we will get a somewhat different result. To see the amount of fluctuation in the result, let us repeat the simulation multiple times and plot their trajectories."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "current time = 25.002535015562486, current protein number = 89\n",
      "current time = 25.008365291579384, current protein number = 92\n",
      "current time = 25.00037835063049, current protein number = 114\n",
      "current time = 25.000301532112346, current protein number = 115\n",
      "current time = 25.002937393015774, current protein number = 100\n",
      "current time = 25.007934515600976, current protein number = 101\n",
      "current time = 25.001950258171757, current protein number = 84\n",
      "current time = 25.003033945598123, current protein number = 96\n",
      "current time = 25.026103730452398, current protein number = 93\n",
      "current time = 25.00334911357203, current protein number = 100\n"
     ]
    }
   ],
   "source": [
    "T = 25.    # total amount of time to simulate\n",
    "trials = 10    # number of simulations to repeat\n",
    "pd_list = []    # list to store simulations\n",
    "\n",
    "for i in range(trials):\n",
    "    pd1 = ProductionDegradation(k, g, N0=0)\n",
    "    pd1.run(T)\n",
    "    print(f'current time = {pd1.time}, current protein number = {pd1.num}')\n",
    "    pd_list.append(pd1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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vEKitZduIkXh7oT51d9Ja7K7fbXh/2oq1IYMyQKnHFxIM7VTY1G/g1DSuylOD/s92lLL/0wdC+7hX/peL9l1EzYHIuhWyrXueSRZhiWooP1p8dRzJTb40msV4837xxssAbF2k2w3qq1op21Fv2K85RT0Y7zAv1OazGzM8VjtPDr0Oz6gan+Lott/9rm7aFDaFqX5c9ft4ZPE+NpTUR9136W7jg98embtsmPKC/uIx5eNgb9NICCuQPnCNvlp44ptT1bGZTqRdf1T8R8kw7i1vRgTP669qw72j81oGnr0NNLy7DxkcnJZsD1NVaPpgXb8ncuXh3rmT4quvJtCsexE9csDovbdtwECeGqgcUn8qXVH7cLDhy60YJJJ0Sz72flMZUKXfF2219Yb9joZBG8Dr9fLoo4+ycOFCWlqMnlNLyw6/JvbmNuNQuXDnAU5fGj22wWOxUBHmv7B4x0oqKnbxt/deY/maVgSCPWsiPdm0lkgPL/+hQ9Q9/wIyoP++lrIqLlyq4avomapsplDoA7R2GMj9XjWLXvrC06G2T56MvVwNhLkoWjSHYdvb76R03F3tZxFo3fQ7fSAYIdqZKsHtdvPyyy9HtF//ZHR1V8egs4CUeGz65/Asi64qSq+tYNbQTMb0S2bu8GykAN/kTLxTMkL7+I7S7Fb6NLRYsRydfBdNn6nVwrKnwlQc9bpNp3pTcsQx+847n7bVa6j590Oh79kaRU3UToKwMCgzge/MNWbsXL6n5kupfJq8TczJ+D4pE79NQZ1ujK366U8N+x0tt9+tW7dSWqq+p/fee8+wbeHyhYb3qc5ULhhywWGdf3FDGwekMY5golsJzMFeL+E5TH46/Gf8cOmn/MFZRA25gHLo6IjsMNnwNzZSdf/9VNx9N+6wCVG/OsEVn2tU7T9KjgkdMIXCCUblvkaD5xCAz+rm3X9v5J83f0LjoTbszshZYF2Fbvdviy+jOldPhmdFn6WMcFqZkRA2uHqju3Q213nYvqKCp37TvcR439y0j7zPNvBCRXR9fSAQqbawEuBQs4cPt0Z6rRwKFo5JCxavGX7ne2hhY6AtoK+eatJ0T462N1/nz3VLeOOWU1RD8BiZrAvD8k5cbTujra2Ejz8ZTF2d7kPhHJYGD04PvZd3p8LmV+BXqUot1FZPTe0SPv5kMD6n+m68i16Dt35EtghbWbSvFNwNnfah5pFH2T5yFNtGjOT1+uiR6e1D/sc/mcNtC4xeLsv31jDw5+90qrqLRtZpNxFvU3YE59jLQu2BDeu4vtHJJfV+3n3tp7CzmwPdM5fCw6dGNC/cXUbup+vZGBZst2nTJhYuXEhbDPXM4ssX85uZv+GMAWcAkOpJ5eJ9F5PkTaI59Qqq+z/VZXc+WHMDoz3qmnscDkQHk+hn6R1icTXJwoULWbEirKBO2D2+MyeNZ351Oy3LlqndPfrnsQd329RgCoU+RW3tMqqq3ut6xw7sWBW5pIzzJbF3nVKnLF68nvzhI/WN+9VNFx593JysZmv24FLeF6ZfTrIKsuzdu20+GhfHbdMdMbePS4wLvX73kBrM/m/bAd4tr+N/S4o5ePAg69atY926ddx7b6SxPEGoPn/7v6tpchtn3Lsq1eqoLsxrRoa5Errt+mfaV3SO4djaRx/FEoxe/fc3Jkdct7Ht8D1x6upWsGz5XAAOlASDuDSJsAio2opNtM/07fBqyNRG4MAy1q9XUazNWetV371jYPVjLNbGhvZ7fbH6DgJVXcdSOEZegK3flJjbo62DzsOOA1h3QAmiRxZ3rdOuKW/mw8e28M+bP2HjGL1amGPg7NBrX8BCumZhIMobaMLmbgZl7XofytdGND9UolRiz3ZQfx1Iy2ZthdGGdvqA0w3v22MXClqUinFq9VTaks827PPU2IFRu7PVDk+n6Cs0gQ9H27qI/TShnp2WxlYkcN/6bTz3ssqZ1OYP8NbMeUhgd246h0oP4CtXcT8Hrr2WuueeA8CpqYmYR/SMsdkUCscp69Z/g02bb4m5/XB0r3P2Xh56/c/990G42uDxswz7tnsXARC86QJhQqE7QT9zkh8CYPnIODRrbBXF7UW5Udu/uWM/P/TV89RTz/Dq62/w+uuvExBRAqrCXi/bYzTcvbJO6dsvm6KHv2hh5ygJs+k2pgyK2cdZQyO9RP79+d4oe3bO2nVXRbRJvwZB4RNnUSsqjXgIi4ptaNHVBpq92bBvlkv/Lbau+Zw7Xt5I3evvh9rSh0dx9bTF4Rx+NnFTY5d0DK2ogvfYKdi4lThuxMmIXDV4ZyR0bTN6/+HN7FylVnGHMsdH3Wdf0bmG98Ife6DrjtouIyjsh9mN98s742ZwcbESaAWJatD/3oTvGfbZUKWihS1SDYtp3kjDv4hyHwL8Ji1yKE2p/itCM9oJ6uNVoKCUkrLULBYNn8i/PRaam5v5c10bf7n62ywZrwvscJVnxa9+DcD0LGXrmljQM5mATKFwnNDcvEOpFuq/oKlJ1++3tZVG7Lvx0xL+9d1PQ0FmT/9yeWjbpk8j9w9nxMHxfPrEv0Pv3y4bDlX69WTYUOsTkaUZtaBQSOpw5+TZ9XP0c2yi/9DYK4R2tv6y8yRkf516Gk9NP5Nmh4tHZp/Pmv7DDNtd6APITU/p5woXmF8br3sTLRtqzJyiBeqjXvfjUQN4+fcqGVl4QjPp1D/0kaSUPnToIy5+6Fy0Zh/eErWiCaAGIK821LDvhprP9OOGBmeUmlJt3aP9NbTtdtuL3LapFXfZSdjyJ5N0wcNkTIj8/YSja/fXhuCAWvaLpZTevph7UMfkYuGjbWq2ndzip+yOJZTermb2F7x2AZe+aXT3DVdJRlwjWc242+IyDe1pVdFtPf9etIehv3iXotvf5ve/+knUfW7Zup+aoEfQwSZdIPosRhXnxOyJ9Evsx6BU42TgkmGXADCrYFbMfrti5D8SUqmmxtaM5eJ9FzOnfA4LShYgLcbUGC9P1lVeb42fCcD2vCI2NbXy32a1Al0y+aTQPlqH6wWaW8gKmgjzUgroCUyhcJzwxeqLAVi79nJq63TviMbGDRH7rnrTuHRvqI6uK00bEZmzfWCNcfm7vTGbwPoXw1o6H+zqLWrmk223YBMwzGnBgnE1YUFDeKMHJK06WVddWYELs1M7vV6bw8XT01Wy3W15Req4FvVUxInoapz3t+gqtPiwNBZ+q3FwkH5V69bqbyP1ssuIP0k9jB67jeINa9GkZERYFa2cAbp64Eizp57SOEn1qVINnO6AUlO5NX321xxvRbPu7Nb5NPTB3l6k1DM+bTDSCk0LAmgJkgMFp+JOGxbrFCE+z46e678tdScj0lV/RnXIj7SnYU8o+2fZjjrWr4/d74M+jTWTlIG5JmOMYZuvtg6W3A+rH1cNyx+E93/BH97V9ed3yOjJ9F6u1G0siy1xfD50PAeT0/HYjMKxtLkUa5QkzFePuppfz/g1+/3pVCRHrhL+PLwQb4fJQEpjHXfvuDu09h7WqL7fTE8mCf7ouZIWDZ0Q8ZTdVlyNJ3iWD6aewqbh6v6QHZwBvLt3YYlX57XE90x8iykUjhO0sJwp4VnD7faMiH393iieC1JGeIX0PynSC6X9J5dC/+kPbCwjJAxia3sA2GBTuu+URA9npyxmZJyVPLtgWrxy8XR5a4mz1NNaYzREFrRqDGsMkO/UVxD9HIKf9Y8ePBSNZpd6CKwtyv4w274Xa1gQT3v8wHee0XXNVcGgK0eUSNL2VVFK4z5Sr/kGuff/1bB9b4PREHv7OaNCrw8n4M7rNRrPWzQLY1uHGNoSbW+qfoodobaVU2LHLQRkOlIKpAS/dBAI06ELZ/vvbsU72UHjeQEaFkh2D7mE0sHnIQG/AKsmuagkMpr896Oju6MOmnYvP5vyD0AyJCP6gAfw2n3rWPqQccUaHzbSdOaUtifBDh/dDW/9EOoPwPs/Ry7vutZBNLbmD+T1ibMNtiQpJcmOZGrdkQ4NLhycP/h8Hs8bxmsT5+C3GIfHi3LSmJSsD8TT13zK/z1/Dw/GHZ46cVt+EW12o+fSTrePfgd1D7L3Tg0GvwmlJm3/yqr+eh/SF7yXbZErwaOBKRSOAzye2Nle//OfZ1m3zmiwCkSZpT67cCUPfseY9z4xJ9pNI/Bk5NI8YhLuHKVv3zvpI/KnKztAU/LuKMdEMvbsMcQlqkErx36AQvtG5n12CzOW/RKHxU2K3WjwvGGPh2eXt+Ju8JLTogZvG4JCR9dqpo5Ygi61dqHxrRI9FcHIu94zGJy/cfIAMhPVw/f6mz+POI+/9QOQGtaAl/dfeZan7r6VhFNOCW1/+A6jmiLR+uXUR4uXTDW8L/cKRriNKzanRaWAsIruZf496PkvZZ43KfO8xb8rn+eduodD26wpSk0mEbROa+Nq8TJPzbwCgBuuKOKOcS4WzE0gYBG8n3f4A0vSyJ9zfo1ue6po6dxfPskCpyfr10kK2pmenasPsJaAEk5+R9j3uuNdKq1Wxg3sz/Q03X36cHnmZL1m19uLl+INeBmcanS1rT5QzH3XX8Wvfv3rUNujs/QkkBNb/0O81UJqmIOCJixUh92+8b7uz9wrkyOTA5blDTC8/3T6As6//7/c+Kt7eeFy5bHlLS2hKuh0IRymUDhhqakxDuZ+v656EULy+uuvd3mO+qAaIt4CAx3qZ220R0ZNeu11eLOVLtKXnoM3Xc3UkwvXYrH48bqMQV/pCalRr/fpE49iHarUFCPjPopwqx+Z8L7hfYVL9WnZb1bwpyUtPLW8hSEuC96wms/jk+Loipq2ZmxNuprApXmwhLn/ldapMjH+QYnccNoQphSl88S1SjXj9PmxaJK0sGA5i+anMak/e1avpKGygt0+XQ+uddBFX7NpH94xaQQynXxRsZJntz3Lk1uejNpPTWo8vPFhqlsjZ6Revz6wZIxsd/1Vgj4gO8+e6c2NrjqJZs8XeDk0VA1Ur8ZdEGr/MM9OffAeabEJxu4y5iTKryzhtX6dDziOsCXlB7siVZzhpNmMnXMG3y4aq/rWEG/hV1fmsrP/aKqy/0VzILg6fvdWDgQHYWeKHo/yTuDLG1g/WLGS5QeXU9lqdGPe9MUqWgePMTgjhFNa/RkPPfwQL730Uqgtzt1KUpudsaXKNpDpzow4bkTxc1h9kRHUVUmpXfZ19Xg1QdkTfF5bHDb85XoWYmHrvKTnl8UUCscB27YbZ7Eup65SEZYAQgTw+TovbSk1N1IGOCXRxrh4KzagvKWcVYVvG/ZrytZndcLvw5Oje+cMdEUWmhmeG+mZo6FhERa8wXQKViHRfMaHydfBbfXUSjX4j3JYGI1gZKNGvEXQcKiNEQlKXVHo6nrm8/q8SwwaLglkenXh99CiPcgUO/6hKfxkl1JhzEjy47NY8Fss5DQ0U1inGc7QnghPINjp188esEbqnbV+8fgmZ/Kjz7/DH1b9gT+v/jP7G/dHJDpbU7mGv6/7Oze//+OIc4z26cZvy5631H/URKB10g87/fz7xi3BG1dNwGq0Iwk0NItRFVTnv55VVn0AFZZIFdoPt7sZEKa2ACjPKeS3Y4wqJNmJ++M9S3TB6I8STxJrUeW3WZDAv89U6q6bfq4S971Tp54HCbQFB2l/2GCtddRx+r3Uu7sXO9I+6Hdc3Xy+Sak7O6p12okLxFFRXsHmzbqNqTEpFQlM3ebEFrAzrnZcxHGz9zs5b8Mq4rzG/lm6oX7MOnTQ8H7FkH4kn302Iri6FpaeGb5NoXAcsmv3H0KvJ0x4n1NmPcvniydS3xDbW8fT8G98LW+FqkMJAb9b+Tu25iij9YHUrbhdFQabgeygk0xzRkaTFuX2Jz9gXOq24cUm7Pi2Kd1+g/8mkB2EQofC5Gm+6A9B+c56vtaq+rFl3wcxP187XodxsPKlZRuMca+vLw/5qi4JZrA8eOcv+XDsQAJWCwfTkmhL1G0DKQ17cQc9YC4deCvnFt5EvFW5XXZcKcTi3FfPZcZzMwxt+xuU+mxno/6bZW2/AkdTAaSFOwoEC7QEA9E8wbi2kjzj54w/NDr0et+sn7F3tlG1lT3tcXadZnQz/fWoQTxq/W7o/fBLvktHRjVqZDRErigBmsM+/t5ZP4u6D4A1SXebveG96w3b7N6mjrvjsggESgg/floyHkdYChELVPuVaufJ5CRuyc0GdOEAYA8LpsTvZdUDpzJiefcCuV6aMq9TXwoZZaWQ1NbC6NrREe2uuEQ82QXIwCFA4NQiBYrX4iWnxcuVKz80tK8p6jr1dUKr8bvz2G14S0qQ3p4tRmQKheOAlBRjIJHfH31VULZvBRs7uJwmpW5CC9QBAfDpg837I1VlK7e9hddHPcAnQ56mJak4yln1J+STjIMRW3NJY55vNOd7dL24V/gZnTbTsF/g7IeMn6GDUPBHX5VjtVuwP7+fKxY1kbTvk+g7AYlhD8i9N/+WsuDy25+QzMB44yxWxumjWe3zy3HvMg56JQMvCr4SbEyLLPBXkDAcgKYENYO9+ZOus4yG18x9ankxi3fVReyTWnoqjrYshD98wA/29Tw93XWp+y1KMoxBc3UpRoGt2Y3unk35yi1Zs+r9eK3AKFhqiHRa0ATkl0cPRNsf96dQXIrfpX+edItk1bCn8NvVfXrZoTP5een1XFl9Nuuq1hv7ldxKtU1XoW207mebtRQrYNFslGUY7xNvUNX0bGIif8nQDe07nQ4W2p7gIsvnnGkNS23y2yxeyOlYCr5z3Akz8bp0r6f6ms5zTl289jMGtOj6/uuWvs0p6xczunwfvoxcsCRSUG8c5Ae7lOqnXVDYtQCXrPqYOWtWGPYbVnGAnBhCOa/a+Dz6UjJYYbHEVHEdLUyh0AsEGjz4qlpDwT8NDeomT0qMnI2Es+nzXSx5Udf/Ss1N9b4P8TY9hwULY9J0/+o4u5/MAAgNDqbswW1vCaoXJA6nciu1WPwkJIY9sA7do2Sydz0XfO0cmj4+gAsHWTKZHLvaLgEvfvxhM7ayx3U1lSadNFlUQZWT1i5iVpWfDE/06ZmUEquEIRU+7DESzV24/H28HVY1b06aS5MzDi0ugTOk0f3RN1Ef/OrWtZEQZZYrrJkg4qlyRhoHJ2bMR2AJeWjNck2M2Mdvy49wF2znl69v4a319RHtsv4Q9pZcpM0dUsc4hOq7GHueYV9ns+6DXrDmxxRsjuJxFhywbUAjyWgIynJip594hUsj2kY0BghIXa3k9OhqqcYZFfidkTaR2/LcpBR9TMUYZd+4rvp8ZjdN5huHzo3Ytyl1B6Up+kpilX03S+07sCeVkdYWqYNvilPf+f0pAyK2XWf7gL86Hopofzr/a6HXs7YvYeq+zlNwNGXeTEP2bbT4WqhsbeD+v/8ttC3aSsHl90W8H9NQgzWodpT+MhbsvB5nm7IHJTYOprFYfQ4Rdo+c+cH/+OkzjxjOlVNdRlZTfdR+HuxnVN268weyY+QISvoXRt3/aGEKhWOM1CQH/7CKyr+uofGDYjxe3QiVmjq1kyMha8ybDDjt96H3/rZgoI908/WBP2Nkqp6xdHZuCXcWtTJzS7jqx0Jm5gFOOukVUlIqGDFiMZMmvRPaesOYvSQlKe8XV0UJEybr/cn50SQcmr6C+a9rES859FnPohp9BVPueZkLJ/0WgKLqKu5b14YVqIniNSU8umBxhC2/B1SrGIJrXvonQzYspqCD3huUV0lNcjp5adFcbxVvOIwJ84QlVX0Ttn6ARq1VI+CJLP4yI/t8tKDONsUnGdlg1JXX5f+RtsQOaRKkDKWWtjqqwjewfe0okBp1A1VW+APTfs8rmf9ABGMthMNoZK/v/zEARct+Q0LNOMY1lUf0sa6/UrdVplr5jnicW/gPF46dQ509urD6TJxmeJ/e5iPRb4xS9zj1fkgg4GzEf9BoSHZa1P4tWZHlM5N8iRFt7dQIfbV3IGEPkxpHUFhtHHDbtZAW2T3VXUdsUjD5wE6GVJZ0ue/gJbsYv3IfTWGfeXO+cSA+besX3b+2T6kdnW3R3ayHlDWT2GZc4eUc2ImzVjd6T9ZW8d33VTqL4tzog3+bq2uHjCPBFArHGBmWi7/ps1KaGvUHKy4+cnbUEVeqPvgGvFuQFitavxHUiCZW2HaGHvDBKfXqf5V+A8W15jJylPJ2GTf+QzIyI6OfU1IqsddWssdfaEjXa8uIQwT1+S1CqSiaLbqqIrffPN658CZ+ffXVhvOFrxCiGRzT1lbia/kAT+NzFFRqfGvJW5y1aTkLtq7iW+tXkteosrDa/NED1ZpdcfRLTufp60+Kur3B0opEYgne6ra4dpdTC8g2qi0avralhhkdQEHCMN6feyEAVgmProqMzg3Ef53Rxbqg06TGu5vVkt/iUv9PTfKBEOR5K5A+PeWBO2UvT2Zuo8JqhUGnGuoUhKuALL4EEq1vRP1sLdnrAdg2UrnoNgr1XZXEd0+9kFa7j499f2TI1yIFLsDj3ETJpqepa3uQF7iS1XTt9ZPX2h+A6iQLL09P4KE5F7Cp3yCW23ay0xop2BI8xiDH9pVCkiedid7LybTfhsvvYrzbE3FsNGyaWlHO3bGO71ftYfG0rnX33oH6b7ux0Bg/ImIYhEXY/eiPT2rfWf1DkJrTPfdUZ6IbSzCZ4RC5gx+JP2JJ7HxY3jFsaKfbjxRTKBxjWtcZk3Lt2/f30Ou83IsP+3zejFxakhN51bmKzbYSGoXRK8WZoNQU1gBUZ0RPM21EYG1rocXr48DyBwnY1ECmoVEezKq5yK4vzw9YDqGhMS59NveeMZdPZxqTy6XXqMFxv0fDH6Xcpa3NT8C7GRk4SL8aK46AnwG1lQjA0XAQi1Wpoaav/SxqbwPCgub14ki2oyXakC4rQzo4ouy1VNEvQUWaWuzBmaBUxrr5o+wgm4mzJcX8Rlqt4NTg3DKjYHK7XNz9nFEo/Oj5DSA82FPWk2nTOD9VHVMf14AQNiw+XUWXbvOzIs4FF/yLNfvruMfSiN9ZR11/3QtMSAvJNhWLkVtp/GB+exOtaTtoyzXqnjekWZHCT7a/84ypX2t6kezZu0jMj56OYp2Ywi/P+w5P3nwWr4uLuU/cZthutI0oTt6vVDmfj4lja3+18ls6ZBxbbCVssUVOQnwOY26gNocSaLP3XsoHQ85hW94Yzik5h1x3HodIpZnOZ8mVKWplbJMavm2bGOJycOl+L/etjZ1yIyO7hNTUg1itkROPjl5CyZq6friTRtuA4WjCp5erlQJXvFHYpdXWIlypiPgM/rhef0YLZ1YwfusXTJJf8AP+jACmTu082WB1eibW67/d6T5HgikUjjHNy4yzpfDVgc0WO0o0HL9VPUipOXloHXTt4Xp+gFFfVzfYlG3pZLZ07fIpLAEQgn4zK9ntvZ/d81RSvg0fvIsIppdwh6WX+MCxgS9sewj3SK106m+SUO5zdQENzR99Rhp2dcO77Mw8CBqss2uiB0htzStioyuB87buwzszB8+cXBYMyw5tDwgLnzo2k5BUiMU+HBE8n+ZX50v5QOmTLZ08CilBz6nTKjrPjrov6HGUNOJurEjuzNMH8bhECRYrKeW6l9IP3gioqybncdWjKxk6/iH2zPkRh4bqvvCv2l7AElyZjd5hHGjctiZKpv6BzXajyiPHLdlb+B+GWteH2sbI9XRkqH0XjiQ1aRgctMucJo2ZeXfnDuR/4htRP29c/ZCItnSPUp14Oqiwmh2RAgT0rKFJwWy2r5+s1E/pbXmhfSSQWHcq/+Cb/AeV3HGtpl87POmcpYNdquHdYm7d7mFWdecV48aO+4gZM/8X0d7cQVXTaImeUqYmZzk+pzJYS62Z4rX3G7ZP+WI1CfN/TeIZf2BCnd6XgLCSHajkJ9xDOsp+Y7NHUVmFpXp/5uQz+f7csyP3OUqYQuEY4++QpygrS0Vbjh3zoKF95YqLCASiB6dornoABk89mXi/UffqFj5jplPg/sJW5uS0YbN0vQRPSz0IWoCs0bpHRuXwp9m/+y3s9dGjbdfZS5l+hj7TPmeurleen6/USa0a+DQ1uKVdMoykuZH6Us2lL7ldLhdnz7kYQecBOiUZubzVYJxt/uOAvhoLBO0CHqvE5poQapea0eNDhKX92JVoYcqZ+udJ9YEn0MophwLMrTQKhtaw2hRNYfmeOqr12w5ZsKYVkbVTz1ibOjOg4j28tdw87jHGZEUaSK+cXmR4/9aK80OvLXFqJdAsjKucO8bH8XphJkvFnFBbCpGrhtRBuo7/Nn7LX+V3aSG2TaAjrZmbaU0zFmdq/xYrUo2/287c/lHPIYXA6fNyQVjK9+rcz9HC4iLq4/Q+1ZGq2qRq8wi7IelcnNd4jzcvKaMr/MF7rIK8iG0dk+l1B80T+TtaNA1hV/eKNWzxESdbsSd0nQJbCwq79hiNDc1HVjO7M0yh0MvI4AwgIUHNfCaMf4zc4m+CJ4UvVl0AQEODMco1b8QHpM/JBikZk2zUpXvx4XdEDgD5k2oIFPkJYKGeVCqInrY6JbUKaTOmnqgf8BHJYz7C4ovuH30gI/q5wvH7a9hSt5R9TZtwjk6jsV+0c+lPy5RZcyg+2ITFoacjuOStJyKOcPh9LJk8N+Z1NSFodMWzOVGCiEcA4+Is5MQVGfazhWWEvW9EpL95rUcNWj/ebhx0tg4cymBRxOjWwfg1P/kInJqD/o4Old82B71RwgyonrESbf5Civc/yNTc9RHXLCz8Jtku3S2zTTpwDo50v4yTkWUcn028LvT6mgN7sEStkqCTQAs5VLKW2HUWAJ7b8z1D8FjJ1D8atjuC3jsdVwqrBo4iGgfSc3D6vGQHy3y2B3mFB+dtLDCuSLxpQ7nd921uTbqHTzL0ldewigMMCzMw9w9EejdFoxFli/mJ0HMsTawNql3DVx7dzGzidy8zvK8NuLAK3SPOHmZca7Im43d3LXj25ihvtFZH9OC6o0mPCQUhxGNCiCohxOawtnQhxIdCiF3B/2nBdiGEeEAIsVsIsVEIMamn+nW8EQga0Npnqo7tQ0jZOQeHtOH3xjH0g8fZuME4EGQNXsYHlS/y2c5qVtmN/uuLGz+gJWlXxHUqyOO+oh/yAlfyB+7idlTyt9J9k6nefL5hX0csXXQMl9EPRkc3QE47pM+APC3v0+yvY9Whd1jy4pNcu/KG0DbdyKsPJL9b/SK3frANIRw4U1Xe+7amSEHS0VU1osvCwrMnncGDp57K3oxtjImzMNBpZW7uZYb90p3RBdu0GvUZ8uKViibfbRwZrFqAf2y9lT/v/wmeba28QBK/rb2I72brwiNvw3cobNCjmJNeDUt46P2ckpLHo1572NA7ESv0FWTc2b/lNxedHLGfH1tI/RON7+1IpaXOmA56goxuX3LS+WryrSGn8mTrLyPafUJ50Z0UrMrnt3Vt7NYQaBYLjfGJpNj2k1vXTEazuvdaw3IglaUZJ0XlVy2iijReqO7PnZ5vhdrn7VhLnN9LhUOt5sb5jY4b/Vui379lRKagLmgLxmeERbVP9seuuxENa3MDBPxsb+jP5tHz9fawW6gfpYwuj1yBTy42BuO5220bYS6z6xtj20mOhJ5cKTwBdJzW3A58LKUcCnwcfA9wFjA0+Hcj8K8e7FevUfNcZNRlTbVyK23PjOotbsRPgGaLG1snVXSn919Mfck+BgxdRla2ytKYmbmfwVM2cSAj0lulGJWA7S1xIaViAD7hxIMDDk7m3xaja+Hc7bHqNR9euuhLS3RVixZm61jz9uvkFWssdaqMoE6rUht5M4KufE0DqIzbQJVNosV7qU6s4IVTS1mUp1cae/h3kQnuovHfGXoRIbfdQrYt+i0/MUN3L3WGad8uLIm0I3z+ka52qUjRZ4CFn9dwYMo9pBYadcJCWhmafyUAnq2vEbdB74OjuYsi8q1haq60gbR9soKhn+h++QEs+ISTsWzgL/J7UU6g6mo3hw3S/5DX8wP+EnXfIXSdqnuZcyyuBj2hXwCND217+Djdww+nxuOLMfFttytUZ57CB2PPZEu+fo4RCR8gLZ5QnIDbqU8oGuOMtrZvfXIB1sStaPE2yiYVRVynPm0LV7lnkStTDe1PrtBXVAv2fs5d8g4Aloo5eNEnF5eXVxDnV4Pwmc1FXOCZyvnuyUwMRK+6Fo4rTD0cV7qbhD2bOatyK4kyLN4jTDWWJyvIbFHHpD6lf3FT9m/nrX76506trkOW7+XViXrVukXbeqYcp/gyRbi7fXIhioC3pJRjgu93AHOllAeFEHnAZ1LK4UKIfwdfP9dxvy7O33OdNzExMTlxWSOljKorPNY2hZywgb4CaI/y6AeER5uUBtsiEELcKIRYLYTojn+liYmJiclh0DO5V7uBlFJ+mZm+lPJh4GGAKVOmyNWrj3/Z4KtoofJ+vfCLc0gqaZcMo+KeVew44zoA5s9TtoHS2xdTaqnhPcd6AG5wz+dR18cMGvwF/fp1vlyUwB+4mwJKuIbHKFz1C97Z+AL3fPueqPtnrK/FWlLH8+/cyfOXX8as2U8ZtrceyCS+f2Ta3y9WXYDbrTxeHppzgWHbT7e5Oa/Uw2PxS0LpAW5wz+f5fX/seBrS04dyeorKQ/So6+PghxAMbhtBUlIdP/K5mOvYwpTSs1jr8DPJa8NvAavUENLCKycnsGXA4Rnebl70Gje4lX53q7WUZXalwprnHcMgLYcXmtz86ZIsw/5nDd9Gc466z4Z98DgCwYF4wUWzlAfMmx9XsdiyjvFzHyYaA5fcg6NV2SxSzi3ikYMHWfCrazj4QGwX18mTnic1dQoLFy40tM9etIi8gxWU507jr9dez5qiYH6mXR5mDbmSJ7iBD4WuMntz99Pk7TmfS2fGszfRyj/k9aRRH9reWDKRjcWjOGWWKpIkAQ9OXHjwYcOChhWNdbUz+HOGnoTv5epf4c5Uase1Ky9m0kkvc5V4Oer33X6PXJQcz71jBnL3vgqePqirxW5a9BoC/V66Ztm7lBVM4eP+6newBfzcsOSt0P41zho+6beCmkI9ZcTXV39CRouKo2n/fVsyNlI6WS+cNPyDJ9DQeKXoCcYOU0GcHfv8I/lH4p+rwdvo4LKBxriM0Gd3rKAuWIFwSGkqBxybQ+nok7ZFH4/Cz9WSvoU5U5Vt6BmpxyZl/cpO9d2R90S07/WkdSu5//xLGTg4diGmzohVaxqO/UqhMqg2Ivi/3XewDAj3USwItp0QNLxrDEZpOdSEp81nSC8Qjksq/eYKX39uCroSlhwYS8mBznMj+XCwRYzjfaECyFz1g0IZQKORUVfKRbs+od3AW19nNLZKb/Q5Q1x6GVOXr8BZYSykM75kF6etfIWtdf8w5Ispbt6MJzOfQAdf9fq6yIpVFquXsUO+YJyWiUDDZ1WGz0nBvtg0FdAFUJsUqbwev31zRFs4u3OVN1OFqAsJBIAkqfzRX5qquxOGUiWEufgW596FRBqMhfcMh4YY/uuAIYOsNckJKSnsSYi6EA7hcGSxtyHy+1k7UflgCElIIAC8mKuM8LMw1ubI2acExANr2hi4bjNVr6QC0FajhKm3JQMp9WFAAK6gsdmOH2vQjpQljPUHkndeob92RBdug6uMwWp5gUoSlt1LQge7TsfhqTopNSQQAPxW432Y6E9As2Ub2trzUCVq+j3m1YxG89Wj/sjzY34bEggA5+82Zi+14UdYYs9VS9pqOcc7Cae0cYV7JjPSJ+GoqQSpEbdfv5+sjtjPqmZz8zv5U26WDxjarfUwaF+kJ1k0BsT5SHKeGPUU3gCuDb6+Fng9rP2aoBfSyUBDV/aErxKeA8YUuKWVXla+ux9fvPFB81W2Rw+rm7JJOkmwFpMYSMDnc1Fc3LlTlr9D3dxySz31A0fG2Bvqx+dz2a5PsBVMZXAgh+pqo7eGPTXyBi2nH38YejuvnHIGjjo9HiCrsY7pe7dQe8nLJH19reGYJd4VeLPyaR08Bo8tLJ2DjAwoKsjfRc2QV9k36zYsrgpsgdiV2SbsNT70Ny96jemVqnJcrNw3Hw0fi1/AW05jHyWSHw/4M3sH6L79p21Xaa+bs/XKd95xJXgSSwxCYWlBNsXR3HKDH09ouhHTUZDEgIwE1mQPj/m5AKy2BM5/7fyI9qRmdS/JDjWGh+5SfbVh9Hm3aOr7y3VLDlal0VYdx/p/j8TXogYUmaTmXq2tyZSX6/WbvU1Z+P32sPMYnQwq3GmUr1AeZLkDo+cHymqqxx7mgpu4+XlY9Efwdu418+7Y6Z1uH+4tpCXVmNzPEoyWn+bX3VcPNBsdJpIKtjEpfy9+n/65BvuNgncro7HFqe/QE2jD18HmutuXhFPa+YZnDgm4cFgEKVmFJG1fiy0sk6894UxcaaqWRsfASM3WShH7mMUiQ7vwgTe7qNPP3k7+8KX4tE4mIkdAT7qkPgcsB4YLIUqFENcD9wCnCyF2AacF3wO8A+wFdgOPAJGJ37+ibPi4BK/b+KC2arB3dQkyWPRkzGg1Y9Ba/ATQeMOplqCXWj9jUkN/nJW6j7fHEzunygGKQq+vEi9zzewCAlGCb+5YqQbMuiQ104ybcgM/mzedhcNvNezn7OC9AYTy37x9yjzDuc9csxgAGSUo2xdWetA79CRk8LiE3FZ2zfwR5XFqQMvMKmbAIL3+gLB4aHTpaoYRl36bEZfq4f1DDkafod606DXmb49de+JzR6SHjVf42RYfOTPPJtJdcIU1smbwxoIh3MIj7EAN9oWlbViDmjerX//NbBlx2KwiFMkbix3bd3Pxvsi0J3nBylut8caZ8uCgC6PWzUfa06iERWOb+sHWrjmXPbt11+Lij3/B8mV6oJ21Q0Dk1rQEbPHKoyYxNfr8zWezcZZ3Iks+VINliUsJTtkW3eV57o61UdsB0g/kMaNeudUWW6vxOccYtmdVTuTkujkM0pSZclPd54jE5ojzANjs+n1jE8Z7yILkzJkqVuK1Aw/wSaP+7Nb6NRo1eKvB+DyfcaOxjkVHRIffuj2RYcR+mkAMPyeifUFl9O/F44usVXE06DGhIKW8QkqZJ6W0SykLpJT/kVLWSCnnSymHSilPk1L5aUnFLVLKwVLKsVLGcKL+CrLkxV1sazE+UC4LeKSFhjwV5PKLx5ay5r8vIwMBWoU++7364Dsk+RORAT3a89XibylX0ih82MEDuNFpi6gFe+U+NzPcSg951ftvgNVhUGKFv84vvYiOvIU+e20LRiBbNI00X2vINbYjgcQUw/vV49WsLnVwI1pCHWLQOpKSqxgwwJiNUxDA4Y+e6ybBAv090V1kRfDvr6ubsGga83caYzmeG5TIwTBX0rq4RFZnGoXtmZtVBthEWkkMGCOG806qoqOG4WBqJvUinY2oNNtWTTLg83Hkbr4eS0CpNCyJShg6rJaoKZrbGTniHl555b2o29qPswaMMRvtM2V3WG6gyz+PHDQ+yZhNfYIPX5L6TdpVR1JaAcGePZNpKhuP5lXCwu1W/20dVgp/mBSPPanzxbwjqEJMG6EmHxUOpcp0lS437HeKTyWts/sjI3sHVauVjF+rCgX+rSwaGZpYDK4qZd6WnWS2QKFDn6RIKSFKfZCOiIDxdziddxBSjxYO/5k3tqnnuONd129EbFWRzTUdZ5y+8vnk4DN4ktWkLLlMr0kS/7n6HQYPjkzzPjfwWdRz18XIMHCkmBHNx4CON5EAMke9E0qjfE5NI/G/v5PGDz5glW13aL+qJckkNpfia34VgNr4JN4ccSqPcVPU61RGiVLuGFj2450+2oNtU5oasQ+cw4GwrJrlYU5foiYfi99F1VI9aGcE+pI8f/R4AG7970MkWBsZMaILn/v2c7iNBWQa+y1hwoT36eh3MECLo6hOzQhtcbqftz2hmtOS7ZyaZOeKRWrgy2o0FkoZ4e/H7Bp4+U9/4aRNxkFoXf/hvD5BD+Z6d+x0fjvROPPOaFZGywAWnDJSMCXHqCTXihIuQlqxp/yYlHL9OglT9JTKB+MzcOzWv/dPm5Q6Z7eWS37+16OeG3Sh0FF9FLBYObAolzz03FpFVT72+owTki3Jo3ltTjm2lOiqh/KyUZQt/V4oori8TA3Ybncil1a8a9i3ItGovrNK46x74KGDWLAQt/duAD7JUMbVmhZ9pTC30kdhsCZzQoeSlQCZwVoDmpD0c1goTc1i3QBd9Ta+dDeTd2uMdFlICStU7bTG4xzUdfpsETD+jk68kKKbN8O3NkRqO1XfDkX2O7tqDZaAF1vcdBwuPQW9NlCvLZH0tL6SydownJQLL8RqjZIjqk2flCS0BbBKH/0oxdqJ7eNIMIXCMSChw7fs0QgtvQHSndNxTb0J38bltAjjg5Z5SJ89t+fxWc4pRGOfiExQFo32e0nGpWGJz8Ad9jDdKh4g9cA81j2XQ1NLG1mf3s+PTrmXq8TLfMBZjGV9aN/BVytVjkwOMHbe+4Zr2GzRI2OnTnuFWbOfYsJN28gaYxzI4+KMM9uLSxYxcr9qE1Z9ZmyP11VKbZZ3WfFBExetW4QQGrNmP8VJJ79IilSD8/LURmw+d0SEaDjtwVHhRXMKByjPmv0UIt31EcfUj/gPq9+PnIlbgsOIzx3pFSWcQf1+iouAxUrGfbqhcI/bwo9L4niovBVvJ+UW24XCU2cYhX1CazO129NoXWHnGXkxT7Z+i+GnJ6IlRk8kGAjWc25tVSuG72jPhrZ5nNXUZik7gc+nPofHk8ADO+6hf1hiwoaA7vnyJhcQCEsVcvOi10h2t+LEhgjotqncOYsMA+3XD/hIwMUN7vlc1GGyANAcXBGUZqehSUlNgrF2RlZTPX5bCwUO40MWK0K9I7JDfjEbPorri0LvO07ospPVc9sangc+AKfs0AXQlL0HGbP1MeYu/hFOdy3BCrmsbW4mY6R+zwu3fr9tm/dbHCOvovT2xQwq/KnxswxaHHo93rWMx7mSfMrp1y92Zt8jwRQKx4COk8q9Xg0h9NttoMzF3m8yNFbQTzOqe2SYPnJDMAdMQNj4ApXzaNPG+Xyx6gL+Vd31DXLNMjXTC6UDTi8Ci52WDikJsnZezhdjk0lxZnAoQVerPCluoBl1nXSbhSu3qQchoSCyOldCQh3Og8UR7S5X97wrAOYcTGWWzc5pSTbyT/pPqF0LMz7PtuRik7DAO57+/dVA7nC4sYQN8K31+xnoi3Tdq4s3Jn9ryNZtKqm5+oy7yRr5mDQULKZViyzjWI5KZ7HTWxhyGBCWGuw59SRMVSuFfmlx+C0WhBRk/d6G+5Bgi9uKhsAv/bS2xjbEtsWpVctnE4059VOb6ki/+BT2ZKpZq93l57PEVxHBYe0vwfrbz31bzda1YJrodvVRtkV3emhK0W0u1dVF7Nk9hYqSgTDpGqaECdeyCr1WQaxMqhoSp8WYIG5dku78cOpg3TvO3mEEdvq8FAcT6f1vwSzWtgYiXJUE4Hc04rIYN/g0XbAmVkVWzgNoK56OZ1srV61+kzOql/OrrY/gwkOrYy2OpMtwJF2FX0KJV+OLFqXaqmpUz+fKZj9apvotNLebOJ+u+rJISb8HVPZdjyudAUGBJYWL+Cx9siTCBEvttlrcW9VzJGuMn0WEiSYRdBEGcHuiq2uPFFMoHAPa79fqlkbabG34JDhTwjxugy6LwiJZZ+uYS13/iXbn6Mva+8WtvFuWR319Pm53Eutt80LbBlVFevOet34x49vUDd2+UtAEyNYaXiw05g+yaA4urr6eOEsSezsU/LCjBpPasCpqCVEyNiYm1mJraaTbWcSi4Jx4OY6CqcRbIS6jONQuLPoDOLtZPfCFWib9B+hL80PBKl8SiUBicUQKheennsYwv54Z0xdWtzcLfZBsdBtz77Tzied+5nVIp93+OFcnp1Ep6gFIXjCFnB99DWuiEmYpcfaQjt5eamHf0/04t/81oXNoHXNMhbu0agFDQrpwtuQcojojKBSc8bxT9hZaUCW3P+9FQDIiT6knFjUL/H47be5EQ7/VsbrQldJKeflI7AcPIr/2ADYtYNjW2GycxHQkQToRGCcCbotaffzIs5b0i3WPp+YOk5OzNi9n5hrdxbZZi8yCCqrSWX2Hqn5b6/WkdM379XxRDcX6RGD6ybdgb6ilaMdgzvrchX+TsqE5Uw5isfXDYlNCfG1rgPIOM7tGDbLPU+7NbRs2Yg3o109p9ZBwsrrmSXVrGOZSqx0NCHjC3H9dqaHX85P1Z9BTbDTEh+ejOgXdnbalZX3Hr+KoYAqFHqRqv9JLjwjeFMt8cTRNVjNJV5ru49+eEE4r/H7EOfYPOBOLfSjW5saIbW8mqdnZruRdeF1q1pba0sQZ24wugvO2rSa/oYZJfpW7xRa8v5eOHotz1AURK4VdiRZm+HJZmmnljvFGfbqlLXKQT0qNXCkkJR9i0rc2MGv207QLhg/6Rfe6iEnQ42XnGd80NGemRwq95kyjkTpHGo3b2TFqRD83L7L9DPkOcbhJaFQPfVyaWhEt/tw4G07u38zCA+sMbTtQv0NzUzpvd3B7bcdps9Jq09VL83dWURBmInjkERWUlVQ/gqyK2WRVziKrYjYSjTVDRjP/X892PCWnXncjOfE5VPrUI+31KiPkbpe6z7zCR1z/R7EGXYJ3N6awfNnl+Lzx/IR/G87l9YXZG4ICyd5Yy8FdOxBhQn53dgHfSXokanCVkCqIzIY1wlZU4splQetWblugktnl/ESpjdIG6qqhn5fdS25jHWO3rAy1rcvexCcjIzMzOLypBjXP8/v+SI1HX+mVhg3ErnQ1wLpXzicj1cXNwzZjseVS6x9AZMQE5Dp1n5fx8XpOsbFzdNtboAkSTv4+l2Rey9kb9mDXNIQtqJZKbWHHGdfRkrGJ4qFxlDdMxtOYw6RRG5HeZoZ/8ATDP3jCeFGr0XhhDft048LUt5Yvkda7O5hCoQfZv7kmom35+1URbVJa2WItIRD245/5brj3iYbrYGQ1poaUk1iTuYYtafvwxisd83kblgAqkKyduGDKa1d/pTt3BS9T41Q//9c6VBRbmqVu6EcGR+rF/XGRN2LCxMioZ6dTnx0KobHH0o+Kkm9F7NcZ9YUfR20f5Aj62CPZcdq32D/tN+wtet2wz/BAPk9mvo3fKolLSo6ooNXOFyIy62hb0IOnY4nOjmSMrGNnvjGKOcHj5umK71JZr8d8CEfkY/Z/C4weK9kr9N+rrU0NykIK/BZ4Y1oCawc50YTkxdnGOstTNizh0jcfo+5gGf0S+1Ef8qaxYNWsrLbs476s59jvPIgtYQ/eoNdSQYueGdR1+l1wxu9IqTW6eQKk1kwg7oBSJ33+zIuEj+87YtRI+LH8A/n56pgUW2SUd473EC1Cv7fsWfFkfGMk088bxjC/m3nyfUbnryCpMt0QH/HmqXMizgWAhKT4DoFcYR31t+kTBC0oNB1tTlhyH/WBfMNhUhP4WvTVz1JN/52co+bRb3iqep1gx5auVl2Ny9Zgyx2LNUm3Y1ji47lnylXsGqdUjPX9FuGxQps/AAh8ngCBSn1la+h6SuzYnHbsHo30QHaX+30ZOhUKQgiLEOLSzvYxiU1cUtc/bnL5DHZbKlhu38n6MNVRcmOYEVMGsMSoUVycVExd1pWh987gfhPChEK7a2DGeSOxprtwDk0lxavhDOo0O3jlhfK9T62NdBEMdHMeYbfrKiUhJItb80m3qu+jY32IjsTVKu+SugEfRt2uBeM7fHFVYNFwp+5hj8voafLCvj+xJW0zra4AhWPGc/64ziOIw6lqT8kVRY4U9NNXC7U7U7FYdOF3slxCjSudd/Pms2zwuFB7u9oonJPPmkmgfYUoBKMfWxKxj5BW9uTa2TDQydtTE5BIRpQbV4wB6hlQtpfxp53F7ILZNPgt1PoFzvzvMLZ2LHmt+SQ1ZYcmwdWtagXhteg6d8vJN8KM7xlqPYS2aY6gGhDKtq9EhLkIp7VErl7PkG8zmdUMGroSzeIl0arsWPEB3U5S5solv8EYKxI3OpOmhhrOf/S3XM/Dqru1H3QhlvU+2r1KeGz3qJl9fKZ+//ndulA4uCoLd0MmrjYJW1+nxmcUbK3VI/C3pYbeh2dPHfq105h16TBSsuIYflIuIugC68jQXU4tKf1xjRtHSW0riwomkj1Spedwp+6l1uNHBnW3UoPsn/2MwCHjChcgOTAjoq0jE7Y0kH4wcoJ5NOj0CZdSasCtne1jEptFz+6IsUWf/eRtvpFAUE1ywKKvLD6b83caE5UNQfMXA2CPUeTGk6B7I4mgv3pc2L7tS35XdiJ5t04l6/qxhpKAd3ZQEd03wsWUM5N4fFDkSsHXIUZigoweJBYXp7vbzTzlOdKcdfxx1q8AaGqMLRTSiheQs03Xr4cXDMrco+Iwqkc8B4AW5pEU32HJPebaHRSu8pDUZgNNY/SMQipOncC/6vdx86LXyKuPXN20s0OoYEGL3U1yirItNDUpt8nhwxeSbfszANnjanHmeXlGXswz8mKDamVbfpH+K0dJ121NTWXM9q00JSby4mWX8u5ZCzhr4FmGfSyak9Qa3c3XbbOxbqCxOlhjcj8sViuZ/YvIS8jjnH0Xs2XZ1fx46f8Y3DQ47FyqDz9frFKOnz88rIJb0KstJSO6s4I9UY9XyajT3ZOdUSYq4am341PuQASDw/YuMX42qy1SUK7ZegpFZ3TtRtpO+2Tnw1m6nn1DuVpdOlIvCLVpPt1ZYqBvNgfe/03IprO4yRh4lpCzjbjMvVhd9eSf/DAXXvgdAD6K8+JPsJLRL5GrfzOd1Jx4sEYRWVYbaZdfztl/W8wH6N+n31XLyXl7SE+oRAgNKSUZ138L+1lnRpxCWxTAXR9Z4yFD6nEJDp+EpO55WB0u3Zn2fSSE+KkQojBYJCddCNG5dakP0rKhim1PbqWt2YuUko1/+RhP2lbq0tfxqOvjMNWQRsLEf4aOqxctbLUqHbmvQ4qCujTdH9tvteGzGx+k/OpKxpadamiL9oOKoOrEGlYwxCrVCmFzSlhu/xWxZx6OVmWn8ISVfpwkV/E9/hqxr8caOSufmqvr3u2ONhoaoi990/efiQzzzKoYpQrQWN2p5Jfpg+6+Gb9QK4UgRU6jodHm0hhd2IzPCYGw+rZJSar/zU6jIEwJREbZDpr8Irm5u4LHKYEdCAQYdlJ0l+CO5Rz3ZPXDVpCIa3Bq1P0BFl90IQCNKSnYy+3Ehw1gEsmBHD3I7ukZF0QcX5k9GC0QtL3s0AfkrDaj4B1Rr2wdexqUF1JLrVrhfO1rXwslR7volhlRE6VZbEoVZrEPJ7XZwdztylYSreLeDPQVT12G+k0OzP862xacxx+H6QOdRcJfLjuXT598hFWvv8Ty5armcOrAyCjk1IZINeyFaz/jsi8+AuDe2SrdRnuuo7gMN/0KVAqJ8pXfRPO7qNp4EXvf/Q1j4t9Fw8balkvwydgr+f5z/0Jyf3XP10x6kXWOAOf9fQlFt7/NU8uLARBRhIItZxzx00+jyeMnHkFKydzQNqdjHy2eRBCSnV+oyUZFfPQiUSWf/ZichIcYOeIPuJz5vDA6ndv5dWi79ez7YcJVMft/JHRHKFwG3AJ8DqwJ/p0wEcdHgtfbRG2tGjTqnttB0rYaPvrPFnxlzbzduIJG5yH8DqUG+sKmHsaE3C0UDlWuk1ITrLTtos6iHgSvMAqF5kR9cK2KUfLyk+ld6+kT3UpH3T4jBCUUGuyC607W81KIpugqKou/CrtHuSI2BPNYDJB7+Ql/JA59mZ6U900qA3GkJeRHnOOy4a+FXldWDKF438SoKTusnhQcbbrAaMleD0Dmngux+fWH0JtYhi9xd8fDDfSbUUVcaguJ6UG3R28rEycqb6W5O40G4pEtOxjsVr/RLfI+9XmydtPakgrA3r0q79SGDRvQtOj1cTvGiXw8aiqu+XkIe+zHrCksJsG+3c5ZpfqM2uaP573pU6MdFuLMz14NvX7++edDrycfMvr8j2ww5sA6uEtF+44Zo9sRUrLiueCCCwz7WTQ7Qggs1kSEsIPUGLoxdpBi+DAp7ZUEUvqxy/cp5a3LSPPp31tzslqNrX3ndZa98iitbbFW1XDRey8YP0t5MTlN9SQEPZGSPq2jKVBHi68egOGX7MM+TP2+AY+aBNRuPwtvUy5Zdl1Fu7rZWH0vHGeyHo8xc8gHIKA8WDL0l69vUZ/VEalucw4/m6q/R6qEADzJjfRLOYCvOZNNn5YiNYnHHT0iLuBNwhoYTX7+pcycuZjZ2f3JDwYm2h0FlOZfgJvoAuVI6VIoSCkHRvk7vLp0JyiLl0xg3foF7NunJ7YqONBIoMGLp0NOFS24UojP1v2869+dRbPQHxR3h2Mqc/QAJZ/TGLQDUJ6VE9EWTlaTMnIN8Kslefgs0B9nDRma2xHGyXaIlOq/hdRSy4WaJf+eyHD8aSPv5MrTN9PaGD1BWjstLWk0NmazauXFtAQH3fZ0CgILlkC0dNgSpNGYWD303Sj7Gcka1ITVZoMd78Hv80jzq9XF7IwUsvz1of2anfH82nkrz8iLDbNdn1/1pbqqCIC6ujrKyyNnrrGwFSZ2vVMMkppKO92ec+gQg8JsR+F0TMIWC5vN+J3m5emrndGucxHB82hSINEAiavZuKp6e5KKmbjifaOxH+Fn5Th9Nr71+R/q103W792CU6IH2LWTr53DKat0+9KMPbqBNkdLIbC1EaEJGnxdp32whk281rZEpnGRWnesGAoRFhvh3R9mE9JkKDVlQ+FnoeYU6+vY7W4SclVWgNfvX8fa9/fHPL/fqz+Qnv26/eaat27l1L8sYX1Jfbf7ejh0eecIIeKFEHcKIR4Ovh8qhDi3R3rzFWLfPj0p2kcf/TM06GfZLfhaI2fcA3LSmBD/GuUFuv5zf2kVAU9kVKyzXuJpeJKAVwkQCbj7qcHl1Z2/5tMvrovZr3PffJPRUs26zty8Eseqat7yjOGmay437OfrsPQVwENXT6afNXL2I4Wdwy3F2Rl+vz7ob9xwBmvXnMO6tecwYNlvSLU9RMund5L1a+MsyNGaR0vgksO+VsbAoFDYrNwmLf86mW9eczUXXngh3rAI3LiwWez+Yt1IPGyYyoHUHuSVk5PD/v2RLrix2NvmocUfYPqKrdy/bgt/u+Zi7ttTRu6n6/F6vWRmxk5t7nMkkSAjv/ehlSV846UHufSNhwA45XJlg0lOjpw4RMOm6YLA2uH3zsjQ1VULbhzD0GDAnRIOGr7mV3F1SEcxKTmeJwrTueuGqw3tJQVxtAn9/s4bqav7asr1ErBpg6MndksfXq9eCBdTNuirE3swVmK0v5AzvRMASLSnEtAiHSP87mQuSLsz6vmjUbEmehCeiHL/t3j0621zqRVJU9YaKkf8F5fwG+xhHXEk2CjbWR/RXulT1xkTZyE+yU7jxwcINHpoXnrsKgl0ZzrxOOAF2k3iZcBve6xHXwH8/ib27rsv9D6g2VhvLQ693701Uvr7G3eRnfYCDUG7gfSqtG3NROag8cZ7kFoNvpZ3ADVgvzHhPACaPS2MbN3HhZ++H3Hcb//1ZwaPLMc1Sc2AEr1uLHVezpx/BnmDRhj2FVlGnfqLEwazYEwuU6IYG22+AxAlzTXAi3WHt4SNbzaubvx+Jy0t6fj9TgJvPUWi7S2SM/dhrzAKLXtbBt2hdedJhvdNZfH4PG7YoqtZ8stfwW5vocGqq84u1j4JvT5wYHzEeS1eJZQryw9hsViI5uG6QHszou2MzSW8WV3PvjYv99T78Hs8/PGAmtG+u2wFKSkpEccA2LxJeJxpJNusDNOMA3dBXRVZjbWhwTk+JRWAtDQ9QK8izjj7TsrRf9czWs+Iek1QKsZhw4Zx3nnnkZTuYvCkdtuEFaQPzR9pCBZCsGBIf9KGDGbYsLtxOvMi9gEQbfrAuis9DVea6v+hbalR9+8/V6m4pp07mKzsoZy+6HVOW/E5Do9SG+VraTjC6oRZLZH3otTsNNqbsASDLqUG0xKNcR5X3KXfM00lUStUkupsICe+kkS7EmBbyxv58QvrCdiUbcaTUkjA2kb5xL9T3/8TchMqY7pUA1S5IyeOe9wBcoKqxsFOK1lS0vjhfqr/vZG2jYfI3fRt4qumEQdkIciM4tV2NOiOUBgspfwTqG9VStlKtCiPPsSizycYGySsDdNVpm6LTFPwoc/NP62Xk2tTD0bDn5SNQOtQlBzAEjYTC/iMoey5XqW6OHvpJ4b2nzz9CJenfkDakFbOPte4LL5uZlHENfJTjfr8U9LUoJFi0wcg1/tluN4vQ2vNARG9oEetX91CroRIf/9o5G09KWp7QnMzWn0xAPV7Ir8Tq1fNgiMCfcL4qNHG7gPGQcvfZiOjYABo+kP4ufffLFmqu/0lyCYKk1YajktIMKaRcLQo+87iZZ9RU9ZMfZ1x4JNSkPhOdLXSD7dH96h5NuAgVo10hzcVgIMBSZbQOPdD3V4gEQQS9EFeCxrSNU2jf5FysWxfDWxK20RhYSHOsGC5uGo1IXA6o+RnEoIrr7ySSZOUDcXnCQSv6UdquhF4/mJdANaU6Z+vsOAaTpkZ6V4LkJKlrwhKxQBGXLqPuMw2NK+6h8KjjcOZ9rXBnHTBmUzY9gU3vvwE3mC/7R3qhwSkn588/5ahTWoWzvLewzedVzLvs1vY/mIe4+P1vuemHiI9X91vPiR/TIS7lt0e0YezBn7M70/5HX879RcAnP3AYqrL32f3vFtoTdtOUpFg9/zvhPafmFCNDEbeO3xGe2BjYy7hs4ryoJpoi1vDHZb6ovElpRr016jxIOXgTArXf5cPSeZVksiL6z2h4BVCxBH02hZCDIawuGsT4uPVMrFaKL1fpaU+6n6p3lSSrBKPBm0O4yDrKtMHf8chfZbna34NgJmrlKfF0Ba1CskZbbxGfVKSEtXXvGFQCfzn2imkxEXOoOLC8vmcmq4PMCvqI3MTtR64AX/ViIh2AL+EXy//KcNH6F5IRUW3ALCqYiLJt4U96AFoe0IPymuf8QGc8b6Kdo4xRoaKxQBkL4y+Ojm3pYUEj3GgEFZpMLBHYyRbI9qGDf2l4b0jLNhr067VbN06h9VfnMeKFRezccPp1L5ZSCCsQlh+ded6coBV2Nm7NzJ/TVL9MOKbi1g+XAVH1e1aR+4hPUI3xd2CJ3cA0mLBnVNIXIpyBtQ0DWswyjXTo9RSUkgqKio4VHaIa9OuNVzH4+n6MTYYjgO62mzilpWctHYRtzzxe5Y9/3SX51HnilTB2OICBIJCQVgjf3xhUcckZ6oVy8FU/X7K1VIBqCv8kNa0HWQ6+7FthNGgPnGF8vT7R0nQBVcKLGG1IWqCTg0X3DmVfyerwbesOXKlM7//5xFto1OVt1fZiD9RMcyYRmWMS7cBjJnyd8O2jz+/jVRNvyfXtQWoGJWBRE/P3R0cR0+ja6A7QuFu4D2gUAjxDPAxfTh2QUZRo7Trm193KgPr+3bd+2DORqObp9fvQJOCyhTjrMji1lcXosPIKIH64INvl2r20VCUatjHqmkE3BYYpKI+p0yZwhVXXMH8kdGN0d8p1F0WHxipB/DkBkv8WSrD1Fqai4C7KOp5ir0W9jf1J86lq3esFjWYTRuYS1Mg7HMGx+vZnynD/PyP9eW1w6dm8m3VkbOfhM+Mt2nBcEtU6ZGOZNL4YkOb1a4hvE1oAmrS7IZ4tJukeliv90VG3cbFFRneC2lcHGuanba2FHzeePIamkiqamHnIL0Y0h1vGz1m2gm//uByva9Dd6oBJqPqZFzuXASCjyao1VxCa5PhOFtwZeDJLsSXnsOO/QeCfdKwdShdKZH4gt9t89pmnGH2nClToqtKwvGGvGMkQWUBoITF7FUfEu9uZefK7qVMj0e/x38qfwdA7pDBxKckIjUoWxZ5r8ZleJBS4tcqAUlphm43ESjjd9XIZyiZ+ge0jIMEUo33RXxjDf2aqpi+Ry/Tag37HL5gTY74NCdtFpgzLIuBmZ07Bwzz78Me8BEX9BzTkjT8VuOqa4I1gDdYWTElTY+KbvAV4fQaVbdnfmccQ84sAtQkq7tYLD2jsOmO99GHwEXAdcBzwBQp5Wc90puvAOvWXxfZGB5Sj57JMTuQRv9BxpKKyd5k3I05aDa7IQOqCEs0pnWIR9g2dDxbhqvlfHselBzNqKroX1GOLV4/x7nnnsvw4bFLPg6Ic1Jx6gQqTp1AlkOfec9MVauGO4ca3UqFO/JWeabGga89N07YyiMlRQ02I/rPpJ+InI3mVVRw2f+eJ8Xr4bL/Pc9l/9NVI75W40w/LfVkUl4wDnQJBVbGbNNVERM3qpVaSqOPgibjSscW7+fgZ0+zbFoa68em8Mls3bA7m894Rl5MOvoM+ItV6vey21M79Dr2A3g5b6FZBC63LkhHDhsadd/KLP173VygB5dNKz/IZf973rAiaseqBYgLmzS0p+zwpSnBvq9UGSEDgUCE4Xima6bh/bkluo/IsGHD6Iq03KCaUTMag6/509+j7N05AkKBfhNRsQ4nX3Qpmf0LkQGBN1gNrn6fPihf8IvvUd+wmn2HvkPGyPoO5xPUDNZtRVXT/0Ll7zskKPTBox//iX0p+uy/8bbIwEUt+J3OH5nNpz+d2+nnuO3s+3h59W3M36975hekG8/ZlLuS5hwV2GmxOBk1UgU8zpmykEF+/TcqGptB0bhMUnPiueWheZx709hOrx2Ovza6a/SR0t3cR3OA+cCpwKwu9j2hqavTsy+217AtKNhGbp6a6fnQB+YD6Zm8OFg3JM485RlSUpSRsWXQaJpHTNJPHLwp1/Qfzv1X/YTmsLTOW4fq3jDtDG7V9biP/O52ZmxcQ3x27Dz83eX7A7JZetIIvjt5AB//ZA6nDlcDj2jQH7a/yO8B8EWrDX+zEjz2MG+mtLRpnHzSh+TnX47W0kLSG9ETd+X/n+4RlTlaDTpVG5VQyvnFHcyY/iljxz4IgGeznnTNHjhAoP16UpJe7+PkL+rIq/SQU+1l9LZGpgllV0kubCGuuRiPM3byMH9YHIEMpnqw2RKwWMIH6M5nZekpLQwIqgBnHFrL4J/+OOp+T10cvdLshjPvYdEpfw69XzxUd6+0BgLEeXSBY+ngkdQaVANVVVVFqMoCdbHVEUOHRhdc4RSMSOfKhUY7UN6wEWQNGMjZ3/tJqK1ky8aOh8bE12Jl3wfKRtPaug9cFUigYOR4alaexoFP8ylM/z0AVmsctTVqZZmQ18rwr+9l0qQwe8bgSON+OO0rPE8wxcqmjIF8/3/rIvYLBJ+/jsF7M6ZHqo0A3GMlWtiCwtJkTGYZsBuD8HJzL+Dkkz4gI8M4fLbbbNrRWmI/wwfSO6hNtcNYVhwG3XFJfRC4GdgEbAZuEkL8s/OjTkx8vgasQY8VKWHzpvmhbUOHKkNlu2uqBJ6YMJr7R7hCCwlLUD9qs3nBGt1w+8VApRP9eKY+o3N5wmYENhfM/CG2LH0VMKR0vypBOaDrnCldYRGCwfFK/TM4K5Gfnjmc00flGIbEFPQ6Ag+eeQ/fmTs44mFKSBgUarPWR7+WdcSs0CrLnqBUIv5W9b20LF1GXFx/7PYUcu++C+9epWpqXfY3EFCaH1yCB6+R0BYIleHMrfaSVKJH907LKMHh7Z4C9qSTZnLdddepPtn1wP1oyfHim/tz6aWXwnl/Z9K8uRSV7mLsttXcV2DH09S1bjinUa1QTpu7gMr9LQRsulrhs0n671sUjEW4+J3/MqR4O0ltRkcGt1u/P7xeL6NG6WqszMxMxo+P9KaCyAEwFmm5CQw7WY/iPrhTuUoPm663vfev+6MeqwUDDttqdPWK1RXAEkzVu2fvvTgTnVjtknP+72fMveI2hkyeQ1ahsmFVVr1DS6ty4ohL9xCX7iEhsZ5JvoHd6ns7Mw4q9ZEAPt9ZTdCMwfj5KpVMuzayXSMzceLTDBr4Q1yuyEBMgEC2xF4a+/sLOI15oYQQJCQMjtivbGc95fW6wBed2L9+UGt0hRau6GPIkdKdlcI84Ewp5eNSyseBs4NtfY7PF08iEGjB53OwZPE3OPfc/4vYp8HSik1aqc3VVwFSgAgzbmmByB9TdMihX5pfFHrtdoaV6LuzEk7/FdY5Ucw63+o6mOtwGZ2fwiPXKHWQJVh28FCwxOOQ1CGcOmQIty2IboQGSDr9dOz7gm52BT8ybrQ6SB3YGnxpnPXETZgQep12xRXk3vULml67kUDVFoSAnGo1O06vC86shp9tPPfez0IvndYArg6RozNX1mL1azg7tM+efTpFRUUA5OepspiJiUbjZTsJzUVqAJ50Dc6L/8GUlBIWLHqNz15axv9+tSrqMeG0188eM9K4EkzK0H/v6e4G8qtUENugAzs5/+MXsEWJXWhuVjPTtLQ0JaiCTJ48mVmzjnxxP3CCHiGdP1wJHavNTv8xSuA0VkdPkbLxPyNY/++RlC3X7QX+NhvuejVzj4vrj8dzEJerHwmpaWQXDeJrP7odV7xS81VVvU11tXJOiMvQVZH9Wr6cPt0dXDG0G2kHjFa2sHb1kTUoKNPTpjNw4PdjCk7RCg1Xdt8obDg2LGtutUVjxj26J6EtJzLKH+BVvBwKsyylXToMR16kl97RoDuiZjfQH2h3vi8MtvVZ7HY1EA0bNozSsJiS4cOXsORgFf7GbPYm6T/urNlPGY4XFuPNtCltEzOkRiDsBmyNS+RA/kCeP+/6qH0IV4bkTasjqaBn9Ivh2NfXIh0WHhhowy5sPLxgYZfH5N/7J3Jqb2dYhgW7L5Gd6ItMe34eOZMbyBjVjK/FqN5JnGfM6WTLVl4iSliUM6C0jbR6H0nXr4W5fkgpAE8TIOBeY8D9ounpBhURgMujMX11HeLq11m8O5jXP/tcbDb9QRs48Aekpp1ESvIkVj+2lPQqFWFem60P+P+8+ROKxmZwzi3jsQRXPYdKS3CmtPK9x//JK1/7FuWZecS7W2l1RT7wHpudZ+5eYWibdelQqFU3VqNdzbCHTJ3O7i+WY/F5id+7hdZBxtTbH32kvNNyc43uj+PHj486sE2eHFn6sjNk2IB0+cJ7Qq/rDupeUZoWwGKx4vf52PT4MGxxenBXc5n+vVqdATx16nO1tSkjeVKiMZ9UXFznWW2X172ExZdAYZWL+OwoNZLvtEOCHTrkE8twN3D7F08RGKoS4RWMVF5DWmil0D1h03Ja9JVn/0FPUrHpNrwJsb3PBt0wjDcf2cwonw1n8Lq+gMaFDy5lc1kj/7tiEgXPqSH2UppwIjgQquMXpIdUR9DJSkEI8aYQ4g0gCdgmhPhMCPEpsC3Y9qURQvxICLFFCLFZCPGcEMIlhBgohFgphNgthHheCNEzTrhHCbvdTuCQMi6V048XuIKsnH2Mn/A+NpsH6dcflhIKDccW75tkeL87eTdfjKhHNutubTcmWWMKBAARTIH89Yr3SB3UFjHT7glEQGJpC+CTglZN4IpWZLwDFpcLe34+LmculgTjzEY4HFgmXYkjMRDhjihsRv1p4qxZpF19NQUP6kIludmPSBsAGYPB5oSETEiIDHLrKBDa0yw7vRJH/nRcLjUAdYxNEEKQnjYda9CzxKq5sGouEhoHk1qjq2SKN9UgpaQpS9e9B3x7iPO00a9azfKdAePg1I67cFREW4lf33dL8Dueet7FoTZrmH2hnfXr16vrBpPjzZs3j8svvzwkEM4+++zQCgggPj76jDQWnpaw+hhhKo6mGt32UVeu7vlDB4oJeK14GoweORb3qODxMqRW0s95eKqQ+MI62gJNSBl9ELfVCkb8N7Kok9diZ07ZBias/xuzrxiGEIJdlU28tk4J4WgyYewYZddK0jq3waSlzWBI4YxOBQKA3W4lPtjv5KDn4nefWcvmMqVyuuaF9dxFK3fSSjmSfWghS+VjeGhF4hrRczlJO1Mf/Rn4C3AXcBbKNXVh2OsvhRCiH/B/KC+mMahJ7+XAH4H7pJRDgDog9oh4HDBixAh2zVbunz8TD/C6uIQ9qJtm4qS3yS7Uo5pvF/cbjm1o0Gdz8XnxaBaNLYMauOk3N4fac7I7z2uE30PFojn8fccfjvCTdI+x/XSDubdOzZhTnNGjcWMhhEDE6Xpza2IiXPgv9bqD07U1xZiyQdjt5N75C2zp3X8YCsoiB0+A2SvCdLM2B4MHqULpiYlde+MAxLf2w+4zfvaNn5ZizdZrAcuAGiw9DjWoe6Kkigb4NDEyW+z1TfpAe4VbeZll9S/ihr//J2LfjrQHw82ePZsRI3S13rRp07j4Yl2w7Nmzp8tzhdNQ1XXcRe1BJQCfv/u2qNsTUpTTggqlMI6+SYmRwrEz2mMbnCme0OuO2PPyyP31rwxtacG0Mun1OxloVc/o6fd9zr3vq9QwHn/kCiA7+0zmz9vDCO//kf/d2HPVfvmXR0iVuLgBEfvtqGxil10N8zuC/z/cqpd/9QY0PsHPZ0ROJB7Dwxk0Ra3RcbSIKRSklIvC/4B1KGNz+9+RYAPihBA2IB44iLJTvBTc/iRwwRFeo0cpKysjIAS/CNwfansD5fHicrWwleiuZV63/mOOGTKYvBm6q1yzX1crrWuMDCLbcUpYZawog0lP8vJ3ZrD112fy3g9n8e5Vf+WjSz4iN+Hw87kPW7GcIYsWMWTRIsPKQXS4E20ZkTP+EL+siX5QB9zOyO1zl0S6I+bkfI2ZM5aQmXl6zHPNu0bZFUbNjJ7CYckLu2ht0D1HAh7lcplXqQbKVqeLq5e/F3FcXWJkVHFT0GZwXnYqZ5eo5GnCYiGlq4kCMGBA5CDUTnjyu+4EroWT3q8wanu7fQFg2QvPAOCPUfcjPErjit/ca9giLIc5yAVPZXNpxG2F3B/bQ0GNIszxxznQaJDObqsPvS654Qa2jRiJ069/F8NzYytBZCC6DSEuTsX5JCdPMCTJczpzOfmkSDuf02ZlvTPAw0lu3og/co/Bo013vI9uFEJUABtRKbOPKHW2lLIMtQo5gBIGDcFz1ksp20VjKRBVqRjsz2ohxOrq6q6zIvYUtbW1NGYNpNimPyxrhJ7V9IAoinrcrpf7I4Ipf/MHDQ5VYgJoCSv+fcgbOUtIsYctsUeeZ9x4obHO7tHGYbMQ77AxIjeZQVkp5CR0PUBFw+J0Ys/Jxp4TJtSuehn7dY+H3tryow+8Iaw2WPBHuPatTneryeg40Ais4RPBc1QUthAClyuvU2+cYSflMHnBAGZcMpRZlw1l0pmRpSir9tdHtCW26SNUYlj6krHblA/7zM2xk+v5DuzDHlxZ2RzGzzK+Xy7jxkW6KufkxP5dwt1Vv/3tb8fcLxpj552Jzenk7P8zZsc99we3MmiSSu996EAxe9fpGXKzBhgH5HGTdFtE/rCRDBr4w9B7LRB9VRdOYuJIEl3KFlJ0ehn5uVlITcVtWNwCW5Ugv+50Jgx6mJy7VES6c2TXK5DRNcWh17FsCr6qKjw7o2ekHTv2X/QvvB6XS923LqfyWBo18k9YLJFC/7KpasxosMpuJwy6Ypp+v10yObIAz9GkO4q8nwFjpJSxS1UdBkKINOB8YCBQD7wILOju8VLKh4GHAaZMmdLzivQwhLAjpY8D+8eSm5uLfcb3DNsTZWR5wo74mm24OEBb4VD69etHepKuDnGHeSCtaIhcKRiw2mBh7CyMXymGnhZ8NlTOmbQw75mYnHxz7G1jLoHNLyE7POCFhd8E/qTeZI+Gqd3XUFqtFk6+QLkUjjtVPdT7NhyirkJ3D21riJwrJTVGH/THbfuCTSMnE+8JADa++adTiE9WA/9vPl0PwLuuNMa89SquxMjZ69Ahgxlz6ukMHjyYV1/VA7g6E2ztK4Xp06fjcnVtDzIca7fzg/++HNGelJHJqdfdxN61Shi8eo+urpn3zZsoGDmGv1ym3KtdcUpgJSWpVXRh4TfZu+9+AJpbjOU51X6jaWpStQumTX2TpKRRNDVtZdUXX8Nik0y6Op/SBrAFkyfm/PJO0i8OFp4JLqqtiV176PgtupNDrCDh3fPmgz+6XSgpcQRJQ+8Ivc/JPZ/9+/8VERXfTqLTxnnj83ljQ3nU7dH4w0VjeW6VMsr/YH7X8SVHQndcUvdAWHz6kXMasE9KWS2l9AGvADOB1KA6CaAAlY31uEHKAFL6sNvOYP/+8VCdwqFk48N6Gnrm0uFyK1bpwyHVquAL2o2QAltzAz/47ncYMGAAI9J1ve/mpq5nSycywzesZ+jyZWTcdNORneiiR2Di1SQ2Gx/ioUPugOuVlw7ph+fnHo1L75jKTQ/oxeSj+ZhbgyoHZwyVioYS/ragMTxagjx3sx5NHJesbBnW4AAfKwYhGlarlV/+8peccUbsLKlfhtScXIZMnR6lXc2cf/jMq/zgaSW4Tp27g6lTlHCx2fToL0sU9dHUKbqwS0oKzvjDVIalTf8DC4hgkXHnYGORo+5ydvHy0OvMKOo8IKZAmH5yZCbUwYN+wuxZazr1oIqzK0F0ztjYq+KXvxP5nQJYeyi9RTvdEQo/B5YJIf4thHig/e8IrnkAODlYp0GgIqW3Ap8C7QnzrwVej3F8rxAIFh4vKz8ICJpaD7EuzehGuYKZ7GUwuxhKKvWAwCvUTXa/uJX6vboQiYvXZzD3zrmXF859gQ9rul5pnMhYnE5saWndDqqKfSILOBINqTAGDLhZnTd/Asz6KZzxmyO7BmBzWLE5rJx6tRLsg0/6QcQ+1qDXUXs+q/lbvyD3UB3JzfUAtFiUf781WMc5PEvmqUvfjjhfu9CwdPDOAkhM7Lqgj9VqPfLvNwpxSZGrmYQ0tQq22uzY7Kq/FosNISKjy4cNjax5IISVadPeZvQoPU290xHFlhZU9VuSvlxBozll0SuldUVi4siQPSEcIUSUNClGbpoziBtOGcjZHYRCewYBiC2g8lIOb5V3uHRHKPwb+ARYgV6OM3q19m4gpVyJMiivRRmsLSh10G3Aj4UQu4EMoGtXi2NIu7nDZlP6wmGBPB4YbvxxKkQ+vxR/YqG4hwBW8imjvywObS/+UNcF2l36D76gaAGHRAFL6yPr07bzvf7H1rD8lScxm4SwjJMDg5lbsdph/i8h/egVDxwwVhnFrbZ0HEnGurkjR49FSI0Jwajk0SVuvvXuLnzB+INFJ6kodEswbcd9xbqXz+D9kSUq3U1q4hDwR+bjnxAW8HesSc6MvD+7I3wGDlSC1OHIiro9KXEEubm6/Syajr5dL2+NIpgAXOPGkTBrFgkz1Hed8e9HIvaxB9T3GXOlEEZeMKjxpGlvIbpwdojFoKxE7jx3FNMGGr3pvh+mGkpLcBDvsHL6KKV2u3iSGj96QqiH0x2bgl1KGT2Ry5dESnk3kW6te4FpUXY/LmhpUS58yUltoFmYbNENenc1/YpfJxk/zmpxEkVyD7fyW76LMqKW5g6goEK5wVk7zPSqfdGXpwA/GpDDbYO6ML6aGEkypiewWg/PL/9waJ/l11e1QodZ8IKrr2PrAw9gDc7wx/efQ3H9IdIzjTPMdq+VA26lZios30daFHtEWl4+dQfLSUyLdM2dP39+RNuxInuQMYVDu/G5KwYN/D8GDYzMDBALS5R4hiTrCGAXwhZ9OCt69hkQAhGWLPCA3UVCWLW9dRdkkThTJQ/07NvH3rPOBpsN/H4K/vWg4XyjRt7DqJH3cDTISnJSfM853PDkF3y0rQqnzcLu352FLyCJc1hZ+8vTcQSTTf7l0vH85dLuqwu/LN0RCu8KIW4E3iSsjoKUsvs1CU8ANm/5IQAW6yoEgwlP5tm8xwITIo+xoJGMrhLaPHxiSCh0JMcR/afIcdj4YdGX8/Tp09Sq5HTT1tTh/VbPaiLtwWR7DVVtIHX3xjNv/gHJyckhgfD1r3+dz/+l1EWOKrWKyauuDbm7AlyQncZrVfWGmsQnX6QXmA+pj8IGuIsvvpiEhIQen0F2hrfVaHY87YZbeuQ6Ikqxp6ybvosYfRBbXvSJUzRhYemQVqbu2edCQqHxzWCSvaAdofQ70ZMYHk3+8vUJvLP5IKPzlc2ovdaVyx47kWNP0Z21zxUE7QroqqMv7ZL6VcXjUaUBPa0nI6SFvw3Tl5nlddFvxr1iqMHjrEGLrfN0xwhbf2XiEJxdFIkxicKwMwFIKlgQkZnyaGMJyxArLGoGf87//Ywxp54eGqjnz5/P6NGj0doT5gcD9u0+D8NP1uM92pMZ2MMM09kD9Vm4t005IzRU6cFOY8eOZdCgo6cO+zLkDjGmaU/KiF17+siw4HQa42OSBkwm41vfPCyh+MKwebitdq5ccBcAzWG1PTR37BiOnF92v97z4ZASbze4nfYmXa4UpJRH7qZxArF+Yxaa1UudQ78BLfWxE2Nd/8EDoMYnDowewefT/8rrkyMjZ6/aqFfguiQnjZcq6/hwyrBQxlKTw6RgCtxVp4zOPUz4YCQscfzff18PrR4sFgsLFy4Mbc8fmkr5rnqEsNKvogyBMBRLKW5TwsAS5oXkStAnE6PnzOeLN17GGd+1q+WxJDUnlx889Qp/+8ZFMQPdjgZCCGbOWIwyJGiA+FJ6/f8NP43nh83jR2eMUCXEwq8Rw7sn6fTTSb/qqqjbTiS6FApCiGuitUsp/3v0u3P84/e7kMAnucomcMaGlfSrjF6DNxorG43L7LWNLfzftgOh9w+PLuKklAQmpyQwJjGu4+Emh0MvrbAsttgz1tO+OYr/3qFqcgjNiwY8v/B2Tr/x+6Tn92NjuVqRxrc2M2rWqQwYP4mCUXp0/IyvX0VGQX8GT4le67o3sTkcnPeTO+g3/PBSVhwuuhD48qqVNXeexk9e3MD35w1he7DNs2sXzqFDwR693KtnX2Tp1BOR7jw1U8P+ZqHyH53X2QEnIqmp0/B4lLGy1aGrjq7aHbs+rX29MruMd0R6NASkxKdJzl6zi92t+nJ1RIKLHKedb/bL7FUdscmXp7MyiUnp+srPIiWaEJRu28zjP1KxGa+1BVM4awEmnHkuo2adargPbA4Ho+fMP27vjaHTZhCfktrb3eiSjEQnT3xzmuF73Ps1NazJtugZh53dKEp0ItCdcpzfD/v7NjAJ+HIOwV9hyppKcLcqI5AWtly1dchB1F5Ws+LUCViDdY7fnxmZj3/o4k0ULor0j86KYXA2Ob75+s/1esddDdjX/0XZOISmGe6lcrduRxg7YzZ5Q2OXUzXpGfy1tdQ+8UTUbV82OO6rxpdZX7egUlT0KWraKkkIKD3ufJ+ecyY9SQ0Acz//Pde+8HdufPav3Lp9adTI1HBaA1rU9jS7KRS+isQlBSNyuzGBb9dZW6TGwdz+7B4wHL/VxlWrtoT28db2Xl6vvkbWD/Wgw7rnnjNsSzlfr7GeefMRRtp/RehOQrw3hRBvBP/eAnYAr3Z13ImGXchQ/d7UsIXSfrfKP7Q7fwff//6PyPB5+O43rqWyMboHQ47DFqry1JHr+/WUx4ZJTxOf5CAuyc6CG8d0ua8WnBD47Mpm9OpZ32DFxDlsC+gSZf/GyDrCJj2DvVA3jB/6+z8M7enfvC70PlYcxIlGdz7ln8Ne+4H9UsrSHurPcUueXdIolK5RBqeD3yu+jz07lb1AE5KCUWP4v/+q7N/vLFF1Zf90iTGTZaXXz/wvIiNVAX4y8PBTUZscH1jtFr51b/dcX9uD3ca3uWh/kJZP0SvNXfLWE0e5dyadESsSesiHqkjPyO3bjmV3ep3u2BTC6yos7YsCAcAnwa9ZcUgbjXYlFF606VGyPrtx9r+rSqWsOG1kZODZtpbohqxU27EPVDE59jhcNi766STmTY3uutm/fB/f/sdjx7hXfZeEGTNCKTDaGfhKZEbYvkJ31EcXCSF2CSEahBCNQogmIUSfy9xmFxBwp+CUNv4yQnmQJPpmxNzfEQxoSo1T7m3f7yJ30ey0xG7XhzX56pM3JJXCnEh1YVJTPU67jeQsM9fVsULYbKRfa/S8dw7rXhW+E5HuGJr/BJwnpUyRUiZLKZOklMldHnUCse/QegCE8JMhk9icGrQtNDXFPObJ5SqdRbt74i8G5zMj1ei0dU6WXtLxhQl9w7PBRMfljAxMvPmZP0etW2DSs9hyjarbvmI/iEZ3PnmllLJvKdU6UFKnSiu6W1MRYe4lo3esDb1+7Ex9uR+IkbJiVKKLZWGZUK/My2BYvIvrC6JniDQ5sem4Mkxuqu+djpjgGm66/7bTHaGwWgjxPPAaxoR4r/RUp4433J6DWAGP30FcmFCI8+hFcQqTCmn2+Gl2+1mzvy7qeb5TmM2jpXoBu5aAZmY/7cMMjndyckpCqMreBe89E7VQj4nJsaQ7QiEZVXktvFyTRFVM6xNYq9QqoMHtwo4eX+Dw6m6nLquLMXe/H3FsOP1cxupS2WagWp8mzW7jtUlDyQ2W38yqrWDYyaf0bqf6MDl33EHl739P/8eOq1Iux5zuJMT75rHoyPGK230w9DqAhbeH6rp/i9RocfnZPetrHGo8PM+h87NTOSnl+EpqZtI7LBk3gH/++k4sUnLOD27t7e70WdKuuJy4cWNxHUaJ0xMRc6raBfuK/x56vT1+KEsKdRdTu8/LmmENrN5dyDkPLIk49hsnD4h53t8O7Xfc5q8xObYMTkuhoGI/BaPGmPdELyLsduJ6sXrd8YIpFLqgvPz50Ov3Rs0Mvc4tfQoBWAMCsOLxR6atOGN0ZIzCt/pl8ljZIVLMmASTIMJi4SfPv9Xb3TAxAb5c7qM+w4s7X4y5rb0Qe31SZK1cgB+fPoyZgyP90O8eks+Kk0fiMA2KJiYmxyHdqafgBC4GisL3l1L+uue6dXzw6+W/5v5g0Om726+BsGSn8+tUDYSANbr76YIxuVFTKDstForiui4ObmJiYtIbdGe6+jpwPirvUUvY35dGCJEqhHhJCLFdCLFNCDFdCJEuhPgwGD39oRAi7UiucTSIE2rAryaLp0eeb9h2dYUqzaGJ6EIhJ8msmGZiYvLVozs2hQIp5YKjfN2/Ae9JKS8RQjiAeOAO4GMp5T1CiNuB24HbjvJ1D4sMmxrwvTgitnma1LamkpugQ6GmnGQnKfHRqzeZmJiYHM90Z6WwTAgxtuvduocQIgWYDfwHQErplVLWo1YjTwZ3exK44Ghd88vQ5m8jzaaMx2XNxqLoIw9u45BHuZPWWyOjkd/8vulrbmJi8tWkO0LhFGCNEGKHEGKjEGKTEGLjEVxzIFANPC6EWCeEeFQIkQDkSCnbgwIqgEjXHUAIcaMQYrUQYnV1dc8VIrnhgxvICq4U/pb0Q8O2c19/hu2NKmGZX6jF1v2XTQBg7vAssk3VkYmJyVeU7qiPzuqBa04Cvi+lXCmE+BtKVRRCSimFiK6sl1I+DDwMMGXKlM7Lmx0BG6s3cn9hpGfRjx++y9gfBFdM688FE/txytBMMhIiVU0mJiYmXxVirhSEEO2ZUJti/H1ZSoFSKeXK4PuXUEKiUgiRF7x2HlB1BNc4Yr4+7Ouh15Zg3WUAq9YhHkEI8lLUyiAz0WkGH5mYmHyl6Ux99Gzw/xpgdfD/mrD3XwopZQVQIoRoT0s4H9gKvAFcG2y7FuX11Gu8teuF0GvNogLNBlRWRt33rDFmxTQTE5MTg5jqIynlucH/A3vgut8Hngl6Hu0FvokSUC8IIa4H9gOX9sB1u40rOOHft28iBO3M1775JG0d9tv7+7OjxiOYmJiYfBXpTvCaAK4CBkopfyOE6A/kSilXfdmLSinXA1OibJr/Zc95tIkPfjWapqejaPMbC86lX3e3KRBMTExOKLrjffQgMB24Mvi+Cfhnj/XoOMEm1WDv9cTH3Kdf/+g1dk1MTEy+qnRHKJwkpbwFcANIKesgSjTXCcbAFpXhVAsKh+t2RtrW81PjjmmfTExMTHqa7ggFnxDCiiqsgxAiC4hMCXoC0ehtZEBLAQBSqq/IQqSaaHR+nypVbWJi0gfojlB4AHgVyBZC/A5YAvyhR3vVyzy99WnawySarSpyudWh0laUZOsFOEz3UxMTkxON7lRee0YIsQZlBBbABVLKbT3es16kqrWKNLsqtRnfOAqA3NoaANqmXgBvb8CRkNRb3TMxMTHpMbrjffSUlPIbwPYobSckNmEjO3sfAF5UmmurJnFZfPz50gm8n/ojzjylb5fsMzExOTHpTpqL0eFvgvaFyT3TneOD5Zs+ZPqQUgCaLSpa2SegMMdJksvOJecdN56zJiYmJkeVztJc/FwI0QSME0I0CiGagu+r6OVo454myZcSep1mU3Kzn0eD9MG91SUTExOTY0JMoSCl/IOUMgm4V0qZLKVMCv5lSCl/fgz7eMzJ9+cjgXc5h9oUFaeQYk0Fu+mCamJicmLTHUPzz4UQ56FqIAB8JqU8YauMB/waVqlRQn+eFt+C4OIgyevHUlDQu50zMTEx6WG6dEkVQvwB+AEqad1W4AdCiN/3dMd6i4e+9xmFjQPYjzHlUz+vDYvDrJNgYmJyYtMdQ/M5wAQppQYghHgSWIcqn3lC4W5R9RPsdg8fc4ZhW6Ifyv2R9RVMTExMTiS6E7wGkBr2OiXWTl91dq9WqbGFxccuMSJi+/4N6451l0xMTEyOKd1ZKfweWCeE+BQVvDabDpXSThQWPbcTAGEJRGzb3biOUafPO9ZdMjExMTmmdCoUhBAWVJ6jk4GpwebbgoVyTkg0/0HszuKI9nU1H/F/X3v52HfIxMTE5BjSqVCQUmpCiFullC+gKqOd8HibXyeuQymd7+70MO70M7Da7L3UKxMTE5NjQ3fURx8JIX4KPA+0tDdKKWt7rFe9iWylJGVQ6O3q91XK7IJ7vtdbPTIxMTE5ZnRHKFwW/H9LWJskVKTyxOM/Bca0ThtqP6OAWb3UGxMTE5NjR3eC13qiRvNxicUq0Gx2/BalJjp90xpgGPnpJ+aiyMTExKQj3cmS6gK+C5yCWiEsBh6SUrp7uG/HHKlptAzVs59O2LsXXMMYNXtSL/bKxMTE5NjRnTiF/6Iypf4d+Efw9VM92aneoLXRi6b5DW2jWw+qF4NP7YUemZiYmBx7umNTGCOlHBX2/lMhxNYjvXAwBfdqoExKea4QYiDwPyADWAN8Q0rpPdLrdJdVb+2jY5VRTQZLUbvMgjomJiZ9g+6sFNYKIU5ufyOEOAk1mB8pPwDCK7j9EbhPSjkEqAOuPwrX6DaeVh+oTB4kywZOk+/hlZlqo1l208TEpI/QHaEwGVgmhCgWQhQDy4GpQohNQoiNX+aiQogCVE6lR4PvBTAPeCm4y5PABV/m3F8Wu8NKc/JOMjP3E8CChQCaVOoka5LjWHbFxMTEpNfojvpoQQ9c937gVqBdL5MB1Esp25X6pUC/aAcKIW4EbgTo37//UeuQ3WXFndjA5FGLaRE/wCo1Ts7KQwOExVwpmJiY9A2645K6/2heUAhxLlAlpVwjhJh7uMdLKR8GHgaYMmWKPFr9CviU6qg9ZbYPOxrK60j6tZjHmZiYmJxIdGelcLSZCZwnhDgbcAHJwN+AVCGELbhaKADKjmWnircWM2HqO5SQC8Cc2rDYBNOmYGJi0kfoburso4aU8udSygIpZRFwOfCJlPIq4FPgkuBu13KM60An5u4iKbmGg+QD4EvfEtpmSzeL65iYmPQNjrlQ6ITbgB8LIXajbAz/OaZXl60APCZuBiC5JfmYXt7ExMTkeKA31EchpJSfAZ8FX+8FpvVGP3bs2EGlbQtpYW0DS1Vohmt4WvSDTExMTE5AelUoHC+8//77CGH8KlLLZ6v/5w/pjS6ZmJiY9ArHk/qo16itrcVm9wBgl+r/RzYouGeWaU8wMTHpU5hCIYyVnIxPOAHY0ubp5d6YmJiYHHtMoRBECMlLXBF6X4EZm2BiYtL36PNCwd3iA0AgcaOrirRkM7WFiYlJ36PPC4Vd2/cCIIRGrcgMtb9569xe6pGJiYlJ79HnhULxXpXFIzt3j6Fd2Pr8V2NiYtIH6fMjn0Wq0psyMRBq++cXrb3VHRMTE5Nepc8LhS+2LsJm87CPQaG2k2oDnRxhYmJicuLS54UCgN3uoZV4AG7d6ib7+xN7uUcmJiYmvYMpFACQ+FFqpOk1fhz9Enu5PyYmJia9Q59Pc+EQ8cQH/GwhC4A4zDTZJiYmfZc+vVLQNA2vbEUgcNEGQGarGbRmYmLSd+nTQqGlpUW9EG4C2HAGTAOziYlJ36ZPC4WqA40AxHlqCGDFJiVJcwt7uVcmJiYmvUefFgrNdUpl5LQK9jAEASTP79+7nTIxMTHpRfq0UBBWZVTOT+iPEzdtFgvC3qe/EhMTkz5Onx4BA76gDSGpHD92+nsqerdDJiYmJr1MnxYKHq+qmVDfbzvbxWgyU3J7uUcmJiYmvUufFgruFi8Ae13ZAIzOMOsxm5iY9G2OuVAQQhQKIT4VQmwVQmwRQvwg2J4uhPhQCLEr+L/HR+jaimYAHuMmAE41hYKJiUkfpzdWCn7gJ1LKUcDJwC1CiFHA7cDHUsqhwMfB9z2KNWhUbq+j0KbJnr6kiYmJyXHNMRcKUsqDUsq1wddNwDagH3A+8GRwtyeBC3q6L62NxjrMp2ck9/QlTUxMTI5retWmIIQoAiYCK4EcKeXB4KYKICfGMTcKIVYLIVZXV1cf0fXbhYJV+jm/6jUSbNYjOp+JiYnJV51eEwpCiETgZeCHUsrG8G1SSglE1eVIKR+WUk6RUk7Jyso6oj7U1VThsdoICBtWr5nzyMTExKRXhIIQwo4SCM9IKV8JNlcKIfKC2/OAqp7uh+Yvx5eqYhVcPk8Xe5uYmJic+PSG95EA/gNsk1L+NWzTG8C1wdfXAq/3ZD80TRLw7yJv9CYA0pPcPXk5ExMTk68EvVFPYSbwDWCTEGJ9sO0O4B7gBSHE9cB+4NKe7ITm13jp9CsoE8p0MbjfgJ68nImJiclXgmMuFKSUSyBmJZv5x6ofXneAsgzdlm2LTzlWlzYxMTE5bumzEc1Nhw4Z3mekDOqlnpiYmJgcP/RZoVB7sJQJzRtC7/vnTO/F3piYmJgcH/RZoeBpaaXSqhLgXbFzMYPinL3cIxMTE5Pep88KhYDfj5Aa8bKF2ZsXYRGxzBwmJiYmfYc+KxRamloRQjKYXdS0tfV2d0xMTEyOC/qsUGisO0RZXD4WNHbZM3u7OyYmJibHBX1WKNR7VC2FZhIZOXloL/fGxMTE5PigzwqFulqV1mIsG5g5alIv98bExMTk+KDPCoUWi0qAJ5AMmnZGL/fGxMTE5PigzwoFj1BCIY1arLbeyPZhYmJicvzRZ4XCqvx+ALgwPY9MTExM2umzU2SvVX30k9zberknJiZ9B5/PR2lpKW63mZX4WOByuSgoKMBut3f7mD4rFNw2G2myhsSaot7uiolJn6G0tJSkpCSKiooQZsBojyKlpKamhtLSUgYOHNjt4/qs+uhgRhYBrFjscb3dFROTPoPb7SYjI8MUCMcAIQQZGRmHvSrrsyuFxEAbdlpwJCf0dldMTPoUpkA4dnyZ77rPrhTanHayqCQn24xRMDExMWmnTwqF1rY2GuwptJJAftHpvd0dExOTryDl5eVccsklAHz22Wece+65ALzxxhvcc889AFx33XW89NJLh3Wu3qZPqo/qWloAKJL7sGRe1cu9MTEx+SqSn58fdcA/77zzOO+887p9Hr/fH/NcvUGfXCmUNKvYhDhhxiiYmPQWQoge+esOTz/9NNOmTWPChAncdNNNBAIBHn/8cYYNG8a0adP49re/zfe+9z0gcrafmJgIQHFxMWPGjIk49xNPPBE6FuCjjz5iypQpDBs2jLfeeiu0z3nnnce8efOYP3++4Vwdjz/33HP57LPPQtf+2c9+xujRoznttNNYtWoVc+fOZdCgQbzxxhuH8e3Hpk8KhS37SgBI8bX2ck9MTEyONdu2beP5559n6dKlrF+/HqvVytNPP83dd9/N0qVLWbJkCVu3bj1q1ysuLmbVqlW8/fbb3HzzzSFvoLVr1/LSSy+xaNGibp+rpaWFefPmsWXLFpKSkrjzzjv58MMPefXVV7nrrruOSn/7pPqopb4ZUuPJbmnu7a6YmPRZpJS9ct2PP/6YNWvWMHXqVADa2tpYtmwZc+fOJSsrC4DLLruMnTt3HpXrXXrppVgsFoYOHcqgQYPYvn07AKeffjrp6emHdS6Hw8GCBQsAGDt2LE6nE7vdztixYykuLj4q/T3uVgpCiAVCiB1CiN1CiNt74hqtjcqmIAj0xOlNTEyOY6SUXHvttaxfv57169ezY8cOFi5cGHN/m82GpqlcaZqm4fV6D+t6HVVa7e8TEqK7w4dfDzDEGdjt9tDxFosFp9MZeu33+w+rX7E4roSCEMIK/BM4CxgFXCGEGHXUL1QTXCG0mjEKJiZ9jfnz5/PSSy9RVVUFQG1tLRMnTmTRokXU1NTg8/l48cUXQ/sXFRWxZs0aQHkW+Xy+w7reiy++iKZp7Nmzh7179zJ8+PBO9y8qKmL9+vVomkZJSQmrVq06zE94ZBxv6qNpwG4p5V4AIcT/gPOBo6fgA3ZmKUnvFeZKwcSkrzFq1Ch++9vfcsYZZ6BpGna7nX/+858sXLiQ6dOnk5qayoQJE0L7f/vb3+b8889n/PjxLFiwIOYMPxb9+/dn2rRpNDY28tBDD+FyuTrdf+bMmQwcOJBRo0YxcuRIJk06trFUorf0etEQQlwCLJBS3hB8/w3gJCnl98L2uRG4EaB///6T9+/ff9jXufeh37OiMJMbky2cOeuGo9N5ExOTLtm2bRsjR47s7W50yRNPPMHq1av5xz/+0dtdOWKifedCiDVSyinR9j/eVgpdIqV8GHgYYMqUKV9Kov3s5juOap9MTExMThSON6FQBhSGvS8ItpmYmJgcM6677jquu+663u5Gr3BcGZqBL4ChQoiBQggHcDlwdCIyTExMjguOJ5X1ic6X+a6PK6EgpfQD3wPeB7YBL0gpt/Rur0xMTI4WLpeLmpoaUzAcA9rrKXRl2O7I8aY+Qkr5DvBOb/fDxMTk6FNQUEBpaSnV1dW93ZU+QXvltcPhuBMKJiYmJy52u/2wqoCZHHuOK/WRiYmJiUnvYgoFExMTE5MQplAwMTExMQlxXEU0Hy5CiGrg8EOaFZnAoaPYna8C5mfuG5if+cTnSD/vACllVrQNX2mhcCQIIVbHCvM+UTE/c9/A/MwnPj35eU31kYmJiYlJCFMomJiYmJiE6MtC4eHe7kAvYH7mvoH5mU98euzz9lmbgomJiYlJJH15pWBiYmJi0gFTKJiYmJiYhOiTQkEIsUAIsUMIsVsIcXtv9+dYIIQoFkJsEkKsF0Ks7u3+9ARCiMeEEFVCiM1hbelCiA+FELuC/9N6s49HmxifeaEQoiz4W68XQpzdm308mgghCoUQnwohtgohtgghfhBsP2F/504+c4/8zn3OpiCEsAI7gdOBUlQNhyuklEe1DvTxhhCiGJgipTxhA3yEELOBZuC/UsoxwbY/AbVSynuCE4A0KeVtvdnPo0mMz7wQaJZS/rk3+9YTCCHygDwp5VohRBKwBrgAuI4T9Hfu5DNfSg/8zn1xpTAN2C2l3Cul9AL/A87v5T6ZHAWklJ8DtR2azweeDL5+EvUwnTDE+MwnLFLKg1LKtcHXTai6K/04gX/nTj5zj9AXhUI/oCTsfSk9+AUfR0jgAyHEGiHEjb3dmWNIjpTyYPB1BZDTm505hnxPCLExqF46YVQp4QghioCJwEr6yO/c4TNDD/zOfVEo9FVOkVJOAs4CbgmqHfoUUulK+4K+9F/AYGACcBD4S6/2pgcQQiQCLwM/lFI2hm87UX/nKJ+5R37nvigUyoDCsPcFwbYTGillWfB/FfAqSo3WF6gM6mTbdbNVvdyfHkdKWSmlDEgpNeARTrDfWghhRw2Oz0gpXwk2n9C/c7TP3FO/c18UCl8AQ4UQA4UQDuBy4I1e7lOPIoRICBqoEEIkAGcAmzs/6oThDeDa4Otrgdd7sS/HhPbBMciFnEC/tRBCAP8Btkkp/xq26YT9nWN95p76nfuc9xFA0HXrfsAKPCal/F3v9qhnEUIMQq0OQJVgffZE/MxCiOeAuai0wpXA3cBrwAtAf1Sa9UullCeMYTbGZ56LUilIoBi4KUzf/pVGCHEKsBjYBGjB5jtQOvYT8nfu5DNfQQ/8zn1SKJiYmJiYRKcvqo9MTExMTGJgCgUTExMTkxCmUDAxMTExCWEKBRMTExOTEKZQMDExMTEJYQoFE5PDQAiRKoT4bvB1vhDipd7uk4nJ0cR0STUxOQyCuWfeas9IamJyomHr7Q6YmHzFuAcYLIRYD+wCRkopxwghrkNl5kwAhgJ/BhzANwAPcLaUslYIMRj4J5AFtALfllJuP9YfwsQkFqb6yMTk8Lgd2COlnAD8rMO2McBFwFTgd0CrlHIisBy4JrjPw8D3pZSTgZ8CDx6LTpuYdBdzpWBicvT4NJjvvkkI0QC8GWzfBIwLZrmcAbyo0tkA4Dz23TQxiY0pFExMjh6esNda2HsN9axZ+P/27tgGYRiKouj7AzBLpqGiZBzmygBIUDMBEhIDmILo9wkUKc7pbbm7smXZyWvZZcAuOT6Cdd5JDlsGLm/gP6rqmHxfv6yq6Z+Lg1+JAqwwxngmmavqluSyYYpTknNVXZPc4ytYdsaVVACanQIATRQAaKIAQBMFAJooANBEAYAmCgC0D4YTVp67iEqzAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "for pd1 in pd_list:\n",
    "    plt.plot(pd1.time_hist, pd1.num_hist, drawstyle='steps-post')    # stochastic realizations\n",
    "plt.axhline(N_eq, color='k', linewidth=2, label='equilibrium')    # expected number at equilibrium\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('protein number')\n",
    "plt.legend(loc='lower right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "We see that, in all repeated simulations, the protein number quickly approaches the equilibrium number, then fluctuates around it. Let us characterize such fluctuation by estimating the distribution of the protein number after reaching equilibrium. From the figure we may safely consider the equilibrium to be already reached after about $t=5$. We will collect data from all repeated simulations after that time, and make a histogram of the protein number."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "source": [
    "Note that, in our simulation, we recorded every change of the protein number. These numbers are correlated in time, as the number can only change by 1 at a time. To collect data properly, we need to first pick a set of time points that are well separated (compared to the average time between events), then retrieve the number of proteins at those chosen time points. This can be done by the following function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def collect_data(time_points, time_hist, num_hist):\n",
    "    \"\"\"\n",
    "    collect data from history of time and numbers, assuming no events happen between consecutive times in history.\n",
    "    inputs:\n",
    "    time_points: list (or 1-d array), time points at which to collect numbers.\n",
    "    time_hist: list (or 1-d array), full history of time of events, assuming no events between times.\n",
    "    num_hist: list (or 1-d array), full history of number after each event.\n",
    "    outputs:\n",
    "    num_points: list, collected numbers at given time points.\n",
    "    \"\"\"\n",
    "    num_points = []    # to collect number at every time point\n",
    "    if (time_hist[0] > time_points[0]) or (time_hist[-1] < time_points[-1]):   # check if data contain all time points\n",
    "        raise RuntimeError('time history does not contain all time points')    # if not, report error\n",
    "    for t in time_points:\n",
    "        i = np.argmin(np.asarray(time_hist) <= t) - 1    # index of time point just before given time\n",
    "        num_points.append(num_hist[i])    # get number at the time point\n",
    "    return num_points"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "Now we can use this function to collect data from all simulations and look at their statistics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean number of proteins = 98.5635\n",
      "variance = 103.25096775000002\n",
      "variance-to-mean ratio = 1.0475578459571748\n"
     ]
    }
   ],
   "source": [
    "time_points = np.arange(5, T, 0.1)    # choose time points\n",
    "num_all = []    # list to collect data at given time points from all simulations\n",
    "for pd1 in pd_list:\n",
    "    time_hist = np.asarray(pd1.time_hist)    # convert to 1d-array\n",
    "    num_hist = np.asarray(pd1.numbers_hist)    # convert to 1d-array\n",
    "    num_points = collect_data(time_points, time_hist, num_hist)    # collect from each simulation\n",
    "    num_all.extend(num_points)    # join the list of all data with the current new data\n",
    "\n",
    "mean = np.mean(num_all)    # calculate the mean\n",
    "print(f'mean number of proteins = {mean}')\n",
    "var = np.var(num_all)    # calculate the variance\n",
    "print(f'variance = {var}')\n",
    "ratio = var / mean    # calculate variance-to-mean ratio\n",
    "print(f'variance-to-mean ratio = {ratio}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "The mean number of proteins is around $N_{eq} = 100$ as expected. The variance-to-mean ratio is very close to 1, suggesting that this may be a Poisson distribution. Let us plot a histogram of our data and see if the Poisson distribution is a good fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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66ivAma4/ISEBgN69e5OSkhL0+gb1BklVXQAsKLTvXp/tbODCIo6bBcwqYv9moEfgIzXGtetL+Pl16HoP1DkB5ztRePruYHe+PdCN6+Pm8NqeIVWj1eJnyyLQCvpYSmvq1KksWbKE+fPn07t3b1asWMEll1xCv379mD9/Pueccw7PP3/seesKT61fEZfCKm3nvTEVLj/XWcCrVkvoHNqdp/56cuclxEXutVaLBwYMGMCrr74KOMsMN27cmHr1fr++z6ZNm+jXrx+TJk0iNjaWbdu2sXnzZk444QRuvvlmhg0bxurVqxkwYABz584lKyuLgwcP8s477zBgwAAvqgXYlC7G/GbjVMhYA/3fgupVY5r5JQe78c2B7lWr1VJJTJw4kSuvvJLu3btTq1YtZs6c+Ycyd9xxBxs3bkRVGTx4MD169GDy5MnMmjWLyMhImjZtyl133UWjRo0YO3Ysffs6Y5muuuoqevbsWSGXvYpi0+YbA84aK++1h0a94fSPjy43XN4144tSUdPm+6tf7TW80eZOJu24+g9Dq23a/KrDps03JtBW3Q25ByBxSuVZw76CFLRaroudQ5Qc9jocEwYssRiTvhw2vQjtb4L6haezqxqe2jmauMi9jImxvhZTfpZYTNWm+U6HfXQcdLvP62g8E+6tlqpwyb88Av3vY4nFVG1bXoH0JZAwGWrU9zoaTxWMEAu3Vkt0dDTp6emWXIqhqqSnpxMdHV1yYT/ZqDBTdR3JhKS/Q8yJ0PpSr6Px3NKDXfl6f3euj32L19LPIlsD9x+Nl+Lj40lNTcXmDCxedHQ08fHxATufJRZTda170BkNduoCEGu8Azy16xLebDOBMTEfMn33cK/DCYjIyEhat27tdRhViv01marpSAZs/A+0usQZYmyA31ot18XOIVqyvQ7HhChLLKZqSn4Bcg9Cx795HUml8+TOS4iNzAi7vhZTcSyxmKonPwd+mgJNToNGPb2OptJZltWVxft7cF3sHMgtfkEqY4pjicVUPVvfhqxU6PBXryOptJ7aOZrYyAxnmhtjSskSi6laVOHHf0PddtA89KcrCZaCVgvrJ1urxZSaJRZTtaR9DXuWQ8e/2kiwEjy1czRk77JWiyk1+8syVcuPj0ONRtD6Mq8jqfSWZXWFJoOt1WJKzRKLqTr2b4LUudD2Wqhe2+toQkO3iW6r5T9eR2JCSFATi4gMEZENIpIsIn9YOUlEokTkDff9JSLSyt3fV0SS3McqETnf33MaU6wNU6BadWg/3utIQkdcf2j6J1j/iDM82xg/BC2xiEgE8CxwNtAZGC0ihaeOHQfsVdW2wBPAZHf/WiBRVROAIcDzIlLdz3Ma80dHMmDzdGg5Cmo18zqa0NL1PutrMaUSzBZLXyBZVTer6hFgNjCsUJlhQMGyaXOAwSIiqpqlqrnu/migYPY4f85pzB9tetG9IdKGGJeatVpMKQUzsTQHtvm8TnX3FVnGTSSZQAyAiPQTkXXAGuA6931/zol7/DUislxEltvkc1Vcfo5zGSzuVLshsqyO9rVYq8WUrNJ23qvqElXtAvQB7hSRUk21qqrTVDVRVRNjY2ODE6QJDVvfhqxt0PE2ryMJXbGnQNMz4IfJ1moxJQpmYtkOtPB5He/uK7KMiFQH6gPpvgVUdT1wAOjq5zmN+Y2qM8TYbogsv273weE0GyFmShTMxLIMaCcirUWkBjAKmFeozDzgcnd7JPCZqqp7THUAETke6Aik+HlOY36z+xvYsww63Go3RJbX0VaL9bWYYwvaX5rbJzIeWAisB95U1XUiMklEhrrFpgMxIpIM3AYUDB/uD6wSkSTgHeAGVd1d3DmDVQcTBn58HGo0hBMuL7msKVm3idZqMSUK6kJfqroAWFBo370+29nAhUUcNwuY5e85jSnSgc2w7R3oPMFuiAyU2JOh6ZlOq6Xd9fbvaopk1wZM+LIbIoOjoK/lp+e8jsRUUpZYTHg6kgGbpkPLi+2GyEAraLXYfS2mGLbmvQlPm16E3AN2Q2Q5tZowv8j9vWqdwf/afsRDT93EtLQLij0+5WEbiVcVWYvFhJ/8XJ8bInt5HU1Y+j6rE1/u78k1sf8jSg57HY6pZCyxmPCzzW6IrAjP7bqQxtUzGdHwc69DMZWMXQoz4UUV1v+2QmRxl3JM+X13sBurs9pyVew7zN5zJmrfU43LfhNMeLEbIiuQ8ELa+bSJ2s7gesu8DsZUIvaXZ8KL3RBZoRZk9if1SCxXN/6f16GYSsQSiwkfBzbbCpEVLI8IZuweTr8660ioucHrcEwlYYnFhI8NU4BqdkNkBXtjzxnsy6vNVbHveB2KqSQssZjwcCTTuSHy+FFQq8glekyQHMyvxavpZ3N2/W9oUeNXr8MxlYDfiUVEmovIySIysOARzMCMKRW7IdJTL+8+lzytxpWN3/U6FFMJ+DXcWEQmAxcDPwB57m4FvgxSXMb4Lz8XNjwFcYPshkiP7MxtzLyMQVzc6COe3HkJmXl1vQ7JeMjf+1iGAx1U1W6xNRXKn/tQzq3/Jc8cv42rfhjLJ5/YfSteeWH3+Yxs9CljGn3Ac2kXeR2O8ZC/l8I2A5HBDMSYslGuip3LlsPH8em+Pl4HU6VtyG7FF/t7cUXjedSQHK/DMR7yN7FkAUki8ryITCl4BDMwY/zRq9aPJNT6iem7h9ud35XAtLQRxEZmMKyBTfNSlfn7lzgPeAD4Bljh8zgmERkiIhtEJFlEJhTxfpSIvOG+v0REWrn7zxCRFSKyxn0+3eeYRe45k9xHnJ91MGHoqsbvkJFbh7f3DPY6FAN8faAHPxxqzTWx7yDkex2O8YhffSyqOtNdY769u2uDqh6zrSsiEcCzwBlAKrBMROap6g8+xcYBe1W1rYiMAgoGCewGzlPVHSLSFWcpYt8xpGNUdbk/sZvwFR/5K2fV/47n00ZwSKO9DscAIExLG8GTLf/NoLorgPO8Dsh4wK8Wi4icCmzESRTPAT/5Mdy4L5CsqptV9QgwGxhWqMwwYKa7PQcYLCKiqitVdYe7fx1QU0Si/InVVB1XNH6PfISZu8/1OhTj4/2MAfxyJIZr7IbJKsvfS2H/Bs5U1UGqOhA4C3iihGOaA9t8Xqfy+1bH78qoai6QCcQUKnMB8H2hEWkvuZfB7hERKerDReQaEVkuIsvT0tJKCNWEmtrVsrio0UfMz+jPztzGXodjfORSnRm7h3FyndWwp8Qr5iYM+ZtYIlX16ERAqvoTFTBKTES64Fweu9Zn9xhV7QYMcB+XFnWsqk5T1URVTYyNjQ12qKaCjWj4GXUjDvHy7qFeh2KKMHvPWezPq+ksYWCqHH8Ty3IReVFETnUfLwAl9XFsB1r4vI539xVZRkSqA/WBdPd1PPAOcJmqbio4QFW3u8/7gddwLrmZKkTIZ2zM+yRltSfpUAevwzFF2J9fm9l7zoKtb8LBrV6HYyqYv4nlepy77m92Hz+4+45lGdBORFq7Hf+jcEaX+ZoHFMxvPhL4TFVVRBoA84EJqvp1QWERqS4ijd3tSOBcYK2fdTBhYkCdlbSJTuXl3dYxXJm9VNCa3PCUt4GYCufvqLDDwOPuwy+qmisi43FGdEUAM1R1nYhMApar6jxgOjBLRJKBPTjJB2A80Ba4V0TudfedCRwEFrpJJQL4BHjB35hMeLi88fuk5TRgQWZ/r0Mxx7AjJw5aXgzJ06DrPVCjgdchmQpyzMQiIm+q6kUisgZnbrDfUdXuxzpeVRcACwrtu9dnOxu4sIjjHgQeLOa0vY/1mSa8HV9jB6fVXc7Tu0ZxRG0yiEqv09/g59cg+QXofIfX0ZgKUlKL5Rb32cZzmkrhspj55FGN/6af7XUoxh+NekGT053LYR1ugYgaXkdkKsAx+1hU9Rd38wZV/dn3AdwQ/PCM+U3tallc2Ohj5mf0Jy23kdfhGH91uh0ObYetb3gdiakg/nben1HEPvvKaCrUiIafUS8ii5np1mkfUo4bAvU7w/rHQP9wRd2EoWMmFhG53u1f6Sgiq30eW4DVFROiMc4Q48tj3icpqx0rs2yIcUgRgY63Q8Zq+PUTr6MxFaCkFstrOJP9vOs+Fzx6q+pfghybMUf1r5NE2+hUZu4+DyhysgVTmbW6BKKbOq0WE/ZK6mPJVNUU4O84o8IKHnVEpGXwwzPGcXnj90jLacD8zAFeh2LKIiIKOtwMv34Ee+1iR7jzt49lPvC++/wpzsJfHwQrKGN8HV9jB6fXXc5re862IcahrO21UL02/GjTvIQ7vxKLqnZT1e7uczucaVS+DW5oxjgKhhi/mj7E61BMeUQ1ghPGQcprkJXqdTQmiMq05J6qfg/0C3AsxvxBrWqHuLDRxyzI6M+u3MITX5uQ0/FWIB82PO11JCaI/JrSRURu83lZDegF7CimuDEB89sQY7tHNyzUaQ0tRkLyVOh6N0TW8zoiEwT+tljq+jyicPpaCi/aZUxgqTI25j1WZbXj+6yOXkdjAqXT7ZCzDzZN9zoSEyT+TkJ5P4CI1HNe6v6gRmUMwK+f0DY6ldu2/hUbYhxGYvpA3ED48UloPx6q2YCMcOPv0sSJ7o2Sq4E1IrJKRBKDG5qp8jZMIS2nAe9nlrQKtgk5HW+HrK2wdY7XkZgg8PdS2Ayc+cJaqWor4EZ3nzHBsX8T7JjPa3uG2BDjcNT8z1CvA6x/1KZ5CUN+XQoD8lT1q4IXqrpYRHKDFJMx8NOzIBG8arMYh7RWE+YX+95FDc/ikRZTGPvQJBbtL/oCSMrDfw5WaCaISporrJeI9AK+EJHn3WWJB4nIc8CiConQVD05B2DzDGg50oYYh7F3Mk4j9UgsN8XNpojlnkwIK+lS2L/dRw+gPXAfMBHoBCSUdHIRGSIiG0QkWUQmFPF+lIi84b6/RERaufvPEJEVIrLGfT7d55je7v5kEZkiItarG25SZkFOJrS/yetITBDlaCRT00bSu/aPnFxnldfhmAAqaa6w047xOP1Yx4pIBPAszvT6nYHRItK5ULFxwF5VbQs8AUx29+8GzlPVbsDlwCyfY/4DXA20cx92O3Y4UXVunmvUGxqf5HU0Jsje2nMGv+Y04ua42V6HYgKopEthf3GfbyvqUcK5+wLJqrpZVY8As/njvS/DgJnu9hxgsIiIqq5U1YIbMNcBNd3WzXFAPVX9TlUVeAUY7m9lTQjY+SnsW++0VqwxGvYOaw2e33UBJ9ZZS9/aa70OxwRISZfCarvPdYt5HEtzYJvP61R3X5FlVDUXyAQKX1S/APheVQ+75X0nGSrqnCaUbZgCUbFw/MVeR2IqyOt7ziItp4Hb12LCwTFHhanq8+4lrX2q+kQFxXSUiHTBuTx2ZhmOvQa4BqBlS5vhPyQc2Azb34cud0NEtNfRmAqSrdG8sPt87jruJXrW+pGVNstCyCvxPhZVzQNGl+Hc24EWPq/j3X1FlhGR6kB9IN19HQ+8A1ymqpt8yseXcM6CuKepaqKqJsbGxpYhfFPh3CHGtLvO60hMBftv+jnsya1nrZYw4e8Nkl+LyDMiMqBgCLI7DPlYlgHtRKS1iNQARgHzCpWZh9M5DzAS+ExVVUQa4MxHNkFVvy4orKq/APtE5ER3NNhlOKtbmlCXc8CZO6rFBVDLrm5WNVn5NZm+exin11tO15rJXodjysnfxJIAdAEm8dsQ5GOuMer2mYwHFgLrgTdVdZ2ITBKRoW6x6UCMiCQDtwEFQ5LHA22Be0UkyX3Eue/dALwIJAObsAXHwkPKf50hxh1siHFV9cruc8nMrW2tljDg753341R1s+8OETmhpINUdQGwoNC+e322s4ELizjuQeDBYs65HOjqX9jGa8e68/o3ykft/8Xh/Dac9++9OI1VU9Xsz6/Ny+lDuaXJ63SM3sKP2a29DsmUkb8tlqJminsrkIGYquvkOqtoH72Vl9OHYrMYV20zdg/lQF5Nxse96XUophyO2WIRkY44l8Dqi8gIn7fqATZsxwTEFTHvkZ5bj/czBngdivFYZl5dXkn/M9fFvk2bqEu8DseUUUktlg7AuUAD4DyfRy+cu9+NKZcWNX5lcL2lvJZ+Noe1htfhmErgxbTzydYa3GitlpBV0n0s7wLvishJqvptBcVkqpBLY+aTj/DqHpvF2Dj25NXn1fSzubLxPNifDHXbeh2SKSV/+1jOF5F6IhIpIp+KSFrBdC/GlFVNyebihh/xYeYp/JrT2OtwTCUyLW0EuRoB6/7ldSimDPxNLGeq6j6cy2IpOEOB7whWUKZqOL/h59SvfpCXd5/rdSimkknLbcTre86CLa/AgRSvwzGl5G9iKVjC78/AW6qaGaR4TBVRjTzGxc5l7aE2LM8qPOm1MfB82gXORKQ/TC65sKlU/E0s74nIj0Bv4FMRiQWygxeWCXfnNlhMm6jtPLvrQmyIsSnKLzmxcMIVzqJvWUXO3GQqKb8Si6pOAE4GElU1BzjIH6fAN8YvQj43xc1mQ3ZLPsw82etwTGXWeQJoHvzwiNeRmFIo6T6W01X1M997WAot2Pi/YAVmwtfZ9b+hXfQ2xv/8f6jfjWZTJdVpDa0vg03ToMudULOp1xEZP5T0Vz3QfT4Pp+O+8LMxpVLQWknOjmdB5ileh2NCQZe7IP8I/PhvryMxfipprrD97kqRawHlt4vhGtSoTNg6s953dKqZwi1b/0Y+EV6HY0JB3bZw/GjY+B/o9HeItqHplV1JLZY6OCtF9gauB44DmgHX4dx9b0wpKDc3mc3mw814P2NgycWNKdDlbsjNgg0Vvt6gKYNjJhZVvV9V78dZUKuXqt6uqn/DSTS2LKMplcF1l9Kl5mae3XUxedZaMaVRvxO0HAkbnoYje72OxpTA357TJsARn9dH3H3G+Mlprfx8uCnv7h3kdTAmFHX5B+Tuhw1TvI7ElMDfxPIKsFREJorIRGAJ8HKwgjLh59S6y+lRayPP7rqIXL+XATLGR8PuED8MfnwScvZ5HY05Bn/vY/kncAWw131coao2iY/xk3JL3GxSj8TxTsZpXgdjQlnXeyAnA3561utIzDH4fROBqn6vqk+5j5X+HCMiQ0Rkg4gki8iEIt6PEpE33PeXiEgrd3+MiHwuIgdE5JlCxyxyz1l4yWJTSQ2os5KetTfw3K4LydHIkg8wpjiNesNxZ8OPj0PuQa+jMcUI2t1pIhIBPAucDXQGRotI4UmhxgF7VbUt8ARQMClQNnAPcHsxpx+jqgnuY1fgozeBo9zS5HV2HGnMnL1/8joYEw663gOHd8PGqV5HYooRzNue+wLJqrpZVY8As/njNDDDgJnu9hxgsIiIqh5U1cXYfGQh76Taq0msvZ7/pI3kiLVWTCDEngRNBsP6RyH3kNfRmCIEM7E0B7b5vE519xVZRlVzgUwgxo9zv+ReBrtHCs0xU0BErhGR5SKyPC0trfTRm4C4pcnr7MxpxJt7zvQ6FBNOut4D2Tth0wteR2KKEIrDc8ao6nYRqQu8DVyKM2rtd1R1GjANIDEx0WYKKKNWE+aX+dh+tdfwRpu13L/9alt22ARWk0EQO8CZUv+EKyGyjtcRGR/BbLFsB1r4vI539xVZRkSqA/WB9GOdVFW3u8/7gddwLrmZSuimuNmk5TRwFmwyJtASHoZDO2Ddg15HYgoJZmJZBrQTkdYiUgMYBcwrVGYecLm7PRL4TFWLbV2ISHURaexuR+JMhLk24JGbcutd6wf6113F82kjyNZor8Mx4Sj2ZGe9lvX/hsz1XkdjfAQtsbh9JuOBhcB64E1VXScik0RkqFtsOhAjIsnAbcDRIckikgI8DowVkVR3RFkUsFBEVgNJOC0eu8haCd3cZDbpufV4Nf0cr0Mx4SzhYaheB5bfBMV/JzUVLKh9LKq6AFhQaN+9PtvZwIXFHNuqmNP2DlR8JjgSam5gUN3vefiXsRyy1ooJpug46PFPWH4jbH0Ljr/I64gMwb0UZqqom5rMZm9uXWZZa8VUhLbXQsOe8P1fIWe/19EYLLGYAOtaM5nB9Zbx4u7hHMyv5XU4piqoFgF9nnM68tc+4HU0BkssJsBujptNZm5tZu4+z+tQTFXS+ERoMw5+fAIyf/A6mirPEosJmM7Rmzmz/ndM3z2cA9ZaMRWtx8MQWReW3Wgd+R6zxGICZnzcbPbl1eJla60YL0Q3hh7/gl2L4OfZXkdTpVliMQHRPiqFcxp8w0u7h7Iv3+6CNh5pcxU0SoSVf7M1WzwUilO6mFIoz5QspXFTkzc4kFeTGbsLzzNqTAUq6Mhf2A/W3A+9/u11RFWStVhMubWJ2saf6y9mZvq5ZObV9TocU9XF9IG2V8OGpyDDJubwgiUWU27j497gUH4UL6YN9zoUYxw9HoLI+s6Nk9aRX+EssZhyaV1jO0MbfMms9HPYm1ff63CMcUTFONO97PoSUl7zOpoqx/pYTLncGPcmRzSSF3ef73UoJgyVp49QaMqW0/rCytuh+blQw774VBRrsZgya1njF4Y3/JxX04ewO7eh1+EY8ztKNacjP3snrJnodThViiUWU2Y3x80mTyN4Pu0Cr0MxpmiNekO76+Cnp2Hvaq+jqTIssZgyOblOEiMbfcpLu4eSltvI63CMKV73B6FGQ+vIr0CWWEyp1ap2iMnxT7P5cDOe2HmJ1+EYc2xRjSBhMqQthi2zvI6mSrDEYkrtjqav0DxyF/+37RYOa5TX4RhTshPGQsyJkHQHHMnwOpqwF9TEIiJDRGSDiCSLyIQi3o8SkTfc95eISCt3f4yIfC4iB0TkmULH9BaRNe4xU0REglkH83t9aq3lisbvMTP9XJZndfE6HGP8I9Wgz7NweDesvrfk8qZcgpZYRCQCeBY4G+gMjHaXF/Y1Dtirqm2BJ4DJ7v5s4B7g9iJO/R/gaqCd+xgS+OhNUaIlm0daPMXWw0145JfLvQ7HmNJp1AvaXg8bn4W9SV5HE9aC2WLpCySr6mZVPQLMBgpPJDUMmOluzwEGi4io6kFVXYyTYI4SkeOAeqr6naoq8AowPIh1MD7+2vQ1Wkf9wt9Tb7Ylh01o6vEA1Ihxp9bP9zqasBXMxNIc2ObzOtXdV2QZVc0FMoGYEs6ZWsI5ARCRa0RkuYgsT0tLK2XoprCEmhu4qvFcXk0fwrcHe3gdjjFlU6Mh9HwUdn8DW17xOpqwFbad96o6TVUTVTUxNjbW63BCWg3J4dEWT/JrTgz/+uVKr8MxpnxaXwqxp8DK/4Mje72OJiwFM7FsB1r4vI539xVZRkSqA/WB9BLOGV/COU2A3Rz3Ou2it3FX6nhbGdKEPqkGic/CkXRY9Q+vowlLwUwsy4B2ItJaRGoAo4B5hcrMAwp6gUcCn7l9J0VS1V+AfSJyojsa7DLg3cCHbgp0qZnMdXFzeGvPn/jiQG+vwzEmMBr2gPY3wcbnYOvbXkcTdoI2CaWq5orIeGAhEAHMUNV1IjIJWK6q84DpwCwRSQb24CQfAEQkBagH1BCR4cCZqvoDcAPwMlAT+MB9mCCIlBwei3+S9NwGPPDLVV6HY0xgJTwMu5fAt5dBnROgUU+vIwobQZ3dWFUXAAsK7bvXZzsbuLCYY1sVs3850DVwUZriXB87h041U7gq5R725dlywybMRETDwHdgYV/4ciictQxqNvU6qrAQtp33pnw6RKcwPu4N3t07iE/29fM6HGOCo2ZTGDQPDu+BL4dDXnaJh5iSWWIxfxBBHo/GP8m+/NpM3HGN1+EYE1wNE+DkWZC+BJZcZRNVBoAlFvMHV8e+Q/daydy7/XpbFdJUDS1GQPcHIOVV+GFyyeXNMdkKkuZ32kRt469NXmVBxsksyOzvdTjGVJwud0PmOlh1F9TvBPGFJwox/rIWizmqGnk8Ev8UWfnR3Lfjeq/DMaZiiUC/GdAoEb4ZYwuDlYMlFnPUFY3fo3ftH7l/xzWk2VLDpiqqXhMGzoXI+vDFeZC9y+uIQpIlFgPA8TV2cHvTWXyyrw9zM071OhxjvFOrGQx8Fw6nwVcjIO+w1xGFHEssBiGfyfFTyNHq3J16I2BL3JgqLiYRTnwZ0r6GZdfZSLFSss57w5iYDzixzlru2HYzO3Mbex2OMZXD8RdB5g+w9n6o3wU6FbU8lCmKtViquPjIndzZ9CW+3N+Tt/ae4XU4xlQu3e6FFiOdmZC3z/c6mpBhiaVKUx6KfwZFuDP1JuwSmDGFSDU4aSY07Alfj4aMdV5HFBIssVRhoxotZGDdlTz8yxVsz4nzOhxjKqfqtWDQu1C9tjtSbLfXEVV6lliqqDPqfcekZlP55kB3Xt0zxOtwjKncasU7w5AP7YDFF0DeEa8jqtSs874KOqveNzxz/GTWZrXl2pS7Uft+YcJUqwnl6xdJefjPv71o3A9OnOHcPLn8Rug7zbmp0vyBJZYqZki9r3n6+EdYndWOy7dMshUhjSmNVpc4076sewjqd4WOt3gdUaVkX1WrkHPqL+aZ4yezKqu9JRVjyqr7AxA/HFbeBjs+9DqaSimoiUVEhojIBhFJFpEJRbwfJSJvuO8vEZFWPu/d6e7fICJn+exPEZE1IpIkIsuDGX84Obf+l0xp+QjfZ3Xk8i33W1IxpqykGpw0C+p3g8UjbWnjIgQtsYhIBPAscDbQGRgtIp0LFRsH7FXVtsATwGT32M44yxR3AYYAz7nnK3CaqiaoamKw4g8nQxss4qmWj7HiYGfGbrmfg5ZUjCmfyDpw6gLnctjikZA0AfLzvI6q0ghmi6UvkKyqm1X1CDAbKDwP9TBgprs9BxgsIuLun62qh1V1C5Dsns+U0vAGn/NEi8dZerALY7dMJCu/ptchGRMeajWDP30Bba911nBZNMSGIruC2XnfHNjm8zoVKLzG7dEyqporIplAjLv/u0LHNne3FfhIRBR4XlWnFfXhInINcA1Ay5Yty1cTD5VnVMuIBp/yeIsn+e5gN8ZtuZdDGh3AyIwxRERB36kQ0weW3QALE2HA/6BRL68j81Qodt73V9VeOJfYbhSRgUUVUtVpqpqoqomxsbEVG2ElMLLhJzzW4km+PtCDKy2pGBNcbcbBGYtB8+HjU2DzzJKPCWPBTCzbgRY+r+PdfUWWEZHqQH0g/VjHqmrB8y7gHewS2R9c2PAjHol/isUHErgq5R6yLakYE3wxfWDICmh8Mnw3FpbdWGVvpAxmYlkGtBOR1iJSA6czfl6hMvOAy93tkcBnqqru/lHuqLHWQDtgqYjUFpG6ACJSGzgTWBvEOoScixst5NEWU/jqQE+uTvkHhzXK65CMqTqiY+G0hc5MyBufg09PhawdXkdV4YKWWFQ1FxgPLATWA2+q6joRmSQiQ91i04EYEUkGbgMmuMeuA94EfgA+BG5U1TygCbBYRFYBS4H5qmoDyV2jG33I5Pin+Xxfb66xpGKMN6pVh56PwilvQMZq+LA37FrsdVQVKqh33qvqAmBBoX33+mxnAxcWc+w/gX8W2rcZ6BH4SEPfXxot4MH45/h0Xx+u//kujmik1yEZU7UdfxHU7wxfng+fnga9noD2N1aJaWBCsfPeFHJpzPs8GP8cH+/ra0nFmMqkQVcYsgyOGwIrboJvL4fcLK+jCjpLLCFubMw8Hmg+lY8yT+SGn++0pGJMZVOjgTPtfrf7IeW/zqixA1u8jiqoLLGEqEjJ4aa415nYfBofZp7EjVv/To4lFWMqJ6nmrEY56D0nqXyYCL985HVUQWOJJeQoZ9T7joXtb+RvTV/l3b2DGP+zJRVjQkLzP8OQ5VCrOXw+BNZMCstLYzZtfgjpEr2Ju5tN5+Q6q9mY3YKxWyayaH9vbElhY0JI3bZw5rew5GpYcx/89Ax0uMXp2K/RwOvoAsISSwiIrb6HO5q+wsiGn5KRV5d/bL+e2elnkWs/PmOCKqALhfmqXhtOeQ3aXQ/r/gWr/+HMN9bueuh4K9Q8rlyf6zX7n6kyy83iprjXuS72bSIllxd2n8+zOy9iX34dryMzxgRC3ADnsTcJ1j0MPz4GG56CE66AzndAnRO8jrBMrI+lMtJ82PJfeL8Df2v6Kl/s78WffvoP//rlSksqxoSjhgnQfzacuwFOuBw2z4D32sHXYyBjjdfRlZollspm12JYeCJ8eylEN+GiTQ9zw9a72HoktJvGxhg/1G0LfZ+HoVug422wfR4s6A6LzoO0r72Ozm+WWCqLA5th8UXwyQA4tB1OnAlnLWXpwa5eR2aMqWi1mjnTwgz7GbpNgvRv4eP+8PFA2PEBqHod4TFZH0uQldT5V7faQW6Me4MrGs8jjwie33UJ09JGcGhJNPBBxQRpjKmcohpBt3ug022Q/KLTB7PoHOfSWecJ0GIkVIso8TQVzRJLCco7KqRoSruorfyp3lLGxc6lcfVM5uwZzKO/XsrO3MZB+DxjTEirXhs63uKMGkt5FdZPhq9HQZ22cMZXULOp1xH+jiWWClK32kFOrrOKU+suZ1Dd72lWw1nC9LsDXRn7y/2sPdTW4wiNMYEW8OHKETWgzRXQ+jJInQs75kN0k3J9RjBYYgkSIZ/O0VsYVHcFg+quoHft9VSXfPbl1eLrAwlM2TWKL/f3YkdOnNehGmNCTbUIaHmB86iELLEEUMOITAbUTWJQnRUMrPs9sZEZAKzJasPUXSP5Yn8vVmZ1tBsbjTF+CdoNmkFm/8OVQzXy6FFro9MqqfM9PWr9RDVR9uTW46v9Pflify++OtCLtNyGXodqjDEVxhJLOSxsP5520dvI02okZbXnyZ2X8MX+Xqw51JZ8Kt9IDWOMqQhBTSwiMgR4CogAXlTVhwu9HwW8AvQG0oGLVTXFfe9OYByQB9ysqgv9OWdFmr57GAfyarH4QAIZefW8CsMYYyqVoCUWEYkAngXOAFKBZSIyT1V/8Ck2Dtirqm1FZBQwGbhYRDoDo4AuQDPgExFp7x5T0jkrzOw9Q7z4WGOMqdSCeed9XyBZVTer6hFgNjCsUJlhwEx3ew4wWETE3T9bVQ+r6hYg2T2fP+c0xhjjoWBeCmsObPN5nQr0K66MquaKSCYQ4+7/rtCxzd3tks4JgIhcA1zjvjwgIhtKEXtjYHcpyoeKcKxXyNbp58nnFvdWyNapBOFYr0pdJ5lc5kML6nV8WQ4O2857VZ0GTCvLsSKyXFUTAxyS58KxXlan0BGO9QrHOkH56xXMS2HbgRY+r+PdfUWWEZHqQH2cTvzijvXnnMYYYzwUzMSyDGgnIq1FpAZOZ/y8QmXmAZe72yOBz1RV3f2jRCRKRFoD7YClfp7TGGOMh4J2KcztMxkPLMQZGjxDVdeJyCRguarOA6YDs0QkGdiDkyhwy70J/ADkAjeqah5AUecMQvhluoQWAsKxXlan0BGO9QrHOkE56yVayef1N8YYE1psoS9jjDEBZYnFGGNMQFX5xCIiHUQkyeexT0RuFZFGIvKxiGx0n0NqJkkR+auIrBORtSLyuohEu4MelohIsoi84Q6ACBkicotbn3Uicqu7L+R+TiIyQ0R2ichan31F1kMcU9yf2WoR6eVd5MUrpk4Xuj+rfBFJLFT+TrdOG0TkrIqP2D/F1OtREfnR/Xm8IyINfN6r9PUqpk4PuPVJEpGPRKSZu79sv3+qag/3gTMg4Fecm4IeASa4+ycAk72OrxT1aA5sAWq6r98ExrrPo9x9U4HrvY61FHXqCqwFauEMOvkEaBuKPydgINALWOuzr8h6AOfgrFEtwInAEq/jL0WdOgEdgEVAos/+zsAqIApoDWwCIryuQynqdSZQ3d2e7POzCol6FVOnej7bNwNTy/P7V+VbLIUMBjap6s/8frqZmcBwr4Iqo+pATff+oFrAL8DpOFPnQOjVqRPOL3WWquYCXwAjCMGfk6p+iTMK0ldx9RgGvKKO74AGInJchQRaCkXVSVXXq2pRM14UN2VTpVNMvT5yfwfBmSEk3t0OiXoVU6d9Pi9rAwWjusr0+2eJ5fdGAa+7201U9Rd3+1eg8q3/WQxV3Q48BmzFSSiZwAogw+cPwneanFCwFhggIjEiUgvnm1QLQvjnVEhx9ShqaqRQ+rkVJZzqdCXON3oI8XqJyD9FZBswBrjX3V2mOllicbn9DUOBtwq/p06bMGTGZbvX54fhNMeb4XwDCempmFV1Pc5lh4+AD4EknCUVfMuE1M+pOOFSj3AnInfj3Gf3qtexBIKq3q2qLXDqM74857LE8puzge9Vdaf7emdBk8993uVZZKX3J2CLqqapag7wP+AUnGZswU2xITcdjqpOV9XeqjoQ2Av8RGj/nHwVV49wnMYo5OskImOBc4Ex7hcBCIN6uV4FLnC3y1QnSyy/Gc1vl8Hg99PNXA68W+ERld1W4EQRqSUigtN39APwOc7UORB6dUJE4tznljj9K68R2j8nX8XVYx5wmTs650Qg0+eSWagqbsqmkCDOYoP/BwxV1Syft0K2XiLSzuflMOBHd7tsv39ej1CoDA+cS0XpQH2ffTHAp8BGnBFIjbyOs5R1ut/95VgLzMIZqXICzi96Ms4lvyiv4yxlnb7CSZCrgMGh+nPC+QLzC5CDc816XHH1wBmN8yzOCKM1+IyuqkyPYup0vrt9GNgJLPQpf7dbpw3A2V7HX8p6JeP0OyS5j6mhVK9i6vS2+3/FauA9oHl5fv9sShdjjDEBZZfCjDHGBJQlFmOMMQFlicUYY0xAWWIxxhgTUJZYjDHGBJQlFmOKISKLCs/KG6TPuVlE1otIQO/gFpFWInKJH+WaicicksoZ4y9LLMYEgc8MB/64AThDVceU4XNERIr7O24FlJhYVHWHqo4sqZwx/rLEYkKa+618vYi84K798ZGI1HTfO9riEJHGIpLibo8VkbnuuicpIjJeRG4TkZUi8p2INPL5iEvdNSrWikhf9/ja7poWS91jhvmcd56IfIZzs2PhWG9zz7NWfltPZirOjasfiMhfC5UfKyLvuvXYKCL3+dR5g4i8gnNTWwt3jZC1IrJGRC52T/EwzsSdSeKszxPhllvmrq1xrc/51vp85v9E5EP3Mx9x90eIyMs+n/G7WI3xVZpvVcZUVu2A0ap6tYi8iTPP0X9LOKYr0BOIxrmT+u+q2lNEngAuA550y9VS1QQRGQjMcI+7G/hMVa8UZ5GnpSLyiVu+F9BdVX83LbmI9AauAPrh3M28RES+UNXr3ClCTlPV3UXE2df9zCxgmYjMB3a7db5cVb8TkQuABKAH0Ngt9yXOui63q+q5bgzX4EzJ0UdEooCvReQj/jjhZYL7b3MY2CAiTwNxOHdjd3XP1aCEf19ThVmLxYSDLaqa5G6vwLkEVJLPVXW/qqbhLCvwnrt/TaHjX4eja1jUc/9DPROYICJJOItYRQMt3fIfF04qrv7AO6p6UFUP4EwMOsCPOD9W1XRVPeQe09/d/7M662MUnPt1Vc1TZxLVL4A+RZzrTJx5n5KAJTjTyLQrotynqpqpqtk4U+gcD2wGThCRp91EuK+I44wBrMViwsNhn+08oKa7nctvX56ij3FMvs/rfH7/d1H427zitDgu0EKLWIlIP+BgqSIvWVGfTxk/R4CbVHXh73aKtCpUrvC/Z3VV3SsiPYCzgOuAi3DWIjHmD6zFYsJZCtDb3S5r5/TFACLSH+cyUiawELhJRMR9r6cf5/kKGC7OjNO1cSZo/MqP484QkUZuv9Fw4Otizn2x2w8Si7P07FJgP1DXp9xC4HoRiXTjbu/GUiIRaQxUU9W3gX/gXPIzpkjWYjHh7DHgTbdvYX4Zz5EtIiuBSH77hv4ATh/MandE1hactTmKparfi8jL/DaN+ouqutKPz1+KM/NsPPBfVV1eRAvjHeAknFmfFfg/Vf1VRNKBPBFZBbwMPIVzme97Nymm4f9Szs2Bl3xGoN3p53GmCrLZjY2ppMRZTCpRVcu1mp8xFc0uhRljjAkoa7EYY4wJKGuxGGOMCShLLMYYYwLKEosxxpiAssRijDEmoCyxGGOMCaj/B0yxlqrDg+pzAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.arange(70.5, 130, 3)    # edges of bins (avoid integers since our data are integers)\n",
    "x_array = bins[:-1] + (bins[1]-bins[0])/2    # center of bins\n",
    "x_array = x_array.astype(int)    # convert to integers, for which Poisson distribution is defined\n",
    "y_array = st.poisson.pmf(x_array, N_eq)    # calculate Poisson distribution with mean = N_eq\n",
    "\n",
    "plt.figure()\n",
    "plt.hist(num_all, bins=bins, density=True, label='data')    # plot histogram\n",
    "plt.axvline(mean, color='k', label='mean')    # plot mean\n",
    "plt.plot(x_array, y_array, 'orange', label='Poisson')    # plot Poisson distribution\n",
    "plt.xlabel('number of proteins')\n",
    "plt.ylabel('distribution')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "We see that the protein number does seem to follow a Poisson distribution. Indeed, it can be mathematically shown that, in this model, the equilibrium distribution of the protein number should satisfy the equation:\n",
    "\\begin{equation}\n",
    "k P(N-1) + \\gamma (N+1) P(N+1) - (k + \\gamma N) P(N) = 0\n",
    "\\end{equation}\n",
    "which has a solution:\n",
    "\\begin{equation}\n",
    "P(N) = \\frac{(k/\\gamma)^N}{N!} \\, \\mathrm{e}^{-k/\\gamma}\n",
    "\\end{equation}\n",
    "i.e., a Poisson distribution with mean $N_{eq} = k/\\gamma$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Transcription and translation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "Let us now consider a more general model that includes the dynamics of both the protein and the mRNA that encodes the protein (i.e., a two-stage model). There will then be four processes --- the production and degradation of both mRNA (denoted by $B$) and protein ($A$). We may assume that the production (transcription) rate of the mRNA is constant, whereas the production (translation) rate of the protein is now proportional to the number of mRNA. The degradation rate of each type of molecule is again proportional to its number. Thus, the processes involved can be represented by the reactions:\n",
    "\\begin{align}\n",
    "\\emptyset &\\xrightarrow{k_1} B \\\\\n",
    "B &\\xrightarrow{\\gamma_1} \\emptyset \\\\\n",
    "B &\\xrightarrow{k_2} B + A \\\\\n",
    "A &\\xrightarrow{\\gamma_2} \\emptyset\n",
    "\\end{align}\n",
    "Note that, in the third reaction, the mRNA $B$ acts as a \"catalyst\" that is present both before and after the reaction. Let the numbers of $B$ and $A$ be denoted by $M$ and $N$, respectively. Then the overall production rate of $A$ will be proportional to the total number of $B$ around, i.e., $k_2 M$. If $M$ is kept at a constant level, $M_0$, then the protein $A$ will be produced at a constant rate, $k = k_2 M_0$, as in the simpler model above. In the current model, we allow $M$ to be dynamic, so effectively the production rate of $A$ will fluctuate over time. Our goal is to see how this will affect the distribution of the protein number $N$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Gillespie algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will again use the Gillespie algorithm to simulate the stochastic processes described by the above reactions. Since there are two more reactions than before, we need to modify the codes for our simulation. To avoid having to customize codes every time, let us write a general purpose class for stochastic simulations using the Gillespie algorithm.\n",
    "\n",
    "In general, consider a model that involves $n$ types of \"chemical species\", denoted by $S_i$ for $i = 1, \\cdots, n$; they are involved in $m$ possible \"chemical reactions\", with rate constants $K_\\mu$ for $\\mu = 1, \\cdots, m$. To describe each reaction, we introduce two stoichiometry matrices, $R_{\\mu i}$ and $P_{\\mu i}$, which contain the stoichiometric coefficients of the reactants and the products, respectively. These coefficients are usually non-negative integers. Thus, for the $\\mu$-th reaction, if a species $S_i$ is not involved, then $R_{\\mu i} = P_{\\mu i} = 0$; else if $S_i$ is a reactant with multiplicity $p$, then $R_{\\mu i} = p$; or if $S_i$ is a product of this reaction with multiplicity $q$, then $P_{\\mu i} = q$. Note that some species can appear as both reactant and product (like catalysts)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "Here is the general purpose code for the Gillespie algorithm, including several implementation methods (the one we have used so far is called the \"first-reaction\" method). It is OK if you do not understand every part of the code right now. We will simply learn how to use it for a given problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "class StochSimulation:\n",
    "    \"\"\"\n",
    "    implement Gillespie algorithm for stochastic simulation, assuming mass action kinetics.\n",
    "    available methods include 'direct', 'first-reaction', and 'tau-leaping'.\n",
    "    based on (D. T. Gillespie, Annu. Rev. Phys. Chem. 58, 2007).\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, stoich, rates, init, record=True):\n",
    "        \"\"\"\n",
    "        general purpose code for stochastic simulation using Gillespie algorithm.\n",
    "        inputs:\n",
    "        stoich: 2-tuple, stoichiometry matrices of reactants and products, (R_ui, P_ui), u = 1 ~ m, i = 1 ~ n\n",
    "        rates: list, rate parameters, K_u, u = 1 ~ M\n",
    "        init: list, initial numbers of every species, N_i(0), i = 1 ~ n\n",
    "        record: boolean, whether to record full history of events\n",
    "        \"\"\"\n",
    "        self.reactants = np.asarray(stoich[0])    # stoichiometry matrices of reactants\n",
    "        self.products = np.asarray(stoich[1])    # stoichiometry matrices of products\n",
    "        self.rates = np.asarray(rates, dtype=float)    # rate constant for each reaction\n",
    "        self.numbers = np.asarray(init, dtype=int)    # current number of each species\n",
    "\n",
    "        self.num_reac = self.reactants.shape[0]    # number of reactions\n",
    "        self.num_spec = self.reactants.shape[1]    # number of species\n",
    "\n",
    "        self.time = 0.                  # time since beginning of simulation\n",
    "        self.nevents = 0                # total number of events that have happened\n",
    "        self.term = False               # whether reactions terminated\n",
    "        self.record = record            # whether to record time series\n",
    "\n",
    "        if self.record:\n",
    "            self.time_hist = [0]                  # list of times at which events happened\n",
    "            self.event_hist = [-1]                # list of events that happened, -1 represents initial time\n",
    "            self.numbers_hist = [self.numbers.copy()]     # list of species_number arrays right after each event\n",
    "\n",
    "\n",
    "    def run(self, tmax, maxstep=10000, nmax=1000, disp=0, method='first-reaction'):\n",
    "        \"\"\"\n",
    "        run simulation until time `tmax` since the beginning of the simulation.\n",
    "        inputs:\n",
    "        tmax: float, time since the beginning of the simulation.\n",
    "        maxstep: int, maximum number of steps to simulate even if `tmax` is not reached.\n",
    "        nmax: int, maximum number of agents of any species at which simulation stops.\n",
    "        disp: int, print messages if >= 0, higher values allow more details.\n",
    "        method: 'direct'|'first-reaction'|'tau-leaping', method to use.\n",
    "        \"\"\"\n",
    "        self.term = False\n",
    "        for n in range(maxstep):                # bound on number of steps\n",
    "            if self.time >= tmax:               # bound on accumulated time\n",
    "                return\n",
    "            if np.any(self.numbers >= nmax):    # bound on number of each species\n",
    "                if disp >= 0:\n",
    "                    print('maximum number of agents reached.')\n",
    "                return\n",
    "            a_j = self.rates * np.prod(np.power(self.numbers, self.reactants), axis=1)    # mass action\n",
    "            if np.all(a_j == 0):\n",
    "                self.term = True    # reaction terminated\n",
    "                if disp >= 0:\n",
    "                    print('reactions terminated.')\n",
    "                self.time = tmax    # jump to final time\n",
    "                return\n",
    "            elif np.any(a_j < 0):    # should not happen\n",
    "                raise RuntimeError('transition rates become negative!')\n",
    "            a_j = np.maximum(a_j, 1e-15)    # if a_j is zero (when N=0), replace by a small number to avoid division by 0\n",
    "            if method == 'direct':  # direct method\n",
    "                dn_i, tau, events = self.direct(a_j)\n",
    "            elif method == 'first-reaction':  # first-reaction method\n",
    "                dn_i, tau, events = self.first_react(a_j)\n",
    "            elif method == 'tau-leaping':  # tau-leaping method, requires parameter tau\n",
    "                tau = keywords['tau']\n",
    "                dn_i, tau, events = self.tau_leap(a_j, tau)\n",
    "            self.numbers += dn_i\n",
    "            self.time += tau\n",
    "            self.nevents += len(events)\n",
    "            if self.record:\n",
    "                self.time_hist.extend([self.time for ev in events])\n",
    "                self.event_hist.extend(events)\n",
    "                self.numbers_hist.extend([self.numbers.copy() for ev in events])\n",
    "            if disp > 0:\n",
    "                for i in range(len(events)):\n",
    "                    ev = self.nevents - len(events) + i + 1\n",
    "                    print(f'event {ev}: t = {self.time}, triggering reaction {events[i]}')\n",
    "                    if disp > 1:\n",
    "                        print(f'current numbers = {self.numbers}')\n",
    "        else:\n",
    "            if disp >= 0:\n",
    "                print('maximum number of steps reached.')\n",
    "\n",
    "\n",
    "    def direct(self, a_j):  # direct method\n",
    "        a0 = np.sum(a_j)\n",
    "        tau = -1. / a0 * np.log(np.random.rand())\n",
    "        prob = a_j / a0\n",
    "        event = np.random.choice(self.num_reac, p=prob)\n",
    "        dn_i = self.products[event] - self.reactants[event]\n",
    "        return dn_i, tau, [event]\n",
    "\n",
    "\n",
    "    def first_react(self, a_j):     # first-reaction method\n",
    "        tau_j = -1. / a_j * np.log(np.random.rand(self.num_reac))\n",
    "        event = np.argmin(tau_j)\n",
    "        dn_i = self.products[event] - self.reactants[event]\n",
    "        tau = tau_j[event]\n",
    "        return dn_i, tau, [event]\n",
    "\n",
    "\n",
    "    def tau_leap(self, a_j, tau):   # tau-leaping method\n",
    "        r_j = np.random.poisson(a_j*tau)\n",
    "        dn_i = np.dot(self.products - self.reactants, r_j)\n",
    "        if np.any(np.abs(dn_i) > np.maximum(1, 0.03*self.numbers)):    # check leap condition\n",
    "            print('Warning: leap condition violated.')\n",
    "        if np.any(self.numbers + dn_i < 0):\n",
    "            raise RuntimeError('numbers become negative during tau-leaping.')\n",
    "        events = np.repeat(np.arange(self.num_reac), r_j)\n",
    "        return dn_i, tau, events\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given this general class (or the so-called `base class` in Python), we can define a `derived class` that is like a specific case of the general class. The derived class inherits all methods from the base class, but one can also redefine certain methods to override (or so-called \"decorate\") the base methods."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us define a derived class of the base `StochSimulation` class to represent the transcription-and-translation model above. We will only modify the initialization of the class object by supplying specific stoichiometry matrices. In our model, we have $n = 2$ for the two species $S_1 = B$ and $S_2 = A$, and $m = 4$ for the four reactions with rates $K_1 = k_1$, $K_2 = \\gamma_1$, $K_3 = k_2$, and $K_4 = \\gamma_2$. The stoichiometry matrices corresponding to the four reactions are:\n",
    "\\begin{equation}\n",
    "\\mathbf{R} = \\left( \\begin{array}{cc}\n",
    "0 & 0 \\\\\n",
    "1 & 0 \\\\\n",
    "1 & 0 \\\\\n",
    "0 & 1\n",
    "\\end{array} \\right) \\,,\n",
    "\\qquad\n",
    "\\mathbf{P} = \\left( \\begin{array}{cc}\n",
    "1 & 0 \\\\\n",
    "0 & 0 \\\\\n",
    "1 & 1 \\\\\n",
    "0 & 0\n",
    "\\end{array} \\right)\n",
    "\\end{equation}\n",
    "A derived class for simulating this model can be defined as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "class TranscriptionTranslation(StochSimulation):    # it is derived from the `StochSimulation` class\n",
    "    \"\"\"\n",
    "    simulate the transcription-and-translation model using Gillespie algorithm.\n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, rates, init, record=True):    # decorate base method\n",
    "        \"\"\"\n",
    "        modify the initialization to specify the stoichiometry matrices.\n",
    "        \"\"\"\n",
    "        reactants = [[0, 0],\n",
    "                     [1, 0],\n",
    "                     [1, 0],\n",
    "                     [0, 1]]\n",
    "        products = [[1, 0],\n",
    "                    [0, 0],\n",
    "                    [1, 1],\n",
    "                    [0, 0]]\n",
    "        StochSimulation.__init__(self, (reactants, products), rates, init, record=record)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "Let us now test the class to simulate the transcription-and-translation model. We need to specify four reaction rates, mRNA production $k_1$, mRNA degradation $\\gamma_1$, protein production $k_2$, and protein degradation $\\gamma_2$. As before, we can set $\\gamma_2 = 1$ by rescaling time, so that the average lifetime of the protein is $1/\\gamma_2 = 1$. The mRNA degradation time is usually much shorter than that of proteins, i.e., $1/\\gamma_1 \\ll 1/\\gamma_2$, so we can choose $\\gamma_1 = 10$. On the other hand, mRNA usually exists in much smaller copy numbers than proteins. If we look at the mRNA part of the model (the first two reactions) alone, the math is exactly the same as for the production-and-degradation model above. Therefore, the equilibrium number of mRNA would be $M_{eq} = k_1 / \\gamma_1$. We can choose $M_{eq} = 2$, so that $k_1 = 20$. At equilibrium the overall production rate of the protein will be $k = M_{eq} k_2$, so the equilibrium number of proteins will be $N_{eq} = k / \\gamma_2 = M_{eq} k_2 / \\gamma_2$. If we choose $N_{eq}$ to be the same as before, $N_{eq} = 100$, then we need $k_2 = 50$. Let us run our simulation with these parameter values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "current time = 25.00400074685411, current numbers of mRNA and protein = [ 2 89]\n",
      "current time = 25.00458051799042, current numbers of mRNA and protein = [ 2 83]\n",
      "current time = 25.00541629813756, current numbers of mRNA and protein = [ 2 82]\n",
      "current time = 25.005845490970565, current numbers of mRNA and protein = [ 0 70]\n",
      "current time = 25.010554039048873, current numbers of mRNA and protein = [ 2 94]\n",
      "current time = 25.008282911286155, current numbers of mRNA and protein = [ 1 98]\n",
      "current time = 25.0054666602822, current numbers of mRNA and protein = [  6 114]\n",
      "current time = 25.01376158688284, current numbers of mRNA and protein = [ 0 77]\n",
      "current time = 25.002804714410043, current numbers of mRNA and protein = [ 4 93]\n",
      "current time = 25.004647264310172, current numbers of mRNA and protein = [ 1 94]\n"
     ]
    }
   ],
   "source": [
    "k1 = 20.    # mRNA production rate\n",
    "g1 = 10.    # mRNA degradation rate\n",
    "k2 = 50.    # protein production rate\n",
    "g2 = 1.     # protein degradation rate\n",
    "\n",
    "M0 = 0    # initial number of mRNA\n",
    "N0 = 0    # initial number of protein\n",
    "M_eq = k1 / g1           # expected equilibrium number of mRNA\n",
    "N_eq = M_eq * k2 / g2    # expected equilibrium number of protein\n",
    "\n",
    "T = 25.    # total amount of time to simulate\n",
    "trials = 10    # number of simulations to repeat\n",
    "tt_list = []    # list to store simulations\n",
    "\n",
    "for i in range(trials):\n",
    "    tt1 = TranscriptionTranslation([k1, g1, k2, g2], [M0, N0], record=True)    # create simulation with given rates\n",
    "    tt1.run(T, maxstep=100000)    # run simulation until time T\n",
    "    print(f'current time = {tt1.time}, current numbers of mRNA and protein = {tt1.numbers}')\n",
    "    tt_list.append(tt1)    # save simulation to the list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,2, figsize=(12,4))\n",
    "for tt1 in tt_list:\n",
    "    time_hist = np.asarray(tt1.time_hist)    # convert to 1d-array\n",
    "    num_hist = np.asarray(tt1.numbers_hist)    # convert to 2d-array, second dimension represents species\n",
    "    ax[0].plot(time_hist, num_hist[:,0], drawstyle='steps-post')    # mRNA number\n",
    "    ax[1].plot(time_hist, num_hist[:,1], drawstyle='steps-post')    # protein number\n",
    "ax[0].axhline(M_eq, color='k', linewidth=2, label='equilibrium')    # expected number at equilibrium\n",
    "ax[1].axhline(N_eq, color='k', linewidth=2, label='equilibrium')    # expected number at equilibrium\n",
    "ax[0].set_xlabel('time')\n",
    "ax[0].set_ylabel('mRNA number')\n",
    "ax[0].legend(loc='lower right')\n",
    "ax[1].set_xlabel('time')\n",
    "ax[1].set_ylabel('protein number')\n",
    "ax[1].legend(loc='lower right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "source": [
    "Comparing the right subplot with the same figure for the production-and-degradation model above, we see that in the transcription-and-translation model the protein number fluctuates much more. This is clearly because the mRNA number (left subplot) fluctuates significantly with time instead of being constant, which introduces extra stochasticity in the protein production."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "Let us collect data on the protein numbers to characterize their distribution at equilibrium."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean number of proteins = 99.4655\n",
      "variance = 630.64880975\n",
      "variance-to-mean ratio = 6.34037741478201\n"
     ]
    }
   ],
   "source": [
    "time_points = np.arange(5, T, 0.1)    # choose time points\n",
    "prot_all = []    # list to collect protein numbers \n",
    "for tt1 in tt_list:\n",
    "    time_hist = np.asarray(tt1.time_hist)    # convert to 1d-array\n",
    "    num_hist = np.asarray(tt1.numbers_hist)    # convert to 2d-array, second dimension represents species\n",
    "    num_points = collect_data(time_points, time_hist, num_hist[:,1])    # collect protein numbers (index 1)\n",
    "    prot_all.extend(num_points)\n",
    "\n",
    "mean = np.mean(prot_all)    # calculate the mean\n",
    "print(f'mean number of proteins = {mean}')\n",
    "var = np.var(prot_all)    # calculate the variance\n",
    "print(f'variance = {var}')\n",
    "ratio = var / mean    # calculate variance-to-mean ratio\n",
    "print(f'variance-to-mean ratio = {ratio}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "We see that the mean number of proteins is still around $N_{eq} = 100$ as expected. However, from the large variance-to-mean ratio, we may conclude that this is no longer a Poisson distribution. In fact, in the limit that protein lifetime is much greater than mRNA, i.e., $\\gamma_1 \\gg \\gamma_2$, the protein number distribution can be approximated by a negative-binomial distribution:\n",
    "\\begin{equation}\n",
    "P(N) = {N+r-1 \\choose r-1} p^r (1-p)^N\n",
    "\\end{equation}\n",
    "where $r = k_1 / \\gamma_2$ and $p = \\gamma_1 /(\\gamma_1 + k_2)$. This distribution can be generated by the scipy function `scipy.stats.nbinom.pmf(x, r, p)`, plotted below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "binwidth = 5\n",
    "bins = np.arange(40.5, 180, binwidth)    # edges of bins (avoid integers since our data are integers)\n",
    "hist = np.histogram(prot_all, bins=bins, density=True)[0]\n",
    "\n",
    "x_array = bins[:-1] + binwidth/2    # center of bins\n",
    "x_array = x_array.astype(int)    # convert to integers\n",
    "y_array = st.nbinom.pmf(x_array, n=k1/g2, p=g1/(g1+k2))    # calculate negative-binomial distribution\n",
    "\n",
    "plt.figure()\n",
    "plt.bar(x_array, hist, width=binwidth, label='data')    # plot histogram\n",
    "plt.axvline(mean, color='k', label='mean')    # plot mean\n",
    "plt.plot(x_array, y_array, 'orange', label='neg-binom')    # plot negative binomial distribution\n",
    "plt.xlabel('number of proteins')\n",
    "plt.ylabel('distribution')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "Let us now look at the mRNA number distribution. Since the mRNA part of the model is mathematically the same as the production-degradation model above, the mRNA number should follow a Poisson distribution. Let us plot that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean number of proteins = 1.933\n",
      "variance = 1.949511\n",
      "variance-to-mean ratio = 1.0085416451112261\n"
     ]
    }
   ],
   "source": [
    "time_points = np.arange(5, T, 0.1)    # choose time points\n",
    "mRNA_all = []    # list to collect data on number of mRNA\n",
    "for tt1 in tt_list:\n",
    "    time_hist = np.asarray(tt1.time_hist)    # convert to 1d-array\n",
    "    num_hist = np.asarray(tt1.numbers_hist)    # convert to 2d-array, second dimension represents species\n",
    "    num_points = collect_data(time_points, time_hist, num_hist[:,0])    # collect mRNA numbers (index 0)\n",
    "    mRNA_all.extend(num_points)\n",
    "\n",
    "mean = np.mean(mRNA_all)    # calculate the mean\n",
    "print(f'mean number of proteins = {mean}')\n",
    "var = np.var(mRNA_all)    # calculate the variance\n",
    "print(f'variance = {var}')\n",
    "ratio = var / mean\n",
    "print(f'variance-to-mean ratio = {ratio}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "binwidth = 1\n",
    "bins = np.arange(-0.5, 10, binwidth)    # edges of bins (avoid integers since our data are integers)\n",
    "hist = np.histogram(mRNA_all, bins=bins, density=True)[0]\n",
    "x_array = bins[:-1] + binwidth/2    # center of bins\n",
    "x_array = x_array.astype(int)    # convert to integers\n",
    "y_array = st.poisson.pmf(x_array, M_eq)    # calculate Poisson distribution\n",
    "\n",
    "plt.figure()\n",
    "plt.bar(x_array, hist, width=binwidth, label='data')\n",
    "plt.plot(x_array, y_array, 'orange', label='Poisson')\n",
    "plt.xlabel('#mRNA')\n",
    "plt.ylabel('distribution')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "Notice that the number of mRNA is 0 about 13% of the time, during which there is no mRNA available for the translation of the protein. According to the Poisson distribution, this fraction is generally given by $P(0) = \\mathrm{e}^{-M_{eq}}$ and becomes even larger for smaller $M_{eq}$. For example, if $M_{eq} = 0.5$, then mRNA is unavailable more than half of the time. In such cases, the production of proteins has to wait for episodes when the mRNA is present. Therefore, we might expect to see \"bursts\" of protein production from time to time, which would contribute to large fluctuations of the protein number."
   ]
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    "Note that, the low copy number of mRNA is only one reason that could lead to bursts in protein numbers. The mRNA number itself may be subject to bursting because of intermittent production of mRNA. This phenomenon is called \"transcriptional bursting\", and may be due to the binding/unbinding of transcriptional factors (e.g., a three-stage model) or mechanical properties (e.g., \"supercoiling\") of DNA during transcription."
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