lectures/L02_probability.ipynb

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    "# Probability & Statistics: I\n",
    "\n",
    "*Davide Gerosa (Milano-Bicocca)*\n",
    "\n",
    "##### Reading:\n",
    "\n",
    "- [Ivezic textbook](https://press.princeton.edu/books/hardcover/9780691198309/statistics-data-mining-and-machine-learning-in-astronomy) Chapter 3. \n",
    "- [David Hogg: \"Data analysis recipes: Probability calculus for inference\"](https://arxiv.org/abs/1205.4446)\n",
    "\n",
    "\n",
    "This course is based on previous work by many people. See [here]((https://github.com/dgerosa/astrostatistics_bicocca_2023/blob/main/README.md) for credits.\n",
    "\n",
    "\n",
    "---"
   ]
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    "## Preliminaries and notation <a class=\"anchor\" id=\"one\"></a>\n",
    "\n",
    "* **\"Statistics\"** = extracting knowledge from data.\n",
    "* **\"Astrostatistics\"** = extracting knowledge from astronomical data.\n",
    "* **\"Knowledge\"** = summary (physical or phenomenological) of data behavior.\n",
    "* **\"Data\"** = result of measurements.\n",
    "\n",
    "In the textbook, $x$ is a scalar quantity that is measured $N$ times to form a dataset.\n",
    "\n",
    "* $x_i$ is a single measurement with $i=1,...,N$.\n",
    "* $\\{x_i\\}$ refers to the set of all N measurements comprising the dataset. \n",
    "\n",
    "Our data can be real numbers, discrete labels (strings or numbers), or even \"missing values\" (we sometimes pad our datasets with NaNs in this case). \n",
    "\n",
    "**Goal of data mining & statistical inference:**\n",
    "> We are generally trying to *estimate* $h(x)$, the *true* generating distribution from which $\\{x_i\\}$ are drawn. \n",
    "\n",
    "* $h(x)$ is the **probability density (distribution) function** or the **\"pdf\"** and $h(x)dx$ is the propobability of a value lying between $x$ and $x+dx$. This distribution can have several levels-- the population distribution of events (e.g. source redshifts), and a measurement uncertainity distribution that blurs our measured data away from true values.\n",
    "\n",
    "* The \"left to right\" integral of $h(x)$ is the **cumulative distribution function** (**\"cdf\"**), $H(x) = \\int_{-\\infty}^x h(x')dx'$. The inverse function of the cdf is the **quantile function**, e.g. what $x$ value has 90% of the distribution below it?\n",
    "\n",
    "* While $h(x)$ is the \"true\" pdf (or **population** pdf), what we *measure* from the data is the **empirical** pdf, which is denoted $f(x)$.  So, $f(x)$ is a *model* of $h(x)$.  In principle, with infinite data $f(x) \\rightarrow h(x)$, but in reality the blurring effect of measurement errors keep this from being strictly true. Likewise, the empirical cdf is denoted $F(x)$.\n",
    "\n",
    "* If we are attempting to guess a physical *model* for $h(x)$, then the process is ***parametric***.  With a model solution we can generate new data that should mimic what we measure.  If we are not attempting to guess a model, then the process is ***non-parametric***, i.e. we are just trying to describe the data behavior in a compact practical way."
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    "### Picturing (i.e. understanding!) a pdf is not a trivial task!\n",
    "\n",
    "Let's see an example. This cell will start with a generating distribution $h(x)$, draw a number of random samples as data $\\{x_i\\}$, and then fit these data with a parametric and non-parametric model $f(x)$."
   ]
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   "source": [
    "# Based on Ivezic v2, Figure 6.8; edited by G. T. Richards, S. R. Taylor, and D. Gerosa\n",
    "\n",
    "# Author: Jake VanderPlas\n",
    "# License: BSD\n",
    "#   The figure produced by this code is published in the textbook\n",
    "#   \"Statistics, Data Mining, and Machine Learning in Astronomy\" (2013)\n",
    "#   For more information, see http://astroML.github.com\n",
    "#   To report a bug or issue, use the following forum:\n",
    "#    https://groups.google.com/forum/#!forum/astroml-general\n",
    "\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy import stats\n",
    "\n",
    "from sklearn.neighbors import KernelDensity\n",
    "\n",
    "from astropy.visualization import hist\n",
    "from sklearn.mixture import GaussianMixture\n",
    "\n",
    "#----------------------------------------------------------------------\n",
    "# This function adjusts matplotlib settings for a uniform feel in the textbook.\n",
    "# Note that with usetex=True, fonts are rendered with LaTeX.  This may\n",
    "# result in an error if LaTeX is not installed on your system.  In that case,\n",
    "# you can set usetex to False.\n",
    "if \"setup_text_plots\" not in globals():\n",
    "    from astroML.plotting import setup_text_plots\n",
    "setup_text_plots(fontsize=14, usetex=True)\n",
    "%config InlineBackend.figure_format='retina' # very useful command for high-res images"
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    "#------------------------------------------------------------\n",
    "# Generate our data: a mix of several Cauchy distributions\n",
    "# In reality nature generates data for you\n",
    "\n",
    "\n",
    "random_state = np.random.RandomState(seed=0)\n",
    "N = 2000 # number of data points\n",
    "mu_gamma_f = [(5, 1.0, 0.1),\n",
    "              (7, 0.5, 0.5),\n",
    "              (9, 0.1, 0.1),\n",
    "              (12, 0.5, 0.2),\n",
    "              (14, 1.0, 0.1)]\n",
    "hx = lambda x: sum([f * stats.cauchy(mu, gamma).pdf(x)\n",
    "                          for (mu, gamma, f) in mu_gamma_f])\n",
    "x = np.concatenate([stats.cauchy(mu, gamma).rvs(int(f * N), random_state=random_state)\n",
    "                    for (mu, gamma, f) in mu_gamma_f])\n",
    "random_state.shuffle(x)\n",
    "x = x[x > -10]\n",
    "x = x[x < 30]"
   ]
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7.527040326782769, 2.7244851381595274, 12.142987334304102, 7.379293030823061, 6.344715294606626, 14.060237942578414, 14.030833802524118, 7.212157658382289, 9.159677910324579, 19.40266628619724, 7.20324169939552, 11.681527514204056, 6.919666787989292, 7.094035716751656, 9.112139144660262, 4.515211867393564, 11.951760210991416, 14.932290991400532, 7.3520398818267365, 6.980632336413033, 16.410835927210968, 7.083354120544382, 8.081825067901997, 6.628398092163631, 10.83582539117231, 11.845790593888747, 6.442209554090313, 12.191060817099471, 11.989911811725406, 8.191794708775989, 14.420554851354701, 7.028620812963018, 6.834816664096059, 12.687579511370483, 7.0867587295109065, 9.03770425908276, 12.596870290270965, 11.775259884666973, 5.724046052793435, 12.566677397392208, 9.00077067128107, 8.79155936488387, 7.412022103888882, 4.959386731546293, 29.020105995534475, 7.745453178837573, 7.132269573724061, 12.707480044991057, 3.56478272196545, 6.844101645708884, 9.551860305193784, 6.7535408422727246, -0.42444058873540946, 6.837195694937949, 8.941869822882767, 26.918184236790392, 6.603832787706708, 12.946956379437092, 12.14213047293747, 7.0692479497292116, 7.268290397592829, 8.194690564935284, 19.686940644739416, 5.141946670285295, 6.851841266238974, 8.470795909583071, 7.571559570133704, 5.868903512405287, 6.303720320931217, 0.5936748268627943, 12.18776171908774, 12.501688795299382, 14.749506443718607, 4.755447020702094, 1.701727391976827, 6.847798730873417, -6.208769716815777, 13.574637539100356, 8.789735202781031, 4.230175095064601, 7.511930632150213, 6.0043613129781, 14.224353341552678, 8.128957373022098, 13.34192034950452, 8.283071385733013, 11.280600586112703, 5.499958782900659, 5.747948387710847, 3.403876220394118, 12.420003186617953, 11.272776668527774, 6.965971767275564, 5.400699113871966, -2.678464182742548, 12.354274698008341, 21.443055052149976, 6.348047767529818, 9.093689221595778, 6.780985936519547, 8.601421038000415, 6.773379659801707, 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7.142947989831098, 11.93851062639482, 9.350397240978578, 5.224175631602608, 8.009413979324806, 3.5920737406412595, 6.553071821522593, 6.964829373609375, 7.309091438016207, 8.750758067834186, 13.516723183062592, 6.2400321000513, 7.150182692497454, 6.802644781466888, 7.348962534767795, 16.418502112979688, 6.361451501165564, 10.694762638041254, 11.660649081727117, 18.996406764531898, 6.800320327241336, 6.953719932766829, 13.52600263246471, 10.992097274671359, 8.585062689395405, 18.329943031404866, 6.883119897986309, 6.866067644182304, 13.34001485887729, 7.763913844525529, 14.879451120371126, 12.71679576941862, 5.4859672907588894, 5.550464820316129, 2.2053300239375595, 15.927700953290536, 6.880627818483194, 3.7095002177272836, 11.838355474408209, 6.664308484995112, 6.528758941487081, 6.897325427051207, 6.833917808895734, 5.695088115065443, 13.970300252121238, 13.777070011087718, 9.008771109947896, 9.049201706004444, 6.555573746982933, 13.55002218306496, 13.720122437932048, 10.654243497002032, 6.744128842606789, 6.228476356530689, 6.383358240270921, 8.945882142548845, 9.018421515966855, 6.4748041537028955, 8.916271218666683, 6.670601064154221, 7.362364989483268, 8.941112738976608, 3.9279532730636753, 26.621080712156292, 8.136313465466051, 8.381281722720757, 4.901195191974905, 4.495089607069853, 7.973305897487838, 9.05740238481852, 3.328681037390001, 6.204301945315569, 11.738488587191947, 13.06523952731087, 10.55872632856024, 4.668890286599242, 14.323466223883965, 9.59282677627662, 12.031433662644167, 13.452716414827501, 6.876723606259362, 8.608081706393484, 11.662332532415515, 13.281593384004495, 7.269418216516551, 12.47025598628555, 16.453817054453275, 2.444492700257686, 8.865603742547062, 14.574358089041656, 8.323486367534782, -6.070028748153771, -9.890167554081579, 7.617056489761675, 6.872524683425343, 2.7940112149664413, 6.832762641171434, 21.507154964395774, 5.230966417354352, 11.043140254661175, 5.522257399696264, 7.4143398563390335, 9.021592805577207, 7.147014278616847, 6.759607370010269, 7.092211259896514, 5.4933828299674925, 12.268860601446303, 13.544907751890957, 12.26364281143595, 9.069853709155282, 15.394331461035968, 3.9208808322448014, 9.22359726535049, 7.325582422888461, 5.179297144607573, 7.339857105465976, 5.824570452601675, 14.962617627403604, 6.836188644776897, 9.00379709213352, 6.400072256337544, 12.38545718143132, 6.383464096069581, 11.5489545803673, 7.362252411772547, 3.800787541968503, 6.09413901524497, 5.934718239958054, 4.764520427347624, 14.715695082662776, 12.683452892222428, 5.94076426708134, 11.973994042296132, 10.561703031292737, 4.790997904108675, 9.880981746696893, 6.931097042196352, 7.751128915148049, 7.234252226516989, 6.932618858371901, 6.588633028841694, 9.039014363998827, 8.607005440320151, 3.714002167778573, 6.438936379322467, 7.38917088500872, 7.938872112269865, 7.349433293564839, 6.906769505168733, 8.977646289727003, 6.823170971667894, 6.68498373712945, 8.031069798938729, 7.320386498278415, 8.254039307746705, 6.84487839228687, 5.3418344124006465, 6.632360345045692, 2.517852797982397, 6.211004958787935, 6.9346061730929645, 14.821356788031794, 11.649036755287021, 5.461389496403894, 5.41456217306307, 12.232148715757424, 6.857484378331105, 7.583569651443824, 7.365328814609054, 9.497959572591814, 6.984766963584178, 7.185114518982949, 7.3710505326263664, 13.297020113021828, 7.058260051534283, 7.13980179008891, 11.97980134803834, 8.24423138156356, 12.638231132029437, 11.354820127644393, 12.46409682406573, 11.529285647438016, 8.265368085888205, 8.975943581617495, 11.563502407571372, 5.384827940780271, 11.882605478539226, 5.0404189042036025, 8.499358529542617, 12.571023172915371, 9.056705171737107, 23.46881308290806, 8.829599789301575, 11.33032053913967, 6.545905209398164, 12.655152309110154, 6.891993604631731, 14.358909876827859, 7.02724265839944, 14.823102645734238, 8.082959695483718, 13.652841404279856, 7.442792786952829, 14.148576998455733, 13.51371325096842, 6.73627972720658, 7.08668955769352, 6.298242977417739, 7.195207775346878, 11.175477090317855, 9.074196232591595, 7.141183554279301, 12.080793508862769, 10.30051870037897, 14.156512584566382, 7.870113285602201, 7.610148689600642, 7.09611383866419, 6.881624668193296, 7.343273894653581, 6.440822576121029, 12.57292868938497, 8.65399202430721, 11.295962966406565, 14.485477429913521, 2.66758226863469, 8.381867153509509, 0.5371123083683118, 11.862297486747686, 7.672035978699446, 0.10520164805877474, 16.426960447949437, 9.382391630022894, 6.453391925264657, 9.019830254515814, 6.9351906687275315, 9.805042740296248, 6.396005193409462, 12.848348744278123, 7.754334614268818, 5.707888278974348, 12.889470793202397, 11.67744751995941, 6.4874766046240655, 8.521922057642746, 9.046523828181666, 6.715841223834883, 6.8531239389147895, 6.218387396430712, 5.080230084675351, 6.785143409083088, 14.838041831914362, 6.675439112401661, -3.081600853820415, 6.758368500050699, 12.287196817726036, 12.944892821782929, 7.65201447173237, 7.578434783536712, 15.240666642513006, 5.878197175842592, 7.436801673260582, 6.104682030078665, 12.347162432949535, 9.21372042437729, 12.929968769666877, 7.434947866471283, 8.116205296935716, 6.789602363569304, 6.579963634645263, 9.062369306820708, 6.931567663476179, 6.849155379436006, 6.1149259013874735, 7.834328068922182, 9.027731382144815, 1.7889182912125707, 12.574122020698072, 8.82775743862172, 11.437348770276529, 5.270943070022271, 14.20644516988937, 8.602315736188753, 11.220931634098434, 4.832344611939629, 10.440511202777989, 11.516271340668943, 12.407219431968901, 3.8211092802090203, 7.712683071767981, 16.157088909883374, 6.377495520111803, 8.150356946548147, 12.990507148619427, 10.219199935627042, 9.031908060389586, 4.772408468814463, 13.948119317178739, 10.491128804986687, 13.62495424149853, -2.3199286774961276, 8.270758674174576, 7.2000916691447765, 13.926527683652703, 9.189088419023468, 12.978946232690268, 14.980301535913041, 3.041372537953364, 6.646710361291593, 10.358636843271864, 11.90928914610556, 8.006549769990198, 7.162829601635287, 7.801200353969058, 8.173449718089426, 7.469819620131897, 7.094863169742908, 14.717539870625144, -0.22208434145476197, 8.233313649869823, 14.112640534037315, 6.580050996624619, 13.318475001594338, 4.597157993705627, 12.640588675987875, 6.0438482768318424, 10.000365441772487, 0.5638530356002223, 8.55817634765807, 8.096845925242254, 11.997541347565734, 6.472746383145977, 8.83007288996728, 6.83608211996286, 6.593815078163559, 6.581913663138388, 7.35690262343712, 8.699686908922214, 12.422411113345163, 7.038061181145389, 4.625967987483422, 10.065816209647924, 7.530046403460814, 4.265180230872969, 9.122109631017844, 0.45576274812529594, 7.424784161706958, 22.022933884706553, 17.978010345827407, 5.585674413995635, 8.87901306020531, 12.829162311557809, 6.617535184002678, 11.866475297634475, 14.892454166973714, 11.257931887152866, 7.434625431049974, 9.042218883388555, 6.546848009680842, 7.240647974686908, 7.597775098177896, 6.762787307539995, 19.57175643884119, 7.295522266417779, 13.395561167897943, 9.259884632083311, 8.697964618636183, 11.293305290283964, 6.369070047507685, 6.99590227476925, 7.232200674516776, 6.320587614392989, 6.406556556020475, 17.405760381709342, 5.33454501068848, 6.721344684286741, 23.97780877805616, 20.135196310298753, 9.03963855386948, 7.684577929603367, 7.223845635693454, 7.5944712711328455, 7.510284175123881, 8.923521894628278, 11.890562258803147, 6.092061155041585, 13.67954218165216, 10.346576294140283, 5.71427257156779, 14.38001414986764, 9.215297467022703, 8.807291291441144, 6.511314347536672, 6.984947082038528, 3.4586304003899997, 8.052046988183365, 5.465289264559419, 7.668516212985683, 15.145575513803074, 6.675018971911318, 6.774074601760693, 6.840510761079168, 14.346811677298343, 6.687808399407786, 6.719939872411122, -4.964142001723934, 7.139168286946017, 7.792086895953264, 11.934796169128001, 6.470324533668289, 10.876262192445099, 11.687022275381139, 7.225354708908462, 5.243927572735473, 6.110167931806957, 7.311045917672502, 9.263042529410649, 9.845114614732449, 11.925008162998129, 9.010188769480273, 8.624337439590557, 5.5804697418420615, 4.725289094277516, 10.869540810496982, 11.40260711270168, 11.990488082609362, 6.2670835961276055, 8.67635445972101, 6.716836576060793, 6.309969664381697, 12.373942687520511, 11.649220332757599, 7.826410029252393, 6.700018949647153, 6.987261592390378, 8.385983733254742, 6.739739025814246, 6.97445687342104, 7.378887017993616, 16.848677113838903, 11.126887545988563, 9.055195022930397, 7.502408676891286, 7.001670034193867, 13.980725472431489, 7.3771576327009845, 12.236366286440324, 8.896528422538816, 6.791497435511148, 12.886578733223205, 6.365483944264434, 6.953764363274848, 12.913850336111903, 8.199510473043242, 15.540490220354933, 6.891136147289275, 12.098747857312238, 21.181856549885353, 6.001765113888735, 11.212581496526711, 7.434007310654368, 11.742590564225052, 8.286908276305988, 5.534029532646235, 13.274517005013454, 20.13754698517355, 8.924556745465944, 8.048308288967826, 6.299199349400904, 12.56638145682066, 9.153726655359803]\n"
     ]
    }
   ],
   "source": [
    "# These are the numbers you have. \n",
    "#Say these are stellar flux measurements, or a time series from a gravitational-wave detector\n",
    "\n",
    "print(x.tolist())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtwAAAH5CAYAAACyIOlxAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAABYlAAAWJQFJUiTwAAAeJElEQVR4nO3dQW5bSZ4n4N9/JoFuzKKH5f0AXcpNe9lS3qBSN5CRN7BukEKewFDewFknmLRvYNcJuqStemNNA7N3CbPqXsUs+OhiKklKIhl8pPx9gPGo9+I9hsgw9VMoXkS11gIAAPTx38auAAAAPGcCNwAAdCRwAwBARwI3AAB0JHADAEBHAjcAAHQkcAMAQEcCNwAAdCRwAwBARwI3AAB0JHADAEBHAjcAAHQkcAMAQEcCNwAAdPTNpheoqkmSn5IcDbsmw/aytfbxgXPPkvyQ5POw60WSi9ba7ab1AgCAfbBR4K6qoyRvk5zPh+Sq+jHJh6p631p7teTcd0kmrbXTuX3HSa6q6tVDYR0AAA5BtdbWP7nqKsn/bq39vODYp0x7vc9ba7/cO/Y606D+h9ba3YJjl0n+eP8YAAAcmk3HcB8nuayq7xccux62pwuOXSZ5vyRQ/5rpsJSfNqwbAACMbtPA/THJbZK/rijzef6LYdjIZDjvd4YQfpfk9YZ1AwCA0W0UuFtrp621b5f0VM96vT/c2//DsP204tK3SSbDGHEAADhYXaYFHIaYTJJct9be3zt8PGxXzUQyOyZwAwBw0LYeuIdpAt8m+dhaO1lQ5MUTLjfZRp0AAGAsG8/DnXwZl32eaY/0d5nOpf3LkuKTJ1z6wXBeVf8nyf9K8l9Livz7E54PAICv278s2f8PSf5va+2PT73gVgJ3a+0608A9C99/rqrzJK82XMRm8ogy/1RV//0f//Ef/8eigy9fvjxetB926ebmJkny8uXLkWvCNlxfX395fHx8/LuvD532yiHRXtm2WZu67z//8z/TWvunda65lcA9bwjfJ8M83J+q6mTYN3O35af8j3/91399cXV1teXLwvacnExHV2mnz0NVfXl8dXX1u68PnfbKIdFe2ZWTk5NcX1//xzrndrlpcnA5bN/d2//5fsEV7rZTFQAAGEfPwD2bm/vo3sI4d8N2suLc2bGnhHMAANg7awfuqnpdVX8blmJf5G7u8fz0frMQveqGyNmx6xVlAABg723Sw32eaU/0xZLjk7nH8zdOzhbC+XbFtY+S3G14wyUAAIxuk5sm/5ppb/XlkuPf3SubJGmtva+qu/x9AZzfGFaXnCRZNq0gAAAcjE0C99skl621j0uOnw/biwVLv79JcllVkwXHzmbnbVA32CvunueQaK8cEu2VQ7D2kJJhqr+3VfVhmHv7i6q6zLQH+5fW2s8Lzv05ycckf7l33nGmPeavFgRxAAA4OBvNwz0MD/mYaW/17MbIF5mO2b4///b9c0+HGy8/ZHpz5GQ4d+V5AABwSDZe+GboiT5/qNySc3+JsdoAADxjPefhBgCAr57ADQAAHQncAADQkcANAAAdCdwAANCRwA0AAB0J3AAA0JHADQAAHQncAADQkcANAAAdCdwAANCRwA0AAB0J3AAA0JHADQAAHQncAADQkcANAAAdCdwAANCRwA0AAB0J3AAA0JHADQAAHQncAADQkcANAAAdCdwAANCRwA0AAB0J3AAA0JHADQAAHQncAADQkcANAAAdCdwAANCRwA0AAB0J3AAA0JHADQAAHQncAADQkcANAAAdCdwAANCRwA0AAB0J3AAA0JHADQAAHQncAADQkcANAAAdCdwAANCRwA0AAB0J3AAA0JHADQAAHQncAADQkcANAAAdCdwAANCRwA2wgaoauwoA7DmBGwAAOhK4AQCgI4EbAAA6ErgBAKCjrQTuqrqsqg9V9Wn4966qjlaUPxrK/VhV3w9fT6rqeLjW1TbqBQAAY/tmk5OHUP02yWVr7WJu37skn6rqorX285LTj5JcLth/l+RPm9QLAAD2xaY93G+TnLfWPs52tNZuW2snSW6TXFbV2ZJzb5NcD4/vknxMctFa+0Nr7XrJOQAAcFDWDtxV9X2S69ba7ZIil/e2971vrZ201moI2acresMBAOAgbdLDfZrkx6paFqhnvd5HVTXZ4HkAAOBgbRK4J8N22ZCRz3OPl95ACQAAz9kmN01eDNu3S47Ph+xlw04AAOBZWztwt9bukpyvKPLdsL0dyv5OVR3fu8aLJG/nb8IEAIBDttG0gA84v7e97yxJWmtfjg9TCl5V1Zun3EB5c3OTk5OThceurkzpDXw9qurL49baiDUBOEzLMuXNzc3a1+yy0mRVvU5ynOlMJIt6qz9nOgXgxfzOYcaTN5lOJ3jco24AALBLte0ekKGX+lOSj6210zXOP05ylemUg4t/xfht+avj4+NjPdnArsz3It83dq+yHm6APk5OTnJ9ff2ofHpfjx7ud5mG5SeH7SSZW/RGDzcAAAdvq4G7qt4myarkX1WTqjp7zNzchpUAAHDotha4q+rHJEeP6Gb/KdNe8D8/4rKmEwQA4KBtJXBX1VmS00XDSIbe7EUL33xYcq1Z2btl0wkCAMCh2Dhwz+bSXjFm+zS/XXXy34byvywp//2w/XXTugEAwNg2CtxDb/RPy8L2ME77u/me6tba+ySnK8ZwXyS5y99XsgQAgIO1duAeAvOHJGdV1Rb9S/K3JadfJHk3f1PkcDPlbJjJnwwnAQDgOdhkpcnLJIvGZt/31/s7Wmu3VfUq0wVujjJd0j1Zc+5uAADYV2sH7mFJ9mXLtj/m/LtNzgcAgEPQZWl3AABgSuAGAICOBG4AAOhI4AZ4Jqpq7CoAsIDADQAAHQncAADQkcANAAAdCdwAANCRwA0AAB0J3AAA0JHADQAAHQncAADQkcANAAAdCdwAANCRwA0AAB0J3AAA0JHADQAAHQncAADQkcANAAAdCdwAANCRwA0AAB0J3AAA0JHADQAAHQncAADQkcANAAAdCdwAANCRwA0AAB0J3AAA0JHADQAAHQncAADQkcANAAAdCdwAANDRN2NXAOA5qaokSWvty+PZ17t4XgD2jx5ugA4EYABmBG4AAOhI4AYAgI4EbgAA6EjgBgCAjgRuAADoSOAGAICOBG4AAOhI4AYAgI4EbgAA6EjgBgCAjgRuAADoSOAGAICOBG6AJ6iqsasAwIERuAEAoCOBGwAAOhK4AQCgI4EbAAA6ErgBAKAjgRsAADr6ZhsXqarLJMdJjoZd10kuWmu3D5x3luSHJJ+HXS8ecx4AAByKjQJ3VR0leZvksrV2MbfvXZJPVXXRWvt5ybnvkkxaa6dz+46TXFXVq9bax03qBgAA+2DTHu63Sc7ne6SHxydV9SnJZVXdttbez59UVa+TnCX5w/z+1tp1VV0keVdVf2yt3W1YPwAAGNXaY7ir6vsk1yuGf1ze294/9n5JoP41ySTJT+vWDQAA9sUmN02eJvlxGL+9yGxIyFFVTWY7h2EjkyQLg/oQwu+SvN6gbgAAsBc2CdyTYXu25PjnucdHc49/GLafVlz7NslkGA8OAAAHa5PAfZHklySvlhyfD8vzvdnHC/bdNzsmcAMAcNDWvmlyGPpxvqLId8P29t5Y7RdPeJrJ02oFAAD7ZSvzcC9xfm87M3nCNR4Vzm9ubnJycrLw2NXV1ROeDuD5qKq01sauBsBBWZYpb25u1r5ml5Umh2n/jjOdiWST+bQn26kRAACMY+s93HOL4XxsrS0a33237ed8+fKlnmwAADa2LFOenJzk+vp6rWv26OF+l+n83KdLjn9esn+Ru82rAwAA49lq4K6qt0nSWls8+GXqbthOVpSZHXtKOAcAgL2ztcBdVT8mOXogbCd/D9GrboicHVuv3x4AAPbEVgJ3VZ0lOV00jKSqzu4tYPNh2H674pJHSe5WLBsPAAAHYePAPSzVfr5izPZp5oaGtNbeZzqs5HhR4SGcT5L8umndAABgbBsF7iEc/7QsbFfVJMl39xa+SZI3Sb4fjt83Wyr+YpO6AQDAPlg7cA9h+UOSs6pqi/4l+duic1trPyf5mOQv9655nOQyyasFIR0AAA7OJvNwX2Y61vohf120s7V2WlWvq+pDpjdHTjK9WfKkteZmSQAAnoW1A3dr7Ty/X7b9qdf4Jckvm1wDAAD2WZel3QEAgCmBGwAAOtpkDDfAV6Oqxq4CAAdKDzfADgjsAF8vgRsAADoSuAEAoCOBGwAAOhK4AQCgI4EbAAA6ErgBAKAjgRsAADoSuAEAoCOBGwAAOhK4AQCgI4EbAAA6ErgBAKAjgRsAADoSuAEeUFVjVwGAAyZwAwBARwI3AAB0JHADAEBHAjcAAHQkcAMAQEcCNwAAdCRwAwBARwI3AAB0JHADAEBHAjcAAHQkcAMAQEcCNwAAdCRwAwBARwI3AAB0JHADAEBHAjcAAHQkcAMAQEcCNwAAdCRwAwBARwI3AAB0JHADAEBHAjcAAHQkcAMAQEcCNwAAdCRwAwBARwI3AAB0JHADAEBHAjcAAHQkcAMAQEcCNwAAdCRwAwBARwI3AAB0JHADAEBHAjcAAHS0tcBdVUdV9emx5arqx6r6fvh6UlXHVXVZVVfbqhMAAIztm01OrqpJkqMk50leP+HUoySXC/bfJfnTJnUCAIB9snYPd1WdJflLpmH7XaZh+bFuk1wPj++SfExy0Vr7Q2vteulZAABwYNbu4W6tvU/yfvZ1VT3l9PettYt1nxsAAA6FmyYBAKAjgRsAADoSuAEAoKONZinZRFUdZ3rD5cyLJG9bax9HqhIAAGzdWIH7LElaa18Cd1UdJbmqqjettZ+fcrGbm5ucnJwsPHZ1ZVpvYH1PvCEcgAO3LFPe3Nysfc0xhpR8znQKwN/MUtJau03yJsnl0PsNAAAHb+c93K21u8xNJ3jPbDjJn5Ms/vVigZcvX+rJBgBgY8sy5cnJSa6v11suZq9umpxb9EYPNwAAz8JOA3dVTarqbFgS/qGyQjcAAAdv1z3cP2W6DPyfH1H2tnNdAACgu7GGlHxYtHOYqSRJ7oax3gAAcNB2Hbj/Lcl5a+2XJce/H7a/7qg+AADQ1U4Dd2vtfZLTFWO4L5LcDVsAADh4WwncQ4CeDI+PVhaehul38zdFDjdTzoaZ/MlwEgAAnou15+EeAvPs5sf5kP2pqmbT+70ZerW/aK3dVtWrTBe4Ocp0Sfck+dhaO123PgAAsI/WDtzDnNmPXpzm3rl3Sc4fKgcAAIdurxa+AQCA50bgBgCAjgRuAADoaO0x3ADwFFX15XFrbcSaAOyWHm4ARldVvwnkAM+JwA0AAB0J3AAA0JHADQAAHQncAADQkcANAAAdCdwAANCRwA0AAB0J3AAA0JHADQAAHQncAADQkcANAAAdCdwAANDRN2NXAGBfVdXYVfgqzb/urbURawKwHXq4ga9GVQnRAOycwA0AAB0J3AAA0JHADQAAHQncAADQkcANAAAdCdwAANCRwA0AAB0J3AAA0JHADQAAHQncAADQkcANAAAdCdwAANCRwA0AAB0J3ADPWFWNXQWAr57ADQAAHQncAADQkcANAAAdCdwAANCRwA0AAB0J3AAA0JHADQAAHQncAADQkcANAAAdCdwAANCRwA0AAB0J3AAA0JHADQAAHX0zdgUA9kVVfXncWns2z3XIqsrrAxw8PdwAO1JVvwnarM9rCRwSgRsAADoSuAEAoCOBGwAAOhK4AQCgI4EbAAA62tq0gFV1lORDa+3bR5Y/S/JDks/DrhdJLlprt9uqEwAAjG2jwF1VkyRHSc6TvH7Cee+STFprp3P7jpNcVdWr1trHTeoFAAD7Yu0hJUMP9V8yDdvvktw98rzXSc6SvJrf31q7TnKR5N0Q5AEA4OCtHbhba+9bayettfMn9khfJnnfWrtbcOzXJJMkP61bLwAA2Cc7vWlyGDYySbJwnPYQwu/yhOEpAACwz3Y9S8kPw/bTijK3SSbDTZgAAHDQdh24j4ftqplIZscEbgAADt6uA/eLJ5Sd9KoEAADsytbm4X6kyRPKPjqc39zc5OTkZOGxq6urJzwlQH9VNXYVDsrs9WqtrTw+b1lZgIcsy5Q3NzdrX3OfV5qcjF0B4LBUlTD7jHlvgUO16x7uux4XffnypZ5sAAA2tixTnpyc5Pr6eq1r7rqH+/PDRb6461UJAADYlV0H7rthO1lRZnbsKeEcAAD20lg93KtuiJwdW6/PHgAA9siuA/eHYfvtijJHSe5aa6vm6gYAgIOw08DdWnuf6bCS40XHh9UlJ0l+3V2tAACgnzGmBXyT5Puqmiw4djZsL3ZXHQAA6GcrgXsIz5Ph8col2VtrPyf5mOQv965xnOQyyavW2t026gUAAGNbex7uISD/efhyPmR/qqrZDY9vhmEkv9FaO62q11X1IdObIyeZ3ix50lpzsyQAAM/G2oF7CMaL17583Pm/JPll3fMBAOAQ7PPS7gAAcPAEbgAA6GjtISUAz1lV7fS5Wmu/ec7W2oPnPBfz38tD39dz+r6Br4fADTx7QtruzF7rh35hAPiaGFICAAAdCdwAANCRwA0AAB0J3AAA0JHADQAAHQncAADQkcANAAAdCdwAANCRwA0AAB0J3AAA0JHADQAAHQncAADQkcANAAAdfTN2BQC2raoefby11rs6rPDQe7XvtCXgMfRwA1+1Qw98AOw/gRsAADoSuAEAoCOBGwAAOhK4AQCgI4EbAAA6ErgBAKAjgRsAADoSuAEAoCOBGwAAOhK4AQCgI4EbAAA6ErgBAKCjb8auAMBjVdWXx621Ltd9jmbf3zZfs32xznvXqx0BLKOHG2BPVdXCQPncf0HYN8veB4DHErgBAKAjgRsAADoSuAEAoCOBGwAAOhK4AQCgI4EbAAA6ErgBAKAjgRsAADoSuAEAoCOBGwAAOhK4AQCgI4EbAAA6ErgBAKCjb8auAMAiVbXVcodm/vuqqrTWRqzN9u3ifZt/jmWv3/16zJe7f2z29XN7L4D+9HADwBNU1aN+YXhsOeD5E7gBAKAjgRsAADoSuAEAoCOBGwAAOholcFfVUVV9qqofq+r74etJVR1X1WVVXY1RLwAA2LYxpwU8SnK5YP9dkj/ttioAANDHmIH7NtNwfTxs/5rkQ2vt5xHrBAAAWzVm4H7fWrsY8fkBAKA7N00CAEBHAjcAAHQkcAMAQEdjjuFOVR0nOZ/b9SLJ29bax5GqBAAAWzVm4D5Lktbal8BdVUdJrqrqzVNmK7m5ucnJycnCY1dXpvQG9l9VjV2FJ5mvb2ttxJostk+v56wu+/g6Ab+3LFPe3Nysfc2xhpR8TnJxf5aS1tptkjdJLofebwAyDW2zfz2u+7V46Hv92l4PYDdG6eFurd0leb/k8Gw4yZ+TLP4V456XL1/qyQYAYGPLMuXJyUmur6/Xuube3TTZWpt9J3q4AQA4eDsP3FU1qaqzqpo8oqzQDQDAQRujh/unJO8yHTLykNvOdQEAgK7GHFLyYdHOYaaSJLkbxnoDAMDBGiNw/1uS89baL0uOfz9sf91RfQAAoJudB+7W2vskpyvGcF8kuRu2AABw0MYaUnKR5N38TZHDzZSzYSZ/MpwEAIDnYKx5uG+r6lWmC9wcZbqke5J8bK2djlEnAADoYbSl3Yce7POHygEAwCHbu4VvAADgORG4AQCgI4EbAAA6Gm0MN8BMVX153FobsSbPW1UtfX3n34Pkae/DqusuuvYheEydD/H7AsYhcAN7RYgB4LkxpAQAADoSuAEAoCOBGwAAOhK4AQCgI4EbAAA6ErgBAKAjgRsAADoSuAEAoCOBGwAAOhK4AQCgI4EbAAA6ErgBAKCjb8auADCeqvryuLV2UM8xf10e77Gv26zcovds0TXu79u396equrXx+edIpq/Zvn3/wLj0cAO/UVVrhYV1z+MweH8B1idwAwBARwI3AAB0JHADAEBHAjcAAHQkcAMAQEcCNwAAdCRwAwBARwI3AAB0JHADAEBHAjcAAHQkcAMAQEcCNwAAdCRwAwBAR9+MXQGgr6r68ri19uiy615z1TUee332x/337JDfw13V/THPs+z/0KJzH/p/+9A1e3no+Tapz6Jzez4f9KaH+4BV1UH/8OPvdvVe9ngO7RDGsen/vUP6v3so9dyFQ3rf+DuBGwAAOhK4AQCgI4EbAAA6ErgBAKAjgRsAADoSuAEAoCOBGwAAOhK4AQCgI4EbAAA6ErgBAKAjgRsAADoSuAEAoKNvxq7A16iqvjxurf3u602vt40y961Tr6e6//zzz7npa/SYa2zyHJu8B/P7N20bq97Dh8rc3/+YawGP99j/e9s4vmjfUz9D1vlZ8ZjvcZPP12X7Nv0Ztc7n3SbPuY0c8JifKZtea1cWPf/Yddq2ZxG4r6+vN77G7I0d+02tqtHrsO/mX6Ntf+jOP8ei6z32Q3mM9iQgA6us+7nU87NlX372bstz+36+Ng+9f5vkTUNKAACgI4EbAAA6ErgBAKAjgRsAADoSuAEAoKNRZympqrMkPyT5POx6keSitXY7Xq0AAGB7RgvcVfUuyaS1djq37zjJVVW9aq19HKtuAACwLaME7qp6neQsyR/m97fWrqvqIsm7qvpja+1ujPrBtp2cnIxdBYBny2cs+26sMdyXSd4vCdS/Jpkk+WmXFQIAgB52HriHYSOTJAvHaQ8h/C7J651VCgAAOhmjh/uHYftpRZnbJJOqOtpBfQAAoJsxAvfxsF01E8nsmMANAMBBGyNwv3hC2UmvSgAAwC6MMUvJ5AllHxPO/zlJqmqduvzOtq6zyfNtUofHnLvO9Xf9ujz0nMuOPbae2y637JxN6nm/zBjvAfD8PPaz5SmfOZuW3fTz7fr6eqvXe4x1fkY9puw2f0Yfys/7h55/H7LZnH9e55qjLnzzCJNHlPl/Sf5nkv9acvzft1YbAACeu39Zsv8fMs2dTzZG4L7b5sVaa3/c5vUAAGCbxhjD/fnhIl/c9aoEAADswhiB+27YTlaUmR17SjgHAIC9M2YP96obImfHrleUAQCAvTdG4P4wbL9dUeYoyV1rbdVc3QAAsPd2Hrhba+8zHVZyvOj4sLrkJMmvu6sVAAD0Mda0gG+SXFbVpLV2d+/Y2bC92G2VYLuq6izJD/ntMKoLf7lhTEOnxofW2qq/Ms6X144ZRVVdZto5N1t1+jqPaHvaLPuoWmvjPHHVhyQvWmsnc/uOk1wleTX0hMNBqqp3SSattdO5fcdJ/pJp+/44WuX46lTVJNPQcp7kdZK01h5cSUI7ZgzDL4Vvk1zO2tiw712mAfyitfbzknO1WfbSaIE7SarqdZJXmf7WOsn0t9A3rTU3S3Kwhnb9Nskf7v8FZzh2meSPC/66A1s39Pb9lOSvmQaWWSBZGbi1Y8YydMidL+qRrqpPmf7y+LuOOW2WfTZq4IbnqKr+luRja+3VgmOTJH9L8nNrzbApdm5on48J3NoxO1dV3yc5Xdau5kL17f1hUdos+2yMWUrg2Rr+dDlJsnCs4NCzcpfhz/qwj7RjRnSa5Mdh/PYisyEhR0OITqLNsv8EbtiuH4btpxVlbpNMhjGJsI+0Y8YyGbZnS47PL4g33/a0WfaawA3bNZvuctXd8LNjPvTZV9oxY7lI8kum93ctMt/e5tunNsteG2taQHiuVq2get+kVyVgQ9oxoxiGfpyvKPLdsL29d/OjNste08MN2zV5Qtmn/ICAXZo8oax2zC6d39vOTJ5wDW2WnRO4YTyTsSsAWzAZuwJ8HYYZSo6TvN9wPu3JdmoEjydww3bdjV0B2IK7sSsA8+YWw1k47V+0WfacwA3b9fnhIl/c9aoEbEg7Zt+8S3I9v4LkPdose03ghu26G7aTFWVmx57yAwJ26W7YTlaUmR3Tjumqqt4mSWvtZEWxu2E7WVFmdkybZecEbtiu2Qf5qptyZseuO9cF1qUdsxeq6sckRw+E7USbZc8J3LBdH4bttyvKHCW5a62tmi8WxqQdM7qqOst0mfffDSOpqrN7C9hos+w1gRu2qLX2PtM/bR4vOj78gJgk+XV3tYKn0Y4Z27BU+/mKMdunmRsaos2y7wRu2L43Sb6vqsmCY7Plii92Vx1Yi3bMKIZw/NOysD20ye/uLXyTaLPssWqtjV0HeHaq6kOSF/PjDocem6skr4beGNipIYj8bfjy24f+tK4ds2tDG73Kw8uvXy8a163Nsq8s7Q4dtNZOq+r18OF/nemfMl8kOWmtuWGHnRnCxp+HL+dDzKeqmrXFN4uCiHbMCC7zcNhOkr8u2qnNsq/0cAMAQEfGcAMAQEcCNwAAdCRwAwBARwI3AAB0JHADAEBHAjcAAHQkcAMAQEcCNwAAdCRwAwBARwI3AAB0JHADAEBHAjcAAHQkcAMAQEcCNwAAdCRwAwBARwI3AAB0JHADAEBHAjcAAHQkcAMAQEf/H1ycJfKFk1ExAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 252,
       "width": 366
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Let's do the easiest thing ever.\n",
    "plt.hist(x,bins=1000);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SlUq4DhRr9/uqzTn77jsDXg8AYBK4FXZ37klq6GHXqsJudkEy09Xj8yPp4kxSuIcdFXYAAADA+JqYwE7VoQ6StNfmnIqkWK0nXcestWlr7WqLSjm/6m53WOsBAEyI0NCJLirsjAkCPklBld3ynWVN14I878TT6cVpf9cLAAAAYCgmKbBL1N62m7zqX9eXgKy2RTYmqWyt3Rn1egAAY+akyZTYow6mxErSHXdb7DtJ0vTUdOg2DJ4AAAAAxtMkBXYrXZwbu+mD1YZFFCQVrbXJUa8HADCGmlTYuVtiW1bYSeE+dsfvgkMGTwAAAADjb2bUC+ijWBfndhOmBWp96bKqVsQ9kJSz1m4NYz2vX79WMtksF5RKpVIXDwUAiAw3sPN72B11GNiFtsTWA7tvLnxTqt3FLw8ZPAEAAAC0ylNev3495JV0bpIq7LoR6+VG1tqytTZrrU1Leigpa4wp9aEHXU/rAQCMOXfoxNyijs+P9eGsGuLNTM3o/tz9FjdUw5bY+qTY0OAJtsQCAAAAY2mSKuy8YT6YtbYsKWmM2ZO0Z4xJ1i4byHo+//xzKukAYNI09LBrnBBrjGl9W7fCztkS+835bwbHVNgBAAAArXcmJpNJlcvlpteN2iRV2O13ca7Xx8fN195uN1w+qvUAAMZFaEvsUmhCbNuBE1K4h13jltga9/4AAAAAjI9JCuy82ttYm3P867oJ067zqvY2XpsaO+r1AADGxWlDhV2n/euklj3slu8sB8cHxwc3XiIAAACA4ZukwM4PvdoNcPCv67je0Rizbow5MMastzjFc47dXnYDWQ8AYIKEetg1VNjdvabCrkUPu+W79cDOO/FuukIAAAAAIzBJgd1u7e1qm3PikjxrbaWL+82qWgmXa3F9zDl273dQ6wEATIpQD7vFUA+76yvsnMDO6WHnBnb7xxRwAwAAAONoYgI7a+2OqtVuiWbX1ya5xiQ97/KuX0kqqhrcNfOg4dxBrwcAMAmsbbsltrsedvUKu9idWHBMhR0AAAAwniYmsKvZkJQyxsSaXLdWe3ulUs4YEzPG5I0xa43XSSpIkrW22OIx/SAvZ631+rEeAMAtcHYoyVaPZ+5K0zPdBXYtetjdn7uvaTMtSfp49lGnF6f9WjEAAACAIZmowM5au6lqNdwL93JjTELVaa6ZJqGaJK1Leqyrk15lrS1LKhhjdmv3495vXtUKuq3aY/drPQCASXcSrq6T1JcedsaYUJUdgycAAACA8TMz6gX0m7U2XRsUsavqMIeYqsMdkrXwrZmiqv3nmlbRWWt3jDFFSfnaVlbV7rNyzf32uh4AwKQ7Dfevk9RdD7u7zXvYSdU+dv59eSeevr347ZutFQAAAMBQTVxgJ0nW2i1JW12cX1b74RCqVcK16mPX1/UAAG4BN7CrbW8NVdj1uCVWYvAEAAAAMO4makssAABj4/Rj/XhuUYdnhzo6P6q+OzWne7P3Wtyw5s4n9eOGwI7BEwAAAMB4I7ADAGAUTtpPiDXGtL99qMLufXXqbM3K3ZXgmAo7AAAAYPwQ2AEAMAqhLbFL3fWvk6SZuep0WUm6PJfOjoKrqLADAAAAxhuBHQAAo3AarrBzK+HcCrm2GqvsatwedkyJBQAAAMYPgR0AAKMQ6mG3FKqE+8TtT9fOHWdSrNPHbvkOgR0AAAAwziZySiwAAJEX6mG3GArsdv7gQP/Rf/r7197FP5y71F+t/ent3/z7/0/9t/ZPJEnTC3+qhb9Yvfw/+2f/XL/3/wrf19c/+p0bLR0AAADAYFFhBwDAKDT0sPOOveBde7HQ0V28t/Xz7plD5/aLwbGZ/igAAAAA44XADgCAUWjoYedW2LmBWzsfNB8cL6k+dCIU2M0cCgAAAMB4IbADAGAUTsKB3cFJvddcxxV2qp93P1RhV7+8WmFne18nAAAAgKGjhx0AAKNwGu5h9/bkbfCuPa8Hbm37zf1n/x/pD/6/kqTf/Z/G9bv/av3c/8F/tKHD80MZcylNHUuX863uBQAAAEDEUGEHAMAoNPaw62FLrO46U2KP34WuWr5bnxRLHzsAAABgvBDYAQAwCqdOiDZ3r6ehE7pzr3580hDY3XECuxkCOwAAAGCcENgBADAKTg+7y7l5vT11tsR2HNg5FXaNgR0VdgAAAMDYIrADAGAUnAq7D8bo0l5KkuzFHUnTnd2HW2HHllgAAABgYhDYAQAwCqfvg8O39jw47rh/nSTd/aR+fPI+dJW7JXaKLbEAAADAWCGwAwBgFJwKu/3L0+C44+2wUtsedrG7seDYTB92vTwAAAAAo0NgBwDAsJ2fShe1kM5Myzs/Cq7qLrBze9i1rrBjSywAAAAwXgjsAAAYttP6wAndWZIXGjjRxZZYetgBAAAAE4nADgCAYXMDu7kleSde8G5XFXZ321TYuYEdPewAAACAsUJgBwDAsJ20CezOuwjs5pwKu9P30uVF8G7sTiw4pocdAAAAMF4I7AAAGDZn4ITmFnVwfBC829WW2KmphtCuHgR+cqc+QdZMHQkAAADA+CCwAwBg2E6d7at3lvT2xO1h10WFnRTeFuv0sbvnBnnTR5Iuu1wkAAAAgFEhsAMAYNhCFXb3dHDiVth1Gdi5gyecPnazU7NamKnelzFWmjrpaakAAAAAho/ADgCAYQv1sFu8WYXdHXfwRHhS7H3nOjPNtlgAAABgXBDYAQAwbO6U2DuNU2K76GEntaywk6RP5pw+dgR2AAAAwNggsAMAYNicwM7OLso79urv36iH3dvQVaEKOwZPAAAAAGODwA4AgGFzetidztzRuT2XJM3PzEt2trv7alNhd3/O3RJ72P06AQAAAIwEgR0AAMPm9LA7nDLBcexOrPv7atfDbo4edgAAAMA4IrADAGDYTuuVcIdT9R/FNw/sGnrY3aGHHQAAADCOCOwAABg2Z0vse10Gxz0FdqEedq0r7EQPOwAAAGBsENgBADBszpbYtzcN7DruYUdgBwAAAIwLAjsAAIbNqbB7Vxs4IUmxu7Hu76tdD7s7BHYAAADAOCKwAwBg2Jwedvv2LDi+cYXd8dvQVZ/M0cMOAAAAGEcEdgAADJtTYbd/eRoch3rOdepu66EToQo7etgBAAAAY4PADgCAYXN62L25PAmO3YCtY+22xNLDDgAAABhLBHYAAAybU2H35sIJ7HqpsLvTpsIuFNgddn/fAAAAAEaCwA4AgGG6vJTO6oHdry/qQVpvgZ3bwy5cYXdvrn6dmT6WnIm0AAAAAKKLwA4AgGFywjrNLurtWb0qrqfAbnZempqpHl+cSOf1ir3pqWndm3UCvanj7u8fAAAAwNAR2AEAMExO/zrNLeqd03eupx52xoSr7NoNnqCPHQAAADAWCOwAABim03pgZ+8s6d1pPbBzt7B2pePBE/SxAwAAAMYBgR0AAMPkBnazCzq7PJMkzU7N6u703d7u864T2DX0saPCDgAAABg/BHYAAAyTsyX2fLYe0N2fuy9jTG/32emk2CkCOwAAAGAcENgBADBMp/WhE2czd4LjnvrX+TreEktgBwAAAIwDAjsAAIbJ2RJ7Mj0bHPc0IdbH0AkAAABgohDYAQAwTKHAbiY4vlFg16aH3SdznwTHBHYAAADAeCCwAwBgmJwedodT08HxzbbEuhV2rYdOiCmxAAAAwFggsAMAYJicHnaHzpCJm22J7bCHHUMnAAAAgLFAYAcAwDCd1nvMfXCGwt6bu9fk5A6162HH0AkAAABg7BDYAQAwTE6F3TtzGRzfrIddvU/dlR52d+hhBwAAAIwbAjsAAIbJ6WH3zl4ExwObEkuFHQAAADB2COwAABgmZ0rsgT0Pjm82dKJND7s79LADAAAAxg2BHQAAwxQK7E6D40FV2C3NLsnaarM8M30i6UIAAAAAoo3ADgCAYXK2xL65OAmOb9bDzrltQw+7KTMlXd4N3jfTx70/DgAAAIChILADAGCYnKETv76oh2fucIiutdkSK0n2Yr7+zhSBHQAAABB1BHYAAAyTsyX2Vxf1nnJ93RJrbehqe3knOGbwBAAAABB9BHYAAAyTE9jt13rYTZtpzc/Mt7rF9aZnJf/29iJUxVe9yNkSS4UdAAAAEHkEdgAADIu1oR52h1PVH8P35+7LGHOz+3b72DUMnrD0sAMAAADGCoEdAADDcn5SrYCTZKdndV4L6e7fucF2WF9oW2xDHzt62AEAAABjhcAOAIBhcbbDXjhbYG/Uv853p8MKOwI7AAAAIPII7AAAGBYnsDufrYdo/QnsnAq747ehq9gSCwAAAIwXAjsAAIbF6V93Oj0XHPclsGvXw46hEwAAAMBYIbADAGBYnAq7k5nZ4Lg/Pew+qR83VNjJqbATFXYAAABA5BHYAQAwLE5gdzw1HRz3p8LOCewahk5QYQcAAACMFwI7AACGxdkSe+QEdvfm7jU7uzt3W1fY0cMOAAAAGC8EdgAADMvpx+Dw45QJjvteYdcY2FFhBwAAAIwVAjsAAIbF2RL7QTY47ksPuzaBndvDjsAOAAAAiD4COwAAhsUJ7N4ZJ7AbeIXdfP0dtsQCAAAAkUdgBwDAsDg97N7Zi+B4aW7p5vd91wn9jhuGTlBhBwAAAIwVAjsAAIbF6WHnqR7Y3Z8d8JZYOyNrq0MuzNS5Ti5Obv54AAAAAAaGwA4AgGFxtsQeXJ4Gx/2psGsT2MmEBk+8P31/88cDAAAAMDAEdgAADIsb2Nmz4HjwgZ1Cgyc+OOsAAAAAED0EdgAADIvTw+6jqb6dn5nX7NTsze977p6k2p2evpcuzkNXuxV2H84I7AAAAIAoI7ADAGBYnMq2j1PVcG1ptg/VdZI0NRUePHHSevAEW2IBAACAaCOwAwBgWJyhEx9N9UdwX7bD+tpsi6WHHQAAADA+COwAABiWk3pQdlirsLs3d69/99+uj90lW2IBAACAcUFgBwDAsDgVdodT1R/B92b7GdjF6sdU2AEAAABji8AOAIBhcXrYHZpaD7thbYmlwg4AAAAYGwR2AAAMw8W5dH4sSbIyOjLD3RIbCuxOCewAAACAKCOwAwBgGJyQ7GxmTvIDu35uib3jTIltsyX23Wl4giwAAACAaCGwAwBgGJz+daczc8HxsLbEigo7AAAAYGwQ2AEAMAxOSHYyNRMcD2xL7Em4is5ezAfH9LADAAAAoo3ADgCAYXACu6Pp6eB4aXb4QyeYEgsAAABEG4EdAADDcOJOiK3/+B3a0IkLpsQCAAAA44LADgCAYXAq7D5OmeB4WIGdqLADAAAAxgaBHQAAw+AMnXgvGxyPYkvsh9MPstYKAAAAQDTNXH8KAABo9P0f/n5X5/870/9E/9vZ6vEvzs4kVQO0f+N/91L2/J/3Z1HtKuzsjOzljMzUuc7tuY4vjjU/My8AAAAA0UOFHQAAQ7Cg4+D441S9us1e9jE0axfY6WqVHQAAAIBoIrADAGAIlkw9sDuavpQkWWuky7n+Pcid+5Jq/fFO3kmXF+HrncET78/oYwcAAABEFYEdAABDEK6wq/34vZxTX38UT03VQruak3ehqy2DJwAAAICxQA87AAD64Osf/U77E/7hP5LK1cNDU62C+437K/rH192uW3c/kU5q22GP30rzy8FV9qK+/ZYtsQAAAEB0UWEHAMAwOFNiD2sVdktzfZwQ67vrVNi1mxR7RmAHAAAARBWBHQAAw+BUtPkVdvdm7/X/cdoNnnD65X08+ygAAAAA0URgBwDAMDgVdn4Pu3tzww3smBILAAAAjAcCOwAAhuGkPuTh41S1wm4wW2LdwK5h6MTFnfoaqLADAAAAIovADgCAYQhtia1V2A15Syw97AAAAIDxQGAHAMAwhIZO1HrYDXlLrC6psAMAAADGAYEdAADDcHK1wm7wW2JbV9gR2AEAAADRRWAHAMCgWRveEjusCrujg/AynB52bIkFAAAAoovADgCAQTs7lGSrh1PTujC1wG4QPezmV+rHR/vh66iwAwAAAMYCgR0AAIPm9K87mpoJjgeyJXbBCewOw4GdvZwLjqmwAwAAAKKLwA4AgEE7eR8cHk3Vf/QOZEtsmwq7UA+7UyrsAAAAgKgisAMAYNBCE2KdwG4QW2IXPq0fX6mwo4cdAAAAMA4I7AAAGDSnwu6DqV88kC2x8zFJtQc59qSL8/p1ztCJj2cfZa3t/+MDAAAAuDECOwAABs0J7N6aeki2NDuAwG5qOjwp9thzrpyRvaz20LuwFzq+OO7/4wMAAAC4MQI7AAAGzQns3teK36bNtOZn5gfzeG0HTzApFgAAAIg6AjsAAAbt5F1w+HGqmtgtzi7KGNPqFjfTZvCELsPbYgEAAABED4EdAACDdlof8PDBVH/0DmQ7rK9dhd1FvcKOwRMAAABANBHYAQAwaM6W2I+1KbGLc4uDe7w2FXb2cq6+llMq7AAAAIAoIrADAGDQ3CmxtS2xo6qw0yUVdgAAAEDUEdgBADBoocCu+qN3YXZhcI/nVtgdvgldZelhBwAAAEQegR0AAIMWGjox5B52V7bEUmEHAAAARB2BHQAAg+ZW2JnRbom1F1TYAQAAAFE3M+oFDIIxZk3SF5L831JWJOWstZUb3m9eUkJSvHZRud39GmPiknYlFWrnVmpritfWl7LWJm+yJgDAGGg2dGJ2WEMnDsLXuRV2p1TYAQAAAFE0cYGdMWZbUsxam3YuS0gqGWMy1tpiD/cZVzV0y1trc85l25L2jDE5a+1mi5vHJeWbXO5JetjtWgAAY6hJD7uRVdg5PezYEgsAAABE00QFdsaYdUlrkpbdy621ZWNMTtK2MeYza63X5V0XJGXdSrracdIYsycpb4ypWGt3mty2omo4l6i9fSVpt03ABwCYNKEKu+qW2OFV2LUO7NgSCwAAAETTpPWwy0vaaRHIPZcUk/Skmzs0xqQkldtsp803vG20Y61NWmuNtXbZWpsmrAOAW6ZZhd3cMCvsbP39i/qWWAI7AAAAIJomJrCrbXuNqVrRdkUtxPMkrXd512lJj2v965rxt9jGjTGxLu8bADDpLi8kp1fcoRlChd3svDQzX3v8My3pKLiKCjsAAAAg+iYmsFN1iIMk7bU5pyIpVus/16lY7e1ai+vdvUbd3C8A4DZwwrqj6RnZYQR2UqjKLmbqa6CHHQAAABB9kxTYJWpv202C9a/rJljLSdqSlGlxvXtfN5pCCwCYQM522KOpeuvYgQ6dkEJ97JblBnZsiQUAAACibpKGTqxcf0og1umJta202TanPKi9rbQaZlHbruvex4qkQi8TawEAYyY0cKL+d7JhVtgtm/f1NnZuhd0pFXYAAABAFE1SYBfr4txuwr3rZBveNlqTJGttcH1tS27JGLPBAAoAmHBOYPe+NiFWGkKFnbsl1q2wY+gEAAAAEHmTFNh1I9aPOzHGrKu6FXenRbXcvqSctXbHvdBaWzHGbEjKG2OK1trydY/1+vVrJZPJpteVSqXuFw8AGI6Td8Hh+3pep8W5AVfYuVtinR52srOaMlO6tJc6vjjW2eWZZqdmB7sWAAAAYIRa5SmvX78e8ko6N0k97LxhPlitSq4gqWitbdrfzlrrNYZ1Dj/gezqI9QEAIsKpsHsX7EuVFmeGvCU2YELbcQ/PDge7DgAAAABdm6QKu/3rTwl4fXi8bUlla226lxtba8umOikwcd25kvT5559TSQcA4yjUw65aYjc/M6/pqenBPm5o6MT70FVLs0t6f1q97MPZB31y55PBrgUAAAAYoVZ5SjKZVLl87abHkZjECrtYm3P867oJ964wxhQkyVrbvKayek7MGLNmjGm3Hv/cjkI7AMAYcgK7D7XAbuD966SGCrvwcAm3wo7BEwAAAED0TFJg54dw7QZK+Nf1HJ8aYx5LircL62qeqFqF18mW10qv6wEARFyTKbEDnxArhSrs3KETjY9/eM6WWAAAACBqJimw2629XW1zTlySZ63tKSAzxqxJSjfbBlurpou3WVfj+f65nrXW62U9AIAx4FbYmSEGdi172IUr/KiwAwAAAKJnYgK72nAHTy16wtUCspik573cf23barZNz7q0wlttX9bO32pxfqr2tqf1AADGhDMl9uNQt8R+GhyuNAR2bmD48ezj4NcCAAAAoCsTE9jVbEhKtegbt1Z7m2u8otZvLl+roLuiFvY9aRXW1R7vgVspVwsQ02162OVUDRivrAcAMEFCPeyGWGG39K3g8Bt6KzkTapfmnAq7MyrsAAAAgKiZqMDOWrspqSjphXt5rTouLynTYvvpuqTHqvacC6kFbruS1owxttk/SQctlpSTtO0OlaiFg/422YdshwWACdcksHMDs4GZW5RqweAdc677qlfSUWEHAAAARNvMqBfQb9batDFmvRaKlVXdBrsiKWmtbTVsoqjq4Idik+vyqva+u86rJmupGGMykvK1Kj2/oVCxzdZaAMAkCQ2dqG6JHUqFnVStsjv4SpL0TfNW72w1KAz1sKPCDgAAAIiciQvsJKnWN65V77hm55fVYliFtTYrKXuDtXg3uT0AYMw1GToxlB52Uiiw+4beaU+/KSkcGDJ0AgAAAIieidoSCwBA5JzUA7GPw+xhJ0mL3wwOv2m84HhhdiE4Pjw/HM5aAAAAAHSMwA4AgEFypsR+GPqW2G8Hh98wb4PjxZn64x+eEdgBAAAAUUNgBwDAoFjb0MNuyBV27qRYJ7BzK+wYOgEAAABED4EdAACDcnYk2QtJ0unUtM5NtcJuaD3s3C2xcirsmBILAAAARBqBHQAAg+JU1x1N1ec8Lc0Na+hE8y2x9LADAAAAoo3ADgCAQXECu8Pp6eB41Fti3R52VNgBAAAA0UNgBwDAoLgDJ2rbYaXRbIkNBXZsiQUAAAAijcAOAIBBcSrs3js/cUdSYae3kuyVxz86PxrOWgAAAAB0jMAOAIBBcQK7d7WwTBpiD7u5Ran2WHfMue6rWk13d+ZucMrR+ZEuLi+Gsx4AAAAAHSGwAwBgUNwKu9qO2Bkzo7mpueGtwZ0UW9sWO2WmtDDD4AkAAAAgqgjsAAAYFCew+zhV/ZG7OLco4/SzGzhnUuw36WMHAAAAjAUCOwAABuWkHpB9qAV2Qxs44VtyBk+oeWB3eEaFHQAAABAlBHYAAAzKsRvYVavqhjZwwrfoDJ5wKuwWZtkSCwAAAEQVgR0AAINy/C44fD+yCjt3S6wXHLs97NgSCwAAAEQLgR0AAINycjWwG3qFXWhLbH099LADAAAAoovADgCAQXEq7EbWw66DLbEEdgAAAEC0ENgBADAozSrs5oZdYVffEvuNFlNiGToBAAAARAuBHQAAg9Jk6MQop8S6PewWZ5wtsedU2AEAAABRQmAHAMCgNBk64W5FHQpnS+yneifJVi+mwg4AAACILAI7AAAGpcmW2KFX2M0t6L2dlyTdMef6RNVqOnrYAQAAANFFYAcAwCBcnEm1yrVLGR2aEW2JlfRLGwuOv2P2JYUDu8NzKuwAAACAKCGwAwBgEJztsMczs1ItsHO3og7Lz+1KcPwdc1Bdh9vDjgo7AAAAIFII7AAAGIST+sCJw+mZ4HgUFXY/13Jw/O1ahZ0bHBLYAQAAANFCYAcAwCA4FXYfpuqB3eLc8CvsfuFW2KlaYRfaEsvQCQAAACBSCOwAABiEEzewM8HxKCrsfhbaEvtGEj3sAAAAgCgjsAMAYBCO61ti39XzupH0sPuFrW+JpYcdAAAAEH0EdgAADIKzJfatscFxZIZO0MMOAAAAiCwCOwAABsHZEntgLoPjhZmFZmcPlBvYNRs6QQ87AAAAIFoI7AAAGAR36ISp/rhdmFnQ9NT00Jfya32ic1tdw6fmvXR2rPmZeRlV9+oeXxzr/PJ86OsCAAAA0ByBHQAAg+BU2L2fqv64HcXACUm61JR+qVj9gvc/kzEmNHji6Pxo+AsDAAAA0BSBHQAAg3DsBYcfaoHd4tzw+9f5fuFsi9X7n0kKb8+ljx0AAAAQHQR2AAAMwrFbYVfdejqqCjtJ+rkzKVbvfiqJPnYAAABAVBHYAQAwCE22xI5iQqzv580q7GapsAMAAACiiMAOAIBBcIdOjLiHnST94poKu4/nBHYAAABAVBDYAQAwCMdvg0O/ws6taBu2UIWdH9jNsCV2ZN79VPrFPxv1KgAAABBRBHYAAAxChKbEStLPxZbYyNivSP/7vyr9g39N+v/93qhXAwAAgAgisAMAYBBCW2KrQydG28PO3RJ7NbCjwm6I/uQfS5dn1eN/9g9HuxYAAABEEoEdAAD9dnYsXZxIki7MlI5NbUrs3CinxLoVdj+VLi9DW2LpYTdEH35eP373k9GtAwAAAJFFYAcAQL8522FPZuYkP7Ab4ZbYY93RW1urqLs8lw5/HR46wZbY4Xn/i/rx2x+Pbh0AAACILAI7AAD6zdkOezQ9FxyPckusdHXwBFtiR6TWQ7B6/HPp/HR0awEAAEAkEdgBANBvJ/UJsR+nZ4LjUVbYSVcDOzdAPDwnsBuaD06FnWx1izIAAADgILADAKDf3IET0/UftaOusPtZKLD7iRZmmBI7Eu9/Hn6fbbEAAABoQGAHAEC/Hdcr7N7X+tdJUQjsPq2/8+4n9LAbhfMT6Wg/fBmBHQAAABoQ2AEA0G/O0Il39bxu5FtifyonsHv7E3rYjUJoO2zN2z8f/joAAAAQaQR2AAD0m7Ml9sBcBseLc1EaOkGF3Ui8bxbYUWEHAACAMAI7AAD6zamwO7AXwfHIK+zcLbFvf0xgNwoffn71MgI7AAAANCCwAwCg35wKu3e1n7SzU7Oam54b0YKqQj3s3v9MizPzwbtMiR2SxoETEoEdAAAAriCwAwCg39yhE1PVH7Wjrq6TpEPd1Vtb61t3caqFk6P6dfSwG45WgZ21w18LAAAAIovADgCAfnO2xPqB3agnxPrcbbHzh29kVJ2KcXxxrPPL81Et6/ZotiX29IN07A19KQAAAIguAjsAAPrNqbD74FfYzY2+wk4Kb4s17xomxbItdvCaDZ2Q2BYLAACAEAI7AAD6LVRhV61gW5hZaHX2UIX62L39iRZn6pV/bIsdArfCbn65fkxgBwAAAAeBHQAA/RbpCruV+jvvfhyusCOwGzy3h91vPqgfE9gBAADAQWAHAEC/HUe3h12owu7dT0Pr+nj2cQQrukUuzqWPv669Y6TfTNSve/vnI1kSAAAAoonADgCAfrK26dCJKEyJlaSfKrwl1q2w+3hOYDdQH38pqTYNduFTafmz+nVU2AEAAMBBYAcAQD+dHUm1aavnUzM6M9UedlEJ7MJbYsM97KiwGzB3O+y970qf/Fb9fQI7AAAAOAjsAADoJ6d/3enMneA4sltiZ+4G79LDbsBCgd23q6Gd78Mvh78eAAAARBaBHQAA/eRshz2amQuOozJ04kRz1e2YkmQv9O3L+nVU2A2YOyF26TvSnDM5+Oxo+OsBAABAZBHYAQDQT8duYDcbHEelwk6SdP83g8Nvn58Hx4fnVNgN1Ptf1I/vfVuaJbADAABAcwR2AAD000l9S+zHqengOCo97CSFArtPT4+DYyrsBuyDE9gtfachsCMsBQAAQB2BHQAA/eT0sPMnxEoKTWMduU/qgd3Kab2yix52A3byvn48H5OmZyVTC3Uvz6SLs5EsCwAAANFDYAcAQD85W2LfT5ngOKoVdp8cfwiOqbAbMHfb6+y8ZAxVdgAAAGiKwA4AgH5yhk54xgbH0QrsfiM4XDohsBsaN5Cbna++ZfAEAAAAmiCwAwCgn5wKO0/1EayRGjpx7zvB4aKzXoZODNh5vV+gZmqBnR/cSdIpgSkAAACqCOwAAOgnp8Ju314Ex0tzEaqwu/fd4PDO4UFwTA+7AWtWYcekWAAAADRBYAcAQD85QycOdC5JMjKan5lvdYvhcwK7ucM3kq1u3WVL7ICFetgthN82Xg8AAIBbjcAOAIB+Cg2dqP6YXZxd1JSJ0I/cO/ek2hbdqfMT3b8ksBuKxqET7luJoRMAAAAIROi3BwAAJsBJ88AuUowJ9bH75kW1EpAedgPWNLBjSiwAAACuIrADAKCfnAq7D1EN7KTQtthvXVR77VFhN2BU2AEAAKBDBHYAAPST08Pu/ZSRJC3NRmjghO++E9idV6fZnlyc6PzyfFQrmmzWhgM5v6fhnBPm0sMOAAAANQR2AAD004kb2EW5wq6+JfY3nP8OsC12QM5PJFV7BWp6TpqeqR67FXanPPcAAACoIrADAKBfrJVO3gfvfqwFdktzEaywc7bE/sZF/eJDtmUOxrlTPedODGZLLAAAAJogsAMAoF9OP0i2ur30fHpO56a6JTbqFXbfurwMjuljNyDN+tdJwbTeK+cAAADgViOwAwCgX5z+daezd4PjSPawu/cbweE3z+t96wjsBqRlYEeFHQAAAK4isAMAoF+cCbEnM3eC46hX2K2cnQbHBHYD4oZxswvNjwnsAAAAUENgBwBAv5zUA7ujmbngOJoVdvXALnZ2LGOrAxEYOjEgHVXYsSUWAAAAVQR2AAD0i1Nhd+hPAZW04FZRRcXsvHQ3JkmatlYrtT52DJ0YkFaB3RwVdgAAALiKwA4AgH5xKuw+TE8Hx5GssJOk+24fu+qoWLbEDkjLCjsnsDslsAMAAEAVgR0AAP1y7AWH72sTYiVpaS6igZ2zLfabFwR2AxXqYcfQCQAAALRHYAcAQL84W2LfTdUDu0gOnZCke98NDr9Fhd1ghSrs3KETi83PAQAAwK1GYAcAQL84W2I9XQbHkd0S61TYfeviXJJ0dE5oNBDu8zpzt37M0AkAAAA0QWAHAEC/HDcP7Maiwo4tsYPVssLODex47gEAAFBFYAcAQL8cvw0O39iz4Di6FXb1wI6hEwPWckosW2IBAABwFYEdAAD94myJ/bU9D46jW2HXZOjEOYHdQHQ0dILADgAAAFUEdgAA9Is7dMJYSdLc1Jxmp2dHtaL2Fj4NDmMX1S28h0wqHYyz4/pxKLBztseefpSsHd6aAAAAEFkEdgAA9ItTYfd+qvojdmkuotthJWnxG8Hh8mU1sGNL7IC0qrCbnpWmZqrH9kK6OBMAAABAYAcAQL84Pew+1AK7yG6HlaS5JWn6jiRp3lrNX15SYTcorYZOSJL7GuH5BwAAgAjsAADon5P3weGHKSMpwgMnJMmY0LbY5YtLHZ4TGA1Eqwq7xvfpYwcAAAAR2AEA0B/WhgK7j+NQYSdJi05gd3nBlthBOXd72DVW2LmBHYEpAAAACOwAAOiP04+SqgMDLqbndGHGoMJOkhbqfexWLi51cnGis0v6qPWdWzk3czd83RxbYgEAABBGYAcAQD+cfggOz2frgcziXNQr7OqBXeziQpJ0dM62zL4LbYltV2HHcw8AAAACOwAA+sPZDns6cyc4HqcKO39SLIMnBiA0dKJND7tTtiQDAACAwA4AgP5wArsTJ7BbaKymihqnh93KBYHdwLQN7BaanwcAAIBbi8AOAIB+cAK74+mZ4Dj6FXbulNjqllgGTwxAx4EdYSkAAAAI7AAA6A+nh93h1HRwHPkpsc22xJ4TGvUdFXYAAADoAoEdAAD94FTYHU7Vf7xGvsJu0Z0SS4XdwHQ8dIKwFAAAAAR2AAD0hxPYfZgywXHkA7sFd0osFXYDcXEm2WoYqqkZaXo2fP0cW2IBAAAQRmAHAEA/OIHd+3pep8W5iG+JXXS3xFZDJYZO9Fm76rrGy9gSCwAAABHYAQDQH04Pu3eywXHkK+zuxiRT/e/A/UurGWsJ7PrNDeFm7l693t0Se8p2ZAAAABDYAQDQH06F3VtdBMeRHzoxNSXNrwTvLl9c6OM5oVFfhSrs5q9eT4UdAAAAGhDYAQDQDyf1Crt9ex4cRz6wk8LbYi8uqbDrt7Pj+jFbYgEAANABAjsAAPrh5F1weGDPguPIb4mVQoMnVi4vmRLbb24I17TCjimxAAAACCOwAwCgH5wedge1Cjsjo/mZJgFN1Cx+GhzGLi6YEttvXW2J5bkHAACANDPqBQAAMBGcHnaHU9W/hy3NLskY0+oW0eFW2F1c6ieERh37/g9//9pz/kdTf6j/61z1+L+ofND/quE2/9rUP9V/XLv+n/zRj/W/aHKfX//od268VgAAAIwPKuwAAOgHp4fdh6lqSLc4Nwb966RwD7tLKuz67a7qW6SPNHfl+iN7JzieNydDWRMAAACijcAOAIB+cCrsPjoVdmNhob4ldvmCHnb9Nq96CHekO1eud0M891wAAADcXgR2AAD0g9PD7qOp/ngdiwmxUkNgd8GU2D6bN6fB8bGdvXL9oRPiEdgBAABAoocdAAB9YBt62FW3xI5Nhd1ieEosgV3vmvaa+ydfS/+oevhv/w//iv7t/0nDOe9/If39f1eS9BfuGX39936no954AAAAmFxU2AEAcEMLOpFkJUnnM3d0URs0MT4VdvXALnZxSQ+7fjs7qh83nRI73/xcAAAA3FoEdgAA3NCS6iHL+Ux9e+PYBHbu0ImL6tAJa+0IFzRhQoHdwtXr3cvOPko89wAAALcegR0AADe0ZOqBzMk4BnZOD7vY5aXs5YWOL45HuKAJc12F3fSMNF0bPGEvpYvTq+cAAADgViGwAwDghtwKu5Pp+lCBpbkx6WE3PSvN3aseSlq0lkmx/eT2BJy92/wcN8g75bkHAAC47QY2dMIY831JKUlJSXFJK5Jitas9SfuSKpJKkorW2q8HtRYAAAZp0dSr0Y6nZ+X3sxuboROSdPcT6bQ6OOPexaWOzo6kJsVg6MG5U63YbEusJM3clfS2dj6TYgEAAG67vgZ2tZAuK2ld1XDOKBzOfVU7NSbpU0mrtfOtMcaTVJC0RXgHABgn91SvoDqcnpZ0LmmMtsRK1cDu3Y8lSfcuL/XxnCqvvglV2LVIQZ2t1LogsAMAALjt+hLYGWPuS9pUNagrS3oqadda+6LD26ck/Q1JaUk5Y8y2pC+tte97XM+apC9UDQqlanVfzlpb6eX+nPvNS0qoWjEoVT/Wa+93UOsBAETDouoVVB9rE2KlMaywq7l/eanDMybF9s11QyckadoJ7M7pYQcAAHDb3TiwM8b8z1UN6J5JWrXWfnXNTa6w1hYlFSX9rjEmLikn6WtjzN+21v4nXa5nW1LMWpt2LktIKhljMrXH6kptTQVJeWttzrlsW9KeMSZnrd0c1noAANHiDp34MFUP7Mauwq7m/uUlPez6yQ3sZlr0sHMr7M4Z+AEAAHDb3SiwM8b8SNXKuM+stW/7saBa1VnWGJOT9NwY8zettU86XM+6pDVJyw33Wa7d37Yx5jNrrdflsgqSsm5FXO04aYzZk5Q3xlSstTtDWg8AIELuOUMn3hkbHI/N0AkpFNjdu7zU4TkVdn3TUYXdXP2YKbEAAAC3Xs9TYo0xf0+SrLX/er/COpe11rPW/nb1ocy/1+HN8pJ2WgRgz1XtnddR+Oerbdctt9m+mm94O9D1AACiZ9GpsHuny+B4YaZFOBNFjYEdW2L7JxTYddDDjqETAAAAt17PgZ2qk11/2LeVtFB7jGt74dW2mcZUHW7R7H48VQdgrHe5hLSkx7X+dc34W1rjxpjYENYDAIiYJafCztNF/XIq7CAxdAIAAABd6zmws9b+YT8X0ofH+qL2dq/NORVJsVr/uU7Fam/XWly/7xy79zuo9QAAImbJ1HuOHVye1y8f06ET9y4tPez6yd3i6m59dTF0AgAAAI6bVNhFTaL2tt3kVf+6bgKynKQtSZkW17v35T72oNYDAIgYt8Ju354Fxwut+pVFEVNiB8fd4upW0rlmnCCPoRMAAAC33o2nxF7HGPPXJVWste8G/FArXZwb6/TE2tbVbJtTHtTeVhp61Q1kPQCA6FmUOyW2+vbu9F3NTs2OaEU9aNgSS4VdH3VbYXdxKmmMXjsAAADou4EGdrXBFHlJl42PZYz5RNKytfbrPj1crItzuwnTrpNteOuLdXEf167n9evXSiaTTa8rlUpdPBQAoN+WnKETH001sVucXRzVcnpDD7vB6ajC7m7D+WP2+gEAAIiwVnnK69evh7ySzg16S+ynkn5X0jtjzPfdK2qTZf+OMeYfGGPuD3gdjWL9uBNjzLqqW193rLXF684f9HoAAKOxpPoWxg9T1R+tYzVwQpLmY8EhU2L7yNrwEInpDrbEMnQCAADg1hv0llhbm/Kaa3HlD2uVdnlJf/eGj+Xd8PZdqQ2KKKg6LbdZf7u+rufzzz+nkg4AIipUYTdlJFFhh5qLek9DTc1IUy3+VhoaOkFgBwAA0E+t8pRkMqlyuTzk1XRm0BV2+7Uedi3VKu1+aIzZuOljdXGud8PHkqRtSWVrbbrF9cNeDwBgRBadCruPU5OxJZYedn3SSXWd1DB0gsAOAADgthtoYGet/V3Vt73+xTbnvdXNt4V6tbft7se/rpsw7QpjTEGSrLXNN0EPeT0AgNExutQ9p8Lu0Ixphd2deneKpUurIwK7/jh3Bk7MtBg4ITUZOgEAAIDbbNAVdlI1uMpKqhhj/tQY8380xvyPm5x300EQfujV7n7863qudzTGPJYUvyasG9p6AACjtaB6NdT5zB1d1gK7pdkx62E3Na3LWt+9KUk6eT/S5UwMt8LOHSzRaIYtsQAAAKgbaGBnjPmRpJSkLUm/p+oQir8jqWiMuTDGvDTGPDPG/Kmkyg0fbrf2drXNOXFJnrW2p8cyxqxJSjfbBmuMWav1tRvaegAAo7ekenXdmRO6jF2FnSR7t15lN338YYQrmSBu+DbdpsKOwA4AAACOQQ+diFtrH7gXGGP+hqS0pC8kJVWdsrpprX1ykwey1u4YY7za/V1RC9NiqoaHXTPGJCRl2/SsS0sKJsUOej0AgGhwB06cOlsex67CTpK5G5Pe/VSSNHNKYNcX7vbWmTY97EJbYgnsAAAAbruBD51ovMBa+4fW2s3altJlSf9hHx9vQ1LKGBNrct1a7e2VibXGmJgxJl+roLuiFq49aRXW1R7vgbXW68d6AADjY97ZEns8PRscL82NYWA3HwuO756f6OzyrPXJ6Mw5QycAAADQvUEHdp4x5vutrrTWvrXW5iT9qA9TYmWt3VS1yu2Fe3mtOi4vKdMkVJOkdUmPVZ38GlIL23YlrRljbLN/kg76vB4AwJhYdAK7k6np+uVjuCXW3I0Fx/cuL3V4dji6xUyKiw6HTrj97Rg6AQAAcOsNdEustfaHxpj/kzHmR9bar9uc99aYWpfumz9m2hizbozZVXWYQ0zV4Q5Ja22r4Q5FVXvoFZtcl1e119x1XvVxPQCAMbFgjoPjw6n638HGcUus7n4SHN6/vNTR+ZE+ufNJmxvgWp1W2Ln97c6PW58HAACAW2HQPexkrf07xpgfGWM+k/Sltfadf50x5hNVt83uSvrDPj7mlrroDVcLzpoOh7DWZlWdcju09QAAxseinMDOGElWkrQwuzCiFd2AE9jdu7zUx7OPI1zMhAhNie106AQVdgAAALfdwAM7Kai0+0SSabj8rTHma0m/rebVbQAARJpbYffR+Sk37hV2bIntEzd8a1thx9AJAAAA1A0lsJOq4VyLy1eNMZ9Za78a1loAAOgXt8LuQ626TpqMwO7jORV2N0aFHQAAAHow6KETHSGsAwCMqwVn6MQ7XQbH4zh0IhzYWSrs+qHTCrtQYEcPOwAAgNsuEoEdAADjyt0S+07nwfG4B3b36WHXH6EKuw6HTrAlFgAA4NbrObCrTX/9i/1cTIvH+b4x5h8M+nEAAOiFW2H39rIe2C3Njf+W2KPzoxEuZkK41XLTbIkFAABAZ25SYfdDSb9njPm3+rWYRsaYh5K2JeUG9RgAANyE28PunaluiZ0xM7o7fXdUS+odU2L7zw3fqLADAABAh3oO7Ky1nqSUpL9rjHlmjPlr/VpUraruuaTHklLW2nf9um8AAPrJ3RJ7aKpjYhfnFmWMaXWT6LobCw7vXVzq8Jwedjfmhm9tK+ycgJcKOwAAgFvvRj3srLWetfa3JZUk/aEx5h8ZY/4tY8z9bu/LGHPfGPM/M8b8I0l7kv7AWvuvt5ouCwBAFLgVdodT1R+rYzkhVqLCbhA6rbBj6AQAAAAcM/24E2vtpjFmS9ITSf9nSZ8YYyqSiqqGb56k/dpbSYpJWqm9XVW1Ui8u6a2k55JWCOoAAONgwdQrqI5qVXVjG9jduS8rIyOre9bq6PTDqFc0/kIVdp1uiaXCDgAA4LbrS2AnBVtkc5JyxpiUpDVJaUlZ9zRJjXuE/GDvh9ba3+vXegAAGIaFJhV2YzkhVpKmpnQ+O6/Zs+pW2Msj/nZ2Y+fulNhOh07Qww4AAOC261tg57LWFlUN4SRJxpjPVK+q8yvt9qmiAwCMO3dKrF9hd2/u3qiWc2PndxaDwE7H3kjXMhHcarlOK+wuz2R0KXuzziUAAAAYYwMJ7BpZa78axuMAADBsi+7Qiana0IlxrbCTdHnnnvThV5Ikc8Lf1W6s0wo7Y6qBXm0L7ZzOdaI25wMAAGCi8adbAABuILQl1lR/rI5zhZ3u1OdGTZ3Qw+7GOq2wk0LbYu/obEALAgAAwDgYSoWdJBlj/rqqW2Ir1tqvh/W4AAAMjg1NiT2agAq7UGB3ypTYGwtV2F0T2DnbYud0PqAFAQAAYBwMvMLOGLNhjLmQVJK0K2nPGPNrY8z/ZtCPDQDAIN3RmaaNlSSdT03rfNynxEqaulsP7KZPj0a4kgkRqrC7ZourE+jNUWEHAABwqw00sDPG/D1Vp8T+nqTfrb19q2ql3e8aY/7EGPPXBrkGAAAGxa2uO3XCmKW58Q3spu98Uj8+J7C7sW4q7NwtsYbADgAA4DYb9JbYB9balcYLa1NjM6qGeWVjTMJa+98MeC0AAPTVgqmHMcfT08HxOFfYzcwvB8ezZ8ey1srUKgfRgwsnsLuuwm6aCjsAAABUDXpL7H6zC621X1lrN621q5L+Q0n/uTHmfrNzAQCIKnfgxMnUZAR2U04Pu8XLSx1RZXcz586W2Gsr7OhhBwAAgKpBB3bX/kneWptTtdIuP+C1AADQV4tNJsRK470lVnfqE24X7KUOzw9HuJgJEKqwu27oBBV2AAAAqBp0YJc3xmxcd5K1dkfSpwNeCwAAfbVgnMBuqv43qnGusNOd+tqXLq0OzwjsbiRUYdf50Al62AEAANxuAw3srLVfSXpljPkHxph715z+ZpBrAQCg39wKuw+ywfFYB3ZOdeDCJRV2N9ZNhR1TYgEAAFAz0KETxpiHkrZr764bY3YlFSUVrbX/tXPeZ+pg+ywAAFGyoHoY895cBseLc4ujWE5/uD3srNXHs48jXMwE6KbCzgn07tDDDgAA4FYb9JTYvKTN2nFS0m/X/tnaxLmiJE+Stdb+rWZ3YIz5B9bavzvgdQIA0DV3Suw7Ww/sxrrCLrQl9lLv2BJ7M11V2LlDJ6iwAwAAuM0GHdi9stb+0L3AGPM3JKWdf/7lGUl+BV65dtt3klIDXiMAAD1xp8R+rNWJz03NaW76mkqqKAttibX62TkVdjdy7gR2102JDQ2doMIOAADgNht0YFcyxvx7krZq4ZustX8o6Q9Vq7yrBXgp1avvfluqNgIyxniSYgNeIwAAPXF72B3Vhk6M9YRYKTQldunyUkdnRyNczAS4cLfEdt7DjqETAAAAt9tAAztr7dNaILdpjFmW9KUf3Dnn+AHe70pXKvAeSk4XbwAAIiQ0JdZU5ziN9XZYKRTYLdpLetjd1DlDJwAAANC9QVfY+YHc3+nyfLcC758PaGkAANyIW2F3OCkVdg1bYg8J7Hp3eSHZi+qxmZKmr/lv1zQ97AAAAFA1NeoFdKA46gUAANCMO3Ti0NQCu3GvsJuZ0/lUNViakXRy7I10OWOtm+o6qaHCjh52AAAAt9nAK+xuylrbcXUeAADDFK6wq/4NbHF2cVTL6dj3f/j7ba8v353RSi0w+o//y3+qv/+ftD/f9/WPfufGa5so7oTYmQ4GkczcDQ7pYQcAAHC7jUOFHQAAkTSvqxV29+butTp9bHxQvdJrybAltmfnzsCJTirs2BILAACAGgI7AAB6tGjcKbHjU2F3nXBgdzjClYy5UIUdW2IBAADQOQI7AAB6tOBuiZ2UHnaSPqq+NXPJ+RjRpVCFXQdbYp1z7lBhBwAAcKtFvocdAABRNS5TYrvtLff2//J/kP7szyRJf/VbM/q//7vNb39dL7xbr+sKO3rYAQAAoIoKOwAAeuROifW3xE5ChZ25U+/DN3X6YYQrGXOhKbGdDJ1wt8QS2AEAANxmBHYAAPRocUK3xE7dvR8cz5yxJbZnF86W2E4q7EJDJ+hhBwAAcJsR2AEA0IMpXWreVAOZS0nHJrpbYrs1fTdWPz47Gt1Cxh0VdgAAAOgRgR0AAD2Yl7Md1kzLTlCF3ezd5eB47pwKu56dd9nDjqETAAAAqCGwAwCgB+6E2KNaWCdJi7OLo1hOX03f/SQ4vntxrrNLwqOeuEMnprsbOjFn2BILAABwmxHYAQDQg0Xj9q+r/zi9N3ev2eljxTg97BYvL3V4djjC1YyxUIVdJ1ti3R52hKQAAAC3GYEdAAA9WHS2xB46P00nocJOTh++RWsJ7HrlDp3opMJu2u1hR4UdAADAbUZgBwBAD9wtsYdT9S2xk9DDTnfqVYKLl5c6PCew60nXFXb1wO6OTtucCAAAgElHYAcAQA9CW2Jrgd38zLymp6ZHtaT+aQjsPp59HOFixli3FXbulFh62AEAANxqBHYAAPTAnRJ7OEETYiWFt8ReWirsetX1lFh3Syw97AAAAG4zAjsAAHrgVtgdTVV/nC7NTUhg51TYLVgq7HoWmhLb3dCJO/SwAwAAuNUI7AAA6IHbw+5o0irsnMBu6ZKhEz07d7bEUmEHAACALhDYAQDQgwVnS+zR1IQFdqEtsZcEdr3qusKuHtjdNWeSbP/XBAAAgLFAYAcAQA/mTb16Kqiwm5QtsTN3dGGq/0WYlXR88m606xlX3VbYTU1LUzPBu7O6GMCiAAAAMA4I7AAA6IE7dOKoFm5NTIWdMTpzAqazo/0RLmaMdVthJ7EtFgAAAJII7AAA6Emoh11tS+zi7OKoltN357PzwfHFiTe6hYyzbivspNDgCQI7AACA24vADgCAHswbt8JuwrbEKhzYXR6zJbYnoQq7DgM757w7BHYAAAC3FoEdAAA9CA+dmLAtsZIu5+rVgpbArjfnTmA30+GWWKcSb86c93lBAAAAGBcEdgAA9CAU2JkJmxIryTqBnU7fj24h4+zC2RLbaYXdDD3sAAAAQGAHAEBPJn1LrO7cCw7NyccRLmSM9VJhF9oSS4UdAADAbUVgBwBADyZ9S+zUnfv149MPI1zJGOupwq4e7N3RaZsTAQAAMMkI7AAA6MF8sy2xE1RhN3X3k+B4+vy4zZloKVRh12lgdzc4pIcdAADA7UVgBwBADxacLbGHU5PXw27aCexmT49GuJIxFpoS2+mW2Pp59LADAAC4vQjsAADowYLqVWd+hd3i7GKr08fO7N1YcDzjBk/o3LmzpdWpnGtrxu1hR2AHAABwWxHYAQDQA3dL7LGp/ji9N3ev1eljZ2Z+OTieOz+VtXaEqxlTF70MnaifN8vQCQAAgFuLwA4AgG5dnGnOXFQPJZ0aychofmZ+tOvqo+k79S2xC5eXOjpnW2zXznsZOlE/b47ADgAA4NYisAMAoFunH4PDI2MkY7Q0u6QpM0E/Vufq23sXrNXh+eEIFzOmLnoYOuFW2DF0AgAA4NaaoN8sAAAYkrN6eHVUGzixODc5/eskSXfqAzQWLi91eEZg17VQhV33W2LpYQcAAHB7EdgBANCtUyewq1XVTdKEWEmS049v8dLq49nHNiejqRtW2LElFgAA4PYisAMAoFtOeOVX2E1eYFevGFy0l2yJ7Za10kUPFXYzDJ0AAAAAgR0AAN07qw9gODK3YUssFXZdawzraq+Ta027QyfYEgsAAHBbEdgBANCt0NCJ6o/Se7P3Wp09ntyhE5dU2HXt3NkO2+mEWImhEwAAAJBEYAcAQPeaDZ2YnbAKO6eH3YK1Ojylwq4rboXdTIfbYRvOpYcdAADA7UVgBwBAt0JDJ6qB3b25Cauwm57R2dRM9VDSyfHb0a5n3PShwo4psQAAALcXgR0AAN1qMnRi4irsJJ051V5nR/sjXMkYOj+uH3dTYTfN0AkAAAAQ2AEA0L1Qhd3/n737jpPrrO/F/3nO9O1F26SVtFr1YluW3O0YG9uAKQZj+0JoCRB6GtxfYshNIYEbMAkJIcm9l24gBLBNcQVXjC3cZMmy1ftKWmlX2/tOPc/vjzN7znN2Z2ann92Zz/v14qXnzHnmzCOxtrXf/ZZ4D7tSy7ADEHX7rXVoxLmDLEa2oRMZZNi51aETDNgRERERlSsG7IiIiDIVmVsSW4oZdjFPwFqzJDYzaklsthl2HDpBREREVLYYsCMiIsqUMoBhKl4SW+Wpcuo0BaN7rYCdDE04eJJFKNsMO5c6dII97IiIiIjKFQN2REREmYrMLYmt8pZewE4qWYMyNO7gSRYhW4YdS2KJiIiIKDMM2BEREWVK7WFXwhl28Cl9+cLMsMtITJ0Sm11JLAN2REREROWLATsiIqJMKVNig6J0A3bCZ/2ehPJ7pjRElZLYTDLsGLAjIiIiIjBgR0RElLnw3KETpVgSq/lqzLUrPO3gSRahPGTYcegEERERUfliwI6IiChTag87zfhPaSlOiXWpAbsIA3YZyTbDzs2hE0RERETEgB0REVHmlCmx00JASg1+l9/BAxWGO1Bvrj3qEAWany3DLpOSWA6dICIiIiIG7IiIiDIXmTV0IuaHiJfGlhKPnwG7rNmmxGZZEsuAHREREVHZYsCOiIgoU7YedhqkXnrZdQDg9teaa78eRSTGEs20xZSS2Ewy7JTgnk/wz5uIiIioXDFgR0RElCllYuq0JiD1DAIyi4jwVZvrSl1iKjqVYjfZ5CHDjiWxREREROWLATsiIqJMKQMYpoSAjJVmhh2UybcVusRUhAG7tGWbYafsZUksERERUfliwI6IiCgTum7rYRcUAijRDDtbwE7qmFQyC2ke2WbYcUosEREREYEBOyIiosxErey6aSEghSjZHnbwWQE7lsRmKOsMOw6dICIiIiIG7IiIiDJjGzhhTIYtj5JYZthlxJZhl13AzitiENDzeCgiIiIiWiwYsCMiIsrErIETACD1gFOnKSwlYFcpmWGXkZgSsHNlUBIrBKB5zEsOniAiIiIqTwzYERERZcKWYRf/z2ipZtj57Bl2HDqRgahSEptJht2s/SyLJSIiIipPDNgRERFlIpKgJLZUe9i5vIjFg5IeAMHgqLPnWUyyzbCbtZ8ZdkRERETliQE7IiKiTIQTlMTGSrQkVgiElaml4eCQg4dZZGwZdhkGdDl4goiIiKjsMWBHRESUiXLKsAMQVYJNUWbYpS+W5dAJAHCrgycieToQERERES0mDNgRERFlwpZhZ/xntGSnxAKIeZSA3fSIcwdZbKK5lMRaAT6WxBIRERGVJwbsiIiIMqFk2AVFiU+JBRDzVFgX4XHnDrLYxHIYOsEedkRERERljwE7IiKiTITnlsSW7JRYALrXCtjpIQbs0pZLhp1aEguWxBIRERGVIwbsiIiIMhFJMHSihHvYwVtpLiUDdunLU4Ydh04QERERlScG7IiIiDJhy7DTIHU3ID0OHqiwhK/aXGtK/z6ahy3DLoeSWMGAHREREVE5YsCOiIgoE0oPuylNlHZ2HQDNV2OuhfJ7p3nYMuwyLYlVh06wJJaIiIioHDFgR0RElAl1SqwQkLHSHTgBAC4lYOeKTDt4kkUmXxl2LIklIiIiKksM2BEREWUiYi+JRYln2Ln99ebaFQk6eJJFJqYE7DLNsGPAjoiIiKjsMWBHRESUCSXLbFoTkCU8IRYAPIE6a61mjVFqUaUkNqcMO5bEEhEREZUjBuyIiIgyMbskVi/tkliPkmHnj0UQ1ZnxNS8pZ2XYZRiwUzLyPCKWp0MRERER0WLCgB0REVEm1JLYMsiwU6fEVug6JiOcFDsvPQpI3VgLF6C5Mnu/i0MniIiIiModA3ZERESZCNt72JX60Al4q8xlhZSY4qTY+UVzyK4D2MOOiIiIiBiwIyIiyoiSYTatiZIfOgGfFbCrZIZdemJq/7oMB04AtpJYBuyIiIiIyhMDdkRERJmwZdgJyFIP2M3KsJuMMmA3r7xm2LEkloiIiKgcMWBHRESUiUi5lcRWmktm2KVJHTiR6YTYWe/xCGbYEREREZUjBuyIiIjSJaV9SmwZDJ2AbeiEZMAuHVGlJNbNklgiIiIiyhwDdkREROmKhQEZAwBEAESFgNRLPcNuVkksA3bzyznDzgrYeRiwIyIiIipLDNgRERGla1Z2HQCg1DPsPAHoMH6vfikxFRpz+ECLQK4ZdkrAzscedkRERERliQE7IiKidM3qXweg9IdOCIGIEnSKTI84d5bFItcMO2VQhZc97IiIiIjKEgN2RERE6Zo1IRZA6Q+dABBxW0HJSHDYwZMsErYpsbll2LEkloiIiKg8MWBHRESUrsisgRNSA6THwQMVR8xjBeyiDNjNL6aUxObYw87LklgiIiKissSAHRERUbrC9pJYY0KscO48RaJ7Kqx1cNzBkywStgy7XAN2zLAjIiIiKkcM2BEREaVL7WGnCaDUJ8TGSa8VsJMcOjE/W4ZdFiWxbpbEEhEREZU7BuyIiIjSpU6JFSKeYVcGvFXmUoYnHDzIIpFzhp31Hp9gSSwRERFROXI7fYBCEELcDuBdAIbiLzUAuFNKeSJPz+8E8LiUcnU6+wB8A8BuACfiZ+qMn+9GKeX2fJyJiIiKIGIfOiHLJMNO+KqttRK0pCRsU2I5dIKIiIiIMldyATshxL0A6qSUNymvbQOwSwhxh5TyiSyfWwcj0PYxAB/N4K2dAO5K8PoIgBuyOQsRETnEVhKrQcayyJ5ahDRfjbVW/gwoiahSEptNhp2bPeyIiIiIyl1JlcQKIT4K4HYAd6ivSyl3A7gTwL3xwFumz70dwJMwgnX3wgi2pesEjOw6xN/3BIxsv/r4uYiIaLEIl2eGnctfa60ZsJtfHjPsOCWWiIiIqDyVWobdXQDuk1KOJLh3D4zS1M/BCN6lTUp5H4D7Zq6FyGgi4H1Syow+j4iIFqjZQyfKpIed219nrSOh5BvJkGuGndLDjiWxREREROWpZDLs4mWvdTAy2uaIB/FGkFk5KxERkcU2dEIrmww7T6DeWkfDkFI6eJpFwJZhl2NJrGDAjoiIiKgclUzADsYQBwA4nmLPCQB18WEQREREmZmVYVcuU2JdSg+7Cj2G6ei0g6dZBHKeEssedkRERETlrpQCdtviv6aaBDtzjwE7IiLK3JweduURsIMyJbZCSkxGOCk2pViuJbHsYUdERERU7kqph11DBnvrCnWIROLluh9TXmoA8I1sJ9YSEZFDImpJrICMVTh4mCLyVprLSl3HZGQSTWhy8EALXDSfQyeYYUdERERUjkopYFeXwd5Mgnu5uh0ApJRmwC5ekrtLCPElKeVX0nnIwYMHsX379oT3du3alY9zEhHRfJQMuylNA2Ll0cMO3ipzWSElJqPMsEsp1ww7N4dOEBEREeVTsnjKwYMHi3yS9JVSSWwm6or0OUMA7pw9JVZKeQLAlwDcFc++IyKixSAyqyS2bAJ2VoZdha5jSvlzoASiOQ6d0NzQpTGR3i10aNDzdDAiIiIiWixKKcNuxOkDzBafTHtfktsz5bDfApA41KvYuHEjM+mIiJymTonVRNlMiVV72FXqEn3sYZeaOiXWnUVJrBCIwA1fvH8ds+yIiIiIcpMsnrJ9+3bs3r27yKdJTyll2A1lsHekUIdIl5Ry5iuCGXZERIuEVDLLgmWVYaeWxOqYiEw4eJhFIKqUxGaTYQcgpPxM1cfBE0RERERlp5QCdiPxX+tS7Jm5l0lwLytCiDohxO1CiFTnmdnLoB0R0SIgw1agagoeQHocPE0R2YZOSJbEzifXDDsAYVhfWxw8QURERFR+SilgNxOESzVQYuZeMfIdPwfgXhglr/M5UeCzEBFRPqhDJ/QymRALzB06ER538DCLQB4y7CJKhh1LYomIiIjKTykF7B6P/7o6xZ5OACPxoQ/F8niiF+OTYhE/z0jxjkNERFlTMsumZGWKjSVG0xBxWZli4ekR586yGNgy7LIL2IWlFbDzCpbEEhEREZWbkgnYSSnvg1EWm7C8NB4gqwNwT5GOtBPAx6SU30xy/8b4r8U6DxER5UKPQYsZmVM6gGm9jAJ2AKJK4CkaHHbwJIuALcMuu5JYNcOOJbFERERE5adkAnZxXwJwY5K+cbfHf71z9o14v7m7hBC3z76XrXgA8aYUPezuhBFgnHMeIiJagJQJsUEhgHIqiQUQ9VgDNqLBUQdPsgjkI8OOPeyIiIiIylpJBeyklF8B8ASAJ9XX40Md7gJwR5Ly048C+EsYPedSigfg6uLrzpSbjWDcvepQiXhwcKZM9gaWwxIRLRJKOex0OU2IjdO9VoBSD405eJJFIKoE7LLMsAvbMuxYEktERERUbtzzb1lcpJQ3CSE+Gg+K7YYRXGsAsF1KmWzYxBMwBj88kehmPOA2MzxCDdIdF0LMPPNL8aw69SwnhBB3ALgrHtybGXrxhJTypgx/a0RE5CQ1YKcJSL28AnbqpFjJgF1q0Xxk2HHoBBEREVE5K7mAHQDE+8Yl6x2XaP9upBhWEb+/PcuzjAD4WDbvJSKiBSSsZthpZZdhJ5VJsWp5MCWglsRmOSXWPnSCATsiIiKiclNSJbFEREQFo06I1cqvJFZTAnaCAbvU1KET7nwMnWBJLBEREVG5YcCOiIgoHUqQyuhhV15DJzR/rbVWgpeUQD4y7JShEyyJJSIiIio/DNgRERGlw9bDTiu7HnYuJWDnikw7eJIFTtcBXQmwuTzJ96ag9rDzMWBHREREVHYYsCMiIkpHuLynxHr89ebaHQk6eJIFbnZ2nRBZPYZDJ4iIiIjKGwN2RERE6YjYS2JRZgE7NcPOH4siHAun2F3G8jAhFgDC0srM8wr2sCMiIiIqNwzYERERpUPNsCvDoRPCZw2dqJASE5EJB0+zgKmBTFd2AyeA2UMnmGFHREREVG4YsCMiIkqDtA2dKL8edlCmxFbqOiY5KTaxfGXYsSSWiIiIqKwxYEdERJSGSGjUXEddHkC6U+wuQV5m2KUlTxl26pRYL1gSS0RERFRuGLAjIiJKQyQ4Yq6lp8yy6wBALYnVdQbskslThp2tJFYww46IiIio3DBgR0RElIZI0Mqwg7fSuYM4xVYSKzEZYUlsQrYpsdln2IUke9gRERERlTMG7IiIiNIQC4+ba00JXpUNNWAnmWGXVFQpic2phx1LYomIiIjKGQN2REREadBDVsDO5at28CQOUbIKK3TJoRPJ2DLs8lQSyww7IiIiorLDgB0REVEa1CmxLl+NgydxCHvYpceWYZdDSSwz7IiIiIjKGgN2REREaRCRKXPt9dc5dxCneK2swkopMamUCJMiTxl2YcmhE0RERETljAE7IiKiNIjItLn2BuqcO4hTXG5E4hljGoDI9Iijx1mwbFNis8+wYw87IiIiovLGgB0REVEaXEogxu9vdPAkzol6Ksx1LDjk4EkWMFvALpD1Y8JKDzsfe9gRERERlR0G7IiIiNLgUQN2lU0OnsQ5MWXwhB4cdfAkC1g0aK05JZaIiIiIssSAHRERURq8MStoUlFRngE7qQyekAzYJWbLsPNn/Rh16IRPMGBHREREVG4YsCMiIppPLAqvHgMA6ACqyjRgB2U6rghxSmxC+cqwU4dOMMOOiIiIqOwwYEdERDSfyKS5nBICNf5aBw/jHKH8vkWIU2ITylOGnb0klj3siIiIiMoNA3ZERETzCSsBO01Dna/OubM4yOWvM9fuyJRzB1nI8tbDjhl2REREROWMATsiIqJ5xJR+bVNCoMZbk2J36XIHGqx1ZNrBkyxgzLAjIiIiojxgwI6IiGgek5N95jrocsOtuVPsLl0uJWDnj4ZgdPQjm0L0sOPQCSIiIqKyw4AdERHRPCYnz5vriNvr4EmcpfmtzMIqXQe0UIrdZSpvU2KtrzNm2BERERGVHwbsiIiI5jE9NWCuozlkTS16PjVgJyEYsJvLlmGXS0kse9gRERERlTMG7IiIiOYRVAJ2MU/AwZM4bFaGnXAFU2wuU3kqiQ0pPex8zLAjIiIiKjsM2BEREc0jND1krqW30sGTOMxXbS4rWRKbWN6GTlgZdj4RAaTM5VREREREtMgwYEdERDSPaHDEXAtvlXMHcZqv1lxW6xJCY4bdHHnKsJPQEJEu64UYy2KJiIiIygkDdkRERPOwBeyULLOyM7sklhl2c+Upww6wZ9khxj9rIiIionLCgB0REdE89NC4uXb5a1PsLHFKsJI97JLIU4YdAISVPna2QCARERERlTwG7IiIiOYTnjCXXn+9gwdxmDolVrKHXUKFyrBjwI6IiIiorDBgR0RENA8RnjLX3kAZB+w8AejC+KuDTwJeMenwgRagfGbYSSXDjiWxRERERGWFATsiIqJ5uCLT5tofWOLgSRwmBMIeK2usWkyk2FymCpZhF87pWURERES0uDBgR0RENA+3kjUVqGxy8CTOi3oqzHW1xoDdHIXqYccMOyIiIqKywoAdERFRClJKeJTspsrKZgdP4zzdW2muq8VUip1lKo8ZdiFm2BERERGVLQbsiIiIUpiOTiOg6+a1L9Do4Gmcp/uqzHU1GLCzk3nNsAvBa10ww46IiIiorDBgR0RElMJoaBQV0grYCSVgVY6EMim2BtMpdpYfD2IApHGheQDNldPzwpJTYomIiIjKFQN2REREKQyHhlGhS+sFb5kH7Py15roSwRQ7y48XEesix3JYYHYPO5bEEhEREZUTBuyIiIhSGAmNoFIpiS33gJ0WqDfX1YJZXyqfLWCXWzksMHtKLP+siYiIiMoJA3ZEREQpjE0Nmp3EYhB5CcQsZm41YCcZRFKpAbugAP56x1/jvY+8F/ccvge6UladLmbYEREREZUv9/xbiIiIytfE1HlzHXF74RLCwdM4z6MM3aiSERg928r7z2SGT1hBtd7QCO4/fj8A4LX+1/DIyUfwhau+gOU1y9N+HnvYEREREZUvZtgRERGlMD3Zb64jZZ5dBwCuQJ25rpY6ICLJN5cZn7CGcIRnBXZ3nd+F9/3qfRiYHkj7ebYMuyj7BRIRERGVEwbsiIiIUghODZrrmCfg4EkWCGVKbJWuQ7gYSDJIVDc+bl6FNQ0f3vJhfHDzB+ESxrTYoeAQ/vnlf077ibYediyJJSIiIiorDNgRERGlEJq2AnbSU+HgSRaI2QE7jQE7AHDXvIrKqoPmdXPNCvz59j/HZy75DL7++q+brz984mE8f+75tJ4ZsmXYsSSWiIiIqJwwYEdERJRCJDhsXfgqnTvIQuGrNpdVug5oDCQBEt4lT8EnpflKU3W7ub62/Vrc3HGzef3FF76IUGz+Pzdm2BERERGVLwbsiIiIUohNj5lrTckuK1t+NcNOsiQWgKvyCFy+PniVgJ1w+217/uLSv0CVpwoAcHr8NO4/dv+8zw1LZtgRERERlSsG7IiIiFLQQ1bAzsWAHUtiE/A2PgMA8EnlRbfXtqepogkfu/Bj5vXPjv5s3ucyw46IiIiofDFgR0RElIIMT5hrj7/ewZMsELNKYss9YKf5z8JdeRwA4NWVG7My7ADg1rW3wqsZgbwDgwdwcPDgnD2qEJSgHzPsiIiIiMoKA3ZERERJRPUoXNFp89oTYMBOzbCrlBJCm06xufR563eYa/fUUuuG2zdnb62vFjeuvNG8ni/Lzp5hx4AdERERUTlhwI6IiCiJ0dAoKnQrbUpTssvKlsuNiMvI/NIAVGrjzp7HQcFoEO6a/ea1a2qVdTNBhh0A3L7udnP98ImHMRWZSvp8ew87lsQSERERlRMG7IiIiJIYDg6jQlcak3k5JRYAIh4rGFVTxgG75889D6EZgTQ9tATeSIV1M0GGHQBc0nIJVtasBABMRCbw2KnHkj6fGXZUcLoO7PhX4BcfB/oPO30aIiIiUjBgR0RElMRQcAiVkgG72aLKn0ONmHTwJM564vQT5joyvgU+RKybSTLshBB459p3mtePdaUK2DHDjgrs+X8Hnvg88OqPgW/fBBz/jdMnIiIiojgG7IiIiJIYCg3ZSmLhZUksAOhKaXA1JlLsLF0RPYLfnLGCG9HxLfAJNWCXOMMOAN6w8g3m+qXelzAdTdwHMKRm2EXLe7gHFcDpF4En/t66Do0CP7od2Df/BGMiIiIqPAbsiIiIkhiaHkIFM+zm0AN15rpOJO/BVsp29uzEeNgoB9YjtdCDy9LKsAOA9up2dNZ2AgBCsRB29u5MuM+WYRdjhh3l0dQQcN+HABmzv65HgYc+zanERERECwADdkREREkMh4ZnZdgxYAcAwm9Ny62T5RmwU8tho+NbAIi0A3YAcG37teb6me5nEu4JSzXDjgEUyqMX/g8w1m2s/XXAhx4DquNTjoOjwImnnToZERERxTFgR0RElMTQ9JB96ASnxAIAtIoGc12H8ivV1KWOp04/ZV5Hx7YAwKyAXfKSWGBuwE6qmZxx9gw7BuwoT6QE9t5rXd/8FWDF5cAF1gRjHHig+OciIiIiGwbsiIiIkhgKDqFCMsNuNndls7muLcOA3dHhoxgMDgIA9GglYtPG1FefUMpW58mw29q8FdUeIwDcM9mDYyPH5uzh0AkqiHOvAMNdxtpXA2x6u7He9A5rz6GHgFhk9juJiIioiBiwIyIiSmIoOCvDjgE7AIC3ygrY1ejlF0h6qfclcx2b6sTMX6cyybDzaB5cufRK8zpRWWxYHTrBDDvKF3WoxIa3AJ54cHnZNqCm3VgHR4CTiUu1iYiIqDgYsCMiIkpiKDiESluGXZVzh1lA3BVN5rpWxgBRXpk4toDd5GpznUkPO8BeFvvs2Wfn3GeGHeWdrgP7f2ldb7nNWgsBbLrFuj5wf9GORURERHMxYEdERJTEcHAIAVuGHQN2ACCUHna1ug6hlU9ZbEyPYVfvLut6qtNcZ5JhBwBXL7vaXL/W/xpCs7LoQpI97CjPul+yhk0E6oHO6+z3Z8pjAeDQw0AsWrSjERERkR0DdkRERAlE9AimQqNmjpPUPIDb6+iZFoyANSW2NqYDrvIJ2B0aPoTxyDgAYElgCfSwlW3oE5ll2C0JLEFHTQcA4+tt38A+2/2QWhLLDDvKB7UcdtPbAZfHfr/9MqCq1VhPDQA9e4p2NCIiIrJjwI6IiCiB0dAoKnWrHFawf53FX2cuyy3DbmfPTnN9aeulAIR57YM6dGL+DDsA2NayzVzvPr/bdo9TYimvpAQO/9q63nzr3D2aBqyySrXR/XLhz0VEREQJMWBHRESUwOD0IKqUgB38Nc4dZqFRMuxqyixgp/avu6z1Mtu9THvYAcDFzReb6919KQJ20ZARcCHK1sARYPS0sfbVACuvTryv/VJr3b0z8R4iIiIqOPf8W4iIiMrPcGgY1Wr/Ol+tc4dZaPzWn0W1rsPlnkLMweMUS1SP2oJqRsBur3mdaQ87ANjevN1c7+nbg5geg0tzAQB0aIhKDW6hA5CAHp1bwkiUrmNPWOvO1yX/Wmq/xFp378TR4aP4zr7voHu8G+vq1+Hi5ovxxo43wutiiwAiIqJCYoYdERFRAkPTQ6i2ZdgxYGdyuTEd7+enAajWxpw9T5EcGjqEycgkAKC1shXLq5fb7mfaww4A2qvbsSSwBAAwEZnAsZFjtvv2LLvyyWSkAjj6uLVec2PyfS1bAFc84DxyCh/95a14+MTDeLX/Vdx75F781Y6/wvt/9X6MhkYLe14iIqIyx4AdERFRAsOhYZbEphDyVJjrOq08vnF/tf9Vc72teRuEELb72ZTECiGwrdnqY7fr/C7b/TAHT1A+hCeBU7+zrlMF7NxeyKUXmZebg9NzthwYPICPP/5xjIXLI1hPRETkBAbsiIiIEhicHkQNM+ySCnutgF29KI9v2vcOWOWvFzZdOOd+NiWxgH3wxCt9r9jucfAE5UXXDiAWD/g2bQRq21Nu3+cPmOsLg2FcvfRqfO26r+GDmz9o7Rnchz9+8o8R1aMFOTIREVG5Y8COiIgogTkZdj5m2Kmi/mpzXSfGHTxJ8ezttwJ2Fyy5YNZdaZ8S68ogYNdsnxQrleES9gw7BuwoS7Zy2BtSbn2x50X8YPSAef0Gdz3+303/DzesvAGfueQz+Nsr/9a890rfK7j/2P15Py4RERExYEdERJQQe9ilFlOGcNSKSQdPUhwjwRGcHjcmbLo1NzY0bLDddyMGl4gH2jQ34Ep/rte6+nWo9FQCAPqm+9Az2WPeC0k1w44lsZQFKe0DJ9belHRrRI/g8899Hnt81tfdyvFBQLfGytyx7g58/KKPm9f/sec/MBWZyu+ZiYiIiAE7IiKiROZMiWUPOxsZUAJ2KP1v1vcN7jPXG+o3zJmQmU3/uhkuzYXNjZvN6wODVnYTM+woZwNHgeGTxtpTCay4MunWB48/iO6JbvS6XBiIB51FeALoP2zb96EtH0JzoNl4/PQAvrf/e4U5OxERURljwI6IiCiBoSAz7FLRAg3mug5zm9KXGls5bNPsctjs+9fNSBawC4EZdpSjI7+y1quvT/r1GYlF8I1Xv2FcCIGJFiWLtHunbW/AHcCfbPsT8/rufXejf6o/b0cmIiIiBuyIiIgSGgoOsYddClrFEnNdK4MOnqQ4Xht4zVzP7V+XW4YdAGxq3GSu9w/uN9e2oRPMsKNsHHnUWq97U9Jtvzj2C5ybPAcAqPfVY+m6t1k3e/bM2f+2zreZpeHBWBD3Hb0vL8clIiIiAwN2REREs0RiEYyHx+0BO2bY2birmsx1nSztQJKUEvsGrJLYhAE7oWS/5ZhhZwTsjHLssFRKYjklljI1NQScfiF+IYB1b0y4LapH8a293zKvP7jlg/C2X2ptOLdnzntcmgsfvuDD5vUvjv4CMaXXHREREeWGATsiIqJZhoJDAIAaW8COGXYqX2WLua6VpV2q2T3ejZHQCACgxluDlTUr5+zJNcOuvbod1V5j8u5oaBTCMwxgdoZdaf85UwEcewKQ8SDasu1AVXPCbTvO7kDvZC8AoMHfgHetfxew9GJrw/n9QCwy532vX/561PnqAAA9kz14sefFvB6fiIionDFgR0RENMtwyAiWVKlDJ3zMsFP5q9vMdY2c+418KZldDiuEmLMn1x52QghbWazLfxbArIAdM+woU4eV/nXrk5fD/vzoz831O9a8AxWeCqCiAahdYbwYCwF9B+e8z+vy4q2dbzWvf3b0Z7mfmYiIiAAwYEdERDTH0LSRYcehE8l51Qw7PQaI0g3aqUMgNi/ZnHBPrhl2gL0sVvN3A5g9JZYZdpSBWAQ49qR1ve7mhNsGpgfwTPcz5vWta261bi69yFon6GMHAO9c+05z/dSZp8wMZSIiIsoNA3ZERESzDAYHASln9bBjSaxKBOrNda2uQ2ilO3ji8NBhc72pYVPCPT6RW4YdgPkz7KKl+2dMBXDqd0Bo1FjXLgdaEgeb7z92P2LxstntLdvRUdth3WxTAnYJ+tgBwNr6tbiw6UIARi+8h44/lOvJiYiICAzYERERzdE/3Y+AlFaoxO3POghTsgJ15rI2pgOuaefOUkBSShwetgJ26xvWJ9zngzp0IvcMO1egG4Dk0AnK3kElcLb+ZiBBKbeUEr889kvzWs2WAwC0KX3skmTYAfasvCdPP5l0HxEREaWPATsiIqJZ+qf67dl1PmbXzeEJYDr+1wgPgEptzNnzFMj5qfPmwIkqTxWWVS1LuC/XHnYAsKxqGWrjvRKFKwjhGUKIQycoG7oOHHrYut74toTbXu1/FV1jXQCMr++bVt5k37B0q7Xu3Zdw8AQAXL/8eggYAcE9/XswHBzO9uREREQUx4AdERHRLAPTA6hWB06wf11Co5qV/VUnSvMbdLUcdn3D+oQDJ4D89LATQthKbl3+s/Yedsywo3Sd2w2MnzPWgQZgxVUJtz126jFz/caONyLgDtg3VC4BatqNdSwE9B9K+JzGQCMuajLKZ3Wp49mzz+Z2fiIiImLAjoiIaDYjYMf+dfMZFV5zXecadfAkhXNoyApQrK9PXA4L5KeHHQBsaNhgrjV/76wedsywozQdfNBar78ZcLnnbJFS4slTVvnqnOy6GWqWXc+rST/ydctfZ66fPvN0mgclIiKiZBiwIyIimmVuwI4ZdomMCiswVSdKsyRW7V+nBtNmy0eGHWA08J+h+XrZw44yJ6U9YJekHPbg0EGcmzSy8Ko91bis9bLEz2vbaq3PvZL0Y69ffr25/t3Z3yEcY4CZiIgoFwzYERERzdI/zR526RiBVT5XsgG7ofkHTgCzh05kn2G3rn6duXb5emf1sGPAjtLQfwgYOm6sPZVA5/UJtz1x6glzfd3y6+BxeRLuwzJl8MSZl5J+bGdtJ5ZXLwcATEWnsLN3Z2bnJiIiIpu5+fFERERlbCoyhcnIJDPs0jCqBOzqxYSDJymMycgkTo+fBgC4hRur61Yn3etF1LrIIcNuVe0quIUbURmF5h1CWO2Zx4wlSseRX1vrtTcCnrlfjx2ffRgVnb+EKx5bvue3dfjvhx+esw8AqjCFV30CLiER69mLCz97HyYRSLjX17wC3sYzAIAP3XM3Dn/66tx+L0RERGWMGXZERESKgekBAJg1dIIZdokMocpcN2DcwZMUxpHhI+Z6Vd0q+FzJM+fy1cPO6/Kio7bDvI64p6ybzLCjdHTtsNZrEvel07x9cPn6AQBS9yA6uTbhPgCYQAUOyxUAAJeQuFg7lnRvdMIamuKuOpJ0HxEREc2PATsiIiJF/7TxTay9JJYZdokMSCuQuQSll2GX7sAJAPCrJbEpAnvpUPvYRd2T1g1m2NF8YlHg9AvWdcc1Cbe5q/eb6+jEekB6E+6bsVO3SrUv1Q4n3RebWgmpG6W1mncI5ybOpXNqIiIiSoAlsURERIqZgB1LYuc3IOvM9RI5lXzjIqX2r0s1cAIAAlCy3zyJywXTta5+HX518lcAgIhnHGa1LTPsyk7HZxOXqSZzkTiG+31G8PysbMTVX9kP4MCcfYGV1td2dHzTnPuzvayvxx/gcQDAdpE8YAe4EZtaCXeVkYX38vmXcUvVLen/BoiIiMjEgB0REZFicHoQwOyAHUtiExmQDea6UQYdPElhHB0+aq7VYRCJBIQSTPNW5vS56mdFvWPA9MwFA3aU2hXaQXP9gr4RgJi7SQvCFThtXsYm16Hry29J/eDRi4B//Q8AwDX+LnR9/g1AgiEVHZ99GLGp1WbA7qWel3DLagbsiIiIssGSWCIiIkX/FDPs0tWvKwE7vbSCSVJKHBuxenWpZaqJBNSS2Dxk2M2IekesG7HS+jOm/LtcCdi9qG9MuMddeQxCGP9+i00vg4xVJdxnU9sO1BoTYBGZBHr3Jt0aneo01y+ffzmNUxMREVEiDNgREREprB52ytAJHzPsEumPNZnrJXokxc7Fp2eyB1NRo8y3zleHRn9jyv0VtpLY3DLsWipaIGPGZM+IS5k+yww7SsGFmK2/3At64lJXV6U1DCI6mTpz1GbFFdb6zItJt+nT7ZC60RPv7MRZnJ04m/5nEBERkYklsURERAprSiwz7OYzrC9BDIALQK2MAdEw4E7dvH6xULPrVtethhAJSgsV9pLYipw+WwiBWLAN7sqTCKsfy6ETZS9l6erZXcC34vXT1UvxzN99EJj1dSulxBt+9jX0xmeZ/OR9f4htLdvS+/DllwN77zXWp58HrvhEko0uxKY6zCmxO3t3YtmaZel9BhEREZmYYUdERKRIPHSCGXaJ6Lofw5r1V4nIRI+Dp8kvNWC3pm7NvPvzOXQCAPRQKwAgpAZcoqXXJ5DyqOt31rrjmjnBOgA4OXoSvZO9AIBqTzUubLow/eevuFJ50LNALHlWbUwpi93ZuzP9zyAiIiITA3ZERESKgSlm2KVPw6DSeH5qpMu5o+TZ8ZHj5jqdgF0+S2IBK2AXtgXsWBJLKahlqh1XJ9yy4+wOc3152+VwaxkU2zRvAqqXGuvpIeDkb5NujU7aA3ZSyqR7iYiIKDEG7IiIiOIisQiGQ8PQpESl+Q2mALzVjp5rIRvQrBLY4MjpFDsXl9klsfPJZ0ksAOihZgBAkBl2lK5+q38d2rYm3PLcuefM9dXLEgf1ktI0YPOt1vW+nyfdqgeXQcaMfzf0TPaYWX1ERESUPgbsiIiI4gaDgwASDJzQ+J/LZAaFz1xHxkqjubwudZwYOWFeZ14Sm3uGXSxsBOxsGXYRBuwoiVgEGD5pXS+ZO9U4Eotgd99u8/rKpVfO2TOvLbdZ64MPpcj6dCEWXGFevTbwWuafRUREVOb4HQgREVFc4oET7F+XyoCw+rVFx0ujh93Z8bMIxozgWIO/AfX++nnfU5HnHnaIVUKPVjLDjtIzdBLQ4xOFa5cD3rlB470DezEdNYZSLKtahmVVWQyCWLYNqFtprEOjwLEnk26NTS8316/1M2BHRESUKQbsiIiI4vqnjIETVexfl7YBoQQGJvqcO0geqeWwa+vmZirNpkGHX8w04Bf5CdjBKIvl0AlKy8ARa50guw4AXup9yVxf3nZ5dp8jBLDlndb1vp8l3RqbVjLsGLAjIiLKGAN2REREcQknxPqYYZfKAKrMtYgP7Fjsjo9aAyfS6l9ny66rSDidMxt6uGVuwI7N+ykRW8BuXcIt6rTWS1svzf6z1LLYw48AU0MJt+lKht2BwQOIpJgqS0RERHMxYEdERBQ3UxJbw5LYtA3C+vNxJ/nGfbE5OnzUXKcXsAtbF3nKrgMAPdQEKYT6dE6KpcTmybALxULY07fHvL6s9bLsP6tlC9C0wVhHpoAn/yHhNhmrwvJqI2gX1sM4NHQo+88kIiIqQwzYERERxfVNGSWd9TElYFfR6NBpFocBvc5c+4Kjzh0kj46PWBl2a+vnL4kNCKVUNQ8TYmfooRYAYFkszW+eDLtX+15FWDdCvx01HWiuaM7+s4QAbvhb63rX3cDZ3Qm3Xth0obnm4AkiIqLMMGBHREQU1zvZCwCo12PWi5VLHDrN4tCPOnMdCE44d5A8iekxnBy1pm121nbO+56KPE+InaHHJ8WGNAbsKAUpgQErKzRRwE7tX5dTdt2M9W8G1tw0cwDgkf8PUDOT4y5cYgXsXu1/NffPJSIiKiMM2BEREcX1TBpTThtsGXYM2KUyGGvAzJ9WIDINxKKOnidX5ybOmZlISwJLUOubf+hIoUpiZbQaMuZnhh2lNnEeCI0Za18NUNUyZ4utf11bDv3rZggB3HwX4PIa12d3Ab+9a862i5ouMtccPEFERJQZBuyIiIgASCnNDLuGGDPs0hXVKzGiGX+d0ABgkQ+eODlmZdetql2V1nsCQsmw8+Yvww4QcyfFRhiwo1lm96+bNfQkGA3aylEvbclDwA4AGlcD13zGuv7tl3Gz9qJty7r6dfC5fACAsxNnzT6hREREND8G7IiIiACMhccwFZ0CADSqgzgrm5w50CIhdT8GXS7rhYk+5w6TB5mWwwJABZQgmid/PewAIBZuZoYdpTZP/7p9A/sQ1Y3M11W1q9AYyGNfzmv/Aui83rz8quf/Yb04bV57XB5satxkOwsRERGlhwE7IiIiWP3rAKBJVwIkHDqRWiyAQZfy14nJxR2wOzF6wlynm2Fn72GXv5JYAHMz7Biwo9ls/evmDknZ07/HXF/cfHF+P9vlBu74HtBgBLcrRAhf8HwPgPVTj82Nm831wcGD+f18IiKiEsaAHREREYDzU+fNdYPaPJ0lsSnJWABDtgy7fucOkwdqht2qmvQCdn6h9LDLa0ksA3aUhnky7Pb07THXW5u25v/zA/XAu38MaB4AwGXaYbxRs3rmbWzcaK4PDB7I/+cTERGVKAbsiIiIAPRMGAMnICWqI0rGFIdOpDS7JFaWUklsXbolsWqGXX5LYvXZJbHsYUezpZgQq0vdlmG3tXlrYc7QvAG47CPm5WfdP4YHRhnupgarJPbAEAN2RERE6XI7fQAiIqJC6vjsw2nt8zbtgG8JUCUl3NLIsJuUPmz+298U8niLn/RgIJ5ZAwDR8XPwpNi+kA0HhzESGgEABNwBNFc0p/U+W8DOm9+AnYzUISSsn69OB4eR36JbWtRiUWDsrHVd32G73TXWhdHQqHHLV4+OGvv9vLr2LzD6/N2oFVNYpZ3H+12PA3g7Omo74Hf5EYwF0TfVh4HpASwJ8AchRERE82GGHREREQDNMwLAPiF2SNY4dJrFZUD4zXV0/JyDJ8mN2r+uo6YDmkjvr0l+UbgMO0BDULf+fAfGu/P8fFrUJvuA+A8YUNEIuH2222o57EXNF0HMmiCbVxUN+Hr0VvPyg65fA1LCrbmxvmG9+Tr72BEREaWHATsiIiIAwh3PQolZ/esGwYBdOs4Lq2+bVLN9Fhlb/7o0B04AhS2JBYCgtJ45NFO6TQQAY8rXQ/XSObdf6XvFXBekf90sP4y9AWPxr9flWj/Q8yoAYGMD+9gRERFligE7IiIiJM6wG2SGXVp6RbW5do0t3gw7W/+62vT61wGFLYkFgKBuBURHGLAjlZrRWtM257aaYZf3CbEJhOHBE/o264WDDwIANjVafewODjHDjoiIKB3sYUdERGWl68tvmfOaLnVs/6+/RlQHGpQMuxu2b0LXO+buJ7seUWuuPRP9gK4D2uL7mWC2GXaBgpbEAkHdCoiOTy3uKbyUZ7YMO3vAbjg4jK6xLgCAR/Ng85LNRTnSo7FL8U7XDuPi4APADX9jD9ixJJaIiCgtJRmwE0LcDuBdAIbiLzUAuFNKeSL5uzJ6fieAx6WUqxfCeYiIKDeD04OI6sZEw6XCa92oZGP0dEzq1RjRNNTpOjQ9Ckz2A9UtTh8rY2oPu4wCdgUuiZ2OWZmeE9ODeX8+LWK2DDt7SayaXbepcRN8Lnt/u0L5rX4hpqQPFSIEDBwB+g+js7ETXs2LsB7GuclzGAmOoM5fV5TzEBERLVaL78ff8xBC3AvgY1LKO6SUH5NSfgzAlwDsEkLcmMNz64QQ24QQ3wBwHEBatTKFOg8REeVPz6SVpbJUUwJ2FQzYpUPGAuh1u6wXRhffYIRgNIhzE0bwQxMaVtasTPu99pLYyuQbsxSMWhmMwelh6FJPsZvKSooMu1f6i9u/bkYQPjytX2S9cOABeDQP1tWvs14aYh87IiKi+ZRUwE4I8VEAtwO4Q31dSrkbwJ0A7hVC1GXx3NsBPAngYwDuBTDi5HmIiCi/eid7zXWLVAJPlU0OnGbxkbofPW4laX9s8QXsTo2dgoQEACyrWgavyzvPOyz2kthAvo+GkLSCgC49avt6pTKXIsPu1b5XzXUx+tepfh271Lo4+AAAYGMjB08QERFloqQCdgDuAnCflHIkwb17ANQB+FymD5VS3iel3B7PkHvC6fMQEVF+qRl2jbq0brAkNi0yFkCva3Fn2J0aO2WuO2o6MnpvoUtiQ/CYa5+U6Brtyvtn0CKVJMMuHAtj38A+8/qi5otQTE/pFyMk40H83teAiT5saNhg3j8ydKSo5yEiIlqMSiZgJ4TYBiMAlrAvXDxoNgLgo+V4HiIiSk7NWKqNRqwbFY0OnGYRigXQq2bYLcKA3enx0+Y6k3JYoAglsbCy/XxSmoMEiDCuBOyUDLsDgwcQ1sMAgOXVy7EkUNwfPkygAq9JpXtM906sb1hvXh4ePlzU8xARES1GJROwgzHUATD6yyVzAkBdfGhEuZ2HiIiSOD913lxXhqesGyyJTYvUA+hZ5D3s1Ay7TAN2hZ4SG5JWhp2fATuaERwDwhPG2uUDAvXmrVf7nSuHnfGKvta6OPMS1tathYAAAHSNdSEUCyV5JxEREQGlFbDbFv811eTVmXvFCJAttPMQEVESM8MGICW8oXHrBkti0yJjFfYedos8YLeiZkVG7w0gbF0UIGCnZth5WRJLM2zZdW2AEOblK33KwInmrUU8lGW3GrDrfhkVngosr14OANCljmMjxxw5FxER0WJRSgG7hgz21hXqEIqFdh4iIkrizPgZAECVlND0qPGip7IgAwRKkYxVLPopsblk2NlLYgvbw86vM8OO4sbUgRPLzKWU0h6wK+KEWJUtYHduNxCL2spi2ceOiIgoNff8WxaNugz2ZhJMy1ZdBnvnPc/Bgwexffv2hPd27dqVwUcREZFqNDSKsfAYAKBNKv9ZZHZd2mQsgH6XCzEALgCY7AOiIcDtc/hk6ZkIT2AoOAQA8GpetFa0pv1eDTp8wuh7qEsBze3P+/mC0p5h1zPZg2A0CH8BPosWkfHEAye6x7vNr+dqbzVW160u9skAAH2oB2rajanRkSmgbz/W1q/F46ceBwAcGWbAjoiIiidZPOXgwYNFPkn6SinDLhN1Th9gljqnD0BEVK5Oj1nDBtb7lSETDNilTcYqEBMCfeqk2LGzzh0oQ6fGrey65dXL4dJcKXbbVSBorqfhtZUl5ostw04aU4y7xxdfFiPlmS3DzgrYvdJvZddd1HQRNOHgX/eXX2qtz7yE9fUcPEFERJSuUsqwG3H6ALOM5PNhGzduZCYdEVEBzJTDAsBqT611o4IBu7RJD6TuQa/bhbZYzHhttBtoWBwtWk+N5qd/3RR8yP+M2Lk97AAjyLimfk0BPo0WDVuGnTUhdiGUw5raLwX2/8JYd+/E+k1vNm8dGT4CKSVEAYLcREREsyWLp2zfvh27d+8u8mnSU0oZdkMZ7B0p1CEUC+08RESUwOlxK8Nuhab0H+OE2IzIWGDW4InFmWGXy4TYaVmYEuBEGXZnxs4k207lYmzW0Im4PX17zLVTE2JN7ZdZ6+6dWFq5FFWeKgBGOwJ1QjcRERHZlVLAbiT+a12KPTP3MgmmZWtk1mcmMnOvGOchIqIE1Ay7NqH2sGtMsJuSWcyDJ9Sy6FwGTkyjMAG72T3sAHugmcrUuFISG8+wGwuP4fjIcQCAS7iwZckWJ05mabsQcMW/fodOQEwNYl39OvM2+9gRERElV0oBu5mgV6oBDjP3ipHvuNDOQ0RECagBuyW6tG4wwy4jRsBOzbBbPBlguUyIDRQhYJcow04NMlKZSpBh92rfq5AwvkbWN6xHhSf/U4sz4vYBbRdZ12d3Y229NT2WATsiIqLkSilg93j811SjsDoBjEgpT5TheYiIKAE18FEXnLBu1Cxz4DSLl4wF0LNYh04oAbsV1Rn2sFNKYqcKVBKbqIcdM+zKXCxqTGOeUWVMNt7Tv8d8yfFy2BltW631+b1Y36AMnhji4AkiIqJkSiZgJ6W8D0YZ6rZE94UQnTBKUO8px/MQEdFck5FJDAYHAQBuzQ3/5IB1s3a5Q6danGSs0t7DbmRxZNiNBEcwFh4DAATcATRXNGf0frUkdqpgGXZWwC4gJSAleid7EYqFUryLStrEeUDqxrqyCXAbXyNq/7qtzVuLf65EWjZb6/P7bSWxR4ePOnAgIiKixaFkAnZxXwJwoxCiLsG92+O/3jn7hhCiTghxlxDi9tn3nDgPEREVR/e41WetvaodQu27VtvuwIkWr7lDJ84AUiZ/wwLRNdZlrldUr8h4YqUasAsWKGCnQwM0qyzWA0BC2r5+qcwkyK6L6BHsHdhrvuz4hNgZrRdY6/P7sabOmm58auwUIrGIA4ciIiJa+EoqYCel/AqAJwA8qb4uhNgG4C4Ad0gpRxK89aMA/hLAvfN9Rjz4VhdfdxboPEREVARqWeGayqXAlJFtB80DVLU4dKpFKlaBMZeGMS0e8IpMARN9qd+zANimBNdkVg4LAP4ilMQCANx+6zN19rEre2o2cJXRb/PI0BFMR6cBAG2VbWitbHXiZHM1bQAQ//fCwFFUwoW2SqPnXlRGbSXpREREZHHPv2VxkVLeJIT4qBDicRjDHOpgDHfYLqVMNtzhCQAn4r/OEQ+wfSt+qQbpjgshZp75pXgZbD7OQ0RERaAGPDa5a6wbNUsBraR+plVwMmY0t+92u7EpHM+YGe4Cqhd24DOXgRNAcUpiAQAePxAeB8A+dgRgst9axwfkqP3rFkw5LAD4qoCGVcDQCUDGgP5DWFO3Bj2TxtCMYyPHsKZ+zTwPISIiKj8lF7ADACnlNwF8M4P9u5FiOET8/vZinYeIiIpDnRDbKaw+YajLPNOq3Ek9ACBBwG7F5c4dKg1q0DbXgF2hSmIB2DPsOCmWEgTsXul7xXxpwZTDzmjZbATsALMs9tmzzwIwAnZEREQ0F9MHiIiobKkBu+UxpXcZ+9dlbCbD7ozH6rWG4ZMOnSZ9uWbYOVESO5Nhd2qcpYRlyxawWwIppS1gt2AmxM5osfexW11n/Zz8+MhxBw5ERES08DFgR0REZUstKWyOhK0bDNhlTC2JNQ13OXOYNEkpbQG7FdWZZ1YWrSQ2QYbdmbHFMYmXCkDtYVfZhN7JXvRNGT0jK9wVWFu/1qGDJWGbFLvXVgLLDDsiIqLEGLAjIqKyNB2dxvnJ8wAATWiomR61bjJglzEzYOdZPAG7weAgpqJTAIBqTzUa/A0ZP8NeEutNsTNHHiVgF/+1Z7IH4Vg48X4qbbNKYtXsuguaLoBbW2Bdb9SAXe8+dNasgogPojg9fhqhWCjJG4mIiMoXA3ZERFSWToycgISRqbSiegW0sbPWTQbsMiZjVg870wIP2HWNdpnrFTUrIIRIvjkJv7ACZsUqiV3qMwKLEhLd492F+0xauGaVxC7oclgAqFsJeKuM9fQQAsExLKtaBgDQpW77Z5GIiIgMDNgREVFZOjJ8xFyvrV8LjCrlhbXLHTjRIic9CLgD6HG7EJ15bbwHiEw7eaqU1JLoFTXZDRqxl8T6U+zMUYKAHcBJsWVLLYmtWIJX+181Ly9uWoABO02bVRa7z1YWe3TkqAOHIiIiWtgYsCMiorKkfoO4tm41MMoMu1zVeGsQEwI9tiy7hTsYIdeBEwBQgaC5ni5oDzvr2Ut99eaak2LLkJS2DLtJbwUODx8GAAgIXNB0QbJ3OmtWWeyaOitgx8ETREREczFgR0REZenYsNXofLOvGdAjxkWgAfBWOnSqxa3OVwdg8ZTFqsGubAN2AWVK7LQsZA+7gLlsif85A8ywK0uhMWCmd6GnEq+NHoMudQBGtnC1t9rBw6Vgy7CzT4rl4AkiIqK5GLAjIqKyZMuw05RSRmbXZa3WVwsAOLNIBk90jXWZ65XV2QXsKpWS2MmClsRaGXZNHisgwwy7MmSbELsEe/r3mJcLsn/djBYl8+/8fqytsybZqj9AISIiIgMDdkREVHaGg8MYmDa+6fW7/GiOKJM22b8uazMBO3uG3UmHTpOaLnWcGbf6Fmbbw65GTJrrMVTkfK6k3FaG3RJPlblmhl0ZmjUhdk/fHvNya/PWoh8nbc0brfXAYXRULYUmjG9Fzk6cxXR04fa7JCIicgIDdkREVHaODlvZdZ11nXCNnbNuMsMua2bAbhFk2PVN9SEUM7Lj6n315tkzVYMpcz0mC1hKrWTY1bl8EDAm2vZM9iAcCyd7F5UiJWAnK+0DJ7Y2bXXgQGny1xjTYgFAj8I31IUV1UagXELixOgJBw9HRES08DBgR0REZcc+cGItMNpt3WTALmu13nhJ7CLoYaeWw2abXQddRxWsrKDxQmbYKT3s3LEYWitbjSNIHWcnziZ7F5UiJWA36vZiMmJkeTYFmrCsaplTp0pPyxZrfX6/bfAEy2KJiIjsGLAjIqKyo2bYra1nwC5fkmbY6bozB0ohHwMnEBqDJiQAYEwGoBfyr1VKhh2i07YgI/vYlZnJQXN5TkbM9dbmrRBCOHGi9LWqAbt9tsETnBRLRERkx4AdERGVnTkZdmoWGHvYZW1mSuyEpmHKEx/AEA0CE+edO1QSp8ZOmeuZsryMBUfM5RgKPFlY6WGHaMh2ZvaxKzNKht3x6Ki5XtDlsDNmTYq1ZdhxUiwREZENA3ZERFRWdKnbSq/W1q0GBpXMjsbVCd5F6ajx1Zjrfp8SwFqAZbFqwG5lbZYZdkErWDIuC1gOC9gz7CLTtqxAZtiVGSVgtz/YZ64X9ITYGWpJbO8+BuyIiIhSYMCOiIjKSs9kD6aixqCAWl8tloSDwMx0wopGoKLBwdMtbjM97ACgx+u3biz0gF117gG7gk6IBWw97BANYXm1lQnKDLsyo2bYRcYAGNOuNzRucOpE6avvADzxf1Ym+7BSC8AtjBL6nskesx8fERERMWBHRERl5uDgQXO9tm4txKCS1dG41oETlY6ZklgAOON2WTeGTxb/MClE9Si6J6y+hVkPnVADdoWcEAsAbiUAGmWGXVmbHDCXQy7jr/Kbl2yGR/M4daL0aS6geZN56Rk4YvtaZh87IiIiCwN2RERUVvb07THXFzZdCKgBuyVr5r6B0lbnrzPXJzVp3VhgGXY9kz2I6lEAxmTNSk+WwTYlYDda8B52asAuhPbqdggYAwbOTZ5DJBZJ8kYqOUqG3aBmBMYXRTnsDFsfu31YU8+yWCIiokQYsCMiorKyp3+Pud7atBUYsAZQYMm6op+nlMxMiQWAIyJs3VhgATvbwIlss+uAWRl2he5hpwTsItPwuXxoqWwBYPRlPDtxtrCfTwuDHgOmrCmxI/EMu8UVsFMnxe63TYplwI6IiMjCgB0REZUPEcGBwQPm5UXNFwEDR6z7LInNiUfzoNpbDQA47VJLYrucOVAStv51NVn2rwOK3MPOnmEH2HvvsY9dmZgaAmBkrw5rGmLCyLK8qOkiBw+VodkZdsrgCZbEEhERWRiwIyKisqH5zyGiG6WDK2tWosHfMKsklgG7XDX4jaEd590uSM1oJo+J80B44TSTV3u+rajOIcNuesRcFruHHQAsr1EGT7CPXXlQymFn+td11nbaslsXPDVg138Ya5TAszrBm4iIqNwxYEdERGXDFbAyqy5qusgIIo3FSwk1tzHBkHJS76sHAOhCIFTVYt0YPpXkHcWnZth11HRk/6BiZti552bYqcFGZtiVCVvAzshi3dayzanTZCdQB9TGg82xMJaHQ+bAjL7pPoyFx5w7GxER0QLCgB0RERVf30Hgp+8D7vswMN5btI9VA3Zbm7fas+vqOwDXIpiyuMDV++vN9UR1k3VjAZXFlkIPO8AesDszfqawn08LgxKwG9aMv8Zva15kATvAlmXn7juEVbWrzGtm2RERERkYsCMiouKREtj9A+Cb1wMHHwT23Qd8/xZgoq8YHw5XhRWoubjpYg6cKAA1YDcSqLNuDJ8s/mESiMQiODd5zrxeXr08xe55qFNiZVUux5pfgh52akksA3ZlYnLAXM5k2G1v2e7UabI3q4+dOnjixOgJBw5ERES08DBgR0RExfP8fwAP/InZgwsAMHDYCNop34gWgvAMQXNPAACqPdXorOu0B+wa1yR5J2VipiQWAPr9Sl+3BZJh1z3RDV3qAIC2yjb41cy1TDlWEmv889Ne1W6+dHb8LKJ6tLBnIOcpGXaDLhfaKtuwtGqpgwfK0uxJsbVWwI6DJ4iIiAwM2BERUXFEw8Cz/2Jd168CRHySaP9B4NefK+jHuwJWj68Lmy+EJjRgUM2w48CJfFAz7Hq8PuvGAgnY5a0cFnCuJDaeYVfhqUBTwCg7jsooeieLV15ODpk1dGLR9a+bYQvYcVIsERFRIgzYERFRcRx9FJgeMtY17cAnngNu/YZ1f//PC9rPzl11xFxf3HSxsbBl2DFglw8zU2IB4JRL+WvGAgzYrVSmU2bFlmFXxCmxkWmjvBz2kl4OnigDs0piF2X/OgBo6LS+psd7sEbJzD0+yoAdERERwIAdEREVyys/stZbfx/wVgAX3gGsuNJ4TY8Cu+4u0IfH4K46ZF5d234toOv2oRPMsMsLNcPuhIhZN4ZPGX/mDjs9ZgW1csqwi0WB8DgAQJcCE8ihtDYdLrcxyRgAIIFYGIA9YNc93l3YM5Dj5KTV73PIpS3O/nWA8fXcvNG8bJ8ctSbFTnFSLBEREQC4599CRESUo4k+4Ohj1vVFv2+tL/sIcPp5Y/3yd4FrPgO4vXn9eFdFF4TL6PvVWtmKDQ0bjIyvyJSxIdAAVDTm9TPLla0kNjph/LlODQKxEDDeA9Quc/B09gy7jpqO7B8UsgIK4whAFuNnoJ5KIBTP6gtPAm6fLeioBiOpNEXHezAzyzrqr0dnbaej55lPx2cfTnrvLnct3hX/TuSL3/0Zgisa4fIbWdZbv/Rf0KcTZ8B2ffkteT8nERHRQsQMOyIiKrzX7gFkPNtqxZVAo9VgHBtvAapajfXEeeDQg3n/eHfVAXN9Xft1EEIA5/dbG1q3AELk/XPLUYPPKokdDg4bvQrNF7qKf6BZTo3nqYddcMRcjsoCl8PO8Cp98uLBZpbElhmlJHZ56zbj32WL1CFpfe1uFKehh5rNa5e3GJPDiYiIFjYG7IiIqPD2/Le13voe+z2XB7jkQ9b1S9/O84dLuKsPmlfXL7/eWJzfZ21RG6BTTur8deZ6ODQMWd9h3XQ4YBeMBs3BDJrQbFNWM39YEfvXzfAoAbuwEbBbUW0FHc+MnynOOcgRPoThiQYBABEAG5dd4eyBcnRIWl+7G7TT0MNWwE7znXfiSERERAsKA3ZERFRYYz1AXzybze0HNr1j7p7tf2hNjD39nPGePNF856F5jWEXMubDpa2XGjcYsCuIgDuAgDsAAIjoEURqWq2bo84GlNSA1tLKpfC4PCl2z6OYE2Jn2DLsJgEA7dVW0LF7vBu6dL5PIBVGA8bN9ZDLhe2tlzh4mtwd1K2A3XrRDS24xLzWfMywIyIiYg87IiIqrJn+dADQfingr5m7p7oF6LgaOPmMcX3kV/asuxyo5bDRifVWkKZXDdhtzstnkaHeV4/pqNEzcKKiAWaR7IizJZu2CbG1i2hC7AyP8jlhI2BX66tFra8Wo6FRBGNB9E/1o6WypTjnoaJa4raGioy43UYvzgUm4/5y//pFYPQMfCKCJ/7HNtz8/E8AAO0tY3j8U8azUvXBIyIiKmXMsCMiosI6/YK1XpGihGu98o3eoUfy8tG61OGp3W1eRyc2GYvQBDB80lgLF9C08L7xXczUwRMjASVAu5ACdtU5BuymR8ylIxl28ZJYgGWx5aLJf9RcRwP1cGsl8HP3pReby9bRs+bvqXeyFxPhCadORUREtCAwYEdERIV1+jlrnSpgt+HN1vrkb4HQePK9aXqm+xloPqNJu4z5ER3faNzos7LusGQt4PHn/FlkUQN2A96AdcPhgJ06lCGngRPArAy7YgXslAy7eEksYB88wYBd6WryWl+/nuo2B0+SR8u2m0t3z6u2yc0nRk84cCAiIqKFgwE7IiIqnOCoNY1VaED7Zcn31q0AWi4w1rEwcOzJnD/+hwd+aK4jI5cB0mdcsH9dQTX4rUmxPW6lT9zYWUCPOXAiQ9dol7lWAwNZUQJ2RZsSayuJtTLsOCm2PDS5rd6eNfWrU+xcRJZts9ZnX0Fnbad5eXzkuAMHIiIiWjgYsCMiosLp3gnMNMFv2ZK4f51KzbI7nFtZ7KGhQ3ip9yUAgJQawkNXWTfZv66g6n1Khl10AqhsMi70KDCev4EimSpchl2RAna2oRNKSWwNS2JLnXBNoFGMmdeNS0qkjL9tKwBhrPsOYH2VFXxmhh0REZU7BuyIiKhwTikDJ1ZcOf/+9UrA7sijQCyS9Uer2XXRsQsgo3XWzZmsP4AZdgVQ568z18PBYSN7coZDZbGTkUkMTBvl0W7NjbbKHEsKnZgS61F72FklsWoPu9NjzLArRa6KLjTErAnAJVMS668x2hIAgIzhIt361uTYyDGHDkVERLQwMGBHRESFk+7AiRltFwE17cY6OGKfMJuBnb078eDxB83r8NA11k1dtwfsWhmwyze1JHY4NAzUWlkzGHEmA0wdONFe1Z57w37He9hZGXbt1e3m+sz4GUgpi3MeKhpX4CQaY0o5+UzWailYapXFdk6MmOsTI8ywIyKi8saAHRERFUY0BJx92bpOJ8NOCGD9zdZ1FtNiJ8IT+Osdfw0JI2gRnVgPPagEjEZPA+H4QItAPVAqmSoLiFoSu1Ay7NTMs5z71wGzMuyK1cMucYZdo78RFW7j3kRkAiOhkeKch4rGVXkCDWrArmKJc4fJN2XwRONQF9zCCKafmzyHKSUwTUREVG4YsCMiosLoeQ2IBo11fQdQk2ZgzNbH7mEgg2whXer4xxf/EecmzwEAarw1CPbcZt90bo+1btliBAkpr9QpsXMDdqcSvKPw1Ay7nPvXAUYGaJzTGXZCCA6eKGHCNQmXv8dWEovKUgrYWRl22rk9tn8+2ceOiIjKGQN2RERUGOdesdbtl6b/vpXXAL74cIqR0/by1RQmI5P4n0//Tzx4wiqF/Zsr/gYyOmvQRfdOa61kdlD+zCmJVQN2o86UxKpBrJU1K3N/oCNTYtUMO3vmEQdPlC5XxQlASnuGXSkF7Fq2ADMl6kPHsaXSKvHmpFgiIipnOTZwISIiSkIN2Ck9iuYzKSMYW7oFbSefAwA88us/wbOrr0C1txptlW1YWrUUSyuXorWyFQAwFh7DM93P4GdHf2bLonpb59vwplVvAvCw/QPO7rLWmQQSKW1qht1QcGhBlMR2jXWZ63wH7JyZEjtpu6Vm2J0ZY8CulLgqjqNKSnhnXvBU2rMtFzuP3wja9ewBAFwec+GB+K3jo8cBrHfqZERERI5iwI6IiArDFrC7eN7tp8ZO4fv7v4+HTzyMayf68U/x11ee24c7xUBGH/2+je/DZy75zJzX3YjOyvy7JKPnUnqqPFVwa25E9Simo9MIVjXDP3NztNsY/KEVN8lf7WGXc8AuGjJLUqNSwxR8uT0vXR4lSDMrw44lsaXLVXm8dLPrZiy/3AzYbZ4cM182MuwYsCMiovLEklgiIsq/0AQwcNhYCw1ovSDpViklfnLoJ7jtgdtw75F7MRWdwo6KACLx+5vDYbREo2l9bMAdwBev/iLuvOxOeDTPnPsbxGmrr17tCqC6NZPfFaVJCIEGn1UWO6SHgED8OhYGJs4X9TyjoVFzEIPP5UNzRXNuD1TOP4BaAEXqg2jLsJtVElvNkthSJNxjcPn6Z/WvK6EJsTNWWkOJ2ga7zDVLYomIqJwxw46IiPKvdy8g499gLlkP+KoSbgtGg7jzmTvx1JmnbK+PRlrxoiuGa2I9AIDrz63D3b4N0DwjEJ5haJ5hCPcYABege6CHmxAZuwDj45vxZ3vd+LPZZbBxF2vHrAtm1xVUY6ARfdN9AIDB6UEsrVsOTA8ZN0fPpD+EJA/UctgVNSugiRx/Xjneay7Py/oUG/NMLYMMT9husYddaXJVGEMX7Bl2JRiwW3GVuQycPwD/ijYEoePcxDlAhAHpTfFmIiKi0sSAHRER5d+53dY6STlsJBbBp5/+NHac3WG+Fgu2InT+FsSmVuFB19O4xvMtAMDtkWP41uRHkGsm01YG7IpmScAq2xuYHjD62PW8arwwchpYflnRztI12mWuO2o6cn/geI+57CtmwC5FSWxzRTO8mhdhPYyh4BAmwhOo8iYOlNPi4ao0/p3VWOolsdUtQEMnMHQCIhbC67VaPKIPQ0JC8/VBD7bP/wwiIqISw5JYIiLKv3n610X1KO589k5bsC48dBWmuj6F2FQnAIGHYldgUhq9wdZr3bhYHJvznEzZnsGBEwWlBuz6p/uNEuQZI6cSvKNw1Ay7/ATs1Ay7utyfl64UJbGa0NBebQU1mGW3+Ekp4a4wSkLrS70kFrBl2f2ebuUUaN4+J05DRETkOAbsiIgo/9SA3bK5E2L/c89/4vFTj5vXH7vwYwidvwWQVt+5SQTwUMzqa/Qu129yOlIdxtGpxQMtmgdovTCn51FqasBucHpw1qTY4gaT1Ay7VbWrcn+gkmFX1JJYjxKwm5VhB9j72HHwxOJ3ZvwMNO8wAKBBbeNZqgE7pY/dFmXwhOZjwI6IiMoTS2KJiCi/gqPAYDyTTXMDLZttt1/qeQnf2fsd8/p9G9+HT239FP75p4/Y9nV9+S3AmSbgO08DAN4d2Il3/3//BfiqszvXkceA/46v2y4EPP6U2yk3c0pi65XA7Uhxg0kFzbCDQz3sIpNzbjPDrrQ8d+45c90Y9gMYNS5KNWC3wgrYLRvuhlaxBLoQcPmKO6SGiIhooWCGHRER5ddMnzIAaN4IeALm5UhwBJ/b8TlISADAlW1X4i8u/QsIkaQ3XfulxtAKwAhQ7L03+3OdsspvsYz96wptTkmsmmE3WrxgUkyP4fSYFSDsqO3I/aFO9bBzeQHhMtZ6FIiGbbc5eKK0qAG7lohyo3ZZ8Q9TDA2dQFULAMATmcbasPGbZoYdERGVKwbsiIgov1L0r/vSS19C35TxzVe9rx7/+5r/nXpipxDAtg9Y10/+AzB2LrtzHVIy+FZfn90zKG1zSmJrl1s3R84AUmb/8JPPAmdeSmvruclzCOtGYKvR34hqb5YZmqpxK+OnqCWxQqTMsltebf0Zq0FKWnwiegQ7e3ea16160LpZs9SBExWBELYsu0tDxj+3wjMEiEiydxEREZUsBuyIiCi/kgTsdp3fhUdOWkGzL1z9BTRVpFHate0DVrBnehj4xccBXU/9ntn6jwCDR421pwLovC6z91PGmgLW/7cD0wNAoA7w1RovRKeByYHsHvzUF4HvvxX4zk3AM/8073bbhNh8ZNcBzvWwA1L2sWMPu9Kxb2AfJiITAAARrkUzrJ5uqG5z6FRF0HGNubwuHqMTQkLz9jt0ICIiIucwYEdERPmVIGAX02O466W7zJff1PEmvG7569J7nr8GuPUbAOJlsyd/C/zqL4HQRPpnOvywtV79eluZLhVGY6DRXPdP90NKCdSpWXZZBJRe+pY9SPfUF+cN2uW9f11kGgiOGGvNg2FU5f7MTKSYFNtW1QZXvGS2b6oPwWgQtDip5bB14+1wiXhGamUz4PY5dKoiWP16c3nR5Bjc8UxcjX3siIioDDFgR0RE+TM1BAx3GWuXF2g2Bk7cf/x+HBw6CADwuXz4zPbPZPbcjquBaz5tXe/8FvDv24CXvzunj1dCajnshrdk9tmUlQpPBSrcRnApokcwFh6bNSn2VGYPPPxr4JG/mPv6U18Edv8w6dvyPyHWGjiB6lbIYv9VyqOUxIbtJbEezYO2Siv7qnu8u1inojyz9a+btMrLS7YcdkZDJ1C3EgDgj0VxYSgEgH3siIioPDFgR0RE+dOzx1q3bAHcXkxHp/H13V83X/7Qlg+hrSqLkq7r/wroVHrPTZwHHvq0Ebjb/cPkPdHGzwPd8V5QQgPWvSnzz6asqCXPg9ODuQ2eeOoLQHxYCZZtt5c1P/f1pP//F3JCLKpbc39eplJk2AEcPFEKRkOj2DewDwAgpUBTSPn/vKZEB07MEMLWY/SqaSNLlBl2RERUjtxOH4CIiBafjs8+nPD1T7rux196jPUPTzfgbz77MDz1O+BvHQQA6JEafOWnbfjKTxK/PyWXB3jfz4HXfmIMn5jpIzZ6Bnjgj41S3Df/E6C57O878iuYgZ4VVwEVDZl/NmWl0d+IU2NGJt3A9AA6a7MsiR06AZw3Ahhw+YDf/6lR1vzP64zBCwNHgN69QNuFc96a9x52Sv86RwJ2KXrYAbMGT7CP3aL0/LnnoUujT6cebEebVDIpS3VCrGr164FddwMArpwO4j/qAZeXGXZERFR+mGFHRER5c4F2wly/JjsBEYG38RnztfDg9YD0Zv8BmgZsfQ/wJ7uAm/4BqFBKxV7+DnDPB4weYzOiYeDFb1rXLIctKnVSbP90/6yS2Ayyvw6pPQivB6qaAF8VsOHN1uv77pvztsnIJPqmjW/03Zoby6ryEOywZdg50Pw/xZRYwB6wY4bd4vRMt/XvzOjEerSJQetmqZfEAsCqa41saACbQ2HUxGIQ3kFOiiUiorLDgB0REeXNhUrAbq/eCU/dy9A8xnRDPVKNyMgl+fkgbyVw9Z8Bf/4acMEd1uuHHgJ+8Hajlx4APPMVoG+/sXYHgM3vyM/nU1rUktiB6YHsh06oATs16Lrldmu97+dzymLVctjl1cvh1vJQWOB0hp0asEuQYadOimXAbvGJ6THsOLvDvI5ObECrGLI2lHpJLAAE6oGl2wAALgCXB0PxSbFZTpYmIiJapFgSS0REebEEo1gWzwQJSg+Oyhb4G39k3g8PXQtIT34/1FsJ3PpNI3Dy3L8br515EfjuG4FNbwee/Rdr741/Vx7ZKQ6aXSrtbRyAr9lY/+OjL+Ff+3zY4zeuJ/tOYPNnH4I5/TeJJRjFS74XoAkgJgUuvceDoXuMz/Egip2+StSJSWD0DN75V1/DbrnOfK+7Zg8C8fjGke6A7XxdX84y29LpDDtbSezcSclqD7vTYyyJXWz2D+7HcGgYgFFSPh5cijZvmQXsAKMs9uzLAICrpqfxeGUFNN956CEH/pkjIiJyCAN2RESUs64vvwU48hjw38a1f/nF+Nr1HvzVjlEAQIO/Ab/+zN8h4A7k/8M1DXjDF4HqpcCjnzNeGzgCPPNP1p4VVwGXfSz/n00p6dFqcy3c4xhBFSalD5UihEoRQh0mMILqFE8AbnDthiaMzLmX5XoMoca8F4Ebv4pdht93/wYAcIvrOeyOWgE7zdtvnSVkZfvlZE6G3XTSrQVhK4mdm2Gnlv32TPYgokfg0fIcKKeCUcthr1l2Dbpe0WZl2JXJDx1Wv97IkAbwe1NBQEpOiiUiorLDklgiIsqPc6+YS7l0K3500Mque+/G9xYmWKe68pPA7d8FXLN65HkqgHf8pxHYo6KSasDONQ5AoFtagbN20Z/gXXZv1Haa68dic0uqH9CvMtdvcu2EOWAEswJ24SXIiwWVYTc3YOd3+9FS0QIAiMkYeiZ65uyhhevZs8+a62vbr4UGHS0YtjY48TXnhPZLjdJYAC2xGDaGI9C8nBRLRETlhd+9EBFRfpzdZS5PVy/B/kGjd5xX8+L2dbcne1d+bbkN+OQLRsbd1X9uZNV94AGgobM4n082claGHQCclVbgbJlI3ZPKhzCu1vab14/ql87Z86K+EWPSCAa3imG0K8/UfGrArjnD0yehBuyqWvLzzEx4lYBdgqETACfFLlb9U/04MHgAAOAWbly59Eo0YQRuYUyMHZA1gMfv5BGLx+UG1r7BvHzd1DQz7IiIqOywJJaIiHKnx4DTz5uXP5mwhk+8ufPNaPA3FO8sjauBq/6keJ9XxubrAzcwPYDr7/k6AKCxNoQDX34L8PBTwM49AIBvvLUJuCrFM06/AHw3PhmyYTV2/OkfJt73g8uBE08DAHa8pwq44C3QpY4r/vvvMR01tuQlwy40DoSNwCNcPjMDqKg8qYdOAEYfu5fPG/2/To+dBsqk7dlip5bDXtxyMaq91WhTymF7ZAPylCe6OKx7I/DaTwEYAbv/WzfASbFERFRWmGFHRES5690LhIxpsLGqZvyk70Xz1ns3vtepU5HD6n310ITxV42R0AgisQhQq0yKHZ1niumZl6z1iiuS72u/zFp3G4Gqvqk+TEeN/nJ1vjogVpngjRkaV0ryqlsBkXpgRkHYMuwSB+zUDDtOil08njrzlLm+rv06AEBbfJAPAPTKxmIfyVlrbgTik523hMNojkWYZUdERGWFATsiIsrdqd+Zy+N1rYgiBgDY3rIdGxo2OHUqcphLc9myKweDg0CdNcUUI/OUa56xAr9on1sOm/BetxHkOzl60nypo6YjnePOb6zbWjvVS8zWw27+klgG7BaHycgkXjj3gnl9/YrrAWBOhl1Z8dcCK60elddOBaH5elO8gYiIqLQwYEdERLnrsgJ2D8dGzfW7N7zbidPQAtIUsIZMDEwPAHUrrZvDXcnfKCXQbQ2cwPLLk+9tV4ZR9LwGRILoGrOe3VHbkfZ5Uxo8Zq0bVuXnmZmaZ0osAKyotoKi7GG3QEXDtsvfnf0dwrrx2rr6dWbQtdUWsCuzDDsAWPcmc/m66Wm4fByiQkRE5YMBOyIiyomAbsuw+41mfNNZ76vH65e/3qlj0QLRGLCCDP1T/UaPwRmDx4BYNPEbR04BE/ESVF8N0JQiU7OiAWhcY6z1CNDzKrpGu8zbecuwGzhqrZeszc8zMzXPlFjAnmHXPd6NmB4r9KkoEw/8KfDFJuA/Lwee/Adg6IStHPb1K6x/by5VSmLLLsMOsAXsrpgOIuA95+BhiIiIiosBOyIiyskGcQYIjgAAxjwBnPQYPYduWX0LvC6vgyejhaC5wprO2j/dDwTqrHLSWBgYOpH4jWeU7Lr2SwBtnr+y2MpidxYmw27giLVesi4/z8yULcMucUlslbfKLEWO6BH0TbHv14IxchrY/X1j3X8IeParkN+4FntPWgG7G1bcYK7VDLtelGHArnE1jkljGnNASlyJ4w4fiIiIqHgYsCMiopxcrh001y94NbMR/zvXvtOpI9EC0lrRaq57JuPlbM0brQ39B5GQ2r8uVTnsjFl97NQMu1U1eSpftWXYLYCAXZIMO4B97BasI4/OeUmExvG6ESObdGnlUqyvX2/ckBIdwurZdrYcS2IBPBnbbq6vCw1jcHowxW4iIqLSwYAdERHlRA3Y7fQbGXXbmrehs67TqSPRAtJaaQXseifjwYcmJWDXdyjxG7uVCbGpBk4k2CPP7DSDgy7hsgWvshaetKbaChdQ71APO8/8U2IB9rFbsI4+Zq3bLjKXb5swsiVfv+L1EDPTh0fPYIkwpm+PyQC6pdUPspyoAbvXTU3j6PCRFLuJiIhKBwN2RESUNQHdFrB72e8DANy69lanjkQLTEtli7k2A3bNSj+6RBl2oQmgd1/8QtiHSiTTvAnwGNlnYvwcmqIRAMCyqmXwuDzZHN1u9sAJt0Pl3rYMu8QlsYA9w44BuwUiPAWcfMa6fvt/QrqMf2duDEewLhy2lcPi7C5z+ZreCVmmf23fJddhRBj/DLfGYhg4+RuHT0RERFQc5flffiIiyosLxEk0iAkAwKCm4bjHA7/LjzesfIPDJ6OFImGGXfMma0OiDLuzuwAZH5TQvBHw187/QS430Hahebk+bATs8te/bgGUwwKzhk6kCNjV2AdP0ALQ9SwQDRrrJeuB1gsw2HGFeft/BCW2tWyz9isBu1elMqylzMTgwjNah3kdOP60Y2chIiIqJgbsiIgoa6/TXjXXOyoCkELguuXXoUINKlBZU3vYnZ86D13qQNN6a8PgUSAatr+pa4e1XnFl+h+mBALXzATs8jYhVh044dCEWABw+wAR/+ubHgFikYTbbBl2Y8ywWxDU/nXrjB9qPFprDZJ4y8QENF239pzdbS5f1cs3YAcAT+pbzfXK3iRl9ERERCWGATsiIsra61yvmevfBfwAgJtX3ezUcWgBqvBUoNZnZMhF9AiGgkOArxqojQeU9CgwNGvyoxqw67gm/Q9ThlmsDRtBwJKaEAsYQ10885fFzu5hJ6Us9MkoFSnt/evWvhFRPYpvTR5Dv8v463hVaBI4ES/3jEWBc6+Y2/foa4p52gXnN+FrEI2v10yNIjZ61tHzEBERFQMDdkRElJUaTOBiYZQJ6gCeD/hR7a3GNcsyCLBQWVCz7KzBE0ofuz6lj114Cjj7snWdScCuZbO5XBMxMs/W1OUp0LFQSmIBwDv/4Ik6Xx2qPdUAgOnoNAaDnKzpqP7D1tASXy2w4gq81PsSBsOjeLhSCcDu/r7x68Bh8//bHtmAPtQX+cALy1isCbt91tf90N6fOHgaIiKi4mDAjoiIsnKNtg8uYWTt7PN5MeJy4aaVN8HrcqgZPy1YifvYKZNi+5USt+6dQCxeIrtkPVDVnP4HKc/sjETgkhKr6/JQSqjH7EMnGh3OdrL1sUscsBNCoL263bw+M36m0KeiVHqtbGR0XA24PHisy8i4+3l1lXXv8K+A8V5b/7o9ZV4OO+Mp9zJzLQ//ysGTEBERFQcDdkRElJVrNZbDUnrmDdipGXbZlsMCQKAe0XiAzyeBra4a1HhrMj3uXKNnrGEBlU1ARUPq/YWmToqNJB88saJGKYtlHztnqQHfpvUIxUJ47JQRsDvp9WBiZmCKHgX2/Mg+cIIBOwDAb2D9O6P+3B4gEnTuMEREREXAgB0REWVBzupfF8CSwBJc2nKpg2eihUoN2PVM9hgLtSRWzbDLJWAHYLR2qbm+0pXGdNl0LKRyWCCtDDvA3seOGXYOU7+GGtfgme5nMB4eBwAsq1qGyis+Zd3f9X3gzE7zspwnxKqOR9bhpMcNAPDEIsDJZxw+ERERUWExYEdERBlbJ7rRJoYAAGOawD6fF2/qeBNcmsvhk9FClDDDzjYp9jgwPZxb/7q47oCVUbdFz9NfcxbKhNgZPqWEMjyRdJttUuw4M+wcNagG7NbiweMPmpdv7XwrxKZ3AP4644WRU0DffgCALgX26quKd84FTA+14reBgPXCkV87dxgiIqIiYMCOiIgy9jrtVXP9fCCAmBAsh6WkbEMnpuIBO28l0LbVWMsYsPsHufWvizvktv5q0xFMnn2WkR6l/1jTxuT7isWnlPkGR5NuUwN2Z8aYYecYXTeC0nGj1c149uyz5vXbVr8N8PiBre+Z89ZX5BpMoGLO6+VIDzfjtwHrz0I/8itj+i4REVGJYsCOiIgypgbsdgT8aK9qxwVLLnDwRLSQJcywA4DLPmKtX/wmsONfreuOq7P6rJ2wero1jvdl9Yw5zu221su25eeZufArpb4pAnZqD7szEwzYOWa8x5rmG6jHr86/iKgeBQBcuORCrKxZady7/ONARaOxrmwGLvsoPhn+MwcOvEBJN3ZpyzCmCQCANnYO6N3r8KGIiIgKhwE7IiLKTGgCl2qHzcvnAn7cvOpmCCEcPBQtZC0VLRAwvj76p/oR0SPGjS23G0McAGCsGzjxm/g7BHDx+zP+nIgewe9CA4jFr32jZ1P2eEtLcMzqPyZcQMuW3J6XD34lwy40lnRbU6AJfpcxEGY0NIrRUPLgHhXQrHLYh048ZF6+dfVbrXv1K4FPvgh84nngfx4C3vxPOA+HB5wsMOHQMuxQy2IPP+LcYYiIiAqMATsiIspM1w74hJEdcsTjQZ/bjTeverPDh6KFzOPyYElgCQBAQqJ/qj9+ww9c8uG5b7jik1llsp0ZO4MJxHA63pheQNoHWmSj9zUA8bK75o2AdwGUJ/rUDLvkATshBNqr283r7vHuQp6KklEGTozXtOLVfiND2S3ceFPHm+x7q5qAlk0A+4EmpIda8VSFErA7+FDyzURERIscA3ZERJSZY0+Yyx0VfsSCrVhTv8bBA9FikLQs9pIPAS6vdV3fAbz+r7P6jGMjx4xfPR7rxb6DWT3LdO4Va710a27Pypc0M+wAex+7U2OnCnUiSkXpX7dHt4aEXNt+Ler99U6caNGKhVrxbEUAoZmE7vN7gaETjp6JiIioUBiwIyKizCgBu98FAoiOXeTgYWixSBqwq24Btn3AWAsXcMu/Z53FdnzECIwc8yoBu1wz7M4q/euWXpzbs/LFNnQidcDO7I8G4NQ4A3aOUEpiHx23gku3rbvNidMsanqwDVOahuf9futFZtkREVGJYsCOiIjSN3gcGD4JAJgSAq/4fYgwYEdpsAXspnrtN9/0ZeDWbwAffhxYdW3WnzGTYXfck8eAnS3DbgEMnADSHjoBzArYMcPOGUpJ7D4EAQDNFc24eml2g1XKmYzWotpTjScrlaD+IQbsiIioNLmdPgARES0iJ542ly8G/AhOr4SMsCk6za+1wgrYnZs4Z7/p8gAXvTvnz5gJ2J3IV4bd9LAZoIbmAVo253C6PMqgJLajpsNcd412FeY8lFwkCIycBgDoAM64ja/Nd6x5B1zsU5cFgbX1a/F0cAQxAC4AOPMiMN4LVLfO814iIqLFhRl2RESUvjMvmcuXmV1HGSj08INgNIiusS4AwCmPF1LEgyEjp4HwZHYPPbfHWrdsBty+nM6YNxmUxHbUdpjrrrEuSCkLdChKaPgkZoaWnHO7EdaM5mvvWPMO5860yK2tX4sRlwsv+5V/HpllR0REJYgBOyIiSlv09PPmeo/Xj+jYhQ6ehhaTFdUrzHUhSjOPjxyHLnUAwNLaDoiGTuvmwJHsHnpuAfavAzLKsGv0N6LKUwUAmIxMYmB6oJAno9mUctiu+PTiy1svtw0DocxsbNgIAHiqQimL3f9LZw5DRERUQCyJJSKi9EwOwD1iBFrCAPZGN0DGqp09Ey0ay2uWQ0BAQuLc5DlEYhF4XJ7535imQ0NW6ev6hvVAqMZq9t93CEBN4jemshAHTgAZZdgJIdBR04F9g/sAGFl2TRVNhTxdWer47MMJX/+E62HcGf8ynwnYPf3yGnT8JvF+mt/GRiNg93hlAHcODRvZB107WBZLREQlhxl2RESUnu6d5vKgz4up8QXSgJ8WBZ/Lh5bKFgCALnWcnTib1+fbAnb164HmjdbNbPrYSWn7msey7TmcLs98szLsdD3ldrUs9uToyQIdihJZLvrM9Rm3B3qkBtHxTQ6eaPFbU7cGbs2NfrdbKYuVwIH7HT0XERFRvjFgR0REaRk59pi53uP1Izq+QBrw06KxstqaWHp6/HRen314+LC5Xt+wHmjaYN3sP5zgHfMY7gImzhtrX409AOg0lxvwVsUvJBAeT7ldHTzBSbHF1S76zfVZjwuRkcsQH5VAWfK6vFhbtxYA8Gt1Wuy+nzl0IiIiosJgwI6IiNIyefJpc70bnYAecO4wtCgtr7H6dp0ey1/ATpc6jgxbfeo2NGwAmtZbG7LJsDvzorVuvxRYaBM9cxg8QcXTrvWa67MubzxgR7myymIroIv4tzNnXjQn8hIREZUC9rAjIqJ5yVgEjUNd5vWu6aucOwwtWurgiXxm2J0dP4vJiDEJtsHfgKZAE+CpAYQGSB0Y7oIfIQSRwZTX0y9Y6xVX5O2seeOvAcbPGet5Bk+oGXZdo12FOxOZur78FkDXEf3i+4F4xfLGzhvxi4/+vrMHKxGbGjbh5/g5RlwuHK1fhvVDZ4wb+38BXP1nzh6OiIgoT5hhR0RE8zp59CH4432yzrvd6J5klghlbkVNYQJ2h4atDLp19esghAA8fqB+VfxVidWiJ7OHqhl2yy/P/ZD5lkGGnfrnfnbiLCKxSKFORYqhgYNw6zEAwIim4bYL/tDZA5WQmQw7APhVlVoW+3MHTkNERFQYDNgREdG8Tuz9qbk+37ASkF4HT0OLlS3DLo8lsYeHrB51GxqU3nVKH7s1ojv9B06PAH0HjbVwAe2X5HjCAvCrAbvRlFsD7gDaKtsAADEZw5nxM4U8GcX9Zu/3zfWQvwrbmjmoJ1/W1a+DSxhl6veIKUhX/L9JPXuAYfZpJCKi0sCSWCIiSkmXOmJnXzKvK1ddB7BNEGVhebXVw+7cxDlE9Ag8mifn56oBu/UNSu+65g3A4YcBAOu0brM0cV7dOwFIY916AeCtzPmMeeevtdbzlMQCRllsz6SRZdg11oXOus5CnYwABKNB7D/2K9wWv65o2mhkflLOOj5r/DNdsWoJXP7zGNcEno6twvUw/j3whX/+Cr4Te3PGz+368lvyek4iIqJcMcOOiIhS2n1+N1ZOWQGBlRve7uBpaDHzu/1oqWgBYGR6nZs4l5fnqiWx6+uVgF2TVTa3QWSQVab2r1uI5bDArJLY1Bl2AAdPFNsDxx9ArfL/S3PbAszSXOT04DJz/Zhnqbl+k+ulRNuJiIgWHQbsiIgopUePP4TVYavnlbv1IgdPQ4udrY9dHspih4PD6J00JnF6Na8tMIW2C83lZq0r/Yeq/etWLNCAnVoSm2aG3QwOnig0HT888EMsi0bNV7T6DueOU6JiQStI93SFHzFpZDBuF0fRhGGnjkVERJQ3DNgREVFSET2Co0cfwkzRYqiqBQjUOXkkWuTyPSl278Bec72hYYO9xLZxDeAxGtK3imE0YWT+B0bDQPfL1vXyBTghFsho6ATADLticlUdQtdYF5ZGYtaLdSuSv4GyogfbzfVoZT9e0o2MWk1IvNH1crK3ERERLRrsYUdEREk9f+55tE0OmdfeZWyaTrnJd4adGrC7oOkC+03NZfSgi2fMbda68LS+NfUDu3cC0WljXd8B1C5Lud0xag+7dEpimWFXNN6GZwEAS5UMOwbsspest9x0dBpX/ve3EJMxuH39uPjmPwIe+xsAwBfXn8QXP5C6J91MLzwiIqKFihl2RESU1K9O/grrwmHzWrRckGI30fxWVq8016fGc5/muLdfCdgtSfD12WaVcG8WXfM/8ORvrfWq1+VwsgLLcOhEa2Ur/C4/AGA4NIzR0PxBPsqc5u+Gu/IkhJSzAnbLk7+JshJwB7Cufh0AQELiQNMq6+bJZ41pz0RERIsYA3ZERJTQVGQKT55+EutDVv86tG5x7kBUEtQMuxMjJ3J6lpTSlmF34ZIL525SAnZbtJPzP/SEErDrXMABuwxLYjWh2f7sWRZbGDPZdUtiMXhnXgw0AL5qx85UyrYssf6btDt43vrnXcaA0887dCoiIqL8YMCOiIgSevL0k5iOTmO9kmGHFgbsKDcdNR1mn7meyZ6cMr1OjZ3CWNgIVtX76tFe3T53kxqwmy/DLjQBnFV6Xy3oDLvMhk4ALIstNOEZgLvmNQDA0ij71xWDmlX7Wv9rQMfvWTe7djhwIiIiovxhwI6IiBJ68PiDaIzG0KjrxgueSqB+Veo3Ec3D4/JgTd0a8/rI8JGsn6Vm121ZsgVCiLmbmjYALiPXabnWj1pMJH/g6ecBPV7G2LIFqFyS9dkKLsMMO4CDJwrNu+RpCCEBANdVKf+uZMCuYNSA3d6BvZArr7JunvqdAyciIiLKHwbsiIhojvOT5/Fi74u2/nVo2QRo/M8G5W59w3pzfWjoUNbPea3/NXM9Z+DEDJcHaN5kXm7WupI/8MTT1nrVtVmfqyiYYbegCM8QPLW7zeub6zdbNxmwK5hVtatQ4TYmQQ9MD6CvaQ2AeOC+59W0g9lEREQLEb/zIiKiOR45+Qh0qWN9WOlfx3JYypMNDRvMdS4Bu3n7182wlcWm6GO3WAZOABlPiQVmBeyYYZdX3sbfQggjGzk6uQrL1IET9R3OHKoMuDSXrY/daxOnrf9WSd2cEE1ERLQYMWBHREQ2Uko8cPwBALD3r+PACcqT9fVWht3hocNZPSMUC+HwsPVe9Zv2OWyDJ7oS75kcBHrjAUDhAtTSuoXIWw0zkyg8AeixlNsBe0ns6bHTiKXxHprf+cnz8NRavQ/DAzcAI8oE5FpOiC0k9Z/9vf17gY6rrZvsY0dERIsYA3ZERGRzePgwjo0cAwCsjyhZIsywozxRS2KPjx5HJBZJsTuxg4MHEY33m+uo6UCtrzb55rat5nKbdhSAnLvn0IPWuv0Se8npQqRp9smjaZTFVnur0ehvBACE9TB6JnsKdbqy8r3934PQjOBnbGoFYlOrgeEuawMz7ArKNnhi4DWg4xrrJvvYERHRIsaAHRER2Tx43AhcuKXEKjVgp/QBI8pFtbca7VXGRNeoHsXx0eMZP2Nn705zfWFTinJYAGi9AGMyAABoFwPYKE7P3bP3Pmu96R0Zn8cRHDzhuIHpAdx3xPraCQ28Hm7EgJEz1qb6lQ6crHyoAbv9A/sRab/UunnuFSA86cCpiIiIcseAHRERmaJ6FI+cfAQAsDwShVvGJ8TWtC/8jCNaVHLtY/dij9Wb6vK2y1NvdnvxtL7VvHyja6f9/nivUjongM23ZnweR3DwhON+sP8HCMVCAIDY9DLEJtejTQwCMl5uXN0GeAIOnrD0tVS2YFnVMgBAMBbEwWCf9QMmPQqceSn/HyolsONrwHfeABx6JP/PJyIiAgN2RESkeKHnBQxMDwAALobPutG8Ick7iLKjlsVm2scuGA3ilb5XzOvLW+cJ2AF4NGZl3bxB22W/uf8XMMtkO64BatoyOo9jbBl2HDxRbMPBYfzk8E/M6/DA6wEIrBR91qb6VcU/WBm6uPlic/1K3yvAcuXfCT2v5vfDYlHggT8Gnvg7Y6jFzz5sL4EmIiLKEwbsiIjINFMOCwBvqFhh3WhiwI7yK5cMuz39exDWjYEoq2pXoaWyZd73PK1fhJD0AAA2aafs32Dv+5m13nJbRmdxlG1SLEtii+2HB36I6eg0ACAWbEV0YiMAYKU4b21i/7qi2NayzVzvPr/bPiTp/L78fZCURoDulf+yXotMAQ992rhHRESURyUZsBNC3C6EuFcI8Y34/+4VQnQW+7lCiE4hxHEhxF8KIW6MX9cJIbYJIe4SQuxK9l4iomKbjEziqdNPmdcXxIMbAIDmjQ6ciEqZGrA7PHQYMoNvdl8494K5Tie7DgAmEcAOXfkm/uBDxq/DXUB3vERWcwOb3p72ORyXY0nsydGTeT5Q+RgLj+HHh35sXhvZdcZfq5erGXYNzLArhm3NVsDulb5XIJs3WzfP78/fBx19DDjwy7mvH38K2Htv/j6HiIgIJ9FF2AAAhjxJREFUgNvpA+SbEOJeAHVSypuU17YB2CWEuENK+USRn9sJ4K4Er48AuCGbsxARFcKjXY8iGAsCANbWr0X1mbPWTWbYUZ61VLSg3leP4dAwxiPjODZyDGvr16b1XrV/3RVtV6T9mY/ql+AGl1FKu/PX38f/eGAlvu35Km5wGfefimzBh/7h+fR/E07LYuhEe3U7PJoHET2Cvqk+TIQnUOWtKtABS9ePDv4IE5EJAEaW52sHrWAwM+yKb1XtKtT6ajEaGsVwaBhdgUqYodKBI0A0BLh9qR6RnmPKX/cvuAMINAAvfcO4/vVngQ1vAbyVuX8OERERSizDTgjxUQC3A7hDfV1KuRvAnQDuFULUFfm5JwDsjq9HADwB4E4pZX38/URE2dFjwK67gRf+r/HNSI7USYe3rnoLxOAx62bT+gTvIMqeEAKXtF5iXj9/Lr1A2Vh4DAeGDgAANKHZnjGfJ2LbEZMCAHCpdgS/8P6dGcADgO/F3pT2sxYEW0lsej3s3JrbVhabzYTecjcRnsB/HbBKIj9ywUeg/pV6BXvYFZ0mNFsfu90jR4G6+HRePQr0Z9YnM6mTz1jrre8BbvgboMYYeIGpQeDIr/PzOURERCixgB2MTLb7pJQjCe7dA6AOwOeK/Nz7pJTbpZQiHqS7SUr5lSzOQERk99hfAw/+mfFT/V98LKf+OYeGDmHvwF4AgEfz4Jb6C4xvcgCgdjngq87HiYlsrlx6pbl+vie9gN3O3p3Q49OLNzZsRK2vdp53WIZQg4d1KyNvq2YFq74ZfQue1S9M+1kLQkWjtZ4aSPttq2tXm+sTIyfyeaKy8JPDP8FY2MhoXF69HDevulm5K+0BO5bEFo1aFru7bzfQeoF1Mx997MZ7gf54v02XF1h+hfHfxm1/YO3Z9/PcP4eIiCiuZEpi4+WpdTAy2uaQUo4IIUYAfBRGVpyjzyUiUnV89uGM9r/X9QT+t+e71gv7f4F/3aPh32KpG+Z3ffktCV9Xs+tuXHkjakdZDkuFd2WbFbDbdX4XwrEwvC5vyvc8021luFzell7/OtVfRj4KALjFZQUId+lr8ZXouzJ+luMql1jryfQDdp11Vvvd4yPMsMvEVGQKP9j/A/P6jy74I7g166/TDRhHtTAGUcBbZQ+qUkHZMuzO7wZargUOxXtV5qOPnZpd134Z4K0w1lveCTz9j8b66ONGebraX5KIiChLJROwAzDzN+1Uf/M8AWCbEKJTSpnuj5QL9VwioqxcJg7i7913z3n9056f4ZBcjkf1yzJ63lRkCg+fsAKGd6y7Azio9OlpZsCOCqO9uh3Lq5fjzPgZTEen8Wr/q7i09dKk+8OxMB4/9bh5ff3y69P+LFuwWt4KPPd14Df/CFS3Yfsf/ALH6pZn9XtwlC1g15/229QMu2Ojx1LspNnuPXIvhkPDAIC2yja8rfNttvtzymGFKObxytrmxs3wuXwIxULonujGcOcy1M/c7N2b+wec/K217nydtV6y1sjm690LxELA4UeAi96d++cREVHZK6WS2Jk8+FQBs5l7mUyMLdRziYiy8j8998ItjJLA1/RVeDZmNTv/c3fm5TiPdj1qNk9fWbMSl7RcAvQftDY0cUIsFY6aZTdfH7sdZ3dgPDwOAFhWtQwXNV2U3YcKAVz9Z8CdXcCf7AYWY7AOACqbrHUGGXZr6taYa5bEpi8UC+Hu/Xeb1x/e8mF4XB7bnhW2gRMri3QyAgCPy4OtzVvN65cRtG6e35dT2whICZxQMuxWXWu/v/md1pplsURElCelFLBryGBvXTGfK4TYJoT4hvK/e4UQN2bwXCIiAMBycR6Xa0YPnajU8PHwp/HHkT9FWBpjLjdqp9GEkbSfJ6XEjw/92Ly+be1tEEIAfYesTcywowKy9bGbJ2D3yMlHzPWbV73Z+FrNhScAaIv4r0K2gF36GXbLa5bDLYwii57JHkxGJvN9spL086M/x8C0ERhtDjTjHWvfMWcP+9c5S50a/ZvxE0ZZMmAMhJg4n+RdaRjuAkZPG2tPJbBsu/3+FiVgd/wpYGoo+88iIiKKK6WS2LoM9hYzuHc7AEgpPzbzghCiE8AuIcSX0h1AcfDgQWzfvj3hvV27dmVwRCJaDJL1msPTdwFPG0v3upvw3Hvjza6/9wPg1A4AwM7fdwMXGe+frzfeK32v4OCQkU3nc/lw65pbgWgYGFK6ACzhhFgqnMvaLoMmNOhSx/7B/RgNjSYcJDEZmcTTZ542r+2N/suUbejEIKDraQUgPZoHK2tWmhNiT46exJYlW+Z5V3mLxCL47j6rb+gHt3wQPpdvzr6Vtgy7jiKcjFRXtl2Jf8O/AQCe730RsnkTRPdLxs3z+4Dq1uwerJbDrrwKmJVZifoOI4h3dhegR4zeeds+kN1nERFRQSSLpxw8eDDh6wvBIv6xck7qivTcIQB3Siltwyjife6+BOCu+FALIqL5SQm8amXDYevvW+vV11nr40+l/cgfHfyRuX5r51tR568DBo8pE2JXAL6q7M5LlIYabw22NBrBIgmJX5/8dcJ9T51+CqFYCACwtn4t1tavLdoZFyy3D5gJbsoYEBxJ+63q4IljI+xjN5/7j9+P3sleAECDvwG3rUs84GeFNquHHRXVhoYNZsB/YHoAo/VKuXtvDpNiu1+21qt+L/EelsUSEVGelVKG3chCe66UcgTAfUluz3R0/xaAxKFexcaNG5lJR1TuzrwIDJ801r5aYJ2SYbT69cBTXzTWJ35jBPfmKRfsnezFk6efNK/fs/E9xkLtX8dyWCqCN3e+Ga8NvAYA+P6B7+P2dbfDpbnM+1JK2yTjN696c9HPuGBVLgFCo8Z6sh+oSK+IYE3dGnOAB/vYpRbRI/j23m+b13+4+Q8RcAcS7mVJrLNcmguXtV5mfm0f9rhgzpLuP5T0ffPqP2ytWy9IvGfzO4DH/pexPvkMMNEPVDUl3ktEREWXLJ6yfft27N69u8inSU8pBewyaRYx4vRzpZS74713mGFHROlRs+u23Ap4/NZ121bAX2dk2EycB/oOAC2bUz7uJ4d+gpiMAQAua70M6+rXGTfU/nVNDNhR4d265lb8nz3/B2PhMZwZP4OnzjyFm1beZN5/8vST2N1n/EXKLdx4y6okJePlqLLJKmGf7Aea0ithVzPsZkpjKbFHTjyCsxNnAQC1vlq8a/27Eu6rwhTaRPyvjZobqF2kw0wWuSvarjADdi9EhqyA3cDR7B4opT3Yl+y/i7XtwIorgdPPGxmvB+8HLv2j7D5zlvnaW+RL0nYcRETkiFIqiR2J/1qXYs/MvWyCcBk9VwhRJ4S4XQiR6n0zexm0I6LUYlHgwP3W9UW/b7+vuYDO66zr479J+biJ8ATuOXKPef3eje+1btoy7DghlgqvwlNhC4Lcve9uyPhEx3AsjH/Z9S/mvXdveDfaqtqKfsYFq3KJtc5g8MTq2tXm+vgIA3bJxPSYLbvu/RvfjwpPRcK960S3dbFk/dw+Z1QU6iCbxyaU7NHBo9lNih3vAUJjxtpXC1Sn+PePrSz2F5l/FhERkaKUAnYzwbJUtSAz9zLJd8z2uZ8DcC+Mktf5sBaFiFLr3glMDxvr6qXA8svn7ll9vbWep4/dPUfuwXh4HACwsmYlXtf+OuumWvrDDDsqkvdsfA88mhHgeG3gNTx80sgo+f7+7+PM+BkARr+7j1/0ccfOuCDZAnYDab9tZc1KuIRRdnx24iymIlP5PllJePz04+ga6wIAVHuqrdYBCWzUTlsXLZsKfDJKZnn1ciyrWgYAOC0jiHni5cvB0Yz+GTH1KT/Ealqfut3EprcDIv7t1anfAWM9mX9eMiIKV+UReJc8Dv/SnyKw4hvG/5Z/D77Wn6Gi9jnU+k4CyCIoSUREC1IpBewej/+6OsWeTgAj8aEPxXru4wlem5kUi/j7RjI4DxGVoyNKI/51b0z8DUOnErA79RwQiyR8VCgWwg8P/NC8/uDmD1r9wqIhYFDJtkmzvI4oV0sCS3DL6lvM6889+znc/sDt+PorXzdf+8RFn0g4QbasVSo9sjIIRnhdXqyoWWFenxjlzw5nk1Li269Z2XXv3vBuVHurk+7fINSAXeqWBFRYVy29ylgIgYGKOuvGYBZlseoPsebr61rdAnRcE7+QwIFfZv55s+wf3A//0p+gat0/oGLFd+FrehKe2lfgrjwJd+VJBCoP4cPak/hd5P/gFfG/8J3aT+Ga2h8DGoPwRESLXcn0sJNS3ieEGEGSnnDxAFkdgG8W6bk7AXxMSpns826M/3pPkvtERJYjj1rrdW9MvKd+pdEzafQMEJ22f5OhuP/Y/RiYNr6xbw40422r32bdHDxm9N4BgLqVgLcyH6cnSsuntn4KL/S8YPYLOzxsfQ2vq1+Hd21I3DusrNkCdumXxALA2rq1ODlqDLI5MnwEW5ZsyefJFr0dZ3eYX4MBdwDv3/T+lPs32DLs+GfppOuWX4d7j9wLADgkomiZuTFwFFh5VWYPU9tEpJN1vvmdxtAJANjzI+CKT2T2eXGHhg7hn3f+M17sfRGeJD+nWB6J4Bu9/VgejZqv3RAawQ14EL9e8iz63vB5vHvje+F1eRO+v1i98YiIKDullGEHAF8CcGOSvnG3x3+9c/aNeL+5u4QQt8++l+1zpZT3AbgpRQ+7O2H0x5tzHiIim+FT1jcMbj+w6nXJ97ZdZK17Xp1zO6JH8N193zWvP7D5A/a/yPexfx05p6miCT99609x3fLrzNc0oeG2tbfh22/4tlkyS4ose9gBsAbNADg6nGVD/hKm9q67be1tqPfXp9gtsV6csS6bWRLrpMvbLjcn+e5D2LqRa4ZdWgG7W43/VgNA717g3J6MPm4iPIF/fPEf8a6H3oUXe1+03dPDjQgPXYnPX/l5fPPGb+Cn0QZbsE71prER1P76f+H2+9+J/YP7MzoDEREtDCUVsJNSfgXAEwCeVF+PD3W4C8AdScpPPwrgL2H0nMvnc+8EcK86VCIeHJwpk72B5bBENK+jj1nrjt8DvIkbngMAWi+01r2vzbn9i6O/sE07vGPdHfYN6UzCIyqgWl8tvn791/HFq7+I9296P+556z34/FWfnydYUsYqlIDd1GBGb11bv9ZcHxk+kq8TlYRd53dZk4k1N/5g8x+k3L8MA6gR0wCAEVkJ1Cwt+BkpOZ/Lh6uXXg0A6PIoBUUDxzJ7kJSZT04P1AGb3mFd7/5B2h+3b2Af7njwDvz40I+hSx0A4BIuREa3YvLkH2Py+P+H0Pm347Z1t+HKwbOo7o0H4jQP8MYvYeqPnsCZlZeZz3v7xCTef/IVvO+h9+Lbe79tPpOIiBaHkimJnSGlvEkI8dF4UGw3jHLVBgDbpZTJhk08AWPwwxP5fK6U8oQQ4g4Ad8VLZ2eGUzwhpbwp898dEZWl2f3rUmlTAnY9rwK41roWEfz9s/+GmSSlvjNXYtPf2KfJ/j/P03hTvJ3dZ34TxM+fZLkMFZ8QAm9f83anj7E45FASq2bYHRk+AiklRKqG+mVEza57W+fb0FrZmnK/Wg57SK7AFfxzdNz1K67HE6efQJdHyczNNMNuvBcIjRprX036gdhtHwBe+4mx3nsv8IYvpvxhm5QS/33ov/HPO/8ZUWllzF3ZdiU+d/nncP2XDtjfEJoAHv9b6/qKjwNXfhIVACr+4FHoD/4ptFeMXrV3jE9gv9eLf9v9bzgydARfuOYL8Ll86f0+iIjIUSUXsAOAeN+4tHvVxQNuqYZKZPXc+HtGAHwsk/cQEZnCk8DJZ63reQN2Skls714I6JDxZGpP/XPQPGMAAD1SjfDQ3D4+a0W3uT4i27M/NxEVRw4Bu6VVS1HhrsBUdAojoREMTA+gqaJp/jeWuIODB7Hj7A4AgIDAh7Z8aN73bFDKYQ/qK3BFwU5H6fq9Zb8HTWg4pWbYDXcZA5lcaZbX92cwIVa18iqgYTUwdBwIjQEH7ge2/n7CrVE9ii+/9GX89PBPzdeqPFX4myv+BjevujkeRJ8VsPvd14Dxc8a6shm49i+te5oG7W1fB6JBI1gI4HNDQ9jr8+JXXb9Cz2QP/v31/446f116vxciInJMSZXEEhGVnFPPAbGQsW7aCNStSL2/us0qkQtPYKU4b6y1afgaf2tuCw/cAEh7E2ofwugQvQAAXQock8vy8lsgogKqaAAQDyJMDyedDp2IJjRbWSz72Bm+s+875voNHW9AR23HvO9RM+wOy+WFOBZlqN5fj4ubL8a0pqHXFU8d16PA0Mn0H5Jp/7oZQhhZdjNe/m7CbVORKfzxU39sC9ZtadyCe992L97c+eaEGa8+hIGXvmW9cOPnAX+NfZOmAW/7utlL0SeBr/YNoELXsad/Dz7y+EcwOpM5SERECxYDdkREC9lxpWR1zQ3z7xfClmW3RXQBAHxNT0C4pwAAergBkZFL5ry1U/TAJSQA4IxsQhAsmSFa8DRXPGgXxz52Oeka7cJjXVbf0A9v+XBa71Mz7A7p8/xghYrm+uXXAwBOZlsW25fhhFjV1vfA7EHR/RJw+gXb7fHwOD7+xMfxu7O/M1+7edXNuPvmu9FenTzD/UZtNxAcMS5qVwAXJc7cg7cCuOP7gMeY9t4RjeLPh4wg3aGhQ/jIYx8BtKnMfk9ERFRUJVkSS0RUMk4oAbvO69J7T9uFwHFjRs5/XO/Cn16yFv/jwRcQM2Jx+OpNn8ObPvKmue977R7g58Zy5Ybt6HrPW7I/NxHlVcdnk/eTfMzrx7r4j2Df9I+/wCGZfsDoS3+oTIodYYbd9/Z/DxLGvyyvWXYNNjamMS07EkSnMMoTdSnYTmABeWPHG/HVl7+KLo8bVwbjLw5k8HWuZtg1Zxiwq2oGLnwXsOe/jOvf/RuwwiiWHgmO4KOPfxQHh6yA4Mcu/Bg+tfVT8/aRvMNlZcsbQcEU+RdN64C3fBX45ccBAL8/Po5Hqyqwy+/DwaGDqFh+N6ZOfwSQnMBNRLQQMcOOiGihGj8P9MX71mgeoydOOpRJsbLnVXzpxS8hJmMAgMtbL8cbVybpg6dOlW3dks2JicgBg7LWXDeKzMrc1tYxw25G72QvHjj+gHn9Rxf8UZpv3GtmJ5+WzZiCvxDHoyy0Vrbi8rbLsx88MaD8M7FkXfJ9yVz9p9b68CNA3yGMhcfmBOvuvPRO/PHFfzxvsK4Vg7hWU/5bvfU985/honcD66wf0v3HBODT4xNoK07Dv/QnADg9lohoIWLAjohooTrxtLVefjngrUzvfUpJbPjsy3i5dycAwC3c+Nzln0v+DUHvXmvdekGGhyUipwzC6l/ViLGM3quWxB4fOY6oHk2xu7R9f//3zd//tuZt2N6yPb03HrVKaHfJLII6VFBvW/02nFQGT8iBY+m9cWoImB4y1u4AUJNF5mTTemD9m83LyI5/wSce/4QZrBMQ+PyVn8f7Nr0vrce90/UstHhwGKuuBepXzv8mIYC3/qsx5RZA1fh5/CBgZQt6avbD18yJ8ERECxFLYomIFiq1HHb1dem/r34V4K0GwuPwhcbREqvGebcb79n4HqyuSzIQW0qgR82wuzDxPiJacAZltbleIjIL2NX6atFS0YLzU+cR0SM4NXYq+b8nSthQcAg/O/oz8/rDF6TXuw4AcOTX5vKJ2LZ8Hovy4MYVN+LbgWoAxhTlWP+hhN8AzS473yaO4OfxVq4Hw024+a9+ldXnd33yz43sOgBi7z04394GuI0T/N2Vf4fb1t2W5pOkvRz24venf4iapcAbvgg8aGT8bTr8FP7iqj/AP50z2md4G3+HWGgpALbCICJaSBiwIyJaiKS0Z9h1vj7992oaZNsFEKeeAwBsDIXhrluJT279ZPL3jJ21Mgl8NUBdGj+1J6KC6fpyBt84P70PePpxAMDfvr4Zf3tD8vcm6oW3rn4dzk8ZE6UPDx0uy4Ddjw7+CNPRaQDA+vr1+L1lv2f8e1iPAa4Uf10ePWu2EwhLF57VmZ280FR4KrCl842YPvX/EJAS7uCIkT03j9XaOXN9XLZlf4AVl0MuvwLizAtwS4n3jo3jXxrq8b8u/18ZBOuAreI4Vmnxye++GmDDWzM7x7YPAPt+Bpz8LSB1vP/oC/in6Eag1sj287f+AgcGb8emxk2ZPZeIiAqGJbFERAtR/2FgvMdY+2uBpVszevsxf4W53hCO4AtXfwGVnhQltbPLYVM1sSaihaVyibWe7M/47RsarPK4Q8OH8nGiRWUqMoWfHPqJef1HF/4RxJFHga9vBf5pNbDz20bwLpGjj5rLF/WNmEBF4n3kqLeuuQWnlbLY4Pl9876nU/SY6+NyadafLaXEfzc2m9d3jE3gL7d8DO/e8O6MnnOL6znrYuMtxhTYTAgB3PJ1wGO8T/QdxEf7PYiFjLMJLYpP/+bTGA1l1geTiIgKh9+REREtRGp23aprAc2V9lsPDB7Afw1Z5a1v8Dbj0tZLU7+J5bBEi1dlk7WeyC1gd3DwYIqdpemXx36JsbBRStxZ0YY37LoP+PG7gOEuIDgCPPw/gfs+CAQTlBsfsQJ2T+kXF+fAlLHLWy9HX8AazvLKwXvmfY8asDuhZ59h97XdX8NdI6/gWHzwRZWUeN9UOKNnaNDxVtcL1gsXpJ+ZZ1PfAdzwd+blp7SHcXn3NsiYUft7bvIcPv/c5yGTBaiJiKioWBJLRLQQqf3rOq9L+22joVF85unPoMJr/TxmdXBq/jfaJsSypItoUalWggmj3Rm/fWPjRnN9cOggpJTzTqssFTE9hh8c+IF5/U8hP7Rj987duP8XRvnrHz4EuOONzcJTth+uPKmzf91C5dJcqF92GTBq9JI7ffIpHP/Hf4Mr1Q/D/uPvgQFj+W+fugP/tiy9/3/VsnNPwzP47r5HACFwd201vjhglOKKF/4vcMUnAU96E4Uv1w6iWYwAAPplDZo6rk3rfQld9lGjp97J30ITEl/Df+HWs3+I/hUPAQCeOP0E7jt6H+5Yd0f2n0FERHnBDDsiogXGjSjQtcN6ofP6tN4X0SP4i9/+Bc5OnMVJjweh+Dfc2thZYHIw9ZvVgF0bM+yIFhV1UuTIqeTlm0m0V7Wj2mMMrhgNjaJ3sjefp1vQnjz9JM5OnAUArBV+rD2hlB1e8D+A7R+0rrtfAh76jPXne/ABIBoEABzTl+K0bCnWsSkLa9fcbK4bJ4fwmzO/Sb45FgWGTljXjWsy/jxP7U74Wx4xryfW3ww5E1yf7ANe+WHaz7pFs74uH45dkbqv4nw0Dbj9u+bU21oxhbsj92JznzUx+q6X7sLxkePZfwYREeUFA3ZERAvMVnEMCE8YF3UrgIbOed+jSx1/+7u/xfM9zwMAokIg2Kg0ju99Nfmbp0eAkdPGWvMAS9ZneXIickRlk9mXCqExYHo4o7cLIbCh0SqLPTB0IJ+nc87x3wCP/CVw7pWEt6WU+P7+75vXfx+rhdAjxsXyK4B3fhN429eAm75gvWnPfwG/vQs4u8sI3sU9pl9SiN8B5ZGvZbO57ohEcff+u5OXfo6cAma+FqpaAX9NRp/lrn4Nvrafm9fbmrfhy9f/C8RVf2ptevarQCQ4/8OiYdzsesm8fCB2VUZnSahyCfCuHyAkjcDfCq0fP5p4Cl8di+LaqWm4ItP46x1/jagezf2ziIgoawzYEREtML/nUpphd15nNIpOQUqJr778VTx04iHztU9c9AnUrvz/27vr8Liq/I/j7zsW1yZ1d6FOjRap4b6wyOIOCyzuiy9LYX8svhRY3HVxaYuVCnVa6u5tksZ95P7+uJOZTJO08UySz+t57pN77j1z7klmcufMd45MCGYqP0fd/sovONF2ADhcNayxiDQpwwhd2Tl7a42LGJBcblhsc5/HzuuG7+6GN0+FBdPhleNgd8UvLZalL2N5hnVv7OqFQ7YvC56ceGfw3nvYdTD0nOC5n/4JL00Cd4GVTurOi54arOorTaNNsAdZV7ebFWnLqu5lt29DcD+lT+V5qmCPWUtkp/cxDCsYOCB5AM9OfpZIRyQcejHE+nti5u2GJa8foCS/tV+TaFivte2+VJaYNatPlTqN5Hr3deSaUVa9DZOj9+3iub3p/LBtJ0M2zePNldWon4iINBgF7EREwswEW7kA2kGGw/pMH48tfCxkDqYz+p7B1UOvhg5Dgxkr+bAaELJCrIbDijRL5YfFZtUiYFduHrs1mc14pVifF94+E+Y9GzzmKYJ3z4X8tJCs5XvX3e+ND/au6zoOehwZzGgYcOKT0Hl0xeu54uCc98gmrh5/CWkQkfGBYJkL6Ojx8K9F/6LUW8kCEBnrg/s1GA67aM8iojq/iWF4AfCWpPLC1BeIc/lfH84omHBj8AGznwB30YELXfBiYPcT3wSg/uaX/M43imNLpvGrd1DI8RjT5M7MLIZ+dRfbdi6o4tEiItLQFLATEQkjcRQy1CibN8YI/dC4H4/Pw/1z7+et1W8Fjk3pOoV7xtxjTRjfvlzAbs8BetjtWBjc1/x1Is1T+R52WVtq/PCByQMD+826h93ab0IX7SkLbuTugA8usOYmA7bmbuWHbT8AkOLxcuietcGHHHVnxZ7Nzki44DOY8gDEtPUXbbfmAms7AGkmyvWy6+H2sD1vO++sfqdivn3lAnbV7GG3In0F1/5wLYbNeo35ShMp2nYZyZHJoRlHXmQNswXI3xMSkKtg93LYOgcAt2nnbc+UatWlJnaRwvnuO/lL6Z1w2HWYyT0C50YUF5P/3jl4fd56v66IiBycVokVEQkjY22rcBg+K9FhCMS0qTRfTkkOt/x8C/N3zw8cO7rb0Tx6+KPBVe/aDbQ+UJpe2LcRSvIgYr9eIKYZusBF13H1+euISGNJ6h7cr8WQ2G7x3YhyRFHkKSKtKI2MogxSolLqr36NZfUXwf3h58OAk+GdPwMmbJtnzUE38iLeXPUmJtaQxdvNBAyvtfAEnQ6FHlWswOmKhgk3wJirYPMvkNhFwbrmJqU3bLXe87q73cwmiunLp3Nsj2NpH9M+mC+j3JDYNgcP2C3as4hrf7iWAv8waZ8njsJtl2F6EkJWjS1zgf0YHnRaPTwLvv8HU75IYjcV3++nOV7kLP+nta99Y0gjqbq/aY2Y2JjjGwxHn4Ax6e9kfH8nSQv+ix0YmJfBd788wDFHPdgg1xYRkaqph52ISBipznDYtZlrOeerc0KCdaf2PpXHjngMp90ZzOiMgtSyBSRM2PMHFaSvtVarA4hKgnaH1PE3EJEmUcchsXabnb5JfQPpZjks1uuGdd8E06Muhb5Hw5G3B4/9+AjZuTv5bMNnAET7fExJ2xY8P/76g84bijPSKlfBuuYnJfgaH2xYc7flu/O5+eebcXvdwXwhPewOPCR29o7ZXD3z6nLBumiKtl2K6a464P2OdzJrfdYqrTFGCfc536iQJ4lcTrXPCaRf9xx9wHrUG0cEKcc/wdpuwYVUkn97kW252w7wIBERaQgK2ImIhJEJtv0WnCjHZ/p4Y+UbnPPVOWzP2x44fs3Qa3jgsAeCPevKKz8n3e5lFc9vmR3c7zYebHpbEGmW6rjoBLSAhSe2/ArFOdZ+QhfoMMzaH/83iOto7efvZcPX11PstVbnvMobg6NsVe7kntD/xMatszSucr3lJkS0w25Y75vL05fz+KLHrROFmZC/19q3u0L/t8oxTZM3V73JtT9cG3g9pUSlULT1Snwl7St9TBkPDu52XxJIH2tfyNG2ctNTYHKH4z0iDCuI+LuvZ/0tNlFNfU56Aa9/SPmooiLe/vavVa+qKyIiDUKfzEREwkQH9tHLtttKOCJDhqduyt7EZd9fxuOLHsftnxg9yhHFE0c9wdXDrsZmVHE77xz8hpyNP1Q8Xz5gV9UwMBEJf+V72GVvA5+vxkUMbBOcx+6PjEp65Ia7NcGVsul/QrCnnCsaJt0TODVo7Q90c7tp7/Fw9r5yC1GM+ytU9sWHtBzlesvF5e7mxpHBBSDeXfMu03+fjll+VfV2gyp9TeSW5nLPnHt4bOFj+Ezrf61DTAdeP/Z1fKXtqlWVRWZ/3vccFUg/5XyOI23WAlHn2WdyluOnwLmXPcdTn4tNVIczpQ+5A4OrH0/c9FvIavQiItLwNIediEiYmGAvNxy261hwRlLsKebF5S/y6spX8fg8gdMDkgcw7Yhp9EjoUUlJ5fQuN0H15l+gtND68ArWB/ry89d1n1APv4WINImIOIhuA4X7wFsKebshoVONijgkJTgkvtkF7Hw+WFNurrD9e8oNPRvmPw97/yDK9PHOrj0UGA6i/MMgM8x4xn/chpKPK843Ji1IYjer15y3FPL3ckH3E/k9/XdmbJ0BwLPLnqWbvQvHluUvv9o6Vk/3H7f9yCO/PUJaUTDYOyR1CE9NfIqUqBS2PNq1+vUpGAsvjIe83UQZpbwe+QR0O8xaaKIs5j7kLJ457WGeOdhQ7QaQNOVhfKu/wmaajC0u4dT5/+TILkcS74qvnwuU9dhrgt9NRKQ5UA87EZEwETocdiKzd8zmtM9O46UVLwWCdXbDziWHXMLbx7998GAdQHKP4Jw9nuLQHnXpq60P92B90E/VfEwizVodh8X2TOhJtMMK6KcVpbGnYE991azh7VpiBSkBopIrLqBjs+M7/nFK/YGBeJ9JB3+wrsR0cIv7SkpwNWaNpSnY7CFztRq7l/LQ+IcY3X504Ji5e2lgf1d8WzKKMliRvoK3V7/NqZ+dyg0/3RASrDu518m8cswrtVukJaYNXPQVJPiDfD43bP4Zyr6gaz8ETnqq6QJayT0wu4wJJPtn7+G5pc/VT9lb5sC07jD98FqtbC0i0hooYCciEgYMfIwvF7Cbtm8B18y6hh35OwLHhqYO5f0T3+fGkTeGLi5xMH3KTVS97rvg/uZywbvuEzR/nUhzVw8LTwxKGRRIr8hYcYDcYWbDzOB+v+PBXnEQya92Dxd0aMtee3CIY7Hp5Ar3zfzkG94YtZRw0GlkcH/nEmKcMbww5QVO6XUKAANKSgOnb1r7OhM/mMi5X5/LowseZXPO5sC55MhknjjqCf4x4R9E2CNqX582veCSb0IWxACseRfPfttaQKoJ2cv11B9XVMx7a9+rnzkuv7sLirNhzwp4/STI2Vn3MkVEWhh9OhMRCQP9je2kGLkAZNpsvJ0VnEMn3hXPfePu443j3qBfcr+qiqha32OC++tnBIegbPopeLz74bWotYiElXpYeGJwyuDA/or0ZhSw27k4uF/FfJyvr3ydlRERnNWpPV84urHE15sLS+/gZ9/QSvNLC1U+YLdjEQBOu5OHxj/E/SNuprvH6t3mAdY7K/a6jHHGcP7A8/nfKf9jarep9VOnhM5wxU9w7gdw3idw2Sy4bhEk1mB4bUPpOSmwO7aoGJ/Py8O/PRyYu69Wdi4OXQgrexu8cTIU7Kt9mSIiLZDmsBMRaWI+08cR0d+A10r/FhWJaRgYGJzS+xRuGHEDbaLa1P4CXcaCKw5K8yBnG6SvAZ8X1n0bzLPfirQi0gwldQ/u13KI2ZCU4MrSyzOWHyBnGDFN2BUcxkinERWyrNq3igV7FgCQYXNyffGtmJ4kALY8ekKF/NKChfSwW2y9fgwDwzD4U1xwJdY9MUl0Te5DWmEabaLa0C+pH8PbDufkXicT64qt/3q5YkK/YAsXHYdBZCIUZ9PO66WX283y9OV8tuEzTutzWu3KXPRKxWP7NsC8Z2DK/XWorIhIy6KAnYhIE1q5byWPzH+Ea1wLoMg6Nj8qkqGpQ7lz9J0hw9NqzeGCXhNh9edWetVnsHMJ4O9p1+cYSOlT5cNFpJmo45BYgMGpwR52q/atwuPz4LCFeXMxZwcUpFv7EfGQ3KtCltdXvh7Y9+QODgTrpBVq0xsiEqAkBwozrN5dZf87u38PZOvc53g+PeX5JqpkGLHZrV6r/jbEuKJiNrpc/Hvxv5nUdRIJEQk1K68oG1Z8HEyPvBgWv2rtb/q5fuosItJCaEisiEgTKPWW8vSSp/nLV39hy96ljC4qDpz7MecM3jzuzfoJ1pUp/639T4/C+rK57AyYfG/9XUdEmk75IbG17GHXNiKJo4jmkuxcrtu7i7QFL0BxTv3Ur6HsWhLc7zC0wnycewr28N2W4PydpZmaAqBVs9mgU7k5C8sPpy4XsNt/hdhWrdfEwO5R/in+skqyeG5ZLRagWP4+ePzfULYbHNoG2bMcSgvqUFERkZYlzL8yFRFpeVbtW8Xdv97NhuwNAEwtKKJsCYllvp5syzsKo75XhBt4Ksx+AjI3EuhZBzDkz9D+kKoeJSLNSWJXsLvAWwp5uyA/HWJTD/iQ7nd8FdgfaazlGdczPGNkBjN8ezfub+7lXe8kHvacRykHX/CmvoaYlq/bgdzm+Ihr/C3aFzYk8uh+j4to+xWuNtacA56CHviKO9dL/aQZ6zQyOI/rzsVwyOnWvgJ2lesZDNiNLC7GYcbhMQw+WPsBf+77Z3on9a5+WUvfDO6PugSik61V6tNXW6vj7lxc5TyUIiKtjXrYiYg0ErfPzXPLnuPcr84NBOsA/uwOrlj4uXd8w1w8IhYu/T50cQmbEybe1TDXE5HGZ3dCx3I9h3YsqPZDT7H9yjuuf9CxfLDOz2l4ucAxgzdd/ySZ3Pqoab0aYmwM7C/39Qg9aSvGmRj8O6h3nQAV57EDKC2EjLX+gwa005dZAck9IMn633J4ivlzjDXs3Gt6eXzR45imeaBHB5XkwZ4/rH3DBoecYe13HRvMs21+fdVaRKTZU8BORKQRpBWmcdl3l/HC7y/gNa2eHlGOKB4YfA0DcjMA8JkGX3rHHqiYuolJgfP/B0fcBm0HwklPhk5SLyLNX5cxwf1qfvD9s/1HnnI9T4RhrY6ZTRSfxcbwYkI8q5zRgXxjbGv4xHUfSWEUtDPwMcS2OZBebobOX+dMXIBhLwHAW5KKN79/o9ZPwlT5gN2uZeD1wLZ5ULbyaUof64suCep2WGD30uTh2AzrY+TcXXOZvXN29crYvZxAL//UARAZb+13HRfMs21ePVRWRKRlUMBORKQh+Hww4174v/7se/t0bvnoJJakBedZGtF2BB+f9DGnlxoY/sbrb74BpNHAE6HbHTDpbrhmHgw/r2GvJSKNr3xPle2/HTR7b2MHDzpeC6TX+TpxYsmD3J2SyjPJiZzVqQ2PeM/AZ1rD9Lvb9vKg87XKC2sC3Yy9xBuFAGSasewwU8qd9eBK/jWQcmcejpq+AkBce4j3D432FFn/K3OfCZ7XkMyKyvXebZu9k9P7nB5IP77wcdw+98HLKL+ac/newF3LfdGwfaG1kr2IiGgOOxGReufzwZc3wBJrVcI2ebt5DfhfbAz/SE3h6hHXc8khl1jfTv/xUeBhn/vGVVqciEi1dR4d3N+1FNzF4IwMHAqZX85dDC9Phr3+D9ptB9L3km/5NTKBv3z9M8vTl4NhMPbyv2DLPR4+ugSAk+zzOensq2DQaUD155qrq0rnxlv+IXxi7Sb3GcuW804MnPpi4xfc9avVGzA5Mpnvb72LCHtEY1RVmoPuE2D5e9b+p1dCznZr37DBuL82Xb3CVfkA264lXHv8o3y7+Vvy3flsyd3Ce2ve4/yB5x+4jJCA3bDgfmI3iOsAebuhNA/2roQOQ+q1+iIizZG+ZhQRqW/f3BoI1pWxAafnF/C90Y3LBl5kBet+fx92LATAbdr5xju6ksJERGogNhWS/cNCvaWhk+jvb9aDsNc/n5QjEv70X4hMAGBk2+CQwcV7F8Mhf4Jh5XrlfnWztahFUyu/Qmy5gIJpmry+MngfPrf/uQrWSaijbgdHlLVfFqwD67We3LNp6hTO2h0CNn9fj30baGM4uHLIlYHT//n9P2QVZx24jJCA3YjgvmFoHjsRkUooYCciUp82z4aFLweS38VE80tUsHdLm02/wKdXwPoZVi88v0+9E8gmrjFrKiItVciw2Co++O5aBr/9J5g++mFoNzCQHNkuGLBbstcfFDv2EYjvZO0X7oNfHq+nCtfBrmXB/XIBgHm757E2y1pAIMoRxVn9zmrkiknYS+5Z+cJLE25s/Lo0B85Ia/7bMrt/59wB59IlrgsAeaV5PLfsuaofX5TtX6keK/DXblDo+fLz2FV13xIRaWUUsBMRqUe+Ra8E9mdGR3FbahveG3E67lGXBjP98TG8fQa4rXmXaNObBzwXNHJNRaTF6lKut+62Suax8/ngq5uCE+z3nAijLgvJMqztMAyseetWZ66mwF1g9b474f+CmZa+CYUVV5VtND4f7FkRTHcYGtgt37vu1N6nkhiZ2IgVk2Zj7DXQYVgw3e/4ioEkCSo/LHbnElx2F7ccekvg0IfrPmR91vrKH1u+t2/bgSFD9YHQ+1b5nngiIq2YAnYiIvXEnb8X36r/BdL/SUrgxN6n8PTkZ3Ae/38wopKgnCMSznydAqIar6Ii0rJ12W/hCdMMPb/kddi52Nq3u6wgnGGEZEmISKBPUh8AvKaX39P8H7b7HmsNjQPrS4eF/22I36B6srda810BRCVDfEcA1mauZe6uuQDYDBvnDzjIvFrSetkdcPqLkNTDmkft6IebukbhLWQeOyuoNrHLRMa0txaN8Jk+Hl/4OOb+95xy+SuUUya1P/i/JCBrizXHpohIK6eAnYhIPXD73Hzx6fk4/D1WVrhcjB56CQ+NfwiHzWF9GD7xKTjjFRhwErhiwR4BpzwH7Q9p4tqLSIuS0hfKepQVZoTOB5W9DWbeF0xPuBHa9Kq0mPLDYhen+QN8hgGHXR/MtGA6EZTWU8VraM/y4H77wYGg4xur3ggcntx1Ml3iuzR2zaQ5Se0Hf1sGNyyv8n9B/DqVm3fOP3+kYRjcNvo2a25erOHov+z4peJjDxawc0ZBYldr3/RB5qb6qrWISLOlVWJFROrINE3un3MfF20LTn6+u99Ubht1G0b5Xis2mzWZ9SF/Aq8HTC84NAm6iNQzmw36HA0rPrDS394Ol/8IPi98eDEU51jHk7ofcL6uEe1G8O6adwH/whNlDjndWrAidwcUpHO6fTbveic30C9zACHDYa0VJfcU7OHrTV8HDl806KJGrpRI83WwFZ+dePgjwkmE4YbsbQy/412yiAcgov0oXEnWEPxrvrmfgk03UP6j5i+uOXT1dxU54eMCVn5U8VqvOJOYZN9qlfHUu3ztG1shT3mVrhwtItKCqIediEgdPbP0GTav+og+bjcApXYnU0/4T2iwbn92h4J1ItJwJt1jDbkHa+6ouc9Ygbudi6xjNgec/pLVq6UK5VeKXZG+ghJviZWwO2Hs1YFzF9i/ByoZAtfQygfs2lsBu3dWv4PH9AAwou0IhqQOafx6ibRQbhysNrsG0oNtmwP7pelTMb3WPccWkYEzeV7gXAL5dLVZq0qXmA7WmZX3et1gdgrs9zZ21WvdRUSaIwXsRETq4L017/HSipc4rqAwcMw5+EyMyIQmrJWItHpJ3WDCTcH0zPug3KI4TL4vdJL3SqRGp9I9vjsApb7S4GqxYM3J6YwGYIBtO4OMLfVU8RrYXX5I7BDyS/P5cN2HgUMXDrqw8esk0sIt9/UM7A8xgsNWTW8sJRnBnrYRKbMw7PkADLRtDRxfa3bBXcUgr41mx8B+b9vOequziEhzpYCdiEgtzdw6k0d+ewRMkyMLiwLHjUPOaMJaiYj4jf+bNex1f32PhXHXVquIcR3HBfbn7Qr2mCEyHgacHEieYa9kzqqGVJABef4eOI5IaNObj9d/TL7bChB0j+/OUV2Oatw6ibQCy81yATtb6Dxz7sxx+EpSADDsxbhSZwIw0AgG7Fb7ulVZ9gZfMGDXSz3sREQ0h52ISE11v+Mr7FFbiOr6MobNpIfbQ1ePNQSrwIxg+Mt5lHLgeWBERBqcM9Ja2Oads8BTDJ1GQt9jYOxfrXnuquGwjocF5rGbu2suN1Gu196wc2H5ewCcap/DPz3nUoqz3n+NSpUfDttuEG7D5K3VbwUOXTDogsAk+CJSuVrNAbe3B/xnOgBHJ+5my82hZfy0PYHrfrgOgMjkBXxx4a30/ckH/oWmzzrxOM4aW8V1C8fBYw8AMMiVxpb7jwu5Vx1sjj0RkZZGLRkRkRoynJlEdn4Dw2YF6Q7PC95KZ/uGNN4HVhGRg+k+AW7fAnfuhEu/h8NvtgJ51TSq/SgchvX97tqstWQUZZQr+3BIsOaiSjLymWhbWlkRDWO/FWK/3fwtewr2AJAcmcxJPU9qvLqItCYpfQPD4cnbBXl7Qk4f2flIxnawFovwmT6mLZiGubf8fJODqy47OhliUq19TxHkbKvPmouINDsK2ImI1ECRp4iozm9ic1hz1vk8sRyeE5y0fZZveFNVTUSkcnZnjYJ05cU4YxjadmggHTIs1maDoecEko06LLZcDztf+8G8vOLlQPrs/mcT6ajd7ysiB2F3QIfgPYFdoYF6wzC4fdTt2A07AEt2/4aZtjqYod2gA5ef0je4n7G+rrUVEWnWFLATEakm0zS5b8592CN3+9N2nNvP4FCCc7j86FXATkRalvEdxwf25+6aG3pyWDBgN9G2jBRyGqdS5QJ2C81iNuVY9+FoRzTn9j+3ceog0lp1LNfW2VWxZ23vpN6c1e8sAHq63dh81ogEErpCVOKByy4fsEtfW8eKiog0b5rDTkSkml5b+RrfbPkmkC7ZcwqTSjNxuHzWgU4jWXS5PiiKSMtyWMfDeHrp04DVw85n+oLzwyX35Ddff8bY1uAwfJxq/xVo4PtgSV7gg7xp2Hh656zAqXP6n0NChFbpFmlQ5QN2O5dUmuWaYdfw9eav6ZtXbrXX9occvOzUfsH9DAXsRKR1Uw87EZFqmLtzLk8ueTKQLs0agzt7NJPt5RqqfY9t/IqJiDSw/sn9SYxIBGBf8T7WZa0LOf+R94jA/hn2X8A0G7ZCO5cA1jUKkrqxPHcDAJH2SC4YdEHDXltEKvawq+R/PiEigeuGX0e/0tLAsbzKVq3eX0qf4H76uqrziYi0AgrYiYgcxI68Hdz6y634TKsnnaewGyV7TsKJh4m2ZcGMCtiJSAtkt9kZ12FcIP3j9h9Dzn/tHUOhGQFAf9t22L2sYSu0Y2Fgd77dG9g/s9+ZJEcmN+y1RQSSe0FEvLVfmAE5OyrN9qc+f2KEGVyI69O8agTgUsr3sFPATkRaNwXsREQOwO11c+vPt5JbmgtA26i2FO84D3Aw1raKeMNafIKErgde+UxEpBmb1HVSYH/W1lkh5wqI4hvfqOCBZe80bGV2LArs/mTmA+Cyubh40MUNe10Rsdhs+y08UfmwWLthY4DbF0i/l7OSRXsWVZo3IKEzOGOs/aJMKMg4cH4RkRZMATsRkQP495J/88e+PwBwGA6emPgEpjcOgGNswV4eDDgRDKMpqigi0uAO73w4TpvVU2Zt1lq2520POf+R98hgYsWH4ClpmIqYZkgPu+URVs++0/ucTmp0asNcU0QqOsjCEwDk78VZnA1AgWGww+Hg0QWP4vV5K88PVluqTa9get/GutdVRKSZUsBORKQKP277kTdXvRlI3zDyBoamWt8oG/iYal8czNz/xMaunohIo4lxxnBYx8MC6R+2/RByfr5vADvMFCtRlAWrPmuYimRtsYbgAbk2gy1OBw6bg0sOuaRhriciles0Iri/fUHlefb8EdjdGBGBaRiszVrLx+s/PnDZbXoH9/dtqEMlRUSaNwXsREQqsTt/N/fMuSeQPrLzkVwwMDiZ+XBjA+2MbCsR3Qa6jm3kGoqINK7JXScH9mdunRlyzsTGe56JwQPz/9Mwi0+UGw673B8AOKXXKXSI7VD/1xKRqnUNzmvJ9gVQWlAxz7a5gV1buR55zyx9hpySnKrLVsBORARQwE5EpAK3z81tv9wWmLeuXXQ7Hh7/MEa5Ia9H28vNwdLvOLDZG7uaIiKN6qguR2EzrKbjsvRlpBemh5x/xzuZkrIJ5nctCRm6Wm9ChsO6sBt2Lj3k0vq/jogcWFx7SB1g7fvcsG1exTybZwd2+w6/lE6xnQDILsnm+WXPV122AnYiIoACdiIiFTy39DmWpS8DwG7YefzIx0mMTAycN/BxbPn56/qf1LgVFBFpAkmRSRza7tBAeta20MUnMonnM29w2Czz/1PvdTD3m7/ulN6n0CW+S71fR0SqoWe5uSs3/Rx6riQ/ZDEKV89J3HLoLYH0e2vfY03mmsrLDQnYaQ47EWm9FLATESlnzs45/PeP/wbS1w6/luFth4fkGW9bSXfbXgByzSjoeVRjVlFEpMlM6TYlsP/Fxi8qnH/Ve2wwseozyNlZfxd3F2Hu/j2QXBsVy9VDr66/8kWkZsq3fzb9FHpu23zweaz9toMgpg2Tu05mTIcxAPhMHw/Oe7DyBSja9AzuZ24En69iHhGRVkABOxERv7TCNO769a5A+rCOh1U6kfmF9u8C+x97jwBnZKPUT0SkqR3b/VgcNgcAyzOWszE7tPfLarMbdD/cSphemPt0vV3bu3UeNtP6cL/Z6eC4QefSPqZ9vZUvIjXUbTwY/ilB9qyAwszguS2/BPd7WPcEwzC4e8zdgRWnV2Ss4MN1H1YsNyoJov2L2HiKIbceA/8iIs2IAnYiIoDX5+WO2XeQWWw1NlOiUnhkwiOB+ZoCMjcz2bY0kHzDe3RjVlNEpEklRSYxsUtwcYn/bfhfxUyHXRfcX/QKZG+rl2tvXPhcsNiYOC4bfFm9lCsitRQZX261WBM2lwvSlZu/LhDEB3ok9ODywZcH0k8teYq0wrSKZWseOxERBexERACmL5/Owj3W3Eg2w8a0w6fRJqpNxYwLX8ZmWCsf/uwdwmZTKxOKSOtyau9TA/vWsNj9hrT1ORo6j7b2vaXw87S6X9RWRMymYDAgeuCfSI5Mrnu5IlI3lQ2LLc6B3cv8Bw3oPj7kIZcOvpTu8d0ByHfn89jCxyqWq4CdiIgCdiIiv+3+jRd+fyGQvmrIVYzuMLpixuIcWPpmIPma95jGqJ6ISFg5rONhtI1qC8C+4n3YY9eGZjAMmHJfML3sHUhfV6drDkz6lE7uUgAKbTYmH3FvncoTkXrSo9zCE+u/B3cRbJ0Hpn/eufaDrSGu5bjsLv4+9u+B9HdbvuPXnb+GltumV3BfC0+ISCulgJ2ItGoZRRncMfsOTKxec6Paj+KKIVdUnvnbu6ygHbDF146ffEMbq5oiImHDYXNwUq/g6tiuxAUVM3WfAL0mWfumD2beVzFPNRnODKa45gTSuV0OJTIyodbliUg96jI6GJDL3Qm/PA6/Bb8EpccRlT5sdIfRnNQzeB95eP7DFHmKghnUw05ERAE7EWm9fKaPu2bfRUZRBgDJkck8evij2G32ipnXfgvL3gokH/OchalbqIi0Uqf1OS2w74hbg821t2KmScEeNKz9GtZ9X4srmUS2/x8TCwsCR9oNu6gW5YhIg3BEwORyPV5n/x9s+jGYHnhKlQ+9ZdQtJERYwfed+Tt5bmlwnkoF7EREFLATkVbslT9eYd7ueYH0IxMeoW1024oZ8/bAF9cHkl94x/K1b2xjVFFEJCx1i+/GpC6TAmlXm58rZuo0AoafH0x/cxu4i2t0HUf8UlKj1jK0xBoOa2Jg9NV0BCJhZcRF0HlUxeNH3Gr1wKtCcmQyN428KZB+Y9UbLEtb5j/ZAzCs/eyt4Cmtt+qKiDQXCtiJSKu0ZO8Snl36bCB92eDLGN9pfMWMmZvglWMg3997JKYtf3df3Ei1FBEJX5cMviSw70hYhuHIqphpyv1QNnw1azPMfbra5Rv2AiLafcWUgsJAg9XoMgZiUmpfaRGpfzYbnPhvMMqNUOh7HBx110Efelrv0xjXYRwAJib3zLnHGhrrjIKELlYm0wdZWxqg4iIi4U0BOxFpdfYV7ePWn2/Fa1orGw5vO5y/DvtrxYxb58F/jwk2Eg07nPIc2cQ1XmVFRMLU0NShHNruUAAMw4erzeyKmWJSKg6Xq8YHb9M0iWj3GQ57Pufn5gVPHGB4nYg0ofaDYeoD1n6XsXD6i1Yg7yAMw+DB8Q8S64wFYGvuVp5e4g/sl194ImNtJY8WEWnZFLATkVbF6/Ny++zbSStKAyAhIoHHjngMh80RzOQugu/uhlePgwIrH45IOPtt6Ht0E9RaRCQ8XTr40sC+M3EBhjOzYqaRF0MH/yI9nmL49s6DlvvZxs9wJixnYmERPdwe62BEAgw/rz6qLSIN4bDr4O69cPE3EBlf7Ye1j2nPbaNuC6TfWv0WC/cshLYDgpnS1tRnTUVEmgUF7ESkVXlh+Qv8tvs3AAwMHj38UdrHtA9m2LEIph8B854F/8qxRCbA+Z9Cv+Mav8IiImFsfMfxeIs6A2DYPES0+6JiJpsdTngimF77tbWQTxW25m7lkd8eAdPkkpzc4IlRl9QoCCAiTcAZWa2edfs7tfepHN7p8ED63jn3UpLcM5ghfXV91E5EpFlRwE5EWo25O+cy/ffpgfTlQy5nQqcJVqIkH2bcC/+dChnrgg/qORGungvdDmvk2oqIhD/DMCjec3Ig7Yxbzc/bK1mAovOhMOKCYPqb26z77n4K3AXc9NNNFHmKOLS4hCH+xSZKTCeMubre6y8i4cEwDO4bdx9xLmvakR35O3gnc2kwQ5oCdiLS+ihgJyKtwp6CPdw++3ZMf6+5Me3HcM3Qa8Dnhd/fg2cPhTlPWRMbAzhjrAmUz/8UEjo3Yc1FRMKbr7grpdmHBtL/XPBPCtwFFTNOvh8iE6397K3w9S0hpz0+D7f+fCvrstYR5fNx977gIhYfew+HuHYNUHsRCRftYtpx5+jgkPnpu8sF/zPW4cTTBLUSEWk6joNnERFpnrrf8ZW1Y3iI7voi9uhsAHzuOGb/ciR3/HIHV9s/p6dtT8jj5vsGcEv+lez4qC189HUj11pEpPkpTTsWZ9xKDHsRO/N3MnL6JRTvOI/9vxs+1XYuT7qetxK/v8tNCxP4xHcEYBLR/jNcSfPBNLl7Xxa93W4AikwXL3hP4tzG/ZVEpAmc2PNEZm2bxaxtsyiw2djtcNLB4wafh+7GHtab+hJVRFoP9bATkRbOJLL9p9ijtwGQ7DG5ekcqvzru4nHniyHBujQzkZtKr+Kc0rvZYbZtqgqLiDQ7pjd2v6Gxq3ClzqiQ73++CXzkPSKQfsj5KkfYlhLZ4aNAsO6C3DxOyQ/20LvXcxHbTPWuE2kNDMPggcMeoGNMRwDWOe2Bc/2M7U1VLRGRJqEediLSojmT5uBMXExbj4dLcnL5U24RkWwHI5gnx4zmNe+xvOQ5nnyim66yIiLNmCd3OKWRO3G1+RWAiJQfAShNn0r574jvdV/EcGM9vWy7iTFKeM31OK/54lid7+Lk/AIOLyoO5P3IewQfeo9qzF9DRJpYQkQCjx/5OBd+cyEbXC6O9N8T+tq2g29cE9dORKTxKGAnIi2WPWYdkW2/5M+5edyYmU2saYac32Um86bnaN7yTiFPgToRkTorSTseW0Qajlhr8Z6IlB+xR+6kZO+J+EqtnsuFRHKV51redD1CewqwAZfk5FUoa4WvO393X9SItReRcDEkdQg3jLyBNT89EDjW37kaTWMnIq2JAnYi0iJtzd1Kx/Zv8H979zK6uCT0ZIdhMOFGOvY/kdvtDm5vkhqKiLQMWx49ISSdXzqRm3++mbm75gLgiF2HI/YJhqQMoUNsB0q8JSzYvYCzSxJ5LM1T8R6NAWOvZvCkv7PapS9TRFqrCwZewLQN30P6lwD0s2/CcGRhepKauGYiIo1DATsRaXHySvOY9vUlvLt3K5093uCJNn3g2H9C7ylgGFUXICIitRbriuX5yc/z3LLneGnFS4HjyzOWszxjeSBdaLdzRfu2XFLq4KzobrSLSLJW6B7+F+h2WFNUXUTCiGEYXD3lCbxLv8QOdPG4Ser8KplbrwXT1dTVExFpcArYiUiLUuIt4cnPzuPRdYuJ91lDYH0YPO85mWuvehGckU1cQxGRls9us3P9iOsZ13Ec76x+h5+2/4THDB3L1iWuCyf2PJGLBl1EtFM96USkooSYdhQndsWevQ0b0Me2g987fkjxTq0bLSItnwJ2ItJieHwenvrqUv62+udAsK4AJ9eXXs8s30iuVbBORKRRjWo/ilHtR5FRlMHv6b9T6i3Fa3rpk9iHvkl9MdTbWUQOIrLDMMjeBkDv0lJWxa/AVzITOLFJ6yUi0tAUsBORFsE0Tf4z60YuXfZVIFi3j0guKLmXlWb3pq2ciEgrlxKVwuSuk5u6GiLSHLUdCKs/B2BgaSmfAxGps/h0/aec1ue0pq2biEgDsjV1BURE6sOrv97Pn+e/TRufD4BiZyTnldynYJ2IiIhIc9ZlVGB3REHw8APzHmDOzjlNUCERkcahgJ2INHsfLnqKo39+hnZea4GJEruTiAu+YLXZrYlrJiIiIiJ10mUMGHYA+nkKiClMBcBrernxpxtZlrasCSsnItJwFLATkWbt/cXPMPK7BwOrwZba7DjO/RCjy+gmrpmIiIiI1FlEHHQcBoDNMBm8azQ+dwIARZ4irpl5DWsy1zRhBUVEGoYCdiItTUkepK+FrC1NXZMG99bCfzPy2wfo6bZWHvQYBpz5OvZeE5u4ZiIiIiJSb7odFtgdZW6jaNulJEcmA5DnzuOK769gbebapqqdiEiDUMBOpKXY8wc8OQT+2RmeGw1PDYXZTzR1rRqEz/Tx4s/3MOb7f9Db7QbAi4H3tBdxDTipiWsnIiIiIvWq24TA7hjbanylbZk+dTpxrjgAskqyuPT7S1m1b1VT1VBEpN5plViRJtb9jq/qXEYEpXzpups+tp2hJ2Y9wO3f7uJ970S2PHpCna/TUGr0NzA8HJHyAk8WzCfZv8CEF7jBfSVfvBMD79T97ykiIiIiYaTrWHymgc0wOcTYTCyF9E/uzwtTXuDKGVeS784npySHy767jGcnP8uIdiOausYiInWmHnYiLcDNjg8DwTqPaSPLjA2ce8TxMpNti5uqagdWkAErPuJM+0/8yfYLE2wrSCK3yuyd7Fv5v4RbeTVvbiBYV4rBje6r+MJ7RCNVWkREREQaVVQiq82uANgNk5G29QAMSR3Cy0e/TLwrHrCGx17+/eXM3DqzyaoqIlJf1MNOpJkbZazhMvvXgfS9nov53DuO91wPc4htC3bD5HHndCi8FqKTm7Cm5exdCb8+Cav+B95SHneGnt5ptmGVrzvrzE64cRBFCSMdfzCUrTiLg/nSjQiuKr6dxWb/xqy9iIiIiDSy33wDGGTbCljDYssMShnEK8e8whUzriCzOJNSXyk3/XQTtxx6C+cPPB/DMJqqyiIidaKAnUizZnKf8w1shgnAL97BvOOdBBhcXHob/4v4O52MfSQb+TDrATjpqaatLsDqL+HjS8FTXGWWTsY+Otn3MZWqewb+auvMLYW3sYeUhqiliIiIiISR33z9uYRvATje9ht4PWC3Ps72S+7HW8e/xdUzr2Zr7lZMTB5f9Dhrs9Zy77h7ibBH1F9FTBO2/AoZ66AwE2LbwqBTITKh/q4hIoICdiJhp0ZzzW2eDa9vsfYdURxx4/tsSegEWPPC3ee+iJdd/2edX/w6DL8AOo+sdd3qOt/eufZZPOR4Bbs/wAiwzNeLDWYnHHjobuxhgLGdCMNdZRnLI6MwJt7NhDHXMb9OtRERERGR5mK2bwjZZgyJRgHdbXutkRqDzwic7xLXhTeOe4Prf7ie39N/B+DzjZ+zPms9/zryX3SN71r3SnhK4aOLYc2Xoce/uwuGnQujr4CUPnW/jogICtiJ1IxpQt5uyNoKiV0goXPT1mfec8H9YeeAP1hXZqZvBLO8w5lsXwqY8NWNcNkPgW8jG9MZ9p95xPnfQHqzrx3Xu69jhdkzJJ8DD6uv7878pS+yauM3eH1uTAzWu5wUdRzGPZOfpEtcl8auvoiIiIg0oUIied17NH9zfGod+PXfcMifoNyQ1+TIZF6Z+DRPzX2YN7Z/D4bB6szVnPnFmdwz9h5O7Hli7YfIekrggwth3TcVz5Xmw4IXra33FDjkDOg1CeLa1e5aIiIoYCdSfcvehe/vgcKM4LGRF8GU+yEqqfHrk7EB1n0bTI+9ppJMBvd7LmCC7Q+r19ru363GzZG3Nlo1AcbaVvGI4+VAepmvJ5eW3so+9h86YGLGruP0315mS+4WSIgBwGbYuHDQhVw37Dqc9v0mvBMRERGRVuE1zzFcbv+aaKME9v4B67+HvsdYJ9NWw/zncS3/gFs9xVwR1473HaW8HhdDLoXc9etdzNw6k7+P+zspUbWYUuXTq0KDdf2Oh+SesGEmpK8JHt8w09oA2g2GXhOh/wnQZUxIcLHRFGWD3QWOSLBpzUmR5kQBO5HqmP8CfHt7xeOLX4M1X8FZb0HXsY1bp9/+A/iHlvY5psru99vNdjzlOZ3bnO9bB35+FPpMhY7DDly+aULOdijOgYg4iG5Tq2r2NHbxgvPfuAwvAKt9XTiv9C7yiS6Xy4cjdjWulB+wR+1kS7mFYnsn9ubBwx5kcOrgWl1fRERERFqGLOJ5xzuJyxz+wNln11pfoO9YCJt+DMmbkLeXK4DjCos5s30bCmw2ftj+Awv3LuT64ddzZt8zsdvs1bvw5l9g5SfB9ISbYPK9VgDu6Idh88/W54V13xJonwPsXWFtc5+GbhNg4l3QfXxd/gTVt2+jNW/0rqVW2u6Cw66HSfc0TeBQRGrMME3z4LmkSRmGsXjEiBEjFi+uegJ+aUDznrPmpSgTEQ+x7WDf+uCxyES4bGat5qzYf164as1hl58OTw0Bd6GVvuBz6HlkleXa8bKx9zOwY4F1ILU/XPxNxVVjvW5Y+zUs/wC2/wYF6SGnV/q68avvEL7zjmKJ2Yctj5544Hpmb4dXjoXcHVY6pi1c/oM1nBhIK0zjy01f8sHaD9iZvzPkoXHOOK4ceiXn9j9XvepEREREWrmytm07Mvkl4gYiDE/VmW1O8AXnRF7drg9/jioOCVT1T+7PTSNvYlzHcQe+sGnCy5Nhp/+z2JCz4LTplQe9MjfByk9h44+wbX5IHQJGXwHH/LNhp6jZtQze+lPoyKAyUx+E8X9ruGuLNDMjR45kyZIlS0zTrP1k7w1EPexEDmTnEmsYbJnOo+G8j6yg3Zov4YsbrDfC4mx4+0y4bBbE1K4nWnUVeYowf5lGtD9YV5zSl3WxiZC+HJthwzAMbNiwRezB9LnAF4HX58I87QWMFyZYQb70NfDikXDGa9BxOGRvgSVvwNK3oSCtymsPsm1lkG0rVzq+YpOvPfy8GoaeBYmVTOKbuxveOCUYrHNGY57zLptxM2fVm/yw7QcW712MSeiXBhH2CM7seyaXD7mc5MjkiuWKiIiISKu1l2Suc1/Hi0lvhX65bNisoadj/2qNJFn8Gnx7BwAD9q7ny7GXc1XBSnbkW23TNZlruGLGFYxpP4arh13NyHZVfFZf/XkwWGePCPasq0xyTzj8ZmsrybNWk139BSx/H3z+AOOCF60VZs98rWGm1dm5GF4/BUrzrLRhA5sDvKVWesa9ENcRhpxZ/9cWkXqlHnbNgHrYNRFPKbx4FKSttNKdR8P5n1jDQ8vsXAKvHg+eIivd/XCrt1sN5ocI9oTzYrgyef2Knuwp2BPY9hbuJbM4k9ySXHJKc4gpLeSb7buI9v/v/q1tCj/ERFd9AT+7YefMghLu3rur2nXzumLxxXfAXlqIkbcHw/RW8Uscbq2M1e848HowV34KPz6EUWyNbfXa7LwwaBIfefeRUVTJN31AQkQCp/c5nQsGXlC7eUVEREREpMWqMCrl4Snwx8ew8n/WKJfRl0NS99AHfX2rFSADsDkovWo2r+6ezcsrXqbYWxySdVjqMM4beB4Tu0zEZXdZB70eeH4M7NtgpQ+7zhoCW1NZW+C7u0NXl207CC78HGLqsd2bn259KZ/rH7kSmQjnfgAdhsJbp8PWOdZxuwuumQ9tetXftUWaqXDuYaeAXTPQaAE704Rfn4D1M6yVUEsL4bBrW2+X6Z8fhx/9b8iOKLhmHiT3qJhv9Zfw/nkE5qs4/l9Wg6EKPtPH9rztrN63mjWZa3hh3lxsrgxiHOnckJ3J0OJSVkW4WBgZwc/RURTtF/y7MTOLS3Ksb8zWuJz8uWN7zBrMQzGpoJCH0/cRV8X//l67nU/jYvgmJobNTkeg7GivyaFFXiYWFHNsUQ6xVQXv9uMBbq4iqGhgMLr9aE7sdSLHdj+WSEdktX8PEREREWk99g/YVYcTDx+6HmCYbSMAX3jHcp37egxHDq6UWTgTF2EYvpDH+DzReHKG484ZxQnuTTzjehaAXDOaw0ueJIfYWv4GJn+zf8KNzo8DR1b7unBu6d1kEV+rEkOm0vG64Y1TYeuvVjoyAS7+FtoNtNJFWdZUNWULZPQ9Ds59r1bXFWl0GeutwDdAQmdoO6DeilbATuqk0QJ2C1+Gr26uePz0l1tfl+mM9fCfw4Jdx4/+hxW8rMrMB6xgJ4AzBq6ZG/iGL6s4i6VpS1matpTl6ctZm7WWAndByMP7lpTyr/QMerhD5+LY6bBze2oKv0dGBPK9tXsvUf7/20e6DWRxm464bC4Mw8Bn+vCZPkxMVu7OxLCVYhilYCvBsAUDbF3dbu7al8Ww4hJiTBMPMCcqko/iYpkdHYX3IAHASJ+PSYVFnJRfwLiiYqqarnebw8HDKUnMi4oKHIt1xjKmwxgO63gYk7pOUm86ERERETmo2gTsAIYaG/gs4t5A+oSSf7DStL6EN1zpuNr8jDNhKYax35fRpsm7OzI5xGO125/0nMaTnrp/JjrNNpt/OV/Abljt+dW+rpxbeletgnaBgJ1pwhd/gyWv+88Y8JePoM+U0AfsWgovTiTQ0eC8j6H3fnlEwklBBnx7J6z4IPT4oNPg5GdCR7/VkgJ2UieNErDbtxHK5jfbnyMSLvnWmuusNTBNePNU2PSTle44wlpQ4kCrSHlKYPoRgW+s0tsP5LnBR7M0fRmbcjYd8HJDikv47540Iqv4XzQNG1lDzsDefgjxPz2GUeJfQrXdIXDl7CqH31Zs1HjAVmoF8ezFGLYisBdhtxVgtxXhdZRi2Iow7EXgP2/Y/ZutGMNeUul12no8nJBfyIn5BXR3uymw2ci22/g+PplvO/ahXXxXeiT0oG9SXwanDKZHQo/qr8glIiIiIkLtA3YALzj/zbH2hQD87B3Che47Qs4bjhyciQtwJi7G5swG4NCiYl7dY83tXGwYTOnQm4yigXiLeuAt6oKvpB1Q/WlwyjvV9itPOP+DzR+0W+Xrxl9K76xx0G7LoydYn12+uR0WTA+emHQPHHFr5Q/67K+w9C1rP6UfXD0HtMCbhKMNM+Hjy6Eos/LzKf3g7LdrtfBjeQrYSZ00eMDO57XmYds+30qnDoA/vQQfXWJNiAoQ3xn++htE1LYLeDOy8lP48CJr37DBFT9DhyFVNxJsxThiNjAs4jfez58V6G32YJskPoyvPOLv88TgK+5ERFEqn+V/QzeyASgwI4g59j4oyrbedItzKr9mRAJc8Cl0qvqeUpdGTeW8/kBesT+IV8Sbl43GbtixGTYcNgcuu4s2kW1Iikwiwh5Rz9cXERERkdaqLm3b3sYOvnPdHujVdnbpPcz3Dawkpw97zEacCYv4T9EsJhZZnRk+jIvlwZTQxdBMnwtvUSd8xR3xlaYGNtMTBxx8uprTbLP5P+cLgaDdal9XLnffzA4ztdq/VyJ53O14mzMdvwSOfeKdwM3uqzCrCCamks0PETcTZ1hzcN/vvoDXvMcGzocMsxWpo9r+3062LeY/zidxlev5utDXFxOD0ba1gWM7zTYcX/JPfn/0rFrXMZwDdlolVmDpm8Fgnc0Bp/0H2g+Gs9+FlyZBSY610ufiV62JVluyknz49q5getTl0GHIfpl82CJ34ohdiz1mPfao7RiGj7XA6/a4wPxyN2dm82tUFLscEfiKOuEt6o63sBve4s6YnnjA4O+Ol+nmyAYg14zi9NIHmDnuSusyIy6ATy6HbfNCLx/T1lr8ov3gA/4qerMVERERkZaizm3b/y2HZVbPsvd6fgeX3lL1aq/p6+C5LwLJz1M7gxk6EsmwleKI2Qwxm0OOxzhjaB/dntToVNpGt6VtdFtSo6z9lKgU4iPiiXfFk+A6GtuKofC/qwGTAbZt/Bp/L5z0pDXcr5K6WcEPk4HGVibZlnKp4xuSjPzA+S+9Y7nVfWWVwTqAdBJ5xnMqdznfBeBGx0d85j2s1vPoidS3KbbFPF8uWLfLTOYu92X85BsGWMHuR5z/JcoopZOxj2nOl8D8c9X/z82YAnatnWnC/BeC6cNvDg59TekNU+6Dr26y0nOftQJYzha8MMC3d0CefxXVmLYw0QrelXhLsMeuwRG7CkfcamyOvEof/lxiIkcVFNPT4ybGNPn7jijOL/k7mK4KeSfalnKu44dA+j73RWwwOwczJHaBi76C9d/Dpp+twF1kPJz4pFZ0EhERERGpiaPusObB8pbCjoWw9mvoX0UQ8Kd/Bvf7Hsvr57zL6n2rmb97Pn9k/MHyjOWkFaZV+tACdwEbczayMWfjQasU5Yji9E7duGXnVhyYVkeJjy4m49tb2dj1UDzxHXFFJpBYWkRCQSZvRSxjIDtJNgoqlPWFdyw3uq/BW+Xs0kGveY/lHPsP9LDtJcEo5GbHh9zjufSgjxNpaGOM1TznfCoQrNvqa8vZpX9nN20CeT71HU6BO5IXXf8GsIa7L/ovjLqsSerckBSwa+22zoX01da+MwbG/TX0/LC/wM+PQf4ea/v9HTj0ksavZ2NY/oHV29CvYNJdzNr1Cz9u+5E5u+YQ3aWoyod6izrhKehDYUFfbi4q5SPXQ9gNk8PZyBW273jRe1JI/nZk8i9nMFD6tXc0n/omVCzYZod+x1mbiIiIiIjUTmIX6wP9/Oet9KyHoO+xFeep3rkEVn4STB9+CzbDxqCUQQxKGRQ4vLdgL3/s+4ON2RvZkrOFLblb2JyzmXx3PtVV5CnibRcs79CWx9Iz6OyxghQp+RmkrPq2Qv62lXQg2m6PYFpsb2ba22D3fo3NE4/PE4vpicf0xFmbN5ry8+2V4uQhz/m84voXAOfYf+Ad72RWmd2rXXeR+tbX2M5Lrv8jwrAWYtzia8fZpfewp1ywrsz3vlG85jmaixzfWwe+uxt6HFnn+ezCjeawawZqModdTceIP+t8mhPt1nDYtz2TubuSb1YutX/F351vA7DNl8rE0ifY+OjJNbpOY6vp36GXsZPPXfcQY1gLK3we0Za72kdh2Cr///B5Yji132TGdxzP2I5jSY4MndOC7++Buc9Y+4YN/vJhcAUmnxfeOAW2zLbScR3gqjkQU/FGJCIiIiIi9aQgA54aCqX+oNqJT8KhFwfPmya8cTJs9s8JN+AkOOutahdvmiZZJVmkF6aTVphGelE6ewv3kl6YTnphOvuK95FbmktuSS65pbl4zeD8XHFeH9dnZXNyfgHRB/mMnm2zMTcqktnRUXwfHU2p7cBDAe2GnTZRbegY05FOcZ3oGNORzrGdmPTL8yTuWATAJl97Ti99gGWPnl3t31fkYPb/XF7l0PacnfDfqZC700rHtoNLv4ek7lWWG0Epn7ruY6Btq3Wwyxi4+JsDLxZZCc1hJ2EplSyOsS0MpN/0Tq0037veyVzr+IwkI5+utnROsM0HwjtgV30+BkYu5DXjRWJMK1i3xeHgH+1dFYJ1vpIUPPkD8eQNxFvUlX9celJlBVom3QvbF8D238D0WQt4nPYidB4FM+4NBusMG5z+koJ1IiIiIiINLSYFxl0LPz9qpb+9w5oOqOMwK73uu2CwzrDD5PtqVLxhGCRHJpMcmUy/5H4HzGuaJgXuAiuAVy6IN6MgjTabfiExfT1GSR620kL2OZzsdDjY4LTxu91knVmCF1+16+U1vaQVppFWmMay9GWB46+Zbt43DKJMk562Pbwcdxv/mLOKrkl96B7fnR4JPegY2xGbUbvVcFsFTyls/RUKM63h1l3GaPqimirKhrfPCAbrXLFWh5cqgnVlSnBxk/tqvnDdjdPwWp+9f5sO465p8Co3FgXsWrGz7T9aL2xgga8fa8yuleYrJJLXPMdwo/NjAC51fAPmP5rxpI4e7DGbcMStYoJjAU/u20qc/1usYsPglrYpFNqsNyVvYddAkM5Xmkp1VnwCwOGCP78JLx5lzYlXnAPvnmW98Zf7Jo0jboMeh9fvryciIiIiIpUbfz2s+h+krwFPMbx/Plz4OWSshw8vCuYbcX6DDq8zDINYVyyxrlg60jH05MBzD/jY/YN92SXZ7CvaR0ZRBhlFGaQXpZNRGNzPLc2ttJzNLid3pbbh32kZABzqzsEz+wXuTWnDbqcVKoiwR9Atvhs9EnpYW3wP+iT1oXtCd5w2Z93/EM1Z+lr44ALrtVTGsMHUB63AcLP9vNyIPCXw3l8gbZWVtjngrDehw9BqPXyN2ZXnvKdwg8M/jH3Wg9B7MqQeOGDeXChg10oZ+DjL8VMg/Zan8t51Zd70TuUax+dEGG6G2jZZ0euuYxu4lvXIVowjdq21aETsGqKMIv6Wlc15GcE5JnJtBteltmdl6WA8mQPx5A3A9MbV/ppx7eDst+CNU6HE/yZZPljX7wQ48rbaly8iIiIiIjXjioGz3oaXJlpt9Jxt8PSw0DwxbeGoO5uketVxwGBfJUq8JaQVprErfxe78nexI38Hu/J3sTN/J9/v3MgTSR5uysoGYGxxCZ/u3M30xAQ+jI8lnxLWZa1jXda6kDIdNgc9EnrQJ7EPfZP60ifJ+tkuuh1GMwxU1XRKpeNt83ncOT0wpVKA6YPv7+Hjb77lTvfllBIMatZ5peOW6OtbrB6KZU55HnpNqlERz3lO5YZO62DvH+ApgnfPhst/gKikeq5s41PAroWr8qaw6Sd4w/omhagknr7nXp52RFRZTvc7vuJT73jOLgvyzXsu7AN2hiMHR+xqHHEriYzfjMdnTV7Zu7SUJ9Iy6OH2BPLmuaJZddxD/OeQc4l2RtdfJTqNhL8usOazW/wquAuhTW+Ycj/0P1HfuoiIiIiINLaU3nDadHjvnIrnErvC+f+DuPaNXq2GEmGPoEtcF7rEdalwrvsdX/G0UYrL9Q7XGN9jA2JMk5uysrkqJ5cPY2N4JTGeTHvovGAen4f1WetZn7Werzd/HTge54qjT2KfQACvLJgX44xp6F+z0Rxn+41nnc9gM6xRWkWmi1m+4fQw9jDIP5/an+y/km9GcZ/n4gMV1botfg2WvBFMT7kfhp5V42LcOKz/5/9OtT5vZ26CDy+Gv3wE9uYd8mretZfaW/ZOcH/wn+EAwboyr3iPCwbs1nwJWVshqVvD1K8WfKaPVftW8evOX4nu/hn2qB2Bcx7/FA8n5hVw775MospN5OrrPZW4k59hbHyHhqlYfAc49hE44hbr5tFhKNhbefdxEREREZGm1P94OOd9mPcs7FxsfdBvPxjO/dBqv7cmpot/lVzED8ZhfNLpXchYC0C0z8eFuXmcV+Rhff9j+L7LINblbWN91np2FeyqtKi80jyWpC1hSdqSkOOdYzvTL7lfIIjXN6kvneM6N7v58cbaVvGk87lAsG6Trz3XuG9gjdkVF24edLwa+Mx8oWMGP/qG85NvWNNVOFztWAxf3xpMDzkLxt9Q+/LaHwKnPh8c1r7pR3j/PDh9OkQm1KWmTUoBu9aoOAdWfR5MDzvwHAll1pldmO09hMPtf1hdfec9B8c/1kCVrJ6s4izm7JrDnJ1zmLtrLpnFmQDYoyrmvcUdxYUZ24IHnNFw3DRsw89vnJ5u0cnWJiIiIiIiTa/fsdbmdUPOdkjo2ux75NTFErMvXDUbfn8X5j0fCNzZ3UX0X/E/+u9ZYy2Y12EI+aX5bMjeEBguW9bbLs+dV2nZO/J3sCN/B7O2zQoci3JEhfTE65fUjz5JfYhz1WFaogZ0iLGJF51PEGFYI7U2+jpwZul9ZBIPQClO7vBcTpKRzzF2a/Xdx53TOaZkWiCPACX58PGl1iIdAO0GWys21/Uz+aDTYO8q+MUfo1j3Dbw0Cc54FToMqVvZTaT13o1as5WfWmO7AdodUu0JHQH+6z3eCtiBNcRz3F8btZed1+flj31/MGfnHH7d+St/ZPyBSeXLnpumDW9hTzx5A1l4eFsSv783eDKlr7UoRNv+jVRzEREREREJS3YnJPds6lqEhe73zARSgXuZalvMzY4P6W/bbp1MX0PJCxN52HMeb3qnYi3IFwMM928mhiMHW8Qe7JF7sEXsxhaxB1tEOoZRcVXbIk8Ry9OXszx9ecjxjjEd6ZvcN6Q3Xte4rtht9gplNJQKU0vtWgZvXAPFhVY6tj29Lv2OJZV9Fi4YB/8ZB/l7STVyeNj5Cte4b6h7pYpzIGMDRMZDbNvm23Nsxr2Qtdnaj4i3Fplw1dO0VEfdaS0mM/dpK71vA0w/AkZcAJP+DrGp9XOdRqKAXWu09O3g/rC/1CiS/ZNvKIt9fRhpW29FxH98xOpm2kC8Pi9rs9aycM9CFu5ZyOK9i8l351eZPzkymfEdx/PB7Bg8+X3BF80xtoUkfl9uSfYuY+G8jyAiPL+5ERERERERaVoGM3yHMqt0BOfYf+Bux9tEGyVEGB4ecr7GAGMb93kusuYPK/cY05OI15OIt6BcxwjDw7e39mNd1jrWZq4N9MorGx21v10Fu9hVsIuftv8UOBZpj6R3Yu9AIK93Ym96JPQgNSq14Re52PiDNSdacba/Molw3sdVd1yJaWMtnvD2nwA43r6AY7wLgVosOmGasPITWPauNQ+9zx0813EEHHYdDDi5+fQM3TATFv03mD7uMUjuUX/l22xw9ENWp6TPrvV3VDJhyevwxydw5K0w5qpqTQkWDprJsyr1ZtdS2LHA2rc5YMifa1iAwaPuc/gw4kErufx96ybR/pB6qV6Jt4TV+1bze/rvLNqziMV7F1fZrRrAZtgYmjqU8R3HM6HzBAYkD8Bm2HjnK2uVny7GXh53vgBlvfA6DIW/fKBgnYiIiIiIyEH4sPG2dwrzfAN5yvksg21bADjX8QO9bLu4uvSGgw/3NB30T+5P/+T+0Ct4OKMog3WZ6wIBvLVZa9mUsymwWGB5xd5i/tj3B3/s+yPkeIwzhh7xPeiZ2JMeCT3oEd+DHgk96BLXBWdd5w3P3AS//AuWlevwEpkIF35+8M+/fabwnueowHx2DzpfhaIbICqx+tfP2QlfXG8FuSqzawl8dLG1qOFJT0H3CdUvuwnEUQif3RI80P9EGHp2w1xs8BnQfgh8d2fw71eaZ/XuW/QKHP1ws1gEUgG71mbus8H9QadDTEqNi1ho9oe+x8K6bwETvrkNLvisxgspmKbJ9rztLM+wukGvSF/Bmqw1ld6gy2sb1ZZxHccxofMExnUYR0JE5V2BnXh41vkM8YZ/+G9iVzjv0+bbdVhERERERKQJbDI7ckbp/Uxzvsip9rkAjLGt4TPX37ncfTNrzK7VK2jfRvjlcdi+gJSSXFIMG4cNPAWOvB1iUnB73WzO3czazLWsz1ofCORlFGVUWlyBu6DSQJ7dsNMxtiOdYzvTKa4TnWM70znOv8V2rvQzZCrZjLatYbhtPTz/D0hbGZohug2c90m1p5R6xHMuk+zLaGtk087I5v1/XMjtniuq8UiT022zud/5BvFGYciZDb6OOPHQwdiHy/BaB/dtgNdOgFGXw5T7wrZzyh2OdyHPv1hJdIoVZDxIwMzr81LsLabIU0Sxp5hSXylurxtb5HYMwwuGBwwPvR9eae3bPP7j1jnD6MkREcdwZ+l8epk5VqFZW+D981hgb8urrv6sTt/asL94HShg15rk7LDmrysz7q+1L2vyfbD+e2vxia1zrKDdCU9U+Q9X5CliY/bGkC7Q67LWkVuae9BLpUalMqr9qMDWNa5rtbo93+F4l6G2TVbC5oQzX7O6J4uIiIiIiEjFudoOxjwV5jwJMx8ATLrY0vk29kE4bhqUW8yv+x1fhT6uKBt+/IfVu2n/DhoLXrSGfE66G+eYqwLz1pW3r2gf67PXsy7TCuBtydnCppxNVU6X5DW9bM/bzva87bC74vk4V5wVzItKZXJ2Ou9GL2eMbzeBNWvT9nvAoNOt3zG27cH/Rn65xHKv+yJecD0JwFmOn1hq9uY976QqH5NKNo84X2aqPbjKrs80eM17DK94j2OHac3B1oYcLnB8z8X2b4MdVBa+BOu+g5Ofgl5VX6O+maZJkacoZCv0FFLkKcIeuwrDVsoYNvGX0uCCI5/2Hc/SZU+HPsZdWKGMEm9JpdeMqcEo2t+AM8x4/pxr45rsHBJ81nyKo71pjC5K44FzTNo17VqaVVLArjX57QUw/VH47odDx2G1L6vdQGtCxx//YaUXvYIvsRtpw85ia942tuZuZXvedrbmbmVzzma25m6tcnGI/XWP787glMEMazuM0e1H0y2+W43nJZhiW8yljm+CB6Y+AJ1G1qgMERERERERKccwYMKNkNofPr4MSvPBXQifX2cNPZz6UIW53Y62LYTnboL8PVWXW5oH395h9RY77jHYb4GJNlFtaBPVhrEdxgaOmabJvuJ9bM7ZXGHbVbDrgL9GXkku7bMW87fMbLp7Kh/hVWIYLI1N5Jf2vdmSFEXC0n+TGJFIQkQCiRGJIfsxzhiiHFFEO6OJtEcGFsj41jeaz73jONk+D4CHHK+y2deB38wB+13N5GTbPB5wvkaSEQxCbvG141b3ldYot3L2kcC/PWfyjmcyvw350j/6DcjZBm+eZi2ycPTDEJmAaZqU+kopchcFequV9Vgr9vjT3v3SVQTgKguuFXuKq/ysH90FIn0+Ht4VfO5/jI7i3uwlkLP0gM9RffIYBu8kxPFlbDRXZ+dwdm5+IBjWNip8h8Uaplm9IEpzYhjGGcBZQNkslsnA7aZpbmqKcutaH8MwFo8YMWLE4sWLD5p3/28yAt+YFGbCU0OhxN+j7Zz3rSXMq6n7HV+CrRibIxfDmcO/zu7OnoLdTJj/GoP3rA3k+zUqkofbJLPTWb1YcLwrnsGpgxmSMoQhqUMYnDK4yiGu1Za9nex/jyHRKABghnckUx+cFfbj00VERERERJqNtNXwwYWQEfw8iM0Bg07nkSV2HHg5yT6PAWWrzJbpNt7q/JHSx5pjfca9kLEueH7gKXDai+CMrHXVijxF7MrfxY68HezI32H99O8XZG3hjrTdTCosCnmMD1gaEcHiyAiWR7pYEBlJkc1W+QUOItIeSWGJHXwuIj123tq3lgEe6/NpnmHn6ejevBPZFa/pYIw7myuKNjDekx5SxlsRPfi/qIEU2RwE5mTHBMOLYXj8wz69HNotjtEZW7lo22rivMFFKdIcTv7Zti2zIhzV7jzTEO7OyOTsPCsImWcYnNq5A2mO6vcdi3JEEeWIIsIegcvuwmlzsnZ3EZgOTNMe8jNk32fHNB1YqxnbwDSsfdNGZ18+Z7vXcIZnDckUYzyQu8Q0zbDr4dPiAnaGYXwIJJqmObXcsRHALOBM0zSrmLGxYcqtj/oYhrF4+PDhI+YtnBd6HKPCfp+7v/Yf8IHhYdHfJ+Lxuon/7Hqi138PQEliF/44+1UKPcUUeAoodBdS4C6gwG3t57nzyC7OJqski5ySHLKKs8goyqp0KW6Xz+S/e/YyrKQ0cMwNzIiJ5p34OH6PcIFhYDNsdIvvFrI0d9+kvnSI6VC/q/p4SuC1EwMLa+w023B8yT/5/dGz6u8aIiIiIiIiAqWF1sT+i187aNZ0M4H73BfytW8MlPss68TDv5wvcIp/bjyA+b4BXF56M3lE12t1p9oW8YjzZVKN4NRMubh40TWIz6NTSXeVYjjyiIspoNBTeICSaqa9x8N7O/fQxhf8TJ1vGNiA6P1iMjsddu5NacOCqJoFLNt4vdyVkcnR+wUiv4iJZlqbJHLs9ioeWXcR9girh6EjOhBgi3JGEbFyE//JDfakmzH0ZDb3OjyYx79FO6ND0/5yIh2R2IzaBU2rxevmlKNG8Pmvfyhg19AMw7gCmA4kmaaZXcm5aUCP/c81VLn1VR/DMBZHdosc0fuB3gAkeL2MLC4h2mdSbDNIt9tZEeHCV0Xg66S8fB7JCC6Z/dd2qfwSHXXQ37u6onw+rs/K5tzcfPb/V8pJ7k7+8HNJHnUlUZGJ9XbNSpmmtXTzsrcA8Jg2/lx6L0vMvjWfm0FERERERESqZ/Mv8NM02PprhVNFpotPvROY5jmbHGIrfbiBj3scb4dMa7Ta15Vb3Fex0uwekteBh0HGFkba1tPWyAZMSnDxh687S3x92EfFEVudjXTudbzB0fbQUWtveybzL8+ZZO230u2WR0+gwF1AWmEa2SXZZBdnk1OaQ05JjpUuyQ7s55TkUOguDBk2WpkBJaU8npZBtyqG4HqBT+Ji+b/kRApq2bMPYGpBIXdnZIYEB/fZ7TzRriPzk9oFgmKR9kgiHZGBwNj+x+Ow0TFnL0mF2dbcfYldIKUvUa64kEBb+SHAIXJ3kfF/Y0jxB0e/9Y7i2AdnhN3It5EjR7JkyRIF7BqaYRhZwEzTNM+s5FwikAU8Zprm7Y1Rbn3VxzCMxcm9Ikf87W/tOCW/gMElpRUCYxl2GzOio/kuJpolkRGYhgGmycTCIh5J30es/3n+MC6WB1OSq//Ll2N6IzC9sfjcCZw2eBDtYtrRLtra2sa0pVtuBrE/Pgrb5lZ8cFJ3az6DASc13D/o3Gfg+3sCyX+4z+Ul74lALSZTFRERERERkZrZvgC2zuHlb38jhmIWm335xjuaAqrTYcTkSvuX3Ol8N+ToD95hrDc7YQBDbJsYamwkyiitvAised+WmH3YYyZjAofa1jHKWIvNCMY+9pqJ3Oq+kl98la/4WpfPjz7TR7GnOBDAK5vvzePz4PMU0fb3j+m87H0cbqsHn8cRwY4e41k74GgK49oDYBgGBkbgZ9kxGzauf3d5uSGgdj666nCcNmfI5irJI+HHR4lc9Vlo5QacbM1tt988gwEl+dZClUvfskatmfuNsottByMuhJEXQUKnqv8I+Wnw6vGwbz1g/b2PLXmUpY+eU+O/Z0NTwK4R+IeZLuYAATB/AA3TNJMautz6rI9hGIv33RE3IjmieoGuNLudLQ4nUabJ4NLgqiq7XFHcOmAMXmcUTpuTaGc0Mc4Yoh3WzxhnDNHOaGKdsSRGJpIUkURiRCJJkUmMfmiedUOohoHGFs63z+BU+5wKN9L5vgE85D6PlWbly7rU+sa48GX46hbKxvZ/5D2CW9xXUtbVWgE7ERERERGRxlFhldgaON32C9OcL+E0vPVYo6B3PROZ5jmbbOKqzNPgnx+9bijKAkcEOGPAXv053Wryt51sW8w/nK/Q3go9AFBq2nnfO5GvfGNZ6utNJKX0NnbyJ/svnGyfR6xRfNByS007H3qP4nnPyewkNeRcJ9J52fWvwNyFbtPOhe7bmes7JCw/l4dzwK4lrRJbNknZxgPk2QSMMAyjZw0WoKhtufVan/LBOq9p8LvZi21mW6IpYbhtA6lGTuB8W6+Xtt79bm5RyXQ8/1Peru3KsNUM1gGsMrtzp+dyHvWcw9n2H7na8XlgAYixttV84bqHj72H87jnLNKoduy0cj4f/PAQ/PpE8FiXMdy1/lLKz4sgIiIiIiIijaNugZkTYO8F8NOjsPrzyrMkdoUuYyG1n7WibEEG7FhkLWLhLamY37BB98PhqDs5p9s4mryfl91pDTNtYLN8I1lY0p+7HG9ztuMnAFyGl/MdMzmfA0+n7zUN1pmdWWd2IYk8Bti2Bub+cxle/uKYxVn2H5njO4QZvpGU4GSgsZVz7bOIMDyBMq53X8tc3yEN+nu2VC0pYDfC//NAga9N/nw9D5KvPsqt9/ps9bXlNe8xfOI9PGTsvw0fo21rONE2j2PtCwNjxAHrxnToJTDxboiu3VDY2sohlunek3jPO5G/OT7hfPsMnIYXm2FypuMXjrf/xkveE3jPM5E9tKn5BTb/At/dDXuWB491HAFnv0vpQ/Pr7xcRERERERGRxtNuEJz1JqStgS2zobQAvKXQpjd0HQvxHSt/nKcE9qyAnYuhJA98XohrD/2Oa5QAWTjKJYY7PFfwsfcIbnO+xyjbugPm3+DryHveiXzqnRAyH6ADD1Nti7nE8U2gDIfh40j7co60L69Qjs80uNl9Nd/4xtTvL9SKtKSAXU2iUYmNUG691uf4LxNYM+UJfBVmrwMfNub7BjLfN5D7PBfRz9hOglFADMW8fOuFVY9PbyQ5xPKg5wLe8k7hLsfbTLFbq8TEGCXc4PiE6+2fssjsyxJfX66/ay67zWQyiaPIjMCNHTs+oo0Sksijq5HGIbYtTLQtpadtT8h1ZnqHc92maylSsE5ERERERKT5a9vf2qrLEQGdD7U2CbHQ7M+ZpfdxuG0Fx9kWMNq2ht62XeSZUaSZiSz29eV971EsNvtS2Wg1Dw6+8Y3hm9LRHGZbyfWOTxlrW13ptZb4evOI+1wWmTV47qSClhSwS6xB3sYI7tX2cZX6aVUGA8z7Kz23ePHiSo/Xp/oba345bPzR6hmXthIAm2Ey2ljLaNvaWpVYZLqY7j2RZzyn4aXhlqoWERERERERaUp1/2x+YnDX6yHO7iAO6AX8uUZl3A7Z22Dl/6xRbzYnuGKg9xRG9D2Gj8JwNdjKrF5dedAxHLSkgF1NJIZZubV9XPPUayJcNRtWfMjsj57hMNtK7EbNFz8pMCP40juOf3v+VLshtSIiIiIiIiKtVQ0Wu6hUYlcYf3391EUqaEkBu+wwK7e2j6vUgAEDGqUnXaOx2WHo2Zz/bhypZHOobS2H2DbT19hJGyOHZPJwGW6cePFgp8h0kUs0O8xUtpntmOcbyG++AZTibOrfRERERERERETCWFXxFP8qsY1cm+ppSQG7zBrkzW6EchuqPi1KTbvzDvP/vKbeayIiIiIiIiIiEh4qrmDQfGX7fyYeIE/ZudoE02pabkPVR0REREREREREWrCWFLArC3odaAGHsnM16e9Y23Ibqj4iIiIiIiIiItKCtaSA3Qz/z14HyNMTyDZNc1MjlNtQ9RERERERERERkRasxQTsTNP8CGsY6ojKzhuG0RNrCOoHjVFuQ9VHRERERERERERathYTsPP7JzDFMIzESs6d4f95+/4nDMNINAxjmmEYZ+x/ri7l1uFxIiIiIiIiIiLSSrWogJ1pmo8BM4FZ5Y8bhjECmAacaZpmdiUPvQK4DfiwPsutQ31ERERERERERKSVcjR1BeqbaZpTDcO4wjCMGViLOSRiLe4w0jTNqhZ3mAls8v+sz3Jr/TgREREREREREWmdWlzADsA0zReBF2uQfwkHXhyiVuXW9XEiIiIiIiIiItL6tKghsSIiIiIiIiIiIs2dAnYiIiIiIiIiIiJhRAE7ERERERERERGRMKKAnYiIiIiIiIiISBhRwE5ERERERERERCSMKGAnIiIiIiIiIiISRhSwExERERERERERCSMK2ImIiIiIiIiIiIQRBexERERERERERETCiGGaZlPXQQ7CMIyCqKio6MLCwqauioS5kSNHArB48eImrok0B3q9SHXptSI1odeLVJdeK1ITer1Idem1IjURHR1NUVFRoWmaMU1dl/2ph52IiIiIiIiIiEgYUcBOREREREREREQkjChgJyIiIiIiIiIiEkYUsBMREREREREREQkjCtiJiIiIiIiIiIiEEa0S2wwYhuExDMM+fPjwpq6KhLnVq1cDMGDAgCauiTQHer1Idem1IjWh14tUl14rUhN6vUh16bUiNbF06VJM0/Sapulo6rrsTwG7ZsAwjM1APLCliasiIiIiIiIiItJSdAdyTdPs0dQV2Z8CdiIiIiIiIiIiImFEc9iJiIiIiIiIiIiEEQXsREREREREREREwogCdiIiIiIiIiIiImFEATsREREREREREZEwooCdiIiIiIiIiIhIGHE0dQVaE8MwzgDOAjL9h5KB203T3BSO5UrTMgxjGjAC6Ok/tIQ6PK+GYfQEZgDT/WVtwnrN9MR6/UwxTXNkXestjaehn1PdW1oWwzBmAB8CH5immV2P5ere0gKUPY+mafaqZn61aVqpWrxW1J5pxar7elGbRmrwWlF7ppWr7ftKs2y7mKaprRE2rJvKjP2OjQCysP75w6pcbU36Wil7s5iy37HFgAncVodyzSq2LGBEU//u2sLnOdW9peVtwMYDvF7236r92tG9pfluQKL//3p62XNWzcepTdPKttq8VtSeab1bHV4vatO0sq2WrxW1Z1rpVpf3lebadmnyP3pr2IAr/C+gxCrOZVV2rqnK1dbkr5cZQM8qzpW9QZ1Ri3J7+h9fdkPL8l+rVg1mbU2/NdRzqntLy9xq0Lj9sIbl6t7SDDfgDP9zNh2Y4n/ezGo8Tm2aVrbV4bWi9kwr3OrwelGbppVtdXitqD3TSrfavq8057ZLk//RW8Pmf6IqvWFgfatgAtPCpVxtTfpamXKg56zcTWFjLcruqddDy9oa6jnVvaXlbf7XygEbrv7ndkYty9broZlvNfigpDZNK9+q81pRe0ZbueerJgE7tWla8VbNe4vaM610q8v7SnNuu2jRiQZmGMYIrCer0vHLpjXuPhvrBdbk5UqTmwrc5h+XX5mZ/p89DcNIbJwqSWuie0uLNQJ4/yB5XgJub4S6SDOlNo3UgNoz0uR0b2mR1J5pvWr1vtLc2y4K2DW8s/w/Nx4gzyYg0T/RZVOXK00r0f/zjCrOZ5bb1/MqDUH3lpYpm2BDpgLDMK4AFpqmuaTRaiTNkdo0Ul2J/p9qz0hT0r2l5clG7ZnWKtH/s6bvK8267aKAXcMb4f95oBVCys7V5IlsqHKlad0OvAicWcX58s+lVrWShqB7SwtkmuZMs4qV1PyNiDNN03yscWslzZDaNFJdas9IONC9pYVRe6ZVq+37SrNuuzhq+0CptuQa5E0Mg3KlCfnfgK48QJZD/T83VfVmdTD+7rvlr5EMTDdNs8pvqyS81fNzqntL6/MhVTd+qk33llZBbRqpFrVnpLbUppE6UHumBavD+0qzbrsoYNfwEmuQNxxeTBLertzvZ02dAWCaZuDx/m+jFhuG8U99I9Us1fdzmliDvLq3NHP+oSMzTdOsaw8X3Vtah8Qa5FWbRg5E7RmpjNo0UitqzwhVv68k1qCMsGu7aEhseElsZuVKI/K/EY0APqrlNzyZwO2maYZMwup/Y/snMM3/jZI0H039nCY2YNnSOKYB0+tYRlO/DiU8JTazcqWRqD0jVWjq5zWxAcuWhqf2TCtWD+8rZRLrp0b1V64Cdg0vu5mVK2HI/83OdKxvjmrV1ds0zWzTND+q4nTZje2l2pQtTaOBntPs2tdImhN/4yazrt9G697SqmQ3s3IlzKg9I1VRm0ZqS+2Z1q0a7yvZDXTphio3hAJ2DS/z4FkCssOgXAlPHwJLTNOc2hCFl1tJSd8atRB1eE51b2k9bgcadBU13VtaHLVppK7UnpEaU5tGDkLtmdbtYO8rzbrtooBdw8v2/0w8QJ6yc7V50uu7XAkzhmFMBzBNc2Qdykg0DOMMwzASq5FXb0TNQAM+p9n+nwcqt+yc7i3NlP/byJ7AwjqWo3tL65Lt/5l4gDxl59SmkRBqz0hV1KaR2lJ7pnWr5vtKtv9n4gHylJ0Lu7aLAnYNr+zJOdBEg2XnavLNQEOVK2HEMIzbgJ51adz63Yn17UN1unHXdbJWaRwN9Zzq3tI6nOH/Wdf/d91bWhe1aaRW1J6Rg1CbRmpL7ZlWqgbvK8267aKAXcOb4f/Z6wB5egLZNRx331DlSpgwDOMMYGpl3Xv93wD1rEWxMyo7WK6s7P2WwZbwV9/Pqe4trUPZfSW7nsrTvaV1UJtGakztGakBtWmkptSeaYVq+L7SrNsuCtg1MP/EldlUMd7d/2JKBD4Ih3IlPPi7Wl95gLH4U6lZ19qF/vJerOL8FP9PvV6ajwZ5TnVvaTXKGjJ1HQKke0srojaN1JTaM1JNatNIbak908rU9H2lubddFLBrHP8EplQxJr6sG+/t+5/wj6Wf5o8g11u5Et78/9x3VnUT8j/fh+7/7c6BXi/+G8rUA8zLcDvWDUevl2aiLs+p7i1CsIF7ULq3yH7UppFqUXtGqkttGqkDtWdakdq+r9Cc2y6maWprhA2ry+Ti/Y6NAEzgjCoec5v/vFmf5WoL3w0rCr+x7Hk/wLa4ksce8PWC9YY2Axix3/Vm+K85or5/H20N/nqp1XOqe4u2cveSg/7f697S8jf/81X2muhZjfxq07TSrbqvFbVntNXk9VKX51X3lpax1fR9qNzj1J5pJVtd3lf8j2+WbRcH0ihM05xqGMYVhmHMwJp0MBFrEsKRZnCZ6P3NxJrUcmY9lyvhaxrV+6ZoUSXHDvh6MU1zk2EYZwLT/N9OlE2COdOsukuxhLE6PKe6t8gSILGaz6XuLS2Qf0hJ2eTa5d93NhqGUfa6+Kdp9ToIoTZN61LL14raM61Ube8tatO0PnV5HypH7ZnWoy7vK8227WL4I4AiIiIiIiIiIiISBjSHnYiIiIiIiIiISBhRwE5ERERERERERCSMKGAnIiIiIiIiIiISRhSwExERERERERERCSMK2ImIiIiIiIiIiIQRBexERERERERERETCiAJ2IiIiIiIiIiIiYUQBOxERERERERERkTCigJ2IiIiIiIiIiEgYUcBOREREREREREQkjChgJyIiIiIiIiIiEkYUsBMREREREREREQkjCtiJiIiIiIiIiIiEEQXsREREREREREREwogCdiIiIiIiIiIiImFEATsREREREREREZEwooCdiIiIiIiIiIhIGFHATkREREREREREJIwoYCciIiIiIiIiIhJGFLATEREREREREREJI46mroCIiIiING+GYUwDEoFkYJNpmrf7j98GtPFn22ea5mNNU0MRERGR5sUwTbOp6yAiIiIizZRhGNOBaaZpbvKnFwMzsQJ4003TXOIP6N0GjDRNc0mTVVZERESkmdCQWBERERGpFX8gLhCs81uEFZyjXHDuCv/P8vlEREREpAoK2ImIiIhIjRmGkQj03C9YB9awWIBp5Y6NNE3TME0zuzHqJiIiItLcaUisiIiIiNSYP2DH/kE4wzCygEzTNHs1QbVEREREWgQtOiEiIiIiNVZZbznDMEZgzV33QWPXR0RERKQl0ZBYEREREakvU/w/P2zSWoiIiIg0cxoSKyIiIiL1wr9C7AjTNI1KziVqDjsRERGR6lEPOxERERGplbJ57MrtjwCWVJJvGsHFKERERETkIBSwExEREZEaMwxjI5BV7tCd/p+b9suXCCRWspqsiIiIiFRBATsRERERqRHDMHoCPYGZ/nSi/9RjWL3sKHd8GnB749ZQREREpHnTHHYiIiIiUmOGYdwGtClLm6Z5u//4NKxgXiaQXXZcRERERKpPATsREREREREREZEwoiGxIiIiIiIiIiIiYUQBOxERERERERERkTCigJ2IiIiIiIiIiEgYUcBOREREREREREQkjChgJyIiIiIiIiIiEkYUsBMREREREREREQkjCtiJiIiIiIiIiIiEEQXsREREREREREREwogCdiIiIiIiIiIiImFEATsREREREREREZEwooCdiIiIiIiIiIhIGFHATkREREREREREJIwoYCciIiIiIiIiIhJGFLATEREREREREREJIwrYiYiIiIiIiIiIhBEF7ERERERERERERMKIAnYiIiIiIiIiIiJhRAE7ERERERERERGRMKKAnYiIiIiIiIiISBj5f8tZKO4HagZZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 595,
       "width": 630
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#------------------------------------------------------------\n",
    "# plot the results\n",
    "fig,ax = plt.subplots(figsize=(10, 10))\n",
    "xgrid = np.linspace(-10, 30, 1000)\n",
    "\n",
    "# True distribution: you typically don't have it! Only have the samples!\n",
    "if False:\n",
    "    ax.plot(xgrid, hx(xgrid), ':', color='black', zorder=3,\n",
    "            label=\"$h(x)$, Generating Distribution\")\n",
    "\n",
    "# A simple histogram\n",
    "# But try changing the number of bins!\n",
    "if True:\n",
    "    ax.hist(x,density=True,color='C0',bins=100,histtype='step',lw=2, label='Histogram, 100 bins')\n",
    "\n",
    "# Something more sophisticated: Kernel Density Estimation\n",
    "# But try changing the bandwith! \n",
    "if True:\n",
    "    kde = KernelDensity(bandwidth=0.1, kernel='gaussian')\n",
    "    kde.fit(x[:, None])\n",
    "    dens_kde = np.exp(kde.score_samples(xgrid[:, None]))\n",
    "    ax.plot(xgrid, dens_kde, '-', color='C1', zorder=3,\n",
    "            label=\"$f(x)$, non-parametric (KDE)\")\n",
    "\n",
    "# Use Gaussian Mixtures with a pre-defined number of clusters (13)\n",
    "if True:\n",
    "    gmm = GaussianMixture(n_components=13).fit(x.reshape(-1, 1))\n",
    "    logprob = gmm.score_samples(xgrid.reshape(-1, 1))\n",
    "    fx = lambda j : np.exp(gmm.score_samples(j.reshape(-1, 1)))\n",
    "    ax.plot(xgrid, fx(np.array(xgrid)), '-', color='C2',\n",
    "            label=\"$f(x)$, parametric (13 Gaussians)\")\n",
    "\n",
    "# Plot cosmetics\n",
    "ax.text(0.02, 0.95, \"%i points\" % N, ha='left', va='top',\n",
    "            transform=ax.transAxes)\n",
    "\n",
    "ax.set_ylabel('$p(x)$',fontsize=14)\n",
    "ax.legend(loc='upper right')\n",
    "\n",
    "ax.set_xlabel('$x$',fontsize=14)\n",
    "ax.set_xlim(0, 20)\n",
    "ax.set_ylim(-0.01, 0.4001)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.34357186498273545\n",
      "[0.12751122]\n",
      "[0.23034853]\n"
     ]
    }
   ],
   "source": [
    "# For instance in a single point:\n",
    "print(hx(9))             # h(x), the true distribution\n",
    "\n",
    "print(fx(np.array([9]))) # f(x) for a parametric model\n",
    "print(np.exp(kde.score_samples(np.atleast_2d(9)))) # f(x) for non-parametric model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A note on uncertainties and errors\n",
    "\n",
    "* Technically, errors are systematic biases that we can not mitigate through collecting lots and lots of data. \n",
    "* Statistical uncertainties are the result of random measurement uncertainty. \n",
    "* But \"error\" will be used for both, and denoted as either statistical errors (error bars) or systematic errors (biases).\n",
    "\n",
    "\n",
    "* Statistical error distributions (error bars) that vary from data point to data point are called **heteroscedastic errors**. If they are the same for all points then they are **homoscedastic errors**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "##  We could summarize the goal of this course as an attempt to \n",
    "\n",
    "1) estimate $f(x)$ from some real (possibly multi-dimensional) data set, \n",
    "\n",
    "2) find a way to describe $f(x)$ and its uncertainty, \n",
    "\n",
    "3) compare it to models of $h(x)$, and then \n",
    "\n",
    "4) use the knowledge that we have gained to interpret/predict new measurements."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Probability <a class=\"anchor\" id=\"two\"></a>\n",
    "\n",
    "> $p(A)$ = the probability of $A$ (or the probability density at $A$; I'm sloppy!) \n",
    "\n",
    "e.g. the probability that an observed object is a galaxy. This does not mean that the object is in some sort of Schrodinger's cat quantum uncertainity...*the probability reflects our current state of knowledge of the object, and our belief that it is a galaxy*. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Probability axioms (Kolmogorov)\n",
    "\n",
    "1. $p(A)\\geq0 \\quad\\forall\\, A$\n",
    "2. $p(\\Omega) = 1$, where $\\Omega$ is the set of all outcomes, i.e. the sum/integral of all possible outcomes is unity\n",
    "3. $p(\\cup_{i=1}^\\infty A_i) = \\sum_{i=1}^\\infty p(A_i)$ if all events are independent\n",
    "\n",
    "$A \\cup B$ is the *union* of sets $A$ and $B$. **Read as A OR B.**\n",
    "\n",
    "$A \\cap B$ is the *intersection* of sets $A$ and $B$. **Read as A AND B.** Different notations $p(A \\cap B) = p(AB) = p(A,B) = p(A\\,\\mathrm{and}\\,B)$. We will use the comma notation throughout. \n",
    "\n",
    "If we have two events, $A$ and $B$, the possible combinations are illustrated by the following figure:\n",
    "![Figure 3.1](http://www.astroml.org/_images/fig_prob_sum_1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   "source": [
    "* The probability that ***either*** $A$ ***or*** $B$ will happen (which could include both) is the *union*, given by\n",
    "$$p(A \\cup B) = p(A) + p(B) - p(A \\cap B)$$\n",
    "The figure makes it clear why the last term is necessary.  Since $A$ and $B$ overlap, we are double-counting the region where *both* $A$ and $B$ happen, so we have to subtract this out.  \n",
    "\n",
    "\n",
    "* The probability that ***both*** $A$ ***and*** $B$ will happen, $p(A \\cap B)$, is \n",
    "$$p(A \\cap B) = p(A|B)p(B) = p(B|A)p(A)$$\n",
    "where p(A|B) is the probability of A *given that* B is true and is called the **conditional probability**.  So the $|$ is short for \"given\".\n",
    "\n",
    "\n",
    "* The **law of total probability** says that (for independent $B_i$)\n",
    "$$p(A) = \\sum_ip(A|B_i)p(B_i)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
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   "source": [
    "It is important to realize that the following is *always* true:\n",
    "\n",
    "$$p(A,B) = p(A|B)p(B) = p(B|A)p(A)$$\n",
    "\n",
    "However, if $A$ and $B$ are independent, then $p(A|B)=p(A)$ and $p(B|A)=p(B)$ and\n",
    "\n",
    "$$p(A,B) = p(A)p(B)$$\n",
    "\n",
    "**EXAMPLE** (classic marbles in bag scenario)\n",
    "\n",
    "If you have a bag with 5 marbles (3 yellow and 2 blue) and you want to know the probability of picking 2 yellow marbles in a row, that would be\n",
    "\n",
    "$$p(Y_1,Y_2) = p(Y_1)p(Y_2|Y_1).$$\n",
    "\n",
    "$p(Y_1) = \\frac{3}{5}$ since you have an equally likely chance of drawing any of the 5 marbles.\n",
    "\n",
    "If you did not put the first marble back in the back after drawing it (sampling *without* \"replacement\"), then the probability\n",
    "\n",
    "$p(Y_2|Y_1) = \\frac{2}{4}$, so that\n",
    "\n",
    "$$p(Y_1,Y_2) = \\frac{3}{5}\\frac{2}{4} = \\frac{3}{10}.$$\n",
    "\n",
    "But if you put the first marble back, then\n",
    "\n",
    "$p(Y_2|Y_1) = \\frac{3}{5} = p(Y_2)$, so that \n",
    "\n",
    "$$p(Y_1,Y_2) = \\frac{3}{5}\\frac{3}{5} = \\frac{9}{25}.$$\n",
    "\n",
    "In the first case $A$ and $B$ (or rather $Y_1$ and $Y_2$) are *not* independent, whereas in the second case they are."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Need more help with this?**  Try watching some Khan Academy videos and working through the exercises:\n",
    "* [https://www.khanacademy.org/math/probability/probability-geometry](https://www.khanacademy.org/math/probability/probability-geometry)\n",
    "* [https://www.khanacademy.org/math/precalculus/prob-comb](https://www.khanacademy.org/math/precalculus/prob-comb)\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Bayes' Theorem <a class=\"anchor\" id=\"three\"></a>\n",
    "\n",
    "In the following figure, we have a 2-D distribution in $x-y$ parameter space.  Here $x$ and $y$ are ***not*** independent as, once you pick a $y$, your values of $x$ are constrained.\n",
    "\n",
    "![http://www.astroml.org/_images/fig_conditional_probability_1.png](http://www.astroml.org/_images/fig_conditional_probability_1.png)\n",
    "\n",
    "We have that \n",
    "$$p(x,y) = p(x|y)p(y) = p(y|x)p(x)$$\n",
    "\n",
    "We can define the ***marginal probability*** as\n",
    "$$p(x) = \\int p(x,y)dy,$$\n",
    "\n",
    "where marginal means projecting on to one axis (integrating over the unwanted variable). The **marginal** distributions are shown on the left and bottom sides of the left panel.  As the equation above says, this is just the integral along the $x$ direction for a given $y$ (left side panel) or the integral along the $y$ direction for a given $x$ (bottom panel).  \n",
    "\n",
    "The three panels on the right show the ***conditional probability*** (of $x$) for three $y$ values: $$p(x|y=y_0)$$  These are just normalized \"slices\" through the 2-D distribution.\n",
    "\n",
    "The marginal probability of $x$ can be re-written as\n",
    "\n",
    "$$p(x) = \\int p(x|y)p(y) dy$$\n",
    "\n",
    "But since $p(x|y)p(y) = p(y|x)p(x)$, we can write\n",
    "\n",
    "> $$p(y|x) = \\frac{p(x|y)p(y)}{p(x)} = \\frac{p(x|y)p(y)}{\\int p(x|y)p(y) dy}$$\n",
    "\n",
    "which in words says that\n",
    "\n",
    "> the (conditional) probability of $y$ given $x$ is just the (conditional) probability of $x$ given $y$ times the (marginal) probability of $y$ divided by the (marginal) probability of $x$, where the latter is just the integral of the numerator.\n",
    "\n",
    "This is **Bayes' Theorem**, which itself is not at all controversial, though its application can be as we'll discuss later."
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## Bayes' Theorem Example: Lego's <a class=\"anchor\" id=\"four\"></a>\n",
    "\n",
    "An example with Lego's (it's awesome, let's have a look!):\n",
    "[https://www.countbayesie.com/blog/2015/2/18/bayes-theorem-with-lego](https://www.countbayesie.com/blog/2015/2/18/bayes-theorem-with-lego)\n",
    "\n",
    "(This example comes from a very nice book: [Bayesian Statistics the Fun Way](https://www.amazon.com/Bayesian-Statistics-Fun-Will-Kurt/dp/1593279566/))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Bayes' Theorem Example: Contingency Table  and COVID Tests\n",
    "\n",
    "We can also use Bayes' rule to learn something about false positives and false negatives.\n",
    "\n",
    "Let's look at COVID tests.  The test can be positive ($T=1$) or negative ($T=0$) and one can either have the disease ($D=1$) or not ($D=0$).  So, there are 4 possible combinations:\n",
    "$$T=0; D=0 \\;\\;\\;  {\\rm true \\; negative}$$\n",
    "$$T=0; D=1 \\;\\;\\; {\\rm false \\; negative}$$\n",
    "$$T=1; D=0 \\;\\;\\; {\\rm false \\; positive}$$\n",
    "$$T=1; D=1 \\;\\;\\; {\\rm true \\; positive}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "All else being equal, you have a 50% chance of being misdiagnosed.  Not good!  But the probability of disease and the accuracy of the test presumably are not random.\n",
    "\n",
    "If the rates of false positive and false negative are:\n",
    "$$p(T=1|D=0) = \\epsilon_{\\rm FP}$$\n",
    "$$p(T=0|D=1) = \\epsilon_{\\rm FN}$$\n",
    "\n",
    "then the true positive and true negative rates are just:\n",
    "$$p(T=0| D=0) = 1-\\epsilon_{\\rm FP}$$\n",
    "$$p(T=1| D=1) = 1-\\epsilon_{\\rm FN}$$\n",
    "\n",
    "Let's assume that $\\epsilon_{\\rm FP}=0.02$ and $\\epsilon_{\\rm FN}=0.001$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "In graphical form this $p(T|D)$ matrix is:\n",
    "![http://www.astroml.org/_images/fig_contingency_table_1.png](http://www.astroml.org/_images/fig_contingency_table_1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    }
   },
   "source": [
    "If we have a **prior** regarding how likely the disease is, we can take this into account.\n",
    "\n",
    "$$p(D=1)=\\epsilon_D$$\n",
    "\n",
    "and then $p(D=0)=1-\\epsilon_D$. Say, $\\epsilon_D$ = 0.01. \n",
    "\n",
    "Now assume that a person tested positive. What is the probability that this person has the disease? Is it 98% \n",
    "because $\\epsilon_{\\rm FP}=0.02$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "We can't just read $p(D=1|T=1)$ off the table because the table entry is the conditional probability of the *test* given the *disease*, $p(T=1|D=1)$. What we want is the conditional probability of the *disease* given the *test*, that is, $p(D=1|T=1)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Bayes' Theorem then can be used to help us determine how likely it is that you have the disease if you tested positive:\n",
    "\n",
    "$$p(D=1|T=1) = \\frac{p(T=1|D=1)p(D=1)}{p(T=1)},$$\n",
    "\n",
    "where $$p(T=1) = p(T=1|D=0)p(D=0) + p(T=1|D=1)p(D=1).$$\n",
    "\n",
    "So\n",
    "$$p(D=1|T=1) = \\frac{(1 - \\epsilon_{FN})\\epsilon_D}{\\epsilon_{FP}(1-\\epsilon_D) + (1-\\epsilon_{FN})\\epsilon_D} \\approx \\frac{\\epsilon_D}{\\epsilon_{FP}+\\epsilon_D}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
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   },
   "source": [
    "where in the final approximation we assume that all $\\epsilon$ values are small. That means that to get a reliable diagnosis, we need $\\epsilon_{FP}$ to be quite small.  (Because you *want* the probability to be close to unity if you test positive, otherwise it is a *false* positive).\n",
    "\n",
    "In our example, we have a disease rate of 1% ($\\epsilon_D = 0.01$) and a false positive rate of 2% ($\\epsilon_{\\rm FP}=0.02$).  \n",
    "\n",
    "So we have\n",
    "$$p(D=1|T=1) = \\frac{0.01}{0.02+0.01} = 0.333$$\n",
    "\n",
    "Then in a sample of, e.g.,  1000 people, 10 people will *actually* have the disease $(1000*0.01)$, but another 20 $(1000*0.02)$ will test positive! \n",
    "\n",
    "Therefore, in that sample of 30 people who tested positive, only 1/3 has the disease\n",
    "(not 98%!). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Transformations of random variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If $x$ is a random variable then $f(x)$ is also a random variable for any function $f$.\n",
    "\n",
    "To transform probability distributions when taking functions of random variables, we can simply use conservation of dimensionless probability, i.e. \n",
    "\n",
    "$$\\mathrm{Prob}(x, x+dx) = \\mathrm{Prob}(y, y+dy)$$\n",
    "\n",
    "$$p(x)dx = p(y)dy.$$ \n",
    "\n",
    "where $y = f(x)$.\n",
    "\n",
    "Thus, $$p(y) = \\left|\\frac{dx}{dy}\\right| p(x)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**EXAMPLE**\n",
    "\n",
    "* Let $x$ be a random variable drawn from a uniform distribution between $0$ and $1$. So $p(x) = 1/(1-0) = 1$.  \n",
    "* Let's transform to $y = e^x$.\n",
    "* So $p(y) = \\left|dy/dx\\right|^{-1}p(x) = 1/y$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![https://www.astroml.org/_images/fig_transform_distribution_1.png](https://www.astroml.org/_images/fig_transform_distribution_1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Bayes' Theorem Example: Monty Hall Problem (or \"Deal Or No Deal\") <a class=\"anchor\" id=\"five\"></a>\n",
    "\n",
    "A very famous stats mind trick... You might have seen this already.\n",
    "\n",
    "The [Monty Hall Problem](https://en.wikipedia.org/wiki/Monty_Hall_problem) was originally posed (and solved) in a letter by Steve Selvin to the American Statistician in [1975](https://www.tandfonline.com/doi/abs/10.1080/00031305.1975.10479121). It became famous as a question from reader Craig F. Whitaker's letter quoted in Marilyn vos Savant's \"Ask Marilyn\" column in Parade magazine in 1990\n",
    "\n",
    "\n",
    "You are playing a TV game show and are shown 2 doors.  One has a car behind it, the other a goat.  What are your chances of picking the door with the car?"
   ]
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   "source": [
    "OK, now there are 3 doors: one with a car, two with goats.  The game show host asks you to pick a door, but not to open it yet.  Then the host opens one of the other two doors (that you did not pick) and that has a goat.  The host offers you the opportunity to switch doors.\n",
    "\n",
    "- One player decides to switch\n",
    "- Another player prefers to stay with the previous choice\n",
    " \n",
    "![https://upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Monty_open_door.svg/180px-Monty_open_door.svg.png](https://upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Monty_open_door.svg/180px-Monty_open_door.svg.png)\n",
    "\n",
    "- Now a third player comes in who has not seen what happened earlier. They pick a door.\n",
    "\n",
    "*Which of the three players is most likely to win?*\n",
    "\n",
    "You might know or remember the answer already... but don't think now! **Let's simulate it**. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Time to get you hands dirty! Open a jupyter notebook and code it up! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulate the Monty Hall Problem\n",
    "\n",
    "- Simulate three doors, one car, and two goats.\n",
    " - Simulate three players: the switcher, the conservative, and the newcomer. \n",
    " - Record who wins.\n",
    " - Repeat it many times.\n",
    " - Which player do you want to be?\n",
    " \n",
    " - What would happen if you had 100 doors to choose from and the presenter opens 98 or them?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[My implementation](https://github.com/dgerosa/astrostatistics_bicocca_2023/blob/main/solutions/S01_monty_hall.ipynb) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pdf of the log\n",
    "1. Use `numpy` to draw $N$ (where $N$ is large...) random samples from a uniform distribution between $0.1$ and $10$, and store these samples as $x$.\n",
    "2. Use matplotlib to make a histogram of these samples.\n",
    "3. Compute the base-10 log of your array $x$, and store this as $y$.\n",
    "4. Make another histogram for $y$. Using the equation to transform probability distributions, write what the theoretical pdf of $y$ is, and overplot it onto your histogram.\n",
    "5. Compute the log of the mean of $x$ and the mean of $y$. Now compute the log of the median of $x$ and the median of $y$. \n",
    "\n",
    "You should note that the means are different, but the medians (as it is a cumulative statistic) are the same. The mean is affected by the scale of the sample values, but the median only depends on the ordering of the samples. Monotonic transformations (like taking the log) do not change the ordering of samples.\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[My implementation](https://github.com/dgerosa/astrostatistics_bicocca_2023/blob/main/lectures/S02_pdfofthelog.ipynb) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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