{ "cells": [ { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# setup... requires numpy and matplot lib\n", "import numpy as np\n", "import matplotlib as mpl\n", "from matplotlib import pyplot as plt\n", "%matplotlib inline\n", "plt.style.use('fivethirtyeight')\n", "\n", "# plot setup\n", "_plt_x = 12.\n", "_plt_y = _plt_x * 0.8\n", "\n", "def normal_pdf(mu, sigma):\n", " '''\n", " PDF of a normal distribution.\n", " '''\n", " def pdf(x):\n", " return 1./(sigma * np.sqrt(2 * np.pi)) *\\\n", " np.exp(-(x - mu)**2 / (2*(sigma)**2))\n", " return pdf\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# MCMC\n", "\n", "Credits: most of this presentation is based off Chapter 11 of Bishop's Pattern Recognition and Machine Learning\n", "\n", "See also: [Iain Murray at MLSS 09](http://videolectures.net/mlss09uk_murray_mcmc/) and [Iain Murray at NIPS 2015](http://research.microsoft.com/apps/video/default.aspx?id=259575)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Outline\n", "\n", "* Motivation - reminder of what we're trying to solve\n", "* What's wrong with the methods we saw last week?\n", "* Simple MCMC example using the Metropolis algorithm\n", "* Why does this work?\n", "* Full Metropolis - Hastings Algorithm\n", "* Gibbs Sampling\n", "* Slice Sampling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Motivation - what we're trying to solve..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recall the problem we're trying to solve:\n", " * In Bayesian inference, we can typically write down a prior, $\\mathbb{P}(\\mathbf{z})$ and a likelihood functions $\\mathbb{P}(\\mathcal{D} | \\mathbf{z})$.\n", " * We're then interested in working with the posterior, $$p(\\mathbf{z} | \\mathcal{D}) = \\frac{1}{Z} \\mathbb{P}(\\mathcal{D} | \\mathbf{z} )\\mathbb{P}(\\mathbf{z} ) = \\frac{1}{Z}\\tilde{p}(\\mathbf{z}),$$ where $Z$ is a normalising constant.\n", " * If we're being Bayesian, we'd then write down a loss function $\\mathcal{L}$ which we can then optimise with respect to the posterior expected loss.\n", " * More generally, we'd just like to be able to be able to evaluate functions of the form $E[f(\\cdot)] = \\int f(\\mathbf{z}) p(\\mathbf{z})\\text{ d}\\mathbf{z}$ for some $f(\\cdot)$\n", " * Why? $f(\\cdot)$ could be:\n", " - Your loss function $\\mathcal{L}(\\cdot)$.\n", " - $f(\\mathbf{z}) = 1$ to get the normalising constant $Z$ (if $p$ is unnormalised, $\\tilde{p}(\\mathbf{z})$)\n", " - $f(\\mathbf{z}) = {z}_i$ to get marginals (by integrating over $\\mathbf{z}_{\\setminus i}$).\n", " - $f(z) = \\mathbb{1}(z \\in \\mathcal{S}) \\Rightarrow E[f(z)] = \\mathbb{P}(z \\in \\mathcal{S})$\n", " - etc...\n", " * Problem - we can't evaluate $$E[f(\\cdot)] = \\int f(\\mathbf{z}) p(\\mathbf{z})\\text{ d}\\mathbf{z}$$\n", " * Solution... approximate it with $$E[f(\\cdot)] \\approx \\frac{1}{N}\\sum_{i=1}^N f(\\mathbf{z}_i)$$ where $\\mathbf{z}_i \\sim p(\\cdot)$\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# How do we sample from $p(\\cdot)$ if it's intractable?\n", "\n", "Last we Ricky showed us two methods...\n", "* Rejection sampling\n", "* Importance sampling\n", "\n", "Both relied on a proposal distribution $q(\\cdot)$ that had to be \"close\" to $p(\\cdot)$ in order to be effective..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Why is this a problem?\n", "\n", "Variant of the curse of dimensionality:\n", "* in high dimensions, it is very difficult to choose $q(\\cdot)$ close to $p(\\cdot)$\n", "\n", "Artificial illustrative example:\n", "* We wish to sample from a multivariate zero-mean Gaussian with covariance $\\sigma^2_p\\mathbf{I}$ using rejection sampling.\n", "* The proposal distribution, $q$, is also a zero-mean Gaussian with covariance $\\sigma^2_q\\mathbf{I}$.\n", "* We need $q$ to \"cover\" $p$, so $\\sigma^2_q\\mathbf{I} \\geq \\sigma^2_p\\mathbf{I}$ to ensure that there exists $k$ such that $k q(z) \\geq p(z)$.\n", "* In $D$ dimensions, the optimal value for $k = (\\frac{\\sigma_q}{\\sigma_p})^{D}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![Normal distribution](normaldist.jpg)\n", "\n", "The acceptance rate is $\\frac{1}{k}$ so if $\\sigma_q$ is just $1\\%$ larger than $\\sigma_p$, for $D = 1000$ the acceptance rate will be just $\\frac{1}{20000}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# MCMC - basic version\n", "\n", "**Like importance** and **rejection** sampling, we sample from a proposal distribution $q(\\mathbf{z})$\n", "\n", "***Unlike* importance** and **rejection** sampling, each sample depends on the current state: $q(\\mathbf{z} | \\mathbf{z}^{(t)})$... so the sequence of samples $\\mathbf{z}^{(1)}, \\mathbf{z}^{(2)}, \\dots$ that you get from the algorithm form a Markov chain.\n", "\n", "Let's start by seeing the algorithm at work for a special case, and then we'll show why it works more generally.\n", "\n", "The basic *Metropolis* algorithm assumes that the proposal distribution is symmetric (we'll relax this later). i.e. $q(\\mathbf{z}_A | \\mathbf{z}_B) = q(\\mathbf{z}_B | \\mathbf{z}_A)$\n", "\n", "#### *Metropolis* algorithm\n", "We draw a sample $\\mathbf{z}^\\star \\sim q(\\mathbf{z} | \\mathbf{z}^{(t)})$ and accept it with probability:\n", "$$\n", "A(\\mathbf{z}^\\star, \\mathbf{z}^{(t)}) = \\min\\left(1 , \\frac{p(\\mathbf{z}^\\star)}{p(\\mathbf{z}^{(t)})}\\right) = \\min\\left(1 , \\frac{\\frac{1}{Z}\\tilde{p}(\\mathbf{z}^\\star)}{\\frac{1}{Z}\\tilde{p}(\\mathbf{z}^{(t)})}\\right)= \\min\\left(1 , \\frac{\\tilde{p}(\\mathbf{z}^\\star)}{\\tilde{p}(\\mathbf{z}^{(t)})}\\right)\n", "$$\n", "\n", "If we accept the sample, we add $\\mathbf{z}^\\star$ to our list of samples. If not, we add another copy of $\\mathbf{z}^{(t)}$ to our list of samples." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def metropolis(N, z_0, p, q):\n", " '''\n", " Very simple (inefficient) implementation of the\n", " metropolis algorithm.\n", " N - the number of samples.\n", " z_0 - some initialisation point\n", " p - unnormalised distribution of interest\n", " q - proposal distribution that samples conditional on the last point\n", " '''\n", " z = [z_0]\n", " for i in xrange(1, N):\n", " z_star = q(z[i-1])\n", " u = np.random.rand() # uniform random number in [0, 1]\n", " A = min(1., p(z_star) / p(z[i - 1]))\n", " if u < A:\n", " z.append(z_star)\n", " else:\n", " z.append(z[i - 1])\n", " return np.array(z)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Simple example\n", "\n", "Assume we know the (unnormalised) density function that generates the CPSC 540 grades.\n", "![](grade_dist.jpg)\n", "\n", "We'd like to be able to calculate the mean and variance of this crazy distribution. Let's use the `metropolis` algorithm defined above.\n", "\n", "We'll use the following proposal distribution: $q(z_t | z_{t-1}) \\sim \\mathcal{N}(z_{t-1}, 0.2)$" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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VRI7eki5H/bpqeaomtYnQ/DgXvSSwBWEEAACgpGSkKeLjyXIvn5frIdMw5OvS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\nBADSihU/TgueQRgBkHFyG6L6VVGd+tXaxxz/9uyA/t6fXdYBAEgXhBE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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Average grade = 0.722681\n", "Standard deviation = 0.179676\n", "P(z < 0.5) = 0.147200\n", "P(z > 0.9) = 0.206600\n" ] } ], "source": [ "# plot setup\n", "plt.figure(figsize=(_plt_x,_plt_y))\n", "\n", "# Metropolis inputs\n", "N = 5000\n", "z_0 = 0.5\n", "\n", "def p_tilde(x):\n", " I = np.array(x >= 0, dtype='float64') * np.array(x <= 1, dtype='float64') # indicator x \\in [0, 1]\n", " z = I * 0.4*np.exp(-((x-0.5)/0.1)**2) + 0.7*np.exp(-((x-0.9)/0.3)**2)\n", " return I * z\n", "\n", "q = lambda x: 0.2 * np.random.randn() + x\n", "\n", "# Get the samples\n", "z = metropolis(N, z_0, p_tilde, q)\n", "\n", "\n", "# Plot the results\n", "n, bins, patches = plt.hist(z, 15, normed=1, facecolor='green', alpha=0.75)\n", "\n", "x = np.arange(-0.01, 1.1, 0.001)\n", "plt.plot(x, p_tilde(x) * 3.1) # the 3.1 just scales the density function so the two plots line up\n", "plt.title(\"CPSC 540 Grade Distribution\")\n", "plt.show()\n", "\n", "# Calculate E[f(x)] using the samples\n", "print \"Average grade = %f\" % (z.mean())\n", "print \"Standard deviation = %f\" % (z.std())\n", "print \"P(z < 0.5) = %f\" % (np.array(z < 0.5, dtype='float64').sum() / float(N))\n", "print \"P(z > 0.9) = %f\" % (np.array(z > 0.9, dtype='float64').sum() / float(N))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# How does the algorithm work?" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false }, "outputs": [], "source": [ "z_i = np.arange(0., 1., 0.1)\n", "i = 0" ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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cjNLSUvTv3x8DBgxw+Oes4tfVXOuCv+zsbMnj0tJSaLVaJCYmAgBat24NURSR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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot setup\n", "plt.figure(figsize=(_plt_x,_plt_y))\n", "# Acceptance probability function\n", "A = lambda x, z: np.minimum(1, p_tilde(x) / p_tilde(z))\n", "# pdf of the proposal distribution\n", "q_pdf = normal_pdf(mu = z_i[i], sigma=0.2)\n", "\n", "# plotting functions\n", "plt.plot(x, A(x, z_i[i]), label='Accept')\n", "plt.plot(x, 0.3*q_pdf(x), label='Proposal')\n", "plt.plot([z_i[i]], [0.], 'ro', ms=10., label='Current point')\n", "plt.legend(loc=2)\n", "plt.ylim(-0.1, 1.1)\n", "plt.show()\n", "i = (i + 1) % 10" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Why does this work?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Markov Chain refresher\n", "Informally: a sequence of random variables where the future is conditionally independent of the past given the present. i.e.\n", "\n", "$P(X_{n+1}| X_{n}, X_{n-1}, ... , X_{1}, X_{0}) = P(X_{n+1}| X_{n})$ \n", "\n", "A simple example:\n", "\n", "![Markov Chain](weather-model.png)\n", "\n", "We specify a Markov chain by giving an initial distribution, $$p(\\mathbf{z}_0),$$ and conditional probabilities of subsequent states, in the form of transition probabilities $$T(\\mathbf{z}_{t} , \\mathbf{z}_{t+1}) = p(\\mathbf{z}_{t+1} | \\mathbf{z}_t)$$\n", "\n", "The marginal probability can be expressed in terms of the marginal probability of the previous variable:\n", "$$\n", "p(\\mathbf{z}_{t+1}) = \\sum_{\\mathbf{z^{(t)}}} p(\\mathbf{z}_{t+1} | \\mathbf{z}_t)p(\\mathbf{z}_t)\n", "$$\n", "\n", "A distribution is stationary (or invariant) if applying the transition operator leaves the marginals unchanged:\n", "$$\n", "p^\\star(\\mathbf{z}) = \\sum_{\\mathbf{z}'} T(\\mathbf{z}', \\mathbf{z})p^\\star(\\mathbf{z}')\n", "$$\n" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": false }, "outputs": [], "source": [ "T = np.array([[0.6, 0.3, 0.1],\n", " [0.2, 0.3, 0.5],\n", " [0.4, 0.1, 0.5]])\n", "#x = np.array([1., 0., 0.])\n", "x = np.array([0., 1., 0.])\n", "#x = np.array([0., 0., 1.])" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 [ 0.44117396 0.23529267 0.32353336]\n", "1 [ 0.44117626 0.23529333 0.32353041]\n", "2 [ 0.44117659 0.23529392 0.3235295 ]\n", "3 [ 0.44117653 0.2352941 0.32352937]\n", "4 [ 0.44117649 0.23529413 0.32352939]\n", "5 [ 0.44117647 0.23529412 0.32352941]\n", "6 [ 0.44117647 0.23529412 0.32352941]\n", "7 [ 0.44117647 0.23529412 0.32352941]\n", "8 [ 0.44117647 0.23529412 0.32352941]\n", "9 [ 0.44117647 0.23529412 0.32352941]\n", "10 [ 0.44117647 0.23529412 0.32352941]\n" ] } ], "source": [ "print 0, x\n", "for i in range(10):\n", " x = np.dot(T.T, x)\n", " print i + 1, x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Detailed Balance\n", "\n", "A **sufficient** but ***not*** **necessary** condition on the transition probabilities for ensuring the required distribution $p(\\mathbf{z})$ is the stationary distribution (as $t$ goes to infinity!):\n", "$$ {p}(\\mathbf{z}) T(\\mathbf{z}, \\mathbf{z}') = {p}(\\mathbf{z}') T(\\mathbf{z}', \\mathbf{z})$$\n", "\n", "why?\n", "\n", "$$\n", "\\sum_{\\mathbf{z}'}{p}(\\mathbf{z}) T(\\mathbf{z}, \\mathbf{z}') = \\sum_{\\mathbf{z}'} {p}(\\mathbf{z}') T(\\mathbf{z}', \\mathbf{z})\n", "$$\n", "\n", "$$\n", "{p}(\\mathbf{z})\\sum_{\\mathbf{z}'} p(\\mathbf{z}' | \\mathbf{z}) = \\sum_{\\mathbf{z}'} {p}(\\mathbf{z}') p(\\mathbf{z} | \\mathbf{z}')\n", "$$\n", "\n", "$$\n", "{p}(\\mathbf{z}) = \\sum_{\\mathbf{z}'} {p}(\\mathbf{z}') p(\\mathbf{z} | \\mathbf{z}')\n", "$$\n", "\n", "#### Useful practical note\n", "We can constuct $T(\\mathbf{z}, \\mathbf{z}')$ as a mixture or sequence of \"base\" transitions, which may not satisfy detailed balance on their own. \n", "\n", "i.e.\n", "$$\n", "T(\\mathbf{z}', \\mathbf{z}) = \\sum_i \\alpha_i T_i(\\mathbf{z}', \\mathbf{z})\n", "$$\n", "or \n", "$$\n", "T(\\mathbf{z}', \\mathbf{z}) = T_1(\\mathbf{z}', \\mathbf{z})T_2(\\mathbf{z}', \\mathbf{z})\\dots T_n(\\mathbf{z}', \\mathbf{z})\n", "$$\n", "\n", "See Bishop for details." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The Metropolis-Hastings algorithm\n", "\n", "Hastings (1970) proposed the Metropolis-Hastings algorithm. It is the same as the original Metropolis algorithm, but doesn't assume $q(\\mathbf{z} | \\mathbf{z}^{(t)})$ is symmetric and modifies the acceptance function as follows:\n", "$$\n", "A(\\mathbf{z}^\\star, \\mathbf{z}^{(t)}) = \\min\\left(1 , \\frac{{p}(\\mathbf{z}^\\star) q(\\mathbf{z}^{(t)} | \\mathbf{z}^{\\star})}{{p}(\\mathbf{z}^{(t)}) q(\\mathbf{z}^\\star | \\mathbf{z}^{(t)})}\\right)\n", "$$\n", "\n", "#### Proof that Metropolis-Hastings algorithm has stationary distribution $p(z)$:\n", "$$\n", "p(\\mathbf{z}) q(\\mathbf{z}'|\\mathbf{z}) A(\\mathbf{z}', \\mathbf{z}) = \\min\\left(p(\\mathbf{z}) q(\\mathbf{z}'|\\mathbf{z}), {p}(\\mathbf{z}') q(\\mathbf{z} | \\mathbf{z}') \\right)\n", "$$\n", "$$\n", " = \\min\\left({p}(\\mathbf{z}') q(\\mathbf{z} | \\mathbf{z}'), p(\\mathbf{z}) q(\\mathbf{z}'|\\mathbf{z}) \\right)\n", "$$\n", "$$\n", "= p(\\mathbf{z}') q(\\mathbf{z}|\\mathbf{z}') A(\\mathbf{z}, \\mathbf{z}')\n", "$$\n", "\n", "i.e. ${p}(\\mathbf{z}) T(\\mathbf{z}, \\mathbf{z}') = {p}(\\mathbf{z}') T(\\mathbf{z}', \\mathbf{z})$ as required.\n", "\n", "This implies that because detailed balance is satisfied, if we're sampling using the Metropolis-Hastings algorithm, as $t\\rightarrow \\infty$, the stationary distribution is our distribution of interest $p(\\mathbf{z})$\n", "\n", "Practical issues:\n", "* **Burn-in**... do we throw away the first $x$ samples?\n", "* Samples are correlated... not an issue for most expectations, but something to be aware of - see **thinning**\n", "* choosing the right proposal distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Choosing proposal distributions" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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0SXD/6h40hJK4dG6bJ7stNmXQML9HxZASrl9vWdKJdxoym/gf1vRgjcApxTTT\nMfuUeiKH4ylcPr8Nz0vMUGg3trg4gPQlTeYkkiSZ/aKfpP1ufJ/bekYcP4BKDc0BXzdbjRfBLj1Y\ny4QwIhiSv1h/BRZPbgwJtT+yGte2xfDN90zJ6rUL2/Hbz7yHBIwkCL7xz1a8UNdrUci2l5vplOwA\nwz6mo84TM+khbS4YUMykCgRmA+YbdslkIkWw2uWUCOg1PhH8TjnYPzFWcjT8X1r18fDaEC6Zm5Fo\nUNLpvwt29+GO5ZmBK6uDt3+i+c94q8XGuL2/q89mqyGb5LyqjE33yLoevCqR8IrAL24v1PXiFsbh\n56UtGZsilifb3pPEjz7ssOX1ovoAMu31xzU92Bk2jfFVnuvZgtL9BWcD52b0zzL7Xr1/WaiYe76L\n3+Ycze74xOwLMUNMrLG0lTHx8OrY9F5bIV7Zaq/3sfUhzErbk2l1K5NG5rTkVTtAP1nGNOcCnTWF\njkTV9/MqbjfQufppSwwr096whGRWiB09STRHkvh4T2ZdcKXVMJ2kRIdTme0lfarTDg99ru/9z5IQ\nMIAHVnfj0rlt8gwcPYDYFIDHDR914PnN5vikgvOvv2syFG72fG6MkIh5buUYUC/MFAu3w2PSZbKJ\n1pIKzQkflCTzwtxQwQ5vD6jOI/4tg7QJmOe9iRSaI0l0RlO2w9aW7gTWZmFnSPs8RZkVmJL11r4k\npv2zRe5PkU4rswtlD3HZRED5t5RMUojU2ISkmcmgXTK5qCmKm5e4e4R5PRRSCtg1QdWPdGK49Rtl\nHB/fEEaKEOWJjn3H183+yTJu//NZN/66KXMiqy4O2P6l2MuppCijMXV2Mz7VCNfA08kOcv6T9uVg\nptXOro9YKnJXlbHgvZsNI209fpGhY1VWpehUKQK7QEaTBLvD9hO3JVUT1MQvrnzYniWMhzmvyiHI\nMMSftkQx7b1WPLY+ZHlfy07LfB+L+PeXtvTila36zCSbRKZ9IJL3vAaB/kltJlPI7YQuIl+LP+YO\njyKwURl0Ngu27alamjB1ETgPLgUaguagIZZMykh6YHW3kyAJsr29I2DIN1meKWKr4A+4MhJljJcs\nvWhfkMGiL/3jl1woN9EYFxW7K5TAuw2Zw5WbFHBbTxLPbQoLHdfYSgiAHT0J9MT1wtEBQKGkclW4\nImda818+bJwKhuS3V96KTf7oFyFMn9eGhlDCUtP/cFH2Hv0ss2hJJgNmvOWOGJHa19Ox2ikRggQM\nYGRJAEXKqnddAAAgAElEQVRBI+PT4cE05p2G/XP5yYBiJmlHn/12ixU3LUUIljdHzU3UMEzJJDOC\nRPZ4WccvFGST2WLxeHJj2LPk6bVtEcckZEswJM8BQzmJ2FAgSQIcMigPxdzqyhuc29XP3r4jwDng\n8OsNywD1t3RIxFxpq3k00wMmw7a2LWZJ2iiszVwqmWTqJZmyVHihLozvzrcvarwqL1tc9YHTC5gt\nuyOawhftcatddUMA9abESwn9VB3PYp00tD1ZG8pwPIVljG2yUApJcgsNxJaXzVV5ulIoOnXZ1HxW\ndn6xNrsZ5oU4JPxuDiZGulwvdmxUAioqmX92NHchAsWHjX0IpyfRhe+2oDlidx/Z3pPE5y5SIva7\nrfo9Sg8c6SX53Q4HlAYCd+dAXQb7zR0R3L9aT7J7+GDThvzpTWFh7NFZ2yM2JveqD9rxsAepsWwY\neVFzZ+nrZCGX7GyLU/ODz1oz44sya9mss2xoKUpjwJBHHKFagIL0e1l8UALgyCEFSBGiFHrISGY1\nFPsSA4qZZDF3VwQ9sRRa+1L472VdSKYlk7zNpGg+dsYIrlvUjje292Lq7GbTLkZjBIoWcPrvZy0x\n/OSjDkceFub9ufqjsDGcdDJeTHbZaS9JCFo0DZ5TRM8zV5ZGZ1JRm8mNHRIPTE2GPFf04xnCAQPA\no+tDVtgmsz4i9MBjIRqftHna+kxvSF61KPLY8/ppv/q0C89xHvkNIWckAgJGFcs8c5WoMX3ML4Lf\nntdq2a3SZFqSSSYNHfrUkJ3vW3af5ueCqKoUMsyqxdS7kyQEVcF7MZ3R5T/d2v2CsUU2NadMgssP\nSxUzSavqihEs2+tUuatInz6vTSveLV/Glq44LnmvFXet6LY2u1CcYGco6V3aJDgkiMpY3hx1eJrT\nZLzq2K1vZYcDttlv+rgzXYckraYUmA86QLtyyZ6o42DDmj7KmpF/HtPbHh15eXMEXeTKTIqITRFi\nW0dZ2pLMOi1q32c2eYusoQO6fgUgv/bxgnfs3u+NCpvsgGEfL7ImbOpNSi832NcYsMzkzlASW7sT\nGUlEesC7eXMD5omwriuBlS3x9N/2xpdJFlSlbulOYIPklhiKtqj3hZB2gOibZKdr13A0TD7z3lRF\nUHGODsA7U2YA6IkR/Odik9nmmeDFe6K4bkMlOqKpfpdM2iXHxPFMBB0bWx6G4fQs/fvWCH5ibRgy\n+pgFjpaV/nd9RwJPbAijN0Fs7ZIv4OxVjlb01ekjM3HiFjVFreD3FHdLwpFY3r/MpuzKBDHPeUn2\n3kgK6y1pksEnt+HlLb1Y3CQP9H9n2izEkqa40QXx+H1yQzinscdm7Y7T4OEa+UhmTOrsobTMpzaI\nHdGChn0z5p2KKDZzTmgSJ14rLy2SSsBYu2u3z3xCQCu/dvFlbOxMWBcqsGPbC5/Bf7PbsriLsT2b\n5xIeRlfNzX+XW4B4UVluaEk7H9E9gvb/Hcu7LJtZwAw9w0pxpVNXQHuuUdro8BIFzpal9VQ+azMp\neH/zx524lQmAzn7bK1t6ceG7rfjVp114aUuGccyVp5WBEFNqD5h7r0wySSMjuGkt6Pxkh5aM9svf\nb3PErN1fGFDMJKumGF4StG1qCUKE3tyiTSWafliYthMyDHvjiwIjE0KUNz7obERe96okYzNJDb53\nMN5pcjW3Gmy+FCFKySRtc9bb3eu5xjDsGwI/qJrSJ64VLTHH7TP9CZbhaIkksVOysD272a6q1glr\nQQgcM7iBKV+q5raVIRaJ8VmpMTx7RZlI/cnDKeV2HzUEmf4h3HO3+hz1s3+kaaHDSsb8/WV9yIpp\nKkrSFbfTJpLcqeyJKcIJwrSh/KvcJM1A5jsflzB8Ilp0JZNUNaq6RtC+8RPr/yyTwEug8wMGFjb2\nYfo8UxoydXazzVGNn5X0hiQdJiMoSCQyM5CBffOP7b3C6+NU4McGANeoEL9NB66mlPOf4CqZ5MOe\nEjMO6U8/dmqv3Jg6t7TUzpneGCbbtH+9stsuaHBpxmwOV2yedR1OxvXKBe42h9nEF3bL8Xl7HKvb\nxIw0vTlqUVMU23v0zHZ0mmZjp/uFBAFDrPVj12ad4U4vBtHRMupeuNHfGFjMJPObv1WF7qv5AcNm\nDyRqNioVeT99dVkA7t5gfPvzm6lO9xDibfNlmWV6A8M/GWlStobGbL4kUQcVF4UaYAe6TrUGnH0n\nAiFAUT9HwxbRlyIEP1/aiRkaC9u+pMOkxZnGsiOUGPENTd/Q42VjcKTXy2Kj72XqdU9Ypk1SimA+\nBQynnRhdYFTMlEi69tKWXjy7Kcy0lUUaAPVpXsQsXnpQsSvTubUrgQvfFQdeFlXHx1UU02JC12ZS\nx4tUtC6wa4kIHdEUtnQl0BxJWc53tK/49nq3ISK8MEEGOqUPq5LHJuWL4FcBeqDIxr5LdMAQHglE\nm7qsUMO0L+bjc9K6+P6sDyURT8HSXh1U7i20FkUsSRy298H0gkqlzTJmjD8IuR2L2H7PRs3NXunp\nNrpXt8bwvXScVp7pWCi5QvLBNd24ZYmTOWdjZdqkqy408FDxtKox/8neKG5d2mndT+7Iy/wuLzCE\nDCDbNzo2/gZM7SLdW1W0HyimbkAxkywsBoWZvKaa266mFnW6IyyEjr0kv9E4yhX3OKta9HoeSBEn\nA8AyWyJJkVckSWYxEr5nvEEtuiRpp85uxnaNoOJeD56EmHeQ5wp2Y/UaYsi1bKiH0e9XdwsN7lky\nNnUmbCFDZAcVS4Um2Bz5tH9c02PZFfK2azpNwHp30xMtYbYZrRic9F8j4xhjtZUlmdSTTLH4gNlk\n+Pxuam6eQSKKPPRWim7N64zoZq4KqM3SAsjn1HOcvZabEx/PNO5hbXiZN7xUmpVWRNgQJhTMpGWd\nPbwcYkUSygxtaqzvyP7KNx0S39+ltuvkKTdgYEdP0pLQiupMkkyL98RStvYfXOS+tYrofn93FN95\n336g4WmTLed8+8s0E/zTD5uiOat8ZeNkQ0ccz28OY0t3Ag1pM4OnuTH/Qp3gOkoAC3ZHsSrtHLOL\nYdy0tFs5Lv8tfSn8daNYur26LY5PW2LWnG6OJPEko6Vg1/jq4qCrp7srM0m82ZkeqLvLBzYzyUj6\n4imzQQsChi0Mia7kzE3KJyuHd8ThMbosaEvrSTJJMiF7eAllNqBqUXYwWWpuCWGigdytULGJpDH8\n4FXdTy4r+d5V5gbmdR6w/UKYZ7qBvL2AL5Gtu1sS35KVYDzyRQjnzmmxgrjL2kLEeFG7RP7V7PoI\nVim8AN0QFQwAwtQj60m2LWj/Bw1D6sigooX1gGVRwKygbN+y/4ryCeti5ib//qlNIUeZLG09cTuj\nwDLPbqC5OiRzgt9YGwSmGbyUkJV00NtE+I/iTTlY0AOkjkE/z7yKQA8QKns9h2TSsL/rj9mq2pTf\n29WHqAf1H6XHGZki/S8xPaGp6pmf+nYHEFnUEXHdsjvR6VNRWxFClOsun5ZHNgyIjhnWW/URPLUx\nrAxaL9vz2APQLCaMkIxU274nrY1J7/J+WXNMecihzbimLY6/MQwxGwGDEHHbqtYvR1qo15q6tH0z\nFQzoHHL3Bfr3zrQcwR+UU4yMhE7G/IBhkwCJJoZj4YL7wHGqwAj3rxh2+0RvJ/mUgC4i+a2Drmgm\nx4aOOFa1xkCgtrNgmR0vIZVYA3+WV13XHpdeaQm4f5PXRa0nzkpmTKTQDx6DArg5FYi+TbTB8RLM\nS+a2YjDjhulmH7m4KYqP9kRx+39UmOkkCbXsfGV5PZRBFy9Rm9NHSjW3JE0wABhJ+zuaROVBzDLD\n7LPGtHTDac9np4PFx3ti+OWnXTh5OBPaRkPVxKNXk5GJJoGxZUFbXFie3kLBhGa/uVlyO0tmfpi/\nkhImnq2TaKxpWjeSuZSRDTND7+/OaCTUlTwmCKtCpbQOySRjusHCcvIDF0wafLoMHljVjXKBB5RO\nKCwRRPNMGB9Ukl90qNI9fLNjQccUgj6XHaaywf5ilbZ2JXD94g4svKhaWD899MsOHBS5S+wyvhX8\netoZTeG6RaYpgHXfuy+Z5AYq7B7IzREzsGpBEK42k6KNxM3oV+d04AavSwMhzAaa/td2ZRmxp3UD\n+4lzGiJ4fEMYfUmiVD+xd+162RPYUyPLTK6VSMms3B4WPR2IAhrLToMAUFPcP0P+b5vl4STYyyRU\nGy3t03gqYyQOyD10Kd7bGbF5av9+jThOnI6KWhiehKlbGk+P/YNKJgPyw5ftkKR5aGGjEGT+NX/V\ndcnNLdr7UljZapcoKNXiIiLToFI3SvJVH7RlJJPyIjNlK/pS1A4pENQUB5XtLtOs0Mf/85n86kQg\nI5lkzSlkh1rW5EFans6hhfs7W3twFj9bag+9k41liyXFkaqOxc9lBxLRn9t6khbjq8giBS/dF0om\nNZ/Z3ksSvLm913bNrZyuDCWLJIc7WsVrHm5Uc61X0ieaViqu5VDIzn+8U6FjHUg//4+h+Vr1uIEQ\n+VojjGyTy4aaAwYWM8n8pg44dMD3JUk6sK7hamidDWOY7SmRRYp4K0WUXuZRrlMuf3oBTOY0oaBr\nXTs93ROtRZ3fHB+fUmUj0M0+pL/HeYHgsliC/h/YC3ZHbRvC/N190m9hY/opIwQwv0vTwcgIIZYp\ngajXCMSSKQD40aRS299ZC4wIu0GLv3JYUca8g1ITNAzH+BB5c/N0yZhn2722EjW/CNsF9/WmCBMC\niXtH/05xb1j7RXqL0I6epPVNWte6Kd7JDsJ5gX1za1TGecT+LyD/Fh06JikcbyjiKeCK91ulcSxz\n2W/5A4e3vOJc9ApYdj37oj1ueYk7x5D9SS5aAR5834gkk7oxKwG4hjN7aG0o44zHwS2AvAper2iV\nob8cbUSPyzXsMXnmXiSZHFsWxMQKc170x2dTYZh1PWz6ueggl+01nbliYDGT7OIG+wShQcsD4CaB\nbDfk/mKNdmWLuKpYN3UgkNsG4Hay9MZMZr61KGhgbFlmseclhzp2LyKa2LQLGqOWN2Y2p7D+GvqW\nepgQKR3Z1vWX9e5hYJbsMTdK1gZItPBbbcgQU1FgWO9YaeauUMJmp0qIPAD1oEJuOmssKm7jmmWG\nXqgLWwHKWUaPksNGDeCL1Qnlw2/IQSPjkMY7GXldMAmIlLFjHbdYTHuvRbqpApqbWrpQ0dqwhwtS\nvKkzjhQB8rgDs1Y1RH9s07ZTqbmtcjXK29Dh7pQXTRI09qYsJwwW/PWf2SKbPVQl7QPs69nCxj68\nVd+Xrsu5x3ixg2PTvLyl12auA5h2cLKwMyItmxc/ABHoHPZi6qSz1tPSaooD0nXL65bh5epGr/BS\nMmXkRLfY2W3Kc6NXddgSrYNu8bD3FQa0zST7zJQqGOmYhpl0QsmkYD4cPSRfqGpQlcPWrzPFUop0\noXgKZYKjmfbc1UgnUh0R2K87pLcy8MUSyE636oppPhoXz9U21eV9LqCk3ruqxzoVytL0T4X2Pylz\nkG9kFP8qLYToIGJuSplN/soF7ajgTstVPNMog8YixkvjMjTY6QLM+8tPrDZtB0USVxszyTOMioaX\nMXNBw0Blgf1ETj2N2RM5X7Toq03JpP2Z4xu4931JCJkfVT08VDbXi7iQKM2RFFLITjJJ4M5NZtZS\n81+Vepoo2jcbUKkwrdtho5iDbNLNWUwnr6x2geJDqy4vbfaX9SEcMsi+XsnMdwCxBGil4CIGNxpE\n9o9eQjN5OUwFDcMWN3d/wI0+4XuNj7J4E4uZtL/nDxW52u8TQZ2QzOExZUG7qdx+xMCSTDK/hZJJ\nkZRH50Tm2NjY32m1oiSNbKMTgRBnwvHpeGNhwX3XppORvHxbqA8PbBjLIIjsoQDg3bTNHVuqaAHj\n8UlzFD9e3C5lslUThz+9i+B13snKoyrKFs27pb2CtRO1nqWJZyWTImaNggh+EwK8krYvot8W4cIJ\nFcvu5xLQ6AbZ/KEjoZMznKfJqed6VyyFW5aYBxQ2NizPDLGl8F7vMgY0GDCZkIKA852K2ZLZlPHq\ndHojkMVkCfKJHGdo+dt6knjf5SaVzLeJ5z8Pev2pbNwskJhXNPU6c8jUz6LQUzKYEk/v3KRU+px+\n4QgSnsOGSxw/vOeV1S/bIEXfJ5rPyrqZRHyQddX1lyJa+duudGjgg8MXBohlQ/9BYxQ98RTiKeKQ\nmlLoRB6hNajSEqIXs5VCd6i4pdumEeZOVS49IDntjYntohRdG1cd8GsVHzz/QDGSwEBjJpnZZRj2\nCUqvIwsYZviMN7b3IkkIHhHcdMB3lIDHs7BkbwyXv9/m2EjcGFIRtIz8JS/EBvrudbJ4daudCTGL\nJ44A8DIy5jS4G0kv2RPDho4Efr60U/jefaI7CdkXJh7t6Qttr5jf1v+Fp8FvsvTb2euzVP3KvlNJ\nMPl3sjbmi2iPppQhOQCFZD+djb9NgT9csXaFrMMMvzmw30pVhZl3REg/lXSyknWLbqZARz8IdlvW\nZpKHyklGhJqSjL2ozPzhD2u6Mac+4qLZENFJkBcwbAGR2bx9ir2Cv8lJNk5421G1A072G5+9zvS/\nkvefNLvf7y1DZoPt/4VEpqLka+ri5poWo8783sw5lKmuv1RFTWDRqLDXBszQRiwxvAlZQ08Sd3zS\nhW9IAvnneTgBqJjjTV0JXP5+m7bpina1Ah8CFtsEt+F4OdPQCwZ4E3Zeqi/69K0eGFmZQAg4cPaR\nIgwsZpL5HYBhcwpJpogV4ueVrRH879qQZVs2osT+GTqME4UV80+SR70Z2CFyqHGTbOqe+nVSLU0b\nt/P2aboTRNQGfEgHVzr6wZylN+HOBIkgastsboXRrk9S2Nmji6zf6uu7nJuPqEiVvaEbntkk9zpX\nlUcAW7iiDC3EkY6CPbQ0cswk2w18zD16yYBo7pjMpJg5pHiRs2sUSgKIM7yQ9U6QXgU2/qXsKs63\n6/vwxo6Isl95Out7EtjencSo0iA6YkQ6B2R9xt7TLCqfgvL/IjWnVYdLXSKopr7FTErKi+YiUFEe\nyNUf4PZ9tKujSYL5u9gg+vZ0967qwb2MF73Ouq5KUZTWPoTiKYFJgBMiBmuPB60MSZfLj4nViugc\nOkODtoMqPJ1b9AoeqnFmE0jpFaddNp/GumFPMHcMJp2ob/7zQ+fNPjIQpgy+jWQxSQ8EBiwzyaqA\ngfRvw25bY7nmCwxg+b9lTW4waXRpU6WRblSCAgwY2nY+bvWzp9As+DAA4hPUQ2s5yYvLjHcbUDqk\nTZ/Xhl+vlF9W/0JdGGe+1ewoz07avjPSloEOw0MZ+6cCxa1qLLl0HLDMu4wR8fJlbuoj2eaekpyo\nHRJ8Jn8eI0FsTm9kGZVQJh1frnVjFUcLYejgmYLWvhSK0zvUgt1RRz4n3URpUsLTqIIXJwUvTNmT\nG8NY1xHH4MIAioKGZ6mD27zPHMzFNLJ4ZavJoHuxcrPZbPN1czT05+zMSCadcL9S0IQbPZs647b7\n0kVdwwYN14qkoOgvKvWLCSLF2fY7BeFe2thkWOw7GMsQiaAan7/9rAt/WttjfaOOJ3d/sEW5luGl\nzegnqex9CXJnsihzSn8DmbEjM0E4EBhQzKTqRoZkyiSW3Wxlg1n0VGZQbgieif/WO2k6vPz6g0vV\nSLe5K86oRZlFD3TxcZdy6FxB6EjBPXCbjDr7YyhO0CIJvAyY1xJadl8SUnQXheOG5QufD3O5Dk2k\n/qJPdA2ubW2R/iMU5/vOXqZK4pGNqYRwriBTJ5+fXm+WYXQzCQYVBqzn1EaYty9in/GQMaqOCA4w\nrzvjbb5UYCWTznfmi11hPdWTqtZEimTuvCb2A4HumAwY5n+UXv56WFn9ukxugl+jBLSxzkls8vGq\nO6c1pE+ZPu4/dlLFsGcz/r3UycKmytUomIBI+4wwaShobNWAimtn4MWJi2qwbGuoSxep2nberije\nZsymVOYZOuXpgveziKZDCupChwRnmB7JfHJRs2cDWlM5jf7RHxx4P2FAMZOfMWoaupjStkoS06h1\n8Z6oML0Nbowh81s2IGR5vYJw/7IwXN7LGCXdOulvncEcT5nmA7nCIclkaSHu30mhcjLpz8k5dWSR\n8PnPjyp3zSvrE5vkQNFx7CvLoJo7CFD1UGVBAFUFhk3loUOP27jpFlwBaTJe6kVYtoHTeTQ2fc0o\nXXjZZLLQHqJ5akkmFbTwENlGNoSSjgsCwP35l/VqkwA+vQi/X9ODb8112piJxr7U6YNhJnviKe3b\nQxzlcz1oraUpcXqdcm88TD4vdNSP9N/+vKGKdvcnzc79QJehkkmXpPbJgjHGOpnoVEtIdh7oIpoW\nNmZvcwqY8zZF7GYbbl3k1raJVKYdxqkOIRYNelCl42PM/mqFXMMlgpdrGDO8CVcGYYUNJDfvMphO\nkAlGrXLk4HxLKzOAeMmBxUzy9kfsyX65YKGg1wepmEXVM0Cu5qZqHhWz56hDkChjpyV4aagnZLYD\nJclsXIRknJlUdYjujtXF18eKGbJsQPtDZWNjm5tE+FNbaiULAK7DscqYA1k4EVV+oQqS2OO/GYaB\nTZ0JPCG4Fk5ah0szrJMEISbQY+L497L5wnqF666tBEgbsHtbjEU0J4nd8STGech7Kp/LwMYD3NQZ\nz9yjDvX6IfsqAwYChrkZd0ZTVngkN8xz8SyndwY7NDouDWB7rSDFLpizF5o5LAGrWmOZO8X7EdT+\nfVxZEPQsKgpgb2ME0z/5IcaH4+IhYjrGlGbMW3SXU7d0qsMjAEd/XDKh2PrtxdyJEKA3FbCtLQFD\nXbdb+ez7wn48PQi6z8LKFvt6tsujd7MXxym3EFu5hLtiMWt7BC8z/IimrGK/Y0Axk/zAZZmiDZ0J\nfUcS0TMi/k3r7OEMWRfs5jxOs65bL2e26phzGGcPfpDTZ7J5zC6q2vZigr+vOqQUhe4Hz34LNiuX\nFrjn5dOUSiSg2VAqUnOrDjYsLexmy6aj173RftzrMdSRmyNAkeD7aQ7+SlNx+fbfvJ0nLZ21J5OG\nW+H/Jib9OtEI2K8QjeWCoP05G/LHa/g71Vxx2CMy7aE7poKG2UavbO3FjAXtTk9rSWPs4J29JBVm\nHHAyTK9yamquDWrJZKaoWdsilidsf+O0EYW489gKjCg1F6R7VjivlmSv4pR5gDsuAOAgyjW8xNt2\nSqDBTJLsNTHZ2PaycDVZUgyMgJUmXVY/LP2JFOm3WJUy4Yme0Ig7KPFnM47X2Bdq7oHERFIMKGaS\nxQeNUdy7yr4QqM1cmb8Ek0jW+LTMHyxstz3nbfKkXq/c5s8nSzHpQgJjWaXkSsIAsxDZz9hsJlUb\nH9EbnI9+EcLCRnrzA0cj7PZdKpTkiZkTr6YE9pNZbtOqVOP6LBko3c+fMRgjS4IZZlKQRphfkM6u\n5iYIBjLvdZiq588YjK/VFAjrcCUija3dCSveoVuF/BjlU9PxyUqAZf4DvHq6L0nwRUdCS0Kqc1rP\naIqITSW5yyWECg+VRIa3R7SuxvQwyKuLAwgYhuWNy49QtwsWKPh89G+RmluXl1QKyTSkWKYKUFFI\nFmDpqyxI37SSfihyULibYTDdukVmR+6WT2c9fKehT273z+0/2SBXtksmWRtTGsRXawqU38iuWypM\nGVFo/XZL++gXIXzrvVZPbUIA4aCdKQgpqEODVSYDvg/pwVGm9exXDCCuckAxk2yfTKrKw3ljMlK3\n44blZ30tkVOalnkiK9HaMHLsLPabLuTidbF7dbZMkUjj65BMQvwZKYb7VS0Mf9/aa1uARdCdhLp7\nqioZ/ea6rji+YK5yy6YFS/pBMmnAvkGyElhd5plXmeSlGUf2hG/AfZMaU5aHCiZIXUgQLN9Wr+BZ\nUTBjmynL7Xa4Ujm0lecHcPPHHfjVp2p7ppa01X5tZZ5r37oy8MQegiSXaa2aq7zghG409G5vFpWS\nYIKGYdgPaNy6p28HyJebptGx+ckLrOBU7Kp5cWVtqfRdfcicp7neOb6qNYYX6uxmHjyjzh4+8gRq\nmU6BnbBD+pv+l6p9HQy94DuI5LcML23pzao9lFnYQ5WHskVJZdvtznDSVYAQ5DLLtGNs+LHPBLf4\nsNgTSToceRyh6zQ/WhbcO5vhKQo/l+2B6fSRhba/jx9WIEmZqWugYEAxkyyOHVqAkaVBa0IUKYzo\nnMwi97dAmkYhY1D5YM26kNUlnKyS58JyJc/p1XoilalVj6Tp7PEL9SgRpQoY+iGO3MqUxdNiQT/n\nt5+pGVy3ugCgVHI1g1d7F5OhNPMEmSJlgbIBXqpt/pEk5kGquthU03WnmUEdRxRaHku56gpRngYK\nVl2fglrSzx9c6J/rO8x6+WtRAaCywMDqtjiWN8eUGzAhwKjSoBnX0WV4smNcHu6IIzZLqDbRFsbu\nmxBiXbEpcpCoSatF+XieBsy2p4yoDiMjAj/vqSmPSLIqGu1HDs7H0MKAdlNdWVti/ebryEQB8OZd\ny+O5zWGHzTC/frCHLlFIGtEBnG8rntnQEWRkwxhKIwykKcvFAdQLPV5pdzvY0mXVal9JOvawcsdy\n9eGyQMCRRiT7dJGL2RXfnXQO6rTDc5vtcW2bBNeyslJJL+Od/cQJ5UFhaDm7EGrgQJuZfPLJJ3HU\nUUdh+PDhmDp1KpYuXapMP3/+fJxzzjkYM2YMJk6ciCuuuAJbt27NmlAvnSK+Y1qc1t0uxP6vMq1m\nvfefWMm8VzAbLuUAwIkClaYzaLkhlyTRPMwzPgi8jKZM+f0jcdQFXQhUtiqyuGZ8/TLJZFYOOOl/\n2XOPaOMWjSmaLpkiCBqGUCpowLAcw1T0uO179tMuwYiSAP4ypcqWht449X9rQ3h2c69rCBPr7/QD\nKvwJcM/ZPLyTFJumujiQURfpqLltNDlTd8ZSmNPQx6TJHrqODSkAb2g4mogPaJnxzXdntrdefJqO\nfpHg1NzStdFwahNUY4tluC6W3Jqyr6PiZWg1f7jdPOrG7MjAh5HipeeqQyQLHQecbEHbemcou2sD\nVVGOl0YAACAASURBVHATIPDtLjuc8zfjiKJLUBQIBEqy8Ti+3HSGktks8ttDZr/IfYei60820klD\n8pv922bSM4C4SS1mctasWbj99tvx85//HIsXL8YJJ5yAyy67DLt37xamr6+vx3e/+12cfPLJWLx4\nMd58801Eo1FMnz7dG3WEU0lLOsdc8FRMmX17uW5RB15O35rhGkvLwwlRlETEOIwsDTrei6BzSmJP\nQLQNqosz3UrvCRVBxqyeWF3oSKukQWOzB+R9NFuw4arKowuTSuJ8xGBx/Ei+KVRBxd1gSQINe7kB\n5i8V4yFq/1CCmGGw0u9pT1LJZLYB6VmcP9butFUYNHDooHzbM4KMuv6ZTWFMn5e5lpIyeiI4ngsk\nkzKwaf776AqbpNUtf8BlgW3qTVnSJh1antss95hfIQtJxiGm21kcwYZh9nuKGV8sslVzU4iZUWfq\nlkgy661VatdJcrOZFB7YkfGop+sdTSZSc7uVp4MVnNfwfwzJt8r6xdHl2u3mFitZuKdoDysz4W9W\numtwvApbTMmknBCq5o6nB6usG/jnrEawptjOnqgifFDQcZcZY94+LCvpsuLvXJbrbT1JfLxHvNYM\nIB7SghYzOXPmTFx55ZWYMWMGamtr8cADD6CmpgZPP/20MP3q1auRSCRw1113Yfz48Tj88MNx8803\nY/v27ejokF8jxDYQrx6jkhK3vNccWiph6uxPN3am1XCKMmW0qSAPjJz5zZ4waDgPUTY++PhLdXoh\nYSZX2RkDnXZjJ4DXxd5LG4rWny86vHl20vqc8b2II417WQa+95USwXM9GmgZYBhKukCOKg0qpeSi\n8DRtfSkEmXP8sWkpIkFmYZZBd4yyC7gqkDebrkUSf4539uLnGe/VqQI/RyzJJNw3UFby4ZVxFeHp\njfK5phvTz60O+k0OsxSYQZ67c7zdQjaPLQccF4ljY28KzZH+vfE66bKOZwP7uDFsUQhEd0JnE6XG\ndT1I30tfUWDgkEH52gyfK/OSQ3vR0dMmufKTq8b5TEGbmzMgVXPLbBNlYNc49lpaGaSOqfQ9gC4P\nNrLZjHWHkCR9YIomiTwWdhYwmH+3dSfSnu0Dh610ZSbj8ThWr16NqVOn2p6fccYZ+OSTT4R5jjnm\nGOTn5+O5555DKpVCT08PXnzxRRx77LGoqqoS5gHUkiYChWSSaGw8DsbD/JeWWRQU21l4OblGEsRx\nT7BosWC/46P0yUN24mbxVr0zjpxNMimgiXoBu0H3O0VF6TCfBQaR0uhgzCRIcHo/dpsbXx7MiSFW\n0SSD7fCDTDgRat8bNIAygbc4ZbhaIs5bRvb0JjEqHfCbkMxpXCVh9kq7XSUsH3tSqQQzyfisfFlW\nf2qML7497WWpC9CxmWRL2h/qIQLg5OFqA3qajoUBoDzfsGwcZRsf7xyjC+olrrOB9nI2abkygrk2\nu8bSbhs7opusRN+QK12mpC79W1NTA+iNVdG96WxoG5nGJ0VMyWebRtB7oVOg4isMFy0J3XOoGZHu\n2hXvp5tyWIfGPoGW3zGniH7ZbtjQmUBTbxJv1UewstUuKDmsKk+SK02Xqp2Yd498EcJrWyMDiJXU\nYCbb2tqQTCZRXV1tez5s2DA0NzcL84wZMwazZs3Cvffei+rqaowbNw4bN27Eyy+/rE2YAeCvm8LW\ngiqzfaCg72UTWdbotAEOHZSPC8YWS1LpDTLeS1JWb0BzSbbFHCS8st4Ea6ck+25ZbeZ1Xs66VNT1\n8XZuLukzdGokcsFZb7cgnsoY8Ks8hr1AyOB6oJdNesTgfCuvNL6noF663FtxJLkyoknRAij+YDfa\nWW/z5kgK9Q7pAUmruSX5JeUKDwuGGRJLR75lYyaNdJsY2dhMutSzn1Zgt3qI40caBlBTEpSquWm5\nY8vUG5MMUQ9zuCgoH2c6GMQxvLq2hNmCcKK8YcXO0crermXNRd2+ksAwYDkXGRrpKdyZSXGC17dH\nmDR20MNsigAbOnSvCPXWL6E4weYufVtM3eVUpX3ROQTQfqSHoHhKbErAzqmrD8loM7PRBYjydMfE\n3+Hm2Kl6z78JJ8h+W8t0sE+8uZubm3HTTTfh8ssvxwcffIA5c+agrKwM3//+95X5RO1CT1Vuam4A\n0gR0kzuJcVah8d9YwYlqE9bpM7EDjlOCQ+tx2wB5T1nlwkPEpyv6Xe4brN6oFGnedCSfAWQkyLmA\nHQfsnsiHPwpLQuLwC0u/qNwM+wZC2yNoiB2fZOpN+o7dkNi2lV2PxxfsRTIpQl/S3IRk84Gq9Jgq\npTQFYIbEWq+zqUl2BpUDmVUPQyufVuaMNVAgUnObn6OWTLp9lvwQ6S2taO3SRXlBAKcMtzsJ9nuc\nSe6DZKHQKE6oLsBVh5Ta8vaLZJL+dlEBs5AFb3eTlLGXF8iqIkR/XRel6k0Q6Z3aK13Ut7rtyQ8F\nHTNjlvGV7YnU9jKZIq4Mu+2++SwGgrsJDlu8OPEPDinFLUeqr/A1uH/F4qUDB9ej7ZAhQxAMBh1S\nyJaWFoe0kuKJJ55AaWkp7r77buvZY489hsMOOwyffPIJTjzxRGG+UCgEwLT3a29vB1CEpj17AJQg\n3BtGX9IQkhyPJ1C3ZQsMUoG21laEkwEAGSeSbdu2o6OjEMmkAcBc2Oq6Eqirq0NjKA9AKSKRCLpI\n0pYPALbvqEekMIWOjiLHO5ZOAGhta7N+U8QSKQAGdtTXAzAHy44d2wFUoLu726Jn23bzGYuGhp0A\nygAA0VgM8aQBfgvZtdNM07RnDxKJIgABtLa1oSsWAFCAcCiMFnQhES9EXV0dgIwn+dYtW7EnlA+g\nBC2tGdq7OjuF3yrCzp07QYqStnJFMEDQtGcPwkkDgF0C3NPTY7VDb28YQD56eyOoq+M9QiuxZcsW\ndHcXAyhAPJGw2iMWi8FkV8yFYUNnhnkxv9vMH46b/UGxZesWtLcVgu+33bt2gba9CLFoFD0kBSAf\n9Tu2IxYrRXNzCH2RfOzY3gagAvFoFIlUAPySGQqb37hwZxh8f/aEw0AfQTwWxI76evSFC622ScRj\n1veZ37UFbLvvbW5BXSKGri7nWDVMRTkAYE9TIwB7TEB+bABArK8PovmWiMeQSBqoq6tDfSRotVMk\nEsFtH/XZaOzrizjKaGwy5zRf/670XATM9o8nSxCPJdDTE8GeZAJ10biDRgqSSoK25Z7mZrBjbFJJ\nHJ+HMnbE9fX1KA0SsPON/X5RW7iBHWMU8XgCoVAUlcEgupIBtKXXB5p2d9hsu2TSPiZ3NjSgt7cI\n0XgQQAAJZpwDwN69ewGUICpoWxaRXvH7rm5zvu3ctQtlHUk0RQOIxUvA9hsFSRHsZObCLsW8ELVb\nPBbDxWVhfJRu647ObpjnPHf1/wkVMSzvzqSrq6vDmjZnH+3anaGpq6sLO3Y0IxYvQ11dnXAudHV1\noTKaAlCMnlAIdXXN6AmVgO49ou/a2ZsZ5yJ0dLQjljKQSuajob4esZi4PXn83+edEB0LGhoaAJRj\nR309enuLbLQ1NjaiM5IHoBCNuxtR15mw2qKrsxOpVAEAA1WBmK3vJpfGsT4s/sZIxDnXf/pxp5Ru\nk0kVnwrq6uoQj5cDCCCaXkNke0prayvYubpz504UtJkcbEe7fV2m+2UoZK6fANDe3oG6uibr+1vb\n2lBX14hYuv5YMoXucCY9RZgpo6mpCfFEMYCA8ICfmdsU9jHexvAAFAFQyYmB5mZzvgJApK9POE+G\n9u3FVwJJLOsx9zYxzDbvjfQCyEd7RydKepPg11I7zd7WsVzgembPz8/H0UcfjYULF9qef/DBBzjp\npJOEeSKRCIJB+0QKBNJxnFJyQXJZmTnojx9WgCGDBwMAampqAADFxSUoLhYb5Obl52HixINhGAaG\nDR2KQZxd5oQJEzCoahDKy+2cf21tLcaMGpUuvxhVgwY5yh43fhxqa2sxSPDur1MHY3CaTgAYPGSI\nI02MmBNu3Nhx1rODJkwAAFRWZjaz8eMnOPKOHD3a+h1BPgJ5zo1hzJgx5reMGYG89PshQ4ZYZZeU\nlqKmphrBvDzU1tba8k48eKLVviztom+VYfTo0aideLBruoABDB8+HMOGDXO8Y/ulpMRkJoqLi1Fb\nW2v7DwAOPvhgDEp/W5xZrIuLCpFfWOjwAARgy0/NAs5NB8SvPfhgVDF9yH6XCoVFhSgrNcfrhPET\nUFhYgGHDhqG4uBgTD5qQ/oZCYXw6+o0VRc6FvaSkFJUVFSgsLMDYseMwmBkjBQX2RebgWnu7V1cP\nM8dqpbP/WDpGjRrpeM+PDQAoKRabfRQUFCAYDJrzJz3+AKCoqBhNMfu8LxaUMWL4cGH9Ixi6xo4Z\njUAgiIKCAlRUVKCmpkZII0Ues97wY6y8zM44jx03DhMmHOSoX/RbF+wYowjm5aG0tBTfOKgMhwzK\nw5utRba0o9JjjK6NFOPGjUVZaSna4uZz+i9FdbU5Z0tL5GY5AFAieV9aZs63UaNGo7a2FuPGjXOM\nLQuGYZsLYyTz4upDS4Xtll9QgIMOyqxt5RUVqChXS2BYOg8ZlFnzZH00clSGpjMOHoavTDwInYkA\nasZNRGWlczMtr6hETVoQUlpahtraWpSWygOus30lw5DBg1E5aBCCwSDGjxuHvHwx08YjlBRvwWPG\njgUAjB83DqUldtpGjhxp7VUjR43EwQdn1oFBgwbBSIvpR1SW2vqudphdWMGiqMjd2YUiaMA6mE6f\nWOwIrP1O33BrzBal9+xBVeI9ZdjQofjzKZn9evSYMdb8GDzEvi7Tdb+Umc+VVYNsY+GNliLU1tYi\nkF4PUjBQVOxktsrLMgeD4SNGIC8oP5SJ9iEWVVXO/SM/aFhrLp2vAFBYVCQsY8xocy5WVMj7iJZX\nWmJ+T2XlIGv/ltG8P6GlALrhhhvw4osv4rnnnsPmzZtx2223Ye/evfjBD34AALjnnntw8cUXW+nP\nOeccrFmzBg888AC2bduG1atX44YbbsDo0aNx9NFHS+uhMaaOGeqciPQcdP9JEskETPWCqdJ12gRJ\n5cGG8KewfB58vGuRuNu6B5d5Rp0q3NTc7LOOaMpW/v87xhx0hgH8x9B85AUkVxVCr5Oz9RstLwho\nqa0iSZO+bpcbWXTKomlY5wDT6J7gm+PVG2yKmEGzj5SEDvJCh3CcIaOOlt0SYdnnCN6xz7Z1J2w2\nqjKjcR2weXW1vjLzhaZwJmSMqy2ZZl2iwqi8TscGja0nBfud62Jbq/5XEO3i4vlZ48FF7Sl6pTId\n4c0pZJBfViCwIVPUpTPORpdKpHDEbp7hZcxGk5oBzpkyjxicj6rCACryDfTExZa6IlV7zmpuI2OC\n48UBxw1C+om9XX7Nhf7JmNHITXq+WmNnAL2s/788psKx1rFg7Tl1cDizFuuo5dlbb2TJaYoEcXeC\nZU05srHAEPIG6VjBjrQ5DIyMmtv8xV6HLMKSPXpRJ/oLWhbc06ZNQ0dHBx588EHs3bsXkyZNwquv\nvopRaane3r17UV9fb6WfMmUKnnzySTz88MP405/+hOLiYhx33HH4xz/+IZRUUKwW3NZBbUo+a43j\n8Kp85Al6iA8N4cU71baxKjpfx84opwXEhbEoCtqTnD6yEL/9TLzZshsAjesmoi2RktjmaM6oY4bm\nY3x5nlY8vSRMInoUQWlZqEoU9qORZj5cuEDROOAdEmR18k3EMgv0b8NgbCYhZvD5qxPt9BGrvP/h\nbvjhP42//YFI0lF6ZeXIIEsm85wWO4g580ttvLi6bXEm3eySjEyP8LEMAxwR+8Jo/acfdwjt31SH\nuVuWmGpEfrNz654MM5md8aF1rSRXXi6QUbIznLT1hZeA6yKmT5zOWWZZvuKiBpKZo7pxhHUOM1a/\nSOa9F7B9Izz4MO3yYZOdadCZX453Xg6mWQw7Xftd2z4moWm9zhW6lKEmQKkgooaMDtXBdfaOiPAg\n5iVGp5tMS0Up3+5v7Ijg1qPkUn7LL2Q/Qdsd8Oqrr8bVV18tfDdz5kzHs2nTpmHatGlZE0aZgreZ\ncDhJIj+pst7cwvcQdxR7fZ/Ky1pngqpOVXVdmY2GbgJsqB8258SKPGztTti9uSGXKFCpnJiJlrfZ\nRf9sxS+ONgdjNjEaqVekbtw2guw3QNXNCEBG+sOXflB5EFNnN2PhRdUWEYZh2G5T4D3UAWc5Wkb1\nlPmhzGRAfCpuTVu1i/pzRUscF4wNavWBLAyhdJynq9ONJqAMNKy5+XjpbRszaWTuB9eR9PCxM23M\nsyRPVWHAcbdvthBdW5lykRxkwEuQDHUfpcdNtn5F1pi0HcIV1SFjc6tzwHC848pSrReFQeDnR1VY\nV6WySdsl8RLthxD7tiyas+/u7ENReu3SZah1nCxSzOmnvw4sphONqD73mZUi4gshzPzZgx132d7G\nROEltyg0nptkEjBj9cqCf1tlUGc/xdr2v5/3CCW48kgVZmE6N9bwt4HJSvOCQp0o7/2IAe7naMcm\nRSgCdpESdYuoExc3RfERIwpW8jnp/FcfkrHXoKoNLokQTzL3ybqp3S4YW4RBBYaSOQ0wa2YgvfFa\nqVmaiPq7cpFOeF1HpKdsF7T1JXHRPzPOOKKF1ACVTJox+ihKOVfeFMxBP4S5D/mkmkJMHal2OFJN\nFF46TNPKAvvS6+xU68e2HvdTZbaqWl1+vkziBs1KXmyHKVFdgmfSgxnH3GSjxpdJrfn6+cNlLuFv\nZMhIitWSKv4dZaDd0ruquSXbDz/ulCp4RjqsrstEuUAKxEuyVYyQ6iDw4Ofim1zshxBnnSI09Jh7\niW58QVfJJO1jw/y65kj/XRwpkt6pPu+qQ0rxlco87Awl8f7u/gmwz4PGOH1tm1qlrSNxywWqm5Z4\nGmRg905Z2ta+pNwUQNJ4Fj+i0bhJl3l2YnWB8K2qaFGM432JAclMyhooJWGMMkyKeJmSdeadn3bh\nH+nJ4CZ5zGwMmXcBGLaTme6G4WZLYUpYDcEd2/Y0svwswgk9u6NsrpGiC6a2ZNJDHWzSKMdX8e33\nm+MrUZ4fsNqI5j1jVKEwLAy7WRsATh5eiLuPc/FGV/SZWV6mv6w4k3Audl+tKbDo89rmOouijFYW\nuv0lC4ptD8OjHv+6kugX6sKCTTMtLYD72KE0UTtV21yR9N2+Xmo7oimAZMJiySCWPCnSp/9168eq\nQvHybql2rX9dmFemrWRmJPRpRYE6SDj7qbaQLIK6+GbZ0yvZziVtS+SvbLbsV7zfiq3dud1fzY7R\noUXy60a1kS7gmoXt+KzVKfVW9dd3a0tx1SGlamkxf8DycnAzDNzjsl5aabl/3UBgBmTvTWiaQ8kk\nk5pCHvrebe2UScV1ytdJS+eyqP5RpUFMm1DMzEG9ugYVBPZrWLQByUwC3hd61SJEn7l1guz1g2u6\nMSttVGy7wJ6XTGqOKlGj81l5RoSeeq2qmd8BTg3I/t4VTtpUurJ6c1n89PuKAASYXJXnCGbspSw+\nzakjCmEY9thrfLo2JmCaAfd7XnNSA1mMjbOUgkCG6ZQxk7K6RRIK0QNRftVBRAY+3cQK0yqGHW/9\nJc9b1RqzH6gM+wKvW49Jm51TlC1ybPdQ+8V9Ahf6HZJJ6DnguKk6rzlU7KGcogyuMnemLnbtlNWo\nslVm33zRHrf+vuXI8oz5CaWNy8B+o4zhsx3UBXWKEEtPvqV7Y2jsTdmuC80GdIwaMO8DV9UvYqJl\nSAg6SaffDMO5xnl1AlPhoIrsAua7gRDgj5/34IJ3WrVo4tdQyjzZHovakNsw3SSTKlqE8YKZsh78\nvEdcLwMVI8YKLQA7jW59KvIx2VcYkMykquNUna2ylzSZTXsCfsGWSTBYWw2WQTCgfwLiN0oRjfRx\nfsBwqNABxUKepmOo4Oqw8nwDw4oCSmN0wF6X1+Hn5vRiqw/AaSOKcO0kecw2mnBnSLx5yBxM4il7\ngGq2f1iTy4DBSlrE1dNvqkozvaLNnV+AaB9SezcRw5qtM4IIOtlpe7D1UunRiBL19JdtibwnpPgP\nBZh0VC3KBrSfVJVn9Z0Bu7RZhkygeHfJpCh4vsj5rz/AzmtpGn6eSzIE2YGmSEdRLjmwJYl9PD+9\nMYQdErOKJAE2d8azDpDOv6wsCFh/1xSrJZOqTl/dmrGBkyVTjZkfuq0/ArpU4PcCA5nDlyita326\nhCnoafGgavdq5uGZRdHMQAA0pG/k0iGJN/Wht9i5mQDJ1jBN/1A7DW7MKvvce/FQ+T3orov7AwOS\nmQRUJ2Dxc9uiTZzvRB1icGlERTskhrZTs30B0VVbCuthFtGhxQFpWBlheemM/zHUDPfASylpuaIL\n72nabJhJO4OiznVEWdwm5VAxxoBpkDxjQTva+pJY0xYTphE9G1oUtE3kxrRHGz/Q3dSv9O1r5w6V\npuElIvwJUj6RzYSdsiu3PCy8or95KeThXBik0jwDc84fipsOd7lxQUIHq7bN1dTwsDRtfFs6qnap\nqDw/gMsPLsHwkqBjLvPOLN3xlKtDV3/ClZkUPBMeXmiba9crrjlFTOcwWs5HCucEAHhsQ9j1Gyw1\nnegd85t1opQd0GyPJRXfzEiSZWYCsiEzqMDAOI9XUara/LQRhVZ9FrkGUBAU377UH/u7mwS2PD+g\ndOrg83mZxsL5mSVEfeTlys0UAabOzlyoIhKOiMAe5FN0Y5LSqGZNZe/EwikXJldWvuHe5866fGbS\nMwgzGLyoxGxzjeht4qy0iZUeXnKQOr6hbbOULaLMgmwyqplc7MCwBeYmdqaWF/ObDjhmxov/yd8o\nwzIFmbqCWYxAt4HEMiAG3NuaqrSW7o3h/tV2NYFQMmnY/6W/qV0nyzoEDH2GTTaBifU/c9Nmxx1r\nv8fi+18p0ZKy6UK6LnGnbn7xNwzTMSks0qGJi7GBZcT5g4ujDJd2pvOJIDPejfT/MpJJ91ArwQDw\no8llKM4znPbFHA23LOnEtYs6+m1DtOoRPKPzukEiZadp+HJEZdExzKa//0S57ZpUmkHSDDbRC4sF\nOOfXjyeX4VhBPGBVXkDvgMw6UnrtI0M2YRmwa60uVGR3RFOOfcdIZxItpTqaHLdmMpg2YkHrK8s3\nUMxsVj9zuarPEzPpgZukBxod73OLFo+HpmzQGLZL4l2ZRSWzKc6jI5zSgcq+241un5kEpK2nalQ6\nwfgFa0dPAl0xgmGC21EoUiBWYzwgCYwOOCWTSY7hk4F9JQr7YTdydwa8ZvPfdaydPrqQWQ4onFOE\nioGxJJNy0rWgI+ljD4C6Y1y02akkk3apnJ2rCjDPA4L0athTilSlQCZGJOBskx8cWkZJ8VATUJTe\nFGSSSFX+zLhyfmmPLLYQLUcmmWSblSFiY6eTYcoTlMHSHUxXwrcnO2bp+E5ocCKWrTFnUyyC6Psq\ncvCAlJnJBCAP4wS4B1UWlZkLkiCW3atOmwLOjWJYccBmi63LnCUJOz/EaawxAb356WDi2HceNnrd\nSnj19edpO1A+vJr9kkw5jdlAVkZQ0hH8Yy/Mnahuz0y+5LljTSPe9iI+/8bOOL47v82TA45bGhfB\npeSdWDWte0hQvuMXeAVd+5PBG7jMpCYqCzJhcTISPXua2z/pwodNUVQLbHQoZKEE+L7iGYQjh5g3\nLpiLh97xRSaZZOs3YDgmlVTygYwoni875SLqZiWYXsEW63YCst67bZxcOfwmLNsIZOGCKJKE2KQr\nrs5YLu9tjLFB+8D8m7XfE+b12NbDJbaNfDGym5WkdqHc30+eVqV8T+HFAcdtXMTTk9U+/o2M2jAd\naoXAfuMRD4PJ6xb5QPU8Fz5NWo/HndccT7mzHLJ6qZobAC6Z2wYAuMxFs2IYjNRYADpCE4LBzX5L\nip2HkrLYm8V02k7IjEPRl1l0MqvoFGmh6Jxg1xizKbLrR92A03zpQaZ+L6ZLuUSWUPaRx88nWdDC\nYnNXArvDSeEaW6jv92SnSVCW7EDNwsu8VwlZWN6GT+PGeHvxZ8gVA5KZVIl12ee1lXm4+YhyWx5z\nERH3rqpZdU9D/Kn03DHFeP3coTAAtOUQPoBV3xpQSyb5cmmcyeZIUsxoGaqF1XyTq2TSbcjSxZ0u\nuLLJ+Gmz3X5LJDmRfSP7L5+QFfkH4M7k8BNXZ73kFwSxiktdrydwTfP1ccW2+m31Cn7z6Q6utKst\n3ZjQJCFKBk9AouPZ0r1mfxPCjANDMGZJJj4nAJSIRJ7pvPyBY1+oekRXvsqr8UaAARfJpOQ3D/66\nV4oUMSVYBJmA/V4jXTjaNP13bYWzXdi0rKJBxjB7jbX81MYQT4a0xQuDmTXIzQFNBrG9peFggtg1\nh4XOeFRdSUgU+wLbduw7K8pBGg6nNHeSbMjmgCSCSNuSCzNJkQL+P3vvHmBXVd79f9e5zpxz5n7P\nJDO5HUIgkAsQQlAIAUXuIIKXgkpo1QqovxZLkWpFXy+lxV58G6tSbKmilVe0vrXV2koq7ZuiLS9a\n36YyCSGBhMwkk+tMJjNnzpzfH/usvddee932PpeZTNbnj2TO3ntd9trr8qxnPetZePvyDK5Z5J05\n3i5xlQXoJ/jqcg4Glik9+HczqQt083Doya9GkVRt5qQwaUoyRg+dL1MuOKnLFVUHXfK0jr6zZJnP\n9RvnN2FJs3x6808KB7FaYZJRi1MbvBmu1xAKTEz8hZlSwA0QdQOiy1elS2d64cw7oYedZfHwq9pC\nWUWRFvuuvhkcE88r42KhW0VQ4xs8ccidQbr1SEzkohakx5IU7ILw8hQ+OYm84Dpj/8tfjuOjPz0W\nPmIBhydnpBMad5mbKfBrBhr8z9C8wdHS+2xnq7Kw6Ic/ylJF6LomCUPPGzdtq7IlT0eY5Fdj1Lnk\nhTS+T6HXP3pBM+45V75T2idMSpJMhBwBfTvRuUlqQFhh+qAwJ4TwghkPgTitqDXvF4KjOX3pSSKO\n+fqeED1NFQS4qlCCa6ZV6ZjUm4kjHvOOm5SbYuk32AQ8LnD3A2EkEfKXu8oeWHTps4kS4U1RKay0\nsgAAIABJREFUOMOz7avEnBQmZVI9EFTbEkJwZHIGe8emnTAqLRyA2yXLOT53IpLZHQGQScTwjas6\ngvlSpGnyLL9EEoOhZrIEjBVm8PF/P44YIb6TXXzxSmr3l8sn81Q6G9QKk8TLT/mKUby8ZvI/Dk4J\nBz72RCBRCrw7FNPd3DLB0FcviLhzF16DvpPk36+rQTyBER0DyTNT8paSVfkS54P77XZmzh/VPPv1\n1fGiW6i8MEUH6n3j+vQICWrZw9hMmjYD07D0rPWwiPK8pew3ku+TwjJTKgXi15qpcAlS8wPvvvMr\nFSeuja8oj2w/K0vS3ZRVQZ+k0oTxKwgm8O2dh19JEgmXuryFyYusDNn5ZJhl7tCaSYPSixmkK0pY\ntNGM59ryZFK6xFxOf/TUjHvUKTsyyjxpmMKGfoZRIl1RPklNKsNwyfKnjEnLlcjlBhF7TkxLNeO1\nYk4KkypkM4Jv7DzJLL/Jw8psCExseej93oxgcOcCXdqb8v02qbpsB8HbvCiSct3fUO0q22GWSiWp\nhgKAu6M36tF8FOMNOCUzTRn1P8h/y++/MqFcxvUJIZyWgm2oRPCMMEJD+M7buRaMhABSB8n8RICy\nolXsxmTLtsOSvPjTfem4XxPLl5XUH56kDOhqgMlgLzoTlw3XxfhGZQd5bxeoJ4B/Y+dJfYKCfJna\njIbB9HzzKOmwm7hYEgRlZ/+VtVWqmfSlaZAnFtkyty4sb7ssgvflGwZ+fJBpjfgJixYmIpUtNNuv\nlARCO5/HKEwW5b01K5uwzzTIzELKhFEm8PVTFjO/WdWEEkoYK+gzk9JISXSCz5rhsPXtyKTXB+v6\nspJgQs5Cx9BFOU4uEFTwKC2Xr68m3hGOTc1YYZISVnvinMvsGe7L4pQVLrvzzrT8VXlc1cbZDmmW\nd1hjbVYzmU0QXDvQ4KvwfPBkOcIZgVr7hEHDBKqgmdTcJ9wP9nnhSrZCs6Dc8Sa5PoMSp5mUx2EK\ne9yfSsA1RSY0NoU8E0umrZBxtiRd2SzZia8662I+21k2bcFopRpAWOGT1wpUWrd/JZ8Jpmf4cWWu\nrNgTmXhkx8YCZpptHazNpBuv5n34vjFGPOfSAGdeohBU2W8hq9XdCq8bleK3yzVvoTptMCHAswcm\n3YkigWI3d4V9z++9cAJ/9aJ4YnXz4mBdBZxxhLU5rkTMMVEGAPJJkYoSgEPlMlQpOErc/4G0EdQW\nm2xE5UmW/bH+9nP6E7LaUryW0eEtzGqo9I3o2C6SDbj4TCiV/6mFiY+MOStMyvAVNtPpnix4gpTM\n6aluNiqaMct2eQfj9t/lOypdU+WXLmKEYKZUwkAujg+vVvsIizNfkT9akS7v6tKPciwki8kyt08Y\nlpSxKl/0tygpr8GJfRLKTkWJ2tRE9SKQbsjIZRqbdV1JfJnbaW0SDyVONAK4VEMU7vkoiDZisYMQ\nm9YlnLZfFh8vjL18QnKSkuCasxHI/yWbBO6CVCci8ddEneyUYsW+qKnjlYrxM/DsXim6TxqYoKBs\nmkDvG9YJ37tJwtBJQwlizZ4KnUJguuRokqIIORTRKoz0RHJBQtUc3llt/VktCVcDya9sJWNEuNOe\nEqZORcm/8eQLYkfvYaGnnLGvLIu2RCUvBYq5nxTRuKDd6CO4L10yh3qibDWTiFaxqa8vqpmQIStc\nE9+9YTRifDq6ma1vNzdxwhfLD1PBtCSIoATv/E1+R7gqPZ6Kd3MbaDbYZSduTiCFH9hlmh536YkX\nWsuwLpLeuiwTuuIHNuDAr+Wg6erKPYpWNU4I8i1mDqJFsMdHOulIpFYNrlYK0QSaJza3Y3N/2hfa\n7wBdvCRF6042wVV8UeYQ/A4sXb4jR83eX9Q30JCfvIjx+apSk3Co3IgVZxQaBaJ34K7j0KliYIIp\nqgo3L/Y0KhMzZSFF8bwbF/eb3VAzUyph93HxqVTVIKAIkK1SwVwo+stfjusFbxL8KZv4VnN8f/6Q\neKMOP6kmxO8NoeLd3CGfN4bJSNFgUFI1OQLHpypFZ4oliyeMcsWd8EnGKV7byj+y46jge5ZNQ0T2\n+7qsVXPir2NOCpMqVAVJCy7KspbP3kWSRpjvEmXmy6ZPNXm6zqhUKrkuQGZAd7MG1ftazWiEMtvN\naHyMTsCB905aP10l33/85QDUjlUm6LAde4yYb8CR/d43XvQJxqJJTNg6EBN0FlHiCU5swr2r9nrE\nHiqTIAF7M1k98LUFODZOJlWUQC2otTPCpMqUwvdbEB3N9/KWhHsiVQhZUq2Nl2jkREGE9tsaJotB\n+1xRHm8YFAiT5Qf5OuWzj1NUj2IJ+MWRgvI59wScCqRmpz3KI5BtmqOwgvRXfjkuzJ/vmiB+mUZJ\n5ualUgJvy7UnlcIkVFlzZXdAsRFPtwJEk6UbV1i+ZeIeSTZZINVZ5qbf0ZSSZNwCgE+vlx+GQhHJ\nLiIFTPCu+I51Wq7QLAQGWsGMULUBR2ozyQqTCgWIjEA++JmfTr3N/eZ3c6tgdz/SdFmDYZOOK8x5\nqBTWobhOYImVp3jCM9IVQfnJ6Uwp6IsS4L9d8F1K8Hdsok7ugTVycwI+i8JGz7ukEbyXzrm6MG36\nfTXPyQhoJjUdPBtOBHUrEzY/oo1gtO62pYi003x1vIiv7zxp1B7cSZgk7/zli7qCS+cmExjRWdRh\nhEmedyz3bN1kGhkqnLBNdbApgYcvbHZ/L24yEy4bEiRwYguPql2G3cBDMfEzSSR/hyGwmqNJJwzG\nm2pKkolXHbRFzqTKD6uVN+nPVHGz4aUuvcyj9B2rWg1IOZe+CapqnFHIDMZpytpEOe5MIriqQE3U\nlKtzgTx5Cek2Dp3xy9wykpyvAX7mRwCAEGkBqwyCHRceYs2QL37FbxZdwfLeXnitDLV5YTU0ouVb\npwycK8VSyd1lynb2dIe3ipLkb1OM/Ey6P8xn5kFHwCW8eMzRiF6xII13r8gGwlD7Fv+uN++4TLrB\nieeaAfkpILplPdHtllS45mVa77TxiCYyrJAbMj5R/JXUEZG2f1W7X6hj34G6QFJ1nF47IdKND6Iw\nnxJoC/h0xCesqPsKNy6IBQqV+6JckoTSokRdohSFk3kU4GlPx3xmB6YCoIm7mkomT34fwWbPieDD\njjEzZ2FI7htTYY7dNczeq/kYLxBs3nduDltWBN1LiX6HiFo6+TFZwBDlw0SvoasjzuoT3LGCXotC\nGE8nvr5NkB7/biYuuWj3LbKplwnypZIzcauWcG7CnBUmRWUcFwiDIo2LbJlL18nx9+ME/qUC7gHe\nQbhpYoQAfdzy1P8ZnmQqC0EMQc3BDBNeBCs0NKf0y3ksrMP1Ekr4o42t+kAMfKNoS6kTNRmEAfXA\nnoh5p1jotG1FRkvgb5hmPYzoKVeTRpzBic3qthu70SIoA6EGiImnGvDRyNyCsAKYCJndb4z7bUpM\nkJa7tE/EQib79yefP65NQ2UeIotXh0hrz3bsqnJ4ZUzsIF/lvmhhLiHXdKFybZtKmOFtVUVhn7mh\nC4NNCdyyxJt8mbYj1a5v9xmif8aUEkq+U1DceEPG/en/e8L922wDjlwoIu4/1UU52SIEyRhBc7lP\nChy4ELIx+wUa/XhrvAGnStKP6PtKN+AIrl3gnnAV7UOx83fVK8U18Q80xSNLhB/96TG/Q/8aM2eF\nSREqf4mA10nKKySRdnoidxx8x83e/sfru3wuW3RVrj/rCY8EQBunAfjfeyYCjc/RsDBSkqalUZvJ\nH7826TpqRfka+yJZjc8xAFjTqd85yxJc5ueEhnIWvFmWWKtBodnltUKswbnIzlUlaNNbdNaqIkoX\nMnxyhjtLXBCLQpqUvUOlA+qCTDxSQ+eT9W04ihIf1SYw31TkZLk5FdN/Tz5u5v+SKpOcNCnaiPDE\ni34bORGm5Xno1IzQ2bos/+5vkVZDFpjNl0lloZMf30TZ/KMSZgLARCn8O5g/s+eiYhqnapXKJKzu\nmjPJkAhZFaRtSqA+cf/zOQuzAZO3+TTZKCN7X7rB8s1LPTMPE9nJs000L2NVHVcJ/pEEXCaMym+m\naLWG5eUTRRwvlKR1plrCdzWYk8KkszQUvM5rJvnlO4rqWDZppUawwQXz4F0Ic+RXXyaG1/X6DYw/\nvLrZ9zvOCVeu8XCIXocKxHvHith13FPv89oTmZPqSuArksipMV3CUGlGKLQB6rddEOZf+aDGThZM\n0hen4sfXkAnwg1dP+YV4w0RYIVd1nyaXY1zVZBMEC7gzhvl6G4+ptQRhhVU3PyE7skwiqAN1hcny\n/+s6kwHb1TDLUzqbycDzgmvf23PK91trIqJ5QHS+fNDBvR+hpgtiTWhorRITH39NVk+IK6J7F2Va\nRlXZm/h6ZR3Ch92qwrZx1WYI+ow0HsU9k0GTnRyFibtaSNOQfBzea4Yucr5vlT1o+q7ntCVxSY+j\nwDASJstP/fBV8RHGMQTrl2ohUVpHBO1NmS9BnfuHV09J41L1bWs6PA8eBHpl12wzJ4VJGTGBJoHv\n/FQzCdEHofhseZiHdDYQFJUPr4CDYAB92bjPbpIXlPnOiK04PoGauSAzuOV3c9eiAvIaEeHMuJww\n4b6jqlz/lhvYWUowFzSK8HbIxkiE/ZSCTHrfQxyb6TX+nkyrICKbJBjI+ScH/PNJrsDlkyU/Mi1X\nDHK75LDxxQB00vNpS475RzYZ4wR/829F240shGyy4XtG0cfwF8PYd6kIlI0gjE44cuIxyA88oTtw\nj/ifc+MVphWsU4Dfmbkq/kqeMY2jFkvNsj6WpQRgeEKs1qiVZtJkrJJNBMO6hqNj5AWdSRQVfp1F\nf6uo1tgkKuMoNpOVCGx8eiJ7ZJXngt/k/Evz44OsDc8Wc1KYlC1TXbXQb/vy4rFpYYVV7UyT1Sf2\n6Cv2o7HnD6vqokrV72gZvUyJshcjXgKEeGHYvIiSYCuT9MQF+FXtovSXNSdww2CD/AENfMORLdOJ\nBOKoHat/Bz4p50M28/Y3wmrZJwJyTWdY7VgUbZpoUOSjScTUDd1E8AL8NqKV9GG+sAS459ycuzvc\na4PhPpBPIwW/xwCZj0DR5FLUOevMa8x05354O8ygfZc8Tf5MdJkpDgDctlS+qYztT2QTGR7ZJJAN\n9xOBtwXRcyaa+Eraqeq7VCLQmezmPqlY2qyFIKmDtykPLA9zP0Wuety4mL9vWNyIW5dmsKEnhX+6\noUuarlEeUT3hSHQuuHTsR3WEWNr30DjZ9D6wKodkzJmE/3zUax+6vkWYTjmIyt/vbMiYc1KYlHHv\nqiZBBXGutKdjjoaIiA3mnWflFUokiBECjDOdglKYDKw9eX/ymkFP4CG+Z/h8+jp7ZooUOG2HJlkS\n+6fjBSzRiR6hljkEBIRJBH+banlDIZgAiGCdlos6mkC0mvdRPUsJ27ioACGqh0D0jpY/Ace06HXa\nDR0begR2t4JypcIpWwcJd98UkaDbKLER3iPRoKk2x/D5iwp7ZjAgcLWjSkAtB/i4bjAoTFJB6lPs\nhibRO0oER4psmdvUzYx0EhOhrvLPs/2NKDuqsUCfRuWdVzUns0bpcenyZTIDIM5c3S05NYqNi3Ln\nWVl89uLWgGAU2nyGtt2qSHbB/RF8/la1MwdBqNKMnJ9geZQAfOBfvaMZc4KxWBRa1A9WOqmvNqeV\nMCmkXMDpuLyhsM8ql7mpYMIIKL5OX9E4ZKp+GkzWoVFWtiZ9HaFznKL3TGEGOF4WbGn+Mgni29jj\n27AjSQcA7lsV9KdYkoQ1RSYAsfedo+oq68hZ2NmfKD72fZyyJG7eotoJSu+LM2AWt0YSpvneX9ZI\n8Y/pGnFSJ+nL8iW7btiJsX7tFmbF/g/ZuuCrg0yZiPKhsoPjbY1vVZyNa1IUKk2USTnwdeO7L0/g\nKOcyRjT54qGvFbAj5iauLB0NZl28rvoK70uEPvXE1HtStiHCmxwroqkCUfs7voyvWJA2Wpnx0tVj\nsklShUl9YimV/McYqnYBRxGEox50EBWRzSTPLw4zmzklz9C+7rI+uaaWf5b97f0Qh+GXspXxC/7/\ni1/qNwvWizkrTEoHMolWjrVbUzktl8H7dKR/FQXaEhGq0wViRG9j1pthnASUhR3RDnOWv7u2C12N\n3iB9bLKErka5XQZlgWBgZ5eUovThfBrKZVWJgBAWnwsYbiIA+JdyZhiH4kSRv7czzqNZWgX2Lrpv\nKttEwUOzHOMviH8Gw2seSMTUcUg1kNx1KiSEEaRE+G2BnXZbmCn56qCvHw5RWYolJy42COsmSydM\nipZW13eH82zAw/dZn/v5icDgGkYYCfpeZdPyI9p0UJgRT/Z4RGMhe+2NCxtw3YBjGuPTTAriUqUT\neEYipJrgey+VuZNmRhvGLnVdZyqU8FYrm0klXLsSuVwzydPnLmnFamZjiM73q1aI5Z5nJyJLFA74\ntaYlgjI28d26vDlofy5Ky8hWWv8IcoYHkRMSnPrUW7utY04Kk6qZrawTpKd8ECicqEL+gXkbBxj8\nZlEJk662hL8uG8QR7gQcGs3+k0UsEgiKJnVO5ZvPhKCtojg21u4Ogr/DIBI+/AOg94u6TQLUroEu\nFJyI8u2rO3G5wIZIZP/JYvpa7jtEiMik7F7Xm65ogKbQ943JelgDAkGJ42R++/CU2KMCwuV3+/AU\nfvjqpFSrFlzC1scuOhednXhVQ4MmmySz0F3qSptwLmBC8n6HTsk3h4jzF6SrMY5fyWcD95V9ocHH\njOrHVJQOu2zKO1mP2g5Ey418bGrNpP9mLbxryMZJmcLAaXv6El/XlTI+43qcWdUzmkSUn6KhmhSC\nlnYiT4JlEHkDTgV9Hft3JROjOSY3CjEWJh977DGsXr0avb292LRpE7Zv364Ns3XrVqxfvx49PT1Y\nuXIlPvGJTxhnzFTAmGa1JeUw9OxXUZzK4xTLibINz7/LW54P1XGEsrOx/R2wX5tCiFyoVs96o1W7\nsLv5eHSaFdcuDsGGZXrqBo/Qz6QkD6yWN0ZIKAGW9wnKI9M0CL9F+ZOG2RAT9ovytebinrRSy2Qq\nw7LxzgDYtl/slkP0PBsX26bevjzjeUJgvlHYjlQ1a/cJkwZxVRtR/vn+IopmkhcQRGnFJRWNXeJj\n45C1H9mEx6tDzMStwkImFYyiom/dkg5GUtHEWZRuiAh5M5t20apH+GwJbY753/T/KU7id06Ai5Cm\n5j5fz3ThS4p7LJ0a8w0CA3d1NB3VGB/mu3K/ezLhV7NMTERkSozHLm9TR15jjEbxp59+Gg8++CDu\nv/9+PPvss1i/fj1uu+027Nu3TxrmIx/5CL7yla/gE5/4BH7yk5/gm9/8JjZu3Fi1jFOmy1IQ3UAz\nqe3JxLXDtwOU6VhNZyWTnIkJGyxGTCoR3JpMymFMfdezDUDYYEwahGZJXUeg4YqSoNIk/IOP7IQW\nHew302n3WLdJhEufJUxO2EYt3KAglyWFO2l1u1tFF0RBhBMXA8FAm67muglOm/JyuKzZO+2F3QTH\n/l/pco7P9EHbnkMO4yWzJTddKgEtijgpn2aX/n9ZXxpvLp9Gw9frsLtF/ZMOErguE9r9ZaxYWQqV\nG3N4JRYtpxKAs8qaZX8biG4hLhKodTLIus6k9J6IKNqwUyEOO/mPQ34hr9KVKRlT5Y7OaEJIzIXJ\nrGZ52MQuXjTsuEcWszKAOhop9zO+pGk/JotLrGzyZ1D3PssFKyj1xEiY3Lp1K+644w7ceeedyOfz\neOSRR9DT04PHH39c+PzQ0BC+/OUv4+tf/zre9KY3YXBwEOeddx6uuuoq44yZDmR0glUqa/YmptUd\nmSzeGU7YoKjskVimOCHWF47onW/7BlLi/C2zYwlt3G3QGtglxiiNRzejYxsl4e5HXUZw5G+zLpCd\niJucgGOcgapAmH/VWjZRSP620H+gNnXBde4G3chjuswl+658m3LrXcnfBlT5UzkgloWpJqL40xIT\nL6HAz5UN3xGL67UTiN/sl4wR1zwjquAdFBt5wVIdjr3fnxUv2/YJNDU6TEMEdsNL/vY9E7KsVrSK\n30u0MqFss9zzqklnGI5OydeXRJpnPr0oVcc4n4pJvixO1aQkis0iP7HiJ2Xs3av6G3zXTMco9jl+\n85uZQC1RchDG/KOcRqHS5cQqo22rhUIBL7zwAjZt2uS7vnnzZjz33HPCMH//93+PJUuW4B/+4R+w\nZs0anH/++fj1X/91HDp0qOIMB2yCym8wI7gXCKt4hncQDgSXp1XR//aaZum9GCQDvExqhbdpJ2yH\nJxpkTdrBq+NF7Dw2bfw8D+8XLzA4lmMuSe5XCk29uzEeuAY4y4o0TUKAdJzgq5vbtfGFTZ9FPEgE\nS9cbkCUdifa3PrfRZAx/KOrGIorAkmcGYt7llS8+btDjzzynvHtFFv/zdd6yjmpDiaKZVQy7hLq2\nMyU0iehsiPndkCBoVmKyIYai2/TA81trzHeMyiOTmNwQ//8AcPfZWeGzYcr+zrMyePvyjHFdYz01\nuOmVwpeVOg3F9RCTmzCCZ1SkfYli/JvtDRQE/u9VSVs9OlkKCGaBSbcgfcqbBhqx7cZu57kq2EzK\n0nSvM0oxUXhRH6ayTZ4NtPVndHQUxWIR3d3dvutdXV0YGRkRhnn55Zexd+9efPvb38af/dmf4Utf\n+hKGhobw9re/3SxTitbF32lOxvDba5qYj6GOWzUzc59hBjTfx1XkS7TblxIjRGuTyC/xEcjdDan6\nHtExj6Y2TD/X2LeoUNl8ZcrrCY5j6pJPgCCI3mnwS9eAM7noEtjTsFpMKm4uzJkbvos7BifnYTYt\nqBBpxlXxy1LR1ZrAQBMyo6aPp8szm+YkwUPrnMmWYwssji+MdiSXDApoMuj73ry4UW9uYpgHugKS\nScQYTYrzrjwxAlzNHbgQmDzyeRZNRMphVJv5ROGuWdQQvMiHF6Qr0p6Z1HWVbZqp4HT32Tls6NG7\nY5GmqZLe6OWw9V7xvHbCFwjrXRCNHKciSAoq2z/C/S8MWwOhlk9f+Qz3UFgh7gPn5dy/z2lLGNtM\nKvMEYGSiiGcPqO3DKSI5gsbjPKB+KdndRCzcvobZOBmnJpORmZkZTE1N4Utf+hI2bNiADRs24Itf\n/CL+/d//Hc8//7w2/JX95p0I4Lj+4O2JRKiEQXaZmyXMN+kRuOUB5DaTvtkG09ESEPds7rD1X2SY\nrBMmL67Q9Qkgd1r+yYta8JVN7YGlTFZwilrxedMAwKnQlwl2XotOy6kUn82k4L5QANVpqA3i0Q1U\npmnoBpjATL4kvi7j9mWOm6VkjPiWmILafm+y4WqPeRWlhPedkxM+xn5jVtCqVh+7lN2BWy6YEoA3\nLGzA45uCGm++/IOaSbUWhYZxTGaC0OeFPjEJwZ9fLtfCs/mTyWC6OiKyyeVh5ZXeCEveOjobVOcG\nhetLVe1ZtPM++Lw8Nep5xH2ySkKccuzTtHZelrzf1P9hlYUWU5tJEfzub9EmUGligOSjE/xs1FzJ\nolrJDL2CxPyIE6Jc9jedWNcSrWqmo6MD8Xg8oIU8ePBgQFtJ6enpQSKRwJIlS9xry5YtQzwexyuv\nvIJ169ZJ03tL9wQmXtuNQ4dTAPynNwwNDeG1yRgAr6K/8sorGC8STBUakZwpYXR0HIB4Jv7aa/tx\nuBALxEsZGR4GkMEre/cCaMLMTBGHRg+78R14bT+GxuQnA8xM50D1XgcPHnTTOTUxgSMzRQBp9z0A\nYGamCXT4PHL0KKankwBi2Lt3D8bG0pgiwEQhhqGhQwBa3HT27NmDqbQ3pJyayAJIoDtVxNjIPgDe\nDA0Adr30EgBvGd5J34vv5Pg4AK8yHj1yFENDB3zPyKDvMj7WCMATSgtTUwDimDz4Ko6PzQBowMFD\nh/B/RtMYLB1BMTkDIAeCEg4f8co4DONj49i//wiGTkzj0KhTX156aReOHmkAkMaxY0dBy/z3f3YC\nAw1FAHEcHBnGUEHcQbw6HgeQw95yHaDvNzqaDuRxYuIUgAR2Du3EyYkMaBnSMMNHkwA8v5VDQ0M4\nfsJfTgBQmnHE4uPl/B496uUbAHbv3o3DiRLo9ygWi6D15tDENPripwAk3XQPH/HndWhoCIWCVzd3\n7dqJdMzL39Gj9HsD7Dc/dMirw877TgBIYPykv77I2L9nN4BmFIvTbt6OHWvEyKmiG+/Lu3dj+GQC\nQAYHDx3E8ekYhoYO4Pg0AdCMUxMTiE+VAunR+HrL/cHJkxO+djI5Oem+7969ewA04ejRozg1mYCn\nmw62hZmZEorT02Dn2fwzAHCs/I2GhoYwXXTa8fj4OI5jGkUy5Xt+ZOQgEqQEti4cOHDA/3t4xC2T\noaEhHBbUt9FDoygUUhgbnwSQxNjYGIaGnH55/1gCQBYTJ51vxJYRAJwol6cMxwSpEYXClFs+u1/e\nHQiz5+U9mGT6nqMFJ969e/ZgMuVc33vK30fT8isUpssT2xgKhWkmf/6yZfM9Pua1KxXFmRl8Zslx\n7Np5BAAweSqLva8cxYkTKRzAEQAZnGBOMxsaGsKpk06/KYJvg06cTnvftWunL8/Dw8NIxUoAsl7c\nRf87/ftBr78ZHxtHqZQAlRb4/jcqpZkZt+z477137x7MNMxg+Ji/T3LDwi/IjI4MC59jvw3QgtcO\nHMDQRMF3TcTo6ChEffzo4cMYGnoNADB2ohGvlb8VAEyUy1vEQa5vaoyVMMy0qYmTE9j36hGwY+HY\niRNg+96yZ1sMl8d9Uiq5/YY7Rk83BdIC6IqlXzicmDiJAgHot9w55NWTkYMHsftUAdPFHPi+5df7\nE2g/fgxDY8DklNdPv7zba3+v7t2DqUIWQAxjY2Pg68sHew75+r9X973qvvslLfLjTauJVphMJpNY\ns2YNtm3bhptuusm9/swzz+Dmm28WhtmwYQOmp6fx8ssvY/HixQCcAbFYLGJgYECZXldnF/LLM3hh\n10lgeMx3L5/PIz02Dbx02L22cNEijBVmED94Ag3pGDo6moGDYq/wC/oWIDFRDMRL6e3zkFjQAAAg\nAElEQVTpAV47gcGBQWD3YSTicbS3twOjJ53wCxYg3yvXmqb2jgIFZ0tdV1eXm04204jmXAI4MuG+\nBwDEdx50DR+aW1qQODUFTM9gcHAQLVPjiMcIJiaKyOcXADs8YX7x4kEMMEu0jSNHgJMF9DU1YGBR\nJ/DyEV++zskvBXZ69qr5fN4XXzaXBca9Ctfa2op8vsn3jAz6Li0njgHHvaWAdDoNTE5jYGAA+dYk\nMPIKmto6cPLgSfT09GJhLg7sOQJCCFpbvTIOQyabRX9/J/I9aTxPTgIjY8gvW47WwhhwZAItLa1u\nmQNAY0MaODWN3p4e5AXHzAHA2KEpYO9Rtw7Q9+ssjQfqVUNDA3BqGvn8cmRHjwLjBV+Z7H7lFPCa\nd2RdPp9H83F/OQFALBYDZkpoa3Xy29rWChz28r10yVK0N8Tc75GIx916M1UiyOVywIlJN922wpiv\nPPP5PNKvjAJTTt3ML1+OdJxg594J4LUTaKPfG/B98+6uLmDEaysNjY3AyQJy2SwwJu+gsgmC8ekS\nli5dCgwdQiKR8OrJ+HF05BJuvEuXLsHxQwVg/3F0dHQiPlVCPp9zTogZOoTGxkZkkySQHo0vecLp\nDzKZRuTzC3DrqRP41u4Jt/4BwOLBQeClw2hpaUVqesrneoFvC4QQJJJxz02E4BkAaG9rAw6fRD6f\nR3yX044bMxl0daWRX5bxl2N3l7N56cAJ71pPD7Df+51o6QCGT+I7V3eiNd2NTgTrW0dnB1LjE2ho\nTAPjBTTlcsjn+wEAR0YmgVeOIZtxvhFbRgBwbMopTxmdnc63TqVSbj1ZumQJsHPU99zixYNYxPQ9\no6eKwM5RLB4c9MxGjhWA3V4fRMsvnkggXiwBxRLiTJ3gy5bNd+7IUWVdo8RiMV+4xgOHsWhRF5oK\nJ9HXlwb2H/c9n8/nkTl4xC0rnpnGZuCov502NjYCEwUsX7Yc+OVB93pfbw9ScQLsO+57Xxm5XBax\nUwV3yaip3H5NOKslgcOTM0I/oSRG3DKg7YcyODiIpc0J7Hn1VKAs3PDM3729zljIw5Yxdoygt7cX\nedaEQ/Le3Z0dwnG5vb0d+bwj9DQdO4beXu9bpdNO/3r9YAP+ds8pXzhaXymxWAy9vb1u2Eym0RkL\n93pHF7Y0N/n6XuoLpKenBzjgHCRA+w36nomXDqGjowkY8eedEILbljTiqZe8fjrTmHHaebm+nnVW\nHvhvpzy6u7uxtC+N2J5Rn7FjPp8HU6JIvTrq9k9LliwBdjntb9mSQcRfOwoUZtz+noVvS70L+nHJ\n5AT2nCjiM5cvDJR7LTBaa7jnnnvw5JNP4oknnsCLL76IBx54AMPDw7jrrrsAAA8//LBP0Ny0aRNW\nr16Ne++9Fz//+c/xs5/9DPfeey/Wr1+PtWvXVpTh4NKbUyXokqd6mVtz5ihnF8THp1NS88vW7HWh\nH0pmaZY/gYfalpksn+qWSbLJGM5qkc8bqrHKwtu58jZW7DYKQvQ2WCawc0P228miZJ2WV4MdR6fL\nabLnLzHphTWbYMwcfJd1y+Amy9yK8C8ek7cJYXqa+x86379ExpdDYBMSodcly7sh1rvuOy+4PEfj\nvHxB2mjpbGRCb52ksmk0eZ5/Jzq+UNtrVcd8eFIgSCjyZYJp3yZd7maXuQ0iqrZNl3BXcEm03c0M\n3g8joHqvcG6G+N4iTNjGBEGDxJWBepk7mFZjXN7PVKmLdDFxUSVzDdSSMjOJ0JkOyIwgSiXggTVN\n+K01zUKXXV/cERSCSwDu4Y4lJgS4QHDoBc1bJWUaJ94IatJ2fuvfjmFpcwLXDIRf8YuK0Ve65ZZb\n8JnPfAaPPvooLrvsMvzkJz/BU089hf5+Z1Y8PDyMPXv2uM8TQvDXf/3X6OrqwvXXX4/bbrsNCxcu\nxNe+9jVtWrpykn2QEj0uT7N779hUiO6FkFADmVSIIeIdqcfLeUnFg4a7MRClI/RqEraSi4QklWsO\n+pu1MaTP6yYAKvx2pl7eZCdKuHaVihde1pzAxp7KbUjZPGmfYyYVlcRDEbmhUsWxbzyEgzp4+W1N\nqXMmc0ciOk4RoJukgmGnq9QO8i0Jow04Im5f6tdk+yaOzP8y21TdN5zm5EOVsCo6N9ndzSxJSSss\nEuBjFzTjg8wAyYbpSokFbDqJVFsrOrCTY9Mvyr4P9aUpjFsQju1vTMKwqOxSRbZ4oYRJ7uEwk1tT\noUQquzHXZXbuol8yt46m31HmPF+eYtA5f5iUnX0HmkGJ4ZqBRrzRYKOajtuWZaRlBYQb69jsJmLM\njm8uFlV9qPakQIXxdtYtW7Zgy5Ytwntbt24NXOvu7sZXvvKVCFkKFndbiuCIRAgsAQAx00wCzsxO\nRrbsZ4idxSm943O8ri+Nr+8MLtfSzTQqTkyVMM2lVRScocvmz/S6joBmS/Lcpb0p/OuBKVzel8Yz\n3OknJid4sPHSmaqjgY0mLPgczdN04XQMv/dCcImGDngqPUJzKoZPX9yKXSG1dSJ0ZeDlq/w89786\nYkbTa5BIFK1D2I1BJvf5Nsq7chGVgcqfmqzM/F4YvGeiuma76+wcvsksaYURAEQa16Bmkh8gggnw\n8XSyG/44IZzH5Ftt7m9wlkfpNYM6QwQPyNoX+4amk/QPnZ/DYFMcXx06Ga5/q3AUDbNRjgChNvUF\n+qwQeY0ppEl+NUyURkxwjRInwTZD6cvEsXcs3KTTH7fZc8L+0bjDUt+eTddHbtYizotbUzHfpFUY\nN0e9d3TPtmupAHwBrOlIYnO/esbAC33S54jnpiYjECpbUp6A48bLpaPiveWdpRd2+Y1jdfnLJWN4\n9sAkjpQ7cgLPx2W1fAiGcWshQ6V9MPEzSQeQErjd3Ibp84icXLMdTyBewTMytDsBNc8zyfkQ1gNX\nEJBolaowvVRFIaubWgHEMGOqZXh2bGR9xbLfdbrC8/l8dSRiVCoBgEap8r6gm7Dxq6q6OvrY5W14\nz0pvc4HxRESDToCUfXKTgYQVhk0FhI6GOFZ3JOUZ8sUuuBrxe+tWhT6wKie8TndBX9Ynt60nxF+O\ntRiERZNsmrYsXZ+gyd2rVC7hl7mp1xG+L2B/z5RKeNuyjOuQPyzdnHcVqcsqRRxR2pNpH6CNh3k+\nESPyuqx4r2p5CjBh7gmTmt+yQZuevayr9PSFRcJkwD0H8auUo36XEtT5ulIgLLPCFyBfuvWFiZjB\n6AeLeSj9vJWh79PTGGOESbEJgAmssG0ymLJOy+uBKB2VXGR6nKIu+zSJv9rcjq9f1REIY6qJDmr7\n/NdNtF2itGXaQZ+NMBMoX+ExYWz6tZyshxmU+IGhaKAyZYMsb0m6fjwBAxtkw8mQ7DFp3RSkK81D\nyVtJeP+5YmFMmAbXxs3C6POjMnnSaci6uMMR6K0lTYlA+qK8VdIFSYs3bDxhFAySyE2FdVPNJJtQ\nCcAbFzU4m5sM4L95mgsnq8NZgW9YNh5T3rwkow2jKy6l6cVsOI8MwZwTJm9W2MUAasHHmdnICzzK\n4OeLroIeQFUPAvaGpHw2NxOIPVUiylKW8p7he6meo+9AT0kRaSZZYcS1mTSYAKgz5fzn2kcxmQw4\nxyb+vFYTUZSy85V5EoJJjC5uXzoS4XBRLoG+TLwcp/eQsdZBWs+IMJ+y8Hybpd/lgs6kuxoA+DtL\nNsS9q3K4oFMtUPJ56WiI442co/BYiInLopz/bEQ+XHj7Vq4MuLu8HZRw4CtFtynXIRT8EawzIh+L\npjgmSU6IKNqmMIPVi8cKeHW8GHlwViwgBN+ZCNpsiIIxPZ4UABri8hFQNVaJJgvK8jSccJpiohVk\nxwK2rIVNQZMhIkhTVHLfuKoDmwV+idl4THjrsgw2lj29iMJQu9pK2q/M1K9OuhEtc06YzCTUWRIN\nhATEyMG3VEgsIzJIjipLlri/VWdzi9KNcZt/WGfk1dAkquBzyi/bi6Cd1VI6M6c2kcwzbBl49ouC\nBEPkk8YvPuNVPEDXovTEHUjwqmgAo8KtdOlPI1waC4cyDE9a8gR2s+jcAYF7npbBpgUNzk748v0Z\niL9RIkZcW+cWzaYfSowANy5uLP/tCb+mk3tdx5gU2FOozAWCS/3+h68blG/wAYDblzVic798N7rb\nDjT3tTAPipa8ZXXPZNk6skAileLkcU8WgUcEdtMsf3BJKz5+odj3ZtiNl3w56CbvhPutoiFO3BWG\n9oaYkaAq+07+dE2nPirEBZXlVv6MdnPDW8pdmI27q42mEO5vXmkgqqO9mbiyHIYNPDuYUo1xZ3FT\nPHBNNbmop6A554RJLYFO2blWQjhpUjjzJMH/VUbNMnj1uu6MWJEwSQBfY6p0aVYVPKDZ4jV6Bm8e\ndAXExcEP5GwZa2MXwx6naILX4VdWmKLzl0VFRC8tysVxX9nGSvSudKejoSwZvK/5fro4TMv/P7nj\nNk3Lnn/sl5Iz4EU2sEGhKoN3nuU5U5Z9SnaiQQJ35Hg7Jvn4/FpTkc1kiUnsU+s9583re9KB9+CH\nqBRXmPx7vf/cJuXxn/R5uswauC8N6b/PD8ja8ILvpBSkDPMjDisPFWUFsKMhjq4G/3K1Kj62boYu\nJ8UzJoMwXWFQpWFiZsEKTqpNk5UKIezRhgDQEJSBArBpdjV6p9pFzQsvwNbTflBGGG8Souw6J+H4\nr5n0gfXgtBAmVeVPCyy8ZjIYK9/REfAfV/9pPntxC957Tg68gjWMPRXg7QB3BSDmKdmsMyq68DKh\n4SJmqao/6x/ERGHoAOr4ZfTSrsRmUvS3jEoGMh37Be51aCPvz8Zx61JHABJpPNid7SJ0+T057Y9U\nZ+9F06HPyebeYdqT6j773L7xIv5tWOyEmncZ5I/L+b2qPYktZwft7WRL6WwGCKLv5pb59gPgnqzC\nJuluGoEjCPCh/xezMxwQTeA8zmeOStNtljqnrTL70myC4IE1Al+ddKevYOLr/M/0TzUa3FRhpwx2\n/AvvMTc/yAhASmWD4DrhKrvWHlHQHgHg3LbgZMC0vw+7iqYy9zG1q5Zd501MVF5UZPGpznJXfR/n\nR3AMqp+wE7EjNyAeUvlyRm/AoRyT9A6isqECiU4w8QmTgvuiJQrfcwYfZkNPGgO5hE/TUEJJuWyy\npjNoP0QIZ0NmMP1VZq988wfXdameUsbLx7+k2Ztu6voKAv/yJxFcp6xoNfNYxWqyROUbsHMrF2K1\nnJazTEybNXGRMBDn6p1osFIRECYN7InCPMejdzhf8t033blagqc5YbVAvv8V4WWwcZlqsGR1h8Yn\nysfRyRn5hIW7kEsSn+lKwHcck97vSpZiRdHrNsrIoMv2hBBcMxC0W5e9F01PY50EgBMOQnxIvi5U\nEzbKy/oasKosjIttJp2n4yTod5F/LVlxrOtMYk1nSqrN/OgFweMIo2gMTSamcULw5JUdRvGF1fzy\nS8dNJo7Hib8fL8EpR9G7mNgemrirqxa6jbq0zwjjM1eUX1E7k7X5n4/W5xhFNx91TS0EXx0SH68n\nnZWVnMauFiaJG4G4s/AT4wafMHWRbTu6+rOqPenT8sUIQQz+mbxKAApjQ8MvwZuE5++LBKcEt1TL\n7tam+DRPCoHkjnw2eFFAiQm/sTeFXz9HvUOUPmvkGsgoBx5CYda3/ll+ThCWFyZ1mCxr68IYhZcE\n0g2YsucBIMnUPz7ZYqmk3XFvqqVh42hNxfDuFVnthMeXJ0WZyjRsrFDP558vq6Yk8Z3ssbgpgd88\nX+ww3Mg9mMBGOQxpwTJkGCGGHeSkfXTYTPH5CfHspb0pvHVZJtSEiTCzhJxgh+9PD06VnyNY25ly\n3QDxk2MVn9vYhusHG33PxUKUM01fiOJdZf3tgqzB+rMucgN6G/3pXLEguFmFwHOR9cuj05H9D9O4\nVK6PAODXVpqNMyKUcobiI05GcNXZzNiJNyVjgbRlyTkntNVQguaYs8IkWwTsOaSigZQQxjWQoWpS\nNfNktSBhlw4oqztSWMfsQFVpJkUDJCHc4BQxHyboKgEvIF7UnSpf93IS2JEsiENUBk4HEq3TODrl\naYIGcgm8dXlG+XwtXQOJNtYIZElh/UwwWiHnf/99Ws63SjwdBO37gqjqj6w4+OsfXs0vf5oVpFQz\nyRVGSSClVehiEgCQjAPvXpEFIeFOtJLBTmJYDvs0k1x7EHxT9lIiRnDDYu/7sgJGmMlPVK27ahmf\njT9Yd5wrJhssdBNzXd7DvNuKlqSrPYxSJA+ta8Y3rpJr7VJx4poyECYRmdB2LXesXRjzqWp0VyL3\nSjSPdEn66naz88FZTLvuFCez0qMI+QkL7UfHp0vYf3Imcl/tmB7wbdD/+1cMlBa6U75C5Sni82e3\nOvXsq5vb8dC6ZhwKbAqSx1w/UXIuC5NMKZg4LaYn4JhiesJBmBNwWHoycXxuY5sTB/Tzuv8+6t/c\ngBLw30en8R+HnNmwyexVa6cTEb4Tp8IPu7PW3USi0CiJlgII8WuTv3x5G9Z3m7kNeWWsGOq9XM1k\niDCmiCactGMsCa5RFjfFcXH5fXXuZkTnTpviH0QCko0RCzl3OaJv/eXL2xj3HsEHVO2AbcP0/0K5\n7dPfHSaW/HDqmkgA0rVDlR3pN67qYL5RZQKAz85OA9vOdPmX+yr1bvD1LBkD1nfL3aMAek2xyTI3\n+7wImUBLr4Zy6VV+Vns6NxNnC6cB6s2o6xrbh/F1ja/7HQ3+Arojn8UNg44QJ7JnNsyyD/ZN+UMk\nRGH4CcjG1gLaRZsLUaleMrjBTARVCrHEjPTy5fCa+yaTkc39aWxiXAWZTJIA+ApIWNYh2ruMhbkE\nmlOxwFJ5PQVGFXNWmGQzpjKaZ5UZ2uVa5lmZloy/ou2MDFH5NCMEmPLvPsBAeVcmPUpO9Wqy5iZy\nIyBLn/LelVncwmnAOhvivufiBPjmGzpw+zJPE3hJTxofWesJOyK7Ol9nR+/D/y3yjEbBhLiih5Bt\naoiym3uRZjlIZbN5H3NaBm8h8BdXdHinZRDffy6i7F7Zn3aXP/j3DHMUnCi9O8u7pfnrvGZXdKa3\nyME42yFvZzbfBDSqpWBbvpT6biv/5gUOmUaOXc0IAy27JU3xQFq9mbjxznudvE4E11j8AobZQAyo\nT6kSxQ04ZdwgOsRB8DefFerui/3Gouw+sqEFn77YswcU5VJkgsOiausqaPlt7BHYppf/X9GaqMjL\nAy9Eir43y23LMvi18glGYZM1WeXmvycNs64z5Z7eQwThChLFzeb+BvzOuqDtrunomGC+3aW9cmVB\nseS08QVUkK9QUmLNx0yi+pV8Fh+/MGi3ykOFbtW7zAXsBhw4NkUuhnaLE9NB0a+R6aDYsCbLXYRE\nX+bm0a2+80tA/ExW11k74fw3fGGUqnDv3tvzWQxy7kUGyhopduDuboz7Ooh0nOCNixoDnSqTiFvm\nwaWNwKNGvGdlVrpZZ2E2jp5yh0Q1AKFsJrlnLlvQgH+8vkuaP5XN5CLGpcv/d75op6zzP62rowpB\n6LqBBty8uBEfvaDFdQPDJ339YEPghBFRnj1zBTEBu7+Qdnn0OdlOzhL3nM8VVvmauzHEzYM6LUpx\nJqjlpGmooLeziRj+6NLWwH3dznsZogkCr+lVPe/mT5J/3YRapf0K8yp8+qkYMZr8re9OY3VHSllu\nlwiEPcDb7BJGM0kQzsNDjPsdBmFaBhHRb6I6xhCo7HsBwMrWBHrKRws2JAjevJQzB2JtuiWF1hgn\nuGqh+lhjGaySYVlzAp9a77Ur9l3+bu8p/On/G0OMeCtdMYjHLt4Gk4/LE5SDdswfOC+Hxze1G+Vd\nVF8JgP9Rdv1102L1ISuivIVFNzGp1YpkWOasMNnDLDH4BDqudFj7pZuXNAa1NJKwReZoLx4aRwzi\nTSNhKUE+CADBzkiktfDZnRnmg+18VbvIdO+l220soicTw6YFaXfHKis0Ou/nDcoBYdKwoK9Y0CBd\nhvjqlR2uEExnpx1pv1AcloSi4EWaZ5FIuFjiBxDwjP753dlsqh9e04w7zsoGrrOc1Zr0aY2dZ4NP\ndws6ZBVRNwo1GkoBIvdevKBi6tjdnw/vpqkmpQTHVulHN/i9H2jLoJxWcCcppymCM7F40yLxAC3t\nm2TJlv+XlU9aMqkGgBMFc88ZfPqJGMEPr+/WhuPv8c32nLYEzmoRt42+8qqArK13NgSHMQKnHf3L\nAU8Trhx0I3QKtNSOTM64G0eo8GISnfutFIJ+pdww2IDf29Aq7lMFl/gz4ik6rbGKsGt7BP4T0kRs\n7k/jYxfIvRzQ/o4dW2h5D2QTWGpwPLGMFa0J145RmLZ0whuuDGVabtGKDssVihN9asmcFSbftcIz\njuVWgP0wA1Cf0MZFPDDPlMTHGAoflqVtSKmk2/3ld0SaTQarXdgdf4D//SqZvdDlpTCavZZUDB+/\nsAXNzI5Vn2sgZlDWnTkqPUrPsCBoRzpYXvavhWsgUSdsapyu6yx02iajZAy//xsWpl3hO8wMmIV/\nb1PNpM/OsfxHkvtYpppJ48zJHivnjl/6/ORFLfgfF+mXwXT5iRHHLu/eVTn8wSVBDWjoOhpC0Ofj\nPjVtnkx1jH7ELG1OCE1zaB1g+7NsgqC7rG0TmTQQotbw88QkA7eKyXKjny6V3LPV+ToNyW/AE461\nmskQeeJZ3ZHy9cE6RGZdF3entMccK+MMWWliRL8SRwgJmrwIHmQ9JtC/+M1AYanGJj4TTPsAdgNr\nbyZWt/zxzFlh8pIeM+marfyiwj/FmHWxt4sl/eBI4DSESgvJZAMO7fa23diNXDIW6EH8y+DijAeX\nJb2/F2UVp2do8sa7+dGdjy6Kk8Czr0owr0eI3pG0bNOFLt+uhpnw/0fvnu9akcVdK4K7AE38XMrg\nZ6AqB9Yi+KPLxGmobnp3H1rXgvM7UvinG4L+SHk7WNN2odspTBEtcyf4NE2FSclzyyTaLz5u2QC4\nriuF1/WlfW2N1QTwyX6uLCjKSiCXjEnOqRaHKGpGCrMNHIaz5AgT2LDPsmHO70jhL64I7qB2l7mZ\nCreuM+V6F7hYsmHvZ5yfvS7F5i0TAWN5c8JnIzdVHltKYDbbcX2OCr2/1iAERBi3LAoTLyL+DYLB\n55Y2JwKTujCElW0cYdL7Owq0TD+8hrXjJ/jC69sqduyv3cSnMUUxpTWtMdAuwy5kfeOqTt9qjrWZ\n5NBtgqHlRX0zSp9jBwsEv5FYAAoOcFHQHqOkuc8aRpvYRTm/vQuq8TyuqQX80l6UFQ9HA+n8vYxZ\nYmCvq8KGuS57jrovMvE3KFvWedeKrM+FC0X0DmE3QNH/+XPcdTtpH1rXjK9dqbYBUr2ySHERJySQ\nrk6DKktTmrbQJMUvWFO/lF5cvDbC/78wAwx/cEmbLDfIGZ7SwUddLAWv0/x0lbVnoiNTVcgG0SNT\nZn3hBoVHhFpo5k2JMrjRncBLmhL4rTWsL07nuqipEgDHpqiAV8J3ru4M2BGzvPcc/WaYL1zW5rP3\ny1K7/hKYZW6HHgMTkgRxJiItGs1hJQKBcuNn+X92fA2r1aqFEmymFPTiEJUM42aAAFjZllSaK5kg\nKlL2ksxUICq63LZwPlErfb+onBbCpOqYNfa7xQjxuXfg4e/IytxdqiDwLaOb2vKx3HNuDq/rTQsb\n6f98nTewBZY2JXkS3TPRFMne9e3LM2gqT2Vky8kJTpqOZnvknALU3RhzXGkwcUVVy+s+h+87wtE+\n/OUV7TjL4ISdvkwc33yD2ekQbFos+ZYknhFo+MIiFabLN5pTscBxlrJnReQkOygKXK/obcAJ1w5e\n1ydeZfC+jxNfSdDWEv6qZ6yZJGwChqRCzJL8wmQwIX1+1WlFHQ5ouPsFRyL+4/VdWNGawHntZpoZ\nYR4qHChlkwKVTR47OF5bPp2nhJKxkFUoOVqeVJzg9y4WmyisUNjAufng0mPtn3lh0uQDEkLwuxe2\nuDbFi5viRm3LcN7kzw9HfzaO88t+MtnqS/vihdk4ztb0k6mYzLSsMk4USljd4fky1vV/FJ/ChblO\nVwcqlkzLlCR/U2T9gUl93bwg/CYn3ozI5ACBWnBaCJMs/AfpSMfdgSdGgFuWqB1Xc7FpnygxaUb5\nMLcty6C7MSbUrg4qNFd8WgsZ1zQyjZGqssoGtXPakm542c60oMZTno5qCZ516szunqzgoAMlNFov\nLYLBJnMXIGE3qIgwcuvC/a/agBM5HxHCDHCbhUw34LyuL40PnJdz6wm1bZNBd+TPlIJ1y9xm0vwN\nmyUTTvaqtkoyD6/pYNyPBIRf4rtuiuz525epbddUJ+EkYgSPXtKKjxkczyiLw6Sphn3Xz17cgntX\n6X2o8m5rVP0e+yg7KeLdC4XpemRtuQSmjsuWOA2M1h+9pNWo7MIsOcu0ZF+7sgO/uVru6md5SxJ/\ndpl6teMfru/GWsFRwLI4AfN+6JKyOQEh5j5MD0+KDabWlc1ImgWnGoWBukbSncxTiWbynSuyuLLf\nP/kOm2v2ABErTHLIKuO1Aw1Y1pLwaQF0u87Yu3ybpJ0Va0Q9UypVvCzECkymcQWX87zfso+mcrAq\nu8e645B1eAFbTGkq8jAEjl/CgxN+x5mZRCywrGuKcVmWn6tgQ2JN8crK+WNRNuHr+KJoxOVphAjD\n/W7k1ISyr5ZLxvDmJRkkYgR/d22nVOtDw3c3xtGUJMJ6wJtgBJeLwwtr331Tl9AEoZVx2Gy6hA84\nE0aKtwuV4E8ubUVvYyzwPOCc3mQaP8vyZnFZ8hMSGblkzLf0ZxImLPSb9AgmEaJ8buhJG+2uZTed\n6yYPvzjsHQLhD+eH/85X9Te4J8KwfEXhSqYEx94T8Oy/w5QpW0qyJXsW4RgnuPSuszKun1ZTRCvu\nlU72lXabkoJilQ0Ls3GsEmjT+aCskC2Kd7nAB24YaJTa/Q+CB8L0T1T7HiUswPWZdRzzTgthUlYZ\n+TbFDjStKYJtN6pdVvC/Rf4OHdvKaNoFNx5CfAKqKP1fPTvrPytUlZasAXLXS7HHuxEAACAASURB\nVIp7lEQsaBsnTa4cYRhtG6UjOYNDp2YCnW172mD3mVQbZQY72agmBM6yeTXiAbz6lYwBn7k4uMOX\nJ0wnH+XV+c/cyNkvmsALLiy8b1V6NCrlXWdlsLwsZITd9BOFhwROmWXI8sH64ju/IyXVFO45od5C\nLWtiOvvmasLmgf4d5hAH8TtEb4RppgHrlrlZ7VAhREO5YXEjPiKoB6Z9RxTByxOwCZpTMXz5crld\nr4x3nZXFHXn/qtxdZ+fQJjnRhoXN8juYk3nqgaxYWY0+IUQ4MeHpZ1fvQqRljGASTZf52WtLm+JC\nN1em6eu8m+gwdcVWbaI7W5oD8MuV7OkPonm/TggS+TtkN+pU8oncJVdJJNR3oAl8s9rcn8ZzI1PK\n/FVSv2g5v3ayWP4dPg6ZIB8j0TfgaOGE32oLk29c2BBw8P5JA7cxHzovhx++egr/74hfoGCFynPb\nk4iT6hlzO0fDFQLXr+xPS3c3ssV1+7JGNKU8LdvHL2zGTAn4xH8cr0r+xqdLOFX0+36962xvw0RJ\nMpGRtc0on3qQcSJ+VLJk5iXgT+GirhTiMfkSJP8ZdR4MZEOnbo+Qt8xeWWX/yqZ24UTAZJxTzoOJ\n/39TvvXGDiPBSMR0tMOQjGHLRKQ0EP323eNMIfhTpHwKCCIW6N8l8DARhXdXKZ5KYU9Ik8HeW9+d\nwoVdKWWfWamM5WommfgHckER6gsC8wAC8zofZg/BrUsaAzbpbPBjun6sipwWmknZ+dj0T7rphhq+\nvu+cHN6zMrhzT7fE4RpRs51DyaxiqyDwO+ymNCYIXi9ZhjDpkClXL3LU4gFNLfO36pxZWVpruQ05\nPy8vHRkNFpo0WFcvusYjOgbNidPsi9ByqMQlkCQDPrIJgtdLNpuw3Lwk43MHw9cv0+WUMHLmhyTn\nen/0ghbcyp+IweUDAAaZTpMQYNOCBmw0dN9lQiZB8C8HpqQd7q7jak1etScK4/y5lxx8cp9a34JP\nKI5h4+u4TiiTTXx1ZwXzR16aIHp0CbfsPDu6Do+Ohnio9ssKXCrTJ1MBo1o2r8Jnuf9l9ymdhufT\nV4tK57O6AztU103Lka4qfPGyNmm4Sk196N9CRRXzdzpOKnLyzsfPx8ROjm5e0hiwW63VHgQdc16Y\njBO5zSQ9z3pheaCjA8Dblmdw/WB4J6s0HXoSyUyphMkis5wSsX6wlZgd9OKE4JPrxQOQekYmvst2\ntn9yaSvyjKr91qWZwGkeujT/cGNbIM+AugOWL1vIr8vOg6VcJtnhFnY3d9U9JjDZXtmWcHdHhoXv\nON1Oq1S9QTzMTmWKbvCupmx+TfkkGFmUMuN6GZEGDkJcI3t+J3vgWe53Kk6UZcwLZ1G18dpl7tmW\n+gBlHqqZPVVcdED9iyvapacMAY4PxT8RHJvJYzpQ6jZniAhbV99/bk66Kz0KtZY9osTPT7CFcTDl\nRnf8dyk2TVa896EcXucaSBreMB1d39BUVp59/9ou31G9orxU202RijkvTCZjRCppX8Q5++0SHKvF\nwjdaPt6ZUgnbbux2/X6VABw4WcSCTBzrOpO+HdVhYDWTprPrKDuzW5ldqud3pFwfd164aK1JplWs\nKI7ylTgheGE0uPwaJU4efsmpljO2P97YZrTETWGzsiAbx8MXNmM99Q3IvFglM9xaUa1y9E0SFbuQ\nAc9BdAA66FRQTNcNeMIGtXmUnDDoJRsyPWpb1VFeqtVtOpPaTEqu8/PdWtWaMIOmKA/VzJeqadB8\nLm5KaDSTxN08ExW2TPjTZjIhDhSQ1inuRnMqhouruCpQzX7x2oGg4O5v52bx0LGKjnVXKyYEIkTJ\nxKpU+3hhb0N3ymBFihj7f1zTkcSWsz1zA1551Jz0zlnXUWsTD5Y5L0wmYv4lC7b42MLcdmO3q6GU\nQfgIynxglbMkzkvxA7kEEjGCgVwcn9vYJvXHp4MQxuYrUgx6nn5jJ+7mlvZvXZoJ5StR1tCDu7nD\nvwUfgrareshK7pmshk7Eo5CKm3cWPDFCcPmCBrd+0fJd3pzAmojazmrgO8KT+Zsaulf66fgNOKo4\nk3Egrfh8leRlg2BgVp1lXwk01qiayYROWxw6R+GouFQ4jVMlnNuexB9u1GsVq0G7QlFBq8oPr+8K\n2FD//oZW3DDYEMk0yL1vns2aEGbT1SKRwiWKtpb7fXF3Gp9e3+I/IlgRTnivUs2k+5f/fT67odX1\ni1kNsskY3snsoQibb7a4a9WPiZjzG3CSMSKtyqYHViRjjqaBf7zE/S/azT0+XapYVUzgaSKqsdQq\nikPU2SVjxMhXoq6y8jGr3kFmJC91ARGyPJqSBCcKZmXJC/C6gbieqKoUzeajG1uN67gJX7uyPZRx\nt05REqU4V7Qm8MujQftHGldOchrIwxJ7RKrpE2Ul6qT8scvblLvQZemFQW8zKb6uW+aOtrxv/myT\nwYS61tpRwGk/MUKwtjOF//XSSeNwA7k42iNs5NHVB4BzTVP+vzFB8Jurm/Hdlyek4epRXvVCVJei\nDJ/ucYpMqWzsTWNZcwIvHnP6D1F/rirDSCe3Vel9aDwfOC+HP/nPsQgxMHFp7tP8fWBVDmsM/IBW\nizmtmbxiQRpXL2pAVuLS3VQTJHvsFCcl0i357GC5b7xYsfYsToD/Ku/cNd2RSJMUnWtcjU5HdJ6t\nLN4WLs+qwUe20SO4zO1gKkx+vmzX9NELPLcd+qBU6HSeNHV+Ww9kwsRV/WlsKp/13JKKIRtRGy6i\nP5sQ2thI0SypRuFqgQ8/Ns7lEn+DaztTQgfJ1E5RVJymk3Lezm15SxILNCYtlcxLYtALhbLbusmh\ndsk0IgTO6k/UHdVsPEDl+ctxx+SZ0tUYx9NXd1aWOIdJNbt2oEG6SkQCfzi0KSZK1WQu2kyaTFj7\nQpqdVVrn6DgS9cQ2AMgw47mJCUQlvHlpxsh/a7WYU5rJDdyu3d8tayPObUtirBD8gqbfwpnd6J2P\n08YbA3B5n3dm6oVdlUn37Ozgdy8ws6tTLX1UY6A4ty2J50ampGlQvndNZ0CgUZVjQ4LgN89vCmxG\n4Ycgb1OM2cucV4VlhDlofhjgdwzrRz2QiQ0y7wZfeH04/3giP6hR67aof1f5a+tqiGPPCZkhpp5K\nqtLHLmzWh5c80JeJB/zn+oMRVfDIxEml/iXL96qQFwDaI1Hru6E1mBr/ngnFKpGsrxe1v1p0YbVe\nCWWj50/Dkm1aM1EyCBcxFP1IKsKyICvwVbKJ3lUOMfH93bVmR+2GzXUYs4RqYjzNfOyxx7B69Wr0\n9vZi06ZN2L59u1G4Xbt2YeHChVi0aJH22c9KHDU3p2JCTYGp1kY2UGUTnlbjRzd0uR7yCSF4+CLv\nzNRKD06nyx/pOLBM4MxUhdDFgeJ5/pzOShGVsS6FGxY3BmyHSHkw4u3tKhLwdMvc5f/p56v0O841\nat1lSG1oJQW/UuKvUk7wDaLqvcLusHxgbRP+ogoO58PSmCDYtKABl2vO4I1aDm3pGJY0xYUrGiym\n53NTru+cjJgjMZW2RK0nh1lyj0IJ5xpIPAEQaecW5urrFqga0HH0O1d34nfWeZPlL17WhrdI3JLR\n5W1Vl02FQ/fsbbAmA/6Af3lFu9I9noxfZXzdVkMz+fq+NC7trVAxYrrOXWeM+qynn34aDz74IO6/\n/348++yzWL9+PW677Tbs27dPGa5QKODuu+/GpZdeWpXM8pjavrAzP1En290QE2rIiCuERM2hn8kQ\nihBVfVHdG2xK4Dshl3HCduw6X3ci9k06DfmPOIP5sPJdh2oXBgdt9JNlc4b0PBMmq3F2uApZaVWq\nRaSwA36lcYo6eFWf2tkQD0x4whAlm39wSSs+stbwXOyIBdHeEMNXrujQuoK6d5U3SOpSWpSLoy8d\nxQJV3qdWyhyyWJEIrs6L9mYMbEwFdT+bIFjC1c8fXNeFW5cEXd69bZlYIDNFK3uEEk78H/i2pY3Y\n3O9MnFrTMZ+yY0VrUrrTXqatZbNClTS+jYLCXCByW39dX9rVgNI4Iy3bl/+PEyI9JEIalnuZOSpL\nmrXJrVu34o477sCdd96JfD6PRx55BD09PXj88ceV4T72sY9h1apVuOmmm6qSWcAryG03dvvO0jUJ\nEyMEv5LP4jHmuKrvX9ul3dZfjY0bUTs/8TK3Oj8m5RLVqWtTkmjtyURMzRBfGnHi+BZslWy4AIC2\nlD9D/3RDl0+za9qojpfPQTZxpVAvqtHg7zk3h7/aXDvtms4pfKTSlGo7zdKUwZcnQWUaBB1RuoQL\nu1I411AjWOuayk6qZaf2RIXGdt1gA67qr54LGxadeUw1P73vmFsBSYXgbrJxRxT6e9d24b7zcr77\n6Tjx9f0fv9CZmLxzRWXCZC3Jt6hdM4n45hs6mDPu5c9Ru2Nh9a1BA1pdPsSjUq338anainuzJUxq\nxfVCoYAXXngB9913n+/65s2b8dxzz0nD/eAHP8APf/hD/PjHP8Z3vvOdynNaAWyFTMeJ78B3lYAx\nPOGoEquxB4IQhPrKslx9WuLkPCxvWNiADo1fThH/+xozOw8e/kxuQggeWNuMr744Lg2TS8VwhHEw\nGFYjSoUJkw79dKQ5FQv4tasmotOmgMpPhKII/UxG1kwGG1ctlzprLezRMn7nWbURFAZycXxqfQv6\nMga7m0OWI/2Gty/LBARVwj0TlbmyyPDly9uwuAINN8Bq4fwvpWvZdLNalJUiU5Y2xXGBYLNmLelu\njGPvmLNhlX+zhdk49o8XfffY969FUZR1EW46lbpunNCcrlUpb12WwYrW+ruU07aC0dFRFItFdHf7\njb67urrwz//8z8Iwr732Gj70oQ/hySefRCYz+7MmqkcL2wG9WHZhsiqkfZGIGKmvN3odvZk4rh3w\nL5nUsn/2jpOsXiq6mGh5X9idwveuqe4OzjMBtnxlp1CFZS2zkeryBZ7WKsb9HxahZjJiWBMa6zRB\nuW4g/EleJhBCcKnkKNdKobZstexP2LgPnaqjZ2YO/hxtSph3ly3NmrrgqnRj4b2rcrhxcSNw9Fjg\n3uNXmPspBtTL0jpWtSfxi/KRve6xoNwzH17T5B5gQMdz0bheU4EtyiyVyWPYDTJhP29XYxxvWFh/\n29qa7OZ+73vfi7vvvhtr164FYH7E1NDQkPaZk0UAaDF61qEFM8UigBj27tmDgmv704KZmRllPFNT\nOQBx7H95l2FaCkrNAIhxvl89GQeQ4/LYgv3792PohPqc4rAcPpwG0ODELT0D2dGImpe7nxKcgWv3\n7pcwmvDqw+iok/a1HaewoaWAoSHaobWgMDUFIB5I88srgV/b0YKXdu1S7rAbPpwC0Bg5z2pacPzE\ncQwNDUcKTcu8NnmrDvsnYwAcV0/Dw8MYmiwAaMGhgwcxVJwqP+VpysO0yd5UESf37wYNMVouj5df\n3o3jybCddQvGxsYxNHTQ/T05NYVXX90HIKvN12vHE0bPsXSXgI8vjTH1tboUCgQXNTfg4Csv4biB\n3Lp3wvlW1a9PLZgqON86TNxbVwC7dwXLhvapO4d2VqBdbMHBkWEMTTmCx8kJJ042fxMTWQCJKpRH\nC0YPjWII+0OFOjRq3vcMl+vfrl07fTuUD04RAM2YLkwL4zlQbp8v7dxZsUaOtuJKy8v/3i04cGAY\nQ6fMTji7qTmOXxzOYWhoCCNTzrvt3LlT+OxBUJmuBa++8goShxwJ05lXtGAZjmBoaKSid/Fgx74W\nFIrFUH0dABx47QCGTjrlcPRYI4CUYRwtGBs74XuX8fEMgGSob5XP542fjYpWmOzo6EA8HsfIiP/D\nHDx4MKCtpDz77LPYvn07PvvZzwJwhMmZmRl0dXXh0UcfxTvf+U5hOJMXHi/MAC8eMi+cHSNIJhNA\ncQaLFw9igPrZ2zGCWCymjCexZxQoFKvyIeIvjqBQNP+oU4cLwJ4jiMeZPO4YQd+CBchXWaPQMTMO\nHBpH/4IFyMuO6doxgl89O4t8Xu6WRMX6yV3420MNWLZ0qc+msxPjwMFxbD6r1++CaccI0qkUMCUp\n/x0jWLZ8mXIJ+z9fOgkMj9WmIe0YQXNTM/L5hZGCtxXGgNGTdWnkUUmdmAZeOgwA6O3pQX6gEdgx\ngp7uLuSXlFccdozg8r40OqaPhWuTqZTv+a6SUw+WLlmiPF9XFl9DJot8vt/9nU6lsKC/HXhFn6/9\n+08B+46H/hYrwuUyNOvPCfHwsQLw8pHq16cdI0glnXZZjbgb9h0GJqeRzy+PfLwrdoygr7cH+UWO\n1jbpxunlr2H4CHCyUHmed4ygo7MD+bzabpLnhdhJYMSs7+mdmsGCvimcu8DftzadLAK7RpFMJoTx\ntJ8qAi+N4qyzqvPNh4aGKi6v5wnz3jtG0EP7DQPyAN5wPgB0IzM+Dew6rM/Pf49gYGAR8uVl3Ynp\nEvDLg1jY14u8xKdtaHY4sg99p1g8HqqvA4C+vl7kyxuRmsaPA0dPmcWxYwS5XJNvnMkdPgqMTc25\nsUMrTCaTSaxZswbbtm3zbaR55plncPPNNwvD8G6Dvve97+Fzn/scfvSjH6G3t7fCLIfH3YDDXa/n\nqjNBSKPJOmLapVeS+5aEeilKtFRTaWnNJbMCnjmcNRf58Zr+G9cPNqD1WDgtgGxJL6q2apnAOa+x\n0/JoSc4psjVcdq9F+VS6BK4zl6lmnpureHCAiKZUTOgqStcWOhrUPkfnAlG/QxhzKCL4W3coQCVU\nuModemPgHDq4TYnRMvc999yD973vfVi7di02bNiAP//zP8fw8DDuuusuAMDDDz+M559/Hn/zN38D\nADj77LN94Z9//nnEYjGsWFH5XD5KwYrcjizIxFyn5HKq1yVNhJRsdOe11oQ6JCZzc8ALk9kEQWdD\nDHvH5P6UdLvs54OQMJvonJZTorixCQiT7v/h4/rh9V3BjR6EVGwofzqxIBvH3xs6QT7d6cvEMNDk\naa9Nzaii8LUr22vugktGtTYr1ZNq5TWUzSkJ/l3LTUlRatt6ZhNT2Ooqm3jPNYyEyVtuuQVHjhzB\no48+iuHhYaxcuRJPPfUU+vudZaXh4WHs2bOnphmlNMZJ6B3NtGKxA9Wjl7RpZy9zQRjh600tTnGp\nR92UGVSLduQBjmuMj/1Ubo/2zA1dWiFGdQJKpVzVn8bFPfXd5ThX4F19VEMJ4K4eRKiMMtc23ZUc\nWXEaUu0DC2oB680hKl+/yr+ZTjRpqFbL78/O3iFxc2XHeiVEPiiiwnev9ji5uDx5ySYIOkIeKbqu\nM+k7/GNmTkgW1ce4pWzZsgVbtmwR3tu6dasy7Dve8Q684x3vCJczCYQQbAxhM/inr2vDvvFpfPr/\nnvBJ9Cbnelb7k79lqfnOTFFb2Pr6NpytOUasEmq6+1KiaWX9ToaLTx+glsvclR57aOpwfzZpScew\nrDmBXcymrMc3tWOwyd92osgFAQ11Dabby1oSc34Z8ExjeraPpqkT1ajOtToas15sfX0bzgp54hul\n0neutjDZU9ZOf+3KjoqF/Eo1k3OVOXU2dy04tz2Jo2VHUbM9fIephCTwB0J7zg+fWB2QpCUqm0rH\nnTctaoh0Hms9ePPSRlxVLQPxGtGUjOHPN7Vj03c9e8ilAtvEapRwJZpJS22ppvg3WgM3PiIbtNme\nrFVDmDnd20Il41UU10rs39Ve5qbfwvSgFBa+es5X85t5L0wC0W1Pqj2JDlXBZ6EjqWWSsmVuekVU\nNpUeWN/REMdtFR41VivihKAtfZqPFmWiDHp8kGod0WiZ29Ti84p6id9e24QPnpcT3KkPV/Y3VCzQ\npsoLANU4ga1eVCunlb5ytTfgdFVgMsPLEXNVwVEpZ4YwORubWQTUwt6xGsymYtJqpE4P6tUBzkY1\nOLs1iRU1NB+x1BiBNJlJxJCZxU/aLNmhHQbq9kx3zvqZDrsXgo71vVXcNPX0GzuRTUb/Bnz1vGdV\nDreHUHKcLnOJM6IHjSqwVFMxed+qHC4OcSwV4f4/3ZGd5tDd6HSYzan58qbzj8c3tWNBRt45R/EX\nKLOdnY1JRW8mji9eVrszzi21Zb4uG57JtKdjuGaRmTDO9hm12AHfHuHYYQqBZ29JaUrG0BTC3VQ1\nT42rJWeUMDmbH+XWpeGWW+spTNajfGQxX9HfgCv657bt4JmOyE6SpRoC4FjBmbrxO8Wjcnp0v6cH\nc33PzFzPnyU8iRjBA2ubtc/9yaWt7k5rlrmy0vXNN3QgU2UvC3Pk1QKcEcIk3YCTCqn5ns1Oqp6q\n7UJYL6oRiCKw2jHi9CBKVeV3b1NfgbX0D2eZn1RqW205fTm/Q7zaN1d6kdCneQkImobNlbfzc0YI\nkxt70/j9DTHkQp5kMBe6qHpUm4X0iMkaJjbflu0tHrkkwanZzgSHlUnPHJY2JzAxbXb+s2V+M5vm\nMrWiNzPbfmjMOCOEyaZkDBd1V/c86/lEXZbS51Hjtnj84/VdSMQIhkKGs9XBUi0+fmFL6CPqLPOT\nuWDSVk2+9cYONGtP6psbnBHCZFT+4JJWjBdmp5eiTSHyCQIVpGmxmFLP+mmZLea2pCY7Acly5jJf\nqkSHwCXRXFXMWGFSweKm2S+eam1IUFHPuhlmWLKG9fOXudohWoJUtRna7z6vme12XYvd3HONjT0p\nHJwoznY2Asy+tGQRMl32d1GXRmHoh7Mag0oYs1UrS1qiMo/HkrqytjOJwVwVhwnbqC01hG7sm8/t\n/00DjXjTgPnRzPXCCpNzlA7q26oOnW+9Gp49J9kiw8oYc5M/3NgGABgaOjDLObFYzJnPmsm5ihUm\n5yhdjXEsysZxXkeNzuMWYBugpV7Uw3zDMgexnz0Uf3ZZG1pPkw0YcwlbzeqPFSbnMH91ZUdd0rEN\nz1JvGq0wabFoObu1fsqEajBXxN75sgHndMIKkxZzjWSd1yLt0uf8JewBAhaLZe5z2YI0Gqt84ovl\n9GCuTCQsc5yNPSlcFOJs8WqQb0mgs4JzUS1zFzvcWCzzj86GOK6ZA5tDYraHqTtWM2lxUTW/T1/c\nWrd8ULasyOLdK7J1T9dSe2rtVNja/1osZy4Jq4OoO1aYtMzZORwhBHY1dH5ihT2LxVILrNeQ2cHK\n7xZXmLRGy5Z6wVc1ax9rsVgspy9WmLS4WFnSUi+sZtJisVjmD1aYtLinBsTsCG+pE7WuabYmWywW\nS/2wwqTFxcqSFovFYrFYwmKFSYuLrQyWesFPXFa1JbGqrXoOmu28yGKxWOqH3c1t8QZeOwJb6gQ/\ncbm4J42Le9KzkheLxWKxVIZVRllcLZGtDJZ6YU0qLBaLZf5g5QeLq5C0A7ylXtTaabnFYrFY6ocV\nJi0u9ggqS72oeU2zVdlisVjqhrEw+dhjj2H16tXo7e3Fpk2bsH37dumz//Iv/4J3vOMdOPvss7Fg\nwQJceuml+OpXv1qVDFtqh9VMWuqGrWtnJPazWyzzEyNh8umnn8aDDz6I+++/H88++yzWr1+P2267\nDfv27RM+/5Of/ATnnnsunnjiCWzfvh133303PvShD+Fb3/pWVTNvqQ5UiLQdvaVeWD+TZyZtabsY\nZrHMR4xa9tatW3HHHXfgzjvvRD6fxyOPPIKenh48/vjjwud/4zd+Aw899BDWr1+PwcFBbNmyBTfc\ncAO++93vVjXzlupij1O01Atb185M+jLx2c6CxWKpAVphslAo4IUXXsCmTZt81zdv3oznnnvOOKET\nJ06gtbU1dAYttcduwLFYLPWgp9EKkxbLfEQrTI6OjqJYLKK7u9t3vaurCyMjI0aJfP/738ePf/xj\n3HXXXdFyaakpVIa0C1CWemHnLWcmCdvJWCzzkpo7Lf+3f/s3vOc978EjjzyCNWvW1Do5SxTsyG6p\nM7XUgl+9qAErW+15DHMR29VYLPMTbY/b0dGBeDwe0EIePHgwoK3k2b59O9761rfioYcewrvf/W5t\nZoaGhrTPWKrP84dTABqxd8/LmEiVapaO/b7zG/Pv24Ljx45haGi4Jvl4Sw7ANGCrW3WpRvs9erQB\nQNr2BXMU+13mJ/l8vuZpaIXJZDKJNWvWYNu2bbjpppvc68888wxuvvlmabh//dd/xdve9jZ85CMf\nwXvf+16jzNTjhS1B/uvlCWD4BFaftRTZZG3WoYaGhuz3nceE+r47RtDa0op8vqm2mbJUjWq137ap\nE8DhCdsXzEFsH22pBCPJ4Z577sGTTz6JJ554Ai+++CIeeOABDA8PuzaQDz/8sE/QfPbZZ3H77bdj\ny5YtuPXWWzEyMoKRkRGMjo7W5i0sVaFWgqTFwmN3c5+Z2JOPLJb5iZFh0S233IIjR47g0UcfxfDw\nMFauXImnnnoK/f39AIDh4WHs2bPHff7rX/86JiYm8PnPfx6f//zn3euLFi3Cz372syq/gqVSSqXa\nLW1bLBYLxYqSFsv8xNhKfcuWLdiyZYvw3tatWwO/+WuWuYsVJS31xrqhOjOx391imZ/YdU2LFSYt\ndcfKFGcm9rtbLPMTK0xarDRpqTtWqDgzsZpJi2V+YoVJC2ZmOwOWMw8rVJyR2M9uscxPrDBpgd1/\nY6k3tuOxWCyW+YPt0y0WS92xy51nJva7WyzzEytMWjBjNZOWOjKYi+OCrtRsZ8MyC1hZ0mKZn9gD\nbC12/42lrvzl5o7ZzoJllrDCpMUyP7GaSQusOGmxWCwWiyUqVpi02A04FoulLsSs0aTFMi+xwqTF\nugayWCx1YW1nEgO5+Gxnw2KxVBkrTFrQl7Gdu8ViqT3nd6TwhLWZtVjmHXYDjgVXLEjj0t6u2c6G\nxWKxWCyW0xArTFpACEHaKictFovFYrFEwC5zWywWi8VisVgiY4VJi8VisVgsFktkrDBpsVgsFovF\nYomMFSYtFovFYrFYLJGxwqTFYrFYLBaLJTJWmLRYLBaLxWKxRMYKkxaLxWKxWCyWyFhh0mKxWCwW\ni8USGStMWiwWi8VisVgiY4VJi8VisVgsFktkrDBpsVgsFovFYomMFSYtMsbtVgAAIABJREFUFovF\nYrFYLJGxwqTFYrFYLBaLJTJWmLRYLBaLxWKxRMYKkxaLxWKxWCyWyBgLk4899hhWr16N3t5ebNq0\nCdu3b1c+/1//9V+47rrr0NfXh3PPPRePPPJIxZm1WCwWi8ViscwtjITJp59+Gg8++CDuv/9+PPvs\ns1i/fj1uu+027Nu3T/j8iRMncMstt6C3txfbtm3DZz7zGXz+85/Hn/7pn1Y18xaLxWKxWCyW2cVI\nmNy6dSvuuOMO3Hnnncjn83jkkUfQ09ODxx9/XPj8N7/5TUxMTOALX/gCVqxYgRtvvBEf/OAHsXXr\n1qpm3mKxWCwWi8Uyu2iFyUKhgBdeeAGbNm3yXd+8eTOee+45YZif/vSnuOSSS5BKpdxrV155JV57\n7TXs3bu3shxbLBaLxWKxWOYMWmFydHQUxWIR3d3dvutdXV0YGRkRhhkZGRE+XyqVpGEsFovFYrFY\nLKcfidnOAMvQ0NBsZ8FSQ+z3nd/Y7zu/sd93/mO/8fwkn8/XPA2tMNnR0YF4PB7QKB48eDCgfaR0\nd3cLnyeESMMA9Xlhy+wwNDRkv+88xn7f+Y39vvMf+40tlaBd5k4mk1izZg22bdvmu/7MM89gw4YN\nwjDr16/H9u3bMTU15V770Y9+hL6+PgwMDFSWY4vFYrFYLBbLnMFoN/c999yDJ598Ek888QRefPFF\nPPDAAxgeHsZdd90FAHj44Ydx0003uc+/5S1vQSaTwfvf/37s2LED3/3ud/HHf/zHuOeee2rzFhaL\nxWKxWCyWWcHIZvKWW27BkSNH8Oijj2J4eBgrV67EU089hf7+fgDA8PAw9uzZ4z7f3NyMb3/727j/\n/vuxefNmtLa24r777sP73//+2ryFxWKxWCwWi2VWIEePHi3NdiYs8x9rjzO/sd93fmO/7/zHfmNL\nJdizuS0Wi8VisVgskbHCpMVisVgsFoslMlaYtFgsFovFYrFExtpMWiwWi8VisVgiYzWTFovFYrFY\nLJbIWGHSYrFYLP8/e/cd31S9/gH8c7KbpCNt00EHs+wlW2YZsocIeAVxiwvhOkCEK1yQn1flXvRy\n1aqgqKCgqCAgILuIbET2KgUKtNB0pTPNOuf3x0lOkiZt0zRd8LxfL18vTM5JTnKa5DnP9/k+X0II\n8RkFk4QQQgghxGcUTBJCCCGEEJ9RMEkIIYQQQnxGwSQhhBBCCPEZBZOEEEIIIcRnFEwSQgghhBCf\nUTBJCCGEEEJ8RsEkIYQQQgjxGQWThBBCCCHEZxRMEkIIIYQQn1EwSQghhBBCfEbBJCGEEEII8RkF\nk4QQQgghxGcUTBJCCCGEEJ9RMEkIIYQQQnxGwSQhhBBCCPEZBZOEEEIIIcRnFEwSQgghhBCfUTBJ\nCCGEEEJ8RsEkIYQQQgjxGQWThBCfvfjii9BoNLh582ZdHwohhJA6QsEkIcRnDMOAYZi6PowGb+3a\ntRgyZAhiY2MRHx+P0aNHY/v27T491vbt2zF69GjEx8cjNjYWQ4YMwdq1a8vdnmVZfPrpp+jTpw+i\no6PRtGlTPPzwwzh69KjH7UeNGgWNRuPxv9DQUJhMJp+OmxDScDF6vZ6r64MghDRMOp0OBQUFaNq0\nKcRicV0fToM0f/58fPzxx4iJicG4ceNgMpmwfv165Obm4t///jeeffZZrx9rxYoVeOONNxAWFobx\n48dDJpNh48aNSE9Px4wZM/D222+77fPkk09i48aNaNmyJYYPH468vDxs2LABBoMBq1evxogRI1y2\nHz16NA4ePIgXXngBwcHBLvcxDINZs2ZBJKI8BSH3EgomCSGkjhw9ehTDhg1D8+bNsWfPHgQFBQEA\nbt68iQEDBsBgMODo0aOIi4ur9LFu3LiBHj16QKVSYd++fYiNjQUA5OfnY+DAgbh+/Tp27NiBbt26\nCfv89NNPmDZtGnr16oWNGzdCJpMBAE6ePIlhw4YhODgYf/31F1QqlbCPPZg8deqUV8dFCLn70eUj\nIcTNtm3bMG7cOLRp0waRkZFo3bo1hg8fjg8++MBlu4pqJj/99FP06tULUVFRaNu2LWbPno2CggJ0\n6NABnTp1ctl2zZo10Gg0eP/993Hy5ElMmDAB8fHxaNKkCR5//HGkp6cDAK5fv45nnnkGCQkJiI6O\nxujRo3H27Fm3505NTcXChQsxcOBAtGjRApGRkejQoQNmzpyJW7du+fGdqp4vv/wSDMPg9ddfFwJJ\nAIiLi8Ozzz4Lo9GI7777zqvHWr16NUwmE5577jkhkASA4OBgvPbaa+A4DitXrvT4/G+99ZYQSAJA\n586dMX78eGRnZ2Pjxo3VfJWEkLsdBZOEEBdff/01pkyZgkuXLmHo0KGYMWMGRowYAYZh8NVXX7ls\nW17N5Ouvv4558+ahoKAATzzxBCZOnIh9+/Zh/PjxsFqtHp+XYRicOHECI0eOhEwmw5NPPom2bdti\n8+bNGD9+PFJSUjB48GBkZWVh8uTJ6N+/Pw4cOICHHnoIJSUlLo+1efNmfP3114iNjcXEiRPx/PPP\no02bNvj2228xePBg3L59239vWDX88ccfAIDBgwe73ffAAw+A4zj8/vvvfnksAC6PZTQacezYMSiV\nStx///1Vfv4dO3Zg2bJl+Pjjj7F9+3YYDAavjpMQcveR1PUBEELql6+//hpyuRwHDhxAWFiYy315\neXmV7n/o0CGsXLkSLVq0wO7du4WM24IFCzB27Fjcvn0b8fHxbvtxHIedO3di1apVGD16tHD7xIkT\nsXv3bgwdOhSzZ8/GSy+9JNz3yiuvYNWqVVi9ejWef/554fZHHnkE06dPh1QqdXmO5ORkTJgwAf/5\nz3+wdOlSr96PLVu24MyZM15ta/fmm29Wuk1JSQkyMjIQGBiIiIgIt/ubN28OgM+yeiMlJQUA0KJF\nC7f7IiMjoVKpkJGRgdLSUigUCly7dg1WqxWNGzf2WONY2fPPnj1b+DfHcdBoNFiyZAkmTpzo1fES\nQu4eFEwSQtxIJBKPE2o0Gk2l+65ZswYMw+DVV191GbqVSCT45z//ieHDh5e7b9++fV0CSQCYNGkS\ndu/eDY1G4xJIAsDDDz+Mb775xi3Yi4qK8vj4iYmJaN26Nfbs2VPp67DbsmULvv/+e6+3ZxjGq2Cy\noKAAAFzeI2f22/Pz8716Xm8er6SkBAUFBVAoFD4//6hRozBz5kx07NgRoaGhuHnzJtauXYuPP/4Y\nzz//PIKCgjB06FCvjpkQcnegYJIQ4mLSpEmYP38+evbsifHjx6N3797o2bMnIiMjvdrfHtj16tXL\n7b7u3btDIin/a6dDhw5ut9kDw3bt2rndFx0dDQDIyMhwu++HH37A2rVrcfbsWej1epfhdblcXsmr\ncEhKSkJSUpLX29/tXnzxRZf/b968Od566y1ERkbijTfewOLFiymYJOQeQ8EkIcTF9OnTERERgZUr\nV+LLL7/E8uXLwXEcunfvjgULFqBv374V7m/PeGm1Wrf7RCIRQkNDy93XU5bMniGt6D6z2exy+9y5\nc/HZZ58hOjoagwcPRqNGjaBQKAAA3333Xb2YhGN/Pfb3qyz77WXb71T0eLm5uSgoKEBISEi5j2d/\nXn8//+OPP4558+bh3LlzKCoqglqt9mo/QkjDR8EkIcTNpEmTMGnSJBQVFeH48ePYunUrvvnmGzz8\n8MP4448/0KxZs3L3DQwMBABkZWUJ/7ZjWRa5ublo1KhRjR17dnY2li9fjnbt2mHHjh1QKpUu9//0\n009VeryaqplUKpVo1KgRbt++DZ1O51Y3aa9VtNcuViYhIQFHjhzBlStXXNr/AEBmZiaKi4sRExMj\nBNX23qBpaWlgWdatbrKqzy+Xy6FWq5Gfnw+DwUDBJCH3EAomCSHlUqvVSExMRGJiIgIDA/Hhhx9i\n586dLpNdyurYsSPOnDmDQ4cOuQWdR48ehcViqdFjvn79OliWxcCBA90CyfT0dFy/fr1Kj1dTNZMA\n0K9fP6xbtw67du3ClClTXO7bsWMHAGDAgAFeP9bhw4exa9cut2DS02PJ5XL06NEDhw8fxsGDB90y\nzjt27ADDMF4/f0pKCvR6PQIDA90mbhFC7m7UGogQ4qK8VjB37twBAAQEBFS4/yOPPAKO4/Dhhx9C\nr9cLt5tMJo8rsPibfab44cOHwbKscHtRURH+/ve/VzmYTUpKQm5urtf/5eTkeP3YTz/9NDiOw9Kl\nS13eq7S0NHzxxRdQKBRuQWZmZiZSUlKQm5vrcvujjz4KuVyOFStW4MaNG8Lter0eH3zwARiGwVNP\nPeWyzzPPPAOO4/DOO+/AaDQKt584cQK//PILtFotxowZ43Jczsdpl52djenTp4NhGEycOJFWwCHk\nHkOZSUKIi8ceewwqlQrdunVDfHw8GIbBn3/+iUOHDqF58+YYP358hfv36dMHTz75JL755hv07t0b\nY8aMgVwux7Zt2xAcHIzo6OgaDTYiIiIwYcIErF+/Hn379sWgQYNQUFCAvXv3IiAgAB06dPDY6Lwu\n9OjRAy+//DI++eQT9O3bF2PHjoXZbMb69euRn5+Pf//7326rzCxcuBDff/893nzzTcyZM0e4vXHj\nxli8eDHmzJmDgQMH4qGHHoJUKsWmTZuQkZGBGTNmuGUsJ0yYgM2bN2PTpk3o378/hg8fjpycHPzy\nyy9gWRbLli1zGa4+cOAAXnvtNfTq1QtNmjSBRqPBrVu3sGPHDhQWFqJLly5YuHBhjb5nhJD6h4JJ\nQoiLRYsWYc+ePTh79iz27NkDiUSC2NhYzJ07F88995xbHaSnpuUffvghWrZsia+//hrffPMNQkND\nMXr0aMyfPx9t27ZFeHi42z7lNUD35b6PP/4YTZo0wYYNG/Dll18iLCwMI0eOxLx58zB16tRyH6su\nLF68GO3bt8eKFSuwatUqiEQidOrUCTNnzhSajTuzv15Pr2HatGlo0qQJli1bhh9++AEsy6JVq1aY\nP38+/va3v3l8/q+++gqff/45Vq9ejRUrVkAul6NPnz6YPXu2W/DZuXNnTJgwAX/99RfOnDmDwsJC\nqNVqtGvXDg899BCefPLJCmfrE0LuTrQ2NyGk1qSmpqJbt26YOHEiVqxYUdeHQwghxA+osIUQ4ndZ\nWVngONfr1JKSEsydOxcMw7g1JieEENJw0XgEIcTvPv/8c/zwww/o27cvoqKikJmZid9//x0ZGRl4\n4IEHMG7cuLo+REIIIX5CwSQhxO8GDBiAM2fOIDk5GXl5eZBIJGjevDleeOEFtxVUCCGENGxUM0kI\nIYQQQnxGNZOEEEIIIcRnFEwSQgghhBCfUTBJakVKSkpdHwKpQXR+7250fu9+dI5JdVAwSQghhBBC\nfOZVMHnw4EFMnjwZbdu2hUajwdq1ayvd5/z58xg1ahSio6PRrl07LFmypNoHSwghhBBC6hevgsni\n4mK0a9cO7733HpRKZaXbFxYWYvz48YiKikJycjLeffddfPTRR/jkk0+qfcCEEEIIIaT+8KrP5AMP\nPCCsEfvSSy9Vuv26detgMBjw6aefQiaToVWrVrh8+TKSkpIwffr06h0xIYQQQgipN2qkZvLYsWO4\n//77IZPJhNsGDx6M27dv48aNGzXxlIQQQgghpA7USDCp0+kQERHhcptWqwXHcdDpdDXxlIQQQggh\npA7Uq+UUqTXB3Y3O792Nzu/djc7v3Y/O8d0pISGhxp+jRoLJiIgItwxkVlYWGIZxy1g6q40XTOpG\nSkoKnd+7GJ3fuxud37sfnWNSHTUyzN2jRw8cOnQIJpNJuG3Pnj2Ijo5GfHx8TTwlIYQQQgipA163\nBjpz5gxOnz4NlmVx69YtnDlzBrdu3QIALFq0COPGjRO2nzhxIpRKJV566SVcuHABmzZtwrJly2gm\nNyGEEELIXcarYPKvv/5C//79kZiYiNLSUrz77rsYMGAA3n33XQBAZmYm0tLShO2DgoKwYcMG3L59\nG4MGDcKcOXMwY8YMr9oKEUIIIYSQhsOrmsm+ffsiLy+v3PuTkpLcbmvTpg22bNni+5ERQgghhJB6\nj9bmJoQQQgghPqNgkhBCCCGE+IyCSUIIIYQQ4jMKJgkhhBBCiM8omCSEEEIIIT6jYJIQQgghhPiM\ngklCCCGEEOIzCiYJIYQQQojPKJgkhBBCCCE+o2CSEEIIIYT4jIJJQgghhBDiMwomCSGEEEKIzyiY\nJIQQQgghPqNgkhBCCCGE+IyCSUIIIYQQ4jMKJgkhhBBCiM8omCSEEEIIIT6jYJIQQgghhPiMgklC\nCCGEEOIzCiYJIYQQQojPKJgkhBBCCCE+o2CSEEIIIYT4jIJJQgghhBDiMwomCSGEEEKIzyiYJIQQ\nQgghPqNgkhBCCCGE+IyCSUIIIYSQWnBMZ0ROqbWuD8PvvA4mv/jiC3Tq1AlRUVFITEzEoUOHKtx+\n9+7dGDp0KOLi4tC8eXNMmTIFqamp1T5gQgghhJCGaPbhfCz+s6CuD8PvvAom169fj7lz52LWrFnY\nv38/evTogUmTJiE9Pd3j9mlpaXj00UfRp08f7N+/Hxs3boTRaMTDDz/s14MnhBBCCGkIis0sAOBk\njrmOj8T/vAomk5KSMHXqVDz22GNISEjAkiVLEBkZiZUrV3rc/uTJk7BYLFiwYAGaNGmC9u3b45VX\nXsG1a9eQl5fn1xdACCGEEFLfHcsy1fUh1JhKg0mz2YyTJ08iMTHR5fZBgwbhyJEjHvfp0qULpFIp\nVq1aBZZlUVhYiDVr1qBr167QaDR+OXBCCCGEkIbAwnJYeLwAQ2LkEDMAx3HCfXojW4dH5h+VBpM5\nOTmwWq2IiIhwuV2r1UKn03ncJy4uDuvXr8e//vUvREREoHHjxrh48SK+//57/xw1IYQQQkgDsfG6\nAQBQYOagkjI4k8sPdb/4ey4e3J5dl4fmFzUym1un02HGjBmYPHky9u7diy1btkCtVuOJJ56oiacj\nhBBCCKm3PjpbBAAotXAoMHGYeUCPRcfzcUFvAeCaqWyIJJVtEBYWBrFY7JaFzMrKcstW2q1YsQIq\nlQoLFy4Ubvv888/Rrl07HDlyBD179vS4X0pKShUOnTQ0dH7vbnR+7250fu9+dI5rxuUSMQA1nosp\nQddAM57PDQYA7M0wCtv8eTEVwRJHQMlyQLZZhAhZ9YfAExISqv0Ylak0mJRKpejcuTOSk5Mxbtw4\n4fa9e/fiwQcf9LiPwWCAWCx2uU0k4pOgLFv+G1MbL5jUjZSUFDq/dzE6v3c3Or93PzrHNYPjOEzb\nnAUAmNK1CQAguSWw7YYB758sBABEBIjwW4kWb3UNRqGJxaV8C2Yd0vPbjvWctKtvvBrmnj59Otas\nWYNVq1bh8uXLmDNnDjIzM/HUU08BABYtWuQSaA4dOhSnTp3CkiVLcPXqVZw8eRLTp09HbGwsOnfu\nXDOvhBBCCCGkHrlR5LlBea9IOQDg4WYB0BlY7Eo3It/EYsxv2UIgCQBmtmEMf1eamQSA8ePHIy8v\nD0uXLkVmZibatGmDH3/8ETExMQCAzMxMpKWlCdv3798fX3zxBZYtW4aPPvoIAQEB6NatG37++WcE\nBATUzCshhBBCCKkHOI4DwzDIMvCjsXM6B7rcHyJjAABNgyT4V49gzDuaj9cO6t0eR2ewIkblVahW\npxi9Xt8wwl7SoNEQyt2Nzu/djc7v3Y/Osf8c15kw67Aen/bT4GaRFUd0RszvGuy2ncnKQSoC7pSw\nmLw7x+3+lsESPNZShX7R8to47GqhtbkJIYQQQvxkyw2+DdCL+/NwWGdERIDY43YyMQOGYRCtEmP3\nGK3LfZ3CpIhSioXH8uROiRWp+Rb/HXg11P/cKSGEEEJIA+E8S3tPuhFTWigr3UfMMJjZXg1tgBg7\nb5ViZLwCVg7YnFZ+MPncvlwUmLl6MUmHMpOEEEIIIX6w6lIxAOCBWMfQdJdwmVf7PtRMiX7Rcrzd\nPRi9IuUIkYlwONOE9GLP2ccCM1+l+Om5omoedfVRMEkIIYQQ4gcrbcHkP7oEY8coLT7pq0G3CO+C\nybKilHyIdta2Wo7OYEWpxTHNpWUwP7j8Q2pJnTc9p2CSEEIIIcTPZGIG7UKlPu8fphCjV6QMeUYO\nVo7Dwztz8Mm5QuH+7FIW0baAM9/E4WoBn8Hck16KxE06fFaLGUuqmSSEEEII8YMu4VJMSVD57fH6\nR8txMtuMB37lG59vTitFRIAYE5spUWxh8e3gcDy6Oxd/25UNY5mWlt+nluCFdmq/HUtFKJgkhBBC\nCPGDfBOHYFsPSX/QKkTILrXCuXf5lxeL0UYjRbRSDKVEhDyj55UFFZ4nkdcIGuYmhBBCCPGDfBOL\nYJn/Qqs4tQSpBY4JOE+14rOesw7pPbYcCleIsG2kFt8OCkWpFWBrqZaSgklCCCGEkGq6XWxFdql/\ng8kopRj5Jj4g/GVYOJ5opcLIeAUAIDKAf55vB4Xi64GhAIDP+2sQIGGEQPOTs7VTN0nBJCGEEEJI\nNf3vLD85Ri723zC3M7WUf9wmgXyFYrSSDxhj1RI0CZQgeWwEwmxj2zLbMfx8rfw+lf5EwSQhhBBC\nSDXpTZ5rF6vrs/4ajG6sgETEB4hjGwegrUaC0Y0DKtzv7x1qZ/INQBNwCCGEEEKq5a2jelzIs2BO\n50C/P3brEClahzhaDCkkDJL6hVa6XxuN722Jqooyk4QQQgi5580+pMd/Txf61AD8YKYJABAqrz9h\nlT9rNytDmUlCCCGE3POOZZlwLAu4P0qGGKUYsWrvQ6QAMYPn26rR2culE2tDtFKMXaO1tfJcFEwS\nQggh5J7mnI2cczgfAN+G54lWlTcgN1g4mFkOYxorwDA1M/nGV/Y6y5pWf/KxhBBCCCF1QG/iEChl\nEKdy9G78yrbONsAHm4mbdHhqb47bvjqDFWqpqN4FkrWJgklCCCGE3NOyDFZEBIgxv2uQy+32jOXA\nzfxyhtcKrUjcpHPZZu6RfOSWswrNvYKCSUIIIYTc03QGFtoAERKCJXihrQqdwqQIEDMoNHM4nmWq\ncN+MEmuF998LKJgkhBBCyD3tVrEVUQFiMAyDR1qosKyPBgYrh7G/ZWPWIT0ACKvMOFuTwg+Fz7vP\n/y2BGhIKJgkhhBByTzuZbUKX8Ir7MsaqxHirSxCCbCvRpOSbsfwCH0zeHymv8WOszyiYJIQQQsg9\ni+U43CiyID7QtcHNoBg+QPx1RDiSx0ZAImLQP1qOEguHi3lmTNuXBwD4X58QBNZiT8f6iFoDEUII\nIeSeNW1fHjJKWGGta7sFXYOxoKvrtjIxAwsHvLA/T7itY1j96S1ZV+7tUJoQQgghDU7S2UL8mFri\nl8dKLbAAAOTie7e1T3VRMEkIIYSQBmXdVQM+OVdU7cfJKOZnYv+rR7DX+9jbB73aMRBPt668qfm9\ngIa5CSGEENLgFZlZ/JllQpdwWYU1jFaOA8sBUhGDKbv5JuQdwiqefONscIwC8WoxWgRJ7ulG5c4o\nmCSEEEJIvaU3sth6w4A4tQTvnyzAFwP4Fj1SEWC0chi2Jctl+67hUjzRSoVN1w14q6t7xnGwrQH5\nm535dj4TmgUgUFq1gdqEYO+Dz3sBDXMTQgghpN46lmXC8gvFuFFkQZGZw7wjfN/HyAAxrhdahO3s\n8aCFA36+asCudGOFj/veyUIAwN+aK2vmwO8hFEwSQgghpN6YdSgPO26WCv//zokCAEBuKb9k4dVC\nvs7xVrEVz//umFVtZoGX26thZYFCM7+theXcHl8lYbCwG1/32FgthlZBoVB1ef0OfvHFF+jUqROi\noqKQmJiIQ4cOVbpPUlISevTogcjISLRp0wZvv/12tQ6WEEIIITXHZOWw+1Zp5RvWoONZZuzNcD+G\nKwWOLORzbRwTX5oEivFESz672F0rw9k8M05kmwEA5/PMwnaDNumw/7YRZpbDgGg53u0ZjOUDQqnu\n0Q+8CibXr1+PuXPnYtasWdi/fz969OiBSZMmIT09vdx95s2bh6+++gpvv/02jh49inXr1qF3795+\nO3BCSNXllrIosbB1fRiEkHrqiM6ExScK8LuHYK42eUgo4lSOGREBfNgyqbkSM9qrAQDXC63oouV7\nPcarXXtFzjygR5GZRaGJBQtg/rF8hCv4ZRPvj5RTOyA/8SqYTEpKwtSpU/HYY48hISEBS5YsQWRk\nJFauXOlx+5SUFKxYsQJr167F8OHD0bhxY3To0AFDhgzx68ETQrx3tcCCh3ZkY8Yf+ro+FEJIFemN\n/IXgutQS5BkdF4RXnbJ1/jD/WD4A4FSuuZIta8budD6IPaIzCbc5x3vz7gtC8tgISEUMEhvxK9R0\nDZeiU5gMPw0NE7KM45sGCPuM3paNi3rH61FJKYD0t0qDSbPZjJMnTyIxMdHl9kGDBuHIkSMe99m2\nbRuaNm2KHTt2oHPnzujYsSNefPFFZGdn++WgCSFVl27rpxZG9UHEA4OFg8HiIR1Uz628WISDdyqe\naNGQcRx/Th7cno2RW7ORdK4I+5yyhk8n5wq9Ev31XINj5Pj5qgFWrvb/Ho5kOoLIUguHNSnFsHLA\nAltvxyCnlj9hCjG+GxyKf/UMAQCEKxxZyZbBEvxf92AobJHo7MP5jse1Nry/8/qu0l+VnJwcWK1W\nREREuNyu1Wqh0+k87nP9+nXcuHEDGzZswGeffYbly5cjJSUFkydP9s9RE0KqhOU4IeOgucfXkCWe\nvXYwDzMP8JMZjmQakV7s34xXTdh/24hVl0uw/EIRdAZrnQQ/Ne3xPbnYesPgcptExOB6oQUXbPWA\n9skm1XXUlg2c1oYfPs4prf2SGNbpHK65UozlF4oBAI1UfKAYXuZiOEYlcRuq3jZSixHxAegbLcdv\no7SY0IzPUg6PU+DVDmp8PTC0Jl/CPalG+kyyLAuTyYTly5ejadOmAIDPP/8c3bp1w4kTJ9ClSxeP\n+6WkpNTE4ZB6gs5v3Sm0MACCECJhkZ5XiJSUTL8/B53fhovlgAsjWYuZAAAgAElEQVR6vh/fxcsp\nmHMxGENCjfhbpCMDVtfn98WLQRgQYsIjUY5jmn+BP+biUhMe3pmDB7WlGBV+d2UpbxYHY8OlPDj/\nXF/JyMJ/TimE/0+5fhMiVdWzk1YO+D1PhvuD+SDyn8f0UIqAwvSr0ErVOHE5Dc2V/sl6VubrjAAE\nSVjkm0WIV4hxo1SMVZf55RJHhpUiPyMNQBAy01JR1W+vLowIPyMQA2Q6hFs4XL3i98Ov1xISEmr8\nOSoNJsPCwiAWi92ykFlZWW7ZSrvIyEhIJBIhkASA5s2bQywW4+bNm+UGk7XxgkndSElJofNbh9IK\nLUBKLmZ2CsEPqSVQNoqERi6CUuKfLCWd34YtvdgCXMwFALxwkQ/QbrIqJCTEAagf59dyQYfdeXLM\n7xcHluOQdK4IAJ+x01v5rNV5kxrPNY312991RfKMLM7mmtEvWl6zT3RBh5smCdpoJJjSQoXvUopR\nKAsG4Aiac5WRSEiofFm/xE06xKnEGB6vwJQWSozYmoVSK7Am01FfOL9LEBJiIxGUnov30vhh5BhV\nza9vcuACH2N0DpNielsl5tiGpefeF4gHYrUQMQyS2wKA57ijIgkAtrZioZRUfV/inUo/cVKpFJ07\nd0ZycrLL7Xv37kWvXr087tOrVy9YLBZcv35duO3atWuwWq2Ij4+v1gETQqruZLYJLYIkaBMixSW9\nBY/uzsWsQ3oUmmhmNwHSCq3oEu66osclvQVvHdXjRlHdD3c7D18nZ5Ri161S/HTVMfRrH+W9nG/B\nyK3ZSNykw7YyQ8P+9uHpQsw/lo9rXk6AsXIcbpdULctnr2EstfINuvtFy/FwcyV225pxbxwejs5h\nUq8+x/ah8JvFVqy4UIx8E4dSD4czKIYPjqOVfHjwzaUSJG7S4ZzThJwr+WaP/Rt9YbJyePWgo1fk\nyRwzgqQiPBArx7OtVRgWFwCRH1r31MYFxr3Mq3d3+vTpWLNmDVatWoXLly9jzpw5yMzMxFNPPQUA\nWLRoEcaNGydsn5iYiE6dOuHll1/G6dOncerUKbz88svo0aMH7rvvvpp5JYQQN39mmTBqaxY+PFOE\nKKUIwXLHl/L5PAvG/EaT4ghwMNOIKKVYqEd7rSO/zNwfd0wuzaPryr4MRxbuTgmLw04zff/XJwQK\nsfs+W27U7HHn2wK4TWneBa3JGUZM3pWDqwUWJG7S4eOzhS6rtzjLLLHiuX25OJfnuF9i++h2CHUE\n/cEyEYbEKlDsxcSpMdtcP+sPbuf/f4gteBSDwzOtVcJs6OfaqtE8SIIdtp6T0/9wBHzP7svDtykl\nlT5nec7nmVFkC253p5fiL1tPSPuxhCtE+EeXYExtWXm2ldQPXgWT48ePx7vvvoulS5eif//+OHr0\nKH788UfExMQAADIzM5GWliZszzAMfvjhB2i1WowePRqTJk1CbGwsvvvuu5p5FYQQj7bcMAg/NP/X\nIwQB1FONgM+SJW7S4XaxFTqDFb+mleK+cBkWdQvGqHgFxjZxDHtuuFazGT5vvP1ngfDvtEIL9tgy\nc8ljI9AxTCYMw6ptLV8ebBKAUHnNZaISN+lwKocPgDZc827Ws33G9dPJfDnBT1cNtqF6BzPL4XSO\nCQuO5+NyvgWpBRYMiZHj/7oH41VbgK8N4CPnlsH8aw5TiLD1RikSN+nw2O6cKr+WKbbhca2MxWNO\nwVu8WoJWIa7D21aOEzKUX18qxg9Xqh5QZpZY8dL+PIzelo1Pzha63DezQyAWdw8WXiNpOLwuhHj6\n6afx9NNPe7wvKSnJ7baIiAh89dVXvh8ZqRXpxfyQ57aRWgRIKNC420htWYYlvfg6OIZhsGu0FmIG\nGLg5CwBwvdCCJoGuXwUcx6HAzCG4Ac/8fm5fLl7pGIi2GilS8s2QMAyaBtV87VdD8IstQJzsFHw0\nCRQjIViKdrbM1/R2auzNKMX5PAvOFklQ2xWTBSYWhzKNwhDnzA5qtAiSYOYBvk/q2iFhwra9ImW4\nU2JFrEqMi3oLBsfIseyMI1ArNrNQSf3zt1zqlAWc0zkQ758sxO1iK2LVFf9t5XsYij6qMyFxkw6/\njgiHWirCS/vzkJLvyEZ+eLoQb3cLQt8ydZlfDNBAbXs9jZ2e92axFfkmFnOP6BEoFeH9XiHIKbXi\n2eRciBlgzeAwXNCbcTbXLJQJRAaIMDVBicCSLLfje6SFEiKGrw+9km/B7WIrFhxztNj59HwR/tai\nautab3fKdP941QCtQoRmgWJ80FuDIJmo5mtQSY1ouL8UxC8O3OGHiz4qc4VI7g43ii1IbCRHV9vq\nEADfVoRhGOwZowUAPLk3F99eLnbZ72SOGeN+y8b+2w2jRYxdlsGKDddKkHS2EJfzLXjvrwJ8fLYQ\n0/bl4ankXOiNrj/oF/PMmOE0fHe3SMk347NzRcgyuBbFFZtZ/N+f+fjorGtGLCJAhIRg15rJSc2V\nWNZHAwDYmStDbVt7pQTv/lWId04UIE4lxtjGAVA51b1FKx3Zq2daq7BxeDhibe1j4tQSXCmwIM/I\n4q9sE0Zty0aOpwJBH2Q6vacj4gPQXSvDLS/6PKYXW7GoG99wO67MKi3rrxqw+1apSyBp5ym4ahEs\nRZTt9dtb5til5FtwPs+CIzoTis0sJuzIQZ6Jg5UDIpViJDZS4KV2fOufWZ0CoZKK8GwbNboEuT93\nvFqCWZ2C8E6PECjEDKbuyUWOkcVjLZXCcDtXhXZMHMdh323X2fZZpSweb6VCSA1mkknNo7N3j7MP\ns/xWw/VFpPb8nlEKK8fhtYN5uJBnwcz2gRB7KGB3Lmr/4qIjmDyuM+HVg3z2Z/6xfPzvTBHmHdFj\nT3r9/xuZtDMHy84UYZ0t63KjyOoyUeN4lsll+/N5Zpypo5U+/CXPyAo/6MVmFlN25WDavjx8n1qC\nSTtzYGY5nM01g+M4/JpWil3p7q1z7o/0nA2Sivi/kfPFUo/316RN1x3nbWyTAEhETLmjJyKGgUTE\noIVt6NcemIzfno1U2wSZCTty+K4G1fT5ef47c7ftYixGJa40mOQ4DocyTYi1DcevHhSGzSPChftX\nXirG4hMFLvs0sk2A8Wbd6L1jtFjULQjD4xSYdcixwlVqOZODRAyD5LERGN04wOP9nqQVOV7j4BgF\nPuqrQYiMQVaZXpSJm3R41jaUn7hJh5R8/m9vTUoxBm7OQmqBBU+1UuGTvhphnwGUjWzwKJgkAIAO\nYVIc0xnxq5fF5KT+SSu0YPBmHRYcL8DFPAtO2IraNfLyf4x+HhqGPlF81sk+DPfeSdcftSM6Ew5m\nmupF7VxFNl93Pb42Ie7Djhf0roGjxBYs5dZBc2Z/Gb89GwM3ZyFxkw6/3zYio8yM4b+yTXj5jzyk\nF1shtyWxJjULwOYR4ViZGIrF3YOFTJUn7/UMRqikdt8fK8e5TCqxZ+GUtmDy/Z7BHveb2EyJzcPD\nXW7TOb0fT+zNrdZxWVgOBzNNeL2j4wItVi1Git6CLIPVY7C66boBeUYOcjHQPNjxNxkoFaFlsERY\nErCsf3QJxtOtvJuAwjAMBjRSuCwZGCRjXGbpP9TU+8CxIq93DBTKYrQBYqy44Mhy20sA7hiswvfJ\nlXwLfrpqEJqPA3zzcHs5Ra9ImVcBM6nfKJi8x2kVIvyvTwhO5Zix+M8C/OcUDXc3VDeKrLCvEva6\nU3aioi/qMIUYszvxy5QttZ37HhEyvNYxEG91CXLZtuzKE/UFx3H4K9uEpacL0T5Uiq0j+WBCxPAT\nNNYOCcOjCUq82kHtUu9msnL44DT/mpdfcB32XXqqwOWHuaE4l+c45nn3BUIlYfCGrV/fjAN6lFo5\nPNwsANPbByJQKkKzIAn6RcvdVhBxFq+WoLZ/6xcd5y9ovhvMr1Rin0xjz0yWNyQqETEItNX57h6j\nRaCUwbqrBjzdWoUnWiqREFy9mll7gNQr0jHsLxUx2H6rFJN25rgFqyUWFh+cLsTco3oYPSQvlw8I\nxcJuwUgeG4GBZYLKdqFSPO5lMGm3pFeI8O8CE4cDtln6awaHCava+GrFAD6TOLqxo1l6erEVO28Z\nhSDa3vooRCbCOFuniI/OFsF59cKl94cg0nZx8Gk/Dd7s7Po9Qxqm+vnrQGqFheWQZ2TR1HaVWWDm\nP/FVqYEh9UeR05JqpVYOLYIkLkNJ5QmRi/ByezV+v21EiYVFiYWDSsJgSKxCqKsEHGt7l3Uu14xr\nhvJnXyZu0vmtXs2TOwZWGJaf3SlQ6CdnfzuilWJMa6NGnFqCLTdKhYDymNOQ96FM16HfzWmlLu1o\n6iu2zGf1eiH/Po9rEoChcQEutbJ5RhafnS9GXhV7i4bIGRRamFr7XjifZ8bvtrq6GJUEm4eHC1ks\nmQj4Z9cgYTi7ImKGEYLkLuEyDIlVICXfUq3+iBf1FjQLFLvMNn4g1jUIdP4c3rANDV/SVz68/o8u\nQXg0QYmdo7XY6/S5qwqt7YLv372C0StChsOZJiglDBqpxNWeYJkQzF+oOV+crhnMT4L6+GwRTuWY\ncDLHhPYaqcuwf4mFg97I4sEmAdg7RuvyN9lGI6VaybtEgz2Ly84U4p0T+ZVvSDziOA4brhkQIhcJ\n7TTsDFYKJv2p0MQicZMOLMch1UOBvb/suFWKITFyIYPYIlgi/AhXxj4ENnJrNs7mmoUfaxHDYN0D\nYVjYLQg3i6zgOP6HwXlYePofefjXdc9ZD5Ptb2nj9ZobIp93hA8k24RI0Nh2YTQsVoGR8QqX7WJt\nkx4u6M24rDfjm0vF6BIuxX96hUAExxCd2RZsZHgxqaKucByHw5lGlFg4KCV8/RsAnM01Y3ILJV5u\nz5+Pt7vzw8GjGyuE7F6X8KpNpgkQM1CKOey/bYSF5XAk04jETbrKd/RCgYkVZm0DfEb4pf38hKh/\n9eCPPdCpowDDMBgYo/BYA+yJ/ausfagUEbYA0Nca2a03DPjH0Xy34Me5GbZGLoLOwH82bhdbccdp\niN2+PnR5JCIG09qoIbVNkPMFwzDoHy1H8yCpELT192M9YtnG3yFyEQY2kiNIxuDvB/RYdqYIMU4T\ngnaN5oPi71NLIGK8q/8kDVODDCbvlFix4ZoBO2/V/8xBfWVigU/OFUEt5b+4vh0Uiv/0CkGUUoTv\nr5TgcgMc4quv7EM/E3fk4Jl91avZqggDYGicQshGViWRJGIYoR4tu5QVgjIAiAjgZ4DKxECOkcXL\nf+ThoR3eNTtfa+tD501mxhe5pSyu2bJxzkHH3C5BeLCpa8uSiAAxOoVJ8WNqCZ77PQ+X8y1opBKj\nW4QMRhb45Bw/5G2fUVt21ml9cqeExZtH8jF6WzZKbEGwPVjpGSETJs4AwMJuQXihrRoRAfz7MzxO\n4f6AFWAYBhEyFguOF+CrS8VCRveWH1bGGftbNsb+lo25R/JxLteMzWn8JK9whQj3R1Z/Brlz5lYu\nZpAQLMFmH+rCb5dYseQk//dxxcMFYfLYCOwarYVCDOy4WYqcUism787BOycKMCxWgQebBGBG+0Df\nX0gVvN09GKEKESba/h6a1XA7rIeaBuBwpiPLHx4gQusQCbQKkVCTDKDCulzS8NXbYPLF33PLbUni\n6cNsb8J71culreqa0Y/ZP5bjcExn9Kpxrl2xbUg7y3YVHauWoFuEDPlGDqsu8z+2NTk0eTep7H3K\ntL3Huba2NCfKzCj2l6xSFlqFGOG2oCFGXbXGv6NsmTz7KhRlxakluFlkdZu56k0tZdlJIf5yNpd/\nL5USxqsMzKkcMw46/fA9ZatJK7Fw2JxWirf/5IMa+2tal+r7Kh81KcfoPlTdypZN7hjmmo1ObKSA\nWipC9wg+OPMlOxQk5p/vu5QSYXa888ov+28b3doQVeS4zuS2tKDzCiurB4X5JYv1n/tD8FEfRx1h\nlsGKPel8OUdVHLjjuLB4INZzMC4RMegdJcf3qSWYsIPv32lmAb2JxSsdayeQdMbYZmyr/dRfszxK\nichlslREgBif9NNgja0PaNdwKaYmKF0CS3L3qZfBJMdxuKC3CEssleUcMNr7xl22ZT7+d6YQaYUW\nPJOc65cr55qw6nIxhm1xNIg9nWMqd1ktb1zIs2D24Xy8edj7Yf9L+fx7+1wb1wJv5yHu1Zfr5w9p\nffDR2UIknS2EmeUwYUcOHtuT41a/Zqcr8yP7mtPkGH8xWjnoDFZEKkUQMwy2jAjHowlVayY8vX0g\nfh4ahnldPBfEx6nEQg2Y/TkNFg7ZtiHvxE06l3q0LIMVBzONeKGtCjeLrC6tXvxFxDDoHSnD1pFa\nr9qc2NcdfqWDGsljIxBmW4fv1Q581mRPuhGfnCuC1haQJ50rwu5blbdEWnWpGL9n1F7rJJ3Biha2\njFOUrYVMYiMFvh4YWu46xlNaqLAyMdSn5xsR7p6lXZfKn08Ly2H+sXxM2lnx6itmlkOBicWVfDNm\nHdZj8i7H9s6tYbaP8t8CCgnBUnQIc2Q4k/rxr//PLP7773SOyWXN6fLklLJ4oqUSyWMjMKND+YFh\ne40jkNfIXZemvFvJy1yzNg0UQ8wwQnZ8aW8Nnq3m5B9S/9W7YHLgJp0wCyzPw9U3wA9D2b98PrY1\n275pCxxP5pjxZ7YJqQUWTN2TKyxuXx+wtuzpSltPvxILC5bjMPOAHk/uzUVBFQvj7exX9Mey+NUU\nCr14nLlH+MBzXNPyAw5fhoPuFT9fNeDnawZk27KON4usbpkWu0yDFU+0VOLHB8LwD1ugVuznv0u9\nkUWQVCTUNKmkIq/rypyFKcTlBiNiEb8ih93SU4U4aMvYSBk+iHTu4zhpZw4u6S0YHMNncj44Xegy\nm9ofDFauwpnIZc3qFIh59wW6DYGX/RwUmDjMu48PAsr2/+M4DtecLmhvFFmw8lIxFhx33a4m/Zpm\nQPMgCTYOD8fn/fkASSZm3FYychYgYXwe8oxXsJjdyREURSsdPx1/ZfPn3F4rdzHPjJR81wCN5Tg8\n8GsWxv6WjWf3uTaJ/6y/Bou6B+PtbkHYOjK8SuezqsJsGef3/ipA4iYdZh7Qu2REPXn3rwLcKLJ4\ntcSfPfu2MjEUG4aF47eRWmHm8t3Kfr7WDw1HiIxWmbpX1atgMstgBQfHrGJ7AbyF5XDR1vLCwnI4\nk2vCtDYqLO4eLDTgtRc9A8D/nJbRKi8grQulZYa2PzlbhJ+dGirfLCp/mOhUjgn7bJkP51U8ks65\nt/J561jFGUp7Bm1RN/cM1GsdAzHNlq30R83S3czKuTYFfnS3ox7SYOHwe0Ypntybg3Wp/A+/NkAs\nDJGN2uZdzaG3ii0cVNKaHUZ6qkybkh23SrH4RAG6aaV4PobPYr95JB8mK4fbTkPh2gAxfrU1aB6+\nNQvv/uW/oOudEwU4qvO+bEApEWFonOcM5u4xWqhsGbHF3YPhPOnXueTmqM6Ep5JzMX57Nv57uhCP\n7/FcB6s3svjjthGvHczDS/tzqzy06vw4ziUsHMfhRLYZARIGwTJRrS152SfKkT38VMjwmTD7cD76\nRMmQXmzFUZ0RL+zPw7QyAeN6px6lQVIGz7Tm/5Ze7aBG6xA+m9e/kcJtgoe/ycUMFncPdhmWBYAx\n29yXElyTUoyks4XYfrMUB+6YXCaWlMe+Ak+8rcREcQ8sUasNEGP7KC1CFSL8MlyLwBoeVif1U706\n6xedivT/2TUI226WguM4bE4z4AXbDL8hv2ZBb+IQq5agT5QMcjEfMKYWWNA3yhH8TGmhRBuNBIWm\n+jMz+Q2nYehYlRhbbpTik3NFiFKKEBkgQloFw/J/P6DHP22Zjwe3Z2PijmzsTS8VhppWDwpFsIz/\n4jqVY3ZpT1GW3si/J56W6RrbJACPJqgwq1Mg/rhjclt+jrh661g+BsfI8XhLPrP1n1MFWJNSjC8u\nFmHB8QKhVYtzRsjfQbqV45Bdaq3x2qgwhRiPNFe61SYezzKjU6BFGM4buiULk3fnIEjmmGWsloow\n2baG73bb5xrg+/atKrOUY1WIGeDvHfwzhCZmGGwZqUXy2Ag0C5Kgd5RcmFH86O5c4eLW3iIpz8ji\nl+sGYeISABzROYaDf0gtwVvH8nEi24zzeRaM3JqNxE26Cmubt94wuH3mHtyejcGbs4Ta3Idtw8lP\nVLEHYXXZZzG/1zNY+Le9n6k9I/qOUxbXXvLAcpzLutQFZg6tQiTYOVqLsU3800i7KvpFyxEZ4PpZ\nKTRz4DgO224YYGE5WFgOyy8UCyspARCC3oo0DZIgeWzEPVcfWJPZZNIw1KtgMqPYignNApA8NgK9\nbVfBOUZWqGm5UmboRMQwYDl+BYi9GUZMTXB8ucaoxOA41Jv2QRzHL2kG8F/Gzi1bFGIG45oEIK3Q\nc2bS/gPVSCkSvpSzS1ks+pP/4m4dIkGsSoyNw7XCEl8V/UDrSvl6q/KGMwEIbVV23CrFP47qkVyL\n9WANgfPauhq5SMja/ZpWiuUXilFidgQMfaJkiFU7gslZnQIRIvPPl2+hicXgzVl443C+8PdVk15o\np8bb3YOFTCPANyEGgDGNXScmhJVpoTLKqVXP9UK+zdC437Kx8mKx0ELIWyzHYdgWHawc0LmKrW68\nFSQTCd9DgGM4t2w5Q4mFw//ZWvDMOZwvBMqKcn5gy6sFB4AlJwvx4HZH1vp0jiPrOu8o/11mX77O\nX39DVbG8vwY9bBN5XneqBXw0QYmR8QrkO128j7Zl31deLMbqyyWY1SkQz9oykqFyUbVa4FTXnM5B\naB4kwesdA4VZxunFVrx/shDjfst2CYrtJVX+quMk5G5Ur4LJrFKr0AtNLmbQIVSKQ3dMwsxFe63N\n3PscX2LOCbgopRg/Dw3D6kGhGBGvQKaBRUYJi/+ervtVXfS2L9lVg0LRK1LuUn/UIVSKMIWo3FnB\n9nWzOUCoJ3X2394a4UtZzDAIkjLQVDD09cLvebhSyax3EcPgwSYBSDpXhAN3TFhYi/Vg9Z2F5Ydx\nP+vHt+AJlIrAMAycf2q23XQE3zFlaqaCZSLoTXw2sbrGePh7qA32LOjjLZVCPzuGYeCckLlW5uIo\n1FavJhXxAZnziiBXnSagZZZYK13eMM/ICvuH1NIwb5HtAuGa7VinOk1waqvh+1UC/Kx9C8vhq0uO\nCzp7hhNwn5DliX0yz9eXXC8Kv7roKOGpi0CsZYhUuAi1rwLzrx7BUEpEmNLCte7UXtZzxFaGEK4Q\nYWCMHAFivol2XeqileHLxFCMaRKAh5srEa0UCW2Jii0c9jo1rP9ntyDsHO1bE3FC7hX1KpjMKLa6\n1P9EBIiw9HShy5X81AQlhjnVPDmv8BEsYxCmECNOzWfd1tq68/9Sgw2TvZVpsKJlsATxtgyVRMRA\nIWagkjB4rWMgtAoxLugtbqtMWFj+i+2xlkrcLnH9gX26tQrz7gt0q8uZ1kbt8uNcVpxa7PbF78m4\nMkNQS08VIN/Ewszyy9fNrKRw/W6VU8oiSCZCa40UT7RUoq8te7V3bITLyhX9ouQY2EiOkWVmGduH\nwN7zU+2gPVNUdk3i2tCoTKD8SV8N3uzsefaqUiLC3jFajIgLQKbBin+f4l//0FgFrhVYkJpvQeIm\nHf62KwcP7cgWJvd8dbEIL+93/VsrcMqAyWp4iO2zfhpMbBaAIzq+WffxLDPWDgnDs23U2DVaixUD\nNAhViNAtQoYOoVLcKLK61IU+3VqF3lFyIdDOMngOlJ3ru1dcLMaZHBNOZJvxXs9gjIhT4JLegm9s\nHRYeaV61mfo1QRsgxleJoULZhj1AjFaKhNZKWQYrtAr+/7tpZYhRSbBtlLbGayOrSipicCHP7PaD\nuHl4OEROM5MJIZ7Vq2lXBzNNeNKpDsh5QopGxiDPxLnVorQKkeCFtip8m1LidqWukDBopBQho6Ru\n6v6MTjNNU/QWod2I3crEUDC2VQHaaKRIL7Zixh96fNzPESAX2rIhQU71cL8MC4eZ5cqdXRitEmNv\nhufXrDNYcbPIioe9+DGyD+WOiFNg281SbE4rFa7eRzdW4HSuGYmbdEjqp0FbjXcrrZzNNaOxWuzS\nYLqh+ZtTS5OnWrvW6zEMg54RMhzRmfB296AKs0euuUzvHdeZcKXAjEm2c7iwWxAkDFPjQVVZy/tr\n3GYHt9FI0UYjRYtgice1iBmGQaRShNQCC3bbJs+FKUTINbJuDd3nHc1H8tgIIYByVmBm0SFUio+8\nWC6yulprpPj0fBFO5TguaqNsn2WJiEFCsONvv3GgGFfyHa/NXjMKAHvGRGDHTQMO2fpcGiwclp4q\nwJv3BeG3m6X4j21t9CktlNibUYoZB/h6xB4RMsjFDA5nGpFn4tAhVIoX6kkDaOeZuyKGwa7RWlg5\n4BHbZ8TeLujLAaH1uo4wo9iKG0VWzOygFiZwPtgkoEF/TxFSm+rdJ8X5xympnwZfJYbi034arB8W\njmdbq9zqsiQiBo+0UOHXEZ6HIVYPDoOYQbXWY/XVsC1ZOJxpxGW9GUtPF+JOmaC2kUqMaFtmx16P\nU7Y4397aaGyTAMzvGoTto7QIkYsqbFMRJhfhRLYZrx10ZHM4jsOvaQYssM309mY9VPuXv4Xj0CTQ\n9fmc6/Ne2u9dhtLCcnj5jzxsuXF311/a249UFEjO7xoEme0tzS1lYbBwXvVFLTKzmHVYj8/OF2Pw\nZn4GqlIiqvVAEuCHPMsLEFoES8tdyjFKKcavtouSxEZyaOSictfBdp5FbV/m8HSOCTeLrMJnpzY4\n9+x8v1dwuec2Xi3Bj1f54NdTf8EopRjpxVb8lW3CiK1Z2JVuxBGdSQgkAeDxliqXUQgRw6/ckmfi\nIBMBS3qFuD1ufSER8ethv1pmUlTToPrdHmeK7fy2CJII9a/PtKndCU6ENGT1KjMJwOXHSSJy7Vk1\ntWXVP9xihoGVA05km9Ajgh+OLDazUEpqp/j7zSOOCUChlQRwAxvJXWp1AL4ovHmQBHIxI/Trq4x9\niOlEthkz/8jD6VwzekfKcDDThMRGcnTTej9hIVDKIFrJLydIK6gAACAASURBVKf3j6OO13K90Ir2\noVKXoDKn1AqZiCn3at5ec/bZ+SI84sUwuyd/ZZvQWC0R6u+qwsJySLeVUngTTHtir2X7dlD5zZ9n\ndQrEtEqa9GoVIuTbZtU/ujtHaBb/7aBQl8k6ZS0qU7vawcu1t+sT5yBwYbdg/JpmwGXbqlabhocj\nSCbC1hsGLDlZ6NJu6ZGdOVg1KBQzD+gRImPwuA/fB76yf3cAQM+I8lfaaawWQ2dgMSpe4XGmcoxK\njMv5Frx60NG43r4aVbxajPldgzy2k7HXqJpYQFG/4zIAfJufVYMk+P5KCe6PlFc42a8+MNhaBbUK\nkUIuZrBmcBi1uCGkCu6JT8vgGDneOJyPxE063C62YtS2bJyoYEalP5TtKdcyWII3yqkls5vcQgm5\n2HU92WwDW2kQWlagTIT5XYLAADhtC/bsS8glZxiFuk1vbBwejqdaqXBfuBRqKQOFGEIpwv2RMiy0\n9ar80baE2Nwj5c+et2dZI8oM95/LNeOl/bk4lWNyqxm1yyi2YuKObLx6UI/VKcVIyTdX2EP0RpHF\nLRv92fkiPLE3t9ImxRWxN6auKDMsYhhh9Yvy8JNw+ON3XnVoajk9C+2OOTUFD5ExtTLM62/2HnzT\nbUO18U4z44NsFyIj490DsRwji2W2IUi9iUNCcO1fC79VzupAdvY1zcvrSRjmIRL8l62+8quBoS5D\n5gCwYZh7HWxdzYCuqni1BG90DvLYgqy+aRcqRZdwqVCWVNcThAhpaOpVMOnrUl+V6ey0nNZR249x\nTTcz/+O240c/TiXG8gGhla6gEKfm68wGbc7C33ZmI+lsIYrMrE+rVgyOVYADoPbQyLrskHVFRAyf\nwVVKRFj3QBh+GhouTMwZFR+AAdFyyMXAJ+f4H/l8p+n1l/WuAftFvQUauQh6I4utNwzYf5vPwh7L\nMuF8ngV/P6AXeviVdUxnFJbt23DNgGn78spdN7nQzOLxPbkuM2H1RlZYU9j+HLMP6ZFWwUSlEguL\nz887Zs/ae3cu6hZU7b5qIXIRbhVbhZm9zsHnH7eNHpdmvFOmJY3Bj+u71ya1VASVhBHKATqGyfDz\n0LBys733R8qEC7EdTksbtq/lrOyeMVoMKWddZjt7/8KKGom3DuE/z5NbKLGgqyM4dV6x6LeRWnw3\nOLTSixLiH4mNFPigd8O7MCOkvqhX31S+LvVVma5Ow7pncmonmLT/LiSPjcBq26zyyjj3Mcs0sFh3\n1YDsUhYaue+BS5FTv0N7c+WWXjTf9UQpEUEtFUEj52flhsj5ljjOmU57FlVvZPHc73nYftMxk/6X\nayUAx6FPlBxLThZi/rF8GK2cS0B3p5yZrvahvz5OjekN5SzNd93W9ujblBKhL+dHZ13bQ/2eUWoL\nYvmA95OzhULmlOM4GK0cxmzLxtorjoD1aoEFLYMlGNDIu3KDigTZgnx7A+oNw8KxfRRf9/vWsXwM\n2pyFqwUWZJZY8drBPCRu0gmTGuzZKk8TXBqKLSO1GORUthGmELsN7+8arcXIeAXe7RmCEXGObduH\nSrHugbBaz9B5M1TLfx7EaFPBhLS3uwfjXz2C8VQrFTqF8duVLVdQSBjEqFzfj28HhVKLGkJIvVTv\naiZrQiOVGDtHa/HOiQJh+cUsP/T4K8+2Gwbkm1hMalb11R0+6hMizOIEgHN5Zjwf7fvMzS7hUpis\nwNk8M6a1UcHop2yW8w+58zB8kZlzWZrsUKZJaOUUpRTjwaZKZJZYhdrQYVuyhOPMKLHip9QSt5pO\nC8shu5TF+KYBeKa1CqO3ZaNruBR/ZvPD4mWDijVXSqCRi5BnZLH4z3w801otzK7dO0aLgZuzhOHq\nn68a0CJYgh+vGiARMTCzHFqFSF2aFpdaOCSdK8IRndFvQ6sMwyBOJcZNp0ysXMygdYhEWAnq6WTP\nQ94auQjRSpFLe5y7kUTE4I3OfObO+Rx/1CekXg/1rhpU8cVjRIAYEbZRihAR/9nxprtCRbW0hBBS\nl+6ZbyepiMFzbdRIzjBicgulsKqOvxWbWbx/ks+CTfNhNmCHMBm2jgzH28cLcFhnwkW9BY19/BGx\ntyW5km/GH3dMGN+0ZnrTjWkcAIkIGN9UiVmHHIEwA+CaU3P0LAOLcIUIHUOl+OKiazNmmZjB5BYq\nfOihwfw7JwqwN8OI6e3UUEtFWJkYCrmYX+Lu+yslmOy08lGxmcWhTBO6a2WIUYnxy3UDjmfxNZL/\n8xCEXCmwCOsIO7KQjmyqQszgWJYJm9L4215sV/2spN3rnQLxykG9y8owH/QOwcit7o3Iy7a4WtZH\ng3rcaaVG2Id963MgWVViWzud+tw2hxBCKlOvhrlrWpRShCAZg+Fxjh6JAD8ku9EPjc1T8y0Ytc0R\nCHg7+7ospUSEd3s6VsyozjA3wLdpebIG1/HtGy3HOz1C3DKK87oE4XaJFSYrh+sGMa4XWaBViBCp\nFOPp1iossk3eeaa1Cm91CcJYW9sn57WJPz9fhJO2Zeya28ogmgVJEG6byPD5Bdeg9JYt0zfnvkCX\nsomR8QqhVU0zW83o2krKD+RifhWPRccdk4qqMnmpMp3CpHi/ZzBmd3bUzSklInzaT4P2oVJh6TkA\nePO+IExpoRSWy4wIEAvvwb0iRiWpd82u/YECSUJIQ3f3fTNXQMQw2DRc61bU/uTeHI8ZMQvLeZwI\nUZ5d6a79E8N9aF9jxzAMEhvJhX83FL8MC8eu0VooxHztWCOVGKtTivHOdTUKTI5G64+3VKGvbZbn\nmMYBUEsdGacHt2fj5T8c2cI823Cuc5souZjBlwPcJ2zcKrIisZEc4QqxMMEjeWwE3ugcJExwWNwj\nGCoJ3zwb4Gferh3iCCztGWWjFXispRIWjl/C85UOajStwuSlyjAMg56R7jNd22ik+LivxqUVVscw\nGZ5rq3aZpEEIIYTUB/fMMLezIBk/M/nhnTmwsBzyy6k9e2pvLlprJPhHl2C3+/53phATmymFFhJJ\n5wqxLtWA+V2DsPhPvt6uuhmHhd2Cy51kUl/Z+zf+ZptMImYYrHZaAs55FrSYYVxWCHF2NtcMM8sh\nSinCnRIWH/fVuF0ENLYFdvaVhjiOw81iK2Jt56RPlBy7PExYiFFJsGUkf7vz8w+KkaNPlByDYxQ4\npjOhSaAE/aPlWH2Zr+P01Nalpm0fpYWpDhruE0IIId66pzKTziICxNDIGOSbWAyMcTQzd3az2Ipz\nuZ5bx6y/ZsBPVx0zfdel8sPk9tmZ/spgBXhoYNyQpNpqJsOkLJ5vW/lQ+4Zh4fhiAN+iY8L2bNwp\nYdEpTIpmHlbQsAfr9lrHH1JL8PWlYiGYdN7GGwu6BgulCf/to8ErHfmh8pnt1XUSSAJ8BpaaJxNC\nCKnPvP6V+uKLL9CpUydERUUhMTERhw4d8mq/1NRUxMbGIi4uzueDrClBMhGSM4xIK+Tr7CY7rbls\nl1FihZXj8L8zhcKQt8k2I3r9NUedpVYhQnetDOEKMR5sEoDJLWgpLgD4YUgY3uwciPdaFHo1XK+R\ni4RaxwJbW6P/9g6psFZu7ZViGK0cPjvP10/G+bGuUcwweKhZzUxcIoQQQu4GXgWT69evx9y5czFr\n1izs378fPXr0wKRJk5Cenl7hfmazGc888wz69Onjl4P1N4YBPjpbJGTPCswckjNKkbhJh3dOOCZd\nrL9qwPprBgzanAULy+GG0xrK9gDTYOXwlq0B8SsdAzE0zn+zfhuySKUYwz2sZlKRsv38KgpCh8TI\nYbQ6WgwB5a8+QgghhBD/8yqYTEpKwtSpU/HYY48hISEBS5YsQWRkJFauXFnhfgsWLED79u0xbtw4\nvxysvxU61Uque4CfgHHwDj9zeOctxxrZ9tVdAOCJvbm4UWRFI9v6wtP25eHTc0Uws5zQiJpUX+9I\nfmZ4XCWBYdsyzZ5XDwr1ed1tQgghhFRdpb+6ZrMZJ0+eRGJiosvtgwYNwpEjR/6fvTuPkqK898f/\nru7pnn1gGGZhB2GEEZFVHMXgCGo0LjAR3K5Glhs1Eq/cX8xVSFyI3wTDCXo8XjEKoqDRKBGDhmjk\nsijqgCaERKOGlmXYhplhmH3t7qrfH0339FLdXV1d1V3V836do0B3LU/XU/XUp56twq73l7/8Bdu2\nbcOqVaviTqReJg60YWSuFW9eWXB2ImELPqvrDSLl3ol9ot2N6lYXZp3tZ3mwxYU3Dnag222uUddG\n9+i0fnjn6oFYKzNi29/3R2Vh5tlR4dlpgqZN3ERERBRd1DtvQ0MD3G43iooCR90WFhbiww8/lF2n\npqYGS5cuxWuvvYasLOP2N/vZlDxIUu8gjbqzr/Iry0/D140uvHBZPgZmWLF8bxPG9rfhnLw0PPx5\nMzYc6MDyyXm4bFA6Pjz7fulV5aEjvkm9dKug+P3Xv7iwH0RJAsc8ExERJZ4u1Th33303Fi9ejMmT\nJwPwvOtYCYfDoUdyFJucmwWnCExO78DXyELjsUNoBLDQWznWBgCeoDGj+QRu7y/ie9kCPm6yI7+5\nGY7mMBsmAMnPX9IX8ze1MX9TH/M4NZWWluq+j6jBZEFBAaxWK+rq6gI+r6+vD6mt9Nq9ezeqqqrw\nxBNPAPAEk6IoorCwEKtXr8YPfvAD2fUS8YMjeers7l2ihO92uDE0J/T3Xd3WAgnAzPN7v7soQekz\nM4fDkfT8Jf0wf1Mb8zf1MY8pHlGDSZvNhkmTJmHXrl0BA2l27tyJuXPnyq4TPG3Q1q1b8eSTT2LH\njh0oKSmJM8n6S7MIGBqm791Dk/NkPyciIiLqixQ1cy9ZsgT33HMPJk+ejPLycrz44ouora3FwoUL\nAQArVqzAvn37sGXLFgDAuHHjAtbft28fLBYLxo4dq3HyiYiIiCiZFAWTlZWVaGxsxOrVq1FbW4uy\nsjJs2rQJQ4YMAQDU1taiurpa14QSERERkfEITU1NHARLumN/nNTG/E1tzN/UxzymeHB2ZyIiIiJS\njcEkEREREanGYJKIiIiIVGMwSURERESqMZgkIiIiItUYTBIRERGRagwmiYiIiEg1BpNEREREpBqD\nSSIiIiJSjcEkEREREanGYJKIiIiIVGMwSURERESqMZgkIiIiItUYTBIRERGRagwmiYiIiEg1BpNE\nREREpBqDSSIiIiJSjcEkEREREanGYJKIiIiIVGMwSURERESqMZgkIiIiItUYTBIRERGRagwmiYiI\niEg1BpNEREREpBqDSSIiIiJSjcEkEREREanGYJKIiIiIVFMcTK5btw4TJ05ESUkJKioqUFVVFXbZ\njz/+GLfddhvGjRuHwYMHY8aMGXj11Vc1STARERERGYeiYHLz5s1YtmwZHnjgAezevRvTp0/H/Pnz\nceLECdnlP/vsM4wfPx4bN25EVVUVFi9ejKVLl+Ktt97SNPFERERElFxCU1OTFG2hK664AhMmTMBT\nTz3l+2zq1KmYO3cuHn74YUU7WrhwIURRxIYNG9SnlkzL4XCgtLQ02ckgnTB/UxvzN/UxjykeUWsm\nnU4n9u/fj4qKioDPZ82ahb179yreUWtrK/r37x9zAomIiIjIuKIGkw0NDXC73SgqKgr4vLCwEHV1\ndYp28v777+Ojjz7CwoUL1aWSiIiIiAxJ99Hce/bswV133YVVq1Zh0qRJeu+OiIiIiBIoLdoCBQUF\nsFqtIbWQ9fX1IbWVwaqqqnDzzTfjZz/7GRYsWBA1MQ6HI+oyZF7M39TG/E1tzN/UxzxOTYnoCxs1\nmLTZbJg0aRJ27dqFOXPm+D7fuXMn5s6dG3a9Tz75BLfccguWL1+Ou+++W1Fi2Pk3dbFzd2pj/qY2\n5m/qYx5TPBQ1cy9ZsgSvvfYaNm7ciAMHDuDBBx9EbW2trw/kihUrAgLN3bt346abbsKiRYtw4403\noq6uDnV1dWhoaNDnVxARERFRUkStmQSAyspKNDY2YvXq1aitrUVZWRk2bdqEIUOGAABqa2tRXV3t\nW/71119HZ2cnnnnmGTzzzDO+z4cNG4Z//OMfGv8EIiIiIkoWRfNMEsWLTSipjfmb2pi/qY95TPHg\nu7mJiIiISDUGk0RERESkGoNJIiIiIlKNwSQRERERqcZgkoiIiIhUYzBJRERERKoxmCQiIiIi1RhM\nEhEREZFqDCaJiIiISDUGk0RERESkGoNJIiIiIlKNwSQRERERqcZgkoiIiIhUYzBJRERERKoxmCQi\nIiIi1RhMEhEREZFqDCaJiIiISDUGk0RERESkGoNJIiIiIlKNwSQRERERqcZgkoiIiIhUYzBJRERE\nRKoxmCQiIiIi1RhMEhEREZFqDCaJiIiISDUGk0RERESkGoNJIiIiIlKNwSQRERERqaY4mFy3bh0m\nTpyIkpISVFRUoKqqKuLyX331Fa699loMGjQI48ePx6pVq+JOLBEREREZi6JgcvPmzVi2bBkeeOAB\n7N69G9OnT8f8+fNx4sQJ2eVbW1tRWVmJkpIS7Nq1CytXrsQzzzyDZ599VtPEExEREVFyKQom16xZ\ng9tvvx133HEHSktLsWrVKhQXF2P9+vWyy7/55pvo7OzEc889h7Fjx+KGG27A/fffjzVr1miaeCIi\nIiJKrqjBpNPpxP79+1FRURHw+axZs7B3717ZdT7//HNcfPHFsNvtvs9mz56NmpoaHD16NL4UExER\nEZFhRA0mGxoa4Ha7UVRUFPB5YWEh6urqZNepq6uTXV6SpLDrEBEREZH5pCU7Af4cDkeyk0A6Yv6m\nNuZvamP+pj7mcWoqLS3VfR9Rg8mCggJYrdaQGsX6+vqQ2kevoqIi2eUFQQi7DpCYH0zJ4XA4mL8p\njPmb2pi/qY95TPGI2sxts9kwadIk7Nq1K+DznTt3ory8XHad6dOno6qqCj09Pb7PduzYgUGDBmH4\n8OHxpZiIiIiIDEPRaO4lS5bgtddew8aNG3HgwAE8+OCDqK2txcKFCwEAK1aswJw5c3zLz5s3D1lZ\nWbj33nvx9ddf45133sHTTz+NJUuW6PMriIiIiCgpFPWZrKysRGNjI1avXo3a2lqUlZVh06ZNGDJk\nCACgtrYW1dXVvuXz8vLw9ttv44EHHsCsWbPQv39/3Hfffbj33nv1+RVERERElBRCU1OTlOxEUOpj\nf5zUxvxNbczf1Mc8pnjw3dxEREREpBqDSSIiIiJSjcEkEREREanGPpNEREREpBprJomIiIhINQaT\nRERERKQag0kiIiIiUo3BJBERERGpxmCSiIiIiFRjMElEREREqjGYJCIiIiLVGEwSERERkWoMJomI\niIhINQaTRERERKQag0kiIiIiUo3BJBERERGpxmCSiIiIiFRjMElEREREqjGYJCIiIiLVGEwSERER\nkWoMJomIiIhINQaTRERERKQag0kiIiIiUo3BJBERERGpxmCSiIiIiFRjMElEREREqjGYJKKofvSj\nHyE/Px/Hjh1LdlKIiMhgGEwSUVSCIEAQhGQnw7ROnjyJ3/zmN1iwYAGmTJmCAQMGID8/H99++23E\n9bq6urBy5UpceOGFKCkpQWlpKRYuXIgDBw7EnAZRFPHcc89hxowZGDRoEEaNGoWbbroJn332Wdh1\nmpqasGzZMlxwwQUoLi5GWVkZfvzjH+PkyZNh1zlw4AAWLFiA0tJSlJSU4MILL8TKlSvR1dUVc5qJ\nyByEpqYmKdmJICJjq6urQ0tLC0aNGgWr1Zrs5JjO1q1bcfvtt8NisWDEiBFobGxEc3MzPvvsM4wZ\nM0Z2nZ6eHsyZMwd79uzBlClTMHPmTJw4cQJvv/027HY73n33XUyZMkVxGhYsWIAtW7bg3HPPxdVX\nX43Gxka8/fbb6OzsxCuvvIJrrrkmYPnGxkZcddVVOHjwIGbOnIkpU6bgwIED2Lp1K4qKivDBBx9g\nxIgRAev87W9/ww033ACXy4U5c+ZgyJAh+Oijj7Bv3z6Ul5fjnXfegc1mi/0AEpGhMZgkItJZTU0N\nqqurcf755yMnJwfXXXcdPv3004jB5JNPPonHH38clZWVWL9+ve/z9957D7fddhvKysrw6aefKtr/\nH/7wB/zwhz9EeXk5tmzZArvdDgDYv38/vvvd76Jfv374+9//juzsbN86S5cuxcaNG/HjH/8Yv/jF\nL3yfv/DCC3jwwQdxxRVXYNOmTb7PRVHExRdfDIfDgddffx3f/e53fd/deeedePfdd/Hoo4/i/vvv\nV3bQiMg02MxN1Ie99957mDNnDsrKylBcXIxx48bh6quvxpNPPhmwXKQ+k8899xzKy8tRUlKC8847\nDz/96U/R0tKCCRMmYOLEiQHLvvbaa8jPz8evf/1r7N+/HzfeeCOGDx+OkSNH4gc/+AFOnDgBADhy\n5AgWL16M0tJSDBo0CNdddx2+/PLLkH0fPHgQjz32GC6//HKMGTMGxcXFmDBhAv7rv/4Lx48f1/BI\nxWfQoEEoLy9HTk6O4nXWr18PQRDw2GOPBXx+zTXX4OKLL8Y333yDjz/+WNG2XnzxRQiCgJ///Oe+\nQBIAJk2ahMrKSpw+fRpbtmzxfd7e3o4333wT2dnZePDBBwO29cMf/hDDhg3D9u3bUV1d7fv8448/\nxoEDBzBjxoyAQBIAVqxYAUmSAoJiIkodDCaJ+qiXX34Zt912G/7973/jqquuwn333YdrrrkGgiDg\npZdeClg2XJ/Jn/zkJ1i+fDlaWlpw5513Yt68efjwww9RWVkJt9stu19BELBv3z5873vfg91ux4IF\nC3Deeefh3XffRWVlJRwOB2bPno36+nrceuutmDlzJj755BN8//vfR0dHR8C23n33Xbz88ssYOnQo\n5s2bh7vvvhtlZWV49dVXMXv2bNTU1Gh3wBLo8OHDOHHiBMaMGYPhw4eHfH/llVdCkiR89NFHUbfV\n3d2Nzz//HFlZWbj44osVbeuvf/0rOjs7cdFFFwXUVgKe/Js9ezYAYPfu3b7PP/roo4Dv/I0cORJj\nxozBsWPHcOTIkahpJiJzSUt2AogoOV5++WWkp6fjk08+QUFBQcB3jY2NUdevqqrC+vXrMWbMGGzf\nvh15eXkAgEceeQQ33HADampqZAMhSZKwbds2bNy4Edddd53v83nz5mH79u246qqr8NOf/hT33nuv\n7ztvk+srr7yCu+++2/f5LbfcgiVLloT0w9u1axduvPFG/OY3v8Hq1asVHY+tW7fiiy++ULSs10MP\nPRTT8ko5HA4AwOjRo2W/P+eccwB4amajOXz4MNxuN0aMGAGLJbT+wLsP/20p2b8kSQHreAcTRVrn\n4MGDOHjwIEaOHBk13URkHgwmifqwtLQ02QE1+fn5Udd97bXXIAgC/vu//9sXSHq3+eijj+Lqq68O\nu+6ll14aEEgCwPz587F9+3bk5+cHBJIAcNNNN2HDhg0hwV5JSYns9isqKjBu3Djs2LEj6u/w2rp1\nK37/+98rXl4QBN2CyZaWFgAIOK7++vXrBwBobm6Oe1vez/23pWb/WqaZiMyFwSRRHzV//nw8/PDD\nuOiii1BZWYlLLrkEF110EYqLixWt7w3sysvLQ7678MILkZYWvniZMGFCyGfewHD8+PEh3w0aNAgA\nZKekeeONN/D666/jyy+/RFNTU0Dzenp6epRf0WvNmjVYs2aN4uWJiMiDwSRRH7VkyRIUFRVh/fr1\nePHFF/HCCy9AkiRceOGFeOSRR3DppZdGXN9bE1VYWBjyncViwYABA8KuK1d75a0hjfSd0+kM+HzZ\nsmX47W9/i0GDBmH27NkYPHgwMjIyAAC/+93vDDUIJxbeY+A9xsG8tXve2r54tuX93H9bavavZZqJ\nyFwYTBL1YfPnz8f8+fPR1taGv/71r/jzn/+MDRs24KabbsLHH3/s65snJzc3FwBQX1/v+7uXKIo4\nc+YMBg8erFvaT58+jRdeeAHjx4/HBx98gKysrIDv//CHP8S0PSP1mSwtLQUQvk/koUOHAITvn+jP\nOzdodXU1RFEM6Tfp3Yf/tpTsXxCEgHW8UxxpkWYiMhcGk0SEnJwcVFRUoKKiArm5uXjqqaewbdu2\ngMEuwS644AJ88cUXqKqqCgk6P/vsM7hcLl3TfOTIEYiiiMsvvzwkkDxx4kTMo4aN1Gdy1KhRGDp0\nKL799lscPXo0ZCDTBx98AEEQMHPmzKjbSk9Px/Tp07Fnzx58+umnITXOctuaNm0aMjMzsXfvXrS3\ntweM6JYkydcX9Tvf+Y7v85kzZ2L16tX4v//7PyxdujRgH0eOHMG3337rmwaKiFILpwYi6qPCTStz\n6tQpAEBmZmbE9W+55RZIkoSnnnoKTU1Nvs97enoCJrnWizfA2rNnD0RR9H3e1taG+++/P+Zgds2a\nNThz5ozi/xoaGjT9PcEWLVoESZLw6KOPQpJ63y2xdetW7NmzB+PGjQsJDI8cOQKHw4HOzs6Azxcv\nXgxJkvDLX/4S3d3dvs/37duHP/7xjygsLMQNN9zg+zw7Oxs333wz2tra8MQTTwRs6/nnn8fRo0dx\nxRVXBLwB59JLL8XYsWPx6aef4r333vN97v0NgiBg8eLF8R0UIjIk1kwS9VF33HEHsrOzMW3aNAwf\nPhyCIOBvf/sbqqqqMHr0aFRWVkZcf8aMGViwYAE2bNiASy65BNdffz3S09Px3nvvoV+/fhg0aJDs\nVDRaKSoqwo033ojNmzfj0ksvxaxZs9DS0oKdO3ciMzMTEyZMkJ3oPFl+9KMf+ebqdDgckCQJjz32\nmK+v4bXXXotrr73Wt/ySJUvwwQcfYMuWLZg9ezYuu+wyHDt2DFu2bEFOTg6effbZkH1cf/31OH78\nOP70pz9hxowZvs9vvPFGvPvuu3jnnXcwc+ZMXH311WhoaMAf//hHiKKIp59+OmRC9UceeQSffPIJ\nnn32Wfzzn//E1KlT8c033+C9995DcXExVq1aFbC8xWLBs88+izlz5uDOO+/EnDlzMHToUHz44YfY\nv38/ysvL8aMf/Uiz40lExsFgkqiPWrFiBXbs2IEvUjyj9gAAIABJREFUv/wSO3bsQFpaGoYOHYpl\ny5bhrrvuCukHKTdp+VNPPYVzzz0XL7/8MjZs2IABAwbguuuuw8MPP4zzzjsPAwcODFkn3AToar77\n3//9X4wcORJvv/02XnzxRRQUFOB73/seli9fjttvvz3stpLh97//fUB6BEHAn//8Z9+/R4wYERBM\n2u12/PGPf8RTTz2Ft956C8899xxyc3Nx/fXX46GHHsK5554bsg9BEMIG8C+99BKef/55vPLKK1i7\ndi3S09MxY8YM/PSnP8W0adNCls/Pz8e2bdvw61//Gn/605+wZ88eDBgwAHfccQeWLVvmG2Hvb+rU\nqdixYweeeOIJ7Nq1C62trRg2bBgefPBBLF26lO/lJkpRfDc3EWnu4MGDmDZtGubNm4e1a9cmOzlE\nRKQj9pkkItXq6+sD+vMBQEdHB5YtWwZBEEImJiciotTDZm4iUu3555/HG2+8gUsvvRQlJSWora3F\nRx99hJMnT+LKK6/EnDlzkp1EIiLSGYNJIlLtsssuwxdffIFdu3ahsbERaWlpGD16NO655x4OtiAi\n6iPYZ5KIiIiIVGOfSSIiIiJSjcEkEREREanGYJISwuFwJDsJpCPmb2pj/qY+5jHFg8EkEREREamm\nKJj89NNPceutt+K8885Dfn4+Xn/99ajrfPXVV7j22msxaNAgjB8/PuTVW0RERERkfoqCyfb2dowf\nPx5PPPEEsrKyoi7f2tqKyspKlJSUYNeuXVi5ciWeeeYZ2XfJEhEREZF5KZpn8sorr8SVV14JALj3\n3nujLv/mm2+is7MTzz33HOx2O8aOHYsDBw5gzZo1WLJkSXwpJiIiIiLD0KXP5Oeff46LL74Ydrvd\n99ns2bNRU1ODo0eP6rFLIiIiIkoCXYLJuro6FBUVBXxWWFgISZJQV1enxy6JiIiIKAkM9TrF//vn\nwajLFNlFZFoTkBjSHKeeSG3M39TG/E19zGPzOuMUsOZ4FkRJCPnule8O0n3/ugSTRUVFITWQ9fX1\nEAQhpMbS30v1/ZGdFnogvM50i7h6WAb+szRHs7RSYjgcDpSWliY7GaQT5m9qY/6mPuaxuX3T6ARO\nteCRqXlJ2b8uweT06dPx2GOPoaenx9dvcseOHRg0aBCGDx8edr3/npCLaUX2sN+/5mhHq5OvEici\nIiLykgBkpAko7WdLyv4VBZPt7e04dOgQJEmCKIo4fvw4vvjiC+Tn52Po0KFYsWIF9u3bhy1btgAA\n5s2bh1WrVuHee+/FT37yEzgcDjz99NN46KGH4k6wxFiSiFJEj1tCtCLNZgEsQvgWG+rbdtd044uG\nnoDPLIKAW0uz0M8eeViE5HdDlaTAf8sReB4aloTkvoVGUTD597//Hddff73vRFq5ciVWrlyJW2+9\nFc8++yxqa2tRXV3tWz4vLw9vv/02HnjgAcyaNQv9+/fHfffdF31aoSjnKU9jIkoVe+u6sWxPM6wR\n7gCiBFwxNAPLJien6YqM772jncizWzAqt/d2/vaRDlxSYscFBeFb+gDgqX+24Z3qzrP/6gd8Ux92\n2e8Nz8D/TOJ5aFSShKQGSYqCyUsvvRSNjY1hv1+zZk3IZ2VlZdi6dav6lIXBiklKNaIkQQCf+vua\nNqeEywan49Fp/cIus7umG+8f6wz7PZEE4DuD0jGjJN332cenuhWt2+IU8ejUPFw+JCNin0meh+aQ\nzDuIod7NHe1A8F5Lqeh7f67HfZ80JTsZlGgKnowtArv2kDo8bfoWb6VEshhqaiAlovcwIjKXLjdQ\n3+lOdjIowSREf0AWAIiJSAyZVjytm0ofVFiPE59WpwinwiLeIgD902Ov5/OcB8nLKUMFk9EPA09p\nIkod0Uo01kymFpco4XRX7+NBtk1Ark37BkI97pQ8D9XpdEmofP80cm3KcqXFKeF/L81HWb6KUdlG\n7zNpKDyhiSgFKKlREsAiL5W8cbADrzk6kGMT4JaArDQBG2cVxLfRMCeI4lpHBQEIu5ip5xIlpFsF\nvH11oaLl7/+kEd3u2K/6JI+/MVifSQVNPixYiSgVKLnZC6yZTCndbgnzR2fhjSsH4pkZ+XCK+mSu\n0uBP6d5571UvUcdNkpIbTJqvZpKISIVWp4hOV2DRniYIGJCRrGfq6LcZCwSIjCZThh61R+H63mp9\n1vAsVC/Wml01x1pJH2w9mSqYFASe0ESkzn/uOgOX6OmH6NXQLeJ3swswKMua8PQoKvxZ5qUUSQrM\nc+Zt6ktk8zNrJs9itwwi0kunW8LGywsCRkresb0BPSr6J2nB0ywVudSzgAFHytH4RpeIYEUwWDt3\nh0vEPxqckCQgzQJMLbTDatCOnYlqfhYl1kwqZrDzmYhMxC0i4ttmEk3RABzBc5Og1BCQlcaMfcIy\n0mn46ake/ParNozpl4Z/nHZizXfyMSrPwOFMAvI62QNwDHX09Yiq/3y0E0db3bBagFvHZCFHh2kY\niOJlpII6VbklCdbgMibZN/Qo+9draqB1X7fhVEfgxHdXDcvA9KL0MGuQFoJrqbTIW7mar1hOayXL\nJvsyCeaWJEwZaMfyKXlYvOsMXAbuV5ywIC/Jh8B8kVWMB+z1bzsgQsJfjnXheBsnhk4lLlHCsr1N\nuP+TRnx5xpns5JDBuUTPgBt/yW7tUDI1kB6Tlv+puhPnD7DhouJ0XFScDhHAvnpeQ3pLZO2Rkvgq\nlknLjRSu+TfpWlh7D8DzQhfWTJ6l14G4dnimp3+FTts3EpcooblH33dm2C0Ccu3Jfw7pdkvYd7oH\nkwvsONLqwvkDVEzyahBGe/JPRW4ptJlbQPKm3lGyW0Hpgir2fdngDOSf7T/a0OVGY3dfKCGTzxsE\naXrNJ6IZ1UCnh4TemjCjB5Ox9plU/TYjsM+kYqpGcxv4JNPDC1+14U9Hu5Ae0p6nnZYeEe9eMxBZ\nafEFlMfbXBiao/4UlABYBQEFGRZDFXRqmDz5itS0u1HflZzWAe/Nxkid9JXcZCyCALFPnB19Q6LK\nKe9p7mh2Yvvx7oDvZg1Jx7n9ex+8FV0RxrlsAITWTCZpDJ0iiaox5OsUE8Ro1fR6aXdJuHd8Dq4b\nkanbPm54rx7OOCs/RUnC7TvO4K2rClCQEd+0LJwyyhxW/r0F7S4JWWnJKfC+Myi0P2Ayzx1F7+bW\nqc9kaHOrAIlvAdedPvNMygcrEoA9tT34d7MT0wvtAIDP63uQmSb4gklJ4dlvsFgSktQ7xZfVDHOx\nxvgQq+rnJPkQGCqY1OvVYoKQ3OasRHJJCB1koDUNbnDemiJXnPcvAanxoGC0wloPbknC/3dBLsab\nuDtCounVZ1IvHS4Rbc7oV+OAdAvSLH3hrA/kCfw8v1vPX++/7fH5Ntxamg3AMz2WWkoDz0QQ0fsb\nrRaj10zG2Myt8sQQ41hXC4YKJvVg4HNMF25R0r2Q1jJ4i2c7qZS3qfRbwukLvzEWSpq5BQFo7RGx\nu6Zb9vsB6RZ1wXlQZmjVN3PZ3mYcaXXBFqEMandKWDA2GzePyQr5zi1JWP9NO7pc8SUmxyZgwdhs\nCAbq1gAA0GEuwHDnkQT5LA3+TMkxSsZR/PvpHizf2+xL7zXDM3D/hFwAgCRJsJxNd6r1mYxnP8kc\nyWCoYDLaSR1X7aLByhS9JKJmUstaXs3KgL5Q7WxyRsyhZLdYRLuPl2RaUdrPhvePdYZ81+MGDre6\n8IerBuqUutj1uCWsvKg/zssPH+Cu+7oNPWHu/h1OCZsOduCu83LiSsezX7bhjnOzkaQeFWF5frUQ\n9O/4qe0rp/zd3ELCr5OmbhFTC21YPiUPVbU92HGiy/edf82kBQjbzN3hErH9eLdutfsCgMsHp0cd\nkJqI1yn6EpQkhgomo1J5oFKlKVQJlyjpXoAKghB3k4cU8hf1GxEg9Im8Je15yoUkvQFHwTL90y1Y\ncWE/2e9Od7lx14eNqvftf4PTqu+o0m2EW04CYLcKmHdOaK1lLNb8qy2u9fWiT59J5V/Gs+9kXCVp\nFgFZaRZkWoWApmz/PpM2i4Dnv2rH77/tCFm/xSmhyyVh0kB9utZ8Xt+D/nYBMwdnhF0mUceNk5b7\n0eNA9JUgY3dNN/5wqAOHW1y6Dr4BtMkn74NkvPkjCByAYxo6NPHFy/NglBzJLvz1YJTfZNTKA/8g\nXtNrIVw7t8x+JDVVjEnIVP9UWi2eN1h5+Y/m/q8JuTjZHn6WiOG5VhRlxjfIM5yHP2vWfJuqpwZK\nUHN6OIYKJqOJ50B5mrOMWLxo40CzE4OzrFg8LhtlEZqYtCAg/j4q3tXjGYWXurlJfUKc5VE8AVNw\n0Jfw4CvMzrQKRhPdfUGUJLSGGXhks6B3GrWgG75eafTuQ7tm9OTwDbIRBLj9DpYoAd7wcHC2FYOz\n9QkWtZCwPpPgAJyYqBrNjeTOv5Qog7KsuKDArvt+jFQT2Je6MJidUWqtjCLZ88Lp0hKkcFCR3tdr\nosuoNw92Yv03bciQ6bDe5Zbw3rWFsOpYCy5fMRncQzM+iS5jA2omg+aSlCAZZnBVtOOiJsgz4/3M\nVMGkmlNHCjgBU5dk0ju1ZqO5UzlzSTfJHICjSU2CysTLrabZYYjjNyW7qU6tM91uLBqXjVvGZId8\nd8W7dQHls+ajuVV+56UkOckeqBYcTIp+fSbNQM+kNveIaOgScarDndRrJ/nvxPOj5CLjaO4IEvQb\ntShYtOozCSirhTjZ7sainQ0BIwKNpC+cnkZ83kl25UZ8XXfiTHySfnvUlgQN0pXo4OfNg52+V1OG\npMVv6prga0CvZuiAwVUBnwcuqfjd3Em+TqyCgG63hIYuNxq63Gh3Jfc91F6KYhad0/CrfS1YtrcJ\nW492orRf8ubwTfmaSS3WpUAWDZqQvOvHW+ArzdfTXW4canXjaFtyXucXDStWkyeZA3CMsA3g7E1R\ng40Z5YEh0c3cVgGoCDOi17+81KPmNVwZKkF+nEA8/WwTym+H+ekWNHaL+E+/2QsWjg2tBTYkNQcu\nhnW63BIempyHyQP17+IWiaGCSSUXWezTeEgyf6N4GWEskzcNSu6DvYW5ARLeRxmxK0ZS+9vG+yAV\nZ8CkV1ZE7TOJyNehZgNwEhjaevtuy38nBA5YFAL+0Gb/Cjcmt1iyax0j8aZtcLbVUPOp+tOjz2Qs\n3FIC3nqngLmCyThyJNl9PhIhUeeTFk/93oeCuLNEUJa3sY4+b+kR8fxXbXG/pmv+OVkY3c9QlxkF\nM3OfyTj27U+roDru7i8apMEjsQdWQvg+fJ6aSU9gq0d4K3fMlHaBUHq8DRCrmFa4d6eHE+uxdksS\nrAZ4IugTdznvXISpLJH3w96n/vhpEuDrkLcnO9z4a30PFsTRlPL+sS78q9HJYNKP0S7DZJYL8QYW\n8QaAuozmRnzHVKtm4ERXHkhS+N8toHfwSCIHGHl/fkg/SbXbS/BDV6rU/eid527RMw9nsim+y61b\ntw7PPPMMamtrMW7cOKxcuRIXX3xx2OW3b9+OX//61/j6669ht9tx0UUX4fHHH8fo0aPD7yTKEVc1\nmjvM31NRwmomYZwBOEp/c8zzYkpAP7sF1wxXPwH8V43OlD/nYmHAVm4ASewzmcSRy8HXbyKb+wVB\n0L27SaL7TPq/3i+YRfAv7xI7cCT4mpNt5lawnWRNB2fE8kKd2H5JLJU1RmnmVhTPbt68GcuWLcMD\nDzyA3bt3Y/r06Zg/fz5OnDghu3x1dTX+4z/+AzNmzMDu3buxZcsWdHd346abboo7wbw5G4ExXl/o\ne/JG9PNCy9HjMUn1vhUml9Q+k94ExCOOxCe7Vlb+c22CrUTmqzcwDttnUgh6mD174LU8/rKbkuS/\nUzNdXjJOlVQqOWPJ61jPC7ckIc0ATa+Kgsk1a9bg9ttvxx133IHS0lKsWrUKxcXFWL9+vezy+/fv\nh8vlwiOPPIKRI0fi/PPPx9KlS3H48GE0NoZ/l6yyjttKUhy8XupPWZ7ImMVoo7mVnBexNstr0Z9N\ni3eGd7kk7KntTomBQ5GaApPFYMmJSTy1RSHrCdqUIZIUPRhM2DFP0CUTrjnZy+K3THBNoTbHPP5t\nKNpPYnZjKsoGDeunwyXiSKsb2bbkl2RRg0mn04n9+/ejoqIi4PNZs2Zh7969sutMmTIFNpsNGzdu\nhCiKaG1txWuvvYapU6ciPz9fk4QrFdDMneJXQ6Ju1Jo0c/v+VL+hWEZze1/rmshTwCL07letfzT0\n4KG9zWgJ86o2ipNGQZQaRm32j5eSR/eIh1yDgiyRzbISIt9IBUHwvTZWr64NwYfM+2+5hwbVknCd\npML1oeY6V3qoO1wS+tsF3d49HouowWRDQwPcbjeKiooCPi8sLERdXZ3sOsOGDcPmzZvxq1/9CkVF\nRRgxYgS++eYb/P73v4+4r6hPtHEUEEarEdFaQq9zLY5lgvtMxhowaHajj/MH+nfcN7sU+Amaijew\niK8pN3BNrYpHJelJRFGc2GbuyPeXkJpJjacGCt9lQMF+FB6kpDRzm6TAiNoqpmPfaFECbAZ5FZAu\nY4Dq6upw33334dZbb8XOnTuxdetW5OTk4M4779Rjd1F5D7VJzk3DS3o/s2ACEC1FYhKCMm2mUAr8\nk7SVzHM52TWTenX+iedNZlodk0SO5hajBAshfSb9aJFEuWPmu+fJDLRSvx+WQsEUV1LF0mcyhoXd\nonFeKxl1NHdBQQGsVmtILWR9fX1IbaXX2rVrkZ2djccee8z32fPPP4/x48dj7969uOiii2TXO3bs\nKIT68A2DdY02NHemweGojZZsH6czF4ePHEZnRxaOn2hEXpMx34ASr8bGdHRbAAdO6r4vZ08Ojhyp\nhjMjtkZch8Ph+3u7WwCQh+rqo0CmusbgZpcAtzsHTY1NcKeJcEjhf/vJ1jQA2Thz5gwcjpqo2z7a\naUV3V0ZAmmNOX1MG7B0iHO6eKEv2g8vpkt2XN90HDx1CvzRjF+bRjlV3dw6OHW0EYjxv9NTdlY1j\nx5qQ3pD4cuF0gx0tLgscjlOq1m93A253nqpzVBTzcPDgt/C+AbD+jB1N3ZHTomQ/3T05qK6uhjtC\nHjecSYdThOx12OT0XNPxXHcAIIq5OHToEHITcM04RQAInw+iKxeHDh9Gs01Cc3Mm6pwuOHqcnt/q\nCv2tx7os6BEFQABGZLiRFiVY6OrMxrHjjcg803sOt7dn4cSJRpzptMJmARwOT9nY0JCObr9j396e\nhZqTjXC0ugCEz+PjHVZ0xlkexupUsw2tbWlwOORbQI2gtTUTNUIjHB3OsMvUdFvg7MlSfOzaOzx5\n52h2RV22rscC0RV926WlpYr2HY+owaTNZsOkSZOwa9cuzJkzx/f5zp07MXfuXNl1Ojs7YbUGtuFb\nLJ5SSxTDFzLDhw+P+G7Jf1d34nSjE6WlQ6Ml2yftyGmMGjkKWc0tGDJkIEoLk/vKIb3kO9uQYxNQ\nWqr/K6bSjzdg+IhCnJOnfP5Eh8MRcEI394jAgdMYNnw4Svure59oQ5cb1qONyM/PQT975N9eW9MN\nHG/GgAEDUFqaE3XbPWecyGhuRWnpYFVpA4D87lYMzLSidHRW5AW/rkOaLU32gj91Nt2jRo1CQUby\n+8WEE5y/ctJPnMHw4QMxJonvjw2WeaoRQ4cORGlBb7nQ3CPii4bwNwettLZ1Iz/Xouh8lF3fKcJy\nqEHVjUI4UIcxo8cg42yk8q/DHWhvdaO0NFd2eSX5CwD24w0YEaVsKJDa0eOWZH93facbacca4775\nWQ/WY9Q554R9X7aWulwSrN/Wh02zvfo0PnEWIVuy4KTYjRnFWSgdnukpv4J+a2uPiHv+chpj+6fh\nWJsbD07Kw6WD0iPuP+NUI4YFncPZDU0YPGQgGs84Ybf2lo0FUju6/I591tnlSovTI+ZxzxknMlri\nKw9jdfhYJ44KPTHd7xMtt7kZJSXpKB0i/ypNALC1upBe16z4nM4+fTZPiiLnOwCkt7mQfkr5tvWk\nKBpYsmQJ7rnnHkyePBnl5eV48cUXUVtbi4ULFwIAVqxYgX379mHLli0AgKuuugrPPfccVq1ahXnz\n5qGlpQWPP/44hg4dikmTJqlOrOqmiz7Szt0X55kEkj+iLhwtmlB9HffjTk3yeUb6GqRNxk/wsd12\nvAubD3VgVAwPS2rNjBIo6EV2nkmNTjJFs3JE+l6DUySRzdzRmubvOS8HNe2eWsOrhmZgml+FRnAS\n3RKQaxOw5jsD8MjnzXCp/BHh5pY02fiblBjroOd5KBpkjklAYTBZWVmJxsZGrF69GrW1tSgrK8Om\nTZswZMgQAEBtbS2qq6t9y8+cORPr1q3D008/jWeeeQaZmZmYNm0a3nrrLWRmhp8EWs9jYpDjrZuE\n9gWEhv1ntJgaSEHfRElFUBbvOaPpqPdUiCaNSCaT3SJwaUk67j1fvpbOKOJ9WNHjRm2U1ylqWkZF\n4ZkbM/zBrBgcvtYqdFu9lJYf4ebmlCT546m6H2WCyyAzFHlKKzLUXmuSJOH1bzvQ7pIwqcCGC4Nq\nK03VZ9Jr0aJFWLRokex3a9asCfmssrISlZWV6lMmI97R3OxArA1BEHC83Q1LDFfI8S4LrC29fUBy\nzs6LFU/vuVhyM9b9aFJjqsE55xs4pEF6ki2eQlUvcskRJSnsnIGpInTKGEGz8jHaoUtIrWEC80+M\nMppbrbjm8xVk/xqSTqXbT94bcFL7OozGKQLrvm7HZYPTcaLdHRJMipBiug/ryVAvDdZtdOHZP1Ph\nhhxJok6p8/LTsOHf7TGt09OTBfvpZgBAQ5eI75/j6UeoxaTlSrbja1aPYX/x10wKhqmpMQKj/pbg\ndIkwztN+JIlsylUq2SPUvRI6NRDU/WZBZpLT4GlklPwGz0OafAqMdn6kmi63hDcPduBUR+AAvnP7\n2TCtqLc7Q8znh1++WS3Adwal48OT3SGLNXaLcMX8rmB9GCqYjEZNAdE715YRijj9JPJ0+snEvJjX\n8e/c/cyXrehxx59i/0nLo4m5ZlKDUliLG5qaIJiUkwvIJMkkwaSGaUzoPJMRarm0mpMvkdmn1/ki\naBQRR6uNVJL0ZEyhZYYyr7rVjZMdbkwe2Bs4nupw42/1PTjTLeL9Y53odMdWe+i/qPcQhKul7nBJ\nyDLA228AgwWTetfWmuDcjItBaruj8i+Y4s0TQZC/Oe040YUn/9nq+7f36U3p/jy1DfEdUC2ahlKp\nmduI5K4ZEcaoXVMirj6TGm7LaITQSj/daFkbK6G3zVyAsofgiPNMRltX4TFKVi24Wa7Du8/rnZng\nr/U9eN3Rji/PODEyNw2XlKSjMEOfWQUkCSgyyCwfhgomFVFxQvtOyFQqLYNIhmlgis6C3iDpHw09\naOwWYbMAFxXZVfVVk3tqbugSMWtwBn5Y1jtd0NtHOtHpStxJoM0AnNQZzQ0Y8wwNPrZmqZn0UHdm\nBL+1RbOfG2f/QS371Sbqmtnw73ZV54vefUvNXmaYI/3yqZTgKbtH5NoCRu+r2aqA8OeCkfqhmyqY\nVHPMfE2hBjnghIB31X7d6MTXjU58VteDV2cXxPSOUSnsPzz/tFuBXHvvE2HMUyjEec5o8gYcrapw\nDcAMzVbA2QE4yU5EEmiRP4qauePfjSH24bXteBd+NiX2rj+A/PHypt1zz1I0nDvsNhRR2s5NivjX\nCmtVH2kRBIgyGW2kKiRTBZOAunuqICSnz0fiGeW0iswiAC4RGJBuwf+b3h8AcPO209CgG6WPXN+r\nRB8dTfpMBv1pdkZ7qJMdzQ3AZrSEyhAgqD4vgm9Ccj/3VIcb9Z2egQXHO6zoPuPE2P5pUd8FrGi6\nlDAJ1+rmmOhm7vPytZ+IP578BeT7lKs9tgKATpeErxt7J/PPShMwIlfnEMLwl2H4BKod5R9y34q0\nDQPdGAwVTEY77vGW7wY67toz0Y+T6wuktrO5AH2mrdDipqZFB3pvdwDRLNV6ERjpKdpLLuiQJEDQ\n/8UphhN8hv1qXwtanSKy0yzo7MpA/ckm/E+UN7IorZnU+2xO6GhulYOGot7vEP6d3gH7R2z3RjVF\nSUGGBf3sFjz9RW8/9APNLmy7rhBWEzx46Sf0YGoRvPu27vdAwGbuGCg5KLHOhdY7mjv1meU3em/g\nwRed2sJfbt1wndITPbl7vG+hNn8IaWxy545okj6T8ZzPSlZzSRIemJiH8QNscDhO45WmIkVvZInr\n0GnZOqHdpqJT+aMjlVvxBAnedeXK2ZBlFWxvYIYV//ud/IDPZr1b5zn/dLxWTHAZypIQ3/yjISPu\nw1SYGOkB3VDBZDRxHbQENntQZAIAtySFDACItfbNfxCBFlP5hGw7zm14bvbK0tXhkrDjRFfI595m\npVQ4dc3yG4xUQEei90TSat6UouR0jzaZvyavU0xg1aReu1H6E8Kdr+HWlQL+rj71eh9ic5QX4U9W\nteWI/zrebYStmdTgPqUVQwWTWhVWfZGZDotFCG2+ieeNI/Jrhl5liX6LgyAIioPJCwvt2F0TOimt\nl5ny12yCj61bMs5bJXSjYDR3cBOaIHPdyq8VV7I0YQGw5l9tyEqLLx+tFuCHZTmo7XAjI03AyDB9\nBLU6W/wfkLXo96l3MyjvxzLN3GfzTctZIcLfu4yTAYYKJqPTOuBILWa5/8k90ap5yo325BfPPJFa\nFMICAHfUpTyjzJdPyQs7sOHb7Q2pUWjH0eyjF4sA/OFgBz482Vsr/K8zTlw9PDOJqUqOkL6jUNcV\nJXoeh3+qC/ee6Vj9dFIeajuUXH2RrfumHbm2Drx3rBNtTgl/umYgstICO9TGUzsU7XgqqpmMYf9y\neRPPoBy9Gay4iEk853LgtSiEvfbYZzLBfNXEyU6Ijsz02yyC4OlP4veZ0s7mcvynGvKSD74ESHH3\nYlROAPBNowubD3dEXC74WMhuKAUY8RxdODYHB/3eGQ8Apf1sKC+OfW44MwkJFGXOsZC5KBXUlHm2\nm/wT1v+NJPF442AHXKKES0s8r7NzyxQfWt6Svq+QAAAgAElEQVTQ/Q+vRZOaSQnBE9T4N23Hs/1E\nd7MwEwne6ye+E8ObV+GuPc+DRPKvN8BkwaRRInCKjzdwDL5Rxcr/2upySWjq9pT0mWmCIfq9TS+y\n40y3iKOtkWtI/qM0K+IcmOEehP7Z0IMPIzSNe2VYBSwal22IUZfJT0Gg8QNsGD9A+2ldEkHrAWVy\nm/LPL0uYZaJtQ26bYfvzGagPGBA4iC7RTY0xVYAEd+nROC3JYoAiSzXVb9IKU3ss17/VCPc5L0MF\nk8pGc8fGf9JyMz/pKGGUkyoaT98rKaRmUm32FGda8NzhDrx/vAtu0TPn2+SBoQGCgNh2Eu/xHJdv\nwzgN5p8LV0PxUU03TnW4Makgci3Mum/acNPoLPSzJ/cMSfHLL+HiftOM/7aULCMoG1BmlnJICU+/\n57N/h7bncLhBQsEDMNSSJEmm63ho7qit2dL6YSZVeI9mcM1+PNuLeKwNcsEZKpgsSI88uZvqvh1n\nV0zl895Mv80iyM8zqbaZ+5rhmbjmbB+3fzb04IWv2+NuejJaISmXHLcETB1ox/fPyYq47isH2g3z\newxS7qUMLbM1eFuhr1yMPom2kqliojePGuss8XZDCTuiFvo0NQpQNoAv5topSfavqnA0d3ha1hqG\nu/ZYMxlGti1yMJmVJmDnyW58cqo+7DLFmRZsmFWgddJIQ3L9I1VdEDE++cXax8coTSzhkuEWFb4i\n0iC/wygBbaqIt6YsWn+ukEFycTzwBWwn/k0klISz05iFSbheTfOWGMqr4P17g9uQEflaJMy7LcHb\n9Gq2HNVXvKO5Q/JSCH8vMlK3EEMFk9FcUpKOrdcUhp0bq9Ml4T+2nwn4zLukUQ64bkx0o7YIwLfN\nrpBCTrNgQ4PtGOlwhjs2LkmC1Qyza5M5BI/mlumKooSS5cL2mYRxHuKA3t8SaRCn2jTLdi0IekBW\nOppb9vNwyytJiAIGyiZD0iLM9u9iIfcgZ6TrxVTBJOAZXBE+i0TIzvukYj+SJMU9Eovkfefs69hK\nsqy+z4QwL7KPRO5i9XZUDvdu7phqJmNKjX4EQZB9gHJLymomte7rpZ4xUpFSVBxSuabTcH0m/efb\nlJsfVoPkKEpLsnhrY73PbFrXrkfaXCwTrwffqvy7dul3PI2UU8kRadBa8LiAeCR6jmQ1UuoNtJH6\n9CjtfwIALlHC5e/Wo7kncdPIaMEsse+Q7DTcMiYbFYMzfJ9pd9FF79elhNEuXNk+k6KkaIS2kTrK\nm+UcNQOtj2VIn0kFy8hRlKwYa9OSxT+eCzeiVkv+wZ8AZa9jVVwDCW3PmUSUK2YtLiR4aw3V/QLJ\n789I1Wds5tZJuKdrwHMRfdviQlZaT9TttLs8l3CXS0I/k0w3Z7RCOFZq+mNFmhQ2XPW/4l0Y6IAK\nAA61uOAKurM0douwmuhx0ECHNGWoOaayNfphLiT/j5XMe6hkBGu0Whaj3By9RAlIE8IPsdHrhq7V\nG3CifRbPwFZdB+CYoMCIdOzUnhdy64SdZxLGeUBPqWASCH8CThpowyc13fjXGafybWmUpkQxyDml\nilZNscZp0tXOxIE2vH24M+RzAcDQbGvoCjLL6V2jooReo177Kq3P9eBzJHQ0t/7XlhEDCN8NO8xd\nO54+k5Fqg60A3qnuxOf1kStATra7YVF4XQUvZeTR3IBxAqVwItUKu1UOwJETrpbaSMOfUiqYjPSk\n9P1RWfj+qMhTqPi7edtpA9x+lTNTWuXE0j/Iy3Pjka9+DFv7onAfWr3WTQv3nZ8b3waMXiJTQoXr\naxwseNJlJV2FlDaDR1zOQKert8yINgBHDzePycLUwuhNYzeNzsLIvOgPlVoTAPPfeHT0TZMTc6Du\ntazeyyzg8MqefMbJgJQKJmXFc7CNk08pT2n/oKjbMUFH5UQzSm2tkfr3pAKtj2VIURn0b6XXVirl\nsadc6q1TD3c70eM3F2RYUZChLkj0pUem24FWzdx6M0KZFY1skzQASEB+uiVgkGk8LGEGYRqptSf1\ng0moO9hmDEqMcUqpo7Z/UNhKN5ltxRJUGakvCpGW5CcWDz3ZPaO5A5fQ5IEP4a91IzXbAYFpDXtP\nUHujkCvzFPQ5VUpJeWrkd3MDxjoX5ET7/ar6TPqvdPZ8sFmAA80u3LGjIWDZY21uXFJsjIEdKRVM\najm6zCj9zJQyUG23KpqN5ob/SDqNNmpyRhrNbfi7g4l4R4rqNY1ZcGCn5IFPq1fIGYZwtrk/wm8y\nclkjG5xreo/Uj1GKrFh5p3LTssw9t18aXqoYAHfQNu/ceQaNBpl1JrWCyXhG7wZvCwa6AfcBAjzz\ncmmxnUhNUTHVTKZI5GOkWvbUOKLmp2Q0d/B1ZAHQ7ZbQ7gx/8wruZ6lo50H7NNI54i1PBIQvW7Ss\nTdVqW7G+GUzVPsB7ZCTxPGT4H1bP2C8BQ3PkwzUt3kqlhZQKJgH5m6a6DDVSkaaQCZPsJQgCXvu2\nAwOOdfk+qxicjguL0sOuE6ngNVpzGRknoE01as51ueXlemT5l52FmRZsPNCBVx0dYbebbgHSo8yk\nb8br0juY20znsK+Fxu+zaP0nKX7+lRbxnutK8scoAX1KBZNaVrubreAwu7vLslHd5vb9e9/pHnxa\n2xMxmJQlyP7V94HiC4+ZrwszBhJGpqbMk33glvnMU8vY+80tY7Jxy5jsGPemPA3ez43UZOxpMfH8\nJdKxVtU3TuYzrWaRiLQNzYo2vfPJKFGSSolKfXDTd7IonvJ43bp1mDhxIkpKSlBRUYGqqqqo66xZ\nswbTp09HcXExysrK8Itf/CKuxKqh9jhbVK770jdteGhvk++/x//WrEnzrRIGKoNjNqHAjutGZPr+\nmzDAFr1/FuSnOJEAxW87isRIN7V4GKU5yghpIA8lXYJ0m4xbh23qJeStakEHyVvOGPHVu55yEJEf\nsOOQiFkizNrVSPL9L/7tRDsCWtzrtKCoZnLz5s1YtmwZnnzySZSXl2Pt2rWYP38+9u7diyFDhsiu\ns3z5cmzbtg2PP/44ysrK0NLSgtraWk0TLyvMKN6YqRxd/GFNN+aMzERxpmdKgEc+b8b/TALSdZ4G\nzBink3YsANwqMkCr6TtS6XgaqZbdgPdcU/Od7zEcV7nrI+zqOuWXQe5/0Qm971iWu460/hmJOC6a\ntd5B3/Sa5RSJJBHlnTGG3ygMJtesWYPbb78dd9xxBwBg1apV2L59O9avX4+HH344ZHmHw4G1a9ei\nqqoKY8aM8X0+YcIEjZItT8ubptqnLrcETBlox4hcz6FV8goyCqXkHdvhbqJangOkHV4GOtDwJA0u\npyTE0HQVg2hJNtJ1570P+AbgBL8lSINty3+jHb2Op9lmPEkoKb7Bv77NKHhQNM0AHKfTif379+O+\n++4L+HzWrFnYu3ev7DrvvfceRo0ahQ8++ADz5s2DKIqYMWMGHn/8cQwcOFCblMtQ1qlc+bbUBIFu\nEfDvf57IWiEjFcLxsgjqLhLvk6AEz0SvAd8httHcqSIRzVGRdLsliBIfqvRgswCLdp2J6doX4XnX\ndIAwo7n1qlkJF4QY7RwR/P4Md08wbLmrMK2q05+Aajejt2REGvCbqEGgRrlmogaTDQ0NcLvdKCoq\nCvi8sLAQH374oew6R44cwdGjR/H222/jt7/9LQDg5z//OW699VZs27ZNg2SHl+wBOG5JgtVvpt/e\npzd9TyujnFBaUVqjq+dRNXg5FpsknR8n2l24Y8cZ2C2A3SIgM8pIX4rNK7MK0OGKPXOz0gLzId0i\n4JNT3Zj/wWnfZw3dIuxavVzYX4QIwUivMfUSfcV3aMr06FeqZQAld+fxL1fjvW/oWaykwi1NbVYq\n7Qc5IseKMf2MMY5al1SIooienh688MILGDVqFADg+eefx7Rp07Bv3z5MmTJFdj2HwxHXfj3Hv1/A\ndkR3Lg4dOoTctNhOzZ6eHFRXV8OdEVuPhG5nLo4eOYw2m2d/kpiHg98ehMq3YinW3JyB+m4RDleP\nvjuKQyz5W9dkQ1NHGhyO8P1sa7ot6OnJCtjusS4Lurqz0NDQBqsAOBwnfd/VN9rR1GWBw3Eq6v5P\ntKahvd0Oh6NecZqNyuXKxeEjh9Fm17d4lsvfY10WDLZn4dFz2gAAp6qbEP3ok96az/7nVSQBj58T\neOtLE4D6o83wXgHxls9edY12NHdZZK/tY10WdAdd08nU1ZUNqVtCk1OEy5mGw0eq0Znee0/wxPF5\nqtLb5QbcYuC6tT0WODX4/W1tmag51YjmDivqOnvvC/Vn7Gju6S0DOzuzcfx4I7IbPTNpxLJf0ZWL\nw4cOo9GmT7kSnFYjcjlzAVgCjtvxTis6uzLQ4xZwpLoanfbYYoj29izU1DTC0e5Cq0uA6M4Jmy8P\nDvFUvDgcdRG3WVpaGlMa1IgaTBYUFMBqtaKuLjCx9fX1IbWVXsXFxUhLS/MFkgAwevRoWK1WHDt2\nLGwwqckP/qYuYDuWb+txzjnnoH96bL1/0o83YPjwQoyOMeoXDp3GmHNG+d6pajlQj3NGj0a2TY/e\nR73yOlpQlJeG0lFZuu5HLYfDEVP+HjrWiRP1PSgtHRp2GXurC+l1zQHbFZqdsJ9uQf6AXNgtAkpL\ne6cy+epwB1pb3CgtzY26//pT3ch2dqK0VH6AmZnYqk9j5MhRGJyt3xNN2PxtdiK9oRWlpYN02zfp\nL9brN5Kvj3TiQE03TueF3j+arG5kpHcZ5nzJrGtEulVAfm4a7N3dGDmyEMP8Jo92ihKEf9erOjYd\nLhGWgw0B62a0uWA/1Rz3sc5taUZJcTrqGpwozrP67gtfHO5AZ2tvGZhZ24hhwwaitMAecx6nHTqN\nkaNGoTBTn3Lly8Md6GhVVl4nS1r1acApBhw3V6MTGU2t6OkRMXLEiLCTjYeT09iMQYPSUTo4A03d\nIqzVDQkJBuMV9VfabDZMmjQJu3btwpw5c3yf79y5E3PnzpVdp7y8HC6XC0eOHMHIkSMBAIcPH4bb\n7cbw4cO1SXkEwa8XU9NsoLZzsVuSYA3adypU1yeaRRAUTQ0ULOJUEmdfc9XXJLujvNGaLSm5xvRL\nw6enurHlcKfs9zNKjPGuYaC3n2TvABxzUHrNxTWASOd7m1mOdTD/8yTeN+CY6RgoCpmXLFmCe+65\nB5MnT0Z5eTlefPFF1NbWYuHChQCAFStWYN++fdiyZQsAoKKiAhMnTsSPf/xj/OpXv4IkSVi+fDmm\nT5+OyZMn6/drztKih+LpbhH/+WEjcm2xbanTJQW8ASKhBZDReyvHwAJlUx6EjCPwL+DiOByJ6jyd\nKMnqUyvqOIiDzOm8fBueKO+f7GQo4j13hbPRZMiI9zj7TOo51VBvORh4PyLtRDqefW1WEUXBZGVl\nJRobG7F69WrU1tairKwMmzZt8s0xWVtbi+rqat/ygiDgjTfewIMPPojrrrsOGRkZuPzyy/HLX/5S\nn1/hJ6SzscrttPV41vzd7IKY1kuzAJlpZsl+4xIUjOaONUDqq7mSzN+dakE59S0C4HvpRLjZQrR+\nWNJyc3ItEsGfqN2f3vNMmqFaTjaJZx86PGVf7EfXrA/fihvzFy1ahEWLFsl+t2bNmpDPioqK8NJL\nL6lPmUpyNYFq8sa7jTx7fH0dhQRWTZr0HJSldmogwP9CVk+vt38kRxJ/iQluCESRBM4zqfO+NNqB\nEObvIfuLcz96Hw+zBlZe8SbfTPchY4wp15j/RJ9qT/ZkT34eq1S7Z1sAnOkW8bf68KPTT3W4Qz6L\nVIiaqc+TlpLZb1ePmhuiRPI+1Aphmrnjo8/ElVZBwEvftKHDJWFcf5uWm+7dFq/riOI5N8x4n0q9\nYFLDE1yLTfXVACZew3LSYLcAv3O0R1yuvCg94N/ewEmL+dNYWMZPr7eoECWCt/wWIlROqG8m1q+A\nuWd8Dk62ex62g+ch1LL2s4+3cssSwv4jdmYaMJpywaSWM/xrEkwonHxbC6kU+4zKS8OTl+THvJ63\ngJMLBuVqFvqCZD7QxPreaCIj8XZT8jZzBzNqn8n8dAvyZabDC9m2wdu5zVp0+EZza7Exk9RqpFww\nCQSe3/EED1rVTCZCXwySwuKxCKB7R3kF+ycyIwFCwACcP1V3YoBfkOYU43tjTzIuS61quwQB2HSo\nI+YZTyJvU8ANIzIxIMNi2mLcezTMmn61Uq4FSssbl1ZvEutrJ5WRMS8SixWTZHbed5TfWpqNzDQB\nnW7J959LAn5YlqNqu2FrOuNKrTbpUGLR2Bzk2S0QBEGz/7Yf78LXTU5Nf18ySJJ2g2fMUn6mXM2k\nbFNmEnMjkbVCJqkN15X/YJP4RnMb7x3BqiXxh4iSpGvfMCK9iWdLlCuHZiQ5JRoIuknEU0t51TDt\nj8eBJmfA/dKMJYf/IVb7whQzSrlgEtCu9kmLmklPlxv9o0nWuHn4+kyGGSR5tNWNd4/Iv3kDAC4o\nsGFEbtrZ5c16WQdK+iCw1DiM1Ad5H07ZXSkx/CsDzHAswqXR228/7u1rsI1ESclgUiuaBBOsLky4\ncPNMjh9gw9dNTvy7Wb4ZpabdjY0H2jEsx4qmbjHmd6oaVTL7TLKZm8xMAHwDcPQg+9Cb4AtGMNA9\nKiQlxklaQpmxdjY17pZ+tBzNrcVzQdJrhfqYSHk9MjcND0zMC/t9t1vCl2ecvvwamm3VNG19kSRp\n1/eYKNEEATje7sZFOgRccpvUfRLwBO8vVv4Dnswg2mnRl4q+lAsmgcCoXu1puXxyHuwaxBLJHknb\nN0mQIMX8xJ1uFTC10K5TmpIn2ZOWE5nVD8fl4EirCxcU2KIvbBJGviaTWVapEa47VbjvlPC/bXkH\nf5lBygWTWh14rToXJ/LiMMk5pyuzFUZ9Ac9LMqvR/dIwup9+t8lEl1XattxpT+6tZWbV1158kXrB\nJLR7kb2ZsPYziAT0jZw3NjM9WRMZgd6XiyQBLT0inKIEl6jzzmIkCL2vrzTDLS1c2Sb5zU2qhhT0\npxmkXDAJCGdHT3uyMdlBFqcGSiwBQu8bcJKdGINIZlcLEcwHIiPpcEmo/Mtp9LNbYBWAfnbjXKHB\nlUHGSZk8+Wbus7GHym0a/TeHk4LBpLEkqtnVTE8wemIf1VCJmp5KFvOCSDG9yy5B8Aw0zLMJ2Pzd\ngfruTAVBrmnRhCSgz92I+sQbcJJZY5ci14Z5CECXW8KJdjdrav0kbwBOCk3+TqShcNeF3teLUwTS\nDDrFggBPawZgjlhM7h7j/czTOqbuOJupdtYr9YLJoDfgGOJ8TFQzd2J2Y2j97RZMHmiHIADj+rPi\nHUjuPHJ9rRM6UTwS0YLgFCXYDHrnD25ZMnrREWnS8r6Gd1udsZk7sTLTBDw2rV+yk2EoAoDf/qsN\nuXb97iCtrZnIbW72/fv7ozJxQYE9rqdzolQnP2m5vteLy8g1k95Z4gH8q9GJ4kyDRr0KaPEgbYba\nWa+UCyaN1qyc1P5qRAAemJiLmg63rvuoERo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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plotting functions\n", "mpl.rcParams['lines.linewidth'] = 1\n", "f, ax = plt.subplots(3, sharex=True)\n", "f.set_figheight(_plt_x)\n", "f.set_figwidth(_plt_y)\n", "\n", "sig = [0.2, 0.005, 10.]\n", "\n", "for i, s in enumerate(sig):\n", " q = lambda x: s * np.random.randn() + x\n", " z = metropolis(N, z_0, p_tilde, q)\n", " idx = np.arange(z.shape[0])\n", "\n", " ax[i].plot(idx, z)\n", " ax[i].set_ylim([-0.05, 1.05])\n", " ax[i].set_title('sigma = %1.3f' % s)\n", "\n", "plt.show()\n", "\n", "# plotting functions\n", "mpl.rcParams['lines.linewidth'] = 4\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Gibbs Sampling\n", "\n", "Idea: if we can cheaply sample from conditional distributions, lets use that for the proposal distribution\n", "\n", "Given $p(\\mathbf{z}) = p(z_1, z_2, \\dots, z_M)$\n", "\n", "Generate a sample by sampling $z_i ~ p(z_i | \\mathbf{z}_{\\neg i})$\n", "\n", "e.g. Given $p(z_1, z_2, z_3)$, we sample as follows:\n", "$$\n", "z_1^{(t+1)} \\sim p(z_1 | z_2^{(t)}, z_3^{(t)})\n", "$$\n", "\n", "$$\n", "z_2^{(t+1)} \\sim p(z_2 | z_1^{(t+1)}, z_3^{(t)})\n", "$$\n", "\n", "$$\n", "z_3^{(t+1)} \\sim p(z_3 | z_2^{(t+1)}, z_3^{(t+1)})\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Gibbs Sampling as a special case of Metropolis-Hastings\n", "\n", "Let $q_k(\\mathbf{z}^\\star | \\mathbf{z}) = p(z_k | \\mathbf{z}_{\\neg k})$ where we keep all $z_i,\\, i\\neq k$ unchanged.\n", "\n", "Also, $p(\\mathbf{z}) = p(z_k | \\mathbf{z}_{\\neg k})p(\\mathbf{z}_{\\neg k})$.\n", "\n", "So,\n", "$$\n", "A(\\mathbf{z}^\\star | \\mathbf{z}) = \\frac{p(\\mathbf{z}^\\star)q_k(\\mathbf{z} | \\mathbf{z}^\\star)}{p(\\mathbf{z})q_k(\\mathbf{z}^\\star | \\mathbf{z})} = \\frac{p(z_k^\\star | \\mathbf{z}_{\\neg k}^\\star) p(\\mathbf{z}^\\star_{\\neg k}) p(z_k | \\mathbf{z}_{\\neg k}^\\star)}{p(z_k | \\mathbf{z}_{\\neg k}) p(\\mathbf{z}_{\\neg k}) p(z_k^\\star | \\mathbf{z}_{\\neg k})} = 1\n", "$$\n", "\n", "i.e. The acceptance probability is just 1. for every sample.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Gibbs use cases\n", "\n", "Gibbs sampling is most useful when we can easily sample from the conditionals $p(z_k | \\mathbf{z}_{\\neg k})$. See the graphical models lectures from last year...\n", "\n", "It is not always useful... e.g. sampling from correlated Gaussian, where we need $\\mathcal{O}((L/l)^2)$ Gibbs steps to obtain an independent sample:\n", "\n", "![](Gibbs.jpg)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Simple Ising Model example\n", "\n", "To illustrate let's perform Gibbs sampling on a simple *Ising* model. \n", "\n", "$$\n", "\\mathbb{P}(X^{i, j} = x^{i, j} \\text{ for all } (i, j)) = \\frac{1}{Z} \\exp\\left(\\frac{1}{T}\\sum_{(i, j) \\sim (k,l)} x^{i, j}x^{k, l}\\right)\n", "$$" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def neighbours(i, j, L):\n", " return [(i + x, j + y) for x, y in (-1, 0), (1, 0), (0, -1), (0, 1) if (0 <= i + x < L) and (0 <= j + y < L)]\n", "\n", "def potential(i, j, X, T=1):\n", " L, _ = X.shape\n", " p = 0\n", " for _i, _j in neighbours(i, j, L):\n", " p += X[_i, _j]\n", " n = np.exp(T * p)\n", " return n / (n + np.exp(-T * p))\n", "\n", "N = 50000 # number of samples\n", "L = 100 # edge length of the image\n", "x = np.random.binomial(1, 0.5, L*L).reshape((L, L)) * 2 - 1\n", "X = np.repeat(x.reshape(1, L, L), N, axis=0)\n", "T = 1.\n", "for i in range(1, N):\n", " X[i, :, :] = x\n", " # we just choose a random pixel to perturb\n", " _i = np.random.randint(L)\n", " _j = np.random.randint(L)\n", " p = potential(_i, _j, X[i, :, :], T)\n", " val = np.random.binomial(1, p) * 2 - 1\n", " X[i, _i, _j] = val\n", " x = X[i, :, :]\n" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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Izda36prXJh5I1zHOh/bkYitf1fnQxOlRFVN7h409o3BLWeUoZF2tw8ZJUDcO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PAAAg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\nAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f, ax = plt.subplots(5)\n", "f.set_figheight(_plt_x*2)\n", "f.set_figwidth(_plt_y*2)\n", "\n", "for i in range(5):\n", " ax[i].imshow(X[i*10000, :, :], interpolation='nearest')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Slice Sampling\n", "\n", "![](Slice1.jpg)\n", "## Algorithm\n", "\n", "For a given value $z^{(t)}$, choose $u$ uniformly in the region $0 \\leq u \\leq \\tilde{p}(z^{(t)})$\n", "\n", "Sample $z^{(t+1)}$ uniformly from the ‘slice’ defined by $u$ (shown by the solid horizontal lines). \n", "\n", "Because it is typically infeasible to sample directly from a slice, a new sample of z is drawn from a region $z_{\\min} \\leq z \\leq z_{\\max}$, which contains the previous value $z^{(t)}$. (see plot below)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![](slice2.jpg)\n", "\n", "#### Why it works\n", "Slice sampling is a **auxiliary** variable method where we augment $\\mathbf{z}$ with and additional variable $u$ and then draw samples from their joint space $p(\\mathbf{z}, u)$.\n", "$$\n", "p(\\mathbf{z}, u) = \\begin{cases}\n", "1/{Z_p}&\\text{ if } 0 \\leq u \\leq \\tilde{p}(z)\\\\\n", "0 & \\text{otherwise}\n", "\\end{cases}\n", "$$\n", "\n", "where $Z_p = \\int \\tilde{p}(z) \\text{ d}z$.\n", "\n", "Given this definition of the joint distribution, we can get the marginal over $z$ by integrating out $u$.\n", "\n", "$$\n", "\\int \\tilde{p}(z, u) \\text{ d}u = \\int_{0}^{\\tilde{p}(z)} \\frac{1}{Z_p} = \\frac{\\tilde{p}(z)}{Z_p} = p(z)\n", "$$\n", "\n", "So we can sample from $p(z)$ by sampling from $p(z, u)$ and then ignoring the $u$ values." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.11" } }, "nbformat": 4, "nbformat_minor": 0 }