{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#Chapter 6\n", "\n", "____\n", "\n", "This chapter of [Bayesian Methods for Hackers](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers) focuses on the most debated and discussed part of Bayesian methodologies: how to choose an appropriate prior distribution. We also present how the prior's influence changes as our dataset increases, and an interesting relationship between priors and penalties on linear regression." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Getting our priorities straight\n", "\n", "\n", "Up until now, we have mostly ignored our choice of priors. This is unfortunate as we can be very expressive with our priors, but we also must be careful about choosing them. This is especially true if we want to be objective, that is, not to express any personal beliefs in the priors. \n", "\n", "###Subjective vs Objective priors\n", "\n", "Bayesian priors can be classified into two classes: *objective* priors, which aim to allow the data to influence the posterior the most, and *subjective* priors, which allow the practitioner to express his or her views into the prior. \n", "\n", "What is an example of an objective prior? We have seen some already, including the *flat* prior, which is a uniform distribution over the entire possible range of the unknown. Using a flat prior implies that we give each possible value an equal weighting. Choosing this type of prior is invoking what is called \"The Principle of Indifference\", literally we have no prior reason to favor one value over another. Calling a flat prior over a restricted space an objective prior is not correct, though it seems similar. If we know $p$ in a Binomial model is greater than 0.5, then $\\text{Uniform}(0.5,1)$ is not an objective prior (since we have used prior knowledge) even though it is \"flat\" over [0.5, 1]. The flat prior must be flat along the *entire* range of possibilities. \n", "\n", "Aside from the flat prior, other examples of objective priors are less obvious, but they contain important characteristics that reflect objectivity. For now, it should be said that *rarely* is a objective prior *truly* objective. We will see this later. \n", "\n", "#### Subjective Priors\n", "\n", "On the other hand, if we added more probability mass to certain areas of the prior, and less elsewhere, we are biasing our inference towards the unknowns existing in the former area. This is known as a subjective, or *informative* prior. In the figure below, the subjective prior reflects a belief that the unknown likely lives around 0.5, and not around the extremes. The objective prior is insensitive to this." ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "import numpy as np\n", "from IPython.core.pylabtools import figsize\n", "import matplotlib.pyplot as plt\n", "import scipy.stats as stats\n", "\n", "figsize(12.5,3)\n", "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\", \"#467821\"]\n", "\n", "x = np.linspace(0,1)\n", "y1, y2 = stats.beta.pdf(x, 1,1), stats.beta.pdf(x, 10,10)\n", "\n", "p = plt.plot( x, y1, \n", " label='An objective prior \\n(uninformative, \\n\"Principle of Indifference\" )' )\n", "plt.fill_between( x, 0, y1, color = p[0].get_color(), alpha = 0.3 )\n", "\n", "p = plt.plot( x,y2 ,\n", " label = \"A subjective prior \\n(informative)\" )\n", "plt.fill_between( x, 0, y2, color = p[0].get_color(), alpha = 0.3 )\n", "\n", "p = plt.plot( x[25:], 2*np.ones(25), label = \"another subjective prior\" )\n", "plt.fill_between( x[25:], 0, 2, color = p[0].get_color(), alpha = 0.3 )\n", "\n", "plt.ylim(0,4)\n", "\n", "plt.ylim(0, 4)\n", "leg = plt.legend(loc = \"upper left\")\n", "leg.get_frame().set_alpha(0.4)\n", "plt.title(\"Comparing objective vs. subjective priors for an unknown probability\" );" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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gwL7+jo6OkJeXx9WrVxEREYFWrVrBy8sLsbGxyM3NxZUrV+Do6Agej8fWUdvjIs35sfzr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\nPGgV8ZTWXrFiBVevXuXTTz+1injupu3p6YmjoyM7d+4E4P777weoknb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"text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The choice of a subjective prior does not always imply that we are using the practitioner's subjective opinion: more often the subjective prior was once a posterior to a previous problem, and now the practitioner is updating this posterior with new data. A subjective prior can also be used to inject *domain knowledge* of the problem into the model. We will see examples of these two situations later." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Decision, decisions...\n", "\n", "The choice, either *objective* or *subjective* mostly depends on the problem being solved, but there are a few cases where one is preferred over the other. In instances of scientific research, the choice of an objective prior is obvious. This eliminates any biases in the results, and two researchers who might have differing prior opinions would feel an objective prior is fair. Consider a more extreme situation:\n", "\n", "> A tobacco company publishes a report with a Bayesian methodology that retreated 60 years of medical research on tobacco use. Would you believe the results? Unlikely. The researchers probably chose a subjective prior that too strongly biased results in their favor.\n", "\n", "Unfortunately, choosing an objective prior is not as simple as selecting a flat prior, and even today the problem is still not completely solved. The problem with naively choosing the uniform prior is that pathological issues can arise. Some of these issues are pedantic, but we delay more serious issues to the Appendix of this Chapter (TODO)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We must remember that choosing a prior, whether subjective or objective, is still part of the modeling process. To quote Gelman [5]:\n", "\n", ">...after the model has been \ufb01t, one should look at the posterior distribution\n", "and see if it makes sense. If the posterior distribution does not make sense, this implies\n", "that additional prior knowledge is available that has not been included in the model,\n", "and that contradicts the assumptions of the prior distribution that has been used. It is\n", "then appropriate to go back and alter the prior distribution to be more consistent with\n", "this external knowledge.\n", "\n", "If the posterior does not make sense, then clearly one had an idea what the posterior *should* look like (not what one *hopes* it looks like), implying that the current prior does not contain all the prior information and should be updated. At this point, we can discard the current prior and choose a more reflective one.\n", "\n", "Gelman [4] suggests that using a uniform distribution with large bounds is often a good choice for objective priors. Although, one should be wary about using Uniform objective priors with large bounds, as they can assign too large of a prior probability to non-intuitive points. Ask yourself: do you really think the unknown could be incredibly large? Often quantities are naturally biased towards 0. A Normal random variable with large variance (small precision) might be a better choice, or an Exponential with a fat tail in the strictly positive (or negative) case. \n", "\n", "If using a particularly subjective prior, it is your responsibility to be able to explain the choice of that prior, else you are no better than the tobacco company's guilty parties. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Empirical Bayes\n", "\n", "While not a true Bayesian method, *empirical Bayes* is a trick that combines frequentist and Bayesian inference. As mentioned previously, for (almost) every inference problem there is a Bayesian method and a frequentist method. The significant difference between the two is that Bayesian methods have a prior distribution, with hyperparameters $\\alpha$, while empirical methods do not have any notion of a prior. Empirical Bayes combines the two methods by using frequentist methods to select $\\alpha$, and then proceeds with Bayesian methods on the original problem. \n", "\n", "A very simple example follows: suppose we wish to estimate the parameter $\\mu$ of a Normal distribution, with $\\sigma = 5$. Since $\\mu$ could range over the whole real line, we can use a Normal distribution as a prior for $\\mu$. How to select the prior's hyperparameters, denoted ($\\mu_p, \\sigma_p^2$)? The $\\sigma_p^2$ parameter can be chosen to reflect the uncertainty we have. For $\\mu_p$, we have two options:\n", "\n", "1. Empirical Bayes suggests using the empirical sample mean, which will center the prior around the observed empirical mean:\n", "\n", "$$ \\mu_p = \\frac{1}{N} \\sum_{i=0}^N X_i $$\n", "\n", "2. Traditional Bayesian inference suggests using prior knowledge, or a more objective prior (zero mean and fat standard deviation).\n", "\n", "Empirical Bayes can be argued as being semi-objective, since while the choice of prior model is ours (hence subjective), the parameters are solely determined by the data.\n", "\n", "Personally, I feel that Empirical Bayes is *double-counting* the data. That is, we are using the data twice: once in the prior, which will influence our results towards the observed data, and again in the inferential engine of MCMC. This double-counting will understate our true uncertainty. To minimize this double-counting, I would only suggest using Empirical Bayes when you have *lots* of observations, else the prior will have too strong of an influence. I would also recommend, if possible, to maintain high uncertainty (either by setting a large $\\sigma_p^2$ or equivalent.)\n", "\n", "Empirical Bayes also violates a theoretical axiom in Bayesian inference. The textbook Bayesian algorithm of:\n", "\n", ">*prior* $\\Rightarrow$ *observed data* $\\Rightarrow$ *posterior* \n", "\n", "is violated by Empirical Bayes, which instead uses \n", "\n", ">*observed data* $\\Rightarrow$ *prior* $\\Rightarrow$ *observed data* $\\Rightarrow$ *posterior*\n", "\n", "Ideally, all priors should be specified *before* we observe the data, so that the data does not influence our prior opinions (see the volumes of research by Daniel Kahneman *et. al* about [anchoring](http://en.wikipedia.org/wiki/Anchoring_and_adjustment) )." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Useful priors to know about\n", "\n", "### The Gamma distribution\n", "\n", "A Gamma random variable, denoted $X \\sim \\text{Gamma}(\\alpha, \\beta)$, is a random variable over the positive real numbers. It is in fact a generalization of the Exponential random variable, that is:\n", "\n", "$$ \\text{Exp}(\\beta) \\sim \\text{Gamma}(1, \\beta) $$\n", "\n", "This additional parameter allows the probability density function to have more flexibility, hence allowing the practitioner to express his or her subjective priors more accurately. The density function for a $\\text{Gamma}(\\alpha, \\beta)$ random variable is:\n", "\n", "$$ f(x \\mid \\alpha, \\beta) = \\frac{\\beta^{\\alpha}x^{\\alpha-1}e^{-\\beta x}}{\\Gamma(\\alpha)} $$\n", "\n", "where $\\Gamma(\\alpha)$ is the [Gamma function](http://en.wikipedia.org/wiki/Gamma_function), and for differing values of $(\\alpha, \\beta)$ looks like:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "figsize( 12.5, 5 )\n", "gamma = stats.gamma\n", "\n", "parameters = [ (1, 0.5), (9, 2), (3, 0.5 ), (7, 0.5) ]\n", "x = np.linspace( 0.001 ,20, 150 )\n", "for alpha, beta in parameters:\n", " y = gamma.pdf(x, alpha, scale=1./beta)\n", " lines = plt.plot( x, y, label = \"(%.1f,%.1f)\"%(alpha,beta), lw = 3 )\n", " plt.fill_between( x, 0, y, alpha = 0.2, color = lines[0].get_color() )\n", " plt.autoscale(tight=True)\n", " \n", "plt.legend(title=r\"$\\alpha, \\beta$ - parameters\");" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": 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RSa6YuyRHzNv+IS4uDrt374Zerwdg7glftGgRBg8ejHHjxqG4uBiffPKJOP/V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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Wishart distribution\n", "\n", "Until now, we have only seen random variables that are scalars. Of course, we can also have *random matrices*! Specifically, the Wishart distribution is a distribution over all [positive semi-definite matrices](http://en.wikipedia.org/wiki/Positive-definite_matrix). Why is this useful to have in our arsenal? (Proper) covariance matrices are positive-definite, hence the Wishart is an appropriate prior for covariance matrices. We can't really visualize a distribution of matrices, so I'll plot some realizations from the $5 \\times 5$ (above) and $20 \\times 20$ (below) Wishart distribution:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import pymc as pm\n", "\n", "n = 4\n", "for i in range( 10 ):\n", " ax = plt.subplot( 2, 5, i+1)\n", " if i >= 5:\n", " n = 15\n", " plt.imshow( pm.rwishart( n+1, np.eye(n) ), interpolation=\"none\", \n", " cmap = plt.cm.hot )\n", " ax.axis(\"off\")\n", " \n", "plt.suptitle(\"Random matrices from a Wishart Distribution\" );" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "One thing to notice is the symmetry of these matrices. The Wishart distribution can be a little troubling to deal with, but we will use it in an example later." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Beta distribution\n", "\n", "You may have seen the term `beta` in previous code in this book. Often, I was implementing a Beta distribution. The Beta distribution is very useful in Bayesian statistics. A random variable $X$ has a $\\text{Beta}$ distribution, with parameters $(\\alpha, \\beta)$, if its density function is:\n", "\n", "$$f_X(x | \\; \\alpha, \\beta ) = \\frac{ x^{(\\alpha - 1)}(1-x)^{ (\\beta - 1) } }{B(\\alpha, \\beta) }$$\n", "\n", "where $B$ is the [Beta function](http://en.wikipedia.org/wiki/Beta_function) (hence the name). The random variable $X$ is only allowed in [0,1], making the Beta distribution a popular distribution for decimal values, probabilities and proportions. The values of $\\alpha$ and $\\beta$, both positive values, provide great flexibility in the shape of the distribution. Below we plot some distributions:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "figsize( 12.5, 5 )\n", "\n", "params = [ (2,5), (1,1), (0.5, 0.5), ( 5, 5), (20, 4), (5, 1)]\n", "\n", "x = np.linspace( 0.01, .99, 100 )\n", "beta = stats.beta\n", "for a, b in params:\n", " y = beta.pdf( x, a, b )\n", " lines = plt.plot( x, y, label = \"(%.1f,%.1f)\"%(a,b), lw = 3 )\n", " plt.fill_between( x, 0, y, alpha = 0.2, color = lines[0].get_color() )\n", " plt.autoscale(tight=True)\n", "plt.ylim(0)\n", "plt.legend(loc = 'upper left', title=\"(a,b)-parameters\");" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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cuEs+i5Jo4lK0byvhg+KG8EFxQ/hqHTs2DxSOng1GJBZiSm5LGp4AiK37K5vu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\nIIzeeFTqSRrMOlaZ9dQZNdQaN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"text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "One thing I'd like the reader to notice is the presence of the flat distribution above, specified by parameters $(1,1)$. This is the Uniform distribution. Hence the Beta distribution is a generalization of the Uniform distribution, something we will revisit many times.\n", "\n", "There is an interesting connection between the Beta distribution and the Binomial distribution. Suppose we are interested in some unknown proportion or probability $p$. We assign a $\\text{Beta}(\\alpha, \\beta)$ prior to $p$. We observe some data generated by a Binomial process, say $X \\sim \\text{Binomial}(N, p)$, with $p$ still unknown. Then our posterior *is again a Beta distribution*, i.e. $p | X \\sim \\text{Beta}( \\alpha + X, \\beta + N -X )$. Succinctly, one can relate the two by \"a Beta prior with Binomial observations creates a Beta posterior\". This is a very useful property, both computationally and heuristically.\n", "\n", "In light of the above two paragraphs, if we start with a $\\text{Beta}(1,1)$ prior on $p$ (which is a Uniform), observe data $X \\sim \\text{Binomial}(N, p)$, then our posterior is $\\text{Beta}(1 + X, 1 + N - X)$. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#####Example: Bayesian Multi-Armed Bandits\n", "*Adapted from an example by Ted Dunning of MapR Technologies*\n", "\n", "> Suppose you are faced with $N$ slot machines (colourfully called multi-armed bandits). Each bandit has an unknown probability of distributing a prize (assume for now the prizes are the same for each bandit, only the probabilities differ). Some bandits are very generous, others not so much. Of course, you don't know what these probabilities are. By only choosing one bandit per round, our task is devise a strategy to maximize our winnings.\n", "\n", "Of course, if we knew the bandit with the largest probability, then always picking this bandit would yield the maximum winnings. So our task can be phrased as \"Find the best bandit, and as quickly as possible\". \n", "\n", "The task is complicated by the stochastic nature of the bandits. A suboptimal bandit can return many winnings, purely by chance, which would make us believe that it is a very profitable bandit. Similarly, the best bandit can return many duds. Should we keep trying losers then, or give up? \n", "\n", "A more troublesome problem is, if we have a found a bandit that returns *pretty good* results, do we keep drawing from it to maintain our *pretty good score*, or do we try other bandits in hopes of finding an *even-better* bandit? This is the exploration vs. exploitation dilemma.\n", "\n", "### Applications\n", "\n", "\n", "The Multi-Armed Bandit problem at first seems very artificial, something only a mathematician would love, but that is only before we address some applications:\n", "\n", "- Internet display advertising: companies have a suite of potential ads they can display to visitors, but the company is not sure which ad strategy to follow to maximize sales. This is similar to A/B testing, but has the added advantage of naturally minimizing strategies that do not work (and generalizes to A/B/C/D... strategies)\n", "- Ecology: animals have a finite amount of energy to expend, and following certain behaviours has uncertain rewards. How does the animal maximize its fitness?\n", "- Finance: which stock option gives the highest return, under time-varying return profiles.\n", "- Clinical trials: a researcher would like to find the best treatment, out of many possible treatment, while minimizing losses. \n", "- Psychology: how does punishment and reward affect our behaviour? How do humans learn?\n", "\n", "Many of these questions above are fundamental to the application's field.\n", "\n", "It turns out the *optimal solution* is incredibly difficult, and it took decades for an overall solution to develop. There are also many approximately-optimal solutions which are quite good. The one I wish to discuss is one of the few solutions that can scale incredibly well. The solution is known as *Bayesian Bandits*.\n", "\n", "\n", "### A Proposed Solution\n", "\n", "\n", "Any proposed strategy is called an *online algorithm* (not in the internet sense, but in the continuously-being-updated sense), and more specifically a reinforcement learning algorithm. The algorithm starts in an ignorant state, where it knows nothing, and begins to acquire data by testing the system. As it acquires data and results, it learns what the best and worst behaviours are (in this case, it learns which bandit is the best). With this in mind, perhaps we can add an additional application of the Multi-Armed Bandit problem:\n", "\n", "- Psychology: how does punishment and reward affect our behaviour? How do humans learn?\n", "\n", "\n", "The Bayesian solution begins by assuming priors on the probability of winning for each bandit. In our vignette we assumed complete ignorance of these probabilities. So a very natural prior is the flat prior over 0 to 1. The algorithm proceeds as follows:\n", "\n", "For each round:\n", "\n", "1. Sample a random variable $X_b$ from the prior of bandit $b$, for all $b$.\n", "2. Select the bandit with largest sample, i.e. select $B = \\text{argmax}\\;\\; X_b$.\n", "3. Observe the result of pulling bandit $B$, and update your prior on bandit $B$.\n", "4. Return to 1.\n", "\n", "That's it. Computationally, the algorithm involves sampling from $N$ distributions. Since the initial priors are $\\text{Beta}(\\alpha=1,\\beta=1)$ (a uniform distribution), and the observed result $X$ (a win or loss, encoded 1 and 0 respectfully) is Binomial, the posterior is a $\\text{Beta}(\\alpha=1+X,\\beta=1+1\u2212X)$.\n", "\n", "To answer our question from before, this algorithm suggests that we should not discard losers, but we should pick them at a decreasing rate as we gather confidence that there exist *better* bandits. This follows because there is always a non-zero chance that a loser will achieve the status of $B$, but the probability of this event decreases as we play more rounds (see figure below).\n", "\n", "Below we implement Bayesian Bandits using two classes, `Bandits` that defines the slot machines, and `BayesianStrategy` which implements the above learning strategy." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from pymc import rbeta\n", "\n", "rand = np.random.rand\n", "\n", "class Bandits(object):\n", " \"\"\"\n", " This class represents N bandits machines.\n", "\n", " parameters:\n", " p_array: a (n,) Numpy array of probabilities >0, <1.\n", "\n", " methods:\n", " pull( i ): return the results, 0 or 1, of pulling \n", " the ith bandit.\n", " \"\"\"\n", " def __init__(self, p_array):\n", " self.p = p_array\n", " self.optimal = np.argmax(p_array)\n", " \n", " def pull( self, i ):\n", " #i is which arm to pull\n", " return np.random.rand() < self.p[i]\n", " \n", " def __len__(self):\n", " return len(self.p)\n", "\n", " \n", "class BayesianStrategy( object ):\n", " \"\"\"\n", " Implements a online, learning strategy to solve\n", " the Multi-Armed Bandit problem.\n", " \n", " parameters:\n", " bandits: a Bandit class with .pull method\n", " \n", " methods:\n", " sample_bandits(n): sample and train on n pulls.\n", "\n", " attributes:\n", " N: the cumulative number of samples\n", " choices: the historical choices as a (N,) array\n", " bb_score: the historical score as a (N,) array\n", " \"\"\"\n", " \n", " def __init__(self, bandits):\n", " \n", " self.bandits = bandits\n", " n_bandits = len( self.bandits )\n", " self.wins = np.zeros( n_bandits )\n", " self.trials = np.zeros(n_bandits )\n", " self.N = 0\n", " self.choices = []\n", " self.bb_score = []\n", "\n", " \n", " def sample_bandits( self, n=1 ):\n", " \n", " bb_score = np.zeros( n )\n", " choices = np.zeros( n )\n", " \n", " for k in range(n):\n", " #sample from the bandits's priors, and select the largest sample\n", " choice = np.argmax( rbeta( 1 + self.wins, 1 + self.trials - self.wins) )\n", " \n", " #sample the chosen bandit\n", " result = self.bandits.pull( choice )\n", " \n", " #update priors and score\n", " self.wins[ choice ] += result\n", " self.trials[ choice ] += 1\n", " bb_score[ k ] = result \n", " self.N += 1\n", " choices[ k ] = choice\n", " \n", " self.bb_score = np.r_[ self.bb_score, bb_score ]\n", " self.choices = np.r_[ self.choices, choices ]\n", " return " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below we visualize the learning of the Bayesian Bandit solution." ] }, { "cell_type": "code", "collapsed": false, "input": [ "figsize( 11.0, 10)\n", "\n", "beta = stats.beta\n", "x = np.linspace(0.001,.999,200)\n", "\n", "def plot_priors(bayesian_strategy, prob, lw = 3, alpha = 0.2, plt_vlines = True):\n", " ## plotting function\n", " wins = bayesian_strategy.wins\n", " trials = bayesian_strategy.trials\n", " for i in range( prob.shape[0] ):\n", " y = beta( 1+wins[i], 1 + trials[i] - wins[i] )\n", " p = plt.plot( x, y.pdf(x), lw = lw )\n", " c = p[0].get_markeredgecolor()\n", " plt.fill_between(x,y.pdf(x),0, color = c, alpha = alpha, \n", " label=\"underlying probability: %.2f\"%prob[i])\n", " if plt_vlines:\n", " plt.vlines( prob[i], 0, y.pdf(prob[i]) ,\n", " colors = c, linestyles = \"--\", lw = 2 )\n", " plt.autoscale(tight = \"True\")\n", " plt.title(\"Posteriors After %d pull\"%bayesian_strategy.N +\\\n", " \"s\"*(bayesian_strategy.N>1) )\n", " plt.autoscale(tight=True)\n", " return" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "hidden_prob = np.array([0.85, 0.60, 0.75] )\n", "bandits = Bandits( hidden_prob )\n", "bayesian_strat = BayesianStrategy( bandits )\n", "\n", "draw_samples = [1, 1, 3, 10, 10, 25, 50, 100, 200, 600 ]\n", "\n", "for j,i in enumerate(draw_samples):\n", " plt.subplot( 5, 2, j+1) \n", " bayesian_strat.sample_bandits(i)\n", " plot_priors( bayesian_strat, hidden_prob )\n", " #plt.legend()\n", " plt.autoscale( tight = True )\n", "plt.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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sjY1ay5B+pQoeIp46EQIoL9ieo33/ORJHi41QtcGSsQ2d5Wz3/d+4XAl1owaR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\n7+ViKInycyoR5WdriFsS41AuhsCCHkrE4ZJm2sw2PCbQszJaTP7/wSTnS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GfVtVv40U6H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FV8q0GBRYGt76LNGKAnPNKo4qONZoSGyuAhXBtyJAFxZC/O9+St7T/6QhwzmxYtF/PsKaV0Sf\nP/wUjdHgc7+i481ExgRRXFCNwyHYuzWTa28eevENu5Dzk5WWlpaSmJjIH//4RxYuXNjV3ZJ0EfUF\nxZx7azXn/rsKa3GZ+0qNQvjV44i7+wYCB/X33EAvotZiZ8OOYgpLGlzLzIE6Jo0Ow+ThJZWttIzc\n3/8VXVgICX/4uWt5kU2wPF+Q32zy4wEGlbuCVQzdX+Vy+HAFdrtg5MhgdK1M1Nae6IYORvu7x2j4\nYCX2HU6XJFFdQ+0zL3Dyf+uo/u5iJo9tu+41BRlJHB5NdmO2vfStmcQkhWMK8hxkPSImgFizgfwq\nK/V2lVVpxdw3NvbSD6wDaNWI2LNnDwMGDKBfv34AzJs3j9WrV7cwIjrJI6pH0t2HrG1VNeS+/znZ\nb6yk7sy5FutNibHE3X0DETMmuk0Sdx6HEGwrdfBhnp3CBvfzJEIPt0TA8AA8PngfOHqw27gzVVfb\nOH26hsLCBrflGg3Ex/sTG+uHppNSz4qqGtJKchhjaz3f9JWE3S6wWlUcjsu/l7SHO1OlqmBQfOuL\nVoE7zCpKFaQ1GhJbq5zn/vxI0AYGEP+rhyl44TXq9jvfxles24KtqIT+f/0tulDf0vcpisKIcfFs\n/Mz55vbw3nNcNS2JAC8KqDvgy2SlEs90d93gK0IIKvYc5uzrH1H4+SaE3d0wVwx6omZfTdwds/GL\n85xa80J6ujtTbqGFjbuKsdQ3OfvGRhkZMzwEvbcHaVVgLykjraGS89OZHakVvFnknM/mPONMKrMD\nVa6AAX8ArFYVu11c+N7ykmiLblD8Tfg9cC/28WNpePt9RKnT6I0/dRzHr/8PywPz8LtrbpuD+/sM\nj6b4bDmWqgbsVgdHvj7F+LnDPD4DaRSF2YPCeXOfcyR75dEibh0eSXAHjEZcKq32JDc3l8TERFc5\nISGB3bvd/RYVRWHHjh2kpqYSHx/Ps88+y7BhPX+q+Z6MEILKA8fIWfEZ+R9/1SK9HkDIuBHE3HIt\nIRNGenTLcAjBjjIHH+XZyat3v/oDtHBdKEwOAV03EUMcIQAAIABJREFUH6quqnIaD0VFDS3WRUUZ\nSUjwx2CQ48G9HY0CtzcaEkcbDYkd1VDjECyKBoOfkdiffp+S/3xI5VebAKg9dIyMRT8l6fk/Ykz0\nPqTdnLg+IYRFBlBWXIvdprJvexbTbhjcUYclkVwytqoaClavJ/s//6P6aEaL9YaIUKJvmk70nGkt\n5grqrdjtKnuPVHD0pPsEY8MHBjGgb4DPo9xWVbCyVLClWTNaBDcFqYwyyZe+bUE3fAja3z+G9ZM1\nWNdvQhECrdWK5V9vYf16GwE/XYZuULLP7Wm0GgZO6MPh9c5rouB0KeeOFdJneIzH+mPig1h7opSC\nait1NpX3DhbwvYntP7v2pdKqEeHLCTtmzBjOnTuHv78/a9as4bbbbuPkyZMe68osHN27bCuvol92\nObnvf8Ge486sAcM0AYAzS4bGz8iMm24k+pZrOVScSyUqExsNiPNZJFJTRvN1sYO3tu2jwi4wJztH\nEqpOH8SowO3jRzElBNKPHeJILq6RhgONWSQuLJ/H2/qOKAsh2LpzHwWF9QT7DwTgbK7TF71v/DBC\nQ/VU1Z2itkGLwdA1WSYAjmZnMGr4kC7Zf3uXT2YepbSkgcTEsZfdXsrQ1MvuT9Xpg+gVAZEpbdr+\ntiGpaKtha9phAA4nj+KFfMHE0oP4aRTGPHAP+ugItrz1FgjBsOxcTj7wCGWLb8M0sD8Txk8EYM/e\nXQAeyyPGxfPff68CQLdTy9jJfTl4eB/QsVk4JJ3LlTgKIVSVsp0HyV3xGQWfb0S1tHz5EpQyiNi5\nMwmdPBqN7tLeqPbEUYjisgY27S6hoqrJ78ig1zB+ZIjHAGpvhPUZxp9zBEXN3JfMGsHdwQ7ifQ+j\n6JFc6gi1YjRivPs2jo0YS/CKFUQVOOMUHKfOULXs5xjnzMK0aAGaEN9GlUOiA4kdGEF+hjMhzdGN\npwlPCCYguKUrr0ZRuGVoBK/uyQPgk/QSbh8RRVSg766wHUmrgdW7du3i97//PWvXrgXgySefRKPR\ntAiubk7//v355ptvCAsLc1suA+i6J6rVRtG67eS+9zklX+9COFr6gJv6xRM7dyYR105Ea/IcyFlu\nFXxRaGddsZ3aC5rw08C0EJgaAqZuPIaqqoL8/HrOnq2lurqlq1BoqJ6EBP8OSdnaFix/fwlH+gn8\nHl6KrtGIuNLJzq4jL89CYqKJ+PiuTV3aoMJfSnQYFMFjka3HRHhCCFhfq2FnXdMIVZwBlsYohOud\n53/NngMUvviGa1I6tFoSfrGUiLtu8qF9wRcfHKa8xJlSOPWqRGbd6lumpq4IrG4NqRd6BpbcQvI+\n+IKc9z7HcjavxXqN0UDEtROJueVaApL7dEEPuy9Wm8o3RytIy6hyc9mJjjAyelgwfkbf3GVqikr5\n4It97J98LWozF5vBBpWbzSoBV+iA+b59ZdjtgrFjQ9Hru/YgdtQqfF0Ft+9ZT9+v1oCtyVJTAgMw\nPTAf49wbfHJxctgd7P/iBJZqp6EdGmtmyj0j0XiYDVsIwbNbsjnbmKlpRnIov5zRr12OCTowsHrc\nuHFkZGSQlZVFXFwc77//fgsf18LCQqKiolAUhT179iCEaGFASLzTFX6vwuGgbOcB8ldvoPDzTdjK\nKlvU0fgZCZ86jqjZVxM0YpDHUSkhBGnVKuuLHewqd3ChO3uAFqYEO40H/0swHjorJsJicZCbW8e5\ncxasVrXF+tBQAwkJpi43HppzTK1FPnp5pqvT3yoKzApUCdQI1tU4lUmeFf6SI3gwBgaaFAInjEb3\nm2Dyn30ZR1UNOBzkPPkilhOnif/FUjR6768MFUVh9MQ+fN0YG3Fkbw7jru5HaHhApxyfpHPo7jER\ntooqCr/YQv6qdZRu3dci2QaAf/8EomZPJWLmJPTmS5tl3RM9ISZCCMHp7Fp2Hyynrr7pZYVWq5Ay\nyEzfeJNP3iBCCA7Wwoc1wVRMnUXV6YOYk0dhUASzA1VG+Qm6uddwp9EeukHVasmbOYuhE1NoeH8l\njqPpAIiaWupe/DcNn3+F/w8Wox89stV2tDotgyf35eBXJ0FAeX4Vx7ZkMmJGS9coRVG4dVgkz293\nxqVuPF3OTUPCGRkbdFnH0h60+lSk0+l48cUXmT17Ng6Hg8WLFzN06FCWL18OwPe+9z0++ugjXn75\nZXQ6Hf7+/rz33nud0nFJ2xAOB+V7j1CwegMFn21smRmjkaARg4i6fgrh14z3OupQaRNsLrGzvthB\nfkNLxRGhd448jDODoZOCjduKwyEoLKwnL89Caam1xXqNBiIijMTE+OHv332MBwDj4m9jTB+JdmBS\nV3el3YiL8yM62oi2G4xUGRR4KNzO5fZkkr8gUONgdZUGFYUaFZ7LE9wTAVPN4DcwiYQnfknB316h\nIdOpHEpXrsFyKot+f34MQ6z3INPYPiFEx5spzK1CVQWb15zgtm9f2Q9Vku6PvbaOoi+3kb9qPSUb\ndyE8JHfQBvoTMWMiUbOnEjCgT69O0eqN/KJ69h4up7DU3d0rItTA6GHBBPioc7LqBZ+UCY5bAJre\nYPfRC241OwjtAZnGU1KcLkI6XdefR2NMgmF+dowKaAKjMD30feyH02j4YCWiyOma5MjMpvpnv0M/\nfjSmRfe2Gi9hjgigf2ocmQedo3dnDuQSEhNIwtDoFnUHRfozJj6I/bnOdL8v7sjhpduHoOviZyw5\n2VwPxlFXT+nWvRSu3Urxuu1YSzxP4W6ICCVy1hQiZ03BFN/y5AVoUAX7K1S2l9n5pkLF7uGs6esH\n00NhRIDTj6+7oaqC8nIr+fn1FBTUe8wEZDBoiI72IyrK2OVDp5KeQbYVPqzUUiuarolJQXB3hIKf\nRkFtsFL06tvUbN/rWq8NDqLP739C8DUTvbZbUljN2o+Ousp3LRxHv4ERrfZFujNJ2kpDcRlFX22j\naO1WSrfuRa1v+dIFRSF49DCiZl9N2OQxHjP1SaCotIF9R8rJLax3W+5n0DBikJl4HycozWsQfFou\nOOQ+TRMBiuC6QJWRcvShUxE2O7YNm7B+/iU0uF8f+qmT8F84H23fRM/bCsGxLZmuSeg0WoVJd6YQ\nntByYrtyi43H12dibXx2uW9MDN8ec/kpXzt0srn2QiqLzqEuO5/SLXsoXredki17PQa2AehDzYRP\nHU/4tPEEDRvgMcOSXRUcqVLZVuZgb7nDLU3cefw0MCYIJgV3z3keVFVQWmqlsLCeoqJ6t5mlmxMc\nrCcqykhoqKHTUrVKeg+VDvigUku+vencitTDwiiFfn6KMw3m5+spXbEK1KYLLfLe24n90UKv7k07\nNpzizPFiAMIiA7j/R1PQtpJLXRoRkoshhKDm+BmKN+yk6MutVOw76tFVCSBgUH8ipk8g/JrxGCOl\nG7MnhBBk51s4cqKK/CJ340FRICkxgCHJgd5TtzZr51Q9bKgQHKmD5r+IgmCcSTAjQMVPvvvqMtSK\nSqyrPse+c4/7NaPRYJg1HdO9d6GNb/nQb7c6OPjlSeqqnOeH3qhjyj2pmCNbuqiuzyhjVZrznq9R\n4Pm5gxkUeXlxhNKIuIK5XL9Xe3UtZTv2U7JpDyWb93icy+E8+hAzoZNHEzFtAuaUwSgeAniq7YKD\nlQ6+qVA5WOloESR9nj5+MNEMo4LA2EEP3ZcaE1Ff76C0tIGSEislJQ3YPQ2bAH5+GiIjjUREGDH6\nGLzWXehqv//uTHeVjU3AZxfMbq0BbgpTuD4EtIqC5fgpCl94HXtZ06ih34B+9Pn9T/Ef2nJyI0ut\nlU/eOYjN5rxQp1w3gEnXep8ESRoRVw6dGRNhLSmnZMteSjbtoXTzHhoKS7zW9e+fQPi0CURMm+Dz\nvA7tzZUQE1Hf4OB0di3HMqqpqLa1WN8nzsTgpEACTK27LllV50zTmyoF2R7eCQ4zqkwPUIlobKa7\n3v+6A50lGzW/gIbVa3Dsd88yiUaDYepE/Obd0cLNqb6mgQNfnsRW73QRNJj0TL57JOYId0NCFYLn\ntp3jdKkz9X5CsJEXbh1MgOHSn2E6LLBa0v2wllZQvucQZbsOUr7rEFVHTrq9ubwQU584QieNImzS\naAIH928x4uAQgqw6wdEqp+FwvEbFm1UZoYfRQc5PdDea6tJmU6mosFFa2kBpqZWaGu+TsOn1CmFh\nBiIijAQG6qS/rqTT0Ctwm1klqV6wpkaDVSiowKdlgm9q4J4IGDRkAIlP/YrCV95yTUxXfyqLk/c/\nTPTCbxG9ZL7bqIQpwEDKhAT2bz8LwM6NpxkwNJrIbhBwJ+m+NBSVUr6rUY/sPkR1Wst5HFxoFIKG\nDyRs0mjCJo3uMsPhSkBVBbmF9ZzMrCYrt66FalYUiI/2Y3BSEEGtJOpQhSCzHnZWC/bXQL0HpTzQ\noDIjQCVGeo51OzSxMZi+vxDH2XNYV32GI82ZBANVxbp5B9bNO9CNGoHfbXPQT56AotXiF2hkxPRk\nDm/IwGFTsVps7PjwMBNuHU5YXNM8KhpF4TtjYnhyYxYNdkFOZQNPbsziD7OS0HaBF4UciejGOOob\nqD52msqD6VQdSqfyQDo1JzNb3UZjNGAeOZjgMcMJvSq1RYyDQwjO1gnSqh2kVakcq1GxtJLFMlgH\nowKdhkOC0be5QzoSIQQWi4OKChvl5VYqKmytGg0ARqOGsDADYWEGaThIugXlDlhVpeWczf1cHBcI\nd4QrBGuh8suNlK5YhbA2vcX0S+5L/M++R9CE0a5lqir4auVRSgprAIiKDWLB9yei07d8MyVHInof\nqtVGdbpTj1QeOEb5nsOtjliDc5b1kNFDCbkqldAJI9EHS6PUG3a7Sm5hPZk5tWTnWWjwkOFPp1Po\nF+9PUmIA/ibPb4wdQpBhgYO1gsO1UOFBL+sQjPQTXOWvEilfAV8xOE6ewrpmPY609BbrlIhw/G6+\nHsPsa9FGRVBVUsuRDadw2J3nkUarYfQNg4gf7G6878upcs1kDXDrsEiWTYq/pOcb6c7UA7BV1VBz\nMpOa9NNUHjpO1aHjVKefRtgvkqdeUQhITiR4zHBCxo4gaNgAV1CbEILCBsGpWpVTtSqnawWZdSoN\n3gcuUIBEPxgW4PzEGbrOcFBVQV2dnaoqO1VVNqqrnf+9uSedR1EgKEhPSIie4GA9/v7aHmU41L/2\nFo6MM/gt+jbaQd5dV64k8vIsFBTUExfnR0xMywl3OpMGFV4p02JQYGl42+eJ8BVVwK46hc11GmzN\ngq51CkwOglkhCkElxRQtf4v6E6fdtjVPm0j8j5dg7BMPQGW5hS/eP+RKFpAyLoHrbx/e4ryXRkTP\nxl5dS/WJM9QcP0N12ikqD6ZTfewUaoOHYOjmaDQEDU0mZOxwgseOIHBgP4/urpLGOLsKK7mFFnIL\n6iksqcfhRaeGmPX0iTORGGtqEfOgCkGBFY5b4ITFaUB4GnEACNcKUv1URpuE1/ke1LJyLE8/hxIa\ngv+jP76MI+xeHD5cgd0uGDkyGN1F4kY6mm8sCttqNYwxqUwNaPujs+NcDrYvN2Dfe6BlnJGioEsd\njvG6adQPH8WxPfnYGppekPZNiWH49GS3l0Or04pZl9GUafP24ZF8f2LbDQnpznSFIITAWlxGXWaO\n02A4mcX2XTtJLqmnIb/YpzYUrZaAQf0wjxiEOWUQQcMHog0wUWGHbIvKuXLBOYuVcxZBtqX1UYbz\nmLWQ7A+DTDA0AII6MZWaEAKrVaW21kFdnZ3aWrvre3rGEfrEDfOpnYAArctwCArSd4tUoR2FqKoh\nrSSHMR7SK16p2O3O88BTxqy20h5+r5WqgkHp2PcrGgUmBwhG+DlYV6MhrTFWwi5gSxVsqxJMCIrg\n6l88QvimTZR98CmiwekUXbV5F9Xb9xE2dxZR37mT4D7xjJncl71bswA4si+HqNggRk/q26HHIOk4\nvMVECCGwlpRTdzaXujM5ToPh+BlqTpyhPrfQp7YVvY7AwUmYUxr1yNBktP5da7y3hc6KiRBCUF1r\np7isgaJSK8VlDZSUW1u9T5n8NMRFmegTZyI4qOmFXqlNcLYBzjYIztY7s7bVt/JCz6QIhhoFqSaV\nBB0Xz7akqoiyco5Zqxh/CcfaXbFaVex24S22v01crm5oUJ26oV4o4NXx2zvaxAS0S+5HvWMuti07\nsG/dgah2jiAjBPaDR7EfPAo6HQMmTCBz6HTqhfMx/eyRAoqyyhk+LYnYgREoisItwyIoqbVyIM/Z\nxv/Siim32Hhkah9MHkaiO4KLGhFr167lxz/+MQ6HgyVLlnicrfqhhx5izZo1+Pv78+abbzJ69GgP\nLfV8VKuNhuIyGgpLqc8vwpKdhyU7H0t2HnXZ+Vhy8ltkSzpsLyVBF+61Tb/4aAIG9kOb3Bdbv37U\n9O1DnmLgQL2gsEGlMEtQ2FDf6s3oQoJ1kOQHA/wh2eSMdeiIN/XnDQSbTaW+XqW+3tH4cf/u7YZc\nUJzl0YjQahUCA3UEBekICtITGKjr0UaDJ7LUejnZnBfOZJ++ogILzVq4M1hljFWwoUZDXmMGJxXY\nVQ27qhWiR8xg8tAxDPriE2zbdgEg7HZKV66h9H9rCb52MvELbqdkUASZJ51BsRs+TUej1ZA6wXNq\nwc7AF/0hcUe12mgoKmXPF+sYWO2gPreIuuw8LGdzqTubh+VsHg5L/cUbaoYxOoLAQf0IGNyfoCHJ\nBA7uf0WnYT126mS7GRFCCBqsKrV1dipr7FRU2aistlFRZaOi+uIj3wBBATpiIo2ERPjhMOkosSvs\nsEFhoUqRDQpteMxueCHBGsFgo2CIUdBHL7gUF/csW22PMiLak+6iGzRhoRhvuwnDzbOx7z+Efftu\nHMdPNo1O2O1od+yg/95vyJtyE5VJIwCwVDew77N0zFEBDByXSMyACB4YFwf78lyGxKYzFZwqtfCj\nKYmMjut4N8RWjQiHw8EPf/hD1q9fT3x8POPHj2fu3LkMHTrUVeeLL77g1KlTZGRksHv3bpYuXcqu\nXbs6vOMdiRACtd6Ko86CvboGW0U1toqqxk/j9/IqrKUVNBSX0lBYSkNRqceZny9GHc47i9DpcMRE\nUx8TQ3ViH0oS+pAbk0ihzp8Ku2iaDToboGWmB2+YNE73pD5+kGh0/jf7ONKgqgJVFTgczo/dLrDb\n1cb/ApvNaQDYbM7lNpuK1dr08ZZO1VfqrXUYDBoCArT4++tc/41GTY9yT7oUzp83kpbU1tVevFI3\npL9BsDjUQaZNYWuthrPN4iUKbfA/guGG7zBw1DVM++JjzGcaXZyEoHLDdio3bCekf1+CZnyLapwT\nRa5blUZlWR2TZw7wGCPRkfiiP3oywuHAUVePvbbO+b+qBmt5ZaP+qMbm+l6FtbTc+fKpoARbWQUA\nx+zFHHh9XZv2qei0mBJjMfWNx79vHAED+xI4sB/6EPPFN76CqKqp8bpOVRv1k12lwapSb3XQ0KBS\n3+D8Xt+gUt/goM7ioKbOTq3F0fYRUIMGNcCAJcBAqclAqUZLhR1sLs8S39rzVwR9DYL+BkF/vSBM\n68OIw0WoEz1nhLq96W66QdHp0E8Yi37CWNSKSux792PfvQ81OwcAra2BhE0rCcw5RcH4WThMzkxN\nVUW1fPPFcXQ4iAiC6QlmzAEmNlcroNGQU9nAo1+cYmx8EDcNiWB8ohljB7mCtWpE7NmzhwEDBtCv\nXz8A5s2bx+rVq92UwCeffML9998PwFVXXUVFRQWFhYVER7ectOzdP3/cZGmJ5sNTAuH2TCSa1Wus\n2+x7U51ml6oQrmWoKjhU53/VAQ4V0VhWVIfTGdmhgsMONjuKzQb2xu+Ny5ztXXA1K54KWtBFQVwU\nxLWo5H4rURTsOj31Jn/qAoOoCwji7MlNrJl6L/X+/ojGzEkuL4oyFTM1mD23htJYVwH0OH0l/TXO\n/yaNczhUB1DrPBybKjjVKFohhFM8zQwF53dc3zsnWsY5suDnp8Fk0uLn5/yYTFpO55kYMya0czoh\nkXQDFAWSDIIkg4NzNjhg0XCsQcHaLGYiI6YvGQsfISHrFOO2riPpZJprnS3zLPG5z3N29r1YIp3x\nEnu2ZHJgy0nMRhupt/TrtGPxRX8ArGimF4T7H/dbnhCude73fU/fPbQhmm/X7MuFNzohnDpCdSAc\nolGHOFBUAQ5Ho345r0ealW12sFkb/9tR7I0Pcx6eCj3fWsMhJhxinKW6/IOUxHlKca0gDHpEQAAi\nKADVHIwabEYNDkYEBUKjHnHtI8MBNJ9otGnvPt/jPdRri3pwq+tlp+K8rldx/dZCCOeQ3Pnnhcb/\nB0/X8MaaPIQqnL+RQyBU1fm9nfWWTaNQadRTZdRTadRTadRh1TUzyB2Nn4tgVASxOkGcHuJ1gji9\nwKy5fKNB0jPQhARjmDUDw6wZqGXlOA4fxX7oKI4TGYSeOow5+yRFo66hbMhYhM45imhHS0E1FKTX\nYqSWGxssaCy1YKtHdVhxINiuKGzTKPj56TGajBiMTs8NjaJBq1VQFIUhNyZdcr9bNSJyc3NJTGwa\nCk9ISGD37t0XrZOTk+PRiMiraTlxRrujANrGTzfHBFhrq0i0Ata6dmvXAdQ0froarRZ0Og16vYLB\noMFw/r9BQa/XYDBo0Go9uVMJCovzsVl9H3XpLahCUCxsOOx2t8w9VzKqw6mFHQ71sn/zgqK8y2rD\nOYCmA0GXnn8xwI1+cJ0RTti0pFu1ZNs1WFFAUcjpP5Cc/gOJKMhl9M5NDDq6H2NDPTprPf3Wvk32\nzLupjXMqBxt6Shs6133FF/0BkNsZeqEtNNchXejxk/v1GQqumu1bZTtQKqC0ukP71F0oK8rHXnWR\nYPE2YFcU6nUaLDottQYdtXottXodtQYdNo3i85O+AUGQRhCiEYRpBeEalTCNIFyrEnBhMw64WN6U\ntiAaY+SK7PU9Sm+6PHxsNhCX9zb9cnWDw6EDtKgOBzZrB474BAbC5InoJk9Ea7Uhss6iPXWGuIzT\nRK7eS1n/FMoHpmILcn/J6jCacBjdY5vOPwrbGz+1HozeIZfR1VaNCF9dRi5M8ORtu2vvkvmlL+Ta\nu37X1V3otvz68V91dRe6J397iN/xUFf3ol0JTvLDtxD6i9Me581TrteZfpfdVnsQAUxxlS581RoH\ncxYAC9yWtpwXtXPxVX9IveAZqRu80/myacvwhoKbp0JnkRQHX7xITztrpiW13z34cnXDbGA2Auej\nc2flJfKDISOAEa4lcZ20Z19oVQrx8fGcO9eUT/rcuXMkJCS0WicnJ4f4+PgWbXWntIISiUQi6Vh8\n0R9SL0gkEsmVS6tjQ+PGjSMjI4OsrCysVivvv/8+c+fOdaszd+5c3nrrLQB27dpFSEiIR1cmiUQi\nkfQefNEfEolEIrlyaXUkQqfT8eKLLzJ79mwcDgeLFy9m6NChLF++HIDvfe97zJkzhy+++IIBAwYQ\nEBDAG2+80Skdl0gkEkn3xZv+kEgkEknPoNNmrJZIJBKJRCKRSCQ9g3ZNHLt27VqGDBnCwIED+ctf\n/uKxzkMPPcTAgQNJTU3lwIED7bn7bs3FZPPOO++QmprKyJEjmTJlCocPH+6CXnYNvpw3AHv37kWn\n07Fy5cpO7F3X4otsNm3axOjRoxkxYgTTp0/v3A52IReTTUlJCTfccAOjRo1ixIgRvPnmm53fyS5g\n0aJFREdHk5KS4rVOZ9+HpW7wjtQN3pG6wTtSN3hG6gXvdIhuEO2E3W4XycnJIjMzU1itVpGamiqO\nHTvmVufzzz8XN954oxBCiF27domrrrqqvXbfrfFFNjt27BAVFRVCCCHWrFkjZeOh3owZM8RNN90k\nPvrooy7oaefji2zKy8vFsGHDxLlz54QQQhQXF3dFVzsdX2Tzu9/9Tjz22GNCCKdcwsLChM1m64ru\ndipbtmwR+/fvFyNGjPC4vrPvw1I3eEfqBu9I3eAdqRs8I/VC63SEbmi3kYjmEwvp9XrXxELN8TYx\nXU/HF9lMmjSJ4OBgwCmbnJycruhqp+OLbABeeOEF7rrrLiIjI7ugl12DL7J59913ufPOO11ZbyIi\nIrqiq52OL7KJjY2lqqoKgKqqKsLDw9HpOistX9cxdepUQkO9T9LY2fdhqRu8I3WDd6Ru8I7UDZ6R\neqF1OkI3tJsR4Wliodzc3IvW6Q03RF9k05zXXnuNOXPmdEbXuhxfz5vVq1ezdOlSwPf881c6vsgm\nIyODsrIyZsyYwbhx4/jvf//b2d3sEnyRzYMPPkhaWhpxcXGkpqby3HPPdXY3uyWdfR+WusE7Ujd4\nR+oG70jd4BmpFy6PS7kPt5v51d4T0/Uk2nKMGzdu5PXXX2f79u0d2KPugy+y+fGPf8xTTz2FoigI\nIVqcQz0VX2Rjs9nYv38/GzZsoK6ujkmTJjFx4kQGDhzYCT3sOnyRzZ///GdGjRrFpk2bOH36NLNm\nzeLQoUMEBQV1Qg+7N515H5a6wTtSN3hH6gbvSN3gGakXLp+23ofbzYhoz4npehq+yAbg8OHDPPjg\ng6xdu7bVIaeehC+y+eabb5g3bx7gDIpas2YNer2+x+ec90U2iYmJREREYDKZMJlMXHPNNRw6dKhH\nKwrwTTY7duzg//7v/wBITk6mf//+nDhxgnHjxnVqX7sbnX0flrrBO1I3eEfqBu9I3eAZqRcuj0u6\nD7dLtIYQwmaziaSkJJGZmSkaGhouGjy3c+fOXhMg5otszp49K5KTk8XOnTu7qJddgy+yac4DDzwg\nPv74407sYdfhi2zS09PFzJkzhd1uF7W1tWLEiBEiLS2ti3rcefgim0ceeUT8/ve/F0IIUVBQIOLj\n40VpaWlXdLfTyczM9Cl4rjPuw1I3eEfqBu9I3eAdqRs8I/XCxWlv3dBuIxFyYjrv+CKbP/7xj5SX\nl7t8O/V6PXv27OnKbncKvsimt+KLbIYMGcINN9zAyJEj0Wg0PPjggwwbNqyLe97x+CKbX/3qVyxc\nuJDU1FRUVeXpp58mLCysi3ve8cyfP5/Nmze4UFDMAAAgAElEQVRTUlJCYmIif/jDH7DZbEDX3Iel\nbvCO1A3ekbrBO1I3eEbqhdbpCN0gJ5uTSCQSiUQikUgkbaJdJ5uTSCQSiUQikUgkPR9pREgkEolE\nIpFIJJI2IY0IiUQikUgkEolE0iakESGRSCQSiUQikUjahDQiJBKJRCKRSCQSSZuQRoREIpFIJBKJ\nRCJpE9KIkEgkEolEIpFIJG1CGhESiUQikUgkEomkTUgjQiKRSCQSiUQikbQJaURIJBKJRCKRSCSS\nNiGNCIlEIpFIJBKJRNImpBEhkUgkEolEIpFI2oQ0IiRdxvTp0/nud7/b1d1olQ8//JDk5GR0Oh2L\nFi3q6u5cUbz55pvo9XpXedOmTWg0GvLy8rqwVxKJpDsj9ULPRuqFnoU0InoIDzzwABqNBo1Gg16v\np1+/fixdupSysrJ2aX/btm1oNBqys7PbpT2AVatW8be//a3d2rsUdu/ejUajYcKECS3WORwOFi1a\nxLx58zh37hz/+Mc/WLJkCTNmzOjQPqWlpXH33XczaNAgtFotDz74oMd6J0+eZPbs2QQEBBAZGcnS\npUupq6tzq5Ofn88999xDcHAwwcHBzJ8/n+Li4g7tv0Qi6R5IvXBpdEe98PrrrzNjxgwiIyMxm82M\nGzeOd999t0U9qRcknYk0InoQ11xzDQUFBZw9e5bnn3+elStXct9997XrPoQQl92G1WoFICQkhMDA\nwHZp61JZvnw548ePZ//+/Rw6dMhtXV5eHrW1tdx4443ExsZiNpsva18XYrPZPC63WCz069eP3/72\nt6SmpqIoSos6NTU1zJw5E4PBwM6dO/nggw9Yu3YtixcvdtVRVZWbb76Zs2fPsn79er766itOnjzJ\nbbfd1q7HIZFIui9SL7Sd7qgXNm7cyO23387atWs5dOgQCxYs4L777uODDz5w1ZF6QdLpCEmP4P77\n7xfXXXed27InnnhCaLVaUV9fL1RVFc8884zo37+/MBgMIjk5WfzjH/9wq79q1SoxatQo4e/vL0JC\nQsSECRPEgQMHRGZmplAUxe0zY8YM13YrVqwQqampws/PT/Tr10/85Cc/EbW1ta7106ZNE4sXLxa/\n/vWvRUxMjIiNjXUtX7Jkiaue1WoVjz76qIiPjxcGg0EMGzZMvPvuu259VBRFPP/882L+/PkiODhY\nzJs3z3WsSUlJwmg0isjISDF79mxhsVhalVlFRYUICAgQa9asETfffLNYunSpa90bb7zR4pinT5/e\nYtl//vMfIYQQ1dXV4qGHHhLx8fHC399fjB49WqxcudLV3nkZvvPOO+LGG28UAQEB4rHHHmu1f0II\nMX36dPHggw+2WL58+XJhMplEVVWVa9nnn38uFEURWVlZQgghvvzyS6Eoijh58qSrTlpamlAURWza\ntMnrPs+fS3/7299EXFyc8Pf3F3fffbcoKytrUac5//3vf4WiKG4y1Ol0rvLGjRuFoigiNzdXCOH8\nvR955BGRkJAgjEajiI2Ndf2eEonk8pF6oWfqhfPMnTtX3Hnnna6y1AuSzkYaET2E+++/X8yaNctt\n2V//+lehKIqoqakRL774ojCZTOLVV18Vp06dEq+88orw8/MTr732mhBCiPz8fKHX68UzzzwjsrKy\nxPHjx8WKFSvEkSNHhMPhEJ988olQFEXs27dPFBYWivLyciGE84YQGhoq3n77bZGZmSm2bNkiRo4c\nKb7zne+4+jFt2jQRFBQkli5dKtLT08XRo0eFEC0fkH/2s5+J8PBw8dFHH4mMjAzx5z//WWg0GrFh\nwwZXHUVRRHh4uPjnP/8pzpw5IzIyMsTHH38szGaz+Oyzz8S5c+fEwYMHxXPPPXdRZfHiiy+KpKQk\nIYQQn376qTCbzS4lZ7FYxN69e4WiKOLTTz8VhYWFoqqqStx7771iypQporCwUBQWFgqLxSJUVRXT\np08XM2bMENu3bxeZmZniX//6lzAYDK6+n1cWCQkJ4t133xVZWVkiMzPzor+rNyPivvvuEzNnznRb\nZrVahVarFe+8844QQojf/va3Ijk5ucW2iYmJ4k9/+pPXfd5///3CbDaLW2+9VRw9elRs2rRJDBw4\nUNx+++2uOg888ECL862tyuKvf/2rSEhIEJs3bxbnzp0Te/fuFc8991xr4pBIJG1A6oWeqRfOM3Xq\nVHH//fe7ylIvSDobaUT0EC58A5CWliaSkpLEpEmThBBCJCQkiEcffdRtm0ceecR1s9y/f7/b24oL\n2bp1q1AURZw9e9Zted++fcXy5cvdlm3evFkoiiIqKiqEEE5lMXjw4BZtNlcWtbW1wmg0ipdfftmt\nzu233y6uvfZaV1lRFLe3VEII8be//U0MGjRI2Gw2j333RmpqqnjyySeFEEI4HA7Rp08f8e9//9u1\n/vwNfvv27a5lixcvFtOnT3drZ+PGjcLPz09UVla6LV+4cKG47bbb3Npq7SbtCW9GxKxZs8S9997b\nYnlkZKR49tlnhRBCPPjgg2LKlCkt6owfP1788Ic/9LrP+++/XwQFBbm9zfrqq6+Eoiji9OnTrjqX\n+8bp4YcfdvttJRJJ+yL1Qs/UC0I477cGg0EcOHDAtUzqBUlnI2MiehCbNm0iKCgIf39/UlJSGDBg\nAO+88w5VVVXk5uZyzTXXuNW/5ppryMrKor6+ntTUVGbPns2IESO44447eP7558nJyWl1f8XFxWRn\nZ/PII48QFBTk+syZMwdFUTh16pSr7tixY1tt69SpU1itVo99TEtLc1t2YbDbt771LWw2G3379mXh\nwoW8/fbb1NTUtLq/3bt3k56e7sqsodFoWLx4McuXL291O0/s3bsXq9VKfHy8mxzeeecdNxl46vul\n4ilOwhPiEn2Vhw0bRlBQkKs8efJkAI4dO3ZJ7Xli4cKFHDlyhAEDBrB06VJWrlzp1R9YIpFcGlIv\n9Dy9sHr1ar773e/y+uuvM2rUKNdyqRcknY2uqzsgaT8mTpzIf/7zH3Q6HXFxceh0zp+3qqrqottq\nNBrWrFnD3r17Wb9+PR9//DGPPfYYH374ITfddJPHbVRVBeD555/3mJkiPj4ecN7YAgICLvWwWnBh\nW3FxcRw/fpyNGzfy9ddf8/jjj/Poo4+ye/duEhISPLaxfPlybDabq4/gvLEKITh06BCpqak+90dV\nVYKDg9m3b1+LdQaDodW+XyqxsbGcO3fObZnNZqOsrIzY2FhXnQ0bNrTYtqCgwFXHGxdTMhqNpkWd\ntt7oU1NTyczMZN26dWzcuJGHH36Y3/zmN+zatctNUUkkkktH6oWepRfee+89Fi5cyL///W/uvfde\nt3VSL0g6GzkS0YPw8/MjKSmJPn36uBQFgNlsJiEhgc2bN7vV37x5M0lJSfj5+bmWjR8/nl/+8pds\n3ryZadOm8cYbbwBNNz2Hw+GqGx0dTWJiIsePHycpKanFx2g0+tz3AQMGYDQaPfYxJSXlotsbDAZm\nz57NX/7yF44cOUJdXR2rV6/2WLeyspIPPviAl156iUOHDrl9pk6d2upbJ4PB4CYDcMqsoqICi8XS\nQgbelNXlMmXKFHbu3El1dbVr2bp161BVlSlTpgBw9dVXk5mZ6fbW69ixY+Tk5HD11Ve32n56erpb\n2zt27ACcb6IAoqKiWuT13r9/f5uPIyAggNtuu43nnnuOffv2kZ6ezpYtW9rcjkQi8YzUCz1HL7z6\n6qssXLiQt956q4UBAVIvSDofORLRS/jlL3/JT3/6UwYOHMi0adP4+uuveeWVV3jppZcA581gw4YN\nzJ49m5iYGDIyMjh8+DBLliwBoG/fvmg0Gj7//HPuuecejEYjwcHBPPHEEyxevJjQ0FDmzp2LXq8n\nPT2dtWvX8sorrwBNb3IupPlyf39/HnroIX7zm98QGRnJyJEj+eijj/jkk09Yv359q8f22muvIYRg\n/PjxhISEsGHDBqqrq103tgt5++230Wg0LFy4sIVCu/fee/nZz37Gs88+63HbpKQkPvroI44dO0ZU\nVBRms5lrr72W6667jjvuuIOnn36alJQUysvL2bFjByaTySVDX7HZbK6h+urqakpLSzl48CAGg8F1\nTAsWLODxxx9nwYIFPPHEE5SWlvKDH/yAefPm0bdvXwCuu+46xowZw7e//W1eeOEFVFXlBz/4AZMm\nTWrhHnAhiqJw33338ac//cnV9q233kpSUhIAs2bN4umnn+all15i9uzZfP3113z44YdtOs5nnnmG\n+Ph4UlNT8ff3Z8WKFeh0OgYNGtSmdiQSyaUh9UIT3V0v/P3vf+cXv/gF//znP5k6dSoFBQWA04AJ\nCwsDpF6QdAGdG4Ih6Sg8ZUW4kPOp/PR6vUhOTnbLeJCWlibmzJkjYmJihNFoFH379hW/+MUv3ILS\nnn76aREfHy+0Wq1bKr9Vq1aJSZMmCX9/f2E2m8WoUaPE448/7lrvLTj4wuU2m0089thjrlR+w4cP\nFytWrHDb5nw6vOasXLlSTJ48WYSGhgp/f3+RkpIiXn/9da9yGDVqlFiwYIHHdcXFxUKv14vXXntN\nZGZmCo1G4xZAV1ZWJubMmSOCg4PdUvlZLBbx2GOPuVIlxsTEiBtvvFFs3LhRCCE8tuWN5qkTNRqN\n63v//v3d6p04cUJcf/31wt/fX4SHh4vvf//7oq6uzq1Ofn6+uPvuu0VQUJAwm81i3rx5ori4uNX9\nnw+Oe/bZZ0VsbKzw9/cXd911l1sqPyGc6RPj4+NFYGCgWLBggfjnP/8pNBqNa/0bb7wh9Hq9q7xx\n40ah0WhcAXTLly8XY8eOFWazWQQGBooJEyaITz755KLykUgkviH1Qs/RC/369XPTB57S6goh9YKk\nc1GEaIdZYiQSSY/hgQceIDc3l3Xr1nV1VyQSiUTSDZB6QeIJGRMhkUgkEolEIpFI2oQ0IiQSiRuK\novicKlAikUgkPR+pFySekO5MEolEIpFIJBKJpE10WnamXbt2UVtb21m7k0gkEskFhISEXHSCr85E\n6gWJRCLpWi5HL3SaEVFbW8uYMWM6a3dXDMuWLXOl05O4I2Xjnd4qG4cq+M1Xp9mX05SrfEC4iVFx\nQZRbbGzLqiD9nadI+tajGLUKz986mP5hpi7scffiUnK2dyRSL3int17jviBl4x0pG++0VTZ/35rN\nmhOlAAQZtfjrtRTWWAGIDTLwrzuHYtRd+VEBl6MXrvyjv8Lp06dPV3eh2yJl453eKptXduW4GRC3\nDovgoasTmZ4cyu0jovjZNX0JjYoDoMEheHxDJnVWh7fmJJJuS2+9xn1BysY7UjbeaYtsSmttfHmy\n1FX+Vmo0o+OaZszOr7ayNbOiXft3JdIuRsSJEycYPXq06xMcHMzzzz/fHk1LJBIJAPtzq1h9rMRV\nvmFwOLMGhaNpFuwXazYyLsGMQetcllPZwKt7cju9rxKJRCK5ctmcWY7aGDF8frTbT+/+yLw9SxoR\n7WJEDB48mAMHDnDgwAG++eYb/P39uf3229uj6R5PcHBwV3eh2yJl453eJpt6u8pz2865yqmxgdw0\nJNxj3ZjIUOaNinaV15wo5Wy5pcP7KJG0J73tGm8LUjbekbLxTltks/F0uev7+EQzABoFmnsv7cup\nwmLr3SPd7e7OtH79epKTk0lMTGzvpnskKSkpXd2FbouUjXd6m2zeOVBAfrXTF9Wk1/Ct1Giv6QYH\nDR3OhMRghkT6A6AK+PeevE7ra29k0aJFREdHu52XP//5zxk6dCipqanccccdVFZWdmEPrzx62zXe\nFqRsvCNl4x1fZZNbWc+J4joAtAqManRjunZAGP+YO5jYIAPgdJlt7l7bG2l3I+K9995jwYIF7d1s\nj+Xqq6/u6i50W6RsvNObZFNaa+N/R4tc5TtGRGH2854TYuxVkwG4bUQk582M3eeqOJTXu2/2HcnC\nhQtZu3at27Lrr7+etLQ0Dh06xKBBg3jyySe7qHdXJr3pGm8rUjbekbLxjq+y2XimyU1pWHQgAQat\n2/rUZrER23q5S1O7ZmeyWq18+umn/OUvf/G4ftmyZa7AluDgYFJSUlw/6rZt2wBkWZZlWZbdyu8c\nLKDk5AEAho+9iol9zHyzewfQZDB4K0/o05/d2VVUnT7IP97P4I1H7uny4+nM8vnv2dnZACxZsoSO\nYOrUqWRlZbktmzVrluv7VVddxccff9wh+5ZIJJL2ZFuzgOlxCUEt1o+KC2RtY9am3dmV2Bwqem3v\nzFPUrpPNrV69mpdffrnFGymADRs2yFR+Hti2bZt8c+AFKRvv9BbZ5Fc1sOjDYzga71LLJiUwLDqg\n1W2+2b3DZUwU1Vh5fH0m529yr901lMQQvw7scfdm//79zJw5s0PazsrK4pZbbuHIkSMt1t1yyy3M\nnz+/xSi11Ave6S3X+KUgZeMdKRvv+CKbyno7d7/tvIdpFHh6zsAWAdVCCH731RnKLHYAnps7iKFR\nreul7szl6IV2HYlYsWIF8+fPb88mJRJJL+aDw4UuAyI53MTQKP82bR8VaGB4TABHC5wTmq1KK+ZH\nU2S8VmfyxBNPYDAYvLq5yhFqWb6UEbbu1J/uVD5y5Ei36k93Kp9/wdFa/UP51UAMAKbCY6TtL/U4\n4p0cbiJr81YA0oviGRoV0OXH1xUj1O02ElFbW0vfvn3JzMwkKKjl8I984ySRSNpChcXGt99Lw9po\nRTw0JZFBkW0zIgBOFNfywvYcAIw6De/OH06QsV3fn1wxdPZIxJtvvsmrr77Khg0b8PNrOQIk9YJE\nIulOvLD9HJ+mO1OJzx4Uxi3DIl3rHKrAoQo0GoXtWRV8eNgZqzetfwj/N7N/l/S3PbgcvdBuTlwB\nAQGUlJR4NCAkEomkrXyaXuIyIBJDjAyMuLSZpwdF+BNvNgLQYFfdUvdJOo61a9fyzDPPsHr1ao8G\nhEQikXQ3DjZLwHHhS6uNp8v5yWcZfHqsmKSwJn10rKi20/rX3eidkSDdiAuHZyVNSNl4p6fLpsGu\n8kmzieVmDgjzmtL1Qs4POZ9HURQm92vKD74+o6x9OilxMX/+fCZPnsyJEydITEzk9ddf50c/+hE1\nNTXMmjWL0aNHs2zZsq7u5hVFT7/GLwcpG+9I2XjnYrIprbVxrrIBAJ1GoX+Y9xdXcWaja1LT4lob\nxbXW9uvoFUTvHNOXSCTdms1nyqmsdwathZp0jI67vBHOsQlmVh4pwiHgeHEd5yrqe3WAdXuzYsWK\nFssWLVrUBT2RSCSSS8MZD+Gkf5gfhlYyLmk1Cn1D/cgocU5kml5YS2SSocP72N2QIxFdjMyi4B0p\nG+/0dNl8frxpFOKapBC0Gt9GIaApzWtzAg1aRsQEusrr5GiEpJvT06/xy0HKxjtSNt65mGwOF9S4\nvg+KuHj8XX/p0iSNCIlE0r04XVpHepFztlCdRmFin+CLbOEbExLNru/rT5Whtl92a4lEIpFc4Rxv\nZggkhV88Bq9/aFOddGlESLoC6b/oHSkb7/Rk2XyeXur6nhoX2OZMShfGRJxneEzTzKMltTaONxoq\nEkl3pCdf45eLlI13pGy805psLDYHWeX1AChAHw/urhoF9FrFNTLeL6ypzplSCw61972YajcjoqKi\ngrvuuouhQ4cybNgwdu3a1V5NSySSXoLF5mDD6SZXo6v7hbRb2zqNwsjYJpemrZkyS5NEIpFIIKOk\njvM2QEyQAZNe26LOtQPC+Pstg5jbmPY1yKjDbHTWa3AI8qsbOq2/3YV2MyIefvhh5syZQ3p6OocP\nH2bo0KHt1XSPRvovekfKxjs9VTa7siux2FQAogMNDPBhSPlCPMVEnKd5gPa2rEraaZociaTd6anX\neHsgZeMdKRvvtCab5iPT/UJ91ztxwUbX9zNllkvr2BVMuxgRlZWVbN261ZWNQ6fTERzcPn7MEomk\n9/D1qabRgfGJZp/TuvrKoEh/TDrnba+wxurKrCGRSCSS3svx4qaYhr5hvmfuSzA3GRGZZfXt2qcr\ngXYxIjIzM4mMjGThwoWMGTOGBx98kLo66W/sC9J/0TtSNt7pibKpqrezL6fKVR6bcGlpXb3FRIDT\npSmluUtTVsUl7UPizqJFi4iOjiYlJcW1rKysjFmzZjFo0CCuv/56KiqkrNtCT7zG2wspG+9I2Xin\nNdm4j0T4bkTIkYh2wG63s3//fpYtW8b+/fsJCAjgqaeealFv2bJlPPXUUzz11FO8/PLLbj/otm3b\nZFmW3cpHjhzpVv3pTuUjR450q/60R3n5x1/SOEE1/kXHyD66z7X+m9073IyDyymPigui6vRBqk4f\nZHujEdEdjr8jytu2beOpp55i2bJlHTrZ28KFC1m7dq3bsqeeeopZs2Zx8uRJZs6c6VEnSCQSSVdT\nUmulpM4GgEGrEBtkvMgWTcS7jUT0PiNCEe3gFFxQUMCkSZPIzMwEcCmuzz77zFVnw4YNjBkz5nJ3\nJZFIeig//SyDI415uu9KiWJ6cmiH7MfmUHn0i1NYGy2WN+4eRnyw70rjSmb//v3MnDmzQ9rOysri\nlltucRn/Q4YMYfPmzURHR1NQUMD06dM5fvy42zZSL0gkkq5mW2YFf9zgfH4dEG7ix1P7eKznUAUO\nVaDRKOgaMzTZVcFPPj3pCsr+330jXVkArxQuRy+0y0hETEwMiYmJnDx5EoD169czfPjw9mhaIpH0\nAopqrC4DQgHGxF/eDNWtoddqGBwZ4CrvPlfZYfvqzRQWFhIdHQ1AdHQ0hYWFXdwjiUQiaUlGaZMr\nU59WXJk2ni7nJ59l8OmxYtcynUYhJqhppuqsXjYa0bYE7K3wwgsvcO+992K1WklOTuaNN95or6Z7\nNNu2bZPZFLwgZeOdniabTaebAqoHR/lj9rv0W9M3u3e0mqEJYHhMgMto2Z1dyR0joi55f5KLoyiK\n1yD5ZcuW0aeP881fcHAwKSkprnP7vItWbyw3d0/rDv3pTuULZdTV/elO5SNHjrB06dJu05/uVH75\n5Zc93l9O1cQCUHX6IPW6cBhxHdAUX3den5w5vJeqrAoYMMNtfby5H3lVVqpOH+Tz9bkM//bN3eJ4\nW7t+tm3bRnZ2NgBLlizhUmkXdyZfkMPWnulpD4PtiZSNd3qabL6/8rgrKO3bY2Iua5ZqX4yICouN\nX395BgCtAh9958obgr4UOtudadOmTcTExJCfn8+MGTOkO1Mb6GnXeHsiZeMdKRvveJKNEIJvvXOU\nino7AL+Z2Z/oZiMLzVmfUcaqtGJmDgjl9mYvns4vB7h5SAQPXZ3YQUfQMXS5O5Pk0pEXu3ekbLzT\nk2STVW7hTJkFRQiCbXYSHQ4Kz5Tx/+y9d3xc13Xv+z3TG3rvAAGikSDAXkSKIqlCWqLcZDu2b+Qn\nW/F78efakWPHiZObdxPnxfaNHSeKE6fYcSzJjiRLsi2JkiiKFHsDSRSCAInee8f0ds77Y4ABQGKI\nNgAG5Pl+Pvhg9sw+ZzYWZs4+a++1fmu0z4Lb6Zn3+WZzIAAi9WpSx/MgvBJc6xyb5QiZ+fLkk0/y\nwgsvAPDCCy/wsY99bIVHtLq4l77jwUa2TWBk2wRmJtsM2Tx+B0KjFIgzqed93qTwSaejdeT+knkN\nWjiTjIyMzHwRvSJHz7SwsWeYKLsblSRxrX1wsoMA0cnhJK+NI70oEdUMVUQXyvpEEx2jvgqjpW1j\nPJi1NInc9wOf/exnOX36NAMDA6SlpfGd73yHP/uzP+PTn/40//mf/0lmZia//vWvV3qYMjIyMtNo\nmJIPkRqhQ7GA2kSJpklhjrb7zImQdyJWmKkxajLTkW0TmNVuG0mSqK3q4Wc/OovlcitxNheqmSIr\nJRjqHOPGqUaO/6yUxrIOJPHuEZh3qxMxlcKEyeTqsk6zXL16Ebz88st0dXXhcrlob2/nmWeeITo6\nmuPHj1NXV8exY8eIjIxc6WGuKlb7d3wpkW0TGNk2gZnJNvWDk4nQaZF3V+lTCKBWCigV0x2NKIMK\njdL33KjDw4jdHYTRrg7knQgZGZllxTzq4L3Xq2hrHLzjNY1ejc6kQaFU4LK5sY1Nruq47G6qTzXR\nXT/AxsfyMEbqFzWOjEgdepUCu0dkwOambcRBRtTizikjIyMjs3poGJjciUiLuHuRuf050ezPib7j\neYUgkGDS0D6+s9024iRSP/+wqNVI0JyIzMxMwsPDUSqVqNVqSktLg3Xqexo5fjEwsm0Cs1pt01Tb\nz7u/vo5jykqNSyHQEW4gKjOKJwtjp6n4uBxuBtpGaK/uxTleDGioc4wz/13Oto+uIyblzgTsueRE\nACgVArlxBiq7fSpN1zrNshMhEzKs1u/4ciDbJjCybQIzk22mhTPNshNxNxLDtFOcCAcbkkwLPtdq\nImjhTIIgcOrUKcrLy2UHQkZG5g7KL7by2xev+R0IQYCuKCPn0mJpiDaxPjX8DhlQjU5Ncm4cW58s\nJGNDoq+IBOB2eLj4+nW6GwYWNaaC+MmQpmsd5kWdS0ZGRkZm9TDm8NBn8c1HKsX8KlXfztRaEfdT\nXkRQcyLkmOL5I8cvBka2TWBWk20kSeLcsTpOvH2TiUuEwaQh66FsbkSZ8CgVhKkVZIXPLKsHoFAq\nyChKouTRXNTjNSREr8TVIzfpax6a1neuOREA+fEG/+Pr3WZcXnEef5mMzNKxmr7jy41sm8DItgnM\n7baZuguRHK69I9dhPshOxCIRBIGHH36YLVu28NOf/jRYp5WRkVnFSJLE2WN1XDrV5H8uJt7ERz61\ngaop6q1Fsfo5qWKExxopeSwX/fiKkSRKlL5Vw1DXwqpOxxo1xBl9satOr0R1r3VB55GRkZGRWV00\nDMw9qXo2EsPuT4WmoOVEnD9/nqSkJPr7+3nkkUfIz89nz5490/rIlUnl9kIqK4bSeEKlPfFcqIwn\nUFvlSaL0dDOtnTUA7Nq1iz2P5XL52mVOlPWiyyoGQNNeRfmAiuJN21EoBCrLfSGRxRu3AUxr601a\niB2mq7WD5OhcRK/Iq//yGsUHcti1/3mKuqEAACAASURBVCE2b991R6XRu7Xz4400Hj8FQFlHPBuT\nw0LGfqFUmVRmeZFj2wMj2yYwsm0Cc7tt6m+Td50NryjhFSUUCgHVbbsWsUY1SsFXd2jA6sbq8t4X\nBUyXpGL1X//1X2MymfjGN77hf06uTCojc39xs7KLd1697m+nZEbx4MFclEoFpd0W/rmiD4BYnZIn\n8dJR00tmcRLp6xPndH672UnF+3X+gnQR8SYe+EzxvGtJXO828x+XuwDIidHzk4/nz+v41cRSVqxe\nCPK8ICMjs1J88bUaf62gb+5NJ3MWYY1AFasn+NsTzXSbXQD805O55E/JuQtlVrxitc1mw2z2JSVa\nrVaOHTtGUVFRME59zyPHLwZGtk1gQt02Hc1DHH29yt9OSAn3OxAAF7os/tc2xBpYQH0f9GFaCvZk\n+o8d7bNQc6ZpXjkRAGtjDUwsKjUM2hm+jzS+l5rvfe97rFu3jqKiIj73uc/hdDpXekirhlD/jq8k\nsm0CI9smMFNtY3V5/Q6EQvDlRCyW+zEvIihORG9vL3v27KGkpITt27fzxBNP8Oijjwbj1DIyMquM\noX4Lv/tlOV6vb5MzIkrP3kN5fgfC6vZS2T+5jbwhduGyqpEJYWRvSfW3Wyq7GeqcX36EXq0kK3py\nDBVdskpTMGhpaeGnP/0pZWVlVFVV4fV6eeWVV1Z6WDIyMjI0DU3mQySGadAoF387nHAf5kUEJSci\nKyuLioqKYJzqvkOOXwyMbJvAhKptnA43v3mxzC/jqtOr2fdEPhrt5KXmSo+Vcf+CFKOaWL2Kxdy2\nJ62NZaTHzEC7z3nw9ETgsLrQGQOrPd1OfpyBxvHKpdc6zOzLvrOgkMz8CA8PR61WY7PZUCqV2Gw2\nUlJSVnpYq4ZQ/Y6HArJtAiPbJjBTbTO1yNxc8iHmgrwTISMjI7NAJEni6Bs3GBlPVlOqFDz0eD6m\n8OkX6IvTQpkWX9xNEATWbk9Ha/CpLLkdHqo+bJjXOabVi+g0y3LVQSA6OppvfOMbpKenk5ycTGRk\nJA8//PBKD0tGRkaGhsGpykyyE7FQgqbOJLMwpirsyExHtk1gQtE2ZRdaqa/u9bd37c8mNmF61c4h\nh4dbQ76Lq4BP2hVAUAgolMIdxebmilqrIndHOlUfNo4rQRXSVddPcm7cnI5Pj9KhVyuwu0UGbW5a\nhh3TQpxk5k9jYyP/+I//SEtLCxEREXzqU5/iV7/6FZ///Oen9ZNV+2ZuT43fDoXxhFL7dhut9HhC\nqV1VVcUf/uEfhsx4Qqn9r//6r/7rS8OAjbFGXwRN2u7DwN1V/ABaqq5gax1Fmbtvxtc7a65hbuwg\nLLuEHrOLk6fPoFYqQubvXwrVviVRZ5oJWYVjZkLxZjBUkG0TmFCzTXf7CC//+2VE0Xc5yStKZOuD\nWXf0e695hJdv+YrDrYnQ8MXC2KCOo+5SG5fPnCUjpRCtUcOBZ7ag0sxtreRnpZ1UjO+S/D87UvjE\nDOobq53lVGd69dVX+eCDD/jZz34GwEsvvcSlS5f4l3/5F38feV4ITKh9x0MJ2TaBkW0TmAnbODwi\nH3uhElHyLWb93eM56Oep6heIv/qgiQGrL5z3Xz+eR3aMYZYjVp4VV2eSWTjylz0wsm0CE0q2sdtc\nvPVyhd+BiI43sumBjBn7Tg1lKo4N/sV1zaZk1uZsAMBpdVF3uX3Ox+bHTYY0lXXKydWLJT8/n0uX\nLmG325EkiePHj1NYWLjSw1o1hNJ3PNSQbRMY2TaBmbBN06Cd8emKeJMmaA4EQKJpakjTva9GF1Qn\nwuv1snHjRg4fPhzM08rIyIQokiRx7LfVmMfjPzVaJQ8+NinlOpUui4uWMZ+GtlKAwujgxKFORaVR\nkbVxMnm3qawDy7D9LkdMkh8/6dRc77bg9opBH9/9RHFxMU8//TRbtmxhwwafY/flL395hUclIyNz\nv1M/Jak6fZGVqm8nMfz+UmgKqhPx/PPPU1hYuOC45vsRWdM5MLJtAhMqtrlV2T0tD2Ln/pw7Eqkn\nuNQ9uQuRF6VDr1qajdCe4XrCY327CqJXovp045yOizVqiBlPznZ4RG722WY5QmY2vvWtb1FdXU1V\nVRUvvPACarV6pYe0agiV73goItsmMLJtAjNhm7ppTkRwF7Om70TITsSc6ejo4N133+XZZ5+VlU1k\nZO4DzKMOjr9V42+vXZdA2pqZpVElSQq6KlNABGFa7YjepiF6m4fmdOjU3YiyzrGgD01GRkZGZmWZ\n5kREBdmJCJediAXx9a9/nR/84AcoFHKaxXyQ4xcDI9smMCttG0mSeP+3N3A6PACYwrVs2jVzHgRA\n86iTXpuvr1YpkHfb6o/oFfF6RH9exWIo3riNsBgDidkx/udunGpEnEN40tS8iHK56JzMCrLS3/FQ\nRrZNYGTbBGb37t3Y3V7aRyYVAudTI8IrSrg8Ip67zFMJU3YiOkedeIMwp4UyQbnjP3LkCPHx8Wzc\nuFHehZCRuQ+4fqWDlroBf3vngRzUmsDJaRenhDIVRutQK6eHPLZW9XD+1Uo6anpvP3TBZJYkoVSP\nV8kettNc2TXrMblxBiZGVttvw+L0BG08MjIyMjIry9Sk6oQwDdp5hNWebBzmj4/U83ZNf8A+erWS\nSL1PEdAjSnSN3dvJ1UGpE3HhwgXeeust3n33XRwOB2NjYzz99NO8+OKL0/rJeuCy3rWsdx18vevl\nfv+RIRu/+I838LhFMlIKKShOorWzhtZO2LZ1BwClVy4BvrZXlHj39DmsHpHw7BI2xOqpLC8FfLsG\nAHX1FfR1DpNZnARwx+vzaU88BsgoyqSprJPWzho6X6/jD9b/X6g0qrvqgadF6rhxzTf+iu4sdmdG\nrvj/OxT0wGWWF1mqMzCybQIj2yYw586doz8y198Odj7EBIkmDSN23wJU64gjaMXsQpGg14k4ffo0\nP/zhD3n77benPS/rgc+M/IUPjGybwKyUbSRR4tWfldLRMgxARJSeQ58uQqUKvAtR2Wfj76/1ABCm\nVvAnmxNQ3Ca+0FzRRXt1L5nFSaSvT1zUGCvLS/3OhegVufL2TZxWnypU3s4M8nYGDrsC+O2NPk40\n+P6+wwWxfPWBtEWNJ5RYzjoRc0GeFwIjX/8CI9smMLJtAnPu3DkueFI5Pn59f6oonoeyo+Z8/PH6\nIX5X3c+BnCg+fpc6Qq9f7+VU0wgAz2xJ4rMli5vTlpqQqxMhqzPNHfnLHhjZNoFZKdtcu9DqdyAE\nwRfGdDcHAuDclNyC4jj9HQ5EsJlwIAAUSgUZRZMX8MZrHTjt7rsenxMzmfQt14uQWSnk619gZNsE\nRrZNYHbv3k3dwKTk95LtRITdPzKvQQlnmsrevXvZu3dvsE8rIyOzwgz2WTh7rM7fXr85hdgE012P\nsbq9lPVOKmFsjFv+6p0JWdF03OzDNurA4/JSX9rG+r3ZAftnRk06EZ1jTnrNLhLCNAH7ywRmZGSE\nZ599lurqagRB4Oc//zk7duxY6WHJyMisIHabi9aGQTpbhxkbceCwuVBrVBhMGhJTI0hfEzPr3LIQ\nbK7bk6qDWyNigsQp80Xr8L3tRMhSSiuMrOkcGNk2gVlu24hekfder8Lr8SkcRcUaWT9FRjUQpT1W\n3ONZbElGNQmGmesECAoBhVIIyi7m1JyIiXNP5FoAtFR0YTcHvrCrlAJTR1EmqzQtmD/6oz/iIx/5\nCDdv3uT69esUFBSs9JBWDfL1LzCybQITyrZpbx7izV+V85PvnuTIK5WUX2yj8WYfna0jtNQPUFPe\nxYdv3+QXz5/jlz+5SE15F1IQ1Y1eP/ohE2dLDNegmWetIoUAaqWAUnH3eWqqE9E+6kS8hwWHgr4T\nISMjc+9x+XQzPR2jACgUArsezp6xKvXtnO+cVGXaGBe4NkTmhiQyNyQFfH2xxKRGEBZjwDxoQ/RK\n1F5opeSxvBn76tVKPrYujt9W+xQ4yjrHOJQXM2NfmcCMjo5y9uxZXnjhBQBUKhURERErPCoZGZnl\nZrDPwqn3ammuDaxqdDs9HaO8+9p1rpxr5sDhQlIz5567EIiOKaFFCwll2p8Tzf6cmWshTcWkVWHS\nKLG4vDg9In0W17QQp3sJeSdihZHjFwMj2yYwy2mb3q4xLn7Y4G8Xb08jKsZ4lyPGj7O6qRvfylUA\nG2KWsMDcFKbmREwgCAKZJcn+dltNL5bhwBWp86YUnavostzTK0lLRXNzM3FxcTzzzDNs2rSJP/iD\nP8Bmk6uAzxX5+hcY2TaBCSXbiKJE6ZkmXvzx+TsciNgEE0VbUtnzWC4Pf6yQfY/ns2V3JmlrolFM\nWenv7zbz6k8vc+5YHd451Pq5G0Jakf/xUuVDTDA1BPZezouQdyJkZGQC4vGIvPfadX8RuNhEEwVT\nbsbvxoUpFarXRmox3aWOxHIQlRhGZKKJkR4LSFB7sZXNH5k5vCY5XEuYVonZ6WXU4aFp0E5O7PLn\nc6xmPB4PZWVl/PM//zNbt27lueee4/vf/z7f+c53pvWTpb/ltty+99o2i4u//9sX6Osyk5FSCEBr\nZw3J6ZF8/NOHiIw2UHrlEr3DsC1nUhpcHwuf3LeZW5XdvHvkOKJXIiOlkEunmjh58jQPPLyW/Qce\nWtD4Lpw/x5jVTXh2CemRurtKfS+2nRimobz0IgBtw8lsS4sImf/PxONgSH8HXeI1ELKU38zIcmyB\nkW0TmOWyzZmjtZSeaQZAqVLw+Gc2EB45+46CJEn8yel2+sa1sj+zNoqi2OXZiZgq8Xo7Y/1WKqYk\nhz/09GbCY2feVfnF1S6udvjyIZ7dmsynixOCP9hlZjklXnt6eti5cyfNzb7Pz7lz5/j+97/PkSNH\n/H3keSEw8vUvMLJtAhMKtunvNvPbl64xNmUFPjreyI6HsomOm30XewKr2cnFEw30dI5NnifOyFPP\nbJnTPDTtXC4vB/73i4Rnl6AQ4IdPrEUzh5DchXKycZg3qvoAOJgbwx8/mL5k77VYVlzi1eFwsH37\ndkpKSigsLOTb3/52ME4rIyOzgnS2DnPlbLO/vWln+pwv3HXDDr8DoVMK5EeHRrGd8DgjUcnh/nbt\nxdaAffOmTHZycvX8SUxMJC0tjbo6n9N2/Phx1q1bt8KjkpGRWUq62oZ55aeXpzkQRVtSOfiJ9fNy\nIACMYVoOfLSQDdsma/UM9Vv59c+uMDZiv8uRd9IwMBlKmRSmXVIHAqYnV8vhTLOg0+k4efIkBoMB\nj8fD7t27Q8IbXg3INgqMbJvALLVtXC4P771excQ+ZWJqBLlFcy+Yc7J98qZ7fYwe9SxqFqJXRJLG\nVZpm6TsbgXYhJsjckMRwl29lq7t+gNE+CxHxk3KCkiTh9kpkT3F8bvRYcHnEeat53O/8+Mc/5vOf\n/zwul4vs7Gz+67/+a6WHtGqQr3+BkW0TmJW0TVvjIL99qQy3ywuAWq3kgUfXLiop2usRKSxJIixC\ny8UTjYiixMiQjVd/Vsrn/u8dGOeYsFw3YCM8uwRYeD6EV5TwihIKhYBqHgpNbSMOJEm6J2uoBW1G\nNBh88cIulwuv10t09OwZ7DIyMqHJmffqGBn0rdyo1Up27s+e8wXQ7PJS2j2ZD7EtYfZcgtaqHs6/\nWklHTe/CBjwPwmIMxKROqgTdvhvh8Ij88ZF6/u50Gwkm30Tg8krc6LUgMz+Ki4u5cuUKlZWV/OY3\nv5HVmWRk7lEab/XxxgvX/A6EVq/ikY+vW7Sq0m9fLOOV/yglKS2SBw/m+heZRofsvPHCNZwOz5zO\nU9Nr9T/OiFqYE3GycZg/PlLP2zWzq0xF6lToxhedLC4vw/a5jXO1ETQnQhRFSkpKSEhIYN++fRQW\nFgbr1Pc0oazpvNLItgnMUtqmqbafistt/vaWPZlzXu0BONNhxjO+g5FqUpNsWt5CbbfXiZiJjCly\nsj2Ngwz3zByulDelON5EfoSMzHIgX/8CI9smMCthm6baft78Zbm/jpDBqOHRj88/fGk2UrOi2XMw\nl4n1rL6uMd5+uRxxFtUmSZKo7rUy1lgBwJplUAoUBGGaQlPrPRrSFDR1JoVCQUVFBaOjozz22GOc\nOnWKhx56aFofWYVj5iz5UBpPKLWrqqpCajyh1K6qqlqS82/etI33f3OD1s4a3+t7drMmP47SK5cA\n2LZ1UkVjpvaWLds52T7mv1hvffQhYPLGfiLU6PZ2XX0FfZ3D/qJws/VfbLuxpYpRTzcRKt/16MhL\nb1H4YJZfZWOssQKHUkHhlkOcaR5hrLGCd/s0fHn754Nq79WkwiEjIyNzO52tw7z13+V+BT9TuJaH\nP1qIKXxp8uDSsqLZ/tAaLp1sAqClfpBzH9Tz4MGZ6/4AdI25GBnfsdCrFdNCjZaSRJPGX7G6fcTB\nxuSwZXnf5WRJ1Jn+5m/+Br1ezze/+U3/c7IKh4xMaCNJEm/9dwX11b6QIp1ezROfLUann7nK9Ezc\nGLDxd1d6fMcrBb61OWFOCWzNFV20V/eSWZxE+vq5514sBtuog6vv3GSihOkDnykmJiUCu9vLn7zT\ngE6l4LsHs/nWuw14xifIlz6zbtrq0mpjOdWZ5oI8L8jIrF76e8y88h+X/SFFxjAtj35iHUZT8Aqr\nvfafV3A6PDz1xS3T5qKKy23cuNrpbz/5uRJyA8wdH9QP8oPTvoWUwgQjX9mZuqCxHK8f4nfV/RzI\nieLj6+Nn7f9B/SBvVg8AcLgglq8+kDbLESvDiqszDQwMMDIyAoDdbueDDz5g48aNwTi1jIzMMlFT\n0eV3IAB27M+elwMB8GHbpBTfxjjDkitgLAZDhI74KfG6tRda7uijUSnInVIf4krH2B19ZGRkZO43\nRoZsvP5fV/0OhE6v5sCTBUF1IO5G8bY0kjMi/e33Xq9isG/mvLXqKfkQa6KXR2ocIHGKLe5Vhaag\nzPDd3d3s37+fkpIStm/fzuHDh0NqtSuUkWM7A7PabeO1OXB092Nt7sBc08BIWTWD567R/+ElBk6X\nMnjuGkOXKhi+WsVoxU0s9S04+4cQ3bMnYAXbNqPDdk68ddPfXrsuYd4JccMOD2V9kzJ6W+eQUD2B\noBBQKIWgqFfMJSdigoyiJBh/y4H2UQbafIshaqWAWul7oTBhMq63tH100eOTkZkLq/36t5TItgnM\nctjGbnPxxi+uYjU7AZ/4xv7DBfOu3TAXlCoFyhlU8QRB4IGH12IK992ou11e3vxl+YyJ1hNOxFhj\nxaKcCIXgmxuUc1QQnBo21X6POhFByYkoKiqirKwsGKeSkVkVeG0ObK2d2Fo6sLV0YmvpxNk3iKt/\nCGf/EK7+Yby2+elYT0VpMqCODEcTE4k+NRF9WtKUn0REtztof4skSrz3+nVcTt/FNyxCx6ZdGfM+\nz+l2M+NRP2SGa4g3zH0XI3NDEplTkp2XC32YlsQ1MfQ0DgJw60ILD3ymmH84nOvvsy7ByOu+FBTK\nu2SpVxkZmfsXr0fkrV9VMDxed0GhFNj7eF7Qk6gn+MQXNgd8TatTsfdQHkffuIHXIzI0YOWD393g\n8c8U+xekLE6PPy9BISxcmQlgf040+3PmrjwaY1SjUgh4RIkhuwez00OYNmipyCHBvfXXrEJkvevA\nhIJtRI8Ha0Mb5poGzDfqGaupx3KrCWfPwJK+r9diw2ux4ejoYazy1h2vC0olZ9ekEVaQTVjBGkwF\n2YQX5aFPmX9V5SvnmuloHvadV4BdD+eg1ijndQ6PKHGyfTLUZ1vC0kwoc2G2OhG3k74+kd7mISRR\nYqhrjP7WYeIzJyeKOJOGOKOafqsbp0ekstvC1rTwu5xRZiper5ctW7aQmprK22+/vdLDWTWEwvUv\nVJFtE5iltI0kSXzwZjXtzUP+5x54eC2JKSsn3RwVa2THvjWc/6ABgFvXe8jKi2PdxhRgeihTwabt\naJdxAUghCCSYNHSO+XZs2kYcrEswzXLU6kJ2ImRkpuDoHWCk9DrDV6sYuXIDc3U9otO1oHMJKiWq\ncBMKrcb3o9Gg1GkQ1CoQJSSviOT1IokikseD1+bAY7bisVjxL+kHQPJ6sda3YK1voeetE/7ntUlx\nRG0pInLLeiK3rCd8fS4KbeBE4K62Yc4dq/e3129OIS5x/goSl7stDDt9+uAmtYLCEKlQPRd0Jg2J\n2TF01/scw1vnW4nLiJoWWrU+0cTJRp+jdbF1VHYi5sHzzz9PYWEhZrMskSsjs5opPd3EjWuTycwl\nO9LJyIlZwRH5yMqNo6djlMabvvoNJ96qISUjishoA+Vdk9edtbFzD7ENFolhU5yIYdmJkAkycmXv\nwCyHbewdPQyevcrguauMlFZhb++e24EKBdqEWHTJceiS49ElxaONi0YdFY460vejNBkWFOMvieK4\nQ2HBNTiCs28QZ8+A73fvII6uXsq7WilU3Lna7+zup+ftD+l5+0PfMHUaorYXE/vgNmL2biWsMAdB\n4VuJsdtcvP1KpV+aLzbBRNGW+atWSJLEu82TuQI7Eo2zVvNcSirLSxewG5FAT+Mgkigx0mumt2mI\nxOzJybE4aYoT0TbK/5RSUdyD1UeDTUdHB++++y5/8Rd/wY9+9KOVHs6qQp4bAiPbJjBLZZvaqh7O\nTllwys6PY92m5KC/z0LZsjuLvi4z5lEHLqeXd399nd/7g21UdE0mW0sdVbB+efN1b69cfa8hOxEy\n9xXuMQuDZ68ydPYqA2evYmtsm/UYTWwUhjVpGNekYcxOx5CVijYpDoVqab4+gkKBymRAZTKgS5pZ\nRs5++RLrI+KwNY/nZTR1YKlvRrQ7p/UTHS4GT19h8PQV+BvQxEQSvWcLcQd2cdkchXn8oqbRKtn9\n6FoUC1BTqh6002727daoFcKKhjItFK1BQ3JuLJ23fCtZty60kLAm2u8EZkXrMWqUWF1eBm1u6gds\n5C1RDPC9xNe//nV+8IMfMDYmq1rJyKxWutpGeO+16/52Qko42x5aExQhjGCh1ih54JG1vP+bG0ii\nRFfbCCc/qKdpyJebqBAgZYlqV9yNxCmFWu/FgnNBuQtqb2/n6aefpq+vD0EQ+PKXv8zXvva1YJz6\nnkdeTQlMsGxja+2i74Nz9B87z9CFMiSPN2BfQaPGlJdFeOFawgqzMeWvQR0ZWqErosvNjuKNKNRq\nwvKz/c9LXi+2lk7MNY2YbzZgrmnE2d037VjX4Ag9vzvOjTozPTse8z+/dWPsgosDHWma3IXYHG/A\noJ6/IyJ6RSRpXKVpkbsY892FmCCtMIHu+kFEr8hYv5X2W/2kF/icOKVCYH2CkcvjeR8XWkZlJ2IW\njhw5Qnx8PBs3buTUqVMB+8lFSGdu7969O6TGI7dXT3uCYJzPanbQWKbA4xFp7azBYNLwqS99FqVS\nMecipItpez1etm7ZgVKl4MrVy3ft39R2A1VYP+7RWAB+98o7iDFhKAq2kBmlR60UuHb5gr+o6LXL\nFwDm3L5y8QKiJLF5xy5UCmFOxw/bPIAvV7H04gXOGrvZs2dP0P4/C2lPPA5GEdKgFJvr6emhp6eH\nkpISLBYLmzdv5ne/+x0FBQX+PnJRIZnlQhJFRstr6Dt2jr73z2G51RSwr6BRE74+l4iNhYRvyMOY\nnY5CHdobdDXf/ntGy6op+O4fE7l5/V37OvsGGS2vYaSsmtHyGjyjFqzxabQcehpJ6Uuejqm+RNLl\nY+jzc4h6bC+Rj+1FkxA3p7HUDzv4m0tdgE8v+rmN8UTr5m+/lSg2NxNN5Z101PgcL6tGxe99ZSfC\nuFNT2WXmp6W+vzUjSsdPP1kQ8DyhynIWm/vzP/9zXnrpJVQqFQ6Hg7GxMT75yU/y4osv+vvI84KM\nTOjisLt5+d8v++svaHUqDj5VRFjE8q3oByo2FwhRlDj+ZjV947kQNpWSi6nRPFIQxxMFsYsay3yL\nzQGIksS33mnA4REB+NVn1xFnDK2CpYuZF4Jyt5SYmEhiom/iN5lMFBQU0NXVNc2JkJkZObYzMPOx\njSSKjFyrpufN4/QcOXlX9SRjTgaRW9YTsbGQsMIcFJr5FVQLBWpEK3P5dmnjY4h/bA/xj+1BEkUG\nbrXx7nU3kuBzIPT9nSRcOQ6A/VYD9lsNdP3TzzFuXEfUwX1EHtiN6i47MW+O5wkAbIjTL8iBCDYL\nyYmYIK0wga66AUSPiNHlobO2n9Tx3YiCeCNqhYBblGgddtA24iA9cvUkkC833/3ud/nud78LwOnT\np/nhD384zYGQuTvy3BAY2TaBCZZtvF6Rt/67wu9AKBQCew/lLasDsRAUCoFdB9byzquVuF1eDB4v\neYMW8uIypu1CLNt4BIHUCC0Ng76wqrp+W8g5EYsh6DN+S0sL5eXlbN++PdinlpGZhiRJjJZV0/3W\nCXrfPomjq2/GfoJaRcTGQqK2FxO1vRht3Nx1nu8lvBKc69DgGo8W0qigJM6FtygfW3UdeMaL9EgS\n1rIbWMtu0PF/fkL4zs1EHXyIiH27UOgm4zubRp1c7/ddGAVgb8r8VZ1CDbVWRWJuHF01vsrdtRdb\nSc6LQ6EQ0KgUFCYYqez2Taqnm4b5/U3LX9titRJK8dMyMjKBkSSJ42/W0DZePwdg54Ec4pNDK7Q3\nEKZwLbnb06k+2wxAqtmOftjKSmVmpUfpJp2IARsPZEbOcsTqIahOhMVi4amnnuL555/HZLpTxkqO\nfZXbwYjtNN9s5MiP/pXB89fIGfIlEteIPi3oCcWiWr1IWEEODz1xiMhN67hSW8MokDjuQFyq8BVH\n3FGyaVW2Aa421PLweDjTbP0vll+j8uYoSuUaANq6aliXG0bCzl3wyC6uXL2E/VYD2a2D2KtrqfH6\nbpQLMTJ2rpRLZ06iMOjZffhJoj/6KFXmAV6pHYJY335ITP9Num51EDe+AzBRNbp4ju26+gr6OofJ\nLE5a0PFT28Ubty3q+MS8OM6eOIVKlMigkI6aXvqtvpC4zanrqey2MNZYwWs9av7Hxs8jCELIfF+W\nMvZ1Mezdu5e9e/euyHuvVuSV/7OVrgAAIABJREFU9sDItglMMGxTeqaZqqsd/nbx9jSychcXCrTc\n9Jh09Bi1JFp99wg3jjew7wtbVmQsU3es68eL9N0rBCUnAsDtdvPEE09w6NAhnnvuuTtel2NfZRaD\ns2+Q7t9+QOdr72G+UT9jH1W4iegHNhHz4FYiivMRlPMrmLZamE9OxATXb41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onOPxrB4P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n2wr8OUN4ijvEEc5Q3iKG+wjvKF3g1E3uC0QoS1iYXKy8v73GckXBBtiY25bdu2YcmSJYOR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\njru5AU9rUyGSlFZfx7MRFbdWTtbnp6PCw87KxWcyqhrKu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"text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we don't really care how accurate we become about the inference of the hidden probabilities — for this problem we are more interested in choosing the best bandit (or more accurately, becoming *more confident* in choosing the best bandit). For this reason, the distribution of the red bandit is very wide (representing ignorance about what that hidden probability might be) but we are reasonably confident that it is not the best, so the algorithm chooses to ignore it.\n", "\n", "From the above, we can see that after 1000 pulls, the majority of the \"blue\" function leads the pack, hence we will almost always choose this arm. This is good, as this arm is indeed the best.\n", "\n", "Below is a D3 app that demonstrates our algorithm updating/learning three bandits. The first figure are the raw counts of pulls and wins, and the second figure is a dynamically updating plot. I encourage you to try to guess which bandit is optimal, prior to revealing the true probabilities, by selecting the `arm buttons`." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython.core.display import HTML\n", "\n", "#try executing the below command twice if the first time doesn't work\n", "HTML(filename = \"BanditsD3.html\" )" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " \n", " \n", " \n", "\n", " \n", "\n", "\n", " \n", "
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\n", "\n", "\n" ], "output_type": "pyout", "prompt_number": 4, "text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Deviations of the observed ratio from the highest probability is a measure of performance. For example,in the long run, optimally we can attain the reward/pull ratio of the maximum bandit probability. Long-term realized ratios less than the maximum represent inefficiencies. (Realized ratios larger than the maximum probability is due to randomness, and will eventually fall below). \n", "\n", "### A Measure of *Good*\n", "\n", "We need a metric to calculate how well we are doing. Recall the absolute *best* we can do is to always pick the bandit with the largest probability of winning. Denote this best bandit's probability of $w_{opt}$. Our score should be relative to how well we would have done had we chosen the best bandit from the beginning. This motivates the *total regret* of a strategy, defined:\n", "\n", "\\begin{align}\n", "R_T & = \\sum_{i=1}^{T} \\left( w_{opt} - w_{B(i)} \\right)\\\\\\\\\n", "& = Tw^* - \\sum_{i=1}^{T} \\; w_{B(i)} \n", "\\end{align}\n", "\n", "\n", "where $w_{B(i)}$ is the probability of a prize of the chosen bandit in the $i$ round. A total regret of 0 means the strategy is matching the best possible score. This is likely not possible, as initially our algorithm will often make the wrong choice. Ideally, a strategy's total regret should flatten as it learns the best bandit. (Mathematically, we achieve $w_{B(i)}=w_{opt}$ often)\n", "\n", "\n", "Below we plot the total regret of this simulation, including the scores of some other strategies:\n", "\n", "1. Random: randomly choose a bandit to pull. If you can't beat this, just stop. \n", "2. largest Bayesian credible bound: pick the bandit with the largest upper bound in its 95% credible region of the underlying probability. \n", "3. Bayes-UCB algorithm: pick the bandit with the largest *score*, where score is a dynamic quantile of the posterior (see [4] )\n", "3. Mean of posterior: choose the bandit with the largest posterior mean. This is what a human player (sans computer) would likely do. \n", "3. Largest proportion: pick the bandit with the current largest observed proportion of winning. \n", "\n", "The code for these are in the `other_strats.py`, where you can implement your own very easily." ] }, { "cell_type": "code", "collapsed": false, "input": [ "figsize( 12.5, 5 )\n", "from other_strats import *\n", "\n", "#define a harder problem\n", "hidden_prob = np.array([0.15, 0.2, 0.1, 0.05] )\n", "bandits = Bandits( hidden_prob )\n", "\n", "#define regret\n", "def regret( probabilities, choices ):\n", " w_opt = probabilities.max()\n", " return ( w_opt - probabilities[choices.astype(int)] ).cumsum()\n", "\n", "#create new strategies\n", "strategies= [upper_credible_choice, \n", " bayesian_bandit_choice, \n", " ucb_bayes , \n", " max_mean,\n", " random_choice ]\n", "algos = []\n", "for strat in strategies:\n", " algos.append( GeneralBanditStrat( bandits, strat ))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 14 }, { "cell_type": "code", "collapsed": false, "input": [ "#train 10000 times\n", "for strat in algos:\n", " strat.sample_bandits( 10000)\n", " \n", "#test and plot\n", "for i,strat in enumerate(algos):\n", " _regret = regret( hidden_prob, strat.choices )\n", " plt.plot( _regret, label = strategies[i].__name__, lw = 3)\n", "\n", "plt.title(\"Total Regret of Bayesian Bandits Strategy vs. Random guessing\" )\n", "plt.xlabel(\"Number of pulls\")\n", "plt.ylabel(\"Regret after $n$ pulls\");\n", "plt.legend(loc = \"upper left\");" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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TpkyBVCpF9+7dsXnzZtSpU0ccIEZEqFu3Lh49eoSvvvoKHh4eCAgIAACMHDkS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\n8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"text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Like we wanted, Bayesian bandits and other strategies have decreasing rates of regret, representing we are achieving optimal choices. To be more scientific so as to remove any possible luck in the above simulation, we should instead look at the *expected total regret*:\n", "\n", "$$\\bar{R_T} = E[ R_T ] $$\n", "\n", "It can be shown that any *sub-optimal* strategy's expected total regret is bounded below logarithmically. Formally,\n", "\n", "$$ E[R_T] = \\Omega \\left( \\;\\log(T)\\; \\right)$$\n", "\n", "Thus, any strategy that matches logarithmic-growing regret is said to \"solve\" the Multi-Armed Bandit problem [3].\n", "\n", "Using the Law of Large Numbers, we can approximate Bayesian Bandit's expected total regret by performing the same experiment many times (500 times, to be fair):" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#this can be slow, so I recommend NOT running it. \n", "\n", "trials = 500\n", "expected_total_regret = np.zeros( ( 10000, 3 ) )\n", "\n", "for i_strat, strat in enumerate( strategies[:-2] ):\n", " for i in range(trials):\n", " general_strat = GeneralBanditStrat( bandits, strat )\n", " general_strat.sample_bandits(10000)\n", " _regret = regret( hidden_prob, general_strat.choices ) \n", " expected_total_regret[:,i_strat] += _regret\n", " \n", " plot(expected_total_regret[:,i_strat]/trials, lw =3, label = strat.__name__ )\n", " \n", "plt.title(\"Expected Total Regret of Multi-armed Bandit strategies\" )\n", "plt.xlabel(\"Number of pulls\")\n", "plt.ylabel(\"Exepected Total Regret \\n after $n$ pulls\");\n", "plt.legend(loc = \"upper left\");" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0\n", "1" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", "2" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] }, { "output_type": "pyout", "prompt_number": 24, "text": [ "" ] }, { "output_type": "display_data", "png": 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Ro3Hp0iU899xzeOGFF/D888/XmZQAAHr16lXlvW+++QbffvstUlNToVarodfr6+zj0pBj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\njh1DcHAwysrKsGrVK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} ], "prompt_number": 24 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.figure()\n", "[pl1, pl2, pl3] = plt.plot( expected_total_regret[:, [0,1,2]], lw = 3 )\n", "plt.xscale(\"log\")\n", "plt.legend([ pl1, pl2, pl3], \n", " [\"Upper Credible Bound\", \"Bayesian Bandit\", \"UCB-Bayes\"],\n", " loc=\"upper left\")\n", "plt.ylabel(\"Exepected Total Regret \\n after $\\log{n}$ pulls\");\n", "plt.title( \"log-scale of above\" );\n", "plt.ylabel(\"Exepected Total Regret \\n after $\\log{n}$ pulls\");" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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w119/8eKLL+Y6NldXV3bt2kVERASTJk1i1KhR3Lx5Uz0eGBiIp6cnV69e5d13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} ], "prompt_number": 25 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Extending the algorithm \n", "\n", "\n", "Because of the Bayesian Bandits algorithm's simplicity, it is easy to extend. Some possibilities:\n", "\n", "- If interested in the *minimum* probability (eg: where prizes are a bad thing), simply choose $B = \\text{argmin} \\; X_b$ and proceed.\n", "\n", "- Adding learning rates: Suppose the underlying environment may change over time. Technically the standard Bayesian Bandit algorithm would self-update itself (awesome) by noting that what it thought was the best is starting to fail more often. We can motivate the algorithm to learn changing environments quicker by simply adding a *rate* term upon updating:\n", "\n", " self.wins[ choice ] = rate*self.wins[ choice ] + result\n", " self.trials[ choice ] = rate*self.trials[ choice ] + 1\n", "\n", " If `rate < 1`, the algorithm will *forget* its previous wins quicker and there will be a downward pressure towards ignorance. Conversely, setting `rate > 1` implies your algorithm will act more risky, and bet on earlier winners more often and be more resistant to changing environments. \n", "\n", "- Hierarchical algorithms: We can setup a Bayesian Bandit algorithm on top of smaller bandit algorithms. Suppose we have $N$ Bayesian Bandit models, each varying in some behavior (for example different `rate` parameters, representing varying sensitivity to changing environments). On top of these $N$ models is another Bayesian Bandit learner that will select a sub-Bayesian Bandit. This chosen Bayesian Bandit will then make an internal choice as to which machine to pull. The super-Bayesian Bandit updates itself depending on whether the sub-Bayesian Bandit was correct or not. \n", "\n", "- Extending the rewards, denoted $y_a$ for bandit $a$, to random variables from a distribution $f_{y_a}(y)$ is straightforward. More generally, this problem can be rephrased as \"Find the bandit with the largest expected value\", as playing the bandit with the largest expected value is optimal. In the case above, $f_{y_a}$ was Bernoulli with probability $p_a$, hence the expected value for a bandit is equal to $p_a$, which is why it looks like we are aiming to maximize the probability of winning. If $f$ is not Bernoulli, and it is non-negative, which can be accomplished apriori by shifting the distribution (we assume we know $f$), then the algorithm behaves as before:\n", "\n", " For each round, \n", " \n", " 1. Sample a random variable $X_b$ from the prior of bandit $b$, for all $b$.\n", " 2. Select the bandit with largest sample, i.e. select bandit $B = \\text{argmax}\\;\\; X_b$.\n", " 3. Observe the result,$R \\sim f_{y_a}$, of pulling bandit $B$, and update your prior on bandit $B$.\n", " 4. Return to 1\n", "\n", " The issue is in the sampling of $X_b$ drawing phase. With Beta priors and Bernoulli observations, we have a Beta posterior — this is easy to sample from. But now, with arbitrary distributions $f$, we have a non-trivial posterior. Sampling from these can be difficult.\n", "\n", "- There has been some interest in extending the Bayesian Bandit algorithm to commenting systems. Recall in Chapter 4, we developed a ranking algorithm based on the Bayesian lower-bound of the proportion of upvotes to total votes. One problem with this approach is that it will bias the top rankings towards older comments, since older comments naturally have more votes (and hence the lower-bound is tighter to the true proportion). This creates a positive feedback cycle where older comments gain more votes, hence are displayed more often, hence gain more votes, etc. This pushes any new, potentially better comments, towards the bottom. J. Neufeld proposes a system to remedy this that uses a Bayesian Bandit solution.\n", "\n", "His proposal is to consider each comment as a Bandit, with the number of pulls equal to the number of votes cast, and number of rewards as the number of upvotes, hence creating a $\\text{Beta}(1+U,1+D)$ posterior. As visitors visit the page, samples are drawn from each bandit/comment, but instead of displaying the comment with the $\\max$ sample, the comments are ranked according to the ranking of their respective samples. From J. Neufeld's blog [7]:\n", "\n", " > [The] resulting ranking algorithm is quite straightforward, each new time the comments page is loaded, the score for each comment is sampled from a $\\text{Beta}(1+U,1+D)$, comments are then ranked by this score in descending order... This randomization has a unique benefit in that even untouched comments $(U=1,D=0)$ have some chance of being seen even in threads with 5000+ comments (something that is not happening now), but, at the same time, the user is not likely to be inundated with rating these new comments. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Just for fun, though the colors explode, we watch the Bayesian Bandit algorithm learn 15 different options. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "figsize( 12.0, 8)\n", "beta = stats.beta\n", "hidden_prob = beta.rvs(1,13, size = 35 )\n", "print hidden_prob\n", "bandits = Bandits( hidden_prob )\n", "bayesian_strat = BayesianStrategy( bandits )\n", "\n", "for j,i in enumerate([100, 200, 500, 1300 ]):\n", " plt.subplot( 2, 2, j+1) \n", " bayesian_strat.sample_bandits(i)\n", " plot_priors( bayesian_strat, hidden_prob, lw = 2, alpha = 0.0, plt_vlines=False )\n", " #plt.legend()\n", " plt.xlim(0, 0.5 )\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[ 0.01086616 0.20672538 0.00137644 0.02843378 0.00809559 0.09709516\n", " 0.00540949 0.02886983 0.1670677 0.01158008 0.06498409 0.15652432\n", " 0.17674427 0.0351021 0.11126791 0.00988438 0.24309639 0.02708666\n", " 0.04342859 0.00825645 0.01890499 0.24829156 0.15444239 0.03984653\n", " 0.00785845 0.00758847 0.08759903 0.02189288 0.0228888 0.18814637\n", " 0.04898048 0.01136161 0.02290211 0.17823588 0.17785098]\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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1a5g7dy6bNm0qtD8iIoIWDT5m0ebaDB/06R3rGLDgD/LyfdDrklg/qm+hY5d+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\nFcoPhgJwc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/Lr2T3F/AYRBjniNOXbU7QaJT64pS/3XYVDhLapgc1vj2J4Uz4K5IQ4u5nL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8zts9AG/K+yU8D9q1B/dz/ZQETNbsYWreHH925m5n1fIh6nws/ijAXIyFw08Cqm3307latS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bmnjv4c/Q+CWAKKJtb8I9qow7rzuASaPQ6Nby0aFU5maOw4xK56iy+LNl6EjmpAYzL7rn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\nFxNu30PM2kJg34vEhvsZ2DyEp6GdnBtXkzR/xpj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bITb5J0Lwja003Pk/IATTHroP78TR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"text": [ "" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Eliciting expert prior\n", "\n", "Specifying a subjective prior is how practitioners incorporate domain knowledge about the problem into our mathematical framework. Allowing domain knowledge is useful for many reasons:\n", "\n", "- Aids speeds of MCMC convergence. For example, if we know the unknown parameter is strictly positive, then we can restrict our attention there, hence saving time that would otherwise be spent exploring negative values.\n", "- More accurate inference. By weighing prior values near the true unknown value higher, we are narrowing our eventual inference (by making the posterior tighter around the unknown) \n", "- Express our uncertainty better. See the *Price is Right* problem in Chapter 5.\n", "\n", "plus many other reasons. Of course, practitioners of Bayesian methods are not experts in every field, so we must turn to domain experts to craft our priors. We must be careful with how we elicit these priors though. Some things to consider:\n", "\n", "1. From experience, I would avoid introducing Betas, Gammas, etc. to non-Bayesian practitioners. Furthermore, non-statisticians can get tripped up by how a continuous probability function can have a value exceeding one.\n", "\n", "2. Individuals often neglect the rare *tail-events* and put too much weight around the mean of distribution. \n", "\n", "3. Related to above is that almost always individuals will under-emphasize the uncertainty in their guesses.\n", "\n", "Eliciting priors from non-technical experts is especially difficult. Rather than introduce the notion of probability distributions, priors, etc. that may scare an expert, there is a much simpler solution. \n", "\n", "###Trial roulette method \n", "\n", "\n", "The *trial roulette method* [8] focuses on building a prior distribution by placing counters (think casino chips) on what the expert thinks are possible outcomes. The expert is given $N$ counters (say $N=20$) and is asked to place them on a pre-printed grid, with bins representing intervals. Each column would represent their belief of the probability of getting the corresponding bin result. Each chip would represent an $\\frac{1}{N} = 0.05$ increase in the probability of the outcome being in that interval. For example [9]:\n", "\n", "> A student is asked to predict the mark in a future exam. The figure below shows a completed grid for the elicitation of a subjective probability distribution. The horizontal axis of the grid shows the possible bins (or mark intervals) that the student was asked to consider. The numbers in top row record the number of chips per bin. The completed grid (using a total of 20 chips) shows that the student believes there is a 30% chance that the mark will be between 60 and 64.9.\n", "\n", "\n", "\n", "\n", "From this, we can fit a distribution that captures the expert's choice. Some reasons in favor of using this technique are:\n", "\n", "1. Many questions about the shape of the expert's subjective probability distribution can be answered without the need to pose a long series of questions to the expert - the statistician can simply read off density above or below any given point, or that between any two points.\n", "\n", "2. During the elicitation process, the experts can move around the chips if unsatisfied with the way they placed them initially - thus they can be sure of the final result to be submitted.\n", "\n", "3. It forces the expert to be coherent in the set of probabilities that are provided. If all the chips are used, the probabilities must sum to one.\n", "\n", "4. Graphical methods seem to provide more accurate results, especially for participants with modest levels of statistical sophistication." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Example: Stock Returns\n", "\n", "\n", "Take note stock brokers: you're doing it wrong. When choosing which stocks to pick, an analyst will often look at the *daily return* of the stock. Suppose $S_t$ is the price of the stock on day $t$, then the daily return on day $t$ is :\n", "\n", "$$r_t = \\frac{ S_t - S_{t-1} }{ S_{t-1} } $$\n", "\n", "The *expected daily return* of a stock is denoted $\\mu = E[ r_t ] $. Obviously, stocks with high expected returns are desirable. Unfortunately, stock returns are so filled with noise that it is very hard to estimate this parameter. Furthermore, the parameter might change over time (consider the rises and falls of AAPL stock), hence it is unwise to use a large historical dataset. \n", "\n", "Historically, the expected return has been estimated by using the sample mean. This is a bad idea. As mentioned, the sample mean of a small sized dataset has enormous potential to be very wrong (again, see Chapter 4 for full details). Thus Bayesian inference is the correct procedure here, since we are able to see our uncertainty along with probable values.\n", "\n", "For this exercise, we will be examining the daily returns of the AAPL, GOOG, MSFT and AMZN. Before we pull in the data, suppose we ask our a stock fund manager (an expert in finance, but see [10] ), \n", "\n", "> What do you think the return profile looks like for each of these companies?\n", "\n", "Our stock broker, without needing to know the language of Normal distributions, or priors, or variances, etc. creates four distributions using the trial roulette method above. Suppose they look enough like Normals, so we fit Normals to them. They may look like: " ] }, { "cell_type": "code", "collapsed": false, "input": [ "figsize(11., 5 )\n", "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\", \"#467821\"]\n", "\n", "normal = stats.norm\n", "x = np.linspace( -0.15, 0.15, 100 )\n", "\n", "expert_prior_params = {\"AAPL\":(0.05, 0.03),\n", " \"GOOG\":(-0.03, 0.04 ), \n", " \"TSLA\": (-0.02, 0.01), \n", " \"AMZN\": (0.03, 0.02 ), \n", " }\n", "\n", "for i, (name, params) in enumerate(expert_prior_params.iteritems() ):\n", " plt.subplot(2,2,i)\n", " y = normal.pdf( x, params[0], scale = params[1] )\n", " #plt.plot( x, y, c = colors[i] )\n", " plt.fill_between(x, 0, y, color = colors[i], linewidth=2,\n", " edgecolor = colors[i], alpha = 0.6)\n", " plt.title(name + \" prior\" )\n", " plt.vlines(0, 0, y.max(), \"k\",\"--\", linewidth = 0.5 )\n", " plt.xlim(-0.15, 0.15 )\n", "plt.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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ByJXbGcRHOy/A7QygYmLmTSTh7Q0BAGpvqMLMuZUSR0NSKS2DqC/v6/ryyy9j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\nW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"text": [ "" ] } ], "prompt_number": 18 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that these are subjective priors: the expert has a personal opinion on the stock returns of each of these companies, and is expressing them in a distribution. He's not wishful thinking -- he's introducing domain knowledge.\n", "\n", "In order to better model these returns, we should investigate the *covariance matrix* of the returns. For example, it would be unwise to invest in two stocks that are highly correlated, since they are likely to tank together (hence why fund managers suggest a diversification strategy). We will use the *Wishart distribution* for this, introduced earlier." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import pymc as pm\n", "\n", "n_observations = 100 #we will truncate the the most recent 100 days.\n", "\n", "prior_mu = np.array( [ x[0] for x in expert_prior_params.values() ] )\n", "prior_std = np.array( [ x[1] for x in expert_prior_params.values() ] )\n", "\n", "inv_cov_matrix = pm.Wishart( \"inv_cov_matrix\", n_observations, np.diag(prior_std**2) )\n", "mu = pm.Normal( \"returns\", prior_mu, 1, size = 4 )" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 33 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we pull historical data for these stocks:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# I wish I could have used Pandas as a prereq for this book, but oh well.\n", "import datetime\n", "import ystockquote as ysq\n", "\n", "stocks = [\"AAPL\", \"GOOG\", \"TSLA\", \"AMZN\" ]\n", "\n", "enddate = datetime.datetime.now().strftime(\"%Y-%m-%d\") #today's date.\n", "startdate = \"2012-09-01\"\n", "\n", "stock_closes = {}\n", "stock_returns = {}\n", "CLOSE = 6\n", "\n", "for stock in stocks:\n", " x = np.array( ysq.get_historical_prices( stock, startdate, enddate ) )\n", " stock_closes[stock] = x[1:,CLOSE].astype(float)\n", "\n", "#create returns:\n", "\n", "for stock in stocks:\n", " _previous_day = np.roll(stock_closes[stock],-1)\n", " stock_returns[stock] = ((stock_closes[stock] - _previous_day)/_previous_day)[:n_observations]\n", "\n", "dates = map( lambda x: datetime.datetime.strptime(x, \"%Y-%m-%d\" ), x[1:n_observations+1,0] ) " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 34 }, { "cell_type": "code", "collapsed": false, "input": [ "figsize(12.5, 4)\n", "\n", "for _stock, _returns in stock_returns.iteritems():\n", " p = plt.plot( (1+_returns)[::-1].cumprod()-1, '-o', label = \"%s\"%_stock, \n", " markersize=4, markeredgecolor=\"none\" )\n", "\n", "plt.xticks( np.arange(100)[::-8], \n", " map(lambda x: datetime.datetime.strftime(x, \"%Y-%m-%d\"), dates[::8] ),\n", " rotation=60);\n", "\n", "plt.legend(loc = \"upper left\")\n", "plt.title(\"Return space\")\n", "plt.ylabel(\"Return of $1 on first date, x100%\");" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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IJvJkGt4+zjzy54G1HtssZT/ffPMN8+bNw9HREW9vb2xtbSkqKiIpKYn+/fsT\nFBTU4AYABAQEkJCQwOXLl3Fzc2Pz5s1s2rSpyjFJSUnGn+fPn8/DDz9cLfEXBEEQhLagpKicLV+d\nJC/7Go4uHXh0YWCNM6zERV7ltx3nqVAbBkCeOHSJwSPFk+y6kPUyu7capm20dbBg2mMD2nziD9C9\nd0ee692xWa5lKAlq+NjOhurVt5Px7wBAUkjMe3pwrbMStRX3P9iDuMirJMVnc+lCNl17Ojf5NWv9\nK+jSpQvh4eFERkby3nvvsXjxYt59913OnTtHeHg4Xl5ejdIIlUrFhg0bGD9+PL1792bOnDn4+vqy\nceNGNm7c2CjXEO5NlY/Z2isRX9vWnuNrz7FBw+IrLixn85cnyMu+hlPHDjy6qObEHwxJz9K3xzFl\nbj+Q4PDeC0SeTL3ra9dVa//+LsZksn71Ptav3kfM2Ss1HhO2L4GE85mYmat45MmBVabJbO3xNVR7\njE+pNDzxSk6Pwdxc1S4SfwCrDmYMGd0dgD9+jePQoUNNfs1ae/4r9ezZk549ezZpQyZOnMjEiROr\nbHv66adrPPabb75p0ra0lIcffpjz588TFxeHqWnVEfTJyckMGDCA+fPns3bt2ir7HB0dsbS0RJIk\nrK2tmTFjBqtXr0ahUNCvXz/Wr1/PyJEjmzMUQRAEoQZFBWVs+fIkBXmlOHeyZvaCwDrNmNKrbyfK\nSzXs2xXD7z+fx9zChJ59XJuhxXWTGJvFnuAokGBiEw9MLswvZddPEcaxEbu3RnJobzwu1wdJ6/Qy\nEcdSDDO8SPDwvP71XqRLaH0mzPQnZHv09TUMWs+A7MYwYJgXp8MukZd9jR3fxeHu3KtJ/4bu+Pxr\n48aNDB06FBsbGxQKBTY2NgwbNox///vfTdaoe1FKSgpnzpzB2dmZPXv2VNsfFBSEr68vO3bsoKKi\notr+w4cPk5KSws8//8y2bdv47rvvAMNg6nu5PrRyYE17JeJr29pzfO05Nqh/fImxWWx4J5T/fHiQ\ngrxSXNxseHRh3RL/Sv2HeDJsbHdkGX7dfI6UxNz6NvuOLpzPYP3qfZzdX86F8xl3PF6v05NwPpOd\nP56lvExDeamG3VsjG71dYJi6MfJkKv/9+Ei16TlLitQkxWdz7EASJw9dMk7taGKipEsPp2rnEr+f\nbU9lCdLaL5a2+HS44cmFzP4hitk/RBGeXFjnfbejUinQaPQAuLv0Mk7921Rq7flfsWIFv/zyCy+9\n9BJ9+/aHxUmmAAAgAElEQVTFxsaGwsJCzp07x7p160hKSjLOyd9WZf0WRtSy9wHw/+g1XB6q/x9M\nY5wjKCiIkSNHMnDgQIKCgpg2bZpxnyzLbNmyhZUrV7J69WpCQkJuO96hR48eDBkyhLi4uHq3QRAE\nQWgau7dGGlculRQSjy4MrNO83rcaOqYbZdcqOHsshR3fn2HOXwbh6l51ikNZb0iSD4bEAxJjpvSi\nz0CP255T1sukXc4nLvIq507cKCna9WMEPft0xLuXC117OmHV4UaZRUlROZEn04g8mWqc+72SulxL\n1Kk0/ANuf836Ki4sZ+/2aC4n5ADQydOO/JxrSJLEQzP8cHTpQNaVIrKvFnMy7JJxsa7K1XsFoTGt\nO5xC4fW/5/f2X2Kwpy0lah3XKnRczC2l8t703dBLLAh0w6+jFd2dLFEpbt8ZW1nWBKCvff3dBqs1\n+f/yyy+JjIysNttLQEAAEyZMoG/fvm0++Y9a9j6aPMOcuWeefKXB54v+6/uMOb+73u/bvHkzK1as\nYMCAAaxZs4bs7GycnQ2DPo4dO0Z2djYPPvgg586dIygoqFryXzkTUlxcHMeOHeONN95ocCztQVhY\n+5qr+lYivratPcfXnmODuscnyzKnwi4bE38Ac3PVXSX+YHiaO2aKL2WlGuIir/LDp+GYmqno3b+T\nYdGijGKyM4qrrGIbsi2asN8T6ORhh6uHDXo9nD56GVkv07mrA5lXiqrM5w6Gumov995ciM7kQnQm\nSIbZVUqKypH1Mnq9bJx5xd7JEo8u9iTEZKGt0KHV6tm7PZqMtELGTPFFeZeDbCsXP9Nq9ciyjFaj\nx9zCxLDKbV/Xak+1HZys6NW3E26edlVmqKmJ+P1su1o6trxSDaU3/X1V6GQOXyqo8ViNXmbj8XQA\nzJQSnWzMuFqkxkSp4OWRXgz1unHjPmGmP3u2RXE57TzPvjC3SWOoU81/Te7lUpLGduzYMa5evcqE\nCROwtrbGx8eH4OBgnn32WQA2bdrE+PHjMTc3Z9q0aXzyySfk5OTg5HTjUeaoUaNQKpXY29vzxBNP\n8Nhjj7VUOIIgCAJQXqYhJDiKi7FZgGGqThNTJRMeaVi9sqSQmDjLnwvnM9DrZCrUWiKO3zIIWAJu\n6jwsKVKTEJNJQkxmlcMq22ZjZ45vPzesrM0I/yMRMwsVD87wQ6fVkxSfTWpSHgU3TTsKhkWK+g/2\nxLObA5IkMf76eqDRp9P4fWcM506kkp1RzNQ/9aeDjXm9YpRlucrTEjCUfTw03e+OAz1byww1QusX\nnlzIusPJyMDyB6om47fSyzK/xubw9amraK537ZspJR7q6UjfTh2wMlXSwVTJxdxS/nvqKjIwtrs9\nZRo95zOvkVao5nK+4SZbrdPx4cFktj/Z13j+br4uPPfGWMLCzJq8rKnW5H/hwoWMGTOGl156iX79\n+hmn+oyIiGDdunWNtthAS/L/6DWi/2oo2enzr7sv+7n5HPW1adMmRo8ejbW1NQDTpk0jKCiIZ599\nlrKyMnbt2sWGDRsM7fX3x9PTk+DgYJ555hnjOQ4ePEiXLl3qfe32rr32fFQS8bVt7Tm+9hwb3Dm+\njPRCfvkpgsL8MszMVUyc5U/3RpyeUalSYGqmMq4MrFQpGP5gD1w62eDcyZqrKQXG3u/xM/ywd7Ii\nI62QjLRCIk6kIl9PXlQqBY8uCqRTZztjp96AYV7AjeR5wFAvKiq0fPH3A8apFs0tTZj22H01tq3P\nQA+cOlqz88ezXEkp4JuPw0AGhUK64yrFWo2O2MirnA1PqZL4m5opmf74fY3W8Xiv/362ZY0VW3qh\nmvf/uIRaa/hbWB2axGP3dWKguzU9nSxR3lSik5hbysdhqcRlG26AB3W2YckwDzrVcCPay8WKKb7V\np+ssKNPw1JYYSq/X9pdpdOhlGcUtv9PN8d3VusgXGAb8fvvtt8TExFBSUkKHDh3w8/PjySefvO1s\nPC2prS3yVVZWRq9evZBl2biQmlqtpqioiIMHDxIbG8vTTz+No6MjSqWhdrGwsJCePXty4MABwDDb\nz+nTp2tM/vv378/69esZMWLEXbWvtX5ugiAIrc3NZSo6rQ69Hjq62/DwvP7YOTT+QkR3uwCT4X1R\nQP0Wiarv9a6VqPllUwRpl/KN20xMlUye0w9bewtsHSxITcwjZFsUsgydvR1Iu5RH2fUbGlNTJXpZ\nRmWibPIZhIS2zdCDnwLAiw94VunBv3nf04PdKNXoCb2YR2xWaY3nArAyVdLZ1ozL+eXoZRmNTkYG\nHCxVLB7qwQNd7O7qRrTySUNRuQ4ZeHmkJw/2cKzz+xtrka87Jv9tTVtL/rdt28Yrr7zCoUOHjNN7\nyrLMggUL6N+/P7GxsXh4eFSp4b9y5Qpjx47l0KFD9O7d+47J/9q1a6vcSZqYmBhvJO6ktX5uddXS\ntYFNTcTXtrXn+NpzbFBzfBveDTX2xAP0H+zJqEk+bXLQaWN9fzqdnk9W7UOr1df5PR3dbLhvqCe9\n+nZqss/uXvz9bC9qim32D1HGAbhKCfp2ssZMJWGmUnA0uRCNrnqqa2GioKeTJRdzS1FKEhN9nLim\n0XEmvZgrtwxiB5jW24mnAtywMm347+S+hDzWHEzGwULF17N7Y3nTOWv77pplhd87SUlJwdPTs8GN\nuJcFBQXx2GOP4e7uXmX7okWLjE9WDhw4YBz8C+Ds7MzYsWPZvHkzq1atuuM15syZU+X18uXLee21\n+pcnCYIgCDW7GJtVJfE3NVMyblrvFmxR66BUKnh4Xn92b41Er5fx6GoPMhTklVKUX4bupqRMqTSU\nILl53l2vqnDv0upv3FzqZDh7pfi2xw7ubMOY7vYM8bTF4jY3lxnFap7eFkfZ9ZvWDqZKlgzr3Gjt\nHdPdnl9is4nNKuWniAwWDXK/85sa0V33/JeXl2NlZYVOp7vzwc2orfX8t3bicxMEQbi98jIN+/8X\na1xlVqGQMDUz1PiLMpXa6fUy58+kcWB3vGEQsyjtaTfCkwv556FkAJaPqH0gbUPdnKibKiWeGOBK\nd0dL1Do9aq1MbFYJe+PzQILnh3kwro5lNrWVEjWG+OxrLN15AaVC4t8ze+Fhe+dB8c3S83/w4MHb\n3n2r1WraWcWQIAiCINRZUnw2v+2IpqRIjUql4IHxPRkw1Auplrm8hRsUCgn/gM74BzRej6rQfCoT\nfI1e5v4utliolORc05B9rYLE3DLjZFPvhl7isxk+eNlbNHobyrV6Vu27RJlWT6CHDasf8q4yUBdg\ndDd7Fg+t/+/YUC9btno13UrCPs5WPNTTgb0X8th4LJ13xndrsmvdqtbkf/To0bi6ut62Plw8lhNa\nu/Zc9wgivrauPcfXXmNLjM1iz7YoEpIi6ezqC4Cbpx0TZvnj4GTVwq1rPO31+6sk4mu4fx5Kpkht\nqP7Yl5B/2+M0epn/2xbH2O72PD6gE242tU/VeieVscmyzL8Op5CYW4abjSkrRntVS/xbuwUBbhy+\nVMDx1CJOpBYyqLNts3x3tSb/Xl5e/PDDD9x///3V9pWXl2Np2fizFwiCIAhCayTLMr9uOUeFWmdc\nQXbkRB8G3t8FRRtLOgShIUorDKvZVjJTSiwIdMPJyhRnKxNSCsr5z4kryLKMj7MlZ9KL2Xcxnz8S\n85ng48if7nPF2cq0QW3YFp3NH4n5mKsUvD3OG2uzBg1jbRH2liY8PqAT/z6ezufh6dznZt0s1621\n5n/WrFmMGDGCpUuXVtunVqvx8fHh8uXLTdm+ehM1/41LfG6CIAiGAaqhv8RyKT7buM3cwoTn3mx4\n/a0gtCVlGh2v700kOuMaEtDBTMlLd6jrv1qs5oczGYRezOP6EhOYKiWGedniaXe91l2SSCso50hy\nIRKGaTkn1zBfPsCZ9CJeC0lEL8NbY7syvKtd4wbZjDQ6Pc9sjyO1UM2iQW482vf264E0y1SfGo1h\n5gITk7tbhrwliOS/cYnPTRCEe5lOq+dU2CXC/0hEq9GjMlEgSRIqE2W95sgXhPagXKvnzb2JnLta\ngpOlCR9O7oG7bd3LeFLyy3l2R5xxhdw76e5owShve0Z42+F6fUGtq8Vqnvs5nmK1jnn9OzI/oO3n\nKKfSDDczFiYKvp7dG0fLmvPuZhnwe6ekX6PRtKkbA+HeI+o62zYRX9vVlmOrXKxLr5cxMVVScn3O\nb9/+nRg1sRdW1maEhYW168S/LX9/dSHiqz+1Vs/bvyVx7moJDpYq1kzuXq/EH8DT3hxLU6VxTn4z\nlYJZ/i7IsmERre1RWahvmv71Ym4ZF3PL+PLkFdxtTMkt1ZJz4QwdvPszqLMNTw7o1JghtpgADxt8\nnCyIzylj2ns/8uH/zWjSGZIUdTlo3LhxXLlypcq2c+fOMXDgwCZplCAIgiC0lN3BkZSValCXaykp\nUmPvZMnsBYFMfrQfVtYNG6woCHURnlzI7B+imP1DFOHJhXV+38GkfKZ/e463fkus1/vupEKrZ9W+\nJM5eKcbeQsWaST3qNDVlTV58wBNbcxW25ipeG92FPw/sxFMBbswPcOO1MV2N+94c24W3x3VllLcd\nZioF6UUVlGv16GVQSLBiVNsb4Fub9KIKALR6mQ8PJjfpteo0z/+rr77K119/zYYNG5g9ezZr1qxh\nzZo1vP/++zzzzDNN2sD6EmU/jUt8boIg3Csy0gs5/kcSCTGZxm0mJkqWvDkWlapOfWXCPehu54M/\nkJjPx2EpyMD4ng642ZhTrtVTptERHJVFxfUecFtzFVsfr33KSY1Oz+64XD4LTzNOsalSSCwf4ckw\nr9svZlWX2P55KJlSjR6tXsbWXMWHk7vTpQmm7axNuVbP3B+jKNUYFt2yNlOy7Ym+zdqGpnbzKsU2\n5kqCH68eX7PU/N/s8OHDPPHEEwC4ubnx3Xff0b179wY3oLGJ5L9xic9NEITmUFlqAzChmRd7Sruc\nz7EDiVy+kAMY5p9XKCRUpkqx8JRwR7O+jzROednBVMlXs32xM1dVmw5do9MTl13K2fRizqQXE5N1\nrU7nV0iwaJA743s6VJvRRqeX+SMxn29PXyWzpKLG95urFPR0tuBiThkqpcTyB+q+6Nb0b88ZE24J\n+OKRXnR1aN7Ev1JTL7rV0uoSX7PU/N8sKSmJoqIivL29KSkpoaysrMEXF6p6+OGHOX/+PHFxcZia\nGqbAWrJkCUFBQfzwww9MnDjReOxrr73Gxo0b+fTTT5k7dy5Dhw4lPT29yvkqKirQarXk5OQQFhbG\ntGnTWLBgAR9++KHxmIkTJ/Lkk08yb9685gmymYm6zrZNxNd21Se2stIKft0SSYXa0Ou1e2skz70x\ntkkXy0qMzWL31kg0FTr01wcfmpgq6T/Yk4DhXe5Y3tOevzsQ8dXV6bQiitU3prwsqdAx58dorM2U\neNiaYaZUEJt1DZ1sSJ5vN9DVRCkxoacj5ioFFiYKMosrOHCpgAqdoczl38fT+fbUFcZ0d6CrvTk/\nRmSg0clYmyrJvGaYnMXLzpxhXWzZHZdL3oUzTH1oNJfyyonJukbk1es3Ghp4f/8lNkyvfdGt9EI1\nG4+nGRN/ACtTZYsl/nBj0a2wsLB2l/hD88ZXp+R/1qxZREVFERISwqBBg/j0008ZOXIkK1as4JVX\nXmmUhoSEhLBs2TJ0Oh2LFi3i1VdfrbJ/586dvPXWWygUChQKBR9++CFjxoxplGu3BikpKZw5cwYP\nDw/27NnDtGnTjPu6d+9OUFCQMfnXarXs3LkTb29v4zHh4eFVznft2jXGjh3LjBkzjNusrKzYsmUL\nS5cupXNnw2p3kiSJxdoEQWgWlb37MtBvUGe0Gh0pSXlkZxTDTTmRulzLV/86zH1DPOkz0B0z88af\nWKJyvv5KQ0Z3Y+D9XlhYNmzuceHeUKbR8dXJK+yKMTwtUkqGJ0YuVibkl2kpVuuIzSqt9j4vO3Pu\nc7fmPjdr1Fo9n4anATX39C4f6YVOL3MitYidMdmcSS9mT3xulWNKNXpcOpjw5IBOjO3ugFIhMT/A\njbCwQoYP9wTgSpGap7fHodYaEnm1TuYv2+LwdbFkfE9HRnrbY2VqKAsqrdCxKSKD7dHZaPQypkoJ\nhSRhplLw4gOejfshCi2mTmU/zz77LOvWrcPC4sYd34ULF3jiiSc4fvx4gxuh0+nw8fFh3759uLu7\nExgYyKZNm/D19TUec+3aNaysDKsnRkVFMWPGDC5evFjtXPUt+2mMR82NcY41a9YQERHBwIEDOXXq\nFJs2bQIMPf+Ojo5s2bKF48ePY2try969e/nqq68oKSnhiSeeqLHXfuHChRQWFhIcHAwYejmeeeYZ\npkyZQklJCRs2bABg0qRJPPnkk8ydO7fGdomyH0EQGsun74ZSVqqptl2plLBzsqQwrwwJCZWpgrLr\nvZkmpkrcu9hzNbUAhSQ1SknQmfBk9v8Sa3xtYWnCkjfEfP1C3ZzPLOHDgylcKVKjlOCJAZ2Y06+j\ncfCpLMvkl2lJLSjnzd+SKL+edNuYKQluQJ16SkE5v8TksDPmprUmVAqCH/fH9A5jUipLSnR6w6Jb\nsVnXjL36KoWEJIFSklApoKTCsP3BHg4sCHS77bSTQvNr1rKfzz//vNq2nj17cuTIkQY3AODEiRN0\n796dLl26ADB37lx27txZJfmvTPwBSkpKcHJyapRrh2yLMv5jtOP7Mw0/3/Zolrxe/ycSmzdvZsWK\nFQwYMIA1a9aQk5NjjNHMzIyJEyeyfft25s+fT1BQEHPmzOGrr76qsdd+48aNnDp1igMHDlTb9+KL\nLxIYGMiyZcta5ZgNQRDaL/1NJQ8KhcSgkd54ejvQydMOk5sGJOr1MolxWZw5mkxqUp6xFh/gl6AI\nxk3tjZOrNY4uHUi5mFvnzhdZljnyewLHDiQBhsG8KlPDfP2CUJvKga9qrZ4KnWFayi725rw6yotu\njpZVjpUkCQdLExwsTfjb6C5V6rgbwtPOnCXDPPDraMXHR1JRKmD5A153TPzhRklJpXKtnrBLBYTE\n5xKZUQKA5vrjNx9nSxYP9cDXxarGcwltX4OmL1CpGmcp5fT0dGMZCoCHh0e1+nWAn3/+GV9fXyZO\nnMj69esb5dqtwbFjx7h69SoTJkygW7du+Pj4sHXr1irHzJkzh6CgIIqKiggPD2fy5Mk1nuvkyZO8\n9957fP3119jb21fb7+Liwvz58/n73//eJLG0NmFhYS3dhCYl4mu9EmOz+PTdUD59N5TE2Kwaj2nL\n8d3JrbHpdXrMr/cgqkwUTHvsPoY/2APPbo5VEn8w3Bj06N2ROYsG8dQL96O8KbnRavSEbIvmh0/D\nWb/yd37+4QxlpRrKSjXsCY66bXv0Oj2/7TjPsQNJSAqJ8TP78MKqB1ny+pi7epLQnr87EPHd6sOD\nyRSpdaivJ/5z+rqwYbpPtcT/VkO9bNn6uD9bH/dvtDruUd3s2fFkX4If73vbc94pPnOVgnE9HFg7\npQcdTG/8/VmYKPh4as9WnfiL382Ga5zsvYHqWnM+ffp0pk+fbpx5KD4+vsbjFi9ejKen4Q7b1tYW\nf3//KvXxN5sw05+Q7dGGn+9ytcbE2Kwq56ivTZs2MXr0aKytrQGYNm0aQUFBPPvss4Dh8xkyZAi5\nubmsXbuW8ePHY25efX7d3Nxc5s+fz1tvvVXrGgxLly5l4MCBnD9//o5tKywsJCkpyTgwqvKXsq28\njoqKalXtEfG1XHyJsVl8/lEQAM8um0s3X5cma//9w+7n1y2RJCRFAsB2iSWvj7nnvr+bX58JTyYy\n6jSWHUx5Z90zmJqp6vz+qfP6E7ItiovJ0bh72uHTvR/ZGcVERJ5C1st4ufcGIP7iOd58MYEpUx/E\nx78T0bGGp7mDBw3lf5vPsX/fAZQqiedffoxuvZru+xev289rvV4mzboHJRU6ihIjAHDzHcjCQe6t\non2N8frlkf6sO5xCfsJZJvXtiELq16rad+vrSq2lPU0ZX1RUFIWFhvUaUlJSWLRoEY2hzlN9NqVj\nx46xcuVKQkJCAPj73/+OQqGoNuj3Zt26dePEiRM4OjpW2d7WpvosKyujV69eyLJsLG1Sq9UUFRVx\n8OBBPvvsM9zd3Xnttdf4xz/+wYcffsgvv/zC0KFDq9Tr6/V6Zs2ahaOjI//5z3+qXScszFDzHx1t\nuEn5xz/+wblz5ygoKLjtuAFovZ+bINTXJ+/sQ12mBcDCyoQlr9etbjIhJpOQ4CgkSWLirNrLStTl\nGqJPpxNxPIX8nBuD/UxMlSx9a1yTzl7TmhXml/HNR2FoNTpmPDmAbr0aZ+pMrUZHxIlUju5LQKeT\nkQCt9sbsJHYOFlwrrkCn06PXy5hbmPDInwfg5ln9qagg3CqloJwPDyYTn234WzZVSliYKHixHlNl\nCkJjavapPptSQEAACQkJXL58GTc3NzZv3mwc8FopMTERb29vJEnizBlDb86tiX9btHv3blQqFYcO\nHTJO7ynLMgsWLCAoKMj4GuDpp59m2LBhDB06tNp5PvjgA65cucL3339fp+suXryYAQMGIMuymO1H\nuCfobkoKy8u05GWX4ODcodb35GQW88tPEcZa9Z9/OEPPPq64e9nh5mVPcUEZv+04j14v06mzHenJ\n+WgqDDPIWFiaUKHWotPJaCp0BP/3FBNn+dPB5u5WxWyrZFkm9JcYtBodPft0bLTEH0BloiTg/i4E\n3N8FMCT+yQk5xEVd5WJMFgV5N6akliSY9/RgHF1q/84FQS/L7IjO5ptTV6jQyThZmbD8AU8Geti0\ndNMEoVHcdc3/qlWrCA0NbZRGqFQqNmzYwPjx4+nduzdz5szB19eXjRs3snHjRgC2bduGv78/9913\nHy+88IIxMW7rgoKCeOyxx3B3d8fZ2RlnZ2dcXFxYtGgRwcHB6PV6Y3JuZ2fHAw88UON51q1bR0pK\nCr6+vnh6elb5r3L8xM1JvrW1Nc8//zwFBQVNH2QLuvUxWnsj4qs7B6cbNayyXub7T8OJOXulxmN1\nWj1HQy/y3YajVQapyjLER2Ww/39x/PBpODt/jKCsVIO6XMvlhBw0FTo8vR2Y+qf+PPu30fz1nfFM\nf2IAFpYmJF/M5dv1R6rU/7fn768ytgvRmSTFZWNqpmLMFN87vKthVCoF3XxdmPxoPxa/PgbTmxZE\nMrMwadTEvz1/d9B+4wtPLmT2D1GMe/s7wpMLq+2b+X0kk7+OYOPxdCp0Mg/1cOA/M33bXOLfXr8/\naN+xQfPEd9c9/3/88Qfff/89rq6ujdLQiRMnVlnECgw93ZVeeeWVRltToDW5dWBvpcrxDbXZvXu3\n8eecnJxajgR3d3djfXGlpUuXsnTp0jq2VBDaLlkvG3uB5y8bTvj+ROIir7J7ayQpSbmMfbg3JtcH\nvV1NLSBkWzS5WYYZMLr0cCIzvRAkiWFjuqFQKkhPzudKcgEFeTdKe1QqBY8vGYZTx6oJZndfF1yX\n3s+e4CiSL+ay4/szdO3pREZaIZdSz9PJsWedxhq15Aq4d0tdrmH//wxTao4Y37NZn3qYmCiZ/Gjf\nBo3HEuouJD6Xz8PTkCRYPsKTB7q2ztKqfx4yDNwtqdDxbugl+rtZU6zWUlKhI71QbVxuQgJWPugt\nynuEdqnBNf9paWl4eHg0VnsarK3V/Ld24nMT2oPsjGK+XX8Eaztznn5lFLIsE3Uqjf2/xKLV6rG2\nNTeU6Gj1xppxO0dLxs/oQ2dvh9ue9/yZdPb/LxaF4s7zz8t6mdNHL3No7wX0uhv/21WZKBh4fxdM\nTJQU5JUSH5UBgN8AdxxdOqDX6dHpZI6GXkSrMZQUmVmoeP7NcY3x0TSp33ee59zxVNw87Zj3f4Pv\n2TEP7ZEsyyTllXE0uZDw5EIu5pZV2T+uhwOjve0Z4G5tnP++pV3IKWXpznhus8huFQ2dk18QmkKL\n1PynpqaSnp7OkCFDjNtaU+IvCIJQkysphvI2d087wFAC1zewM5062/HLpgjysq9VOX7QiK4MHdu9\n2hSUt/Ib4I7fAPc6tUFSSAQM70pnb0d++PQold0uWo2e49fnnb9ZxLGU255LXabluw1H8R/ojm9/\nN8wtWt8iPFdS8jl3IhWFQuLB6X4i8W8HjiYX8OHBZDQ6GUsTJQXl2tseuy8hj30Jediaq+jpZEFM\nVikqBS0yWFanl9kSmcl3p6+il0EhgalSwSQfR+5zt6aDmRJrMxUXsq+x8bihFFCsZiu0Z3VK/lNS\nUpg3bx4REYZprq5du8bWrVvZu3cvX375ZZM2UBAaIiwszDiNVnsk4qubKyn5ALhdT/4rObta8/ji\noXz63n7jgGAzCxUjJvg0+Jq309HNhilz+7N3ezSXUqN5aMJY7Bws0Wp0nD5y2fjkQalS0GeAO0ql\nAoVSojC/jEsXskE23EhkXSki9EoRB/bE4+phS3ZGMco6PIFoapXlSfEXz+Hp1puAEV1wdrVusfY0\nlXvpby/3mobfEnL59nryDFCh0+JgoWKIly1DPW2p0OlZfyQNgD8PdCW/TMsfifmkFao5mVZsPO/7\n+y+x7uGedHe0aNBkE5Ur1oIhUb/dDUVGsZo1B5KJzjTc4M/wc2ZBoBsnjx1l+NB+VY71tDNnXI+2\nP5EItO/fz/YcGzRPfHVK/v/v//6PSZMmcfjwYeMMOw899BDLly9v0sYJgiA0hsqe/5qmeDQ1UzF1\nXn/2bItCkmDCI/7VjmlsPv6u+Pi7EhZmzvDhN67n5mlXp3VHtBodF2OziDqVRnJiLumX84379gRH\n8dybDX8sfLcqV02XZcMMO0PHdG+xtgj1V5lU5yUk8oS5N0l5ZZxILapWKtPBVMlPf+qD4qYE/tY6\n/8fvcyUxt4xlv1yg4nqpm1ons+TneDxszRjlbY+dhYrvzxhK3WpL4m+19lAyxWpDGdwHBy7zzkPe\nuNua42Ch4lhKEesOJ1Ohk9HpZSp0Mg6WKl4a4UVAGxu4KwhNoU41/w4ODuTk5KBQKLC3tyc/3/AP\njUgmYdQAACAASURBVK2trXHxgdZC1Pw3LvG5CW1d6bUKPntvPyoTBc+/NQ6lskELm7c6hjn0D6PV\nGJ4YKBQSf33noQZP4Xs3A4xlWebjlb8b22JmruL5t1r/2AThhlnfR1J0PamupJRgWBc7utibsyvG\nMLlEfRL1yhsKnV6md0dL4rPLKKyhZMjGXEnw47XX2au1erZGZfHd6as17rcwUaDW6qvcrAzvYsuy\n4Z7YmLeK2c0F4a41a82/q6srCQkJ+PjceBQeExODl5dXgxsgCILQlK5e7/V3dbdtd4k/gK29BQ/P\n7W/scdfrZRLOZ9Kzj2uDzrsnOJLy64ui/S/oHM+/PQ5FLXX7sl5m/6+xxsTf1EzJpNliwGRbIcsy\nB5IKjL3pYKiNXxjoxrgeDthfH1fyxIBO9T73UC9btnrdeMKl08tEXCnmQFI+ey/kGbcXlev49Gga\n0/2ccLetOjOULMsculTAlyeukFlSAYCJQkKpkPBxtqBCJ5NWqK7SfjDcDLw5tqtYz0YQblKn5P+l\nl15iypQp/O1vf0Or1bJp0ybef//9WlfgFYTWQNQGtm2NEZ+x5MfL7g5HNr/G+v66+bqw5I2xnD2W\nQuiuGA7tvUC3Xi4oVfW/2VGXazl2INGY+ANoNDqC/n2cSbP7YudoWe09er3MbzuiiT6djlIp8fC8\n/mTkJbSJ6UjvVn2/u/0X81h/JBWABQGdmOTrjKqVDIJOyi3js/A0IjMM09sqJSi/HMn7i6YxtAn+\nbpQKiYEeNgz0sGFQZxv+eSiFCp2MVi+zMyabXTHZDOpsg4+zJTtjstHpwcFSRUqBGgBvB3OeHeJB\nP7fqY0mKyrXsvZDLj2czUCkklo/wqjHxF//vbLvac2zQimr+FyxYgKOjI1988QWdO3fm22+/5Z13\n3rnjPPSCIAgtLf36YF/3Gur925u+gR6cDU8mL/saEcdTGHh95du6kPUy0WfTObz3AqXXe1aVKoVh\nwLHCcBP17SdHGDWpF30DPYwJlU6nZ/eWSOKjMlCZKJj++AC69HAiIyyhKUJs1SrLW2RkHr/PFROl\ngtjMa8RkXSOtUG08bkN4Ol8cv4K7rRleduYoJDiRWoRCknh5pGejJNx1GRBbrNby3ekMfonN/n/2\nzjysirL945+Zs7JvgiIIuKAB4r6v5ZJL21tm669Ne7PSSivrLVvUrMxsz8qyrLTUynLJJcMlxdw3\nUFAQZFHZdzjAWWZ+fxw5iCCCLALO57q4rjNzZp557plzDvfzPN/7vpFkcNGrmdTHmzFdPPh3d1GD\nOP6XMrS9my1WIC7LwJoTGWyLy2Ffcj77kvNtxxUaLbjo1Tzax5uxnT0umz7UWa9mYrfWTOzWusH7\nrqDQXKmR5n/fvn3079+/0v79+/fTr1+/BunY1aJo/usX5b4pNGcsFonP5m7FbLLw9KsjsHfUXusu\nNThx0en8sewwejsNj784rNo0oGW6fkmSsbPX2AqhebdzYcRtwXj7Wh3GYoORreuiOBlhDcxs38WT\nMXeGoLfTsH7FUeJOZqDVqbjr4d74tr98XYSWzoRlEZVkJ1UhCHC5/7wCMKy9K6HejoS2cSSloJSP\ndllXDGqiszdZJE5nFfPyxtOUXMgcpRYFBvu7oFOL6NQiWQYTh87mY7TIyFjlPbcFefJw7zY46a69\nLj632MTGk9bsQmW3SacSWPFAVxybQP8UFK4Vjar5HzVqFAUFBZX2jxkzxhb8q3B1tGvXzjaDVlRU\nhF6vR6Wy5hb/6KOPGDVqFLNmzWLr1q0UFRXRpk0bHnzwQZ577jkAPDw8OHToEAEBAVW2X1hYSFBQ\nEAMHDuSXX35pFJsUFJoKGakFmE0W3DzsrwvHH6DDDZ606+BOcnw2e7fHceP4Gy57bFmcAFjlPo7O\nOoaN7UJQd+8KUgk7ey233teDTkEphK2L4sypDL6avwNRFJAkGb2dhgmP9bENFq43jBaJ1ZHpFRx/\nQbA68cFeDgR5OZBZZOSTC6kwnx/qR4+2jiTnlpKYW8yn4cmUXsiGIwP/nMnlnzNWuZpwYR/Au9sT\neKK/Dw5aFQ5akTPZxaw6lo4ky/TxcSa3xMzJjCJbZp0yzJJsa+9SVKLAoju60MHDrl7vSV1wtdPw\nQM82+LvpWbgzCVGAF4f5K46/gkI9Ue03SZIkyhYGJEmq8F5cXBwaTdMrLNPcSE5Otr3u0aMHn376\nKcOGDbPtmzp1KiUlJezbtw9nZ2diY2OJjo6ucfvr16/Hx8eH3bt3k56ejpdXy9XgVoWiDWze1NW+\n84lNV+8PDfP8BEHgxnFdWPbFHo7sSaTHAD9c3Svr9GVJxmQsd1bVGpFJM4aircbBuqG7Nz4Bbnyz\n8B8ki4x0IaXKvY/3w9O7ov76evls7kvK48u95zifb5X1aEQBvUbkxWGXFrNyYMglqTA7e9rT2dMe\nR63aJtF5qFcbVKJAZEohkamFZBSZbMeXmCVb3MCl7Ewod+7buejwdNASnVGEKMAdwZ4EuNlRapEo\nNUss2X/etirgqFVV6fg3hec3OMCVwQEN891tCvY1JC3ZvpZsGzQBzb9ara7yNYAoisyaNathetWI\nHDq9k682zQHgyXFv0rvTsCuc0TBtXI6jR48ya9YsnJ2tuYkDAwMJDAys8fkrV67koYceIiwsjF9+\n+YVp06bVW98UFJo6tmDfdk3T+W8oWvu4ENyjLVFHzrNzcwy3P9CjwvuSJPP3mhO2gmJanZpb7ulW\nreNfhpOLHp1ObVsx0NtpKjn+LZkyLX3mqThCMlsRk2mVSvm56nl6oA+9fGqfR/7SbDgAt9zQCoBN\nJ7NYvO8skgy9fJxw0asxGC0UmSwcOVdA2SS/TiXw6oj2BLd2wOUKKS09HbQV4gEUFBSuL6rV/Cck\nJAAwbNgwdu3aZVsFEAQBT09P7O0rzyZda2qr+f/vZyMpKK56OfRqcLZ34+tpYVd1blUz/8899xwH\nDhxg2rRp9O/fn44dO1Y4pzrZT3JyMr169eLo0aOEhYWxZMkSdu3aVas+KZp/hebM1wt2kJ9bwiPP\nDm6RVWaroyCvhG8/2InZLPHAk/1tBc4ki8Sm1ZFEH02pEKBbG+Ki02tUjKwlcmkefHuNyEO9vLkj\npPGz99S0yq2CgkLLoFE0/2UOZVJSUp0vpHB1vPfee3z55ZcsWbKEGTNm0K5dO+bPn8+oUVcunLNq\n1Sp69eqFj48Pt912GzNnziQyMpLQ0IavYKqgcK0pzC8hP7cErU6Nh5fjte5Oo+PkoqfPkAD27ohn\n+4aTPPDkACSLzJ+rjhF7Ig2N1hqg265D7QN0OwZ5MXXWiAboddPmVEYRhRdJpTQqgaUTg3GzvzYS\n2KpWDBQUFBSuRI2jZ9auXcs///xDVlYWkiTZgsF+/PHHButcY/DkuDdZvHkuAFPGvnHVsp+L26hP\n9Ho9M2bMYMaMGRQUFPDJJ58wadIkIiMjcXGpfpZn1apVPPbYY4C1SvPgwYNZsWLFdeX8K9rA5k1d\n7CuT/Hi3c6m2ONWVaMjZ1YZ+fv2GdyDiwFlSkvOIOnqeUxGpxJ/KQKdXM+HRPrT1azg5VEv6bBrN\nEsuOpPJrRBqSbM2OU5oQwZzH/3PNHP+GpiU9v6pQ7Gu+tGTboHHsq1EFmDlz5jBlyhQkSeKXX36h\nVatW/PXXX7i6Nn8dbe9Ow/h6WhhfTwu7aq1+fbRRE5ycnJg+fTpFRUUkJiZWe+y+ffuIj4/ngw8+\nICgoiKCgIA4ePMjq1auxWK6cik5BoblzrkzvX0cH94OdieSVmMkrMfPBzuq/d00NrU5N567WfOeb\nfo0k/lQGdvYa7pnct0Ed/8vxb2IuE5ZFcNePEfwVk4XRXJ5IYk9iHhOXRzJxeSR7EvMavC81vV50\nehFPrznFqmNpANwd6sXaR7rz1piOisxGQUGhWVKjPP9+fn5s2LCB0NBQXF1dyc3NZf/+/bz11lus\nX7++MfpZY5pznv+qNP/vv/8+o0aNIiQkBEmSWLRoEV988QWRkZHY29vj4eHBv//+i7+/v+0cjUbD\niy++SHJyMl9++aVtf3FxMUOGDOGbb75hzJgxNepTc7hvCtcXNZ2J/+nLPaQk53H3Y31qrWkvo6DU\nzD3LI7k4c2KwlwO9fZ3o4+tMtsHEx+FV52BvKnrsRfO22oJzEeDRZwfTqnXDxT/sSczjg52JmCWZ\nwQGu6NQiqQWlpBYYKxS6KsNOI+KsU5NZZKwQvPpon7a426txs9OQlFvCj4dSEAR4fuilWXSujotz\n8qtFgbFdPGhlr8HDQUN6oZE/jmdgtEiYLuTCb+ei48Xh/gR5OdT52goKCgpXQ6Pm+c/Ly7NJRbRa\nLUajkX79+vHPP//UuQMK1SOKItOmTePs2bOo1Wq6du3KypUrKwRbDxo0yPZaEATmz5/P2rVr+eqr\nr/D09KzQ3r333svKlStr7PwrKDQ13v8n0aa7fnd7AgtvCaRTKzvEi/LSm00W0s/ng2CV/VwNhaVm\nXtkUh0W25mwXBZAliEq3Vmxddji1wvHztp1hWHtXJBlkWWZ3Qh6mC6kw39uRwAe3BtLORY9WXaMF\n1wZBr9c0qOMPsHBnos2p/js2+7LHCVhzzBebJIpNxgrvlVpkFu87V+V587ae4flhfvT1dcb5Cllt\nqqLEXDknv1mS+TM687Ln3NvNi4d6eV/TZ6egoKBQX9Ro5r9nz54sX76ckJAQbrrpJv7zn//g5ubG\nG2+8YcsI1FRozjP/TZHmft8UbWDz5lL70guNPLTyBJf+aLno1fTyccJVryLsdA7OxUZCEjJp1dqR\nR5+r/f0pLDXzv01xxGQaaOOkZeEtgXg5aikyWohIKeTg2XwOnSuw5XavKaIAbZx0OOlUJGQXkxd3\njAljbyLIywG9RiQhu5g/TmQiADOGtmPoJXnhr4bGzMyTbTDxwIrjSDLkxx2lVeeeTO7bljZOOto4\naUnKLeHzf8sLXQ3wc8ZgksgrMbM7IZefj6QiAYP8XXDSqckxmMgqNhGVVoR0yUMXBQhu7YC3k449\niXmoxOpXBSRZJiw2m+8PppB5YSVELQro1AK33uCJu72abIOJTIOJHfE5WC4okhy1Kn5/uFul9q63\n715LQ7Gv+dKSbYPq7WvUmf958+aRmWmdFZk/fz4PPPAAhYWFfPHFF3XuQBmbN29m+vTpWCwWHn/8\ncV5++eUK7//0008sWLAAWZZxcnLiyy+/pFu3yj/ICgoKLZMio4VZf8UhY3XatCqBIC8HzuaVklZo\nZHtcebVx9/wS4Or0/oWlZl7ZXNnxB3DQqhjo72JzMDeezOTrfeeQgbGd3Qls5WBbJTidWcyGk5lY\nZOjgrqeg1ML5/NIKAwajRWLDySw2nMyq1I+3tibQxTOdIC8HbvC0p8QssfTgeUCoQmKUywc7rRKj\nFy4pLtVYmXkyi4y8tPG0LSDWQSMya0T7Cn1p727H8A4VBzTWarUqJnZrzcRuratsu0xCJckyQwJc\nSC0wEpFSyPHUIo6nFtmOe2vrGcZ0dsfbWUdbJx0ZRUZ+OpKKRZJx0qtJLbCuMHTysOOJ/j70aFv1\nKsiw9m5KHnwFBYUWS41m/hsai8VCly5dCAsLw8fHh759+7JixQqCgoJsx+zZs4fg4GBcXFzYvHkz\ns2fPZu/evZXaUmb+6xflvik0BUwWidf+iuPI+UL8XfV8dFsgjhcKUsmyzNm8Ug6ezeeb/ecxSzLd\nU3NpbSglP9CTCWM6083b0ZahrDrKHP9TGZUd//rAaJE4m1vKjD9jKDZdKLClEhjW3pUSs8TepHzM\nl05xV4FaFAhw01NktFBktFTIO69VCax+qBu6RpSopBcaeWljLOfzjXRwt2P+uI642jVsFpwio4WD\nZ/NZsCPRJq+6Eq0cNEzq05YRndwqyMQUFBQUmgMNPvMfHx9fowY6dOhQ507s37+fTp062eoK3Hff\nfaxdu7aC8z9w4EDb6/79+3P27Nk6X1dBQaHpI8syn+5O5sj5Qtzs1Lw1poPN8QdrnEs7Vz3tXPW0\ncdLxwT8JuJZaZR0RxRJ7N56ma2sHevo4sS4qg6pnzq1BqkVGCxYZWjtqeX98/Tr+AFqVSAcPO/53\nY0CVwcAXBwlPHeiLs17FyXQD0elF7E/Ot8mdzJLM6aziKq9htMhMXXOKl2/0J7BV9YUY6yMoObWg\nlJkbTpNWaCSwlR3vju10VVr82uKgVTG8gxtalWhbFbg9qBXOejUpBUZS8ks5cDbfJhfSq0WWTgxu\n1EGRgoKCQlPksr/QnTp1uuLJgiDUS9rIc+fO0a5dO9u2r68v+/btu+zx3377LePHj6/zdRVaPtez\nNrAlEB4eToJDJ/6KyUanFnnr5o60cdJd9viB/i4suTWQJQtT0NtpmNDfhzVRmRxPK+J4Wrk85O1t\nZxjXxQNBEBAE2BCdidFSVsEcFt4SSGun+nX8L+3nr/6hhIeHV3C4qyra1MvHGbBKexbuTEKSZO7u\n1pq+vs44aEXstSqOpxby6e6zWCQZvVogKbeE59bF8FCvNtzTrTWqKuocyLLMgn+sAx6wBizPGOJH\n97aOeDrUzPbz+aXM3BBLRpGJGzzteWdsR9vArLE+m9UVurp0cFOfjv/18N1T7Gu+tGT7WrJt0Dj2\nXdb5l6Ty/MvfffcdYWFhzJkzBz8/P5KSkpgzZ069LD0ANVqOL2P79u1899137N69+7LHPP300/j5\nWXWaLi4uhIaG1ssKxfVIbm4u8fHxtg9ieHg4QLPZjoyMbFL9ud7sW7z6L1YeTcUtsCczh/tjSa5d\nf1dv28ue4lhcOvbg1ZsCSD91mPRT1Z+feDoT0OPj74pncTxP+Upkundm6YEU8uKOAuDcsQdrozLJ\nv2gbrEGq9hqR1k49G+X+1Ob5DfR3ZUZ7a+DukJ7dK7w/dMgQhrZ3Izw8HKNFIlrTnrVRmXyyahPr\ntuj58Km78HbSER4eTn6JmQLPIP6KySIl+pDNfpNF5rXv1gIQ1LM/3k5a/v13N6IAz98/ns6tHNi9\nO5wSswQ+IWw6lU3GqcPIwICBg3l7bEeO7N/ToPerttuW5EieC2g6/VG2lW1lu+7bZTSV/jSkfZGR\nkeTlWeuQJCUl8fjjj1Mf1Ejz7+vrS0xMTIX0kgaDgc6dO9eL/Gbv3r3Mnj2bzZs3A/Duu+8iimKl\noN+IiAjuuusuNm/efNmVictp/tPS0nBycqpgg0L1GAwGCgoKaN266iA8BYUrcdePEba0nCoRZgzx\nY2h7V+w0qmrP25OYx4J/EigyWichnhrgw51da5alJmxdFEf3JjH05kD639jRtv+f+Bw+2pWELMOI\nTm74u9khyTKSDAnZxew8k4tWJVQKmG2uHDybz8KdiWQbzADo1CL+rjpOZxXbpDCOWhGTRUatEhkS\n4EJusZnI1EIMJqmaliuiEgV+fyj0is9UQUFBQaFuNGq2H0mSSEhIIDg42LYvMTGx3irF9unTh9jY\nWBISEmjbti2rVq1ixYoVFY5JSkrirrvuYvny5TWSJF2Kl5cX6enp5Obm1kufrwdUKhVeXg2XFlCh\n5WO5KBDTIsHCnUks2nOW4e3d8HHR8ltkOiDw3GBf2jrrOZNTTEJOCasj022Br1qVUGPHH+C8rbJv\nxawywzu4Vco0czEvDve/7HvNkT6+znx9VxD3/XwcsyRTapaIySxGJcBgfxfGdPGgr69zJUmQRZKJ\nyTTw8sbT1ll+rNl7Orjb4aBVYa9VcTA53xZk66gVFcdfQUFBoRlRI+d/xowZjBgxgkmTJtGuXTuS\nkpL4/vvvmT59ev10Qq3m888/Z8yYMVgsFiZPnkxQUBCLFy8GYMqUKcydO5ecnByeeuopwFrFdv/+\n/TW+hiAIVz2DHR7ecvVlLdk2UOy71nTzdmRfcj46tcjYzu6czirmRFoRm2MqpracuzWhwrZnUQld\nM/JJPBeFpd/gGl/vZESKtbgXYCgyXuHoa09DPz9nvRoHrUheiXWiRq8W+eHeYNyqycSjEq0pVF+5\nqeqgZKispa+Kpv7ZrCuKfc0bxb7mS0u2DRrHvho5/zNnziQ0NJRffvmFI0eO4O3tzdKlSxk7dmy9\ndWTcuHGMGzeuwr4pU6bYXi9ZsoQlS5bU2/UUFBQanrKZ49dHBtDvQqXd5NwStsRk8UtEeoViXT7O\nOtq76/F30ZGx9jhIMhpJpktaXo2v99eFYlZglf90CW1TL3Y0Z54f6l/BUa/O8b+Y6gJpq3tPQeF6\nI31LOJHT3wEg9ONX8bq55TqmCi2DJpHnvz65nOZfQUGh8Zm4PJK8EjPL7wuplDZzd4I1e40ATB/a\njmHt3SgpNrHupyMkxWdXOHb8xG4E97x8vQmTycLWdVEcP3TOts/OQdsoxa0UFBSub7YGj8OUbZ2k\n0Lg6M+LEBgSVIoVTqH8aVfOvoKCgUFtyik1os4q4KTOfXz/exdgJoXQMKtfuDw5wZXBAeQXevJxi\nfv/hEFnphWj1agTAYpYwmyU2/hpBRloBQ2/ujHiJRj0328C6n4+Sfj4fURRQa0RUahVj7+raWKYq\nKDQr0jbvJPK5txFEgdBPXlNmquuIxVBie23KzSes02icugbi3K0Lgihy7pdNCCqVsiqg0GRQqp3U\ngEvTL7UkWrJtoNh3LUnILiEkIw+NRaLYYGLjrxFcbqEx9VweP3+1l6z0Qtw9HXjkmUE888Yo+txs\nz6jbgxFEgQM7z7Bm2WFKS8y28+JOprPs839JP5+Pq7s9/zd1IM++OZqps0ZUGGg0VZry86srLdk2\naBr2pW8JJ6zLGMICR5PwzSqMWbm271j6lnC2Bo9na/B4UjfsIOdgJPGfL+fQ/73IkcdewZxXgCkn\nn2NPvYlcRfKOquxL27yTsMDR/N1xFDHvfUPOgUgKTydizMolbdNO2/XSt1z7e3Ml6uv5GRLPIZmt\nv0mCRoPGwxVLcQm5ByJJ+vY3Er/5xXqvs3M5+sRrZO7Yh2Q01cu1q6MpfD4bipZsGzSOfcrMv4KC\nQoOQkFOMeJGvX1pi5tsPdnFDd2+Cunvj4eUIWB349SuOYTZZaNfBnTse7In+Il16jwF+uHs6sO7n\no8SfymDpx7swmyyYzRLmCykpOwZ5Me7u0ArnKSi0dCKemYs5rxCAk69/wsnXP0HUadG1aUXJuTRk\ns9WpPzr51cu2YSkqZt8dT9H1w1dx7BxQ5TGyLJO5Yx9HJ8+yDRTiP1pK/EdLqzz+2FOzGX5gNVr3\n5p8y90qcmrsIzBba3j2Wbp+/AYAxK5f8yFPkHTvJ6Q++Q77g7EslRg7eNwO1kwOtRg5E39aLcys2\ngCAoqwIKjUqNNP8LFy7kxRdfrLT/ww8/5Pnnn2+Qjl0tiuZfQaFp8NGuJAr+Pom9WUJUCWi0KkqL\ny2ftXd3tKMgvxXIhKDi4Z1vG3NkV1WWqsOZmGfhj2WGy0gsr7B86pjP9hrZHqKKKrYJCS6U0I5vt\n3W+jrGiDoBJROTpgziuo8niHwADcB/bArX93LKVGYt/+0joDrRIx5xYgaDV0ev4x2k/9P0RN+bxg\nzsFIYt7+ipw9Ryq0J2jUOId2wZSTZ/3LrXhdQa2i1fB+eN85Gq+xQ1E7OtTzHbj2ZO0+zIEJ01DZ\n6Rn67yr03p6VjknfEs7xGe8gmS20Gt6PwtgECqPjKh2ncrBn6L8r0bdu1RhdV2im1Jfmv0bOv5OT\nEwUFlX9Q3NzcyMnJqXMn6hPF+VdQaBq8uCKCNpHnUevUTHv1JkSVSHJ8FtHHUog5noaxtHwgoNao\neG72qCtW+y4tMbPo7a1IFuvPlk6v5pk3RjWoHQoKTQ3JaOLAPc+Ss/cYglqF2sWJ0I+sM8fmIgMl\nKRmkrd9G/KKfEASB4HdfpO3dY6psy5RXwKm3FnF2+ToA7Py8MeUVAAIOHXzJOxINgMbVCa8xQ0kP\n+xcB6PpRxZnqtE07Of7Cu0hGE/YBPhRGx9tWCQSNGgQBUa3C5/7b8BjSC42LMxpXJ3KPnSTmrUVA\n85r9li0W/h39GAVRpwl8+b90nPFYjc81JJwlbfMuYuZ9YVudAUAQcO0dQutxw1E5ORA7/2ugdhmE\nUjfs4PiMdxDUKkI/ntVs7qdCzWgU53/btm3Issxtt93Gn3/+WeG9uLg45s2bR2JiYp07UZ80hPPf\nknPKtmTbQLHvWiHJMi++v4u2uQaC+/oy/s6Kwbcmk4Uv39mGsdT6j+9ymXmqsi82Ko3Nv0UiiALj\nLgkibm401edXH7Rk2+Da2hf1ygckLV2Nrk0rBm1Zis7Lo85tZoUf5Pjz8ylOOm+9hlREsOiAyk6P\n/5R7af/UA2hcnGrcXmlGNml/bidlTRg5+47V6By1swMjT2254iRAfVDX55f04xqiXlqA3rcNQ3et\nQGWnq3Ub1hShbyMZTTh08qcwOg6ptHJ9Eo27KyOjNlbblixJpKwNI2LqXJAkoqQiurm1YdSpv2rd\nr6bO9fzb0ijZfiZNmoQgCJSWljJ58mTb/rKCWZ999lmdO6CgoNDySMktxjO/GIA+/SsXgdJoVNxy\nT3c2X8jLX5vMPIHBrQl84+oK9ikoNHfO/vwnSUtXI2g19Pzu3Xpx/AE8hvRh8PZlbAsZj1RSCoCo\n1zFs369XdQ2dpzt+j03A77EJbL1hLKZca/E9Uael1Y39MOUWYMrNpzAmAS7MQZrzi9h7yxN0enEy\nrW7qX+0goGyGmwsZi1qPGVp7o68SU16BbVa+y+tTr8rxB/C6eQgjozbZts1FBjK37SVt805Sft9C\nWSEUU04ese99g9+kCeg83Su0IcsyWf/sJ+btL8mPjKnwnjmvgJNzPidw5uOo7PVX1ceWQNkgC0mm\n6yezGvWzUnVfrn1NiBrJfh566CGWLVvWGP2pM4rsR0Hh2rN+axyntsZictDxyqybrnV3FBSaNOlb\nwomYNtfmnLS55cYqj8s9fIJ9/3ka2Wii64ev4vvArQ3Sl8hn51mDUD+pH9lIme4dKsuF0reEWITO\n3QAAIABJREFUEznjHaTiUgSViLmgCADXPl3p9OJkPIb3QxAEJJOZ/IiTZO0+TPbuQ2T9c6D8AoKA\nx/C+uPQIwqVHkFXKNGcR0DAO1sk3PyVh8UrcBnSn3x9fNMhKReqGHRyf/jaW4hKbNEjUa/G55xac\nugYSO/9rZLMZvU9rWwyBvq0XXuOGk/LH31gMxdZVBFnGvr0vXT94BfdBPeu9n82BrUFjMeVYB58I\nAt53jsZjSG/cB/fCzq9to6w02fpyUU0IrYcrI05Uv6JzKY2q+ZdlucLN2b59O6IoMnz48Dp3oL5R\nnH8FgEOnd/LFhjewyBZu7fsQfQNvxNneDSc7Vzbv3MTK/QsBuK/fi9x60+3XuLctj88+Cac0rRBt\nqDfP3t/9WndHQaHJIssyYR1HlueKFwTaP/0Avv93Bw7tfW3HlaZn8e/Nj1Gamonfo3cRPL9yEo7m\njrmomOTvfyd+0U+YsnMBa+AwgoAgilVKYq6E2tmREVEbEdX1k9ywKC6J8OEPIlskBv71HS7dutRL\nu5dDlmVy90cQv+gnMi6TQlXt4kTHZx/Gb9LdFVYh8o5EETnjHQpPxgPWVReVvV29DeqaA4bEc+wc\neC9IUpXvazxcsRQaEDUaQhe90WCrAgXRcZz9eT2JS361rXQJWg0jozejdrCrcTuN6vwPGzaMd999\nl8GDB/Pee+/x4YcfolKpmDp1KrNmzapzJ+oTRfNfO1qibXlF2Uz76hZMFiPZicW4+1/yxZKBC2NZ\nteTAhLYfobPToNOrMRQaiT+ZgagSGD+xW5PXkzfF55ebbWDJwp1YBAi5rye3hl69RKcp2leftGT7\nWrJtUD/2SaVGjr/4Hud/3VTl++5DeuPc7QbOrfwTc34hstmCW//u9P31U0Rtw6a1vZbPz1xkIOm7\n34h5Z7HNUQKw7+iHx+BeuA/qhWQycWq2VXocOOspNM6O5B2NJu9oNNm7D9kkMwDaVm60uWMk3neO\nxrV3VwRBuGr7Dj00k4y/d+P7wG10/fCVOttaGwpjEjjz5c+cW1Eegyna6bjpyFo0rs4Vji2zTzKa\niPvkB+I++M72ntrFqVnHAtT02eUfj+HQAy9Qmp6FoFKhdnak08zHQZbJ3n2I7H8PV8hSpbLXMzp+\nW537Z5P2yDJt7hhJ/oXPZRmCSoUsWUAG525d6PXDggqZoq655r+MEydOMGDAAAC+/vprtm3bhrOz\nM4MGDWpyzr/C9YvZYmLLkV/5bfdiTJbyGSKVqKatuz95hmwKDLnIQvl/BRkLcSczKjdmgvUrj/Lc\nm6NrlEIyLjqdzasjASpVsr3eOH7oHABpDnpub+14jXujoNA0Kc3I5sjkV8ndH4Go1SDqtIhaDe2n\nPkhhTAIpa8PIDj9Edvih8pNEgR5L3m5wx/9ao3awp8MzD3PmixWYcqwSCY2bC8N2r6xwnM/EcRW2\n29xqlRimbd5plcyUmlA7O2JMyyTp299I+vY3tK3cMBcaOCmW0vmrBbWaAc/YvpeMv3ejcrQn8JUp\ndbSy9jh2DiD0o1dxG9Cd6FkfWWerP5lVyfG/GFGrIXDm4yQu+dWWBtacX0Du4ShcewU3Vtcbnazd\nhzny6MuYC4pwH9KbXkvno3YqTzfrP/luZIuFrcHjbLUyLIYSzq74E9/7r05OV5KaQX7EKY5OeQOp\n2LqSl/z974B1Bcr7ztH4PnAbzt26UBSbyKGHXiQ/4hR7xk6m1/fzcenZeM+jRjP/bm5uZGZmkpCQ\nwM0330xcXByyLOPk5ERhYeGVTm9UFNlPy6KmTnVEwl5+2LqQc1lnAAhofQOZeecRRRVTxr5B707D\nADh+OJnla5eTaL8GWTDj59ydJ4a9S0mJmdJiE7u2xNgKRwF0uMGTW+7pjk5f/Tj5s7lhtsqzdvYa\npr5W95F5c0SSZL5e8A+F+SUc8HZj6ZQ+2GtV17pbCgpNioLoOA49NJOSs6no23rR64f3cA6tKB8x\n5Rdy/re/iH79I7BYf5Oa+4xtbakuVqCmyLJMfsQpUn7fQsq6rZSmlE/2iHotw/b8WmV+/ktJWRPG\nsamzwSLR9p7xdPv0tVr35VpSFlthKShCMloHRX1WftwiBwCp67dxbOocZKOJNrePpNtnryPqtFUe\nW/YZs5SUYikqRlCp6PXjAjxHDqz2Gulbwol45i0kownHLu0pTcmgNC2z0nGCRk3ox7NoPf7GSoHh\nxuw8jkx+lZw9RxD1WkI/fg3v/1SfurpRZT+33nor7dq1IyUlhU6dOrFw4UJOnz7N6NGjOXPmTJ07\nUZ8ozn/L4vO3tlJSbK2OqFIJjPpPCB26eOLgqLPq+je+SampGLPFekxrV18eHvECvToOrRTEczYh\nh1+/3Y/FIhM6wp6lh2fgqHfhq6l/oVZZZ9LiotPZ/PtxJIuEJMmYjBbcPR248+FeuHlULlJTcmHA\ncGxfsm2fSi0yfc7oRg0iaiqciclg9feHMKhVxAZ5s+z+mmfxUVBoyZRJAWSTCcloQio14tIrhF7f\nz682m07aX7uIfHYegiAQ+ulr141WuyGQJYmtN4zFnF8+aSnqtfg9OoEOzzyE1sO10vHZuw9zduWf\npKzeYtuv8XBlZC0DNZsKksnMsafeJO3P7aidHem76uNGnXFuKMq+X1Kp1YkH8Jt0N0HzpiOIVReO\nvJSYd74i/tMfUdnp6ff755e9L7LFQljg6PI4nQuonR1xDu2MxsWJrF0HrbUWPqn+OysZTUS9+oGt\nzoZop0dlp79soHqjOv9ZWVksXLgQrVbLzJkzcXR0ZMOGDcTGxjJ9+vQ6d6I+UTT/taO2tsVFp7Np\ndSSyJDe4Jj45PptVS/ZXfkMA97YiWw1vYJFNtt33D5vG+D4PolGXj/DL7MvNNvDTF3soNpjoOcCP\nkbcHM/O7e0jOjGPmXR/ZVgYu5uKKsno7Dbfd3x3/Ttbqi7IsE3XkPDs2naK4yIgggEolYr5QrXbU\n7cH0GFA5xWV909Q+m+t+PkLM8TRi3Rxo3b0tc2/uWKf2mpp99U1Ltq8l2wa1t29r8HhbECuA952j\n6frhq1edJrKhaanPr2ym93hxLv1CQsk9YF1ZVjnY4zlqEFk7D4As4TGsH7mHjlNyLq1SG1eTpaWx\nqe75SSYzx558g7QNO5rlAKAq2y79fgX+7wk6PPdIrSbhZFkm8tl5nP91E1oPV/r/+XWFoHsAQ1IK\nkc/OJWdvee0KlaM9g7YsxT7Ap8YDjUuvm/jNL5x84xPAWmOju6dPlQPMRtP8m81mnn/+eRYvXoxe\nX54n9pZbbqnzxRWaF7Is8+eqY5iM1rRj61Yc5elXb0Knr1/9qSzLHAxPYOdf1pzFoiig1anoHOpN\ndnYOB86v43DhLiSh3PFXy/bc0ucR1OrKX7zSEhO//3CIYoOJgM6tuOmWGwAYHDyWlTsXsTt6c5XO\nv6uHPQ88OYCNvxwj7mQGvy49iEajQhQFHJ11ZKVbU9L5Brgx6o5gWrV2IvrYeTasimDbhmi82jrT\n1s+1UrstFUOhkdPR6QCcd7Kjv1vNMxgoKLR0pJLyWUKVvZ5uX8y+LlcHrzVeNw9hxImNaMPDGTBk\nCHkRp4id/zWZ2/aQujbMdlzquq0A6H3b4HPvePTensS+uxiwSpCaM6JGTfev5toGAAfunU7fXz7B\npUdQpWNT12/j+AvzkS0WOs96Gv9JE2p0DVtufVm+4ux3XZGMJixFBtu2ytGejtMfrXU7giDQ9cNX\nMGZmk7l9H4fun0H/9YvRebojyzLnVm4g+vWPsRQaULs4gSwhajR0/ehVHDq0u+r+C4JAwBP3cvr9\nJbZUt7LJfNXt1eiaNZn59/b2JikpCY2m6QcZKbKfhiEzrYCwtVGcTcipsN/JRc+4u0Px61h9EZia\naveNpWY2/RZJ7AnrbItXj2x2pX0LQN/Amzh4egf5BmsfHCw+lAjZCIgEGO7E174HfYe2J7SvL1qt\ndVwrWSR+//EQCbFZeHg58sCT/W2DlfTcczz79e3oNHoWTw1Dr63aWZUlmd1hsezdEV9hv72DluHj\nuxDco2Ke4G3rozm8JxFHZx0PTRuEg2PTnNmrbw6GJ7Bj40nM7g5sc3Xkfzf6M6KT+5VPVFBo4ST9\n8AdRL78PWB2T7l/MVuQ7TYycfcfYP2FaeU59nZbeP32A+6CeVzWb2xy4eAUAQUDt7EDIgpdQOzuS\ns+co2XuPkrs/osI5DoH+tB4/nNbjb8S5W5dKA1hDUgqZ2/cS/dpHNgdW0GgYsmMZDh3rfzXcXFDE\nkcmvWldsALWTA90WvVmn75e5sIj9d00jP+KUNUuQkwP2HXzJOxwFQOtbbiRkwUuVZGJ1pazGhmQ2\nX/Y3olFlPwsWLCAnJ4c5c+ag1VYdNNFUUJz/+sVYambPtjgO7U5AkmS0OjUgI4oiensNuVnW0Xbv\nwf4MubkzGk3l4M7cbAPffxJuC6QVBIGQXm3x9nWhTTtX8nIM/P3HCSRZRqNWUVhQilanZtzEUBZs\nfYCC4twK7XX26c4Dw59BU+DD5t+PYzFL6OzUFORaZ9bs7DUEdG7FmZhMTEYLFrOEnYOWB58agKu7\nfYW2Xl/+GLHnI3jm1rcZHDy22nvx6Zy/MZZa/zGo1SJPvnITervKA2KLWWLVkv2cT8qlXQd3Jj7W\nB1HVMv95lCHLMt9/spus9EKSAlpxUlTx1Z030MFDmf1XuL45u3IDx6e/DUDwuy/g91jNZk4VGp+0\nv3ZZn5UgXtPqq42JZDLzd8eRyEbTlQ8WhAqpVzUertYgWbUK98G9MMQnUxSbWPWpGjX+k+6m4/OP\noXFxqpe+l6RkcOjBFyiIOo22lRu9ly+scvXiaihNz2J7jzsq1AdQOzkQ9M7ztL177DVbtWtU59/X\n15e0tDREUcTT09NmtCAIJCUl1bkT9Ymi+a8ZZTPxZ5JP8NT0++gY5IUsyyDD6ZPpbPn9OBaLjEol\nUGwwgQDd+7Vj6M2dbQ6vZJHYuyOePdvjkCUZd08Hxt/TjTY+LhhLzcScSOPEoXMkn8muVd9atXbk\n9gd74uqu59GPh2I0Xyg1L4g8/5+F9O40rNIXT5Zk4k5lsHd7HKln82z7E89F4e8TzP1T+uPj71bp\nWpsPr+L7sAX06jiUlyZ8fMV7tml1JMgw7u7q03kW5pfw4+f/Yig00m9Ye4aNbZhCME3ls5mSnMtP\nX+7FzkHLei9XEAXWPdodbR0HPU3FvoaiJdvXkm2DmtmXsuZvjj09BySJLrOfof2T9zdS7+qO8vya\nN7Wx7+KqswAuvUJwH9ADtwE9MBcZOPnaRwAEv/8yGicH0jbsIG3Tziqz26idHPAY1hedlwcpa/4G\nBJxCO5O96yDIMhp3VwJf/i/t/u92BNXVZYILDw+ne6u2HHrwBUrOpWHf0Y8+P3+Avb/PVbV3OcJu\nGIP5Qh0AQa1m2J5V2LXzrtdrVEWTyfO/fPnyOl/oSmzevJnp06djsVh4/PHHefnllyu8f/LkSR57\n7DGOHDnC22+/zQsvvNDgfWrJbF4dSbHBRGmJmT+WHa722NY+zoy6IwRvX5cK+0WVyKCRnejQxZON\nv0aQnVHE8kV7EFUCgiBguRD8qtaItPF1ISOlAFEU6DusPWq1SMrZPFKT88jJukirpxZ54KkBGCUD\n762ebnP8dRo7pt06jz6BVVeVFkSBTkFedLzBk6S4bFZ/fxBJso5rtTpVlY4/wIAuo/hx6wccO/Mv\nBcW5ONldfhmvY5AX02qYwtPRWc9t9/Xgl+8OsH/nGbzbuRIYcvXFrmpDdRKrhqhHEBedzroVRwFw\nbeOEJAv4u+jr7PgrKDRn0jb+Q8TUuSBJBP7viWbl+CtcX4R+PIvjM95BMlsIef8lvG+v+H+u7Z2j\nK2x7DO1D0DvPV8icJNrp6fPzB7j2CUXUWF3L4HfL/bS8iFOcfONjcvYeI+rl94l69QPU9naEfl7z\nqrplGX2OG7IxCPZIxSW49g2l1w8L0Lq7XLmBWtLt09eJfG4estlC6GevN4rj31jUaOa/obFYLHTp\n0oWwsDB8fHzo27cvK1asICiofPkmIyODxMRE1qxZg5ub22Wdf0X2UzM+fvNvzCbLFY/TaFU888Yo\nxCsUujKZLCx6a6st2w2Aj78rIb186BLaptqg4Kij59m6zqqlG3d3KDqvQj74/QVSc5NxsnNh+u3v\nEeLft4aWWYmLTmfjbxEgc8WsRO/+Oo1jZ/bw+M2vMqpH/S7JH9h1hn82nQJAb6dm3N0NXzX44vSo\ngijQuq0zKpWISi1yNiEbyWL9yts5aJg6q2aDmZgTqWz+NRJJlmnf2RMnZz0mkwWzycKp46m2NlVa\nFZt8WzG8vSuzRrZvGAMVFJo4GWH/cvix/yGbzHSY/gid/9f4BaEUFBqa2tZhkGWZtPXbOfrk63Bh\ncg5RoN3/3YHnqMF4DOmNyl5f5bkl59PZNewBLIXlk4Wtb7mRbp+/2WQzZjUEDT7zP2/ePF57zVrE\n4vXXX0cQBMrGCWWvBUFg7ty5de7E/v376dSpEwEBAQDcd999rF27toLz7+npiaenJxs2bKjz9a53\nThw5Z3P8tTo14ydaZ4DLpDRlue4Bxt7V9YqOP4BGo0KjVdmcf72dhvunDKhRf4J7tCW4R1sADsRu\nZ9GyNygxGQjw6sLzdy7Ey6VtrW3sGOTFM69XXyyjjEFBYzh2Zg+7o/+qd+e/z5AAwrfEYLHIlBSb\n2bQ6ssarB1fDucQcm+MPVjnUxTKoiykxmDmXmHPZVZEyEmIzWf/zUZvUsywYuyrKhn7+7orWX+H6\nI31LOBFT59gydgRMuY/Al5+4xr1SUGgYyjIn1RRBEGhz+wg0/3u/XGYkyST/uIbkH9cg6rU4dm5P\nUVwSgkpFmztGYSksImd/RKWUq6JeR4+v37pq6dD1zmWd/3PnztleJycnV9ZYX3D+64Nz587Rrl15\nmiRfX1/27dtXL23XBy1JG5gQm8lfq62O/U233ECxfJZOwRXlKB2DvJg6a0St2x47IbTCoKGmHDq9\nk682zaHUVILRbA3aHRQ0hiljX0enqZsTWZNn1zfwJpao3uFk8mEy81Np5dymTte8GEEQ0OjUWAxW\nh7y02ERBXglOLlXPbtSWi+2LPHiWv9eeAMrTow4Y0Ym27VyxmCUsFomzZ7I5vCcRk9GCLMusWLyP\nrr19GDa2C/YOFYP5c7MMbN94krgL6TvL0GhUDLk5EI1WhVqjIiutkKP7khBFgfT2raBYIsCt/u1r\nibRk+1qybVC1fceeetNWYEjUa+ky+5lmm87zenx+LYmmbF+ZzAig/bOPYCksIuPv3eQdjSY/4pTt\nuLPL1theq50csAvwwRCXRJRczP2LW67j3xjP7rLOf3BwecGHWbNmERgY2GCdqO8fx6effho/P2tK\nKRcXF0JDQ203Mjw8HKBW25GRkXU6v6lsp53L45P3lmM2SUy4bzy9Bwfw5Zeb6q39jkFedB9udSDL\npC01Of/91S9g522dM85OLGZUjwk8c+tcBEGos/2RkZE1Or5Xp6HsO7WV71YtYlDQmHq9/17tDaSf\nsae0xExC8gnefi2OV+ZOwsXNrl7skyQJU24rjuxNIvFcFIEhrZn2wv2IKpHw8HDik87ajj+bdpJe\nI+3o338g+3bE8+uKP0lcF8XpqHSGje1MXnECZouEytiGQ+EJxCedQK0RGT1mBGdiMjiTfIJ+Q9vT\ne3CArT+CAzzzhnWVZcycZeSXmGk/Mahe7l9Nn1/Z9vqPvuTM58sJ0bkQ+vGrxFxI7tQUvn/1YZ+y\n3TS3B/XtR9SsD4kssAZABosOqB3s2b17d5Pon7KtbDep7QsrBuHh4Zy78H6nFyaxff1Gjk2dzQ1G\nNQDRqlL8HpvAzQ/cg2OX9uzeswc7oDfgNWRI07GnnrfLCA+3+p95edZVkqSkJB5//HHqg8tq/p2d\nncnPz6/0uiHYu3cvs2fPZvPmzQC8++67iKJYKegXYM6cOTg6Oiqa/1qSm23g5y/3YigyEtTDm/F3\nd0OogZynodl78m8+XvcKYP0Y2usc+e65fxq9H/tjtvHhmpkEeHVh/qM/N8g1ig1Gflt6kLRz+Ti5\n6rl3cj9cPeyvfOIV2lz381GS47MRVQKj7wghtI9vjc/PzigkbF00SXFZ5KqjSbD/HYAAw124moMI\n7tmWYWM64+h85Zn8wlIzdy2LRKcSWPNId1TX4PMV1vlmWwCaxt2VkVE1W5IuCyQDrpsUf9eC9C3h\ntgC6oHeex2fiuGvdpTpTkprBkcmvknfoBIJGjajTotJpa6SBVlBQqEht4wiuNxpc89+hQwdeeOEF\ngoODMZlMfPfddxWkPmWvJ02aVOdO9OnTh9jYWBISEmjbti2rVq1ixYoVVR7bBOKTmx2GQqvTaSgy\n4t/Jg7F3hV61418m0QF4ctybVVbGrQmFJfl8H7aA8CjryoNaVKPXOvDU+NlX1V5d6dFhMHZaBxLS\nT3Eu6ww+HvUfrGpnr+WeyX1Z/f0hziflsvKbfdwzuS/uno61bisuOp2Nv0ZgLDUjy2DvqOWOB3te\nUb9/Ke6ejkyc1IdTEam8tWkeFtEqWYhzWMHAwPEUeXmzJy6GzPxU/j76K6Kg4qnxs6t87ok5VsmW\nn5ve5vjX1+flShiSUoh5a5HN8Qcw5eQR9/H3+E26G43z5e+xZDRV0Gkfn/FOrXSsCjVDMps59uSb\nWAzWz1jkM29xZtFPeAztg8fQPlgMJUS9+iHQfAZgOfsjOPr4LErTs9D7tKbnd+/i0v2Ga90tBYVm\nS23jCBSujsvO/J86dYoFCxaQmJjIjh07GDq06lRM27dvr5eObNq0yZbqc/LkybzyyissXmwtpT1l\nyhRSU1Pp27cv+fn5iKKIk5MTUVFRODpW/Keu5PkvpywvfWmJGVmS8fJ24t7/9kenLx/z1da2/342\n0lZ0S6+159tnt6MSLzuGrJKIhL18tXEO2YXp6DR6HrxxOqN73N0g2tja2PfVpjnsiFzHhEH/ZeKQ\nJ+utDwdj/+GLjW8iCPD0+LmEthvE7z8c4mxCDvaOWiZO6otnm9oVPflsbhilJWYSz0UR0C6EJ2YO\nr1McQb4hhyc+Gw3ClQfXAgJdA/rh5xmIv2cghSX5/LHnW4xmiWz1OLr6+NLPu4S03GR2ndiARbIG\nlzvbu/H1tLBa9etKz89cWET8Z8tI+GolUqkRQatGEFXIZrOtUqfaxQn/yRPx/+89aN2cAbAYSsjc\nsY+0jTtI37K7wqBB4+rMyJOba9XPq+VS+1rSCsTFtuUdjebESwsq6HmrQ+PuwsgLEwNNjbJnFFmY\nyQ1mLUgS7oN70WPxW2hb1W7w3ZRprv/3aopiX/OlJdsG1dvX4DP/Xbp04dtvvwVgxIgRbNu2rc4X\nq45x48YxblzFJeApU8rTo7Vp04bk5OQG7UNLY/PqSEouBJoKAkx4tE8Fx/9qMFvKM8mUGA28vPR+\n7hs2rcrCWxdjnQGeTYmpBNOF3P2BbUN5evxcvN3rv+T31TA4aCw7ItexO2ozdw+eUufBiCzLRCTs\n5aO1M20O8FebZvPNM9uY8Ggf1iw/TOLpLH74dDc6vfqKKUnLSD6TTWmJ2batt1PX2fGft+pJq+Mv\nC6jQMajTrXQMaE+eIZu8oix2Ht+AWbI+exmZyIR9RCZUDsp3MK3izGk4c7rydepr1a7M+ZJKSxHU\nasx51iIsbe8eQ+dXn0Lf1lqwLjv8EKc/XErOniPEffgdZ75YDgjIkoSAdca/DL1Pa0pTM5EtFlCJ\nlKRkoPf2rHFfoH6c9cjpb9uyYBx5fBa+99+K3tsTXRtPSs6nk7B4JYIoEvrJrGYxMDAXFBEzfzFJ\nS38HSULj7opsMiFqNQQveAmtmwtZuw6SFX6Q3AORtvNMOXmcXvgtAVPuQ+3kcA0tqIi5oIhjT8/G\nUmhAkkpBVOM/5V66vD4VUV2331YFBQWFxqJJ5PmvTxTNvxVZlvn4zb9thbb0dhqmvV630eL57ET+\n9/39GM2laFRa7HWO5Bms1Xu7+HTngeHP0sW3R4Vz0nLPciR+N8u2fYhFKndY7xs2ldv6PVzrVYOG\nRJIsPPXlOPKKsnj7oR/p6B1yVe3IssyxM3tY/e/XxJ6PrPCeVq3jx+f/BcBssvDp3DBbjnytzlpT\nobpBR1J8Fr//cBizyYJKLaLVqRl7V9errh1Q5vgnZZymrXsAb9y3GFfHVpWOO3R6J4s3W9P63jt0\nGi72biRlxJKUEcv+mG1IsvVzJiMS6DuIG7zb08atHfmGHFb/+w0WyczNPScyafT/rqqfZUilRraG\njK+Q69mldwhBb03HtVfVzyt771HiPlpK1j8HKux36RFE61uG03r8jTh09MNcZODA3c+SdyQKx87t\n6bf2S9tKweW4OMZA5WBP318+xvGGDqgdahfLIcsymVv3cOiRl8AiXfkEQcAppBN2vm2w822D2VBM\n6rptCCoVoZ++VuuiOVC7wUt159kGZ0YjglqFObcAQaXC/7/30Gnm5Mvem5S1YZx48T0sJaXIJutv\nhcbdhQ7PPozfI3fVey7v9C3hRD47D9liodNL/6XthDFo3JwRBKGCfUHzpiMZTaRt2EHmP/uRLxo0\nqhztGX26dqtZCgoK1y91lcLW18y/4vy3UA6GJ7Bj40mAWs0qX44SYzGvL3+E5Mw4BnQZxXO3z8ds\nMRF2bDW//7vEJgVSixo0ai3Bfn1IyU7gfHZipbYc9M58+2z9yMXqmwWrp3M4bhdatY7nbp9f4y9m\n2RfabDHh4uBBak4SAE52LvTsMISDp3diKC1AJar5bMqfuDtZZ5UXzdtKsaHcmQgMac3Nd4ZgZ6+t\ndI3E01n8sewQZpNESC8fxtSwBsPlqKnjfyXKbM8vtVBo/wjfP/IgnhelDd15YgNfbHiDjt4hvP3Q\nj7b9tXE8i8+mkrxsDWd/Wo8xM8e2X+Voz6jYv2u0SlMhGNjNmZHRlaU9xuw89v/naQp/Nh1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3+eWsnwTpMKS9zsef4/+eQTatasyahRowpDpjyRmec/s+o8kiShTTHg7xvG8b3+GA0Szm42PI5M\nzDR5N22d/Fc2XCPuyRilKFDd1RqtwYjOIHE/NjlD8QxRgCYe9lRwtOBQYDQgmBcNccl6QuJS+Gxv\nIJonYRWikHUBDnsLBbZqEQdJopxvKMonj1AnClQd3BB7SyX2FkruxyTzv6uP0BmNpOhNYzpWceKj\nthWwzMJDn7ZyjbWFLasnHn++MMCdKA2zDt8hNE6LAFiqRN5o6E6tsjYYjBJ6o8SNRwlsuR6BIAh8\n2r4CLb1fXIawoDhzL5b5x+9hMEp0qOJIWVsLNHojyToDe/yj0D1ZqdkrorCImobRaGDO8A1UerL7\nk0pYdDAfr34FoyTx7Vu/U6FM9ksZ/rR7Bif8dtOxXn/e7Tkj33Rbc+g79l/ahCiI2Fja56qOMMDV\n0HjmHg0iWqPH0VLJ5x0r0sjD5NGXJIkroQlsuR7OufvpdxgcLJX8OexpSIzJ8zobfXwikk7P6f4i\nAVU02QqnkklPbutDF6fYfRkZGZnSQOrfY0mSqOv9En7B54nXmAqe2Fk5otWnoFZavPBv9Z2H/zJt\nw3AEBOaO2Ii3W/Us71uoYT9t2rTh/PnzeHt74+7+NPxBEAR8fHzyLER+kpnxv2TWIXNHVEEwGfLJ\nyfoMSbupOLpY41XJGQtLJdcvhSAIAj0G1sVYxpY9NyPZfTMqW7IoBBjbwpN2lR1xssrojU/LswmV\n9cvZcjdaw+0oDavOh5gN0mcpk5hCnQjTC+dXxoEIm+d73Ue/VJ5X67m9cAfnr1Or+OvUSkRBZNKA\n72larX2W4wESUvQM/u06+myUDRQFk44dqjihziQvoSAJjklm3Jab6LJZ3rCZ3W5u39tKnQrNmP7a\n8nTfXWrpzg71+jM2hwZ8WHQwk399xTTP6L/zJdv/wq2jLNj6MQpRydfD1lL5mcXKizC9g/dI1kto\n9UYkoL67LZ93qoiLdebvb0hsMu9uuWlOHn/W+D9Uo7u5Ay+CQNm/p/Ptyek42riwdOxulIqsfxcy\nJpK1SYz9qTvJOtMOi7WFHasnHitaoWRkZGT+ozxb3huginsdejcbxkvVO+bo37ZUp1218vX56o1f\ns8wbLNSwn9GjRzN69OgMnxf3MCCD3sjpI4Fmwx9MlVNSK++o1Ap02qdefoVKwehJbbFzsARMxtCx\nKC0R/pe5cK0sofEhAFS+6Uu3LRsRBNB9PIE6AzuiUoioFQJ+DxNZ808oAJPbeWdZPz8tLb0d+NM7\nfRJhXXdb6rrb4marNi8MJrb2pK67LYlaAwlaAxfux/GXbzgS0MrbAUdLJbEpBuKS9VxME25koxYZ\nXD9jYmVmsWWPYh4AMLDVmGwZ/gC2Fkps1CKxyabvUyFALTcbFKKAKAj4PkwwLwyMEnzvE8zqf0IZ\nUKcMfWq6YmtRMPHHqfo9itey8XIYB29Fp9tVUSsEBtV1w1IlYqVSEBqXzIGAaLQG047FP7HtcRIP\n4Bd8gct3TtK4iqlzqn/IVc4HHEattGBwm7E5lquccwXa1e3NMd8dbDnzC+N7fZUn/SLjHrJiryk0\n6fX2E3Js+IcnaJl3NAiN/ml32aENyjK8STlznkdmeDhYMq1TpXQL1+SwCMK2HiT0r31PDX9A5WBL\nw5Y9KH/jF0Kjg7hy5xRNq3XIln6llaz0kySJgJCrHPXdwdmbB82GP4DeoM30muLEf/nZlQZk/Uo2\npVm/4qCbwfjUdlQqVHzx2gqqezTIlV38WttxnPM/xK3Qaxy7th11fJkC1y9bFtdbb71VoEIUBBEP\n49nz5zUiwkzGh1IlolCItO1enep13FFbKLj1OJl5m3yp8eiJ59zZjlM7AsxzxKcYkIAUg5HQeC12\nFgq6VHOm6ve/Y0gyxUHbfr+IOuP6mq+p6GRF71p5q5n+LJktDByf7CTUKGPDsMaZx04/u5uQHZK1\nGs4HmCrAtKndM0dyTmrr/dxykGll6VTFkSuhCdx9nMzqC2FsvGRKJlUrRIY2LEs1V2uS9UY0OiN+\njxI4EBANQO+aLjTzssfBUomjpYqbEYksOnk/y/tFBdymdWI5LobEozdKKARo5mGHf2QSgiBkWrZy\nfEuTF/5SSByrzoUQmtIba81m5u+YT7KzLUpRgaf2e5NMzYbhbJe7ngwvtxyFz/Vd+FzfxcVAH8b3\n+ipXIToGo56lu6aTmBxHo8qt6dn09eeOTZuT0r9OGRK1Bi4+iOdeTHK6cTZqkbebZd4j4lmq+Psy\ndvZsjFodRu/yHPv3trk+qcLGCslgQGFpSb3F0xEEgU71B7Dx2CKOXNv2QuP/v0bqVrJWn4y12o7H\niRHmc+WdKxIRF4ZOn4K7U/Z+zzIyMjIy+YveoMPawpaklHjUSksm9ptLDc+GuZ7P2sKONztOYsmu\nafx+fAmv1i74nkjZCvuRJIk1a9awYcMGQkJC8PT0ZNiwYbz99tvFzvt/+PBh9AlOnDoYgMEg4eBs\nRc9X6uNZ0QmAiEQth25Fc/BWNA9is9/EyVolsumNeiScvcSFwR+aa3QDVJsyhsofvlXsvovccNJv\nD0t3f0G18vX5etiaAruPJElcDInnL99wLoXEv/iCFyAK4O1oiVIhoBJF/CMS0yVZC0Cnqk682bgc\n5e2zn5BsMErsvfmQjXvfBkMEidbDMYo22CUsx8rCkU8Hb6aqmxP/PIjPsg7+83hzQUtzgzB7aydW\nvZ+9jsJp+fPkCv4+/TNONq58+/b/sLd2SnfeKEmExaVwK1LDAp97pGQSQmalEqngYElwTDIqhfDC\nXStJkki4eYfIo+cImLMCSZ+mW6pahVvX1pR/tQdlOrVM1x0XIDYxmvHLe2KUjPw0dneuF0+lkWe3\nkh1tXGhXtw8d6vajvEtFwmNC+GBVP5xsXFn+3v4ilFRGRkbmv8m2s6v5n89PlHX0ZP7bm1CrLPM8\npyRJTFk7lOCIW6gUaj7s/22mzsBCDfuZM2cO69evZ/LkyVSoUIHg4GDmz59PaGgo06dPz7MQ+Y3P\nPn8A6jfzpEOvmlwIS+C9dVfRPQnlSMXJSkktNxuuhSUgCjC2hQdNPU0dNgVB4J8HcSw/+wABgY8a\nuXDrs++edsVUKBAtVBiSkrn17c/o45Oo/sX4Er8AOPGkMkbbOr0K9D6CINDU056mnvYMXH+NBO3T\ncKE6ZW2xVIlYKkXOBMea8x1UokDtsjbEJOuJ1eiJSRPOZZTg7uPkTO+lFAV+GlCDSs5WmZ7PCoUo\n0Kd2OWwNH7Ji7zSsNNuQBNPiIVLRm4m7g1EIwUg8TdL+3ucef79ZP1vzW6gszca/3pD9RnCp+AX/\nw5YzvyIg8F6fr7FUO7DFN5x1l8IwGCXK2VkQkag11+hPp5sAr9YvS1NPO2q52aSr2/8s4QdO4jvx\nG4w6PQ4Na5EYeI+Uh5EZ57SxpsOlragcnt8YzcHGmabV2nPO/zDHr+/k5ZbFv5BAUWCpsuancXvM\nHbIBXB3KoVZa8DgxkoTkOGwtn98RWEZGRkYmfwmLDubvUz8DMLrb1Hwx/MFkE0XFm5pb6gxalu2e\nwa8FmNeVLeP/559/5vjx43h7e5s/6969O23bti2Wxj+CqeRlxequ+NyJYdPynYzYshGAAwOH4dmz\nLd2qO9PEwz7LeObOVZ3pXNWZnQtXkDJsLw/CIkxdMT96i0rvv4moUhK27RDX3v+Ku8t+Q5+QRO15\nkxHE4lXrPivSxs7FJERyLegcClFJy5pdC02GT9pnL1zo2XOngmJYeMJkeI9oXI467jbon1QXuhaa\nwGbfR8QGXuGrUQNyZfinpX3d7vzvxHJiEh6ABEqVM02q9yEoRk9YXAppfenxKQbGbrlJK28HWld0\noLKz1XMXheN6fcXinVNJ0WkQEIhLepzBc58Zv53ey45Tc4kOisLF25Iy7oNYeN6WkLir6XIaUsN5\nXKxVVHWxwkolcv5+HEoxo3f/aU10qPX1RNQujsRe8yfu6k0e7fUx73ZFn7wIgIWbCy4dmqN2dSTk\nf7sRBIG6C6dmafin0qn+AM75H+bote30b/H2cxOcchrbmduKOEXFs/oNajWGtYfnP1nMzUpn+IOp\nK7OHSyXuPrpJSNRdang0KGyRs01xiMstSGT9SjayfiWXotJNkiR+OTAHnUFLuzq9s13eO7uk/jsY\nfU+DXc2CrYiYLeM/KSkJV9f0cewuLi4kJ2fuaS1qLK1URNtY8P02fwKjNIz/ax2WyaZa+j3/Xk/f\neS9ucGNITiFo1SZuf/8rt5JjqC3a4NC4DvUWTsW2RiXzuHIDuqCwseLK6GncX78VQ1ISdRdNK/AG\nOgXBqX/3I0lGGlVpi51V4ZXizCynITvnWld0pHXFzOWsU9aWoY3cOXkyPtshOFkhCAJa3dNwDJWg\nZWY3U0kujc7A7puRbLj0EL1BQhDgTrSGO9EaNl5+iKOlkiSdAbVC5JP26Q3uJlXbsWbicb7+31j+\nfXCJlfu+5uOXF2S5g6TRGdhxah6ClIiAhIQC/5RuoE1BFNKXirVRi6x+pTZOz6nWA2BISib22k2u\njp2BIcn0m7723vMTkBXWVrTYtRLbWlXMctackbOynfUqtsDOyonw2BBGL+7Ie72/zhdDfdnuGSSm\nmMLIVuydxc8Tch5GVZSklorrWL8/zap1zHSMp2sVk/EfeadYG/8yMjIypQkfv134BV/AzsqRYR0/\nyvf5x/b8kpX7ZpFsqWRszy/zff60ZMtC7dGjB8OGDWPu3Ll4e3sTFBTEtGnT6N69e4EKl1tul3Nk\nx77bADS6dQ2LJ4Y/gIUmiSN1euParhmuHVuAKOA/6yeQJLxHv4JRp+fx2SvEXLqB9KQtfG3RxmTw\n7FyBoMjY1deta2ua/LaAS8M/JfSv/egTNTRcMQvRImdNlYqCtKvnk09CftoUcMhPYZKf3oG0XliV\n8qkxbaVS8Eq9srxSz1RNSWswcjU0gdP3YjhzL5Zojf7J5wa+OXyX1a/Wpqzd03dDFBW812cWn64Z\nwsXA4xy+uoUuDQdluL8kSRy9/Zifz90HyWSkO3tbIQmWfNy+EpWcrajgaMmlkPT5B2kN/0f7T+A7\n8RsknQGnl+qjjYwm/sZtJEPG3haOzephX78GDvVrok9IJPCHNQiYasXb1a6ah2/S5OFI0Zl+l0kp\nCSzc/imvt/+A2l5NqOBWzewByenzS53TNG88sYnRONg450nWguRZ/c4HHAbgperPj+n0dDE5Hx5E\n3S04wfKB0up1TEXWr2Qj61dyKQrd4pIes+HIQgCGd5qcrR36nNKkartc5f3lhmwZ/0uWLGHChAk0\naNAAnU6HSqVi8ODBLFmypKDlyxV+koidWuTN6z5Yrv8DwJR0KIooHWzRPori4c4jPNx5JN11gfN/\nfXogCAgKEclgCnVQWFlkavin4tKmCc3+/JHzr04kfK8PB6t2ocGymbj37ZT/ChYADyLvcPfRTawt\nbM3lLGXSk7oqB3i3x/Pr+qsVIs287GnmZc+E1hKDNviS+CSnQWeUGPXXDQbVc2NIg7JYqUzvlKt9\nOUZ3m8rinVNZf2QBtbwa4+HydIcpMDKJZWcecP1hLDaJv2CB3hRqJFjTr/XndKvuYh777G5JSkQ0\nUSf+IcrnAiGb95i3BSKPnjUNEEXs6lbDoowLjy9cQ1QqqbtwKmV7pvfEe496NdffXabfk9ICrd60\niNEbdKw/sgAAG0t7yjl5cT/yDiqlmnE9Z2ZrV+Duo5vojan9PAQMRj3TNrzJJwMXvrBxSnEgNPoe\n9yNvY21hS13vZs8d5+FSGYAHkbcLSzQZGRmZ/zTrjywgITmWehWb57gSYnEkW8a/g4MD69evZ82a\nNURGRuLq6ooiC0O4qLGWdHx+cieROw6DIGD8rDt/i6YutWN7fkJNRWUij54j8uhZIg6eMl8nKBV4\nj3kN55YNcWxWn5gL17j+0Ryup8QyZOHUF97XsUldRJUSIyDp9Fz74Jtib/ynxs6lJvq2qNEFtTL7\n1XCKO/kZG5ibVbkoCHz6JKdBkiS8nSzxfZjIH1cesT8gipFNy9OlmjOiINCqVpPpHgEAACAASURB\nVHcu3znFCb/dLNk5jT7tfmThqTBS9EZTEy1Jj5PmZwTtRazUNkwd/BOP7sTSplV6/cK2H8Lv428x\n6vSoXZ1IfvAwU9kU1lY0+e177OvXRGmTt5yI3DCu10xW7puF0WikbZ1eJKbEcyP4HyLjHhIY5gdA\nWGA0K4VZ2fret54xLd57NX2Dfi8NZ8G2j7kV6suM30byXu9ZvFS9+P0W076fqV7/JlXbZ9kgxtP1\nifFfzD3/pTnmGGT9SjqyfiWX/NTtYqAPy/d8id6o5432E+nScFCGsNurd09z8sZe1EoLRnebWuCF\nXQrj2eUoMF2hUFC2bMZGUfnBvn37+PDDDzEYDIwePZopU6ZkGPPBBx+wd+9erK2tWbt2LY0aNcp0\nrvf+WEbkjQAUNtZ4//ghswPmkpJi8jD+uONzRnefikfPWtQZ1pOTW9aw0X8NCPBmrdHUfPVpwya3\nbm3o5LcH9cmTuGXzQaTdHTAmp6BP1BSJYZUTjJKRUzf2AtCmdu5DfswJo5JE3UVTKdtd3kGAjJ54\nv0cJrDgbgn9EEt/7BLPwRDAqhUij8rYo1K+hUF0gKNyf+bsWobE2dQFG0lFNXENU8kVsLOwY6z2G\n4C5T8EuJpeqP36BytCf61EWiTvxDzD/XzfdKfvAQ0coC5xYNcWnbDEGl4M6idYApfMe5Zea/ocLg\neYup8NhQPl39mrmplVb/4pK89yMCOR9wBJVCTd+X3sTR1pUvhqzk5/2zOeG3mx+2fcLgNuN4ueWo\nYluR67y/aSey+QsWKW4O5VEp1ETHPyIpJQFrC9vCEE9GRkam1LFi71ckJMcB8OvBuWw+uYzq5RtQ\n3aM+ErDr/AZzHtmrrcdS1tGzCKXNP7JV57+gMRgM1KhRg0OHDuHh4UGzZs34448/qFXraZfSPXv2\nsHTpUvbs2cO5c+eYOHEiZ8+ezTDX4cOHedj7PSKbOhLySgV8wy9jlDLGM6ciCCKSZArtyW2d9bSE\nHzjJ9Y/moIuNR9IbqDV7Et6jXsnTnAXNjeCLzPrfO7jau7P43Z1ZtpbOisO1e6GLfpoUa1PNGyuv\n8lh5uWNMTuHh7mMISgX1F3+BW7ei80ikrWpTb9FU3Lq1QZ+oQRMcStj2Q9xbtRlEgXo/Tse9d4cC\nkcEoSRwJfMz84/d49geo1AViF/8tAPF2k9Erq+CYtBwx5Ro2lvZMHbiEu50moY9LeOF9lPa2dPLd\nVSLyT9JyMdCHpbumo9EmYqW2Zsm7u7C1en7i9uIdUzl9cz/dGg1mZNenjgNJkth1fgO/H1+MhIRS\nocJKbVPsKgGFx4bywcq+WKis+Pn9Qy8sHzdl7VDuhQfw9bC1VCufeUK8jIyMjEzWDP+htTn8VHhS\nQiMzREHBhsmnM1RgK2zyq85/sahJef78eapWrUrFihVRqVQMGTKE7du3pxuzY8cORowYAUDz5s2J\niYnh0aNHmc636V0te9qGc/XRPwgCVCtfHyu1LVZqG1rW7E6LGl3xcq2CQlSaDX8wdbfV6bV50iV1\nt6Dhqm8ACFr5v0yTKYsTJ/x2A9C6ds9cG/5AukZPAIm37hF55Az3120lZNMeDAlJ6GPiuTJmOtro\n2GzNGX7gJIdr9+Jw7V6EHziZa9nS4vvhHHTRMeiiY7g88nOO1O3NoSqdOdXxTe4sWochSYMhIYkr\nY6Zz/7cdGHX6F0+aBQ93HeVQ1a4cqtaVR/tPAKZwoC7VnLGzeLpTZKkUmdLBmzn9e9CtydsISNjH\nfY9L5DjElGtYY8nAy1W4025iBsPfrnZVvN99jcbr59NgxSzULo6oXRypv3RGiTP8wbQrsHricepU\naIpGm8T/Tvz03LGhUUGcuXkAhaikX/MR6c4JgkDf5sP5eOAPgCm3IF4TY87dKC5ceNJVu1HlNtmq\nG52aDxJSzEN/ZGRkZIorYdHB6I2mwi7WFnZMfnkBi9/ZwXu9v6Zrw1cQhaf/PluprYvc8M9PioXx\nHxISgpeXl/nY09OTkJCQF4558OBBpvOlWENZR0+Gtp/AT+P28vWwNaz58DhrPvRhYr85fNh/HvNH\nbmb9pFOM6voZFkrTP7ZafTLTN47gfkRguvlOnsy50enWvQ3WFT3QBIfyaM/xHF9fWBw9fpSz/qbd\njrZ5CPkBsPQwhYSJVpY0WDGL1kc30Hjdt9T85kNEy6d5BMYULSfaDCVk0x5etPHkO3G22VC/9v6s\nHBvizz47SZIwap6WqJX0BrSRjxHUKqyrVEBQpflxG434TZ7HidZDePDHLoz6nN077noAN6b+wJUx\n09EnJKKPT+TKqGnEXLphHjO5nTcOlkocLJV83rEinas607C8HSM6vINgBASQFIAEXdcbUOy9gSFJ\ng0W5MoiWavwtjdRb8gWtj6yn1lcTcevWmnIDutDJbw+d/PYU6Q5LXhEEgbp2nVGICg5f2cLtsBuZ\njtt2djUSEu3r9sXV3j3TMU2qtsPG4mn/gdw0VCsIUt/Pc0+M/+Y1speX4OVaBTAl6hdXcvN3syQh\n61eykfUrueSHbpIk8evBuRiNBjrU68fqicdoWq09bo4etK3Ti1HdPmfyy99jZ+WInZUj43sXnsOo\nMJ5drpcxkiRx4sQJ2rXL+9Z5dmNwnzUUn3fdv7ujadDzFf49+pDQS5upV6+eOXki9Utt06YNClGJ\nVWI5xrz0LWUrO7B013QuX7jKu5cG8f7wKfRoMoTTp07j6+ub6fUvOq747hD+mjKLe/MW806fjgiC\nkKPrC+N437EdhIRH0uSlRni6Vs71fLUkSxL+vY2/lUSD5VMo16MLAFejwqBmeRqu+tqUPK2JQeXi\nQKX7MfhO/IY9K9ZQ8d3X6DrkFfN8kiRRR2HLg993cjUqFDCVW9XHJbCkWhvs69egy2uDEESRLdPn\nAjBk+be4dWuTQT5fX1/zsWQ08vvoyTxKjHpSvtWSx/1b49r+JTr2640giuxcuJy7P22kroUD5Qf3\n5Mi2nSQH3ULz0RwC5q7gWkwEokqZ4X7Vk0w7Cn4psTi3bETl8ETirvlzw5holh/ATxuLX4+hdB40\ngOpTx2K4f5uJFZ/Ke8LHh5h/fClz5CqqZvAw3FS60r2sFfV7DSLQWY19nWp07GtaqN1evpy75ezw\ngGLxPuX38cPgKKpatMJfc4LVh+bRveJoREE0n9+5byvb927Bxdua/i3eynK+8b1nMWPJRHT6FBxq\nOZOi03Dh3MUi1c/X15e4pBgCQq6iUlqgCRM5GXnyhdd7uJk8/6dPn6aiqmmxeV7ysXwsH8vHBX2c\nSl7mO/XvPnx8jmOltuH19z/IdLzmociIRl8VqX6+vr7ExpoiJYKDgxk9ejT5Qa5j/pOTk7G2tsZo\nNL548As4e/YsM2fOZN++fQDMnTsXURTTJf2OHTuWDh06MGTIEABq1qzJ8ePHMyQgHz58GMk+IVfx\nvMnaJNYfWcCRa9sAqFCmGtHxjxAEMVcxwoakZI41fRlddCzNd6zA6aX6OZapoJm/ZRIXA48zvNNk\nejV9PVdzSJLE2V5jiL18g2pTx1Llg+EvHB/61z5ufrnElCOgVCCqlCgs1Lh2aUXsP9dJCnq68yOo\nlAgKBSonB1LCwjOdU+XsQOcnScuZYdTpuf7RbEL/2o+gUtLgp5m493uxl1UyGAjbepDABatJuvvg\n6QlBwMLNBVGtQrRUk3TnQYbwLqWDHeUHdce6kgd3Fq1DkiScWzUi4uBpjClaRAs1Zbq0Ivr0ZRCg\n3MvdiPI5T+KtewCE1Fbi0z4JAXiz9mg6p0lG/y+hSUlk0q+DeJwQwTvdp9Opwcvmc6v2fc2Ra9to\nV7cP43s9vzFZKnqDjqnr3yQ44hb9W7zN0HY5a05WEOy/tJk1h76ladX25vCkFxEaFcSkXwfhal+O\npWN3FbCEMjIyMqWHhOQ4Jv8yiNikaN7tMYOO9fsXtUjZJr9i/pVZnVy3bt1zvetabd5i49PStGlT\nbt26RVBQEOXLl2fTpk388ccf6cb069ePpUuXMmTIEM6ePYujo+NzKw/lNpHPUm3NOz2+oHGVtqzc\n9zXBEbfM51buy165wYuBPqzYazJCxvb8kgojBnJ74RruLv+9QIz/1PsZJSNvd/mEVrV6mOP2n5Ul\n7fdiKm81k4TkWECgVc1uuZYhfP8JYi/fQO3qlK1a8IIg4PFqT8p0aU3ANz/x4LedGPUGjJoUwv7a\nD4BFuTJ4vNYLzyG9sa7oab5Wcz+MiCNniTxyhvD9T1fJuuhYbn65mErvvYGFm0u6+xmSkrnyznQi\nDp1GYW1FozVzcW3/UrZ0ExQKyr/SA/cBXThcoweGRFMFGiSJlEeRmV+jUlJv8XTK9myP4km4U8Ux\nr5nPJwWHcWvuCsK2HuTR7mPmz4N//RMwhU9VfHcIXd7oyygb62zJWZqxsrDhzY4fsXjnVP7wWUKz\n6h2xs3IkMi6M49d3IQgiA1qMzNZcSoWKMd2nMWPj2+w6v542tXuaQ2iKCnNjrxrZ/4Ne1skThagk\nMi6MZG0Slmr5PZGRkZHJDpt8fiI2KZoang1pX69vUYtTJGTp+VcoFDRu3BhLy4wJaEajkbNnz2LI\np2TWvXv3mkt9jho1is8//5yVK1cC8O677wLw/vvvs2/fPmxsbFizZg2NGzfOMM/hw4cz/TynxCRE\n8t6K3hiMeqLvafCuWY6fJxx+4XVjlnQmXmOqeGOltmHFG9s43nQgRq2Otif/wKZKhTzLptWncDvM\njxv3L7Ll9C8YnjQ2AlNGup21I/ZWjoRG3zOfUykt6FjPtLoVBIEj17ah06cQfU+DWyU7Nn58Lley\nSAYDpzoNJ8H/LrW++Qjv0TlvBHWoejdzAqugVtF4zTxcO7yUZVM1gIe7j3H9ozkYNClIOlMMt2ip\nxmtYfyq9PwxL9zIc238Aq2VbeXzuKione5r89gOOjWvnXFGeVnKSJKj1zYc4t2qEMUWLMVlLxLHz\n3P5hNcKTKkHZibWPueTHuX5jkfSm35CgEKm7cBrlXu6KqMpyXW7m5MnSW8sZnuonSRLfbBqLX/A/\ndGkwiNHdp7L64DwOXP6TVrW680HfOTma95cDczh05W9qeDbky6E/5ynRPS/sP7SXtZdnIAoiq94/\nhI2l3YsvesInqwdzP/I2s9/cQJVyuXunC5L/yrtZWpH1K9mUZv3yotutUF9mbHwbURSZN+J3vMpU\nzWfp8k5W+hWK579atWp8++23dOqUMTwiNewnv+jZsyc9e6bvmpZq9KeydOnSfLvfi3C0dWViv7ks\n2v4ZAJXK1nrBFSbSrqU02kRWnv2elq92JGrjfoJWbqLOd5/kSI5krYajvtvYfGI5BqMBN0cPHj2+\nj86Q2c6LgFEyEJsYRWxiVLozOn0KBy5vzvQeqjw09QrbepAE/7tYerrj9Wbuts7qL53B9Y9Mxlvd\nhVMp07lltq5z793BXIozztef2wvX8mjPce798ifBa7ciKET8UmKphRWW5d1o+r9F2FavmCsZ4Wkl\np8ywrVGJSu++lum55+HYuA4Nf52D74SvAai35Au5N8JzEASBt7tMYcraIRy+uoWGlVtz9JqpItjL\nLUfleL6h7SZw4dYx/B9c4ZjvDjrVH5DfImcL/5ArSJKRuhVb5MjwB1On3/uRtwmJulMsjX8ZGRmZ\n4oTBqOfXA3ORkOjdbFixNPwLiyw9/++88w4NGzZk/PjxGc7pdDq6du3KsWPHClK+HJNfnv9U7kcE\n8vn6YegNOj5/dQkNKrV67liDUc+Uta/zIPI2oqBAFEX0Bh0OFo40/V8C3mFWdPhnK2pXpwzX/nPr\nuLnLXA2P+ugMeh4+DuZxQkSm96pQpiq1vJpgobLk6LXtCILAuz1mUL9iC+I1McQlPebibR92nd+A\nJEm0rt0TrzJV4MnjDo4I5PS/+xAEkfG9Z9GsWoccfzdGrY4TbYeiuRdK3UXT8BzSO8dz5DdxfrdM\ni4BdR59+qBBpf+4vrDwzrwQjU3LYeHQRuy5sMB9X96jPrDfW5GquUzf2sWTXNGwtHfhh9N/YW2f8\nXULW4XN5Ze6fE7h693SGXIbs8PepVfx5aiX9mo/g9fYf5JtMMjIyMqWR3Rd+Y8PRH3C1L8f3I//E\nUl28G7BmRn55/otFk6/8JL+Nf4DtZ9fwh89SnG3dmD9y83M9dJtPLGfLmV9wtHFh3lt/kKxNYsXe\nr7j54DIAVfxEhtQbSb2PxwGmXYJ74QGc9T/E9rNrMm0uoVSoMBoNGJ/0I7BS27D43R3YWTnmq45p\nyawJVmYEr9vKjSnzsanmTeujGxCV2QtVKQwO1eiOPtbUle9FycAyJQdNSiIjf2xv/q3YWNrz6wdH\nX3BV5kiSxJw/38M36Bzt6vTOtJSbTq/lnaVd0GhNVZvyoxFgKonJ8byztAtGycjK9w48d/HxPM76\nH2LR9ik0qdKOTwYtzBeZZGRkZEobphzHL82dfD8ZuLBYNXnMCaWqyVdxx0lbmarl6hKdEM76Iwsy\nHeMbdI6tZ35FQOD9Pt/gaOOCu5MXM4auYninyahEFbfrGJlt+IW3FrZl4fYpfPTLQD5b97q5Tnkq\nSi18/spSFr+zg/UfnWLyywuwt3bC3tqJ9/t8k6+G/7OlpSB9E6xrE77OtBa/ISmZ2z+YPK7VPh1T\nrAx/gPpLvkDt4kiArUC9RdOKWpwCI7PnV5p4Vj8rC5t0ya0KMeu8kKwQBIFRXT9HpVDj47cbv3sX\nzOfuPrrJ2kPfMW5ZD7PhD+RLdbNULt72IeJuPLW9GufY8AfwdKkMwP2o2/kmU37yX3s3SxuyfiWb\n0qxfTnVbtmeG2fBXKlTF3vAvjGeXpcUWFBSESqXCw8NURTw+Pp5Zs2bh6+tL3bp1mT59Oo6OBeeB\nLi6IooJxvWby2bo3OH59Jy9V75Tu5YlJiGTp7i+QkBjU6h3qej+tJCMKIr2avk6DSi35+OdXkERI\n1iVx7kljLVuFLVXCbBEDIvi3sSnxs/UBJYZbW7Gf+zGio4ImVdvlm7fxRSSHRaBPeGrs6GPjOd31\nLbzeHED5gd1Q2pnq1Qev+ZuUR5HY169J2T4dC0W2nJAan68+eRK3Upr09F/l/T7fsGzPl4iCyLs9\nZuRpLncnL15uOYrNJ5cze/N4VEoLHKydCY99WmrWzcGDyPiHGI0GbCzt0epTUOchTyaV8/5PqvxU\nz50Xx93JC4WoICImlBSdBgtVydvClpGRkSkojEYDuy/8RmJyvPkzS5VcGQ1eEPbTrFkz5s2bZ95i\nGD58OJcuXeK9997j4MGDSJLE1q1bC03Y7FAQYT+p7L6wkQ1HF+Jo48L3I//E1soBo9HA7M3v4Rd8\ngToVmjJt8DLE53gjR37biiQhBQClUaTHUWecr8UhSgKCWokgiAgKBZJkxKhJQWFrTY3p4/EaPgBB\nLNhNGslgIHjtVgLmrsCQYCpnKVqoEVRK87HC2grHZnWJvfwv+vhEkCSa/PEDZTq2KFDZZGQKEp1e\ny4iFrc2hdQC2lg60qdOTDnX7UbFsDeKSHjNtw3AiYkNpV7cP43rOzHZzwsw4c/MgP+4wFRMY23Mm\nHXJZbm7yr68QEnWXuSN+o1LZmrmWR0ZGRqY0ERYdzPK9MwkIuQqASqHGUm2d73lbhU2BV/s5fvw4\nAQEBGI1Gjh8/jsFg4M8//2TOnDnUrl2bqlWrMnToUHx8fPKly29JoGeToZwPOIJ/yFXWHp7P+32+\nYevZ1fgFXzCH5DzP8Adoc9gSn1Ym47/1ARHXO/HYVKuI1/ABeLzaE5WjPWDyvt/4/HvC953gxmff\nE7rlAHW//yxPlWqyIu56AH4ff0vslX8BcOvRllqzJ2HlURZDcgqP9hzn/obtPD5zmajjT0MjBKUS\n1w7NC0QmGZnCQqU0/aOQlGIqN2ultmH5+H2olGrzGHtrJz5+eQFfbHwLn+u7qFS2Jj2bDM3V/ZK1\nGpbv+dJ8/PvxH3Nt/Hu4VCYk6i4hkXdk419GRuY/j1EycuDSZn4/vhitPgUnG1fe6fEFjarIEQBp\nea47+e7duwiCQFBQEEFBQWzfvh1ra2ucnZ0JCgoiJCQEQRC4e/duYcpbJKTGX5nCf75CrbTg5I29\n/HbsR/46tQoBgfd6f42TbZks5/F+YMmQFRYMWWGB9wNLmv29lDY+v1NxzGtmwx/AslwZGq2ZR8Nf\nZmPh5kLM+WucbPc6Byp14uHe4/miU/iBkxyu3ZOFns043W0ksVf+xbK8G43WzKXx2m+x8jA1UFNY\nWlB+YDeab/2JNid+R7R8Gu6gsLHKk/ezMCjNcY8g65dfvNf763R5NWkN/1S83aoztudMADYcWZgu\nRyA76A069l3axMSf+6PVm5wA0fc0eZLb06USAA+iit/fYfndLNnI+pVsSrN+mel2MdCH0Ys78eaC\nlqw9PB+tPoU2tXsyf+TmEmf4F8aze67x/9Zbb9GyZUvOnz+Ps7MzFy5cYNCgQYwYMYIRI0bQt29f\n7O3tGTFiRIELWZxwd/Kibe1eAOw8vx5JMtK/xds0qPTi2vT1Fk1F7eKI2sWRhr/MxqV14+caz4Ig\n4N6nI218fkO0MBkiRk0y18Z9men4nHJtwtfoomORtFowGvEeM5g2Pr9Rtmf7515jW60iDVd9jcrF\nEZWzA/WXfJEvssjIFDWpeTWr3j+U5ZZwq1rd6Nd8BEbJwKIdUwiPDX3h3EajAZ/ru/jol4GsPfQd\nsYlRuDtVwNrCFmtLuzzlLXg+6U4cEnUn13PIyMjIlHRW7P2KhORYDEY9AgKTBpiiM2ytHIpatGJJ\nljH/9+/fZ/Lkyfj5+dGkSRN+/PFHnJxMVSl++OEHoqKimD17dqEJmx0KMuY/lbRdfBWikvWTTqEQ\nC67azeHavdBFx5iPa8/7mApvDcz1fKFbDnBt/EzzsdLBji7++/MioozMfwaj0cC3f0/k6t0zVHSr\nwVdv/Jppsu2ZmwdZte9rUnQacz6Bp0tlXms3nqZVO+TLrllwxC0+XTMEd6cKLBpTvPKvZGRkZAqL\ntHZZXkpAF3cKpcOvl5cXmzdn3hV20qRJeb55acDawrZADX8w7Rhc/2gOhhQthoQk/p22EJuq3ri0\naZKjeYwpWm5+uZjgtVsAEC1UKGxsqLdoakGILSNTKhFFBRP6zmHa+jcJCvdn1OKOWCgt6VCvH0qF\nigeRd7gfeTtdxSBBEBnX80va1O6ZZV5QTinn5I0giDyKeZBvVYhkZGRkShrDOn7I8j0zAVMzRpms\nkev8Z4Nn46/G9vzSHB9cGC9ZatnKroGHqDT+DSSDgStjppF0L+TFFz9Bcz+Mc/3HEbx2C4JaRe1v\nP6Fr0DEsVj2/iVdpoDTHPYKsX1Fha2nPxwN/AEyx/Ikp8ez+5ze2n1vLxds+6Qx/03gH2tXtk8Hw\nz6t+KqUad0cvJMlIWHRwnubKb4rrs8svZP1KNrJ+JZfMdLO3MkWl1PJsTLNqHQpZovylyOv8y2RO\nYdbdf5bq08aSEHCXiEOnuTT8U1rsWmWuvf8sqZ16JZ0OyWjEkKjB0tOdRr/MxqFhrUKWXEamdOHl\nWgUrtY25CZhSoaJ/87fwcq2Cp2sVQqOD+OWAqVN2XvsRZIWnayXCHt8jJOoO3m7VCuw+MjIyMsWV\noHB/ACrKVc+yRZYx/yWRwoj5L2r08Ymc6TWGxFtBlOnWhsZr5iIoMoYSHKrRDX1sgvm4TJdW1Fsy\nA7WTfYaxMjIyOedioA8r980CTAZ+UdSP/p/PT2w7u5qBLUczuO24Qr+/jIyMTFHzw7ZPOB9whPG9\nvqJd3T5FLU6BkV8x/88N+1m6dKn5/wMDA/N8I5n8Q2lnQ+P136FytCPiwEkC5q0ynzPq9IRtO8jZ\nvu+mM/wV1pY0Xv+dbPjLyOQj2a0SVJAU53KfMjIyMoVB0KNUz3+NIpakZPBc43/q1KdJoKXdk/4i\nimPsnE0lTxr+MhtEkbtLNnCwcmeujp/J8WYDuTr2S2Iu+CJaWSJaWqBysqfBilmZdgkujrrlJ7J+\nJRtZvxdTXMt9ys+uZCPrV7Ipzfo9q1ticjzhsSGolBZ4PHGGlGSKNOa/cuXKTJ48mdq1a6PT6Vi9\nejWSJJnL06X+/8iRIwtcSJnMcWnTFIWlBYYkDYYkDWFbDgBgW70SFUa9QvlXuqO0sS5iKWVkZAqS\n8s7eCAg8fByM3qBDqVAVtUgyMjLZ4GKgDyv2fgWYCokU1e5hSSc13r+Ca9UCr75YWnhuzL+/vz/f\nffcd9+7d49ixY7Rt2zbTCY4eLV61VP8LMf9pSdsDQFCraPrbApzbNCn2nXdlZGTyj4mr+vMo5gHz\nR27G68lOgIyMTPFm5I/tSUoxhefaWzsVWSGRks7uCxvZcHQhnRsMZEz3aUUtToFS4HX+a9Sowa+/\n/gpAp06dOHLkSJ5vJpP/pPYAkIB6C6fi0rZpUYskIyNTyHi6VOZRzANCIu/Ixr+MTAng6t0zZsMf\nQKfXFqE0JZu7T+L9K8mVfrJNtur8HzlyBL1ej4+PD3/88Qc+Pj7o9fqClq3YUJxj51J7AHT225Or\nev3FWbf8QNavZCPrlz08XItf0q/87Eo2sn4Fx8VAH+Zv+QgAUTBV6kvWajgfkH9O1tL8/J7V7WmZ\nz9KR7FsYzy5bxv/NmzepVasWr7/+OosXL+b111+nZs2a/Pvvv3kWIDo6mq5du1K9enW6detGTExM\npuNGjhxJ2bJlqVevXp7vKSMjI1Oa8HSpDMCDyOKV9CsjI5Oe8wFH+GHbJ+gNOro1GszGj88yoMVI\nJIz8uONzLt8uvUZ7QZCi0xASdRdRUFDBtWpRi1NiyJbxP27cON555x3u37/PmTNnuH//PmPHjmX8\n+PF5FmDevHl07dqVgIAAOnfuzLx58zId9/bbb7Nv37483y83tGlTejvglmbdQNavpCPrlz08nhj/\nxanij/zsSjYlWb+LgT6MWdKZMUs6czHQJ9MxRaHfqRv7WLT9MwxGPb2bSvQqPQAAIABJREFUDePt\nLp8iCiKvtR1Pr6ZvYDDq+WHbJ/jeO5/lPMVVv8IirW7BEYFIkhEPl4qoVZZFKFX+URjPLlvG/5Ur\nV5g0aZI5iVQQBCZOnMjly5fzLMCOHTsYMWIEACNGjGDbtm2Zjmvbti1OTk55vp+MjIxMaSO1vF1o\n9D30Bl0RSyMjU7Qs2/Ml8ZoY4jUx5iZ8Rc0x3x0s3TUdo2Tg5ZajGNbhw3Q21ZsdP6Jrw1fQGbR8\nv+Uj/r2f0b4yGg34P7jCjzs+M+uXWi3ov8rT+v5yvH9OyJbxX758eY4dO5busxMnTuDh4ZFnAR49\nekTZsmUBKFu2LI8ePcrznPnNfyl2rrQh61eykfXLHn7BFxAEEYNRz5FrmTtQChv52ZVsSqp+jxMi\n0iXSpuiSMx1XWPpdDPThrYVtWLH3KyQkBrcZx2ttx2eoyCcIAm93nUKHev1I0SUz98/3GPljB8Ys\n6czmE8tZte9rxi3rwZe/j0KrTzFfF6+JZdOJZcQlPS4S/Z5HdnYnckta3e4+uglARbfSEe8PRVzn\nPy1z586lf//+9OnThwoVKnDv3j12797Nxo0bs3WTrl278vDhwwyfz549O92xIAj5UqJy/PjxVKhQ\nAQAHBwfq1atn3kZJ/VJzcuzr65un64vzsa+vb7GSR9ZP1k/WL+fH6y5/hSQZib6nYcm6uXRr9Gqx\n0E8+lo8L8/jg4f2sOzwfydGIIIhEBSUCGo5c3UqnBi8XiXzf/vUhNuVNdk18iBE341MP9bPjT586\nTW2bjmhrpXD63/08vG3Kgdyi+QWA6HsaHG1dada8KTeC/yHs9mOMRgNb+ZXdFzZSQdmYljW60bt7\nvyJ/Hsv2fMl9f5Mz9yfjF6yeeDzf5k/7/Z06dRrsTJV+ivr9Kwj9fH19iY2NBSA4OJjRo0eTHzy3\nzv+zBAQEsGnTJsLCwihfvjyDBw+mevXqeRagZs2aHDt2DHd3d8LCwujYsSM3b97MdGxQUBB9+/Y1\n/4OZGf+1Ov8yMjIyY5Z0Jl5jMhRUSgs2TDpdxBLJyBQuydokvtk0jsCw63i4VOLLoT9z+t/9rD08\nHwGBCX3n0KpWt0KVyWDU8+aClhglI5D9Wv56g463FrU1h/CJgoJBrcfQrFoHvFyrpnOS+odcZfvZ\nNVy6feLJWBGFqEQUFXRtOIj6lVpiZ+VI0CN/fj++GCi4hmKSJOEfcoWd5zdwMfB4unPjes2kfd2+\n+Xo/vUHH24vaoTNoWT3xGNYWdvk6f3GkwOv8P0v16tX54osv8nzDZ+nXrx/r1q1jypQprFu3jgED\nBuT7PWRkZGRKM2N7fsmyPV+SmByHKIjo9FpUSnVRiyUjUyho9Sl8v3UygWHXKeNQnmmDl2Fv7USP\nJkPQaBPZdGIZP+2ejqXaisZVMm9YWhAc992JUTLtQthZOvBujxnZuk6pUPFB3zms2PsVoqBgXK+Z\nzzXWa3g04NNBi7gXHsD2s2s5fXM/RoMWDLDrwkZ2XdiY4ZoFWyfToFJLyjiUp4xDeeI1sRy68jei\nIGZ5r2dJ26G4Y/0B3Aj+h8Cw6wDmBYiA6fks3zOT6PhwBrQYmW9NSEOigtAZtLg5evwnDP/8JFsx\n/wXJZ599xsGDB6levTpHjhzhs88+AyA0NJTevXubxw0dOpRWrVoREBCAl5cXa9asKTQZn92KKU2U\nZt1A1q+kI+uXPZpUbcevHxzF2606KTqN2QtYlMjPrmRTUvQzGPUs2TmV6/fO42DjwrTBy3C2czOf\nH9BiJH1fGoHBaGDhtk/xu3cBKHj9UnQa/jy1EoAJfb5h1YRDOfK2v1S9E6snHueXD45k6zpvt+p8\n0G8ONpb2gClESKlQUadCMyqUqYbAU4PbKBm5fOcUBy7/yW/HfmTHubUkpcSTkBzLou1TMuQPPI8V\ne78yJx7vOLeWwLDr2Fo6MLDlaJaN28uGSadZP+k0b3X+BAGBTSeW8euBuRiM+mx/D5mR+uyCwk1R\nIqWtuVdh/Pay7fkvKJydnTl0KOM2WPny5dm9e7f5+I8//ihMsWRkZGRKHO3q9GFD+A/4XN9F8xp5\n3xqWkSnOGCUjK/fO4sKtY9hY2DH11Z9wd/JKN0YQBF5vPwGNNoFDV/5m/pZJTHttWYHLtu/SJh4n\nRFCpbE1a1Oxa4PdLZXyvr1i5bxbJlko+6v+deeFwMdCHlftmIUkSA1uNxtXenYjYMMJjQzh0+W/0\nRlOIkc6gZdIvgxja/n061h+AKGTuI/a7d4HE5HjzsSCIvNX5E9rX7Yul2ird2B5NhuBkW4alu6Zz\n6OrfPE6I4IN+c7BQWT07bY4wV/pxK13Gf2GQ7Zj/koIc8y8jI/NfJSYxivHLeiIIsGzcPhxsnIta\nJBmZLEkbOvJsLHrac6O7TaW6R30SkuNI0MRx7e4Zdl3YgM6gRalQMWPIKqp71H/ufYySkWW7Z3Dy\nxl5AwMbClvG9ZxVI7HuCJpYPVvUjKSWBaYOXUa9i83y/R36SujAwGg0425UlOOIWAFXL1WVU18+o\n5F7LPDYk6i6/H1vMxdumCj6CIGCpsmZ871k0q9Yhy/vcfHCZ+VsmmcITRQXWatschRk9y8zfR3Pz\nwWWmvLKYRpVb52qOkkZ+xfzLxr+MjIxMKeK7vz/k0u0TDO80mV5NXy9qcWRksiRtsrpSoaKWZ2OS\ndRpSdBruR95GepIsmxXWFrasnnj8heP0Bh1vLWxr9nLbWzmxasKLE3Bzysaji9h1YQP1vJsXyi5D\nfiJJEmduHmTDkQU8TowEBFRKNWqlBdXK1+fa3TMYJQMWKisGtHibXk1fz5EHPyTqLh+vHmx+rlZq\nG3794CiiqMiRnEbJyKgfO6DRJrLivQM42rjk6PqSSn4Z/9mK+b9z5w5Dhw6lVq1aeHl5mf9LLadZ\n2ikpsY+5oTTrBrJ+JR1Zv5zTrm4fAHyu78r3uXOC/OxKNoWln06vNf+/3qDD9945boVeIzjiVgbD\n38HGBQ+XSlT3aIBSfBq1rFSosnUvpUKFlYUNYIqJT1svP7+IjHvI/kubABjafkK+z59dcvv8BEGg\nVa1uLBj9N72avgFI6PQp/L+9+46Oquj/OP7eTYc0QkgoASKRKiVAgJ+00EJVQBR4QJAaQKUJUqQI\noigKjwjBhyJNBKkqIEVKgNAUkCYdEiCFHkgh2dTd+f0RdyWUGNJu7mVe53COW7L7/bizc2d3Z+Ym\nJsdz6upBBIIWNd9gTuBG3nh1wHNP3SlT/CWKPrI4Nyk1keGLOvHrkRUkJMVl6zEOHjzI3dgbJKUm\nUqyou+YG/oVmzn/Pnj15+eWX+frrr3FwyN0cLUmSJCn/1PVpSlF7Z67fvUT43SuU96iodEmS9FSp\nackZA/c0sLW2p13dHlQrVxd7GwdsbewJvXmWtQf+h06nY3Dbj/Gr6G/5W/NUFSDbu+hAxtSieVsm\nA0kIIYg3xOBcpFieZdpwaCFpxlRerdKaCo9Ml1GbInaOvNNiFCFnNpOYkjG331pvzRd9VlG2xMu5\neux3209lwfZPSEtPwd62KNHxt1gVMof1hxZQxas2YbfOoddbZbkl6bU7FwDw9tTOyb0KUram/Tg7\nOxMTE4OV1fP9LKMEOe1HkqQX3ZKdX7Dr1AY61OtF7+YfKF2OJD3VpiPLWR0ShLdHZT7vs/KZi0vz\nmhCCz9e/z5nrR2jl+yYDW0/Ik8eNjA5j7LL/oNfp+O+An55YfKxGlvUAwsS77XI+P/9ZTMLE6auH\n+e3EGk5f+z3TbU4Ornw3LPipf7c6JIhNR5bzxqsD6N7kvTytqTAr0Gk/TZs25eTJk7l+MkmSJCn/\nmaf+HDy/Pcfb6h0P3U9gUEsCg1pyPHR/XpYn5RE1v0YJSXFs+iNjy+6ezYYX2MAfMqa29GnxIXqd\nFcGnfyH87uU8edw1+79FCBMta72piYE/ZGwjvGjobhYPy96Wo89Lr9NT26cxH3Wdx9cDfsLG2s5y\nW1JqIs/6fvr63YydfrS2zWdByda7rXz58rRt25ZBgwYxefJky7+PP87+T21qpuW5nVrOBjKf2sl8\nOfNyqeqUditPXOJ9/rr2R44e49E9vL/d+vx9vXzt8t+jr5F5V5y8kt/5Nv6xDENKAjXKN6Cm9//l\n63M9zfWLN2lTJ2Ph6fLdM585yMyui1EnOR4agp2NA10aDsyjKnOuMLTP51W6uDcjO87A0d4FyFgD\ncvjCjifud+DAAa7dydjj39tDe9N+CuK1y9bg32Aw8Nprr5GWlkZUVBRRUVFERkYSGRmZ3/VJkiRJ\nz0mn09HklYxv/0NyuPDXZDJa/js5NTHTwkypcDA9siA2OdWgYCXPJzr+lmVRbE8FF8W+1WgwTg6u\nXIg6wR+XdmV532f9yiKE4ND5HXy6ZjAAdXyaaG4BakGq+3JTFg/fw6A2kwBYtvsrYhPvZ7rPw6RY\n4g0xFLVzooRLaSXKVL1/XfBrNBrx8vJi4sSJ2NvbF0RNhU7jxo2VLiHfaDkbyHxqJ/PlXJNX2rPu\nwP84HhpCQnI8jn+f+TM7TMKEc9HiloV+JmFiy7EfeOPVAdl+DPna5b/mNTqy5dhKIOPkTPvPbaXp\nKx3y5LHzM9+6gwtIM6bSsGqbTHvIFyRzvu5N3mfxzums3PsNdXyaPHP3mv9tm0JicjwAX28cg6dr\nGcs5B0zinw/KZ8OP5n/x2VAY2mduNK/Zmd8v7eLM9SMs3TWDDzp9hU6XcZZizwoucCpjsa/5Oi0p\niNfuX7/5t7KyYv78+dja2uZ7MZIkSVLecHcuySvl65FmTOWPi1l/q/m4Pad/4daD6xQr6s7oN2YB\n8PPvS7gTG5UfpUo5ZPp7qkp5j0pAxkLvmw/CFaklu+sPIu5d4cDZrVjprQvFQs0WNTvh7VGZ+w/v\nsPnIiiduT0lLYt2B+ZaBP4DRlM7NB+HEG2IyDfwBTQ5GlZCxw9Nk7G2KcPTynky/zFzX8JSfgpKt\naT/vvPMO8+fPz+9aCi01zp3LLi1nA5lP7WS+3DEv/H2eqT8xCff4MWQuAH1ajaFexeY0qtqWtPQU\nlu/+Kttzo+Vrl//Cbp8DoEfTYTSs0oaUtCTmbv4oT6ZoPS3fowP8nSfXczx0P9v+/JGlu77k641j\nLOsP5m+b+szHXR0ShEAQUPstPF29cl1nTpnz6fVW9Gk5BoDNR7/nXtwtIGM6z7Erexm9pCs//74Y\nABsrWxxsi/KfpkOZ1X89C97fycrRfzCmy2ycixTDuUix59p2ND8VhvaZW+7OpejVfCQAS3d9Sbwh\nBoCQ/fsA7S72LTT7/B85coSgoCC++uorypYta/lkq9Pp2L9fXTsMSJIkvSjqV2zBUpsZXLn5Fzcf\nhFParfy//s2KPV9jSEmgdoXGNKiUsaVc7+YfcPLqQU5ePcSxK3upX6lFfpcu/QuTyWj5BrRCyapU\nKlOD0NtnuX73EqtC5tD37wFtXpq/bSoJyRknYlq6a8Yz75eQHMcvvy/htXq9sbH+Z9bAuYg/OXn1\nEA62RenyqvKLYs2qlq1NwyptOHxxB6v2fUP3Ju+zPHgmp68dBqBciYr0DxhHFa/aT/178444Ut5r\nWasLv1/cxbmIYyzd9SUjO83gVkwkVu7grdHBf0HI1j7/y5cvf/of63T06dMnr2vKFbnPvyRJ0j/m\nb5tKyNlfs7Uf9smrh/hyw3DsbOyZ1X8DJVxKWW7bcWIdy3Z/iZuTJ18P2IC9bZH8Ll3KQuS9UMYs\n604Jl9IEDf4VgLBb5/h4VT+MJiMfvvF1ppNiPep46H7L7kBZnUjpUTEJ93h/fnvLImOdTk+N8vUp\nWawsnq5eJCTFs/PkOlLSU0g3ZvzyULJYOfq1GkOtlxoihGDSyj6E3TpH18ZDeLNhYF78b8gz0fG3\nGbmoE+mPbI1bxM6Rbk3eI8D3Taz02fquVMoHd2NvMGZZd1LSkghsM5HvdkzH1tqO5SMPoNcX/vNP\n5aW82uc/W625b9++uX4iSZIkqeCZ9xvf+MdSKpSsRr2KzZ56v5S0JMu3uV0bDck08AcI8H2TkDOb\nuXrnAhsOLbL8HC8pI+z2eQB8SlazXOdT6hV6NB3Gyn3fsGD7J8zw/BF355KW203CxIWI43yzaRxp\nfw/Q/7dtCkuG783yuWIS7vHpmsGYhAm9zoqi9k5P/dDQvWnGh8uz4UdZuutLbj64zhfrh1GxdE0i\n7l0hJS2JInZOdPDrlSf/D/KSu3NJ9Hpr+Hvwb2Nly+yBv+BS1E3hyiQP1zL09B/Ost1fWvqo8h6V\nXriBf17K1pz/JUuWsHTp0qf+exFoYe7cs2g5G8h8aifz5d62P38EMuYwB/06gfsP7zz1fj8d/o57\ncTcp71GJdn49nrhdr7diQOsJ6NCx7c8fibh3Jcvnla9d/gq7lTHf36fkK5mub1/vbXwrNCIhOY4R\nizoRGNSSHSfW8mPIXIYueI1P1w6xDPwBEpPj+e34mifWcpjzZQz8h3DzQTjlSlRkwfs7+G5YcJa/\nFlQvX5+v+q3hbf8R2Nk4cOXmX6SkJQEZ05XsbZ++o05BetrrZ2fzz46GDnZFVT3wV7p95rWA2m/h\n5e6D0WTkQXgSRe2clC4p3xSaOf8//PBDphXst2/fJiwsjEaNGtG/f/98K06SJEnKO6npKQxb8Dr1\nK7WgXd3/UKlMLXQ6HeF3r7Dl6Ep06AhsM/GZUxx8SlUjoPZb7Dy5niU7v2BKz8VPnJnVPKXk7tV4\nHEr+N1/OCirB1dsXgIz5/o/S6/S81/4TBs8LwGhK52FSLMt2f2W5vYRLaXxKvsKZ8COkpqdkLOQO\nnsnZ8KMMaTcFRwcXy31jE6L/Hvhfp1yJikzqPh/nIsWyVZ+1lQ2vN3iHhtXaMGJRJ9KNaQDYPnIG\n18JmSLspLPxtGkChWbgrZdDr9MQk3LNcvnjjlILVqF+25vw/zdKlSzl//jyzZs3K65pyRc75lyRJ\n+sfx0P0s/G0aRmM6Xu4+XLl5xrI9oadrGeIMMaSlp2A0GWlTpzv9Wo3N8vESkx8ybOHrGFIeYm9T\nhKGvfUbZEj6E3jxL6K2z7Dy5DuPfJwjT6fQ0r9GJ6uXr80o5P1V/k1qYpBvT6PtNE4zGdJaM2EcR\nO8cn7tN/jj+GlIS/L+loWesNmrzSnkplamX6wHbkUjALf5uGISWB4k6eDO/4BZXL1CI2IZppawb/\nPfB/mUndF2R74P+446H7mb9tCjqdPttrDCTpcYFBLXmYFAuAk4Mr3w0LVriigpdXc/5zPPg3Go24\nu7sTExOT6yLykhz8S5IkPdv9h3fYdXIDwad/4mFSnOV6nU7HkuFPH0g+ru83TSxnlNWhQ5C9w4i7\ncyniDA+w1tvwXodPnrn+QMpa2K3zTPyhN6XdvPl64E9Pvc/x0P18u/VjhBAMafcxDSo/e8BwN/YG\nc3+dQOits+jQY2NtS7oxFZMw5XrgL0l5xfxFBmT8MvMifojMq8F/tub8m0ymTP8SEhJYtGgRxYrl\nvjN48OABAQEBVKpUidatWxMbG/vEfSIjI2nevDmvvPIK1atXZ+7cubl+3uehtblzj9JyNpD51E7m\ny3vFnTz5T9P3+XbINuxt/tmxx8G2aLYG/pCxGNJMIHBycKV2hcZ0bTyEtxoNwsnBleTb1vRq9gE9\nmg6lRvkG2FjbER1/i7T0FJJSE5i9cSxHL+/J9nkDChsl2+bVvxf7Vnhkse/j6r7clKUj9rFsZEiW\nA3/IWFA5tediXq//DgITqenJRF9PRK/Ta3bgL/sW9TFvqfqO71RND/wLzZx/a+sn71amTBm+++67\nXBcwY8YMAgICGDt2LF9++SUzZsxgxozM+wfb2Ngwe/ZsfH19SUhIoG7dugQEBFC1qjKnBZckSVI7\nWxt7hr0+nYW/Tfv72+Ep2f7bIe2msGD7JxhN6bzdbCQtanbOtC7srUaDOXjwII3rZ5ymvtP/9SM1\nPYUh37a2TEUxCSNfbxyDt0dlujYeQh2fJvLsqNlk2emn1LMH/8/L2sqGt5uNYPepn0hKTQSgqL2z\nJgf+kvSiy9a0n+vXr2e6XLRoUUqUKJEnBVSpUoWQkBA8PT25ffs2zZo14+LFi1n+TefOnRk2bNhT\nf/qQ034kSZIKJ/PP9kII6ldqwYnQ/cQkRgNQ0rVcxpQgK2s5L/xfjF3WnYh7oUx7exmVytTM08c+\nHrqfhdunge7FnVohSYVVgc75Hz58+FOn2owcOZJvvvkmVwUUK1bMsm5ACIGbm1uW6wiuX7+Ov78/\n586dw9HxyZ+o5eBfkiRJHVLTktl9+mc2/bGMOMMDy/Uv6mK+7EhJS6LvN03RoWPZyBDsbJTfNlOS\npIJRoHP+ly1b9tTrV6xYka0nCQgIoEaNGk/827x5c6b76XS6LH/2TUhI4K233mLOnDlPHfjnFy3O\nnTPTcjaQ+dRO5lOv7GSztbGnvV9P5gzanGkQ++g+9IWVUq/d9TuXEMJE2RI++Trw13LbBJlPzbSc\nDQrBnP8lS5YAkJ6eztKlSxFCWAbnYWFh2Z76s2vXrmfeZp7uU7JkSW7duoWHh8dT75eWlsabb75J\nr1696Ny5c5bP995771GuXDkAXFxcqFGjBo0bZ8w9Nf9PfZ7LZ86cydXfF+bLZ86cKVT1yHwyn8z3\nYl4e/vrnTJk3ktS0ZOo1eEXxegrr5T8u7QYyzuxbGOqRl+Xlgr5sVljqyc98Z86cIS4uY1e2iIgI\nBg4cSF7IctpPs2bN0Ol0HDhwgCZNmvzzRzodnp6ejBgxgv/7v//LVQFjx46lePHijBs3jhkzZhAb\nG/vEgl8hBH369KF48eLMnj07y8eT034kSZLUKSbhHu/+ry021nYsHhYsp7Q8xbwtkzh4fjsDW0+g\nle+bSpcjSVIByqtpP9ZZ3bhv3z4AJk6cyPTp03P9ZE8zfvx4unXrxpIlS/D29mbdunUA3Lx5k8DA\nQLZu3cqhQ4dYuXIlNWvWpHbt2gB88cUXtG3bNl9qkiRJkgpeMccS+JR6hbBb5zhz/Sh+Ff2VLqnQ\nCbv1904/WWzzKUmSlJVszfmfPn069+/fZ8WKFXz1VcZpwm/cuEFUVFSuC3Bzc2P37t1cvnyZnTt3\n4urqCkDp0qXZunUrkPGTiMlk4tSpU5w8eZKTJ08W6MD/8Z9itETL2UDmUzuZT71yms3v5YwB//HQ\nkLwsJ88p8dolJj/kVkw4Nla2lC3xcr4+l5bbJsh8aqblbFAw+bI1+A8JCaFy5cr8+OOPfPrppwBc\nuXKFd999N1+LkyRJkl4s5q0lT4QdwCRMCldTuFy7cwGAch4VsbayUbgaSZLUKltbffr6+jJr1ixa\ntWpl2ZozOTmZcuXKcffu3YKoM9vknH9JkiT1EkIwfFFH7sXd5NNey6lYuobSJRUam44sZ3VIEK1r\nd6N/wDily5EkqYAV6Faf4eHhtGrVKtN1NjY2GI3GXBcgSZIkSWY6nc7y7f+fhXzqT0GzzPfPwzP7\nSpL04snW4L9q1ar89ttvma4LDg6mRo0X4xsZLc8v03I2kPnUTuZTr9xkq2uZ978/r8rJc0q8dldv\nZwz+KxTAYl8tt02Q+dRMy9mgYPJluduP2ddff81rr71G+/btSU5OZtCgQfz6669s2rQpv+uTJEmS\nXjBVvWpTxM6RqOgwbsdEUrJYWaVLUly8IYbo+FvY2ThQxs1b6XIkSVKxbM35h4zdfVauXEl4eDjl\nypWjV69eeHl55Xd9z03O+ZckSVK/uZsncPjiDt5pMZr2fj2VLkdxJ8MO8uVPI6jqVYcpPb9TuhxJ\nkhRQoHP+AcqUKcO4ceP43//+x/jx47lx4wZdunTJdQGSJEmS9DjzvP/CvuVnQflnyk9VhSuRJEnt\nshz8x8fHM3bsWDp06MC0adMwmUwcPXqU5s2b06JFC0qWLFlQdSpKy/PLtJwNZD61k/nUK7fZalVo\niJXeiguRJ0lIjs+jqvLO8+Y7HrqfwKCWBAa1tKxlMJmMxBti2HFiHf3n+DNwbvNnrnMIu21e7PtK\n7grPJi23TZD51EzL2aAQzPl///33OXPmDK1bt2bDhg2cPHmSPXv2MGzYMNavX4+7u3u+FyhJkiS9\neBztnaniVYdzEcc4dfUQjau1U7qkXFmw/RMeJsUC8N9fRlPU3omEpHgEmWfezv11AstG7kev++e7\nOSGEZfBfEIt9JUnStizn/JcsWZLTp0/j6elJVFQU5cqVY9++fTRt2rQga3wucs6/JEmSNmz780dW\n7PkvDau0YXjHz596n+Oh+5m/fSpCmHiv/TTLdKHCpt83/iSlJjxxvaO9C4aUh5lOaFa7QiPebf8J\nzkWKARAdf5uhCzpQ1N6ZxcP2oNPpCqxuSZIKjwKZ85+YmIinpycAXl5eODo6FuqBvyRJkqQd5oH8\nqWuHSDemPfU+87dNISEpjsTkhwRtmViQ5WWbISUBa6uMH9ptre3p12osC9/fxaoPj7B4+B5Gv/Ff\nnIsUw8HWEXubIpy8eohxy3twLuJPIPN8fznwlyQpt7Ic/BuNRvbs2cOePXsIDg5GCGG5bP73ItDy\n/DItZwOZT+1kPvXKi2yerl6UdffBkJLAhaiTT9web4jBkPLPt+nJqQYuRJ7I9fNmx/PkWx0SxMOk\nWCqUrMaykSG0qdMdl6JuWOkzPhDUfbkpi4buZtnIEGYNWE9lL19iEu7x2ZohrD+4gCs3zwLgU7Jg\n5vuDttsmyHxqpuVsUAjm/Ht4eDBgwADL5eLFi2e6DHDt2rX8qUySJEl64dV92Z/I6DCOh4ZQo3x9\ny/WGlId8vu59TMKEXmeFlZU1aekp/PeXD/m013JKuZVTsOp/nIv4k12nNmClt2ZIu48tA/5ncXcu\nycf/WciGQ4vY+PtSfjr8z7ae2dyZW5IkKUvZ3udfLeScf0mSJO24cvMMk1f2pYRLaeYO2oxOpyMl\nLYnP1w/lUtQpPF29+KTnEpyLFGPWL6M5EXaAUsXK82mvZTg6uCi2n56kAAAgAElEQVRae3JqEmOX\nd+du7A26NhrMm40GPdffnw0/yvS171kWBTvau7B4+Ivxi7skSU8q8H3+JUmSJKmg+ZR6BZeixbkX\nd5PI6FDSjWl8vXEsl6JO4ebowcTu83F1dEevt2LYa9MpV6Iit2LCmb1p7DPXCRSUtQf+x93YG5Qr\nUZFO/9fvuf++evn6FLV3tlzW6+UhW5Kk3JM9STZoeX6ZlrOBzKd2Mp965VU2vU5PXZ8mABy7vJd5\nWyZx+tphnBxcmdj9f3i4lLbc18GuKGPf/AbXosU5F/Eni3d+8cypMk/bd/95/Fu+SzdO89vx1eh1\nVgxpNwVrK5vnfg6Ad9tPxblIMZyLFGNw249z9Bg5oeW2CTKfmmk5GxSCOf+SJEmSpDSXosUBWH9o\nIQAOtkWZ0HUeZYq/9MR93Z1LMqbLbD5ZHci+M5so7Vaejg36WG4XQnA37gZBWyaSnGoAYM7mjxjc\ndjJlS/hQ2s2b09d+Z8H2TwAY0m7Kc28fmpqewsLtnyAQdGzwTq7OymteDCxJkpRX5Jx/SZIkqVAL\nDGppOUEWwJQei6latnaWf3P08h6+3jgGAHsbBxpWbYsh5SGXok4Rkxj9zL/T66wAYdl33962CGO6\nzMbDpQzFnTw4efXQv34wWB0SxKYjyynt5s2Mvj9ia233vJElSZKekFdz/uU3/5IkSZJqFLFz/NeB\nP0D9Si2ws7EnJS2Z5LQk9vz1i+U2JwcXPF29iIy+il6np9ZLDTGa0oi8F8ad2KhMZ91NTjXw6ZrB\nAFjprTAJgfj7g8GczeN5s9EgnB2K4eTgys0H4fzy+2KSUhOBjA8HcuAvSVJho/jg/8GDB3Tv3p3w\n8HC8vb1Zt24drq6ume6TnJyMv78/KSkppKam0qlTJ7744osCq/HgwYM0bty4wJ6vIGk5G8h8aifz\nqVdeZhvSbgoLf5uGEIIh7aZk++9srTMG/wA2Vrb0azWWyl6+lHbzfubJslLSkgg+9TPrDy3EaDLi\nU6oaRpORe7E3Mv1i8CA8CbfyGd/yP/257ahUpuZzpCxctNw2QeZTMy1ng4LJp/iC3xkzZhAQEMDl\ny5dp2bIlM2bMeOI+9vb27N27l1OnTvHXX3+xd+/eAl3wcebMmQJ7roKm5Wwg86mdzKdeeZnNPO/9\nu2HBzzX/fki7KZbFsiM7fUmLWm9QpvhLWZ4l187Ggfb13mbZyP2sGHWIKT2+Y9rbS5n//g5WfHCI\nAQHjKWLnSNJ9QdNXXqNDvV40faUDtSs0+nvK0D+Po2Zabpsg86mZlrNBweRT/Jv/zZs3ExISAkCf\nPn1o1qzZUz8AFClSBIDU1FSMRiNubm4FVmNcXFyBPVdB03I2kPnUTuZTr8KQLa8Xy9ra2BNQuysB\ntbsyI2kG73UYn+n246H7WfjbNIAC3ZknPxSG1y8/yXzqpeVsUDD5FB/837lzB09PTwA8PT25c+fO\nU+9nMpmoU6cOYWFhvPvuu1SrVq0gy5QkSZKkLMmdeSRJUoMCGfwHBARw+/btJ66fPn16pss6ne6Z\nP8fq9XpOnTpFXFwcbdq0Yd++fTRr1iw/yn1CREREgTyPErScDWQ+tZP51EvL2UDmUzuZT720nA0K\nJp/iW31WqVKFffv2UbJkSW7dukXz5s25ePFiln/z6aef4uDgwIcffvjEbcHBwflVqiRJkiRJkiQp\nRhNbfXbs2JHvv/+ecePG8f3339O5c+cn7hMdHY21tTWurq4kJSWxa9cupkx5+o4PefE/RZIkSZIk\nSZK0SPFv/h88eEC3bt2IiIjItNXnzZs3CQwMZOvWrfz111/07dsXk8mEyWSid+/ejBkzRsmyJUmS\nJEmSJEl1FB/8S5IkSZJWCSGy3FpUkiSpoCm+z7+kDvIzoiQpw2QyKV2ClAty4K9eWj/uyb5FvXLb\nNuXgPw8kJiYqXUK+kwcwqbAxGAwcPHiQrVu3kpSUBGjrYG00GoGMnc5MJpOmsgHEx8fz888/s3bt\nWqVLyRc3btxg1KhRpKena+61A3ncUzPZt6hfbtum1dSpU6fmTSkvpvDwcPr160erVq2wt7dHr9fW\n56n79++zcOFCjh8/TtmyZXFyclK6pDyVkJDAgQMHuHTpEikpKZhMJhwdHZUuK09oORtA3759OX78\nOIsXL+bAgQP4+/trqn1OmjSJvXv3Ur16dRwdHdHpdBiNRs30MX369OHKlSt89913REVF4e/vj7W1\nNWlpaVhZWf37AxRyI0eOxN3dnZYtWyKEIDk5GRsbG03kk8c9dZN9i3rdu3ePpUuXUqJECYoVKwZk\n/ILzvB8G5Jz/XOrduzdlypRhxowZPHz4kMTERG7cuIGPjw+urq5Kl5dr3bt3x97enoiICGrWrMln\nn31Gamoq9vb2FC1aVOnycq1z5844Ojpy7do16tSpQ/HixWnQoAHNmzfH3t5e6fJyRcvZQkJC+PDD\nDzl27BgAH3zwAe7u7kycOBFQ/zzrffv20aVLF/r06UNoaCivv/46gYGBlkypqanY2toqXGXO7d27\nl48++og//vgDgA4dOmBjY0OxYsXo3LkznTp1UrjC3AkODmbChAkcOXIEgJkzZxIcHEypUqU0kU8e\n99RL9i3qfu99+OGH/Pjjj3Tu3Jnq1avTu3dvnJycMBgMFClSJNuPo/hWn2p27949bt++zbx58wAY\nMWIEd+7cwcPDAycnJ0aNGoW3t7eyRebCiRMnCA0N5fjx40DGNqq9evXCzc2NV155hcGDB6v6G5HL\nly8TFhbGmTNngIwB5e+//86uXbuws7OjRYsWCleYc1rOBhkHsN69e1su9+3bl169ejFkyBCKFy/O\nypUref3111U7EImIiGDIkCGMHDmS/fv3s3nzZoKDg+nXrx9t27Zl8eLFdOrUiTJlyihdao7s27eP\n9957D4AlS5Zw4sQJDh06xPbt25k4cSJlypTBz89P4Spzbs+ePRw7doydO3diMBgIDg5m5syZhISE\n8NFHH1G6dGnq1aundJk5Io976j7uyb5F3X3L6NGjiYqKom7duly4cIHp06fz8OFDqlatytChQ7P9\nOHLaTy4ULVqUY8eOER8fz8OHD9m/fz9r166lfPnyHDlyBDs7O6pXr650mTkWGhrKkSNHeOmll9i2\nbRtbtmxh69atODg4sG7dOkqXLk3FihWVLjPHUlJS+PXXXylRogSVK1fG29sbX19fbt68ycSJE2na\ntCklS5ZUuswc0XI2IQQVK1bE29sbNzc3dDodJUuWZOfOnTRo0IDjx4/zxRdfMHz4cKVLzbFatWpR\nr1493NzcqFixIr6+vqSlpbFt2zZmzpzJ7t27mTRpktJl5tirr75K3bp1AYiJiWHw4MFUqVKF+vXr\nEx0djcFgoE6dOgpXmXMtW7bk1VdfZdiwYcyfP59FixbRoEED6tevz507dzAYDJb8aiOPe+o+7j3a\nt1SqVIlatWrJvkUl0tPTcXR05Pz58xiNRgIDA7lw4QLffPMNZcuWpVSpUpQqVSpbjyUH/zlknmPl\n4uJCUFAQR48epX79+jRv3pwyZcoQGRnJ4cOH6dixo9Kl5lj58uW5d+8eixcvJjo6mu7du9OsWTOq\nVKnCjRs3OHv2LK1bt1a6zBxzcnKiSJEibNmyhdjYWDw8PChevDh+fn6WA7RaOwknJyecnZ3ZsmUL\nMTExmsqm0+mwtbXF09MTnU5nmccZExPDsWPHWL16NdOmTaNChQpKl5pjCQkJlm8XrayscHNzo3bt\n2lSuXJmvvvqKH374QdX5rK2tLX1ohQoV8PT0tNw2fvx4OnfujI+Pj4IV5pwQgoSEBKpVq8awYcNo\n1KgRzZs3t0yr+Oijj+jSpYsq88njnrqPewaDgaSkJJydnYGMBb+yb1EPvV6PXq+nQoUKLF++nAED\nBrBo0SIqVqxI1apV+euvv2jevHm2HksO/nNIp9Px8OFDXn75ZWrVqsX169dZuHAhMTExlC1blnHj\nxjFy5EhefvllpUvNFT8/P/r06YOHhwcLFizAzc2NEiVK8NFHHxEYGKjafMnJySQmJuLn50dcXBx/\n/fUXJ06c4Pz587i7uzN27Fi6d++u6m94ypcvz8OHDzl79iwnT57URLagoCDWrFnD7NmzSUlJoW7d\nuuj1essHgh49elCnTh3Gjx+vdKk5MnPmTH766SdmzJjBlStXqFevnmV9hpWVFWvWrCElJYWPP/5Y\n4Upz5ty5c6SmpuLs7GwZDD+6PuOzzz4jMTGRjz76SMkycywoKIi1a9cyZ84cEhISqF+/PhUqVMiU\nLyEhgQkTJihcac7I4556j3szZsxg7dq1fP7553h7e2fKIPsWdTAYDNjY2ODi4sL9+/dZtmwZBw4c\nYP/+/VSsWJF69eple1MPueA3B2bOnMmtW7c4cuQI/v7+jB07Fmtraw4dOsTmzZtJS0ujbt26DB48\nWOlSc+TcuXO4uLjg5eVluc5gMLBgwQJOnz5NVFQUtWvXZtasWQpWmXMzZszg+vXrHDt2jNmzZ9Ok\nSRMuXbrEvn37OHz4MPfv37e8rmpz7tw5XF1dLfM1hRAcPnyYs2fPcvToUW7fvq3abJcvX6Zr1658\n9tln6PV6Vq1axbRp0zIdxD7//HN69+5N2bJlFaw0Z8LCwggICGD16tXY2toydepUIiIiGDp0KAMG\nDADg7t276PV63N3dFa72+V24cIFGjRoxbNgwmjVrRq1atXBzcwMyvlGOjo7mt99+o2XLlqqcb/y0\n9vnJJ59YPmQnJCSwY8cOXn31VUqXLq1wtc9PHvfUe9y7cuUKXbt2ZdGiRVy+fJn79+/j4+NDUlIS\nXbt2BWTfUpgFBQVx7do1Tp8+TdeuXRkyZAhnz55l0qRJ9OzZk27duj33Y8rB/3N69ABtY2PD1KlT\nuXHjBiNGjOCdd94BMuZlWVurcy11Vm+iuLg44uLicHBwwMnJSZU7xjzaCV66dIl79+5RtWpVhBC0\nb98egKSkJOzs7FS37dnjr12NGjUsHbl5B4fExEQcHBxUlw2gX79+VK9endGjR5OWlsb48eOJjY1l\nyZIlADx48MDSVtVo1apVbNiwgV9++cVy3c6dOxk+fDgNGzYkKChI1TuNjBs3jgsXLlCvXj2uXLmC\nn58fjRs3plKlSjg6OhIdHa3KgYeZltunPO6p+7jXv39/qlatypgxY1izZg0DBw5k6NChrFu3jmrV\nqrFq1SpcXFyULjPHtNy3ZPWlV3x8PM7OzpbzNDzPDndy2s9z2r59Ow8ePGD06NGUKlWKHj164O3t\nzYQJEzh+/DgBAQHY2dmpdpvBWbNmUaRIEcqWLUtwcDDR0dFYW1vj6OiIi4sLSUlJeHp6WqZaqM2Y\nMWNo0aIF3bp148KFC3zwwQeUKFGCmTNnsmvXLl577TXLvsdq8/hrd//+faysrCxrG27cuEHx4sVV\nmc1gMHDnzh1atmyJp6cnVlZWVKpUidWrV9OrVy8OHz7MyJEjefvtt5UuNcd8fHw4dOgQer3e8m2x\nj48PgYGB7Nixgzp16lj2dVYbo9GIq6srvXr1okOHDhQtWpSQkBD+/PNPbGxsOHr0KH379mXo0KGy\nfRZC8rin3uOewWAgLS2N/v37Y2VlxaJFixgxYgTDhw9nxIgR7Nmzh7p166r2g6nW+5YPP/yQgIAA\n+vbty0svvcSRI0fYtWsXHTt2xN7enrt37+ZszCKk55KQkCAGDx4stm7dmun65ORkERgYKK5evapQ\nZbmXnp4ujhw5Im7duiWEEGLHjh1i0KBBIjAwUGzatEmsWLFCVK5cWZhMJoUrzZnExETx448/itTU\nVCGEEMOGDRPr16+33D5gwAARGhqqVHm5ovXXToiMjDExMZbLKSkpomPHjuLq1auia9euYvny5QpW\nlztGo1GYTCaxcuVKUb9+fTFlyhRx7949ER8fL4QQonbt2mLjxo0KV5k7JpNJGAwGy+Xk5GSxbNky\nERgYKNzc3MTChQsVrC73tNw+5XFP3X2nuXaTySTOnTsnhBAiLS1NCCGEv7//E6+r2mi1b0lMTBRB\nQUHir7/+slx39epV0aZNGyGEEIcPHxbt27fP0WPLwf9zkAdo9b6JzLTcCWr5tXv8wJueni6EEGLO\nnDnC2dlZtGvXTomy8sWFCxfEG2+8IZo0aSJGjRolunTpIlq1aqV0WXnK/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"text": [ "" ] } ], "prompt_number": 37 }, { "cell_type": "code", "collapsed": false, "input": [ "figsize(11., 5 )\n", "returns = np.zeros( (n_observations,4 ))\n", "\n", "for i, (_stock,_returns) in enumerate(stock_returns.iteritems() ):\n", " returns[:,i] = _returns\n", " plt.subplot(2,2,i)\n", " plt.hist( _returns, bins = 20, \n", " normed = True, histtype=\"stepfilled\",\n", " color = colors[i], alpha = 0.7 )\n", " plt.title(_stock + \" returns\" )\n", " plt.xlim(-0.15, 0.15 )\n", "\n", "plt.tight_layout()\n", "plt.suptitle(\"Histogram of daily returns\", size =14);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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27Thw4AAAIDw8HH369JF9I0JOfefkmmtuwkmU/F2gvoJCgmO3IFg62tdxZLon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\ndPO28p89mLaGU2IGEGzD9jhz8QZu9wz9a2QHgBmx4zFmlD13yQx6AHH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"text": [ "" ] } ], "prompt_number": 38 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below we perform the inference on the posterior mean return and posterior covariance matrix. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "obs = pm.MvNormal( \"observed returns\", mu, inv_cov_matrix, observed = True, value = returns )\n", "\n", "model = pm.Model( [obs, mu, inv_cov_matrix] )\n", "mcmc = pm.MCMC()\n", "\n", "mcmc.sample( 150000, 100000, 3 )" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " \r", "[****************100%******************] 150000 of 150000 complete" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] } ], "prompt_number": 39 }, { "cell_type": "code", "collapsed": false, "input": [ "figsize(12.5,4)\n", "\n", "#examine the mean return first.\n", "mu_samples = mcmc.trace(\"returns\")[:]\n", "\n", "for i in range(4):\n", " plt.hist(mu_samples[:,i], alpha = 0.8 - 0.05*i, bins = 30,\n", " histtype=\"stepfilled\", normed=True, \n", " label = \"%s\"%stock_returns.keys()[i])\n", "\n", "plt.vlines( mu_samples.mean(axis=0), 0, 500, linestyle=\"--\", linewidth = .5 )\n", "\n", "plt.title(\"Posterior distribution of $\\mu$, daily stock returns\" )\n", "plt.legend();" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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GYPfu3YiLi8O5c+cwefJkFBUVYcWKFdDpdLY/Y86cORPPP/88rrvuOnFHQUREivjTn/4E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\naWqKLMuwXPY+YzE7nxVIAqDzc/1Mucni3kXvrth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"text": [ "" ] } ], "prompt_number": 41 }, { "cell_type": "markdown", "metadata": {}, "source": [ "(Plots like these are what inspired the book's cover.)\n", "\n", "What can we say about the results above? Clearly TSLA has been a strong performer, and our analysis suggests that it has an almost 1% daily return! Similarly, most of the distribution of AAPL is negative, suggesting that it's *true daily return* is negative.\n", "\n", "\n", "You may not have immediately noticed, but these variables are a whole order of magnitude *less* than our priors on them. For example, to put these one the same scale as the above prior distributions:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "figsize(11.0,3)\n", "for i in range(4):\n", " plt.subplot(2,2,i+1)\n", " plt.hist(mu_samples[:,i], alpha = 0.8 - 0.05*i, bins = 30,\n", " histtype=\"stepfilled\", normed=True, color = colors[i],\n", " label = \"%s\"%stock_returns.keys()[i])\n", " plt.title( \"%s\"%stock_returns.keys()[i] )\n", " plt.xlim(-0.15, 0.15 )\n", " \n", "plt.suptitle(\"Posterior distribution of daily stock returns\" )\n", "plt.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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NzJkzK71Wy8NbtXLvaSFPLeQIkqeoqMqvTwMCAti5cydZWVkVxrpGRkbStGnT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\nXzN27FhcXV3x8/OjY8eOHDx40IbhCyG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"text": [ "" ] } ], "prompt_number": 43 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Why did this occur? Recall how I mentioned that finance has a very very low signal to noise ratio. This implies an environment where inference is much more difficult. One should be careful about over-interpreting these results: notice (in the first figure) that each distribution is positive at 0, implying that the stock may return nothing. Furthermore, the subjective priors influenced the results. From the fund managers point of view, this is good as it reflects his updated beliefs about the stocks, whereas from a neutral viewpoint this can be too subjective of a result. \n", "\n", "Below we show the posterior correlation matrix, and posterior standard deviations. An important caveat to know is that the Wishart distribution models the *inverse covariance matrix*, so we must invert it to get the covariance matrix. We also normalize the matrix to acquire the *correlation matrix*. Since we cannot plot hundreds of matrices effectively, we settle by summarizing the posterior distribution of correlation matrices by showing the *mean posterior correlation matrix* (defined on line 2)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "inv_cov_samples = mcmc.trace(\"inv_cov_matrix\")[:]\n", "mean_covariance_matrix = np.linalg.inv( inv_cov_samples.mean(axis=0) )\n", "\n", "\n", "def cov2corr( A ):\n", " \"\"\"\n", " covariance matrix to correlation matrix.\n", " \"\"\"\n", " d = np.sqrt(A.diagonal())\n", " A = ((A.T/d).T)/d\n", " #A[ np.diag_indices(A.shape[0]) ] = np.ones( A.shape[0] )\n", " return A\n", "\n", "\n", "plt.subplot(1,2,1)\n", "plt.imshow( cov2corr(mean_covariance_matrix) , interpolation=\"none\", \n", " cmap = plt.cm.hot ) \n", "plt.xticks( np.arange(4), stock_returns.keys() )\n", "plt.yticks( np.arange(4), stock_returns.keys() )\n", "plt.colorbar(orientation=\"vertical\")\n", "plt.title(\"(mean posterior) Correlation Matrix\" )\n", "\n", "plt.subplot(1,2,2)\n", "plt.bar(np.arange(4), np.sqrt(np.diag(mean_covariance_matrix)),\n", " color = \"#348ABD\", alpha = 0.7 )\n", "plt.xticks( np.arange(4) + 0.5, stock_returns.keys() );\n", "plt.title(\"(mean posterior) variances of daily stock returns\" )\n", "\n", "plt.tight_layout();\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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6i3xJwpX9LSwN2Oov3fpsvpFuXSr3AFhKuL6JkyYhRMtTScR68OABhg59OBRK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\nVFZWYtOmTQ7nWiwWbN++HR999BG8vLzs9qlUKuzatQsHDhw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"text": [ "" ] } ], "prompt_number": 47 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looking at the above figures, we can say that likely TSLA has an above-average volatility (looking at the return graph this is quite clear). The correlation matrix shows that there are not strong correlations present, but perhaps GOOG and AMZN express a higher correlation (about 0.30). \n", "\n", "With this Bayesian analysis of the stock market, we can throw it into a Mean-Variance optimizer (which I cannot stress enough, do not use with frequentist point estimates) and find the minimum. This optimizer balances the tradeoff between a high return and high variance.\n", "\n", "$$ w_{opt} = \\min_{w} \\frac{1}{N}\\left( \\sum_{i=0}^N \\mu_i^T w - \\frac{\\lambda}{2}w^T\\Sigma_i w \\right)$$\n", "\n", "where $\\mu_i$ and $\\Sigma_i$ are the $i$th posterior estimate of the mean returns and the covariance matrix. This is another example of loss function optimization." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Protips for the Wishart distribution\n", "\n", "If you plan to be using the Wishart distribution, read on. Else, feel free to skip this. \n", "\n", "In the problem above, the Wishart distribution behaves pretty nicely. Unfortunately, this is rarely the case. The problem is that estimating an $NxN$ covariance matrix involves estimating $\\frac{1}{2}N(N-1)$ unknowns. This is a large number even for modest $N$. Personally, I've tried performing a similar simulation as above with $N = 23$ stocks, and ended up giving considering that I was requesting my MCMC simulation to estimate at least $\\frac{1}{2}23*22 = 253$ additional unknowns (plus the other interesting unknowns in the problem). This is not easy for MCMC. Essentially, you are asking you MCMC to traverse 250+ dimensional space. And the problem seemed so innocent initially! Below are some tips, in order of supremacy:\n", "\n", "1. Use conjugancy if it applies. See section below.\n", "\n", "2. Use a good starting value. What might be a good starting value? Why, the data's sample covariance matrix is! Note that this is not empirical Bayes: we are not touching the prior's parameters, we are modifying the starting value of the MCMC. Due to numerical instability, it is best to truncate the floats in the sample covariance matrix down a few degrees of precision (e.g. instability can cause unsymmetrical matrices, which can cause PyMC to cry.). \n", "\n", "3. Provide as much domain knowledge in the form of priors, if possible. I stress *if possible*. It is likely impossible to have an estimate about each $\\frac{1}{2}N(N-1)$ unknown. In this case, see number 4.\n", "\n", "4. Use empirical Bayes, i.e. use the sample covariance matrix as the prior's parameter.\n", "\n", "5. For problems where $N$ is very large, nothing is going to help. Instead, ask, do I really care about *every* correlation? Probably not. Further ask yourself, do I really really care about correlations? Possibly not. In finance, we can set an informal hierarchy of what we might be interested in the most: first a good estimate of $\\mu$, the variances along the diagonal of the covariance matrix are secondly important, and finally the correlations are least important. So, it might be better to ignore the $\\frac{1}{2}(N-1)(N-2)$ correlations and instead focus on the more important unknowns.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conjugate Priors\n", "\n", "Recall that a $\\text{Beta}$ prior with $\\text{Binomial}$ data implies a $\\text{Beta}$ posterior. Graphically:\n", "\n", "$$ \\underbrace{\\text{Beta}}_{\\text{prior}} \\cdot \\overbrace{\\text{Binomial}}^{\\text{data}} = \\overbrace{\\text{Beta}}^{\\text{posterior} } $$ \n", "\n", "Notice the $\\text{Beta}$ on both sides of this equation (no, you cannot cancel them, this is not a *real* equation). This is a really useful property. It allows us to avoid using MCMC, since the posterior is known in closed form. Hence inference and analytics are easy to derive. This shortcut was the heart of the Bayesian Bandit algorithm above. Fortunately, there is an entire family of distributions that have similar behaviour. \n", "\n", "Suppose $X$ comes from, or is believed to come from, a well-known distribution, call it $f_{\\alpha}$, where $\\alpha$ are possibly unknown parameters of $f$. $f$ could be a Normal distribution, or Binomial distribution, etc. For particular distributions $f_{\\alpha}$, there may exist a prior distribution $p_{\\beta}$, such that:\n", "\n", "$$ \\overbrace{p_{\\beta}}^{\\text{prior}} \\cdot \\overbrace{f_{\\alpha}(X)}^{\\text{data}} = \\overbrace{p_{\\beta'}}^{\\text{posterior} } $$ \n", "\n", "where $\\beta'$ is a different set of parameters *but $p$ is the same distribution as the prior*. A prior $p$ that satisfies this relationship is called a *conjugate prior*. As I mentioned, they are useful computationally, as we can avoided approximate inference using MCMC and go directly to the posterior. This sounds great, right?\n", "\n", "Unfortunately, not quite. There are a few issues with conjugate priors.\n", "\n", "1. The conjugate prior is not objective. Hence only useful when a subjective prior is required. It is not guaranteed that the conjugate prior can accommodate the practitioner's subjective opinion.\n", "\n", "2. There typically exist conjugate priors for simple, one dimensional problems. For larger problems, involving more complicated structures, hope is lost to find a conjugate prior. For smaller models, Wikipedia has a nice [table of conjugate priors](http://en.wikipedia.org/wiki/Conjugate_prior#Table_of_conjugate_distributions).\n", "\n", "Really, conjugate priors are only useful for their mathematical convenience: it is simple to go from prior to posterior. I personally see conjugate priors as only a neat mathematical trick, and offer little insight into the problem at hand. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Jefferys Priors\n", "\n", "Earlier, we talked about objective priors rarely being *objective*. Partly what we mean by this is that we want a prior that doesn't bias our posterior estimates. The flat prior seems like a reasonable choice as it assigns equal probability to all values. \n", "\n", "But the flat prior is not transformation invariant. What does this mean? Suppose we have a random variable $ \\bf X $ from Bernoulli($\\theta$). We define the prior on $p(\\theta) = 1$. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "figsize( 12.5, 5 )\n", "\n", "x = np.linspace( 0.000 ,1, 150 )\n", "y = np.linspace( 1.0, 1.0, 150 )\n", "lines = plt.plot( x, y, color=\"#A60628\", lw = 3 )\n", "plt.fill_between( x, 0, y, alpha = 0.2, color = lines[0].get_color() )\n", "plt.autoscale(tight=True)\n", "plt.ylim( 0, 2);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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ykhVSyAtZ5X1i5rjvhDc3N0d/f3/ceuutMTY2Fhs3boxFixbFtm3bIiJi06ZNsWPHjti6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\nRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 48 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let's transform $\\theta$ with the function $\\psi = log \\frac{\\theta}{1-\\theta}$. This is just a function to stretch $\\theta$ across the real line. Now how likely are different values of $\\psi$ under our transformation." ] }, { "cell_type": "code", "collapsed": false, "input": [ "figsize( 12.5, 5 )\n", "\n", "psi = np.linspace( -10 ,10, 150 )\n", "y = np.exp(psi) / (1 + np.exp(psi))**2\n", "lines = plt.plot( psi, y, color=\"#A60628\", lw = 3 )\n", "plt.fill_between( psi, 0, y, alpha = 0.2, color = lines[0].get_color() )\n", "plt.autoscale(tight=True)\n", "plt.ylim( 0, 1);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 49 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Oh no! Our function is no longer flat. It turns out flat priors do carry information in them after all. The point of Jeffreys Priors is to create priors that don't accidentally become informative when you transform the variables you placed them originally on.\n", "\n", "Jeffreys Priors are defined as:\n", "\n", "$$p_J(\\theta) \\propto \\mathbf{I}(\\theta)^\\frac{1}{2}$$\n", "$$\\mathbf{I}(\\theta) = - \\mathbb{E}\\bigg[\\frac{d^2 \\text{ log } p(X|\\theta)}{d\\theta^2}\\bigg]$$\n", "\n", "$\\mathbf{I}$ being the *Fisher information*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Effect of the prior as $N$ increases\n", "\n", "In the first chapter, I proposed that as the amount of observations, or data, that we posses, the less the prior matters. This is intuitive. After all, our prior is based on previous information, and eventually enough new information will shadow our previous information's value. The smothering of the prior by enough data is also helpful: if our prior is significantly wrong, then the self-correcting nature of the data will present to us a *less wrong*, and eventually *correct*, posterior. \n", "\n", "We can see this mathematically. First, recall Bayes Theorem from Chapter 1 that relates the prior to the posterior. The following is a sample from [What is the relationship between sample size and the influence of prior on posterior?](http://stats.stackexchange.com/questions/30387/what-is-the-relationship-between-sample-size-and-the-influence-of-prior-on-poste)[1] on CrossValidated.\n", "\n", ">The posterior distribution for a parameter $\\theta$, given a data set ${\\bf X}$ can be written as \n", "\n", "$$p(\\theta | {\\bf X}) \\propto \\underbrace{p({\\bf X} | \\theta)}_{{\\rm likelihood}} \\cdot \\overbrace{ p(\\theta) }^{ {\\rm prior} } $$\n", "\n", "\n", "\n", ">or, as is more commonly displayed on the log scale, \n", "\n", "$$ \\log( p(\\theta | {\\bf X}) ) = c + L(\\theta;{\\bf X}) + \\log(p(\\theta)) $$\n", "\n", ">The log-likelihood, $L(\\theta;{\\bf X}) = \\log \\left( p({\\bf X}|\\theta) \\right)$, **scales with the sample size**, since it is a function of the data, while the prior density does not. Therefore, as the sample size increases, the absolute value of $L(\\theta;{\\bf X})$ is getting larger while $\\log(p(\\theta))$ stays fixed (for a fixed value of $\\theta$), thus the sum $L(\\theta;{\\bf X}) + \\log(p(\\theta))$ becomes more heavily influenced by $L(\\theta;{\\bf X})$ as the sample size increases. \n", "\n", "There is an interesting consequence not immediately apparent. As the sample size increases, the chosen prior has less influence. Hence inference converges regardless of chosen prior, so long as the areas of non-zero probabilities are the same. \n", "\n", "Below we visualize this. We examine the convergence of two posteriors of a Binomial's parameter $\\theta$, one with a flat prior and the other with a biased prior towards 0. As the sample size increases, the posteriors, and hence the inference, converge." ] }, { "cell_type": "code", "collapsed": false, "input": [ "figsize( 12.5, 15)\n", "\n", "p = 0.6\n", "beta1_params = np.array( [1.,1.] )\n", "beta2_params = np.array( [2,10] )\n", "beta = stats.beta\n", "\n", "x = np.linspace(0.00, 1, 125)\n", "data = pm.rbernoulli(p, size=500)\n", "\n", "plt.figure()\n", "for i,N in enumerate([0,4,8, 32,64, 128, 500]):\n", " s = data[:N].sum() \n", " plt.subplot(8,1,i+1)\n", " params1 = beta1_params + np.array( [s, N-s] )\n", " params2 = beta2_params + np.array( [s, N-s] )\n", " y1,y2 = beta.pdf( x, *params1), beta.pdf( x, *params2)\n", " plt.plot( x,y1, label = r\"flat prior\", lw =3 )\n", " plt.plot( x, y2, label = \"biased prior\", lw= 3 )\n", " plt.fill_between( x, 0, y1, color =\"#348ABD\", alpha = 0.15) \n", " plt.fill_between( x, 0, y2, color =\"#A60628\", alpha = 0.15) \n", " plt.legend(title = \"N=%d\"%N)\n", " plt.vlines( p, 0.0, 7.5, linestyles = \"--\", linewidth=1)\n", " #plt.ylim( 0, 10)#\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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/LJvcZWsB8GkTSWi/JEL6JxLaL4nAHp1Ru+ldshBCCCGaB5fN852dnc2wYcM4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PGEXTgGdbAYwCX0HnaXTHGdg8JaO0V1dgprHRTV2imtb90AYa1KIslkoH+4gdRwo/cRbuz5M7AI\n3VOXTDXoCxF8Cy1xVNV60ko+W0XNzoPNnhM4MJmYy6YTNXMyurCQTq6h0NdZXUpDUN0QZFvdFFs9\nzyvtcpsHngWqIVKvIsqgIlIvEaVyE5l1AuP+/bh37ceZV9Tyi9UqAjLSCbpwHIGZYwgYOQRJK2by\naUltbQ2vv/w3Hnzsia6uitBKLlmhuCEYL6ixU1hrp6DWM7i4Nb97oQaNNyDv3/BINhnEfOVCu4ng\nW+gR3DY7ZWt/ouiLf1P6n00ojsavGw/JZtJVgWhCgoieOZmYy6cRNCi1C2srdGf+yvmuc3qC6pKG\n4LrIKlPcEGRXO9p+ezRpJaL0UkOArSJaL3kCbr2KAM3P98I5i8sw79iHZfs+LHsPo7QwpziAKsBI\n4IQMAieOIWjSWPRpKaKX7wy9dZ7vvszplj0Bea2dgho7+TU28mvsVFl9n6NeJdHQS94YkPeP8PSS\nb9q0SeR8Cz7p0tlOBOHnKG43lZt3U7jiX5R89wOuunPnhpXUakKGD2HoomsIzxyNSqftgpoKvZGs\nKFQ5ZIq9QXVjcF1klTG72hZgS0C4TiLaoPIE2Q2BdZTBE2Tr2pF7qo2NwjTnIkxzLkJxurAePoFl\n534suw5gP2sqQ9lipW7dFurWbQFAHW4icHwGgeNHEThxFPr+ySIYF3oVrVrlGYQZ1nSQvdnhpqDG\nTl6NrWFrJ7/Gjt0ln3MNWYFTVTZOVdlYl9U4T3+oQYOxpIBD2gL6hxsZEGEkySRyyQX/anfP969/\n/Wu+++47oqOj2b9//znHRc9336TIMtU7D1L89VqKv1qLvbSi2fOChg7wLPV+8SS0JpFWIrSNU1Yo\ntXmC6pLTAbbNsy2xunGc+9nrE7WEJy3kdGDd8DzaoCJcJ3XJB7KruhbL7oNYdx/CsucgrhZ+t05T\nR4R5gvFxIwgYNxJDWkqHLvTT3ZSVlnDdnFndZnl5oXPJikK52Ul+Qw95XrWdvGobpeaWB3meTauS\n6Bdm8Abjp3vJg/Wi/7Kv67K0kx9//JGgoCBuuukmEXz3cYosU73rIMVf/5eSb9dhKyxt9jxDfDRR\nl3hW/AtISejkWgo9kaIo1LkUSqyNAXaJN9iWKW9H/rVWhSegbkgLObMnO0wn+W2Z846gKArOolJP\nIL77IJZ9h5Fr63/2NargQALGDPcE42NGYBw+CJVB30k17nwi+BaaY3PJTYLxvBo7+dW2Vk2HGBWo\nbRKMDwg3Ehei79b3DMG/uiztZMqUKeTk5LT3MkIPJbtcVG3ZS+nqDZSs2tDsTCUA2rBQoi7KJGrm\nhQSnD2z2a/CeMG+z0HFsboUymyeYLm3otS5tKJfYZKxnfSjWZu3xLt5xPgFqT4Ad2ZAWEq1vzMMO\n0Uo9Ni1DkiR08THo4mMIvXwGiizjOFWAde9hLPuOYN1/BPmsNC+5zkz9+q3Ur9/quYZWg2HoQAJG\npRMwehjGUelo46J77L9Jcxw/M5OM0DcZNCoGRgQ0mRJRVhTKzE7+s249gamjGoJyGxWW5nPJy8xO\nysxOtuQ2ToNo0KhIDff0kqeGewLylHAjgbq+822TcH7iOxOh1VxmK+U/bKV01QbK1mzCWV3X7Hma\n0GAip15A5IwJmMYOF9MD9nF2t2fu61Kbm9KGbZlN9gbbNc62fwknAWE6T891pHdgo+QNuAPPM8Cx\nt5BUKvSpSehTkzBdNdMTjOfkY91/FOuBo1gPHMN91kI/itOFdd8RrPuOUPHeFwBoosIxjhiCceQQ\njCMGYxw+GE0PTQsLCg7m2htu6upqCD2ASpKICdIxOCqQC4ZHeffXO9zkN/SO51V7essLau24mplP\n1OaSOVxq4XCppcn+2GCdd7aV1HADqWFG4kP0qEUueZ/kl9lOcnJyuOKKK1pMO3njjTfE8vI9vDw6\nvh9lazez5rMvqTt4gqFuz+p7p5d3P7189lGjQmjGEC6+dj6hY4exde9uoHss/y3KHVeeOGYc9S6F\n/2zdRrVDIWbQKMpsMrv27KTa4UaVnEGNU2nTcuiny3oVkLuPUC2MGDmWSL1E+fE9hGpVTB83Fq1K\nYueenQCMHTUWQJTPKu/YvQNXRTVDZR22A8fYsWs7rtIK7+/v2b/PZ5Z1/RI4Fh2Avl8iE2dfijF9\nELuPeaYI7Q7LoYuyKHdm2SUr/Pu/6ymtdxKQOpK8Gjv7tv+E2Sn7fH+zndxLdLCOiZkXkhJupPbE\nbmKD9cy+aBqSJHWbz39R/vnl5btsqsHzBd8i57vncdWZqfxpD+Xrt1K+9icsOQUtnquLDidiygVE\nTB1H6KihqDTiC5Xexu5WKLfLlNvcDVtPnnWFXabMJlNud2Nzt+891JJn9pAInYoI/Rm92DoVEXoV\nQRp6VSpEd+Guq8d2OAvb4RNYD5/AdjQbxWrz6bXauGgMQwZgGNwfw2DPVtcvQXzLJfRZ1VbP4M7T\nveT5NXaKau2tWiwo1KChn8lASriBfiYD/RpW8gwxiM/W7kZMNSi0i2x3ULV9P5WbdlLx4w5qdh9G\ncbccTQX0TyJiyjgipl5A0OBUvwRFIue7850eyFjVEEhXNmzPftS3cTq+M6kkCNNKROhVROg82/CG\nVJEIvYRJ27rBjTv37PT26Aptpw4OapiaMAMAxS3jyC/CfjQb27GT2I5mYz+ZC65z7wfOolKcRaXU\nrfvJu0/SadGnpWAYmIJ+YD/0DVtdQmyXzbKyfctmb++lIJxPe9qLyajFZNQyPLZxFVqnW6aozuGZ\ncaUhIM+rsVNjaz6XvMbmYl9xPfuKmw6eDjNq6BdmINnkefQzGUgOM2AyiBU8e5p2B98LFy5k/fr1\nVFRUkJSUxFNPPcUtt9zij7oJHchZU0f19v1Ubd9H1dZ91Ow5hGxreVCSyqjHNHY44ZmjCZs4CkNs\nZCfWVmgtRVGod3nmt66yy1Q5FCrtsqfs8ATZlXaZSoeMs43T8J1Nr/LkXYfrPEF1eEOQHa5TEd6G\n4FroGpJahb5fAvp+CYTMnAKA7HDgyCnAnnUK+4kcbCdO4cjOQ3GeO12b4nBiO3gc28HjTa+r16FP\nTUKXmoQ+JbHxeWoi6uCgc64jCL2FVq3yBsz0C/Xur7W7GhYJalwsqKDG3uKMK1VWF1XWevYUNg3K\ng/VqkkINJJn0DVsDiaF64kL0Yn7ybkqscNkHyE4X9UezqdlzmJo9h6necYD6oyfhPP/1gWkpmMYN\nI2zCKEIzhoiFb7qY3BBQ1zoUqh0yNU6ZaodM9elyQ2B9uuyHzmovteRZsTFMJxGmUzVsGwPtMJ2K\nALVIC+lLFLcbR14R9pN5OE7mebeu8qrzv/gs6rBQdMnx6JLiPdvTzxNj0USF96l5yYW+TVYUKixO\nCmrsFDas4FlQa6eo1oGzmQGeP0clQWywnsRQPQmhehJCPI/4UD3RgTox2NMPxPLyAgAus4X6I9nU\nHcmm7uAJavYcpu7gcWT7+afaMiTGYho7HNO44ZjGpItFbzqYw61Q55KpcyrUORVqnTK1ToVaR8PW\n6Qmoa50KNQ3HWnnv9YlBBaE6CZNWRWhDgG3SSYRpVZh0nh7rYNFrLfjIXVuPPScfR24BjtxCHKc8\n27NnWfGZRo02LhpdfAzahFi08dFoY6PQxkajjY1EGxuFKiiwxT/8amtreP3lv/HgY0+046cShK51\nerGgwlpPUF5U6/A+b83c5KepJYgJ1hMfoiM+RE9skI7YYD2xwTpig3UEiQWEfCJyvvsYR1Utluxc\nzFl5mLNOeQLuw9lYcwt9u4BaRdDAFEJGDiYkYzChIwajiwzr2EqfR0/M+XbLCha3gtnledQ7PcuV\n17sUzE6FepcnX7rO6Tl2+nmdU8bup3SPlhjUEKKRCNVKhOo8gfXpR4hWwqRTYdJKGNQ9M6gWOd/d\nkzokiICRQwgYOaTJfndtPY78Ipz5xTjyi3AUlODML8JZWNps+oqXy40zrwhnXlGLp6gCjGiiI9BE\nR6CNCkcTFYEmKhxtVAT1atj4yWfcd/s9aMJCkbTiY0/4ed1xjIBKkogO0hEdpGNUfLB3v6IoVFld\nFNU5KK7zBOXFdQ6K6uxUWZvPKQdwK3iDdzh3uuAgnZqYYM/7RQfqiArSEh3oKUcFaQk3akXPeTu0\n+y60evVq7r//ftxuN7fddhsPP/ywP+rV57mtdqz5RVjzi7HlF2PNL8aaV4zlVAGWk/k4K1vXi6SP\njSRoSH+Chw4gaEh/QtLTUAcYOqj2bXPw6NFOCb4VRcEhexZ1sbkVrG4Fq6the1bZcubWpWBuCLQt\nLgWzS273DB+tZVRDkMYTPAdrPD3SIRqJYK2KkDMC6xCNhK6HBtW+OnrimAi+exB1SBDG9DSM6WlN\n9iuyjKuiCmdhqXcAp+dRhqu0HHdN8+sInEm2WHHk5OPIyW/2+CSXmqNTrvHUwxSCOiwUTVho4/OG\nrTo0CHVIMOrQYNQhjc9VgUaR+tKHHDl0oNsF3y2RJInwAC3hAVqGxQQ2OWZ3yZTWOyipd1BS56C4\n3kFpw6PmPB9e9Q439RVWsiqszR5XSWAyaogM0BERqCWyoQ7hRg1hZzw3GbUi77wZ7Qq+3W4399xz\nD2vWrCEhIYELLriAK6+8kqFDh/qrfr2G4nbjrDXjrKrBUVmNs7IGR2UNzsoa7GWV2EvLsZdUeB6l\nFbh8+MBpllpFQFI8AQOSCByQTNDgVIIG90cX1r1TSGRFoaq2DrPLMwDQKXsCZM9WwSl70jQcMjga\n9jka9tllBbtbwX5W2eamYb8nyD69z+ZW6OBOZ5+oJAhSSwRqJII0NGwlgrQN24ZHyBllrbiJedXX\n//wy6kLPIKlUaKMi0EZFQMa5nx2yzY6rtAJnaTnOknJcZZW4yitxlVfhKqvAVV6Fcp60OssZv/Hu\n6lrc1bU4Tua1qp6qwABUwYGogwNRBwV6yoFG71Z9umw0oDIaUQUYkIyGhrIBlV7nKRt0SHo9KoMe\nSa8T4yS6obra2vOf1APoNSqSTJ4BmGezu2TKzJ7AvKzes1JnudlBudlJhcWJ4zypLLIClRYXlRYX\nlP98PYJ0akINGs/DqMFk0BCiVxOs1xB8xjZIryZQ53kEaNW9ume9XcH3tm3bGDhwICkpKQBcf/31\nfPXVV+cE34VZLc8R3WZnpqo3eap4jimKZ7+ioChn7lNQ5NNbGUWWwe3ZKm43iltGcblRXK6G7enn\nLhSHE8XuQHY4URyerWy1I1ttyFYr7tPPLTZkswV3nRl3nRm53oxsaf6vxzbT61DHx6COj0WdEIeU\nGIc6JQkpKR40GuyAVYEyQHaDXOZAQUFRQMbzi+Nu+CeSFU8u8el9Mkrjc8Vz3N1QdiuNx1wNz12y\nZ79nnycVw6WAS27c5zpj3+mtU/EE1y7Zc07BKSubf2z9YK2uZlBDgFryPDQSAWoI0EgY1RKBDfsC\nNZzx3PMwqMQARUE4H5VB7x2E2RxFUZDrzbgqqnFX1uCqrMJVWYO7shpXVQ22sgrq9pegDg3GXVt/\n3oHmLZHNFmSzBVdxWXt+nHNIOi2SXucJzvU6JK0WSadD0mpQ6bSe41otklbjea5Re8oajWc+da3G\n81ytbjimAbXaW0alarKVVGpQq5BUqoat2tMToJK8zyWVClSqxueSBNLp/RIgIakkzzmS5FliltPn\n4j0fSWo4JDWe593fcO87ve/M807v5+x75BnPz9wvNbOvyT9y8/tbuv/K9RacZ/8/97JbtQqIAWI0\ngAkwqQEjYPRMQWuXqbI6G2ZYcVLdsK2yuqixuTA7WteFVdPwaA29WkWAVoVBq8KoUWPQSujVKvRa\nFQaNGp1aanio0GoatioVWrWERgVqlYRWpUKjllCrJNSShEoCteQpn27CKiQkqeHXAKmx7TXshzOa\nuZ+0K/guKCggKSnJW05MTGTr1q3nnLfvwmva8zZ9kluloj7ERK0pglpTOHWmcGpN4dSEhVMVEUN9\nSKin1ZypFjjo5yC/E9mrijvtvTQS6NWgV0noVRIGNRjUEnqVZ+t5gFF1xvOG/fO3oaMAACAASURB\nVMaGYNuoltCrEQMRu0hhsY/jG4ReTZIk1MFBnukKUxLPOV5eUc76G/7N05+8guJ2466pw11bj7u2\nHrm2HnftGeV6M+56M3KdpWFrRrZYkC2+LTrUForDieJwIteZO+w9hNY57Czk6Ps/dHU1ugVjw6P5\nP327JwVwNjw67jfXI/r7V9r0unYF37702tXX17e5csL5dOhENZ1vzEN0/s/U9vdzAA6lXZcQ2uGB\nh35LjdzG9Cyhz9CG6fn+++89bUXC08NnCgUa51tWNzwEAUDMiyP4qq3pj+0KvhMSEsjLa8yby8vL\nIzGxac/D3Llz2/MWgiAIgiAIgtBrqM5/SsvGjRvH8ePHycnJweFw8Mknn3DllVf6q26CIAiCIAiC\n0Ku0q+dbo9HwyiuvMGvWLNxuN7feequY6UQQBEEQBEEQWtDhK1wKgiAIgiAIguDRrrSTM61evZoh\nQ4aQlpbGs88+2+w5v/nNb0hLSyMjI4Pdu3f7662FHuZ8beXDDz8kIyODkSNHcuGFF7Jv374uqKXQ\nXfhybwHYvn07Go2GL774ohNrJ3QnvrSVH374gdGjRzN8+HCmT5/euRUUupXztZfy8nIuvfRSRo0a\nxfDhw3nnnXc6v5JCl/v1r39NTEwMI0aMaPGcVse3ih+4XC5lwIABysmTJxWHw6FkZGQohw4danLO\nd999p8yePVtRFEXZsmWLMmHCBH+8tdDD+NJWNm/erFRXVyuKoiirVq0SbaUP86W9nD5vxowZyuWX\nX658/vnnXVBToav50laqqqqU9PR0JS8vT1EURSkrK+uKqgrdgC/t5YknnlAeeeQRRVE8bSU8PFxx\nOp1dUV2hC23YsEHZtWuXMnz48GaPtyW+9UvP95mL7Wi1Wu9iO2f6+uuvufnmmwGYMGEC1dXVlJSU\n+OPthR7El7aSmZlJaKhnGrAJEyaQn9/8ktFC7+dLewF4+eWXWbBgAVFRUV1QS6E78KWtLF++nKuv\nvto7K1dkZGRXVFXoBnxpL3FxcdQ2rHZZW1tLREQEGk27hsoJPdCUKVMICwtr8Xhb4lu/BN/NLbZT\nUFBw3nNEUNX3+NJWzvTmm29y2WWXdUbVhG7I13vLV199xZ133gmIVUP7Kl/ayvHjx6msrGTGjBmM\nGzeO999/v7OrKXQTvrSX22+/nYMHDxIfH09GRgbLli3r7GoKPUBb4lu//Ann64edctbYTvEh2fe0\n5v983bp1vPXWW2zatKkDayR0Z760l/vvv5+lS5ciSRKKopxznxH6Bl/aitPpZNeuXaxduxaLxUJm\nZiYTJ04kLS2tE2oodCe+tJenn36aUaNG8cMPP5CVlcUll1zC3r17CQ4O7oQaCj1Ja+NbvwTfviy2\nc/Y5+fn5JCQk+OPthR7El7YCsG/fPm6//XZWr179s1/3CL2bL+1l586dXH/99YBngNSqVavQarVi\nzYE+xpe2kpSURGRkJEajEaPRyNSpU9m7d68IvvsgX9rL5s2beeyxxwAYMGAAqampHD16lHHjxnVq\nXYXurS3xrV/STnxZbOfKK6/kvffeA2DLli2YTCZiYmL88fZCD+JLW8nNzWX+/Pl88MEHDBw4sItq\nKnQHvrSX7OxsTp48ycmTJ1mwYAGvvvqqCLz7IF/ayty5c9m4cSNutxuLxcLWrVtJT0/vohoLXcmX\n9jJkyBDWrFkDQElJCUePHqV///5dUV2hG2tLfOuXnu+WFtv5xz/+AcAdd9zBZZddxvfff8/AgQMJ\nDAzk7bff9sdbCz2ML23lqaeeoqqqypvDq9Vq2bZtW1dWW+givrQXQQDf2sqQIUO49NJLGTlyJCqV\nittvv10E332UL+3l0Ucf5ZZbbiEjIwNZlnnuuecIDw/v4poLnW3hwoWsX7+e8vJykpKS+N///V+c\nTifQ9vhWLLIjCIIgCIIgCJ2k3WknzzzzDMOGDWPEiBEsWrQIu93uj3oJgiAIgiAIQq/TruA7JyeH\nf/7zn+zatYv9+/fjdrv5+OOP/VU3QRAEQRAEQehV2pXzHRISglarxWKxoFarsVgsYgYTQRAEQRAE\nQWhBu3q+w8PD+d3vfkdycjLx8fGYTCYuvvhif9VNEARBEARBEHqVdg24zMrK4oorruDHH38kNDSU\na665hgULFnDDDTd4z3nnnXearPwjCIIgCIIgCD1dfX09c+fObfXr2pV2smPHDiZNmkRERAQA8+fP\nZ/PmzU2C76SkJMaMGdOetxH6iLvuuov/9//+X1dXQ+ghRHsRfCXaitAaor0Ivtq1a1ebXteutJMh\nQ4awZcsWrFYriqKwZs0aMWeq0GbJycldXQWhBxHtRfCVaCtCa4j2InS0dgXfGRkZ3HTTTYwbN46R\nI0cCsHjxYr9UTBAEQRAEQRB6m3avcPnQQw/x0EMP+aMuQh8XGhra1VUQehDRXgRfibYitIZoL0JH\na/ciO4LgLyNGjOjqKgg9iGgvgq9EWxFaQ7QXoaN1+PLya9euFQMuBUEQBEHocxwOB+Xl5V1dDaEd\n9Hq9d2KRs+3atYuLLrqo1ddsV9rJ0aNHuf76673l7Oxs/vSnP/Gb3/ymPZcVBEEQBEHo0RwOByUl\nJSQkJKBSiUSDnqqiooL6+nqCgoL8ds12tYbBgweze/dudu/ezc6dOwkICGDevHn+qpvQx2zcuLGr\nqyD0IKK9CL4SbUVoDX+1l/LychF49wLh4eHU1NT49Zp+axFr1qxhwIABYkEdQRAEQRAEEIF3LyBJ\nEpIk+fWafmsVH3/8MYsWLfLX5YQ+aPLkyV1dBaEHEe1F8JVoK0JriPYidLR2TzUInrymb775hmef\nfbbZ43fddZd30vrQ0FBGjBjhbdynv94RZVEWZVEWZVH2d7m2tpaPPvqI999/v1vUR5T7Trmmpob4\n+HiE3mHjxo3s37/fm4KSm5vLbbfd1qZr+WW2k6+++opXX32V1atXn3NMzHYi+Grjxo3em5YgnI9o\nL4IviouLufDCC8nKyurqqgg9hL/uLYWFhT0q+I6IiOCuu+7iT3/6EwAvv/wyFouFhx9++LyvzcvL\n46abbkKWZRwOBzfffDNLliwBPIsv7t27F41Gw5gxY3jxxRfRaDQd+rP4W0v/l22d7cQvaScfffQR\nCxcu9MelBEEQBEEQhE6m0+n47rvvqKysBGhVnnNsbCz//ve/Wb9+PWvWrOHVV1+loKAAgGuuuYat\nW7eyadMmbDYb77//fofUvydpd/BtNptZs2YN8+fP90d9hD5M9GIKrSHai+ArnU7X1VUQepC+em/R\narXcfPPNvPrqq216rVarBcBms6HVagkICADgkksu8Z43evRoCgsL/VPhHqzd/f6BgYFiAnlBEARB\nEIQe7te//jVTpkzh3nvvbbL/888/5+WXXz7n/P79+/P2228DUFBQwHXXXcfJkyd56qmnCAsLa3Ku\n0+nks88+45lnnum4H6CH6FlJN0KvJnJ4hdYQ7UXwlcPh6OoqCD1IX763BAcHc9111/H6669jMBi8\n+xcsWMCCBQt+9rUJCQls3LiR4uJirrjiCmbMmEH//v29xx988EEmTZrExIkTO6z+PYUIvgVBEIRe\nKywsjEceeaSrqyEIPcadd97J9OnTm0wf/dlnn/HKK6+cc25qairvvPNOk32xsbFMnDiR/fv3e4Pv\nZ599lqqqKpYtW9ahde8p2h18V1dXc9ttt3Hw4EEkSeKtt94Sf9UIbdJXexqEthHtRfCFXq/n9ttv\n7+pqCD1IX7+3mEwmrrrqKj744AN++ctfAp5Bk9dcc02LryksLCQsLAyj0Uh1dTXbtm3jvvvuA+C9\n995j3bp1rFy5slPq3xO0O/i+7777uOyyy/j8889xuVyYzWZ/1EsQBEEQBEHoAnfffTdvvPGGz+cf\nO3aMP/7xj97VIB944AEGDhwIeNJNkpOTmTVrFgBXXHEFDz74YIfUu6doV/BdU1PDjz/+yLvvvuu5\nmEZDaGioXyom9D19Oc9OaD3RXgRfibYitEZfbS+5ubne51FRUeTn5/v82unTp/Pjjz82e6y0tLTd\ndett2jXV4MmTJ4mKiuKWW25hzJgx3H777VgsFn/VTRAEQRAEQRB6lXatcLljxw4yMzPZvHkzF1xw\nAffffz8hISE89dRT3nPWrl3LG2+8IZaXF2VRFmVRFmVRFuU+Uz58+DBDhw5F6PkKCwvJzs5udnn5\ntqxw2a7gu7i4mMzMTE6ePAl4Gt7SpUv59ttvveeI5eUFQRCErlJZWcl9990nVtUTOl1PW15eaFm3\nWl4+NjaWpKQkjh07BsCaNWsYNmxYey4p9GGnew0EwReivQi+cDgcbN68uaurIfQg4t4idDRNey/w\n8ssvc8MNN+BwOBgwYIB3pSNBEARBEARBEJpqd/CdkZHB9u3b/VEXoY87nScnCL4Q7UXwlU6n6+oq\nCD2IuLcIHa1daSeCIAiCIAiCIPhOBN9CtyHy7ITWEO2l+1FkGVe9GUdFNbLD2dXV8XI4HF1dBaEH\n6Sv3luPHjzN16lSSk5N5/fXXufvuu/m///u/LqvPiy++6F0Vs7drd9pJSkoKISEhqNVqtFot27Zt\n80e9BEEQhG5EdjgxZ+dhPp6D+cQp6o+fwnwiF2dNLW6z1fOw2pq8Rh1gRBsWgtYUgjY0GH1cJMFD\nBxI8bCAhw9LQRYUjSVKH1jssLIxHHnmkQ99DEHqil156ialTp7JhwwbAs6qlr7+PV1xxBddeey03\n3nij3+rzwAMP+O1a3V27g29Jkvjhhx8IDw/3R32EPkzk2QmtIdpLx3JbbFRu3UPFhh1U/Lid+sPZ\nKG53K69hxW2xYiso8e4r4t/e57oIE8HD0ggbP5KoiycRMnIwksq/X8jq9Xpuv/12v15T6N36yr0l\nPz+f8ePHN9nn6+zT/v6j2e12o1ar2/Ral8uFRtPucLZT+eUu146pwgVBEIRuov54DlnL3mXb1few\nZsgsdi78LTmvLqfuwHGfA2+VUY8mOBBU5/9wdlRUU7FhOyeef5OfLr2VdRlXsv++P1P89X9x1ta3\n98cRBKEFc+fOZePGjTz88MMkJyeTlZXV5Hh1dTXXX389gwYNon///ixcuJDCwkIA/vznP/PTTz95\nX9vcN0u5ublERETw7rvvMmzYMNLT03nllVe8x5cuXcrNN9/MkiVL6NevH8uXL2fp0qUsWbLEe86q\nVavIzMwkNTWVK6+80jutNXgm+3jppZeYPHkyycnJyLLs73+iDuWXnu+LL74YtVrNHXfcIXoYhDbb\nuHFjn+lxENpPtBf/cJRXUbRyDQWfraJ275GfPVcfG0lASgIB/RIwpiQQkByPLjIMtdGA2mhAZdB5\ne64VWcZtseGqrcdVZ8ZZU4e1oBjziVzMJ05hzspFttqb1qWskoJPvqfgk++RNGqiZ00hcdEVRE4f\nj9TGXjHonW2l1uaiqM5Ond1Nrc1Fnd1Nnd2zdcoKWpWEVi2hUUlo1Cp0KomwAA3RgTqig3VEBerQ\n+PAHUl/UWe1l5hu7/Xatf982ulXnf/XVV1x55ZVce+21/PKXvzznuKIo/PKXv+Sdd97B5XJx7733\n8vDDD/P+++/z+OOPs23bthZfe6ZNmzaxY8cOTp48yVVXXcWIESOYNm0aAKtXr+add97htddew2az\nsWzZMu/rTpw4weLFi/nggw+YPHkyf//731m0aBFbtmzx9nJ/8cUXfPrpp0RERKDy8zdmHa3dwfem\nTZuIi4ujrKyMSy65hCFDhjBlyhR/1E0QBEHoALLLRenqHyn4dBXl//0JxdV8r3ZAaiKmcSMwXTCc\n0FFD0QQG+PwekkqFJigATVDja8IY6X2uyDK2wlLqDmdRtWUvVVv24KyubTzuclPy3Q+UfPcDhoQY\nEq6/nMTrL8eYFNeGn7jnsjrdHCm1kFNlJbfaRm61ndxqGzU2V7uuq5IgPEBLbLCOQZEBDI0OZEhU\nINFB2g7Pwxe6j5YyF8LCwpgzZ463/Nvf/pa5c+f69NozPfTQQxiNRtLT01m0aBErVqzwBt/jx49n\n9uzZABgMhibX+/LLL5k5c6b33HvvvZd//OMfbNu2jUmTJiFJEosXL+6xK4i2O/iOi/PcCKOiopg3\nbx7btm07J/i+6667SE5OBiA0NJQRI0Z4/6o8PapYlEV58uTJ3ao+oty9y6K9tL68/j9rKFvzE5Fr\nd2PLL+aQbAYgXRUIwGHJRvCwNH4x7wpMY4ezKzeLUmDA2LEA/LTTs6ZD5tgL2l2WVCr2lORBuI7M\nP96FIsv898uvqT14gpScSuqPZjfWr6CErBfe4pvnXyF0VDrznvw94Zmju/zfsyPKVqeb4AGj2FdU\nz5ofNpBfYyOo/ygAarP2ABAyoP1lWYHsfdvJBg4MGAWUUZu1h2C9mkkXTmZETCCaooNEBuq61b9P\nTyrX1NR0++CwpT+0LBYLjz32GP/973+prq4GwGw2oyiK9zW+/JGWkJDgfZ6YmMihQ4e85Z/7tyku\nLiYxMbFJPRMSEigqKmr22p1h48aN7N+/n5qaGsCTWnPbbbe16VqS0o6EbYvFgtvtJjg4GLPZzMyZ\nM3niiSeYOXOm95y1a9cyZsyYtr6FIAiC0E62ojJOvfkZee+txNVMLnXw8DRiLp1K5EWZaEOCuqCG\n57LkFFD87X8pWbUBV3XdOcfDJmTQ/76biZwx4WeDgMrKSu677z7ef//9jqxuu+RW29iUU83mUzUc\nK7Pgy4eyTi0RHaQjRK8hUKciUKf2PrRqCbes4Drj4XQrVFldVFicVJid1NhcPr1PsslAZr9QJvUL\nZXBUACrRK+6zwsLCbh18n512cvfdd5OQkMCjjz7KX/7yF3788UfefPNNoqKi2L9/P9OnT6esrAyV\nSsXcuXO55pprWkw7yc3NZfTo0WzZsoW0tDQAnnzySaqqqli2bBlLly4lJyeH1157zfuaM/c9//zz\nHDp0iLfeegvw9LIPHz6cf/7zn0yaNIlRo0Z5Z2vpDC39X+7atYuLLrqo1ddrV893SUkJ8+bNAzyj\nTW+44YYmgbcgtEZvzMsUOo5oL+dnzSvixF/fpvDz1SjOpmkKGlMwcXMvJmb21G6ZyhGQkkD/e24k\n5Y6FVGzcQck366jatg8a+ouqtu5l56LfEjJyCP3vu4mY2VObnSnF4XCwefPmzq7+z1IUheMVVjbl\nVLMpp4bcaluL50pAYqielHADccF64kP0xIXoiAjQtisQdskKlRYnhbV2siutZFfYOFlpxepqOnDN\nk+pi45O9JYQbNUwbEMZlgyPoF2Zs83t3d33p3nJ2/+vpstlsxmAwEBISQlVVFc8991yT86KiosjJ\nyTnv9V944QVefPFFcnJy+Oijj/jHP/7hU73mzp3LsmXL2LBhA5mZmbz22msYDIZzZmfpqdoVfKem\nprJnzx5/1UUQBEHwA3tZJdnL3iX3vZUoZy12Y0yKJeG6y4mePRW1Qd9FNfSdSqshasZEomZMxJpX\nRN4HX1O6eoM3T7123xH23PoowcPTGPLEvURMGdfFNW5ZpcXJmuOVrD5WQX6NvdlzVBL0MxkYHBXA\noKgABkYGEKRr+2DTlmhUnp7z6CAdo+KDAZAVhaI6ByfKLewrqudgiRmHuzE4q7S6+PJAGV8eKGNY\nTCCzB0cwtX8YBk3PGuwmNDr7W6PT5SVLlrB48WLS0tKIi4vjzjvvZNWqVd7z7rjjDu6++27eeust\nrrvuOp555plmrz9p0iTGjRuHLMvcc889TJ8+3fs+zb336X1paWm89tprPPzwwxQVFTFy5EiWL1/e\n46YUbEm70k58IdJOBEEQOoezpo6Try7n1Ouf4rZYmxwLGTmYxEVXEH7hGL/Ppd3Z7CXl5C//luKv\n156zkmbURZkM+uPdBA/pD3hyR2fMmMHhw4e7oqq4ZIVteTX862glW/NqkJv5xNWpJUbEBjEmIZiM\nuCACOiDYbgu7S+ZQiZndhXXsKayn3nHuwNxAnZqLBoYxb1g0CaHd/4+5ztTd00460um0k9NpKj1d\nt0o7EQRBELqe7HSR+/YKsv76Fs6z8qODh6eRcsf1mMYM66La+Z8+JpIBD/yKpF/No+Dj7yj8/F/I\nNk9Pctnanyhbt5XEG64g7fdtGwzlD1VWJ98dLufbw+VUWs+dmcSgUTE6IZixCcEMiwlE3w17j/UN\ndRydEIysKBwqMbM+u5o9hXWc7hA3O9x8fcjzc05JNXF9RgwDInyfFUcQ+iK/BN9ut5tx48aRmJjI\nN998449LCn1QX8qzE9pPtBeP8h+2cviPyzAfz2myP2BAMimLr/P0dPfSQXK6sFBS71xE/IJLOfXG\np5R8t96TEy7L5L//FUVf/IeYxQtw2h2dVqfsCitfHizlvyeqcDbTzT0oMoApqaGMSwzplgF3S1SS\nxPDYIIbHBlFjc7E5p4b1J6sorfd88yArsD67mvXZ1VyQGML1o2IYEds9Bu+2lri3+Edvve/4g1+C\n72XLlpGenk5d3bkj0gVBEAT/s+Tkc+TJlyld/WOT/Yb4aPrdfi1RF0/q8eklvtJHhTPoD0tIuGY2\n2a98QPX2/QC4zRYKX3yPe6L6UbVtH2HjR57nSm2jKArb82v5fH8pewrPnU0m1KBhckook1NMxATr\nOqQOnSnUoGH2kAguHRzO4VILq49WcKDE7D2+Pb+W7fm1jIgN4tYL4kmPCezC2gpdITk5mfLy8q6u\nRrfV7pzv/Px8fvWrX/HYY4/x17/+9Zyeb5HzLQiC4D9ui42sZe9w8tWPmgymVAcYSb5lPvHXzEal\n7bsZhYqiULV1Lydf/gBLTn6TY4mLrmDQ43ehCw/1y3vJisLGnGo+2lNCVoX1nOOp4QZmpoUzNjGk\n168mmVNl5fsjFezMrztnCsML+4VyywXxJJsMXVK3rtKXc757m26X8/3AAw/wl7/8hdra2vOfLAiC\nILRZ2botHHr4eay5hU32x1w2jZQlC9FFmLqoZt2HJEmETxyFadxwCj9Zxam3Pvfmg+cv/4aS1RsY\n/Me7Sbj+8jZ/Le6WFdZlVfHRnmLyzpq1RCXB2IRgLhkUzsA+lPucEmbkrsxEiuvsrDpaweacGm9e\n+KZTNfyUW8OlgyO4cXQcEYHarq2sIHSxdn0n+e233xIdHc3o0aN9WmZUEH7O6dXBBMEXfam92Msq\n2XvnE+xc+NsmgXfQ0AFkvP4nBj12pwi8z6LSaEi84QrGfvgC+cOTvPudlTUceOBpdlx/P9a8op+5\nwrncssLqoxXc8tkhnlt/qkngrVNLXJIWzrOXDeTOzMQ+FXifKTZYzy3j4vm/SwcwISnEu19W4Psj\nFfzq04O8t7MI+1nziXcnfeneInSNdvV8b968ma+//prvv/8em81GbW0tN910E++9916T88Ty8qIs\nyqIsyq0v/7hhA2VrfyLk4//iqqnzLrc+MjSa1LtuIDsuiIO2ajLx8Ofy772pnLL4WgZZVXz1zIs4\nK2tIVwVSsX47/7jwKpJumsv8px5BUqla/P/InHQh67OrePGj7ymzOJss165Xq5h/6QwuGRTO0d3b\nyN6XRcTESQBs3+JZ3OeCPliODtIxhlMkmOwc0Q3gUKnZu7z9B+5R/Od4JRdq8hgWE8iUKVOa/Ht3\n9e/faX1heXnBd91mefkzrV+/nueff17kfAuCIPiBOSuXA797hqote5vsj5o5mf6/uRFdmH/ylvsS\nt9XGqTc+o+CT770rZQKETxrD8L8+QkBKYpPzZUVhU04N7+0s4tRZq1AG6tTMTAvnooFh3WZe7u7s\nYEk9n+0rJbe6aZrOuMRg7spMJDG09+WDi5zv3sPfOd9+HQovppURBEFoH9nlIvuVD9j0i5uaBN6G\nhBiGv/goQ564RwTerVBVXc1tv38AALXRQP97byTjtacw9mv8IK3cvIuNM24k55+foMgyiqKwI7+W\ne1Ye5U9rTzYJvAO0KuYPj+K5ywZwRXqkCLx9NCwmiP+5OJWbx8Y2WbFzR34di1cc4c3thdi6cSpK\nb5SRkcH69eubPfbTTz8xYcKETq3P8uXLueyyy/x2vRdffJH77rvPb9fzJ78NiZ82bRrTpk3z1+WE\nPkjMrSq0Rm9sL3WHTrD//qep3XfEu09Sq0lcNIekW65Gre/509R1NofLydZdO5vsCxmexpi3l5L7\n9gryln8DbhnZaufIH5eR8/V61i64ka3Opj2xeo2KmWnhzBoULgLuNlJJEtP6hzE2MYQvD5TyQ1Y1\nCp5VQD/ZW8L67Cp+c2ES4xJDznutjtQb7y3NaW6J99MyMzPZunVrJ9fIvx544IGurkKL+u58VIIg\nCN2E7HCStexdspe9i+JqXMI7cFAKg/6whKBBKV1XuV5KpdeRsmQhEdMncOzp17Bk5QJg276HcfuO\nYJ59NQfGZqLTqPjFwDBmD44gWC8+Mv0hSKfmxjFxTE018cHuxmkai+scPLo6i4sGhnHHhARMRjEr\nitA2brcbtbptfyS7XC40mo79Xe8bKzAIPUJf6GkQ/Ke3tJeavUfYPOvXZL3wljfwlnRaUu64nlH/\n/LMIvP1Ap235GwNnagrbH/oD26bNQm7oBdTbbcxc+SG3fvEGfx5n4tqRMSLw7gD9woz8YUY/bhkX\nR6C2MRxZe6KKWz8/zL+PVXTJTGq95d7ii127dpGZmUn//v255557sNs9OfkbN25k+PDh3vP+9re/\nMXbsWJKTk8nMzOS7777zHsvOzmbOnDmkpKSQlpbGrbfe6j127Ngx5s2bx4ABA5gwYQIrV670Hqus\nrGTRokX069ePiy++mJMnT7ZYz9zcXCIiInj33XcZNmwY6enpvPLKK97jS5cu5eabb2bJkiX069eP\n5cuXs3TpUpYsWeI9Z9WqVWRmZpKamsqVV17JsWPHvMcyMjJ46aWXmDx5MsnJychyx6ZAtetuYrPZ\nmDZtGna7HYfDwdy5c3nmmWf8VTdBEIReS7Y7OPHi25x8+QMUd2Nvd8iI6wKmjAAAIABJREFUQaT9\n4Q4C+iV0Ye16P6tL4ctcK1/nWbHLwCVXkjVkBLNWvEd4eSkAobv3UHbNErRP3k/o7OldWt/eSiVJ\nTEk1kREXxMd7S9iS61kzpM7u5vkNuaw9Ucn9U5KJC9Z3cU39b3XsJL9d69Liza1+jaIofP7556xY\nsYKAgAAWLlzI888/z2OPPXbOuampqXz//ffExMTw5ZdfsmTJEnbu3El0dDRPP/00F110Ed9++y0O\nh4Pdu3cDYDabmT9/Po899hgrVqzg4MGDzJ8/n6FDhzJ48GB+//vfYzQaOXLkCDk5OSxYsICUlJSf\nrfOmTZvYsWMHJ0+e5KqrrmLEiBHelOfVq1fzzjvv8Nprr2Gz2Vi2bJn3dSdOnGDx4sV88MEHTJ48\nmb///e8sWrSILVu2eHu5v/jiCz799FMiIiJQdfDqwO26usFgYN26dezZs4d9+/axbt06MT+m0Gai\n7Qit0ZPbS82ew2yeeQvZf3vXG3ir9Dr633cTI//+pAi8/czhdHifu2SFVQU27txSxWenGgLvBiHp\nA4l+6X8xzb3Eu89dXUve/U+R9+DTuGvPXTpe8I8Qg4bFExJ4YEoSkQGN6Sa7C+u5Y8URvjpYhtxJ\nveA9+d7SGpIkcdtttxEfH4/JZOK3v/0tX3zxRbPnzp07l5iYGADmzZtH//792bVrFwA6nY7c3FwK\nCwvR6XTegZr/+te/6NevHwsXLkSlUjFixAjmzJnDV199hdvt5ttvv+UPf/gDRqORoUOHsnDhwvN+\n0/HQQw9hNBpJT09n0aJFrFixwnts/PjxzJ49G/DEp2de68svv2TmzJlMmzYNtVrNvffei9VqZdu2\nbd5/i8WLFxMfH49e3/F/6LU7tA8I8Cwk4HA4cLvdhIeHt7tSgiAIvZFsd3Ds6dfYcvli6o82fsUa\nMmooY957joRrL0NSi2xAfzKFhPK7O+5CURS2lNm5b1s1rx8zU+Ns/GBOMKq4N83AfYMMpIYHEHXn\nL0l49hE00RHec2q+WcPxK26l/qddXfFj9BkjYoP406z+zBoUzumhgDaXzN9/yufB745TUGP72dcL\nrZOQ0PiHfmJiIsXFxc2e9/HHHzNt2jRSU1NJTU3l8OHDVFRUAPDkk0+iKAqXXHIJkyZN4sMPPwQg\nPz+fnTt3el+TmprKihUrKCsro6KiApfLdc77t6e+PzetY3FxcZPrS5JEQkICRUWNC22dee2O1u4k\nNlmWGTNmDFlZWdx5552kp6f7o15CH9SX8uyE9utp7aV610H23/d/mI/nePepDHpS71xI3PyZSB38\nNWdfpdfpmDjrah7dVcuRWleTY2E6iSvjdYyP0KA6a9aHgIyhJL/6Z8pe/ZC6NZ6eUFdxGTm/epCI\nm+YT87vbURl6XypEd6DXqLguI4YLkkJ4a3shhbWeby4OFJu544sj/GpsHPOGR6NWdcz0xp11b2lL\nqoi/FRQUeJ/n5+cTGxt7zjl5eXk88MADrFy5kvHjxyNJEtOmTfP2LEdHR/O3v/0NgC1btjB//nwm\nTZpEQkICkyZNarY33e12o9FoyM/PJy0tzfv+53P2+XFxcd5jPzfddVxcHIcOHfKWFUWhoKDA59f7\nW7vv9iqVij179pCfn8+GDRv44Ycf/FAtQRCE3sFttXP0qb+zZc4dTQLv0NHpjHnvOeIXXCoC7w5S\nYHHz7IE6/nBW4G1Uw7wEHU8OD2BipPacwPs0dWAAsQ/eTtzj96IKCfLur3jvC7Lm3YF1/9EO/xn6\nsv7hRp64OJU5QyM4HWc73Aqvbyvkd98eJ69a9IK3h6IovPHGGxQWFlJVVcVf//pX5s+ff855ZrMZ\nSZKIiIhAlmU+/PBDDh8+7D2+cuVKbxAfGhqKJEmo1WpmzZpFVlYWn376KU6nE6fTya5duzh27Bhq\ntZo5c+bw7LPPYrVaOXLkCB999NF5A+AXXngBq9XK4cOH+eijj5g3b55PP+vcuXP5z3/+w4YNG3A6\nnbzyyisYDAbGjx/fin8x//Hb8O3Q0FAuv/xyduzYwfTp05scE8vLi7Iv5TPz7LpDfUS5e5d7QntZ\n9cZ7ZL/yAQOKPbnCh2Qzkl7HnN/cQdxVF7Nl904ozu3y5dd7W3nI8LF8mmPh841bkRuyS0IGjMKc\nvYdRJg2LfzGBII3Ezj2e+b/HjhoL0HJ58jgM6QNZ8+RS7EdOkK4KxJ6dyzcLfoXpyku45On/QdJq\nutXy7r2pPH/iJMYmhPDsB99SanYSMmAUh0rNLPrLx1w6KIJHbpyDWiX5dXn5M+8xvXV5eUmSuOaa\na7j66qspLi7msssu43e/+12T4wBDhgzh7rvvZtasWahUKq677jomTpzoPW/Pnj089thj1NXVERUV\nxTPPPOON+VasWMHjjz/O448/jizLjBgxgj//+c8APPfcc9xzzz0MGTKEQYMGccMNN7Bp06afrfOk\nSZMYN24csixzzz33eOPN5uYsP3NfWloar732Gg8//DBFRUWMHDmS5cuXt2pKwW6zvHx5eTkajQaT\nyYTVamXWrFk88cQTTZbaFMvLC77qKwsbCP7RnduLy2zh+NLXOfXGZ02WMTeNG07aI4sxxEV3Ye16\nL4tL5qs8G1/nWbE1TiBDbdYefnHBOOYm6IjUt/1bBkVRqF29nrLXP0KxNva6GoalkfjcHzAMTGlH\n7YXzcckK3x8p55tD5bjPiFzSowP53dRkkkz+WaLeX/cWsby8/+Tm5jJ69GjKyso6fCaS5vh7efl2\nBd/79+/n5ptvRpZlZFnmxhtv5Pe//32Tc0TwLQhCX1L+w1YOPPgstvzGgUDqACOp99xA7JUXdWpe\nYV/hlBX+XWjj0xwrtc6mH2mDgtXMT9TRL9B/q1I6i0opfuGf2A40zhMs6bTEPHArETdfjdTGxT0E\n3+RV23hzeyG51XbvPp1a4uaxcczvwFzw1hLBt/+I4LuVRPAtCEJf4Kis4cgTL1H42aom+8MmZDDw\nodsxxEZ2Uc16L1lR2FjqYHm2hRJb00UxEowqrkrQkYCZp1/4P/7yp+f8+t6KW6Z65b+oeGcFitPp\n3R8wZjgJT/8efWqSX99PaKqlXvCh0QH8bko/ksP80wveHiL49p/c3FzGjBlDaWlprwi+xSgfodvo\nK3OrCv7RXdqLoigUrVzDxikLmwTempAgBv3xLoa98IgIvP1MURS2ljl4YHsNLx6qbxJ4h+skfpWq\n59F0I8NNGtxuJ7v27fZ7HSS1irCrZ5P08pPoB/bz7rfsOsCJubdT/vZnTRZPEvxLo5K4Mj2KP16c\nSrKpcdaZw6UW7lx5hE/2luCW29a32F3uLUKj5ORkysvLuyTw7ghivVxBEIQ2suTkc+gPf6V83ZYm\n+6MunkT/+29GFxbaRTXrvfZVOfkw28Kxs6YNDFTD7DgdU6O1aDsx7UCfkkjS3/6Hyo++ofLjb8Dt\nRrE7KF76KjX/Wk/i0w+h75/cafXpa5JNBh6/KLVJL7jTrfDm9kI25lTz2ynJpIYbu7qagtCESDsR\nBEFoJdnu4OSry8n62zvItsbVE3XR4Qx88FYiLhzbhbXrnQ5XO/k4x8q+KmeT/XoVXBSj5eIYHUbN\nuUF3eUU5v7zjJlZ//n2H19GedYriF97AkZ3r3SfptETfdwuRv7oGSSNywTtSfo2NN7cXcaqqcTCs\nRiWxaHQs142MRtvJC1gVFhYSGxvba3pr+ypFUSgsLGx2EZ4uSTvJy8tjxowZDBs2jOHDh/PSSy+1\n53KCIAjdXsXGnWy66CaOL329MfCWJOLmz2TsB8+LwNvPjtQ4eXJPLY/urm0SeGskT9D91IgArkjQ\nNxt4dzb9gH4kv/QE4TfOg4ZAW3E4KfnL62RdcyfWMwZoCv6XGGrg8V+kcPWIKDQN3364ZIX3dhZx\n98qjHC41d2p9IiMjKSgoQJbl858sdFuVlZWEhvr3W8x29XwXFxdTXFzMqFGjqK+vZ+zYsaxcuZKh\nQ4d6zxE934KvuvPUcUL309ntxVZUxtE//52iFf9usj9ocCoDf38bwUMHdFpd+oIjNU4+Pmll71k9\n3SpgUqSG2fE6wnXn7z8qryjnul8vZO1X/+mgmjbPnp1LyQtvYM861bhTpSLipvlE/+YW1IEiFaIj\nFdTaeXt7IdmVjb3gEjB3WBS3jIvDqG35Wwh/3lscDgfl5eV+uZbQNfR6PREREc0ea2vPd7tyvmNj\nY71LkQYFBTF06FAKCwubBN+CIAg9mdtmJ+cfH5O97D3cFqt3vzrASL/F1xE/fyZSJ3+d3VspisKB\nahcrTp0bdEvAhAgNs+N0RBt8//cOCQ7hjlsW+7mm56fvn0zSsv+h6vNVVC7/CsXhBFmm4p3Pqf33\nBuKfuJ/g6RPPfyGhTRJC9Dz6ixTWnqhixf5SHG4FBVh5sIzNp6r5zYVJjE/q+DEZOp1OzHginMNv\nOd85OTlMmzaNgwcPEhTUuAyv6PkWBKEnUhSF0lUbOPLky1hzC5sci/zFRPr/5ib0UeFdVLveRVYU\ndlQ4WXHKes5ASgkYH6HhslYG3f+fvfsOj6pKHzj+vdOSSS8kIRUSCCShd4LUFRSUYsMV9Ccr0kRR\nEJGmi4oFsYO7orKuFRvgigqoIC0UKaEJSAkphCSkt5mUKff3x8CESEuZZGaS83mePMm59c1wuPPm\nzrnndSSVGRfIXv4JZQePVVvudetAWs6dhia0pZ0iax5ydZV8eiCLPy5UH3YyMNKHqX1DCXDX2Cky\nwdnZdZ7v0tJSBg8ezDPPPMMdd9xRbd3mzZtZuXKlKC8v2qIt2k7T7uwbxJ+LlpGwfTsAcQp3AJKC\n3Am951aGjb8XcJxy6s7aTti3j6OFBk54x3FOZ6I46RBgKQUvAaE5R+ntr2ZY757Adcq/O0FblmV2\nfPQphT9sIrbc8kfEcbMOSa1m0PTJtJh0n3V7e5dzb4ptWZb55PtNbD6Tj7pVZ8BS+VSjVDDj3uHc\n2TGQPbsspc3tff0RbcdtX628vF2Sb4PBwMiRIxkxYgQzZ868Yr248y3UlBjzLdRGQ/QXfWoGp5d+\nQObaX6uVhVd5edBq8r0Ej75ZzFhhAzqDmV8yK1ifXk5uRfWH0VQS9PVXMayl7e50Hzh0wJoQ25up\nqIScD7+iZFP1uaTVoUG0nPcIXsMGiCqoDai4wsjXh7PZnVpUbXkrX1cevymcTi09xHuRUGN2GfMt\nyzIPP/wwcXFxV028BUEQnEFFTj5Jb3/MuU//h2y4bNiDUkHwHcNoNWksai+Pax9AqJHMMhM/nStn\nc1Y55X+pP+OigAEBam4OUuNTgwcpnZXS25OWT03Ge8Qgcv79ufWBTMP5C5yb8Rzu/XrQcu40tDHi\nAd6G4OWiYnLvEAZGevNZYhYZxZYZi1ILypn942mGtvWlg9Fwg6MIQv3U6853QkICAwcOpHPnzta/\n1F955RWGDx9u3Ubc+RYEwVEZikpI+eBrUlZ8hUmnr7bO76YetJ52H+5Rokx4fZhlmSMFBjaeL2dv\nroG/vuF4qCQGB6oZHKjG3QGmC2xMsslM8c/byP14Nebi0qoVkoT3yJsJeuIhNOHB9guwiTOaZTad\nzuf7YzlUXFaj3kUpMbZzEGM7B153VhRBsOuY7+sRybcgCI6mMq+QlA+/Ju0/qzGWVH8Iy6tze1pP\nG4d3lxg7Rdc0FBvM/JZZwS8Z5WSWXTnPcbCrgqEt1fTyUzVoRcrCoiJeev0lXlu8tMHOUV+mklLy\nPvuOoh83w2Ul0SW1Cr9xowl45AFUfj52jLBpy9cb+OrwBfanl1Rb7u+m5qGewQyN9kMhhgIJVyGS\nb8HpiXF2Qm3Upb9U5OST8t6XpH28ttq0gQBukWG0njYOv5u6izG3dSTLMieKjPyaUc7OnEoMV6kt\nEuelZGiQmhgvZaO8zvaa57suKlLSyfvvt+h+P1RtucLdjRYTx+L/f3eh9Pa0U3RN34lsHV8fvsAf\nB37Hq01X6/K2/loe7hVC91BPcW0QqrHLmG9BEARnoEtKI/XDb0j/6sdq5eABtBEhhE+4g8Bh/cV8\n3XWUU25ia1YFW7IqrnqXW6uEvv5qBgSoCdaK1/haXFqHEfL8LMr+OEXuR19TfvwMAGadnuzln5D7\n0bf43T+GFv+4B5W/r52jbXpiA93559BI/lt6hj9UKorKLc9/nMkrY/7GJDq2dOcfPYLpHCz+ABLq\np953vidOnMhPP/1EYGAgR48evWK9uPMtCII9yLJM3vZ9pH7wNTmbd1+x3q1NBBET7qTF4D4i6a6D\nMqPM77mVbMmq4GjBlWO5AVq5KRgYqKaHrwoXpX3uGObm5fLA1AfZuHq9Xc5fV7Iso9tzkLz/fkvl\nX+aZl1xd8Lv3dlpM+jvqoAA7Rdi0lRvNbDyZx8aTeVSaqvfuriEeTOgRTIcg8RB2c2e3YSc7duzA\nw8ODBx98UCTfgiDYnVGnJ3PtL6R++C2lp5KvWO/RPorwf9yJf/8eSAqRdNdGuUlmf24lO3MqScyr\npPIqw0q0Sujhq6J/gJpW7vZ/WM1Zk+9LZJOZkq27Kfj6xyuTcLUa75F/w/+BO9F2bGenCJu2gjID\nP57IZfvZQv6Sg9MzzJO/dw6ic7CHGI7STNlt2MmAAQNISUmp72EEQYz5Fmrl8v4iyzKF+/8gfdUP\nZH2/+Yrx3EgSfv26E/r3EXh37yDeKGtBbzRzMN/AruxK9l8j4ZaAWC8lfVuo6OKjQtOAD1DWhcHg\nvFPHSUoFXjffhOeQeEp3HaDgy3VUJKUBIBsMFH73M4Xf/Yy2Wxz+D9yJ1y0DUWjUdo7aue3bs8ta\nqMdXq+b/ugczor0/647nsiu1yPpM7P70EvanlxDdQss9nYIYGOmD0sH6vuCYxJhvQRCcVkV2Hhmr\nfyb9yx/QnU69Yr1S60rQyMGE3DMcbZgo4V1T2eUm9udWsi/XwB+FBozX+Hw0TKugp5+KPv4qh52b\n28vTi6kPTbF3GPUmKRR49u+Fx0090e89TP5XP1B+4ox1fdnB46QfPI4qYAW+f78d3zuHoxF93mZa\nuGuY2CuE22NbsO5YDnvSiq1DrU7nlvHKlhQ+2qfhzo4BDG/nj5vG/p/6CI7LJrOdpKSkMGrUqGsO\nOxHl5UVbtEXbVm1DYTFt8irIWreZhISdIJut5d+Pmy3TBvaIjCZ49M0kh3mj1Lo4TDl1R2336NqT\nE0UGvkv4ndMlRvQhVeW3AevMD8VJh/DXKBjepyfd/VSc//Pgxf3tX769ObZ3r/uB0p37aX3sHBhN\n1v5/6f9DUruWePbvxaBHp6D0cHeocu/O3s4qqWDl2l/4I0uHW1QXoOr/S2D77gyO8iWo6BQRPi4M\nGDAAcIzrp2g3kfLycOPkW4z5FgShPsov5JL9cwIXfviNvJ2JYL5y7INS60qLm+NpOWoInh2ixdCS\n6zDJMimlJo7kGzhcYOBEkeGqw0kuCXdT0NlbSXc/FSFacUfP0RjzCynasJWin7Zgyi+8Yr3kosFr\nWH+8b/8bHjf1ROGisUOUTVNxhZEtZwrYfKaA0krTFetb+7oyor0/N7f1w8tVDDZoauw6z7dIvgVb\nEGO+hUvMRiNFB46Rs3k3Ob/tpuSP01dsc9ysI07pgVeXGIJuG0TAkL4o3VztEK3jqzDJnCo2cqLI\nwIlCIyeLjZT99emxy6gkaOeppLOPik4+SvwcdEhJTR04dMB6t7gpkw1GSncfoPjXBPQHjlYr2HOJ\nws0VjwG98RraH89BfcS84Vdx+Zjvmqo0mdmVUsSmM/nWkvWXUysleoZ6MSDSh/hW3riLYSlNgt0e\nuBw3bhzbtm0jLy+P8PBwXnjhBR566KH6HlYQhGZENpsp/fMs+bsPkb/7IHk79mMsKrn6xpKEV+f2\nhLQNoPf/jcMlwK9xg3VwJrPMOb2JM8VGzpRYvlJKTVfM1PBXQa4SsV4qYryUtPdU4mqnqQGFupPU\nKjwH9sFzYB+M+YWUbNlD8aYEKpPPWbcx68sp/nk7xT9vB5US915d8LipJx7x3XGNbYOkFElhXWiU\nCga38WVQlA9J+WVsP1vI3nPF1mkKDSaZ3WlF7E4rQq2Q6BHmycBIX/pGeOHhIu6INzeiwqUgCI3O\nqNNTfPQURQeOkb/nEAV7j1w72QYklRKvzjH4D+xFi8G9RcJ9UanBTKrORGqpiVSdkdRSE8mlxusO\nIbnEWy0R7akk1ktJjJfz390Wrq3ibBolW3ZTuisRw/msa26n9PbEvU9X3Pt2x71PF1yiIsR0nPVQ\nZjDxe1ox25MLSSkov+o2CslS3KdHqCc9wrxo18JNzJjiRER5eUEQHJKhsJjSk8kUHfmT4sN/UnT4\nJLozqXCDS48m0A+/+G749u2KT4+OqNy1jRSxYzHLMrkVZjL0potfZs7rTZzTm8irqEGWfVGwq4K2\nngraeChp66HETyM1i3HxhUVFvPT6S7y2eKm9Q7E7WZYxnMukdNcBSncnUnHy7HW3V3i4o+3UHm3n\nGNw6x6LtEota/OFbJxdKKtmXXsz+9GLSCiuuuZ2HRknXEE86tXQnNtCdNv5a1KIImMMSybfg9MSY\nb+dlNhopz8ihLC0D3ZlUSk+lUHoqGd2pFCqy82p0DLWfN95dY/HuEoN39w64RYZdNzncfWCfddYO\nZ2aSZYoqZfIqzGSXm8guv/i9zGz9uSZ3si/nq5Fo5aaglbuSVu4KItyUuKuafqJ9Nbl5ufx94jg2\nf/+rvUNxOIacfPSJf1B26Dj6Q8cxFRTdcB9VC19coiNxjW6NS7tIXKMjcWnbCqWHeyNE3DjqMua7\nNi6UVrL/XDH7z5eQeo074peolRLR/m7EBLrRPsCd1r6uhHm7iITcQdhtzPfGjRuZOXMmJpOJSZMm\nMXfu3PoeUmimjh49KpJvByTLMsaiEsozcyjPyqEiM5eKCzmUZWRTlppBWVoGZelZyMYrn/S/JoWE\nW6tQPNpH4d0lBq+uMWjDg2t1J/bYyZMOm3ybZRmdUabEIFNUaabQYKaosurnggqZ/Aoz+ZVmCirN\nV3surkZUErR0VRDqpiBEqyBUqyDcTYGXWrwxX85oNNo7BIekDvDD+9aBeN86EFmWqUw9T9nhE+gP\nH6f8RNJVk3FjbgHG3AJ0uxOrLVf6eqOJCEETHowm3PJdHRKEOrAFqqAWKD3cGuvXqrc/j//RoMl3\nkIeG22NbcHtsC4orjBy/oOPYBR3HsnQUllfvqwaTzPFsHcezdUAOAEoJwrxdaeXrSmtfV0K9XWnp\nqaGlhwYfrapZfKLl7OqVfJtMJh577DE2bdpEaGgovXr1YvTo0cTGxtoqPqEZuTR3pmB7sixjrqjE\npCvDqCvDpNNjLC7FUFSCoagEY1EphuJSDIXFVOYVUJlXiCG/iMq8QirzCjCXX/n0fk1JGjVuEcG4\nt22NR0wkHu2j8IhuhVJbv5lJikuvPUa8LmRZxihbZgapNFu+l5tlyo0y5SbLV9nF7zqjjN4oozdZ\nvuuMl5JtMyUGy8+2/EjRQyUR5CoR5Kog0EVBkKvlK9BVQineaG+ogT/gbRIkScKldRgurcPwGTPM\n8v8hO4/yk0mUnzxL+Z9nqTiTglxx9WuBqaCIsoIiyg6fuOp6hbsbqkB/1EEtUPn5oPT1QunrjcrX\n29L29kTh4Y7Swx2FpztKT3ckVxe7JJIlxcWNdi4vFxV9I7zpG+GNLMtkFFdyIlvH2fwyzuaVka27\nsjqrSYbUwnJSC8vZnlx9nYtSIsjThSAPDX5uKvy0anzd1PhqVfhq1fi4qnB3UeKpUaJRiT/S7aVe\nyffevXtp27YtrVu3BuC+++7j+++/vyL5/v37HfU5jdBMnD+ZZpu+cq332au+AV9j48u3lf+yrNo6\n2fLGLssXt7vsZ1kG2WxZZDZX7Wc2g8nSls1mS9ssg9mEbDKDyQRms/Vn2Wi6+N0IRqNleWUlssEI\nBgOywYhcaYBKA3JFBXJFJXJFBZRbvsvlFchlZZZzNiRfb6TAAKTgIAgPgbAQCA9FDgygTKlAL0P2\nxZdTLgK5qOLiyyRjpuplM1u/y5aX5bLlZlnGJIMZOFJg4NMkHWYZjLJl+IbJbHljMl3czmAGoyxj\nNFuWGcxgMF/8flm70ixTabIc1x48VOCjVuCrkfB3UdDi4nd/Fwl/jQK3ZjpkRLAfSZJQB7VAHdQC\nz4F9AMt1zJCVQ2XqeSpT0qlISacyJR1DRjay4cok8XJmnZ7KZH21mVduSKVEoXW1fLlpLd9dXZDc\nXFFo1EgazcUvNQoXDZJahaRSIalVoFIiqdVIKqXlS6EEpRJJqaj6rlBYknulwvJgqSSBJFGRlErx\nrzus7UtfkiSBBHBxmeWFuriMqj8UrvUHQw3+kPAG+gJ9JQn8QO9pIrO4gvPFleToDOSWVlJccf1P\nGWUg6+LX9SgVoFUrcVUpcFFJaJRKNErp4pcCtVJCpZRQSRIqRdXPSoWEQgKFQkKBhEIBCklCwvIA\n6aXXSWl9YSzLLT9WvV4XV131+5UNx6QOr9twq3ol3+fPnyc8PNzaDgsL4/fff79iu4KpYiiKcGNp\nhgwKNhyydxjCVVRqNJR6+VDq6UOplzc6L8v3It8WFPn6U+Trj1HjcuWO+UC+vkFiOpucTlHa9cdL\n2pNWCW5KCU+1hKfK8t3r0ne1hI9agY9GwlstoRazGzQok7kWQ6KEa5IUCjQhQWhCgiC+6lku2WzG\nmFeIITMbQ1Y2hoxsDFk5GHPzMeUVYMwtvGFyflVGE+YSHeYSnQ1/ixs7Y8gg7ZdjjXrO61ECERe/\nHJEZ+924sLfA9e/Wab96Jd81+TiotLS0zsEJzcsiewcg1FMjf7Tf/enGP2et3Tg+PTTfd65GoPZ1\nYf369RSZbTtMSfgLfzX4h0LHUNSA2t7x1IN4LxJqqrS0tE771Sv5Dg0N5dy5qo+Qzp07R1hYWLVt\nxowZU59TCIIgCIIgCEKTUa/R9j179uT06dOkpKRQWVnJ119/zeidE0yvAAAgAElEQVTRo20VmyAI\ngiAIgiA0KfW6861SqXj33Xe59dZbMZlMPPzww2KmE0EQBEEQBEG4hgYvsiMIgiAIgiAIgoXNJnnc\nuHEjMTExREdH8+qrr151m8cff5zo6Gi6dOnCwYMHbXVqwcncqK988cUXdOnShc6dO3PTTTdx5MgR\nO0QpOIqaXFsA9u3bh0qlYu3atY0YneBIatJXtm7dSrdu3ejYsSODBw9u3AAFh3Kj/pKbm8vw4cPp\n2rUrHTt25OOPP278IAW7mzhxIkFBQXTq1Oma29Q6v5VtwGg0ym3atJGTk5PlyspKuUuXLvLx48er\nbfPTTz/JI0aMkGVZlvfs2SP36dPHFqcWnExN+squXbvkwsJCWZZlecOGDaKvNGM16S+XthsyZIh8\n++23y6tXr7ZDpIK91aSvFBQUyHFxcfK5c+dkWZblnJwce4QqOICa9JdFixbJ8+bNk2XZ0lf8/Pxk\ng8Fgj3AFO9q+fbucmJgod+zY8arr65Lf2uTO9+XFdtRqtbXYzuXWrVvHhAkTAOjTpw+FhYVcuHDB\nFqcXnEhN+kp8fDze3t6Apa+kp6fbI1TBAdSkvwAsX76ce+65h4CAADtEKTiCmvSVVatWcffdd1tn\n5WrRooU9QhUcQE36S3BwMMUXq10WFxfj7++PSlWvR+UEJzRgwAB8fX2vub4u+a1Nku+rFds5f/78\nDbcRSVXzU5O+crn//Oc/3HbbbY0RmuCAanpt+f7773nkkUeAmtUfEJqemvSV06dPk5+fz5AhQ+jZ\nsyefffZZY4cpOIia9JfJkydz7NgxQkJC6NKlC++8805jhyk4gbrktzb5E66mb3byX57tFG+SzU9t\n/s23bNnCRx99xM6dOxswIsGR1aS/zJw5kyVLliBJErIsX3GdEZqHmvQVg8FAYmIimzdvRq/XEx8f\nT9++fYmOjm6ECAVHUpP+8vLLL9O1a1e2bt1KUlISw4YN4/Dhw3h6ejZChIIzqW1+a5PkuybFdv66\nTXp6OqGhobY4veBEatJXAI4cOcLkyZPZuHHjdT/uEZq2mvSXAwcOcN999wGWB6Q2bNiAWq0WNQea\nmZr0lfDwcFq0aIFWq0Wr1TJw4EAOHz4sku9mqCb9ZdeuXSxcuBCANm3aEBkZycmTJ+nZs2ejxio4\ntrrktzYZdlKTYjujR4/m008/BWDPnj34+PgQFBRki9MLTqQmfSUtLY277rqLzz//nLZt29opUsER\n1KS/nD17luTkZJKTk7nnnnt47733ROLdDNWkr4wZM4aEhARMJhN6vZ7ff/+duLg4O0Us2FNN+ktM\nTAybNm0C4MKFC5w8eZKoqCh7hCs4sLrktza5832tYjvvv/8+AFOnTuW2225j/fr1tG3bFnd3d/77\n3//a4tSCk6lJX3nhhRcoKCiwjuFVq9Xs3bvXnmELdlKT/iIIULO+EhMTw/Dhw+ncuTMKhYLJkyeL\n5LuZqkl/WbBgAQ899BBdunTBbDazdOlS/Pz87By50NjGjRvHtm3byM3NJTw8nOeffx6DwQDUPb8V\nRXYEQRAEQRAEoZHUe9jJK6+8QocOHejUqRPjx4+noqLCFnEJgiAIgiAIQpNTr+Q7JSWFDz/8kMTE\nRI4ePYrJZOKrr76yVWyCIAiCIAiC0KTUa8y3l5cXarUavV6PUqlEr9eLGUwEQRAEQRAE4Rrqdefb\nz8+P2bNnExERQUhICD4+PgwdOtRWsQmCIAiCIAhCk1KvBy6TkpIYNWoUO3bswNvbm7Fjx3LPPfdw\n//33W7f5+OOPq1X+EQRBEARBEARnV1paypgxY2q9X72Gnezfv59+/frh7+8PwF133cWuXbuqJd/h\n4eF07969PqcRmonp06fz73//295hCE5C9BehpkRfEWpD9BehphITE+u0X72GncTExLBnzx7KysqQ\nZZlNmzaJOVOFOouIiLB3CIITEf1FqCnRV4TaEP1FaGj1Sr67dOnCgw8+SM+ePencuTMAU6ZMsUlg\ngiAIgiAIgtDU1LvC5dNPP83TTz9ti1iEZs7b29veIQhORPQXoaZEXxFqQ/QXoaHVu8iOINhKp06d\n7B2C4EREfxFqSvQVoTZEfxEaWoOXl9+8ebN44FIQBEEQhGantLSUoqIiJEmydyhCHSmVSgIDA6/6\nb5iYmMjNN99c62PWa9jJyZMnue+++6zts2fPsnjxYh5//PH6HFYQBEEQBMGp5eXlARASEiKSbyem\n1+vJzs4mKCjIZses17CT9u3bc/DgQQ4ePMiBAwdwc3PjzjvvtFVsQjOTkJBg7xAEJyL6i1BToq8I\ntWGr/lJRUYG/v79IvJ2cm5sbJpPJpse02ZjvTZs20aZNG1FQRxAEQRAEQRCuod6znVzy1VdfMX78\neFsdTmiG+vfvb+8QBCci+kvjkWWZiuw89Mnplq+UdPQp5ylLy0Tp5oo2PPiyr5a4tQ7DNTjA3mFb\nib4i1IboL0JDs0nyXVlZyQ8//MCrr7561fXTp0+3Tlrv7e1Np06drJ370sc7oi3aoi3aou1Y7c3/\n+4HczbsJ2nWC8vMXOG7WARCncAe4bturcwyZvdriP7Ang2+9xW6/T0FBAUuXLmXHjh12fz1Fu3m1\ni4qKCAkJwVn4+/szffp0Fi9eDMDy5cvR6/XMnTu3Rvunp6fz+OOPk5GRgSRJfPPNN9VGQ8ybN49V\nq1aRlpbWIPE3tISEBI4ePUpRUREAaWlpTJo0qU7HsslsJ99//z3vvfceGzduvGKdmO1EqKmEhATr\nRUsQbkT0l4ZhNhrJ2bSL9M++J2fL72A21+t4ClcNQbcNJmz8SPz6dUdSNO4Mt1lZWdx0000kJSU1\n6nkF52Wra0tGRoZTJd/BwcEEBwezadMm/Pz8ePfdd9HpdDVOvkeNGsVTTz3FoEGD0Ov1SJKEVqsF\n4ODBg3zwwQf89NNPTpl8X+vf0i6znVzy5ZdfMm7cOFscShAEQbAD2WQi9b9rSF7+ORUXcq9Yr3TT\nom0VgjYsCNeQILRhLXENCcRUXkFFZg7lWTmUZ+ZQkZlD6ZlU5EoDAObySjLX/kLm2l9wiwwj5oUn\nCBx2U2P/eoIg3IBarWbChAm89957LFy4sFb7/vnnn5hMJgYNGgRYHlK8xGQy8dxzz1mTb8EGybdO\np2PTpk18+OGHtohHaMbEXUyhNkR/sZ2iIyc59tSrFB/584p1Pj070XL03/Af0BOFRl2j4xmKS8n5\ndScXftpK6clk63J9cjqJ/zeHoJFDiH1xJq4tG2dcuKtvIFuTCvjjQiknsnXoK82YZBmzLGMyg8ks\no1RIRPq5EhPgTvsAN2IC3fF2tcn9KcHJNOdry8SJExkwYAAzZsyotnz16tUsX778iu2joqL473//\nS1JSEt7e3jz44IOkpaUxaNAgFi1ahEKh4MMPP2TEiBE2narP2dX7yuLu7k5u7pV3SQRBEATHZtTp\nObN0JSkfflNteIna34eWtw0iaOQQtGEta31ctZcHIXffSsjdt1J6KoULP20l++cdGEssY8Iv/LiF\n3K2/027BI0RMuANJqbTZ7wRgNMskJBeyL72Yw+eLCJ32b17eknLD/fL0Bvanl1jbwZ4aOgd7cHtM\nC2IC3W0aoyA4Ik9PT/7+97/zwQcf4Orqal1+zz33cM8991xzP6PRyO7du9m+fTuhoaFMnDiRVatW\ncfPNN7Nu3Tp++OEHGrimo1MRf9YLDkOM4RVqQ/SX+sn+dSfH571O+fkL1mWSRk3EP+4ibPwoFGrb\nvD14tGuNR7t/EPHQXST/exUXftoKgKlUz4kFb5Dx7QY6vD4Xrw7R9T5XaYWR9Sfz+N+xHHJ1Buvy\n4qRDeLXpWuvjZZZUklmSz8+n8okLdOeODgH0j/RBpRDzNjdlzf3a8sgjjzB48OBqM9h9++23vPvu\nu1dsGxkZyccff0xoaCidOnWyTq5x++23s3//foKCgkhOTqZHjx6ApWBNr1692LdvX+P8Mg5KJN+C\nIAjNiNlo5OTz75L64TfVlnv36ED0nElow4Mb5LxqHy/aLZhG4PABnHntP5SlZQBQdPA4e26bTMe3\nFxBy5y11OnZmSQX/+yOHjafyKDNc+YCoUoKYADeiW7jRLkCLn5sapSShkEAhSSgVEuUGM8kFZZzN\nK+NsfhlphRUYzVV36o5n6zieraPFXjWj41pwW/sWeIlhKUIT5OPjwx133MHnn3/OAw88AMDYsWMZ\nO3bsNffp1q0bRUVF5OXl4e/vz7Zt2+jRowfDhg3jxIkT1u0iIiKafeINNki+CwsLmTRpEseOHUOS\nJD766CP69u1ri9iEZqY532kQak/0l9ozFJVwaOqz5G3da12m8vYkasb/ETh8QKNU4vPp3oHun7zK\nuc/Xce7T75ANRswVlRx55Dl0p1JoO2dSjWdEKakwsnJvBj+fysP8l0+0vVyUDIrypVOwO63vjrnh\n3WpvVwjy1NA3whsAg8lMSkE5284WsvdcsTURz9UZ+GhfJt8eyWZqn1CGRfuJCoZNjLi2wKOPPsrK\nlStrvL1SqeSFF17gjjvuQJZlunbtyoMPPtiAETq3ek81OGHCBAYNGsTEiRMxGo3odDq8vb2t68VU\ng4IgCPanS0ojccLT6M5UTfPlP7AX0XMno/bxsktM+tTzHJ//BmWpGdZlQbcPptOyZ1G5a6+5nyzL\nbDtbyHt70ikoM1ZbF+Kl4ZZ2/sRHeKFW2mZaw6JyI1uSCtiaVEBxRfUy091CPHmifzghXi42OZfQ\ndDjbVIPCtdl6qsF6XZmKiorYsWMHEydOBEClUlVLvAWhNi4VKBCEmhD9peZyt+1l922TqyXe4f+4\ni9iXZtkt8QZwaxVK1w9exLdPF+uyCz9t5fcx0yi7bCz65S6UVPLsL2d5eUtKtcQ7NtCNWQPCWXxL\nFAMjfaol3vv27KpXnN6uKu7oEMBrt7fl4V7B+LtVzfpyMKOEqWtO8M3hC5j+evtdcEri2iI0tHol\n38nJyQQEBPDQQw/RvXt3Jk+ejF6vt1VsgiAIQj2lfrSGA+NnYyyyzOKh0Khp//zjtJ58b6MXvLka\nlYcbHZY+TcjYEdZlJX+cZvfwhyk6eNy6zGSWWXM0m0lrTrD3XLF1uY+rikf7hTJnUCs6tfRo0CEg\naqWCm1r7sPjWKG6J9uPSmSpMMiv3ZfDY9ydJzi9rsPMLgtA01GvYyf79+4mPj2fXrl306tWLmTNn\n4uXlxQsvvGDdZvPmzaxcuVKUlxdt0RZt0W7k9jezniX9i3XW8u+nPBW0nvJ3br5rDAC7D1gefIrv\n0csh2j8ue5+MrzcQi2WKs5OuZtr/8zH6jb+PV7aksGX7DgC82nRFAtqUJTEwysf6+166w92rb79G\naa/7ZQsbT+ZR3rIDYJlVRaNU8PLDY+gf6WP3f3/Rtm/7xIkTxMbGIji/jIwMzp49e9Xy8nUZdlKv\n5DsrK4v4+HiSky1FFBISEliyZAk//vijdRsx5lsQBKHxnXnjI868VvXAlEdsG+JemY1LgJ8do7qx\nwsRjnFj4FsbiUgAUHm6sn/Q4x1uEW7cJ9XLhHz2DaeN/7XHhl+Tl5DD1wXGs3rCpQeI1mmV+OZXH\n98dyMVw27OSBbi15oHtLFOJhzGZLjPluOhxqzHfLli0JDw/n1KlTAGzatIkOHTrU55BCMybG2Qm1\nIfrL1cmyzOlXP6iWeHv36EDn5c86fOINltlQOi9/FpWPJwDmUj1D3nub4LSzANwe48+iYZE1SrwB\nzLKZrMyMG29YRyqFxG0xLXh2aGsC3KvGgn9+MIvnNyWjrzRdZ2/BEYlri9DQ6j3gb/ny5dx///10\n6dKFI0eOsGDBAlvEJQiCINSSLMucenkFSW99bF3m07szHV6bi1Lreu0dHYwmKoI/n5yN3s0DAJeK\ncu7+5F887lXC3Z0CHbLITZi3K88OjaRDUFUlzN2pRTyx7hTniyrsGJkgCI6m3sl3ly5d2LdvH4cP\nH2bt2rVithOhzsTcqkJtiP5SnSzLnHz+XZKXf2Zd5hvfjQ5LnkLporFjZLVTXGnm2YPFrFMEsHri\n49YEXFNRjmbe8+gT/6j1MTWaxvn9PTRKZvYP55Z2VZ8wpBaWM+P7kxy7UNooMQj1J64tQkOz/6Pu\ngiAIQr3IsszJF/5Fyoovrcv8+vcg7uUnUThR4p1dZmJ+YhEniy1TCOa2DOXYrCdReF8cgqIvI+Xh\nueiP/GnPMK9LqZC4r0sQk3qHWO/Ql1aamL8hiYPnS+wcnSBUOX36NAMHDiQiIoIPPviARx99lJde\neslu8bz11ls88cQTdjt/YxLJt+AwxDg7oTZEf6mS/O5npLy3ytr2H9iL2BdnodCor7OXY0kuNTIv\nsYiMMkt5eAm4O0zDuP5RhL06D+XF+cjN+jJSpy6gIiW9xseurKxsiJCvq18rb+YPaYWXixKAcqOZ\nZ35OYndqUaPHItROc7m2LFu2jIEDB5KWlsaUKVMAajxV56hRo/jss89uvGEtzJo1i3feecemx3RU\n9U6+W7duTefOnenWrRu9e/e2RUyCIAhCDZ37Yh2nXlphbfsP7EXM4idQqFV2jKp2/igw8ExiMQWV\nltlCVBJMinJlaEsNkiTh0jqM0CVzUXhaxlOb8gtJeXguhpz8Gx7bz78Fzy95vUHjv5ZIPy1zh7TC\nV2v5tzCYZZ7fdJYtSTeOWxAaWnp6Ou3bt6+2rKYT4Nl6Pn2Tqe4PJhuNxhtv5GDqnXxLksTWrVs5\nePAge/futUVMQjMlxtkJtSH6C2T9tJVjc5Za297dOxDz3AwUKudJvHdlV/D84WL0JsubvqsSZrTT\n0t2v+u/g0jqMkOefRLo4jMaQnknqlHmYSnXXPb5SqeTm4bc1TPA1EOzpwvwhrQm8OBOKWYYlW1JZ\n/2eu3WISrq85XFvGjBlDQkICc+fOJSIigqSkpGrrCwsLue+++2jXrh1RUVGMGzeOjAzLrEEvvvgi\nu3fvtu47b968K46flpaGv78/n3zyCR06dCAuLo53333Xun7JkiVMmDCBadOm0apVK1atWsWSJUuY\nNm2adZsNGzYQHx9PZGQko0ePts6sB5bnDZctW0b//v2JiIjAbDbb+iVqUDYZdlKPqcIFQRCEOshL\n2M/hRxbBxTcdj/aRxC2Z7VRjvDeeL+f1Y6UYL76FeKslZrfX0s5TedXttXFtaTl/OlyszFl+/Axp\njy3CbIdhJbXRwl3NvCGtCPVyAUAG3k44x5qj2fYNTGi2vv/+e+Lj41m6dClpaWm0adOm2npZlnng\ngQc4cuQIR44cwdXVlblz5wLwzDPPVNt3yZIl1zzPzp072b9/P6tXr2bZsmVs27bNum7jxo2MGTOG\n1NRUxo4dW+1u+pkzZ5gyZQpLlizhzJkzDB06lPHjx1e7y7127Vq++eYbkpOTUThAtd7aqPftEUmS\nGDp0KEqlkqlTpzJ58mRbxCU0QwkJCc3ijoNgG825vxQd/pPECfOQKw0AaMOD6fDGPFTubnaOrOZ+\nOFfGR2f01naQq8SMaC3+Ltd/E/Xo243Ax/9B9tsfAaDbncj5ea8S9vpCpGu8Ae/bs8taldJefLRq\n5g6O4M0d50gpKAfg/d/Po1ZKjI4LsGtsQnWNdW25ZeVBmx3rl0nd6rTftW6e+vr6MnLkSGv7ySef\nZMyYMTXa93JPP/00Wq2WuLg4xo8fz5o1axg0aBAAvXv3ZsSIEQC4urpWO953333HLbfcYt12xowZ\nvP/+++zdu5d+/fohSRJTpkxx2iJG9U6+d+7cSXBwMDk5OQwbNoyYmBgGDBhQbZvp06eL8vKiLdqi\nLdo2aJdnZKN4fiUmnZ7jZh0qb0/uf3sBGl9vu5eHr2n7QkBHPknSU5x0CIDOnbvzaFstJ48lkgL0\n6NoDgAOHDsDV2sMHYcovZMfHlge+4n7agirAn/QhXYEry8Ff0tjl5//aPnFwL39zNZPQIoxTuWUU\nJx3i5aRDuDw0mlvb+TtE/xLtKvU9XlFRkcMnh9cau63X61m4cCG//fYbhYWFAOh0OmRZtu5Tk3Hf\noaGh1p/DwsI4fvy4tX291yYrK4uwsLBqcYaGhpKZmXnVYzeGhISEq5aXr4t6lZf/q+effx4PDw9m\nz55tXSbKywuCINhGZW4Be0ZNRZ9smelD5elO538/h3tU+A32dByrU/R8kVxmbUe5K3isnRatsnYP\ncMmyTM6/PqPox83WZcH/fBz/+++wWawNpcxg4s3t50jKt7wOEjBvSGuGtPG1a1yCbd2ovLy973yP\nHj2ae++9lwceeACARx99lNDQUBYsWMBrr73Gjh07+M9//kNAQABHjx5l8ODB5OTkoFAoGDNmDGPH\njrXu+1dpaWl069aNPXv2EB0dDcBzzz1HQUEB77zzDkuWLCElJYUVK6oeFr982euvv87x48f56CPL\nJ1yyLNOxY0c+/PBD+vXrR9euXa2ztTQGW5eXr9edb71ej8lkwtPTE51Oxy+//MKiRYvqc0hBEATh\nKkxlFRyY8LQ18VZo1HR4fa7TJN6yLPNNShlfpVQl3tEeCqZHa3GtZeINljthAY88gLGgCN3O/QBk\nvvgumvAQPAdWzbyVl5PD1AfHsXrDpvr/EjaiVSuZNSCcpdtSSSusQAZe3ZqCRilxU2sfe4cnNJK6\nDhWxpb/ef73U1ul0uLq64uXlRUFBAUuXLq22XUBAACkpKTc8/htvvMFbb71FSkoKX375Je+//36N\n4hozZgzvvPMO27dvJz4+nhUrVuDq6tpkZtWr1wj1CxcuMGDAALp27UqfPn0YOXIkt9xyi61iE5qZ\n5jK3qmAbzam/yGYzRx57nqIDxywLJIn2z83Aq2M7+wZWQ7Issyq5euLd3lPJo3VMvC+RlApazpmC\nS7tIywKzmXMzX6D85FnrNmbZTFZmRp3P0VDcNEpmD4wgxMvygKxZhpd/S2F/erGdIxOa07Xlr0NH\nLrWnTZtGeXk50dHRDB8+nJtvvrnatlOnTmXdunVERUUxf/78ax6/X79+9OzZk7vuuovHHnuMwYMH\nW89ztXNfWhYdHc2KFSuYO3cu0dHR/Prrr6xatQqVE83kdD02HXZyNWLYiVBTzfkBOqH2mlN/+XPR\nMlLe/8rajnriQULvtd/0ebUhyzJfJJexJrUq8Y71UjKtrSsahW3mCjbmF3Ju5gsYs/MAUIcEEvXN\nv1EH+JGTfYE7bxlCwqHjNziKfRSWGViyNZXsUsvDsxqlxMvD29A52NPOkTVftrq23GjYSVN2adjJ\npWEqzs7Ww06c/xURmozmkkgJttFc+kvqym+rJd4hY0c4TeIN8HVK9cS7o7eSR2yYeAOo/HwIeX4W\nCjdXAAwZ2aQ9shBzmWVWEY3Gcadf9NGqmTOoFf5ulnnAK00y//zlLEl5+hvsKTSU5nJtEexHJN+C\nIAgO6sLG7Zx49m1r239gL6Jm/J8dI6qdb1L0fJ1SPfGe0sYVtQ0T70tcIsNpueBRuHjssqMnSZ+7\nBNkJim/4u6mZMygCb1fLR+p6g5kFG5PIKK6wc2SCUHe2roLZlNgk+TaZTHTr1o1Ro0bZ4nBCM9Wc\nxtkJ9dfU+0vRweOWIjoXRwZ6xrWl/aLHkJTOcc9kTWoZX142q0kHr4ZLvC9x79mZgEeq/jgp/nk7\npR98TaWDF+EBCPTQMHtgOG5qy79vQZmR+RvOkKc32Dmy5qepX1saQ0REBLm5uU1iyElDsMmr8s47\n7xAXFyf+yhEEQbABfVomB/5vDuYyy51P15BA4pbOQenqYufIaua7tDI+P1s1bCLWS8nUtg2beF/i\nM+pmfO6oevBf/8U65t9x9enQHE2YtyuP9w+3vk6ZJZUs3JhEaYXxBnsKguBM6p18p6ens379eiZN\nmiTKzAv1IsbZCbXRVPuLoaiEA/fPpjK3AACVlwcd3piHxtfbzpHVzA/nyvg0qSrxbu+pZFoD3/H+\nqxaTx+HWu4u13Xr1VnT7jzTa+eujXQs3HokPvTR6hrP5Zfzz17NUGB1/+ExT0VSvLYLjqHfyPWvW\nLF577TXx0YIgCEI9mSsNHJw4H93pFAAktYq4V2bjFuEcMyasT69eMj7aQ2F5uLIe0wnWhaRUEDzv\nETStLRXyZIORtEf/SUXa+UaNo666hnjyUM9ga/uPLB0v/5aCySxucAlCU1CvjPnHH38kMDCQbt26\nibveQr2JcXZCbTS1/iLLMn889Sr5OxOty9otfATvrrF2jKrmfj5fzoenqxLvNhcL6Lg0cuJ9icJN\nS8jzs1D6enPcrMNUWEza1IWYikvtEk9t3dTah3s7B1rbu9OKeDshTbzXNoKmdm0RHE+9ZivftWsX\n69atY/369ZSXl1NcXMyDDz7Ip59+Wm276dOnExERAYC3tzedOnWyfqxzqZOLtmiLtmg353bSWx+z\n6atvAYhTuNNqyt9J8tOQdGAf8T16AbD7wD4Ah2vrgjux4pSO4qRDAHTt3J3HorUcO2r5Q6JH1x4A\nHDh0oFHbRzJTqRw3DGnFF2CGg2dOcGLCdEZ98xGSWsW+PbsA6NW3H4DDtf0LThJTWcCfmigAvt3w\nG3mnfHl50h2AY/XfptS+pL7HKyoqarbzfDdFCQkJHD16lKKiIsAyl/mkSZPqdCybFdnZtm0br7/+\nOj/88EO15aLIjiAIwvVlrN7IkcdesLaDRg4het4Up3iI/bfMct79U8elN5LW7goej9aiVTlO7CVb\n95C15D1r2+++UQQ/N9MpXl9ZlvloXyY7U4usyx7pG8qdHQOvs5fgCBy9yE6XLl1YtmwZgwYNumLd\n7t27mTlzJr///nujxbNq1So+//xz1q9fb5PjXSpr/84779T7WA5dZMcZLmSCIAiOJHfbXo7OfMna\n9unZibZzHnaK6+m2rIpqiXe4m4IZDpZ45+XnMfXz5fg9cId1Wf5XP5D38Wo7RlVzkiQxoWcwnYM9\nrMve23OeLUn5doxKaAquVuL9kvj4+EZNvBvCrFmzbJJ4N4ccP5kAACAASURBVASbJd+DBg1i3bp1\ntjqc0AyJcXZCbTSF/lJ89CQHJy5ANpoAcIsKJ/alWShU9RoR2CgSLlSw7ESpNfEO0yp4op0WNwdK\nvMFy5/hCTjZ+99+Bx+C+1uVZr66g6Oftdoys5lQKiUf6htLGX2td9tq2NPanF9sxqqarKVxbmjuT\nyVTnfY3Ghp/aU0xRIgiCYAf61AwO3P8UJp3lIUWXIH86vjkflYebnSO7se0XKnjreCmXJr8LuZh4\nuztY4n05SZIIevJhXOOiLQtkmfQ5L6M/fMK+gdWQi0rBE/3DCfHSAGA0y7ywKZmTOTo7RyY4s8TE\nROLj44mKiuKxxx6josJSWyAhIYGOHTtat3v77bfp0aMHERERxMfH89NPP1nXnT17lpEjR9K6dWui\no6N5+OGHretOnTrFnXfeSZs2bejTpw//+9//rOvy8/MZP348rVq1YujQoSQnJ18zzrS0NPz9/fnk\nk0/o0KEDcXFxvPvuu9b1S5YsYcKECUybNo1WrVqxatUqlixZwrRp06zbbNiwgfj4eCIjIxk9ejSn\nTp2yrrs0BKd///5ERERgbuDKuCL5FhyGmFtVqA1n7i+VeYXsH/8kFdl5AKg83enw+jxcAvzsHNmN\nbc2q4J3LEu9gVwVPtHPFQ+24ibdarQZAodEQsugJ1KFBAMgVlaROW0jluQx7hldjHholTw6IwE9r\n+WSk3Ghm4cYkUgvKbrCnUBvOfG2pDVmWWb16NWvWrCExMZGkpCRef/31q24bGRnJ+vXrSUtL4+mn\nn2batGlkZ2cD8PLLL3PzzTeTkpLCsWPHmDJlCgA6nY677rqLe++9l9OnT7Ny5UrmzJnDyZMnAZgz\nZw5arZY///yT5cuXs2rVqhsOt9u5cyf79+9n9erVLFu2jG3btlnXbdy4kTFjxpCamsrYsWOrHevM\nmTNMmTKFJUuWcObMGYYOHcr48eOr3eVeu3Yt33zzDcnJyQ0+fXa9jl5eXk6fPn3o2rUrcXFxzJ8/\n31ZxCYIgNEkmfTmJE55Gn5QGgKRRE7fkKdyjwu0c2Y1tybIMNbk88Z7Z3hUvtfPcx1F6exKyeDYK\nL8sYalN+ISmT52MsdI4hHH5uap4cGIG7RglAcYWJ+RuSyCqpsHNkQm1tbNnPZl91IUkSkyZNIiQk\nBB8fH5588knWrl171W3HjBlDUJDlj9Y777yTqKgoEhMtsxlpNBrS0tLIyMhAo9HQp08fAH7++Wda\ntWrFuHHjUCgUdOrUiZEjR/L9999jMpn48ccfmT9/PlqtltjYWMaNG3fDqTSffvpptFotcXFxjB8/\nnjVr1ljX9e7dmxEjRgDg6upa7Vjfffcdt9xyC4MGDUKpVDJjxgzKysrYu3ev9bWYMmUKISEhuLg0\nfCXhel0xXV1d2bJlC4cOHeLIkSNs2bJFjJUS6kz0HaE2nLG/mI1GDk9fROH+PywLJIn2/3zUKeby\n/i2znOWXjfEO1SqY1V7rFIm3wWCo1taEBBHy3Eyki3fEK5PPkfbYPzFXVtojvFoL8XJh1oBwXFSW\n1z5Xb2DehjPk6Q032FOoCWe8ttRVaGio9eewsDCysrKuut1XX33FoEGDiIyMJDIykhMnTpCXZ/nk\n7rnnnkOWZYYNG0a/fv344osvAEsF9AMHDlj3iYyMZM2aNeTk5JCXl4fRaLzi/PWJ93ozy2RlZVU7\nviRJhIaGkpmZedVjN7R6XzXd3CzjEysrKzGZTPj5Of7HpoIgCI1NNpv548klZG/cYV0W9cSDBAzp\ne529HMOmv0wnGKpVMLOdFk8HHmpyia+PLwtnL7hiuTYumqA5U6xt/b4jnJ/3KnIDj/W0lSg/LY/f\nFIbqYh36jOJKFmw4Q3F5wz8sJjQd589XVX1NT0+nZcuWV2xz7tw5Zs2axdKlSzl79izJycnExsZa\n7ywHBgby9ttvc+zYMd58803mzJlDcnIyoaGh9OvXj+TkZOtXWloar732Gv7+/qhUKtLT06ud/0b+\nun1wcFUl2OsNWQkODubcuXPWtizLnD9/vsb721q9H6k3m810796dpKQkHnnkEeLi4mwRl9AMNZdx\ndoJtOFN/kWWZE8+8TcY3VfPXho0fRejYEXaMqmbWp5fz4emqh/rCtAqeaK/Fw4EfrrycUqnkbwOH\nXHWd58DeGC/kkvufrwEo+mkLSl9vgp+Z4RRTPcYGuvNIfCj/2pWOWYbkgnKe/SWJJSPaolUr7R2e\n02qsa8vwrF2Ncp5rkWWZlStXcsstt6DVannzzTe56667rthOp9MhSRL+/v6YzWa++uorTpyoelD5\nf//7H7169SI0NBRvb28kSUKpVHLrrbfywgsv8M0333DnnXcCcPToUTw8PGjXrh0jR47k1VdfZfny\n5aSmpvLll1/SunXr68b8xhtvWOfv/vLLL3n//fdr9LuOGTOGd955h+3btxMfH8+KFStwdXWld+/e\nNX/BbKjed74VCgWHDh0iPT2d7du3s3XrVhuEJQiC0HScXvI+aR9VzSvdctTfaD19vB0jujFZlvk2\nRV8t8Q53UzDTiRLvmvC5ZwTeo6qKZOR//j9y/vXpdfZwLN1CPHm4V9XH7Sey9Tz3azKVJue4gy/Y\njyRJjB07lrvvvpvu3bsTFRXF7Nmzq60HiImJ4dFHH+XWW28lJiaGEydO0Ldv1Sd2hw4d4pZbbiEi\nIoIHHniAV155hYiICDw8PFizZg1r166lQ4cOxMbGsnjxYuswsKVLl6LT6YiJiWHGjBncf//9N4y5\nX79+9OzZk7vuuovHHnuMwYMHW2P96x/Mly+Ljo5mxYoVzJ07l+joaH799VdWrVqFyk7TutqswiXA\n4sWL0Wq1PPXUU9ZlmzdvZuXKlaK8vGjfsH35ODtHiEe0HbvtLP0lY+3PeK3aDMBxsw6fHh25952X\nkJQKhykP/9d23+49+SRJz2db9wDg1aYrke4K+umPo1VKdisXX9f2pWXXWt+9czeyXl3B3i2/ARCn\ncCf42RmcbWt5wMxRys1fr735TD7vrf4ZsPx79Qn34m/a86gVCof6/+AM7UvL6nu8EydOEBvr+M9z\nOIO0tDS6detGTk5Og89EcjUZGRmcPXv2quXl61Lhsl7Jd25uLiqVCh8fH8rKyrj11ltZtGhRtUBE\neXmhphISEpxqKIFgX87QX1I/WsOJBW9Y23439SD2ZccuomOSZVac1LEps2r2jBhPJVPbuuKqdM47\n3gcOHbAm3NciG4xkPPc2+gNHrcvCXl+Iz6jav7Hayw/Hc/nuWI613Sfci2eHRqJROv5DsY7EVtcW\nRy8v70wcIfl2mPLymZmZ/O1vf6Nr16706dOHUaNG1SkIQQDnGsMr2J+j95fzX6+vlnh79+hA7OIn\nHDrxNphl3jxWWi3x7uqjZHq08ybewA0TbwBJrSL42Rm4xrSxLkuft4SSbXsaMjSbGhnrz+0x/tb2\n7+eKeXFzMgYxBKVWHP3a0lw5w3MYNVWv5LtTp04kJiZapxqcM2eOreISBEFwWue+WMfRmS9Z254d\noumwZA4KF40do7o+ndHMS0dK2JVTNd1eX38Vk9q4olY475teXn4e4yfdeCwpgMLVhZDFT6JpdXHK\nMaOJtMefR7f3cANGaDuSJHFXx4BqCfietGJe3JwiEnDBqUVERJCbm2uXu94NoWn8FkKT0JzmVhXq\nz1H7S+p/VnNs9hK4OKLPvW0rOrw+F6Wbq50ju7bschPzE4s5XFA1T/SQQDX/19oFpZPfbZJlmQs5\n2TXeXunpQehLT6EKamHZv7yClMnzKN2d2FAh2tSlBPy2yxLw3WlFvPibSMBrylGvLULTIZJvQRAE\nG0n+1xecWPimte3RPopOy55BfbGaoiM6U2xk3oEizulM1mUjQzSMDdegcPLEu65ULfwIfXkOSj8f\nwJKAp05dQOmuAzfY0zFIksTdHQMY0f6yBDy1iJd+S6HSKBJwQbC3eiXf586dY8iQIXTo0IGOHTuy\nbNkyW8UlNENinJ1QG47UX2RZ5swbH3Fy8b+syzw7RlsSb29PO0Z2fb/nVLLwYBEFlZa79EoJ/hHp\nwu0hmiY1vlJ9sZJlbWhCWxL22nxULXwBkCsqSZ22kJId+2wdXoOQJIl7OgUwvH1V4btdqUUs/DkJ\nXaXpOnsKtry2mJ2kaJNwbbIs37DsfW3VK/lWq9W89dZbHDt2jD179vCvf/2r2sTrgiAITZ0sy5x6\neQVnXltpXebdLY5Oby1E5eFmx8iuTZZl1p0r49U/Sqi8mBu4KeHxdlr6+Nc+UW2qNKEtCV06H1WA\nJYGVKypJm/6M0zyEKUkSYzsFVkvAD2eWMuen0xSUiVL0Da1FixacP39eJOBOLj8/H29vb5ses16P\n3bds2dJaitTDw4PY2FgyMjLEvJZCnTjD1HGC43CE/mI2GDk+7zXSv/jBusynd2fiXpmN0tXFjpFd\nW4VJ5oNTOn7LqprRpIWLxKPRWlq6Ns2RiJeKetSFJiSIsNcWkP70EozZuciVBtIeXUT4skV4/a2f\nDaNsGJcScA+NktVHLdMQnskrY9YPp3llRBuCPR2zn9qTra4tGo2GoKAgsrKybBCVYC8uLi54eNh2\n6KDN5rxKSUnh4MGD9OnTx1aHFARBcFiGohIOTVpI3o791mV+/XsQu3gmCo1j3j3OLDOx9I8SUkqr\nhh1EuSuY1laLp7rpDDO5nK+PLwtnL6jXMdQtAwhbOo/0uUswXshFNhhIe+yfhDz/JH5jb7NRpA1H\nkiRui2mBh4uKT/ZnIgMZxRXM+uEUrwxvS6Sf1t4hNlkajUbM9S1cwSYVLktLSxk8eDDPPPMMd9xx\nR7V1osiOIAhNjT41gwMPPIXudIp1WeDwgUTPn+Kw83jvza3knROl6I1Vl/w+/irub+Xi1FMJNiZD\ndh7n576CIbOqkE3AtPsJnDnRacbIJ54vYcWe8xjNln7goVHy3LBIOgc77rMJguCo6lpkp97Jt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MtaqaqqMptmD7wFEqDhzFknf+N0bW0jKqjpZRdfRE/fIzGtC6u6H1cEfr4YbWxYjGaETjYkTr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\n6/26RqWdnD9/nsGDB9OzZ0/69evH3XffXSvwFkII0XqZLpdw8q0FWjn2d+O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"text": [ "" ] } ], "prompt_number": 50 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Keep in mind, not all posteriors will \"forget\" the prior this quickly. This example was just to show that *eventually* the prior is forgotten. The \"forgetfulness\" of the prior as we become awash in more and more data is the reason why Bayesian and Frequentist inference eventually converge as well." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bayesian perspective of Penalized Linear Regressions\n", "\n", "There is a very interesting relationship between a penalized least-squares regression and Bayesian priors. A penalized linear regression is a optimization problem of the form:\n", "\n", "$$ \\text{argmin}_{\\beta} \\;\\; (Y - X\\beta)^T(Y - X\\beta) + f(\\beta)$$\n", "\n", "for some function $f$ (typically a norm like $|| \\cdot ||_p^p$). \n", "\n", "We will first describe the probabilistic interpretation of least-squares linear regression. Denote our response variable $Y$, and features are contained in the data matrix $X$. The standard linear model is:\n", "\n", "\\begin{equation}\n", "Y = X\\beta + \\epsilon\n", "\\end{equation}\n", "\n", "where $\\epsilon \\sim \\text{Normal}( {\\bf 0}, \\sigma{\\bf I })$. Simply, the observed $Y$ is a linear function of $X$ (with coefficients $\\beta$) plus some noise term. Our unknown to be determined is $\\beta$. We use the following property of Normal random variables:\n", "\n", "$$ \\mu' + \\text{Normal}( \\mu, \\sigma ) \\sim \\text{Normal}( \\mu' + \\mu , \\sigma ) $$\n", "\n", "to rewrite the above linear model as:\n", "\n", "\\begin{align}\n", "& Y = X\\beta + \\text{Normal}( {\\bf 0}, \\sigma{\\bf I }) \\\\\\\\\n", "& Y = \\text{Normal}( X\\beta , \\sigma{\\bf I }) \\\\\\\\\n", "\\end{align}\n", "\n", "In probabilistic notation, denote $f_Y(y \\; | \\; \\beta )$ the probability distribution of $Y$, and recalling the density function for a Normal random variable (see [here](http://en.wikipedia.org/wiki/Normal_distribution) ):\n", "\n", "$$ f_Y( Y \\; |\\; \\beta, X) = L(\\beta|\\; X,Y)= \\frac{1}{\\sqrt{ 2\\pi\\sigma} } \\exp \\left( \\frac{1}{2\\sigma^2} (Y - X\\beta)^T(Y - X\\beta) \\right) $$\n", "\n", "This is the likelihood function for $\\beta$. Taking the $\\log$:\n", "\n", "$$ \\ell(\\beta) = K - c(Y - X\\beta)^T(Y - X\\beta) $$\n", "\n", "where $K$ and $c>0$ are constants. Maximum likelihood techniques wish to maximize this for $\\beta$, \n", "\n", "$$\\hat{ \\beta } = \\text{argmax}_{\\beta} \\;\\; - (Y - X\\beta)^T(Y - X\\beta) $$\n", "\n", "Equivalently we can *minimize the negative* of the above:\n", "\n", "$$\\hat{ \\beta } = \\text{argmin}_{\\beta} \\;\\; (Y - X\\beta)^T(Y - X\\beta) $$\n", "\n", "This is the familiar least-squares linear regression equation. Therefore we showed that the solution to a linear least-squares is the same as the maximum likelihood assuming Normal noise. Next we extend this to show how we can arrive at penalized linear regression by a suitable choice of prior on $\\beta$. \n", "\n", "#### Penalized least-squares\n", "\n", "In the above, once we have the likelihood, we can include a prior distribution on $\\beta$ to derive to the equation for the posterior distribution:\n", "\n", "$$P( \\beta | Y, X ) = L(\\beta|\\;X,Y)p( \\beta )$$\n", "\n", "where $p(\\beta)$ is a prior on the elements of $\\beta$. What are some interesting priors? \n", "\n", "1\\. If we include *no explicit* prior term, we are actually including an uninformative prior, $P( \\beta ) \\propto 1$, think of it as uniform over all numbers. \n", "\n", "2\\. If we have reason to believe the elements of $\\beta$ are not too large, we can suppose that *a priori*:\n", "\n", "$$ \\beta \\sim \\text{Normal}({\\bf 0 }, \\lambda {\\bf I } ) $$\n", "\n", "The resulting posterior density function for $\\beta$ is *proportional to*:\n", "\n", "$$ \\exp \\left( \\frac{1}{2\\sigma^2} (Y - X\\beta)^T(Y - X\\beta) \\right) \\exp \\left( \\frac{1}{2\\lambda^2} \\beta^T\\beta \\right) $$\n", "\n", "and taking the $\\log$ of this, and combining and redefining constants, we arrive at:\n", "\n", "$$ \\ell(\\beta) \\propto K - (Y - X\\beta)^T(Y - X\\beta) - \\alpha \\beta^T\\beta $$\n", "\n", "we arrive at the function we wish to maximize (recall the point that maximizes the posterior distribution is the MAP, or *maximum a posterior*):\n", "\n", "$$\\hat{ \\beta } = \\text{argmax}_{\\beta} \\;\\; -(Y - X\\beta)^T(Y - X\\beta) - \\alpha \\;\\beta^T\\beta $$\n", "\n", "Equivalently, we can minimize the negative of the above, and rewriting $\\beta^T \\beta = ||\\beta||_2^2$:\n", "\n", "$$\\hat{ \\beta } = \\text{argmin}_{\\beta} \\;\\; (Y - X\\beta)^T(Y - X\\beta) + \\alpha \\;||\\beta||_2^2$$\n", "\n", "This above term is exactly Ridge Regression. Thus we can see that ridge regression corresponds to the MAP of a linear model with Normal errors and a Normal prior on $\\beta$.\n", "\n", "3\\. Similarly, if we assume a *Laplace* prior on $\\beta$, ie. \n", "\n", "$$ f_\\beta( \\beta) \\propto \\exp \\left(- \\lambda ||\\beta||_1 \\right)$$\n", "\n", "and following the same steps as above, we recover:\n", "\n", "$$\\hat{ \\beta } = \\text{argmin}_{\\beta} \\;\\; (Y - X\\beta)^T(Y - X\\beta) + \\alpha \\;||\\beta||_1$$\n", "\n", "which is LASSO regression. Some important notes about this equivalence. The sparsity that is a result of using a LASSO regularization is not a result of the prior assigning high probability to sparsity. Quite the opposite actually. It is the combination of the $|| \\cdot ||_1$ function and using the MAP that creates sparsity on $\\beta$: [purely a geometric argument](http://camdp.com/blogs/least-squares-regression-l1-penalty). The prior does contribute to an overall shrinking of the coefficients towards 0 though. An interesting discussion of this can be found in [2].\n", "\n", "For an example of Bayesian linear regression, see Chapter 4's example on financial losses." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### References\n", "\n", "1. Macro, . \"What is the relationship between sample size and the influence of prior on posterior?.\" 13 Jun 2013. StackOverflow, Online Posting to Cross-Validated. Web. 25 Apr. 2013.\n", "\n", "2. Starck, J.-L., , et al. \"Sparsity and the Bayesian Perspective.\" Astronomy & Astrophysics. (2013): n. page. Print.\n", "\n", "3. Kuleshov, Volodymyr, and Doina Precup. \"Algorithms for the multi-armed bandit problem.\" Journal of Machine Learning Research. (2000): 1-49. Print.\n", "\n", "4. Gelman, Andrew. \"Prior distributions for variance parameters in hierarchical models.\" Bayesian Analysis. 1.3 (2006): 515-533. Print.\n", "\n", "5. Gelman, Andrew, and Cosma R. Shalizi. \"Philosophy and the practice of Bayesian statistics.\" British Journal of Mathematical and Statistical Psychology. (2012): n. page. Web. 17 Apr. 2013.\n", "\n", "6. http://jmlr.csail.mit.edu/proceedings/papers/v22/kaufmann12/kaufmann12.pdf\n", "\n", "7. James, Neufeld. \"Reddit's \"best\" comment scoring algorithm as a multi-armed bandit task.\" Simple ML Hacks. Blogger, 09 Apr 2013. Web. 25 Apr. 2013.\n", "\n", "8. Oakley, J. E., Daneshkhah, A. and O\u2019Hagan, A. Nonparametric elicitation using the roulette method. Submitted to Bayesian Analysis.\n", "\n", "9. \"Eliciting priors from experts.\" 19 Jul 2010. StackOverflow, Online Posting to Cross-Validated. Web. 1 May. 2013. .\n", "\n", "10. Taleb, Nassim Nicholas (2007), The Black Swan: The Impact of the Highly Improbable, Random House, ISBN 978-1400063512" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython.core.display import HTML\n", "def css_styling():\n", " styles = open(\"../styles/custom.css\", \"r\").read()\n", " return HTML(styles)\n", "css_styling()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "" ], "output_type": "pyout", "prompt_number": 1, "text": [ "" ] } ], "prompt_number": 1 } ], "metadata": {} } ] }