{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "15bb94b3-1e30-4b1e-949d-75ed8256a42f", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "id": "61921132", "metadata": {}, "source": [ "#### Maximum likelihood estimation\n", "\n", "Maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.\n", "\n", "If the likelihood function is differentiable, the derivative test for finding maxima can be applied. In some cases, the first-order conditions of the likelihood function can be solved analytically; for instance, the ordinary least squares estimator for a linear regression model maximizes the likelihood when the random errors are assumed to have normal distributions with the same variance." ] }, { "cell_type": "markdown", "id": "c2e23cc2", "metadata": {}, "source": [ "As a very simple MLE example, consider the following experiment:\n", "\n", "I have a bag that contains 3 balls. Each ball is either red or blue, but I have no information in addition to this. Thus, the number of blue balls, call it $\\theta$, might be 0, 1, 2 or 3. I am allowed to choose 4 balls at random from the bag *with replacement*. We define the random variables $X_1$, $X_2$, $X_3$ and $X_4$ as follows\n", "\n", "$X_i$ = 1 if $i$th chosen ball is blue or $X_i$ = 0 is the $i$th chosen ball is red\n", "\n", "thus, $X_i \\sim$ Bernoulli($\\theta$/3), where Bernoulli is a discrete probability distribution wherein the random variable can only have 2 possible outcomes. \n", "\n", "After doing the experiment, the following values for $X_i$ are observed:\n", "\n", "$x_1$=1, $x_2$=0, $x_3$=1, $x_4$=1\n", "\n", "i.e. we found 3 blue balls and 1 red ball. Our goal is for each possible value of $\\theta$ (the number of blue balls), find the probability of the observed sample, ($x_1$, $x_2$, $x_3$, $x_4$)=(1,0,1,1)\n", "\n", "The probability of $x_i$ is \n", "\n", "$P_{X_i} = \\theta/3$ for $x$=1 or $(1-\\theta/3)$ for $x$=0\n", "\n", "so the joint PMF is\n", "\n", "$P_{X_1 X_2 X_3 X_4}(x_1,x_2,x_3,x_4) = P_{X_1}(x_1)P_{X_2}(x_2)P_{X_3}(x_3)P_{X_4}(x_4)$\n", "\n", "therefore, \n", "\n", "$P_{X_1 X_2 X_3 X_4}(1,0,1,1) = (\\theta/3)^3(1-\\theta/3)$\n", "\n", "which maps as:\n", "\n", "$\\theta$ ``` ```$P_{X_1 X_2 X_3 X_4}(1,0,1,1;\\theta)$\n", "```\n", " 0 0\n", " 1 0.0247\n", " 2 0.0988\n", " 3 0\n", " ```\n", "Note that $\\theta$ = 0 or 3 are impossible. So the highest probability is $\\theta$=2, this is call the maximum likelihood estimate of $\\theta$." ] }, { "cell_type": "markdown", "id": "dec581a4", "metadata": {}, "source": [ "\n", "---\n", "\n", "Suppose that the lifetime of a lightbulb is modeled by an exponential distribution with (unknown) parameter $\\lambda$. We test 5 bulbs and find they have life times of 2, 3, 1, 3 and 4 years, respectively. What is the MLE for $\\lambda$?\n", "\n", "Notation is important here. With five different values it is best to use subscripts. Let $X_j$ be the lifetime of the $i$th bulb and let $x_i$ be the value $X_i$ takes. Then each $X_i$ has pdf $f_{X_i}(x_i) = \\lambda e^{-\\lambda x_i}$. We assume the lifetimes of the bulbs are independent, so the joint pdf is the produce of the individual densities:\n", "\n", "$$ f(x_1,x_2,x_3,x_4,x_5|\\lambda) = (\\lambda e^{-\\lambda x_1})(\\lambda e^{-\\lambda x_2})(\\lambda e^{-\\lambda x_3})(\\lambda e^{-\\lambda x_4})(\\lambda e^{-\\lambda x_5}) \n", "= \\lambda^5 e^{-\\lambda(x_1+x_2+x_3+x_4+x_5)} $$\n", "\n", "Note this is a conditional density, since it depends on $\\lambda$. Viewing the data as fixed and $\\lambda$ as variable, this density is the likeihodd function. Our data has values\n", "\n", "$$ x_1 = 2, x_2 = 3, x_3 = 1, x_4 = 3, x_5 = 4 $$\n", "\n", "So the likeihood and log likeihood functions are\n", "\n", "$$ f(2,3,1,3,4|\\lambda) = \\lambda^5 e^{-13\\lambda} $$\n", "$$ ln(f(2,3,1,3,4|\\lambda)) = 5 ln (\\lambda) - 13 \\lambda $$ \n", "\n", "Finally, to find the MLE, we take the derivative and set it to zero, such that\n", "\n", "$$ {d \\over d\\lambda}({\\rm log\\, likeihood}) = 5/\\lambda - 13 = 0 \\rightarrow \\lambda=5/13 $$\n", "\n", "therefore, the typical half-life is 1/$\\lambda$ = 2.6 years, or the same as the mean of the lifetimes." ] }, { "cell_type": "markdown", "id": "738a6fc2", "metadata": {}, "source": [ "When you approach a new problem, the first step is generally to write down the likelihood function (the probability of a dataset given the model parameters). This is equivalent to describing the generative procedure for the data. In this case, we’re going to consider a linear model where the quoted uncertainties are underestimated by a constant fractional amount. You can generate a synthetic dataset from this model:" ] }, { "cell_type": "code", "execution_count": 4, "id": "9f379bcd", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# https://emcee.readthedocs.io/en/stable/tutorials/line/\n", "\n", "np.random.seed(123)\n", "\n", "# Choose the \"true\" parameters.\n", "m_true = -1\n", "b_true = 5.\n", "f_true = 0.5\n", "\n", "# Generate some synthetic data from the model.\n", "N = 50\n", "x = np.sort(10 * np.random.rand(N))\n", "yerr = 0.1 + 0.5 * np.random.rand(N)\n", "y = m_true * x + b_true\n", "y += np.abs(f_true * y) * np.random.randn(N)\n", "y += yerr * np.random.randn(N)\n", "\n", "plt.errorbar(x, y, yerr=yerr, fmt=\".k\", capsize=0)\n", "x0 = np.linspace(0, 10, 500)\n", "plt.plot(x0, m_true * x0 + b_true, \"k\", alpha=0.3, lw=3)\n", "plt.xlim(0, 10)\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\");" ] }, { "cell_type": "markdown", "id": "bf367366", "metadata": {}, "source": [ "The true model is shown as the thick grey line and the effect of the underestimated uncertainties is obvious when you look at this figure. The standard way to fit a line to these data (assuming independent Gaussian error bars) is linear least squares. Linear least squares is appealing because solving for the parameters—and their associated uncertainties—is simply a linear algebraic operation. Following the notation in Hogg, Bovy & Lang (2010), the linear least squares solution to these data is" ] }, { "cell_type": "code", "execution_count": 5, "id": "7afcba31", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Least-squares estimates:\n", "m = -1.191 ± 0.016\n", "b = 6.450 ± 0.091\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "A = np.vander(x, 2)\n", "C = np.diag(yerr * yerr)\n", "ATA = np.dot(A.T, A / (yerr**2)[:, None])\n", "cov = np.linalg.inv(ATA)\n", "w = np.linalg.solve(ATA, np.dot(A.T, y / yerr**2))\n", "print(\"Least-squares estimates:\")\n", "print(\"m = {0:.3f} ± {1:.3f}\".format(w[0], np.sqrt(cov[0, 0])))\n", "print(\"b = {0:.3f} ± {1:.3f}\".format(w[1], np.sqrt(cov[1, 1])))\n", "\n", "plt.errorbar(x, y, yerr=yerr, fmt=\".k\", capsize=0)\n", "plt.plot(x0, m_true * x0 + b_true, \"k\", alpha=0.3, lw=3, label=\"truth\")\n", "plt.plot(x0, np.dot(np.vander(x0, 2), w), \"--k\", label=\"LS\")\n", "plt.legend(fontsize=14)\n", "plt.xlim(0, 10)\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\");" ] }, { "cell_type": "markdown", "id": "21f39976", "metadata": {}, "source": [ "

This figure shows the least-squares estimate of the line parameters as a dashed line.\n", "This isn’t an unreasonable result but the uncertainties on the slope and\n", "intercept seem a little small (because of the small error bars on most of the\n", "data points).

\n", "\n", "#### Maximum likelihood estimation\n", "\n", "

The least squares solution found in the previous section is the maximum\n", "likelihood result for a model where the error bars are assumed correct,\n", "Gaussian and independent.\n", "We know, of course, that this isn’t the right model.\n", "Unfortunately, there isn’t a generalization of least squares that supports a\n", "model like the one that we know to be true.\n", "Instead, we need to write down the likelihood function and numerically\n", "optimize it.\n", "In mathematical notation, the correct likelihood function is:

\n", "
\n", "\\[\n", " \\ln\\,p(y\\,|\\,x,\\sigma,m,b,f) =\n", " -\\frac{1}{2} \\sum_n \\left[\n", " \\frac{(y_n-m\\,x_n-b)^2}{s_n^2}\n", " + \\ln \\left ( 2\\pi\\,s_n^2 \\right )\n", " \\right]\n", "\\]
\n", "

where

\n", "
\n", "\\[\n", " s_n^2 = \\sigma_n^2+f^2\\,(m\\,x_n+b)^2 \\quad .\n", "\\]
\n", "

This likelihood function is simply a Gaussian where the variance is\n", "underestimated by some fractional amount: \\(f\\).\n", " \n", "In Python, you would code this up as:

" ] }, { "cell_type": "code", "execution_count": 6, "id": "b854eb9b", "metadata": {}, "outputs": [], "source": [ "def log_likelihood(theta, x, y, yerr):\n", " m, b, log_f = theta\n", " model = m * x + b\n", " sigma2 = yerr**2 + model**2 * np.exp(2 * log_f)\n", " return -0.5 * np.sum((y - model) ** 2 / sigma2 + np.log(sigma2))" ] }, { "cell_type": "markdown", "id": "982956f0", "metadata": {}, "source": [ "In this code snippet, you’ll notice that we’re using the logarithm of $p$\n", " instead of $p$\n", " itself for reasons that will become clear in the next section. For now, it should at least be clear that this isn’t a bad idea because it will force $p$\n", " to be always positive. A good way of finding this numerical optimum of this likelihood function is to use the scipy.optimize module:" ] }, { "cell_type": "code", "execution_count": 7, "id": "668bb913", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Maximum likelihood estimates:\n", "m = -1.019\n", "b = 5.114\n", "f = 0.441\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.optimize import minimize\n", "\n", "# seed this for demo\n", "np.random.seed(42)\n", "\n", "# define function for log likelihood\n", "nll = lambda *args: -log_likelihood(*args)\n", "\n", "# pass an initial prior, randomized off of real slope and yerr\n", "initial = np.array([m_true, b_true, np.log(f_true)]) + 0.1 * np.random.randn(3)\n", "\n", "# find minimum of d(log_likelihood)\n", "soln = minimize(nll, initial, args=(x, y, yerr))\n", "m_ml, b_ml, log_f_ml = soln.x\n", "\n", "print(\"Maximum likelihood estimates:\")\n", "print(\"m = {0:.3f}\".format(m_ml))\n", "print(\"b = {0:.3f}\".format(b_ml))\n", "print(\"f = {0:.3f}\".format(np.exp(log_f_ml)))\n", "\n", "plt.errorbar(x, y, yerr=yerr, fmt=\".k\", capsize=0)\n", "plt.plot(x0, m_true * x0 + b_true, \"k\", alpha=0.3, lw=3, label=\"truth\")\n", "plt.plot(x0, np.dot(np.vander(x0, 2), w), \"--k\", label=\"LS\")\n", "plt.plot(x0, m_ml*x0+b_ml, \":m\", label=\"ML\")\n", "plt.legend(fontsize=14)\n", "plt.xlim(0, 10)\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\");" ] }, { "cell_type": "markdown", "id": "f9698304", "metadata": {}, "source": [ "It’s worth noting that the optimize module minimizes functions whereas we would like to maximize the likelihood. This goal is equivalent to minimizing the negative likelihood (or in this case, the negative log likelihood). In this figure, the maximum likelihood (ML) result is plotted as a dotted red line—compared to the true model (grey line) and linear least-squares (LS; dashed line). That looks better!\n", "\n", "The problem now: how do we estimate the uncertainties on m and b? What’s more, we probably don’t really care too much about the value of f but it seems worthwhile to propagate any uncertainties about its value to our final estimates of m and b. This is where MCMC comes in.\n", "\n", "This isn’t the place to get into the details of why you might want to use MCMC\n", "in your research but it is worth commenting that a common reason is that you\n", "would like to marginalize over some “nuisance parameters” and find an estimate\n", "of the posterior probability function (the distribution of parameters that is\n", "consistent with your dataset) for others.\n", "MCMC lets you do both of these things in one fell swoop!\n", "You need to start by writing down the posterior probability function (up to a\n", "constant):

\n", "
\n", "\\[\n", " p (m,b,f\\,|\\,x,y,\\sigma) \\propto p(m,b,f)\\,p(y\\,|\\,x,\\sigma,m,b,f) \\quad .\n", "\\]
\n", "

We have already, in the previous section, written down the likelihood function

\n", "
\n", "\\[\n", "p(y\\,|\\,x,\\sigma,m,b,f)\n", "\\]
\n", "

so the missing component is the “prior” function

\n", "
\n", "\\[\n", "p(m,b,f) \\quad .\n", "\\]
\n", "

This function encodes any previous knowledge that we have about the\n", "parameters: results from other experiments, physically acceptable ranges, etc.\n", "It is necessary that you write down priors if you’re going to use MCMC because\n", "all that MCMC does is draw samples from a probability distribution and you\n", "want that to be a probability distribution for your parameters.\n", "This is important: you cannot draw parameter samples from your likelihood\n", "function.\n", "This is because a likelihood function is a probability distribution over\n", "datasets so, conditioned on model parameters, you can draw representative\n", "datasets (as demonstrated at the beginning of this exercise) but you cannot\n", "draw parameter samples.

\n", "\n", "In this example, we’ll use uniform (so-called “uninformative”) priors on \\(m\\),\n", "\\(b\\) and the logarithm of \\(f\\).\n", "For example, we’ll use the following conservative prior on \\(m\\):

\n", "\n", "
\n", "\\[\\begin{split}\n", "p(m) = \\left \\{\\begin{array}{ll}\n", " 1 / 5.5 \\,, \\mbox{if}\\,-5 < m < 1/2 \\\\\n", " 0 \\,, \\mbox{otherwise}\n", " \\end{array}\n", " \\right .\n", "\\end{split}\\]
\n", "

In code, the log-prior is (up to a constant):

" ] }, { "cell_type": "code", "execution_count": 8, "id": "20f8759d", "metadata": {}, "outputs": [], "source": [ "def log_prior(theta):\n", " m, b, log_f = theta\n", " if -5.0 < m < 0.5 and 0.0 < b < 10.0 and -10.0 < log_f < 1.0:\n", " return 0.0\n", " return -np.inf" ] }, { "cell_type": "markdown", "id": "dabca7e1", "metadata": {}, "source": [ "Then, combining this with the definition of log_likelihood from above, the full log-probability function is:" ] }, { "cell_type": "code", "execution_count": 9, "id": "aaa3ffe0", "metadata": {}, "outputs": [], "source": [ "def log_probability(theta, x, y, yerr):\n", " lp = log_prior(theta)\n", " if not np.isfinite(lp):\n", " return -np.inf\n", " return lp + log_likelihood(theta, x, y, yerr)" ] }, { "cell_type": "markdown", "id": "12019de2", "metadata": {}, "source": [ "After all this setup, it’s easy to sample this distribution using emcee. We’ll start by initializing the walkers in a tiny Gaussian ball around the maximum likelihood result (I’ve found that this tends to be a pretty good initialization in most cases) and then run 5,000 steps of MCMC." ] }, { "cell_type": "code", "execution_count": 10, "id": "2d1a43f9", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "You must install the tqdm library to use progress indicators with emcee\n" ] } ], "source": [ "import emcee\n", "\n", "pos = soln.x + 1e-4 * np.random.randn(32, 3)\n", "nwalkers, ndim = pos.shape\n", "\n", "sampler = emcee.EnsembleSampler(\n", " nwalkers, ndim, log_probability, args=(x, y, yerr)\n", ")\n", "sampler.run_mcmc(pos, 5000, progress=True);" ] }, { "cell_type": "markdown", "id": "3158a836", "metadata": {}, "source": [ "Let’s take a look at what the sampler has done. A good first step is to look at the time series of the parameters in the chain. The samples can be accessed using the EnsembleSampler.get_chain() method. This will return an array with the shape (5000, 32, 3) giving the parameter values for each walker at each step in the chain. The figure below shows the positions of each walker as a function of the number of steps in the chain:" ] }, { "cell_type": "code", "execution_count": 11, "id": "676e44a3", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(3, figsize=(10, 7), sharex=True)\n", "samples = sampler.get_chain()\n", "labels = [\"m\", \"b\", \"log(f)\"]\n", "for i in range(ndim):\n", " ax = axes[i]\n", " ax.plot(samples[:, :, i], \"k\", alpha=0.3)\n", " ax.set_xlim(0, len(samples))\n", " ax.set_ylabel(labels[i])\n", " ax.yaxis.set_label_coords(-0.1, 0.5)\n", "\n", "axes[-1].set_xlabel(\"step number\");\n" ] }, { "cell_type": "markdown", "id": "640905ec", "metadata": {}, "source": [ "As mentioned above, the walkers start in small distributions around the maximum likelihood values and then they quickly wander and start exploring the full posterior distribution. In fact, after fewer than 50 steps, the samples seem pretty well “burnt-in”. That is a hard statement to make quantitatively, but we can look at an estimate of the integrated autocorrelation time" ] }, { "cell_type": "code", "execution_count": 12, "id": "15f955a2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[43.80102132 43.38549646 38.78637146]\n" ] } ], "source": [ "tau = sampler.get_autocorr_time()\n", "print(tau)" ] }, { "cell_type": "markdown", "id": "6f2045b1", "metadata": {}, "source": [ "This suggests that only about 40 steps are needed for the chain to “forget” where it started. It’s not unreasonable to throw away a few times this number of steps as “burn-in”. Let’s discard the initial 100 steps, thin by about half the autocorrelation time (15 steps), and flatten the chain so that we have a flat list of samples:\n", "\n" ] }, { "cell_type": "code", "execution_count": 13, "id": "0e9b9aee", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(10432, 3)\n" ] } ], "source": [ "flat_samples = sampler.get_chain(discard=100, thin=15, flat=True)\n", "print(flat_samples.shape)" ] }, { "cell_type": "markdown", "id": "a6d5e9b5", "metadata": {}, "source": [ "Now that we have this list of samples, let’s make one of the most useful plots you can make with your MCMC results: a corner plot. You’ll need the corner.py module but once you have it, generating a corner plot is as simple as:\n", "\n" ] }, { "cell_type": "code", "execution_count": 14, "id": "07bde33b", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import corner\n", "\n", "fig = corner.corner(\n", " flat_samples, labels=labels, truths=[m_true, b_true, np.log(f_true)]\n", ");" ] }, { "cell_type": "markdown", "id": "b8daa48b", "metadata": {}, "source": [ "The corner plot shows all the one and two dimensional projections of the posterior probability distributions of your parameters. This is useful because it quickly demonstrates all of the covariances between parameters. Also, the way that you find the marginalized distribution for a parameter or set of parameters using the results of the MCMC chain is to project the samples into that plane and then make an N-dimensional histogram. That means that the corner plot shows the marginalized distribution for each parameter independently in the histograms along the diagonal and then the marginalized two dimensional distributions in the other panels.\n", "\n", "Another diagnostic plot is the projection of your results into the space of the observed data. To do this, you can choose a few (say 100 in this case) samples from the chain and plot them on top of the data points:" ] }, { "cell_type": "code", "execution_count": 21, "id": "ae552730", "metadata": {}, "outputs": [ { "data": { "image/png": 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+mGQIYr1ipkSqNWZL//3ZXGB1QiYOqTCkoyJmNMpAURRFUYYFo0fEhHZASQWMmQHZBLS9DU0vyrK74ASZRnK4RYjYvf1iJtEtE0qJLuM2vn4xYzKJ8LG5pSKT6JHFeQ7fqIgyUBRFUZSRzOgRMa4SyBegZ7sIjzHTIZOGjvXQ+CJ4KyA4DjwVYI/0ixlfhZh6Ez0QbZVWk7sEHH5ZlAf9UQY2N2RiIngsdrkPi20on7WiKIqiHLOMHhGz6V9QfRyUToRcCkK7wOKEihNlfLp9PTS+Ipt7g7UiamwRaSPZPf1iJt4FkVYRKq7eyowhZnqjDGweaS/FO6W9ZPcN9tUoiqIoinLEGT2fvJkYtKyC7k1QNA5KJkM+A+Fmaf2UHwcFRMw0vQyuUiiZKG0lmwdcfhEo/iox/Ma7INoCiU7Z8mv3DhYzveInHZXxbqtzcCvqMONwOPj617+Ow6GeHEVRFEWB0bTs7uH/xG9JyKK7XB7sTgjUiJixmCEZkWqJu0R2wHRshHib7JEpnmBUZgaIGZtLxq3jnTKlZHUabSbvnsvwclnZEpxNye/ZB1RvFEVRFEXZg8Ox7G70VGJcPnCXQSoG6R7IpKBzkyy5C4yFkkniX4m1AyYonQTmaWIA3vkaOIuhpBZS5SJUXAHxxQTGyrh1vBPCO0XMeEoHb/btjTLIZUTwxNoMQ7BHxYyiKIqiHCFGj4gpngp0Q8EkrZ9UFNJhmVTq2AQ9W8FXDWVTwWaX7b0mE5RNBI4z2kyvSURB8USpzDhC4pNx+CBQLWIm1gGhJrC6wFsqZt8+MWOTfTTZtLSZ0u3DNspAURRFUUY6o0fEpMNQWgMBE0SbwZSXBXW5NMR7IJeA7u0QapSFeCV14AxCvFvCH0smQNlkaTPtfF3Gr0vqwNtbmQnuKWa6G2UHjadU2ki9QsVqB2uxtJdS0f6lewMFj6IoiqIoh8ToETHhFnDZwGIBdzl4xkCqS6aUrHbIZCDVIwbg0C758peLZ6Y3XymfhuLxclnXJtjVADa/TDx5y8TM27v5t6hGFuHFOqVlZfeIZ2ZgTMEwjzJQFEVRlJHM6BExkV2QbZdRaV8KzMYel/LjRTyEGkVQ5NKQ6YFEDMJtEGoBbwkE6yBQJRlLubSIlOI66NkMzW8YYqbWqMz4ZRPwQDET7TB21PjkOpur/2yDogwGVmZc+3gyiqIoiqK8G6NmOumCU4/jP649h4uPK8KUzYA3CN4x4PQY488eSKchvAPSCchmpAWVish0kQnxvxRNFDGTz0g7yF0iXpee7Yax1yutJ1+55C71ihmLXXwwsU5Jw3b45Hd3z1wqFETMpKNgMmuUgaIoinJMcjimk0aNiLnjoxfyi0dfprTIx+3XnMfHZtXgMiWlauKrkpaRxSI/F/JSmUmGIZ8SUZOIiCHXVACnV6IKisYPFjNmG4S2Q2intIWKxoO/QszAntL+Db7pqHhmMklpQXlK9xQqhYJUZNIxjTJQFEVRjjlUxDDgRfjjLdjtdv7wwnYWPfQCLV1hPveBc/n8xcdR6UyLD8U3RsSI1SrCAyC8SyIH0inIxSERhkJaIgzsblmcVzRBjMLZlFRrLE4IN0JPo3hhAuMh0CtmyvrFTCoiYiaXFqOwu3gfYsZoMWmUgaIoinKMoCKGAS/CS3/En26FnkYK+QJPrW1j0d9e5emGjfy/957BvPefwvQKs7SNPGPFO2Ozy4QSyNbdWJvkLaVikDEqM4UsWN0QGCO7Zkwmo13kF09LeJeET9rcImb8RnyB2zACm61GZaZd9si4iqQqtHvVJZ+X22XiGmWgKIqijHpUxDDgRXjtIfzFlSIwurZA53bIJljXHOXuZav47ZOvcfbJk5n3gVm87wQ/5kJWEq69ldI+snjA4ZKR68guSCdlkikdkcV5hZxUSorGQHCytKZyaREqVqf8Ts8O2R8TGAf+SnAH5TGcfjBZIBUWsZTLiJBxF+9ZdcnnDDGTOOJRBoqiKIoyVKiIYcCLsPYZ/NasmHStTqmARHZJinWsm45Imvue2sA9f3+JoN/D7VfO5rqzqnGb0rIDxl8lLR+7W4RIOgHRnZCKQ7K3MmPEGpisIlKKp0i8QT4tVRmrB2ItYgK2uKCoWvw47qAszxsoZmLtcl+u4L7FTCqsUQaKoijKqERFDANehH//FP+YOhldziQhHZfWj80rE0PdmyDcTCqV4o8vNrLo4ZfZ2RHms++fzc0XT6XKlTV8M1UycWR1id8ln4VIs/hmMkmZaEonjYkmE/gqZVrJ4RPhYXXI70Vapc1kdcl9BqrEj+OtAGeAVDrDwm/exR2fvw6HzSqP6Qzu2ULKZUXM5NLSshoYRKkoiqIoIxQVMQx4ER75Jn6PXTKPPJUiLgo5SIbku90rVY2eHdC1iUImxTNvtbBo6Rv88/VNfPjCmcy74mRmVJrBZBMPjKdCRqQdAZloiuyUdlMmBsm4tH3yWRmV9pZA8SSp5hQyhuAwxEzPDrkfbxUEKsFdQrjgJTBmAqHuLvx2IN4uJl938T7EjJHLlMuI2LLvJYhSURRFUUYIKmIY6In5G36iEG2XsWiLXUy2nkoRFGmjNWN1isck1AydGyDRw/qmEHc/9ha/frKBM0+cyPwPnsGlx/sxFwpiAPaPAbsL7H4RLLF2MQGnopCNS+spkwRM0joqnSSel4GVmZixDM/mBHclYauPwIzLCO3air+8WgRJMmQEVCJVG1dwTz9Mb5RBPjtqogxSqRQLFy7kjjvuwOHQnTmKoijHAipiGPAibGnA7/NCpAWibdICyiTkRq7i/jZRNiUVDROyuC7ZLb6ZcAud4Rj3P7WRe5a9hs/j4vYrZ3P96VV4bFlwlUh1xuGTUWqbTVpMkV0Qj0h1JhWVSgmFAdlLpVJhsdjA5pOKS2gH4WSOwKX/Tej1Zfgrx0GgRu7bZJL7jXcAJtkx4wzsKWYySakEFfIjPsrgcPxDVhRFUUYWKmIY8CKs+Sd+v0eqFyaLCIrwLmnnxLtESNgNf4qvXHwliRDkclIdyeegZxt0bCOdCPOnl7az6O8NbG/r4bNXnM3NF05irC9vhECOBWexbAG2OWUkO9YiraZUTMakcxmpCDn8EKwV4zAFMRzbA4TbdxA451OEHvs2/rJx4pnxlMhkk9Mv5030QKJTqj/uXjGzmx+mN8oARmyUgYoYRVGUY4/D8d4/ehaRBGvBaZYP/WxKqhPlUyX/KNoM0VaItEHXVmnreEplvNpTDJmobO4NjofSydhDu7jOV8rHzq7l32vbWLx8DRP/9AzXXHAK8y47iVMqw7LwLjDWWG7ngeAk8CclWDLRZQQ+JsRg3LwaOjfK/QfGQbKz3/PiLpPFebFWGceOtEnYZNE4aU25iiDRLeePd+wpZmwu+UrHB4dM7h53MIxZvXp13/fZs2cP8WkURVGUkcLoqcS0bMfvtkMB8YvEu+VD3Wzp95bEO6X9E26VCkYhKz4Xf4V4UPI5iSIwFWRcOtUDnZsg1MzGnZ384PG3+eWTq5k5rZb5HziNy47zYrZZRAwFqmQSqndKKdIiPphkSHbXZJOS12RzQrCGsKmUwAWfIfTcL2W/TbxLxIzZJsLGX2GImVqjMpOX2yS6pZrjLdtz7LpQkCpQKjpiogwaGhq49NJLaWlpoaqqiuXLl1NfXz/Ux1IURVGOMFqJGUgmCc5y+bDPxMWL4isTUZLoFmHh8EPldChJSphjtAViXdC+GawDqjNWu+GbMUNVPVScxOTSrdxTU8E3rjyJnz69hc/96BG+6HRy2wfP4MYzs3h7dsj4tH+MTEj5q8A/VozGkV1yjmxCxrPbNkBmo5w7mRDBZbFC+UmQ6oZQkxh8PWVSmfGVSfSBp1Sml+JdUvGx2EXM9HppTCYxEdvc4pdJdA37KIOlS5fS0tICQHNzM8uWLVMRoyiKouwXo6cSs/UN/A6zfIB7iuV7NinippCXCIFkl3hWrE5pyZhMUjGJNIsZOJMSw29vBpKrRPKU0lERAQWL3K5zHelQD39+aRuLHlnNlpYePnPZGdxyYS3VPjM4fUY7qFgqPVabiJOenSKasinC3RECn/gloV9dh79inFRc7B7ZBGzzSAUn3CiL9dyl4uPxlUNwojHGnZNKT6JHRJdngJjpZWCUgcUuIm6YRRk0NDQwd+5cmpubtRKjKIpyDKHGXnZ7EdxOqbrEu4GcEbpYIjfMJMQrkzd2xyTDQEFaTVaHLJTraRJRk4qJSLA5xWzrrZBWTe9Uk8kucQSdGymEdrLirWYWP7aWR1/ZzFXnncy8S6ZxWpVVvDK+aqmkOH2SwZSKQGQnK196nTlf+QMrvnkZs+tKpOrjK5f8JVdAfrZ7IRWCcJMhZsrkPL5ymXxyFknrLNYByR7jvGV77pAZ5lEGK1euZM6cOaxYsUI9MYqiKMcIKmLYx4tQKIgvJNElYsXqlKqIw2dUZxLy4Z9NSmsmk5APfkdALo/uhHALRDvEN9Prq3GXyO0ycWkNmZ1AXszCXdvY1LiLH/5jIw88uYZTptYw7/IZXHGiF4vJDoFqCJSDvYiGLa1c+rm7aOnooSroYfl/XUb9+CDkjIwmT6kYlV3F8th2ozITbUF20ZRKtclXIcZlV9AQM+1yO5tLTMJ2955iJhWR521zGdt/h17M6HSSoijKsYeKGPbjRchlpDqT6JY/OwP94iATl3ZTPittmVRYxrPdQTHYxjulOhNtg1xCTMMOr7SZXEUyQp2OSpXEYoFwG3RupLu9hZ8/s4kfProGu83Gbe+fycdnleFz2sBTxoKHVnPXA4/2HXHBJy/lzg+dLNWdXBqyWdn66wxC8Xh5PKtDWmTJHqm8FHIiVDzF4C2Hksn9Z4q1i3jrFTMOz26vSVYeK5saFlEGKmIURVGOPY4ZEfPoo49y8803s3Xr1j2uO6AXIRUVYZIMiyhwBUXU5FL97aZ0XLwz2YxUZuweERahHdJqiocBYxOvwy/tG7NJfq+QA4tD2lHt68l0N/HQy9tYtPwtNuzs5tOXzuQLF4yns7ubuf/7NM3dcapKAyy/92vUHzcREh3QvUPaYfkUZLJynw6fjGe7y8Dh7J+cirSL38drtJm8ZYaYCYqYibSKWLF5jWmm3Rbi9UUZpOV5DlGUgYoYRVGUY49jQsR0d3czc+ZMstks27Zt2+P6g3oR8jnDO9MlAsbhkxaNxSbVmXRCWi5JY3md1W4YgW2yQC/aLNWOXE68Kw6fCBqnX9pM2SSYHSIwOjdT6Gnk+be2sejRdTzyymY+OPskLpwa5Kb7nmHFN97P7LPOEJHhCkhVJxGG0BaIdorQyOVE1Ni9stnXb2Q62b2GAbhVvDruUhEwgQoonmxsKE7KhFQ6Krf3lMnSv4Fk0yJm8llDzHiOqpjR2AFFUZRjj2NCxNx8881UVFTwwAMPvLOI6WjBX1x+4B++6bhUZxI9MrnjMgIY82mjOpMQUZEMAXkRGhZjhDnUCOFmET4FZG+LwyXtn3xWWlB5k9xvuA06N7BleyM/fGIDv/jnW0QTaX5z+yV8ZGYQi91tmIAr5DGsLsNsvEMEUyZptJnSMmkUHAe+MdIycvikzRRtlXaYq1jEjL8cSqeIlyeblLZYKipiy1O250K83kiG3igDm2tY5jKp6FEURRn5jHoR87e//Y2enh4A7rrrrncWMTs34/e5xcRrc0m750DI54w1/4bR1+EXM7DVaVRn4tKaSfQYRmA3OIrERBzaLkbgpJxVhITfWEbnECGUz8ifM3Ho2Ejj1g2M+9yD1JT6sdps3Hr5DD5xRgV+l02iEYqqwFkCTq88dmgH9OySwMlCQVpAFrMhfMaC2wdmL+Qi0vYyI9EIrmKZZiqbIpWaTELETDom1SVv2Z6v1T6iDIaLeND2k6IoyshnVIuYjo4O7rjjDn72s5/xq1/96l1FzJgxYzCZTFAoMP+WzzD/ls9IpcHqOvCttZmk4Z3pAczG+v9iqa5k4pCMSjsqHTauL5Lx6XgH9DSKiCjkpdXk9EtEgdMnbSoygIVwNEbg7Bvp/M0n+ecbW1i0fD3rmrr41MX13HpBDeOL7fKYffEDAREvPTvkMdJRqf5k01It8VdKZcYdlGDLTFT235hM0lZyBkWwlE0Ws28mIZWbTMLYi1O65+uUNnbkGOPe4UR6WIgHFTGKoigjn1G9sfdrX/sa//M//7Pft1/3+gv4Syr7P4izhlk30S0f5FanTOLsz7I3m5GL5B/TX52JtkmLxV0MRWPBE5RqRty4PtcugqXqZCg5DsI7INQsYshklSqO1SFJ1uSk8gNY687hmrp6rjlnMy+s2cSix95myryXef9Z05h/8STOHN8pHpWSWnCXQ1GNmHzDzdC5A+gW829Pk1zmKoHiGhFAxRNEiITbINYphuFIG/jLoGSKjHGnYxCTqao+odO73dfulipMJi7ttFhi//8CFUVRFOUIMyxFzJ/+9CfOO+88Kisr9/+XTKbdBItLRo4LBRE02YRUSszW/uvfbUeKySSVDXdQKh7xTjH2gnhOXCXyPV1hjD53ik/G4ugLk5Qk7WZpN5mTYDEMthhek1wOfCVQW86sqpP486kb2bZlKz98fB0XffMxTqitYP6lJ/DBk0JYnR7ZN+OtFJ+Lt0rO1L0JYt1yX5F2SLTLuXzVxsRSrQi6SItMQCW65HbeMjljUa0IlWgrdGwQAeQxjM4DowySzXLmeBe4ncM+l0lRFEUZ3QzLdtL555/Pv/71r71e98wzz3Deeef1/TyoHOXziVckExfhYrL0t5QsVkPQGMvucmnZBdN7/YHsSUn0yAd5Oiof8K5iiQrIJcUYG++UeAHyIiYcXply6t4q1Zl8hnAiQ+Di/yD07M/xB4tlpLuQlTNns9C9lXDLFn7x1Dp+8Ng6MJm5de50PnlmOQGP3agUjTXaRy5IRKB7I0SMBX15o9rj9EpLylMmPp9sXKpKJpMhxILGBuApsm8mHZNE7WzaEHBlfdWrvs26/3yM2afPGLJcJm0nKYqijHxGrSdm06ZNRKPRvp+XLl3Kfffdx6OPPsqkSZPwer191+3zRdhDsFgNw69TKjD5vFRnMkkx3Vrs/dfv70ROLiOCJW60dJxF0m4ymUVIxTpk6286KkLGHZTrurcTbtpA4MIvEHrsu/iDJfK4FpsYcrMZuZ3JBOFmsm2b+dsLa1n82AbWbO/gk++dzq3nVTGh1CXTTP4aESlOr/huujdDaKcstcvlgQw43OAxWmSuXjHTjmwADg7wzEwxPDMxqczkMuAupmFDE5dednl/2vQjj1B/fJ0RZeAQE/NRymVSEaMoijLyGbWemEmTJg36+Y033sButzNjxoz9vxOTSUSJzWUIlqSx+8VYdGc1KjB2j1QseidykiHjemPC6Z0EjcUGvkr5SkWkndS5yWhlBcVz4q+CREgEQWiXdJE8FTChTO7DUyIiJ22IAZcRBWCxypm8ZVi9lVw15kSuOn8zL73xNosf38BxX36dy8+Ywvz3TmDWxBZMjiAUVctYdcVxUHYcdG6WqaYUkE5BchNEdsg0k69KKjSZpPhk4l2y5C/aKllRpZMk0iAdgUgrS//4y8Fp0488Qv0pdxr5ThFp1R2lKIPVq1f3fdesJUVRlGOXYSliDjtms5hU7e5+wZKJyx6W3gqM3SPVklzGEDRhSBb61/2/m//D4ZOvXE48J7FOw2gbkNFmb5mYbKPNUqHpapffqzoZPE7o2iLVk3CLscjOqGyYrCK+HB4YU88Z5Sfwx1M3s2P7Zn70+Ftc8t2nOK6mjHmXTOHK6e3YXD7ZIeOvksTr0jrobpR8p3QMMhn5c2iHIcDGivjJJmUfTbxblvxFW6UiUzoZiuu44soPc/9v/0xzaztVlRVcftlc47W1iPeoN8og1n5EowwaGhq4+uqrAbjmmms09VpRFOUYZli2kw6EQypH5bL9LaVCbs8dM9l0//UDDcP76wFJRSFhxBxYHEYIpcQcpHpaWfid73DHJ67A4fSKkdbmgFCTmIPjnWBxGYLGLW2hQl7GvE1mGa+O7CTSspkHnlzDDx57m2wevvC+4/n0WeUU+Zxi7C2qkWqPxSECqn0jJI3tvCBCw1Mmt/OWipco2iHXuYvEQOwuhdI6Vq7azJzzzmfF0t8x+4xT5PdcxYPFyhGOMliwYAF33XXXoJ/vvPPOw3b/iqIoytFh1HpiDoTD5o/orcBkk+KnGbhjpne53L4Mw+9630Z1JtEtv+/0iziw2MV70rMT4m0iltwlInSycejYLNNNJmQPjd0vfy7kIReXKkjBCslucm0b+fsLb7F4+du8sa2DT1x4PLeeW0VduVuqMv5qiSuwuo2210bDE1OQdpvFIp6eovFi9M3lZPS6kJeQSVcp4byDwCmXE+rqwO8wiUGYglRsXMHBYuYIRRk0NDQwd+5cmpubxZujlRhFUZQRiYoYjpDJs3fHTDa1546ZfU44OffPC5I2Rr2TITEbu4tFPOSz0ooJNRm+HJdUOjDLRuDuRsjGRIQ4vfK4uQJkDQN0wSpCrHsTr6xey+LH3uahF7Ywd+ZE5l1Yw+yJPkzeYghOED+MwydxCt0boacZKe0g3x1+aTF5KwGTCKxcnnDBQeCiLxF6/RH8E06S61NGCwlkuslZtJuYGRhlYIxqH6KY6ZuSWrFCPTGKoigjFBUxHOFJlYE7ZrKpPXfMDDQMZ1MDDMPOd/eD5POyWyZuxBw4fdKasTrFu9K9Q0adC1kjvdonXpqe7WLEtdj7Kxz5nDx+IQ0FY6op1Ejj5g3c8/ga7v/nBiaPKWbexZO4+uQibO6AVFz8VeAtgVRSJpp6Go1R7wKYC0bgZLWMchcKhDt2ErhiAaEn/g9/eY3hmZlgiJmoMbptlokpZ2CwWMkY4+cU5LnYXPt6Zd4VnU5SFEUZ+aiI4Sh+oL3bjplew3A2KVUVi90wBL/LhBPsFnNgGGVdQSAvgiW0TaomDp8ImnxWjMDhJqm+OI2cJpBU7nQcMEvlKNZNtHkjv/rnKu5+7G2SmRxfeN9x3DSrlKDPC8GxEBgnxuMCcr/d22SaqZCT52Zzgr+SlLOahb95lDuuOgOHwyxj2Z5SqcAU18pUUzoqYstsMSozu4mZ3igDTIaY2S2Ecj9QEaMoijLyURHDEH2gvduOmXczDL/T/aZCMiHUu1vGVSxiKB0VcRFpEUHlLRfhEtopS/SSIVm45/CJiTefluqIqSDVmWyCXMc2Hnn+TRY9+havbWnnxvOmcNv5VUyu8Ek1xV8DgQp5Pj2N0LFJRIfZJK0rhw28YyAwXsRNshPyBWkh+UqlMhOslUpMKiptM4tNzurw94uZQsGYDouK2HH4DiiwU0WMoijKyEdFDMPgA233CszuO2beyTD8TmRS/WZgEKHgChqtop0SBJkKi8hxB2UjcM8WGdHGLLe1+8Rgm4lBLgFYxZsS3sFrq9exePlb/PmFrbyvfjzzLxzLOZMCmDxGTIFvjLSqwi3QuV42Ahcych9Ws1SEiidItScZEgHmDICvzBAz4wdsAO6Q18NbIcJsoJhJx+TLYpP21X5EGQz537miKIpyyKiIYZh9oOWMlOtewWJ17DayvZth2OZ69wmnQkHESm/MgdUlI9M2j4xud22FaIv4dTxlRhVlu4xpZxIy0eQOGonXMUjG5X5NeYh0snP7eu55bC33//Ntasv9zL9oAtfMCGL3BsU3E6yR9la4E7o2ysRSHsPwbAJniYgZm1PCMAt5Gc32lMkemqIaaTmlY/IcrA653NG/dZl8XoRWOrZfUQbD6u9cURRFOShUxDCMP9DeacfMuxmG3+k+412yjK5Q6B/VRoy8dG+FVNyIESiRSk73ZhmptrpFjFid8pjJHqkcmU2QSBBr3cyvn1nF3cvfJpbKcst7JvGZs0ooDvogUAvF42WPTCIM7Zsh1ixVqIJJ7sNtBE66/P2VGVdA2lS+SigaI8ImFZXqks1ttJl2EzPpqAjBd4gyGLZ/54qiKMp+oyKGEfKB1leBSe49lLL3umzK8Ne8SyhlodC/SC8Vld9xl0gFIxmW6INoC5gdsvOlYOqfPjIBjmIRGL27XDJxI+YgRr67leUvrGLxo+t4aWMbN5xTx+3nljOlyi/bfYsnQKBKfqdrC/TskokmMyLWnD7wjwdPkQieQlZaYf4KSd0OVMnyvExMgjTtHmkz2d39zy+fk3NlkyK6HL5B4m5E/J0riqIo74iKGEbYB1pvBSYT7w+l3GNk+wBDKXMZqWwkuuXDv9cMjNmozmyTNo2nVMy10VYjgiAiS/V6b5uOSNuqUJAKTbyLhjVvsnj5Wpa8sIX3Tq9m/gWVnDc5iMlbCSXjZKopX4DwdrnPTNo4Z0HESaAGXCWQiRiJ2gHwG1EHgSrx7aRjUrlxeKViM3D0ujfKIJsaFGWQSqVYuHAhd9xxBw7H/huCFUVRlOGDihhGmIgZyLvtmOnLeEoYE07vEkrZa5KNd0M6LALJVSItp2S3bP+NNIuXxlMmo9idm2W3i9kuPpveMMdUWK7PmyDZya7tm/nx42u578m3qSn1MP8947j2lBLsniAUTxQTr9WITOjaLCbjggksiPjwjTGyo2JAFuwBCBiJ2v5KqdRk4lJFcvhkummQmNktysDmOSK5TIqiKMrRQ0UMI1jEDCSfM3bQ7Gtk+wAnnHJZES7xHvngd/iMvTNm2TnTvV2Ek6sU7C4RH93bjNZPibSmskmpkPTudEmFiXfu5DdPreHux94mFE9zy4UT+MyZQUqDxWLgLZ8sQijcAh0bRZRgMnbNWMFTZQioDJAGR5G0mIpqpN3kDPRPKzkD4pkZuEcmm5bz5DKHNcpAURRFOfqoiGGUiJiB7LFjxkjRttjlA/tAQil7/TbxLqmumC2yoM7pl+V63VtFcDiMbcGpCHRtEtOv3Sej0iaT7K5JRaXNlE6QD7fx2EtvsvjRt3l+fSvXz6nl9nNKOW5sQFpFpVOlfZXolMDJeLd4ZvJ5OaevAjwVItjyOcNHYyzdC1SIEErH5Hk6AtJmGijYeqMMettnhyHKQFEURTm6qIhhFIqYgbxbKOXACad3C6XMZY1R7W5pFdlcIlxMZqnC9GyT27jLRBD0bIdwszG6XQo2r3hbkiFIpSCfgmgnq9Zv5O7H3uYPz23mwhOrmHduORdOC2Jyl0HJFCgaK4KkczNEWoGciCmzRao+3jLjgEa2kn+sjHYHKo0lf3HIJaXl5K0YLGYGRhnYvYPNwYqiKMqwRkUMo1zEDORdR7bfIRJhIL3VmWRIKi4ms7RuHH4JcuzeIVuBHT6p2MS6oGerkbAdFJHTO6KdjokgivfQ3LiNe594m5/8cz1jgm7mXTCWj5xagsMXhOJJ4pshJ2Im3CyCyWSSx3cFJceJApAXweSvlrFuf6U8j3RMthC7glLFsQ6oPGUShpg5+CgDRVEU5eiiIoZjSMT0stcKjGvPUMpeQfNOoZS5rHz4J7pEJFkdkqpdQIRLT6NMH7mDcn3PdmlDWT0SM2ByQKpbRqlzGUj1kOjcxW//tZa7H99AVyTFzReM47NnBikrLQL/BPHNmK1yXz07jT05BTECu4LSwrJYkMqMV3bPlNSKyLHYRcwUcv237RUzvVEG6ZgIowOMMlAURVGOLipiOAZFzEAOVyhl7/0kevrHrJ1+YyS7QwRNtFMuszhka29oh4gdb6nsnUmHxEycTUMqQT60iydeXc+ix9az4u0Wrps1jtvnFHN8TYl4XCpPAItLJqZCO2SiCYzKkBF0abXJIj2bWyozJXUymm2yiGAp5KUl5i3vb6ENjDIwWw0x8+5RBoqiKMrRRUUMx7iIGcjAHTMDKzA214GFUuayMgGU6BZhY7GJUMjnRGz0NAEmaUElYxDaLrtcXEaidTYrv5uJi58l2saa9Zu4+/EN/P65LZw3rZz555Ty3hOKMbkroOI4uf94p3hzkkalxVwQc7G71HgOgMPYPVM8STwzYIxtm8Rb4y7tFzMHGGWgKIqiHF1UxKAiZq/sVyhlXAQN7H1ku7dtlQxJdSafk/aOwyeVmO7tcp3dA3mzxBBE28Bml1Fqs8PYKBwWL0u0k9ambfzkyXXc+8+NlPudzLtgDB89pQintwTKDBNwMixiprdFZTVJ+8pVbHiALOKZCdZAcR0ExgAFaYv15kd5yvpbZ/sZZXAo6PI9RVGUA0dFDCpi3pVBFZj8O4RS7iUSoZd8TioaiW65rcUqo9qZFIR3SkvIBFicImzCu6Qa5C0HezFkQ/2VnXiYZGcjv392HYse20B7OMnnz6nhc2cVUVEchNKJEJwo49fdW2SaKpsRUWK1S8XH6gW7VdpMgfFQOkkEUC4jgsVsk8ceJGZyhphJ7DXK4FDQf4OKoigHjooY9APkgBg44QTvPLK9r1DKTFKqK0mjOmNzyQbdWJsszUtF5D7zKZlySvSAPQj+MhFRsQ4JqcwkKYQaefKVtSz6x2b+vbaF46q8/OKacZwysVjESckksBom4GinTEKZTHIeV7Gxvdd4DkXjoPw4qcxkk9LKsljFEOwq6Rczg6IMXFKZOcTtv/pvUFEU5cBREYN+gBw071SB2T0SYeAG4UGVDSP3KJMwtvL65PbRXbITxmQCLJDsEkFjskqqtc0N8Q4ROPkMRNp5adUazvz6kzhtFuZMKWH+OWVcPM2PyVcFZZPFZBzaBfE2qQBRkMd0GOPhdqO6FJwI5VMk1iCbkDNanWImdpf0G5oHRhkMyGU6GPTfoKIoyoFzON47D685QBk5WB3yNbACE+8YXIGxuwcYhhNSgRkoaJx++epdOpcKibjxjYGiWtk7E2kGux/KglIdibVCKC4m4JI6qYrY3Ew7JQA8yZvfncvvV2zmht9vpsTrYN55nXzs1CZc3mIonwaV02ViKt4KyagIpES3bO51+GTKqWsLBGtFzARrIJ3o30/jHyNj5BabfO+NMoi1a5SBoijKCEMrMUo/e63ADBjZ3lskwkDDcD4nBtpEj4gek0laTbmUUUXp7H+ceKv4XWxe8FURjiYIzL6O0NIF+G15kp3b+cMzb7L4iY009yT53Dlj+fyZASpLAuKbCYyHZAQiO41U8JyMZ9tcImYc3v4k7crjIThORE/aCJn0jxF/Ta9gyab6oxUOMMpA/w0qiqIcOFqJUQ4vZrNUXwZVYIwqS28FpndCqTcSIRWG5IBIBIdPvnrzjXonmwJjJegx3gXRFjBVyLK6RA/07ICosSemZDJYEjidXj5+zURuvKSVp15+k0WPb6D2iW38v5lVzJvdyfTajeCplAmlfA6izSJQUlEZrU46pb2V6pEx8MB4Q8zUip+n7W05Z1GNjIv3VqZ6n286tkeUgU4hKYqiDC+0EqO8O70j25nE3isw7xSJkM9LpSQZlu8U5PfSCYi2iqemkGXlC68z59PfZMXdn2b2mTNl50s2AeFWSCUg0826tW9z96Nv8dvnd3BWXTHzzynlfdP8mD0VUFonfp54GyRCkE6DxWSILy84veDySy5T5QkifhLd0gJz+KVS4wz0P+dMQgQRGJUZ1z7/ra1cuZI5c+awYsUKZs+efXT/bhRFUUYoauxFRcxR52BCKW1umSjKpgwzcFjaNmYLFKDhlee59Lov0NLRTVVpEcu/91nqxwWkCuKtAlNBPCvJECQidDRv577HV/Pjf24m4LIy77wKrjs1iNsfEJ+NvcgQM2E5JxjGYy+4AuDyQWACjDkJiieImEmGxN8THN8vZnpzptJRMJkJpwoESsoH/VtraGjg0ksvpaWlhaqqKpYvX059ff3Q/N0oiqKMILSdpBx9LDZj862/vwKT6B5cgXEFB0cipNv7IxGcRfKViRttmzhLn36Jlo5uAJo7elj26g7qT7lSYgx6tgNZSbD2jYV4F6WuAP9902T+48pm/vivVSx+bD3/9Ugjnz27gptntVNV4oPiWgmQTEYh2i4L91I9kAlDzC1tre5NUDRRxExwouRA7VoNriJDzPhFSNmMAMqeFnkNsum+l2Pp0qW0tMjlzc3NLFu2TEWMoijKUUIrMcqhUyjIqHImPrgCM2hkex+RCLkMDa88z9wPXkNzaztVFWUs//191E8aayzIMwy38Q7IxsBhxBvk87KXJhujEGrnmdffYvHydTz5VhsfPq2cebOLmTHeL9uD/dVAGiKdckZTvl90Of3gLIbicVA1Q9pMqR4JxXQVi4fG6QMgHAoRKCoi1LQBf7AEHD4aVr/J3LlzaW5u1kqMoijKAaDtJFTEDDv2GUrpNFK29x6JsPKFl5hz7nmseOxvzJ55ElCQiaNsDGIDsphi7dKOsthksZ3ZJpWWRBckIqzfuJ67H1nNr5/bzpm1AeadW8bc432YPeViLjaZ5fdTIdkyXCiAySYtJncJFE+EMTMgWGckdHfJ5cFawumC/Fvr7sbvNPdFGax8eRVzzjt/yD0xajxWFGUkoSIGFTHDmt1HtnsrML1L8/pGthOEQ2EC1ZMJdbbh9weMdlNYblPISwsn0SVVmXQckp0Q6zHiDSrBXSQ7Z3p2QjpCZ3MT9z++inue3IjPaeG2c8q54dQAHn9QxIzFBdkoJKJgyspZzTYjQTsoIZNjZsi0VKoL4l2Ec04CU8/q/7dmRBmEO9sIVE8h1N2Fvyg4ZC+3GowVRRlJqIhBRcyIYfcKzMCleSYT4a4OAiVlhJo24vf7+qs3+az4UdLGpFAmZaRs9/RHIMTaRdzY/eCrALIQaoZEF+medpaseItFy9eyrSPGZ84q55azixlb6gdflYxhkzHMxhkoZMFklw3AbmMhX/WpUDqZcPsOAlNnE9rwHP5xJ0uqNhDu6SYQLJY2U0m5sf338OQy7S9qMFYUZaQx6o2927dv56abbuL5559n0qRJLFq0iPPPP3+oj6UcDGaLsVXX21+BSUVlKsjqBAwt7SsHl0MET6Lb8NcY+2lyaTBHROA4/P17alxFxsh2G3RukqRrTzkUVWP3d/GxKyr46HtO5d+vrWPxo28x8VtvcfWMEuaf08kp4/3gLpOWUT4HmaiMZ8d75HzRVujYCKV1rG6xAbD6rfXMNiXFmxOc2C9Yeu8j1n7IUQYHihqMFUU5Fhm2lZhCocDFF1/Me9/7XiorK/n+97/Pxo0bWb16NXV1dX2300rMCMcY2Q53tRMYO4lQ6w78xRWDR7YzcUPAWMHiAAr949rkJWogFZVqSi4pk0eRNsgnwVlm7JyJS+J2tJ2NW3fwg+Wr+eWKbcwc52XeOcVcNs2LxVsqtzVbpdqTTcteHLOFhp0JLv3BK7T0JKgqK2b5Q78T83Gsg3DBRWDKgDZTXy5Txlge6D3iUQYNDQ1qMFYUZUQxqttJa9asoa2tjQsvvBCAtrY2Jk6cyLe+9S1uu+22vtupiBkdpFIpFn7rf7hj/hdwWBgwsu3eeyil1SFVmkJeNvTmMv2TTOmwLMhLRSS7KRWR+/KOETNvtBUizXS1t/Kzx1fxo39uxGWF22aXcuNpRXj9PnCXy2Pk0pBNsuDv67lr+da+8y647jzu/M+vQvlxhDt2iVdm/XP4x0+XahMcUpTBwaCeGEVRRhKjup00depUTjrppL6fy8vLOf7443XqYpTicDi46xvflB/eNZQyZ0xAJcXHYnXJdfm8MbZdLNNHqai0nXIpaTWFtgIF2TkTqKe4JMxXKquZ/8F2/vzsWyx6bB1fe7yFm2aV8oVZ3VSX+WXM2uHmilPHcf+KnTSH01T57Vw+PgGv/hpKJkLJDONZFKDxZfCUyRI9h7c/yiAd3WuUweFk5syZfP3rX2fmzJlH5P4VRVGGG8O2ErM3Jk+ezDPPPEN1dXXfZb1KbsyYMZiM/8udP38+8+fPH6pjKoeTfY5s7yOU0mQGTHLbXlNwokdaTtmERBJEmiEXA6sPPBVAGnp2UgjvYuWqrSx6ZA2PrmnhyulB5s8Jcto4H7gDrNySZs73XmDFl05ndp1XHscEKVsRC59q4Y4vfxHH2JNlSireZXhmavv2zOwtykBRFOVYZVS3k3bn2WefZfny5Xz3u98ddLm2k44hBi7Ny2f2mHAaFImQz/fvgclnROwkuvqjCDJRCLdD3Ngm7CmT+4m1QU8jm7Zt54fL3+SBFduoH+Ni/rnFnFfnofhr6wjdfYFMUGUTUhXK5cFilsV5pXVQey5UHC9trGS3sX+mtt8bk473RRlg94ooUxRFOcY4ZkRMJpPh1ltv5e67796jnaQi5hhlH0vz9hpKWciJqCEv31MRqc6ko3KbaBdEOyCXkMgEd1Cmpnp20tPayM+eWMMPn9yE1VRgW1eKpv+eTGmRl4VP93DH5cfhMGflPIU8YJJ07NI6mHgOlB8vj5EMGXEGtXI9GLtwotIu6209KYqiHCMcMyLmO9/5Dh/96EepqanZ4zoVMcoeoZRWh1GhcQz212SSUpGhIIIjl5FKSbwbslnZ0Btpk9gBi1NaTaYc9DST6Wrkt0+9wSd/8RoBp4XrTw3yo+c6CH3rRPyBYP8Cv3wasjkxHdudsixv4hyoOknOlwyJUCoaJ5UbMPwycdlC7PAZ2VSKoiijm2NCxPz85z/ntNNOY8aMGYBMsVitViwW2c2hIkYZxMAKzMBQSottsL8mE+/fBoxJqjPxTqmMZBPiaYl1iNBxB8HqJdy5k8Dld/GPL5/LPY+vZdnqdj50YoCvXFDM6TUeIyzSLe2pnFGdMZtFTJVMgNo5UHNK/9SSMwBFNf2VmXRUzmWxiyHZMmx994qiKIfMqJ5OArj33ntpamqiurqaxx9/nHg8zsMPP8yvf/3roT6aMlyx2uXLGTB2zCREnAwMpXS7IF8kYiVtjGI7PGD3SGsq0QVOL3jLZfdMpB0SO6AgxvEzz7+EM0+ZTuDaH1FRGuDC+3cwvcrBvDklfOA4L1aXMS1ldoEpI7trWt+Czo2w5RlpM1XVy2O1viln9VeLAdjuETET7xDx4/Af9e2/iqIoI4VhK2IeeOABbr75ZgAWLlzYd/kXvvAFzEdpC6oywrE6BrSUjApMOgZmK6mciYXf/wF3/Od/4XAHjeuiUiFxF4OrRMy/8U7xsqRi0L5T7jfZA/4qAL5zyzUsvKGFnz/2Ol9cvoX/WN7KrWcH+eRpAfweu5Hk7QKLSVpWbeuhcwsEn4bas6F6plRt2teKmPGNkTaT3SviKtbev7FYxYyiKMoghn076d3QdpJyQBhL88JdbQSqJhBq3oq/uHxwKGUmbmQzxZHtwBlIhUn1tLLw/j9wx0fPJdXTTuCK/yH0tzvxl5RBKkK2azt/ffp1Fj2+nrXNUT59epAvnBWgtsgu/hirR8SMySytJqtdwisnzIbas8BkiC1HQHbZOANy5nREqkpHOcpAURTlSHJMeGLeDRUxysHQ9++mfRd+l22voZRk08bOlx5pCeVz4rWJd4kIOvsGQo9+G78lJdFPDp94bMJNvPDaWyx6ZDVLV3fw/hP8zJtTxKxxLjDZJDrB4gCbpS/WAG8ljDuL1JiZLLzv19zxuetx+Iol0LLXM5OKyP4bu+eoRBkoiqIcSQ7H57f+L52yT1KpFHfddRepVGqoj3LksHtkKZ27VMy/vaGPiW6gIBt7S+uguE48Mk4f+Meyepe8Jqtb81A6GbxlkE9J5IG3jFkXXMKfv/Fx1i/+INVlAS7+eROzfrydJau7yKZCMgmVjEiLKZeD8C5Y+zCppxeyYNFPScUMv07nFujcLALG7pHzZNOygTgVlVaZoijKMcoBiZg//vGPR+ocyjAklUqxYMGC0S1iDFLZHHct/D4pm1+W05ksMg4dbZPvJjP4KqHsOBoaw1x9y38BcM1XFtOwKyFTRsFa8I+TKks6DFY7tSeewaIvfZymn36UD8+q5SuPdlD3v9v4/rMdhCIh2SCcDBnTUjlZwAewchGsW2p4deLQvRW6tw8QM0XSeoq1y/UqZhRFOQY5IBEzb948rrrqKn7zm98QjUaP1JkU5agzSLBZbGKu9ZbLTpdCQSoz0TZIRVj66D9oaRWx0dzWybKVb8p0UdF4CIyVr+A4Gc3OpYA8/opJ3P6Jj7Dxp5/i+x+p569rE1R/exu3P9LC1vYYJKKQ6IB4WA6U7IbNz8DT34Y1f4FIl1ReenZAT1O/mHH4xKwc6xDBoyiKcgxxQNNJTzzxBMcddxz/+Mc/mDdvHvl8nssuu4y5c+dit9uP1BkVZejoHdkesDTviovmcP9PK2huaaWqspLLP3wDVJ0gQidhLM/LxMBmfE9FpHVUSGF1F3HVBy7jqvedzUuvr2Xx0tc57vvbuOw4D/PPCXJiqTGBFOkAU0BMxVufg50NUH4CTDpfKkKZqPhinAERM4WCPE5vyKRGGSiKcgxwSMbeeDzOLbfcwsMPP8yHPvQhPvKRj3DBBRf0BTEeDdTYe+QYza/t7s/tgJ5rocDKfz/FnPPfy4rH/8bs2bMHh1KmorJrJtYlS/NS3ZCMGRt7DaGRTUneUjbDju1b+NHDL/HTlU1MKrbx+q4UHf9ZS4nfCjmzMWJtB5sRrVB2HEw8D4I18rh2r+y5sRnp2MYYuUYZKIoynDnqxt6tW7cC0NnZyf/+7/9y0kkn8eCDD3LJJZdw3XXX0dnZyWc/+1kWL158UIdRlBGBycT0U04HYPoZ54qQyCTFEBzvEv9MoEaiBsbOgMqToXSSVFB8peCvAF+57I8xWxhXO4nvzfsYTfdfx4fPHA/Ayfc08b1/99CTykAuDLEeiIVkb83O1+CFH8NLD8DO1RJaGW2HWKcImN4NxYkeOU82fchP+ZgweSuKMuI4oErMzJkzqamp4dFHH6WmpoabbrqJj3/845SWlg663Ze+9CUSiQQ//vGPD/uBd2c0VwuGmpUrVzJnzhxWrFgh1YZRxO7P7UD/He319u8USplLS6spYgiOeBvEQyIwMnFpO2VThFM5Alct4nefOZX7nlxPQ1OMT5zq57azAtSVWiCPCBSrFxwOGQcvqoUJZ0PFNPHh2DxGG8xoKWWTRpTBwecy6X9niqIcbo567MBrr71GeXk5y5Yt473vfe8+b7dr1y4effTRoyJilCNDQ0MDV199NQDXXHMNy5cvp76+fohPdXjY23OLxWIArF69+uAFm9kiLRyHV5bmZROQCkPSCKV0BcFTLoIl1gWRZvmKdkLGCZk0ZEIAXH7+HD568Vm8suZtFi99nePvbuTSKW7mz/YzuyaPKZuCtEXymlIx6NkC3hqonQVVJxr7ZbLSVrI4gIJUcawOsPs0l0lRlFHBAbWTvv3tb7N8+fJ3FDAAt99+O7/97W8P6WDK0LJ06VJaWloAaG5uZtmyZUN8osPH7s/t/vvvHyRqGhoaDv1BLFapfPROOJlM0t6JtctCvMAYGFsv3pYJs6DqZPCVsXqXTP2tbgqD08fM+pN58M7r2HT3h5gyNsgVv2tl5n3NPLgqTiaTFY9NrF2MwB3rYPWf4Pl74c2/Q+v6/kDLXFqqMfmc5DIlQ/Ln3dC2kaIoI4kDEjFf/epX9+t2p59+OpdffvlBHUgZHlxxxRVUVUk+UFVV1aj6+9z9uQFHVrD1BlL6KmS/S8GoiiTDInZKJkPNTBoSY7h6we8BuGbhX2hoikoApN1HzfgJfPcLV9F433XceM5E7nw6xITv7+S7K0J0R43NwrFOGbXu2Ahv/x2e/zG88SfYtRqSUWld5bNgsoqxONYuZ8jn+476yiuvsGDBAl555ZXD+xooiqIcAXRjr7JX6uvrWbJkCQBLliwZNa0k2PO5feYznzlgweZwOPj617+Ow3GA0z9WhwgZrxEnkMvIJFM2ydInn6WlvROA5s4wy9aEoKhadtY4vGD34i2t5JYPv4/1P76eH183g0c3Zqn+v13csrSLje0pSIRFzIQ6oGMzrFsulZnXfgWNr8gWYPJSDcIkfpxYG6lwB5/5zGcOf0VKURTlCKLZSco+Gc2v7e7PbUhNzEYoZcNrLzP3gx+mubWNqspKlv/tL9QfVwuRFtnW27NLluDlEpDJySK9XJrX1qxj8SOr+fMbXbxvsot5Z3k5t9qKyWIT0WRzg8Ml4qnyBBh/Bqmyk1j4owe4Y/7NOOx2wqEwgXHHDTrWggULuPPOO/f6eimKohwqGgCJvrkeSUbza3tIe2KOICuffZY5557LiiceYfaZp4qPxWwRoRNthdAu6NkmE07JMBTSkExDIcfOph3c88hr3P9cC7VFFuad6eHDJziwWy1gcYoJ2O4AZ4CweyKBG35OaHMD/spxhLu7CFRPpqK8jNa2dhFRy5dTf8ope329FEVRDhUNgFSUUcb0GTPk+xlz+kMps2mpunjLYMzJUHch1F0AVadKVpOnCGwOxtZOZOFnLqfx3g9z49njuP3xMLV3t7Pw2TBdkaj4cKKdEG5l9cvPArD61/8Fa/7G6tdeBuBrX54PwJJf/Ij6yWP7ogxWr1496LuiKMpwQEWMogxX+iacyiSU0myDQk6W65XUwsSzoO48mHAOVJwgC/YcPjxFxdx42Wy6EnkWf/h4ntyep2ZxO597pIf1LWEaNjdz9a83AXDN4if4w33f5errPwnAN//3+9z0iY8z84wzZYFfpJWG555Sr4yiKMMSXRahKCMBi81YVOeXykw2AfmkjHB7yiRwMtYmvpl4G+QbAbhkdj0ffs9pNKzbwN3L13Ly/V2M81toicpEUnMky0//3UhLKAlAS1sHY3NNOOKtUDqZVDzMvK/81x7TW6PJ6K0oyshFKzHKPjnoCRzlyNI7su0tl+82Bzh9EJwA406DmjNg3Ey5belkcBdRP/0Efv3Fy9iy8GLOmRSgN90s4ICPTzdR5ZW3giqflcvLdsE/7oJ/f5/Uzrf593MvUVFeJtdXlHH5e+YcligD0L00iqIcGipilH3icDi46667jgkRMyIFm8kkrSVXUEa23UERNYGxUD5NbjO2HmrOhIrpUFTLmAkT+Pltl/GPL54FgN9h5itPJZk7WdKzl1zloz6QhHAjrP8H/Ou7APzqm7fL9b95gPqpNdCzQ8zFucwhPYVUKsWCBQtUxCiKclBoO0lR6BdsIxaTSYIfbS6ZZEobtZbiCeCyymRTrAPi3RDv4oxTXcDzrF54Kc+t2sT3ntgGZPhFQ4wSV55pZSGwuIEIACd2PgbAdH8UbF6JM0h2Sx6UOwjOoEYZKIpy1NFKjKKMNsxmGacGiTforcxUTocxJ0H5cVAlnhZz+RTmvmc2//jqRXzm7EpyJgf194e49Pch/rmxm0KsWe4n2irfX7gXnlwA658Ak00qP/Eu6NoslZm9RBkcKNpiUhRlf9H/dVKOSUZk++hgGBhK6QpCtgICNThcjXz95o/iGHsimDI4iru4b34NxDr5352N3PvPt7n2L11UeqWikwobIibUAjui0PY2bHkGxp0pX84iGeGOd4KnBFwlIqYOgt4W0/z580f/34+iKIeELrtTlGHE4fr3/K73k8tAOi4RBT07ZCtwKiIZS9FdEG0j0dHIz554i9uWtVHqNtERL7D5Vg8Tg36we8DhkUiEkklQfSqMOx08pZLSbbbI1JSr+B3FzN7Oqf9NK8qxgS67U5RRxuGqEL3rcjqLDVwBKJ0ItbNgyoUiRErGQ9lUUmUz+O6LeU48Vaacbp0t00kn3Bvj00s7eKupGSI7oWsn7HwF3ngQVvwA3vq7CKMC0LNTKjaxDgm9VBRFOcyoiFGUo8T+eD0Ox0RYQ0PDgS2nszqkajK2HqZeApMvIhWsZcHv/81HfiCbfX/8chSAp2+eSh47p/0sxvt+180TG1oohJuhcyc0vQ6r/wwv3Adrl0l1J5+Gzq3QsmavYkY3ASuKciioiFGUo8TRGideunTpHsvp9guTCewuKB4nsQZAa7dMJ7X2xAE44exL+MWXrmTbN07jzHFePvbXBCf9pJtfvNZKMtIMHdtgZwOseQhefUBStCMtkpbdvlGui7ZDoXDgYktRFGU3VMQoyijjiiuuoKqqCoCqqiouv/zyA78Tkxh6Kyoq5HtZqVweqIYx06g45VLu+tzV7Pj2bObNKWXRixnGLQ5x1786aG3fBV07pDKz5q/w2q9g3eMSXplJQPt6aHyVpUsePDixpSiKYqAiRlFGGfX19SxZsgSAJUuWHFJEwK9+9SsAHvzjn8Src+YnoO69UDIRSibinHYhn/zo1bz5rYv53YfH8GJTgfF3R/jk3zt5c0ezmIYbX4M3H4aG38Pbj0PXVkiFuWLWFKrKSgCoqqzsE1vaYlIUZX/R6SRFOUoczX+rh/pYvb/f2NhITU3NnvdTKEBPIzSvho71kIzIV/d23lrzBnc/3cTv1qSYM87CvDPtXDzJgdnklsV4ZZMksLJ4PCs39jDn+q+w4o/3MPu9l9KwuY1Lr/gALS0tVFVVsXz5cs1pUpRRyuF4T9Q9MYqiHDgmk4ROBsdB6nxoXQutb4EzwAnFdfysvolvbV7Dfc9s4ca/xylxpZh3ZpKPTY/iindA2zoonsT0wFQApo/zQ8cWlv5+zxaTihhFUfaFtpMURTk0HB4JnDztBjjlOqibDWNnUD7zMu686Sq2/8+Z/MfZfn70cppxd0f42tPdtLTvgp0vwZsPyX1sfwV2NXDF6ROoKgsCUFVeyuXvOeeQ8pl0+6+ijG5UxCjKUWIkeD0O6UPfZILSCXD85XDGTTDtMqg9E+fx7+XjH72WVV8/lz9cU8brLXlq744y98Fuzv1po/zumj/Dmr9R72hjyX9dA8CS732R+jEO6NgI4WZZzneA3W8NmFSU0c2wbyctXLiQLVu2EI/H+eQnP8kFF1ww1EdSlANm93Hi4er16P3Q/9SnPnVod+QKQO1ZUH06dG6CljcxFVfznuqTeM+Zm3jo2Ve4fkk78azc/L6XuvjS2SnM3VuYbisHYLo/DI0vgb8aAlXgLpWAS6exMdhiO8RnqyjKSGdYi5h77rmHjRs38sADD5BMJpkxYwbLly+nrq5uqI+mKAfE3na3DEcR08ubb7456PtBY7VCxXHyFWmD1jchuIY3n+0hnm3vu9k3nk3zwBtZbj8zwQeOS8iFa/4GE0+FYKcIocBYCNaCfwwkwxJyaXOB1XXQOU2Kooxshu1/+el0mrvuuosbbrgBAKfTycUXX8y3vvWtIT6Zohw4h2V3y1HkxhtvBODjH/84N9100+EJYvSVw6QL4MzPcMUNt1JVGgDA67Dy+CcnccdsJ/e9mub4H/cA0Ny6EzY+CW/+Bba/DLtWwaZ/woYnoGMzJEKSoB1rI9XTyl13fm2PttFIaOHtL+rvUZQ9GbYi5rnnnqOzs5MTTzyx77KTTz6ZRx55ZAhPpSgHx+Hc3XI0aG2V1OqWlhbGjh17eNOkbU7qL/owSx5aCsBjP/0Gs6/+BDd85Foa7jiNX39ARi1Pvi/M9Q930bB5F2xfKVEG21+FlrWyb+bNh6F5DSTCpKJhFvzPN0l17YJ0DPL5UbcRWP09irInw1bErF27FrPZTDAY7LssGAzS3t5Od3f3HrefNm0a1dXVVFdXs2jRoqN5VEXZL6ZPnz7o+5HkUIMkezf1Hsmq0cwzzuDrX/86Mz88H2bdDDM/jqn+Y5w79yoAnvtEGV47nP1AmAl3d/DX1xrJN70KG/4Bza9DxyZY/ySs+iOrH/8dAKtXr5GtwLE2lj60RDcCK8ooZ9h6YkKhEEVFRZgH9Lp735Dj8fggcQOwbt06XXanKAa9QZIHy69+9SsuueSSI1o1GnxGB0yYDePOxDFhLV//dDcnXjSGe0/bzJfffpMJi5u4+bEkX30qxe1nhrnh5BCeri3gr6Uh7OPq/30SgGs+eh3Lf/ND6mdfxBVz38f9v3iA5pY22Qh82WVH5HkoijJ0DNtKTHFx8R5l00RCDH+7CxhFUQ4Pu3tHjkbVaBAWK46a6dx1/0M4LvoanHMrTWPOA+DBa8dy57lOfv56mprFbdzxSBM7N73O0if+RUu3BFQ2d4ZZ9vufQsMfqQ/EWfKzHwKw5Dc/p37yGEj0QDZ9dJ/TYWI0+XsU5XAxbEVMXV0dsViMZDLZd1l7ezvV1dW43e4hPJmijE4Gekh6jb1DhskE/goaEpVc/X2psnz0ryFOOPkMXrt9Cg9/OMDajjwTf9jDS41RSo23hCq/jcuP88humc3PMJ11AEyv8csUk8kEiW5J0ja8MyOB0ebvUZTDxbAVMeeddx6lpaW88sorfZetXbuWuXPnDuGpFGX0MnAMvNfYO9TImeQszV0RlsWnY5pzO+de+D7+/tmTefNzZUwMmokYRdsvnArT82/BjpehfSO0b5Ur1j8Bq/8ETW9APiuj2ZkkxNpE1Azz6szeRvQVRRnGIsZmszFv3jz++te/AhCLxXjyySf56le/OsQnU5TRycAx8F5j71Czx2j6tTfArJvgAz+EC77C5Nlzuedjp/D2LZUA3PNqlqk/aOaeJ98iuul5aHpV7qhrOzS/LVNOb/0dNj8DsU4RMwX6qzOp6LCszoy0EX1FOVoM6xTrXC7HV7/6VdLpNKFQiE9/+tOcffbZg26jKdbKSGEk/FtduXIlc+bM4bHHHuOSSy4ZFmftPdOKFSuYPXv24CvTCdj+EqnX/sjCXy/nS6dZWbq2jUUvJNncneeT9XZyeTPfef94HMGx4KkCfym4guAJgm+shFgWjQOzFShIpcbqAJtbvg8xqVSKhQsXcs4553DhhRfu/XVQlBHI4XhPHNYiZn8YCR8MigL9H0Z33HHH4d27chjp/e+psbGRmpqaYfHf1X79N57Pwa43YfWfYfuzFLp3sXJjO4tejPPoxixXTrMy70wfM+tKwVsO/irwV4CrGJxF4KuE4lr57vACJijkwGSRao3NPWRbgYfj34miHA4Ox+f3sB2xVpTRxqGOPR+r7NfOG7MFqk+GsdOhawemVX9iTtlTzJm6jc27OvnBSxHO/3U39VVh5p3Zyvun78LiKQFvJZSMlc2/oUbwVkDJRBEzNo803FMRSEeHVXVGURRBKzGKovQxqv6vP9ZF6rU/sXDRYu6YaSERCfGz17r44ctpbGa47QwXnzi9FF9xCXjKpLXkKQOXF3wV4B8n1Rm7x6jCFCRF2+o8qtWZUfV3oigD0EqMoijKvvAUk5rxURb8/fPM/+KvKdqxnP8oW8/tc7p5aHUHi15Icue/dvDpU1q4dVYp46rawFsqbaZED3TtgI71EKiBkjrwlohvJpOUrcCmHnB4jlp15lC3MCvKaERFjKIoezDqPjBP/gCcfhVsex7b67/jWv9bfPiULp7f1MHiF+NM/sEuPnhcG/POCnLG5HIRLN4qCZmMtEDbRiiqgtLJUFQNVjfkkiJ24t1SmXH4jmh1RtuRykjkSHsBtZ2kKEofI8F8fCDs9f0hm4Idr8EbD8KuNyDSxtaWLn74UoSfN6SZXmFh3pkePnDKWKz+YvBUihnY4QOnR3wzwQlQPBE8JVDIQzIsRmCzBRx+MQcfpuqMvscpI5l3+ver00nof+CKouybd3x/yKag+S1YtQR2vATRVkJdXfz89R5++HIaE3DbGR4+eUYZ/rIKMfu6y8AVALsb3CXgK4Oy4yBYC1a77JlJRWRayuYCd9CozliOzHNQlGHOkRYx2k5SFOXYxOqAmlOg6gRJxH7z7wS2PssXy5u5bVYHf13bzeIXE3z9X1v51CnN3HpWCbU1lVKZ8Zcbadnt0N0kO2eCE6FsinhocimpzoSawGSW6owrCDbnUD9rRRlVqIhRFOXYxuqAyhOgdBKc8AHY8CjWLc9xTUkT19R38MLmTha/mGDqD3ZyxdQ25p+9k1nHlYPb2DfjLYN0HKKd0L5Ofi6dJvfnq5DqTLIbOjtFxDiLpZpzCNUZRRkpDAwuPRJLGodt7ICiKMrRIpVKcdc3F5IqroOzboFLvgP1N8CEs5hVfxJLrqtl/S1BxvlNXPzrFs5c9BZLnnqNbONrsPMVmWKKtBiVme2w5Rl44/ewZYW0rYIToGSy+GpibdC2Tm6Xirzr2TS9WhmpHI3gUhUxiqKMWvZXAKRSKRYsWEAqlZJqSeVUOPNTcOFdMPMGmDiH2ikz+P4HJtA0v4RrT7TylX/2ULfwbb7/8BuENr4Kja/AzjegY4fkMiUjIlbWPASr/izJ2o5iKJsqosZkFiHTug7CLXsNodT0amUkczSCS1XEKIoyKjlkAWBzQvlkOOV6OO8OmHkj1J2Hf+Jp3H7hZDbeWsGii5z89e041Qs3cvvvGtiyZhVsfx52vAJtb4k4yech2QPbVsDrv4SN/5INwEU1UHEC+CshE4f2t6FjM8Q7+0IoNb1aGckcjeBSFTGKooxKDpsA6BUzM66B878Mp14Hky/AOv5UrjxzKs/dVMU/r/PREk0z7QfbuPLnb7HylVUUtr0MjS/I5FPHFshmwGyDns2w+i+wegm0vCUbgEsmQtk0Gc2OtkPrW9C9gyve9x6qKiWheyjTq1OpFHfddZdUqhRlP6mvr2fJkiUALFmyhPr6+sP+GDpirSjKqKShoYG5c+fS3NxMVVUVy5cv3+eb6AG9j2SSEN4FO16GXa9B+2aZQop3sKOtmx+9FOenr2eYWmJl3tkBrjq1FJurWDYBB8dD0ViZcCrkIZ8QYVM0AcqPE1OwxQrpmOQ5pSKsfOl15rz/OlY8809mn3sBmExH4NV6Z/R9VjlYdE/Mu6D/cSmKsi9WrlzJnDlzWLFixTtORhzU+0gmCaFdsPNV2LlKxrTDzRDdRSQU4ZdvhPnBS2nSObj1zACfPquUIq8PiiplDLu4FgJjweKGbEQ8MZ4y2QocrAG7V87W1kSgqpbQxpfwB0skdfswLtPbH/R9VjlYdE+MoijKQTJ9+vRB3w8rNieUToTAGBh7GrSsgZ2vQ+cOfD3buDXYws0ze1i6PsriFyMseKaHT5zq47Y5PdSVN0HH2+AdB5WTxejr9kEmBdtfhOZVUDQOSibIEj2A4glgy0OiU6ag7B7ZP2N3g8V2+J/fAI70mKyiHCwqYhRFUQ6FgWKm6mRoXg3Na6B7M5buXXzQ38wHj+/glaY4i1+Mc/yiLVw6xc28OSXMqWvD1LkB/GOgYiqUTgFPOalUnIULv88dH78cHEXyOKmosTW4BLIJyW2KtsqUk90rYZRWl7SjDiO7G6TfqS2nKLtzpHPYVMQoinLMc1gqDTYnlNTKtFHVdKnMNL8F3dsg3MjMwC4eHNdFY1eMe16O8f7fNFFXYmfe7GKumRHG1rMNml6FimmkPJNY8PO/M/+T10CsW+5/+4uQmSS+GWdAWk8gk03JMGRiYLJIhcbmkq/DsFBvbwZpFTHK/nKkg0t1OklRlGOaw76LpVfMTHkP1F8LJ1wBE8+DmrNg7MnUTJjId+eOpXFeCTdOt3HXk21MWLiR7zy5k66WRti0At74g9xXTxN4iuTPuRS0vgmNL8v37u0yjm0yy2Zgb4VMOqVjcnl4l5iD0/G+ke2D4WiMySrKwaKVGEVRjmmOWKXB5jIqMxVQMQ3a3pav7q0Q2oU3tItPn9VOW6yZ6eVm7nm1h//5Zzs3nhbkk6cH5T5WL4GACAisHgiWQjIkI9td28FXLq0ou1cez+4W028+I+IlHYN0AsxmMQLbXCJ0DmDCqXdMds6cOUdsTFZRDhatxCiKckxzxCsNNpcYdCedByd9EKZdBnXnwPhZpCpO5n+ejXHR9Cr+dWMZKz4eIBxLMOuezQCsWN9JoX2T3M/zP4a3HoNcTnKZvGXiidnxCuxaI2PeiS6pvuSyhk/GJ8bgQh6yyX4fTaJb4hD2czj1iBqkFeUQ0EqMoijHNEet0mBzyVi1txzKp0L7BnCvBh6CypMh28kpng5+O7aH/5oTZdqPu/jYgzuoKZLppHSoFTY9BjtWQMXxMG4OVE0TcRJrk4kmuxf8Y8FXBTY7MKACU8hDPguYZJy7N+bA5hRDcO8UlKKMIFTEKIoyatnfyYijWmmwu8E+npTVz8J7/yqX1c6CTKvEFIR2McbaAnSx9vMl/HldhgX/SjN90SZumVPOZ2ZCSfpVyWkK1kLtbBh/JhRZZfS6cwN0bgTfGIk2cAUAo31ktgEFETQAZivkMrLzxmSSVpPNdcRHthXlcKHL7hRFOeYZiveR3scECG1djT/TJgvzupsIt24n8InfEvrOqfjzEfLJGI9uSrHoxRgvNia54bRSbj+nhKlldhEfnhIxDtfNlipMMiTtpUwMXMUidnyVA6aVjLf93rd/i00mmyhALi1/HjDhlEqlWLhwIXfccccRG5VVjj102Z2iKMooYHVTiNmnz4KSOujcBo7VwG+h8gTI9mCOtXOZp5vLjvPyRkuSxS9Emf5/63nvVD/zz63k/IkdmN5eBluellbTxPfA2OmQTkNkhyzhszqlMhOsBbsLMIOpIJWYXn+MxSbCxWQWMZOOgtmGw+bkrjvvFIOwogwjVMQoiqIMAb27aWC3JXKeMrAVyxU1Z0CmA2ItEmkQaWWGK8yvx7hZeFGae1+KcvWvN1Fd5GD++ZVcOx0cja/Arjdkw++42TDxbCg7TiISerZD5yapyhTXGo9lTCv1iplcEjCBzQN2H1CQdlMyfEATTlq9UY4GKqsVRVGGgOXLl/f9eVDKtsPD6qYwAKsTJTDpHKg+HWpOhepToeIECIxhTFkJ37yogsYvV/P50z0sfGIntd9ayzef7qIjmoHWt+H1X8Hj/wmv/VZ8MLXnQFW9iJVtz8PmZ8RgnIqJP8bhkygDsw1SEZlkSoZkC7C7GCx2GdvunXDKJPc54ZRKpViwYIEmXytHFPXEKIpyzDMU7yO94ZTAoJTthoYGLr30UlpaWuTyh/9C/aRK6NkhC+56mmQaKdIJ4Z2Q7IZ0inwuzeMbEyx6Pszz2xJcd3oZt88pZ1qZDcx5ESel06DuXBh7CljM0LVN7oOChFEWTQSnTyouZqvsm0lGIJ8GTFKZcXhF5GQTMhlVKAyo0Dj6KjA333wz5eXl+t6s7BP1xCiKoowCBo5277F87x//pP6MO2Ujb9E46GmE7iYI7wB/OUS7ILQTc6qLS09wcelxflY1J7n7+TD1//cmF0wpYt55lbxnUgRT08sShxAYC+PPgglzoGwaRHaKQOp6RlpMRePk8WxOyWoymWR5XiokFRirHVxF4AqKiOnNcjKZSMXTLFiwgE996lND94IqxwwqYhRFOeY50iF1uzMw6mB3rrjiCu6//36am5sHL99zeMAx0RAzNdAzDrp3QLhR8ppi7SJwEj2cPM7JL6u9LLwkyL3PR/jIbzZS5Xcw7/wq/t/JFpyZzeKP2fAEjJ0BteeJqElFoXsL7HpdWkdFtSJo7E7xwfjHQiEn/phIG9ACdr8IGm+5mIFjrXLeWKd8z2WP7IupHNNoO0lRFOUos2DBgkGheHfccQff/va3+37ubTWtWLFi34GUqah4U0LNEGoUARPvhngPhLdDrEuW22WyJNJJfvdGmMUre+iM5fj8nCo+N6uEcp8JMIPTDyWTYPzZMO50cHqhc6sIpFQc/FVQPF7GtXsnmMz2/gpMOirj264iwmkLgZIyGrdupGbCZEJNG/AXBft30ByGUEpldHA4Pr9VxCiKohxlGhoamDt3Ls3NzQB7iJUDel8bKGbCO6U6k+yGRBS6N0sUQTYD+QL5bIonNkRYtDLEii0RPjqznHnnVHBCpQ0wg8MNngoYfzqMO0uES6xT7ifWKRNLReOlHWW1GV4Yt+yVSYYg0UW4u4PAlLNo3LCGmiknEeruxu+2i38mm5LfsRqVHR3ZPqZRT4yiKMoIZGDUwcc//nFmzpx58Hfm8MqXt0LCIv3VUpkJ7QS3X4y5Pdsh2o7ZbOZ90z287/gga3bGufu5bk77/hrOnRxk3vkVXFSXw5ROQGQXbP43lE/rn2iiAF1boGszdL4tS/WCEw2jr9WIVZjI6jd3APDmqy/I+SLN4B4v0035HGQSkIlDKiwtq4MIpVSUXoZtJeaZZ57htttuY9u2bZx99tn85Cc/oba2do/baSVGUZSRyDu9dx3S+1oqApFWCLeKYbenUUaok2Ho3iZVm1wGsEIuQWsozk9eDHHv8x2UeR3Uldj57cdqCbisUjVxeMQLM34W1JwJnlIIN4kROBkSc2/RePBV0PDmW1x65cdoaW2juLiYrq4uVixfwuz6qSJYXMXgDkpLKpeVdlQmKT6b3naTVXfKHCuM2nbSrl27uPLKK/n0pz9NLBZjwYIFVFRUsGrVKqzWwcUjFTGKooxEjpiI6SUZhmgbhFogukuW3SUjUgXp3gbRFkglZNIolyIZS/D1J1v532faCLis3HZ+NZ8/q4QKvw1MdnA6wV0KFdNhwlmyXTgVlSpPpAVMFhb8+p/c9cNfDjpGVWWljI9PHSf+mUwc7B6pzDj84pHJZaRC0zuyraGUxwSjtp309NNPs2zZMkpLSwGoq6tj7ty5vPXWW5x88slDfDpFUZQRgNMvX95yiFaAd4yIjUgTuDyQqIOebXJZIce6Hgu/ebUbAIupwJPruvjuEzv4yOljmHduKSdVZiCVhGgHNL0sG4HHz4KqGVB+PPTs4IqzpnL/gwGaO0J9x2huaWHZw0uov/PrMq6dS0O8Sx43vEuEjLtYEridfvHNZBIyyt0XSumWhXuKshvD8l/FNddcg93er8DPO+88AF1drSiKcqD0iZkKiJZDpEraTaEd4PGJmAntYOk//k1LJANAVzzH+6b4+NnVY7l7ZTen/99qZk8uYf45FVw81YM5k5SdMZ2bwPeECJma06l/38dY8rNK5nzwRkoCXjpDUarKSrj8PecYe2TMUmXxlEn0QSoqYqV7u1RknEXGeSUYk2xKWk7xDvHd6ISTshvDUsQMFDAALS0tnHDCCRx33HH7/J1p06ZhMoxh8+fPZ/78+Uf0jIqiKCMKp19iBbyV4CsDX4WIg65t4PJwxfvs3L/ytzT3JKjy27n85HJOqC3hZ9VBvnVpBfe90M2ND26k2GNn3gVjua4+gMuVgWRMKio7XoLSSUwffyIAv7v/h1xy7SdY8t1bqPeHoHUtBKqh4JPFeb2m3qIaGQVPhUXQ9C7TcxSJH8dZJOfPJqVCk4oYv2u0nHTC6ZhmSETMF7/4RVatWrXP62+//XYuu+yyvp9/97vf8b3vfe8d73PdunXqiVEUZcRwtBfsAdKe6RMzFdLS8ZRCpI36k508/O1P8tX7HuE7Hz6Z+krDp2KzUV5cwp1zi/jKBeX84fUeFv17F//59y187twabj67lEpfWvw18Q7Y8joAJ/qjAEy/8MNAXHw5O1+VKot/DHjKIZcS8WJ1SqSBq1geMxmW0fBEp1zn9ItgcRdDPt9vCO4TNDrhdKwyJCLm+9///n7fdseOHaRSKS655JIjeCJFUZSji8PhGLTw7qhiMomYcPilreNpAV85ZwRqeObEqVBIi/8l0gQ9OyEbhyw4PEFunFPEDaeX8dTGHhb/q4PaJ7Zy7cyxzDunnJNrXJAyhMTb/5Dva5fB1LOh8iSppvQ0Qccm6NwG/grwVkk4ZWZAdcZbDoUSuSwZkh01JpMIGbtbbmP39I9sp6JyO6vDMAQ7VNAcIwzLdlIviUSCn/zkJ3zjG98Y6qMoiqKMPvYhZoi0yZ4ZR53EDoR3ys/pGGRzmNx+3nOSn/dMLWVda5QfPNvBrEVvMGtSCV84t4o7L6nBkTHMvdtWQng9BGthzAwomwLFdRBrMUbBm8BZIo/vCkA2DeZI/yK9gF+ESjoOmRgkUuKvsbn6vxze/gmnVBiShf7f1wmnUc2wFTG5XI7vfOc7fPWrX8VmswEQi8XweDxDfDJFUZQjy1FvNQ0UM94KaTF5yyWPKbQLSpzgr4GwsRU4HZdqjcPNtFo/940J8M1LKrn/xW4+9+B6Am4bRV7jvToRhnBOIhE6NkBgHFRMgfIToGq6RBaEdkL7OmkJ+Sql1ZTPQzohU0k2t+yXKQSkOpM22km5lLSerA7xyPRNOKWNSISBE04u2U+jjCqG5Z6YXC7HTTfdxOzZs6mqqgKgra2Nt99+e1C+COieGEVRlMNOoSDtmWgrxDqkMhNuhnwGslmINovwSEYgn5bYASNLKZWK8aeGEP/3zybWNIWYVRfk9zcez4RyJ5ht0jJyesFZBqUToeoEETaFvOyuiXUBBXCXiQHZ4QNMhhjpra44jM2/CREyhYJMPkF/rIHNJT/n0iJ8sik5Z68hWEe2h5xRu+zuhhtu4De/+c0elz/00EN86EMfGnSZihhFUZQjRK+YibRAvFN2xIR3Qi4n7ZvILrkuHRGRUEBERC5DqKeHov+Q6AG71cyHT69m3gVjqR9jLLEzWyWLyR2QjKbSKVAyWURGMixp2NmUVIg8ZbIZuHe02mLr3x8D0mbKGIvyzGY5B/nBHhnon3DKpfujEqxOHdkeIkatiDkQVMQoiqIcYQoFSPaIhyXeJdWZ8E6pwuRMEGsWw246LlWPQoFwzk7gc8sAePWO0/jFS138+rkdnD6xmHkX1nDZCUHMVpuICYsTXF7JYyqdBMWTpKVVyMhjpqNS6fGWS1vJ7u6vvlgdRqvIIVWZdFwqRmYLYIFCVm7bezurw5hwSmoo5RCjIgYVMYqiKEeNQkF8JtE2ETPRDqnG5DLS7gm3QrQJUnFS4TB3LVvPdx7fSujey/FbUnRGEvz0hU7ueXorHoeV2y6o5cZZVXicVhEPFhvYvOAtEyNw6WQIjAGLGWLdMnZdyMvmX2+5TCj1tpHMVqni2AwvTiYuVReT2RA0JqnAwOBYg94Jp2xS9tUM45HtVCrFwoULueOOO0bF8lcVMaiIURRFOeoUCkZFpt0QM+2SVp3LiJiItEN4B+HubgKf+SuhH74Hv88HJivkYqSTSZa83s2if25jW0eMm86t5ZbzaqgusolvxmoWMeMukmV4RXVQPE7aR+kEJDulgmJzi5hxFcnjYlRnLI5+IZJL9beQrA7xxRSMSszuHplhHko52j7vRm12kqIoijKMMZnAUyLL5+Jd8t1b3i9mPEHZCGxtAv4KziCYMpBLgNmF3e/jY7PcfPT0Mp7dEmXRkzuo+89nuPr0Gua9dwKn1vrFNJyKQrgDOrbI1FTJBCiqla3DFGTiqXsr9NikeuMpEeGRNSorZouxSM8r4mZgdcbmkeuzSRkd74s1cIuZuHdkOxkaNqGUq1ev7vs+e/bsITvHcEIrMYqiKMqhsbfKTLRV3p8v/g9Cf/tv/PkuSEQhGyUVS7DwH1u54/0zcJCEXJKNrUl+8K+d/HLFFk6bUMK8907k8pPLsZjNYDFBwSK+GXeZ7K4pmSjCyWKFVBySXZBHds14ywzhMqAdZLGLl8biFC/PwOqM1SnPodcjs3usQW8oZTYl92lzHfUJp4aGBi699FJaWlqoqqqSZPD6+qP2+EeCw/H5rQ4mRVEU5dDorcyUTZVldmVTZEOvv0audxXBmHqoPB781aScxSz4+9uk4j1SDfGUMrmmhHuunULT9y/k0umV3PL71Uz9r2f40dPbiCbyQEF2znRuhcaXYf0/YPMz0L4JyIsp2FcuVZiOjdD+toipfBYwiQCJ90CsTcSK3QPuUmkpJcNSjbHYZRLK5pSWUszw/hTyMiXlLZddOvmsRCzEOqRalM8d8Zd46dKltLS0ANDc3MyyZcuO+GOOBLSdpCiKohweTCaZKnKXyEh21viI8Y8FU0zaNGOmg71VLveUgSUjIsJsAVcxQWeWr7zPwfwLxvLnN7pZ9I+NfO2vb3HTeXV84T0TqSn1QToJqSaJI+jaAt4xEBwn+2acRVAwQyYi24Aju0SsuEuMqaY8pGLyZbUbi/RKZKIpk5BJKKtDtgCbrdKC2j3WoDeUstcQfBRCKa+44gruv/9+mpubqaqq4vLLLz/sjzES0XaSoiiKckQIh0IEiooIbXwZvzUrlYtoK+FIhMB75xN6bCH+bAfEw5A1dr1gArsL8gVIRykUsqzcHGPRE1t49I0mPjRzHPMvrmPmxFLjUXKAFZweaSP5q6XV5AyISTiXNKolWREfXmOBnsncX6Uxm/v9ML3CJZMwWkdGVlMh3y9advfIDAylzGeO2ITTypUrmTNnDitWrBgVnhg19iqKoijDl94P8LIpUnFxBaTlw3a53OKE0ulS5QjtktTqVFKW1+UBZwATMGeqgzmT/WxuP54fPL2d8xf+mxm1xcy/eDLvP60Gi9kCyahUdMIt0LUZAmMhUAtFVbJbJp+XiknnJple8pSLIdnm6N/q2xtCaXVKonYhZ8QcRA1PjeedYw2OcCjl9OnTB31XVMQoiqIoR4i+aZo1a6Ry0DvNlDJu4K+CXET2w1SdJJ6XSJOMaGfTImYoyLg1FuqqEvzwwy6+8f4p/PzZRm7//Sq+9MdV3HbxFD4xuw6f3y2xCN07ZZdNx2Z5jKLxEBwvAqRQEJER2gmRnXImT5k8hgkRNNkUmKP94sThFzGT6Ok39tq9cnk2JYIm3jl4ZHtvoZSHOOF01DO1RgDaTlIURVEOO+80TRPu6SEQDBLa8AJ+e8HIZ2qVD32HT3bBRHZKZlM2KT8XslLpsFhlK282SSZn5qHXW1n0+HrW7+rh0+dP4gsXTWZ8eVCqKLkcWDDiDcok3iBYK/tn8jlDgCTlwDaXVGdcQRFVubTcByZjCZ8hQAp5ETS5tNE2cst1vdNNfbEGtt0mnNL9LScNpQR0OklRFEUZprzjNE2v8bXsOCiZBMUToPIE8bPkkmDKyrbesadCcS34SsHpk+uSIVma5y7D5nBz7ekVvHTnuTz6H+exrSPBlC89wod/9G9e3NACdidYXCIuerZC44uw4R+w9TkRTTa3VGfsbhEXPVuhdQ307BCRY3NL1SSXkceNtckUk9UpZmGLTaos0bb+lpO7WMSQzSUiKWpENeSzYPeBt5wUDu76n2+R6t4lE1SpiCzaUw4YrcQoiqIoh52Ghgbmzp3bN00zqBKz+/t2Pi/tmEiLiIFIB8RbjQ/+gGQodTeKIMgkpBKTy4j4sDmlUpNPQgG2tqX44VOb+PnTGzhpXJB575vCB08bj9XpFGGSy4p51+GRBXrFE8Q7Y7cZLayEsXnYIi0jf4UYgs2W/k2+mORnm0uEzr6qM7DXWINwIkugtIJQTw9+t33f1ZtRjsYOoCJGURRluLKvaZp9Ttnk87IwL9oqFY9Iu1Q/8hlwlcj13dshtgsyRisoFe831eZSImgoEEpm+cWKHfzgsXWYgNveN4VPnleH31+E7I2Jy2NaPbLHprgWgnXgKdqtLYSICleJiB6bU0ROLiUtJDC2ArslpDJn/C70i5zelGwj1iDc2U5gbB2hlu34SyoGh1LuvoRvFIdSqohBRYyiKMpwZW/vz/u1eXZ3MdPrmTHlwR4E8hBqgnBz/1RRJg1WK1h9xlSRLKHL5gs8/Forix5fx1uNXXzq/MncetEkasdUSkUmn5TftRuCIzAOSurAP0Z8ONm4CKZCAaw2Y+ldhXw3IdWZXAbxzgyszhT2WZ3pe11aG6USs8fI9t5CKd2HZcJpOKEj1oqiKMqIYm9emT1EjNks2UueMhEzdo8s0Yu1i9mXvDE+XSuVmUizITaSkOmGnMUw7+axZuJcfeZYrj6jmhc2drL4iY1M/dJyrjhtPPMuqmPWtGpMrqCIjUSPZDZ1bZF9MiUTobgO7EWQjshjRFols8nukS3FnnKZROptRaUiMu5tc4jwsHulapMKy5fN1b/h1+kHr78/1mDQyLbbmHAyQilTEUj2DLtQyqFGKzGKoijKEWFflZh9eWX2ST4vbaVIq7SLEh1ShcEk+1xMFjHlhlukcpMzBAUF8dRYTP0L74BtbRF+9NQ2fv7UOqZVB5l3UR1Xnj0Rqy0I5oKxdC8rgsERgNKJEJwoQioTF0GRScqklNUD7oBc5yoaUIHJyNlN5v7qDEAmTri7k0D1FEIdrfiLy/qrK4VC/8h2NjUglNJlhFUOmHCCYRFKeShoOwkVMYqiKMOVfb0/H/Tm2VwO4u2GATgp+UWRZhE5XqM91LMVwjshGZPU7EwKCoDLZ8QRGLtnslnCiTQPPLeDHzy6jnwhzxcumsKnzq2jqNQIlsykRDhYrOJ5KRoLRZOheKzcRzIkgiZv7I5x+aQ64yo1ppoMMdVrBjZ8LuFYikBpOaGdm/D7vP2enl7vDAwe2X7HUMpkv1A6yqGUh4qKGFTEKIqiDFd635/b2tr48Y9/zB133IHD4Tj09+0+MdNsiJlO+XMhD74xspG3e7NMNKXj8oGfS4jYsXtFYGRi8nMuTzab4e+rWlj06Nus3tbOJ8+bzK0XTWbiuAq5fT4noshkEt+NtxxKJ0l1xuGWJX2psOF/cciuG1eRVGccfmBwZEE4Gicw7nhCHS34/YE9vTO7e1/eKdYA3rl6M4xREYOKGEVRlOFK7/tzY2MjNTU1fe/Th+19O5eTNlO0BdIpwwDcDKYC+Gpkj0v3FujeYYgAQ8zksmD1im8lHZc2kykP+Rwvbepk8RObefiFjcw9dRzzL57M2SeOw+QsltukknIfFpvEKATHQckUMfvmEhDrhmwUsImnxRmQ2ANPSd/00sp//Ys5l36IFcv/LJUou0vETz4rgqZQ6G9B7V5Z6TX99lZ4BsYa9FZvssm9V2+GGSpiUBGjKIoyXDniIqaXXjETaTE8M92y8RfAP14qL52boKdJPDPZlJh083nZF2N1yAd/LglZE5BlR0eEHz21nZ89+SaTq4qY/74pXHXmeGz+cjAZC/BSUbCaRCT4qqC0TkSN2QaJLgm2JCsbg11F4PDRsLmFS6/6mExnVVaw/I+/pP7kE4ABYZMm827VmX2ESfbGGvSGUlod/abfoxRKeSjodJKiKIqiWCySkeQpM8SMS0RDohtCO6QyE6yF8mnQuQG6m4xpIyMnKRU1BESRBFXmkoyrLOd71/q587LJ/PLFXfz3Q2v48h/f4AvvO45PnzuBYEk5+Er6W00dm+Wx3GVQMkGmmkonQSYMsS4INYLVydI//bV/OqullWVPv0D96bOkIpSOyZfFamwTLpLqTCoi4Za7V2csNiO2YGAoZc+eoZR9E06HP5RyqFERoyiKohxR3nzzTUACIQ/IyHugWKyy38VTPkDMFMsHd/c2+cAuHg+lU6BzM/Q0Gl4Wj3hkEl3GB38AyEImj6/Iwa0XOrn5glqWNrSy+PG3+cZfVvHx86dy20UTmVRdIcLFbDIyn5plv03rm7JzpnQS+GsA2Up8xdnHc/8fgjR3dFNVXsrl59aLEPKUScUkkzAmoEL9wsXuAcxSKYp37L2qYrXLl8PfbyjeI5TSd9hDKYcabScpiqIoR4Te9+eKigpaW1v7Rqrr6uqOzvt2LmuImWZIpWTPSrhJ2jUldSIEesVMstuoZhi+FKtD2kCmgkQhYAWSkMnx6tYuFj+5hb+sXMclp9Qy/6I65pxQjclTKkbfTAbSIWlz2RzgNVpNgfHg9LHyX08x59qbWfGLrzN71umyL6bXO+MqlupKr5jJpGSpntmYkLI6+30xhfy+vTOwl1DKdxjZHoJQSvXEoCJGURRluJJKpbj44ov597//3XfZggULuP3224/u+3YuK9WRXgNwvMfwzBSkKmP3QOdGaTOlegwDsDHCbLGB3S9j2tkoYIZsBgoZmrri3PNMI/c/1sDEygDzL5nK1WeMw+4tBmexCKBUTKo8JsBbCkUTCNsqCNRfSmjtv/FbkhIQaXFIC8xZJGGXnhIJjOw1+6bjg0e17W6psuRSA0y87+B56Y016DX9Dow1MJkGTzj1Vm8GRiYcAVTEoCJGURRlOLO35XZHrRKzO7msmH+jLSJE4t2yU8aMIWa84m3p2QaxsLR38r3m2AK4goAJcsYEUb4A+QTRWJpfvdjCDx5ZRTyZ4guXTOOmc2spDhp5SxaLTC4lwpDPE87bCVx9N6FX/oK/sk7StiNtMjaez4qIcRSJqHEF5cti6xcz2RRQMEIojepMIb9/1RnYR6zBwJHtgdWbIxdKqSIGFTGKoijDnd2X26VSKRYuXNi3N+aok82IkIm2StUlHoJIk4iCkkniHenaAl1bDeGRMXwmcaAgvhOzrX8822yCdJxcLssjb/awePkaXlnfxI3nT+O2905kSk0puMtl+28hTbizmcC19xL6/WfxV9ZKvEHReIlKiHdLvEImKqLCGZTqjMsvrSaHd3B1xthC3N8msvZXZ8y2/hbUvgy8vabf3oRuqxGXYDEynXqvGxhKaXMdFkOwihhUxCiKogx3hu37dDZttJlaJQQy3gWRXRL0WDoZbF4RMn1ixjDM5jNSzbB75UM9GxfhgFXMvYU0rzcmWfyPt1ny7zVcfMpE5l08ifOmVWBylxLGQ+D9CwgtmY/fmgTM4Ck2wicnyjI9kKpRrFNaUc4io90UAHex+GjMNkNkJIx2U16EmN0YGy/kDXGSN9pDnnfe6Lv7yPY7hVIehgknFTEM4/84FEVRFGAEvE9n00abqVX+HO8eIGamiCema7NMOCVCImLSSSgkIZcXcWB3yu+mk9I+MtoxO0NZfvzUVu579DXGl/uZf+nxXHJSGWU3/YnQ3/4bv79IkrRjnVLtsLvBPxaKJ0JgrIiVaDvEjERvh7+/xeTwiRnY5pEqSjpmVGcy4uGx2uX+zFa5797qjM317tWUvliD1J6m377qTWLP/TQHgIoYRsB/HIqiKMc4I+Z9OpuSEMlYq7ScEt0Q3iVioPQ4qbx0b5MtwMkemULqbd3kMuBwSSBkLi0VC7PFSNZOEMua+c1LzSx++BUi8SQtXRG2/vBKascarSZPqVQ4Yh0yXm1xiJ8mOE5aTZ5SeazwThkZN1vAUSzhk04/uEvkfH2TTQkRNRQAU391BgZ4Z/ajOrN7KKXJ0i+C9hVKaXPv14STihhG0H8ciqIoxyhD7oE5UPrETIu0mVIhCO2SakT5VLD5IbQNOjbJcrlcxgiaTMvtrUZ+Uj5jjC8jt8kmyBes/H11B/N/8TSt3VGuv+Akbn9vLcdVG+PVvioRFckeqc6QA2cpFFVBsE6Ejd0h4ireJWd1FkmbydkraIpFZORzhnfG2FJswvDJeKQ6k88aYms/qzN7jGzvZvodFEo5YD/NPkSSihhUxCiKoihHiN3FTLIHws1SaSiuEyNuTxN0rodEVCoSuaTsh8kkjVFoj3FfcSmK5DOQSoDJxBu70ix+dA1/+tcq3lM/kXmXTOWCqSWYXD7wVkuVJR2DaDOk4mLq9VXJRmD/WDH9ZsLQs1M2EFud4CwRE7DTZxiBfUbFJNUvaPpGtV2S21TA8MHk97+SMjDWYHfTb+9r1xudsI9QShUxqIhRFEVRjjCZpHhmIi3SPkmFRMxYnVA2VYIge3ZKpEG8W6ouubRRfYmDySaiwmTu3/dSMEO6B0xmmhNWfvz4On6y7CWqSwPMu/xk/t/MMhwOL/grpfpSMBb3xbvlfnxV4pkpHg/uUjlnpFlaYPmsCBxXUf8iPVfRgFFsY7Ipk5Dfs1gHVGdyB1adgXc2/e4eSjlgP004Gj02RMyXv/xl2tra+NWvfrXHdSpiFEVRlKNCn5hpFs9MskfMwDaXJFm7iiC0Ezo2iAE4Z/hICjmZWjKZxbdidsj+mWxWWjypCBQKxAtOfvvcNhY//AI90QQ3X3oKnz13LGUBN3iLIVArFZJ4l+yVyadFrASqxTvjqxSxFOuQc6VjYux1FYEjKNe5g8YZBlRnUrH+UW2bS6oxmESI5bMD9s7sxybfdzL99gokI5QyHEsSqJowukXM888/z8UXX8yVV16pIkZRFEUZejJJETIRY5op2QPRNvmwLptKChcLv/c97rhyJo5czEjINhbUJeOSfG3zimG4N2W6YJKqTSZN3urh8bc6WPTwizz35jaue8/J3P7eOo6vcsuumaIa2eibikOkUUSQ3SXxBsFx0mpylxjtsJ1yPQVpL/X6ZpxF8t3m7G8NpY0KDQXxuNi9Up0p5IzJJuuApO39GKveI9bA0S+GclnCXa0EyqtHr4iJx+N8+tOfxmQyYbVaVcQoiqIow4dMQtpKkVYRKckQRDsIp00Ezvkkoc2v4y/ExDMT75HKTCYl1Yp8WsazHcam3F5PSt5kjEknwe5i9c4Ui5e+yh+efoPz6ycx/9ITeM8ULya7B4qqJfCSvLSzou0iPnwVUpUpGgeeShkVj7bJEr1sSlpHbmOJXt+YthExkMsY1ZmoVGIYID7A2JGTlTPbPfufs7QX0284niFQXDJ6RcxXv/pVbrjhBr773e8CqIhRFEVRhh99YqYFChnCbS0EzryW0IoH8I87SaomsVZoXQfRLhEomZSIll7/TG/LpneRXm/rJRsDs5uWlJV7l7/BTx55icpiP/M+cCofqS/C6XSCt1LGsB1uETLhJql+uIrANxaC1eCvkn036ZjswElGwGwXc7JzoBHY2+9lGTSqnQfMcv0e1Rnj7PtTnekd2c7ECXd3Eqieckif3+8wHD60/Pvf/6aiooJp06bt1+2nTZuGyXgB58+fz/z584/k8RRFURRFsLlk066/Sto30ZRcbnVB82oRCMUToO588aq0vi0tqHRchIrVLq2XWKcszXN4RcSYzXLfuSyV+TDfuGoad3zoNH63ciP/99Bz3PHLOJ+/4gw+d26a8nCjiJDiOhh7CiSjENoBbeugZ6tUZAKGGTg4UcIpIy1iBI51yGM62wZvBra5xVPjDPRPNiVD8twsvSGUJhE6qcj+VWdMJmMCygnpQ89iGpJKzBe/+EVWrVq1z+tvv/12/vznP/PLX/4Ss9nMjTfeCGglRlEURRn+hDtaCJRVEVrzBH6XTUy+yW75gA9OFL9KvAM63oZYl4xcF1KQzcmIdjYHVqukWFMw/DQm+Z6KgclE3ubnibUtLP7LSp5dtZWPvvdU5r1vMieUWkSQFI2HwBj5vUiTYQTOgq8MPFXSivJWgsMjRuFYi5zD6uyfaHL6jJ0zHhFaA6oopKL9o9p2j2QtYUwi9VZn3iU0ctSOWP/Hf/wHn/vc55g4cSKAihhFURRlxND3udTejL8QlkpHNi1VjFSPbPUtniBbeOOd0P62CIm0kcFUyIqQyaZlosnhkQpGNiU/5zIy5l0AXAHebEpw99+e4/f/fINzZkxm/hUnc9EkByaLTUzARePB5pN9M5Gd8jh2P/jKpTLjHyNVnJwxfZWMyBNx+sQz4/CCq8QwAhum3t6x6nTMCMZEKjA2T//1+YyxH8YtImhfr9NoEzGmd+ir7X5cFTGKoijKcGKPz6V0TJbixXvFTFhEiM0DwVrwlhliZr14WjJJw/ibMb6yIgzsXhEx+RRgFi9NOipiweajLWXjJ8te5sd/f4GyoJ95HzyTj54SxGUtiGAprgNvqdFq2g7RDrDZxQTsqZTKjadc9sbE2qTVlElJ28jukTaT3SvVGbu3fxPvwOpMPguYBo9k51J7rc6MWhHzxhtvDPr5zjvvBOAb3/gGM2bMGHSdihhFURRlOLFy5UrmzJnDihUrmD17dv8VvWIm1i4f7ImIbNp1eCBg5CMlevrbTOmosTAvY0wupWQc2uGTdlMmI96WXM4Yz46D3UvS5OH3z6xh8UPP09od5fPvn83nLxhDhSMrnpdgLRSNlSmh7kYZF89nJEnbXQHBsTKu7fCJ1yXWLufsXYDnDIqJ2F1inMVpVF8GjmrHpP1ksRjiy7h+QHUmHE+OThGzO9pOUhRFUUYCDQ0NXHrppbS0tFBVVcXy5cupr68ffKN0DHoapc3U63NJRWXXS2AceMogHYa29VIR6U2mzqaBvLF3ptC/ZZe84U/Jy+6YdBzsPgo2N0++2cjiJSt55o3NfOTiM5h3yTROKjaERLAWguOl0hJrg55GUqFuFv59FXd8/AM4ymqMVlOJCJJ4q1SRslkRMQ6PpGo7/dKOsnv6YwUGjmpnDaOz3W14Z2SRXjgSIzC2bnROJymKoijKSGPp0qW0tLQA0NzczLJly/YUMXYPlB8nH/ChRmkh2d0iZtrXy4STfyxUnw7pELRvlKmmTEyqLiYLWApGWna8P5conwOHWURFMowp0cZFUwNc9D//j7U7I9z91xWcPu9XzJ4xlfnvP5WLJ27A3LFBfDEldTD2dFLuNhb8/kfMf//JOFKt0uryVsruGW+lnCveJa2mSAckwvLYjk5wGt4Zh1emjywBETnZpAirVFS+m3tjDkbodNLhRCsxiqIoynChoaGBuXPn0tzcvO9KzEAKBaMys6PfAJxJSCvJ7hWB4SkTAdC5EcKtEvqYz4lfBZNUaXJpqXJY3dJiymcAs/hf0jHxp7h8tMcK3LfsBe7524sUF/m5/crZXHdaEe5CCtylhN3VBN57O6EX/4A/1yVp2dmU+GDcJeKf8VeBo0geM9Zm7JxBDMt2l2EENrKbepfogXh7+lK1E4TDEQITZoz+dtI7oSJGURRFGU7s0xPzTvSJme2GmEmJwTebFCHgHyOemXQMOrfKQrtkXCaZcknJYMpkRLz0mmhNJjHaFsyyLTgZAVMenMWkCk7+8MxrLPrL8+zqivDZD5zLzReMw5PrJvDxPxBa/h381ZOlQhRtl50z8R5wusFdLgZhbyW4y2QjcKxDxshzWTHvWuwy3WT3ym3tHlmi10smSbizZfRnJ70bKmIURVGU4cQhfS4VClKF6dkB4TYoZIzNvWkRAb4x0uLJJqBzi7Se0nHDg2KETGYzMt1kNssEFGYgCyarsbAuLEZhh5+Cw8vTDZtZ9JfneOr1jZx/6vE8/sIqViy4hNknVIvhuKQOXD5Ip2VxXrRDqj3uEknY9pbJVJPTJy2xWIdUXAZOJDk8srnY4TeqM+bRO510IKiIURRFUYYTh+VzqVCQyaDuHZJ71NsyyqXFb+KpEJ9KOi7Vm54mERC5DOTjgEUMuPkskBffjMUm15stcnkqImLIWQR2H39d+SbXfesPxP9/e3ceHHWZ53H83d3p7nSuzmUgEGGGU1nlUKnxwAGdZRAP1lXE2XVldAF1CxxEHXDUEc9iR8foukpkdBimdmotHCcqTjz/kEXxwCMQLWY8Erk0gSTd6Rzd6aSP/eP5ETY7ozA08Ou2P6+qlOaXPr6ki/p9eJ7v8zzRfjzuHO6/7iKunz4UZyxippHKxoJ/KOA07xfaY4JTXrEZJcovNzXllgMxE2b2n5C9fydfj3WIZUE5nZEY/rLj1NgrIiLyreJwmAbdoX8Hvceb1Uxde81oTCxqRmrC+8zUTsUJUPJdE3g6dkG/x4zG0At4zKhMwhrR8eQBDrPHS14xJIrNnjWhPXz05ybC0X4A+vpj3Pbki6x+oYwb5p3L/NPC5HduMn0u5WPNCE3x8abBt2MXBBoh1Ax5X0F+iZlqKqiwGoHbTWCKdJgpsmgPRALQG0v516QQIyIikq4cDvD5TaApPt4ElZ69puck3g+hL80mennlUDEWSkaYwNO52zT1JqLQj7WaKWH1zcTMGU0uNzhNjwy5MOeMHta89CHNwTCVpYU8e++/8smuFqr/sJHb13Rw7aV/z5JzSxjW+wG0fAzF34GKcTB8kglNgS+sXYFbIK/F7CdTWGFGZ4pHmimm3qBpUu7vhkgi9V+PppNERESOnKN6X0omTU9LcKc1zZQwfTPxuNl9N6/c9KgkYmZkpGOneXwiam2alzR7yiT6zdEGLo9pzHU6IZngzW07OPuGGt7498uZNmEE5BWTdHrYuK2R6mfe5NUtf2berGksu2gSp5RHzGsWj4Dy8WYFk8NhVjSFvjT9N7kFpncmt9jsCOwrM307vUE6Ay34T7lE00kiIiJZYWBk5mRrKsfaZ8aVMIGmq9lM3+SVm1GZomHQ3QKBnebspnivtfzaBW5rg7z+HrMbr9PDxFGVAEyceDK4YhDpwJFMcM5JwzlnytV8sqOZ/3juHc5e+jhTTx7HjZeezYXjAjhDr4KvHI4bb5qP/cMh2gmBXaZ/xrnXhC5fiVmtlF8B/u+k/OtQiBERETmCvF4vK1euxOv1HvzBh8vhMCMfucXQ2wHBHeZ4AGeuGWnpaj4wzeQfbnpUevaaEZxwBziiZgQnmQCHG7MTsLWZHuZbfD5zmnXUOh4hHGT8MD+rb/gH7rl6Jr+q28K/Pfjf3OTL44Z/msVV34uTv3Oz2S+mYqw5sbvyZLPsunOn6enpbjehKrcMEu7Ufw2aThIREclwicSBMNO9z+wN48QECJfbHAtQUG4CTvc+01sT6TAjM/H9q5gc5iiAOXcReu5WigqLrI3qHOYr2WcFGmtFk9tHXxyefn0rD/3hTZqa27l27nksmTmGqpx285yS75hVTXnF5vuuvdD1FfR109nvxH/hnZpOEhERyWpO54GRmXDgwOolp3Wb79kHkTbTk1Iw1Hx1t5rH9QZMMInHD5xM7fBae9T0gctrjjpwus2UUa4VmLo78Xh8/MsPp3DFzFPZtLWRh2o3M/q/nmfuD6ex7B+/x2k5LRD4HAoroXycOViysNKM7DR/mvIfWyFGRETk28LpNCMueaUmzAR3QLjVCiEu0y8TCVq9KceZIw3CbdaOvEG8MScrr5qF1+uBHI8ZoUlYJ2i7PGZUx+U0y6gTJaZpuHsvDqeH6RNHMP3UsXy2q4VHnn2X6Use5tSTxrFs3rnMGRvB1fQ/ZnqqbDyUWs3AKdJ0koiIyLdVImFCSmCHCTCOHHC5BqaPBsJMIml+HtoD4aDZNTiZMGc0kbRWNcWgr9c63DEHcJreHBwHNs4jYRqPHbkEu7r4Vd37/GftG3i9udzwz+dz9ZkVFPS2Qo6bTm8l/gvv0I69CjEiIiLfIBE3ISXwhRVm3GZpddzacM5XAgXW8ufugDldO9IG0bB5biJmWmMScRN4YlGzpNtxYHk2OZ4DxxoQA08x5OTSH4/z+40NPPTMm3y2Zx/XXDab68+bgD/ajP/KJxRiFGJEREQOQSJujgPYH2ZcXhM+Yn3m5/83zPQEzZ4vPa1mgzoSZoM9EpBwWHvU9ALWFJPLAzhM2In1mZ2AY1FzXpInn2QyyeaGL6iufYu6zQ1cdM4Z/OHVN9TYKyIiIofA6TI76OaXm8beQJM5AsCVa6aJop2mZyavFPJLzaqi3pAJM91tZpop0Q/ErRGYfHMydn+fGdVxuiEnx4zSuIea67FO6NqLw5PPtMnfZdqkUTR+2coDv9+c8h9HIzEiIiLZKmEtuQ58YXphcnLB4zMjKIn4gTCDE6Id0Nliwk9vNxCz9pWxjg9IJCEeNSM0OS4TjBwOSLqsfpoeE4JcbvAV0xnuwz/7Fo3EiIiIyGFwuqCo0qxS6t4H7U1muslbYE6ejnaa5dS5fhNojis2uwB3tUJPC0Q6rSATB2cSXHlmRCYeg3iPWeKd4zHv4ysyIzvRLrNiqkcHQIqIiEiqXDnmbKOCCujeC+2NZlWTpxDcPusUamtpdl4ZlBdB4XFmiql7L0RCZpopmTTBxWXtAtzfb61acpkwkwTcBeD1QzKQctkKMSIiImK4cqxjCoaY3XUDn5uRGU+RNTLTbY3MlJhdgMuKzBLtnnZzgnVPCBzWaqakE9xewA2xGPSFzYhM0gkkrJ+lRiFGREREBnPlQPFwKKwwfTCBz00vTG6JCTTRrgPTTL4yKC00zcKRAHS1mGXWsV7TV+NwgTsHPB6IJ0xvTNwBfYmUy1SIERERkb/O5YaS46FoKHQ2Q/tn0NUBvmIzMrN/X5hcvxmZyS0wYSYcMI+PhiDaC44k4ASnA3ILrTOcgimXpxAjIiIi38zlhpIRUPh/wkwkaIKLr9CMzEQ7zZ4wvlIorrKOPuiwemYCZrffZNzsQYMDfAUpl6UQIyIiIocmxwOlI60w8yUEGiEUsA6G9EGvFWZy/WbqyT8M8krMidnd+8wGe/091tJrZ+rlpP4nEhERkazi9kLZKCgabs5bCjRCbxv4KsCTa6aYejsht8iEmaJKMwUVCZlVT92t4OxLuQyFGBERETk8bi+UjwZ/FXTsMpvmRfaBb4gJM1ErzHgLzdLsIp85ILJwCDh2pfz2CjEiIiKSGrcXjhtremE6dlmnZvdB/hBrmqkTOnaCp8CEGbcPSh0pv61CjIiIiBwZbh8cNx6KR5hRmeAuCMegoNKczRQJQccO0wDsSD2CKMSIiIjIkeX2wZAJUPpdaGuE0G4gCQVDIcdvRmY6tcRaRERE0pXbB5UnmTATaISO3WaJdeFQc15TihRiRERE5Ojy5kPlRCgdDe2fm5GZntRXJ6W+SFtERETkUHjzYdgkGDXdnLmUIoUYEREROba8hSbMpCjtp5M+//xznn/+eUaOHMm4ceOYOHGi3SWJiIhIGkjrEPPiiy/y2muv8cADD5CTk9alioiIyDGWtslgy5YtPPbYY2zYsAGXy2V3OSIiIpJm0rInJpFIcM0113DqqaeyaNEiTj/9dNauXWt3WSIiIpJG0jLEbNq0iU8//ZSZM2eydu1alixZwoIFC3jhhRe+9jknnngiVVVVVFVVUV1dfQyrFRERETs4kslk8li/6U033cS2bdu+9ufBYJBIJML27dsHro0dO5ZRo0bxyiuvDHpsZ2cnfr+fUChEUVHRUatZREREDk00GmXVqlX87Gc/w+v1/tXHHIn7ty0h5mCuvfZaPvzwQ957772BawsXLuT111+nsbFx0GMVYkRERNLLodybj8T9Oy2nkwoLCwkGB5+pUFFRQUlJiU0ViYiISLpJyxAzffp0mpqaaGtrG7gWCAT4/ve/b2NVIiIicigaGhoG/fdoScsQc8EFFzB16lTWrFkDmLm1TZs2sXTpUpsrExERkW9SX1/PZZddBsC8efOor68/au+VliHG6XSyYcMG6uvrue2221i6dCk1NTWMHDnS7tJERETkG2zYsIGWlhYAmpubv3FlcarSdrO7IUOG8Mwzz9hdhoiIiPwN5syZw5o1a2hubqayspKLLrroqL1XWo7EiIiISGaaMmUKTz/9NABPP/00U6ZMOWrvpRAjIiIiR9T+w5qP9qHNCjEiIiKSkRRiRERE5Ijyer2sXLnya3frPVLScsfev4V27BUREck839ode0VEREQORiFGREREMpJCjIiIiGQkhRgRERHJSAoxIiIikpEUYkRERCQjKcSIiIhIRlKIERERkYykECMiIiIZSSFGREREMpJCjIiIiGQkhRg54qqrq+0uQSz6LNKHPov0oc/i20MHQMoRV1VVxZ49e+wuQ9BnkU70WaQPfRbpQQdAioiISNbKsbuAVO0fSOrs7LS5EtkvmUzq80gT+izShz6L9KHPIj3s/wxSmRDK+OmkPXv2cPzxx9tdhoiIiByG3bt3U1VVdVjPzfgQk0gk+OqrrygsLMThcNhdjoiIiByCZDJJV1cXw4YNw+k8vO6WjA8xIiIikp3U2CsiIiIZSSFGREREMpJCjIiIiGSkjF9ivWrVKpqamgiHwyxYsIBzzz3X7pKy0s6dO7nmmmt46623GDNmDNXV1Zxzzjl2l5X1XnzxRRYvXswXX3xhdylZLxQK8dvf/pbS0lKGDx+uvx/HWHd3NytWrKCoqIhYLEY0GuWBBx7A6/XaXVpWaWtr4xe/+AU9PT2sXr164Ho4HGbp0qX4fD4CgQD33XcfI0eOPOjrZXRj76OPPsqHH37I2rVr6e3tZfLkydTV1TF69Gi7S8sqyWSSWbNmMXPmTIYOHcqDDz7IZ599RkNDgz4LGwWDQaZOnUosFmPHjh12l5PVGhsbuf3223n00UcpKyuzu5ystHjxYkaPHs2NN94IwJIlSygpKeGee+6xubLs0d/fT11dHcuXL+fMM89k3bp1Az+bO3cuc+bMYf78+Xz00UdcccUVfPDBB7jd7m98zYydTurr6+POO+/kxz/+MQC5ubnMmjWL++67z+bKss/HH3/MihUr+OlPf8qVV17Jq6++isPh4I9//KPdpWW122+/nfnz59tdRtYLBoPMnz+fhx9+WAHGRhs3bhz0L/uTTz6ZhoYGGyvKPm63m4svvpipU6cOuv7BBx9QV1fH5ZdfDpjPxuFw8NRTTx30NTM2xGzevJn29nZOOumkgWuTJk3SjdMG48eP5wc/+MHA9xUVFUyYMEHDtDZ67rnnmDp1KiNGjLC7lKy3cuVKRo0axapVqzj99NNZvnw5sVjM7rKyzsSJE1m9ejWJRAKA999/n+uuu87mqrLT/x9d2bBhA2PGjBl0z5g0aRIvvPDCQV8rY0PM9u3bcTqdlJSUDFwrKSmhtbWVYDBoY2XZx+Px/MW1YDDIhRdeaEM10tbWRl1dHVdddZXdpWS9cDjMk08+ySmnnMJDDz3EunXrqKmpYcWKFXaXlnWqq6tpampi/vz5vPXWW1x88cXMnj3b7rIEcz8vLy8fdK2kpIRPP/30oM/N2BATCoUoLi4etMvf/hQXDoftKkuATZs2cckllxz2NtKSmp///Oea508T7777LpFIhCuuuAKHw8EJJ5zA5ZdfTk1NzcCIgBwblZWVrF+/Hr/fz/nnn6/ffxoJhUKUlpYOuub1eg/pXp6xIaa0tJRoNDroWiQSARg0OiPHVn9/P0899RR333233aVkpfXr1zNjxgyGDh1qdykCtLS0AJCfnz9wbcaMGUQiEb788ku7yspKf/rTn3j77bd57LHH+OUvf8kll1zCK6+8YndZwtffzw/lXp6xIWb06NH09PTQ29s7cK21tZWqqiry8vJsrCy7Pfjgg9x6663qh7HJ448/zo9+9CMcDgcOh4Orr76anTt34nA42Lhxo93lZZ3CwkKAQVPcFRUVgP6xdawtXLiQs88+e+D/lyxZws0332xzVQLmft7W1jboWmtrK+PHjz/oczM2xMyYMYPy8nLee++9gWvbt2/nggsusLGq7Pbkk09y3nnnDZwqHo1GicfjNleVXZ544gnq6+sHvu666y4qKyupr6/ntNNOs7u8rHPGGWfgdrvZsmXLwLVAIMCUKVMoKCiwsbLss23btkH9ewsWLGD37t02ViT7zZ07l4aGhkGjMYd6P8/YEON2u1m2bBm1tbUA9PT08Nprr3HLLbfYXFl2Wr16NU1NTbS0tPDyyy9TW1vLwoULdbL4MTZmzBgmT5488DVixAg8Hg+TJ0/WTdMGZWVlLF26lJqamoFrzz77LLfddpuNVWWn2bNn89JLLw18/8knn2jxgU3i8fignqQpU6Ywbdo0Xn75ZQC2bt2K0+nksssuO+hrZfRmd/F4nFtuuYW+vj5CoRCLFi3irLPOsrusrLN27VoWLFjwF9evv/56HnnkERsqkv3WrVvHnXfeqc3ubBSLxVi+fDnhcJiioiJGjhzJ4sWL7S4r64RCIW6++WaGDRtGQUEBLS0t3HHHHfj9frtLyyrr169n+fLlOJ1O7r///oGg0tbWxrJly6isrKStrY17772XYcOGHfT1MjrEiIiISPbK2OkkERERyW4KMSIiIpKRFGJEREQkIynEiIiISEZSiBEREZGMpBAjIiIiGUkhRkRERDKSQoyIiIhkJIUYERERyUgKMSIiIpKRFGJEREQkIynEiIiISEZSiBGRtFNbW0tZWRler5ePPvqId955h7y8PH7961/bXZqIpBGdYi0iaam2tpZLL72UN998k5aWFgKBAIsWLbK7LBFJIwoxIpK2zj//fNrb25kwYQK/+c1v7C5HRNKMppNEJG098sgjbN26lbPOOsvuUkQkDSnEiEjaCgaDnHjiidx999309PTYXY6IpBmFGBFJS/39/dTU1PDGG28AcO+999pckYikG4UYEUlLq1at4ic/+QmFhYXcf//9VFdXs337drvLEpE0ohAjImnnd7/7HdXV1fT39wPgcrno6+tj3rx5vP322zZXJyLpQquTREREJCNpJEZEREQykkKMiIiIZCSFGBEREclICjEiIiKSkRRiREREJCMpxIiIiEhGUogRERGRjKQQIyIiIhlJIUZEREQykkKMiIiIZKT/BfMHw3CAfafkAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "inds = np.random.randint(len(flat_samples), size=100)\n", "for ind in inds:\n", " sample = flat_samples[ind]\n", " plt.plot(x0, np.dot(np.vander(x0, 2), sample[:2]), \"C1\", alpha=0.1)\n", "plt.errorbar(x, y, yerr=yerr, fmt=\".k\", capsize=0)\n", "plt.plot(x0, m_true * x0 + b_true, \"k\", label=\"truth\")\n", "plt.legend(fontsize=14)\n", "plt.xlim(0, 10)\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\");" ] }, { "cell_type": "markdown", "id": "5010b26d", "metadata": {}, "source": [ "This leaves us with one question: which numbers should go in the abstract? There are a few different options for this but my favorite is to quote the uncertainties based on the 16th, 50th, and 84th percentiles of the samples in the marginalized distributions. To compute these numbers for this example, you would run:" ] }, { "cell_type": "code", "execution_count": 22, "id": "c1eccd0a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-1.10354321 -1.02208053 -0.94290577] [0.08146268 0.07917475]\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\mathrm{m} = -1.022_{-0.081}^{+0.079}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "[4.73900459 5.13166154 5.52574266] [0.39265695 0.39408113]\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\mathrm{b} = 5.132_{-0.393}^{+0.394}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "[-0.94173763 -0.78947967 -0.63445383] [0.15225797 0.15502583]\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\mathrm{log(f)} = -0.789_{-0.152}^{+0.155}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from IPython.display import display, Math\n", "\n", "for i in range(ndim):\n", " mcmc = np.percentile(flat_samples[:, i], [16, 50, 84])\n", " q = np.diff(mcmc)\n", " print(mcmc,q)\n", " txt = \"\\mathrm{{{3}}} = {0:.3f}_{{-{1:.3f}}}^{{+{2:.3f}}}\"\n", " txt = txt.format(mcmc[1], q[0], q[1], labels[i])\n", " display(Math(txt))" ] }, { "cell_type": "markdown", "id": "52e3c979-f0b5-40a7-9f6f-e546cc4306fc", "metadata": {}, "source": [ "\n", "---\n", "\n", "In a particle physics experiment, a lot of data is produced and must be analyzed to extract useful information.\n", "This data typically consists of many independent observations of a “physics event” inside of some detector, which records information about the event.\n", "Often the analysis boils down to classifying a large dataset of events into a few categories, with the most simple example having only ‘signal’ and ‘background’ types of events.\n", "For instance, in a neutrinoless double beta decay ($0\\nu\\beta\\beta$) experiment, the ‘signal’ would be the $0\\nu\\beta\\beta$ events, while everything else (radioactive decay, solar neutrinos, $2\\nu\\beta\\beta$, self destructing dark matter, etc.) would be backgrounds.\n", "Once the events have been classified, it is straightforward to turn numbers of events into (relative) rates or probabilities of each event class by taking ratios of the different classes.\n", "This higher level information can be be used to constrain (or disprove) theoretical models for how particles interact.

\n", "

There are several methods for performing such a classification. Particle accelerator experiments like the LHC provide a lot of information about each event, and these experiments often write complicated algorithms to directly label each type of event as belonging to a certain class.\n", "Bolometer experiments like Cuore, which provide only information about the total energy of an event, and optical neutrino detectors like SNO+, which provide information about the position, energy, and perhaps direction of an event, often have to rely on statistical methods.\n", "This is largely due to the fact that the data collected is not sufficient to uniquely classify every even.\n", "For example, even if a signal occurs in a specific energy range, like $0\\nu\\beta\\beta$, backgrounds, such as radioactive decay, can have very similar energies and be much more common.\n", "Detector energy resolutions complicate matters further by smearing out the measured energies relative to the true energies.

\n", "

These statistical methods don’t directly classify any particular event, but can still give a high precision answer to the overall content of a large dataset.\n", "This is possible because events of different types tend to have different distributions.\n", "For instance, radioactive backgrounds will occur more frequently near areas higher in radioactivity, while solar neutrino interactions would tend to be uniformly distributed in a detector.\n", "Similarly signals like $0\\nu\\beta\\beta$ will occur at discrete energies, while a background like $2\\nu\\beta\\beta$ will have a wide distribution of energies with a known shape.\n", "As long as one accounts for all possible types of events present in a dataset and can reliably know how these events should be distributed as a function of some parameters, one can statistically extract the makeup of a dataset.\n", "The one caveat is that event classes have to look sufficiently different as a function of the parameters chosen.

\n", "

Fully accounting for all possible event classes present in a dataset is no small task, and indeed this is one of the largest difficulties of any statistical analysis of this style.\n", "Choosing parameters is another difficulty.\n", "Energy is an obvious choice, since physical interactions typically have characteristic energy distributions, but this may not be sufficient to well-separate all event classes.\n", "The final big hurdle is knowing how the different event classes are distributed as a function of your chosen parameters.\n", "To do this, one must typically generate a fully calibrated simulation model where physical interactions can be simulated independently to generate a probability distribution function as a function of the chosen parameters for each class of events.

\n", "

" ] }, { "cell_type": "markdown", "id": "4d560d4b-fb9f-4ed6-9829-80b7eb588f83", "metadata": {}, "source": [ "

This will be a one dimensional analysis, i.e. one parameter will be used to distinguish event classes.\n", "More dimensions will likely enhance the ability to distinguish events, but higher dimensions require more simulated data, more processing time, and more complicated code.\n", "Higher dimensions use the same basic framework though, hence a one dimensional example is a good starting point.\n", "Now choose and region of interest (ROI) for this analysis on the chosen dimension.\n", "We’ll be working with totally made-up events as you see, but let’s assume they’re distributed in the low tens of mega electronvolts.

\n", "

Now create a Monte-Carlo (MC) simulation model for two classes of events.\n", "Reality here is much more complicated, but for the purposes of this demonstration, assume:

\n", "
    \n", "
  • Class A has a mean energy of 10 MeV and is described by a Gaussian distribution with width 2 MeV
  • \n", "
  • Class B has a mean energy of 15 MeV and is described by a Gaussian distribution with width 3 MeV\n", "
  • \n", "
\n", "Generate 10000 of these events for building PDFs for these classes later." ] }, { "cell_type": "code", "execution_count": 23, "id": "023194dd", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# https://ben.land/post/2021/01/09/maximum-likelihood-python/\n", "\n", "import numpy as np\n", "from scipy.stats import poisson # To calculate poisson probabilities \n", "import scipy.optimize as opt # Function optimizers and root finders\n", "import matplotlib.pyplot as plt\n", "\n", "binning = np.linspace(0,25,40) # 40 bins from 0 to 25 MeV\n", "\n", "# make fake data, two gaussians at 10 and 15 MeV\n", "np.random.seed(42)\n", "def class_a(nev):\n", " return np.random.normal(10,2,size=nev)\n", "def class_b(nev):\n", " return np.random.normal(15,3,size=nev)\n", "\n", "# generate and save 10000 MC events for each class\n", "mc_class_a = class_a(10000)\n", "mc_class_b = class_b(10000)\n", "\n", "plt.hist(mc_class_a,bins=binning,histtype='step',label='Class A')\n", "plt.hist(mc_class_b,bins=binning,histtype='step',label='Class B')\n", "plt.xlabel('Energy (MeV)')\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "1c5ec8b8-681e-46f4-af07-6ba7b6d910a7", "metadata": {}, "source": [ "

Note that these distributions overlap significantly, and particularly for events in the 10-15 MeV range, it would be impossible on an event-by-event basis to distinguish the two classes.\n", "To make this more obvious, generate a fake sample of data with 100 class A and 200 class B events.\n", "This is a stand in for real data, and testing an analysis with artificially constructed datasets is an important step in any real analysis.

" ] }, { "cell_type": "code", "execution_count": 24, "id": "b7e53957", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# a fake dataset containing 100 class A and 200 class B\n", "data = np.concatenate([class_a(100),class_b(200)])\n", "\n", "plt.hist(data,bins=binning,histtype='step',label='Data')\n", "plt.xlabel('Energy (MeV)')\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "39f9ae8e-7f08-4738-838c-b63bad36bf81", "metadata": {}, "source": [ "To determine the number of each class of event in the data, a likelihood function needs to be constructed and optimized. This function will be parameterized by a hypothesized number of events for each event class \n", " for class $\\mu_j$ for a class $j$. A binned fit will be performed, so this function will need to construct an expected number of events for each bin according to the expected distributions for each class. This is particularly useful when you have a large amount of data, since it is less computationally intense than an unbinned fit. An unbinned fit is certainly possible, and can be thought of as letting the bin width go to zero. This may be necessary if your PDFs are not smooth compared to the size of your bins.\n", "\n", "To do a binned fit, the simulated datasets for class A and B will be binned and normalized, then the bins will be scaled by the hypothesized number of events for each class. Mathematically, bin $i$ of the normalized PDFs for each event class $j$ \n", " can be written as $H_{ij}$. So the expected number of events in each bin, $\\lambda_i$,\n", "can be written as:\n", "\n", "$$ \\lambda_i = \\sum_{j} \\mu_j H_{ij} $$\n", "\n", " \n", "\n", "Finally, the Poisson likelihood $L_i$\n", " of observing the number of data events in each bin $k_i$\n", " will be calculated according to the calculated expected events $\\lambda_i$\n", "\n", " $$ L_i = {\\lambda_i^{k_i} e^{-\\lambda_i} \\over k_i!} $$\n", "\n", " \n", "\n", "You may be tempted to directly calculate this using power, exp, and factorial functions - don’t! Both the power and the factorial will overflow easily for even moderately sized datasets. Fortunately in python, the scipy.stats.poisson module provides a pmf (PDF) function that calculates this without having to worry about intermediate large numbers.\n", "\n", "Finally, to arrive at the total likelihood $L_i$, the product of the likelihood of each bin is multiplied together\n", "\n", "$$ L = \\prod_i L_i $$\n", "\n", " \n", "\n", "All of this is encapsulated in a Python class where the __init__ method performs the initial setup and a __call__ method evaluates the likelihood function." ] }, { "cell_type": "code", "execution_count": 25, "id": "364a2727", "metadata": {}, "outputs": [], "source": [ "# using python object-oriented style\n", "\n", "class LikelihoodFunction:\n", " \n", " def __init__(self,data,event_classes,binning):\n", " '''Sets up a likelihood function for some data and event classes\n", " \n", " data is a 1D array of quantities describing each data event\n", " event_classes is a list of 1D arrays with quantites for each event \n", " class. These should be derived from simulation, and will be \n", " used to generate PDFs for each event class.\n", " binning is a 1D array of bin edges describing how the data and PDFs \n", " should be binned for this analysis.\n", " '''\n", " # First step is to bin the data into a histogram (k_i)\n", " self.data_counts = np.histogram(data,bins=binning)[0]\n", " # Create a list to store PDFs for each event class\n", " self.class_pdfs = []\n", " for event_class in event_classes:\n", " # Bin the MC data from each event class the same way as data\n", " pdf_counts = np.histogram(event_class,bins=binning)[0]\n", " # Normalized PDF (H_ij) such that sum of all bins is 1\n", " pdf_norm = pdf_counts/np.sum(pdf_counts)\n", " # Save for later\n", " self.class_pdfs.append(pdf_norm)\n", " \n", " def __call__(self,*params):\n", " '''Evaluates the likelihood function and returns likelihood\n", " \n", " params is a list of scale factors for each PDF (event_class) passed\n", " to the __init__ method.\n", " '''\n", " # Observed event histogram is always the binned data\n", " observed = self.data_counts\n", " # Expected events are normalized PDFs times scale factors (\\mu_j) for each PDF\n", " expecteds = [scale*pdf for scale,pdf in zip(params,self.class_pdfs)]\n", " # Sum up all the expected event historgrams bin-by-bin (sum over j is axis 0)\n", " expected = np.sum(expecteds,axis=0)\n", " # Calculate the bin-by-bin poisson probabilities to observe `observed` events\n", " # with an average `expected` events in each bin (these poisson functions operate bin-by-bin)\n", " bin_probabilities = poisson.pmf(observed,expected)\n", " # multiply all the probabilities together\n", " return np.prod(bin_probabilities)" ] }, { "cell_type": "markdown", "id": "1abacb79-e1bd-4a54-ba34-b36902b660fe", "metadata": {}, "source": [ "Using the fake data and MC generated above, this class can be used to create a likelihood function:" ] }, { "cell_type": "code", "execution_count": 26, "id": "c48a1659", "metadata": {}, "outputs": [], "source": [ "# Build the likelihood function for the data and with our two event classes and binning\n", "lfn = LikelihoodFunction(data,[mc_class_a,mc_class_b],binning)" ] }, { "cell_type": "markdown", "id": "6c666f59-d3e4-47f0-83e2-9fdc7ad385e5", "metadata": {}, "source": [ "This likelihood function can be __call__ed to calculate the likelihood for some scale factors. Here the ’true’ scale factors are passed to see their likelihood." ] }, { "cell_type": "code", "execution_count": 27, "id": "46a503dc-db58-4b86-8e67-8343953b2951", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.72414260865059e-30\n" ] } ], "source": [ "print(lfn(100,200))" ] }, { "cell_type": "markdown", "id": "cd9dc187-514e-4361-90a6-dd60581ee2c7", "metadata": {}, "source": [ "Note that these likelihoods are typically tiny. With many bins, you can easily run out of precision even with 64bit float values, which is one reason people tend to work with the logarithm of the likelihood (next section) instead.\n", "\n", "#### Likelihood space\n", "\n", "The likelihood function here is a two parameter function because two event classes were used. It calculates the likelihood (probability) of observing the data given the expected (MC simulated) event classes scaled by factors that represent the number of events of each class in the dataset. Because this is a 2D likelihood space, we can make a nice contour plot of the likelihood as a function of the two scale factors around where we constructed the true answer to be: (100,200)." ] }, { "cell_type": "code", "execution_count": 28, "id": "2a70ba00", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# A numpy recipe for creating a 2D grid\n", "X,Y = np.meshgrid(np.linspace(80,120),np.linspace(180,220))\n", "# Evaluate the likelihood at each point on the grid\n", "Z = [lfn(x,y) for x,y in zip(X.flatten(),Y.flatten())]\n", "# Reshape the Z result to match the recipe shapes so plotting functions can use it\n", "Z = np.asarray(Z).reshape(X.shape)\n", "\n", "plt.contour(X,Y,Z)\n", "plt.colorbar()\n", "plt.title('Likelihood Contours')\n", "plt.xlabel('Class A Events')\n", "plt.ylabel('Class B Events');" ] }, { "cell_type": "markdown", "id": "0a7a68c4-8bd0-41b4-9fa0-11a68dfbad39", "metadata": {}, "source": [ "Note that the largest likelihood is, in fact, near the true answer. It is not exactly at the true answer because this is a small data set used for this exercise, and the statistical uncertainty of the analysis is correspondingly large. With more data, the maximum likelihood will be arbitrarily close to the true answer. With different data of the same size as this exercise, the maximum likelihood point will fluctuate around the true answer.\n", "\n", "#### Maximum likelihood\n", "\n", "It is now a computational exercise to find the point of maximum likelihood. Typically, function optimizers are designed to find minimum values, and it is trivial to adapt our likelihood to this domain: simply minimize the negative likelihood to find the maximum likelihood. The scipy.optimize.minimize routine encapsulates several robust optimizers. Here, I have opted to use the Nelder-Mead simplex method which is a good general purpose algorithm that makes very few assumptions about the function it is minimizing, and works well even with higher dimensional and rough functions." ] }, { "cell_type": "code", "execution_count": 29, "id": "a17c0b90", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " message: Optimization terminated successfully.\n", " success: True\n", " status: 0\n", " fun: -1.745999493614505e-30\n", " x: [ 1.013e+02 1.977e+02]\n", " nit: 52\n", " nfev: 103\n", " final_simplex: (array([[ 1.013e+02, 1.977e+02],\n", " [ 1.013e+02, 1.977e+02],\n", " [ 1.013e+02, 1.977e+02]]), array([-1.746e-30, -1.746e-30, -1.746e-30]))\n" ] } ], "source": [ "# Many minimizers require an initial guess (50,50) \n", "# for smooth functions with one global minimum, this need not be a good guess\n", "result = opt.minimize(lambda x: -lfn(*x),x0=(50,50),method='Nelder-Mead')\n", "\n", "# Note fun (minimum value), nfev (number of times lfn function called), and x (the minimum location)\n", "print(result)\n" ] }, { "cell_type": "markdown", "id": "5f6f78dd-e2e4-4cc3-91a5-54247093bc54", "metadata": {}, "source": [ "This indicates the point of maximum likelihood is (101,197) which is quite close to the true value for this data set. You could go on from here to integrate the likelihood around this point to find a region containing e.g. 0.95\n", " total probability, which would give a 95% confidence limit interval. For problems that are sufficiently close to having Gaussian errors (likelihood described well by a Gaussian distribution), there are easier methods using the negative logarithm of the likelihood.\n", "\n", "#### Binned negative log likelihood function\n", "\n", "To avoid very small numbers in likelihoods, one can opt to minimize the negative logarithm of the likelihood instead. This can also simplify the procedure of finding confidence intervals significantly. To start, first examine the Poisson likelihood $L_i$\n", " for one bin in the histogram, with $k_i$\n", " observed events and an expected number of events $\\lambda_i$\n", "\n", "$$ L_i = {\\lambda_i^{k_i} e^{-\\lambda_i} \\over k_i!} $$\n", "\n", "The negative logarithm of this, expanded out is\n", "\n", "$$ -log L_i = \\lambda_i - k_i {\\rm log}(\\lambda_i) + {\\rm log}(k_i !) $$\n", "\n", "The observed events $k_i$\n", " is a constant in the likelihood function, while the $\\lambda_i$\n", " is constructed from the PDFs and changes with the scale factors, which are the parameters of the likelihood function and change. This means the final term log $(k_i !)$\n", " is a constant term and only shifts the likelihood function, so these terms can be omitted during the optimization process without affecting the minimum found. I’ll use $L_i$\n", " to refer to this modified negative log likelihood.\n", "\n", " $$ L_i = \\lambda_i - k_i {\\rm log}(\\lambda_i) $$\n", "\n", "\n", "The total negative log likelihood $L$ \n", " is now given by the sum of $L_i$\n", " for all bins\n", "\n", " $$ L = \\sum_{i} L_i $$\n", "\n", " \n", "\n", "This can be implemented in a very similar Python class:" ] }, { "cell_type": "code", "execution_count": 30, "id": "790e5b29", "metadata": {}, "outputs": [], "source": [ "class NegativeLogLikelihoodFunction:\n", " \n", " # This is the same as before\n", " def __init__(self,data,event_classes,binning):\n", " self.data_counts = np.histogram(data,bins=binning)[0]\n", " self.class_pdfs = []\n", " for event_class in event_classes:\n", " pdf_counts = np.histogram(event_class,bins=binning)[0]\n", " pdf_norm = pdf_counts/np.sum(pdf_counts)\n", " self.class_pdfs.append(pdf_norm)\n", " \n", " def __call__(self,*params):\n", " observed = self.data_counts\n", " expecteds = [scale*pdf for scale,pdf in zip(params,self.class_pdfs)]\n", " expected = np.sum(expecteds,axis=0)\n", " # Calculate the bin-by-bin -log(poisson probabilities) sans constant terms\n", " # Note, regions in your ROI with no expected counts (0 bins in PDF) must be excluded\n", " mask = expected > 0\n", " bin_nlls = expected[mask]-observed[mask]*np.log(expected[mask])\n", " # multiply all the probabilities -> add all negative log likelihoods\n", " return np.sum(bin_nlls)" ] }, { "cell_type": "code", "execution_count": 31, "id": "4120227e", "metadata": {}, "outputs": [], "source": [ "nllfn = NegativeLogLikelihoodFunction(data,[mc_class_a,mc_class_b],binning)" ] }, { "cell_type": "code", "execution_count": 32, "id": "3f4ba7d6-bdcc-4617-bae5-5c94d9ef1fac", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " message: Optimization terminated successfully.\n", " success: True\n", " status: 0\n", " fun: -462.6357466223414\n", " x: [ 1.013e+02 1.977e+02]\n", " nit: 52\n", " nfev: 103\n", " final_simplex: (array([[ 1.013e+02, 1.977e+02],\n", " [ 1.013e+02, 1.977e+02],\n", " [ 1.013e+02, 1.977e+02]]), array([-4.626e+02, -4.626e+02, -4.626e+02]))\n" ] } ], "source": [ "# Minimize like before\n", "nll_result = opt.minimize(lambda x: nllfn(*x),x0=(50,50),method='Nelder-Mead')\n", "\n", "# Note fun (minimum value), nfev (number of times lfn function called), and x (the minimum location)\n", "print(nll_result)" ] }, { "cell_type": "code", "execution_count": 33, "id": "85185cb3", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Class B Events')" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#A numpy recipe for creating a 2D grid\n", "X,Y = np.meshgrid(np.linspace(80,120),np.linspace(180,220))\n", "#Evaluate the likelihood at each point on the grid\n", "Z = [nllfn(x,y) for x,y in zip(X.flatten(),Y.flatten())]\n", "#Reshape the Z result to match the recipe shapes so plotting functions can use it\n", "Z = np.asarray(Z).reshape(X.shape)\n", "\n", "plt.contour(X,Y,Z)\n", "plt.colorbar()\n", "plt.title('Log Likelihood Contours')\n", "plt.xlabel('Class A Events')\n", "plt.ylabel('Class B Events')" ] }, { "cell_type": "markdown", "id": "ed889019-ac05-43c6-85e9-394fa0fac4b9", "metadata": {}, "source": [ "#### Confidence intervals\n", "\n", "Finding a maximum likelihood is not the end of an analysis. One also needs to understand the statistical uncertainty in the optimal parameters. As mentioned earlier, the likelihood function represents probabilities for a particular set of parameters, so integrating the likelihood function in a region directly gives the probability that the answer lies in that region. Poisson likelihoods, as we are dealing with here, are incidentally closely related to thi^2$ \n", " statistic. As is shown by Wilks’ theorem, -2\n", " times the logarithm of a likelihood ratio (where one likelihood represents a null hypothesis (the best-fit) and another likelihood is for an alternative set of parameters) is approximately Chi-squared distributed for sufficiently large datasets (where statistical error is small and the likelihood is well described by a Gaussian distribution).\n", "\n", " $$ \\chi^2 = -2 {\\rm log} L_{alt}/L $$\n", "\n", "Or, for the notation used for negative log likelihood:\n", "\n", "$$ \\chi^2 = 2(L_{alt} - L) = 2 \\Delta L $$\n", "\n", "So, a difference in log likelihood can use to get a $\\chi^2$\n", " p-value, which can be used to set a confidence limit. This means a one-sigma confidence for one parameter ($\\chi^2$ of 1) corresponds to $\\Delta L = 1/2$.\n", "\n", "To arrive at this $\\Delta L$\n", " value, it is easiest to “profile” the likelihood, which means scanning one parameter while maximizing the likelihood (floating) the other parameters. A more mathematically rigorous approach again involves integrating the likelihood directly to “marginalize” away other variables. Python code for functions that returned the profiled negative log likelihood for the class A and B scale factors is as follows:" ] }, { "cell_type": "code", "execution_count": 34, "id": "474d0d22", "metadata": {}, "outputs": [], "source": [ "def profile_class_a(nev):\n", " '''Profile away class_b scale factor to get 1D delta NLL for class_a'''\n", " return opt.minimize(lambda x: nllfn(nev,x[0]),x0=(50,),method='Nelder-Mead').fun - nll_result.fun\n", "def profile_class_b(nev):\n", " '''Profile away class_a scale factor to get 1D delta NLL for class_b'''\n", " return opt.minimize(lambda x: nllfn(x[0],nev),x0=(50,),method='Nelder-Mead').fun - nll_result.fun" ] }, { "cell_type": "markdown", "id": "94c9265d-ff65-498e-a495-e8340ec8e20f", "metadata": {}, "source": [ "The profile for the class A scale factor:" ] }, { "cell_type": "code", "execution_count": 35, "id": "8bdb4e9b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '-$\\\\Delta$ Log ${\\\\scr L}$')" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(80,115,50)\n", "y = [profile_class_a(nev) for nev in x]\n", "plt.plot(x,y)\n", "plt.xlabel('Class A Events')\n", "plt.ylabel('-$\\Delta$ Log ${\\scr L}$')" ] }, { "cell_type": "code", "execution_count": 36, "id": "1a000e1b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$\\\\Delta$ Log ${\\\\scr L}$')" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(180,215,50)\n", "y = [profile_class_b(nev) for nev in x]\n", "plt.plot(x,y)\n", "plt.xlabel('Class B Events')\n", "plt.ylabel('$\\Delta$ Log ${\\scr L}$')\n" ] }, { "cell_type": "markdown", "id": "bcb51970-3830-446c-9074-22b92fc6d532", "metadata": {}, "source": [ "It is then easy to use a root finding algorithm to look for the where these functions cross \n", "1/2" ] }, { "cell_type": "code", "execution_count": 37, "id": "22bec975", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\mathrm{Number\\ of\\ A\\ events} = 101.337_{-13.123}^{+12.370}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\mathrm{Number\\ of\\ B\\ events} = 197.663_{-16.472}^{+15.702}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def confidence_interval(delta_nll_fn,central,step):\n", " ''' Finds 1sigma confidence interval for a delta_nll_fn of one parameter\n", " around a central value with a max distance of step.'''\n", " lo = opt.brentq(lambda x: delta_nll_fn(x)-0.5,central-step,central)\n", " hi = opt.brentq(lambda x: delta_nll_fn(x)-0.5,central,central+step)\n", " return lo,hi\n", "\n", "from IPython.display import display, Math\n", "\n", "central = nll_result.x[0]\n", "lo,hi = confidence_interval(profile_class_a,central,50)\n", "#print('Number of A events = $%0.2f^{+%0.2f}_{-%0.2f}$'%(central,hi-central,central-lo))\n", "txt=\"\\mathrm{{{0}}} = {1:.3f}_{{-{2:.3f}}}^{{+{3:.3f}}}\"\n", "txt=txt.format('Number\\ of\\ A\\ events',central,hi-central,central-lo)\n", "display(Math(txt))\n", "\n", "central = nll_result.x[1]\n", "lo,hi = confidence_interval(profile_class_b,central,50)\n", "#print('Number of B events = $%0.2f^{+%0.2f}_{-%0.2f}$'%(central,hi-central,central-lo))\n", "txt=\"\\mathrm{{{0}}} = {1:.3f}_{{-{2:.3f}}}^{{+{3:.3f}}}\"\n", "txt=txt.format('Number\\ of\\ B\\ events',central,hi-central,central-lo)\n", "display(Math(txt))\n", "\n", "# txt = \"\\mathrm{{{3}}} = {0:.3f}_{{-{1:.3f}}}^{{{2:.3f}}}\"\n", "# txt = txt.format(mcmc[1], q[0], q[1], labels[i])\n", "# display(Math(txt))" ] }, { "cell_type": "markdown", "id": "8f3f98e2-96ba-49c5-a323-e3f5f5ae33ed", "metadata": {}, "source": [ "These results are nicely consistent with the initial conditions, as the estimated parameter error covers the true value. To demonstrate a rigorous fit, one would repeat this procedure for many different fake datasets and record the results. The results of this meta-analysis can be used to demonstrate both that the one-sigma confidence intervals actually contain the true values the correct fraction of the time and that there is no bias between the true and estimated number of events on average.\n", "\n", "#### Final Results\n", "\n", "The fitted number of events can be used to generate the \n", " expected events for each bin, as well as the breakdown by event class. It is straightforward to plot this, both to demonstrate that the best fit agrees well with the data, and show how the total fit is built from the PDFs of the event classes. This is done with the following Python code, which also shows the data with Poisson error bars." ] }, { "cell_type": "code", "execution_count": 38, "id": "968b1eab", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Plot binned data with errorbars\n", "bin_centers = (binning[:-1] + binning[1:])/2\n", "plt.errorbar(bin_centers,nllfn.data_counts,yerr=np.sqrt(nllfn.data_counts),marker='x',linestyle='none',label='Data')\n", "#Borrowed from the NegativeLogLikelihoodFunction class\n", "expecteds = [scale*pdf for scale,pdf in zip(nll_result.x,nllfn.class_pdfs)]\n", "#Plot each event class as a separate hisotgram\n", "for class_name,expected_class in zip(['A','B'],expecteds): \n", " plt.plot(binning[:-1],expected_class,drawstyle='steps-post',label='Class %s Fit'%class_name)\n", "#Sum the histograms to plot the total fit\n", "expected = np.sum(expecteds,axis=0)\n", "plt.plot(binning[:-1],expected,drawstyle='steps-post',color='k',label='Total Fit')\n", "plt.legend();" ] }, { "cell_type": "code", "execution_count": null, "id": "c1ecc105-8b97-4072-a4b1-aab76c703847", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 5 }