{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Machine Learning and Statistics for Physicists" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Material for a [UC Irvine](https://uci.edu/) course offered by the [Department of Physics and Astronomy](https://www.physics.uci.edu/).\n", "\n", "Content is maintained on [github](github.com/dkirkby/MachineLearningStatistics) and distributed under a [BSD3 license](https://opensource.org/licenses/BSD-3-Clause).\n", "\n", "[Table of contents](Contents.ipynb)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns; sns.set()\n", "import numpy as np\n", "import pandas as pd" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import scipy.stats" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Load Data" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from mls import locate_data" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "blobs = pd.read_hdf(locate_data('blobs_data.hf5'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Statistical Methods" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The boundary between probability and statistics is somewhat gray (similar to astronomy and astrophysics). However, you can roughly think of statistics as the applied cousin of probability theory." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Expectation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Given a probability density $P(x,y)$, and an arbitrary function $g(x,y)$ of the same random variables, the **expectation value** of $g$ is defined as:\n", "$$\n", "\\langle g\\rangle \\equiv \\iint dx dy\\, g(x,y) P(x,y) \\; .\n", "$$\n", "Note that the result is just a number, and not a function of either $x$ or $y$. Also, $g$ might have dimensions, which do not need to match those of the probability density $P$, so $\\langle g\\rangle$ generally has dimensions.\n", "\n", "Sometimes the assumed PDF is indicated with a subscript, $\\langle g\\rangle_P$, which is helpful, but more often not shown.\n", "\n", "When $g(x,y) = x^n$, the resulting expectation value is called a **moment of x**. (The same definitions apply to $y$, via $g(x,y) = y^n$.) The case $n=0$ is just the normalization integral $\\langle \\mathbb{1}\\rangle = 1$. Low-order moments have familiar names:\n", " - $n=1$ yields the **mean of x**, $\\overline{x} \\equiv \\langle x\\rangle$.\n", " - $n=2$ yields the **root-mean square (RMS) of x**, $\\langle x^2\\rangle$.\n", " \n", "Another named expectation value is the **variance of x**, which combines the mean and RMS,\n", "$$\n", "\\sigma_x^2 \\equiv \\langle\\left( x - \\overline{x} \\right)^2\\rangle \\; ,\n", "$$\n", "where $\\sigma_x$ is called the **standard deviation of x**.\n", "\n", "Finally, the **correlation between x and y** is defined as:\n", "$$\n", "\\text{Corr}_{xy} \\equiv \\langle\\left( x - \\overline{x}\\right) \\left( y - \\overline{y}\\right)\\rangle \\; .\n", "$$\n", "A useful combination of the correlation and variances is the **correlation coefficient**,\n", "$$\n", "\\rho_{xy} \\equiv \\frac{\\text{Corr}_{x,y}}{\\sigma_x \\sigma_y} \\; ,\n", "$$\n", "which, by construction, must be in the range $[-1, +1]$. Larger values of $|\\rho_{xy}|$ indicate that $x$ and $y$ are measuring related properties of the outcome so, together, carry less information than when $\\rho_{xy} \\simeq 0$. In the limit of $|\\rho_{xy}| = 1$, $y = y(x)$ is entirely determined by $x$, so carries no new information.\n", "\n", "We say that the variance and correlation are both *second-order moments* since they are expectation values of second-degree polynomials.\n", "\n", "We call the random variables $x$ and $y$ **uncorrelated** when:\n", "$$\n", "x,y\\, \\text{uncorrelated}\\quad\\Rightarrow\\quad \\text{Corr}_{xy} = \\rho_{xy} = 0 \\; .\n", "$$\n", "\n", "To obtain an **empirical estimate** of the quantities above derived from your data, use the corresponding numpy functions, e.g." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "x0 6.920270\n", "x1 4.502004\n", "x2 8.492347\n", "dtype: float64" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(blobs, axis=0)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "x0 12.684951\n", "x1 6.807913\n", "x2 15.503924\n", "dtype: float64" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.var(blobs, axis=0)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "x0 3.561594\n", "x1 2.609198\n", "x2 3.937502\n", "dtype: float64" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.std(blobs, axis=0)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "assert np.allclose(np.std(blobs, axis=0) ** 2, np.var(blobs, axis=0))" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "assert np.allclose(\n", " np.mean((blobs - np.mean(blobs, axis=0)) ** 2, axis=0),\n", " np.var(blobs, axis=0))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The definition $\\sigma_x^2 = \\langle\\left( x - \\overline{x} \\right)^2\\rangle$, suggests that two passes through the data are necessary to calculate variance: one to calculate $\\overline{x}$ and another to calculate the residual expectation. Expanding this definition, we obtain a formula\n", "$$\n", "\\sigma_x^2 = \\langle x^2\\rangle - \\langle x\\rangle^2\n", "$$\n", "that can be evaluated in a single pass by simultaneously accumulating the first and second moments of $x$. However, this approach should generally not be used since it involves a cancellation between relatively large quantities that is subject to large round-off error. More details and recommended one-pass (aka \"online\") formulas are [here](https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Covariance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is useful to construct the **covariance matrix** $C$ with elements:\n", "$$\n", "C \\equiv \\begin{bmatrix}\n", "\\sigma_x^2 & \\rho_{x,y} \\sigma_x \\sigma_y \\\\\n", "\\rho_{x,y} \\sigma_x \\sigma_y & \\sigma_y^2 \\\\\n", "\\end{bmatrix}\n", "$$\n", "With more than 2 random variables, $x_0, x_1, \\ldots$, this matrix generalizes to:\n", "$$\n", "C_{ij} = \\langle \\left( x_i - \\overline{x}_i\\right) \\left( x_j - \\overline{x}_j\\right)\\rangle \\; .\n", "$$\n", "Comparing with the definitions above, we find variances on the diagonal:\n", "$$\n", "C_{ii} = \\sigma_i^2\n", "$$\n", "and symmetric correlations on the off-diagonals:\n", "$$\n", "C_{ij} = C_{ji} = \\rho_{ij} \\sigma_i \\sigma_j \\; .\n", "$$\n", "(The covariance is not only symmetric but also [positive definite](https://en.wikipedia.org/wiki/Positive-definite_matrix)).\n", "\n", "The covariance matrix is similar to a pairplot, with each $2\\times 2$ submatrix\n", "$$\n", "\\begin{bmatrix}\n", "\\sigma_i^2 & \\rho_{ij} \\sigma_i \\sigma_j \\\\\n", "\\rho_{ij} \\sigma_i \\sigma_j & \\sigma_j^2 \\\\\n", "\\end{bmatrix}\n", "$$\n", "describing a 2D elllipse in the $(x_i, x_j)$ plane:\n", "![Ellipse Parameters](img/Statistics/Ellipse.png)\n", "\n", "Note that you can directly read off the correlation coefficient $\\rho_{ij}$ from any of the points where the ellipse touches its bounding box. The ellipse rotation angle $\\theta$ is given by:\n", "$$\n", "\\tan 2\\theta = \\frac{2 C_{ij}}{C_{ii} - C_{jj}} = \\frac{2\\rho_{ij}\\sigma_i\\sigma_j}{\\sigma_i^2 - \\sigma_j^2}\n", "$$\n", "and its [principal axes](https://en.wikipedia.org/wiki/Semi-major_and_semi-minor_axes) have lengths:\n", "$$\n", "a_\\pm = 2\\sqrt{C_{ii} + C_{jj} \\pm d} \\quad \\text{with} \\quad\n", "d = \\sqrt{C_{11}^2 - 2 (1 - 2\\rho^2) C_{11} C_{22} + C_{22}^2} \\; .\n", "$$\n", "For practical calculations, the SVD of the covariance is useful:\n", "```\n", "U, s, _ = np.linalg.svd(C)\n", "theta = np.arctan2(U[1, 0], U[0, 0])\n", "ap, am = 2 * np.sqrt(s)\n", "```\n", "The above assumes $C$ is $2\\times 2$. In the general $D\\times D$ case, use `C[[[j], [i]], [[j, i]]]` to pick out the $(i,j)$ $2\\times 2$ submatrix.\n", "\n", "A multivariate Gaussian PDF integrated over this ellipse (and marginalized over any additional dimensions) has a total probability of about 39%, also known as its **confidence level (CL)**. We will see below how to calculate this CL and scale the ellipse for other CLs." ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden", "solution2_first": true }, "source": [ "**EXERCISE:** Sketch the ellipse corresponding to this covariance matrix:\n", "$$\n", "C = \\begin{bmatrix}\n", "1\\,\\text{m}^2 & 1\\,\\text{m s} \\\\\n", "1\\,\\text{m s} & 4\\,\\text{s}^2 \\\\\n", "\\end{bmatrix}\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden" }, "source": [ "The relative scaling of the $x$ and $y$ axes in our sketch is arbitrary since they have different dimensions.\n", "\n", "However, the correlation coefficient is always dimensionless,\n", "$$\n", "\\rho = \\frac{1\\,\\text{m s}}{1\\,\\text{m}\\cdot 2\\,\\text{s}} = 0.5 \\; ,\n", "$$\n", "and can be interpreted geometrically as telling us where the ellipse just touches its bounding box along both $x$ and $y$.\n", "\n", "The half-width and half-height of this bounding box are $\\sigma_x = 1$ m and $\\sigma_y = 2$ s." ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden", "solution2_first": true }, "source": [ "**EXERCISE:** Calculate the empirical covariance matrix of the `blobs` dataset using `np.cov` (pay attention to the `rowvar` arg). Next, calculate the ellipse rotation angles $\\theta$ in degrees for each of this matrix's 2D projections." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "solution2": "hidden" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 1 123.3\n", "0 2 -138.2\n", "1 2 151.0\n" ] } ], "source": [ "C = np.cov(blobs, rowvar=False)\n", "for i in range(3):\n", " for j in range(i + 1, 3):\n", " U, s, _ = np.linalg.svd(C[[[j], [i]], [[j, i]]])\n", " theta = np.arctan2(U[1, 0], U[0, 0])\n", " print(i, j, np.round(np.degrees(theta), 1))" ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden" }, "source": [ "Recall that the `blobs` data was generated as a mixture of three Gaussian blobs, each with different parameters. However, describing a dataset with a single covariance matrix suggests a single Gaussian model. The lesson is that \n", "we can calculate an empirical covariance for *any* data, whether or not it is well described a single Gaussian." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Jensen's Inequality" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Convex functions](https://en.wikipedia.org/wiki/Convex_function) play a special role in optimization algorithms (which we will talk more about soon) since they have a single global minimum with no secondary local minima. The parabola $g(x) = a (x - x_0)^2 + b$ is a simple 1D example, having its minimum value of $b$ at $x = x_0$, but convex functions can have any dimensionality and need not be parabolic (second order)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Expectations involving a convex function $g$ satisfy [Jensen's inequality](https://en.wikipedia.org/wiki/Jensen's_inequality), which we will use later:\n", "$$\n", "g(\\langle \\vec{x} \\ldots\\rangle) \\le \\langle g(\\vec{x})\\rangle \\; .\n", "$$\n", "In other words, the expectation value of $g$ is bounded below by $g$ evaluated at the PDF mean, for any PDF. Note that the two sides of this equation swap the order in which the operators $g(\\cdot)$ and $\\langle\\cdot\\rangle$ are applied to $\\vec{x}$." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def jensen(a=1, b=1, c=1):\n", " x = np.linspace(-1.5 * c, 1.5 * c, 500)\n", " g = a * x ** 2 + b\n", " P = (np.abs(x) < c) * 0.5 / c\n", " plt.fill_between(x, P, label='$P(x)$')\n", " plt.plot(x, P)\n", " plt.plot(x, g, label='$g(x)$')\n", " plt.legend(loc='upper center', frameon=True)\n", " plt.axvline(0, c='k', ls=':')\n", " plt.axhline(b, c='r', ls=':')\n", " plt.axhline(a * c ** 2 + b, c='b', ls=':')\n", " plt.xlabel('$x$')\n", " \n", "jensen()" ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden", "solution2_first": true }, "source": [ "**EXERCISE:** Match the following values to the dotted lines in the graph above of the function $g(x)$ and probability density $P(x)$:\n", " 1. $\\langle x\\rangle = \\int dx\\, x P(x)$\n", " 2. $\\langle g(x)\\rangle = \\int dx\\, g(x)\\,P(x)$\n", " 3. $g(\\langle x\\rangle) = g\\left( \\int dx\\, x P(x)\\right)$\n", " \n", "Is $g(x)$ convex? Is Jensen's inequality satisfied?" ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden" }, "source": [ "Answer:\n", " 1. Vertical (black) line.\n", " 2. Upper horizontal (blue) line.\n", " 3. Lower horizontal (red) line.\n", " \n", "Jensen's inequality is satisfied, as required since $g(x)$ is convex." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Useful Distributions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are many named statistical distributions with useful properties and/or interesting history. For example, in the [scipy.stats](https://docs.scipy.org/doc/scipy/reference/stats.html) module we find a large number of 1D continuous random variable distributions:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "93" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(scipy.stats.rv_continuous.__subclasses__())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and a smaller number of 1D discrete distributions:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "14" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(scipy.stats.rv_discrete.__subclasses__())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and multidimensional continuous distributions:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "9" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(scipy.stats._multivariate.multi_rv_generic.__subclasses__())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You will likely never need most of this distributions, but it is useful to know about them. Most have special applications that they were created for, but can also be useful as building blocks of an empirical distribution when you just want something that looks like the data.\n", "\n", "It is useful to group the large number of 1D continuous distributions according to their general shape. We will use the function below for a quick visual tour of some PDFs in each group:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "def pdf_demo(xlo, xhi, **kwargs):\n", " x = np.linspace(xlo, xhi, 200)\n", " cmap = sns.color_palette().as_hex()\n", " for i, name in enumerate(kwargs):\n", " for j, arglist in enumerate(kwargs[name].split(';')):\n", " args = eval('dict(' + arglist + ')')\n", " y = eval('scipy.stats.' + name)(**args).pdf(x)\n", " plt.plot(x, y, c=cmap[i], ls=('-','--',':')[j], label=name)\n", " plt.xlim(x[0], x[-1])\n", " plt.legend(fontsize='large')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, the centered symmetric peaked distributions, including the ubiquitous Gaussian (here called \"norm\") and Lorentzian (here called \"cauchy\"). Each of these can be re-centered using the `loc` (location) parameter and broadened using `scale`:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pdf_demo(-5, +5, laplace='scale=1', norm='scale=1', cauchy='scale=1', logistic='scale=1')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are also some more specialized asymmetric \"bump\" distributions that are particularly useful for modeling histograms of reconstructed particle masses (even more specialized is the Cruijff function used [here](https://arxiv.org/abs/1005.4087)):" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pdf_demo(0, 10, crystalball='beta=1,m=3,loc=6;beta=10,m=3,loc=6', argus='chi=0.5,loc=5,scale=2;chi=1.5,loc=5,scale=2')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, the \"one-sided\" distributions that are only defined for $x \\ge 0$. Most of these smoothly transition from peaking at the origin to peaking at $x > 0$ as some parameter is varied. These are useful building blocks for quantities that must be positive, e.g., errors or densities." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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RcfYV8i4pKWHPnt2MGzeh/rmVK3/k3/9+mSVLlnWjZO4lJ+coCQnxHRqjVeeyoigNLMszfVo1NTU8/PDDvP/++yQlJfHee+/xwAMPsGjRIpeFKC6uQFG63sJUFJXaWjuFheXU5ueBpKGkWotUW47qFYVkDqTk95XUhDpj1of0DUCS4Js16Vwx3r2K0rrPGZJWZepFTWG5W8cGUMOSQaOlfMdKTmiD3T5+TyU42EJhJ7yePZm2rFlRlLOybJ7DofLQQ//HvHm3c955kygpKeKtt95k8uSpZ+V6mkNRlCbfS1mWCAw0uzRGq+6asLAwCgsL6x8XFhYSEhJS//jAgQMYDAaSkpzhS7NmzWLTpk0uTd7dOKNrnH8bhs/APPfV+lhySZLR9R+DcjwP1e70o/lbDMRHB7BuVx6Km90eSuFh0JuQfENa79wOJIM32ujhVKT9Wr8egeBsRRTydp1WLfkxY8bwyiuvUFJSgpeXFytWrGjgqunTpw95eXlkZGTQr18/Vq5cSWLi2RGqd2aq4TOLc+iHTkM/fAaSdOq3cGxiGIu+3sP+o6UMcmM4paPwMJrgvg3mcje6geOpPrQB+5Gt6GJHddo8AkFXIAp5u0arSj40NJR7772XOXPmYLPZmDlzJklJScybN4/58+eTmJjI008/zT333IOqqgQGBvLUU0+1NmyP4PTompp1H6EJH4iu34j6dklrqO9X92MwrH8wJoOWX3fmuk3Jq3YrSnEW+iEXu2W85tBEDkLjE4Qt/Teh5AUCD8GlgO/p06czffr0Bs+99dZb9X9PnDiRiRMnuleyLqAud42qOLDtWeW05E9T8gC29A3Ubv4S76ufQNIa0Os0jE4IY/WOHK6vtmH20nVcjuJjoDqQg/t2eKyWkCQZc/xYjm/8BrWmAsnomk9PIBCcvXh0MpO6Qt5qZSmoClITqX0loxm1vBBHzr765yYkR2B3KPy22z1VoxyFhwHQdLKSBzAnjAfVgS1jc6fPJRAIuh+PVvJ1hbyVimIA5CYOIWnCBoBWj/3YqYRMvULM9A33Yc2OHLfEnTsKDyOZ/JC8Oz/sVB8ajewXjv3Qhk6fSyAQdD8ereSVk7lr1JNKXjI39rFLWj3ayATsmTsbKPSJyRFkF1VyKOdEx+UoyDi56dq5x63BeYhEGzsKR+6B+h83gUBw7uLRSl5VVSQZ56lWnbHZSkyaXkmo5UUNSumNHBSCQa9h9fbsjslgq0U5no/cxoLdHUEXMwpQsR86O0JdBQJB+/F4JS9LEvr48zHf9Hp9NM2ZaHsnoRt0PpKsqX/OqNcyKj6UzXsLqKqxt1sGpTQbUJEDO54/3lVk31Dk4L7Y0oXLRiA41/FoJX96ZaiWXCWyORDj+LnIvqENnp8wJAKrXWHjnvZvwDpKnJVkNG4oEtIWdLGjUIqP4ijL6dJ5BQJ3kZubw7hxw8nISG+9swfj2UpeUZGQqP55EdbdP7bYV1UVHIWHUW019c9Fh1noHWLml+3t34BVijNBa3B75snW0MakAhL29I1dOq9AIOhaPFbJ1yllSXKW3Dvd394UjryDVP3vH9izTuWFliSJ84ZFkllQwaHs9m3AKiVZyAFRnXrStSlkkx+aiDhs6RtEZkqB4BzGg5W8839ZklDttaDVt9hfExoDei8cxxrWthwdH4aXQcuqrVntkEHFUZLZ5a6aOrQxqagn8lGKj3bL/AKBu7BarbzzzptcffVlTJo0httuu4W0tN0N2hcseJqLLjqfadOm8J//vMesWVewdesWAO6880+8886bPPjgX5k8eSzXXXcly5Z95fL4M2dO57XXXuLKKy/lyisv5cSJE4wbN5yffvqBuXOvq78mNzeH559/lqlTJzJjxiUsX/5tp782Hlv+TznNksduRWpFyUuyFm3UYOyZuxqkOTDoNYxNDOPnrdnMmtwfX++WxzkdtaoMaiuRA6Na79wJ6PoOp3btf7Af2oQmKLpbZBD0PGwH1mHbv6ZL59QNnIBuwNh2X79gwbNs2LCe++9/kPDwSD777BPuvfcOPvnkS4KCgnjppQVs3ryRp59egJeXiQULniYnp2Fk3Mcff8Add9zDbbfdxeefL2bBgqcZM2YcgYFBvPjiv9i48bdmxwf4+uuveOGFV5Blub4y3htvvMpDDz2KxWLhgQf+ws0338Dll1/J229/wJIln/Pcc08xYcL5mEym9r94reDxlryWk5ExrSh5AG2vJNSqMpTShlb7+UMjcSgqa3a0bRNTKXZuusrdZMlLRjOaqARsGZuEy0Zw1lJeXsG3337NXXfdy+jR44iO7st99z1ISEgoX365mKqqKr77bhnz5/+FoUNTiIsbxN/+9s9Gn/nk5BSuuuoaeveO5tZb78DhcHDoUDrl5eV8992yZsevY/LkC4iPH0xc3Kn871deeTXDhg2nf/+BjBkzHi8vL/785zvo3TuaWbNmU1tbS25u5wY/eLwlL6Mg+0cge/m2eo0majAA9mO7GrhYwgO9iY/255dt2VwyqjeaZgr8nsmpyJruseQBdDEjqfnlbZTCDDQhMd0mh6DnoBswtkNWdVejKA4cDgeDByfVPyfLMomJSRw5ksGxY0ew2WzExSXUt/fpE43Z3LDece/evev/9vZ25nWy2+0cO3a0xfHrqKvnejqRkaf0hNFoJDw8ot4LoNc7DUubrXNTf3uwJe9U8orWiPfVTznroLaC7O2P1/QH0Q+e0qht0rAoSstr2ZHu+ilSpSQLyTsAyeDeKlNtQRs9DGQtNnEwSnCWYrH4NPm8qqooioJGoz35uOVUxFpt42SDqqpiMDR9fqZu/Dqa6qfVNrSju+JU+5l4sJJ3/i/RthddGz6wSf/9kNhAAnwMbdqAVcpykf0j2jS/u5H0JrS9ErFnbGr1SyAQ9FS0Wi27d++sf6yqKmlpu+jTJ5qoqF7o9YYG9VWzsjKpqHCtelZUVK8Wx+/peKy7ps6SN9UWUbX0P+hTr0YbNqD166zVWHd+jyYyAW34wPrnNbLMxORI/rcmg5yiSiJaqQGrqgpKWS66uAkt9usKtDEjsR/dhiPvYIM1CQRnA7IscfXV1/LKKy9iNBqJiIjiyy8Xk5OTzfTpM/Dy8uKyy67g1VcX4u1txmw288IL/wJcs6yNRiNXXTWr2fF7Oh6r5OtKyuqUahz5B8FW69qFGh3WnT+gq6lopBAnJkewbN0RftySydyL4locRq0sBXstsl94e8R3K9reyaDRYT+0SSh5wVnJ7bffharCU0/9k6qqSgYNSuDll9+kVy+nn/222+6iurqaBx74C3q9jtmzb2L37p3odK7Vg7j11juRJKnZ8XsyktoDwiq6o5B3eZWVu19ey22pGuIOvofX9AddVnDVP7yEoyQT72ufa2QJvP/9Xn5Ly2fB7WOwmJqP2LFn7ab6uwV4TXsAbcSgDq2lLTRX5Ln6x1dx5B3Ae/bC+jq35wKikHfL5OUdJSys65LjdRatlf9bvXoVw4aNwGJxbraWlpYyffoFfPHFN4SFhXWVmG2muffHrYW8z1XqflNk1QbQapz86Wh6JaKWF6Eez2/UdsHwXtjsCr9sbzksqu6EbU+w5MHpslGrT+DI3dd6Z4HgLOODD97lhRee5dixo2RkHOL5558mISGxRyt4d+GxSr7uBkajuh4nX4c2ylmo3J61q1FbZLCZhL4BrNqahd3RvGWhlOWC3oTkQuhmV6DtPQS0BpF+WHBO8uijT1BWVsof/ziH22+/BUmSeeqp57pbrC7BY33ydU4qRaNHDu6LpHf9xJnsE4wcFI1aW9Vk+9QRvXjxsx1s3lvA6MFNWwpKWS6yX3i3hFQ1haQ1oO0zFPvhLajjbkCSPfajITgH6dMnmhdf/Hd3i9EteLwlX+Efh/eMR5HbWHrPNONRDCmXN9mW0DeA8EATKzZnNnuSVCnNQfbr3vDJM9HGjEStrcCRvbf1zgKB4KzAY5V8g9w17aDOAlcVR6M2WZK4YHgvjuaXcyCzrFG7WluJWn28x/jj69D2SgSdlzgYJRCcQ3iskq8zsIPzN1D55d/bfBBIVVWqlj1N7dr/NNk+enAYZi8dyzcea9RWt+mq6WFKXtLo0EYPw35kC6rD1t3iCAQCN+CxSr7OktdZj6OU5rQ5n7skSUhGC/Zj25v8gTDoNExJiWLHoWKyCisazn0yKkf263k7+7qYkWCtxnFa3nyBQHD24rFKvj6fvGJrU2TN6Wj7DHVmpSxqOh/7pJQo9DqZ7zc0tOaV43kgSUiW4HbN25loIhPA4C1cNgLBOYIHK/mTIZSKrU0x8qej7T0EJAn70W1Ntpu9dEwYEsGmvfkUHa+uf145UYBkDkLS9LwIFkmjRRedgv3oNlR752bHEwgEnY/HKnnFDZa8ZDSjCe2P/ej2ZvtcOMJ57HnFpsxTcx/Pb1QUvCehjUkFWw32zJ2tdxYIuglRyNs1PFbJ11nyVlMomrD252vRJV2IPmFKs6GSgb5GUuNDWbMzh4pqmzM96Yl8ZJ+eq+Q1EXHO/QbhshEIzno8VsnX5copjZ6M13m3tHscXXQKurgJLR5quji1N1abwsrfs1BrysFajewb0u45OxtJ1qDtN8K5qexq4jaBQNAj8VglX59P3g0nTpWKkmb98uBMdZAcG8RPWzKpKTqZs6YHu2sAtP1Ggt3a4roEgp6CKOTdPD1v56+LUHFq+Yid71CTF4pxwh/aPZZ11w/Y0lZinvMKkt6ryT7TxkTzxIdb2LN7HwOhR7trADRhA5BMftgzNqGLHdXd4gi6mKplTzd6TttvJPqEyaj2Wqq/f6FRu27AOHQDx6PUlFPz46uN2+MnoYtJRakopubnRQ3aTNMf7JC8opB387hkyS9btoxLLrmEqVOn8vHHHzdqz8jI4MYbb+Syyy7jlltu4fjx424X1N3UWfK62lLU2soOjaXtMxQUO/YWYsv7RfgwuF8A2RmHe2z45OlIsux02WTuRLVWt36BQNBNiELeLdOqJZ+fn8+LL77IkiVL0Ov1XHvttaSmphIbGws4NzBvu+02Hn74YSZMmMCCBQtYtGgR999/f6cK3lHq0xo4bKBtuoajq2jC+js3Kg9vQddvRLP9Lhvbl6wlX1Gj88PSA8Mnz0TXbyS23T9iP7L1rCrsLOg4LVnWktbQYrtstLTcbg7ssOV+OqKQd8u0asmvX7+eUaNG4efnh8lk4sILL2T58uX17WlpaZhMJiZMcJaxu/XWW5k9e3bnSewmTh2GsrY7Tr4OSdag7ZuC/eh2VHvzG5Wxkb708qois8ZEra1xzpuehhwag2QOxJYhomwEPRdRyLtlWlXyBQUFBAefci2EhISQn3+qWMaxY8cICgrioYceYsaMGTz66KOd6l9yF3XRNU5LvmNKHk5tVDryDzXbR1VVguQT5FnNrGmlqEhPQJKcLhtH1u4Ou7QEgs5EFPJunlZ9BoqiNPj1UVW1wWO73c6mTZv46KOPSExMZOHChTzzzDM888wzLgvhahkrd5J/wmlxOyKS8Os7EEuwpZUrWkYNHI6j35tofQKb7eOorqDCXoPeP4zlm48x84KB6HWaDs3bHoLbsNbalPPJ3rkcY1EaPsmTO1GqzqMt6z1XcHXNBQUyWu3ZGWSn0Tjl1uk09YW8vb1NRERE8sUXi8nJyeGKK67CYvHm8stn8OqrC/Hx8cFsNrNgwbMAaLUatFoZSZKQZanRa6HRSJjNphbHr7umuetPb5ekU4/r/tdomn8PZFnu8Oe3VSUfFhbGli1b6h8XFhYSEnIqxjs4OJg+ffqQmOisljRt2jTmz5/fJiG6o8Zraamz4Ed+/PUEhPlT45Y6oHpoYRzHyRw3sQP7UbKqls9/3M/UEb2a7d8ZtLXmqaoNQbIEU7p9NbWRIztRss5B1HhtGUVRWqyN2pNxnKy85nAo9YW8H3/8sdMKbb9BREQUdrvCrbfeSVVVFffdd099Ie9du3YgyxrsduWk60Vt9Fo4HM7n/vSnO1ocH2jx+rp2VT31uO5/h6P590BRlCbfy7bUeG21kHd+fj7XXXcdX3zxBV5eXlx77bU8/vjjJCU5NyFqamqYMmUKb7/9NnFxcSxatIiDBw/y3HOul9bqDiW/90gJz23MNcYAACAASURBVP13Ow9cP5SBvdtWMKQ5lOoT1PzyFrq489D1TWnUbjv8OzU/voLpysd44cdSsgorePbW0Rj1XbcJ2x6lV7vpC6w7vsP7hoXIXk37P3sqQsm3jCjkLQp5Exoayr333sucOXO44oormDZtGklJScybN49du3ZhNBr597//zSOPPMKll17Kxo0b+X//7/+1fTVdjAL4SFWE/fQgtgPr3DKmZDCjFB3FfmhDk+1qeREAsjmIKyf2o7zKxo9bstwyd2eijRkJqoL98JbWOwsEPRBPLuTtkgk5ffp0pk+f3uC5t956q/7vIUOG8MUXX7hXsk5GVVT0kh3ZXuO2MSVZRtt3BLb9v6LaapF0DXfblYoi0BnB4E1MhERybBDLNx5j0rBIvI2Nd/Z7CnJAL2TfMOyHNqGPn9Td4ggEbebRR59g4cLn+OMf5yDLEiNGjBKFvM91FBX00skwRjdE19ShjRmJbc9K7Md2OAtwnIZaXoRsCarfuJ4xoR+PvbuJ5RuPcdXEGLfJ4G4kSUIbk4p169coVWXIJr/uFkkgaBOikLcHoqoqOuwAHY6TPx1NaH9nOoBDGxu1KeVFSOag+se9QsyMGBTCj1syOV7Zs3O3a2NGAir2jM3dLYpAIGgDHqzkQdcJlrwky+iTLkQTPuCM+VSUk5b86Vwxvh92u8o36464TYbOQOMfiRwQJdIPCwRnGR6s5FUqVQO1vUYhe7snuqYOfdLF6BMvbPiktQps1ciWhnH0YQEmxg8J55ft2eSXVLlVDnej7TcSR/5BlIri7hZFIBC4iMcqeUWFXIc/VcNmI/u6f4ddtdc2qBilnIysOd1dU8cV4/qi1ch8sbr507I9AV1MKgB2keZAIDhr8Fgl7zweoCJ3Ui4J2741VP+wEEeJM0SyTsnLTWSf9DUbuCi1N7/vLyQ9u+dm8JR9Q5GD+ogi3wLBWYTHKnlFVRlrOIDP0vkoVe5XrNrYUSBrsB1YC5wWI29pbMkDXDiyF77eej5bld5sKcGegLZfKkrhYZQTBd0tikAgcAGPVfKqCjocSKri1uiaOmSjBW3vZOwH16Mq9gYx8k1h1Gu5Ynxf0rOPs/VAodvlcRe6GGcqZZGZUtBTmTlzeoM872dy551/4tVXF9Y//uabpcyePZMpU8bxhz9cz7p1v3aFmF2GByt5FZ3kDKGkiRSj7kA3cBxq9QkcmbucMfLmoBZTjY5LCiciyJvPfzmE3dEz84nIlmDkkH4iykZw1vLUU89x883zAFiz5hdeeOFf3HjjH/jgg/9y0UWX8tBD97Fv355ultJ9eLCSdx6GUiUZSe6cM2GaXolIXj7Ys/c4Y+QtzWeoBNDIMrMmxVJQWs1PPTjdgS4mFaX4GEpZbneLIhC0GR8fX0wm5x31N998xSWXTOOiiy4lMjKKWbNmM3RoCitWfN/NUroPj1XySp0l3wmumjokWYvpyn+gH3VdkzHyTZHYL5CkmEC+XneY4xXNFyDpTrT9RgKS2IAVdCt5ebk8+OBfmTp1IhdfPIWFCxdgtzvvzrOzs7j77tuYNGkM11xzOatW/VR/3enumj/8YR6zZjUsciRJErW1PfO71x48WskftoXgiD2vU+eRvf2RbNUnY+RbV/IA103uj82u8OXqjNY7dwOytz+asP7YMzb26E1iwbmL1WrlnnvuoLa2ln//exHPPLOAtWtX8+67zgLhX3/9Py699HL+85/PGDEilSee+DuVlRWNxhk0KIFevU6V/UtPP8jWrVsYMmRol62ls/HY3DWqCjtsfVCSxnT6XLXbv3X+YQpwqX9ogIkLRvRi+cZjnD8skr7hPS+9rzZ2FLVrP0QpPoYm6OxPVSs4xcbc3/ktt2vTV4wOH0FqeOP03M2xZcsm8vNzef31d/D390erlbn//ofIyckGYNq0y5k69SIA5s69haVLl3D06BHi4wc3O2ZRUREPP3w/8fEJTJp0QccW1IPwWEteVVW0OJAUWxfM5txsVdtwUnT6mGh8vPV88tOBHmkt6/qNBFlbHyIqEHQlR45kEBoajr//qdPqqamjmTFjJgAREaeKatcV7G7JBZOTk82dd85Dq9Xy1FPPN6rNejZz7qykjagqXOe9Hu33K+D6zk05Khmdyf0dR7dB8iUuXeNl0HLVxH68990+1u/OY2xieGeK2GYkoxlt9FDsB39DTZ2FpPHYj9I5R2p4Spus6u5Aq9XR0jnGutKAp9OcsXT4cAb33HM7/v4BvPjiqw1+OM4FPNqSr9E6SDd0fvV0tbIEZC2O/IP1J2BdYWxiODGRPixelU5FdVfccbQN3YBxqLUV2I/t6G5RBB5Gr169yc/P48SJUwcZv//+G+bNm9OmcQoK8rnnntsJCQnl5ZffwN/fNZfq2YTHKnlFhf1BNt7xhy8OfI1DcXTaXGp5EZIlGDQ6bGk/tX7BSWRJ4sapA6mqsfNlD8xro4kajOTli124bARdzMiRo4iMjOLJJx8jIyOd7du38e67bzFq1Ng2jbNw4QIcDjsPPfQoNpuV4uIiiouLKC8/d0pGeuw9tqKqKLKKpMLPWWvJqsjhlsE3YNG7VjexTXOVFyH7hqAbOg25jZuUvUMtTBkexYrNmYxNDCc20tft8rUXSdag7T8G264VKNUnzrr6r4KzF41GwzPPvMCLL/6LefPmYjZbuOiiS5k79xa+//4bl8awWq2sXbsaRVG48cZrGrSdd94knnjiX50hepfTaiHvrqA7Cnmv2JzJrsxXKbGoXDZ4Fp/u/xKzzsyfEufQ2yeq9QFcRFVVKt6/Hd2AMRjH3tiuMapr7Tzy9kbMXjr+ftNwNHL7b8DcXdjaUZJN1RcPYxh9XeP0yj0AUci7ZTylkPfZSpcU8j5XUVWVYsWMrPMiNTyFv6TcDsALW19jY+7v7puoPo+8M0beUZJNzZr3UB12l4fwMmi5bnJ/MgsqetxJWE1AJHJwXxFlIxD0UDxYyUOx6o3mZMKw3pYoHhgxn2if3ny4dzGfH1jqFj/9mXnk1apSbPtWYzu4rk3jpAwMJikmkP/9mkFBWXWH5XInugFjUYozcRQd7W5RBALBGXiwklfRSnY0nIqusejN3JU8j/N7jeOXrHW8tG0RZbUdS0N8Zh55TWQCclA01h3foSqu315KksScCwciSxIffL+vR8XO62JGgUaLbd+a7hZFIBCcgccqeUVV6aMrRKooafC8RtYws/9l3BR/HZkV2Ty9aSF7Sw60ex61omEeeUmS0Cdfino8H/vhLW0aK8DHyNXnx7L3aClrd/ac5GCS0Yy273Bs6etR7edOzg+B4FzAg5U8KBJomjlRMSJsKA8MvwuL3sy/t7/DtxkrUNS2b+wo5Y3zyGv7piD7hWPdvqzNFvnE5AgG9PLjv6vSKS3vOQpVF3ceWKuxZ3TtcXiBQNAyHqvkVVVFlUCm+cNQYd6h3D/8LkaGDeO7Iz/x6va3OWFtW6RGU3nkJUlGn3IF2l5J4GjbISdZkvjDxXHYHQofrdjfY9w2mvCBSL5hWPf+0t2iCASC0/BgJQ8qagOffFMYNHpuHHQNs+OuJuP4EZ7etJCDpa4fTFIqms4jr4tJxTDy6nZVpQoNMHHF+L5sO1jEhrT8Nl/fGUiShH7QRJT89Dad6hUIBJ2LByv5k5a8C4W8JUliTMQI7h9+F0atgZe2LeK7wz+6FH3TUh55VVWxH9uOPWdfm+W/cERvYiN9+ejHA5ScqGnz9Z2BdsA4Z9Kyfau7WxSBQHASj1XyiqpSpnqhNfm5fE2kOZwHhs9neGgy3x7+kYXb3qS4urTZ/mptJVhbyCOvOqhZ/ym16z5qU6QNOA9D/HHaIBRF5b3v9vYIt41stKCNHobtwDpUu7W7xREIBHiwkldVqMCIpg1KHsCoNXJTwnXMjb+WnIpcnt78IlvytzfZ98wY+TORZC2GEVeilGZhP7ShbQsAQvxNXDMplrQjpfy8LbvN13cGukHngbWqzZFDAoG7EIW8G+KxSl45GScvt9GCrmNk2DAeHHkPYaZQ3kv7hA/3LKbG3tBtolQ0jJFvCm2/EciBfajdsgS1jZuwAOclRzC4bwCfrUonr6Sqzde7G01EHJJPKNY9q7pbFIGgSUQhbw9BVSFAcwKpA8Wog7wCuXfYrVwcPYVNeVt5etNCDh8/dmqO8oYx8k0hSTKGkTNRy4uwtSMyRZIk/nDJIHRamTeXpmHr5vwdkiSjj5/k3IAtOtKtsggETSEKeXsIp0IoO/YSaGQN0/pN5Z5ht6Kg8sLW1/gm4wfsir3JGPkmx4gajDZ2dH1xkbbibzFw86WDOJpfzue/pLdrDHeiGzgOtHqsu11PqywQtBVRyNs1XNJwy5Yt45JLLmHq1Kl8/PHHzfb75ZdfmDRpktuE60xUFRRci65xhVi/vjw44h5GhA7l+yMreW7Lq2SX5zaKkW8KSZLwmvRndLGj2z3/0P7BTEmJ4qctWWw7WNjucdyBZPBG138s9kMbUKpPdKssgnMTUcjbdVrNJ5+fn8+LL77IkiVL0Ov1XHvttaSmphIbG9ugX1FREc8++2ynCepuFEV1nnh1482MSefFnPhZDAkezKf7vuQlbQVTfS1crDjQyJpWr1cVB7Y9q9BGDUb2a3u5v6vPj+VAVhnvfruXf9xsIcDH2J5luAVdwhRse3/Gtm8NhqHTuk0OQftYuPWNRs8NC0liQtQYrA4rr+14t1F7avhwRocPp8Jaydu7/9OofXzkKFJCkymtKeODPf9t0HbPsFvbJJ8o5O06rWq49evXM2rUKPz8/DCZTFx44YUsX768Ub9HHnmEO++8s1OE7AxUFRRJQpbc77EaEpzAI6l/Jb7Kxvfacp7f+hp5lQWty1RbSe2WJdSs/7hdIZE6rcxtlw/Grqgs+joNRzs3ld2BJiASTcQgbHtWoXZi1S2BZyIKebtOqyspKCggOPhUdEhISAg7d+5s0OfDDz8kPj6eIUOGtEsIV5PfuxODUUtNjQ7voAiCgy1uHz+gRmZ2bimHRk3l0xMHeWbLS1yXeBmX9J+E3GzRDwvHz7uO4hXv4l26F++BqW2eNzjYwh0zh/DCJ1tZuS2X2RfFNdmnK6gccxn5XzyLqXQv5rj2u6I6Slettyfh6poLCmS02safx/tG3t7sNVqtscV2P62lxfZgc0CL7a5gMOiRZamB7Kf/rdNp6h/X/V/XX5KkBtcePpzBXXfdir9/AC+99BoBAT2nzqssyx3+/Laq5BVFaeBTVlW1weMDBw6wYsUK3n//ffLy8tolRHdUhqqqtmGTZBzazqkcVJdbPcHcn4cGTufT/V/w4fYvWX1oE7MHzSTS3LQ7Ru09Ftl/BQXL38HbJ7ZdaQ8G9/Zj7OAwFv+4n6hAL+KjT31ou7JSkuo3EMkSRPH6ZVQHNn+b3JmIylAtoyjKWVlRKSKiF3l5uZSUlOLj44tWK7Ns2dcsWfIZ4HTH1q2r7n+Hw7lWVVXr2wsK8rnzzlsJCQnl+edfwcfHp0e9HoqiNPleurUyVFhYGIWFpzbyCgsLCQkJqX+8fPlyCgsLueqqq/jTn/5EQUEB119/vUuTdyeqoiBJCnI7YtNd4fQYeV+DhT8n3sQfEq6nuKaEZza/xLJDy7E1MbckazCMvQG1ohjrtmXtnn/21AGEBZp4Y2kaRce7p8iIJMvo4yfjyN0vCooI3Ioo5O06rSr5MWPG8Ntvv1FSUkJ1dTUrVqxgwoQJ9e3z58/nhx9+YOnSpSxatIiQkBA++eSTThXaLagOtJIdSnM6Z/jyxnnkh4cm87dR9zEidCjLj67iqc0vcrA0o9G12og49EOno4lqv/Vr1Gu588pEHIrCv5fsxmrrHr+4Lm4C6IxYd5w7cceC7qeukLfD4WDevLk8/PADTJo0hblzb3F5jLpC3mVlZdx44zVcfvlF9f+effbxTpS+a2nVXRMaGsq9997LnDlzsNlszJw5k6SkJObNm8f8+fNJTEzsCjndj0NBkeiUjVdoOo88gFnnzZz4WYwIG8qn+5awcNsbjItI5YrYS/DSetX3M4y4qsMyhAd6M296Ai9/sZMPlu/nj9MGdXjMtiIZvNENOg/brhUoI69q8fSvQNAWIiOjWLDgZaBhIe8vvmh4B2wymVi79lSajVdfXVT/95o1m7pA0u7FpS3k6dOnM3369AbPvfXWW436RUVFsWrV2XGcXVXtOCQJrdR6aGO7xm8ij/zpDAoYwMOpf+HbjBWsyvyVHUVpXBk7jRGhQ+uvURWF2g2fIhktGIZd1i45kmODuGJcX75ae5jocAvXXxzf7jW1F/3gqdh2/4h11wqMY2a3foFAIHAb506cUFtRne6L5iNdOkZzeeRPx6DRc2X/aQwPTea/B/7HB3v+y/qcTcwaOINw71AkWUatPuGMnY8eiiagl0tzf/vbEfJLqikpr6Gqxk6tzUGwn5HFK9NJHBDCG1/uQFXB7KXDx1uPxaQjvk8Ayf2driW7Q0Grcd/rIpsD0MaOwrZvNYZhl7f7ZK9AIGg7HqvkVdV5/FnuJEteKS9CFzbApb69faK4L+UO1udsYumh73lq04tM7jWBi6InYxh7A47sPdT88jamy/+GpHG+ZQ5FIT3rODsOFXMwsww/i4E7ZjhdZ7/uyKXW7iDQx4jFpCdIJ9Mvwpdfd+bw7Ieb6Rfug6pCebWVwzknOF5lRSvLJPcPotbm4M4X1xAeaKJXiIU+oWZio/zoHWrukOLXJ12M/cA6rHtWYhh2ebvHEQgEbcNjlbxV0gGg8w1z+9it5pFvAlmSGRc5iiHBg1l66Ht+PPYLm/O3MbP/ZSSMm0vtT69Su/lLjKNm8eXqQ/yyLZvKGjsaWSImwodeIaes4yf/lIqmiTuUIbGBPPmf3yksq+bBG1LwMjjfflVVcZwMYVUUlYtSe5NZUMHeoyX8luYMi501KZYLR/amqsZGZkEFMZG+bVL6moAoNL2HYNv9E/qki9sVGioQCNqOxyp5m3ryoISXr9vHbi2PfEtY9GZuGHQ1YyJG8N/9/+Pt3f8h1jeG0SHJJOxZhT7pQvzMBobEBpEcG0RC34B6ZV1HUwoenBuxD84dwWNvbeC1r3Zz98wktBrn4RCtxrkP4GXQctXEmPpryipqOZh1nD5hzgMZe46U8tpXuzHqNQzuG0BSTBBJMYH4eLeutPVDLqF62dPY9q9BnzClza+NQCBoOx6bhVJSnUecJbv74+RdySPfGv18o7kn+Q4SdONJLz7Gh5YcPoobSZVWx+SUKP44LZ7hcSGNFHxrJA8IYc6FA0k7XOJSIXA/s4ERcSGE+Dkjf+KjA7jzykRGDgolPfs47363l3tfWUtRmTMW3+5o/iCJJmwAmtD+WLd/167c+YLOoSdUFRM0xl3vi8da8ka7MzuidNz9hbBdySPfEoqqsmZ7DkvXHuZ4pTfxMZfjF3uUHWW/89iGf3GRXzwTE2ag07TP5TF+SASFx2v4Zv0Rgny9mDYm2uVrTUYtwwYEM2xAMKqqciy/gv2ZZQT6OpOhvffdPvJKqhg5KIQRcSENkqRJkoQ+5XKqv1uAbf+v6OPPjoyl5zIajRabzYpeb+huUQRnYLNZ0Wg6rqI9VsmrnNx4dSE7ZFtxNY98s9crKqu2ZhPq78VtVwxmQC8/YCS5lRP4Yvd/+V/R76z9NY2Zg68jITCu1VTGTTFjfF+KyqpZsiaDIF8joxLavjchSRJ9wiz1rhyAfhE+5BRVsnhVOotXpRPX24/JKVGkDHSektZEJiCHxmLd9g26geORNLo2zytwH2azH2Vlhfj5BaPT6dv1WRK4F1VVsdmslJUVYrH4t35BK3iukledboXOiK5pLUa+KRyKwsotWYxLCsdk1HH/dcmYvXQNxgj3DuWOEXexbfXLfF1zjNd3vkd/v35cEXsJ0T69Wxi9MXUVpUrKa3n3u734WwwM7N3xD9TklCgmp0SRX1LFxr35rN+VR3r2cVIGhqAoKhk5J+gz7ApqvhfWfE/Ay8tpiBw/XoTDYe9madqPLMso3Zh11d1oNFosFv/696cjeKySB2ecfHOblB3BlRj50zlRZeXNpWnsPVqKXqfhvKGRWExNu2JkWWbY+NuJXfY0G8uLWKnN5bktrzI0OJHpMRcRanJ9H0CnlbnzykSe/uh3XvpiJ/dfN5S+4T4uX98SoQEmLhvbl+ljorGePIm492gpzy/eToifkTvNvfDZukxY8z0ALy9vtyiT7sQTE9G5isduvKonD0NpJPf/zinlRS774w/nnuCf72/mYNZx/nBJHOcNjWz1GkmrxzJ1PmNqZP4vt5pL+kwirWQ/T2x8nk/3L+F4revVmMxeOv46y3nX8MLi7WQXNq6e0xEkScKgc94txUb6csulgwjwMfJx3kCkqlJ++uwzTlRZ3TqnQCA4hccq+XLZGVeu9Ql167htiZHfeqCQpz/aigQ8dOMwxidFuDyP7O2P19S78Bl5DZfGXMQ/Rj/AuIhRrM/ZxGO/PcuyjB+otte4NFaAj5H7rk1Gq5VZsHg7BWWdk7XSoNcwNjGc/7t+GDf9YQalhkgSytdj0jot/YycE1TVnL0uA4GgJ+KxSr72pAWvcfMR+7bEyEeHWRgRF8zfbxpBdFjb3SSa0Fh0fYcD4H2ihGsGXMbfUu8jMSie5UdW8thvz/LTsdVYHa1byiH+Ju6blYzdrrDg022UlnduIePQQG8iLrgRC5U49qzEoSi8smQnf/33Oj5cvo9j+eLWWyBwB5rHHnvsse4WorraSleH6v62ew/HTUcZGZhAiMV9p14dBYewH9qEfsilyN5+TfbZdqCQUH8TJqOOlIEh9e6Mds9ZkkXVkn+g2mrw7TuSoSFJDA6MI7cyn7U5G1ifswlJkogyh+NjNlHVjHvEx1vPoD7+/LItm20HCxkxqOOytYRsCcJReBh7+m8YBp3PwL4hWG0Kv+3JZ9XWbPYeKSE0wERgB2rVensbml3vuYpY87mPJEmYmtm3OxOPVfK7d/1GvnchI7x7ERIQ7bZxHZm7cGTtxjByZqOj+6qqsmRNBh/9eIBAXyN9Qt1Tlk4yWpyJzHb/iKT3QhMai5/Bl9TwFAb6x5JXVcDanA38lrsZjSwTrA9ptrC4v8VAbKQvK7dmszO9yPkjpO9ERR/QC9vuH1EVB8GDhjN0QDDnD43Ex1vPniOlJMYEEuLnRUW1DYeiomuiVF1LeNqXH8SaPQGh5F1gy+5tFHgXMco/jmD/Pm4b13ZoI0ppDvrhMxqFUH6/8RhL1x5mYnIE08ZEuy0mWZIkNFGJKCVZ2HavQDYHoglyrinA6E9qeAoD/GLIrcxn1ZF1bMjdjCxpiDKHN6nsg3y9iInwYdXWbLYeLCRlYDBGfecEYslePqgVxdj2rUHXfzSSwRu9TkNspC+TUiIJ8fNCkiSWrMngrWV7OFFpIyzAhLfRtYgcT/vyg1izJyCUvAts3rWVAnMxowMTCPRzLYWvK9j2/Awq6BMmN3h+3a5cPv7xACMHhXDzpYOQ3XzoRJIktH2G4ig8jG3XCrS9kpC9T8W9B3r5Myp8OCOjB5NRnHnSst+CRtIQYQ5rpOyD/bzoH+XLz9ty+P1AISkDgtucQsFV5KBobGk/oVYdr99jAJAlqf6H0GzSUVltZ92uXH7ckklmQQX+FkOrrhxP+/KDWLMnIJS8C2xJ20KBdwljggYT4Nt62KKrWHd8i2QORBc7uv65imobLyzeTv8oP26/ItGtudpPR5I1aPsORzIHou2T3OSdQnRIBEm+SfT360tWRS5rczawLmcjdsVBpDkM3Wkx60G+Xgzs7ccv27LZsq+Aof2DMRndr+glvRfYa51588/4carDz2wgZWAI45Mi0Gpkft9fQHWtg5SBznMBDkVp8ofT0778INbsCQgl7wJbdm+mwLuUsUFJ+PuEu23c2k2fow0fiLb3kPrn9DoN8dEBTBoW1an+bXAqek2w0xWklOVizz2Axv9UaGbdlyHQK4DRESMY6B9LSU0Ja3M2siZ7PZX2KsK9QzFqnRZyoI+RuD7+rN6ew6a9+ST3D3LZVdIWNMH9sO3/FUd+Orq48c26srwMWuKjA5icEsXA3v4Y9RqO5pXz+AdbsDsUIoKc7p4z1+tJiDWf+wgl7wLfp2VQ6Z3DhN7j8fXq+HF+cMbIW7cuRRczEk1ofyqqbew8VExEkDf+FkObNw07Ss2vH2DduhTJ2x9NUDTQ+MsQYPRnRNhQkoMHU2mrYn3uZlZnrqOkpoww72C8dd4EWIwk9PVnzY4c1u3OI76PP75m9ya0kjQ6JC8fbHtWNthTaA6tRsZ48gfzeIWVrIIKVu/IZeXWLEoragn1N2H20nnclx88T+GB561ZKHkX+CFtP7XeWZzXewIWvXti5ZWyXGx7f0EXdx6SXwSvf7Wb7zceY0xCGKZOsH5bQ9tnCI6iI9h2/YCkM6IJjW32y+Cjt5AcksjIsKHYFTsb837n58x15FTm42/wo29QCENiAtmwJ5/V27PpF+FLsJ9XE7O2HzmgF47sPdgzNqGLm+hyYRE/s4Exg8NJGRBMjc3B+l25rN2Vx9QRUVgsRo/68oPnKTzwvDULJe8C69M2U+FdwMTwEVgM7snXcnqM/Hc7jrN6ew7XTxnA4H6u57FxJ5KsRdtvJMrxXGy7VoDDjqV/cotfBpPOxOCgQYyJGIksyWwt2MGa7PXsLd5PsI+ZS4clsCO9hJW/ZxIaYCIy2H2HySRJQg7qg233ClRbTQOXlyv4eOsZ2j+YCcmR9I/yJTzQG5NJz8L/bsNqUwgPNCHL536WRU9TeOB5a26LkvfYBGUBajF5gGx33wdDPeE87XqwVOarX9NJjQ9l0jD3beq2B0mjxTjpNmr1Jhz5B0FxLW2Aj97C5TEXc2Gf89mQ9zu/ZK7l3bRP8Df4Mfr8VLZvMPHm0jROVFqZMtx90UmaoD7oBk3CrvWNXgAAIABJREFUtmcVuriJaALbll0TwNdbT+LJH9ay8lqOFVSwYU8+n/+SzuSUKCYmR2L2EknRBJ6Bx1rym3evp9C7kkkRozEZ3VMC0Jb+G0pZHs/v642/xcj8mUnotJ270eoKkiSh6Z2MLmYkZh8LlSUlqPZaJG3rfnWtrCXapzcTosbQxyeKguoiNuRtptb3EP6BsGFbObVVGgb18Xdb3L8mNBbbvjU48g46s1R2YNzAAG9SBwYRE+lLYWl1vd9+ULQ/AZb2n6TtyXiaVQuet2ZhybuAijMplkZ230ugnChE9gnm2lEDCPU3ddoBovYgSRJoDaiqSvXK11HKi/C6cD4af9fuNGRJJjEonsSgeLIrcvk5cy2b87ZhTDrAqrJ9HPw6nrsvugCzseMbspLBG8OY2dSsegPb7h/QJ13csfEkicR+gST2CySroII1O3LqTxtvPVCIyaBlYG8/UTBDcE7isZb8xt1rKfKuZkqvCRj1JreMWbv1azS+YUSPmoSfm6NP3IW3t4EajS/2g+uwpa1C9g1zWdHX4aO3kBScwLjIVIwaA9m1GZQa0ll1eAOV1hoifULqQzDbi+wfiVJ8DNu+1ehiRiK1M5HcmRaej7eexJjAet/8oq/38N2Go2xPL0KvkwkP9D7r/faeZtWC561ZbLy6wKY0p5Kf2nsiel3Hb9srqmuxbfyMQu8Y/AcMdYOEbcehOMipyKOwupi8ynyyKnLJqcgFwKI3U2OvZVvRDo5aqynpFUdBRT6FB1cjV5bhHTkYh6pQUlMGqGhkTauWrUGjp79/Pyb3GY9U7cuBgjyOWNP4OXMt2RV5eOtMBBjb58aRJAlN+EBse39GKTyMdsDYdo3T2pd/zOAwAn2NHMw6zpoduazZmUOAxeDWDeWuxtMUHnjemoW7xgWyCQJKkF0M02uNr1dsZ7rkwCvIfRkt61BUBVmSsSt2fjq2msKqYo5bT3DCWk65tYKxEalM6zeVGkctT29e2Oj66f0uJMIcRqWtitc2fXiqwQSY/LgsfwdT7VdRYD3Bk5teqG82aox4aY1c1X86Q0MSKa4u4efMtfjoLVgMFnz0zn/BXoFcmjCK4RFJvPjVesoMB9kjHWR74S5CvIIYG5lKalhKm0NVZW9/DKOupXbNe9j2/tIppQL1Og0TkyMZPySCtMMlrNh0rN7NdrzSSnWtnbAA99zpCQTdgccq+dqTS9e6wSe/92gphw9mgA8ER7U9GuR0yq0VHDlxjGMnsjhWnk1WRQ5xAf25cdA1aCQNK47+jFFjwM/gh7/Bjz6WXkRZnCdajRoD8xLnYNDoMWgMGDR6NJKMWedUrn4GH1699HEKi09gVxzYFBt2xYG/pEPSm7AoNq4PHUOtTyDVtmqq7TVU2avx0Tv91yU1ZazP3UTtGfnpb026icSgeE6QS+Dg/ahFUJoTRkiQBrzK+V/6tyw99D1JQfGMCh9OfMDAZrNgnolu4AT+f3vnHR7HcR783+7t7nVcAQ69N/bei0RJlkiZVDftUJIt2bKVz45ixfr8xHEUx7ETNylK5BbLcWI7bp9tOVa11Siqi5TYxN5BgujAATgcrrfd748FDwRJkCAFgBSxv+fZZ293ZvZmDot3Zt55533TDZtJvPN7pJKpiK7R70RB95NzQm9/gpe2NPHCO03Mqs1j5YIyQ29v8IFkwgp5J2F60BcU3w8ZVeW3Lx+i3qFHYRKdI4+xChBPx+mIdmUDcf/btv/AH+tBQKDAnk+du4Z6dw2gT9EeWv5PQ/zLnIxJNDHbN33Y7zKJJnwON0LszOsF5oNvM/Pdp5CnXoN50V8gyEPz1Xmq+fcV3yCRSRJKhuhPhuhPhKjI0U0oNTRkkwmzqw/F3EcAFWJwa/la+rUu3mp7lx3+PciiRJmzlFl5U6lxV1PmLB62sxUEAcuKe4j88avEXvlPbDf9A4JpfF7blfPLkE0ir2xvZceRbsoLHFy/qJzFU8emozEwGAsmrJDPFXtHRcgfag7S6o/wqdkSNAsIjnNvfAonI7zn38Wu7n0c6j2CRbLwneVfRRAE1tbdhEWyUOYswWw6XZU0nIAfDeTp16FGg6R2v0i6eTeWFfcgFU85LZ/ZpGC25pJnHdrWek8t9Z5aQFcxbWto5lev7uB/d4S4e+V8Pj65nBcaN9AV6+ZosJGjwUYAPlJ7I0uKF7C9ayeHAg3kW/MosOdTaMsn3+ZDceRiueKTxF/+D5LbnsS88KNj9hucjMth5pYrqlm9uIJNezt4aUszOw53Z4V8OJYy7O0NLnkETRvvJc/T6ekJo6rjW43v/uHrHPGG+eGH/vV9P6utO4Jn16/IdB7BcfsjZ837RstG/vfws2S0DHkWLzN905iRN5Vad9X77nBGwkii2qfbDxJ//Wdo/Z2YF69DmXn9BX9fXzjBj5/ey6HmPq6YWcTt19ZhUSS6YwHeaHmbbV076UsEkUUJnzWPUDJMOBVBQ38fFJPCv135z4iCyObXvkuk/QClC2+npHwhNvncbhVG0t6Romoa8UQGm0WixR/m6z/fwrxJPq6ZW0pdqeuSUeWMZps/KEy0NouiQG7uyNa4RjSSf/bZZ3nsscdIp9Pcfffd3HnnnUPSX375ZX7wgx+gaRqlpaV8+9vfxuUanQ1GY4WG+r4D3Pb2x/HmWCjOsxMJdZ9RVRNLx3ir9V2m5U6m2FFImbOEFaVLWVQ4jxJH0SUjGE5GKpqEfe0/k9j6JKbSGQBoahrhAtYv3A4zf3v7bJ568xjPbTrOweY+7r1xKjXFHm6ru4Fba9fQ2N/E5o732N61k3Aqgs1kpd5bQ7G9ELtsz3Z+G51mDqs5cPzPcPzP5ChOJnvruHvqOgDawh3kmJ04ZPvo/RgnIQpC1tWyzSxxzdxS3trdzub9XZTlO7hmbglLphUO8YJpYHCxOed/bWdnJ48++ihPPPEEiqKwbt06Fi1aRG2tPi0Ph8N87Wtf449//CMFBQV873vf4wc/+AFf+cpXxrzy7wtBw/Q+Jg8nRnL3rJ7CkumFaP1dmCpmZ9PDyQgvHX+Vt9veJZ5JoKFR7CikylVBlWv0IlGNFYJkxrJ4XfY6/up/g5rGvOR2xBGopE7GJIp8ZEUN06u8/Pef9vPtX23nhqUV3LisEpMoZn+TtXU3sr/3EFs632OXfy87/HvwWjwEk/0sKJjD5+f8Jf72PRx//cd05xbSU1iPQxkU6D/e9XN64gFcipMieyHFjkIWpWdSKo3+7+3NsXD7tXXcdmU1m/Z18Mq2Vn674TALJuejyCZS6cwlsdvZwOCcdvLr169HFEXWrFmDLMv09vZy5MgRFi5cCEAkEqG+vp6ZM2cC0NfXx7Zt21izZs2IK3FRAnnve4WQOc2qmpUXVP4XLxwgEE5y58p6ZNIkt/wRqWo+UtEkXm56nf/a/SuO9B1ldv50PjH1Y8zNPz9nW2PFhdgTa5qme9g8+CapvRsAFZOvGmGEFjInyHNZWT6jiN5Qgg3bWthztJfJ5e6sXlsURPJtPubkz+Cq0uUU2QvoT4TY3LmdN1o3sr1rN5rFTrWnmsl7NjLLU8+Mmbdmn19oK6DEWYTZZKY3EWBfzwFkk8IU9yRUTeVbmx/lYOAw7ZFOwqkIIgJWyfK+1GSSSaSyMIer5hSzaGohboe+q/gbv9rG9oN+zIoJn9s6rhusJprNOEy8No+qnXxXVxc+36AaIj8/n127dmWvPR4P1113HQDxeJyf/OQnfOITnzjfOo87zVoemui/oLLH2vt573A3t15RhcMqk+k+DoDoKgAgmOin3lPDzTXXU2gvGLU6XywEQcA89ybk+mUk3vkdya1Pkjr4FtZr/wqTr+q8nmWzSNx741Rm1+XxyxcO8E8/28wtV1Rz3YJSTOKgsLVIZhYWzmVh4Vz6kyF2dO3hva5dvND4Cs+j4astZXrz68zL8VA5+VoEQWBKbj1Tcuuzz1A1lRyPmXBfing6Tr7NR1uknZ3+vVmd/43Vq7i+8kNEU1HebttMsaOIEkchLiXnvFRpgiCQP+B6OaNqzKnL47X3WvnhE7tx2RWWzyxixaxi8kbZPbOBwbk4p5BXVXXIy65p2hlf/lAoxH333cfkyZO59dZbT0s/GyNdQBhNUpiQBQmfz3neZX/09F6cNpl110/BZpFpbevgN4U53OCSmONz8pe56xDF8Q0Qcj5cSJv1gk6o+jKxxt30vv478srLkRxO1GQMUTk/4bXa52TRzGIe++MuHn/1CNsP+7n/L+ZQVXz6Wo4PJzUlxXyElfTF+9nSspNNTVt5TUvyavt6Cvq2sqRyIYtL51DlKT/t/bT6LICTB4v/CoBkOklLfwdNwVaqPeX43E72+zt4quG5bBm7YqPcVcKdM2+hPq+aRDqJqqlYR7g7+tO3zOSTN05n24EuXninkeffOU5dhZcpdfkkUhlEQRjTIDIX/Df+ADMR2zwSzinkCwsL2bp1a/ba7/eTn58/JE9XVxef/vSnWbx4MQ8++OB5V+JiWNfkiCFSavq8V+QDoQS7jvi5cWklkVCcNxs289uDT5Owm5kejVF6ia/wj4oVgr0SZfWXCcRAi/YTffobCIoV88K12QhUI+Uvb5jC3Lo8fvPSQR549HWuX1TOTcsqz6LPFpjtms3sGbMJ9rWydcMj7E708sz+l3hq/4vkWjzMzBu0WCoscJ+xvU48THN4IAV+f4g8Cnn4iq/RFu6gLdJBW7id1nAH4f4kfi3E5o7t/GLf78i1eCl2FFLiKKLYXsi03Eln9dNTlW/nczdNo/eqGhxWGb8/xEubm/jzO8dZNkMf3ReM8o7aiWZpAhOvzedjXXNOnbzX6+W73/0uN954IwAPPfQQn/rUpygo0NUQmUyGu+++m1WrVvHFL37xgqxFLoZOfvuB50jJKT50njp5q1niylnF1Jbk8OfGF/nfw89QhMw93QlmL713jGo7eoy67lJTIRkjdXQzqT3rUQOtiK4iRNvIrKsEQaAkz87ymcUEIwk2bGtly/4uCrw2CjxnF34WSw4VefXM2LaBpSYvpdPXEMnEec+/i03tW3it5W2agq0kUincZtc59xgoJplcq4fKnDJm5E1lafFCXAMBZQQE3OYcREGkM9LFru59bO/axYrSpVgkC++2b+OV5jfpjvWSyCRQRAWzScn+P1jNEqaBAO4ZVaMvnOTt3R28vK2Fg00BRFGgLH90ZrQTTT8NE6/No6qTLygo4IEHHuCuu+4ilUqxdu1aZs6cyb333sv9999PR0cH+/btI5PJ8OKLLwIwffp0vvnNb76/VowxmqAhaOfXIUXjKaxmiRy7wpaO91jf9BpXlizl+v07kR0TcxekIJpQZn0YecoKkjufJ7lnPemjW7Cu+hukipE7anNYZT69ZiqLpxby65cO8ujjO5lTl8e6D9WdNcygKb8a64c+B+u/z+y977Jk5f0ktQwHeg+zu3sfuzv383bTVkRBpNZdzcwBd8l5Vu95tbPYoVvrnCCVSdER9eNS9E4gmOxnf+8h3u3Yls3jUnL4xrIHEQWRY8EmREGgyF5AfZmb+jI3feEEb+9u542dbby1q50l0/TnN3WGKM13IF6C5rUGHzwm7Gaoh576MlGrytdXPTziMv/62/ewmE18/raZaJrGgcBhJnvqCP/iPuTaxViW3zWGNR4dxnpaqyUiJPe/ijJ9JYKkkG7aAaKEqWTaiGd5qbTK+q3NPPt2IxlVY/XiclYvrjir/Xly78sk3v617pJh2Sey35Wba2fL0X26wO/eR3ukE4AiewFTcycx1TuJGncV8ijFFQglw1mVTzgV4cbqVQB8b/t/cqivAQEBnzWXYkchte5qri5bjqZphKJJcuxmguEEX/yPjXicZpZML2TZ9MLzVudMNNUFTLw2j/pmqMsRTdA4n3HS8Y4QB7qayJ91gM5IIQX2fKZ461HjIUhGs5Y1Ex3BbMc8+4bsdXLHc2Q6DiF6SpGnX4tct+ScEalkSWT14goWTy3g8VeP8Mzbjby9u53brqxh0bSCM45wlWnXooZ6SO16HkGxoixYq8eMFUWqXRVUuyq4uebD+KM97O7Zx+7u/bze/DYbmt5AEWXqPTVMyZ3EVG89PmveBW9ScyoOJnlrmeStHXL/zilraQm10Tqg728Ld5BS01xdthxBEPjR3scQBRNF9gKWXeOgtTnBnzf386eNjdSWuLjzunoqCo2FRYPzZ8IKedAQz0PMP71lF+bJW8BkRmVw1qH1dQCMmXfEDzrWNX9L+sg7JPesJ/Hm/5DY/AfMiz6GMnnFOct6cyx89ubpXDU7wO9fOcJ//WkfL25u4qNX1zKt6nR1i3nRxyAVI7njz2BSMM+7+bQ8Plsu19iu4JqyK0hkkhwONLCv9yD7eg6yp+cAAHkWb1bg13tq3ncAFIC8AV8/s5mRvadqenQyTdOo99TSHG5jT89+wqkIuGHpyrkUR5fw9t52NvW+SrtWTCpkR864mFtbYOysNRgRE1bIN2e8eJSRmbA1+Ns5IL+AIpn4wrzPUmAb3DegBg0hfzYEk4w86Qqk+uVkOg6R2rMewaxPM9VoH5muo0jlM8/qMmFyhYd//OR8Nu/r5Ik3jvJvv9/BtCovH72qhvKCwdGtIAiYl9+FlkmT3PYkmCS4bt2wzzWbFKbnTWF6nu6EzR/tYX/vQfb1HuTdjm282boJURCpzClnkqeGek8tVTnlo+Yk7sQmLEEQuK1ucPbTnwzRGm7HLtsod5ayZI6br216hjc79CDsmibwy2M2KpnHqvrFTKrIIZwO4bV4xsX/kcEHiwmpk9c0jc899TA+r8K/rHjgrHlj6RhffeNRIukI9828l2mFlUPSE5v/l+TO53F8+ifnvQP0YnAp6S6TO58n8e7vEawu5EnLkSddeU61Vyqt8ur2Fp7d2EgknmbeJB83L6ui9CTLFE1Vib/6n6Qb3sV79Z2k6q4777ql1DTHgo3s6znEob4GmvpbdFfKokS1q5J6Ty2TPDWUO0tH7Bv//ZBRM/hjPbSE2tjd1siRnhaCxwuJdnspr07iz3sFs0mhyF5ITV45XimX2b7puM2Xtg+p0eJSeq/HA0Mnfw40IMcUQUmnR5S/0ltInXnOaQIe9JG8mOP7QAj4Sw15xkpEdyHJ/a+T3PkcyR1/xlRYj/WGvxv295QlkZULy1k2s4iXNjezfmsz2w76mT85n5uWVVLqcyCIIpar7yWOQO+rv0HpDaAs/Oh56dllURriOjmWjnGk7xgHA0c4FGjg2aMv8Cx6oJYadxX1nhrq3NWUOorHROibRBOF9nwK7fnML9R9JKUzKvsaewmlQuD00BxqY+ORw7T0byFNghJ7EW6ziz3d+3m9dSPF9kIKbfkU2gsotOdjHQU1lMGlz8QU8pqGU4xhTp1dyGuahlWyct/se4bNowbaEN1Fo13FCYEgmpAq5iBVzEGNBEgd3ogW7csK+MS7jyN6SpAq5yKcsqPWbpG59cpqrltQxktbmli/tYVtB7qYNzmfNYsrqCh0Yrn6LxFcOYS2P4eWiGJefhfCBe5EtkpWZgyYX4JuRXO47yiHAg0cChxh74A+XzEpVOWUU+OuotZVRaWr/IxxAUYDySQysyYPyAOqCIQS9B44zK7tfpJCjO/vaWJOTYLySWGCiX4OBRpIq4Pv/L8s/Xu8Fg+HAg10Rv0U2QsotOUPcfpm8MFnggp5UAXOuvB6KHCEZ4++ROLwLFbNqWfepNPdCGuZFGqwA6lq3lhWd0Ig2j2YZw86tdPSCVJHt6CFngOTjFQ+C6lyLlL5LATzoBByWGVuu7KGlQvKeXFzExu2tbD1QBdTKz18eHEFV666l4SqkNzxJ7REGMvV957TumckOBUHc/NnMjd/wDFfIkhDXyMNwWMc6TvG88deRkNDFETKnCXUuqqocVdS46oaMyHqcZr5q1um48ix8trm42w/5GfboS6unjuHa2sXcKw9yOGuNjy+NIFUd1aVs61zB2+1vZt9jkO2U+wo4vOzP4MoiHRFuzGbFHIU5yXpGtvg7ExQIa+hCcNb18TScX6x7/doGRMdTRFWDbOnR+1rB01F9JaOYW0nJoJkxr7uYdSuBlKHN5E+tpX0sa2Yl96JMv06tGQMLRnNuj12WGU+sqKGDy+q4LUdrazf0sy//W4HT755jGvnLWf2Igepd39PNNyDddXfINrco1pft9nFvIJZzCvQvY1GUzGO9R/nSN8xGvqO8XrL22xofgOAfGsela5yKnPKqcopp8RRNKoqHqtZYv7kfOZPziedUTENeMB8Z28X67e2YxIFplR4UHrbmV2Xx19MupWVFdfQEe2iI9JJR6STeCaRXcR9/NBT7O89hFWyUGjTVT1VOeUsK1kEDO/PyuDSYEIuvCaSGb718t/hEa184fp/OS398UNP8UbLJkr6VuJvM/Ovf7V0iIfEE6QObyT+6k+wrf0mJm/JeFT9ffNBXaDSNBW16yhCTj6iNYfUwTeJv/5TxLxKpIrZSKXTEX3VWXVMKq2yaW8H67c20+qP4HIorK0JM6P9SUSzDeuqL2DKGz+//qlMiuOhFhr6jtHY38yx/uOEkmGAbMzbqpxyKl264HebLzzS1HB/Y1XVaGgLsv2Qn+2H/Pj74rgdCv923zIEQcDfFyM3x3KaW+SjwUaaQq10RE50Al0U2vP5wtzPAvCdLd8jlUlRYPORP3CUO0uyAebHgw/qe32hGAuv50DVNLRh1DXHgsd5o2UTi/IX8dpmgRuWFp9RwAOovS0gmhDdxkaosUYQREwFgxuMTMWTURZ+lHTjNpLbnia57Skw23GsexjBbEcSVK6cVcyt19TzyruNbNjewk93JimTVvI592tknv4m1ivuRqlfNi71l00yte4qat26a2ZN0+iN99HYf1wX+sEmXm/dmB3tuxQnla4KKnPKKHeWUuosft8Rr0RRoK7UTV2pm49dXUuLP0JvfxxBENA0je/8ZjvJVIYZ1bnMqMllepUXp02h2lVJtatyyLNSmVT28/TcKbSF2+mM+tnTc4CMlmFBwVw+OW0dmqbxwx3/jcucQ4HNl+0IfNbcMY1XbDDIhBTymgbdmh1HzulqlvXHXyNHcWLtnQq0ccWs4RdVM70tiO7iCwqLZ/D+EJ0+zLPXYJ69BjUeItOyF7W3Oauvj294DDXYiVA7k6nuambcNAl/tJ5X32vlu7vt/IX8KrWv/Rcte9+j4LpPYXeM72KjIAjkWj3kWj3MKxiwllHTtIbbOdbfRGOwicb+Jnb692TL5Fo8lDlLBo5Syp0lOJULc2omCLpDtBNO0TQN/uKaWnY19LDnaA/v7OtEAG5bUc2aJZWomgYa2VH+yQL6hupBJ38ZNUNPPJC9TqopVE3lQO/hIX59VlZczc01HyaejvPs0RfxWfPw2XLxWXPJtXjHxSx1ojAhpZM2EDJCEE8fSXxy2h34Y930dMqIS2XyXMM7x1J7WzAV1Q+bbjA+iBYnYu1iYHH2nqlkKloqTui9l9HSunfCnJrFrPvQZ7n1imo276zmnR0vsNi/leZfNbAt/1ZmzZnG1ErvuEZxOhlJlKjIKaMipwxK9RlGJBWlOdSaPZpCLew4SfC7za6s4C93llDqKCZPO3/BL4oCC6cUsHBKAaqmcbwjxO6GHmpL9MXZps4Qj/x2B5PK3Uyt9DK10kOh13aaSskkmsi35WWvzSaFv5n7fwCIp+N0xbrpivgpGAimE0gE2di+hWRm0IOkKIh8fPJHWVQ0j75EkG2dO/EN7BjOs+aiGDOA82JC6uTDsRRfff0fqTIX8fmr/wbQt5irmoo0wlG5logQ/sV9KAvXDvHVcqkz0XSXeV4Lnft2k24/iGB1okxegZZJEf6f+xAcXhKKG7G7AU3N8Gx0LruV2SyZXsTS6YUU5V6apoSxdIyWUBtNWcHfSlfUn412ZVdsFNsKs1Guiu1FFDsK35cpZ2t3hJc2N7GvMUBPfxzQrXke+OgsSvMdqKp2wZ2jpmn0J8N0x3rwx7rxx3qYmz+TEkcRu7v38eNd/zMkv9vs4tPT76TaVYk/2kNzuJX64nJMccuEsf03dPLnQNU0ZDGNkurP3tvh38NTR57jgbmf5eDROJPKPHicw5vaZQJtAJgMy5pLGsEkYyqsw1RYN3hTzaDMu4VM+wGUziOgpUCA2+xbWSx18KvNczi+NYzqrWT61CrmT/addUY33lglK3WeGuo8Ndl78XSC1nA7zeFWAukeGrqb2HTSCFlAIM/q1QW/fSDoiaOIPKt3RK4QSvLsfGr1FDRNw98XY9/xAAeOB7JuoJ95+xib93cxpcJDXZmL+lI33pyRCVxBEHCZnbjMTmrclUPSZuRN5eErvqZ3AFG9A/DHesgZcPG8t/cAfzj0NAxMbhyynVyLl3tnfAKPxU17pJNAvI9cqxevxTNq3kY/SEy8FgOaqqECIoMv92vNbyEAmYTCfz27ndWLK/jIipphn6H2NgMgegwh/0FDkC2YZ6+G2avRNBUt2Em6swE10kPxzuf5kud5BDUNKejZ7uDAFi9RWxFK/XJmzqwbsfAaTyySWbfDd1dmZ2uqptIbD9Aabqd1wPNla6SdXSfFuJVFiQKbvpO20JZPgT2fInsBPmvuGWe1giCQ77GR77Fx1exBi7LiPDt5bgsb93bw6nutAJT6HHz9ngUIgkAomsRhlS/IYsgu27DLNl2NdQpLihZQ66oiIUdo6GyhO9ZDTyyQHdG/276N9U2vZfO7lBxyrV4+P/teFJNMU38L8Uwcr8WLx+y6LNcCJqSQVwc2Q5k0Xcg3h1ppCDZyW+0NbNzTiabBlbPObv6V6TqGYHEiDNhpG3wwEQQRwV2EMrBrWalbRuzNX6K27EKwunA7C7D2dWNLvstDm/L55Vt+ri/oYrH5MPbiapylNZhyyxBdBZfcArwoiFk99izf9Oz9ZCZJe6ST1nA77ZFOOqJE+vQxAAAbx0lEQVRdHA0eZ2vnjiFlfdbcIW4QTnQCZ1L7nNDnZ1SV5q4wh5qDxBPprFB/5Hc76AsnqCt1U1/qoq7MTVm+A8n0/hyqmU0Kpc5ifD4nNZa609I/VH4l0/Om0BPrpSfeS08sQH8qlNXrb2h+I9tuURBxm10U2wv53KxPAXA40EBGU/GYXXgsbpQx2r08llxab+U4oWkaqiAgDIzkX2t5G0WUWVw4n2+9uIv6MvdZoxEBqF0NiPnVxiaQywzRmYd99f8l1bidxMbfYOo6RE71QpQ5N/B5vGw52E14XxvhvgDO0AYSh9YDoAkmrB//HrLVQbrtAFo8hOgtQcwpuOT8GikmZXCB9yQSmSSd0S46Il10RrpoH/i8u2d/1i0ygMfspsDmw2fLw2fNJd+Wh8+aR57ViyRKVBbmUFmYM+TZ184r5WBzH4ea+9h+yA/A4mkF/OWN09A0jW0H/VQUOslzWUb1f8qpOHAqjqzp6qncWruGpUUL6YkHBjqB3iHf/+zRl2gIHsteO2Q7dZ4aPjP94wBs7XgPQRDwWDx4LW5yFOcl5wl0ggp5dHWNIJLMJNneuZMFhXPo7VNp74ly7byzq2C0RAS1rw2ldvFZ8xl8cJEr5yKVTCO5888kd75AunEbrmnXsmbujQhLP05v/1p2Hurg+KHDxLqO4ybMWz/ezvRqL2tSL+DuHVASixKiuxCTrxrLCt0HkhrqRjDbEJTRDeD9fjGbFMqdpZQ7h77/aTVNd6yHjkgX7ZEuOqNddMW62da5g2g6ls0nIOC1eLJCP3+gE/DZ8lg6o4ArBmbHgVCCI61BXHYle/2jp/Tfy2mTqSrKobo4h/mT8inOG9vFb7fZdVZPnZ+cto6eWC+BRJDeeB+BeGCI2eozR18YYjIqCiLzC2Zz91TdxfVLx1/FYjLjMufgNrtwmXPGvSOYoEJeIyWIpNy1iILIp6bdQa7VS0NDP5JJZN6k/LOWz/j1nv3kzTkGlx+CbMY8/zbkKVeT3PoEqd0vkTrwOsq0a3HPXMVV8ythfiXxZJq9xwJEj3Sz62gPOyIzKDCVM8kVY7IjRrEQxBEdXOSPvfJj1M4jCNYcRFchoqsAU0Ed8uQrAdAyaQTTpfOvKYnSgMqmgNmnpIVTEfzRbrqi3fhjg+djwSbimXg2nyiIeMxucq1e8iwecq1ekL0cDXpwK26+evd8jnWEONoW5Fi7br6Z77ZSnGenuSvMM28do7zQSUWBg/ICJ27H+/c/NBK8Fg9ei2fY9L9f+AUC8SC98QCBRB+BeDAbP1jTNF5o3EAiMzTA+LLihdwxeS2qpvLfe36NS3HiGugA3OYciuwFo+oi+tJ5k8aRjKoiCBqiaEISJWb6pgFQMgsWTM7Haj77z5LpbAAETL4zTwENLi9EuwfLik8jz7ie5PanSe74M8m9L6NMvQZ52rVYHF7mTfIxb5IPTdNo9UfY29jL3sZe3mjqI5nW/cdUdm+lvtTNrMIVFJfMRIp0owY7SDftQouHs0I+8rsvgZpGcOYhOn2IzjxMRZOQynRnaJdSJ+CQ7ThcdqpcQ11EaJpGOBWhK9pNV6wbf7Sb7lgPvfEAu3v2Z106nEAWJbwWL7mlHmbUelkquRGtHTT1p/GHBJr8IbYNqHkAXHaFBz42i/ICJ33hBGlBRNS0cQ9+bpWsWB3WIUHeTyAIAo9c+c+EkhGCiSDBZD99iSD5Vt3ZYTydwB/t5nCgYciMaE3Vdayuuo5gIsR3tz+Gy5yTnQm4zS6meOsodo48SNGEtJNv8wf45u5vs0SZjK+0krn5s8izekesC4w+/+9o4V7sH/3GGNd09JlodvJj0d5MoJXk9mdIH90MCEhV81FmrDzjzC6VznCkJcjexgAHmwM0tofIqHp84RKfnboyN/WlbupLnHhcNjRNI7nzz2j9XaihbtRQN1qoB3nKCizL70JT04R/9n/0WYAjT+8IHLmYymYgFU1C01Ry7dATES7p9aJkJqnrwWO9dMd76Y0N6sS74wFiJwk90FVJLsWFBQdC2koyorB8ShUFzlze2xvm5U3dmE1mivPslPjslObZuXpuCbJ0aa2HDEcykyKY0DsBt9mFz5ZLIN7HE0f+RF+in2Cin2AiSFrLcOfkj7K8dOGI7eQnpJBvau/gof3/zmzy2UEX90y7g4Z9Dlq6wnzhY7POOhrQNI3wL/8auXJeVsf6QcIQ8qOHGvKT3LuB1IHXIRlD9FWjTL8WqWresO6ME6kMx9r6OdTSx+HmPo609pNIZQDIc1moLtYXLauKnLpPfEVCU1XIJBFkC1o6QXLn8wPC36+fIwGUBbdhnn0DariHyP/7IogSgt2DaPcg2L3IU1YgFU9BSyVQA60Idg+C1XnJWQSdIJqKDVkM7Y0H6EsECcSDBBJ99CdP/5tKmhkhbSUdU8gkLNy0cApei5sd+yP4u1RKvbmU53kozrVTlGvDNU4qn9FC0zQiqSiSaMKmWI3NUGcjk9b/qXpJYBJMTPbW8//2vUd5vuOc0z21rw0SEcSC4W3oDSYGotOHZfE6zPNuIXXoLZJ7Xib+6k/gLSty9QKk+mWYCuuHjKjNsonJFR4mV+h63oyq0tQZ5lBzH0dagzS0Btm8vwsAQdDtz6sGhH5lUQ6lPjvmebcMqYemqqDp77Qgmcld+WlCne2okV60SIBMVwNSpe4vW+1pIvrMN7NlBYsTwerCvPQOpJKpqP1dpI9tQ7DmINhcCFaXfrY4EMZxsdAmW7HJVsqG8WSZVtP0JfoJxPsIJPpISXFaejqzevHeeDd/OvbiYIF8aAc295jQOszImpXZFaXkmJ10dGSQNBtFOR7KvHlU+/JxWeyX3ExIEIQLikUwIYW8quoLIVF096itHUkCoQRrrzq34M407QRAKp0xpnU0+OAgyBaUadciT72GTPtBUofeJtXwLqmDbyA4fch1S5Gq5iN6S8/g60WkqiiHqqIcVg3cC0aSHGvvp7G9n2PtIXYc6eat3e0AiIJAUa6N0gHnYqU+/ex26JYqgsWBa8FqksPMXkR3EdZVf4MaCaDF+tGiQbRYf9bSJ+NvJPHu708rZ73x75GKJpFu3kVy90t652Bx6sLf4kSuWYhgtqMlIvqagcU+prMESZTIs3qzi5xnmrElM0kCiSB9cV0fHkz00xkK4I/0EU6HaA610tfTn90VvLsX6AWOgKCZyLXqi6HJmIxTcZJnz6HA6cFjzdFNM2UHTsWO2WS+5DqEk5mQQj6T0Uc9cdIUW3PZsr8LWRKZXZt3jpKQbtqJmFuO6PCOdTUNPmAIgohUPEVXiyz7BOljW0kdfpvk9mdIbn8aISdfj25VOQ9TQc2wI2OXXWF2bV72fdQ0jZ5gnGMdIZq7QrR0RTjS0se7+zqzZRxWmVKfnVKfg7pKLw7FpKsk7MoQASRYHEgVw0TBAaTqBTjKHkOLBVGjQbRYEC3anw1xqWVSuglxsBMtHoKUbkEjlU5HMNtJ7n+N5OY/6A9TrNmOwHb9/0WwOEi37CHjb9Q7B7MNQbEjmG2IeRUIgjiqAUgUk5J1b3w24uk4/kgfx3v8tPT10BXqAzmO06USTPTT1N8GUgIhnIbO08ubMGGT7OQoDtxDOgBH9rNDceCQbdhl+7g7WJuQQv5EnMs4aXItHt462MWsmtxzWtVo8TCZjsMoJ4WpMzA4E4JsRq5fhly/DDXaR/r4DtKN20jtWU9q1wsI1hxMJdOQSqdhKpmGaB/eTE8QBPLcVvLcVhZMHjTvjcZTNHeFafFHaO4K09wV5s1d7by8rSWbxzIg7Au99oGzjaJc3S2BLJ3eyQiCoAtnxYroOt2CQ66ch1w5GO5Sy6TQ4mEEq775SSqboa8dxMNo8ZB+ToRB1vXf6ebdpHa/eMpTBRz3/hSAxFu/IHXkXb0DONEJ2FxYP/Q5AFKN29HCvdl0FDuCxQ6+SXp9LqCTsEgWylyFlJ2hvZqmEYmn8ffF6AiEaAkE6OwPUJgvUVas4I8EeebdAyTkJH1Skma5DZOSQpATqKhn+DZQRBm7bM+6a7DLNhzZ6zPft5gufJPYxBTyA3qtq4o+zIfKFuBc1E15gfPc5Vr2gKYiVZxqLWxgMDyizY0y5SqUKVehJaOkm3aRPr6DTMse0kc26Xk8xZhKpmEqrMdUWDei8IQ2i8ykcg+Tygc7CE3TEBWZPYe76OiJ0tETpb03woGmAJv2dmTzCYAnx4zPZcXntpLntuBzW7NHjm1kfmYEk4xwUgdlyi3HlFs+bH7LktsxL7gNLR5BS0bREhFIxbOzGlPJNDDJaIkoDKRr0WC2fOrAG2Sadgx5puD0Qd2PAYg99wiZzsMIsjXbWZm8ZVkjieSuF9DiYZAtCIoFQbYiOPOQivROQg11g2hCkC0gmRFEEYdVxmHVN2nB0AhwqqqxIHcx/r4Y/kCM7v44gf4EC6vzqa90cKCtgx89ux3kBIKUQpCSaOY0ZRU2rGaVYDxMc5+fNAmSWpzhEAURuzQo/IucBdy/7JPn/PvABBXymYFFKlmUybHaWLVw+JfyZNLHdyBYnIiGfbzBBSIoNuTaxci1i/WQhj3NZFr3km7ZS2r/a6T26G4SBKcPU0Gt7kEzrwLRW4YgndtvyolR/7RKL9Mqh6oU48k0nb0x2nsidPRG6Q7G8ffF2HOsh77w0A07iizic1nJc1nw5ljwOM14nGa8TjOegWuzfGHmiYJkRnCYgdNVnnL1AuTqBcOWtV7312jJKCSiaMmI3kmcpPaSahYi5pZBMqbHAU7F4aTIbunG7fo+lwEZAHrsAWnNlwCI/ukhtNCgPT4mCalqAdZrdJ/40ecegUwaZLPeDtmMt2gSBfXLoQqSe1+GQhlBCCG0mpkhKfzrRxbRqzrpCcboDwToCWdYXFlGRZGLXQ3dfPcPuwa+TAMphSCluH1VBQU+icPtfnY2tiOZ04ikEEgSSScJSIMd37mYkEJei+k/0D7/OzgTxSycVHpOVY0aD5Fu3IZct2xcrQwMLl8EQcSUV4EprwJl1mq0TBq15ziZjsP60bo3O9JHEBDdRYi5FZjyyvVzbjmCZeQBQiyKREWhbpp5KslUhp5+Xej7+06cY3QH4zS09ROOpU4rY7dIeJwWvDnmbCfgcZjJsSvk2BVcA+f364TsZASTpKuGrDlnTFcmrzhredtND6JpGmRSegeQjOlmTAOYF31MX2tIJ9BSSbRUHJNn0MJHkMxo6SRatA81lYB0AmQLcv1yNE0j8fZvgKHm4Nbp11Gz9E6qC6yEf/Zl/eZxCIkSVZLMf1y3mkjttfQH+nBu+hFJzYTzyAHkZgu5MY1QdxE7oqWkYyGWKwdIYWLNNdUj/s0mpJBXUxEAjic7OPD8YVw2xzkXXVP7XoFMCnnGdeNRRYMJiGCSMOXXYMqvgZnXo2kaWribTHeTLvy7j5NpPzAo+NFNIEV3EaK7cOBcREqqQ1Mt5+UYTZFNFOXahw2UkkxlCIQTBPoT9IbiBEIJekP6dSCUoLG9n/7o6R0B6J3ByUI/xzbYCThtCg6rjN0qYbfKOCzymEfmEgQBJEWfGZ3SWZxtFgFgXfn5s6Y77v4h2oDw11IJtHQC0eo68cWYl30c0km0dErPk0kh+crIc1nxmtPE3W7s6SRaOooaD5KTTnD70pncPWU5qd5W4v+rWz5J+1vgQzeOqL0TUshnMvrCq6xKCIqZ6VVnt5TR0klSezdgKpuJyVNy1rwGBqOFIAgITh+i0wdVg4udaqwftacJtbcZta8Dta+ddON7aHE9CHgzgCDqm6GceQiO3JPOPkRHLoLDi3AeVh6KbKLAY6PAM7xTtVRaJRhOEIwm6Y8kCUb088nH8Y4Q/dEksURm2OfYzNKA4JcH9OFS9rPdop+tZgmbWcJqNmE1S9idllG1zLkQBEEAsz0bZ/i0dJOMMu3aYcuLFie2D39x2HTZW4L0mZ/pG+O04X+/U5mQQl5VBzaOJE3MneQ753QydeB1tFg/yszrx6N6BgZnRbTmIJZOh9LpQ+5r8TBqsANbupf+tmZ9N2y4h0zbAdLRgO5+9WTMdkSbe8imJ9HmQrC59WuLE8Fs180dR7AeIEti1groXCRTGfojSUKxFJFYivBJRySWJhzXP4eiSdp7IkTiqbN2DKBrXayKhPUk4T/YGQzetygSiixiUSTMsohZNmFWTPpZNmFRTCiyaVTVTKOFIIogWs5rtjMiIf/ss8/y2GOPkU6nufvuu7nzzjuHpO/fv59/+Id/IBKJMH/+fL7+9a8jSZdu/5EZMKEUkxILZ53D42TXURLv/B5T6XRMxVPGo3oGBheEYHFgstSS43OSKBm6MUhT02jhAGq4Gy3Ure+GjQbRokHUWBC18whatA8yZ1a5YJIHBb7ZjmB26BuezA7dikW2IChW3WplyGcrgmIByaILqAEU2TTiDuEE6YxKJJ4mEksRS6SJJdJEB86iJOHvjWTvnziC4SQdPdFsvsx5uE+RTMJpHcCJa1kSkSURRRKRTSZkWUQ2iSgDZ1k2DV5n8w6WO/VaMgmYxLHpVM4piTs7O3n00Ud54oknUBSFdevWsWjRImprB50x/e3f/i3f+MY3mD17Ng8++CCPP/44d9xxx5hUeDRIDkx1pIyFKRXD2ydnOo8Qe/lHup3uNZ+9pHe1GRicDUGUEHJ8iDnDbwzSNA1SMV3wR/sGbNwjaIkwWjwCiYHrgRmD1jlgA6+OUHUgmQdMExUESQbTgF7cJGfPWV35SfcESdHvm2RsJhmbaNJ300omMEsgmvDk5tDXL4Jo1dNEEwycBZMEooQmiKRUgWRaJZHMkEhliKcyJJP6+cS9oWkq8VSaRGqwTDCcJJVRSaUzJNMq6bRKMq2SSp/ZLn7EfyMBJJM4cAinnAc6ApPeieS6LfzdXQtH9rOfK8PGjRtZvHgxbrdut7tq1SpeeOEF/vqv/xqA1tZW4vE4s2frtuO33XYb3//+989LyP9mww8JhgOQjTupkG8vQgDawy1Zk8cTmEUFn13fuNAWbkLVdK9+g+kWfDZ9hN4abuLUvjsmADa4qbCMzIHXyZySQ4uHyXQeIdO8C8HmxrrqgfOyYjAw+CCib4TSg5mc2OF6LoZYqqTig2aLqRhaMn6Gz3G0dFJffMyk9HMqprtYyCQhnRpMyyRPVzENQ+zcWU5qqAmzaMIsiuQIgr5+IYi6KaY4cB44BEEYvGcygSyCfbgyAhoiKgIaAqomoCLo4UZPPVTInHLvxLWmDU3LqCd9ToOaBIvsAkZJyHd1deHzDfb++fn57Nq1a9h0n89HZ+cZ9v6ehYPWEH6tf+hNtUc/D7fOc9b0MGjd+sez+PMpOLyBRPLMoxDZW4Rz2UdwL70VURn5lPKDgM937o1flxMTrb1webRZ0zRQ02ipJGo6qZsuZtKQSaNlMroKKpOCTAYtk0ZT9TNqWr/OnHqt5yGTRlPToKpomjrkjDbMPVUFNaPfOyVd0zKgpgbznfQM0KW2pg1Ib00DTrkeCK2onQixqKn6eFdT9XycnFdDQ0NSRx5b+pxCXlXVIWqKU1ewz5U+Eq6WphGRwgPjaQFFMlPg1UOQtfc0kR6whmEg3Sxb8Hl1K5e27kZUdeg0yWK2k+fRRyKtXUc52ZuyJoBNcVJRWMX81VX09EZOqY2AIOvTygzQE0wDl49rXsPV8OXP5dlmiay4EjhNco1mm4VTzpcio7rwWlhYyNatW7PXfr+f/Pz8Iel+/+AOse7u7iHpI+HqhTcN609+Jme3W501ad7Z0+vO4ozJ6USMj6+zIAMDA4Px5JzLuUuXLmXTpk309vYSi8V46aWXuPLKK7PpJSUlmM1mtm3bBsDTTz89JN3AwMDA4OJxTiFfUFDAAw88wF133cUtt9zCDTfcwMyZM7n33nvZvXs3AI888gjf/va3uf7664lGo9x1111jXnEDAwMDg3MzIcP/neDy1F2enYnW5onWXjDaPBEQRWHE4f8uvS1dBgYGBgajhiHkDQwMDC5jDCFvYGBgcBlzSTiYGWvXopfqd18sJlqbJ1p7wWjz5c75tPWSWHg1MDAwMBgbDHWNgYGBwWWMIeQNDAwMLmMMIW9gYGBwGWMIeQMDA4PLGEPIGxgYGFzGGELewMDA4DLGEPIGBgYGlzGGkDcwMDC4jDGEvIGBgcFlzIQU8s8++yyrV69m5cqV/OY3v7nY1Rk3wuEwN9xwAy0tLRe7KuPCD3/4Q9asWcOaNWt4+OGHL3Z1xoXvfe97rF69mjVr1vDzn//8Yldn3HjooYf48pe/fLGrMS584hOfYM2aNdx8883cfPPN7Ny586z5LwnfNeNJZ2cnjz76KE888QSKorBu3ToWLVpEbW3txa7amLJz506+8pWv0NjYeLGrMi5s3LiRt956iyeffBJBEPjMZz7D+vXrue666y521caMzZs388477/DMM8+QTqdZvXo1K1asoLq6+mJXbUzZtGkTTz75JFddddXFrsqYo2kajY2NvPrqq0jSyMT3hBvJb9y4kcWLF+N2u7HZbKxatYoXXnjhYldrzHn88cf5p3/6p/OOv/tBxefz8eUvfxlFUZBlmZqaGtra2i52tcaUhQsX8stf/hJJkujp6SGTyWCz2S52tcaUvr4+Hn30UT772c9e7KqMC0ePHgXgnnvu4aabbuLXv/71OctMuJF8V1cXPp8ve52fn8+uXbsuYo3Gh29+85sXuwrjSl1dXfZzY2Mjzz//PL/97W8vYo3GB1mW+f73v8/PfvYzrr/+egoKCi52lcaUr371qzzwwAO0t7df7KqMC/39/SxZsoR//Md/JJVKcdddd1FVVcWyZcuGLTPhRvKqqiIIg246NU0bcm1weXH48GHuuecevvSlL1FZWXmxqzMu3H///WzatIn29nYef/zxi12dMeMPf/gDRUVFLFmy5GJXZdyYM2cODz/8ME6nE6/Xy9q1a3n99dfPWmbCjeQLCwvZunVr9trv908YFcZEY9u2bdx///08+OCDrFmz5mJXZ8xpaGggmUwyZcoUrFYrK1eu5ODBgxe7WmPGc889h9/v5+abbyYYDBKNRvnWt77Fgw8+eLGrNmZs3bqVVCqV7dg0TTunbn7CjeSXLl3Kpk2b6O3tJRaL8dJLL3HllVde7GoZjDLt7e3cd999PPLIIxNCwAO0tLTwla98hWQySTKZZMOGDcybN+9iV2vM+PnPf86f/vQnnn76ae6//36uueaay1rAA4RCIR5++GESiQThcJgnn3zynMYEE24kX1BQwAMPPMBdd91FKpVi7dq1zJw582JXy2CU+elPf0oikeA73/lO9t66deu4/fbbL2KtxpYVK1awa9cubrnlFkwmEytXrpwwHdxE4eqrr2bnzp3ccsstqKrKHXfcwZw5c85axogMZWBgYHAZM+HUNQYGBgYTCUPIGxgYGFzGGELewMDA4DLGEPIGBgYGlzGGkDcwMDC4jDGEvIGBgcFljCHkDQwMDC5jDCFvYGBgcBnz/wEgCt7yLArcfAAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pdf_demo(-0.5, 5, gamma='a=1;a=2', lognorm='s=0.5;s=1.5', chi2='df=2;df=3')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another useful group are the \"bounded\" distributions, especially the versatile two-parameter [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution):" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pdf_demo(-0.1, 1.1, beta='a=.7,b=.7;a=1.5,b=1.5;a=.9,b=1.5', cosine='loc=0.5,scale=0.159',\n", " uniform='scale=1')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "All of the 1D continuous distributions share the same API (via a [common base class](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.html)), and allow you to perform useful operations including:\n", " - Evaluate the PDF, log(PDF), CDF or log(CDF).\n", " - Generate random values from the distribution.\n", " - Calculate expectation values of moment functions or even arbitrary functions.\n", "\n", "The API also allows you to estimate the values of distribution parameters that best describe some data, but we will soon see better approaches to this \"regression\" problem." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "def rv_continuous_demo(xlo, xhi, dist, seed=123, n=500):\n", " x = np.linspace(xlo, xhi, 200)\n", " P = dist.pdf(x)\n", " plt.plot(x, P, ls='-', label='PDF $P(x)$')\n", "\n", " g = lambda x: (0.7 - 0.3 * (x - xlo) / (xhi - xlo)) * np.percentile(P, 95)\n", " plt.plot(x, g(x), ':', label='$g(x)$')\n", " print(' =', dist.expect(g))\n", " \n", " gen = np.random.RandomState(seed=seed)\n", " data = dist.rvs(size=n, random_state=gen)\n", " plt.hist(data, range=(xlo, xhi), bins=20, histtype='stepfilled',\n", " alpha=0.25, density=True, label='Random')\n", " \n", " plt.ylim(0, None)\n", " plt.grid(axis='y')\n", " plt.legend(loc='upper left', fontsize='large')\n", " rhs = plt.twinx()\n", " rhs.set_ylabel('CDF')\n", " rhs.set_ylim(0., 1.05)\n", " rhs.grid(False)\n", " rhs.plot(x, dist.cdf(x), 'k--')\n", " plt.xlim(xlo, xhi)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " = 0.21420671411482317\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rv_continuous_demo(-4, +4, scipy.stats.norm())" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " = 0.8840573776021254\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rv_continuous_demo(0, 1, scipy.stats.beta(a=1.5,b=0.9))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The [chi2 distribution](https://en.wikipedia.org/wiki/Chi-squared_distribution) ($\\chi^2$) is especially useful for confidence interval calculations. Here are two handy utilities that you will likely need at some point (using the CDF and [inverse-CDF](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.ppf.html#scipy.stats.rv_continuous.ppf) functions):" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "def nsigmas_to_CL(nsigmas=1., D=1):\n", " return scipy.stats.chi2.cdf(x=nsigmas ** 2, df=D)\n", "def CL_to_nsigmas(CL=0.95, D=1):\n", " return np.sqrt(scipy.stats.chi2.ppf(q=CL, df=D))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For example, a \"1-sigma\" error bar contains ~68% of a Gaussian distribution in 1D, but a 2D \"1-sigma\" contour only contains ~39%:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.68268949, 0.39346934])" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nsigmas_to_CL(nsigmas=1, D=[1, 2])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To find the number of sigmas required to enclose a specific integrated probability (aka \"confidence level (CL)\") in D dimensions:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1.95996398, 2.44774683])" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CL_to_nsigmas(CL=0.95, D=[1, 2])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Scale $\\sigma_i$ and $\\sigma_j$ both by `nsigmas` to adjust the ellipses we drew above to enclose a desired CL (or, equivalently, scale the covariance matrix by `nsigmas**2`)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, there are some essential discrete random variable distributions, where the PDF is replaced with a **probability mass function (PMF)**:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "def pmf_demo(klo, khi, **kwargs):\n", " k = np.arange(klo, khi + 1)\n", " cmap = sns.color_palette().as_hex()\n", " histopts = {'bins': khi-klo+1, 'range': (klo-0.5,khi+0.5), 'histtype': 'step', 'lw': 2}\n", " for i, name in enumerate(kwargs):\n", " for j, arglist in enumerate(kwargs[name].split(';')):\n", " args = eval('dict(' + arglist + ')')\n", " y = eval('scipy.stats.' + name)(**args).pmf(k)\n", " plt.hist(k, weights=y, color=cmap[i], ls=('-','--',':')[j], label=name, **histopts)\n", " plt.legend(fontsize='large')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The one-sided [Poisson distribution](https://en.wikipedia.org/wiki/Poisson_distribution), which describes the statistics of (uncorrelated) counting measurement (which are ubiquitous in astronomy and particle physics):" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pmf_demo(0, 10, poisson='mu=2;mu=3;mu=4')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The bounded [binomial distribution](https://en.wikipedia.org/wiki/Binomial_distribution), which is related to the beta distribution above, and describes the statistics of ratios of counting measurements (efficiency, purity, completeness, ...):" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pmf_demo(0, 10, binom='n=10,p=0.2;n=10,p=0.5;n=10,p=0.8')" ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden", "solution2_first": true }, "source": [ "**EXERCISE:** Fill in the function below to generate `nsample` samples of size `size` from an arbitrary 1D continuous distribution, and then display an `sns.distplot` of the mean values of each generated sample:\n", "```\n", "def central_limit_demo(dist, nsample, size, seed=123):\n", " gen = np.random.RandomState(seed=seed)\n", " ...\n", "```\n", "Test your function using:\n", "```\n", "central_limit_demo(scipy.stats.uniform(scale=1), nsample=100, size=100)\n", "central_limit_demo(scipy.stats.lognorm(s=0.5), nsample=100, size=100)\n", "```" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "solution2": "hidden" }, "outputs": [], "source": [ "def central_limit_demo(dist, nsample, size, seed=123):\n", " gen = np.random.RandomState(seed=seed)\n", " means = []\n", " for i in range(nsample):\n", " data = dist.rvs(size=size, random_state=gen)\n", " means.append(np.mean(data))\n", " sns.distplot(means)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "solution2": "hidden" }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "central_limit_demo(scipy.stats.uniform(scale=1), nsample=100, size=100)\n", "central_limit_demo(scipy.stats.lognorm(s=0.5), nsample=100, size=100)" ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden" }, "source": [ "This exercise provides a numerical demonstration of the [central limit theorem](https://en.wikipedia.org/wiki/Central_limit_theorem), which asserts that the mean (or sum) of samples drawn from any distribution tends to have a Gaussian distribution.\n", "\n", "Here is a nicer [interactive demonstration](http://students.brown.edu/seeing-theory/probability-distributions/index.html#section3) you can experiment with." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For a more powerful statistical toolbox than [scipy.stats](https://docs.scipy.org/doc/scipy/reference/stats.html), try the python [statsmodels](http://www.statsmodels.org/) package. Going beyond python, the [R language](https://www.r-project.org/about.html) is designed specifically for \"statistical computing\" (and [integrated in jupyter](https://irkernel.github.io/)), and [RooFit](https://root.cern.ch/roofit-20-minutes) is a \"a toolkit for modeling the expected distribution of events in a physics analysis\" integrated into the [ROOT framework](https://root.cern.ch/).\n", "\n", "We will be soon be talking more about the general problem of \"fitting\" the parameters of a distribution to match some data." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.7.5" } }, "nbformat": 4, "nbformat_minor": 2 }