{ "cells": [ { "cell_type": "markdown", "metadata": { "toc": true }, "source": [ "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n", "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#-Discrete-Uniform-Distribution\" data-toc-modified-id=\"-Discrete-Uniform-Distribution-1\"><span class=\"toc-item-num\">1 </span><font face=\"gotham\" color=\"purple\"> Discrete Uniform Distribution</font></a></span><ul class=\"toc-item\"><li><span><a href=\"#-Discrete-Probability-Mass-Function\" data-toc-modified-id=\"-Discrete-Probability-Mass-Function-1.1\"><span class=\"toc-item-num\">1.1 </span><font face=\"gotham\" color=\"purple\"> Discrete Probability Mass Function</font></a></span></li></ul></li><li><span><a href=\"#-Binomial-Distribution\" data-toc-modified-id=\"-Binomial-Distribution-2\"><span class=\"toc-item-num\">2 </span><font face=\"gotham\" color=\"purple\"> Binomial Distribution</font></a></span><ul class=\"toc-item\"><li><span><a href=\"#--Example-1\" data-toc-modified-id=\"--Example-1-2.1\"><span class=\"toc-item-num\">2.1 </span><font face=\"gotham\" color=\"purple\"> Example 1</font></a></span></li><li><span><a href=\"#--Example-2\" data-toc-modified-id=\"--Example-2-2.2\"><span class=\"toc-item-num\">2.2 </span><font face=\"gotham\" color=\"purple\"> Example 2</font></a></span></li><li><span><a href=\"#-Binomial-R.V.-Generator\" data-toc-modified-id=\"-Binomial-R.V.-Generator-2.3\"><span class=\"toc-item-num\">2.3 </span><font face=\"gotham\" color=\"purple\"> Binomial R.V. Generator</font></a></span></li><li><span><a href=\"#-Moments-of-Binomial-Distribution\" data-toc-modified-id=\"-Moments-of-Binomial-Distribution-2.4\"><span class=\"toc-item-num\">2.4 </span><font face=\"gotham\" color=\"purple\"> Moments of Binomial Distribution</font></a></span></li></ul></li><li><span><a href=\"#-Poisson-Distribution\" data-toc-modified-id=\"-Poisson-Distribution-3\"><span class=\"toc-item-num\">3 </span><font face=\"gotham\" color=\"purple\"> Poisson Distribution</font></a></span><ul class=\"toc-item\"><li><span><a href=\"#Example\" data-toc-modified-id=\"Example-3.1\"><span class=\"toc-item-num\">3.1 </span><font face=\"gotham\" color=\"purple\">Example</font></a></span></li><li><span><a href=\"#-Poisson-R.V.-Generator\" data-toc-modified-id=\"-Poisson-R.V.-Generator-3.2\"><span class=\"toc-item-num\">3.2 </span><font face=\"gotham\" color=\"purple\"> Poisson R.V. Generator</font></a></span></li><li><span><a href=\"#-Moments-of-Poisson-Distribution\" data-toc-modified-id=\"-Moments-of-Poisson-Distribution-3.3\"><span class=\"toc-item-num\">3.3 </span><font face=\"gotham\" color=\"purple\"> Moments of Poisson Distribution</font></a></span></li></ul></li><li><span><a href=\"#-Geometric-Distribution\" data-toc-modified-id=\"-Geometric-Distribution-4\"><span class=\"toc-item-num\">4 </span><font face=\"gotham\" color=\"purple\"> Geometric Distribution</font></a></span><ul class=\"toc-item\"><li><span><a href=\"#Example\" data-toc-modified-id=\"Example-4.1\"><span class=\"toc-item-num\">4.1 </span><font face=\"gotham\" color=\"purple\">Example</font></a></span></li><li><span><a href=\"#-G-D-Moments-and-Generator\" data-toc-modified-id=\"-G-D-Moments-and-Generator-4.2\"><span class=\"toc-item-num\">4.2 </span><font face=\"gotham\" color=\"purple\"> G-D Moments and Generator</font></a></span></li></ul></li><li><span><a href=\"#-Hypergeometric-Distribution\" data-toc-modified-id=\"-Hypergeometric-Distribution-5\"><span class=\"toc-item-num\">5 </span><font face=\"gotham\" color=\"purple\"> Hypergeometric Distribution</font></a></span><ul class=\"toc-item\"><li><span><a href=\"#-Example-\" data-toc-modified-id=\"-Example--5.1\"><span class=\"toc-item-num\">5.1 </span><font face=\"gotham\" color=\"purple\"> Example </font></a></span></li></ul></li><li><span><a href=\"#-Continous-Uniform-Distribution-\" data-toc-modified-id=\"-Continous-Uniform-Distribution--6\"><span class=\"toc-item-num\">6 </span><font face=\"gotham\" color=\"purple\"> Continous Uniform Distribution </font></a></span><ul class=\"toc-item\"><li><span><a href=\"#-CDF-and-PDF-of-Continous-Uniform-Distribution-\" data-toc-modified-id=\"-CDF-and-PDF-of-Continous-Uniform-Distribution--6.1\"><span class=\"toc-item-num\">6.1 </span><font face=\"gotham\" color=\"purple\"> CDF and PDF of Continous Uniform Distribution </font></a></span></li></ul></li><li><span><a href=\"#-Normal-Distribution\" data-toc-modified-id=\"-Normal-Distribution-7\"><span class=\"toc-item-num\">7 </span><font face=\"gotham\" color=\"purple\"> Normal Distribution</font></a></span><ul class=\"toc-item\"><li><span><a href=\"#-Inverse-Normal-CDF\" data-toc-modified-id=\"-Inverse-Normal-CDF-7.1\"><span class=\"toc-item-num\">7.1 </span><font face=\"gotham\" color=\"purple\"> Inverse Normal CDF</font></a></span></li><li><span><a href=\"#-Normal-R.V.-Generator\" data-toc-modified-id=\"-Normal-R.V.-Generator-7.2\"><span class=\"toc-item-num\">7.2 </span><font face=\"gotham\" color=\"purple\"> Normal R.V. Generator</font></a></span></li><li><span><a href=\"#-Bivariate-Normal-Distribution\" data-toc-modified-id=\"-Bivariate-Normal-Distribution-7.3\"><span class=\"toc-item-num\">7.3 </span><font face=\"gotham\" color=\"purple\"> Bivariate Normal Distribution</font></a></span><ul class=\"toc-item\"><li><span><a href=\"#-1st-Method-of-Formulation\" data-toc-modified-id=\"-1st-Method-of-Formulation-7.3.1\"><span class=\"toc-item-num\">7.3.1 </span><font face=\"gotham\" color=\"purple\"> 1st Method of Formulation</font></a></span></li><li><span><a href=\"#-2st-Method-of-Formulation\" data-toc-modified-id=\"-2st-Method-of-Formulation-7.3.2\"><span class=\"toc-item-num\">7.3.2 </span><font face=\"gotham\" color=\"purple\"> 2st Method of Formulation</font></a></span></li></ul></li></ul></li><li><span><a href=\"#-Beta-Distribution\" data-toc-modified-id=\"-Beta-Distribution-8\"><span class=\"toc-item-num\">8 </span><font face=\"gotham\" color=\"purple\"> Beta Distribution</font></a></span></li><li><span><a href=\"#-$\\chi^2$-Distribution\" data-toc-modified-id=\"-$\\chi^2$-Distribution-9\"><span class=\"toc-item-num\">9 </span><font face=\"gotham\" color=\"purple\"> <span id=\"MathJax-Element-503-Frame\" class=\"mjx-chtml MathJax_CHTML\" tabindex=\"0\" data-mathml=\"<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>&#x03C7;</mi><mn>2</mn></msup></math>\" role=\"presentation\" style=\"font-size: 109%; position: relative;\"><span id=\"MJXc-Node-4478\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-4479\" class=\"mjx-mrow\"><span id=\"MJXc-Node-4480\" class=\"mjx-msubsup\"><span class=\"mjx-base\"><span id=\"MJXc-Node-4481\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.496em;\">χ</span></span></span><span class=\"mjx-sup\" style=\"font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;\"><span id=\"MJXc-Node-4482\" class=\"mjx-mn\" style=\"\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.39em; padding-bottom: 0.355em;\">2</span></span></span></span></span></span><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mi>χ</mi><mn>2</mn></msup></math></span></span>$\\chi^2$ Distribution</font></a></span><ul class=\"toc-item\"><li><span><a href=\"#-$\\chi^2$-PDF-and-CDF\" data-toc-modified-id=\"-$\\chi^2$-PDF-and-CDF-9.1\"><span class=\"toc-item-num\">9.1 </span><font face=\"gotham\" color=\"purple\"> <span id=\"MathJax-Element-542-Frame\" class=\"mjx-chtml MathJax_CHTML\" tabindex=\"0\" data-mathml=\"<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>&#x03C7;</mi><mn>2</mn></msup></math>\" role=\"presentation\" style=\"font-size: 109%; position: relative;\"><span id=\"MJXc-Node-4808\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-4809\" class=\"mjx-mrow\"><span id=\"MJXc-Node-4810\" class=\"mjx-msubsup\"><span class=\"mjx-base\"><span id=\"MJXc-Node-4811\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.211em; padding-bottom: 0.461em;\">χ</span></span></span><span class=\"mjx-sup\" style=\"font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;\"><span id=\"MJXc-Node-4812\" class=\"mjx-mn\" style=\"\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.378em; padding-bottom: 0.336em;\">2</span></span></span></span></span></span><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mi>χ</mi><mn>2</mn></msup></math></span></span>$\\chi^2$ PDF and CDF</font></a></span></li></ul></li><li><span><a href=\"#-F-Distribution\" data-toc-modified-id=\"-F-Distribution-10\"><span class=\"toc-item-num\">10 </span><font face=\"gotham\" color=\"purple\"> F Distribution</font></a></span></li></ul></div>" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "from texttable import Texttable\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy as sp\n", "import pandas as pd\n", "import scipy.stats" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this chapter, we will only be dealing with special distributions which are frequently encountered in practice." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# <font face=\"gotham\" color=\"purple\"> Discrete Uniform Distribution</font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have seen PMF and PDF in last chapter, here we review an example of discrete uniform distribution." ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 864x504 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "unif_d = sp.stats.randint.rvs(0, 10, size = 1000)\n", "fig, ax = plt.subplots(figsize = (12, 7))\n", "h, bins, patches = ax.hist(unif_d, density = True, bins = 30)\n", "ax.set_title('Discrete Uniform Frequency Distribution', size = 16)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## <font face=\"gotham\" color=\"purple\"> Discrete Probability Mass Function</font>" ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "<matplotlib.legend.Legend at 0x5fee348>" ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 864x504 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = np.arange(1, 11)\n", "unif_pmf = sp.stats.randint.pmf(x, 2, 10)\n", "fig, ax = plt.subplots(figsize = (12, 7))\n", "ax.scatter(x, unif_pmf, s = 100, color = 'green', label = 'Low = 2, High = 9')\n", "ax.plot(x,unif_pmf, lw = 3, color = 'k')\n", "ax.legend(fontsize = 18, loc = 'center')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# <font face=\"gotham\" color=\"purple\"> Binomial Distribution</font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The binomial experiment has 4 properties:\n", "<font face=\"gotham\" color=\"red\">\n", "* A sequence of $n$ identical trials\n", "* Only two outcomes are possible: $success$ or $failure$\n", "* The probability of success $p$ does not change from trial to trial\n", "* Trials are independent events\n", "</font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The PMF of binomial ditribution is \n", "<br>\n", "<br>\n", "<span style=\"color:red\">\n", "\\begin{equation}\n", "_nC_k p^kq^{n-k}\n", "\\end{equation}\n", "</span>\n", "<br>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## <font face=\"gotham\" color=\"purple\"> Example 1</font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use a simple example to explain the PMF.\n", "\n", "<font face=\"gotham\" color=\"purple\"> Every month, a personal banker might meet 50 people enquiring loans, emperically 30% of them have bad credit history. So calculate probability from 1:50 people that have bad credit history.</font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we can asnwer what the probability is that the banker meet exactly $14$ people who have bad credit history?" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The prob of meeting 14 persons who have bad credit history is 11.89%.\n" ] } ], "source": [ "n = 50\n", "k = 14 # what is the prob that exact 14 ppl she met had bad credit history?\n", "b = scipy.special.comb(50, 14)\n", "p = .3\n", "f_bino = b*p**k*(1-p)**(n-k)\n", "print('The prob of meeting {0} persons who have bad credit history is {1:.2f}%.'.format(k, f_bino * 100))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or we can use ```scipy.stats.binom.pmf```. To show the probability from $1$ to $50$ persons." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x432 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "n = 50\n", "p = .3\n", "bad_credit = np.arange(1, 51)\n", "y = sp.stats.binom.pmf(bad_credit, n, p)\n", "fig, ax = plt.subplots(figsize = (10, 6))\n", "ax.plot(bad_credit, y, lw = 3, color = 'r', alpha = .5)\n", "ax.set_ylim([0, .13])\n", "ax.set_title('The probability that from 1 to 50 persons who have bad credit history', size = 16, x = .5, y = 1.02)\n", "ax.set_xlabel('Number of Person Who Has Bad Credit History', size = 12)\n", "ax.set_ylabel('Probability', size = 12)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Because there are the $30\\%$ of people who have bad credit history, thus we can see the mean of the distribution is $15$ out of $50$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## <font face=\"gotham\" color=\"purple\"> Example 2</font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we can formulate another question using ```scipy.stats.binom.cdf```. \n", "\n", "If a trade trades $n$ times a month, he has a $p%$ chance of winning the trade, find out the probability that he can win at least $k$ trades a month." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also ask what are the probabilites he wins more than $k$ trades, or between $(k_1, \\ k_2)$ trades." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "n = 20 # number of trades\n", "p = .55 # winning odds\n", "k = 12 # at least win k trades\n", "k1 = 14\n", "k2 = 4\n", "\n", "win_less = sp.stats.binom.cdf(k, n, p)\n", "win_more = 1- sp.stats.binom.cdf(k, n, p)\n", "win_betw = sp.stats.binom.cdf(k1, n, p) - sp.stats.binom.cdf(k2, n, p)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "+----------+------------+----------------+\n", "| Win Less | Win More | Win btw 4~14 |\n", "+==========+============+================+\n", "| 0.748 | 0.252 | 0.943 |\n", "+----------+------------+----------------+\n" ] } ], "source": [ "table = Texttable()\n", "table.set_cols_align([ 'c', 'c', 'c']) \n", "table.set_cols_valign([ 'm', 'm', 'm'])\n", "table.add_rows([['Win Less', ' Win More ', ' Win btw 4~14 '],\n", " [ win_less, win_more, win_betw]])\n", "print(table.draw())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What if the probability of wining changing from 0.1 to 0.8, what is the probability that he wins less than 6 trades, assuming every month he trades 20 times." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x432 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "chance = np.arange(.1, .81, .05)\n", "win_less = sp.stats.binom.cdf(6, 20, chance)\n", "\n", "data_dict = {'win_rate':chance, 'win_less':win_less} # I am using annotation, that's why i am using pandas to locate the index\n", "df = pd.DataFrame(data_dict)\n", "df.plot(figsize = (10, 6))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To show the idea in a scatter plot." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 864x504 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize = (12, 7))\n", "ax.scatter(chance, win_less)\n", "txt = 'This point means if the winning rate is 40%,\\n then the probability of winning less\\n than 6 trades is 25%.'\n", "ax.annotate(txt, xy = (df.iloc[6][0], df.iloc[6][1]), \n", " xytext = (.35, .5), weight = 'bold', color = 'Tomato', size = 14,\n", " arrowprops = dict(arrowstyle = '->', connectionstyle = 'arc3', color = 'b'))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## <font face=\"gotham\" color=\"purple\"> Binomial R.V. Generator</font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```sp.stats.binom.rvs()``` is the randome generator for binomial distribution. " ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "n = 1000 # number of trials\n", "p = 0.3 # probability of success\n", "bino = sp.stats.binom.rvs(n, p, size = 1000)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 864x504 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "txt = 'This line is the $y =p \\cdot n$ \\n and where highest draw should be.'\n", "fig, ax = plt.subplots(figsize = (12, 7))\n", "h, bins, patches = ax.hist(bino,bins= 80)\n", "ax.axvline(p*n, color = 'Tomato', ls = '--', lw = 3)\n", "ax.annotate(txt, xy = (p*n, h.max()*0.7), \n", " xytext = (p*n ,h.max()-5), weight = 'bold', \n", " color = 'Tomato', size = 14,\n", " arrowprops = dict(arrowstyle = '->',\n", " connectionstyle = 'arc3', color = 'b'))\n", "ax.set_title('Generated Binomial R.V.s', size = 18)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "According to the example, if success rate <font face=\"gotham\" color=\"red\">$p=.3$</font>, total trials of <font face=\"gotham\" color=\"red\">$1000$</font>.Then the counts of successes have the frequency distribution in the histogram. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## <font face=\"gotham\" color=\"purple\"> Moments of Binomial Distribution</font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also calculate all important moments of distributions by using ```sp.stats.binom.stats(n, p, moments = 'mvsk')```. The text table library is used to format the output." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "+------+------------+------------+-----------+\n", "| mean | variance | skewness | kurtosis |\n", "+======+============+============+===========+\n", "| 300 | 210 | 0.028 | -0.001 |\n", "+------+------------+------------+-----------+\n" ] } ], "source": [ "n = 1000 # number of trials\n", "p = 0.3 # probability of success\n", "bino_stats = sp.stats.binom.stats(n, p, moments = 'mvsk') # mean, variance, skewness, kurtosis\n", "table = Texttable()\n", "table.set_cols_align([ \"c\", \"c\", 'c','c']) \n", "table.set_cols_valign([ \"m\", \"m\", 'm','m'])\n", "table.add_rows([[\"mean\", \" variance \", ' skewness ', 'kurtosis '],\n", " [ bino_stats[0], bino_stats[1], bino_stats[2], bino_stats[3]]])\n", "print(table.draw())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# <font face=\"gotham\" color=\"purple\"> Poisson Distribution</font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When $n\\rightarrow\\infty$ and $p\\rightarrow0$,binomial distribution converges to Poisson distribution, i.e. when $n$ is large and $p$ is small, we can use Poisson to approximate Binomial." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## <font face=\"gotham\" color=\"purple\">Example</font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For an ordinary traders, every trade has $1/1000$ probabilty to encounter a 'Black Swan' shock, a trader sets $20$ trades per month, what is the probability that she will encounter $2$ 'Black Swan' within 5 years?\n", "\n", "This problem can be solved by Binomial, the formulation as below\n", "\n", "\\begin{equation}\n", "\\text{Number of Trades} = 20\\times 12\\times 5=1200\\\\\n", "P(x=2) = \\binom{1200}{2}\\Big(\\frac{1}{1000}\\Big)^2\\Big(\\frac{999}{1000}\\Big)^{1198}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of course, we can employ Poisson PMF to approximate it, the parameter for Poisson distribution is\n", "\n", "\\begin{equation}\n", "\\lambda = np = 1200 \\times \\frac{1}{1000} = 1.2\n", "\\end{equation}\n", "\n", "\n", "that means every 5 years, there is in average 1.2 times of Black Swan shock.\n", "\n", "\\begin{equation}\n", "P(x=2)=\\frac{\\lambda^ke^{-\\lambda}}{k!}=\\frac{1.2^2e^{-1.2}}{2!}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To use the PMF directly" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.21698280952603388" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sp.special.comb(1200, 2)*(1/1000)**2*(999/1000)**1198" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or use the built-in function for Poisson ```sp.stats.poisson.pmf()```." ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The probability of having 2 BS shock(s) in a span of 5 years is 21.69%.\n" ] } ], "source": [ "k = 2\n", "n = 20 * 12 * 5 # 20 times per month, and 5 years span\n", "p = 1/1000\n", "lambdaP = p * n # lambda in Poisson\n", "p = sp.stats.poisson.pmf(k, lambdaP)\n", "print('The probability of having {0} BS shock(s) in a span of 5 years is {1:.2f}%.'.format(k, p*100))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suprisingly high probability of having 1 BS shock, and one BS shock could possibly wipe out the whole account. Take care, traders,<font face=\"gotham\" color=\"red\"> the survival is pivotal</font>!\n", "\n", "So what's the probability of having more than $k$ times BS shock?" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The probability of having more than 2 BS shock in 5 years is 12.051%.\n" ] } ], "source": [ "k = 2\n", "prob_sf = 1 - sp.stats.poisson.cdf(k, lambdaP)\n", "prob_sf_inv = sp.stats.poisson.cdf(k, lambdaP)\n", "print('The probability of having more than %1.0f BS shock in 5 years is %3.3f%%.' % (k, prob_sf*100)) # double % can escape formating" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## <font face=\"gotham\" color=\"purple\"> Poisson R.V. Generator</font>" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 864x504 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "poiss = sp.stats.poisson.rvs(lambdaP, size = 10000)\n", "fig, ax = plt.subplots(figsize = (12, 7))\n", "h, bins, patches = ax.hist(poiss, density = True, bins = 10)\n", "ax.set_title('Poisson Frequency Distribution', size = 16)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## <font face=\"gotham\" color=\"purple\"> Moments of Poisson Distribution</font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again we can compute all most important moments" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "+------+------------+------------+-----------+\n", "| mean | variance | skewness | kurtosis |\n", "+======+============+============+===========+\n", "| 2 | 2 | 0.707 | 0.500 |\n", "+------+------------+------------+-----------+\n" ] } ], "source": [ "poiss_stats = sp.stats.poisson.stats(k, moments = 'mvsk') # mean, variance, skewness, kurtosis\n", "table = Texttable()\n", "table.set_cols_align([ \"c\", \"c\", 'c','c']) \n", "table.set_cols_valign([ \"m\", \"m\", 'm','m'])\n", "table.add_rows([[\"mean\", \" variance \", ' skewness ', 'kurtosis '],\n", " [ poiss_stats[0], poiss_stats[1], poiss_stats[2], poiss_stats[3]]])\n", "print(table.draw())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# <font face=\"gotham\" color=\"purple\"> Geometric Distribution</font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The PMF of G-D is <font face=\"gotham\" color=\"red\">$f(k)=p(1-p)^k$</font>, where <font face=\"gotham\" color=\"red\">$k$</font> is a non-negative integer. <font face=\"gotham\" color=\"red\">$p$</font> is the probability of success, and <font face=\"gotham\" color=\"red\">$k$</font> is the number of failures before success." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## <font face=\"gotham\" color=\"purple\">Example</font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "So G-D is trying to answer 'How many times you have to fail in order to embrace the first success?'\n", "\n", "If each trade has 1/1000 chance to encounter a BS shock, what is the prob of encounter a BS shock after trade <font face=\"gotham\" color=\"red\">$k$</font> times." ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The probability of observing exact 10 times of safe trading before a BS shock is 0.001.\n" ] } ], "source": [ "k = 10\n", "p = 1/1000\n", "\n", "geodist = (1 - 1/1000)**10*1/1000\n", "geodist\n", "print('The probability of observing exact %1.0f times of safe trading before a BS shock is %3.3f.' %(k, geodist))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or use built-in ```sp.stats.geom.pmf()```" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.000991035916125874" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sp.stats.geom.pmf(10, 1/1000)" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The probability of observing 10 or fewer than 10 times of safe trading before a BS shock is 0.001.\n" ] } ], "source": [ "sp.stats.geom.cdf(k,p)\n", "print('The probability of observing %1.0f or fewer than %1.0f times of safe trading before a BS shock is %3.3f.'%(k,k,geodist))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## <font face=\"gotham\" color=\"purple\"> G-D Moments and Generator</font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The moments and randome generator are as following" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "+-------+----+------+------------+------------+------------+\n", "| p | k | mean | variance | skewness | kurtosis |\n", "+=======+====+======+============+============+============+\n", "| 0.001 | 10 | 1000 | 999000 | 2.000 | 6.000 |\n", "+-------+----+------+------------+------------+------------+\n" ] } ], "source": [ "mean, var, skew, kurt = sp.stats.geom.stats(p, moments='mvsk')\n", "table = Texttable()\n", "table.set_cols_align([ \"c\", \"c\", 'c','c', 'c', 'c']) \n", "table.set_cols_valign([ \"m\", \"m\", 'm','m', 'm', 'm'])\n", "table.add_rows([['p','k',\"mean\", \" variance \", ' skewness ', ' kurtosis '],\n", " [ p, k, mean, var, skew, kurt]])\n", "print(table.draw())" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 864x504 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "geomet = sp.stats.geom.rvs(p, size = 10000)\n", "fig, ax = plt.subplots(figsize = (12, 7))\n", "h, bins, patches = ax.hist(geomet, density = True, bins = 30)\n", "ax.set_title('Geometric Frequency Distribution', size = 16)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# <font face=\"gotham\" color=\"purple\"> Hypergeometric Distribution</font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The main difference between hypergeometric and binomial is that the former sampling is not independent of each other, i.e. the <font face=\"gotham\" color=\"red\">sampling is without replacement</font>. \n", "\n", "The formula is \n", "\\begin{equation}\n", "f(x) =\\frac{{K\\choose x} {M-K \\choose N-x}}{{M\\choose N}} \n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## <font face=\"gotham\" color=\"purple\"> Example </font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is 100 candies in an urn, 20 are red, 80 are blue, if we take 5 of them out from it. What is the prob of having exact 4 red candies?\n", "\n", "Solution:\n", "\n", "\\begin{equation}\n", "\\frac{{20\\choose4}{80\\choose1}}{{100\\choose5}}\n", "\\end{equation}\n", "\n", "To solve it:" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The prob of have 4 red candies by taking 5 out is 0.514826%.\n" ] } ], "source": [ "C = sp.special.comb(20, 4)*sp.special.comb(80, 1) /sp.special.comb(100, 5)\n", "print('The prob of have 4 red candies by taking 5 out is %1.6f%%.'% (C*100))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or with built-in function ```sp.stats.hypergeom.pmf()```" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.005148263616599428" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# pmf(x, M, N, n, loc=0)\n", "hgeo = sp.stats.hypergeom.pmf(4, 100, 20, 5,loc = 0) # the arg order the same as MATLAB, not recommended\n", "hgeo" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What is the probability that at most $4$ red candies are taken? i.e. The sum-up of probabilities of drawing $1$, $2$, $3$, and $4$ candies." ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The prob of have at most 4 red candies by taking 5 out is 99.979407%.\n" ] } ], "source": [ "hgeo_cdf = sp.stats.hypergeom.cdf(4, 100, 20, 5,loc = 0) # the arg order the same as MATLAB, not recommended\n", "print('The prob of have at most 4 red candies by taking 5 out is %1.6f%%.' %(hgeo_cdf*100))" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 864x504 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "hgeo_rv = sp.stats.hypergeom.rvs(100, 20, 5, size = 10000)\n", "fig, ax = plt.subplots(figsize = (12, 7))\n", "h, bins, patches = ax.hist(hgeo_rv, density = True)\n", "ax.set_title('Geometric Frequency Distribution', size = 16)\n", "s = ''' It can be interpreted as: if 100 candies in the urn, \n", " 20 are red, take 5 out of 100.\n", " \n", " The chance of getting from 1 to 5 red candies, \n", " is shown in the chart.\n", " \n", " As we can see it is nearly impossible to get 4 or 5 candies. \n", " But getting 1 red candy is the most possible outcome.'''\n", "\n", "ax.text(1.6, .5, s, fontsize=14, color ='red')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "+-----+----+------+------------+------------+------------+\n", "| M | k | mean | variance | skewness | kurtosis |\n", "+=====+====+======+============+============+============+\n", "| 100 | 20 | 1 | 0.768 | 0.629 | -0.010 |\n", "+-----+----+------+------------+------------+------------+\n" ] } ], "source": [ "mean, var, skew, kurt = sp.stats.hypergeom.stats(100, 20, 5, moments='mvsk')\n", "table = Texttable()\n", "table.set_cols_align([ \"c\", \"c\", 'c','c', 'c', 'c']) \n", "table.set_cols_valign([ \"m\", \"m\", 'm','m', 'm', 'm'])\n", "table.add_rows([['M','k',\"mean\", \" variance \", ' skewness ', ' kurtosis '],\n", " [ 100, 20, mean, var, skew, kurt]])\n", "print(table.draw())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# <font face=\"gotham\" color=\"purple\"> Continous Uniform Distribution </font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The PDF of Uniform Distribution is\n", "\n", "\\begin{equation}\n", "f(x)=\\frac{1}{b-a}\n", "\\end{equation}\n", "\n", "And its r.v. generator is one of most frequently used function in NumPy: ```np.random.rand()```" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 864x504 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "unif = np.random.rand(10000)\n", "fig, ax = plt.subplots(figsize = (12, 7))\n", "h, bins, patches = ax.hist(unif, density = True, bins = 30)\n", "ax.set_title('Continous Uniform Frequency Distribution', size = 16)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## <font face=\"gotham\" color=\"purple\"> CDF and PDF of Continous Uniform Distribution </font>" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 1224x504 with 2 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# pdf(x, loc=0, scale=1)\n", "# cdf(x, loc=0, scale=1)\n", "x = np.linspace(-.2, 1.2, 100)\n", "unif_pdf = sp.stats.uniform.pdf(x)\n", "unif_cdf = sp.stats.uniform.cdf(x)\n", "fig, ax = plt.subplots(nrows = 1, ncols = 2, figsize = (17, 7))\n", "ax[0].plot(x,unif_pdf, lw = 4, label = 'PDF of Continouse U-D')\n", "ax[0].set_xlim([-.1, 1.1])\n", "ax[0].set_ylim([0, 2])\n", "ax[0].legend(fontsize = 16)\n", "\n", "ax[1].plot(x,unif_cdf, lw = 4, label = 'CDF of Continouse U-D')\n", "ax[1].set_xlim([-.2, 1.2])\n", "ax[1].set_ylim([0, 2])\n", "ax[1].legend(fontsize = 16)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "+-------+------------+------------+------------+\n", "| mean | variance | skewness | kurtosis |\n", "+=======+============+============+============+\n", "| 0.500 | 0.083 | 0 | -1.200 |\n", "+-------+------------+------------+------------+\n" ] } ], "source": [ "mean, var, skew, kurt = sp.stats.uniform.stats(moments='mvsk')\n", "table = Texttable()\n", "table.set_cols_align([ \"c\", \"c\", 'c','c']) \n", "table.set_cols_valign([ \"m\", \"m\", 'm','m'])\n", "table.add_rows([[\"mean\", \" variance \", ' skewness ', ' kurtosis '],\n", " [ mean, var, skew, kurt]])\n", "print(table.draw())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# <font face=\"gotham\" color=\"purple\"> Normal Distribution</font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The most convenient method of creating normal distribution plot is to use ```sp.stats.norm.pdf()```.\n", "\n", "The PDF function single normal distribution is \n", "\n", "$$\n", "f(x)= \\frac{1}{\\sigma \\sqrt{2 \\pi}} e^{-\\frac{1}{2}\\left(\\frac{x-\\mu}{\\sigma}\\right)^{2}}\n", "$$" ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 1224x504 with 2 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mu = 2\n", "sigma = 1\n", "x = np.arange(-2, 6, 0.1)\n", "norm_pdf = sp.stats.norm.pdf(x, mu, sigma)\n", "norm_cdf = sp.stats.norm.cdf(x, mu, sigma)\n", "\n", "fig, ax = plt.subplots(nrows = 1, ncols = 2, figsize = (17, 7))\n", "ax[0].plot(x,norm_pdf, lw = 4, label = 'PDF of Normal Distribution', ls = '--')\n", "ax[0].legend(fontsize = 16, loc = 'lower left', framealpha=0.2)\n", "\n", "ax[1].plot(x,norm_cdf, lw = 4, label = 'CDF of Normal Distribution')\n", "ax[1].legend(fontsize = 16,fancybox=True, framealpha=0.5)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## <font face=\"gotham\" color=\"purple\"> Inverse Normal CDF</font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The inverse normal CDF is commonly used in calculating $p$-value, the plot below is useful to understand the idea." ] }, { "cell_type": "code", "execution_count": 72, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 1224x504 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "norm_95_r = sp.stats.norm.ppf(.975) # ppf mean point percentage function, actually inverse CDF\n", "norm_95_l = sp.stats.norm.ppf(.025)\n", "\n", "x = np.linspace(-5, 5, 200)\n", "y = sp.stats.norm.pdf(x)\n", "\n", "xl = np.linspace(-5, norm_95_l, 100)\n", "yl = sp.stats.norm.pdf(xl)\n", "xr = np.linspace(norm_95_r, 5, 100)\n", "yr = sp.stats.norm.pdf(xr)\n", "\n", "fig, ax = plt.subplots(figsize = (17, 7))\n", "ax.plot(x,y, lw = 4, label = 'PDF of Normal Distribution', ls = '-', color = 'orange')\n", "ax.set_ylim([0, .45])\n", "\n", "ax.fill_between(x, y, 0, alpha=0.1, color = 'blue')\n", "ax.fill_between(xl,yl, 0, alpha=0.6, color = 'blue')\n", "ax.fill_between(xr,yr, 0, alpha=0.6, color = 'blue')\n", "\n", "ax.text(-.2, 0.15, '95%', fontsize = 20)\n", "ax.text(-2.3, 0.015, '2.5%', fontsize = 12, color = 'white')\n", "ax.text(2.01, 0.015, '2.5%', fontsize = 12, color = 'white')\n", "\n", "ax.annotate('±%.4f' %norm_95_r, xy = (norm_95_r, 0), xytext = (-.4, .05), weight = 'bold', color = 'r', \n", " arrowprops = dict(arrowstyle = '->', connectionstyle = 'arc3', color = 'b'), fontsize = 16)\n", "ax.annotate('±%.4f' %norm_95_r, xy = (norm_95_l, 0), xytext = (-.4, .05), weight = 'bold', color = 'r', \n", " arrowprops = dict(arrowstyle = '->', connectionstyle = 'arc3', color = 'b'), fontsize = 16)\n", "\n", "ax.set_title('Normal Distribution And 2.5% Shaded Area', size = 20)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## <font face=\"gotham\" color=\"purple\"> Normal R.V. Generator</font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To generate a normal distribution histogram" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "data": { "image/png": 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ODi4TDTA/RoQBAOiSIAwAQJdMjQDYi5VOQwBgfTEiDABAlwRhAAC6JAgDANAlQRgAgC4JwgAAdEkQBgCgS4IwAABdEoQBAOiSIAwAQJcEYQAAuiQIAwDQJUEYAIAubVp0AQCrtWXbjkWXAMA6ZkQYAIAuCcIAAHRJEAYAoEuCMAAAXRKEAQDokrNGAGxgKz2zxq7tW9eoEoCDjxFhAAC6JAgDANAlQRgAgC4JwgAAdEkQBgCgS4IwAABdEoQBAOiSIAwAQJcEYQAAuiQIAwDQJZdYBuBWLskM9MSIMAAAXRKEAQDokiAMAECXBGEAALokCAMA0CVBGACALgnCAAB0SRAGAKBLgjAAAF0ShAEA6JIgDABAlwRhAAC6JAgDANAlQRgAgC4JwgAAdEkQBgCgS4IwAABdEoQBAOiSIAwAQJcEYQAAuiQIAwDQJUEYAIAuCcIAAHRJEAYAoEuCMAAAXRKEAQDokiAMAECXBGEAALokCAMA0CVBGACALgnCAAB0SRAGAKBLgjAAAF0ShAEA6NJMQbiqTq6qq6vqmqratsz6Z1TVFVV1eVW9p6qOnX+pAAAwP/sNwlV1SJJzkpyS5NgkT1om6L6htfYvW2vHJXlRkpfMvVIAAJijWUaET0hyTWvt4621m5JckOS0yQ6ttc9NLN41SZtfiQAAMH+bZuhzRJJrJ5Z3J3n4dKeq+tkkz05yaJLHzqU6AABYI7OMCNcybbcb8W2tndNa+/Ykz0nyX5fdUNUZVbWzqnbu2bNnZZUCAMAczRKEdyc5amL5yCTX7aP/BUmesNyK1tq5rbXjW2vHb968efYqAQBgzmYJwpclOaaqjq6qQ5OcnuSiyQ5VdczE4tYkfze/EgEAYP72O0e4tXZzVZ2Z5NIkhyR5dWvtyqo6O8nO1tpFSc6sqpOSfC3JZ5I8ZS2LBtaHLdt2rKj/ru1b16gS1spKn+PE8wwcPGb5slxaaxcnuXiq7fkTPz9zznUBAMCacmU5AAC6JAgDANAlQRgAgC4JwgAAdGmmL8sB3BFWcwYC1h9nEwEOFkaEAQDokiAMAECXBGEAALokCAMA0CVBGACALgnCAAB0SRAGAKBLgjAAAF0ShAEA6JIgDABAlwRhAAC6JAgDANAlQRgAgC4JwgAAdEkQBgCgS4IwAABdEoQBAOiSIAwAQJcEYQAAuiQIAwDQJUEYAIAuCcIAAHRJEAYAoEuCMAAAXRKEAQDokiAMAECXBGEAALokCAMA0CVBGACALgnCAAB0adOiCwCAfdmybceK+u/avnWNKgE2GiPCAAB0SRAGAKBLgjAAAF0ShAEA6JIgDABAlwRhAAC6JAgDANAlQRgAgC4JwgAAdEkQBgCgS4IwAABdEoQBAOjSpkUXAKwPW7btWHQJADBXRoQBAOiSIAwAQJcEYQAAuiQIAwDQJUEYAIAuCcIAAHRJEAYAoEuCMAAAXRKEAQDokiAMAECXBGEAALokCAMA0CVBGACALgnCAAB0adOiCwAWY8u2HYsuAQAWyogwAABdEoQBAOiSIAwAQJcEYQAAuiQIAwDQJUEYAIAuCcIAAHRJEAYAoEsuqAHAhrLSi8Xs2r51jSoBDnZGhAEA6JIgDABAlwRhAAC6NNMc4ao6OcnLkxyS5LzW2vap9c9O8lNJbk6yJ8lPttY+MedaAWDuzCmGfu13RLiqDklyTpJTkhyb5ElVdexUt79Ncnxr7buTvDHJi+ZdKAAAzNMsUyNOSHJNa+3jrbWbklyQ5LTJDq21d7TWvjQuvjfJkfMtEwAA5muWIHxEkmsnlnePbXvztCRvXm5FVZ1RVTuraueePXtmrxIAAOZsliBcy7S1ZTtWPTnJ8UlevNz61tq5rbXjW2vHb968efYqAQBgzmb5stzuJEdNLB+Z5LrpTlV1UpLnJXl0a+2r8ykPAADWxiwjwpclOaaqjq6qQ5OcnuSiyQ5V9dAkf5Dk1Nba9fMvEwAA5mu/Qbi1dnOSM5NcmuSqJBe21q6sqrOr6tSx24uTfGuSP6mqy6vqor1sDgAADgoznUe4tXZxkoun2p4/8fNJc64LAADWlCvLAQDQJUEYAIAuCcIAAHRJEAYAoEuCMAAAXRKEAQDokiAMAECXBGEAALokCAMA0CVBGACALgnCAAB0SRAGAKBLgjAAAF0ShAEA6JIgDABAlwRhAAC6JAgDANAlQRgAgC4JwgAAdEkQBgCgS4IwAABdEoQBAOiSIAwAQJcEYQAAurRp0QUA87Fl245FlwBdWOnv2q7tW9eoEuBAGREGAKBLgjAAAF0ShAEA6JIgDABAlwRhAAC65KwRcJByFggAWFtGhAEA6JIgDABAlwRhAAC6JAgDANAlQRgAgC4JwgAAdEkQBgCgS4IwAABdEoQBAOiSIAwAQJcEYQAAuiQIAwDQJUEYAIAuCcIAAHRJEAYAoEuCMAAAXRKEAQDokiAMAECXBGEAALokCAMA0CVBGACALm1adAHQiy3bdiy6BGABVvO7v2v71jWoBJhmRBgAgC4JwgAAdEkQBgCgS4IwAABdEoQBAOiSIAwAQJcEYQAAuiQIAwDQJUEYAIAuCcIAAHRJEAYAoEuCMAAAXRKEAQDokiAMAECXBGEAALokCAMA0CVBGACALgnCAAB0SRAGAKBLgjAAAF0ShAEA6JIgDABAl2YKwlV1clVdXVXXVNW2ZdafWFUfrKqbq+qJ8y8TAADma79BuKoOSXJOklOSHJvkSVV17FS3TyZ5apI3zLtAAABYC5tm6HNCkmtaax9Pkqq6IMlpST661KG1tmtcd8sa1AgAAHM3y9SII5JcO7G8e2xbsao6o6p2VtXOPXv2rGYTAAAwF7ME4Vqmra1mZ621c1trx7fWjt+8efNqNgEAAHMxSxDeneSoieUjk1y3NuUAAMAdY5YgfFmSY6rq6Ko6NMnpSS5a27IAAGBt7TcIt9ZuTnJmkkuTXJXkwtbalVV1dlWdmiRV9T1VtTvJjyT5g6q6ci2LBgCAAzXLWSPSWrs4ycVTbc+f+PmyDFMmAABgXXBlOQAAuiQIAwDQJUEYAIAuzTRHGAC442zZtmNNt79r+9Y13T6sF0aEAQDokiAMAECXBGEAALokCAMA0CVBGACALgnCAAB0SRAGAKBLgjAAAF0ShAEA6JIgDABAlwRhAAC6JAgDANAlQRgAgC4JwgAAdEkQBgCgS4IwAABdEoQBAOiSIAwAQJcEYQAAuiQIAwDQpU2LLgDWwpZtOxZdAgBwkDMiDABAlwRhAAC6JAgDANAlQRgAgC4JwgAAdMlZIwCgMys9s86u7VvXqBJYLCPCAAB0SRAGAKBLgjAAAF0ShAEA6JIgDABAlwRhAAC6JAgDANAlQRgAgC4JwgAAdEkQBgCgS4IwAABdEoQBAOiSIAwAQJc2LboAAODgtmXbjhX137V96xpVAvMlCLMurPSPMADA/pgaAQBAl4wIAwBzZSoF64URYQAAuiQIAwDQJUEYAIAuCcIAAHRJEAYAoEuCMAAAXRKEAQDokiAMAECXXFADAFiolV6AI3ERDuZDEGYhVvNHDwBgnkyNAACgS4IwAABdMjUCAFh3VjrFzpxilmNEGACALgnCAAB0SRAGAKBLgjAAAF3yZTnmwnmBAYD1RhBmWYItALDRmRoBAECXjAh3wOguAMDtGREGAKBLgjAAAF0ShAEA6JI5wgDAhrfS78vs2r51jSrhYCIIAwBMEZz7IAivQ84CAQBw4LoMwmv9Lk9QBQA4+M0UhKvq5CQvT3JIkvNaa9un1t85yWuT/Ksk/5TkR1tru+ZbKgDAwemOGAQz/WL+9nvWiKo6JMk5SU5JcmySJ1XVsVPdnpbkM621ByV5aZLfmnehAAAwT7OMCJ+Q5JrW2seTpKouSHJako9O9DktyVnjz29M8oqqqtZam2OtC2OqAwCw0a113jkYR7RnCcJHJLl2Ynl3kofvrU9r7eaq+mySeye5YbJTVZ2R5Ixx8QtVdfVqiu7U4Zk6nqyaYzk/juX8OJbz41jOj2M5Pwd8LGudf94+x/pXcywfsFzjLEG4lmmbHumdpU9aa+cmOXeGfTKlqna21o5fdB0bgWM5P47l/DiW8+NYzo9jOT+O5fzM81jOcmW53UmOmlg+Msl1e+tTVZuS3CPJp+dRIAAArIVZgvBlSY6pqqOr6tAkpye5aKrPRUmeMv78xCRv3yjzgwEA2Jj2OzVinPN7ZpJLM5w+7dWttSur6uwkO1trFyV5VZI/qqprMowEn76WRXfKlJL5cSznx7GcH8dyfhzL+XEs58exnJ+5HcsycAsAQI9mmRoBAAAbjiAMAECXBOF1pKp+pKqurKpbqsopWFahqk6uqqur6pqq2rboetarqnp1VV1fVR9ZdC3rXVUdVVXvqKqrxt/vZy66pvWqqr65qt5fVR8aj+ULFl3TeldVh1TV31bVmxZdy3pWVbuq6oqquryqdi66nvWsqu5ZVW+sqo+NfzcfeSDbE4TXl48k+eEk7150IevRjJcLZzbnJzl50UVsEDcn+cXW2ncmeUSSn/W6XLWvJnlsa+0hSY5LcnJVPWLBNa13z0xy1aKL2CC+v7V2nHMJH7CXJ7mktfYdSR6SA3x9CsLrSGvtqtaaq/Gt3q2XC2+t3ZRk6XLhrFBr7d1xrvC5aK39Q2vtg+PPn8/wR/2IxVa1PrXBF8bFO4033whfpao6MsnWJOctuhZIkqq6e5ITM5ytLK21m1prNx7INgVherLc5cIFDg4aVbUlyUOTvG+xlaxf40f5lye5PslfttYcy9V7WZJfSnLLogvZAFqSt1TVB6rqjEUXs449MMmeJK8Zp+ycV1V3PZANCsIHmap6a1V9ZJmbkcsDN9OlwGERqupbk/xpkme11j636HrWq9ba11trx2W4CuoJVfVdi65pPaqqH0xyfWvtA4uuZYN4VGvtYRmm5v1sVZ246ILWqU1JHpbk91prD03yxSQH9H2f/V5QgztWa+2kRdewgc1yuXC4w1XVnTKE4Ne31v5s0fVsBK21G6vqnRnmsvtS58o9KsmpVfX4JN+c5O5V9brW2pMXXNe61Fq7bvz3+qr68wxT9XzfZ+V2J9k98UnPG3OAQdiIMD2Z5XLhcIeqqsow3+2q1tpLFl3PelZVm6vqnuPPd0lyUpKPLbaq9am19tzW2pGttS0Z/la+XQhenaq6a1XdbennJD8Qb85WpbX2qSTXVtWDx6Z/k+SjB7JNQXgdqaofqqrdSR6ZZEdVXbromtaT1trNSZYuF35Vkgtba1cutqr1qar+OMnfJHlwVe2uqqctuqZ17FFJfjzJY8dTK10+jsKxct+W5B1V9eEMb3z/srXmtF8s2n2TvKeqPpTk/Ul2tNYuWXBN69nPJXn9+Ht+XJLfOJCNucQyAABdMiIMAECXBGEAALokCAMA0CVBGACALgnCAAB0SRAGAKBLgjAAAF36/3uxf+eTlSrJAAAAAElFTkSuQmCC\n", "text/plain": [ "<Figure size 864x504 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# rvs(loc=0, scale=1, size=1, random_state=None)\n", "norm_rv = sp.stats.norm.rvs(mu, sigma, size = 5000)\n", "fig, ax = plt.subplots(figsize = (12, 7))\n", "h, bins, patches = ax.hist(norm_rv, density = True, bins = 50)\n", "ax.set_title('Normal Frequency Distribution', size = 16)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "+------+------------+------------+------------+\n", "| mean | variance | skewness | kurtosis |\n", "+======+============+============+============+\n", "| 2 | 1 | 0 | 0 |\n", "+------+------------+------------+------------+\n" ] } ], "source": [ "mean, var, skew, kurt = sp.stats.norm.stats(mu, sigma, moments='mvsk')\n", "table = Texttable()\n", "table.set_cols_align([ \"c\", \"c\", 'c','c']) \n", "table.set_cols_valign([ \"m\", \"m\", 'm','m'])\n", "table.add_rows([[\"mean\", \" variance \", ' skewness ', ' kurtosis '],\n", " [ mean, var, skew, kurt]])\n", "print(table.draw())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## <font face=\"gotham\" color=\"purple\"> Bivariate Normal Distribution</font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The multivariate normal distribution density function is \n", "\\begin{equation}\n", "f_\\boldsymbol{X}(x_1,...,x_2)=\\frac{1}{\\sqrt{(2\\pi)^k|\\Sigma|}}\\exp{\\Big(-\\frac{(x-\\mu)^T\\Sigma^{-1}(x-\\mu)}{2}\\Big)}\n", "\\end{equation}\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### <font face=\"gotham\" color=\"purple\"> 1st Method of Formulation</font>" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x432 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "mu_x = 0\n", "sigma_x = 2\n", "\n", "mu_y = 0\n", "sigma_y = 2\n", "\n", "#Create grid and multivariate normal\n", "x = np.linspace(-10,10,500)\n", "y = np.linspace(-10,10,500)\n", "X, Y = np.meshgrid(x,y)\n", "pos = np.empty(X.shape + (2,))\n", "pos[:, :, 0] = X; pos[:, :, 1] = Y # more technical than next one\n", "norm = sp.stats.multivariate_normal([mu_x, mu_y], [[sigma_x, 0], [0, sigma_y]]) # frozen \n", "\n", "#Make a 3D plot\n", "fig = plt.figure(figsize = (10, 6))\n", "ax = fig.gca(projection='3d')\n", "ax.plot_surface(X, Y, norm.pdf(pos),cmap='viridis',linewidth=0)\n", "ax.set_xlabel('X axis')\n", "ax.set_ylabel('Y axis')\n", "ax.set_zlabel('Z axis')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### <font face=\"gotham\" color=\"purple\"> 2st Method of Formulation</font>" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x720 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#Parameters to set\n", "mu_x = 0\n", "sigma_x = 7\n", "\n", "mu_y = 0\n", "sigma_y = 15\n", "\n", "x = np.linspace(-10,10,500)\n", "y = np.linspace(-10,10,500)\n", "X,Y = np.meshgrid(x,y)\n", "\n", "pos = np.array([X.flatten(),Y.flatten()]).T # more intuitive than last one\n", "\n", "rv = sp.stats.multivariate_normal([mu_x, mu_y], [[sigma_x, 0], [0, sigma_y]])\n", "\n", "fig = plt.figure(figsize=(10,10))\n", "ax0 = fig.add_subplot(111)\n", "ax0.contourf(X, Y, rv.pdf(pos).reshape(500,500),cmap='viridis')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# <font face=\"gotham\" color=\"purple\"> Beta Distribution</font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The PDF of Beta distribution is \n", "\n", "\n", "\\begin{equation}\n", "f(x, a, b)=\\frac{\\Gamma(a+b) x^{a-1}(1-x)^{b-1}}{\\Gamma(a) \\Gamma(b)}\n", "\\end{equation}\n", "\n", "where $0\\leq x \\leq 1$ and $a>0$, $b>0$, $\\Gamma$ is the Gamma function.\n", "\n", "Beta distribution is a natural good choice for priors in Bayesian econometrics since its range is bounded in unit." ] }, { "cell_type": "code", "execution_count": 89, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.5" ] }, "execution_count": 89, "metadata": {}, "output_type": "execute_result" } ], "source": [ "params[0][0][1]" ] }, { "cell_type": "code", "execution_count": 98, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "(0.0, 1.0, 0.0, 3.0)" ] }, "execution_count": 98, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 648x648 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 1, 100)\n", "\n", "fig = plt.figure(figsize=(9, 9))\n", "ax = fig.add_subplot(111)\n", "\n", "params = np.array([[[.5,.5]],\n", " [[5,1]],\n", " [[1,5]],\n", " [[2,2]],\n", " [[2,3]],\n", " [[3,2]],\n", " [[1,1]]])\n", "for i in range(params.shape[0]):\n", " beta_pdf = sp.stats.beta.pdf(x, params[i][0][0], params[i][0][1])\n", " ax.plot(x, beta_pdf, lw = 3, label = '$a = %.1f, b = %.1f$' % (params[i][0][0], params[i][0][1]))\n", " ax.legend()\n", "\n", "ax.axis([0, 1, 0, 3])" ] }, { "cell_type": "code", "execution_count": 97, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0, 1.0, 0.0, 1.0)" ] }, "execution_count": 97, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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yvx6ieK2Cr+sNs3//fnx9fcnNzWXMmDGEhIQQHR1d55w6nY6CggLmz58PQL9+/cjPt3xR18e25rJPovOhN+g5mnuUX9J/YfeF3eRX5tc5TiFTMNh7MNH+0QzzG0ZXx67t4gtEomUpKagkKSaL5P0X6/QF8Qp0Imy4L8EDvNpMCG59qDhyhOw330Jz2jIBmW1ICF4v/gP1bbfd8PwLScfZ+vF7VJaYk/gFRvbnrqf+joOT8w3OvDlVKYXkr0mGmvBnmaMSz8ciUHa5ydboVZE0YyUxYl3WrFlDXFwce/bsQa1WEx0dTViYpeqsz+qDv78/GRkZpmOZmZn4+vpec86VPi8vLyZNmkRcXNx1v+yTk5MJDg7GpmYp7ujRo0RGWu7T1XdlpDnsk+gciKLIqcun2HpuK9vTtpNXWXfCOycbJ6L9oxkRMILbfG+TVj8krkvehVKO7jzP2SO5V/tworSV03uoN2HDffHwr8N3oQ2jy88n94NFFG/ZYtGv6NIFz+eew3nCvQhy+Q3nOP7rDnav+hxDTZivIMiImjqdIfc9gCBrWibYypMFFPznJNRUHJY72eDxeARKz5tvd4lZR7nycyJB7MGTHVWM3GwrpblITEwkKioKtVrN5s2bOXDgABFX7d/VZ/Vh0KBBpKamkpaWhp+fH+vXr+fbb7+1GFNeXo7BYMDR0ZHy8nJ27tzJa6+9Zjo+atQo1qxZg5+fH2D0F0lLS0Oj0aDValm4cCFLlixpsG3Wsk+ic3Gp7BJbz21l67mtnCs+V+cYNzs3RncdzZjAMQzsMhCFrM1+xEi0Mlf8QY7+cp6M5MvXHHfysKPvyABConysVtm2pRB1Ogq/XUfe0qUYyspM/YK9PR5zHsdt1ixk9jd2sDUY9Py2ZiVHt//P1Ofg7MI9z75EQFjfJttYmZRPwbpTZiHiYovn4xEo6uP4W10BuclGO0WBXFUITnZNy1Tbvp7hFmDmzJlMnDiRTZs2MX78eIKCglCpGu7Jr1AoWLZsGWPHjkWv1/Poo4+aVljGjx/PihUrqKqqYtKkSYBxC+ahhx5i3LhxABgMBs6cOYObm5tpzoSEBKZPn05UVBSVlZUsWLCAoUOHNupxNtU+ic5Btb6aPRl7+CH1B/68+Gedycfc7NwY020Md3a7kwFdBiCX3fiXnkTnRhRF0o/nc/jndHLPX7uK6x/iSt87AugW7t4m84HcjMoTJ7i0YAGaZEunbcc776TLKy+jrGMF+mo0FRVs+/g90uLNWyFegT2476UFOLo3PbKx4ngel9efgpogHrmbnVGIuNbTcTz7OIJoXKk5J/rg06VLk20S6vIdaAkGDhwoXp2z4uTJk4SGhraKPW2NpKQkVq1axeLFi1vblHohPXcdi9TCVDalbGJb2rY6i83ZK+y5o+sd3N39bob6DkUpk+q5SNwYURRJTyzg0NY08i5YihBBgB4DvOh/Zzc8u7avrZgrGCoryVu2jMurv7HInGoTGEiXf/0L9bAb+4VcoTg3hx/eW0hB5gVTX8/BUdw17wWUdk2PMis/mkPhdylc+V2h8LDH4/EIFM629Z/kz8/gl1cB2KwfTuKg93hjQhiCIBwRRXFgY+ySVkbaKOHh4e1GiEh0DLR6Lbsv7GbdqXUczb22EqeAwK2+t3Jvj3u5I+AOHJRtP4xSovURRZHziQXE1SFC5AoZIVE+3DImAOd6+Cm0VcoPxnLptdfQXjALCMHWFo8nn8Ttr7OQ1TPkNu98GpvfeY3yokJT35BJU7lt6sNN9g8BKD+UTeH3qWYh4mWP52N9kTc0JX4t59V4Qw96N9FfBCQxIiHR6ckpz+G7lO/YnLq5zmgYX5Uv9wXfx8Tgifiqb77ELCFxhYuphRz4/iw5aZYF1ORKGeG3+3HLmK6oGvKLvI2hLysn9/33Kdq40aLfYfBgfN56E5tu9c+9kXkyiR/ffwtNhTGUWa5QcOfcZ+gTfYdVbC07eImiH8+Y2kpvBzwei0CubkRuklpi5LghiLslMSIhIdFYThacZE3yGnak7UAnWoZRKgQFI7uO5IFeDzDEZwgyoem/yiQ6DwVZZfz541nOJxZY9MuVMsKH+3HL2PYtQgAqDh/m4iuvos3MNPXJHB3xevEfuDzwQINC188eiWXrkvfQaY3VcW3sHbjvpQUE9Kk7+VlDKd2fRfFPZqdzpa8Kj9kRyFWN2F6tuAyFaQBUi3JOit3oKYkRCQmJhmAQDezL3Mc3yd9wKPvQNce97L2Y0msKk3tNxsvBqxUslGjPlF6uIu5/5zgVm01tX2eZQiB8uB/9x3Vr9yLEUF1N/tKlFKxcZVFLRj16FN4LXkPZpWHvmxO/7eaXLz5GrEkJ7+DswuT5b+IVGGQVe0t/z6T45zRTWxngiOdfw5A5NNLP66J5CzdZ7IbKwQF3ddOfU0mMSEh0AnQGHdvTtrMicUWdYbn9vfrzcJ+HGREwQnJGlWgwWo2eozvPc2znBfTaWnVWBOg9xJvB93Zv87Vi6kPVqVNcfOllNCkppj6ZkxPeCxbgdM/dDU7kd2Tbj8SsWWFqO3fxZsr8t3Dx9rGKvSW7L1Cy67ypbdPNCY+/hiFrSsK4THPgSYKhBz29rONwLIkRCYkOTLW+mh/P/MiqpFVklWVZHJMLcu4MvJOZfWYS5tG0dNISnRNRFEk9lMOB789SXqSxONYtwp2hE3vg4d/+k92Jokjh2rXkfrAIUas19auibsXnnXdQens3eM64LZvY9+1qU9uzW3fuf3Uhale365/UAHtLdp2ndI85saVNd2c8ZoUhs21i6H0tMXLM0JMeVtiiAUmMSEh0SDR6DZtSNrEqcRW5lbkWx1RKFVN6TmF66HR81Nb5BSbR+cg9X8K+Dalkn7MM/fbs6shtU4Lx6+XaSpZZF11hIZdenU9ZTIypT7Czw+vFf+D64IONinKJ/fE7/lj3jantF9KH+156DTtV07/YRVGkZEc6pb+ZfVlsg11wf6QPMpsmChFRhEzz9u4xMZhHJDEiISFxNVq9lh/O/MCXx78kt8JShDjbOvNw6MM8GPIgzrZNq2ch0XnRVGg5uOUcSb9nWfiF2DsqGXpfD0Ju9WmXycrqojw2josvvogu1/xesuvTB99Fi7AN6t6oOQ9+v4H9G9aa2gF9Ipj08utWySEiiiLF29Io+8O8CmrX2xX3h/sgKK3ghF5wFqqKALgsqjkvdrGK8ypIYkRCokOgN+jZlraNz+I/u2Y7xsPeg1lhs3ig1wNSbhCJRiOKIilxOezffIbKkmpTv0wuEHlHAAPHB2LTztK2Xw9Rryf/00/J//wLCydVt5kz8fz7C/XOG3I1f25ex4GN/zW1A8L6Muml16wjRAwiRf87S/nBS6Y+u1A33KeHIiisFA1Xe1XE0BMQmlyt9wod45XTRgkMDMTR0RG5XI5CoeDqjLMAO3bs4Nlnn0Wv1/PYY4/xyiuv3HDOmJgYVq5cydq1a284rj48+uijbN26FS8vL5KSkuoc01D7JFoWURT5LfM3lhxZco1jqrudO4/3fZwpvaZgK2/fEQwSrUthdjm/rUsh63ShRX/XMDeGT+2FS5eOI3J1BQVk/eMfVPx50NQnd3XF991/o7799kbP++emdRz4zixEuoZHct9LC1DaWkmI/HCG8kPZpj77cHfcpoVYT4jAVWIkGJWNHB/nptsPkhhpdvbu3YuHR921BPR6PfPmzWPXrl34+/szaNAgJkyYQJ8+fa47X3x8PLfccotVbJs1axZPPfUUjzzyiNXsk2g5ThSc4MPDH14Touts68zs8NlMC5mGvaL9RzBItB56vYFjOy9waFsaBp15hUDlbMOwqb3o0d+zwREkbZmKo8fIev55dDk5pj6HoUPxfe+9Bofs1ubw1h8shEi3vrcw8cV/obRp+o8E0SBSuCmFiqPmrST7SE/cpvZGkFv5uaklRuLFYIK91FZ7/iUxUgebNm1i0aJFVFZW4ujoyA8//ICnp6fVrxMXF0dwcDBBQcZ48mnTprFly5YbftknJCTg5ubGkCFDyMvLY9WqVYwYMaJR14+OjiY9Pd2q9kk0P5fKLrH02FK2nttq0a9SqpgZNpMZoTNQ27T/CAaJ1iXvQil71p4kP6NW1VmZQN+R/gy+tzs2TQkPbWNciZbJef8D0NUkABQEPJ58Eo8n/4Ygb7zj5/Hdv/Db2pWmtlWFiF7k8sbTVCbkmfoc+nvhOqUXgrX9dqrLIecEYKzUm2Dowf0BLlabvu2+mt5oRge7N64t/FWbkSNHMmXKFAAWLlzIxo0bmTdvnun48OHDKS29ttrkokWLGD16tKktCAJ33nkngiAwd+5c5syZYzE+KyuLgIAAU9vf35/Y2Ngb2hYfH8/EiROJjY1l586dLFiwgH379jXYtvrQGPskmo8qXRVfJ33NyqSVaPTmMEq5IGdq76k8EfkEbnZNDwuU6NzotHoObUvn2M4LiAbzaohXN0dGPByCZ0D7LGR3PQzl5Vz8178o3b7D1Cd3dsZ30Qeohw9v0tynDvzOruXLTG2/kDAm/uOf1hEiOgOX15+iMsmc5VY1yBuXScHWFyIAF+OhplLvGdGXUhx4YGDATU6qP21XjLQiq1evZsOGDWg0GrKzs3nnnXcsjtf+8r8R+/fvx9fXl9zcXMaMGUNISAjR0dGm43VVTL7RkpdOp6OgoID58+cD0K9fP/LzLWuJ1Ne2+tBQ+ySaB1EU2Zuxl/cPvX+Nc+rIgJE8P+B5ujs3zrNfQqI2Oekl7F6dTGF2halPrpQx5N4gIkf5I5N3rLIA1ZmZZD45zyKJmV14OP4ff4TSz69Jc587eojtyz40OcB6de/BpJdfs46PiM5AwX9PUnXysqlPNdQHlwk9mkeIAGRZ5hfp4+NEuJ/1Fg0kMXIVa9asIS4ujj179qBWq4mOjiYszDIhVH1XH3x9jUXFvLy8mDRpEnFxcRZixN/fn4wMc1KazMxM0zl1kZycTHBwMDY1ntxHjx4lMjKyUbbVh4baJ2F90ovTeffQu+zP2m/RH+oWyouDXmSQ96BWskyiI6HXGziy/TyHf063WA3x7enCyIdDOpSD6hXKDx4k67nn0RcVmfpcpv2FLvPnNzpa5goZJ47z0+J/Y9AbVxLc/bsyef6b2DqomjQvgKjVk7/2JJoUszOxepgfznd3b94fi1flF5k22HqrItCWxchNtlKai8TERKKiolCr1WzevJkDBw4QEWFZrKg+qw/l5eUYDAYcHR0pLy9n586dvPbaaxZjBg0aRGpqKmlpafj5+bF+/Xq+/fZb0/FRo0axZs0a/GoUekJCAmlpaWg0GrRaLQsXLmTJkiUNtq2+3Mw+ieajWl/NysSVLE9cjtZgzvjobOvMs/2f5f7g+5HLmpjASEICY6TMr18nk3ve/CNGYSvntvt7EDbcr/l+abcSoihS+J//kvPuu1AjFgSlEu83Xsdl8uQmz5+bfo4fP3jLVPTOuYs3U/75Fg5OTV9FMFTrKViTjOaMWUA53u6P07jA5hUiooj2fCxXCkUkCb14NbJpK0dX03bFSCsxc+ZMJk6cyKZNmxg/fjxBQUGoVA1Xszk5OUyaNAkwbq889NBDjBs3DoDx48ezYsUKfH19WbZsGWPHjkWv1/Poo4+aVmEMBgNnzpzBzc3sA5CQkMD06dOJioqisrKSBQsWMHTo0EY/1gcffJCYmBjy8/Px9/dn4cKFzJ49u172STQfR3OO8safb5BWbC5uJSAwtfdUnur3FC521nMak+i8iKJIYkwWB74/Y1FPxqeHM6Nm9cHZs+NFYhmqq8leuJDizd+b+uSeHvgvXYqDFaIUS/Jy+f7dN6iurARA7erGA/96G7Wbe5PnNmh05K8+QXVaianPcVRXnEZ3bf7t85IslDVJFMtEO3qGDcC5sYX2roNQl19ASzBw4EDx6rwbJ0+eJDQ0tFXsaWskJSWxatUqFi9e3Nqm1AvpuWs6JdUlfHTkI75L+c6iv69HX/459J/0cZeimCSsQ2VpNbvXnOR8otn5USYXGDIhiH5junaYDKq10RUWkvn001QePmLqs+vbF/9PlqLs0qXJ81eWlbJ+wYtcvmhMw27roGLawvfw6BrY5LkNVTryVyVRfSWxM40AACAASURBVMG8euU0thtOI7s2ee76UH18MzbfPwrAAX0fmPUTUT2uTVkhCMIRURQHNuYa0spIGyU8PLzdCBGJphOTEcObf75JXmWtED2FA8/2f5a/9P6LtCUjYTUyT11m19fJVBSbs6i6+6kY/dc+ePh3rEiZK2jOpZHxxBNoL1ww9TlPnIj3mwuR2TY9skVXXc2WD94yCRG5QsHEF/9lHSFSoSVvVRLaTHOItfP47jhG+zd57vpyIeE3gmvun7UNZXr3pq/0XI0kRiQkWpHS6lLeP/Q+P5750aJ/RMAI/jnkn3irGl4NVEKiLvR6A4d+SuPIL+ctaspEjgrg1vt6ILdG7ZI2SPnBWDKfeQZDSc32hiDg9fcXcJs92yrbGwaDnp+XLSLrVLKpb9y8FwjoE3GDs+qHvlxL/spEtBfLTX3O9wbheJt1/TVuascFs/OqW+/bmmXlTBIjEhKtxMFLB1mwfwHZ5eYUzu527swfMp8x3cZIYdQSVqP0chU7V5ywqLBr76jkjkdCCYyoO0N0R6Bo82Yuvf6GKZGZYGeH7wfv4zRmjNWuEbNmBamxB0zt22fMJiQq+gZn1A99WTX5KxLR1gqzdpkUjHpIy1baPp9bSLfqVKj5OBp0m/X+7WojiREJiRamUlfJ4sOLWX96vUX/XYF3MX/IfMlBVcKqXEguYNfKZKrKzVFZ/iGujP5rH1TOHbNmkSiK5H/yCfmffW7qU3h64v/ZZ9hHhFvtOsd2/MSx7T+Z2gPunsjAeyY1eV59STV5K46jyzU6wiKA6+SeqAa2/Erpb/tieEQwvnbyFN54+TaPn4okRiQkWpDTl0/z4u8vWkTKuNi68M+h/2Rc4LhWtEyio2EwiBz+OZ1D29JM2zKCTGDIhO70v7NbhwvZvYKo1XLp9Tco/t4cMWMbEkLA55+h9LHeqkJa/BH2rl5uavcaOozbH57d5Hl1xRrylyeiy68lRKb2RnVL42vjNNoWvYGcZHO6CJ1Po3xT64UkRiQkWgBRFPn21LcsPryYaoPZcXBEwAhev/V1POw77lK5RMtTWVbNrlXJZCSbM3Q6ONsw9vFwfIM77sqbobyczOeep7xWviXV8OH4LVmCXN30hGNXKMi8wNaP3kMUjSHRPsG9GTfveQRZ0/xudIVV5C1PRH+5ytghA7e/hOAQaf3aaPXh15M5BFefghr/ea8+w5rtWpIYkZBoZgqrCnlt/2vEZMaY+uwV9rwy+BUmBU+SfEMkrEru+RK2f5FIWaG5fpFfbxfunB2Og1PTMou2ZXT5+WTMfYKqEydMfc7334/PwjcQlNbLiVFRUswP7y2kutLoy+Ho7mmVwne6gkqjECmqed7kAu4PhmAf3jo/VERRZOnuM3wmnDH1yQOaL+OzJEYkJJqRw9mHefn3l8mtNJf3DnEL4f3o96V6MhJW5/TBS+z9z2n0OnMSswHjujF4QlCHzB1yher0dC489jjazExTn8eTf8Pj6aetKvZ1Wi1bFv0fxbk5ACht7bjvpQWoXFybNK82r4L85YnoS2pWTeUC7g+HYh9q/RDa+vLLiRyyL2USaGd8rKLcBsG76RFC10MSIxISzYAoinxz4hs+OvoR+ppKlwAPhz7M8wOex0becX+hSrQ8Br2BA9+fJWG3uZaUrYOC0bP6ENi3Y28BViUnc+HxOegLahK4yWR4v/46rn+ZatXriKLIrq8+4eLpmhBeQWD8My/iFRjUpHm1OeXkrUjEUFrjYKyQ4fFIH+x6NU3gNAWDQeSjX1PoJzOvigg+kaBoPofnjhlY3kZ49NFH8fLyIjz8+t7bO3bsoHfv3gQHB/Puu+/edM6YmBhmzJhhFfsCAwOJiIigX79+DBxYt2NSQ+2TMOYOeSHmBT488qFJiLjZufHpqE95efDLkhCRsCpVZVp++iTBQoi4+qiY8srADi9EKg4d4vwjM01CRLCzw3/ZMqsLEYAj234k+fc9pnb0Q7MIHjikSXNWXyon7yuzEBGUMjxmhbWqEAH45UQ2p7JL6S9LNXf6N29RTkmMNCOzZs1ix44d1z2u1+uZN28e27dvJzk5mXXr1pGcnHzd8QDx8fHcYoUaClfYu3cv8fHxXJ2av7H2dXZSClN4cNuD/HrhV1NfpGckG+/ZSLR/03MPSEjUpiCrjO/ePUTmKXMF1+6RHkx5eQAuXh2v0m5tSvfs5cJjj2MoM2YmlTk50XXVShzvGGn1a51PjOf3/3xtaoeNGM3Ae+9v0pzVWWXkLz+OoSbkWrCR4/FoOHat7GBsXBUxipCBshTzgYDBzXpdSYzUwaZNmxg6dCiRkZEMGzaMvLy8m59UB9HR0RaF7q4mLi6O4OBggoKCsLGxYdq0aWzZsuWGcyYkJJCVlcWQIUMICgoiJiamUbbVh8bY15n5+dzPTN82nfMl5019D4c+zNdjv6aLqum1LyQkanM+qYDNHxyhJL/K1Df43u7cNTcCG7uOvQNfvGULmU8/jagxOnvKPT3otnYNDv37W/9auTls/fh9c+RMz96Mfmxek3xRqjNKyVueiKGiJhmbrRyP2eHYdm96Zd+msj0pm9M5pSjQESmcNR8IaHxR1vrQZl+xEd80n6NM4szEGx4fOXIkU6ZMAWDhwoVs3LiRefPmmY4PHz6c0tLSa85btGgRo0ePrrcdWVlZBAQEmNr+/v7Exsbe8Jz4+HgmTpxIbGwsO3fuZMGCBeyrFcbWENsEQeDOO+9EEATmzp3LnDlzmmxfZ8QgGvjk2CesSFxh6rNX2PNm1JuM6y7lDpGwPsf3ZvDHxlSu1DlV2soZ/dc+BPVrnRDQluTyf/5Lzttvm9rKgAC6rlqJTa3PKmuh1VSx5cP/o6rUmEpe5eLKhBfmo2hCdI4mvZj8r08gaoxbuIK9As/Z4di0gbpABoPIx7uNqyGhwgXshRqHWueu4NS8mV/brBhpTVavXs2GDRvQaDRkZ2fzzjvvWByv/eXfFOqqmHwjta3T6SgoKGD+/PkA9OvXj/z8/Ebbtn//fnx9fcnNzWXMmDGEhIQQHW3eSmiofZ2Rcm05r+x7hZiMGFNfoFMgH438iB4uPVrPMIkOiUFv4I+NqST+lmXqU7vZcs+8SNz91K1oWcuQv3w5eR+aC4ja9upFwIrlKL2snxBMFEV2fvkJeennAJDJFdz7wnzUbo2PcNGcKyJ/9QnEauMqi8xBgcdjEdj4to3n7uekS6TkGLe9blWanVebe4sGJDFyDWvWrCEuLo49e/agVquJjo4mLCzMYoy1Vkb8/f3JyDA7nWVmZuLr63vd8cnJyQQHB2NjY3SAPHr0KJGRkY227cq1vLy8mDRpEnFxcRZipKH2dTYySzN5es/TnCkyv2mH+Q3j/ej3cbRp/V85Eh2L6kodv6xI4sIJcyKzLt2duOuJiA6b1v0KxvTuy8j/7DNTn32/fgR8+QVy5+bZ2ji89QdO7f/N1B41+wn8eoc2er6qM4UUfJOMqK0RImolno9FoPS2XjK2pqA3iHz8q9lh9X7PTKgJUCKgaY669aHNipGbbaU023UTE4mKikKtVrN582YOHDhARITllpG1VkYGDRpEamoqaWlp+Pn5sX79er799lvT8VGjRrFmzRr8/IwVGhMSEkhLS0Oj0aDValm4cCFLlixplG3l5eUYDAYcHR0pLy9n586dvPbaaw2yrzNzOPswz8c8T5GmyNQ3K2wWz/V/DrlM3oqWSXREygo1bF2WQEGWuYx88AAvRs0MRWHTsV9voiiS+/4HXP7a7EDqMHgwAZ9/hkzVPF/kF5KOs++/q03tvqPH0XdU47dcq05fJn9tMuiMq80yRxs8H49A2YacjLfEZ5Gaa3x9qW0V9KquFazQAisjkgPrVcycOZOlS5cyfPhwUlJSCAoKQtXIF/yDDz7IrbfeyunTp/H392flypUAjB8/nosXL6JQKFi2bBljx44lNDSUqVOnmlZhDAYDZ86csXCATUhIYPr06URFRTF48GCeeeYZhg5tnFNRTk4Ow4YNIzIyksGDB3P33Xczbty4etvXmdmetp05u+aYhIhSpuTt297m7wP/LgkRCatTcLGMze8fthAiA8cHcufssI4vRAwGct56y0KIqIYPJ+CrL5tNiJRezmfbUrPDqm+vUO7469xGz1eZXED+GrMQkTvb4Dm3b5sSIqVVWv69/ZSp/fQAe2SlF40NpQq6WK+44PUQ6vILaAkGDhwoXh1OevLkSUJDG78M1pFISkpi1apVLF68+OaD2wCd4bkTRZGvT3zNkiPm1Sh3O3c+GvkR/bz6taJlEh2VrJRCtn+RiKYm6kImExg5I4SQW1u2jHxrIBoMXHrtNYo3bTb1qUePwm/xYmQ2zZOrR6/T8d1b88k6ZVwVcHB2Yca7HzfaT6QiMZ/L606BoUaIuNjiOacvCjc7q9lsDf5vWzLL9xmLd3o52vL7+ELstjxmPNg9Gmb+dIOzzQiCcEQUxUZV02uz2zSdnfDw8HYjRDoDOoOOd+PeZcPpDaa+IOcgPh/9Ob5qyY9GwvqkHs7h19XJGGp+UStt5YybG07XPq2XIrylEA0GLv1rgUXlXafx4/F9712r1pm5mn3rvjEJEUGQcc+zLzVeiCTkcnnDaajJzC93s8Pz8QgUrm1LiKTmlPL1/nRT+593h2J3aal5QAv4i4AkRiQkbkqFtoKXf3/ZotDdwC4D+WjkRzjbtn5eAImOx/G9GezbYHYmdHCy4Z6nIvHs2vEdo0W93ihEfvjB1Od83334/N/bCPLm25ZKjT3Aka3ma942bQYBYX0bNVf50RwKv0uBmo0HhYc9no9HIG9jjsaiKPLGTyfQ1azcDO7uxoRIX4g9aB4kiREJidanWFPMk78+yfH846a+uwLv4u1hb0tp3SWsjiiKxG1N4/C2dFOfq7cD9zwViZOHfesZ1kKIej2X5v+T4lrJFZ3vvx+ft99CkDWfi2PhpSx2fP6RqR00YDCDJ0xu1Fzlh7Ip/D7VLES8HIxCxLHtfV5sT8pm/xljyIxcJrBwQhiCtgKyawWQ+Ddq16XBSGJEQuI65FXkMWfXHIvQ3UfDH+XZ/s8iEyTfbwnrIhpE9m1Iscgh4h3kzN3z+mKnar6tibaCUYjMp3jL/0x9zlMm4/Pmm80qRLTVGn5a/G+qKyuM1/Tqwl1PvtCoa5b9eZGiLeaspUpvFR6PhSNXtz0hUlGt4+2t5oiZGUO7EerjBGn74EpxT89QsG+ZOjmSGJGQqIOM0gzm7JxDZpm5JPmrg1/lodCHWtEqiY6KXm9g9+qTpB7KMfV1DXNj3JwIlLYdO2IG6hYiLg9MwXvhwmYVIgB7V39F3oV0AORKJfc+/yp26oYnISv9I4viredMbaWfGo9Hw5G3USH56d4zXCw2lhJwV9nw/JhexgMZtbJst0BI7xUkMSIhcRVnCs8wZ9cc8iqNNYnkgpy3h73NPUH3tLJlEh0RbbWeHV8mceFEgamv56AujJoZilzR8VfgTFEzFkLkAbwXvtHsQuTUgd9J3P2LqX3HrLl0CQpu8Dylv2VQvD3d1LYJcMTj0XBk9m3zKzYtv5zlv6eZ2i/fFYKzfY1oshAjLeMvApIYkZCwIDEvkb/t/hvFmmIAbOW2LLp9ESMCRrSuYRIdkuoqHVuXJXDpTLGpL/x2P6L/0gtB1vFLL4iiSPabb1K82Rw101JCpCj7Eru++sTU7h0VTcSosQ2ep2T3BUp2mYtj2gQ64TErDFkbLVZoMIi8vOk41XpjmE+/ABem9Pe/chAy4syDJTEiIdHyxOfG88SvT1CuLQdApVTxyR2fMMh7UCtbJtER0VRo+emTBHLSSkx9A8cHMvje7p2iBpQoiuS882+K1pvD5Z0nTWoRIaLTatn68XtUV1YC4NLFhzGPP9Wgf3dRFCnZdZ7SPeaSGbZBzrjPDEPWhrfWVh9IJy7dWFJALhN4a2I4sivCtyAVqmqySju4g3vL1deSxIiEBHAs9xhP7HqCCp3Ric3F1oUvRn9BmIeUcVbC+lSWVfO/j+PJzzBnVb1tSjD9RndtRataDlEUyf1gEYVr15r6nO65p9mjZq6w79vV5JwzOqbL5ArufvYlbB3qnxFVFEWKt6dT9rvZp8y2pwvuM/oga8NZcdPyy3n/F3Om1SdH9CDCv1Z6gqu3aFpQFHf8DclWIiMjg5EjRxIaGkpYWBgff/xxneN27NhB7969CQ4O5t13373pvDExMcyYMaPN2tceOZJzhLm75pqEiJudG1+P/VoSIhLNQnmxhh8XH7MQIrc/2KvTCBGAvKVLubxqlantOG4cvu/+u1nziFzh7JFYjv5sDh2Onv5XvHv0rPf5oihSvPWchRCx6+2KxyNhbVqI6A0iL36XQFVNob4Qb0eevuOqx32hdZxXQVoZaTYUCgUffvgh/fv3p7S0lAEDBjBmzBj69OljGqPX65k3bx67du3C39+fQYMGMWHCBIsxVxMfH88tt9zSZu1rbxzOPsyTu5+kUmdcrnW3c2fl2JX0cGm55UmJzkNZYRVbPoqnKMcofBHgjhkhhEZ1niy+BStWUPD5F6a2etQo/D54H0HR/F9HpQX57PjMMp9I//ET6n2+aBAp+t9Zyg9eMvXZ9XHH/aEQhDbubPz1/jQOny8EQCETWPRAJDZX29xKzqsgrYzUyaZNmxg6dCiRkZEMGzaMvLy8Bs/h4+ND//79AXB0dCQ0NJSsrCyLMXFxcQQHBxMUFISNjQ3Tpk1jS61kP3WRkJBAVlYWQ4YMISgoiJiYmAbb1pz2tScOZR+yECIe9h6sGrdKEiISzULp5Sp+WHzMJEQEmcCYR/t0KiFSuH49uYs+NLVV0cPxW7K4WVO8X8Fg0LN92YdUlZUCoHb3YNzfnqu3n4hoECn8PtVCiNhHeOA+ve0LkbN5ZXzwy2lTe97IYML9rsoeXV5g9BkBkCnAt+k/ehtCm10ZORnSfEXXQk+dvOHxkSNHMmXKFAAWLlzIxo0bmTdvnun48OHDKS0tvea8RYsWMXr06Gv609PTOXbsGEOGWCrNrKwsAgICTG1/f39iY2OvPt2C+Ph4Jk6cSGxsLDt37mTBggXs27ev0bZZ2772QnxuPPN2zzMJEU97T1aOXUl35+6tbJlER6SssIoflxyjJM/4epPJBe58LIwet3i1smUtR/FPP5G98E1T22HQIPyXLm22ondXc+h/35ORbMwsKggy7n76H9g7OtXrXFEvUrgphYpjuaY++36euD3QG0Hetp2N9QaRf3yXgEZn3J7p4+PEvJF1hC9nHjLf94kEZctm/G2zYqQ1Wb16NRs2bECj0ZCdnc0777xjcbz2l//NKCsrY/LkyXz00Uc4OVm+8OuqmHwjla7T6SgoKGD+/PkA9OvXj/z8/EbbZm372gsnC07y5K/mFREvey9Wjl1JoHNg6xom0SEpKzSuiNQWIuPmRtC9r0crW9ZylO7ezcVXXoWazxS7vn3x//xzZHYtUzQu+0wKBzb+x9Qecv9U/EPD63WuqDdwecNpKo+bP2sd+nvhOqV9hF9/8dtZjl0wRsgo5dfZngG48Kf5fgtv0YAkRq5hzZo1xMXFsWfPHtRqNdHR0YSFWToy1nf1QavVMnnyZKZPn879999/zXh/f38yMsxhYZmZmfj6Xn/JNjk5meDgYGxqfkkcPXqUyMjIRtnWHPa1B84WnWXurrmUao3/Rm52bqwYu0ISIhLNQlmh0Vm1MwuR8gMHyHruedAbU4zb9uxJ16++RK5Wtcj1q6sq+XnZIgw11/fp2ZtbJz9Yr3NFnYGCdaeoqpWQTjXYG5f7gtuFEDmcfpnFu1JM7afv6Ekf3+usBtUWI11vbWbLrqXNipGbbaU0F4mJiURFRaFWq9m8eTMHDhwgIiLCYkx9Vh9EUWT27NmEhobywgsv1Dlm0KBBpKamkpaWhp+fH+vXr+fbb781HR81ahRr1qzBz88PMPqLpKWlodFo0Gq1LFy4kCVLljTYNmvZ1964kuK9UGN04nK0ceSrMV9JWzMSzYJRiByluLYQmRPeqYRIZUICGU89jajVAqDs1pWAlSuQu7i0mA17Vy+n8NJF4/Xt7Bn/9IvI6hG1I2oNFPz3JFWnLpv6VLf64HJvj3YhRIoqqnlm3TH0NRV5B3Rz5W8jruMPp62ErKPmdtehLWChJW3b66YVmDlzJkuXLmX48OGkpKQQFBSEStVwBb9//37Wrl3Lnj176NevH/369ePnn38GYPz48Vy8eBGFQsGyZcsYO3YsoaGhTJ061bQKYzAYOHPmDG5ubqY5ExISmD59OlFRUQwePJhnnnmGoUMb96Jpqn3tjezybB7f+Ti5lcY9XweFA1+M/oLebr1b2TKJjkh5sYYtHx2zECJjHw+ne6RnK1vWcmjOniVjzlzECqPDrsLbm26rVqH0ajk/mZTY/STt3Wlqj3r0CVy6eN/0PFGrJ3/NCQshoh7mh8uE9iFERFHkpU3HTbVnnO2VLH3wFpTy63zlZx0Fg1Ew4h4M6pb3ZRLq8gtoCQYOHCgePnzYou/kyZOEhjaf42p7IikpiVWrVrF48eLWNqVetOXnrrCqkEe2P0J6STpgTPH++ejPpcyqEs1CVZmWHxYf5fJFYyZfmUxg7Jxwgvp1HiGivXiR9Iemo8vOBkDu4kK3b/+LbVBQi9lQWpDPmhefoqrcmM+ld1Q0dz/z4k393gzVegq+OYHmrDlFv+OIAJzGdms3PnOr96fxxk/mirxfzhjA2LAbiLDfF8Get4z3b5kBE5c16rqCIBwRRXFgY85ts9s0nZ3w8PB2I0TaMpW6Sp7a85RJiChkChaPWCwJEYlmQVOh5X9L401CRJAJ3Pl4WKcSIrrLl7kw+zGTEBEcHAhY/lWLChHRYGDHZ0tMQsTJ04vRjz15cyGi0ZH/9Qmq080p+h1HdcVpdNd2I0SSsop552dzltVZUYE3FiJg6S/SLaqZLLsxkhiR6LDoDDpe/O1FjucdB0BA4N/D/020f3QrWybREblS9C7vQo0DuQCjZ4V2qvBdfVk5GXPmUp1mrAgrKJUELPsE+6v87pqbY79s5UJSgrEhCNw17wXsVOobnmOo0pG/KonqC+YAAKex3XAa2X4y45ZpdDy97pipCF6YrxOvjg+58UkGvWVxvFbwFwFJjEh0UERR5O2Db/Nb5m+mvpcHv8y4wHGtaJVER0VXrefnz46Tfc78i3rkwyH0Gnxz/4SOglhdTebTT1GVlGTsEAR8P/gAVVTL/tIuyMxg339Xm9qDJ0y+aRivoUJL3qoktJnmFP3O47vjGO3fTFZaH1EUeXnzcdLyawp92shZ9lB/bBU3cdbNOQGamtet2htcW8ehXxIjEh2SzxM+Z3PqZlN7dvhspodOb0WLJDoqep2B7V8mkZVSZOob/pee9LmtfYfBNwTRYODiq/Op+POgqc/7jTdwGje2Re3Q63Rs//RDdNpqADy7dSdq6o3f9/pyLfkrEtFeKjf1udwbhPo2v2a11dp89fs5th03Z4f9v0kRdPeoR/CFxRbNrS1aHK82khiR6HB8l/Idnyd8bmpP6DGBZ/s/24oWSXRUDAaR3auTuVArD8Wtk3rQd2TADc7qeOR+sIiSbdtMbc9nn8H1L1Nb3I6D3683VeOVKxSMf+rvyBXXTzWvL60mb0Uiuiu1ggCXScGoh/g0u63WZF9qHu/tMPuJzBjajftuqaeYOn/AfL8V8otcQRIjEh2KfZn7ePvg26b2bb638UbUG+3G+Uyi/SCKIvvWp5B62JwifOD4QPqP7daKVrU8BatXc/nrr01tl2l/wf2JJ1rcjkupp4n9YaOpfdu0R/DoGnjd8foSDXnLE9HVhF8jgOvknqgGtq+ttYzLFTy97hg16UQY2M2VBffUs5ipKMIF82qWJEYkJKxAamEqL/7+IgaxxnnLPYzFIxajlDV/ES6JzkfcT2kk/W4uLhlxux+D7+1cCfSKt20j9933TG316FF4L1jQ4uJfW1XF9k8/RDQY3/v+oeEMuHvidcfrijTkLz+OrsCYhwMB3Kb2xqGdORtXVuuZs/YIRRXGHCFdnGz57OH+dad7r4vCNCgzRj1h6wRdWi+PlCRGJDoE+ZX5PLX7Kcq1xn1fH5UPy0Ytw0Hp0MqWSXREEnZncPjndFO756AuDP9Lr061Ald+8KCx3kwN9v3747doEUI9sptam9+/XW3Ksmpjb8+4J59HJqvbDt3lKvJWJKK/XCNEZAJu03rj0Ld9hV9fcVg9ecnofGojl/H5wwPwcmxAvZ/zV9Wjuc6/WUsgiRGJdo9Gr+HZvc9ysdz4YeSgcOCTOz7Bw77zpN2WaDlOHbzEH9+lmtpdw9wZNSu0XWTmtBZVp1PIfOppqEnzbtOjBwGffdpihe9qcyEpgfhftpraI2fNxdmrS51jdQWV5C1PRF+kMXbIBdwfCsE+rP19Vnz1+zn+l3DR1H5zYhj9u7o2bBKLejStE9J7BSkdfDORkZHByJEjCQ0NJSwsjI8//rjOcTt27KB3794EBwfz7rvv3nTemJgYZsyY0WT7qqqqGDx4MJGRkYSFhfH6669bxb6WRhRFFuxfYMolIhNkfHD7B1Kad4lm4XxSAXvWmB0FfXo4M25uOPLrpdnugGhzcsiYOxdDmTEMVuHlRdflX7VovZkrVFdW8MsX5s/WoAGDCbt9VJ1jtXkV5H553CxEFALuM/q0SyHyy4ls3q3lsPrQkK5MG9yIfChtINnZFTrPO6iFUSgUfPjhh5w8eZKDBw/y6aefkpycbDFGr9czb948tm/fTnJyMuvWrbtmzNXEx8dzyy23NNk+W1tb9uzZQ0JCAvHx8ezYsYODBw9ajGmMfS3NFwlfsD1tu6n94sAXpaRmEs1CTnoJO75KRKzxFHT3U3P3vL4obVpvabul0ZeVkzH3CVN2VZlKRcBXX6JspWrev61dRUme0YHYTu3IO/9PlwAAIABJREFUnXOernOrTJtTTt6XxzGUGEN+UcjweCQM+xC3a8a2dRIzi3lufTxXKrkMCnTl9Xvr6bBam7JcKDBGHiG3Ad/+1jOyEUhipA42bdrE0KFDiYyMZNiwYeTl5TV4Dh8fH/r3Nz65jo6OhIaGkpWVZTEmLi6O4OBggoKCsLGxYdq0aWzZsuWG8yYkJJCVlcWQIUMICgoiJiamwbYBCIKAWm3MSKjVatFqtde8iRtjX0uyM30nnyV8ZmpP7TVVyiUi0SwU5Vaw7dMEdNVGB0lHNzvufToSW4fO4xwtarVkPfccmlM1v8gVCvw+/hi7kJtk+Gwm0hOOcnz3DlP7jkefQOVy7TZF9cUy8r46jqHMuKUkKGV4/DUMu14N3NJoA1wsqmT2N4eo1OoB6ObuwJczBt48sVld1I6i8e0PypbfYqtNm/UZ+fSJPc0297wv7rjh8ZEjRzJlyhQAFi5cyMaNG5k3b57p+PDhwyktLb3mvEWLFjF69Ohr+tPT0zl27BhDhgyx6M/KyiIgwJyPwN/fn9jY2BvaFh8fz8SJE4mNjWXnzp0sWLCAffv2Nco2vV7PgAEDOHPmDPPmzbOKfS1FamEq/9r/L1N7qM9QXhnySqdyIJRoGSpKqvnpkwQqS41fZrYqBfc+E4nKxbaVLWs5RFEk+803Kf/jD1Ofz8KFqIfd1ir2VJWX8cuXS03tnoOjCIm6dkW0OrOUvJVJiJU6AARbOR5/DcM20LnFbLUWZRods785TG6pcZvJ2V7JqlmDcFPZNG7Cq5OdtTJtVoy0JqtXr2bDhg1oNBqys7N55513LI7X/vK/GWVlZUyePJmPPvoIJycni2N1VUy+0ZepTqejoKCA+fPnA9CvXz/y8/MbbZtcLic+Pp6ioiImTZpEUlIS4eHmtMkNta+lKNYU8+zeZ6nUGfMDBDgGsOj2RVIIr4TVqa7Sse3TBEpqclHIlTLufjISV+96ZLbsQBR8+RVF320ytT2efBKXyfe3mj0x36ygrMD42Wfv6FRnETzNhRLyVyUhVhlXEQQ7OR6PhmPb1ema+do6Or2BZ9YdM0XOKGQCXzw8gB6eN663c0Mskp21rr8ISGLkGtasWUNcXBx79uxBrVYTHR1NWJhl7HV9Vx+0Wi2TJ09m+vTp3H//tW9cf39/MjIyTO3MzEx8b7D3mpycTHBwMDY2RiV89OhRIiMjG2VbbVxcXBgxYgQ7duywECMNta8l0Bv0vLLvFTJKjXbZK+z5eOTHONu2v186Em0bvd7AL8uTyD1vfD8JAox9LAyfHp3rtVa8bRt5H31kajtPnIjH00+1mj3njh7ixG+/mtqjH3sSB2dL51lNejH5X59A1NQIEXsFnrPDsfF3bFFbrYEoiry5NZk9p8zJ9d65P4Jbe7g3flJNKWQfr2kIEDC4aUZagTYrRm62ldJcJCYmEhUVhVqtZvPmzRw4cICIqypO1mf1QRRFZs+eTWhoKC+88EKdYwYNGkRqaippaWn4+fmxfv16vv32W9PxUaNGsWbNGvz8jGl9ExISSEtLQ6PRoNVqWbhwIUuWLGmwbQB5eXkolUpcXFyorKzk119/5eWXX26Qfa3BZwmf8UeWean4rdveoqdrz1a0SKIjIooiv69L4cKJy6a+2x/qTffI9pWLoqlUHD3GpVfnm9oOQ4fi89abrbZCWlVexq6vPjG1e0dF02voMMsxZ4so+OYEYo1/j0ylwGN2BDa+TVhFaEU+iznLmj/Pm9pPjujB1IFNLDeQeQhqkkPSJQzsWz4S6mokB9armDlzJkuXLmX48OGkpKQQFBSEStXwJdn9+/ezdu1a9uzZQ79+/ejXrx8///wzAOPHj+fi/7N33uFRlNsf/8yW9EIapNFCAoQUehHpxYIICor0jl7lqj/LtTcs6LXr9eq1UAQFREBFRURAegeBFEghlFRI72XL/P6YMJsgJYQks5udz/P4PHvenZ09kt2dM+8553syMtDpdHzyySfceuuthIeHM2HCBHkXxmw2k5ycjLe3pdr72LFjTJkyhf79+9OnTx8eeeQR+vWrX294ZmYmQ4cOJTo6mt69ezNy5EhGjx5dZ/+UYMvZLXxx/AvZnh05m1vbNe0gLhX74K9N54jfZdFw6DWqHREDbWtw2o1SlZpK2j//iVgldaA4hIQQ/PFHCA71rFFoALYvX0xJvhQguni2YNisB2o9X5GUT+7SGoGImx6/+6NtNhD57uA53vk9Qbbv7BrIk7c0gGxBTbEzBSXgayJcri6gKejVq5d46NChWmsnTpwgPDxcEX+sjdjYWBYvXsz777+vtCt1orH/dimFKUz6ZRJlRmmgVf/A/nw6/FO0CioGqjRPkg6dZ9NXcbLdsW8rRszsYhX1Uk2FqaiIM5MmU3XqFABaLy/arf4Oh9bKDQA8c+wIaxe+JNt3Pv4sHftaCmjLT+aR+008GKVrmsbDAb95Uej9bFOFeXP8ee5ffkieOXNzqA+LZ/auX+fMpSwZBWd3S4/vWQKRDVP/IwjCYVEUe9XntVabprF3IiMjbSYQaWzKjeU8se0JORAJcgvi7UFvq4GISoOTeaqQLUtPyHZgWAuGTQ23q0BENBhIe/RRORARHBwI/u9/FQ1EqsrL2FQjPdOx7821A5G4XHJXnACTdOXWejriNy8Kna9zk/vaEBw+m8f8FUfkQCQi0IP/Te3ZMIGIoVxK01ykrTIdUZeiBiMqVs/C/QtJLpDEeRy1jmrBqkqjUHChjA2fHsdklLb4vfxduP0fUWj19pPNllp4X6Nsr0WDImDhQlx63LjQ4o2wY8XXFOdIek9O7h4Mm22ZClx2PJu8VQlcvHJrvRzxmxeNzltZ3Yz6knS+mNlLD1FZ/Tls4+3C0ll9cHdqoG7BtENgqhZ/8wkD98tL5zc1dfqWCYJwmyAICYIgJAuC8Mxlnm8jCMKfgiD8JQjCcUEQRjW8qyr2yE/JP/Fj8o+y/WyfZ1Wpd5UGp6LUwK//PU5FqaQl4uyu5475XXFyta928bylX1Pw/fey7fvIw3iOvkNBjyA17jjHNv0q28Nm3i+Lm5UdvUDeypNyIKLzccLvga42G4icyy1j6qL9FJZLn0NfNweWze6Dn3sDatpcTM8AtBtw5eOamGsGI4IgaIH/ArcDXYBJgiBcqj37ArBaFMXuwETgU1RUbpCk/CRe3/e6bI8OGc24MOW0DVSaJyaTmY1fxFBwXkoDavUaRj0UjaefbW7x15fibdu48M47su0x5k58H3xQQY/AUFFRS9wspGcfOt88GIDSw+fJ+y4BqlMZOj9n/B6IRmejYnRZhRVMWbSP80WSqJmLg5YlM/vQzreBNW3OWLoRbSoYAfoAyaIopoiiWAWsAsZecowIXFSS8QQyUFG5AcoMZTyx/QkqTNKY7xDPEF7s96Jd5e5VGh9RFNmxKpH0hAJ5beSsLvi3t680YEViIhlPPAlmKTXg3L07Aa+/rvj3bffq5RSel+bgOLq4yuJmJQcyyV+TaAlEWrngd380Wg/bDERySiqZ8tU+UvMkcT0HnYavpvciKriBP4fGSqusF4G61YwEAak17DSg7yXHvAJsEgThYcAVuKy6liAI9wP3A7RpU48Jgyp2gSiKvLbvNU4XngYkYbP3Br+Hi942q+JVrJfjW9OI32m5d+o7NoQOPVoq6FHTY8zLI+3BhzCXlgKgCwwg+JP/oFGwhRcgMzmBIxt+lu0h0+fi7u1Lyd4MCn46Ja/rA1zxnROJ1k1Zf+tLYbmB6YsOcCq7+t9fI/C/qT3oH9oI04TTD4NRusHDOwQ8Ahr+PepJXXZGLhcaX9oPPAlYKopiMDAKWC4Iwt/OLYriF6Io9hJFsZefn32JB6nUnR+Tf+SXlF9k+/m+zxPqFaqgRyrNkTMxOexekyTbHfu2oudtbRX0qOkxV1WR9vAjGKqHeAouLrT+7DN0Pjeg7tkAmIwGNn3+H8RqYa620d2JGDKC4p1ptQORIDf85kXZbCBSWmlk5pIDxFfLvGsE+HBiN4Z1bqSi0jPWWS8CdQtG0oCaPV3B/D0NMwdYDSCK4l7ACWiEsE6luXOu6BxvHnhTtu8KvYuxoZdmBVVUbozc9BI2LYqTx7D7h3gwdGpnxdMSTYkoimS9soDyw4elBUEg6N13cOqkfIH4wfXryDl3BgCdoyMj582neHsahb+elo9xaO2O39woNDY6Obm8ysTcrw/x1zlLivDf46MZHd2IIzfO1FDobmt7wchBIEwQhPaCIDggFaiuv+SYc8BwAEEQwpGCkeyGdFSl+WMwG3h6x9PyALx2Hu14ru9z13iVisr1UV5cxa+fHsdQPUDNzduR2/8RjU5vX7o1eV9/TeG6dbLd8onHcR+mzBiOmuSmp7Jv7UrZvvneqQjHKynaeEZec2jnge/cSDTOtqlOUV5lYs7XB9mbkiuvLRgTwb03KvN+NYxVkHrAYreznnoRqEMwIoqiEfgn8DtwAqlrJk4QhFcFQRhTfdgTwDxBEI4BK4GZolLSrlZCRUUFffr0oWvXrkRERPDyyy9f9riNGzfSqVMnQkNDeeutt6553m3btjFt2rQb9i81NZWhQ4cSHh5OREQEH330UYP4dyN8dvQzYnNjAdBpdLw96G2cdfbV0aDSuEidM7EU50p5c72jljse6oqLh21u89eXkp27uPC2pXPGc+xYvOfMUdAjCdFs5o8v/oPJaATAPySMUH1Xijafk49xDPHEd3YkGkfbDEQqDCbmLTvEnlOWQOTp2zozo3+7xn3jjL+g+kYPr3bgGdy473ed1OmvKYriBmDDJWsv1XgcD1hXmKUwjo6O8uRfg8HAgAEDuP3222vNkjGZTMyfP58//viD4OBgevfuzZgxY+jS5dLOaQtHjx6le/cbFyDS6XS899579OjRg+LiYnr27MnIkSNrvXd9/Ksvh7IO8VXMV7L9aPdHCfdRRwOoNCy7VyeRkVS9LS7AyNld8A22zbkl9aXy9GnSn3jC0jnTrRv+Cg6/q8mxzRtJPxkPgEarZVj0dEq2pcvPO4a1wGdaFzQOtrmLdTEQ2ZWcI6/969ZOPDikQ+O/uRWnaEAdlHdZ1qxZQ79+/ejatSsDBgwgO/v6M06CIODmJv3IGQwGDAbD377sBw4cIDQ0lJCQEBwcHJg4cSI//fTTVc977Ngx0tPT6du3LyEhIWzbtu26fQMICAigR48eALi7uxMeHk56enqtY+rjX30orCzk2V3PIlbXRfcN6Mv0iOkN/j4q9k3cznRitls+433HhNjdFF5TcTFpD83HXCQVTOpatSL4Px8r3jkDUJybw84VS2T71h73YzpWIttOnb3xnR5h04HI/csPszOpdiAyf2gTFefXEjuzvr0Dq93neu++0Y127ie+++Wqzw8dOpR77rkHgAULFrB69Wrmz58vPz9w4ECKi4v/9rp3332XESMsXc0mk4mePXuSnJzM/Pnz6du3dkd0eno6rWvMewgODmb//v1X9e3o0aOMHTuW/fv3s2nTJl588UV27rREvHX1rSZnzpzhr7/+ahD/rpeLbbxZpZKWgKejJ2/c/AaavzdjqajUm4zkAnasSpTtDj1a2l3njGgykf7kk1SdlopABUdHgj/5BJ0VdDaKosiWxZ9RVS6lEfq3GYdHjof8vFMXH3wmd0bQ2ebvQoXBxAPLD7Mj0XJj+8TIjk0XiJgMcK7Gb7cV6YtcxGqDESVZunQp3333HZWVlWRlZbFw4cJaz9e8+F8NrVbL0aNHKSgo4O677yY2NpbIyEj5+cuV1Vxtq9RoNJKbm8tzz0lFnd26dSMnJ6fWMXX17SIlJSWMHz+eDz/8EA8Pj1rPXa9/9eGXlF/4/czvsr3gpgW0crWOWQkqzYPivAo2fh6DuXqImk+wG8Nn2NfwO4DsDz6gdPsO2Q544w2coyKv8oqmI/nAXk4d2o+AQC/f22itDZOfc472xfu+Tgha2wxEyqqMzP26do3IYyM68vDwsKu8qoHJOAoGSccEzzbgZX2BuBqMXMKyZcs4cOCAXO8xaNAgIiIiah1zvbsPLVq0YMiQIWzcuLFWMBIcHExqqkVPLi0tjcDAK7d1xcfHExoaikP1luqRI0fo2rVrvX0zGAyMHz+eKVOmMG7c32XWr9e/6yWrNIs391vaeMeHjWd42+ENdn4VFWOVid/+F0N5sTTrw8lNz6gHo9A72uZWf30p/OVXcr9aJNs+8+YpPnPmIpVlpWxZ8j8EBPr4jaKdm+U30qV7S7zu6Yigtc3AsbjCwOylBzl4Jl9e+78RYTw6ogkDEYCzNSXgrW9XBKw4GLlWKqWxiImJoX///ri5ubF27Vr27NlDVFRUrWPqsvuQnZ2NXq+nRYsWlJeXs3nzZp5++ulax/Tu3ZukpCROnz5NUFAQq1atYsWKFfLzw4cPZ9myZQQFBQFSvcjp06eprKzEYDCwYMECPvjgg+v2DaRdjzlz5hAeHs7jjz9+2WOu5d+NIIoir+x5hWKDFDgFuwXzVO+nGuTcKiogfca2rUgg+5z0GdNoBG67PxIPH/vq0Ko4cYLMF16QbbfBg/H7v0cV9Kg2O1cuoyy/gH5+d9LGzVK07tKzFV7jwxA0thmIFJYZmL7kAMdSLToiT93WiYeGKCDgWFPszApTNKAWsP6NGTNm8PHHHzNw4EASExMJCQnB1fX6BxVlZmYydOhQoqOj6d27NyNHjmT0aKkOZtSoUWRkZKDT6fjkk0+49dZbCQ8PZ8KECfIujNlsJjk5GW9vb/mcx44dY8qUKfTv358+ffrwyCOP1OrOuR52797N8uXL2bp1K926daNbt25s2LChzv7dKGuT1rI7Q/qCCAi8PuB1Ve5dpUGJ3Z5Owr4s2R4wIYygjl4KetT0GPPzSZv/T8QKqZXZoX17At99B0FrHTtDGYkniPljI/1bjqkViLj29bfpQCSvtIpJX+6rFYi8OLqLMoGIyQjn9llsK90ZEZSSA+nVq5d46NChWmsnTpwgPFxt5wSIjY1l8eLFvP/++0q7Uieu52+XXpLOuJ/GUWaUpqRO6zJN3RVRaVAykwv48f2/MFePlu/cP4Bh0+xMYdVo5NzceZTtky5EGldX2n2/GseQEIU9kzAZjax45jE6VfUg0MVykXbrH4jnnSE2+7c6X1TBtEX7STxv6QR6/a5IpvZTqE4j/TB8WS1m5xEEj8VBI/3bCoJwWBTFXvV5rdWmaeydyMhImwlErgezaOal3S/JgUg7j3Y80v0Rhb1SaU6UFlay8YtYORDxa+PO4IkdbfbiVl8uvPOuHIgABL7zjtUEIgCHflpH56reBLi0l9fcBgXheXt7m/1bncstY+qi/ZzLk37fBEGSeJ/QmMqq1+LSFI2V/tuqwYhKk7Lq5CoOZEmSxBpBwxsD3sBJ56SwVyrNBZPRzMbPYykrqgKkgtXbHohEZ6PaFPWlcP168r7+WrZ9H/4n7sOGKuhRbfJS09DvNNCyRiDiPrQ1Hre0tdlAJPF8MVO/2s+F4koAtBqB9yd0ZWy3IGUdqyl2ZqUpGlCDEZUm5FzROT488qFsz4qYRbRftIIeqTQ3dn+fRFZKISDdAN4yN8LuClbL4+LIfFEWyMZtxHB8H3xQQY9qY6owkPXZYVo6tZHX3Ie3xnNkO+WcukGOphYwc8kBCsqkri1HnYZPp/RgeLjCMgUmA5zdY7HbD1LOl2ugBiMqTYJZNPPynpflIXihLUJ5qNtDCnul0pxI2JdZS2G1390daN3Z+yqvaH4Y8/NJf/gRxErp7tyhQwcC33oLQWMdvQrmciNpH+3Fw2z5u2j6uNt0ILInOYd5yw5RWlU9eNFRx1czetEvxEdhz5Dm0VRV1654tgav9lc/XkGs4xOq0uz5IekHDp2XCpa1gpbXB7yOg1Z5CWqV5kFuegnbvk2Q7Q49WtJ9ZJurvKL5IZpMZDzxJIaMDAA0bm4Ef/IftG7WMXvHXGbgwhfH0BZY0jDZLc8TOK6bgl7dGBtiMpm55KAciHi56Fk5r591BCIAp7dbHrcfZLX1IqAGIypNQHZZNu8dek+2p0dMJ8KnYVqEVVSqyo389nkMRoM0+M3L34Vh0+2rcwYg+6OPKd1j2ZIPfPvfOLa3jjthU6mB7C9jMGaWyWux5buJeHCUgl7dGMv3nmH+iiNUmaTPXYCnE9//4yaigj2Vdawmpy2Ku7QfrJwfdUBN06g0Om8eeFMWN2vt3poHu1pP/lrFthFFka3LT1B4QUr/6Ry13HZ/FA5O9vXTVrRpE7lffCHbvg89iPuwYQp6ZMFUXEX2VzEYz0uBiCiKHMr9nch5d+DgbHvaQqIo8t6mRD75M1leC/FzZdnsPgR7WdH/j6Gi9jya9gOV86UO2Nc3VqXJ2XJ2C3+c/UO2X77pZZx19lVQqNJ4HN+axqkjluFjQ6d2wjvw+kUKbZnKlBQyn3lWtl0HDcS3xmBPJTEVVUo7ItlSsCiKIgdyNqDp6Exon5sU9u76MZrMPP9DLN8dsozJ6Na6BYtn9sbb1crSzmkHwCTVDuETBh4NN8qjMVCDEZVGo6iqiDf2vyHbd4feTd+Avld5hYpK3clMLmDPWsvdadTgIDr29lfQo6bHVFJC2j8fxlwm7TroW7cm6O23rUJh1VhQSc6XxzHmSuqvZtHM/uxfyDCmMGv2ZzaXRiuvMvHwyr/YfOK8vDa0kx//ndIDFwcrvJTWStFYbxfNRdSakUZk9uzZtGzZstZwvEvZuHEjnTp1IjQ0lLfeeuua59y2bRvTpk2zWv9q8uHhD8kul+5afZx8eKLXEzfkr4rKRcqKqvj9qzhZ2KxlOw9uvqeJh48pjCiKZD73PFUpKQAITk4E/+djtC1aKOwZGPMqyP78WI1AxMTeC+s5V3qCm8ZPwsOvpcIeXh85JZVM/HJfrUBkfI9gvpjeyzoDEVCDERULM2fOZOPGjVd83mQyMX/+fH777Tfi4+NZuXIl8fHxVz3n0aNH6d69u9X6d5HD5w/zfeL3sv1s32fxdLSiwi4Vm0U0i2xeEkdpgbQF7eSq57b7I9Hq7evnLG/JUoo3bZLtgNdexalzZwU9kjDmlJP9+XFM+dLfx4yZ3Rd+JK0sAd/Wbel5x10Ke3h9pGSXMO7TPbXmzDwwOIR3741Gr7XSz1xlsSQDf5F21l0vAmowclnWrFlDv3796Nq1KwMGDCA7O/vaL7oMgwYNqjXo7lIOHDhAaGgoISEhODg4MHHiRH766aernvPYsWOkp6fTt29fQkJC2LZtW718ayz/AAxmA6/tfU22h7Qewi1tb6m3nyoqNTm88SypJ6pHsgswYnYX3L3tS8W37OBBLrxn6VDzmjIFzzvvVNAjCcOFMi58cRxToRSIiBrYmbWWjDIpnTZi3j/R6qx0J+EyHD6bx/jP9sjy7hoBXh0bwbO3h1t3munsXjAbpcetosDVSlqNr4LVfirSntl57YPqSfBbV48Shw4dyj333APAggULWL16NfNrFIQNHDiQ4uLiv73u3XffZcSIEXX2Iz09ndatLTMLgoOD2b9//1VeIe2MjB07lv3797Np0yZefPFFdu60/Fs1lG/19Q/gm/hvOFV4CgAXnQvP933eur+4KjZDemI+B35Oke2et7albYT1/9A2JIYLF0h77HEwSdoWzl270upp5QdNGs6Xkv1lDOYSSYUUnYaDxRvIKpf+XlHDbiGok+0MQt0Ym8mjq45SaZRad530Gj6e2J1bImygLulSfREbwGqDESVZunQp3333HZWVlWRlZbFw4cJaz9e8+N8Il5uYfLWLttFoJDc3l+eeew6Abt26kZOT0yi+1cc/gKzSLD479plsP9TtIfxdbeDLq2L1lBVV8ceiOC5+LANCPelzp3XoaDQVosFA+mOPY6r+3mu9vQn66EMEB2U7OaoySshZFIO5VLobFxw0ZLRO4/TmYwA4uXswcPJMBT2sO6Io8uXOFN787aT8WfNxdeCrGb3o3sZLWefqio3Vi4AajPyNZcuWceDAAbZu3YqbmxuDBg0iIqK2QFdD7T4EBweTmmppEUtLSyMw8MrtV/Hx8YSGhuJQ/cNz5MgRunbt2ii+1cc/gLcPvl1L8n1y+OTrek8VlcshmkU2L42ntNAyAO+WOZForDVn30hceO99yg9X1wJoNAS99y56f2WD/aq0YrIXxSKWVwcijlr0o/3Y9cE78jGDpszE2d1DKRfrjMFk5qWf4lh54Jy81t7XlaWzetPWx0ZaxsvyICtGeixooW1/Zf2pI1YbjFwrldJYxMTE0L9/f9zc3Fi7di179uwhKiqq1jENtfvQu3dvkpKSOH36NEFBQaxatYoVK1bIzw8fPpxly5YRFCRNfTx27BinT5+msrISg8HAggUL+OCDDxrFt7r4dym70nfV0hR5od8L6DX6BvNHxX45/PtZUuPzZHvErC64eTkq6FHTU7Txd/KWLpVtv0cfxfUmZbU6Ks8VkbMoFrFSShkJTlp8Z0Xy09I3MZuk4CSwYziRg6/vRkgJCssNzP/2CLuSLbvNvdt58fm0XtanIXI1zuwCqrd0AruDk/UHgaAWsP6NGTNm8PHHHzNw4EASExMJCQnB1bV+EfGkSZO46aabSEhIIDg4mEWLFgEwatQoMjIy0Ol0fPLJJ9x6662Eh4czYcIEeRfGbDaTnJxcq8D02LFjTJkyhf79+9OnTx8eeeQR+vXrV+//1xvx71JEUWThfks6a0yHMfRs1bPevqmoXCQjKZ8D6y11Ij1us786kcrTp8l8/nnZdhs2DJ95cxX0CCrPFJLzlSUQ0bjo8JsXTcq5w6TGS3fmgkbDiLkPWc2gviuRmlfGPZ/tqRWI3N09iG/m9rWtQARsMkUDIFyuLqAp6NWrl3jo0KFaaydOnCA83HYKnBqT2NhYFi9ezPvvv6+0K3XiwLEDzDk6BwB3B3fW37UeX2dfhb2o0HDHAAAgAElEQVRSsXUqSgysev2A3MYbEOrJXY91t6v0jLm8nDP3TaQyMRGQhM3ar12D1kO5O96KUwXkLo1DrJ4HpHHV4zs3CrOHyJLH/kFZodQG2/OOuxgyXdmg6VocPpvH/csOk1taJa89NqIjjwwPtc3C+0/6QE710MhpP0KHoU321oIgHBZFsVd9Xmu1aRp7JzIy0mYCkSpTFSUXx1QDj3R/RA1EVG4YURTZsuyEHIg4uuq4ZU6EXQUiAFmvviYHIoKDA8EffahsIJKYT86yeKjuMtG46/GbG4W+lStbFv9PDkTcvH3of69114ytPZzGs+ti5GF3DloN79wbzdhuQQp7Vk+KsyyBiNYBWtuO4rUajKjcMFmlWYjVOcouPl24t+O9Cnuk0hyI2ZbOmeOWbfPh08Nx87IvPZGCtWsp/OEH2W714gs4demimD/lJ/PIXR4PJun7rvFwwG9eFHo/F86nJHNs0wb52KEz5lntIDyTWeTt30/y+XZL+s/b1YHPp/Wkd7sray9ZPadr1Ay27gsO1vnvfznUYETlhiipKqG4SureERB4oe8LaDXKz8VQsW2yU4vZvTZJtqOHBtO+q5+CHjU9FSdOkPWqRTzQc+xYWlTrHylBeVwOuStOyoGItoUjfvOi0Pk4I5rNbFn8GaIo7TC0je5OWN+bFfP1apRUGvm/VX+x+cQFea1TK3e+mtGL1t62c/G+LKe3WR7bUL0IqMGIyg1gFs1klWbJ9tjQsUT5RV3lFSoq18ZQaWLTV3GYjdJFz7e1G/3HhSrsVdNiKi4m7dH/Q6ysTlGFheH/8kuK1TCUHc8mb1UCVM8C0no7SYFI9U5V7LbNZCZJ6QGtTsfw2f+wynqL1Lwy5i07xMksi/zB8M4t+WhSd9wcbfxyKIpwapvFVoORG0MURav8EKv8nfyKfCpNlbI42qM9HlXYI5XmwI7vEik4L8lv6xy13DInwq7mzoiiSObzL2A4J2ldaFxcCProIzQuyty1l/11gbzVCXK3qM7XGd95Ueg8pdbq8pJidqxYKh/fe8x4vAKsr+Ziz6kc5n97hPwyg7z2wKAQnrqtM1pNM7jm5J6CojTpsYM7BNlWN6NVBSNOTk7k5ubi4+OjBiRWjtFsJLssG1EUqSquQuegU4tWVW6YxINZnNyTKduD7uuIl7+NiE01EPnLv6k9AO+N13EMUUZptvRQFvlrkyyBiJ8zfvOi0XpY2l13r1pGRXERAB5+Lelzl3XVjImiyLK9Z3n1l3hM1Ts7eq3AwrujuLdX62u82oZI+dPyuP1A0NqWxpNVBSPBwcGkpaXVezCdStNRWFlIqaEUEZEcQw5jeoxR2iUVG6cop5zt3ybIdsc+reh8k32NEig/fpzz71iUS70mT8bj9tsV8aVkfyYFPyTLtq6VC35zo9C6WwKRrFNJHNtsmfw9dMb96B2tp8i40mjipR/j+O6QRUnaz92R/03tSc+2NiLtXldO1QhGQpqunbehsKpgRK/X0769fc2asEWS85P5x8//wCRKYkcfDv0QFycbL/xSURSzyczmJfFUVUifKQ9fJwZP6mRXO6SmwkLS/+8xMEhpBKeICFo+87QivpTsTqegxkBCfYArvnOj0Lpa7rbNZhNbFn3KxQEu7bv3okMv62klvVBcwYPfHOHw2Xx5rWuwJ59P64W/p/UETA2CyQhnanTSNKG2SENhVcGIivUjiiJvH3xbDkT6+vdlWOthCnulYusc3niWzFOFAAgagZFzInBwtp+fJ1EUyXjueQwZGQBo3N0J+vADNAoMwCvekUbhhtOyrQ92w292JBqX2tv+sVv/IOuU1PGk1esZNvMBqwkeD5/N58FvDnOhuFJeG9c9iIXjonDSN8Nuv/TDUCmlyvAIBh/bK/i2n2+7SoOwLXUbezP3AqARNDzV5ymr+QFSsU2yUgo5+OsZ2e4zuh3+7T2Vc0gB8r7+mpItW2Q7YOEbOLRu+nqGoj/PUfT7Wdl2aOuB76wINE61LxXlxUXsXPm1bPcecw8t/AOazM8rIYoiKw6c45X1cRguaqEI8NyocOYMaN98f6tq1ot0GAI2+P+pBiMqdcZgNvDe4fdk+96O99LRq6OCHqnYOlXlRv5YHIdYXVgYEOpJj9vaKetUE1N+9CgX3rV8r7ymT8Nj5Mgm9UEURYo2n6N4i2VarUN7D3xnRqC5TMvrrpXLqCiR2mM9/FrR5y7l9E8uUmEw8fJPtetDWrjo+WRSDwaENfPiehuvFwE1GFG5DtYmruVskXTX5K53Z363+Qp7pGLrbF+VQFFOBQAOzjpGzOqCpjm0WdYRU2EhaY8/DkZpwq1TdDStnnyySX0QRZGi389SvM1yEXfs4InPjAg0Dn9PaWSdSuL41t9le+jM+9E7KDtBObOwnH98c4RjqQXyWpcADz6f1tP2hcyuRUURpB202CFDlPLkhlCDEZU6UWoo5bNjn8n23Oi5eDk1s2p0lSYl8WAWifvPy/aQyZ3w8HFW0KOm5WKdiDFDamXWeHgQ9P77CE1YJyKKIoW/nqZkV7q85tjRC99p4QiXqa0QzWa2Lv5f7aLVnn2azN/LsSc5h4dX/lVr0N1d3QJ5c1w0zpcJppodZ3ZBdQ0f/tHgapu7QGowolInlsYtJa8iDwB/V38md7buAVgq1k1xXgXbVyTKdqd+/oT1bqWgR01P/vJvatWJBC58A4fgphMLE80iBT+fonSvRdfFKdwbnynhCLrLi8zFbttMZrJFaXXozPsVq8MQRZHPd6Tw9saTF4Vh0WoEnh8Vzqyb2zXf+pBLqVUvYpspGlCDEZU6kF2WzddxlmK1h7s/jJOumbXGqTQZollky9fxVJVLqQkPXycG3WdftUflMbG19USmTcN9xIgme3/RLFLwYzKlByzjHJwjffCe2PmKgUhFSQk7ayit9rpzPF7+gY3t6mUpqjDwr++P8XucZWfN182R/07uTt8QH0V8UoxmUC8CajCiUgc+PfYp5cZyADp5deKO9nco7JGKLXN0SyrpCVJuXxBgxCz7auM1FReT/vjjtfVE/tV0dSKiWSR/TSJlRyyD4py7+uE9oROC9sq7CbtXL6e8WmnV3dePvncro7SakFXMg98cJiWnVF7r2daLT6f0oJWHnd0kFaZBbvVASZ0TtLlJWX9uAPv5BVCpFykFKaxLWifbj/d8XJ3Kq1JvctJK2PfTKdnucVtbAjrYTxuvKIpkvvQShlSpWFTj6krQB+83mZ6IaBLJ+z6B8qMWlWuX7i3xurcjwlUKhy+cSeHYpt9ke+j0eYoora47ksZzP8RQYTDLazP7t+O5UeE4XGFHp1lTc1ekTT/Q224wpgYjKlflgyMfYK4eC35TwE30D+qvsEcqtorRYGLzEss0Xr827vS+w74Ulwu++47i3yzy6QGvv4ZDmzZN8t6iyUzeqgTKY3LkNZderfAaF3bVQEQURbYs/h9i9e9A2+juhPZp2jvwCoOJBT/Hs/KApfXYWa/lrfFRjO1mfUP5moyU5pGiATUYUbkKh7IOsS11GwACAo/1fExZh1Rsmv3rT5ObLm2ta/UaRszqgtaO7mYrEhI4v/BN2W4x8b4mmzsjGs3krjhJRXyuvObaL4AWYzpcNRABOLHzTzIS4gHQaHUMm9W0Sqvncst48NvDxGUUyWsd/Fz5bGpPOrZybzI/rA6zGVK2W2wbLl4FNRhRuQKiKPLB4Q9ke3TIaMJ9whX0SMWWSU/I5+hmy11t/3GheAfYzzRec1kZ6Y8/gVgltZ86duxIq2eeaZL3Fg1mcr+JpyLBMqPF7eZAPEeHXDOoqCwrY8e3S2S75x1j8Q4MbjRfL2VTXBZPfH+M4gqjvHZn10DeGheF62XE2OyK87FQVr3L5eILraKU9ecGsfO/psqV2Ja6jeM5xwFw0Djwz+7/VNgjFVulstzI5q/j5TH0bbp4EzXEvrbWsxYupOqUVCsjODtLdSJOjZ/fN1eZyF0WT2WyRQzMbVAwnrfXrfV137pVlBZIQYyrlzf9xt3XaL7WpMpo5t8bT7JoV40ZOVqBl0Z3YWq/tvbTtns1aqVoBoPGtncZ1WBE5W+YRTOfHP1Etid0mkCgmzItfCq2z67vkyjJkwaWObrqGDY93K4uJoW//ErhmrWy7f/CCzh26NDo72uuNJH7dRyVKYXymvuw1niMrNvFPDc9lSMbfpLtwVNm4eDc+Gqmafll/HPFXxytoaYa1MKZ/07pQbfWLRr9/W2GU1stj228XgTUYETlMvx+5ncS8yVBKmedM3Oi5ijskYqtcvp4Dif3WES1Bk/qhGsLZaXDm5Kqs2fJevll2fYYPRrPcXc3+vuaK4zkLImj6qylzsJjZFs8htetWFYURf5c+gVmk6TsGdS5C50HDGkMV2vxR/x5nlh9lKIaaZkR4S15996utHBp+gnGVktVKZzdY7E72P7kdDUYUamF0Wzk06OfyvaU8Cn4OtumvLCKspSXVPHnNydlO6xXS8J62Y/KqlhVRfrjT2AulYp29W3b4P/KK42+K2QuN5KzOJaq1GJ5zfP2drgPrvsU4OSDezl7/C8ABEHDsFn/aFS/q4xm3t54kq9qpGV0GoFnbu/cvKft1pczu8FULX/fsgt42n7aUw1GVGrx86mfOVN0BpCG4c2MmKmoPyq2iSiKbF+RQHmR9IPp4unAoEmdFPaqabnw/gdUxMVJhl5P0Hvvo3Vr3KJdc5mB7EWxGNJL5DXP0SG4D6j7xcpQVcm2ZYtkO3rk7bRsF9KgftbkXG4ZD688wrE0Szop0NOJ/0zuQc+26vyry5K82fI4dLhyfjQgajCiIlNlqqo1DG9GxAw8He1HkEql4Ug6eJ5TRyzCWkOndsbJVa+gR01LyY4d5C1dKtutnnwC58iIRn1PU0kVOV/FYsiyKJO2GNsBt5uur97r4E9rKcqWZNad3D24+b6pDepnTX49nskza49TXGlJywzvLKVlvFzVtMwVSf7D8ji06cYINCZqMKIiszZpLZmlUn7fy9GLqV0a70dIpflSkl/JjlWWIXhdBgTSLsp+Un3G7GwynnlWtt0GD8Zr+vRGfU9TcRXZX8ZgvFAmLQjgNS4M197+13WewgvnOfjTGtkecN80nN0aXsujwmDitV/i+Xa/pd1brxV4+jY1LXNNck9BXor0WO9i0xLwNVGDERUAyo3lfHH8C9meEzUHV7396ECoNAyiKPLnNyeoLLMMwbv5nlCFvWo6RLOZjKefwZQnTbjW+fkR8ObCRr24mgorpUAkR5ofhQBe93TEtef11+ds/2YRRoOUWmvZrgNRw29pSFcBSDpfzMMr/+JklqWmpbW3M59M6kFXtVvm2tTsomk/CHTNoyBcDUZUAFh1chU55ZKATkvnltzXqWn0BFSaFyf2ZHIuTroQI8DwGV1wcLKfn5m8JUso3VPd5SAIBL79b3Te3o32fsaCCrK/jMGUWyEtaMD7vk64dG153ec6G3OUpP2WDo1hsx5A04BzqERRZNXBVBb8HFdrtswdUQG8OT4KDyf7SePdELXqRZpHigbUYEQFKDOUsTh2sWw/0PUBnHS2O3BJRRmK8yrY9X2SbHcd1prAMPu50y0/fpwLH3wo2z7z5uF6U+NtoRvzKsj+8jimfEnDBY2A96TOuNQjJWYyGvlzqWVnNHzgUII6d2koVyksN/Dcuhh+jbG0eTvqNLw4ugtT+rZR0zJ1xVgJp3dY7GZSvApqMKICrEpYRUGlJDAU5BbE3aGNr4Og0rwQRZGty05gqJB0KVq0cqHf2MbrwLA2TCUlpD/xJBil9JRT12j8Hm481WJDTjk5Xx7HVFjd3qkV8JkSjnMXn3qd79gfG8hNk+o39I5ODJo8s4E8hcNn83hk5VHSC8rltY6t3PjPpB508rfj2TL14dxeMFTXBXmHSP81E9RgxM4pM5TxddzXsj0vah56rbpdqnJ9xO3MIO2kJBsuCDB8Rjg6h4bb4rd2sha8iiE1FQCNmxtB772HoG+c75HhQhnZX8ZgLq4ORHQCvtO64NSpfumgsqJC9qz+Vrb7jZ+Im3f9gpqaGE1m/vvnKT7emoTJLMrrk/u24cU7uuBsR5+PBqOZpmhADUbsnu8TvyevQsrxB7gGMKbDGIU9UrE1inLK2b02Wba7jWiDf4j9tIQXrl9P0c8/y3bAqwtwCG6cYXKGrFKyv4rBXGIAQNBr8JnRBafQ+utx7Fq1jMoyqR24hX8APUaNvWE/0/LLeOy7oxw8YxnO5+Gk49/jo7k9KuCGz2+3JG+xPFaDEZXmQrmxnCWxlomcc6PmqrsiKteFaBbZuvwExkopPePl70KfMe0V9qrpqDp3jqxXFsi257hxeIwa1TjvlVFCzlcxmKs7lQQHDb4zI3AMqX9dzvmUZGK2bpLtoTPuR3eDOzq/HM/g2XUxtSbt9m7nxQf3dSPYq/Fn2zRbCtPhQrz0WOsA7QYo608DowYjdsyaxDXkVuQC0MqlFXeF3qWwRyq2RuyOdNITpHojQYBhM8LR6e1j+100GEh/8l+Yy6QcvkPbtvg//1yjvFdVWjHZi2IRy6sDEUctvrMjcWzrUe9ziqLIliX/A1FKobTv3ouQHr3rfb6SSiML1sfx/eE0eU2rEfi/4WE8NDQUrUYtUr0hTtXYFWnbHxyal/SCGozYKRXGilodNHOi5uCgVRUPVepOUU45e344Jdvdb2mLf3v7Sc9k/+cTKo4flwy9nsD33kPj2vAXiMqzReQsjkWs3n0SnHT4zYnEofWNFX+e2LWNzERpdpBGq2PI9Hn1PteRc/k89t1RzuaWyWvBXs58NLG7KuneUDTjehFQgxG7ZV3Sulq6IuPCxinskYotIYoiW5eftKRnAlzpM9p+0jOl+/aT++WXst3y//6vUeTeK1MKyVkah1gl/TtrXHT4zonCIcjths5bVVHOzm8tKdoeo8bgHXj9w9auVKQ6tlsgr90VqWqHNBQmI5zaZrHVYESlOVBlqmJRrGUQ1uyo2Thqm4eKn0rTEL8rg/SEGt0z08PR6jUKe9U0GPPzyXj6aTm94dr/JrxnzWzw96lIzif363jEaoEwjasev3lR6P1vfPdl/w+rKcmXCtddW3hx0/iJ132O1Lwy/u+7oxw+aylSdXfU8frdkYztZvtTZK2K9ENQWT1I0CMI/Dor608joAYjdsgPST9woewCAL7OvowPG6+wRyq2RHFexd+6Z1q1r3/tgi0hiiJZL72E8bw0SE7r5UXAW28haBo2EKtIzCdnWTwYqwMRdz1+c6PQt7rxQKQgK5PDv/wg2wMnz8TBue6FpaIosvZIOq+sj6OksnaR6vsTutHaWy1SbXAundLbDEXi1GDEzjCYDHwV+5Vsz4qYpaqtqtQZURTZ9u3JWuJmfe60n/RMwervKf7DcmEIWPgG+pbXL71+NcpP5JL7zQkwSTsvWg8HfOdFofdrmIv8tuWLMFWLs/mHdqTLwKF1fm1+aRXP/RDDb7FZ8ppWI/DYiDAeHKIWqTYaSTWn9I5Uzo9GRA1G7IxfT/9KVqn0Q+Lt5M29ne5V2CMVW+Lk3qxas2eGTetsN+JmlSkpnH/zTdn2mjwZ96F1v5DXhfLYHHJXnrQEIi0c8ZsXhc7HuUHOf+b4X5w6tE+2h818oM67OtsTs/nX98e4UFwpr7XzceHDid3ppg64azyKsyDzqPRYo4OQwcr600iowYgdYRbNtTpopnWZhrOuYX7kVJo/pQWV7F5jmT0TPTSYgFD7uAiJVVVkPPkvxAppIJ1jWCgtn/pXg75H2bFs8r47CdUz5LTeTlIg4tUwO5eXzp+JGDyCgLBO13xdeZWJf288ydI9Z2qtT+7bhhfuCMfFQb2MNCpJFh0Y2twETs2zY039FNkRf6b+yenC0wC46d3UybwqdUYURbatSKCyWnDLw9eJfmM7KOxV03Hho4+oiJcEpwQHBwLffReNU8OlN0v/ukD+6gSobkjR+TrjOy8KnWfDFZYf2/QreemSZL2DszMDJ8+49mtSC3hs9VFSskvlNV83B94aF82ILq0azDeVq5D4u+Vxx1uV86ORUYMRO0EURRbFWDpoJnSagLuDOqRKpW4kH77AmeM5sj1sWjh6R/tIz5Tu3UveIsuOYssnn8Cp07V3FOp8/oNZ5K9LsgQiLV3wmxuF1qPhdH/KigrZ8/0K2e43biKuLa6s/2Ewmfnvn8n8Z2tyrZbdEeEteWt8NL5uavddk2CshJRtFjtMDUZUbJyDWQeJyYkBwEHjwNTwqQp7pGIrlJdUsfO7RNmOGBREUCf7ELKS2nifkW3XAQPwmtpw352SfZkU/GjpTNL7u+A7NwqtW8MKEO5etVyeP+MVEEiPUVeeQZWSXcJjq49xLLVAXnNx0PLS6C7c17s1QjPs5LBazu6BqhLpsVc78A1T1J3GRA1G7ISauiJjQ8fi5+KnoDcqtsSu75MoL5YGs7l5OdL/bvtIz0htvC9jvCC1wWu9vAh8c2GDtfEW706n8OcU2dYHuuI7Jwqta8MKhZ0/fYrjWy1b/UOmz0Or+/t7mM0iy/ed5c3fTlBRrW0C0KutF+9N6Epbn+YlP24T1KwXCbu1Wbb0XkQNRuyA+Nx49mTsAUAjaJgVMUthj1RshbOxuSTuPy/bgyd3wsHZPn42CteupfgPS0tlwMI30Pk1TBBfvD2Nwt9Oy7a+tTt+syLQuDRsICKKolS0enH+TLeel50/k1FQzr/WHGN3cq7FJ63AYyM78sCgDmrLrlIkbrQ87niLcn40Afbxq2Ln1OygubXtrbT2aK2gNyq2QlWFkW3fnpTtsN6taBflq6BHTUfVmTNkLbS08baYNLHB2niLtpyj6I+zsu3Q1gPfWRFonBr+5zhx3y7ST8YBoNFqGTx9bq3nRVFkXbWAWXENAbNOrdx5/76uRAQ2z84NmyAnGfKqd870rtC2eU3pvRQ1GGnmnC06yx9nLXd3s6NmK+iNii2x74dTlORLmhJObnoGTmi++eqaiAYD6f96CvHiNN6QEFo99dSNn1cUKfrjLMVbU+U1h/ae+M6MQNMIxcCGygq2L7fciHS/bTQ+QZYbkZySSp7/IYbf4yw7XxoB7h/UgcdGhuGos48CZaslqUYXTcgQ0DdvcUo1GGnmLIldglmU8r83B91MZ+/mN9NApeHJSC4gZnu6bA+8Lwxnd/uY6pz96adUxEjF3uj1BL37DhrnG9PjEUWRoo1nKN6eJq85hrbAZ3oXNI0kGndw/TqKc7MBcPbwpN/4SfJzG2IyeeHHWPJKq+S1tj4uvHdvV3q1824Uf1Suk1otvc07RQNqMNKsySnPYf2p9bI9N3LuVY5WUZEwGkz8udySnmkb5UNYL/vQlCg7fJjczy3CYC0ffQSnLl1u6JyiKFL4SwoluzPkNadOXvhM7YLQSMMFi3IucHD9WtkeMHEaTq5uFJRV8dJPcaw/llHr+Cl92/DcqHBcHdVLglVQUQRnd1vsMDUYUbFhVpxYgcEsdUFE+0XTs1VPhT1SsQUO/3aWgvNSikLvpGXwpE520c5pKi4m46mnwSztJLr06YP3rBsr9hbNIgXrT1G6L1Nec+rig8/kzgi6xptyvOObJRirpBRby3YdiBw6kq0nz/P02hiya8i5B3g68e/x0QzqqHbXWRUpf4K5uobHPwo8ApX1pwlQg5FmSrmxnNWJq2V7ZsRMu7igqNwYueklHNloKa686a4OuHs371z1RbJeew1DupSa0nh4EPjvtxC09U+hiGaRgh+SKT1oGSrnHOWL98ROCNrGC0TSTsSSsHenbPeZNJun18by/eG0WseN7xHMS3d2wdO5YTt4VBqAxBotvR1vU86PJkQNRpopP5/6mcLKQgCC3IIY1nqYwh6pWDtms8if35zEXK24GdDBk8hBQQp71TQU/vorRet/lu2ABa+gDwio9/lEs0j+mkTKjlyQ15y7+uE9oROCtvFuCsxmE1trzJ/xiuzDzN9yyCyskNd83Rx5c1wUI1U5d+vEbP67vogdoAYjzRCzaGZ5/HLZnho+Fa1GrYxXuTqx29M5f7oIAI1WYMiUzgh2oC9hyMwka8Grsu05dgwet99e7/OJJpG81QmUH8uW11x6tMTrno6N/u8Z++cfZJ+R2kFFrZ73CztSorMEIqOjA3h1bCTervZRjGyTZP4FpdVBrIsPBPVQ1p8mQg1GmiE70nZwpugMAO56d+4Ou1tZh1SsnuK8Cvb9eEq2e97WFu/A5q+4KZrNZDzzLOYiKQjTBwXR6sUX638+o5m8VScpj7WIh7n28afFXaGNHohUlJawa5XlJuSAe1dKdNL8KW9XB16/K5JRUfXf7VFpImqmaEJHgp3cSKrBSDNkWfwy+fE9He/BVd/8Lyoq9UcURXasTMBQaQLAy9+Fnre1U9apJiLv62WU7d8vGRoNgf9+C62bW73OJRrN5H57gooTefKa600BtLizQ5PsMO1YvYLyIik1W6x144hnNwBuj/Tntbsi1eF2tkKSfbX0XkQNRpoZ8bnxHMw6CIBO0DE5fLLCHqlYO8mHL3AmxnInP2RqZ7SN1HJqTVQkJJD9/vuy7TNvHi69etXrXKLBRM7yE1Qm5strbgOC8LyjfZMUjv+++zjHN/7Cxb/abu+bcHNz4dWxkdwZHaAWr9sKRRmQ8Zf0WKODDsOV9acJUYORZkbNXZFb2t2Cv6u/gt6oWDsVpQZ2rk6S7chBQQSGtlDQo6bBXFlJxpP/QjRIre9OERH4zX+ofueqMpG7LJ7KZMuUW/chwXjc2q7Rg4CiCgNvbjhByfr/0Q6pJTndMYCQPv1ZcXc0fu7qbohNkfCb5XHbm8G5+X8XL6IGI82IrNIsfj9t2eKb3mW6gt6o2AJ7fzxFeZGkwunq6UA/O5nIm/3+B1QmSUGY4ORE4DtvIzhcf1GnudJEztI4qk4Xymvuw9vgMaJNowci25InxFgAACAASURBVBIu8Oy6GBwyExhTfg4AEbhpyhzuuaWXuhtiiyRssDzuNEo5PxRADUaaEStOrsAoSkI5PVv1JMI3QmGPVKyZjOQC4ndalDgHTeyEox1M5C3du5e8r7+W7VZPP4VjSMh1n8dcYSRnSRxVZ4vkNY9b2uIxrE2D+HklCssMvPZrPGsOp6ERTUzO2yM/13HQCMbc2q9R31+lkagshtM7LHZnNRhRsUHKDGWsSVgj2zO6zFDQGxVrx2Q0s+3bBNlu39WXkO7NX4XTVFhIxjPPyrbr4EG0mDjxus9jLjOQvTgWQ1qJvOY5qj3ug4IbxM8rsTn+PM/9EMOFahXV6KJYvAxSesjB2YURU2c26vurNCLJW8BUPSuoVRS0aNyg1tpQg5FmwvpT6yk2FAPQxr0Ng1sPVtgjFWvmr01nyc8sBUDvqGXgfR0V9qhpyFrwKsbz0pRarZcXga+/ft3pDFOpgZxFMRgySuU1zztDcL+58QTi8kurWPBzHD8etexkOZvK6F90RLZvGj8RF0/7qTFodtRK0dRf58ZWUYORZoAoiqw8uVK2J4dPRiM0/24IlfpRcL6MQxssku99x4TYheR74c+/ULTB8oMf8Nqr6PyubzfIVFJFzlcxGLLK5LUWd4Xi1q/x9Ds2xGTy0k+x5JRYJuz6ujnwkD6O/HOSoJlXQBDdb7+z0XxQaWRMxtpTeu0sRQNQpyuWIAi3CYKQIAhCsiAIz1zhmAmCIMQLghAnCMKKhnVT5Wrsy9xHSqGkuuiic2Fsh7EKe6RirYiiyLYVCZiMUudFy7buRA1t3NSCNWDIzCTr1Roqq+PH4T5ixHWdw1RURfYXxy2BiABe48MaLRC5UFzBP5Yf5qFvj9QKRMZ2C2TV+Dbk/2WZPzNkxly0OnXGjM1ybi9UVHdjuQdCQDdl/VGAa+6MCIKgBf4LjATSgIOCIKwXRTG+xjFhwLPAzaIo5guC0LKxHFb5OytOWmK/saFjcXOon2iTSvMnYX8W6QmSFoagkSTfNc1c8l1WWS2W0pj61q1p9exz13UOY2ElOV/GYMwplxYE8Lq3I649Gn6+iyiKrDuSzqu/xFNYbpDX/T2ceOPuSIZ1bsnqBc+CKM0QatetJyHdeze4HypNyKUpGjvshKpLmqYPkCyKYgqAIAirgLFAfI1j5gH/FUUxH0AUxQt/O4tKo5BWnMb21O2yPanzJAW9UbFmykuq2L0mWba7DgvGr427gh41DZdXWa27KrExv4LsL2Mw5VXPeNGA932dcena8AW/6QXlPLcuhu2J2bXWJ/VpzbOjwvFw0pOwdxdpJ2IlV7Rahkyb2+B+qDQhoggnf7XYdpiigboFI0FAag07Deh7yTEdAQRB2A1ogVdEUdx46YkEQbgfuB+gTRv7qhRuLL5L+A4R6Q6pf2B/2nu2V9gjFWtl77pTVJRId9pu3o70ufP621ltjYrExL+rrPao++AxY265FIgUSN0raAV8JnXGOdK3Qf00m0W+3X+Wt347SWmVSV4P9nLmrXHRDAiT3s9QVcn2bxbJz3e7dTQ+wa0b1BeVJubCCSioruFycId2A5X1RyHqEoxcbr9IvMx5woAhQDCwUxCESFEUC2q9SBS/AL4A6NWr16XnULlOyo3lrEtaJ9uTO6vS7yqXJyOpgBN7MmV78MRO6B2b9wAuc1UVGU89bVFZ7dLlulRWDTnl5Hx5HFNhdb2GVsBnajjO4T4N6ufpnFKeXnucA6ctM20EAWb2b8eTt3TC1dHyM33o53UU50i7Js7uHtw0Xt0JtXkSauyKhA4HnX2q5tYlGEkDaobewUDGZY7ZJ4qiATgtCEICUnBysEG8VLksv6b8SlGVJLgU7BbMgKABCnukYo2YjGa2rbBoioR096NddMPe2VsjOf/5D5UnTwIgODpel8qq4UIZ2V8ex1xcXbOh0+A7vQtOHb0azD+jycyXO0/zweZEqqoLigE6+Lny9j3R9GzrXev44twcDvxk0RK6+b5pONVzqJ+KFVFTAr7zHcr5oTB1CUYOAmGCILQH0oGJwKW34D8Ck4ClgiD4IqVtUhrSUZXaiKJYq3B1YueJaO1k1LTK9XF087namiITwhT2qPEpO3SI3K8s6YyWTzyBY4e6Sd0bskrJ/jIGc6kUiAh6DT4zuuAU2nCBSGx6IU+vPU5chkW9VasR+MfgEB4eFoaT/u/f5Z0rlmKslNJFfm3aETXcfia6NluKMiH9sPRY0ELYSGX9UZBrBiOiKBoFQfgn8DtSPchiURTjBEF4FTgkiuL66uduEQQhHjAB/xJFMffKZ1W5UQ6dP0RSvjRbw1nnzF2hdynskYo1UphdzsFfz8h23zEhuHk1b00RU0kJGU8/I3ebuPa/Ca+pU+r02qr0EnIWxWAuk8YqCA5afGdG4Bji2SC+VRhMfLwlic93pGAyWzLVkUEevDUumsigy79PesIJTuzaJttDZ96PRr35sH0Saw7G6w/ODRfw2hp1Ej0TRXEDsOGStZdqPBaBx6v/U2kCaoqc3RFyB56ODfNjqdJ8EEWRHasSMBmkFIBvazeihjSeSqi1cP7NNzGkpwOg8fAgYOFCBM21JZWqUovJXhSLWFEdiDhq8Z0diWNbjwbxa19KLs+tiyElx6Lc6qjT8NjIjswd0B6d9vI+imYzfy79QrbD+vandUR0g/ikojBqikZGVWC1QbJKs9h6bqtsq+28Kpfj1JFszsVVF0UKMGRyZzRXuOA1F4o3b6ZwraWo2//ll9D7+1/zdZVni8hZHItYKXWyCE46/OZE4tD6xlufiyoMvLnhJCsPnKu13qe9N2+NiyLE7+p1H3E7tnI+RdoF1er1DJ46+4Z9UrECKoshxSLLYI8S8DVRgxEbZG3SWkyi9KPZ2783Hb3sY66ISt2pKjeyc3WibEcNCqJV+4a5w7dWjDk5ZL4ob9jicccdeN5x7bvNypQCcpbGIVZJO0gaFx2+c6NwCLzx4tDf47J46adYzhdVymtujjqeub0zk/u0uabgXFV5GbtWWiYM9xo9Ds+W1w6uVGyAxN/BVP25aBUFXu0UdUdp1GDExjCYDaxNXCvb93W6T0FvVKyV/etTKKtuSXXxcKDvXXUr3rRVRFEk84UXMeVL6rK6Vq3wf+nFa76uIjmf3K/jEatTWRo3PX5zo9D7110U7XJcKKrglZ/j2BCTVWt9RHgrXr8rEn/PutXt7P9hNaUF0v+Tm5c3fe6654b8UrEiTvxsedxljHJ+WAlqMGJj7EjdQXa5pDPg4+TDsNbDFPZIxdrIPldMzLY02R5wbxiOzs37q16wZg0l27bJdsDCN9B6Xr2OqiIhj5zlJ6C6rVbj7oDfvCj0LV3q7Ycoinx3MJU3NpyguLr2BKTBdgvGRDIqyr/OU4ILsjI5/OuPsj1wyiwcnJzr7ZuKFWEoh6Q/LHa4OuSwef9CNUNWJ66WH48LG4deqw7HUrEgmkW2r0y42EhCcGcvQns171FRVampXHjzLdn2mjoVt5tvvupryuNzyf32BJikfyitpwO+86LR+9b/Yn86p5Rn1x1nX0perfV7egbzwh3htHCpm8bJRbZ/swiTUQpoAsI6EX7z4Hr7pmJlnNoKhupCZp8w8OusrD9WgBqM2BCpxansydgDgIDA+I7jFfZIxdqI25XB+dOSdoVGJzB4Uqc634nbIqLJRMbTz2AukybpOrRvT8snrt7UVxaTQ97Kk1DdWqtt4Yjf/dHovOvX8mwwmfliRwofbUmqJV7W1seFhXdHcXPo9QvMnY05SvLBfbI9dOb9deoIUrERaqZowu+0y8F4l6IGIzbEmkSL+uKAoAEEuTX/Nk2VulNWVMW+H0/Jdo9b2tKiVf1TDrZA3pIllB85IhlaLYFv/xuN85V3N8qOXiBvdQJUxwxaHyf85kWha1G/QORoagHPrD3OyaxieU2rEZg3MIRHh4fh7HD9WiBmk4ltX38p210GDSMgtFO9/FOxQkyG2lN61RQNoAYjNkOVqYofky354wmdJijojYo1snddMpXVYl0evk70vK2twh41LhUJCWR/9LFs+z74IM5RUVc8vvTwefLXJMqTtXS+zvjNi0Lref2zQEorjby7KYGle87IKTG4tnhZXTi+eSM5qdLgNL2jEwMnzaj3uVSskNM7oKJQeuzZGgK7K+uPlaAGIzbClnNbyKuQctH+rv4MDLLPyY4qlycjKZ+T+yydG4MmdkJXj7tyW8FcVUXGv56yDMGLisL3gfuveHzpwSzy1yVZApGWLlIg4n59dRwAf568wAs/xpJeUC6vOeu1PD6yI7NubndF8bK6UF5SzO7V38h237sn4ObdsIP5VBRGTdFcFjUYsRFWJ1gKV8eHjVfn0KjImExmtq2waIp06O5H28jmfQHL+fhjKhOl/2fByYnAf/8bQX/5Yu6SfRkU1Ehf6f1d8Z0bidbt+gKRC8UVvPpzPL8cz6y1PjDMl4V3R9Ha+8ZTYntWf0tFiZTy8WzZip53qGMemhVmE5ysMaVXTdHIqMGIDZBSkMKh84cA0ApaxoWNU9gjFWvi2JZUeRCezlHLgGY+CK/s8GFyFy2W7ZZPPoljSPvLHlu8K53CXywzO/VBbvjOjkTrWvcuNLNZZPWhVBZuOEFRjXZdb1cHXhwdzl3dghqkSDjn3BmO/fH/7J13YFRV2oefmUnvvRJqCi303ouAgqKCoq69ru66+llWsay9667bdHdFxF5QUbGAoPTeIYWSQCCk916m3e+PG+9NqCGZmTuZOc9f5z25M/cdSGZ+c96m5hJMvvF2PNo5ZVjQRTi5A+pL5LV/FCSM1tYfJ0KIkS7Al0e+VNZTEqYQ5efapZqC9lNX2dRmEN6oS3u59CA8S139KUPwxhH6uzOPQ6hdf5LqFccV2yshkIjbBqK/gJ4r2SV1PP5NGjty2pbrzhsWz5Nz+hPmbxuxIEkSaz9YhGSVM2u7DxxE4sixNnlugRNxcLm67jsHxAm3ghAjTk6TuYnvjn6n2AuSReKqQGXTl1mYW+aphMX5M2haN409si8lr76KKU9u6CYPwXvxjCWvNb/mUrP6hGJ79Qgi4tYB6H3a95bXbLbwn3VHeXvtUYwWtVy3e5hcrjsh6cLLdc/F0V3byU3fD4BOp2fKzXe5dEm2WyJJp+eLCBSEGHFyVp1YRa1RjiF3C+jGmLgxGnskcBZyM8s5uqdUsSdfl4zBhQfh1a5bR9WX6ilhzF/+ctoQPEmSqFl9gto1J5U9797BhN88AL13+76F7sip4LFlBzhaqk7XNeh13DWpN/dN61i57rkwm0ys++hdxR488xIiu/e06T0ETkDhPqhu+b30CYZek7T1x8kQYsTJWZalTiCdnzwfvc51P2wE7cdisrLhczVpNWV0DHFJoRp6ZF/MlZUUPqnOmgm8+GKCLm07BE+SJKpXHqduvdoK3zsphPAb+6Nvh4CobjDx8oqDfL7zZJv9wd2CeXneIPrH2WfQ4J6fvqO6WK6E8vEPYNzV19vlPgKNyWwVokmZDaJ7dhuEGHFiTtScYHfxbkBOXL0iUWTWC2T2rs6lukQuLfXyMTBufqLGHtkPSZIoeuZZLGVlABgiI4h5+qk2YQxJkqj+4Rh1mwuUPZ+UUMJv6I/O89wCXpIkvj9QyHPfZ1JWp07X9fcy8OdZKdw4tieG80zX7Sh1lRVsW/aFYo9bcD2+ga49XdktESGa8yLEiBPzTdY3ynpit4lE+No2Ti3omtSUNbK7VWLm6Mt74xfkulUXNT/8QO3PPyt23Asv4BGqngJJVomq5Uep36aW3Pr0Dyf8d33ReZxbiJysaODJb9NZf6S0zf6M/tE8O3cAcSH2HUy36bMPMDXJojK8W3cGXXSJXe8n0IiSTCjPktee/tBHDDg9FSFGnBSz1czyo+qx3rxEUc4rkNn0ZRbmlpH3EQkBDJzkumMBTEVFFD33vGKHLFhAwGR1YJxklahclkXDrmJlzzc1grBrU9CdI3/GZLGyeFMOf//lCE0mNUE1OsibZ+cO4OKBsTZ+JadTmHWYjPW/KvbUm+/C4CHekl2SDPWLJSkXg6eYvnwq4jffSdmUv4nSRvnbWoRvBBO7iY6rAjieVkbO/jLFnnxdCnoXTVqVrFYKH38ca62cwO2ZkED0o4+oP7dIVH51hIa9Jcqe75BIwq5OQWc4e1hlb24lj3+TzsHCGmVPp4ObxvTg4VkpBPrYP5YvWa2sff8dxU4cOYYeg4bY/b4CDZCktmJkwJXa+eLECDHipLROXL2sz2V46MV/lbtjNlnY+IWatNpvfCwxvTs+A8XZqfzsM+q3bJUNnY64V15G7+8PgGSxUrH0CI371fCK3/BoQucnoTtLfkdNk4k3fj7MR9tOtJkn0zcmkJfnpTK0u+MSgDM3rqUw+zAABg8PJt9wu8PuLXAwxelQni2vvQIg8SJt/XFSxCecE1LWWMaGvA2KfWWiUNIC2Lsql5qyJgC8/TwYe0UfjT2yH8bjxyl5/Q3FDr/9NvyGDwdAMlup+OwQjRnlys/9R8UQckXiGYWIJEmsTC/ime8zKK5RE1R9PPXcPz2ZOyb2wtOBp0vGxgY2fvaBYg+fcwUhMfYPCwk0ok2I5hIRojkLQow4Id8f/R6LJDeyGhY1jF7BZ251LXAfasoa2b1SbeI15vLe+HZgyFtXQDKbKXh0IVJTi/BKSiLivvtafmal/JODNB1UO6L6j40lZG6fMzYJy6ts4OnvMvj1UEmb/cnJkTx/+UC6h3d+nsyFsv3bL6mvlP33Dw1j9JWikaHLIkI07UaIESdDkqQ2IZork8QvrwA2Ls3C0pJoGdk9kP4TXTdptfzdxTTul7uR4ulJ3GuvovfyQjJZKPvoIM1HKpVrAybEEzyn12lCxGyxsmTzcf62+giNJouyHxHgzdOX9efSQbGadDitKipk9w+tquSuuxkvX8cLIoGDKDoAFS2zkbyDoM90bf1xYoQYcTL2le7jeM1xAPw9/ZnZY6a2Dgk053haGccPqEmrk65NRm+nvhda03TwIKVvvaXYkffei0+/fliNFso/yKD5aLXys8ApCQTN6nGaqNh3sorHl6WR2SpBFeD60d155OK+BPtq12xq/ceLsZjlYXuxiSn0nzhVM18EDqBNiGY2eLru3KjOIsSIk9H6VOTinhfj5ym+NbkzpyWtjnPdpFWr0UjBI4+CyQSA75AhhN9+G9ZmM2VLMjAeV8VF0EXdCZzevY0QqW1JUP3wlATVlOhAXpo3kOE9whz2Ws7EiQP7yN65TbGn3nLXGefqCFwESYJ09f1chGjOjRAjTkS9qZ6fj6vNneYlid4i7s5pSatXum7Satk//0lzltwYSufrS9wrLyOZoey9dIy5tcp1QbN6EjQ1QbElSWJFehHPOkmC6pmwmM2s/UAt5R0weTqxSSkaeiSwOwV7oaolz8s7GPqIU7BzIcSIE/Hz8Z9pNMvdGBNDEkmNSNXYI4GWnJq0Onqu6yatNuzeTfni9xQ76s8P4xEVT+m7aZjy6pT94Nm9CJykTiY+WdHA08szWHNKguqk5Ehe0ChB9UzsX/0T5Xm5AHj6+DLhups19khgd1qHaPrOAQ9v7XzpAggx4kS07rh6ReIVYoS4m7PpSzVpNSIhgAEu2mnVWl9PwcLH+C224j9uHEFzr6J0URqmQnVybsjcPgSMiwPkDqpLNufw5uqs0xJUn7qsP5dplKB6Jhpqqtmy9BPFHjPvGgJCtQ0ZCeyMJEHGt6otQjTnRYgRJyGvNq/NULw5veec5xECV+ZERvnpnVZdNGm1+LXXMZ2UJ+XqAwOJeuJZyhalYS5ukC/QQcgViQSMlntx7Mmt5PFlaRwqqm3zPM6QoHomNn/+Ec0NsqgKiYll2OzLNfZIYHfy90C1fBKGTzD0nqKlN10CIUachO+PqRMdx8ePF0Px3BiL2cqmpVmK3XdsjMsmrdZt2EDVF+rU2qhH/0LVt0WYS+VwJToInZ+M/4hoqhtNvLbyEJ/uyD2tg+qLV6YyvIfjOqi2l+KcoxxYo+aBTbnpTjw8nUssCexARqvE1b6XgYdrhldtiRAjToAkSXx/VBUjl/UR46Xdmf2/nqSq5VTAy8fA2CsTNfbIPliqqih84knFDpw5l6acGCzlqhAJW5CC75BIlu8v4LnvMymra5ug+n8XJXP7BO0TVM+EJEmsff9/Svip55Dh9B42UmOvBHbHaoXM71RbhGjahRAjTsDekr2crJWPqQM9A5maILKu3ZW6ymZ2/nRcsUdd1hu/INf8VlX03POYS+XZMh5xfTDEXomlXK4cQq8j7NoUSuP9ePK9HWzMKmvz2KkpkTx3+UASwpwjQfVMHN6ygfxDmQDoDQam3HSH0+SxCOxI3g6olt/P8QmB3pPPfb0AEGLEKWiduDqr1yy8DSLr2l3Zsiwbc7OckBkW50/qFNdMWq1ZsYKan34CQOcXid+kR7BUy/1FMOgIvjaF90qr+NfSXTSbrcrjooO8efqyAVwyMMapP9hNTU1s+OR9xR568WWExyec9XqBC5H2pboecAUYRFiuPQgxojFN5qY2vUUu7yOS29yV/COVZO0sVuxJ1ySjd8LwQ2cxlZRQ9MyzAOgCogm46AmkphZh4aGjfEYCt6zOJLtELenV6eDmsT15aGYygT7O/+a+Y/lX1JbLpz5+wSGMveo6jT0SOASLqW1Jb+rV2vnSxRBiRGPWnVxHnUl+0+0e2J3BkYM19kigBVaLlQ2fq51Wk0ZEEZ/ifAmZnUWSJAr/8hcs1dXoA2Pxm/gw0NIi20PHN718+euK9DaPGRgfxEtXpjKoW4jjHe4A1SVF7Fz+tWJPuO4mvP38NfRI4DCOrYOGlmnSgXHQfZym7nQlhBjRmO+OqolOl/W5zKmPngX2I219PhUFcvmnh7eBcfNdM2m16quvqF+/AX1QN3zHP4DOKxAAi0HHXwxNbMhSZ8/4exl4aGYKN43tgUcXOiFa9+FiLC0t7aN7JzFw8kUaeyRwGAeWquvU+SDa/bcbIUY0pKyxjC0FWxRbVNG4Jw01RnZ8n6PYIy7pQUCo6w3UMublUfLyK+iDu+M3/gF0XvJpQZMOHrTUccCiNi+bNSCaZ+YOIDbYVyt3O8TxA3vJ3rlVsafd+nsxf8ZdMNbDoR9VW4RoLgghRjTkx2M/YpXk5LwR0SOID3DNZEXBudn23VGMjfIk1+AoX4ZM766xR7ZHslopXPgYeEfjN+5+dC0DIOuQeEhqIANZiMSH+PLc5QOY3i9aS3c7hMVsZu37befPxCX31dAjgUM5vAJMLR2DI5IhZpC2/nQxhBjRkNZVNHP7zNXQE4FWFB+v4eCWQsWeuCAZg6frfZOu+OBDmo9V4Tfu/9B5yqcdNUg8QD2HsWLQ67hjYi/un56En1fXfFvav+pHKvLlkk4vXzF/xu1I+0pdpy6Qs64F7aZr/tW7AIcqDnGkUk5Y9DH4MKPHDI09EjgaySqx8Ysj0NJNtGdqOD0GhmvrlB1ozs6m4oMf8B13HzoPOfxUiZUHaCAbK8O6h/Dilan0iw3S2NOO01BdxZYvP1XsMfOuFfNn3ImGCsherdqp87XzpYsixIhG/HD0B2U9rfs0ArwCNPRGoAWHthVRnFMDgN5Dx/irkzT2yPZIJhMFz76Nz4h70LW0xK6QrNyva6DcR89Llwzg2pEJXX7uzqbPP1Tmz4TGxjNstjjpdCsyvwWrHGolfgSE9dbWny6IECMaYLFaWJGzQrEv7X2pht4ItKC50czWb7IVe+hF3QmJct5uoh3lyMsf4BdzKbqWxk+VVjP36psYNiSGJ+b0JzKw6zf4KzqaRdpa9Vvx1JvvxODh/L1QBDakTYhGJK52BCFGNGBPyR5KGksACPMJY0zcGI09EjianT/m0Fgrl3/6h3gz/JKe2jpkY+qbzax4azWj6/qgM8hvMzWmBl6I9OKl+SOZkOQagyAlq5U1S/6rzJ/pPWwkvYaO0NgrgUOpzoMTm+W1Ti9m0XQQIUY04MdjavnXzB4z8dSLb1HuREVhPWlr8hR7/PxEPL0NGnpkW1ZlFLFq6QHub/RFp5dfV1NTFRum9OKDOf3w8XSd15q5cS2FWYcBMHh4MOXmOzX2SOBw0tUGd/SaDIFdrxLMGRBixMEYLUZWnVil2HN6z9HQG4GjkSSJTUuPYLXK36TjkkJIHBGlsVe2Ib+qkae/y4CD5Twl+Sj9NSz1JXBtX+4eP0BjD21Lc0M9Gz5ZotjDL72S0Jg4DT0SaELrWTQiRNNhhBhxMJvyN1FrrAUgPiBetH93M3L2l3HyYCUgV/5NvCa5y3fdNVmsLNmcw5urs5hs0vO45Iu+5TVZagvxHwMRLiZEALZ+9RkN1VUABISFM/rKBRp7JHA4JQehKE1eG7yhn2hc2VGEGHEwP+X8pKxn95rd5T+IBO3HbLSw6cssxR44KZ6Ibl27impPbiWPL0vjUFEtl+LJI5KPKkRq8tGZtxB+wz809tL2lOedZO/K7xV78g234eXTtbrFCmzA/s/UdcrF4NN1y9O1RogRB1JvqmfdyXWKPbvXbO2cETicfb/kUlveBIC3vwej5nbd8r/qRhOvrTzEpztykSSYhycP4gst2tpSfZKmA+/Se9lnLie4JUlizfv/w9rSvr5bv4GkjJuksVcCh2O1tJ1FM/h32vniAggx4kDW5K6h2dIMQHJoMomhrjkMTXA6tRVN7F5xQrHHXN4HH/+ul7gsSRLL9xfw/A8HKauTf5cX4MV9qLN0LJXHadjyd+JeehbPaNdL5sveuZXctH0A6HR6pt5yl8sJLkE7OLYOalu6J/tFQOJ0Td3p6ggx4kB+zFGraMSpiHuxZVk2ZpM8hyi8WwD9J3S9RMcT5fU8+W06G7PKlL3r8eKe1kKk4igNW/5J4PRJBF3qesnZJmMz6z5crNiDZ15CVM+ue8Il93uKhQAAIABJREFU6AT7P1fXgxaAoet9uXAmhBhxEOWN5Wwr2KbYl/S6RENvBI4k/0gl2btKFHvSNUldquNos9nCO+uP8a+12RjNVmX/Xm8/rm1W30LMZVk0bvsnhpBAYp552iVPC3Z+9xU1pcUA+AQGMW7BDRp7JNCEpho4qOYMMfha7XxxEYQYcRA/H/8ZiyTHmIdFDSMuoOt9MxZcOFaLlY1fqEmrSSOiiEsK1dCjC2PbsXKe+CaNo6X1yp4e+Gd8FEPym5Q9c+khGrf9GyxGYp9/E4/QrvMa20tVcRE7vlM7bU689iZ8AwI19EigGQeXg7lRXkcNEBN6bYAQIw6idRWN6C3iPmRsLKA8vw4ADy89Y+d1jTyhinojL/10kK9257XZHxgXxJvREfjuVUM1lorDihAJnj+PwKlTHe2uQ1j34btYTHLX3OjeiQycJoZbui37WlXRDL5WTOi1AUKMOICTtSfZX7ofAA+dh5jQ6yY01ZvY/v0xxR5+cU8Cw3zO8QjtkSSJL3fn8fJPB6lsMCn7Ad4ePDQjicvLrTRsLVSvN+bRsOkfYDXjGRdH9GOPaeG23cnZu4uju9Qw67Rb70avd51OsoILoPIEnNgkr3V6OV9E0GmEGHEAK3NWKutx8eMI9XG9I2zB6exYfozmenmSZ1CED0NmJGjs0bnJLqnjiW/S2J5T0Wb/koExPHVpf3zW5lG/vUjZNwQ3UfXhi9ASfox96SUMAV27b8qZMJtMrP3gHcUeMOUi4pL7auiRQFNal/P2mQaBMdr54kIIMeIAfj7+s7IWiavuQXl+Hekb8hV7/PwkPJx0JkuTycJba7P57/qjmCySsh8f4stzlw9gWkoUlV9nUb+7WPmZd6If5f95UBEioTfdiP+Y0Q733RHs/vFbKgsLAPD282fidTdr7JFAMySpbaOzwddp54uLIcSIncmpzuFwpTxIy0vvxdQE14ynC1QkSWLj0iO/DXKlW99Qeg1xzim1m7LKePLbNI6XNyh7Br2OOyb24v7pSfgaDFQuPUzDvlLl576DI6j98SWkejkXxqt3b6IefNDhvjuC2vIyti1TSzjHLbge/xBxsum25O2EiqPy2jsI+or8P1shxIidWXVcHYo3sdtE/D39NfRG4AiO7S0l/7A8s0Sn1zFhQZLTlbmW1TXzwg+ZfLuvoM3+0O4hvHRlKv1ig5AsViq+OETjATVZ1W94NNaazTTu2iVvGAzEvfoKeh/nzoXpKOs/Woy5WW7uFpHQgyEzxYePW7PvU3U94ArwFCMAbIUQI3Zm5XE1X2RWz1kaeiJwBGajhc1fZSv2wMnxhMc5Tx6F1SqxdNdJXl5xiOpGNUE10MeDRy/uy+9GdUev1yGZrZR/doimjHLlGv/RMfgOkDg+/01lL+L3v8c3NdWhr8FR5KYf4PDWjYo97ba70RucM9QmcACmJshYptoiRGNThBixI0erjpJdJX8weRu8mdxtssYeCezN3tW51FbI/Td8/D0ZdWkvjT1SOVJcy+PL0th1orLN/tzBcTx5aT+iAuXTDclkpfyTgzQdUhNZA8bFETSrG8evuw6ppbzVp39/Iu6523EvwIFYzGbWLPmvYqeMm0RCf9cUXYJ2cvhHaKqW1yE9oPtYbf1xMYQYsSOtQzSTuk3Cz9NPQ28E9qa2ook9K9X5M6Mv7+0U82eaTBb+tSaL/60/htmqJqgmhPnywhWpTE6OVPYkk4WyDzNpzqpS9gImxRN8SS/K/vUvmjMPAqDz8iLutVfReWr/+uzB3hXLKc/LBcDTx5fJN96msUcCzdnzkboecr3oLWJjhBixI62raGb2nKmhJwJHsLXV/JmIBOeYP7Mxq5Qnvkknt0JNUPXQ67hzUm/um5aEr5cadrAaLZS/n0HzsWplL3BqAkEze9CUlkbZ/9Ty1sgHHsA7sWs0cLtQ6irK2fKVWjEx9qrrCAxzzgRkgYOoypUH4wGggyFiQq+tEWLETmRXZnO0Ws669vXwZVK8GDHuyhRkVZHVav7MxAXazp8pq2vm+R8y+e6UBNXhPUJ56cpUUmLatjG3NpspW5KB8XiNshd0UXeCLuqBtbGRgkcXgkUu4/UbMYKwm2+y/4vQiPUfv4epSW71HRafwLBL5mrskUBz9n4CtJwq9pkGIc7dM6grIsSInfj5hHoqIkI0ro3VKpfy/kaihvNnzpagGuTjwWOz+3HNiITTRJK10UzZknSMubXq9Rf3JGiK/IZb8rc3MebkAKD38yP2lVfQ6fUOeDWO52TGAQ5tXq/Y02+7G4OHeJt0a6wW2PeJag+7UTtfXBjxV2YHJElqE6IRVTSuzaEthZSdbJk/46lnnEbzZ7KKa3n8mzR2Hm+boHr5kDienNOfyEDv0x5jbTBR+l46prw6ZS94Tm8CJ8YDUL91K5UfqbHy6Ccex6tbvJ1egbZYzGZ+fa9V0urYiXQfOFhDjwROwbF1UH1SXvuGQcpsTd1xVYQYsQNHKo+QUy1/k/T18GVC/ASNPRLYi+YGE9u+O6rYQ2f1cPj8mbN1UO0e5scLVwxkUqsE1dZY6oyULU7HVKhO5A25vA8BY+VcF0tNDQWPPa78LGDKFILnzbPTq9CevSu/V5NWvX2YfNPtGnskcAr2tkpcHXwteJwu6gWdR4gRO9D6VGRKtyn4eojGOK7Kzp+O01grh0MCQr0ZOrO7Q++/JbuMJ75NJ6dMFRQeeh13TerNfdOT8DlLC3pLrZHSd9MwF7cktuog5MpEAkbFKtcUv/gS5iJ5Fo0hJITY559zuuZttqKusoKtX6kNrUTSqgCA+nI49KNqDxUhGnshxIiNkSSJVSfUkl4RonFdKovqSVuTp9jj5ifi6eWYplgV9UZe+DGTZXvy2+yfLUG1NZaaZkoXpWEulZM00UHoVcn4D49WrqlZtYrq775T7Jhnn8Uj8swnLK7A+o8WY2xsSVqN68aw2SJpVQAc+AIsRnkdPxyi+2vrjwsjxIiNOVx5mBM1cq8JPw8/xseP19gjgb3Y9GU21pa+HbGJwSQOj7L7PSVJ4us9+bz4YyaVDWfvoHo2zFXNlC06gLlcbsyGHsIWpOA3RPXdXFZG0dPPKHbQ3MsImuW6pem56fvbJq3efg8GD9fsnyK4ACSpbYhGnIrYFSFGbEybEE3CFHw8XHNmh7tzPK2M3N9apetg4oJku4cwcsrqeeKbNLYcLW+zP2dQLE9f2p+ooHP/rpkrmihddABLpTxrBb2OsOtS8Ett1fRMkij8y1NYKuUkWI/oaGKefNK2L8SJsJhN/Lr4P4qdMm6SSFoVyOTvgZJMee3pBwPna+uPiyPEiA2RJInVJ1Yrtmh05ppYzNY282f6T4gjsvvZwyKdxWi28s6Go/xzTTZGs1XZjw/x5YUrBjK17/lPZMxljZQuSsNS3SJEDDrCf9cP3wHhba6rXraMurVrFTv2pRcxBAXZ5oU4Ibt//I6KAjnU5uXry5QbRdKqoIW9H6rr/leAj+v+HTgDQozYkKNVR5UQja+HL+PjRIjGFUlbl0dVS+Knl68HY+b2ttu9dp+o4LFlaRwpVktv9Tq4fUIvHpiRjJ/X+f+ETaUNlC5Kw1rTEvv20BF+Y398U8LaXGfMy6P4xZcUO/T66wkY77q/wzVlJWz9Wu20Ou7q6wkICz/HIwRug7Ee0r5WbdFbxO4IMWJDfsn9RVlPjJ8oQjQuSEONkZ0/5Cj2yDk98Q30svl9appMvLbyEB9vy22znxofzMvzUhkYH9yu5zEV1VP6bhrWOjm/ROepJ/ym/vic0pRNslopXPgY1oYWkdWzJ1EPP2SDV+K8rPvgXczN8klRRPeeDL34Mo09EjgNGd+CsaUJYHiiGIrnAIQYsSG/nFDFyEU9LtLQE4G92L78GMYmuS16aIwfqVO72fweK9MLeeq7DEpqm5U9Py8DD85I5pZxPfEwtK/7qbGgjrLFaVjrzQDovPRE3DIA794hp11b8f4HNOzaJRsGA3GvvYre13VL0nP27SZrxxbFnn77PegNjqmEEnQBdr2nrofdJIbiOQAhRmzEyZqTHK48DICn3pNJ3cQsGlejNLeWzM3qrJfxVydhaKcwaA+F1Y08/V0GqzKL2+xPTYnk+SsG0i20/SMFjHm1lC5OR2psESLeBiJuHYB3z9NPVJqOHKH0zTcVO+L3d+E7aFAHX4XzYzYaWbNE7bQ6YPJ0uvUdoKFHAqeicD/k/ybMveQJvQK7I8SIjfg191dlPS5uHP6e/hp6I7A1ktQyf6alwWmP1HB6DLBNfoHVKvHx9hO8tvIwdc1mZT8iwJtn5vZnTmrsBVXqNOfWUPZeOlLLCY7Ox0DEbQPx7n56Ap5kNFKwcCGSSQ7j+PTvT8Q993TyFTk3O5d/TVVRIQDe/v5Muv5WjT0SOBW7lqjr/peDv2h+5wiEGLERq3PVKprp3adr6InAHmTvLqEwuxoAvV7HhKuSbPK8R4prWfj1AfbkVrXZv25UAgsv7kew34X1u2g+Xk3ZexlIRlmI6P08iLg9Fa/4gDNeX/r22zRnHgRA5+VF3GuvovN03R4blUUFbP92qWJPuOYm/IJPD1sJ3JTmWkj7UrVH3KadL26GECM2oLi+mAOlBwAw6AxMTZiqsUcCW2IyWtjytVrKO2haN0KiOzeFuclk4e212fznlHkyvSP9efnKVEb3vvBTl6ajVZS/n4Fkkst/9f4eRNwxCK/YM5/SNezdS/k7ixQ78sEH8E7UZsifI5AkiTXv/RdLyylQdO8kBs24WGOvBE7FgaVgbKlci+wrElcdiBAjNmDNyTXKekTMCEJ8xDctV2LvqlzqWhqF+QZ6MmJOr049346cChYuO8CxUnWejKdBxz1TEvnDlD5nnSdzLpqOVFL2YSa09CHRB3gSeWcqntFnFiLWhgYKFi4Eq3y93+jRhN10UwdeTdcha/tmju/fIxs6HRfd8Qf0epG0KmhBktqGaEbcJhJXHYgQIzagTRVNd1FF40rUVjSx9+cTij3m8j54+3bsz6a60cQrKw7x2Y625brDe4Ty8rxUkqM71jit8VAF5R9nglk+YdEHeclCJPLspzfFr72G6YTshz4ggLiXX0Knt10yrrNhbGxg7QfqKdCQmbOJ6WObUJvARcjfDcVp8trDFwZdo60/boYQI52ksqmSXcW7FHta92kaeiOwNVu/OYq5JewRkRBA33Gx53nEmVmZXsRT36W3KdcN8Pbg0YtTuH50j3POkzkXjRnllH96EFpCPYZgbyLvSsUj/OxluXUbNlD1+ReKHf3kE3jGxXXo/l2FLV9+Sl2F3EbfLziE8deIJlaCU2hdzjtwPviKE25HIsRIJ1l3ch1WSf6wGhI5hCg/+w9LEziGguwqsnaqZbYTFyRfsGgormniqe/S+TmjbbnujP7RPH/5QGKCO94Yr+FAKRWfH4aWYX2GMB8i70jFI+zsz2murKTgiScUO3DGDIIvv7zDPnQFSk/ksGfFcsWecuPt+PifOaFX4KY0VkJ6q46rInHV4Qgx0klad10Vjc5cB8kqsWlplmInDo8iLqn935SsVokvdp3kpZ8OUtuklutGBnrz3NwBXDwwplOD9Rr2llCx9LBSauwR4UvEHal4hHif9TGSJFH07HNYSssAMEREEPPcs3Yf8KclktXKL+++jdSSG5MwYBB9J0zR1imB87H/czC3TLKOGQTxw7T1xw0RYqQT1Bnr2FqwVbFFiMZ1OLi1kNJcuR20wVPP2Hl92v3YnLJ6Hlt2gG3HKtrsXzsygccuufBy3VOp31VE5ddZqhCJ9CXyzkEYgs7dlr7mhx+oXblSsWNfeB6P0NBzPKLrk7Z2NQVH5NJlvcGD6bff49LiS9ABJKltiEYkrmqCECOdYEPeBkxWuUywb1hfEgITNPZIYAuMjWa2fXtUsYfO7E7QOXIwfsNssbJoYw5//+UIza2m6/YM9+OleamM69P55kl12wup+kYtM/aI9iPyjlQM55mPYyoooOi55xU75OqrCZwypdP+ODMNNdVs/EStjhhx2ZWEx4u/UcEpnNgMZUfktVcgpF6lrT9uihAjnaBNiEZU0bgMu346TmOtLDIDQr0ZNrPHeR+Tnl/No18fIKOgRtkz6HXcObE3/3dRUofKdU+lbksBVctVkeQZ60/EHakY/M990iJZrRQ89jjWWvmkxzMhgeiFj3baH2dn/UeLaaqXe0YER0UzZp6ojhCcgR3vqOtBV4N3x6raBJ1DiJEOYrQY2Zy/WbFF11XXoKq4gf1rTir22Hl98PQ+u5BoMln4x69ZvLPhGBar2rxsQFwQr84f1O7puuejdkMe1T+p04I9uwUQedtA9O0I+VR+9BEN27fLhl5P3Kuvovd37XEFuekHyNyg9v+Zfvsf8PQWU7QFp1CdBwd/UO2Rd2rni5sjxEgH2VG0gwazPG49ITCBPiHtzykQOC+bv87G2lImG9snmKQR0We9dvuxchYuSyOnTG1e5u2h54EZydwxoVe7p+uej5q1udS06nXi1T2QiNsGovc5/59vc1YWJX/9m2KH33UnfsOG2sQvZ8VsMvHL4rcVO3nMBHoNGa6hRwKnZdd7IMmjE+g5EaL7a+uPGyPESAdZm7tWWU9JmCKS4lyA3Mxyjh8oU+wJC5LO+P9a22Ti1ZWH+Hhb2+Zlo3uF8cr8QfSKsM2pgyRJ1PySS+2v6n28egURccsA9N7n/9OVjEbyH3kUyWgEwLt/PyL/8Aeb+ObM7Fz+FZUFeQB4+fox9WbxbVdwBkxNsPt91R79e81cEbRTjOh0uouBfwAG4F1Jkl45y3VXAV8CIyVJ2nWma1wBq2Rl3cl1ii1m0XR9LBYrm75UE0P7jo0hqsfpU27XHi7hiWVpFFQ3KXuB3h48Nrsf145M6HDzslORJIman49Tuy5P2fPuE0z4zQPQe7Uv/6T032/RfFAdghf/2mvovM6d6NrVqSzMZ/s3rQbhXXsjAWG2ma4scDEylkGD3AiP4ARIvkRbf9yc84oRnU5nAN4CZgB5wE6dTrdckqTMU64LBO4DttvDUWfiYPlBShpLAAj2DmZolGsfe7sDGRvyqSyUwy2e3gbGXNE27FZZb+T5HzJZtje/zf5F/aJ44YrUTjUvOxVJkqj+MYe6Teq9vJNDibixH7p2JsI27NlD+bvvKnbUww+59BA8kP/dfj1lEN7gmbM19krglEgSbP+fao+8HQwiUKAl7fnXHwVkS5J0DECn030OXA5knnLd88BrwMM29dAJaT0Yb1L8JDz04pe4K9NYZ2TH92py6IjZPfEPlpuHSZLET2lFPL08nbI6o3JNmL8Xz8wdwGWDYm0aopOsElXfH6V+a6Gy59MvjPDr+6HzaF8OiqWujoJHHlWH4I0dQ+gNN9jMR2fl0Ob1nDiwFwCdTs+MO/8oBuEJzkzeTijcJ689fGDYzdr6I2iXGIkHTray84DRrS/Q6XRDgQRJkn7Q6XRnFSM6ne4u4C6A7t27X7i3TsLak2q+yNTuIkTT1dnxfQ7NDXKX1KBIXwZPk3tRlNQ28dS3GazMKGpz/eVD4njq0v6EB5y922lHkKwSVd9mU79DvZ/vwHDCru3bbiECUPzSy5jy5PCOPiiIuJdfdukheACNdbWs+1A9CRpy8Ryie7v2SZCgE7Q+FUm9CvzCtPNFALRPjJzpa59Sw6jT6fTAm8At53siSZLeAd4BGDFihHSey52SvNo8sirlNuFeei/Gx43X2CNBZyjPryNjgxoOmXBVInoPHcv25PHs95lUN5qUn8UE+fDCFQO5qP/ZK2w6imSVqPzqCA17SpQ938GRhC1IQWdo/8lLzapVVC9bptgxTz+FZ0yMTX11RjZ+soSG6ioAAsLCGb9ADMITnIXaIsj8VrVH3aWdLwKF9oiRPKB128JuQEErOxAYCKxrOa6OAZbrdLq5rpjE2jpxdXTsaPw8zz6mXeDcSJLExqVZSC2yOKFfKN49/Lnt/Z2sPVza5trrRiXw2Ox+BPl0rpX7Gf2wSFR8eZjGfeo9/YZGEXp1MroLSIg1l5ZS9NTTih00Zw7Bc+bY1FdnJO9gOmlrVin2tNvuxttP/F0KzsKuJWBtmReVMAZiB2vrjwBonxjZCSTpdLpeQD5wLfC7334oSVI1oPS51ul064CHXVGIQNsQzZSEKdo5Iug0OfvLyD9cCYBOr6O6bwCz3txIbbM62K5bqC+vzh/E+MTOt3I/E5LFSsXnh2lMU0uK/UZEEzov6YKEiCRJFDzxBJYq+XTAIyaGmKf+YnN/nQ2zycTqd/6t2Ikjx5A0cqyGHgmcGrMRdqsjAhgtTkWchfOKEUmSzDqd7l7gZ+TS3vckScrQ6XTPAbskSVp+7mdwHaqbq9ldvFuxhRjpuphNFjZ/pU7lLYgw8PHaI4qt08HNY3vy51kp+Lejp0dHkMxWyj89RFNmubLnPyaWkLl9LkiIAFR9/jn1GzYqdtwrL2MItk33V2dm5/KvqGjpKeLp48u0W+/W2COBU5P5LdQVy+vAWOg3V1t/BArtepeVJOkn4KdT9p46y7VTOu+Wc7IxfyOWlm59qRGpRPlFaeyRoKPs//UkNWVyr5AmncRXTbXQkuPZK8Kf164axMie9ktqk0xWyj/OpKnlZAYgYHwcwZf2vuDqnOZjORS/+ppih918M/5jxtjMV2elouD0niKB4fY5wRK4AJIEW9VTNEbcBgbbh10FHUPUpF4Ap3ZdFXRN6qua2fnTccXe5GOiSQ96HdwxsTcPzki2yWC7s2E1Wij/KJPmrCplL2ByN4Iv7nnBQkQymSh45BGkJllYeSclEfngAzb11xmRJIlf3n1L6SkS0yeJIbNcPz9G0AlObIbC/fLaw0cWIwKnQYiRdmK0GNmUv0mxRdfVronVKvHxov1YjHIPjlK9lX1eFhKjAnj9qkEM7R5q3/s3Wyj/IIPmY9XKXuC0BIJm9OhQv5LSt9+mKT0dAJ2nJ3Gvv4be27Ylx85IxvpfOZlxAACdXs+Mu/4keooIzs3Wt9T14OvAX5yiORNCjLSTnUU7lcF43QK6kRgiehh0NU6U1/P8B/sYerRZ2Vvnb+aeqX24b3qSXU9DAKxNZsqWZGA8UaPsBc3oQdD0jvXcadizh/L/qePPIx94AJ++fTvtp7PTUF3F+o8WK/bwOVcQ1bO3hh4JnJ6ybDi8QrXHuP6Mpq6GECPt5NQqGjEYr+tgtUp8uPU4r644zLxKD35LDikMgH/eP4ZB3ULs70OjmbL30jGerFX2gi/pSeDkhHM86uyc1mV19GjCbnGPLpJrP1hEU5387xgUGc24q353nkcI3J5tb6O0x0qaBZHJmrojOB0hRtqBJEliMF4XJbe8gT9/tZ/tORX0NxqIs8hCRNLD/Q+NIjI2wO4+WBtMlC5Ox5Rfp+wFX9qbwAnxHX7O4hdfattl9RXX77IKkLN3F4c2r1fsGXf+EU8f280FErggDRWw71PVHnevdr4IzooQI+3gSOURihvkcrBAz0CGRovBeM6O1SrxyY5cXv7pIA1GC54STG5UM+eHz+jhECFiqTNS9m46pqJ6ZS/kij4EjInr8HPWrPyZ6m++UeyYp5/CMza2U352BYxNjax+V43795s4lZ6Dh2nokaBLsGsxmBvldUwq9JyorT+CMyLESDvYmK/2bxgXPw5PvSgHc2byKht49OsDbM5W+3eMafYgQJJDa35BXgy/pIfd/bDUGildlIa5RM41Qgeh85LwH9nx9uym4hKKnm7VZfWyy9yiyyrA5i8+prZM7lLrExjElJvu0NgjgdNjboYdi1R77J/kJkICp0OIkXawIW+Dsp7cbbKGngjOhSRJfLHzJC/8eJC6Vl1UB4X4M/akhNQSMx57ZR+8fOz7q2+pbpaFSFnLNzIdhF6VjP/wjs+1kaxWCh9biKVarsTxiIsl5i9P2sJdp6cw+zB7Vqj9FafedAd+Qa7f1E3QSdK+atvkbMCV2vojOCtCjJyHqqYq9pfKtek6dIyPF4PxnJHimiYe/foA61rNlNHr4M5JvUnNMXHCIrdbj+oRSMpo+w6OM1c1UbooDUt5U4sjEHZNCn6DO9ckr+LDD6nfslU2dDriXnkFQ1BQJ711fixmM6v+9y9+GyLUY9BQ+k0UeVuC8yBJbct5R/8ePLy080dwToQYOQ+bCjZhleSKhdTIVMJ8xKhpZ0KSJJbvL+Cp7zLaTNjtHeHP61cPJqpRYvl3+5T9iddc2PC5C8Vc0UTpOwewVLWUD+t1hF3XF7/UzvU0aDp0iNK//k2xw++4A/9Rozr1nF2FXd8voyz3OAAe3t7MuPOPoppNcH6OrYWSDHnt6Q/Db9HUHcG5EWLkPIgQjfNSXtfMk9+msyK9qM3+reN78sisvngbdHzx4k5lP2V0DDG97Xe0byprpGzRASzVRnnDoCP8+n749g/v1PNam5oo+POfkVq6jfr070/kn9yjIqA8/yRbv/5MscdffT3BUfY92RK4CJv/oa6H3gC+9m1oKOgcQoycA7PVzOb8zYo9qdskDb0RtGZVRhGPf5NGWZ1R2esW6svrVw1mbB/5wz9tXR4VBXIVi4e3gbFX9rGbP6aSBkoXpWGtbfHHQ0fEjf3xSen8SVrJX/9Gc1Y2ADofH+LeeB2dl+sfN0tWK6v+9y+l5Xt07ySGzb5cY68EXYL8PXBsnbzW6WHMPZq6Izg/Qoycg/2l+6kxyt0yo/yiSAlN0dgjQU2TiWeXZ/L1nrw2+9eN6s4Tc/oR0DJht6nOxPblx5Sfj7ikB/4h9mmTbiqqp/TdNKx18oemzlNP+M398Uns/Dexuo2bqPzoI8WOXrgQ797u0W103+qfKDicCYDeYGDW3fehN4iW74J2sPnv6nrgfAjrpZ0vgnYhxMg5aB2imRg/UcSpNWZLdhkPf7mfguomZS86yJtX5w9iSkrb5NAd3x+juUGuqAmK8GGHjGanAAAgAElEQVTw9I51Oj0fxoI6yt5Nw9pyL52XnohbBuDdu/NdXc0VFRQ8/phiB0ybRsg1Czr9vF2BmrISNn76gWKPuvwqInuIDxRBOyjLgky18orx/6edL4J2I8TIORD5Is5Bk8nCqysPsWTz8Tb7cwfH8dzlAwjxaxuyKM+vI31DvmKPvyoJDzvMnTHm1VK6OB2psUWIeBuIuG0g3j06X+EiSRKFT/4FS6lcBWSIiCD2hefdQhBLksQvi97C1CSXRYfFdWP0vGs19krQZdj8D9TW7zMhZqCm7gjahxAjZ6GgroDsKjlO76X3YnTsaI09ck/S8qp5YOk+skvUVuqhfp68cEUqcwad3nVUkiQ2Ls36rQqUbn1D6TXY9tM5m0/UUPZeOlKzBQCdjweRtw/EKyHQJs9f9cUX1K1Zo9hxL72IR5h7VHId3LSOnH27ZUOnY+bd9+PhKRoNCtpBTQHs/1y1JzygnS+CC0KIkbPQ+lRkZMxI/Dz9NPTG/TBbrPxn3VH+8WsWZquk7E9NieTV+YOICjrzPJKcfWXkH64EQKfXMeHqJJufJjTnVFO2JAPJKAsRvZ8HEben4hVvm/byzUePUvzKq4odeuONBExyj+Tphuoq1r6vTiIeOutS4lP6aeiRoEux9S2wtpT4J4yBHuO09UfQboQYOQtt8kW6iVkGjuR4WT0PLN3H3twqZc/Py8CTc/pz3aiEs4oLs9HCpq+yFHvgpHjCbSQQfqMpu5LyDzKRTHLvGb2/J5F3puIZ42+T57cajeQ//GekJjkvxjspiaiHH7LJc3cFfl3yP2Uib2BEJBOuu0ljjwRdhoYK2P2+aotTkS6FECNnoNHcyI6iHYotSnodgyRJfL7zJM99n0mjyaLsD+8Ryt8WDKZH+Lk/8Pf9kkttS9dTH39PRl1m24THpiOVlH2YCeYWIRLoSeQdqXhG20aIAJS++XeaDx4EQOflRdxf30DvbZ8qIGcja/sWjmxV50DNvPNevHx8NfRI0KXYuRiMLeHcqP5yvoigyyDEyBnYWbSTZovcQbN3cG8SAu1TiSFQKatrZuHXafxysFjZ89DreGBGMndP7oPhPF1T6yqb2L3yhGKPntsLH3/b5Rk0ZpZT/slBsMghI0OQFxF3puIZabvwXd3mzVQsWaLYUX/+Mz7JyTZ7fmemsbaGXxa/rdgDplxEzyHDNfRI0KUwNsD2/6j2+P8DvV47fwQXjBAjZ2D9yfXKWpyK2J9fDxbz6NcH2jQwS4wK4O/XDGFgfPs6pm5ZdhSzUT6xCI8PoP/EeJv515heRvmnh6Ald8UQ4k3knal4hNvuW7u5spLChWoZr//kSYTecL3Nnt/ZWfvBIhqq5bCcf2gYU24UE3kFF8Dej6ChZUp3cHcYOE9bfwQXjBAjpyBJEhvz1aNiIUbsR6PRwgs/ZvLJ9tw2+7eM68nCS/ri085y3ILsKrJ2qicqE69JQm+j+TMN+0up+OIQyDoHQ5iPLERCz5xA2xEkSaLwiScxl8pD/gzh4cS9+KJblPECHN29g4Mb1yr2jDv/iE+AbXN9BC6MuRk2tWpyNu5PYBDVV10NIUZOIac6h8L6QgACPAMYEjVEY49ck/T8au7/fC9HS+uVvahAb16/ejCTkyPb/TxWq8TGL44odp9hUcQn22YGRf2eYiq/PKK0LPCI8CXyzlQMwbbN4aj6/PPTy3gjbF+O7Iw01dfxy6J/K3a/CVPoM1yU0QsugL0fQW2BvA6IhmE3auuPoEMIMXIKm/I3KesxsWPw1AuFbUusVolFG4/xxqrDmCxqye7FA2J4eV4qof4XNnPl4OYCyk7KSWsennrGzbfN/Jn6nUVULstShUiUH5F3pGIIsu1MmOasrNPLeCe7T4O99R8tpq6yAgC/4BCm3nKXxh4JuhTmZtj4pmqPvx88RdJzV0SIkVPYXKAOxhsfP15DT1yPwupGHlq6ny1Hy5U9Py8Dz1w2gKtHdLvgsERzg4lt36nzZ4bO6kGQDfI46rYVUvVttmJ7xvgRcUcqhgDbChFrczP5Dz2M1CwnS3unpLhVGe/xfbtJX7tasafffg++gZ3vXitwI/Z9CjUtc6r8I2H4rdr6I+gwQoy0otHcyK6iXYo9Pk6IEVuxMr2QR79Oo7rRpOwNTgjhH9cMoWdEx0pjd/yQQ1PLcLqAMG+GzuzeaT9rN+dT/b0qcDzj/Im4PRWDDStzfqPk9TdoPiKHmHTe3sS7URlvc0M9q95RwzPJYyaQPFr8vQkuALMRNv5Ntcf9CbxEc8quihAjrdhVtAujVa7o6BPch9iA09uNCy6MBqOZ5384yGc71CRVvQ7+ODWR+6Yn4WnoWPldeUEdaetazZ+Zn4SnV+fmz9Suz6N6RY5ieyYEEnnrAPR+thcitevWUfnxx4od/dhCvBMTbX4fZ2Xdh4upLZcTdn0Dg5h+290aeyTochz4HKpb3lf8wmHE7dr6I+gUQoy0QoRobEt6fjX3fb6XY62SVONDfHnzmiGM6tXxOSuSJLFpaRZSS6ltfEoIfYa1P+n1TNT8mkvNarVPiVePICJuHYDex/Z/IqaSEgofe1yxA6ZPJ+Saa2x+H2clZ+8u0teuUuzpt/8Bv+DOTzkWuBEWE2x4Q7XH3gveogKrKyPESCs25wsxYgskSeK9zcd5dcUhjBarsj9nUCwvXZlKsG/nThqO7Ssl75A6f2biguQOl8FKkkTNL7nU/qqe3Hj1CibilgHovW0/6VeyWilc+BiWStl/j6got5nGC3L1zKr//VOxk8dOJGXsBA09EnRJDiyFqpYvD76hMOpObf0RdBohRlo4WXuS4zXHAfAx+DA8WnR/7Ahldc38+cv9rD1cquz5eRl4Zu4Arh5+4Umqp2I2Wtj8pZpcOnByx+fPSJJEzcrj1K7PU/a8E0MIv6k/+k6GfM5GxXvvUb9li2zodMS9+goeobYpRe4KrPvg3TbVMyI8I7hgLGbY8Lpqj/0jeNtmWrZAO4QYaWFL/hZlPTJmJN4G90gktCWbs8v4vy/2UVrbrOylxgfzz+uG0quDSaqnsnd1LrUVrebPXNqx+TOSJFH9wzHqNhcoez4poYTf0B+dp33aSDceOEDJ3/+h2OF33on/2LF2uZczcnT3DjLW/6LYF93+B/yC2tdhVyBQSP8KKltyu3yCYZQoB3cFhBhpYVOB2l9EhGguDJPFypurj/Cf9UeR1NYh3DWpNw/PTMHLwzYf7jXljW3mz4y5oneH5s9IVomq5Uep31ao7Pn0CyP8+n7obOTrqVjq6sh/6GEwm+X7DR5E5J/utcu9nJHGulpWt2pu1nf8ZJJGi/HuggvEYoJ1r6j2mD/KgkTQ5RFiBDBZTGwv3K7YE+JFDLu95FU2cN9ne9mTW6XsRQR48cbVg5mSEmXTe235+igWk5yDEpEQQL/xcRf8HJJVouqbbOp3Fil7vqkRhF2bgq6DlT3nvackUfTMs5hOngRAHxBA/F//is7TfRrqrV3yP+pbhWem3fp7jT0SdEn2fdL2VGS0+D1yFYQYAfaW7KXR3AhAt4BudA/sfL8Kd+DnjCL+/OV+aprMyt7EpAj+umAwUYG2m90CkH+4kqN7ShR70jXJFzx/RrJKVH51hIZWz+M7OJKwBSnoDPZLIK3+7jtqfvhBsWOefQavbt3sdj9n48j2zRzctE6xZ9x5r2huJrhwTE2w/jXVHn8/+IoqLFdBiBFOD9G4S2VDR2kyWXj5p4N8sFUNmRj0Oh6emcLvJ/W22ZC637BarGxoNX8meVQ0sYkX9iYkWSQqlh6mcX+rxNphUYRelYzOxv62xnj8OEXPPa/YwfPnETxnjt3u52zUV1WyetFbit1/0jQSR47R0CNBl2X3Eqhp6S3kHwmjRfKzKyHECG1LekWI5tzklNVz76d7yCioUfbiQ3z553VDGd7DPlUhaevzqSiQe5V4ehsYN+/CmoNJZisVnx+iMV1tQ+8/MoaQKxPtKkSsRiP5Dz6E1NAAgFevXsQ88YTd7udsSJLE6kX/pqlW/l0JCI8Qs2cEHcNYDxv/qtoTHwIv2yTFC5wDtxcjJQ0lHKmUv3V76D0YFTNKY4+clx8OFLDw6zTqmtWwzMz+0bx+1WCC7dClFKChxsiO79WuqCNm98Q/pP2VTpLZSvknB2k6WKHs+Y+JJWRuH7sKEYCSN96gKTMTAJ2np9zu3c992lVnrP+Vo7vUXKyL7/4/fPxFYypBB9j+P6hvOdUMihczaFwQtxcjrU9FhkcNx8/TfT4s2kuTycKLPx7ko22tOpQa9Dw+uy83j+tp17DWtm+PYmyUxU9ItB+Dpye0+7GSyUL5xwdpOlyp7AVMiCd4Ti+7h+Jq16yh8sOPFDvqkUfw6d/frvd0JmpKS1j7/juKPWTWpfQYNERDjwRdlsYq2KyWxDP5EfC0bU6aQHuEGBEt4M/JifJ6/vBJ27BM9zA/3r5+GAPj7VtSV5xTw8EtavnthAVJGNpZems1Wij/MJPmbLXKJ3BKN4Jm2Vc8AZiKitq2e582jdAbrrfrPZ0JyWpl5X/+jrFRDk+FxsYx6fpbtHVK0HXZ+hY0tfwdh/aCIe7zt+ROuLUYsVgtbC3YqthCjLRlRVohj3x1gNpWYZnZqTG8Mn8QQT72LUuVrBIbPj+s2D0HRdBjQHi7HmtttlD2fgbGnGplL3B6d4Iu6m53ISKZzeQ//DCWavneHjExxL74glslRe/9+QdOZhwAQKfTc/EfHsTTW3yTFXSA+jLY9rZqT30cDO5TEu9OuLUYySzPpMYof+OP8I0gKSRJY4+cA6PZyisrDvHeZjVXw8ug54k5/bhpbA+HfLAe3FpIyYlaAAweeiZc3b7/G2uTmbIlGRhPqCc5QbN6EDTVMeXaZf/5L427dsuGXk/8G6+7Vbv38rxcNn7yvmKPvHw+ccl9NfNH0MXZ9CYY6+R1ZD8YOF9bfwR2w63FyNZC9VRkbOxYt/r2ejYKqxv54yd72jQxSwjz5a3fDWNQN8fU9Dc3mNj27VHFHjqzO8GRvud9nLXBROmSDEwna5W94Nm9CJzkmJ4e9dt3UPaf/yh2xL1/xG/ECIfc2xmwmE389K+/YjYZAYjs0YuxV/1OY68EXZbKE7BDzTti2hOgt8/MKIH2uLcYaRWiGRvnPjNCzsbGrFLu/3wfFfVGZW9G/2jeuHpwpyftXgg7vs+hsdYEQECoN8Mu7nHex1jqTZQtTsPUUgIMEHxZbwLHx9vNz9aYKyooePhhsModYv1Gjybi9+7VHXLLl59SclwWkQZPT2bf+xAebtRlVmBj1r4Ilpb3ovgR0PdSbf0R2BW3FSMNpgb2le5T7DGx7tuIyWqV+NeabP7+6xFltoxBr+ORWSncNam3Q0+MyvLqSFunTtEdf1USnueZoGupM1L2bhqmogZlL+TKRAJGx9rNz9ZIVisFjzyKuVQuPTSEhhL32mvoDO7zLS7vUAY7v/tasSdedzMR3Xtq55Cga1O4Hw58odoznwdxcu3SuK0Y2V28G7NVTsxMDEkk0i9SY4+0oarByANf7GPtYbUzaVSgN//+3TBG9QpzqC+SJCet/iaIuvUNpc+wc/+/WGqMlL57AHOJ3M4fHYTOS8J/ZIydvVUpX7yY+k1qF9+4117FM9q2c3mcmeaGBlb8+29Iknwq1H3gIIZdMldjrwRdmtVPqeuUOdBDDFV0ddxWjLTJF3HTEE16fjV3f7ybvMpGZW9s73D+ed1QIgPb31jMVhzZUUxhtlyFotfrmHhN8jlPZczVzZQtSsNc1kqILEjBf6jjhEDDnj2U/l3tgRB+5x0ETJzosPs7A2s/eIea0mIAvP39mXXPA+j09hk6KHADsn+FY+vktc4AFz2joTMCR+G+YqSgbfKqu7F010me/DYdo9mq7N0zpQ8PzUjGw07Ta8+FsdHMlq+zFXvQ9ATCYs/e7tlc2UTpojQsFU3yhh7CrumL32DHnXCZKyvJf+hhsFgA8B06lMj77nPY/Z2BrB1byFj3i2JPv/0PBEW45ymjwAZYLbD6adUedhNEJmvnj8BhuKUYKW0oJbtK/uDz1HsyPHq4xh45jmazhWeWZ/LZjlxlL8DbgzeuHszFAx0X2jiVnT/m0FAjJ6v5BXsxck7Ps15rLm+UhUhVs7xh0BF+XV98B0Y4wFMZSZIofPwJzIVyUzZ9cDDxf30DnRslbNZVlLPqnX8rdt/xk+k3frKGHgm6PAeWQnGavPb0hymPaeuPwGG4pRjZVrhNWQ+JGuI2LeCLa5q4++Pd7G1VtpscHcB/bxhO70jtZoZUFNRzYE2rpNX5iXj5nPlX01TaQNmiNCwtwgWDjvAb+uHbr30N0WxFxQcfULd2rWLHvfwSnnFxDvVBSySrlRVv/a3NELzpt92jsVeCLo2pEda8oNrj7oXAaO38ETgUtxQj7hii2Xm8gns+3kNZXbOyd9ngOF6Zl4q/t3a/BpIkseGLI1itctZqXFIISSPP/AZkKq6n9N00rC1lv3joibipPz7Jjm0q1rhvHyVvqBNEw26+mcBp0xzqg9bs+vFbctP3y4ZOx+x7H8InQAzBE3SC7f+FmpYvJf6RMO5P2vojcChuJ0YkSWpzMuLqyauSJPHxthM8+30m5pYPfINex2OX9OX2CfYfGHc+sneXkN8yyE6n1zHp2jMnrRoL6yl7Nw1rvSxEdJ56wm8egE+iYxqx/Yalqoq8Bx8Es1yJ5ZOaStRDDzrUB60pPpbNps8+VOxRl19FQv9UDT0SdHnqSmCDKvCZshC8A7XzR+Bw3E6MZFdlU9ool7EGeQXRL6yfxh7Zj2azhb98m87SXWoIJMzfi3//bijj+jguv+JsGJvMbP4yS7FTp8QTHn/6t2tjfh1li9OwNsgCQOdlIOLWAXj3su+gvlORrFYKFj6GuaAlTyQoiPg330Tn5eVQP7TE1NTEj/96A6tF/r+I6ZPEuKvF4DJBJ1nzPBhbOidHJMOwm7X1R+Bw3E6MtA7RjI4djcFF2wuX1DTx+1PyQ1Ljg/nvjcOJDzl/a3VHsOvH49RXy7kfvkFejLqs92nXGE/WUro4HampRYh4G4i4bSDePYIc6itAxZIl1K1bp9hxL7+EVzfHdHh1FtZ9+C6VBbK49fT2YfZ9f8bg4XZvIwJbUrgf9nyk2rNeFsPw3BC3exdxhxDNvpNV/P6jXRTXqPkh84bF89KVqfh4Oof4Ki+oY/+vJxV7/PxEvH3b/jo2H6+mbEkGUrNcOqvz8SDy9oF4JTj++LZhzx5K/vamYofdcguB06c73A8tydq5lQO/rlTsabf+ntAY90naFdgBSYIVC4GWTodJMyHpIk1dEmiDW4kRk8XEruJdiu2Kyatf787jsW/SlP4hBr2OJ2b349bxPTXPD/kNSZLY+LmatBqbGEzyqLZJq83Hqih7PwPJKL8OvZ8HEXek4hXn+CRJc2Ul+Q88qPYTGTzY7fJEasvLWPXffyp28pgJDJgiPjQEnSTzW8jdIq/1HjDrJW39EWiGW4mRfaX7aDTL3ToTAhPoFuiYaa6O4P/ZO+/wqKqtD79nSnqvJCR0CAQSQrUgRZooiF0RG1VUUCzXftX76fWKFbGhgAV7QxGlKV2KdAgECAkQQkjvPdPO98eJcxIFgbQzM9nv8/g4e81kZqUw5zd7r/VbFquNl1Ye4cPNJ+wxf08j707sy2Vdta8PqUvKrhxOH1WOjySdxNBbY+oJpeqUIgo+PYRsrhUiPkZCp8VhbHN2E7TmQrbZyHz8cSw5isOozt+ftm+83qr8RGw2KyveeY3qcuVM3yc4hFHTZzmMuBU4KeYq+PUZdT1wBoR01S4fgaa0KjHiqi29pdVm7v9yLxuPqvNluoX7sPDO/rQPbvkL+D9hqrKw5fs6TqvDo+oVrVYnF5L/2SGwKLsmOl83QqfHYQzTxgumYMECKjb9bl9HznkJY9vWVSey/YdvyTh0EABJ0jH2/n+JNl5B49n6DpTUHtV6BcPQx7TNR6AprUqMuGK9yMmCCqYu3kVqbrk9Nio2nLm3JOCjoX/I2djxywkqS1Sn1YFjO9rvqzpUQMEXh8Fa24Ls70bI9HiMIdoU3Fb88Qd5b71tXwdPm4rv5ZdrkotWZBw6yLbvv7KvL7nxVqJ69NIwI4FLUJoJm99Q18P/DZ4t26YvcCwc72rVTJSaSkkqSAJAJ+kY0GaAxhk1nm3HCrj3i90UV5rtsVmXd+HhUd3Q6RxvC73gdDmJ6+s4rd7YBbfaotXKA/kUfnUE/vRCCXAn9O54DEEemuRqzslV5s7YlKMir/79CX3wQU1y0YqqslKWv/OafRpvVGwvLrr+Zo2zErgEvz0H5krldngv0coraD1iZFf2Lmy1b6qxQbH4u7esR0VT89WOdJ5ZetBuZOZm0PHKDfFc28cxjxBkm8zGL5ORa/NtGxNA1/5K0Wrl/lwKv0mG2pl9+iAPQu+OwxCgjRCRzWZOP/ww1oICJZ/gYCLfeB2pFbWwyrLM6vfforwgHwAPH1+umvUvdC7aCi9oQdI2w4Fv1fWYl0D8XbV6Ws27647sHfbbAyMGaphJ47DaZOasPMzC39VC1VBfdxbc0Y8+7VrWFv1COPJHNlnHSgDQ6SSG3KIUrVbszqHo+6P2zj5DiCeh0+PQ+7trlmvum29StXs3tcnS9vXXMYaFaZaPFuz7dTnHdqnHmlfc+yC+wY5VCC1wQqxmWP4vdR17LXQcol0+Aoeh1YiR7Vnb7bcvanORhpk0nEqThQe/3sevh3LssZ6Rfiy8sz+RDmJkdiaqK8xs/UEtWk0YFU1QpDcVO7Mp+iFFFSJhXooQ8dXO0bRs7VoKP/zIvg594AG8L3bOv5eGknPiGBs/+9C+7jPmarr0b10/A0Ez8cd8yDus3HbzUXZFBAJaiRjJr8ontVi5GBp0BhLCEjTO6MLJKa1m2uJdHDhdYo+Njg3nzQkJeLk59q9x29JjVJcrdS0+Qe70v6oj5X9kUrz0mP0xxjbehEzrhd5HOyFiSk8n8wl1ZLn30CEE3z1ds3y0oKaykl/enIPVrPy+Qtt3ZMhtkzXOSuASlJyGDXPU9bAnwE+Y5gkUHPsq1kTsylaNzuJD4vEyatMm2lAOZZYydfFOskqq7bG7h3TiiTHdHbJQtS7Zx0s4tDnTvh58czeqd2ZT8stxe8zY1oeQKb3Qe2vn3WGrqiLjgdnYyhQvDUNkBJFz5iDpdJrl1NLIssxvC96mOFuZvWP08GTcg09gaEWzdwTNyOonwVyh3A7tARfdo20+AoeiVYiR7dl1jmginGu7eUNyLjO/2EOFSXH/1OskXrimFxMvaqdxZufGZrWx8atk+zFMh7hgQoqrKVmVZn+MW7QvIVN6ofPU7k9RlmWy/+95ao4cAUAyGomaNw9DoOPW4DQHiWtWkrxN9VQZdfcsgiIdsyBa4GSkroVDP6nrcW+I+TOCerQKMbIjq07xahvnKV79ekc6Ty89iLW2A8XX3cB7t/dlcNdQjTM7Pw5uOk3+KcX/RG/UMbCdD6V1hUh7P0Im90Tnoe2fYfG331GydKl9Hf7003jGxWmYUcuTm3ac9YsX2tfxI8fQY9BQDTMSuAzmalhRp2i1963Q/lLt8hE4JC4vRrLKs0gvSwfAQ+9BfGi8xhmdG1mWeeO3o7y9Ti36bBvgyceTB9AtvOWHxDWEipIatv+kHsUM6xFIzRb1uMa9kz/Bd/VE565tS1/VgYPk/Pe/9rX/tdcScEvr8tI4U53IsLtaV62MoBnZ+hYU1r4XePjDqOe1zUfgkLi8GKnb0tsnrA9uesc+/zZZbDyxJJEf9p62x3pG+vHxpAGE+Wnju9EQtnyXgqlaOVrqG+yOT3qp/T73LgEE3xmLzk1bIWIpKuL07NnItRdh9+7dafPcs61q5oosy/y28B2KshSh+GediNFNu9ZqgQuRnwqbXlPXw58Bn9bVJi84P1qVGHF0f5HSajP3fr6bLakF9tjQbqG8d1tfvB3Q2v1spB8qIGVXLgC9PHVEW232+zxiAgm+PRbJqG1hqGy1kvnY45gzlYuwzteXqLfmofN03Bbp5mDfr8tJ3rrJvhZ1IoImw2aDn2eDtUZZRyRA/yna5iRwWJznCtcAZFl2Gn+R3LJqJn20k0NZ6g7ChAHRvHBtL4x65+nosJisbPzqKADxnjo61jmG8YgNJnhidySD9t9P/rvvUvF7nQF4L7+MWzvHLwpuSrJSktmweJF9HT9C1IkImpC9n8LJzcptSQ/j3xZOq4Kz4tJiJL0snZxKxSDMx+hDj+AeGmd0Zk7kV3DnR9s5VVhljz0yqhuzhndxuiOD3atOUppXRYKnnvbuqujwjAshaEIMkgMIq7J168h/b759HTxjBr7DW9cAvMrSEn6eOweb1QJAWMfOXD7pbo2zErgMpVnw67PqetADEOH49XoC7XBpMVJ3V6R/eH8MOsf7dhMzipn88U4KKpRJtnqdxEvXx3Fz/2iNM7twirIr2Lv6JH299ES7qaLDKyGUwJtikPTaC6uaEyfIfOxx+9p70CBCH7hfw4xaHpvNysp3XqesIA8Ad29vxj/8pPATETQdKx+FmlqDxqBOMPTxf368oNXjeFfnJqSuGHHEepFNR/O45/PdVNZ6iHgYdbw7sS8jeoRrnNmFI8syGz8/QoK7jqi6QqRfOIE3dEVyAHM2W0UFGfffj61caTc2tm1L5GuvIulb19bxH0u+IW3/Hvv6ypmP4B/WRsOMBC7FoWVw+Gd1ffU8MLauWizBheOyYsQm29iZvdO+djR/kZ/3Z/LQN/vsU3cDvIx8eNcA+rV3TqOt5G1ZRGaWE1lHiHgPbEPAtV0cQojIskzm0//GlKpY0Evu7kS9/VarMzZL27ebbUu+sq8HXnsTnfs51r8NgRNTVQwrHlXXfe4Qg/AE54XLipGUohSKaooACHQPpGtgV40zUs/YwIIAACAASURBVPlyezpPLz2AXOtMGunvwadTB9IlzDk8RP5KVXENlUuP1Rcil0QQML6zw9S8FH70MWWrVtnXbf7vP3jExmqYUctTmp/L8nde588/vOie8Qy6+XaNsxK4FGueg/Js5bZ3GIx+Qdt8BE6Dy4qRui29A9oMQCdpXzgJMH/DMV5edcS+7hLmw2dTBxLh75zbmLLZSvo7ewmr8+P1dDAhUrF1K7mvv25fB06cSMC112qYUctjNtWw7PX/UV2mdGt5BwYx9oFH0bWyIypBM3JsPez+RF1f9Sp4tq6dR0HDcV0xUscC3hHm0ciyzCurk5m/QZ1UGx/lzyeTBxLk7ZyFgzaTlcz5+/GuncgLYI0NJsiBhIgpI4PTDz2seB4Ann36EP5E6yqmk2WZtYvmk3NccfTV6fVc/eATeAeIC4WgiagugZ9mqeuYsRB7jXb5CJwOlxQjFpuFXTnqpF6t60WsNplnfzrIF9vT7bGLOwWx8M7++Ho457AoW42F/I+SIKvCHssJ8KDvHT0cRojYKivJmDkLa4lS1W8IC6PtvDeRWlnXSOKalSRtXGNfD7trOm27t64jKkEzs/opKM1QbnsGwri54CDvAwLnwCXFSHJhMuVmpWMizDOM9n7tNcvFYrXx6PeJ/FjH3n1kjzDemdgXD6NzbpHbqi3kf3QQU3qZPZZstnHRjHiHESJKwerT1CQnA7WTeN+ahzGsdVlRZx49zLqPF9jXsUOGkzB6rIYZCVyOo6th7+fqeuzr4Ot8HYECbXFJMVK3i6Z/m/6aXSDNVhsPfr2P5Qey7LFrEyJ59abeTuWqWhdbpZm8jw5izii3xw5WWWl7XRd8Ah1nnknBokWUraxTsPrcs3gmJGiYUctTUVzEsjdeUo3NOnRm5PSZDiMYBS5AZSEse0Bdx14LvW7QLh+B0+KSYqTuEc2ANgM0yaHGYmXmF3tZczjHHpt4UTv+e00vdA7Q6toQrBVm8hcdwFznaCax0kplWx96DnGceSblv/9O3htz7euAWycQcOONGmbU8lgtZn6e+xIVRYUAePj4Mv6Rp8QAPEHTsvLxOt0zoTD2DW3zETgtLidGrDYre3JUQ6f+4f1bPIdqs5UZn+1m49E8e2zyoA48Oy7WaT+VWstM5C06gCWn0h7bV2nllEXmptu6O4zAMqWlcfqRf9nbVz379aPNk09qnFXLs/6ThZw+cggASdIxdvZj+IeJrXNBE3L4Zzjwrboe9yZ4B2uXj8CpcTkxklyUTJlZqWUI8Qxp8XqRSpOFqZ/sYttxdfLuPUM78/iYGOcVIqU15C08gCVPmZ0jyzL7qqykm2T6XtGekCgfjTNUsJaXc2rmLGylSvuqITycqFZYsLr/t5Xs/22FfX3ZrXfSIb6PhhkJXI7yXPj5QXUdfwv0GKddPgKnx+XEyK5s9Yimf3jL1otUmixM/ngn208U2mOzR3TlwZFdnVaIWIpryF+YiKWgGgAZ2FNpJcMs4xfqyYCxHTTN709kq5XMR/6F6Vitw6qbG1HvvI0hJETjzFqWjMMHWffx+/Z1zKVDGDBenOELmhBZhqX3QWW+svaNgCtf1jYngdPjemJEo3qRKpOVKZ/UFyKPXhHDzMu7tFgOTY2lsJq8RQewFtYKEQl2lVvINCtHIMMmxmBwc4yOoLw351G+caN9HfHif/GMi9Mwo5anND+3tmBVmXUU1qEzV9zzgNMKYYGDsmMBpP6mrq95V5ibCRqNS4kRm2xjd85u+7ql6kWqTFamLt7JH8dVIfLkld2ZMbRzi7x+c2ApqCJv4QGsxTVKQCeRaMMuRGIuakN0jyANM1Qp+WU5BQsX2tfB06bif/XVGmbU8phrqvnp1RepKlU8VTz9/Lnm0acxuntonJnApchJgl+fUdeXzIIuI7TLR+AyOGd/6VlIKUqh1KTUCwR5BNHRv2Ozv2a12cq0T3ey9ZhaI/KEkwsRc14luR8kqkLEIJHV3o+0YhMAnr5GLrvJMWb9VB1MIuvpp+1r76FDCH3oIQ0zanlkWWb1+2+Rm6YcUen0esY//CR+Ia3LU0XQzJirYck0sNa+L7SJgxHPapuTwGVwKTFS94imJepFqs1Wpi3exZZUVYg8NiaGe5xZiORUkPdBIrZSRXhg0CGNbM+Ovfn2xwy+uRsePto7x1ry8siYNQu5RnlzdOvYkbavvYbUyuatbP/xW5K3brKvh0++h6gevTTMSOCSrHkOcpUOLQwecMOHYBCt4oKmwaXEyF/NzpoTk8XGPZ/vZnOqepF+9IoY7hvmvDUipqwK8hYcwFY7a0Yy6gi8owcbN6jusR3igunSX/tP3Lbqak7NmoUlW/E40Pn6EvXeu+h9nXPycUM5un0LW775zL7uPepKeo+6UsOMBC5Jym+wXS2M5ooXITRGu3wELsd5iRFJksZIkpQsSVKqJElPnOH+hyVJOiRJUqIkSWslSWpx//WWrBexWG3M/novG5JVH5FHRnVz6mJV0+ly8hcmYquoFSJuekKm9OJgcjFF2Yq3iNFDz5BbtW9RlmWZrKf/TfX+RCWg09H2jTdw79j8x3KORM7xVFa+o5pMRfeM5/JJMzTMSOCSlOXA0nvVdcxV0H+qdvkIXJJzihFJkvTAu8CVQCxwqyRJf52ytRfoL8tyPPA98EpTJ3oujhUfo7imGIBA90A6BzTPUYnNJvPYkkRWHsy2xx4Y3oX7RzhGDUVDMJ0qI2/hAWyVim245KEnZFovyox69qw6aX/cJdd2xjdI+4LIgg8+oHT5cvs6/Ikn8Bl8mYYZtTzlhQUsfeV5LCbliCqgTQRXP/wkeoNL1aQLtMZmhSVToaL2g5dPOIx/WwzBEzQ557MzMhBIlWX5uCzLJuBroN5saFmW18uy/Kc15x9AVNOmeW7q1ov0C++HTmr6EyhZlnluWRI/7FGPLaYM6shDo7o1+Wu1FDVpJeQtOoBcXStEPA2ETovD2NaH9Z8dxmZTumciOvvTywEs30tX/0rem/Ps64BbbiHwjts1zKjlMddUs/TVFyivtXp39/bmusefw9OndR1RCVqADXMg7ffahQTXLwDv1uXdI2gZzueK3RY4VWedURs7G1OBlWe6Q5KkuyVJ2iVJ0q68vLwzPaTBNHe9iCzLvLwqmc/+UHcKJgyI5plxPTQ/tmgo1ceKyf/oIHKN4kuh8zYQOj0Otyhf9q09Re5JxclWZ5AYdnt3JI0t36uSksh8/HH72uuii2jz76ed9uffEGSbjVXvziXneCoAkk7H1Q8+SVBki+t/gauTuhY2vaquhz0BnYZplY3AxTkfMXKmd3r5jA+UpNuB/sCrZ7pfluUFsiz3l2W5f2ho6PlneQ5kWW72epH3Nhzj/Y3H7OvxvSN58bo4p70QVqcUUfBJErLJBoDOx0jo9HjcIn0oyq5gx7IT9scOGNuRoAhvrVIFwJyTS8Z9M5GrFQM2Y/t2tH1zLpJR+66elmTLt59zdPsW+3r45HtoH9+6phELWoDSLPjhbuxv9Z2GwZBHNUxI4OqczwFzBhBdZx0FZP71QZIkjQSeBobKslzTNOmdHydKTlBYrWxZ+7v70zWwaes3vt15ildXJ9vXI3uE8/rNvdE7yHC4C6UquZCCzw6BRXmj0fm6ETo9DmOYF7JNZv1nR7BaFJESEu1Dn9HttEwXW2UlGffdhyVHmYCs8/Ulev58DIGty/Uxce1qtv+oDiZLuGIcCaOv0jAjgUtitcD3U1S7d59wuH4h6FpXy7ygZTmfnZGdQFdJkjpKkuQGTACW1X2AJEl9gA+A8bIs5zZ9mudIsM4RTd+wvk1aL7L2cA5P/njAvr6kUzDvTOyDUe+cXdFVSQUUfKoKEb2/O2Ez4jGGeQFwYGMGWccUF0+dTmL4nT3Qa/i9ylYrpx97jOqkJCWg19N27lzcO3XSLCctSNu/hzWL3rWvO/bpz+V3TdcwI4HLsv5FSN+q3JZ0cONH4KN9O7/AtTnnVUaWZQswC1gNHAa+lWU5SZKk5yVJGl/7sFcBH+A7SZL2SZK07CxP1yw01zya3SeLmPnlHqy1RZyxEX4suLMfHkbn/IRQeSCPgi8Og7VWiAS6EzojHkOIJwCl+VVs+1E9iuo7pj2h0doWRea+/gbla9ba122eeQafywZpmFHLk5eexs9zX0K2KbtVYR06M+7Bx9G1MnM3QQtwZAVsVtvFufwp6NC6OtUE2nBefYCyLK8AVvwl9myd2yObOK/zRpblvzmvNgWpuWVMXbyTarNyAYgO8uSTKQPw9XDOGoXKfbkUfpsMyreDIdiDkOnxGAIUB0VZlln32REstTUkQZHe9L+yg0bZKhR98y2FH31kXwdNmkTghFs0zKjlKS8s4Mc5/4epqgoAn+AQrnv8Wdw8PDXOTOBy5B2trROppfMIuOwR7fIRtCqc3pTgZOlJ8quUs01foy/dAhvfZptVUsWdH+6guFIxAAv2duOzKRcR5qu9x0ZDqNidQ9H3R+21aIZQT0Knx6H3U62cD23O5HRyEaBYCAy/swd6o3bHMxVbt5L9/PP2tc/w4YQ9+i/N8tECU3UVP778PGUFSueZm6cn1z/+HD5BwRpnJnA5qkvh64lgUjroCGgHNywCnXMeRwucD6cXI3ty99hv9wnvg76RRVblNRYmf7yTzBKla8PLTc/HkwfQIUTbbpKGUr4ji+IfU1UhEu5F6LQ49L5u9seUFlSxZUmqfZ0wqh3hHfxaOlU7NampZMx+EKxKy7F7bA/avvpKq5o5Y7VY+HnuHPvwO0mn4+qHniS0fetymRW0ADYb/HgPFKQoa4Mn3PIFeDnGVG5B68D5xUiOKkb6hvVt1HNZrDZmfbmHI9nKpwOjXuKDO/oRHxXQqOfVivJtmRT/pNaAGCO8CZnaC72PKkT+7J4xVysX/oBwLwaO0+6CZ87NJf3uu7GVKb8DQ3g40fPno/N2TjHYEGRZ5rcFb5O2T21XHzntPjr0btzft0BwRja9CsmqozHj34aIeO3yEbRKnF+M1NkZ6Rfer1HP9cIvh+rNm3np+ngGd206P5SWpOz305QsP25fG6N8CJ3SC51X/ZqXpN9Pk3FEPZ4ZcVcPDG7a7EDYKirIuOdeLJlZSj5eXkTPfw9jeLgm+WjFlm8+I2mjWrR78Q0TiB8xRsOMBC5L8irY8D91fcksiL9Ju3wErRanFiN5lXmcKlPMYd10bsQG/3Vkzvnz8ZYTLN6muqvOurwLN/ZzTlfL0g2nKF2VZl+7tfMlZEovdB71f90leVVs+UHdOUkY1Y42nfxbKs16yBYLGQ8/TPWh2hHlej1Rb87FI7bhv1NnZN/q5fW8RHpdPppLb7pNw4wELkteMvxQpz284xAY+X/a5SNo1Ti1GKm7KxIXGoeb3u0fHn121h7O4YVfDtnX4+IjeNgJ583IskzZ2nRK16TbY24d/AiZ3BOde/1ftWyTWffpYSy1VvCBEd4MvFqb4xlZlsn+73+p2LjJHmvz3LP4DBmiST5akbJ9K2s/Vse0d+o7gFHTZzqty6/AgakogC9vhppSZe3fDm78BPROfUkQODFO/ZfXFPUiSZkl3P/VXmqtROjTLoDXbuqNzsncVWVZpvTXk5StV8cIuXfyJ3hST3RnOHZJ3JBBZooy5VjSSYyc1AODRv4pBYsWUfz1N/Z18IwZBN58sya5aEXGoYMsf/tVkJU/xDZdujFutvASETQDlhr45jYoSlPWRi+Y8Dl4iy4tgXY4txipszPSN/zCxUh+eQ3TF++i0qTsDkQFerLgjv5OZ2omyzIlK09QvkmdJuzeNYDgO2LPKESKcyr5o465Wb8x7Qlrr033TMkvy8l7XTVZ8hs3jtAHZ2uSi1bknDjGj688j9WstJIHRkRy3ePPYfRwzlZygQMjy/DzbEjfVhuQFKv3iN6apiUQOK0YKTOVcbToKAA6SUdC6IUNCzNbbcz8Yo+9hdfX3cBHkwYQ6ut+jq90LGRZpuTn45RvVccFeXQPIvi2Hkhn8Amx2WTWLj6MpdbMLbitD/2v6tBS6dajYts2Mp980r72GjCAiP+92KqOJYqyTvPDS89hqqoEwDsgkOuffB4vP21qdwQuzu+vw/6v1PWo/4Me47TLRyCoxWnFyP68/dhk5YIaExiDj5vPBX39SyuOsP2EMlxPkmDerQl0C9fW+vxCkW0yxT+lUrE92x7ziA0meGJ3JMOZzYr2/nqS7OPq7JkRk3qgP8tjm5Pqw4fJmHU/1O4GuHXpTNQ7b6Nza1jdjzNSVpDP9y8+Q2WJclzm7u3NDU89T0B4G40zE7gkSUth3Qvqus8dcOkD2uUjENTBacVIvXqRCzyi+XFvBh9tOWFfPzyyG8O7O1f7qGyTKVqSQuXuHHvMMz6EoFtikM4y2C7vVBk7fla/7/5jO2gye8aUkaF4iVRUAIqXSLuFC9H7t57dgKqyUpb871lK85S5kgY3d6577DlhaiZoHk7tVIzN/qTDYBj7hvJJTCBwAJxWjOzOUQ2h+oT1Oe+vO3i6hCeWqFN4R8eGM/PyLk2aW3MjW2WKvj9K5V51QLJXnzACb+yGpD/zm4vFbGXNx4ew1Q7JC+/oR78x7Vsk33p5FBVxatp0rHmKhb/O15fohQswRkS0eC5aYaqu4oc5/6EgQ+l60un1jH/kKdp2b11tzIIWIj9F6ZyxKPONCOoMN38KhtazCylwfJxSjJisJg7mH7Svz9fsrLDCxIzPdlNjUY53Ood68/rNztU5I1ttFH6TTFVivj3m1S+cwBu6Iv3D97H9p+MUZtbuRLjpGDkpFt1ZdlCaC1tVFRn33IspLQ0AyWgk6t138OjmfG3UDcVsqmHpKy+QnarUOyFJXDnzYTomNM6wTyA4I2XZ8Pn1UKUcSeMZBBO/FVbvAofDKcVIUkESJpsJgHa+7QjxDDnn11htMvd/tYfTxcqnA193Awvu7O9UU3hli42Cr45QnVRgj3lf1IaAa7r8oxA5nVzEvrVqy++gG7oQEO7VrLn+FdlsJmP2bKr271cCkkTkq6/iPXBgi+ahJRazmZ9f/x+nkhLtsRFT7qX7oKEaZiVwWapL4fMbobjWd8joBbd9ByHOtRMsaB04pRhpyBHNe+tT2ZKqXsTn3pJA59ALK3rVEtlso+CLw1QfKbTHfC6NxP/qTv/YfVJTZWHN4kP2QXntegbRc0jb5k63HrLNRuZTT1Ox6Xd7LPypp/Abc0WL5qElNquV5fNe4USdeTOX3XoXCaOv0jArgctiMcE3t0NO7ZG0pIebPoGo/pqmJRCcDacUI3tz99pvn88RzY4Thcxdc9S+nnV5F0bGOk/Bqs1kpeCzQ9TUmpQB+AyJwv/KDudsg938zVHKC2sAcPc2MPzOHi3aOivLMjlz5lD688/2WPA9Mwi64/YWy0FrbDYrK999g9Sd2+yxi2+YwEXXihkggmbAZoOl98KJjWrs6nnQrfWIf4Hz4XRixCbb6omRc3XSFFWYmP216rA6sEMQD47s2pwpNik2k5WCT5KoqW3HBfC9PBq/0e3PKSpSd+dy5A+17XfYxO54+7esj0rBBx9Q9Oln9nXALbcQOrv1mJrJNhtrFr7LkS3qhaHfuOvEvBlB8yDLsOpxOPi9Grv839D3Du1yEgjOA6cTIylFKZSZlPHyQR5BtPNtd9bHyrLMv77bT1atsVmAl5F5tyZgaOHCzYZiq7GQ/3ESprRSe8xvVHv8Rpz9e/6TssJqNnxxxL7udlE4XfqFNUueZ6Po62/Ie3Oefe17xRW0efaZVmNqJssy6z75gAPrfrXHeo+6iqG3T2k1PwNBC7P2edixQF33nwJD/qVdPgLBeeJ0YuSvRzT/9Kb+8ZY01h5R219fu7E3Ef6ezZpfU2GrspD/8UFM6WX2mN+YDvgNiz7319pk1nx8iJpKCwC+wR4MmRDTbLmeidJVq8j+P3UCqNclFxP56itIrWTWiizLrPv4ffatXm6P9Rw6ghFT7hFCRNA8bHoNNqujFeh5PVz1mvASETgFTidGznc43oGMEl5aedi+njKoo9PUidgqzeR9eBDz6XJ7zH9sJ3wHn1/h6Z7VJ9UheBKMmtITd8+W+1WXb9zI6Ucfsw998+jVi6i332k17qqKEPmgnhCJuXQIo+95AEnnHLtyAifjj/fru6t2GwPXLwBd6xD/AufHqcSILMvszlW7Ec5WL1JpsnD/V3sw1xp8xbX15/ErW3ZnoKFYy03kf3gQc1aFPRZwTWd8Lok8r6/POVHKzrouq1d1IKJzyzmbVuzYQcYDs1Wb944diV7wAXof7xbLQUtkWWb9JwvYt/oXeyzm0iFcNesRdOLCIGgO9nym1In8ScchcNNi0DuPbYFA4FRiJLMik9xK5djFy+BFt8Azm2W9siqZtAJl8JiPu4F3JvbB3eD4FwJrmYm8RQew5Ci5I0HgdV3xHnh+s0pM1RZ+/SgJW221bptO/i06BK8qMZGMe+5FrlG6d4yRkbT7+CMMQa3DYOlPIbJ3ldo5FHPJYEWItJLjKUELk/gd/Fxnvkz0RTDhKzCKic8C58KpxEjdepHeob0x6P6e/rZjBXyyNc2+fu7qWNoHO/6ncmtJjSJE8motmyUIvLEb3v3O/2jp929TKK39ejcPPaOmtJzLanXyUdKn342tUhFShtBQ2n3yMcY2rWPom2yzsX7xwnpCpNslg7nq/n8JISJoHvZ/A0vvgdqBobSJV9xV3Z3HP0kg+BOnEiP7cvfZb5/J7KyixsJjS/bb1yO6h3Fjv6gWya0xWIqryVt4AGuB0vWDDoJujsEr4fy7X47uzObI1iz7esitMfiFtEyxrunkSdKnTsVWorQf6/39affRh7i1O3fXjytgs1lZs/Ddel0z3S4ZzFghRATNxb6vFC+RP90Mw2Lhjh/BM0DTtASChuJUYmR/nio0eof1/tv9c1Ye4VShsjPg52Hgf9fHOXzngqWwmryFiViLlKMNdBJBt3bHK+7cFvd/UpxbyYbPk+3rrgPCibmoZXYkTBmnOTlpMtb82sF33t5EL1qEe1fn8XJpDDarlVXz3+Tw7+vtMSFEBM3Kvi9h6X2oQqQn3LUMvM//PUMgcDScRoxUmCs4WqS4qOokHfEh8fXu35qaz2d/nLSv/++anoT7Ofa5qSW/StkRKakVInqJ4Nt64BkbfN7PYTXb+HVREuYaKwB+oZ4Mm9gyxbrmrCzS77oLS5ayIyN5eBD9/nw843q1yOtrjdViZsVbr3F0+xZ7LHbIcK64d7YoVhU0D3s/h59mYRci4b3gzmXgff7vGQKBI+I0YuRA/gFstWejXQO64uOmnouW11h49Ht1+Nio2HCuTWjZ+SsXijm3kryFB7CVKQP/MEgE3xGLZ8yFFXtu/SGVvFovEp1BYsz0Xri1QBuvOSeXk3dNwnz6NACSmxtR776D14ABzf7ajoDFZOLnN+dwfPcOeyx+5BhGTr1PtO8KmoddH8MvD2EXIm3iFCEiJvAKXACnESN1i1cTwhLq3fe/FYft03gDvIy8eF0vhz6eMWdXkLfoALZypf1VMuoIvjMWj66BF/Q8x/flkbg+w76+9PouhLbzbdJcz4QlP5/0yZMxp/85DdRI1Ntv4TNoULO/tiNgqq7ip9deJP2AWsPU98rxDLtrukP/3QmcmM1zYc1/1HWbeLjzJyFEBC6D04iR/bl16kVC1XqRXWmFfLk93b7+v/E9CfN13OMZU2Y5+YsOYKt1R5XcdATf1ROPzhdWeFZWWM26T1VTt469Q4i/vPmLdS2FhaRPnozp+HElYDAQ9eZcfIYObfbXdgSqykr5Yc5/yE5VBy8OvOZGLrv1LiFEBE2PLCsiZMubaiyyD9z+gxAiApfCKcSITbbVK179c2fEapN59qcke3xUbDjje5+fOZgWmDLKyPvwIHJVrRBx1xMyuSfuHS7MlMxqtfHbh0l2u3efQPcWmcZrKSoiffIUalJSlYBeT9vXXsN3xIhmfV1HoawwnyUvPktBhip+L735Ni6+foIQIoKmx2aF5Y/A7o/VWIfBcOtX4N78O6ACQUviFGLkWPExys2KNXqIZwhRPsoOwJc70jmUpQyR8zDqeO7qWIe9KNSkl5L/4UHk2kJTyUNPyJReuLfzu+Dn+mPpcbKOKW20kk5i9NSeeHg3r9uipbCQ9EmTqTlauyMgSUTOmYPfmNYxlrwo6zTfv/gMpXm1s44kiRGT7yHhirHaJiZwTSwm+HEGJP2gxmLGwo0fCUMzgUviFGJkX556Np8QmoAkSRRWmHhttdrOOnNYF6ICvbRI75zUpJWQ/1ESskkRIjovAyFT43Bre+HmRMf35rHvN/WT+UXjOxLRpXm9BSwFBYoQSUlRApJE5JyX8L96XLO+rqOQc+IYP7z0HJUlyrwfnV7PmJkP02NQ6ziaErQw1aXw7R1wfIMai58A17wLeqd4yxYILhin+Muua3b25xHNq6uPUFKlFIC2D/Zi+pBOmuR2LqqPFVPwSRKyWekE0nnXCpHICxcixTmVrF18yL5uHxdM39HtmyzXM2HJz+fkpEmYUo8pAZ1OESLjxzfr6zoKaYl7+fmN/2GqUgqkDW7ujH/kKTom9NM4M4FLUpoJX9wEOQfV2MAZMGYOiC4tgQvjdGKkd2hv9p8q5uudp+yx566OxcPoeL4O1UeLyP/0EFhqhYiPkdDpcRjDL9ye3mKysmrBQUzVyu6Kb7AHIyfFIuma71jqjELk5ZdbzY7IoU3rWP3+PGxW5Wfu7u3NdY//h7YxPTTOTOCS5CQpQqT0tBq7/GkY8qgyflsgcGEcXowUVBWQXqYcS7jp3Oge2INbFuz6czo9I7qHMbz7+c9vaSmqjhRS8NkhqJ0crPNzU4RIaMOOkjZ+fZSC00rdjM4gMebuXs1aJ2LOySF98hS1a0anI/KVV/Af5/o1ErIss2Ppd2z++lN7zCc4hBue+A8hjT5MxwAAIABJREFU7Tpol5jAdTm+Ab65A2qUGjh0Bhj/NiRM1DQtgaClcHgxUreLpmdIT5bty2X/KeXs3k2v49mrY7VK7axUJeVT8OURuxDR+7sTOj0OQwNnxRzakllv7szgm7sR1v7CC1/PF1PGacVH5FTt7pNeT9tXX8Hvqqua7TUdBZvVyrqP32f/byvtsZB2Hbj+yf/gGyTstgXNwN4vlMm7NqU7DjdfuOVT6Dxc27wEghbE4cVI3eLV2KA4Xl51xL6eMbSTw03krUzMo/DrZLDVCpEgD0KnxWEIalgFfF56GZu+Uj0tul0UTs/Bzde+bEpL4+SkyViys5WAwUDb115rFV0zpuoqls97heN7dtpj7XrFM/6Rp3H3cqy/M4ELYLPCb8/CtnfUmG8k3PYdtGkdIxUEgj9xfDFSp14kNy+CggrFPr1tgCf3DeuiVVpnpHJvLoXfJtvdmg0hnoRMi8MQ4N6g56sqM7Hi/USstTUnQZHeDJvYvdnal2tSUjg5ZQrWPGXoneTmRtt5b+J7+eXN8nqORGl+HktfeZ68kyfsse6DhjLmvgfRG5q3bVrQCqkqhiVTIXWNGgvrqQgRf8ceZSEQNAcOLUZMVhNJ+aqp2W971N2Fh0Z1w9PNcYpWK3ZlU7QkRRUioZ6ETo9D79cwIWK12li98CDlhcoQPTcPPWPu7oXRvXm+56qkJE5NnYa1WDkCkzw9iX73HbwvvbRZXs+RyE49ytJXX6CiuMgeG3DNjQyecKeYMyNoegqOwZe3QEGKGosZC9d/IMzMBK0WhxYjhwsPY7IpOyF++jacrlRqLjqGeHNtguM4rZZvz6L4x1T72hDuRei0OPS+bg1+zq3fp3L6qCIMkGDUlJ4Etmmeo4LKnTs5de992MprC2S9vYn+4H28+vdvltdzJI7+sZmV787FYlJEn06vZ+S0mcQNH61xZgKXJHUNfD8FqkvU2OB/KV0zQvgKWjEOLUbqHtGUFqtbl/cP74JB7xj/cMu3ZlK87Jh9bYzwJmRaHPpGdLoc+SOr3gC8i67uSIf45imeLFu3ntMPPYRcU3sx9vOj3aKFeMbHN8vrOQpn6pjx8PZh/CNPEd3Ttb93gQbYbLDpVdjwEur2qYdiZBZ3o6apCQSOgEOLkbqdNNXl7QDoFOLtMPNnyjZlULJCrTEwRvkQOqUXOq+GC5Hck6Vs+Fx1lu2UEEq/MR0ak+ZZKfnpJzKfehpqfTT0oSG0W7QIj5iYZnk9R8FcXc2q9+dxdNvv9lhAmwiue/w/BEWK83pBE1NZCD/cDam/qTHfCJjwJbTtq11eAoED4bBiRJZl9ubuta+tVYrT6AMjujrErkjp+nRKV5+0r93a+RIypRc6j4b/SCtLTax8/4C9YDUwwpsRk3o0i7FZ4aefkvO/l+xrY3Q07T5chFu7dk3+Wo5ESW42P736X/LS0+yxqNhejH/4KTx9m69dWtBKydwL39wJJeoIBzoMVmbM+IRpl5dA4GA4rBg5XX6a/Cqlq0O2umOrCaNTqDdXa7wrIssypWvSKVurvrm4dfAjZHJPdO4N/3FazFZWvp9IeVFtwaqngavuicOtEeLmTMiyTN5bb1Ew/317zL1bN6IXLcQY5tpvjukH9/Pzmy9TXVZqjyVcMZZhd04THTOCpkWWYddHsOoJsJrU+KAHYfgzYsaMQPAXHPZfRN0jGmtVO0DH7BFd0Tej/fm5kGWZ0tUnKdugWtG7d/Yn+K6e6BrR2SPLMus+PUL2ceUiKUkwakosAeFNO/hPNpvJeu4/lPygTgL1TEgg+oP30fv7N+lrORKyLLNnxTI2fv4hsq3Wml9vYMTUe4kf4fr+KYIWprJQMTE7/LMac/eDa+dDj9YxSkEguFAcVowk5iXab1ur2tElzIdx8drtisiyTMnyE5RvVudGuHcLJOSOHkiNnIuza0UaKTtz7OtBN3alQ1zTFqzaKirIeOghKjapdRLegwcTNe9NdF6OOe24KTBVVbL6g7fr1Yd4BwYx/uEniewmZswImpi0LfDD9PrzZcJ6wi2fQXBn7fISCBwchxUje3Pq74w8MF67XRHZJlP88zEqtqmW7B7dgwi+rQeSsXH1Kym7ctjxs1oEGzs4kvjhUY16zr9iyc/n1Ix7qE5SPVv8r72WiBeeRzK67vFEfnoay+bOoShT7UyK6BLD+EeewicoWMPMBC6H1aJ0y2x6BWSbGh8wDUb/F4wNGwUhELQWHFKM1FhrSC5SO0o6+HRnbFyEJrnINpnipalU7Mi2xzx7BhN0a3ckQ+OESE5aKWsXH7av28YEMmRCtyZ1WDWlpZE+/W51zgwQfO89hD7wQLM5uToCh35fz28L38FS27IM0Hu0Uh9icGEBJtCAgmPw4z2QsUONeQbC+HfEsYxAcJ44pBg5XHAYG8rQKGtNKNMG9dJkV0S2yRQtSaFyt3qE4hkfQtAtMUiN7OgpK6xmxfxErGblU1RAuBdj7u6Fvgk7hSp37SJj1v12V1V0Oto8+yyBE25pstdwNMymGjYsXkjimlX2mMHdndF330+Py4Zpl5jA9bDZYOciZb6MpUqNt78Mrl8gbN0FggvAIcXIypTt9ttSTTvGxbf8rohslSn8LpmqfXn2mFefMAJv6tboVtuaSjO/vLOfyhKlyt7dy8DY++LxaIRR2l8pWbaMrKf/jWw2AyB5eND2jTfwHe66c2byT51k+bxXyD+ltlwHRkYx/uEnCYlur2FmApejOB1+mgknNqkxnQGGPgGDHwad44yqEAicAYcUI+vT1KmpvYLj8PVo2W112Wqj8Otkqg7k22Ne/cMJvL5ro4WI1WxjxfwDFGZWAKDTS4yZEddknTOyLJP/9tvkvzffHtMHBxP93rt49u7dJK/haMiyzIG1q1m/eKHd1h0g5pLBjJ5xP26erlugK2hhZBn2fAqrnwZTmRoPi4Xr3ocI1/w3JhA0Nw4nRipqLGRWJSPV6o+b4wa16OvLFhsFXx6h+lCBPeZ9cQQB4zs3WojINpk1nxwiM6XYHhtxVw+iYgIb9bx/YqupIevJpyhdscIec+/ahaj57+MW5ZpbxtXl5fy64C1Stm+1xwxGNy6fdDdxI65w6boYQQuTnwo/z4aTm9WYpINBs2HYk2Bo2FBMgUDggGLk6z0HkYy1F2vZyPjYfi322rLZRsHnh6hOVqe3+gyKxH9cpya5qG1Zkkrq7lz7+pLrOtNtYJtGPy+AOTeX0/c/QNV+tQvJ+7LLaDv3DfS+rjkJNP1gIqvmz6UsXz1KC4luz9jZj4ljGUHTYTHB1nmw8VWwqjtvBHVWdkOiB2qXm0DgIjicGPnmwBao/YAR6dkNo75ljmhsJisFnx2ips6uhc+QKPyv7NAkQmTfmnT2r1U7WuIuj6LP6KaxXq9KTCRj1v1YclWhEzjxVsKfegrJ4HC/4kZjNtWw5etP2b38p3rx3qPHMvSOKRjdxCdUQRNxaoeyG5J7SI1Jerj0fhj6OLiJI0CBoClwqCtVam4ZaWWHca+9lgxp1zK7IrYaKwWLk6g5ro719h0ejd+o9k0iRI7uyGbL96n2dac+oVx2U9cmee7ipUvJfvY5ZFOt5bROR/gTTxB4x+0ueUSRczyVle++QUGGasfv4ePL6Bn303XgpRpmJnApyvNgzX9g3+f145F94Oq3IEJMdhYImhKHEiPf7DyF3lO9yFwc2fwTLW3VFvI/TsJ0Up1X4jeqPX4jmmbX4sT+PNZ8onqJRHT2Z9TkWHSNrT+xWMh99TUKFy+2x3T+/kTNfQPvS13vomy1WNj50/dsW/IVttopwwAd+/Rn9IwH8AkM0jA7gctgtSjtuuv/BzXqhxOM3jD833DRDNEpIxA0Aw4jRkwWG0v2pKOPUt0y40LjmvU1bVUW8j86iOmUWhXvf2VHfIc2jQPqqSOFrF6YhGyTAQiK9Oaq++IxNGKODYClqIjMRx6hYus2e8y9axei3n3XJafu5pw4xur355GXdtweM7p7MOzOaaJIVdB0nPgdVj4OuUn1493HwZiXIMD1/m0JBI6Cw4iRdUdyKLacwlun+GJEeEcQ5tV8U2RtlWbyPjyI+XS5PeY/rhO+lzVN10n28RJWzD+A1aKYmvmFejJ+dkKjvUSq9u8n48GHsGSp1vQ+I0cQOedl9D7ejXpuR8NiMrFtyVfsXLbEPuAOILJbD66c+TABbbRx5RW4GPkp8NtzkLy8fjyoM1z5CnQdqU1eAkErwmHEyNd/OaKJC2m+XRFruYn8RQcxZ1fYYwHXdsbn4qYZxJefUcYv7+zHUqMcJ3gHuHPN7AS8/RteWCnLMkVffknOnJeh1sgMIGTmTEJm3oekazrnVkfg9JFDrP7grXpzZQxGNy695Xb6jb0GndgqFzSW8jzYOAd2fQyyevSH0RuGPgoX3yfadQWCFsIhxEhWSRWbjubh1kYVI/GhzVMgZi0zkbfwAJbcSiUgQeD1XfEe0DQttkXZFSybt4+aSsXO3sPHyDUPJuAX0vBBWbaKCrKefY7S5eonN52/P5Evz8F32LDGpuxQVJWXsfnLxSSuW60YTNUS1aMXo2fcT2CEa/qlCFqQmnLY/j5sfrO+cRlA/AQY8aywchcIWhiHECO/H83HJoPOU2197R3a9E6G1pIaRYjk186RkCDwpm549w1vkucvyq5g6Rt7qSpTdi7cPA2MfyCBwDYNPz6pPnqU0w8/jCn1mD3m0bMnbefNcykjM1mWObRpHRs/+5CqMrWY2M3TkyG3TSZ+xBiX2/0RtDDmKtj1Efz+BlTm17+vw2Blum5kgja5CQStHIcQIym5ZaCrRO+umFcZdAa6B3Vv0tewFFeTt/AA1oJqJaCDoFti8OrdNHUphVkVLJ27l6pSpcXW4KZj3Mx4Qts1zHBMlmWKv/mGnJfmINeZPBtw882EP/0UOnfX2T7OP3WSNYve4/SR+oWDnfoOYMTU+/ALCdUoM4FLYDHB3s9g02tQlln/vpAYGP0CdB0NohBaINAMhxAjqbnl6OvsinQP7I6HwaPJnt9SWE3egkSsxbUXdZ1E0K3d8YoLaZLnL8gs56e56o6IwV3P1bPiiegS0KDns5aUkPXMs5T9+qs9Jnl40ObZZwm4/romydkRqC4vZ9uSr9i3+pd67bq+waEMnzyDLgMu1jA7gdNjrlZ8QjbPg5L0+vf5R8OQRyHhNtA7xNugQNCqcYh/hal55fWKV5uyXsScX0X+wkSstRNy0UsE39YDz9jgJnn+gtPl/PSmKkSM7nrG3d+byAYKkco9ezn9r0ewZKrdMu4xMbR943XcO3dukpy1xmazcmDtajZ/8znVdY5kdHo9fa+6hktuvBU3j4bX2AhaOaYKpSh169tQnl3/Pp9wRYT0vVMUpwoEDoTmYqTKZCWjqAqPKHVnpKnEiDm3kryFB7CV1QoRg46QO3rgEdM0Bln5GWX89OY+qstrhYiHnqtn9W7QjohsMpE3fz4FHyyAOm2sgRMnEvb4Yy5zLJN+MJENixeQl55WL962e09GTL2X0HYdNMlL4AJUFiqGZX/Mh6rC+vd5BcOgB2HANGHhLhA4IJqLkWN55ciyrf7OSEjjxYg5u4K8RQew1QoFyagj+K5YPLo0zYTczJRilr+XiKlK6ZoxeugZ/0ACbTr5X/Bz1aSkkPn4E1QfUudf6Pz9ifjvC/iNGtUk+WpNfnoav3+1mON7dtaL+4aEMvT2KXS7+DJhXiZoGPmp8Md7sO9LsFTVv883Qpkj028SuLmWD49A4EpoLkZSc8vRueUj6ZXC0kD3QKJ8G+eAasosJ3/RAWy17bWSm46QST1x79Swo5O/ciIxn9ULD2I1KzsYbh56rm6AEJFtNgoXf0re3LnqbBnAa8AAIl+egzGyaXxPtKQ0P5et335B0qZ19Vp1De7uXHTNTfS7+jox2E5w4cgynNwC296F5JWAXP/+gHZw2UNKTYg4jhEIHB7HECN1ilfjQuMa9QnZdKqMvA8PIlfXChF3PSFTeuHe3q/RuQIc2ZbFus+O2C3ePf3cGP9Ab0KiLqxrxnTyJFn/fobKnepOgeTmRujDDxF0551O38ZaWVrCjp++Z9/qX7DWMWlDkoi9bBiXTbwL36CmKSAWtCJqyiDxG9j5Yf1Jun/SJg4uuR96XQ8tNPFbIBA0HocQI3qPOvUijTiiqTlZSv5HB5FrnU8lDwOhU3vhFt2w9tq/sve3dLYuUafv+oV4MH52Av6h538GLVssFC5eTN5bb9dr2fWIjSXylZdx79KlSXLVisrSEnb98iP7Vv2Cuaa63n0d+/Rn8K13Edq+o0bZCZyW3MOKANn/9d+NygC6XgGXzlL8QsRxn0DgdGguRlJyy9B7q5bfvUJ6Neh5ao6XkP9JErJJESI6LwMhU+Nwa+vT6BxtNpltP6Syb40qmoLb+nD1A70vyOK9+vBhsv79DNVJdfw09HpCZtxNyD33ILm5NTpXragqK2XXLz+yd9UvmKvrn9u36dKNIRMnEd1TjF0XXAA1ZXDwB9j7OWTs+Pv9Rm+Iv1mxbQ/t1vL5CQSCJkNTMWKy2DhZWIpHsNrG2hAxUp1aTMHiJOTaGg6dt5HQ6XEYG+F8as+x2sJvHyaRdqDAHovo4s/Y++Jx9zq/bWBbVRX589+n4MMPoY6fhnv37kT897949urZ6Dy1orywgN0rfmL/byv/JkJCottzyU0T6TrwUlGcKjg/ZBnS/1BMypJ+BHPl3x8T0k3piuk9ATwuvGBcIBA4HpqKkZMFFdiMmUiScoGO9o3G3/3C3lyqjxaR/+khqJ2Oq/M1EjotDmN444VIaUEVK95LpOC0OlCvU0Ioo6bEYnA796A2WZYpX7eOnP+9hPn0aXtccnMjZOZMgqdMRjI657l2YWYGO5f9wOHf12G1WOrdFxLdnktuvFURIU5e+yJoIfKSIfFbOPAdFJ/8+/06A8RcpYiQjkPEUYxA4GJoKkYU59WGH9FUHSqg4IvDYFWKSfV+boRMj8N4ATUcZyPrWAkr30+0m5kB9L2iPRdf0wlJd+43QlN6OtkvvkjFxk314p79+xHx/Au4d3K+uglZlsk8eoTdv/xIys5t9bpjAIKj2nHJjRPpdpEQIYLzoCQDkpbCgW8ha/+ZHxPaHfrcoeyCeIuCZ4HAVdFUjKT8pXg1LiTuvL+26mA+BV8egdquFn2AO6HT4zAEN9658/DWLDZ8eQSbRXlunV7i8tu70/2SiHN+ra2ykoJFH1KwaFG9dl29vz+hDz9MwE03Ot2F2mI2c3Tb7+xZuYyc46l/uz+iW3cGXnMTnfsOcLrvTdDCFJ2Ew8vg0E+QsfPMj/Hwh9hrFZfUtv3ELohA0ArQfGdE14Cdkcr9eRR+cwRqjUr1QR6KEAls3Dwbs8nKpq+PcmSrWsPi4WPkynvizmnvLlutlCxdSt68t7Dk5qp3SBIBN91E6EMPYghsGsO1lqK8sIDEtavY/9tKKkuK/3Z/xz79GXjNjbTt3lPUhAjOjCwrLbjJK+DICsjcc+bH6d2h2xVKQWrX0cIbRCBoZWgqRo7m5qHzVyb16tCf16Teij05FH131O5xZAjxJGR6HIYL6Go5E0XZFaxacJDCTLU+JCjSm7H3xeMX8s+7LeWbt5D7yivUHD1aL+4RF0ebZ5/BM+78d3y0xmazkrZvD4lrV3N8zw7kOtb0AHqjkR6XDaPvleNFi67gzFhMkL5VMSNLXgHF6Wd+nKSHTkOh53XQYzx4No0poUAgcD40FSNp5ckYAxRV0cm/M56Gf77oV+zMpuiHFFWIhHkSOi0evV/jWmKP7shm/RfJWGrUTpeYi9owdGIMRvezF6pWJSWRN/dNKjZvrhfXh4YQNns2/tdf7zTHFqV5uRzcsIaD63+jrCDvb/f7BAWTMHoscSOuwMtPdDAI/kLhCTi2FlLXwolNYCo/8+N0Rug0DHpeqxSkejXNnCiBQODcaCZGTBYbNjf1E1PvsH/ePSj/I5Pipcfsa2MbL0KmxaH3abgQqamysOW7FA7XOZbRG3UMmdCNHpdGnPXoofrIEfLeeYfyNWvrxSVPT4KnTiV48iR03o4/B6OmsoKjf2zh0KZ1ZBw+eMbHRMfGET/qSroOvBS9QXNbGoGjUFmoiI4Tm+D4Big8dvbHuvtBl5GK+Og6Ejyd67hSIBA0P5pdXWosVnTnWbxatvk0Jb8ct6+Nkd6ETI1D793wttj0QwWs/+wI5UWqC6p/mCdj7u51Vmv36qNHyX/3PcpWr65/h05HwA3XE3L//RjDwhqcU0tgMZlI27+Hw1s2cnzXdixm098e4+nrR89hI4kbPpqgyMbNCRK4CJWFiv/HyS1wYiNkH/jnxwe0V2pAYq6C9oPA4LyGfgKBoPnRTIxUm234nEfxatnGDEpWnrCvjdG+hE7uie48Dcf+iqnKwpYlqRzanFkv3rV/GMNu646b599/JJV79lLw0YeUr133t3ZW3yuuIHTWTNy7dm1QPi2B2VRD2v49HN22mWO7d/zNnAxAknS0792HnkNH0GXAJRic1P9E0ATIMhSlwakdkL5N+S/vyD9/jcETOg5WdkC6jISgTqILRiAQnDeaiZEqiwk/Y4mShORG54DOf3tM6bp0Sn9VDZDc2vsRMrknOo+GpX0yqYANXxyhvLDOTBgfI0NvjaFLv/o7GrLNRvn69RR8+BFVe/7eAeAzcgShs2bh0f3cRbdaUFVWyom9uzi2ewcn9u0+owABCO3QidjBl9N90FB8AsX5faukugQy9yqtthm7lP8q8//5ayS90nbbcYgiQqIvBmPjutkEAkHrRbudEUs1oGzdtvfphkGnpiLLMqW/naRsnXqM49bRn5BJPdH9Q0Hp2SjOqWTz9ymcrGPpDtC5TyhDbo3Bq04BrLWsjJJlyyj6/AtMJ0789anwufxyQmbNxLOnY1m4y7JMwamTnNi3m2O7t5OZfARZtp3xsQFtIuh28WV0HzSU0HYdWjZRgbZUFkJ2ImTug6x9yv+L/v53/jd0BojsA+0uhg5DoP0l4N40AygFAoFAMzFitlUDfgAkhKkD1GRZpnRVGmUb1SMc9y4BBN8Zi+48LNjrUlNlYdeKNBLXncJmVY9X3L0NDJ0QQ5f+YfYi1epDhyj66mtKli9HrvzLPAyjEf9x4wieMtmhjmMqios4eWAfJxP3cvLAPiqKCs/62MCISLpdfBndLr6M0PYdhS+Iq2MxQUGq4vGRcxBykiD7IJRlnvtrQTEea9tP2fFofwm07Q9ujXc2FggEgjOhXXuEpBZODozsDShCpOSX45RvUd8wPWICCb49Fsl4/i2yFrOVw1uy2Ln8RD07dyTocWkEF1/TGS8/N6zFxZSu/pXiH5ZQvT/xb8+j8/EhcMItBN5xB8bw8AZ8k01LeWEBGYcPknE4iYzDBynIOIt/A4AkEdE1hs59B9K530CCo9sLAeKK1JQpoiM/FfKPQt5hZc5LwTGQref+elB2PcJ6QNQARXREDYDgLuAkbekCgcD50U6M6FQxEhcSh2yTKV52jIo/6rif9ggi+LYeSIbze1M011hJ+v00e39Lp7KkfpdIRGd/Lru5KyFt3CnfsIFTPy+jfOMmMJv/9jzuXbsQMGEC/tdcg97Hp4HfYOOwWizkp6eRlZJMVmoymcmHKc7J+sev8fD2IbpXPJ36DqRTn/54+QsTKZegukTx8ShKU45UCk9A4XHIT4Hy7At7Lr27IjwiekNkAkQkQHhP4XgqEAg0RcOdEaWewYgPbb3bUrw0lYod6hurZ69ggiZ0Py8hUlNl4eDGDPatOUV1eX1x4RPozsVXRdOm/DAV731Lyrr12MrK/p6O0YjvmDEETrgFz759W3QXwWoxU5Bxity04+SmHSP7WAp5J46fse22Ljq9gciY7rSP60P7+ATCO3VBp7vwmhqBhsgyVORD6Wnlv+JTUHJKmVxbnK78V1XUsOcOaKcMmgvvpQiONnEQ1Bn0wi9GIBA4Fpq/K0V6dKN4SQqVe9R5Lp69Qwm6OQZJf3ZBoEyQLebw1iyO7cnFYq5frOnlo6f7/7d37zFyVXUAx7+/3Z3d7cw+23100y59uCwtEBILKiamavFBaqExQakJEZRIAtHER0wkJkr0D0VjjCYkWJQoJCLiH9oYlD8ExCAFahAiRWqFut1ud7uPmX3M7Lx//nFu2+l2OnN327t32P19kpNz750zd0/2l5n97Tn3ntuboPfIE2TveZ6RMiMgAM3XXEP7nj207fkEDWuDvZukWCwwPTbK5IlhJoeHmBoeYnzoGJPDxykW8lXf3xBppG9wGxu3X8XG7VfTN3AFkWa7g6EmqbokYu4UJE/B7BjMnoTZUTeaMTvqJSAjUKicdFZUF3G30a4bgK4B6N4O3VdA1yA0hTOqZ4wxixVqMlKndXx5ZC+psbOJSHRHD523DCJ15RORmYl5jrw0xhsvnGRm/PzbVaMyz6bRZ+l57s/UF/Nkypwj0t9P+0030XbTHpq2XNrnqxTyOWYnJ5keGyUxNkJibJTE6AiJ0ZPER0coXCApKqetu5e+gUHWDwzSd/k2ercO2PofYVCFXMolF/Nxd0fKfBzmpyA1CclJV6cm3ChHctyVYvUE05f6JujcBJ1bYO0Wr97qko/2y2ykwxjzjufrW0xEbgR+AtQDP1fV7y94vQl4BLgWmARuVdVjFc+JcO+Jz7NttvvMsdh71tPxyYFzEpFctsDIkQRDr08ydHiKxFiq3OmIzZ2gf/hp1o+9RF2ZW1qbtm2jddcuWnbtovmqKxc9DaOqZOdTzMWnSMbjJBNTJBNxkok4sxPjzEycYnZinLlE/LyF0fxo711Pz6atdG/eQs/mrax/1yCxDls2+6IUC5BNukQim/TKHGTmIDvr9jNzkJlxF4Kmp12dmXHb6WmYT7i66D+JXLTmdmjb4Er7Bje90rEJ2vvddkuvXUxqjFnRqiYGrc/3AAAGpklEQVQjIlIPPAB8FBgGXhaRA6p6uKTZnUBcVQdEZB9wP3BrpfP2Zbv4wOyOM/ux6/to2tXPiSNxJt+eYuJ/caZOppgYz1Mslk8cGvIpescO0Xfy77TOHae0lUSjRK+9lpadO4nu3EldTxf5bJZcNkvqxHGy6Xly6TTZdJrcfIp0KkkmmSSTSpJJzpFJJpmfnTmnFAs+706ooKVzLWs39LNu42Ws2+jq7k1baIrW/rNsylJ1IwDFglfnQYtntwu5c+tiDgp5NzVRzLnjhZzbP6fkIJ/xShoKmXP382nIpUu2U5Cb94q3nU+H+7tpaoNYN7T0uISidb1X+tx+2wZo67P1Oowxq55olf/iReT9wH2q+nFv/14AVf1eSZunvDYviEgDMAp0a4WTX9O3TZ+8/SEA/jPzb/45/SognHkk7xlaUitogYZ8ikhujvp80r0ioCIQqUMjdWh9HUWgUHSluPiBiovS0gxta4TOmNARq6M9JnTGoCMmNEdkwciJt73wmGr511UXHNPytRbLHCs9Xjy7f045fazgJRWFs/vF03XhbH1evFao+kZYs9Y95C3q1Ws6IboOYl2ujnp1S7dLQiKVn0JtjDEriYj8Q1WvW8p7/UzTbACOl+wPA++7UBtVzYvINLAOqLKmNLyROMhr8b/6660nK5BtBBrL3I5Y9EoAIlIg2pAl1pClxatjDVlaIxnaIhlaGzK0RLLUy4I/0PNeqfrbMJeWQCQKjTG3YFck5i7qbGzx6lb3WnObG51oKqnXdLjpk+Z2aO6wpc6NMSZAfpKRcnMkC/8d9tMGEbkLuMvbzfTfv7P8c+tNWLpYcSnTdNgduBgrMB7vaBaP2mMxqS1XLPWNfpKRYaC/ZH8jsHBN6dNthr1pmnbgvLXJVXU/sB9ARA4tdTjHBMNiUlssHrXF4lF7LCa1RUQOLfW9fi7Rfxm4XES2iEgjsA84sKDNAeB2b/sW4OlK14sYY4wxxpxWdWTEuwbki8BTuFt7H1bV10XkO8AhVT0A/AJ4VESO4kZE9gXZaWOMMcasHL7WGVHVJ4EnFxz7Vsl2GvjUIn/2/kW2N8GzmNQWi0dtsXjUHotJbVlyPKre2muMMcYYEyRb1tEYY4wxoQo8GRGRG0XkTRE5KiLfKPN6k4g87r3+oohsDrpPq5mPeHxVRA6LyGsi8hcR2RRGP1eTajEpaXeLiKiI2N0DAfITDxH5tPc5eV1Efr3cfVxtfHxvXSYiz4jIK9531+4w+rkaiMjDInJKRMouzSHOT71YvSYiO8q1O4+qBlZwF7z+F9gKNAKvAlcuaHMP8KC3vQ94PMg+rebiMx4fBqLe9t0Wj/Bj4rVrBZ4DDgLXhd3vlVp8fkYuB14BOr39nrD7vZKLz5jsB+72tq8EjoXd75VagJ3ADuBfF3h9N/An3Ppj1wMv+jlv0CMj7wWOqupbqpoFfgPsXdBmL/Arb/t3wA2y2KfYGb+qxkNVn1HV008jPIhbV8YEx89nBOC7wA+AkB+4s+L5iccXgAdUNQ6gqqcwQfITEwXavO12zl8Ly1wiqvocZdYRK7EXeESdg0CHiPRVO2/QyUi5peQ3XKiNquZxS2auC7hfq5WfeJS6E5fhmuBUjYmIvBvoV9U/LmfHVik/n5FBYFBEnheRg95TzU1w/MTkPuA2ERnG3fn5peXpmiljsX9nAJ+39l6ES7aUvLkkfP+uReQ24Drgg4H2yFSMiYjUAT8G7liuDq1yfj4jDbipmg/hRg7/JiJXq2oi4L6tVn5i8hngl6r6I+/hro96MQnoSWWmgiX9TQ96ZGQxS8lTaSl5c0n4iQci8hHgm8DNqppZpr6tVtVi0gpcDTwrIsdwc7AH7CLWwPj9zvqDquZU9W3gTVxyYoLhJyZ3Ar8FUNUXgGbcc2vM8vP1d2ahoJMRW0q+tlSNhzcl8DNcImJz4cGrGBNVnVbVLlXdrKqbcdfx3KyqS34GhKnIz3fW73EXeiMiXbhpm7eWtZeri5+YDAE3AIjIdlwyMr6svTSnHQA+691Vcz0wraonq70p0GkataXka4rPePwQaAGe8K4jHlLVm0Pr9ArnMyZmmfiMx1PAx0TkMFAAvq6qk+H1emXzGZOvAQ+JyFdwUwJ32D+1wRCRx3BTlF3eNTrfBiIAqvog7pqd3cBRIAV8ztd5LV7GGGOMCZOtwGqMMcaYUFkyYowxxphQWTJijDHGmFBZMmKMMcaYUFkyYowxxphQWTJijDHGmFBZMmKMMcaYUFkyYowxxphQ/R8HN6v5yYlTDwAAAABJRU5ErkJggg==\n", "text/plain": [ "<Figure size 648x648 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(9, 9))\n", "ax = fig.add_subplot(111)\n", "\n", "x = np.linspace(0,1,100)\n", "params = np.array([[[.5,.5]],\n", " [[5,1]],\n", " [[1,5]],\n", " [[2,2]],\n", " [[2,3]],\n", " [[3,2]],\n", " [[1,1]]])\n", "for i in range(params.shape[0]):\n", " beta_cdf = sp.stats.beta.cdf(x, params[i][0][0], params[i][0][1])\n", " ax.plot(x, beta_cdf, lw = 3, label = '$a = %.1f, b = %.1f$' % (params[i][0][0], params[i][0][1]))\n", " ax.legend()\n", "\n", "ax.axis([0, 1, 0, 1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# <font face=\"gotham\" color=\"purple\"> $\\chi^2$ Distribution</font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\chi^2$ distribution is closely connected with normal distributions, if $z$ has the standard normal distribution, then $z^2$ has the $\\chi^2$ distribution with $d.f.=1$. And futher,if\n", "\n", "\n", "\\begin{equation}\n", "z_1, z_2, ..., z_k \\sim i.i.d. N(0, 1)\n", "\\end{equation}\n", "\n", "Then summation has a $\\chi^2$ distribution of $d.f. = k$:\n", "\n", "\n", "\\begin{equation}\n", "\\sum_{i=0}^k z_i^2 \\sim \\chi^2(k)\n", "\\end{equation}\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## <font face=\"gotham\" color=\"purple\"> $\\chi^2$ PDF and CDF</font>" ] }, { "cell_type": "code", "execution_count": 99, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 864x504 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "k = 1\n", "x = np.linspace(0, 5, 100)\n", "chi_pdf = sp.stats.chi2.pdf(x, k)\n", "\n", "fig, ax = plt.subplots(figsize = (12, 7))\n", "ax.plot(x, chi_pdf, lw = 3, c = 'r', label = '$\\chi^2$ distribution with d.f. = 1')\n", "ax.legend(fontsize = 18)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 100, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 864x504 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize = (12, 7))\n", "for i in range(1, 6):\n", " x = np.linspace(0, 5, 100)\n", " chi_pdf = sp.stats.chi2.pdf(x, i)\n", " ax.plot(x, chi_pdf, lw = 3, label = '$\\chi^2$ distribution with d.f. = %.0d'%i)\n", " ax.legend(fontsize = 12)\n", " ax.axis([0, 5, 0, 1])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# <font face=\"gotham\" color=\"purple\"> F Distribution</font>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If $U_1$ has a $\\chi^2$ distribution with $\\nu_1$ d.f. and $U_2$ has a $\\chi^2$ distribution with $\\nu_2$ d.f., then\n", "\n", "\n", "\\begin{equation}\n", "\\frac{U_1/\\nu_1}{U_2/\\nu_2}\\sim F(\\nu_1, \\nu_2)\n", "\\end{equation}\n", "\n", "We are using $F$ distribution for ratios of variances." ] }, { "cell_type": "code", "execution_count": 101, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 864x504 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 5, 100)\n", "fig, ax = plt.subplots(figsize = (12, 7))\n", "\n", "df1 = 10\n", "df2 = 5\n", "f_pdf = sp.stats.f.pdf(x, dfn = df1, dfd = df2)\n", "ax.plot(x, f_pdf, lw =3, label = '$df_1 = %.d, df_2 = %.d$' %(df1, df2))\n", "\n", "df1 = 5\n", "df2 = 10\n", "f_pdf = sp.stats.f.pdf(x, dfn = df1, dfd = df2)\n", "ax.plot(x, f_pdf, lw =3, label = '$df_1 = %.d, df_2 = %.d$ '%(df1, df2))\n", "\n", "df1 = 8\n", "df2 = 15\n", "f_pdf = sp.stats.f.pdf(x, dfn = df1, dfd = df2)\n", "ax.plot(x, f_pdf, lw =3, color = 'red', label = '$df_1 = %.d, df_2 = %.d$' %(df1, df2))\n", "\n", "df1 = 15\n", "df2 = 8\n", "f_pdf = sp.stats.f.pdf(x, dfn = df1, dfd = df2)\n", "ax.plot(x, f_pdf, lw =3, label = '$df_1 = %.d, df_2 = %.d$ '%(df1, df2))\n", "\n", "\n", "ax.legend(fontsize = 15)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.7.4" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": true, "toc_position": { "height": "calc(100% - 180px)", "left": "10px", "top": "150px", "width": "165px" }, "toc_section_display": true, "toc_window_display": true } }, "nbformat": 4, "nbformat_minor": 2 }