{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline\n", "\n", "import pandas as pd\n", "\n", "import sys\n", "import fmt" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Lecture 6: Monte Carlo\n", "\n", "Topics:\n", "\n", "* Foundation of Monte Carlo\n", "* Random number generation\n", "* Discretize stochastic processes\n", "* Least square MC \n", "\n", "$\\renewcommand{bt}[1]{\\tilde{\\boldsymbol #1}}$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Foundation of Monte Carlo\n", "\n", "Monte Carlo: a town in Monaco principality in SE France, gambling resort." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Introduction\n", "\n", "$\\renewcommand{hs}{\\hat{\\bs s}}$\n", "Monte carlo simulation: \n", "\n", "* one of the most important and widely used numerical methods in scientific computing\n", "* invented in the 40s, born with computers\n", " * first used in Manhattan project, then for the development of Hydrogen bomb\n", "* widely used in quantitative finance, more popular recently with the rise of GPUs" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Common steps in Monte Carlo:\n", "\n", "* generate random samples from probability distributions or stochastic processes\n", "* perform deterministic computations on the samples\n", "* aggregate the results\n", "\n", "Typical applications are:\n", "* integrals and expectations \n", "* quantiles, and other statistical metric" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## A classic example\n", "\n", "Compute the value of $\\pi$ using Monte Carlo:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def sim_pi(ns) :\n", " es = np.random.uniform(size=[ns[-1], 2])\n", " d = np.array([x*x + y*y < 1. for x, y in es])\n", " \n", " return np.array([4.*np.sum(d[:n])/n for n in ns])\n", "\n", "ns = 4**(np.arange(8))*100\n", "ps = sim_pi(ns)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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3CyjJ9Sc99smRUh51fdwIuNOUugG7pZR7pZRFwFvAtVbZqjIDFeGQmppKXl6e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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure(figsize=[10, 4])\n", "subplot(1, 2, 1)\n", "\n", "es = np.random.uniform(size=[500, 2])\n", "d = np.array([x*x + y*y < 1. for x, y in es])\n", "dn = np.logical_not(d)\n", "plot(es[d,0], es[d,1], 'r.');\n", "plot(es[dn,0], es[dn,1], 'b.');\n", "x = np.arange(0, 1.01, .01)\n", "plot(x, np.sqrt(1-x*x), 'k');\n", "\n", "subplot(1, 2, 2)\n", "\n", "semilogx(ns, ps, '.-');\n", "axhline(np.pi, color='r')\n", "legend(['Simulated', 'True Value'], loc='best')\n", "\n", "xlabel('Number of dots')\n", "title('Simulation of $\\pi$');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "* randomly throw dots to a 1x1 square, and count the percentage of dots falling into the quarter circle\n", "* the percentage should be $\\frac{\\pi}{4}$ in the limit\n", "* with a large number of dots, $4 \\times$ the percentage $\\rightarrow \\pi$. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Population and samples\n", "\n", "Given a random variable $\\renewcommand{bs}{\\boldsymbol} \\renewcommand{var}{\\text{var}} \\renewcommand{std}{\\text{std}} \\renewcommand{cov}{\\text{cov}} \\tilde{r}$, its true statistics are referred as the population statistics:\n", "\n", "* population mean: $\\mu = \\mathbb{E}[\\tilde r]$\n", "* population variance: $\\sigma^2 = \\mathbb{E}[\\tilde r^2] - \\mu^2$\n", "\n", "We use $\\bs r = [r_1, r_2, ..., r_n]^T$ to represent samples of $\\tilde r$:\n", "* samples can be multiple observations of the same R.V\n", "* or multiple draws from the population distribution\n", "\n", "The samples themselves are random as well, we can define their statistics:\n", "\n", "* sample expectation is $\\mathbb{E}[\\bs r] = \\mu \\bs 1$\n", "* for independent samples, covariance matrix: $V = \\mathbb{E}[(\\bs r - \\bs 1 \\mu)(\\bs r - \\bs 1\\mu)^T] = \\sigma^2 I$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Sample mean\n", "\n", "$\\hat{\\mu}$ is the mean of the samples:\n", "\n", "$$\\hat{\\mu} = \\frac{1}{n}\\sum_{i=1}^n r_i = \\frac{1}{n} \\bs 1^T \\bs r$$\n", "\n", "$\\hat \\mu$ is an unbiased estimator of the population mean $\\mu$: \n", "\n", "$$\\mathbb{E}[\\hat{\\mu}] = \\frac{1}{n} \\bs 1^T \\bs 1 \\mu = \\mu $$\n", "\n", "the variance of sample mean:\n", "\n", "$$\\var[\\hat{\\mu}] = \\cov(\\frac{1}{n} \\bs 1^T \\bs r, \\frac{1}{n} \\bs 1^T \\bs r) = \\frac{1}{n^2} \\bs 1^T V \\bs 1 = \\frac{1}{n^2} \\bs 1^T \\sigma^2 I \\bs 1 = \\frac{\\sigma^2}{n}$$\n", "\n", "* the std dev of $\\hat{\\mu}$ decrease at a rate of $\\frac{1}{\\sqrt{n}}$\n", "* this is the foundation of the Monte Carlo method" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Sample variance\n", "\n", "$\\hat \\sigma^2$ is the variance of the sample:\n", "\n", "$$\\hat{\\sigma}^2 = \\frac{1}{n}\\sum_{i=1}^n (r_i - \\hat{\\mu})^2 = \\frac{1}{n} (\\bs r - \\bs 1 \\hat{\\mu})^T (\\bs r - \\bs 1 \\hat{\\mu})$$ \n", "\n", "$\\hat{\\sigma}^2$ is an biased estimator of the population variance $\\sigma^2$:\n", "\n", "$$\n", "\\begin{array}\n", "\\\\ \\mathbb{E}[\\hat{\\sigma}^2] &= \\mathbb{E}\\left[\\frac{1}{n}\\left(\\bs r^T \\bs r - 2 \\bs r^T \\bs 1 \\hat \\mu + \\bs 1^T \\bs 1 \\hat \\mu^2\\right)\\right] = \\mathbb{E}\\left[\\frac{1}{n}\\bs r^T \\bs r - \\hat \\mu^2\\right] \\\\\n", "&= \\mathbb{E}[\\tilde r^2] - \\mathbb{E} [\\hat \\mu^2] = (\\sigma^2 + \\mu^2) - (\\frac{\\sigma^2}{n} + \\mu^2) = \\frac{n-1}{n} \\sigma^2\n", "\\end{array}\n", "$$\n", "\n", "$\\hat{s}^2 = \\frac{n}{n-1}\\hat{\\sigma}^2$ is therefore an unbiased estimator of $\\sigma^2$.\n", "* $\\hat s^2$ follows Chi square distribution, converging to normal distribution for large $n$ (central limit theorem)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Sample standard deviation\n", "\n", " $$\\hat s = \\sqrt{\\hat s^2} = \\sqrt {\\frac{1}{n-1}\\sum_{i=1}^n (r_i - \\hat{\\mu})^2} $$\n", " \n", "* $\\hat s$ is routinely used as an estimator for $\\sigma$\n", "* $\\hat s$ follows Chi distribution, which converges to normal for large $n$\n", "* error and standard deviation $\\hat s$ are often used interchangeably\n", "\n", "Is standard deviation is an unbiased estimator of $\\sigma$?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "* No, because of Jensen's inequality:\n", "\n", "$$ \\mathbb{E}[\\hat s] = \\mathbb{E}[\\sqrt{\\hat s^2}] \\le \\sqrt{\\mathbb{E}[\\hat s^2]} = \\sqrt{\\sigma^2} = \\sigma$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Variance of sample variance\n", "\n", "$$\\var[\\hat s^2] = \\frac{1}{n}(\\mu_4 - \\sigma^4 \\frac{n-3}{n-1}) \\approx \\frac{\\beta - 1}{n} \\sigma^4$$\n", "\n", " * $\\mu_4 = \\mathbb{E}[(\\tilde{r} - \\mu)^4]$, population's 4th central moment\n", " * $\\beta = \\frac{\\mu_4}{\\sigma^4}$ is the population's kurtosis\n", " * the derivation is rather [tedious](http://math.stackexchange.com/questions/72975/variance-of-sample-variance)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Monte Carlo error\n", "\n", "The MC error of $\\hat \\mu$ can be estimated as $\\frac{\\hat s}{\\sqrt{n}}$:\n", "* the true MC error is $\\frac{\\sigma}{\\sqrt{n}}$, but $\\sigma$ is usually unknown\n", "* $\\frac{\\hat s}{\\sqrt{n}}$ is a biased estimator to the true MC error, but good enough\n", "\n", "The error of MC error is therefore $\\std(\\frac{\\hat s}{\\sqrt n}) = \\frac{\\std(\\hat s)}{\\sqrt n}$: \n", "* we know the var of sample var, but we need std of sample std\n", "* can we simply compute $\\std(\\hat s) \\approx \\sqrt{\\std(\\hat s^2)} = \\sqrt[4]{\\var(\\hat s^2)} $ ?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Std dev of sample std dev\n", "\n", "Use normality: $\\hat s = \\mu_s + \\sigma_s \\tilde \\epsilon$, where $\\tilde \\epsilon \\sim N(0, 1)$:\n", "\n", "$$\n", "\\begin{array}{l}\n", " \\mathbb{E}[\\hat s^2] &= \\mu_s^2 + \\sigma_s^2 = \\sigma^2 \\\\\n", " \\var[\\hat s^2] &= \\var[ 2\\mu_s\\sigma_s\\tilde\\epsilon + \\sigma_s^2 \\tilde \\epsilon^2] = 4\\mu_s^2\\sigma_s^2 + 2\\sigma_s^4 \\approx \\frac{(\\beta-1)\\sigma^4}{n}\n", "\\end{array}$$\n", "\n", "Note that $\\var[\\tilde \\epsilon^2] = \\mathbb{E}[\\tilde \\epsilon^4] - \\mathbb{E}^2[\\tilde \\epsilon^2] = 2$ and $\\cov[\\tilde \\epsilon, \\tilde \\epsilon^2] = 0$, then:\n", "\n", "$$\\sigma_s^4 - 2 \\sigma^2 \\sigma_s^2 + \\frac{(\\beta-1)\\sigma^4}{2n} = 0$$\n", "\n", "thus $\\sigma_s = \\std(\\hat s) \\approx \\sigma\\sqrt{\\frac{\\beta-1}{4n}}$, not even close to $\\sqrt[4]{\\var(\\hat s^2)} \\approx \\sigma\\sqrt[4]{\\frac{\\beta-1}{n}}$\n", "* $\\mu_s = \\mathbb E [\\hat s] = \\sigma \\sqrt{1-\\frac{\\beta-1}{4n}}$\n", "* the other root of $\\sigma_s^2$ is greater than $\\sigma^2$, ignored" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Population and sample statistics\n", "\n", "| | Definition | Mean | Variance |\n", "|:--:| :--:|:---:|:--:|\n", "| Population | $\\tilde r$ | $\\mu$ | $\\sigma^2$ |\n", "| Sample mean | $\\hat u = \\frac{1}{n}\\bs 1^T \\bs r$ | $\\mu$ | $\\frac{\\sigma^2}{n}$ |\n", "| (adjusted)
Sample variance | $\\hat s^2 = \\frac{1}{n-1} \\sum_i (r_i - \\hat \\mu)^2 $ | $\\sigma^2$ | ~$\\frac{\\beta - 1}{n} \\sigma^4$|\n", "| Sample stddev | $\\hat s$ | ~$\\sigma \\sqrt{1-\\frac{\\beta-1}{4n}} $ | ~$\\frac{\\beta-1}{4n}\\sigma^2$ |\n", "\n", "\n", "$\\sigma^2$ can be well approximated by the unadjusted sample variance:\n", "\n", "$$\\hat\\sigma^2 = \\frac{1}{n} \\sum_i (r_i - \\hat \\mu)^2 = \\frac{1}{n}\\sum_i r_i^2 - \\hat \\mu^2 $$\n", "\n", " * easy to implement, just keep track of the cumulative sum of squares\n", " * the bias in $\\hat \\sigma^2$ can be safely ignored as $n$ is large" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Numerical examples\n", "\n", "Consider the example of computing $\\pi$ using MC:\n", "$$\\renewcommand{ind}{1{\\hskip -2.5 pt}\\hbox{l}}$$\n", "\n", "$$\\frac{\\pi}{4} = \\mathbb{E}\\left[\\ind\\left(\\sqrt{\\tilde x^2 + \\tilde y^2} < 1\\right)\\right]$$\n", "\n", "where $\\mathbb{\\ind}(\\cdot)$ is an indicator function, the population mean, variance and 4th moment are:\n", "\n", "$$\\begin{array}{l}\n", "\\mu &= \\mathbb{E}[\\tilde \\ind] = \\frac{\\pi}{4} \\\\\n", "\\sigma^2 &= \\var[\\tilde \\ind] = \\mathbb{E}[\\tilde \\ind^2] - \\mu^2 = \\frac{4\\pi - \\pi^2}{16} \\\\\n", "\\mu_4 &= \\mathbb{E}\\left[\\left(\\tilde \\ind - \\mu\\right)^4\\right] = \\frac{\\pi}{4}(1-\\frac{\\pi}{4})^4 + (1-\\frac{\\pi}{4})(\\frac{\\pi}{4})^4 \\\\\n", "\\beta &= \\frac{\\mu_4}{\\sigma^4} = 2.933\n", "\\end{array}\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "The variance and error of sample statistics:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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Rk3jH+PenKLm4ffs2vXr1olmzZvj4+LBixQomTJjA2bNn8fPz4+233wbg448/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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "u = np.pi/4\n", "v = u*(1-u)\n", "u4 = np.pi/4*(1-np.pi/4)**4 + (1.-np.pi/4)*(np.pi/4)**4\n", "\n", "ns = 2**(np.arange(1, 14))\n", "var_u = v/ns\n", "var_var = (u4 - v*v*(ns-3)/(ns-1))/ns\n", "\n", "beta = u4/v**2\n", "\n", "fig = figure(figsize=[12, 4])\n", "subplot(1, 2, 1)\n", "loglog(ns, np.transpose([var_u, var_var]), '.-')\n", "legend(['var of $\\hat \\mu$', 'var of $\\hat s^2$']);\n", "xlabel('Number of random samples')\n", "title('Sample Variance');\n", "\n", "ax = fig.add_subplot(122)\n", "loglog(ns, np.transpose([np.sqrt(var_u), np.sqrt((beta-1.)/4./ns)*np.sqrt(v), np.sqrt((beta-1.))/2./ns*np.sqrt(v)]), '.-');\n", "title('Error Estimate')\n", "legend(['std of mean', 'std of $\\hat s$', 'err of MC err'], loc='best');\n", "xlabel('Number of random samples');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* it is prudent to monitor the error of MC error (most people don't)\n", "* the err of MC err is more pronounced for fat tailed distributions, with large $\\beta$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Estimate mean and volatility\n", "\n", "Let's revisit the estimation of stock return's mean and volatility, suppose:\n", "\n", "* we have 10Y daily return data, $r_i$\n", "* the true volatility is 25% annualized, i.e. $\\sigma = .25$\n", "* the returns are roughly normal, i.e. $\\beta = 3$\n", "\n", "The historical mean estimator $\\hat u = \\frac{1}{n}\\sum_i r_i $ has an error of:\n", "* $\\std(\\hat \\mu) = \\frac{\\sigma}{\\sqrt{10}} = 0.079$, the error is large because we only have 10 independent sample\n", "* using daily return does not help either: $\\std(\\hat \\mu) = 250 \\frac{\\sigma/\\sqrt{250}}{\\sqrt{10 \\times 250}} = 0.079$\n", "\n", "The vol is estimated as the standard deviation $\\hat s$ of the daily return $r_i$:\n", "* error in annualized vol is $\\sigma{\\sqrt{\\frac{\\beta-1}{4n}}} = 0.0035$, very accurate\n", "* we used all 2500 daily samples" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.00353553390593\n", "0.0790569415042\n" ] } ], "source": [ "print(.25/sqrt(2500*2))\n", "print(.25/sqrt(10))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Batching\n", "\n", "Advanced MC techniques often involves dependent samples \n", "* the MC error estimate of $\\frac{\\hat s}{\\sqrt{n}}$ is no longer valid\n", "\n", "Batching is a generic method to estimate MC errors with dependent samples\n", "* Repeat the MC simulation $b$ times, and obtain $\\hat{\\mu}_i$ for $i = 1 ... b$ \n", " * each batch has **different** random seeds, *ceteris paribus*\n", "* $\\hat{\\mu}_i$ are independent between batches, \n", " * the variance of $\\hat \\mu$ can be estimated directly $\\hat s_b^2 = \\frac{1}{b-1} \\sum_i (\\mu_i^2 - \\bar{\\mu})^2$ \n", " * $\\bar{\\mu} = \\frac{1}{b} \\sum_i\\hat{\\mu}_i$ is the batch mean estimator, its error is $\\frac{\\hat s_b}{\\sqrt{b}}$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Why Monte Carlo?\n", "\n", "The MC example of $\\pi$ is really to solve the integral of: \n", "\n", "$$\\int_0^1\\sqrt{1-x^2}dx = \\frac{\\pi}{4}$$\n", "\n", "* MC is inefficient, only converges at $\\propto \\frac{1}{\\sqrt{n}}$\n", "* In comparison, Simpson rule converges at $\\propto \\frac{1}{n^4}$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "However, MC shines because its convergence is dimension independent:\n", "\n", "| Dimension | Simpson Integration Points | Equivalent MC samples | Cost Ratio (MC/Simpson) |\n", "| :----: | :----: | :----: | :----: | :----: |\n", "| 1 | $10$ | $10^{8} $ | $10^{7}$ |\n", "| 5 | $10^5$ | $10^{8}$ | $1000$ |\n", "| 10 | $10^{10}$ | $10^{8}$ | $0.01$ |\n", "| 20 | $10^{20}$ | $10^{8}$ | $10^{-12}$ |" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Curse of dimensionality" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "In Finance, we routinely run into very high dimensionalities, every source of randomness is a separate dimension:\n", "\n", "* interest rate: LMM models 3M forwards up to 30Y\n", "* basket options: often have tens of names\n", "* synthetic CDOs: hundreds of issuers in the portfolio\n", "* mortgage securities: monthly payments up to 30 years\n", "\n", "Most numerical methods fail at high dimensionality\n", "* PDE: 4 dimension is the practical limit\n", "* Tree: rarely more than 3 dimensions" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Randomness is dimensionality proof" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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LwH4ze9Ldn5uyz0rgd4E3u/sLZnZNK9rS1kkIxSEo7IHsDhjcGjT0yKkR8ifz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\nr6sbgRMc/ogAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.arange(0, 10)*.1\n", "y = np.arange(0, 10)*.1\n", "xm, ym = np.meshgrid(x, y)\n", "\n", "figure(figsize=[12, 4])\n", "subplot(1, 2, 1)\n", "plot(xm, ym, '.');\n", "xlabel('x')\n", "ylabel('y')\n", "title('100 Grid Samples');\n", "\n", "subplot(1, 2, 2)\n", "xs = np.random.uniform(size=[2, 100])\n", "plot(xs[0,:], xs[1,:], '.');\n", "title('100 Random Samples');\n", "xlabel('x')\n", "ylabel('y');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Monte Carlo is effective in combating high dimensions:\n", "\n", "* the same set of random samples cover all dimensions equally" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## $\\mathbb{Q}$ measure applications\n", "\n", "#### Derivative pricing:\n", "$$ \\frac{v(t_0)}{m(t_0)} = \\mathbb{E}^\\mathbb{Q}\\left[\\frac{v(t)}{m(t)} \\bigg| \\mathcal{F}_{t_0}\\right] $$\n", "* $m(t)$ is a numeraire seccurity, $\\mathbb{Q}$ is the measure induced by the numeraire $m(t)$\n", "* Often used for pricing high dimensional exotic and path dependent derivatives\n", "\n", "#### XVA adjustments: CVA/FVA/DVA\n", "* an active research area\n", "* XVAs can be expressed in expectations" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## $\\mathbb{P}$ measure applications\n", "\n", "#### Market Risk\n", "* Value at Risk: $\\mathbb{P}[v(T) < \\text{VaR}_\\alpha] = \\mathbb{E}_t[\\ind(v(T) < \\text{VaR}_\\alpha)] = \\alpha$\n", "\n", "#### Counterparty credit risk: \n", "* EE (expected exposure): $e_t = \\mathbb{E}[\\max(v_t, 0)] = \\mathbb{E}[v_t \\ind(v_t > 0)]$ \n", "* PFE (potential future exposure): $\\mathbb{P}[v_t \\ind(v_t > 0) < \\text{PFE}_\\alpha] = \\alpha$\n", "\n", "#### Capital allocation\n", "* a new area where the MC method is successfully applied" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Advantages of Monte Carlo\n", "\n", "There are good reasons why Monte Carlo is widely used in quant finance:\n", "\n", "* dimensionality independent\n", "* generic: widely applicable\n", "* robust: can handle complicated payoff\n", "* easy to implement and modify\n", "* precise error estimate\n", "* easy to add more samples on the fly\n", "* can be made very fast for many problems (next lecture)\n", "* often used to test more advanced pricing technique, like PDE" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Random number generation\n", "\n", "Robert Coveyou: the generation of random numbers is too important to be left to chance." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## True and pseudo random numbers\n", "\n", "True random number generators (T-RNG) observe random physical processes:\n", "* often involves quantum effects: radioactive decay, electrical/thermal noise etc.\n", "* costly and slow\n", "* mostly used in cryptography that requires a high level of security\n", "\n", "Pseudo random number generators (P-RNG) are computer software that \n", "* produce number sequence that only appears to be random\n", "* cheap and fast\n", "* can be initialized (seeded) to different states\n", "* states can be stored and recovered, convenient for MC" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Pseudo random number generators\n", "\n", "Building good P-RNG requires highly specialized skills:\n", "\n", "* must pass rigorous statistical tests \n", "* numerical scientists have devoted their careers to build good P-RNGs\n", "* always use a good P-RNG library and never write your own\n", " * ```random()``` in Excel is implemented [incorrectly](http://www.pages.drexel.edu/~bdm25/excel-rng.pdf), don't use it for anything serious" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Mersenne Twister (MT19937)\n", "\n", "The most popular P-RNG:\n", "* often the default P-RNG for MC\n", " * the default choice of Python's ```numpy.random.uniform```\n", "* very long cycle of $2^{19937} − 1$ and excellent statistical properties\n", "* suitable for MC applications, but **not** good for cryptography\n", "* very fast: ~100M random numbers per second on a modern PC" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Non-uniform random numbers\n", "\n", "P-RNGs produces uniform random numbers between [0, 1]\n", "* RNs of other distributions can be built by transformations\n", "\n", "Given the cumulative distribution function $F(x)$, $\\tilde x = F^{-1}(\\tilde u)$ transforms a uniform $\\tilde u$ to the desired distribution:\n", "\n", "$$\n", "\\mathbb{P}[\\tilde x < x]= \\mathbb{P}[F^{-1}(\\tilde u) < x] = \\mathbb{P}[\\tilde u < F(x)] = F(x)\n", "$$\n", "\n", "* a universal method to produce non-uniform RNs\n", "* works the best when $F^{-1}(\\cdot)$ can be compute cheaply and accurately" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Box-muller\n", "\n", "Normal random number is the most important of all:\n", "* most quant Finance models are driven by Brownian motions\n", "* fast and accurate inversion of normal CDF weren't known till recently\n", "\n", "Box-muller is a classic method to transform independent uniform RNs to independent normal RNs:\n", "* takes 2 independent uniforms and produce 2 independent normals\n", "* its [polar form](http://en.wikipedia.org/wiki/Marsaglia_polar_method) is faster and more stable, which is behind Python's ```numpy.random.normal```\n", "* the polar form is a rejection algorithm: the number of output normal RNs is less than the input uniforms\n", " * about 21% of input uniforms are rejected (wasted)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Normal inversion\n", "\n", "Numerical inversion of normal CDF is an effective alternative to generate normal random numbers:\n", "* fast and accurate numerical inversion of the normal CDF were [discovered recently](http://home.online.no/~pjacklam/notes/invnorm/)\n", "* based on polynomial approximation, accuracy is ~$10^{-9}$\n", "* every uniform RN produce a normal RN output, more convenient than the polar Box-muller\n", "* works well with low discrepancy sequences (next lecture)\n", "\n", "Normal inversion is often preferred over the Box-muller." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "How to create correlated normal RNs from independent normals RNs?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Discretize stochastic processes\n", "\n", "Mark Twain: if you must be indiscrete, be discrete in your indiscretion" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Discretization\n", "\n", "To simulate a stochastic differential equation (SDE) numerically, we have to discretize it first.\n", "* $\\bs \\tau = [0, \\delta, 2\\delta, \\cdots, n\\delta]^T$ represents a discretized time grid\n", "\n", "$s(t)$ is the true 1-D stochastic processes as defined by a SDE \n", " * same for multi-dimensional processes\n", " * $s(\\bs \\tau)$ is a vector of the true stochastic process valued at discrete time\n", " \n", "$\\hat s(t; \\delta)$ is a discretization of $s(t)$\n", " * $\\hat s(t; \\delta)$ is only defined at discrete time grid $t \\in \\bs \\tau$\n", " * discretization is a form of approximations, $\\hat s(t; \\delta) \\ne s(t)$ in general" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Discretization error\n", "\n", "The discretization error are application specific:\n", "\n", "European style of derivatives: $\\mathbb{E}[f(s(t))]$\n", " * only depends on the distribution of $s(t)$ at a single time horizon $t$\n", " * $f(\\cdot)$ is the payoff function \n", "\n", "Path dependent derivatives: $\\mathbb{E}[f(s(\\bs \\tau))]$\n", " * payoff function $f(\\cdot)$ depends on the full path of $s(\\bs \\tau)$\n", " * $\\bs \\tau$ could be daily grid\n", " * e.g. Asian options, barrier options, MBS/ABS and CDOs etc" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Order of Convergence \n", "\n", "####Weak convergence:\n", "\n", "* is the accuracy in the distribution of $s(t)$ at a specific $t$:\n", "* a discretization has n-th order weak convergence if\n", "\n", "$$\\mathbb{E}[s(t) - \\hat s(t; \\delta)] = O(\\delta^n)$$ \n", "\n", "####Strong convergence:\n", "\n", "* defined to be the accuracy in capturing the whole trajectory of $\\bs s$:\n", "* a discretization has n-th order strong convergence if\n", "\n", "$$\\mathbb{E}\\left[\\left\\Vert s(\\bs \\tau) - \\hat s(\\bs \\tau; \\delta) \\right\\Vert\\right] = O(\\delta^n)$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Diffusion process\n", "\n", "Generic multi-dimensional diffusion SDE: \n", "\n", "$$ d \\bs s(t) = \\bs \\mu(\\bs s, t) dt + \\Sigma(\\bs s, t) d \\bs w(t) $$\n", "\n", "* $\\bs{s, \\mu}$ are vectors, $\\Sigma$ is a matrix \n", "* $\\bs w$ is a multi-dimensional Brownian process \n", " * with correlation matrix $C\\;dt = d \\bs w d \\bs w^T$\n", "* $\\Sigma$ is rectangular if the dimensions of $\\bs w$ and $\\bs s$ are different " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Euler discretization\n", "\n", "The main workhorse for MC applications in quant finance:\n", "\n", "$$\\renewcommand{hs}{\\hat{\\bs s}} \\hs(t + \\delta) = \\hs(t) + \\bs \\mu(\\hs, t) \\delta + \\Sigma(\\hs, t) L\\bs \\epsilon\\sqrt{\\delta} $$\n", "\n", "* generic and easy to implement\n", "* $L$ is the Cholesky decomposition of the correlation matrix: $C = LL^T$\n", "* $\\bs \\epsilon$ are *independent* standard normal random numbers, $\\sim N(0, 1)$\n", "* $\\mathbb{E}[\\frac{L\\bs \\epsilon\\sqrt{\\delta} (L\\bs \\epsilon\\sqrt{\\delta})^T}{\\delta}] = \\mathbb{E}[L\\bs \\epsilon\\bs \\epsilon^TL^T]\n", "= L\\mathbb{E}[\\bs \\epsilon\\bs \\epsilon^T]L^T = LL^T = C$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Convergence of Euler discretization\n", "\n", "But Euler discretization is slow in convergence:\n", "* order 1 weak convergence, $O(\\delta)$\n", "* order $\\frac{1}{2}$ strong convergence, $O(\\sqrt{\\delta})$\n", "\n", "For processes with known analytical solutions, more efficient sampling method can be devised" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Geometric Brownian motion\n", "\n", "The most common process to model asset prices:\n", "\n", "$$\\frac{dx(t)}{x(t)} = \\mu dt + \\sigma dw(t)$$\n", "\n", "its analytical solution is:\n", "\n", "$$x(t) = x(t_0) e^{(\\mu - \\frac{1}{2}\\sigma^2)(t-t_0) + \\sigma w(t)}$$\n", "\n", "* its trajectory can be **exactly** sampled using arbitrary time steps ($\\infty$ order of strong convergence)\n", "* extends trivially to multi-dimensional GBM" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Ornstein-Uhlenbeck process:\n", "\n", "$$dx(t) = \\kappa(\\bar x - x(t)) dt + \\sigma dw(t)$$\n", "\n", "* commonly used in interest rate modeling (a.k.a. Vasicek model) and empirical studies\n", "* the most tractable and widely used process to capture mean reversion\n", "\n", "The analytical solution is\n", "$$\\small x(t) = x(t_0)e^{-\\kappa (t-t_0)} + \\bar x (1 - e^{-\\kappa (t-t_0)}) + \\int_{t_0}^t\\sigma e^{\\kappa(s-t)}dw(s)$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "the Ito integral $e(t) = \\int_{t_0}^t\\sigma e^{\\kappa(s-t)}dw(s)$ is normally distributed:\n", "\n", "$$e(t) \\sim N\\left(0, \\frac{\\sigma^2}{2\\kappa}(1-e^{-2\\kappa (t-t_0)})\\right)$$\n", " \n", "the trajectory of $x(t)$ in the OU can be sampled **exactly** with arbitrary time steps by drawing $e(t)$ instead of $w(t)$:\n", " * extension to multi-dimensional OU process requires some care as $\\cov(e_i, e_j) \\ne \\cov(w_i, w_j)$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## CIR process\n", "\n", "Cox-Ingersoll-Ross (CIR) process:\n", "\n", "$$dx(t) = \\kappa(x(t) - \\bar x) dt + \\sigma \\sqrt{x(t)} dw(t)$$\n", "\n", "* $x(t) \\ge 0$, zero is attainable if $\\sigma^2 > 2\\kappa\\bar x$ \n", "* no known analytical solution for $x(t)$\n", "* often used to model interest rates and volatility, e.g. Heston model\n", "\n", "Euler discretization could lead to negative values for $x(t)$\n", "\n", "* In practice, ad-hoc floors or reflections are often used to avoid negative values, at the cost of significant bias in $x(t)$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Log-Euler scheme\n", "\n", "A better solution to prevent CIR process from becoming negative is to apply the transformation $y(t) = \\log(x(t))$:\n", "\n", "$$\\small dy(t) = \\frac{1}{x(t)}\\left(\\kappa(x(t) - \\bar x) - \\frac{\\sigma^2}{2} \\right) dt + \\frac{\\sigma}{\\sqrt{x(t)}}dw(t) $$\n", "\n", "* Euler scheme can then be applied to sample $y(t)$, without added bias\n", "* it can be easily extended to sample any bounded processes\n", "* But in practice, we still need a reflective bound for $y(t)$ otherwise it goes to $-\\infty$ quickly." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Milstein sampling\n", "\n", "For a diffusion SDE of the form:\n", " \n", "$$ dx_t = u(x_t)dt + \\sigma(x_t) dw_t $$\n", " \n", "Observe that both $u(x_t)$ and $\\sigma(x_t)$ are stochastic through $x_t$:\n", " \n", "$$ d u_s = (\\cdot) ds + \\dot u_s \\sigma_s dw_s, \\;\\; d\\sigma_s = (\\cdot) ds + \\dot \\sigma_s \\sigma_s dw_s $$\n", " \n", "where $\\dot u_s = \\frac{du(x_s)}{dx_s}, \\dot \\sigma_s = \\frac{d\\sigma(x_s)}{dx_s}$.\n", " \n", "All corrections are higher order than $d t$ except the $dw_s dw_t$ term (note $t < u < s < t+\\delta t$):\n", " \n", "$$ \\delta x_t = u_t \\delta t + \\sigma_t \\delta w_t + \\int_t^{t+\\delta t}\\int_t^{s}\\dot\\sigma_u \\sigma_s dw_u dw_s $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ " The last correction term can be approximated as:\n", "$$ \\small \\begin{eqnarray}\n", "\\sigma_t\\int_t^{t+\\delta t}\\int_t^{s}\\dot\\sigma_u dw_u dw_s &\\approx& \\sigma_t\\dot\\sigma_u \\int_t^{t+\\delta t}\\int_t^{s} dw_u dw_s\n", "= \\sigma_t\\dot\\sigma_t \\int_t^{t+\\delta t} (w_{s}-w_t)dw_s \\\\\n", "&=& \\sigma_t\\dot\\sigma_t \\left(\\int_t^{t+\\delta t} w_{s}dw_s - \\int_t^{t+\\delta t}w_t dw_s\\right) \\\\\n", "&=& \\sigma_t\\dot\\sigma_t \\left(\\int_t^{t+\\delta t} w_{s}dw_s - w_t(w_{t+\\delta t} - w_t)\\right)\n", "\\end{eqnarray}$$\n", " \n", "Note that $\\int w_t dw_t = \\frac{1}{2}(w_t^2 - t)$, the term in the bracket becomes:\n", "$$ \\small \\frac{1}{2} (w_{t+\\delta t}^2 - w_t^2) - \\frac{1}{2}\\delta t - w_t(w_{t+\\delta t} - w_t) = \\frac{1}{2}(w_{t+\\delta t} - w_t)^2 - \\frac{\\delta t}{2} \\approx \\frac{1}{2}(\\delta^2w - \\delta t) $$\n", " \n", "This term vanishes for infinitesimal $dt$ but not for finite sample size $\\delta t$. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Properties of Milstein\n", "\n", "Therefore, if we sample $\\delta w_t = \\tilde z \\sqrt{\\delta t}$, we add the following correction term:\n", " \n", "$$\\delta x = u(t) \\delta t + \\sigma(t) \\sqrt{\\delta t} \\tilde z + \\frac{1}{2}\\sigma \\dot \\sigma (\\tilde z^2 - 1) \\delta t $$\n", "\n", "* Milstein sampling is 1st order in strong convergence and weak convergence\n", "* But it is non-trivial to extend Milstein to multi-dimensional " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Stability of Euler discretization\n", "\n", "Consider a one-dimensional OU process, and its Euler discretization:\n", "\n", "$$\\small \\begin{array}\n", "\\\\ dx(t) &= \\kappa(\\bar x - x(t)) dt + \\sigma dw(t) \\\\\n", "x(t_{i+1}) &= x(t_i) + \\kappa(\\bar x - x(t_i)) \\delta + \\sqrt{\\delta} \\sigma \\epsilon_i \\\\\n", "&= (1 - \\kappa \\delta) x(t_i) + \\kappa \\bar x \\delta + \\sqrt{\\delta} \\sigma \\epsilon_i \\\\\n", "\\mathbb{E}[x(t_{i+1})] &= (1 - \\kappa \\delta) \\mathbb{E}[x(t_i)] + \\kappa \\bar x \\delta\n", "\\end{array}$$\n", "\n", "the expectation explodes if the $| 1 - \\kappa \\delta | > 1$, i.e., $\\delta > \\frac{2}{\\kappa}$" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import proc\n", "\n", "u = .05\n", "k = 10.\n", "dt = 2/k\n", "n = int(20./dt)\n", "sigma = .02\n", "\n", "ou = proc.OU(k=k, u=u, sig=sigma)\n", "es = np.random.normal(size=[1, n])" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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MnYNmZvYBvB3ANVDLd99k5geJ6K1E9Fa929UAHgOwB8DnAPy+9RLv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\nQkQAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "et = .01\n", "figure(figsize=[12, 4]);\n", "subplot(1, 2, 1)\n", "dt = 2/k - et\n", "paths = ou.draw(es, u, dt)\n", "plot(np.arange(n)*dt, paths.T)\n", "xlabel('Time(Y)', fontsize=14);\n", "title('Euler sample path with $\\delta = %g, \\kappa=%g$' % (dt, k), fontsize=16);\n", "\n", "subplot(1, 2, 2)\n", "dt = 2/k + et\n", "paths = ou.draw(es, u, dt)\n", "plot(np.arange(n)*dt, paths.T)\n", "xlabel('Time(Y)', fontsize=14);\n", "title('Euler sample path with $\\delta = %g, \\kappa=%g$' % (dt, k), fontsize=16);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Discretization vs Monte Carlo error\n", "\n", "Suppose we draw $n$ independent paths of $\\hat s(\\bs \\tau; \\delta)$, where $\\bs \\tau$ consists of $m$ discrete time samples.\n", "* the total computation cost is $\\propto mn$\n", "\n", "There are two types of errors in Monte Carlo simulation of SDEs:\n", "\n", "* Discretization error: $\\epsilon_d \\propto (\\frac{1}{m})^\\gamma$\n", "* Monte Carlo error: $\\epsilon_{s} \\propto \\frac{1}{\\sqrt{n}}$\n", "\n", "The two types of errors are independent, thus the total variance is:\n", "\n", "$$ \\epsilon^2 = c_1 \\epsilon_d^2 + c_2\\epsilon_{s}^2 = \\frac{c_1}{m^{2\\gamma}} + \\frac{c_2}{n}$$\n", "\n", "* where $c_1, c_2$ are constant (likely unknown) " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Optimal choice of $\\delta$\n", "\n", "Given a fixed computation budget of $mn = c$, the best allocation between $m$ and $n$ can be found by solving:\n", "\n", "$$\\begin{array}{c} \\min_{m, n} \\left(\\frac{c_1}{m^{2\\gamma}} + \\frac{c_2}{n}\\right) \\\\\n", "\\text{subject to: } mn = c\n", "\\end{array}$$\n", "\n", "apply the Lagrange multiplier:\n", "\n", "$$\\small \\begin{array}{l} \n", "l &= \\left(\\frac{c_1}{m^{2\\gamma}} + \\frac{c_2}{n}\\right) + \\lambda(mn - c) \\\\\n", "\\frac{\\partial l}{\\partial m} &= -c_1\\frac{2\\gamma}{m^{2\\gamma+1}} + \\lambda n = 0 \\\\\n", "\\frac{\\partial l}{\\partial n} &= -c_2\\frac{1}{n^2} + \\lambda m = 0 \\\\\n", "\\lambda mn &= \\frac{2c_1\\gamma}{m^{2\\gamma}} = \\frac{c_2}{n}\n", "\\end{array}$$\n", "\n", "therefore the optimal strategy is to maintain $\\frac{m^{2\\gamma}}{n} = \\frac{2c_1\\gamma}{c_2}$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Richardson extrapolation\n", "\n", "Recall Euler discretization is of 1st order weak convergence:\n", "\n", "$$\\mathbb{E}[f(\\hs(t; \\delta))] = \\mathbb{E}[f(\\bs s(t)] + c \\delta + O(\\delta^2)$$\n", "\n", "Richard extrapolation can be applied to get 2nd order weak convergence: \n", "\n", "$$\\begin{array}{l} \n", "\\mathbb{E}[f(\\hs(t; 2\\delta))] &= \\mathbb{E}[f(\\bs s(t)] + 2c \\delta + O(\\delta^2) \\\\\n", "2\\mathbb{E}[f(\\hs(t; \\delta))] - \\mathbb{E}[f(\\hs(t; 2\\delta))] &= \\mathbb{E}[f(\\bs s(t)] + O(\\delta^2) \\\\\n", "\\mathbb{E}[2f(\\hs(t; \\delta)) - f(\\hs(t; 2\\delta))] &= \\mathbb{E}[f(\\bs s(t)] + O(\\delta^2)\n", "\\end{array}$$\n", "\n", "Therefore the estimator $2f(\\hs(t; \\delta)) - f(\\hs(t; 2\\delta))$ is 2nd order weak convergence." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Cost of Richardson extrapolation\n", "\n", "The variance of the estimator with Richardson extrapolation is:\n", "\n", "$$\\small \\begin{array}{l}\n", "\\var[2f(\\hs(t; \\delta)) - f(\\hs(t; 2\\delta))] \\\\\n", "= \\var\\left[2f(\\hs(t; \\delta))\\right] + \\var\\left[f(\\hs(t; 2\\delta))\\right] - 2 \\cov\\left[2f(\\hs(t; \\delta)), f(\\hs(t; 2\\delta))\\right] \\\\\n", "= 4\\sigma_\\delta^2 + \\sigma_{2\\delta}^2 - 2\\rho\\sigma_\\delta\\sigma_{2\\delta} \\gtrsim 3\\sigma^2\n", "\\end{array}$$\n", "\n", "* Given $\\sigma_{2\\delta} \\approx \\sigma_\\delta \\approx \\sigma$, the minimal variance is ~$3\\sigma$ when $\\rho = 1$\n", "* Richardson extrapolation increases the MC cost by a factor of 3 at least." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Richardson extrapolation implementation\n", "\n", "The following implementation maximizes the correlation between $f(\\hs(t; \\delta))$ and $f(\\hs(t; 2\\delta))$: \n", "\n", "1. draw $m$ independent standard normal random vectors: $\\bs z_1, \\bs z_2, \n", "\\bs z_3, ..., \\bs z_m$, \n", "2. use $\\bs z_1\\sqrt{\\delta}, \\bs z_2\\sqrt{\\delta}, \\cdots , \\bs z_m\\sqrt{\\delta}$ as the Brownian motion increments to simulate $\\hs(t; \\delta)$\n", "3. use $(\\bs z_1 + \\bs z_2)\\sqrt{\\delta}, (\\bs z_3+\\bs z_4)\\sqrt{\\delta}, \\cdots $ as the Brownian motion increments to simulate $\\hs(t; 2\\delta)$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Least square MC\n", "\n", "Lewis Carroll: it's a poor sort of memory that only works backwards." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Early exercise\n", "\n", "Early exercise (American or Bermudan option):\n", "* the option holder can exercise before the option expiry\n", "\n", "The value of American put at time $t_i$ is:\n", "$$ v(t_i) = \\max\\left(\\left(k-s\\left(t_i\\right)\\right)^+, \\mathbb{E}\\left[v(t_{i+1})e^{-r\\delta}\\biggr|\\mathcal{F}_{t_i}\\right]\\right)$$\n", "* the first term inside the $\\max$ is the exercise value\n", "* the second term is the continuation value\n", "\n", "Similarly, the value of American call at time $t_i$ is:\n", "$$ v(t_i) = \\max\\left(\\left(s(t_i)-k\\right)^+, \\mathbb{E}\\left[v(t_{i+1})e^{-r\\delta}\\biggr|\\mathcal{F}_{t_i}\\right]\\right)$$\n", "\n", "these equations are commonly known as the Bellman equation." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Exercise Boundary\n", "\n", "Is it optimal to early exercise?\n", "* it is never optimal to early exercise call option when the underlying stock does not pay dividend\n", "* it may be optimal to early exercise a deep in the money put option\n", "\n", "The optimal exercise boundary of American put is a function of stock price and time: $b(s(t), t)$\n", "
\n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Free boundary problem\n", "\n", "The American option's value can be expressed as an optimization of:\n", "\n", "$$ v(b^*(t)) = \\max_{b(t)} [v\\left(b\\left(t\\right)\\right)] $$\n", "\n", "* $v(b(t))$ is the option value with an exercise boundary of $b(t)$\n", "* $b^*(t)$ is the optimal exercise boundary that maximizes $v(b(t))$\n", "\n", "This types of free boundary problem poses a serious challenge to MC\n", "* if $b^*(t)$ were known, the problem is trivial\n", "* naive approaches for solving $b^*(t)$ leads to MC inside an optimizer, which is prohibitively expensive" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## The stone age\n", "\n", "Before 2000, it was generally accepted that MC cannot solve these free boundary problems.\n", "* American and Bermudan options were priced using PDE and trees\n", " * more natural for solving $b^*(t)$ as they go backwards in time\n", "* However, PDE and trees can't deal with high dimensionalities" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Stock paths\n", "\n", "We draw 100,000 stock paths to 1Y with time grid $\\delta = 0.01$ from the GBM:\n", "* we can store all paths in memory ($100,000 \\times 100 \\times 8 \\approx 76$MB)\n", "* European option is priced to adequate accuracy" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "76.2939453125\n" ] } ], "source": [ "print(1e5*100*8/1024/1024)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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b85geH0RMgPuvcs7irBq+eSmRzQuyyE+rwqOHE8OuDmf67wcw+/nhZ5Wsg638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\nMLLifRov/5zeqRm43U8CoFabfrco1a7GZh6vr+LwU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Xpu9Y/iU28Bz+/wAb9MAqyCz+dt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\nkJW6j/6CKKZoFtEzpVwe3UWcMglXJERK4QL0Hg0OmYZufT5dzhAAEiGGS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2fTc/YQ7qQ5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\nV0oZgZeAsUAX4AalVJf/2W0s0KHlcifw8lkt8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t, m, r, s0, k, vol = 1., 52, .1, 100, 100, .25\n", "\n", "dt = t/m \n", "n = 400000\n", "\n", "ts = np.arange(1, m+1)*dt\n", "\n", "gbm = proc.GBM(r, vol)\n", "spath = gbm.draw(np.random.normal(size=[n, m]), s0, dt)\n", "spath2 = gbm.draw(np.random.normal(size=[n, m]), s0, dt)\n", "\n", "eputs = np.maximum(k - spath[:,-1], 0)*np.exp(-r*t)\n", "u = np.mean(eputs)\n", "e = np.std(eputs)/sqrt(n)\n", "\n", "fig = figure(figsize=[12, 4])\n", "subplot(1, 2, 1)\n", "plot(ts, spath[:100].T);\n", "xlabel('Time(Y)')\n", "title('First 100 simulated stock path');\n", "\n", "ax = fig.add_subplot(122)\n", "ax.set_axis_off()\n", "ax.text(0, .5, \"Europan put price is %.2f, MC err %.2g\" % (u, e), size=\"xx-large\");\n", "ax.text(0, .6, \"True value is %.2f\" % (5.46), size=\"xx-large\");" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Path-wise optimal exercise\n", "\n", "Given the simulated path, one may propose the following simple method to price American option:\n", "1. for each simulated path, determine its optimal exercise time $t^*$\n", "2. then compute the American put's value as \n", "\n", "$$v(0) = \\frac{1}{n} \\sum_i e^{-rt^*_i}\\left(k-s(t^*_i)\\right)^+$$\n", "\n", "This algorithm is easy to implement, but ..." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "
\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Pathwise OptimalTrue Value
American Put12.2536.523
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import fmt\n", "\n", "truv = 6.523\n", "\n", "disc = np.exp(-r*ts)\n", "to = [np.argmax(np.maximum(k-p, 0)*disc) for p in spath]\n", "v = np.mean([np.max(np.maximum(k-p, 0)*disc) for p in spath])\n", "\n", "ne = 1000\n", "te, se = map(np.array, zip(*[((o+1)*dt, spath[i, o]) for i, o in enumerate(to[:ne])]))\n", "me = np.argmin(se)\n", "\n", "df = pd.DataFrame(np.array([v, truv]), index=['Pathwise Optimal', 'True Value'], columns=['American Put'])\n", "fmt.displayDF(df.T, \"3f\", 4)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Perfect foresight" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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fRqPRgI5uodFoii/57ZMcBtgOP560lt2WLD62mNhrsTxe53HEOtUIUD6gPF/e9SX9a/Zn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ohnQtfGF10t3LlbaM0R1tPWumR76bbpS7al8vzQ9lh8UZGnESMn2aDaUrBvH0dG30itAQOIeeP1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\n/tCqzR+A7wdXMp4G7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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure(figsize=[12, 4])\n", "subplot(1, 2, 1)\n", "nidx = np.array([0, 1, 2, me])\n", "plot(ts, spath[nidx].T)\n", "plot(te[nidx], se[nidx], 'o')\n", "\n", "xlabel('Time (Y)')\n", "title('Pathwise optimal exercise')\n", "\n", "subplot(1, 2, 2)\n", "plot(te, se, \"o\");\n", "xlabel('Time (Y)')\n", "title('Exercise points');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "the reason is that it uses the future information, i.e., with supernatural ability:\n", "* it gives an upper bound of the option value\n", "* it does not define an exercise boundary" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Least square Monte Carlo\n", "\n", "Least square is an important breakthrough in MC, it is the method of choice for early exercise.\n", "* invented by quants in Solomon brothers, also known as the Longstaff-Schwartz MC after the creators\n", "\n", "The key insight is that the conditional expectation in Bellman equation can be solved by regression and backward-induction.\n", "\n", "$$ v(t_i) = \\max\\left(\\left(k-s\\left(t_i\\right)\\right)^+, \\mathbb{E}\\left[v(t_{i+1})e^{-r\\delta}\\biggr|\\mathcal{F}_{t_i}\\right]\\right)$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "We present it using a numerical example of American put:\n", "* maturity 1Y, stock price $s(0) = 100$, strike $k=100$, vol $\\sigma = .25$\n", "* continuous compounded discount rate of $r = 0.1$\n", "* the exact value of this American put is 6.523\n", "* the European option worths 5.460" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import mc\n", "\n", "put_ev = lambda x : np.maximum(k - x, 0)\n", "v_b, e_b, b_b, cvs = mc.amer_opt(spath, exp(-r*dt), put_ev, mc.fit_ex)\n", "v_u, e_u, b_u, _ = mc.amer_opt(spath, exp(-r*dt), put_ev, mc.opt_ex)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Initialization of LSMC\n", "\n", "The key idea of LSMC is to work **backwards** using the stored paths,\n", "\n", "First, initialize the value at maturity $t_m$ as $\\bs v(t_m) = \\left(k - \\hs(t_m)\\right)^+$\n", " * here $\\hs(t_m)$ represent a vector of $n$ simulation paths at $t_m$\n", " * the terminal value is the exercise value\n", " * $\\bs v(t_m)e^{-r\\delta}$ is therefore the continuation value (c.v.) at $t_{m-1}$" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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SL6bdDiKIzfmJ64QJE3juuedoaGi4avtvpZRSaiTTkWel+qG2tpbMzEwSEhLw\n9vZ2dTj9Uvo/GVRvynPZ9UVEE2ellFI3HU2eleqHtLQ07HY7SUlJrg6lX9oqGmktrqP+aCn2xjZX\nh6OUUkrdNDR5VqoPbW1tpKWlERsbO2J2FGw6XWX9oc1OQ0aZa4NRSimlbiKaPCvVh8zMTOrr60fM\nqDNA06kq3EZ54x7hS8ORS64ORymllLppaPKs1DUYY0hJSSE8PHzEbC1tWttpPlONz7RQ/BIjaCmq\npbW0oe8XjhAlJSWcOHHC1WEopZS6RWnyrNQ1FBYWUlJSQlJS0ogpt9acX4NpteM9LQTfhNFgg/q0\nm2f0+fPPP2fjxo3k5OS4OhSlenWkoIpf7czjSEGVq0NRSg0yTZ6VuoaUlBR8fHyIj493dSj91nSq\nCvGw4TUpCLcAT7ynhdJw9BKm3bg6tBvW2trKuXPnANi8eTNVVZqYDJSIuInIURH5s+N5qIhsE5Fc\nx88QV8c40h0pqOJrv03hPz87xdd+m6IJtFI3GU2elepFVVUVOTk5zJ8/H09PT1eH029NpyrxmhSE\neLgB4JcYgb22labTlS6O7MYVFBTQ1tbGfffdhzGGDRs20Nam1UQG6K+A7E7PXwa2G2OmAtsdz9UN\nSMmvoKXNjt1Aa5udlPwKV4eklBpEmjwr1YvDhw8DcNttt7k4kv5rLW+kraIJ7+mhV9q8p4di8/Og\n4SaYupGXl4ebmxtz587l4Ycf5vz582zfvt3VYY0YIjIO+BLw207NDwNvOf78FvBlZ8d1s0meNApP\ndxtuAh7uNpInjYwqPUqp/tEdBpXqQUtLC+np6cycOZOgoCBXh9NvTaes0WXv2C++eRc3G75zR1N3\n8ALt9a24+Xm4KrwblpeXx4QJE/D09GTmzJksWLCAgwcPMmHCBKZPn+7q8EaCnwF/BwR0aoswxlx0\n/LkEiOjtxSLyIvAiQHR09FDFOOLNnxDCH59PJiW/guRJo5g/QWfCKHUz0ZFnpXqQnp5OU1PTiCpP\nB9Z8Z/dwH9xH+XRp90uMgHZDw9FSF0V246qrqykvL2fKlClX2u6++26ioqLYvHkz1dXVV9pra2s5\nfvw4H3zwASkpKa4Id9gRkQeAUmPMkd76GGMM0OvkeGPMa8aYRGNMYnh4+FCEedOYPyGEby6boomz\nUjchHXlWqpP29nZ2797Nnj17iI6OZvz48dd9LmOMUyt02Fvaac6vxj95zFXHPCL98BjrT8ORSwTc\nMdZpMQ3S9k+tAAAgAElEQVSmvDxrq/HOybO7uztf/epXefXVV3n33XcZP348+fn5lJVZG8O4ubnR\n3t5OSEgI06ZNc0ncw8gi4CERuR/wBgJF5A/AJRGJMsZcFJEoYOR+wlJKKSfQkWelHKqrq3nzzTfZ\ns2cPCQkJfO1rX7uu5Leqqor169fz05/+lLq6uiGItGfNZ6qhzeA9reeRLr/ECFov1tNy3nkxDaa8\nvDwCAwPpPuIZGhrKQw89xIULFzhy5AgBAQGsWLGCF154ge9///tERkayadOmLiPTtyJjzA+MMeOM\nMTHA48AOY8xTwAfAGke3NcAWF4WolFIjQp8jzyLyBtDxdd+sbsf+GvgPINwYU+5o+wGwFmgHvmOM\n+XTQo1ZqkGVlZfHBBx9gjOGRRx65rtJ0ra2t7N+/n3379gHWtt6ZmZkkJycPdrg9ulKibmLPc7R9\n54RT/ed8Go5cwnOsv1NiGizt7e3k5+cza9asHj/QxMXFMWbMGAICAnB373pbW716Na+++irvvfce\nzz777FXHFT8B3hWRtUABsNrF8dwyjhRU6bxopUag/vwr8ibw38DvOzeKyHjgbqCwU9tMrBGNOGAM\n8LmIxBpj2gcrYKUGk91uZ+vWraSlpTF27FgeffRRQkND+35hJ8YYcnJy+PTTT6murmbWrFmsXLmS\ndevWcfz4cackz8YYq0TdlGDEvecvlGy+HvjEjaL+cAlNZ6oxrXZMazumxY5pN4Q8NBm/BZFDHuv1\nKCoqoqWlpcuUje5CQnpOPkJDQ3n44Yd59913+fzzz7n33nuHKswRwxizC9jl+HMFcJcr47kVddSC\nbmmzYxOIGxPEY7dF82SSLsRUarjrM3k2xuwRkZgeDv0X1qrtzl/xPQysN8Y0A2dFJA9YABy88VCV\nGnxFRUWkpaWxYMEC7rnnHtzc3AZ8js2bN5ORkUF4eDhr1qxh4sSJAMyePZtt27ZRUVHBqFFDW6qq\nrayR9qpmApZce452wNLxmBY74iaIhw3xdEM8bDSdruLy7iJ8EyMQ2/DbSTEvLw8Rue4t0mfOnElS\nUhIpKSlER0czc+bMK8c65kcr5Uyda0HbDWQU15BRbG07rwm0UsPbdX1/KSIPA+eNMRndvkIdC3Re\n2l7saOvpHFrySLlcdnY2bm5uLF++vM/EuTm/hsp3T+F3WyQBS8Yh7jby8vLIyMhg4cKFrFixoss5\nOpLnEydOsHTp0iF9H1dK1PUy37mD5xh/wp6Ju6q9IaOUynWnaM6r7lLmbrjIy8tj/PjxeHt7X/c5\nVq5cSXFxMVu2bCEyMpK2tjb27NlDZmYmMHJqeaubQ0ct6KZWe5f2jzMvavKs1DA34AWDIuIL/D3w\nzzdyYS15pFzNGEN2djaTJ0/uMylrr2+lcn0O9sY2Lm8r4NLP02nIreTTTz8lJCSEu+6666rkOzAw\nkJiYGI4fP45VAWzoNJ2qwj3CF/eQ60sufeLCsPl7UHfwwiBHduPq6uooKSm55pSN/nB3d+crX/kK\nIsLrr7/Or3/9a06dOsWiRYsGKVKl+q+jFvTKmV3LasdFBfKrnXm6pbdSw9j1VNuYDEwEMkTkHDAO\nSBeRSOA80Pl743GONqWGnQsXLlBTU8OMGTOu2c8YQ9V7p2mvbyX8xXhGPRuHaTfsf/NTysrKuGvx\nsl4XocXHx1NZWcmFC0OXlLbXt9J8tqbPUedrEXcbfrdF0pRTSVtVEwB79uzhrbfeGvLEvy9nzpwB\nuOHkGax50Y888ghubm7ccccdfPe732XlypU3fF6lrsf8CSH85uuJ/HjVbBZPDeMv75zEmwfP8Z+f\nneJrv03RBFqpYWrAybMx5oQxZrQxJsZR8qgYmGeMKcEqefS4iHiJyERgKnBoUCNWqg+NjY2sW7eO\nrKysa/bLzs5GRPqs/1u3/wJNOZUE3T8Rz7H++EwLJfilmaT7FBBpDyb4gzouby+ktbThqtfOmDED\nNzc3jh8/3uv529vbaWi4+rW9sTe20ZhdQfXWfC7991Eu/igF2g0+M29sXrVfkrVYsP5QCefOnWPH\njh2cPXuWwsLCPl45tPLy8vDz8yMycnAWM8bGxvK9732PFStW4OfnNyjnVOpGPJkUzdtrkwjw8bgy\nD7q1zU5KfoWrQ1NK9aA/perWAUuBMBEpBn5ojHm9p77GmCwReRc4CbQB39RKG8qZmpub+eMf/0hx\ncTElJSVMnz69x7nMHVM2YmJi8PX17fV8LefrqPn4LN4zQvG//YvNR/alHKCxrYknVq/GK7Wey9sK\nuLytAPfRvvjMGoXPrDA8ovzw8fEhNjaWzMxM7r777qtiMcawYcMGCgsL+d73vnfNedftdS1Ubcqj\n6WSFtQecm+A5PoCApePxjg3BK+bGthF3D/bGe8Yoqg4VsSkrjZCQEOrr6zl27BgTJky4oXNfL7vd\nTl5eHlOnTsVm07L06ubWMQ+6tc2Oh7uN5EmjtJydUsNQf6ptPNHH8Zhuz38E/OjGwlJq4FpbW1m3\nbh3nz58nMTGRtLQ0cnJyiIu7eoFcWVkZFRUVvZaRs9vt2JvbqFyXg5ufByFfib1SX7iyspKUlBTm\nzJlD9KxJMAvaapppyqqgMbOc2p1F1O4owiPSl7AX4pk9ezbZ2dmcPXv2qqkHhw8fJjs7G4CCgoJe\nq0k0ZldQtTEXe1MbAUvG4TU1BK/oAMRj4NVBrsU/OYpPcvdw2X6Z5557jiNHjpCVlcV9992Hp6fn\noF6rPy5evEhjY+OgTNlQarjrmAfdkSwDV8rZebrb+OPzyZpAKzUM6G4B6qbQ1tbGu+++y7lz51i1\nahWzZ88mPz+fgwcP9pg8dySs06dPv+pYfX0969ato+JiGXOaJ7B4zd24+XlcOf75559js9m4664v\nSuO6B3nhf/sY/G8fQ3tdC42ZFVR/eIaaj/KZumoqXl5enDhxoksSePHiRT799FMmRk2gsKSIkweP\nEzN2AjavLxJie0s7NR/lU59agkeUH+HPz8YjcuimGuQ2F5PnVkKi73TGjx9Pe3s7x44dIzs7mzlz\n5gzZdXvTsSX35MmTnX5tpVxh/oSQKwnyr3bmdZnG8X56sY5CKzUMaPKsRjy73c6mTZvIzc3lgQce\nuJLkJSUl8fHHH1NUVMT48V3rH588eZLx48cTEBDQpb26upq3336bmqpqQtv8SXE/TfafL7F06VLi\n4+MpLi7m5MmTLF26lMDAwB7jcfP3xD85ivbLzdTuKMI3YTQzZ84kKyuLL33pS3h6etLc3MyGDRvw\n9fZhcckkdrTVcfrUKeb871F4xwThPS0U9zAfaraepa2iEf87xxF094ReN0Dpj5aWFtLT0zl//jxz\n5sxh8uTJXXbrq6mp4aOPPiIqMJz40ihaLtYTHR1NSEgIx44dc1nyPGbMGJ2brG5JnadxuLnZeC+t\niDa70VFopVxMk2c1YjQ3N1NbW3tV+759+8jKymLlypUkJiZeaU9ISGDnzp0cPHiwS/JcWVnJpUuX\nuPvuu7ucp7S0lLfffpuWpmbubU4gOjqa2rv82b5jO1u2bGH//v0ABAQEcPvtt/cZb+DyaBpPlFO1\nKZdZq2Zx9OhRTp8+zaxZs9i6dSuVlZU8FHwHXrUezFo6l0/2fk7rHH88Clup2XoWALcgL8Ken433\n5ODr+p2BtYDy0KFDpKSk0NjYiKenJydOnCAyMpJFixYxc+ZMRITNmzfT3t7OI6u/QvMredSnXCBk\n1VTmzJnDrl27qK6uJjj4+uMYqCNHjlBUVDTkNbKVGq46T+M4X93I+kOF2A20tNr52een+e6KWE2g\nlXIBTZ7ViGC323n99dcpLS3t8fiSJUu61Ottq2rCM8CT+fPnc+DAAaqqqq5s39wxZaNzibrCwkLe\neecd3MWN+xvnERkZQdiaOEZ7uzNp8iRycnLYsWMHZWVlrFq1ql/zf8XdRsijUyl75Tihp6yk+/jx\n47S3t5ORkUHy2DmEn/Ek5Ikp+Md48cnez7kQUc8dj95BW00zrcW1eE0KxuZz7f9Nm5ubOXToEDab\nDR8fH7y9vfH29sbT05Ps7GwOHz5MS0sLU6dOZfHixYwZM4bjx4+zf/9+Nm7cyI4dOxg3bhxnz57l\nwQcfJHxcBJVzamg4WkrQfROvJM8ZGRksWbKkz/d9o4wx7N69m127djFlypR+fVBR6mbVMY3jSEEV\n76cX09Jqxw7syy1nf145Ly6exMv3X7vcplJqcGnyrEaE06dPU1payh133MHo0aO7HPPz87uy0M4Y\nQ93+C9Rszcc7NpQFqxZw8OBBUlNTuffeewEreY6KirqSTJ8+fZp3332XQN8AVtbEERISTNizcdi8\nrf89RIQZM2Ywbdo0ysrKiIjouqnBtXjFBOGXFEn9gQvMTJzG4ax0zp07x/jwMcw8E4pfUiS+c6z3\nExkZyenTp7njjjtwD/LCPcirX9c4cOAAu3fv7vGYiBAXF8cdd9zRpdTbvHnzSEhI4NSpU+zbt48T\nJ04wbdo05s2bB4D/wigajlyiIb2UkNvHEBMTw7Fjx7jzzjvptqvooLLb7WzdupW0tDTmzJnDQw89\ndF1bpit1s+kYhf7Z56fZl1uOAYyBV/bkEz3KT3clVMqJNHlWw54xhr179xIcHMyyZct6TabsLe1U\nvZ9L47Ey3Ef70JRTic/pUcTFxZGens7SpUtpbm6muLiY5cuXA1bVjfXr1zN6VDgrK2bg6+NL2POz\ncfO/emTZZrMNKHHuEHTfRBqzK4k+50eq3Y6bzcbi8ql4RQYQ/MAX1TViY2PZu3cvDQ0N1yyf11lj\nYyMpKSlMnz6dVatW0djYSFNTE01NTTQ2NhIREUFoaGiPr7XZbMyYMYPp06dTUlJCWFjYlcTYc1wA\nHuP8qUu5gN/CKBISEti8eTOFhYVDVrautbWV999/n+zsbBYtWsSKFSuGNFFXaqSZPyGE766IZX9e\nOZ33LnptzxmmRQboFA6lnEQLp6phr6CggPPnz7No0aJeE+e2ikbKfn2MxowyAu+ZQMR35+M1KYjq\nP+ezIG7+lcVyOTk5wBdTNrZv3467mzt3V8fhY/Mm7PnZ/R7x7S+btzshD08msMyN28bN5m6fRPza\nvQj92vQupeamTZuGMYbc3Nx+nzs1NZXm5maWLFmCl5cXwcHBREZGEhMTw4wZM3pNnDsTEaKiovDw\n8OjS7p8URVtpIy1FtcycORNPT0+OHTvW/zc+AE1NTfzhD38gOzube++9l5UrV2rirFQP5k8I4cXF\nXUtanqto4InXDvIPm07oroRKOYEmz2rY27dvH35+fiQkJPR4vDGnkku/PEZbTQthz84icFk0YhNC\nvhILBrz3XmbChAmkpqaSlZVFWFgY4eHhFBUVkZOTwxxi8Gr1IGztbDzCfIbkPfjEheE7K4w5eaMJ\nv+hFyCNT8AjvOrocFRWFv78/p06d6tc5m5qaSElJYdq0aURFRQ1+zPFhiIeNhrRLeHp6XqkY0tLS\nMujX2rNnD4WFhTz66KO91t5WSllevn8GP141m5hRX9xDWtoN76QWahKtlBNo8qyGtYsXL5KXl0dy\ncvJVI6NgJc4Vb2XhHuJFxLfn4h37xdeW7qHeBD8wieYzNcwNnkZNTQ2FhYXMnDkTYwyfffgJPngS\n1zqesOfi8Iwa2nJowQ9NwebvgV9yFL4Jo686brPZiI2NJS8vj7a2tj7Pd+jQIZqamoZsEZ/Nyx2f\n2WE0ZJRhb2knISGBlpaWKwsuB0traytHjx5l+vTpzJ49e1DPrdTN6smkaP5zdQLeHjY6vqMxWEn0\nH1MLWf3qQd5JLXRliErdtDR5VsPa/v378fLy4rbbbuvxeO2OQtxCvQl/aQ7uod5XHfe9LQLvaSGE\npdsJCbLKrM2YMYMTHx2iqPQ8871jGfetRLyie67ZPJjcAj2JenkBIV/ufbe82NhYWlpaKCgouOa5\nmpubOXjwILGxsYwZM+aafW+EX2IkprmdxsxyoqOjCQ4OHvSpG9nZ2TQ2NnYpM+hMprXdJddV6kZ1\nLCJ8IikaT/cvkmiAdrvhn7Zk6gi0UkNAk2c1bFVWVpKVlUViYiLe3lcnxs0Fl2kprCXgjrHYPHue\nCy0ihDw6FXF3I5lpxM+OxzOlll2H9hLo7seSbz+I+xBN1egxnj42OZk0aRLu7u6cPn36mv0OHTpE\nY2PjkJeO85wYiPsobxrSLmGz2UhISODs2bO9lgy8HkeOHCEkJISJEycO2jkHouFYmUuuq9RgmD8h\nhB+vms26F5KJHxfU5Vi73fDX7x7TEWilBpkmz2rYOnDgADabrdc5sHV7iinwruTnO37Hz3/+c956\n6y22bNnC7t27ycjIoL6+HgC3QC9CHp7M2Ev+LMwdx4nDGVTa6ljx0D14+A3u4sAb5enpycSJEzl1\n6hSm83L6Tpqbmzlw4ABTp05l7NixQxqPiOA7P4Lm/BraKhpJSEjA09OTV199lY8//pi6urobOn9Z\nWRkFBQXMmzcPm835tyNjDLV7zzv9ukoNtvkTQvjnB+Po/vn8XEUDf7/pBD/ZOrjTrZS6lWnyrIal\n2tpajh49SkJCwlVbaINVXaPhZDnpPmfx9fVl7NixtLa2kpuby86dO9m0aRO//OUvSUtLw2634zMn\nHJ/4MFpqmzgaXEhkZCSzZs1ywTvr27Rp06iurqasrOcR0cOHDztl1LmD7/wIEKg/cong4GC++c1v\nMmfOHA4dOsQvfvELdu7cSVNT03Wd+8iRI9hsNubOnTvIUffN2A01H+XTVtrg9GsrNRTmTwjhT39x\nO08mRRMZ2HVg4LW9+TqFQ6lBonWeb3H2hlZsvlcvxHO1lJQU7HZ7r7vL1e2/QKFbORWN1Txy3yPE\nx8dfOdba2kppaSnbtm3jz3/+M0ePHuWBBx4g8rHpnN5XSc3OWh585GGXjHT2R2xsLACnTp26akOY\njlHnyZMnM27cOKfE4x7khdfUEBqOlBK4YgJBQUE89NBD3H777ezYsYPdu3dz6NAhli9fTmJiYr9L\nzLW2tpKRkcH06dPx9/cf4nfR7dplDVRtzKXl3GWwCdidenmlhkzHjoTvjAni7zeduNJuN+iW3koN\nkuGZPSinaDhWyoV/TaH8zSzaKhpdHc4VVVVVpKWlMXPmTEaNGnXVcXtDK3VpF8nwLyYkJIS4uLgu\nxz08PBg7dixr1qxh1apVVFdX89prr/HJZ5+wN3U/MTExTJ482VlvZ8ACAwOJiorqMu/Zbrdz8eJF\nPvnkExoaGli6dKlTY/JLjKC9ppnmvOorbWFhYaxevZoXX3yRyMhIPvroIzZs2EBzc3O/znny5EmX\nLBRszq/m0s/TaSmpBwH/RUO34FIpV3kyKZq/vHMStk6fZffllmspO6UGgY4836Jaimqp3HAa99G+\nNOfXUPJ/jxBw5zgClo3vdfHdUGtvb+fgwYPs2rULm83GnXfe2WO/ukMlFLeVU9pUyYMrH+x14xQR\nYc6cOcTGxrJ9+3ZSU1MBRsTOdbGxsezevZuUlBSKioo4e/YsDQ3W9IL4+HjGjx/v1Hh8Zo7C5utO\n/ZFLXcoBAowZM4ann36a/fv3s2PHDi5dusRjjz1GeHj4Nc/ZsVAwJiZmCCPvyrTZqXo/D7cgL3ym\nh1J34AL+C8fA3ltjPqiIeAN7AC+s+/8GY8wPRSQU+BMQA5wDVhtjNLsa4V6+fwYr4yK7bOndUQ96\nY3oxf3w+WUehlboOmjzfgtprmin//UncAjwJfzEe2g01H5+ldmcRDemlBD0wEZ9ZYU5NMAsLC/nw\nww8pKytj+vTp3HfffQQFBV3Vz7TZqTtwgeP+xQR4BTBnzpw+z+3j48MDDzzA3Llzqa6udtp0hxsx\nffp0du/ezSeffEJAQABTp05l0qRJTJw4kcDAoS+r15242/BNGE3doYs9TvWx2WwsXryYsWPHsmHD\nBn7zm9/w0EMP9TqvvLS0lMLCQlasWOHU6TO1u4tpK29k1NdnUrUxF+/poT2WOLyJNQPLjTF1IuIB\n7BORj4FHgO3GmJ+IyMvAy8D3XRmoGhwdW3ofPldJc6sdg1UPurnVztq3DvN44nhevn+Gq8NUakTR\n5PkWY1rbKX/7JKa5nfC1c3Dzs5Kg0Mem4ZcUSfWWM1T+MQfPmEAC74rGa0rwkCbRjY2NbNu2jfT0\ndAIDA3n88ceZPn16r/0bjpdxofYSF7zKuXf5vbi79/+v8NixY4e8OsVgiYqK4utf/zoBAQGEhTn3\ng0xvfOdHUHfgAg0ZZdZobQ8mTZrEX/zFX/Dee++xYcMGioqKWL58OV5eXRcvdSwU7G3XyKHQVt7I\n5Z2F+MSHYW9sw17fiv/tt9aUDWOVcOkokeLheBjgYWCpo/0tYBeaPN80OupBb0wvZsORYlrbrCS6\nuqGVV/bkU3K5iZ897vxFu0qNVJo834SMMT0mW8YYKjfm0lpcx6inZ+IR2XVHPa+YIEZ/ay71hy9S\nu6OI8tcz8RwfQMBd0XhPCxn0BK6kpIT169dTU1PDwoULWbp06VVJVvf46/aeJ8O3CF8vX+bNmzeo\n8Qw3kyZNcnUIXXiO9ccjyo/6tEu9Js8AQUFBPPPMM3z22WekpqaSkZHBggULSEpKws/P78pCwRkz\nZjhtoaAxhqoteYibjaAvTaTi7Wzcw33wmhLslOsPJyLiBhwBpgC/MsakikiEMeaio0sJEOGyANWQ\n6FhI+Oi8cax96zDVDa1Xjm0+dgFfL3cenTdOp3Eo1Q+aPN9k2utauPRf6dh83PGaGoz31BC8Jgdh\n83KndncxjcfKCLx7Aj5xVy/EAxA3wT95DH6JkdQfuUTtziIq3szCY4wfgcuj8Y4bNShJdFZWFps3\nb8bb25u1a9f2aypF85kaLpRcpMirjLsW3oWnp+cNx6EGxi8xguoP82kprsVz3NUlBDu4u7tz//33\nEx8fz759+9izZw8HDhxg/vz5BAQE0NTU5NSFgo0nymnOrSb4wUm0XmygtbiO4IcnD4sRfWczxrQD\nCSISDGwSkVndjhsR6bHIuIi8CLwIEB0dPeSxqsE3f0IIjyeO55U9+V3a30ktZMORYta9oPOgleqL\nJs83mbq957E3tOIx1p+GtEvUH7wINsFznD8tRbX4zAknYFnfi83E3YZ/UhR+iRE0HC21kug/ZOM1\nOYjgL0/BI9z3uuKz2+3s2rWLPXv2MG7cOB577LEe6zj3+N72nSfDuxBvL+9et+tWQ8t37mgu7yii\ncv0pRn9jTp9lDseNG8fjjz9OaWkp+/fv5/Dhw9jtdkJDQ522UNDe1Eb1h/l4jPXHPcKXirdO4h7h\na9WvvoUZY6pFZCdwL3BJRKKMMRdFJArocQtJY8xrwGsAiYmJPe/io4a9l++fQcnlJrYcu0Dn/4gt\nbXa+v/E4//ZovCbQSl2Dlqq7ibTXt1J38CI+8eGEPzeLMT9cSNgLswm4cyym3eA1KcjaqnoAo23i\nZsMvMZKI7yUS/PBkWs7Xceln6dR8dg7T2j6g+JqamvjTn/7Enj17mDt3Ls8880y/E+e2mmYuni7k\nnLnEggULetyuWw09m68Ho56eQVtVExXrcjDt/cufRo8ezapVq/jOd77DHXfcwf333++0Ud/LnxVg\nr2vBLymSit+fxC3Ei/AXZrusqowriUi4Y8QZEfEBVgI5wAfAGke3NcAW10SonOVnj89lw0u3M6fb\nlt55pXWsfuWAbumt1DXoyPMA2JvbaK9upq26mfaqZtprW/CODcFrgvOrH/Sk7sAFTEs7gY6RZXG3\n4T05GO/JwQTde2PnFjfBf+EYfGaFUfNRPrU7img4Vkbww5PxmRba5+ubmpp4/fXXKS8v57777mPB\nggUDSp4a0i+R4VaAh4dHr9t1K+fwigki5MtTqNqYS83WfIIf7H/N7ODgYFasWDGE0XXVcr6OuoMX\n8I4bRc2fz+IW6EX48/G4+d+yU36igLcc855twLvGmD+LyEHgXRFZCxQAq10ZpHKOji29V79ygM6f\ng9sN/POWTKZFBugItFI90OS5HxqzKqjccBrT2HbVsdrthXjPCCXonpirFuA5k72pjbr95/GJGzWk\ncbgFeBL6+HR8EyOp3pJHxe+yCLp/IgF3XnvO8vbt2ykrK+Opp55iypQpA7qmMYbKw8Xku5WSODcR\nX9/rmzKiBo/fbZG0Xqynbv8FPCL98Lst8obOd/nTz6j58APG/sd/YLuObxXaWho5e/IXjB33dXxG\nRSIitF9uoXJ9DuLjRnNuNbYAD8JfmI1b4C2bOGOMOQ5cVVbBGFMB3OX8iJSrzZ8Qwr9+eTb/tCWT\ndvsXGbTdbkjJr9DkWakeaPLcD3UHzmPzsOG/NAa3YG/cgr1wD/ZCvNyoO3iB2l3FXPp5Or5zRxO4\ncgLuIc6fUlB34AKmqZ2A5c5ZxOM9JZiIv5pH+e9PUrurCL/kqF6/Bi8oKODw4cMkJycPOHEGaDl7\nmdyaAuwedqeWNlPXFvSlSbSWNlC1Oc+qXBFzdV3u/qg/dIgLf/M3mNZWarZ8QMhjfQ96GmNoq2ii\n+VQlTbnVXGrYTMn0N6g/fInw81/FI9yH1rIGTKsdcbNh8/cg/IV43IJ6r+ai1K3qyaRopkUG8Oru\nM2zPvoQx4OlhI3nSKI4UVJGSX0HypFGaSCvloMlzH9ovN9OcX0PA8mgClly90C5wWTR+C6Ko3V10\npQZu4IpoApc5byW6vbmdun3n8Z4eiudY55T+AmtaSODy8ZS9cpyGtEs91sxtbW3lww8/JCgoiGXL\nll3XderTSshzv0R4WDhRUVE3GrYaJOImjHpyOqW/OkbFH7IZ/a0E3IMH9sGx+cwZir/1bTyioxEP\nDyp/9zuCv/oVpJeNU4wx1KeWULunmPbKJgDcRnlRk7AbgPopRxgX8AJNmRXQZo2i2QLcCX9+Nu7B\nmjgr1Zv5E0J47euJXZJlgK/9NoWmVjs2gRcXT9INVZSiHwsGReQNESkVkcxObf8uIjkiclxENnUs\nQPDv2vEAACAASURBVHEc+4GI5InIKRG5Z6gCd5aGjHIw4JvQ+1bDbn4eBN8/ici/uQ3vqSFc/qyA\ntppmp8VYn3oRe0MbAcudu2UzWPNfPaMDqN13vsfFY3v37qW8vJwHH3zwmjWce2NvaqPkRAGXpJo5\nCXNuydJifWnOy6PopW/QUnze6de2+Xowak0cptVO1bunB/TatrIyil54EfH0ZPyrrxL24gu0nDtH\n3Y4dPfY3bXaq/x975x0eRbn98c9s3+wmm02vpJBGCxB6RxQEBCzYuXaUoqKCV0Es2L0WrChVVMCO\nSFVApPeaAFICIWXTNrtJNtvr/P4IIhEQQe79WfbzPHkCM/O+c3Z2dnPeM+d8z6Jj1H97DGmYgvCr\nmxP3746o75XglB5Hp8vDJRpoMOUjSCVEjcklbmJn4iZ0+Kd1EQwS5KLpkKLn/ssy6JCiZ1uRGZc3\nAEBAhOkbinhlxT+jlX2QIL/F71Hb+IhGKaPTWQ20FkUxFzgKTAIQBKElcDPQ6uSY908WpvxlceQb\nkSdqf5c0myxcSfjQdBDBsav6f2BdY8dA6wYDyoxwlM3+fwoXQ3sn4a914TxoarK9qqqKTZs20bZt\n24tK1wBwFpgoFCsQBIHc3NxLYe7fCtHvp+KJydjWrsX46qv/LzbIY0II65eMu8iC1+gAwF1YSPn4\n8Rxun0f5hEdx7t/fZEzAbqds1Gh8dXUkT5+OIimR0AEDkCcmYv5w7hnn8Nu91Mw5gH1HFaF9k4m+\nLxdttwRkkWoM5fORyUJpkfgaBKTUh20kemQbVCm6xvQq+V/6KyhIkP83uqZHIvlVvGLmxiJ2l9T9\n/xgUJMifhPM6z6IobgBqf7VtlSiKP1fPbQN+rha7GvhcFEW3KIongGNA50to7/8Ub01jM4WQtueO\nOv8aWaQaZboO++5qxMB/XwbVvqOKgM1L2P8o1/lsqFpGIotSY91goLH7b6Oe85IlS1CpVFx55cU/\ngLDtrOSYvJr09HTCwv53iwNRFBEDgf/Z+S6WuvnzcRUUENKxI9ZVq7Dv2PH/YkdIXixIBBpWHaJ8\n/HiKhl2Nbd16Qi/ri23dOopvuJHiEf+iYdUqRI+H8vETcB0+TOKbU1G3bgWAIJMRcccdOPfswbF3\n76m5vdV2jNP24SlrQDc0HalOQf23x6j94ghVn27GWPUd4aY+WGZVoa1thz1lN/KkYFFpkCB/lA4p\neu7r1bTTqSjCwj0Gpq09FnSig/xjuRQ6z3cD3538dyJQdto+w8ltf0mc+TUggPoCnGdoVCLw17pw\nF1n+S5Y1IvoCWNcbUKSGoUy/uGKtS4EgEdD2TMRrsJ16zdu3b6eiooJBgwZdtDqG1+ig1FCGVXTS\ntm3bS2nyeamYMIET1w3HX1//Pz3vheAxGDC+9TaaPr1Jnj0LWUI81S+9jOi/MP3tS4G3vAh8Buy7\njdjWbyLyvvtovuYHEqdOJWP9OmInTcRXVUX5uIc42qMntvXriXv6KUL79m0yT/jw65DodNR++CF+\nqwf7XiPG9/YRsHmR6lVYlhZRv/g4zoMm3CUNGMVliIKPiLqBKJqFkpR7Ex5/DXV12//n1yBIkL8j\nEwe3YHTvdCQCCIBcKvD1bgNvrDrCiNnbgg50kH8kf6hgUBCEyYAPWHARY//UbV5FUcSxrwZlmg7Z\nBVboq1tHIiyWYt9VhSoj/PwDLhL7nmr8DR70N2Rd1HhRFLFv3oKmaxcE2YXfCj6fj08//ZSGhgZC\ntVqkajehi8uI7NyM9evXk5WVRevWrc8/0Tmw76qmUFaFQq4gJyfnwmyrq0OQSpFeRLTa+uNaGlY0\nrgcND44jec5sJP/DVuABjx93kQVPmRVt13ikoWeeWxRFqp6ZgiAIxD/zDBKVithHH6V8/ATqFy5E\nf+N/X6Y34HTSsOI76r78Ald+AfLk9qg6jCHhnS8I7ZF26jipVkvEHXegHzEC65ofqftyGSHtW6O/\n+eZTx/gtbqxbKvDVONH2f5aAS0Lli00dYKlahmZgKuqWkchjQggEfBzf+jARml4k9xvUOI8/ncLq\nZ6muXkpERPff9Tqsvv/9YiNIkL8SEwe3oH+rOLYVmamod/LZjlICIni8Ad764SgPX5EVVOII8o/i\nop1nQRDuBIYAl4s/P6uHcuD0qrWkk9vO4M/e5tVbYcdncqLtfeGBc0EuJaRdDPZdVQQc3vO2ML4Y\nxICIbUM58kQtyot00K0//ED5g+OInTSRiDvuOP+AX7FlyxaKiorIzMzE5XJRq7BywlKN/4ejKJVK\nrrrqqosu8BP9ARp2V3BCZqRVq9YoLsB59dfXc3zgIAIWC/LERJQtclC1aIGqRQvU7dohizh3U5eA\ny0X1Sy+haN6cyHtHUjlxEpWTnyTh1f/814oVRVHEW2nHXViPq7AO9wkLP3csCNi96K85M1/csngx\n9s2biX3qSaQRMVhWlyAJzSWkx/WY53yDpucVyOP0CL9OWLwEuI8do+6zz7EsWULAakWRnk7spImE\nDRtGzcxCXD9ZCe1x5jhBJkPTrQ/WLVo8ZgHnARPq1lGI3gCmjw7irXYgi1KhaBaNfcsWZHGtEVQK\nwgakENI6+gx9ZpPpB9zuKrKznj21TSpVEx3dH2PN92RlPo35rWn4rTaiH34Imf7sf9yX1fx5ny4E\nCfJnoUOKng4penaX1LFwjwGPN0AA2HzMxM7iWhaM7Bp0oIP8Y7go51kQhIHAY0AfURQdp+1aAnwq\nCMJUIAHIBP5/kjD/II59RpAKhLSOuqjxmk5x2LdV4sivQdvtTAm3P4rrcC0+k5OIm7Mv2qmr//Ir\nAMyz5xB+881ILkANw2QysX79elq1asUNN9wANBZ1Vb6yHWmr8MbOg2r1RdkF4DpSxwlnBV6F74JT\nNswff0zAYiFy1Ci8ZaW4Dh3GtuZHEEUkGg0p8z5B1bLl2cfOnoPXYKDZR3PRdO2Kr6qamrfeQp6U\nSMxDD1306/ktrOsNNHxfDIAsNgRt9wRUmXoce404dlejG5DSZAHmM5sxvvwK6vbt0d9yCw0/lGL9\nsTFbSho9AGn0AIzvHASJgLZrPLqh6ZfM8bdv3UrpPSMRpFJCr7wS/U03ou7Y8dT8mo5xNKwuwWdy\nIos68/2vX34C0R9AHhmCef4hNF3iEP2Ni4fIO1qiyonAtqkcd1Eu/gYDcaP6oUw7ewMWg2EeKlUi\nUVFNJRDjYodRVfUtx94dTWD2DhAErKtWEfvEJMKGDDnjWnxVFXzsHCTI76VDip4FI7vy1g9H2XzM\ndCoC/dzSg7RO1HFdXlLQiQ7yt+f3SNV9BmwFsgVBMJxs3/oeEAqsFgRhnyAI0wFEUTwIfAn8BHwP\n3C+K4l/umagYEHHk16DK0l901FiRqEUer8G+s+oSW9eIbVM5Up0SdZuLc+49hnLsmzYR0rUrvpoa\n6hcuPLWvqqqK6upzq4WIosiyZcuQyWQMHPiLEItUI0fTMQ7//noU3j+WTm/fVc0xZTU6nY6UlJTf\nPc5fX0/dvPmEXnklMY88TOLUqTT/bgXZu3aSMn8ekrAwykaNxlv+ywMRn8mJGBDxGAyYZ80idNBA\nNCdbgEeOuo/wG67H/MH0JtfoUiEGROxbK1Ck6Yif1Jm4RzoQflU6qiw9oX2SEL0BbDua3kPVL75E\nwOEg/oXnET0BbFsa208nPN2VmHHtEdiFa//nKJursW2pwLqm9JLY6jObKX/sMRRpaWSsX0fi668R\n0qlTE2dU0zEWJJz1vncdq8eZX0Non2RixrZD2ycJ+/YqHLuqCekYiypT39jye/kJFKlqHOv/Q8Oy\nr89qi812lLr6bSQmjuDXgj7hYV2QepSYfFuIuv9+0r5dhDw5mYp/P0bZvfc1kfQrc3nYUm+7JNcn\nSJB/Ch1S9Dx8RRYKmQQJEADyDRYWbC9l+AdbuH1OsOYgyN+b36O2cYsoivGiKMpFUUwSRXGOKIoZ\noigmi6LY7uTP6NOOf1EUxeaiKGaLovjdb839Z8V9wkKgwUNIu5g/NI+mUxzeCjue8kv7x9lT3liY\np+2RgCC9OCe1fuHXIAgkvPQi6nbtMM+ajejxYLPZ+Oijj5g5cyZ7T1M8OJ38/HyKi4vp378/oaGh\nTfaF9kyEgIhtc8V5bfBW2SlesJd9b6ym6r29GKfnUzN7P6a5BzAfrsQgmsnNzUVyjoYZZ6P2k08I\n2GxEjR3bZLtEoyGkY0eazZxBwOWi9L5R+C0WPBU2qt7YhW1zOdUvvQxSKbGPP05AFBFFEUEQiHv6\naTQ9elD5zBRsmzf/blt+D57iBvwWD9oucWd0v5PHaVBmhGPfUoHob1T+sK5dS8OKFUSOGY2yeXNs\nWysRXX7CLktGEiJHkaAlZvwI/JXbcO2ZS0iHWBp+KMW++49JJ4qBABWTJhGwNJA4deo5U1+kOiWq\n7IhGtRn/L2oloi9A/eJjSCNUhPVNQpBJ0HSIBZkEpAKOvdUYp+3Dsaua0H7JRN/XEW3vHtQtWEDA\n6TzjPIbyBUgkChLib2hqp99P9ZPPoNzixd1eQD/mTlTZ2aR+9imxkyfj3LOHoqFDMU59k8pnpjBr\n6nt/6LoECfJP5ecIdI/MKH79XGtDoSnoQAf5W3Mp1Db+djjzaxAUElQtzp0b+3sIaRcNMgH7rksb\nfbZuNCAopWg6n/1x9vkQfT4sC79B26sX8oQEosaOwVdZSf3ixaxatQqPx4Ner2fx4sWsXLmSwGmS\nbXa7nZUrV5KcnExeXt4Zc8si1ahbR2HdWE7Nhwewba/Eb/X8cm5RxHWsjpoPD1D21g4WHl3Ft9bN\nfGlZyyFnCV6PF7PLy6Q8Oesz2rAjPo2FVbVsrbdR6nRj9/nxi2dPkfdbLNR+Mo/QAQNQZZ+9iFKZ\nmUnSe+/hLS3FcP8D1Kwr4f3mCsZUVjKybQ/uefk92h0zkbQun+v2HcMTCCDI5SS+/RbK5s0pH/cQ\nDatW4ykrw7p2LaZZs6iYOImG7y5unejINyLIJahaRp51v7ZnIv4GD879JkSvl+qXX0GR0ZyokSMJ\neBo7Syqz9CiSflnEyGNiiBw1CtuaNSgSTCgzw6lbWIir8OLTE2o//gT7ho3ETHz8nNf2ZzSd4wjY\nvLgO/aJwad1Ujq/GSfiw5ghyKQGPH/OCQ0iUUmLub4cqQ4+3pjENSTcgFUEiEHn3Xfjr66l5513E\n095zn89KVdUiYmKuQqH45TMq+nxUPD4Ry+IlJKTdhCjxU1OzGgBBKiXitn+RvnwZmi5dMM+ciWXF\nCr5v2Z6OtmDOc5AgF8PPEWi59My0sA2FJj7dfmmeegUJ8mcj2J77V4i+AI79JtQtI5Eo/lhzBUmI\nHHWrKBx7awgfnHZJmjX46t04C2rQdk9Eorq4t8+2YQM+o5HwZ54GQNOrF6rWrTn4+RcUtGlUxzCZ\nTISFhbF161ZqamoYPnw4arWalStX4na7GTp06DkjwuFXN0eqV+E8aDrVEU7eLBRBEAg4vPiMTiRa\nOTubGbDVuOjbpy+HDh1ibfUetocc5mjHXmwhFHUghLerG6C64YxzqCQCIVIJaomESLmMwdE6+n23\nBLnNRtT9Ywm4fAhK6VlzfTVdOhP/8suUTvkPU4Y62JKuIMUeINwbQXZ8DFFKBRJB4KNyE28UVzMp\nPR6pVkvMhAkYxo2jfNy4JvMJKhUNK1eizs1Fnnj2AlNfQGRLvY3vTRaGxoTTLVyL6Avg3G9C1erc\n95oqS48sWo11Uznuwg14S0tJen8agkKBbVM5AbuXsLN0loy48w7qv/wS4xuvk7LgC0wz9mOef4jo\n0W1RxGvOeq5z4TxwEOPUqYT2vwL9Lbec93hVVgRSnQLbjirUraPw1buwrilF1TISdU6js1u/+Dg+\no4Oou1ujSNASeWdjl8LTr4O6Y0fCb7ie2rlzCTgdxD31FIJUSmXVIvx+O0lJt506NuByUfnEZBpW\nrCD6kUeIvPNeDFs3Ul29hPj4a08dJ4+PJ+mD9/HX1pIvVVK69xgP5yTzxOZtF3RNggQJ0kiHFD2f\n3deNCV/uo9jsaLLviUX7+XavgccHtQjmQQf5WxF0nn+F62gdotOH+g+mbPyMplMszvwanAfNfzgN\nBMC2pTFfU9vj4osQ67/4Ell0NNo+fQAQBAH96FF8s3wFMp+P8Lg4OnXqxNq1axEEgePHjzNr1ix6\n9epFQUEBvXv3Jibm3K9FqlUQPjgN3aBUfNUOnAdM2PcY8de6QCYQfk0GRaoaDn17nD59+tC3b1/6\n9OlDcXExq3fs5PuAnEyTganN42iZ14YKl5cKt5dyl4d6nx+HP4DDH8AZaPx9wunmlRNVvJLTmY7P\nvsEIlZ6OU3cSmRlJxDlk/DSDB/OKW8/mCDmP/biK660tUaboiM1tDsBe415KrT7eLammf2QYLY8f\npXzCBCQ6HYqcHJz79yPRaIidOBFNl84cHzKUqhdfIvn9aQTsdpwHD+KtreNQh84srrOz1FiP2dvY\nV+irqlqW5GWSWuog4PD95n0hSAS0PRKo//Y4tlXLULVpg/ayyxo1vjcYUKTpUKaeqfEtUSqJeuAB\nKidNwr5xLZF39aFm2j7Mcw8QfX+73y2/6LfZKZ8wHllUFPHPP3/OwkOvtx5RDKBQRCBIBUI6xmH9\nsRRfrQvL8iIAwoemN+Z4b6/Esbua0Mubocps/IMqCALCrxYQgiAQ99xzSHU6zLPn4K+3EP+flzEY\n5hEWmosurLGQ1L5tG5XPPIO3pJSYRycQOXIkALGxQyktnYnHY0KhiGoyrywykq+OGlBJBIZGh/PE\n77oaQYIEORsdUvSs+/dl3D5nOxsKm3aa3VFcx/UfbGFU73QmDm7x/2RhkCCXlqDz/Csc+4xIQmSo\nMi+NPrMyPRxphAr7zqoznCQxIILA71ZCCLh82Lc3RvNketVF2eOtqMC2cSORo+5rou28RyLBqguj\n085ddP1oLpHR0bRu3Zo1a9awZ88eamtrWbx4MSEhIfTs2fOc84uiyMGDB6mqqqJnz56o4jTI4zSN\nzt46A/hELA0Wlq9dTlJSEr179wYar0FaWhrVASX+UiOPpMbSrl075FIpmRopmZrffr17p8/iyyMn\nWHvtTTxSVIGys4qrDfX8+4iZ5OymKREBUeShA8WsiQhhwpEaBn01F8lVj+A16vDVutjtzmfMD2MQ\nJBriUt/n/r1HmD7xfsIiImj20Vzk8fG4jhylcvJkKp94gtABA9D26oV11SqO9bscb1UVG9vk8e6N\nd1JzoARVIED/aB3XxkfSQqPm2r3HGFFQxIIyCbrfca+F5MVSv/QokvD2RN/bAUEQsO2uItDgIew3\nNL51Q4dgnjED07vvkXbFFUTe1Zqa6fmY5x4g5oH2CLLzZ21VPfcs3jIDKZ98jDT83HYW7B+Lz2el\nc6clCIKApmMs1h9Lqfv6aGN+fu9EHLurse+uxl/nRpkRTtjl59d3FwSBmEcfRaqPwPjaazSEFOG4\nooiWLd/AX19P9auvYfnmG+TNmtFs7odounU7NTYudiglJR9QbfyO5NOi1ADuQIDF1XUMitIRKgu2\n7w4S5FLwyT1d+HR7KZMX7ef05DoRmL6hiGaRGm7t8ufr6xAkyIUSdJ5Pw1fnwnnQjKZz3EUX4v0a\nQSKg6RBLw+oSTB8dJODwEnD4Gn87fcjjNIRfm4Gy2fmbedh3ViO6/YT2SjrnMaIoYl25EnVeHvKz\nRIfrF34Dokj48OtPbTObzWzcuBG1w0H68ePIduyAq65Co9EwbNgw8vLyWLJkCUajEYfDwbx58xg6\ndOgZ0WeDwcD333+PwWAA4MCBAwwfPpzk5GRch+tQpOlAIbBw8/eICpHhw4cjlf7iuJg9PuaWm7gm\nJpzrWqWe93r8jL+hgZA5s7i/axde6NSSVR/sZnGGmoXN5CwtK2WMzM3YlFi0MimiKPLYEQMLzRbG\nHnXz0NAuOONfQd2+O8bphyleW8A41zjiNfGUWcvoY17O15oBzLrpTt7513XIohu7Taqys0j9/DPM\nc+dievc9RI8HJBK8JhMrJk3h9aQMWhHgwbXL6Lj4a0J1OiLuuB1vZRWzBwzkJqec0WoXC3Kjzn+v\nBbx4SzYhS+yFsmUHRL+Idb0BedJva3wLMhlRDzxAxaOP0vDdd+iuuoqIm7Ixf/IT9h1VaLuf++mF\n6PFgmj2bhiVLiXrwAUI6djznsW6Pifr6HYCI1XaQsNDWyPQqFBnhuAvrEeQSbBvKQQBl83B0A1JR\nt466IA3qyHvuRhoRwQHDv5E6ZCg3uzk+dQj++noi7x1J1P33I1E1XWBptdlotTkUF79PuC6P0NBW\np/atMTdQ5/NzY9wfq2sIEiRIU27t0oxSs53pG4rO2PfFztKg8xzkb0GwYPA0Gn4oBQFC+56ZQ/pH\n0HSKQx6vwW9xIyikyBM0qHOjCe2TRMDhpeaDfOqXHCfg9p1zDtEvYttcjiI1DEVy6NmPEUWMr75G\n+cOPUHzDjbiOHDm1LxAI4HW7qV+4EE2PHiiSEk+NmTdvHqIo0m3wYBQZzTFPn454WpFgUlISo0eP\n5uGHH+bqq6/GZDIxffp0fvjhBzweDxaLhYULFzJ79mzq6uoYNmwYd911F6Io8uGHH7J25RrcVTbU\nOREcTDBSLdTTO6wt4b+KZE4vM+L0B3gk9cIKIWs/mUfAaiVq7FjsWyppY/TyTofmrIpNpHuNj6ml\nRrpsO8RsQw1PHStnfqWZu8t8jJFrUCSGobv6ahTNoglkqPDuqSVaEcXcgXPpp2zD9qoFXHdgO9+0\n68JGSdNUB0EmI+ree2m+ejXp360g8ZN5vHPNLbyWlMng6HCW9m7Pvc9OJnvGDOQJ8Rhfe526+fMJ\nHTuatwNyjmkkTIgL4Av8do+g+i++wH1gOYJEgn1LBY6CGvy1LsL6NTvvU4uwwYNQZmZiem8aos+H\nqkUEirQwGtaWEvCcqSIpiiLWH9dSNHQYpnfeJXTAAKJGjz7LzL9gMq2hMbYkobLym1PbFXGNudWC\nSkrYFc2Ie6wT0SPbENI+BkF+4V89iivb4m4VIGSDhOrJU5DHx5P29VfETJhwhuP8My1bvI4gSNi1\n+yaMNStPbf+yqpZYhYxe+rN/loIECXLxTBzcgpeubUPor+pyYsNU7C6pY9raY8G23kH+0gQjzyfx\nGh049lSj7ZF4we24z4c0TEHsQ2cqU0Cjo25ZWYxtawXOgyY0V6VyzFeOz+dDIpGc+vGV2wmvd5M4\nNP2c5zG9N43auXMJGzIEx86dlNw6gsS33yakezc+++wzjh87RlSLHLI6dUJeWUlsbCzff/899fX1\nJCcn07tvXyxWGxX//jfWH34gbMCAU3NLJBLCw8Np3749WVlZrF69mk2bNvHjll0o8CIVoFevXvTs\n2RPlyWYrY8aMYfny5azfupHDCh095Fo2rNtETlxzUopDcebXnEplMXt8zCk3cXVMOFnnSNE4YDqA\nTqEjOeyXxY2/oYHajz9Ge8XlKNIzqf1qJ6qcCBSJWlolanmnoJadO2uZ0TeSJwsb88XvkoUw5qdq\nQkc2PzVPpa2S18SZPO6/nfcTXkP5404GfrCPNXdLyG7nJUtU8cjhMtZ2zkYvb/qxkcfGYPf7edAm\nsvKygdywZgX/GXEt6pMRZVlMDD6TGeRy5LGxeA0GWs9bz8QOrXmxpcCkQgOvZiWd1REOOByYZs5C\n3S6HkLbR2HdVIz1ShzwuBFXO+aOmgkRC1IMPUD7uISxLlxF+7TXoBqRSM6MA+7ZKQnv/8hTDXVhI\n9cuvYN+yBUVaGknTZqDK7Ygg/e20hpqa1ahUyYSFtaG6egmZGRORSBS4ixuQRamJHd/hknQ6LDPM\nQxDkZN86A7GLCd01V5/XttDQFnTquIiC/aPZv38szdP/jSb+Hn4wN3BvUjSy/0IHxiBBgjRGoLPj\nQrlp5lZ8fhGZVKBvdgwjZm/D4wsgEQSeu7p1MBId5C9J0Hk+ScOqYgS5lNC+506J+G8gUcnQX51B\nSPsY6hYW8v2XS/lJZjjrsVEhYYzO6n3q/1aPlf01++ma0JW6D+dimjYN3XXXEf/C8/iMRspGjaZs\n9GiKx46h0GgkzeWiLiSETaWlbJoxA7VajdPpRC6Xc/vttwONkUrT++9T+cRkRKeTsGHDznDqNBoN\n11xzDUd9kVQXbMcmhjBs0AAu757T5DiVSsXw4cOJq1KzrmYP36xagk6n4+rbr6dh7hHqlxZBgoIG\naw2zfIpzRp2P1h3l7T1vs8GwAb1Sz7zB80gJa2ycYp7zIQGrleixY7FtrSTg8DXJpQ2/Kp02b9Qy\no8DNgWvTKHZ4GPRlCZJELcrmjZHvWlct962+D7PKTCBCinK3k+oFz5OT3pa+CXq+OP4FUweOYHh+\nGY8fNTApLR6pAFJBQCoIOPwBxv5UQoHVwQtJEfT+cTnVhfmkfvYZzn37MIwZC1IpqQvmo87NxTB+\nEqIsh8FrVlBcqWXe5YOJ9/t4pEXqGde6dsEC/GYz0e++iywmEce+GnxuJxG3ZP9uhzS0f3+ULVtg\nev99dEOuQpmmQ5mlx7qurFHu0O/G+OZb1H32WWMR5BOTCL/hJsrfKyDw4x6iHu2I5hw59j6fjbq6\nzSQm/osIfXeMxhWYzevQebrjLbM2dje8BA6qz2elsnIhsTGD0bXqDe1+/1ilMoa89p/y06HH2Fb0\nEe+WZREQIxgeJae8/HOqqpcAI/6wjUGCBGlKhxQ9X9zXjW1FZrqmR7KtyIzHFyAgNtaeTF60n1Kz\nPVhIGOQvR9B5BjwGK84DZkIvb4ZUq/ivnONI7RHSdGkopI3zi4EA1jVrkGq1aLp1Q9ksDPGGeA7N\nXkYLSTKd5FmIcgnIBUQZVAXq+MG8k7Xr1tK/f38AXt/1Ot8UfsNth6MZuqiSsMGDiH/+OQSJBHlc\nHCkL5rP18cfZbjSSIwjkLllK1D33oL7vXvbv38+aNWuQSCTcfPPNyOWNnRQFqZTkWbOoeOwxAa31\nMQAAIABJREFUKh6fiHXtOuKeeRqZvqnM0AmTndl7bfRv1Q+31c1T352gZWo8rRKaKj+I3gCpVTpG\ntB7CXsUJOnfujDpEjfS6TIzv7uXIeytZXvw1M0c8SsuqYvZt+JzShCRiUtOJ6NSaD/ZPZ1nRMrQK\nLaNyR/HV0a8YtXoU8wfPJ8zsboy0DxuKIiOb2oU7UWbpERJVfHzwY3Kjc2kf0x7dwFTqFx+na5mb\nbnIp5honulsa25rXueoYvXo0VfYqZvSfgf5YLJalRYjoiH1yMvfFBLh1xa0cLF/MhNTB/OdEFUuM\nZ+oCqyUCc9ukcWWUDsvEx6l47HEqJk7E+v1K5PHxJM+aiaJZo1Ovu3oUlu/KEN0nGGeJomrHZl7t\n3IOCHV/zYmQI8f36ItFo8Nts1M6eg6ZXL0Ly2gOgTNfht3pQt4n+3feeIAhEjxuHYfQY6hctQn/j\njej6p2Ccto+6hXuo++QpvKVlhN98E9HjxiHT66ldVIhgdiEFVr6wg5xrM2jRPf4MR9hcu4FAwEN0\nVH90ujwUimgqK79BVpiGIJegyYv93Xb+FpWV3+D320hKvuOixkulKuoTXuAZ8xG8Xg+T5DMw7l1L\nteglJCTtktgYJEiQM+mQom8iUycRBAInddt/LiQEgg50kL8UQecZsKwsRhIiI7TX2TV6ixxuar0+\nOuouTB/3Z7488iXPb3ueCFUE12cO5xpTKt7pH+H+6RAAkffeS9S4B1mx8jvUIWqGPXgrarW6yRwZ\nQO0SP5s3byYzMxN9vJ4VRSu4vTiZIYtOsCtDYMsAKw9ZCsmJaIwA17vdbExKIsrppPXXCxECAcJv\nuB5RoSA/Px+ZTMbIkSOJjm7qiCmSEkmZ9wnmOR9S8+67OHfvJv7ll9H27AE05sU+vfgASpmEZ4a2\nREBg2HubGDVvN0sf6Ile88sCxH3CgugNENu2Gdfm/BIuVMRrUHWJJHqrSMWAu/AqlNxj9xPpicO9\nr57SHTt4e8PrFGQ3cGfrO7mn9T3olDouS76Mu1bexZgfxvDamniQSIgZPx779koCdi+B7qHcs/Ie\n9hr3IpPImNJtCsO6DMO+u5r6ZUVIw5VI9UrUraMpbShl7JqxVNoqefOyN8mLzcPjMyL63Wh6/Qt1\nq1a0AbrFd+Pjgx+zrN91ZKrCcSRr8UsFAiL4RRE/0D1cS/bJdJOwoUOp/2YRDUuWom7XjqQP3m+y\n+HD+ZEESCt7j+wjrP4pZQwfy+pa9TE9uzn5TNc/cNIIOWemIggS/xUL0abrSkXe0BL94wdFcbZ8+\nqNrmYvpgOrprrkEer0aisuDYo0AMyGj28UdoOncGGhVnHNurOOH2k6qSkhymYO38wxzZXkXfEdno\n4375HNTUrEYuj0Cny0MikREXO4wywyfoDl5DaNt0JOo//hUjigHKDJ8QFtbulDzdhY0XmWWo4dnj\nFTRXh/J6fDGC0Ui47nZi44YRqm0F3674w3YGCRLkt+mQoue5q1ufocYxY0MRVreP6/KSgnrQQf4S\n/COc56+qavGJIrfEn9nFzXW8HndhPbrBaU2ajhy1u1heU8+ymnoO2lwAjIiP4KWsJJQX0C76gOkA\nr+x4hY6xHcks8ZL42HRsBpGGKDXKSaOIPV6LedYs9hcdpyw6mmHDhp3hOP/MlVdeSXFxMYsWLSK8\nbzjZhQ6GfFWCuntXeLAX+498yI1Lb2RI+hAeyH2Ab7/4FolEwohHHiGQnk6gwYosKYkvv/wSo9HI\nrbfeeobjXNJQwvPbnidUHsqzdz5LWs8elP/7McpGjkR/223ETprI8gNVbCw08eywVsSENjqM0//V\ngRtmbOWBz/bw8V2dkZ3M93UdrgWZBGX6mVrEJcIRfEhZGZvE5VVeepcmA8lwsoZLYVbzZN+rSU9q\nXAz4zGZy5Em81fct3v5oDM7vD6AfOxpZZDTWOTtxJ0v4V/4dOHwOnu3+LCtOrODJzU9S0lDCfdfc\niWlaPgGbF93QdPLN+Tz444MAzLlyDu1iGh372o9n4zWAIr0XAYcXQSXjAd09HNmxk/p9BbQTBeTJ\noUTd0fKcTykEQSDhlZdpWL4c/YgRTYrZfLUuPCUNhF2ZCtZrMM+eQ9igQTx92/X0r7UytkBg7CNP\nM2bJF1y7cgkCYBg7FmV2NsrsLFRZWYR06YIk5MKKKgVBIOahhyi9+x5M77yDfedOPCfMaPo9Q9SD\nU9F0zgbAW22nbmEhFkGgIkJNTnwIyQ0eNFfksGXhMT5/YQcdrkyh4+BUEHyYzWuJjr4SiaTxsxMf\nP5zSsjk0RG4hvmuPC7LxXJhrN+B0FpOe9uYFj3X6Azx2tIyvqhpl6d5t0QytLAeaDbwktgUJEuTC\nOJsahwgs2F7K5zvLeD6YBx3kL8Df3nmu9/p4/KgBX0Cklz6UJNUvDo8oijSsLEYapkDbLR6A2WU1\nfFxuotDpBqCzTsNzGQkYPT7eKzVyyO5idqtUElTnT++od9Uzft14slx6nvpagnvTboSoCAruyOHd\n5J+o98+hZ++eTG79NDv35BNpsZDtP1MB4WeUSiXXXXcdc+bMoWh9EbfvCEGeFEGz96ZxW0gIV7e6\nnjn75zD/4Hzqd9YTY43htn/dhl6vhzvvBGDNmjUcPnyYgQMHkpmZeWrugBjgs8Of8dbut5BL5Dh9\nTm5dfitvX/Y2aQu/pvqVV6ibNw9Jh448t1tCq4Qw/tU15dT4tsnhvHBNax77uoBXVx7hiZOP4FxH\nalE11zXpHOcLiBy0O5lpqOJgp3TsMoFHWyVhbVnNC/kvUYOZN22TyCnuxLFv1pA+Lgfnvn2UjhqN\nALScNJGJ22Iwhxr4OOcET2yvJGD1MiXibUIVocweMJsMfQZDmw/lxW0vMmv/LMpSy5jYexSe/XVs\niznIxJWTiNPE8cEVH9AsrPGL2lteTv1nnxN29QgCPqj9uhCf0UGEyUMbeRbLYjcxovsdNCwppuaD\nfKLuao0s6uwLHXlcHJH33HPGdkd+DQAhbaMJafcYtg0bqHzyKVI//4wuIXIWVhzhsQYf715zC3ta\n5vKaw4SqqhJX4VEcn8xD9HqRhIQQ/9KLhA28MAcwpFs3Qjp2xDx7DpKwMOKnPIO3PgrHLhNh/Ro7\nYJrnHyIgEdhW76bP9VmonF4sy4rIahFB6pSubPqqkJ3Li1GoZSTnleLzWYmO/qWwVKPJQuVIoyF1\na5OW4dBYlLnBsIFNFZtQSVW0j2lPXmwemeGZSCXnLvwzlH2MQhFNTMzvf71+UWSxsZ43TlRx3Onm\nsbQ4Hk6JRfI7NdX/rgiCkAx8AsTS6LPMFEXxbUEQIoAvgFSgGLhRFMWgHEKQ/wo/p2jM3FjE6WJD\n/oDIE8E86CB/Af72zvPH5WYc/gByQeCN4irezPllRes6VIun1Er4tRkIcinzyk08eayccJmUFzIS\nuComnHjlL05y+7AQxh0qZcCuo8xqnUq3cO05z+sP+Jm4cSIZu6t4YLUcr5hPzKMT0I8YQY5azRCv\ngy+PfMnU3VN50xVCqCqUfkcLKb3zLqLuH4uqZUskCgXCzz9KJcqMDJKSkkjPS0fcLRIIRKC/5RYk\nISEAhCnCeDjvYdLr0tlbtJeDEQfZ6t5KupiOIAgUFBSwceNG8vLy6NKlyylbDVYDT295mp1VO+mZ\n2JMp3aZQbitn/Lrx3Lr8Vl7q+RL9Jk/GtnYdB6d9SE3r25hxWwekv0oduLFjMgfKLczcUESrhDAG\nJ+rxmV1oeyaeenS+0tTAngYHzkAAWnQlWvQxKS0eI/uYvGkykSGRTLt8OmkkU/HqdpRHpZxYtBD3\ncy8ii45GFhFB5cRJqICyey9nVfl6RhQNoFxdTWR2Eh/0fAGtovF9kUvkPNPtGVLCUnhz95tU6Ivp\n1SqCaVu20C40lXdyH0LvcoBQDaGx1Lw3DQSB6AfuoO7balw/mVGkhBFxeTNKIo/y/trPiAnPZsi9\n/TF/fBDjB/uIvKPVeTW6RVHEX+vCfdyCfXslipQwZBEqQEXs5CeomPAo5Q8/jGPPXvxmM6+1a8fy\n7HReymrFJ8nRTMk4KSvo9eI+doyqKc9S/vAjOO/YR8yjExBO5qufD0EQiH36Keo+/ZSo0aORx8Xh\nrXHg3G/Cus6A3+rBZ3JyQClDHRtC8/bR+MxOLMvAdbQWbdcEBtzTCnu9m4IfDaiSViGRqInQ/xJh\n9pxoIKy0O8acBdhsRzjudLG2dC0byjdQWFcIQKI2EW/Ay/fF3wOglWtpG9OW7vHduTnn5lN1AQB2\nexHm2g2kpT2MRHL+BatfFFlirGdqcRWFDjc5GhWf5qbTL/L8Our/EHzABFEU9wiCEArsFgRhNXAn\nsEYUxVcEQZgITAQe/3+0M8jfnImDW9C/VRzPLT1IvsHSZN/0DUVUNbh46+b2/0/WBQny2wii+Nsa\ns/8LOnbsKO7ateuSz+vyB+i07SdaadRkaVTMNtSwoUsOGSEqxICI8Z09jfm44zvwk9PNgJ1H+Dnu\n+1p2ErclRJ0x5xG7i7v3n6DE5WZKRiL3JEadVWJsxra38E+dyWUFIqq2uSS+/jqK5DP1o7/Y9QUH\nlx3EEevg2Vsep+7pF7CuWnXW16Pp3p3kmTMYt/4R4lYB0jDGjB5FSEwMRUVFFBYWcuzYMaxWK5nZ\nmWyP2c5aw1oGpQziXzH/YvHCxSQlJXHbbbchk8moddWyqngVb+5+E0EQeKzTY1ybce2p11Nlr2L8\nuvHsN+1nVO4oLlvtQ/LhDBY/8iYTR509CujxBRgxexv5ZRZmt0oivaCemruUrLRW8JY1lViPmbZR\nISQdLUSxZhWPvv4OC0q+4r1979Euuh1vXfYWkerG9JraZUdxbKpm+/FZtPNYSJk9G0Gl4thl/QjY\n7QghIRSNuJtcYxt29TMwrM91eA0GPCdO4DEY0PbsiTIjA4A1W/7DxCPzcEkEBtjsvGQyozzt1g/E\ndaZkXjEhQ0cSO/Fx/DYPAbsXeWxjfq9oKefmpTfQ4LawtN/7iNpOmOYeJGD1EHFLDqoW4fh8Nrwe\nCx6rGXedGcEiR1YSh7uoHr/FA4BEKyfixmxUWY15faIoYhgzFtu6dWh69iTyvnsJ6dQJQRB44KcS\nltdY2NGtBdGKXxxk0eOh+tXXqJs/H3VeHolvvok89uJbv9d+dRTHnmoQwZ8bxbINlVxxV0uyu8Qh\niiJVr+1CHhNC1J2NTUaK9tXw3fR8Wt00mYioDuS2ef/UXObPDmMrKuF493G4tT157KcdyAQZ7WPb\n0yepD72SepEW1ligV2mvZI9xD3ur97K3ah9l5nJSYpJ4pdcrZOgb37cjR6dQXv45PXpsQqk48/N4\nOsuM9fznROUpp3lCahxXRet+V7Q5deLyM7YVv3LV776GgiDsFkXx3J1k/qQIgrAYeO/kT19RFCsF\nQYgH1omimP1bY/9b39tB/lnsLqnjhulbOJvc/UvXtgmmcAT5r/BHv7P/1pHnhdV11Hh83N8ihhZa\nNQsqzfynqIqZOc2oX3ocb5WDiJuzsQQCjMg/jh+4KkSGWZDydGE53cK1ZIQ0lejK1qj4rmMWD/xU\nwpOF5WyotfJyVhKJp6VxbF0zj4wnZxBfD5GjRxN9/9izRgdFUcReYEeukLNetZ5x2+t45/V3iDY8\nRMBmQ/R6ET0eRI8H16FD1Lz1NkUvPM3OxPW8uSGEHwdcyZwvvsDpdBIIBFAqlTRv3pyMjAzatGnD\nUNdQZtfNpmJzBd94v0EVpsLZysn4DeM5VHuIKnsVUlFCp4TOPNf9OeK18U3si9PEMXfgXF7c9iLT\n82fyle1+3pVIubViB3B251khk3DrZXWc2PoW9cdupEQRxuhtL9AQOQZBHY2/+t/srfSSsTaR2lAP\nvZZcjk/0MSR9CFO6T0EpPU1j21aA1xNCeuIgvMOikUVHU/PuewRsNhLenIrl293kGtvgtuTT+o2l\nHHnkRTgt7aVG/Q4JL79ImGQLl295h3kJrdnf/gaGpwxE4raC2wIuC9QWIf7wGmn93QSS88F0DGlU\nRmNOs90Em95E2DGL0So542IiGLPmfv5z/TJixrbF+PFe9h28C0fVwbNej/i6UcQ2G4qyuQ5lejiy\naHWTxZYgCCS+ORVvVRXKtKaqDw+lxLKwuo4ZZTU82fyXboCCQkHck5NRt2tH5VNPceK660icOhVN\nl85nteF82HrFM1bSwPUBBZpCK2FRKjI7xpyyT5Wtx7GrGtEbQJBLSM2NIiq9Cr9oIirqilPz+K0e\nnAdM6LpmoNP3pKxmA+2juzDtig8IVZzZjCRBm0CMIpZmJe1otqMEW52bQ802cnPdLTzUaRw3NB9I\nZeU3xMZedV7HeW+Dg5EHi8nWqJjZKpUhJ51mvzeAKOWSyOX93RAEIRVoD2wHYkVRrDy5q4rGtI4g\nQf7rdEjR88I1bZj87X5+Hcv7YmcpdQ4PXdMjg4WEQf5U/G2d54Ao8kGZkTZaNT31WgRBYFRyNFOL\nq1m/q56Mw1a0fZJQ5kYxsuAE1R4f4VIJ8WuWkqBSc6hjP8b+VMKyvEwUvyoQDJNJ+ahNGjPKanj1\nRBW9dhxmYloc9yRFU/rxdLSvvoMQKiP+ww/Qd+t5Tvvu3JpPpVzHywNyaR/RnmfWPcHb74zgTlU/\n4u4dhUT5iyOp7dMHf109tR9/zD0tBcLrLAzu2o3d5Qbat29PZmYmSUlJ+Coq2ffuu3y1azfHqioJ\nBAIkxyWzWdjMUcVR/If8pIal0j6mPd39eeStSUTXrBlhmrMXoCmlSqZ0m0JZSTvWepTkt0ym09LF\n+P89Hqn2zLSVgpoCXtjxNKnaFHKdWXytKCXBN546ZWuu/SmfsYfbc+joXkojZCQN7UNqmprk0GSu\ny7zulFMpiiK1H36I8bXXCbniTqK13dm7ZC0pmVmY58xp7JqX0RVJZCiSEAeSE5uR57QgbNAglOnp\nKNLSkIaGUj35YWRLbocYD2KHu8gZ+Ao58jP1ip3791P6zWySbmuBpngdTOsMebeDJgq2fQBeB+Te\nzGV9H+eZowt5+dBcblgynNevnI2y7zc4qg8SWTsEpTwehSocuSYcRWgk5a65VGV/SELe5Wh1587f\nk6jVTRxnt8dETc0qXHVbGRxxLx+WmxiTHEOkounHVTfkKlTZWRjGPUTp3XeTPH062l49sfv8fFZV\ny4cGE5kaJW/nNCNcfvaP+gmHmxtOlGKIkHEAkbu3O7j+miwkp7UMV+VEYN9aifuEBVWWHolEoFnH\no9gDEgLWjnByzWXfVQ1+EU2XeHYWysiUBhifeeVZHWev28+BDeXsW12Ko8FDfIaOhKxw2N6LVGsr\npjun4ayYQXOpi9SUsee8dj+z3FiHFHiqQkagwMCi2mM0mF04LB5Sc6O4amxuk+NFv/+8DVb+zgiC\noAUWAg+Lothw+oJOFEVREISzPpIUBOE+4D6AZs2CEcEgl4afG6o8uWg/h6qsp7b/VNlAgcGCIMB9\nvdKDedBB/jT8rZxn0eejftEiQq+4gjV+Ccccbj5omXLKKbtbrmGOV+QdjZ/5N2UT0j6G105U8mNd\n44f1joANt8eNWiqh37ECFqW15rUTVUw+Ler3MxJRZEzdWq5q3ZuJBgdPH6vg8wOFPLRgCc7mMrq9\n/xn65NbntPWVQgOr3EBScxqsDeR9tYlPVkuROI5g4Qg+awPNJj3ZZEz4+HFs3PQpPX7yokhLo8Wg\ngZyeEVa0fDkrv/ue6qhIVGWldOnZk7y8PKKjo7nNdRslDSVkhmeiVWgb01be34c3YMO6qhTR5kM3\n5MyGFqIo8uYPhawtUNIlK8BCXRkdD/ip/eZrom+/s8mxRoeRB9Y8gF/0E1kVgkyU0KpLR94rqcYn\nk9MrJoGWI9/j8F0jkPlcXBfdjfAOfZvM4Tp8mOpX/oNj27ZG3eqXHqb8rV1k1rRn08SJJAcC6O94\nEPP8Q4hhAge0h6jJiOe6iVNQh56W11q8iaR2BxBtAcq3hiPWQcLlASS/egDgNRoxvvY6QmgkqvsX\nAHZY/yrsngsBH7S8Gi6bDNGNT7Cv7zKBVpZqxpcuYeamEVyvd5OSMpaMfhPOeI8jvZ3Yues6CgpG\n06njt6jVZ5dCBHC7qzHWrMRo/J76+p1AAEGQ0l9hYrn/cWYZapiYHn/GOGVmJqlffUXJrbdS8PyL\nrHn9HeZbXFh8fnK1an40W7ly11HmtE6ldWhIk7GHbE5uyj+OTxT5pE0ao/cWsbRHKI93aRp0VKXr\nQCbBdbj2VLoJ6m24SnM4cNxCUhaIARH79kqU6TqKZGXMPL6Vl5KUSG07gNuazFew1sDO5Sdw2bwk\n5egZMLIViSfnTW8bzdr5h7mn/F80y3yJTbYQNA01dNU057dYXFZLSpWXwk1laPVKQiPVpLSKxFbn\nomS/CUeDh5AwBX6LBePrr2NZuoz4559HN3TIb877d0QQBDmNjvMCURR/7qdeLQhC/GlpG8azjRVF\ncSYwExrTNv4nBgf5R9AhRc93D/fm0+2lfHegErVcyuqfqhEBUQzqQQf5c/G3cp6tq1dT9dTTWL/7\nnmn3P06SSs7Q6MYucs4DJtxfHuGuNCVvpcrITwvBZrLwRnE1MgF66LTI1vxAUvPm9OvXj48++ogO\n+pjGRMCIUHroT4ueiSJ8/zjsmEmzNjcw/9qZLJj3OS/pEnjq/kfpIRq5KanVOe1cabLwTrmZjOoy\nakPCeN5k5IO1a9EPHMzRvGgOfj2bvp8s4FDnFrS4fPipcavLf2RJnp9Wx8FbXY23vBx5YiJWi4UV\n77/PIZcLRbiOXqKU2IVfkXnHHShPStGFK/Xoo/WnFhLO/Bq8Bhv6G7LwVtqxbSrH7/CiH55J7Ucf\n4iooQJ7enNnyDGYZBG7KS+Dl69ux8JiLwlVPY5n1DiF9+iDz+lGkp+MVfdz1/V3Uueu4aaeSG+xt\nccc4mWV9jIj48dTUOZmyXyApt5YKhYREr5SqRyag/Ggu6txcfDU1GN9+G8vCb5CGhRH75JPob7kZ\nd2EhgnE9WkUvfOpsJCN7Yvy6GJ/bzarCj/ErfHhcLvasWEyPm046aUXrCMwfjjssHu/IFahSfsL4\n2msUl5YSP+UZ3CdO4Ni5E8euXXhLSgGIfepJpFoNoIGrXoeeD4PXBVEZZ7x/LS5/kTkLNnIw3Mgh\np4TlpQaeTbaeEWGVy8NpmzuLXbuHU7D/PjrkfYlM1lQr3Oks59jxVzAaG3WGNZpM0lLvJyZmED6f\nlT17b6WX4gSzDRJGJ0efNYJsUSp588mXWGRx4jfZGBylY0xKLB11GnZb7Iw8WMyQPYW8mp3M8Mhw\nqksaKFKI3FtiQCmRsKh9BqEVTq7cYWdRdy3TymsYf1qnR0EuRdVch+tILdAcu70Ih/M4Ydr7ObCu\nBkuNE4XZib/eTdigVB7d/n/svXd4VNXav3/v6ZlJ770HQkgChBpq6EW6UkSKAiIINhREURRERUQR\nQaWLFEW6gIAU6R1CTQLpvU/qTGYmU/bvjyCIoOe85/29p3xP7uuaa2CvvdasPXvNzmc/+ymz0Cic\n8PPpQnnJbszmSuTyBnF8+ecsLu3Lwj/ShfaDQ/H+QwrDsDhPPILsOX/uI6xGR8QbzzKr8k3WDVpD\nE5cmj/093SypIQ8ro80yXliegOR3N4DaAh1bP7hExrVSgozJFC/8AGtFJYrAQApnz8ZaXY3r2P+e\n6oJCwwVgHZAiiuLnv2vaC0wAFt17/+lfML1GGmFM+0DGtA/kak4lR1NKHnLlaBTQjfy78P+UeK7a\nsRNBoeBSURmXaupYGOGHVICaoznUHM2FIAd69g1mQ0YeLybloLdacZRKMIkiE4U6zut0tB88GD8/\nP0aMGIHhx23ktu/NlNtp9BF3szB+DhqZGo7Mg0urwSkQ8fZuypJ8aPP9DqZ29qckqAsKq435Tmd5\nr3unR4IJ0+uMTE/Kxr22kokHdmKMbc2C1l1I2b2fYX4e+AIubePRjp6Ebe673PUwMzR2NABb72zl\nibtqJPZgQ+DkrDUUNe1IrvkCFomFGJtInxdeoWZNKqZYgYotW/B57z0A5qcXsq+siiVNA0hw0FB9\nKAu5nz3qVp4Q1xDIVnMoG1N6LtU/rEDq4cr6Ajlbm0TQL/sC43/aRcYKd2KNRqw1IGAgt+8AADQD\n+vFqtxxya3MZluHGk0dLUPePwlKYzLC7MOsVF8ZcO8o159Z89d1PtDUZiXvldazvzidn/ARUzZph\nvH0b0WbDvkcPXEYMRcg4Qv7UX9GdPodEo0HVrxmRrp3QZ1Ujl9tItb9J9+lTCW/TnkNfLSXx4D5a\nDxyGqjod2w9PkyEVeNZRpObXyXg5eNF7agz9N9whe1TDdylxckLdujUuo0ajbtcOu+g/3Ow4/XmZ\ndpOlkoxgC2qdDUetH79qj1N7Yiare69+TCnzMKKbL+f6jYkkJc8k1mkCgls4VjsHcnJWk5O7ChAI\nDpqGt/dQNJqHxXpoyEz6Zy7ntPA5a/LLmBXysPW5xGRm5I0MsuosjMZIv3lziRk8EK/ZswBo7aTh\ncJsmTE3K4eWUXLaXZhOUpGNbZwfU9TYm3rKQfv0u1WUG2upFbO5OfJ5dTE83R1r8zlKtinSl6qcM\nzOUGyvVHAGjeZjhJP2dx89dcmlYakdjLOam+TGJpIu/Fv0eIbwxlxTtIz1hCs8gPuXoom0v7sojs\n4E2P8c3+1A9ZX38ImSYNO/MsPAub0EPnwAzVS2weuAlP9aOBkWtOZ4MbTO0R+pBwBnD11eDsriB5\n6xlkx+ejjGpGwMqVKMPDKZj5OiULF2KtrAT+a6oMdqLhUcAtQRCu39v2Ng2ieZsgCJOAHGDkv2h+\njTQCNFiip3QJfSgfNDQI6GMpJRx5PeFfM7FGGuE/ONuG9loJ1twKPIc03IGaCwpI79Ub92nTeNkt\nkCtObpzzsceSqmS5voYTQSpyZCK/z6LsLpdRbrYwJ8Qb+6P7qaurY8aMGUju+TgnJiZZTCTLAAAg\nAElEQVSy9tdT7I7rgtxwkwS7LL4V7JCeXARtJiF2mE7xsz2oSleT0ac5R7388ZB4UG/nQH1tDa5D\nRjIr9oG1TGexMuDyHfJqdIw+/wszfL3xmjyZvldTqbZYOdOuGap7vqZFZ3+lcvJ0jrYUqHhpJEPD\nhzJj+1hWfS2iGv08ifUtKNSK1CnAyVBF9/ZGIp97mpqjudQea7CmGm//QMj3i7Da2xNzNgmd1YpV\nhOVlMuITK3Gb3Jz8yrsEx7ZCrlRR8eN59In1YK1gZ7emfHE2i1FNnXjLuxZzRibmwkIkGg0StR2l\n331Lsbs9fi2mY0PKDddilGIdsSfvoPMPwMOrH6ZY+Lg4maNRLfhu3ovcaOVHnVaJRjDRK70ADIa/\nPMdSlYDLs8/h+twUbCY5xUuvgAiapwJxbRN8f7/S7Ew2vfkynQYNoH3R52jNOqYEhPBywsdkVWeR\nWpnK3cq71GVmEJln4+UxXxLSqhvC/6DYzW/YbPUkXnuG2toU2qqewf7QIra0f4ZFpadZmrCUXkG9\nHtsvL28DqWkfEJRrwAFX0sOdMNYX4+n5BBHhc1CpHnUNgobqetdvTOTdyk7clbblascYHGUNvrq5\nBhMjb2RQWm9hY0wInV0cKF6wgMrvf8D/qxU49Ox5f5yaahPT9t3mmF9D30CkzKtWIS0xUl1aR43W\nSMdhYfh19Kb7pbs4yCQcbtMUu3vr0aI1UPzpFZwGhXJH+QqiaKZd25848m0Swu1yIuUS1EMDeSr3\nOTzVnmwZsAWpREpa+sfk5q7FwbqMyzvVRLT1otdzUY+I3N+wWGo5f6E3KpUfbVpv5+6FEo59l0KK\nzzlK426yod8G1PIHoj43ScvQlCw0zkpO94p5ZLyagwc5881psnx6MKRVPn6TxyLIGmwGosVC0bvz\nqN69m/5DlzzS978h28b/hsZsG438M1h0IOURAQ3QNcKdjZPaP6ZHI438bf5rs20UHdiBU200vzjL\n6NM1nKo9ewDQDhzMiZxKxp09Qfppf+bGh5DsraS7qz1DHNQ01agIVyuZdDubHGM9EWolQ2UWNuTn\n069fv/vCGSC6RTTC5XV0yHDjfHgrDtOKpmYtA+JX0y22F02Xr0CarkaItbA70BF/nRMjnxmJq5sb\ny75ZSfbhn/nG3p5pob6Iosgr19NIqzPxRMoVnggMQN7zSaoK9cwL9WXUzUzW5pcxI6jB39SnUw+E\nZ5+l97cb+OjQdiZF7GPoTSmFXu25qmvF5VAlVztLMUslTDsq4VquioAKI/rLxSgjnLHp9Ii2EWg3\n/8ztUU9QbbGyunkwycXVxB7N5aKPAtmNo6Rv20hEu470HTGW8qUzkYd0QBI8nA5ny3gp2pfXxrR8\nrNCxWdU45nljVNiRrE4jtiYQJ9wQWnfht7Ihz3o5kuveit6pSWiaBtP1bCq/RgWhqbFi6TuAoK4d\nkfk0lNhWBgdjrarCmn4J67YZ2NxjsJcnIZFtB8l4pJ5OODzZBIWdDHXzhzMveAaHEtqiBVcP7qN5\nMxMTvZyZFD+HhIAEEgIS7u9XbihnwK4BKHQHWSzp/g+tu9S0D6muTiS6+TLsPZ+AjERGXd3JjmZt\nWHJlCZ39OqOSPRqU6O83Ht21FeQEAhiwrzUTF7cGF68ef/l5giChedQSRlx8kTctbVmTW8jroQGk\n1xkZeT0DvdXG9hZhtL5XOt5zzhwMN25S+NbbhOzaicLfn9oKI3u/uEbXKhN9ng3josrG/HDfh9Lf\n/Z4vmgUw+kYmH2UW8kFEgwVe5maHzMOOqoxb1PhfIzTkNQBio90x3dFi9FSzTbqTMkMZX3T/4n7R\nk9CQV8jP3U+5/mPC4lbQ69lmfyqcAbKyv6K+vowWsasRBAmR8T5oC3RwtCNlKfnMVs9mWfdlSCVS\nzPVW9u5KpbCzHW8GeTwyVn1uLoVz3iIgKp4sQUJlZC/8ZQ8ueYJMhs9HHyJ1dobGciCNNPJvyW8u\nGn8U0GfSyhmy4gyj2gY2prNr5J/Of6x4doj3QjhsQXLoLOPTypm7Yxea+A6sMEtQCAL+Hh0Y206B\nBCtrm4fSy8WR63lVnL9ZxveZWkoNBmjuTLTWSmLBZeRyOS3DvGHP9IYUZh7N+NSYySnlJabLmxN2\n/hD5HjIuejvys2Nrtt3Jg4QhuHXsg2jW4lQnwezmyK8qJzzNAsFPDKHk12PsPXUak6Qr1blF/GyV\n0DEjmYhKE7fSo7hxqcFqo1BJie3uxOcZRXQ3ymga6owgCLhMe4mqs5d59UQ1H7prqHcaxYKJYaT7\nNogedXkdRmc7Tvb3wGNXOac/TyTGasN+aDjKYEcK5v2CKd2JX7PKsJdK6OPmSJczZehEgc0hIm22\nb0Ph4ETapXNczi8leewLFEfE4nK8lA+lGkbd0WO4UoK6rddD7gimnBqstdEgVHK6/AsOtdXz/pZS\n9GoHvp+7lNJ6Jc+HelFQV45JoqBnWCBtZuzixKaViPv3syJmOHUaGaui7ekW+CDkUepgD4fGQ4QT\nzNgJxbcQt4ykbnVfFrp/ws5UGwGudmzwaUeA6++C34zVdJCe4XuLAx+YgnELCGdw2OBH1oy7nTtj\nm41lza01TIqZRFPXv0xj+xCiKJKVvYKCgs0EBj6Pl9e9QLPBK5B9E88crZbJSj3fJX3HCy1eeKS/\nkH6UptfSkHTvg8YhEt993yAp+hTGxYP88VUKf0OhcGdw9Ey2XrvCytwYOrk4MykpBwHY3SqcKHs7\nbKINiSBBolDg98VSsoY/ScGrr+G4dA37v06i3mhl8Cut8AlzYsLfONYEV0cm+rmzJr+cPm5OdHFt\n8OVWNLUn3TIbmcwZX9+R2EwWbCdyMUslnC3RsTlpC0MjhhLr8SCzRcqZCnJOjSKg6zKCYk4ikf55\n0QO9PpO8vA34+IzA0fHBGPHDw6ko0tM1ZQQ/2S3nE/tPeKvdW1w5kM1VlQ2AAV7OD40liiJF772H\nIJcT+cX73FqZTUZiKTEJD7vjCIKA5+xZ8NaBv/GtNNJII/8q5gxoxrGUEtLK9Pe32YAb+dXcyL8F\n0CigG/mn8h8rnj0690d3YTXNamJxTzyLWFTI9iefZ2uhFl+9jY+aqGhaXcv7i9/mfJtBvO4Yg8li\nQyJAc18nXpAVI6xfxlHPXni6VNDaX4VqTWewmcHRj0O5v7LV040JNTVMrpjH8fo4Lpg7EFFSTZ7s\nJ4acknK770ASWzUhTyenWiPnjMyRw+mFDybZqisA17JKAAkRRVpiCtLxV3clOMYfz2BHbFaRwvQq\n+t+pZnEbBW+eTKP/0rr7Q9j8XiQpXsHdIDvOxUhxttjoqdNivp3JxRo/ZAFmbkU5M3pSOD6bMzBK\nBExudtip5dh3UKC7INDtSDE1A/2QlhnQXy7GoaMvU0oPk2Q2sTu+gshcd6Ky0lFGxmLO0pMstTGq\nvR0/5klgVxqmrGqch4UjUUgx3KmgYksKUkcFmXnfE5uYRXx5OIJUy6XgEFa7avgowo/W/h747kkj\n08GJTxw8iTeYyEtKwSs0nDF9mrLiFx1Tdm5mQMvdvNnuTbw13nB5HRRdhyfXkVwhsOOWKzm2OSyr\n+ZCpta/g1OJrfkipZ9jXZ1k3oS0t/J2gMgv2voyP6TZy7y44Ztvz/EtvPrZwDcCz0c+y9e5Wll9b\nzoqeK/6utSaKNtLSPyIv71u8vYcRFvrGg0YHLxi8nPZbx9C7WXvW3V7HkPAhDcfzG1YLHHkXiUsY\nTTtuAZkC5C1hxyTY/iyM2gzSv64S6OLSgem+KUwuUjLsejoeUjNf+aVjX3GZHcmXOJZ3mlybK+72\nIQQ4BNDyhQT8V93iyIIzSBRy+va1w8vn76tECPBOmC+nKmuZeTePCx2aIRUESry2YqrNIdLhUywS\nDdnfX0BdYWNvYCKKG7G0Lu7DoKBxnNmRRmWhnooiPbpKE8Ex3fD0yCQ3dyU+3gMf8esGsNls3E39\nAIlESVjYGw+1SSQCfSY1Z8cnVxmcMY0tyg9xM/hiOxxE/kBXQu0UNFErH+pTvecn6s5fwPu9eci9\nvAiP03P5QDb6ijo0CR2gZ0+YNw9cXP50rTTSSCP/Phx5PYHx6y5yLkOL5Q8VVVafyqCpt0NjLuhG\n/mn8x/o8v3lgCspbmUypfBcFx9hcUs6nY59HClgkAg6ZtVjSqlh0djVNqvL4dcpc/Jr44q60Yqit\nJnPfNizVlZg8/al388aDcuQKFXL3MKSOGn4u/xkHZwWfhvXiyI+HyCuqxapQUR8QjkWhwqGsiCbt\nW3A+Ow+kNt42f4vm6U3cMrbizKk8Cor1GGQilS7ZmORWHCr1uNkq8YtwZ/rTj89b+0ZSDj+UVrLc\nYI8fUs7ILfwgNZAv2AgoKWfM+RN0HDuUvfsPcFBog6+bA819HdksNeHsqmL74WqKTSK5Uin9pkTj\nFajh8Euf0NypK5XRLnibROrzdSif8Wbju69gifHke9/LqIw2Ot/wwrNKxd7wCPrFjyPJz4mLlbUc\nNTigOFWIzEONOs6TmsPZyH3ssY505421g3h3kwkEAaePP6aXxBkvg54jT/YhubCEPhllPFuUxd7A\ncPxL8+n741d0f3YKrfoNYty6i1zKLsM+bCn2dhbWxS8kYssY6rzieFn6LkfvlCKXCvSM9GJiUClt\nzzyPoHGnpNXL/HrqBCHmdForcpGbG9IMZvaYw/NXdzLggjfdn51CXP9HLc+/sfbWWpYlLmNT/020\n9Gz5l+vMZrNw587bFBXvxN9/Ak0i3kEQHuMrvf81Cq5/x5CgYHoE9WJx18UP2q6sh/2vNYjkZoMe\nbL+8Fn5+HWJHwdCV8Dd8sEXRyoizu8mot+NNPsCDsofaraKEHIMn6ZmtsMtpi4c+AKlZS5vrX6HR\nl4BMhio6Gln7dvi+9BJS2V/fO2+8sIvZhlCeVt8g1HKBKNNhHPITyNC25LzsGrMLnmOL+wEuhN8h\n4dwkZDUNTwOkcgku3mpcfTR4BDoQ080fq1jB+Qt90WjCUTVZz5lKPXnGevKM9eQajOQa6pDZ9Cy0\nXaafNRZEG9hsIJGg6dwFqb2GymI9Oz65Qq2ykkprOWqrD8sH+fK8vzvzIx5U77RotWQOeAJFaChB\nWzYjSCRoC3VsXXCJ7v09iBrRGqTShtdbb8FrrxG84Pgjx9/o8/zXNPo8N/Kv4GpOJaNWncNie3i7\nRIBQdw0TO4c2WqEb+Zv8b6/Z/7HiOXV0J8rTK3DsO4ktoR34NrShYIeHwUa0TqSXryutAp3xMWrZ\numol1Q4PCnqoaquR56ch1Wio9glDZqvHqNSgxZkITzXllbnIzQ+sdJJ6Ix4enijkMgyZGdQgUO9w\nL8WWKOJcnkukkIXatRW3tYNxdFXhY87E7tR2RFkZv3TvhkSixCizcMz/F77u9zVtvds+ckzl9Rbi\nLyQTplZRa7GSYTARpVExM9CDlksXI23dmm/T00mWhXOmQsPOafFoZDb6bEjEHO/BsAILC9qHs39d\nEvrqesLiPDmkKcK92o5ncxvOs9PAUI6cXk3B3RS2x2fRPKOONyT9uDK6FSnLtiKzWDnatZIn205m\npa4D3koZe5w8qf0xFZvejDLcGbdxzZh76V2OZB/mx7u9cIvrwCfRbfkuv4yvF82l67gxfKhxY5u9\nO5fD3NB6+bB6wTt4luQxZtkaQpydyNHq6bP0FO1CNZQ4LmRWVhoJdbX0MX5CucKfF7qF8kz7IFw0\n9yo35l+BTcPAVIMoVZImBHHZFEBoTCfadO3LUxfmYrKamHAzhprSUiZ9uRbZY6o6AtSZ6+i/qz9h\nzmGs67PuTy2PVquJpORXKSs7TEjIK4QEv/TnVsr6OlidwAqJjlUaKd/1+444rzgw1cKXrcAtAp47\nAH/sf/JTOL4QmvRvyPBhNYGl/sF7va5hjHsvs7EWUTRQKxGY6+HKNTsV4yv1tK2Ko8wPFAFJSGRm\n6kuCEfI17HbTcdVaSv/aEAZkeSC7eBP7Gj23wvyhfVt8m0TiExGJT0RT1I4P0sbVZJ1i1K8zuB68\nEnvDFZYol2NEjvON1wmqCUApKrC6S/GYEouTnRNVpXVUFtfh6qPGwc3usX7NhUU7OJHyOW9JVmAS\nJdhLBbwltTiZ7uIuFHPb2IIyqSfvrV1Gx1uJ9/vZtWxJ4IZvkahU5CZp2b/iBqIIRzqnc8GvHSGV\ny5nWtBtPNXkKtVxNwazZ1Bw6ROjuXffLswP8sOAiboZi+ix/BvT3Hv+q1aBQ8Ha7MWyL7YNF+uCG\nolE8/zWN4rmRfxVXcypZeTKDW/lVFNeYHmmf2rWxoEojf81/bcCg/+wvqJ40lVeaNiEpwJ5BRWlE\na/0Z3ykUl7iGoLuKigo27tqPwcWZns7OuBqN2FVVcqYwDa3NRnhBFVcCFUjzsrncKocSOwdOWmxI\n/Yv5rO2n5O88Q1FxMR5RLahHoKKqCqPaAes9i51gs2FnqiVK6UBZblMyLANQGnJpfmk1Kn0V5oEJ\nvBCawWB/NfXXRU6Hx+Eiv8Erx19hc//NhDqHPnRM7goZrwR5sTCziCiNinXRwfR3bygzbPv4YzZu\n3EiNTcHFanuGt/KldfoKuLKekU6fYcpxYnuwkoleCsbM78D1I7lcO5pHaL2UUscSbBIBpU8w5apC\nsq5fRelkpVJlZJhDF0Jmf0R5gY5FLiLPlO2mb6KK9ZIveTpOw4qqZixxMTDv5VYY7lSgae1FcnUK\n+zP3MzlmMmHjXuF6TR0brqYy0d+DuEA/8pcvZ+/7n5OQn4l3n7aQkUZgzl0udujDxcxSdrV0JMhN\nwyu9Ilh86C6vhQykt/5dPrM8SVSLUD4Y1AlXjeIPJ7wNvHQVdKUIHk3xtwp88v015iaWEm9MIsOW\nyde9viIowpEdH75D8sljxPZ6fAlxtVzNlNgpLLq0iAtFF4j3jX9kH4tFx81b06isPEdExDsEBjz3\n1wtSoYan1jFxbU/2aPxYdOljfnhiK9IzX4C+DJ7+8VHhDND1jYYKhpfWgFQGUiVIFVhkci7LZTjK\n1YTYuaJ2CcZgFki5fJVswcZXTUArhxGZznjpJ3C5pjXO+jrChCqcQ09T5n2eeq9sJleb6V/uxkdO\n+fwUl03boABeO2ikWWkVN2trufTTDkRbgwmn95SXiO3ZF5uujDlHX6RYLtCzPp2zdm1QCHb0bLcd\nHB2p2p2OoJTiNS4OmV1DcKSzpxpnT/Wjx/c7vL2GsyFNjsRqZKt3ImLhN9gEI6qbAh6FrbEb3ovJ\nViXzXpzFYlclTzkoMdy4SdHbb1M4+038vlhKYHM3uo9rRlleLdebh+BcUUWkBj698ilrb61lrdMM\nrPv24f7iiw8JZ4Dw1p5kr7+KKJVy/0zU1UFdHXOPr+flc1v5oMfzHIjshPi4pwuNNNLIvwWtg1xY\nM77NPSv0+UfcOFadyiTQTdNogW7k/4z/WMvzlNtZnE7PodregZeSi5hQaEYtOYJTCx1C3w8pMSnY\ntGkTVquVsWPH4unjyZ70PXx7cRUJB5TofOrw0HTBaKhDXpKOxUlJ+iBXrhRmYyhrySy9BO3dm/Sd\n+grRCb2oz8kha9hwlFHN8Fu7lprr1ymeOhWJ0US5a3NuRT+Pva6AlrdWUCsXcX1zJq/Lf0A06dhV\nWIZVV0F8132Eqi1UZb+FncyOzQM2427XkDlCFEXSqtLYl7afU8V5THHvg5/aB4lEgiAIFBYWcv78\neZJcO5NcbuH0GHtcfxwEoo1y5QS0uhEM7+mIp72Sw22aIpcIHMupYPO2FNpkGJFaTLQfGkLi3o+o\nLy/jl3aFiP5e7HnmMABPrTxPfmUdm/q6sH/JfEz2Anc9q3Do8BzbNS34sWU43VwdEEWRSYcnkV6Z\nzs/Df0Ytt6f/lVRK6s2cbt8MVVEhq9/7iIXjXmBDvZZ+fXuy59MPKEhJwnPeZ7yUVcacEG9eDfbG\nbLXx5JfHWF75IgqlgikhsRTb0lnWfRkd/Tr+5fmvt9ZzR5vKwv1pXEpV0LlNIpufehdRFPnhnTfQ\nV1cx8YtVf+qaUG+tZ+Dugbip3Piuz0p0uiR0ujvodCnU6u6g16cDVppFLsLHZ/jfvzDPf8XBMwuZ\n7enOvJYvM2LfOxA5EJ5a93d1N1qM7Enfw4akDRToCu5v97LzQllkwNmgJNO/DgkC01RP4VIgIedO\nJFZzCfW1OwBQajR4h4fh3kyPVX0AicSKW7qNDZ7dOKJLpEuZGy+tLcH95ZdwnjiR4sw0Tm/ZQE15\nKZOXrWbVj31ZSSVvR47HzimQqUVNWVD6GVN6vINVGULJims4DwxFHftohou/YnOhljfu5jHJtpoe\nwi+orgu43W1CwIR30HRsON86i5WJt7M4Vanj/TBfpgZ6ov12A6WffILrxIn381ebbDaiztxmmKcL\nSyIDuF56nen7J7NsPbg4eBLy0x4kiodvwCqK9JyZ/BVPnFyIVF/7yPwA9HIVxQ5uzOs9jS1b5/7d\nx9ZoeW6kkX8N31/M5Z09t/iDfkYAekd58UK3sEZf6EYe4f/c8iwIwnpgIFAqimL0vW2uwI9AMJAN\njBRFsfJe21vAJMAKvCyK4i//6OT+itIaEwYHJxZ/+SGtDWpscc8jlVcipJ0gP+M2m8VhyFVqxk4Y\ny2XdZVbvWU1ebR59MjyQ2gSGe4xjjymX9oInquxzJPq6Mkr3BIUaMzU5leSlauk5firRCb0Q6+sp\neP0NkMvx+/RTxJIStDNfR+nhSekTk7h5xxWJwsiArik4N8nn27IBXMjfQp57AWuKSshUdea63Ifx\nefv5LGA4S9t9yudnp/PSkam833o2x8sTOZR1iIzqDAQEJDYJ88vO0qWoCw6WB1XrBN/mXM40MbdP\nCK5HJ4CDL/SYi/XHOqASnyIFt31F1uSX8WKgJ4eMek62d2B+J0fOfnGSUzvuYDFUEuSkIMNH5O02\nExEEgaPJJVzNqeSjYTE0aR3I4Jlvc+nnXcjvJCOk72C6/SE2n4/BuW9vSpTFXC66zNsd3kYu1fB1\nbik3dQZWNQ/CUSZF9Pdnx+jxBFZq6f1EZ0qyMsi4cpGOI5+hQ5Avx/RmvknP5AndLSIqb7LD/jCK\n6lIYs48N3s154cgLzPh1Bku6LaG1V2vKDeVoDVq0Ri1ag5aM6gySypNIq0rDYrMgCjKk8rcwVyT8\ntl5pP3wUexYv4Pbxw7ToPeCx60chVTCtxTS+ufwOp8/Gg9jw6E+h8MDePhJX1054uPfC2fl/+Ntq\nP41+aUfZakhm+fUVxEsE/HvO+5vdakw1bEvdxqbkTVQYK4j1iGVm65lIBAmp5Xc5cWYXpVITJX5G\nghyD+aL7FwQ4BHD1UDbZKZk8OWcIckUCxempFKenUpSRSuK2bFwDO9CkZy5lTfOZUH2O0W3mMjdl\nC5eaSWmzaiXOTz5JQFQMnUaPY8fCd9j7/RhWSSsY7RJOQlATklLewkv4hl+VPZjy41gkk4/h1EvA\nnHWOils6bPo6bHo9Nr0eqZMT6rZtsGvRAondwxlEcrKyeT+jnFa5WTz1468o3QPwH/smDq/2fSjf\ntr1MyqbYUKYn5/B+RiEVZgtzJozHnJdHxfr1yP39cB0zhjOVOvRWG/08GlxNWnq25NVELzTlmXh8\nPu8R4Qzg6qPBTVOPzWJD+ifnQWM2ElZRwOpdH0CHfbBiBbT5r9LEjTTyH8WY9oE09Xbgk4MpXMp+\nkHNSBA4nl3A0pYTtUzs2CuhG/n/lb1qeBUHoCuiAjb8Tz4uBClEUFwmCMAdwEUXxTUEQooAfgHaA\nL3AUaCKKovVPhgf+MQvG3g1J3LhVRkxBEk2vr0DVbyF2dgb0wUf5scgPO/SoQnPZpqyg3Kgl0iWS\n6RYNd3cWEOETT5LaiTqhjhGmzthubuSYcwlVCOzpUkiN3A592pu42qv5pHcQ4WsWYzx7Fv8Vy7GL\niyP76aexVdcg/WgtR3aXoXaRkic7i4uLivHaTzgiD+c9vyo6VtvRwjqEkhozAqCQGNnSdQSRTk68\n6JjKq6dnI957lB/nGUdTsSk1V2qIjY/l6/KvkUvkfN7hc/zV/tRbrIzdcgcBOBJ7HOm5L2DsTurt\nOlC6/BpOstVMsUVjGjaMa3VGvo0O5sXkHLq4OrCqeTB3xk7ggLkWqdwD7XOeHCr+hV9H/IqdTMOA\nZaept9o4/FpX5NIHQia9MIV5m6fjX6wGgxe1Di6E5dzBJhHROXtR5uhKpaMbdu06s75XZwRB4Eh5\nNeNuZfFFZACjfdzY+9lH5N6+weTFi1Fd+Rpr1mkoTUHKvWgPt3BoNRY6N+QNrjZVM/XIVG5rbz/2\nvDsoHIhyi6K5W/OGl3tz9lyu49NfUjnwcheifB0RRZHtH8yl4E4yw+e8T1Ds44MC6y0Gdhxvg4Ng\npkPL1Tg5RqNQuD9237+isqgAUQRXX7+GDbUlZKzuxHgXBRqFPeuG7CTA4UFAW73RQllOLSXZNRRn\nVZOdVkKNtYod0UtoE9SKSTGTaOPVBkEQsFos7P5kPrm3bzB8zvsExrZEQEAQBOoNFja+cw7vECcG\nzmjxyLwsZjNSqRQEyEv+mIyi9UitIt6e49ideZHuezOpaupBxDPPIdqMJJ//lgqXarzkIrJ7y0Cl\n9OWE53d8lV/NtQsjkOQGUX688OEPkkqRaDTYdLqGID+5HLuYGNRt2iD396P64EFea9mZxMhoth7e\nSXT/Pth364bwJz7pAFZR5K3UfDYWaklwcWB+mDfq2bPQnTyJ/1crWOAbzq6SSm7FhWI+foLqfXvR\nnT7D0RbQ4tNv6BbQ7bHj5sxYiO/Khcitj/pJPoIggEoFCQmwdCk0/fPUho2W50Ya+dfzZ1ZoD3sF\nK8e1aRTQjdznnxIwKAhCMLD/d+L5LpAgimKRIAg+wAlRFJveszojiuLH9/b7BXhfFMXzfzX+P3IR\nzrhzlhurlmG264XL9UPYqbwJafI0p4p3UKIpZ1dcOlWyOjqaYULb14kvyyH1wJnwIEoAACAASURB\nVEaOFbclpFUMFX4n8XPKJejmJER9HC97LKDzRXuKNRqOdUoh1DadpDs+WCQyYoy1TPNwpkOLMHT7\nf8ZSUYUsoQeZaRZuSbXk9L6Cj50neRfzCLDIOOZ+mHJBQe+Cvni5eNG1WzcKjEquHthMWlAoR0Li\nSKzeyO3U7ymQKegh9cDWbyMbt+4gMjKSkSNHkl6VzuTDk5EIEtb2Xsuh6yKf/nKXHYOVtDkyAlqO\ngSFfUbkzjbrrpXi6z6GyIo/PYjex19OZSkvD/UpbRzXj/dwRdm0m5+QRFI5jueufhkcfK+/Fv8eu\nxHxmbrvBijGtGBj7oMqdKIrcrTOyJiuFHwsLscgb8uNG3F1Pc60cH5MSTZUWibYUuVzO8Lfm49sk\nkkGJaRTXmznfPoqq/Bw2zppBh65xdNJvAWM1hHQl1z2WOXU+RER0Yn5s9CPnVlevY0fqDqQSKW4q\nN9zs3O6/OyudHwnaq64z03HRMXpHefHF6IY8wka9jh/fn0N1aQkj532Ed1gEoihiEUF+L5gtO/tr\nMjI/Y325An/vwcxsPRMvTYO/fOLBfZRmpdP56QnYu7j+6TqsNlaxevpEJLp6Qlq2pvXAYQRGt0DI\nOknK+aU8LynHTq7m6/jV6FOkpF4qoTyvlt9+dhaHOrIVdwitaIFXlJoRMzrePz5RFDm86ktuHz9C\nn6kvE9O9z0OfffnnLC7ty2LEW23wDHL8m7+Ziowj3E2eRp3m8b95nQWK6yUEWtvgIO9CTZEnCmkY\nvoOb0ONGGrPSzzDgs69w6tQU93nLkNjbI9FoEJTKBqFfW4shMZG6K1eou3QZQ1ISWCyc6PME84eN\n5V1PB6Y3D/ub8/wNURRZV1DO4qwi9FYbz3o6M2LhOyjupDDy01W0LCngnSULEOvqkPn4YP/EAMZ5\n7CEuuCOLuy1+7JiGt+ejXLQAiWh7bPtjkUpBLocRI+Djj8HP75FdGsVzI438e/D9xVze3n3rsW1D\nW/re/xvRyH83/yrxXCWKovO9fwtApSiKzoIgrAAuiKK4+V7bOuCgKIo7HjPmFGAKQGBgYOucnJz/\n0cT37+qPyimVopt+lF50QBClDPJ7HqtQyc/527DEuTN84EAiDr8P1fmYpXDAvgUOIfWIjqXYLFJk\nRiv1UglBlxZRjpGlpel0rLhMsa8FpSgh+rYes0974n37oRLkiKINbFYEuQyzKCK1CWS6l/BJ6Hry\ndfkPzS9B2xW/OzqeeuFFdpQ6sfJkBj7KeqLIoqKFBztuvsytSi+KhWD6Op3njhDOYacxTH1xBkpl\nQ87aszlJzDw1FaPFSm3WZPqENmWl/nUwVsGLF9haXE/btXcRYtwJTbBgWdWdU7ZYmr7+MzMzCzhT\nqcPlXglyRBueVjMWmwSMEuycpNiplORq9cgEgRhvR9RSCSqJBJVE4LbOQFqdCQEIVxopLNqOSdMR\nicKbW13a4yRv8PipKS9l+wdz0VdW4v/qO7xYDYua+POsnzv7liwg+9plJoeew84/GoZ+A15RACxI\nL+TrvFI2xoTQx92J/y0f7E9mw7lsTs5KwN+lIXBNV6Hlh3mzMJtMPL1gMV/q4YeiCr6JCqKtsohL\nl4fg4dGb4/URbEjagFSQMqH5BJ7yGsjWWa9itVhQajR0GzeJ6ITej4j2a6XX+HjnHNqfkJPrbSBc\n70F9rQ6PoBBaPzGU8LadOH8xhSNHLuJTEY6ABM8gB4Ki3ZB5W1iS+wG3dTd4seWLtC3ux4XdmXQf\nF0lUp4aKlBd2buXc9i10ePJpOo185qHPNtWZ2Tj3PH5NnBkwLZa/wmyycuNYLomHc5GZy4iLPIij\n4Q6upgyyjzqSYy9h/lMSrIKEYdf8cSzzRuk0HhdvDdUldbj6aVjTxoqhpIQf9yzGL+YOwtObIPKv\ns1HY6uooysmjt7aeIJWS/a0jkP4DOZXL6y0szipic6EWR6lA73Mn2d6+K+/8sJYnvVxxHDQQdZs2\nCBIJCy8s5Kf0nzgx6gQauebRwWbObLAi/yNIJNClC5w48UhTo3hupJF/H17deo091wsf29YooBuB\nfwPxfO//laIouvxPxPPv+Ucuwgtnv0pYi5t4+uQgMQcTangG8+qrqGJHU1S3j9Mld+j6zAQiOwWT\ne2UmxbJCRMGGqcaTgsJgoremUO9hwPK8BdHgQJNLn7PRZsU+YwVmpRmDzEYHdQLNHDtSYS7nQsku\ndJYqRMDOPQBzrSehfqHEEYr3rLZU2+m5WXaTs1lnkZgkvN51JhvfmM5Nhyj2iZEMiPHmTmEVuVod\nP6vm4iSv4+fguYx9cgwXPh9Lt/qjXKgMISfqOYQIGztS47iUrUNQlOEcuhaFDOY7RhF/fTtOo7dy\nxqMjJ/YdYpDhEnN9hjKhXTM63/wOn3Pvc6bJbKYGDiHe2Z6FDiJLv1hCcUx7VO26cDr/DB7lISik\nKgxucjIq6mgZ5IJKJcNos2Gw2jDYbASoFDzh4cwAdyc8lXKWX1vOqru/ovV6j0n+7iyMeFCpTVdZ\nwY6F7/BNq17o/UO40qUF+jOb2PD1Ntq7F9J55Bjo/OpDhUBMNhsjTqTQ7KSW8DoDCaN8CGvVHIn0\nz7xR/5qCKgPdFh9nfHww8wZF3d9eUVjA1nmzEBVKlg54DquDM2armdXKedjbSunQ/hAKhRsFugKW\nXV3GweyD9LrlS0CxiuFz5nNx51byk28TGN2C3lNewtnLG4vNwpqba1h5cyXd7/oRlKNgX/9KvOy9\nmWP/HNcO7KWi2IrSfhgICuT2ItddT1Pgm8zy4Uso0hfxxsk3sNgsLOqyiG4B3RBtIj8tu05JVjVd\nRjhx8+gPFNxJJqprD/q9+Nojwv3ivkyu/JzNyLlt8Qhw+OPXAYDVaiPlTCGXfs7GUFNPSAt3OgwJ\nw9W3QVQaa+oo/eoz9N99z49PyHGM6k6MrSs3j37L4NffJaJde3KTtFyZ/y0pLvksH/0sx6K8aP7T\nmIZiNgO/gNYTyK+sY+a2G3g4KPlqTNxDc5iWlM3+smqOtG1CpObxlRStZhu3TxVQlldLXJ+g+/P7\nI0k6A++mFXCuSocMkVvtI3FRPzzmtdJrjD84no86f8SgsEGPDvLMM/D9948d/0+xtweZrEF4T5sG\n7o+69jSK50Ya+feiUUA38lf817ptbFm2g9vaFPy80mjS9AoKuZL6w/aEFz6N3CuacsezFAX8hNKv\nDGwCpnRXlBUjOV2vQ6ZNZH/zTNwFOe9e0qN7xoqkIIbQ269Re20V1UIBhV1GEq+LRYhyYeeeVfRI\nOcb+Ju255hVEXF0BUnMJaqmagQFTqfUyED61G0r1w6m6Vm89xEfXLHT0U7JpRi8sNhtnP3mSHubj\nvGB9jcSIHkxXVXH0VjaT7U+TYDjMt6FtCfTP4nppe1Se8xnSyg+rtIznD06gyKgFIMA+FDtjOC+5\nHseqrKbC5sZXlhGEOofR7txSfKxZfNZkIa+17EPF5+9hNhoZu2gZScY0Jh+ezLzgjyn9Qc01pQXP\nBB8+Ghbzd33nunodC7Or2FhQzuE2TYh2UEPRTcg5x7nyGoZr+tD9/AHm124nrVxOht6DyQvmoQ5v\n/9A4oiiSfKaQU9tSMYgigihikVhI9U4jzNuODuFhtG3ZEo2T85/M5PG89uN1fkkq5vycnjipHwj1\n/LS7bJn/FrWOrkxZuIRtaV/RSr+eRJf3eaXFMyh+F7B25upBLi7+ihth1eS1lBHt1pyIXHtsJ1LB\nBjGDB7FVPMaFuhsMDHmCwC35+Ec2Rz68FbNOzuL11q8zofkENr59HF2FAYvhIBZTNqZAe/ZGZyCT\nKai16ghxDOGL7l8Q7BR8/7NTL13n6LfFWM0VyGWHaT/sKVr06v/IDYVRb2bj3HMENnOl3wsx2Gwi\nWTfKqCqpo7bChK7CSG2FkVqtEbPJik+4E/HDwvEJe9TCL1qtZD01Amt1FWEHDiDKZKx/dQr2Lm6M\nXrAY3cmT5E+fQZ5Pc559aw7jXZ1ZFOUB2ydA+lHuNpnB8ORO6C0iolRgTv9IJEH23Kg1cKOmjgyD\niVnB3rwe4v3oZ4si6VdLubAng5pyI1K5BFEUaTsgmFZ9gpDKHk0XJ4oiv5TXYLDZGOb1qP+iKIr0\n39WfYMdgVvZe+Wh77z4IR488fgH9DhsCEo0a/P3h3XcbXDYeE4T4G43iuZFG/v34/mIuc3ff4nEq\nx89ZxfTuEY3p7P5L+VeJ508B7e8CBl1FUZwtCEJz4HseBAweAyL+LwIGDSlaCu6UsC7jNE6Wu4Q3\nP46LpgYhVY3EBawedUhNTkgzWmE9XIxD+DgOO6RTKyvHs18ACUE9iXaLJvfkx5Qd3Iiuvw2H1GH4\nlQxDopJhrjKy0+0AQxPzMSYmktShH8nDJqHMrcM+Scfx4B108fYlKtmFcJpyqOxbonv3plW/wSjU\njtwqqWXMmgu4m8qZJL3Ocx8vob4wBenqzqTXuTHGaQkVugfJTjzsBNY7f0hpdBFWgx1StRF1aXPa\n+3ZDUnKb+uzT3JRJ2O46imOSND5xLECw0/JTpZLOLrU4S0WO1Mj4pUaODQGZDUantkSeU8PIeR/h\nH9mcmSdmcqn4EjufOMAHCy7TrFag74wYwqP//pRjVWYLnS7eIcROwd4gCZJv4sFaz7iYT7jsGM2c\nn5ZSUW5CFKHtoGF0HTvpof66SiPHN90hN7kCKCTbr5iCuF60OlwJIvzQ1YFCNxlKk4EOadcZUJmP\nt6cXLj6+uPj44h8Vg5394y2tKUU19F92mll9mzK9+4Mcv6vySll//BQjD20isIUPbu1OoLXrzEuG\nGXRw0rAuOgQ3hex+oGF5bjZhs57heOlpkrXJZFdnY2eQ0CHJlcDShhskiVKOq5cf5bnZxPbqT6dR\nY5lz5V3OFZ7jS/8NXNtaCkBIS0eCo2q4c+4U1zIv8EvrYryqVPTNa4Krkwf2rm5oXFzR5ueSl3QT\ntUtLbPSgZS9/Oj3V5LHHeWFPBld/yWH0O+1w87O/b4UGUNnLcXBVYe+ixN5VRWCUK0HRbn9Zglp/\n8RK5EyYgKJVI3Vypl0oor6rEN6411guXUEZE4LBoBSOu5pHvIOFYaDAWk5Hin6bT0fYra4WhfBfz\nEmnO0vu5rL3lMlqqJbSX1jK5eWvkf0gZWJhWydkd6ZTm1OLmp6Hj8HDcAxw4sy2VtCuluPnZ02N8\n5N/ly/1Hvkz8knW313FsxLH7qSB/oya6BY5JN/+0r0kiQxQEzgfF0n3jMujY8fH5uf9Ao3hupJF/\nT67mVPLO7lukFD8+PeVHw2IaBfR/If/n4lkQhB+ABMAdKAHeA/YA24BAIIeGVHUV9/afC0wELMCr\noige/FuT+EcvwlnVWXxw/gPK0stoWRFDSNAtggKSkcjDyc3rTNuUYuxMQ5FLVByXJ5ElKWTqUz3w\njEm4P4Yoinw+bSodIo5hbCHid3MmjnWtKQhOxbL0YxwtCvwXfojToIHoqivYs+YbZH6ncPbIQi6x\nYrXJcc/twd07wRTmnkZAiqiJ4oBHJFZXfxa2MHNx/XKGznoXh4NTcKrPQ6uOwt5BoKXLx1jrbbQN\ndWdAmAdRJbMxVpwi/ko1qSEqSj0UxCbV4mJyR2sN51ThAL5uF8dkxxV4a87jpphFoV8AlmoDxswt\nuLncINvmT2qSP46FqaiyvbgSVUVkn94MCRvCc4eeY0yzMWSn9uTY7WJmC07IBIHR77ZDofr76+Vs\nLdLy6p08Pq/cy5i7a0ga/ys9U/XMDvHmJW9n9nz6AcWZ6Ty9YDkyhT31Rgsmg4XKojou7s3EZrUh\nk15HX3GWMQuX4B4QRHVZHXuWXaeuuh5LbyeOqfRckNvjUG+g2/XTNL12Bolow8HNg6fe+QBXX//H\nzm38+kskF9Zw5s3uqORSCoz1dLl0h47O9rxdk016/kvYuYh07nKcg7UKXruTi6dCzocRfoTlprLn\nk/n0eO4FWvV78Mhfb9aTok3hdvltSrIy6CCJwlJSRerFc9RVNaRG8g6LoOfbb/L0jrEMuzwbqVVG\n866+JJ0qZMCLsYTEumOorSHtygWqi4vQVWjRVVagq9Cir6xAplTSdtCTxPbux5ltWSSfLWTIq63w\nb/qwddWgq2fj3PMEx7jRd3I0pTk17PjkKuGtPek+NhK58h9ze6k59AuGmzexarWYteUUX7+GSgTn\nZlH4Lf8SmYsL2zJLeTmnkKEnq7mpq6NQZmVi8C1+CO2IUaYmRm9ClX6dqZVXaM1FnCT3Hpl6x2BM\nWERRfSQlWdUUpVdTmFaFxllJ+8GhNO3g/VBFwqwbZZz8/i51NfW07BVIu0EhyBR//3FlVGUw9Keh\nzGk3h2eaPewrXurpj2dZwSN99HIVAiJbY/uwru0wCpw8GysM/g0axXMj/0n8mRtHlwh3Nk1q/5ge\njfy/zH9tee61N5bz9c1vUclUvNb6NZrJOrD5h+1obFoMFgW1oh11opyeXMdqakKG2kyUo46RM5c8\nNM7pu8WM+/YKh4vfoKi7Bas3uJe0xXQhkVpngaz2XnRu1hODIRtt+VkQLOgsCsIDRnE+2x9bzX7C\n3G8j2GQYch0xXrMjt1yDTZTg7OpAbNeuXD9zkSDS6eNxi5yAcQTFxcNPL3Jz9M9sEoI4XlGD2nCL\n95jLBdtAuuWU4uQbSYXsF+ptZaTuaQLW4aQPi8eO7+mp/AGf2vFEDXnv/nGIosi1Mz9SWvcxgtSI\nsUSO1CKS4+FFgbmYGouNrHoJg4O+5eO95czu15Rh/u7s+iyRmAR/uo5q8ruxbICIIDxesNhEkaFn\nL5GuN3DWIZU3nfpwXFvDlfgonOQyLvyUzpWfUxH+P/bOOzyqau3b99T03nsjPaTRQ29SpSoCFlQE\nC4oVEGzYC8eCWADFgkhHQXpRCCUQIJDeE0jvZTIlmbq/P4IUE1HOe77zvurc1zUXZJe1114zs+e3\nn/2s3yO27LKvV4gDIk5SmnaEKYteJKTXtYuWpk3Hnk8yaKxUMeK+CNSR9rxaUs1ZhZpQSzmjMspx\nTPkGmYWE6UtfxSO4R5f2U4obmf1lKm9P68msvv7cn1XK8aZW9oQ1oK3bSHPLSS4f9sHLexLjFjzD\n0eImFpZV0SQ2MW/HZziJTMx9/zPsLbv2XdncQcqOYqIHe+Md6sCaR+fgExmDf3QsP6/7jAkLnyf5\nkBp9nRTLCB0PPD6GrW+dQ6sxMOuVflhY/f4NiiAIV6PDeq2RrW+dQ681Ej3YG12HEV27AV2HgdY6\nDU2VKma90g87F0u2vnkOXYeRmS/1xdLm963fbpXUH7dycvN67nlnJR5BnQ4ZHUYTMSez0VepsCxs\nI2JUAKl6LfEiFZ+kPkKP9orO7cS2NIt6UtoSjtzJmWjDt9iImshvH8Zp9RysvXzp0cuduBF+vyuK\nte0GUnYUk3uyGhcfG8bMi8HJs/tc6O64c/edyMQyNk64lt9cWlaDQ2QELu1tV5ep5RaoLWz4pN+d\nbO85Co38Wg61WTzfHLN4NvNX4519eWxNq6RZrbu6bEioK4V1SvydrVkyLtJsZ/cP4R8rnlcdv5e0\nuvPM9vbF37U/jg590DQ5sX3/aUzySkQGMYLekw5NB4jACQVfdgzgoVEJLBzZ46pQufP9/WTXqjg8\noh7h+3conibHdF2qrVEAmdQWmdiF6uxwMtRi4iYOZoaqHQ6+AHo1TfLelPp70eZ1GowixJdsscsx\nUqBwprbDDonIRJBtM36ORqJfO4qFTAIfRGHyHQHT1oCFmJSz01CrS9nW8iDHHPqgktrgJDTxpmkx\nGGFH9hTa4j14ivewrulF3ik7tMYOHNw8uP3Zpdg5dz6eLjj3CxnnnsfSQYebXQutMmukcgNikQmT\nAF9kzwfLIWya1x+JWMTxLYVkHatk2rOJePVwRKut52L6HKys/ImLXdP94Os05K67g9HhrzPU2YGj\nLSqe8HdnWYg3Bam1HPk6l5AEN3wjnJBZSpFbSelQ6Ug7UIaDSw6FKTsZNGsO/abc2bXpDgP7V2dR\nmd/CyDmRhPf3ZF+DghfSy6iVCUSUq5iW8hUirYqpS17GN/JGqztBELj9k5NotEaeneXJ3oL1TJIe\nRWaoRy53xc/vQWrSHEjZsgEX/yRUbf0wiUU0exRjl/cTu26bRW1YT+72cmG+nxteFtfyXPd9nsml\njEYAfMPVFJ9Zw+3PLKVH7/58+9wC1G06kM4GkYhdfd5nw8yvod6KHe+dJ2qwD8Nm/75P8G9pKFey\n66OLaDUGpHIx8ivjKLeU0KO3Bwmj/Tm1vYj0IxXc/kQc/tEuf7rtP4NWo2btYw8QGJfI7U8/D0Bz\nRzNDD6bRYO2CtUSLVmTF04GePBnggezSMajPZXmGA/sa3Di+ZCQXjxeTkVxGoLcdCbLtuFevB5kl\nomHLoNf9nSXN/4CynCaOfJ2LQW9i2Oxwwvt1zZ3ujm+yv+H9tPfZM3UPAfYBlKSl8so3R/hy9atI\nTXoMUjEdQUHs9g1meeICjOKuNzZm8XxzzOLZzF+Vjanl7M+uQQQcL2q8YZ05jeOfwT9WPCvasmhp\nPkFr6zlaW9MwmtQAmIwiTDox7cVjGDx9ESe2NdBSWcLEBQm8c17DjguVPDAwkJcmRFHSoGL0h8cZ\nbiriq3cWwprB1J5qpSrOFmVvFV5hK5hxZAnzes7HL3kgZZfq2NPnQ/aI7LAoPgLBw6D3XEyOQVz+\ntJUWWTWpURsId82l5uRruEis6dWnluyUFPKKmukwiJDIZPjHxBFqqcC5dghiO3dEvTeSIzuAb74J\ng+EuLinCOK0JocbLiDyujcnGpVTiR4CxChuVF8KlGaitOxCJRRSkHMfWyYUZy98h59gRTm5ej52L\nBzr9OGaErMS2PY+B7R+RFK6gn8sG3KwaCQr/nHD/EUCnWN382lkkMjFTFgeQmTUHjaYEgIT49Tg7\nD+w6+L+8Ccff4+Xbj7C2TYaVWMS5AdGYajT88K8LeATaM+mpeCRXCq40VanY9dFFVE156NU/ERCX\nxPSlS383D9eoN7Hn0wyqi1qZtDCemlIFKT+VUj7Jkw2WOkLqO7jnzHp0DbXc/uxSghP63LD/7vQq\nLmQtIsn7LGKRgJPTIHx9ZiE1RNJc3UhdmT3nd2/A0J6Gb/RYwpPG8fOXy3Bwdyfutbf5oqqRvQ2t\neMhlHOsbgb1UwuWsRvZ+mkmfiUEY9UZSf/wKoy6Pic98THhfPw6v+4nMQ2uR243BO74vbzsuIN4t\nnuH+w1En26JPt0M0uRyTp4qBPgNJcP/jmd5GgwlEXB3H66kuauXHDy4QfYui/FY4tXUDZ3ZsZtLz\nL3FClsOa9G+oqVqErq8fEn01Mbr9rB3yHAH2AVf3OVHUwL3rzjJzsI7jihUo9UpiXWNZNXIVzqpm\n2L8YSn7u3NjSEZOdF21SV2oFJ2otgoiZ+iyujjdObFS1aDm0LpuaYgVRg7wZPCO024h1c3UVunYN\nUrmcFpOS6cdmMzfifmJyrLl4cA/fRQ9i87rXqA10pueKDbj2HUZLTRVPr9rJMVNgl/bM4vnmmMWz\nmb86w1Yc5XKTpsvyR4YE8/z4yP+FHpn5b/GPFc8ARoOBjMP7SNm2AalNK2HDg3APdUJTEUjq1l8w\n6LREDh5LaWYQwQk+jH4wmjf25/H1qcvc0csXTXMTB0uUfDfKhqTbRkHOTtg2B0PSo2STjMJCw/ea\nOCRZ/sSUjuBE0DZG2vzMvFYFjH4N+swDsZii83WUfJdHjJWE/NscaNfPRiLEc2nngwyZGUbPYb6Y\njEaqCnIpPneG0vOpJIiH42zhhSAycjnpJTQGBfnbgkHoFJR2Dl6MsD9OSIg7NeMfJa/kJSRaRyI0\nq/CcnnR1DCrzstn+5stIpFJ07RrC+g1k9MMLOZ/8LWLdB/RPbyDDbQxTK+ZgI1PzzqBXsbUQSEzY\ngINDp61YeW4T+9YmEzbhY8SSGmIzm8gLs0Umd6XPsFOIpBbXBr25FD7tD1GTUE5ew7i0Qqa4O/Go\nsxPb3j6PWCzizqW9sbLrjNg2VanY+eFFTPpKNM3bEYldsHaZyYxlA7B37d66DDodJX5YkYayuQOD\nzkRYPw9G3R/FV4W1vFhVS7DKxJyzm1CXFjH20aeIGDTsqhivqf+F3Ox5HKsdyPgRSwk32XFmx2by\nTiWDICC1SiJyyCS0bQcpPH0U77BIqgvzsHGdzZx378DKVk6aQs3tF4qY6eXMeyE+bHrtLBKJiLte\n7ItIJPDZvHsQS/0RxGPwi3SiIr8FY/sm9FoVM175mOPCId45+w4AUqOcGRlLMIlMbIt9D6NEzzDf\nYSxMXEioU+gtf+51HQa2vHEWgLtevLV89VtBr9Wy5rmHUCib+WFQBV7Se8jOj+aN+xPxsC7i1ZRl\nGEwGlictZ2zgWADKFeWM+/gU7QYVQ/qnMD54HO+dew8Paw9Wj1qNn50v6ck/UJd/Gl1zFRbtdbiL\nWvC88irCj9z+7zNh9Gik1900mIwmzu6+RNqBsm7TOIr2r0f688ucrA+kXmsLwIG+taitjExL9qZ6\nRAKHLPbgbR3IptvX4WJ1LVKv0eqIeqWrA4dZPN8cs3g281fnnX15rD5e2u06s53d35v/6TX7/8+v\n7n+B8uxMfvl6NU2V5QTEJjB8znxcfK+UQO4JMQNncnLzerKO7kNmYUP+qWi0qhwemhCHjdifT06U\nAxCvL6PfiEc794ucBP4DkKZ8TjzQJHjTVzkArSacWudsLrmdZIbBEx7eA26dOcLtSh3HNxfi5GGN\nqENPQr2clYYxDPXeiX/8ZM7sKiU4wQ0bBwv8onriF9WTeKfhqFNqONuahzToHDZ2DTin309Y/yCc\nvByRyrVkHN7NropQPBrV9K/ejp/Xs8h1Prg/0veGcZBbWWNpY4u6tRl7Nw9GzHuA4ssvorX8CW17\nNEXIiW88zFfjH6PQFIqz3BWtto709AdJTNyInV0UHiFGQsetxCg0EJwmF6WGZgAAIABJREFUw8p9\nFB7KFsrciqnePAT7wV9j4RGEzMIS0YGlnX7No1/HTirheN8IBIPAzg8votXomb641+8KZztXN8Y+\n+hL7Vpew97NMpi/u9bvCz9JGRp+JQRz6MgeJTMyAKSGIRCLmhnvRUdvOmzYK1g+/j/stt7Hvk/dJ\n/v5rfGMTKYzug5PpX1gbXdiYNR19+Snc038CkQSJPBErWwOqphTkUjdGLliIydBO8bkz+PfsQ2O1\nF6d/LGHEvZH0crBhgb87q8rrCb/UgaGhnUlPxiORiinLTEerVjLx6UmoFb6c3X0JJ09r2hXDaa3a\nSH1JCndPuJuJwRMRBAGZREZdPxX7V+WwymEjBWEn+SrrK6b/NJ1JIZNYEL8AL1uvP/3ZP/1DCW1N\nHUx9JvH/m3AG+DjrE3b3yGXiaS8Wtk7kK6EP8X5y7g73RCTyIsZ5G4uOL2JR8iLO157H19aXT9M/\nRerYG1PVROaHvUdSiBthTmE8/svj3L3vHobavMV3pyyxtxxNnJ8jCX6OBLqLOGE4hbw4hRmFhxl7\nejZfpd9Hwl0v0CeoMx1JLBHTf0oIXqGOHPk6l82vnyVqkDe9xgbSXpWGx8lF2Nt24O3twuV+yzEY\njEhbTvClYgfKB3pyuG43Yq0fm2Z8g4vVjRaI1ha/b0FnxoyZvy/Pj48kt6atS+oGcHVyoVlAm+mO\nv2zk+dj6Lyg6e4Zhcx6iR+/+iEQiBEGgXanHyk52NQpZV1rMsfVfUpmXA9e5PWa7JHLWOpo3e0uZ\nMnP6tYYFAaGxhMwDOZw+bYUYLacDfuC8x3nutY9g8eSNNxT7OPRlNiUXG5ixrA+StDpUZ2o4N8YR\nUftsbCyjKd4+nx6J7ox+MBqA1tPVqHaVUNxhpD3SBpuox5HrPPA5/ByO44OxG9LpImE06MlJ/oWK\nXaeJthyMUdBS6V6IykKPUa/HoNNi0OmoKSrA0taWuNHjyTqzhsARDYgtdAQHLUSun8WBD08wx2sB\n0qB+cO8PNDQcIjPrUaRSB0QiCT1jVpFf8BId6jKqk+djavWmvm4TiEzEzijC2kJHzGk1eyqicHa0\nYJxTKox+HQYuvDJcAkc35JN3qoYx82Lo0csdgMbKzlQNk74CTfMO7F3dmPHK29g4OlGR28zuTzII\niHFh3CM9b3Ba+JXWeg073k1DKhfTrtThHmjP5CcTrnoBv7M+g099BPwt5SzX13CgsoG9jt742JTz\nAsvJujyIrZmDaJE5Mbc5HxurBAbdEUf0IC+ObfiSi/t3Ez10FCMeeJiMw/uIHDSMjKMtpB8uZ/ri\nXngGO9BhNDEyNZ+Glg7eqZEx7aFOP+xDa1eRf+o4j36xAZncArVCS3VRK4e+zMHWbh/q1hoe+vgL\n5FY35vT+vD6PgjO13LGkF3IPE+uy17Exr3NC291Rd7MgfgEWEosuY3E95blN7P44g/hRfgy849aj\n1n+WirYKJu2axPig8YytDGfTwbPs8xjXpYy73qRnZdpKvs39FoChvkN5rtcypq3KoVeAE1/c13lj\nX9xSyvSvtqFoiGFQuIzPZw/mVE0yu4p3kVKdgkkwIRaJSbQN5PV68K09RooxisPhr/LE1GE421wT\nuGqFlnN7LpF3qgYLUQNTHJ7GRtrBBd97GVD9NYx7D/o9TJuujWFbhqE36TGqQ5gZ8AovT+j+hzDw\n+b1dlpkjzzfHHHk283fBXFDln8f/9JotWb58+X+wO/8ea9euXT5//vxb2sc7PIqEsROxsPagNL2B\ni4fLOb6pgHN7L6Ns7iAgxgWxWIStkzMxw0bR+/bpNNf6oGzxJDwpjkC5JzHNzojULlTktdBQrkTZ\n1E67Us/RH+rJSRfwi3Jj5MOuZGtXcUkHzw2Yh7tj3FVhXpreQOpPl+h7exA9enkgdbVClVJNqKcL\nG+taCXU4gm/AcHKO6vEOdURd2opmZwnNBhNW44Px7n2Ypuaj9Ez8BGmbI6qUamQ+tsjcrBEJIixz\nxTjXumFy0HGu6nMqa0vQaHRoNWqMBiMisRifiCjGLXwcnfVOZF5n6FBI0JeNpc/IF3Bws6FNATWX\nNfirfwSf3lj7jqal9Qw6XRMiJFRVb8CoVRCf2UxrrT01usH4RkYy6em5yCz9aTGcwAoLBknK8ZHV\n0SG2Rz77W0TizpzTrGOVpO0vo/f4QGKHdwr/a8K5HHXTDhw9PJnx8ltYO9gjEolxcLPCwlpG5i8V\nmAwCfpHOAJhMAk1VKkrTG0neVIjRYGLqc4l4BDmQcaSCtuZ2guPdEIlE9Ap2RrmznJPuYraLbciy\ndyPW1ZmnTauQGjSIcxJw01mSKnHH1rUHixYNxj/aBZFYTGBcL0QiMRf27aK5qoIhdz+Ipa0dnsH2\nFJyppaqwhahB3sgkYjRHqvnZFWxD7Rnn4YTRYODQmlUEJ/QmImkIAHJLKSe3FmE0CIyaO5D0A7uR\nyuX4Rd1YfMa7hyMFqbUUnK0jIsGHEWFDmRQyiRZtC5sLNnO04ii93HvhbOXc7WdeMAns+zwLSxsZ\nY+bFIO4mF/o/xZtn3qRCWcGqEasI69mHFamtCCYjr4wP48LeH3Hy8kFuZY1EJCHJJ4l493hGB4zm\nsfjHcLKyR6U1sPlcBVMTfJBJxCzdVkJ+uS1evplUWX7ElsJN7Cndg9aoZVbELF4b+BqDfAbxXdF2\nkh2tGR0zj+Dy3fRu3MXGi02E9uyPlaXF1fEOjHUlNN6a4Ky7cZK28VzHEt5q7U9vSTGel3Yiip+N\npY0rHcYOVGp7yvOn8f4dfXCy6T7K/NGRoi7LnhrVvc92d7z66qs1y5cvX/vvjfZfk3/num3GzP9F\nxsZ44W5nSUZVKxrdjWUp8muV5Fa34e1ohbfj76camvlr8T+9Zv9l0zZyTzaQdayStsYOAKzt5fhF\nOiO3lJJ9vApls5ZxD8dgcaXSnNzSggmPD2P3x45cylQA4BvhhIWVlJY6DRW5zZ0TtAC5lZQR90UQ\nMcALkUjEIpv1DM1eREPJS5xv2EFIyGKaSgI5vrkQVz9bEsYEYDRqaTYeR+fbBCfgQbvbuOx5GKnt\nt9i7PM2xddn0RUAsFuE5tyeC41Fy81bh7j4eJ6femO40YmjuoHlTAS73RtL2czm6y23YDvTGYXwQ\ngSnZ8POr8MhJ8Lwmyhobj5KVPxOdvpHAwAW0aoM4tn0dUuEjxj72NAOm9WBz5hRiOYTtxrvA1oMo\niS1KSQUNgh8KLxmRFQ1kF/uS0+aAlaOB2jJH0g6qcfUfioXVbspCyvCSRGJ9+STbynyJSTlJ1JAR\n5Jyo4sTWIgJjXek7MQi44hKx8iImQzmaph04eXpz50tvIrbQcPzEcORyD9zdRhOQeBtNNd5cOFhG\nu0qHsqmDuktt6LWdFy4bBznjH43F0d0aR3drFPXtpP5UilQqpt/kEKzt5Tw0IQzT5hyKk5yYam+P\nT3k6eodMWopm01g9HBeZmBEBck7WKWiTCPw6DU0kEjHgjllY2Nhw9Ju1/PDOcnpPnIqVvT0Jox05\nsbWS7OQq7F0tEac2Md3Piy1NCqY1KwmoKKJD2Ub4gMHX3oNKJZX5LQyYGoJveAA9+vTn/O4fiBs9\nHmv7a5PfLG1kTH4qnh/fv8CuDy8y5dlEvNy9eGPQG9wWeBsvnXqJmXtnsqj3ImaEz+gyobIsp4mW\nGjWjHojqMmHOaGynvb0cjeYymvbLtGsuo2kvw9Pjdnx8Zt3SdyunMYf9l/czr+c83KzdSK9opVzk\nzJC20+z74Cw1xQU0lF1i8nMvXt0nyTvphjbu7R/A6uQSPjpSREmDiuwqBW9MiWFqr2G8eroFsUjM\n5JDJ9PXsi+TKjViAfQBrb1vLgiMLmFX7E1/N2YL9vjdZULeahpU70IxeinXf+zqf/Bh0CBsn4yZt\n4F8WT/OTLobh7TI2OjxGn44nSFn9KAHzNvJE/EK2HzlK/yArgt1sb2kczJgx889hdj9/Zvfz7zYK\nfSi3jiN5dcwfbJ5IaKaTv2zaRvqRcqoKW/GNcMI3wglnL5urYiP/dA1HN+Tj4G7NxMdjsXfpvFts\nV+rY93kmtaVtiCQipj2XiGdQp7gRTALK5g4UDe04e9tg43Dj43NBMFJT8wNFRR9gMNajqo5FV383\n/SY7o9IdoqHhAAaDErnIC5vKWGxre9FhXUZD5Pf45i7DUBaKnUSE80MxKG1+ITdvCc5OScTGrkUi\n6fQUNii01H+SjkmpQyQT4zQ9FOv4zjQI2lvhw2iImADTOm+Wqqu3kpe/FBubMKIi38PevlNUn96x\niZSt35M4bhLD5szjUkYjKV8coLfPGcSqGiyFRhxtS7EyqRAZ4LSiJ/qE57G0C6elTk1ZVhMIIAhg\n6VxC4Kh3aMy+HSoHo9Yl06FqpM+U5ZzdU4l/tAvjHo5BKpdQX9bGTyvTEUxlqBt/wNnLhzteehNr\newfy8pdRU/MjDg4JKBTnEQQjFhZeKKsSqL7YG1vbSDyDHa6+7F0tbxCPgiCQsqOYjJ8rkMglxA33\nJX60P2d2lZJzvLPohd+QlVg5l9OYtpIOhRhnHxsCBngy66cMRkS68+ndiV0+R7nHf+Hg6pWYjL8p\ngimSIZU7Y2kXzthnpnF3o552o4mXso5RcfoYj679HqlcjiAIHFqXw+XMRua8PRBLGxmNFWWsX/QE\niRMmM+zeuV2O2VStYucHF5HKxEx5JhEHt87PZ2N7Iy+efJFT1acY7jecV5Nexcnymufozg8uoGho\n567l0Wg0eSiVOSiV2SiVOWg0l7g+LUkmc0EskmIwqkgacAy5vPto9m8RBIF5h+ZR0FLA/mn7sZXb\n8vjGCyQXNLAyppWL27/rrLgnCExb+ipB8b0AMBk7n4Rc/549syWdHy5WYSkT88msREZFeaBqbuLQ\n2lX4hEfRb+qMbvtQ0FzA/MPzEQSB1aM+R5tdgOiXN4kXF2NyDEA8dAnKc1uwq05mjehe3m4fx8sT\no/DMUlJZ2EL/hH3Elq7mQdNLeCeOYcOZclbOjGdyvE/3J33pBIFr2ros/jumbYhEoq+AiUD9dRVj\nnYEtQCBwmc6iVy1/1JY5bcPM3xVzGsffn3+028bNqCxoYf/qLCQyMRMXxCKRitn7WSaaNh0D7+jB\nxUPl6DuMxI7wJbS3B44eN/ecVSu0pO4qJf/sZdyjj+Ecvh+BTns8icQWd7fb8PCYhJPTADo6KsjO\neQp1Yxl6kQlrgzcBKS/gPD2MNu9T5OYt7iKcf0VXqaTtaAUOowOQ/bYoxIGlcHYtPJmBYO/N6TOj\nkMkc6ZW4CbH4itjXqhB+eoJj1X5cSLnAwBn30H/6TA59mc2lrCZC4t0I7e1G0fl1CN5fIqiCGX77\nbmTyazcLNcWtHFqXg6ZNR89hvkg836Fdl0pL+sdU5zdg1BUjsxpASKIbox+MRiIVU3epjZ8+Tgfh\nMqqGH3Dx8eOOF9/A2t4BjeYSZ1LH4ONzD+FhL6PTNdPY+AsNjYdobjqBgEBM9Erc3cf84fvaUqvm\n3J5LFJ2vR24lJW6EL44e1jQ3XURt8Tj1mdNozh+HZ7ADrfUaOlR6BBsJx40dPD0vngHRHmg1emqK\nFVQVtVJd2EJDhRIHNxkegSIc3DVoWhpJP1yAUV+DYKwBBBQRcXwx9A4SCy+ywNDC+MefxaA3cvS7\nfArP1tFrXAD9J4dce6s++5C8k8cISuhDWL8kgnv1xdLmWuSzsVLFzg8vILOQMPWZxKvOIybBxIbc\nDXx44UOcLZx5JekVhvgOob6sjW1vnyP2jh/QiQ9cbUcu96RcBxcVTQS49OWumCdwto9AKrVDpS4i\nNXUcAf7z6NFjyR+OLcCpqlM8cuQRlvRZwj1R91DZomHoimPMHRTEQ9GWfLf4CaRyOWKJFJPJiKOH\nFxpFK5o2BU6e3oye//jVdJWSBhWv7Mrh2dvCSPB3orowj5/efwv1laqMU5e8QnBin277UdZWxrxD\n81DqlKwZvYbqWle2bf6KF61+IMjQaaX4vX4cLxjv5cmRoTw9OozGSiVb3jhHn7GeJF6aRb3awFDV\nW9haW3F66UgsZd0UZMneAT8+QqD6my6r/qbieQigAtZfJ57fA5oFQXhHJBI9DzgJgvCHHxizeDbz\nd2ZjajlbzpWTUanosi7e14Gdjw/6X+iVmf8UZvF8E5pr1Oz5JIP2Nh0iiQiZhYTxj8TiEWRPa52G\nYxvzqSpsBQHcA+wI7eNBj14eWFhLaalV01KroblGTUuNmsqCFox6E7Ej/Og9PhCxVEl19VYsrfxw\ndRnRRQSbTDpyC/5FXc06AMJ6vIJUZkdu3qIrwnkNEskt5k+1lsPKeOj/KE29byM940Gioz7E03PS\ntW32LYazaxAsnTlgMZfcM2cYOfcx4kaNwyQImIx69n28guJzZ0ic7YLJ7iTx8d/i4nzjhaBDrefo\nhnxKLzbgF6fBJvxpfLzvIXf3RGpKFBi02SRNTaDPpMHUlirY/XE6Ii6hrN+JW0Ag0194HStbOwCy\nc56ioeEISUnHsJC73nAcvb6VjMx5KBTpREa8hbd318Ip3dFYqeLs7tKrRUt8Bn6KjXsRTsJmwvsG\nY+dsiVFvojS9gczkSmqLFZhE4OJpTUutBgQQS0V4BNrj5mdHTYmChnIlAF49HLB1ssTWyYK4ES6U\npJ2l+NxpvrFy52xsEk9aGnkyOob9q7OpLVXQb3IwvcYG3BB1bVcpObN9E4VnU1A1NSKWSPHvGYd/\nXA9ihozHytblaiEUC2spU55JxM752mcorymPpSeWUqIo4baA2xhaMJsO3XZcorfi4zMbN9fRFLfr\neeH02zS1NzHcfzhHyo4Q6BDIiiErCHfu9H7OyXmG+oaDJA04hoWF203H1CSYmLF7Biq9ip+m/IRc\nIueNPbl8nXKZE4uHk79zPRmH9mPj7Iy+vZ0OlRJnH198I2KwdnAg71Qyirpa4kaPY/DsB7CwvnZD\nmvnzQX5e9zl2rq5MfHIJh1avRNnSzH3vfoydi2u3/alV1/LAgQfQGXVsuX0LJ/LaeWZrOrONh/EX\nGnhbeg/3JwXyyu1RV8f+wNosynObuX+uBvmOmWRFPEVD/GOMiPDoeoCUT+DQC+CfRGDh411W/x3F\nM4BIJAoE9lwnnguAYYIg1IhEIi/gmCAIf2gebhbPZv4JzFidwtnLXR/ERHra8cbUnuaKhH9RzOL5\nD9C06di/OgtBEBg7vye2TjemY6hatBSn1VF4tq5TPIm4/uk3YrEIB3cr3APs6T0+8A8j1L/l0wPr\nCZW9hkTU2aijY1/i4766deH8K9vnQuFB0seNRKkuYGDSccTiK5Ogys/AV2Mh8nYo/hmjZwK7m/pR\ncuEc4594jsC4RHa++xrVRfkMnzOP2NEjOZ92Bx0d1fTutRVb2xt/LwVBIO9UDSe2FuKRuB47/2SM\nOivEIiu0qnaMeglWtiHUZQ2ho94BZe1O3INDmL7statRVqUyj7PnJhIY8CghIc91e0pGo4bMrMdo\nbj5BD/vJBJQ2QVkKTP4Uwm676XDUXW7jcv45VPL5BAU+SXDwwm6323KkhAO7SxjoZk9svAc+oY54\nBNnfkDvcWq+h+Hw9RefraK5WIxaLCIp3JXqQD74RTijb1TycWUpWnZ6HUtRYtpsYdX/UVYeR7hBM\nJmpLiihMPUVh6gna6huw9xFx35sbsbCyo76sjV0fpWNlK+OOJb2xtL3m5KI36vk652u+T93KfeVT\nCBj2Ee7uY4iI+pDVGav5MutL/O39eXfwu0S7RpNak8rSE0tRaBUs6rOIu8Lvor39MmdSx+Drcy9h\nYS/ddCx3l+xm2cllvDP4HSYET6CtQ0/S278wIsKd96dFsuaROQQl9GbCwkUA7PrXG5RlpvPAh6ux\nc3FFr+3g1JYNXNj3E7bOLoya9xgBPeM5+s0XZBzeR0BsAhOeXIyVrR3N1ZVseP4p3INCmPHyW4gl\n3ZfpLmwp5O69d9PbFEb/bCeON1nws1tngZ9pCT786864G9xamqpUbH7jLL3GBNBfuxyKDsOCVLDz\nBK0StG2d/6ZvgtTPIWoyTF1L4Es/dzn2P0g8twqC4Hjl/yKg5de/u9l3PjAfwN/fv1dZWdl/pc9m\nzPxvkVbWwp2rUzD9jlQaEurK+rn9/rudMvM/xiye/wS/nuPvVbT7ldY6DcUX6kEQcPK0wcnLBgd3\nq24rvP1Z6pUdvLBhOTPDtwEgFlvj7/8A/n5zkckcbr5zd9RkoPl2GKf7OhMUuJDg4Cc7l+s7YPUg\nMGjhsdOQtxt2PoJh0PPsOKWguiAPO1c3VE2NjHv8OcIHdEaaOzqqOXd+OmKRlN69d2Bh0VUIttSq\nOfzNOUxWu/EKE+EWKEHRUEHtpWwsHMXIbdSUHvDD1iqR6UtfxcL6WrpJRuZ8WlvPkTTgWPfnazJB\n+WlMWZvJ6dhDvYuYgBqBkEZbRKoGuH8P+PT6/fFoKSMr42GaRNUMTDrxu2NqMglM/vQUtW0dfDe3\nLxGe9jcd5qYqFfmna8g/XUuHWo+9qyVRg7yxc7Xk0Pp81GKB7LFufDAiHDe57KZt/crlsrWcP/A5\nZb944x7mwOxX1iORSqkpUbDrw4t4hthz+8L4Lp+3fRsPIXFcTLO4nQOmBPSCmKzGLKb2mMrzfZ/H\nWnbthq6pvYkXT73IyaqTjPQfycKEhaiqPqOpYS8D+v+CpWX3ftI6o47bf7wdBwsHNk/cjFgk5v1D\nBaz6pZifHh+IuPg8Bz//iBmvvH01LUNRX8s3zzxGSJ/+THxy8dW2aooKOLh6JU2V5di5uqFsbKDP\npOkMmnUfYvE1kZx74ij7P3mf/tNnMnDGPd32q12l5Ps1r9F6NhdsLZg0/1mypAHkVLexdHwEsm6+\nmwe/zOZyVhNzlvhj+fVA0Gu44Y74V/o9CmPeArH4H2VVdzPxfOXvFkEQ/jCcZo48m/mnkFbWwoLv\n06ht03a73tfRkpPPj/wv98rM/wSzeP4L8MKPmWSXHmHpxP7Y6DdRX78PicQWf/+5+Ps9gFRqd0vt\nFe3qS4VtEwP7J2Nh02kPx5FX4eQHcM8P0OPKl/iHhyFrK9q7drD1m10o6mqZvOjFLhZqbcpsLlyY\nhbV1EIkJm5BKf5NrTWfJ7KZqFe4B10Tn3o9XUJyWTMjEUiwcjCQmbMDF7VoOq0JxgfNpdxIS/ByB\ngY92PRFlLWydAxVnQGaNEDGBAl8DVeoTeLtNJuLnQ4h07fDQYXAO7rp/ZRrKnTM4GykQWCsiJPoN\niJvZOaHttygqKTi8jvsyolGJbFk1O6H7R/ndnHdpegNZJ6qoKWwFwNrNErt7QniuthYXmZT1scFE\n2978SYIgCJxJHYtMakdLgQ+ZP5UQ1CeEqc9+hEgkouBMDUe+ySNmiA9Dryu3rVGqOXpwKhaO1XT4\nPsl76d9hEAwsH7Cc2wK7j8qbBBPf5X7HR2kfYRAMOEtMLPPqIFfvRI4oHndrdzxtPK++vGy8SK5M\nZuWFlawdvZYB3gNYe7yEt/blMznem5UzE9j44rNo1Wru/+DzG25CU7Zt5PT2jcx4+S38omOvjZtB\nT+qP28j65SBD73mQiIFDu+3rgc8/Iif5Z+544XUCesZfXa5qaSb94F4yDu9Dq1FjSPBkk8sZ3h75\n3tVqhr9Hc42aTa+lkjDan6TE2s7os6U9yO0QLGypKNWTmyGgdYzF1c8OV19bxuy80KWdf5B4Nqdt\nmDHzJ3hq80X2ZdWgM3bVTeYI9F8Ls3j+C1DRrGHKp6doUuvoG+TMw0km3IQNNDQeQiZzITR0GZ4e\nk/8wMg6dKQ4nj/fDua6FnhHvQfxsqMmAtcMhbhZM+fTaxlolrBkK+nYMDx1DL7G+mof8Wxobj5KR\nOR8Xl6HE9lyNWPzHLoYaRSvfLnoc12A3vAafx2TqoLff61ir2xEQcaFjC5r2UpIGHEUi+U26S3kq\nbL2v8zH6mLcgdgbIbRAEgdLS97lc9jmu9v2JOZqCxMIR5h4Gm+tyY/N203bgYdKjrUBuS/9SZ+Tl\nFyBgIEx4H9yv2Ak1lcDJDyFjM5j01ApOzLNZRU6LmGXjI5k7KOgPxz2vpo2nt6RTV6UixCTBIdKR\ndQ/1I0Op4f6sSygMRtZEBTDa9fefJPx6IxEZ8TaentP48dOZXD7ZQeyYIYx+sDNqe/rHYi4cLL9a\n0h3g5OFn0Ep24e+5gtCoaaj1agwmAw4Wf/zU4pLiEtmN2dRr6rFu+RFXQz6bVf3JrbVHY5GKCd0N\n2w/wGsDa29by+bES3j2Qz4SeXnw0M56Wist8t2Qhw+6bR68Jk2/YR6/T8s0zjyG3tOSed1Yikd6a\n+6W+o4MNy56mQ6XkvvdWoW5t4cK+XeSdTMZkMtKjdz8G3DEbJz8/Hjz4IAUtBWyasIkQx5Cbtnv4\nqxxK0xu4940krO0705oMOiPJmwrIP12Le4AdggDN1WqMBhMrHNu7tPEPEs8rgKbrJgw6C4Kw+CZN\nAH//67YZM92RVtbCHZ+ndPcsi7em9mR2P///ep/M3Dpm8fwXQX2laMS6E6VUKzoI97DjsYE6vESf\nolRm4uTYn/Dw17CxubkoqKraTH7BC/Qqc8SxXQ7zk+HLEaCq78zttPrN09bqdFg3GkJGwqxN3Udl\nr1BZtZGCgpeuuGIs/2Mx31qO7tiHyOrS0XRcIi1ChNQg0Cu9FbWNlIuxDoRZjsWv74cgvZKXLQhw\n/ivYvwQcfGDmRvCI7tJ0ReV3FBa+hp1FAHEns7FwjoY5u0FmBWc+ozl1OZkxDsgsPUlI/A5rywC4\n+B0ceaXzpqHfI6CsgZwfQSyDxPsg6XH4/k7aseQZhw/Zn1PHrL5+vDY5ptvH/0aTwBcnSvngUCH2\nVjLend6T/FolKw4WsHfhIKK9HajT6rk3q5QitZZ9vUKJ/J0IdF7eUurq9zBo4GmkUlu02ka2/WsW\ndZkWDJx5F/2n3ttZBGV1FmXZTdy+MA6x3THyCxaha5jEuLs+vPnhRNLAAAAgAElEQVR78Qd0dNRw\nMHkSH1xcRFmrDf7O1jwy3JNI/w7q2uto0DQwyn8UP5xTs+JgAbfHefPhjDikEjFHvvyM7GOHeXj1\n+m5vvorPnWHXv96g//SZ9J8285YFdGP5Zb5f9gwyKyva2xTILCyJGT6ahHG34+R5rZphvaaeGbtn\nYCe3Y9OETVhILShtLSW3KZecphxq1DXMjZlLokcirXUaNi4/Q9zIzkqMioZ2DqzNorFCRcJELSLX\nj7C3i8HJaSBiQwL9P8vt0q+/o3gWiUSbgGGAK1AHvALsBLYC/kAZnVZ1zX/U1j/hum3GTHdsTC1n\n2Y9Z3a4zTyT8a2AWz38x9EYTuzOqWZNcSkGdEgsJTAo7zwifHUhFWgzWs3H1mEedCsqbNVQ0t1PR\nrKGqtZ2HBgXSQ7wAENFXNgvRrsegx2goPgx3beicKNgdZ1bDgSVw25udAvImFBW/Q3n5F4SGvoi/\n3wPdb6RuhBPvw7kvAREEDACnIBSOllzQ78TG0g+MevSaagacqUNs7weDnoaed8LBpXBxQ2e/p3/R\nVexfR2PjL2TnPIkMC+JSL2HrdxvY+1B36VtyIh2wtgkhIWE9FhbXpV+om+DIy53HkNtCn7nQfwHY\nXdkmYwv8OB/TjA18UBHGJ0eLGRDswqR4b6RiEVKJCKlYjEQs4utTlzh3uYWx0Z68OTUGF1sLFO16\nBr3zC0PC3fh0dqdvdJ1Wz23nC7CWiDnQKwwH2Y3i0WBQc/LUANzdxxEV+e7V5YrWdHaseJKWYjsG\nzboP34gYjLRw7uh+ZI4Z2LgXoG7oQVzM1wTE/HGKyc1oVGmZ/sluatokPDXSj12ZGgrqlCT4O/LC\n+Eh6Bzqz6uci3j9cyOR4b96/s1M46zraWfPIffToM4BxC57ptm1BEPjp/TcpPncGGydn4kaNI3bU\nWGwc//yPR+7xX0jduY3ooSOJHTkWS9vuC5qcqz3HvEPzcLFyobWjFZ2pM3puI7PBQmKBWq/mg2Ef\nMMR3CD9/k0tRWj1DZ4VzantnBcFRD0TRYngGRVsGYrEcvb5TI8499HGXY/0dxfN/kn/SdduMmd+S\nVtbCM1vSKWvWdFknBrY9mmQW0P+HMYvnvyiCIHCssIEzpU2U1Kuoaq4myW0zSd5nadC48HXObApa\nQnGxkePrbE1DWwchjsXcH/4eERFv4eM+FVbGdkZXo6bAjG9vdjDYfDcU7O2MwI55Gyy6FyeCYCIr\n6zEam47Ru/d27O1irq3UKuH0p5CyqnMSVvzdMOx5cPC9uklj41Eysx5GEIxERryLt9oBjr0DVec7\nI8AmPQxZBMOWgrh7h4XraVNmk5ExD6NOQWxmPRorCQU9bHFw6EVc3Be/P+my5TJYOnQV50YDfNIb\nLOzg4eP8mF7F8zuy0F6pLnk9dhZSXp0czdQEnxui8O8dyOfz5BJ+fmbo1ap15xRqpl0sZoiTHd/F\nBiG+bvvqmu3k5S2hV+IWHB1v/K5WlG9h/8rPUVbe+H6IxAJimRSp3Ieew/rgERSMe1AITp7eiMS3\nNoG1UaVl9hdnKG/W8ET85wyLCCUi8l9sT6vg/UOF1Cu1xPk6kFGpYFqCDyvujENyxcEi8+cDHF77\nCTNfW4FPeCSCYELRdhF7u57XXF7odBW5lJFG+oE9XEpPQyyREtZ/IAljJ+Id1plCIwhG6ur2Ula+\nFkfHvoSFvvSnUpV+y/un13Po8kH87XoQ4xrNAN84Erx6oNQreOzIY+Q35/P6wNcZYj+S719JRTAJ\nuPrZMnZ+TwR5LmlpM+jRYyn+fg+iUuXR1HySYZ/7djmOWTzfnH/idduMmd/ye1FoZ2sZvQKdeWRo\niFlE/x/ELJ7/RnTojeSXJdNU9RoYK/DwupfIsCVIJFZsOVfOpaKn6etdytDBKZ1WdxfWw6mV8MB+\nsP19uzQADDo49nZn/q9TIEz7Avy6L1Ch17eSmjoeidSWvr13ImkohqxtkP49aJogchKMeAncwrrd\nv65uD01Nx4mIeKszd1oQoOSXznSNuFkQOfHWxqWjmoyMh1CrCxEQcHEZTs+YVf++3d/FDbBrAcze\nCmFjUGsNKDsM6I0mDCYBo8mE3ijg5WCJo7W8y+6NKi0D3/mFyfHevHdH3NXlX1c1srSwkmcCPVgc\ndM3VIi2ts3x6/36HuxWLh04tQVNxCGtZT6yl4UiM3rRUayk+fwlreyXKxmpMRgMAMgtL/GJi6Tdl\nBt5hEX94qtcL56/m9MGddZSVf0Hfvnuws41AozPw5YlLrEkuYUKsF29Pi70qnAG+e/5JTEZjZz6y\nupD8gpdQKNJwcOhFz56fdfHtBmipqSLj8D6yjx5Bq1ETlNCL6LHBNHdsQKMpRS53Q6drILTHMvz9\nu1ZgvBnfp5bx8q4cjL/xjZJJRAS72vLGtFDW5L9Eam0qS/osIapiMGqFlgFTQpDKJVxMvx+lMoeB\nSck35OH/k9w2/lOYr9tmzHRys4qEYuANcy70/znM4vlviNGoobhkBZWV67GyCiQ6agU6wZ2L54dT\na5zMfWP+dW1jQbhpHnMXylI6XTjaqjojwEOeA0lXq7Xmsu1cLFmCb7Ml4dmVIJZC6G2d29/MOu4/\nQFtbFrl5iwgOegp3905nBYNBSV7+MmQyJ8JCX0Is/nP2cN1i1MOqRLBxg4d+vrXxu8Lyn3LYcKaM\n5MXD8XHsFPGCIPBUfgVbaptZ3zOI21w7qyuePjOKkJDFBAY83KUdncHEsBVHqVZ04O9szVf396aH\ne2descloQiwRYzToKS+5xNFTF8nLzsW1Phepvh3/mDj6T5/ZxT3lV34rnJN6uKLXK0g5PQI7uygS\n4tdfFfMGownpb/K+a0uK+H7Z0wyb8yD2YYVUVHyFVGqPt9edVFSuRyZzIi52LXZ2Ud0eX6tRcerH\nD8g8mIpRB56xMOiuufgHTyY7+0nqGw4QG7sGN9c/tngymgTe3JvHV6cuMSzcjY/uikfZYaC8WUN5\ns4ayJg0/XKjEzlLKjwv68crpZRwpP8L82Pk8Hv84IpEIhSKd82nT6RGymIDfvBdm8XzrmK/bZsxc\n42YCWgQ8PCSY58dH/nc7ZeZ3MYvnvzHNzSnk5T9PR0cNdnaRtLXl8q/019n79MwbooO3TIeic8Je\nxqZOReMScqWAhBK0qs71bZUUBttQ4WtFnNVduMY9B9bO/7mT+x2MxnbOnpuERlMKiAgPfw1fn9n/\n+QOd/wr2PH2jtd8tUNXaztD3jnJP/wCWT7o24bHdaGLyxSIuabQc6B2GULOK8vIvGJh0slsP7a3n\nK1i8PZNnR4fx7ekytAYjn92dyOBQN0wmgdOlTWxPq2R/dg0dehPBbja0qzV41lykvzoLqVaFT0Q0\nA6bPIiC20+qtolnDtvMVbD5XQVuH/qpw/pWKim8pLHqN2Ni1XYRrh1pF6YVzFKWmcDkjDUQCcfc3\nYKQGb68Z9OixGJnMiTZlNpmZD6PXK4iKWoGH+7irbej1bVTXbKGyYj0d2mosxOG05sRReDIHmYUl\n/abOwDcqgsy0Zaha6/FwuhejVo5ILCF21NgbJgkCqLQGFm66yC/59dyfFMiLEyK7CH2AE0UN3Lvu\nLA8PCWbx2DBeP/M6O4p2MMx3GFNDp+LY/B0qZRZJA5K72DGaxfOtY75umzFzI2llLaxJLuFQbl23\n66fEe/PRzIT/cq/MdIdZPP/NMRiUFBW9RXXNVoyyJObvncmmef0ZEOLyP28850c4+lZn9NrC7saX\neyTGqImcK3wcvb6Ffn33Ipf/B475B+QXvEJV1QbiYr+gsmojTU1HCQp6kqDAJ/6t/NjfxaCFjxPA\n0b8z7eXfaHvRtgx2Z1ZzcskIXG2vVa6s6NAx5nwBjlIJk3WfMsLBRJ+4z7vsbzQJjP4gGUuZhL0L\nB1HV2s6D35yjuF5Fn0Bnyps11Cg6sLOUMinOmzt6+RLv54hGZ2RNcgnrkgsJU+QyUJ2JSKPA+47H\n2NfmwsnizpLlg0PdeHJkaJd8O5NJz5kz49GpBcICVqJuVdDW0MDljDTKszMwGY3YODnjFiZF7nsG\n94BAwsNf65KvrdU2kJX1KIq2iwQFLsTTcxIVleupqdmO0ajB0bEf/n4P4Oo6EpFITFNVBce//5rS\ntLNdxkJmYYHRYEQwmYgYOIS+U+5EYltHacUuVp4O51SZK8snRXNv/4CbvifLfsxi09lytj8ygER/\nJ77I+oINuRuwFRp51kNLiSSWqB7P0s+rH7Lrnl6YxfOtY75umzHTPRtTy/nq1CWK61Vd1j1ijkD/\nn8Asnv8htLVlgsSL/u+mMTneh7endf+o/j+NUpXPuXNTcXUZSs+en/9nBexvaGw6RkbGXPz8HiQs\n9AVMJj35+cuoqf0BH5+7CQ97BZHojycZ/mlS18L+RTBnDwQNvuXdSxpUjPogmUeHhrB47I35x6db\nVTySXUCdXoK9xMR0T3fu8nQmzs7q6hjuzaxhwcYLfDgjHqMg8HNeHcmFDWh0RgD8nKx45rZwxsV4\nYinret41inZWHCxgZ1o5M6u2IRGMHIu+n+l9A7mzt9/VdJLrKb1wjsNffoqqubFL0T1HDy9C+yUR\n2jcJnfwUxSVv4ut7H6E9lv1umozJpCU//yVqancAIBLJ8PCYgJ/fAzdONr2+30UFqBWtWNs7IEgb\nyCt5DAfHHoQHfcb5vT+QeeQQRp0BhyAlHomNtFk54Re+jSFh3t22dz0qrYExHx5HLhWzb+FgrOQS\n9CY9J8/NQqvO4d06Bxp1ahwsHOjn2Y9+Xv3o79WfIW91nfBjFs83x3zdNmPm5sxYncLZyy03LBOJ\nYFZff6Yn+ponEv4vYhbP/zCe3HyR5MIGzi4bhVz675cNvxXKy9dRVPwWkRFv4+V1J4Kgw2TSYTR2\nYDLpsLDw+FNFVW6GTtdM6tnxyGSO9Pl/7d13eFTF+sDx75veCySUBAih9450REFpXsCOHSuKvVzs\n9VrvxY4NESwo6g9FLCCKKL1Ib6GThIQACaSRnuz8/jgbDCFlQ8om8H6eZ5/snjN79p3NZvLunDkz\nvebh6mr15Bpj2Lfvv8TETqNB6Eg6dnwdFxfPco7moLwseLsrhLa15pA+A3d/uYGluxNZ/tiFBHqf\nmmBu3DKJ5cmZbA95ll+T0si2Gdr5evFki8YMqx/A6HeWk5mbT4ifJ+tikmkY4MnQ9g25sG0Dlu1J\n5LNVMTTw9+SGvhFc26cZ9f1Krve2+FR+XvAX7r9/zMBrJtBn3BWnFrAVWMu6b/+dT79YhrdrLq0b\nCSmNMikIyKRXyKW4hbYjtPcYXNw8SEz6gy1bJhIaejGdO01FpOzPmTGG+EOzyc1JJDz8mhKHp5Ql\nMfE3tmydhI9PC7KyDpKXWUDanvYcXCeYvHwan3eU/lfcWuKY8ZKs3JvEtdPXcOvASJ6+pANp6dv4\n+++xtIh8kPBmd7AifgWLYhexOmE1RzOPApAe9eppx9HkuWzabitVtvUxyVz54UpsJaRZOg7auTR5\nPsf8EXWEWz9bx4wJvRxaXroqGGNj46YbSU5ejfUnf+q0buHh19Ou7fOVOL5h67a7SUpaTO9ec/H3\nP70xKUzgGzQYTedOp8/JW5bsvAJW7E1iUdQRsvNsvHp5Zzzd7D25K6fCb0/C0Geg163gHVT6gWwF\n1tSAAeEnh3lsi0/lkneX86+uYdw+KJLO4YGICDm5SaxYMYCmTSfQutXjpOblM+9oCp/EJ7E7I5vx\n/v58P2cn3ZoGsvlgKm9c1fW0KfGW7E5k+rL9LNuThIebC2O7hnHzgEg6hAWUGN7c/77Awe1bufXt\nafh6u8O272DPbxC9DJOVyk/x7dl3oj5elwwk2c+Ho6aA/YFe5OX4kp/nTUCBYViX9vgdnEwbHy96\n9Zx95jOaVFDswZnExHxEwwajCQu7CptbCy58+VdGpy4j4PAOWow4wojxP+DtHe7Q8Z6Zt40vVsfw\nzR398Ep/guSUNQzovxQ3t38WeTHGEJ0WzZqENTz26emLv2jyXDZtt5Uq3/qYZF5bEMXfMcmUlG7p\nqoTOocnzOSY330bvlxYxpG0ob9fghQe5uUnExc3CYMPVxQsXFy9cXDw5dnwpx44toX+/xXh5lX9a\nvSQJCd+xI2pyibMgFHXgwLvsP/AW3brOpH79wWUeM+lEDot2HGFR1BGW700iO8+Gr4crGbkFXHNe\nU165rIu9Yhkw+xo4sATcfaDL1XDe7f+seliQB9HLYMePsPMXyDgKbUZaS4AHWonccz9u54vVMRTY\nDOFB3ozs1IjO9Rbjk/UW/fouwM+39cm4MgtsPLgzlnlHU/DefBxzOItHR7TjriGlryy592g6M1dE\n8/2GeLLyCk5Z/a+o5IR4Pn14Eh1a+DPcd4m19HlQM4g8n51Zzfhl7lJ2DhrFTx374yYQ7O6GT8Ex\nPPMP4ZriQopPEAn2BWfqubnQL9ifwcH+jAoNJNSjErObnIHCBVt+mHgeWz96nqS4/Zw3oREDhs1w\n6PkZOfmMfHsZjXwOMrHD80RG3k+LyPtKLa9jnitO222lHLc+JpkXftrO5rjUU7Z7u7vy9CUdNIGu\nYZo8n4Me/34L8zYdYv1TF+HtUYVjgM9AVlY8q1ZfSHj4NbRt89wZPP8ga9Zegr9/B3p0n1XmmGab\nLYc1a0djjKFvn/klDt8wxjBnfRzPzNtOVl4B4UHeXNShIUPbN6BPZH3eWrSb9//axyuXdeaa84o0\nVgmbYe002DoH8rOh+SAIbAq7F0BWMrj7QuuLrJlJVr1vTd037Fmrt9rFheSMXH6POsKCrQks25NI\nvg1CfbJ5ZGRvrujZ9JTZUdbsP8YV32/CNSmboMgAfr2pD428Tp9PurjUzDw+XrafqX/u5fq+zfjP\n2E5WT7UxVmK/9iOWrD7IuuPhXD8shIbDJ0HT88hITWHmw5NI9A9m5pjbmNm1FRfW80dE2BEXzf4d\no8i2taFx7mYOejUms9U0Nub4szL5BPE5ebgA/YP8GNswiFEhQdT3KLaCos1wPC8ffzdXvEuYBaOi\n0rLzGPTan/RuHsz0m3qTfjyJzydPxEY64566j6bNT58nPCs9jZ0rltC2/2B8AqyFc1bt2sS2HQ/S\n1D+JCwcvw8Oj9LMKmjxXnLbbSlXM+phkLv9gZYn7zmsezKMj2+s46BpS2Ta7Uv/pRORBEdkuIttE\nZLaIeIlIPRH5XUT22H/qJ6GK/atrGJm5BSyKKnk6nJrk7R1O40aXcejQN+TkVCyeExl72LhpAgAd\n2v+v3IsBXVw8adP6WbKyoomJnX768XLyeejbzfx7zha6Ng1k/n2DWP7oBTw3piODWofi4ebCwxe3\nZXCbUJ6dt52NsUUu5GjcFca+Bw9FwbDnITnGSkhbD4fxX8HkfdYqjkOfgUmroElPmP8IzBwJibsJ\n9vXgql5NmTGhNzPGfMPErnMIrxfCo99tZeTbS1m88wiFX1Rf+iUK16Rs2jYLJKVNACM37GF1ygny\nSxoYV0SgjzuPDG/LxMEtmLU6lunLDlg71n8K31wHxw/Q9/Jr8AkIZPHBhpim52GA3z6eSlZWFnMG\nj+OdjpEMrR9wcnjIG38ksujgCII9tpLt68pFUbuJ3LaRd9tHsK5fB/7s3Zb7IxpyKCePf++Ko8vK\nbVy+cS9XbtrLkLU76bh8G02XbKbLyu1ctnEvVfFl/LMV0aRm5XH/UGsRHv96IYyb/Dx5me78+u5U\ncnPST5a1FRSw8defmHH/HSye+RFfP/Nvko/EEx39IdkJ1xIRkMT0rVfz4oK4UmM7Gr2/0jErpVR5\nekYEc+fgFiXuWxudzBUfrOSrNbE1HJU6E2fc8ywi4cByoIMxJktEvgXmAx2A48aYV0XkMSDYGPNo\nWcfSHoyKKbAZ+r3yB12bBvHxjc7v7MrKimXV6mE0aXIjbVo/5dBzjhxdQFTUZFxcvOnc+T2Cg0pe\n7bAkW7feQ9KxP+nbZyHe3tayytviU7l39kZijmVw/9A23HNhq1Lnwk7JzOVfU5eTl2/46d6BhPqX\ncCGeMdattKWwjbHmyf71cWup8vMnw4AHOXT0B6KiHj15ceWv2w7z34W7OJCUQZ/IegxuE8r/Fu4i\nxM+DxY8MITYvj5u2HiA+Jw93EZp7e9Dax4tWPp608fViVGgQPsV6c202w72zN/LL1gSmXx7BsD9G\nQ6POcOM8cHFlyx8L+X3au4y+fzK2ggIWTH2dv/qO4NIrr+aWJqEnj/N39HGu/HAVky+OZEDIW4TW\nGwoznye7AAIfXEv9QL8i1TXsyMhm3pFkfkpIJsjLjUaeHoR6uBHi4cax3Hw+O3SMLzpHclFIKUum\nO6B4r3NRfy/4mKWfziOybziXPfgRMVs28edn0zgWF0uzTl3oOOQiFs94HyNZRI7cT7N2Q2jT+hne\nXJzMR0v3c33fZrwwphMuRT4XyQnxzHp6Mq+HnD6XuPY8l03bbaXOzFdrYpmxfD97EzNK3K/T2VW/\nyrbZlZsiwXq+t4jkAT7AIeBxYIh9/2fAX0CZybOqGFcX4ZIuYcxaHUNqVt5pszzUNG/vZjRqOJb4\n+NlERNxZ4pLNhYwpYN++14mJ/YiAgO507jwVL89GFXq91q2f4NjxJeze8x+6dP6Qz1ZG8/L8ndTz\n9eCr2/vSt0XZ81EH+Xjw0fW9uOyDFdz95Qa+vL0P7sWHG4iUPfezCHS7FloNgwWTYfGL5O2ax942\nGQQG9qRx4ysQEUZ2bsywDg35ak0sby7azZoDxxHgy9v6EODlTicvd37v3ZbfklLZl5nD3swc9mRm\n89uxVPINdDmYyMzOkYQXGdbh4iK8flVXDqdlk/rTExjXE8jo18HF6rnvdMEwNv82nyVfzCA9K5ND\nDZsyeMylpyTOxhheXbCTBv6e3DywLd4e0wA4dJEbLX69hR++nsK4ic8Vqa4Q7uLKnqVxJOxKpHfX\nMN4e3+ZkD3aezbD4eDpvxhxhWJGe7Yoq3utcVO+RtxO7aykHVsXzxWN3c/RADAENGnDRpOtp0M6f\n1JQlNB+9gwMLmrH/53Z07XgXXl6NeGxkQ1xchA/+2keBDV4aZyXQ6ceT+PzZJ0jPzDmjWJVS6kxc\n26cZ1/Zpxqvzo/hw6elnvj5cup/Dadm6oEotdsbDNowx8cAUIBZIAFKNMb8BDY0xCfZih4ESp4QQ\nkTtEZJ2IrEtMTDzTMM5ZY7qFkVtgY+G2w84OBYDmzSdhs+USW8JwikJ5ecls2nQLMbEfER52DT17\nfFnhxBnAyyuMyOb3kJS0iIc+f5/nftrBoNYhzL9/ULmJc6EOYQG8dnkX1kYf56Vfoiocw0l+DeDK\nT+HKz9gbcIj8vFTaZbTGFFgzfLy9aA+3fbaO13/bRUpmHgATBjSnbaN/Zsyo5+7G+Mb1ebJlGDM7\nR7KsT3sODO7KzE7N2Z+Vw/B1u/k79dQeCi93V2ZemM/lLkuYyb+IcWlycp+LiysXTLidE8eTyM/N\nxefqW3mkxakXcy6KOsr6mGQeGNbmlHHzYX0uI9q/J4MOTWfznuiT2zcfTGH0O8tZvjeJYe0b8uPm\nQ3y87J9G391FuC+iARvSMlmSbA2ryMkvYO2B4w4P5UjLzmP68gMMa9+Azk1K7r0edefrBEZkk3Tw\nAOF9U2j+r6UkFjzJ9u33ERc/i1adL+P6lz/Av35Dvnv5GfasXYmIMHl4W+65oBWz18byxNytnEhJ\nYdrjj5KZlsbe7tc4FJ9SSlWlx0a1L3UYxw+bDvHA1xtrOCLlqMoM2wgGvgOuBlKA/wPmAFONMUFF\nyiUbY8oc96yn/yrOGMOQKX/RNNiHWbf1cXY4AGzf/hCJSb/Tv98SPDxOXco7JWUd23c8RE5OIu3a\nPk9Y2FVn/Dp7j55gyq/bGBD0EJ5uBZiQWVzVu9UZ9Xa+8NMOZqw4wKQhLXnwojYne6CNMRU6XkrK\nOtZvuJqIzDBardvCId+O3HB8AvsJp00Df3pEBNG9WTA9mgXTqoFf+Qe0252RzU1b9xOXncdrbZtw\nbWP7l4OCPPhoMPlZqQw68SpevgG8Pb4bXZpYf3q/JKbwwZezaNOkCVMuH4tLkboU2Awj3lpKgc3w\n24ODT5u1IzNmA14zL+R7r0u5dPIMvloTwws/76CBvxfvX9eDLk0CufurDfy67TCf3nweg9tYPdo5\nNhv9VkfR1MuDz9pGMHHWetYcOM6UK7tyRc8mlKdwho2f7hlYavIMcPjwAg7FfY9vQFO8vZvi7RWO\nl1dTvL2bnJyKLis9jbmvPc/hvXvoOGQonr5+uLm7syYmjeUHUuiYcwD/rCTSBk3gmYljaPvUr6e9\njg7bKJu220pVjdJ6oAHaN/LnxUs764WEVcxps22IyJXACGPMrfbHNwJ9gaHAEGNMgog0Bv4yxrQt\n61jaCJ+ZN3/fzTuL9/Dh9T0Z3rHiPbhVLSNjL6vXjKB5xJ20bPkIADZbLvsPvENMzEd4ezWhU6e3\nCQjockbHP5qWzdt/7OHrvw/i7e7KQ+enEsHj5U5DVshmy8WYglPmLs4rsPHk3K18uy6OTuEBTLms\nMR65Czh06GtcXX3o1PEt/P07lnPcPNb+/S8K8jPo2+dXopd9R72/HsfPJZfcK7/At8OIM6pvoZS8\nfCZuj2FJcjq3NQnhuZbhuK1+z5qfevxXrPPqx22fryMlM49h7RswekAED8Ufpr2fF993a4VXseT4\n23UHmTxnC+9f14NRnRuX+JoHZ0ygQcxP3Bn4IX8e9WFI21DevKobwb7W8JGMnHwu/2AlCanZ/HjP\nACLq+wLwSVwiT+6Jp/meExyLSaNRoBe5+TYWPzwEX8/SR4mVNdb5TOXlZLPwg7eJ2bKR/Pw8CnLz\nMMaaozxfXAkYdQt33jAGEdHZNs6AtttKVZ31Mck8NXcrUYfTT9vn6gLfTuyvCXQVcmby3AeYAfQG\nsoBPgXVAM+BYkQsG6xljJpd1LG2Ez0x2XgHjp61m5+E0vpN5FWIAACAASURBVJ3Y72SvozNt3XYv\nx44tZUD/JeTkJrJj+8Okn9hO/dDLefavYbRs0IBbB0XSMcyxi8qMMWyITeGLVdH8sjUBY+C6Ps24\nd2hrQvw82brtPo4e/QV39/p4eoTg4RGKh2cIHu71KbBlkZNzhJycw2RnHyYv7zgAfn5tCQzoTmBg\nDwIDu+Pt3YzfNvxM1P7P6RC8BVcXG8HBA8jM3Ede3nHatnmBsLArS4nPxv4DbxMdPZUuXabh438+\no95ZRpDtON8HvIlr0i5rWEc7xxOxkuTbDC/sO8S0uET6+7nz3pJraBzWHq75GkRIz87js5XRfLg6\nhqRuQXi5u/J5m2YMjrB6qm02Q06+jRM5+YydupzQAC9+mNS/1N51kxpPzlvdWZnfgV2D32Xi0FMv\ntAOIPZbJv6Yup2GAJ3MnDcDX042/Y48zNioa14w8vu3aCg83Fy7/YCX3XdiKhy4u/Tt04RmA8nqd\nK8tWUEBBXh45BTb8fH1ObtfkueK03Vaq6j3w9UZ+2HTotO0Xd2jItFowQcDZwqnzPIvI81jDNvKB\njcBtgB/wLVYSHQNcZYw5XtZxtBE+c4npOYx7bwW5BTbm3T2AsKCaWRGuNCdO7GLN2lEEB/UlNW0j\nrq6+tG/3Ep9vjODdxXvx8XAlM7eA/i3rc/ugFpzfJvS0pAwgK7eAnzYf4rNV0Ww/lIa/pxuX92zC\nhP7NaR7ie7JcXl4qcXFfkJ2TQG5ukv2WSG5uEq6uPnh6NrTfGuHp2QiMjdS0TaSmbqSg4ARgTYFn\ns+Xg6hbMluMDmbW5G23C2/PKuCYkHnyM5OSVhDW+ijZtnju5bLjNlseRIz8SHfMRmZn7aNBgFJ07\nvctTP2zlyzWxfH17X/o0doFZl1tzSF8+HTpeWun395uE4zwWtQ+v/CzeaN2IkZH/XFiXXWBj3IY9\nbE/Pwm/DMbKSsgnycSc7r4DsvFNXhfzq9j70b1n6hZ0AOcvexfOPp6B+KxgzFSL6nVZm2Z5Ebpqx\nlos7NOKKnk24d/ZGXFr6cyzClx+7t+K8ID/um72RhdsPs/iRIYSX8PlctOMIt32+jhv7RfDC2E5n\n+M5UjibPFafttlLVo6QE2s1WwPJvH0GGDqXhlJchWHuhK0MXSVHsPpLO5e+vJDzYmzl39cevjNPj\nZTHG8PuOI3y4ZB8tQv347+VdSkxsy7Nl6yQSExdSv/4FtG/3ClkFgQx67U8GtQnhlcu6MHttLJ+u\niOZwWjatGvgxpE0oadl5JGfmkZKZS3JmHgkpWWTkFtCmoR839mvOpd3DyzztX/G6FpCRsZfU1I2k\nn4giKLAnDRoMR8SD2WsP8p+fd+AiMGlIJMOa/kjcwQ/x9+9Ixw5vcDx5JbExH5Odcwg/v/Y0j7iT\nBg1GsmzPcW6csZbbBkby1CUdrBfKToOvroKDa2Dch9D16soFvnshe+c+zKTz3mcLAdwYVp/nWoXj\n7SLcGxXLnCPJfNKpOYP8fflqTSwJKVl4ubvi6e6Kt7srXu4utGrgx6DWoeW/FsC+P+Gn+yAlFnrf\nbi0M43nqUtYfL9nHpwuWcQJvmoWHM/WGHozatp8u/t7M7tqS+JQsLpzyFyM6NTptVcxDKVmMemcZ\nYYHefD+pP17uzln0R5PnitN2W6nqU3wcdFBWGn9PvYF8F1dc3VzxeOpJePBB8PEp4yiqNJo8K8Dq\nAZww828GtQ5h+o29TrkILCMnnzUHjpGWlU/nJoFE1vc9JSm22Qy/bj/Mu4v3EpWQRn1fD45l5PLA\nsNY8MOz0KcPKk5t7nLS0zdSvPwQR4Y3fdvHO4r38+sAg2tlnmcjNt/HL1kN8svwAu4+cINjHnWAf\nD4LsP0P8PBndpTF9Iuud8bRnlRF7LJOX5u9g4fYjhAd58+TQY/hmvUR+vjUeLTCwB80jJp2sY2pW\nHsPfXIqflxs/3zvw1CQwNwNmj4cDy+Bfb0PPmyoWjDEQuxpWvG2teBjShtw7lvHaweO8F3uU1j6e\nDAr2Z0Z8Eo9GNuLB5lU8/j3nBCx+EdZ8CIFNYOR/wc0T4tdD/HpM/HokI5GjHk3xvX81vr5+vBtz\nhJf2JzC/Z2t6BPjy+m+7eHfxXr6f1J8ezawek/wCG+OnrSYqIY2f7h1Ii1DHL6Ssapo8V5y220pV\nr6/WxPLMvG0U2AzNkg8xf+Z9+OZlA5Dj4YWnjxe8/DLcdhu4O3fK2rpGk2d10ldrrGm4bugbwWU9\nwlm+J4lle5PYGJtMXsE/v2d/Lze6NgmiW9MgGgR48sWqGPYcPUGLEF/uvqAVY7qF8dh3W/luQxwf\nXNeDkaVcVAZWAuTqIqUmuKmZeQx8bTEDWoXw4Q09q7zO1W3lviRe/DmKHQlpXNAql1u7/02HFmMJ\nDjrvlDo/9M0m5m0+xNxJ/Usee56XBd9cD3sXwXl3wID7rUS0LDYb7JpvJc1xa8G7HvSZaD3fx5rN\nZOnxdO6NiuFIbj7jGgTxQYeI6vuyEbsGfrwHknbbNwiEtIEmvcC/ESx7HYY8AUMe5UR+Ab1X7aBX\noC9fdGlBRk4+F0z5i7Agb+bax1pPWbiLqX/u5a2ruzGue3j1xOwgTZ4rTtttparf+phkvtsQx/Z5\ni/hi9lME5Gaesj/P2wf34CB480244orSF/ZSp3D2IimqFrm2TzOij2Uwbel+vlgdA0DHsABuGRjJ\noFahhPh7sOVgKpviUth8MIUPluyjwGZo3cCPd67pzujOjU+uyvfSpZ3Yn3SCh77dTER9XzqEBZz2\nevO3JvDUD9sY1DqEN6/qVuIQjxkrDpCek899Q1tXb+WrSf+WIfx070DmrD/I/xbu5vr/G4CfZwqR\nIStoGep7srf0+43x3De0dekXbbp7W8t8L5gMf38C62ZaQzgGPAghrf4pV5BnDfHYvRB2/gzH90NQ\nBIyaAt2uA49TT9ENrufP4t7t+CUxhSsbVXMvfbM+MHEZRP1kzW8d1g28ilzcd/yAlUB3uRK/ei24\no2korx04zPLkdAYG+/Pv4W3595wt/Lj5EPV8PXjvr71c1auJ0xNnpZSqrXpGBNMzIpivt6/BlNC+\nu2dlQlYm3HILPPMMTJ0Kw4Y5IdJzi/Y8n2VsNsNnq6Kp5+vBgFYhhPiVsPS0XVZuAXHJmbQM9Ssx\n8T2als2YqStwdRF+vGcA9e3HSs3K49l52/hh0yHCg7yJT8ni5gHNeeaSDqckb6lZVq9z/5b1+eiG\nut8pdyInn3mb4tlz5AT7Ek+wPzGD+JQsADqFBzB30oDTVyosSXIMrHwXNn4B+TnQcRy0GGKNL973\nJ+Skgos7RPS3hni0HwuudeB7bloCTO1tJdnXzSGjwMbw9btJzy/gj97tqOfmypj3lpOUnku+zUaQ\njwc/3jMAHw/n1017nkFERgBvA67AdGPMq2WV13ZbqRr0zTdkTbgV7+ySl/Q+ydcXOnWykuhedbpJ\nqlba86xO4eIi3Dwg0qGy3h6utG7oX+r+BgFeTLuxJ1d+uIq7vtzArFv7sC76OA//32aOpudw/9DW\n3HNhK16eH8XMFdE0CvBi4vktTz5/5ooDpGfX3V7n4vw83biuT8Qp2zJz84lOyiQ82NuxxBkgOAJG\nT4HzJ8Pq92HtdNg+F/waQYcx0Ga4lUx7lv67qZUCGsMFT8DCxyHqR3w7jOWjjs0ZtX4390bF8GWX\nFjxzSUeu+mgVnm4ufHlb31qROCsQEVfgPeAiIA74W0R+NMbscG5kSikAkpPxFlv55TIysK1ZS26/\ngezv1Iupl0wiKbw5rRr6E+DpxqKdR0lMz8bVRegUFogBOjYOID0nnw0xycSlZBLo5c4lXcL4YWM8\nR9JzcHMVXARsBlxECPXzoFfzemyLTyU1Kw8j4OXqgr+XO0kncsjJtxEe5E3TetaZ0l2H0zmano2P\nuyt5NoO/tzv/6tyY9Jx8jqbnIMDB45kcScsmwNsdN1cX8vJt5OQX0CjAi5SsPLo1DcLH042Ve5OI\nS84EBJvNYAMa+Xsyrns4i6KOkJVvI9DLjdx8G/V8PUjPzudIeg4N/T3x83IjOSOXer4euAU2bFaZ\nX4f2PKtyzdsUz/1fb6JD4wB2JKTRIsSXN67uRrem1hAFm81w79cb+WVLAm9e3ZVLuzchLTuPga8u\npk+L+nysc1OWLSsF0hMgpG3dH69WkA/ThkDmMbhnLXj682l8Eo/tjuOpFo25J6Ihnyw/QGSIDxe2\na+jsaE8613ueRaQf8JwxZrj98eMAxphXSnuOtttK1aBXXoGnn4aCAoefki8u5Lu6Mb/tAF47/yaO\n+Jc9Pem5JOGzB8hJ2HPG4xy120eVa2y3cHYfSee9P/dxU78IHhvZHm+Pf2aTcHER3riqK8dP5PLv\n/9tCfV9PNh1MIS07n/vPkl7nauUdZN3OBq5ucMkb8MlFsOQ1uPhFbgqrz/LkdF49kEDfID9uHejY\nmRFVo8KBg0UexwF9ihcSkTuAOwCaNatUx41SqiISEyuUOAO4GRtu+bmM2/4XjdMSuebaMkdiqQrQ\n5Fk55JGL2zKhfySh/iWPofZ0c+WjG3ty1YeruGvWelxchGHtG9IpvPpWi1O1VNPzoMdNsOp96HoN\n0rAjr7dtypb0LCZuj+aP3m0Jctempy4yxkwDpoHV8+zkcJQ6dxw5UuGnnHD3psDFhem9xzGr+6hq\nCOrcpf/BlENEpNTEuVCAlzuf3XIel72/kviULO11PpcNe86alePnh+DmBQS6u/FRx+aM2bCHB3ce\nZEan5k6Zv1uVKh5oWuRxE/s2pVRtkJjoUDEbQpa7J4mBISy7+k5+aNUfVy9PRuqY51PGPM/NSnfs\nDS2FJs+qSjUM8OLbO/sRdSiNzk201/mc5VMPLv4PzLsb5j8Co6bQPcCHJ1s05rl9h3h5fwKTIxvj\nfgYrWKpq8TfQWkQisZLm8cC1zg1JKXXSsWNl7/fwABcXXC64AN8nn8S3f3+ai3BDsWKPjWrv8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "idx = -1\n", "\n", "fig = figure(figsize=[12, 4])\n", "ax1 = fig.add_subplot(121)\n", "plot(ts, spath[:20, :].T, label=None)\n", "axvline(ts[idx], lw=5, label=None)\n", "plot(ts[idx], k - b_b[idx], 'r>', ms=15)\n", "xlabel('Time', fontsize=16)\n", "title('Stock Paths', fontsize= 18)\n", "\n", "subplot(1, 2, 2)\n", "plot(spath[:500,idx], cvs[:500, idx], '.')\n", "xlim(40, 120)\n", "ylim(-10, 60)\n", "plot(k, 0, 'r>', ms=15)\n", "xlabel('Stock price $s(t = %g)$' % ts[idx], fontsize=16)\n", "title('Payoff $v(t = %g)$' % (ts[idx]), fontsize=18);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## One step before of maturity" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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X7BwcHLhx4wZKKVq3bs2WgppvM9ySmJgYUlNT8fDwsJnv4uKCi4tLhjRXV1eG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\noUOHcixnnz59mDFjRvoGj9b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9xTKUEH788Uf8/Pzw9vbmiSeeICUlhbi4OJo2bcqZM2dI\nTU2la9eurF69OsvyAK6urrzwwgu0adOGLVu2pNcfExODn59f+ufY2Nj0gAOTJ0+mffv2eHh4MGbM\nGJTKvFQF3N3dOXPmDKBdNAMCAgC4fPkywcHB+Pn54ePjw9KlSwvl/hRXzFDbYCgi4uPjOXnyJPff\nf3+JCcF37cjfqORUXJpXxamOK3+v/JPLEaeocm/p2Nly7dq1HDp0CCcnJ1q0aGFvcfKEUsoYVEoR\nZV1d+SY6mjYDB/LC0qV0dHdn2bp1NO7YMUO5LVsgLAwCAiBTlsHOPPfcc0RGRhZond7e3kyfPj3L\n/OjoaObOncvmzZtxcnLiySefZPbs2YwYMYJXXnmFcePG4efnR6tWrejdu3e25dNmbT/88MMMbbRo\n0YLr16/z559/0qhRI+bOncuwYcMAePrpp3nzTT0599hjj/Hrr7/ywAMP5OjapkyZQo8ePZg1axYX\nLlzAz8+Pu++++7ZZoG86cIOhiNi6dSvlypXDy8vL3qLkmKQD5xEnB8o2roxjRWdcmlfjyq5TqJSb\nrR0ljeTkZGJjYwFYsmQJ58+ft69AJRARcRSRXSLyq+VzNRFZIyIHLa9V7S1jSUQcHHh2yRJWTZ7M\n8aQk2nfuzLqZM9Pzt2yBnj1h4kT9amW0NNymhIaGsmPHDtq3b4+3tzehoaEcOXIEgFGjRnHx4kVm\nzpzJtGnTblne0dExy23thw4dyty5cwEyKOLr16+nQ4cOeHp6sm7dOvbt25dj2VevXs3UqVPx9vYm\nICCApKQk4uPj83wvShrGIm4wFAHnz58nJiaGzp074+zsbG9xckzSgXOUbVwZcdI+ghV83UiKPkfS\nH+co17JkLDbNiri4OG7cuME999zDunXrWLBgASNHjqSM8cnNDc8C0UAly+dXgVCl1FQRedXy+RV7\nCVfSuXviRMJ9fOg3YAC9x41jekQET331FWFhwvXrkJIC169ry7ixihcfsrNcFxZKKQIDA3nvvfdu\nyrty5QoJCQkAJCYmUrFixWzLu7i4ZOkXPmzYMIYMGcLAgQMREZo2bUpSUhJPPvkkERER1K9fn0mT\nJpGUlHTTuWXKlCE1NRUgQ75SioULF9K8efM8XXtJx1jEDYYiIDw8HID2JShGcPKZq9w4m4RLi2rp\naS4tquFQwYkrESXfb/XQoUM4Ojri4+ND//79OXbsGKGhofYWK9+IyBiLlfqKiKRkPgqwnXrAfcDX\nVsn9ge8s778DHiyo9m5Xmtx/P1v27+e+KlV45ptvGO3nR6eOSTg7g6MjODtr9xTD7U3Pnj1ZsGAB\np0+fBuDcuXPExcUB8MorrzB8+HAmT57M6NGjb1k+O5o0aYKjoyPvvPNOujU8TamuUaMGiYmJWUZJ\ncXd3Z8eOHQAsXLgwPb1Pnz7MmDEj3a98165dub7+koxRxA2GQub69evs3LmTVq1aUblyZXuLk2OS\nDpwDwKXZP94F4uhAeZ87uBpzjpTLJXtb7kOHDtGwYUOcnZ1p1aoVfn5+bNmyhZiYGHuLlmdEZAQw\nAwgHXIBvgR+Bi+jt7ScXYHPTgZeBVKs0N6XUCcv7k/yzo6ctWceISISIRPz1lwmLmR2VmjZlcUIC\nb7RqxTcREbw+tAELZsfzzjsQGmqs4QZo1aoV//d//0fv3r3x8vKiV69enDhxgt9++43w8PB0ZdzZ\n2Zlvv/02y/I5YdiwYfz4448MHToUgCpVqjB69Gg8PDzo06dPlgant956i2effRZfX98MFveJEyeS\nnJyMl5cXrVu3ZuLEifm/ISUIsbWytSTj6+urIiIi7C2GwZDO1q1bWbVqFcHBwTRo0MDe4uSYv2ZF\nkXI+iVov+GZITz55mVPTd1L5/sZU7FLXTtLljwsXLjB9+nR69+5Np06dAB3j/ZtvvuH8+fOMHTuW\nKlWqAHon1D///JPY2FjuuOMO/P390+txf3U5ALFT7ysw2URkh1LK99YlbZ67E1gGvAMkA75KqZ0W\nX+0w4Cul1KcFIOP9wL1KqSdFJAB4USl1v4hcUEpVsSp3Xil1Sz9x02/nEKWYP2wYgfPnU93ZmaUr\nVtC2Z097S2VAL5Zs2bKlvcUwFDK2vuf89NlgfMQNhkIjJSWF3377jQ0bNtCgQQPq16+f57qUUkUa\naSX1egrXjlzA1b/OTXlOtSrgVNeVKztOlVhF/NChQwDceeed6WllypRhyJAhfPHFF8ybN4/69etz\n5MgR0qy1jo6OpKSkULVq1eLsy9gU2IC2UqcCzgBKqfMiMgWYAuRbEQc6A/1E5F605b2SiPwInBKR\n2kqpEyJSGzhdAG0Z0hBhyLx5NH3/ffq/+ipdevVi1vvv89BLL9lbMoPBkEeMa4rBUAhcuHCBkJAQ\nNmzYgLe3N8OHD8+TIn3+/HnmzJnDv//9bxITEwtBUttcO3wBbihcmts2ZlbwdSP5xGWuHys6mQqS\nQ6xN4j4AACAASURBVIcOUalSJWrWrJkhvVq1avTr14/jx4+zY8cOKlasyN13383o0aN55ZVXqFWr\nFosXL+bChQt2kvyWXAXKKD3VeRKwDlifCNw8ssoDSqnXlFL1lFLuwEPAOqXUo2hrfKClWCBwewUE\nLiK8X3mF8JUr8S1Thodffpl/PfRQ+iI4g8FQsihSi7iIzALuB04rpTwy5b0ATANqKqXOWNJeAx4H\nUoDxSqn/FaW8BkNe2LdvH8uWLUMpxcCBA/MUrjA5OZnNmzezadMmQLtNREVFZXCLKEzSwxY2su3T\nXr5NTS78eoQrO07hXNe1SGQqKFJSUjhy5AgeHh42B0etW7emTp06VKxY8aYIKkOHDuWLL75g/vz5\njBw5sqhEzg17gWbAamAj8C8R+RO4gd7Mp7Ad4KcC80TkcSAOGFrI7d223NG3L2ujoxnfoQPvzZ3L\n3qgoZm/eTKXKlU2McTtR1DOXhqKlsFy5i9o1JQQ9Lfq9daKI1Ad6A/FWaa3QlpbWaCvOWhFpppQq\nsFX/BkNBkpqayooVK4iIiKBu3boMGjSIatWq3fpEK5RSxMTE8L///Y8LFy7g4eFBr169+Pnnn9mz\nZ0+RKOJKKR228M4qSBnbk2YO5Z0o17o6l8NPknT4Aio5FZWcgrqeikpRVO3XhAp+tQpd1rxw9OhR\nrl+/nsEtJTNVq9qeCahWrRr9+/dn3rx5rF27Nsvzz5w5g4hQvXqRh3j8EmhieT8RWAtssny+RCFE\nMVFKhaH9z1FKnQWM03IR4dykCTPj4mjTuTPjd+/G392dt/+7mcBRrbh2DRwc4L//hTFjbl2XUd7z\nh4uLC2fPnqV69epGGS+FKKU4e/YsLi4uBV53kSriSqkNIuJuI+s/6NX31tOY/YE5SqlrwJ8icgjw\nA8zWBYZiydGjR4mIiMDPz48+ffpkGYf1/9k77/CoyrT/f57pyWTSKwkhhBYChAChSZUmomBBLL91\nRV07rLrquyu6rrpNt/m6u+qrqGAvKAoIKL0nEGqAEAihpfc6yfR5fn8MCYQUEggJ6vlcV66ZOc85\nz3lmGGbuuc/3/t6tsWzZMtLS0ggJCWHu3Ln07OnpYDlo0CDWrVvX8EF/JXGWWHBV2DBNaF3TbprY\nHWl3I9QCoVUhdGqEVoU1s4LqLTl4J4UhVFffF1JWVhZCCGJjYy++czPEx8czcuRIdu7cCTR2Bygp\nKWHr1q0cPnyY+Ph45syZ0wErbjtSyi/Pu58lhBgAjAa8geT6q40KPyGMRh7dt4/+d9/NbZ9/zgO/\nHIzG/QUWZuN2w/z5MGhQ68F1fYMgu91jh6g4sbSfqKgocnNzURyAfroYDAaioqI6fN4uL9YUQtwE\n5Ekp0y74FRkJ7Dzvce7Zbc3N8RDwEPCjcqVQ+GmRkZGBWq1m0qRJFw3CbSerKF9yDOPwcEwTohAa\nFVlZWaSlpTF69GimTJnSaI76QPzQoUNMvMKmwQ22hS3ow+vRdfMh+N4BTbbXpRVT/vkxbFmVjawP\nrxaysrLo3r37ZWU2pk6d6mmQccLzuLi4uCEA12q1jB49usGNpTMRQqjPv2oopazFkxVX+CmjUjHx\ns8/YPXQoN/3Pb0nnNoJZQCl/weUSF234s3kzSoOgy0Sr1TYkThQU2kOXFmsKIbyB54A/XM48UsqF\nUsokKWXShcVXCgqdgZSSjIwMevXqddEAz1XroPyLo7gtTqrXnaHo3/uoO17OmjVrCAgIYPLkyU0C\neV9fX2JiYjh48OAV06nVYz1WgSbMG03ApQWqXgOCUfloMafkd/DKLh+z2UxhYWGrspS2oNFouO22\n2xoev/XWWxw7dowxY8bwxBNPMG3aNHx8ukQ7ny+EeF0IMawrTq7QtfR85hmS165hpkZHKa8QwXR0\nOmujhj8pKfDKK57beiZORGkQpKDQRXS1a0ovoCeQJoQ4DUQB+4QQ4UAecP618aiz2xQUrjry8/Op\nqqq6qI+slJKKrzJx1ToIeSiBoPsGIF2SHR+soaSkhMnjrm2xxXpCQgLl5eXk51+5ANdV68B2quqi\n2fDWEBoVxuHhWI+W46zwdFzbunUrH3744RX/EXExTpzwpLAvNxCHxjrysWPH8uSTTzJ16tSuCsDr\nWQrcDaQKIY4IIZ49W4Oj8DPBZ+pUvjmWwfMBoRSwlriA/vTo4fnMqJegvPCC57Y+GB892iNHURoE\nKSh0Pl0aiEspD0kpQ6WUMWdtsHKBoVLKQjw2WHcKIfRCiJ54/HFTu3C5Cj9DLBYLn3/+Oenp6a3u\nl5GRgRDiov7S5h35WI+W4zejJ7pIH7z6BeL/aDz7vM4Q7vbHf4WZ6g3ZOIrrmhzbv39/1Go1Bw8e\nbHF+l8tFXV3TY1vCbXFiySijcvVJit7YT8FfdoJL4hV/eTp040hPoWZtaiGnT59m48aNnDp1iuzs\n7IsceWXJysrCaDQSHt6xhaRTpkzBaDR26JyXgpTyMSACmA1kAC/iqbHZJIS4Vwhh6tIFKnQKqthY\n/nz6OEuHDuV4wWmG9+1LanJysxKUekaPhgULlCBcQaGz6dRAXAjxOZ5iy35CiNyzFlfNIqVMB5YA\nR4AfgHmKY4pCZ2Kz2fj00085duwYa9euxeVq/u1XL0uJiYnB29u7xfnseWaqvj+FoX8gPtecs3Pe\nvjMZi9PKjNtnoe9u8shVXttL4Wt7qVp7Gnu+GSklXl5e9O3bl8OHDze7FiklX3/9NW+++WaLa63H\nZbZT+vER8v+YQtmHRzDvyEdoVJgmdifkkQT0Mc3bFrYVjb8BQ/8gKlJz+PabbwkICECn03HgwIHL\nmvdycLvdZGVl0atXL1Sqrr4YeOWQUjqklMuklLOBcOAxQA28B7Sth7XCjx9fX25NTSV57lx0tbWM\nHzcOW8Xb7ZKgNCdjUVBQ6Fg62zXlrouMx1zwuL4TnIJCp+JwOPj888/Jy8sjKSmJPXv2cPToUQYM\naFqcWFJSQllZWYvWgm63G7fNSfnnR1EbtQTc1rfB3qq8vJydO3cyePBgogfGwkBwVtmwppdhOVxK\nzaYcajbmoA33JvjBBAYNGkRGRganTp1qIq/YvXs3GRkZAJw5c6ZFVxBLRhkVS4/jtjoxTYhC3ycA\nfbQJoW2/y0tr+IyK4IfjW6l2V3P//fezd+9e0tPTuf7669HpdB16rrZQUFCAxWLpEFnKjwUpZZUQ\n4nsgCE9zn4guXpJCZ6JWk/DBB+weMoQ5v/kNL//jUX554276jVrIpElqxUlFQeEq4KebFlJQuESc\nTidLlizh9OnT3HzzzcyYMYPAwEBSWkgL1Qe/cXFxTcZqa2tZtGgR//rnvzhQmYnvnF6ojdqG8fXr\n16NSqZg8+Zz1ssZPj8813Qh5KIGI50fif3NvHCUWqladpE+fPuj1eg4dOtToPAUFBaxZs4aeET1Q\nCxVHUg7itjXOirvtLiq+PU7Zh0dQm3SEzR+C3/SeGHr5d3gQDnDclkuWupBh3v3o3r07iYmJ2O32\nhters6lva9+rV6+L7PnjRwhhEkLcL4TYBJwCfo+nwc/Mrl2ZQlcQ/MQTrF2/nnl6PR+vXMT25aPp\n379pd9jzM+CtyVgUFBQ6DiUQV1A4D7fbzbfffsvx48e58cYbGTx4MCqVipEjR5Kbm0tOTk6TY44c\nOUL37t0xmRrLbysrK1m0aBGF+QWYHAZ2ajJZuPJj9u/fj8vl4syZMxw5coQxY8bg6+vb7HrUPjp8\nRkVgmhBF3b5iXKfMxMfHk5GRgd1uBzwSmq+//hpvgxfjCmOJcAaQeewYeX9MpuTdg9RszcVypIzi\n/+ynNrUQn/FRhM5LRBt+6Zpmu93Ozp07Wbp0KVlZWU2KMKuqqli1ahURviEklEVgL6glOjqagICA\nLpOnZGVl0a1bt6tCy32lEELcKIT4Ak97+3fPbn4ICJdS3iWlXN11q1PoSrSTJvHGkSO8ExHB+t27\nGRkXx7FjxxrGLyzkDApSnFQUFDqDLvcRV1DoCmw2GzU1NU22b9++nfT0dKZOnUpSUlLD9sTERDZt\n2kRKSgrdu58zoSgvL6eoqIhp06Y1mqe4uJiPP/4Yu9XGdFsi0dHR1Ez2YcPGDSxfvpwdO3YAYDKZ\n2uQ37TspGsuhUiq+Pc7AWwayf/9+MjMzGThwIKtXr6a8vJxZ/mPR12gZOHEIP2xbj2OwD9psB1Wr\nTwGg9tMT/MAgDL38L+k1A0/xampqKjt37sRisaDT6Th06BDh4eGMGTOG+Ph4hBAsW7YMl8vFrbff\nhu3tLGp35hNwSx8GDx7M5s2bqaysxN//0tfRXvbu3UtOTs4V92C/ClgBHMMj6ftEStm11bEKVxex\nsTx09ChR11zHvek7GT4wgS+++ZoZM2c2yYCXlXnkKEq3TQWFK4sSiCv87HC73bz//vsUFxc3Oz5h\nwgTGjBnT8NhZYUVn0jFs2DCSk5OpqKhosK6rl1mcb1uYnZ3NZ599hkaomWEZSnh4GMFzBxBq0BDb\nK5ajR4+yceNGSkpKuOWWW9qklxYaFQGz+1Dy9kECj3kC+IMHD+JyuUhLS2NU5GBCTugIuKs3PjF6\nfti2nvywWsbOHouzyoYjtwZ9rD8qr9b/y9tsNlJTU1GpVHh5eWEwGDAYDOh0OjIyMti9ezd2u50+\nffowbtw4unXrxsGDB9mxYwdLly5l48aNREVFcerUKWbOnElIVBjlg6uo21+M3/U9GwLxtLQ0JkyY\ncNHnfblIKdmyZQubN2+md+/eXdJkp5MZIaXc09WLULj6qJebBAX58tSJ7TzFI6x0vseNs2bx6ksv\nMWHqH9DpRIMmvD74vlgAXj+vEqwrKFwaSiCu8LMjMzOT4uJixo4dS2hoaKMxo9HYUOQopcS8I5+q\n1Scx9A1kxC0jSElJYdeuXUyfPh3wBOIRERENgXlmZiZLlizB19vE1KoBBAT4E3zfAFQGz381IQT9\n+/enX79+lJSUEBYW1uZ162P8MI4MpzY5n/ikfuxO38fp06fpHtKN+BOBGEeG4z3Y83zCw8PJzMxk\n7NixaPz0aPz0bTpHcnIyW7ZsaXZMCMGAAQMYO3ZsI/u/oUOHkpiYyLFjx9i+fTuHDh2iX79+DB06\nFACf0RHU7S2ibl8xAdd0IyYmhgMHDjB+/Hgu6KbbobjdblavXs2ePXsYPHgws2bNumjH0x87ShCu\n0BznF14KAW63mj/xLnMZSm8xj9+99BL/b88eVq9eQkqKV5uDaqWgU0Hh8lECcYWfFVJKtm3bhr+/\nP9dee22LgZnb7qLim+NYDpSgCfXCerQcr8wgBgwYwL59+5g4cSI2m43c3FwmTZoEeNxTvvjiC0KD\nQpha1h9vL2+CHxiE2qdpxlulUrUrCK/H7/qeWDLKiT5tZJfbjVqlYlxpH/ThJvxvPOeS0rdvX7Zt\n20ZdXV2rlornY7FY2LlzJ3Fxcdxyyy1YLBasVitWqxWLxUJYWBiBgYHNHqtSqejfvz9xcXEUFhYS\nHBzcEGTrokxoo3ww78zHODqCxMREli1bRnZ2Nj169Gj3a9AWHA4H33zzDRkZGYwZM4YpU6Zc0aBf\nQeFq5nzZiUrl0X0LAUt0j7LrH/Ek/s/1/H7lSjIzE/l2wwaioqIaHd9S1ru5gk4lEFdQaB9KsabC\nz4ozZ86Ql5fHmDFjWgzCnWUWSt46gCWtBN/rehD25DD0sX5UrjzJiAHDsNvt7Nu3j6NHjwLnZCkb\nNmxAo9YwrXIAXioDwQ8ManMmuq2oDBoCbuqFb4ma4VGDmOaVhNGlJ/AXcY2cT/r164eUkuPHj7d5\n7l27dmGz2ZgwYQJ6vR5/f3/Cw8OJiYmhf//+LQbh5yOEICIiAq1W22i7z8gInMUW7Dk1xMfHX1FP\ncavVyieffEJGRgbTp09n6tSpnR6EV31/irqDJZ16TgWFlji/hb1eD2+8ca6L5qB5E3guPZ3l0dEc\nzcwkKT6+wSEqJQUefdRz/IXdOC+cVynoVFC4NJRAXOFnxfbt2zEajSQmJjY7bjlaTtF/D+CsshN8\n30B8r41GqAQBt/UFCYZt1fTo0YNdu3aRnp5OcHAwISEh5OTkcPToUQYTg96hJfhXg9AGe12R5+A1\nIBjvgcEMzgolpEBPwK290YY0znpHRETg4+PTyBWhNaxWKzt37qRfv35ERHS81bRXQjBCq6JuTxE6\nnY74+HjS09MbnF86kq1bt5Kdnc3s2bNb9Ha/kjgrrNRszcWRX9vp51ZQaI4LW9g/9NAFXTR79mTm\noUPsnDABn5oaJo4dy+8XvMfkyfDOO+ey3lYrfPRRy/Mq2XAFhfajBOIKPxsKCgrIyspi1KhRTTK2\n4AnCyz5MRxOgJ+zXQzD0DWgY0wQa8L8xFtuJKob496Oqqors7Gzi4+ORUrL2ux/wQscAR3eC7x+A\nLuLKWuT5z+qNykeLcVQE3omhTcZVKhV9+/YlKysLp9N50flSU1OxWq1XrIBSpdfgNSiYurQS3HbX\nFfMUdzgc7N+/n7i4OAYNGtShc7cV884CEGAcpfTOUbh6aKmFfYN3eLovAzZsYNlt8xnvdvOXVx9E\nWh5BynOfH1LC4sWNs+ItzaugoNA2lEBc4WfDjh070Ov1DB8+vNnxmo3ZqAMNhDw6GE2gocm49/Aw\nDP0CCN7nJsDPY73Xv39/Dq1KJac4j2GGvkTNT0If3bwneEei9tUR8ewIAm5uuUtk3759sdvtnDlz\nptW5bDYbKSkp9O3bl27dunX0UhswJoUjbS4sh0uJjo7G39+/w+UpGRkZWCyWRtaTnYl0uKjbXYhX\nfBAa/46VJSkodDQXeocvfF/NiFX/pRvvMx8VVt7ByHhUqnLq1V1Op9LcR0GhI1ECcYWfBeXl5aSn\np5OUlITB0DTItp2pxp5dg2lsJCpd89pxIQQBs/sgNGpG0Y+EQQnodtawOXUbvhojE349E80VkqM0\nux5N6/99Y2Nj0Wg0ZGZmtrpfamoqFovlitsJ6nr6ogkyULenCJVKRWJiIqdOnWrRRvJS2Lt3LwEB\nAfTs2bPD5mwPdQdKcNc50YR6Y8uu7pI1CCFihRDPCiHeEkIsuuDv/S5ZlMJVyYXFlkuXem4/4n4O\nqLbxptaEgxTCTAPR6dKb1YKf342zNdq6n4LCzw3FNUXhZ0FycjIqlapFzbB5ay5nDOV8uHErPqk+\n+Pv7N/rr3bs3RqMRta+egJt6Ib84RrQtiEPVaZTrzNw661a0xqsrA6rT6ejZsyfHjh1j+vTpzRYs\n2mw2kpOT6dOnD5GRkVd0PUIIvIeFUb32DM4yC4mJiSQnJ/POO++QlJTEuHHj8PHxueT5S0pKOHPm\nDJMnT0al6vwcg5SSmm15CL2amo05uCpsnXJ15HyEEDcDS/AkWYoB24XL7NQFKVzV1Bdb1tsPzp4N\n27Z5Hu/VXcPrnx5m828nc0tWFhrtMObc+QWPzbu5QYaycCHMmwdut6cItCWduGJzqKDQMkogrvCT\np6amhv3795OYmNikDT14XFLqjpSyz/8U3jpvIiMjqays5Pjx45jNZgAMBgNTpkxh6NCheA0OwetI\nGeb0Evb7ZxPuG87AgQM7+2m1iX79+nH8+HFKSkqaeKYD7N69u1Oy4fV4Dwujet0ZavcW4T8thnnz\n5rFlyxZSU1PZv38/o0ePZvTo0c1etbgYe/fuRaVSMWTIkCuw8taRbknV6pM4i+tALfC7IRafMVdO\n5tMKfwI2A7+QUiq2LQqtUl9seb414aBB5x4PGx0NU/ezZ84cbvnhBz759Bbi+rzEqFF/YOdOwfz5\nHqkKgM3Wsn2hYnOooNAySiCu0GG46xyovJsWQXY1O3fuxO12t9hV0bwjn2x1KWWWSm69/lYSEhIa\nxhwOB8XFxaxbt46VK1eyf/9+brzxRsLviCNzezlVm2qYeetNXZKBbQt9+/YF4NixY00C8fpseK9e\nvZr4Bl8pNH569H0CqNtbjO+UHvj5+TFr1iyuueYaNm7c2BCUT5o0iaSkpDbbDjocDtLS0oiLi7us\nrPqlUrLwIPbT1aAShD0+BG3YlS3WbYVY4GklCFdoKxd2z2zSTdPHh6hVq9j63HM88Le/8fuXXuLg\nvn3ED/0Ml+vc+1ylampfeK6bZ+PMu2JzqKBwDiUQV+gQ6g4UU/7lMQz9AvGfGYsmqPO00q1RUVHB\nnj17iI+PJygoqMm4u86BeU8BaT65BHgFMGDAgEbjWq2WyMhI5s6dy8GDB1m7di0LFy5kxIgRHDp0\niJiYGHr16tVZT6fd+Pr6EhERQWZmJuPGjQM8HSeLiopITU2lrq6OiZ38rWhMCqP8s6PYsiobnGmC\ng4O5/fbbyc/PZ926daxatYrTp08za9Ys9PqLS36OHDnSpUWa9sJaEOAzpltXBuEAR4Gmb3QFhctB\npcLr1Vf5ZPBgEu+5h9+tWEHfA8PQatficESjVnu8yc8P4C+Urbz+OpSVNW0KpKDwc0cJxBUuG3tO\nDeVfZ3oK1E5WUfjaXkzjozBd273FwscrjcvlIiUlhc2bN6NSqRg/fnyz+5lTC8l1llJsLWfm1Jkt\nNvkRQjB48GD69u3Lhg0b2LVrF8CPomNj37592bJlCzt37iQnJ4dTp05RV1cHQEJCAt27d+/U9XjF\nB6Hy1lC7t6iRRSRAt27d+OUvf8mOHTvYuHEjRUVF3HHHHYSEhLQ6Z32RZkxMzBVceWOk091w32dY\nGObkfHxGd4kc5Xx+C7wuhNglpTx5JU8khDAAWwE9nu+Sr6WULwohAoEvgRjgNHC7lLLiSq5FoXMQ\nd93F//Tpw4DrruOu7GMYjYOYfc9K7rtvXKPgOiWFJrKVsjKPzaGCgkJjlEBc4bJwVdko/egIapOO\nkIcSwCWp+v4UNZtyqNtXjN+NPfEaGNypwWp2djbfffcdJSUlxMXFcf311+Pn59dkP+l0Y07O56BP\nLia9icGDB190bi8vL2688UaGDBlCZWVlp0k6Loe4uDi2bNnCDz/8gMlkok+fPsTGxtKzZ098fTu3\nmBA8bi/eiaGYUwualTOpVCrGjRtHZGQkX3/9Ne+++y6zZs1qUYdfXFxMdnY2U6ZM6VSJUM2W3Ib7\ndQdKMMQFNmt72cm8hCcjniGEOA6UXzAupZQdVRBgAyZJKc1CCC2wXQjxPXArsEFK+aoQ4lngWeB3\nHXROha4mKYkZhw6ROn06sw4d4oNF15I07E1Gj364YZfNm88F4dC8bKWeevlKfab8wscKCj91lEBc\n4ZKRDhelHx9B2lyE/GowaqMnoAq8ox/GkeFULj9B+adH0cX44js5Gn1v/ysakFssFtatW8e+ffvw\n9fXlzjvvJC4ursX96w6WkF9TRL6+lOmTpqPRtP2/Q2Rk5BV3GekoIiIiuOeeezCZTAQHd+6Popbw\nPptBrksraTGLHBsby8MPP8xXX33F119/TU5ODpMmTWoiVakv0mypW+qVwFlqoXpTdsNjd60Dn2u6\nPBsO4ALa1k71MpFSSsB89qH27J8EbgImnt3+IZ7iUSUQ/ynRrRv9du1i1z33cNfXX/PwI4+Qtm8f\nr7/xBlqtlqAgT/Ofeu6445z3+IWZ8/PdVF5/HZ58UnFXUfh5oQTiCq0ipWw2cJNSUr70OI5cM0G/\njEcb3lgXq4/xI3T+EGp3F1CzMYfS9w+j627CNDkaQ7+ADg8GCwsL+eKLL6iqqmL06NFMnDixVW2x\nlBLztjzSvHPw1nszdOjQDl3P1UZsbGxXL6ERukgftBFGavcUtSrn8PPz495772Xt2rXs2rWLtLQ0\nRowYwciRIzEajQ1Fmv379++0Ik0pJRXLsxBqFZzN+mlCvND39u+U87eGlHJiZ55PCKEG9gK9gTel\nlLuEEGFSyoKzuxQCYZ25JoWOo9XstJcX/kuWsPLVV1nw3HP8Y+FCjhw6xFcrVlBWFoxK5dGHCwFL\nlnjuXxhct+RjrrirKPycaHcgLjwR1ExgPJ5LoC9JKc8IISYAx6WU+R28RoUuwmW2U/S/+1B5adD3\n8cfQJwB9Lz9Ueg01W3KxHCjBd1oPvAY0Xxsm1AKfUd0wJoVTu7eImk05lH2QjrabEd9J0RgGBHVI\nQJ6ens6yZcswGAz86le/apNcxHaiivzCAnL0JUwePRmdTnfZ61BoH8akMCq/O4k9twZdVFNbyXo0\nGg0zZswgISGB7du3s3XrVpKTkxk2bBgmkwmr1dqpRZqWQ6XYjlfiPzMWvvNIn32u6XZVXGnobKSU\nLiBRCOEPfCuEGHjBuBRCNOtdLoR4CHgIIDo6+oqvVaF9tMn7WwjUCxbw94EDSbj9dh5ISWF4QgJ/\n/NsP6PUJ2O2eQNzl8gTiVit89NG5eVrzMVfcVRR+LrQrEBdCBACrgZFADeAD/Bc4AzyIR4/4eAev\nUaGLMG/Lw13nQBvpQ92eImpTCkAl0EX5YM+pwWtwCKZrL17oJzQqfEZGYEwKo25/sScg/yQDfS8/\n/G/ujTbE+5LW53a72bx5M1u3biUqKoo77rijWZ/wZp/b9jzSDNkY9IYWW94rXFm8h4RSvTGH8i+O\nEfrY4ItaX0ZFRXHnnXdSXFzMjh072L17N263m8DAwE4r0nRbnVR+dxJtpA+asHPvW+9hV0/SVwgR\nATwNTAAC8XwubwJek1IWXolzSikrhRCbgOlAkRAiQkpZcHYtzbZOlVIuBBYCJCUlKY2GrjIuzFZ/\n9FEr2fGZM7l7zx76TZvGzfn5PPrgCF548TPgVoKC4PHHPQWbUsKiRXDPPedsEi/0MQdPZnz2bCUb\nrvDzoL2VTf8AugNj8GTDz08BrQcmd9C6FLoYV60Dc0oBXgkhhNw/kG4vjib4wUGYxkciXRJ9rJ+n\n3Xs7soBCrcKYFE7YU0n439QLe56Zotf3UbX2NNLhatf6rFYrX375JVu3bmXIkCHce++9bQ7CnVU2\nCjKzOS2LGDFixCU1j1G4fFTeWoJ+2R9nhZWyz48iXW2LxUJDQ7nlllt4/PHHGTt2LDNmzOi0di33\nhQAAIABJREFUbHT12jO4zXaMI8Mp++hIw/aucge6ECFEX+AAnoSIGUg9e/sEcEAI0acDzxVyNhOO\nEMILmIrHPnEFMPfsbnOB5R11ToXOoz5brVaDRuMJoF94wZMlP79NfUPr+uoBDD94kD3XXMMgm43n\nnpuNzfIHHnjAzX33eTLj4Ans6/Xi4Am2Fyw4V6j55JOe4PzJJxufR0Hhp0p7pSk3Ac9IKVPOagPP\nJxtPkK7QBtw2J65KG85KG64KG64aO4a+Aeh7dL6LRXOYk/ORdhe+ZzPeQqPC0MsfQy9//KZf3txC\nLfAZ3Q2vgcFUrTpJzcYc6g6U4H9TL7z6BV70eKvVyvvvv09paSnXX389I0aMaFcgVreviDT1GbRa\nbYst7xU6B32MHwE396Zi6XGqVp/Ef2bbPdn9/f2ZMmXKFVxdY+x5Zswp+RgGBFG18hRqXz2Udtrp\n28rfgGpgpJTydP1GIUQPYO3Z8Vs76FwRwIdnvwtUwBIp5UohRAqwRAjxKzxXS2/voPMpdCLnZ6uz\ns+Hdd5tqt5vKV4IYvXkzm+bP55GFC3n5T3/i4P79zHvycz780OeikhOlA6fCz5H2BuI+QF4LYwYa\nZ8gVmsGSXkb515lIi7PJWM2GbAz9A/G7LqZJ8WNn4rY6Me/Iw2tA0BVdh9qkI/DOOLyTwqlcnkXZ\n4nT8ZvTENL51jfeGDRsoKSnh7rvvpnfv3u06p5SS8t25nFQXkzQkCW/vS5PFKHQcxuHhOApqMe/I\nRxtuxDg8/LLmq16zlqrvVhD5z3+iuoSrHU67hVNH/kNk1D14BYUjhMBVbaf8i6MILzW245WoTFpC\nHhwErxRd1lqvANcCj5wfhAOcreN5CXiro04kpTwIDGlmexnK1dGfBPXykZQU+PDDptrt5gNnLYZ3\n3mFxYiKJ8+fz9MqVZB1P4uOPvyczs2ertoQXasYVjbjCz4H2BuLHgGl4ZCgXMgE4dNkr+oljTs5D\npVXhMzEGtb8Btb8ejb8eoVdjTsmnZnMuRf/eh/eQUHyn9kAT0PmyCXNyPtLqwjSpcwqoDL39CXti\nKKUfHaFmcw7GUREtXuo/c+YMu3fvZtSoUe0OwgHsp6o5XnUGt9bdqXZ3Cq3jd0MsjuI6KpZleRxI\nYpr6vreF2tRU8p95BulwULV8BQF3XDwZK6XEWWbFdqwc6/FKiuqWURi3iNrdRYTkzUEb4oWjpA7p\ncCPUKlQ+WkIeTEDtd/GOn12ADk/9TnPUnB1XUGgXLWm5WwucxaOP8mT//sTPmsUdmZk8fH8iXy1b\nxujR17b7PBeieI0r/JRobyD+FvCGEKIK+OzsNn8hxH3AfM5WwCs0j6vahu1kFaZJ0ZgmNFXx+F4b\njXFEBDVbcho8ln2nRON7bec5CrhtLszb8zDEBaKL7Bw7OPBIX3wndafk7YPU7Slq1pPZ4XDw3Xff\n4efnx7XXtvxh3hq1ewrJ0hQREhxCRETE5S5boYMQakHQ/4uj+M0DlH2SQej8RDT+7fsRajtxgtz5\nv0YbHY3QailfvBj/ObchWmjyI6WkdlchNVtzcZVbAVAH6alK3AJAbe+9RJkexHq4DJwe/brKpCHk\ngUFo/K/KIBw8+vBfCyG+l1I2tP4863b12NlxBYV2U58dv3Bbq4HzxIlMS0sj9brruOn4caZOmcK/\n//1vHps3j507RcNx0HiO1oLrNrm5KCj8iGhXIC6lXCiEiAVeBv54dvM6wA38XUr5aWvHCyEWATcC\nxVLKgWe3/QOPHaIdOAHcJ6WsPDu2APgVniYVj0sp17RnvVcbdWmlIME7seV23WqjFv8ZsfhcE0nl\nsiyq157Be2gYmk7KvtXuKsBd58Q0qfPl/voYP3TRJmq252EcGYFQN1Y6bdu2jdLSUu6+++5WPcJb\nwm11UnjoDEXqSqYkXv2t6bsCW1YWxf96jbDnn0cX1bkNi1TeWoLmDqD4zQNULMn0dGptI86SEnIe\nfAih09H9nXewHkwj76mnMW/ciKkZHbl0uqlccYLa1EJ0Mb6YxkVi6BuAWZ2OZd8J/PyGUlW1j+rS\nNPTqaIIeHIDGz4DaqEFoL16YmWG20NNLj0HdeZ0+z/JHYCWezppfAgVAODAH6APc0NkLUvhpc7HA\nmZ496bN3LzvvuotfrFrF/F//mnVr9rNm/f/hcOhQqz2FnE5n2wLrzZs9Dixut+dW0ZEr/Nhp97eE\nlPJZoBfwMPB7PFmWflLK59tw+Ad47K3OZx0wUEqZAGQCCwCEEPHAncCAs8e81UyB6I+KurRitJE+\nbbLr0/jrPT7FEur2dI4OVTpc1GzNRd/bH3101xSNmsZH4Sq3YklvXAVXWFjI9u3bGTx48CVJUgAs\nB0s5LvMRQpCQ0PYg7+eCdLnIf+55zJs2Ufz3v3fJGrSh3vhO6o7tZBWO4joAbMePk/fUUxwdMpS8\np5/BcqixAs5dW0vOw4/grKig+9tvo4uKxDRtGtrISMoWLW5yDletg5L3D1ObWohpYndCHkrAZ3Q3\nNEFe5OZ9gkZjon/kP8CtptJ3GyEPDMLQw88jIWtDEO50S+5IO8GTR7Mvum9HI6X8AU+yowZ4HngT\nz+e0GbhRSrm20xeloGAy4btiBcuef54FwPKVi3BZx+FyFeFwNNWZt0ZQkCcIB89tUPNtLBQUfjRc\nUrpGSnlGSvmelPKvUsp3pJQn23jcVjyetudvWyulrK9c3AnUV+rdBHwhpbRJKU8BWcCIS1nv1YCj\npA5HrhnvwS1nwy9EE+SFPtaP2r1FSPeVt9mtTS3EbXbg20na8OYwxAehCfaiZmsu8myPZLfbzYoV\nKzAYDFx33XWXPLd5dwFZ2iJiY2Px9e28HxpSSqTbffEdu5iKTz7BevAg3klJ1KxdS21qapesw3to\nGKgE1WszyHvqKU7Ougnz5i2Yrp2IefNmTs+5ndO/uJvqtWuRdjt5Tz2N9ehRIv/3NbwGDgBAaDQE\nzp2LZd8+6vbvb5jbUVRL8ZsHsOdU4zczFrWfjsplWZR/eYzCz3ZQXPg9/qUTqHq3EJ/yRGp77EUb\n1b6C3m0VNRTbncwM7ZpOm1LKH6SUSYAJj5OVSUo54sd+RVHhR45KReoNf2b4XUv4RK1FzW50DEat\n3t9gk9iWAs2yMqhXm6lUnscKCj9m2hWICyHuO1t539zYS0KIuc2NtYP7ge/P3o8Ecs4byz277UeJ\nJa0EBHi1IxAHj6OEq9yK7WTVFVqZB+l0U7MlF12ML/rYSyuU6wiESuAzNhJHrrnhOe/atYv8/Hyu\nv/76S3Y5cRTXkZ2bQ420MHjw4I5c8kXJf/ppTt06G1dlZaeetz3Yc3Mpfv3fGCeMp/t776LpFkHR\nX19Butrn794ROPJOgjOX2r3FmLdsJ+ihh+i1YT2Rr71G7y2bCVvwLM7CQvIef4LMMWMxb9lC+B9e\nwHTBN7j/7FtR+flRvmgRrho7tfuLKX7jAG6zA3WAgarvTlK5/ASW9FJsZ6opliuRwklgxXR00Sai\nEu7A7iqhomJXu9b/VVEF/ho1U4K61opUSlknpcyTUtZ16UIUFDin7Z6zZA5vaHaxzhRKKMVoxCie\nf/5L/vSntum9J04Evd4TuOv1irOKwo+f9hZrPgG838JYMfAk8OGlLEQI8TzgBFrVmbdw7FXdKllK\nSd2BEvQ9/dqt9fYaGIRYrqZ2TyGG3lcuw1a7rwhXtZ2AOX0v6XgpJbU7kjGOGonQtPdtBU6nk88+\n+4zq6mpMPj6ovWyYlucQNCKaLVu20LdvXwYOHHjxiVqgdk8RxzWF6LQ64uLi2re2igqEWo36ErLo\nNRs3Ub3a89sy99eP0/3991DpOs+4wm13YTtZhT2nBp9REahNTc8tpaTwxZcQQhDx4ouoDAbCnnmG\nvKeepnLpUgJuv/I20G6LherV31Ox5EusaQfRdh+CYdijdPvPl5jG9GzYT+3jQ+DcuQT84hfUbNhI\nxZKVeA8ZSMCddzbs46qyUZOcj7PEgs/Ul3FbVRT8pXEwrfbSYJweg1d8ENpQb9xuJydSniTQOI7u\nk673zOOK5XjRyxQVfUdg4DVteh41Thffl1Rye3gg+haKRDsaIcQfgPeklPln77eGlFL+qTPWpaBQ\nT0oKvPTSOW33boaw9+mD7Fk/k9mpqfzhD3fy3II0Ro78MxfLD7bVWUVB4cdCeyOm3kB6C2MZeLTj\n7UYIcS8eXeNkWa9H8PiVn18xGEULHuZXe6tkR34tzlILPuPbn9AXWjXeiaHU7inEXee4aBvwS0G6\nJeateWgjfdBfYrBfs349eb9+nLAFzxI4t/0XRpKTkzl58iR9+vTBarVSrqvhVFURrvWZ6PV6brjh\nhksurpQuN9V78zmlKWbAgIHo2hEIuyorOTH9etxVVWgjI9H3j8PQvz+G/v3xSkxEE9hyAyK31UrR\nX/+Krlcvgh58gIJnF1Dw/O/p9ve/XbFCUSkljoJabMcrsR6vwHaqCs52rHTXOgi4uam+vmr5cmp3\n7CDshd+jDgylat0ZVKYEvMfcRtn732AcOwVteABC1fFrtmVlUfH5F1StWIG7pgZdbCxhC57Fd9Ys\nShYex3qkBtOYpscJjQbj6AnUJPtgLxNYDpfiNTAY6XBT+kE6jqI6NMEGdNEh1CYnowkfiDDo8J3W\nA++BIah9G78HSkvXY7MV0q/vyw3b1GovQkKmUlzyA337/IGy19/EVWMm5Mkn0AQENPt8VpZUYnFL\nbg+/eGOqDuQl4Acg/+z91pCAEogrdBr1mfD6IFyl8khQRtwYStiL29j4yCPMW7yYv77yCocOHOCT\nL764qHTwogWiCgo/ItobiDuB4BbG2qe5OIsQYjrwW2DCBZdQVwCfCSFeA7rhqfjvGtHqZVJ3oBjU\nAu+BLb10rWMcHk7tzgLq0krwGd3U1u9ysR4tx1lqIfDOfpccIFYu+QqAsvfex//OO1G1w9WktLSU\nLVu2MGDAAObMmQN4CuoKXt2FeoC/p+Oml9clrQvAeqyCU5Z8HDpnu2UpZR9+iLuqiqCHH8aRk401\n4yjmDRtBSlRGIz0+/ghDfHzzx773Po7cXKI/WIxx1CichUWUvP462qhIQp944pKfT2vUbMml+ofT\nAGjCvPG5phuGPgHU7S+mbm8RftN6NPox5ywro/iVV/EaMoSAu+6ien02NRs9ijB1yDTUIdMo/k86\nqAQ+oyLwmxnbYT8ialNSyP7VAwi1GtN11xFwx+14JSU1zG9MCqd63RmcpRY0wU3//StXnUK63GiD\nvCn7JAPjyHCky/NDJGhuPIa4QMzb87CdTMBVnUv4w5PQ92y+WVBu7scYDJEEBze2xQwPm0Vh4TKy\n/vsI7vdSQQhq1q4l7LkF+N54Y5N5viqsINZLz1DfzmsUJaVUNXdfQeFqoL7pT30QPmWKJzsO8Mq/\ndEx84H0WDhlC4hNP8MT33zN62DBe+uv3ZGX1VjLeCj8L2vuhnQo80sLYI8Du1g4WQnwOpAD9hBC5\nZ1sgv4GnqGidEOKAEOJtACllOrAEOIIn2zNPStn5gtXLRLoldWklGPoGXHI2WxfpgzbCSO3uwg5e\nnQfz9jzUfnq8Bl3aDwV7bh6127fjPWoUzpISKpcubRgrLCykqKhl1xcpJStXrkSj0TB9+jlDHbVR\nizEpHNehSnSOy4stavcUkaUvws/Pjx49erT5OFdlJRUff4LpuusI/c2TRL72Gr2+X02/Pbvp8cnH\nqHx9yXn4ERx55y7UOEstSLfEnptL2bvvYrp+OsZRowAIevgh/OfcRtn/vd3oNeoopFtSm5KPrqcf\nEQtGEP6bYfjfEIuhbwCmCVFIhxtzauP3UNFf/oq7ro6IP/8JaXdjTva0cO/2h1GEPj4EwR6sh75A\n38sLc3I+NRs6xgnEWVZG3m9/i65nT3pv2UzkP/+B9/DhjYJ8Y1IYqGj2fW/NqsSSVoJpQndCH0vE\nZ0IUtbsKqdtThHdSGIY+AVQsPU7VqlPoYryo2/I3qld+3exazOZMKip3Ehn5Cy40ZvL3HYnarqfU\nmUzwvHn0XPYt2u7dyf+f35LzYOO2CTlWO8mVZm52W6n46CNqNm7qgFeqfQghooUQzX7QCCE0Qoir\nT7un8JOmvulPvaa7PgifPBleeAEmTxHsTPo189avZ63JRGHWCf7f7UN5/vl1XHstPPqoJ6t+Pikp\n8MorTbe3h46YQ0GhI2hvhPMXYJwQYpcQ4kEhxIyzt7uAcVzkkqeU8i4pZYSUUiuljJJSvi+l7C2l\n7C6lTDz798h5+/9FStlLStlPSvl9a3NfrdhOVeGutuOdGHpZ8xiHh+PIr8WeZ+6glXmw53mKIn3G\ndENcoudx5dKvQQi6/fUveCUmUvbue0i7HbPZzAcffMDChQvZf55zxfmkpaVx+vRppk6dislkajRm\nGhsJbol5R/5F1+AorOX0p/s58K91FL6xn+K30yh57xCliw9TdrSAXFlGQkICqnbodss/+gi32Uzw\nY4812q4yGvFOSiJ64Tu4rVayH3oYV1UV9nwzhf/ag3lHHkV/fQXUasJ+9zvcUiKlRAhB+B/+gHHM\nGApefAnzjh1tXktbsJ+uxlVlx2dkeJOuj9pwI/re/tQm5yNdHgeXmk2bqF69mqBHH0HfqxfmlAKk\n1YXvtd1ReWvRdfMh9Klf4CrYiXXfYryHhVG9PpvavZdnpyndbvIXLMBdVU3ka6+1KO9R++kx9Av0\nuAa5zrnOSKebyuVZqAMN+E6MQmhUGIeFgUYFakHd/iKK3zxA3Z4iTJO6E/JQEj7jx1Dx6ae4LZYm\n58nN+xSVSke3iDmN1+lyUfT7F9EnO7ANEQQ8ei+Gfv2I+fwzwp5/Hsu+fQ37Frz4Eu++9gYAw595\nnKJXXsW8aeNlvU6XyCmaaTt/lsFnxxUUOo16Tff5xZj1WfJGloWTJuG/6ACf0Ic4akBeh832v7z9\ntmTy5HMBc73U5YUXaLS9PXTEHAoKHUW7Ii8p5RbgNiAUeAdP44h38MhSZkspN3f0An/sWNJKEDoV\nhv6Xpxn1TgwBjaB2T8dmxWu25SL0aowjmr9kfzGk00nV0m/wGTcObbduBD/2KM6CAiqXL2ft2rXY\n7XYCAgJYvnw5a9aswX2ejV9tbS1r1qyhe/fuDB06tMncmiAvvAYGU7Mtj5JFhzHvKsBVYz93bimx\nZlVQsugwOa+nsjRzLctqdrCkahMZljM47A7KrA4WDNWypfcgUiN6srSwnJRKM9kWG7VOFy7ZfEmB\nq6qK8o8+xjRtGoZ+zRew6vv0IeqNN3BkZ5M7bz4lm8/wVi8djxYU8MDgMfzqlTdIzColanMatx7I\nwu52I7RaIv/9Ovpevch7/Amq167DnpNDzaZNlL77LvnPLqD6+0v7zVmXVozQqjDEN2+s6zM2Ele1\nHcuhUqTDQdErr6Lr3YvgBx7Abfd0VNX3DUAXde4HkTY0lKCHH8a8YQO6bqXo+/hTsfQ41uMVl7RG\ngPIPP6J26zZCn/1di69tPcYR4bjNDqwZ51xPa7bn4Syx4D+rF0Krxm13UfZpBiq9mtB5iRh6B+Ao\n8Uit/KbFIFSCoPvvw1VZScl//os879/c6ayhsPBbQkNvQKc7939UOp3k/+5ZqpavoFvPO5AqFyUl\n6wAQajWBv7yb2FUrG/avWr2aH+KHkGSuJOnPL9N76xYi/tQlUuzWdENaPM3XFBQ6ldGjYcGCczKT\n87Pk51sWvrshljns5VlmcjMSeAoVc7HZbA3+4s0G8c3QWsa7rXMoKHQG7ba3kFIuB5YLIfoBQUCp\nlDKzw1f2E0A63dQdKsUrPgiV7vJ6Eam8tXgNCKZufwn+M3q2qbHIxXBW2rAcLMHnmkhUhvY7nQCY\nt27FWVyM/4seswbjuHEYBg4k/YsvOTjI43JSWlqKr68vKSkplJSUMHv2bLy8vFizZg02m42ZM2e2\nmKn2v6kX6gADlvRSKr/NonJZFtpoE0II3HUOnMUWVD5adkfnYi6xMnHCRDIyMthUtI9d3kfJTBpH\nMia83N78u6gaiqqbnMOgEnirVXipVARpNcwI8WPS9yvQms0Ez3sMt9WJ0Kub1UYbR44g4pVXyH7p\nb7w0s47kWB09at34OwLpFxFKsF6HSgg+yCvlX6eLWBAbgdrHh9Cnnyb38cfJe/zxRvMJg4HqNWvw\nSkhAG9l8ca/TLUmuNPNDaRUzQ/0Z7e+DdLqxHCrFMKDl95qhbwCaEC9qtudhO74VR3Y2UW+9idDp\nMG/Pw13rwLeZjqqB986lcskSiv/1T3p8+iWl7xyi7JMMQh4ZjC7C2Oy5WsJyOJ3i117DNHUKAXfd\nddH9DX0DUfvpMKcW4jUwGGellZoN2Rjig/CK8wTOlctP4CyuI/j+gei6+RB07wCkw93odfBKSsJ/\nzm2UL16M21JH+AsvINRqCgq/xeWqJSrqlw37uq1WCp57nurVqwn5zW8IuvdBclO2UVS0goiIWxr2\n00ZENNyvXbeR7P1ZPBnXHVNE53YYEUL4A+f/0o882wH5fLyAucCV0bcpKLSD1pxPavHhlyzjBV4m\ngT/yMh+jl0cYOPA7IIKJE0Gj8WjONZrG9oUpKZ45g4LgySc9QbZOB6+/7vEbrz9X/Q+B+nHFAlGh\nK7m06AuQUh7ryIX8FLFmViAtTrwuU5ZSj3F4GJa0EizpZZctdQEwJ3u0zT5jLr0AtPLLJWhCQvCZ\nMAEAIQQBjzzMN6tWo3E68Q8PZ/jw4WzatAkhBCdOnODdd99l3LhxHDx4kPHjxxMa2vJzUfvo8J/R\nE7/rY3AW1WE5XErtvmJc5VbQCPxv7s1JQwkZy04wYcIEJk6cyIQJEzh9+jTrUnfzg1tLn9JcXusV\nTvzQQeRbHeTbHORZ7VQ6XdS53NS53FjcnttTFhuvnirk1bgRJL38L35hCCDptd0E9QkisAVrR+OM\nGbxqC2BHoJbfblzLbTXx6Hv4EZbgMRHaX7yf7Bon/z1TxNQgX+JPZJL39NOo/PzQxcVhOXQIldFI\n2LPPYhw5ghM3zqTwL3+l+1tv4q6txZKejqO8goxhI1heUct3xZWUOTw9sL4qLGfF0D7EZNfhrnO2\n+r4QKoHPmG5ULjuBee1KDIMG4XPttR4P+a256Hr6oY9p6iGv0usJnj+fggULqN22iaD7JlDy5gHK\nFh8mZF5imy05XeZa8p5+Ck1wMBF/+lOLRZ8ORyVSutHpAhFqgXdSODUbs3GWW6la5ekd5j8z1qOJ\n31VA3d4iTJOjMfTxOJkIIRAX/BgRQhD+xz+i9vOj7L33cVVWEfG3V8jN/RhfUwJ+vp4i3tqdOyl4\n8UUcZ7IJfeZpgh54AICwsJlkZy/Ebi9Fp2taS/FVcSUGlWBmSJc08XkCeBGPI4oEmhfDe7LlL3bW\nohQUWqM555N77oFFi8DhUPFX9cv8eUgCn+39BQ+49/HorwYTvmoVMJz6i1rnX9A8352lfkxKz+P5\n8z2Bu053Th6jWCAqXC1cNBAXQtwDrJJSlp293ypSyo86ZGU/AeoOFKPy1mDo0zFfzvpYf9SBBmp3\nFzYJuKRbgqDNjhZuq5PaXZ4soybAcEnrceTnY962jaCHH2rkHb5PpaLGz5fhu/cw6oPFBIWEMHDg\nQDZs2MC+ffsoLy9n+fLleHt7M3bs2Bbnl1KSnp5OYWEhY8eOxRBuRBtu9ASOm3PBKamqrmLVplVE\nRUUxfvx4wPMa9OzZkyK3Hld2Mb+JCSMxMRGtWk0fo5o+xtaf7/6332XJsVNsuuUOfnMyH/0IAzfl\nVvI/x8ro3q9xttMtJU8cPs2GQG+ePlbC9V8tRnXDb3AU++Est7LXlsaj6x9FqIyEx7zFvP3HePvZ\nefgGBhL9wWK0ERFYj2VS8PzzFDz3HKZp0/AZN46atWvJmjQZR2Eh2wYN5b+330vJ4TMY3G6mhvhx\nS0QQ/Y1e3LI/i18cPMmnOSr82vBe8x4aRuV3maj8hxDy4DCEEJj3FuKutuPbioe838wbKXvnHUr/\n+wY9p0wh6L6BlLydRtniw4TOH4LQXFzlVvjHl3Hk5NLjow9R+7e8zoOHHsPprGHE8BUIITAmhVGz\nMZuKrzM99QzjI6nbW0Tt3iJcFTb0vf3xnXzxGkQhBKHPPIM6IJDif/yDau+T1E05SXz8v3BVVlL0\n939Q9c03aKOjiV68CON5387hYTM5c+b/KCr+nu7nZc/rWV5UwfXBfpg0l3+l6hJYBpzGE2gvAv4M\nnLhgHxtwREp5sHOXpqDQdur14x99BIsXw/P7ZjNU24dNpuu5vSSfcWPGMOvmRbhcdyOlR1qyefO5\n4+otEusRwvPncnm218tQ6n8EKAG4wtVAWzLiHwCjgLKz91tDAkogDjgrrFjSyzCOCL/kIsgLESqB\ncVgY1evOUPpBOu46B+46p+fW4kQbbsT/lt7ooy/eeKZ2dxHS5sI0LqrFfaSU1KxZg9fQoWibyVpX\nLv0GpMR/9m0N28rKyti2bRtedXXEnjiBJjUVbrgBo9HIrFmzGDp0KCtWrKC4uJi6ujo+/vhjZs6c\n2SQrnpubyw8//EBubi4Ahw8fZvbs2XTv3h3r0Qp0Pf1AJ1i64wekTjJ79mzU6nNBUJndyeK8Um4O\n9efWATEXfT3qcVVX4/3+u8wbNZI/D49n7f/tZXlvL5ZGa/kuJ5tHNTYe6xGGj0aNlJLfHstlaVkV\nj2XaeGLmSCwRr+I15BqK3z7K6U0Hedz6OBHGCHJqcphQtoqvjdN49457+c/dt6IJ8Th+Gvr1JeaL\nzylbvJjS/76BtNtBpcJRWsrqBS/xz6jeDMDNrzetJGn515j8/Aicew+OgkLemzadOyxaHvGy8mlC\n8MXfa24HjjPb0USOQx8/DOmS1GzJRRvVuoe80GgInj+f/Geeofr77/G74QYC7+hH2UdHqE0txOea\nlq+qSLud0vfeo3rFdwT/ej7eSUkt7muzl1JZmQpIaszp+JoGogkwoOvtj+14JUKrwrykLbBKAAAg\nAElEQVQ1DwToe/njNy0Gr4HB7fI4D/rV/agDAzmc+z+o6zTod9g48dqNuCorCXrwAYLnzUNlaPxj\nzcenHz4+cZw+/Rb+fkMxmQY0Gq9wujrbO7wBKWUakAYghJDASiml0vhb4UdJfVDtdHoC6H0kkPxw\nGrs338ycHTv46qtfolUfQKr+hk6nbpCVTJzosUc8PxCX0rOtPhhXZCgKVyNtiRB7AgfOu9/a34W6\nxJ8t1euzQYBpYlPN7eVgHB6ONsKIq8qG0KnRdjPilRCCaUIU7joHJf+XRuWKE7htzhbnkC6JeUce\nuhhfdN1Nze8jJcV//wd5T/6G03Nux3rsnBLJ7XbjsNmoXLoU45gx6KIiG475+OOPkVIyesYMdL17\nUfb228jzPhmjoqJ45JFHePLJJ7npppsoLS3l7bffZv369djtdqqqqli6dCnvvfceFRUVzJo1i/vu\nuw8pJYsWLWLTmg3YCs14xQWS3q2YIlHJeN/B+F+QYX07pxiLy81vYtpXhFr+0cf8f/bOOzyKsuvD\n92zPZrPpvfeEkEAg9CJNehNEFBBBOiIqFlCKqNh5RQQsFBEBQapSlA7SewmEAOm997K72TLfH0sV\nUHhf9C1f7uvKlWQyzzPP7s5uzpz5nd+xVFXhMnEiNUfziC408kXTYHa5e9O6yMRnmYW0OJ7I0uwi\nZibnsCqvhOezTEyQ26Lw1mLfrx8KP1csISqMZ0txVbiwvPtyOimjOZG/mgGXTrCpcQsOSe6Ucwgy\nGS5jxhC8ezdBv/6C9/cr+aL/M3zqE0pPVwe2to9lzDvTCf/mG+RenhR+OpeyVauwmzie+RY5ybYS\nXvWwYLL8cT+r8h9/xHBpO4JEQs3RXGrjizCX6tF28vvTuynanj1QhoZSvHARosmEKtIJRaCWyv2Z\nWOrudhYVRZGqfftJ7dOX4i8WYNe1Ky7j7+d+aqW4eC/W63kJeXmbbm5XeFi16IJKiraLHx5vNMN1\ndDTqWDcE+cNf6Cq6NcIQZUF9UELB9NnIPT0J3LAet1dfvSsIv0GDyLkIgoTTZwZTWLTzjr+5K2S0\nc7z3e+nvRBTFFfVBeD3/7fy+mLNFLxdc9+9n98SJTACM5n8QFtidn34qv5nVbtUKpkyxBt63Y7HA\n88/f6dpSTz3/SfxpRlwUxQyA6960jYF4URTrLbD+AGNhLbVnC9C08X7olvZ/hlSrwP2lux1GwBr0\nV+xMp/pYLrqEYmx7BZBsysFkMiGRSG5+mXJqcCg34N3n/tdNxQsXUbp8Odrevak9dYqMIUPxnj8f\ndetWrFmzhpTkZFwiIwhr1gx5Xh7u7u7s2LGD8vJyfH19ad+hAxVV1eS+/jpVe/ag7dr15twSiQQH\nBwdiY2MJCwtj9+7dHD58mH1HT6PAiFSAdu3a0bZtW5TXGwNNmDCB7du389uxQ1xR2NNGruHggcNE\neATjn26H7kLRTblOSZ2JZTnF9HNzIOw+MpRLxZewV9jjq711oWSurKR0xQo0XTqjCAqldP0pVBFO\nKLw1RHlr+CK+lFOnSvmmgzMzkqz6+pEyNRMuF2A3+lZT2bzqPD4VFzPVPJwvvT5Fue8U3b86z97n\nJYQ3NhImqnjlShb7m4fjKL/zLSh3d6PGbObFapGdHbszaO8vfDz0CWyuZ7plbm6YiktALkfu7o4x\nO5uGK39jWtOGvN9A4M2kbD4J87lnUG2praV48RJsGkegbuRKzekCpFfLkHuoUUX8eTZXkEhweXES\nOZNfomLrNhye6I991wCKvomn5ngedu1v3V0xJCVR8OFH1Bw9iiIwEJ9F36CKiUOQ/rF0o6hoNyqV\nL1ptNAUFWwgNmYZEosCQXonMxQb3KU0fSYfPrOyVCIKc8CHfILYoxr5/vz9dm51dJM3iNhN/cTwX\nL04kOOh1bjT/HeDuiOz6uvSGfAoKtqG2CcDVtcu/vNaHRRCEKGA0EA78/g0giqLY+W9fVD31PAT3\n1nDLkS9axKv2TYj+aCyTU/bw4rhYtuzYQXh4OMeOwYIF1vFS6a3suEJh1Z7XB+D1/KfywMWaoiga\nBUFYB3Sn3ov2D6nclY4gl2LX4f6yj78CiUqGY78Q1LFulG1MYse6rVyWZd9zXxe1lvFh7W/+XlVX\nxcWii7T0aknZt8spXrQI+wED8JzzHqbCQrLGjSdr/HjSJ04gqbCQQL2eMrWaw5mZHP7mG2xsbNDp\ndMjlcoYPt5YSaHv2oPjLL8l7azqiToe2b9+7AkRbW1v69+/PNZMzBfEnqBbV9O3Rlc6tI+7YT6VS\nMXDgQDzybThQdJZNu7Zgb29Pv+FPUrn8KuVbU8FLQWVVEUtMivtmw6+VXWP+2fkczD6Io9KRlT1X\n4q+1NvkpWfYtlqoqXCdOpPpYHpZa0x3aY4deQUT/o5Rv4g1ceiKQ9No6eqzLQOKtQRlszciX6ksZ\nu3ssJaoSLE5SlGd0FKx+j4igRnTwcuTHlB/5rPtQBl7IYuq1bN4M9EQqgFQQkAoCtWYLEy9nEF9V\nyxwfJ9rv205B0gUC1qxBd/482RMmglRKwOpV2MTEkD3lTURZBD33/kJ6noaVnXviaTbxSmTAXc91\n6erVmEtKcF2wAJmbN7XnizAZdDg9E/7Awa3d44+jbBBJ8ZdfYt+7F8pAe5RhjlQdyLJaYJoNFM77\nnLI1a6wFqG+9icOgweQsjMey7ywur8Vhe5+aBJOpmrKyI3h7D8PJsTWFhb9QUnIA+7rWGLOqrF09\nH0EQbjJVkZe3EXe3nthHtbemFx4QpdKNJrE/cDnxDY6nfgfMBGCgi5ycnLXkF2y5Ka3x9h76twfi\ngiC0AH7DqhkPBeIBR8APyAaS/9YF1VPPP8m9NNzHjkGHf4wiToxkHb0Zm55OiyZNWLNhA+fP97jZ\nwVMqhVGjwM/vnyvGvOG+Ul/IWc/fwcPe003F6iFez32oy65Cd6kETTtvpBrFX3KMq6VXqTPf5qdt\nsVC5ezc11w1TlX5axEGeJMpyiJT4MlzZmWc1j/OsY1eGuXali3Mzii2V7D9wq/Pf3NNzGbdnHHPf\n6kLhp3PR9uyB53vvIkgkyD088F+9ipLH2nOisJAIQaDZlq0M8fLm1VdfpWvXrtTV1SGRSHj66aeR\ny62N/QSpFN8lS1CGhZE7dRo5r0zBVHa3/3RacQ1Lz1UjieiEwacZM39NIyG34q79RKOFgHx7hkb2\nplGjRjz11FPYqG1wHBCKRWfi6sKdLH3nLRan59Mg8yrn585m95KFXNj9C1nlmbx16C2e3PIk5wrP\nMS5mHIIgMG73OIp1xdRl51jvAPTtgyIknOpDVk9twVvFioQVnCs8h1SrwL57AHXJFbTMMvBMpQRz\nkQ679t4IgkCZvozxu8eTX5PPwi4LcWzjjzG3FhF73GdMZ2zj8VTWVZKQ8zOvBniwpbCcVicSaX48\nkabHLtP4aAKtTyRytUbH8uhARof64T5tKvoL8eROm0bmiJFIHRwIWLsGm5gYAOz7jUOQSBENaUyu\nyKPzySN8UlDByBUbyNm6HUtNDQDm6mpKly7Dtl071E1iUfjYoQyyR+Zqg0206wOfe4Ig4Dp5Msas\nLMo3b7au4XF/LLUmyjaeJXXAAMpWr8bhqUEE79yB0/DhlO/IRCjRIzWL7JxzksuHc63Fxb+jpPQg\nFksdri6P4+TUDoXClby8TdQcz0OQS7Bt4v7A6/wj8vI2YTZX4+P73D81XipVUe41h7elC25uKzzX\nnitXp1NXV0hg4Eu0armHiPB3H8l6H5IPgE1AFNbizVGiKAYAXQAp1kLOeur5r+T7760Fl0dpzYvE\ns9kpmoDaWnr16kVO9ifI5eJNOUvs/dpa/Qn1zX7q+bt5WPvCT4DpgiDsE0Wx6K9Y0H87FTvTkahl\n2LW7twd0aq2BUqOJOPuH81++wbqr63jv+Hs4qZx4MnQg/YsDMH79HYbLiQA4jxmDy+QX+WXnr9io\nbej74hBsbGzumCMEKN1i5siRI4SGhuLo6cgvqb8wPN2X3pvTOB0icLRrFS9VJBHhZM1MlxsMHPLx\nwUWno+GGjQgWCw6DnkRUKLhw4QIymYzRo0fj6npnUKfw8cZ/5feULPuWogUL0J05g+eHH6Jp2waw\n6ohn/XwJpUzC230aICDQd+Fhxq08w9ZJbXG0vXUxY0irQDRacG/kxxMRt9KYCk9bVC2ccT0mktt1\nJEaFklE1ZpzrPDCcLyfz5EnmH5xLfHglIxqOYFTDUdgr7eno25GRO0cyYc8EPt3rCRIJblOmUHMi\nD0uNEUtrO0btHMW5wnPIJDJmt5pN3xZ9qTlTQPm2VKQOSqSOSmwaupJZmcnEvRPJq85jXsd5NHFv\nQp2pENFswLbdMGyioogGWnm2YkXCCrZ1GkCoyoFaXw1mqYBFBLMoYgZaO2gIvy6p0fbpQ/mmzVRu\n2YpN48b4fPUlMkfHm49dd7kCiR0YU86jfXwcS/p0Z+7Rc3ztG8zF4gLeHjyUpmFBiIIEc0UFrrf5\nljs/1wDM4kNnmTWPPYaqUQzFX32Nff/+yD1tkKgqqD2rQLTI8FvxHbbNmwNW56DaE/mkGcwEqKT4\nahXsX3WFqyfy6TA0HEePW++DoqLdyOVO2Ns3QSKR4eHel6zs77FP6I9doyAkNv+02+pNRNFCVvb3\naLWNb1oWPtx4kSXZRbyTkkuwjR2ZFALg6zMcd4++2GmiHti56C8iBqtf+I0rHSmAKIr7BEGYA3wI\ntPg3ra2eeh4ZOfiwbsAJjlQ/z8i1a1n05VS6dz5Lq/bL8fCwucNHfO9e65gHyXLfq9lPfVa8nr+S\nh/3P1glr44g0QRCOA3nc+sAHq/7wn0sz/ZewPr8UkyjyzD2aduhTyjEklWPfM/COBjnXavRsLypn\nW1E5CdV6AIZ6OvFBmA/Kh2i5fqn4Eh+d/Ig49zhCM4x4v/E11dkilS42KN8ch3tKKSVLlnAxNYUs\nV1f69u17VxB+g27dupGens7mzZtx6OBAeFItvddnYNO6JbzYjotXv+WprU/RO6g3k2Im8dOPPyGR\nSBj6yitYgoKwVFYh8/Fh3bp1FBYWMmTIkLuC8IzKDN47/h52cjveGfEOgW3bkPP6G2SNHo3js8/i\n/uY0tl/K51BSMe/0jcLNzhp8fj2sKYO+OcakNWdZMbI5suv6aP2VUpBJUAbd7XWdIVzFhJSd7j50\nzjfSPtMX8IXr9XOKEhtmdOhHkI/1wsJUUkKE3IfPO3zO/O8moNtxCceJ45E5u1K17BQGXwnDLjxH\nramWd1q/wy9pvzDjyAwyKjMY238ExYsuYKk2Yt8niAslF3hx34sALOu2jMZu1ouE0hVLMWaDIqgd\nllojgkrGJPtRXD15ivLz8TQWBeS+drg81+C+d08EQcDrow+p3L4dx6FD7ygkNJXqqcuoRNstAKr6\nU7J0GdoePZj17JM8XlrFxHiBia/MYsKWH3li5xYEIHviRJTh4SjDw1CFhaFu0QKJ+uEKWgVBwO2l\nl8h8fhTFX3xBzalT1KWVYNvpbVxe/Azb5uEAGAtqKNuYRIUgkOtkQ4SnGt/KOmy7RHB0YzJr55yk\naTd/4noGgGCipGQ/rq7dkEis7x1Pz4FkZi2j0vkoni3bPNQa70dJ6UF0unSCAuc99Fid2cIb17JY\nn2+1KlwQ6UfDzVaXwNDQtx7J+h4BCqBGFEWLIAilgOdtf7sKNPz3LKueeh6Oe8lDhg+32hrW1Vmb\n+RhlNsS/+AM/NmtGzGuvMXPvjxQXXqZzz1+pq/O+GUx//z2sWHFnYH6/4Lq+2U89fzcPG4i3A4xA\nERB8/et2/tiy4b+ccqOJqdeyMVlE2jna4aO6FTyJokjlznSkWgWaVtb/fUuziliRU0ySztphoLm9\nLe+GeFFYZ2JhZiGJNXqWRgXgpfpzCUu5vpwpB6YQpndk5gYJhsNnEFyciH8uggW+lyk3L6Nt+7ZM\nbziLU2cv4FxRQbj5bieLGyiVSgYMGMCyZctI/S2V4SfVyH2c8Fu4iGfVavpFPcmyi8tYlbCK8lPl\nuFW58eywZ3F0dIQRIwDYu3cvV65coXv37oSGht6c2yJaWHNlDZ+f+Ry5RI7OpGPI9iHM7zifwI0b\nKPjoI8pWrkTSNI53z0iI8tIyrKX/zfGNfB2Y078hb2yI55OdV3mrZyQA+qulqILt7+iYaLKIJNTo\nWJydT0KzIGpkAq9F+VDVoIA5Fz6giBLmVb9JRHozkjftJWhyBLrz58kcNx4BaPDmNKYdd6PELpsV\nEWm8dSIPS5WR2U7zsVPYsbTrUkIcQ+gT3If3j7/PkotLyArIYlr7cdRdLOO4WwLTdr6Jh60HX3X5\nCj+tVVNuzMmhfM1atP2GYjFB6YYkTIW1OBXXES0PY5v7YYa2fo7KLekUfXUBl5ENkbnc+6JJ7uGB\n86hRd22vvWC9KaVu5Iq68RtUHzxI3oyZBKxdQwu1nI25V3mj0sSC/s9wtkEMn9YWo8rPQ590jdrv\nVyIajUjUajw/eB9t9+5/eg7ejrpVK9RxcZQsXYZEq8Vz9tsYy12oPV2MtpO182vJqkQsEoHj5QYe\nezIMlc5IxbZUwiKdCJjdksPrkzi1PR2FjQzfJpmYTFW4ut4q6rW1DUNVG0hlwDEUPnc6kuRV53Ew\n+yCHcw+jkqqIdYuliXsTQh1CkUruX3SZnbUChcIVN7cHf7xmUeTnwnL+kZZPis7AG4EevOzvjuTf\nm/m+H8lY9eBg1Yc/LwjCtuu/j+QRdtYUBMEXq12tO9bP/sWiKM4XBMEJ+BEIwKpVf0oUxbs1afXU\ncx9uyEPuFTiPHAmXL8ORI7B4MaxYIbB37xRm7Iohun9/hl28SHpGDDLZdqAliuv/Xh80y317oaiz\ns/X7je311PNX8LCBeBxQLYqi/q9YzH86K3JKqDVbkAsC/0jPZ17ErUI+fWIpdZlVODwRgiCXsjKn\nmBnJOTjIpMwJ8aKXmwOeylsBd6xWzeTETLqevsaShgG0ctDc97hmi5lph6YRciafSbvlGMULuL32\nKo5DhxJhY0NvYy3rrq7jszOfMU+vxk5lR6drSWSOGInLCxNRNWiARKFAuPGlVKIMCcHHx4egJkGI\nZ0QsFiccn3kGiVoNgFah5eUmLxNUFsS51HMkOCVwzHCMIDEIQRCIj4/n0KFDNGnShBYtbt3pzq7K\nZtbRWZzKP0Vb77bMbjWbnOocphyYwpDtQ/ig7Qd0mj6d6v0HSFj0LUUNn+WbZ5si/Z084qk4Xy7l\nVLD4YCpRXlp6ejtiKtGjaet9Ux6ws7iSs5W16CwWiGyJq2jizUBPCjnP9MPTcVY7s6jz1wTiS+4n\nJ1Bek5K2eSOGd99H5uqKzMmJvGlvogKyxnRmV85vDE3tSo5NAc7hPnzVdg4ahfV1kUvkvN3qbfy1\n/sw7M49cx3TaRTmx6OhRGtsF8EXMSzjqa0EoADt3ihYuAkHAddJzlP1UgP5yCQp/LU6d/chwvsaX\n+9fg5hBO7zGPU7IigcKvzuP8XNSfesCLooi5VI8hpYKaE3ko/LXInFSACvfpb5H76mvkvPwytWfP\nYS4p4dPGjdkeHsQHYVF87+vK7JDrVpNGI4bkZPJnv0POy6+ge+48bq+9inBd3/9nCIKA+6yZlP3w\nAy7jxyP38MBYVIvuYjFVB7IxV9VhKtZxSSnDxl1NcKwrphIdFdtAf60UTUsvuo6KoqbcQPy+bFQ+\nu5BIbHByvJX5rkurRJvZmsKI1VRXXyVFp2d/5n4O5hwkqSwJAG+NN0aLkR3pOwDQyDU0cmtEa8/W\nPB3xNArprfdcTU0qJaUHCQx8GYnkzy9+zaLIlsJyPkvPJ6nWQIStih9igujk/Oc+/f9GtgLtgZVY\n9eLbgUrADGiAyfcf+tCYgFdFUTwrCIIdcEYQhN3ACGCvKIofCYIwDZgGTH2Ex63nf5x7yUPgVufM\n273CDYbrgfWbXegXH8/xbt3om5xMhaQtEZFLmTx5BNHRd2bE75XlvlcG/n4XA/XU8yh5kM6aUqzW\nAC8BWsAsCMJWrEVA5X/x+v5j0JstLM0pooOjHWG2KpZmF/GCnxshahWiRaRyVzoyZxW2ce4kVOuY\nds3qVlJuMqOUSu4IwgF6uToQolbx/MU0Bp1PZnaIN6O8Xe6pL116cgExSw7SMV5E1SgS77lzUfje\nst1Ty9WMaDgCG70NCdsSqHavJurbrymbNYfiLxbcNR+AbevW+C7+hpPqk3jo4EzTOJp37oReryc1\nNZWkpCSSk5OpqqoiNDyUUrdSPj71MfGF8QxzG8bPP/+Mv78/PXv2RBAESvWl7Erfxbwz8xAEgXda\nv8MTIU9YAzZbd9b2XsuUA1N4+cDLjIsZR8de/fH49hvG9R5BrJ/jPdc4o1cDEvMqeX19PI5RPgQB\nSU7Z7Dxzks+rAnCvK6Gdixqfa0ko9u7itblfsDpjPa+dX0hj18Z83vFznG2sEiJNG08CDks48cMS\nGvv54r90KYJKRXLHTlhqagj74Thzho7B0WhHSrsKPmvzMcasbKrSjlOXnY2mbVuUISGMbDgSv8pC\npl1dSbxEoGt1DR+kH0QZf/Dmui0ezTEcTMdxyGhrNnuYE5YaI3J3qx66dYWRBlI7lh6aRb9OLrhO\naEbx8gSKl1zE6ZkIVJEOmEzVGOsqqKsqwVBWglAhR5bhgSG1HHOFtVBXopHf4eqi7dmTyq3bqNq9\nB9u2bXEeOwZ1s2ZMEgSuXM5gRU4JL/i54aqQI8jlqCIj8V/5PQWffErpihXoLl7Ee9485O4PVo+t\nCgvDc/bsm7/LXdWom7hTfSQHRDDHuJB6MI8uIxsgSARkLjZInVTor5ShaWltANSosy+/fn2B/Lyd\nOLu0Ryq9Jb2pPpGHtqwNRcKPHEr8hDcun0QmyIh1j+W1uNdo59OOQG0gAHk1eZwtPMu5gnOcyz/P\ngvQv2ZKyhY/afUSIYwgA2TnfIwhyvL2f+dPHtq2wnI/T8m4G4EuiAujlav+fmgW/iSiKs2/7eY8g\nCC2BgYAa2CGK4q5HeKw8rPJERFGsEgQhEfAG+gEdru+2AjhAfSBez0NwL3nIjeD89iAcrDaFNwPr\noCCizp1jR/dnmHBkG3sTRjJ54hl275/H3r2y+2rE75WBr9eK1/N38SAZ8fHALGA/cBqrHKU/1izL\nyL9uaf9ZbCwoo6jOxAuRbkRqbFidV8LHqfksjvCjfGsKxvxanJ4Op8JiYeiFFMxAL7WMEkHKrKQc\nWjloCFHfadsWbqvi17gwJl3OYEZSDgdLq/gwzAfv26Qqx/auJGTGN3iWg/P48bi+MPGeWUtRFKmJ\nr0GukPOb6jcmnyjji7lf4Jr9EpbqakSjEbGuDrGuDn1iIkWfzyd1zixOef/GvINq9nXtxrIff0Sn\n02GxWFAqlQQHBxMSEkJ0dDR99H1YWraU3CO5bDJuQqVVoYvSMeXgFBJLE8mvyUcqSmjm1Zx3W7+L\np8bzjvV52HqwvPty3j/+Pl9fWMz66hdYIJEyJPckVkfMu1HIJAzpWEbasc8pT36KDIWW8cfnUOk8\nAcHGFXPB65zLMxKy35tSuzrabemMSTTRO6g3s1vPRim9zcO9Oh5jnZog7x4Y+7oic3WlaMFCLNXV\neM37jIqfzhBTGI2h4gIN/7GVq6+8b/0Evk6RzRd4ffg+WslROh/9gpVeDbkYO4iB/t2RGKrAUAH6\nCihNRdzzKYGPG7D4XoDiZKQuIVYNeE0xHJ6HcHIJ41VyJrs5MWHvC3z85DbcJjaicMU5zieMpDY/\n4Z7Ph2fZONz9+qAMtkcZ5IDM1eaOCzdBEPCe9xnG/HyUgYF3jH3J352NBWV8k1XEjOBbXTAFhQKP\nGdOxadyYvJkzSRswAO/PPsO2RfN7ruHPqG7nyURJJU9aFNgmVaF1UREa53ZzfapwR2pPFyAaLQhy\nCQExLrgE5WMWi3FxuWX1Z66qQ3epGPuWIdg7tiWr6CCxri1Y1OUr7BR3N87x0njhpnDHL6Mxficz\nqC4zkOh3iKfLnuGlZpMZFNydvLxNuLv3Qqlw+cPHcK6yltEJ6YTbqlgcFUDv6wG42WhBlPJILBT/\nLkRRPAec+6uPIwhCABALnADcrwfpYJXCPBq7m3r+33BvH3FrkHwjIy6RWG0KFy78XYCs0bCh5xZa\nHHmPBrzNAvNCxg6/wJEzP9Gq1d39Eo4dg9mzb817I+iu14rX83fxIIH4GGCJKIrjbmwQBGEcsFAQ\nhHGiKNbdf+j/BhZR5KusQqI1NrR11Fht73xd+Sy9gN9OlxNypQrNYz4oY1wYHZ9GQZ0JB6kEz71b\n8VLZkBjXiYmXM9jWJBTF74oztTIp30UH8k1WEZ+k5dPu5BWmBXowyseVzBVfo/nkCwQ7GZ7ffoVj\nq7b3Xd+IYxfIk9vzYdcYYp1iefvAW8z/YigjVJ3wGDMOifJWUKp57DHMZeWUrljBqAYCDmUV9GzZ\nijM52cTGxhIaGoqPjw+m3DzOL1jA+tNnSM7Pw2Kx4OvhyxHhCNcU1zAnmgnQBhDrFktrcxOa7PXG\n3s8Pre29i/+UUiWzW80mK6Mx++uUXGjgS7OtP2N+fQpSzd3SnPiieOacnEWAxp8YXRgbFJl4maZQ\npmzIE5cvMPFKLInXzpHpJMOnz2MEBNrga+fLgNABNwNUURQp/fZbCj+di7rLCFw1rTm3ZT/+oWGU\nLFtm7RYZ0hKJsx0SdS2StCPIIyLR9uiBMigIRWAgUjs7Cqa/jGzLcHCrQ2w6kojuHxEhv9sPW3fx\nIpmbluLzbCS26QdgUXNoMhxsXeD4V2CshZin6dhhKm9f28iHicsZtGUgc7stRdlhE7UFCTiX9kYp\n90ShckBu64DCzpkc/XLyw7/Fq0lnNPaR9z1XJTY2dwThhrpiiop2oS87Rk+nMXybU8wEXzecFXe+\n9e1790IVHkb25JfIfP55fL/+Gk27ttSYzKzJL+Xb7GJCbZXMj/DDQX7vj420WvjNVdYAACAASURB\nVAOD0jLJdpJxCZHnT9TyZP8wJNJb57wqwomaY3kY0ipQhTkikQj4xV2jxiLBUhV3s7Sw5nQBmEVs\nW3hyKklGqNTClNBu9wzCjQYzlw7mcH53JrWVdXiG2OMV5gAn2hFQFcXXukXocr8hWKonwH/ifZ+7\nG2wvLEMKzMyVYYnPZnNpMpUlemor6giIcaHXxJg/neP/E4IgaICNwMuiKFbefnEoiqIoCMI9a4cE\nQRgLjAXw8/O71y71/D/m9z7iv9dul5TcP7udmSWwXDmL7sZYFlqe4pX0Q8RGxPDEkF0MHtzg5pgb\nmfDbg/sbQff9LgbqqedR8yCBeBDw2u+2/Qh8BfgDSY96Uf8JiCYT5Zs3Y9elC3vNEpJrDXzVwP9m\ngPe83JZlRpEvbM2sGhyOOtaNT9Py2FdWBcBzlmoMdQZspBI6JcezObAhn6blM/22bOQNJKLIhLL9\n9GrYnmnZtcxKzmXtpSReWr0FXbCMVl+uwdH3/mYHHyVls8sA+ARTWVVJk/WH+X63FEntVSq4iqmq\nEr83Z9wxxmHKZA4d/oE2l40oAgOJ7NGd221XU7dvZ+evOyhwcUaVlUmLtm1p0qQJrq6uPKt/lozK\nDEIdQtEoNIgWkcIvz2O0VFO1KxOx2oR977ubr4iiyLw9SeyPV9IizMJG+yziLpkp3bQB1+Ej7ti3\nsLaQSXsnYRbNOOerkYkSolrEsTCjAJNMTjs3LxqMXsiVkUORmfQMcG2FQ9MOd8yhv3KFgo8+pvb4\ncasv+gcvk/P5aUKLYjk8bRq+FguOz71IyapERK3AJU0iRSGeDJg2Gxu723TA6YfxaXwJsdpCzjEH\nxDLw6mxB8rsbE8bCQgo/nYtg54zqhdVADfz2CZxZDhYTNOgHHaeDq9VV5MkWrxJVUcCUzC0sPjyU\nJx0N+PtPJKTTq3e9xs7GZpw6PYD4+PE0i/sJG5t722MCGAwFFBbtpLBwB+XlpwALgiDlcUUx281T\nWZJdxLQgz7vGKUNDCVi/nowhQ4h/7332zv2CVRV6KkxmYjQ27CupotvpayxrGEBDO/UdYxOrdQy+\nkIJJFPk+OpDx51LZ2saOqS3uTIaqguxBJkF/pRRV2HVJks1x9JkRXEqpwCcMRItIzYk8lEH2pMqy\nWJxyjA98lEirTwLP3jFf/P5sTm1PQ19txCfCka6jo/C+Pm9QI1f2r7rCqJxh+IV+wOFqNbaVRbS0\n/X2N+Z38nFWKf76RpMNZaByV2Dnb4B/lTHWZnoyLxdRW1qHWKjBX3PK6r9i6Dfs+vf9w3r8DQRDS\n+OOieVEUxT9+Ah7ueHKsQfhqURQ3Xd9cIAiCpyiKeYIgeMJ1j8e7F7IYWAwQFxf3P13oX8+j4V5N\nfm7ndomJVAqeY/vQuv05dr7SlWcKsvhyflMWLfqR0aP7Mnz4nXIXiQS6dLFmx28c48+OV089j4IH\nCcQ1WGUot1N1/fvd6an/Eap27yZ/5iyqft3Bohem4qOS08fV2j1Rd6kYw7qrjAxU8nmAjAuBaqqL\nK/hHegEyAdrYa5Dt3YNPcDCdOnXiu+++o6mjGwuBDk52tHG87WkTRdgxFU4uxi96EKueWMzqlWv5\nwN6LmS+8RhuxkME+Ufdd587iCr7IKSGkIItStZb3igv5av9+HLv35FoTVxI2LKXD96tJbB5JZOeB\nN8ftztnHliZmolLAWFCAMScHubc3VRUV/PLllyTq9Sgc7GknSnHfuJ7Q555Ded2e0EHpiKOr482L\nEt2FIozZ1TgOCsOYV0P14RzMtUYcB4ZS+t236OPjkQcFs1QewpJsgcFNvPjwycZsTNaTtGsWFUu+\nQP3YY8iMZhRBQRhFEyN3jKTMUMbgU0oG1TTC4KZjSdUbOHlOoahMx+yLAj4xpeQqJHgbpeS/8irK\n75ZjExODqaiIwvnzqdi4CalWi/uMGTg+8zSGpCSEwt/QKNphsglHMrothRvSMRkM7EpagVlhok6v\n5+wvP9Nm8PWAL/UAllUDMWg9MY7+BZX/ZQo//ZT0zEw8Z7+NIS2N2lOnqD19GmNGJgDuM2cg1dgC\nttBrLrR9GYx6cAm56/WL7Pw+y1YfIsGhkESdhO2Z2bzjW3VX5lcud6BRzBJOnxlI/MWxNG2yDpns\nTi96nS6H5JSPKCz8BQBb21ACA17Aza0HJlMVZ88NoZ0ijaXZEsb7ut4zs12hVDJvxgdsrtBhLq6m\np4s9E/zdibO35UxFDaMT0ul9NolPwn0Z6OxAQUYlqQqRMRnZKCUSNseGYJero9vJGja31rAop4gp\nt3U4FeRSVMH26K+WAsHU1KRSq0tBq3mBSweKqCjSoSjRYS43oO0RwGsnXsdWYY+3ZzuKCzZjNJYh\nl1sD7VPb0zi5NQ2fCEda9A3C43e2lsFN3HD113Ds6AeY9VrECyN4vWwqy/osIcwx7J7vp/iCSrIw\n87RRxrgFHZDcdjFZklPN2vdOknKuEH/9ZfLnvAdtpgGQ+8YbmCsqcBo29J7z/o38xt2BuDPQGqgG\n9j2qAwnWD4BlQKIoip/d9qctWL3MP7r+/edHdcx66vkjDhy4ld0WRWtnzdhnIvgsMZ5P3hvAF+zn\nrKkfS75+h+++m8n8+QIymXV/ufzOILyeev4uHtQ1xVsQhKDbfpfetv2Ogk1RFFMfycr+zZRv2Iig\nUHAyr4iTlbXMCfVGKkDlngwq92SCvx2duwXwXUoWExMyqDGb0UolGESR54VajlVX06JvX7y9vRk0\naBC6H9eR2eJxxl5Koqu4mTmtpmErU8PuWXByMdj7IV7aTFGCJ3E/bGB8Wx8K/NuhMFt4x/4Ib3ds\nc1chZ3KtnhcS0nGpKuP5Xzaij2nKu03bkbh5G094u+IFODZrRcnTo7BMn8lVVyP9Y54GYO2VtfS6\nqkaiAQsCv72+hLzw1mQaj2OSmIi2iHQd9xKVS65hiBEoXb0az7ffBuCd5Fy2FpUzN9yXDna2VOxI\nQ+6tQR3rBk2sRYSVO9IxJGdSsWYhUlcnvs2RszYslO7pxxn+8yZSFroQo9djrgQBHZndegJg27M7\nLz+WQWZVJk+kODNwTwHqHg0w5V7miavw+kuODDm3h3MOTVm04meaGfQ0eelVzDPfIWP4c6giI9Ff\nuoRosaDp1AnHQf0RUnaTPX4f1YeOIrG1RdU9kginNtSkVSCXW7imiafjC+MJiWvBjkXzOPvrVpr2\nfgJVRTKWNc+QIhUYoRWp3Dcadzt3Hh8fTY/vrpA+2PpcSuztUTdtiuPgp1E3b45Nw99dONn73Pc8\nM5jKSAkwoa62oC3xZl/JfqoOTGHx44vver1tbYNpGLWA8xeeJ+HyFGLsn0NwDsFsY0dGxmIyMr8B\nBAL8J+Dh0R9b2zsD/6DAKfRIXcAh4TOWZBfxeuCdWfECg5GnLqSQVmviafR0nzWd6L69cX/jdQCa\n2tuyKy6M8QkZTE7MZH1hOv4J1axra4e6zsLzF00kn79KRZGOZjUiFhd7PkvPp7Ozlka3ZdBVEU6U\n/5yCsVhHcc1uAKLiBpCwPY34fZmEl+mRaOT8pj7F2cKzvN3qbQK9oinK30ByylwiI97nzI50Tm5N\nI6KlB52GR95Xt11TtwOZbRI2xtdxyw2jU7Udk1Qvsqr3StzUdxelLjmUDs4wvlPQHUE4gJOXLQ4u\nCi6vPYxs/zsoG9ySCGk6daJgzhzMZWW4THrh39bURxTFEffaLgiCA7AD2PMID9cG6y2Ki4IgnL++\n7S2sAfg6QRBGARnAU4/wmPXUc1+cnW8Vc1osUH49OmnVw4HOH+/m9bq3COcTfuBt5PozbN26BlG0\nfjaJ1y9f69vb1/N3I4jiH98RFATBwr1vdQr32i6K4v1NfP8G4uLixNOnTz/UmJJzBZgzS3HrZ/3H\naszJIbnL47hMmMBkZz9O2ztz1FOD6ZqSBTWVHPBXkSGzdkG8gYtcRrHRxLRADzR7tlFbW8ukSZOQ\nXNeEnz17lqX7DrK5STvkung62KSxXLBB+ttHEDcKseUL5I/oRHmympSuUexx98FV4kqdjR11VZU4\n9XuK12NuZfGqTWZ6nrpCVmU1Tx/bySQvD9xHj6bbmWtUmMwcbh6J6ro2N+/IPspGv8CexgKlLz5F\n/5D+TFo/jG++FFE9PYazdY3ILRGpVYC9rpyOLfREjHyGyj2ZVO21Znn1l9YQ+MNHmDUaoo8kUG02\nYxZhQZGMVmfLcB4dRXbZVQJiYpErVZT+eIyas3VgLmXjY+F8fiSNweH2vOlRhTElFWNuLhJbWyRq\nGwpXLCffRYN3oxewIOWCUz5KsZaY365Q7eOLq3t3DDHwYf5l9jRoxIpZE7kQ601tiRJbwUCX5BzQ\n6f7wNZaqBBxHjMRp5FgsBjn5806DCLZP+uEUF3Bzv8L0VFZOnUybPj1pkfcZJcZqxvoGMrnDh6RV\npHGt7BpXy65Sm5pCRJaFyUO+IDD2MYSHaMx0A4uljrPnhlJVlUgz1VA0Oz5idYuhfFR4iHkd5tHF\nv8s9x2Vlfce1pPfwz9RhhxPJIfbo6/Jxc+tFaMg0VKq75U9g7Sp5/sLzzCxrw1VpM860jkYrs75d\nM3UGnrqQQmGdie+jA2nraEf+u+9S9sMafBYtxK5z55vzVFYYmLD1Enu9rWP9kDKrQoW0QE9FYS2V\nJXpaPxGMd2sPOp68ip1Mwq64cGyun4+mEh35n57Gvk8QV5QvIYpGmjf7md3LExAuFRMhl6Du78eT\nmSNxU7uxuudqpBIpSckfkpm5FDvzfE5tVBPazJ0uIxvcFTDfwGSq4tjxx1GpvIlrup6rxwvYuyKR\nRM+jFDaJ57vu36GW37pAyEwooX9iGrYOSg51ib5rvspff+XwV4dI8+xEv9hsvEcPI3DGTgDS5nQj\nb+YsKjZvxnHIENxnTP+nzgkAQRDOiKIY908N/uN5BwLvi6IY8ajn/lf5Zz6366nn93z4IUyffiuo\nlsvht9+sP7dvDyYTDGQdjRnGLIyoCaNW2I0o+iGVwpgxD974p556bvCvfmY/SEb8f94ZJe+XDdhX\nNWSng4yu7UMo/+knAEp69+VARhnPHjlA8iEfprcK5LKHko5OGvrZqQm3VRGiVjLqUjoZ+jpC1Ur6\ny0x8l51N9+7dbwbhAA0bNUQ4tYyWKc4cC4llF7GEG0vo2Woxj8V0IXzBQqTJaoQYE5v9tPhU2/PU\n0KdwcnZm/ldfk75rO19pNEwI8kIURV46n0RSrYFeiafp5eeLvPNAynNrmBXkxeD4VJZmFzHJ36rP\n9WzTCWHECB5f/h0f7FjPqNCt9I+XkuvegjPVsZwKUnKmrRSjVMKEPRLOZarwLdVTcyofZagDluoa\nRMsgSlZt59LgXlSYzCyOCuByfgUxezI54alAdmEPyeu+J7R5a7oNGkbxvCnIA1siCRhAyyNFvNjQ\ni1eGNL5n0GQxq9FmeaBX2HBZnURMpR/2OCM0bceNFjcj3LVkusTy+LUEbMMDaH/kGvsa+GNbacbU\nrSf+7Vsj87S2qVcGBGAuL8ecfBLzuklYXKLRyBOQyNaDZDhSN3vsBoahsJGhjrrTQcMtIIigRo04\n8+tWoiINPO/uwKhW0+jg24EOvh1u7lesK6bnpp4oqn/lE0nHf+q8u5b0PhUVZ2kYNR+NWy9IOcvg\nMxvZEBnH3NNzaevdFpXs7oJQH+/hVJ9bSIYfgA5NlZEmTZbg6N7pD48nCBKiGsxl0ImJTDU1Y0lm\nLq8G+ZJcq+ep8ynUmC2sbxRMU3ur5MVt2jR0F+LJffMtAjdtROHjQ1Wpni2fn6N9uYGuI4I5obLw\nTogXrop7+49/HunL0xdS+SA1l/dCrXcGZM42yFxtKE+5SKXPOYICXwEgpqELhisl6N3UrJNupEhX\nxOcdP7/ZoCco8CWyM7dRXPMhwU0W0mVE5H2DcIC09EXU1RXRKGYxgiAhopUnJTnVsKc1RYnZvKF+\ng/kd5yOVSDHWmdmy6Rq5bW2Y6u9611x1mZnkTnsT3watSBMklEV0wUd26+NTkMnw/OB9pA4OlC5f\njrmiAq8PP0BQKO6a69+IHrj/7Zl66vkvp0MHq9b7huGV2XzLg/zGto08xVUiWcLjTOEaSrEhBuEX\nFAqrGcI/Y1lYn0Wv51/hTwNxURRX/B0L+Xdi18odYZcJyY4jDE8qZvqGTdi2aslCowSFIODj2pJh\nzRVIMLM0KogujlrOZ5VzLL6IH1JLKNTpIMqBhiVmzuacQi6X0zjYA356wWpr5xrJp/pUDipP8oI8\niuBjO8h2lXHCQ8t2bVPWXcmCDv1wbt0V0ViCfa0Eo7OWfSp73IwCAb36UbBvL1sOHsIgaU9FZh7b\nzRJap1wmtMzAxeQGXDhpzSYpVFJiOtrzWUoeHfUywoMcEAQBxwkvUn7kFC8fqOB9F1vq7Afz7vPB\nJHtZAyh1cS16Bxt+6+GK66ZiDn12lmizBU3/EJQBWnJm7cSQbM++tCI0UgldnbW0O1xEtSiwKlAk\nbv06FHb2JJ08yqnsQi4PG0d+aAyO+wt5X2rL4Cs16E4XoG7mfsdte0NGJeaqhiCUcaj4c3Y0q2H2\n6kJq1Hb8MH0ehXVKxgS5k1NbjEGioHOwH3GTNnFg5deI27axMHoAtbYyvmmo4TG/W+WmUjsN7BgO\nofYwaSPkX0Rc/RS1i7sxx+VjNl6z4Otkw3eezfF1uq3wUF9BS+lhfjDZ8Z4hAGffEPoG973rnHGx\ncWFY5DCWXFzCqOhRhDuFP/D5JooiaekLyclZhZ/fGNzdrxf59V2I7KtWTCspYbSyhhUJKxjXaNxd\n44XkPYSfS0LSsSu2dhF4bf0KSd6n8GwrkN+7O+cNFAoX+jacwtpzp/k6M5o2jg6MSshAADbHhtBA\nY4NFtCARJEgUCrw/n0fagIHkvPwK2nlL2PZlAnV6M31fisUz2J7n/uSxdnDS8ry3C0uyi+nqbE87\nJ6v2XRGuIdn0BjKZA15eT2ExmLAcyMQolXCkoJpVCavpH9qfGNdbDiWJh0vJODgY3/bz8Y/+DYk0\n9n6HpaYmlays7/D0HIRWe2uOVgNCKM2roX3iIH62WcDHmo95s/mbnP4lnTMq6z3tnu4Od8wliiJ5\nb7+NIJcT8flsLn6dTsrZQqI73BnTCoKA2xuvI3VypOgfnyHIZHh9/NGfPEN/PYIgyLC2tp8N3Nsb\ns556/ke4PRCXy2/ZDsrl1uAa4BLRvMFl/kFvPuEYqeJjPPnEIoYPH/+njX9+zx91Aa2nngfhYTtr\n/k/i2rYH1ccXE1kZg8vZI4h5uawfOIa1uSV41Vj4IExFeEUVsz95i2NxfXhVG43BZEEiQJSXPeNk\n+QjfzmePWxfcHEtp6qNCtaQtWIyg9WZH5j7WujnzXGUlo0tnsb+uCceNLQktqCBL9jP9Dkq51K03\nZ2PDyKqWU2Er57BMy67k3FuLjG0PwLm0AkBCaF4J0TnJ+KjbExDtg1uAFotZJDe5nB5XKvgkTsHU\n35LoMa/25hQW74kktFJw1d+Go9FSHEwWOleXYLyUyolKb2S+Ri42cODpUSF4rkpBLxEwONtgo5aj\naamg+rjAY7vzqeztjbRIR82pfOxaezG2cBcJRgObW5USkelCg7RklBExGNNquCy1MLiFDT9mSWBT\nEoa0ChyeCEGikKK7Ukrp6kSkWgWpWT8QczaNVsUhCNISTgYEstjJlg9CvWnq44rXT0mk2tnzsZ0b\nrXQGshIScQ8KYUjXcBburGbsxlX0bLyZqc2n4mHrAaeWQd55GLiMy6UCGy46kWGZxvzK9xlf9RL2\njb5kTWIdT3x5hGXPNaORjz2UpcGWyXgaLiH3aIc2XcOYF6feV+87ouEI1l5dy4JzC1jYeeEDnWui\naCEp+QOyspbj4fEEwUG3GRLZuUPfBbRYO4THI1uw7NIy+oX0sz6eG5hNsHsmEsdgwluvBpkC5I1h\nwyhYPwIGrwLpH3fHdHRsyQteiYzOU/LE+WRcpUYWeSejKT3Fhssn2Zt1iEyLEy6aQHztfGk8rgM+\n31xk97uHkSjkdOtmg7vng3XgBJgR7MXBsiqmXM3ieMtIpIJAgftaDFUZRNh9ikliS/oPx1GXWtji\ndxbFhRia5nelj/+zHN6QRFluDaV5NVSXGQiIfgw311QyM7/G06P3XTp4AIvFwtVr7yGRKAkOvtPw\nSSIR6Doqig0fn6FvygRWK9/HWeeFZZc/2b2dCLJREKZW3jGm4qefqT12HI+3ZyF3dyekSQ2nfkmn\npsJw17EFQcBlzBhkTk6oIu9vM/lX8QdSQrAW3ff6G5dTTz1/KwcO3NKICwKMHHkrKD5wAL7/3vpz\nbCxs3OjExN0HmS6+wjEWsvKHCWhVp9i582sOH5bfzG7/Wba7vvFPPf8qf6oR/2/jn9EaTv1lLMqL\nqYwtm4mCvawqKObTYWOQAiaJgF1qFaakcj46spiw8iz2jZ2Od5gXLkozuqoKUreuw1RRhsHNhzpn\nD1wpRq5QIXcJRqq1ZXvxduwcFHwa3IXdP+4gK68Ks0JFnW8IJoUKu6I8wlo04lh6FkgtvGVcju0z\nK7moj+XwwSxy8mvQyUTKHNMxyM3YldXgbCnDO9SFF565ty/yawkZrCksY4FOgzdSDstNrJHqyBYs\n+BYUM+TYAVoP68+Wbb/wqxCHl7MdUV5aVkkNODipWL+rgnyDSKZUSvexDXH3s2XXix8TZd+esoaO\neBhE6rKrUQ714PuZL2GKduMHr1Oo9BbaXnDHrVzFlpBQurd6lgRve06UVbFHZ4fiYC4yVzXqJm5U\n7kpH7qnB/JQLry3tw8yVBhAE7D/8kC4SB9x1Newe2JXLuQV0TSliRF4aW/xC8CnMptuPi+g4Yiyx\n3fvw7LITnEwvQhM8D42NiWWt5hC6egi17k2YLJ3JniuFyKUCnSPced6/kGaHxyDYulAQO5l9Bw8Q\naEymqSITudFqBpTaaRpjzmyk53EPOo4YS5Med2fEb7D04lLmn53Pyh4raezW+A/PM4vFxJUrb5GX\nvxEfn+cIC52BINxDR7ztFXLOr6CffwCd/LvwSftPbv3t9Lew7RVrwB3Z59b2U0th+6sQMxj6f21N\nC/0Bomhm0JHNpNTZMJX3cKXojr+bRQkZOjeSU2OxyWiGa40vUmMJcecXYVtTADIZqoYNkbVojteL\nLyKV/fE1/ffHN/GGLohn1BcIMh2ngWEXdtkdSClpzDHZOd7IGclql184HnKFDkdHIau03qWQyiU4\neqhx8rTF1c+O6Md8MIulHDveDVvbEFRh33K4rIYsfR1Z+joydXoydbXILDXMsZyiuzkGRMtNfzLb\ntu2Qamwpy69hw8enqVKWUWYuRm32ZEEfL8b4uPBO6K2utaaSElJ79kIRFIT/6lUIEgkludWsffck\n7Z8Oo8+OCwCkf/To4tt/RW8oCMJs7g7E9ViLJn8VRbHirkH/AdRrxOt5FDxMdvr2fYcIK3ERn2ee\n2URceFO6PbmDXr2sssXHHgOj8Zbe/EG6ctYH4v+/+Fc14vWBOHDt6TYUJ5ei7TaK1UEtWR70f+yd\nd3gUVfu/79maZNN77yQhBVLovXdQQBCpFkABu4KiKHYRsYKFjoiCNOkd6S20EEghvfeeTbbv/P5Y\npAjW96tv+eW+rrmyzp5z9szZw/iZZ59iKS7jpjETrRbp5+1MnL8jXtpqNiz9mnq7W8VnrBrrkRdl\nIlWpqPcKQWbWo1WqqMaRVu42VNUWIDfcsh5K9Frc3NxRyGVocrJpQEBvdyPtmijiWFVAhJCLjXMc\n16pHYO9shZchB+vjmxBllezv3ROJRIlWZuSw736+HPQl7T3b33VNVXojnc+mEmJjRaPRRLZGR6TK\niuf93Yj9ZCHShARWZ2WRKgvlZI2KLTM6o5KZGbDmEobObowsNvJWx1B2rUyhqV5PSLw7+1SluNZb\n83CBZc84DAvm4IllFF9PY1PnXKKym3lRMogL4+JI+2wDMqOJQz1qGd1+Kl+rO+GplLHNwZ3GHzIw\nNxlQhjriMqk1rya+xsG8A/xwvR8u8Z34ILo93xRV8uWCV+kxaTzvqlzYaOvK+RAXqj28WPbWPNzL\nCxn/2XKCHB3Ir25iwCfH6RCsotz+HWbnZtKruZEB2g+oUvjyeM9gJnQMwEl1w1+36AJ8OxJ0DYhS\nJZlCAOd1fgTHdKVdj4E8cPZVdCYdU5JjaKio4LHPVyC7RzVTgGZDM4O3DibEMYSVA1b+qvXcZNKR\nkvoslZUHCAp6hqDAp349s4a+GZb1YolEzVKVlG8GfUO8RzzoGuHzOHBpBY/ssZh8bufYh3DkHQgb\nbMnUYtKBUX/rr15tGePGYdA2IooaGiUCr7o5c9naism1TbSvi6fSBxR+KUhkBvTlgQhFKn50UXPR\nVMHgxiCG5LohO5eMbUMTV0N8oWN7vMMi8GoVgVercGzsb6USbMg9zoM/PUlS4NfYai6wSLkYLXIc\nr7xAQIMfSlGByVWK2/Q2OFg7UFfRTG1ZM85eNti5WN/TD7ykdDNH0z5mrmQJOlGCrVTAU9KIg+46\nrkIZ17RtqZS6M3/FZ3S5eulmP+vYWPzXrEZiZUVBSjW7llxBFOFgtyzO+nQgqHYxM8J78kDYA9jI\nbSiePYeGffsI/nErytBb1vf1b53DSiXnuUpLAcn/FCH+30qLEG/h/4o/4699R1ury6zs3Z9Z9dXI\nccWg/ImOHWM4fvxW+/vvhzlz7h6/xUf8/2/+iWDN/3l853xK/WNP8Ex4GCl+tgwvzSS62pfJXYNx\nircEPNbU1LB26y40To70dXTEWavFuq6WkyWZVJvNhBbXccFfgbQwj/Nx+ZRb23HMaEbqW8ZH7T+k\naMtJSsvKcItsix6Bmro6tDZ2mG5YEgWzGWtdI5FKOyoLwsk2DkGpKSAqcRlWTXUYhvXi8eBsRvja\noE8SOREaj5P8Cs8ceYZ1g9cR7Bh8xzW5KmQ8E+DBOzmlRKqsWBkdyGBX+hWNowAAIABJREFUS6lu\n8/vvs3btWhrMCs7V2zIqzpuErCVwYRVjHT5Cl+/ApkAlj3ooGP9mJ5IOFnD5UCHBeikV9uWYJQJK\nr0CqrErITbqI0sFErZWWkXbdCZrzHlXFahY4iUyo/JGBl6xYJfmch+JVLKlrzSInDa8/HYcmvQZV\nggep9WnsytnF1JiphEx6hqSGZtZczOBRXzfi/X0oWryYHW98TK+iHDwHtIfsTPzzr3Ou0wDO5VSw\nNdaeABcVz/RrxcJ913kuaBj9m17jI+NoItsG8/bwrjirfhEw59sOnroI6goEt3B8TQIffH+ZVy9V\n0FmbQrY5hy/7fUFAK3s2vzuP1GOHadNv0D33jo3chultprMgcQFnS8/S2fvuu7DRqCb56gxqa0/T\nqtU8/P1+J/5ZYQMPrOTRFX3ZpvJhQeL7rB+6AenJT6GpEh764W4RDtDjRUvlzsTlIJWBVAlSBUaZ\nnPNyGfZyG4KsnbFxCkRjEEg7f5E8wcwXYVAthzE5jng0TeF8QwKOTc2ECHU4Bp+g0vMMeo88ptYb\nGFzlwnsORWyPz6N9gB/P7dXSuqKO5MZGErdvRrzxu3D/6U/Rpu9AzOpKXj40kzK5QF99Fqes26EQ\nrOnbYRPY21P3YxaCUorHpHhk1pbAVEd3Gxzdbe6+vtvw9BjFmkw5EpOWDZ6XEEu+wixosUoWcCtJ\nwHpUP6aalLw+czYLnZU8YKdEcyWZ0ldeoWTOS/h8+gn+US70ntSaysJGkqKCcKypI0IFH174kBVX\nV7DC4UlMO3fiOnPmHSIcIDTBncRdueDwKxNsoYUW/i38mSI8d7aNo/HJdD5+dxDvcJFqXQJp174D\nxtxsn5Fxb+v3z8eZM5bMLS2CvIU/Q4sQB55VuHJi/kfU29rxzNUippTIsJF8i0OmGoLfpVyn4Ntv\nv8VkMjHlkUdw93JnW9Y2Vp/bR69sJWo/Dbmq7qjUauT6Zvql+5I13JkLJXloyodS/MNxaq4nM+KJ\nZ4ju1Q99fj65I0ehjGyNz4oVNCQlUfbEE0i0Oqqco6iPnoZdYxGxV5fQKBexemMuL8vX46hz5tmM\n7zGZa9jssRNXm7no8uYy8/BM1g1Zh6u15ac0URTJrMtEV76Ljo2FTFcOwKdYy7VSCYIgUFJSQl5e\nHtnO3VDojcxrq4YfPgHRzMvmY1SXjuGnACtmXy/kQLtwOgwPprGNI+s2ptEu25E9Rh0du1pzadl7\n2BiM7A8uIVjqSf95XwGwcP91FK5ejJjwKrsWvcnYs0Fcz/maMZ0eYWlBW/o429OzoxeiKPLRhY9w\nUjrxaPSjmESROdcLcVfIeCnYC6v5r7Nj/ns0WquY4GO5trNbN2ClsmXMyNE8lVvJkoJyng30ZFr3\nYPZdzuX+4sWUKn05GqahzDiH9LrP6KLqcveXbutuOQAZep4ZYk2jWc+ZVFu6tRtLD98eiD4iXqHh\nnNu2iahe/X7V/WJM2Bi+SfmGzy99ToJrJGp1Cmp1Omp1Go3qdJqasgATka0/xMtr1B/blJ4x2PSd\nzwsn32EORrZeXcWYM0sg+gHwTbh3H0GAfvMtB6A1atmWtY01KWsoVhcDGjBX4yF6oKzU4OjhQo5v\nMxIEXrR6ACdHCfllEZiNBZTlbaYsD5QqFZ6hw3Bt3USDzR4cAutZkWVmjXtPDkou8eVgF55aoWZA\nUGsc3/6QspxMTny3htMb1xHZtQdLt4zmhELglYjJWDsoOVRqQ2FFW2w1YGrtQsPhAhyHBSNzvjs7\nzG/xfVktyaYAHjMvw1S6H6srAi7Xw/GbMg9VF8v3vcVo4tFrubxQo6bRyYUnRt6Pqa6Oig8+oGLR\nR3jMmU3rLl4Emz145OQ1Rrq7sihiJUkVSczaNZWGJQtxCgrC5Ym7A2ZD4t1J3Jn7p+b8TyEIQk/g\nIcAf+OXCiqIo9r27VwsttNBxqCsDPjrLi9qZ7GE5iTVjsWEOzbwPSAgLg/R0i6ebTnenP3iLi0oL\nf5V/VIgLgrAKGAZUiKIYfeOcM/ADEAjkAWNFUay98d5c4DHABDwtiuL+v2NeFQ06NHYOLPz8XRI0\nNpjjpyGV1yJkHqUo+xrrxJHIrWyYOGUi59XnWbZtGYWNhQzIdkNqFhjlNoltugI6Cu5Y5Z3mkrcz\nD6qHUqIy0JBfS2FGNX0nP0F0r36Iej3FL7wIcjk+H36IWF5O9fMvoHRzp2LoYySnOyNRaBnSIw3H\nsCJWVw7hbNF3FLoWs7y0nByrbiTJvZhcuIuP/EbxSYcP+fjULJ46+ARvJMzhSNUl9uXuI7s+GwEB\niVnCm5Wn6F7aHTvjrWqNgncU53N0vDogCOdDU8DOG/q8iumHZqAWr1IF17xFlhdVMtPfnX3aJo51\ntOPNrvac+vQYxzenY9TUEuCgINtL5JV2jyIIAodSy7mYX8t7I2MIS/BnxPOvkLh7K/L0VISszcyy\n3ce6MzE4DuxPubKM86XneaXTK8ilKr4sqCBZrWFpVAD2Mimiry+bx03Gv7aa/kO7UZ6bTfaFc3QZ\nO4FOAd4cbjLwVVYOQ9VXaVWbzGbbAyjqK2D8TtZ4RvH4wcd58qcnWdRzEQkeCVRpqqjWVFOtraZa\nU012fTYpVSlk1mViNBsRBRlS+VwMNb1+3q90HPUg2xa+xbUjB2jbf8g9949CqmBG2xl8dX4eJ051\nBtESxKdQuGFrG4Gzc1fcXPvh6Pgnf7nqOINBmYfYoEllcdISOksEfPu+/rvdGnQNbMzYyLep31Kj\nraGNWxueT3geiSAho+o6R09upUKqo9xHS4B9IJ/2/hQ/Oz8u7ssjLy2H0S/fh1zRi7KsDMqyMijN\nzuDSxjyc/TsR1reAyvAiptSfZly7V3k17TsSW0tpt/RrHEePxi8yhq7jJrH5nXns+H48S6U1jHMK\npVdAGClpc/EQvuInZR+m/zARydTDOPQTMOSepuaqGnNTM+amJsxNTUgdHLBp3w7rtm2RWN+ZCSY/\nN483squIK8jlgR9+Qunqh+/El7B7duAdubttZVK+bRPMrNR83sguocZg5OUpkzEUFlKzahVyXx+c\nx4/nZK2aJpOZQW4W83aseyzPXvJAVZWD28evI7lHCkJnLxUuPipo+u389f80giA8DnwF1AAZwC8j\nSv89lYZaaOG/gM6d4cBPMo4eXcZKdScWLpjGt+aFOHIBtWw7YWG2dxQM2rfvlvV77VrQai05zFuC\nNlv4M/yjPuKCIPTAUmZ57W1CfCFQI4riAkEQXgacRFF8SRCESGA90AHwxlIRLkwURdOvDA/8NV/D\nHWtSuHK1kpjiFMKTlmA16B2srTU0BR7ih1IfrGnCKriAjcoaqrTVRDhFMMuo4vqWYlp5dSbFxoFm\noZkxum6Yk9dy2LGcOgS2dS+hQW5NU+ZLONva8EH/AEKXL0R76hS+SxZjHR9P3kMPYa5vQPreCg7+\nWImNk5RC2SmcnKyYXP0BB+WhzPepo0u9NW1N91HeYEAAFBIt3/UYQ4SDAzPtM3j2xBzEG+4K8e7x\nhIvhNFxooE3nNnxZ9SVyiZyPO32Mr40veqOJid+lIwAH2xxBevpTmLgFvXUnKhZfxkG2jOnmaHQj\nR3K5Wcvq6EBmpubT3dmOpVGBpE+cwh5DI1K5G9WPuLOvbD8/jfkJa5mKIZ+dQG8yc+C5Hsilt0RR\nVkkar6+bhW+ZDWg8aLRzIiQ/HbNERO3oQaW9M7X2Llh36Maqft0QBIGDVfVMuprLpxF+jPNyYcdH\n71Fw7QpTFy7E6sKXmHJPQEUaUm7cGV1CIW4idLPkpa7X1fPEwSe4Vn3tnt+7ncKOSJdIolyiLIdr\nFNvON/Ph/gz2PN2dSG97RFFk09uvUpyeyqiX3yCgzb0DMvVGDZuPtMNOMNApdhkO9tEoFK73bPtb\n1JYWI4rg7O1jOdFYTvayrkx2UqBS2LLyvi342d0KJtRrjVTmN1Ke10BZbj15meU0mOrYHL2IdgFx\nPBbzGO082iEIAiajkR8/eJOCa1cY9fIb+LeJRUBAEAT0GiNr553GM8iBYU+2vWteRoMBqVQKAhSm\nvk926SqkJhFP90n8mHOO3jtyqAt3o9WERxDNWlLPrKbGqR4PuYjsxjawUnpz1P0bviiq5/LZMUgK\nAqg6UnLnB0mlSFQqzGr1zbrT1jEx2LRrh9zXh/q9e3kuthuXIqLZcGAL0YMHYNuzJ8Kv+PADmESR\nuRlFrC2pppeTHW+GeGIzZzbqY8fw/WIJb3mHsrW8lqvxwRiOHKV+5w7UJ05yqC20/fArevr1vOe4\nF/bk8sDxVOA/x0dcEIQMIBF4VBRF/f/ZpP5mWnzEW/g7+bM+3D+3N1+4iHZrP96jDgf8iO5+nJMn\nA7ldNikUsHgxPP20xUr+87kWIf7/D/91wZqCIAQCu24T4teBXqIolgqC4AUcFUUx/IY1HFEU37/R\nbj/whiiKZ35r/L9yQ89OP8WVpZ9hsO6HU9I+rK08CQp7iONlmylXVbE1Pos6WTNdDDCl/Qt0rswn\nY89aDpe1JyguhhqfY/g4FBCQ/BhiUzxPu71Ft3O2lKlUHO6aRrB5FinpXhglMmK0jcxwc6RT2xDU\nu3ZjrKlD1qsPOZlGrkqrye9/AS9rdwrPFeJnlHHY9QBVgoL+xQPxcPKgR8+eFGuVXNyzjsyAYA4G\nxXOpfi3XMr6nWKagj9QN86C1rN2wmYiICMaOHUtWXRZTD0xFIkhY0X8F+5JEPtx/nc0jlLQ7OAZi\nx8N9X1C7JZPmpArcXV+mtqaQj9p8yw53R2qNlmef9vY2TPZxRdi6jvxjB1HYT+S6byZuA0zM7zyf\nrZeKeH7jFZaMj2NYm1vVHUVR5HqzluW5afxQUoJRbsm/3Or6KqKq5XjplKjqqpFUVyCXyxk19028\nwyIYfimTMr2BMx0jqSvKZ+3sJ+nUI56uTd+Bth6CelDg2oaXm71o1aorb7aJvuu7VevVbM7YjFQi\nxcXKBRdrl5t/HZWOdwVM1jcb6LLgMP0jPfh0nCVPtbZJzQ9vvEx9RTljX38Pz5BWiKKIUQT5jUDC\nvLwvyc75iFVVCnw9R/B8wvN4qCzxBZf27qQiN4tuD03B1sn5V/dhvbaOZbMeRaLWExSbQMKwkfhH\nt0XIPUbamU+YJqnCWm7Dl52X0ZQmJSOxnKrCxpv/UzDaNZOnSCe4pi0ekTaMebLLzesTRZEDSz/n\n2pGDDHjiaWJ6D7jjs8/vziVxZy5j5rbDPcD+d//N1GQf5HrqDJpV975/qI1Qppfgb2qHnbw7DaXu\nKKQheI8Io8+VTGZnnWTIR1/g0DUc19c/Q2Jri0SlQlAqLQ8NjY1oLl2i+cIFmhPPo0lJAaORowOG\n8ubIibzmbsesqJDfnefPiKLIyuIqFuaW0mQy87C7I2PemYciPY2xHy4ltryYeYveQmxuRublhe3Q\nIUxy20Z8YBcW9lx4zzFry5qI+/QocLcQ35OzhwiXCIIdgu/R87f5F4V4EzBCFMXDf6X/v4sWId7C\n38XvuYz8UqQvWwazZt20A+BiruQZQz/eJxnkVjQZd2IQ76x6PGCAZVyTyeIh+Pjj8NVX/+hltvBv\n5H9BiNeJouh447UA1Iqi6CgIwhLgrCiK6268txJL+q3N9xhzOjAdwN/fPyE/P/9PzWnX1sFYOWRQ\nmuxDxTk7BFHKcJ9pmIRadhdtxBjvyqhhw2h14A2oL8IghT22bbEL0iPaV2A2SpFpTeilEgISF1CF\nlk8qsuhSc54ybyNKUUL0tSYMXh3p7D0IK0GOKJrBbEKQyzCIIlKzQI5rOR8Er6JIXXTH/HpV98An\nXc0Dj89kc4UDXx/LxkupJ5Jcatq6sTn5aa7WelAmBDLQ4QzpQigHHMbzxMwnUSotOZFP5afw/PEn\n0BpNNOZOZUBwOF83vQDaOph5lg1letqvuI4Q40pwLyPGpb05bm5D+Au7eT6nmJO1apzkMqoMRhDN\nuJsMGM0S0EqwdpBibaWkoLoJmSAQ42mPjVSClUSClUTgmlpDZrMOAQhVaikp3YRO1QWJwpOr3Tvi\nILd4SDVUVbDp7Vdpqq3F99l5zKyHBWG+POzjys5Fb5F3+TxTg09j7RsN938FHpEAvJVVwpeFFayN\nCWKA678ePff2rlTWnM7j2Oxe+DpZggbVNdWsf302Bp2Oh95ayOdNsL60hq8iA2ivLCXx/H24ufXn\niL4Va1LWIBWkTImawgMew9gw+1lMRiNKlYqekx4julf/ux4ALldc5v0tL9PxqJwCTw2hTW7oG9W4\nBQSRMPR+Qtt35cy5NA4ePIdXTSgCEtwD7AiIdkHmaWRRwdtcU19hZuxM2pcN4uyPOfSeFEFkV0sl\n1rNbNnB603d0Gv0QXcdOuOOzdc0G1r56Bp8wR4bMaMNvYdCZuHK4gEsHCpAZKomP2Iu9Jh1nXTZ5\nh+zJt5Xw5gMSTIKEkZd9sa/0ROkwGSdPFfXlzTj7qFjezoSmvJwfti3EJyYd4aFvIeK3Lcrm5mZK\n8wvpX60nwErJroRWSH8t68xvUKU3sjC3lHUl1dhLBfqfPsamjj2Yt34Foz2csR8+DJt27RAkEt45\n+w7bs7Zz9MGjqOSqe44X+PJuADLeGYxCJkEURfZk7WP+iTfoF9CXBX3f+9Nz/BeF+HHgW1EUl/+V\n/v8uWoR4C38X778Pr71mEclSKbz9Nsyda3nvlyL900/hySct6QrBkgV2+nQI8DHS7cxUpu35hkwE\nrFmAmjk3P2POHItV/Lf8w1syq/zv8j8lxG/8d60oik5/Rojfzl+5ob8z51lC2ibj7pWPxBBIsGYC\nhmUXsWozjtLmnZwoT6fHhClEdA2k4MLzlMlKEAUzugZ3iksCid6Qht5Ng3GaEVFjR1jix6w1m7DN\nXoJBaUAjM9PJphet7btQY6jibPlW1MY6RMDa1Q9DozvBPsHEE4zn7PbUWzeRXJnMqdxTSHQSXujx\nPGtfnEWyXSQ7xQiGxHiSXlJHQbWa3Vav4iBvZnfgq0wcPZ6zH0+kp/4QZ2uDyI98BKGVmc0Z8STm\nqREUlTgGr0AhgzftI+mctAmHcRs46daFozv3MVyTyKte9zOlQ2u6JX+D1+k3OBk2hyf876Ozoy3v\n2Il88ukiymI6YtWhOyeKTuJWFYRCaoXGRU52TTOxAU5YWcnQms1oTGY0ZjN+VgqGujkyxNUBd6Wc\nxZcXs/T6T1R7zOcxX1feaXWrQqG6tobN78zjq7h+NPkGcaF7W5pOfsuaLzfS0bWEbmPHQ7dn7yha\nozObGXM0jdbHqglt1tDrQS9C4qKQSKV/ah/8THGdhp4LjzC5cyCvD4+8eb6mpJgNr89GVCj5ZMgj\nmOwcMZgMLFO+jq25gk4d96FQuFCsLuazi5+xN28v/a5641dmxaiX3+Tclg0UpV7DP7ot/ac/haOH\nJ0azkeXJy/k6+Wt6X/chIF/BzsG1eNh68rLtI1zes4OaMhNK25EgKJDbiiQ5n6DYO5XFoxZR2lTK\ni8dexGg2sqD7Anr69UQ0i2z/LIny3Hq6j3Eg+dB6itNTiezRh0Ezn7vrIeDczhwu7M5j7KvtcfOz\n++VyAGAymUk7WULi7jw0DXqC2rrS6b4QnL0tAlXb0EzFFx/R9M33/DBUjn1kb2LMPUg+tJoRL7xG\nqw4dKUip5sKbq0lzKmLxuIc5HOlB1PbxlsJLwz6FhCkU1Tbz/MYruNkp+WJ8/B1zmJGSx67Keg62\nDyNCde8KoiaDmWvHi6ksbCR+QMDN+f2SFLWG1zKLOV2nRobI1Y4RONncOeblistM3juZ97q9x/CQ\n4fcc52ch/qLaBhkCJqP55nvhXd3pN+nuX2l+j39RiMcC3wEzRFE8/nvt/1NoEeIt/F38lkX8lyK9\nb184dOhWUSCZDI4fv9V+/chlrN02g32YcWUUVaxHEBR0727xD/f2tojyllzj/3/xv5C+sFwQBK/b\nXFMqbpwvBvxua+d749z/OUE+3Ui+7oJPXSZh4RfIdVqMPs6W0JIoPD2G0butE6X1H1J/pRKkArpM\nZ5Q1Y0nUq5FVX2LleCOugg2vbWpCPaGR7MjPmXTtORobVNQLxZR0H0ukug1CpBPHtm2iT9oldoV1\n5LJHAPH1xUgNlynKv06s3xNcX3OE0Cd60tu/N739e9+co9htDDsvG+nio2DxQ/EYzWZOfTCacEMh\nj2uf45KpFdIdBzmk6YloK6EXB0iz3ok/uXR07EjPAW9yX1xvTNLeTNs7hdm1ZyDAF7+rX2KtPcBT\nbkeoUtYzxXyML5LGsNcxhA72bfAq/gpnlQ9D/Aaw6+P5BGq1zBs5jBRtJqcuLmRW4PtUrLfhstJI\n915evNc54nfX+6m4p3gk6hHeyatjVVEV4zydibazgdJkbPNPE9Y7kHxVML1P76Fg/6NkVsmRS92I\nf+5rCO14x1iiKJJ1qpTBP1agEUXUooxt35SSsf84IZ7WdAoNoX1sLCoHx3tP5h74OFozvK03G84X\n8EzfVjjYWES/s7cPI16az3dvzmXcnrVMf2cRGzO/QNmUzjmnN+gkc7L0t/VhYc+FjLDtzbk9X5AU\nUsPO1OeI7hZFK/9oio+msebFmcSMGM4G8TBnm68wLGgo/ieL8I2PYk7XOGYfm83lkDKmLPqCta8c\nQV2jwdi8FW1tHr6CLZd8chm/8yEaTWqC7IP4tPenBDoEAiBIBCK7CpRkaDn8TQlyWQV9Hn2Ctv0G\n3yXCtU0GrhwuJCTODTc/O8xmkdwrldSVN9NYo0Ndo6WxRktjtRaDzoRXqAODH4/BK+TOXx6s7G3w\nm/MKuYmXmXC5jpB3P0CUyci7spsLOzcT2r4DTpVXaZ2yBluvKCRmkW9LtCyYshM2TYGdT3P9egaj\nUrvSZBQRpQLRJ3OQBNhypVHDlYZmsjU6Zgd63lOEi6JI1sUKzm7LpqFKi1QuIfNCOe2HBBI3IACp\n7M4CR1G21myJDWF/VQMas/kuEQ4Q6xaLj60Pu3N231OIm8y3jBhJMgNdo6ScrDiIi8qJB1qPxivg\n192Q/kZ2AvbAEUEQLJHXdyKKohjwz0+rhRb+PXTubBG+98r9XVBgEdtgEcijR8OJExZfb6kUliy5\nUzAHzplO3Z44Zuj78RVbcSeGCvEEx4+732wzePDdIrul+mYLv8V/gkX8Q6D6tmBNZ1EU5wiCEAV8\nz61gzcNAq78jWFOTVk1xejkrs0/gYLxOaNQRnFQNCBk2SJzA5NaMVOeANDsO04Ey7EInccAui0ZZ\nFe6D/OgV0Jdol2gKjr1P5d61qAebscsYiU/5SCRWMgx1Wra47OH+S0VoL10ipdMgUkc+hrKgGdsU\nNUcCN9Pd05vIVCdCCWdf5Wqi+/cnbtAIFDb2XC1vZPzys7jqqnhMmsQj7y9CX5KGdFk3sppdGO+w\niBr1rWcqN2uBVY7vUhFdikljjdRGi01FFB29eyIpv4Y+7wTJMgmbnB/ksCSTD+yLEayr2V6rpJtT\nI45SkYMNMvY3yDEjIDPDuIxY5PkNjH39PXwjonj+6PMkliWyZege3n7rPK0bBQY+GUNotNsfXvc6\ng5Gu59IJslawI0CC5KvOYNIzKeYDzttH8/L2T6ip0iGK0H74SHpMfOyO/upaLUe+TacgtQYoIc+n\njOL4fsQdqAUR1vewo8RFhlKnoVNmEkNqi/B098DJyxsnL298I2Owtr23BTittIHBn51g9sBwZvW+\nlUN6aWEFq44cZ+y+b/Fv64VLh6NUW3fjKc2TdHJQsTI6CBeF7GaQZ1VBHiGzJ3Ck4gSp1ank1edh\nrZHQKcUZ/wqL24tEKcfZw4eqgjza9BtM1wcn8vKF1zhdcprPfddweYPl2TQo1p7AyAbSTx/ncs5Z\n9ieU4VFnxcDCMJwd3LB1dkHl5Ex1UQGFKcnYOMVipg+x/Xzp+kDYPa/z7LZsLu7PZ9y8Drj42N60\njgNY2cqxc7bC1kmJrbMV/pHOBES7/HohIqDpXCIFU6YgKJVIXZzRSyVU1dXiHZ+A6WwiylatsFuw\nhDEXCymyk3A4OBCjTkvZ9ll0Mf/ECuF+vol5ikxH6c1c6Z5yGbE2EjpKG5kalYD8F2kkSzJrObU5\ni4r8Rlx8VHQZFYqrnx0nN2aQeaECFx9b+kyO+EO+77/k80ufs/LaSg6POXwzPejPHLlewSOrzwNg\n55iH4LmScOcQVgxcgYPyr7tI/YsW8TX8eol7AERR/J1E9v88LRbxFv5JbrdQS6Xw6KMwefIfK2l/\n5gxsWVqF8puefEwq1tjRwGFMWArrDRgA+/ff3afFIv6/y3+VRVwQhPVAL8BVEIQiYD6wANgoCMJj\nWMowjwUQRTFFEISNQCpgBGb9ngj/q1i3dkHq3UC59TmuZVXSdHkwQQFXCQhLRZSHUlTYjfZpZVjr\n7kceacUReQoG9Dx7//24x/S6OU5Q73n8uLGITpcP09j2Rxqbg7BvTqA8Kp9On+yg2ajA98MPaT18\nGOr6GrYt/wpZz+NMdctFLjFh8pVTW9AHR9qSuGML53dsQ1RFssctAi9nX95p6865VdfJuZiI3d7p\nOJjB3tmDo3aLiA16H5PeTPtgV4aEuNFUHoa0poxuV8vJCLKiwu0a1UlncNK5UmtqTW7hEBLd4nnO\nfgmoSnFWzGZgqB/Geg21Od8x0OkK4XaeZKT4Yl+SgSyvlvORdTTWbua+CgNHCo4wvvV43tqRxWGZ\njnhnB06vz8T/NScUVn9sWznKZbwW4sWz6YVsOL6D8TIrUh49zcGMJuYEeTJh0Xds+/BtynKyiOw5\nnLryZvRaIzqNkdrSZs7tyMFsMmNlnUxTzSleengRrn4B1HdoZttnSUw7psbY34HDViaORXfmkl5D\nz6QThB9di0Q0Y+fixgPz3sbZ2/euubX2sqdHmBurT+XxWLcgrORSirV6Psgto0tsPIODnckqegqT\nXsKwju8ibVTwXHoBgy5m8G4rH0IKMihMSabPI48TFz6UgeEWH+jtlJsBAAAgAElEQVQmQxNp1Wlc\n63aN8txsOkkiMZbXkXHuNADJh/ZSkZvFK6+8wkObJ3JhUwlSZET18CbleAmtu7Rh1Mt9GNzYwJgL\nZ6kvK0VtW426tobq4kIKrl1BplTSa/I02vQfxMmNuSQdLiIgxg3fcKc7rlGj1nPlSBGhCe64+NhS\nkd/Axb35tGrvQe+JEciVf961R9WxAz6ffoomORlTdTWK6irUtbU0X7iIY0wMPos/R+bkxAyJwNP5\nJby34SrJ6mZKZI/xaGAH1gd3QSsT6dDUhFVWEk/UXiCBczhIbmRXORODttcCSvURlOfWU5pVT0lm\nHSpHJX0mtya8k+fNSpwDpkbTqn0lx76/zuYFF4jt50+H4UHIFH/8uoYGD2X51eXsz9vPhNZ3+tav\nP1dw87XMcxU6vRPDPOb/SyL8X0UUxYf/bR/eQgv/JdxuoQbw978ljH+vIFDnznD0qCvzhSvMEh9m\nM9+hoRMqvqaBaYwefe8+97LKt9ACtJS4B2DFlcV8mbwaK5kVzyU8R2tZJ9at34TKXI3GqKBRtKZZ\nlNOXJEy6MLJtDETaqxn7/KI7xjlxvYxJqy9woOxFSnsbMXmCa3l7dGcv0egokNvRg26t+6LR5FFd\ndQoEI2qjglC/BzmT54u5YRchrtcQzDI0BfZoL1tTUKXCLEpwdLajTY8eJJ08RwBZDHC7Sr7fJALi\nO8P2mSSP2823QgBHahqw0VxlPq9y1jyMnvkVOHhHUCPbj95cSca2MDCNImtkZ6z5nr7K9Xg1Tiby\nvvk3r0MURS6f/IGK5vcRpFq05XKkRpF8Nw+KDWU0GM3k6iWMCFjN+zuqmDMonJG+rmz96BIxvXzp\n8WDYbWOZARFBuLf4MYsi959KJKtJwym7DF5yGMCR6gYudI7EQS7j7PYsLuzOQJDcXfDFK8QBgZPk\nXDzE/bPnEZJwy22luUHPriVXqCpS02dyBE2t7Xkzu4TE+iZaWSnod6UAx9NrkCuljJ77Jh7BoXeN\nfzqrivErzvH+qBge6uDPw1dzOF5dx66wSnTl31NTe5K8gz54eY9g8KznOZJVzdP5xVRLzEzb8iVO\ngpnHPvoSe6u7595Yo+X0liyiunvj3cqBpTOm4NM6Gv+oNhxe+SVDn36ZYweaMJTLsIrQ88iTA9n4\n3nl0zUYemt8RpfWvP+yIonjTam3Qmdj43nkMOhNR3b3Ra03oNUb0WiN15c1UF6l5aH5H7Fys2Pju\nefRaE+Ne64CV6tfTAf5Zzv24kZMb1jJxwWd4BFkynWhNZqJPXsNQrMYqo4GIfgGcM+iIFdQsOfcE\noZpCSzuJLTVCDDm14SicnIkyfoNKqCZd04szTVOw8fIlNMGdtn38flVg6zRGTm/JIvVkCS4+KgZO\ni8bJ896+4/dizM4xyCVyvh/6/c1zOfml9PvqIuYbabm9/echK5tJg9Sfn17sfXc11z9BS4n7Flr4\ne/lXLdRnzkDv3hYXlpF8RSlPchYzD3R5hGcXruD4cclvCu4/YnVvEe3/PfzXBWv+3fyVG/ri45O4\nWH6B8d6++Lt2wtGhPc3VTmzeewazogjBKEE0eKJt1oIATtSzQtuZqf3ieLpv6E3RM+ajvVwrU3Ow\nTwXidwvIGqXAfJtrskkEucwWucSFkmvhXGmS0HZYd8aqNbD/VTA0Ua1oR46/Fw1eZ8AkIMm1xS7F\nxPV6Z8q0dkgFM0G2Nfg5moh66whKuRQ+jsTs2wdGLQWlhNOJo2hqymFT7aMcdWiPWqbCSazmXfMc\nMMGWa/fTEOvBsyzEpjSBtFN26ExaHNw8GP7CXOycLT/BXz//E1fOv4yVgx43u1rq5DbIFEYkghmz\nCMuvTQerHqyf1gmpROD4DxlcPVrEqBfi8Qp1RKer4HLSFKyt/WnbZum9F1/fTOrKB+gf/jY9nR04\nUqvmKX93Xgnx5vq5Mg6tTiUkzg3fCCfkVjIU1jK0aj0X9+Xj4JJCxultdHtoCh3vH3P30Foje7++\nSlF6LX2nWKyleyrreTUpnzK5SESBmlGnVyHo1Ix86XV8W98ZWCeKIsOXnKRZZ+KFhzzZfX0tI2RH\nkBsrUChc8fN7lNKLDpz+YR0u/l1QN3TELBGo8cjCLm0H2wc8RFlYDBO8XJju54aX8pY42/NVMrlX\nqgDwDW8i6+xShj8/l9B2nfjmxVk0NehBNh4Ege3tP2LduNVQYc2WhReI7O5Dr/Hhf3h/VxY0sv3T\ny+iajcgUEhQ31lFhJSW0nQdx/f05tTmTpEOFDH+qLf5RLn947D+CrrmJZTMfIbBtPMOfexmAGm0N\nPfdfpNLGBRupDp1gzXOBnjwT4IE89yhUpPLGFQf2VLpx/KW+XD6exZVj+QR62xEn34x7yVqQWyH0\negUSHgaFze/OIz+lmkOrUzEazPQaH054R88/NP8119bw0cWP2DVyFwH2AWRfPMf8NYc442qPSWNJ\nT7i8Ww3HtxzlO/f76e0rZ8WTA3/Thee3+LM3dUEQJgO7RVGsvvH6NxFFce1fmtjfSIsQb+Gf5l8R\nu2fOWPoZDJYUh2ueP8+ej/uwTq8mUIilQDiOUmnHU09BUpLF93z69Ft9fy+dYosby38XLUL8F/yV\nG3p9w1Vqa05QV3eeurqLmMxNAJhNAma9BE3WQLqPns2JTZXUFmUzbFYcCy40s+VSEY90DeS1oZFk\nV6rp/8lxepszWbXgaVjanbJTdRS3taWxnRqvsA8Ze+glpsVMx+9YV/Jzy9nV/hN2CXYosw5BcC9o\n9xhmxyDyvqijVl7Cuch1hLumUnryLVykNiS0L+Pa6dOkZdagNQpI5XL8o9vSyqoe57IeSOzcEdp9\nT4p8H77pZozGB8mtD+NMcwilXiYUbRu4zzSXIvwIMBWjUnsh5o6lyUaLIBG4fvo4tk4ujH1jASlH\nD3Fyw1rsXDzQGwYzNuQzbDVpdNV8Spfwejq6rMPNuoqg8K8I9+8DWITvhrcSkcol3D8ngOSrU2hu\nzgYgLnYtzs5d7178n96F4wt5ffghljXIsZYInO8chbm0ma2LLuERaM+IZ2OR3igOVF2sZvunl1FX\np2Fo2kFA2y6Mnjv3V0WPyWBm1xdXKMmsY8TTsZTm1HN6Rw4FIzxZZ6UnpELLxLNr0VeWMfyFuQTH\ntb+j/86kYi5dnU0X70QkgoiTUzd8fR5CZmxNTUkV5fn2XNi5DqPmIr5RgwjvMpjDK17Bwd2dtm+9\nz/LiKnZX1uGhkHO0QwT2Mil5V6vY/UUy7YcFYTKYOPfjKkz6NIY9/znhHfw4uHIHyQeWobAbiHds\nB953nEWsWyy9/XvTdMwWQ5Idwn0FmD3VdPXpSpx73O/ucZPRDAI31/F2SjLr+PHjS0T9SYH/Zzi1\ncR1nt2xgxMuvcUKewtKkNZQWz0bfwQ+poYRo/V6W9XiRAPtbcYQnMiuZtDKRcd31HK//kEZDI21c\n27C472Kc1TWwdw5k30iXbeWI2c6LBpkrZaITZcogoke+gKvjnW4i6lodB1ZeozSrnshu3nQf2+qe\nlvSakmL0mmZkCgW15kZGHx3PYxEPE51iw+X9u/g2qhui/0Ya0t8GLHnEa0uLeW7xNo6aA5lpn8WT\ns6Zg8yeChH/mLwhxM9BJFMXEG69/C1EUxb+WTuhvpEWIt/CfzC9F++3ZVgTBcjiYqxhHd5aRjjtO\nVHMSPbeybi1dahHjv5VOEX7//Rb+82gR4r/gr97QTUYjVw7u4fSmdchUdYT1DsK9lRPNhYGc2/gT\nRr2O1t0HkZMcRHCcD/0fjeKdvWmsPpXHAwm+NNdUsz+7kW/7qegyoB+kbINNUzB2mcE1jlGvbOa7\n5rZIr/oTndOHE0Gb6Ks6zLS6euj/FrSfBhJLpofsb9OItpaSPsABjWE8UjGW3G2P0mNcGDG9fDGb\nTBRfTyXr/FlyLpwjTtIbZ6UXomAir8trNBvrSd8UDKJFnNo5eNHH/jghIe6UDplBWvZrSHWORDQv\nxnN0l5trUJR2jc3vvo5UJkOvaSasY1f6P/40F459g0T/MZ2SKrniNpCRhVNQyZtY0O1NbJUi8XHr\ncHCwpJorSK1mz7JjhA39HIm0lDbJ1aSF2SJXuNK+1ykEmfLWotfkwBedIHIEjfctZfDFDO53d2KG\nsxOb3r+ARCIwZm47rO0sluTqYjXbPrmM2VBEc81mBIkLNi7jGPtKZ+xd753ODiyZQbZ+eJHGGi1G\nvZmwjh70eziSVRllzCsuI1htZkrieppyMhk041kiuvW6KexLK34i9do0jpZ1ZUifuYSb7Ti7ZQNp\np46BKCKz7kLrHiPQNewn48wRvMNaU5KRhsp1PFM+eABrWwUX65sYfimTcV7OLAzxYf1biUilAg/O\n64AgiHw5bSISmT+iZCB+rZ0oTK/FpFmPQadm7PzPOS4eYEHiAgBkJgVjr7yEWTCzqc1CTFIDvXx7\n8XT807RyavWn971ea+SHdxIBeHBehz/s3/9nMeh0LH1xKvWNNWztVoiXbCLX0qN45+F4PGwyefP0\nKxjNRt7o8gaDAgcBUFBfwODPT6ExqunR6TRDggez8PxCPGw8+Lrf1/jZ+ZJ0bCvl6WfQ1xSj1JTj\nLtTieePIxI/UTh8xtH9/ZLc9gJhNZhJ35nJxX/49XVUy965Fdvh1TlYEUqGzBWBfhzKarE2MOuZN\nSZ84Dih34W0TSMalacCtgj7NOj193t+PtrGR132LGPXcrVzDf5S/IMQDgFJRFPU3Xv8moij+uUIL\n/wAtQryF/1TuZaEGy7mfS9r/jAQTDzORbWzAgBQ566hhHHAriPOvWsRb3FX+c/mvCtb8T6XgWjI/\nrf6a6qICAtrE0XvKdFx8b2ROjIHoruM4uWEtV4/sQa5UkX4qCp06halD26KS+LPkhCVoK9aQT8c+\nMyz9Wo8A/87ITn9FLFAtetOhsTO65nDKnK+R63aSsUZPeHwXuFl8qjWNeo5vyMDJwwZBayCuQsFn\nxoH09N6Gf+x9nN2eQ3CcGyoHJX6RMfhFxhDr1Jum06Uk1qUhCzqPyq4S56SHCesUhJOXIzKFjisH\nd7K9sBUeVU10KtmMn9cLKPQ+uD/R4Y51UFjbYKWypamuBns3D/pMe4SsvHnorHag00SRiYLYqoOs\nGjKTDHMrnBWu6HTlJCU9Snz899jZReIRYqLV4M8wiZUEX5Rj7d4Pj8Za8t2yKNnQA/vuq1F6BCFX\nWiHsm2vJB97/bexkUo53iEA0imz75DK6ZgOj5yT8qgi3c3Vj0IzX2PN1Nru/TGb0nIRfFZFWKjnt\nhwVxYEUKUrmEzveHIAgCj4V7oS3T8K6qnrW9J/Ow1Sb2LPmIY9+txrdNPBlR7XEyL8LG5ML3V0dj\nKDiFe9IOEKRIFfFY2xpRV59GIXOj76ynMRs1ZJ0/i39Me6pKvDjzYzZ9JrUmwUHFLH93FhdUEJ6r\nxVipYcQzsUhlEvKTk9A1NTLsuRE01fuSuDMXJ08bNPW9qSv+nors00wYOoFhwcMQRRG5VE55RzV7\nF6ew2OF7roedZNXVVYzeMZoRISOYFTsLL1uvP7z3z2zNpqFay8jn4/82EQ7w+dUl7AxNZdgZL56u\nG8YqsT2xfgomhHsiCF5EO29i9vHZzD42mwtlF/C19eWLpC+QObbDXDyM6WEL6RLiRphTGE/+9CQT\n9kykp+o9vj1lhb1Vf9r6ORLn50igu8AJ4ykUWacZm3GQQWfGsyppMnEPvkr7IIvLlUQqodP9IXi1\ncuTQ6lQ2vJ1IZDdvEgYFoim+iMfJ2djbavH2diGv4xsYdXqmPDqJPeEmiqf25GDzTiQ6P9aPXUPC\npVN3XKeNUsFHEzszYcU50oNa/23reTu3C+v/RJHdQgv/zdwr9eDcuZbiPzNm3CnEzUhZxXqejejG\ngfSnuM5DBHGWfBbxfUo8PNeXzq+/zuHDTr8pqqdMsfy9PZPLr4n3FoH+30+LRRw4unY5mYln6TVl\nKqHtOiEIAqIoomk0YG0nv2kdLc/J4ujaFRSlpXB7hrBrLvEk2kTxbjsZ94+7LWRaFBGrsknel8KZ\nM9ZI0HEmYCsXPC4wyT6COfd9f0dhmgMrrpF9uZKxr7RHerEc9dlSzg90RNCMR2UVRdbm6YTGu9P/\n0SgA6s6UoN6eTZbWhKa1ClXkkyj0HvgcfBHHIcHY9bBkAzEZDaQc+4nC7WeIsuqOSdRR5J6BWmnA\nZDBg1Osw6vWUZl7HytaWtv2HcPXsUgL7VCJR6gkOehqF4SH2fXKCKV6zkAV1hElbqaw8QPLVGchk\nDgiClJjoxaRffw1tUz4lx6ZjrvOmonw9CGbajM3ERqkn+kwTuwojcXZUMtjpHPR/G7o+fWO5RI6s\nSyftVCkDp0UTmmDJzVpVZHFHMRsKaa7Zgr2rG2Pnv4/K0YnC1Bp2LrlCQLQLg5+IuZkx43bqKprZ\n8sFFZAoJmkY97oH23PdMHFK5pRLigrVX+MJHxN9KwRuGUvYVVbLb0RsfVQGv8gZX87qxMbkbtXIn\nHqtJR2UdR7cH2hLVzYuj61Zwee9Oonr2o88jj3Pl4B5ad+vFlSO1JB0sYPScBDyDHdCazPQ9l05l\nrZYFpXJGTY2xfOfLFpN+6jgzlq9DrlDSVK+jJLOOAytSsLXbQ1NdKVM/X47C+k4f6MNr07h+towH\nXkpA4WFm5bWVfJ9mCSacEDmBWbGzUEqVd63F7RSkVrPz8yvE9vOj6wN/3pr+RylsKGTE9hEMCRrC\noKJw1u9PZI/HYJaMj2NYG++b7QxmA59d/IxvUr8BoKdvT15MeIVRi1NICHBi+WSLwSGrNofRqzZR\nXxlNt3A5X43vzqnSY2zP2s7pktOYRTMSQUK8bSBvV4Bv2VFOmyI5GP4mT43sdUcgZVO9jvO7ckk7\nVYpSqOR+h+dQybRc8p1E55LVMHghhD6A6OWFDiNmCSzvH07Twyt5ZXSXmwV9flni/t3dqcT5OzEk\n5o8/FP3Mv5i+0AR0FkUx8R7vJQCJLa4pLbTwx/k1ETxjhsXd5JcSSqmEI0cgWprIuO592KNvYpx/\nO74vvYJZkGJCStnDc/H/5DmwsflDn/Vr7iot/uT/GbRYxP8P6DJ2Il3HTUbTYCbtdClF6bUUpdeg\naTQQ0dmTXhMikMokeASH8uAbC9Brdez96iT5V3MJbafEv05Oh2In1Km27P4yGUcPGxzdrbF1suLS\n/gZKMu3wj3Khwyj5/2PvvMOjqNo+fM+WbHrvPYQUkpBQA6GGKk2QKqBiQUCxICgo2LAgNkAUlaKg\niCgqCiK9hRp6SIH03nvflC3z/bGQQkK1vK/vt/d15Up2d+bMmbObs7955neeh/TzF5FXwYju4xEl\nMq7LxrTLxSRfKKLXWC9sXExRG0qpicxjYI0xy4tGMMJjOyEjphH1h0invs5IK+tp3JlKuVqL1ZgO\nuHf4jfSMEjp3+xxtgQmVe9OR2Rlh1MkGiSDFXdkRa2Nj1OZ1XEhZR0WhBpmlE1K5HJmBApmBAb5h\n/ejz4CRyiz6jg1UWdaUKxLRReAx8GolUinc/f85emkTf1G8g+SC2HYdhaRlKTU0iiAKXoh5CopXQ\nJaYMVUU0yY3d8Oz6OAOmdaW07Bi55e9Q7mXONHkcdWoJVVhh1uuppjGIjcgh/lQ+PUZ5tiPCs6gt\n3Y6lgyOTX1+GsYUuJ7RbgDX9JvtwYlsSZ3emETZel5VDqxUpy6uhIK2KqINZIMC4+V0pzqrmwFdX\nOLIlnqGPBSAIAvPGB1D7+QW+6wEzZLbgaktPc2OeUX6C0GCGU44TY6RK1kucuOrej1Vze2Fhp7PC\nDHp0Nkam5pz++XsalDWMfn4RMgMDeo62IPl8Icd+SGTy4p4YSiVMTVTxnofAsVBTJqCzQyWfi8S7\neyhyA51oNrFQcPVkHiaWCoY8PpNtbyzk4p6dhE2c1uoz23diR7KvlvHH5zGMX9CVF3u8yHT/6Xx+\n+XM2xW3iZO5JPuz/IR2t2maDARC1Iid/TsHSwZheYzv8Zf9L7fFZ1GfIJXJe6PYC1r0teTVKwFxT\nQz8XBad//p7gISMwtbZBLpHzUs+X6OPSh3p1PYPcBiEIAg/1qmbN0RQyS2uxNVWwbEcJlcVBOLnG\nECvZxn2/GlPdWI2DsQMzg2YyruM4squzmX90Pk/bO7Ax8B16HH2PwOTH2LLmEaY/9RpWFmZN4x3+\nkD9dwq1o+KIv5lIlC+pf4fe0QLYoLhJ64G1kBp2RGBhgWKurez1rXzqKE6Oh6D3Avd1zfrW/FRjd\nvT/8L+BWK0Sl3CbHuB49elrTXurByEjYtKlZhEsk0K8fBAQ0R7EhlF35WSzt3ZutyReoA4xRIQVs\n1r+H+oePkX3wHjz5pG7FJzcv/BMerhPa1wV3eDi33F7Pvwu9EAeuniwmNiKHqpJ6AIzNDXDrZI2B\noYy447lUlzUwck4QimsVFg0MFYx+Npxdn1qSHlMJgKu/FQojGeWFSrKvljWVujYwkjF4hj/+YU4I\ngsBCk80MjFtIcerrXCjejrf3IkpTPTn+YxK2bqZ0vc8DjaaBMs1xGl1L4QQ8YTacDMeDyEy/xdxm\nPhFfxxGKiEQi4DizM6LlUa7Gf4a9/SisrHqgnaxBXVZP2Q+J2DzSiarDWTRmVGHa1xmLUV54no6D\nw2/BUyfBsXPTOJSUHCU2YSqNqhI8PZ+hosGLiF++RiZ+woi58wmb0JEfYx4gmAOYbn0QTB0IkJpS\nLc2mWHSj0klOp+xi4lJcuVJlgZGlmoJMSy7ur8XWfSAKo11kemfiJO2EccZJfs50Jej0SQIGDObK\niVxO/JSMZ7AtoWO8gGvZPlZHoVVnoSzdjpWjM5NfX4ZEoeT4iUEYGDhgbzcMj27DKc135tL+TOpq\nGqkuracwvQpVgy5JrImFAaOeDsbS3hhLe2Mqi+o4+3saMpmEXuO8MTY34MnRvmh/vEJKHyvGm5vj\nknUZlUUM5cnTKckbhI1cwmAPA04WVlIlFbm+BFAQBMImTUNhYsLRb9bz6/tL6TFmPEbm5nQdZsmJ\nn3KIO5aLua0hkrOlTHRzYltpJRPKqvHITqa+ugq/sP7N70FONTkJ5YSN98bVz4OOPXtzYdevhAwb\nhbF588JDQxM5417owm8rLrFzVRQPvNgNJ3sn3u33LsM9h/P6qdeZunsqC3ssZIrflDaLWTOvlFKe\nX8vQxwPaLFbUaOqoq8tCqcxAWZdBnTIDZV0mjg734+LS+oLgdlwpucLejL3M6jwLO2M7LmdXkCVY\nM6Aqkj0rz5GfkkhxZjrjXnqtaZ8+zn1atfFIbw/WHkvlk0PJpBbXEJdbybsPBDG+ezhvRZYjESSM\n8x5HqGMoUonuXDzMPVg/fD3PHHqGaQW/s/HRbZjvWcYzhWspXr0d5bDFGIfO0N2RUjcibh2HnayY\njxXz+b0xiEF1crZazKVn/XPEfL2YYKmU6y5zY3UDVDbAwoXw7Dbdk1qt7tsYoPAqfD8JvAbC+C/v\narzuFUEQJDSLcMm1xy0xAkYCJf9Ih/To+R/ixtziERGgVuv+FgTdIswvW/yrN9tFrHk7IYHgXsNR\nXTjc9LoJSqhW6uaQd9+FVatg0iTCwyVNglsq1VX+jIy8eR7ymwl0Pf8u9NYU4PKhLHKTKnD1t8LV\n3wprJ5Mm4ZIQmc/RLQlY2Bsz5tlgzG10kdC66kb2fBlDQVoVglRgwkvdcPTSCSVRK1JdVk9lcR3W\nziaYWLS2CIiihvz8X0lOXolaU0RNXjCNRQ/Ra5w1NY0HKC7eh1pdjYHghElOMKYF3ak3zqS40/e4\nXl2COtMHM6mA9ZNBVJsc4Wr8y1hb9SE4eD1SqS5ntbqygaI1l9FWNyLIJVhN9MG4y7UyvHUVsCoQ\n/EfDhPUA5OX9RHzCYkxMfAno9CHm5jqBHrn9B07/9D3dRo4l/NFZpEeXcHrDPnq4nEFSk4+hWIKl\naRpG2hoENURWdkbV9RUMzfwoL6wlM7YURF3kwNA6Fc+h71MSdz/k9Ke28Rj1NSX0fGAp5/7IwT3Q\nhpFzgpAZSCnKrOL31ZcRtZnUlvyKtZMLk15fhrG5BfEJS8jP/w0Li65UVl5AFDUoFE5U53YlL6oH\npqadcOxg0fRjbmvYSoiKosjp7SlEH85GaiAlZJArXYa5c2ZnGleO5wLgNmA1RtZZlFxcTX2lBGsX\nEzzCHJn2ezSDO9nz+UPd2nyOrh4/wv61q9FerxJxHUGOzMAaQzM/RiyYwEMlKuo0Wl6PjSA7MoKn\n13+PzMAAURQ58PUVMmJKeHR5XwxN5JRkZ7J54XN0Gz2O8EdmtjlmaV4NO1ZGIZNLeGBBt6ZIfUld\nCa+dfI1TeacY5DaIt/q8hZVhc0GfHSsvUVlcx4NLA1Eq46muvkJ1dRzV1VdQKtNpGTiVy22QCDLU\nmhr6hEVgYHBnpdtFUWTWgVkklieyd8JeTA1MeXbrJY4lFrM6qIKoX77TfYuJIhMWv4VXl+4AaDUa\nBImk1Xu2YNtlfo3KxVAuYc20bgwNcKCmrJQD6z/DxS+AXuOntNuHxLJEZh+cjSiKrB36JQ1xiQhH\nltFFkoLW0gPJwJepPr8Ns7xjrBMeYXndSN4YE4BjbDU5SeX07rqH4INrUP6sxbihvk37ni//AUDG\njhd19bC9FfDjQyA3god+BqfgOxqrltzDYs03gTfucPMvRFF87q471f5xNwJjgKIWlZKtgW2AJ5AB\nTBFFsfx2bemtKXr+TdxsAWdEBNjYwAsvNL/2yScQt/IAyxLHYUbbOQQAExNwdYU1a4g0GcrmzbqI\nu1p9e8uJ3iP+n0efNeUG/o4JPSexnL1rY5HKJYx5JhipTMLuL2JQVjXSd1JHog5koarXEDzYFZ8e\nDlg63DqncW1lA2d3ppFwLgP7wAis/fYiokuZKJWaYm83HAeHsVhZhVFfn03clReoLclEJWgxVjvj\ncfpVrCf6UuV8iqvxi9qI8Os05lRTdTQbi2EeyG8sYLJvMStBp64AACAASURBVJxbD/OiEc2diTwz\nFLncku7dfkAiuXbh0FCD+PtzROS5cen0JfpOeZjeE6dy4Ks40mNL8e5ih08PO5IvfI3o/BViTQcG\n3b+ryWYBkJ9SwYGvr6CsaqRzuCtSx/epazxL+eVPyUsoRtOYgtwoDO9udgx7IhCpTEJhehW/f3oZ\nxAxqin/FxsWNSa+9i7G5BUplOmfO3oeLy8P4+b5BY2MZJSVHKC45QFnpCUREggJXY29/323f1/KC\nWs7/kU7yhSIMjGSEDHbF0sGYstIoahXPUhQzgbKEkTh2sKCiSEl9jQrRRMpxTT3zZ3UhLNCBBqWK\n/JRKcpMryEsqpzi7Ggs7OQ6eAhb2SpTlJVw+mIhGlY+oyQdEKv1D2DBwEt2SonhGXc6oZ19ErdJw\n9LsEks4V0n2kB73HeTe/VV+sIv5kBF5de+Lbqw8duodiaGLa9HpJTg07Vl1CrpAyfkG3pgwyWlHL\nlqtbWHVpFdYKa97s8yYDXAdQlFnFz8vPEzzpVxol+5raMTBwJKsRoipL8bAJ5cGg57A290cmM6Om\nNpmzZ0fi4T6Ljh1fvu3YApzKPcVTh57i5Z4v83DAw+SUKxn4UQQz+3nxZKAh3y16DpmBARKpDK1W\ng6WDE8rKCpRVlVg5OjNs9rO4BeguCFOLa3hz5xVeHO5LV3cr8pLi+X3Fe9RW6DTe+JffpEO3nu32\nI7Mqk1kHZlHdWM26YevIK7Dl5x838prRr3ipdek1v1eN5FXNI8wb4sP8Yb6U5FSz7d3z9BzhSPdf\nRyJsy0HS2DYzYJMQ/2AMGCnARgPTfGHJXrBs37ZyO+5BiA9EV7FYQCfIvwZybtisAV2V4j9EXZWt\nP40gCAOAGmBzCyH+IVAmiuL7giC8AliJonjbD4xeiOv5t9FSAEOzMJdIdFYRrVYXZwCYLG5jPbOw\noPqWbTbKTWjwDeKXgWuYta6HPoXhvwS9EL+Bv2tCL8uv5Y810dRVNSJIBeQKKaOeCsbBy5yKQiUR\nWxPITaoAEew9zPDp6UDH7g4ojGWUF9RSXqCkLL+W8vxachLL0ai0BA92o8coTySyavLyfsLQyA1b\nm8FtBLVW28jVxI8pzP8aAN+ObyKTm3E1fuE1Eb4OqfTm6fvapSILVneB3k9T2mM4l6OfIDBgFY6O\nY5u32bMIzq1DNLRmn2ImV8+cYcjMuYQMHYlWFNFqVOz59CNSzp+h23QbtGYn6dLlW2ys+7U6VH2t\niqNbEkiLKsYtRImJ33xcnB/m6q4x5KdWom6Io8/4rvQc25+CtEp2fXoZgXSqi3Zg5+HJxFffwchU\n5+mNu/ICxcWH6NMnAoWBbavjqFQVRMfMorLyMp3838PZuW2Rn/Yoyanh3K60pgI7Ln0/x8Q+GSvx\nR/xCO2BmbYhGpSXtcjExx3IoSKlEK4CNozHlBUoQQSITcPA0x87NjPzUSoqzdBOuU0cLTK0MMbVS\nEDLYhtSL50g5H8k3RvacC+7DPEMN8wKD2Ls2joK0SnqN60D3ER6tosF1NdWc+eUHks6dpqa0BIlU\nhnvnENxDOhI0YBRGpjZNRXsUxjIeWNANM+vmz1B8aTyLTywmtTKV4R7DGZg4nfrGX7AJ/AkXl+nY\n2Q4jpU7Fq5HLKa0rZZD7IA5lHsLTwpOPBnyEn7Uut/iVKwsoKt5Pn7AIFAq7W46pVtQyZdcUalQ1\n/P7A7xhIDXj3j6tsOp3BiUWDSNixmegDezGxtkZVV0d9TTXWLq64+gdhbGFB/KljVBYWEDJsJP2n\nP46ixaKmmMP7Ofz1l5jZ2jJm3sscWLua6vIyZnzwKWY2tu32p6C2gMf3PU6jppFt92/jRHwdC366\nzHTNQdzFYpbLHuaxPp68eX9A09jvWx9L1tUynjD7Gdn7n4O6bbuthPh1jIx0386rVoHf3edl/5OL\nNd8ENoiimHcv+9/D8TzRifvrQjwRCBdFMV8QBCcgQhTF2w6CXojr+TfTcjGlRKIT4C1vjM5hLStY\ngAl1t21Li4BWbsghTTgLWEWGwk+/CPO/HL0Qv4G/c0JXVjWyd20soigyYnZnTK1aW05qyhtIuVhI\n0rlCnRATaLU0SiIRsLA3wt7DnB6jPG8bOb+Rz/dtxkf+NlJB16ilZShdQjbevQi/zi8zIWk/l0cO\nobo2kb59jiORXMsokXUGNo6ATvdDymE0jl3ZVdqL1EvnGfXcS3iGdGPHB2+Tl5zAoEdnETxsCBcu\nTqK+Po8e3X/C1LT1d68oisSfyufET0k4dNuMmfsxNI1GSAQjGmrq0KikGJl6Uxg7gPoiC6oLdmDf\nwZuJS95uiv5WV8dz7vwYPD2extv7pXZPSaNREhM7l7KyE3Q0H4dHWilknoZxn4Pv8FsOR2FGFRkJ\n56kxmI2X5zw6dHi+3e22HUpl365U+tqZE9zFARcfSxy8zFt5rSuKlKRcKCL5QiFlebVIJAJeXWwJ\n7OeCq78V1XW1zIlJI7ZQxZOnazGs0zL0sYCmRartIWq1FKQmk3T2FElnT1BVVIy5i8CMZVtRGJlR\nlFnFzk8uY2QqZ9LLPTA0bc7Io9Ko2HRlE9+f/YkZWQ/gEf4J9vb34R+wirXRa/kq9ivczd35oP8H\nBNoGcjb/LItPLKayoZKFPRfyoN+D1NVlcObsfbi6PIKv7+u3HMtdqbtYcnIJ7/d/n9EdRlNVr6LP\n8iMM9rdnxYROrHvqUby69mD08wsB2Pnxu2TGXObxVWsxs7FF1VDPqW1buLTnd0ytbRg6ay4enbtw\n9JsNRB/cg0dwV0bPW4SRqRlleTlseeUF7L28mfLGe0ik7ScFSSpP4qHdD9FD60vvOCuOlyo4bKcr\nRjWhqwsfTw5plXWnNLeGH989x/01e3DfuhK0befKdoU46MJYcjlMnqz7lnZxueV4teTfVOK+HSFe\nIYqi5bW/BaD8+uN29p0NzAZwd3fvnpmpz7yo599JS6uKTKYT4eoWF+6vsJy3eR05mps3cgNqpKiQ\nczVgMt0PLCcyy0VvQfkvRS/Eb+DvjqxcH6/bla+uKFSScqkIRBErRxOsnEywsDdqt7LhnVJUXc+r\nW5Yy1e9nACQSY9zdH8fdbSZyucWtd26P/GiU34YTGWqNl+fzdOgwT/e8qh7W9gN1A8yNhPhdsOMp\n1P1eYfupSvIS4zGztaOmtISRz76EX5guAl5fn8f5CxORCDJ69NiOQtFWVJYX1HLwm/NojXbh5Ctg\n5ymlsjibgvQ4FJYSDExqSdvnhqlRNyYufguFcbOlJjpmNhUV5+kTFtH++Wq1kBWJNvZHrtT/QZGN\nBI98Ee8SU4SaYnjsD3DpfvPxKM8kNnoOpUIeffucuOmYarUi4z4/RUFVPd/NDMXf0fyWw1yaW0NC\nZD4JkQXU16owtzUkoJ8zZraGHNicQK1EJG6EHSsH+2FnIL9lW9fJyFzPhX1fknnEGXtfC6a/uRmp\nTEZ+aiU7V0Xh6G3O/c93afN527P1AFLLRZRJ6tin7YpKlBBbEsv4juN5JfQVjOXNF4eldaW8duo1\nTuaeZIj7EJ7v+jw1uV9QWrybsN5HMDRsPzVfo6aR+3+7HwuFBT+O+RGJIGHFgUQ+O5LC78/2RZJy\ngf1ffsKUN5c3WU8qiwr4ZsFcvHv2Zsy85iI4+cmJ7F+7mtKcLMxs7aguKabn2In0mzYDiaRZcF89\ncZS9a1bQe+JU+k55uN1+1dVU8/26t6k4dxVMFYyd/SKxMg+u5FWxeJQ/8nb+N/d/FYfT528TfPnn\ndtu8qRC/jkQC/fvr7mHfIX96UtdZVaahS+lieMPLoiiKQ+617XaO5clNhPi1x+WiKFrdZPcm9BFx\nPf92rltVsrJgw4bWEfEVLGABq+6pXQ0SMtz607kkomkR5xNP6LKzwO394XoP+d+PXojfwP/6hP7q\nbzHEpR1i8ZjemKh+oKhoD1KpKe7uM3F3exyZzOyu2kveGUq2aSl9ex9DYaLLO86ht+DkSnj4V+h4\n7Tv71zkQ+xMND27np292UllYwLiFrzUJqetUVcdx6dI0jI296Nb1B2SyG7zp6MrOl+bVYO/RLGB3\nf/oRKReP4T0mDYWFhm5dt2Bj1+z5ray8xIWLk/Hu8BKenk+3PZHqAvjpUcg+A3JjRP/RJLqqya09\ngbPdOPwPH0BorIMnD4J1O+n6ci5SvWMK5zqJeBYIeAe+CyFTm01+LanMIfHg18yIDqRGMOWz6V0Z\n7O9w27G+bm+JPZFLflIFAMZ2hpg97M1LBQXYyGVsDu5AoOmt73CIosiZsyOQy8woT3Qh5vdUvHp6\nM/7FTxAEgcQz+Rz6Jp6gAS4MbFGyXlldy9H941FY5lHvOo8PL3+HWlSzNGwpwz3bv1ugFbV8d/U7\nPrn4CWpRjbVUyxKneq6qrLgidMHe2B5HE8emHycTJ47lHGP1pdWsH7aeMOcw1h9P5b09CYzr4szq\nqV3Z+tqLNNTW8tjKL1td0J7+eSuRv2xlyhvv4RbYvMhRo1Zx9refiT2yn4EPP4F/34Ht9nXfl59w\n5dhhJr36Dh6duzQ9X1NexuX9u4k+uIcGZS3qro78YHOG5UM+bKrieTPK8mspHjAWv5Qj7b5+MyEu\nmpoiyGSwYIEu4bBt+5aZ9viT1pQ5wJdAGZCEzhveum+iOOhe2r7J8TzRW1P06GmiZXT82lp0Nmse\nYjpb76qdakxRI2MlC9jv9TSXsmybxL0g6G64CcKtF3Tq84z/M+jziP8/46mBHXkgrpCpm8oJ9ZrO\nnD5TsRa3kJ6+mpycLfj4LMHRYdxtI/ags3HkmddhV9iAIvk4dJkO+dFwajV0ebhZhAOM/hhyzqPY\n/QzTFkegkho3+bZbYm4WRFDgp0THzCbuyjyCO69FImn9MZPKJa1EOMCgR2eRFRdNXep9WPa/wJWE\nufSofQfj2jpEBFLqt2FgYIub26NtTyTrLPw0AxqqYMwnEDwFwcAEP1FEnraCjMwvaezXm6Cjp5Fu\nmQgzD4JJC2EUv4uqfXO4HGiEXGqGW4M17HgKor6D0SvA/lqFxNJUOLkKon/ET6tip8SKWSaf8eS3\nF1gyqhMz+3ndctylcglqVyPWS2ooNKvHWyvFwsOEr/0c8HE247HYdO6/lMy6AA+G2d78DkdVVRRK\nZQqd/JfTrdsEqsqmkn4ylUObPmLYE4vw6+1EWX4tl/ZnYe1sQudw3QXWpTOvY2idirvjR/j4T2CQ\n93TUWjUWipsfSyJIeDTwUQa4DiCuJI4iZRFl5b8RJCQQV1PP0cwKlIr9aGlstV+YUxhhzmF8GZHK\nB/sSGN3ZiY8nh1CUkUZ+ciLhM2a1Gaue4yZy5dhhjmxax8Pvr0Yq031upDI5fSZPp8/k6TftJ8CQ\nx58iPzmRPZ99zIwPP6O2opxLe3YSf/IYWq2Gjj16ETZpOlZubsTuf4I3Tr2Bj6UP3pbeN23T2skE\n0eD2vk7QeTs1MgU1JnZc7PkIRk9Mp++0wDva9y/kRWAr8IQoio232/hv4HfgUeD9a793/gf6oEfP\nf5RHW3xNbdgAthTf0X5aoAGBbDrwFm/xM5NRYcCiyRD3GdTX64S9KIJKV9YAUbx5DnF9nvF/B/qI\n+L+Q2gY1P57P5usTaeRV1uPnYMbcvo04CZ9TXR2DlWVv/PzexsTk5gIDIDf3RxISX6V7piWWdQYw\n+xh8NRhqiuCZs2B0wx3lvMvw9TDwHgLTfmg/WnyNnNytJCa+fi27ydLbXxhUZNEYsQp54WWU9elc\n9BeQqUW6X66g1kRGVLAFvoYjcAtdBbJrPnZRhAsbYe/LYOECU7eCQ1vhk53zHUlJb2Om8CDkZBwK\n60B4dJcuxdyZLyg7u5SYIAvkho507fYdxoYeOhF+6E1oqIZeT0F1Plz5DSRy6DYD+jwL30+mDkMW\nWKxi75VCpoW68fa4oHYtDhqtyIYTaaw8kIS5kZwPJnYmoaCaj/Ynsvv5fgQ6W1DYoOKR2DSSaxvY\n092HTjeJjMfHL6aw6A/69Y1EJjOloaGEnz+eRmGMgr5TH6T3+EcQtSJ71saSGVfK/c+HIDGLICFx\nIY3FYxn54L3dIr1OfX0++4+NZWXUQjIrTHC3NuapQY50cq+nsK6QYmUxQ92H8uv5Wj7an8j9Ic6s\nmhKCTCrh0FdfEBdxkDlrN7d7IZdy/gw7P36X3hOn0nvC1CYxfqeUZGXw/ZIFyI2MqKuqRK4wJGjQ\nMLqOvB8rx+YqnkXKIqbsmoKZgRk/jP4BhUxBWkUaV0uvcqX0Cvm1+cwMmkk3h26oQ7oii7nc7vGu\nR8TTVo2jsW8wtc8sptS1HyU5tdi6meIb6nhX/Yc/HRGvBcaKonj4thv/SQRB+AFdthZboBB4E9gB\n/ITOFpOJLn1h2e3a+v8wb+v53+fGCPRzz+nWbEequtOdSzfdTyszQIOEeEMznq4pphYDNOyi2mM4\nHh66QkFdu0JUVHNaQ6lUHxH/b0FvTbmB/08TukqjZVd0HuuOpZFYWI1CCmN9LzDYZTsyoQG18XRs\nHWZRWANZZUqyy+rILlOSW1HHk/086Sh5BhAIlU9D2DkXOg6DlIPw4BbdIs32OLMW9r0Mw5fpxOgt\nSE55n6ysDfj4vIa72+Ptb1RbAidWwPmvAAE8wsDKi0pLQy6pdmBi6AYaFSplHmFnCpGYu0G/+dB5\nMuxfDFFbdP2euKHthUMLSkqOEHdlHnIUhJxNx9RtOJi7UJj+LVc6WWBs4k3XrptRKFpYTGpL4dAb\numMYmELPmdD7GTC7tk30NvhtNtopW1iZ7cuaoymEdbBhbBdnZBIBmVRAJpEglQhsOpXO+YxyRgQ6\nsmx8EDamCirrVPR7/wgD/Oz4fLouL3lhg4rhFxIxlkrY190XC3lrIapW13LyVBj29iMJ6PRB0/OV\nFZfZ/tE8ylPM6DdtBq7+QWgo5/zRvcgtozGxT6S2uCMhQZvwCLq9jeZWlNQ0MHHNLvKrpLwwxI2d\nMUoSC6vp6m7Jq6M60cPTms8OJ7PiYBLjujizYrJOhDfW17HuqRl07BnGyGcWtNu2KIr8vmIZKefP\nYGJlTcjQkQQPHYGJ5W1txk1cPX6Eszt+JnDgEIKHjMDQ1LTd7c4XnGfWgVnYGNlQUV9Bo1YXQDaR\nm6CQKqhV1bIyfCUDBj4OaWlt9tcaGdPh+Z8A2NZ9MTU2uhSkpiZ+WFv3w85uOJaWdz83/0khfhz4\nThTFDfey/3+K/0/ztp7/XW7MniKR6JYuJWm98abtHFKDCQoDWK+ZyQpxAQUKD54f8T5rfluCOSJd\nJW+yR7sUAIUCjh7V7dcybeKt/N+RkbB5s+7v5oqfev5q9EL8Bv4/TuiiKBKRVMyZtFJSi2rILcuj\nj92P9HE+R7HShk1XppNY7oONiQGu1sYUV9XjbZnCY34f4u//Hi7242F1sC7qG/AATPn2VgfTFSxJ\n3K2LDN+3HBTtCx1R1BIbO5eS0gh69PgFc7Og5hcbqiHyczj9GaiU0OUhCH8FLFybNikpOUpM7BxE\nUUMn/w9wrrWAiPch94IuMq1VwYCFEL4YJO1nymhJVXUc0dGz0DRWEhxThNJISmJHUywsuhMSsuHm\nC17LM8DQoq3Q16hhTQ9QmMGc4/x2OZdXtsfSoG6bptlMIeOtcYGM7+rS6u7Ah/sS+PJYKocXDKSD\nnW4cz1fWMiEqhQFWZnwX7IWkxfZ5+b8QH/8y3bttayPysrO2sXf1l1TntH4/BImIRC5DZuBC5/Ce\nOHh1wN7LGytHZwTJ3S0eLqlpYPqGM2SVKXmuy5eE+/vg3+ljfrmYzYoDSRRVNxDiakF0TiUTurrw\n0eQQpNcykcQc3sfB9WuY+vZHuPh1QhS1VFZFYW7WuTlbD7rsMOnRF7m87w/SL19EIpXh27svXUeM\nwdlXZxMSRQ2FhbvJzFqPpWUovj6v35Ed60ZWRG7mQMZ+3M06EmQbSJhrCF2dOlKtqmTuobkklCVw\n9oV0FOVVTfuoDIyRWllQ/+LDBJTq/Orpy0dSUxNPadlJyspOUFFxEWfnKfj7vXXXffqTQrwL8D3w\ntCiKx++ljf8E/x/nbT3/e7SMQLfMJ16EHXYtito2KkxRSs3Z13UxZ/wfY803pq1yho8Ji2D0sJEU\nqeuZxFB+YjdqwYBly5rzid9uEaY+Gv7PoRfiN6Cf0HXUqzQkZB6jNPdt0GTj4PQInXxfRio1Ytv5\nLNKT5xPqnMbA/qd16Q8vbdZ5wx/fC6Y3T6EHgLoRIpbr/NJWnjBhA7i1X0xFparg7NlRSGWmhPbY\ngbQ4BWJ/hsvfg7IUOo2Fwa+DnW+7+xcW/kFp6XH8/d/Tec1FEVKP6CwpIdOg002yVdxsXOrziI5+\nktraJEREbGwG0Tnos3tPARm1BXY+A9N/At/7qG1QU12vRqXRotaKaLRaVBoRJwtDLI0N2uxeUtNA\n3/ePMK6LMx9OCml6flNuCYuTcljg6cAir+bsJBcvTqVRVULvXgfbFZ4HTr2MMvsAxvLOGMv8kGqc\nKc9rIOVCOsbm1VSX5KHV6PJqyRWGuAUF0+uBKTj7+t/2VFuK8I2P9sSer8nM2kBo6B+YmfqjbFTz\n1Yl01h1LZXSwE8snBDeJcIDvXpmHVqPR+bdrk0hIfJ3KyotYWHSnc+cv2uSFByjPzyX64B7ijh6i\nQVmLV9fuBI7oQFn9FpTKNAwM7GhsLMan4xLc3dtWHr0V35/N5I2dV9DckJZQLhXoYGvKuxN8WJfw\nOmvu34iBRgCZATXufph89DbSsWOIinmC8T/qctVnvD+6VRsaTR0aTS0G7ZzT7fiTQjwbMAdMASVw\nY1VLURRFj3tp++9EP2/r+V/hukBuWWGzWmOEQlBRLxoQQzDvy15nnzAStVZyU4vJvl35PDe2Fylk\n8yDORMrP8OMxN8LCbi6yW4rziIjm6Ly+KNDfi16I34B+Qm+NRqMkJfUjcnI2Y2TkSWDARzSK9kRd\nGESBZhwz7vu4eWNRvKXvuw2Zp3XZVKpydZHpAS+BtG36vbLMX4hKfRnXMkP84nJAIgOf4brtb5VO\n8C+gqiqWq/EL6eD1Avb2ugwZanU18QlLkMut8PV5HYnkzlIGtotGBZ91AxM7ePLw3Y3fNZb+foUt\nZzI5tmgQLpa6CwJRFHkhIZttBWVs7uzFcFtdVdHIM0Px9l6Ep8ecNu00qrWEf3SUvMp63K2N2fhY\nDzra63zYWo0WiVSCRq0iKzWdo6eiiI+7im3RVWSqOtyDQug9cWqbLDjXuVGE9+loi0pVyenIwZiZ\nBdC1y+amCwO1RovsBp98QWoy3y+ZT/ijT2Dum0R29kZkMnOcnSaTnbMZudyKkOD1mJkFtHv8BmUN\np35bScz+s2gawTEY+j04E/cO44iLm0dR8T6Cg9dhZ3v7zHwarciy3fFsPJVOuJ8dnzzYhep6NVll\nSrLKlGSWKvn1Ug5mhjJ+e6YXVZ09uGzXSOX8p5k+6T0EQaCy8jIXLk5k5oFPgbZC/M/wJ4X4N7Sq\nXtAWURRv4hP7z6Gft/X8L3JdGD/3TTcyjAN4KOYVYrRBTV8ToqgTybNmgbt7c3T7+n6Wlip+eW8M\nR3IOMExuwLadO7AaObKNBWboUJg4sVn4GxjAJ5+0fqyPiP996IX4Degn9PYpKztNfMIr1NfnY2bW\niaqqq3x8+R12z5/aKmp519RX6hZLRv+gU0c23jrbSUM1NNToXq/KIamDCdmuRoQYPYhtyEtgbP3X\nndxN0GjqOHd+LEplGiDg5/c2ri63zrxxT1zYCH/Mb53u8S7Irahj4IdHebi3B0vHNi82rdNoGReV\nTLqygX09fBHzPyMrawN9+5xsN0f7TxeyWfRLDC8O8+XbyEwa1Bq+eKgb/X3s0GpFItNK+eViDnvj\n8qlXaelgZ0JdrRLH/Ch618Yia6jBxT+QsInT8AjWpf/LLlPy84VsfjyfTVW9qkmEXyc7+1uSkt8m\nOHh9GxFcX1tD2qXzJJ89TUb0RRBEQh4rRkM+zk5T6NhxEXK5FVXVccTEzEGlqiQg4CMc7Ec2taFS\nVZGXv42c7M3UN+ShkPhRcSWEpJNXkCsM6TV+Cq4B/sRcXEJNRREOVo+gaTBAkEgJHjqi1QJNgJoG\nNc//EMWRhCIe6+PJa6M7tbloADiRXMwjX59jzoAOLBrhyztn3mF78nbCXcMZ7zMey7LvqKmOZcZu\nnfXkv0WI/1vRz9t6/te5seiPKOqE9I0i+cbtHn8c7FRv8f7XS/EEfl+yhPLR7zJkqEBDg8760tKP\nrtU2R8BtbGD7dp1Inz27/T7pc4z/efRC/Ab0E/rNUaurSU5+j7z8n9DI+zB791R+mNWbMG+bP9/4\nld/g6Hu62UVh1vrHvhOagDGcT3oWlaqcXqG7MTD4C455GxIS3yQ3dwshwRvIyd1KaelRvLzm4eX5\n3D35iW+KugE+7QqW7jprzz20vfDnaHbF5HHy5cHYmjZXbM2ub+S+C4lYyqSMa/ycwRZaeoZ82WZ/\njVZk2MpjGMql7H6+H7kVdTzxzXlSimro6WlNVpmS/Mp6zAxljA1xZlJ3V7q4WaJs1LDuWCpfH0vC\nt/IqfWtjEJSVOE+ay54qG06m6HyN/X3smDfEh+4erX3yWq2KM2dG0Vgr4uuxmtqKSqqKi8mIvkhW\nXDRajQYTK2vsfGUYuJ7B3sMTP7+32/jbGxqKiY19msqqKLw8n8fRcSzZOZvJz/8FjUaJpWUv3N0e\nx9Z2CIIgoTQ3m+PfbyLt4rk2YyFXKNCoNYhaLf59BxD6wGSkpoWkZe9kdaQfpzJtWTo2kEd639qh\nseS3WH44l8UvT4XRzd2KDbEb2HJ1C6ZiCS86NJAqDea9vU8CeiH+Z9HP23r+bdyLiG25D7S/f8to\nN+i+TgwN4ZNl+3j9lXHUNzaydeBAbN/YzRsfmHDoULMYl0p1f99JRFzvIf/r0AvxG9BP6LenqioG\npE70/uAi47q4sHxC+3aEv5rqmgTOnx+Prc1AOnf+b5+dcAAAIABJREFU8q8VwzdQUhpBdPRM3Nye\nwNfnVbRaFQkJS8gv+BUXl4fw830TQbj9As875ux62LsQHv0DvPrf9e6pxTUMXXmMpwd6s2hEa792\nZEUNT8UlUqiSYi7VMtHRngcdrQkxM2oaw90x+Tyz9RKrpnRBI4ocji/kWFIxykbdbO5mZcSC4X6M\nDHLEUN72vPMr6/hofyI7LmYxNfdnpKKGiMDHmBjqyeQebk2WmZakXTrPwa8+p6aspI0ZwtLBCZ9e\nffAJ7UOjwSlSUpfh6joDn45LbmoF0mobSEh4nfyC7QAIghwHh9G4uT3eeqFvy34nJ1JbWYGxuQWi\nrJj41LlYWHbEz+sLLuz+lZhDB9A0qrHwqsahWwlVRla4+f3MAF/ndttrSU2DmvtWHcdAJmHP8/0x\nMpCi0qo4eX4aDbVX+KDQgvTo1wGYOOIIvZx60dupN25mbn/qs/0XVNbsjC6V4EDACp1P/CjwjiiK\nsffcsb8R/byt59/E3ylir7d9PWc4NEe4H5qWwQN9+nA5P5/ljo4MW32cfo/5tLKjlJbemUe8PXvL\n0qV6MX4v6IX4Degn9Dtn3o9RHEsq5tySoRjI7i57xr2SlfU1ySnv0cl/OU5OkxHFRrTaRjSaerTa\nRhQKhzYFgO6WxsYyzp4bhVxuSc8eO5FKdRFmURRJTf2QzKz12NuNJDBwBRKJ4jat3SGqOlgdAnZ+\nuhzl98Az31/ieFIxJ18ZjIVRa7EaFTOXk+VKrti+yb6SKuq1Iv4mhrzawYmhNuaM/vQkykY1tqYK\nLmSW42CuYEgnBwb72XMiuZhvIzOxN1PwSG8Ppvdyx8a0/fOOy63kj70RyA9uoN+0x+j1wKTWG2g1\nkB+N8spBvvnuBEbSRnwcBSoclWjMlfSwHY/Mzh+7nmORyAwoLjlMTMwc7OyG0zloDYJw68+ZKIrk\n5v1AY0MxLi7T2rXg3Iri4gPExM7F2LgDdXXZqJQaqpI7kX1BQFSpcQotos+kme167NvjdEoJ0786\ny8x+Xrw+JoCq6jjOnx9HB6/5uLjPxvfVgwB4d19JkbIIAGcTZ3o59WKYxzD6u979Rdmf9Ij3BI4B\ndeiK6xQAjsD9gBEwQBTFi/fS9t+Jft7W82+ipYj9qxZCtoyWx8bC11/DpUs6Md5S7CuVSmaOGsWP\nx44xTS5n4Ztb2SeZ1CayfuPFQkuR3nLBZ0t7i0Khj4zfC/rKmnrumbEhzuy8nMfJlOI7KtH+V+Dm\n9jglpUeJT1hCfMKr6GqJNePi8vA9pXy7jiiKJCS+hkpVQZeQTU0iHEAQBDp2fBkDA1uSU96DqxI6\nB316V+3XqzScSinhUHwh9Sot70/sjEIm1RUH6vM8HHhVlxe9x0wwsrx5Q1qNLl2kuUuTleXpcG92\nx+bz2o44ZvX3orOLBYIg0NBYQnnpYUa4PcZzHb2oVKnZWVTB17klzIhNZ6qZGVfyq+jiZsGFzHJW\nTglplSZxaIADgzs58NWJNFYcTOKzoymMC3Hm8b5eBDi3rnAa5GJB0JPj+K0smrO/bSMofAgmRnKI\n2w7JByDjBGJdJYdyO9GgskG4bxDHTY0pEjWkWRiytsEEdbEW812/MTS4E6bZH+FrGkRgwIrbivDr\n79Gf8fHb2Q3Hx+dVMjPX4eoyHWfnKWiHdGDwe/sYXXkCzkGU9Vc4TB2DkZHLbdvr09GWGWEebDyV\nzn2BjhhWr0EmM8fN7VFk0uYsOIcmHSKjKoOz+Wc5k3+GQ1mHMJGb3JMQ/5MsB+KAIaIoVl9/UhAE\nM+DQtdeH/9Od0qPnf4nwcJ24vS5yr1tN7pWWorllFhWZDEaOBMcWdcGMjY3ZevQowYsW8erHH5P0\n2mR2PP88rqErgea7nWFhOlF9YwaXlqL+8GFdFPy6vaWxETYfiSRCHUG4ZzhhbnpF/k+gj4j/P6ZR\nraXnskOE+9mxemrXf+64jSXk5GxBRItUYohEYohEoqC07DilpcfoE3YEQ8PbWwfaIz9/O1fjF9HR\nexEet4h6pqd/Rlr6J3QJ2YSNzYBbtllS08Chq4Ucii/kZEoJ9SotJgZSahs1TAt1Y/mE4GsnVgs/\nTIP0YyA3huAHIXRWc7VPjQoyTsDV3yFhN9QWge9IGL1CVxkUXQaV785kotGKuFgaMTLIkc7WRzCu\n+4Sw3nsxNfFp6pdSo2V+QhY7iyowii5DLKjj5RH+PB1+84qqKUXVbDqVwa+XcqlTaVpVvWxJeX4u\n37w4l4AOZtxncgwaqnQeeK+BJNS5s/u34yT0H8WuwD7IBLCSyzDWlKJQ5yGtkFBhbEn+teJI1jIJ\nYVZmDLAyY5SdBXYGfyJLzT1wvbjQjjmhxK57i5KcNEIfc6Tv0I13tH9tg5qRq0/gaJzNnIC38PKa\nRwev5wHwfGU30NYjnhF3GWMHW+ztXNu0dzv+ZES8BnhEFMXf2nltAvCtKIptS5r+h9HP23r+bfyV\nCx1bRthbZlS5vgjzxqj4df7Yvp3p06ZhrFLxa2goffbs0anuG3j6aVi3rjlLS8sIfquLAM9IxBnh\nqEUVcqmciEcj9GL8DtBHxPXcMwYyCaM6O7Lzch51jRqMDP5Cz/StjmtgS4cOL7R53sYmnMjSwWRm\nrcfPd+ldt1tXl01i0ttYWobi7v7kLbf18JhNQeFOEpPeonevPe1aVERR5JeLObyx8wp1Kg0ulkZM\n7enOkE729PKy4ZNDSXwRkUqwqyXTQt3BwAQe/R3yo+Hcel0mmYubwLM/WLhB0l6oKwe5CfgM02WY\nifwCPu8FQ9+EHjNZOjaQeUN8OBhfyN7YfL45nY5a64Wd8Qe8ZK5gUnexKcuNsVTCE0Zm7LmYilhS\nj6WXOeN7u93yvDvam7FsfGcW3efPhhNprDmagoWRjHfGBeki6KIICbuxOreObhbZXEh2ocvQwTjc\nNxfcQqmtrODQi3OpcnJnf0Bvvg/uwGBrMwRB4GpOBmlXn6be2BenxmiyJU4oO64nqsGM0+U17C6u\nZHFSDn0sTRnnYMkoW0tsDG6oHKoVKVOpMZNJMWonm8ndUlWv4quT6QztZE8XLzu8Fy1l86I5XPox\nB/eOf+Dm2TYPfV11FQmnjuHXZwDG5haYKGR8MM6KuKtvo9Ia4+oy45bHzE24ys4P3sara0/GLvjH\nE/feLrLyvxV50aPnP0RY2F9n4WgZYW8ZEZdIdL9FUWchiYhofcwxEydyJiqKcYMGEX7uHF/6+jLz\nwAHo3pwWODISNm5s9pvLZK0j+C0j5+fsNrMjV1dhuFHTyObozXoh/g/wzxiD7wBBEOYLgnBFEIQ4\nQRB+EATBUBAEa0EQDgqCkHzt953XudZzR9wf4oyyUcOh+ML/dFcwMnLByXECeXnbaGi4u/7U1CYT\ndfkxAAI6fXTbhZgSiQJfnzepq8sgM+urtu01qFnwUzQLf4khxM2CPc/35+TLg1g6NpD+PnYYyCS8\nONyPAb52vLnzClFZLeqmOIXAuM9hQTwMfQvKM3URcJ/7YOpWWJSqq1465A2YGwmu3WHPS7BpJBQn\nYWViwJQebmx8rCcbx25jTsgvuFjb8vL2WEauPs6RhEKu38latjseaUk9fu4WVPiaM/JSMmcqalBr\nb623LIzlvHSfH3MGdGDLmSy+OpGue+HiN7DtIShLp/fEaRibW3Ak2wHRLRQROLBhDXV1dfwy4AE+\nDfRiiI15kwVm5eFiDmWPwMoglnoTKcPik/CKi+KzTh5cCAvgaE8/5nk4kNegYmFiDsGn45gYlcLk\nyymEn0sg8GQcbseiCT59hQlRKfwVd+u+PZVBZZ2KeUN0BaPMrG15YNFbqJRy9n22hsaGJvcGWo2G\nqH272DhvNkc2rePHNxZSXphLRsZa6vOn42FewlexD/Lu3pyb9q0oI43t7y+lSmpKvNfQP93/e+As\nsOSaFaUJQRBMgJeBM/+JTunRo+fmXBfD77yjE8RHj+r+nj+/WUBrtVBRofs7MlIXRY+MhIDAQM4l\nJhIeGsqTZWU836sX6g0bmtqOiGidgeXxx9teQISFXYuQmxW0er6gtvlxZHYky08sJzI78q89eT3/\nHRFxQRBcgOeBAFEU6wRB+AmYCgQAh0VRfF8QhFeAV9B9mej5i+jlZYO9mYLfo/O4P+Te7CB/JZ6e\nT5NfsJ3MrA34+rx2R/sUFu0lPn4REokRISFfYWR0Z3YAG5v+2NuNJCPjCxwdxjXtF5dbyXM/RJFZ\nWsv8ob48O7hju7nWpRKBT6d24f41J3l6yyV2PdcPO7MWkXVja+j3AvSd13yf8UasveCRHbro+b7F\nsLYvDFwEfeeTX7QDlfIUjw5czitOA9gXV8CH+xN54psL9PKyZoCvHTG5ldiaGvDzE73IUql4NDad\nB6JSkAsCnkYG+Bgb0tFYga+JIaPsLDG+Icr88gh/csrrWLYnHi8jJUMPL9VF8GfsRCGR0lfYz8H1\nn5EYeQKtRkPahbMc7z2CF0O78oBD83Xx+YwyDsUXsWj4k9ja1mBnPYSG02/hcWk5pQPHY2NhSidT\nIzqZGrHIy5GrtfXsLCxnV345loYyvIwUhFqYYGsgo7RRzbd5pRwqrWKYrcUdvZft0TIa3tm1uR0X\n3yD6P/IAx7/ZyR9fvMSE+evIjLnM0W/XU5qThXtQMIHhwziy8Qu2LJ6D18g03P3D8fV5g4sN5aw7\nnoZWFHl7bOtMLuX5uWx793Uq1RJ+d7ufZb63vjvxN7EEiAAyBUH4A8hHt1hzFGAMhP8nOqVHj55b\nc2OEPSxMJ7av36gEWLkSvL3b+r3BigH3n8LW+Vk+27GOK7Nns+bXE+wKW4+No2ErP/uMW9zQczRx\nbPdxZHYkQzYPoUHTgFSQsmbUGmZ3bycxuZ574r9CiF9DBhgJgqBC94WRByym+YvjW3RfMHoh/hci\nlQiMCXZmy5lMKutUbbJ1/NMYGbnj6DCO3Nwf8PB4qt2y59cRRQ2pqSvIzFqHuXlXOndeg6HC8abb\nt4ePzxJKy46RlPwOwZ3X8u3pDN7bk4C1iQFbZ/Wmd4db5zu3NDZg3cM9mPDlKZ75/hLfz+qF/EZL\nhSDcOre4IECX6dBxKOxdBEfeRZW4kxTfWiwsuuPkNAlBEBjZ2YmhAQ5sPZvFqkNJnE0vQwC+f7IX\n5oZyggzlHOzpx4GSSlKVDaQoG0hW1nOgtBK1CMHZxWzq7IWLYfMiQ4lEYMWUEAqq6qnctQRRWoMw\negVIdHcUggYNJfrAHo59t5HqOiV5Dm4MGDueJ1ztWrwPIu/vTcDeTMHj/fwwMlgPQN4wGR32PcGO\nHz/mgTlLW5yugItESvLxHPITi+kZ4szqqb5NkXWVVuRIWTWrMgsZ2iLifrfcGA1vSc+Rs8hKPE56\nZC7fvfIMRemZmNvbM2zuw9j7m1FZcQzP0VdJ3+tO2h/+hAQ+jaGhI6+MdEAiEfgyIhVNi3XG1WUl\nbH5zCdXKBk76TmXznOF0cjJvc9y/G1EUzwmC0Bt4A7gPsAbK+C9PX6hHj562hIfrrCQqle6xVqvL\npnI9tWFDA2zeDN9+C42NMgwM1vLq4lA++mA2Y/Z9x7J9F3lTsYdPPvVolTHlZswImcHGyxtRaXQe\n8RkhOtUekRFBg6YBrahFK2p5Zs8zdLbvrLet/EX8V1hTRFHMBT4GstBFcCpFUTwAOIiimH9tswKg\n3dQegiDMFgThgiAIF4qLi/+RPv8vMbaLM40aLfvjCm6/8T+Ap+dctNpGstqxjFxHpSrn8uUnyMxa\nh4vzNLp3+/6uRTiAoaEzXp7PUlJyiAWbv2Dprqv097Flz7z+txXh1wlwNueDicGcyyhj2e74u+5D\nE6b2MPkbmPwtKeZ5qFWV+Nf6IGp0mVpWH0rmyW8vsOJAIhVK3cz8WF9P/BybBZ+1XMZUJxte9XZm\nU2cvTvTqRPqAEDYFeZJW18B9F5I4X1nbegzkUjYNVjNRcoxN3E+mpPmOgkQiZdBjs6gpK0Hd2Ijx\ngzN5qUPrOyeH4ou4mFnOC0N9W60zcO41gQyz7vT/v/buOz6qMmvg+O+kh4QQSKihdwHp0gSN4C6i\nrg27Ai4I9r62VV/brl0ExMZaEQUbKiqKgtIEQXpVaugdQighCcl5/3huYAhpQJKZxPPlk08yd245\nzwy5OfPcc59n89ssXJl0ZPnCDclcMGw601ft5NzTqjJu4Wb+N23NkedDg4Q761RhXspBpuxxpSNp\nhzOZvXZ3octV8uoN93X+zS9Toc4hdm5YS0KnZOr+Yyo7Mh9h6dI72bhpFA1Pv4zrn3mD8nFV+eKZ\n/2Pl7BmICA/0bMLt5zRk9Oz1R/Y14uEHOZiSwqo21/DRv/7hlyQ8m6ouUtXLVbWqqoZ636+0JNyY\n0qVzZxg+3CXjQUHue/aQhuAS86lTXUKemel6vaPK96f/oOlsoiIDWcajaS2I+e1HHn644Jr2zrU6\nM7nfZG5qdxP9W/c/sjyxbiLBPuWeWVlZTE6aXAwt/msKiFFTvNrvL4CrgGTgM+BzYLiqxvqst0dV\n860Tt7vvT5yqkvjSZGpVLMeoGzv6OxwAli69lx07f6JL5ymEhVU65rnk5DksXXYvaWk7aNrkSWrU\nuPKkj7Nq+35e+mEJZ8beS3hIJho/iivPaHhSvbBPfbOMd39dy62JDbjnb42P9Iyr6gntLzl5DnPn\nXUWdgzVoOGcRm6Oa02f3DawhgcZVytO2Tixtalekbe2KNKwSXej9rjhwiH6L17DxUAbPN6nJtdW9\nDxqZGfDWWRxO3Uu3/c8RERXD0Ktb07Km+9X7bkcyb3w0isY1a/JS74sJ8mlLZpZy3pCpZGYpP95z\n1nGjrxxcN4+I97ozNuJSLn3gXT6etY6nvl1GlfIRvH5dW1rWrMBtH8/jhyVbef+fHTirsetpT8vK\novNvy6kVEcYHTepw06i5zFq7m5euaMXl7QouPcoeKeWb27vmmYgDbN36PZs3jiUqphaRkbWIjEgg\nIqIWkZE1CQlxZdap+1L48vkn2bpqJc0TexAeFU1IaCiz1qXw6p56ANySNIKUbjfwfzdd5IazPAUn\nege+uHEhLwDWquqSPNY5Hairqic3yH0xs/O2MXnLHqFl/fqjo59kyy5d8R0HHKB7903ooV6ksZgn\ngceefBJ59FFmzgrKd7SX7DKU9Mx0woLDmNR3Ep1rdWbE3BHcNv42srKyCA8JP7I837g3zGRyUtkf\nCrGsjJpyLu6PyA4AERkLdAG2iUh1Vd0iItWB7f4MsqwSES5pncCwn1cyYelWejY/8Z7lola37q1s\n3TaODRvepUGDfwGQlZXOmrXDWLfuLSIjatK+3SfExLQ8qf1vTznE0EkrGfP7BiJDg+lw9t3U4GHq\nVf4ekTsL3D4rKx3VTIKDj844+fD5TdmflsHrk1czdeUOXrqsOmHp37N58xiCg8vRovkQypdvXsB+\nM/jjz0eJCK9BvbN+YHXUF1Sa/DA/RDxC+hUfEtUs/6EW89M4KoLv2zXmpqXruPePDSzbn8oTDRII\nmfUWbF9GyNUf82pEZ24cOYeLhv/KuadV4YIz63Dvpq2c1u3vPNO64TFJOMAX8zaycvt+Xr+u7XFJ\nOEC5Om3ZUPsS/rFuHDcO+ZxftpcjsUllXrmyNRWjXInMi5e3Ys2OA9wxej7jbj+TOnFRhAcFcVvt\nKjyychPnfTSbXetTqFUpkhcn/EGvFtWICs/71FWY3vBs1ar1olq1XvmuE1k+hise+y8T3hjKqtkz\nOXw4g8z0DNAsqHcLADHn9+eBPhcV62yx+bgOeAPIffpRZx8wWkQGqurokgnLGFMUshPmkSOPLVWB\no0l4zpkxhw5N4LbbZhFyuD+PM4bFjz/OK+Nn0HvhaLZnVMxzRtDJSZNJz0wnUzNJz0xncpIbwnBQ\nu0GcXuX0QifWeSX05niBkoivBzqJSDncjHA9gDnAAaAf8Jz3/Wu/RVjG3ZLYgCkrdnDXmPl8elPn\nI72h/hIV1ZAqVXqxYeOH1K59I2npO1i29D727V9KXOXePD75XBpsyGJAt700r1G4G/pUlXnrk/lw\nZhLfLd6CKlzfsTZ39GhEfHQ4i5dMZ+3aoWzcOIrwsHjCwioTFh5PWGgcmVmppKVtIy1tK4cObSUj\nYzcA0dFNqBDThgoV2lKhQhue792CHvWSWL5mCOuXLyI4KIuKFc/k4MHVzJl7OU0aP0WNGlfkEV8W\na5OGc+DASlq2HMGhzHD6z6lFbLlhjI15hagv+kDQ+9D0gly3L4zY0BA+almfp1ZvZsTGHSxL3str\nM0ZQvfF50OR82osw7YFz+GBGEm/+to5vV6wnIjSYh+LjiPAS7awsJe1wFvvTDjPkpxW0qhVLrxZ5\nf3ir2fu/pA0ZT589r9Ghx6vc1KMFQT43v0aFhzCiT3v+MXw6A0fO4ctbzyQqPISWWcEEpWexKT6U\nT3t0JCwkiN5vzOCtKau59+9N8jzekJ9W5lkbfrJCwyO48O5jb0/Jyszk1Ud+AOCWvhcX2bFOQh/g\nPVVNymsFVU0SkXdw51FLxI0pRXJO+HPWWbBjB6xa5cpTwsKOn55+1y5QjSSTjxFpy1h9kJWzJjCG\nVtzJOJaktz5uOERwZShhwWFHEujEuolHnutcq3Ohk+m8EnpzvIBIxFV1loh8DswDDgPzgRFANPCp\niAwA1gEnX4Ng8hURGsz/+rbnktd+ZcAHc/j6tjOpERtZ8IbFqF7d29m+fTyLF9/G3pT5BAdH0fL0\nNxg5vw4LN61i5Y6tjJ2/iS4N4hjYrT5nN658TIKXLTU9k28WbuaDmUks3ZxC+fAQrutYhxu61KVu\nfNSR9Zo2eZroqMYcSttCevpO0tN3cjB5LenpOwkOLkd4eFXCw6tSvnwLwsOrgWaxN2UBW7d9w6bN\nLrcJCgonJCuN1lUrsmj3BYxa2JrGCafx7CU12bHhIZb/8RB7986jceMnjsz6mZWVwbZt40ha9xYH\nD66mSpXzqRzfg0e/Wsz63Qd5YWAiwdW7w6je8Glf6P02NL/0pF/XkCDhqUYJNI+O5KHlq+necjiD\nG1Wjl9ebWz4ilBvPbsC35bPYuy+VyHm76DtpM7HlQjmUkcmhjGNnQ33pylb59gRLhQSk+2N0n/Qo\n3f+4ARoPhzrHnpBrx5Vj+LVt6PfubO77dCGXt6vJHaPnU7FBeXbViSI4Lpx2sdFc1KoGb01dw1Ud\napOQy//Picu28e6va+nbuU6BveGnKii4ZMbdL4S2wKuFWG8irvfcGFOKTJ7skvDMTNcDPmPG0cl5\nBg50I6Ecl1Anut7zrCwhLOx+nn32dB5/5AouS93EaDryadAIEhP7HXeszrU6M6nvpFMuKckvoTfH\nCoga8aJktYanZsW2ffR+fQYJFSP5/JYuROdTApAfVeWnZdt4c8pq6leO5oXeLXNNkguyaPGt7Ngx\ngbi4czit6bOkZlag2/O/0K1xPM9e1pLRs9fz/q9JbE05RMMq0SQ2rkzKoQz2HMwg+WA6ew5msCU5\nlQPpmTSuGk3fznW5tE1CvqUNJ97WTA4cWMXevfPZt385sRXaUaVKT0TCGD17A09/u4wggVsT63Fu\nrXFs3PAm5cs3p3mzwezeM4P16/7HobTNREefRt06N1OlSi+mrdxN33dnc2PXejx6YTN3oEMp8PGV\nsGEWXPImtLrq1AJfMYFVX97HrR1eZxEx9K0RxxMNE4gMEu5Yvp7Pt+3hnRZ16VY+io9nrWdLcioR\nocGEhwYTGRpMRGgQDatE061R5YKPBbD6F/jmTkheD2cMdJMYhR87yeP/pqzm/e+nsZ9IaickMLxP\nW85fsoaW5SMZ3aoBm5JT6f7SZM5rUe242WA3J6dy/rBp1KgQydhbuxARWvyJcl4za56Kk6gRT8NN\naT+9gPW64oaDPX72Kj+z87YxefPtEQ8Kcgl5Vtbxs2Tm3Obss10ZS2goTJkClSr9Sc9zL2TTxtUM\nR7lp0CAYNswVl+d23FOs8bYa8UJub4m4yWnayh3c8N7vdGsUz9t92x9T+3sg7TCz1u4iJfUwp9es\nQL24qGMS7Kws5YelW3n151Us35JCXFQYuw6kc/e5jbj73BMvFUhP301KykLi4hIREQb/+CfDfl7F\nD3d3o6k3Wkj64Sy+W7yZd6avZcW2/VQsF0rFcmHEet/jo8O5oGV1Otar5Jca3vW7DvLf8cuYsHQb\nCbGRPNJjF1Gp/+XwYTciSIUKbalb59YjbdybmkHPV6YSHRHCt3d0PTahTD8Ao6+GtdPgH0Oh3fE9\nGvlShfW/wa9D3Uyf8Y1JHzSN5zfs5rX122lULpxuFcvz7qadPFivGvfULeL7BdL2w8//gVlvQoWa\n0OsFCAmHTXNh01x001zkwA62h9Ui6q7fiIqK5tV12/jvmi2Mb9eItjFRvPzjn7z68yrG3tqFtrXd\nvduHM7O4esRvLN+Swjd3dKV+5cLfxHoqAiQR3wQ8oKofFbDetcCLqppwqjEWNTtvG5O/7Bs24+Lc\nOOJpaS4pf+01GJTLkN633AJvvnn08c03wxtvQHJyMtdecw3f//ADtwBD27YldOxYqFPn2OP51HiH\nBIXwz9b/pG+rvmU6oT5ZlojnYCf0ovHxrPX8+8vF9OlUh8vaJjB95U6mrdrJ/PV7yMg8+n+mfEQI\nrWrG0rpWLFViwvlw5jpWbt9P/fgobjunIRe1rsFDXyzmi3kbeeO6tvQ6vXqexzycmUVwkOSZLO89\nmEHX53/mzIbxvNmnXa7rBLIZq3fyn2+Xs2xLCuc0TGdAm99pVv9iKsZ2OKbN936ygK8XbubLW7vk\nXqufkQqfXA+rJkKHQW7CoAoFjCSSlQV/jncJ+MbZEFkJOt7kti/nRqWZunsfdyxfx7b0w1xSJZY3\nmtUpvg8u62fBuNth5wpvgUB8Y6jZHspXg2kvQ+K/IfFB9h/O5IyZy2hfIYoPW9bnQNphznlpMjVi\nI/ny1i6ICC9N+JPhv6xiyFWtuaRNyeWZAZL0zUcbAAAgAElEQVSIfwJUVNW/F7Dej8AeVT3FSylF\nz87bxhTeiBFw++2uZzx7pJScpSl5JeIAmZmZ9Ov3bz766AW6STCjwsuz/5kxNLun55H1n532LI/9\n8hiZ6qblFISIkIgCb7r8q/SC+yoro6aYAHNtx9ok7TrAiKlr+PC3dQA0rxFD/6716NawMvHlw1i0\nYS8LNiazcEMyb0xZTWaW0qhKNMOuacMFp1c/Mhvlfy9twZqd+7n304XUiYuiWY3jx1gev3gLj361\nhG6N4nnlyta5lrG8++ta9qUd5s4ejYq38cWkS4N4vrmjK5/P3cCLE1Zw/WdnEh2eTL34X2lQOepI\nL+7Y+Zu4s0ejvG+YDY2Eqz92k//8/g7Mec+VqZx5D8Q3PLpeZoYrY1kxAf74Fnavgdg6cP5L0Po6\nCCt3zG7PqlSen89oync7krmiWjFfPajdEW6aBsu/ceOn12gNET413bvXumS85RVEV6rPoFqVeX7t\nVqbv2UfXiuW5v2cT7v98EeMWbqZSVBivTV7Fle1rlmgSHkCGANNF5BXgQVVN931SREKBF4HuQFc/\nxGeMKUK7drm+lawsV66S202XffvCu+8eLU3xnVFz9uxgxo59HpGWTNcBdD50gG/vPY8Ny56k1luP\nQlAQceXiCJIgsjQL9f4VdNOljZRyciwRN3l66LymVK8QQaWoMM5sGE989LF1ZE2rxXDlGW4a79T0\nTDbuOUiDytHHJdERocG8dX07Lhr+KwNHzmHc7WcS5+1rb2oGj3+9hK8WbCYhNpKvF7jE6v8ubHZM\nIrg3NYN3f11Lz+ZVc03kS4vgIOGqM2pzQcsafL1gEyu37Wf1jv38nrSHrxZsBqBFQgx3dG+Y/45C\nwl1pStd7YcarMP9DmP8RNL8E6ie6euzVv0DaXggKhTpdoPujcNrFEJz3r31cWAh9E/KezbRIhUZA\ny9xHkKHnM7DyJxh/P1z3OYNqVuaLbXu4bdk6Jp3RlN5ta/LBzCSeHf8Hh7OyaFA5micuyn9oyLJK\nVWeKyH3Ay8B1Xs/3Ou/pOsDfgDjgPlX9rSRiEpHzgKFAMPC2qj5XEsc15q8gMZFjpq1PTMx9vfPP\nh82bYcCAYxP17Js/Va8DmrCZi+nENj5++3FqbfqN35+/i7t/uJvMrEyCJOhIQl7QTZc2UsrJsdIU\nU2IWbUzmijdn0qpWLKMGdGRO0m7u+2wh2/elcfs5Dbm9e0OeGb+c935N4uFeTbnp7AZHth0ycQVD\nJq7kuzu7Fnq4wtLmYPphknYeJKFiJBUiQ09s4/3b4bfXYfbbkL4PoqtBo79B454uMc9xU2SpMPN1\nmPAwXDkSml3M0v2pnD93BV1io/moZX3mJO3hyrdmEh4SxLjbu9KkWsm3MRBKU3y2Owt4EEgEsoeU\nSQUmA8+p6rSiirGAOIKBFbgPABuB34FrVHVZXtvYeduYwvGtFZ8/3y1r08b1ksfFHf1+552ujhxc\nsv7qq0ef++gjmDbNd2KgLYj0RnUmj4gwIDaIy3tnMs+bRLlV1VZ0TOjItgPbqBpVlTbV27Dr4C6S\n05L5bOln7EzdSXxkPI3jGvPTmp+OxBpfLp6MzAwy1SX0gnAg4wB1Y+tySdNLmJI0hT2pe0g9nEqN\n8jXYvG8z9SvVJyI4gqnrphIaFErnWp1JPpRMREgEm/dtZv3e9YgI1aOr81DXhxjYbiB9xvbhqz+/\nAoWwkDCiQ6PZn7GfIIKoGl2VuzreRYsqLfhw4YdsO7iN3Qd3s+PgDjIyM9h5cCexEbE0jmvM7M2z\nycjMoFFcI2LCY9h5YCd70/ayL20fCTEJpKSlEBkSSWhwKFXKV6FZfDNiImJ44eoXUnSnnnRiYom4\nKVFfL9jEXWMW0Kx6DMu2pFA/PorBV7WmdS1XhpGVpdwxZj7fLdrCK1e14tI2NUk5lEHX536mY/04\n/tf3pMuw/hpSk2HfFohv4u7kKc0yD8OIRDi4C26fDeHleX/TTh5asZFH61fn9jpVeWf6WurFl6N7\n06p+CTGQEnGf7YOA7Msau1S9Is8SIiKdgSdUtaf3+GEAVX02r23svG1MwXKOJy7iSk+yso6dYTM4\n+NhJf8CVp2SPtpKT21cahyt0h10zSqYxpVkscLfP47dAN+tJ13JaaYopURe3TmDFtn289stq+nWu\nw0O9TiMy7OioIEFBwuArW7F7fzr3f7aIuKhwFmxIJuXQYe4qpbXhJSoy1n2VBcEhcOFgeOdvMOV5\n+Pt/6Fcjjul79vHc2i10io1mQNd6/o4y4KhqFv6dhTgB2ODzeCPQMedKIjIIGARQu3btkonMmFLM\ndzzx7IQ6uy81+3v28uBgt57vz7kl4Ue3CYfzoiANIrfA5cug0R6YXw2+aQyHA2bahGNll82UqIii\n3Z0l4qbE/evvTbihSz0ql8997NLwkGDe6tuOK9+cyS2j5hIUJJx7WlVaJJTNkhSTj1odoG0/V6bS\n6hqkanNeblKLRftSuWlpEpPOaEJsqJ3GSiNVHYGbuI327duXrUuzxhQD39rw/HrEw8NhyJBjS1ey\nhzzMmYyLuH2qQsYfl6MX/kRqC/ioB/zfFBg7BRYqXHGlsDIu8H5N29doz+zNswtcL1iCj4wAE2js\nL5gpcSKSZxKeLSYilA/6d+Cy12ewKTnVesP/ys59wo2u8u298M/vqRAawlvN63LRvJXc88cG3m1R\n1y/jw5s8bQJq+Tyu6S0zxpyCzp3dUIWTJx+9QTO7Xty3Rjwx8fhRVE4//ei633/vbuJMTITYWN99\nDSK5ASxI+4LezXqzuttqBjT9kGEf72HZ+8G8fUdXFnaud0yN+KdLPj1SI35m7TOZv2U+W/dvJUuz\niA6LZn/6/lxrxC897VImr518SjXiD3d7mEHtBnH92Ov58o8v86wRv7vT3Zxe5XRGLhzJ1gNbi6RG\nvHJU5aM14q++kHIq76vViJuAtik5leWbUzi3mX9qgE2AmD8Kvr4N2g9wwy8GBfHm+u08sXozd9Su\nwgP1qhN6EjO3nqpArBH3NxEJwd2s2QOXgP8OXKuqS/Paxs7bxgSwpCS44gqYMwfuvx+eeQZCrB83\n26mes0v53VymrEuIjbQk3Lhxz8+8G+a8A+Pvg6wsbqpVmauqVeLV9dvpOedPFqQc9HeUBlDVw8Dt\nwARgOfBpfkm4MSbA1a0L06e7WYFefNHdMbpli7+jKjMsETfGBD4RV6LS9R6Y8y6Mvw9RZehptXm/\nRT12Z2Ry/twVPLFqEwcyA7MO8K9EVceramNVbaCq//V3PMaYUxQe7qbmHDkSfv8d2raFqVP9HVWZ\nYIm4MaZ0EIEejx9Nxr+7F7KyOK9yBaZ2bMr1NeJ4c8MOzpn9J99sT2bRvoOsOZjG9rQMDqSnoTNe\nczd9rp8FGan+bo0xxpQ+ffrA7NkQEwPdu7se8jJW4lzSrMjHGFN6ZCfjCEwf7JZdMJiYkGBeaFKL\nS6tW5F9/bGDg0qTjNg3J6sjNGz/h3xP+TVBQMFRpBjXbQ9MLoWGPEm2GMcaUWi1auF7xAQPggQdg\nxgx47z1356c5YZaIG2NKFxHo8X/u5+mD3YQ/FwyG6Mp0jo1m0hlNmJNygH2HMzmQdoj9s99h/54N\nLGl0OcNrX8eWxpfyysFJhG2aA4u/gLnvw3WfQcNz/dosY4wpNWJi4NNPYehQdwNn+/bw+efQurW/\nIyt1LBE3xpQ+2cl4ZCz8/B9Img69nofTryAiOIiuFctD2j74eACs+xUuGoa26UGz9dt5Zs0WdsZd\nyztn/5vorEPwTk/4vD8M/AXiGhxzmO1pGczee4DZew8wa+9+dqYfJixICAsKIsxnyMSfd6VwTqXy\nNoyiMeavQ8QNUN6hA1x5pRsz8bXXoH9/f0dWqliNuDGmdBKBM++Cm6a5BHrsQPj4Kti7EVL3wMhL\nYP1M6P02tO2LiHBnnaoMaVqL6cn7uGz+KnYQBld/BBIMo69h5749jN22h7uXr6fzb8toOWMpNy5N\nYuTmnUQFB3NmxWjaxETRsFw41cNDj4Ry7aI1XLFgtY3cYoz56+nSBebNg65dXblK//5w0M6FhWXj\niBtjSr+sTJg9AiY95ZLq8tUgeR1c/h6cduFxq0/clcLAJUlUCQvhyYYJLNjwB79sXMui6CaoCBVD\ngukUG02HClF0rBBFi/KRhAUd32+RPY74o7d3YHDSVnZnZHJxlVgerl+dupH5T1qVl9I+jvjJsPO2\nMWVAZiY8+SQ8/TS0bOlKVRqV/cn4bBxxY4wJCoZOt8AtMyChLaRsgmtG55qEA5wbF8MXbRqwLzOT\nG5as5dWUcMIr1OD+pHcZz68s6dqC906vxy21q9C2QlSuSbivG2tWZlanZtxTpyo/7kyh66zlvLx2\na3G01BhjAlNwMDz1FIwfDxs3urrxsWP9HVXAsxpxY0zZUake9P3aDU8YVi7fVdvGRDHpjCYs3X+I\nM2LKUSEkGPaMgSn/hqq1oNlFJ3To8iHBPFi/OjckxPNy0tZjSleMMeYvo1cvmD/fzcbZuzfccw88\n/zyE2jkxN5aIG2PKFpECk/Bs1cPDqB4ednTBBYNhxx/w5U0w6004nAaZ6ZCZAZlpULsLXPAShEbm\nuc+q4aG80KTWqbbCGGNKr9q1Ydo0+Ne/4JVXYNYs+OQTqFnT35EFHCtNMcaYbKERcNUoqJ8ICETE\nQEwNiG/oxh1fMApGXgwHd/s5UGOMCXBhYTBsGIwZA4sWQZs28NNP/o4q4FiPuDHG+Iqp4erLc7P0\nSxh7E7zzN7ju85KNyxhjSqOrrnLji/fuDT17wuOPw6OPuppyYz3ixhhTaM0vdTXoB3a6ZNwYY0zB\nmjRx5SnXXw9PPOHqyHfs8HdUAcEScWOMORF1OsOAn/KtEzfGGJNDVBR88AGMGAFTp7pSlV9/9XdU\nfmeJuDHGnKjKjWHAxKOPh7SEsYNgzruwbRlkZfkvNmOMCVQiMHAgzJwJ4eGQmAiDB0MZm9PmRFgi\nbowxJ6N81aM/V28Jq3+Bb++BNzrDC3Xhl2f8FpoxxgS0Nm3cbJz/+Afcd5+rH09O9ndUfhEwN2uK\nSCzwNtACUKA/8CfwCVAXSAKuVNU9fgrRGGNyd9Uo16Ozew1smAXrf3M3fRpjjMldhQrwxRcwZAg8\n8AC0a+dm42zTxt+RlahA6hEfCvygqk2BVsBy4CFgkqo2AiZ5j40xJvCIQFwDaH0tXDQM2t3g74iM\nMSawibgJf6ZOhfR06NwZ3nrrL1WqEhCJuIhUAM4C3gFQ1XRVTQYuBj7wVvsAuMQ/ERpjjDHGmGLR\nubObjTMxEW6+Gfr0gf37/R1ViQiIRByoB+wA3hOR+SLytohEAVVVdYu3zlagam4bi8ggEZkjInN2\n2HA4xhhjjDGlS3w8jB8PTz8No0fDGWfA0qX+jqrYBUoiHgK0Bd5Q1TbAAXKUoaiq4mrHj6OqI1S1\nvaq2r1y5crEHa4wxxhhjilhQkJvs56efYM8e6NABRo70d1TFKlAS8Y3ARlWd5T3+HJeYbxOR6gDe\n9+1+is8YY4wxxpSE7t1dqcoZZ0C/fnDjjZCa6u+oikVAJOKquhXYICJNvEU9gGXAOKCft6wf8LUf\nwjPGGGOMMSWpenWYOBEeeQTeeQc6dYIVK/wdVZELiETccwfwkYgsAloDzwDPAX8TkZXAud5jY4wx\nfiQiV4jIUhHJEpH2OZ57WERWicifItLTXzEaY8qAkBD4z39c7fimTW6Iw08+8XdURSpgxhFX1QVA\n+1ye6lHSsRhjjMnXEuAy4C3fhSLSDLgaaA7UACaKSGNVzSz5EI0xZUavXq5U5aqr4Oqr3XCHgwe7\n2TlLuUDqETfGGFMKqOpyVf0zl6cuBsaoapqqrgVWAR1KNjpjTJlUqxZMmeJm4nz9dejSBdas8XdU\npyxgesSLyty5c3eKyLoCVosHdpZEPH5S1tsHZb+N1r5SRJ7PdfHJtrHOKQXjXwnAbz6PN3rLjiMi\ng4BB3sM0EVlSzLGdjED9f2pxnRiL68SUjrjmzYMGDfwXzVFNCl4lb2UuEVfVAscvFJE5qppbGUyZ\nUNbbB2W/jda+0q+0t1FEJgLVcnnqEVU95RvnVXUEMMI7VkC+VhbXibG4TozFdWICOa5T2b7MJeLG\nGGNOnaqeexKbbQJq+Tyu6S0zxhiTC6sRN8YYU1TGAVeLSLiI1AMaAbP9HJMxxgSsv2oiPsLfARSz\nst4+KPtttPaVfmW2jSJyqYhsBDoD34nIBABVXQp8ipsH4gfgtkKOmBKor5XFdWIsrhNjcZ2YMhmX\nuJnjjTHGGGOMMSXpr9ojbowxxhhjjF9ZIm6MMcYYY4wflNlEXETO86ZYXiUiD+XyvIjIMO/5RSLS\n1h9xnopCtPE6r22LRWSGiLTyR5wnq6D2+ax3hogcFpHLSzK+olCYNopIoogs8KYUn1LSMZ6KQvwf\nrSAi34jIQq99//RHnCdLRN4Vke15jYFdFs4zxUFEgkVkvoh86z2uJCI/ichK73tFP8SU5J0rF2QP\nRxYgccWKyOci8oeILBeRzv6OS0SaeK9T9leKiNzt77i82O7xziVLRGS0iEQESFx3eTEtFZG7vWUl\nHldu56z84hCRh73z158i0rOE47rCe72yRKR9jvX9GdeL3u/jIhH5UkRiTykuVS1zX0AwsBqoD4QB\nC4FmOdY5H/geEKATMMvfcRdDG7sAFb2fe5WmNhamfT7r/QyMBy73d9zF8B7G4m58q+09ruLvuIu4\nff8Gnvd+rgzsBsL8HfsJtPEsoC2wJI/nS/V5phhft3uBj4FvvccvAA95Pz+U/X+ihGNKAuJzLAuE\nuD4AbvR+DvPOCX6Pyye+YGArbiIqv8aFmzxqLRDpPf4UuCEA4moBLAHK4YaNngg09EdcuZ2z8ooD\naOadt8OBet75PLgE4zoNN1nOZKC9z3J/x/V3IMT7+flTfb3Kao94B2CVqq5R1XRgDG7qZV8XAyPV\n+Q2IFZHqJR3oKSiwjao6Q1X3eA9/w43pW1oU5j0EuAP4AtheksEVkcK08VpgrKquB1DV0tTOwrRP\ngfIiIkA0LhE/XLJhnjxVnYqLOS+l/TxT5ESkJnAB8LbP4otxCSfe90tKOq48+DUuEamASwTeAVDV\ndFVN9ndcOfQAVqvqOgIjrhAgUkRCcInv5gCI6zTch/CDqnoYmAJc5o+48jhn5RXHxcAYVU1T1bXA\nKtx5vUTiUtXlqvpnLqv7O64fvfcRjs2tTiquspqIJwAbfB7nNs1yYdYJZCca/wBcz1xpUWD7RCQB\nuBR4owTjKkqFeQ8bAxVFZLKIzBWRviUW3akrTPuG4/5IbQYWA3epalbJhFciSvt5pjgMAR4AfN/n\nqqq6xft5K1C1xKNyHwoner9ngwIkrnrADuA9r5TnbRGJCoC4fF0NjPZ+9mtcqroJeAlYD2wB9qrq\nj/6OC9cb3k1E4kSkHO5KWa0AiCtbXnEE6vk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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def show_lsmc_step(idx, ne=500) :\n", " fig = figure(figsize=[12, 4])\n", " ax1 = fig.add_subplot(121)\n", " plot(ts, spath[:20, :].T, label=None)\n", " plot(ts[idx], k - b_b[idx], 'r>', ms=15, label=None)\n", " axvline(ts[idx], lw=2)\n", " xlabel('Time', fontsize=16)\n", " ylabel('Price', fontsize=16)\n", " title('Stock Paths', fontsize=18)\n", " legend(['LSMC fit time'], loc='best')\n", "\n", " subplot(1, 2, 2)\n", "\n", " s = spath[:, idx]\n", " cv = cvs[:, idx+1]\n", " u = mc.fit_u(s, cv, put_ev(s))\n", " sd = np.arange(10., 120., 1)\n", "\n", " itm = np.greater(k, s[:ne])\n", " otm = np.greater(s[:ne], k)\n", "\n", " plot(s[:ne][itm], cv[:ne][itm], 'b.');\n", " plot(s[:ne][otm], cv[:ne][otm], 'g.');\n", " plot(sd, u(sd), 'r')\n", " plot(sd, np.maximum(k-sd, 0), 'k')\n", " plot(k - b_b[idx], b_b[idx], 'r>', ms=15)\n", "\n", " legend(['in the money', 'out of the money', 'LS fit', 'exer value']);\n", " xlim(40, 120)\n", " ylim(-10, 60)\n", " xlabel('Current stock price $s(t=%.2f)$' % (ts[idx]), fontsize=16);\n", " ylabel('Continuation value', fontsize=16)\n", " title('Least Square Fit @ t=%.2f' % (ts[idx]), fontsize=18);\n", " \n", "show_lsmc_step(-2)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "* the red line is a polynomial best fit to the continuation values (in the money paths only, blue dots)\n", "* the option is exercised if the exercise value (black line) is greater than the best guess (red line)\n", "* $\\bs v(t_{m-1})$ is known for each simulated path using the exercise decision\n", "* $\\bs v(t_{m-1})e^{-r\\delta}$ is therefore the continuation value (c.v.) at $t_{m-2}$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Two steps before maturity" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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cXFi7di0ffvhhmiJesWJFypcvz9GjR29rFS8IUi3zTk5OuLi4pCl2Tk5O3Lx5\nE6UUbdq0YUt+jbcZbktUVBQpKSl4eHjYzXdzc8PNzS1dWvny5Rk6dCjBwcEsWrSIESNG4FRCFkhJ\nSkpi/vz5JCYmMnbs2DTLjbu7O61atWLTpk34+PikuXYZii+PPPIIzZs354EHHqDLPfcQ/NVXDK1T\nB/71L62Mf/45mNV7DUWMgABtCU+1iAcE5G/9qc9p0C+t2Y2klXqc7TFKKRYtWkSLFi2y3aaTk1M6\nXSE77dsenzqCq5Ti5ZdfZoKdEa5x48YRHBzM6dOnGTNmzG3rL6qUjKduMWX16tVpVsrTp09z/vx5\n6tatm67MG2+8wb///W+cnZ3Tpb/88ss8+eSTXL6s3Wzi4+PtRk3JjAoVKnDlypUc52WHFi1acPbs\n2TRFPCkpiX379uW6PsPtiYyMpEqVKjkeeahfvz79+vXjyJEjrF+/voCkK1yUUvz888+cOHGCBx98\n8Ba3m169epGSkkJISIiDJDTkN+3btycsLAwfHx+GDR/Oq3fdRcprr0FwMPTvD3nozwyGgqBTJ+2O\n8uab+e+Wkl2y+6zv06cPs2bNSlOOd+3ales2O3fuzPz58wGYO3cu3bp1u23bs2fPJj4+HtDuhn/+\n+ScADz74IKtXryYsLIw+ffrkWiZHc8dZxB1FQkJCuomZzz77LLGxsTz99NNplsr33nuPWrVqpU2Q\ngMzDEU2aNIn4+Hh8fX1xcXHBxcWF5557LtvyeHl54ezsTNu2bQkKCmLKlCmZ5qUOCWUXV1dXFi5c\nyOTJk7l06RI3b97kmWeeoU2bojUaUVKIj4/njz/+oGvXrrlacKB9+/acPHmSTZs2Ubt27WJ/n/bu\n3cuePXsICAigdevWt+RXrVoVf39/Nm/ejJ+f3y0vv/YwkVaKPrVq1WL9+vU8+eSTvPX22+wdMIBv\nZ82i4jPP6FjjK1aAcZEzFCE6dXKMAp5KUFAQEydOpEyZMlmOYE+dOpVnnnkGLy8vUlJSaNSokd35\nZdlh1qxZjB49mvfee48aNWrw9ddfZ1m+d+/eHDhwgE7WhSpfvjzfffcdd911F66urvTo0YPKlSvf\nYqwsTkhJe8B06NBBhYeHp0s7cODALb5MhqKBuTd5JywsjBUrVjBx4sRcT7q8efMmwcHBnDlzhscf\nf5y77rorn6UsPBYuXEh0dDTPPvtspq42iYmJzJo1i6pVqzJmzJjbvsBs2rSJR5dfAiDsOT9q1KiR\n73KnIiIQ06r6AAAgAElEQVQ7lFIdbl+y5GCv384tSik+/vhjpkyZQosWLVj27LM0mTwZatSA1auh\nZct8acdgsMU8ywqflJQU2rVrx48//kizZs0KpU179zmvfbZxTTEYijmRkZFUr16dmjVr5rqOUqVK\nMXToUEqXLs38+fO5fv16PkpYeCiliImJoWHDhln6u7u5uREYGMjx48dv6zZ18OBB1q1bl7b/yy+/\n5Ju8hvxHRHjqqaf4v//7P06fPo3v88+z7t13ISEBOneGzZsdLaLBYMgj+/fvp2nTpvTs2bPQlPCC\nwijiBkMx5vLlyxw7dow2bdrkyi3FlooVKzJkyBAuXLjA5mKqrFy6dInLly/ToEGD25b18fGhZs2a\nrFixgt9//91umbNnz7Jo0aJ0vveRkZFpPoqGokvPnj0JCwujTp069H36aT6aOBFVrZqOGWdFbTAY\nDMWT1q1bc/ToUd5//31Hi5Jn7hhFvKS54JQEzD3JO/v37wfINFpKTmnYsGFaxJu8TNh1FMeOHQPI\nliLu5OTEkCFDqFChAvPmzWPFihVpk6cBrl27xvfff4+LiwsPP/xwWrqrq6uxihcTGjduzJYtW+jf\nvz9Pv/km4/z8uN62LQweDLNmOVo8g8FguDMUcTc3N86fP28UvyKEUorz58/fElLPkDMiIyOpWbNm\nvvosBwYGkpyczK+//ppvdRYWMTExlC5dOttuOtWrV+fxxx/H39+fsLAw/ve//3Hq1CmSk5P58ccf\niYuLY9iwYVSqVCntmI4dO7Jv3760OLeGok2FChVYvHgxU6dOZfa8efQQ4XTv3jB5Mjz/PKSkOFpE\ng8FwB3NHRE2pV68esbGxnD171tGiGGxwc3NLF0nGkDPi4uKIjY0lMDAwX+utVq0a7dq1Y8eOHfj7\n+xerRRKOHTtG/fr1cxQPPXWhn6ZNm7JkyRK++OILGjRoQHR0NAMGDLjFut6pUye2bdvGL7/8wtCh\nQ/P7FAwFgJOTE2+88QZeXl6MGjWKDlWqsGTwYDrMmKFjjQcHg00MY4PBYCgs7ghF3MXFhUaNGjla\nDIMhX0mdZJhfbim2dO/end27d7NhwwYGDx6c7/UXBFevXuXcuXN4eXnl6vimTZsyadIkfv75Z6Ki\noujYsSPt2rW7pVzZsmXx9/fn119/5fTp07mOVGMofAYPHkzTpk0ZOHAg3ZYv56uHH2b4/Plw8iQs\nWQJVqjhaRIPBcIdxR7imGAwlkX379lG7dm2qVq2a73VXqFABf39/IiMjOXnyZL7XXxAcP34c0H7u\nuaVcuXIMGzaMSZMmZblARKdOnShdurTxFS+GeHt7Ex4ejp+fHyPmz+fF++8necsW6NIFrDkGBsOd\nQHBwcI7796ioKLy9vfHx8eHIkSPp8t5+++2079HR0QViJCqJGEXcYCiGnDx5kpMnT+ba+psdunTp\nQpkyZdKF7ivKHDt2DGdnZ+rUqZOnekSEmjVrZuneUqZMGfz9/Tlw4ACnT5/OU3uGwqdGjRqsXbuW\nCRMm8O7PPzOgfXsunTypV1fJw6qBBkNxIjeK+JIlSxg8eDC7du2iSZMm6fJsFXFD9jGKuMFQDNm2\nbRsuLi54e3sXWBtubm5069aNo0ePcvTo0QJrJ7+IiYmhbt26uLi4FEp7/v7+lC5dmtDQ0EJpz5C/\nuLq68tlnn/Hpp5+yJjycjlWr8rtScPfdeuEfg6GA2XJ8C+9sfIctxzNf1TInfPDBB3h4eODh4cHM\nmTOBWy3TM2bMYNq0aSxcuJDw8HBGjBiBt7c3165dS1dXREQE/v7+eHl58eCDD3Lx4kVWrlzJzJkz\n+fTTT+nRo0e68i+99BLXrl3D29ubESNGAJCcnMzjjz9OmzZt6N27d1obR44coW/fvrRv355u3bql\nW008lWnTpjFq1Ci6detGw4YNWbx4MS+88AKenp707ds3LcJVSEgIPj4+eHp6MmbMmLQ1MNzd3Xn9\n9ddp164dnp6eaW1cvXqVMWPG4Ofnh4+PD0uXLgXg7rvvJiIiIq39rl27snv37tzfjBxgFHGDoZhx\n5coV9u7di4+PD2XKlCnQtnx9falUqRJr164lpQhHl7hx4wanTp3KVtjC/KJMmTJ06tSJqKgofvrp\nJy5evFhobRcVRCRaRPaKSISIhFtpVUVkrYgcsj6LtOP1xIkTWbduHeevXMEvIYHVd90F/fvDV185\nWjRDCWbL8S30nNOTqRum0nNOzzwr4zt27ODrr79m27ZtbN26lS+++IJdWYzuDB48mA4dOjB37lwi\nIiJueZaMHDmSf//73+zZswdPT0/++c9/0q9fPyZOnMiUKVPYsGFDuvLTp0+nTJkyREREMHfuXAAO\nHTrEk08+yb59+6hcuTKLFi0CYPz48cyaNYsdO3YwY8YMnnjiCbsyHjlyhPXr17Ns2TIeffRRevTo\nwd69eylTpgwrVqwgMTGRoKAgFixYwN69e7l58yaffvpp2vHVq1dn586dTJo0iRkzZgDw1ltvERgY\nyPbt29mwYQPPP/88V69eZezYsQQHBwPw+++/k5iYSNu2bXN2E3KJUcQNhmJGWFgYKSkpdOzYscDb\ncnFxoUePHpw6dSotZnlRJDY2lpSUlEJVxEG773Tq1InIyEhmzZrFypUri2X89TzSQynlbbPE80tA\niFKqGRBi7RdpunfvTlhYGA3d3bkvOpr3mzZFjRsHr70GJuytoQAIjQ7lRvINklUyN5JvEBodmqf6\nNm3axIMPPki5cuUoX748gwYNYuPGjbmq69KlS8TFxdG9e3cARo0alatwto0aNUobtW3fvj3R0dHE\nx8fz22+/MWTIELy9vZkwYQKnTp2ye/y9996Li4sLnp6eJCcn07dvXwA8PT2Jjo7m4MGDNGrUiObN\nm9uVc9CgQenaBlizZg3Tp0/H29ubgIAAEhMTiYmJYciQISxfvpykpCRmz55NUFBQjs83txRq1BQR\nmQ30B/5USnnYpD8FPAkkAyuUUi9Y6S8DY630yUqp/ytMeQ2GokZSUhLh4eE0b9680MIKenl58dtv\nvxESEkLLli0pVaroBVuKiYkBoH79+oXarouLC3369EmLohIWFsbOnTvx9/dP87G/AxkIBFjfvwFC\ngRcdJUx2cXd357fffiMoKIi/L1zI7iZN+PzNN3GLjoYvvwRXV0eLaChBBLgH4Orsyo3kG7g6uxLg\nHlAg7ZQqVSrdaGZiYmKBtGOP0jYhQZ2dnbl27RopKSlUrlw5nRvI7Y53cnLCxcUlbfVoJycnbt68\nme3jnZ2d08orpVi0aBEtWrS4pXyvXr1YunQpP/zwAzt27Lj9CeYThW0RDwb62iaISA90x91WKdUG\nmGGltwYeBtpYx3wiIs6FKq3BUMTYu3cvCQkJdOrUqdDadHJy4p577uHixYuEh4cXWrs5ISYmhpo1\nazpM8a1UqRL3338/f/vb32jVqhWbNm1i+fLlDpGlkFHAOhHZISLjrbSaSqlUE9dpwO7qSiIyXkTC\nRSS8qKzxUK5cOX744QfeeOMNvj1yhO5163Ly22+hXz+4dMnR4hlKEJ3qdyJkZAhv9niTkJEhdKqf\ntz69W7duLFmyhISEBK5evcpPP/1Et27dqFmzJn/++Sfnz5/n+vXr6fqlChUq2B3Bq1SpElWqVEmz\nqH/77bdp1vGscHFxSbc6sT0qVqxIo0aN+PHHHwGtGOfWF7tFixZER0dz+PDhbMvZp08fZs2albbA\no637zrhx45g8eTK+vr5UKcRQpoWqiCulfgUuZEieBExXSl23yvxppQ8E5iulriul/gAOA36FJqzB\nUMRQSrF161Zq1qyJu7t7obbdrFkzGjVqxC+//HLLpB5Hk5yczPHjx/MUtjC/qFatGg899BATJ068\nZTJTCaWrUsobuBd4UkTuts1U+mln17dDKfW5UqqDUqpDfq4Mm1dEhKlTp/LTTz+x/9IlOlSuzLbQ\nUOjaFawQmQZDftCpfide7vZynpVwgHbt2hEUFISfnx8dO3Zk3Lhx+Pj44OLiwmuvvYafnx+9evWi\nZcuWaccEBQUxceJEu5M1v/nmG55//nm8vLyIiIjgtddeu60M48ePx8vLK22yZmbMnTuXr776irZt\n29KmTZu0CZM5xc3Nja+//pohQ4bg6emJk5MTEydOzPKYqVOnkpSUhJeXF23atGHq1Klpee3bt6di\nxYqMHj06V/LkFinsZd9FxB1YnuqaIiIRwFK01TsR+LtSKkxEPga2KqW+s8p9BaxSSi3Mqv4OHTqo\nomq1MxjywtGjR5kzZw4DBw7Ex8en0Ns/deoU//vf/+jSpQu9evUq9PYz48SJE3zxxRcMHjy4QOPW\nur+0AoDo6fcVWBsAIrLDxt+62CAi04B44HEgQCl1SkRqA6FKqVvHgW0oqv12ZGQkAwYM4ERsLJ87\nOzOqalVYuRIKaRKXofhw4MABWrVq5WgxDHng5MmTBAQEEBUVlWn4Wnv3Oa99dlGYrFkKqAr4A88D\nP0iqI1A2KYpDnAZDfrNlyxbKlSvnsEUSateujZeXF1u3biUuLs4hMtjjmLUIS2FP1LzTEZFyIlIh\n9TvQG4gElgGjrGKj0IaWYomHhwdhYWF07daNoMREnrt8mZtdu8KaNY4WzWAw5CNz5syhY8eOvPXW\nW1muIVEQFAVFPBZYrDTbgRSgOnACsJ15Vc9Ku4WiOsRpMOQX586d49ChQ/j6+hZanGx7BAYGArB+\n/XqHyZCRmJgYqlSpQsWKFR0tSpFBRJxExENEultKckFQE9gkIruB7eiJ9quB6UAvETkE3GPtF1uq\nVavG6tWreeqpp/ggPp77gIv33guzZztaNIPBkE+MHDmS48ePM2TIkEJvuygo4kuAHgAi0hxwBc6h\nrSoPi0hpEWkENEN39gbDHce2bdtwdnamQwfHeixUrlwZf39/9uzZk+MV2QoCpRQxMTHGGm6DiDyJ\nniS5G1gPtLDSl4jI5PxqRyl1VCnV1traKKXestLPK6V6KqWaKaXuUUplnBdU7HBxceGjjz7iyy+/\nZMP16/i5uXFg7FiYOtWENzQYDHmisMMXfo8Oa1VdRGKB14HZwGwRiQRuAKOsCT77ROQHYD9wE3hS\nKZVcmPIaDIXNTz/9RGxsLFWqVKFy5cpplt6IiAg8PT0pX768o0WkW7du7Ny5k7Vr1zJy5Ehy6EmW\nr5w7d46EhIQiMVGzKCAijwMfovvVNcAPNtkbgYeAjxwgWolg7NixtGzZkkGDBtExKYl5//oX/aOj\n9eI/JryhwWDIBYWqiCulHskk69FMyr8FvFVwEhkMRYdz586xe/duateuzdWrV4mNjU0X89Xf39+B\n0v2Fm5sbAQEBrFq1ikOHDqUtpuAIUuOHG4t4Gs8C7yulXrQT7jUKPQ/HkAe6dOlCeHg4DzzwAAN2\n7eKt777jpePHkZ9+gkIMeWYwGEoGRW9lDoPhDmXXrl2ICMOHD6dChQqAXnwhLi6OlJQUatWq5WAJ\n/6J9+/Zs27aNtWvX4u7ujuttrIGJiYkcO3aMq1evcvXq1bRYtzdu3KBnz57kdm5HTEwM5cqVK7TF\njYoBjYDMFj67ClQuRFlKLPXr12fjxo2MHTuWf8yfz55ff+WrTp0ou3o1FHJoUYPBULwxirjBUARI\nTk5m9+7dNG/ePE0JB219LkoKeCqlSpWib9++fP/993z77beMGDECNzc3u2XPnz/P3LlzuXDhL1dh\nFxcXypYtS0JCAleuXGHs2LE5nql+8+ZNjhw5QoMGDRzqHlPEOAe4Z5LXgkwmvBtyTtmyZZk3bx5t\n27blH//4B78fPswSX1/qr1oFDp7LYbgzKV++PPHx8enSDh48yIQJE4iLi+P69et069aNzz///JZj\nn3/+eVauXEm/fv1o0qQJZcuWZeTIkQQHB9O7d2/q1KlTWKdxx2EUcYOhCHDo0CHi4+Np166do0XJ\nNs2bN2fw4MEsWrSIb775hkcffZRy5dIH6IiNjWXevHkopXjkkUeoWbMmZcuWTbOg79mzh8WLFxMW\nFkbHjh1z1P6uXbuIj4+nffv2+XZOJYDlwGsiEgocs9KUiFQHpqAnxxvyCRHhpZdewsPDg+EPP0yH\nCxdY3LUrXX74AQYMcLR4BgOTJ09mypQpDBw4ENCrM9vj888/58KFCzg7p/doCw4OxsPDwyjiBUhR\niJpiMNzx7Ny5k/Lly9O0aVNHi5Ij2rRpwyOPPMLZs2f5+uuvuXz5clpeVFQUwcHBlC5dmrFjx9Ki\nRQsqV66czo3F09OTJk2aEBISkqPY5Ddv3mTjxo3Uq1ePJk2a5Os5FXNeBa6j43mvQ69q+RFwAEgG\n3nCcaCWX/v37s3X7dio2bEiPGzf4cuBA+MjMiTU4nlOnTlGvXr20fU9Pz1vKDBgwIM2osWDBAqZN\nm8aMGTNYuHAh4eHhjBgxwu7qm4b8wVjEDQYHc/nyZQ4dOkSXLl1usUYUB5o1a8ajjz7KvHnzmD17\nNiNHjuTw4cOsWrWK2rVrM3z48EyjvYgI/fv355NPPmHFihUMHz48W24mu3bt4vLlywwYMMC4pdig\nlDonIh2AZ4A+wBF0P/8x8B+l1OWsjjfkntatW7N9xw4eHjKEx0NC2P3003xw6BAuM2dCMfxfG/LA\nM89ARET+1untDTNn5viwKVOmEBgYSOfOnenduzejR4+mcuX0U0WWLVtG+fLlibBknjZtGgCDBw/m\n448/ZsaMGQ4PnVuSMRZxg8HBREREoJRyyLL1+YW7uzujRo3i+vXrfPbZZ6xcuZLmzZsTFBR025CL\nVapUITAwkEOHDrFv377btpVqDa9fv76xhttBKXVFKfWmUqqrUqq5UqqTUuqfRgkveKpUqcKK1auZ\n8vTTfAz0+fhjzg8YAAkJjhbNcIcyevRoDhw4wJAhQwgNDcXf35/r1687WiyDDcYibjA4kJSUFHbt\n2oW7u3uxj/xRt25dgoKCWLBgAc2aNaNPnz7ZnoDZsWNH9u7dy6pVq2jcuDFly5bNtOzOnTu5fPky\nAwcONNZwQ5GjVKlSfDBzJm19fBg/diy+K1eyzM8Pj5AQqFnT0eIZCoNcWK4Lkjp16jBmzBjGjBmD\nh4cHkZGRZm5NEcJYxA0GB3Ls2DEuXrxYrCZpZkXNmjWZPHky9957b46ioDg5OTFgwAASEhJYs2ZN\npuWSkpLSrOGNGzfOD5FLFCKy/jZbiKNlvFMYNWoUv27eTGLVqnTat48lnp6wf7+jxTLcYaxevZqk\npCQATp8+zfnz56lbt262j69QoQJXrlwpKPEMGEXcYHAoO3fupHTp0rRq1crRojicWrVq0aVLFyIi\nIjh69KjdMjt37uTKlSv06NHDWMPt4wRIhq060AVobu0bComOHTsSvncvrVq35sGzZ3mzXTtUiHkX\nMhQMCQkJ1KtXL2374IMPWLNmDR4eHrRt25Y+ffrw3nvv5SgkblBQEBMnTjSTNQsQ45piMDiIa9eu\nsX//ftq1a4eLi4ujxSkSdO/enf379zNv3jw6duxIly5d0txUkpKS2LRpEw0aNKBRo0YOlrRoopQK\nsJcuIk3QoQvfLlSBDNSpU4dfd+xg/IgRvLZ4MXt69SL4008pN2GCo0UzlDBSUlLspn/wwQe3PdY2\n/njqZE2Ahx56iIceeijPshkyx1jEDQYHsWfPHpKTk0uMW0p+4OLiwqhRo2jdujWbN2/mo48+YuPG\njdy4ccNYw/OAUuoIMB14z9Gy3Im4ubnxzcKFzHjzTRYrRZeJE4l+6ilQytGiGQwGB2Ms4gaDA1BK\nsXPnTmrXrk3t2rUdLU6RolKlSgwaNIguXboQEhJCSEgI27ZtIyUlhYYNG+JulhDPLWfR7ikGByAi\nPPfqq3j4+DBs0CB8P/6YRVFR3L18OZQu7WjxDAaDgzAWcYPBAZw8eZIzZ84Ya3gW1KxZk+HDhzN6\n9GiqVKlCQkKCsYbnEhGpBjyLjitucCB97ruP7Xv2UK1GDXquW8dnbdrA+fOOFstgMDgIYxE3GBzA\ntm3bcHV1tbvKWVFEJaeACOJU+Epww4YNGTNmDAkJCZQrV67Q2y9OiMgf6NU0bXEFUuPmGWfPIkDz\nFi3YdugQw3v0YNKuXUQ0bsxHv/2Ga5s2jhbNYDAUMsYibjAUMleuXCEyMhJvb2/c3NwcLU62+PPT\n3cT9dNhh7YuIUcKzxy92tp+BqUBLpdQyB8pmsKFSpUosCwvjxUcf5X+XL9PL25uzP//saLEMBkMh\nYyziBkMhEx4eTkpKCh07dnS0KNni5vlrJMXGk3Q6gUr9GuFUxnQbRRWlVJCjZTBkH2dnZ6Z/+y1e\n7dox9rnn8B0wgKX/+hdtX3nF0aIZDIZCwljEDYZC5ObNm4SHh9O8efNis5Jm4u8X9ZebKSTsPutY\nYQyGEsjwKVPYuG4dN11d6fzqqywcOtREVDGUCIKCgli4cKGjxSjSGNOWwVCIREZGcvXq1WJjDQdI\nPHgR52puSCknEnacoby/ifJSlBCR13JQXCml3iwwYQy5pkNgIOGHDjGoQweG/PgjU6OimLZtG05l\nyjhaNMMdTHJyMs7Ozo4Wo0RjLOIGQyGhlGLr1q3UqFGj2CzPrpKSuX4kjjItqlKuQ01uHL9C0p8J\njhYr3zh9+jR79+51tBh5ZVoON0MRpVaDBmyIiWF0u3a8uXcvD9Wvz5XoaEeLZSgmfPfdd/j5+eHt\n7c2ECRNITk7m2LFjNGvWjHPnzpGSkkK3bt1Ys2ZNpuUBypcvz3PPPUfbtm3ZsmVLWv1RUVH4+fml\n7UdHR6cFHHjjjTfw9fXFw8OD8ePHo+yM6Li7u3Pu3DlAu2gGBAQAcPXqVcaMGYOfnx8+Pj4sXbq0\nQK5PUcVYxA2GQiImJobTp0/Tv3//YhOC7/rRS6ikFNxaVMGlTnkurfqDq+FnqNyvZKxsuW7dOg4f\nPoyLiwstW7Z0tDi5QillDColiNJubnwVHk7boCCemzOHTi1asGzlShr37Olo0QzZ5JlnniEiIiJf\n6/T29mbmzJmZ5h84cIAFCxawefNmXFxceOKJJ5g7dy4jR47kxRdfZNKkSfj5+dG6dWt69+6dZfnU\nUdv3338/XRstW7bkxo0b/PHHHzRq1IgFCxYwbNgwAP72t7/x2mt6cO6xxx5j+fLl3H///dk6t7fe\neovAwEBmz55NXFwcfn5+3HPPPXfMBH3TgRsMhcTWrVspU6YMXl5ejhYl2yQevIi4OFG6cSWcK7ji\n1qIqCbvOoJKLv/9qUlIS0Za1ccmSJVy8eNGxAhVDRMRZRHaJyHJrv6qIrBWRQ9ZnFUfLWBwREZ7+\n5htWz5zJyaQkfHv1Yv1//uNosQxFmJCQEHbs2IGvry/e3t6EhIRw9OhRAMaNG8fly5f57LPPmDFj\nxm3LOzs7Z7qs/dChQ1mwYAFAOkV8w4YNdOzYEU9PT9avX8++ffuyLfuaNWuYPn063t7eBAQEkJiY\nSExMTK6vRXHDWMQNhkLg4sWLREVF0aVLF1xdXR0tTrZJPHiB0o0rIS7aR7Bch5okHrhA4u8XKNOq\neEw2zYxjx45x8+ZN7r33XtavX8/ChQsZPXo0pUqZbjEHPA0cACpa+y8BIUqp6SLykrX/oqOEK+7c\n8/TThHl6MuDee+n97LPM3LmTJ+fMKTYjancqWVmuCwqlFKNGjeKdd965JS8hIYHY2FgA4uPjqVCh\nQpbl3dzcMvULHzZsGEOGDGHQoEGICM2aNSMxMZEnnniC8PBw6tevz7Rp00hMTLzl2FKlSpGSkgKQ\nLl8pxaJFi2jRokWuzr24YyziBkMhEBYWBoCvr6+DJck+SeeucfN8Im4tq6alubWsilM5FxLCzzhQ\nsvzh8OHDODs74+Pjw8CBAzlx4gQhISGOFivPiMh4y0qdICLJGbd8bKcecB/wpU3yQOAb6/s3wAP5\n1d6dSpPAQLb8/jv3Va/OU999x+Pt2nH92jVHi2UoYvTs2ZOFCxfy559/AnDhwgWOHTsGwIsvvsiI\nESN44403ePzxx29bPiuaNGmCs7Mzb775Zpo1PFWprl69OvHx8ZlGSXF3d2fHjh0ALFq0KC29T58+\nzJo1K82vfNeuXTk+/+KMUcQNhgLmxo0b7Ny5k9atW1OpUiVHi5NtEg9eAMCt+V/eBeLsRFmfu7gW\ndYHkq0mOEi1fOHz4MA0bNsTV1ZXWrVvj5+fHli1biIqKcrRouUZERgKzgDDADfga+A64jF7e/o18\nbG4m8AKQYpNWUyl1yvp+mr9W9LQn63gRCReR8LNnTVjMrKjYsCEvLoxlXG1vvoqIoGeDBpwxkzgN\nNrRu3Zp//etf9O7dGy8vL3r16sWpU6f45ZdfCAsLS1PGXV1d+frrrzMtnx2GDRvGd999x9ChQwGo\nXLkyjz/+OB4eHvTp0ydTg9Prr7/O008/TYcOHdJZ3KdOnUpSUhJeXl60adOGqVOn5v2CFCPE3szW\n4kyHDh1UeHi4o8UwGNLYunUrq1evZsyYMTRo0MDR4mSbs7MjSb6YSK3nOqRLTzp9lTMzd1Kpf2Mq\ndK3rIOnyRlxcHDNnzqR379507twZ0DHev/rqKy5evMjEiROpXLkyoFdC/eOPPxgw7zgA0dPvK1DZ\nRGSHUqrD7UvaPXYnsAx4E0gCOiildlq+2qHAF0qpj/NBxv5AP6XUEyISAPxdKdVfROKUUpVtyl1U\nSt3WT9z021mzZQv07Ak3risG8iirUuZRzdWVpcuX065XL0eLZ0BPlmzVqpWjxTAUMPbuc176bDAW\ncYOhwEhOTmb9+vWsXr2aBg0aUL9+/VzXVdgvzCk3krl+NA63FlVvyXOpVQ6XuuVJ2FF83VMOHz4M\nQNOmTdPSSpUqxZAhQ1BK8cMPP7Bq1Sr++9//8v7777N48eK0cgcPHix0eXNAM+BXtJU6BXAFUEpd\nBN5C+3TnB12AASISDcwHAkXkO+CMiNQGsD7/zKf27mhCQ+HGDUhOEZbKXN64dwZOSUl07dOH+e+9\n5xQWCQEAACAASURBVGjxDAZDHjCKuMFQAMTFxREcHMyvv/6Kt7c3I0aMyNUEq4sXLzJ//nzeffdd\n4uPjC0BS+1w/Egc3FW4t7Bszy3WoSdKpq9w4UXgy5SeHDx+mYsWK1KhRI1161apVGTBgACdPnmTH\njh1UqFCBe+65J82vEuCnn34iLi6usEXOLteAUkq/uZ0GbAPWxwN18qMRpdTLSql6Sil34GFgvVLq\nUbQ1fpRVbBRwZwUELiACAsDVFZyd9WeXqc8Rtno1HUqV4pEXXuAfDz+cNgnOYDAULwo1PICIzAb6\nA38qpTwy5D0HzABqKKXOWWkvA2OBZGCyUur/ClNegyE37Nu3j2XLlqGUYtCgQbkKV5iUlMTmzZvZ\ntGkToN0mIiMj8ff3z29x7ZIWtrCRfZ/2sm1rELf8KAk7zuBat3yhyJRfJCcnc/ToUTw8POy+HLVp\n04Y6depQoUKFDBFUdFxgpRQ//vhjUY2wshdoDqwBNgL/EJE/gJvoxXwK2gF+OvCDiIwFjgFDC7i9\nO4JOnSAkRFvGAwL0PvRm3YEDTPbz450FC9i7bx9zN2+mYsWKWVdmKDCUUiaiTQmmoEamC/spEgx8\nDMyxTRSR+kBvIMYmrTXa0tIGbcVZJyLNlVL5NuvfYMhPUlJSWLlyJeHh4dStW5eHHnqIqlVvde3I\nCqUUUVFR/N///R9xcXF4eHjQq1cvvv/+e/bs2VMoirhSSoctbFoZKWV/0MyprAtl2lTjathpEo/E\noZJSUEnJqBspqGRFlQFNKOdXq8BlzQ3Hjx/nxo0b6dxSMlKlSuZuzQMHDuSHH35g3bp19O3b126Z\nc+fOISJUq1boIR4/B5pY36cC64BN1v4VCiCKiVIqFO1/jlLqPGBWnikAOnVKVcD/wrVJEz6LjqZt\n585MjozE///ZO+/wKKu0D99n+mRSJj0hhRBICAklQCiRXgUELKi4nwUr1rXvruzqquuu7q6r6667\nrg17RVBARAHpPdQAIUBCS+89mZlMOd8fA6EkgSSkiL73dXHN5C3nfWaYTH7vOc/ze3r0YMnmzcRc\nps2pLmcMBgOlpaX4+/srYvxniJSS0tJSDAZDu4/dqUJcSrlBCBHVxK5/4q6+P3sZ82rgCymlDTgu\nhMgEhgJbmzhfQaHLyc7OZufOnQwdOpQrr7yyWR/WC7F48WJSU1MJDAxkzpw59Ojh7mDZr18/Vq1a\n1fBF35E4ii04y214jblwTrvX2AhkvQuhFgitCqFTI7QqrEfKqVqfjUdSMEL10/uDlJmZiRCC6Ojo\nix/cBPHx8QwbNoxt27YRGRlJfHx8w77i4mI2bNjAgQMHiI+P54YbbmivsFuElPLLs55nCiESgGTA\nA9hyerVR4WeElxf3791Ln9mzuX7RIob268eXX33F5Gsufs+1dev5s+wKbSU8PJycnBwUB6CfLwaD\ngfDw8HYft8vXVYUQVwO5UsrU8+4iw4BtZ/2cc2pbU2PMBeYCl5UrhcLPi/T0dNRqNePHj7+oCLcd\nq6RswWFMQ0LwGhOO0KjIzMwkNTWV5ORkJk6ceM4Yp4X4/v37GTt2bIe+jgbbwmbyw0+j6+ZJwO0J\njbbXpRZR9vlhbJkV51gf/lTIzMwkIiLikmY2Jk2aRE5ODkuWLCEkJASHw9EgwLVaLcnJyQ1uLJ2J\nEEJ99qqhlLIW96y4ws8ZtRr9Ewv5R+WfefXHZ5h67bX845lnePT555udnW1wYql3552vXq2I8UtB\nq9U2TJwoKLSGLi3WFEJ4AL8H/ngp40gp35ZSJkkpk84vvlJQ6AyklKSnp9OzZ8+LCjxnrZ2yLw7h\nsjioWnWSwn/tpi6jjBUrVuDr68uECRMaCXlvb2+ioqLYt29fhzuoWA+Xown2QOPbNqFqTAhA5aml\nZmteO0d26dTU1FBQUHDBtJSWoNFouP766xFCMH/+fN544w0OHz7MiBEjeOSRR5g8eTKenl2SO58n\nhHhNCDG4Ky6u0DWcFtV3r32aMO1irlZrePyFF7hj+vQmOxzCWU4sTvfjunWdGrKCgsIputo1pSfQ\nA0g9ZYMVDuwWQoQAucDZa+Php7YpKPzkyMvLo7Ky8qI+slJKyr86grPWTuDc/vjfkYB0SjZ/sILi\n4mImjBrXbAFg//79KSsrIy+v4wSus9aO7XjlRWfDL4TQqDANCcF6qAxHuVsEbNiwgQ8//LDTbRjP\n5+jRowCXLMTBnUd+3XXXoVarGTlyJI8++iiTJk3qKgF+mkXALUCKEOKgEOKpUzU4Cj9jzhbVq1xX\nM/nBPTxnNvPh8uWM7devye+M851YOnihTUFBoRm6VIhLKfdLKYOklFGnbLBygEFSygLcNlg3CSH0\nQogeuP1xU7owXIVfIBaLhc8//5y0tLQLHpeeno4Qgt69e1/wuJrNeVgPleEzrQe6ME+Mvf0w3x/P\nbuNJQlxmzEtrqFqdhb2ortG5ffr0Qa1Ws2/fvmbHdzqd1NU1Prc5XBYHlvRSKpYfo/A/e8j/yzZw\nSozxl5aHbhrmLtSsTSngxIkTrFmzhuPHj5OVlXWRMzuWzMxMTCYTISHtU0gaGxvL448/zsSJEzGZ\nTO0y5qUgpXwACAVmAenAs7hrbNYKIW4XQnh1aYAKHcL5onrATX159sgRFsXFcSAzkyFxccx/dzsv\nveSePYczTiwvvKCkpSgodCWdbV/4OTAWCBBC5ADPSinnN3WslDJNCLEAOIjbeutBxTFFoTOx2Wx8\n+umn5OTkUFBQQFxcXJO536fTUqKiovDw8Gh2vPrcGiq/P46hjx+eV5yxc960bQsWh5Vf3Xgj+u21\nVK06SdWqk2iCPDD29cfYNwBtqAmj0UhsbCwHDhxg8uTJjWKRUrJw4UKysrJ4/PHHL5in7qypp/yb\nTKwHS0ECaoEuwguvsREYYn3RRzVtW9hSNGYDhj7+lKdk803aTnx9famtrWXv3r107979ksZuKy6X\ni8zMTGJiYlCpunoxsOOQUtqBxcBiIYQPMBv3LPm7uF2rLi+/SYWL0rS9YSDX7d1Lr+uv5+ply7j/\nnisQ4h3UhjsbhHdTTiwKCgqdS2e7pvzqIvujzvv5L7i7wSkodCp2u53PP/+c3NxckpKS2LlzJ4cO\nHSIhoXFxYnFxMaWlpc1aC7pcLlw2B2WfH0Jt0uJ7fWxDAVVZWRnbtm1jwIABRPaNhr7gqLRhTSvF\ncqCE6rXZVK/JRhviQcA9/enXrx/p6ekcP368UXrFjh07SE9PB+DkyZPNuoJY0kspX5SBy+rAa0w4\n+hhf9JFeCG3rXV4uhOfwUH7I2ECVq4o777yTXbt2kZaWxtSpU9HpdO16rZaQn5+PxWJpl7SUywUp\nZaUQ4nvAH3dzn9AuDkmhHTnf9aSRqNbr6b90Ka+Nf5rX1r3IOnkXHpadrFnzOsnJ7fv7rqCg0DZ+\nvtNCCgptxOFwsGDBAk6cOME111zDtGnT8PPzY+vWpp0zT4vfuCa8e2tra3nvvfd45R+vsLfiCN43\n9ERt0jbs//HHH1GpVEyYcMZ6WeOjx/OKbgTO7U/oH4ZhvqYX9mILld8dIyYmBr1ez/79+8+5Tn5+\nPitWrKBHaHfUQsXBrftw2c5dQHLVOyn/JoPSDw+i9tIR/NBAfKb0wNDT3O4iHCDDlkOmuoDBHr2J\niIggMTGR+vr6hversznd1r5nz54XOfLyRwjhJYS4UwixFjgOPI27wc+Mro1Mob04XaD5zDPux2a+\nnkAIgl78C8Haz7kXNXX8j+ULxjR0h926lXNSVhQUFDoXRYgrKJyFy+Xim2++ISMjg+nTpzNgwABU\nKhXDhg0jJyeH7OzsRuccPHiQiIgIvLzOTb+tqKjgvffeoyAvHy+7gW2aI7y97GP27NmD0+nk5MmT\nHDx4kBEjRjTbDU/tqcNzeCheY8Kp212E83gN8fHxpKenU19fD7hTaBYuXIiHwciogmhCHb4cOXyY\n3D9tofidfVRvyMFysJSif++hNqUAz9HhBD2YiDak7TnN9fX1bNu2jUWLFpGZmdmoCLOyspLvvvuO\nUO9A+peGUp9fS2RkJL6+vuzdu7fN170UMjMz6dat208il7ujEEJMF0J8gbu9/TunNs8FQqSUv5JS\nLu+66BTak9a4niQnwyPrb2LYA9v4r6cPKfs2M6xvX7744nDLxLyCgkKH0eU+4goKXYHNZqO6urrR\n9k2bNpGWlsakSZNISkpq2J6YmMjatWvZunUrERFnTCjKysooLCxk8uTJ54xTVFTExx9/TL3VxhRb\nIpGRkVRP8GT1mtUsWbKEzZs3A+Dl5dUiv2nv8ZFY9pdQ/k0Gfa/ty549ezhy5Ah9+/Zl+fLllJWV\nMdM8En21lr5jB/LDxh+xD/BEm2WncvlxANQ+egLu7oehp7lN7xm4i1dTUlLYtm0bFosFnU7H/v37\nCQkJYcSIEcTHxyOEYPHixTidTq678Xpsb2ZSuy0P32tjGDBgAOvWraOiogKzue1xtJZdu3aRnZ3d\n4R7sPwGWAodxp/R9IqXs2upYhQ7jdIHmaR/wi3203akrSTDvAD2Tx3NrTgZ33pKIzbUQl7yqQcwr\nOeMKCp2LIsQVfnG4XC7mz59PUVFRk/vHjBnDiBEjGn52lFvReekYPHgwW7Zsoby8vKEF+uk0i7Nt\nC7Oysvjss8/QCDXTLIMICQkmYE4CQQYN0T2jOXToEGvWrKG4uJhrr722RfnSQqPCd1YMxW/uw++w\nW8Dv27cPp9NJamoqw8MGEHhUh++veuEZpeeHjT+SF1zLyFkjcVTasOdUo482ozJe+FfeZrORkpKC\nSqXCaDRiMBgwGAzodDrS09PZsWMH9fX1xMTEMGrUKLp168a+ffvYvHkzixYtYs2aNYSHh3P8+HFm\nzJhBYHgwZQMqqdtThM/UHg1CPDU1lTFjxlz0dV8qUkrWr1/PunXr6NWrV5c02elkhkopd3Z1EAod\nT9MFmhdna3Y4N5fs4UVm8aZzBXuZjlq8iFb7FGPH/vQ64Soo/NxRhLjCL44jR45QVFTEyJEjCQoK\nOmefyWRqKHKUUlKzOY/K5ccwxPox9NqhbN26le3btzNlyhTALcRDQ0MbhPmRI0dYsGAB3h5eTKpM\nwNfXTMAdCagM7l81IQR9+vShd+/eFBcXExwc3OK49VE+mIaFULslj/ik3uxI282JEyeICOxG/FE/\nTMNC8Bjgfj0hISEcOXKEkSNHovHRo/HRt+gaW7ZsYf369U3uE0KQkJDAyJEjz7H/GzRoEImJiRw+\nfJhNmzaxf/9+evfuzaBBgwDwTA6lblchdbuL8L2iG1FRUezdu5fRo0c32/WvPXC5XCxfvpydO3cy\nYMAAZs6cedGOp5c7igj/ZdEW15N166DCbuI+lvMcvyOGf7BA/p6Ybrux2T4CjC0a5/xCUQUFhbah\nCHGFXxRSSjZu3IjZbGbcuHHNCjNXvZPyrzOw7C1GE2TEeqgM4xF/EhIS2L17N2PHjsVms5GTk8P4\n8eMBt3vKF198QZB/IJNK++Bh9CDg7n6oPRvPeKtUqlaJ8NP4TO2BJb2MyBMmtrtcqFUqRpXEoA/x\nwjz9jEtKbGwsGzdupK6u7oKWimdjsVjYtm0bcXFxXHvttVgsFqxWK1arFYvFQnBwMH5+fk2eq1Kp\n6NOnD3FxcRQUFBAQENAgsnXhXmjDPanZlocpOZTExEQWL15MVlZWh1kZ2u12vv76a9LT0xkxYgQT\nJ07sUNGvoHC5cCalRcVfdS+zbHY/Ej64k+eOLWTq+ENcf/P3PPBA+AXF9elC0dNpMYoPuYJC21GK\nNRV+UZw8eZLc3FxGjBjRrAh3lFoofmMvltRivK/sTvCjg9FH+1Cx7BhDEwZTX1/P7t27OXToEHAm\nLWX16tVo1BomVyRgVBkIuLtfi2eiW4rKoMH36p54F6sZEt6PycYkTE49fjfHneN80rt3b6SUZGRk\ntHjs7du3Y7PZGDNmDHq9HrPZTEhICFFRUfTp06dZEX42QghCQ0PRarXnbPccFoqjyEJ9djXx8fHo\ndLoOK9q0Wq188sknpKenM2XKFCZNmtTpIrzy++PU7Svu1GsqKLSE8xv5bI+9jR9V6/kQbzTyAAs+\n6c/YsVsvWLjZmkJRBQWFC6MIcYVfFJs2bcJkMpGYmNjkfsuhMgpf34ujsp6AO/riPS4SoRL4Xh8L\nEgwbq+jevTvbt28nLS2NgIAAAgMDyc7O5tChQwwgCr1dS8Bd/dAGtGyJt7UYEwLw6BvAgMwgAvP1\n+F7XC23gubPeoaGheHp6cvjw4RaNabVa2bZtG7179yY0tP2tpo39AxBaFXU7C9HpdMTHx5OWltbg\n/NKebNiwgaysLGbNmtWst3tH4ii3Ur0hB3tebadfW0GhJSQnw7x57sexY2GnfgR/JJWP6EUE5Tjq\nR/PKK+83e/75nTx//jXQCgodhyLEFX4x5Ofnk5mZyfDhwxvN2IJbhJd+mIbGV0/wrwdiiPVt2Kfx\nM2CeHo3taCUDzb2prKwkKyuL+Ph4pJSs/PYHjOhIsEcQcGcCutCOtcgzz+yFylOLaXgoHolBjfar\nVCpiY2PJzMzE4XBcdLyUlBSsVmuHFVCq9BqM/QKoSy3GVe/sME9xu93Onj17iIuLo1+/fu06dkup\n2ZYPAkzDld45Cj99Ts+QT7kvint0u3mByYzHwaJFd9Kr58Ns3Nj4++P8WXUlLUVBoe0oQlzhF8Pm\nzZvR6/UMGTKkyf3Va7JQ+xkIvH8AGj9Do/0eQ4Ix9PYlYLcLXx+39V6fPn3Y/10K2UW5DDbEEv5Q\nEvrIpj3B2xO1t47Qp4bie03zXSJjY2Opr6/n5MmTFxzLZrOxdetWYmNj6datW3uH2oApKQRpc2I5\nUEJkZCRms7nd01PS09OxWCznWE92JtLupG5HAcZ4fzTm9k1LUlDoKJKT4X//g2/XebHw6uVM4HEe\nAY4ee50JYyayYkVZk+ecnlVXUFBoO0qxpsIvgrKyMtLS0rjiiiswGBqLbNvJKuqzqjFf3ROVrunc\ncSEEvrNiKPjnbobTm9x+FnTbqlm3ZyPeOhNjfj0DjanzxJfQXPg+Ojo6Go1Gw5EjRy7YTTIlJQWL\nxdLhdoK6Ht5o/A3U7SzENCiYxMRE1q1bR1FRUSP3mraya9cufH196dGjR7uM11rq9hbjqnOgCfLA\nllXVKTdl5yOEiAZuBCKB8z/sUkp5V6cHpXBZkJwMNRY183iFO0jgbebyoNzArbMH8s//LicrK+Ec\nl5TTzin+/lBaqjioKCi0BUWIK/wi2LJlCyqVqtmc4ZoNOZw0lPHhmg14pnhiNpvP+derVy9MJhNq\nbz2+V/dEfnGYSJs/+6tSKdPVcN3M69B2oghvCTqdjh49enD48GGmTJnSZMGizWZjy5YtxMTEEBYW\n1qHxCCHwGBxM1cqTOEotJCYmsmXLFt566y2SkpIYNWoUnp6ebR6/uLiYkydPMmHCBFSqzl/sk1JS\nvTEXoVdTvSYbZ7mt04W4EOIaYAHu1c4iwHZ+mJ0akMJlx6xZsHIlvM+dZNKLJczgjsps5twyBKn6\nHL3+alavdh87YQLYbOBygUoFer2SqqKg0FoUIa7ws6e6upo9e/aQmJjYqA09uF1S6g6WsNt8HA+d\nB2FhYVRUVJCRkUFNTQ0ABoOBiRMnMmjQIIwDAjEeLKUmrZg95ixCvEPo27dvZ7+sFtG7d28yMjIo\nLi5uctZ5x44dnTIbfhqPwcFUrTpJ7a5CzJOjePDBB1m/fj0pKSns2bOH5ORkkpOTm1y1uBi7du1C\npVIxcODADoj8wkiXpHL5MRxFdaAW+FwVjeeIjkvzuQAvAOuAm6WUim2LQquZO9f9OH8++HcbTfDN\ne1hx3xTuKs1gl+sarNY/s3bt7xFCUF/vFuHgflS6cyootB5FiCu0G646OyqPxkWQXc22bdtwuVzN\ndlWs2ZxHlrqEUksF1029jv79+zfss9vtFBUVsWrVKpYtW8aePXuYPn06IbPjOLKpjMq11cy47uou\nmYFtCbGxsQAcPny4kRA/PRves2dPwsPDOyUejY8efYwvdbuK8J7YHR8fH2bOnMkVV1zBmjVrGkT5\n+PHjSUpKarHtoN1uJzU1lbi4uEuaVW8L9uI6yhdlUH+iClSC4IcHog3u2GLdCxANPKGIcIVLYe7c\nM4Icokkx7+SZyTeyQK7gM/k0a35M5fdPv49OZzpnRlxxUFFQaD2KEFdoF+r2FlH25WEMvf0wz4hG\n498x1n2tpby8nJ07dxIfH4+/v3+j/a46OzU780n1zMHX6EtCQsI5+7VaLWFhYcyZM4d9+/axcuVK\n3n77bYYOHcr+/fuJioq6YP51V+Pt7U1oaChHjhxh1KhRgLvjZGFhISkpKdTV1TG2k/9ympKCKfvs\nELbMigZnmoCAAG688Uby8vJYtWoV3333HSdOnGDmzJno9RdP+Tl48GCXFGnajlVQ/N4B0KhAgOeI\nbl0pwgEOAY0/6AoKl8DQid5s3fAdv37qtyRufpXfrf2K0pJDfPrpMg4dimzIEff3P+MprsyKKyi0\nDEWIK1wy9dnVlC084i5QO1ZJwau78Bodjte4iGYLHzsap9PJ1q1bWbduHSqVitGjRzd5XE1KATmO\nEoqsZcyYNKPZJj9CCAYMGEBsbCyrV69m+/btAJdFx8bY2FjWr1/Ptm3byM7O5vjx49TV1QHQv39/\nIiIiOjUeY7w/Kg8NtbsKz7GIBOjWrRu33normzdvZs2aNRQWFjJ79mwCAwMvOObpIs2oqKgOjPxc\npMNF+deZqH30GOP8qNmSh2dyl6SjnM1vgdeEENullMc68kJCCAOwAdDj/luyUEr5rBDCD/gSiAJO\nADdKKcs7MhaFjid5pJqtL79Cn1f6svSbe7g5LY27bh/I9bMXM3as+yb//G6b4BbmShGngkLzKEJc\n4ZJwVtoo+eggai8dgXP7g1NS+f1xqtdmU7e7CJ/pPTD2DehUsZqVlcW3335LcXExcXFxTJ06FR8f\nn0bHSYeLmi157PPMwUvvxYABAy46ttFoZPr06QwcOJCKiopOS+m4FOLi4li/fj0//PADXl5exMTE\nEB0dTY8ePfD27gJXD40Kj8QgalLym0xnUqlUjBo1irCwMBYuXMg777zDzJkzm83DLyoqIisri4kT\nJ3ZqilD1+hwcJRb8b4unfFEGhji/Jm0vO5nncM+IpwshMoDzfeeklLK9CgJswHgpZY0QQgtsEkJ8\nD1wHrJZS/lUI8RTwFPC7drqmQhdxpq39HYzRxLBBO5Prqyp4953xfPDBf7nrrrnndNv86CP48MNz\nhbkixhUUGqMIcYU2I+1OSj4+iLQ5CbxrAGqTW1D5ze6NaVgIFUuOUvbpIXRR3nhPiETfy9yhgtxi\nsbBq1Sp2796Nt7c3N910E3Fxcc0eX7evmLzqQvL0JUwZPwWNpuW/DmFhYR3uMtJehIaGctttt+Hl\n5UVAQOfeFDWHx+BgarbkUZda3OwscnR0NPfeey9fffUVCxcuJDs7m/HjxzdKVTldpNlct9SOwFFi\noWptFsb+AbgsDly1djyv6PLZcAAn0LJ2qpeIlFICNad+1J76J4GrgbGntn+Iu3hUEeKXOWe3tV/P\nSF4Ztpv3N17FnznICvu9bNywF632X4AWnc59ztnCXCniVFBoGkWIK1wQKWWTwk1KSdmiDOw5Nfjf\nGo825Ny8WH2UD0EPDaR2Rz7Va7IpmX8AXYQXXhMiMfT2bXcxWFBQwBdffEFlZSXJycmMHTv2grnF\nUkpqNuaS6pGNh96DQYMGtWs8PzWio6O7OoRz0IV5og01Ubuz8ILpHD4+Ptx+++2sXLmS7du3k5qa\nytChQxk2bBgmk6mhSLNPnz6dVqQppaR8SSZCrcLnqh6UfpyOJtCIvpe5U65/kdjGdub1hBBqYBfQ\nC/ivlHK7ECJYSpl/6pACILgzY1LoGE63tT89wz3yliiu3bGdt6w305+lvHzwfwxKPMjUqxZy1VUB\nwLkz4koRp4JC07RaiAu3gpoBjMa9BPqclPKkEGIMkCGlzGvnGBW6CGdNPYX/3I3KqEEfY8YQ44u+\npw8qvYbq9TlY9hbjPbk7xoSma8OEWuA5vBumpBBqdxVSvTab0g/S0HYz4T0+EkOCf7sI8rS0NBYv\nXozBYOCuu+5qUbqI7WgleQX5ZOuLmZA8Ad3pKRyFTsOUFEzFt8eoz6lGF97YVvI0Go2GadOm0b9/\nfzZt2sSGDRvYsmULgwcPxsvLC6vV2qlFmpb9JdgyKjDPiMaeX4c9pwbz1T1/EisNnY2U0gkkCiHM\nwDdCiL7n7ZdCiCa9y4UQc4G5AJGRkR0eq8Klcbqt/dk53/36ebJuzTc8fOQZ+n/0InenbqCsbDA3\n3vgt/fv3b3S8goJCY1olxIUQvsByYBhQDXgCrwMngXtw5yM+3M4xKnQRNRtzcdXZ0YZ5UrezkNqt\n+aAS6MI9qc+uxjggEK9xFy/0ExoVnsNCMSUFU7enyC3IP0lH39MH8zW90AZ6tCk+l8vFunXr2LBh\nA+Hh4cyePbtJn/AmX9umXFINWRj0hmZb3it0LB4Dg6hak03ZF4cJemDARa0vw8PDuemmmygqKmLz\n5s3s2LEDl8uFn59fpxZpVnx7DG2YJ5pgD0o/PIgm2AOPwT+dSV8hRCjwBDAG8MP9vbwWeFVKWdAR\n15RSVggh1gJTgEIhRKiUMv9ULEXNnPM28DZAUlKS0mjoMiA5+VxB7f5ZBfyFW65MoPftt3NNbi5X\nDB/OR598wnXXXQec66RyuhunIs4VFNy0dkb8ZSACGAHsAOrP2vcj8Jt2ikuhi3HW2qnZmo+xfyD+\nv4pDOlzYTlZhyyjHmlGBPtoH31kxrZoFFGoVpqQQPAYGU5uST+WKExS+thuvMeF4j4tAaFvusGK1\nWvnmm284fPgwAwcO5Kqrrmpxjrej0kb+kSxO6AoZPXR0m5rHKFw6Kg8t/rf2ofid/ZR+foiA51aJ\nBAAAIABJREFU2/si1Bf/PAUFBXHttdcybtw4du7cSVRUVKfORrtq6vGeFEnpRwdR++oJvKdfl7kD\nnY8QIhbYCPgCm4FMIAR4BLhNCDFKSpnRTtcKBOynRLgRmAT8DVgKzAH+eupxSXtcT6HruaCI/r//\nY0hMDDunT+e6khJmzZrFnXc+y2ef/RG7XYVOB6+9Bo8+qhRwKiicTWuF+NXAk1LKradyA88mC7dI\nV2gBLpsDZ4UNR4UNZ7kNZ3U9hlhf9N0738WiKWq25CHrnXifmvEWGhWGnmYMPc34TLm0sYVa4Jnc\nDWPfACq/O0b1mmzq9hZjvronxt5+Fz3farUyf/58SkpKmDp1KkOHDm2VEKvbXUiq+iRarbbZlvcK\nnYM+ygffa3pRviiDyuXHMM9ouSe72Wxm4sSJHRhd0xgS/Klcdhy1t57Au/uj9vxJpTX9DagChkkp\nT5zeKIToDqw8tf+6drpWKPDhqb8FKmCBlHKZEGIrsEAIcRfu1dIb2+l6Cl3IGdeUC4joIUMI3bOH\ntTNnct+uXbz33vPAPuAjrFZP5s9vWwGnMouu8HOmtULcE8htZp8B+OUlSbYSS1opZQuPIC2ORvuq\nV2dh6OOHz5VRjYofOxOX1UHN5lyMCf4dGofaS4ffTXF4JIVQsSST0vfT8JnWA6/RF87xXr16NcXF\nxdxyyy306tWrVdeUUlK2I4dj6iKSBibh4dG2tBiF9sM0JAR7fi01m/PQhpgwDQm5pPGqVqyk8tul\nhP3jH6jasNrhqLdw/OC/CQu/DaN/CEIInFVnFv9sGRWovLQE3tMPtfdPSoQDjAPuO1uEA5yq43kO\neKO9LiSl3AcMbGJ7KTChva6j8NPgbNeUC4robt0wbNzI+3fdReLnn/M4i4FkpFzKzp09ON2qoaUF\nnC26AVBQuIxprRA/DEzGnYZyPmOA/Zcc0c+cmi25qLQqPMdGoTYbUJv1aMx6hF5NzdY8qtflUPiv\n3XgMDMJ7Unc0vp2fNlGzJQ9pdeI1vnMKqAy9zAQ/MoiSjw5SvS4b0/DQZpf6T548yY4dOxg+fHir\nRThA/fEqMipP4tK6OtXuTuHC+FwVjb2ojvLFmW4HkqjGvu8toTYlhbwnn0Ta7VQuWYrv7ItPxkop\ncZRasR0uw5pRQWHdYgri3qN2RyGBuTegDTRiL65rOF5l0hJ4T3/UPhfv+NkF6HDX7zRF9an9Cgqt\nxt8fhGhhK3ujEfHppzzavz9x8+ZxI+nUMhiXaxFCjOOee+C225oX1GfPgLf4BkBB4TKltd0v3gAe\nFUL8ATit0sxCiDuAh4D/tmdwPzecVTZsxyrxGBKC15gIPAYEou/ujdpHj8qgwXtcJCG/HYLnqDDq\n9hVT8I+dVK3N6tQYXTYnNZtyMcT5oQvrHDs4cKe+eI+PwFXnoG5nYZPH2O12vv32W3x8fBg3blyb\nrlO7s4BMTSGBAYGEhoZeSsgK7YhQC/z/Lw6NWU/pJ+k4KqytHsN29Cg5D/0abWQk+rg4yt5/H+ly\nNXu8lJKabfkUvLyTwn/spOLbY9iLa6mMWQ9Aba9d6OPM1OfXIK3OhvMC7+6HxvyTFOEAe4FfCyHO\n+W4/5Xb1wKn9CgqtYutWd263ywVqtTvX+6JiWAh46imi/r6U9ejpSRUwCZfrv0REyAuK8AkT4Jln\n3I/+/m7hr1YrNogKP09aJcRPVbm/CjyPuwgIYBXuyvfXpJSfXuh8IcR7QogiIcSBs7a9LIQ4JITY\nJ4T45pQN1ul984QQmUKIw0KIK1sT60+RutQSkOCR2Hy7brVJi3laNCFPDsEQ40vVypM4Km2dFmPt\n9nxcdQ68xnd+ur8+ygddpBfVm3KRzsYmChs3bqSkpIQZM2Zc0CO8OVxWBwX7T1IoKhiQOOAXaTd3\nMWyZmWTf/wD1Oc1loHUcKg8t/nMSkHYX5QuOtOpcR3Ex2ffMReh0RLz1FgFz76H+xAlq1qxp8njp\ncFHxTSYVizNRe+swX92TkN8kYbxHhUV9FB+fQVhlDlUlqQi1ioD7+zec25Lumek1FqzO5m8COpA/\nARNxd9b8kxDifiHE80Aa7mLK57siKIXLm9Oz0i6X+19pacvPjfvNDDKfTWEBEUxDIuVDbN9+L/X1\n9U0ef/4MeGmpOx3lhReUtBSFnyet7gctpXwK6AncCzyNe5alt5TyDy04/QPc9lZnswroK6XsDxwB\n5gEIIeKBm4CEU+e80USB6GVFXWoR2jDPFtn1acx6zDOiQdLsDHF7I+1OqjfkoO9lRh/ZNUWjXqPD\ncZZZsaSVnLO9oKCATZs2MWDAgDalpABY9pWQIfMQQtC/f/+Ln/ALQzqd5P3+D9SsXUvR3//eJTFo\ngzzwHh+B7Vgl9iJ3OogtI4Pcxx/n0MBB5D7xJJb952bAuWpryb73Phzl5US8+Sa68DC8Jk9GGxZG\n6XvvN7qGs9ZO8fwD1KYU4DU2gsC5/fFM7obG30hO7idoNF70CXsZXGoqvDcSeHc/DN1bnirjcElm\npx7l0UOdu5oFIKX8AZiOOw3lD7hXKZ/G3QFzupRyZacHpXDZc7qZT1tnpcOvTOCT23fycuho5gFL\nl77D+HHjKCxs/LfN39+d/nJ2CkxyMsybp4hwhZ8nbeqsKaU8CbzbhvM2CCGiztt29h+GbcD1p55f\nDXwhpbQBx4UQmcBQYGtbYu5q7MXuxh8+03q0+ByNvxF9tA+1uwrxGheBUHXsDG5tSgGuGjvenZQb\n3hSGeH80AUaqN+Rg7Odux+5yuVi6dCkGg4Err2z7wkjNjnwytYVER0fj7d15NxpSSpASoWr1fW+n\nUv7JJ1j37cMjKYnqlSupTUnBNHRop8fhMSiYyhUnqVqZjnX3p1R9/wMqoxGvcWOpWbeOqu++wzh4\nMH5zbsNr7FhyH38C66FDhL/xX4x9EwAQGg1+c+ZQ+OKL1O3Zg8dAd02hvbCWkg8P4qyy4TMjGqES\nVCzORNpd1DtLKAr+Hv/KKVSuL8CzdyK13XehDW9dQe/G8mqK6h3MCOqaTpunxPgPQggP3DaG5VLK\nuoucpqDQLE0182kpZ4ot/Xlbu5LD1z9O/4X/4c5t2xgyeDBLvv2Wgad+P0+nwDidbiHeohQYBYXL\nnFYpAyHEHacq75va95wQYs4lxnMn8P2p52FA9ln7ck5tuyyxpBaDAOOA5tNSmsI0JARnmRXbscoO\nisyNdLioXp+DLsobfXTbCuXaA6ESeI4Mw55T0/Cat2/fTl5eHlOnTm2zy4m9qI6snGyqpYUBAwa0\nZ8gXJe+JJzh+3SycFRWdet3WUJ+TQ9Fr/8I0ZjQR776DplsohS++hHQ6L35yO2PPPQaOHGp3FVGz\nfhP+c+fSc/WPhL36Kr3WryN43lM4CgrIffgRjowYSc369YT88Rm8zpumM8+6DpWPD2XvvYezup7a\nPUUU/Wcvrho7al8Dld8eo2LJUSxpJdhOVlEklyGFA7/yKegivQjvP5t6ZzHl5dtbFf9XheWYNWom\n+netFamUsk5KmauIcIX2oK2z0menmtTZtXww6HVueustNgmBLCxkxBVX8OWXX7J1Kzz3HNhs7vQX\nKd1pKVu3wksvuR8VFH6OtHZG/BFgfjP7ioBHgQ/bEsipAlAHcME882bO/Um3SpZSUre3GH0PHzSt\ndFow9vVHLFFTu7MAQ6+Om2Gr3V2Is6oe3xti23S+lJLazVswDR+GaGFjnbNxOBx89tlnVFVV4eXp\nidpow2tJNv5DI1m/fj2xsbH07dv34gM1Q+3OQjI0Bei0OuLi4loXW3k5Qq1G3YZZ9Oo1a6la7r63\nzPn1w0TMfxeVrvOMK1z1TmzHKqnPrsZzeChqr8bXllJS8OxzCCEIffZZVAYDwU8+Se7jT1CxaBG+\nN3a8DbTLYqFq+feUL/gSa+o+tBEDMQy+n27//hKvEWdWkdSenvjNmYPvzTdTvXoN5QuW4TGwL743\n3dRwjLPSRvWWPBzFFjwnPY/LqiL/L+eKabVRg2lKFMZ4f7RBHrhcDo5ufRQ/0ygixk91j+OMJqPw\neQoLv8XP74oWvY5qh5Pviyu4McQPfSetgAgh/gi8K6XMO/X8Qkgp5QudEZeCApxJazltPzh2LJA8\nl0Fxcey89lpmVVZy0003odHsw+l8ASlVDWkp/v6KdaHCz5/WKqZeuIt+miIdd+54qxFC3I47r3GC\nlPJ0lV4u5zYICqcZD/Ofeqtke14tjhILnqNbP6EvtGo8EoOo3VmAq85+0TbgbUG6JDUbctGGeaJv\no9iv/vFHcn/9MMHznsJvTusXRrZs2cKxY8eIiYnBarVSpqvmeGUhzh+PoNfrueqqq9pcXCmdLqp2\n5XFcU0RCQl90rRDCzooKjk6ZiquyEm1YGPo+cRj69MHQpw/GxEQ0fs03IHJZrRS++CK6nj3xv+du\n8p+aR/4fnqbb3//WYYWiUkrs+bXYMiqwZpRjO14JpwpfXbV2fK9pnF9fuWQJtZs3E/zM06j9gqhc\ndRKVV388RlxP6fyvMY2ciDbEt0NSo2yZmZR//gWVS5fiqq5GFx1N8Lyn8J45k+K3M7AerMZrROPz\nhEaDKXkM1Vs8qS8VWA6UYOwbgLS7KPkgDXthHZoAA7rIQGq3bEET0hdh0OE9uTsefQMb+X+XlPyI\nzVZA79gztYxqtZHAwEkUFf9AbMwZfesoL0fj69vk61lWXIHFJbkx5OKNqdqR54AfgLxTzy+EBBQh\nrtBpNJvWMno0wbt3s2bGDB7Yv5/5jheB/QjxCRMnevPcc4p1ocIvg9YKcQcQ0My+1uVcnEIIMQX4\nLTDmvCXUpcBnQohXgW5ADJDSlmt0NXV7i0At8Ojb3Ft3YUxDQqjdlk9dajGeyd3aOTqwHirDUWLB\n76bebRaIFQu+AqD03fmYb7oJVStcTUpKSli/fj0JCQnccMMNgLugLv+v21EnmN0dN43GNsUFYD1c\nznFLHnado9VpKaUffoirshL/e+/Fnp2FNf0QNavXgJSoTCa6f/wRhvj4ps99dz72nBwiP3gf0/Dh\nOAoKKX7tNbThYQQ98kibX8+FqF6fQ9UPJwDQBHvgeUU3DDG+1O0pom5XIT6Tu59zM+coLaXopb9i\nHDgQ31/9iqofs6he484IUwdORh04maJ/p4FK4Dk81J1X3U43EbVbt5J1190ItRqvK6/Ed/aNGJOS\nGsY3JYVQteokjhILmoDG//8V3x1HOl1o/T0o/SQd07AQpNN9I+I/Jx5DnB81m3KxHeuPsyqHkHvH\no+/RdLOgnJyPMRjCCAg41xYzJHgmBQWLyXz9Pk43iDw27SqCfz8P7+nTG70XXxWUE23UM8i78xpF\nSSlVTT1XUPipkJzcWEC7vcK7E3zPVqY8PIeBLOJhliHlcEaNWkpysnvSoNFs+kVQunAqXG609ks7\nBbivmX33ATsudLIQ4nPcxZa9hRA5p1og/wfwAlYJIfYKId4EkFKmAQuAg7hnex6UUnZ+wuolIl2S\nutRiDLG+bZ7N1oV5og01UbujoJ2jc1OzKRe1jx5jv7bdKNTn5FK7aRMew4fjKC6mYtGihn0FBQVN\nVsafRkrJsmXL0Gg0TJlyxlBHbdJiSgrBub8Cnf3StEXtzkIy9YX4+PjQvXv3Fp/nrKig/ONP8Lry\nSoIee5SwV1+l5/fL6b1zB90/+RiVtzfZ996HPffMQo2jxIJ0Sepzcih95x28pk7BNHw4AP73zsV8\nw/WU/u/Nc96j9kK6JLVb89D18CF03lBCHhuM+apoDLG+eI0JR9pd1KSc+xkq/MuLuOrqCP3zC8h6\nFzVb8jAk+NPtj8MJengggp1Y93+BvqeRmi15VK9uHycQR2kpub/9LboePei1fh1h/3gZjyFDzhG2\npqRgUNHk596aWYEltRivMREEPZCI55hwarcXULezEI+kYAwxvpQvyqDyu+PooozUrf8bVcsWNhlL\nTc0Ryiu2ERZ2M+cbM5m9h6Gu11Pi2NKwTRsRQd5vfkv2PXPPsXnMttazpaKGa1xWyj/6iOo1ay/1\nbWo1QohIIUSTXzRCCI0Q4qeXu6fws+Nied1ne4Xf+7iJ2eIr8nmBVUi8OMKzzyTxr3+taphNb6l1\n4dtvw+jR8PTTbiF+//1KbrnCT5/Wzoj/BfhRCLEdt2tKLu4CyruBQbh9aptFSvmrJjY3l3OOlPIv\np6552WI7Xomrqh6Pq4IuaRzTkBAqlh6lPremXRvt1Oe6iyJ9pvVAqNsmeCsWLQQh6PbiX8h9/AlK\n33kX3+uvp7a+ng8++AC73c706dMbKuPPJjU1lRMnTjB9+nS8vLzO2ec1MozabfnUbM7DZ+qF3Wbs\nBbXkrj5CRUEJIfoAVBoVQqNCqAWlGYXk6EoZ2X8kqlbk7ZZ99BGumhoCHnjgnO0qkwmPpCQi336L\nE/93M1lz7yXqs09x1qopen0PPtN6UPH5S6BWE/y73+GSEgEIIQj54x+x5+WT/+xzaEJC8BzRRN5F\nG6k/UYWzsh6fqT0adX3UhpjQ9zJTuyUPr1FhCLWK6rVrqVq+nICHf42+Z0+q1mYjrU68x0Wg8tCi\n89AS9PjNHJsyFetugWnsw1T9mIXa14BpcHCb45QuF3nz5uGqrCLy3fnNpveoffQYevtRu6sQ78nd\nGz6f0uGiYkkmaj8D3mPDERoVpsHB1GzOAymp21OIPbcGe34tXuMj8J7YHVvqCMo//RT/u+9Cdd7q\nSk7up6hUOrqF3nBunE4nhU8/i15vxzJaNPQTjvr8M8o/+5zif/6TYzNm4HfrrTgrK3lH7w3J4xny\n5MMUlpVgvuF6vMa3rfHUJXAcSKbp1cMBp7Zf1jawCj9tWtKS/uyUE5UK1BrBi46n2S/7sZH/Yza1\nPPbYFKR8hUceeYTk5KZX4c6e/QZ46CFwONzP6+vhrbfgww+V3HKFnzatbeizHre9YBDwFrDs1GMg\nMEtKua69A7zcsaQWI3QqDH0uLWfUIzEQNILane07K169MQehV2Ma2vSS/cWQDgeVi77Gc9QotN26\nEfDA/Tjy86lYsoSVK1dSX1+Pr68vS5YsYcWKFbjO6nRYW1vLihUriIiIYNCgQY3G1vgbMfYNoHpj\nLsXvHaBmez7O6jNNIKSUWDPLKX7vANmvpbDoyEoWV29mQeVa0i0nsdfbKbXamTdIy/pe/UgJ7cGi\ngjK2VtSQZbFR63DilE2XFDgrKyn76GO8Jk/G0LvpAlZ9TAzh//kP9qwsch58iOJ1J3mjp4778/O5\ne8AI7nrpPyRmlhC+LpXr9mZS73IhtFrC/vUa+p49yX34EapWrqI+O5vqtWspeecd8p6aR9X33zd5\nvYtRl1qE0KowxPs3ud9zZBjOqnos+0uQdjuFL/0VXa+eBNx9N656d0dVfawvuvAzN0TaoCD8772X\nmtWr0XUrQR9jpnxRBtaM8jbFCFD24UfUbthI0FO/a/a9PY1paAiuGjvW9LKGbdWbcnEUWzDP7InQ\nqnHVOyn9NB2VXk3Qg4kYevliL3anWvlMjkKoBP533oGzooLif7+OPOv/3OGopqDgG4KCrkKnO/M7\nKh0O8n73FJVLltKtx2yk6sxinFCr8bv1FqK/W4Zp2DBK336byuXL+SF+IEk1FST9+Xl6bVhP6Atd\nkop9obwhLdAlXYYUfjk0ldd9Pmf7kuv18J//wL33wgr91dyiSmEB4VyN5LHHHuPOO+/EZmvc1O78\nDpwffeS+5tlI2XwMCgo/FVptbyGlXAIsEUL0BvyBEill69rg/UKQDhd1+0swxvuj0l3aJJTKQ4sx\nIYC6PcWYp/VAaC99UstRYcOyrxjPK8JQGdpkKU/Nhg04ioowP+suZjONGoWhb1/SvviSff3cLicl\nJSV4e3uzdetWiouLmTVrFkajkRUrVmCz2ZgxY0azM9Xmq3ui9jVgSStp6ISojfRy+4vX2XEUWVB5\natkRmUNNsZWxY8aSnp7O2sLdbPc4xJGkUWzBC6PLg38VVkFhVaNrGFQCD7UKo0qFv1bDtEAfxn+/\nFG1NDQEPPoDL6kDo1U3mRpuGDSX0pZfIeu5vPDejji3ROrrXujDb/egdGkSAXodKCD7ILeGVE4XM\niw5F7elJ0BNPkPPww+Q+/PA54wmDgaoVKzD27482rOniXodLsqWihh9KKpkRZCbZ7Il0uLDsL8GQ\n0PxnzRDriybQSPWmXGwZG7BnZRH+xn8ROh01m3Jx1drxbqKjqt/tc6hYsICiV/5B90+/pOSt/ZR+\nkk7gfQPQhZqavFZzWA6kUfTqq3hNmojvr5paIDs/Zj/UPjpqUgow9g3AUWGlenUWhnh/jHFu4Vyx\n5CiOojoC7uyLrpsn/re7u3Oe/T4Yk5Iw33A9Ze+/j8tSR8gzzyDUavILvsHprCU8/NaGY11WK/m/\n/wNVy5cT+Nhj+N9+DzlbNzaKTRsaSvj/3sBZVkaqWk/WnkwejYvAK7TpG6GO4lQ34rPv9MOEENHn\nHWYE5gAdk9+moHCKJl1SzqO5As7bboN16xKwDtrFopdv5E+rV/P8Bx9wKD2dr7/5htDQ0IYxzhf8\n4Bb1NhsI4Z5pd7na1oBIQaEzaZv6AqSUh9szkJ8j1iPlSIsDY+KlpaWcxjQkGEtqMZa0UjzaYcya\nLe78Vs8RbS8ArfhyAZrAQDzHjAHc6Re+993L198tR+NwYA4JYciQIaxduxYhBEePHuWdd95h1KhR\n7Nu3j9GjRxMU1PxrUXvqME/rgc/UKByFdVgOlFC7uwhnmRU0AvM1vThmKCZ98VHGjBnD2LFjGTNm\nDCdOnGBVyg5+cGmJKcnh1Z4hxA/qR57VTp7NTq61ngqHkzqnizqnC4vL/XjcYuOvxwv4a9xQkp5/\nhZsNviS9ugP/GH/8mrF2NE2bxl9tvmz20/LbNSu5vjoefXcfgvu7TYT2FO0hq9rB6ycLmeTvTfzR\nI+Q+8QQqHx90cXFY9u9HZTIR/NRTmIYN5ej0GRT85UUi3vgvrtpaLGlp2MvKSR88lCXltXxbVEGp\n3b3++lVBGUsHxRCVVYerznHBz4VQCTxHdKNi8VFqVi7D0K8fnuPGuT3kN+Sg6+GDPqqxh7xKryfg\noYfInzeP2o1r8b9jDMX/3Uvp+wcIfDCxxZaczppacp94HE1AAKEvvNBs0afdXoGULnQ6P4Ra4JEU\nQvWaLBxlViq/OwaAeUa0Oyd+ez51uwrxmhCJIcbtZCKEQJx3MyKEIORPf0Lt40Ppu/NxVlQS+reX\nyMn5GG+v/vh4u4t4a7dtI//ZZ7GfzCLoySfwv/tuAIKDZzT9ngqBxt+fr47kYFAJZgR2SROfR4Bn\ncTuiSKDpZHj3bPmznRWUwi+Tljb/aaqA88w2P5jwA8/95jf0e+01btuxgyGDB/PNkiU4HENYt85t\nbXi24L/tttNC/ozwVoo2FS4HLirEhRC3Ad9JKUtPPb8gUsqP2iWynwF1e4tQeWgwxLTPH2d9tBm1\nn4HaHQWNBJd0SRC02NHCZXVQu909y6jxNbQpHnteHjUbN+J/79xzvMN3q1RU+3gzZMdOhn/wPv6B\ngfTt25fVq1eze/duysrKWLJkCR4eHowcObLZ8aWUpKWlUVBQwMiRIzGEmNCGmNzCcV0OOCSVVZV8\nt/Y7wsPDGT16NOB+D3r06EGhS48zq4jHooJJTExEq1YTY1ITY7rw693z5jssOHyctdfO5rFjeeiH\nGrg6p4LfHC4love5s50uKXnkwAlW+3nwxOFipn71PqqrHsNe5IOjzMouWyr3/3g/QmUiJOoNHtxz\nmDefehBvPz8iP3gfbWgo1sNHyP/DH8j//e/xmjwZz1GjqF65kszxE7AXFLCx3yBev/F2ig+cxOBy\nMSnQh2tD/eljMnLtnkxu3neMT7NV+LTgs+YxKJiKb4+gMg8k8J7BCCGo2VWAq6oe7wt4yPvMmE7p\nW29R8vp/6DFxIv539KX4zVRK3z9A0EMDEZqLZ7kV/Ol57Nk5dP/oQ9Tm5uPct/8BHI5qhg5ZihAC\nU1Iw1WuyKF94BNuxSjxHh1G3q5DaXYU4y23oe5nxnnDxGkQhBEFPPona14+il1+myuMYdROPER//\nCs6KCgr//jKVX3+NNjKSyPffw3TWX++Q4BlAZpPj2lwulhSWMzXABy9Nl6RfLwZO4Bba7wF/Bo6e\nd4wNOCil3Ne5oSn8EjjfqaQpkd1qNBr45z+ZlZhIr7vv5uriYkaOGIlkPi7XLajVMG0ahIS4Bfjp\n6519XUWAK1wOtGRG/ANgOFB66vmFkIAixAFHuRVLWimmoSFtLoI8H6ESmAYHU7XqJCUfpOGqs+Oq\nc7gfLQ60ISbM1/ZCH3nxxjO1OwqRNideo8KbPUZKSfWKFRgHDULbxKx1xaKvQUrMs65v2FZaWsrG\njRsx1tURffQompQUuOoqTCYTM2fOZNCgQSxdupSioiLq6ur4+OOPmTFjRqNZ8ZycHH744QdycnIA\nOHDgALNmzSIiIgLroXJ0PXxAJ1i0+QekTjJr1izU6jMiqLTewfu5JVwTZOa6hKiLvh+ncVZV4TH/\nHR4cPow/D4ln5f92saSXkUWRWr7NzuJ+jY0HugfjqVEjpeS3h3NYVFrJA0dsPDJjGJbQv2IceAVF\nbx7ixNp9PGx9mFBTKNnV2Ywp/Y6Fpsm8M/t2/n3LdWgC3Y6fht6xRH3xOaXvv0/J6/9B1teDSoW9\npITl857jH+G9SMDFr9cuI2nJQrx8fPCbcxv2/ALenTyF2RYt9xmtfNo/4OKfNZcd+8lNaMJGoY8f\njHRKqtfnoA2/sIe80GgIeOgh8p58kqrvv8fnqqvwm92b0o8OUptSgOcVza+qyPp6St59l6ql3xLw\n64fwSEpq9lhbfQkVFSmApLomDW+vvmh8Deh6mbFlVCC0Kmo25IIAfU8zPpOjMPYNaJXHuf9dd6L2\n8+NAzm9Q12nQb7Zx9NXpOCsq8L/nbgIefBCV4dybNU/P3pwW4tXVaXh5JTTsW11aRbkLe2aCAAAg\nAElEQVTD2dne4Q1IKVOBVAAhhASWSSlLuyQYhV8cLSnObMuYDcJ+zhwG9OnDjpkzub6omA3yVmAf\nTudLLFmiRqWCggKYOtXdifPsGXDFylDhcqAlQrwHkH/Wc4UWUPVjFgjwGts45/ZSMA0JwXKgBGel\nDZVJi9asR+WhRWVQU7eniOL/peKZ3A3vK7uj0jf93yudkprNueiivNFFeDV9jJQU/f1lyt5/H01w\nMBFvv4Whd28AXC4XTrudikWLMI0YgS48rOGcjz/+GCklydOmoTt4kNI338R76lTEqRzw8PBw7rvv\nPqqqqjh+/DgrV67kzTff5IorrmD0/7N33uFRVVsffs/0zEwy6b2TBoFAQg3SQZp0RBSkSUdARaWI\nIjYscAUElI4ICFKVJh1EeicQWkJ6SO9lMplyvj+GFgEFL+p37837PPNAzpyz954z55xZe+3fWqtF\nC/R6Pfv27ePSpUt3jXcnJyc2b97M8uXLadGkGTUy5Th0CuRMxXWykgtpZ9cQ+994WBemZqM3W3jD\n/8mCUPO/W4WlpATnMWMoO5ZBnWwjbfvWZlxhOTNikvlSms3KjHze8HcjSW9gdUYer6SaGC3XoPCy\nQ+HV3XqOgpIwnsvDpZ4zyzuuYMbWNziWuYZeeh2b6kXTR6Lk/nwagkyG8/Dh6Lp1x1JehiGvgElb\n97DFO5jnXHTMr+mHqlUU5Z2fJWfObLJnzgLA9scfmTvzO0ZqzLypsbDGIiL7HaO08IcfMFzegdyn\nJWXHbiH3tsWcX4F9l1p/uJpi17mT1Ss+fwF2HTqgqumIIsCO4oMpqBu4PaBNF0WR0oOHyP78cyqT\nk7Ft3x7nUY/KfmolN3c/1vm8hIyMzdjZWuMMFO4aKuMKEVRSbFt6o67v9qdXcgAUHepiOGHBdpeM\nrK3TUdWuje/SJahq1vzDY8+c7Ut4+L9wdekAwPrMfNwUMpo7PPxe+jsRRfFPVTauppo/y9MuuvNw\nw74RLufPs6VdD969copvmAlcQhTXYjbb8+OP8OOPVl24Umk9Bv7aqpzVRn41T4s/NMRFUUwGuJ2b\nth4QI4pi4l89sP9kjNnllJ/LQvuM1xOXtP8jpHYK3F57MMMIWI3+ot1JlB6/hT42F81z/sSb0jGZ\nTEgkkrsvU3oZ9oUGvLr+Np7rHrnzF5C/YgV2XbpQfvo0yf364zV3Luqm0axdu5ab8fE41wwjpGFD\n5BkZuLm5sWvXLgoLC/Hx8aFFq1YUlZRy6+23Kdm3D7v27e+2LZFIsLe3JzIykpCQEPbu3cuRI0c4\ncOwMCoxIBWjevDnNmjVDebsw0OjRo9mxYwe/HP+Vawodz8i1HD50hDD3Gvgl2aK/mHNXrpNXaWJZ\nei7dXe0JeYQM5XLuZXQKHT529yZK5uJi8leuRNuuLYrAYPI3nEYV5ojCS0u4l5avYvI5fTqfRa2c\neDfOqq8fIlMz+koWtsPuFZXNKM1gpriYSeaBfO05E+WB03T85gL7X5EQWs9IiKjijWupHGwUioO8\n6i0od3OlzGxmXKnI7tYd6bN/J5/374nNbU+3zNUVU24eyOXI3dwwpqVRe9UvTK5fm09qCUyJS+OL\nEO+HGtWW8nJyFy/Bpl4Y6roulJ3JQnq9ALm7GlXYH3tzBYkE53FjSR//GkXbtmPfswe69v7kLIqh\n7EQGti3ura4Y4uLI+vQzyo4dQxEQgPeCRagiGiBIf1+6kZOzF5XKBzu7OmRlbSU4aDISiQJDUjEy\nZxvcJtR/KhU+U9NWIQhyQvstQmyci65H9z8c2x202hAuXRpDjcC30XgMZV9eMcO9Xe5OgCoMmWRl\nbUdt44+LS7t/e6xPiiAI4VhTyoYCv70BRFEU2/7tg6rmv5bHCc58Eh5p2Ht44HjuMO/3eZW625bx\nKrux0BCR7VgvdWtw5v1ZUv6qqpx/xSpANf+7PHawpiiKRkEQ1gMdseaqreYRFO9JQpBLsW31aNnH\nX4FEJcOhexDqSFcKNsWxa/02rsjSHrqvs9qOUSEt7v5dUlnCpZxLNPFsQsHyFeQuWICuVy88Pv4I\nU3Y2qSNHkTpqFEljRhOXnU1ARQUFajVHUlI4smgRNjY26PV65HI5AwdaQwnsOnci9+uvyXhnKqJe\nj123bg8YiBqNhh49enDD5ERWzElKRTXdOrWnbdOwKvupVCp69+6Ne6YNh3LOsXnPVnQ6Hd0HPk/x\niusUbksATwXFJTksMSke6Q2/UXCDuefmcjjtMA5KB1Z1XoWfnbXIT96y5VhKSnAZM4bS4xlYyk1V\ntMf2zwVS51/5LIoxcLlnAEnllXRan4zES4uyhtUjn1+Rz4i9I8hT5WFxlKI8qydrzUeEBdallacD\nP9z8gS879qf3xVQm3UhjSoAHUgGkgoBUECg3WxhzJZmYknI+9nakxYEdZMVdxH/tWvQXLpA2egxI\npfivWY1NRARpE6YgysLovH8nSRlaVrXtjIfZxBs1/R841/lr1mDOy8Nl3jxkrl6UX8jBZNDj+FLo\nYxu3ts8+i7JWTXK//hpdl+dQBuhQhjhQcijVmgLTbCB79hwK1q61BqC+MwX7Pn1Jnx+D5cA5nN9q\ngOYRnmyTqZSCgqN4eb2Mo0NTsrN3kpd3CF1lU4ypJdaqnk/BCDeZSsjI2ISba2d04S2s7oUnICry\ne65cnciJhG+ZlxqCRXSkt7Oc9PR1ZGZtvSut8fLq/7cb4oIgNAZ+waoZDwZiAAfAF0jjUUL3aqr5\nkzxucObj8ruGvVKJ209LGPlNFKFjx9NLTKSIhlj4AeiERFL1mKc5Qbifp70KUM3/Nk+aNSUBaw7x\nah5BZVoJ+st52Lb1RapV/CV9XM+/ToAuAIXU2r5osVCyfz9SrRZNdDRKXzvEPh5cXbqdmhIfGspD\nEOUSkAuIMsi0FLAv7zQHDx3k2WetNZhmnZnF5rjNDLjmQtctGdh17oTHRx8iSCTI3d3xW7Oa45Mm\ncTI7mzBBIGLrNpyHDsVmxHAuXbrE/v37kUgkvPjii8jl1sJ+glSKz5Il3Jo4kVuTJlNy8BDu709D\n5uBQ5fMk5pax9Hwpz4a3wVBi4L2fE6nl70G4Z9UMHqLRgn+mjv61u3BekUijRo2wUdsg7RVM9rzz\nXJ+/mx1JG1nc/y1qZSZx4fA6Ujy9cfUPxLFhbb65tJDtCdvRKrSMjBjJhhsbGLl3JKs7r8Yuz2Bd\nAejWFUVQKPmbTqMMcUDwUrEydiURLhFEukai6+hP4U83aZJqIFouJS9Hj+6lUARBoKCigFF7R5FZ\nlsmiZxfhEO9G0bYERHS4vTuVEa4W+u3sR2z6T7zp35nPEzPZml34wPdrIxFYUSeADs46iiZP4tbE\nSdyaPJmSXbuRe3jgs2QxCl/rBEHXfSRFP6ciGhIZX+RM5qmjfNHoGWJObeQTJzUebVoh0Wgwl5aS\nv3QZmubNUUdZCyspA3WYSyqxqePy2NeeIAi4jB9P2qjRFG7ZgsMLL6B71o/sBRco2HSOgu/ew5iS\niv2LfXEZPx6ZgwP5W+IQ8iqQArs/PkVYzyBqNvV4wKjOyz+MxVKJi/Oz6HRRKBQuZGRsRhYXgCCX\noIn680WE7icjYzNmcynePoP+1PFSqYpCz495P+86RmMlU+SLyD5/kCzRiFodQEDAa7i7dUGt/keU\nfDOAzcAAwAgMFUXxnCAIbYBVWAM5q6nmqfJUgjPva+t3DXtBgDFjaBUezqluPelVUsRl8Tl69vqc\n+vXfonVr4e4xd9pxcrrnJX8a43zaqwDV/G/zpIb4F8BUQRAOiKKY81cM6D+dot1JSNQybJs/PAd0\nQrmBfKOJBrony798h/XX1/PRiY9wVDnyfHBveuT6Y1z4LYYrVwFwGj4c5/Hj2Ln7Z2zUNnQb1w+b\n31QSDALyt5o5evQowcHBOHg4sDNhJwOTfOiyJZEzQQLH2pfwWlEcYY5Wz3ShwcCv3t446/XU3rgJ\nwWLBvs/ziAoFFy9eRCaTMWzYMFxcqhp1Cm8v/FZ9R96y5eTMm4f+7Fk8Pv0UbTNrRUlRFJn202WU\nMgnvd62FgEC3+UcYueos28Y2w0FzbzJjSCxCNFpwq+tLz7B7bkyFhwZVYydcjovcaj8Eo0LJ0DIz\nTpXuGC4UknLqFHMPzyImtJjBtQcztPZQdEodrX1aM2T3EEbvG83M/R4gkeA6YQJlJzOwlBmxNLVl\n6O6hnM8+j0wiY3r0dLo17kbZ2SwKtycgtVcidVBiU9uFlOIUxuwfQ0ZpBrNbzybKLYpKUzai2YCm\n+cvYhIdTB4j2iGZl7Eq2t+lFsMqech8tZqmARQSzKGIGmtprCb0tqbHr2pXCzVso3roNm3r18P7m\n6yoTGf2VIiS2YLx5AbtnR7Kka0dmHTvPQp8aXMrN4v2+/akfEogoSDAXFeFyX95yp0G1wCw+sZdZ\n27IlqroR5H6zEF2PHsg9bJCoiig/p0C0yPBd+S2aRo0Aa+ag8pOZJBrM+Kuk+NgpOLj6GtdPZtKq\nfygO7vfug5ycvcjljuh0UUgkMtzdupGa9h262B7Y1g1EYvOns63eRRQtpKZ9h51dvbspC5+UxanZ\nfHDzFjVsbJnlkYSQnY29biBu7t2w1YY/duaiv4gIrPnC71QtkgKIonhAEISPgU+Bxv/Q2Kqp5rF4\nLMO+ZUuCYs6zt103xsXHsGHzRNTqGJo2Xcynn9pUMeIfJSP5szrvp70KUM3/Nk/6y9YGa+GIREEQ\nTmAN4ry/NKEoiuKfczP9h7AhMx+TKPLSQ4p2VNwsxBBXiK5zQJUCOTfKKtiRU8j2nEJiSysA6O/h\nyIwQb5RPUHL9cu5lPjv1GQ3cGhCcbMRr4kJK00SKnW1QThmJ28188pYs4VLCTVJdXOjWrdsDRvgd\nO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PO8RYEmrgQ7ZxXBDVzvjk8V6kD5mSxEowVBLsE/whnnwEzMYi7OzvdS/ZlLKtFfzkXX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\n4UeNMVnAfOAqT+gqoM0qSMdA4EtjTLoxZju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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show_lsmc_step(-3)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Keep going back in time" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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FM2V/Cp0inhXLdU5StWpVhg0bxrBhw2jatGmSafPKlSvj5OTE+vXr+fTTTxMV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Xc1Q6IqpOyKAtEoo86677Fo1gwwOQeVnc8gQWvAWyXFU63g+MY73D2fQfuhQdi6VJ4H2dmHkcvt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T0kMukVOtrOa70O/oYt+Fv3+OJyWigK4jPDn1VwoAPV/zprRhKuUV0YjFMpRKjd7U1/PE1LQT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\niDQTkR9E5LCIpIhItIh8l+0ikld5InKpiCx1NCeIyI8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show_lsmc_step(-20)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Until ..." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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Zu3YtAC+88AKVK1fOc7lTEJHdSinffGugAJKX/bZSis8++4zRo0fTqFEjVqxY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+oUppx0Jc8mjTVhibx3KgNziYGZjouwUdiwotMKghyC6FmrJx+f/Jjll5eT6p/KlNZjqLhcwEnX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KJnzyDQ7ePgiCGln5TYyN/BGLtevHENRqbkVcJ/zIAW6FX0cskeIV1I12g4dj76VJExIEFfn5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\nmvDk1c1ze8aVUiUqLy5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aW5Z6ywLTbhsMFc+sWbO49957qV27NnPnziU5uUOpfMSLG+qw\nNJMh10StYebWmQCM7DDSKQ14Y4jnwTTopSM/Qzw7W/HVmghqervTq2kggT4Fu5ampGcRfSaZJrV8\n8jWiTyakcsP7/+BiE+Y90osAq6z4lAz+O3cHv245Sqi/F0fiUhjTqyH/ua71eb2x8Sm6N7xnkwCm\n31Xqz7vTkJiWydwtRwg/kciBmEQOxiRxJE77rbUN9eOXh3pduEJnfpw5DKvfg81fa+O8zY3QOEz7\nYx9YDmnxYHODBj21G0urIeDiLMGSCiHhGLzfDep3hzvmkJSVzYCN+zibmcWybi2p6erCDR+s4tTZ\ndDKzs/Gv5s68R3pRzb0S1K0IStOoi8gTwDtALLAEPbkdoAFwNRAAPKWUmlaWWgvRcy0wDXABPlVK\nvVFYftNuGwwVQ16/8Q0bNnDjjTdy5swZZs6cydChQ0tc5ut/v86Ly18kS2XhIi68cuUrTOgzocR5\nLtAatYawr8JIz9J9Cx4uHiwftdzpjHFjiOfBNOilIz9DvKzZFh3HLR+voUM9f765pzsbIk7z1I9b\nOXk2jUeubMojVzXltYW7+eKfCCYMbMn9VzTJPXfq0n1MXRrOgsd6FztcYWUjOT2TiFPJhNbworqX\nW8lOTjwJaz+E9Z9C+lnwCYZmV0PzAdowzzMpslKw5kNYPAGGz4TWQ9iZmMKgjfvo6e/DrPaN2RBx\nhuHT1+DhamPeI71pEVwJ65gPpW3URaQv8CwQBuSElEkBVgBvKKX+LiuNRehwAfah/wBEA/8Ctyml\ndhV0jmm3Dc5KQZFE1qyBmbqjlk6d9HxA+zxFRSCZMUOvoJmUBGPGwJtvnkufOlW7Ltevr9P27dNu\nzD4++jrp6TqMtpcXBAfrgCBhYXoe4rJlelHLatUgMVFPC2pvLbeRnq4jA2Zna7fnfv20zsTEYyg1\nFFhDYOMxhN4dS7pfOIHegbQKaMVfkX+xL3Yfnq6eCEK2yibIOwiFIjI+EhE5b9VjV5urXm2zXi8a\n+Tdi3ZF17IrZRUZ2Rm6e6p7VaVi9IX6efqRmpNK0ZlP2n97Pvth9xKfFYxMbXq5eJGWcHxHFxeaC\nm80NFHi5e5GakUp6djo+bj6kZaWRnpmOu6s7Nb1qkpSehJebF81qNiM+LZ5Tyae4osEV+Lr78ueh\nPzmRdIKWgS05mXSSuNQ4FIrkjGSCvIO4rtl1dKrTic3HNgPg5+nHgn0LSMpIIis7i9jUWGxiw9vd\nm5jXY2LV6dJHozKGuAGoGEMcYO6WIzz+3RZa1/Fj17EEGgd6M/nWjnSsp32hs7MVj363mQXbjjHl\n1g7c1KkuCakZ9H7jT7o3DuCTkZW/N7xcSYmDs8cgsIWeZFKZycqEGWGQHAuPrAcPX748corx+6J5\noXEdHmlQm89WHaJRYDWualnb0WrLjIvuXdErbeb8KMQqpbIKy1/WWK4yE5VSA6z9CQBKqdcLOse0\n2wZnpKBIImvWaMM33c4JzGbTc/mWLdP7hflbz5gB999//rWeeUaHxs6bXnGkQbWhkLzAUQIqD/7A\nE3b700EdVaWeUFX5x3ENlYohHUPZd+IsHyw/wKgeDRg/sBVe7ueigthswuThHTidmM7//biNAG8P\ntkTFkZCayeP9mjlQeSXBy19vVQEXV7huMnx2Nax8E675H6NCAlh15ixvHDrG5f4+3NO7kaNVOh1K\nqWwcuwpxKBBltx8NdM+bSUTuA+4DqJ/T9WcwOBEFrXSpF8s5P2929rk8UPgKmT/9dOG1fv4ZGjcu\nl2oUEw/o1BOCF0Chq7UY8Czb4owhbqhwnr6mBaN7NqKWb/4+5x6uLkwf2YXhH6/hwW82YrMJ/VvV\npm1o1XRJMRRCvcug8yjtptLhNqR2G95pUY9tZ1O4f2cEy7q1wN/NNGOVEaXUDGAG6B5xB8sxGC6g\noJUuw8LAze3CHnH7PIWtkDl0KCxZcn7azTfrHvG86RXK4SvhSjdwyYCKj/R7yWJ+wQwVjogUaITn\n4Ofpxld3X8bNH67mSFyK6Q2/lOk/UUdX+W0cjPmd6m6uTG/TkBs2hfPknig+b9vQIfHhDQVyBKhn\nt1/XSjMYKhU9emi3kry+3jm94oX5iOd3Xg733adf8/MRh/LzEff0hJo6Wi3BwXp9m3nztAabDWqr\nHvitX4nHlW+R7ruPQO9AWge2ZuXhlYX6iNvERq1qtYhJjkEphZuLG642V3rV60XjGo1ZG72Wfaf2\nkaEy8HX3JaBaAPGp8YT4huT6iDcLaEZ4bPh5PuK1qtUi2CeY9Ox0ElITOJVyChs2FKrUPuJhDcPw\ndfdl2cFlhfqIX9/8+gt8xH/b+1uuj/ip5FPnfMRTY2Iv5nNmfMQNQMX5iJeUI3Ep7D6aQP/WVccH\n2FAKNn8Dcx+GrvfAoElgs/Fx5EkmHjjKo/WDeKZRHdxKsXKrM3KxPuKORkRc0ZM1+6EN8H+B25VS\nOws6x7TbBoOhsnKxbbbpETc4NaH+XoT6exWd0VC16XgHnAqHf6YCCga9w/31arE7KZX3Ik+yLDaB\nyS3r09HvwtjohopFKZUpIo8Ai9HhCz8vzAg3GAyGSxljiBsMBudHRLuoiMCqKTpp0DtMa1WfgYHV\nGb8vmkEb93FfvVr8X6NgvF1cCi3OUL4opRYCCx2tw2AwGJwdY4gbDIbKgQj0+69+v2qKdn4cPJlr\na1WnZw0f/nfgKB9HxbAwJp4Xm4TQwMsdHxcXfFxseEs21TZ8qn3JQ7tAnfbgZkZaDAaDweBYjCFu\nMBgqD7nGuMCqyTpt8GT8XF14q0U9bqpdg6f3RDF2Z8QFp7pmd+eB6O95bvFz2GwuENQa6naFltdB\n034VWg2DwWAwGMAY4oYKICMjg+joaFJTUx0txWCHp6cndevWxc2thKt4OhoR6Pcf/X7VZL3gz+DJ\n4FOLHv4+LOvWgg0JSZzNzCIpLZXE9Z+ReCaKHc2G8X79OzjW/CamJC/D/cgG2P4TbPwS7vgRmvZ3\naLUMBoPBcOlhDHFDuRMdHY2vry8NG5owc86CUorY2Fiio6Np1KgSLoqTY4x7+cOf/4OIVTDwTWh3\nC54uNnrX8IW0s/DtPXD4H7jhXVSnfrSOPMlrB49xKuB2PrviOXyyU+GzATDnbhi7HAKanHeZk2kZ\nrI9PYn18EuviEzmVnom7TXC32XAXwc0mVHd1YWzdWlxZ09d8vg0Gg8FQIowhbih3UlNTjRHuZIgI\nAQEBxMTEOFpK6RGBXo9DswEw7xH4eSxsn6NX43T3hm+GwdHNMPRTaDcMAR5rUJsgd1ee2hvFzZv3\nM6tDY2qNmAUzwmD2bZwatZi/kuGv02dZF5/IoRS9YoenTejs502LGp5kKkjLziYjW5GhFPuSUrl9\n20F6+/vwQpMQE7nFYDAYDMXGGOKGCsEY4c5HlXkmQS3h7sWwfgYsexk+uBx8gyHuMAyfCa2uOy/7\niDoBBLq7MXZHBNdtDOelpqFsufo7lkcfYtu/ESgRari6cLm/DyNDAule3Zu2vl6422z5Xj49O5uZ\nR2OZHHGcazfuY0iQPxMa16GhV+GLVhkMBoPBYAxxg8FQ+bG5wOUPQvNrYf7jEP0v3Da7QL/v/gF+\n/NSpCXduO8joHYdwEQ+6VA/h/w58TlijlnTo/RAuxfyj4m6zcW/dWtwaXJMPI0/ycVQMC2LieLJB\nME81Ci7LWhoMBoOhipF/F4/BUMXw8fG5IG3v3r2EhYXRsWNHWrVqxX3WusMrVqxARPj0009z827Z\nsgURYdKkSblpkyZNomXLlnTs2JFu3boxM2e9Yzv27NlDx44d6dSpEwcOHKBnz54ARERE8O233+ar\nNe+xDRs28Nhjj5Wu4pcaNRvByLnwfweKnHzZ2c+bZd1a8E37xuzq1ZZ5ffswrmYWnVc+h8vu+SW+\ntK+rC882rsPay1txe50A6nhUskmwBoPBYKhwTI+44ZLlscce48knn2TIkCEAbN++PfdY27Zt+eGH\nH7j33nsBmD17Nh06dMg9/vHHH/PHH3+wfv16/Pz8SEhI4JdffrngGr/++ivDhg3jhRdeAGD16tXA\nOWP79ttvv+CcvMe6du1K166VdsXzikcE3Ivnp13Hw506Hu7nEgZPhpg98Mv9sO5jyEyDrHTIyoCs\nNKjfEwZPKjQGeW0PN95qUe9ia2EwGAyGSwBjiBsqlJfm72TX0YQyLbN1iB//vb5Nic87duwYdevW\nzd1v165d7vsGDRqQkJDAiRMnCAoKYtGiRQwaNCj3+GuvvcaKFSvw8/MDwM/Pj1GjRp1X/sKFC5k6\ndSouLi4sW7aM5cuX4+PjQ2JiIuPHj2f37t107NiRUaNG8eSTT+ael/dYp06dmDRpEr/99hsTJ07k\n0KFDHDx4kMjISKZMmcLatWv5/fffCQ0NZf78+bi5ubFx40bGjRtHYmIigYGBfPnll9SpU6fE9+iS\nw80Tbv0GFjwFqQng6Qcu7uDiphcQ2vINxIbDbd9BtZqOVmswGAyGSo4xxA2XLE8++SRXXXUVPXv2\n5JprrmHMmDH4+/vnHh82bBg//vgjnTp1onPnznh46Ml3CQkJnD17lsaNGxda/qBBg3jggQfw8fHh\n6aefPu/YG2+8kWtc5yXvsRUrVpx3/MCBAyxfvpxdu3bRo0cPfvrpJ9566y1uuukmFixYwODBg3n0\n0UeZO3cutWrV4vvvv+f555/n888/L81tuvTwC9H+5fmx8xf4+X747Gq4Y452hTEYDAaDoZQYQ9xQ\noZSm57q8GDNmDAMGDGDRokXMnTuX6dOns3Xr1tzjw4cP59Zbb2XPnj3cdtttuW4ljmbgwIG4ubnR\nrl07srKyuPbaawHdox8REcHevXvZsWMHV19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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show_lsmc_step(-40)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Finally" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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IopTi008/5YUXXqBRo0asXLmS+vXr54PUBsNfHDlyxKa7hiH/SElJoWXLlixe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\nZsygbt26xX6NLjtunnDbLPj9KUhPBk8/sLi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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show_lsmc_step(0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We reached the first time step $t=\\delta$, where the option value can be computed as the average of discounted $\\bs v(t=\\delta)$, i.e., $v =\\frac{1}{n} e^{-r\\delta}\\bs 1^T \\bs v(t_0)$." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
LSMC MCTrue Value
American Put6.4936.523
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import fmt\n", "\n", "df = pd.DataFrame(np.array([v_b, truv]), index=['LSMC MC', 'True Value'], columns=['American Put'])\n", "fmt.displayDF(df.T, \"3f\", 3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* the LSMC result is surprisingly accurate" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Details of the least square\n", " \n", "at time $t_{m-1}$: $\\hs(t_{m-1})$ and the corresponding c.v. $\\bs v(t_m)e^{-r\\delta}$ are known:\n", " 1. construct a smooth function $u(s; t_{m-1})$ that minimizes \n", " \n", " $$\\left\\Vert \\ind\\left(\\hs(t_{m-1}) < k\\right) \\odot \\left( u\\left(\\hs(t_{m-1}); t_{m-1}\\right) - \\bs v(t_m)e^{-r\\delta} \\right)\\right\\Vert_2 $$\n", " \n", " * $u(\\cdot)$ is an estimate of the option's c.v., based on $\\hs(t_{m-1})$\n", " * $u(s; t_{m-1}) = c_0 + c_1 s + c_2 s^2$, coefficients are solved by least square\n", " * $\\ind(\\cdot) \\odot$ excludes OTM paths $\\rightarrow$ better accuracy\n", " 2. exercise decision is: $\\bs e = \\ind\\left(\\left(k - \\hs(t_{m-1})\\right) > u\\left(\\hs; t_{m-1}\\right)^+\\right)$\n", " 3. option value: $ \\bs v(t_{m-1}) = \\bs e \\odot\\left(k-\\hs(t_{m-1})\\right)^+ + (\\bs 1 - \\bs e) \\odot \\bs v(t_m)e^{-r\\delta}$\n", " * $\\bs v(t_{m-1})e^{-r\\delta}$ is therefore the c.v. at $t_{m-2}$\n", " \n", "$\\odot$ is element wise vector multiplication." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Exercise boundary" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(ts, k-b_b, '.-')\n", "xlabel('Time', fontsize=16)\n", "title('Exercise boundary', fontsize=18);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "Exercise boundary is defined by:\n", "\n", "$$ u(s; t_{m-1}) = c_0 + c_1 s + c_2 s^2 < k - s $$\n", "\n", "* it can also be directly obtained from the MC simulation\n", "* the exercise boundary from LSMC is not very accurate (smooth)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Bias of LSMC\n", "\n", "One would think LSMC is biased low because of the inaccurate exercise boundary, is it really?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Consider the following two ways of pricing American option:\n", "\n", "1. draw 100,000 paths, estimate the exercise boundary using LSMC \n", " 1. draw 100,000 new paths, and price the option using the boundary from step 1.\n", " 2. use the same 100,000 paths from step 1 to price the option" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Lower bound\n", "\n", "we can conclude the following (barring the discretization and MC errors):\n", "* 1A clearly is a lower bound of American option\n", "* 1B gives a higher value than 1A, because it makes use of the aggregated information of future paths during the least square\n", "\n", "Therefore, 1B is not necessarily a lower bound, due to the offsetting effects.\n", "* 1B is preferred over 1A because of faster speed and less bias " ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "def fixed_b(s, cv, ev) :\n", " fixed_b.idx -= 1\n", " return np.greater(ev, fixed_b.b[fixed_b.idx])\n", "\n", "fixed_b.b = b_b\n", "fixed_b.idx = -1\n", "\n", "v_a, e_a, b_a, _ = mc.amer_opt(spath2, exp(-r*dt), put_ev, fixed_b)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Upper bound\n", "\n", "Given that 1A is a reliable lower bound, it is useful to find an upper bound:\n", "* so that the true solution can be bucketed\n", "* the perfect foresight estimator is an upper bound, but it is too crude.\n", "\n", "We present a simple upper bound that is the most useful when the exercise boundary has simple topology.\n", "* more sophisticated upper bound is available in the literature" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "A more precise upper bound can be found by solving for the optimal exercise boundary $b^*(t)$ by going **backwards** from the simulated paths:\n", "\n", "1. set $b^*(t_m) = k$, $v(t_m) = (k-\\bs s(t_m))^+$, same as before\n", "2. step back to $t_{m-1}$\n", " 1. the exercise decision $\\bs e = \\ind \\left(\\bs s < b^*(t_{m-1})\\right)$\n", " 1. the option value is therefore $ \\bs v(t_{m-1}) = \\bs e \\odot\\left(k-\\hs(t_{m-1})\\right)^+ + (\\bs 1 - \\bs e) \\odot \\bs v(t_m)e^{-r\\delta}$\n", " 2. find the $b^*$ that maximize the average of $\\bs v(t_{m-1})$, this can be easily solved by 1-D direct search\n", "3. repeat till reaching $t_0$, and the option value is the average of $\\bs v(t_0)$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Bounded values\n", "\n", "\n", "This results in an upper bound because we did use the future information when solving for $b^*(t)$. \n", "* the resulting boundary is more optimal than the true exercise boundary for this set of stock paths\n", "* the resulting valuation bounds are very tight, they did bracket the true value of 6.52 (subject to Monte Carlo noise)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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GZSeWM68XCO9dnqRRkg4uKaGkzSS1VGgwuYrwe/PtlGSHA5OBgyVNJ7zuFZIG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\nWfGVXvMNvHwhNOnk9xWI3Mk3V7wbkhURWETtJK+b7ud85G4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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = figure(figsize=[12, 4])\n", "subplot(1, 2, 1)\n", "\n", "plot(ts, k-np.transpose([b_a, b_u]), '.-')\n", "xlabel('Time(Y)')\n", "title('Exercise Boundary')\n", "legend(['LSMC', 'Optimize $b^*$'], loc='best');\n", "ylim(75, 100);\n", "\n", "ax = fig.add_subplot(122)\n", "ax.set_axis_off()\n", "ax.text(0, .6, \"Option value is bounded by [%.3f, %.3f]\" % (v_a, v_u), size=\"xx-large\")\n", "ax.text(0, .5, \"LSMC (1B) value is %.3f\" % v_b, size=\"xx-large\");\n", "ax.text(0, .4, \"True value is %.3f\" % truv, size=\"xx-large\");" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Error of LSMC\n", "\n", "The path-wise LSMC values are dependent\n", " * through the estimate of exercise boundaries\n", "\n", "To estimate the exact LSMC error, we have to use batching\n", "\n", "* repeat the LSMC 10 times using 100,000 sample paths each\n", "* we also report the MC error using the independence assumptions\n", "* the (incorrect) independence assumption only leads to a slight over-estimation of the MC error" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def lsmc_batch(b, n) :\n", " bvs = []\n", " errs = []\n", "\n", " spath2 = gbm.draw(np.random.normal(size=[n, m]), s0, dt)\n", " disc1p = exp(-r*dt)\n", " \n", " for i in range(b) :\n", " spath = gbm.draw(np.random.normal(size=[n, m]), s0, dt)\n", " \n", " v_b, e_b, b_b, _ = mc.amer_opt(spath, disc1p, put_ev, mc.fit_ex)\n", " v_u, e_u, b_u, _ = mc.amer_opt(spath, disc1p, put_ev, mc.opt_ex)\n", " \n", " fixed_b.b = b_b\n", " fixed_b.idx = len(b_b)\n", " \n", " v_a, e_a, b_a, _ = mc.amer_opt(spath2, disc1p, put_ev, fixed_b)\n", " \n", " bvs.append((v_a, v_b, v_u))\n", " errs.append((e_a, e_b, e_u))\n", " spath2 = spath\n", " \n", " return np.array(bvs), np.array(errs)\n", "\n", "bvs, errs = lsmc_batch(10, n)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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Batch 1Batch 2Batch 3Batch 4Batch 5Batch 6Batch 7Batch 8Batch 9Batch 10Batch MeanBatch Std
LSMC - LB6.5076.4926.4866.4986.5196.5116.4976.5176.4866.5176.5030.012
LSMC6.5066.4996.5146.5306.5266.5076.5286.4966.5286.5376.5170.014
LSMC - UB6.5486.5406.5546.5736.5636.5506.5686.5336.5716.5826.5580.015
LSMC err0.0120.0120.0120.0120.0120.0120.0120.0120.0120.0120.0120.000
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import fmt\n", "import pandas as pd\n", "\n", "df = pd.DataFrame(np.concatenate((bvs.T, errs.T)), \n", " columns = ['Batch %d' % (i+1) for i in range(10)],\n", " index=['LSMC - LB', 'LSMC', 'LSMC - UB', \n", " 'err - LB', 'LSMC err ', 'err - UB'])\n", "sd = np.std(df.T)\n", "u = np.mean(df.T)\n", "\n", "df['Batch Mean'] = u\n", "df['Batch Std'] = sd\n", "idx = [0, 1, 2, 4]\n", "fmt.displayDF(df.iloc[idx, :], \"3f\", 2)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Final words on LSMC\n", "\n", "The main application is exotic options whose exercise decisions depend on multiple factors.\n", "* no need for pricing vanilla 1-D American options, there are far superior methods\n", "* great care are needed for high dimensional applications" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Assignment\n", "\n", "Recommended reading:\n", "\n", "* Andersen and Piterbarg: Chapter 3.1-3.3\n", "\n", "Homework:\n", "\n", "* Complete [homework set 6](http://yadongli.github.io/nyumath2048)" ] } ], "metadata": { "celltoolbar": "Slideshow", "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": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 1 }