{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Numerical Methods I\n", "\n", "# Lecture 4: Roots of Equations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Learning objectives:\n", "\n", "* Identify nonlinear equations\n", "* Solve these equations using the `scipy.optimize` functions `bisect` and `newton` \n", "* Explain the algorithms that underlie the Bisection, Newton and Secant method\n", "* Explain why these methods are considered *iterative* and *approximative* and how this relates to *tolerances*\n", "* Explain three types of *convergence* errors" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# some imports we will make at the start of every notebook\n", "# later notebooks may add to this with specific SciPy modules\n", "\n", "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# scipy's optimization\n", "import scipy.optimize as sop" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Nonlinear Equations\n", "\n", "A **system is said to be linear** if it can be represented by a **linear function** (*i.e.* a straight line in 1D):\n", "\n", "\n", "$$ f(x) := a + kx, $$\n", "\n", "\n", "where $f(x)$ is a quantity of interest that depends on some variable $x$, which can be quantified through measurements or observations.\n", "\n", "To a linear system we can associate a **linear equation**, which can be written in the form:\n", "\n", "\n", "$$ f(x) = 0 \\;\\;\\;\\; \\text{where} \\;\\;\\;\\; f(x) := a + kx. $$\n", "\n", "\n", "We've set the *function* equal to something (here we chose zero) to obtain an *equation*.\n", "\n", "[Our aim will be to find a solution $x$ to this equation. Note that for linear problems this is trivial if the problem is scalar valued, in the following lectures we will consider linear systems for vectors - i.e. matrix systems. Here we consider how to deal with the complexity when the problem is not linear (but for simplicity still scalar valued).]" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Examples of nonlinearity\n", "\n", "Note that the majority of real world systems cannot be expressed in such simple (linear) terms. \n", "\n", "[Note also that discretisations of nonlinear ODEs or PDEs (e.g. being nonlinear in order to accurately represent the nonlinear real world) results in nonlinear discrete systems for which we need to make use of techniques such as those introduced in this lecture.]\n", "\n", "They are then called nonlinear systems, and equations representing them contain terms like:\n", "\n", "\n", "- $ x^2,\\; x^3,\\ldots\\;\\;\\;$ e.g. higher ($>1$) order powers that would appear in polynomials.\n", "\n", "\n", "- $ \\sqrt{x},\\; x^{1/3}, x^{\\pi},\\ldots \\;\\;\\; $ e.g. roots, radicals and other non-integer polynomials.\n", "\n", "\n", "- $\\tan(x),\\; \\sin(x), \\; \\log(x),\\; \\text{erf}(x), \\ldots \\;\\;\\; $ e.g. trigonometric and other [*special functions*](https://en.wikipedia.org/wiki/Special_functions).\n", "\n", "\n", "You should be familiar, for example, with quadratic equations $f(x) := a x^2 + bx + c = 0$, for which there exist the well known analytic solutions:\n", "\n", "$$\n", "x^*_{1,2} := \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}\\,.\n", "$$\n", "\n", "The solutions $\\,x^*_{1,2}\\,$ are commonly referred to as the **roots** of the equation - this means that $\\,f(x^*_{1}) = f(x^*_{2}) =0$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## An example nonlinear equation\n", "\n", "An example of a nonlinear problem without trivial solution is:\n", "\n", "$$ x = \\tan(x). $$\n", "\n", "There is no exact analytic solution to this equation, so we have to devise methods to find approximate solutions of this equation.\n", "\n", "That is, we are looking for $x_{\\text{approx}}$ such that \n", "\n", "$$x _{\\text{approx}} \\approx \\tan(x_{\\text{approx}}), $$ \n", "\n", "to a set *tolerance* (or *precision*). \n", "\n", "Note that we can of course equivalently look to solve the problem \n", "\n", "$$ f(x) \\approx 0 \\;\\;\\;\\;\\text{where}\\;\\;\\;\\; f(x):= x - \\tan(x), $$ \n", "\n", "[or of course equivalently we could instead choose to define $\\,f(x):= \\tan(x) - x$].\n", "\n", "We will often do this (move all terms of our equation to one side and set equal to zero) to make our presentation of the theory below, as well as our implementation of solvers, generic. In this context a solution to the problem $f(x)=0$ is called a **root**.\n", "\n", "\n", "Q. Why is this equation nonlinear ? How many roots does this equation have ?\n", "\n", "\n", "We will see a plot of this problem in a couple of cells." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Picard's method of successive approximations (or fixed point iteration)\n", "\n", "\n", "## Fixed points\n", "\n", "Before moving on to problems written in the completely general form $\\,f(x) = 0\\,$, in this section we will consider equations that can be written as:\n", "\n", "\n", "$$ x = g(x), $$\n", "\n", "\n", "where $g$ is a given function.\n", "\n", "[Of course if we're given a problem of the second type we can make it look like the first simply by defining $\\,f(x) := x-g(x)\\,$ or $\\,f(x) = g(x)-x,\\,$ as we did for the problem involving $\\,\\tan\\,$ above]\n", "\n", "An $x$ that satisfies this equation is sometimes called a **fixed point** of the function $g$.\n", "\n", "It's called this since if we keep applying the function $g$ to the output, then the output never changes, i.e.\n", "\n", "\n", "$$x = g(x) = g(g(x)) = g(g(g(x))) = \\ldots $$\n", "\n", "\n", "As an example, consider the function\n", "\n", "\n", "$$ g(x) := x^{2}-3x+4. $$\n", "\n", "\n", "This has the fixed point 2, since $g(2)=2$.\n", "\n", "While the example\n", "\n", "\n", "$$ g(x) = x+1, $$\n", "\n", "\n", "clearly has no fixed points - every application of the function adds another one to our $x$.\n", "\n", "If we plot the function $y = g(x)$ as a curve in $(x,y)$ space then the fixed points (if they exist) are the locations where this curve intersects with the line $y=x$.\n", "\n", "Let's see some examples." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(15, 5))\n", "fig.tight_layout(w_pad=4)\n", "\n", "x = np.linspace(-1,4,100)\n", "ax1.plot(x, x**2 - 3*x + 4, 'b', label='$y = g(x) = x^2-3x+4$')\n", "ax1.plot(x, x, 'k', label='$y = x$')\n", "ax1.plot(2, 2, 'ro', label='intersection')\n", "ax1.set_xlabel('$x$', fontsize=16)\n", "ax1.set_ylabel('$y$', fontsize=16)\n", "ax1.set_title('Fixed point example 1', fontsize=16)\n", "ax1.legend(loc='best', fontsize=14)\n", "\n", "x = np.linspace(-1,4,100)\n", "ax2.plot(x, x+1, 'b', label='$y = g(x)=x+1$')\n", "ax2.plot(x, x, 'k', label='$y = x$')\n", "ax2.set_xlabel('$x$', fontsize=16)\n", "ax2.set_ylabel('$y$', fontsize=16)\n", "ax2.set_title('Fixed point example 2', fontsize=16)\n", "ax2.legend(loc='best', fontsize=14)\n", "\n", "x = np.linspace(-1,10,1000)\n", "y = np.tan(x)\n", "# don't plot large values - comment out next two lines to see issue\n", "y[y>100.] = np.inf\n", "y[y<-100.] = -np.inf\n", "ax3.plot(x, y, 'b', label=r'$y = g(x)=\\tan(x)$')\n", "ax3.plot(x, x, 'k', label='$y = x$')\n", "# I know that tan(0) = 0, so I already know one of the roots \n", "ax3.plot(0, 0, 'ro', label='intersection')\n", "# NB. the following values found below using bisection\n", "ax3.plot(4.493409156799316, 4.493409156799316, 'ro')\n", "ax3.plot(7.725251197814941, 7.725251197814941, 'ro')\n", "ax3.set_ylim([-10,10])\n", "ax3.set_xlabel('$x$', fontsize=16)\n", "ax3.set_ylabel('$y$', fontsize=16)\n", "ax3.set_title('Fixed point example 3', fontsize=16)\n", "ax3.legend(loc='best', fontsize=14)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Observations\n", "\n", "The first example has a single unique fixed point, the second has no fixed point, and the third has infinitely many." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Algorithm (Picard iteration)\n", "\n", "The simplest method to find approximate fixed points/roots to this kind of equation consists in guessing $x$, plugging it into the right-hand-side $g(\\cdot)$ and evaluating the function. \n", "\n", "The resulting new value for $x$ is then used as an updated guess. \n", "\n", "A sequence of $x^{(k)}$ values are thus defined via the iteration:\n", "\n", "$$ x^{(k+1)} = g\\left(x^{(k)}\\right), $$\n", "\n", "starting from some initial guess $x^{(0)}$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "This procedure can be repeated until some stopping criteria is met, e.g. when two consecutive values for $x$ differ by less than some user-defined tolerance. \n", "\n", "Note that here \n", "\n", "$$x^{(k+1)} - x^{(k)} = g\\left(x^{(k)}\\right) - x^{(k)}$$ \n", "\n", "and so the 'change in $x$' value dropping below our tolerance is equivalent to us satisfying $x=g(x)$ to that same tolerance!\n", "\n", "This strategy is often referred to as (Picard's) method of successive approximations. \n", "\n", "A pseudo-code description of this solution strategy looks like\n", "\n", "```\n", "guess x\n", "x_previous := x + 2*tolerance # so that the initial evaluation in the while loop is true.\n", "while ( abs(x - x_previous) > tolerance ) do \n", " x_previous := x\n", " x := g(x_previous)\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 4.1: \n", "\n", "Complete the implementation of the method of successive approximations below to solve $x=\\mathrm{e}^{-x}$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Current iteration solution: 0.9\n", "\n", "Picard used 1 function evaluations\n", "\n", "Solution from Picard: 0.9\n", "\n", "Check this against the solution from SciPy: sop.newton(f, 0.9)= 0.5671432904097843\n" ] } ], "source": [ "def picard(f, x, atol=1.0e-6):\n", " \"\"\" Function implementing Picard's method.\n", " \n", " f here is the function g(.) described in the lecture and we are solving x = g(x).\n", " \n", " x is an initial guess.\n", " \n", " atol is a user-defined (absolute) error tolerance.\n", " \"\"\"\n", " # record number of function evaluations so we can later compare methods\n", " fevals = 0\n", " # initialise the previous x simply so that while loop argument is initially true\n", " x_prev = x + 2*atol\n", " while abs(x - x_prev) > atol:\n", " x_prev = x\n", " \n", " \n", " # ONE LINE OF MISSING CODE HERE\n", " \n", " \n", " fevals += 1\n", " print('Current iteration solution: ',x)\n", " print('\\nPicard used', fevals, 'function evaluations')\n", " return x\n", "\n", "\n", "\n", "def g(x):\n", " return np.exp(-x)\n", "\n", "\n", "print('\\nSolution from Picard: ', picard(g, 0.9, atol=1.0e-7)) # 0.9 is our initial guess\n", "\n", "\n", "# let's check our answer against a SciPy function: sop.newton.\n", "def f(x):\n", " return x - np.exp(-x)\n", "\n", "print('\\nCheck this against the solution from SciPy: sop.newton(f, 0.9)=', sop.newton(f, 0.9))\n", "\n", "# NB. if we tighten up the atol toelrance in our call to picard the answer gets closer to SciPy \n", "# but of course takes more iterations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To get a better idea of what is going on here let's look at the progression of the intermediate results $\\,x^{(k+1)}\\,$ from $\\,x^{(k+1)} = g\\left(x^{(k)}\\right)\\,$, and plot them on top of the curve $y = \\mathrm{e}^{-x}$.\n", "\n", "NB. I include the plotting code here for completeness, but you can ignore the details if you're not interested." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x_00 = 1.00000. g(x_00) = 0.36788. |x_00 - g(x_00)| = 0.63212\n", "x_01 = 0.36788. g(x_01) = 0.69220. |x_01 - g(x_01)| = 0.32432\n", "x_02 = 0.69220. g(x_02) = 0.50047. |x_02 - g(x_02)| = 0.19173\n", "x_03 = 0.50047. g(x_03) = 0.60624. |x_03 - g(x_03)| = 0.10577\n", "x_04 = 0.60624. g(x_04) = 0.54540. |x_04 - g(x_04)| = 0.06085\n", "x_05 = 0.54540. g(x_05) = 0.57961. |x_05 - g(x_05)| = 0.03422\n", "x_06 = 0.57961. g(x_06) = 0.56012. |x_06 - g(x_06)| = 0.01950\n", "x_07 = 0.56012. g(x_07) = 0.57114. |x_07 - g(x_07)| = 0.01103\n", "x_08 = 0.57114. g(x_08) = 0.56488. |x_08 - g(x_08)| = 0.00626\n", "x_09 = 0.56488. g(x_09) = 0.56843. |x_09 - g(x_09)| = 0.00355\n", "x_10 = 0.56843. g(x_10) = 0.56641. |x_10 - g(x_10)| = 0.00201\n", "x_11 = 0.56641. g(x_11) = 0.56756. |x_11 - g(x_11)| = 0.00114\n", "x_12 = 0.56756. g(x_12) = 0.56691. |x_12 - g(x_12)| = 0.00065\n", "x_13 = 0.56691. g(x_13) = 0.56728. |x_13 - g(x_13)| = 0.00037\n", "x_14 = 0.56728. g(x_14) = 0.56707. |x_14 - g(x_14)| = 0.00021\n", "x_15 = 0.56707. g(x_15) = 0.56719. |x_15 - g(x_15)| = 0.00012\n", "x_16 = 0.56719. g(x_16) = 0.56712. |x_16 - g(x_16)| = 0.00007\n" ] }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def plot_picard_convergence(f, x, ax, max_labels=6, atol=1.0e-4, flabel=''):\n", " \"\"\" Function to demonstrate/plot the Picard algorithm and its convergence\n", " \"\"\"\n", " # variables to store solution iterations for plotting purposes\n", " xs = []\n", " fs = []\n", "\n", " # the following is identical to our iteration above, apart from storing iterations\n", " x_prev = x + 2*atol\n", " while abs(x - x_prev) > atol:\n", " x_prev = x\n", " x = f(x_prev)\n", " print('x_{0:0>2d} = {1:7.5f}. g(x_{0:0>2d}) = {2:7.5f}. |x_{0:0>2d} - g(x_{0:0>2d})| = {3:7.5f}'.\n", " format(len(xs), x_prev, x, abs(x_prev-x)))\n", " xs.append(x_prev)\n", " fs.append(x) # as x = g(x_prev) at this point we can store this\n", "\n", " # plot the iteration results\n", " ax.scatter(xs, fs, marker='x', color='red', s=30)\n", "\n", " # plot the convergence pattern\n", " x_pattern = [xs[0]]\n", " f_pattern = [fs[0]]\n", " for i in range(1, len(xs)):\n", " x_pattern.append(xs[i])\n", " f_pattern.append(fs[i-1])\n", " x_pattern.append(xs[i])\n", " f_pattern.append(fs[i])\n", " ax.plot(x_pattern, f_pattern, 'g--')\n", "\n", " # plot the function over the x values considered\n", " idx_sort = np.argsort(xs)\n", " ax.plot(np.array(xs)[idx_sort], np.array(fs)[idx_sort], 'b')\n", "\n", " # add some labels\n", " # figure out a reasonable offset for labels\n", " dxt = (np.max(x_pattern)-np.min(x_pattern))/50.\n", " dyt = (np.max(f_pattern)-np.min(f_pattern))/50.\n", " ax.text(xs[0]+dxt, fs[0]+dyt, '$x_0$')\n", " # only plot a maximum of max_labels labels, so plot doesn't get too messy\n", " for i in range(1, min(max_labels+1, len(xs))):\n", " label = ''.join(['$x_{', str(i), '}$'])\n", " ax.text(xs[i]+dxt, fs[i]+dyt, label)\n", "\n", " ax.set_xlabel('$x$', fontsize=16)\n", " if not flabel:\n", " fl = '$f(x)$'\n", " else:\n", " fl = flabel\n", " ax.set_ylabel(fl, fontsize=16)\n", " ax.set_title('Successive Approximations', fontsize=20)\n", "\n", "\n", "def g(x):\n", " return np.exp(-x)\n", "\n", "# set up a figure for plotting\n", "fig, ax1 = plt.subplots(figsize=(8, 8))\n", "# set an initial guess - you can try different values for x_guess\n", "x_guess = 1.0\n", "# call our plotting function with above choice of function g(.), use the default stopping criterion\n", "plot_picard_convergence(g, x_guess, ax1, flabel=r'$g(x) = \\exp(-x)$')\n", "\n", "# add a y=x line without extending the axes limits\n", "ax1.autoscale(False)\n", "xlim = plt.gca().get_xlim()\n", "ax1.plot(xlim, xlim, 'k--')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is an example of a so-called [\"cobweb plot\"](https://en.wikipedia.org/wiki/Cobweb_plot):\n", "\n", "- We start from $x^{(0)}=1.0$ - shown as $x_0$ in the plot.\n", "\n", "\n", "- We evaluate $g(x^{(0)}) = 0.36788...$. The red cross marked as $x_0$ is plotted at the location $(x^{(0)},g(x^{(0)}))$.\n", "\n", "\n", "- We set our new iteration value, $x^{(1)}$, to this '$y$' value (i.e. $0.36788...$) - the lowest green dashed horizontal line takes us from $x^{(0)}$ to this new $x^{(1)}$ - we jump horizontally to the $y=x$ line given by the black dashed line.\n", "\n", "\n", "- We then evaluate $g(x^{(1)}) = 0.69220...$ - the left most vertical green dashed line takes us to this value on the $y$ axis where the second red cross marked with $x_1$ is plotted at the location $(x^{(1)},g(x^{(1)})$.\n", "\n", "\n", "- We set our new $x$ value to this (0.69220), and this is indicated by the top most horizontal green dashed line taking us back to the $y=x$ black dashed line.\n", "\n", "\n", "- Evaluate $g$ of this value giving us 0.50047, this is our next vertical line\n", "\n", "\n", "- and so on, converging to our fixed point" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "This plot shows that our algorithm *converges* to the point where $x = g(x)$, which in our case is $x = \\mathrm{e}^{-x}$.\n", "\n", "For this example this is the point where both $x$ and $g(x)$ equal ~0.57. \n", "\n", "It should be obvious that this method is iterative in nature and that the solution can be expected to be an approximation accurate to a tolerance of $e \\leq$ `atol`. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "As we said at the start of this lecture, another way to visualise this is to plot the functions $y = x$ and $y = \\mathrm{e}^{-x}$ in $(x,y)$ space and find the intersection." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Fixed point as the intersection of two curves')" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(6, 6))\n", "ax1 = plt.subplot(111)\n", "\n", "x = np.linspace(0, 1, 100)\n", "\n", "ax1.plot(x, np.exp(-x), 'b', label=r'$y(x) = g(x) = \\mathrm{e}^{-x}$')\n", "ax1.plot(x, x, 'k--', label='$y(x)=x$')\n", "# our solution from Picard above: 0.5671430835570621\n", "ax1.plot(0.5671430835570621, 0.5671430835570621, 'ro', label='intersection')\n", "ax1.legend(loc='best', fontsize=14)\n", "ax1.set_xlabel('$x$', fontsize=16)\n", "ax1.set_ylabel('$y(x)$', fontsize=16)\n", "ax1.set_title('Fixed point as the intersection of two curves', fontsize=16)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Roots of equations\n", "\n", "This graphical method shows the intersection point, $x = \\mathrm{e}^{-x}$, also at ~0.57. \n", "\n", "This value is also termed a *root* of a closely related problem, as it satisfies \n", "\n", "$$ 0 = f(x) := x - \\mathrm{e}^{-x}. $$\n", "\n", "[So a \"fixed point\" can always be defined as a \"root\" of a related problem, but the opposite is not strictly speaking true. However, we will see below how it is possible to update the problem of finding a \"root\" to finding a \"fixed point\", and hence reapply this sort of fixed point iteration approach to this more general problem].\n", "\n", "In this expression we rearranged $\\,x = \\mathrm{e}^{-x}\\,$ to $\\,0 = x - \\mathrm{e}^{-x}\\,$ and defined $\\,f(x) := x - \\mathrm{e}^{-x}$. \n", "\n", "Thus, another solution strategy is to find a value $x^*$ such that $f(x^*) = 0$, or, in our case, $x^* - \\mathrm{e}^{-x^*} = 0$. \n", "\n", "We can of course plot a similar intersection figure for this modified problem." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(6, 6))\n", "ax1 = plt.subplot(111)\n", "\n", "x = np.linspace(-1, 2, 100)\n", "\n", "ax1.plot(x, x-np.exp(-x), 'b', label='$y(x) = f(x) = x - \\mathrm{e}^{-x}$')\n", "# add a zero line extending across axes\n", "xlim = ax1.get_xlim()\n", "ax1.plot([xlim[0], xlim[1]], [0., 0.], 'k--', label='$y(x)=0$')\n", "ax1.plot(0.5671, 0., 'ro', label='intersection')\n", "ax1.set_xlim(xlim)\n", "ax1.legend(loc='best', fontsize=14)\n", "ax1.set_xlabel('$x$', fontsize=16)\n", "ax1.set_ylabel('$y(x)$', fontsize=16)\n", "ax1.set_title('Fixed point as a root of $f(x)$', fontsize=16);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Subintervals and initial guesses\n", " \n", "It is often important to start from a good initial guess for a root can be very important - how can we establish a good initial guess?\n", "\n", "The graph shows the root of $f(x)$ at our solution $x^* \\approx 0.57$. By visual inspection, we see that $f(x)$ has a root $f(x^*) = 0$ in the interval $x^* \\in (-1,1)$. \n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## Exercise 4.2:\n", "\n", "\n", "Let's consider an example:\n", "\n", "$$2\\,x + x \\, \\sin(x-3) = 5\\;\\;\\;\\; \\text{for}\\;\\;\\;\\; x \\in (-10,10).$$\n", "\n", "\n", "By means of visual inspection (i.e. do some plotting) find a subinterval $(a,b)$ such that \n", "\n", "\n", "1. there exists an $x^* \\in (a,b)$ such that $f(x^*) = 0$, and \n", "\n", "\n", "2. $f(x)$ is [monotonic](https://en.wikipedia.org/wiki/Monotonic_function).\n", "\n", "Where we define $f$ such that the solution to the above equation is a root - i.e. move all the terms on to one side and set equal to zero. Below we make the choice to define $f$ as $f(x) = 2\\,x + x \\, \\sin(x-3) - 5$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": false }, "outputs": [ { "ename": "SyntaxError", "evalue": "invalid syntax (, line 4)", "output_type": "error", "traceback": [ "\u001b[1;36m File \u001b[1;32m\"\"\u001b[1;36m, line \u001b[1;32m4\u001b[0m\n\u001b[1;33m return ..............\u001b[0m\n\u001b[1;37m ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n" ] } ], "source": [ "# for this problem we can define f as 5 - (2*x + x*np.sin(x-3)), or (2*x + x*np.sin(x-3)) - 5.\n", "# it makes no difference to the root-finding, just the plots\n", "def f(x):\n", " return ..............\n", "\n", "# plot the function over the whole interval being considered\n", "x = np.linspace(-10,10,100)\n", "\n", "# now plot the function over a smaller interval\n", "x = np.linspace(..... ,..... , 100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You should find that in $(0,5)$, i.e. an interval with upper and lower bounds $a$ = 0 and $b$ = 5, there exists a root, and also the function is monotonically increasing over this interval - we have excluded any local maxima or minima that we see do occur in the function outside this restricted interval.\n", "\n", "[Note the caveat that in general we will assume the evaluation of $\\,f$ (or $g$) is expensive and so we want to do this as few times as possible - generating a nice high resolution plot like this is not something we will be able to do in general].\n", "\n", "We can make use of this knowledge to help us identify a good starting guess for the root." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Root bracketing\n", "\n", "Where the root lies can be important.\n", "\n", "By visual inspection we can identify if roots exist for a function, and narrow down the interval in which a root can be found. \n", "\n", "For the equation \n", "\n", "$$f(x) := x - \\text{e}^{-x},$$ \n", "\n", "we have shown by plotting (above in two images, see also below, where we noted a root around $x\\approx ~0.57$) that a root is bounded in $(-1,1)$, and that $f(x)$ is monotonically increasing over this interval. \n", "\n", "With this in mind, we can define a [*root bracketing algorithm*](https://en.wikipedia.org/wiki/Root-finding_algorithm#Bracketing_methods) that marches along $f(x)$ in increments of $\\Delta x$ and identifies a new, tighter (i.e. smaller) bracket around the root by detecting a *change in sign of $f(x)$*. \n", "\n", "This algorithm is also referred to as *incremental search*. \n", "\n", "The approach can be visualised as follows:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def plot_root_bracketing(f, a, b, dx, ax, xbounds=(-0.1, 1.4), ybounds=(-5, 6), flabel=''):\n", " x = np.linspace(a, b, int((b-a)/dx)+1)\n", " y = f(x)\n", " # plot the sub-intervals in blue\n", " ax.plot(x, y, 'bo-')\n", " for i in range(1, len(x)):\n", " if np.sign(y[i]) != np.sign(y[i-1]):\n", " # plot the sub-interval where the sign changes in red\n", " ax.plot([x[i], x[i-1]], [y[i], y[i-1]], 'ro-')\n", " ax.set_xlabel('$x$', fontsize=16)\n", " if not flabel:\n", " fl = '$f(x)$'\n", " else:\n", " fl = flabel\n", " ax.set_ylabel(fl, fontsize=16)\n", " xlim = ax.get_xlim()\n", " ax.plot([xlim[0], xlim[1]], [0., 0.], 'k--')\n", " ax.set_xlim(xlim)\n", " ax.set_title('Root bracketing\\n' + '(red indicates the bracket containing the root)', fontsize=20)\n", "\n", " \n", "def f(x):\n", " return x - np.exp(-x)\n", "\n", "\n", "fig, ax1 = plt.subplots(figsize=(8,5))\n", " \n", "lower_bound = -1.\n", "upper_bound = 1.\n", "dx = 0.4\n", "plot_root_bracketing(f, lower_bound, upper_bound, dx, ax1, flabel=r'$f(x) = x - \\mathrm{e}^{-x}$')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 4.3: \n", " \n", "For $2x + x \\mathrm{sin}(x-3) = 5$, use the subinterval $x \\in(a,b)$ you found in Exercise 4.2 and complete the code below to implement a function for the root bracketing algorithm. Derive the concept from the Figure above" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "def f(x):\n", " return 2*x + x*np.sin(x-3) - 5\n", "\n", "\n", "def root_bracketing(f, a, b, dx):\n", " \"\"\" Function to perform root bracketing on the function f(.)\n", " between a and b, with fixed interval size dx.\n", " Returns the bracket of size dx that contains the root.\n", " \"\"\" \n", " # The sign function returns: -1 if x < 0; 0 if x==0; 1 if x > 0.\n", " sign = np.sign(f(a))\n", " while ...\n", " .....\n", " return (a-dx, a)\n", "\n", "\n", "a = 0.\n", "b = 5.\n", "dx = 0.1\n", "# print out the output from our root_bracketing function\n", "print('Bracket = ', root_bracketing(f, a, b, dx))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Bisection method\n", "\n", "Once we know that a root can be found in $x \\in (a,b)$, we can close in on it with an algorithm similar to root-bracketing/incremental search described above, but with a smart switch to gradually *decrease* $\\Delta x$ *by a factor* of 1/2, and *change the marching direction* depending on the sign of $f(x_1)f(x_2)$, where $x_1$ and $x_2$ are the local bounds considered during the marching process.\n", "\n", "\n", "The algorithm works as follows:\n", "\n", "\n", "- If there is a root in the interval $[x_1, x_2]$, then $f(x_1)f(x_2) < 0$ (as $f(x_1)$ and $f(x_2)$ will be of different signs)\n", "\n", "\n", "- In order to halve the interval, we compute $f(x_3)$, where $x_3 := (x_1 + x_2)/2$ is the midpoint of the current interval. \n", "\n", "\n", "- If $f(x_2)f(x_3) < 0$, then the root must be in $[x_2, x_3]$, and we record this by replacing the original bound $x_1$ by $x_3$,\n", "\n", "\n", "- otherwise, the root must lie in $[x_1, x_3]$, in which case $x_2$ is replaced by $x_3$. \n", "\n", "\n", "- In either case, the new updated interval $[x_1, x_2]$ is half the size of the original interval. \n", "\n", "\n", "- The bisection is repeated until the interval has been reduced to some user-defined convergence tolerance." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "You can find pseudo-code here.\n", "\n", "\n", "A visualisation of the method illustrates the narrowing in of an ever-smaller bracket:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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zEckxa72uzEcegVKlvHlmN93kd6qCr8AXaOvXr6ddpv0kbrnlFgYMGEBKSgrdunU752v69OlDnz592LNnD7///e/POd+/f3969+7Ntm3buOuuu845/8gjj9C9e3fWr19P3759zzn/5JNP0rFjR1asWMGgQYPOOf/cc8/RsmVLFi9ezBNPPHHO+Zdeeom4uDhmzZrFP//5z3POv/rqq9SvX59Jkybxv//975zz7777LtWrV+fDDz9k5MiR55z/5JNPqFixIqNHj2b06NHnnP/iiy8oUaIEI0aM4KOPPjrn/Lx58wB44YUXmDx58lnnLrvsMqZOnQrAP/7xD2bPnn3W+QoVKvDpp58C8Pjjj/PVV1+ddb5atWq89957AAwaNIgVK1acdb5evXq89tprADzwwANs2LDhrPNxcXG89NJLANx5551s3779rPMtWrTg3//+NwA33XQTe/fuPet8hw4d+Nvf/gZA165dOXr06Fnnb7jhBh599FGAc/7eQf783WvXrjudO3/HV1/1ozbfs4xttAeoXp0n336bjp066e+e/u6dc17vexf+u1dY7d0L990HEyd62zW99ZY3tCmXnpoERAqQAwfg2mst33yVRn2+o3rVNGjbFqpW9RY+GznynO5OEZGszJvndXtPnQpDh8LkySrO8pOxQfxmbYwZDNwPWGA1cK+19tj5rk9MTLTJycmZj5H5mEhB9MMP3mbEO348xccnenD9wLreu6oxXlE2eDAkJXm98Gq3Ermowvrvx6lT8MwzXjNAVBSMG+d1bErgGWOWWmsTszoXtEOcxpiqwMNAQ2vtUWPMR8CtwGhfg4kEoRUrvOGHEydgzrwwmu+83+vmPD3nLL1xgLZtveMiIlnYuRNuvRXmz/f20Bw+3Jt3Jvkv2Ic4iwKXGWOKAiWAn3zOI+Kf8yxAO2+upW2rk4SHWxYtguYtjPeELHNDgDnPcRERvKIsPh6WLIF33oG331Zx5qegLdCstTuAF4AfgZ+Bg9baGf6mEvFRFgvQfvKxpXOnVKqlbGDx36bRoIHPGUUk5FgL//0vdOgApUvDN994y2mIv4K2QDPGlAN6AJHAVUBJY8ydWVz3gDEm2RiTvHv37vyOKZJ/MixAy+DBjBxhueUWi5P6NQv7jqXa/V38TigiIebAAe+t5c9/9n7+c11vw3PxX9DOQQM6Aj9Ya3cDGGM+A1oC72W8yFr7GvAaeE0C+R1SJN+kzyOzFp5OKsezGLoziXEDFlLi5f9q6FJEcmTdOujRw2swSkqChx7S20gwCeYC7UeguTGmBHAU6AAUvnYakQxS0wwDjg7lNQz38Sav0peiL5/Uu6qI5MjEid5uAJddBnPnQuvWfieSzIJ2iNNa+w3wCbAMb4mNIqQ/KRMpjI4dg5tvtrz2uuEJ/sUb3E9RUs+akyYiciFpafDss96Ts/r1vU3PVZwFp2B+goa19u/A3/3OIeK3AwegRw/LwgWWYTzMQwPDYGjab2ubwW9rnomIZOHXX73J/xMmeK+jRnlP0CQ4BXWBJiLw00/QpQt8t87yAbfRe2CV34qxoUO9i5KSvDXOtACtiGRh61bo3t3b8Pyll+Dhh/XzXLBTgSYSxNat8xag3bsXvvjC0PHwrVqAVkRy5OuvvSHN48e9bZs6dfI7kWRH0M5BEyk0zrMA7cIFllbNTnDsmGX+fOjYSQvQikjOfPABtGsHl1/uFWoqzkKHCjQRv2WxAO1HH1o6tk/lysOb+fqZGdoHT0RyJC0N/v53uP12uPpqb/HZ6Gi/U0lOaIhTxG8ZFqC1Fl6sPpRHHzO0YTET+k6j/AP/8juhiISQ48fh3nu9p2f33QcjR0JEhN+pJKdUoIn4LX0eWWqaYfCwSIZjuIUPeef/XIoPf15DlyKSbfv3ezMe5s+Hf//b2yFAbyGhSQWaSBA4esxwx/YXGY/hEV7gv/yJIsNT9c4qItm2ZQt06wabN8P778Ntt/mdSPJCc9BEfLZnD3ToYJkw3pLEw7zAYxTBagFaEcm2pUuheXP4+WeYMUPFWUGgAk3ER5s3Q8uWluVLTvIJv+fhgUW82b0ZNkVXkSYiFzJ1KlxzDRQvDosXe6vuSOjTEKeIT5YsgRtugLRjJ5idei0tBzbTArQikiNjxniNALGxMGUKVKnidyIJFBVoIj6YNAl69/beTKcujKDe2se0AK2IZJu18MIL8Kc/QYcO8NlnULq036kkkHJVoBljKgIPAw5gga+Bl621+wKYTaRAGjkSHnwQmjaFyZOhUiUD9bN4QnZ6AVoRkQzS0uCxx+DFF+GWW7ynaMWK+Z1KAu2ic9CMMfuMMQkZPq8OLAceB2oAtYCngKXGmCsvUU6RkJeWBo8/DgMGwPXXw9y5UKmS36lEJJScOOFtdP7ii/DQQ95aZyrOCqbsNAmU5ewnbUOACKCZtbaRtbYh0BwoBTwd8IQiBcDx43DXXTBkCPTr5w1HlCzpdyoRCSUpKd6Mh7Fj4V//8qaoFlGrX4GVmyHOzsCz1trlpw9Ya5ONMUPwhj1FJIMDB7yRynnztHCkiOTOwYNeU9GXX8Krr8IDD/idSC613BRoZfGGODNbBlTOWxyRgmXbNujaFTZsgPfegzvu8DuRiISa3buhc2dYvdob0uzd2+9Ekh+yW6AlGmNKpX+8G8iqV6QskBKQVCIFwMqV3qrehw/DtGnQvr3fiUQk1GzfDp06wdatMHGi9wOfFA7ZLdCGp7+eHphpC0zJdE0CsDUQoURC3cyZcNNNUKaMNyTRuLHfiUQk1GzaBB07evtrTp8Obdr4nUjyU3YKtGuzOHYwi2ORwLi8xREJfe+8A/ffDw0bwhdfQNWqficSkVCzdq23vtmpU17Hd0LCxb9GCpaLFmjW2vnZuZG19s68xxEJXdbCP/8JTz3l/dT76adaOFJEcm7FCm9YMzwc5s/3ftiTwkcNuiIBcPKk11X11FPeGkVTpqg4E5GcW7IErr0WSpSABQtUnBVmKtBE8ujwYbjxRnjjDXjySRg9GiIi/E4lIqFm0SLv6Xv58l5xFhXldyLxk/biFMmDnTu9XQFWroTXXoM//tHvRCISimbP9n7Qq17d+1hzV0UFmkgurVvntbzv2eO1v3fr5nciEQlFM2ZAjx7eE7NZs+BKbZooqEATyZWFC7031IgIbxJv06Z+JxKRUDRtmrd9U3S0V5xVrOh3IgkWuZ6DZoyZY4ypFsgwIqHg44+9DqtKleCrr1SciUjufPGF94New4besKaKM8koL00C7YASAcohEvSshRdfhFtugcREWLwYIiP9TiUioWjyZG+P3pgY78lZhQp+J5Jgoy5OkWxITYVBg+CRR+D3v/feUMuX9zuViISiiROhVy9o0sTbdUTvJZIVFWgiF3H0KNx8MwwbBoMHw4cfQvHifqcSkVA0aZL3Q158vNccUK6c34kkWKlJQOQC9uzxWt+//hpeegkGDvQ7kYiEqilTvD164+K84qxMGb8TSTBTgSZyHps3e8tobNvmNQbcdJPfiUQkVE2d6g1rxsaqOJPsCeohTmNMWWPMJ8aY74wx64wxLfzOJIWD60KLFrB3r9ddpeJMRHJr+nSvIaBxY2/OWdmyfieSUBDUBRqQBEyz1kYDTYB1PueRQmDyZGjXDkqV8jo1W7b0O5GIhKqZM72lNBo08D7WnDPJrqAt0IwxpYFrgDcBrLUnrLUH/E0lBd2oUb+tS/TVV1C/vt+JRCRUzZvnzWGtX1+d35JzQVugAbWB3cDbxpjlxpg3jDEl/Q4lBVNaGjz+OPTv7807mzdP262ISO59+SXccAPUrq11ziR38lKgdQJ+DFSQLBQFEoCR1tp44Ajwl8wXGWMeMMYkG2OSd+/efQnjSEF14gTcfTcMGQJ9+8KECVBSPwqISC4tWeL9oFe1qjeH9Yor/E4koSjXBZq1dra19lggw2SyHdhurf0m/fNP8Aq2zDles9YmWmsTr9D/BXI+1sL48d5rBgf2W7o03c3YsfDcczByJBRVb7OI5NLy5dC5s1eUzZkDlSv7nUhCVdAOcVprdwLbjDGnZwF1ANb6GElC2YQJXo/74MFnirRtP1pa193JojVleHdgMo8/Dsb4nFNEQtaaNd4+vaVLe8VZ1ap+J5JQFuzPCh4CxhpjIoDvgXt9ziOhqmdPb5XZpCQAVvYZSrfWBzl8pATTer1O+6EDfA4oIqFswwbo2BGKFfOKs5o1/U4koS6oCzRr7QogMS/3SEtLC1AaCWnGwNChAMxKWkOvpF8pzWEW3TGWmHf/pEdnInIWm2k6xIVs2QIdOnjNRvPmQZ06lyyWFCJBXaDl1ZEjR1i/fj116tShZMmSRERE+B1JgsJS6uEt433vd03B+djnPCISbA4ePMiePXsuet1PP3nF2ZEjXnEWHX3ps0nhkKMCzRjTHOgCNAeuAi4D9gDrgfnABGvt/kCHzK2SJUuyb98+Vq5cieu6GGNwHIfY2FiKFSvmdzwREQlCP/74I5988gn9+/e/4HW7d3vDmrt2ed2asbH5FFAKBZOdx7jGmHuAR4FGwCFgFd4aZUeB8kAkUA84DnwEPGOt/eESZT6vxMREm5ycnOU5ay1btmzBdV1++OEHYmJicBwHdX6KiMhpp06d4tVXX+Xaa6+lYcOG571u/35o3x7Wr4dp0+Caa/IxpBQYxpil1tosp3Jd9AmaMWYlUAkYA9wNrLBZVHXGmDLADcAdwLfGmHuttR/mKXkAGWOIjIwkMjKSQ4cOkZyczJgxY6hYsSKO4xAdHU2RIkHb1CoiIvlg4cKFVKxYkQYNGpz3msOHoVs3+PZbmDRJxZlcGhd9gmaMGQSMysmaZ8aYJkBla+30PObLkQs9QctKamoqa9euxXVdDh48SEJCAk2bNqVUqVKXMKWIiASjXbt28c4779CvXz8uv/zyLK85dszbIWDePPj4Y28TdJHcutATtGwNcYaKnBZoGe3cuRPXdVm7di1RUVE4jkP16tUx6u4TESnw0tLSeOutt4iPj6dp06ZZXnPyJNx8M3z+ObzzjrcDiUhe5GmIs7CoXLky3bt3p1OnTqxYsYLPP/+c8PBwHMchJiZGHaAiIgWY67oULVqUhIRzNqwBvCU07rvPK86GD1dxJpdetgo0Y0x14PfASWCctXaPMaYG3t6YUcAm4EVr7aZLljSfFC9enObNm3P11Vfz/fff47ous2fPJjY2FsdxqKAdb0VECpQDBw4wf/58/vCHP2Q5amItPPQQvPce/POf8OCDPoSUQic7c9AaAF8BpdMP/YS37dIsoBRecRYNnADirbWXcgP1C8rLEOeFHDhwgOTkZJYvX06VKlVwHIe6deuqqUBEJMRZaxk7diw1a9akTZs2WV7z1796e/U+9hj85z9a11oC50JDnNmpMJ7G27g8Gq+b8xtgIrATqGWtdfCeou3Ce6JW4JQtW5aOHTsyePBgYmJiWLhwIcOGDWPRokUcOXLE73giIpJLq1ev5vDhw7Rs0QLGjz+zV+9pLzxvee45+OP9VsWZ5KvsFGgtgX9bazdYa/fgFWF1gRestQcBrLW/AC8B116ypEGgaNGiNGnShPvvv59bbrmFvXv3Mnz4cMaPH8/27dtztDWIiIj468iRI8yYMYMbb7yRsEmToFcvGDz4TJH25huWx/5kuIUPGdl5goozyVfZmYN2BZBx2HJL+uv3ma5bD1QPQKaQcNVVV9GjR48zTQWfffYZxYsXx3EcGjduTHh4uN8RRUTkAqZPn05sbCxXXXUV9OwJAwdCUhIAn7YeygMPWLowjXcfXELYTS/4nFYKm+wUaPvxirTTUoGleDsKZFQabx5aoVKiRAlatmxJixYt2LRpE67rMmvWLJo0aYLjOJQrV87viCIiksnGjRvZtm3bb9s5GQNDhwIwM+lbbk86QXOS+WTAXCKGvaCxTcl32SnQ1gJXA58BWGvTACeL62KBzYGLFlqMMdStW5e6deuyb98+kpOTeeONN6hatSqO4xAVFaU11UREgsDx48eZMmUKN95449lLKBnD172H8rukI9RnPZO5gZIv71NxJr7Izhy0/wDLs3FdAt4+nIVe+fLlue666xg0aBANGjRg7ty5DB8+nMWLF3P06FG/4wpUduAAACAASURBVImIFGpz5swhMjKS2rVrn3X82zWWbtemUJmdTKcz5Thw1pw0kfx00Sdo1toZ2bmRtbZX3uMULOHh4cTHxxMXF8eOHTtwXZdhw4YRHR2N4zjevAcREck327dvZ+3atb8Nbabb8oPluuYHKX48hRl9PqDKWz95xVn6nDSGDtWTNMlX2kkgHxhjqFatGtWqVePIkSMsX76cjz76iFKlSuE4Do0aNaJoUf2nEBG5lFJTU5k4cSKdO3emRIkSZ47v2gXXtTpCyhHLgjvepfZbT541J42kJGjbVhtvSr7SXpw+SUtLY+PGjbiuy86dO4mLiyMxMZGyZcv6HU1EpECaP38+P/30E7feeuuZOcGHDsG118K6dZZZf1tAy79cc/aTMmthwgSvy1NP0CTAtFl6kNu7dy+u67Jq1Spq1KiB4zjUrl1bTQUiIgGye/duRo8eTd++fSld2tsY59gx6NoVFi3y9tjs1s3nkFLoaLP0IFehQgW6dOlC+/btWb16NTNnzuTkyZM4jkNcXBzFixf3O6KISMiy1jJp0iTatWt3pjg7dQpuvx3mzfP22FRxJsFGBVoQiYiIoGnTpiQkJLBt2zZc12X+/Pk0bNgQx3GoXLmy3xFFREKO67oAJCZ6Dyqshf79vZ2dkpLgjjv8TCeStVwXaMaYOcDd1trtAcwjeE0FNWrUoEaNGhw+fJhly5bxwQcfUKZMGRzHoWHDhoSFhfkdU0Qk6B08eJB58+Zx7733npk28uST8MYb3uvDD/scUOQ8cj0HzRiTBkRbazcENlLuheoctOxIS0tj/fr1uK7L7t27iY+PJzEx8czjehEROZu1lg8++ICqVavStm1bwHtiNmgQPPAAjBqlef/iL81BKwCKFClCgwYNaNCgAbt378Z1XUaOHElkZCSO41CrVi01FYiIZPDtt99y8OBBevfuDcDYsV5x1qsXjBih4kyCmwq0EHTFFVfQrVs3OnTowKpVq5g6dSrWWhzHoUmTJhQrVszviCIivkpJSWH69On07t2bsLAwpk2DPn28JTXGjgXNEpFgpwIthBUrVgzHcUhMTGTr1q24rsvcuXNp3LgxjuNQqVIlvyOKiPhixowZNGrUiGrVqvHNN3DTTRAT4y1ppsZ4CQUq0AoAYwy1atWiVq1aHDp0iKVLl/Luu+9SoUIFHMchOjpaTQUiUmhs3ryZLVu2MGDAANat85bQqFIFpk4FTduVUKEmgQIqNTWVdevW4bou+/fvJyEhgaZNm3L55Zf7HU1E5JI5ceIEI0eO5Prrr6d48ShatoQTJ2DxYsi0N7qI79QkUAiFhYXRuHFjGjduzC+//ILruowYMYI6dergOA41atRQU4GIFDhz586lRo0alC8fRZs2cPAgzJ+v4kxCjwq0QuDKK6/khhtuoGPHjqxcuZJJkyYRFhaG4zjExsYSERHhd0QRkTzbsWMHq1evpk+fAXTvDps2wfTpEBfndzKRnFOBVogUL16cq6++mmbNmvHDDz/gui5z5swhJiYGx3GoWLGi3xFFRHIlNTWViRMn0rFjZ+69twRffQUffwzt2vmdTCR38lKgdQJ+DFSQ8zHGhAHJwA5r7Q2X+vsVBsYYateuTe3atTl48CDJycmMHj2aSpUq0axZM+rVq0eRIkX8jikikm1ffvklpUuXJimpMZMnw8iRXuemSKjKdYFmrZ0dyCAXMBBYB6j35hIoU6YMHTp0oG3btqxdu5Yvv/ySqVOnkpiYSEJCAiVLlvQ7oojIBe3Zs4evv/6a/fv7Mnq04emnoV8/v1OJ5E1QD3EaY6oB1wP/Av6fz3EKtKJFixIbG0tsbCw///wzruvy8ssvU7duXRzHoVq1amoqEJGgY61l0qRJWNuWIUPK0K8fPPWU36lE8i7Xy2zkB2PMJ8C/gcuBR7Ma4jTGPAA8AFCjRo2mW7duzd+QBdjRo0dZsWIFruueWRQ3JiaG8PBwv6OJiACQnJzM7Nkrefzxe+nVqwgffqhdAiR0XGiZjRwVaMaYBGvtsoAlu/D3ugHoZq0dYIxpx3kKtIy0DtqlYa1l8+bNuK7Ltm3baNKkCY7jUL58eb+jiUghdujQIYYPf5VXXrmH+vUrMXWqdgmQ0BLIddDmGmN6WmvnBiDXxbQCbjTGdAOKA6WNMe9Za+/Mh+8tGRhjiIqKIioqiv3795OcnMybb77JVVddheM4REVFqalARPKVtZb33/+C+fO9be20hZMUNDl9gjYS6APcaa39NNO51sAQa23rgCb07t0OPUELKqdOnWLNmjW4rktKSgqJiYnEx8dTokQJv6OJSCEwe/a3TJw4jylT+rJwYVGqVPE7kUjOBewJmrW2vzHmZ2CcMeYha+0oY0wM8BzeZP51eY8roaBo0aLExcURFxfHjh07cF2X4cOHU79+fRzHoWrVqn5HFJEC6ocfjjJjxjTmzr2FqVNVnEnBlOMuTmvts8aYHcBIY8xteEOR24D7gDEBznf6e84D5l2Ke0veVa1alapVq5KSksLy5cv55JNPKFGiBI7j0LhxY4oWDepmYREJIQcPwrPPzmDfvga89VZ16tb1O5HIpZHjfzmNMeWBekAq0AZYDLSz1p4KcDYJMSVKlKBVq1a0aNGCTZs24bouM2fOJC4ujsTERMqVK+d3RBEJYceOQZ8+3xMZ+T29ew8gMcuBIZGCIUcFmjHm78Dg9K/7H7AJGAW8CDwc8HQSkooUKUK9evWoV68e+/btw3VdXn/9dapXr47jONSpU0drqolIjqSmwl13naRGjck0aHA9XboU8zuSyCWV0yaBE8AbwDPW2l/Sj7UHxgPT8JoHTl6KoNmhJoHgdfLkSVavXo3rupw4cYLExETi4uK47LLL/I4mIkHOWhgwADZvnknbtof461+1h5MUDIFcZqOBtXZzxgPW2jnGmGuBL/CKtA65iykFWXh4OAkJCcTHx7N9+3Zc12XBggU0aNAAx3Goolm+InIe//gHfP75TzzwwEoGDervdxyRfJHTLs7N5zm+LH2ZjekBSSUFljGG6tWrU716dY4cOcKyZcsYN24cpUuXxnEcGjZsqKYCETnj1VfhmWdS+fOfJ9GzZyftDyyFRsD+JbTWbjLGtAzU/aTgK1myJG3atKFVq1Zs2LAB13WZMWMG8fHxJCYmUqZMGb8jioiPPvvMG9q8996viI4uSZMmsX5HEsk3AX1UcXpemkhOFClShOjoaKKjo9mzZw+u6/Lqq69Ss2ZNHMchMjJSTQUihcz8+XD77dCu3V7q1VtM9+5/1PuAFCoXLdCMMZ8DT1trl2fnhsaY4sAAIMVaOyqP+aSQqVixIl27dqVDhw6sWrWK6dOnk5qaiuM4NGnShOLay0WkwFu5Em68EWrXttx66yQaN26jZXqk0MnOE7Qfga+NMSuAscAiYFXGdc+MMVcBzYDuQC9gB97CtSK5EhERQWJiIk2bNuXHH3/EdV3mzZtHo0aNcByHK6+80u+IInIJfP89dOkCpUvDsGHL+eGHk1x99dV+xxLJd9laZsMYUwcYBNwBlAEscAg4DpQDwgEDLAFGAu9aa9MuUebz0jIbBduvv/7KsmXLWLp0KeXKlcNxHBo0aEBYWJjf0UQkAHbtglatYN8+mDHjV+bMGcXdd9+tH8ikwLrQMhs5XQctAmgBXA1cBRQH9gLfAQustVvzHjf3VKAVDqmpqaxfv54lS5awd+9eEhISaNq0KaVLl/Y7mojk0qFDcO21sG4dzJ4N27Z9RMWKFWnfvr3f0UQumUBuln4CmJ/+S8QXYWFhNGzYkIYNG7Jr1y5c12XkyJHUrl0bx3GoWbOmJhOLhJDjx+F3v/Pmnk2cCGXLrmPp0l306tXL72givtGCUxLSKlWqxPXXX0/Hjh1ZuXIlU6ZMwRiD4zjExsZSrJi2gxEJZt4WTjBnDrzzDrRvf4wRI6Zy0003aU1EKdRys1n6PcBtQA28Ic6MrLW2TiCCieREsWLFaNasGY7jsGXLFlzXZc6cOcTExOA4DldccYXfEUUkE2vh4Yfh44/h+efh7rth0qSZ1KtXj5o1a/odT8RXOd0s/W/AM8AaYAVek4BI0DDGEBkZSWRkJIcOHSI5OZkxY8ZQsWJFHMchOjqaIkWK+B1TRIBnn4URI+DRR71fW7ZsYdOmTfTvr+2cRHLaJLAFGG+tHXzJEuWBmgQkK6mpqaxduxbXdTl48OCZpoJSpUr5HU2k0BoxAv7v/6BPH3jrLTh16iSjRo3iuuuuo379+n7HE8kXgdwsvQIwKe+RRPJPWFgYMTExxMTEsHPnTlzX5ZVXXiEqKgrHcahevbqaCkTy0UcfwYMPwg03wOuvgzEwf/58KleurOJMJF1OC7T5QBNgziXIInLJVa5cme7du9OpUydWrFjB559/Tnh4OI7jEBMTQ0REhN8RRQq0WbPgzju99c4+/BCKFoWdO3eyfPlyDW2KZJDTAm0Q8JkxZi/wBbAv8wV+LFArklPFixenefPmXH311Xz//fe4rsvs2bOJjY3FcRwqVKjgd0SRAsd1oWdPiI72ltMoUQLS0tKYOHEiHTt21LQDkQxyWqBtSH99+zznbS7uKeIbYwx16tShTp06HDhwgOTkZN566y2qVKmC4zjUrVtXTQUiAfDdd9C1K1xxBUybBqe31vz6668pXrw4cXFx/gYUCTI5LaaexSvCRAqcsmXL0rFjR9q1a8e3337LwoULmTp1KomJicTHx1OyZEm/I4qEpG3boFMnCAuDmTPhqqu84/v27WPRokXcf//9mgcqkkmOujiDnbo4JdB++uknXNdl3bp11K9fH8dxqFq1qv4xEcmmPXugTRv46SeYPx9OPyiz1vLuu+8SFRVFy5Yt/Q0p4pNAdnGKFCpXXXUVPXr0ONNU8Nlnn1G8eHEcx6Fx48aEh4f7HVEkaP36K3TrBlu2wPTpvxVnACtWrODYsWM0b97ct3wiweyiBZoxJhVoYa1dYoxJ48JDnNZaq6JPCpwSJUrQsmVLWrRowaZNm3Bdl1mzZtGkSRMcx6Hc6Qk1IgL8tr/msmUwfjxcc81v5w4fPsysWbO46667NMdT5DyyU0w9C2zP8HHBGRMVySFjDHXr1qVu3brs27eP5ORk3njjDapWrYrjOERFRWn4Uwq9U6fgjjtg9mxvf83u3c8+P3XqVOLj46lcubI/AUVCgOagieTRyZMnWbNmDa7rcuzYsTNNBZdddpnf0UTynbVw//3e7gBDh8KgQWef/+6775g5cyb9+vXTFAEp9DQHTeQSCg8PJz4+nri4OHbs2IHrugwbNozo6Ggcx+Gq0y1rIgWctfDYY15x9tRT5xZnx44dY+rUqfzud79TcSZyETndLL0IUMRaeyrDsc5AY2COtXZ5gPOJhAxjDNWqVaNatWocOXKE5cuX89FHH1GqVCkcx6FRo0YULaqfiaTgGjIE/vc/bxunp58+9/ysWbOIioqiVq1a+R1NJOTk9F+LD4DjwN0Axph+wIj0cyeNMddba2cFMJ9ISCpZsiStW7emZcuWbNy4Edd1mTlzJnFxcSQmJlK2bFm/I4oE1KhR8MQT3tyzpCRvf82Mtm7dyoYNGxgwYIA/AUVCTI7moBljtgJ/ttaOS/98MzAbeAR4Dahsrb32UgTNDs1Bk2C2d+9eXNdl1apV1KhRA8dxqF27tpoKJOSNGwe33w7XXw+ffQaZRy9PnTrFqFGj6NChAw0aNPAnpEgQCuQctErAjvSbRgGRwMvW2l+NMW8D7+cpqUgBVqFCBbp06UL79u1ZvXo1M2fO5OTJkziOQ1xcHMWLF/c7okiOTZ4Md93lLUb70UfnFmcACxYsoFKlSirORHIgpwXaIeD0LtLtgD3W2lXpn6cCAfsXxhhTHRgDVAbSgNestUmBur+IXyIiImjatCkJCQls27YN13WZP38+DRs2xHEcLT0gIWPePLj5Zm8B2kmTIKvG5V9++YWlS5fSr1+/fM8nEspyWqAtBv5ijDkFDAK+yHAuit/WSwuEU8Aj1tplxpjLgaXGmJnW2rUB/B4ivjHGUKNGDWrUqMHhw4dZtmwZH3zwAWXKlMFxHBo2bEhYWJjfMUWytGSJt75Z7dre5uelS597TVpaGhMnTqR9+/Zcfvnl+R9SJITltED7EzAFmAh8Dzyd4Vxv4KvAxAJr7c/Az+kf/2qMWQdUBVSgSYFTqlQprrnmGlq3bs369etxXZcZM2YQHx9PYmIipbP610/EJ2vWQJcucMUV3ubnFSpkfd0333xDREQECQkJ+RtQpADIaZNAQvoTrQrW2r2ZzsUAO621uwMe0phawAKgsbX2UKZzDwAPANSoUaPp1q1bA/3tRXyxe/duXNdl9erVREZG4jgOtWrVUlOB+GrzZmjdGooUgYULvSdoWdm/fz+vv/46f/jDH6hwvgpOpJC7UJNATgu0g0BPa+3cQIXLxvcsBcwH/mWt/exC16qLUwqi48ePs2rVKlzXxVqL4zg0adKEYsWK+R1NCplt27xmgMOHYcECaNgw6+ustYwdO5ZatWrRunXr/A0pEkIC2cX5PvCFMeZOa+2nmb5Ja2CItTZg/zcaY8KBT4GxFyvORAqqYsWK4TgOiYmJbN26Fdd1mTt3Lo0bN8ZxHCpVquR3RCkEdu6EDh1g/36YM+f8xRnAqlWrOHLkCC1atMi/gCIFTI4KNGttf2PMz8A4Y8xD1tpR6UObzwHXA+sCFcx44zhvAuustS8G6r4iocoYQ61atahVqxaHDh1i6dKlvPvuu1SoUAHHcYiOjlZTgeSNtTBhAvTsedZKs3v3WDpdfYgde0ozY4ahadPz3+LIkSPMnDmT22+/XX8fRfIgV5ulG2P+AIzEawpoBWwDngHGWGvTAhLMeyK3EFiNt8wGwBPW2i/O9zUa4pTCJjU1lXXr1uG6Lvv37ychIYGmTZuqY05yZ/x46NULBg70djo3hkMHLR3qbWP1rkpMeTqZDn+/8CDJp59+yuWXX851112XT6FFQldAN0s3xpQH6uGte9YGb+mNdhn35wwEa+0iQLOhRS4gLCyMxo0b07hxY3755Rdc12XEiBHUqVMHx3GoUaOGmgok+3r29IqzJG/JySP/HMr1Db9nxa4ajO/+Nh2e+uMFv3zDhg3s2LGD/v3750dakQItp00CfwcG4xV2LwGbgFF4i8g+fEkS5oCeoInAsWPHWLlyJa7rEhYWhuM4xMbGEhER4Xc0CQXWwuDBHEsaxY1MZDYd+KDru9wy5Z5zN9jM4Pjx44wYMYIePXpQ+3ytnSJylkB2cZ4A3gCesdb+kn6sPTAemAbcaa09mffIuaMCTeQ31lp++OEHXNdly5YtxMbG4jgOFStW9DuaBLkTxy29ik9hCjfwNn3ok/b2BYszgC+++IKTJ0/So0ePfEopEvoCOcTZwFq7OeMBa+0cY8y1eLsKTAM65C6miASSMYbatWtTu3ZtDh48SHJyMqNHj6ZSpUo0a9aMevXqUaRIEb9jSpA5ecJya6NVTOEGRtGXPrwDg8uemZOWlW3btrFu3ToGDBiQz2lFCq6cdnFuPs/xZemT+qcHJJWIBFSZMmXo0KEDbdu2Ze3atXz55ZdMnTqVxMREEhISKFmypN8RJQiknrLcHbOc8ZsTeOmaz+g7bxQMvuzMnLSsirRTp04xceJEunTpwmVZbcYpIrmS4yaB87HWbjLGtAzU/UQk8IoWLUpsbCyxsbH8/PPPuK7Lyy+/TN26dXEch2rVqqmpoJBKS4M/XPcj4zYkMKTVJAbO+51XjA0d6l2QlARt28LvfnfW1y1atIgKFSrQ8EILo4lIjuVqmY1gpTloIjl39OhRVqxYgeu6ZxbFjYmJITw83O9okk/S0qB/f3jtNXi69zr+/kH02U/KzrM+2q5du3jnnXfo27ev9osVyYWANQkEOxVoIrlnrWXz5s24rsu2bdto0qQJjuNQvnx5v6PJJWQtPPggjBgBf/kLPPfcRfsBAEhLS+Ott94iLi6OxMQs/30RkYsI6DpoIlIwGWOIiooiKiqK/fv3k5yczJtvvslVV12F4zhERUWpqaCAsRYGDfKKs0cfzX5xBpxZxqXphbYVEJFc0xM0ETmvU6dOsWbNGlzXJSUlhcTEROLj4ylRooTf0SSPrIVHHvGmmA0aBC++mP3i7MCBA7z22mvcd999WrZFJA8C/gTNGFMEmAX0tdZuzEs4EQleRYsWJS4ujri4OHbs2IHrugwfPpz69evjOA5Vq1b1O6LkgrXw5z97xdlDD+WsOLPWMmXKFJo3b67iTOQSyu0QpwHaAdrwT6SQqFq1KlWrViUlJYXly5fzySefUKJECRzHoXHjxhQtqhkTocBaePJJeP55rzEgKSn7xRnAmjVrOHToEK1atbp0IUVEc9BEJGdKlChBq1ataNGiBZs2bcJ1XWbOnHlmsni5cuX8jijncbo4e+45eOABePnlnBVnKSkpTJ8+ndtuu42wsLBLF1REVKCJSO4UKVKEevXqUa9ePfbt24frurz++utUr14dx3GoU6eO1lQLItbCX/8K//439O3rNQbktOdj+vTpxMTEaGhbJB9ku0AzxjyV4dPT/1s/YIz5KeN11tpnAxFMREJH+fLl6dy5M+3bt2f16tXMnj37zE4FcXFxWmHeZ9bCE0/AkCG5L842bdrEjz/+SP/+/S9NSBE5S06eoN2bxbHuwIkMn1tABZpIIRUeHk5CQgLx8fFs374d13VZsGABDRo0wHEcqlSp4nfEQidjcdavH7zySs6LsxMnTjB58mS6d+9ORETEpQkqImfJdoFmrY08/bExpiheYdbdWrvsUgQTkdBljKF69epUr16dI0eOsGzZMsaNG0fp0qVxHIeGDRuqqSAfWAuPPw7/+Y/XEPDyyzkvzgDmzJlDrVq1qFOnTuBDikiWcvsOWXAWTxORS6pkyZK0adOGVq1asWHDBlzXZcaMGcTHx5OYmEiZMmX8jlggZVznLC/F2fbt21mzZg0DBgwIfEgROS/9CCsi+aJIkSJER0cTHR3Nnj17cF2XV199lZo1a+I4DpGRkWoqCJC0NHj4YW84c+BAr0jLzR9tamoqkyZNonPnzlqcWCSfqUATkXxXsWJFunbtSocOHVi1ahXTp08nNTUVx3Fo0qQJxYsX9ztiyEpL8+aavf46PPaYN7yZ27p30aJFlClThsaNGwc2pIhcVK4KNGttqjHmWmB9gPOISCESERFBYmIiTZs25ccff8R1XebNm0ejRo1wHIcrr7zS74ghJTUV7r8fRo/2ltT4xz9yX5zt3r2bb775hr59++rJpogPcv0EzVo7P5BBRKTwMsZQs2ZNatasya+//sqyZcsYO3Ys5cqVw3EcGjRooIVRL+LUKbjnHnj/fXjmGXjqqYt/zflYa5k0aRLt2rXTHEERn2iIU0SCyuWXX07btm1p3bo169evZ8mSJUyfPp2EhASaNm1K6dKl/Y4YdI4fh1tvhQkTvIVo//KXvN0vOTkZay2O4wQmoIjkmAo0EQlKYWFhNGzYkIYNG7Jr1y5c12XkyJHUrl0bx3GoWbOmht6AlBTo1QumT/f21Xz44bzd7+DBg8ydO5d7771Xf74iPjLWZn/FDGNMQjCve5aYmGiTk5P9jiEil8jx48dZuXIlrutijMFxHGJjYylWrJjf0Xxx6BB07w4LF8Ibb8B99+XtftZaxo0bR5UqVWjXrl1AMorI+RljllprE7M6l9MnaHONMT2ttXMDkEtEJEeKFStGs2bNcByHLVu24Louc+bMISYmBsdxuOKKK/yOmG/27YOuXWHpUm/e2a235v2e3377Lfv37+fmm2/O+81EJE9yWqC9D3xhjLnTWvtpxhPGmNbAEGtt64ClExHJgjGGyMhIIiMjOXToEMnJyYwZM4aKFSviOA7R0dEUyc2qrCFi507o3Bm++w4+/RR69Mj7PVNSUpg+fTq33HKLdnkQCQI5GuKEM5um/w14yFo7yhgTAzwHXA+ss9Y2CnzM7NEQp0jhlZqaytq1a3Fdl4MHD55pKihVqpTf0QJqyxbo1Al++gnGj4frrgvMfSdMmECxYsXo2rVrYG4oIhcVyCFOrLXPGmN2ACONMbcBrYBtwH3AmDwlFRHJpbCwMGJiYoiJiWHnzp24rssrr7xCVFQUjuNQvXr1kJ/0vnatV5ylpMCsWdCiRWDuu3nzZrZs2UL//v0Dc0MRybMcF2jGmPJAPSAVaAMsBtpZa08FOJuISK5UrlyZ7t2706lTJ1asWMHnn39OeHg4juMQExNDRESE3xHPz1pvvYyePc9aZdZdYunS4SQRpcJZsMAQExOYb3fixAkmT57M9ddfX2ibLUSCUY4maRhj/g58D/wf8D+8p2aJwIuBjyYikjfFixenefPmPPjgg3Tq1ImNGzfy0ksvMW3aNPbu3et3vKxNmOCtmzF4sFesAXPnWNq3Pk6Zw9tZ9NTMgBVnAHPnzqV69erUrVs3cDcVkTzL6TIbJ4A3gGestb+kH2sPjAemAXdaa09eiqDZoTloInIxBw4cIDk5meX/v707j66qPPc4/n1kkBkLCiiDWCapAwETFJGpDCKiUnHC6SJ2YWmxgFOrVr10sK1VGZwtWi0qhQqioIAoqFAEggwCgha4DIGiFRGZZMpz/3hPTJgkCSfsnZzfZ629cs7eJ/s8uI/JL+9+hwULOPnkk8nIyKBRo0ZJGVQwdOhQtmzZkoQqc33ySVPGjr2catW+4oYbRlKlyrZCn6tq1aoMHDjwu+fr169n1KhR9OvXj4oVKyajXBEpgGT2QWvq7ivz7nD3aYl1Od8ihLSOhSvzYGbWFRgGlAJGuPufknVuEUlNJ5xwAp06daJ9+/YsXbqUGTNmMGnSJNLT02nevPlRBZUtW7bwwAMPFOyb3ENv/zlz4KGHYMAAePRRGDSIp4fvYjD3cR6zmZg2nGoPuRzBNAAAG0lJREFUjyr84prA4MGDv3u8b98+JkyYQJcuXRTORGKoQAHtwHCWZ//8xDQbU5JSFWBmpYAngM5AFpBpZm+4+yfJeg8RSV2lS5emWbNmNGvWjA0bNpCZmcnjjz9O48aNycjIoHbt2sdmUMH48dCzZ3iclgbDhuHZzuDZFzKYbnRnAqO5mgqTtx1VODvQrFmzqFSpEmcl836piCRNgafZ+N6TmdXMufWZhHO1Av7X3S9MPL8bwN3/eLjvqVy5sp9zzjn77bvqqqv4+c9/zo4dO+jWrdtB39O7d2969+7Nl19+yRVXXHHQ8X79+nH11Vezbt06brjhhoOO33777VxyySV8+umn3HLLLQcd/81vfkOnTp1YuHDhfrcWcjz44IOcf/75zJo1i3vuueeg40OHDiUtLY133nmH3//+9wcdf+aZZ2jSpAkTJkzgkUceOej4yJEjqVu3LqNHj+app5466Pirr77KiSeeyAsvvMALL7xw0PG33nqLChUq8OSTTzJmzJiDjr/33nsAPPzww0ycOHG/Y+XLl2fSpEkA/O53v+Pdd9/d73j16tUZOzZMp3f33Xfz4Ycf7ne8Tp06vPTSSwAMHDiQhQsX7ne8cePGPPvsswD07duXzz77bL/jaWlpDB06FIDrr7+erKys/Y63atWKP/4xfJx69ux5UJ+kjh07ct999wFw0UUXsXPnzv2Od+/enTvuuAPgkLOu67NX/D57pUuX5uSTT6ZevXqceuqpZGRk8OKLL+b7s7d69Wrq169f8M/enDmwfj0AXrESO7Z3YB5vcBPPs4Gb+Ragdm1o2BAo/Gcvp77rrruOzZs3c8UVV9DnEMsP6LOnn3ugn3vH4rP3/vvvH/YWZ747XZhZezO7zsxaHOZ4beDg/1qFV5swfUeOrMS+A9+3r5nNM7N5e/ZE1v1NREqAvXv3sm7dOtasWUOHDh1YtmwZVatWpUGDBpQrV67o3rhhQ6hdm2yMT7bXYx4Z3M2DPMfN2IUXhnC2fj2sWJGUt9u0aRNt27bVwvMiMXbEFjQzqwS8DZwLGODAVKCPu2/I87pzgVnuXiophZldCVzo7j9NPL8BaOnutx7uezRIQESS7auvvmLevHksWrSI2rVrk5GRQcOGDQ95+3Pw4MFH7oN2mGk0Nv03m0trfMiHtGIoA/klj4UDOX3SbrstrIY+bhz85CeF+rcMHjyY7t27s2DBAvr06VOiV1sQKQ6OdpDAPUBToDeQCbQHBgNzzOzCIuwTlgXUzfO8DrDhMK8VESkS1apVo0uXLnTo0IElS5Ywffr0/QYVlC9fvmAnzJlGY8AAGDIEzFi1IpuLzljLGs7hn1xJT8aF1yb6pAEhpLVrF4LdUZg2bRo33nijwplIzOUnoF0OPODuIxPPl5vZBOB14AMzu8jdM4ugtkygkZmdBqwHrgGuLYL3ERE5ojJlytC8eXPS0tJYv349mZmZDB8+nNNPP52MjAxOOeWU/J2oR48QzhLBK7PXo3S/YDN791bmXTrSOm0HtLkVHnsMFi7MDWnt2hW65Qwg525Jeno6NWvWLPR5ROTYyE9AqwcsyLvD3debWTtgAvCumV0K7DzUNxeWu+81s/6EkaGlgOfdfWky30NEpKDMjDp16lCnTh22b9/OggULGDNmDJUrV87vCULLGfDmsH9z1bCd1OAbJtOVJhc3gjdmhNeYwfDhIaTddddRt5ytTwxCaNOmzVGdR0SOjfz0QVsN3O3uow5x7HhgHNABeBi4N1l90ApDfdBEJArZ2dlkZWUxbty4fE9UO3duBpMmdaVWrY1ce+0rVK68vYirhCpVqjBo0KAifx8RyZ/v64OWn4D2KrDX3a85zPHSwCvAFYAroImIHN6+fXDbIGf4Y8YlvMErXEsltu/XJ01EUsP3BbT89BIdBZxqZtUPdTCxSPrVwDPA2kJXKSJSwm3dCpddFsLZIB7ltVunUyl7a26ftDzrb4pIajtiHzR3HwuMPcJrHOiXrKJERIq1Q0ylkZUF3bs7Sz7O5kn602/A8bktZok+ackYDCAiJYPGWYuIJFvOVBqJFrHMTGjZ0lm1bBcT/WL63VVl/9uZOSFt3LijHgwgIiWDApqISLLlmUpjVLeRtG3rlN22mX/tzqDrgNPhT386uK+ZWWg5Ux80EUEBTUQk+czIfmQI92ZM4drJN5Lx7QwytzbhrAEdNRBARPJFAU1EJMm2boXLexoPZnbhp/yVd+jESXypcCYi+aaAJiKSRKtWQevWMHGiM7zdWJ6lL2XZEw5qlKaI5FOBA5qZHWdm08ysUd7HRVGciEhxMmUKpKdDVpYz6ZKnuPX9K7ABAyA7W1NpiEiBFKYFzQgLplc+4LGISEpyhz//Gbp1gzp1IPMPU+k8/hf7Tz47ZEhuSBs/PuqSRSTm8rMWp4iIHMa2bdCnD/zzn3D11fDcc1CxQmeoNW6/edC+C2nt2mkqDRE5IgU0EZFC+uwz6NkTPvkE/vIXuP32nDxmh55s1g6zX0TkAApoIiKFMHYs3HQTlC0LkydD585RVyQiJYlGcYqIFMCePXDbbXDFFfCjH8H8+QpnIpJ8CmgiIgdyh9deO2i05fosp8PZmxgyBPr3hw8+gHr1IqpRREo0BTQRkQMdsJYmwNS3nRaNt7Fw+fGMum0ujz0Wbm+KiBQF9UETETlQnrU092Yfx/0VH+FPf3Kaspb3bniDpg//OuoKRaSEU0ATETlQYkqMtd+cQK/HOjML46eMYNjPP6PC4w9puSYRKXIFDmjuvs/MOgCf5n2c/NJERKLzxgSj9/gH2MM2XqEXvfgHPJ6tcCYix0Sh+qC5+/vuvv3AxyIixd3OnWEAwGWXwWllslhA8xDOQMs0icgxo0ECIiIJCxfCOefAE0/AoObvMeuLhjQc0F1raYrIMaeAJiIpLzsbHn4YWraEr7+Gt++fyaMLOnD8gH5aS1NEIqFBAiKS0rKyoHdvePfdsArTX/8K1au1hjStpSki0VELmoikJHf4+9/hzDNh9mwYMSIs31S9OrlrZh44IOBw+0VEkqxALWhmdh7QFTgPOAUoD3xJGMX5PjDe3Tcnu0gRkWT6/HO45RZ4/XVo0wb+9jdo0CDqqkREcuWrBc3M/sfMFgOzgIFABeDfwBxgM3AuMAJYb2YvmNlpRVSviMhR+ec/4YwzwgLnjzwC06crnIlI/ByxBc3MFgE1gL8DNwIL3Q8ewmRmVYHuwHXAUjO7yd1HJ7leEZFC+fxzuPXWENAyMuDFF6Fp06irEhE5tPzc4vwb8LS7f/t9L3L3LcDLwMtm1gyolYT6RESOijuMHAkDB8L27fCHP8Bdd0FpDZESkRg74o8odx9a0JO6+yJgUaEqEhFJkjVrQl+zKVPg/PPhuefg9NOjrkpE5MgKNIrTzFoUVSEiIsmyd2+YruyMM2DmTHjsMZgxQ+FMRIqPgk6zMT2x9maRMrO/mNlyM/vYzF4zsxOK+j1FpGTIzIRzzw23NC+4AJYsCUs3HadJhUSkGCnoj6xXgLfMrOeBB8zsAjObmZyymAqc6e5nA58BdyfpvCJSQm3ZEoLYuefCf/4Do0fDpElQv37UlYmIFFyBApq79wP+CPzDzH4GYGZnmdkE4APgB8koyt3fdve9iaezgTrJOK+IlDzu8Mor4fblk0+GkLZsGVx1leaTFZHiq8DjmNz9t2a2HnjKzHoBrYF1QB/CVBzJ1gfQdB0icpBFi8LUGTNmhEXOJ0yA9PSoqxIROXoFDmhmVg1oDOwD2hAmr22fp8Urv+d5h0NPxXGvu7+eeM29wF7C9B2HO09foC9AvXr1ClKCiBRTmzbBfffBM89AtWrw7LPQpw+UKhV1ZSIiyVHQpZ4eAAYlvu8RYAXwNPAo8MuCnMvdOx3hvf6HMPFtx0NNjJvnPM8CzwKkp6cf9nUiUvzt2RPC2P33w9dfwy9+AYMHww+S0rlCRCQ+CtqCdi9hSafB7v45gJmtBV4zs5rA9e6+52iLMrOuwK+Adu6+42jPJyLFmztMnAh33gmffgrt28Pw4XDWWVFXJiJSNAo6irOpu/88J5wBuPs0oAPQDpicpLoeByoDU81soZk9naTzikgxs2ABdOwIl14agtr48TBtmsKZiJRsBWpBc/eVh9k/38wuAKYkoyh3b5iM84hI8bV6NTzwQFimqVq1MNnsLbdAmTJRVyYiUvSSthqdu68ws/OTdT4RSU2ffx7Wy3z66dDp/4474J574ARNVy0iKeSItzjN7HUza56fk7n752ZWzsxuy5knTUQkP7ZsCSMzGzQI85nddBOsWAEPPaRwJiKpJz8taGuA2Wa2kLCSwAzg47zTapjZKUBL4BLgcmA9Yf4yEZHvtWVL6PD/6KNhZOY118BvfwuNGkVdmYhIdPIT0HYTBgH0Ah4AqgJuZt8AuwirB5QBDJgLDARGunt2kVQsIiXCli1hQfMhQ0Iw69Ej9DlLS4u6MhGR6OUnoA0Exrj7rWa2lTBSsxVwMlAO2AQsBz5w9zVFVqmIlAibNoUO/8OG5Qaz+++H5vnqSCEikhryE9C+IneNzV8B4939z0VXkoiURFlZ8MgjYaLZHTsUzEREvk9+AtpM4GEzO4lwG1Oz9YtIvi1fHjr6v/QSZGfDddfBXXfBGWdEXZmISHzlJ6D1B15MbA68Y2YfAwvybEuTsYKAiJQM7vDuu6F/2VtvQfny8LOfwe23w6mnRl2diEj8HTGgufsGoLOZ1QI2AKOBE4CuwC8SL9tjZp8AC9z95qIqVkTibdcueOWVEMwWL4YaNcJamf36wUknRV2diEjxke+Jat19o5m9Bgxx92UAZlYJSAOaJ7YWRVKliMTa2rXwzDMwYgR88UVYhun556FXLyhXLurqRESKn4Iu9dTzgOfbCH3UZiazKBGJv+xsmDo1TCo7cWLYd8kl0L9/WDvTLNr6RESKs6Qt9SQiqWHDBnjxRXjuOVi5Mty6/PWvwzqZ9epFXZ2ISMmggCYiR7R3b+jsP2JE+LpvH7RrF2b879kTjj8+6gpFREoWBTQROSR3WLgQRo6EUaNg40aoVQvuvBP69NFSTCIiRUkBTUT2k5UFL78cgtnSpVCmDFx8MfTuDd26heciIlK0FNBEhI0b4dVXYfRomJkY8tOqVRgAcNVVUL16tPWJiKQaBTSRFLVxI7z+eghl778fRmWecUboV9arFzRsGHWFIiKpSwFNJIWsWAHjx8Nrr8GHH4Z+Zk2awG9+E1rKtPySiEg8KKCJlGB798Ls2fDmm2GusiVLwv7mzcMM/z16wJlnas4yEZG4UUATKWG++CJMIPvmmzB5MmzeDKVLQ5s2YQmmHj2gfv2oqxQRke+jgCZSzH37bejYP3UqvP12mBoDwjqYl10WRmB27gxVq0Zbp4iI5J8Cmkgxs3s3ZGbC9OlhmzUrhLQyZaB1a3jwwRDIWrSA446LuloRESkMBTSRmNu+HebODa1kM2bAv/4FO3aEY82ahSWWOncOM/tXqhRtrSIikhwKaCIx4h4mip0zJ4yynDkT5s8Pnf3NQof+m2+GDh2gbVvNTyYiUlIpoIlE6JtvQgCbOzeEstmzw2LkENa3bNkyLK10wQVh4tgf/CDaekVE5NhQQBM5RjZvhkWLQiD76COYNw8++yz3eIMG0L49nHde2Jo1g7JlIytXREQipIAmkmTZ2bBqFSxeDB9/HEZVLlgAa9bkvqZOHUhPhxtvhHPOCdtJJ0VXs4iIxIsCmkgh5fQXW7oUPvkkTAK7eHF4nNOJ3yzM1N+qFfTrB2lpYatZM9raRUQk3hTQRI5g925YuRI+/RSWLw/bsmUhiG3blvu6GjXgrLOgb9/w9ayzwtJJFSpEV7uIiBRPCmgihNuS69fDv/8d+oXl3Vatgn37cl97yilw+ulw003wox+FENa0KZx4YnT1i4hIyaKAJilj3z5Yuza0hq1cGcLYihVhW7kyTPaao3x5aNQodNS/8soQyE4/PdyurFIlun+DiIikhlgHNDO7A/gLcJK7fxl1PRJ/O3aEFq+VK3O/5myrV8OePbmvPf74MHKyUSPo2jV8bdgwhLBTTtEs/CIiEp3YBjQzqwt0BtZGXYvEhzts3JgbwPKGsVWrwrG8qlYNISwtDXr2DI8bNAhBrHZthTAREYmn2AY0YAhwF/B61IXIsbV7d2jtytv6lbP93//Bzp25rzWDunXhhz8Mi4KfdlpuCGvQIEzsahbZP0VERKRQYhnQzOxSYL27LzL9di2Rdu06uB9YzrZ2bei0n6NChRDAcm5F/vCHuVv9+uFWpYiISEkSWUAzs3eAWoc4dC9wD9Aln+fpC/QFqFevXtLqk6O3bx+sWxemp8jZckZJrl0bblfmqFYt3HY8/3y44YbwOKcVrGZNtYKJiEhqMc/7WzIGzOws4F0gMdUndYANQEt333jYbwTS09N93rx5RVyhHGjnzhC6li3L3ZYvD/t27cp9XZUq0Lhx2Bo1yt0aNgwBTUREJJWY2Ufunn6oY7G7xenui4EaOc/NbDWQrlGc0du9OwSvpUvDtmRJ+LpqVe4tyeOOC/3AmjaFCy8MYaxJk7DVqKGWMBERkfyIXUCTeNi4Mawh+fHHuduyZbB3bzheqlQIX2lpcN11IZA1bRr2lSsXbe0iIiLFXewDmrvXj7qGksw9LOI9b15Y0DtnyztdRd26cPbZ0L17WL7ozDNDEFPnfBERkaIR+4AmyfWf/8DcuSGQZWaGr5s2hWOlSoWli7p0gRYtQuvY2WeHqSpERETk2FFAK8F27YL582H27NxtbWLa31KlwhqSPXpAejqcc05oHdPtSRERkegpoJUgmzfDrFkwc2bYMjNzR1HWqwfnnQcDB8K554bWsQoVoq1XREREDk0BrRj78kv44AN4772wLV4c9pcuHVrE+vcP84qdd15YW1JERESKBwW0YmTrVnj/fXjnHZg2LTeQlS8PrVvDlVdCmzbQsqVax0RERIozBbQY27cP5syBqVPDNmdOmOaiXDm44AK45hpo3z70IStbNupqRUREJFkU0GJm40aYPDlsb78d+pWZhRB2553QqVO4banO/CIiIiWXAlrE3MO8YxMmhO2jj8L+WrXgssvgootCKNNSSCIiIqlDAS0Cu3eHPmSvvw4TJ0JWVmgla9UKHnwwhLJmzbQskoiISKpSQDtGtm+HKVNg3LgQyrZsgYoVw3qVv/sddOsW1qoUERERUUArQjt2hDA2Zgy89Rbs3AnVq0PPnnD55dCxo/qSiYiIyMEU0ArKHcaPD1Pw570Hmdj/bdceTJ5ijB4d+pRt3w41a8JNN4Vg1rZtmKdMRERE5HAUFQpq/PjQ/DVgAAwZAmZk73M+uPoJXhpbjlcr7GHLjrKceCJcfz1cfXUIZaVKRV24iIiIFBcKaAXVo0cIZ8OGsXRTLUae8iteefJr1m3rT6Uy39LzyjJcey38+MdqKRMREZHCUYQoKDMYMoTte8qS8eQv2c0+uvIvHuq6iUtfvZEKFTX0UkRERI6OAlphmFHx8T8z7smLaMF8avBfeCtb82KIiIhIUhwXdQHFkjsMGkRXpoRwBjBoUNgvIiIicpQU0AoqEc4YNiz0RcvO/q5PmkKaiIiIJINucRbU+PG54SwxipMhQ8KxYcOgXTv4yU+irVFERESKNQW0gurRIywHkHcetJyQ1q5d2C8iIiJyFBTQCsrs0C1kh9svIiIiUkDqgyYiIiISMwpoIiIiIjGjgCYiIiISMwpoIiIiIjGjgCYiIiISMwpoIiIiIjGjgCYiIiISMwpoIiIiIjGjgCYiIiISMwpoIiIiIjGjgCYiIiISMwpoIiIiIjFj7h51DUljZv8F1hzjtz0R+PIYv6ccnq5HvOh6xIuuR7zoesRLFNfjVHc/6VAHSlRAi4KZzXP39KjrkEDXI150PeJF1yNedD3iJW7XQ7c4RURERGJGAU1EREQkZhTQjt6zURcg+9H1iBddj3jR9YgXXY94idX1UB80ERERkZhRC5qIiIhIzCigFZKZdTWzT81shZn9Oup6Up2ZPW9mX5jZkqhrSXVmVtfMppvZMjNbamYDoq4p1ZlZOTOba2aLEtdkcNQ1pTozK2VmC8xsYtS1CJjZajNbbGYLzWxe1PWAbnEWipmVAj4DOgNZQCbQy90/ibSwFGZmbYFtwN/d/cyo60llZnYycLK7zzezysBHQA/9/xEdMzOgortvM7MywExggLvPjri0lGVmtwHpQBV37x51PanOzFYD6e4em3np1IJWOC2BFe6+yt13A/8ALou4ppTm7h8AX0Vdh4C7/8fd5ycebwWWAbWjrSq1ebAt8bRMYtNf5xExszrAxcCIqGuR+FJAK5zawLo8z7PQLyCRg5hZfaA5MCfaSiRxS20h8AUw1d11TaIzFLgLyI66EPmOA2+b2Udm1jfqYkABrbDsEPv016hIHmZWCRgLDHT3b6KuJ9W5+z53TwPqAC3NTF0BImBm3YEv3P2jqGuR/bR29xbARcAvEt1mIqWAVjhZQN08z+sAGyKqRSR2Ev2cxgIvu/u4qOuRXO7+NfAe0DXiUlJVa+DSRJ+nfwA/NrOXoi1J3H1D4usXwGuErkyRUkArnEygkZmdZmZlgWuANyKuSSQWEh3SnwOWufujUdcjYGYnmdkJicflgU7A8mirSk3ufre713H3+oTfHdPc/fqIy0ppZlYxMaAJM6sIdAEinxFAAa0Q3H0v0B+YQugAPcbdl0ZbVWozs1HAh0ATM8sys5ujrimFtQZuILQMLExs3aIuKsWdDEw3s48Jf2BOdXdN7yAS1ARmmtkiYC7wprtPjrgmTbMhIiIiEjdqQRMRERGJGQU0ERERkZhRQBMRERGJGQU0ERERkZhRQBMRERGJGQU0ERERkZhRQBMRERGJGQU0ERERkZhRQBMROYCZNTSzPWY2+ID9T5nZVjNLj6o2EUkNCmgiIgdw9xXACGCQmZ0IYGb3A32An7j7vCjrE5GST0s9iYgcgpnVAlYCTxIWFn8W6OXuYyItTERSQumoCxARiSN332hmQ4HbCT8rf6lwJiLHim5xiogc3r+B44EP3f2JqIsRkdShgCYicghm9mPgGeBDoLWZNYu4JBFJIQpoIiIHMLMWwHjCQIH2wFrgwShrEpHUooAmIpKHmTUEJgFvA7e6+25gMNDNzNpGWpyIpAyN4hQRSUiM3JxFaDG70N13JfaXApYAm939/AhLFJEUoYAmIiIiEjO6xSkiIiISMwpoIiIiIjGjgCYiIiISMwpoIiIiIjGjgCYiIiISMwpoIiIiIjGjgCYiIiISMwpoIiIiIjGjgCYiIiISM/8PftWsE+GrcKQAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from mpl_toolkits.axes_grid1.inset_locator import zoomed_inset_axes\n", "from mpl_toolkits.axes_grid1.inset_locator import mark_inset\n", "\n", "def plot_bisection(f, x1, x2, ax, tol=1.0e-2, inset=True, ixmin=0.4, ixmax=0.7, iymin=-0.25, iymax=0.2, zoom=5, loc0=4, loc1=2, loc2=1, flabel=''):\n", " # start by plotting the function over the given bounds (x1, x2)\n", " x = np.linspace(x1, x2, 100)\n", " y = f(x)\n", " ax.plot(x, y, 'b')\n", " # initialise the first interval\n", " f1 = f(x1)\n", " f2 = f(x2)\n", " x1s = x1\n", " x2s = x2\n", " # plot initial interval\n", " ax.scatter( [x1, x2], [f1, f2], marker='x', color='r', s=50)\n", " # plot midpoint, and update the appropriate interval limit\n", " while abs(x1-x2) > tol:\n", " x3 = 0.5*(x1 + x2)\n", " f3 = f(x3)\n", " ax.scatter( [x3], [f3], marker='x', color='r', s=50)\n", " if f2*f3 < 0.0:\n", " x1 = x3\n", " f1 = f3\n", " else:\n", " x2 = x3\n", " f2 = f3\n", "\n", " # add a zero line to the plot to help identify the root\n", " xlim = ax.get_xlim()\n", " ax.plot([xlim[0], xlim[1]], [0., 0.], color='k', ls='--')\n", " ax.set_xlim(xlim)\n", " \n", " # add a zoomed inset if 'inset=True'\n", " if inset:\n", " x1, x2 = x1s, x2s\n", " ax_ins = zoomed_inset_axes(ax, zoom, loc=loc0)\n", " # same code/algorithm as above\n", " x = np.linspace(x1, x2, 100)\n", " y = f(x)\n", " ax_ins.plot(x, y, color='b')\n", " f1 = f(x1)\n", " f2 = f(x2)\n", " ax_ins.scatter( [x1,x2], [f1,f2], marker='x', color='r', s=50)\n", " while abs(x1-x2) > tol:\n", " x3 = 0.5*(x1 + x2)\n", " f3 = f(x3)\n", " ax_ins.scatter( [x3], [f3], marker='x', color='r', s=50)\n", " if f2*f3 < 0.0:\n", " x1 = x3\n", " f1 = f3\n", " else:\n", " x2 = x3\n", " f2 = f3\n", " ax_ins.plot([ixmin,ixmax],[0.,0.], color='k',ls='--')\n", " ax_ins.set_xlim(ixmin, ixmax)\n", " ax_ins.set_ylim(iymin, iymax)\n", " ax_ins.get_xaxis().set_visible(False)\n", " ax_ins.get_yaxis().set_visible(False)\n", " # draw a box of area covered in main image and lines from corners to indicate zoom\n", " mark_inset(ax, ax_ins, loc1=loc1, loc2=loc2, fc='none', ec='0.5')\n", " \n", " xf = (x1 + x2)/2.0\n", " ax.set_xlabel('$x$', fontsize=16)\n", " if not flabel:\n", " fl = '$f(x)$'\n", " else:\n", " fl = flabel\n", " ax.set_ylabel(fl, fontsize=16)\n", " ax.set_title('Bisection', fontsize=20)\n", " \n", "\n", "# Let's see what it looks like for our example.\n", "\n", "def f(x):\n", " return 2*x + x*np.sin(x-3) - 5\n", "\n", "\n", "fig, ax1 = plt.subplots(figsize=(10,6))\n", "plot_bisection(f, 0., 5., ax1, tol=1.0e-2, inset=True, \n", " ixmin=2.6, ixmax=3., iymin=-0.25, iymax=0.2, zoom=10, loc0=2, loc1=3, loc2=4, flabel=r'$f(x) = 2x + x\\sin(x-3) - 5$')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This algorithm has been implemented in the `scipy.optimize` module:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.5671432904109679\n" ] } ], "source": [ "def f(x):\n", " return x - np.exp(-x)\n", "\n", "a, b = -1., 1.\n", "print(sop.bisect(f, a, b))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 4.4: \n", "\n", "For $2x + x \\mathrm{sin}(x-3) = 5$, use the subinterval $x \\in(a,b)$ you found in Exercise 4.2 and complete the code below to implement a bisection algorithm. Derive the concept from a pseudo-code description and compare the result to `scipy.optimize.bisect`" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": false }, "outputs": [], "source": [ "def bisection(fct, a, b, atol=1.0E-6, nmax=100):\n", " n = 0\n", " while n <= nmax:\n", " \n", " # complete\n", " \n", " raise RuntimeError('no root found within [a,b]')\n", "\n", "def f(x):\n", " return # complete\n", "\n", "a, b = # complete\n", "\n", "print(bisection(f, a, b))\n", "print(sop.bisect(f, a, b))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Newton Method\n", "\n", "So far, above iterative algorithms use only one part of a functions information: its value, $f(x)$. Newton's method additionally uses $f'(x)$ to infer the trend of the function in the vicinity of $x$. This slope, together with the function value $f(x)$, is used to find the intersection of the tangent at $x$ with zero to get an improved guess of the root. The formula can be derived from the Taylor series expansion:\n", "\n", "\\begin{equation}\n", "f(x_{i+1}) = f(x_i) + f'(x_i)(x_{i+1}-x_i) + O(x_{i+1} - x_i)^2\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Let $f(x_{i+1}) = 0$ to find\n", "\n", "\\begin{equation}\n", "0 = f(x_i) + f'(x_i)(x_{i+1}-x_i) + O(x_{i+1} - x_i)^2\n", "\\end{equation}\n", "\n", "assuming $x_{i+1}$ close to $x_{i}$ we drop the higher order terms to find\n", "\n", "\\begin{equation}\n", "x_{i+1} = x_i - \\frac{f(x_i)}{f'(x_i)}\n", "\\end{equation}\n", "\n", "which is the **Newton-Raphson formula**." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "A pseudo pseudo-code for the algorithm looks like this:\n", "\n", "```\n", "guess x[0]\n", "do\n", " x[i] = x[i-1] - f(x[i-1])/dfdx(x[i-1])\n", "while abs(x[i] - x[i-1]) > tolerance\n", "```\n", "\n", "The expression of the associated error indicates quadratic convergence:\n", "\n", "\\begin{equation}\n", "\\epsilon_{i+1} = -\\frac{f''(x)}{2f'(x)} \\epsilon_{i}^2\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Illustrated, for $f(x) = x - \\mathrm{e}^{-x}$, this approximation looks like the following.\n", "\n", "Note that the green dashed lines extend off from the current iteration in the direction given by the slope of the blue line:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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WrVrRrFkznJySdbqQdIYPh7NnIX9+I4nLn994Pny4wy6Z0gc71AbOaK3PASil5gPtgWPRyrQHvrT97gf8VymltNZxvuiTJ0/SpEmTp7Z169aNIUOGEBoaSps2bZ45pl+/fvTr1487d+7QpUuXZ/YPHjyYN998k8uXL9O7d+9n9n/44Ye0bduWkydPMmjQoGf2f/HFFzRv3pwDBw4wdOjQZ/Z//fXX1K9fnx07djBixIhn9k+aNIlq1aqxfv16xo8f/8z+KVOmULZsWZYvX87333//zP6//vqLIkWK4OPjw2+//fbMfj8/P3Lnzs2sWbOYNWvWM/tXrVpF5syZ+fXXX/H19X1m/+bNmwH47rvvWLFixVP7MmXKxOrVqwEYN24cGzZseGp/rly5WLhwIQCfffYZO3fufGp/4cKFmTNnDgBDhw7lwIEDT+0vU6YMU6dOBWDgwIGcOnXqqf3VqlVj0qRJAPTq1YsrV648tb9evXpMmDABgM6dO3P37t2n9jdr1oyRI0cC0Lp1ax4/fvzU/jfeeIOPPvoI4JnPHchnTz578tmTz17y+ewppShdujQFChTg3XffJXfu3In+7M2cOZNNmzY9tT+pPnvr96zHa6AX+V3zkzF9xn/3v/Rnr1AhQq9cwSVLI7Jmn8kHwXcYnz49FCoE0f7G7PnZi4iISNF95AoBl6M9vwLUiauM1jpKKRUE5ALuRC+klBoIDARwcXFxVLxCCCEAjSbSEsnWi1u5c+vOiw8QpnNxcaFixYpEREQQERFB7ty5zQ7ppV17eA3PpZ7M3jAb6wMr6ZzSUSRbkUSd8979KE5dfER4RC24OIqCGTMQTBaoXxMctKKF1hqlFFZrnHkc6jkVV6ZTSnUFWmqtvWzPewO1tdbvRitz1Fbmiu35WVuZu7GdE8DDw0MHBAQ4NnghhEijwqPC6bW4F5GWSE7cOUGVfFXw7fpsjZVIPi5evIifnx+1a9emYcOGdl1qa8yYMYwePdpu54uPTj6dWH1mNX2r9mVK4BS+bfEtH9X/KMHnCTx9md9nhLJ9aVlOnAAnlxCq5PXliwdT6PRoNwogd264cQMcMKdeZGQk//nPfxg5cmSg1tojtjLJvdH7ChA9hS4MXIurjFIqPeAG3EuS6IQQQjzlUfgj2sxrg98xP14p9gpOKrl/zaRtWmt2797NggULaN++PY0aNUqR66Ueu32Mtxa9xam7RhPyDy1/4Pz75/nt9d8IGRHC+3Xej/e5wiIiGTn1H/LX3o5HufxM/09ZsufQzJgBQQXrsf9yfzq7nEVFRRlJ3J07ULasQ16XxWJ54aTLyf0vbC9QWilVXCnlDHQHlsUoswzoa/u9C7Dxef3jhBBCOMbtkNs0/bMpWy5s4c8Of/JBvQ/MDkk8R2RkJIsXL+bAgQMMGDCAUqVKmR1Sgh2+eZg3/d6k0q+VWHpiKQdvHATAPbs7+V3zo5Qic4bMZEiX4YXnungRug45SpZ8Nxk/qAG3j5Wnbue9rNt5jZ07FP37g+v3Y6Bkyf/VwN24YTz/9luHvD6LxUL69M/vBZes+8jZ+ry9A/gD6YA/tNZHlVJjgQCt9TJgBvCXUuoMRk1cd/MiFkKItElrTQefDhy9fZTFby6mbdm2ZocknuP+/fv4+PiQL18++vfvT4YML050khOtNb0X92bu4blkdc7KZw0/Y1i9YeTO/HS/vvCocD5d/yntyrajafGmz5wn+HE4o34PIGBFVbZvcgUqkLvyAQZ8eZORA6uROVP9pw/o2NH4eSJdOjhzxgGv0BCfGrlkncgBaK1XAatibBsV7fcwoGtSxyWEEOJ/lFL88NoPRFgiaFSskdnhiOc4c+YMS5YsoVGjRtSuXTtFNaWeuHOCcrnLoZSiqFtRRr4ykqF1h5IzU85Yy0daI5m0exKFshV6KpFbs/sco76/SMDqiujgBmTN84CRI8HTU+HuXj2pXs4LpYpETgghRPK168outl3cxvAGw6lTOOakAjCj3QxcnV1NiEzEpLVm+/bt7Nmzh65du1KsWDGzQ4q3PVf3MHbLWFaeXsnmvptp7N6Yr5t9/fyDdu6EL0eArVItLNSKX+2JvB/emntnqoNTUQrUDGTwwMt80rcazsmwUlISOSGEEA7jf8afTr6dKOBagLc93iarS9ZnytQrUs+EyERM4eHhLFmyhODgYLy9vcmWLZvZIcXLzss7Gbt1LGvOrCFnppyMbzqeavmrxe/gUaNg62YoWZHJY0ry9YZH3LeMIEfWi7QcuIX/DC9P1VLP/ucjOZFETgghhEP8ffhv+izpQ6W8lVjz1ppYkziA1adX45bRjfpF6se6Xzje7du38fHxwd3dnc6dO7+w83xyERYVRrv57QCY2GwiQ2oNifNzFlNoKPj28GfKzoPwW3UuOUXQJv1iPnDfSNMTv+GUPmXURkoiJ4QQwu5+2fML765+l1eKvcLS7ktxy+gWZ9kP135IpbyVJJEzyfHjx1mxYgXNmzenevXk0/crLlsubGHWwVlMbzudjOkzsrLnSirkqRDv5vlDh2DqVJgzB4KCnChTphofXfuQ/pbZlH98B05ZIAUtNyaJnBBCCLtzdXalQ7kOzOs876llj0TyYbVa2bRpE4cPH6Znz54UKlTI7JDipLVm4/mNjN06lq0Xt5LfNT9n7p2hbO6y1C5U+4XHh4SAry9MmQK7d4OLC3TuDIO8rTQaWhMVHG35spo1ITAwxSRzksgJIYSwC4vVwuFbh6mWvxp9q/WlT9U+KWq0Y1oSGhrKokWLsFgseHt7kyVLFrNDitON4Bt08e3CP5f/oWDWgvzc6me8aniRKUOmFx576JCRvM2ZAw8fQrly8OOP0Ls35MoFtGgJBw9AtWpG8lazJhw4AC1bwrp1jn9xdhAVFSWJnBBCiMQJjwqnz5I+LD2xlGP/d4wSOUpIEpdMXb9+HV9fX8qXL0/z5s1xSoY1T1prLgZdxD27O3ky5yFzhsz80uYX+lfv/8Ia3tBQ8PExmk937TJq37p2hYEDoWHDGEuejh1rPPr7GzVwgYFGEvdkewogNXJCCCESJTgimI4+HVl/bj3ftviWEjlKmB2SiMOhQ4fw9/endevWVKpUyexwnqG1ZsWpFYzdOpbz989zYegFXJ1dWdt77QuPPXLEqH376y8ICjJq3374Afr0sdW+xaZevadr3pycUkxN3BMpfmUHIYQQ5rkTeoc2c9uw7/o+ZrafSb9q/RJ8jvld5pM5Q2b7Byf+ZbFYWLt2LWfOnKFv377kzZvX7JCeYsXK4uOLGbd1HPtv7Kd49uL8p/l/cEnn8tzjwsLAz89I4LZvB2dn6NIFBg2CRo1i1L6lUlIjJ4QQ4qVNDZzK4VuHE7XkVpV8VewclYguODiYBQsW4OLigre3NxkzJr/BJ9e4xljfsZTKWYpZ7WfRs3LP5659euqU0XQ6cybcuwelS8N330HfvsYa9WlJfBI5lRbXl/fw8NABAQFmhyGEEMmSVVtxUk5YtZXjt49TMW/Flz7XwmMLyZEpB68Wf9WOEQqAy5cv4+fnR/Xq1WncuHGy6bdosVrwO+bHpaBLDG8wnEmTJhEQFEAJSpCO2JMSi8WJEyfKEhDgwfnzJXByslCu3Ak8PAIoXvxCmqh9e54vv/wyUGvtEds+SeSEEEL8a8/VPQxcPpCl3ZdSLHviJ02t8EsFKuWthG9XXztEJ8DoaxYYGMimTZto3749ZcqUMTskAKKsUfgc8WH8tvGcuHOC6vmrs8d7D+md4m78u3gRpk2DGTPgxg0oVswYuNC/P+TPn4TBJ1N79uzh9u3bvPHGG3EmctK0KoQQAoB1Z9fR0acj+VzzEWWNMjscEYuoqChWrlzJ1atX6d+/P7ni7OmftLZf2k7/pf05fe+0kbh38aVzhc44qWdHzVosxkDS336DVatAa3j9dRg82BhU+oKWxDRFBjsIIYSIF58jPvRe3Jvyecqz5q01FMhawOyQRAxBQUH4+vqSI0cOvLy8cHZ2NjWeSEsk98PukzdLXvJlyUdWl6ws7LaQDuU6xJrA3bpl1LxNnQoXLkC+fPDZZ+DtbdTEiWfJYAchhBAvtOTEEnos7EHDog1Z1mMZ2TNmNzskEcP58+dZtGgR9erVo169eqb2h4uwRPDngT/5evvXVM1XlSXdl1A6V2kCvAOeiUtr+Ocf+PVXYwRqZCQ0bQrffAPt2xsjUUXcJJETQgjxQq8Wf5WP6n/EmCZj4jWjvkg6Wmt27tzJjh076NSpEyVKmDePX3hUODMPzGTC9glcCrpErYK18Krh9e/+6Enco0fGnG+//WbMAefmZjSdvv02lC9vRvQpU1RUFBkyxD3CFySRE0KINMmqrfy06ycGeQwim0s2vmnxjUOus7zHclzSP3++MBG7iIgIli1bxr179/Dy8iJ7dnNrSr/f+T2fb/ycuoXrMuWNKbQs2fKZGrgjR4zat7/+guBgqF4dpk+H7t0hGa8UlmxZLJYXTikjiZwQQqQxEZYI+izug89RH7JnzI5ndU+HXatkzpIOO3dqdvfuXXx9fSlYsCCenp4vrJVxhMeRj5m2bxrlc5enRckWDKo5iFoFa9G8RPOnEriICFi82Ejgtm41ls16800YMgRq104bE/c6ijStCiGEeEpwRDCdfTuz9uxavmn+jUOTOIDZB2eTK1MuXi/zukOvk5qcOnWKpUuX0qRJEzw8PJK8P1xIRAhTAqfwzT/fcDPkJkM8htCiZAtyZc5Fi5It/i139aqx6sK0acbUIcWLG33fPD3T3sS9jiKJnBBCiH/dDb3L6/NeZ++1vfzR7g+HJ3EAE7dPpFLeSpLIxYPWmi1btrBv3z66d+9OkSJFkjyGGftm8NmGz7gdeptmxZvh84oPjd0bR4sRNm+GX36BJUvAaoU2bYzat1atjOVMhf1IIieEEOJf98Pucz34Oou6LaJ9ufZmhyOiCQsLY/HixYSFhTFw4EBcXV2T7NoPwx/iks4Fl/QuRFojqV6gOqNeGUWDog3+LfPoEcyebSRwx49DzpzwwQfG4AUTx1+kepLICSGE4NqjaxRwLUCpnKU49c4pGXyQzNy6dQsfHx9KlixJt27dXvjFbS9BYUFM3jOZH3b+wPhXxzOk1hAG1RzE2x5v/1vm+HEjeZs920jmatY01kB9803IJAOcHU4SOSGESOP2XN1Dm7lt+KDeB4xoNEKSuGTm6NGjrFq1itdee42qVasmyTXvP77PT7t/YtKuSQSFB9G2TFvqFa4HGFOIWCywfDn897+wYYMx19ubb8L//Z8MXkhqsrKDEEKkYU+W3MqbJS/dKnYzOxwRjdVqZf369Rw/fpxevXpRoEDSraTRdUFXNpzfQMdyHRn5ykiqF6gOwJ07xsoLv/4Kly5BkSLw1Vfg5QV58yZZeCIaqZETQog0yveoL70W9TJ9ya0NfTaQIV3ST52RnIWEhLBw4UKUUnh7e5M5c2aHXu9O6B0m7ZrE0LpDyZ05NxOaTcA5nTNV8xs1gPv2GbVv8+ZBeDi8+ipMmgRt28ILKoOEg0kiJ4QQadDVh1fps7gPdQrXYXmP5aYuuSVrtj7t2rVr+Pr6UqlSJV599VWcHDjM81bILb7b8R2/7v2V0MhQKuapSI/KPahVqBaRkTB/PkyeDDt2GJP1enrCO+9AxYoOC0kkkCRyQgiRBhXKVojVb62mTuE6ZM7g2NqeF/lt72/kyZKHLhW6mBpHcrB//37Wr1/P66+/ToUKFRx2Hau28vG6j/l176+EW8LpUakHnzf6nPJ5ynPzpjH32++/w/XrULIk/Pgj9OsHJi8cIWIhiZwQQqQRVm3lA/8PaFCkAV0rdqVp8aZmhwTA5D2TqZS3UppO5CwWC6tXr+bChQv069ePPHnyOOQ6QWFBuGV0w0k5cTHoIl0rdmVEwxGUzV2WvXuh9wfg62usxNCqlbF0lsz9lrxJIieEEGlAhCWCfkv68feRv8mYPiNdK3Y1OyRh8+jRI3x9fcmSJQteXl4vXDfzZVwOusx//vkPMw/MZN/AfZTNXRafLj5ERTrh5wd9f4bdu8HVFQYNMppPy5SxexjCASSRE0KIVC4kIoTOvp3xP+vPxGYT+bjBx2aHJGwuXrzIwjg3oJQAACAASURBVIUL8fDwoFGjRnZfauvig4tM2D6BP/b/gUbjWc2TLM5ZuHULpkxx4rffjObT0qXh55+hb1/Ils2uIQgHS9GJnFIqJ+ADuAMXgG5a6/uxlLMAh21PL2mt2yVVjEIIYabHkY9p/ldz9lzdw/S20xlQY4DZIQmMpbb27NnDtm3b6NChA6VKlbL7NYIjgqn8W2XCosIYUH0Anzb8lHvni/HFe/D339J8mlpERUWl3EQO+BTYoLWeqJT61Pb8k1jKPdZaV0va0IQQwnyZMmTiVfdX+bj+x3Qs39HscAQQGRnJihUruHnzJgMGDCBHjhx2O/fpu6fxO+bHZ40+w9XZlRntZuCRvy6Bm4rQqy1s326MPvX2NppPy5Wz26WFSVJ0jRzQHmhi+/1PYDOxJ3JCCJGmnLxzkrCoMKrmr8pXzb4yO5zn2uW1i3QqaZacMtv9+/fx9fUlT5489O/fH2dnZ7uc9+Sdk3y17SvmHp6LczpnulfqTnaKc2FVVz76rzF5r7s7fP899O8vo09Tk5S+skM+rfV1AK31daVUXPNKZ1RKBQBRwESt9ZIki1AIIZJYwLUAWs9tTaGshdg3aB9OKnm3mWVzSRudss6ePcvixYtp2LAhderUsUt/uJvBNxnmP4z5R+aTMX1GhtUdRvtcn/Dt53n4808IDYUmTeCnn4zJe5NoiVaRhJJ9jZxSaj2QP5ZdnyfgNEW11teUUiWAjUqpw1rrs7FcayAwEKBo0aIvFa8QQphpw7kNdPDpQO7MuVnQdUGyT+IAvtvxHfld89OrSi+zQ3EIrTXbt29nz549dOnSBXd390SfMyQihCzOWXB1dmXXlV0Mr/8xNR9/yqxJ2fl+Nbi4QM+e8P77kETLswqTJPtETmvdPK59SqmbSqkCttq4AsCtOM5xzfZ4Tim1GagOPJPIaa2nAlMBPDw8tB3CF0KIJON3zI+3Fr1FmVxl8O/lT8GsBc0OKV7+2P8HlfJWSpWJXHh4OEuWLOHRo0d4e3uTLZFDQg/eOMi4reM4cusIR4ccxcmShY8znmby0HR8cwzy54exY40pRGTt09RPa43Van3h6h/J+b9zy4C+tt/7AktjFlBK5VBKudh+zw00AI4lWYRCCJEEtNb8sf8PahWsxdZ+W1NMEpea3blzh+nTp5M5c2b69euXqCRu3/V9dPTpSLUp1Vh3bh2t8/dnxOdWihSBwW+nw8UFZs+GCxdg5EhJ4tIKi8WCk5PTC5vpk3MfuYmAr1JqAHAJ6AqglPIA3tZaewHlgSlKKStGUjpRay2JnBAiVdBaExoZShbnLPh29cVJOZm+5JaAEydOsHz5cpo1a0aNGjUSda7NFzbT9M+mZM+YnYEFfufBZk9+GeVMVBS0bw/DhkGjRmDnKehEChCfgQ6QjBM5rfVdoFks2wMAL9vvO4DKSRyaEEI4nFVbGbZmGDuv7GRT3024OruaHVKaZ7Va2bRpE4cOHaJnz54UKlTopc6z8/JOrjy8QteKXalfqBFemZdzfHkrpm5Lj6srDB4M771nrIMq0q749I+DZJzICSFEWhVpicRzqSdzD89lWN1hZMqQyeyQ0rzHjx+zaNEiIiMjGThwIFmyZEnwObZf2s7YLWNZd24dpV2rc2NjZ37+OR1nzrxB0aLw3Xfg5QVubg54ASLFkUROCCFSoJCIELou6MrqM6v5+tWv+bThp3Zf2ikpHR58OEXHD3Djxg18fX0pW7YsLVq0eGHn85j2X9/PR+s+YuP5jeSMrEzTizvZv6IO7z1Q1KkDX30FnTpBPFrRRBoiiZwQQqRAg1YMwv+sP1PemMLAmgPNDifR0jml7MnNDh06hL+/P61ataJy5fj35NFaE2GJwCW9CyGRIRw8oPA4fpQD68uzxaro1Mno/1a/vgODFymaJHJCCJECjWs6ji4VutChXAezQ7GLMZvHUDBrQbxrepsdSoJYLBbWrVvHqVOn6NOnD/ny5YvXcVpr1p1bx9gtY6mcpypvOP3C99835O6m9YS7wv/9n9H/rUQJB78AkeJJIieEECnEqbunmLFvBhOaT6B4juIUz1Hc7JDsxueoD5XyVkpRiVxwcDB+fn5kyJABb29vMmV6cR9FrTVrzqxh7Nax7Dq/n+yn3uNcwGf8fh4KF4ZvvjHWQJXls0R8SSInhBApQOC1QFrNbYVCMaTWEIplL2Z2SGnalStXWLBgAdWqVaNJkybx7t83dstYvlw1GbfDn5F1zwYe3MtM8erw7Rzo1g0yZHBw4CLVkUROCCGSuY3nN9J+fntyZcrF2t5rJYkzWWBgIBs3bqRdu3aULVv2uWWt2sqyk8sokaMEmR5W4dTsoTjP+5yg8PS0aQMffWSsg5rCx3kIE0VFRUkiJ4QQydXi44vpvrA7pXOWxr+XP4WyvdycZCLxoqKiWLVqFVeuXMHT05PcuXPHWdaqrSw+vpixW8dyKCAz7kd/5eJuyJDBjd694YMPoEKFJAxepFpSIyeEEMmYW0Y3GhRpgF83P3Jmyml2OA6TMX1GnNM5mx1GnIKCgvD19SV79uwMGDAAFxeXOMsuPbGUzzeM5Oi2EmTcMxPO1yAoh2bECHjnHWMtVCHsJcWv7CCEEKmN1prA64F4FPTg1eKv0tS9aYqfY+1F9g3aZ3YIcbpw4QILFy6kbt261K9fP9b3wmK14KScCAtTTJ2qOD1nGdx2J7+75oOfwdNT4SqLbggHiG+NXMJmNRRCCPFSrNrKB/4fUGtaLbZd3AaQ6pO45Eprzc6dO/Hz86Njx440aNDgmfciyhrFXwf/ouy39eg19ATu7rDqx3ZULlqM+fPh9GnFu+8iSZxwGGlaFUKIZCLSEkn/Zf2Zc2gO79V+jwZFG5gdUpL5ZN0nFM5WmHfrvGt2KABERESwfPly7t69i5eXF9ljzAcSaYlkzqE5fLl0JpfWdMLpwGbOhmemTRsYPhwaN1YygEEkCUnkhBAiGQiNDKXrgq6sOr2K8U3HM6LRiDRVE7f81HIq5a2ULBK5e/fu4ePjQ4ECBfD09CRDLHOCNPh6MHsXNIGjG0nn5ETPnorhH0ECFnUQwi4sFku8loOTRE4IIRxo2cllrDmzht9f/51BHoPMDifNOn36NEuXLqVx48Z4eHj8m0yHR4Xz18E5FLnfmx+/c2av/3QyZY7i7ffTMWyYokgRkwMXaZYMdhBCCBNZtRUn5UT3St2pnLcyFfNWNDukNElrzdatWwkMDKRbt24ULVoUgLCoMKbt/YMvpxzk3roBcM2ZfPng669h8OD0sgKDMJ00rQohhElO3z1NZ9/O/NH+DzwKekgSZ5KwsDCWLFlCaGgo3t7eZM2aFYvVwqTtvzNu8kWCNnrBvSEULBbKqN81ffsqMmY0O2ohDJLICSGECfZf30+rua2waqvZoSQLuTLnws3FLcmve+vWLXx8fChZsiRdu3ZFOSmCguC335wYNeFNIh/mpmzlh4z7XdOpU2bi8X0pRJKSlR2EECKJbb6wmXZ/tyNHphys672OMrnKmB2S6bZ5bkvyax49epRVq1bRokULSlUoxZiVU5g8WWHZM4hHD51o2syNL0ZA06bZZASqSLakRk4IIZLQ3qt7aTWnFSVzlmRtr7Wy5JYJrFYrGzZs4OjRo3To1oGpu9YzefA+wvf2B2sGWrcLZfwoV2rUkBXsRfJnsVhwdn7xqiiSyAkhhB1Uy1+NYXWHMbzB8FS95FZCvbPqHYq5FWN4g+EOvU5oaCh+fn4AVPHoQaUO24k4OBCVzkr77vf4dnQ+SpeW2XtFyiE1ckII4WBaa34P+J1O5TuRzzUfE5pPMDukZGfj+Y1UylvJode4du0a833mE+yUnT3r+rFypRPOmd6g16Bb/GdkAQoWzOfQ6wvhCJLICSGEA1m1leFrh/PDrh+4EXyDMU3HmB1SmrR993b812xiyeYKHNncmZy5LIwbB//3fy7kyFHA7PCEeGmSyAkhhINEWiLxWu7F7IOzebf2u4xuMtrskNKcm0F3GP/jHFRQFPPnDiLY6sTH464yalghsmQxOzohEk8SOSGEcIDHkY/p5teNFadWMLbJWL545Ys0teSW2SIiNLNnB7P/wFLu3c3Pup11eX9EBJ8MKUw8+oULkWLIyg5CCOEAoZGhnLt/jl/b/MrgWoPNDifZK+JWhHxZEt9H7fztG3h9uYNLW0vQ7rWN3LntQYs3qjJnjpvMASdSJamRE0IIO7oVcovsGbOTK3Mu9g3ch0t6F7NDShH8e/kn6vhT164zYNQetvvUplb5wnR6Yw0VK7bju+8qyBxwIlWTRE4IIezkzL0zvPbXazR1b8qM9jMkiUsC9+/DsDHn+HNqdtJHtqFH77lULvuQgV4DyZVLpncRqZ8kckIIYQf7r++n9dzWRFmjeNvjbbPDSXH6L+2Pe3Z3RjUeFa/ygacvM2mSYulfhXn0qASVmu6iV5sAShUvQNu2PeM1QaoQqYEkckIIkUhbLmyh3fx2uLm4sbnfZsrlLmd2SCnOriu7CI4IfmG5nUcvMXDEKY6srg9RGXmzm8bL6xwHDmynQYMG1K1bVwaViDRFEjkhhEiE0MhQ3vR7k0JZC+Hfy58ibkXMDilV2nboEgM/OcuJdfVBF6Rc0wB+nVCUDOHn2L17N507d6Z48eJmhylEkpNETgghEiFzhsws77GcEjlKkCtzLrPDSXVOn9ZMnKj4c3ZhLDo/lV4LYOrEEtQoW52lS5cSFBSEl5cXbm5uZocqhCnim8g5JUEsL0Up1VUpdVQpZVVKeTynXCul1Eml1Bml1KdJGaMQIvX59p9v+eafbwCoVaiWJHEva+dOaNHif8+tVmjRgpUzVlC88XbKltPMnQuD34bAow84vKo+pQumZ/r06WTMmBFPT09J4kSaFhUVleJr5I4AnYApcRVQSqUDfgFaAFeAvUqpZVrrY0kTohAitdBa8/G6j/lu53d0r9QdrbX0yUqMUaNg/XrKlXCjWOc2LKnVjvdv9+eSVxvI8JgGXfayYFIdChRwAvJy8uRJli1bxquvvkrNmjXNjl4I06X4plWt9XHgRf+Q1gbOaK3P2crOB9oDksgJIeItyhqF1zIv/jz4J0M8hvBz658liUssf3+oWZMvp1p4a1EdvrvzHTg/ol73rfwxsTLlitUBwGq1smXLFg4cOECPHj0oXLiwyYELkTyklZUdCgGXoz2/AtQxKRYhRAqktabrgq4sObGELxt/yajGoySJs4P9B50YW2wfSw4ostwNomGxcczcOoRSRZv8W+bx48csWrSIyMhIvL29cXV1NS9gIZKZFFEjp5RaD+SPZdfnWuul8TlFLNt0HNcaCAwEKFq0aLxjFEKkbkopWpZsSYsSLRhSa4jZ4aR4gYEwdiwsWwbZ0z1iND/wvv6JHBcfQPtFRgEnJ27evImPjw9lypShRYsW8frCEiItSRGJnNa6eSJPcQWIPidAYeBaHNeaCkwF8PDwiDXZE0KkHdcfXefk3ZM0cW8iE/3aQUAAjBkDK1ZA9uwwtsQs3jv3Pm7VSkDgXahZEw4cgJYtOfzDD6xZs4aWLVtSpUoVs0MXIllK8aNW42kvUFopVVwp5Qx0B5aZHJMQIpk7e+8sDWc25E2/NwmJCDE7nBQtIADatoVateCff2DcOLhwAUbOKYtb89r/1sARGIilRQv833qLTZs20bt3b0nihIiD1jrlJ3JKqY5KqStAPWClUsrftr2gUmoVgNY6CngH8AeOA75a66NmxSyESP4O3DhAgz8a8CDsAcu6LyOLcxazQ0qRoidwO3bAV18ZCdwXX4CbG1CvHqxbZyRxQMjjx/zVsye306fH29ub/Plj61UjhABjEJCTk1O8+usm28EOWuvFwOJYtl8D2kR7vgpYlYShCSFSqK0Xt9L277Zkc8nGpr6bKJ+nvNkhpTiBgfDll0YTas6cRgL3zjuQLVvcx1y9ehVfX1+qVq1KkyZNcHJKtnUIQiQL8a2Ng2ScyAkhhL35HvWlgGsB1vZeS1E3GfSUEPv3GwncsmWQIweMHw/vvvv8BA5g3759bNiwgbZt21KunKxVK0R8SCInhBDRhESEkMU5Cz+1+omH4Q/JkSmH2SGlGAcPGgnckiXGIIZx4+C9916cwEVFRbF69WouXbqEp6cnuXPnTpJ4hUgNEpLISf22ECJV+27Hd1T6rRI3gm+QzimdJHHxdOQIdOkC1arBpk3GiNQnfeBelMQ9fPiQWbNm8fjxY7y8vCSJEyKBpEZOCJHmaa35ZP0nfLvjW7pV7EaOjJLAxcfx40bS5usLrq4wciR88IFRGxcfFy5cYOHChdSpU4cGDRrI5MpCvARJ5IQQaVqUNYqBywcy88BMBnsMZnLryaRzkglnn+f0aSOBmzcPMmeGzz6DDz80BjTEh9aa3bt3s337djp27EjJkiUdG7AQqZgkckKING3slrHMPDCT0Y1HM7rxaKkVeo4LF4yVGGbPBmdnGD4cPvoI8uSJ/zkiIyNZvnw5t2/fZsCAAeTIIbWfQiSGJHJCiDRtWN1hlMlVhl5VepkdSrJ15YoxdciMGcZUb+++C59+CvnyJew89+/fx8fHh3z58tG/f38yZMjgmICFSEOioqJksIMQIm25GXyTd1a9Q1hUGDky5ZAkLg43b8LQoVCqlJHEeXnB2bPw448JT+JOnz7NjBkzqFGjBh06dJAkTgg7kRo5IUSacu7+OV776zWuB1+nX7V+eBT0MDukZOfuXfj2W5g8GcLDoW9fYyCDu3vCz6W1Ztu2bQQEBNC1a1eKFStm93iFSMssFgvp08cvRZNETgiRoh26eYiWc1oSYYlgY5+NksTF8PChUdv2ww/w6BH06GHMC1e69MudLywsjCVLlhASEoK3tzdZs2a1a7xCCKmRE0KkETsu76DN3DZkdcnKhj4bqJCngtkhJRuhofDLLzBxIty7B506GaNSK1V6+XPevn0bHx8fihcvTteuXeP9RSOESBhJ5IQQaUL2jNmpmLcif3f+W5bcsomIgOnTjSW0rl+HVq2M32vWTNx5jx07xsqVK2nevDnVq1e3T7BCiFhJIieESNX2XN1DrYK1qJCnAts9t8v0IoDFAnPnwujRxpQijRqBj4/xmBhWq5WNGzdy5MgR3nrrLQoWLGiXeIUQcZMluoQQqdYPO3+gzvQ6zDk0ByDNJ3Faw6JFULmyMYAhZ05Yswa2bEl8EhcaGsrcuXO5du0a3t7eksQJkUTsmsgppV5NdERCCJFIWms+W/8ZH679kC4VutCtYjezQzKV1rBuHdSuDZ07G8/9/CAgAFq2hMTmt9evX2fatGnkz5+fXr16kSVLFvsELoR4IXvXyE1WSrWJvkEplbb/BRVCJKkoaxTey72Z+M9EBtUcxPzO83FJ72J2WKbZvRuaNYPXXoNbt+CPP+DwYSOhs0cF5cGDB5kzZw7NmzenRYsWODlJ440QScnefeRaACuVUpmAK8CPQDrA96UjFEKIBNh7dS+zDszii0ZfMLbp2DTbnHrsGHz+OSxZYiyh9dNPMGgQuNgpp7VYLPj7+3P27Fn69u1L3rx57XNiIUSCJGRlhxcmclrra0qp/sA/wANgqNZakjghhMNZtRUn5US9IvU4PPgw5fOUNzskU1y8aMz9Nns2ZMlirI06dCjYcwq3R48e4efnR8aMGfH29iZjxoz2O7kQIkHs3UfuW2A1MAG4iVEbJ4QQDnUz+CZ1p9dl2cllAGkyibtzB4YNgzJl4O+/jd/PnTNWZLBnEnf58mWmTZtG8eLF6d69uyRxQpjM3k2rWYHKWuvbSqlfgdVKqSxa6+mJCVIIIeJy/v55XpvzGlcfXiWDU9pbvzM42FiN4dtvISQE+vUzauSKFLHvdbTWBAQEsHnzZtq3b0+ZMmXsewEhxEuxWCy4xLPPRHyaVt+O9vtdpVQLYCUgiZwQwu4O3zxMyzktCYsKY0OfDdQrUs/skJJMRARMmwbjxhmL23foAF9/DeUdUBkZGRnJqlWruHbtGgMGDCBnzpz2v4gQ4qU4ZEJgpVQhrfVVrXWQUuq1l45OCCHicCnoEq/MeoXMGTKzzXMbFfNWNDukJGG1woIFxkCGs2fhlVdg8WKo56Ac9sGDB/j6+pIzZ04GDBiAs7OzYy4khHgpjlrZYT+QF0BrHfoScQkhxHMVyVaE4fWH07NyT9yzu5sdTpLYsAE++QQCA41JfVeuhNat7TONSGzOnTvHokWLqF+/PvXq1UuzI4CFSM4clcjJX7sQwiHmHZ5HtfzVqJCnAiMajTA7nCSxfz98+imsXQtFi8Kff8Jbb4Gj1qHXWrNjxw527dpF586dKV68uGMuJIRINIvFQvr08UvREjLLo365cIQQIm4/7vyRtxa9xYTtE8wOJUlcuAC9e0ONGsYqDN9/DydPQp8+jkviIiIi8PPz49ixY3h5eUkSJ0Qy56gaOSGEsButNZ9v/JwJ2yfQuXxnprdN3eOn7t2Dr76C//4XnJyM5tRPP4Xs2R173bt37+Lj40OhQoXw9PSM9//yhRDmkUROCJGsRVmjGLxiMNP3T2dgjYH8+vqvpHNKnVNUhoXB5MnG6NOgIGMqkTFj7D+VSGxOnjzJsmXLaNq0KTVr1pT+cEKkEJLICSGStShrFGfun+HzRp8zrum4VJlgWK0wb54xEvXSJWjTBiZONAY0OJrWms2bN3PgwAF69OhB4cKFHX9RIYTdOCqRu/xy4QghhOFR+CMs2kL2jNnx7+WPc7rUOe3Fhg0wfLgxoKFGDZg5E159NWmuHRYWxqJFiwgPD8fb2xtXV9ekubAQwm7sukTXE1rrmi8dkRAizbsVcoumfzalo09HtNapMok7csSoeWve3OgTN3cu7N2bdEnczZs3mTZtGjly5KBPnz6SxAmRQknTqhAiWbnw4AIt57TkctBl/Lr5pbqm1OvXYdQo+OMPyJbNWFrrnXcgKZcsPXLkCKtXr6Zly5ZUqVIl6S4shLA7h9TIPaGUqq6UWqSUuqOUilJK1bBt/1op1Sqh53vOdboqpY4qpaxKKY/nlLuglDqslDqglAqw1/WFEPZx5NYRGvzRgFsht1jXex1tSrcxOyS7CQkxBi6ULm3MA/fee3DmDHz0UdIlcVarlbVr17JhwwZ69+4tSZwQqUBUVJRjauSUUg2B9cA5YB7wTrTdVuBtYE1CzvkcR4BOwJR4lG2qtb5jp+sKIexEa02fxX3QWrO131Yq50uCnv5JwGIxErcvvjBq47p0gQkToFSppI0jJCQEPz8/0qVLh7e3N5kzZ07aAIQQDuHIptWJgD/QAUjH04ncPqBPAs8XJ631cSDVNcEIkZYopZjfZT7O6ZxTzZJb69fDhx/CoUNQty74+UH9+kkfx9WrV1mwYAGVK1emadOmODkluIFFCJFMOWplB4AawG9aa82zKz3cAfIk8Hz2oIG1SqlApdTAuAoppQYqpQKUUgG3b99OwvCESHvmHprL/638P7TWlMlVJlUkcceOweuvQ4sW8PAhzJ8PO3aYk8Tt27ePefPm0bJlS5o1ayZJnBCpjCNr5MKAuOruCwBBCTmZUmo9kD+WXZ9rrZfG8zQNtNbXlFJ5gXVKqRNa660xC2mtpwJTATw8PGS5MSEc5KddPzHUfyhN3ZsSFhVGpgyZzA4pUW7fhi+/hClTwNUVvvkG3n03aQcyPBEVFcWaNWu4cOEC/fr1I08eM/7vLIRwNEcmctuBoUqp6EnWk6RoALAxISfTWjdP4PVjO8c12+MtpdRioDbwTCInhHAsrTWjNo1i/LbxdCrfibmd5pIxvQnZjp2Eh8PPP8P48caghsGDYfRoyJ3bnHgePnzIggULcHV1xdvbGxcXF3MCEUI4nCMTuZHAP8BBwA8jieurlPoBqAnUSuD5EkUplQVw0lo/sv3+GjA2KWMQQhg+8P+ASbsn4VXdi9/f+D3FLrmlNSxcCB9/DOfPwxtvGNOJlCtnXkwXL17Ez8+P2rVr07BhQ+k7LEQq57BETmt9UCn1CvAt8DmgMAY8bAMaa61PJjDWOCmlOgKTMfrdrVRKHdBat1RKFQSma63bAPmAxbZ/1NID87TW9ho1K4RIgNdKvkYW5ywpesmtwEAYNgy2bTOW0lq3zpjc1yxaa/bs2cO2bdvo0KEDpZJ6WKwQwhQOnRBYa70PaKaUygjkBB5orUMTep54XGcxsDiW7deANrbfzwFV7X1tIUT8PAp/xOYLm2lbti2tS7emdenWZof0Uq5dgxEjjClF8uQx+sMNGADx/HfUISIjI1mxYgU3b95kwIAB5MiRw7xghBBJxmq1AsR7ENNLr+ygtQ4Drr3s8UKIlO12yG1az23N4VuHOfPuGYq4FTE7pAR7/Bi+/96YAy4qymhOHTEC3NzMjev+/fv4+PiQN29eBgwYQIYMGcwNSAiRZBJSGweyRJcQ4iVcfHCR1+a8xqWgSyzstjDFJXFag6+vkbhdugSdOhn94EqUMDsyOHPmDEuWLKFRo0bUrl07xTZTCyFejiRyQgiHOnrrKC3ntCQ4Iph1vdfRsGhDs0NKkMBAGDoUtm+HqlWN5tQmTcyOyugPt337dvbs2UPXrl0pVqyY2SEJIUwgiZwQwqHWnl2LRVvY6rmVKvlSzrqeN24YzaazZhn94KZNA09Pc/vBPREeHs6SJUsIDg7G29ubbNmymR2SEMIkksgJIRwiOCIYV2dXhtYdSp+qfciVOZfZIcVLeDj89JMxH1xYmLG81siRkFxypdu3b+Pj44O7uzudO3eO97I8QojUKaGJ3Euv66KU2qiUKvyyxwshUo6/D/9NiZ9KcPTWUZRSKSKJ0xqWL4dKleCTT4zm06NHjb5wySWJO378OLNmzaJ+/fq88cYbksQJIZK0Rq4JcS/XJYRIJSbvnsx7a96jcbHGFM6WMv7vdvy40Q9u7VooXx7WrIGWLc2O6n+sQ86lUwAAIABJREFUViubNm3i8OHD9OzZk0KFCpkdkhAimYiKipKmVSFE4mmtGb15NOO2jqN92fbM7zI/2S+59eABjBkD//0vZMkCkybBkCGQnGbvCA0NZdGiRVgsFry9vcmSJYvZIQkhkhHpIyeEsItZB2Yxbus4+lfrz5S2U0jvlHz/ubBYYOZMYzDDnTvg7W30iUtua8rfuHEDHx8fypcvT/PmzeM94acQIu2wWCwJ6maRfP9lFkKY6q0qb2HVVvpX75+s5zLbuRPefdeYVqR+faMZtUYNs6N61qFDh/D396d169ZUqlTJ7HCEEMlUkg12EEKkPo/CHzF4xWDuht7F+f/bu+/wKKq3jePfk0DoTUFAWkQFRZCgwSAdlKIgSEc6CAiKguX9WVAQRKwoKtIVpCi99yZFmnSkd0IRpHdIO+8fExQ0QALZnd3k/lxXrmR3Z2fu2SSbJ2dOCQzixcde9Nki7sgRaN7cKd7+/BNGjHDmhvO1Ii46OpqZM2eycOFCmjVrpiJORG5KhZyI3JbjF4/z1LCnGLR2EEsPLHU7zg1FRjrLahUoAL/8Au+8A9u3Q+PG4Gs15/nz5xk2bBinTp2ibdu2ZM+e3e1IIuLj1EdORBIs/Ew4lYdXZv+Z/UxsMJHnCj7ndqQ4zZsHr73mjEp99llnMMODD7qdKm4HDhxg3LhxFCtWjHLlyvlsy6aI+BYVciKSINuPb+fp4U9z7so55jSZQ5l8ZdyO9B/h4c5EvuPGwf33O/PDVa/udqq4WWtZs2YNv/76KzVq1KBgwYJuRxIRP6JCTkQSJFPqTARnDqbPM30omqOo23Guc/mycxn144+d2x99BG+9Bal9dBaUqKgopk+fzqFDh2jVqhV33+37EyeLiG/xZiFXCQi/g+eLiItWHVpFSI4QcqTPweIWi33u0t/Mmc5o1N27oU4dp6Dz5XXkz5w5w5gxY8icOTOtW7cmKCjI7Ugi4oe8NtjBWjvfWnv5dp8vIu4ZvWk0pX4sRc8lPQF8qojbtw9q1XL6wAUGwuzZziVVXy7i9u7dy+DBgylUqBB169ZVEScit00rO4jITfVd1ZcOMzpQJl8ZOpXo5Hacv12+DF9+6VxGDQiATz6B11+HVKncTnZj1lqWL1/OsmXLqF27Nvnz53c7koj4OfWRE5E4WWvptqgb3RZ1o0bBGoyqM4o0KdO4HQtwWt06dIBdu6BuXfjqK8iTx+1UNxcREcGUKVM4efIkrVu3JnPmzG5HEpEkwKOXVo0xPjbVpojEV/iZcHot70XLkJaMrz/eJ4q4Awec/m9VqzqtcHPmwNixvl/EnTx5kh9++IGUKVPSsmVLFXEikmg83SL3qzHmeWvtrwl8noi4JDommsCAQPJlzsfqNqspcHcB1/vERUTA119D9+5grXM59c03ffsy6lU7duxg8uTJlC9fntDQUNdfSxFJWqKjo0mZMmW8t0/oYIefgRnGmDr/fsAYU9oY81sC9yciHnQ+4jzPjHyGb1d+C0DBrAVdLzwWLoSQEGdFhkqVYMsWZ7F7Xy/irLUsXLiQadOm0bBhQ4oXL+76aykiSY9HL61aa9sDnwCjjDHtAIwxRYwxU4HFQJaE7E9EPOfExRM8NewpFuxdQIagDG7H4ehRaNoUKlSAS5ecSX0nTYLgYLeT3drly5cZNWoUe/bsoU2bNuTx9Wu/IuK3PD7YwVrb3RhzCOhnjHkBKAUcAFoBwxK6PxFJfAfOHKDKiCrsObWHCQ0mUKNgDdeyREfDwIFOq9uFC9C5s/N12rSuRUqQv/76i9GjR3P//fdTv379BL3BiogkVHR0NClSxL88S3AhZ4y5CygARANlgGVAeWttVEL3JSKJ73zEecoMKcOpy6eY03QOZfOVdS3L2rXQrh2sWgUVK0LfvuBPK1Zt3ryZGTNmULlyZYoW9a1VL0QkafJoi5wxpivweuzzegG7gP7AV8BrCdmXiHhG+qD0vFv6XcJyhxGSI8SVDGfPwgcfQJ8+kC0bjBwJL7wA/tKlLCYmhnnz5rF161aaNGlCzpw53Y4kIsmEpy+tdgYGA92stUcBjDHhwERjTHagibU2MoH7FJFEMHf3XFIEpKDCfRV4KfQlVzJYC+PHQ8eO8Oef8PLL0KMH+NPsHBcuXGD8+PEYY2jTpg1p/eUasIgkCZ4u5B621u6+9g5r7QJjTAVgBjALeCqB+xSROzRm8xiaTGjCE7meYEnwEldGU+7Z40zqO3MmFCvmDGQoXtzrMe7I4cOHGTNmDIULF6ZixYoEBNz2KoYiIrfFo4Xcv4u4a+5fa4wpDcxOyP5E5M71W9WPV2a8Qqm8pZj6wlSvF3GRkc6C9t26QYoU0Ls3vPKK87U/WbduHfPmzaNatWoUKlTI7Tgikky5tkSXtXaXMaZkYu1PRG7OWkv3Rd35cNGHVC9QndF1R5M2pXcvAy5dCi+9BJs3Q+3a8M03kDu3VyPcsejoaGbNmsXevXtp0aIF2bJlczuSiCRjHp1H7lau9ptLDMaYL4wx24wxG40xE40xcfayMcZUNcZsN8bsMsa8k1jHF/F1FsvuU7tpVrQZE+pP8GoRd+oUtG0LpUvDuXMwZYrTN87firhz584xdOhQzp07R+vWrVXEiYjrXGuR84C5wLvW2ihjzGfAu8Db125gjAkEvgcqAQeBVcaYKdbaLV5PK+IlEdERHL94nHsz3MuPNX8kwAQQYLzTl8taGDUKOnWCEyfgrbega1dIn94rh09U4eHhjBs3jtDQUMqUKaNVGkTEJ0RFRSWNQs5aO+eamyuAunFs9gSwy1q7B8AYMwqoCaiQkyTpQsQF6oypw55Te9jQboNXF77fuxfat4fZsyE01Pkc4s7sJnfEWsuqVatYvHgxNWvW5MEHH3Q7kojI35JSi9y1WgGj47g/F86qElcdBMK8kkjEy05cPEG1n6ux6vAqBlYf6LUiLjLSWeD+ww8hMNDpB/fKK87X/iYyMpJp06Zx9OhRWrVqxV133eV2JBGR63hjZYcAYB7wErD76tfW2p23sa95QI44HupsrZ0cu01nIAoYGdcu4rjP3uBYbYG2AHnz5k1oVBFXHTx7kMrDK7Pn1B7G1RtHrYdreeW4q1dD69awYQPUqOFM8Ouvy4yeOnWKMWPGkDVrVlq1akVQUJDbkURE/sMbLXIGKA9k+NfXCWatffqmBzKmOVAdeMpaG1eBdhC49s9KbuDwDY41EBgIEBoaGmexJ+KrOs7qyMGzB5nVZBblg8t7/Hjnz0OXLk7rW/bsMG6cMyrVX7uR7d69m4kTJ1K6dGnCwsLUH05EfFaSubRqjKmKM7ihnLX24g02WwU8aIy5DzgENAQaeSmiiNf0r9afw+cOUzSH59f7nDnT6Qu3f7+zTuqnn0KmTB4/rEdYa1m6dCkrV66kbt26BAcHux1JROSmXJ1+JJH1wWnpm2uMWW+M6Q9gjLnXGDMDwFobBXTAmYh4KzDGWrvZrcAiiWnennnUG1uPiOgIsqXL5vEi7tgxaNwYnn0W0qaFJUugXz//LeKuXLnC2LFj2bZtG23atFERJyJ+Icm0yFlrH7jB/YeBZ6+5PQNneTCRJGPs5rE0ntCYglkLcubyGbKl89z8ZtbCiBHw+uvOYvcffgjvvAOpUnnskB53/PhxRo8eTd68ealdu3aCOg6LiLgpyRRyIslV/9X9eXn6y5TMU5KpL0wlS5osHjvWvn3O5dPZs6FkSRg0CPx9dapt27YxdepUKlasyOOPP+52HBGRBFEhJ+LHeq/ozeuzX6fag9UYU2+Mx1ZriI52RqC+9x4EBDhft2/vfO2vYmJiWLhwIRs2bKBRo0bkypXL7UgiIglirSUmJoaABLwZq5AT8SHlg8vTPrQ931T9hpSBKT1yjM2b4cUXYeVKpz9c//7+O6XIVZcuXWLChAlERkbStm1b0qVL53YkEZEEu9oal5CR9X78/7dI0hAZHcnoTc581yE5Quhbra9HiriICOjeHYoVg127YORImDbN/4u4I0eOMGjQILJmzUrTpk1VxImI30roZVVQi5yIqy5EXKDe2HrM3DWT4MzBhOX2zMIkv//utMJt2gSNGkHv3pAU1of/448/mDVrFlWrVqVIkSJuxxERuSNeKeSstdHGmArA9mu/Tuh+RJK7k5dOUv3n6qw8tJJBzw3ySBF38aKzqP1XX0HOnDB1KlSvnuiH8bro6Gjmzp3Ljh07aNasGdmzZ3c7kojIHfNai5y1dlFcX4tI/Bw6e4gqI6qw8+ROxtYbS+2Hayf6MRYvdlrhdu2Cl16Czz+HjBkT/TBed/78ecaNG0fKlClp06YNadJ4Z81ZERFP06VVET+x6vAqDp07xKzGs6hwX4VE3fe5c848cH37Qv78sGABVEjcQ7jm4MGDjB07lpCQEMqVK5egkV0iIr4uKipKhZyILzt35RwZUmXg+Yeep2y+styV5q5E3f/cudCmDYSHQ6dO0KMHJJW+/2vWrGHBggU899xzPPTQQ27HERFJdLfTIqd/Z0W8ZMHeBQR/E8z8PfMBErWIO3PGKeAqV4bUqeG33+Drr5NGERcVFcWUKVNYsWIFLVu2VBEnIklWdHR0gleiUSEn4gXjt4znmZHPkDN9Th7KmriFyMyZULgw/Pgj/O9/sG6ds0pDUnDmzBmGDh3K5cuXad26NVmzZnU7koiIx3i8j5wxpgRQFSgB3AukAY7jjFpdBEyy1p5KUAKRJG7QmkG0m96OErlLMPWFqYnWEnf6NLzxBgwZ4iyrNX48PPFEouzaJ+zbt4/x48dTokQJSpYsmaAJMkVE/JHHLq0aY5obY/4AlgGdgLTATmAlcAoIAwYDh4wxQ40x9yUohUgS9eveX2k7rS1VH6jK3KZzE62ImzHDaYUbNgw6d4a1a5NOEWetZfny5YwbN47nn3+eUqVKqYgTkWTBIy1yxpgNwD3AMKAZsN5aa+PYLhNQHWgMbDbGtLTWjk5QGpEkpnxweX6o8QNNH22aKKs1nD4Nr78OQ4c6hdzkyZCU1oWPiIhg6tSpHD9+nNatW5M5c2a3I4mIeI2nWuSGAPdZa9+21q6Lq4gDsNaesdaOtNY+CzwJnE5QEpEkIjI6ko4zO7LzxE6MMbQq1ipRirirfeGGD3da4VavTlpFHMD8+fMJDAykVatWKuJEJNkJCgoiWwKX3blli5y1tndCg1hrNwAbEvo8EX93MfIi9cfWZ/rO6RS4uwAP3v3gHe/zzBmnL9yPP8Ijj8CkSRAamghhfVDTpk0JDg6mR48ebkcREXHFvn37OH78eLy3T+hgh8estWsTnEokGTh16RTVf6nO8gPL6V+tPy+FvnTH+5w711md4dAhePddZ7mtVKkSIayPCg4OZvXq1W7HEBFxTWgC/1NP6PQjv8aurSoi1zhy/ghlh5Zl9eHVjKk35o6LuHPnoF07Z164tGlh2TLo2TNpF3EiIpJwCS3kfgZmGGPq/PsBY0xpY8xviRNLxL9kCMrAvRnuZUajGdQtVPeO9rVoETz6KAwcCG++6cwLFxaWSEFFRCRJSVAhZ61tD3wCjDLGtAMwxhQxxkwFFgNZEj+iiO/aeHQjZ6+cJV1QOmY1nsVT+Z+67X1duuSMSC1fHgIDnUXvv/wStCa8iIjcSIJXdrDWdgfaAd8aYxYB64DCQCugSOLGE/Fdv+79ldI/lqbDjA4AdzTX2e+/Q7Fi0Ls3vPIKbNgApUsnVlIREUmqElzIGWPuAgoA0UAZYAXwoLV2qLU2JpHzifikiVsnUnVkVfJkysMnT31y2/uJiID334cnn4SLF53BDX36JI01UkVExPMSVMgZY7oCe4BXgF44rXChwFeJH03ENw1eO5i6Y+vyWM7HWNJyCbky5rqt/Wza5PR9+/hjaNoU/vgDnn46kcOKiEiSlqDpR4DOOEtxdbPWHgUwxoQDE40x2YEm1trIRM4o4jPOXTnHhws/pPL9lRlXbxzpghLedBYdDV9/7UzqmymTMy9czZoeCCsiIkleQgu5h621u6+9w1q7IHZKkhnALOD2e3uL+KiY2F4DGVJl+LsVLigwKMH72bsXmjeHJUvg+edhwAC4557ETisiIslFQket7r7B/WuB0kBwImQS8SmR0ZG0mNSC12e9jrWW+7Lcl+Aizlr44QdnWpENG+Cnn2DCBBVxIiJyZxI82OFGrLW7gJKJtT8RX3Ax8iK1Rtdi+MbhZEuXsPXvrvrrL6hVC1q3huLFnb5wzZrBHQxyFRERAeJRyBljJhtjisVnZ9bao8aY1MaYN67OMyfir05dOkXl4ZWZsXMG/ar14/2y7yd4ipEpU6BIEZg1C776CubNg7x5PRRYRESSnfj0kdsPrDDGrMdZ2WEJsNFaG3V1A2PMvcATwHNAbeAQzohWEb8UY2OoMqIK64+sZ3Td0dR7pF6Cnn/+vDO57+DBEBICCxY4C96LiIgkpvgUchFABeAFoCuQCbDGmLPAFZzVHFICBvgd6AQM15xy4s8CTACdy3QmXVA6ns6fsDlBli93phPZs8dZ6P7DDyEo4eMiREREbik+hVwnYIy19lVjzDmckalPAjmB1MAJYBuw2Fq732NJRbxg/ZH1bD22lReKvEDNhxI2J0hkJPTo4XzkzesssaXVGURExJPiU8id5J81VN8GJllrP/NcJIcx5gucS7URwG6gpbX2dBzb7QPO4aw0EWWtDfV0NkmaFu1bRI1RNciaNiu1Hq5F6hSp4/3cHTugSRNYtcqZXuTbbyFjRg+GFRERIX6jVn8DvjTGNMG5fGo9G+lvc4HC1tpHgR3AuzfZtoK1NkRFnNyuSdsmUWVEFXJlyMWiFoviXcRZC4MGOeuk7toFY8bA0KEq4kRExDviU8h1AI4AP+EUcfOMMUuMMd8aY1oaY0KMMSkTO5i1ds41AypWALkT+xgiAD+u+5E6Y+oQkiOEJS2XkDtj/H7Ujh93phVp29ZZK/WPP6BewsZEiIiI3JFbFnLW2sPW2kpALpwWudHAn0BVnOW61gDnjDFrjTE/eChnK2DmjSICc4wxa4wxbT10fEnCws+EUyl/JeY1m8fdae+O13PmzHGmFZk5E3r1cm7nur0lV0VERG5bvJfostYeMcZMBL621m4FMMakB0KAYrEfjyXk4MaYeUCOOB7qbK2dHLtNZyAKGHmD3ZSy1h42xtwDzDXGbLPWLo7jWG2BtgB5NZFXshdjYwg/E05w5mC6lutKtI0mRcCtfx0uX3ZGovbuDYUKOfPDFS3qhcAiIiJxSNBaq9baOv+6fR6nD91vt3Nwa+1N53UwxjQHqgNPWWvj7JtnrT0c+/mv2ELzCeA/hZy1diAwECA0NNRb/fzEB0VGR9Jmahum7pjKpvabyJkhJynMrX8VNm+GRo1g40bo0AE+/xzSpPFCYBERkRtItCW6EpsxpirOKNka1tqLN9gmnTEmw9WvgcrAJu+lFH9zKfISdcbU4acNP9ExrCM50sfVIHw9a6FvXwgNhT//hGnT4LvvVMSJiIj7EtQi52V9gFQ4l0sBVlhr28WuIjHYWvsskB2YGPt4CuBna+0stwKLbzt9+TQ1fqnBb+G/0ffZvrQv3v6Wzzl2DF58EaZOhapVYcgQyHHr2k9ERMQrfLaQs9Y+cIP7DwPPxn69B1APJYmXjxd/zIqDKxhVdxT1H6l/y+3nznUWtz950ukT9+qrEOCzbdgiIpIc+WwhJ5LYulfoTu2Ha/Nknidvul1EBLz/PnzxhQY0iIiIb1P7giRp64+sp8qIKpy+fJo0KdPcsojbuRNKlXKKuHbtnJUaVMSJiIivUoucJFmL9y/muV+eI2OqjBy7cIzMqTPfcFtrYfhweOUVSJkSxo+H2rW9GFZEROQ2qEVOkqQp26dQZUQV7s1wL8taLePBux+84bZnz0LTps4aqY89Bhs2qIgTERH/oEJOkpzxW8ZTe3RtitxThCUtl5AnU54bbrt6tVO8/fILdOsGCxZAnhtvLiIi4lNUyEmSE5Y7jKZFmzK/2Xyyps0a5zYxMfDVV1CypDO4YdEi6NIFAgO9HFZEROQOqJCTJMFay4iNI4iOiSZ3xtwMqTmEDKkyxLntsWNQvTq8+SZUqwbr10Pp0l4OLCIikghUyInfi4qJotWUVjSd2JSxW8bedNtff3VGoS5YAN9/DxMmwF13eSmoiIhIIlMhJ37t6pJbQ9cPpWu5rjR4pEGc20VFQdeu8NRTkDEjrFwJL78MzqIgIiIi/knTj4jfOnP5DDVG1WDJ/iV898x3dHiiQ5zbHTrkLHa/eLEzMrVPH0if3sthRUREPECFnPitHSd2sOHIBn6u8zMNCzeMc5vp053i7fJlGDbMmWZEREQkqVAhJ37n7JWzZEyVkeK5irOv0744J/qNjITOnZ0VGooWhdGjoWBBF8KKiIh4kPrIiV/ZeHQjD/V5iCHrhgDEWcSFh0O5ck4R1749rFihIk5ERJImFXLiN5bsX0LZIWUJDAgkLHdYnNtMnQohIbBpk9MK17cvpE7t5aAiIiJeokJO/MLU7VOpPKIyOdLnYGmrpRTKVui6xyMj4a23oEYNCA6GtWuhfn13soqIiHiL+siJz9t1che1x9QmJEcIMxrNIFu6bNc9Hh4ODRo4l1Bffhl69VIrnIiIJA8q5MTnPXDXAwyvNZxqD1b7z2oN06dDs2ZOi9zo0WqFExGR5EWXVsUnWWv5YMEH/Bb+GwANCze8roiLioJ33nGW2sqTB9asUREnIiLJj1rkxOdExUTRblo7flj3A1eir1A67/ULoR4+DA0bwpIl0LYt9O4NadK4FFZERMRFKuTEp1yOuswL419g0rZJdCnbhQ/Lf3jd4/PnO6s0XLgAI0ZA48bu5BQREfEFKuTEZ1yIuED1X6qzcN9Cvq36La+Gvfr3YzEx0LMndOkCDz0ECxfCww+7l1VERMQXqJATn5E6RWruzXAvI2uPpFGRRn/ff/y4s7TWrFlOC1z//lorVUREBFTIiQ/Ye2ovKQNTkjtjbkbWHnndYytXQr16cPQo9OsHL70ExrgUVERExMdo1Kq46o+jf1Dqx1K8MP4FrLV/328tfP89lCkDgYGwbBm0a6ciTkRE5Foq5MQ1S8OXUnZoWQJMAP2r9cfEVmnnzzuXUDt0gMqVnalFHn/c5bAiIiI+SIWcuGL6julUGl6Je9Ldw9JWS3nknkcA2LYNwsKcyX0//himTIG77nI5rIiIiI9SHznxuhgbQ9eFXSmUrRAzG8/8e8mtceOgZUtnTrg5c+Cpp1wOKiIi4uNUyIlXRcVEkSIgBdMbTSdtyrRkSJXh71UaevWCEiVg7FjIndvtpCIiIr5Pl1bFK6y1vDf/PeqMqUNUTBTZ02cnQ6oMHDkCTz/tFHEdOsCiRSriRERE4kuFnHhcdEw0L017iU9++4Qc6XJgcAY1LF0Kjz0Gv/8Ow4fDd99BUJDLYUVERPyICjnxqMtRl6k/rj6D1g6ic5nO9K/enwATSJ8+UL48pE0LK1ZAkyZuJxUREfE/PlvIGWM+MsZsNMasN8bMMcbce4PtmhtjdsZ+NPd2Trm5ZhObMWHrBHpX6U2Pij24dMnQvDm8+ipUrQqrV8Ojj7qdUkRExD/5bCEHfGGtfdRaGwJMA7r8ewNjzF1AVyAMeALoaozJ4t2YcjP/V/L/GFFrBB1LdGTPHihZ0lnsvnt3mDwZMmd2O6GIiIj/8tlCzlp79pqb6QAbx2ZVgLnW2pPW2lPAXKCqN/LJje07vY8+v/cBoHiu4jR+tDGzZkFoKOzfD9OnwwcfQIDP/vSJiIj4B5+efsQY8zHQDDgDVIhjk1zAgWtuH4y9L659tQXaAuTNmzdxg8rfNv21icrDK3Mp6hJ1C9Ule7ocfPIJvP8+FCkCEybA/fe7nVJERCRpcLVNxBgzzxizKY6PmgDW2s7W2jzASKBDXLuI4764Wu6w1g601oZaa0OzZcuWeCchf1t2YBllhpQBYHGLxaSzOahbFzp3hhdegOXLVcSJiHhVeLizTM7VtaytdW6Hh7ubSxKNqy1y1tqn47npz8B0nP5w1zoIlL/mdm5g4R0HkwSbsXMGdcfUJVfGXMxtOpeIv4IJqwA7dsBXX0GnTlrwXkTEq5Yvh6ZNYfduOHbMmbDzvvvgQOyFrM6d3c0nicJnL60aYx601u6MvVkD2BbHZrOBntcMcKgMvOuNfHK94xePUyhbIWY0nsHvv95D48bOnHBz5kDFim6nE3+xfft2ypcvf9199evX5+WXX+bixYs8++yz/3lOixYtaNGiBcePH6du3br/ebx9+/Y0aNCAAwcO0LRp0/88/uabb/Lcc8+xfft2Xnrppf88/v777/P000+zfv16OnXq9J/He/bsScmSJVm2bBnvvffefx7v3bs3ISEhzJs3jx49evzn8QEDBlCwYEGmTp1Kr169/vP48OHDyZMnD6NHj6Zfv37/eXzcuHFkzZqVoUOHMnTo0P88PmPGDNKmTUvfvn0ZM2bMfx5fuHAhAF9++SXTpk277rE0adIwc+ZMAD766CPmz59/3eN3330348ePB+Ddd99l+fLl1z2eO3duRowYAUCnTp1Yv379dY8XKFCAgQMHAtC2bVu2bt/KyYsn/162LyQkhN69ewPQpEkTDh48eN3zn3zyST755BMA6tSpw4kTJ657/KmnnuKDDz4A4JlnnuHSpUvXPV69enXeeustgP/83EES+Nm7fJlC+3YzLv19dP5mEvd+05eUREKqVDB3LgPq1tXPHs7P3o4dO6573O2fvYTw5e7mn8ZeZt2IU6B1BDDGhBpjBgNYa08CHwGrYj+6x94nXrLn1B4AmhVtxrJWKxjw1T089xw88IAztYiKOBG5lYuRFwG4FHmJLce2cCHygsuJ/Ju1lr/OH6d+8GNkzzWHxuf7s49gThE7TUBYmLsBJVEZa+PsUpakhYaG2tWrV7u5JnUmAAAfEklEQVQdw69Za3l/wfv0Wt6Lla1Xkj9dUZo3h4kTnZb8AQMgTRq3U4q/CQ0NRb+byce+0/vouaQnk7dPZuerO1m4byE1R9VkTds1PJbzMbfj+Z29p/bSY/xEfhmWlktr6sDFbGTMdobXjvXmRYYQzH5nw44d4euv1d/FR8X1PmiMWWOtDY1re5+9tCq+Kzommpenv8zAtQNpXaw1qc8WpsRTsH27897QsaPeH0Tkxnaf3E3PJT0ZtnEYASaANo+1ITI60u1YfulK1BXOnrNMHp+ant+mYe8fb2ACIylV6Tjvdoii6ouFCOTwP0/ImhW++QayZVMfuSRChZwkyJWoKzSe0JjxW8fzbul3KRv5MSXCDAEBMHs2PPWU2wlFxJftObWHgn0KkjIwJS+Hvsz/Sv2PXBnjnDVKbmLrsW10HzGXiT9ngc0NuHIJHno4G116nqFD60xky5YTKlWCo4chRw44eNCZzHP9emf6gDj67Il/UiEnCfLDuh8Yv3U8vSp9RfTS16n2DhQuDJMmOYOhRET+bdvxbSw/sJyWxVqSP0t+vnvmO55/6HlyZsjpdjS/Yq2l78Jx9Or/F3sXVIDjrxKY6jLP1jrJex2zExYWiDGZ/nlC9+7O59mznRnY16yBKlWc+zWfapKhQk4SpF1oOx7M+Cg/fVSakSOhXj0YMgTSpXM7mYj4ms1/babHkh6M3jSaTKkzUe+ReqQPSk/74u3j3L7g3QXpWq4rOdOrwLtW+KlDbFqeix9+MEycXAsbnYK8hQ/RqdsZ2jTLRPr0qeN+4pNPwty5/9wOCLj+tiQJKuTklvaf3k/LyS35seaPpDgfzHtNSrNmjTOn5Lvvqj+ciFxv76m9/G/e/xi3ZRzpg9Lzdqm3eePJN0gflP6mzyuYtSAflv/QOyF93IWIC3w/ZwbfDjjPocVPw1mne1u7VyJ4uW0AhR/R5WhxqJCTm9r812aqjKjChcgLzFl4ni7t4OJFZ8H7555zO52I+JKI6AiCAoOwWBbsXUDnMp15vcTr3J327ng9/3LUZU5eOknWtFkJCgzycFrftONoOK/0msevE/ITvbsemGgeKhHOe69dpEHttAQFpXU7ovgYFXJyQ8sPLKfaz9VInSI1rwf9wasNcpMnDyxYAIUKuZ1ORHzF6sOr+WjxR0THRDOt0TTyZ8nPoTcOkTrFDS753cCc3XOS5fQj566cY/ma80wfnZOfhuXizOlWpLvnGA3f2E+XjnnJm1cdkOXGVMhJnJYdWEal4ZXImTYPZbevpGv/TFSqBKNGwV13uZ1ORHzByoMr6b64OzN2ziBL6iy88eQbxNgYAkxAgou45MZay8Lta+ny3WaWTXmYmIPFCQqCWrUCadz8EtWqZCPAl6fsF5+hQk7iVOSeIjyfryWHh/RiyPxUdOwIX34JKfQTIyLAsA3DaD6pOXenuZueFXvyyhOvkDFVRrdj+TxrofuIuXzb/wInV1WCyMfJnPcQLT/cR+cOwdx9N4BmU5f4059luc7oTaOpXqA6h/dlYHX3PuzdC4MHw4svup1MRNy2eP9iAMrmK0uNgjX4otIXtAttd8tBDMmdtZaZG1azaV4xhv6Ygq1bKxGQ6iKlnt1PtzfyULFMLg0ak9umQk4A542m68KufLT4I1qk/4WJHzUkKAjmz4cyZdxOJyJusdaycN9Cui3qxqL9i6iUvxJzms4hc+rMvFXyLbfj+bRj50/yweBF/DIsLWc3VICYFJQoAQMGRtGwQRoyZnzY7YiSBKiQE6JjoukwowP9V/cn7NDPDPuxAYULw5QpkC+f2+lExC2/hf/Gu/Pf5bfw38iZPie9q/SmzeNtPHa8QtkK8WWlL8mVwb+n1ti88xyNPpjLxlmhcKYWKdKf5ukXttPzrfspHpIW/emVxKSfpmTuStQVmk5sytg/JhKydgUrp4fx/PMwfDik19USkWTHWkuMjSEwIJDtx7ez7/Q++jzThxcfe9HjAxgeuOsB3iz5pkeP4SmHTh1j8C9HWTG1MLNnp8fa2uQptpUO7fbRsXkwqVJldjuiJFEq5JK5I+ePsHDLH9w/fQ/r1+bh3XehRw80WkokmbHWMmPnDLov7k7jIo15Lew1mhVtRpNHm5AqRSqvZDgfcZ7D5w6TN1Nevxj1GmNj+GneSj777jjbF4TBhcLkzm15/31DixaW/Pl16VQ8T4VcMnX2ylkyBGXg4p/5SD9sEwcPBTJ8ODRp4nYyEfEmay1Td0yl+6LurPlzDcGZg8meLjsAKQNTejXLgr0L/GIeuYsXoUufDXw/IILLe56EgEjuL7GFtzpcok39fAQGAmj0gniHCrlkKPxMOJWHV6bYhXeY0bMFqVMH8uuvzrJ8IpK8tJnahh/W/cD9We7nxxo/0uTRJl4v4PxBdEw0/aauYNnkQsyYkIUzZ4qSJvsBGnZax6dvPUy+XEXdjijJlAq5ZGbrsa1UHlGZ4wvrs2t6cx55BKZOhbx53U4mIt4QY2MYt2Uc5fKVI3v67DQv2pyy+crSqEgjUgToT8K/bTt4mP99tY7ZY/MQcbAUgSkjeaEBtG4NZcvmwZg8bkeUZE49oZKRlQdXUmpwOU5O6MrlKb145hnDb7+piBNJDqJjovnlj18o0q8IDcY14Md1PwJQJl8ZmhVtpiLuGtbCsmVwf8XFPJw/E1O/rkaQSUfL99Zy8FAMw4dDuXJo7jfxCfrNTSbOXD5DlR/qEzFqHJe2leXNN+Gzz4jtyyEiSdnPf/xM90Xd2X5iO49ke4RRdUZRt1Bdt2P5nHW7D9Dt293snFeOLVsMQWnCCKm0gS6v38vzT92vwk18kgq5ZOLUkUxkGrGJw/vSM3AgtPHcVFAi4gOurnkKMGnbJFKlSMW4euOo9XCtv+/3NY9mf5QB1QeQN5P3LhNciYzkk2ErGTA4miOrSkB0Hh59/CKDB6elQYNUpE//hNeyiNwOFXJJ3Pe/f8+pnQX57o2niYjIwOzZULGi26lExFMioyMZtmEYny79lMkNJ1MoWyEGPTeIDKky+GwBd1Vw5mDaPt7WK8c6fBg++e4I/QZeIfpkaUzaUzxRcy3d38hHlVL3eiWDSGJQIZdEWWvptqgb3b7fSsDkNtyX1zJ9uqFgQbeTiYgnXIm6wk8bfqLnkp7sP7Of0HtDuRBxAYBMqTO5nC5+Tl8+ze6Tu3k428OkTZk20fd/8UoE3QavZP64/KxbnIuYmBxkL7yJpp3X0rXdo6RPq6H74n9UyCVB0THRvDrjNfp9nRkWjObJ0pZJEw1Zs7qdTEQ8ISomiqL9i7L9xHbCcoXRt1pfnnngGYyfdepavH+xR+aRW7BuD52/3MPv0x4h5mwZgjKd4O23oVUreOCBwol2HBE3qJBLYqJjomk4uhnjPqsEG1rQpIll8GBDKu9MzC4iXnIp8hKTtk2iYeGGpAhIQcewjuTPkp/K91f2uwLOEyIinPWi//fpDvaueQBMMNlD1tG2zZ+816ooqfWeKEmECrkk5uyZQFZ+1h023E+3bvDBB0YjrUSSkIuRFxmwegCfL/ucI+ePkD9LfsJyh9G+eHu3o/mEGSt20aVXOPsWlePEsUDuyZmXp1ot5bP/K8jjDz3udjyRRKdCLok4fvE4qzedpFOzAhzdez8jRkDjxm6nEpHEcinyEt+v+p4vln3BXxf+okJwBX6p8wthucPcjua6k+cu8u53qxk1LD1ntz8GAcEUL/8nw9/KTeXKqQkMLON2RBGPUSGXBISfCads97c5MKAPmVNZ5s41lC3rdioRSQzW2r8vlfZa3oui2YvyQdkPKJNPxcmmTdBvQBT9friCvVSWlFnDeealxXz+f49Q+P7cbscT8QoVcn5u67GtlH7rG07+PIRcuSwL5hgKFHA7lYjcqbNXztLn9z5M2jaJpa2WkiZlGja220i2dNncjuYxj+V8jJG1RxKcOfiG2xw9dZ53eq9l5pg8HN12H0FBKQgpe4ymLQ/wWoMiBAZqqRpJXlTI+bEVB1ZSsd0MLs3oT9HiF5g7PR3Zku57vEiycPryab5d+S1fr/ia05dPU71AdU5dPsU96e5J0kUcQO6MuWlUpFGcj42YtZWe3/zF1l+LwZWyBGXfwyefXaF1q1Rkzar/XiX5UiHnp6KioPGLp7g0txvP1DzP+F/SkyaN26lE5E5sPbaVEj+U4OyVs9QsWJMPyn7A4/cmgw76y5dDly4cnziSTce38Hj2YmSoUZezb3/Mz7ue4LNvT7Bv68OQIpj7y6zlzVcy8lKtwgQEaCSXiAo5P3T6bBRNGqVgz9yqvNzxPN99lZ4A356wXURu4PjF42w8upGK91WkYNaCtAxpSYuQFoTkCHE7mvd06QLz5rGsXglqhu3l7V+rM2FfQ8KrFuZKNDxSJBP13lrEF2+GkC9HKbfTivgUny3kjDEfATWBGOAvoIW19nAc20UDf8TeDLfW1vBeSu/7dOZPfNQujMsHC9K3r6F9+/RuRxKR23DswjG+XPYl36/6nlQpUnHojUOkTpGa3lV7ux3N+2bP5nTRckxfWxTWteGzo0Uh5XmKP7OTPh8UpXjxFBhTzu2UIj7JZws54Atr7QcAxpjXgC5Auzi2u2StTfL/ulpreXVYP77v+CyBl7MzdkIEtWtqRksRf/PXhb/4fOnn9Fvdj0uRl2hYuCGdy3QmdYrUbkfzOmth2TIYNCiAMbsXc+mSIUuW1Tybty2f/f4FubIXdTuiiM/z2ULOWnv2mpvpAOtWFrfF2BjqfvEtE7s2J3XqABYuSUlYcZ/91onITew5tYevV3xN4yKNea/MezyU9SG3I3ndyZMwfDgMHAhbtkCGDJbmacfR5tInPHZqHZwCqq6CNWtQvxGRm/PpasAY8zHQDDgDVLjBZqmNMauBKOBTa+2kG+yrLdAWIG9e/xqe/vz7vzD1s/bcde9pVi3KRv779MYm4i8Onj3I50s/B+DbZ76lRO4S7O+0n9wZk9c8Z9bCkiVO8TZuHFy5AmFhMHgwNBhRg/QLp0FICKyJhscfh/XroUoVmDvX7egiPs3VisAYM88YsymOj5oA1trO1to8wEigww12k9daGwo0AnobY+6PayNr7UBrbai1NjSbn8zRYS306gVTezYmf+ET7FyfXUWciJ8IPxPOy9Nf5v5v76ff6n5ExURhrXNhITkVccePO+9jDz8M5crBtGnQurVTp61YAS++COl7vgdPP/1PC9yaNc7t7t3dji/i81xtkbPWPh3PTX8GpgNd49jH4djPe4wxC4FiwO7EyuiWv86doGbL3awY/wT16sGwYfeSOvl1oRHxSyM2jqDV5FYAtCrWindKv3PTSW6TmpgYWLgQBg2CCROcBexLloShQ6FePUib9l9PePLJ61veAgLUEicSTz57adUY86C1dmfszRrAtji2yQJctNZeMcZkBUoBn3sxpkfsPHKQx6tu4dyGyjR96RhD+2ZTNxERH7f75G4iYyJ5KOtDlM5bmjaPteHt0m+TN5N/deW4E3/95RRrgwbBrl2QJQu0bw9t2sAjj7idTiRp8tlCDvjUGFMQZ/qR/cSOWDXGhALtrLWtgYeBAcaYGJzLxJ9aa7e4FTgxrNi5g3JVThOx72le+WAXfbo/4HYkEbmJnSd28vGSjxmxcQTVClRjcsPJBGcO5vtq37sdzStiYmDBAqfv26RJEBkJZcvChx9CnTroSoKIh/lsIWetrXOD+1cDrWO/XgYU8WYuT5q2aiPPV09F9ImifNpvP2+/pCJOxFdtO76Nj5d8zM9//EyqwFS8FvYa/1fy/9yO5TVHj/7T+rZ7N9x1F7z6qtP69lDyG4gr4hqfLeSSm40bocVzBbHnrjBiwnEa17jP7UgichNjNo9hwtYJvFHiDd4q+RbZ02d3O5LHxcTA/Pn/tL5FRTkDGD76CGrVUuubiBtUyPmAkVMO8XLTXGTIkIrVywMpVjSj25FE5F82Ht1Ij8U9aPBIA+oUqkOnEp1oH9o+yS9kD3DkyD+tb3v2wN13Q8eOTutbwYJupxNJ3lTIuaztZ3MY1Lkcee47x9IFGciTR98SEV+y/sh6ui/qzsRtE8kQlIGK91UEIGOqjJCEF1e52vo2YABMnuy0vpUvDz16QO3akCoJn7uIP1HV4BJrLc+9Povp31QhS4GtLFt8H7mT/pUZEb/y2szX+O7378iUKhNdynahY4mO3JXmLrdjedSRIzBkiNP6tncvZM0KnTo5c7+p9U3E96iQc0F0TAwlGs1l9ehnyF18LZsXFCFj+pRuxxIR4PdDv1P4nsKkTZmWknlKkjVtVl4Le43MqTO7Hc1jYmJg3jyn79u1rW89ezp939T6JuK7VMh5WVQUVHvhMKvHVaFw1RWsmfIEQSk1SZyI25YfWE63Rd2YvXs231b9llfDXqVh4YZux/KoG7W+tWkDBQq4nU5E4kOFnBddvAgNG8Kcqblp9tp+hnwdRkCAcTuWSLK2ZP8Sui/uzrw988iWNhufPf0ZLUJauB3LY+Lq+1ahAnzyCTz/vFrfRPyNCjkv2XP4FI9XOMiZnYXp08fwyiv53I4kkuxZa3ln/jvsPrmbLyt9SbvQdqQLSud2LI+4Ou/bwIH/jDxV65uI/9M1PU8ID4ePP3ZWvQdWbztEoWJHOL27IG/2Ws0rr7icTySZstYyb888Kg+vzJHzRzDGMKLWCPZ03MObJd9MckXc1da3+vUhTx545x3n888/w6FD8MUXKuJE/J1a5Dxh+HB4/304doxZDV+letUURF/KzRdNvuWt199yO51IsmOtZfbu2XRf1J3lB5eTK0Mudp3cRY70ObgvS9KbfPvYsX9a33btclZd6NAB2rbVqgsiSY0KOU947z04doxJQ5ZQe9B7AAyv+ylNhvRwOZhI8nMl6grlfyrPioMryJspL/2q9aNlSEtSpUhancGshUWLnL5vEyZARASUKQNdu0Ldulp1QSSpUiHnCcbA11/zyzejSZ/mIuOCKlN5xHbnfhHxOGstqw+vpniu4qRKkYqSuUvSKqQVzUOaExQY5Ha8RHX8OPz0k9P6tmMHZM4M7ds7rW+FCrmdTkQ8TYWcJ1gLr7/OEAZy5lImcl46Aq+/Dl9/rWJOxINibAyTtk3io8UfseHIBja9vIlC2QrRq0ovt6MlKmthyRKn9W3cOKf1rWRJ6NwZ6tWDNGncTigi3qLBDp7Qsyd88w1pO7YlZ8xhZ1HCb75x7heRRBdjYxi7eSwh/UOoM6YOFyIuMPT5oRS4O2n15D95Enr3hkcecRarnz7daXnbuBGWLoVmzVTEiSQ3apHzhKZNnc/vvff3ZVayZfvnfhFJVCcunqD5pObky5yPEbVG0KBwA1IEJI23N2th+XKn9W3MGLh8GcLC4McfoUEDSJvW7YQi4qak8U7na/Lmda5xXGXM9bdF5I5ExUQxatMo5uyew0/P/0S2dNlY9uIyitxThMCAQLfjJYozZ2DECKeA++MPyJABWraEl16CokXdTicivkKFnIj4jaiYKEZuHMnHSz5m58mdFLmnCCcunSBr2qyE5AhxO16iWL0a+veHX35xVoN57DFnIMMLL0D69G6nExFfo0JORPzClmNbeO6X59hzag8hOUKYUH8CNR+qSYDx/66+5887hVv//rB2rXO5tFEjp/UtNNTtdCLiy1TIiYjPioiOYO+pvRTMWpD7Mt/HQ1kfoneV3lQvUB2TBEaAb9jgXDodMQLOnYMiRaBPH2jSBDJlcjudiPgDFXIi4nOuRF3hx3U/8slvn5AiIAXbO2wnTco0TG803e1od+ziRWfQwoABsGKFs0h9gwZO69uTT2qGIhFJGBVyIuIzYmwM3638js+Wfsahc4comackXct1TRIjULdscYq3YcPg9GkoWNAZ0N6smbOElojI7fD/d0cRSTLOXjnLa7Neo0zeMvz0/E9UvK+iX19CvXIFxo93+r4tWQIpU0KdOtCuHZQtq9Y3EblzxlrrdgavCw0NtatXr3Y7hoj8S9asWQkODnY7hoiIa/bt28fx48evu88Ys8ZaG+fQJ7XIiYjP+Pebl4iI3Jz/j9sXERERSaZUyImIiIj4KRVyIiIiIn4qWQ52MMYcA/Z76XBZgeTc8Se5nz/oNdD5J+/zB70GOv/kff5w569BPmtttrgeSJaFnDcZY1bfaKRJcpDczx/0Guj8k/f5g14DnX/yPn/w7GugS6siIiIifkqFnIiIiIifUiHneQPdDuCy5H7+oNdA5y/J/TXQ+YvHXgP1kRMRERHxU2qRExEREfFTKuQSmTGmnjFmszEmxhhzwxEqxpiqxpjtxphdxph3vJnRk4wxdxlj5hpjdsZ+znKD7T6PfZ22GmO+Nf68Mvq/JOA1yGuMmRP7GmwxxgR7N6lnxPf8Y7fNaIw5ZIzp482MnhSf8zfGhBhjlsf+Dmw0xjRwI2tiu9X7mjEmlTFmdOzjK5PKz/xV8Tj/N2J/1zcaY+YbY/K5kdNT4vt3zRhT1xhjb/Y30h/F5/yNMfVjfwY2G2N+TozjqpBLfJuA2sDiG21gjAkEvgeeAQoBLxhjCnknnse9A8y31j4IzI+9fR1jTEmgFPAoUBgoDpTzZkgPu+VrEGsY8IW19mHgCeAvL+XztPieP8BHwCKvpPKe+Jz/RaCZtfYRoCrQ2xiT2YsZE10839deBE5Zax8AvgY+825Kz4nn+a8DQq21jwLjgM+9m9Jz4vt3zRiTAXgNWOndhJ4Vn/M3xjwIvAuUiv3d75QYx1Yhl8istVuttdtvsdkTwC5r7R5rbQQwCqjp+XReURP4Kfbrn4Dn49jGAqmBICAVkBI46pV03nHL1yD2FzyFtXYugLX2vLX2ovcielR8fgYwxjwOZAfmeCmXt9zy/K21O6y1O2O/PoxTxMc52acfic/72rWvzTjgqSTUGn/L87fW/nrN7/kKILeXM3pSfP+ufYRTwF72ZjgviM/5twG+t9aeArDWJso/7yrk3JELOHDN7YOx9yUF2a21fwLEfr7n3xtYa5cDvwJ/xn7MttZu9WpKz7rlawAUAE4bYyYYY9YZY76I/Y8uKbjl+RtjAoBewP95OZs3xOf7/zdjzBM4/9Ts9kI2T4rP+9rf21hro4AzwN1eSed5CX1ffxGY6dFE3nXL8zfGFAPyWGuneTOYl8Tn+18AKGCMWWqMWWGMqZoYB06RGDtJbowx84AccTzU2Vo7OT67iOM+vxk+fLPzj+fzHwAe5p//RucaY8paa294OdrX3OlrgPO7VwYoBoQDo4EWwA+Jkc/TEuH8XwZmWGsP+GODTCKc/9X95ASGA82ttTGJkc1F8Xlf8+v3vluI97kZY5oAoSStLiU3Pf/Yf96+xnmfS4ri8/1PATwIlMf5+7fEGFPYWnv6Tg6sQu42WGufvsNdHATyXHM7N3D4DvfpNTc7f2PMUWNMTmvtn7F/pOJqOq4FrLDWno99zkygBDfpV+hrEuE1OAiss9buiX3OJJzXwC8KuUQ4/yeBMsaYl4H0QJAx5ry11i8G/iTC+WOMyQhMB9631q7wUFRvis/72tVtDhpjUgCZgJPeiedx8XpfN8Y8jVPwl7PWXvFSNm+41flnwOkTvTD2n7ccwBRjTA1r7WqvpfSc+P78r7DWRgJ7jTHbcQq7VXdyYF1adccq4EFjzH3GmCCgITDF5UyJZQrQPPbr5kBcLZThQDljTApjTEqc/0qT0qXV+LwGq4Asxpir/aIqAlu8kM0bbnn+1trG1tq81tpg4C1gmL8UcfFwy/OP/b2fiHPeY72YzZPi87527WtTF1hgk85kprc8/9hLiwOAGonVP8qH3PT8rbVnrLVZrbXBsb/3K3Beh6RQxEH8fv4nARUAjDFZcS617rnjI1tr9ZGIHzitTQeBKzgd+GfH3n8vzqWkq9s9C+zA6RfT2e3ciXj+d+OM1NsZ+/mu2PtDgcGxXwfivJltxSlevnI7t7dfg9jblYCNwB/AUCDI7ezePP9rtm8B9HE7tzfPH2gCRALrr/kIcTt7Ipz7f97XgO44f7DBGeQ0FtgF/A7kdzuzl89/Xuzfhavf8yluZ/bm+f9r24U4I3hdz+3F778Bvor9u/cH0DAxjquVHURERET8lC6tioiIiPgpFXIiIiIifkqFnIiIiIifUiEnIiIi4qdUyImIiIj4KRVyIiIiIn5KhZyIiIiIn1IhJyIiIuKnVMiJiNwmY8wDxphIY0y3f93fzxhzzhgT6lY2EUkeVMiJiNwma+0uYDDweuzaiRhjugCtgFo26awjKSI+Skt0iYjcAWNMDpy1FfsC24CBwAvW2jGuBhORZCGF2wFERPyZtfaIMaY38CbOe+prKuJExFt0aVVE5M7tBFIBy62137sdRkSSDxVyIiJ3wBhTERgALAdKGWOKuhxJRJIRFXIiIrfJGPMYMAlnwEN5IBzo6WYmEUleVMiJiNwGY8wDwExgDvCqtTYC6AY8a4wp62o4EUk2NGpVRCSBYkeqLsNpgatirb0Se38gsAk4Za0t6WJEEUkmVMiJiIiI+CldWhURERHxUyrkRERERPyUCjkRERERP6VCTkRERMRPqZATERER8VMq5ERERET8lAo5ERERET+lQk5ERETET6mQExEREfFT/w/+C9cbCnNMGAAAAABJRU5ErkJggg==\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def plot_newton(f, dx, x_0, atol, ax, inset=True, ixmin=3.0, ixmax=3.2, \n", " iymin=-0.1, iymax=0.1, zoom=8, loc0=1, loc1=3, loc2=2, maxiter=100, resfct=100, flabel=''):\n", " x_n = [x_0]\n", " y_n = [f(x_0)] \n", " \n", " # Newton iteration\n", " i = 0\n", " # iterate until we hit break either as we hit tolerance or maximum number iterations\n", " while 1:\n", " # approximate gradient - computed using a dx value - note comments below on quasi-newton\n", " dfdx = (f(x_n[-1]+dx) - f(x_n[-1])) / dx\n", " # Newton-Raphson update\n", " x_zero = x_n[-1] - ( f(x_n[-1]) / dfdx )\n", " x_n.append(x_zero) \n", " y_n.append(0.)\n", " if abs(x_n[-1]-x_n[-2]) < atol:\n", " break\n", " x_n.append(x_zero)\n", " y_n.append(f(x_zero))\n", " i = i+1\n", " if i >= maxiter:\n", " break\n", " \n", " # the iteration results\n", " ax.scatter(x_n, f(np.array(x_n)), marker='x', color='red', s=30)\n", " \n", " # the convergence pattern\n", " ax.plot(x_n, y_n, color='green', ls='--')\n", " \n", " # the function\n", " x = np.linspace( np.min(x_n), np.max(x_n), resfct)\n", " ax.plot(x, f(x), 'b')\n", " \n", " # zero line\n", " xlim = ax.get_xlim()\n", " ax.plot([xlim[0], xlim[1]], [0., 0.], 'k--')\n", " ax.set_xlim(xlim)\n", "\n", " # zoomed inset\n", " if inset:\n", " axins = zoomed_inset_axes(ax, zoom, loc=loc0)\n", " axins.scatter(x_n, f(np.array(x_n)), marker='x', color='red', s=30)\n", " axins.plot(x_n, y_n, color='green', ls='--')\n", " axins.plot(x, f(x), 'b')\n", " axins.plot([ixmin,ixmax],[0.,0.], 'k--')\n", " axins.set_xlim(ixmin, ixmax)\n", " axins.set_ylim(iymin, iymax)\n", " axins.get_xaxis().set_visible(False)\n", " axins.get_yaxis().set_visible(False)\n", " mark_inset(ax, axins, loc1=loc1, loc2=loc2, fc=\"none\", ec=\"0.5\")\n", " \n", " ax.set_xlabel('$x$', fontsize=16)\n", " if not flabel:\n", " fl = '$f(x)$'\n", " else:\n", " fl = flabel\n", " ax.set_ylabel(fl, fontsize=16)\n", " ax.set_title(\"Newton's method iteration\", fontsize=20)\n", "\n", "\n", "# case 1\n", "def f(x):\n", " return x - np.exp(-x)\n", "\n", "fig, ax1 = plt.subplots(figsize=(10,6))\n", "x0 = -1.\n", "plot_newton(f, 1.e-3, x0, 1.e-2, ax1, loc0=4, loc1=2, loc2=1,\n", " zoom=4, ixmin=0.4, ixmax=0.65, iymin=-0.2, iymax=0.2,\n", " flabel=r'$f(x) = x - \\mathrm{e}^{-x}$')\n", "\n", "# case 2\n", "def f(x):\n", " return 2*x + x*np.sin(x-3) - 5\n", "\n", "fig, ax1 = plt.subplots(figsize=(10,6))\n", "x0 = 2.0\n", "\n", "plot_newton(f, 1.e-3, x0, 1.e-2, ax1, loc0=4, loc1=2, loc2=1,\n", " zoom=4, ixmin=2.7, ixmax=2.9, iymin=-0.2, iymax=0.2,\n", " flabel=r'$f(x) = 2x + x\\sin(x-3) - 5$')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This algorithm has been implemented in the `scipy.optimize` module:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.567143290409784\n" ] } ], "source": [ "def f(x):\n", " return x - np.exp(-x)\n", "\n", "def dfdx(x):\n", " return 1 + np.exp(-x)\n", "\n", "x0 = -1. # initial guess\n", "print(sop.newton(f, x0, dfdx))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 4.5: \n", "\n", "For $2x + x \\mathrm{sin}(x-3) = 5$, use $a$ from the subinterval $x \\in(a,b)$ you found in Exercise 4.2 as initial guess $x_0$ and complete the code below to implement a Newton algorithm. Compare the result to [scipy.optimize.newton](http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.newton.html)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": false }, "outputs": [], "source": [ "def newton(f, x0, dfdx, atol=1.0e-6):\n", " \"\"\" Function to implement the Newton-Raphson method\n", " \n", " f is the function we are trying to find a root of\n", " \n", " and dfdx is another function which return the derivative of f\n", " \"\"\"\n", " x = [x0]\n", " fevals = 0\n", " while True:\n", " x.append( ...............\n", " fevals += ...................\n", " if abs(x[-1]-x[-2]) < atol:\n", " print('Newton (analytical derivative) used', fevals, 'function evaluations')\n", " return x[-1]\n", "\n", "\n", "def f(x):\n", " return # complete ...\n", "\n", "def dfdx(x):\n", " return # complete ...\n", "\n", "x0 = 0. # initial guess somwhere in interval\n", "print(newton(f, x0, dfdx))\n", "print(sop.newton(f, x0, dfdx))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## (Quasi-) Newton with approximate derivative \n", " \n", "The implementation of the Newton method above assumes that the derivative $f^\\prime(x)$ is readily available. \n", "\n", "[Although note that this was not the case in the plotting function `plot_newton` where we computed an approximation to it].\n", "\n", "For many problems, however, the derivative is not easy to express analytically or we just don't want to bother working it out and writing a function to implement it. \n", "\n", "In these cases $f^\\prime(x)$ can be replaced by a difference approximation such as\n", "\n", "$$ f'(x) \\approx \\frac{f(x+\\Delta x) - f(x)}{\\Delta x}. $$\n", "\n", "Use of an approximate derivative renders the corresponding root finding algorithm a co-called *quasi-Newton* method.\n", "\n", "\n", "Note that since we only have an approximate derivative we cannot in general expect this method to converge as well as Newton when we supply it with an exact derivative. This manifests in a reduction from perfect quadratic convergence - but still generally closer to quadratic that linear!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 4.6: \n", "\n", "Extend the Newton algorithm to compute $f^\\prime(x)$ using a finite difference approximation. Compare the result to `scipy.optimize.newton`" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": false }, "outputs": [], "source": [ "def quasi_newton(f, x0, dx=1.0E-7, atol=1.0E-6):\n", " \"\"\" Function to implement quasi-newton\n", " \n", " f is the function we are trying to find a root of\n", " \"\"\"\n", " x = [x0]\n", " while True:\n", " ......\n", " ......\n", " if abs(x[-1]-x[-2]) < atol:\n", " return x[-1]\n", "\n", " \n", "def f(x):\n", " return # complete ...\n", "\n", "x0 = 0.\n", "print(quasi_newton(f, x0))\n", "print(sop.newton(f, x0))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Secant Method\n", "\n", "The Secant method replaces the local derivative in the Newton method by a difference approximation based on two consecutive $x_n$. It follows that\n", "\n", "\\begin{equation}\n", "f'(x_n) \\approx \\frac{f(x_n) - f(x_{n-1})}{x_n - x_{n-1}}\n", "\\end{equation}\n", "\n", "which leads to the secant method\n", "\n", "\\begin{equation}\n", "x_{n+1} = x_n - f(x_n) \\left ( \\frac{x_n - x_{n-1}}{f(x_n) - f(x_{n-1})} \\right )\n", "\\end{equation}\n", "\n", "The algorithm can be visualized as follows:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def plot_secant(f, x_0, x_1, atol, ax, max_labels0=1, inset=True, ixmin=3.0, ixmax=3.2, \n", " iymin=-0.1, iymax=0.1, zoom=8, loc0=1, loc1=3, loc2=2, maxiter=100, resfct=100, flabel=''):\n", " # variables to store to convergence pattern, initialise with two initial guess values\n", " x_n = [x_0, x_1] \n", " y_n = [f(x_0), f(x_1)] \n", " x_its = [x_0, x_1]\n", " # iterate secant method and store iteration convergence pattern\n", " i = 0\n", " # iterate until we hit break either as we hit tolerance or maximum number iterations\n", " while 1: \n", " # Secant update\n", " x_zero = x_its[-1] - f(x_its[-1])*( (x_its[-1] - x_its[-2]) / (f(x_its[-1]) - f(x_its[-2])) )\n", " x_n.append(x_zero) \n", " y_n.append(0.)\n", " x_its.append(x_zero)\n", " if abs( x_n[-1] - x_n[-2] ) < atol:\n", " break\n", " x_n.append(x_zero)\n", " y_n.append(f(x_zero))\n", " i = i+1\n", " if i >= maxiter:\n", " break\n", "\n", " # the iteration results\n", " ax.scatter(x_its, f(np.array(x_its)), marker='x', color='red', s=30)\n", " \n", " # the convergence pattern\n", " ax.plot(x_n, y_n, color='green', ls='--')\n", " \n", " # the function\n", " x = np.linspace( np.min(x_n), np.max(x_n), resfct)\n", " ax.plot(x, f(x), 'b')\n", "\n", " # zero line\n", " xlim = ax.get_xlim()\n", " ax.plot([xlim[0], xlim[1]], [0., 0.], 'k--')\n", " ax.set_xlim(xlim)\n", "\n", " # zoomed inset\n", " if inset:\n", " axins = zoomed_inset_axes(ax, zoom, loc=loc0)\n", " axins.scatter(x_its, f(np.array(x_its)), marker='x', color='red', s=30)\n", " axins.plot(x_n, y_n, color='green', ls='--')\n", " axins.plot(x, f(x), 'b')\n", " axins.plot([ixmin,ixmax],[0.,0.], 'k--')\n", " axins.set_xlim(ixmin, ixmax)\n", " axins.set_ylim(iymin, iymax)\n", " axins.get_xaxis().set_visible(False)\n", " axins.get_yaxis().set_visible(False)\n", " mark_inset(ax, axins, loc1=loc1, loc2=loc2, fc=\"none\", ec=\"0.5\") \n", " \n", " ax.set_xlabel('$x$', fontsize=16)\n", " if not flabel:\n", " fl = '$f(x)$'\n", " else:\n", " fl = flabel\n", " ax.set_ylabel(fl, fontsize=16)\n", " ax.set_title('Secant method iteration', fontsize=20)\n", "\n", "\n", "# case 1\n", "def f(x):\n", " return x - np.exp(-x)\n", "\n", "\n", "x0 = -1.\n", "x1 = x0+0.75\n", "fig, ax1 = plt.subplots(figsize=(10,6))\n", "plot_secant(f, x0, x1, 1E-3, ax1, loc0=4, loc1=2, loc2=1,\n", " zoom=4, ixmin=0.4, ixmax=0.65, iymin=-0.2, iymax=0.2,\n", " flabel=r'$f(x) = x - \\mathrm{e}^{-x}$')\n", "\n", "# case 2\n", "def f(x):\n", " return 2*x + x*np.sin(x-3) - 5\n", "\n", "\n", "fig, ax1 = plt.subplots(figsize=(10,6))\n", "x0 = 2.\n", "x1 = x0+0.1\n", "plot_secant(f, x0, x1, 1E-3, ax1, loc0=2, loc1=3, loc2=4, inset=True,\n", " zoom=4, ixmin=2.7, ixmax=2.85, iymin=-0.35, iymax=0.1,\n", " flabel=r'$f(x) = 2x + x\\sin(x-3) - 5$')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 4.7: \n", "\n", "For $2x + x \\mathrm{sin}(x-3) = 5$, use $a$ from the subinterval $x \\in(a,b)$ you found in Exercise 4.2 to find $x_0 = a$ and $x_1 = a+0.1$ and complete the code below to implement a Secant algorithm. Compare the result to `scipy.optimize.newton`" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": false }, "outputs": [], "source": [ "def secant(f, x0, x1, atol=1.0E-6):\n", " \"\"\" Function to implement the secant method\n", " \n", " x0 and x1 are the two required guesses\n", " \n", " f is the function we are trying to find a root of\n", " \"\"\"\n", " x = [x0, x1]\n", " while True:\n", " dfdx = .....\n", " x.append(.......\n", " if abs(x[-1]-x[-2]) < atol:\n", " return x[-1]\n", "\n", "def f(x):\n", " return 2*x + x*np.sin(x-3) - 5\n", "\n", "x0 = 0.\n", "x1 = x0+0.1\n", "print(secant(f, x0, x1))\n", "print(sop.newton(f, x0))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Potential convergence Issues\n", "\n", "It's important to understand the ways some of the methods we've introduced can go wrong, and again to emphasise the value of a good starting guess.\n", "\n", "Let's start by illustrating the basic concept of Newton root-finding methods for a well-behaved function\n", "\n", "$$ f(x) := x^4 - 5. $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's first reillustrate the basic concept of Newton root-finding methods for a well behaved function\n", "\n", "\\begin{equation}\n", "f(x) = x^4 - 5\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def f(x):\n", " return x**4 - 5\n", "\n", "fig, ax1 = plt.subplots(figsize=(10,6))\n", "x0 = 4.0\n", "plot_newton(f, 1.e-8, x0, 1.e-7, ax1, loc0=2, loc1=3, loc2=4, zoom=5,\n", " ixmin=1.45, ixmax=1.85, iymin=-5, iymax=15, flabel=r'$f(x) = x^4 - 5$')" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "We've said several times now that the convergence of many algorithms often depends on the initial values provided to them. \n", "\n", "Complex equations, or systems thereof, provide plenty of situations that prevent convergence all together, lead to slow convergence, or cause convergence to an undesired root (e.g. one that is far from, and not the closest to, the initial guess). \n", "\n", "Their solution strongly depends on having a *good* initial guess. \n", "\n", "For example,\n", "\n", "$$ f(x) = x\\, \\sin(\\pi x) - e^{-x}, $$\n", "\n", "provides for ample pitfalls, in particular for gradient-based methods (e.g. Newton and Secant)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "We will illustrate these convergence issues below. \n", "\n", "\n", "They mostly fall into one of three categories:\n", "\n", "\n", "1. Multiple roots in the vicinity - the algorithm converges to one of them, but this \"one\" could change with only slight changes to the initial guess.\n", "\n", "\n", "2. Nearly singular/numerical overflow - the local gradient at guess $x^{(k)}$ is near zero, so that $x^{(k+1)}$, the intersection of the local gradient approximation with the $x$ axis is beyond the representable range. Even if we don't get overflow, we can still jump to a location a long distance away from our initial guess and end up converging to the wrong root.\n", "\n", "\n", "3. Oscillations - the algorithm bounces back and forth between (near) identical $x^{(k)}$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Multiple roots\n", "\n", "For many functions multiple roots exist, and the algorithm depends on and can be sensitive to the initial guess.\n", "\n", "Let's see an example where we choose two initial guesses (0.0 and 0.1) and visualise how this relatively small difference leads to convergence to different roots." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def f(x):\n", " return x*np.sin(np.pi*x)-np.exp(-x)\n", "\n", "fig, ax1 = plt.subplots(figsize=(10,6))\n", "x0 = 0.0\n", "plot_newton(f, 1.e-8, x0, 1.e-7, ax1, inset=False, flabel='$f(x)= x \\mathrm{sin}(\\pi x) - \\mathrm{e}^{-x}$')" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def f(x):\n", " return x*np.sin(np.pi*x)-np.exp(-x)\n", "\n", "fig, ax1 = plt.subplots(figsize=(10,6))\n", "# a small perturbation to the initial guess\n", "x0 = 0.1\n", "plot_newton(f, 1.e-8, x0, 1.e-7, ax1, inset=False, flabel='$f(x)= x \\mathrm{sin}(\\pi x) - \\mathrm{e}^{-x}$')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see from the first plot that this problem has roots at just under 0.6 and just over 0.8. The initial guess of 0 leads to convergence of the Newton iteration to the larger root, whereas a slightly higher initial guess of 0.1 leads to the smaller root!\n", "\n", "We confirm this behaviour is not a product of an issue with our implementation, and print the two actual root values, using calls to the SciPy function below." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.8191177934425945\n", "0.578262577864515\n" ] } ], "source": [ "def f(x):\n", " return x*np.sin(np.pi*x)-np.exp(-x)\n", "\n", "x0 = 0.0\n", "print(sop.newton(f, x0))\n", "x0 = 0.1\n", "print(sop.newton(f, x0))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Nearly singular/numerical overflow\n", "\n", "In this case the gradient $\\,f'(x^{(k)})\\,$ is close to zero, so that the new iteration value, $x^{(k+1)}$, is orders of magnitude offset, perhaps too big even to be representable on our finite computer ([*overflow*](https://en.wikipedia.org/wiki/Integer_overflow)).\n", "\n", "We see this with the following example." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def f(x):\n", " return x*np.sin(np.pi*x)-np.exp(-x)\n", "\n", "x = np.linspace(-1, 2, 100)\n", "y = f(x)\n", "\n", "fig, ax1 = plt.subplots(figsize=(12, 6))\n", "\n", "ax1.plot(x, y, color='b', zorder=0)\n", "xs = [0.57, 0.83, -0.27]\n", "texts = ['$root_I$', '$root_{II}$', '$nearly singular/overflow$']\n", "for i in range(len(xs)):\n", " ax1.scatter([xs[i]], [f(xs[i])], marker='x', color='r', s=60)\n", " ax1.text(xs[i]+0.03, f(xs[i])-0.15, texts[i], fontsize=16)\n", "xlim = ax1.get_xlim()\n", "ax1.plot([xlim[0], xlim[1]], [0., 0.], 'k--', label='$y(x)=0$')\n", "ax1.set_xlim(xlim)\n", "ax1.set_xlabel('$x$', fontsize=16)\n", "ax1.set_ylabel('$f(x)= x \\mathrm{sin}(\\pi x) - \\mathrm{e}^{-x}$', fontsize=16)\n", "ax1.set_title('Near singularity/overflow example', fontsize=20);" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def f(x):\n", " return x*np.sin(np.pi*x)-np.exp(-x)\n", "\n", "fig, ax1 = plt.subplots(figsize=(10,6))\n", "x0 = -0.2\n", "plot_newton(f, 1.e-8, x0, 1.e-7, ax1, inset=False, maxiter=100, resfct=1000,\n", " flabel='$f(x)= x \\mathrm{sin}(\\pi x) - \\mathrm{e}^{-x}$')" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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wDGM7Z8UKqMookLTCzQu1kSOhV69wwg10W1+fLl5oTLgZhmEYhlGW+noVNSGordWWUpC+H6gfU//+2l80hHDr109v9+kDGzemixcaE26GYRiGYZTlqKN03teyZelj1dbC6NEqkNK2lPLCbcAALShIm9rMddz69AnTjSEkJtwMwzAMwyhJYyO8/rrefvPN9PFqa2HYMBg8OJxwC+W41ddnHbe+fc1xMwzDMAyjizFnTvb27Nnp4+UKt9Wr08Vav17ny/Xpo65bGsetuVl/+vTR+5YqNQzDMAyjy/H++9nbH36YLlZjo4qtoUPDOW79+oGIbtOkNjdt0m3v3rrt29dSpYZhGIZhdDGWLNHtkCEwf366WF6oDR4cTrj5OWlphZYXbr166dYcN8MwDMMw2oWWFnjtNWhtTR/LdyfYY4/s7aTkFhNUQrilWb5j82bdmuNmGIZhGEa7cumlcNBB8Ne/po9VW6sVmyNHhhNu/fuHm+MW2nHzws0cN8MwDMMw2oXnn9ftzJnpY/ligqFDwwgtyLaV2rRJ3cGk1Ne3FW4bNyZ3GfNTpea4GYZhGIZRcZyDuXP1dm5f0KSsWqWibehQve1c8li5ws0vu5FGHG3YoAILslsvwOKSnyr1jlua3zc0JtwMwzAMYxtj1arsema5fUGTkuu4NTamE1q+afuAAVnhlmZe2saN2eU70grBQqlSyAq6zkCXEG4iUi0ir4nIw5n740XkJRH5UETuE5EeHT1GwzAMw+gsLFyo2x131L6gaVm1SitKhw7N3k9KIcctlHDzjlto4daZ0qVdQrgB/w28m3P//wG/cM7tDqwBvtQhozIMwzCMgDzyCCxenD5Oba1uJ05Uh6uhIV28ujotThg8WO+nqQQNLdw2bQov3PwcN79N+/qFpNMLNxEZC5wC/D5zX4Bjgfszp/wR+ETHjM4wDMMwwnD//XDqqXDxxeljeeG25566TeOQOZet3PRFAGmElhdu/fpVznFLGi9/jpsXbpYqjceNwDcBXyMyFFjrnGvO3F8E7NARAzMMwzCMUDz7rG5DtJTyQm3iRN2uXJk8VkMDNDXpnDQv3Lz4SsL69SqwqqrSC7fWVnXJctddg3CpUnPcYiIipwIrnHOv5u4ucGrBeg8ROV9EXhGRV1amedcahmEYRoXxraTefVcLANLgHbcJE9reT0JuajOEcNuwISvY0go374Tl9haF5FWl+anSnj3bPk9noFMLN+AI4HQRqQHuRVOkNwKDRKRb5pyxwJJCD3bO3eqcm+ScmzR8+PD2GK9hGIZhJMI7bc3NsHRpuli1tTofbdQovZ/Guwgt3DZuzDpjaYWbXxzXC7a0qU1LlabEOXelc26sc24c8GngSefcZ4GngE9lTvsC8GAHDdEwDMMwUuMc1NRkU5vLl6eL59dd88UEfmmQJOS2qAol3PKX7+gswi0/VeodN0uVpudbwGUiMhud83ZbB4/HMAzD2A655x4tKkhLfb2mR/fZR++nFW7r1sGgQSq2ILt2WhL8Y0M6bqGKCSoh3Lp3h+rqMPEqQbfyp3QOnHPTgemZ23OBj3bkeAzDMIztm3nz4DOf0dtpV9b3c9D23lt7i6YVbnV1KrL69NEigDTCLTdV2q2biplQwq1nTxBJ75CFTJX6GLnxzHEzDMMwjC7Oiy9mb6edk+arQPfaS7dphdv69eq2ieg2hHDz7l3//umW79iwISu0RFQcJS0mqITj5tOkYMUJhmEYhrHNMGdO9vbrr6eL5R23HXZQgZS224F33CC9cPMizc9H698/nOMGKraSCiMv3EIVE+QLt86YKjXhZhiGYRgJyBVuoRy3YcN0blqaYgLIOm6QXrj5NdFyK0FDLZgLKpRCLd/h56elEW6WKjUMwzCMbZB58+Dgg/X2koKLUkXHO27DhmlrqXXr0sUL6bjlpyPTCC0fL5Rw84IqX2ylmeNmqVLDMAzD6CRMnQqXXBIm1ooVsNNO2nw9rePmHbaBA9MLt9xOBxBGuIlkRUxo4ZZWaPkYIeIVS5Wa42YYhmEY7UxLC5xyCtx8M8ydmz7eqlXqkI0Zk95xq6vTVGR1dXrhlrt8B4RJlfbpo+INVNh4Fy4uznVux82KEwzDMAyjk7BgQfb2P/+ZLlZra1a4jRoFy5ali1dXl3XI0gq3/CrQfv3CdTqAdEKrsVFfu9COmxdYIeLlisCqKp03Z8LNMAzDMNqZefOyt31f0KSsW6cOnu9OsGZNuniVEG6+CrRPn84zJy1/vlzaeJV23Hw8S5UahmEYRjvj06M9esCiReli5VaBDh6cvgq0kHBLuqivF0feJevTJ3lq08erVBWov91ZHLdCwq1nT3PcDMMwDKPdmTtXV/4/9FBYuDBdrNwq0NDLdwwcqI3m04ojL0B691bHqLU1WbzcBXN9vLQOWa44ShtPRNOZnpCp0rTxKoEJN8MwDKPT8tprMGUKrF6dPtayZTByJIwbl164+fEMHqw/DQ3p0pH5y3f4fUnIT0f6bZr0ZijhFroKdPPmbNus3HhpRG8hx81SpYZhGIYRgQsvhOnT4a670seqrYXhw7UKdOnSdP1FvagaOFAdN0jnuuWmSn2KM2l6M99x86IrabxCxQlJHbxCqc20QjCkQ1Zsjps5boZhGIYRgZoa3T71VPpYtbWa2hw6VFORaVb/98JtwAB13CCccAshtHLjeCES0nGDZGKmkOOWNlWaKwJ97CRjc654PHPcDMMwDKMMGzZkm63nVoQmxQu3IUP0fpr0a65w845bmsrS9euzqdLQwi1tvA0btp6TBsnEViU6HYRy3JqadJsv3Kw4wTAMwzAi4MXa8OHqvKVJbUJ44SaiS24MHKj7kjpuTU3qAPp0pN/6HqFxCZ0q3by5reOWZs5cMcetqUmXV4lLSMfNC7cePcLEqxQm3AzDMIxOiRduxx6rQilNKrK5WR2xkMJtwAAVb94pS5p69YIq5Jy03DhpixPyXa00jlux5Ttyj6UZm4+XJFZjo24LCTdLlRqGYRjbJCtXwoEHwrPPpo+1eLFuDz9ct7mdD+Li05hDhoQVbhBOuOULrTSOW3V1dokML7TSOG6FhFuSeMUcN0ieeg3luBUTbpYqNQzDMLZZ/vQneP11+Pzn08fya6Xtuadu/aK3SfCdCAYNCi/cfIeCUMItbVVpfjFBGgfPubCOW7E5bhDecYubWvfCLXdNuNx4nQUTboZhGEYwpk/X7YoVYeakDRgAO+yQvZ+UQlWgoYVb0n6goYsJQgo3L2YqmSoN7bj17q1LlTQ3x4tVynGzVKlhGIaxTeLbSuVWhCZl5crs8h0QTrj16qWuStIFbn08nyLt0UPjhXbc0qRKQ1WBhk5tFluAN/dY3HiFHLck8aw4wTAMw9iucE4LCnxqM20j99x11yBMqnTgwGxBQVKHDLZelLZ//3DCLe2ctJCOW3sIt0rMcct9rqhYcYJhGIaxXbFypbpExx+v9737libesGHqZg0YEM5xgzDCLVcc9esXLlVaXa1iJE3nhFzHrTMJNy+AQqVKQzpuVpxgGIZhdHpaW+Hoo+GGG9LHWrRItx/9qG7TpkpXr866bcOGpRNu3nHzwm3AgHSp0g0b2jpu/fqFc9xAYydNlRbrdNAZHLLNm1WIV+WojzSp0ko4boWKExoa0s/ZDIUJN8MwjO2YV16BZ56Bb30r3TppoA4ZwPjxenH395OSWwAweHD6llKQXSy3MzluXgDlpzdDpUqrqpI7eJUQbvkOWWd33Hw8f7yjMeFmGIaxHTNtWvb2O++ki+UdseHD9WfFiuSxnGsr3AYOzLpmSVi3Ti/I3p0ZMCCscEsjBAs5bn36hCtO8PE6q3BL67hVujjBv2c6S7rUhJthGMZ2zJw52dvvvpsulnfYhg+HESPSCbfNm7UFkq/cTJvazO0FCno7aTzfoipfaKVp4g5txVbfvuEctzTjK1UFmnSOW2jHrdLFCSbcDMMwjE7DvHk6J61XrzDCrbpaF7lNK9y8e+XFVlrHLX9OWgiHLDde797hWlT526GKE9KMr5BwS5t6DSW0WlpUQLdHcQJkHbmOxoSbYRjGdsy8ebDrrjB2bLbFVFL88h1VVeq6pZnj5kVVbjFBGuGWv3xHmlSpT2GGdNy6dWs7KT5kcYIfXyjhBioEO3qOW6EK1dz7ceMVK07wQs7muBmGYRiJuOQSOP309Kkb52DhQth5Zxg1CpYtSxevtjZbBRqqmCDXcaurS17ZV8xxSxKvkEOWVMj4eKGEVuh4oYVbqTlpSYVbfrykDlkxx82Em2EYhpGYTZvg5pvhH/+AqVPTxVq7VlNNI0aEEW51ddmqzYEDVRi1tCSLlZ8qHTBARVbSJTc2bNjaIXMu2cKqoVObIYVWS4sKjEKp0lBz3NLGy4/lhVHcv0Wh9llp4hUrTjDhZhiGYSTmxRezt19/PV0sPwctlHBbvz6b2hw0SLdJCwAKzXFLEy8/VZpmUdpic9w2bUru4OULt6Sp0kJLi/j7IR23NMUO+UJLRPfFFUbFHLekQsscN8MwDCM4s2frtn9/eO21dLFyq0BHjVIHLk36NXf5Di/ckqZL8zsd+G3SeW75qdI0wq3QHLfevdM5eKGElhdTlVwOBJJ3EyjkuIGKo1COm79vws0wDMPocObO1cnTxx6bvqVUruM2YoTeTlNQkNt4Pa1wy3fc/DZkqhTSOW6F4iVxoTZtKuy4hRqbvx9auCURqYXmuCWNVynHzYoTDMMwjGDMm6fFBDvumL4KNNdxGzxYb69Zkzxe/oK5EE64ebcsTaVl6FRpqLZSxRy35ub4YqFYqrRXr+QOGRR2tZIIt1KOW9zfNfQcN3PcDMMwDABuvRV23x1mzkwfa/58FW477KBpw6RCBrKdDoYNSy/cWlsLz3FLmtr0wq1fP916IZL0920vxy1pvELCLUk8f34oh2zzZhUuVXlqIU28fKGVNF4pNxDiCy1fnNDlHTcRObY9BmIYhrGt8vvf69y03/0ufazly3U+2g476P00rltdnV7kevaEIUN0X1Lh5gVVKMetrk4dsupqvZ/GcWttVScq9By3/OIESO64FZqTlvtcUSmWPkzjuIVKbYaOV2wdNy+8kqRKu3XbWqR2OeEG3CwiJ+fuEJGzKjQewzCMbYr167WRO8ALL6SPt2KFzkcLIdzWrcsKrLSOW34xQdo5afktqrxISjNhvz1SpaEcNy9uQokZL4ziVr2GFm7F5rglSZUW+12rqlSAJUmV5qdJ/dj88c5AtwjnnAA8IiK9gUXAL4Bq4C+VHJhhGMa2wJw5erHcfXd4+22dt9QtyidvATZs0J8RI3ReGqQvJvBCywu31auTx4JsPJ/iTCPcfCxI57gV63QA6YRbrgBJU5zQXsINNB1YSJwUo5RwSyJkQgpB//yFUq9JhGBj49ZpUh8r9/k6mrKOm3NuCfBF4C7g78CNzrlDKj0wwzCMbQFf+Xn88bo46pIlyWN5kTZihM5LA1i1Knm8XOHWv786FWkdN++S9eql63OFctzSzHErtO5aWuHWu3fblFro4oTQ/TaTxgsptFpaVDgWm+MWavmONPG6guMWZY7bT4BHgR8By1G3zTAMw4jAnDm6nTxZt/PnJ4/ll+8YOTLbWiqNcMtNlVZVaUFBqFSpiLpuSYsJcpcWgawwSuO4hRRuubHSxHOu8Bw3L27iCq1yjluSAoBKL98BydZxKyXcksQr5kZ2OeEG9Af2dc79ADge+JqI/Gdlh2UYhtFxPPecpg6vuSZ9rPnzVRDtt5/eX7AgeSzvuA0bpheTfv3COW6QrvF6flN40PGFctyqqlQchUqVppkzl1+hCskdt+ZmLZ7IF25JHbJiwq0zOG6lhFuaVGkxsbXdOm7Ouf9yzq3M3F6Fznk7t8LjMgzD6DDuu0+rIW+5JXlTc4+vAt1xR72fRrj5Ck0/H23o0HCOG6hQSiq08h03UHEUSrj5eKFaVHnxEKqYIKlwCy20KuG4hV6+I+ScNP/YQuPbboVbPs65dcDHKjAWwzCMTsGTT+p26VKoqUkXa/lyTW327as/Pt2ZBJ/G9GukpRVu+Y5bv37JHbdCwi1NqnTDhmyBgydp/85CqVKR5N0EQq67Vk64hS5OCFvYHqUAACAASURBVJkq9W5hVEoVE3QWx22bKE7wiMgO/rZzLsFb3TAMo/PT0gIffghHHKH3338/Xbzly7PtpIYPT1cF6oVbruOWtArUua2FW//+6YVbrkuWJlVaSDAkTZWGbgNVaI5bZ3Pc2qM4Iff5olAJhwyKi61Qy4FUV2uqvssJNyBlO2PDMIzOz+LF+gF9wgl63xcXJMU7bhBGuPXtm71QDRyYFUxx2bhRRWpuqjSN0Kqr0wt87kU0qUMGKoDy532FdNwguXDbsKH4nLRQjlvS4oRirlYlHLe48YqJSr+vMzhuxZZKSRKvUsQRblKxURiGYaSkqSnMB6sXakccoResNI3cGxp0Hlko4bZ2bTZNCuqWJRVuhVKbaRy3/HXXILkQbGnRv2W+YEg6x61QcYK/n7Txer5wE9F9ncVx64zCrZzjlkS4iWS7a+THS9LyalsTbimn6BqGYVSG2lrt33nwwemLCfyctl12gfHjtal7mnFBds21EI6bT5OCCq2kws33EM0Xbmkct1DCzV/AQzluhYoTIJ1wKyRmkgi3YhP20wg33zkgRLxSxQn++aIS2iHzQksK2EohU6WgTnJXFG6GYRidkkcf1UKCN9+Et95KF2vZMt2OHg1jxmTvJ8HPSfNrrg0frsUJScVlvnDzy3ckiecFX36qNI3jFqqYwIuf0KnSUI5bQ0NhMZMkXqneopBMuIUSWlDY+UwarxLFCSEdsm0xVWoYhtEpeeqp7O0ZM9LFWrZMxUzv3priTCPcfOGAF1uDB+uHf5Jm31B43TXnkomZYqnSpqZkPSgLzUlL6rj51ydkcUKvXls3D+8Mjlvo1GYx4ZZGCBZLbcYdX5TihDhfQkoJraTFDoUKHcCEm2EYRlDefReOPVZFSNoq0KVLdd010O3y5ekcMoAhQ3Tr3S2fpoxL/tpm/naSdKkfQ/46bpBMbBUrJmho0GUj4saCsI5bvtsGyYVgMXEUUrhVValY6EihBcXFUSVSpaBfHNKOzcczxw0WVmwURRCRHUXkKRF5V0Rmich/Z/YPEZF/isiHme3gcrEMw9h2+fBDbeK+557phduyZW2F28aNyed9ecetUsLNu2VJhFuxddf888Rl06atxZGPF1ccFXPckhYnbN5cXLiFdNzSpEqLpQ+TVJWGSpU6V7q3aNx45Ry3JPFKCa1QLa98vC4n3JxzH6nkQIrQDFzunJsIHAp8RUT2Aq4ApjnndgemZe4bhtGFaGhIv7gtqKu1ahXsthtMmAAffJAu3rJl2SpQv02aLs1fd61Swi2J0CpWnADhHDcv3OLGK+W4NTRo1WkcQgot59rHcQMdc6g5bklSpaGFVqnlQHy8OOKoEqnSbUq4dQTOuaXOuZmZ2+uBd4EdgDOAP2ZO+yPwiY4ZoWEYSXAODjpIKzfTLLcBbatAd9wRliyJt5p7PqtXty0mgOTdCVav1qUKvDhKI9xaWlRkhHLcvNjLXzA391gciqVKIb7j5sVPIcctSbyQws13Cyg2xy2k4xZSuFWimCBpvFKp0pCOmwm3DCJyoIj8TURqRaRZRA7K7L9eRD4efohbnncccCDwEjDSObcUVNwBIyr1vIZhhOf99+Gdd1TA3XlnulhLl+p2zBj9aW5OvuSGc7pWWm4xAWSds7isWaNizS9XkEa4ebGSW7mZZo7bxo06ETt3MnZncdy8WMmP59OdHSncygmtkP07k8QLKdyiOGQdnSotVUyQZD7fNlecICJHAi8AewJ35z2+FfivcENr87z9gAeAS51zkT+iROR8EXlFRF5ZmWbxJMMwguJ7gQ4YAC+9lC7WkiW6HT0adtih7b64rF+vzpYXbH6xW9/cPUm83Mn/aYRbIYcsTaq0UL9NHzuU41aJVCmEE269e+vFOE7qtdj8O78vaW/RYvFCOW7dumnBQ0emSqM4bqFSpea4Zfkx8DiwN3BZ3rGZwEEhBpWLiHRHRdufnXN/y+xeLiKjM8dHAwXbNjvnbnXOTXLOTRrucx6GYXQ4s2apiDnjDF17LQ3ecRs1Sh030LZVScifk5bWcaurayu0KiXckjhupYRWR6dKSxUnQHyXrNgiskkauYcuJqhEvELiQyT+WmmVSpWGjBdyjts2V5yQ4SDgN845x9adFGqBoOpIRAS4DXjXOffznEMPAV/I3P4C8GDI5zUMo7J88AHssQfst5+6Y0kbpYM+fuhQ/aD2ws2LubjkC7e0jluhddcgnHBLmyot5rjFdciam/WiV2nHzY83iXAr5mj543Fi5T42lySLyIae41asqjRJvK6QKi0ltFpboy9F49y267htBgoUVQMwGkhYK1WUI4BzgGNF5PXMz8mo83eCiHwInJC5bxhGBWluhunT003893zwgVaA7rKL3p8/P3ms5cuzy3f4ooKkxQT5wq1nTxUPSR23/P6d1dUqZkIJt5499YISSrglddyKCa20c9xCdRMIKdwqUUwQOl4x4dZZHLdQqdJyDlmceF7gbYvC7VngUhHJbenqnbcvAU8GGZUP7Nyzzjlxzu3nnDsg8zPVObfKOXecc273zDbF93XDMKJw/vkwZQr89rfp4jQ1wcKF2gd0p51034IFyeOtWpUVbL176wUlqYOXL9xAXbc0jluu0AJNlyYRbl785Mfzba/iUii12auXisuOdsiKxfP3O1K4VcJxq64u3Cg9ZHFCkvGFdtwaGko3hY8br1yq1J8TNRZsg8UJwHfRdOkbmdsO+IKIPIWus3ZN2OEZhtEZaGqCBx7Q27femi7WsmWalhg7NoxwW706u8CtiIq4kMJt8OBwjhskF25enOX3Ax0wIJzjJqLCMJTj5u/HXdusWDwvlpI0ci8l3ELNcevVSy/ucVzpUkIrtOMWN16lUpuFmsKHXsctruNW6nf1+7ukcHPOvQEcDSwHvg0I8NXM4WOccynXLDcMozPy6qsqDiZO1CbuSdoEeXzhwA476DppPXuGE26gtzuT4xZauOU7bv37hxNukKy/aDnhlmROmsjWF9E0/Tbby3GDeBf4YqLSP0dnTZVWYt21joznW21tc8INwDk30zl3HNAfGAsMcM5Ncc69Fnx0hmF0Ct5+W7cXXqhuwmsp/ttzhZuILuORtpF7vnBLM8eturqtOErquLW0qMANlSotJtxCpkpBxVwoh6xbN009JYnXq9fWzkxSB6+YOPKCJOQct9xzosYrJbRCVZX6eKFSpVVV+rcNndoMLdy2e8ctF+fcZufcEudcgk5vhmF0Jd59Vy9KJ52k99P0A80VbqCuW21tslibNumFLVe4pUmVrl2rDluuYEjquHnXKrTj5pfE8IR23JKs/l9MuPl9oVObnXmOW9x4oVOlIatKSzlufn9HCa1y8ZLOcdumhZthGJ0b5+B//zd5F4Fc3ntPq0DHjVNHKk2bqhUrNIYvKBg2LPkY85u4+9tpUqW5aVJI7rh5MRXScevXT52OXPr1S5a6LibcknQT8MKsmBBM4rgVEoFJhFZzs7qf7VFVmnTCfnvNcQvpuCWJV0pUVspxixpvWy5OMAyji3DrrfDJT8Lpp6ePNW8e7Lqrpr523jmdcFu1SsWVFyBpHDcv0LwIhGyq1OWvNBmBQsJt0CAVWnGXQfEOWb7j5uPFpb5+axEIKpaSCLdSqdLQjluSeMU6HeQ+XxTKdTrIPacj4pUTbnGEjHPtV5wAYR23SrS88udEjZX7uELxmpqSfa6ExoSbYWyj3HWXbl98Md3kf+d0+Q5fAZq2MXxtrbpsntCO29Ch+uEf1+WB4o5ba2v8eWTeccsXbgMG6EUi7rd377jl07dvfGEElXHcQqZKC8Xq3l3T2EmEVqk5aZ3ZcWtpib6IrJ9g3x7FCUnilZp/19Gp0ijFCbnndSSJhZuIPCkiY0MOxjCMMNTXq2A79VS9P3168ljr1mm8HXfU+2PHJu8FCm3XXQN13DZuTCY+iqVKc4/FoZhwg/jz3IqlSpO2gVq/vrDj1rdv/FhNTSoG2kO4JS12KBRLRPeHdsjiiI/2dNzizpkrJSr9/o5OlYZy3KJ0OvDPGXVsuY9LG6+SpHHcJlO8i4JhGB3IrFn6Tf288/TCOXNm8lgLF+rWC7cxY7SlVNIOCoUcN78/LqWEW5LK0kLLd/i2V3HnuRVLlSbtJlBMuPXpoxf2OI3SywmtuMLNn1/p4gTQ/R2ZKg3tuJX7XeOMr5zQ6szFCXEdsiidDiD+HLdtXbgZhtFJmTVLt/vtB3vuqcUFSfFVoGMz/vqYMSoSkqY3CzlukEy4eXGWnyqFZI5boXlkSRu5l3Pc4gq3DRuKp0ohnpjxQquzpkqLOW4QX3yErgItlXqtRKo0zvgqkdqE9nHcqqt13muoddfi/i2iFCfEiVdJTLgZRifi4Yc1xZmWd97RD/3x49MLtxUrdDtihG7TNHJ3rrjjlkQIrl6tH7S5S2QkTZW2thYWR2kcMijuuMVNb27YsPVSIJAs9VpKuFViOZBQTeF9vI523KqrtVAnVLxQlZahU6Whl8goJdzixis3Ni/Aos5JCx2vkphwM4xOwvPPw2mnwWGHpSsmAH38TjvpBWbCBG3invSbohdU3hkbPVq3Sea51dfrB2Qox80vvpu77lrSVOmmTSos84Wbd8ySFieEctxKFRNAPOEWZU5anOq5TZsKdzrIjReHzu64FROVoR230MItidDyjwsVr72EW9zU5nZRnGAYRljuvjt72/cFTcqiRdnU5s47Z/clYeVK/dDyzlGI1GZIxy2/mGDgQN3GTW16IVVMuMUVWnV1eoHPT70kddyKCTcvBOO4WuVSpRBPzHihVagHZUenSr2YKSS2ROJ3JwiZ2iwXr1KOW1RR3tCQreQtFi+ucCs2NqiMcAvtuNkcN8MwtvD44+q47bUX/POf6WLlCjdfVOCLDOKyYoWKNf/h7d2yJMLNPybXcRs0SJ3BJPHq6rJCzdO3r441rkNWTLj5+3HjFSsmSJp6LSfcQqVK/b44QrCU0ApdnBAyVer3by+Om98fR8yUE1qh5rj5eB3luIUWgpXEhJthdALq6mD2bDjkEDj4YHj99eSxWlo0jekFm19/LWn6deXKrMsGKpSqq5NVbRZy3KqqVMglcdwKiaOqqmRtoEILt3LFBHGEVmuripX2SpVCxwq39kqVJokXxXHraOEWasJ+qXXX/PPEcaDKxYvj4FVKuBUrTjDHzTCMNrz1lm73319/li6F5cuTxVq2TMVbKMctX7iJqNAK5bhB8m4CxVytAQPCCbfu3fWCkqQKtJDQSuK4eWHRnqnSkMJt48Z4c+bKOW6hhVuo5TuS9ioN5eCVqypNskRGKKEVJV5ndtysOMEwthGefhp+/et4a2gV4p13dLvPPvoD2tg9CX4umxduvXqpMEoqBFesyFaUeoYNC+e4QfJG7u0h3ECfI4njVqoKNI5wKyW0Onuq1MeLKhZaWvTiWMpxC5kqDTnHLckisps3t+8CvBBPzISak+bjhRZuoRyyrlScUKCgOTInAClr3wyj67JiBUyZomks5+ArX0kea/58TT+OHZtd2HbuXJg8OX6sfOEGKrz8sh5xyXfcILnj5pfo8IvaetI0Xm8P4davXzLHrZBw69lT/9ZJhFaheKFTpX5fXOFWSATmxivWf7TY2ELOSYNw/TtDOm5RWlRB+DluIVOl28sct20iVeqcm+aci/F2N4xtiwceUJHVrRvcdlu6WDU1KrS6ddM5ad26wZw5yWLldzoAFW5JHLfNm1WwFBJuSTsT9OunwiWXJMLNueLCLeQcNx8vlOMmovtDO26dOVXqz4mCFz2l4nXWOW5+fbeOFFoh45Vz3DpzqtQv6BuqqrQzOW6WKjWMhDz2GOy6K1x9Nbz2WvyWSLnMnw/jxuntbt10CY+kwm3RIr0Y5XYTSOq45a/h5hk2LFwVKCRLlTY0aNubzpoq3bixsHDzzxHHIfPndsVUaVwHr5QbCOFTpSEdt7jxygmtuMUOHeG4ddRyIOVSm3HjWXGCYWzjOAf/+hccfrgumAvwwgvJ49XUZNdbA3Xdkq67VlurQi137aWkwi2/a4LHO25xJpxD4V6gkMxx80KqmHALtRyI3xcqVZokXimh1auX/q3jpkr9Gmb5+OeI20IrtOMWUmiJFL8gh3TcIF53gko4ZBA2fRgqVdrSoj/t5bglieddukJYcYJhdHGWLNHqzUmT9AfgjTeSxWpq0njecQPtTpCkpRSooMp12wBGjtT9vjFzVLyrll9MMGyYjjuuOFq3rrhw27gx3odiOeGWxHGrqiosGJKmSovN++rbN5xDJhK/v6gXWoUWVq1UcUJU4VbOcevdW8WCnwtaDu+QFVtEthKOW1zhFqqqtL1TpT166N8hSnFWJYRW6HjlYuU+b0diws3Yrpg1Cy67TB2uNPgq0P32U5Ewdmx2X1wWLdIPv1zHbcwYFXNxHS3ItoHKZcSIbJ/QOPj0ZX53Ar+cR9x5bsUcN1+sEMd1iyLc4rx+9fXqhBW6wPfrF26Om48XynGDZEKwWKzOMsetlOMG8cRMKaGVpPF6OcctdBVoZ02VxqlS7Qjh1r17vNRruVj+vI7GhJux3dDaCp/8JPziF/DZzyYTRR7ftH3PPXW7117Jl+/wIjJfuG3enGyJjGLCDeKnS/3z51eBegcurhAsNsfN7wsp3JyLJ2bq64sLrf794wmt5ma9YBSLF7I4we+Pmyot55B1lHCL4rhBdHEUck5alHhxhGC5iteOFm5RHLeo8TrKcYtTnBDFcetywk1EDhWRq0XkMRF5U0Q+FJEXROQOETlPRAaXj2IYHcOMGfDhhzov7fnn1X1LyvvvqzgYOVLvT5igsZPgOxr4DgeQbeSeJF26evXWC9yGFm5J216Vc9ziCNVyws0/X1S841YInyqNKva9iApVnBDFcYubKi0Wy4uSji5OKOe4xXHwQgq3co5byOKEqqpkVaqh5rhFKU6IGq+rp0q7XHGCiHxBRN4CngcuBfoAHwIvAWuAQ4DfA4szIm58hcZrGIl55BH9x7zjDr3/6KPJY82ZA7vtlk2r7byzioQka5H5ys1Ro7L7xozR7ZIl8WI5V9hx8wIziXDr3n3ri7JPncatpC01x80fj0p7Crd+/bIuWhRKrbvm93fWVKmf5xdVaLW06OsSao5bueVA4jZy78yOWznhliRejx6lm8LnPm85onRO8OdFiQXhih0qIdyKFbBAF0uVisgbwI+BqcBHgMHOuaOdc2c65z7nnDvZOTcRGAJ8GRgBzBKRsys5cMOIyzPPwEc/CrvvDnvsAc8+mzzWggVtU5v+dpJ+oCtX6gdMrmjwjltc4bZ+vQqMYqnSuGu5rV2rblj+hSDJnLTWVh1fewg3vy+k45b7nOWolONWLF7IVKmPF1W4RVl3zT9n1LFFiddRwq09HTd/LLTQ2p5SpdtrccLtwHjn3Lecc685VzhZ4Jxb55z7s3PuZOAwIMHsHMOoDI2NMHOmpklBK0FffTVZLOdUoOWmNtM0cvedCXLFUdJUqe9MkC/cBg3SlEvcRu7r1m2dJoVkQss7TMXWcYPOmyqN22g+inCL67hVVRW/sIR03CCecIsqtEIXJ8SJF0VoRUmDNzerw9jejlscIVguVu7zRokXOlUaah23cuuuxY23TRUnOOdu9B0SROSgKEGdc2845x5POzjDWLYMLroI7r03XZz33tMP3QMO0PsHHQSLFydb22ztWr3oFhJu8+fHj1eopVS/fio+4jpuXrjlz3ET0fRm3NTm2rWFhVbv3ioE4wg3f257pkrjVIJGcdyiiq1SC+aCCq3GxugXAS+0iqXA+vaNv+5aKeHWu3d4hyxUvEqkSp2L9reoRGrTjyFUvFAOGUTrnODPizK23DEUG19HVZVGnePWJYRbHk+JyJSKjMQwCvClL8FvfgOf+Qy8+WbyOP6x++2n24kTdfvBB/FjeXGWmyodOVL/sZM4brW1W6+TBuq6JRVu+Y4bqHDzx6PiU6X5iMTvduDdr0LCze+LK9x69iz8jTuJ47ZhQ/s5bnHbVJVaEw5U5IQqJvDxOlJo5T6u0NhynzdKvHLCKOr4yo3NH+uoVGlUxy10cUKoVGmcFlpRHbdQVaVVVbpAb1dJleZyNzBVRM7MPyAiR4pIillDhtGWOXNg6lT42tf0H/rWW5PHevdddYgmTND7u+2m29mz48cqVAVaVaW9QdOkSvMZOTK+I+jXVSsm3JI4boWEG8TvdlBKuFVXq6sVN1VayG2D8HPc/P6o6chywi3ukhshU5tR4sURgl5AFYtXXa0X187suEE08RFaaJVbDsSPL7RwCzVnrhJVpVEX9G1q0vdVMRfaxwtVnODjdTnHzTl3IfAj4F4R+S8AEdlXRP4BPA3YciBGMB56SLeXXAKnnAJ//3vytdfmzFGHzP9jjhunF5QkS3gUEm6g8UOlSkH3xZ2TVs5x6wzCrVDqNUm8KMItVKrU74+aKo1SVQrRhWBo4bZpU/l4UYWWf96QDl5VVekWVRBeuG0rjlsoh8ynj0M5eFGFW5x4pWL5eKFSpRAv9VpJYi/A65y7Fvgv4CYRmQG8BuwDfBHYN+zwjO2Zf/5Tqz/HjYMTTtC0YdK10ubM0Ybwnu7dYfz45MKtZ8+txdZOO8V33BoaVNAUEm5JGrmXEm5DhiRbvqOUcIvjkJWa4+b3x3HISgk3n0KNKrT8fLNiws0Lrbhz3Mo5bqGFW9QvNqV6i0LYVCnEawxfrkVV6FRpHOFWqTluIatKS8XygjhkFSiEj9cRwq1ccQLoa9flHDcAERkCTABagKOAF4HdnXN3OOcido8zjNI4By+/DEceqfePOkq3L76YLN7s2dn0qGf33ZOnSseO3boZ8ZgxWkwRtYciZFObhea4DRumx+PEW71axUKhD++4jltjo17gizlkgwaFS5X6/XEcslLCDeK1qSrVYD53f6hUadw5blGEm3PRnZRyjlto4da7d3QXqtz8u7iOW7mWV5Vw3DpyHbdSsSC6mKmE0AodL6RDFloIVpK4nRO+D8wFvgL8DHXZJgE/Dz80oyuycSNccIEWFcRt8p3LokXqNh2UqWOeMEE/EJMUKKxerc5QruMGKuQ+/DB++nXpUthhh633jxqllatxxJFPhRZLlba2xotXaPFdjxduUYWgF2XtlSoN6bhBvMbwUYVbqKrSSjhuEE1sefEReo5bKAevnENWiXXcosarxPIdUeKFFG5R40UdG3Re4VaJVGlXdNy+jRYo7Oqc+45z7g7gZOALInKfiJSZ2mds63zzm1pE8Ic/wOWXJ4/j11jzwq1bN9h772TCbc4c3eYLt9131wtx3AKAZcuynQhy8fuWLYseq5RwS9IPdNWq0sLNuejiqFi7K0/cVKl/3mLiqBLCLarQKifcvMiJI9y6dSu97hqEc9zitJWKMictzhy30KnSqI5bZ60q7dlTvxw1N5eP19CgYiDfvc+P1xHCLXSqNIoQrIRwi1NVuk0WJwATnXMXOee2rL/unHsSmAIcAzwWcnBG12LVKvjd7+D88+GrX4Xbb48/ud4zc6Z+mPnlO0BvJxFuPh2aL9ySdjtYvrxteyqP35dEuBVLlUI84VbOcYPoDl454TZokAqZKBVgoO5c//7FL1L9+4cVbiFTpdXVKibipEqLpUkhWXFCqXhxqlTLtc+Cjk+VhnLIWlv1gtyejlvceKGEVuh4URfMzT03Sryu7rh1uVSpc25Okf0zgSOBcQHGZHRRHnhA39QXXghf/rJe0O+/P1msmTN1rbXci8t++6loitu2ae5c3e6yS9v9Y8fqdtGi6LE2b1YBUshx88Itzvi8KCuWKs09JwqFGsx7vKCLKtyipEohutgq1mDe05lTpf5YHMctlNDy50VJlUaJV275DqiMcIvjkJWK5ZcXiSO02nOOW5wlN8p1dfDxQlWVQnQxE2XB3I5OlUZxyLb74gQReVREdip0zDk3Gzg8yKiMLsnUqVqpuf/+sO++6mg98USyWO+9p6nRXLz79tZb8WItWqTuVf6FKolw86KskOOWNFUqUtgl845bHNcyiuMWdRFe77iVWr4Dos9zq6srHguyxQlR5hw6pyKqvVKl/lic5UBCOm7lFuBN4riVE1pNTdHSfaGFW7lUKURPvUZdJw3Cpfs60nErV1UaJ962UJwQ2nHrksUJwInA+SJymIgU+og7PsCYjC5Iays8/TQce6wKERE4+mht7B538n9TE9TU6By0XPbcU7dxux0sWpQVabkMH67/iHGEmxdlhYTbwIH6oRhXuA0dqi5CPnFTpc6Vn+MGYVOlueeVI4rj5lw0MbNhg57bXqlSiNcPNKTj5lxYxy1qqhSiiSN/Tqi1zcrNSYsTL2oVaO65aePFcdyiCrdQvUp9vNBz0jrrciChq0q7pOOW4SrgWWCtiMwWkQdE5Hsi8lUgxdr2RkfQ3AxXXKHN1x98MHmcN99UQTB5cnbf0UerMHn//Xix5s/XNGv+nLTRo/WCMqdgwr44CxcWFm4iun/hwuixvONWKFUqooIubqq00Pw20Atrnz7RhVt9vf4920u4xXXc1q0rL9wgWrq0VJ9ST2dOlfp1yqIIwcZG/WIUqqo0Sqo0brxS665BeMctarzQwi1OpWVI4dZZixMqlSqNOr4oDplz0ebhbsvFCaCu2xTgMuAZYFe02vQmIOYl1ehofvhD+H//Tyfw//u/w9tvJ4szfbpujzkmu+/oo3X79NPxYnlhlr/umojOU4sr3Io5bqD7QzluoIIuruNWaH6bZ9iw6KnSUovv5u6PI9yqqoqLmSSp0lLCLU6bqqjCraNSpeVSmyLRux3EcchCpkohunALJbSg6ztucYVgud/VC60omYuo67iFKk7o1q3tueXi+X6fpcYWNV6UOWlR4zm3DRcnZFjnnHvaOXeTc+4859wBQF9gJ+DgsMMzKsnatXDDDSrY3n1XHYLvnFgLdQAAIABJREFUfz9ZrBdf1M4BO+6Y3bf77ioWXnklXixfBZov3EBduDiL5m7apOnDYsJtxx2TCbcRIwofHzWq44VbseKE3r31gylOccKgQcWdlCSp0nJz3Px55Ygi3Pr10wtUlG/IXpCVm5cWKlUaJ14U4daRqdJyaVwIuxyIH1/o1GZnddz82KO8j6M6bqGKE0SiC8GohRMQdo5blHjekduWU6Vb6X7nXLNzbpFzLqKha3QG/vhH/dC94gq92F9wgaZLly6NH+uNN+CAA9ruE9FChbhLeMyerReCQq7WrrtqlWjUeXOLF+u2nOMWdVHa5ctVjBb7Bw8t3IYOzXZXKEc5x01E06VxihNKCa1KpUqjpDejOm5R49XX6wWylBsQMlUKYR23SlSVxokXSmhFjRdVCHZEVWklihP8uaVoadGfcuIjZKrUx4sqtKK4gbnPXS5eKOEW9XftqsUJAD8RkR+KyFkisqdIqZkNRmfm1lvh0EOzi9x+/vP6j++bu0dl0yYtGNh//62P7befVoHGadvk+4oWemfttps+X1Rx6d20UsKtqSn6IrzFFt/1jBihc9Ki/L6trSrKis1xg3jCzZ9XTLhBvLZXpRrMQzzh1tKioqe957hBNLFVqsG8J2RVKXS841ZuAV4ImyptaIj2f9HeqdJu3TSFF1VoVVVlU4SFqMRyIFHiRUlt+uOhihMgXgutzuq4RRVuXdlxGwJcCNwLzALqReRfIvK7TIGC0QWoqYF33oGzz87umzhR55A9/HC8WG+/rR/IxYTbxo3ZtdSiUKivqMcXLESd5+aFW24KNxffuiqqECy2+K5nxAh9LaK4Wr79VLlUaSjHzR8LJdx69NALYpRUqRc87SncvBCL6riVE26hU6VxHbdS8ZLMcQtZVRrFIYNo4ihqvFDCTSR6f9GoojL3uUsR0nGLKrRCO25x5sxFce9ynzttPF9sEFW4bavFCfcA/+GcG4IutvsJ4HqgBjga+EXIwRmFmToVzjwTLrkkeWeCxx/X7cc/nt0nAqeeqmuvRV0YFDRNClunSiG79lrUdGlrq4q8YsLNL6IbV7gV6i0K2hgeYMmSaPGiOG4QzcEr1e7KM3SoCqMo62lFEW4hHTeI3mi+XJ9SqExxAoR13DZsKO8a+SVN2tNxq67Wi16cqtL2Lk6A8mKmuVnd2fZ03CD6khshhVboeJVwyELH6yjHrZzYiuO4dblUqXPus865WZnbC5xz/3DO/dA5d5Zzbg+gxPdpIwS33w6nnKLFALfcopWbcRp9ex57TIsJ9tij7f6TT9YPsGefjR7rjTf0ojZ+/NbH9tpLUwte3JVj8WL9AMpfCsSz004qMGtqosVbtEjFSrGLaFzhFsVxg3jCrVyqFKKJrdWr9eJe6iIVZ46bL04oRdRG8/6c9qwqDe24+ePlvtT4lGC5CftRhVu5hvWeOA5e9+6l032VmOPmzy0XK/f8YoQWbnHiRRGB0HmFW9xUacg5bp01VeqFXcjep5UkSaq0KM65iHVDRhLeew++8hU4/nh1pR57TOeWfe978eI0NcG0aeq25c8jO/xwFVrPPRc93htvqLNWqAdlnz4q6N59N1qsUhWloB8SY8bEE27F5rdBVoRFEW719foTynEr1e7K44VblHRpqa4JnriOWymHDKILNy/GSgm3nj31J05xQimxFbc4IUqqFMqLLX+8PYsTQMVO1HhRRCCEd9yiCrf2dtyipkor4biFEoLbQqq0Ei2vosTb5hw3EXlQRA6MGlBEeonIZSLyX+mGZuTinPYA7d0b7rxT//mmTIEvfQl+85t4a5u98IJezE48cetj/furCHv++ejjeuONwvPbPHvtpfPpolBOuIEKwVDCrXt3FVtRhFupdleeSqRKIZpwK9U1wTN4sAqtcgtSNjfreyRKqjTKHLcoqVKI3q90/XoVRsUa1kNlUqVR4kUVbiFTpf54VIcsigj050aJF2qOmz8e2nEL1Z0gSjFBR89xC1VVGjr12pmXAykr3F54AU44ge7dnDpura1wwgm6vwOI4rgtAF4UkZdE5BIROUhE2pjsIjJGRD4hIrcBS4EvAjMrMN7tliee0EVur75aOwh4rrlGL14//3n0WI8/rnNijjuu8PHDD9dUbJR5VTU1eqEtJdwmTlRnMEq8OXNUTJUSW+PGRRduxbom5DJ6dDjhNmSI/j1Cp0qjOm7F1nDLHR+Ud8m8eAqVKo3iuPnjUYVbqTQpVC5VWk64RSkmgPCOW5x4oRwyf872kioN6ZD5c6IKt3LjizMnramp/FzN7XE5kKIO3ve+B088QY97/0hjo4OPfEQvynHTXYEoK9yccxcDewH/Aq4GXgY2i8hqEVkqIpuBhcDfgL2BS4H9nHP/qtioARH5uIi8n2m7dUUln6ujcQ6+/W2d33X++W2PjR6tlaF33hm9vc/jj8NhhxV3P444Qi9OUZq5+7lr5YRbU1O0ytLZs7UAodR6WuPGqSArN9egoUEFVDnhNmZMNOHm12crlSqtrlYhFjVV2q9f6QtB6FRp1EVzy7W78oSc4wYqxkIJt86eKu0oxy1KqrSj5rhFFVohF+D1x9t7+Y7Q8eKkSiHchP2QqdLqap2+E2XB3NbW8FWlReNNmQIi1NctpnFzC7z+ug50ypTSgStEpDluzrk5GQE3CjgW7Vd6J/Ag8DPgXGC8c+5Q59wfnXMxVu2Kj4hUA/8DnISKyv8Qkb0q+ZwdyUMPwcsvq7gv9E950UV64fnzn8vHWrECXn21bTVpPkccodso6dI33tD37777Fj9n4kTdRpnnVmopEM/48fpPW67jgRdjUYRblOVAojhuoOnSqI5bqTQpZIVblH6lUee4Qfl5bl5odWXHrXdvdT87a6q0Tx+9cJdzPqKsu+bjhUqVdu+ur13oVGlIx833cC1F6FRpFMfNX/zLxfNtljpKuEWJ17176R60ELaq1HdiCFlMkHt+4njXXQfO8eBejbTSjWZE/4DXXVc6cIUoUVe0Nc65RmBG5qcj+Sgw2zk3F0BE7gXOAIrOpHr//feZnNsBHTjrrLO46KKL2LhxIyeffPJWjzn33HM599xzqa2t5VOf+tRWxy+88ELOPvtsFi5cyDnnnLPV8csvv5zTTjuN999/n89//gKWLdMPph499OJ+ww3f4fjjj+f111/n0ksv3erx119/PYcccjiXXfY8vXtfxZ13wl13ZY/feOONHHDAAdTVPUHfvtfxzW/Cvfdmj99yyy3sscce/OMf/+BnP/sZkBUff/sbfP7zd7Hjjjty33338Zvf/KbNc/foAU8+eT9f+cow7rjjDu64446txjd16lTeeKMPw4f/mlNO+ctWx6dnGpj+858/BR7ma1+DX2QWjOnduzePPvooAD/4wQ+YNm0aoC5fbS2ceeZQHnjgAQCuvPJKXsiZS6Bu0Fhqav7E+PFw6aWX8vrrr7d57gkTJnDOObcCcP/953PnnR+0OX7AAQdw4403AvDSS59j6dJFHHNM9kPqsMMO40c/+hEAZ555JqtWrdqSnv30p+H444/ju9/9LgAnnXQSm3KuSIsWQX39qcDXAbZ634G+91auvIghQzYyeXLx915DQy3wKW6+GR55JHu80Htv+XItWJk8ue1774ILLtjyOC+ypk37Dh/5SPH33plnXg8czsKFzzN58lVbHffvvdraJ9i06bo2rx1s/d7zr93pp+v2rrsKv/fefls/tGtr72fYsOLvvaamqfTv34df//rX/OUvhd97ItC9+0+5/faHeeaZ7LH8994TT0xj0yb461/1C9LQoYXfe16w/fCHY/nYx/4EFH7v9e49AbiVPn3g/PPP54MPCr/3VNh9jmOOWdTGYc5/77388ipE4Nhj9fhxxxV+7731lr52P/3pqXz968Xfe4sXn8UOO5T/3Ovdu5Y77/zUVoVK+e+9zZvhL3+Bf2VyLIXee/61u/xyqK4u/rmn/9vX06vX4Tz//PNcdVXh916vXgcATzB58nVbzXPMfe/94Q8/a/PaQeH33ptv6lSOyZPh/vuLv/dmzoSDD54KlH7v9ewJzzzzUyZPbrsoZu577+qrfwBM4667YEbmilrovee/CFxxBdx331j+9KfC7z2tFp9Az576uVfsvbfbbvq598Uvfo7a2rbffg859BCu++F1dKvqxv33f4qWllUcdUwLOHA4jp58NJdfcTlD+wzlpJNOYv2G9cx6u4qmRuGwIxs59uPHcsHFF7DTwJ2YPHkyjS2NNLfqHJlZb/VizI6f4L3ak9mpz06cfPLJbGrepMcz8U/+95Pp1v0a1q1bw+TJn6K+sX7L4x2OUz5zCqd98jQGrh8LnMPNv9nEn/+2EZdp6HTaF07jxFNOZHTDaC644AIW1a4DBvLli9fSb9BmTvvP0zjxYycyrG4Yl156Kcvrl9PiWthQ1wMYxm8fO57GnSYxYMUArrrqKhbVLcI5h5swEubVsKRaX69HpJpfuGaYNEnfNBkKXXNzKfa55yn13ssllnDrROyApmc9i4BD8k8SkfOB8wF6lvsaUiFWr4brr9cLgnPZFcQXL4af/hSOPLL04+++W1OMe+1V/JuPiKbv5s4tnwZZvVqXASjnVgwcGK3H6BtvFF8jzdOrlwrBcm6A/wYd9dv7vHmlnWrvyPXtW/q5/etVrmmxr2Iq9w20e/doLs/KlSrgS30zV/FR/htjS4u+v8pVWfklIMqNL0rTdci+ds3NpZ+7ubl0+jt3fFFco/p6nTpQjp49yxdieNem3Pj88ajf3qM4bv75Sz13S4sed87hcDS1NLGhcQN9e+gTtLpWWl0rUlVFS4tQ31jP8vrljOynOf2m1iZaWrMvwsbNTdA9+yI3NDfQ7LIXzwXrFjBrxSx69RpJSwtsbNpIc2vzlovjuyvf5dUlrzKCEVteu4aWTazOCMiXF7/M0IVDGYraxWs2rWFDgwOGsHZTHU/Oe5LuNd0ZiM7VWLlhJS2uBYdjwwb9nH579ct8JDOXd8n6JVt+d4A7X7+TTfW9trx2i9Yv0GOZ8d/04k2cVn1a5rgDccxdU7Pl8dfOuJYzDz0TgObWZuatmcfG5tG0NHXng1Xz+dpjX+Nzh34OgMaWRuaumbvlsRsbx/POmpk8MVf/aTc1b2LO6mxlmMNxyt2n0K3HgzQ3w6aWeuasmbNlbFU9qjj69qO5/rjrt7wvl9QvYuVS/UZdXVfNAb89gN+d9jsAVm1axeyVi4H9+HDVHBa89yq7/HIXHvz0gwAs37CcuWvmgoOWjYOBCZxy33G8vOctACyuW8y8tfO2jP/ZxmeRmkbg17S2wvy186lZW7Nl/DNaZnDDdTdQd0Udra3gpIVn52fXhnru2ef40U9+ROv39A8/d81c1jYMhqY+vLjoFV58+kV+WfVL6q/SD5A5q+ewYkMm/dA4idlr3mXKH3/CnAv1NZu9ejarN2bXJ3rt6deocpdvcdxmr57Nus1ZS//NZ97k8V6P84dD/heA2k0rWbJi3pbjs56bxQt9X+CWw/T3X7R+AbAvi+sWQ3Mt7z//Pu8NfI8fTPyBjm/NHJpammDTEGAYf33vz1S/MYuLR18MwLy182j1b/LBQLWKyFbXDWjWb0ul5glVCHFRmz76B4h8AfgPtKl8vmnsnHNFVuAKh4j8O3Cic+4/M/fPAT6aSecWZNKkSe6VuN3Oo7BggdpgV12lV1nn4PrraTjrHH7zyE5ce626HF/6Elx7rabZ6utVzP34x7oO24MPFp5v1tAAe+6p6a+XXy5dQbdsmaYEv/ENyHxZ34rWVp0Td/zx5dOqP/sZfP3rpRec9U3Dr7tO5+CV4oQT9Nv0yy8XP+e551TITp0KJ51U/LymJhVv3/62vqbF+MlP4JvfLN8j86GH4IwzdGyTJhU/7xOf0OKJt97Si2ira6VKqhARmlqaaG5tptW18vXLunPPn7ozf1kdA3vpH7auoY5NTZtwuC0X2kP2HsUJx3Xjjjtg6fql1DfWbznunKNbVTd2H7o7++wDY8bV8+PffbDleVtdK32692HfkZqjnvry25zy0X34+o/f46SzltDqWhnUaxCTxugvNKNmBusb17NiSU++NOUELrzmNT533iYO3/FwfQ3ef4gNjRu2xJ7xv7tw29VHMG+ezim84/U7aGhu0LFlxrjX8L1YMONYzjsPrvrrbQwes2bL2FtdKwfvcDDH73I8jS2NHHLqLOa+uguX3PvTLY+fMm4KJ+x6AnUNdVwz/RocjiduOpPZz+/Ll/78bc7Y8wyO3+V4ltcv57tPfTf7u9PKA//1Yw4+2DHtoVHMWzOPq568qs1zt7pWLj30Ui74+NHsPGEt1Wd/ts1xh+Payddy2I6H8dDLr3DGRyex6zk/YeTk/91y3q9O/hWTxkzisdmPceW0K2lYO5h3r3iS0Wf/gEFH3cNf/v0v7DNiH+57+z6+/eS3t8Ste+mTrL7n50x7tYZjDxrHb1/5Ld+f/v0t4/I/1wyaz9cuHMRl9/6KX8/+xpb9foxrr1jLgJ4D2OfEfzHrxVFw2c5t3o+t32tFRLjgHxdw68xb4e+3Q81k+Np4+nbvu+Xi+ZkHPsM9b9+TfeD/vEXPUTVsfvNUAE6/53T+8cE/2sTebchuNP70QyZPhgXHTmF6zfQ2xw8cdSAzL5iZbdn28Uvg0Ju3HD9656OZca7aSHv8ag8+mN0Iv5wHZ5wHB97BKbufwsOfUTdqzM/GsLQ+M1fhnU/CX/7GiT/9Fo9d/v8A6P+j/tQ3tv2mccTyO3nuN+ewZAmMuXXrb1JfO/Rr/PzEn/Of5zdx292r6XXlOAShSqqokiquOPIKrjrqKpbXL2fvX+9N/Z9/T/PSvRn+raOpkiq+c9R3uPDgC5m3Zh7H3nnslsct+OGj9Bg9m9/dtZZP7/Np3ln5Dp++/9Nbjovoc3x4xbP8x1k9Of97r3Hxoxdv2e/HcN2x17F7r8MZMQImfuF/GP+xqW3G94MpP2Dfkfvy3ILn+NEjd/PIRf/DRy+8hd2PfwYR4ZrJ17DL4F2YUTODu968C0GoeW4ST9xwAWf96jpu+sKXGdlvJE/Ne4qH3n9oy/NXSRWz/u8jTP3p2cyZA/PlKZ6qearN2ESEbxz+DS6+qCcP/G8DV/z9pi2P9ccv/qj+TjNqZvD1C3ZgwXvD+eHf/0qVVNG9qjvn7K9ZgOcWPMf8dfOpkiouO+1kxk9cy5U3vsmpE/S999Kil1ixYUWb1+5zR0zh387oya23wmtLX2Ndw7rscyP069GP4a37s8MO8P2fLuH0zyxrM/5+PfoxfrAuKvrkKws57uAd+dlvl/OJszZQJVX06d6HEX21/H95vQrmRx/uyXn/MYgnn1vLwZO60a+HfmOtb6zX2M8+R9UJH+NzYy7h/oW/5KXBQzhw3Rq6PzVDL+IVQkRedc5tdVWK5biJyHeBa4C3gdeBjmoqvwjIbWI0Foi4hGpg7roLvvMdlsxrYNoZ57Ls9w/w5lPVPPKjQazZAIcevZ5bf9WfffeFFxe9yNtz62l1rRz9xVaah43i59/aj2OPreLxx+GVtY+xsWnjlg/ve27ai5qavbn1VhVt975971YXzwlDJ3D0zkczahRMPLSG3942jJGn3Y5U6UXgwNEHMnmcWtZf/+OfWbHiPBp2fojrnn6TVtfKUTsdxZTxU1jfsJ4fP/vjLXEXVO8IfIXfPfQm3/nyfqzcsJJrZ1zbRngsnbUL8E3231+/uX1/+vfbHHfOcdHBF3HkTkcyctwqnrqrD5+49zNA9uL57aO+zaFjD+WlRS9xwZ0zgG9y7Vtf4IYVC3DO8fMTf85Bow/iiblP8N2nvrsldrdBD/Gr/3uVs746jn1G7MP979y/5eLoL3wrHv42ffudw4ABVfx+5u+5dsa1bV67VtfKaxe8xpjMKryTb/4M1RMfaRNj2deXMaDnAL71z2/x4Kv/Bj3qkGs+tuXP3/K9FgTh4kcv5pZX9Vse714F637I6BvGsfF7Opnswkcu5O637s6+bxywbCPDh+u/4AUPX7DVxXPXwbsy+5LZDB0K/5o9h//f3nmHx1me6f5+Rt2S3OQmy5YtN8AGN5qptrENhOWEJGwISfaEkEIIJJTNJoGQhcAe2OUcdtm0k4RUNgeWJWwaCQklJJSEEsBOaAYbcO9FlmUVq7znj2dezzejr73v945mRnp+16Vrimae+ayx5rt1P+34u47P+v7CSQux+lOrAQCff/CfAdyDO1Zfjzu6+K/RM5rPwJOXPnkk/ht73wC6awG041tP34uNs17Drz/06yPHt+2g51fomWsAnHakxu2q31yFg4ezq/w/segTOG8U56Bue+wbQGN2yvCak685ItzWbHwLQCVuferWIx/CVWVVWDVzFbp6u/CdF7+DFKXQ3d6Mw+2Lce8r9+KocUdh5YyV6OjpwINvPpj14X2oPQVV2QpgEjp7O/HS9peyTnwpSqGtuy29X5TQfWhX1okpRakjKZjuLn4Pqkb0YETFiCOPK0/x/SMqRqB5VDP6qmrwOoCG8mk4esI8VJfz360TaidgyZQlR+K++dpCPAtg3Ci2jmeNnYX3Hf2+ASf3UXvYojx65GJcddJVWd8jECrL2P4dX9GMcaPLce1Zt2b9GxQUCISL5l2EuePn4oG/LsaaTRNw+3nfREUqY39edvxlWDlj5ZG4n//uNBw9PWO5f+G0L+B/zv+fWa9fV1mHz3yTSzv+ZcW/oLWrNevkX1/Jz9cVAl9cdhXe8+EPHXmN+qpM/F9e/Ets296Ps74K3Hjqbfjgx7545MQIAM9+4lkopUBE+MUDtbjqfuCWlZkU6YarN4CIst7f/7qnCn8Eu9VdN3QNEBaavp4KNDdMxMYb/IvrJtZNxJ4v7MElrwJPtgHvfC672LVlTAveuTrj6My4Ezjt2Fm4+Fi+PXf8XPz10wPXwjT/Ex/bosZFePpj/tPMdUbg70+/Ep/40JW+jzmt+TR8772nofEK4KPHfQqfft+nsr6/dPpSLJ2+FABwz0HgMQD/tOrLmJj+8S5vWY7lLdlpifv2Ag+BjYHlxwz8vubwYaB+RBU+f9rnfb+vX39eI7D7DeATiz/he/yngYumr1PArPEjcf6cjFV+8pQBiTLU1WTq7xY1+k8i06UX0xsmY3Hj5MDjmzmeZcKYyomYMWbg97UrPSJtikwYNRp1nqzLkf+nf3MB0Af0VfBnxskfr8D67wMzzz3XbM2QI0xTpR8H8FWl1LX5OBgD/gxgNhG1ANgK4GIAHyrIkXzpS8Du3bjzq/W44/szAHweoD5g1m+AU+5E2dLDOO44LrC59BeXYu2etVlPP/7qG/HKN27G0qXAvr+9ATtS6Skqb60A/t9vMW3pE1i1in8xP/WrT6GtO7ty++OLPo4zp7Hif2Xy54E//gTXfutBYNajAPjkuWz6MvT09eDr/4/t6f8+fBn++/f8l8aXz/gylrcsR0dPB27/4+2ZD7/eEUDqMvzh6S58+ZP8l8c9L9+T9eHY+dzHALBT3Ha4/chfbt6/fvZ2cDvk1Jnt6OtuwNq3DqG6YdeRk0BXL6cc+lQfWreNA6gPqTGb0NffhxRlLMbyVDlGVo08Er9uwh6gtQWVZXyCGl09GnPHz836cH+qcx5qp/YBSKF5VDNWzliZ9X0iQk15zZHxKifVvwcLFk7MOnnqE+DyluX4Ts8cNB+zEe8988YBJ4j3Hv1etIxuQYpSeL5zPh54HLhuUabG4aMLPorTpp525LUPd1biszfXHGlOuHbJtbho3kVZPzt98mtoAMbumIW7P/DzrGMfVZWxaa889h9xJYA733MjFp9yLQh0xO0DgPvffz+6e7tBSGHJ/1a45Oh/wA3vyrQ0/uGSPxxxEFOUwtc6xuLrjyiMHMn/xrWfWQsCZZ28q8ur8Xz6nPSr9z2NpctU1s+3LMX5v9qKWqyaciHaRxP+dNPAavIJtROOuEP/qw/4xyeB7dfsPZK2bhnTgu05J9QRNwCLp/MPb+74uXjjM28MiAsA/1YP9BwehT9/MtjqnVXHu9pue9eXcMEFA2uqzpx2Js6cdianNC8F3jfzI7j5/R858v3ck+Md64FnAcxIW9UrZ6zEyhkrB8TVNYsLGk7FJ086NfD46mgSpjYAXzpj4LEBwIoZK7BixgpsbgFWPwxcceIVWd9fNn0Zlk1fduT2F3uBYxozwur0Zv96jREjWJj5nVw1Wrgd2zQLS6b4dxUdNe4oTErryFHljTh6XGPW95tHZU7kuspj0pjM/92GEQNn3NSn09BdXUBVeXAZTJxNB4DblVc6XiGaCVzHiyr+B9x2lep4LgfmAg46aG+8EbjlFlS+/wLgdgB9FUB1FfCFwowDMRVuDQAejHxUnlFK9aYX2j8MoAzAD/QqrkGHCLjzTlz61XloHPcYUtX7Me2Xt6J2ZCVSdD3GVGdk/o/f+2N09XZlnZxHV4/Gtr/hou2Kbz6Hqz61G0SE7zwwAc1HH8bP/mP2keev+dSa9EtmhIX3L9dN3/4m5j/WjxWHH8R3v9DBrkb6Q21ExQgsOnALKk/ux5O3b8oSWAD/5dF7Y/agtRN+BagtJwHgk+e+L2bvSrrsMuCBMZyiJZqHjddsDPwxnXvKNPwLgK+e8Ijv4N9Tp56KM+tPxbPTgT9+8vcDvp978vnoI7z9YU76M93v5Hj8bcCEdHbp7Jln4+yZZ8OP+on8Np4+9iLccu5Fvo85Z+a56GoFzl04BjcvH7iU9ZxZ5+CcWfwP+8Ue4AEA5zd97Mj3V81chVUzVx25/c47wGeRmeEW9FcvwMKts60WFxx9QeBjxtPRAIAV8xbhuGkDvz9/4vwj18eMAap6s/8Cnd0wO+vx1M3pZZ2en1zv/1etTvH3dtZm/aWaFYsIbW3RHapAJqV98GDwTLreXhYMUXWaAD9m06bwx8St50ulWMzEHQcSdztB1B9GZwwXAAAgAElEQVTsccZ36HgdHVytEVaHGaerFOBaU1ddoK7HgZgM9I0j3FyuvALiCTeTjldg8IWbS6Gl48URvS6Fm7OVV9ddB1x3Hapuepxv91UCr7wKjM17ZZgvpsLtCQALADyeh2MxQin1ENjxLfSBANdei7l4HXP3pOdd3P1rbp/M+fTU9Ua5HLWcB95efnk5vnYb/zW6YgVwzz3VmDgxc8LUefsgpo6dgA99EPjBD6qQOlyVVTe3eTNh9UuE22/HkRRMFEuWAHffnSmOzuXFF3kOYVSxPpA9EsRPuAFcPxa0ozSX6dO5wSPsw2Xz5vCaNU15OdfxhY0EOXCAP+iiRoEA8bYnxFl3pWlo4DluYSdkvX80agAvEG/tVZx1V0DmMVEjQQ4ciNdMEEe4aaEVR7jV1UXPcYsr3PRj4owD0aNIwog7F66jI96/dcSIeCMm4gzgBdwKN93UEyWOTMaBAPGEWxyx4HLllY4XdWyFctxMhtLGdRddjQPRx5d4YK4nlvfxUfGihWD6A7g/4oXzjOmu0msAXEpEHyGicUSUyv3Kx0EWNbfdBnz1q8DVV3P1/9VX8+3bbjMKM28e8NRT3AywaRMPZQ4b9BrEJZfgSHu+l5/8hC/f8574sZYs4ZOU37qqri4u0j/xxHixxo/nJougWW5K8XaFOXPixZs+nZ8T5KZ0dnLX5tSp/t/PJWoIrx6+60q4xVl3pWlo4L8IwwSDFm5jfOo4comzpqq1NZ5DFle4tbVFz3ADMo8Jm+UWZ8G8pr7erXCrrY0n3OI4Wlq4xXHc4gqtqHg9PexYxnXcoo4trtAiiicEC+W46VRpVK+eS8ctrtAqK+MvSZVmx9KPjYrlfXzSeJNGpQdl9sUzP/KFqeOmh8L8MOD7yiJmaaPnt+mu0jvv5LOxz1y3ONiINS8nnsju1o9+BHzyk3xffz/w7W/zKqu4wggATk6Xtjz33MABuy+/zCeBOI4WwD+asJ2le/awWIh7fC1p83HDBv+Bvbrw10S4hQ30zZdwC1t3pfEO4Q0SK/v28Ykxzgk+ruNmktqMI9ziOHiuhVsch8zUcYuTKo0aBQJkxFMcx80kXkdHsICPK7R0PFeOm35MnHhlZdFOiolwi/P/pLqaRVvYSKDeXs4+uK5xcyUETVZUeV8/LF7c1GZPT3hGQDvBcYRbHAfPtMbNlYN3wlQe/fH5k2/AuBExPrzzhKnIugWA2fyQoU5zc/YsDKLo2Rh5hIgF29//PfDoozyG47e/5Y0EYaMz/Jg1i12yZ58FPpHTMKQnq8QVbgALyp/+1P97ek6kieMGBO8s3Zye8mci3PQAUT90GtW7JzYIvcbKZaoU4HRpS0C2PM7WBM3o0dG7XuOmNquq+CtMaPX1sTiK47jpk6xLx62jIzjdD+QnVRrXvQOiXS1TIRgWL+76LMBtqhTg34k48eLGAuIJtzi/YzpemMtkKrSi/p/Edcj0Y+KkXlOpzKzGsFje1w+LF+d3zLtCK+hnp+dMxnXcon4n4m5O0G6lawfvwqMvxqgY/w/yhenmhK/k6TgEh1xxBfDNbwKf+Qzwq1/xtPJp04ALLzSLQ8Q7Tb1T5zXPP89uUVxhBLBw27vXf9WTqXBrauJfyCjhFkd8ACzIdu3iDwS/v7pMHDei6LVXu3fz68QRM9qVC9tXundvfOE2Zky8VOn8+eGP0UStvdJCq1CpUoDFT9Dr6xNsHHEUN1Xq2nGL25ygHx8Wy/vYMFwLtzj7RU2aCfTjXcTzLnIP+n9lIrRc1rjpx8QRWnEdMu/rB2GS2ox6fFxhpB8T9flkEi/OAHP9/SjH7eU9LwFYjAdfexgLj18W2tGcT4ZfTdowoKoK+O53uXNxzhx2277//Xj/yXNZuZJF1UZPw6hSwOOP89zBOI0JmrCdpW+8wb802kmLorycRdk77/h/X9e+Re0p1aRHuR0RaLns2ME/vzjpQyCecBs/Pt7PL86i+X374jUmAPxv2L8/vJ4nbnMCEC3ctAgzSZWG1aWZpkqj4rW38x8BcU56hUiVunTcTIWWqxo3/ZjBdtzi7BaNGy9u/R3gtsbNJF7cWIC75oQ4QlB/b7Br3EziaXcujFR6c8Ktf7gdW9oilmXnkUjhRkR9RHRS+np/+nbQV29UPGFwWL6cXbFbb+UatRUr7OKsSk+wePTRzH1vvcXCyDTm3Ll86Sfc3nyTU7Nx1iJppk8Pd9zGj4/3IQtkhFtQg8KOHey2xRWqcYRbnPo2IL5wM3HcenqCT6L9/SzE4orUuMKtkI5blHCrq4v33satmYsjtFIp/v/pqplAPyZMHJk4brrGLUzg63iuUqWFcty8qdIgXAutuONA9PG5Fm6umhPiCMF8CC0g2iEziRfn2Kqr0ieoEmhOuAW8qUBflxq3EmHhQv5Kwty5LGoeeSRT55beB28s3KZO5ROaX4PC2rVmjRMAC7eHH/b/3ubN8dOkQEa4BY0E0cItLhMmcANHEHv2xKu9ATKF5i6FG8Cum98J/OBBPlm7Em76e3GEW20tCyjXwi1MbGnhFoe4qVKTeGGOm6nQ8j4nabyaGhbxYbVLrlOl+ahxM02VhsXyvnZUvGJNleajOUE/PiyW97Wj4sUVbi7jxRGBR4RbgceBRAo3pdTNnutfyevRCEUHEXDeecB992VqbX7zG05BmgotIt69muu4dXay4/a3f2sWr6WFHTK/D+fNm4HZs/2f50ccxy2oMcAP7bgFdVrt3h2/saO8nEVUkHBTyqzGTQuy1lauFcxF15eYCLewGXgmjlsqxaLHZVep9zl+mAg3l6lSIDM0NywWEC9enHEgpkJLP8eVcIvqZu7sLKzjFhbPtMZtsFOlJl2b3tcPOz6TGrewePlwyLyv7SJenFg1ReK4SY2bEMmHP8wnt/vvZzHy0EPARReZ1bdpjjlmoHB75RXuOlrkv5YuEF0P5zfLbdMms8aJ8eM5TRuVKjWJ190dLBhMUqVAZgivHx0d/METt8bN67j5oR0y16nSuDVzI0dGC7dUKp5YMEmVxqGuLtOlGoSJcCt2xy0qXmcnC4GoYcM6XpxUaZz3VZ9kw4SWUuaOW5j4yFeNm8t4rhwy/X1XqVITkVoI4RbmKnsZX5/+UOwroQG86SG75Tn3nUNEnyMiw9OuUCosXcodhrfcAnz603zS0jPiTJk7l+eleU/0q3lPunFaN2gkyP79fKI2SZWWlfEMPT/h1tvLQss0VQr417l1dfG/32RmX0NDZoRILibDd4GMIAsSbtpxM2lOCBNaJo6bflxUc0J9fbw/HPKRKgXCxUzcGjcg2nErBuEWJrbipjaBeJ2WceMRRcfTs8UK4bhpoRVWH1jsXaUuhWC+atxcdZXGFal6af0nF16B8bUxa13ygKnj9p8AfqBvENHlAH4D4P8AeJaIBm5SFkoeIuAb32DB9dOfAtdcwylPG/SmhWefzdy3Zg2frON2lGp06jK3s3TdOr40TeUGbU/YvZs/gF0JN32fqXALctz0/XEdPC3wglrubYTbwYPBLpRJjZt+XJTjFidNCuQnVQoEu2Q9PfzlqsbNJFXquqs0TrODiXCL67jFbSiKanYwLf4H3Dlu1dVcH9gb0q5n0mnpUrgRxdt24LKrNF81boOdKtWp3pMbz8TIqpgfaHnAVLgtQfZ+0M8D+B6AUQB+CqBwk2eFvHLGGcCrr/IYkDvusI9zyilcs/Xkk5n7Vq9mt8009drYyL9IuY6bnglnUuMGBAs3k+G7mjDhtnMnX7oSbtqJiyvcohw3fX/cmrmoER5tbfzexnWhXAq3fKRK9XP8MBFa+nGDmdospOPmchyIjueymcD7HD9MHTLvc4LiVVbG+9xzKdzixItqSvESx3ErhXEgcervdnVuBQDc/dK96OqNsI/ziKlwmwBgKwAQ0SwALQC+oZQ6CF6DdVzIc4USZ/ZsHjNiU9umqa0FFi/OCLeODl5Wr9drmVBWxunQXOG2bh3X3MyYYRYvSLjpVVi6gSEOroXbuHHuhVuQ46aFW9zUa9S+0gMHWIzFqYMCWGy5Em5aQLlOlQbFMxnmC7CAcuW46Vl0rsaB5CNV6tpxcyXc8jHHDYh28FwJLf1aceNFiRkThywf40B6e1k8RsUb/HEg/CH21NvPYmvb1ugn5AlT4dYGQJdALwOwRyn11/TtPgAFXAIhlApnnskz5jo6gKef5r/szjrLLlZLy8BU6Ztvcto17oeYZvJkFke5H5B6+PC0afFj6VEfLh239nb/DyAt3OI2J5SXs1AJctz27WNxbpIqBYKFW9y9p5ooxy3u3lOAxWJtbbTjFldoRaVKC+m4AdFDczs7+b2N87sRtznB1CELq/tyWTNnI9xcznGLE89EuEXVB8YVHzqey9Qm4D5elBAsL4/3x6DL5oTa6vSDCjwOxFS4/QnAdUR0PoBrkJ02nYXMvDdBCOTcc/kX6Ve/Ah54gE9eZ55pF2vGDHbYvCeDdevM06RA8Cy3jRv5gz3u3DWAP6BGjXIr3AB/103fFze1CYSvvdq/n4VWXIcsjuMWV2gB0c0JbW3x6+UAdueC4inFws20Zi4qVRrXwYty3EyFW5xmh5qaeK55PmrcdArORTyXws31HLe4zQ6Fctyi4pmmNgG3qdI48eKK1MpKd80JI6rTvZml1FUK4AsAxgL4Jdhd+4rnex8A8IybwxKGMsuW8aiOq64C7r6bd6jGPTHlsnAhO0R6JIhS7LiZNiYAmfEhueNFNm3ilKxpijhoe8LOnSwU4p6ggHDhtmcPC7Go5dJexowJr3GLmyYF8ue4BTkzbW3xhRbAjw0SWh0dLCZcpV5dO26m8eIINxP3DnCbKg2LZzK+Q8eLU5NWqK5S73OC4sX9txZKuBUqVRonXlzhVlHhLlV6xHErsTlu9UqpOQDGK6VmKaU2eL53NVjYCUIoZWXAv/4ri5qaGuCmm+xjLV7Mly+9xJdbt7K7ctRR5rF0Tdxbb2Xfv3GjWZpUM2ECd6TmsnOnmdsGRAs3k5lwAAupIMdt3z474RaU3rRx3Pr7gwWIqeNWVxfsuGkBZuq4BblktjVuQSLVteNm6pDp57iMFySOenr4fS/WVKnrGjcToeVy5RUQ3VVayFRpXCFo4ri5ak6oqawEqL/kUqW/J6LlSqkBpw+l1MtKKZ/TlCAM5P3vB95+G1i/3ryJwMv8+SwEtXDTl1rQmTBtGsfyE24mM+E0QY7brl1uhdvevfHr2zRRjptJ2jVOqtTEcdMiyk8I9vezCHOVKtX3F7KrVKngk56OF9eZyYfjFif1ahIvSAiaCCP9OFfCLc5AX9PNCXHimTpkUXPhTOINdmrTZbx8CLc48cpSZaisJFww6yJMrDP8EHeIqXC7F8BDRHRh7jeI6HQietrNYQnDgenTzZ2iXGpqeKivFmwvvMC1WQsWmMeqqGCB5hVuXV3skNk6bkGpUlvh5jeE19ZxC2tOcJ0qNXXcAH/hpt0pU8ctSGiZrM8C4qdKTWrcvM/LRQutuPWGejF8ECbCLR81bmHxTGbMAW6FWyrFJ+6oeETxnJl8NCcoFT0XzlVzwlBKlbpsTgCAygpCy8g5qKuM+UueB4yEm1Lq0wD+GcB96eG7IKLjiOhBAE8CMPi4FwQ3LF7MXap9fcATT3Ddm23N3MyZ2cJt82a+tHHcJk7kVGluYWwxpEqjmhNMHLfqaj6Z+Qk3pexSpYC/cNNCy5XjZpoqjRJaNo4bEOxqmQgtIF5XaaFSpVEulH6dQjhu+nFxhFbcuWv6OVHx4hAnXtyBuTqeK+FWqK7SQjhuANDetxd3r74XHT0hv2h5xnhXqVLqFgCXA/gaET0BYDWAYwF8DDLHTSgAZ5/N4uWRR4BnngFWJtjfkSvc9KgR060OAIs9pTJz4AA+qe7dC0yZYhZrxAg+sbiscTt4cOBf8EqZNycQsZDyE27t7ZzeNG1OAPzFlun6LCC8OcE0VarHi7ic4waEC8G4sXQ8V6nSsjIW5IPluGmh5dpxczVyw6RxIh9z3MLi6XS7K+Hm2iHLR6rUpJ7PVVcpACDVg/3t7dh+cHv0Y/OEsXAjorEA5oDntp0B4FkAs5VSP1JKhYzME4T8cN55fDI67zz+Bf3AB+xjzZzJqULtRq1dy5c2zQ46vertUk3i4PltT+jo4BOhaY2bdtRy06Xt7SzmTIQbELxoXt/nynGzEW5hzQmmqVIgXLhpARZXfGhRFpUqjYtL4QaEO3hK8f89V12qhUyVxoln2kzgPYageK6EoBYmrgbw2jhuxZoqjdtVGicFDgAoO1xa40CI6CYAbwO4EsC/gl22EwD8m/tDE4R4jB4N/OM/8vWLLrJrTNDMmsWXem3W2rUsOkxTm0BGnHmFm75uI9z8tifo26bCTTt0uTVzpuuuNEHCTQtgV80JSRw3v8Ju01QpwEIwyiGLW5PmOlXqsqsUCF9TpU/ursaBFLI5AYh2oVw7bi5TpSZCSz/OVaq0rIy/ohw8ongji4o9VYqynoKPAzGY/ASAd5F+D8DNSqmdAEBEmwD8jIgmAvg7pVSEKSkI7rnuOuCDHzRPQeYyfz5f/vWvwEknAa+9BhxzjN2aLz0XTm9e8F63aXZoaBgotHbs4MtJk8xiBQm3ffv40sZx8xNaxeC41dezaOvoGJh2NE2V6seGOW6mqU39PFfxXDpuYc0Opg5Z1DiQoeS4lbpwM3HI9OPiDMyN8zmaL+GmVPDrmzQnINVTcuNAjlFKXaFFGwAopR4HsBzAUgC/dXlwgmCCHueRhJYWFgWrV3Nt1ksvAYsW2cWqqeHO0lzHLZUy23uqaWwcuEtV3zaNp7dA5M6ZM91TqnHpuOUjVQr4p0tdp0pN1mfpWIBbx62zM3wunGmq1LVwc+m49fRwU5KreK4ct3yMA9HPCYoFFKarVD/OpdDSz3EVT6ng/yfG8aqo4I6baVfpWwH3vwTgdADTHRyTIBSMVAo4/njgT38C3niDT+wnnWQfr7l5oHCbPNmgnsJDUxMLNe/y5WIRbkEDfW0ct6oq/hB12ZwA+Mdrb+fXM3k/4qRK4+LacdNrpYJOei5TpTYOmfd5ruKFiZmysvgbRaKaE4rBcQs6PpOuTcBtjZuO56rjNR/CLSyeUmbxjprQgpMaT0djfWO8J+QB4+aEIJRS6wGc6iqeIBSKFSuANWuAH/+Yb59xhn2s5uaBqVKbNCnAwq2nJzu9uW0bi80JE8xi6VRprnDTt032sgJcE+fX8WrjuAHBi+b1faYrrwB/l+zgQbM0KRCdKjWJlw/HLShef79ZMwEQ3pxQDKnSsHgmDpmON5hdpcMxVRo3lvcYgo7PNF5QZ2lfH4u3uH+8jagqx8jysRhRYTlzygHOhBsAeFOoglCqvPvdfPnP/8w1bzNn2sfSwk2nrvTeUxuamvhy69bMfdu2ceOEaYq4qooFTW6N2870b7CpcGtoYNGSezKwcdwAPrYg4VZdbVCPguhUqYkI1PEGq8bNpXAzHbeh4xVzqtT7PL94psLNldCKM9vM5TiQQjYn6Me5FlpRwtKkq1Q/JyiW93WjWL37eTy27km0Hw74EBgEnAo3QRgKHHcc8NGPspN1663JYs2ezSeqLVv4L75Nm+xmwgHBws2mXg5gcZbruO3axWlSE2EEBA8Ibm3lWCYnUCDccTMVWlGpUtN4LmvcwoQWYC8E/eKZDgcGwlOl+jUKnSp1JdxcznGL2sTQ38+fB6Yi1aVw6+3NLrtIEi/KcSvmVKl24uLGO6wOAX0V2NleOJ9KhJsg+PDDH7JbdP75yeLMm8eXr73GI0Z6ezP3maKFm7dBwbVws9nqAAQLt7177daahQk3k/o2ID+pUlc1aRUV/OUXT3fCunLc9H2uhJu+P268KDFjszkBCBduccWCjueqxg0Id7VMa9JcNydEuVo2qdIoB6/QqVJXjhvPcSuh5gRBGE6YntD90CLtlVf4CwCOPdYu1qRJ3M7u0nHLTZXu2mVeLwcECzebrQ4Ai7Og5gRT4ZaPVGlnp3+XmmmNG8DCJyi1qZSdcPMTW7aOW1j9nfc148aLEoJx48VZoWWSFo7TVWoSL0y46ftd1czZxgsSMzZdqsXcVRoWz1i4leA4EBBRiogeJ6LZ3uv5ODhBKHXGjeOatueeA154gd0Vmy0MAD934sSMcDt8mIWRrXAbN86d46YH9uo5cJo9e8yHAwPBjtuBA/aOm8tUKeDvkpk6bgALFb9YNg6Z61RpWI1bPoRbZWX84cVxmh1MhZarVGlUPJt1XIDbVGlUvIqK+O9FKaRKg5oT9OsM2c0JaQjAMgD1OdcFQfDhjDOAp54CHn8cOOUU83ovL01NGeG2Pb0qL2mq1Dvzq1gct6DmhP37zbc6aAfMZaoUGCi2lDKvcQOCHTdbYeR9rhd9vK6Els3xVVeHxzN1yIBw4VaorlIdL0gY2Wx1AAZPuBltEoDbVGmUG2h6fK4dt8ZR4yRVKghDnfPP5w0HL70EnHtusljNzcCGDXz9nXcy99kwfjx/oGpBc/gwCyOXws11jdu+febCrbycT5AuU6XAQCHY3c3F3q4cN1uHDHBf4+Y30NdWWIYJLVMRCIS7Wi5TpaZCcDBTpfkQgib1fC4dNz13z9XctaiuUtPmhNNblqCxthlNI5viPSEPiHAThDxz4YXAWWfxWJErrkgWa/Zs4K23uL5q3brMfTboNVl6bZZOm9qkSkeM4JOGV7j19bHQshVunZ3czOHFRrgBLM5yhZtSLA5NR5Vo4ZMr3LTQclXjZiOM8tFVCviLo3ykSl07bqap0qBNDErZpUqjhFahUqVRLpRNI4Yrh4woXAjquWuFctxqqlJQvRWoLk+QOkmICDdByDMVFcDvfgesX28uEnKZM4dPLhs3crzKSnvHTadYdepVz3CzcdwAdt28wq21lR0oW+EGZIutzk4+oZhudQD8Z6+1t/PxmQ4HDkqV2ggj/fiwGrdiEG5+Yqujg2ugTLZOhKVK8yHcTFObgL846ulhseAq9Sqp0uh4roSWa+H2u40PY8eBvWjr9kkJDBIi3AShhJgzhy9ff52/Zs6038+aOxdu1y6+tHHcgIHCTXesJhFu3nSpbnxw5bjZbnUISpXaLKwHghfDu06V2tS4hXWp6lElcRaHa8JSpaajT1ynSsPEjM3wYpep0vJyFslB/9Z8NCcUKlUaFa/Qwm1391agvwK7D+2OfnCeEOEmCCXEwoX8Af788/x1wgn2sXKFm252cC3cbLtKgez9p0mFW67QshVuQalSLTJtUq+uHLcwhywfjpvJsel4xZoqDYtn6pABblOlceMVqsbNZaoUyI9wc9VVWlbeL80JgiDEp76e58Ddey+nNk86KVms+nre6gBw+pUImDrVLl7uvtIkjpt+jnfO3P79mdcxpa7OveOWK7b0ei/TcSVBzQlaGJoIrbIyPlG57lItZuHmOl6Y4+ZauLludnC1kquYU6W2w4ZdCcGyir6SHAciCEIBOe88rm8DgHe9K1ms6dMz3akbN3Ldm+m6K03uJgbXwk07bjY1boORKk3iuPkJLX28pl2vYanXmpr4s7mA8PEiNsItrO4rH12lpsIoKJ7pVgf92KjUpqvxIt3dLNrjlk3EGcA7VFKlrrtKy8r7gf5K9Pu1Wg8SItwEocT4zGeABQv4cubMZLFmzgTefpuvb9gATJtmH6uxkR03/QGZRLjpJfdeIVjsqVLXjls+hJup0IpT42ZC1Fw4E4csrO6rt5e/hkuq1Ca1qZ/nKl6YcBtKzQmzx00HAPT0lJBwU0r1AVgO4A3vddcHJgiCP01NwJo1wNe/njyWFm79/Xw5fbp9rMZGvtTjRfbs4Q9005M7wOKMKFu4FUuqtKaGjy1XbCVx3Hp7B9bgHDzIwsRGbAUJN9OO12JOlRIFu1qmC+uB0k6V2rqLg5UqLYYaN1fxzj9mFQBgUo1lO78DrBw3pdQTSqlDudcFQSgtZs/mD/1XXwU2bbLfowpkhJtuctB7VE26DjXl5ZwSzU2VlpWZO1BAZqBvf3/mPi3cTIVWKsUCyM9xI7IbBwIMFIJ6OLDpzy9IuHV0FF64uRwHouO5dMi8z00az3Wq1KXjFlXjZhOvv99/Bl5/P/9hUuxdpXGbEyoq+BdS9ZXHe0IekFSpIAxjFi3iyx/+kC+PO84+Vu5A361bM52rNuTWzO3bx2LORgg2NPAJxDtepLWVhYzJHDKNn3Bra2OBaFJDBmSEaO6mCJutDkDwftEkjpurGreamuAht6Y1bkB+HLcw4eZqHEixpEpdDuANime8xB3hDl6+ukoj4z3zDLBqFR7e8CAAYP2uDcCqVXz/ICPCTRCGMQsWsHC5806+rYWcDXqgr+5S3bIFmDLFPt64cQNTpTZpUiAzksTr4LW2mqdJNXV1/l2lpvVtQMbxyxVubW12wq2mprhr3ICB4qi/33zuGiCpUo3rGjeb1GZQPFvhFuWQxf33OmtOuPFG4LHHsO31pwAAWz5xCfDYY3z/ICPCTRCGMVVVvI4LABYvTuaQTZrE8TZu5CnzLhy33FSpTUcp4L9LNalwC3LcTPEbNgwkc9yKtcYtaISHjaOl47nqAnXdVVpVxc5i7to2gAVOKpXZyxk33mDVuNmmXsMct2LtKo0d7+GHgYULUX6Yf/G7Nm7hwZoPPxzvQBwiwk0Qhjk33QQsWQLcfnuyOKkUd6Vu2MCCq6srmeOWmyrdvduuQxXIPM+VcAuqcbNZaRYm3GyEYDHXuAU5bjq+q1SpjRB03VUa5eBVVZml/Yu9qxTwF0emc9f0Y53NXUuPSUkcL5UCXnwRX16zBZMbfofTt/YAL75oXhvhAKPqOiJaAuBcAEsATAZQA2APuKv0CQA/V0rtd32QgiDkj1NOcVemoefCvfkm39YrumwYN44FYH8/fzZu326/KSLIcdMNFabU12fHAlh4JdkSoceJaA4ezHcDI2YAACAASURBVNQNmuAnKgE7x02Lj1whqFQy4ZYrBG1Sm/r4ijlVquPl/txNHTIdz5XQ0k5fmJgp9lSp63iRta79/cDxx+PDHWvw4Y7H+L7jjy+IeIv1akR0CRG9DOBPAK4BMALAOgDPAdgP4GQA3wOwlYh+REQteTpeQRCKmJkzgXXrgLVr+fZRR9nHGj+eU00HDvDl7t32Qst1jdvYsZnxJJp8OG42qVK/YcOAXY1bKsWCIFdo6QYDV8JNC0NT4RY0XsRGuLnuKg1ztbq77YRbWJeqiXAjyk+XqqtUadhcOFvhFtackErFGF58zjk8h2nhQv7Pv3Ah3z7nnPgH4ohIx42I/gJgAoD/APARAGuUGjgymIhGATgfwIcBvEpElyql/svx8QqCUMQsWgR861vAQw/xh2WSuXA6vbl7N5+w+vvtHCiABVUq5S5VOnZsZiCwxrbGzXVzwsiRLNyUyk7F2ThugH+Xqs36LCA4HWnruI0YMfB98Ma3SW0OVurVpePW1WXu9gbFU2popUqj4vX0xIx1yy18+fDDR9KmOOeczP2DSJxU6Q8BfFspFaD1GaXUAQD3ALiHiBYAsPyIZYjo/wD4HwAOA3gLwKVKqdb0964H8HEAfQCuUkoNfnWgIAgDWLyYL3/6U07Bxl3B44d217Zty4gbW+GWSvGJTQu3vj4WbkmaHVpbOY7+N9o6brW1LLC8wk2pZI5bX1/2eA3dtWkj3PxcLVvhFpUqdTVsOInjFpYqdVVHpmvcTHDpkIXF080UQylVWlERPvok1kigU04BHn00czuVyr49iESmSpVS/x4l2nye8xcHYupRAMcqpeYDeBPA9QBARHMBXAxgHrje7v8SUYLTgyAIrpg/P+M6nX12sljN6cHkmzZxhyqQGTlig1e47dvHYmbCBLtYY8eyuNJ1aT09LBZsHLdUisWWt8atu5tPoEm6VL3pUluhBfiPF3Et3GxTpS6FW9gKrc5Ou2YCIFi4mTpuUbtKTYVb0Kw004X1OhZQnF2lceKZ/uwKjVFFHREtzteB5KKUekQppRupnwWg+9MuAHCfUqpbKfUOgPUAThqs4xIEIZiKCk6Vvv/9wGc/myyWFm4bN3LDAwC0JKiebWjI1LjpbtUkwg3IpOls111p9GYHje2eUu9zvPH0dRshWFs7cGZd0lSpq+aEIOFmkyoNW6Flm9oE3Na4haVKbRy3sNTmcEmVDnnhBuD3RLQ8L0cSzscA/CZ9vQnAZs/3tqTvEwShCPjQh4D777frsPRSXQ1MnMiO29tv80naVmgB2Y7brl18qZfZmxIk3GyEEcCCz7Vw8zpuSYSlX7NDUsfN1TgQl46bfrxfs4OtQ6af6xfPdarUlRC0FUbe57qIN1jCrbvbLFYxYCrc7gXwEBFdmPsNIjqdiJ42CUZEjxHRKz5fF3gecwOAXnD9HAD4mdUDmiXSz72MiF4gohd2ewdCCYJQEsyYwV2q77zDbpvNuivNuHEZ4ebKcdPxdIepbbODS8fNr0s1ibCsrx84XkQ7cIUeB6IbJ7w7aL3xTMWMS+HmOlVaVZXZ+5mLyxq3JKnSMCFoGq+nh8sRguK57CotNcfNaI6bUurTRLQdwH1E9Fml1LeJ6DgAtwH4GwCvG8ZbGfZ9IroE3Km6wtPJugXAVM/DpgDYFhD/LgB3AcAJJ5zgK+4EQSheFiwA7ruPmwiSrOMCMqlSpZI7btpN1I6bFnC2A4JHjswsvQeSCy0g2yXT9XO28TZsyL7PVlgGpUqT1LgBLIS8IrKzk2vWTDYT6HhBqVfTY8tHqlQ/N/ffVWjhlo9UKeDf8Rl7fEdOvOHsuEEpdQuAywF8jYieALAawLHgdGaCFdXZENG5AL4I4N1KKe+v0i8BXExEVel5cbMBPO/qdQVBKB4WLWJB88473NSVhMZG/pDev5+H+ZaV2adzc1OlunbONt7IkdnNCfly3GxSpXV1A1OltseXD8cNGCi2bISWjhck3GyFlstUKTBQbPX327lGQWKmWFKlYfFMhVZYV+mQd9wAgIjGApgDHsVxBngo7zJPI4ErvgGgCsCjxPmRZ5VSlyulXiWi+wG8Bk6hXqmU6nP82oIgFAErPZ780qXJYk1N+/SbN3PdXFOTuSOj0SnRXMctiXAbjBo3W8ctSLiZxgsSWjr1ajquRD8+N15np51wy0eNm8tUqV88LUhs4uU2nXjjFzpV6n1ubjxT4VZZGT68uNQcN9OVVzcBuDb9vH8Fd3R+G8C/AbjK5YEppWaFfO9WALe6fD1BEIqPGTOA225jgXXiicliaeG2aRN/6a5VG8rL2b3Kddy0E2dKbnOCTpva1Mz5jQPRbp5tc0J7e/ZAX1thWV7OAiO3Zq69nU+epifQICHY2WkuZHS8oGYHm3o5/dxckqZKc2N5v28Sz294setxIElSpUFC0Ea45Q64ThKv0Jj+vXkDeLXVzUqpnQBARJsA/IyIJgL4O6VUQAmgIAiCOddf7yaO13HbvBk4+eRk8bzbE/buZZFl6+CNHMniRQ/01c0ONgOCR4zgGiC/VKmtg9ffn72kvq2NX8PG1aqr8xdudXXmscKEm22qNHcHLWC3mSBMuCVJleY6R0mEm6uu0rAat2JIlUZ1qdr83yskpjVuxyilrtCiDQCUUo8DWA5gKYDfujw4QRAEV0yaxC7H2rUs3KZNSxavoSHbcUsy/iTXJdu3j4/VRnwQDUxvtrWxKLERllrsecWW3upg0+Xrl3p1LdwOHbKL5zJVGnRstvGCHDebmXVAsJgZqqnSoK7SUkyVGgk3pdRbAfe/BOB0ANMdHJMgCIJzUing2GO5S7WnBzguYSvV2LGZFOmOHZkVXTZoZ00Lwf377ddxASyOvI6b7TouICOAvGLr4EH7mXX5cNxya7WS7GV1lSoN6qDVu0CLIVU6GJsTkqRKg+K5dtxKrTnBuKs0CKXUegCnuoonCILgmgULMjPcko4XmTyZ96gCfJl0HReQvZLLtl4OyCya17S12Qstv2YH2z2qwOCkStvb3Qo3b5o4LqkUC4Jc4dbby6lnU7EQ1OxQDKlSveszLFUaax8osl97MLpKh6TjRkS/IKJYH3FKqZ1EVE1Ef09Elyc/PEEQBHecc07m+pw5yWJNmcJjRfr6eJdqEuGm579pB2/fPreOWzEJN7+BvrbxBitV2tHhbs+rbWqzmB03ouDdp4cPs3BKGdhEUTVz4rhFsxHAs0T0HBFdTUSLiSirUoKIJhPRe4jo+wC2g2e6vZSH4xUEQbDmwguBz30OeOIJswGefkyZwqJt3ToWCi4dt/373TpuSVKlQeNFkjhug1HjlsRxy53YnyRe0Mw6UyGYjxo3V8JNx3OZ2gQGR7iVouMWp1T1MLj54IMAbgIwCoAiojYA3QDGAKgAr6J6HsA1AH6slOr3DycIglAYUingjjvcxGpKb0h+7jm+dOm47d2bLJVbX59J4wIstGxr8IIcN9t/b7GnSoHsAb49Pfxl67i52hKRD8fNVRdoVLxiEG5hK6+GonC7BsD9SqnPEtFBcOfoKQAaAVQD2AtgLYAnlVIb83akgiAIRcT06Xz561/zZZLU6+jRLCr37mW3Z+dOYOJE+3i5mxhcO27FXuNm65B5R3jo6zq2bbzcY9O3XTlutlsnqqrYMdYjaDRJHLegVKlNLP1cv3im78VQS5XGEW77wK4awCuofq6Uuj1/hyQIglD8zJnDtTs/+QnfPvpo+1ipFKdGd+/mNGlPD48vsWXs2MwsOCBZjZsWVH7jQGzwq3GzFW6Vlfyz84qjnh772VxeIahT1bZCSz8nyHErBuGm43mPpRRSpab1n/rYvEOkkxxfoYlT4/Y0gDuI6O/A6VBZ1i4IwrCnshI45hi+3txsL2Q0jY2c3tyZnpKZxHEbO5Zdp+5u7mBMMr4j13FTKnmNW3d3JnXV38/HahOPaGAnqO36LMDfwUsSLyxVWkzCzS+eTfNEsaZKKyr4/21fznLMvj67Dt9CE0e4fQbADgB3g0XbY0T0FBF9jYguJaKFRGTQ6CsIgjA0OOssvvTuVLWlqYm7U3fs4NtJHDdvs4NeV2Ur3PSaKi3curr4hOfKwdPCyHZ6vUvh5rftIInj5pcqdd2cYFszFySOOjv5tUy6QHU8V3tZo4Sbq9SrzYy5YiAyVaqU2gZgFRFNArANwH8BGA3gXABXph/WQ0SvAVitlPp4vg5WEAShmPjKV3gul4u1XE1NwOrVbhw3Ldz27cucnJJsdvBuO7DdU+qNBbBwGzMmI+BshVttrb9wc1Uzl9TBy3dzQj66VG32vAalSl0Lt+5us5lwufG8PyebrQ7FQOwFKEqpHUT0MwB3KqVeBwAiqgOwEMCi9NfivBylIAhCETJqFPD1r7uJ1dQE7NoFvPkm325uto+l67P27s0IjwkT7OO5FG65jltS4ZbvVGlSx811qjR3V2k+UqU2q9aCUqX5EG627mJuZ+mQddy8KKUuzLndDq6Be9rlQQmCIAw3mps5pfm733G9W5LF195UqT4pjR9vH8/bpepKuOk4roWbjucqVVosNW7l5VzT5ye0iOyX1rt03IJSpabvbZhw6+pylyq1HX1SaJytvBIEQRDs0btTn3wSmD07WSwt3Pbsyaz4SiLcvF2qeiODqxo3LeCSCDfvrlLXqdKkXaWuxoFoceYn3KqrB3ZLRhFW42bjuFVXD3QDAfeOm8t4th20hUaEmyAIQhFw7LGZ67pb1RZdH7d9u3vh1trKl0nnwuWmSm0dvNra7PEixd5ValuTBrBgcZnaBNzFq6lxL9xyj00pvs80XtAuVXHcBEEQBGtGjACmTuXr73tfsliVlSzUtm3jurnqajvhoRk7lhsdgMxaLttmB9c1bt76O2+8YukqPXw4ewxFR0dmt6cpQY6bzbG5TpVWV/vvebWJFyS0envtxndEpUpLzXEzqnETBEEQ8scf/wjcey+wYkXyWE1NLNxqa/m6aSrNixZuSrkTbq5q3HKFW7E5bgALGv3v0wvrbd4PP+HW0VHcjptO5ZqQSnFNX67QSrKXFRhG40AEQRCEwWHqVOCLX3QTa/JkFm4VFUBLS7JYY8dyR96hQyzcysuLp6s0SLjZxMtdc6WvE9m5UFoI+gk3G4IcNxuhFZSO7OzMdCWb4NJx08cXtJfVVrjldpWWquMmqVJBEIQhyJQpwMaNwDvvZPaq2qJP5Pv2sXBraLB38Orq+Lm6S1U3OyQRbu3tnEIDMkLQRhxVVLAoze0qtXXIglKvtsItqGYuiePm52rZpkpd1bjpeEGO23AfwCvCTRAEYQhy7LEssnbtSi7cvF2qWrjZkkoBo0dnmh327eM0pO3JUzt/2mk7dIiFjOnkf01ul2pSoaVjuIhXW5t9bEBxNSfkikql3NbMJXXcpDlBEARBKFoWLMhcX7QoWSy9fmvHjuTCDeCNCVq47d9vl5rT5O5SPXQo2Qy8urqB40VsGzu8qVKNbTOBjpdv4ZZEaPX1cQOBRgsjV+NFbGvcgpodZByIIAiCUDQs9uyxWbYsWazJk/ly2zb+amxMFm/MmEyX6r59fNsWP+GWpIM2t2bOheOWmyq1ETLAwPVeOrbLrtIkjpt+vsZWaOnnBAk3GcArCIIgDDnq6oD164Gnn7YXHhrtuG3bBmzZwvVzSfDOhXPtuB08mNxxy212sBWCg5EqtRWC+RjAC2SLrSTCza9LVZoTGBFugiAIQ5SZM4HTTkseR8+Fe+UVPrHreXO2eB23/fvdOm4HDnANXZJ43oG+SYSWX6o0aTxXqVI/odXfz2LGVmjp49Ekddxya9xs4wXteZXmBEEQBGHI0tTEc+YAN8LN25yQRLjpDQ66S7W1NZlwy4fj5kq4BaVKkwg3bzwtbFwJQf3vLnSqVL9+blpYHDdBEARhyDJvHqdKAWDatGSx9EDf/v7kwk2LNO9KLpeOmx4HYoPfQN8kzQkuu0pTKX5e7rEByWrcXKVK/YSbbarUT1R644njJgiCIAw5vF2q8+cnizVpEncgvvMOn0x1DZ0NWvR5hZvtHlXAreOWO2wYSN6c0NubcYr6+vi6KyGYVGgB7lKlfjVutvGChJs0JwiCIAhDllWr+HLlyuQnOt2l+uKLfJmkS3XkSB6Ou38/zw1zUePmFW4HDtgLwSDh5srBS5La1PFcOW6umxNcpkqjatxKLVUqK68EQRCESBYuBN5+O9moDY0Walq4aSFng3egr96gkFS4dXSwm0XEIs5WuFVX8/Fp4dbXx2IhiUMGsEs2enQyoaXj+Qk3180JtkLQ1QDe8nL+8nPcUimgrMz8+AqJCDdBEAQhFkl3nmpcOm5AptmhtZVvJ21OADIpRKXY1bOBKDv1qoWIC+EGZERXEsfNL1Va7I6bq3iHD5ee2waIcBMEQRAGGS3Unnsu+7YtWrjpOrckwi23S9V7nw3eZgctklylSpM6bi5TpYMxgDdJajMoXqnVtwFS4yYIgiAMMtXV7N61t7NoSyKMgMxcuJ07+faECfaxtOhrbQXa2vi6reMGsOOmhVvSeLmOm4tUqevmBNcDeJUaGM+VcLPtyC00ItwEQRCEQUev5Dr++OSxJk5k0aaF28SJ9rG8XaradUvapaqFm06ZuhZuSRy8fDpuSee4KZW92aGrix2ylIVyCUq92hxboRHhJgiCIAw6K1bw5fLlyWM1NgLbt7sRbl7HzZVw04JNO25624MprlOluY5bsXWV5sbr7ravSRtKjpvUuAmCIAiDzqc/DXzgA8mG72oaG/mk/sYb7MgkEVpex02LhySp0vp6YOtWvu7acdNOnm2nb67jljS1CbitcdMx9PuZxCEbSo6bCDdBEAShICRZLu9FNzesWcPDfInsY/kJt6Rdqrk1braOW5BwSxLPVaq0ooJ/7n6Om41LFrSJwaVwK1XHTVKlgiAIQkmjhduf/wxMmZIslnZ3WluB3bv5+rhx9vFGjsykXF05blps6Xh6hIkpehyIbgBIUpNGNHDbgRZaNkJ6MFKlpeq4iXATBEEQSpqjj85cP/bYZLHKylhY7d/Pwm3kyGSzvkaPzgg3VzVuLh03pTJjNpLWzOUOzU3qkHmPyUW8oeK4SapUEARBKGm8u07nzUseb/x4YNeuzPUkjB7Nwqirix2yVMq+C7SykjcAaOGmHbckNW4Ax6uu5svycvvZZrniyIVwk1TpQMRxEwRBEEqej36UnbHzzkseS3ep7t7tRrgB7OC1tbE7lqQGz1uX1t7Ot23GY+hYQHa8ujr746upceeQ+dW4SaqUEeEmCIIglDzf+x47ULNmJY81eTILtz173Am31lYeEpy0i9a7purgQfv6Nh0LyMQ7dCjZLtpccdTZmUxoAeK4+SHCTRAEQSh5ysq4s9EF2nHbvj3ZTDggI9RaW4G9e4GGhmTxvLPX2tvt69t0LGCg42ZLruPW0WEvBAejxq1UHTepcRMEQRAED42N7Ga5cPC8jpsL4eYd6OvKcXMl3HLF0aFD9vV8MoA3GHHcBEEQBMHDzJmZ63PmJIvlWrh5u1STOm6uU6U1Ndlz4ZLEy3eqVHfTlqLjJsJNEARBEDycfHLm+uzZyWJpobZ7tzvh1trK1w8cKK5UaV1d9gqtJMLNrzmhszOZcOvrA3p7s+OK4yYIgiAIJc6UKey6zZ8PzJ2bLFZDA9febdnCgsulcNu/P9n2Cb+5cEkct9zdpy4cN9c1c1qwJZ1ZV0ikxk0QBEEQPBABf/kLn+xtR21oUimeM/fKK3zbtXBL0qWa67gdOpTMcautzQwF1nFdpko7OtzUzNXVJdujWmhEuAmCIAhCDkmcp1wmTwaeeYavNzcnizV6NDclHD7MAi6JcPNz3IolVVpZmb37tK+Pa9JcNTuUsuMmqVJBEARByCONjRmXbMaMZLF0s8OmTXyZJFWqRVV7Oxfru0iVdnQA/f38lcRxI8puKNBCK6lw03HEcRMEQRAEwZeWFv/rNmjh9vbbfJnEcauoYCF04AALmt7eTHwbtFvX0ZHZvmArtAAWVTqNqy+lxq0EHDci+gciUkQ0Ln2biOhrRLSeiP5KRIsLfYyCIAiCEMSpp2auJ0lFAhmHbf16vky6iUGPF9GOYBLh5nXwdMrUhYMHZC5dp0rFcXMMEU0FsArAJs/d7wIwO/11MoBvpS8FQRAEoeg44wy+/PKXk8dqbOTLV1/lSxfCrbXVjXDTovTQoUxTh6suVX3pSriV8jiQohZuAO4E8AUAv/DcdwGA/1BKKQDPEtFoImpUSm0vyBEKgiAIQggTJ7IwGjUqeSwt3F54gS+bmpLFcynctEhzKdx0l2q+HLdSFG5FmyoloncD2KqU+kvOt5oAbPbc3pK+zy/GZUT0AhG9sHv37jwdqSAIgiCE40K0ASwCiYDnn+fLpMJt1Khs4ZbkOL2pUr2Wa+RI+3jeLlXXwk2aEywhoscATPL51g0AvgTgbL+n+dyn/OIrpe4CcBcAnHDCCb6PEQRBEIRSobwcmDAB2LmT58NVViaLN3o0sG5dZo2Wi1Rpezt3lQLJhFttLW+cAMRx81JQ4aaUWul3PxEdB6AFwF+IW1OmAHiJiE4CO2xTPQ+fAmBbng9VEARBEIqC5mYWblOnRj82CpepUu3WtbXx3DXvfTbU1gIbNvB1V8JtKIwDKcpUqVLqZaXUBKXUdKXUdLBYW6yU2gHglwA+ku4uXQLggNS3CYIgCMOFBQv48qijkscaPZo3MOzbx7eTCC0t+lpbWbwljeeyOUE/TwvAUnbcilK4RfAQgLcBrAfwXQBXFPZwBEEQBGHwuOgivrz88uSxJk1id+zVVzmtmUTIeIWbTr0mrXHTzQn6sr7ePhaQEYAyDiTPpF03fV0BuLJwRyMIgiAIhWPVKi7+TzoTDuB1XAB3qSZtdKir427S1lZunCBKvvtUCy3t4NkKt9z1XpIqFQRBEARh0HAh2oCMcFu3LnPdFiJOjR44wEJr5MjMWBAbamt5P2lfHwvV8nJ7oVVWxs/1Om7V1ZkND6VESThugiAIgiC4xyvWkgo3INPsUFaWfASKdy5cWxu7bUmEltfB6+oqTbcNEOEmCIIgCMMWPdAXcCvcysuT1bcBmee3tbHjljSed6Bve3uy4cCFRISbIAiCIAxTqqoy1/VqriRo4dbfz/PmksYCMqlX2/o2jddxa29PHq9QSI2bIAiCIAxjbr2VL1esSB5r/Hhg1y5gxw7uWE2CTrW2trpz3LRwc9XcUQhEuAmCIAjCMOb664HeXjc1X01NwNatPCB44sRksXLnwonjxohwEwRBEIRhDBE3E7hg8mQWR4cOuRVu4rhlEOEmCIIgCIITvLPgXKVKDxzgL5fCTRw3QRAEQRCGPd7O1JaWZLG0cNu/n5fNjxuXLF5dHTttgAg3QRAEQRAELF6cuX7iicliVVfz16ZNQE8PNz4kYfTozCquUk6VyjgQQRAEQRCcUF8PXHopCyMXC9zHjgVef52vuxBu7e3A4cO8bL5UHTcRboIgCIIgOOMHP3AXq6kJWLOGr7sQbgCwbRtflqrjJqlSQRAEQRCKkilTMnVpSYWbrpnbuJEvkzY7FAoRboIgCIIgFCXeLlVXmxjeeosvkzY7FAoRboIgCIIgFCVauKVS7L4lIVe4NTQki1coRLgJgiAIglCULFnCl/39LN6SoFOlpS7cpDlBEARBEISiZOlS4OKLgVWrkscaM4Yv163jSxFugiAIgiAIDiEC/vM/3cTSmxz++le+HDvWTdzBRlKlgiAIgiAMeaqquMGht5dnuFVWFvqI7BDhJgiCIAjCsEA3ODQ3F/Y4kiDCTRAEQRCEYcHUqXw5b15hjyMJItwEQRAEQRgWHHccXzY2FvY4kiDNCYIgCIIgDAuuuw7YuRO4/PJCH4k9ItwEQRAEQRgW1NYCd91V6KNIhqRKBUEQBEEQSgQRboIgCIIgCCWCCDdBEARBEIQSQYSbIAiCIAhCiSDCTRAEQRAEoUQQ4SYIgiAIglAiiHATBEEQBEEoEUS4CYIgCIIglAgi3ARBEARBEEoEEW6CIAiCIAglggg3QRAEQRCEEkGEmyAIgiAIQokgwk0QBEEQBKFEIKVUoY9hUCCi3QA2DuJLjgOwZxBfT/BH3ofiQd6L4kHei+JB3ovioBjfh2lKqfG5dw4b4TbYENELSqkTCn0cwx15H4oHeS+KB3kvigd5L4qDUnofJFUqCIIgCIJQIohwEwRBEARBKBFEuOWPuwp9AAIAeR+KCXkvigd5L4oHeS+Kg5J5H6TGTRAEQRAEoUQQx00QBEEQBKFEEOHmGCI6l4jeIKL1RHRdoY9nOEFEPyCiXUT0iue+sUT0KBGtS1+OKeQxDheIaCoR/Z6IXieiV4no6vT98n4MIkRUTUTPE9Ff0u/Dzen7W4joufT78F9EVFnoYx0uEFEZEa0mol+lb8t7UQCIaAMRvUxEa4johfR9JfH5JMLNIURUBuCbAN4FYC6ADxLR3MIe1bDiRwDOzbnvOgC/U0rNBvC79G0h//QC+JxS6hgASwBcmf5dkPdjcOkGcJZSagGAhQDOJaIlAG4HcGf6fdgP4OMFPMbhxtUAXvfclveicCxXSi30jAEpic8nEW5uOQnAeqXU20qpwwDuA3BBgY9p2KCUehLAvpy7LwBwd/r63QDeM6gHNUxRSm1XSr2Uvn4QfKJqgrwfg4pi2tM3K9JfCsBZAB5I3y/vwyBBRFMA/A2A76VvE+S9KCZK4vNJhJtbmgBs9tzekr5PKBwTlVLbARYTACYU+HiGHUQ0HcAiAM9B3o9BJ52aWwNgF4BHAbwFoFUp1Zt+iHxODR7/DuALAPrTtxsg70WhUAAeIaIXieiy9H0l8flUXugDGGKQz33StisMW4ioDsB/A7hGKdXGBoMwmCil+gAsJKLRAH4G4Bi/hw3uUQ0/iOh8ALuUUi8S0TJ9t89D5b0YjdxgFgAAAzZJREFUHE5TSm0jogkAHiWitYU+oLiI4+aWLQCmem5PAbCtQMciMDuJqBEA0pe7Cnw8wwYiqgCLtnuUUj9N3y3vR4FQSrUC+AO45nA0Eek/3OVzanA4DcC7iWgDuIzmLLADJ+9FAVBKbUtf7gL/QXMSSuTzSYSbW/4MYHa6S6gSwMUAflngYxru/BLAJenrlwD4RQGPZdiQrt35PoDXlVL/5vmWvB+DCBGNTzttIKIaACvB9Ya/B/C36YfJ+zAIKKWuV0pNUUpNB58bHldKfRjyXgw6RFRLRPX6OoCzAbyCEvl8kgG8jiGi88B/RZUB+IFS6tYCH9KwgYj+E8AyAOMA7ARwE4CfA7gfQDOATQDer5TKbWAQHENEpwN4CsDLyNTzfAlc5ybvxyBBRPPBRdZl4D/U71dK3UJEM8Cuz1gAqwH8nVKqu3BHOrxIp0r/QSl1vrwXg0/6Z/6z9M1yAPcqpW4logaUwOeTCDdBEARBEIQSQVKlgiAIgiAIJYIIN0EQBEEQhBJBhJsgCIIgCEKJIMJNEARBEAShRBDhJgiCIAiCUCKIcBMEQRAEQSgRRLgJgiAIgiCUCCLcBEEQBEEQSgQRboIgCAYQ0Swi6iGim3Pu/xYRHSSiEwp1bIIgDH1EuAmCIBiglFoP4HsAriWicQBARDcC+BiA9yqlXijk8QmCMLSRlVeCIAiGENEkAG8B+L8A1gK4C8AHlVL3F/TABEEY8pQX+gAEQRBKDaXUDiL6dwCfA3+OXiWiTRCEwUBSpYIgCHasA1AF4Bml1DcLfTCCIAwPRLgJgiAYQkRnAfgOgGcAnEZECwp8SIIgDBNEuAmCIBhARIsB/BzcoLAMwCYAtxXymARBGD6IcBMEQYgJEc0C8BsAjwD4rFLqMICbAZxHRGcW9OAEQRgWSFepIAhCDNKdpH8CO2znKKW60/eXAXgFwH6l1KkFPERBEIYBItwEQRAEQRBKBEmVCoIgCIIglAgi3ARBEARBEEoEEW6CIAiCIAglggg3QRAEQRCEEkGEmyAIgiAIQokgwk0QBEEQBKFEEOEmCIIgCIJQIohwEwRBEARBKBFEuAmCIAiCIJQI/x8D+pGi8EwzDwAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def f(x):\n", " return x*np.sin(np.pi*x)-np.exp(-x)\n", "\n", "fig, ax1 = plt.subplots(figsize=(10,6))\n", "x0 = -0.25\n", "plot_newton(f, 1.e-8, x0, 1.e-7, ax1, inset=False, maxiter=100, resfct=1000,\n", " flabel='$f(x)= x \\mathrm{sin}(\\pi x) - \\mathrm{e}^{-x}$')" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def f(x):\n", " return x*np.sin(np.pi*x)-np.exp(-x)\n", "\n", "fig, ax1 = plt.subplots(figsize=(10,6))\n", "x0 = -0.268\n", "plot_newton(f, 1.e-8, x0, 1.e-7, ax1, inset=False, maxiter=100, resfct=1000,\n", " flabel='$f(x)= x \\mathrm{sin}(\\pi x) - \\mathrm{e}^{-x}$')" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\Matt\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:11: RuntimeWarning: invalid value encountered in double_scalars\n", " # This is added back by InteractiveShellApp.init_path()\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def f(x):\n", " return x*np.sin(np.pi*x)-np.exp(-x)\n", "\n", "fig, ax1 = plt.subplots(figsize=(10,6))\n", "x0 = -0.269\n", "plot_newton(f, 1.e-8, x0, 1.e-7, ax1, inset=False, maxiter=100, resfct=1000,\n", " flabel='$f(x)= x \\mathrm{sin}(\\pi x) - \\mathrm{e}^{-x}$')" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4.999570827870424\n", "24017.65375762087\n", "0.578262577864515\n", "0.8191177934426116\n" ] } ], "source": [ "def f(x):\n", " return x*np.sin(np.pi*x)-np.exp(-x)\n", "\n", "# do we converge for a slightly larger initial guess?\n", "x0 = -0.2684\n", "print(sop.newton(f, x0))\n", "\n", "# but see what happens if you make this x0 very slightly smaller!\n", "x0 = -0.2685\n", "print(sop.newton(f, x0))\n", "\n", "\n", "\n", "# we converge to the first root in the image above if we start with an appropriate value\n", "x0 = 0.5\n", "print(sop.newton(f, x0))\n", "\n", "\n", "# and similarly the second root shown in the above plot\n", "x0 = 1.0\n", "print(sop.newton(f, x0))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Oscillation\n", "\n", "In this scenario the iterations are trapped in a region with gradients of approximately equal magnitude but opposite directions." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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ALdCUUkoppfhlyhVIf4IerSo6HQXQAk0ppZRSqVxUFBzfWI1GjaPIEJbW6TiAFmhKKaWUSuWWLoVTJ4N48pHcTkf5j06zoZRSSqlU7YNhWwgJLUnDhsGAsOaJNaQJTuNoJr2DppRSSqlUyxhYODsT4aVXEx4uAGRPn51MaTM5mksLNKWUUkqlWvNXHeby8QLUa3T2v20Dlg9g4paJDqbSAk0ppZRSqdiXP/4LwPOdbvtv2+DVg5m+fbpTkQAt0JRSSimVii2em5m0hTdSq2xxp6PcQAs0pZRSSqVK+/cbzuwqTbV7DyEiTse5gRZoSimllEqVpk2zRdm3rzZyOMnNtEBTSimlVKo08RcXpUtDmTKBdfcMdB40pZRSSqVCx45f5feFhtrtVwD33LBv6zNbHW/y1DtoSimllEp1vhj5D7hCaNTs/E370oakJTQ41IFU12mBppRSSqlU5+dfLkPmvTzdvPpN+/ou7MtPf/7kQKrrtEBTSimlVKpy/jzsXF2MAtXWkCVd5pv2/7jxR+b+M9eBZNdpgaaUUkqpVGXEhMOYK2E8+KBxOkqctEBTSimlVKqy4LcsZMhygRfb3el0lDgFRIEmIj+IyFER+SvatmwiMldEdrg/ZnUyo1JKKaWSv8uXYf7sMNq1Ss9t2Qs5HSdOAVGgASOAxjG2vQbMN8aUAOa7P1dKKaWUSrTpsyM4cwYaNb0Q5zEhQSEES7AfU8WSwdGruxljFotIkRibWwB13f/+EVgI/M9voZRSSimV4nw98jCE5iZ3+S3AzSM4AXY8u8O/oWIRKHfQYpPbGHMIwP0xV1wHisiTIrJGRNYcO3bMbwGVUkoplXxcvQrL5+UgbZkF1CoWuP3PILALtAQzxgw1xlQ1xlTNmTOn03GUUkopFYCWLI0i8nQW7mp4kCCJuwTqNbcXw9YN82OymwVygXZERPICuD8edTiPUkoppZKxwaMOQvAlnmxX8JbHTdgygSV7l/gpVewCuUCbBnR2/7szMNXBLEoppZRKxoyBeb+GE1RsPi0q1HM6TrwCokATkbHACqCUiOwXkW7Ah0BDEdkBNHR/rpRSSinlsQ0b4PThrHz0bA0yhGZwOk68AmUUZ/s4dtX3axCllFJKpUgTJkBwMHR5OHlMqxoQd9CUUkoppXzFGBg26jQ5y20iS7aoeI/PnDYzGdI4e5ctIO6gKaVUoHK5YM8e2LQJ/voL9u2DCxdufADkyWMfefPaR8GCULUqhIc7Gl8pBWzcCMf2Z6FQ3UGEBJWP9/gNT23wQ6pb0wJNKaWiiYqCJUtg6lRYudIWZefPX9+fIwdkzAjp019/GAPr1sGhQxARcf3YoCCoUAHuucc+atWCAgX8/zUpldr9OOY8SFratQl1OkqCiTGBu5J7YlStWtWsWbPG6RhKqWQkIgJmz4YpU+DXX+HUKQgLg7vusgVWuXJQvjyULRv/HbGICDh8GHbtguXLYelSWLXqepFXowZ07Ajt2kH27L7/2pRK7YyBvEXPcCRoNeuWZady3srxPueZX5+hTM4y9KzW0+f5RGStMaZqzO16B00plWrt2QNffgnDhsG5c5AtGzRrBg8+CPfdBxkS0QUlY0YoXtw+GjWy26KibBPLvHnw00/wzDPwwgtw//22WGvRAtKk8eqXppRy27QJjvybmSxt5lEpzwcJes7MnTOJuBIR/4E+pAWaUipVMQZWrIDPP4dJk2wzZNu28PjjtgkyxAe/FUNCoEoV++jVC/78E0aNgjFjbFNq0aLw2mvQpQuEJp8WGKWShYkTQYJcdO+YCxFxOk6C6ShOpVSqsWIF1Kxp+4PNmwevvgq7d8Po0VCvnm+Ks5hEoGJFGDDADjiYNg1y5oTu3e1dt8GDITLS9zmUSg2MsdNr1KsbxIctXnI6jke0QFNKpXj79kGHDnD33bZZc9Agu+3DD53ttB8cbJtUV66EWbOgUCHo2RNuuw1++MGOIFVKJd7mzbB1K7RsddXpKB7TAk0plWJduAB9+0KpUjB5Mrz5JmzbZvuAZczodLrrRGx/tSVLYMEC2+TZrRvUrm37zyilEufnnw3IVRak86yzf77wfGQLy+ajVAmjfdCUUinS/PnQtau9U9a2LXz8MRQu7HSqWxOxTa1LlsCPP9om2MqV7YCCvn0Dq6hUKjkYPT4SCq+k+R3VPXresseW+ShRwukdNKVUihIZCS+9BA0a2FGYixfD+PGBX5xFFxRki8tt2+Cxx+DTT6FMGZg50+lkSiUfW7bAP9vTwe0Tub/E/U7H8ZgWaEqpFGPjRrjzTjtC85lnYO1aOzIzucqeHYYOtfOpZc0KDzwAL74Ily45nUypwDdhAiAuqjbYS64MuTx6bucpnRmwfIBvgiWQFmhKqWTP5bJ3mapVg+PH4bff7ECA9OmdTuYdNWrAH3/As8/CwIH28+3bnU6lVGAbM/4KFFpC6zvv8fi5i/9dzKajznYA1QJNKZWsRUTAQw/BK6/YO0ybNkHjxk6n8r6wMDup7tSp8O+/cMcdMHKk06mUCkx//w3b/07Dc13z0bFCR6fjJIoWaEqpZGvPHjun2ZQp8Nln8Msvdq3MlKx5c9uUW6UKdO5s+6ppk6dSNxo3zg66ee3JEhTIlDwXwNUCTSmVLC1ZYvub/fuv7Tz/4ov2F3JqUKCAnY7jrbdgxAg7IOLYMadTKRUYjIHRY1wUrLiDc6HJty+AFmhKqWRn2DCoX9+unfnHH9fXvExNgoOhXz97p2DNGqhe3U7KqVRqt3497NoZxN6CH7H/7P5EnaNEthLkD8/v5WSe0QJNKZVsGANvvAFPPAH33gurVkHJkk6ncla7drBoEVy8aFdKmDXL6URKOWvsWAgKiSK80jxqFUrcMO45j87h/frvezmZZ7RAU0olCy6XXQbp/fdtgTZjBmTJ4nSqwFCtmr2TeNttdqDEoEFOJ1LKGS4XjBtnCCkxn6YV7yZNcBqnIyWaFmhKqYAXFWU7xH/9tZ1d/9tv/bOweXJSsKDtl9e0qZ2Oo18/e8dRqdRk2TLYv1+4XOZHmpVslujztPm5De8tfs+LyTynv+KUUgEtMhIefthOL9G/P/TunXoGA3gqY0Y7kvXxx+Htt+HMGRgwQF8vlXqMHQuhYVFkqryCxsUHJ/o8aw+tJUNoBi8m85wWaEqpgBURAQ8+aNfV/Oor28Spbi0kBH74AcLD7dQjZ8/CN9/YQQVKpWRRUXb1gJYtQhjzxi6CJHk3EmqBppQKSBcvQrNmdi3NH3+ETp2cTpR8BAXZSW0zZ7Z3Hc+ds5PahoY6nUwp35k/364k0r49yb44A+2DppQKQJcvQ+vWdnTiyJFanCWGCLz3Hnz0kV0svnVrndBWpWxjx0JYxku88k85zkSecTpOkmmBppQKKFFR0KGDXU/z22/hkUecTpS89eplB1fMmGH78l254nQipbwvMhImT4aslRcQmtaQOSxzks5XKU8limUt5qV0iaNNnEqpgOFywWOP2Y7un39up9NQSdejhy18n3sOHn0URo/WPmkqZZk50/a3jCj6BZ2SMHrzmsntJnshVdJogaaUCgjG2EEAo0bZKSJeeMHpRCnLs8/afn3/+x+kTQvDh9u+akqlBGPHQuZskZwpPI/mpfo4HccrtEBTSgWEN9+EIUNsk9ybbzqdJmXq1cs2Bb39NqRLZ19vnYJDJXfnztkm/EL1FpEmPCvV81dP8jmbjG7CHXnuoH/9/l5ImDhaoCmlHPfdd9dXCPjwQy0afOmtt+ydtA8/hLAw25Ssr7dKzqZMsX94dOmYjmwl3yM4KOnt91uPbyVXhlxeSJd4AV+giciLwOOAATYBXY0xkc6mUkp5y+zZto9U48a2M7sWC74lYovhyEgYOBBy5YLXX3c6lVKJN2oUFC0Kr7WvjUhtp+N4TUD3QBCR/MBzQFVjTDkgGHjY2VRKKW/ZuBEeegjKlYOff9blm/xFBD791I6QfeMNGDHC6URKJc6BAzBvHtRuvoedJ3c4HcerksOvwxAgnYhcAdIDBx3Oo5TyggMH7MLemTLBr7/ame+V/wQF2RUHjh61S0Plzg1NmjidSinPjB5tBxj9Ht6NI7NC+e2R35yO5DUBfQfNGHMAGADsBQ4BZ4wxc5xNpZRKqnPnbHF25owtzvLndzpR6hQaaqc0qVAB2rSB1audTqRUwhljVxmpfOcF9oYsoHnJ5l47d81CNSmbs6zXzpcYAV2giUhWoAVQFMgHZBCRjrEc96SIrBGRNceOHfN3TKWUB1wuuxTLX3/ZdfMqVnQ6UeoWHm7nkMqVyxbNO3c6nUiphFm/HrZsgSJ1lgDQrFTS5z+7ZlTLUfS6p5fXzpcYAV2gAQ2A3caYY8aYK8Ak4O6YBxljhhpjqhpjqubMmdPvIZVSCff22/au2Zdf2oEBynl58tjBGi4XNGoE+neuSg5GjbJ3gQ8WGkjlPJUpkKmA05G8KtALtL3AXSKSXkQEqA/87XAmpVQiTZpk14d87DE7clMFjpIl7VxSB/e7aFniLy5ddNkdLhc0bAgrVjgbUKlorlyBMWOg8QNXWH9mAc1Lea95E6D28Nq8MucVr57TUwE9SMAYs0pEJgLrgChgPTDU2VRKqcTYsgU6d4Zq1WDwYJ1OIxDddReMKPk+D//1Jk/mn86IYw8gVavAhg32gLlznQ2olNucOXaAS7cuaRje8BAu4/Lq+fed3UfRrEW9ek5PxVugici9xpgF/ggTG2PM28DbTl1fKZV0p0/Dgw9Chgz2LlpYmNOJVFzabXydrfmH0PdwD8qEvMZrbIBKlWwbqFIBYuRIyJHDdpMIDc3mdByfSEgT51cicn/0DSLS1kd5lFIpjMsFHTvC7t0wcaKO2Ax4QUH02d+dsrnG0psPmcyDsHatLtypAsbp0zB1KjzU9iotJjRh3j/znI7kEwn5H9cQ6C8irUWkuogsB172cS6lVArRt+/1QQE1azqdRsXL5UKqViHsgcfIlGMlbYN/YmT1lrbSVioATJwIly5B6fp/MGvnLC5fvex0JJ+It0AzxhwEHgNGAZOBgcaYpK9EqpRK8WbPhnfftYMCnnrK6TQqQRo1gg0bCMoURLHX+mHSn6Dr1sGsvq+V08mUAmzzZunSsC3taNKnSc+9Re/1+jUaFWtElbxVvH5eTySkD9onwKPAB0Ar7HJLSil1SwcPwqOP2mWcvvpKBwUkG/362Y9lz5AnPbw55TKtG+el7q632BcRQbaMGZ3Np1K13bthyRLo39/wzfZp3FfsPsJCvN+p9Zum33j9nJ5KSBNnOFDeGPMudl6yF0Xkcd/GUkolZ1FR0KEDXLhgJ6NNn97pRCrBatS4YbRmq3uL8/qAHVzYU4U7Wi7hquuqg+FUajdypP1jr/J9W9h3dh/NSnpvctpAk5AmzqeMMcfc/z6B7ZPWxce5lFLJ2DvvwKJFMGSIbYpQyU/WdFnJHJYZgP7PVaLBo2v5d14T3h14yOFkKrW6etWuH9ugAWTNc446hevwQIkHfHKtKkOr0HNmT5+cO6E8ngfNGHNGRO7zRRilVPI3dy707w9du9omTpU8ze5447Qas4ZXod7+SD7oXYDGd9s505Typ/nzYe9e+OQTuKvAXSzsstBn1zp58STnLp/z2fkTIsHjpkXkv8HxxpgLvomjlErODh2CRx6B22+HQYOcTqO8KTgYpkwMI39+aNz8PJNWL3c6kkplhg2D7NmhfpMITl085XQcn/NkYpv1PkuhlEr2rl61xdn58/Dzz9rvLLl7dc6r9FvU74Zt2bLBuAmRnD0jtGsbxN+HdzmUTqU2x47BlCnQqRP8sn0MOT/Jye5Tu52O5VOeFGg6BkspFacBA+D33+2IzdtvdzqNSqpF/y5i5f6VN22vViWMz78+S9Seu7jn4eWciTzjQDqV2owaZdff7NYNpm+fTqHMhSiSpYjTsXzKkwLN+CyFUipZW7cO3noLWre2fc9UyvZ8tzy06baPU4sepdbLg4lyRTkdSaVgxsD339t+j0VLXmDeP/NoXqo54sO5e1qWbsk9Be/x2fkTQtfuUEolyYULtmkzZ0749lud7yy1GDOkIMUqHmHTd88xfM7Nd9qU8paVK2HLFnj8cZj3zzwioyJ9PqRpjLwAACAASURBVL3GZ40+48kqT/r0GvHRAk0plSSvvgpbt8KPP9oOvCp1SJMGFv2am6yZwvj8pZpERDidSKVUw4ZBxozQrh1M2zaNzGkzU7twbadj+ZwWaEqpRPv1V/j6a3jpJTs3kUo58mfKT56MeW59TH6YMD6EbdvgwY5HmLsrZS5arZxz9iyMG2eLs4wZ4bWarzGq5SjSBKfx6XVLDSrF49OcnZPfk3nQ9vkshVIq2Tl61K6xWaECvP++02mUt01uNzlBx9WvD++84+Ktt3KzzHzM+u8LUDqHzk6svGP8eNuN4nF3rVQ8W3GKZyvu8+tevnqZK64rPr/OrST4DpoxxtlVQ5VSAcMYO5rqzBkYMwbSpnU6kXLS668Hce99F4j89QMafPA6Jy6ccDqSSiG+/x7KloXq1eHnzT8zYfMEpyP5jTZxKqU8Nnw4zJgBH31kf3mqlOeZX5/h9fmvJ+jYoCCYMDY9efK6OPDD5zQb3onLVy/7OKFK6TZtglWr7N0zEXhv8Xt8veZrp2P5jccFmohUFpFJInJcRKJE5A739vdFpLH3IyqlAsnevfDii1C3Ljz7rNNplK+sPriaDYc3JPj4bNnsSgPBEQVZMehxflg33IfpVGowbJgdjNKxI+w5vYdNRzel6MXRY/KoQBORmsAKoDQwJsbzXcBT3oumlAo0xti/Zq8tWhyk9+BVNNWrwycfB8HWlkQue8LpOCoZi4iAESPgoYcgRw6Yvm06gN8KtEcrPEr9ovX9cq24eLpY+ofAbOBBIBiIvtT7OqCTl3IppQLQ0KF2MfQhQ6BoUafTqED0wguwcCH06hVEkfIHyFj0bxrcpkN8lWdGj7YjOJ95xn4+bfs0SucoTYnsJfxy/X71+sV/kI95+vfvHcAQY4zh5pUFjgM5vZJKKRVwdu+Gl1+202l07+50GhWoRGwfxbx5oUP7YB4c0YU/j/zpdCyVjBgDgwdDpUpQowZEuaI4HHHYr82bV65ecXyFDE8LtEggriWQ8wK6KJtSKZDLZUdtBgXZUVW6WkDKVyJ7CW7Leluinpstm50e4cqp3Fyd8i1NxzTjSMQRLydUKdXSpXaAwDPP2N81IUEhbOqxiffufc9vGUoOKkm3ad38dr3YeFqgLQVeEJHgaNuu3UnrBizwSiqlVEAZMsQuhP7551CokNNplD+MbjWaQfcPSvTz77oLPvxQiNz0AIfnt+bB8Q8SGRXpxYQqpRo8GLJkgQ4d7Oe20Q5Cg0MdTOV/nhZob2GbOTe6/22AziLyO3AX8I534ymlnPbPP9CrFzRubCemVSqhXnoJmjYFM+cTVv5xif6L+zsdSQW4Q4fgl1+ga1dIn942b5b4qgTfrPnG6Wh+51GBZozZCNQGjgBvAML1gQJ1jDHbvBtPKeUkY+CJJyAkBL77Tps2U5OuU7vy4qwXk3SOa/3RcucKJu/sRTxT8TUvpVMp1XffQVQU9OhhP1++bzm7Tu0iR/oczgZzgMeD5I0x64wx9YFwoACQyRhTzxiz3uvplFKOGj4cFiyAjz+GAgWcTqP8afPRzWw7kfS/uXPksKtNHNkXzqsvZODcpQiW/LvECwlVSnPlCnz7LTRqBCXcgzWnbZtGaHAojYo1cjacAzydZuM/xphI4KAXsyilAsjBg7aJqk4dexdNqcSqXRvefts+9mb/mdU5e7K462Kq5qvqdDQVQKZOtb93vonWmjlt2zTqFqlLeNpwv2Z5qspTFM3q7FxCOs2kUipWPXvCpUu2yUEnpFVJ9cYbdvWJ1d91JWtEDZqPbc6BswecjqUCyODBULgw3H+//Xzb8W3sOLmD5iWb+z3L/2r+j7Zl2/r9utHpr12l1E1++QUmT4a+fa83NSiVFMHBdvLRDOmFjNNmcPb8FZqPa875y+edjqYCwF9/2QmOe/SwPysAYSFhvFzjZZqX8n+BdjryNBGXI/x+3ei0QFNK3eDkSTv/0B132IlpVepUMXdFbs95u1fPmS+fXb5n+5Z01Nm6hg2HN/Di7KQNRFApw9dfQ9q0dr7FawpnKcyA+wZQMHNBv+ep/G1lnpn5jN+vG12i+6CJyAKgkzFmvxfzxHadLMAwoBx2Wo/HjDErfHlNpVKzV16B48dh1iw7elOlTt81/84n533gAdu38bPPCvPcpwt4qVYRn1xHJR8nTtjCvUMHO6gE7B2sDYc3ULNQTUKCUucvoqTcQatL3KsKeNMXwCxjTGmgIvC3H66pVKo0b54dudmrl11mRSlf+OADqFIFRr5bBzlbGJdxsf6QTgSQWg0ZAhcv3njHfvq26dT7sV6q/rkI6CZOEcmEnXftewBjzGVjzGlnUymVMl28CE89BcWLw1tvOZ1GOa3dxHZ0n+6bRVdDQ2HcODvfVYcO8N7vH3LX93exbO8yn1xPBa7ISPjqK2jSBMqWvb592vZp5M2Ylyr5qjgXzmEBXaABtwHHgOEisl5EholIhpgHiciTIrJGRNYcO3bM/ymVSgH694ddu+wQ93TpnE6jnLb71G72nd3ns/MXL27nvFq2DM7OeZFCmQvRcnxL9pze47NrqsDz009w9KjtWnHNpahLzN45m6YlmxIkgV6m+E6gf+Uh2KWlhhhjKgPngZumojbGDDXGVDXGVM2ZM6e/MyqV7G3ebCejffRRqF/f6TQqtejQwS7p89nH6Xiz4HyuuK7QdExTzl4663Q05QcuF3z6KVSuDPXqXd++6N9FnLt8zpHRm9e8XONlWpdp7dj1IfALtP3AfmPMKvfnE7EFm1LKS1wu27QZHm5/WSrlT199BSVLwuvPFOK7e6ew9fhWOk/p7HQs5QczZ8LWrfbuWfRl5GbtnEW6kHTUL+rcX4s9q/V0tECEAC/QjDGHgX0iUsq9qT6wxcFISqU4338PS5fCgAGgN6CVv2XIAON6b+TE4cuM6Fub75oN48Vqz0PDhrBCB+ynZAMGQMGC8NBDN27/qMFHrHp8FenSONfX4sDZA5y4cMKx60MSptnwo2eB0SISCvwDdHU4j1IpxpEjdsRmnTrQpYvTaVQgqVGgBpnSZvLLtSr99AqfukrSc+Zg6tV7lK6jq8KGDexJe5EiM5b6JYPyr9WrYdEie9c+TZob96UJTkP53OWdCeZWc3hNaheuzY8P/uhYhoAv0IwxGwBdsE0pH3jpJbhwwQ4MiN7EoNQXTb7w38Vmz+bpO6owdsdkXvnfA1RME8yxBwrTufofzN79O/WK1ov/HCpZ+fRTyJQJHn/8xu3frf2O7Se281HDj1L1AAEI8CZOpZTvzJkDY8ZA795QurTTaVSqFhSErFvLgyW7QcbDdLsyjprD1lMiewla/9ya7Se2O51QedGePTBxInTvbou06L5b9x2L9y5O9cUZJK1Aawjs9VYQpZT/REba5ZxKlIDXbhoXrRQ0HdOUTpM7+ediLhdUqUIucwratOeAqwjt71jCtLZTCQ4KptnYZpy6eMo/WZTPffGFvWP/3HM3bj907hCrD652ZHH0QJToAs0YM98YE+nNMEop//j4Y9i5EwYPhrAwp9OoQHT0/FGOXzjun4s1agQbNkChQlBoObUqfMKyQ83p3/RHJrWdxO5Tu2kzoQ1XXVf9k0f5zNGjMHQotG8PBQrcuG/G9hkAjo+eDBQB3wdNKeVdO3fC++9Du3Z2oJxSjuvXz3585xGY1pUhs1tRo9oihq/rTev9RxjWfBiRUZEEBwU7m1Ml2aef2jv4b7xx877p26dTOHNhyuUq5/9gMbxd523yhedzNIMWaEqlIsZAz552qZ3PPnM6jVJuNWrA3Lmk/Ws82dNlJywsLQvml6JK5fO0aRvFgb/bki2TvdV78uJJsqXL5nBglRjHj9u79g8/DKVK3bw/V4ZcdKzQEQmAEUtdKnVxOoIOElAqNZk0CWbPhnffhXzO/nGo1E3alWvH8V7HKZKlCJVL5KHvF/8QebAEtduuA2DZ3mUUGViE33b85nBSlRiffmpHjb/5Zuz7hzUfxnv3vuffUHHYfmI7+8/udzSDFmhKpRLnzsHzz0PFinaAgFK3Ur9ofWoVquVohj7dqlO340o2z76bMWOgYp6KFMtWjHYT27H56GZHsynPnDgBgwbZrhVlyty832/9HROo0U+NeGNBLO2wfqQFmlKpxDvvwIEDMGQIhGjnBhWPDxp8QO9avf16zYV7FtJqfCsORxz+b9vc4Xdxzz12SobdO0KZ9vA0MoRmoNnYZhw7f8yv+VTiffYZnD8f+90zl3FRfkh5nvvtuZt3pmIeFWgicpeI9BWRWSLyp4jsEJEVIjJCRLqKSFZfBVVKJd6mTTBwoJ0UskYNp9MoFbu9Z/YyeetkLly58N+2kBAYNw6uBp3nrsZ7yRKSl6kPT+VQxCFa/dyKS1GXHEysEuLkSbvmaps2ULbszfvXHFzD4YjDVMtfzf/hAliCCjQR6Swim4DlwAtAemAHsAo4BVQHhgEH3MVaUR/lVUp5yBh4+mnIkgU+/NDpNCq5uPfHe3lowkPxH+gHBQrAM+//wYX9xanbfj3V8ldjRIsRVMxdUUd2JgMDB9ouFm+9Ffv+6dumEyRBNCnexL/BAly8DR0ishHIBYwEOgEbjDEmluMyA02BR4DNItLVGDPey3mVUh4aPdouhj50KGTP7nQalVxEXI4gLCRwJsn75Jl6zJo/k3WT76fPV5vp92w72pVrB0BkVGRAZVXXnTplJ6Zt3RrKx7G85vTt06lZqCbZ0+svqOgScgdtOFDUGPM/Y8z62IozAGPMGWPMaGPM/UAN4LQ3gyqlPHfmDLz6KlSrBt26OZ1GqaRZMqoOYUXX8d6rhVi54SQAu07uovSg0kzZOsXhdCo2X3wBZ89Cnz6x7//39L9sPLKRZiWb+TdYPD5q8BHdKjv7SzPeAs0YM/DaigEickdCTmqM2WiMmZ3UcEqppOnbF44csXMPBemQIBXgMoZmpEiWIoQExd64kyVDBqZMCIPgy3R4OA0XLkC+8HzkyZiHRyY9wvpD6/2cWN3KiRO2ebNlS6hQIfZjsqfPzphWY2hbtq1/w8Wjbdm21C5c29EMnv7K/l1E6vkkiVLKqzZtsh1zn3gCqlZ1Oo1S8WtVphW7n99NocyF4jymUZXbmfxzevZsD6dHDwgLSceUh6eQPV12mo9rzqFzh/yYWN3Ku+/avmfv3WJqs4yhGWlfvv0tv+dOWH9oPTtP7nQ0g6cF2hhgpoi0jrlDRGqKyFLvxFJKJYUxdq6zzJntsk5Keap5qebcV+w+p2PEqsUD6ejTxzByJLw5YA95MuZhevvpnLp4ihbjWnDxykWnI6Z6u3bB11/brhW33x77MecunePT5Z8GZFHd6udWvLv4XUczeFSgGWN6AB8A40TkKQARKS8i04HFgE6zoVQAGDMGliyBDz7QgQEqcd6s/SYv3PWCX685d9dc7ht1X4LesF/833nCSvzOB73zsHj5OSrmqciYlj8RvmUnkSsW+yGtupXeve2Scu+8E/cxs3fN5pW5r7Dj5A7/BUtGPO6VYozpBzwFfCkii4D1QDngMSCOMRpKKX85exZeeQXuvFMHBqjk5VDEIeb+M5eLUfHfAcucLiMTSvbHZDjG/Y1OcvL4VZp3eId5A0+R9d0BuIzLD4lVbFatggkT7O+hvHnjPm769ulkS5eNuwve7b9wyYjHBZqIZANKAleBWsBKoIQxZoQx+j9CKae98871gQHBOkWUSqQa39eg6ZimTse4pabT5vDknU9x/kJest8zk6gNG5FKlTg1ZRx1R9Rl7KaxTkdMdYyxhVnu3PZjXK66rvLr9l95oMQDcQ4KSe08XUngbeAf4BngU+xds6rAZ96PppTy1JYt8OWXdsWAO+90Oo1Kzq66rgb+XaigIL6eNQUavQzbm1Gn+Ouwdi0ZwsIREbpO7cqq/aucTpmqTJ1q51185x3ImDHu41bsX8GJiycCbnqNQOLpHbQ3sAMFihlj3jTGjADuBzqLyHgRSePtgEqphDEGnnvO/lLs39/pNEr5gctF8J3V+HX7IKgwiuU7+9G/ypOESgi/tP2F/Jny02JcC/ae2et00lThyhX43//sYujxda/YdGQT6ULS0ah4I/+E89CgJoN45s5nHM3gaYFWxhjztDHmyLUNxpgFQD2gDjDLm+GUUgn3yy8wf74d0p4zp9NplPJclrAslM9VntDg0IQ9oVEj2LCB+8MrceT3FoTl2kifLZ+yrWZXcqTPwfT207kYdZHmY5sTcTnCt+EVw4bB9u3w0Ud2DdVb6XFnD469eoxMaTP5J5yHHij5gONrg3o6inNXHNvXATWBIl7IpJTy0IUL8PLLdjLI7t2dTqNU4jQv1Zw/e/xJgUwFEvaEfv2gQQOmjH6LzWfW0v+HnbiCr9Bw05ucO+Pi9py383PrcVzYs4MjS37zbfhU7vRpOzF2nTrQNIFdFzOEZvBppqRY8u8S/jr6l6MZPO2D9puIxDqbnDFmJ6BDMZRywIcfwt69dmLa+P5yVSohHi73MC1KtXA6xq3VqAFz5/Lmwj4MXj2Yno1bUKJpF/adL0r1srNwRblo1PZ1Nn9ygWIfDnU6bYr2xhtw/Dh89hmI3PrYL1d9Sb0f6wX0fHWdpnTik+WfOJrB0ybORsCTIlJDRGLr/tfAC5mUUh745x/4+GPo0AFqO7syiUpBXqrxEt2r+vd27MwdM6nxfQ0OnD2QqOeHBocy8+vP4L5X+fvA/RSt/hZs2ECaCpW4MnMGT05/kuHrh3s5tfrjDxgyBJ59Fu5IwIKQk/6exMmLJ0mXJp3vwyVjiVmd73VgKXBaRHaKyC8i0kdEegL6J4pSfvbii/au2ccfO51EpSSRUZFcirrk12sev3CclftXculq4q9bPEdJfvygEpT/ib3r3qVzmaawdi0EBbH79G66z+jO4n91IltviYqy3Sry5rUtzvE5efEkS/cu1dGbCZCYAq0RdlDAS8ASoBh2dOeXQKx91JRSvvHbbzBtGvTpA/nzO51GpSS1h9em5fiWTsfwnMtFp8cGQrMnIe86Ru4cy+8VHyKNBDPhoQnclvU2Wo1vxa6T+nblDYMGwYYN8MUXkCkB/f1/2/EbV81Vmpdq7vtwyVxiCrQzxpjFxpgvjTFdjTGVgAxAIUBnXlLKTy5fhhdegJIl7UelFP+N7Lz7XBBZHusMYadpuutzDtd9mCxhWZjRYQYu46LZ2GaciTzjdNpkbf9+eOstaNIEWt+0Qnfspm2fRp6Meaiar6pvw6UAielObG7aYEwUsD/pcZRSCTVwoB3S/ttvds07pVKrSe0mkTY4rf3E3c62bOBsCAqiZY53mPbqK9Q6/Dnrz1+leLbiTGo3iVbjW/HX0b+4p9A9DiZP3p5/3jZxDh4c/8CAa+4tci/V8lUjSBJzf8h/RrQYQdZ0zi4vnphX6BMR6S8ibUWktEhCvy1KKW85eBDefReaNYPGjZ1Oo5R35EyfkxoFalwvthKoZPaSFM5S2H7iHtlJkH17a3hPTlytH2HnjryUabgKlwvqFqnLnhf2aHHmqRUroGFDcLmYMQMmTYI++b+n6OEVCT5F96rdefnul30Y0jvqFKlDhdwVHM2QmAItG9ADGAdsBiJE5A8R+c49UMDrRCRYRNaLyAxfnF+p5Oa112wT5+efO51EKe9pUqIJy7stJ38mzzpUjv5zNDN3zLxhW/fp3flk2Sf0qNqDli2DoOH/2L/ibhp2Wwrw3wSpg/4YxDdrvvHOF5DS9ekD8+YRUakmPXsabg/bxcu7etjtCbDu0DpOR572cUjvmLVzFmsOrnE0g6cF2ligvTEmG3ZS2geB94E9QG3AV28XzwN/++jcSiUry5fDqFF2IeJixZxOo1KqrpW68nC5h52OkSAfLP2AH9b/cMO23/f8zvrD6xERvm/+Pdw9ACp/z4IRNXnr8x0AuIyL2btm03NmT+bumutE9ORl9myoVIkuO7qy91/DN5FdCK1U1m6PhzGG1j+3pvOUzn4ImnQ9fu3BV3985WgGT1cSeMQYs9n9773GmOnGmP7GmLbGmFKA19dsEJECwAPAMG+fW6nk5upVO9dQ/vzQu7fTaVRK1uPOHnSq2Mmv15y2bRrlvi7HvjP7vHrerOmysvSxpfBADyg6n/deKcK0GVcIkiDGtBrD7Tlv56EJD7H1+FavXjfFCQri7ce/55fIJ6hd4GNqsfS/KUzis/nYZvac3kPTEglcZkAlqokzTsYYX0wLPBDoBbh8cG6lkpUffoB162DAALsoulK+cvLiSb83R52OPM3mY5u54rri9XPfU+ge1vRYwb29B0GuTTz0EKxaBeFpw5nefjppQ9LSdExTTlw44fVrpxQ7/4ng3VcKQ9611LrN3axZpQq44n97nrZtGgBNS2qBllDxFmgiMlVEKif0hCISJiIvichTSYsGItIUOGqMWRvPcU+KyBoRWXPs2LGkXlapgHTqFLz+OtSqBe3aOZ1GpXSNf2pMh186OB3Dq6rkq8LsbhOo/MqbZMp+kcb3R7F1q6FwlsJMaTeFg+cOMmfXHKdjBiSXC56+cyshl9NBq0fI1P89qFTJToLWqFG8z5+2bRp35ruTvOF5/ZA2ZUjIHbS9wEoRWSUiz4nIHSJyw/QcIpJPRB4Uke+BQ8BjwDov5LsHaC4ie7CDEu4VkZ9iHmSMGWqMqWqMqZozZ04vXFapwPP223DypF1vU8dOK3VrRbIUIU/GPDdtF4RzoTs43uoOTl86wd31znHgANQoWIOdz+2kffn2DqQNfAO/cDH3ZFU+LfktTe8uTrHsxW3zZoMG8S4hcOz8Mf448IdOTushMeamac1uPkikGPAC8AiQGTsX2lngEpAVSAMI8AcwBBhljPFqk6SI1AVeMcbc8v5o1apVzZo1zo68UMrbNm2CypXhySfh66+dTqNSg2rfVSNH+hzMfGRm/Ad7yciNI+k8pTO7ntvFbVlvS/DzDpw9QJrgNOTKkCtBx/+24zfuH3M/HKwMIxZRtIiwblVGsmSx+xfsXsDW41t5+s6nE/NlpDhLV5+l9t1hVKl5nD8W5EvUH4jbT2wnPDQ82dxBW3NwDZnSZqJk9pI+v5aIrDXG3DRzb4ImqjXG7AKeFZGXgRpAdSAfEAacALYCi40x/3ovslIKwBh47jnInNnOfaZUSpUvPB/3FbuPdCGeLaLt6bQcTUo04eUaL/Ppik+hXUt2j57JvfdFsnBeGJkywbB1wxj31zgKZipIs1Kpe83IyEho1uYMJuwC/b84gki+RJ3HH4WONwXCSgeejuK8bIxZZIz52BjzgjHmKWPMG8aYUb4uzowxC+O7e6ZUSjRxIixcCP37Q/bsTqdRynca3NaA2R1ne3yXZejaoUz6e9IN2x6d/CjvLX4vzue8X/99+yZcbD481I71a4Np1NjFuXMwrPkw7sh7Bx0mdeDPI38m6mtJCYyBJu32cXpvQR5+fQ73VajMhSsXyPtpXr5enbBb+RevXKTT5E6OzynmqUl/T2Lp3qWOZgjstRaUSuUuXICXX4aKFeGJJ5xOo1KTntV60rVSV6djJMiXq75kzKYxN2xbtX8VW45tifM5ocGhjGs9ji6VukCZKdDmYVb/ITRpAlcj0zP14alkSpuJZmObcSTiiI+/gsD09rvnWTitIHmaDeLHXnZOPGMMhyMOc/7y+QSdY8HuBYz6cxQnL570ZVSve3nOy3y37jtHM3hcoIlIZxGZJSJbROSfGI9dvgipVGr14Yewb58dGBAc7HQalZp0qtiJh8o+5Ndr/rLlFwoPLMzeM3v9cr1i2YoxvMVwtvfcTrYqC3n+k5WsXOHigWzLyezKzbSHp3Hs/DGGtikKQ4f6JVOgmDoV3uubHik/nt++rUVocOIW/J22bRoZQzNSp3AdLydM+TxaLF1E3gLeAf4CNmAHCSilfGD3bvj4Y2jf3k6toZQ/7T+7n2AJ9mun7vNXzrP3zF6iXFF+uyZASFAI4aHh5LlzKWmbfcGyqaNpnGMZM49VZ82Qq5Q5cBlW97ajdFKBP/+ERx6BqlWFH6dUp0zeIok6j8u4mLFjBo2LNyZtiGfrqyoPCzSgG/CFMeZFX4RRSl338ssQEgKffOJ0EpUatRrfyu+jOJ2SK0Mu0qdJT/8l/blQ+QyECMsm/UT28svZdTQ9EhbErq3Lmb92KE9WSYFF2tChdmmSI0c4ejKEBx6IIsOlI0xp8zv58nVM9GnXHVrHwXMHaVYydQ+0SCxPmzizA9N9EUQpdd3cuTB5Mrzxhl3WSSnlmbK5ylI0S9EEHZshNAPj24wnMirSbig/Dlq3J+pQdUqGL2bzhgN8vvorus/ozoTNE3yY2iG9e8PJk1zKmJ1WLV0cOnSZcx2bk27gszcdGhwUTPty7SmTs0y8pz1x4QSlc5Tm/hL3+yJ1iufpHbRFQEVggQ+yKKWAK1fg+eftQugvveR0GqUC39LHlhIsN3bSnNxuskfnKJ+7PJ83+pynZ7rnPis3AdIf59K4KVSuepplC99jfcH1dJ7SmaJZiwbENAxec+QIF8OzUj3sRzYtD4I2XXjnnz/Juvfm1RvDQsIY03pMLCe5WaPijfi7+N/eTusXMzvMJGOos+vpeXoH7QWgq4h0EpEcIhIU8+GLkEqlJl99BX//DZ9/Dmm124ZKRQplLkTrMq3JkCaDR8/LEpaF8LThSb7+U1WfotXONKS56t5w2+/0K9aAsEuhNLrT8Hrh6eTKkIsW41pw4OyBJF8vUFy6GkzpCovYdPpBaPIsd2eawEtzI2wfi0S6eOWi3/sSelOZnGUomLmgoxk8Lai2A+WA4cAR4EqMx2WvplMqlTl8GPr2hSZNoKnO+qdSmbpF6jKx7URyZ8zt0fMGrhzI6D9H37Ct1fhWvDH/DY/OIyKMuGcAEUOy/retxNjnWZe+CdlzBtG6aWYeTTuRs5fO0uf3Ph6dO1Bdvgz5MS+L2AAAIABJREFU7lrK3j/ugCY9ofogRkyB4MxZIOrmAuv85fNkfD8jA1cOvOV5h28YTs5PcnI44rCvovvUyI0jmffPPEczeFoe98Mu86SU8oHeve3M3QMH6nqbylm97ulFWEiY0zESZNi6YZTOUZpHKjzy37a/jv6VqPzhTz0HTz0H79j/gFUKVKP1hy4+q7aVNg+m5b2nq9L6qRUMfDHhS1EFqkuXoEqDfzi5oRbh9z7Duep28tkSF8LsL6LcueHEiZued/7Kea5cvXLLc0/fPp0c6XOQO4NnxXageHvh29QuXJsGtzVwLINHBZoxpq+PciiV6q1cCSNGwP/+ByWT16ooKgVqc3sbv19z3F/jePrXp1nXfR1FshTx+/VjM+nvSfx55E+aT7+LX2bMpP1jf/PLN+05si2CUT+dY+nxqXSskPiRjk65dAkK1FjB8fU1qNj8ff5YPpa0taFcrnJwbr0tzj74IFHnPnfpHAt2L6DnnT0R/Usz0bTPmFIBwOWCZ5+FfPngzTedTqOUXdx610n/zj1++eplTkWewmVcfr3urbw2/7X//v3uitdZOrUE4a1eZeniNJStdJFHBw1k1MZRDiZMoBUroGFDcLk4cgQK37GV4+trwP1PU+rRjfy+YiwVc1ekWNZitu/ZiROJnvdtzq45XL56mealmnv5i0hd4i3QROSqiFRz/9vl/jyuR/LtEaiUg4YPhzVr7MS0GZ0dOKQUAB0ndeTZ326eZiG1ib5w+4bDGxiy5mtWf/s4OXu2QkwwMnw5XfusZOm/yxxMmQB9+sC8eaws3YWyFSI5sr0QtOpAnzyz+Hnzz+w+vZuNRzay8+TOJF9q+vbpZA3Lyj2F7vFC8NQrIXfQ+gH7o/37Vo93fZBRqf+zd99hUVxdAId/Q2+CFQtW7AVFEKwRjSj23nvDFlvUmJiYhNijxh41Ro0Ga+xiwy4qFrBgFxRBBcWG0vv9/ti4cQWkiKz63fd5eMLO3Jk5uyHhcss5n7WXL1Vrzxo0gJ49tR2NJH0eHKwcqFSw0nvf5+8Of2u8/uvyX1iZW3FpygoCrpnj5KSQvPt3vnROxuvyw3TuoiVvjJrh6cnvxd2oG/gnzxNCqdC+Hr7PLzC3bBguZV3oV6MfQIbTtXo6egyxG0KNIjXSbTPUfiiLWyxGTyf7u0ClTKxBE0L88sb3bh80Gkn6P/Tzz6rZhMWL5cYAScqOS0MvpTq2vuP6NFpmnqudK39e/JPm5Zqzuu1qXMq50HdHX47cO0LQyyDVWi1z2LA9jDJ9ZhF/4Bca1zZg9gxVHsP3yFCRc/4dNYupWYfRDmdZ9fBnKHsAOvXk2LJwui/8Av2wMFa2XZnptWKGeob80eaPd7apW6IudUvUzYl3oDUn+p/Q+iYZuQZNkrTo2jX4/XcYOhRsbbUdjSRpV9l8Zelv2z/LCUL1dfXR19XP0VgqFPhvp86AmgMolqcY6zuuZ6TDSAqbFqbntp4EhgeiowPlmx+Gr6pQrfZjJkyAunXB72+//0avQPXPpk1Vo1q5xdOTRTX6UThoDatW6cAX06BXK1xvhnO6BJy8f5KFLvMpbl5cfcmS80ve65F7/fdyMvjk+0audSUtSmJpaqnVGLLUQfs3Ga3eW8dcFEUZryhKzZwNTZI+b0LAyJFgYQFT5eIASaJ+yfr81e6vLP9inHFyBqsurtI45rLOhfGe47Mdy+Lzi1Mdc/Vw5cKjC7yIfcHGaxtps7ENpgamHO93HLtKhbnhXIGxc88SEBiPXb9q9Drcn5tVO6s6Z/b2cPiwalTrQ3hzOhPwD4jHqvx+xvitIUrXEHq1gCY/gk4Kjaa609mgBvvWQd+JmiONIZHvTsAbnRCN8ovCnNNpFwn+5tA3/HLilzTPfUqW+Sxjj/8ercaQ1RG0jcDq1y8URRkG7AfmAGcVRdFewhBJ+sRs3gwnTqh2shcooO1oJEmTWyM3xtfNfgcnN224uoH9d/ZrHLsXfo9HUY+yfc+QiBD61einUdWgl00vzjw8w1zvuQDceHqDvjv6ks84H0f6HsHBqhYLouryanAxmva9yi6dDlS5tZVKVps54R+vGib39Mx2TO/073RmZM16DBkXQsUqKYQ+aARffg8jqkL5Awy+oGr6MDIE5cJFWpR2RpmSc38d3nlxh5vPbn4Wuzdne89myw3t1l3NagetDrDvjdffACsBC2A7kLW0zZL0fyoyEsaPV/1RPWiQtqORpNRalm9JE+smufrMdVfWYTDVgMDwwFx9blqM9Y0pYFxAY21Wt2rdGFxzMKsurVJPC+64tYOpJ6aS1ygvB/scpL9tf+zKluZIOQfcz/pCg1+5/aI1jWKuUcHsL9y3vSThA9TcufabJ18Xcsc8YA9/zreCSjthZEVoOBP043Es5sg3L1SbJr498h1BEffh0CHVfCxgoGsAgF1Ru2zH4HHbA4A2Fdq857uRIOsdNEsgBEBRlHJAGWCJECISVfknm5wNT5I+T9OmQWgoLFkCuroZt5ek3Hb58WWuP7meq89MESkkprw7Q31uiUqIYt7ZecQnxWscX9hiIZUKViIyPpJieYoB4HbCjYj4CMwMzPir3V8c7XuUMnnL0HGfE3OTv+evUmWoXn4mAb6l6Ns1P4ULw4ABcOAAJL7H242IgCXL4yhVLRSbGjr8/rIXlDkKAxqwkZ6Y5n+hbjvTeSYx/6imM9sUakApi1Ia99JRdKhRuAYlzLNff3K3/26qWVajTL4y2b6H9J+s7jOJAF5PxjQCngkhrvz7Ohn4NOqCSJIW3bqlKoQ+cCDUqaPtaCQpbUM8hlDQpCD7eu3LuPFnLDElEUMM1a9N9E3Y3Hkz3bd1Z2aTmXTf2p28RnnR1/lvk4KFkQUtrsURUAwmuEDy5Mf0r+XATaNfOGUzmlOV57J1WzJr1uhiYZFCzZo6VK2K+qtKFTAyUi0nS0mB5GRVR+72bbh4ES5cAN8Lyfjf1kEIIygUDi5zsCy/mZCCj6gWBtsrQ3RyLHWs6nA25CyJyYkM9BiMpaklq/vvSLVrMzklGb8wP0Q2qznGJcVx7ck1XO1cs/dBS6lktYPmDXz3b0LasWhOd5bjv3xpkiSlQQgYPRpMTLJdRUWSpLfo6+qnyrnVqHQjyucv/0GeZ1PYhqvDr6Kj6PBPl39YdG6RasTtzDyG1RpGAZMCzO27nh17mvLAKJ6eO3qz0deXys2bU3lKJ1zrQr0R7oxYtJPI2225+agxPr6liI7K3KSWeaEIYgueRjQ8B+U8ofhZUED3JZSM0eda4USuFYYxZ6GjSSJO1WH6yelcenwJG0sbQiNDKWhSUOOer0cue1Tr8c5n6+noMb7ueBysHDSOG+kZEToulNik2Cx8ktK7ZLWDNhHYC+wGAgG3N851A3Jx/7AkfXp27FAt+1i0CCy1u4Nbkj4baeVBW9FmxXvdc1ydccw7Oy/d8zqKDnFJcRwOPMyUxlMIiw5jitcUjgYdxbO3J/r1v+Be3Wj0puqx+fpmwqLDOHrwqHrkamjt/jRb4sSMkzNY4zcUBR0Gl55Mx4I/cvu2asRMVxd0dFT/TBJxVCpvhJ0djD01lE3XNmnE07SAAxvPGlOwjhcAfav3Yf6pUE4O7Ai+FwiLDqO2VW3OhZzj2pNrVC9cPVufi6GeIXObzU3z3IdId6Itvq6+Wn8vWV2DlkcIUQEoJIQoJ4QIeuPcGFQdOEmS0hATA19/DdWrw/Dh2o5Gkj4+lQpWYpTjKMwNzbUdCkXzFM2wTVxSHDtv7aTHth4Y6BqQkJzA0XtHmXBwAgC6OrrqnG7Hg44z/qDmrtgy+crwZ9s/CRgVwADb/uSxDKdFCxg7FvoOD2PcOOjl+pTQypP4OdqSIraXKFwYfmn0C8Z6xuQzygfApAaT2D/iDAP6WqjvvardapRDh8lbqwFflvmSTZ028Ve7vzJ8T3O8006f8ZoQgsj4SBKS/9vpkJCcgOOfjmy5rt1djzmpgEkBrf8cZnUE7ZiiKO2FEMfePiGEuJpDMUnSZ2nGDLh/H9zdP5Is45L0kXG0csTRyjHL1/1w5AeK5inKSMeR6mMNVjegeuHqLG21NFuxzDyV8RqEvEZ52dhpI1/89QUj9o6gpEVJ7r+6z8JzC6lRuAYDag5AR9FhlOMojgcdZ+G5hTS1bkrzcs011oCVzluaP9r8gRCq9V9ewV44rXFSn1dQaFepHTtv7cS2iC0FjAtwa+QtSlqU5PLjy9gWsWWpz1I8/FW7KGO+j1FP+Z4MPsmcpnOoWbQm/s/9M3xPL2JfvPN8TGIM5rPMme08m2/qf6N+hk+oj9ZHnHLSXO+5lM5bms5VOmsthqyOoG0A9imK0untE4qiNFAU5VTOhCVJnxd/f5gzB/r0gYYNtR2NJGVsdtPZ/Njwx1x9ZnJKMvFJ8eqOSmbtur2L40HHNY49iX7Cy7iX2Y4lNjGWkQ4jNfKgpaVuibpM+3IaR+4doXnZ5ugqqm3Zow+MVj9fV9HFe5A3NpY2tNzQEts/bElMTr1983Wn7c3M/qBK+XE48DBTvKbQdWtXyiwso763bRFbRu0bxVf7vqJNhTY8/eYpMYkxAJx9eJbRB0az3Hd5tj+HzPDw98BQ15Cm1k0/6HNy0+8+v6s7vNqSpQ6aEGI4MBPY9G+SWhRFsVEUxQPwAvLlfIiS9GkTAkaNUu3Kmj1b29FIUuY0Kt0o1+sprr+6HqPpRtx7eS9Xn5sWXR1dDHQNMlWjcmL9iThbO7P91nbmNFVNETYs1ZC8RnnVbcwMzPDoofqFfyXsCq03ttZI4XH/1X1mnJyBEALrfNZs67qN/b1UyXdjEmOISojCWM+YrTe20qxsM8rkVaWy8HvsxxIfVXmmzZ03M8RjCI3XNiYmMYZ+O/uRIlLYeWsnZx68e4n46zxodYpnbWu5EILdt3fjbO2MqcG7O7NS1mS5FqcQYgowDFikKMoJ4BJQDRiIzIMmSals2wYHD6pynxUpou1oJClzvB944xvqq+0wtCa9PGhp0VF0cO/gjld/L8bWGcsA2wH4P/cnJjGGAbYD6G/bH4ASFiU4N/gcdkXtOHj3IO03t+fG0xsM8RhCuUXlcDvuxrUn1wDoWLkjs0+r/qJ73RmLT45n+pfTKZ+/PE9jnnL6/mlc1rlQ3Lw4wWODMdY3Vsf0w5Ef8H/uz08Nf+JpzFNik2Ipl78cUZOi6Fq1a5rvoUbhGhQ2LZylz+nG0xvce3lPJqf9ALK8EkZRlPxABVR5z75AlXqjkRAiKYdjk6RPXlSUamOAra3cGCB9WsYeGCvzoJE6D1p6ipgVoYhZEYQQ9LLpxW/NfuNe+D0WnVvE89jn/N3+bxRFwdHKkQtDLjDn9BwmHp7IgTsH0NPRY6j9UL6t/y2FTAuRlJKkTmcxsf5ETgSd4M+Lf7Kp8ybyGeWj/ur6zDo9S/3sGyNuUNKipPr11SdXufbkGiNqjaCJdROmeE0BVJ2w9Ea5klKS8AvzQ0fJ8rgNPar1oHWF1lm+Tnq3rBZL/xlVeo2vgN9QjZrVAtLfiyxJ/8emTYOHD+H33+XGAEn6UCyMLNS7JV9rVb4VdYvn7hQtwKZrm3B2d+Zw4GHK5S+HQLDuyjrmn50PqIqNAxpltILHBrOk5RJCI0Ox+8OOeWfmkSJSsClsQ/NyzZnSeAqXh13G2doZ+2L2HOh9QOOZs71n8yrulfp1pYKVmNN0Dr82/VWj3ZPoJ3x94GsuhF5IFXdSimqMJa3RtTfp6+rzs9PP1CtRD4CqllXZ0GkDVuZWmf2IpEzK6q+MH1DV3vxFCBEGoCjKfWCHoiiFgd5CiI+jTockadnNm/Dbb6qSLvXqaTsaSfp8nR54OtWx+c3nv9c9f2z4I1O9sl5IvHOVziw8txBXD1f1Yn2A8QfHM81rGnkM8+A/0p+aRWrSuUpntt3YhlewF7/7/M6p+6cobl6cUhalaLOxDVfCrnB9xHXMDc3VGwcevHpAv539yGOQB7dGbtx/dZ8TwSfUHdTnsc/R19FnfL3Uhe5fxr1kwbkFOFg5YF/MPlufi4GuAW6N3AB4FfeKsOgwKhSokK17fcxufXUrU+sPP6SsjmVWFkKMeN05AxBCHAUaA07AgXSvzAZFUUooinJMUZSbiqJcVxRlTE7eX5I+FCFg5EgwM4Nff824vSRJUM2yGpMaTNJYXK8t2c2Bpa+rz8ZOGxEIll/Q3D0ZHhdOi3ItSExJRFEU/m7/NzqKDj229eDUfVUShPku8/n+6PccunuIyV9MJo9BHvX1kfGRlFygSuVxov8JxtUdx4LmC/B19UVXR5edt3biFezF1SdX1Sk1ChgXoF3FdqkqB6Rnyokp7zyfIlIIjQwlKiGK7Te3U3FJRa6GfX5Ztgz1DNUbJ7Qlq7s476Zz/CLQACidAzG9KQkYL4SoDNQBvlIUpUoOP0OSctzmzXD0qCr3WaFC2o5Gkj4NdkXtmNFkBvmN82fpurEHxjLntGaC1Zp/1GTgroHZjuWnYz9l+9oy+cqwss1Kzj48q3G8v21/lrderh7tMtY3ZksXzeSuXbZ0ITA8EK8BXgytNVQ9ipMiUhi6ZygAox1HU7NoTfU1ujq6vIp7Rb+d/QBV3rTKv1emz44+6OnosbP7zkxXDsioVFNsYixW86xY5rOM3f67KW5enGqW1TJ170+J23E31l1Zp9UYsr4aMB1CiDtAjk7kCCEe/dv5QwgRCdwE5ES39FF7+VK1MaBWLRgyRNvRSFL2LGm5hOlfTs/VZ8YlxfEs5hnJKclZuu5w4GHOhZzTOBadEE1cUly2Y9HV0WVcnXGp1rZl5MyDM/zt9zddqnbhm3qqRK5tK7allEUpfEJ8SBEprLq4ipknVYlwO1TugI+rDxPqTsBQV7UZwUTfRGM3ZWxiLA1WN2DjtY3MajKLhS0WpnruOM9xRCVEsav7LnxcfRhXZxzbb26nytIq3Hp2K7sfQ7rikuI4ePcgbSq00fpU4Iew1m8thwIPaTWGHOugAbw59ZnTFEUpDdQEzqVxboiiKL6Kovg+ffr0Q4UgSZkyeTI8eQLLl6tq6EnSp8jRylFjlCY3/HP9HwrNKUTwq+BcfW5O8Ar2oql7U+qtrofbcTeSUpKY3XQ25obmWOe1Zke3Hbh3cKfdpnYM9hjM90e/JzI+kkeRjyhuXpw5zeYQNiEMjx4eGOgasNRHVQEhMTkRkxkmnHl4ht7VezOxfuqKinv997L68mq+rf8tay6vYcCuAcxpNod7Y+7Ry6YXTmucOBl8kr/9/k43fgNdA8wMzGhYKnOZtI8GHSUmMYa2Fdtm7wOTMpSjHbQPRVEUM2AbMFYIEfH2eSHECiFELSFErUJyPknSIl9fWLpUtf7MPntrcCXpo3A48DBewV7aDkNrXudBy2gU7vLjyzRa0winNU5cCbvCnKZzuDL8irrU0qE+h1AUBWd3Z7pt7cYe/z3qa3869hP2K+zVU5NxSXEM3zucNhXaMMt5FikihY7/dFS3f52q421bb27FxtKGn51+1jhuaWrJYLvBPIl+wqv4Vyz3XY6Cgoe/Bzee3tBoq6PoUDZfWXV9z4wcDzqOqb4pjUo3ylR7Kes++o3/iqLoo+qcrRdCbNd2PJKUnuRkGDpUlYx2atY3f0nSR+X7I99T0KRgpkdUPlev00+8SQhBbFIsJvomAAS8CGCBywJc7V3Vx15ztHLk2L1jvIh9wYvYF/Sy6cX6q+sBWHBuAYA6bYalqSVNrZvy1+W/aFm+JVtubGGP/x7ql6jP8f7H051KXN12Nc9inmGol36+NhN9E26NvMVv3r+xxGcJm69tpkvVLsxsMhPrfNbqPGivO5YZmdRgEs3LNcdIzyhT7aWs+6hH0BTVT+Mq4KYQQuZakz5qS5fCxYuwYAGYZ28DmCRJ2VAsTzEKmWjOnnSt2pUvy3yZo88RQrDXfy91VtVRL9i3LWJL0JggxtQZk6pzdv3JddZdWUej0o0oYFwAgF42vTTaWBhaqFNoKIrCslbL+KLkF/TY1oPtN1VjEteeXMMnxCdVPCeCThD8MhhFUShkmvHsUVJKEk9jnrK582YmNZjEwbsH1ev9Xo8UZlQc3EDXgLlN59KhUofPuvOup6OnrquqLVnuoCmKoqMoylFFUcq/+f2HCA6oD/QBvlQU5fK/Xy0/0LMkKdtCQ+GHH6BZM+jSRdvRSNL/l4N9DrKs9TKNY9O+nMZgu8HZvuds5/8K576uZ1nrz1q03tiaJ9FPaFSqkfq8vq6+xrUxiTGM8xyHzTIb+uzow6Zrm7gz+g6lLErRc3tPjbYDaw7EwtBC/dpQz5Dxdf/LYXag1wEKmRaiqXtTjYLwT6Of0mVLF/rv6p/p9xQRH8GqS6t4GfeS6U2mEzIuhPIFVL++u25RJai9+uTdKTP0dfWxNLXk9IPTWS5q/ykJGBXA6nartRpDdkbQFKARkOet73OcEOKUEEIRQlQXQtj++/X/XXdE+iiNGwcJCaqKAZ/hhiZJyhU1i9RkxpczMr0O6kN6czpx1qlZdNjcgYj4CFa3XY3/SH8G2Q1K87pT909RY3kN5p+dz/Baw9Wlk649ucba9muJTYzFvYM7+3ruQ0HhRewLdZoMUKV3aL+5PQBflPwCRytHvPp7USpvKVqsb4FXsBdCCIbvHc6r+FcsbrFY4/mudq788MUP6teWppb0sumVZo3N1yN+Qgh1qowNVzfQ6Z9O+D32S/P9pYgUhu8dzooLKz7L3Zsfk49+DZokfew8PVV5z6ZMgXLltB2NJH26bArbYFPYJsvXue52paRFSX50+lF9rMLiCtQqVosNnTZk+X7JKcl8c+gb9et+NfpRyqIU3ap1e+carSknpuB23I3SeUtztO9RGpdpjPsVdxacW8DCcwtxa+RG4JhAiuUpBsDsprOpVLASgeGB1F9dn7xGedUpMYLHBqvra8YnxXO071EmHJpANctqbLq2iW03tzGryaxUOchalG+h8bpSwUqs66jK5/U6ee3bFEVhSuMpzPFW5ZI7HHiY7Te3497Bnd7Ve2u0DXgeQHRiNE+in2T4OX7KJh6aSIUCFd5rFPZ9yQ6aJL2HmBhVEfQKFWBi6t3vkvTJWt1udaYXjOeUyPhInsU8o7h58VTThu9y5uEZwuPC3/v5SSlJrL+ynhmnZqiPmRmYYWZgRq/qvd5xpUo1y2p85fAVM51nYmZgRkR8BJEJkQB0r9ad8XXHq4uVH7p7iBblWlDVsirJKck8jnrM46jHAJwffF7dOYtJjKGpe1MalGiAewd3HkU+wtXDFYAJ9SakiiHoZRDxSfFULFgx259D0JggFp9fTItyqs7euYfnMNA1oGbRmupdqJ97eo0tN7bQsFRDrXbQPupNApL0sfvlF7h3D1asAMP0N1BJ0ienmmU1KhWslKvP3HFrB9aLrHkQ8SBXnwuw+dpmKi6pSP9d/THWMwZgbO2x77wmOiGaMfvHqKsYdKzckcUtF2NmYMatZ7dw/NNR3XZ9x/XqzllMYgz9dvaj29ZuxCTGMGLvCI37FjErov7eWM+Y6pbVme09mzWX12BqYEp0oqrg+lq/taliGuc5ji5b/lsIe+r+KUymm3A86Dg6ig7mhubo66Tu/BrqGlLUrCjO1s7kM87HT04/UcBEtbHhh6M/YLfCjnab2uF2wg0g1382/h/JDpokZZOfn6oY+qBB4OSk7WgkKWfturULzzue2g7jg4pPilen0Qh+FUx+4/zs7r6bS0MvAao0GLGJaZc+8gr2osbyGiw6vyjd6b5kkczSlksJHReqsV7LRN+ENe3XcP3pdYbtGcaKiysAVS4yU31T2m9ury60rigKi1osokmZJgzxGMLlx5eJ/j6aZmWbMWj3IH4///s732OKSCE2KZYUkUK5/OV49d0rulRNvZNJURQsTS0x1TdNdW5b121MaTQFr2AvohKiAFX+N+nDkh00ScqG5GRwdYUCBWD27IzbS9KnZvrJ6Sw8l7qk0OcgNjGWxecWU3ZRWTZd2wTA13W+5vzg87SpqFm6KFlolp2KTohm9P7ROK1xQiA43u84c5qpRtCSUpLYfG0zQggqFazEza9uMtxhOEXzFE0VQ7Oyzfi6zte4X3EHoEqhKqSIFMrmL4tVHiuN/Gv6uvrMd5lPYkoiTmuceBT5iN3dd9OuYjtG7h/JXO+57/2ZJCYn4hfmx6OoR6nOWRhZ8KPTjwSNCeK7+t8BqOuMfs47ObVNdtAkKRuWLgUfH1XOs/xZq+ssSVIOK1+gvHrN1msDbAfQsrxmVqbohGjmnZmH9SJrRh8YjXU+a8rkLQOoOkGZ2ZV4/el1lvkuY0ztMVwZdgWn0qrh86fRT2m+rjndt3VXp8PQ09Fjue/yNCsyPIp8xPyz89WvD/c5jKudK1fCrjCo5iDMDc1JESmAqhM04ZBqvVkhk0IkpSRhqGfIli5b6Fq1KzNOzsjUov3QyFC6be3GqfunUp173RHtUKlDutcb6RmpNhM0ncPmzpsBWO67nJbrW3LuYaoqjJ80C0OLNEcTc5PcJCBJWfTgAXz/Pbi4QPfu2o5GkqQd3XakOjbpi0mpjrXa0IoTwSf4ssyXbOq0Sd25SsucpnPUOzmjEqLYH7CfLlW74GjlyJ1RdyiVt5S6rW+oLx03d+RJ9BNWt11N4zKN1ee+PfwtA20HaiR1DY8Np9g81U7O2la16VujL0XMirCoxSKuhF0h6GUQYVFhtNvUjp+cfuLBqwccvHuQpS2XMqzWMBRFQQiBjqLDho4bCAwPxNLUEiEEgvRHtKISovjn+j+0q9juHZ9m2pJTkrFeZM3wWsOZ3HCy+riuji7nQ85TZ1Udmpdrzs9OP1OneJ0s3/9jc3mY9qdwZQdNkrJo1CjVFOeyZTLnmSTlJEcrRxa3WKzOuv8+ohOiiU6M5q9LfzHCYQR5DPPwk9NPGOga0KBkg0zf59i9Y4xNCYC1AAAgAElEQVQ5MIbgV8HYFbWjbP6yGp2zdVfWMXj3YAqbFeb0wNPYF3t3Ed7ohGhab2wNQPXC1Tkz6Ix65C4+KZ5TA0+hp6NHTGIMCckJtNrQCgBna2d15yxFpDB492DMDMxY1GKROtns9JPTCQwPZNqX09TPK2pWlGH2w7DKY5Wp9zvpyCS+a/BdquPnQ84TGhmKdT5rfEN9KW5enCJmRRhiP4Qe1Xqw1Gcpc8/Mpe6quoyrM47fXH7L1POk9GV5ilMIkQw0Bm6/+X1OByZJH6MdO2DXLtXuzTJltB2NJH1eKhWsxEjHkVgYWWTc+A29tvfi+yPfq1+Hx4ZjNtOMwnML892R79gXoMpv/mWZLzPdOXs9etZ2U1t0dXQ53u84ZfOXTdUun1E+GpZqyIUhFzLsnCUkJ+Ds7szZh2fZ2mUrl4deVnfOzoecp/TC0hy9dxRQbUJ4c9p2XrN56rY6ig75jPKx+PxilvmoKigIIXgZ95IrYVfwuO2hLuFUvkB5lrVe9l5pNwB2396Nno4eTqWccPjTAXc/d/W5PIZ5+LbBt9wbc49fnX/FpZwLAM9jnnP6/un3eq62fLX3K5acX6LVGLK1Bk0IcUIIEf3295L0OQsPhxEjwNYWxr57970kffI2dd7E8tbLc/WZ4bHhXAm7QnxSfJau83vsh/9zf5JTkpl8dDKlF5ZWn/N19aVbtW5Zut/rzg2oNg/4DfPji1JfqI89jHjIxqsbAWhVoRWevT0paFIww/vOPDmTsw/PMqb2GDpV6aSx5s3G0garPFb02dGHx1GP8QnxYdftXXSs3BGA7458pxHX7KazaV2hNaP2j+LQ3UMoisKcpnPoXKUzKy+tpO/OviSlJCGEIDkl+b0X83v4e9CwVEPyGuVNt42ZgRkT60+kWdlmACw5v4QGfzWgqXvTNNe9fcz23dmHT2jq+qe5SW4SkKRMmjABnj6FVatAP/M5NCXpk2SdzzrVwvsPzcPfgxrLaxASGZKl62KTVKkwdHV0ORdyTt1B6FGtR4ajWm+KSYxBCIGujqpItqOVI/Nc5mkUQT8edBz7FfaM2DeC8FhVctyMNhcIBPsC9jHt5DRsi9gyo8mMVG2M9Y3Z3HkzkfGR9N3Rl97Ve1O/RH08bnvQr0Y/AsMDeRrzVN1eV0eXDR03UKVQFbps6cKtZ7dQFEXdidtwdQM9t/XEK9gLval6HAs6hp6OHlZ5rNR53t5kqGtIhQIVUm2sAAgMD+T60+u0rZC15LQT6k1gbtO5XAm7whd/fYHz386cDD6ZpXv8P5MdNEnKhEOHYPVq+OYbsLPTdjSS9OFtvLqRnbd2ajuMd3oU+YjxnuMJDA9UJ7fd23MvW7psoXz+8lm615HAI1T5vQobrv5XGup8yHl1HjQhBPPPzMf5b2fyGeXDe6A3+Ywzrhl6dfhVjtw7QqsNrbCxtOFE/xMY6Rml2baqZVUWNl/IocBDWC+yJvhVMMXyFONw4GE8e3tqJLAF1dSiRw8PCpkWIiTiv06tjaUNC1wW0LJ8S43Oo3U+ax6Oe0iHyql3aiqKgrGecZpJbM0NzZnbdG6a172LqYEp4+uN596Ye/zW7DeuPbnGvLPzsnSP/2eygyZJGYiKgiFDoGJF+PlnbUcjSblj/tn5rLiwQtthpOlhxENG7x+N9SLrVLnaDHQNsnSviPgIhu0ZhrO7M4Z6hljns9Y4nyxU04N9d/Zl3MFxtK3YlvOu56lcqHKm7j/lxBSuPbkGwIHeBzA3NH9n+zdLC81qMosd3XbwPPY5G69uJDYxlkG7BnEh9IK6Tam8pbj51U2aWDcBUO/iHFNnDP1t+6vbRSe8eyXS6zxoaaXrKGhSkPH1xmd7RNVE34RxdccROCaQpS2XAqqank3+bqJOSSKlJjtokpSBH36A4GDV1KZR2n/4SpKUS8Jjw6m4pCLLfJfRy6YXt0feppdNL5qUaaLRbqTjSPX6rfQcu3cMm2U2rLiwggl1J3B56GXqlqibqp2iKFS3rM7MJjPZ1nVbhp2s1/688CerLq0C4O7ou1iaWmZ4zY2nN9BRdOhQqQM9bXpSs2hNLg65yMT6E4lMiORQ4CHab25PWFSY+prXNVMXnl3Izls7NVJtPI1WTYu23dSWG09v0GpDqzQ7Ra/zoL1dY/NV3Cs2Xt1IRHwEAIZ6hmzouIHWFVpn6jN4k4m+iTpp772X97j59CaN1zbGaY0Tx+4d+6iS3hbLU4z8RtpNcpmlDpqiKHUURXFTFOWAoihXFEUJUBTljKIoaxRFGaAoSsbjvZL0CfH2hsWL4auvoH59bUcjSf+f7r64y6JziwDIZ5yPpS2XEjAqgJVtV1I2f1nWdVyXal3X6Nqj6Vyl8zvv+zLuJcZ6xpweeJo5zeZgrP/f2qw5TVXVAQ7ePQjAN/W/4bsG32UqmS2oFsgP2TMEgBG1RqQamUtLYnIi/Xb2I79xfpa3Xs7VJ1f59tC3VCpYCUVReBX3iq8cvuJ5zHM6b+lMQnKCxvXPYp4BqEfsAAqZFlJ/X3dVXfYF7CM0MjRT7wFg/5399Nzek+tPrgOqzmAPmx6ZHkFMT7Oyzbg7+i6Lmi8i4HkAX/79JS7rXNTJebXt9MDTzG8+P+OGH1CmOmiKovRTFOUq4A2MBUyAAOAcEA7UBlYCIf921mQCAumTFxenqrNZogTMnKntaCTp81e/RH3WtFtDIRNVp8L/uT/9dvaj4pKKfHv4W3XHop9tP0rnLf3Oez2JfqJexP+mQ3cPqaduO1TuwJXhV1KNmqWIFH4+rlrPMMd7TpZHdsJjwxm1fxQAuopupqddoxKiKGRaiGWtlmFpaonnHU9me8/mz4t/AjBi3wimn5zOpAaTOHX/FKP2jdKI7ZfGv1DCvAQAe/z3AFDcvDjf1PuGBS4L1KNg76o6MOmIZoJfD38PCpkUwtFKVfg9OSWZ40HHuf/qfqbe07sY6xszqvYoAscEsrjFYhqUbICOouqWnA85/1GNqGmFEOKdX4Af8Aj4FagJKOm0swB6AfuAGKBbRvf+EF/29vZCknLC998LAUJ4emo7EknKfQ4rHESLdS208uyQiBDRc1tPofOLjjCeZiy+PvC1CI0ITbd9+03txdcHvtY4Vn5RedFjaw/161dxr4TrbleBG8J2ua1ITE5M814vYl6IlutbCtwQuCGeRT/LUuxPo5+K+qvqC/0p+sLzjqcwn2kuxu4fm+nrU1JS1N8npySLZu7NhNE0I3E17KoIfhksCvxaQFRbWk2M3jda5J2VV9x/eV/j+uiEaGH/h70wm2Em/B77aZz7/fzvAjdEpSWVUj03NjFW/Z5fS0hKEHln5RX9d/ZXH4uKjxK4IWafmp3p95RVXkFeAjdEvVX1hOcdT43PJLf03dFXzDk9J1eeBfiKNPozmRlB+wsoI4T4Vghx6d+bpdXReyWEWC+EaAnUBV6+Z99RkrTGxwd+/RX694dmzbQdjSTlPo8eHqxtvzZXn3n/1X28H3gDqvVh4+uqdgDOc5mXZsHx1wKeB7xzRMfzjifVllZj1aVVTKw3kTODzqjXbb3pafRTav1Zi0N3DwGqHGgFTDJf1eDio4sUmlOI0w9Os77jenW6j4zEJ8UzYu8Igl8Ga0yh6ig6/N3+bywMLei2tRsFTQqysdNGrj+5Tlh0GH7D/ChhUULjXree3WJi/YnkNcrL2YdnSUpJ4mXcSxKTE3G2dgbghy9+ADIudH7q/ilexr3McnqN9+Vo5cjSlkt58OoBLutcqL+6Pp53PHN1RM0r2IurT67m2vPSkmEHTQixQAgRl5WbCiH8hBCe2Q9LkrQnLg769YOiRWG+dpcgSJLWFDYrrLF+6UO69OgSHTd3pNSCUtRfXZ+4pDiCxgYxu+lsCpsVfq973wu/R8sNLTEzMMN7oDe/Nv013TQXBU0K0rZCW473P46ZgRkKma/ldufFHexXqHKufd/ge7pU7ZLpa6ecmMIy32VpdggKmxXGvYM7N57eYMHZBTQt25Spjaey+fpmvIK9EEKw4OwCgl8GAzDNaxrTvKZx86ubDLEfgvcDb/L9mo+T909ioGtApYKVyGuUl6CXQTT4qwEBzwMAVSH0GoVraNTpPP3gNAa6BjQt2zTT7yUnGOoZMtxhOAGjAljWahkPIx7Se0dvYhJjcjUObcvqJgGZAUr67P38M9y8CStXQt70k2ZL0mdt9aXV6mz5H8r5kPO02dgGuxV2HL13VGNdWVbTZbwt4IWq41EmXxn29NjDxaEXqV28dqp2icmJfHf4O24/u42iKMxvPp96JeoRlRDFvLPzMtUpCIkIoam7qhMzvu54pjeZrj4XNCZIozbm286HnGfW6Vn0t+2f7s7IpmWbsq/nPibUmwCoCsEvbrGYTpU7ERoZittxN9ptaqeRSsPMwAz4b5ODEILSeUtz86ubtK7Qmoj4CAKeB9BwTUP1BoC3TW44mcDRgep75TZDPUOG1RrGndF3ONznMKYGpiSnJNNzW0/2B+z/7NeoZTXNxjFFURp/kEgk6SNw5gzMnQuuruDiou1oJEl7lvsux/2Ke8YNs2mP/x5qr6yN9wNvpjaeSvDYYH5p9Mt73/dl3EsG7hoIoC4v1KJ8izRHzR5HPcbZ3ZlfT/+Kh79HmvfLaFdhRHwExecXJywqDB9XH+Y2m6txPp9xPkwNTNO8NjYxln47+1EsTzEWuCx453NalG+Bga4BL2JfEBIRwkjHkRjrG2NmYMaSlku4+uQqA3YN0EixAeAb6guoCqm/qXrh6pzofwIFBac1Tpx7eA6/MD+exz7XaGdlnrki6x+Sga4BNYrUACDoZRBnHp6h5YaW1F5Zm73+ez/bjlpWO2gbgH2KonR6+4SiKA0URfm0im1J0htiYlRTmyVKwG+/aTsaSfr8nAg6we7buwFVmoUFLgsIGhPE5IaTs1wg/U31StSjRuEa7A/YT7Wl1VjrtxZLU0vmu6S/RuHMgzPYr7DHJ8SHdR3WqUensupvv78BVU3OWsVqpTrvdtxNvaPybXO853Dr2S1WtV2VqfefIlJotKYRnbd0JjE5keSUZBqtbcSqS6uY1ngaW25sSVX9YVID1a7MY0HHmH9mPg3/aqheY1e5UGW8BnhhamCK0xon1fso3wqApT5L6bW9F4nJiRr3M9QzxKOHR4Y55j6UsvnL4j/Sn5VtVvI05imtN7bGcaVjllKHZEb5/OWxyqPdzmmWOmhCiOHATGCToijDABRFsVEUxQPwAmQeNOmTNXkyBASoSjrlyaPtaCTp8yCE4EjgEZzWONFobSOmek1FCIGBrgFj6owhj+H7/8e2os0KnkQ/oeWGlqrF8YPOEjYhjE5VUo0lAKoNCE5rnDDSM+LMoDP0qt4rVZvXedDSE5cUx+zTsxm9fzRtK7ZlY6e0p4Pnn53PkcAjaZ4bW2cs7h3cM72ZQEfR4Sennzgfcp7JRyejq6PL13W+5njQccLjwullo3ofQS+D1Ne8uelg3MFxnLx/UqOmZ7n85Tg54CTNyzXXeNaGqxu49ewW+rqapZ/0dPRoXaE1ZfOXzVTMH4K+rj6D7AbhP9KfVW1XYWlqSWFT1VrFwPDAHBlRO9jnYJo1U3NTlisJCCGmAMOARYqinAAuAdWAgYBNzoYnSbnj5ElYsECVkPbLL7UdjSR9HrwfeFN/dX2c3Z1VyWabL8Krv1e6yV6dSjmxres29S/brKhcqDLfN/ieC0Mu4GDlwL3wezyKfJRm27ol6jLKcRS+rr7qqbOsSEpJIv+v+fn28LfULFqTTZ02pbkrND2xibHEJ8VjbmhO7+q9s/TszlU6M9R+KLO9Z+N5x5O+NfoyzH4Yc7zn0KJcC5a0WMLBPgfV7UtZlGJKoymcHXQ23XuWtCjJps6bAFUetN23d+P9wJs2FdqkapuUkoTHbQ/uvLiTpbg/BH1dfQbWHMjennvR1dElKiEKxz8dsV9hr6qo8IlPfWa5g6YoSn6gApAMfAGcBcoLIdYI8ZGkAJakLIiMVKXTKFMGZs3SdjSS9GkTQhCXpNr4/zLuJSGRISxrtYy7o+8yqvYojWz9byuVtxQdK3dMd83Wm8Jjw+m/sz/rrqyjmXszroZdZXqT6RjqGQLgss6F8QfHq9sHvQyi29ZuvIp7hZGeEb+5/PbOYuffHPoGQJ049bUUkUKv7b2ITVIVUT/a9+g731NaJh6aSO2VtdWfU1bNd5lPNctq9NnRh0eRj1jQfAGOVo4M3zscZ2tn6hSvw6G7hwiPDadU3lL86PQjtYvXxqu/V6bu325TOwQiVdknUKUEabupLTtu7shW7B+SkZ4RvzX7jYj4CDps7kDNP2qy4+aObFUn6PxPZ6Z5pb+5IzdkdRfnz0Ag8BXwG6pRs1qALE8vfbLGjoWgIFi7Fsy0s1lJkj46R/oe4Z8u/2S6fYpIYfvN7ditsMPtuBsALcq1IGBUAMNqDVN3nN4lJCIEzzueGe6c3OO/h6pLq7LuyjpCI0MJjQzVmLZ726G7h7BfYY/nHU9uPL2RqfdjZmDGuDrjMNE3UR8TQjDh4AT+uf4Prcq3ImxCWJbXzh29d5QlPktoVLpRuuk+MmKsb8ymTpuoW6IuOooOhnqGbO2ylUalG+EX5sfay2tpu6kt3bd1JyYxhocRD4lLilOnLAl4HsB4z/EZdlxep+D4VOjp6NHPth+3Rt5ibfu1xCTG0PGfjviE+GT5XhceXVDvBNaWrI6g/YBqo0BZIcRkIcQaoCXQT1GUzYqi6L/zakn6yOzYoVpz9t130KCBtqORpI9HHsM8mUqvkJySzOZrm6mxvAad/ulEdEI0tkVsAdX6p6ykyzhy7wjN1zfncdTjNM+Hx4bTb2c/2mxsQwGTApwbfI6J9Semez+BYNapWTRf35xieYrh4+qTZjH0zPrx2I/MPzuf0Y6j8ejhkani52+KiI9g4K6BlM9f/r3XN1W1rMqu7rsobFYYIQQlLEqwu8duNl3bxBzvOaqpzrsHaby2MSXml8D7gTeGuobUKlYL30e+zDs7jx+P/qi+35t50L6u8zUAPbf3ZO3l3E1WnBP0dPToW6MvN766wf5e+9XpVeZ6z2XbjW0fTb3PjGS1g1ZZCDFCCBH2+oAQ4ijQGHACDuRkcJL0IT16pEqnYWenyn0mSdJ/Fp9bzOpLqzNsN85zHN23dSc5JZn1Hddz46sbdK/W/YPEdPL+SdZfWc/kLybj6+qLfTH7d7bfdG0Tk45MokuVLpwZdIbyBcpn+llv50F7HPWYlRdXAqr8YJktmv7sm2fq1BsTDk7gQcQD1rZfqzEy9z4eRz2mqXtTzjw4A0B0YjTXn14nOjGakQ4jOR9yXt22VN5S+Lj6sLv7blztXJlxagbrrqxLdc95LvOImhRFkzJN+Pbwt+oanp8aPR099eaHpJQk1l1ZR+ctnamxvAZbrm/56DtqWd3FeTed4xeBBkDpHIhJkj44IWDgQFVqjfXrweD9cmJK0mfH/Yo7W29sTXU8MTmRNZfXcPvZbQBc7V3Z3HkzV4dfpadNzywtls+MF7Ev1Gkq2lZsS8CoAKZ+OTVTU6YNSzVkcYvFbOy0MdvJVlNECltvbKXB6gZEJURxdtDZLFVY0NfVR1dHl5jEGHxDfRlfd/x7jeK9zVjPmMDwQHps60F4bDjGeqr1cOMPjqdzlc7qNXR3X/z361tRFJa0VE2zDto9CO8H3iQkJ+AX5seFRxdISknC1MCU3T124zXAC3ND8xyLV1v0dPS4MOQC6zuuJyklia5bu1J9WXXOPkx/84S2ZXmTQHqEEHeAejl1v9cURWmuKMptRVHuKIryXU7fX/r/tHQpHDgAc+ZApUrajkaSPn4JyQn8eeFPKi6pyIBdA1jrp5r6qmZZja5Vu6Kro5vjz9x9ezdVl1al+9buvIh9AagqA7zN2dqZ2laqaaztN7fTdUtX3Bq58VPDnxjpODLTo11p2XJ9C122dOFu+F22d9ueZjWCd5lwcALbbmzDRN+Ec4PPMbXx1GzHkhYLIws2dtpISGQIrh6uKIpCCfMSlLIoRc/tPVnSYgkA1vmsCX4ZTM0/arI/YD8GugZs67qNkhYlmXFyhno06WHEQ/ru6Auopj0rFKgAwA9HfmCa1zSM9Iw41u8Y3ap1y9H3kRt0dXTpadOTa8OvsbHTRnQUHQqaFARUfwgkpySr29oWsaVsPu2lEgFIVT397S9gF1Azo3ZvtDcCxgHDMnvNO+6lC9wFrAEDwA+o8q5r7O3ts1pIXvo/c+OGEEZGQjRvLkRKirajkaSPk8MKB9FiXQshhBCrLq4SJeaVELghHFY4iN23douUD/Afz9rLawVuiPMPz4te23oJ3BA1ltUQF0MvZnhtUnKS+O7QdwI3hOOfjuJ5zPP3imXO6TkCN9RfKy+szNZ9zGeaC9PppuJFzIv3iicjs0/NVsdqs9RG+D32E8bTjIXipgjcEEcCj4i9/nsFboj1V9arrwsKDxIxCTEiNjFWff3qi6s17p2ckiz6bO8jcENMOjzpg/y714Y330fbjW1F5SWVxYYrG0RSclKuxgH4ijT6M5kZQQsGziqKck5RlDGKotgpiqIxhq0oSjFFUdorirIKeIRqd+fFHOg/OgJ3hBCBQogEYBPQLoNrJCld8fHQuzeYmqo2B7zHH9aS9FmLS4pTlw3ye+xHcfPi7O+1n3ODz9GmYpv3GpVKj7O1M9u6bsNlnQubr2/mZ6efOe96nppFa77zumcxz2i+vjmzTs9iqP1QvPp78TDiIYHhgdmO5eIj1a+wEuYlOD3wNIPsBmXrPhHxEUQnRvPHhT+yHUtmjK83HpeyLujr6LO2/VqqF67OijYrEAhGOozEwtCCVhtUVQLEG/nBSuUthbG+Ma/iXqmPtarQSuPeOooOa9qvYYjdEGaemonlXMt063d+St78Ge5t0xsdRYee23tSbVk1NlzdoDGipg3Km/+i0mygKHOB7UAPoBdgAQggAohHVT1AH1CA88AywF3kQE40RVE6A82FEIP/fd0HqC2EGJneNXny5BH29poLR7t27cqIESOIiYmhZcuWqa7p378//fv359mzZ3Tu3DnV+eHDh9OtWzcePHhAnz59Up0fP348bdq04fbt2wwdOjTV+cmTJ+Ps7Mzly5cZO3ZsqvMzZsygXr16eHt78/3336c6v2DBAmxtbTl8+DDTpqXOy/LHH39QsWJFPDw8+C2NGkXu7u6UKFGCzZs3s2zZslTnt27dSsGCBVmzZg1r1qxJdX7fvn2YmJiwdOlS/vkn9bb748ePAzB37lz27NEsaWJsbMz+/fsBmDp1KkeOaGbULlCgANu2bQNg0qRJnDlzRuN88eLFWbdOtYh17NixXL58WeN8hQoVWLFiBQBDhgzB399f47ytrS0LFqhq3PXu3ZsTJx7y8CFUrQoFC0LdunWZOXMmAJ06deL5c806dE2aNOHHH1U7nVq0aEFsbKzG+datWzNhgqpETKNGjVJ9NvJnT/7sgepn7+HDhxrnP/afveDywbTu0JqJNhPp1btXqnxgH/JnLyQyhGm/TqObc7dM/ex1HdeVuMQ49c7TiPgIoltH0+eLPrRKaJWtn70T9U+AAbiZuHFs77FU5zP7s6d8qUCgaj3c6w7Bh/rZS0xJREGhll0t9c9etx7dCHuk2td3+/ltHkc+pk2TNuxepSq59fpn73HUY/W6wimDpqT7sxfwPIDQoqHM/Gkm3zX47rP7/97TmKckOCdwx/AOvU1782DPg1TX5/T/906cOHFBCJGqTlhmVnOOBf4RQoxSFCUS1U7NukBRVNOZz4FbgJcQIjgT98uKtP5ES9WjVBRlCDAEwNAw44Wj0v+nkBB4+BCKFVN1ziRJSt9XDl/hYu8CCamTtX5oVnmsqFiwYrrnYxNj2X17NwlhCVSnOlUKVuH60+tExkcSkxiDuaE5AxwGMLrhaC4ezt5kzoZOG4jXiSfG+9052TIy0HYgNxNvfpARx7fp66TOdPVmqaaKBSpSwLiAel3Zm4qYFSEhOYF8Ru+u2Fi+QHlcarowxH7I+wf8ESpkUoh5XebxwuIFT64+YQUrtBZLZkbQngB9hBCeiqIkA3WFEOffeVFOBacodQE3IYTLv68nAQghZqZ3Ta1atYSvr29uhCd9QkJCwNYWrKzg7Fkwyl5+SEmSctHr30+KorD1xlaW+y7HN9SXV/Gq6TgzAzOeTHiCsb4xV8OuYqxvTNl8ZXOlMyRJOUVRlGyPoJ0C5iqKUgjViFZuFrfyAcorilIGCAG6Az1z8fnSZyA5WbXuLDYWNm+WnTNJ+lg9i3mGT4gPPqH/foX44D3IG+t81oTHhhMeF073at1xKOaAg5UDVQpVUaf1sCksS0FLn5fMdNBGAmv//RLAYUVRrqAqkv7667oQIjGngxNCJCmKMhLwRLWjc7UQ4tNfmSjlqhkz4PhxWLMGKqY/ayJJUi6KjI/k4qOLlM1fluLmxdnjv4c2G1XFuRUUKhWshEs5F3X6B1d7V1ztXbUZsiTlqgynONUNFaUIEAqsBPICtsDrJCGJwA3gkhAie1tdcoic4pTedPIkNGoEPXqAu7vctSlJ2hIZH8lav7XqkbFbz24hECxsvpDRtUfzOOox7n7uOFg5YFfU7rNIjipJmZHeFGemO2j/3mQbMFkIcfPf12aoOmo1X38JId69H/oDkx006bVnz6BmTdWU5sWLkCePtiOSpM9fUkoSN5/eVHfEahSpwbBaw4hKiMJilgWFTArhYOWgmqYs5kDt4rXJb5xf22FLkta8zxo0NSFEp7deR6Fao3bq/cKTpJyVnAy9esHTp+DtLTtnkvQhCCF4EfuCAiYFAGizsQ1H7x1V1680NzRXj4SZGZjx8OuHFDErIhfxS1Im5GzRNEn6SEyZAgcPwooVqmLokiS9v0eRjzgXck69kN831JcSFiXwG+YHgAyZntsAABrWSURBVHVea6xrWqtHyMoXKK+RoqNonqLaCl2SPjmygyZ9dvbvh6lToX9/GDxY29FI0qfpecxzfEN9ufrkKuPrjkdRFMYfHM/GaxvRVXSxKWxD5yqdqVO8jvqahS0WajFiSfq8ZGkN2qdArkH7/xYcrBoxK14czpwBExNtRyRJn47jQcf548IfnA85r1EmKXRcKEXzFOXSo0vEJcVhW8QWY31jLUYqSZ+PHFmDJkkfs/h46NwZkpJg2zbZOZOktCQkJ3Al7Ao+IT6cDz2PT4gPf3f4G7uidoRGhnL6/mkcrBxwtXPFoZgD9sXsyWuUFyDDmpiSJOUc2UGTPhtjx4KvL+zYAeXKaTsaSdK+5JRkbj27hYWRBcXNi3Pu4TkarmlIQnICgHpH5etcYz2q9aCnjcwFLkkfA9lBkz4Lq1fD8uXwzTfQvr22o5Ek7UhITmDHzR3qTPwXH10kKiGKXxr9wk9OP1GxYEXG1B6DQzEHHK0cKWlRUmNHpdxdKUkfD7kGTfrkeXurktE2agT79oGe/LND+j/wKPKROtdY0TxFGeEwgqSUJCxmWZCckoxtEVt1SaSGpRpSOm9pbYcsSVIa5Bo06bP04AF07AglS8KmTbJzJn2e4pLiMNJTFZEdsXcEu2/vJiQyBABdRZfu1bozwmEEejp6XBxykTL5ymCga6DNkCVJek/y15n0yYqNhQ4dICYGjh6F/DIZufQZiE6I5tLjSxpFw5NSkrg35h4ABroGOJV2Umfir1m0Jib6/+2IqVhQFpyVpM+B7KBJnyQhYNAgVQmnXbugShVtRyRJWZeYnMjVJ1fxDfVlYM2B6Ono8c2hb1jmuwyA4ubF1R2xFJGCjqLDguYLtBy1JEm5QXbQpE/S7NmwcSNMnw5t2mg7GknKPL/Hfqy8uBKfUB8uP75MfHI8APVK1KOaZTUG2w2mRbkWOFg5UMSsiJajlSRJW2QHTfrkeHjApEnQrZvqn5L0sRFCEPwqWGOackqjKXxR6gseRjzkr8t/YV/MnpGOI9UL+cvkLQOAXVE77IrK+mSS9P9OdtCkT4qvL3TvDvb2qtQaMiuA9DF4Ev2EpJQkiuUpxp0Xd6i7qi7PYp4BqjVjNQrXIDYpFgCXci68+u4Vujq62gxZkqSPnOygSZ+M4GBo3RosLWHPHlkpQNIOIQTHgo5pjI7df3WfsbXHMr/5fEpalKRthbbUKlYLBysHbCxtMNQzVF+vpyP/tytJUsbk/ymkT8LLl9Cypaqc07FjULiwtiOS/h/EJsZy+fFlfEJ90NfRZ7jDcAB6butJWHQY1vmsqVu8LqMdR9PEugmgGjFb1W6VNsOWJOkzIDto0kcvIUGV6ywgADw9oXJlbUckfY5e75IEmO41na03t3LtybX/tXfv0VWVdxrHv79cCAQCgSQgJ0ASB7mqGDgHKigqopWhIjcvo2VU6uhoq4y2tmqpltbadqqldtaMl1FKvVIUaKsFR60iKl4SUlQEqTAqQriEWyEgISG/+WMfT8FBESVnn+Q8n7WyAjvuk+ddyMnDfvf7bhoaGwAY1n0YV8auxMyYf9F8SjqUUJBbEGZkEWnBVNAkpbnDv/xLcNXsgQfgtNPCTiQtQaM38u6WdxM78VdUV/D+9vdZe91aMiyDbXu2UZRbxHeHfpdYcbDNRXH74sT5uolfRJqaCpqktB/8IChm06bBpElhp5HmyN35cMeHVKyrYNQxo8jNzmXawmn8aNGPAMjNzmVg14FccOwF7GnYQ252LrefeXvIqUUk3amgScqaPj3Y5+yyy4KiJvJ5vbftPR5880FeX/c6FdUVbNq1CYBFlyzi5JKTGdtnLCX5JcQiMfoW9dWN+yKScvSuJClp5ky47jqYOBHuvlvbacjB7ajbwZLqJYnVlJeVX8ZXe36V9bXr+eHCH9KnsE+w6Wt8r7EBXQYAUN61nPKu5SGnFxH5dCpoknJ+//vgMU5nnAEPPQSZ2i5KCB4YvrNuJ0Vti9i8ezMn/+ZkVm5eieMAlOWXMbb3WABikRjbb9hO+5z2YUYWEfnCVNAkpTz/fPCEgMGDYe5cyMk59DnSMr218a3EFGVFdQVvbnyTScdPYsY5MyhoU8CALgO48NgLiRXHiEaiFOYWJs7NzswmOzM7xPQiIl+OCpqkjIoKGDMGevWCP/0J2rULO5Ekg7uzausqKqorqN1by+WDLgfg3MfOZeWWlXTI6UA0EuU7J36HkUePBMDMmDVxVpixRUSalAqapITKSjjzTCgqCvY669Qp7ETS1O6vup9Zb8+isrqS7Xu2A9CjQ49EQZtxzgwKcwvp2alnYn8yEZF0oYImoVuyJLjfrGPHYIozEgk7kRwpW3ZvOWCvsTc2vsHKb62kdVZrVm1dxZbdWziv33mJvcb6d+6fOHdo96EhJhcRCZcKmoRqyRIYORLy84NyVlISdiL5omr31lK1vooBXQbQoXUH7qq4i6vmX5X4ep/CPgwvGc6Ouh20zmrNT0f+lJ+O/GmIiUVEUpcKmoRm/3K2cKHKWXNTs6uGx5Y/lrhCtmLzChq9kT9e8EfO7n02J/U4iZ+P/DmxSIxBkUFaUSkichhU0CQUH09rqpylvn2N+1ixeUVimvKsnmcxpvcYanbX8M3536Qot4hYcYyJ/SYSi8QY1mMYAMd1OY7juhwXcnoRkeYpZQuamf0COBvYC6wGLnX37eGmkiNh0SI4++y/33OmcpY63J3avbXk5eRR11DHmQ+dyZLqJeyq3wVAXqs8/qHjPwDQu6A37095nx4demDaSVhE5IhK2YIGPAPc6O4NZvZz4EbgeyFnki/pySfh3HOhtBSeeQa6dQs7UXpbv3P9ATfxV1ZXcnLJycw7fx45WTkU5hYyuXxyYif+XgW9EisqMzMyKclXuxYRaQopW9Dc/en9fvsqMDGsLHJkPPQQXHIJlJfDggVQWHjIU+QI2vrRViqrK1m3Yx2Xll8KwLjfjeO1da+RaZn079yfsX3GcnrZ6Ylz5pw3J6y4IiJpLWUL2idMBn73aV80s8uBywF69OiRrExyGH79a5gyBUaMCB7llJcXdqL08MTKJ3h02aNUVFewausqAHKzc5k0YBJZGVn8bOTPyM7IprxrObnZuSGnFRGRj4Va0MzsWeCog3zp++7+h/h/832gAXj4017H3e8F7gWIRqPeBFHlC3KHW26BH/8Yxo2DRx6B1q3DTtWy7N23l7c2vnXAVOXCSxbSqU0n3tj4Bi+ueZFYJMY3yr+RWFGZlRH81T+19NRww4uIyEGFWtDcfeRnfd3MLga+Bpzu7ipezcyePcFDzx95BCZPhnvugazmcs02Re1r3MfKLSvp2q4rHdt0ZO6KuVw450Lq9tUBUNCmgFhxjG0fbaNTm07ceNKNTB0+NeTUIiJyuFL2x6WZnUWwKOAUd98ddh45PDU1MHYsLF4Mt90GN9wAWuh3+Gr31jL/3fmJK2NL1i+hdm8tD4x9gEkDJnFs52O5evDViZ34S/NLD1hRmZmRGWJ6ERH5oixVL0yZ2SogB9gSP/Squ//roc6LRqNeWVnZpNnks61YAaNHw/r18MADwapNObQNtRsSReyEo05gfN/xVO+spviXxbTKbMUJR50QrKaMxBh59EiK2xeHHVlERL4kM1vi7tFPHk/ZK2ju3jPsDHL4/vxnmDABcnKCDWiHDAk7UWpqaGwgKyMLd+eCORew+MPFrN2xFoAMy+Dar1zL+L7jieRFqLq8iv6d+9Mqs1XIqUVEJFlStqBJ8+IOt98ON94IffoE+52VloadKjXsrt/N0g1LE1fHKqorKM4r5rmLn8PMqN9Xz8k9Tk7sNVZ+VDltW7VNnF/etTzE9CIiEgYVNPnSduyASy+FuXODq2czZkD7NH3sYv2+epZtWsbKLSu54NgLAJg4eyILVi0AIJIXIRaJcUrJKYlz5p4/N5SsIiKSulTQ5Et5+20YPx5Wrw6uoF13XfotBlj84WJmLZtFRXUFSzcsZU/DHgxj9DGjycvJ49snfpsrBl1BrDhGJC8SdlwREWkGVNDkC5s1Cy67DNq1C+49O+WUQ5/TXLk7H+748IBpyvvH3E9pfilV66uY8ZcZDOw6kKuiVyVWVLZr1Q6A048+/RCvLiIiciAVNDlsO3fCNdfAzJkwbBjMng2RFnZhqGZXDVkZWXRs05GX1rzEhNkT2LRrEwDZGdkc3+V4tuzeQml+KZcNvIwro1dqSwsRETliVNDksLzyCnz96/D++zB1Ktx8M2Rnh53qy9m7by8vr3k5cWWsYl0FH/ztA3591q+5esjVlHQoYVTPUYmb+Ad0GUBOVk7i/NZZejSCiIgcWSpo8rk0NMCttwYf3bvDCy/ASSeFnerw7WnYk1hRGcmLMKHfBPbu28vIB0fS6I2U5ZcxpNsQvjX4W4mpye4dujNz7Mxwg4uISFpRQZNDWr48eGTTq6/CP/9z8ODzDh3CTnVo7p7YVf/6p6/nz+/9mbc2vUVDYwMA5/U/jwn9JtCuVTuev/h5+hX1ozC3MMzIIiIigAqafIa6OvjZz+AnP4G8vGBRwPnnh53q4NydVVtX8fq61xNTlQAvT34ZgNXbVlOQW8D1Q69PTFUW5/19J/7hJcNDyS0iInIwKmhyUIsXBys0V6yACy+E6dOhc+ewUwXcnbU71rJ0w1LO7n02AJP/OJmZS2cC0CarDQO7DmRo96GJq2jaa0xERJoTFTQ5wLZtwc3/d90V3Gs2fz6MGhV2Klhes5w5y+ckro5tqN0AwNpr11LcvpiLjruIYd2HMbh4MP2K+pGVof+1RUSk+dJPMQGCRQD//d/wgx/A1q3BNhq33hrscZZMO+t2UrW+KlHEbh5+M/0796dqfRW3LLyF3oW9OePoMxhcPJhYJEbntsFlvZFHj0xuUBERkSakgiY8+yxcey0sWwanngq/+hUMGND037euoY66fXW0z2nP8prlnPvYuayoWYHjAJR0KKF6ZzX9O/dnXJ9xbL9hO+1z0vQZUiIiklZU0NLY8uVwww3wxBNQVgZz5sC4cU3zqKZGb+TtTW8n9hmrqK7gzY1vMnX4VG4+5Wa6tutKWX4Z5/U7L7ETf1HbosT5+z88XEREpKVTQUtDf/0rTJsGjz4KbdsGKzWnTIHWR2i/VXdn9bbVVFZX0iqzFeP7jqfRGxly3xA+aviI9jntiUaiXHfidZxeFuw11rFNR5688MkjE0BERKSZU0FLI++9Bz/6ETz4IOTkwPXXBx+FR2jrr1++8kueWvUUldWVbNuzDYBh3Ycxvu94sjKymHv+XMryyzim4BgyLOPIfFMREZEWSAUtDSxbBnfcAQ89BJmZwQKA730PunQ5/Nfa+tFWKqsrE9OUm3ZtYvE3FgPw2rrXqNldw8R+E4lGosQiMY7tfGzi3LN6nnWkhiQiItKiqaC1UO6wcCH84hewYAHk5sKVVwbFrLj4kKcDsGvvLqrWVzG0+1AyMzKZ+txUfvLiTxJf71XQi1gkRv2+erIzs5k1YVZi534RERH54lTQWpiPPoLHHw9WYlZVBZvL/vjHQTkrKPjsc9fuWMsTK59IbHGxvGY5jd7IsiuX0b9zf0aUjaBdq3bEIjEGRQaR3zr/gPNVzkRERI4MFbQW4p134J574Le/DTab7d0b7r0XJk36/zf/72vcx8otKxPTlJeccAnRSJQ3NrzBVfOvojC3kFgkxvg+44kVxyjJLwFgRNkIRpSNCGF0IiIi6UUFrRmrrYV58+C++2DRIsjODrbJuOIKOO20YLsMd+ej+j20yW7Duh3ruGjuRSxZv4TavbUAtGvVjhO7nUg0EuXU0lN5b8p7lHQo0dUwERGREKmgNTP19fD00/Dww/CHP8Du3XD00cFWGZdeCo25G6hYV8EtCyt4fd3rVFZXcvGAi7njq3dQmFtIfWM9Fw+4OPHA8N4FvcnMyASCvca035iIiEj4VNCagfr64Ib/efPgscdg82bo1AnOv6iO40e+Selx6xnbdwzuzlF3DGDTrk1kWAb9i/pzTu9zOKX0FABysnJ4efLL4Q5GREREDkkFLUXt3g3/8z8wdy48+SRs3x6sxDzupDX0G/gY1Z1n8Jsdy2EF9NrUi7F9x2Bm3D36boraFlF+VLmuhomIiDRTKmgpwh1Wrgy2xFiwoJEXFsHeugxy8mrpcPyLzPvOWZx5pvGtZ37I06ufJhaJcWn0ImKRGNFINPE64/qOC3EUIiIiciSooIVo40Z47vlG5s3/G68tymfNB8GN+Va0Ei9fAL2eJLfPMsq7D+TUs04kt3U+d42+i5ysnJCTi4iISFNSQUuijRvhqedqefSJDVQubseWD44CMqBVJieftpWbbiwgv/9rvL5rNoOLBxMrvo+y/LIDVlSqnImIiLR8KmhNxB1eWbqF381fx6KX9rF5ZR/WvtcGaAfZXbGSxXQb/zhDhu1m1PAunN13FJ3bAgzhfIaEnF5ERETCpIL2ea1ZEzxl/KabPt5gDG67LdgJtkcPNm9ppLIigxdequM3f1pOzV/LaNxdABRAm830H7SOa67sSXRIHa17vMPAbsPJyToj7FGJiIhICkr5gmZm3wF+ARS5++bQgjz4IEydCjU1bJ12G4//62089cpO/jL7Ldatb6S+pjSetxU5kXaUnriEQbEGxpzRiXOG9SUvp2f8hXKAQWGNQkRERJqBlC5oZtYdOANYE3YWbroJamr44Z35TPuPbGi8FYCMDtV0PmYNXzmvhmsmxIhGjby8Y4Bjws0rIiIizVZKFzRgOvBd4A9hB8EMpk8ndufXGNfp3+md8zoTn72LQX0iQCTsdCIiItKCpGxBM7MxwDp3fyMlngvpDtdey2jmM3rz/ODY3WUwfXpQ3kRERESOkIwwv7mZPWtmyw7ycQ7wfeDmz/k6l5tZpZlV1tTUNE3Y226DO++EKVOgsTH4fOedwXERERGRIyjUK2juPvJgx83sOKAM+PjqWTegyswGu/uGg7zOvcC9ANFo1Jsk7KRJweePV3FOnw5FRX8/LiIiInKEmHvT9JkjyczeB6KfZxVnNBr1ysrKpg8lIiIi8iWZ2RJ3j37yeKhTnCIiIiLy/6XsIoH9uXtp2BlEREREkkVX0ERERERSjAqaiIiISIpRQRMRERFJMSpoIiIiIilGBU1EREQkxaigiYiIiKQYFTQRERGRFKOCJiIiIpJimsWjng6HmdUAHzTxtykEDvnYqRYqXceeruMGjT0dx56u44b0HXu6jhvCH3uJuxd98mCLK2jJYGaVB3tuVjpI17Gn67hBY0/HsafruCF9x56u44bUHbumOEVERERSjAqaiIiISIpRQfti7g07QIjSdezpOm7Q2NNRuo4b0nfs6TpuSNGx6x40ERERkRSjK2giIiIiKUYF7TCY2Qwz22Rmy8LOkkxm1t3MnjezFWb2tplNCTtTsphZazN73czeiI99WtiZksnMMs3sL2b2ZNhZksnM3jezt8xsqZlVhp0nmcws38weN7N34n/nTww7U1Mzs97xP+uPP3aY2b+FnStZzOza+PvbMjN71Mxah50pGcxsSnzMb6fin7emOA+DmQ0HaoEH3P3YsPMki5l1Bbq6e5WZ5QFLgLHuvjzkaE3OzAxo6+61ZpYNvARMcfdXQ46WFGZ2HRAF2rv718LOkyxm9j4Qdfe02xfKzH4LvOju95lZKyDX3beHnStZzCwTWAcMcfem3lMzdGZWTPC+1s/dPzKz2cB8d58ZbrKmZWbHArOAwcBe4CngSnd/N9Rg+9EVtMPg7ouArWHnSDZ3X+/uVfFf7wRWAMXhpkoOD9TGf5sd/0iLf9WYWTdgNHBf2FkkOcysPTAcuB/A3femUzmLOx1YnQ7lbD9ZQBszywJygeqQ8yRDX+BVd9/t7g3AC8C4kDMdQAVNDouZlQLlwGvhJkme+DTfUmAT8Iy7p8vYfwV8F2gMO0gIHHjazJaY2eVhh0mio4Ea4Dfxqe37zKxt2KGS7ALg0bBDJIu7rwNuB9YA64G/ufvT4aZKimXAcDMrMLNc4B+B7iFnOoAKmnxuZtYOmAP8m7vvCDtPsrj7Pnc/AegGDI5fGm/RzOxrwCZ3XxJ2lpAMc/eBwCjgm/HbG9JBFjAQuMvdy4FdwA3hRkqe+JTuGOCxsLMki5l1BM4ByoAI0NbMvh5uqqbn7iuAnwPPEExvvgE0hBrqE1TQ5HOJ3381B3jY3eeGnScM8amehcBZIUdJhmHAmPi9WLOAEWb2ULiRksfdq+OfNwHzCO5TSQdrgbX7XSV+nKCwpYtRQJW7bww7SBKNBN5z9xp3rwfmAkNDzpQU7n6/uw909+EEty+lzP1noIImn0P8Rvn7gRXu/suw8ySTmRWZWX78120I3szeCTdV03P3G929m7uXEkz5POfuLf5f1QBm1ja+GIb49N6ZBNMhLZ67bwA+NLPe8UOnAy1+MdB+/ok0mt6MWwN8xcxy4+/1pxPcZ9zimVnn+OcewHhS7M8+K+wAzYmZPQqcChSa2VrgFne/P9xUSTEMmAS8Fb8XC+Amd58fYqZk6Qr8Nr6yKwOY7e5pteVEGuoCzAt+VpEFPOLuT4UbKamuBh6OT/f9L3BpyHmSIn4f0hnAFWFnSSZ3f83MHgeqCKb4/kKK7qzfBOaYWQFQD3zT3beFHWh/2mZDREREJMVoilNEREQkxaigiYiIiKQYFTQRERGRFKOCJiIiIpJiVNBEREREUowKmoiIiEiKUUETERERSTEqaCIiIiIpRgVNROQgzKynmdWb2bRPHL/LzHaaWTSsbCLS8qmgiYgchLuvAu4DrjWzQgAzuxmYDIxz98ow84lIy6ZHPYmIfAozOwpYDfwX8A7BMwr/yd1nhxpMRFo8PSxdRORTuPsGM/sV8G2C98trVM5EJBk0xSki8tneBXKAV9z9P8MOIyLpQQVNRORTmNkI4B7gFWCYmQ0IOZKIpAkVNBGRgzCzgcDvCRYKnAqsAW4LM5OIpA8VNBGRTzCznsAC4GnganffC0wD/tHMhocaTkTSglZxiojsJ75yczHBFbOvuntd/HgmsAzY5u5DQ4woImlABU1EREQkxWiKU0RERCTFqKCJiIiIpBgVNBEREZEUo4ImIiIikmJU0ERERERSjAqaiIiISIpRQRMRERFJMSpoIiIiIilGBU1EREQkxfwfsHlEzJbUOmcAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def f(x):\n", " return 2*x + x*np.sin(x-3) - 5\n", "\n", "fig, ax1 = plt.subplots(figsize=(10,6))\n", "x0 = 1.\n", "plot_newton(f, 1.e-8, x0, 1.e-7, ax1, inset=False, maxiter=14, \n", " flabel='$f(x)= x \\mathrm{sin}(\\pi x) - \\mathrm{e}^{-x}$')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What happens if you increase the number of iterations?\n", "\n", "Another similar example:" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def f(x):\n", " return np.arctan(x)\n", "\n", "fig, ax1 = plt.subplots(figsize=(10,6))\n", "x0 = -1.3917\n", "plot_newton(f, 1.e-8, x0, 1.e-7, ax1, inset=False, maxiter=10, \n", " flabel='$f(x)= \\mathrm{tan}^{-1}(x)$')" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.7.7" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": false, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": { "height": "calc(100% - 180px)", "left": "10px", "top": "150px", "width": "427.513px" }, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 1 }