{
 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "(section:newtons-method)=\n",
    "# Newton's Method for Solving Equations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Last revised on August 25, 2025**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**References:**\n",
    "\n",
    "- {cite}`Sullivan` Section 2.4, [Newton's Method](https://numericalmethodssullivan.github.io/ch-algebra.html#newtons-method).\n",
    "\n",
    "- {cite}`Sauer` Sections 1.2, *Fixed-Point Iteration*, and 1.4, *Newton's Method*.\n",
    "\n",
    "- {cite}`Burden-Faires` Sections 2.2, *Fixed-Point Iteration*, and 2.3, *Newton's Method and Its Extensions*.\n",
    "\n",
    "- {cite}`Dionne` Section 2.5, *Newton's Method*.\n",
    "\n",
    "- {cite}`Chenney-Kincaid` Section 3.2, *Newton's Method*.\n",
    "\n",
    "- {cite}`Dahlquist-Bjorck-v1` Sections 1.1.3, 6.3.1 and 6.3.2."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Introduction\n",
    "\n",
    "Newton's method for solving equations has a number of advantages over the bisection method:\n",
    "- It is usually faster (but not always, and it can even fail completely!)\n",
    "- It can also compute complex roots, such as the non-real roots of polynomial equations.\n",
    "- It can even be adapted to solving systems of non-linear equations; that topic will be visited later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using PyPlot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Derivation as a contraction mapping with \"very small contraction coefficient $C$\"\n",
    "\n",
    "You might have previously seen Newton's method derived using tangent line approximations.\n",
    "That derivation is presented below,\n",
    "but first we approach it another way: as a particularly nice contraction mapping.\n",
    "\n",
    "To compute a root $r$ of a differentiable function $f$, we design a contraction mapping for which the contraction constant $C$ becomes arbitrarily small when we restrict to iterations in a sufficiently small interval around the root: $|x - r| \\leq R$.\n",
    "\n",
    "That is, the error ratio $|E_{k+1}|/|E_k|$ becomes ever smaller as the iterations get closer to the exact solution;\n",
    "the error is thus reducing ever faster than the geometric rate $C^k$ seen in the section on\n",
    "[fixed point iteration](section:fixed-point-iteration).\n",
    "\n",
    "This effect is in turn achieved by getting $|g'(x)|$ arbitrarily small for $|x - r| \\leq R$ with $R$ small enough,\n",
    "and then using the connection between $g'(x)$ and $C$ given in {prf:ref}`a-derivative-based-fixed-point-theorem`.\n",
    "This can be achieved by ensuring that $g'(r) = 0$ at a root $r$ of $f$ — so long as thr root $r$ is *simple*:\n",
    "$f'(r) \\neq 0$ (which is generically true, but not always).\n",
    "\n",
    "To do so, seek $g$ in the above form $g(x) = x - w(x)f(x)$, and choose $w(x)$ appropriately.\n",
    "At the root $r$,\n",
    "\n",
    "$$\n",
    "g'(r) = 1 - w'(r)f(r) - w(r)f'(r) = 1 - w(r)f'(r) \\quad\\text{(using } f(r) = 0,)\n",
    "$$\n",
    "\n",
    "so we ensure $g'(r) = 0$ by requiring $w(r) = 1/f'(r)$ (hence the problem if $f'(r) = 0$).\n",
    "\n",
    "We do not know $r$, but that does not matter!\n",
    "We can just choose $w(x) = 1/f\"(x)$ for all $x$ values.\n",
    "That gives\n",
    "\n",
    "$$g(x) = x - {f(x)}/{f'(x)}$$\n",
    "\n",
    "and thus the iteration formula\n",
    "\n",
    "$$x_{k+1} = x_k - {f(x_k)}/{f'(x_k)}$$\n",
    "\n",
    "(That is, $g(x) = x - {f(x)}/{f'(x)}$.)\n",
    "\n",
    "You might recognize this as the formula for Newton's method."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To explore some examples of this, here is a function implementing Newton's method."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:remark} On Julia\n",
    ":label: julia-remark-keyword-parameters\n",
    "\n",
    "This function uses optional keyword parameters with default values for the first time;\n",
    "these will be described in [Functions, part 2](functions2-future) in {ref}`section:julia-language-notes` once they have been written.\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "function newton_method(f, Df, x0, error_tolerance; max_iterations=20, demo_mode=false)\n",
    "    # Basic usage is:\n",
    "    # (rootapproximation, error_estimate, iterations) = newton(f, Df, x0, error_tolerance)\n",
    "    # There is an optional input parameter \"demo_mode\" which controls whether to\n",
    "    # - println intermediate results (for \"study\" purposes), or to\n",
    "    # - work silently (for \"production\" use).\n",
    "    # The default is silence.\n",
    "    \n",
    "    if demo_mode\n",
    "        println(\"Solving by Newton's Method.\")\n",
    "        println(\"max_iterations = $max_iterations\")\n",
    "        println(\"error_tolerance = $error_tolerance\")\n",
    "    end\n",
    "    x = x0\n",
    "    global error_estimate  # make it global to this function; without this it would be local to the \"for\" loop.\n",
    "    for iteration in 1:max_iterations\n",
    "        fx = f(x)\n",
    "        Dfx = Df(x)\n",
    "        # Note: a careful, robust code would check for the possibility of division by zero here,\n",
    "        # but for now I just want a simple presentation of the basic mathematical idea.\n",
    "        dx = fx/Dfx\n",
    "        x -= dx  # Aside: this is shorthand for \"x = x - dx\"\n",
    "        error_estimate = abs(dx);\n",
    "        if demo_mode\n",
    "            println(\"At iteration $iteration, x = $x with estimated error $error_estimate and backward error $(abs(f(x)))\")\n",
    "        end\n",
    "        if error_estimate <= error_tolerance\n",
    "            if demo_mode\n",
    "                println(\"Done!\")\n",
    "            end\n",
    "            return (x, error_estimate, iteration)\n",
    "        end\n",
    "    end\n",
    "    # Note: if we get to here (no \"return\" above), it completed max_iterations iterations without satisfying the accuracy target,\n",
    "    # but we still return the information that we have.\n",
    "    return (x, error_estimate, max_iterations)\n",
    "end;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:remark} A Julia module\n",
    ":label: module-numerical-methods\n",
    "\n",
    "This and many other functions defined in this book are also gathered in the module `NumericalMethods`;\n",
    "see the appendix {ref}`module:NumericalMethods`.\n",
    "It can be made available with the commands\n",
    "\n",
    "    include(\"NumericalMethods.jl\")\n",
    "    using .NumericalMethods: newton_method\n",
    "\n",
    "The dot at the start of the module name is a litle surprising;\n",
    "that is needed whe the module is defined locally; in this case by that `include` line.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:example}\n",
    ":label: example-newton-x-cosx\n",
    "Let's start with our favorite equation, $x = \\cos x$.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:remark} On Julia style\n",
    ":label: remark-julia-style\n",
    "\n",
    "Recommended style for Julia code is that function names be alpha-numeric\n",
    "(possibly with the underscore `_` as a \"special guest letter\"),\n",
    "so I will avoid primes in notation for derivatives as much as possible:\n",
    "from now on, the derivative of $f$ is most often denoted as $Df$ rather than $f$.\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "f1(x) = x - cos(x)\n",
    "Df1(x) = 1 + sin(x);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solving by Newton's Method.\n",
      "max_iterations = 5\n",
      "error_tolerance = 1.0e-8\n",
      "At iteration 1, x = 1.0 with estimated error 1.0 and backward error 0.45969769413186023\n",
      "At iteration 2, x = 0.7503638678402439 with estimated error 0.24963613215975608 and backward error 0.018923073822117442\n",
      "At iteration 3, x = 0.7391128909113617 with estimated error 0.011250976928882236 and backward error 4.6455898990771516e-5\n",
      "At iteration 4, x = 0.739085133385284 with estimated error 2.77575260776869e-5 and backward error 2.847205804457076e-10\n",
      "At iteration 5, x = 0.7390851332151607 with estimated error 1.7012340701403256e-10 and backward error 0.0\n",
      "Done!\n",
      "\n",
      "The root is approximately 0.7390851332151607\n",
      "The estimated absolute error is 1.7012340701403256e-10\n",
      "The backward error is 0.0\n",
      "This required 5 iterations\n"
     ]
    }
   ],
   "source": [
    "x0 = 0.0\n",
    "error_tolerance = 1e-8\n",
    "r_e_i = newton_method(f1, Df1, x0, error_tolerance; max_iterations=5, demo_mode=true)\n",
    "root = r_e_i[1]\n",
    "error_estimate = r_e_i[2]\n",
    "iterations = r_e_i[3]\n",
    "println()\n",
    "if error_estimate > error_tolerance\n",
    "    println(\"Warning: the error tolerance was not achieved!\")\n",
    "    println()\n",
    "end\n",
    "println(\"The root is approximately $root\")\n",
    "println(\"The estimated absolute error is $error_estimate\")\n",
    "println(\"The backward error is $(abs(f1(root)))\")\n",
    "println(\"This required $iterations iterations\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we have introduced another way of talking about errors and accuracy, which is further discussed in the section on {ref}`section:error-measures-convergence-rates`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:definition} Backward Error\n",
    ":label: backward-error\n",
    "- The **backward error** in $\\tilde x$ as an approximation to a root of a function $f$ is $f(\\tilde x)$.\n",
    "\n",
    "- The **absolute backward** error is its absolute value, $|f(\\tilde x)|$.\n",
    "However sometimes the latter is simply called the backward error — as the above code does.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This has the advantage that we can actually compute it without knowing the exact solution!\n",
    "\n",
    "The backward error also has a useful geometrical meaning:\n",
    "if the function $f$ were changed by this much to a nearbly function $\\tilde f$\n",
    "then $\\tilde x$ could be an exact root of $\\tilde f$.\n",
    "Hence, if we only know the values of $f$ to within this backward error\n",
    "(for example due to rounding error in evaluating the function)\n",
    "then $\\tilde x$ could well be an exact root,\n",
    "so there is no point in striving for greater accuracy in the approximate root.\n",
    "\n",
    "We will see this in the next example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Graphing Newton's method iterations as a fixed point iteration\n",
    "\n",
    "Since this is a fixed point iteration with $g(x) = x - (x - \\cos(x)/(1 + \\sin(x))$,\n",
    "let us compare its graph to the ones seen in the section on [fixed point iteration](section:fixed-point-iteration).\n",
    "Now $g$ is neither increasing nor decreasing at the fixed point, so the graph has an unusual form."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "g(x) = x - (x - cos(x))/(1 + sin(x))\n",
    "a = 0.0\n",
    "b = 1.0\n",
    "# An array of x values for graphing\n",
    "x = range(a, b, 100)\n",
    "iterations = 4;  # Not so many are needed now!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Starting near the left end of the domain\n",
      "x_0 = 0.1\n",
      "x_1 = 0.9137633861014282\n",
      "x_2 = 0.7446642419816996\n",
      "x_3 = 0.7390919659607759\n",
      "x_4 = 0.7390851332254692\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 700x700 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Start at left\n",
    "description = \"Starting near the left end of the domain\"\n",
    "println(description)\n",
    "x_k = 0.1\n",
    "\n",
    "figure(figsize=[7,7])\n",
    "title(description)\n",
    "grid(true)\n",
    "plot(x, x, \"g\")\n",
    "plot(x, g.(x), \"r\")\n",
    "println(\"x_0 = $x_k\")\n",
    "for k in 1:iterations\n",
    "    g_x_k = g(x_k)\n",
    "    # Graph evalation of g(x_k) from x_k:\n",
    "    plot([x_k, x_k], [x_k, g(x_k)], \"b\")\n",
    "    x_k_plus_1 = g(x_k)\n",
    "    #Connect to the new x_k on the line y = x:\n",
    "    plot([x_k, g(x_k)], [x_k_plus_1, x_k_plus_1], \"b\")\n",
    "    # Update names: the old x_k+1 is the new x_k\n",
    "    x_k = x_k_plus_1\n",
    "    println(\"x_$k = $x_k\")\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Starting near the right end of the domain\n",
      "x_0 = 0.99\n",
      "x_1 = 0.7496384013287254\n",
      "x_2 = 0.7391094534708724\n",
      "x_3 = 0.7390851333457581\n",
      "x_4 = 0.7390851332151607\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 700x700 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Start at right\n",
    "description = \"Starting near the right end of the domain\"\n",
    "println(description)\n",
    "x_k = 0.99\n",
    "figure(figsize=[7,7])\n",
    "title(description)\n",
    "grid(true)\n",
    "plot(x, x, \"g\")\n",
    "plot(x, g.(x), \"r\")\n",
    "println(\"x_0 = $x_k\")\n",
    "for k in 1:iterations\n",
    "    g_x_k = g(x_k)\n",
    "    # Graph evalation of g(x_k) from x_k:\n",
    "    plot([x_k, x_k], [x_k, g(x_k)], \"b\")\n",
    "    x_k_plus_1 = g(x_k)\n",
    "    #Connect to the new x_k on the line y = x:\n",
    "    plot([x_k, g(x_k)], [x_k_plus_1, x_k_plus_1], \"b\")\n",
    "    # Update names: the old x_k+1 is the new x_k\n",
    "    x_k = x_k_plus_1\n",
    "    println(\"x_$k = $x_k\")\n",
    "end;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In fact, wherever you start, all iterations take you to the right of the root, and then approach the fixed point monotonically — and very fast.\n",
    "We will see an explanation for this in the section {ref}`section:newtons-method-convergence-rate`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:example} Pushing to the limits of standard 64-bit computer arithmetic\n",
    ":label: example-2\n",
    "\n",
    "Next, demand more accuracy; this time silently.\n",
    "As we will see in a later section, $10^{-16}$ is about the limit of the precision of standard (IEE64) computer arithmetic with 64-bit numbers.\n",
    "\n",
    "So let's try to compute the root as accurately as we can within these limits:\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "The root is approximately 0.7390851332151607\n",
      "The estimated absolute error is 0.0\n",
      "The backward error is 0.0\n",
      "This required 6 iterations\n"
     ]
    }
   ],
   "source": [
    "x0 = 0.0\n",
    "error_tolerance=1e-16\n",
    "r_e_i = newton_method(f1, Df1, x0, error_tolerance)\n",
    "root = r_e_i[1]\n",
    "error_estimate = r_e_i[2]\n",
    "iterations = r_e_i[3]\n",
    "println()\n",
    "println(\"The root is approximately $root\")\n",
    "println(\"The estimated absolute error is $error_estimate\")\n",
    "println(\"The backward error is $(abs(f1(root)))\")\n",
    "println(\"This required $iterations iterations\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observations:\n",
    "- It only took one more iteration to meet the demand for twice as many decimal places of accuracy.\n",
    "- The result is \"exact\" as fas as the computer arithmeric can tell, as shown by the zero backward error:\n",
    "we have indeed reached the accuracy limits of computer arithmetic."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Newton's method works with complex numbers too\n",
    "\n",
    "This book will work almost entirely with real values and vectors in $\\mathbb{R}^n$, but actually,\n",
    "everything above also works for complex numbers.\n",
    "In particular, Newton's method works for finding roots of functions $f:\\mathbb{C} \\to \\mathbb{C}$;\n",
    "for example when seeking all roots of a polynomial.\n",
    "\n",
    "(See the notes on [Complex numbers in Julia](complexnumbers).)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:example} All roots of a cubic\n",
    ":label: example-3\n",
    "\n",
    "As an example, let us seek all three cube roots of 8,\n",
    "by solving $x^3 - 8 = 0$ and trying different initial values $x_0$.\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "f2(x) = x^3 - 8\n",
    "Df2(x) = 3x^2;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**First, $x_0 = 1$**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solving by Newton's Method.\n",
      "max_iterations = 20\n",
      "error_tolerance = 1.0e-8\n",
      "At iteration 1, x = 3.3333333333333335 with estimated error 2.3333333333333335 and backward error 29.037037037037045\n",
      "At iteration 2, x = 2.462222222222222 with estimated error 0.8711111111111113 and backward error 6.92731645541838\n",
      "At iteration 3, x = 2.081341247671579 with estimated error 0.380880974550643 and backward error 1.0163315496105625\n",
      "At iteration 4, x = 2.003137499141287 with estimated error 0.07820374853029163 and backward error 0.03770908398584538\n",
      "At iteration 5, x = 2.000004911675504 with estimated error 0.003132587465783101 and backward error 5.894025079733467e-5\n",
      "At iteration 6, x = 2.0000000000120624 with estimated error 4.911663441917921e-6 and backward error 1.447482134153688e-10\n",
      "At iteration 7, x = 2.0 with estimated error 1.2062351117801901e-11 and backward error 0.0\n",
      "Done!\n",
      "\n",
      "The first root is approximately 2.0\n",
      "The estimated absolute error is 1.2062351117801901e-11\n",
      "The backward error is 0.0\n",
      "This required 7 iterations\n"
     ]
    }
   ],
   "source": [
    "x0 = 1.0;\n",
    "error_tolerance = 1e-8;\n",
    "rei1 = newton_method(f2, Df2, x0, error_tolerance; demo_mode=true)\n",
    "root1 = rei1[1]\n",
    "error_estimate1 = rei1[2]\n",
    "iterations1 = rei1[3]\n",
    "println()\n",
    "println(\"The first root is approximately $root1\")\n",
    "println(\"The estimated absolute error is $error_estimate1\")\n",
    "println(\"The backward error is $(abs(f2(root1)))\")\n",
    "println(\"This required $iterations1 iterations\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Next, start at $x_0 = i$ (a.k.a. $x_0 = im$):**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solving by Newton's Method.\n",
      "max_iterations = 20\n",
      "error_tolerance = 1.0e-8\n",
      "At iteration 1, x = -2.6666666666666665 + 0.6666666666666667im with estimated error 2.6874192494328497 and backward error 27.23670564570405\n",
      "At iteration 2, x = -1.4663590926566703 + 0.6105344098423685im with estimated error 1.2016193667222377 and backward error 10.211311837398133\n",
      "At iteration 3, x = -0.23293230984230884 + 1.1571382823138845im with estimated error 1.3491172750968106 and backward error 7.206656519642179\n",
      "At iteration 4, x = -1.9202321953438537 + 1.5120026439880303im with estimated error 1.7242127533456901 and backward error 13.405769067901167\n",
      "At iteration 5, x = -1.1754417924325344 + 1.4419675366055338im with estimated error 0.7480759724352086 and backward error 3.7583743808280228\n",
      "At iteration 6, x = -0.9389355523964149 + 1.716001974171807im with estimated error 0.36198076543966584 and backward error 0.7410133693135651\n",
      "At iteration 7, x = -1.0017352527552088 + 1.7309534907089796im with estimated error 0.06455501693838851 and backward error 0.02463614729973853\n",
      "At iteration 8, x = -0.9999988050398477 + 1.7320490713246675im with estimated error 0.0020531798639315357 and backward error 2.529258531285453e-5\n",
      "At iteration 9, x = -1.0000000000014002 + 1.7320508075706016im with estimated error 2.107719871290353e-6 and backward error 2.6654146785452274e-11\n",
      "At iteration 10, x = -1.0 + 1.7320508075688774im with estimated error 2.2211788987828177e-12 and backward error 1.9860273225978185e-15\n",
      "Done!\n",
      "\n",
      "The second root is approximately -1.0 + 1.7320508075688774im\n",
      "The estimated absolute error is 2.2211788987828177e-12\n",
      "The backward error is 1.9860273225978185e-15\n",
      "This required 10 iterations\n"
     ]
    }
   ],
   "source": [
    "x0 = im;\n",
    "rei2 = newton_method(f2, Df2, x0, error_tolerance; demo_mode=true)\n",
    "root2 = rei2[1]\n",
    "error_estimate2 = rei2[2]\n",
    "iterations2 = rei2[3]\n",
    "println()\n",
    "println(\"The second root is approximately $root2\")\n",
    "println(\"The estimated absolute error is $error_estimate2\")\n",
    "println(\"The backward error is $(abs(f2(root2)))\")\n",
    "println(\"This required $iterations2 iterations\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This root is in fact $-1 + i \\sqrt{3}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Finally, $x_0 = 1 - i$**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "The third root is approximately -1.0 - 1.7320508075688772im\n",
      "The estimated absolute error is 3.62974830495685e-15\n",
      "The backward error is 1.9860273225978185e-15\n",
      "This required 10 iterations\n"
     ]
    }
   ],
   "source": [
    "x0 = 1-im\n",
    "rei3 = newton_method(f2, Df2, x0, error_tolerance; demo_mode=false)\n",
    "root3 = rei3[1]\n",
    "error_estimate3 = rei3[2]\n",
    "iterations3 = rei3[3]\n",
    "println()\n",
    "println(\"The third root is approximately $root3\")\n",
    "println(\"The estimated absolute error is $error_estimate3\")\n",
    "println(\"The backward error is $(abs(f2(root3)))\")\n",
    "println(\"This required $iterations3 iterations\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This root is in fact $-1 - i \\sqrt{3}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Newton's method derived via tangent line approximations: linearization\n",
    "\n",
    "The more traditional derivation of Newton\"s method is based on the very widely useful idea of *linearization*;\n",
    "using the fact that a differentiable function can be approximated over a small part of its domain by a straight line — its tangent line — and it is easy to compute the root of this linear function.\n",
    "\n",
    "So start with a first approximation $x_0$ to a solution $r$ of $f(x) = 0$.\n",
    "\n",
    "### Step 1: Linearize at $x_0$.\n",
    "\n",
    "The tangent line to the graph of this function wih center $x_0$,\n",
    "also know as the *linearization of $f$ at $x_0$*, is\n",
    "\n",
    "$$L_0(x) = f(x_0) + f'(x_0) (x - x_0).$$\n",
    "\n",
    "(Note that $L_0(x_0) = f(x_0)$ and $L_0'(x_0) = f'(x_0)$.)\n",
    "\n",
    "### Step 2: Find the zero of this linearization\n",
    "\n",
    "Hopefully, the two functions $f$ and $L_0$ are close, so that the root of $L_0$ is close to a root of $f$;\n",
    "close enough to be a better approximation of the root $r$ than $x_0$ is.\n",
    "\n",
    "Give the name $x_1$ to this root of $L_0$:\n",
    "it solves $L_0(x_1) = f(x_0) + f'(x_0) (x_1 - x_0) = 0$, so\n",
    "\n",
    "$$x_1 = x_0 - {f(x_0)}/{f'(x_0)}$$\n",
    "\n",
    "### Step 3: Iterate\n",
    "\n",
    "We can then use this new value $x_1$ as the center for a new linearization\n",
    "$L_1(x) = f(x_1) + f'(x_1)(x - x_1)$,\n",
    "and repeat to get a hopefully even better approximate root,\n",
    "\n",
    "$$x_2 = x_1 - f(x_1)/f'(x_1)$$\n",
    "\n",
    "And so on: at each step, we get from approximation $x_k$ to a new one $x_{k+1}$ with\n",
    "\n",
    "$$x_{k+1} = x_k - {f(x_k)}/{f'(x_k)}$$\n",
    "\n",
    "And indeed this is the same formula seen above for Newton's method."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Illustration: a few steps of Newton's method for $x - \\cos(x) = 0$.**\n",
    "\n",
    "This approach to Newton's method via linearization and tangent lines suggests another graphical presentation;\n",
    "again we use the example of $f(x) = x - \\cos (x)$.\n",
    "This has $Df(x) = 1 + \\sin(x)$, so the linearization at center $a$ is\n",
    "\n",
    "$$L(x) = (a - \\cos(a)) + (1 + \\sin(a))(x-a)$$\n",
    "\n",
    "For Newton's method starting at $x_0 = 0$, this gives\n",
    "\n",
    "$$L_0(x) = -1 + x$$\n",
    "\n",
    "and its root — the next iterate in Newton\"s method — is $x_1 = 1$\n",
    "\n",
    "Then the linearization at center $x_1$ is\n",
    "\n",
    "$$\n",
    "L_1(x) = (1 - \\cos(1) + (1 + \\sin(1))(x-1),\n",
    "\\approx 0.4596 + 1.8415(x-1)\n",
    "$$\n",
    "giving $x_2 \\approx 1 - 0.4596/1.8415 \\approx 0.7504$.\n",
    "\n",
    "Let's graph a few steps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "L_0(x) = -1.0 + x;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_1 = 1.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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pUEpKSnj11VeZNGlSrfbr0aMHrVu35u23366nykRERESkqVN4qgHDMCgur/DIh2EYtap1wYIF+Pv7k5yc7G6bNGkSPXr0IC8vr07eD5fLxb/+9S/atWuHn58fLVu25PHHH3e/XlZWxm233UZ0dDT+/v6cddZZ/Prrr+7XP/jgA7p3705AQAARERFccMEFFBUVAfDll1/i4+PDgAEDan1do0ePZsGCBXVyjSIiIiIif+Xj6QIagxKHky4PL/HIubc+NpxA35p305VXXsmTTz7JzJkzef7555kxYwZLlizh559/JiwsrE5qmj59OnPnzuW///0vZ511FikpKWzfvt39+j333MOHH37IG2+8QatWrXjqqacYPnw4O3fuJDMzk2uuuYannnqKMWPGUFBQwIoVK9wh8YcffqBPnz4ndF19+/Zl5syZlJWV4efnVyfXKiIiIiL1o9ThxN9q8XQZtaLw5GVMJhOPP/4448aNw2azMXv2bFasWEF8fHydHL+goIDZs2fz/PPPc/311wNw2mmncdZZZwFQVFREUlIS8+bNY8SIEQDMnTuXZcuW8dprr9GvXz8qKioYO3YsrVq1AqB79+7u4+/fvx+bzXZC1xUfH09ZWRmpqanuY4uIiIhIw1Je4WLml9v4dX82H0wd2KgClMJTDQRYLWx9bLjHzl1bo0aNokuXLsyYMYOlS5fStWvXard79NFHmTFjxjGP9euvv1a5E7Rt2zbKyso4//zzq91+z549OBwOBg0a5G6zWq307duXbdu2MXHiRM4//3y6d+/O8OHDGTZsGOPGjaN58+ZA5TNP/v7+J3RdAQEBABQXFx/zmkRERETEM1LzSrnlnbWs+T0HgOU7MriwW6yHq6o5hacaMJlMtRo652lLlixh+/btOJ1OYmJijrrdrbfeypVXXnnMY/11xrs/AsrR/DH8zmQyHdFuMpmwWCzu4XZLly7lueee44EHHmD16tW0adOGyMhIcnJyTui6srOzAYiKijpmjSIiIiJy6q3cncn/LVhHVlE5If4+PHNFT4Z2Ofrvqg2RJozwMmvXruXyyy/npZdeYvjw4Tz00ENH3TYyMpJOnTod8+Ovd4Hat29PQEAA33zzTbXHbNeuHb6+vvz444/uNofDwW+//Ubnzp2BymA1aNAgZsyYwbp16/D19eXjjz8G4IwzzmDr1q0ndF2bN2+mRYsWREZGHv+NEhEREZFTwuUyeHH5bq59dTVZReV0jgvl8/87q9EFJ9CdJ6+yf/9+LrroIu677z4mTJhAly5dOPPMM1mzZg29e/euk3P4+/tz7733cs899+Dr68ugQYPIyMhgy5YtTJw4kaCgIBITE/n73/9OeHg4LVu25KmnnqK4uJgbb7yR3377jdWrVzN8+HCio6NZvXo1GRkZ7mA1fPhwpk+fTk5OjnsoX02va8WKFQwbNqxOrlNERERETl5eiYO73tvA19vSABjXuwX/vLRbo3rO6c8UnrxEdnY2I0aMYPTo0dx///0A9O7dm4svvpgHHniAr776qs7O9dBDD+Hj48PDDz+M3W4nLi6OqVOnul9/8skncblcTJgwgYKCAvr06cOSJUto3rw5ISEh/PDDD8yePZv8/HxatWrF008/7Z5conv37vTp04f33nuPm266qcbXVVpayscff8ySJZ6ZFVFEREREqtpizyNx/loOZBfj62PmsdFdGX9mwhGPdzQmCk9eIjw8nG3bth3RvmjRojo/l9ls5oEHHuCBBx6o9nV/f3+effZZnn322SrtLpeLjh078uWXX2I2H33E6EMPPcTdd9/N5MmTa3xdr776Kv369aN///4ncEUiIiIiUpfe++0gD32ymbIKFy2aB5B0TW+6t6ibZXM8SeFJGpyRI0eya9cukpOTSUhIqNE+VquV5557rp4rExEREZFjKXU4eWTRFhb+dhCAIR2j+O/4njQL9PVwZXVD4UkapNtvv71W20+ZMqWeKhERERGRmjiQVUzi22vYYs/HZIJpF3TgliHtMJsb7zC9v1J4EhERERGRk/L11jSmvbee/NIKwoN8mX1lTwa3977lYxSeRERERETkhFQ4XTyzbCcvLt8DwBktm/HC1b2wNTv22qCNlcKTiIiIiIjUWmZhGbctWMfKPVkA3DCwNfeP7Iyvj/cuJavwJCIiIiIitfLr/mxufWctafllBPpaePKyHow+3ebpsuqdwpOIiIiIiNSIYRi8+uM+Zn65HafLoF10MEnX9KJ9TIinSzslFJ5EREREROS4Ckod3PPBRr7cnArAxafbeHJsd4L8mk6kaDpXKiIiIiIiJ2R7aj6J89eyL7MIq8XEgxd14boBrTCZvGca8ppQeBIRERERkaP6cM0hHvhkE6UOF7Ywf164phdntGzu6bI8wnunwpCT9uKLL9KmTRv8/f3p3bs3K1as8HRJIiIiInKKlDqcTP9oE3e9v4FSh4uzO0Tx+W2Dm2xwAoUnOYqFCxdyxx138MADD7Bu3ToGDx7MiBEjOHDggKdLExEREZF6diCrmMuSVrLglwOYTHD7+e15/YYzCQ/y9XRpHqXw5CUyMjKIjY3liSeecLetXr0aX19fli5dWuvjPfPMM0ycOJFJkybRuXNnZs2aRUJCAklJSXVZtoiIiIg0MMu2pjHquRVssefTPNDKG3/ry51DO2AxN63nm6qjZ55qwDAMiouLPXLuwMDAGj2IFxUVxWuvvcall17KsGHD6NSpE9deey0333wzw4YNY8WKFYwYMeKYx7j//vu5//77KS8vZ82aNdx3331VXh82bBgrV648qesRERERkYapwuniP0t3Muf7PQD0atmM56/uha1ZgIcrazgUnmqguLiY4OBgj5y7sLCQoKCgGm07cuRIJk+ezDXXXMOZZ56Jv78/Tz75JAB9+vRh/fr1x9w/PDwcgMzMTJxOJzExMVVej4mJITU1tfYXISIiIiINWnp+KbcuWMcv+7IBuHFQG+4b0QlfHw1U+zOFJy/zn//8h27duvHee+/x22+/4e/vD0BAQADt2rWr1bH+esfLMIwmNx2liIiIiLdbtSeL/1uwjszCMoL9fHhqXA9Gdo/zdFkNksJTDQQGBlJYWOixc9fG3r17sdvtuFwufv/9d3r06AFQq2F7kZGRWCyWI+4ypaenH3E3SkREREQaJ5fLIOn7PTy9dAcuAzrFhvDiNb1oG+WZEVeNgcJTDZhMphoPnfOk8vJyrrnmGsaPH0+nTp2YOHEimzZtIiYmplbD9nx9fenduzfLli1jzJgx7teXLVvGJZdcUp+XICIiIiKnQG5xOdPe28C329MBuKxXC/55aTcCfC0erqxhU3jyIg888AB5eXk8++yzBAcH8+WXXzJx4kQ+//zzWg/bmzZtGhMmTKBPnz4MGDCAl19+mQMHDjB16tR6vAIRERERqW8bDuZy89trSc4twdfHzD8u6coVfRL0eEYNKDx5ieXLlzNr1iy+++47QkNDAXjrrbfo0aMHSUlJJCYm1up448ePJysri8cee4yUlBS6devG4sWLadWqVX2ULyIiIiL1zDAM3vr5d/7x+VYcToNWEYG8eE0vutrCPF1ao6Hw5CXOPfdcHA5HlbaWLVuSm5t7wse8+eabufnmm0+yMhERERHxtMKyCqZ/tInPNtgBGN41hn9ffjqh/lYPV9a4KDyJiIiIiHixHakFJL69hr0ZRfiYTdw3ohMTz2qjYXonQOFJRERERMRLfbjmEA98solSh4vYUH+ev/oM+rQO93RZjZbCk4iIiIiIlyl1OHlk0RYW/nYQgMHtI5k1vicRwX4erqxxU3gSEREREfEi+zKLuPnttWxLycdkgjvO78Ct57XDYtYwvZNlru8TvPjii7Rp0wZ/f3969+7NihUrjrrt8uXLMZlMR3xs3769ynYffvghXbp0wc/Pjy5duvDxxx/X92WIiIiIiDR4X25K4eLnfmRbSj4RQb68eWNfbr+gvYJTHanX8LRw4ULuuOMOHnjgAdatW8fgwYMZMWIEBw4cOOZ+O3bsICUlxf3Rvn1792urVq1i/PjxTJgwgQ0bNjBhwgSuuOIKVq9eXZ+XIiIiIiLSYJVXuJjx2RYS315LYVkFZ7Zuzhe3DWZw+yhPl+ZV6jU8PfPMM0ycOJFJkybRuXNnZs2aRUJCAklJScfcLzo6mtjYWPeHxfK/lY5nzZrF0KFDmT59Op06dWL69Omcf/75zJo1qz4vRURERESkQUrOLeGKl1bx+k/7Abjp7La8M7k/sWH+ni3MC9XbM0/l5eWsWbOG++67r0r7sGHDWLly5TH3PeOMMygtLaVLly48+OCDDBkyxP3aqlWruPPOO6tsP3z48GOGp7KyMsrKytyf5+fnA+BwOI5YG8nhcGAYBi6XC5fLdcw6pXYMw3D/1xPvrcvlwjAMHA5HlUAuJ+eP76G/fi9J46U+9U7qV++jPvU+J9Kn3+3I4J4PN5Nb4iDU34enxnbj/M7R4HLicDnrq1SvUpv3u97CU2ZmJk6nk5iYmCrtMTExpKamVrtPXFwcL7/8Mr1796asrIy33nqL888/n+XLl3P22WcDkJqaWqtjAsycOZMZM2Yc0b506VICAwOrtPn4+BAbG0thYSHl5eU1ulapnYKCAo+ct7y8nJKSEn744QcqKio8UoM3W7ZsmadLkDqmPvVO6lfvoz71PjXpU6cBiw+a+Tq5ciBZQpDB3zqUUrbvNxbvq+8KvUtxcXGNt6332fb+uviWYRhHXZCrY8eOdOzY0f35gAEDOHjwIP/5z3/c4am2xwSYPn0606ZNc3+en59PQkICw4YNIzQ0tMq2paWlHDx4kODgYPz9dauzLhmGQUFBASEhIR5ZlK20tJSAgADOPvts9W0dcjgcLFu2jKFDh2K1apVyb6A+9U7qV++jPvU+Ne3T9IIy7nxvI78k5wAwoV8C917YET+fep8Lziv9MSqtJuotPEVGRmKxWI64I5Senn7EnaNj6d+/P/Pnz3d/HhsbW+tj+vn54ed35Jz2Vqv1iC9Mp9OJyWTCbDZjNjetL8CsrCw6d+7ML7/8QuvWrY+7/bhx4xg4cGCVYHosfwzV++P9PdXMZjMmk6nafpeTp/fV+6hPvZP61fuoT73Psfp05e5Mbnt3HZmF5QT5Wnjysh5cfLrtFFfoXWrz/VNvv8H6+vrSu3fvI247Llu2jIEDB9b4OOvWrSMuLs79+YABA4445tKlS2t1TG83cOBApkyZUuv9Zs6cycUXX1yj4ATw8MMP8/jjj9cqrYuIiIhI7TldBrO/3sU1r64ms7CcTrEhfPZ/Zyk4nWL1Omxv2rRpTJgwgT59+jBgwABefvllDhw4wNSpU4HK4XTJycm8+eabQOVMeq1bt6Zr166Ul5czf/58PvzwQz788EP3MW+//XbOPvts/vWvf3HJJZewaNEivv76a3788cf6vJRGw+VysXHjRq677rpa7VdSUsKrr77K4sWLa7xPjx49aN26NW+//TaJiYm1LVVEREREaiCzsIw7F65nxa5MAK7o04IZo7sR4KsJsE61eh07NX78eGbNmsVjjz1Gz549+eGHH1i8eDGtWrUCICUlpcqaT+Xl5dx999306NGDwYMH8+OPP/LFF18wduxY9zYDBw7k3Xff5fXXX6dHjx7MmzePhQsX0q9fv/q8lEZj+/btFBUV0atXr1rt9+WXX+Lj48OAAQPcbQsWLMDf35/k5GR326RJk+jRowd5eXkAjB49mgULFtRN8SIiIiJSxeq9WVz07ApW7MrE32rmP5efzlPjTldw8pB6nzDi5ptv5uabb672tXnz5lX5/J577uGee+457jHHjRvHuHHj6qI8r7N27Vp8fHzo0aNHrfb74Ycf6NOnT5W2K6+8kieffJKZM2fy/PPPM2PGDJYsWcLPP/9MWFgYAH379mXmzJmUlZVV+1yZiIiIiNSey2Xw0g97+c/SHThdBu2ig3nxml50iAnxdGlNWr2HJ29QuS5RzacwrEtmc2CtZqZbu3YtXbp0qXY2uc8//5y77roLl8vFvffey6RJk9yv7d+/H5ut6phZk8nE448/zrhx47DZbMyePZsVK1YQHx/v3iY+Pp6ysjJSU1PddxRFRERE5MTlFJdz70fr+G5HBgBjzojnn5d2I8hPv7p7mnqgBlyuYlasCPbIuQcPLsRiCarx9mvXrq12yF5FRQXTpk3ju+++IzQ0lF69ejF27FjCw8OBymeeqgtco0aNokuXLsyYMYOlS5fStWvXKq8HBAQAtZsfX0RERESqt68AnnzxZ1LySvH1MfPY6K6MPzPBI8u8yJGa1lzcXs4wDNavX0/v3r2PeO2XX36ha9euxMfHExISwsiRI1myZIn79cjISHJyco7Yb8mSJWzfvr3aBY8BsrOzAYiKiqrDKxERERFpWgzD4NWf9vPsFgspeaW0jgjk45sHcmXflgpODYjuPNWA2RzI4MGFHjt3Te3Zs4e8vLxq7zzZ7fYqw+1atGhRZSKIM844o8p6WlB5F+vyyy/npZde4t133+Whhx7i/fffr7LN5s2badGiBZGRkTWuU0RERET+J6/YwV3vb+DrbWmAiZHdYvjXuNMJ8df6XQ2NwlMNmEymWg2d85S1a9cCYLFY2Lx5s7vdarViGMYR2//5rxjDhw9n+vTp5OTk0Lx5c/bv389FF13Efffdx4QJE+jSpQtnnnkma9asqXJna8WKFQwbNqwer0pERETEe60/mMstb68lObcEq8XEpS0rePyKHvj6Kjg1RBq250XWrVsHQP/+/enevbv744YbbiA+Pr7KnaZDhw5VWXy4e/fu9OnTh/fee4/s7GxGjBjB6NGjuf/++wHo3bs3F198MQ888IB7n9LSUj7++GMmT558iq5QRERExDsYhsFrP+7j8jkrSc4toWV4IO9P6cdZsYaG6TVguvPkRWbOnMnMmTOrfa2iooLNmzeTnJxMaGgoixcv5uGHH66yzUMPPcTdd9/N5MmT2bZt2xHHWLRoUZXPX331Vfr160f//v3r7iJEREREvFxeiYN7P9jIV1tSARjRLZZ/jetBgAV+X+/Z2uTYFJ6aCB8fH55++mmGDBmCy+XinnvuISIioso2I0eOZNeuXSQnJ5OQkHDcY1qtVp577rn6KllERETE62w8lMst76zlYHblML0HL+rCdQNaYTKZcDgcni5PjkPhqQkZPXo0o0ePPuY2t99+e42PN2XKlJMtSURERKRJMAyDN1bu5/HF23A4DRLCA3jh6l70aNHM06VJLSg8iYiIiIjUo/zSymF6X26uHKY3vGsMT407nbAATQrR2Cg8iYiIiIjUk02H8rjlnbUcyC7GajFx/8jO3DCwtSaFaKQUnkRERERE6phhGLy56nce/2Ib5U4XLZpXDtM7PaGZp0uTk6DwJCIiIiJSh/46TG9Ylxj+Pe50wgI1TK+xU3gSEREREakjGw/lcus769zD9O4b0ZkbB2mYnrdQeDoKwzA8XYLUMfWpiIiI1Je/zqanYXreSeHpL6zWytupxcXFBAQEeLgaqUvFxcXA//pYREREpC78ddFbzabnvRSe/sJisdCsWTPS09MBCAwM1G3WOuJyuSgvL6e0tBSz2XzKzmsYBsXFxaSnp9OsWTMsFsspO7eIiIh4tw0Hc7l1wf8WvdVset5N4akasbGxAO4AJXXDMAxKSkoICAjwyA+UZs2auftWRERE5GQYhsFrP+3nyS+16G1TovBUDZPJRFxcHNHR0TgcDk+X4zUcDgc//PADZ5999ikfOme1WnXHSUREROpEbnE5d7+/ka+3pQEwolssT17WQ8P0mgCFp2OwWCz6hbsOWSwWKioq8Pf313NHIiIi0iit+T2H2xasIzm3BF+LmQdHdWZC/1YaptdEKDyJiIiIiByHy2Uwd8Ve/r1kBxUug1YRgbxwdS+6xYd5ujQ5hRSeRERERESOIbuonLveW893OzIAGNUjjpljuxPir5E0TY3Ck4iIiIjIUfyyL5vbFqwjNb8UXx8zj17clav6JmiYXhOl8CQiIiIi8hdOl0HS8t08s2wnLgPaRgXxwtW96BwX6unSxIMUnkRERERE/iS9oJRpCzfw4+5MAMaeEc8/Lu1GkJ9+dW7q9BUgIiIiInLYj7syuWPhejILywiwWvjHpd0Y17uFp8uSBkLhSURERESavAqni9nf7OL573ZjGNAxJoQXrjmDdtEhni5NGhCFJxERERFp0lLySrh9wXp+2Z8NwFV9W/LIxV3wt2q9T6lK4UlEREREmqxvt6dx13sbyCl2EORrYeZlPRh9us3TZUkDpfAkIiIiIk1OeYWLp77azis/7gOgW3woz13VizaRQR6uTBoyhScRERERaVIOZBXzfwvWsuFQHgA3DGzN9JGd8PPRMD05NoUnEREREWkyPt9oZ/qHmygoqyAswMpT43owvGusp8uSRkLhSURERES8XqnDyWOfb+Wd1QcA6N2qOc9edQbxzQI8XJk0JgpPIiIiIuLVdqcXcOs769ieWgDAzeeexp1DO2C1mD1cmTQ2Ck8iIiIi4pUMw+D93w7xyKdbKHE4iQz25ZkrenJ2hyhPlyaNlMKTiIiIiHidwrIKHvh4E4vW2wEY1C6C/47vSXSIv4crk8ZM4UlEREREvMqmQ3n834K17M8qxmI2MW1oB6aecxoWs8nTpUkjp/AkIiIiIl7BMAxe/2k/M7/chsNpYAvz59mrzqBP63BPlyZeQuFJRERERBq9nKJy/v7BRr7elgbAsC4xPDWuB80CfT1cmXgThScRERERadRW783i9nfXk5pfiq/FzAMXdea6Aa0wmTRMT+qWwpOIiIiINEpOl8Fz3+7i2W924TKgbWQQz119Bl1tYZ4uTbyUwpOIiIiINDopeSXc8e56Vu/LBuCyXi147JKuBPnp11upP/rqEhEREZFG5Zttadz9/gZyih0E+Vr455hujDmjhafLkiZA4UlEREREGoWyCidPfrmd13/aD0C3+FCeu6oXbSKDPFuYNBkKTyIiIiLS4O3NKOT/Fqxjiz0fgBsHteHeER3x87F4uDJpShSeRERERKTBMgyDD9cm8/CizRSXO2keaOU/l5/O+Z1jPF2aNEEKTyIiIiLSIBWWVfDgx5v4ZL0dgP5tw5k1/gxiw/w9XJk0VQpPIiIiItLgbDyUy/8tWMfvWcVYzCbuvKA9iee2w2LW2k3iOQpPIiIiItJguFwGr/64j6eWbMfhNIhvFsDsK3vSp3W4p0sTwVzfJ3jxxRdp06YN/v7+9O7dmxUrVhx1248++oihQ4cSFRVFaGgoAwYMYMmSJVW2mTdvHiaT6YiP0tLS+r4UEREREalHGQVl/G3erzy+eBsOp8GIbrEsvm2wgpM0GPUanhYuXMgdd9zBAw88wLp16xg8eDAjRozgwIED1W7/ww8/MHToUBYvXsyaNWsYMmQIF198MevWrauyXWhoKCkpKVU+/P019lVERESksfphZwYjZq/g+50Z+PmY+eel3Xjxml6EBVo9XZqIW70O23vmmWeYOHEikyZNAmDWrFksWbKEpKQkZs6cecT2s2bNqvL5E088waJFi/jss88444wz3O0mk4nY2Nj6LF1EREREToHyChdPL93BSz/sBaBjTAjPXX0GHWJCPFyZyJHq7c5TeXk5a9asYdiwYVXahw0bxsqVK2t0DJfLRUFBAeHhVW/VFhYW0qpVK1q0aMGoUaOOuDMlIiIiIg3f/swixs1Z6Q5OE/q3YtGtgxScpMGqtztPmZmZOJ1OYmKqzsEfExNDampqjY7x9NNPU1RUxBVXXOFu69SpE/PmzaN79+7k5+cze/ZsBg0axIYNG2jfvn21xykrK6OsrMz9eX5+5eJqDocDh8NR20uTE/THe6333LuoX72P+tQ7qV+9T2Pv00UbUnjk060UlTsJC/DhiUu7MqxLDODC4XB5ujyPaOx92ljV5v02GYZh1EcRdrud+Ph4Vq5cyYABA9ztjz/+OG+99Rbbt28/5v4LFixg0qRJLFq0iAsuuOCo27lcLnr16sXZZ5/Ns88+W+02jz76KDNmzDii/Z133iEwMLCGVyQiIiIiJ6vUCR/sNfNrZuUAqNNCDCa0d9Lcz8OFSZNVXFzM1VdfTV5eHqGhocfctt7uPEVGRmKxWI64y5Senn7E3ai/WrhwIRMnTuT9998/ZnACMJvNnHnmmezateuo20yfPp1p06a5P8/PzychIYFhw4Yd9w2SuuNwOFi2bBlDhw7FatXDn95C/ep91KfeSf3qfRpjn248lMed72/kQHYJZhPceu5p3HxuW63ddFhj7FNv8MeotJqot/Dk6+tL7969WbZsGWPGjHG3L1u2jEsuueSo+y1YsIAbb7yRBQsWcNFFFx33PIZhsH79erp3737Ubfz8/PDzO/LPGVarVV+YHqD33TupX72P+tQ7qV+9T2PoU5fL4OUVe/nPkh1UuCrXbpp1ZU/O1BTk1WoMfepNavNe1+tse9OmTWPChAn06dOHAQMG8PLLL3PgwAGmTp0KVN4RSk5O5s033wQqg9N1113H7Nmz6d+/v/uuVUBAAGFhYQDMmDGD/v370759e/Lz83n22WdZv349L7zwQn1eioiIiIicgPT8Uqa9t4Efd2cCMLJ7LDPH9NAU5NIo1Wt4Gj9+PFlZWTz22GOkpKTQrVs3Fi9eTKtWrQBISUmpsubTSy+9REVFBbfccgu33HKLu/36669n3rx5AOTm5jJlyhRSU1MJCwvjjDPO4IcffqBv3771eSkiIiIiUkvfbU/nrvc3kF1Ujr/VzKMXd2X8mQmYTBqmJ41TvYYngJtvvpmbb7652tf+CER/WL58+XGP99///pf//ve/dVCZiIiIiNSHUoeTJ7/czryV+wHoHBfKc1f1pF20piCXxq3ew5OIiIiINB270gr4vwXr2J5aAMANA1tz34hO+FstHq5M5OQpPImIiIjISTMMg3d+OcA/Pt9KqcNFRJAv/7n8dIZ0ivZ0aSJ1RuFJRERERE5KTlE59320kSVb0gAY3D6Sp684negQfw9XJlK3FJ5ERERE5ISt2pPFnQvXk5pfitVi4t4LO3HjoDaYtXaTeCGFJxERERGpNYfTxayvd/Li8j0YBrSNDOLZq86gW3yYp0sTqTcKTyIiIiJSK/szi7h94Xo2HMwF4Io+LXjk4q4E+elXS/Fu+goXERERkRoxDIMP1ybzyKLNFJU7CfX34cnLejCye5ynSxM5JRSeREREROS48kocPPjJZj7bYAegb5twZo3via1ZgIcrEzl1FJ5ERERE5Jh+25/N7e+uJzm3BIvZxJ0XtCfx3HZYNCmENDEKTyIiIiJSrQqni+e+3c1z3+7CZUBCeACzrzyDXi2be7o0EY9QeBIRERGRIxzMLub2d9ex9kAuAGPOiOexS7oS4m/1bGEiHqTwJCIiIiJVfLzuEA99soXCsgpC/Hz455huXNIz3tNliXicwpOIiIiIAJBf6uChTzazaH3lpBB9WjXnv+N7khAe6OHKRBoGhScRERER4bf92dyxcD2Hckowm+C289tz65B2+FjMni5NpMFQeBIRERFpwv46KUSL5gHMvrInvVuFe7o0kQZH4UlERESkiTqQVcwdC/83KcSlPW08dmk3QjUphEi1FJ5EREREmhjDMPhobTKPfKpJIURqQ+FJREREpAnJK3HwwMeb+HxjCgBntm7OM1doUgiRmlB4EhEREWkiVu/NYtp7G0jOLcFiNnHnBe1JPLcdFrPJ06WJNAoKTyIiIiJezuF0Mevrnby4fA+GAa0iApk1vidntGzu6dJEGhWFJxEREREvtjejkDsWrmfjoTwALu/dgkdGdyXYT78GitSWvmtEREREvJBhGCz45SD/+HwrJQ4nYQFWZo7tzsjucZ4uTaTRUngSERER8TJZhWXc99Emlm1NA2BQuwj+c/npxIUFeLgykcZN4UlERETEiyzfkc7fP9hIRkEZvhYzfx/ekYlntcGsSSFETprCk4iIiIgXKHU4efLL7cxbuR+A9tHBzL7yDLrYQj1bmIgXUXgSERERaeS22PO449317EovBOCGga25b0Qn/K0WD1cm4l0UnkREREQaKZcBr/y4n2e+3oXDaRAV4se/x/Xg3I7Rni5NxCspPImIiIg0Qil5pby41cyu/J0ADO0Sw5NjuxMR7OfhykS8l8KTiIiISCPz6QY7D368ifxSMwFWM49c3JXxZyZgMmlSCGkcCgrWkpOzjJYt7/V0KbWi8CQiIiLSSOSXOnhk0RY+XpcMQKtgg1cmDaB9bDPPFiZSA05nCenpC7Hbkygo+AWA8PCRBAd393BlNafwJCIiItII/Lw3i7ve20BybglmE9x8TlvaluykdUSQp0sTOabi4p3Y7XNITZ1HRUUOACaTlcjIsZhMVg9XVzsKTyIiIiINWFmFk2eW7eTlH/ZiGNAyPJD/ju9JD1swixfv9HR5ItVyuRxkZX1KcnISubnfuNv9/Fphs91EXNyN+PrGeLDCE6PwJCIiItJA7Uwr4PZ317MtJR+A8X0SeOjiLgT7+eBwODxcnciRSksPkZLyMikpr1BennK41UR4+Eji4xMJD78Qk6nxTqGv8CQiIiLSwLhcBvNW7ufJr7ZTXuEiPMiXmWO7M7xrrKdLEzmCYbjIyVlGcnISWVmfAS4ArNZo4uImEhc3hYCA1h6tsa4oPImIiIg0IKl5pfz9gw2s2JUJwLkdo3hqXA+iQ/w9XJlIVeXlmaSmvo7d/hKlpXvc7WFh5xAfn0hk5BjMZl8PVlj3FJ5EREREGojPNth58JPN5JU48LeaeeCiLlzbr6WmIJcGwzAM8vNXYbcnkZ7+PoZRBoDFEkps7PXYbFMJCuri4Srrj8KTiIiIiIfllTh4ZNFmPllvB6BHizD+O74np0UFe7gykUoVFQWkpc3Hbp9DUdFGd3twcC9stkRiYq7CYvH+mR8VnkREREQ8aOWeTO5+bwP2vFLMJrh1SDv+7/z2WC1mT5cmQmHhRuz2JNLS5uN0FgJgNvsTHX0VNttUQkLObFJ3RhWeRERERDyg1OHkP0t28MqP+wBoFVE5BXmvls09XJk0dU5nKRkZH2C3J5Gfv9LdHhDQEZttKrGx12O1Ns2vU4UnERERkVNsqz2fOxeuZ0daAQBX9W3Jgxd1JshPv5qJ55SU7MFun0NKyutUVGQBYDL5EBk5BpttKs2aDWlSd5mqo+9QERERkVPE6TJ4+Ye9PLNsBw6nQWSwL0+O7cEFXRrfYqHiHVyuCrKyPsduTyInZ6m73c8vgbi4KcTFTcTPL86DFTYsCk8iIiIip8DB7GKmvbeeX/fnADC0Swwzx3YnMtjPw5VJU1RWZicl5RVSUuZSVnbocKuJ8PDh2GyJhIePxGxWVPgrvSMiIiIi9cgwDN7/7RAzPttCUbmTIF8Lj1zclcv7tGjyQ6Dk1KpczPZb7PYkMjMXAU4ArNZIYmMnYrNNISCgrWeLbOAUnkRERETqSWZhGdM/2sSyrWkAnNm6Oc9c0ZOE8EAPVyZNicORRWrqG9jtcygp2eVuDws7C5stkaioyzCbdQe0JhSeREREROrBsq1pTP9oI5mF5VgtJu4a1pHJg9tiMetuk9S/ysVsVx9ezHbhnxazDSEmZgI221SCg7t7uMrGR+FJREREpA4VlDr4x+dbee+3yudIOsaE8N/xPeliC/VwZdIUVFQUkp7+DnZ7EoWF693twcE9sdmmEh19DT4+Wnz5RCk8iYiIiNSR1XuzuOv9DRzKKcFkgimD2zJtWAf8fCyeLk28XGHhZuz2OaSlvYnTWTkFvsnkR3T0eGy2REJD++kZuzqg8CQiIiJykkodTp5ZtpO5K/ZiGNCieQBPX346/dpGeLo08WIuVxkZGR9ityeRl/ejuz0goN3hxWxvwGrV12BdUngSEREROQlb7HlMW7jBveDt+D4JPDiqMyH+Vg9XJt6qpGQfdvtLpKa+hsORcbjVQmTkJdhsiTRvfh4mk9mjNXqren9XX3zxRdq0aYO/vz+9e/dmxYoVx9z++++/p3fv3vj7+9O2bVvmzJlzxDYffvghXbp0wc/Pjy5duvDxxx/XV/kiIiIi1apwunjhu91c+sJP7EgrIDLYl7nX9eFf43ooOEmdMwwnmZmfsXHjSFavPo2DB/+Fw5GBr288rVs/yoABv9Ot24eEh1+g4FSP6vXO08KFC7njjjt48cUXGTRoEC+99BIjRoxg69attGzZ8ojt9+3bx8iRI5k8eTLz58/np59+4uabbyYqKorLLrsMgFWrVjF+/Hj+8Y9/MGbMGD7++GOuuOIKfvzxR/r161eflyMiIiICwL7MIqa9t551B3IBGHZ4wdsILXgrJ8G0Zg0DH3oIU0wM9O8PQFlZKqmpr2K3v0xZ2QH3ts2bD8NmSyQiYpQWsz2F6vWdfuaZZ5g4cSKTJk0CYNasWSxZsoSkpCRmzpx5xPZz5syhZcuWzJo1C4DOnTvz22+/8Z///McdnmbNmsXQoUOZPn06ANOnT+f7779n1qxZLFiwoD4vR0RERJo4wzCY//PvPLF4OyUOJyF+Pjw6uitje8XrYXw5aab584natAnn/PnkdCw5vJjtxxhGBQA+PhHExf2NuLibCAxs5+Fqm6Z6C0/l5eWsWbOG++67r0r7sGHDWLlyZbX7rFq1imHDhlVpGz58OK+++ioOhwOr1cqqVau48847j9jmj8DV2BiGQXFxsafLOCUcDgelpaUUFRVhtWo4g7dQv3of9al3Ur+evNS8Eh78ZDM/7c4CoH/bcB4f0x1bswCP/FuuPvUOpgMHMGVlgcmE38J3AXC+M4c9PV4AA3zDwNquP1FRkwgPvxSz2R/DgKKiIg9XXjcCAwMb1R8e6i08ZWZm4nQ6iYmJqdIeExNDampqtfukpqZWu31FRQWZmZnExcUddZujHROgrKyMsrIy9+f5+flA5Q8dh8NRq+uqa0VFRTRv3tyjNYiIiEjtHQTe/z9PVyGNnVHN/1tznPS56X/tJn4GfgYmnbrCTpGcnByCgoI8WkNt8kC9D5D8a5I0DOOY6bK67f/aXttjzpw5kxkzZhzRvnTpUgIDA49e/ClQWlrq0fOLiIiIyKnn5wfnnQffxMKQN8HshD9+m/3jvw7gBs+Ud8osWbIEf39/j9ZQmzvH9RaeIiMjsVgsR9wRSk9PP+LO0R9iY2Or3d7Hx4eIiIhjbnO0Y0Llc1HTpk1zf56fn09CQgLDhg0jNNSzq30bhkFOTo5HazhVHA4H3377Leedd56GF3gR9av3UZ96J/Vr7X23PYMZX2wju8iBj9nElLNbM2lQa3wsDWMmM/Vp41RauoPMzNfJzl6Ay1U5GmrdAB96T6k4ctvly3nh9NN54VQXeQo1hGF7f4xKq4l6C0++vr707t2bZcuWMWbMGHf7smXLuOSSS6rdZ8CAAXz22WdV2pYuXUqfPn3cPxQGDBjAsmXLqjz3tHTpUgYOHHjUWvz8/PDzO3L2G6vV2iB+2Pj6+nq6hFPC4XDg7+9Ps2bNGsT7LnVD/ep91KfeSf1ac/mlDmZ8upUP1x4CLHRKCOOZK3rSLT7M06VVoT5tPFyucjIzP8FuTyI3d7m73d+/LTbbVOICegEXYJjNmFwu939DQkKgWTNPld1k1Ob7p16H7U2bNo0JEybQp08fBgwYwMsvv8yBAweYOnUqUHlHKDk5mTfffBOAqVOn8vzzzzNt2jQmT57MqlWrePXVV6vMonf77bdz9tln869//YtLLrmERYsW8fXXX/Pjjz9WW4OIiIhITf20O5O/v78Be14pJhNMGdyWO4d2wN9q8XRp0giVlv6O3f4yKSmv4nCkHW41ExFxMfHxiTRvPrRyTSbzIYiNxYiPZ0PfvvT45RdMyckQHe3R+uVI9Rqexo8fT1ZWFo899hgpKSl069aNxYsX06pVKwBSUlI4cOB/89W3adOGxYsXc+edd/LCCy9gs9l49tln3dOUAwwcOJB3332XBx98kIceeojTTjuNhQsXao0nEREROWEl5U6e/HIbb6z6HYCW4YE8fcXpnNk63MOVSWNjGE6ys5dgtyeRlbUYcAHg6xtLXNxk4uIm4++fUHWnFi1g/36cJhO/f/klXWfNwmwYlQ9GSYNS7xNG3Hzzzdx8883VvjZv3rwj2s455xzWrl17zGOOGzeOcePG1UV5IiIi0sSt+T2bu9/fyL7Myqmfr+3fkukjOhPkp4VHpebKy9NJSXmNlJSXKC3d725v1uw8bLZEIiMvwWw+xvAwPz/4Y9Y3kwmayGMdjY1+KoiIiEiTVFbh5L/LdvHyD3twGRAb6s+/xvXgnA5Rni5NGgnDMMjL+xG7PYmMjA8wjMrw4+PTnNjYG7DZbiIwsKOHq5S6pPAkIiIiTc7m5DymvbeenWmFAIztFc8jF3clLEATL8jxVVTkkZr6Fnb7HIqLt7jbQ0L6YrMlEh09HoslwIMVSn1ReBIREZEmw+F08cJ3u3n+291UuAwig315Ykx3hnWN9XRp0ggUFKzFbp9DWto7uFyVwzzN5kBiYq7GZkskJKSXhyuU+qbwJCIiIk3CzrQCpr23ns3JlWu6jOweyz8v7U54kJ4tkaNzOktIT1+I3Z5EQcEv7vbAwC7YbInExk7Ax6dhTWMv9UfhSURERLya02Uwd8Venlm6k3Kni7AAK/+4tBsX94jz+OKc0nAVF+/Ebp9Dauo8KipyADCZrERFXYbNlkhY2GB9/TRBCk8iIiLitfZmFHLX+xtYdyAXgPM6RfPk2O5Eh/p7tjBpkFwuB1lZn5KcnERu7jfudj+/VthsNxEXdyO+vjEerFA8TeFJREREvI7LZfD6yv089dV2yipchPj58PDFXRjXu4XuFsgRSksPkZIyl5SUuZSXpxxuNRERcRE2WyLh4cMxmbRQsig8iYiIiJc5kFXM3R9s4Jd92QAMbh/Jvy7rga2ZZj+T/zEMFzk5y0hOTiIr6zP+WMzWao0mLm4SNtsU/P1bebZIaXAUnkRERMQruFwGb/9ygJmLt1Fc7iTQ18IDF3Xm6r4tdbdJ3MrLM0lNfQ27/SVKS/e625s1O/fwYraXYjZrEhGpnsKTiIiINHqHcoq598ON/LQ7C4D+bcP597jTSQgP9HBl0hAYhkF+/kqSk5PIyHgfwygHwGIJIzb2emy2qQQFdfZwldIYKDyJiIhIo2UYBu/+epB/fr6VonIn/lYz917YiesHtMZs1t2mpq6iIp+0tLex25MoKtrkbg8O7k18fCLR0VdisQR5sEJpbBSeREREpFGy55Zw74cbWbErE4AzWzfn3+NOp3Wkfhlu6goLN5CcnER6+ts4nYUAmM0BREdfic2WSGjomR6uUBorhScRERFpVAzD4P3fDvGPz7dSUFaBn4+Zey7sxA0DW2PR3aYmy+ksJSPjfez2JPLzV7nbAwI6YrNNJTb2eqzW5h6sULyBwpOIiIg0Gql5pdz30UaW78gAoFfLZvz78tM5LSrYw5WJp5SU7MFun0NKyutUVFQ+82Yy+RAZOQabLZFmzc7VhCFSZxSeREREpMEzDIP31xy+21Raga+PmbuGdmDS4La629QEuVwVZGV9jt2eRE7OUne7n18CcXFTiIubiJ9fnAcrFG+l8CQiIiINWmpeKdM/2sh3h+82nZ7QjKcv70G76BAPVyanWlmZnZSUV0hJmUtZ2aHDrSbCwy/EZptKePhIzGb9eiv1R19dIiIi0iAZhsEHaw7x2B93myxm7hzagcmD2+BjMXu6PDlFKhez/Ra7PYnMzEWAEwCrNZLY2InYbFMICGjr2SKlyVB4EhERkQYnNa+U+z/exLfb04HKu03/GdeD9jG629RUOBzZpKbOw26fQ0nJLnd7WNhgbLapREVdhtns58EKpSlSeBIREZEGo7q7TXcMbc+UwW11t6kJqFzMdjV2+xzS09/FMMoAsFhCiIm5DpttKsHB3TxcpTRlCk8iIiLSIKTklTD9o03umfR6tAjjP5efTgfdbfJ6FRWFpKe/g92eRGHhend7cHBPbLZEoqOvxsdHMyqK5yk8iYiIiEf9dd0mPdvUdBQWbsZuTyIt7S2czgIATCY/oqPHH17Mtp+mGZcGReFJREREPMaeW8J9H23ih53/m0lPzzZ5N5erjIyMD7Hbk8jL+9HdHhDQ/vBitjdgtYZ7sEKRo1N4EhERkVPOMAwW/nqQf36xjcKy/63bNPEs3W3yViUle7HbXyI19TUcjszDrRYiIy/BZkukefPzMJnU99KwKTyJiIjIKXUop5jpH21ixa7KX6DPaNmMf487nXbReqbF2xiGk6ysL7Dbk8jOXgIYAPj6xmOzTSYubhJ+fvGeLVKkFhSeRERE5JRwuQze/uUATy7eRlG5Ez8fM3cP68iNZ7XBYtZzLd6krCz18GK2L1NWdtDd3rz5MGy2RCIiRmkxW2mU9FUrIiIi9e5AVjH3fLiBn/dmA3Bm6+b867IetI3S3SZvYRgGubnLDy9m+zGGUQGAj08EcXF/Iy7uJgID23m4SpGTo/AkIiIi9cblMnhj1X6e+moHJQ4nAVYL91zYkesHtMasu01eweHIITX1jcOL2e5wt4eGDsRmSyQqahwWi78HKxSpOwpPIiIiUi/2ZhRy74cb+XV/DgD924bzr8t60CoiyMOVSV3Iz/8Vuz2J9PR3cblKALBYgomJufbwYrane7hCkbqn8CQiIiJ1qsLp4tUf9/HMsp2UVbgI8rVw38jOXNO3pe42NXJOZxHp6e+SnJxEYeEad3tQUHdstkRiYq7Fx0fTzIv3UngSERGROrMjtYB7PtjAhkN5AAxuH8kTY7qTEB7o4crkZBQVbcNuTyI19U2czsq+NZl8iY6+4vBitgO0mK00CQpPIiIictIcThdJy/fw3Le7cDgNQvx9eGhUFy7v3UK/VDdSLlc5mZkfk5ycRF7e9+52f//TsNluIjb2b/j6RnqwQpFTT+FJRERETsrm5Dz+/sFGtqXkA3BB52geH9OdmFBNEtAYlZb+jt3+Mikpr+JwpB1uNRMRcTHx8Yk0bz5Ui9lKk6XwJCIiIiek1OHk2W928dIPe3G6DJoHWnl0dFdGn27T3aZGxjCcZGd/RXJyEtnZi/nfYrZxxMVNJi5uMv7+LTxbpEgDoPAkIiIitbbm92zu+WAjezKKALioexwzLulKZLCfhyuT2igvTycl5VVSUl6mtHS/u71Zs/OJj08kImI0ZrPVcwWKNDAKTyIiIlJjRWUV/HvJDt5YtR/DgKgQP/55aTeGd431dGlSQ4ZhkJe3Ars9iYyMDzEMBwA+Ps2Jjb0Bm20qgYEdPFylSMOk8CQiIiI18uOuTO77aCOHcirX9Lm8dwsevKgLYYG6M9EYVFTkkZr6FnZ7EsXFW93tISH9iI9PJCrqCiyWAA9WKNLwKTyJiIjIMeWVOHjii20s/O0gAPHNApg5tjtnd4jycGVSEwUFa7Hbk0hLeweXqxgAszmQmJhrsNkSCQk5w8MVijQeCk8iIiJyVEu2pPLQJ5tJLygD4LoBrbjnwk4E++lXiIbM6SwhPX0hdnsSBQW/uNsDA7sSH//HYrZhHqxQpHHSTz4RERE5QkZBGY9+uoUvNqUA0DYyiCcv60HfNuEerkyOpbh4J3b7HFJT51FRkQOAyWQlKmocNlsiYWFnaSZEkZOg8CQiIiJuhmHw0dpkHvt8K3klDixmEzed3Zbbzm+Pv9Xi6fKkGi6Xg/T0RdjtSeTmfutu9/dvTVzcTcTF3Yivb7QHKxTxHgpPIiIiAsChnGLu/3gzP+zMAKBLXChPjetBt3gN72qIysoO4uf3Dr/9lojDkXK41URExEXYbImEhw/HZFLgFalLCk8iIiJNnNNl8Naq/Ty1ZAfF5U58fczccUF7Jg9ui9Vi9nR58ieG4SInZxnJyUlkZX2Gv78LhwOs1mji4iZhs03B37+Vp8sU8VoKTyIiIk3YrrQC7v1wI2sP5AJwZuvmPHlZD06LCvZsYVJFeXkGqamvY7e/RGnpXnd7RUU3unadTkzMOMxmXw9WKNI0KDyJiIg0QeUVLpKW7+GF73ZT7nQR7OfDvSM6cU3flpjNmlCgIahczPYn7PY5ZGS8j2GUA2CxhBEbez3R0RNZvnwfkZEjMZu11pbIqaDwJCIi0sSsO5DDfR9uYkdaAQDnd4rmH5d2w9ZMC6Q2BBUV+aSlzcdun0NR0SZ3e3Bwb+LjE4mOvhKLJQiHwwHs81yhIk2QwpOIiEgTUeaExxdv542fD2AYEBHkyyOju3JxjzhNX90AFBZuIDk5ifT0t3E6CwEwmwOIjr4Kmy2R0NA+Hq5QRBSeREREmoAVuzJ5coOF7LIDAIztFc9DF3WheZCek/Ekp7OUjIz3sduTyM9f5W4PDOyEzTaVmJjrsFqbe7BCEfkzhScREREvll1Uzj8+38rH65IBE/HN/HlibA/O6RDl6dKatOLi3aSkvERKyutUVGQBYDL5EBk5FpstkWbNztHdQJEGSOFJRETECxmGwSfrk3nss63kFDswm+DsWBezJg6kWbCebfIEl6uCrKzPsNuTyMlZ5m7382uJzTaF2NiJ+PnFerBCETmeel28IScnhwkTJhAWFkZYWBgTJkwgNzf3qNs7HA7uvfdeunfvTlBQEDabjeuuuw673V5lu3PPPReTyVTl48orr6zPSxEREWk0DmYXc/3rv3Lnwg3kFDvoFBvCe1P6Maa1iyA//d30VCsrS2b//hn8/HNrtmwZezg4mQgPH0m3bp/Sv/9eWrV6QMFJpBGo15+gV199NYcOHeKrr74CYMqUKUyYMIHPPvus2u2Li4tZu3YtDz30EKeffjo5OTnccccdjB49mt9++63KtpMnT+axxx5zfx4QoL+iiYhI01bhdDFv5X6eXrqTEkflYre3n9+eKWe3BZeT5I2errDpqFzM9lvs9iQyMxcBTgCs1iji4iYSFzeFgIA2ni1SRGqt3sLTtm3b+Oqrr/j555/p168fAHPnzmXAgAHs2LGDjh07HrFPWFgYy5Ytq9L23HPP0bdvXw4cOEDLli3d7YGBgcTG6i80IiIiAFvsedz34SY2JecB0LdNODPHdncvdutwOT1ZXpPhcGSRmjoPu/0lSkp2udvDwgZjsyUSFTUWs9nPgxWKyMmot/C0atUqwsLC3MEJoH///oSFhbFy5cpqw1N18vLyMJlMNGvWrEr722+/zfz584mJiWHEiBE88sgjhISE1OUliIiINHgl5U5mfbOTV1bsw+kyCPH3YfqIzlx5ZoIWuz1FDMMgP381dnsS6ekLMYwyACyWUGJjryMu7iaCg7t5uEoRqQv1Fp5SU1OJjo4+oj06OprU1NQaHaO0tJT77ruPq6++mtDQUHf7NddcQ5s2bYiNjWXz5s1Mnz6dDRs2HHHX6g9lZWWUlZW5P8/Pzwcqn7GqXGBOToU/3mu9595F/ep91KeNx097snho0VYO5pQAcGHXGB66qBPRIX44nRU4/3SzSf1a95zOQjIyFpCa+jJFRRvc7UFBPYmNvYmoqPFYLIfv/NXD+64+9T7qU8+ozfttMgzDqM3BH330UWbMmHHMbX799VeWLl3KG2+8wY4dO6q81r59eyZOnMh99913zGM4HA4uv/xyDhw4wPLly6uEp79as2YNffr0Yc2aNfTq1avGNb/zzjsEBgYesw4REZGGpsgBn/xu5peMynmfmvkajGvjont4rf5JlxNkNv+Or+9X+Poux2SqDK6G4YvDMYjy8hE4ne0B3fUTaSyKi4u5+uqrycvLO2bmgBO483Trrbced2a71q1bs3HjRtLS0o54LSMjg5iYmGPu73A4uOKKK9i3bx/ffvvtcS+iV69eWK1Wdu3aVW14mj59OtOmTXN/np+fT0JCAsOGDTvusaXuOBwOli1bxtChQ7FarZ4uR+qI+tX7qE8bLsMw+HRDCv/+cgc5xQ5MJri2bwJ3XtCeEP9j/5Oufj05LlcZWVkfkZr6Mvn5P7nb/f3bERs7hejoCVitEae0JvWp91GfesYfo9JqotbhKTIyksjIyONuN2DAAPLy8vjll1/o27cvAKtXryYvL4+BAwcedb8/gtOuXbv47rvviIg4/g+iLVu24HA4iIuLq/Z1Pz8//PyOfDjTarXqC9MD9L57J/Wr91GfNiy/ZxXx4CebWbErE4AOMcE8eVkPerVsXqvjqF9rp6RkL3b7y6SmvobDkXG41UJk5CXYbIk0b34eJlO9rvxyXOpT76M+PbVq817X2zNPnTt35sILL2Ty5Mm89NJLQOVU5aNGjaoyWUSnTp2YOXMmY8aMoaKignHjxrF27Vo+//xznE6n+/mo8PBwfH192bNnD2+//TYjR44kMjKSrVu3ctddd3HGGWcwaNCg+rocERERj3A4XbyyYh+zvt5JWYXLPf345MFt8fXx7C/t3sownGRlfYHdnkR29hKgcjikr288NtsU4uIm4ucX79kiRcQj6nWdp7fffpvbbruNYcOGATB69Gief/75Ktvs2LGDvLzKaVUPHTrEp59+CkDPnj2rbPfdd99x7rnn4uvryzfffMPs2bMpLCwkISGBiy66iEceeQSLxVKflyMiInJKrT+Yy30fbmR7agEAA0+L4PEx3WkTGeThyrxTWVkqKSmvkJLyMmVlB93tzZsPw2ZLJCJiFGazFhkWacrq9SdAeHg48+fPP+Y2f56vonXr1hxv/oqEhAS+//77OqlPRESkISoodfD00p28sWo/hgHNA608eFEXxvaKx2TSRAR1yTAMcnOXH17M9mMMowIAH58I4uJuJC5uCoGB7TxcpYg0FPrziYiISAOyZEsqjyzaQmp+KQBjz4jngYs6ExGshVXrksORQ2rqG9jtcygp+d/MwKGhAw8vZjsOi8XfgxWKSEOk8CQiItIA2HNLeOTTLSzbWjlTbauIQP55aTcGt4/ycGXeJT//18OL2b6Ly1U5zbjFEkxMzLXYbIkEB/fwcIUi0pApPImIiHiQ02Xwxsr9PL10B0XlTnzMJm46py3/d157/K16lrcuOJ1FpKUtwG6fQ2HhGnd7UFAPbLZEYmKuwccnxIMVikhjofAkIiLiIZuT87j/401sPFQ5cVLvVs2ZObY7HWL0i3xdKCrait0+h9TUN3E6K99jk8mX6OgrsNkSCQ0doGfIRKRWFJ5EREROsaKyCp5ZtpPXf9qHy4AQfx/uG9GJq85sidmsX+ZPhstVTmbmxyQnJ5GX978Jpvz9T8Nmu4nY2L/h63v89SpFRKqj8CQiInIKLd2SyqOfbsGeVzkhxEU94nhkVBeiQzU5wckoKdlPSsrLpKS8isORfrjVTGTk6MOL2V7g8cVsRaTxU3gSERE5Bey5JTz66RaWHp4QIiE8gH9c0o1zO0Z7uLLGyzCcZGd/RXJyEtnZi/nfYrZxxMVNJi5uMv7+LTxbpIh4FYUnERGRelThdPHGqt955k8TQkw+uy23ndeeAF9NCHEiysvTSUl5Fbv9JcrKfne3N29+weHFbC/GbLZ6sEIR8VYKTyIiIvVkw8FcHvhkE5uT84HKCSEeH9ONTrGhHq6s8TEMg7y8H0hOTiIz8yMMwwGAj09zYmP/hs12E4GBHTxcpYh4O4UnERGROpZf6uDpJTt48+ffMQwI9ffhvhGdufLMBE0IUUsVFXmkpr6J3T6H4uKt7vaQkH7ExycSFXUFFkuABysUkaZE4UlERKSOGIbBF5tSeOyzraQXlAFwaU8bD1zUhagQPw9X17gUFKzFbk8iLe0dXK5iAMzmIGJirsFmm0pIyBkerlBEmiKFJxERkTpwIKuYhxZt5vudGQC0iQzin5d2Y1A7TYtdU05nMenpC7Hbkygo+NXdHhjYFZttKrGxE/DxCfNghSLS1Ck8iYiInITyChdzV+zl2W92UVbhwtdiJvHc00g89zT8rZoQoiaKi3ccXsx2HhUVuQCYTFaiosZhsyUSFnaWFrMVkQZB4UlEROQErdqTxYOfbGJPRhEAg9pF8I9LutE2KtjDlTV8LpeDzMxF2O1J5OZ+6273929NXNxNxMXdiK+vpnEXkYZF4UlERKSWMgvLeOKLbXy0LhmAyGBfHryoC5f0tOkOyXGUlh4kJWUuKSmvUF6ecrjVTETERdhsiYSHD9ditiLSYCk8iYiI1JDLZfDOLwd46qvt5JdWYDLBNf1a8vdhnQgL1LpCR2MYLrKzl2K3J5GV9TngAsBqjSEubhI22xT8/Vt6tkgRkRpQeBIREamBzcl5PPDJZjYczAWgqy2Ux8d0p2dCM4/W1ZCVl2eQmvo6dvtLlJbudbc3azYEm20qkZGXYjb7erBCEZHaUXgSERE5hoJSB88s28kbK/fjMiDYz4e7hnVgQv9W+Fg0vOyvKhez/Qm7PYmMjA8wjHIALJYwYmNvwGabSlBQJw9XKSJyYhSeREREqmEYBp9tTOGfn/9vzaaLesTx8KguxIT6e7i6hqeiIp+0tPnY7UkUFW12t4eE9MFmSyQ6+koslkAPVigicvIUnkRERP5ib0YhDy/awo+7MwFoHRHIY5d04+wOUR6urOEpKFiP3T6HtLT5uFyVsw6azQFER1+FzZZIaGgfD1coIlJ3FJ5EREQOK3U4eeG73bz0/V7KnS58fczcOqQdU85uqzWb/sTpLCUj4z3s9iTy8392twcGdsJmm0pMzHVYrc09WKGISP1QeBIREQG+257Ow59u5mB2CQDndoxixuiutIoI8nBlDUdx8e7Di9m+TkVFNgAmkw+RkWOx2RJp1uwcTdUuIl5N4UlERJq0QznFzPhsK8u2pgEQF+bPIxd3YXjXWAUBwOWqICvrM+z2JHJylrnb/fxaYrNNITZ2In5+sR6sUETk1FF4EhGRJqmswskrK/bx3Le7KHW48DGbmHhWG247vz1BfvrnsawsGbt9Likpcykvtx9uNREePgKbbSoRESMxmTSUUUSaFv3rICIiTc6PuzJ5+NPN7M2onOCgX5tw/nFpNzrEhHi4Ms8yDBc5Od9gtyeRmfkp4ATAao0iLm4icXFTCAho49kiRUQ8SOFJRESajNS8Uv75xVY+35gCQGSwHw9e1JlLetqa9BA9hyOL1NR52O0vUVKyy90eFjYYmy2RqKixmM1+HqxQRKRhUHgSERGv53C6mPfTfmZ9vZOicidmE1w3oDV3Du1AWIDV0+V5hGEY5Of/jN0+h/T0hRhG5VpWFksosbHXERd3E8HB3TxcpYhIw6LwJCIiXm3VniweXrSZXemFAJzRshn/uKQb3eLDPFyZZzidhWRkvEdychJFRRvc7cHBZ2CzTSU6+mp8fII9WKGISMOl8CQiIl4pPb+UxxdvY9H6yskOwoN8ue/CTozr3QKzuekN0Ssq2oy//0v8+usEnM4CAMxmf6KixhMfn0hISN8mPXRRRKQmFJ5ERMSrOJwu3li5n1lf76KwrAKTCa7p15K7h3WkWaCvp8s7pVyuMjIyPsBun0Ne3o/4+YHTCQEBHbDZphIbez1Wa7inyxQRaTQUnkRExGv8vDeLRxZtYUda5Z2VngmVQ/S6t2haQ/RKSvZit79EauprOByZh1stOBx96dnzESIjh+kuk4jICVB4EhGRRi8tv5THv9jGpxsqh+g1D7Ry34hOXN47ockM0TMMJ1lZX2C3J5GdvQQwAPD1jcdmm0Jk5PV88816mjU7T8FJROQEKTyJiEij5XC6eP2nfcz+ehdF5c4mOUSvrCyFlJRXSEmZS1nZQXd78+bDsNkSiYgYhdnsg8PhANZ7rE4REW+g8CQiIo3ST7szeeTTLexugrPoGYZBbu53hxez/QTDqADAxyeCuLgbiYubQmBgOw9XKSLifRSeRESkUbHnlvD44m18cXih2/AgX+4b0Ylxvbx/Fj2HI4fU1Dew2+dQUrLD3R4aOvDwYrbjsFj8PVihiIh3U3gSEZFGoazCySsr9vH8t7spcVQudDuhfyumDe1IWKD3LnRrGAYFBb9ityeRnv4uLlcpABZLMDEx12KzJRIc3MPDVYqINA0KTyIi0uB9tz2dGZ9tYX9WMQB9WjVnxiVd6Wrz3iF6TmcRaWkLsNuTKCxc624PCuqBzZZITMw1+PiEeLBCEZGmR+FJREQarN+zivjH51v5els6AFEhftw/shOX9oz32hnjioq2YrcnkZr6Jk5nPgAmky/R0VdgsyUSGjrAa69dRKShU3gSEZEGp6TcyYvLd/PSD3spr3DhYzZx41lt+L/z2hHi731D9FyucjIyPsJuTyIv7wd3u7//adhsNxEb+zd8fSM9WKGIiIDCk4iINCCGYfDFphSe+GIb9rzKZ3sGt4/kkYu70i462MPV1b2Skv2kpLxMSsqrOBzph1vNREaOxmZLpHnzCzCZzB6tUURE/kfhSUREGoQdqQU8+ukWVu3NAiC+WQAPjerM8K6xXjVMrXIx2y8PL2b7Jf9bzDaOuLjJxMVNxt+/hWeLFBGRaik8iYiIR+UVO/jv1zt56+ffcboM/HzMJJ57GlPPOQ1/q8XT5dWZ8vI0UlJexW5/mbKy393tzZqdT3z8zUREXIzZ7H1DEkVEvInCk4iIeITTZfDebwf595IdZBeVAzCiWywPXNSZFs0DPVxd3TAMg7y8H0hOTiIz8yMMwwGAj09zYmP/hs12E4GBHTxcpYiI1JTCk4iInHK/7c/m0c+2sDm5cja59tHBPDq6K4PaecekCA5HLmlpb2K3z6G4eJu7PTS0PzbbVKKirsBiCfBghSIiciIUnkRE5JRJzSvlyS+38cl6OwAh/j7ccUEHrhvQCqul8U+MUFCwhuTkJNLTF+ByVa5JZTYHERNzDTbbVEJCzvBwhSIicjIUnkREpN6VVTh5ZcU+XvhuN8XlTkwmGN8ngbuHdyQy2M/T5Z0Up7OY9PR3sdvnUFDwq7s9KKjb4cVsr8XHJ9SDFYqISF1ReBIRkXpjGAbfbEvnH19s5fesyjsxvVo2Y8bobnRvEebh6k5OUdF27PY5pKW9QUVFLlC5mG1U1DhstkTCwgZ51SyBIiKi8CQiIvVkd3oBMz7byopdmQBEh/gxfWQnLu0Z32hDhcvlIDPzE+z2JHJzv3O3+/u3+dNittEerFBEROqTwpOIiNSpvGIHs77ZyZurKqce97WYufGsNtx6XjuC/RrnPzulpQcPL2b7CuXlqYdbzUREXITNlkh4+HAtZisi0gQ0zn/FRESkwXG6DN799QBPL93pnnp8aJcYHryoM60igjxcXe0Zhovs7CXY7XPIyvoccAHg6xtLXNykw4vZtvRskSIickrV65/JcnJymDBhAmFhYYSFhTFhwgRyc3OPuc8NN9yAyWSq8tG/f/8q25SVlfF///d/REZGEhQUxOjRozl06FA9XomIiBzLz3uzGPXcjzzw8Wayi8ppHx3MWxP7Mve6Po0uOJWXZ3DgwL9YvbodmzaNJCvrU8BFs2ZD6NLlPfr3P0CbNv9QcBIRaYLq9c7T1VdfzaFDh/jqq68AmDJlChMmTOCzzz475n4XXnghr7/+uvtzX1/fKq/fcccdfPbZZ7z77rtERERw1113MWrUKNasWYPF4j2r0YuINHQHs4uZ+eU2Fm+qHMoW6u/DtKEduKZ/45p6vHIx25+w25PIyPgAw6i8c+bj04yYmOux2aYSFNTJw1WKiIin1Vt42rZtG1999RU///wz/fr1A2Du3LkMGDCAHTt20LFjx6Pu6+fnR2xsbLWv5eXl8eqrr/LWW29xwQUXADB//nwSEhL4+uuvGT58eN1fjIiIVFFYVsGL3+3mlR/3UV7hwmyCq/u1ZNrQjoQH+R7/AA1ERUU+aWnzsduTKCra7G4PCTkTmy2R6OjxWCyBHqxQREQaknoLT6tWrSIsLMwdnAD69+9PWFgYK1euPGZ4Wr58OdHR0TRr1oxzzjmHxx9/nOjoytmL1qxZg8PhYNiwYe7tbTYb3bp1Y+XKldWGp7KyMsrKytyf5+dXrmjvcDhwOBwnfa1SM3+813rPvYv61fscq09dLoOP19t5etkuMgor784MbBvO/SM60jE25Kj7NTSFhetJTZ1LRsY7uFxFAJjNAURGXklc3E0EB/cCwOWqnGHPG+h71fuoT72P+tQzavN+11t4Sk1NdQeeP4uOjiY1NbWaPSqNGDGCyy+/nFatWrFv3z4eeughzjvvPNasWYOfnx+pqan4+vrSvHnzKvvFxMQc9bgzZ85kxowZR7QvXbqUwED9RfFUW7ZsmadLkHqgfvU+f+3Tvfnw0X4LB4sqpxmP9DO4tLWLbs3T2bM2nT2eKLJWyrFaf8LX9yt8fHa4W53OFpSXX0h5+bnk5ASza1cqsNhzZdYzfa96H/Wp91GfnlrFxcU13rbW4enRRx+tNoj82a+/Vq6wXt06HoZhHHN9j/Hjx7v/v1u3bvTp04dWrVrxxRdfMHbs2KPud6zjTp8+nWnTprk/z8/PJyEhgWHDhhEaqlXfTxWHw8GyZcsYOnQoVqvV0+VIHVG/ep+/9qk9t4R/L93F51sq/0AV5GfhlnPbcl3/Vvj5NPznmkpKdpGa+grp6W9QUZENgMlkJSLiUmJjbyI0dHCjXXeqNvS96n3Up95HfeoZf4xKq4lah6dbb72VK6+88pjbtG7dmo0bN5KWlnbEaxkZGcTExNT4fHFxcbRq1Ypdu3YBEBsbS3l5OTk5OVXuPqWnpzNw4MBqj+Hn54efn98R7VarVV+YHqD33TupX71PuctE0nd7efmHvZRVuDCZ4IreCdw9vCNRIUf+TG1IXK4KsrI+xW5PIifna3e7n19LbLYpxMVNwte35v8WeRN9r3of9an3UZ+eWrV5r2sdniIjI4mMjDzudgMGDCAvL49ffvmFvn37ArB69Wry8vKOGnKqk5WVxcGDB4mLiwOgd+/eWK1Wli1bxhVXXAFASkoKmzdv5qmnnqrt5YiIyF+4XAa/ZJh4YvZPpBVUPi/ar004D43qQrf4MA9Xd2xlZcnY7XNJSZlLebn9cKuJ8PAR2GyJRESMwGTSrKwiInJi6u2Zp86dO3PhhRcyefJkXnrpJaByqvJRo0ZVmSyiU6dOzJw5kzFjxlBYWMijjz7KZZddRlxcHPv37+f+++8nMjKSMWPGABAWFsbEiRO56667iIiIIDw8nLvvvpvu3bu7Z98TEZET89v+bGZ8toVNyRagjITwAB4Y2ZnhXWMb7NA2w3CRk/M1dnsSmZmfAU4ArNYo4uImEhc3hYCANp4tUkREvEK9rvP09ttvc9ttt7lnxhs9ejTPP/98lW127NhBXl4eABaLhU2bNvHmm2+Sm5tLXFwcQ4YMYeHChYSEhLj3+e9//4uPjw9XXHEFJSUlnH/++cybN09rPImInKCD2cU8+dV2vtiYAoCfxeC28zswcfBp+Fsb5s9WhyOLlJTXSUl5iZKS3e72sLCzsdmmEhU1FrO5YQ8vFBGRxqVew1N4eDjz588/5jaGYbj/PyAggCVLlhz3uP7+/jz33HM899xzJ12jiEhTVlDq4MXle3j18HpNJhNc3iue7vzOlYPbYG1gwckwDPLzf8ZuTyI9/T0Mo3JYocUSSmzsdYcXs+3q4SpFRMRb1Wt4EhGRhsnpMlj460GeWbaDzD/Wazotggcv6kL7qAAWL/7dwxVWVVFRQFra29jtcygq2uBuDw4+4/Bitlfh4xPswQpFRKQpUHgSEWliftyVyT+/2Mr21AIA2kQGcf/IzlzQORqTydSgFmcsLNyE3Z5EWtp8nM7Kes1mf6Kjr8Rmm0pISN8G+yyWiIh4H4UnEZEmYnd6ITMXb+Ob7ekAhPr7cPsFHZjQvxW+DWi9JqezlMzMD0lOTiI//yd3e0BAB2y2qcTGXo/VGu7BCkVEpKlSeBIR8XJZhWXM/mYXb68+gNNl4GM2cW3/Vtx+fnuaB/l6ujy3kpI92O0vkZr6Og5H5uFWC5GRlxIfn0izZufpLpOIiHiUwpOIiJcqq3Ay76f9PP/tbgrKKgC4oHMM00d24rSohvF8kMtVQXb2FyQnJ5GT878Jg/z8WhAXN4W4uIn4+dk8WKGIiMj/KDyJiHgZwzBYvCmVJ7/axsHsEgC6xIXy4KjODDzt+IucnwplZXZSUl4lJeVlysoOudubNx9OfHwi4eEXYTbrnygREWlY9C+TiIgXWXsgh8e/2Maa33MAiAn14+5hHRnbqwUWs2eHvBmGQW7utyQnJ5GVtQjDqLwb5uMTQVzcjdhsNxEQcJpHaxQRETkWhScRES9wIKuYfy353yK3AVYLN53TlilntyXQ17M/6h2OHFJT52G3z6GkZKe7PTR0EPHxiURGXobF4u/BCkVERGpG4UlEpBHLK3bw/He7eGPl75Q7Dy9y27sFdw3rSEyo5wKJYRgUFPx6eDHbd3G5SgGwWEKIiZmAzTaV4ODuHqtPRETkRCg8iYg0QuUVLub//DvPfruL3OLKdZkGt4/k/pGd6RwX6rG6nM4i0tIWYLcnUVi41t0eFHQ68fGJREdfjY9PiMfqExERORkKTyIijYhhGHy5OZWnvtrO/qxiADrEBHP/yM6c0yHKY1N5FxVtxW5PIjX1TZzOfABMJj+io6/AZkskNLS/phkXEZFGT+FJRKSRWPN7No9/sY21B3IBiAz2Y9rQDlzRpwU+llO/yK3LVU5GxkfY7Unk5f3gbg8IaHd4MdsbsFojTnldIiIi9UXhSUSkgdufWcS/vtrOl5tTgcrJICYPbsOUc04j2O/U/xgvKdlPSspLpKS8hsORfrjVQmTkaGy2RJo3Px+T6dSHORERkfqm8CQi0kBlF5Xz7De7mP/z71S4DMwmuLx3AtOGdTjlk0EYhpOsrC+x25PIzv4SMADw9bURFzcZm20yfn7xp7QmERGRU03hSUSkgSl1OHntp30kLd9DQWnlWkjndoxi+ojOdIw9tZMtlJWlkpr6Knb7y5SVHXC3N28+FJstkYiIUZjN1lNak4iIiKcoPImINBBOl8FHaw/xzLKdpORVTu3dJS6UBy7qzKB2kaesDsMwsFg2sX37fLKzP/nTYrbhxMb+DZvtJgID25+yekRERBoKhScREQ8zDIPvd2bw5Jfb2Z5aAEB8swDuHt6BS06Px2w+NbPUORy5pKW9SXJyEsHB28nKqmwPDe2PzZZIVNTlWCwBp6QWERGRhkjhSUTEgzYn5zHzy238tLsyqYT6+3Dree24bkBr/K2WU1JDQcEakpOTSE9fgMtVOf25YfgTG3stLVrcQkhIz1NSh4iISEOn8CQi4gEHs4v5z9IdLFpvB8DXYua6Aa24ZUg7mgf51vv5nc5i0tMXYrcnUVDwq7s9MLArsbFTWLcukrPOuhyrVc8ziYiI/EHhSUTkFMouKuf5b3cz/+ffKXe6ABh9uo2/D+9IQnhgvZ+/uHgHdvscUlPnUVGRC4DJ5EtU1DhstkTCwgZRUVHBunWL670WERGRxkbhSUTkFCgpr5xBb87yPRSUVU7AMKhdBPdd2JnuLcLq9dwul4PMzE+w25PIzf3O3e7v3wab7SZiY2/E1zeqXmsQERHxBgpPIiL1qMLp4sPDM+il5ZcB0DkulOkjOjG4fSQmU/1NBlFaegC7/WVSU1+lvDz1cKuZiIhR2GyJhIcP02K2IiIitaDwJCJSDwzDYNnWNJ5asoPd6YXAqZlBzzBcZGcvwW5PIivrC6ByaKCvbyxxcZOIi5uMv3/Lejm3iIiIt1N4EhGpY7/uz+bJL7ez5vccAJoFWrnl3HZMGNCq3mbQKy9PJzX1dez2lygt3edub9ZsCDZbIpGRl2oxWxERkZOk8CQiUkd2phXw1Ffb+XpbOgD+VjM3DmrDTeecRlhA3QcXwzDIy/sRuz2JjIwPMAwHAD4+zYiJuR6bbSpBQZ3q/LwiIiJNlcKTiMhJSs4tYdaynXy49hAuAyxmE1f0SeCOC9oTE+pf5+erqMgnLe0tkpOTKC7e4m4PCTkTmy2R6OjxWCz1P3OfiIhIU6PwJCJygnKKynnhu928+fPvlFdUPls0olssdw/vyGlRwXV+voKCddjtSaSlvYPLVQSA2RxAdPTVxMcnEhLSu87PKSIiIv+j8CQiUktFZRW89uM+Xv5hr3va8X5twrl3RCd6tWxep+dyOkvIyHiP5OQkCgpWu9sDAztjsyUSEzMBq7VZnZ5TREREqqfwJCJSQ+UVLhb8coDnvt1FZmE5AF3iQrl3RCfOruNpx4uLd2K3v0Rq6utUVFROPGEyWYmMHEt8fCJhYWfX6zTnIiIiciSFJxGR43C6DD7bYOfpZTs4mF0CQKuIQO4a1pFR3ePqbNpxl8tBVtanJCcnkZv7jbvdz68VNtsU4uIm4usbUyfnEhERkdpTeBIROQrDMPhmWzr/WbqD7akFAESF+HH7+e0Zf2YCVkvdLDBbWnqIlJS5pKTMpbw85XCrifDwkcTHJxIefiEmU/1McS4iIiI1p/AkIlKNn/dm8e8lO9xrNYX4+zD1nNP426DWBPqe/I9Ow3CRk/M1dnsSmZmfAU4ArNZo4uImEhc3hYCA1id9HhEREak7Ck8iIn+yOTmPfy/Zwfc7M4DKtZpuGNiGqee0pVmg70kfv7w8k9TUedjtcygt3eNuDws7B5ttKlFRYzGbT/48IiIiUvcUnkREgD0ZhTyzbCdfbKwcNudjNnFl3wT+77yTX6vJMAzy81dhtyeRnv4+hlEGgMUSSmzs9dhsNxEU1PWkr0FERETql8KTiDRpybklzP56Jx+sqVzg1mSC0afbmDa0A60igk7q2BUVBaSlvY3dPoeiog3u9uDgXoenGb8Ki+XkziEiIiKnjsKTiDRJGQVlvLh8N2//fIByZ+UCtxd0jmba0I50sYWe1LELCzcdXsx2Pk5n5UQTZrM/0dFXYbNNJSTkTE0zLiIi0ggpPIlIk5JX4mDuD3t57ad9FJdXTtLQv204fx/eid6tTnyBW6ezlMzMD0lOTiI//yd3e0BAR2y2qcTGXo/VWrcL6IqIiMippfAkIk1CUVkF81bu56Xv95BfWgHA6QnN+PuwjgxqF3HCd4JKSva4F7N1ODIBMJl8iIy8FJstkWbNhuguk4iIiJdQeBIRr1bqcDL/599JWr6HrKJyADrEBHP3sI4M7RJzQsHG5aogK+tz7PY55OQscbf7+SUQF1e5mK2fX1ydXYOIiIg0DApPIuKVHE4X7/12kOe+2U1qfikArSMCuXNoB0b1sGEx1z40lZXZSUl5hZSUuZSVHTrcaiI8fDg2WyLh4SMxm/VjVURExFvpX3kR8SpOl8En65KZ/c0uDmQXA2AL8+e289tzWe8WWC3mWh3PMAxyc78lOTmJzMxP+N9itpHExt6IzXYTAQFt6/gqREREpCFSeBIRr+ByGXyxKYVZX+9kT0YRAJHBftwy5DSu6tsSf6ulVsdzOLJJTX0Du30OJSU73e2hoYOIj08kKmocZrNfnV6DiIiINGwKTyLSqBmGwbKtaTyzbCfbUyunBW8WaGXK2W25YWBrAn1r/mPOMAwKCn7Bbp9Devq7uFyVw/0slhBiYiZgs00lOLh7vVyHiIiINHwKTyLSKBmGwfc7M3hm2U42HsoDIMTPh0mD23LjWa0J8bfW+FhOZxFpae9gt8+hsHCtuz0o6HTi4xOJjr4aH5+QOr8GERERaVwUnkSkUTEMg1V7snhm2U5++z0HgEBfC38b1JrJg9vSLNC3xscqKtqC3T6H1NQ3cTrzATCZ/IiOHo/NlkhoaD9NMy4iIiJuCk8i0mis3lsZmlbvywbAz8fMhP6tmHruaUQG1+z5I5erjIyMj7Db55CX94O7PSCg3eHFbG/Aao2ol/pFRESkcVN4EpEGb83vOfx32U5+3F25CK2vxcxVfRO4eUg7YkL9a3SMkpL9pKS8RErKqzgcGYdbLURGjsZmS6R58/MxmWo3E5+IiIg0LQpPItJgbTiYy3+/3snyHZVhx2oxcUWfBG4Z0g5bs4Dj7m8YTrKyvsRuTyI7+0vAAMDX14bNNoW4uEn4+cXX5yWIiIiIF1F4EpEGZ9OhPGZ9vZNvtqcDYDGbGNerBbee146E8MDj7l9Wlkpq6qvY7S9TVnbA3d68+VBstkQiIi7WYrYiIiJSa/U6RiUnJ4cJEyYQFhZGWFgYEyZMIDc395j7mEymaj/+/e9/u7c599xzj3j9yiuvrM9LEZFTYHNyHpPe+I2Ln/+Rb7anYzbB2DPi+WbaOfxrXI9jBifDMMjJWc6WLeP5+ecE9u17kLKyA/j4hNOixV307buT009fSlTUGAUnEREROSH1+hvE1VdfzaFDh/jqq68AmDJlChMmTOCzzz476j4pKSlVPv/yyy+ZOHEil112WZX2yZMn89hjj7k/Dwg4/hAeEWmYtqXkM+vrnSzZkgaA2QSjT7fxf+e357So4GPu63Dkkpb2Jnb7HIqLt7nbQ0P7Y7MlEhV1ORaLfj6IiIjIyau38LRt2za++uorfv75Z/r16wfA3LlzGTBgADt27KBjx47V7hcbG1vl80WLFjFkyBDatm1bpT0wMPCIbUWkcdmems+z3+xi8aZUAEwmuLiHjdvOb0+76GOHpoKCNSQnJ5GevgCXqxgAszmImJhriY9PJDj49HqvX0RERJqWegtPq1atIiwszB2cAPr3709YWBgrV648anj6s7S0NL744gveeOONI157++23mT9/PjExMYwYMYJHHnmEkJDqF7EsKyujrKzM/Xl+fuV6Lg6HA4fDUdtLkxP0x3ut99y7nEi/7kgt4Pnle/nq8J0mkwlGdo3lliFtaX84NFV3PKezmMzM90hNfZnCwt/c7YGBXYmNvYmoqKvx8QmtdT1Slb5XvZP61fuoT72P+tQzavN+11t4Sk1NJTo6+oj26OhoUlNTa3SMN954g5CQEMaOHVul/ZprrqFNmzbExsayefNmpk+fzoYNG1i2bFm1x5k5cyYzZsw4on3p0qUEBh7/4XOpW0frJ2ncatKvyUWw5JCZDdmVj1uaMOgZYTCshQtb4CF2/XaIXdXsZzYfwtf3K3x9v8NkKgLAMHxwOAZSXj6CvLxOpKSYgB/r8IpE36veSf3qfdSn3kd9emoVFxfXeNtah6dHH3202iDyZ7/++itQOfnDXxmGUW17dV577TWuueYa/P2rruMyefJk9/9369aN9u3b06dPH9auXUuvXr2OOM706dOZNm2a+/P8/HwSEhIYNmwYoaGhNapFTp7D4WDZsmUMHToUq9Xq6XKkjtSkX7enFvD8d3tYsrVy9jyTCUZ0jeGWc9vSIab6O8YuVznZ2YtISXmZ/Pzv3e3+/m2JiZlETMz1WK1RdX9Bou9VL6V+9T7qU++jPvWMP0al1UStw9Ott9563JntWrduzcaNG0lLSzvitYyMDGJiYo57nhUrVrBjxw4WLlx43G179eqF1Wpl165d1YYnPz8//Pz8jmi3Wq36wvQAve/eqbp+3WLP47lvdvPVlv890zSyexy3ndeejrHVh6bS0gPY7S+TkvIKDscfP0PMRERcjM02lfDwYVrM9hTR96p3Ur96H/Wp91Gfnlq1ea9rHZ4iIyOJjIw87nYDBgwgLy+PX375hb59+wKwevVq8vLyGDhw4HH3f/XVV+nduzenn378h763bNmCw+EgLi7u+BcgIvVuc3Ies7/ZxbKtf3qm6RihyTCcZGcvxW5PIivrC8AFgK9vLHFxk4mLm4y/f8KpvAQRERGRI9TbM0+dO3fmwgsvZPLkybz00ktA5VTlo0aNqjJZRKdOnZg5cyZjxoxxt+Xn5/P+++/z9NNPH3HcPXv28PbbbzNy5EgiIyPZunUrd911F2eccQaDBg2qr8sRkRrYcDCXZ7/Z5V7c9o/Z8249r121w/PKy9NJSXmNlJSXKC3d725v1uw8bLZEIiMvwWzWX95ERESkYajXdZ7efvttbrvtNoYNGwbA6NGjef7556tss2PHDvLy8qq0vfvuuxiGwVVXXXXEMX19ffnmm2+YPXs2hYWFJCQkcNFFF/HII49gsVjq72JE5Kj2F8CkN9fy/a5MoHKdpkt6xnPLkHZHTDluGAZ5eSuw2+eQkfEBhlE5w42PTzNiY2/AZptKYODxZ+MUEREROdXqNTyFh4czf/78Y25jGMYRbVOmTGHKlCnVbp+QkMD3339f7Wsicmr9si+b2V/v5Kc9PkAmFrOJS3vGc8uQ02j7l8VtKyrySE196/Bitlvc7SEhfbHZphIdPR6LRbNfioiISMNVr+FJRLyPYRis2pPFs9/u4ue92QCYTQZjz2jBree1p3VkUJXtCwrWYbcnkZb2Di5X5TTjZnMgMTFXY7NNJSSk9ym/BhEREZETofAkIjViGAY/7MrkuW928dvvOQBYLSYu6xVPh4r9TBjT1T1bjdNZQnr6Quz2ORQUrHYfIzCwMzZbIjExE7Bam3niMkREREROmMKTiByTYRh8vS2d57/dxYZDlc8n+vqYubpvS246py2RgT4sXrwfgOLindjtc0hNnUdFRWXAMpmsREaOJT4+kbCws2u8zpuIiIhIQ6PwJCLVcroMvtqcynPf7mJ7agEA/lYz1/ZrxZSz2xIdWrl4dVlZMT4+K9m8+Vny8r517+/n1wqb7Sbi4m7E1/f4a7uJiIiINHQKTyJSRYXTxacb7Lzw3W72ZFQ+oxTs58N1A1px41ltiAyuXHC6tPQQKSlzsdvnEhSUQuWkmSbCw0cSH59IePiFmEyaAVNERES8h8KTiABQVuHkwzXJzPl+DweyiwEIC7Dyt0Gt+dvANoQFWjEMF9nZS7Db55CZ+RngBMDlCqNly5uIj08kIKC15y5CREREpB4pPIk0ccXlFSz45SBzf9hLan4pABFBvkwa3JZr+7ckxN9KeXkmBw7Mw26fQ2npHve+YWHnEBMzmV9/9aNVq0vcE0aIiIiIeCOFJ5EmKr/UwVurfufVH/eRXVQOQGyoP5PPbstVfRMIsFrIz1/Ftn1JpKe/j2GUAWCxhBIbez0221SCgrrgcDiAxR68EhEREZFTQ+FJpInJLirntR/38cbK/RSUVQDQMjyQxHNPY2yveCwUk5Y2ly32ORQVbXTvFxzcm/j4RKKjr8RiCTra4UVERES8lsKTSBNhzy1h7oq9LPjlAKUOFwDto4O5ZUg7RvWIo7RkM7/vnUla2nyczkIAzOYAoqOvxGZLJDT0TE+WLyIiIuJxCk8iXm5vRiFzvt/Dx+uScTgNALrHh3HLkHZc0CmMzMwP2bghifz8le59AgI6Eh+fSEzMdVitzT1VuoiIiEiDovAk4qU2J+eRtHwPizenYFRmJvq3DeeWIe3oHZ9HSsrT/Pzz61RUZAFgMvkQGTkGmy2RZs3O1WK2IiIiIn+h8CTiRQzD4Jd92by4fA/f78xwt1/QOZqp57SmVdBP2O2P8ssvS92v+fklEBc3hbi4ifj5xXmibBEREZFGQeFJxAu4XAbfbk/nxeW7WXsgFwCzCS4+3caUQYEEORdit7/MlvLkw3uYCA+/EJstkYiIkVrMVkRERKQGFJ5EGjGH08VnG+zM+X4PO9MqJ3nw9TFzeW8bE3odpKLgn2TsWUTG4cVsrdZIYmMnYrNNISCgrSdLFxEREWl0FJ5EGqGScifv/XaQl3/YS3JuCQDBfj5c3z+MUe2/Jz/rdlL37XJvHxZ2FjZbIlFRl2E2+3mqbBEREZFGTeFJpBHJKSrnzVX/3969R0dV3+8ef+aayZ2QQDKTxAQwGFFAIYJEOIACWqv0pmCxohY8gKKitS5buhTPamXVrqo/L1hbqaCAoiIt/cktKreAF4jh7sFKAiFAiOGWGySTzD5/ROZXJMBMTiY7mbxfa+WP7PlO1jP5OLKf7GR/92v+p/v8G9smxTj0wNBKDUxaphPH3tOR0tOSJJstVsnJd8njmaqYmL5mxgYAAAgLlCegAzh44pRe31Ckd744oFPepl/B65UkPXDtNqVFvK/amkIdq2haGxNzlTyeaerefYLs9hgTUwMAAIQXyhPQju0pq9Jr6/Zq2bZDavA13W98WOZR3dV/jSIbPlBjQ6VqGySr1aVu3cbL45mquLjB3GYcAAAgBChPQDtz5nbjr60v0if/t1ySZLd4dVf/7bohY4VU/5lUJzVKiozMksczVSkp98jh6GpucAAAgDBHeQLaiUafodW7yvTa+iJtPXBCktQtqky/vHqD+sR/KMNXIdVLkk1JST+SxzNNCQnXy2KxmhkbAACg06A8ASY77W3UB18e1N82FKm4okYWNSon5UvdccXHSnJslGTI8ElOZ6o8njOb2aaaHRsAAKDToTwBJjleU68FnzXdOa+iul7xzuO67bKPNDozTxGWQ/51CQljvtvM9hZZrbxlAQAAzMKZGNDGDhyr1esbivTullKd8jYou+sO3X3NKl2ZuFEWNUiS7PZEud33yu2eoqioS01ODAAAAInyBLSZbQdO6K8birRix2G5bNUamvqxbuqxSomuEv+auLjc7zazvU02m8vEtAAAAPg+yhMQQj6foTV7yvXX9UX6vPiYesR9rXuuWKFcz3rZrXWSJJstRsnJv/huM9v+JicGAADA+VCegBA4cxOI1/OLVHr0qK51r9esIcuVGf+Nf010dF95PNOUnPwL2e2xJqYFAABAIChPQCs6Wl2ntz7br7c+3S+n9mpk+nIN7feJohw1kiSLxalu3W5Xauo0xcXlspktAABAB0J5AlrBN+XVmptfrH8WFuuKxE2a3Ge5Lk/c4X/c5eopj2eKUlLuldPZzcSkAAAAaCnKE9BChmHo071H9Xp+sbbu26kR6as0e+gqxUec+G6FVYmJtyo1dZoSEkazmS0AAEAHR3kCglTf4NO/th3S3PxvZPeu1fWXLNcvhhfIavFJkpxOt9zuyXK775PLlW5yWgAAALQWyhMQoOM19Vr0RYne31yoPl3+W/dmrVK3qCP+x7t0uV4ezzQlJf1IVqvDxKQAAAAIBcoTcBHflFfr7xuLtL1opYZ6PtTMnE2yW5s2s7XZEuR23yOPZ4qioi4zOSkAAABCifIENMMwDOV/U6E3N+6Qr/ZdjUxfoTED/2cz25iYQUpNnabu3cfLZos0MSkAAADaCuUJ+A+nvY3659aD+rBgtXpFv6fb0tYpwt60ma0sUXKnTJDHM02xsQPMDQoAAIA2R3kCJB2pPK2Fn+3RnuIFGpS8TL/M/tr/mCMiWxnpDygl5S7Z7fEmpgQAAICZKE/o1LYdOKF3P1sro2a+cj0facBl1ZIkQw4lJP5EmekPKD5+GJvZAgAAgPKEzqeh0aeVOw9o/Y4Fyox8V6O7bZe+27fWZ01Xj0umKdXzSzmdyeYGBQAAQLtCeUKncaymXu9v/lwHSv+qAUnLdXPaMUmSYVjkjBmj7J4PqWvXG2Wx2ExOCgAAgPaI8oSwt/vQCX24+W056t5Uv25fqHda02a2XiNRbvckXZp5v1yuDJNTAgAAoL2jPCEsNfoM5e3crcI9r6pX9BJdE1/mf8xrG6I+lz4od/LPZLU6TUwJAACAjoTyhLByrLpO/9ryTx3/9q+6InGdhnRr2sy23hej6PgJ6n/Zw4qJ6WNySgAAAHRElCeEhZ2lB7Vu66uKNxYqI3afMr67AUSN7wr1zHhAvTMnymaLNjckAAAAOjTKEzosb6NPedvWqGj/K+oVu1JXxJxqOu6LUIPzx7qmzyNK6jrY5JQAAAAIF5QndDhHTp7U6oK/qbF6njLjdunKhKbjld5MJSX/b+VmT5HT2dXckAAAAAg7lCd0CIZhaMveL7V1z38pxfFPpTsrpTip0WfTSWO0+l82Qz1Tx7CZLQAAAEKG8oR27VR9nVZ9+aaOf/s39YjdrKzv/mypsj5ZjtiJGtr/YcVGpZobEgAAAJ0C5QntUlHZN9q4/QXFGovVJaJCXWIln2FRRX2uemY+oOG9x7GZLQAAANoU5QntRkNjo9bv/EAlpXOUHrle6c6mzWxrvPE67Riv3H6PyJ2YbXJKAAAAdFbWUH7xP/zhD8rNzVVUVJS6dOkS0HMMw9CsWbPk8XgUGRmpESNGaNeuXWetqaur04MPPqikpCRFR0dr7NixKi0tDcErQGtasGOB7txxpxbsWHDW8fKTh7V47W/1j7wMWY+PU2b0WtmsPpWd6q/GuDkaM7JMPxvxGsUJAAAApgppeaqvr9ftt9+uadOmBfycZ599Vs8995xefvllbd68WSkpKRo9erSqqqr8a2bMmKGlS5fqnXfeUX5+vqqrq3XLLbeosbExFC8DreT5z59XTWONXvj8Bfl8Pn2xZ5XeXDFW27ZkKFmzleQ6qNMNUTrs/bk8l36uO36wVTcMmCaH3WV2dAAAACC0v7b39NNPS5LmzZsX0HrDMPTCCy9o5syZ+ulPfypJmj9/vpKTk7Vo0SJNmTJFJ0+e1Ny5c/XWW29p1KhRkqQFCxYoPT1dH330kW688caQvBa0zMaSjSo+XiyL1aKd5TslSXsqtmv2Eo+SXEcU75AcNqn81KVyxU/S9YOnKSYy3uTUAAAAwLna1d88FRcXq6ysTGPGjPEfi4iI0PDhw7Vp0yZNmTJFBQUF8nq9Z63xeDy68sortWnTpmbLU11dnerq6vyfV1ZWSpK8Xq+8Xm8IXxGGvjH0nGN1Pul3u4/4P/9s/Ar9qMdIWa1NF0KZScdyZl7MLXww0/DEXMMPMw0/zNQcwXy/21V5KisrkyQlJyefdTw5OVn79+/3r3E6nUpISDhnzZnnf9/s2bP9V8H+0+rVqxUVFdUa0dEMr8+rH3brpxXfbpfvPGtuSrxJZXvqtHLPyjbNhtaXl5dndgS0MmYanphr+GGm4YeZtq3a2tqA1wZdnmbNmtVsEflPmzdvVk5OTrBf2u/7G50ahnHRzU8vtOY3v/mNHn30Uf/nlZWVSk9P15gxYxQXF9finGjeN4d3a8tXL6qLZYke63NSY6ukKV+eu27+2Pn6+ZU/b/uAaFVer1d5eXkaPXq0HA6H2XHQCphpeGKu4YeZhh9mao4zv5UWiKDL0/Tp03XHHXdccE1mZmawX1aSlJKSIqnp6pLb7fYfLy8v91+NSklJUX19vY4fP37W1afy8nLl5uY2+3UjIiIUERFxznGHw8F/mK2kvsGrNdsWqbzsNaVGfab0CEOSdLIuSSX1AyStPuc5NruN738Y4f0UfphpeGKu4YeZhh9m2raC+V4HXZ6SkpKUlJQU7NMC0qNHD6WkpCgvL09XX321pKY79q1bt05//OMfJUkDBw6Uw+FQXl6exo0bJ0k6fPiwdu7cqWeffTYkuXB+xUeKtHH7fym68W0luL5VenTT8YO1g5XinqKb+94pz5Ftmr3rI7nsLuVE52hLzRadbjit3l17mxseAAAACEJI/+appKREx44dU0lJiRobG7V161ZJ0qWXXqqYmBhJUnZ2tmbPnq2f/OQnslgsmjFjhp555hllZWUpKytLzzzzjKKiojRhwgRJUnx8vCZNmqRf/epXSkxMVNeuXfXYY4+pb9++/rvvIbTqGxq1dvtSlR76iy6JWqs0R6PkkGq8saq03K7BV8zQCHdf//prUq/R8cePK8ISoZUrV+qmm25SnVGnOBe/MgkAAICOI6Tl6cknn9T8+fP9n5+5mrRmzRqNGDFCkrRnzx6dPHnSv+bxxx/XqVOndP/99+v48eMaPHiwVq9erdjYWP+a559/Xna7XePGjdOpU6d0ww03aN68ebLZbKF8OZ3evvKDWr/9ZbnqF6p71AH1bOq/OnKqrxK63adR/ScpwtH8DTjiXHH+O5lYrVbFOShOAAAA6FhCWp7mzZt30T2eDMM463OLxaJZs2Zp1qxZ532Oy+XSSy+9pJdeeqkVUuJC6ht8+mTHKpUcmKOM6DxdYq+T7NLphkid1FgNyJ6hEWnXmh0TAAAACLl2datytB97y7/V2q2vyVn3ptJj/63e310oOlbXSzFdJ2t432mKdLGZLQAAADoPyhP8Tnsblbc9X/tK5qhXzIfq5ayRnFKDz6ETxk3qlzVDw9NHXvS28QAAAEA4ojxBXx2u0CeF8+Wsf1NZXbar73d3gK/ypiqyyy91Xd/pinR1NzckAAAAYDLKUydVXdeg5YVfqPjAa8qOW6Yrok5IUZLPsKrSGKk+lz6krPRbZLFYzY4KAAAAtAuUp07EMAwV7K/Qmm2L5fK+pSsSt6h7N58k6VRjkiLjJ+raPg8rKuoSk5MCAAAA7Q/lqRP4tqpOy77cpn0HXle/rst0TfwR/2M1ylV2rwfVI/VnslrZyRoAAAA4H8pTmGpo9GndnnJ9smOZ4nyLNDB5o3qlNUiS6n1xioq/U1dnP6To6GyTkwIAAAAdA+UpzBR9W60PCr5S6cH5yun+L41OLvE/Vm+9SlmZ03VJ6gTZbJEmpgQAAAA6HspTGKiua9CH2w9p7c6PlWJ/R9e61ymnV50kqdGIVGzCeF3e60HFxg4wOSkAAADQcVGeOijDMPRF8TEtKfhG3377roZ6/lvje3ztf9xn661eGdOV6pkou53NbAEAAID/X5SnDqb0eK0++PKg1uz6VJfFfaD/5flYMd2qJUmGHIpP+LF6ZkxXfPwwNrMFAAAAWhHlqQOorW/Qyp1lWlKwT3XVH+r6S5br4X7b/Y9b7JcoM32q3O5JcjrZzBYAAAAIBcpTO2UYhjbvO64lBaXa+PV2XdP9Q92WvloJrmNNj8uihISblZ52v7p2vVEWi83kxAAAAEB4ozy1MyVHa7Xky1ItLSxRnHWTrk9fof8z5AtZLU2b2drs3ZXquU8ez31yuTJMTgsAAAB0HpSndqDqtFfLdxzWkoKD+upgsYam5Wn6lSvVParMvyY+foRSU6cpKenHslqdJqYFAAAAOifKk8nmrP1GL378tdKjd2rkJSt0X+98OaxNm9nabPFKSblbHs9URUdfbnJSAAAAoHOjPJksNWKVZg76k9Jj9/uPxcbmyOOZpu7d75DNFmViOgAAAABnUJ5M1ie5Ugfr9stqjVT37j+XxzNNcXE5ZscCAAAA8D2UJ5NlpE1WpDNKyckT5XAkmB0HAAAAwHlQnkzmdHZTWtrDZscAAAAAcBFWswMAAAAAQEdAeQIAAACAAFCeAAAAACAAlCcAAAAACADlCQAAAAACQHkCAAAAgABQngAAAAAgAJQnAAAAAAgA5QkAAAAAAkB5AgAAAIAAUJ4AAAAAIACUJwAAAAAIAOUJAAAAAAJAeQIAAACAAFCeAAAAACAAlCcAAAAACADlCQAAAAACYDc7gBkMw5AkVVZWmpykc/F6vaqtrVVlZaUcDofZcdBKmGv4YabhibmGH2YafpipOc50gjMd4UI6ZXmqqqqSJKWnp5ucBAAAAEB7UFVVpfj4+AuusRiBVKww4/P5dOjQIcXGxspisZgdp9OorKxUenq6Dhw4oLi4OLPjoJUw1/DDTMMTcw0/zDT8MFNzGIahqqoqeTweWa0X/qumTnnlyWq1Ki0tzewYnVZcXBz/QwhDzDX8MNPwxFzDDzMNP8y07V3sitMZ3DACAAAAAAJAeQIAAACAAFCe0GYiIiL01FNPKSIiwuwoaEXMNfww0/DEXMMPMw0/zLT965Q3jAAAAACAYHHlCQAAAAACQHkCAAAAgABQngAAAAAgAJQnAAAAAAgA5Qmtas6cOerRo4dcLpcGDhyoDRs2XHD9unXrNHDgQLlcLvXs2VN/+ctf2igpghHMXD/44AONHj1a3bp1U1xcnIYMGaJVq1a1YVoEItj36hkbN26U3W7XVVddFdqACFqwM62rq9PMmTOVkZGhiIgI9erVS3//+9/bKC0CFexcFy5cqP79+ysqKkput1v33nuvjh492kZpcTHr16/XrbfeKo/HI4vFon/84x8XfQ7nSu0L5QmtZvHixZoxY4ZmzpypwsJCDRs2TD/4wQ9UUlLS7Pri4mLdfPPNGjZsmAoLC/Xb3/5WDz30kJYsWdLGyXEhwc51/fr1Gj16tJYvX66CggKNHDlSt956qwoLC9s4Oc4n2JmecfLkSU2cOFE33HBDGyVFoFoy03Hjxunjjz/W3LlztWfPHr399tvKzs5uw9S4mGDnmp+fr4kTJ2rSpEnatWuX3nvvPW3evFmTJ09u4+Q4n5qaGvXv318vv/xyQOs5V2qHDKCVDBo0yJg6depZx7Kzs40nnnii2fWPP/64kZ2dfdaxKVOmGNdee23IMiJ4wc61OX369DGefvrp1o6GFmrpTMePH2/87ne/M5566imjf//+IUyIYAU70xUrVhjx8fHG0aNH2yIeWijYuf7pT38yevbsedaxF1980UhLSwtZRrScJGPp0qUXXMO5UvvDlSe0ivr6ehUUFGjMmDFnHR8zZow2bdrU7HM+/fTTc9bfeOON2rJli7xeb8iyInAtmev3+Xw+VVVVqWvXrqGIiCC1dKZvvPGG9u7dq6eeeirUERGklsx02bJlysnJ0bPPPqvU1FT17t1bjz32mE6dOtUWkRGAlsw1NzdXpaWlWr58uQzD0JEjR/T+++/rhz/8YVtERghwrtT+2M0OgPBQUVGhxsZGJScnn3U8OTlZZWVlzT6nrKys2fUNDQ2qqKiQ2+0OWV4EpiVz/b4///nPqqmp0bhx40IREUFqyUz//e9/64knntCGDRtkt/PPRnvTkpkWFRUpPz9fLpdLS5cuVUVFhe6//34dO3aMv3tqJ1oy19zcXC1cuFDjx4/X6dOn1dDQoLFjx+qll15qi8gIAc6V2h+uPKFVWSyWsz43DOOcYxdb39xxmCvYuZ7x9ttva9asWVq8eLG6d+8eqnhogUBn2tjYqAkTJujpp59W79692yoeWiCY96nP55PFYtHChQs1aNAg3XzzzXruuec0b948rj61M8HMdffu3XrooYf05JNPqqCgQCtXrlRxcbGmTp3aFlERIpwrtS/8CBGtIikpSTab7ZyfhpWXl5/zE5MzUlJSml1vt9uVmJgYsqwIXEvmesbixYs1adIkvffeexo1alQoYyIIwc60qqpKW7ZsUWFhoaZPny6p6cTbMAzZ7XatXr1a119/fZtkR/Na8j51u91KTU1VfHy8/9jll18uwzBUWlqqrKyskGbGxbVkrrNnz9Z1112nX//615Kkfv36KTo6WsOGDdPvf/97rlJ0QJwrtT9ceUKrcDqdGjhwoPLy8s46npeXp9zc3GafM2TIkHPWr169Wjk5OXI4HCHLisC1ZK5S0xWne+65R4sWLeJ37duZYGcaFxenHTt2aOvWrf6PqVOn6rLLLtPWrVs1ePDgtoqO82jJ+/S6667ToUOHVF1d7T/29ddfy2q1Ki0tLaR5EZiWzLW2tlZW69mndjabTdL/XK1Ax8K5Ujtk0o0qEIbeeecdw+FwGHPnzjV2795tzJgxw4iOjjb27dtnGIZhPPHEE8Zdd93lX19UVGRERUUZjzzyiLF7925j7ty5hsPhMN5//32zXgKaEexcFy1aZNjtduOVV14xDh8+7P84ceKEWS8B3xPsTL+Pu+21P8HOtKqqykhLSzNuu+02Y9euXca6deuMrKwsY/LkyWa9BDQj2Lm+8cYbht1uN+bMmWPs3bvXyM/PN3JycoxBgwaZ9RLwPVVVVUZhYaFRWFhoSDKee+45o7Cw0Ni/f79hGJwrdQSUJ7SqV155xcjIyDCcTqcxYMAAY926df7H7r77bmP48OFnrV+7dq1x9dVXG06n08jMzDReffXVNk6MQAQz1+HDhxuSzvm4++672z44zivY9+p/ojy1T8HO9KuvvjJGjRplREZGGmlpacajjz5q1NbWtnFqXEywc33xxReNPn36GJGRkYbb7TbuvPNOo7S0tI1T43zWrFlzwX8jOVdq/yyGwXVcAAAAALgY/uYJAAAAAAJAeQIAAACAAFCeAAAAACAAlCcAAAAACADlCQAAAAACQHkCAAAAgABQngAAAAAgAJQnAAAAAAgA5QkAAAAAAkB5AgAAAIAAUJ4AAAAAIACUJwAAAAAIwP8DOuj/wr1t6xkAAAAASUVORK5CYII=",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x600 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[10,6])\n",
    "title(L\"First iteration, from $x_0 = 0$\")\n",
    "left = -0.1\n",
    "right = 1.1\n",
    "x = range(left, right, 100)\n",
    "plot(x, f1.(x), label=L\"x - \\cos(x)\")\n",
    "plot([left, right], [0, 0], \"k\", label=\"x=0\")  # The x-axis, in black\n",
    "x_0 = 0\n",
    "plot([x_0], [f1(x_0)], \"g*\")\n",
    "plot(x, L_0.(x), \"y\", label=L\"L_0(x)\")\n",
    "plot([x_0], [f1(x_0)], \"g*\")\n",
    "x_1 = x_0 - f1(x_0)/Df1(x_0)\n",
    "println(\"x_1 = $x_1\")\n",
    "plot([x_1], [0], \"r*\")\n",
    "legend()\n",
    "grid(true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "L_1(x) = (x_1 - cos(x_1)) + (1 + sin(x_1))*(x - x_1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_2 = 0.7503638678402439\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x600 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[10,6])\n",
    "title(L\"Second iteration, from $x_1 = 1$\")\n",
    "# Shrink the domain\n",
    "left = 0.7\n",
    "right = 1.05\n",
    "x = range(left, right, 100)\n",
    "\n",
    "plot(x, f1.(x), label=L\"x - \\cos(x)\")\n",
    "plot([left, right], [0, 0], \"k\", label=\"x=0\")  # The x-axis, in black\n",
    "plot([x_1], [f1(x_1)], \"g*\")\n",
    "plot(x, L_1.(x), \"y\", label=L\"L_1(x)\")\n",
    "x_2 = x_1 - f1(x_1)/Df1(x_1)\n",
    "println(\"x_2 = $x_2\")\n",
    "plot([x_2], [0], \"r*\")\n",
    "legend()\n",
    "grid(true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "L_2(x) = (x_2 - cos(x_2)) + (1 + sin(x_2))*(x - x_2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_3 = 0.7391128909113617\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x600 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[10,6])\n",
    "title(L\"Third iteration, from $x_2=$\"*\"$x_2\")\n",
    "# Shrink the domain some more\n",
    "left = 0.735\n",
    "right = 0.755\n",
    "x = range(left, right, 100)\n",
    "plot(x, f1.(x), label=L\"x - \\cos(x)\")\n",
    "plot([left, right], [0, 0], \"k\", label=\"x=0\")  # The x-axis, in black\n",
    "plot([x_2], [f1(x_2)], \"g*\")\n",
    "plot(x, L_2.(x), \"y\", label=L\"L_2(x)\")\n",
    "x_3 = x_2 - f1(x_2)/Df1(x_2)\n",
    "println(\"x_3 = $x_3\")\n",
    "plot([x_3], [0], \"r*\")\n",
    "legend()\n",
    "grid(true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How accurate and fast is this?\n",
    "\n",
    "For the bisection method, we have seen in {ref}`section:root-finding-by-interval-halving`\n",
    "a fairly simple way to get an upper limit on the absolute error in the approximations.\n",
    "\n",
    "For absolute guarantees of accuracy, things do not go quite as well for Newton's method,\n",
    "but we can at least get a very \"probable\" *estimate* of how large the error can be.\n",
    "This requires some calculus, and more specifically Taylor's theorem,\n",
    "reviewed in {ref}`section:taylors-theorem`.\n",
    "\n",
    "So we will return to the question of both the speed and accuracy of Newton's method in {ref}`section:newtons-method-convergence-rate`.\n",
    "\n",
    "On the other hand, the example graphs above illustrate that the successive linearizations become ever more accurate as approximations of the function $f$ itself, so that the approximation $x_3$ looks \"perfect\" on the graph —\n",
    "the speed of Newton's method looks far better than for bisection.\n",
    "This will also be explained in {ref}`section:newtons-method-convergence-rate`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{exercise-start}\n",
    ":label: newtons-method-exercise-1\n",
    "```\n",
    "\n",
    "a) Show that Newton's method applied to\n",
    "\n",
    "$$ f(x) = x^k - a $$\n",
    "\n",
    "leads to fixed point iteration with function\n",
    "\n",
    "$$ g(x) = \\frac{(k-1) x + \\displaystyle \\frac{a}{x^{k-1}}}{k}. $$\n",
    "\n",
    "b) Then verify mathematically that the iteration $x_{k+1} = g(x_k)$ has super-linear convergence.\n",
    "\n",
    "```{exercise-end}\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{exercise-start}\n",
    ":label: newtons-method-exercise-2\n",
    "```\n",
    "\n",
    "a) Create a Julia function for Newton's method, with usage\n",
    "    \n",
    "    (root, error_estimate, iterations, function_evaluations) = newton_method(f, Df, x_0, error_tolerance, max_iterations)\n",
    "\n",
    "(The last input parameter `max_iterations` could be optional, with a default like `max_iterations=100`.)\n",
    "\n",
    "b) based on your function `bisection2` create a third (and final!) version with usage\n",
    "\n",
    "    (root, error_bound, iterations, function_evaluations) = bisection(f, a, b, error_tolerance, max_iterations)\n",
    "\n",
    "c) Use both of these to solve the equation\n",
    "\n",
    "$$ f_1(x) = 10 - 2x + \\sin(x) = 0 $$\n",
    "\n",
    "i) with [estimated] absolute error of no more than $10^{-6}$, and then\n",
    "\n",
    "ii) with [estimated] absolute error of no more than $10^{-15}$.\n",
    "\n",
    "Note in particular how many iterations and how many function evaluations are needed.\n",
    "\n",
    "Graph the function, which will help to find a good starting interval $[a, b]$ and initial approximation $x_0$.\n",
    "\n",
    "d) Repeat, this time finding the unique real root of\n",
    "\n",
    "$$ f_2(x) = x^3 - 3.3 x^2 + 3.63 x - 1.331 = 0 $$\n",
    "\n",
    "Again graph the function, to find a good starting interval $[a, b]$ and initial approximation $x_0$.\n",
    "\n",
    "e) This second case will behave differently than for $f_1$ in part (c): describe the difference.\n",
    "\n",
    "```{exercise-end}\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{exercise-start}\n",
    ":label: newtons-method-exercise-3\n",
    "```\n",
    "\n",
    "The normal convergence rate behavior of Newton's method to a root $r$ of function $f$ fails when $f'(r) = 0$:\n",
    "a *multiple root*.\n",
    "Let us investigate what happens then.\n",
    "An often useful strategy is to study first the simplest non-trivial case and seek a conjecture or intuition for more general situation.\n",
    "\n",
    "Thus, consider a very simple case of a multiple root, $f(x) = (x-a)^2$.\n",
    "Work out explicitly the behavior for this case, seeking an error relationship relating $e_{k+1}$ to $e_k$.\n",
    "This should show linear convergence, with convergence constant $C \\neq 0$.\n",
    "\n",
    "a) Based on the above, a plausible conjecture is that this behavior is general for any *double root*\n",
    "$f(r) = 0$, $f'(r) = 0$, $f''(r) \\neq 0$, so try to verify this.\n",
    "\n",
    "b)(*)\n",
    "Seek a conjecture about what happens more generally for multiple roots of order $p$:\n",
    "all derivative of order less than $p$ vanish at the root $r$ and $f^{(p)}(r) \\neq 0$.\n",
    "Mimic the strategy above, by studying the simplest case that is neither a simple nor a double root.\n",
    "\n",
    "```{prf:remark}\n",
    ":label: remark-11-newtons-method\n",
    "\n",
    "A possible solution for this slow-down is studied in {ref}`newtons-method-convergence-rate-exercise-2`\n",
    "```\n",
    "\n",
    "```{exercise-end}\n",
    "```"
   ]
  }
 ],
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