{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "instrumental-peace",
   "metadata": {},
   "source": [
    "(section:least-squares)=\n",
    "# Least-squares Fitting to Data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "695fb14c-34d1-4c12-acf1-7b1497ebd67e",
   "metadata": {},
   "source": [
    "**Last revised on August 27, 2025**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b6fe15e-a215-40b1-bab6-d06b76e2b752",
   "metadata": {},
   "source": [
    "**References:**\n",
    "\n",
    "- {cite}`Sauer` Chapter 4, *Least Squares*, Sections 1 and 2.\n",
    "\n",
    "- {cite}`Burden-Faires` Section 8.1, *Discrete Least Squares Approximation*.\n",
    "\n",
    "- {cite}`Chenney-Kincaid` Sections 9.1, *Method of Least Squares*, and 9.3 *Examples of the Least Squares Principle*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "another-saying",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib.pyplot import figure, plot, title, legend, grid, loglog\n",
    "from numpy.random import random\n",
    "from numerical_methods import solve_linear_system\n",
    "from numerical_methods import evaluate_polynomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e31e3991-b3bf-4eba-be46-cfbe227e266c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numerical_methods as nm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "romance-premises",
   "metadata": {},
   "source": [
    "We have seen that when trying to fit a curve to a large collection of data points, fitting a single polynomial to all of them can be a bad approach.\n",
    "This is even more so if the data itself is inaccurate, due for example to measurement error.\n",
    "\n",
    "Thus an important approach is to find a function of some simple form that is close to the given points but not necesarily fitting them exactly:\n",
    "given $N$ points\n",
    "\n",
    "$$(x_i, y_i),\\; 1 \\leq i \\leq N \\quad \\text{ (or $0 \\leq i < N$ with Python!)}$$\n",
    "\n",
    "we seek a function $f(x)$ so that the errors at each point,\n",
    "\n",
    "$$e_i = y_i - f(x_i),$$\n",
    "\n",
    "are \"small\" overall, in some sense.\n",
    "\n",
    "Two important choices for the function $f(x)$ are\n",
    "\n",
    "(a) polynomials of low degree, and\n",
    "\n",
    "(b) periodic sinusidal functions;\n",
    "\n",
    "we will start with the simplest case of fitting a straight line."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "pressing-garbage",
   "metadata": {},
   "source": [
    "## Measuring \"goodness of fit\": several options\n",
    "\n",
    "The first decision to be made is how to measure the overall error in the fit, since the error is now a vector of values $e = \\{e_i\\}$, not a single number.\n",
    "Two approaches are widely used:\n",
    "\n",
    "* *Min-Max*: minimize the maximum of the absolute errors at each point,\n",
    "$\\displaystyle \\|e\\|_{max} \\text{ or } \\|e\\|_\\infty, = \\max_{1 \\leq i \\leq n} |e_i|$\n",
    "\n",
    "* *Least Squares*: Minimize the sum of the squares of the errors,\n",
    "$\\displaystyle \\sum_1^n e_i^2$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "hungarian-taiwan",
   "metadata": {},
   "source": [
    "## What doesn't work\n",
    "\n",
    "Another seemingly natural approach is:\n",
    "\n",
    "* Minimize the sum of the absolute errors,\n",
    "$\\displaystyle \\|e\\|_1 = \\sum_1^n |e_i|$\n",
    "\n",
    "but this often fails completely.\n",
    "In the following example, all three lines minimize this measure of error, along with infinitely many others: any line that passes below half of the points and above the other half."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "early-wesley",
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xdata = [1., 2., 3., 4.]\n",
    "ydata = [0., 3., 2., 5.]\n",
    "\n",
    "figure(figsize=[12,6])\n",
    "plot(xdata, ydata, 'b*', label=\"Data\")\n",
    "xplot = np.linspace(0.,5.)\n",
    "ylow = xplot -0.5\n",
    "yhigh = xplot + 0.5\n",
    "yflat = 2.5*np.ones_like(xplot)\n",
    "plot(xplot, ylow, label=\"low\")\n",
    "plot(xplot, yhigh, label=\"high\")\n",
    "plot(xplot, yflat, label=\"flat\")\n",
    "legend(loc=\"best\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "environmental-saturday",
   "metadata": {},
   "source": [
    "The Min-Max method is important and useful, but computationally difficult.\n",
    "One hint is the presence of absolute values in the formula, which get in the way of using calculus to get equations for the minimum.\n",
    "\n",
    "Thus the easiest and most common approach is **Least Squares**, or equivalently, minimizing the root-mean-square error, which is just the Euclidean length $\\|e\\|_2$ of the error vector $e$.\n",
    "That \"geometrical\" interpretation of the goal can be useful.\n",
    "So we start with that."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "material-monitor",
   "metadata": {},
   "source": [
    "## Linear least squares\n",
    "\n",
    "The simplest approach is to seek the straight line $y = f(x) = c_0 + c_1x$ that minimizes the total square sum error,\n",
    "\n",
    "$$E(c_0, c_1) = \\sum_i e_i^2 = \\sum_i (c_0 + c_1x_i - y_i)^2.$$\n",
    "\n",
    "Note well that the unknowns here are just the two values $c_0$ and $c_1$, and\n",
    "$E$ is s fairly simple polynomial function of them.\n",
    "The minimum error must occur at a critical point of this function, where both partial derivatives are zero:\n",
    "\n",
    "$$\\frac{\\partial E}{\\partial c_0} = 2 \\sum_i (c_0 + c_1x_i - y_i) = 0,$$\n",
    "\n",
    "$$\\frac{\\partial E}{\\partial c_1} = 2 \\sum_i (c_0 + c_1x_i - y_i) x_i = 0.$$\n",
    "\n",
    "These are just simultaneous linear equations, which is the secret of why the least squares approach is so much easier than any alternative.\n",
    "The equations are:\n",
    "\n",
    "$$\n",
    "\\left[\\begin{array}{cc} \\sum_i 1 & \\sum_i x_i \\\\ \\sum_i x_i & \\sum_i x_i^2 \\end{array}\\right]\n",
    "\\left[\\begin{array}{c} c_0 \\\\ c_1 \\end{array}\\right]\n",
    "=\n",
    "\\left[\\begin{array}{c} \\sum_i y_i \\\\ \\sum_i x_iy_i \\end{array}\\right]\n",
    "$$\n",
    "\n",
    "where of course $\\sum_i 1$ is just $N$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "necessary-fluid",
   "metadata": {},
   "source": [
    "It will help later to introduce the notation\n",
    "\n",
    "$$m_j = \\sum_i x_i^j, \\quad p_j = \\sum_i x_i^j y_i$$\n",
    "\n",
    "so that the equations are\n",
    "\n",
    "$$M c = p$$\n",
    "\n",
    "with\n",
    "\n",
    "$$\n",
    "M = \\left[\\begin{array}{cc} m_0 & m_1 \\\\ m_1 & m_2\\end{array}\\right],\n",
    "p = \\left[\\begin{array}{c} p_0 \\\\ p_1 \\end{array}\\right],\n",
    "c = \\left[\\begin{array}{c} c_0 \\\\ c_1 \\end{array}\\right].\n",
    "$$\n",
    "\n",
    "(0-based indexing wins this time.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d42ab0a2-36d3-42ab-88fd-6e46d53bdeff",
   "metadata": {},
   "outputs": [],
   "source": [
    "def line_fit(x, y):\n",
    "    m0 = len(x)\n",
    "    m1 = sum(x)\n",
    "    m2 = sum(x**2)\n",
    "    M = np.array([[m0, m1], [m1, m2]])\n",
    "    p = np.array([sum(y), sum(x*y)])\n",
    "    c = solve_linear_system(M, p)\n",
    "    return c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "brief-edward",
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The coefficients are [3.04698488 1.94139219]\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 10\n",
    "x = np.linspace(-1, 1, N)\n",
    "# Emulate a straight line with measurement errors:\n",
    "# random(N) gives N values uniformly distributed in the range [0,1],\n",
    "# and so with mean 0.5.\n",
    "# Thus subtracting 1/2 simulates more symmetric \"errors\", of mean zero.\n",
    "yline = 2*x + 3\n",
    "y = yline + (random(N) - 0.5)\n",
    "\n",
    "figure(figsize=[12,6])\n",
    "plot(x, yline, 'g', label=\"The original line\")\n",
    "plot(x, y, '*', label=\"Data\")\n",
    "c = line_fit(x, y)\n",
    "print(\"The coefficients are\", c)\n",
    "xplot = np.linspace(-1, 1, 100)\n",
    "plot(xplot, evaluate_polynomial(xplot, c), 'r', label=\"Linear least squares fit\")\n",
    "legend(loc=\"best\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "streaming-defendant",
   "metadata": {},
   "source": [
    "## Least squares fiting to higher degree polynomials\n",
    "\n",
    "The method above extends to finding a polynomial\n",
    "\n",
    "$$p(x) = c_0 + c_1 x + \\cdots + c_n x^n$$\n",
    "\n",
    "that gives the best least squares fit to data\n",
    "\n",
    "$$(x_1, y_1), \\dots (x_N, y_N)$$\n",
    "\n",
    "in that the coefficients $c_k$ given the minimum of\n",
    "\n",
    "$$\n",
    "E(c_0, \\dots c_n) = \\sum_i(p(x_i) - y_i)^2\n",
    "= \\sum_i \\left( y_i - \\sum_k c_k x_i^k \\right)^2\n",
    "$$\n",
    "\n",
    "Note that when $N=n+1$, the solution is the interpolating polynomial, with error zero."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "colored-sweet",
   "metadata": {},
   "source": [
    "The necessary conditions for a minimum are that all $n+1$ partial derivatives of $E$ are zero:\n",
    "\n",
    "$$\n",
    "\\frac{\\partial E}{\\partial c_j} = 2 \\sum_i \\left( y_i - \\sum_k c_k x_i^k\\right) x_i^j = 0,\n",
    "\\; 0 \\leq j \\leq n.\n",
    "$$\n",
    "\n",
    "This gives\n",
    "\n",
    "$$\n",
    "\\sum_i \\sum_k \\left( c_k x_i^{j+k} \\right) = \\sum_k \\left( \\sum_i x_i^{j+k} \\right) c_k = \\sum_i y_i x_i^j, \\; 0 \\leq j \\leq n,\n",
    "$$\n",
    "\n",
    "or with the notation $m_k = \\sum_i x_i^k$, $p_k = \\sum_i x_i^k y_i$ introduced above,\n",
    "\n",
    "$$\n",
    "\\sum_k m_{j+k} c_k = p_j,\\; 0 \\leq j \\leq n.\n",
    "$$\n",
    "\n",
    "That is, the equations are again $Mc = p$, but now with\n",
    "\n",
    "$$\n",
    "M = \\left[\\begin{array}{cccc}\n",
    "m_0 & m_1 & \\dots & m_n \\\\\n",
    "m_1 & m_2 & \\dots & m_{n+1} \\\\\n",
    "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
    "m_n & m_{n+1} & \\dots & m_{2n}\n",
    "\\end{array}\\right],\n",
    "\\quad\n",
    "p = \\left[\\begin{array}{c} p_0 \\\\ p_1 \\\\ \\vdots \\\\ p_n \\end{array}\\right],\n",
    "\\quad\n",
    "c = \\left[\\begin{array}{c} c_0 \\\\ c_1 \\\\ \\vdots  \\\\ c_n \\end{array}\\right].\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1a06227-f597-4646-b387-2caab92b629c",
   "metadata": {},
   "source": [
    "```{prf:remark} Alternative geometrical derivation\n",
    ":label: geometrical-derivation-of-least-squares\n",
    "\n",
    "In the next section {doc}`least-squares-fitting-appendix-geometrical-approach`,\n",
    "another way to derive this result is given, using geometry and linear algebra instead of calculus.\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ec6ba21c-b9c6-41a1-87e5-153495d8232e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def fit_polynomial_least_squares(x, y, n):\n",
    "    \"\"\"Compute the coeffients c_i of the polynomial of degree n that give the best least squares fit to data (x[i], y[i]).\n",
    "    \"\"\"\n",
    "    N = len(x)\n",
    "    m = np.zeros(2*n+1)\n",
    "    for k in range(2*n+1):\n",
    "        m[k] = sum(x**k)\n",
    "    M = np.zeros([n+1,n+1])\n",
    "    for i in range(n+1):\n",
    "        for j in range(n+1):\n",
    "             M[i, j] = m[i+j]\n",
    "    p = np.zeros(n+1)\n",
    "    for k in range(n+1):\n",
    "        p[k] = sum(x**k * y)\n",
    "    c = solve_linear_system(M, p)\n",
    "    return c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "armed-baghdad",
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The coefficients are [ 1.74358819e-06  9.99724141e-01  2.09252099e-03 -1.72087272e-01\n",
      "  5.99447486e-03  5.74628644e-03]\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1400x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N =10\n",
    "n = 5\n",
    "xdata = np.linspace(0, np.pi/2, N)\n",
    "ydata = np.sin(xdata)\n",
    "\n",
    "figure(figsize=[14,5])\n",
    "plot(xdata, ydata, 'b*', label=\"sin(x) data\")\n",
    "xplot = np.linspace(-0.5, np.pi/2 + 0.5, 100)\n",
    "plot(xplot, np.sin(xplot), 'b', label=\"sin(x) curve\")\n",
    "c = fit_polynomial_least_squares(xdata, ydata, n)\n",
    "print(\"The coefficients are\", c)\n",
    "plot(xplot, evaluate_polynomial(xplot, c), 'r', label=\"Cubic least squares fit\")\n",
    "legend(loc=\"best\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "informed-failing",
   "metadata": {},
   "source": [
    "The discrepancy between the original function $\\sin(x)$ and this cubic is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "excess-there",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1400x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[14,5])\n",
    "plot(xplot, np.sin(xplot) - evaluate_polynomial(xplot, c))\n",
    "title(\"errors fitting at N = 10 points\")\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "advanced-january",
   "metadata": {},
   "source": [
    "What if we fit at more points?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "proud-token",
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The coefficients are [ 1.07391198e-05  9.99651567e-01  2.26782013e-03 -1.72246629e-01\n",
      "  6.03896848e-03  5.74935574e-03]\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1400x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 50\n",
    "xdata = np.linspace(0, np.pi/2, N)\n",
    "ydata = np.sin(xdata)\n",
    "\n",
    "figure(figsize=[14,5])\n",
    "plot(xdata, ydata, 'b.', label=\"sin(x) data\")\n",
    "plot(xplot, np.sin(xplot), 'b', label=\"sin(x) curve\")\n",
    "c = fit_polynomial_least_squares(xdata, ydata, n)\n",
    "print(\"The coefficients are\", c)\n",
    "plot(xplot, evaluate_polynomial(xplot, c), 'r', label=\"Cubic least squares fit\")\n",
    "legend(loc=\"best\")\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "accepted-laundry",
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABJcAAAHBCAYAAADU5lqlAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8hTgPZAAAACXBIWXMAAA9hAAAPYQGoP6dpAAB240lEQVR4nO3de1xUdf7H8fcMDFdhEJGb4jXzkpq3UjRTM5XMLLtYubHZutZm1s/VtpvtRrWr271drWxbN9usbHfLrVZzNVPLFc0MU7yg5l1BvCCgCAzM+f0BM4JcBAQOMK/no3nAnPmeM5+ZvhycN9/v91gMwzAEAAAAAAAA1IDV7AIAAAAAAADQeBEuAQAAAAAAoMYIlwAAAAAAAFBjhEsAAAAAAACoMcIlAAAAAAAA1BjhEgAAAAAAAGqMcAkAAAAAAAA1RrgEAAAAAACAGiNcAgAAAAAAQI0RLgEAgAZv//79uvHGGxUaGiqLxaJp06Zp//79slgsWrBggbvdunXrlJCQoNOnT5c5xptvvlmqbcljX3ichmjWrFn697//XeX2FotFFotFf/zjH8s8tmDBAlksFn3//fe1WGHVa7rwVl6N6enpmjhxosLCwhQQEKDY2FitXLmyXustqV27dpo4cWKN9v3www/1+uuv12o9AAA0JBbDMAyziwAAAKjMuHHj9O233+qvf/2rIiMjFRUVpcjISCUlJaljx45q2bKlJOnll1/Wb37zG+3bt0/t2rUrdYzu3bsrLCxMq1evLrU9Ly+vzHEaombNmun222+vcghmsVgkSXa7XXv37lVoaKj7sQULFui+++7Txo0b1a9fv7oot8Kabr/9ds2YMaPU9jZt2ig6Otp9Py8vT/369dPp06f1xz/+UeHh4XrjjTe0ZMkSffXVVxoyZEi91eySlJSk4OBgdezYsdr7jhkzRsnJydq/f3/tFwYAQAPgbXYBAADAfA6HQxaLRd7eZf9pkJOTo4CAgBof2zAM5ebmyt/fv8bHSE5O1tVXX61bbrml1PYBAwbU+Jguvr6+tXKchuj666/X6tWr9Yc//EGvvPKK2eVIkiIiIi76fs+fP1/Jyclat26dYmNjJUnDhg3TlVdeqccee0wbNmyoj1JL6d27d70/JwAAjQXT4gAAaEJ2796tCRMmKDw8XL6+vurataveeOONUm1Wr14ti8Wi999/XzNmzFCrVq3k6+urPXv2aOLEiWrWrJm2bt2qkSNHKigoSMOHD5cknTp1SlOmTFGrVq3k4+OjDh06aObMmcrLyyt1fIvFoqlTp2revHnq2rWrfH199d5770mS3nrrLV155ZVq1qyZgoKC1KVLFz311FMVvh5XrXv27NGXX37pnka1f//+MtPZEhIS9Jvf/EaS1L59e3fb1atXq127dtq2bZvWrFnj3u4a2VTetLiEhARZLBZt27ZNd999t+x2uyIiIvSLX/xCmZmZpWo8ffq0Jk2apNDQUDVr1kw33nij9u7dK4vFooSEhEr/f+Xm5mrGjBnq1auX7Ha7QkNDFRsbq88++6zMe3r27Fm999577vqHDh1a6bElqXPnzpo0aZLeeOMNHThw4KLtG4rFixerc+fO7mBJkry9vXXPPffou+++05EjRyrdf+jQoerevbu+/fZbDRgwQP7+/mrVqpV++9vfqrCwsFTbqvbrC6fFufrmRx99pJkzZyo6OlrBwcG6/vrrlZKSUqqWJUuW6MCBA6WmArpU92cCAICGiJFLAAA0Edu3b9fAgQPVpk0bvfLKK4qMjNR///tfPfLIIzpx4oSeeeaZUu2ffPJJxcbGat68ebJarQoPD5ck5efna+zYsXrggQf0xBNPqKCgQLm5uRo2bJh++uknPfvss+rZs6e+/fZbzZ49W5s3b9aSJUtKHfvf//63vv32W/3ud79TZGSkwsPDtWjRIk2ZMkUPP/ywXn75ZVmtVu3Zs0fbt2+v8DX16dNHiYmJGjdunDp27KiXX35ZkhQVFaXU1NRSbX/5y1/q1KlTmjNnjj799FNFRUVJkrp166bFixfr9ttvl91u15tvvimpaMTSxdx222268847NWnSJG3dulVPPvmkJOlvf/ubJMnpdOqmm27S999/r4SEBHe9cXFxFz22VDT969SpU3r00UfVqlUr5efn66uvvtKtt96qd999Vz//+c8lSYmJibruuus0bNgw/fa3v5UkBQcHV+k5EhIS9P777+u3v/2t/v73v1dpn5IKCgqq1M7Ly6tUaFKRDz/8UPPnz5fT6VT37t01depU3XfffaXaJCcna/DgwWX27dmzpyRp27ZtatWqVaXPk5aWprvuuktPPPGEnnvuOS1ZskS///3vlZGRoblz50pStft1eZ566ikNGjRIf/3rX5WVlaXHH39cN910k3bs2CEvLy+9+eabuv/++/XTTz9p8eLFpfatyc8EAAANkgEAAJqEUaNGGa1btzYyMzNLbZ86darh5+dnnDp1yjAMw1i1apUhybj22mvLHOPee+81JBl/+9vfSm2fN2+eIcn4xz/+UWr7Cy+8YEgyli9f7t4mybDb7e7nK1lHSEhIjV5b27ZtjRtvvLHUtn379hmSjHfffde97aWXXjIkGfv27StzjCuuuMIYMmRIme3lHeeZZ54xJBkvvvhiqbZTpkwx/Pz8DKfTaRiGYSxZssSQZLz11lul2s2ePduQZDzzzDPVep0FBQWGw+EwJk2aZPTu3bvUY4GBgca9995b5WNJMh566CHDMAxj5syZhtVqNX788UfDMAzj3XffNSQZGzdurPQYrvemKrdVq1ZdtKYJEyYYH3zwgfHNN98Y//rXv4wbbrjBkGQ8/fTTpdrZbDbjgQceKLP/unXrDEnGhx9+WOnzDBkyxJBkfPbZZ6W2T5482bBarcaBAwcMw6hev27btm2p99/1czR69OhS+/7jH/8wJBmJiYnubTfeeKPRtm3bMnVeys8EAAANCdPiAABoAnJzc7Vy5UqNGzdOAQEBKigocN9Gjx6t3NxcrV+/vtQ+t912W4XHu/Cxr7/+WoGBgbr99ttLbXdNE7rwKl7XXXedmjdvXmrb1VdfrdOnT+vuu+/WZ599phMnTlT3Zda7sWPHlrrfs2dP5ebmKj09XZK0Zs0aSdL48eNLtbv77rur/Bz//Oc/NWjQIDVr1kze3t6y2WyaP3++duzYcYnVn/fYY48pNDRUjz/+eLX2i46O1saNG6t069u370WP98EHH2jChAkaPHiwbrvtNi1dulRjxozRH//4Rx0/frxU28pGQVVlhFRQUFCZ/38TJkyQ0+nUN998I6n6/bo85fURSVWahtgYfyYAACgP4RIAAE3AyZMnVVBQoDlz5shms5W6jR49WpLKfHB1TRu7UEBAQJkpVydPnlRkZGSZD/Xh4eHy9vbWyZMnL3rs+Ph4/e1vf9OBAwd02223KTw8XP3799eKFSuq/XrrS4sWLUrdd02lO3funKSi98Xb27vUldikokWrq+LTTz/V+PHj1apVKy1cuFCJiYnauHGjfvGLXyg3N7cWXkGR4OBgPf3001q2bJlWrVpV5f18fHzUq1evKt2aNWtWo9ruueceFRQU6Pvvv3dva9GiRZk+JRWtjySpzPtdnvL+H0RGRkqS+9jV7dfluVgfqUxj/JkAAKA8hEsAADQBzZs3l5eXlyZOnFjhyBJXyORS0eiP8ra3aNFCx44dk2EYpbanp6eroKBAYWFhVTr2fffdp3Xr1ikzM1NLliyRYRgaM2ZMo1psuqQWLVqooKDAHXq4pKWlVWn/hQsXqn379vr44491yy23aMCAAerXr1+ZxaRrw4MPPqj27dvr8ccfL/P/sSL79+8vE1ZWdHON4qouVy1W6/l/lvbo0UNbt24t09a1rXv37hc97rFjx8psc/1/cQVC1e3XdaGp/UwAADwTC3oDANAEBAQEaNiwYUpKSlLPnj3l4+NTq8cfPny4/vGPf+jf//63xo0b597uWiDadUW5qgoMDNQNN9yg/Px83XLLLdq2bZvatm17yXVWNmrE19e3SqNJqmPIkCF68cUX9fHHH+vBBx90b1+0aFGV9rdYLPLx8SkVxqWlpZW5Wpx06fX7+Pjo97//vX72s59VOTRxTYuris6dO9eorvfff182m63UtLpx48ZpypQp2rBhg/r37y+paGHxhQsXqn///oqOjr7ocbOzs/X555+Xmrb24Ycfymq16tprr5VU+/26IlX5f1dXPxMAANQHwiUAAJqIP/3pT7rmmms0ePBgPfjgg2rXrp2ys7O1Z88effHFF/r6669rfOyf//zneuONN3Tvvfdq//796tGjh9auXatZs2Zp9OjRuv766y96jMmTJ8vf31+DBg1SVFSU0tLSNHv2bNntdl111VU1rq2kHj16SCp6L+69917ZbDZ17txZQUFB6tGjhxYtWqSPP/5YHTp0kJ+fn7t9TcXFxWnQoEGaMWOGsrKy1LdvXyUmJrrDiZKjccozZswYffrpp5oyZYpuv/12HTp0SM8//7yioqK0e/fuMq9t9erV+uKLLxQVFaWgoKBqBzp33323Xn75ZX355ZdVau/j46N+/fpV6zkq8tJLL2n79u0aPny4WrdurfT0dM2fP1/Lly9XQkJCqcDrF7/4hd544w3dcccd+uMf/6jw8HC9+eabSklJ0VdffVWl52vRooUefPBBHTx4UJdffrmWLl2qd955Rw8++KDatGkjqXb6dVX06NFDn376qd566y317dtXVqtV/fr1q5efCQAA6gPhEgAATUS3bt30ww8/6Pnnn9fTTz+t9PR0hYSEqFOnTmWmxFWXn5+fVq1apZkzZ+qll17S8ePH1apVKz366KN65plnqnSMwYMHa8GCBfrHP/6hjIwMhYWF6ZprrtHf//53tWzZ8pLqcxk6dKiefPJJvffee3rnnXfkdDq1atUqDR06VM8++6xSU1M1efJkZWdnq23bttq/f/8lPZ/VatUXX3yhGTNm6I9//KPy8/M1aNAgLVy4UAMGDFBISEil+993331KT0/XvHnz9Le//U0dOnTQE088ocOHD+vZZ58t1fZPf/qTHnroId11113KycnRkCFDtHr16mrVa7FY9MILL2jkyJHVfKWXrkuXLvr888+1ZMkSZWRkyN/fX7169dJHH32ku+66q1RbX19frVy5Uo899pgefvhh5eTkqFevXvryyy81ZMiQKj1fZGSk3njjDT366KPaunWrQkND9dRTT5V6X2ujX1fF//3f/2nbtm166qmnlJmZKcMwZBhGvfxMAABQHyxGVSfdAwAAoEo+/PBD/exnP9P//vc/DRw40OxyPM7QoUN14sQJJScnm10KAAAegZFLAAAAl+Cjjz7SkSNH1KNHD1mtVq1fv14vvfSSrr32WoIlAADgEQiXAAAALkFQUJAWLVqk3//+9zp79qyioqI0ceJE/f73vze7NAAAgHrBtDgAAAAAAADUWOWXMAEAAAAAAAAqQbgEAAAAAACAGiNcAgAAAAAAQI2xoPclcDqdOnr0qIKCgmSxWMwuBwAAAAAAoFYYhqHs7GxFR0fLaq18bBLh0iU4evSoYmJizC4DAAAAAACgThw6dEitW7eutA3h0iUICgqSVPRGBwcHm1xNzTgcDi1fvlwjR46UzWYzuxygXtH/4cno//Bk9H94Mvo/PBn9v3qysrIUExPjzj4qQ7h0CVxT4YKDgxt1uBQQEKDg4GB+uOBx6P/wZPR/eDL6PzwZ/R+ejP5fM1VZBogFvQEAAAAAAFBjhEsAAAAAAACoMcIlAAAAAAAA1BjhEgAAAAAAAGqMcAkAAAAAAAA1RrgEAAAAAACAGiNcAgAAAAAAQI0RLgEAAAAAAKDGCJcAAAAAAABQY4RLAAAAAAAAqDHCJQAAAAAAANRYnYdLb775ptq3by8/Pz/17dtX3377baXt16xZo759+8rPz08dOnTQvHnzyrT55JNP1K1bN/n6+qpbt25avHhxtZ/XMAwlJCQoOjpa/v7+Gjp0qLZt23ZpLxYAAAAAAMDD1Gm49PHHH2vatGmaOXOmkpKSNHjwYN1www06ePBgue337dun0aNHa/DgwUpKStJTTz2lRx55RJ988om7TWJiou68807Fx8frxx9/VHx8vMaPH68NGzZU63lffPFFvfrqq5o7d642btyoyMhIjRgxQtnZ2XX3hgAAAAAAADQxFsMwjLo6eP/+/dWnTx+99dZb7m1du3bVLbfcotmzZ5dp//jjj+vzzz/Xjh073Nt+9atf6ccff1RiYqIk6c4771RWVpa+/PJLd5u4uDg1b95cH330UZWe1zAMRUdHa9q0aXr88cclSXl5eYqIiNALL7ygBx54oEqvLysrS3a7XZmZmQoODq7GO9NwOBwOLV26VKNHj5bNZjO7HKBeNZT+bxiGCpyG8gucchQ6lV/olGFITsOQ05CcTqPE/aJthmHIdfK2WiTJIotFslosskju71X8vbfVKi+rpdTN2/W9xSJr0UHgQRpK/wfMQP9HXXL9Xi8oNFTgdBZ/Lf19odMpR2Hx73Vn2d/xhc7z3zuNot/lRb/fS/y+t5z/N4C1eJu3l0U+Xlb5eFtl8yq6+Xhb3du8rBb6Pzwa/b96qpN5eNdVEfn5+dq0aZOeeOKJUttHjhypdevWlbtPYmKiRo4cWWrbqFGjNH/+fDkcDtlsNiUmJurXv/51mTavv/56lZ933759SktLK/Vcvr6+GjJkiNatW1flcAmA5yl0Gso851BGTr5O5+Qr42zR92fzCnQ2v1A5+QU6m1f8Nb9QOSW25+QXKs9RFCAV3YoCpfxCp9kvqziAKgqbbFarvL0s8vayymYt+urtVRRGeVutsnkXbbd5FX3v41Viu1fR/jbvosd9iv9h6+1V8r6l+Bjn29lc2y/43ttqlU9xmwvrcddptchiIRxrKFwfhAqdRR+OCpzO4q/G+a+FFWwv/uBV7nbX/cLS28u2LfrqdH01ivZxGq7nVPF+xV+LA9zCEu0LS3wtLLXt/AfAQmfJD4ClH3M6zwfAJT8sutq4wmIV/edu69puSMWPlf3738X+JOj6USiKmaULvrg/kFqKv5el7DbXB9eiW9GHWav1/Lbzjxd9dQXWFotFXhbJy2pxb7cWh9fe7m1FYbfV6mprlZdVJUJvq/sD8oUhuJeX677Vvd193vKylrpftH/pdt5e5+8bzkKln5MOnsqRn69PqfPf+efh/NIQFToNOQqLzgmOEn+UcRQWbXf9ocZ9v8S2kl/zC40y2/NKPX5h28IKn8O1rcBpuLc3VFaL5ONtlbfhpZd3fqtmfjY18/VSoK+3An291cyn+Kuvl5r5eSs00FctAn3UopmPWjQr+t7P5mX2ywDQANVZuHTixAkVFhYqIiKi1PaIiAilpaWVu09aWlq57QsKCnTixAlFRUVV2MZ1zKo8r+treW0OHDhQ4WvKy8tTXl6e+35WVpakovTT4XBUuF9D5qq7sdYPXApXv8/Pz1dGTr7SMvOUlpVbdMvM07HsXJ06m6+MHIdOF98ycx0X/XBXG4o+lBV/qLNc+IHv/KgkF9cHVteHWZX43vXBtrJ/7BqGiv+RbChX5odd1eVd/GHS21oUTLk/TBZ/EC37obPkh93zH3pLflB2jejycn3Atp5/78v+vzk/Ysz9l2WV+KBvcX/UV3mfU8vrU+7QoZwAwijeqaLwwmlIhrN0mFF4QWhSUOjUiRNWfZS2UYbkDk8uDFbO3y8dxriDm3ICHTQE/H+4OG/9YfPai7ayFgdm5QVb1gtCrpLnFdfNWhzeu84n57eff9wV3HlZJasrlCtxXnKdQ0r+Pih1DpIkS1GoeP48VFS/pegB97nJpeTkBaPMN0XhZslzSMkRtJJKnW+cTkOFhnH+a4nQtmQ4e2GoXBQUlQ2YHcXnKEeJkT+O4uCmPn4H1xVbiYDU9bvK68Lf71ZLmd8zrt8grv8nhlF+KO16z/NLhWql3zCnIeU6nJIsOpNxTtK5ar+OQF8vhQYUB06BRbfoEH+1DvFT6+b+at3cXy2b+TIqGg0Sn3+rpzrvU52FSy4X/rXHMIxK/wJUXvsLt1flmLXVpqTZs2fr2WefLbN9+fLlCggIqHC/xmDFihVmlwDUqZwCKf2clH7OovRci07nSafzpYx8Lz26fpUcRvX+AeTnZSjQWwr0lgK8Dfl7Sz5WydfLdTPka5V8XPetko+XIZtFRX+5t0heFsnbWvarVeUHELXB9Y/SwuKAotBwfUAouhUa57cVlrlZ5HSW3V5QvK2geL+i+5ai+86i7SXbXbhPodNS9rmcJY5XYltR3WXfnAJ3qNH4gjFzWaXMjPp7NoshL7k+IBd/aLcU9XevEvetF7Rxt5NRut2FN5U9nrXM8YxS2yzlPZ9cU0sr+L746/nvDfcH/1IhY8nvLecXunRtU4k2ru91wf3KTgUXnidKfug2Lvha8vFSIWWJ+1LxT5Ar0Cze7izR/nyIbTm/vUQbp86fZy7cVup2QTtn8TnGfX4ypMLy9ivn/FX6PGYpu73CtufPOUV1lP9uOw3JWegK6DnHNDQWGUW/U12/R0v8nrUW/171dn81yvwOdj/u3u98G9djZfaxSF4XHOvC770s52+uc4sZDKP0796C4q95TimvUMottBR/Lbpfctu5QumsQzpTYFG2QzrjKPo5PZtXqLN553Qoo+JgyttiKNRXCvU1FOontfA11MJPivI31NK/6H0BzMTn36rJycmpcts6C5fCwsLk5eVVZpRSenp6mRFDLpGRkeW29/b2VosWLSpt4zpmVZ43MjJSUtEIpqioqCrVJklPPvmkpk+f7r6flZWlmJgYjRw5slGvubRixQqNGDGCOado9ByFTh06dU77TpzV3pNnte9ETtH3J87q1NmLp+6hgTZFBvspMthPUXY/RQQXDf8OCbApJMCm5gE+ah5gk93fJptXnV9sExVwOs//VbvA9dftEmtbuP4KXnqa1AXTpwrPj7Qp+df2wuJ1Ly58rOjD9PnpThdOb3KNHDr/4bv0iCMX17aq/pvaNTrBHU5UMEKh1AirKkxhslqKpgXt2L5NPXv0kM3bq/RIihIjMIpGXKjMiIuSI8FK3b9w/+KpSK7agIagvH//uKY5FhafYy4cYVPgdBYF5hdO1Swxas894q/M6D+VOq+4thuGURyeu74/v/5O0baiUYeukSpOo+ToldKjFVXiHCSdPw8VfV8yfDx/Fir5I3lhuCkV/dzLPXqm7Kgpi86Ptjk/2lPuEV3uUVwW1xTI0ucK99fikaeuaZMXTn12Tcd2nU9KTqP2YnRMtdX03/+GYehMXoFOns3XyTP5RV/P5utEdr4Onz6nI6fP6XDGOaVm5qrAsCg9V0rPtUiZpY/j421Vp/BAdY4IUpfIIHWOaKYukUEKDfSp5VcKlMXn3+pxzdaqijoLl3x8fNS3b1+tWLFC48aNc29fsWKFbr755nL3iY2N1RdffFFq2/Lly9WvXz/3//jY2FitWLGi1LpLy5cv18CBA6v8vO3bt1dkZKRWrFih3r17SyqaFrNmzRq98MILFb4mX19f+fr6ltlus9kafcdsCq8BnsVR6NTuY2e09chpbTmcqa1HMrUzNbvS9Ysig/3UPixQHVoGKiY0QC0Dbdq/I0m3jByqVqHNWEOgESl7JkZ1ORwOLT2erNF9WnP+h8fi3z/wZDXp/6E+PgoNClCnSto4Cp1Ky8zVoVM5OpSRo8MZ53ToVI72n8zRrmPZyskv1Laj2dp2tPRVusODfNUlKlhdo4LUr22orm4XKnsAP5+oG5z/q6Y671GdToubPn264uPj1a9fP8XGxuovf/mLDh48qF/96leSikYCHTlyRH//+98lFV0Zbu7cuZo+fbomT56sxMREzZ8/330VOEn6v//7P1177bV64YUXdPPNN+uzzz7TV199pbVr11b5eS0Wi6ZNm6ZZs2apU6dO6tSpk2bNmqWAgABNmDChLt8SADVQ6DT00/EzRSHS4dPaciRT249mKa+gbJAU4ONVHCA1U4fiIKljy2ZqHxaoQN/SpzyHw6GlR5LUJjRANoIlAACAS2bzsiomNEAxoWWXDXE6DR3KyNGO1GztSM3SzrQs7UzL1oGTOUrPzlN69nF9s+u43tZeWSxS54ggDejQQv3bh+qq9qEKa8afl4CGqk7DpTvvvFMnT57Uc889p9TUVHXv3l1Lly5V27ZtJUmpqak6ePCgu3379u21dOlS/frXv9Ybb7yh6Oho/fnPf9Ztt93mbjNw4EAtWrRITz/9tH7729+qY8eO+vjjj9W/f/8qP68kPfbYYzp37pymTJmijIwM9e/fX8uXL1dQUFBdviUAqsAwDO06dkZr95zQuj0ntGHfKZ3JKyjTLsjXWz1a29WjtV09W4WoRyu7YkL9mXoDAADQAFmtFrVtEai2LQIV1z3Svf1sXoFSjmVrZ2q2th45rQ37Tmnv8bPamZatnWnZWrBuvyTpsvBmurp9qPq3D9WADi0UEexn0isBcCGLUXIxCFRLVlaW7Ha7MjMzG/WaS0uXLtXo0aMZFghTHc7I0bo9J4sCpZ9O6sSZvFKPB/p46YpWdvVsVRwmtQ5R29CAS7oSCf0fnoz+D09G/4cnayz9Pz07Vxv3ZWjDvpPasPeUUo5ll2nTo5Vdcd0jFdc9Uh1bNjOhSjQ2jaX/NxTVyTzq/GpxAFCec/mFWrMrXd/sLhqdtP9k6SsR+Nu8dFX7UA3q2EKDLgtT16hgFu0EAADwEOFBfrqxZ5Ru7Fl0AaaMs/n6bv8pfbfvlDbsO6ltR7O09UjRupsv/TdFl0c0U9wVkYrrHqWuUUGMZAfqGeESgHpzLr9Qq1LStWRrqr7eka5zjkL3Y15Wi3rFhGhQxxYaeFmYercJka836yABAABAah7oo1FXRGrUFUXT6Y5n5+mrHcf0ZXKa1u05oV3HzmjXsT3689d71LZFgOKuiNSo7pHq1Trkkka6A6gawiUAdaqyQCkm1F/Xd43QNZeF6er2oQryY2gqAAAALq5lkK/uvrqN7r66jTJzHFq585iWJadpza7jOnAyR29/s1dvf7NXUXY/3dEvRhOubqNIO2s0AXWFcAlArbtYoDS6R5Ru7BGlHq3sDFkGAADAJbEH2HRrn9a6tU9rnc0r0Jpdx/Vlcpq+3nFMqZm5+vPK3Xpj1R6N7Bah+AFtFduxBf8GBWoZ4RKAWrPrWLYWrj+gT384UurqbgRKAAAAqA+Bvt4a3SNKo3tEKddRqOXbj2nh+gP6bt8pfZmcpi+T09ShZaDiB7TVrX1ay+7PyHmgNhAuAbgk+QVOLd+epvcTD2jDvlPu7a2b+xctwkigBAAAABP42bw09spojb0yWilprj+CHtbe42f17Bfb9eKyFN3SO1r3DGirK6LtZpcLNGqESwBqJDXznD7acFAfbTyk49l5kooW5R7RNULxsW01kOHGAAAAaCA6Rwbp+Vu66/Ebumhx0hEtTDyglGPZ+ui7Q/rou0Pq0yZEjwzvpCGXt+TfsEANEC4BqDLDMLTup5N6P/GAVuw4pkKnIankgooxirL7m1wlAAAAUL5mvt6KH9BW9/Rvo+8PZOj9xAP6MjlVPxw8rYnvbtTV7UL16KjOurp9qNmlAo0K4RKAi3I6DS3Zmqo/r9yt3eln3Nv7tw9VfGxbjewWKR9vq4kVAgAAAFVnsVh0VbtQXdUuVOnZXfXXb/fpvXX79d3+Uxr/dqKGXN5Sj47srB6tmS4HVAXhEoAKOZ2G/rstTa9/tVspx7IlSYE+Xrq1T2vFx7bV5RFBJlcIAAAAXJrwID89NbqrfjGoveZ8vVsfbzykNbuOa82u4xrdI1LTR1yuy8L5dy9QGcIlAGUYhqGvdqTrtRW7tD01S5IU5OetyYM7aOKgdgr246oaAAAAaFoi7X76w7geuv/aDnr9q9369+YjWro1TcuS0zSud2tNu76TYkIDzC4TaJAIlwC4GYah1buO67UVu7TlcKakonnpvxjUTpOu6SB7AKESAAAAmra2LQL12p299KshHfXK8hQt335Mn/xwWJ//eER3X91G00dcrpAAH7PLBBoUwiUAMgxDa/ec0Ksrdinp4GlJkr/NSxMHtdP9gzuoeSC/PAEAAOBZOkcG6S8/76fNh07rleUp+nb3Cf098YCWbk3T8zdfoRt6RJldItBgEC4BHi4lLVu/+yxZG/adkiT5elv189i2emBIR4U18zW5OgAAAMBcvWJC9P6k/lq354R++1myfjp+Vg9+8INu6B6pZ2++QuFBfmaXCJiOcAnwUDn5BfrTyt2a/+0+FTgN+XhbNeHqNpoytKPCg/kFCQAAAJQ08LIwLXlksOZ+vUfz1vykL5PT9L89J/TbMd10e9/WslgsZpcImIZwCfBAX20/pmc+36Yjp89JkkZ2i9AzY69QqxB/kysDAAAAGi4/m5ceHdVZN/SI1OOfbFHykSz95l9b9PmPRzVrXA8W/IbHsppdAID6c+T0Od3/9+/1y79/ryOnz6lViL/e+Xk//eXn/QiWAAAAgCq6Itquf08ZpCdu6CJfb6u+3X1Co17/Rgv+t0+FTsPs8oB6x8glwAM4Cp1a8L/9eu2rXcrJL5S31aJfDu6gR4ZfpgAfTgMAAABAdXl7WfWrIR01sluEnvh0q77bd0oJX2zXF1tS9cJtPXRZeJDZJQL1hpFLQBO36UCGbpqzVn9YukM5+YXq17a5ljwyWE/c0IVgCQAAALhEHVo206LJA/T7W7qrma+3Nh3I0Og/rdXHGw+aXRpQb/hkCTRROfkF+sOSHfpgQ9EvtZAAm566oatu79taViuLDQIAAAC1xWq16J4BbXVdl3A9tXirVqcc1+OfbNWWw5l65qYr5OPNuA40bfRwoAlKScvWzXP/5w6Wxvdrra9nDNX4q2IIlgAAAIA6Eh3ir7/de5V+M6qzLBbpgw0Hdfc763UsK9fs0oA6RbgENCGGYeij7w5q7Ny12p1+RuFBvvrwl/314u1XKjTQx+zyAAAAgCbParXooWGX6W/3XqUgv6JpcmPmrNX3+0+ZXRpQZwiXgCYiO9ehhz9K0pOfblVegVNDLm+ppf83WAMvCzO7NAAAAMDjDOsSri+mXqPOEUE6np2nu99Zr4XrD8gwuJocmh7CJaAJ2HL4tG7881r9Z0uqvK0WPXlDF7078SqFNfM1uzQAAADAY7ULC9SnUwbqxh5RchQaevrfyXr8ky3KdRSaXRpQqwiXgEbMMAzNX7tPt721TgdP5ahViL/+8atYPTCkI2srAQAAAA1AoK+35k7orSdu6CKrRfrH94d159uJSs08Z3ZpQK0hXAIaqYyz+Zr89+/1/H+2y1FoKO6KSC19ZLD6tGludmkAAAAASrBYLPrVkI5acN/Vsvvb9OPhTN00Z6027D1pdmlArSBcAhqhjftPafSfv9VXO9Ll423V8zdfobfu6SN7gM3s0gAAAABU4NrLW+qLqdeoa1SwTpzJ18/+ukFf/HjU7LKAS0a4BDQyn2w6rLv/sl6pmbnqEBaoxVMGKj62nSwWpsEBAAAADV2bFgH69MGBurFnlAqchv5vUZI+2XTY7LKAS+JtdgEAqsYwDM39eo9eWbFLknRjzyi9eFtPBfryYwwAAAA0Jv4+XppzV28F+Xpr0cZDmvHPH5VX4NSE/m3MLg2oET6VAo2Ao9Cp3/47WYs2HpIk/WpIRz02qjOLdgMAAACNlNVq0axxPeTrbdV7iQf01OKtyiso1H2D2ptdGlBthEtAA3cmr0APffCD1uw6LqtFevbm7oof0NbssgAAAABcIqvVooSxV8jP5qW3v9mrZ7/YrlyHUw8O7Wh2aUC1EC4BDVh6Vq7uW7BR245myd/mpTl399b13SLMLgsAAABALbFYLHrihi7ytXnpzyt364VlO5XrKNS06zuxrioaDcIloIHafSxbE9/dqCOnzymsmY/m33uVrowJMbssAAAAALXMYrFo+ojL5ett1Uv/TdGfVu5WbkGhnojrQsCERoFwCWiAEn86qfvf/17ZuQXqEBaoBfddrTYtAswuCwAAAEAdemjYZfKzeen5/2zX22v2Ks/h1DM3dSNgQoNHuAQ0MJ9tPqLf/HOL8gud6te2ud75eT81D/QxuywAAAAA9WDSNe3l623V0/9O1oJ1+5VXUKg/3NKDi/mgQSNcAhqQt9f8pNlf7pQk3dgjSq+Mv1J+Ni+TqwIAAABQn+4Z0Fa+3lY9/skWffTdIeU5nHrpjivlRcCEBspqdgEAiry1+nywNHlwe825uzfBEgAAAOCh7ugXo9fv6i0vq0WfJh3RrKU7zC4JqBDhEtAA/G3tPr2wrChY+s2ozpp5YzeGvQIAAAAebuyV0Xp1/JWSpPlr9+nvifvNLQioAOESYLKF6w/ouf9slyT93/BOemjYZSZXBAAAAKChuLlXK/1mVGdJUsLn27RyxzGTKwLKIlwCTPTP7w/p6X8nS5J+NaSjpl3fyeSKAAAAADQ0U4Z21J39YuQ0pIc/SlLykUyzSwJKIVwCTPLZ5iN6/JMtkqT7BrXT43GducQoAAAAgDIsFot+P667rrksTDn5hZr03kalZp4zuyzAjXAJMMGy5FRN/8ePchrSz/q30e/GdCNYAgAAAFAhm5dVb97TR53Cm+lYVp7ue3ejsnMdZpcFSCJcAurdyh3H9PBHSSp0Grq9b2s9f3N3giUAAAAAFxXsZ9O7912lsGa+2pmWrakfJqmg0Gl2WQDhElCfvtl1XA8u/EGOQkM3XRmtF27ryVXhAAAAAFRZ6+YBmn9vP/nZrFqz67h+9/k2GYZhdlnwcIRLQD1J/Omk7n//e+UXOhV3RaReHX+lvAiWAAAAAFTTlTEh+vNdvWWxSB9uOKh3vt1rdknwcIRLQD3YdOCUJr23UbkOp67rEq4/391bNi9+/AAAAADUzMgrIvX0jd0kSbOW7tSXW1NNrgiejE+3QB3be/yM7nt3o3LyCzW4U5je/Fkf+XjzowcAAADg0vxiUDvdG9tWkjTt48364WCGyRXBU/EJF6hDmTkO/fK975WVW6A+bUL0l/h+8rN5mV0WAAAAgCbAYrHot2O66bou4corcGrye98rNfOc2WXBAxEuAXWkoNCpqR/9oL0nzira7qe34/vJ34dgCQAAAEDt8fayas7dvdUtKlgnz+br1x9vVqGTBb5RvwiXgDry+yU79O3uE/K3eemde/upZZCv2SUBAAAAaIICfb31xs/6KMDHS+v3ntK8NT+ZXRI8DOESUAc+3HBQC9btlyS9dmcvXRFtN7cgAAAAAE1a+7BAPXdzd0nSqyt2adMB1l9C/SFcAmrZ+r0n9bvPkiVJj468XHHdI02uCAAAAIAnuK1PK429MlqFTkP/tyhJWbkOs0uChyBcAmrRwZM5enDhJhU4Dd10ZbQeGnaZ2SUBAAAA8BAWi0W/H9ddrZv763DGOc1cnCzDYP0l1D3CJaCWZOc6NOm9jcrIcahna7teur2nLBaL2WUBAAAA8CDBfjb9+e7e8rJa9MWPR/WvTYfNLgkegHAJqAVFw043a3f6GUUE++qdn/eTn40rwwEAAACof33aNNf0EZdLkp75fJv2Hj9jckVo6uo0XMrIyFB8fLzsdrvsdrvi4+N1+vTpSvcxDEMJCQmKjo6Wv7+/hg4dqm3btpVqk5eXp4cfflhhYWEKDAzU2LFjdfhw6TS2Ks9tsVjK3ObNm1cbLx0e5sVlO/X1znT5elv1l/h+igj2M7skAAAAAB7sV0M6KrZDC+XkF+rhj5KUV1Bodklowuo0XJowYYI2b96sZcuWadmyZdq8ebPi4+Mr3efFF1/Uq6++qrlz52rjxo2KjIzUiBEjlJ2d7W4zbdo0LV68WIsWLdLatWt15swZjRkzRoWF539Yqvrc7777rlJTU923e++9t/beAHiEf206rLe/2StJeumOK3VlTIi5BQEAAADweF5Wi167s5eaB9i07WiWXlqWYnZJaMK86+rAO3bs0LJly7R+/Xr1799fkvTOO+8oNjZWKSkp6ty5c5l9DMPQ66+/rpkzZ+rWW2+VJL333nuKiIjQhx9+qAceeECZmZmaP3++3n//fV1//fWSpIULFyomJkZfffWVRo0aVa3nDgkJUWQkV/NCzWw6cEpPfbpVkvTwdZdp7JXRJlcEAAAAAEUi7X568fYrNfnv3+uva/fpmk5hGto53Oyy0ATVWbiUmJgou93uDnckacCAAbLb7Vq3bl254dK+ffuUlpamkSNHurf5+vpqyJAhWrdunR544AFt2rRJDoejVJvo6Gh1795d69at06hRo6r13FOnTtUvf/lLtW/fXpMmTdL9998vq7X8AV15eXnKy8tz38/KypIkORwOORyN8xKPrroba/1mOnk2X796f5PyC50a0TVcU4e0531sZOj/8GT0f3gy+j88Gf3f8wztFKp7+sdo4YZDmvGPH/WfqbEKa+ZrdlmmoP9XT3XepzoLl9LS0hQeXjYRDQ8PV1paWoX7SFJERESp7RERETpw4IC7jY+Pj5o3b16mjWv/qj73888/r+HDh8vf318rV67UjBkzdOLECT399NPl1jd79mw9++yzZbYvX75cAQEB5e7TWKxYscLsEhoVw5DeSbHq+BmrIv0NjQg6qmXLjppdFmqI/g9PRv+HJ6P/w5PR/z3LlYa0MsBLqWfzdd+8VXqgq1NWD76wNf2/anJycqrcttrhUkJCQrkBS0kbN26UpHIvw24YxkUvz37h41XZ58I2VXnukiFSr169JEnPPfdcheHSk08+qenTp7vvZ2VlKSYmRiNHjlRwcHCl9TVUDodDK1as0IgRI2Sz2cwup9H44LtD2rZ+h2xeFv3lvlh1jQoyuyTUAP0fnoz+D09G/4cno/97riv6n9G4t9ZrZ6aUHtJFvxjUzuyS6h39v3pcs7Wqotrh0tSpU3XXXXdV2qZdu3basmWLjh07Vuax48ePlxmZ5OJa+ygtLU1RUVHu7enp6e59IiMjlZ+fr4yMjFKjl9LT0zVw4EB3m+o+t1Q0dS4rK0vHjh0rt52vr698fcsOH7TZbI2+YzaF11Bfdh/L1uwvixbDezyui3q2CTW5Ilwq+j88Gf0fnoz+D09G//c83Vo11+9u6qaZi5P18orduq5rpDpFeOYfyen/VVOd96jaV4sLCwtTly5dKr35+fkpNjZWmZmZ+u6779z7btiwQZmZme4Q6ELt27dXZGRkqSFq+fn5WrNmjXufvn37ymazlWqTmpqq5ORkd5uaPLckJSUlyc/PTyEhIdV9W+Ah8goK9ciizcorcGpwpzD9YlB7s0sCAAAAgCqZcHUbDe8SLkehoaf/nSzDMMwuCU1Ena251LVrV8XFxWny5Ml6++23JUn333+/xowZU2pB7S5dumj27NkaN26cLBaLpk2bplmzZqlTp07q1KmTZs2apYCAAE2YMEGSZLfbNWnSJM2YMUMtWrRQaGioHn30UfXo0cN99biqPPcXX3yhtLQ0xcbGyt/fX6tWrdLMmTN1//33lzs6CZCkF5elaEdqlkIDffTKHVfK6skTlQEAAAA0KhaLRc/efIXW/XRSG/ad0qc/HNFtfVubXRaagDoLlyTpgw8+0COPPOK+stvYsWM1d+7cUm1SUlKUmZnpvv/YY4/p3LlzmjJlijIyMtS/f38tX75cQUHnh+u99tpr8vb21vjx43Xu3DkNHz5cCxYskJeXV5Wf22az6c0339T06dPldDrVoUMHPffcc3rooYfq5L1A4/fNruOav3afJOml23sqPNjP5IoAAAAAoHpaNw/QI8M76YVlOzVr6Q4N7xqukAAfs8tCI1en4VJoaKgWLlxYaZsLh+FZLBYlJCQoISGhwn38/Pw0Z84czZkzp8bPHRcXp7i4uEprA1xOnsnTjH/+KEmKH9BWw7tWvHYXAAAAADRkk65pr09/OKzd6Wf04n9TNGtcD7NLQiNX7TWXAE9jGIYe+9cWHc/OU6fwZpp5Y1ezSwIAAACAGvPxtur3t3SXJH303UElHcwwuSI0doRLwEUsXH9AK3emy8fLqj/d1Vt+Nq+L7wQAAAAADVj/Di10W5/WMgxp5uJkFRQ6zS4JjRjhElCJXcey9fslOyRJj8V1VrfoYJMrAgAAAIDa8dToLrL727Q9NUt/TzxgdjloxAiXgArkOgr1yEdJyitwanCnMP1iUHuzSwIAAACAWtOima8ej+siSXp1xS4dy8o1uSI0VoRLQAVe+m+KdqZlKzTQR6/ccaWsVovZJQEAAABArbrrqhj1bhOiM3kFeu4/280uB40U4RJQjm92Hdf8tfskSS/d3lPhwX4mVwQAAAAAtc9qtej3t3SX1SIt2ZKqb3YdN7skNEKES8AFsnMd+s2/fpQkxQ9oq+FdI0yuCAAAAADqzhXRdk0cWLQMyO8+S1auo9DkitDYEC4BF3hl+S4dy8pT2xYBemp0V7PLAQAAAIA6N33k5YoI9tX+kzl6a/VPZpeDRoZwCShh6+FM/T1xvyTp97d0l7+Pl7kFAQAAAEA9aObrrd+NuUKS9Nbqn7TvxFmTK0JjQrgEFCt0Gnpq8VY5DWnsldEa3Kml2SUBAAAAQL0Z3SNS117eUvmFTv3us2QZhmF2SWgkCJeAYu8n7tfWI5kK8vPW02OYDgcAAADAs1gsFj039gr5eFv17e4T+s+WVLNLQiNBuARIOpaVq5eX75IkPRbXReFBXB0OAAAAgOdpFxaoh4ZeJkl6/j/bdTavwOSK0BgQLgGSnvtiu87kFejKmBBNuLqN2eUAAAAAgGl+NbSD2rYIUHp2nt793z6zy0EjQLgEj7cqJV1LtqbKapFmjesuL6vF7JIAAAAAwDS+3l6aPuJySdLb3+xVZo7D5IrQ0BEuwaOdyy/U7z5LliTdN6i9roi2m1wRAAAAAJjvpp7R6hIZpOzcAr39zU9ml4MGjnAJHm3uqt06dOqcoux+7mQeAAAAADyd1WrRjJGdJUnv/m+/0rNzTa4IDRnhEjzW7mPZ+ss3eyVJCWOvUKCvt8kVAQAAAEDDcX3XcPWKCdE5R6HeXMXoJVSMcAkeyTAMzVycLEehoeu7hmtktwizSwIAAACABsViseixUUWjlz7ccFCHM3JMrggNFeESPNI/Nx3Wd/tPyd/mpYSxV8hiYRFvAAAAALjQwMvCNLBjC+UXOvXnlbvNLgcNFOESPM6ps/mavXSHJGna9Z3UunmAyRUBAAAAQMP1aPHopX9tOqyfjp8xuRo0RIRL8Dizl+5QRo5DXSKD9Itr2ptdDgAAAAA0aH3aNNf1XSPkNKRXV+wyuxw0QIRL8Cgb9p7UPzcdliT9YVx32bz4EQAAAACAi5kx8nJZLNKSLanadjTT7HLQwPDJGh6j0Gnod59tkyTdfXUb9W0banJFAAAAANA4dI0K1k09oyVJryxn9BJKI1yCx/j0h8NKOZYtu79Nj8d1NrscAAAAAGhUfj3icnlZLfp6Z7q+33/K7HLQgBAuwSPkOgrdc4MfGtZRIQE+JlcEAAAAAI1L+7BAje/XWpL00n9TZBiGyRWhoSBcgkd4b91+pWbmKtrup5/HtjO7HAAAAABolB6+rpN8vK3asO+U1u45YXY5aCAIl9DkZeY49MaqPZKk6SM7y8/mZXJFAAAAANA4RYf4657+bSUxegnnES6hyXtzzR5l5Raoc0SQxvVuZXY5AAAAANCoTRnWUQE+XtpyOFP/3XbM7HLQABAuoUk7evqc3v3ffknS4zd0lpfVYm5BAAAAANDIhTXz1aRr2kuSXlmeokIno5c8HeESmrTXVuxSfoFTV7cP1bDO4WaXAwAAAABNwi8Hd1Cwn7d2p5/R5z8eMbscmIxwCU1WSlq2PvnhsCTpyRu6yGJh1BIAAAAA1Aa7v02/GtpRkvTqil1yFDpNrghmIlxCk/XSf3fKaUg3dI9U7zbNzS4HAAAAAJqUiQPbKayZjw6dOqcvk9PMLgcmIlxCk/TdvlP6ake6vKwWPTqqs9nlAAAAAECTE+DjrfgB7SRJf/12L1eO82CES2hyDMPQ7C93SJLuvCpGHVs2M7kiAAAAAGia7hnQRr7eVm05nKnv9p0yuxyYhHAJTc5/tx1T0sHT8rd5adrwTmaXAwAAAABNVotmvrq1T2tJ0jvf7jO5GpiFcAlNSkGhUy/+d6ck6ZeD2ys82M/kigAAAACgaZt0TXtJ0sqdx7T3+BmTq4EZCJfQpPxz02HtPX5WzQNsuv/aDmaXAwAAAABN3mXhzTS8S7gMQ/rb/xi95IkIl9Bk5OQX6LUVuyRJD1/XSUF+NpMrAgAAAADP8MvBRX/c/9emw8o4m29yNahvhEtoMt79336lZ+epdXN//WxAG7PLAQAAAACPMaBDqK6IDlauw6mF6w+YXQ7qGeESmoRTZ/M1b/VPkqTfjOosX28vkysCAAAAAM9hsVg0uXj00nuJB5RXUGhyRahPhEtoEt5YtUfZeQXqFhWsm3pGm10OAAAAAHicG3tGKcrupxNn8vTZ5qNml4N6RLiERu/EmTz3sMvHb+giq9VickUAAAAA4HlsXlZNHNhOkjT/230yDMPcglBvCJfQ6P1t7T7lFTh1ZUyIru0UZnY5AAAAAOCx7rq6jQJ9vJRyLFvf7j5hdjmoJ4RLaNSych16P7Fo1NKUoR1lsTBqCQAAAADMYve3afxVMZKkd77da3I1qC+ES2jUFq4/oOy8AnUKb6YRXSPMLgcAAAAAPN4vBrWX1SJ9u/uEdqZlmV0O6gHhEhqtXEeh/rZ2nyTpV0M6stYSAAAAADQAMaEBuqF7lCTpr9/uM7ka1AfCJTRa//z+kE6cyVerEH+N7cUV4gAAAACgoZg0uL0k6bPNR5SelWtyNahrhEtolAoKnXr7m6L5u/df20E2L7oyAAAAADQUfdo0V9+2zeUoNPT34nVy0XTxiRyN0hdbjupwxjm1CPTR+H4xZpcDAAAAALjA5OLRSws3HFBOfoHJ1aAuES6h0XE6Db21+idJ0i+uaS9/Hy+TKwIAAAAAXGhEt0i1CQ3Q6RyHPtl02OxyUIcIl9DorNyZrl3HzijI11v3DGhrdjkAAAAAgHJ4WS36xaB2kqT5a/fJ6TTMLQh1hnAJjYphGHpj1R5J0j2xbWX3t5lcEQAAAACgInf0i1Gwn7f2n8zRVzuOmV0O6gjhEhqVxL0ntfnQafl6W/WLQe3NLgcAAAAAUIlAX2/9rHjGyV+/3WdyNagrhEtoVFxrLY3vF6OWQb4mVwMAAAAAuJiJA9vJ22rRd/tPKSUt2+xyUAcIl9BobD2cqW93n5CX1aL7r+1gdjkAAAAAgCqICPbT8K7hkqSPNx4yuRrUhToNlzIyMhQfHy+73S673a74+HidPn260n0Mw1BCQoKio6Pl7++voUOHatu2baXa5OXl6eGHH1ZYWJgCAwM1duxYHT5ceuX5P/zhDxo4cKACAgIUEhJS7nMdPHhQN910kwIDAxUWFqZHHnlE+fn5l/KSUYfeXF201tLYK6MVExpgcjUAAAAAgKq686oYSdLipMPKKyg0uRrUtjoNlyZMmKDNmzdr2bJlWrZsmTZv3qz4+PhK93nxxRf16quvau7cudq4caMiIyM1YsQIZWefHzo3bdo0LV68WIsWLdLatWt15swZjRkzRoWF5ztofn6+7rjjDj344IPlPk9hYaFuvPFGnT17VmvXrtWiRYv0ySefaMaMGbXz4lGr9qSf0bJtaZKkB4d2NLkaAAAAAEB1XNuppSKCfZWR49BX29PNLge1zLuuDrxjxw4tW7ZM69evV//+/SVJ77zzjmJjY5WSkqLOnTuX2ccwDL3++uuaOXOmbr31VknSe++9p4iICH344Yd64IEHlJmZqfnz5+v999/X9ddfL0lauHChYmJi9NVXX2nUqFGSpGeffVaStGDBgnLrW758ubZv365Dhw4pOjpakvTKK69o4sSJ+sMf/qDg4OBafT9wad5e85MMQ7q+a4QujwgyuxwAAAAAQDV4e1l1e9/WemPVT/r4+0O6sWeU2SWhFtVZuJSYmCi73e4OliRpwIABstvtWrduXbnh0r59+5SWlqaRI0e6t/n6+mrIkCFat26dHnjgAW3atEkOh6NUm+joaHXv3l3r1q1zh0tVqa979+7uYEmSRo0apby8PG3atEnDhg0rs09eXp7y8vLc97OysiRJDodDDoejSs/b0Ljqbsj1p2bmanHSEUnS/YPbNuha0bg0hv4P1BX6PzwZ/R+ejP4PM43rFaU3Vv2kb3cf14HjWYoO8a/X56f/V0913qc6C5fS0tIUHh5eZnt4eLjS0tIq3EeSIiIiSm2PiIjQgQMH3G18fHzUvHnzMm0qOm5Fz3Xh8zRv3lw+Pj4VHmf27NnuEVElLV++XAEBjXsNoBUrVphdQoU+3WdVgdOqTsFOpW5dp9StZleEpqYh93+grtH/4cno//Bk9H+Y5bJgq/ZkWfXHj1crLsYwpQb6f9Xk5ORUuW21w6WEhIRyA5aSNm7cKEmyWCxlHjMMo9ztJV34eFX2qUqbiz3PxY7z5JNPavr06e77WVlZiomJ0ciRIxvtNDqHw6EVK1ZoxIgRstlsZpdTxsmz+Xri+28kOfXUuKt0zWUtzC4JTUhD7/9AXaL/w5PR/+HJ6P8wmyP6qB79JFlbzwTq9bjBslqr9zn+kp6b/l8trtlaVVHtcGnq1Km66667Km3Trl07bdmyRceOHSvz2PHjx8uMGHKJjIyUVDSqKCrq/PzL9PR09z6RkZHKz89XRkZGqdFL6enpGjhwYJVfR2RkpDZs2FBqW0ZGhhwOR4X1+fr6ytfXt8x2m83W6DtmQ30NH363V+ccTvVoZdfQLhHVDhCBqmio/R+oD/R/eDL6PzwZ/R9mGdOrtZ5dslOHT+fq+0NZGnRZWL3XQP+vmuq8R9W+WlxYWJi6dOlS6c3Pz0+xsbHKzMzUd9995953w4YNyszMrDAEat++vSIjI0sNUcvPz9eaNWvc+/Tt21c2m61Um9TUVCUnJ1crXIqNjVVycrJSU1Pd25YvXy5fX1/17du3ysdB3cl1FGrhhoOSiq4QR7AEAAAAAI2bn81LN/cqWvv4442HTK4GtaXa4VJVde3aVXFxcZo8ebLWr1+v9evXa/LkyRozZkypxby7dOmixYsXSyqapjZt2jTNmjVLixcvVnJysiZOnKiAgABNmDBBkmS32zVp0iTNmDFDK1euVFJSku655x716NHDffU4STp48KA2b96sgwcPqrCwUJs3b9bmzZt15swZSdLIkSPVrVs3xcfHKykpSStXrtSjjz6qyZMnN9opbk3N0q2pOnU2X9F2P43sVv5oMgAAAABA43JnvzaSpGXb0pSZw+LaTUGdLegtSR988IEeeeQR95Xdxo4dq7lz55Zqk5KSoszMTPf9xx57TOfOndOUKVOUkZGh/v37a/ny5QoKOn/5+ddee03e3t4aP368zp07p+HDh2vBggXy8vJyt/nd736n9957z32/d+/ekqRVq1Zp6NCh8vLy0pIlSzRlyhQNGjRI/v7+mjBhgl5++eU6eS9QfX9PLFrE/WcD2srbq85yUAAAAABAPereKlhdo4K1IzVL/958RPcObGd2SbhEdRouhYaGauHChZW2MYzSq8NbLBYlJCQoISGhwn38/Pw0Z84czZkzp8I2CxYs0IIFCyp97jZt2ug///lPpW1gjq2HM7X50GnZvCwa3y/G7HIAAAAAALXEYrHozn6tlfDFdn288RDhUhPAcBA0SO+v3y9JGt0jSi2Dyi6iDgAAAABovG7p3Uo+3lZtT81S8pHMi++ABo1wCQ3O6Zx8fbb5qCTp57FtTa4GAAAAAFDbQgJ8NOqKoivGs7B340e4hAbnX5sOK6/Aqa5RwerTprnZ5QAAAAAA6sCdxUug/HvzEeU6Ck2uBpeCcAkNitNp6P31RQt5/zy2rSwWi8kVAQAAAADqwsCOLdS6ub+ycwu0LDnN7HJwCQiX0KB8s/u4DpzMUZCft27uFW12OQAAAACAOmK1WnRH36LRS0yNa9wIl9CgLCwetXR739YK8KnTixkCAAAAAEx2e7/WslikxL0ndeDkWbPLQQ0RLqHBOHQqRyt3pkuS7hnAQt4AAAAA0NS1CvHX4E4tJUn//P6wydWgpgiX0GB8+N1BGYZ0zWVh6tiymdnlAAAAAADqwfh+rSUVXdyp0GmYXA1qgnAJDUKuo9A9xzY+llFLAAAAAOApRnSLUPMAm9KycvXN7uNml4MaIFxCg7B0a6pOnc1XtN1Pw7uEm10OAAAAAKCe+Hp76ZberSRJ/2Bh70aJcAkNwvvFC3lP6N9G3l50SwAAAADwJHdeVXTVuK92HNPJM3kmV4Pq4lM8TJd8JFNJB0/L5mXRnVe1MbscAAAAAEA96xIZrCtb2+UoNLQ46YjZ5aCaCJdgur8n7pckje4RpZZBvuYWAwAAAAAwxfji0Usfbzwkw2Bh78aEcAmmysxx6LPNRyVJ8QNYyBsAAAAAPNVNV0bL19uq3elntDMt2+xyUA2ESzDVPzcdUl6BU12jgtW3bXOzywEAAAAAmCTYz6ahnVtKkpZsSTW5GlQH4RJM43QaWli8kPfPY9vKYrGYXBEAAAAAwEw39oyWJC3ZmsrUuEaEcAmm+XbPCe0/maMgP2/d3Cva7HIAAAAAACYb3iVcvt5W7TtxVttTs8wuB1VEuATTvF+8kPftfVsrwMfb3GIAAAAAAKYL9PXWdV3CJUlLtzI1rrEgXIIpDp3K0cqd6ZKke1jIGwAAAABQbHSPKElF6y4xNa5xIFyCKT787qAMQ7rmsjB1bNnM7HIAAAAAAA3EdV3C5Wezav/JHG07ytS4xoBwCfWuoNCpf206LEm6Z0Abk6sBAAAAADQkJafGLWFqXKNAuIR6t3bPCR3PzlPzAJuu6xJhdjkAAAAAgAbmxh7FV41jalyjQLiEevfpD0ckSTf3aiUfb7ogAAAAAKC0YV1ays9m1cFTOUo+wtS4ho5P9qhX2bkO/XdbmiTp1j6tTK4GAAAAANAQBfh4a3jxTBemxjV8hEuoV19uTVNegVOXhTdTj1Z2s8sBAAAAADRQN/Ysvmrc1qNMjWvgCJdQr/71Q9FC3rf1aS2LxWJyNQAAAACAhmpY53D527x06NQ5bT2SaXY5qAThEurNoVM5+m7fKVks0i29o80uBwAAAADQgPn7eGl41+Krxm1halxDRriEerM4qWgh70EdwxRl9ze5GgAAAABAQ3djj6Kpcf/hqnENGuES6oVhGPrUNSWuLwt5AwAAAAAubmjncAX4eOnI6XPacpipcQ0V4RLqxQ8HM7T/ZI4CfLw06opIs8sBAAAAADQCRVPjuGpcQ0e4hHrxyQ9FU+Ju6B6lAB9vk6sBAAAAADQWrqlxS5ga12ARLqHO5ToK9Z8fj0piShwAAAAAoHqGdm6pwOKpcZsPnTa7HJSDcAl1buWOdGXlFija7qcB7VuYXQ4AAAAAoBHxs5WYGsdV4xokwiXUOddC3uP6tJLVajG5GgAAAABAY3Njz6KpcUu3MjWuISJcQp06cSZPq3cdlyTd2qe1ydUAAAAAABqjIZcXTY07mpmrJKbGNTiES6hTn20+qkKnoV4xIerYspnZ5QAAAAAAGiE/m5dGdGNqXENFuIQ65ZoSd1sfFvIGAAAAANTc6B7np8Y5nUyNa0gIl1BndqZladvRLNm8LBrTM9rscgAAAAAAjdi1l7dUM19vpWbmKulQhtnloATCJdSZT384Ikka3iVCzQN9TK4GAAAAANCYlZ4al2ZyNSiJcAl1oqDQqcVJReHSrUyJAwAAAADUghuZGtcgES6hTvzvp5M6np2n5gE2De0cbnY5AAAAAIAmYPDlYQry9VZaVq5+OMjUuIaCcAl1wrWQ9829WsnHm24GAAAAALh0vt7np8b9h6vGNRh86kety8516L/biua/MiUOAAAAAFCbbuxZNDXuy2SmxjUUhEuodV9uTVOuw6nLwpupRyu72eUAAAAAAJqQazqFKdDHS8ey8rQ9NcvsciDCJdSBT4qnxN3ap5UsFovJ1QAAAAAAmhJfby8NuixMkvT1znSTq4FEuIRaduhUjjbsOyWLRRrXmylxAAAAAIDaN6xL0YWjCJcaBsIl1KrFSUckSYM6hinK7m9yNQAAAACApmhY8VXJfzx8WifP5JlcDQiXUKu++PGoJEYtAQAAAADqTqTdT92igmUY0ppdx80ux+MRLqHW7D6Wrd3pZ2TzsmjEFRFmlwMAAAAAaMKuY2pcg0G4hFrzZXKaJGlwp5YK9rOZXA0AAAAAoCkb1qWlJOmbXcdVUOg0uRrPRriEWuMKl27oHmlyJQAAAACApq5XTHM1D7ApK7dAPxw8bXY5Ho1wCbVi34mz2pGaJW+rRSO6MSUOAAAAAFC3vKwWDbm8aPQSU+PMRbiEWvFlcqokKbZjC4UE+JhcDQAAAADAEwwrXndpFeGSqQiXUCuWFU+JG90jyuRKAAAAAACeYsjlLWW1SCnHsnXk9Dmzy/FYdRouZWRkKD4+Xna7XXa7XfHx8Tp9+nSl+xiGoYSEBEVHR8vf319Dhw7Vtm3bSrXJy8vTww8/rLCwMAUGBmrs2LE6fPhwqTZ/+MMfNHDgQAUEBCgkJKTc57JYLGVu8+bNu5SX7JEOncrRlsOZslqkkUyJAwAAAADUk5AAH/Vp01wSo5fMVKfh0oQJE7R582YtW7ZMy5Yt0+bNmxUfH1/pPi+++KJeffVVzZ07Vxs3blRkZKRGjBih7Oxsd5tp06Zp8eLFWrRokdauXaszZ85ozJgxKiwsdLfJz8/XHXfcoQcffLDS53v33XeVmprqvt17772X9qI9kGvUUv/2LdSima/J1QAAAAAAPAlT48znXVcH3rFjh5YtW6b169erf//+kqR33nlHsbGxSklJUefOncvsYxiGXn/9dc2cOVO33nqrJOm9995TRESEPvzwQz3wwAPKzMzU/Pnz9f777+v666+XJC1cuFAxMTH66quvNGrUKEnSs88+K0lasGBBpXWGhIQoMpKrm12KpcXrLY3uwfsIAAAAAKhfwzqH66X/puh/P51QrqNQfjYvs0vyOHU2cikxMVF2u90dLEnSgAEDZLfbtW7dunL32bdvn9LS0jRy5Ej3Nl9fXw0ZMsS9z6ZNm+RwOEq1iY6OVvfu3Ss8bmWmTp2qsLAwXXXVVZo3b56cTme1j+HJUjPPKengaVks0qgrCJcAAAAAAPWra1SQIoP9lOtwav3ek2aX45HqbORSWlqawsPDy2wPDw9XWlpahftIUkRE6XV7IiIidODAAXcbHx8fNW/evEybio5bkeeff17Dhw+Xv7+/Vq5cqRkzZujEiRN6+umny22fl5envLw89/2srCxJksPhkMPhqNZzNxSuumta/5Ifj0iS+rYJUXN/r0b7PsAzXWr/Bxoz+j88Gf0fnoz+j6ZqyOUt9PH3R7Rye5oGdWhebhv6f/VU532qdriUkJDgnnJWkY0bN0oqWjD7QoZhlLu9pAsfr8o+VWlzoZIhUq9evSRJzz33XIXh0uzZs8t97cuXL1dAQEC1nruhWbFiRY32+yjZS5JFMZaTWrp0ae0WBdSTmvZ/oCmg/8OT0f/hyej/aGqCsi2SvLR080H1texTZfEA/b9qcnJyqty22uHS1KlTddddd1Xapl27dtqyZYuOHTtW5rHjx4+XGZnk4lr7KC0tTVFR5y9pn56e7t4nMjJS+fn5ysjIKDV6KT09XQMHDqzuyyllwIABysrK0rFjx8qt8cknn9T06dPd97OyshQTE6ORI0cqODj4kp7bLA6HQytWrNCIESNks9mqte/x7DztXb9GkvTr24cpyu5XFyUCdeZS+j/Q2NH/4cno//Bk9H80VUPyCvTe7FU6mSd1uXqIOrYMLNOG/l89rtlaVVHtcCksLExhYWEXbRcbG6vMzEx99913uvrqqyVJGzZsUGZmZoUhUPv27RUZGakVK1aod+/ekoqu+rZmzRq98MILkqS+ffvKZrNpxYoVGj9+vCQpNTVVycnJevHFF6v7ckpJSkqSn5+fQkJCyn3c19dXvr5lr4Zms9kafcesyWtYueuoDEPqFROiNmFBdVQZUPeaws8wUFP0f3gy+j88Gf0fTU2IzaYBHVro290n9O2eU+oSHVJhW/p/1VTnPaqzNZe6du2quLg4TZ48WW+//bYk6f7779eYMWNKXSmuS5cumj17tsaNGyeLxaJp06Zp1qxZ6tSpkzp16qRZs2YpICBAEyZMkCTZ7XZNmjRJM2bMUIsWLRQaGqpHH31UPXr0cF89TpIOHjyoU6dO6eDBgyosLNTmzZslSZdddpmaNWumL774QmlpaYqNjZW/v79WrVqlmTNn6v777y83QEJZX27lKnEAAAAAgIZhWOdwfbv7hL7ema7J13YwuxyPUmfhkiR98MEHeuSRR9xXdhs7dqzmzp1bqk1KSooyMzPd9x977DGdO3dOU6ZMUUZGhvr376/ly5crKOj8yJjXXntN3t7eGj9+vM6dO6fhw4drwYIF8vI6f7nB3/3ud3rvvffc910joVatWqWhQ4fKZrPpzTff1PTp0+V0OtWhQwc999xzeuihh+rkvWhqTp7Jc6/Cf0P3qIu0BgAAAACgbl3XJVzP/We7Nu4/pexch4L8GJ1UX+o0XAoNDdXChQsrbWMYRqn7FotFCQkJSkhIqHAfPz8/zZkzR3PmzKmwzYIFC7RgwYIKH4+Li1NcXFyltaFiy7cfk9OQurcKVkxo417MHAAAAADQ+LULC1SHsEDtPXFWa3ef0A09GAhRX6xmF4DG6cvkNEmMWgIAAAAANBxDO4dLkr7emW5yJZ6FcAnVdjonX+v2nJAk3dCd9ZYAAAAAAA3DdV2KwqVVKcfldBoXaY3aQriEalux/ZgKnIa6RAapQ8tmZpcDAAAAAIAk6ar2zRXo46UTZ/K07WiW2eV4DMIlVBtT4gAAAAAADZGvt5cGXRYmialx9YlwCdWSlevQ2t1FU+JG92BKHAAAAACgYXFNjfs6hXCpvhAuoVq+3pGu/EKnLgtvpk4RQWaXAwAAAABAKcOKw6Uth0/rxJk8k6vxDIRLqJalW1MlsZA3AAAAAKBhigj2U7eoYBmGtCbluNnleATCJVTZ2bwCrdlV9IPJeksAAAAAgIaKqXH1i3AJVbYqJV15BU61axGgrlFMiQMAAAAANEyuqXHf7DouR6HT5GqaPsIlVNmXW4uuEhfXPUoWi8XkagAAAAAAKF+vmBA1D7ApO7dAPxzIMLucJo9wCVVyLr/QfRlHrhIHAAAAAGjIvKwWDbm8pSSmxtUHwiVUyZpdx3XOUahWIf7q0cpudjkAAAAAAFTKNTVu1U7CpbpGuIQqWZZcdJW40T0imRIHAAAAAGjwru3UUhaLtOvYGaVn55pdTpNGuISLKnQaWl18lbjru0aYXA0AAAAAABfXPNBHXSODJUmJP500uZqmjXAJF7X5UIZO5zgU7Oetvm2bm10OAAAAAABVEtuxhSRp/V7CpbpEuISLWrWzaNTStZe3lLcXXQYAAAAA0DgMLA6XGLlUt0gKcFGuq8RdV7wYGgAAAAAAjcFV7UNltUj7T+YoNZN1l+oK4RIqlZaZq+2pWbJY5L6MIwAAAAAAjUGwn819xfP1e0+ZXE3TRbiESq1OKRq1dGXrELVo5mtyNQAAAAAAVE9sxzBJ0vp9hEt1hXAJlWJKHAAAAACgMTu/qPcpGYbJxTRRhEuoUF5BodbuOSFJGtaZcAkAAAAA0Phc1a65vK0WHc3M1ck8s6tpmgiXUKGN+zKUk1+olkG+uiI62OxyAAAAAACotgAfb/WKCZEk7c60mFtME0W4hAq5psQNvbylrFZ+AAEAAAAAjZNratzuLD7b1gXCJVTItZg36y0BAAAAABozd7iUaZHBwku1jnAJ5dp/4qz2njgrb6tF13QKM7scAAAAAABqrE+b5vLxtirLYdHeEzlml9PkEC6hXK4pcVe1C1WQn83kagAAAAAAqDk/m5f6xNglSev3nTK5mqaHcAnlWsWUOAAAAABAE9K/fagkacNewqXaRriEMs7mFbh/2IZ1aWlyNQAAAAAAXLoBHYrCpfX7TsnpZN2l2kS4hDLW/XRS+YVOxYT6q2PLZmaXAwAAAADAJevZyi4fq6GMHId2pWebXU6TQriEMlzrLV3XOVwWC5dpBAAAAAA0fj7eVnUIKhqxtG7PSZOraVoIl1CKYRhaXbze0lDWWwIAAAAANCGd7EXhUuJewqXaRLiEUnamZSs1M1d+NqtiO7QwuxwAAAAAAGpNp+CicGnD3pMqZN2lWkO4hFJcU+IGdQyTn83L5GoAAAAAAKg9rZtJgb5eysot0PajWWaX02QQLqEUpsQBAAAAAJoqL4t0dbvmkqTEvSdMrqbpIFyC2+mcfG06kCFJGta5pcnVAAAAAABQ+wa0D5VUdKV01A7CJbit2XVcTkO6PKKZWjcPMLscAAAAAABq3YAOReHSxn2n5Ch0mlxN00C4BLfVKcclScOYEgcAAAAAaKK6RAQpJMCms/mF2nok0+xymgTCJUiSCp2Ge72l6zoTLgEAAAAAmiar1aL+xVPjEpkaVysIlyBJ2nI4Uxk5DgX5eatP2+ZmlwMAAAAAQJ0Z2DFMEuFSbSFcgiRp9a6iVfKvvbylbF50CwAAAABA0xXbsYUk6fsDp5RXUGhyNY0fKQIkSat3Fa+3xJQ4AAAAAEAT1ym8mcKa+SjX4dTmg6fNLqfRI1yCMvOl7anZslikoZ1bml0OAAAAAAB1ymKxaECHotFLiXuZGnepCJeg7RkWSVLP1iEKa+ZrcjUAAAAAANQ919S4day7dMkIl6Dtp4vCpWGMWgIAAAAAeAjXot6bD55WroN1ly4F4ZKHyy9wKqU4XLquC+stAQAAAAA8Q7sWAYoM9lN+oVObDmSYXU6jRrjk4b4/kKE8p0VhzXzUPdpudjkAAAAAANQLi8VSYmrcCZOradwIlzzcml1FP0DXdgqT1WoxuRoAAAAAAOqPK1xKZN2lS0K45OHO5hfKy2Jo6OVhZpcCAAAAAEC9ii2+YtyPhzN1Jq/A5GoaL8IlD/f7m7tp9lWFuo7FvAEAAAAAHiYmNEAxof4qdBrauP+U2eU0WoRLkK+X5GvzMrsMAAAAAADqnWv00nqmxtUY4RIAAAAAAPBY5xf1JlyqKcIlAAAAAADgsQYUj1zanpqls6y7VCOESwAAAAAAwGNF2f0VZfdTodPQj4dPm11Oo0S4BAAAAAAAPFqfts0lSUkHT5tbSCNFuAQAAAAAADxanzZF4dKmAxkmV9I41Wm4lJGRofj4eNntdtntdsXHx+v06dOV7mMYhhISEhQdHS1/f38NHTpU27ZtK9UmLy9PDz/8sMLCwhQYGKixY8fq8OHD7sf379+vSZMmqX379vL391fHjh31zDPPKD8/v9RxDh48qJtuukmBgYEKCwvTI488UqYNAAAAAABo2vq6Ry5lyDAMk6tpfOo0XJowYYI2b96sZcuWadmyZdq8ebPi4+Mr3efFF1/Uq6++qrlz52rjxo2KjIzUiBEjlJ2d7W4zbdo0LV68WIsWLdLatWt15swZjRkzRoWFhZKknTt3yul06u2339a2bdv02muvad68eXrqqafcxygsLNSNN96os2fPau3atVq0aJE++eQTzZgxo27eDAAAAAAA0CB1iwqWr7dVGTkO7Ttx1uxyGh3vujrwjh07tGzZMq1fv179+/eXJL3zzjuKjY1VSkqKOnfuXGYfwzD0+uuva+bMmbr11lslSe+9954iIiL04Ycf6oEHHlBmZqbmz5+v999/X9dff70kaeHChYqJidFXX32lUaNGKS4uTnFxce7jdujQQSkpKXrrrbf08ssvS5KWL1+u7du369ChQ4qOjpYkvfLKK5o4caL+8Ic/KDg4uK7eGgAAAAAA0ID4eFvVs7VdG/dnaNOBDHVo2czskhqVOguXEhMTZbfb3cGSJA0YMEB2u13r1q0rN1zat2+f0tLSNHLkSPc2X19fDRkyROvWrdMDDzygTZs2yeFwlGoTHR2t7t27a926dRo1alS59WRmZio0NLRUfd27d3cHS5I0atQo5eXladOmTRo2bFiZY+Tl5SkvL899PysrS5LkcDjkcDiq8rY0OK66G2v9wKWg/8OT0f/hyej/8GT0f3iyi/X/K4vDpe/3n9ItV0bWZ2kNUnXOE3UWLqWlpSk8PLzM9vDwcKWlpVW4jyRFRESU2h4REaEDBw642/j4+Kh58+Zl2lR03J9++klz5szRK6+8Uuq5Lnye5s2by8fHp8LjzJ49W88++2yZ7cuXL1dAQEC5+zQWK1asMLsEwDT0f3gy+j88Gf0fnoz+D09WUf93nrRI8tI32w5pqW1/vdbUEOXk5FS5bbXDpYSEhHIDlpI2btwoSbJYLGUeMwyj3O0lXfh4VfapqM3Ro0cVFxenO+64Q7/85S8rfZ6LPdeTTz6p6dOnu+9nZWUpJiZGI0eObLTT6BwOh1asWKERI0bIZrOZXQ5Qr+j/8GT0f3gy+j88Gf0fnuxi/f+q7Dz97cU1Ssu1aPB1IxTk59k/I67ZWlVR7XBp6tSpuuuuuypt065dO23ZskXHjh0r89jx48fLjBhyiYwsGnaWlpamqKgo9/b09HT3PpGRkcrPz1dGRkap0Uvp6ekaOHBgqeMdPXpUw4YNU2xsrP7yl7+Uea4NGzaU2paRkSGHw1Fhfb6+vvL19S2z3WazNfoTc1N4DUBN0f/hyej/8GT0f3gy+j88WUX9PzrUpphQfx06dU7JqWd17eUtTaiu4ajOOaLaV4sLCwtTly5dKr35+fkpNjZWmZmZ+u6779z7btiwQZmZmWVCIJf27dsrMjKy1BC1/Px8rVmzxr1P3759ZbPZSrVJTU1VcnJyqeMeOXJEQ4cOVZ8+ffTuu+/Kai39UmNjY5WcnKzU1FT3tuXLl8vX11d9+/at7tsCAAAAAAAaub5tigax/HAww+RKGpdqh0tV1bVrV8XFxWny5Mlav3691q9fr8mTJ2vMmDGlFvPu0qWLFi9eLKlomtq0adM0a9YsLV68WMnJyZo4caICAgI0YcIESZLdbtekSZM0Y8YMrVy5UklJSbrnnnvUo0cP99Xjjh49qqFDhyomJkYvv/yyjh8/rrS0tFJrKY0cOVLdunVTfHy8kpKStHLlSj366KOaPHlyo53iBgAAAAAAaq5PW1e4dNrcQhqZOlvQW5I++OADPfLII+4ru40dO1Zz584t1SYlJUWZmZnu+4899pjOnTunKVOmKCMjQ/3799fy5csVFBTkbvPaa6/J29tb48eP17lz5zR8+HAtWLBAXl5ekopGIO3Zs0d79uxR69atSz2fYRiSJC8vLy1ZskRTpkzRoEGD5O/vrwkTJujll1+uk/cCAAAAAAA0bH2KRy4lHcyQ02nIaq18/WcUqdNwKTQ0VAsXLqy0jSvscbFYLEpISFBCQkKF+/j5+WnOnDmaM2dOuY9PnDhREydOvGh9bdq00X/+85+LtgMAAAAAAE1fl8ggBfh4KTu3QHuOn9HlEUEX3wl1Ny0OAAAAAACgMfH2sqpna7skadMB1l2qKsIlAAAAAACAYn1d6y4RLlUZ4RIAAAAAAEAx17pLm7hiXJURLgEAAAAAABTrXRwu7T1+Vhln802upnEgXAIAAAAAACgWGuijDmGBkqSkQ4xeqgrCJQAAAAAAgBL6uNddOm1uIY0E4RIAAAAAAEAJrnWXfmDdpSohXAIAAAAAACjBdcW4zYdOq6DQaXI1DR/hEgAAAAAAQAmdwpspyNdbOfmFSjmWbXY5DR7hEgAAAAAAQAlWq0W92oRIkn44wNS4iyFcAgAAAAAAuMD5dZdOm1tII0C4BAAAAAAAcAHXFeM2MXLpogiXAAAAAAAALtArJkQWi3TwVI5OnMkzu5wGjXAJAAAAAADgAnZ/mzqFN5PEuksXQ7gEAAAAAABQjr6uqXEHCZcqQ7gEAAAAAABQjt7Fi3onHThtbiENHOESAAAAAABAOVxXjPvx8GnlFzhNrqbhIlwCAAAAAAAoR4ewQIUE2JRX4NSO1Cyzy2mwCJcAAAAAAADKYbVa1DsmRJK0iUW9K0S4BAAAAAAAUAHXot4/sKh3hQiXAAAAAAAAKuBadynp4GlzC2nACJcAAAAAAAAqcGVMiKwW6cjpc0rLzDW7nAaJcAkAAAAAAKACgb7e6hIZLImpcRUhXAIAAAAAAKiEa90lFvUuH+ESAAAAAABAJfq0DZHEyKWKEC4BAAAAAABUwrWod/KRTOU6Ck2upuEhXAIAAAAAAKhEm9AAhTXzkaPQ0LajmWaX0+AQLgEAAAAAAFTCYrGodxvWXaoI4RIAAAAAAMBFuBb1/uHAaXMLaYAIlwAAAAAAAC7Cte5S0iFGLl2IcAkAAAAAAOAirogOlsUiHcvK0/HsPLPLaVAIlwAAAAAAAC4i0NdbHcICJRVdNQ7nES4BAAAAAABUQY9WdkmESxciXAIAAAAAAKiC7sXh0lbCpVIIlwAAAAAAAKqgOyOXykW4BAAAAAAAUAVXRAdLko5m5urkGRb1diFcAgAAAAAAqIIgP9v5Rb2PZplcTcNBuAQAAAAAAFBFVzA1rgzCJQAAAAAAgCrq0apoahzh0nmESwAAAAAAAFXEFePKIlwCAAAAAACooiuii8KlwxnnlHE23+RqGgbCJQAAAAAAgCqy+9vUtkWAJGkbi3pLIlwCAAAAAACoFqbGlUa4BAAAAAAAUA3do7liXEmESwAAAAAAANXQo3jkUvJRwiWJcAkAAAAAAKBaurcKliQdOJmjzHMOk6sxH+ESAAAAAABANYQE+Kh1c39J0jamxhEuAQAAAAAAVBdT484jXAIAAAAAAKim81eMyzK5EvMRLgEAAAAAAFSTK1ziinGESwAAAAAAANXmmha378RZZed69qLehEsAAAAAAADVFBroo1YhxYt6H/XsqXGESwAAAAAAADVwRXSwJKbGES4BAAAAAADUQA/WXZJUx+FSRkaG4uPjZbfbZbfbFR8fr9OnT1e6j2EYSkhIUHR0tPz9/TV06FBt27atVJu8vDw9/PDDCgsLU2BgoMaOHavDhw+7H9+/f78mTZqk9u3by9/fXx07dtQzzzyj/Pz8UsexWCxlbvPmzau11w8AAAAAAJqu7q1dV4wjXKozEyZM0ObNm7Vs2TItW7ZMmzdvVnx8fKX7vPjii3r11Vc1d+5cbdy4UZGRkRoxYoSys7PdbaZNm6bFixdr0aJFWrt2rc6cOaMxY8aosLBQkrRz5045nU69/fbb2rZtm1577TXNmzdPTz31VJnne/fdd5Wamuq+3XvvvbX7JgAAAAAAgCape3RRuLT3xFmdySswuRrzeNfVgXfs2KFly5Zp/fr16t+/vyTpnXfeUWxsrFJSUtS5c+cy+xiGoddff10zZ87UrbfeKkl67733FBERoQ8//FAPPPCAMjMzNX/+fL3//vu6/vrrJUkLFy5UTEyMvvrqK40aNUpxcXGKi4tzH7dDhw5KSUnRW2+9pZdffrnUc4aEhCgyMrKu3gYAAAAAANBEtQzyVWSwn9KycrUjNUtXtQs1uyRT1NnIpcTERNntdnewJEkDBgyQ3W7XunXryt1n3759SktL08iRI93bfH19NWTIEPc+mzZtksPhKNUmOjpa3bt3r/C4kpSZmanQ0LL/k6dOnaqwsDBdddVVmjdvnpxOZ7VfKwAAAAAA8Ezdi9dd2nrYc6fG1dnIpbS0NIWHh5fZHh4errS0tAr3kaSIiIhS2yMiInTgwAF3Gx8fHzVv3rxMm4qO+9NPP2nOnDl65ZVXSm1//vnnNXz4cPn7+2vlypWaMWOGTpw4oaeffrrc4+Tl5SkvL899Pyur6FKDDodDDoej3H0aOlfdjbV+4FLQ/+HJ6P/wZPR/eDL6PzxZXfX/bpHN9NWOY9p6OEMOR+taPbaZqvM+VTtcSkhI0LPPPltpm40bN0oqWjD7QoZhlLu9pAsfr8o+FbU5evSo4uLidMcdd+iXv/xlqcdKhki9evWSJD333HMVhkuzZ88u97UvX75cAQEBldbX0K1YscLsEgDT0P/hyej/8GT0f3gy+j88WW33/3MZFkleSkw5qqVLD9Xqsc2Uk5NT5bbVDpemTp2qu+66q9I27dq105YtW3Ts2LEyjx0/frzMyCQX19pHaWlpioqKcm9PT0937xMZGan8/HxlZGSUGr2Unp6ugQMHljre0aNHNWzYMMXGxuovf/nLRV/bgAEDlJWVpWPHjpVb45NPPqnp06e772dlZSkmJkYjR45UcHDwRY/fEDkcDq1YsUIjRoyQzWYzuxygXtH/4cno//Bk9H94Mvo/PFld9f9+2Xl6Z+capedaNPT6kQrwqbNJYvXKNVurKqr9isPCwhQWFnbRdrGxscrMzNR3332nq6++WpK0YcMGZWZmlgmBXNq3b6/IyEitWLFCvXv3liTl5+drzZo1euGFFyRJffv2lc1m04oVKzR+/HhJUmpqqpKTk/Xiiy+6j3XkyBENGzZMffv21bvvviur9eLLSyUlJcnPz08hISHlPu7r6ytfX98y2202W6M/MTeF1wDUFP0fnoz+D09G/4cno//Dk9V2/28ValPLIF8dz87TnhO56tu2+cV3agSq8x7VWZzWtWtXxcXFafLkyXr77bclSffff7/GjBlT6kpxXbp00ezZszVu3DhZLBZNmzZNs2bNUqdOndSpUyfNmjVLAQEBmjBhgiTJbrdr0qRJmjFjhlq0aKHQ0FA9+uij6tGjh/vqcUePHtXQoUPVpk0bvfzyyzp+/Lj7+Vyjo7744gulpaUpNjZW/v7+WrVqlWbOnKn777+/3AAJAAAAAACgPD1a2fX1znQlH8lsMuFSddTpWK0PPvhAjzzyiPvKbmPHjtXcuXNLtUlJSVFm5vkV1R977DGdO3dOU6ZMUUZGhvr376/ly5crKCjI3ea1116Tt7e3xo8fr3Pnzmn48OFasGCBvLy8JBWtgbRnzx7t2bNHrVuXXkzLMAxJRQncm2++qenTp8vpdKpDhw567rnn9NBDD9XJewEAAAAAAJqm7sXh0tYjnnnFuDoNl0JDQ7Vw4cJK27jCHheLxaKEhAQlJCRUuI+fn5/mzJmjOXPmlPv4xIkTNXHixEqfNy4uTnFxcZW2AQAAAAAAuJju0UXrMCd7aLh08YWIAAAAAAAAUKEere2SpN3pZ5TrKDS5mvpHuAQAAAAAAHAJIoP9FNbMR4VOQztSq36VtaaCcAkAAAAAAOASWCwWXRFdNHop+SjhEgAAAAAAAKqpR6vicOmw5627RLgEAAAAAABwiboXh0ueeMU4wiUAAAAAAIBL1L1V0RXjdh3LVl6BZy3qTbgEAAAAAABwiVqF+Kt5gE0FTkMpadlml1OvCJcAAAAAAAAukcVi8dipcYRLAAAAAAAAtcAVLiUf8awrxhEuAQAAAAAA1AL3FeMYuQQAAAAAAIDqcoVLKWnZyi9wmlxN/SFcAgAAAAAAqAWtm/vL7m9TfqFTu455zqLehEsAAAAAAAC1oGhR72BJnjU1jnAJAAAAAACglnjiFeMIlwAAAAAAAGpJ9+jiRb2Pes4V4wiXAAAAAAAAakmPVnZFBPuqdYi/DMMwu5x64W12AQAAAAAAAE1Fu7BAbXjqerPLqFeMXAIAAAAAAECNES4BAAAAAACgxgiXAAAAAAAAUGOESwAAAAAAAKgxwiUAAAAAAADUGOESAAAAAAAAaoxwCQAAAAAAADVGuAQAAAAAAIAaI1wCAAAAAABAjREuAQAAAAAAoMYIlwAAAAAAAFBjhEsAAAAAAACoMcIlAAAAAAAA1BjhEgAAAAAAAGrM2+wCGjPDMCRJWVlZJldScw6HQzk5OcrKypLNZjO7HKBe0f/hyej/8GT0f3gy+j88Gf2/elxZhyv7qAzh0iXIzs6WJMXExJhcCQAAAAAAQO3Lzs6W3W6vtI3FqEoEhXI5nU4dPXpUQUFBslgsZpdTI1lZWYqJidGhQ4cUHBxsdjlAvaL/w5PR/+HJ6P/wZPR/eDL6f/UYhqHs7GxFR0fLaq18VSVGLl0Cq9Wq1q1bm11GrQgODuaHCx6L/g9PRv+HJ6P/w5PR/+HJ6P9Vd7ERSy4s6A0AAAAAAIAaI1wCAAAAAABAjREueThfX18988wz8vX1NbsUoN7R/+HJ6P/wZPR/eDL6PzwZ/b/usKA3AAAAAAAAaoyRSwAAAAAAAKgxwiUAAAAAAADUGOESAAAAAAAAaoxwCQAAAAAAADVGuOSBMjIyFB8fL7vdLrvdrvj4eJ0+fbrSfSZOnCiLxVLqNmDAgPopGLgEb775ptq3by8/Pz/17dtX3377baXt16xZo759+8rPz08dOnTQvHnz6qlSoPZVp/+vXr26zHneYrFo586d9VgxcOm++eYb3XTTTYqOjpbFYtG///3vi+7DuR9NRXX7P+d+NCWzZ8/WVVddpaCgIIWHh+uWW25RSkrKRffjd0DtIFzyQBMmTNDmzZu1bNkyLVu2TJs3b1Z8fPxF94uLi1Nqaqr7tnTp0nqoFqi5jz/+WNOmTdPMmTOVlJSkwYMH64YbbtDBgwfLbb9v3z6NHj1agwcPVlJSkp566ik98sgj+uSTT+q5cuDSVbf/u6SkpJQ613fq1KmeKgZqx9mzZ3XllVdq7ty5VWrPuR9NSXX7vwvnfjQFa9as0UMPPaT169drxYoVKigo0MiRI3X27NkK9+F3QO2xGIZhmF0E6s+OHTvUrVs3rV+/Xv3795ckrV+/XrGxsdq5c6c6d+5c7n4TJ07U6dOnq/TXP6Ch6N+/v/r06aO33nrLva1r16665ZZbNHv27DLtH3/8cX3++efasWOHe9uvfvUr/fjjj0pMTKyXmoHaUt3+v3r1ag0bNkwZGRkKCQmpx0qBumOxWLR48WLdcsstFbbh3I+mqir9n3M/mrLjx48rPDxca9as0bXXXltuG34H1B5GLnmYxMRE2e12d7AkSQMGDJDdbte6desq3Xf16tUKDw/X5ZdfrsmTJys9Pb2uywVqLD8/X5s2bdLIkSNLbR85cmSFfT0xMbFM+1GjRun777+Xw+Gos1qB2laT/u/Su3dvRUVFafjw4Vq1alVdlgk0CJz7Ac79aJoyMzMlSaGhoRW24XdA7SFc8jBpaWkKDw8vsz08PFxpaWkV7nfDDTfogw8+0Ndff61XXnlFGzdu1HXXXae8vLy6LBeosRMnTqiwsFARERGltkdERFTY19PS0sptX1BQoBMnTtRZrUBtq0n/j4qK0l/+8hd98skn+vTTT9W5c2cNHz5c33zzTX2UDJiGcz88Ged+NFWGYWj69Om65ppr1L179wrb8Tug9nibXQBqR0JCgp599tlK22zcuFFS0RDZCxmGUe52lzvvvNP9fffu3dWvXz+1bdtWS5Ys0a233lrDqoG6d2G/vlhfL699eduBxqA6/b9z586lpkbHxsbq0KFDevnllyscSg40FZz74ak496Opmjp1qrZs2aK1a9detC2/A2oH4VITMXXqVN11112VtmnXrp22bNmiY8eOlXns+PHjZRLbykRFRalt27bavXt3tWsF6kNYWJi8vLzKjNJIT0+vsK9HRkaW297b21stWrSos1qB2laT/l+eAQMGaOHChbVdHtCgcO4HSuPcj8bu4Ycf1ueff65vvvlGrVu3rrQtvwNqD+FSExEWFqawsLCLtouNjVVmZqa+++47XX311ZKkDRs2KDMzUwMHDqzy8508eVKHDh1SVFRUjWsG6pKPj4/69u2rFStWaNy4ce7tK1as0M0331zuPrGxsfriiy9KbVu+fLn69esnm81Wp/UCtakm/b88SUlJnOfR5HHuB0rj3I/GyjAMPfzww1q8eLFWr16t9u3bX3QffgfUIgMeJy4uzujZs6eRmJhoJCYmGj169DDGjBlTqk3nzp2NTz/91DAMw8jOzjZmzJhhrFu3zti3b5+xatUqIzY21mjVqpWRlZVlxksAqmTRokWGzWYz5s+fb2zfvt2YNm2aERgYaOzfv98wDMN44oknjPj4eHf7vXv3GgEBAcavf/1rY/v27cb8+fMNm81m/Otf/zLrJQA1Vt3+/9prrxmLFy82du3aZSQnJxtPPPGEIcn45JNPzHoJQI1kZ2cbSUlJRlJSkiHJePXVV42kpCTjwIEDhmFw7kfTVt3+z7kfTcmDDz5o2O12Y/Xq1UZqaqr7lpOT427D74C6Q7jkgU6ePGn87Gc/M4KCgoygoCDjZz/7mZGRkVGqjSTj3XffNQzDMHJycoyRI0caLVu2NGw2m9GmTRvj3nvvNQ4ePFj/xQPV9MYbbxht27Y1fHx8jD59+hhr1qxxP3bvvfcaQ4YMKdV+9erVRu/evQ0fHx+jXbt2xltvvVXPFQO1pzr9/4UXXjA6duxo+Pn5Gc2bNzeuueYaY8mSJSZUDVyaVatWGZLK3O69917DMDj3o2mrbv/n3I+mpLy+X/JzrWHwO6AuWQyjeLUqAAAAAAAAoJqsZhcAAAAAAACAxotwCQAAAAAAADVGuAQAAAAAAIAaI1wCAAAAAABAjREuAQAAAAAAoMYIlwAAAAAAAFBjhEsAAAAAAACoMcIlAAAAAAAA1BjhEgAAAAAAAGqMcAkAAAAAAAA1RrgEAAAAAACAGiNcAgAAAAAAQI39P61Q/BFHzjPpAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1400x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[14,5])\n",
    "plot(xplot, np.sin(xplot) - evaluate_polynomial(xplot, c))\n",
    "title(\"errors fitting at N = 50 points\")\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "compatible-republican",
   "metadata": {},
   "source": [
    "Not much changes!\n",
    "\n",
    "This hints at another use of least squares fitting:\n",
    "fitting a simpler curve (like a cubic) to a function (like $\\sin(x)$), rather than to discrete data."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "musical-illness",
   "metadata": {},
   "source": [
    "## Nonlinear fitting: power-law relationships\n",
    "\n",
    "When data $(x_i, y_i)$ is inherently positive, it is often natural to seek an approximate power law relationship\n",
    "\n",
    "$$ y_i \\approx c x_i^p$$\n",
    "\n",
    "That is, one seeks the power $p$ and scale factor $c$ that minimizes error in some sense.\n",
    "\n",
    "When the magnitudes and the data $y_i$ vary greatly, it is often appropriate to look at the relative errors\n",
    "\n",
    "$$ e_i = \\left| \\frac{c x_i^p - y_i}{y_i} \\right| $$\n",
    "\n",
    "and this can be shown to be very close to looking at the absolute errors of the logarithms\n",
    "\n",
    "$$ |\\ln(c x_i^p) - \\ln(y_i)| = |\\ln(c) + p \\ln(x_i) - \\ln(y_i)| $$\n",
    "\n",
    "Introducing the new variables $X_i = \\ln(x_i)$, $Y_i = \\ln(Y_i)$ and $C = \\ln(c)$,\n",
    "this becomes the familiar problem of finding a linear approxation of the data $Y_i$ by $C + p X_i$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "conditional-cream",
   "metadata": {},
   "source": [
    "## A simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "rural-arlington",
   "metadata": {},
   "outputs": [],
   "source": [
    "cexact = 2.0\n",
    "pexact = 1.5\n",
    "x = np.logspace(0.01, 2.0, 10)\n",
    "xplot = np.logspace(0.01, 2.0)  # For graphs later\n",
    "yexact = cexact * x**pexact\n",
    "y = yexact * (1.0 + (random(len(yexact))- 0.5)/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "determined-compromise",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[12,6])\n",
    "plot(x, yexact, '.', label='exact')\n",
    "plot(x, y, '*', label='noisy')\n",
    "legend()\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "constitutional-realtor",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[12,6])\n",
    "loglog(x, yexact, '.', label='exact')\n",
    "loglog(x, y, '*', label='noisy')\n",
    "legend()\n",
    "grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "interim-montgomery",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "C=2.124828507552144, p=1.468500681953282\n"
     ]
    }
   ],
   "source": [
    "X = np.log(x)\n",
    "Y = np.log(y)\n",
    "Cp = fit_polynomial_least_squares(X, Y, 1)\n",
    "C = np.exp(Cp[0])\n",
    "p = Cp[1]\n",
    "print(f\"{C=}, {p=}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "clinical-accused",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[12,6])\n",
    "plot(x, yexact, '.', label='exact')\n",
    "plot(x, y, '*', label='noisy')\n",
    "plot(xplot, C * xplot**p)\n",
    "legend()\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "institutional-shame",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[12,6])\n",
    "loglog(x, yexact, '.', label='exact')\n",
    "loglog(x, y, '*', label='noisy')\n",
    "loglog(xplot, C * xplot**p)\n",
    "legend()\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16f4319d-5617-48b9-b7a0-2feecfc2f9b5",
   "metadata": {},
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38168895-9488-4d6e-a3f8-41ea2ebc29c1",
   "metadata": {},
   "source": [
    "```{exercise-start}\n",
    ":label: :least-squares-exercise-1\n",
    "```\n",
    "For the following data, find:\n",
    "\n",
    "1. A linear least squares fit\n",
    "\n",
    "$$\n",
    "\\text{(Blood Pressure)} \\approx P_0  + P_1 \\text{(Weight)}.\n",
    "$$\n",
    "\n",
    "2. A power law fit\n",
    "\n",
    "$$\n",
    "\\text{(Blood Pressure)} \\approx P \\text{(Weight)}^a.\n",
    "$$\n",
    "\n",
    "Illustrate your results with graphs, and compare how the two methods perform.\n",
    "\n",
    "| Species    | Blood Pressure (mm Hg) | Weight (g) |\n",
    "| ---------- | ---------------------- | ---------- |\n",
    "| Cow        | 157                    | 800,000    |\n",
    "| Cat        | 129                    | 2,000      |\n",
    "| Dog        | 120                    | 5,000      |\n",
    "| Duck       | 162                    | 2,000      |\n",
    "| Frog       | 24                     | 50         |\n",
    "| Giraffe    | 300                    | 900,000    |\n",
    "| Goat       | 98                     | 30,000     |\n",
    "| Guinea Pig | 60                     | 100        |\n",
    "| Human      | 120                    | 90,000     |\n",
    "| Monkey     | 140                    | 5,000      |\n",
    "| Monkey     | 128                    | 150,000    |\n",
    "| Snake      | 55                     | 100        |\n",
    "| Turkey     | 193                    | 15,000     |\n",
    "\n",
    "\n",
    "This can be done using Python or by hand; for those who wish to do it with a notebook; I will provide a notebook version of this table.\n",
    "\n",
    "Be sure to provide final verbal comments and explanation of your results, not just numerical output.\n",
    "```{exercise-end}\n",
    "```"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.12.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
