{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "instrumental-peace",
   "metadata": {},
   "source": [
    "# Least-squares Fitting to Data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b6fe15e-a215-40b1-bab6-d06b76e2b752",
   "metadata": {},
   "source": [
    "**References:**\n",
    "\n",
    "- Chapter 4 *Least Squares* of {cite}`Sauer`, sections 1 and 2.\n",
    "- Section 8.1 *Discrete Least Squares Approximation* of {cite}`Burden-Faires`."
   ]
  },
  {
   "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 numericalMethods import solveLinearSystem\n",
    "from numericalMethods import evaluatePolynomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e31e3991-b3bf-4eba-be46-cfbe227e266c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numericalMethods 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": {
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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 linefit(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 = solveLinearSystem(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 [3.1081582  1.82658183]\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 = linefit(x, y)\n",
    "print(\"The coefficients are\", c)\n",
    "xplot = np.linspace(-1, 1, 100)\n",
    "plot(xplot, evaluatePolynomial(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": 8,
   "id": "ec6ba21c-b9c6-41a1-87e5-153495d8232e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def fitPolynomialLeastSquares(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 = solveLinearSystem(M, p)\n",
    "    return c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "armed-baghdad",
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The coefficients are [-0.00108728  1.02381733 -0.06859178 -0.11328717]\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 = 3\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 = fitPolynomialLeastSquares(xdata, ydata, n)\n",
    "print(\"The coefficients are\", c)\n",
    "plot(xplot, evaluatePolynomial(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": 11,
   "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) - evaluatePolynomial(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": 12,
   "id": "proud-token",
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The coefficients are [-0.00200789  1.02647568 -0.06970463 -0.1137182 ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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MXL9uZFNXr8KBA3fvpqcnFC4MRYoYx52/L1LECIYy0I+pIsmkaeBz/fp1jhw5Yn98/Phxdu/eTa5cuShcuDDDhw/n9OnTfPXVVwD07duXKVOmMGjQIHr37s2WLVsIDg5m/vz5adnNB/JQv1mmgslksi9nGjVqFEWKFGHRokVJlrPdjypVqrB/f/K/BQcPHoyLiwvLly+nRYsWtGzZMllx5r1799KuXbu7PnfZsmXZunUr3bp1s5/bunVrkjYbN25k2rRptGjRAjCWmF24cCFJGzc3NxISEpLd1717d3sx5+vXr3PixIl/f8MiIiIi4lD33LHKaoXTp7EePsLl7Uf4+6dQLm4/RiDH8eIEcAkADyB5VU/DDbw5RSFOU4BwChJOQbKXLkjO8gXxKF4Q3zL5yFU6D/kKmslhgWqlkgc4H05N+d/1D/Ifvg/680LBgvf3s0Vat08TiUlK4cL3bmezGTOGTp26fYSFJX0cHg4WCy6nwvA6FYYXa8kLPHrn8/j4QPHiUKEYPFuKm4VLE5mzDCc9SxMWlZPTp0lyhIcbeVNMDBw+bBwpcXExZgIVL24cxYol/X3OnA/n4xJ5UGka+Gzfvt1eJBiwhxMvvPACc+fOJSIigrCwMPv1wMBAli1bxsCBA5k6dSr58+fns88+y5BbskP6fbPctm0bq1evJigoiLx587Jt2zbOnz9P2f9QMKhp06bMmzcvybmlS5cye/ZstmzZQtWqVRk2bBgvvPACf//9t3352IkTJzh9+vQ9d8V6/fXXeeGFF6hevTpPPPEE3377Lfv27bPvvAVQokQJvv76a6pXr05UVBRvvvkmXl5eSZ6naNGirF69mjp16uDh4cEjjzxCiRIlWLhwIa1atcJkMvH222//5x3XRERERCRtBQfDS71tBNjOUIZDDGl7hDLmUKyHj+AVHsojl4/iYY3BBcgNNEjhOS6Si+MEctq1KFcfKUpMvqKYAgPxKl2YhPyF6DHAN/kSqt/u/u/19AhwMkS4kpmZTJArl3FUqpRyG6vVmB10/DgcO2YcR4/e/v2ZM8Zys127jAPwAgJvHfj7Q5kyRt2Oerd+LVOGuPxFCT/jcmuJmJEzJf4+8XFc3O3Ha9Yk71quXLfDn1KljKdO/PUu5VBFHqo0DXzq169vL7qckrlz5yY79+STT7Jz58407FXm4+Pjw4YNG5g0aRJRUVEUKVKEiRMn0rx58wd+zueff56hQ4dy6NAhSpcuzfnz5+nZsydjxoyxb40+evRoVq1aRd++fVmwYAFgbOceFBRkLx6dko4dO3L06FGGDh1KTEwMzz77LC+//DIrV660t5k9ezYvvfQSVapUoXDhwrz//vu88cYbSZ5n4sSJDBo0iC+++IICBQpw4sQJPv30U1588UVq166Nn58fQ4cOva+iVSIiIiLycNx1xo7FAkePErPrAJc2HyRq2wEq/HmQyxzEh2tGm4XJn8+CK8cJ5KipBKG2EhylOMcJ5DiBnKQIE2f50K4dVH8k5f7EZ1eA45RcXCBfPuOoXTv59Zs3b4dBR44Y03UOHoRDh4ww6OxZ41i/Pslt7t7eFCtXjmIVKkCFClCnAvStYBT24XbOdGe+dPTo7ePcOaNk0aVL8OefybsVEJA8BCpd2giHXDNU4RXJzEy2eyUymVBUVBS+vr5cvXo1xV26jh8/TmBgYLruOPQgrFYrUVFR+Pj4pFkx4iFDhnD16lVmzpyZqvaxsbGULFmS+fPnJ9kpS7IuR33NWCwWli1bRosWLTJU/S6RtKaxL85M4z9zCQ6Gfr0tFLeFUpE99K61h2LR+/AOO0juK0dwtcWneF88Zo5RjFBKEpm9JJYiJTCVLEG2yiXxf6wwJcq64eJi/NCbrF7OiX8PW4xdutKn5MLDpPHvIFFRtwOgxBDo4EHj3N1qhObNawRAiUeVKlCuHLi7J2l2/frtEOjIESMcPXTIeOrIe2xo5u5uBD+PPmo8beKvxYtn3XpBGv/3516Zxz8pO3RiI0eOZOrUqSQkJGA2m/+1/cmTJxk5cqTCHhERERFnYrPBqVPEbN/DhbV7uLZ5L9V37iGKg3hw64fiLUlvuU42DlKG4x5luJCnLCHhZTlIGY5QAgvuuLjAybvsWAUPvkGKZuDIffHxgerVjeNO8fFGSrNnT9Lj2DFj6s7q1caRyN3dCH+qVjWOatXIXqECFSt6UrFi8pe9ejVpAHTnr9HRt1/uTm5uxkygxBCoYkXjCAzkoe0ULVmPAh8n5uvry4gRI1LdvlSpUpQqVSoNeyQiIiIijmBfnlUkjgJX9nFx9W6i1u/CvGc3fmf+Ilt8FJ7AP7OU62RjL+XZQwWuFSlP9uplyfFYGQrXLkjpsi5Uv7WBk3swLEmHgsciD4Wrq1HXp0wZaN/+9vkbN2D//tuJzN9/w86dcOUK7NhhHInMZiOduRUAUaMGVK4M7u74+qacM1mtRm2g/fth376kv964Yfx+376k92TLZmRNlSrdDoEqVDC2nRdR4CMiIiIi4oyiorD8uZvfPt5N5IpdVGY3edmHCQt+wJ2bbVtw5RClOexegfMBFVgaZoQ8JymCDRdjydWmuwczqpcjWUK2bPDYY8aRyGYz1hvu2GGEPzt3Gr+/cMEIhP7+GxJr13p4GAFQzZq3j0KFjOLUGDN1ihY1jlubGQNGEBQefjv82bvXeNp9+4wgaOtW47hTkSJGCFSlyu2JRwUK2F9KnIQCHxERERGRLCZZQeUbN4jbtouz//uTmE3byXHoTwKiQnED/rkNyGVy8pepMuF+VYguUwXvmpXI37AM5aq4Uy6v8QOjazAs6wO2+1hypQBHsiSTyVhXFRgI7doZ52w244swMQTavh22bTMqOG/ZYhyJ8uWDxx+/HQDVqAH/2L3YxeX2LvZ37tsTH298nf/9N/z11+186dSp27uHLVlyu32ePLfDn8QjMFAhUFamwEdEREREJAuZMyOW6S//TXX+5DG286T3nxSJ3o87Vgr9o+0pCrKLKuyiCrupzC6qcJIirFpp4vkmd38NLbkSuQeTyZi5U6gQPPOMcc5mM75gEqfjbNtmpDQREbB4sXGAUaznscegbl2oV8/YeSxnzhRfxtUVypY1jo4db5+/fNlYcZa4E/3OncbMoPPnYeVK40iUM6cxC6hGDeNla9Qwvp4VAmUNCnxERERERDIrmw3biZOc/WUrV5ZvwW3nVrpc2EUPLLfbRBu/nCEff7k9xrkij0H16vg1rUau0nl4po7xs2gis9n4AfLfaMaOyH0wmYwpdyVLQteuxrnoaCONSQyBNm82AqDNm43jww+N+ypWNMKfunWNIyDgni/1yCNG83r1bp+7edMIgXbuvB0C/f23UX5o7VrjSBQQkDQAeuwx4zkl81HgIyIiIiKSwSUu0SpV4AY+oTuIWLgF65at5D22lVyxkQQAd/4IeJFc/Mljt+b4VKfeoMdo1z8/zQon/5/7L754sB2xROQ/8vaGJ54wDjCS1+PHYcMG2LjROEJDjZlAf/0Fn39utCtZEho2hEaNoEED8PO7+2vc4uVlhDc1atw+FxcHBw4YK87+/BP++MMIgSIjjaVgdy4HK1nSuLdmTWPSUcWKxgwjydj0RyQiIiIikkFZw8+waPAmzvywidr8jj9/4UoCOe5oY8GV3aYqnPCvyeUyNflwXU2OEQgYyY7ZDFMHPtyCyiKSBkwmKFbMOLp3N85FRMCmTbdDoL//NkKg0FAjnQVj969GjYyjbl3Inj1VL+fubhR2rlTJ+D4AxkygXbtuB0B//GF8b0h8yW+/Ndp5exsBUO3aUKuWceTO/VA/DXkIFPiIiIiIiGQENhuxfx0k7LtNxKzeRJ6DGwmIPs6z/2h2mvz85V2Ly6Vr4vFkLYq0qUrFx714zMO4bg6+/xk7Wp4lkkHly2dsDZ+4PfyVK0bws2YNrF5trNPavds4Jk40pt3UrHk7AKpZ06gLlEpeXkaIU7v27XMXL96uO51Yc/rqVVi3zjgSlSp1+94nnjB2tVctIMdS4JMFdO/enStXrrA4sdBXKq1Zs4Z+/fqxf/9+XFxc/rX9nj17aN68OYcOHSJbtmwP2FsRERER52bfQSswnuyhuwj/bj1s2kTBE5vIGX+Rkne0TcCFv6jEJp7gd+qwmdqEU4i1S6FF/ZSfXzN2RLKwnDmhVSvjADh71ijAs3q1cRw/bswI2rQJxo4FHx9o3NjY3qtZswf6hpA7t/E9pWlT47HVCgcPGmWGtmwxfj14EA4fNo7EXej9/IzgJ7H8UOXKWgaW3vRxZwGTJ0/GdmelvVQaMmQII0eOTFXYA1ChQgVq1KjBp59+yltvvXXfryciIiLi1OLj+e7NXeyetI4nWYcPG/HhGjnvaHITT3a61ySi2BO41HsC70a1aNHJJ1lR5RIl7v1SmrEj4iT8/aFTJ+MAI/BJDH9++w0uXICFC40DoHx5I/xp3hzq1DHWdd0nFxd49FHj6NXLOHfpklF3essWI2vautV46Ts3IMue3Vj6lVh7+vHHk+1ALw+ZAp8swNfX977v2bx5M6GhobRPnBqYSj169KBv374MHz4cs9l836/7oCwWC273MRVRRERExOHi4zm/ahfh36zD9fd1BIZvpLP1Gp3vaHKZnOzMVpfL5evhHfQEpZ+rSu0y7kmWQXxxTUWVRSSVAgONFKZXL2Mqzo4dsHw5rFhhrMnau9c4PvrISGAaNTLCn1atIH/+B37ZXLmgRQvjAKMg9I4dt2tPb9pkrEYLCTEOMLKmxx+HevVc8PTMTcOG97X6TFIhdVM7sjCbDW7ccMxxP5NyfvrpJypUqICXlxe5c+emcePG3LhxAzCWdD3zzDP2tvXr16d///4MGTKEXLlyERAQwJgxY5I83/fff09QUBCenp63PgcbjRs3plmzZvbZQleuXKFw4cKMHDnSfl/Tpk25ePEi69evv2d/lyxZQvXq1fH09MTPz4+2bdvar5lMpmTLz3LmzMncW3P/Tpw4gclk4ocffqB+/fp4enoybdo0vLy8WLFiRZL7Fi5cSLZs2bh+/ToAp0+fpmPHjjzyyCPkzp2b1q1bc+LEiXv2VUREROS/CA83VlSEn7JxaeM+dnWfzF9FnuaaR27ytKxBlflDqBC2jOzWa1wmJ7/wNAP5hCrsxI8LmP+3hHZb36DFOzUpXtY9Wc2Lnj3hxAnjNU6cuF1cVUTknlxcjD3VR40y1l2dOwfz50O3bpA3L1y/Dr/8An37QoECRttx44zC0A+wguRO7u7GbJ4hQ+DXX406QH/9BVOmQMeORrYUF2eEQe+9Z+btt58gTx5XGjaEd981zsfFPaTPwYk5/Qyf6OhUFzF/6K5fh9SUwomIiOC5555jwoQJtGnThmvXrrFx48Z7LuOaN28egwYNYtu2bWzZsoXu3btTp04dmjRpAsCGDRt47rnn7O1NJhPz5s2jQoUKfPbZZ7z++uv07dsXf3//JGGRu7s7lSpVYuPGjTRs2DDF1166dClt27Zl5MiRfP3118TFxbF06dLUfSh3GDp0KBMnTmTOnDl4eHiwceNGvv32W5o1a2Zv891339G6dWuyZ89OdHQ0DRo0oG7dumzYsAFXV1fGjRtHs2bN+Pvvv3F/gOmKIiIiIvcy991TbBj1Gw1ZTRlWk4tIct1x/TI5+cu3Hlcq14cn69PunYokcHuWdGqWZ4GWaInIQ5A79+3lX1arUeh5+XJYutRYg7V9u3G8/TYULQpPP20c9er956k3Li7GVu4VK8Irrxh50tGjieWHrKxaFcfly56sXWucA2O5V506xg70jRtD1arG90xJPacPfDKDiIgI4uPjadu2LUWKFAGMejr3UrFiRUaPHg1AyZIlmTJlCqtXr7YHPidOnCD/P6bsFShQgJkzZ9K1a1fOnj3Lr7/+yq5du5ItpSpQoMA9Z8289957dOrUibFjx9rPVapUKdXvN9GAAQOSzAzq0qUL3bp1Izo6Gm9vb6Kioli6dCk///wzYMxacnFx4csvv8R067/G5syZQ86cOVm3bh1BQUH33QcRERGRO8WevcLhGWuIXvIb/vtW0z32MN3vuB6NFzuz1eVSlcbkfLYRlbpVon6u2z+hzCys5VkikgG4uBgJStWqMHKkUfz5f/8zZvyEhBjTCT/7zDh8fY21Wq1bG7/myPGfX95kMsLuEiWge/cEli5dSfHiLfj9dzd76HP+vFGG6LffYMQIo151w4bQpIkRABUvrl3A/o3TBz7e3sZMG0e9dmpUqlSJRo0aUaFCBZo2bUpQUBDt2rXjkUceues9FStWTPI4X758nDt3zv745s2b9uVcd2rfvj2LFi1i/PjxTJ8+nVKlSiVr4+XlRXR09F1fe/fu3fTu3Ts1b+2eqlevnuRxy5YtcXV1ZcmSJXTq1Imff/6ZHDly2IOcHTt2cOTIEXL84xtQTEwMR48e/c/9EREREedg30WrJBQISOD4Tzs4O28FvltXUurKNiqQYG+bgAt/UIPVNOI3GrOFWqz8nwdP10/5ubWDlohkSP7+xjeonj2NZTAhIbBkibEe6/x5YynY/Png4WHs9tW+vVH3x8fnoby8yWRs416hgrHCzGaD/fuN4GfNGuO4ciVp/ekiRW6HPw0bQp48D6UrWYrTBz4mU+qWVTmS2WwmJCSEzZs3s2rVKj7//HNGjhzJtm3bCAwMTPGef87KMZlMWK1W+2M/Pz8uX76c7L7o6Gh27NiB2WwmNDQ0xee+dOkSxYsXv2t/vf6l1LrJZEq2HM1isSRr98+t393d3WnXrh3fffcdnTp14rvvvqNjx4643trbz2q1Uq1aNb799ttkz5VHX/0iIiKSCsHBMKrXGYJYSVNWEmQKoZjtEsXuaBNqLsPxEk2Irt2Y7nOe5Cq3N9DQDloikul5exuzeVq3NqYjbttmzPxZuNBIq3/5xTjc3Y0Eu107Y+lXzpwPrQsmE5QrZxyvvgrx8UYR6JAQY8bP5s1w8iR8+aVxAFSpYmRRzZoZ9YNUAFpFmzMNk8lEnTp1GDt2LLt27cLd3Z1FixY98PNVqVKF/fv3Jzs/ePBgXFxcWL58OZ999hlr1qxJ1mbv3r1UqVLlrs9dsWJFVq9efdfrefLkISIiwv44NDT0njOG7tSlSxdWrFjBvn37WLt2LV26dLFfq1q1KqGhoeTNm5cSJUokOR5kJzMRERFxDvE3Lez5bC2/VR3CY70qcpoCzOFFOrGAXLZLXMWHTXnbsqrdTA6uOEEJywGCDn7GM7OfZuKXvvaaElqiJSJZjtkMtWvDhx/C4cNG5eW33oLSpY2qyr/+Ci+8YBSBbtkS5swx9mh/yFxdjR293noL1q0zXmLZMhg40JgVBLBrF4wfD08+aZQratsWZs2CsLCH3p1Mw+ln+GQG27ZtY/Xq1QQFBZE3b162bdvG+fPnKVu27AM/Z9OmTZk3b16Sc0uXLmX27Nls2bKFqlWrMmzYMF544QX+/vtv+/KxEydOcPr0aRo3bnzX5x49ejSNGjWiePHidOrUifj4eJYvX86QIUMAaNiwIVOmTKFmzZpYrVaGDh2a6i3Xn3zySfz9/enSpQtFixalZs2a9mtdunTho48+onXr1rzzzjsULFiQsLAwFi5cyJtvvklB/etLRETEKd25RCvxnwPn90RyePJyzCuX8Wj4KioQRWKFRCsmtlOdlTRlBc0YvfRxglqk/M9mLdESEadhMt2uvPzOO8aaqx9/hJ9+gn37jARm2TIjnWnWDLp0MZZ9pcGSmuzZjd3kmzc3HkdGGrN/VqyAlSuNXcEWLTIOgLJlb8/+qVcPUqhukiVphk8m4OPjw4YNG2jRogWlSpXirbfeYuLEiTRPHN0P4Pnnn2f//v0cOnQIgPPnz9OzZ0/GjBlD1apVASO4yZ8/P3379rXfN3/+fIKCguzFo1NSv359fvzxR5YsWULlypVp2LAh27Zts1+fOHEihQoVol69enTu3Jk33ngD71QWNDKZTDz33HP89ddfSWb3AHh7e7NhwwYKFy5M27ZtKVu2LC+++CI3b97E5yGtLRUREZHMJTjYqPPQqKGVZwv9wfxSo9mX7THyVMxHneAXqRn+Ez5Ecd6UhzUFu/Ec88nLOR7nD0bxLtvMdXi04r3/j7RgQahfX2GPiDiRxDVXY8bA3r1G+PPuu0YYFB9vFIB+7jmjNtDzzxtBUAplPB6WgADo2hW+/daoP/3HH0YmVbu2UZ/6wAH49FMjoM+VC1atSrOuZCgm27329s6EoqKi8PX15erVq8l+yI+JieH48eMEBgamWLA4I7FarURFReHj44OLS9rkckOGDOHq1avMnDkzVe1jY2MpWbIk8+fPp06dOmnSJ8lYHPU1Y7FYWLZsGS1atEj17C+RrEBjX5xZWoz//duuMarmKlqxhOYsJy/nk1zf512dc9Va4PdCSx7tVh2zmwvBwcl30erZ86F0R+Su9P1fspQDB4wCz99+C8eO3T7v5wcdOkDnzkaRnVs/56b1+L982aj7s2KFcZw5Yxz58j30l0oX98o8/klLupzYyJEjmTp1KgkJCZjN5n9tf/LkSUaOHKmwR0RERDKs4xvDOTb5V7KvXULlS2v4iTj7tav4sIogaN6CJz9oTrmKAZT7x/1aoiUi8h+VLWtMrxk71phq8+23sGABnDsH06YZR5EiRvDTrZuxv3oaeuQRY1Ox9u2N3b8OH868Yc/9UuDjxHx9fRkxYkSq25cqVSrFbdpFRERE0ss/6/HEW2z8/fVfXAj+hQI7llAudid37mEaSgmW8DT/4yk28QQ2sxsnZkHeewQ52kVLROQhMJmMSsuPPw6ffGLsrf7dd8ZuXydPGhWWx4/H/PjjFKla1Vh/lca7K5tMRr1pZ6HAR0REREQyheBgeOklcLFaqM96+vgvpub5JVS1nrK3sWJiv28trtR9msKvPs2GU2UY2teUZImWwhwRkXTm6gpBQcYxfbqxu9fXX8Py5bhs20blbduwzZkDbdpA9+7QqBGkYhWK3JsCHxERERHJ8Pb8cZNfe60imEU8zRJycRnOGtei8WJ/wSCsLZ+m9OCnKF8yr/2+nkDTZlqiJSKSYXh5GbV8OnSAyEgSvvqKG1On4hMWZtT+mT/f+GbdrZux5btWmTwwBT4iIiIikiGF7bnK/o+W4rliEY+dX8Ziou3XzuPHL7QmT69naPlJI6rn8Lrr82iJlohIBhUQgHXgQNaWKkXLgABcv/nGWPYVHg7vv28cdepA795GEZ5U7u4sBgU+IiIiIuIwiTV5ihY1Hh/+/TzHP11KznWLqBH1G4W5vY1vGIVYSFsW0YbfqQNmV06MBtccjum7iIg8JCYTtmrVoGZNmDgRliyBuXONbbV+/904Bgww9l5/6SUoX97RPc4UFPiIiIiIiEMEBxv/aetnO0cbFvKc6w+Ujt9AORLsbU54l+Vs7TYUfK0tIeeq8obq8YiIZG0eHre31TpzBubNgy++gOPH4fPPjaNWLejTR7N+/oUCHxERERFJVzYbrP3+LNt7LeQ3fuRJ1mPGCvHG9VCfqlxp3I5ig9pQtE4Zit66T/V4REScTP78MHw4DB0Kv/0Gs2bBL7/Ali3G8frrt2f9VKjg6N5mOC6O7oCkr3Xr1mEymbhy5cpd28ydO5ecOXM+8GuMGTOGypUrP/D98nCMGTMGf39/TCYTixcvpnv37jzzzDOO7paIiDgpmw12LY9kUdA0tnk34MnO+ZlOPxqyFjNW/qQ6Q/iQVdMPUfLqDh77eTi565RJ9jwFC0L9+gp7RESciouLscPXTz/BqVNGbZ/AQLh6FaZMgYoVjW3dv/0W4uIc3dsMQ4FPJhIZGclrr71GsWLF8PDwoFChQrRq1YrVq1c/1Nfp2LEjhw8ffqjPmZb+a0CVFR04cICxY8cyc+ZMIiIiaN68OZMnT2bu3Ln2NvXr12fAgAEO66OIiGRN4eGwdq3xq80Ge9ZdZGHzWWzxbkilFvlpE/IKNWPWYcbKHzzGm0wgkGPU4E8murxByaaBjn4LIiKSkQUEGLN+jhyBVavg2WeNbd+3bIHnn4fChWHUKGM5mJPTkq5M4sSJE9SpU4ecOXMyYcIEKlasiMViYeXKlbzyyiscPHjwob2Wl5cXXl533+lCHi6LxYKbm9tDfc6jR48C0Lp1a0wmEwAeHh4P9TVERET+KTjYmFWfzRpFa36hu/t86sWFUCFxrRZwONfj3GzZnhLD2rFnSxE+7cOtmjw2+vb9i4IFVYhTRERSwcUFmjQxjshI+PJLmD7dCHrefRfGj4e2beHVV+GJJ+DWz0XORDN8Mol+/fphMpn4448/aNeuHaVKlaJcuXIMGjSIrVu3AkYoZDKZ2L17t/2+K1euYDKZWLduXZLn+/3336lUqRKenp48/vjj7Nmzx34tpRkzS5YsoXr16nh6euLn50fbtm3vq/9z5syhbNmyeHp6UqZMGaZNm5bk+tChQylVqhTe3t4UK1aMt99+G4vl9q4cf/31Fw0aNCBHjhz4+PhQrVo1tm/fzrp16+jRowdXr17FZDJhMpkYM2ZMin2423Pc+b4LFy6Mt7c3bdq0YeLEiUk+h5SWRA0YMID69evbH69YsYInnniCnDlzkjt3bp566il7+AK3/4x++OEH6tevj6enJ998882/fkZxcXG8+uqr5MuXD09PT4oWLcr48eNTfJ9jxoyhVatWALi4uNgDnzv73717d9avX8/kyZPtn9uJEydSfD4REZHU+D0kmpW9fuQH67OcIy9f041GcctxI55jvlX4q/OHRO87TqmLW6n01WCyPVqEnj3hxAljRlBoaDxNmoQ5+m2IiEhmFBAAb71l/KXyww9Qty7Exxu/r1cPqlQxAqHoaEf3NF1pho/N5rg/dG/vVKWMly5dYsWKFbz33ntky5Yt2fUHWc705ptvMnnyZAICAhgxYgRPP/00hw8fTnGmydKlS2nbti0jR47k66+/Ji4ujqVLl6b6tb744gtGjx7NlClTqFKlCrt27aJ3795ky5aNF154AYAcOXIwd+5c8ufPz549e+jduzc5cuRgyJAhAHTp0oUqVaowffp0zGYzu3fvxs3Njdq1azNp0iRGjRrFoUOHAMiePXuK/bjbcwBs27aNF198kffff5+2bduyYsUKRo8efV+fKcCNGzcYNGgQFSpU4MaNG4waNYo2bdqwe/duXFxu56tDhw5l4sSJzJkzBw8Pj3/9jD777DOWLFnCDz/8QOHChTl16hSnTp1KsQ9vvPEGRYsWpUePHkRERKTYZvLkyRw+fJjy5cvzzjvvAJAnT577fr8iIuLcTp+w8Me4VXgu+o66l37hB27Yrx2gDPN5joYzOlK/T+m7PkfBgsZhscDff6dHr0VEJMtyc7u9w9dffxn1fb791vh9794wZAj07An9+0OhQo7ubZpLl8Bn2rRpfPTRR0RERFCuXDkmTZpE3bp179r+22+/ZcKECYSGhuLr60uzZs34+OOPyZ0798PvXHQ03CUgSHPXr0MKAc4/HTlyBJvNRpkyyQsXPqjRo0fTpEkTAObNm0fBggVZtGgRHTp0SNb2vffeo1OnTowdO9Z+rlKlSql+rXfffZeJEyfaZwUFBgayf/9+Zs6caQ983nrrLXv7okWLMnjwYBYsWGAPfMLCwnjzzTftn0HJkiXt7X19fTGZTAQEBNyzH/d6jsmTJ9O0aVOGDRsGQKlSpdi8eTMrVqxI9fsEePbZZ5M8Dg4OJm/evOzfv5/y5W9PUR8wYECSWVL/9hmFhYVRsmRJnnjiCUwmE0WKFLlrH7Jnz24PAe/2mfj6+uLu7o63t/e/fm4iIiJ3unLZxsaPtpLw1bfUOb2ANlywXztGIN/Tie/pxB4qYDabeKmlAzsrIiLOq1IlYzv3Dz+EOXNg6lRja/ePP4ZmzZwi8EnzJV0LFixgwIABjBw5kl27dlG3bl2aN29OWFjKU3Y3bdpEt27d6NmzJ/v27ePHH3/kzz//pFevXmnd1QzLZrMB2JfmPAy1atWy/z5XrlyULl2aAwcOpNh29+7dNGrU6IFe5/z585w6dYqePXuSPXt2+zFu3LgkS51++uknnnjiCQICAsiePTtvv/12kjEyaNAgevXqRePGjfnggw+S3Jta93qOAwcOJPlMgGSPU+Po0aN07tyZYsWK4ePjQ2CgUXjyn+O9evXq9t+n5jPq3r07u3fvpnTp0vTv359Vq1bdd99ERETuV2IB5iNHYNVnB/mxzNtcylWCVuNr88zpqeThApfc8vJ3/f5cXr6VtV8cZZT5ffZQEbPZxMyZ2k1LREQcLFcuGDwYQkPh11+NmT4NGzq6V+kizWf4fPLJJ/Ts2dMe2EyaNImVK1cyffr0FGuQbN26laJFi9K/f3/AmOnQp08fJkyYkDYd9PY2Zto4grd3qpqVLFkSk8nEgQMH7rmtduKSocSACEhSB+ff3C1Q+i8FnK1WK2As63r88ceTXDObzYDxZ544g6hp06b4+vry/fffM3HiRHvbMWPG0LlzZ5YuXcry5csZPXo033//PW3atEl1X+71HHd+Znfj4uKSrN0/P99WrVpRqFAhvvjiC/Lnz4/VaqV8+fLE/WNrwDuX5qXmM6patSrHjx9n+fLl/Pbbb3To0IHGjRvz008/pfr9i4iI3I8vvoDRL0XQke/pwrcEscN+LdolG0crtSXP610I6NKIXK7GPyl7Ak2bGQFRiRIKe0REJAMxm+Gpp4zDSaRp4BMXF8eOHTvsy2QSBQUFsXnz5hTvqV27NiNHjmTZsmU0b96cc+fO8dNPP9GyZcrzgWNjY4mNjbU/joqKAowfxP/5w7jFYsFms2G1Wu0/ZAPgqB2pbDbjSPGSzf5rzpw5CQoKYurUqbz66qvJ6vhcuXLFXiQY4PTp0/YlVzt37gSwv+fE971582YK3vpX2OXLlzl8+DClSpVK0ibx14oVK/Lbb7/Zl1/9+9uy2e/PkycPBQoU4OjRozz33HPJ2lqtVjZt2kSRIkUYPny4/XxiAeE7/5xKlCjB66+/zuuvv07nzp2ZPXs2rVu3xtXVlYSEhKR/pndxt+coW7YsW7ZsSfIcW7ZsSdIHPz8/9u7dm6RNYh0gq9XKxYsXOXDgANOnT7cvWdy0aZP9Of752Sb+PjWfERhLtdq3b0/79u1p27YtLVq04MKFC+TKleuu99zZV5vNZh//AG5ubsTHx9/zc7NardhsNiwWiz18Sg+JX7v3E1iKZAUa+5IR7N8ezZ9v/49Cq7/mFCGYMf6esODKgcJBZH+pEwX7taJMduPfIxabzSjAc4u/v3FAktP/SuNfnJnGvzgzjf/7cz+fU5oGPhcuXCAhIQH/xL/1b/H39ycyMjLFe2rXrs23335Lx44diYmJIT4+nqeffprPP/88xfbjx49PUlsm0apVq/D+xwwaV1dXAgICuH79erIZFxnVtWvXAPjwww9p2rQpNWrUYPjw4ZQrV474+HjWrVvH7Nmz2bZtGwCPPfYY77//Pn5+fly8eNFeeDg6OpqoqCiibxWoHjt2LF5eXuTJk4dx48aRK1cuGjZsSFRUFDExMdhsNnt4NnjwYFq3bk3BggVp27Yt8fHx/Pbbb7z++usp9jk2NpaEhAT7/UOGDGHYsGG4u7vTuHFjYmNj2b17N1euXOGVV14hf/78hIWFMWfOHKpWrcqqVatYtGiRvQ83b95k1KhRtG7dmsKFC3PmzBn++OMPWrVqRVRUFHny5OH69ev8+uuvlC9fHi8vr2R/9v/2HC+++CJNmzbl3XffpWXLlqxZs4YVK1Yk+Rwef/xxPv74Y2bNmsVjjz3GDz/8wJ49e6hYsSJRUVGYzWZy5crFtGnTyJEjB+Hh4faxefPmTaKiorh+azbZjRs37M+bms9o2rRp+Pv7U6FCBVxcXJg/fz7+/v64uLgkeZ473y+Q5JrFYiE+Pt5+rkCBAmzZsoW9e/eSLVs2HnnkkSSFpcEIbW/evMmGDRuIj48nvYWEhKT7a4pkBBr7kt6uXHLl7E/nKLpxDc2u/UIlrtmvbaYW3/A8P9Ke13sfokL5i+zZsD7N+qLxL85M41+cmcZ/6kTfx6ZT6VK0+Z9LhWw2212XD+3fv5/+/fszatQomjZtSkREBG+++SZ9+/YlODg4Wfvhw4czaNAg++OoqCgKFSpEUFAQPj4+SdrGxMRw6tQpsmfPjqen50N4Z2nHZrNx7do1cuTIgclkokKFCuzYsYP333+fUaNGERERQZ48eahatSrTp0+3v9c5c+bQq1cvGjZsSOnSpfnggw9o1qwZ3t7e+Pj42IOQDz/8kBEjRhAaGkqlSpVYsmQJfn5+AHh6emIymezP2aJFCxYsWMB7773HpEmT8PHxoW7dusk+30QeHh6YzWb79VdffZVcuXIxceJERo8eTbZs2ahQoQL9+/fHx8eHTp06sWvXLoYOHUpsbCwtWrTg7bffZuzYsfj4+ODp6cm1a9fo168fZ8+exc/PjzZt2jB+/Hg8PT1p0qQJffr0oWfPnly8eJFRo0Yl22Hr356jUaNGzJo1i7Fjx/Lhhx/SqFEj3nrrLcaNG2d/H23atOGtt95izJgxxMTE0KNHD7p168bevXvtbebPn8+AAQOoXbs2pUuXZtKkSTRs2BAvLy98fHzsO4hly5Ytyef3b59R7ty5mTJlCqGhoZjNZh577DGWLl161x3aEpfh3fkabm5uuLq62s8NGzaMHj16ULNmTW7evMnRo0cpWrRokueJiYnBy8uLevXqpevXjMViISQkhCZNmqS4c5xIVqWxL2ktPByOHDFRooQNPz9Y98URrk//jnpHviGQE/Z2kZ5FmRXTla/oxlFKAGA22+jSJWeaLdPS+BdnpvEvzkzj//6k9B/+d2OypaZ4yQOKi4vD29ubH3/8MUmtlddff53du3ezfn3y/x3q2rUrMTEx/Pjjj/ZzmzZtom7dupw5c4Z8+fLd8zWjoqLw9fXl6tWrKQY+x48fJzAwMMMHPlarlaioKHx8fJLNupD0MXfuXAYMGMCVK1cc3RWHcdTXjMViYdmyZbRo0ULf9MWpaOxLWgoONupU+tiu0JEF9HCZR03rFvv162YfTtboQIHh3cjZsg7Bc1zo0wcSEoyyBzNnGjvZphWNf3FmGv/izDT+78+9Mo9/StMZPu7u7lSrVo2QkJAkgU9ISAitW7dO8Z7o6GhcXZN2K7F2SBpmUyIiIiJZ1vY/rHzfaw1fM4e2LMSLGLBCAi4cKd6U7C93o0C/1pS7o65hz57QtKkKMIuIiGRWab6ka9CgQXTt2pXq1atTq1YtZs2aRVhYGH379gWMJVmnT5/mq6++Aoxdjnr37s306dPtS7oGDBhAjRo1yJ8/f1p3V0RERCRLiI2F3748zpVJc3niyFxCCLNf20N55tKdNj905on2d589XbCggh4REZHMKs0Dn44dO3Lx4kXeeecdIiIiKF++PMuWLaNIkSIAREREEBZ2+x8g3bt359q1a0yZMoXBgweTM2dOGjZsyIcffpjWXRVJonv37nTv3t3R3RAREUk1mw12/36DPWN+JnD9HFrGr7Nfu0xO5vMcs3mRHVTDbDYxsJbj+ioiIiJpK12KNvfr149+/fqleG3u3LnJzr322mu89tpradwrERERkcwtPBxCQ8Evt439c//Add6XNLm0gCq3dtmyYuJoYGOyv/YiK72eof+rnklq8mj2joiISNaVLoFPRqNaQCKpo68VEZGM64svYNhLl+jCN/TiSzqyx37tbLZiRLXtTrGxL1AysDAA3YHGT6kmj4iIiLNwqsAnseJ3dHS0fdtqEbm76OhoAFXLFxHJQM6EW/n1jfXkWPAFp1mIJ7EA3MST0ErtCXz3Rfxb1sM/hV0+VZNHRETEeThV4GM2m8mZMyfnzp0DwNvbG5PJ5OBepcxqtRIXF0dMTIy2ZZd0Z7PZiI6O5ty5c+TMmdO+U56IiDhGfDys/iaCsx/OpfbBYPpw1H5tN5X4gt58R2cWTXqEivUd108RERHJOJwq8AEICAgAsIc+GZXNZuPmzZt4eXll2FBKsr6cOXPav2ZERCT9nTyWwPqRq8i7aCaNY/+HKwkAXHfJwbfWznxBL3ZQDTBhNhtLtURERETACQMfk8lEvnz5yJs3LxaLxdHduSuLxcKGDRuoV6+eltOIQ7i5uWlmj4hIOkoswBwYCAfXRnB2/GyeDP2Cbpy0tzleoA6er/QiX//2uH6fjd19ABVhFhERkRQ4XeCTyGw2Z+gfZs1mM/Hx8Xh6eirwERERyeKCg+GlXlYaspq+zOBpluBGPADXXHMS0eQFio5/icBKj9rv6dkTmjZVEWYRERFJmdMGPiIiIiKOlpAAP049x+HX53CYWRTnmP3aUf/aZBvUh4DX2pPjLptNqAiziIiI3I0CHxEREZF0djbSxqq3N+L73TTaRi+kE8Yy8yv48jVdmUkfpnxfnvr1HdtPERERybwU+IiIiIikA5sNtqyM4uBb3/D4jml0ZZ/92lYeZyZ9+IEORJNNBZhFRETkP1PgIyIiIpIGEosw58sHf32zB6ZPo8Wlb6jNdQCiXbIR/mQXiox/mX17K/N1H2OJlwowi4iIyMOgwEdERETkIQsOhld6xdKGhfRjGh3ZZL92JmdZEl7qR6ERXSnl6wtAz8dVgFlEREQeLgU+IiIiIg+JxQLff3SKyJEzOMmX+HPOOI8rh8u1ocgH/cjf8kkwmZLdqwLMIiIi8jAp8BERERH5j86dtbFyxHpyfTeF52IW40oCAKfJz0z68CW9+G5KfsrVd2w/RURExHko8BERERF5QDs23OCvId/y2B9T6GrbYz+/hgZM5RWW8DTxuKkIs4iIiKQ7BT4iIiIiqZBYhLlwYdiz+Cg3Pp5Gi8jZVOMKADddvDlVvytFP3qV47vK84uKMIuIiIgDKfARERER+RfBwdC7l40mrOI1PudpluGCDYCzOYoT0/MViozuQamcOQHoWVVFmEVERMSxFPiIiIiI3MOKn2+wvddX7OMzynLQfv5g0WYEvPca/p2agYtLsvtUhFlEREQcSYGPiIiIyD/Ex8OKL8K4+t4UWpz+gma3lm1FkYM59GAqrzBrTinK1HdoN0VERETuSoGPiIiIyC2XLtpY/tbv5Jw3meY3F2LGCsARivMZ/ZlLd67hoyLMIiIikuEp8BERERGnlFiEuWRJuHEpls0Df6Dy2kl0se20tzlWtCE5xwxgQ1wLpr1sVhFmERERyTQU+IiIiIjTCQ6G3r0hl+0CfZjJq0yhB5EAxJg8OVn3eYpO7E+x6hUAeBEIaq4izCIiIpJ5KPARERERp3LsGHzU6xBTmcQLzMObmwBc8MhP1POvEDj+JUrn8Ut2n4owi4iISGaiwEdEREScwqWLNlYMXYvfV59wkKX28zuoyicM4qVf2/NkE3cH9lBERETk4VHgIyIiIlnakf1xbO7/PZXXfEJn218AWDHxK634hEFsoB5ms4kPyzq4oyIiIiIPkQIfERERyZL+WHGJw4Nm0PDAFLoRAcBNkxcnG/Zgd73Xef6dUirCLCIiIlmWAh8RERHJ9BJ33CpWDA4uP87VsZNoERlMDW4AcNEjH1eef41iH/ahTO5clAGeeFFFmEVERCTrUuAjIiIimVrijltVbdt5g49pz4+YsQJwKldFzG8OJv+gTuR2T1qfR0WYRUREJCtT4CMiIiKZ1p6/rCzqtZw1fER91tvPHyjUBP+P3qRQh8ZgMjmwhyIiIiKO4eLoDoiIiIjcr2MHYvmm4Wxcq5TnfzxFfdZjwZWv6EoldnP2q1Xk6thEYY+IiIg4Lc3wERERkUzj741X2fvaDBr8NYnniQQgihzMpA+f0Z9wCmE2G3V5RERERJyZAh8RERHJ0Gw22PxzBKffnETTEzOoSBQA5z0KcOWFAWwu15vhg3y145aIiIjIHRT4iIiISIYTHg6HDsHFLYdx/+wjmp//ijrEGdd8ymIdPITCwzqTx92dkkCjttpxS0REROROCnxEREQkQ5kxA+a+vI03mUA7FuGCDYCjAXXI9s5QCvZsCS5JyxBqxy0RERGRpBT4iIiISIZw/ZqNn/uspMz8D9h6x45bS2hF2TlDKdm9jgN7JyIiIpK5KPARERERh7p0PoHV/X6m1KIPeCFhFwAWXPmG5/mYN9hPOdYWhZKO7aaIiIhIppIu27JPmzaNwMBAPD09qVatGhs3brxn+9jYWEaOHEmRIkXw8PCgePHizJ49Oz26KiIiIunkzIk4fmgazEX/srT/qSOVEnZxw5SNTxlIIMd5kTnsp5x23RIRERF5AGk+w2fBggUMGDCAadOmUadOHWbOnEnz5s3Zv38/hQsXTvGeDh06cPbsWYKDgylRogTnzp0jPj4+rbsqIiIiaSQ8HEJDoWRJsFy5wfaXZlFry0Q6cBqAq+ZHCG/TnzJTX8Pn19xE9gG065aIiIjIA0vzwOeTTz6hZ8+e9OrVC4BJkyaxcuVKpk+fzvjx45O1X7FiBevXr+fYsWPkypULgKJFi6Z1N0VERCSNBAfDSy+Br/USrzKF/nxGey4CcMEtH+dfGEyZiS9RzicHAD17QtOm2nVLRERE5L9I08AnLi6OHTt2MGzYsCTng4KC2Lx5c4r3LFmyhOrVqzNhwgS+/vprsmXLxtNPP827776Ll5dXsvaxsbHExsbaH0dFRQFgsViwWCwP8d2kr8S+Z+b3IPKgNP7FWWXFsR8eDm/1usAHfEJfZpCD6wCc9izOtX5vUHzs8/h6eBAPcMf79vc3jn+cliwsK45/kdTS+BdnpvF/f+7nc0rTwOfChQskJCTgn/gvtlv8/f2JjIxM8Z5jx46xadMmPD09WbRoERcuXKBfv35cunQpxTo+48ePZ+zYscnOr1q1Cm9v74fzRhwoJCTE0V0QcRiNf3FWWWXsn95iwWfGSo7zNZ4Y/znzFxUZz3AqDAugfOWrHFq92sG9lIwmq4x/kQeh8S/OTOM/daKjo1PdNl126TKZTEke22y2ZOcSWa1WTCYT3377Lb6+voCxLKxdu3ZMnTo12Syf4cOHM2jQIPvjqKgoChUqRFBQED4+Pg/5naQfi8VCSEgITZo0wc3NzdHdEUlXGv/irLLC2LfZ4I9vj3B1xEf0jvwaN2PuDluoyXuMZCktMZthfLd4LdWSJLLC+Bd5UBr/4sw0/u9P4qqm1EjTwMfPzw+z2ZxsNs+5c+eSzfpJlC9fPgoUKGAPewDKli2LzWYjPDyckiWTbsrq4eGBh4dHsudxc3PLEoMlq7wPkQeh8S/OKjOOfZsNNk7fS8yo92l0cQFmrAAczNeAnS3eotucBiRYTfYizIGBmev9SfrJjONf5GHR+BdnpvGfOvfzGaXptuzu7u5Uq1Yt2dSskJAQateuneI9derU4cyZM1y/ft1+7vDhw7i4uFBQ/xUoIiLicOHhsHat8avVCms/2s66R9pQ75UKBF2cjxkr+4q0IPLn3ylzZg2dv2zIiZMm1q6FEyeMoswiIiIikrbSNPABGDRoEF9++SWzZ8/mwIEDDBw4kLCwMPr27QsYS7K6detmb9+5c2dy585Njx492L9/Pxs2bODNN9/kxRdfTLFos4iIiKSf4GAoUgQaNoQOhbaw3rs5DYY8RoOri7Fi4u+Sz3J+5U7KnVhKQNvb/7lTsCDUr68dt0RERETSS5rX8OnYsSMXL17knXfeISIigvLly7Ns2TKKFCkCQEREBGFhYfb22bNnJyQkhNdee43q1auTO3duOnTowLhx49K6qyIiInIP4eHQuzfUsW1kFO/QhN8gFuIxs7f8cxSZMZyKdR51dDdFREREhHQq2tyvXz/69euX4rW5c+cmO1emTBlV6BYREclA4i02Vgxdx2rbOzRgHQAWXJnHCwTOHE6jl4o7toMiIiIikkS6BD4iIiKSOcVbbKwd+RuPfP4OvWI2ARCHG7N5kQ8YRri5KCdaOLiTIiIiIpKMAh8RERFJxhJnY93Q5eSZ/g5NYrcBEIMHa4r15uXjQwizFbLvuKW6PCIiIiIZjwIfERERsYu32Fj75jL8Z4yhSex2AKLxYv8TfSgT/CYtSuXn93A4cgRKlFDYIyIiIpJRKfARERFxcuHhcPCAjes/LKPY13cGPd7sffIVys0eTPVi/vb2BQsq6BERERHJ6BT4iIiIOLFZM2382ncpoxhLY4yg5wbe7Kv/KuXmvEGNonkc3EMREREReRAKfERERJxQQryNpf2WUvWLMbzEDsAIeqbyKs9ueYMaNRX0iIiIiGRmCnxEREScSEK8jY3DluI3ZQxPx94OeqbwKh/zBhfIQ40Y0CbrIiIiIpmbAh8REREnYE2wsemt5TwyaTT1Y24v3ZrKq3x0K+gBMJuNYswiIiIikrm5OLoDIiIiknZsVhu/jwlhj09t6n3Qkgox27mBN5vrDsF69AS5v/yQy+bbYY+2WRcRERHJGjTDR0REJIsJD4fDh8ESspa8U0ZR5/omwNhefXftVyg/701ql8gLQM9i0LSptlkXERERyWoU+IiIiGQhX34JX/XeyFhG0ZR1AMTgwY7HXubReUOpXTYg2T3aZl1EREQk61HgIyIikkWseW8LRd4axQZ+AyAWd76kN/VXDqdOUAEH905ERERE0pMCHxERkUxu77wdRA9+m4YXlwNgwZVgevI+IzhFYda6O7iDIiIiIpLuFPiIiIhkUod+3sul10ZTK2IhAPGYmUt3xvEWJykKaNctEREREWelwEdERCSTORESyuneY6h1cj4u2LBiYmuxLhQOHo3paAnC+wAJ2nVLRERExJkp8BEREcnAwsMhNBRKlgTTyRMce/Fdah2eR1ESANhSsB3+08dS+6lHAehZX7tuiYiIiIgCHxERkQwrOBheegn8rWcYyXv05gsKYAHgj7xP4TPpHWo9VyXZfdp1S0REREQU+IiIiGRA4eEwrNcFPuQDXmEqXsQA8KdvYzw/epcavWs6uIciIiIikpEp8BEREclgbkREsfOZzznKJ/hwDYBN1OEtxjFmcX0eq+/Y/omIiIhIxqfAR0REJIOIu3qTuPEbSPijJ0/bLgKwkyqM5D1W0Ayz2aQdt0REREQkVVwc3QERERFnlxBjYWuPGVwLKEv7bZ+Q23aRI25lmN7wR2qYtrOC5pjNJu24JSIiIiKpphk+IiIiDmKLT2Dnm/PJO3U0NS3HAAhzKcyh50bz5KxuvOztSqtw7bglIiIiIvdPgY+IiEg6Cg+H0MM23FcsIWDKSKrd3AfAWZM/u1uOIKpjIZ7p+BRubsZf0dpxS0REREQehJZ0iYiIpJPgYHi+0Ho8G9WmzkfPUPzmPi6Tk5X1x+Nx6igNF76Mew791SwiIiIi/51m+IiIiKSDXbN3kb/XCNaxAoAbePMZr9Ni3RCaPpkTAIvF4sAeioiIiEhWosBHREQkDZ3fcoSTL7xN9dDvAbDgyixeYhxvEUk+atkc3EERERERyZIU+IiIiKSBa4fOcKDzu1TZ+SV5iMeKie/ozGjGcoziAJjNaJt1EREREUkTCnxEREQeotjIy/zVZQLl10ymBjcB2OTbEveP3yPWVImTfYAEI+zRNusiIiIiklYU+IiIiPwH4eEQGgolCtzk3KgplPjxfWpYrwCww6sO10eMp97IuphMUANo2lTbrIuIiIhI2lPgIyIi8oCCg6Fvr3i68hVjGU01wgE44FqesL7jafRJS1zdTEnu0TbrIiIiIpIeFPiIiIg8gPBTNn7ttYTdjKAc+wE4SWG2tXyXp+Z3oWwOs4N7KCIiIiLOzMXRHRAREclsTv/wO1fKP8FinqEc+7lILgYxkdIcIu8b3fBW2CMiIiIiDqYZPiIiIql0ccM+znQfQYXjSygAROPFJAYwgSFcJad23RIRERGRDEOBj4iIyL+IPhzO4edGU2HnXHJjJR4zqwr25ECH0YyanJ8E7bolIiIiIhmMAh8REZG7iL94lb1dP6T08k+pTAwAa3K2xfvT92jRvQwtgI4DteuWiIiIiGQ86VLDZ9q0aQQGBuLp6Um1atXYuHFjqu77/fffcXV1pXLlymnbQRERkVvCw2Htilj+6DKZa/7Fqbx8PF7E8KfHE6was5n6F3+mZvcy9vYFC0L9+gp7RERERCRjSfPAZ8GCBQwYMICRI0eya9cu6tatS/PmzQkLC7vnfVevXqVbt240atQorbsoIiICQPAXVt4s9D1FmpelxncDeCThIoddyrCk5y9UvLKBoNG1cNF2ByIiIiKSCaT5P1s/+eQTevbsSa9evShbtiyTJk2iUKFCTJ8+/Z739enTh86dO1OrVq207qKIiAh7P19DpZdqMJ/nKMZxIgjgJWZh2bmHp798Gg9Pk6O7KCIiIiKSamlawycuLo4dO3YwbNiwJOeDgoLYvHnzXe+bM2cOR48e5ZtvvmHcuHH3fI3Y2FhiY2Ptj6OiogCwWCxYLJb/0HvHSux7Zn4PIg9K41/SU9TvezjbYyTlT6wwHpODCQzhUwYSTTY6nI+nVDqNRY19cWYa/+LMNP7FmWn835/7+ZzSNPC5cOECCQkJ+Pv7Jznv7+9PZGRkiveEhoYybNgwNm7ciKvrv3dv/PjxjB07Ntn5VatW4e3t/WAdz0BCQkIc3QURh9H4l7RkjryM78Ql1A79hdxYseDKDPrwLqM4T14AXFysnDy5mmXLYtK1bxr74sw0/sWZafyLM9P4T53o6OhUt02XXbpMpqTT4G02W7JzAAkJCXTu3JmxY8dSqlSpVD338OHDGTRokP1xVFQUhQoVIigoCB8fn//WcQeyWCyEhITQpEkT3NzcHN0dkXSl8S9pyRZ1jcO9JlL8l0/xst0EYJVPO9w+egcPSnKpnxkSwGy2MW2alW7dGqZb3zT2xZlp/Isz0/gXZ6bxf38SVzWlRpoGPn5+fpjN5mSzec6dO5ds1g/AtWvX2L59O7t27eLVV18FwGq1YrPZcHV1ZdWqVTRsmPQf3h4eHnh4eCR7Ljc3tywxWLLK+xB5EBr/8lDFx3Nk2Jfkmjya8vHnAPjTrTZn3/yY5u/UwmyGBkCLFonbrJsoWDBd/l8kGY19cWYa/+LMNP7FmWn8p879fEZp+i9Zd3d3qlWrRkhICG3atLGfDwkJoXXr1sna+/j4sGfPniTnpk2bxpo1a/jpp58IDAxMy+6KiEgWEx4OoYdt5N32K77jh1Li2kEAjphKsKvDB7T4si2PZU8647RgQW2xLiIiIiKZX5r/1+WgQYPo2rUr1atXp1atWsyaNYuwsDD69u0LGEuyTp8+zVdffYWLiwvly5dPcn/evHnx9PRMdl5ERORegoNhZq8/+Yg3KMcGAC6Qm99qj6b+/D60L+zu4B6KiIiIiKSdNA98OnbsyMWLF3nnnXeIiIigfPnyLFu2jCJFigAQERFBWFhYWndDREScyMkNJ/HsNYI/+A6Am3gyiQHUWjyMTq19Hdw7EREREZG0ly7FCfr160e/fv1SvDZ37tx73jtmzBjGjBnz8DslIiJZju3KVQ52H0/gL5PoQiwAX9GVtxjHKQqzVlmPiIiIiDgJx1SjFBEReZgsFo6P+IKck0ZTNv4CAGupz2AmsouqAJjNUKKEIzspIiIiIpJ+FPiIiEjmZbNxNvh/xA8aQuCtgsyHTKXZ2ekjLtd5ir9fN93aYh1mzlQxZhERERFxHgp8REQkU7q2YRdnuw6mRNhaAM7jx4qaY2n0fW+eK2JsV/l068Qt1hX2iIiIiIhzUeAjIiKZRng4HN90Gp8JI6mw6ytKYCMGDxYWGUj5r4fRtW7SIj3aYl1EREREnJUCHxERyRTmTbvBiVc+4k0m4M1NAH716Yz3p+/zXI8imEwO7qCIiIiISAaiwEdERDI2q5V9Q7+iyccjyE8EABt5gjeYyPe7axAY6OD+iYiIiIhkQAp8REQkw7qyeB1RvQdR7sIuAI5SjCFMYCFtARMnT6LAR0REREQkBQp8REQkw4nbF8rJjkMouW8xOYGr+PAub/M5rxGHB6Bt1kVERERE7sXF0R0QERFJZLt0mdCnBmIq/ygl9y0mHjM/+PVj3+IjlP3yDRLMt8MebbMuIiIiInJ3muEjIiKOZ7EQNmIGvpPGUDL+EgC/ebTg2tsf0W74o7i4QG2gaVNtsy4iIiIikhoKfERExGHCw+H4tOUEThlE4WsHAdhnKseOzp/QdkYQ2bMnba9t1kVEREREUkeBj4iIOMT3b+8j57jBNGMlAOfx49ca42jyfU+6BeqvJxERERGR/0L/ohYRkXRlO3+Bve1G027DTFxJIA43JjGA8aaR7PnZVzN4REREREQeAhVtFhGR9BEXR9jAT7merwQVNkzDlQQW0oZH2c9QJnDF5suRI47upIiIiIhI1qAZPiIikrZsNi7O+x+W/oMpfC0UgL9NlRhg+5S1NLA30zbrIiIiIiIPj2b4iIhImonZvpdjJYPI3eNpAq6Fcpa8BNf6ktwndtDlywaYzUY7bbMuIiIiIvJwaYaPiIg8dLYLFznaZRSBq2ZQDCuxuPNDgYE8+vUIejbwAaBnT22zLiIiIiKSVhT4iIjIQxEeDkcOWPD/eRoFg8dQIv4KAMu82pIw/iOe718MkynpPdpmXUREREQkbSjwERGR/yw4GH7qtYJPGEhZDgLwt6kiu1+YRLupDfD2dnAHRUREREScjGr4iIjIf3Lqt0ME9GrJcppTloOcx48+zCTm9510m6OwR0RERETEERT4iIjIA7FdvsLRpwcS0KQ8LVmGBVcmMoiShDKLl4iONTu6iyIiIiIiTktLukRE5P4kJHDm3WC83x9JccsFAH7lKQYzkVBKAdpiXURERETE0RT4iIhIql1buoGr3V+n4IXdABygLFs6fMrNek059jqQoC3WRUREREQyAgU+IiLyrxKOneR4+yGU2PkDOYAr+PJzhbE0+LEfL5Z2A6B1a22xLiIiIiKSUSjwERGRFIWHw9E90fjNnkDxnz+khC2GBFz46ZGXCJj1Dj3b5UnSXlusi4iIiIhkHAp8REQkmeAvbYT0/oEJvElhTgHwu2s9wt+YzLPvVsZVf3uIiIiIiGRo2qVLRESSOPnLbkr2fpLv6URhTnGSwnTgB3x2rKPjeIU9IiIiIiKZgQIfEREBwHb+AqGNX6bgM9Wox0ai8WIUYynDQX6kPRcvmRzdRRERERERSSX9P62IiLOLj+fUyBnknPg2JROuAPA9HRnCBE5RGNA26yIiIiIimY0CHxERJ3Z18Vqu9+xPoUt7AdhjqsiuFz/nRrV6nHkNbbMuIiIiIpJJKfAREXFCliMnOdH+DUru/glf4CK5WFxtHEE/9qZboPFXQ6tW2mZdRERERCSzUuAjIuIkErdZz/XlBEou+pCSt7ZZ/zH3yxSZ9w49W+ZK0l7brIuIiIiIZF4KfEREnEDwlzaW917IxwymKCcB2ORan4hhk2k/piJms4M7KCIiIiIiD5UCHxGRLO7ksn0U6f06P7EagDAK8QYTGbWzHU9U0M5bIiIiIiJZkbZlFxHJomxXrnK45UAKtKxEY1YTgwfv8LZ9m/ULFxX2iIiIiIhkVekS+EybNo3AwEA8PT2pVq0aGzduvGvbhQsX0qRJE/LkyYOPjw+1atVi5cqV6dFNEZGswWol/N05XM5bilLLJuFKAot4hkfZz2je4Sbe2mZdRERERCSLS/PAZ8GCBQwYMICRI0eya9cu6tatS/PmzQkLC0ux/YYNG2jSpAnLli1jx44dNGjQgFatWrFr16607qqISKYX9dsfnMhfi4KjXiSX5RyHTKX5+vmVRExdRJi5GKBt1kVEREREnEGa1/D55JNP6NmzJ7169QJg0qRJrFy5kunTpzN+/Phk7SdNmpTk8fvvv88vv/zCr7/+SpUqVdK6uyIimVJCxDmOtB9O6d9n4wNcIzuLKoym3k/96VrKHYCnn9Y26yIiIiIiziJNA5+4uDh27NjBsGHDkpwPCgpi8+bNqXoOq9XKtWvXyJUrV4rXY2NjiY2NtT+OiooCwGKxYLFYHrDnjpfY98z8HkQelMb/vwsPhyNHTJQoasE6ZQZ5p46ldMJVABb7dsN32jieax8A3P4c/f2NwzjnkG7Lv9DYF2em8S/OTONfnJnG//25n88pTQOfCxcukJCQgH/iTxi3+Pv7ExkZmarnmDhxIjdu3KBDhw4pXh8/fjxjx45Ndn7VqlV4e3vff6czmJCQEEd3QcRhNP5TFhJSmGnTKlPXtoHPeY2K7AFgl6kKK1oOpFR3X6Jcd7JsmYM7Kg9MY1+cmca/ODONf3FmGv+pEx0dneq26bItu8mUdCcYm82W7FxK5s+fz5gxY/jll1/Imzdvim2GDx/OoEGD7I+joqIoVKgQQUFB+Pj4/LeOO5DFYiEkJIQmTZrg5ubm6O6IpCuN/7sLD4dXnjnLN3ShM/MBuEgufqr2Hk8t7M4b+cwO7qH8Fxr74sw0/sWZafyLM9P4vz+Jq5pSI00DHz8/P8xmc7LZPOfOnUs26+efFixYQM+ePfnxxx9p3LjxXdt5eHjg4eGR7Lybm1uWGCxZ5X2IPAiN/3+IiyPs1Ukc5B2ycwMrJmbQl7d5l58/zk2Bwo7uoDwsGvvizDT+xZlp/Isz0/hPnfv5jNJ0ly53d3eqVauWbGpWSEgItWvXvut98+fPp3v37nz33Xe0bNkyLbsoIpIpRH61itO5K/DksqFk5wabqUV1tvMK07hqzq0t1kVEREREJIk0X9I1aNAgunbtSvXq1alVqxazZs0iLCyMvn37AsaSrNOnT/PVV18BRtjTrVs3Jk+eTM2aNe2zg7y8vPD19U3r7oqIZCgxB09wvM0gyh5cBEAk/sx7dAIjDzxPgs1FW6yLiIiIiEiK0jzw6dixIxcvXuSdd94hIiKC8uXLs2zZMooUKQJAREQEYWFh9vYzZ84kPj6eV155hVdeecV+/oUXXmDu3Llp3V0RkQzBdjOGAy9OoNiC8ZS1xRCPmUUF+1Puh9EMreVLl3BtsS4iIiIiIneXLkWb+/XrR79+/VK89s8QZ926dWnfIRGRDCY8HEJDoWRJ4H//w2XQ6zx68xgAmz3qE/XeFNoNKkdivfuCBRX0iIiIiIjI3aVL4CMiIncXHAwvvQRFrMeYzOu04n8AnCY/G9t8QquvOpAt+7/vbCgiIiIiIpIoTYs2i4jIvYWHw2u9bvK2dQz7eZRW/A8Lriwo8iYxuw7SaWFHhT0iIiIiInLfNMNHRMRRbDb2f/ArexlAMY4DEEJjXuNzZswtQ/HKju2eiIiIiIhkXgp8REQc4OqOI4Q/+zpBJ5cBcIqCDORTfuZZzGaTtlkXEREREZH/REu6RETSkfV6NLtajcKzejnKnVxGHG7MCRjOo6aD/Ew7zGaTtlkXEREREZH/TDN8RETSg81G6Ce/km3E61SJOwHApmxBuEz9nB4vlKKJtlkXEREREZGHSIGPiEgau/TnUcKffZ2Kp5YCcMpUiF3dJtF8Vhvc3I2CzNpmXUREREREHiYFPiIiaSA8HA7/dRO3iR/w2NoPqUgscbixotwb1PhlJE8Xz+boLoqIiIiISBamwEdE5CELDobFvf7HZPrbd9/akr0JbjM+5+kupR3cOxERERERcQYq2iwi8hDt+/UYeXo9za+0ohjHOUVB2vMj+f5eSXWFPSIiIiIikk4U+IiIPATx12PY2uIdij1djqf5FQuufMBQynKAn2jHiZMmR3dRRERERESciJZ0iYj8R3smLMf37deoGXcUgNU05FWmcJCyAJjNxu5bIiIiIiIi6UWBj4jIAzr7Zxhhzw7gsVOLAIgw5Wdfz084/lgHQvuZIMEIe2bO1A5cIiIiIiKSvhT4iIjcJ8uNOLZ2+ISqy97lMaKJx8zaigOo+stoGhfNAUDzFnDkiDGzR2GPiIiIiIikNwU+IiKpEB4OoaFgWruGQh++Qt24gwDsylEXt1nTaNKpfJL2BQsq6BEREREREcdR4CMi8i+Cg2F0r9N8xBs8x/cAnDPl5cCLH1N35vO4mFWQWUREREREMhYFPiIi93DscDz7en3OfkbjwzUScGE6/Wiw8V2erJPT0d0TERERERFJkbZlFxG5i+2TfyemfDU+YRA+XGMLNanOdl7jc85bcjq6eyIiIiIiInelGT4iIv9wevd5DrcZSoMTcwC4SC6GMIE59MCGi7ZZFxERERGRDE8zfEREbomLsbKi7Sy8qpS2hz2bH+3FwvcPMc/c0x72aJt1ERERERHJ6DTDR0QE2DptJ16DX6ZZzB8AhGarhG3qdGq/UIvaQPOu2mZdREREREQyDwU+IuLUTu25wp42b9P06DTMWLlmysGBzuN4bE4/TG63v0Vqm3UREREREclMFPiIiNMJD4d9e21cnvodDf43mBacBWBHqecouWQiNUrnc3APRURERERE/hvV8BERpxIcDEGFDuDWvBGd/vc8/pzlpFdpjs5aTbVD3+GjsEdERERERLIABT4i4jT+XB/N2V4j2E0lGrKWaLwYwfu47Pmb4r0bOrp7IiIiIiIiD40CHxHJ8mJj4cduv5K3/qOMYDzuWPiVpyjHPsYznKOn3B3dRRERERERkYdKNXxEJEtb/9VJLP360/7GEgBOUpj+fMYSWgNgNhs7b4mIiIiIiGQlCnxEJEsKOxLHhmc+oe2+d/DmJhZcOdzqDf5s+hZLX88GCUbYM3Omdt8SEREREZGsR4GPiGQpsbHw06vrqBrcj+dtBwA4UuBJ/H+eRrnHH6Uc0Lg1HDlizOxR2CMiIiIiIlmRAh8RyfTCwyE0FC7sP4fb8Dfocu1rAC675eH6mImUGP48mEz29gULKugREREREZGsTYGPiGRqwcHwUi8rvfiCDxjGI1zBionQRn0p9cN7PJLrEUd3UUREREREJN0p8BGRTOvoUZjaaxe/8zI12QbATqqQc/4MSneq4eDeiYiIiIiIOI62ZReRTGn1oijWVh7An1SnJtuIIgf9mUwN/iAsQGGPiIiIiIg4N83wEZFM5VSYjR86/EinbQNpxBkAvqcjg/iECPJrm3URERERERE0w0dEMom4OJjx5lEOBjZn8LaOFOAM53OWYPHLK3ne/L097NE26yIiIiIiIukU+EybNo3AwEA8PT2pVq0aGzduvGf79evXU61aNTw9PSlWrBgzZsxIj26KSAb129JYpud/l+4fl6OJdSVxJnfO9h1Nnog9PDMtiBMnYO1aOHECevZ0dG9FREREREQcL80DnwULFjBgwABGjhzJrl27qFu3Ls2bNycsLCzF9sePH6dFixbUrVuXXbt2MWLECPr378/PP/+c1l0VkQwiPBz27PHjjz9g7JNrKPhUJV6/OApPYjlTvgluB/fiP30MeHoCxoye+vU1s0dERERERCRRmtfw+eSTT+jZsye9evUCYNKkSaxcuZLp06czfvz4ZO1nzJhB4cKFmTRpEgBly5Zl+/btfPzxxzz77LNp3V0RcbDgYOjd25U8thIU4UVG8w0AV70DcPv8U/L36Agmk4N7KSIiIiIikrGlaeATFxfHjh07GDZsWJLzQUFBbN68OcV7tmzZQlBQUJJzTZs2JTg4GIvFgpubW5JrsbGxxMbG2h9HRUUBYLFYsFgsD+NtOERi3zPzexC5X+Hh8FIvF17iC8YznEe4ghUTYU/1pcDssZAzJ5b4eEd3UyTN6Hu/ODONf3FmGv/izDT+78/9fE5pGvhcuHCBhIQE/P39k5z39/cnMjIyxXsiIyNTbB8fH8+FCxfIly9fkmvjx49n7NixyZ5n1apVeHt7/8d34HghISGO7oJIurhwwZNl77vzO8OpyTYAdlCVvsyg9eOxVLhLSCySFel7vzgzjX9xZhr/4sw0/lMnOjo61W3TZVt20z+WX9hstmTn/q19SucBhg8fzqBBg+yPo6KiKFSoEEFBQfj4+PyXbjuUxWIhJCSEJk2aJJvVJJKVxMXB9Ak38Hh/LD/Ef4YZK1HkYCTvMY1+mMwu/NAlXvV5xCnoe784M41/cWYa/+LMNP7vT+KqptRI08DHz88Ps9mcbDbPuXPnks3iSRQQEJBie1dXV3Lnzp2svYeHBx4eHsnOu7m5ZYnBklXeh0hKfgux8Uv3RQw905+CnAZgb7kOND/wCeHWApjNNmbONBEYqK8BcS763i/OTONfnJnGvzgzjf/UuZ/PKE136XJ3d6datWrJpmaFhIRQu3btFO+pVatWsvarVq2ievXq+sMXySLCw+HVp04QE9SKz888S0FOcy1PMWzLllN+7wI2HMnLu+9uIjQ0Xtusi4iIiIiIPIA035Z90KBBfPnll8yePZsDBw4wcOBAwsLC6Nu3L2AsyerWrZu9fd++fTl58iSDBg3iwIEDzJ49m+DgYN5444207qqIpLG4OPh4vIWZxT5kwtJHeYqlxLu4EfPGW+Q4uRdT82aAsb16hQoXtYxLRERERETkAaV5DZ+OHTty8eJF3nnnHSIiIihfvjzLli2jSJEiAERERBAWFmZvHxgYyLJlyxg4cCBTp04lf/78fPbZZ9qSXSSTW70aZr+4ieFhfSnPPgCuV69P9q+n41qmjIN7JyIiIiIikrWkS9Hmfv360a9fvxSvzZ07N9m5J598kp07d6Zxr0QkPZw+DaNfvUjNxUP5lmAAbubIg8fnE8ne7Xm4RwF3EREREREReTDpEviIiPOJi4PJk2wceXseH8S9gR8XAYh9oTden3wAuXI5uIciIiIiIiJZV5rX8BER57NmDbQte4AaQ+szM64HflzkZskK8PvveMydpbBHREREREQkjSnwEZGH5vRp6NruJpsbvcXCY5V4kg1Y3L2xfjgBr3074C6784mIiIiIiMjDpSVdIvKfxcXB5Mmw6e2VfBLbj+IcA8DSrBVuMz6HW0XaRUREREREJH1oho+I/Cdr1kDjchEUGtKJX2KbUZxjxOUtAAsX4rbsF4U9IiIiIiIiDqAZPiLyQE6fhjcGJpDrxxn8ygh8icJqcsH0+uu4vzMWcuRwdBdFRERERESclgIfEbkvicu3Fo3axaSYPtTgTwDiqz6G65czoUoVB/dQREREREREtKRLRFJt9WqoVf4arkMGsjGmOjX4k4TsPjBlCq5/bFHYIyIiIiIikkFoho+I/KvwcBg8GGJ/WMxiXqMQ4QDY2nfAPOlTyJ/fwT0UERERERGRO2mGj4jcVVwcTJgAjUuF0fmH1iymDYUIJ6FIICxfjumHBQp7REREREREMiAFPiKSotWroWrFeM4Oncj2m4/SmiXYXF1h+HDM+/dCs2aO7qKIiIiIiIjchZZ0iUgS4eEwaBCc/HEb39CHyvwFgO2JJzDNmAHlyjm4hyIiIiIiIvJvNMNHRABj+daHH0KN0ld58sdX2EItKvMX1pyPwJdfYlq/XmGPiIiIiIhIJqEZPiJCSAi89qqNiod/ZAevk49I40LXrrh8/DHkzevYDoqIiIiIiMh9UeAj4sTCwozlWzt+Ps40+tGcFQDYSpY0lm81bOjgHoqIiIiIiMiD0JIuEScUGwvvvw8Vylgo8fMH7KMczVmBzd0dxozB9PffCntEREREREQyMc3wEXEyK1ZA//7gF7qZTfShAnuNCw0aYJo+HUqXdmwHRURERERE5D/TDB8RJ3HyJLRtC881v8zg0D5spg4V2IvNzw+++srYh11hj4iIiIiISJagwEcki4uJgXffhTKlbXgu+o6DlKEPs4yLPXtiOngQunYFk8mxHRUREREREZGHRku6RLKw//0PXn8dTMeOsISXacJvxoWyZWHmTKhb17EdFBERERERkTShGT4iWdDRo9CqFbRtFcdzx8axl/I04Tdsnp7w3nuwe7fCHhERERERkSxMM3xEspDoaPjgA5gwAWrEbuAv+lKWA8bFoCBM06ZB8eKO7aSIiIiIiIikOQU+IlmAzQaLF8PAgXDt5EWmMoSezDYu5s0LkyZBp06q0yMiIiIiIuIktKRLJJM7fBiaNYO2bW3UO/kVh13K3A57XnoJDh6E555T2CMiIiIiIuJENMNHJJO6fh3GjYNPPoGilsOsMb1MA9sasALly8OMGVCnjqO7KSIiIiIiIg6gGT4imYzNBt9/D2XKwKcfxjLM8g77XCoYYY+Xl1HEZ+dOhT0iIiIiIiJOTDN8RDKRvXvh1Vdh/Xqox3rWu/WhuOWQMaunaVOYNg2KFXN0N0VERERERMTBNMNHJBO4cgUGDIDKlWHv+gvMM/dgPfWNsMffH+bPh+XLFfaIiIiIiIgIoBk+Ihma1Qpffw1DhsC5cza68RWfuw/GJ+6i0aBvXxg/HnLmdGg/RUREREREJGNR4COSQe3caSzf2rIFSnGIJV59efzmOogDKlSAmTOhVi1Hd1NEREREREQyIC3pEslgLl40Ju5Urw47tsQyzm0s+8wVjbAnsSjzjh0Ke0REREREROSuNMNHJINISIBZs2DkSLh8GZ5kHd/l6Ev+a4eMBs2awdSpqtMjIiIiIiIi/0ozfEQygE2bjBk9/fqBy+ULLH6kB+toYIQ9AQGwYAEsW6awR0RERERERFJFgY+IA0VEQNeuULcu7N5to6/3PE5lK0Pry3ONBn36wIED0KEDmEwO7auIiIiIiIhkHlrSJeIAcXHw2Wcwdixcvw6lOcTifH0pE7HOaKCizCIiIiIiIvIfaIaPSDpbtQoqVoQ334S467HMKjCW/W4VjbBHRZlFRERERETkIUjTwOfy5ct07doVX19ffH196dq1K1euXLlre4vFwtChQ6lQoQLZsmUjf/78dOvWjTNnzqRlN0XSxfHj0KYNNG0Khw5Ba991nPOvSO/TY3CxxBlFmffuhaFDwc3N0d0VERERERGRTCxNA5/OnTuze/duVqxYwYoVK9i9ezddu3a9a/vo6Gh27tzJ22+/zc6dO1m4cCGHDx/m6aefTstuiqSp6GgYNQrKloXFiyGvywW2lu3B4qsN8D17GPz94fvvVZRZREREREREHpo0q+Fz4MABVqxYwdatW3n88ccB+OKLL6hVqxaHDh2idOnSye7x9fUlJCQkybnPP/+cGjVqEBYWRuHChZPdExsbS2xsrP1xVFQUYMwWslgsD/MtpavEvmfm9+DsbDZYuNDE0KFmwsJMgI3xZebyRuSbuB64CEDCSy9hHTcOcuaE+HiH9jcj0fgXZ6WxL85M41+cmca/ODON//tzP5+TyWaz2dKiE7Nnz2bQoEHJlnDlzJmTTz/9lB49eqTqeX777TeCgoK4cuUKPj4+ya6PGTOGsWPHJjv/3Xff4e3t/UB9F/mvwsJy8MUXFdizJw8ANR/ZzTfZe1L81E4AogoXZne/flwuU8aR3RQREREREZFMJDo6ms6dO3P16tUUM5I7pdkMn8jISPLmzZvsfN68eYmMjEzVc8TExDBs2DA6d+581zcyfPhwBg0aZH8cFRVFoUKFCAoK+tc3n5FZLBZCQkJo0qQJbqrnkmlcuQLvvuvCtGkuJCSYyOEew6LHx9Nw2weYLsdh8/LC+tZbeA0YQC39ud6Vxr84K419cWYa/+LMNP7FmWn835/EVU2pcd+Bz91m1Nzpzz//BMBkMiW7ZrPZUjz/TxaLhU6dOmG1Wpk2bdpd23l4eODh4ZHsvJubW5YYLFnlfWR1VivMmQPDh8P588a5t55Yx9tn+uK+8ZBxolkzTFOnYi5WDLPjupqpaPyLs9LYF2em8S/OTONfnJnGf+rcz2d034HPq6++SqdOne7ZpmjRovz999+cPXs22bXz58/j7+9/z/stFgsdOnTg+PHjrFmzJlPP1JGsb8sW6N8ftm83HtcseZGfir1JgZVzjBMBATB5MrRvD6kIO0VERERERET+q/sOfPz8/PDz8/vXdrVq1eLq1av88ccf1KhRA4Bt27Zx9epVateufdf7EsOe0NBQ1q5dS+7cue+3iyLpIiIChg2Dr74yHvvksPH9U1/TLGQwppUXjHCnb194/32jKLOIiIiIiIhIOkmzbdnLli1Ls2bN6N27N1u3bmXr1q307t2bp556KskOXWXKlGHRokUAxMfH065dO7Zv3863335LQkICkZGRREZGEhcXl1ZdFbkvsbEwYQKUKnU77Bn+7GHOV2xE8/kvYLpwASpUgN9/h2nTFPaIiIiIiIhIukuzos0A3377Lf379ycoKAiAp59+milTpiRpc+jQIa5evQpAeHg4S5YsAaBy5cpJ2q1du5b69eunZXdF/tWyZTBgAISGGo+feCyW+ZU/pOC89yAuDry8YMwYGDgQtP5UREREREREHCRNA59cuXLxzTff3LPNnbvCFy1alDTaJV7kPwkNNTKcpUuNx/7+MO/F9QQt7IPpi9tFmZk2DQIDHddREREREREREdI48BHJ7K5dg3Hj4NNPwWIxJu2M6HOREVfexH38raLM/v5GUeYOHVSUWURERERERDIEBT4iKbBa4euvjaLMkZHGuWZNbcxu8DX5Ph4MFy4YJ/v2hfHjVadHREREREREMhQFPiL/sG2bsc36H38Yj0uUgFlvHKb+gr6Yhq01TpYvDzNnwj12nBMRERERERFxFAU+IrdERMDw4TBvnvE4e3YYMzyW129+gGv/928XZR49GgYNUlFmERERERERybAU+IjTi42FSZOMWj3XrxvnuneHia3WkWtEXzh0qyhz06ZGUeZixRzVVREREREREZFUcXF0B0QcxWaDX381VmcNG2aEPY8/DjtWXmAOPcj1bAMj7PH3h+++g+XLFfaIiIiIiIhIpqAZPuKUDhwwtllfudJ4HBAAH35g43nrV7h0HgwXLxoXVJRZREREREREMiEFPuJULl+GMWNg6lRISAB3dyP4eavDIbIP7gvr1hkNVZRZREREREREMjEt6RKnEB8P06dDyZLw2WdG2PPMM7B/VywfeI0le62KRtjj5QUffAA7dyrsERERERERkUxLM3wky1uzBgYMgD17jMflyhlFmhu7roO2dxRlbtbMmPqjOj0iIiIiIiKSyWmGj2RZx45B27bQqJER9uTKZeQ5u3+7QONve0CDW0WZAwJgwQJYtkxhj4iIiIiIiGQJCnwky7l2DUaMgLJlYdEiMJvhtdcg9LCNft5zcS1fBubOBZMJXn7ZqODcoYPxWERERERERCQL0JIuyTKsVvjqKxg+HCIjjXNNmsCnn0I580F4ti+sX29cqFDBKMpcq5bjOiwiIiIiIiKSRjTDR7KETZugRg3o0cMIe4oXh8WLYeUvMZT7YTRUqmSEPV5eMGEC7NihsEdERERERESyLM3wkUzt5EkYMgR++MF47OMDb79tLOHy+H0NVOoLoaHGxRYtjCI+RYs6rL8iIiIiIiIi6UGBj2RK16/Dhx/Cxx9DTIxRfqd3b3j3XchrOg8vvWGs7wLIl8/Yi/3ZZ1WnR0RERERERJyCAh/JVKxW+OYbo07PmTPGufr1jW3WK1Wwwpw5xpSfS5eMcKdfP3jvPfD1dWS3RURERERERNKVAh/JNDZvhoED4Y8/jMfFihkzfJ55BkwH9kP9vrBxo3GxUiWjKPPjjzusvyIiIiIiIiKOoqLNkuGdPAnPPQd16hhhT/bs8MEHsG8ftGl2E9Pbb0HlykbY4+1tpEDbtyvsEREREREREaelGT6SYV27ZgQ7n3xyu07Piy/CuHEQEACEhMDLL8PRo8YNrVrB559DkSIO7beIiIiIiIiIoynwkQzHaoV582DECGOLdTDq9Hz6qTGRh7Nnocsg+O4742KBAkbQ88wzKsosIiIiIiIigpZ0SQazfj1Ur27M5ImMhOLFYdEiWLMGKle0whdfQJkyRtjj4gKvvw4HDkCbNgp7RERERERERG7RDB/JEI4eNTbXWrjQeOzrC2+/Da++Ch4ewN690Lcv/P670aBqVZg1C6pVc1ifRURERERERDIqzfARh7pyxQh6Hn3UCHtcXIyyPKGhMHgweCREw7BhUKWKEfZkz26s7dq2TWGPiIiIiIiIyF1oho84RHy8MUFn9Gi4cME4FxQEEydC+fK3Gi1bBq+8AidOGI/btIHPPoOCBR3RZREREREREZFMQ4GPpCubDZYvhzfeMErvAJQtawQ9zZrdKsNz5oxRm+enn4wGhQvDlCnGLlwiIiIiIiIi8q+0pEvSzZ490LQptGxphD1+fjBtGvz9NzRvDiZrghHslCljhD1ms5EM7dunsEdERERERETkPmiGj6S5yEgYNQqCg40t193dYcAAY9t1X99bjXbtgj594M8/jcePPw4zZ0KlSo7qtoiIiIiIiEimpcBH0szNm0Z95fHj4fp141z79vDBB1Cs2K1G164ZhXwmTzbSIB8f44Y+fYwZPiIiIiIiIiJy3xT4yENntcJ33xkzeE6dMs499pgR/tSpc6uRzQaLF0P//hAebpzr0AEmTYJ8+RzQaxEREREREZGsQ4GPPFTr1xvbqe/YYTwuVMiYsPPcc8aW6wCcPAmvvQa//mo8LlYMpk41qjaLiIiIiIiIyH+mos3yUBw6BK1bQ/36RtiTI4cR9Bw6BF263Ap7LBb46CN49FEj7HFzg5EjYe9ehT0iIiIiIiIiD5Fm+Mh/cv48jB0LM2ZAQoJRdqdPH6MsT968dzTcsgX69jW25AKoW9e46dFHHdJvERERERERkaxMgY88kJgYo87y++9DVJRx7qmnYMIEKFv2joaXL8Pw4TBrllG3J3duY5ZP9+5gMjmi6yIiIiIiIiJZngIfuS9WK3z/vVGQ+eRJ41yVKvDxx9Cw4R0NbTaYPx8GDoRz54xz3bsbYY+fX3p3W0RERERERMSppGkNn8uXL9O1a1d8fX3x9fWla9euXLlyJdX39+nTB5PJxKRJk9Ksj5J669ZBjRpGTZ6TJ6FAAZg7F7Zv/0fYc/gwNGliNDx3zpjys24dzJmjsEdEREREREQkHaRp4NO5c2d2797NihUrWLFiBbt376Zr166punfx4sVs27aN/Pnzp2UXJRX274dWraBBA6Mgc/bsMG6ckeu88MIdu2/FxBgFfSpUgNWrwdMT3nsPdu+GJ5905FsQERERERERcSpptqTrwIH/t3fnwVVW9x/HPzfJJYCGyxIDQULALSCLQhASClpAAyhW0FqpNILTQQHDItQS0Vaw1pSOinREQAaZUWh1KkuxWCQWkuCQsBmIFBL1JwgKgUDJIqmQ5fz+eEpszHpD7pLnvl8zmfF5ch7v9+LXM+PH85xzRFu3blVWVpaGDBkiSVq1apXi4+OVl5enmJiYOp/95ptvlJSUpA8//FD33HNPvZ9z8eJFXbx4seq6+L8bypSVlamsrKwZvolvXK7dl98hP196/vkgvflmkCorHQoONpo6tVLPPltZtSHz5fIc27crOClJji++kCRVJiSoYulS6frrqw8EGsEf+h/wBXofgYz+RyCj/xHI6H/3uPPn5LHAJzMzUy6XqyrskaS4uDi5XC7t2rWrzsCnsrJSiYmJeuqpp9SnT58GPyclJUWLFi2qcX/btm1q27Zt07+An0hNTfX6Z373XbA2bbpBmzbdoO++C5YkDRlySo88cljXXvut9u37fmxoYaH6rFmjqPR069kOHfTpL3+pkz/6kXUme16e1+uHffii/wF/QO8jkNH/CGT0PwIZ/d84paWljR7rscAnPz9fEdXO5bZEREQoPz+/zucWL16skJAQzZo1q1Gf8/TTT2vu3LlV18XFxYqKilJCQoLatWvnfuF+oqysTKmpqbrrrrvkdDq98pnl5dJbbzm0aFGwTp2yTtC67bZKLV5cqWHDwiXd/v3gykoFrV6toGeekaOwUMbhUOWMGQpeuFC3uly61SsVw6580f+AP6D3EcjofwQy+h+BjP53z+W3mhrD7cBn4cKFta6o+V979+6VJDlqOXbbGFPrfUnav3+/li5dqk8++aTOMT8UGhqq0NDQGvedTqctmsUb38MY6e9/l5KTrf16JOm666SUFOnBB4PkcPxgq6eDB6Vp06SsLOt64EA5Vq5U8KBBCvZopQg0dvn3GHAXvY9ARv8jkNH/CGT0f+O482fkduCTlJSkiRMn1jumR48eysnJ0enTp2v8rqCgQJ07d671uZ07d+rMmTPq3r171b2KigrNmzdPr776qo4dO+ZuuWjA7t3Sr38tZWRY1x07Ss8+K82YIdXI0UpKpIULpaVLpYoKKSzM2pR5xgwpmKgHAAAAAAB/4XbgEx4ervBGHK0dHx+voqIi7dmzR4MHD5Yk7d69W0VFRRo6dGitzyQmJurOO++sdm/06NFKTEzUo48+6m6pqMcXX0gLFkh//at13bq1NHu2tcqnffsfDDZG2rRJmjVL+vpr696DD0pLllhnswMAAAAAAL/isT18evfurTFjxmjq1KlauXKlJOmxxx7TuHHjqm3Y3KtXL6WkpGjChAnq1KmTOnXqVO3v43Q61aVLl3pP9ULjnTkj/e530ooV1p49Dod1tPrzz0tRUbU8cOyYNHOm9c6XZL3rtWyZNGaMN8sGAAAAAABuCGp4SNOtW7dO/fr1U0JCghISEtS/f3+9/fbb1cbk5eWpqKjIk2VA0oUL0gsvWKekv/aaFfaMHSsdOCCtWVNL2HPpkvSHP0g332yFPU6n9a7XoUOEPQAAAAAA+DmPrfCRpI4dO2rt2rX1jjHG1Pt79u25MuXl0ptvWlvvnDpl3YuNlf74R2nkyDoeysiQpk//fgfnH/9YWr5c6tXLCxUDAAAAAIAr5dEVPvAdY6T166U+faTHH7fCnp49pb/8Rdqzp46wp6BAevRR6Y47rLDnmmukt96Stm8n7AEAAAAAoAXx6Aof+EZamjR/vhXsSFJ4uPSb31jBTy0n2EuVldYyoPnzpX//27r3+OPSiy9ax3YBAAAAAIAWhcDHRnJyrFO2/vEP6/qqq6R586yfdu3qeWjaNCkz07q+5Rbr9a34eK/UDAAAAAAAmh+vdNnAsWPSI49It95qhT0hIdKMGdbR64sW1RH2fPut9KtfSQMHWmHP1VdLr7wi7dtH2AMAAAAAQAvHCp8WrKDAeuvq9detQ7Uk6aGHrNO4brihjoeMkTZulGbPlr7+2rr3wAPSq69K3bp5o2wAAAAAAOBhBD4tUEmJtGSJ9NJL1l9L1ibMixdLgwbV8+DRo9LMmdKWLdZ1z57SsmXW+ewAAAAAAMA2CHxakIsXpRUrpN//3lrdI1lvZKWkSHfdJTkcdTx46ZKVDr3wgvSf/0hOp7VB84IFUps2XqsfAAAAAAB4B4FPC1BRIa1dK/32t9Lx49a9G2+08puf/lQKqm8nph07rA19cnOt6xEjrHfAOGYdAAAAAADbYtNmP2aMtHmzQ/37S1OmWGFP167SG29I//qX9LOf1RP2nD4t/eIX1rteublSRIT09tvSP/9J2AMAAAAAgM2xwsdPpac7lJw8XHl51j+iDh2kp5+WkpIaeAurokJaudJ6XauoyHrPa/p06z2w9u29UjsAAAAAAPAtAh8/tGqV9NhjIZI6qk0boyefdOippxqR1+zbZ4U7+/ZZ17Gx1qY/9e7kDAAAAAAA7IZXuvzQAw9I4eFGY8ceVW5uecOLcwoLpSeekAYPtsIel8s6fWv3bsIeAAAAAAACECt8/FDHjtJnn5UrIyNHkZHd6h5ojPTnP0vz5ll79kjSpEnWiVxduninWAAAAAAA4HcIfPzU1Vc3MODIEev0rbQ067pXL+v0rREjPF0aAAAAAADwc7zS1dJcuCAlJ0v9+1thT5s21obMBw8S9gAAAAAAAEms8Gk5jJH+9jdp9mzrfHZJuvde6U9/knr08GlpAAAAAADAvxD4tARffinNmiVt2WJdR0dbQc9PfuLbugAAAAAAgF/ilS4/FlRWpqAXX5T69LHCHqdTWrBAOnyYsAcAAAAAANSJFT5+yvHRRxoxe7aCT560bowcaR213quXbwsDAAAAAAB+jxU+/mjVKoXcfbeuPnlSpksX6+j1jz4i7AEAAAAAAI1C4OOP7r9fpnNn/d+4cSr/9FPp5z+XHA5fVwUAAAAAAFoIXunyR506qfzwYR3auVP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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 = fitPolynomialLeastSquares(xdata, ydata, n)\n",
    "print(\"The coefficients are\", c)\n",
    "plot(xplot, evaluatePolynomial(xplot, c), 'r', label=\"Cubic least squares fit\")\n",
    "legend(loc=\"best\")\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "accepted-laundry",
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "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) - evaluatePolynomial(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": 14,
   "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": 15,
   "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": 16,
   "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": 18,
   "id": "interim-montgomery",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "C=2.0413344277069996, p=1.474126908463272\n"
     ]
    }
   ],
   "source": [
    "X = np.log(x)\n",
    "Y = np.log(y)\n",
    "Cp = fitPolynomialLeastSquares(X, Y, 1)\n",
    "C = np.exp(Cp[0])\n",
    "p = Cp[1]\n",
    "print(f\"{C=}, {p=}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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": 20,
   "id": "institutional-shame",
   "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",
    "loglog(xplot, C * xplot**p)\n",
    "legend()\n",
    "grid(True);"
   ]
  }
 ],
 "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": "3.9.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
