Week07_NumericalDifferentiation&Integration.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numerical Methods Week 7\n",
    "# Numerical Differentiation and Integration\n",
    "## Based on Tim Sauer's \"Numerical Analysis\" (Chapter 5, 5.1-5.2, 5.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Importing required Python modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import sympy as sp\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from IPython.display import Image\n",
    "import warnings; warnings.simplefilter('ignore')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.1 Numerical Differentiation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.1.1 Finite difference formulas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By definition, the derivative of $f(x)$ at a value $x$ is:\n",
    "\n",
    "$$f'(x) = \\lim_{h \\to 0} \\frac{f(x + h) - f(x)}{h},$$\n",
    "\n",
    "provided that the limit exists. Moreover, Taylor's Theorem says that if $f$ is twice continuously differentiable, then\n",
    "\n",
    "$$f(x + h) = f(x) + hf'(x) + \\frac{h^2}{2} f''(c),$$\n",
    "\n",
    "where $c$ is between $x$ and $x +h$. This leads to the following important formula for approximating the derivative of $f$ at $x$:\n",
    "\n",
    "<span style=\"font-size:large;\"><b>Two-point forward-difference formula for the derivative</b>:\n",
    "    <p/>\n",
    "<span style=\"font-size:large;\">\n",
    "$$f'(x) = \\frac{f(x + h) - f(x)}{h} - \\frac{h}{2} f''(c),$$</span>\n",
    "\n",
    "<span style=\"font-size:large;\">where $c$ is between $x$ and $x + h$.</span>\n",
    "\n",
    "Thus, in the two-point forward-difference scheme, the approximate derivative of $f(x)$ at $x$ is:\n",
    "\n",
    "$$f'_{\\textrm{two-point forward-difference approximation}}(x,h) = \\frac{f(x + h) - f(x)}{h}$$\n",
    "\n",
    "and the corresponding error made by this approximation is:\n",
    "\n",
    "$$f'_{\\textrm{two-point forward-difference approximation}}(x,h,c) = - \\frac{h}{2} f''(c).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Moreover, according to Taylor's Theorem again, if $f$ is three times continuously differentiable, then\n",
    "\n",
    "$$f(x + h) = f(x) + hf'(x) + \\frac{h^2}{2} f''(x) + \\frac{h^3}{6} f'''(c_1)$$\n",
    "\n",
    "and\n",
    "$$f(x - h) = f(x) - hf'(x) + \\frac{h^2}{2} f''(x) - \\frac{h^3}{6} f'''(c_2),$$\n",
    "\n",
    "where $x - h < c_2 < x < c_1 < x + h$. Subtracting the two equations gives the following second formula for the approximation of the derivative:\n",
    "\n",
    "<span style=\"font-size:large;\"><b>Three-point centered-difference formula for the derivative</b>:\n",
    "    <p/>\n",
    "<span style=\"font-size:large;\">\n",
    "$$f'(x) = \\frac{f(x + h) - f(x - h)}{2h} - \\frac{h^2}{6} f''(c),$$</span>\n",
    "\n",
    "<span style=\"font-size:large;\">where $x - h < c < x + h$.</span>\n",
    "\n",
    "Thus, in the three-point centered-difference scheme, the approximate derivative of $f(x)$ at $x$ is:\n",
    "\n",
    "$$f'_{\\textrm{three-point centered-difference approximation}}(x,h) = \\frac{f(x + h) - f(x - h)}{2h}$$\n",
    "\n",
    "and the corresponding error made by this approximation is:\n",
    "\n",
    "$$f'_{\\textrm{three-point centered-difference approximation}}(x,h,c) = - \\frac{h^2}{6} f''(c).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Proceeding similarly we have the following approximation of the second derivative:\n",
    "\n",
    "<span style=\"font-size:large;\"><b>Three-point centered-difference formula for the second derivative</b>:\n",
    "    <p/>\n",
    "<span style=\"font-size:large;\">\n",
    "$$f''(x) = \\frac{f(x - h) - 2f(x) + f(x + h)}{h^2} - \\frac{h^2}{12} f^{\\textrm{(iv)}}(c),$$</span>\n",
    "\n",
    "<span style=\"font-size:large;\">for some $c$ between $x - h$ and $x + h$.</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def two_point_forward_difference(f,h):\n",
    "    return (f(x+h)-f(x))/h\n",
    "\n",
    "def error_two_point_forward_difference(f,h,d2f,c):\n",
    "    return -h*d2f(c)/2\n",
    "\n",
    "def three_point_centered_difference(f,h):\n",
    "    return (f(x+h) - f(x-h))/(2*h)\n",
    "\n",
    "def error_three_point_centered_difference(f,h,d3f,c):\n",
    "    return -h**2*d3f(c)/6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <span style=\"color:#19bfc2\">EXAMPLE 5.1</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-size:large;\">Use the two-point forward-difference formula with $h = 0.1$ to approximate the derivative of $f(x) = \\frac{1}{x}$ at $x = 2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The approximate derivative of f according to the two-point forward-difference formula is -0.23809523809523836\n",
      "The error of this approximate derivative of f is -0.01190476190476164\n",
      "The error predicted by the formula is between -0.0125 and -0.010797969981643452\n"
     ]
    }
   ],
   "source": [
    "f = lambda z: 1/z\n",
    "x = 2\n",
    "h = 0.1\n",
    "adf = two_point_forward_difference(f,h)\n",
    "df = lambda z: -z**(-2)\n",
    "d2f = lambda z: 2*z**(-3)\n",
    "print(\"The approximate derivative of f according to the two-point forward-difference formula is\",adf)\n",
    "print(\"The error of this approximate derivative of f is\",df(x) - adf)\n",
    "c1 = x\n",
    "e1=error_two_point_forward_difference(f,h,d2f,c1)\n",
    "c2 = x + h\n",
    "e2=error_two_point_forward_difference(f,h,d2f,c2)\n",
    "print(\"The error predicted by the formula is between\", e1,'and', e2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <span style=\"color:#19bfc2\">EXAMPLE 5.2</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-size:large;\">Use the three-point centered-difference formula with $h = 0.1$ to approximate the derivative of $f(x) = \\frac{1}{x}$ at $x = 2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The approximate derivative of f according to the three-point centered-difference formula is -0.2506265664160401\n",
      "The error of this approximate derivative of f is 0.0006265664160400863\n",
      "The error predicted by the formula is between 0.0006250000000000001 and 0.0005141890467449263\n"
     ]
    }
   ],
   "source": [
    "f = lambda z: 1/z\n",
    "x = 2\n",
    "h = 0.1\n",
    "adf = three_point_centered_difference(f,h)\n",
    "d3f = lambda z: -6*z**(-4)  \n",
    "print(\"The approximate derivative of f according to the three-point centered-difference formula is\",adf)\n",
    "print(\"The error of this approximate derivative of f is\",df(x) - adf)\n",
    "c1 = x\n",
    "e1=error_three_point_centered_difference(f,h,d3f,c1)\n",
    "c2 = x + h\n",
    "e2=error_three_point_centered_difference(f,h,d3f,c2)\n",
    "print(\"The error predicted by the formula is between\", e1,'and', e2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.1.2 Rounding error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <span style=\"color:#19bfc2\">EXAMPLE 5.3</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-size:large;\">Approximate the derivative of $f(x) = e^x$ at $x = 0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$h$</th>\n",
       "      <th>Two-point forward-difference formula</th>\n",
       "      <th>Two-point forward-difference formula error</th>\n",
       "      <th>Three-point centered-difference formula</th>\n",
       "      <th>Three-point centered-difference formula error</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.000000e-01</td>\n",
       "      <td>1.051709</td>\n",
       "      <td>-5.170918e-02</td>\n",
       "      <td>1.001668</td>\n",
       "      <td>-1.667500e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.000000e-02</td>\n",
       "      <td>1.005017</td>\n",
       "      <td>-5.016708e-03</td>\n",
       "      <td>1.000017</td>\n",
       "      <td>-1.666675e-05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.000000e-03</td>\n",
       "      <td>1.000500</td>\n",
       "      <td>-5.001667e-04</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.666667e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.000000e-04</td>\n",
       "      <td>1.000050</td>\n",
       "      <td>-5.000167e-05</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.666890e-09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.000000e-05</td>\n",
       "      <td>1.000005</td>\n",
       "      <td>-5.000007e-06</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.210232e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.000000e-06</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-4.999622e-07</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.675549e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.000000e-07</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-4.943368e-08</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>5.263558e-10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.000000e-08</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>6.077471e-09</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>6.077471e-09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.000000e-09</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-8.274037e-08</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-2.722922e-08</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            $h$  Two-point forward-difference formula  \\\n",
       "0  1.000000e-01                              1.051709   \n",
       "1  1.000000e-02                              1.005017   \n",
       "2  1.000000e-03                              1.000500   \n",
       "3  1.000000e-04                              1.000050   \n",
       "4  1.000000e-05                              1.000005   \n",
       "5  1.000000e-06                              1.000000   \n",
       "6  1.000000e-07                              1.000000   \n",
       "7  1.000000e-08                              1.000000   \n",
       "8  1.000000e-09                              1.000000   \n",
       "\n",
       "   Two-point forward-difference formula error  \\\n",
       "0                               -5.170918e-02   \n",
       "1                               -5.016708e-03   \n",
       "2                               -5.001667e-04   \n",
       "3                               -5.000167e-05   \n",
       "4                               -5.000007e-06   \n",
       "5                               -4.999622e-07   \n",
       "6                               -4.943368e-08   \n",
       "7                                6.077471e-09   \n",
       "8                               -8.274037e-08   \n",
       "\n",
       "   Three-point centered-difference formula  \\\n",
       "0                                 1.001668   \n",
       "1                                 1.000017   \n",
       "2                                 1.000000   \n",
       "3                                 1.000000   \n",
       "4                                 1.000000   \n",
       "5                                 1.000000   \n",
       "6                                 1.000000   \n",
       "7                                 1.000000   \n",
       "8                                 1.000000   \n",
       "\n",
       "   Three-point centered-difference formula error  \n",
       "0                                  -1.667500e-03  \n",
       "1                                  -1.666675e-05  \n",
       "2                                  -1.666667e-07  \n",
       "3                                  -1.666890e-09  \n",
       "4                                  -1.210232e-11  \n",
       "5                                   2.675549e-11  \n",
       "6                                   5.263558e-10  \n",
       "7                                   6.077471e-09  \n",
       "8                                  -2.722922e-08  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = lambda z: np.exp(z)\n",
    "df = f\n",
    "d2f = f\n",
    "d3f = f\n",
    "x = 0\n",
    "hv=[10**(-i) for i in range(1,10)]\n",
    "adf1=[two_point_forward_difference(f,h) for h in hv]\n",
    "adf2=[three_point_centered_difference(f,h) for h in hv]\n",
    "e1=[f(x)-two_point_forward_difference(f,h) for h in hv]\n",
    "e2=[f(x)-three_point_centered_difference(f,h) for h in hv]\n",
    "df=pd.DataFrame(\n",
    "    {'$h$': hv,\n",
    "     'Two-point forward-difference formula': adf1,\n",
    "     'Two-point forward-difference formula error': e1,\n",
    "     'Three-point centered-difference formula': adf2,\n",
    "     'Three-point centered-difference formula error': e2\n",
    "    })\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The reason that the approximations lose accuracy for very small $h$ is loss of significance. Both formulas subtract nearly equal numbers, lose significant digits, and then, to make matters worse, magnify the effect by dividing by a small number."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.1.3 Extrapolation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $F(h)$ be an order $n$ formula for approximating a given quantity $Q$, i.e.,\n",
    "\n",
    "$$Q \\approx F(h) + Kh^n.$$\n",
    "\n",
    "Then the **Richardson extrapolation** formula for $F(h)$ is:\n",
    "\n",
    "$$Q \\approx \\frac{2^n F(h/2) - F(h)}{2^n - 1}.$$\n",
    "\n",
    "*Examples*:\n",
    "\n",
    "1. <b>Five-point centered-difference formula for the derivative</b>:\n",
    "    <p/>\n",
    "\n",
    "$$f'(x) = \\frac{1}{6h}(f(x-h) - 8f(x - h/2) + 8f(x + h/2) - f(x+h)) + O(h^4)$$\n",
    "\n",
    "2. <b>Five-point centered-difference formula for the second derivative</b>:\n",
    "    <p/>\n",
    "\n",
    "$$f''(x) = \\frac{1}{3h^2}(f(x-h) + 16f(x - h/2) - 30f(x) + 16f(x + h/2) - f(x+h)) + O(h^4)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.1.4 Symbolic differentiation and integration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle f{\\left(x \\right)} = \\sin{\\left(3 x \\right)}$"
      ],
      "text/plain": [
       "Eq(f(x), sin(3*x))"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = sp.Symbol('x', real=True)\n",
    "f = sp.sin(3*x)\n",
    "F = sp.Function('f')(x)\n",
    "sp.Eq(F,f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\operatorname{f'}{\\left(x \\right)} = 3 \\cos{\\left(3 x \\right)}$"
      ],
      "text/plain": [
       "Eq(f'(x), 3*cos(3*x))"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Fp = sp.Function(\"f'\")(x)\n",
    "sp.Eq(Fp,f.diff(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\operatorname{f'''}{\\left(x \\right)} = - 27 \\cos{\\left(3 x \\right)}$"
      ],
      "text/plain": [
       "Eq(f'''(x), -27*cos(3*x))"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F3p = sp.Function(\"f'''\")(x)\n",
    "sp.Eq(F3p,f.diff(x,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\int \\sin{\\left(x \\right)}\\, dx = - \\cos{\\left(x \\right)}$"
      ],
      "text/plain": [
       "Eq(Integral(sin(x), x), -cos(x))"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = sp.sin(x)\n",
    "t1=sp.Integral(f)\n",
    "t2=sp.integrate(f,x)\n",
    "sp.Eq(t1,t2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\int\\limits_{0}^{\\pi} \\sin{\\left(x \\right)}\\, dx = 2$"
      ],
      "text/plain": [
       "Eq(Integral(sin(x), (x, 0, pi)), 2)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t1=sp.Integral(f,(x,0,sp.pi))\n",
    "t2=sp.integrate(f,(x,0,sp.pi))\n",
    "sp.Eq(t1,t2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\int \\sin^{7}{\\left(x \\right)}\\, dx = \\frac{\\cos^{7}{\\left(x \\right)}}{7} - \\frac{3 \\cos^{5}{\\left(x \\right)}}{5} + \\cos^{3}{\\left(x \\right)} - \\cos{\\left(x \\right)}$"
      ],
      "text/plain": [
       "Eq(Integral(sin(x)**7, x), cos(x)**7/7 - 3*cos(x)**5/5 + cos(x)**3 - cos(x))"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = sp.sin(x)**7\n",
    "t1=sp.Integral(f)\n",
    "t2=sp.integrate(f,x)\n",
    "sp.Eq(t1,t2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{16}{35}$"
      ],
      "text/plain": [
       "-16/35"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t2.subs(x,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle -0.457142857142857$"
      ],
      "text/plain": [
       "-0.457142857142857"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t2.subs(x,0).evalf()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.2 Newton-Cotes Formulas for Numerical Integration"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Trapezoid Rule"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-size:large;\">\n",
    "$$\\int_{x_0}^{x_1} f(x) \\, dx = \\frac{h}{2} (y_0 + y_1) - \\frac{h^3}{12} f''(c),$$</span>\n",
    "\n",
    "<span style=\"font-size:large;\">where $h = x_1 - x_0, y_0 = f(x_0), y_1 = f(x_1)$ and $c$ is between $x_0$ and $x_1$.</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Simpson's Rule"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-size:large;\">\n",
    "$$\\int_{x_0}^{x_2} f(x) \\, dx = \\frac{h}{3} (y_0 + 4y_1 + y_2) - \\frac{h^5}{90} f^{\\textrm{(iv)}}(c),$$</span>\n",
    "\n",
    "<span style=\"font-size:large;\">where $h = x_2 - x_1 = x_1 - x_0, y_0 = f(x_0), y_1 = f(x_1), y_2 = f(x_2)$ and $c$ is between $x_0$ and $x_2$.</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Simpson's 3/8 Rule"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-size:large;\">\n",
    "$$\\int_{x_0}^{x_3} f(x) \\, dx \\approx \\frac{3h}{8} (y_0 + 3y_1 + 3y_2 + y_3),$$</span>\n",
    "\n",
    "<span style=\"font-size:large;\">where $h = x_3 - x_2 = x_2 - x_1 = x_1 - x_0, y_0 = f(x_0), y_1 = f(x_1)$, $y_2 = f(x_2), y_3 = f(x_3)$.</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2f6fU+LdEBPxG4LGlNfbLz6vs3XV1fuua+iMCIhAAAs+sqLGfza60V9bUJq23yyq22mHjy+zD9Zn5u5WVNNIBPdBWLJ8vxUWS1yagJ6Bui4AIpJTAzM31Vgu97TM8d85rldK+6OAiEI7AvYuq7fMt9dbK8uzITrotCMdI74mACDRN4IXVtfb8qlqb3Xmrndw1u+kN4/gJFcaJUN5O/rDclp9YYsVZmTW/ygLXzMXUNd+9IKrqzTbV0hlKIgIiIAItJzB9E348IL2LWmfcBNNyStoylQS6hBYW1lTJQpzKcdCxRSCoBLhQSRmxR3KsHVTcnl3pWvtu6J+XkXOrFLhmvi2dc3cg+lKTWzO09LEIiEBjAp4CN7xtcia2xsfXaxFojkCXPHee+7JKi5TNsdLnIiACOxMordtmi0PhAcOToMDRM+6amZVOJ3oXtrar+uTu3KEMebVDO8mQE470NLs2cHlao8ktUnzaXgQyngBd0yjDpMBl/LXgVwDePKdFSr+OkPolAv4lMAvWN2/pJxnz3N+W19gnIc+WPwzJt5wM1WQy9LRb/kXoBAuc51a7qlLuJS0npy1FQAS4Mrky9LsxsEQWOF0R/iTQLWSBWyUvE38OkHolAj4mMLfUvTdmrghaxBIpZZhTmXCJcnjHLDutW3Li7RJ5TtG2nVjS0fbKR/u1Rghc19DktloWOB+NjLoiAv4nsLBB1sn+xfq59f+IZWYPu+e71+bX1dusRuuUmXkR6KxFIEoCc0JeJvsVtTHeMydSfje/2ugp0AbHuWdofiIP5fu2lW6qBUPEyW0FVtFlgWsBLG0iAiKwncD+iAfYeEpb4wplH0xuEhHwI4FuoVABukExkcneBVps8OM4qU8i4EcCp8IKVgRXtfY5idXelpRvtXsWuta3C3rl2NAMD0uQAteCb4MXHyAFrgWwtIkIiMBOBEqyW9mY9lLedoKiF74i0C1kgWOnOM9JgfPV8KgzIuBrAod1yDI+Ei3Xo2xANTwE2mJO/c3AzLa+kXXiiSd6RJPQ/rl759ihuDgzXdtPAmodQgREQAREIMkEGAPXE0pcN5TNaZXYRfQkn5kOJwIikA4Exn9VZy+gzhzlRpQN6JirH6pW2yDpMLg6BxEQAREQAREQAREQAREQgfQhwLIBI98tNdaa64t6qrOOLrFseXmbEKTPNa4zEQER8BGBtUgI8RTSHU/bWG9InCURAREQAREQgbQikIykR48urXGUN4K7C4lLpLy5l5AUuLT6KulkREAE/ELg4/V19oNpFTbmvVIrlwbnl2FRP0RABERABOJE4Lxp5db11c32C8SnJUI21W6zm+a4bR/TOctO6pK5ZQMa85UC15iIXouACIhAHAh4Bbx7ILaIQdcSERABERABEUgnAnO2bLV18DZJ1BrlrXOr7Cu0z3rMmV42oPF1IwWuMZEwr9fXbLO+b2yxkpc22wdf14XZQm+JgAiIwM4EZsBfnzJIBbx3BqNXviTwISzGN8+pst/Oc9N0+7KT6pQIiIBvCNB9ckFZ4ua5eaX19uAX1c75Xt471wYUK5tzw8GXAteQRhN/c/Wc9SfoBrVWxbyboKS3RUAEGhJg7BtlVDtNOg256G9/Epi0vt5R3v6ypMafHVSvREAEfEXgMyxSejFwI1DzNN5y9WeVVgslsQPqy/1qQF68mw98e1LgWjCENN3uGSpQ+CWLUEhEQAREYDcE6PKxrML9rRgpBW43pPSRXwh0CRXzXoc5Tjl3/DIq6ocI+JfAtI2uR1p+m1Zx9zR5ZU2tvbnWbf83g/JtD4Uh7HIhSIHbBUn4N7xCpyrmHZ6P3hUBEdhBYPom1/rGdw6QArcDjP7yLYGuqAVH4Yo3FyAkIiACIrA7AtNC8xytbzR0xEto1bt2lpu4ZHjbNnZRr5x4NZ1W7UiBa+FwdkciAsrKSk1sLUSmzUQgYwnM2uIqcHT9YJFkiQj4nUB3FPH2RAuVHgk9i4AINEVgVijOm0pWPOWehVW2qMz1YLlnWL613vHTFM/DBL4t3Vm0cAh7hCa31ZXuRdXC3bSZCIhABhLwJrbBcZ7YMhClTjlJBLxFSh5OClySoOswIhBQAiyu/TkyUFKGxHGe42/P7fPdxCXf7ZFjh3bICiihxHdbClwLGXcPraKvlALXQmLaTAQyl0AuflmL4FMyRBkoM/ciCNiZF+N6LQn5QWmeC9jgqbsikGQCi5DYr7Le9UgbXBI/VeJns6usDAkDC/FbdOcQJS7Z3bBKtd0dnQafsZYTZVWVLHANsOhPERCBMAT+sn+BPTTCrDw0wYXZRG+JgO8I9ChobXPg/rtK2ZZ9NzbqkAj4iUAv/FZMPLzIpm6ot2FxssBNQJmup1e4WXB/sV+ueffdfjpvP/VFClwLR8NzL6lCaMsG1IVrH8pK2cLdtZkIiECGEaDfPq0aEhEICoFuyEQ5ZwtjvbVQGZQxUz9FIBUEcmDTOKh9lvOIx/G51vnjmW7ikt6Fre2avrK+NcdVClxzhEKfD27b2u4amm9dcltZXnzjNVvYA20mAiIgAiIgAokjMBQr6Ztqt9leIY+TxB1JLYuACIjADgJ/RsFu1pWjMHEJwxAkuyfQahtk95voUxEQAREQAREQAREQAREQARGIL4F1KFsy4M0tzuLRSV2y7aWxhfE9QJq2Jgtcmg6sTksERCA1BH4xu9IpOnpy1+y4FzdNzRnpqCIgAiIgAiLgEqCVfmnFVhtY3MboShmrcM5km7S60fomaRkBKXAt46StREAERKBZAixA+sdF1VaN546YjQYpC2WzzLSBCIiACIhAcAi8s67OvjO53FHe1p/S1graRB/rPWlDnT25zE1ccl2/PGP8m6RlBESqZZx22kqJ5XbCoRciIAIhAjPgw0/ljXJAOwXLuiT0vwiIgAiIQLoQmLqxzjmVvZCJMhbljffSV06vNMZxMavlz5F5UtJyAlLgWs7KLv60wvZ4abOd/0lFBHtpUxEQgUwhMBmriRTWgBss61umDHvanOcWuDH9em6VXTa9whajzpNEBERABBoTmIzSAZTR7WJz4mPiEi56Uug6mR+DJc9pJMP+i41+hsGitluKAoNKsZxhA6/TFYEWEvAmtpGwvmkuaiE0beYbAq3gCXUrFDgKYzjlzuSboVFHRMAXBGg1m7bRVboObB+9l8laJC65aY77W3MiEpecit8bSWQEZIGLgJdXVHAlgjclIiACItCYwKebXAvcKLlPNkaj1wEgwLqFJaHahSs0zwVgxNRFEUgugbml9VYRiiMajTpw0cp1syptMyz+LMv1RyUuiQqjFLgIsHkK3KoqKXARYNOmIpARBMpgnV9Y5v42jNgj+pXJjIClk/QtgR6IRaGsrFSFId8OkjomAikiMH2Ta33jOs+QkuhUiPFf19k/lruJS36OxCX7KnFJVKMZHf2oDhX8nXqGJrYqXL9fwfwrEQEREAGPACe2raGfhRF7RL8y6bWnZxFIBYEe+W5GuRWVWqhMBX8dUwT8TODTkAI3ACUE8qKIE6jFz8qVMyqdU+xT1Nqu3y/Pz6fr675JgYtgeLqHJjbuoji4CMBpUxHIAAIfhwK722W3sr6YmCQiEEQCnqeJ5rggjp76LAKJJTAlNM9Fm2X5HpTZmbPFteL9aViBU/stsT1O39a1TBzB2HoTG3dZhdVJuUlFAE+bikCaE+hf3Nq+2S3biqHARV8VJ80h6fR8T6Bnvrv4wDlOIgIiIAIeAYa+sYA3ZeyekasPy7Dvb0JJks7okW3HdI68Da8vejYTvQiuAgZ4Mz04Y13WVMmFMgJ02lQE0p7AKciixYdEBIJMoFtIgVutOS7Iw6i+i0DcCdBjcuWJJTYfiUw65UbuZXLVzEonAQrvpe8emh/3/mVag5GPQKYRanS+XfPctfU1SmTSiIxeioAIiIAIBJ2AN8eVY6GSZXMkIiACIuAR4B1wf8S/tc+JzM/k5TW1xgfl1wPzrFue1A8HRgz/yQIXIbxbBuQZzcjR+v9GeDhtLgIiIAIiIAJJI0AXSoYHdMENViVCVYp1l5A09jqQCKQjAS4G/RjWN8rwtm3syt656XiaST+nVtsgST+qDigCIiACIiACIiACIiACIpDWBK5Hzbe7FlZbaxjtJh5WbGNiKACe1qAiPDnZMCMEps1FQAREoDGBYyeW2ZEflNkLq1wXkcaf67UIiIAIiIAIBJXA1zXb7BYkIHnvqzqriSC/0czN9fZHZJ6kXLJPrpS3OF4AUuDiCFNNiYAIZB6BKvhUT0BhUhYnXY9JTiICIiACIiAC6USAcxwzSB49ocw21bZsnmNd1Es/rTCG0tIl+/ZBqvkWz2tCClyUNOnT27JLOMoDaDcREIFAEJiOFUZvRXLcnm0C0Wd1UgREQAREQARaSuDD9XXOpvuhXE6n3JYlMHnoi2qbstGt+XYPsk62RYkdSfwISIGLkCWr0Hd8ZbOVvLTZVoTqYUTYhDYXARFIIwKfhCYolhhhdi5JZhJgcquHl9TYGZPLAw/gxdW1dsWMSrtzgev6FPgT0gmIgAjERGBaaJ4b3a5lWY1Woo7kLz+vco55Qpds+w7qvkniS0AKXIQ890Tq1A0hN6kVKnQaIT1tLgLpR2DyBneF8QBk7mOQtiQzCTBF9mXTK5w4yGdXBjsW8n3EufwZq+f/WV2TmYOpsxYBEdhOgItTNF5QRrVr2SLllVgAYhmSQixsPjBcNd+2w4zjH1LgIoTZHSmWvZs0WeAihKfNRSANCTA2gHLQni1bmUxDBDolEDitW/b2AP3rZ1ciBX9wnexZSoCyoiK45+CcgP4TARGImcAMhAkwbIgyun3z89xzSObl1Xy7FTXf9i6QqhHzIIRpQFTDQNndW1hMsK6hAoQrKjW57Y6VPhOBdCfwRflW8yzxh3dofmJLdx6ZfH40vt47rMD4vBzu9b8PsPthzwLXlPxl9VarjSDjXCaPv85dBNKVwAewyFOKcQO8PzxNdicbkeDkqlDNt5Gw1v1INd92hyumz6TARYGvR747ua2SC2UU9LSLCKQPAS+wmws7Y5XAJH0GNsozGY0blvP2znH2/sOCKlsa0DjpHiELHLPIra6SBhfl5aDdRCAtCDDDMmUcvEzauLe/TZ7XTz+rtC/xm8E58eH9C5rdvsmG9EGzBKTANYto1w08C5wmtl3Z6B0RyCQCH4fi34a0beP4+mfSuetcwxO4fXC+leDupQohI7yZCaJ0C3mZsO+a54I4guqzCMSPwOQNngK3e+vbO+vq7Illbtzsdf3ybBjmRUniCEiBi4KtN7mtqZILZRT4tIsIpA2Bn/TJdVYZr8azRARIoDNSbN80wK13xGyOb651b36CRKdbyALHPq9RqECQhk59FYG4EqhALO8RHbNtn8LWiPFtOkyAMXKXoOYbhaUGvN/AuHZGje1EoOnR2GkzvWhIoFvIhXK1XCgbYtHfIpBxBPoWtba+Ra7LXMadvE64SQKM+3gcK9FzttTbj2dW2MyjSyw3QMul7CszLrMwvSxwTQ6zPhCBtCdQAJ/Jf44uaPY8b0DJALqMM8nfI3CdDNLvXbMn59MNAjSl+IegZ4HTxOafMVFPREAERMAvBLIxs/5pmJs6e2HZVrtzvlsPyS/9a0k/dsxz8jRpCS9tIwKZSmAiinw/iLIjlMv3zXVi5TKVRTLPWwpcFLQPRba5xw8osJfHFhmDvCUiIAIiIAIi0JDAYR2z7Oy9XOvsHUhosgiKXJBkLBIWHNs5y/rAdUoiAiIgAuEIsFzKxZ9UOPfCdLO8fZDrPh5uW70XXwKttkHi26RaEwEREIH0JzBtY731h69/EdNtSUQgDIF11dtswJtbbBNSax/dKcveOLgozFZ6SwREQASCSeC6WZV298Jqp3zKW4cUIV5OkVnJGkktrSWLtI4jAiKQNgRQHssOGV9q7V/ebCxaKhGBcAQ6IaHJ75CVkvI2MrQ9vcLN0BZuW70nAiIgAn4iwGLcB79fZj+FkhbO0jMJ2SnvXeS6Tl68T46UtyQPnhS4JAPX4URABIJP4CP4/NdAiYP3iA0q0c9o8Ec0cWfAG5uDQtnbrkFZgQ1IDCIRAREQAb8TeBcFvKmkvfZlrWNha9hfuk5eMM11ndy7oLXdOcRdqGq4jf5OLAHdecTAl6vwmoxjAKhdRSCgBN6CNYXSHenWBxSr1k1AhzEp3aaD7Z/3zzcmNqFL5fWzg1kbLimwdBAREAHfEKDXAIVlBBrLjcg6uSAU18usk8UKJWiMKOGvpcBFifh8BG0W/meT/XC6W/ciyma0mwiIQAAJvLfOdZtkXJNEBJojMLikjf20rxvc//jSGnsPK9t+l1LUdboaFsPTPy63WSiHIBEBEcgcAsyyzjIolGMazXMTvq6z+xa7rpM/3CfXjmr0eeZQSu2ZSoGLkn9brDbQEWaVasFFSVC7iUAwCbCw6fTN7sTGjLQSEWgJgRv751o/1A2k/BAFb+mC5GfJRUGn+xHf8l8UI59fGqwMmn7mqr6JQBAIfPi1O8fRg4AZdT1hwe4LG2SdvHOIsk56bJL9LAUuSuLd4DpFWV3p70k4ytPTbiIgAk0QmLKh3mpD97NMtS4RgZYQyENB3D/D1Yg3RIvLt9rNc/xdGy4HU1wHJGGhaKHSwaD/RCBjCHyE2DfKAHgPtMt2fwf4+vrZVc7vF995FOW0lIWZVFIjUuCi5N49z72g18DMrFpwUULUbiIQQAJe/FvXvNbbLSoBPA11OQUEDoPFlklNKH+EdWsKSlH4WbrjGqfQnUoiAiKQOQTeC8W/jdtzR4z3W2vr7M+hgt0/7pNr/D2TpI6AFLgo2XsWOFiT7StlFYuSonYTgeAReHOtG/92DIocS0QgUgK/R1mBHvDgoAflRXBFYjZTv0rXkKfJKnma+HWI1C8RiDsBWty9uNdjO7kJTDailuWFcP2m9Efirt+qYHfcuUfaoBS4SImFtu8WWpnkS7mXRAlRu4lAwAgw8+xmTGSU4wISuL0I7novr6nbHrcXMORp190SuCP9BVkpKZ8jScCtc/3rSul5msgCl3aXoU5IBJok4GWfZGJJL0HJlTMqnXtdvvfEyALLh0u4JLUEtIQcJf9u+Tsu3tVYrdh/jx1m5iib1G4iIAI+J5CLJa8Fx5XY8oqt1j5nx2+AX7o9r7Te5m5B9jA8M4PYPKR5noPXNfDzvmLfHBsxvMAvXc3ofhzfOdvO3TvH/rasxv6woMpO757tyznE8zThHCcRARHIDAIndMm2p0YV2FIs/rXFgtO/V9baMytqnJP/Rf88G9VO97t+uBKkwEU5Cqx5wcBOmpWX4mZOIgIikDkE9kLh0lQK426ppM1DdkAqanPwPNd5rm8yJncL/b0lviFwz9B8exsxJbRusSDulCOLjYlD/CQ9Qy6UK6DA8erx35KFn2ipLyKQHgQ6IXnR93q6sbr0MLs8VC5rJBS3G6HASfxBQApcDOPA6vMbkU58mRS4GChqVxEQgd0RoMcmlTRXQXMVtrkh5a2p/QYUo8A4socNRKzCQDzzNZ8l/iGwBxYAHxqRb6dNcuus3Tavym4d6K+bo16hhYoq5FphEfLOoayU/qGonoiACCSKABdtWPOYhgq6TD4J10m6UEr8QUAKXAzj8DsEo2/DP90YxQBRu4qACGwnwNpgdHmkguYobXCBpEvkwrLw2QoZhuAqaFTUoKRBYetPZQ3PrTTRbufq1z9O7ppt398rx/6+vMZ+P7/KTuuWbQf4yB2/N+rWHY4aUFysrN8mG5xfryP1SwQSQeA+ZMp9J5SNkvXemLxE4h8CrbZB/NMd9UQEREAE/EngWcQBsDbOCYhfOjYOGShL4dI4d7vr4w7L2hLEHYQTFlamkuYpaJ5lbT9NquFwBeY9rm4PfavUcaXkmE6DKyVjLSUiIAIikGwCH3xdZ4PwO8QSWWPeKzVa34/DnPfauMJkd0XHa4aAFLhmAOljERCBzCbwNcqETMSkdguyBc6Cy/QRyD759sFFEUHZhJt0x6K2PWbNTTbC2KJwUoCFzh2WNbpCui6RvQt1Zx+OV9Df+9+XtXbyR+XOaVzbN9fuHOJmqQz6ean/IiACwSHAxaSer22xagRZswYk56cOSNY18+hi69Ig83pwzii9eyoFLr3HV2cnAiIQJQHW6bphdqXdDTeSAvgqluMN+iswedFbhxTZiCZc3ajw7YhZg6JWSktbvTWVya8EQQWOshZygeTf/eG61kvKWpQjF8zdfogaS39dWmMwtNo7uL4OVZHcYA6kei0CASLA0jgvra6xB76osQ/X1+2SBOvFgwrtVLh6S/xHQApcjGPCxG40NXfEKkWe6mLESFO7i4B/CNz4eZXdtbAqbKHlIihdc44pNn7lnUyQO1nW6p2ED+HOhKUHPAWNz55ljYWdJZlNoAyTyfB3So0utEweMv2oYmPNOIkIiIAIJIrAtz8ut1e+rLNapjZuJIdjEemdQyPzNmnUhF4mkIAUuBjgUnHb639bnBWLd3GRH6YV0xhoalcR8A8Bfrf3xnebVrhwQnWrIzLywePENsDiFk64qNPYsjYA8Wpd8nRTHo6X3jObiBXwIz4oc+aUc5DchAVzUy0vr6m1f6AGVCFWKx49IPX9STUPHV8E0oXAq3Dd/hYUuNrwnvxWiIXKZSeUOF4n6XLO6XQeykIZw2h2QqS5dyvGWhkSERCB9CDAhCW0rjWlwPHbvhZp1T3piviAAQ1cIJ00/ohb66hsFB4iPbeAwMF7Ztn1/fLsDmSkfAqZKZml8tso8p1KWYRMqPw+qIRAKkdBxxaB+BN4YHG17a48KI1yz6+qtYt6uTXh4t8DtRgLASlwMdDjDR5v3FZCeVtZueNmLoYmtasIiECSCSxGiv55ZW7cGotjs97aZ0jdX9PMmkwOgpXuH5a3vd5aO1jcJCIQK4FbBuTZm2tr7dNN9XYp4uLGtC82r6B2rG1Hs7/n3ss6cPxO+K3YeDTnpH1EQATMFpW7cd1NsaiDBsf5UeJPAlLgYhyXvRCrQAVOxbxjBKndRSAJBBY4ddVQY82ps7aj3hoDuSMR1lgb1a61XbRPbiS7aVsRaJZANvxz/z6q0Ea+W+oU0D1vaoW9jaQmTG6SCulR4B6YS5T0NNlHyXVSMQw6pgjEnUB3uPMvLmu62Sz8FnVTfHbTgFL8iRS4GAeABU4/Wm+2tInaTTE2r91FQASiJNA4bb+XbISriuGkDzI/MkbNSy7yf4tqbD6scTVhtmc505sHKNV7OI56L3YC+8H99u6h+Xbp9AobjxIWdKm8oX9e7A1H0QITqniytEIKnMdCzyIQdAIXwDVy8oZ6p2xAuHNhbNzp3VLrwh2uX3rPJSAFLsYrwVuN5MQmEQERSD4BKmRzkAXSVdBgXYPSxQLZfG5K+kNR82LW3Hg1Km6t4R62w8xxCJISDX+71LF8sJgphUkBaX27oFeuHY16cBIRSBSBi/fJsdfhSvmf1bX2a9QgPLxjlo1FjFyyhfWf8rBiwe+As1DZMdk90PFEQAQSQeDsnjl2/axKZE3etXWGCN02KN+6ywK3KxyfvJP82cAnJx6vbuwTWp2kCyXX9Xfc/sXrCGpHBETAI0BXR1dBo6IGJS0Us0bXyHDSGtrWgGI+PMvaDsWtga4WblejdX3x8SVOPNLdC6sdpfBqFFk+BYklRrajDU4iAokl8Mj+BfbJxlKnoO734Ur5KUoL7JHk0gKc0/hdmI9FkSVaqEzsgKt1EUgigX+trNle8iYfGhuSL6PW6TYbhMXMWwfm22myviVxNCI/lBS4yJnttIfnXlKJdHVrcfWrWv1OePRCBKImUI70WLSsMamIG7PmJhtpKqia97Vu2n63vprzNxS3/nBHi1ZYt+1MrFJyYvvLF9WY1FLjxhZt/7VfsAnw+ntqVIEdNaHMibO+6JMKe+7AwqSfVK+CNo4CJ0+TpKPXAUUgIQSYXfay6ZVO21yQ/ODQYhvzXqmxfMm1/RTbnRDocW5UClyMQPduENC9HJkou+j+Lkai2j0TCWxGQTVa1uZhUuGzp7g1lRyIq4V0efQsawMYv4bXfYtkGcvE6yedz5muvDcjM+Wv5lTZi3CnZOrvK3on9wbLW6hcpljvdL7UdG4ZQoDZZM+aUm6lWCQtQa23p0cXWi6mznw8uGgkCQYBKXAxjtNe8A9+aWyh4yfcHzeREhEQgd0TYOFr1/XRdYF0XCKhtK2qCp9cpBgTjBOnVrKzZc2LP9390aL/lMojpzJmmpWIQCoJ3LBfnr3/VZ29h8d1iFk5ELFwB+yRvMWKgzu0wc1ejg1rm7xjppK3ji0C6UyAvyEsU0L5C9y0921giEjn8063c2sFf9fwd03pdqY6HxEQgaQTYO2oHTFrSC6Cemt0ifySPolhhPE9rutja+d5oJNspA3qYCV/VfBCuKs9sazGvoE4AMa90YVy0hHFYXqtt0Qg8QT4ndn/nVKngDxvuKYdWWxtkxwPl/iz1BFEQAQSSYBW/G9/XO4c4mKUwZmxqc6GYmHmR31y7RLMeZfgvfNVuDuRQxC3tmWBixtKNSQCmU1gNWpEuS6QO5KLUHn7Gha3cNIhF8paSEFznkPJRvxQd4YuJpzoKINh+ZOIQKoJML6a9eGO+7DMvoAr4wW42Xo+BfFwqeag44uACERHYDF+N7gwSaHSdkb3bHtkSbVN3Vhv5+6dE12j2itlBKTApQy9DiwCwSWwAsra3FAWyB0Wtq22CbFs4YQ3n0wmMpAPxxWS2SDbWCcocX6UD1B7i3F5lDN6ZNs0THASEUg1gSNRuuJm1IO7BWUFWF6A2VGvQWZUiQiIgAjsjkAVEu19d3K5M68VISzhX2MK7SF4lVB6IhRoXApKlOyuv/qseQJS4Jpn1KIt6N5CdzGuakhEIJ0ILMGq3Vyk66eitr3eGv5mAHQ46Q53Ry+5iGtho+LWJlDB0bw5pjDOjhY4KXDhRlrvpYLAL6HAfbihzt5aW2e/mF1po9u3sYN185WKodAxRSAwBK6aWWnTQ3FvD++fb/2Qs+GVNe48dyrCBPy5lBoYvCnpqBS4OGC/d1G1XftZpWNNWHNS2zi0qCZEIDUEFpYhE2Spm2TEsaw5Slu9VTZhgGJ9KFrSqKAxKyQT+dDCFuTYHLpP/hv1cSinqw5Oai5EHbVJAqxfSFfKkYiHoyX8zMkViIcrSngJm2swx30CS/Q5cLW6SDEyTY6PPhABvxF4ErHcf13qzmmX75tr3+2RY1PwXaYrNuVUxHhLgkdAClwcxswr5k0LHGtXFcI8LREBvxOYxxpr2y1rSDBCl0gobE14QVpvpOjvX+QmGXEta25WyHS73t9YW2vrQ3F7vFmViIDfCHRAqm+6QB3+QamtgffHmVMq7O1DiiyRU8+UDfU2CZa/wfIy8dvloP6IQJMEZmyutytmuPXexsBaf9fQfGfbvy93FbquCG84oqNUgSYB+vgDjVocBqdXgxSsXyD1+BBYICQi4BcCW+Hp6Kbtd10gqaRReeN7/Cyc0L2ioWXNc4nMzYCM+s+u2pG8RN/lcFeH3vMDAd6M3YObMd6cTUDM5vVIDX536OYsEf2jO/GkDWZ0qZaIgAj4n8BGrMYy42Ql4t+8RZ8czOGc958PzXNn9sw2lFWVBJCAFLg4DFrDGhqc3HTTFweoaiIqAjX4ZZ4DS9qOgti0rLkKW1MNNk7b7yUbyaKvVoYJ4/q8+LdvI0OXRAT8TOBSuEN9DMvYU1hN/yNc+Ue1a2Nn9UyM1dib55aUN+FP7WdQ6psIZBgBKmlnwzLPe1IqaP9EsW4mK6GwpqRXyueM7on5vcgw3Ck5XSlwccDOQsN7wqWFblcs/isRgWQQYFxaY8salbVFTayQZ7Wi+6OXDdKNWfMsa8nobxCO8TXcoMfu2cbeW1entMpBGDD10R4akW+z8b1ngoKLP610LOfDE+DmSAschXMcDfeZt7zjnL7+E4FAELh5TpUxHIBy26B8OwoZbD3xSuT0hacNLfmSYBLYMaLB7L9ver0Xkjmsr6m35VLgfDMm6dQRWoacpCJ0fcTNmuMGWba1SXcmujq6ljVXUfNi1ugaKWmaAG9SXx9XZF9Bkevo0xIHTfden2QigXwsr7Me3Oh3S52ai9+aVG6TUeSbLlPxFCYsolRjjXIt4u5YGkQiAiLgPwIvwD3yjvlVTse+BU+S6/vtXGrkvuH5dhoSdNG1UhJcAlLg4jR2NE1zBVQWuDgBzeBmNsKSS8uaF6dGl0ha1phxLpwwiQjrq+2IWXOTjTDpiCQ6AlLeouOmvVJDgMrVM0hqctzEMluKRUTWe3rj4PgmNfHcr3iGyyu3QYFLzbnqqCIgAk0TmIV7hfNRrJuq2SDkY3jsgIJdNubSztENLHK7bKA3AkFAClychslbnVwhC1yciGZGM19TWcMP7twGljVmhlxTFX5ljOn5aVlz0/W79dWouHnXX2ZQ01mKgAg0JsBMcn8Ykm9M988YFz7fN8zNONd422he94SSyBs//jJxnhuNeDuJCIiAfwgwjOd0WODL4LHTDvcKLx5UaCzaLUlPAlLg4jSudKGkcGVSIgLhCDBoeLui5lnYYF1bR5+kMNIeLlCu66OrqHnJRrqHApHD7KK3YiDASU+TXQwAtWvKCVzVJ9eYNvxvqPv0wOJqG4ZYuAvjVLONbtmd4Fa8Fu7F8jRJ+VCrAyKwEwFMX47lnbXdmLTkaSQt6d0gQ/pOG+tFWhCQAhenYTyjR7Yd3CFLX5g48Qx6Myvh7ki3x7mIU/NcIOkWuQErZOGEN0YNXSDpEslskIozCUcr/u9NXF9nx08st5O7ZtmDwwuMyrNEBIJI4M8jCmw+fmsmIzvlFTMqjHGvh2BuioewLiKz241W4oN44FQbIhA3Aj+ZWWnvwfJO+f3gfDum867feRbz/goLxmeikLeXlChuHVBDSSew6wgnvQvpcUDGB/SMn7dKekDJkLPgavR2y5rjDskkI1ttC5fEwkg3XCtu9kc8N6i31kFJM8LQSs5b9yMFOwO6p+Kmdw+4nkhEIKgEaCljUpMx75XZKiwknYF4uI+PKLZeIS+RWM6LN4YSERABfxH48xfV9hAelHOxyHJ1352TlvB93o78Zm6VcXF5ARaWHw8TG8ftJMEhIAUuOGOlnvqAwGK4J9CyRmuaU28tVBC7vAllrWf+zpa1AbCq0RVSSoIPBjPUhXVwCfNqv13RO9cysPydfwZDPYkLga7IEMn4l8PGlzkZVU/7qNwmHl5kLHkjEQERSB8C76LkzVWwvlHG7plltMCHk5dW1zrKGz+7HPUjJcEnIAUu+GOoM0gQAbohuQWx3dT9TC7ChCNNhKw5LgmeZc1L28/nIn3LEjRC8WmWRZCpf2fDcsHVS4kIpAOBA/Zo46yynzWl3KkTdxaK+v4XSh3jYyQiIALBJzAfC8i0sHP+YiIzWt5pgQ8njyEuljISyYdGKQFROESBe0+3lnEcso2127ZXvWfwuCQ4BObgh3CHZQ2xa3CBpJWtqTIpfZGifwCKYjuKGlP4Q1FjkWzWZJIEhwDH90Eke6B8A3Vx4l07Kzgk1NN0JMDY7HmleXYLXKf+92WtXYvMlPfGMTNlOjLTOYlAEAgw4+Spk8psE+47mXzrP1icYSx9OGFiE6+o9/lapAyHKJDvSYGL47BdOaPSnllRYyd2ybaXxxbGsWU1FS8CXKly0/a7LpBeQWw+NyVMJuIqaFDS+DdcIKm40WIjCTaB19fWOnWzeBY/gvukRATSjcBNA/IcTwLOTfdjsWI//IZdFqUL1RbcLH4LK/7LEff7KGJoDobLlkQERCC5BGqQuPpbH5fbIsSy0eX/n6MLbOhujAYPIj6OyYdYhuj7e8nLJLmjlbij6dc3jmz3QrwThZObJPUEqmBecQtiu7XW+DctawvKwitr/CF0XR8bpu13LWvh17VSf47qQWwEHljsupUMgVI+TjejscHU3r4lwGK+y7AKP2mDGy/DDHTHd86OuL9c6Z/wdZ3VYopbgvYO3jPiJrSDCIhAjAQuRKFufg8pd6H240kwGjQlvA9iWRHKuVDeVCqnKVLBe18KXBzHzCumrBo5cYTawqbKoZPtsKy51jXGrNF1IJzkwHrm1lWjggZ3yCI32Uh/WNYkmUHgM9TL8txKrkT9LIkIpCsBxsUwqcnY90ud38QzJ1fY+MOKnDpxkZwzF7mYcZm/q5rnIiGnbUUgPgR+NafK/glrOoXJSH7czNz1JGK86W7JRehL9pH1zQGXJv9JgYvjQHoKXCn89OiXrEyDcYTboKnNYOtZ06i0uVa2pm8oCrBqvCNdv5sFki6RfZDCX5K5BDipUXlfj6w058itJHMvhAw5846Ij6Fr/8HvlxnjtU9BZsqPkJmyBxSySKQnkiVIgYuEmLYVgfgQeAKWtNvmVTmNMVSnJfGsT6D2G+UEbM/5TpI+BKTAxXEs92pQZ4fuJSOQBUwSGwHeZHuWNbfWGmuu1Tv1jcK1zDTZTCayI2bNTTYSjxpI4Y6n94JL4IiOWTbr6GIntXJTmbuCe3bquQjsSoAeBsxUd/yHbo04KnHjDy2ykghqH3oLlbLA7cpX74hAogi8tbbOfvhphdM87y2fRtxbS3KmvX1Ikf1rZa1zX5Sovqnd1BCQAhdH7r0RV0AzNWJFjfXCpMBFBpf1uNxU/W7aftfKVm9r8X44aZcDZQ03JG5SESptruLGFWKJCLSUQKQWiJa2q+1EwI8EDsPCxV/3L7Bzp1UY3Yi/jaQkr44tanFSpn1Dv6+LkUBBIgIikHgCM/A99coF0FBAS3pLY9kKsah9QS+5TiZ+lJJ/BClwcWSeh+UQ3gyuQKX7hU6ijKYDS+N42EA2tbqKafvdVP2Ohc1xhdzq+GqHO6GOMJEMKIYrJBQ2ugF4yUZYsFYiAiIgAiLQcgJnw2WYFrSbEE/zDgoBX4SV/SdHhi8A3LjVviHX8+WY55gNj/HEEhEQgcQQ4Pf05A/LjaE5DMt5Fcqb7nsSwzporUqBi/OI9cbk5ipwWp300DIrp1cEe26pZ2Wrd+IEvW0aPnfJ21VRo8LGGA6JCMRK4MP1dShmmtVkwdNY29f+IhAEAjf0z3OUuL8iRubvSHTAxcffDsprtut9UAOTwrTkXyB7lBI/NYtMG4hAVAQ2IITkRChva7DgTTf/F5CISHFsUaFMy52kwMV5WLk6+f5XZkubyH4Y58P5rrklVNbCWNbKWIAtjPCmwXOB5A9Tf/Djc3u4R0pEIN4EOBEeNaHMSuBW8jgsDrtLvxzvY6s9EfAbgQdHFODmcJu9iiLfd8yvsu4ohcPMdruThsmfWIdKCtzuaOkzEYiOQCXS/5+KGNV5iPnn3dCTIwvtsA4tu2UfjxIDF8BF+leoAXlWz5wWu0dH11PtlSoCLbsaUtW7AB73Jqxq3ohHtwxw7VuIyduzrM2B0ub9jXvksNILMYKegua5QPI5kgD6sA3rTRFoIYHfz692alhVouzE7gqftrA5bSYCgSbAJAjPjCmwo7GoMXlDvV01s9I6Y6n/W92bdv+nG9dP++U620l5C/Twq/M+JcD17u+i1AfrNlLuHppvZ/Ro+jvZ+DR+PqvSlmIx/TfIWEkFTpKeBKTAxXlcu0eYkjnOh09Yc1TO5jJOjYoaFbdQzFot/WjCCBO6NLSsebFrBUrMGYaW3koGgZWI2Xk0lFL50n1znHpWyTiujiECfiZQAC3uJSQxOQQ14hbgt/2cqeXwgCgyZmltSn4/OL+pj/S+CIhADAR4R3UJYlJpFadcj8WS5mq9ORuG/mNM65SNWKGE/A7f02zFqIbIpN9T07/Q6XeuOqMWEKDxrKE1zU3h72aFDK+qme3HTJDIAOklF+mPZCP8O5dVXyUi4BMCN35eZRVwS2H2rmv67t5NzCddVjdEICkEOsBl/X8HU4krMyaY+uakcmP68ZHttOKWlAHQQUQgROBnsJ49iXpvlPP2znGUsNBHzT5xPf067E+hdfz0bi232jXbuDbwHQEpcL4bkuR1iBnEvFT9VNq8v+djFTactII+RpfH/lTW8Nyw3lpL6pGEa1PviUAyCNCC/M8V7qTIFU1l8UoGdR0jSARYK/O1gwvtiPFuoe+TUCvuPdSI42KcRAREIPEE7lxQbXctrHYOdHLXbHsY5T4ikWdX1dhMlByg3Dkkz7SGHgm94G0rBS4BY8bYsPm4YdwbboRDfDL50fLQ0LLGoth8LHLKHewKAUYKZ+JuaFmjSyRfS0QgaASu+azS8BVwMplG4o4StPNUf0UgFgKcr14eV2jHTii3r5EB77iJKPR9WJHti7ksnNArQ34W4cjoPRGIjACzwf5itms9OwTJSp5BoW7eh7VUqjDB3TC7ytl87J5ZStDVUnAB3k4KXAIG74yPy20WYsSuhZvWnUOSHytQirhXz5pGF8g5VNbwzKDWcJKHBVY3qYhbX42WNSYb6Qcrm0QEgk7gzbV1xgflNwPzrTiSWTHoJ6/+i0CEBA5qn2UvHFhop05y3SmPnVhm78MS17Dg/fRN9fYDZLlbhDICy09oa3sqa3CElLW5COwg8OzKWrtseoXzxvC2bey/KBeQH6Fb032La5x7POp8tL5J0p+AFLgEjHFfWKmowNESl2jZWEvLGhKMQElzlDXn73pbWRk+Yo3xP3SJ6V/kPnuKW1MrrInuv9oXgUQTuA2ZuCiDcN1f0EsZuRLNW+0Hn8AxnbPs6dGFyIRXbktQEucYZKmkO2WXUHZlLoLMxlxDWQAvDip9EhEQgcgJvLG21s6ZVu7UVWQZqtcQi9oWmV4jEdYe/m1onvsusk7q+xgJveBuq1/dBIxdX6fQaW3cFbivqqGsbc8GCaWtDEWxMYmytlU44Y/AQCiTbjZIxqy5LpB7IdZBIgKZQuCVsYV2y9wq+yYCuiNc1MwURDpPEdiFwDfwfXkCtRLPhaWN2SmPgTvlu0hs0jG3le0Dl0pmt6vF1LMQi4cHtd9ld70hAiLQDIEJqNf27Y8rnO8RLdxvQHnrjO9XpMKF+bOhuD2NOO87Bsv6Fim/oG4vBS4BI9czVEpgIVYmP/iqzsbAHxmldSISKmXzaFULWdbctP31RiUunNCFxVXQ3OQiXrKRdC1rEI6B3hOBcARYZ5B1dCQiIAKREWANqWooaRd9UuF4eNAS9zYsccxaSa+N+Zif5iXB0ySyXmtrEfA/galI9c9C3cxPwEWRN6G87R3l4no7zHEPjsi32wbloQRI5Aqg/2mph+EISIELRyWG9+5BBqGfhwJJWYzxBHxBC7Hs//dR+XZs5/ApXVmfamcXSNcdku6R4aQz3Fi85CIDYHL3LGt8XyICIiACIiAC8SLwA6Qyp6WNMToMDTj6gzL7Rf882+gmdbU/LKiyz/H+lfvm2lGdspT5Ll7g1U7aEmCmyBMQW7oFN4l7QPn637gilGOK/f5NylvaXjJhT0wKXFgs0b35GLII3YBaU3XbdihezAzExylQ5D4+otjaYXXEsaZhwqN1zbWy1duWJpS1bnmtGrhAUnFzXSEVNB7dGGmvzCDAJAvD92ijDHmZMdw6ywQTuHifHGRx3WZXzKh0lLizUezbm+ZYe+qVNbX2OhIF3bBfnv1qgGosJng41HyACTB29FhYsrlAT9fHV5H1dQTmKokIREpAClykxJrYnm4m16KAYg1nszACHc4OH19qW3FLSZN5OGFsmquguXXWnNg1xK211SiFw6X3RCAsgRlY3Rz5bqmNRhHiJ0cVWj9YqSUiIAKxEbgUFjZ6i/xufvV25a1hi3WY+347r9LO6pmt71xDMPpbBEIEqLwdDeWNJToK4Jn1MuKzD4wyAdBzq2rtLli/HzmgwAbjPlGSeQSkGsRpzF9cXWPlbqbysC1SZXNLrrnKG+MHvOQidIf0XCK5IiMRARGIjsBmrGp+B2U8KEtQNiPSbF7RHVV7iUBmEGCJGiYCamINEnWrWtnfltfYbQOVSCEzrgidZUsJ0P2YMaTMY8ASAVTeDkW9t2iECylXwKWZiuD3p1TYjKOLo2lG+wScQHRXT8BPOpbuU/1qnLafQdyMAWjC+LbT4R5GoOmIdllO3JpC1nZCoxciEDOB85FsYTHSnrfGTeY/YH2LJqNXzJ1QAyKQpgTo8t+U8sZTrsYkOA9zoUQERGAHAXqFHBeyvHnK2+Edo7v9ZjzqmZNd5Y1tPTmqYMeB9FdGEYjuCsoQRLWYjLbHqWFSclP4M+FIdBMU08ReuI/iAzLk8tFpJpnAHfOr7L+ra52j3oQkC0yoIBEBEYgfgV7wHNmdBQ75GKLOpBe/XqolEfAPgSnINnkiEpYw5s1zm4xWeeNZXT+70iZtcN297h+Wb8NQ+FuSmQR0hxMad5ZScy1rUNS2uFkgqag1VYybk9iOtP2or4bC2E+tqLW319U5SUsaX04sI3DTALmVNOai1yIQDwL/RP2bG5FAiHIsihDfCAVOIgIiEF8CZyO+7Yml1U02SuscSw9IREAEzD5AnTeWCihFtslihMfQbfKQKN0myZOJ8u5b5H7/mB32/F76rmXydZaRClwZvky0rO3IBlmPbJDb7Ivy8Ja1XGhrTNc/oMRNLuIpbo3Tvh6DMgEj3im1r/H9Kg/5mWTBlyvLttkRnbLtQn3ZMvm7pnNPEIGJ6+vsfBQbpntzf2RpfWZ0oVKZJ4i1ms1sAozZ+U6PHPv3yhpkW96VBUO4a730lLt+rHdEIGMIvL621inSXYl7QZYKYLbJaBOWEBqNAxd/WuHwG9O+jf1puGqbZszF1MSJpr0Ctwlma8+yNhdKmvf3ciQ4CCcFsEZ7ChqfBzLBCJ57w3WkOWHChFkIJn0XxbsfX1bjuHP9qHeOndo128aimDfmNokIiEAcCfD7ffqkcudmshOKoT5/YIESl8SRr5oSgcYEHkXWu0M6tHGyUa7gPIqJrQtcTDbWbDV6shw7odyew/fwuCbqnjZuT69FIN0I/HtlrZ07rdypn8gi3a+jSPfwGFwd6Yb5rVByri5InvDsmEInEUq6cdP5REYgrRS49cjI48WpUVFz/6631VVhlgrBqQQK10Cs2HuWNTcbZBujn3+0UoglyFOgsPWBxY7xOP0K21geLHhKLhktUe0nAk0T4Mrm/w3Jt6s/q8QKZ5FjgWt6a30iAiIQK4EcTI+XIJabjx/A8s3SOQ+OKLBFSOZ10oduivTTsKjyBBS9M+VOGStu7R8wAg99UW0/nlnpJLXribwHb0B5a+ytFekp0ajNu9J2mO/ePqTQuqNdiQgEVoFbi1SsDV0gGbfGmLV1eD+ctMesM6AYrpChQtie4sbEIomUy2ZU2PX9clGTSubuRHJW25lL4FzEApyMRZP2ObJxZ+5VoDNPBQFkM7eXV9fZv1Zutq9ObmvjDyuy4yeW2wp88P2pFc58/OM+StyVirHRMZNP4Ndzq+xWPChU2l7HoiLr+8YqdJmkFQ9VOpx72Fjb0/7pQSAQCtwqTAZUzlwlzfu73mhxCyc0WbsKmusC6bhEwg2yC95PhXyBtOYSERCB+BBgDGvjeolS3uLDVq2IQCQEWAqHpQMonOdGtmtjEw4vshOgxHHOpmV8Dfwqbx+crxCCSMBq20ARYMqDy1GX7a9IMkLh9+CVsUXGe9F4CZU4iQg0JOA7BW555c6WtbnMCImJgAV6w0lXzCCeCyQVtf5wXRyIZCMdmfbRJyIFzicDoW4EmgB/Ae5dWG3/h8cErPTvG4Orc6BBqPMi4BMCDEPwZElIgaPb2Af4fjL7HtOd37mg2lYhjOHR/Qss2z/TstdtPYtATAQqoL2xLturX7olbI5BFuTnEKPWeJExkoM8iRwKzKnwjW7ZkeymbTOMQEoVOCo2rmXNs67xuR4ZHMOPQk+Yol0FbUdyESpt9Av2s8xHbABvPv3dSz8TVN8ynQCTlVyCDFzPr3InyStnVNpryOolEQERSB0B2gR4o0qr+PwyTtzuDSct4m8iVuesKRX2yppa+8fyGvsSljje2DZU+lLXcx1ZBGInwFCe0z4qs6lIMkI5e6+cmBYqquGs9SOE3TwKSx6LdL9/aJFjzYu9p2ohHQmkRIGbDSXt/GmVjmWtKpRuvzHcXlDWmP2RWSAdF0gndq21U0uj8bZ+f12OyW0ZsnXxnCQiIAKREXgH6ZPP/6TC6EpNYZ23v40qiKwRbS0CIpAQAlxAdUrzwFumobBo8QsHFtoVuCF9ZEmN8Xt86PgyewULL4mOPW/YD/0tAokgQOPDyR+W29JQRvOf75dntw3Ki3qhfubmeicp0Gd4pgyGJ1nXPC37J2Ls0qXNlChw7fGDz5prnvLGjI0Nk4v0R7IRKm2cANJF5uHLLgUuXUZT55EMAothob/x80rUnHKtbvw5+CUKdN+EB8orSkRABHxAoB2sbSsqzfGmadwdfmf/jAyVe8Gt8qY5VTYLi7cHvVdmL0OJiyWteuPj6LUIJJPAu1iMOGNyudEzhNf4n4YXICtrdEW1ucB/N8ICbp9fhYyu7llcvm+u3T00Xy7HyRzUAB4rJQpcN/yY3zE4z3G98BQ3piZOR+mAye1rJFthLN/xndPxDHVOIhBfApjP7CJY3J5BseDa0ITWD4s8T44qRDZXBXLHl7ZaE4HYCLCUB2UBXCiZzyTc4soNWHTZGx4oF8ENejVcKQ+DJe7p0QV2YhfF+MRGX3snmwATlVyBhCWcp4rhPvyvMdHVPOR35S9Lqu22edWOezHPg7VMH0asKEtRSUSgOQIpUeDYqYtRQyYTpB9cP79eX2cLEQcnEQERaJ4AayauhLsklTe6Z/0MrilMRe6jvETNn4S2EIEMIcBkC5QqeH4tx/e2KU8TxgfRdZIFiTfCcvEN1Iq7B1aGK3pnxr1AhlwOaXuajPa5blal/XFRtXOOLA/w34MKbWiUBbpfQmwoY7kpXPQ4GzUT/4CapvHMXOk0rv/SlkDKFLi0JdroxHojU96islaWK8NBIzJ6KQLmJC2aggDwH6CWW0P59cA8229Frd0yIE8TWkMw+lsEfEagpMFdxGIsVDalwLHbh3XMsg8PL7aTkfiBScxY8Hhe6Va7d1i+44rms1NTd0TAIcAs6EzI88Za152fniAvQnnrwjoaLRDoflYBk10hVydDciqsbINCSX8oXJgAAEAASURBVPj+NCLfhuBviQhEQqDBT28ku2nblhL46wEF1uA729LdtJ0IpB0Bupx8AmXtY6QWvwb1oZhSnFY2rj7SZWRPuBt7Mm7PLONDIgIi4G8CBZjgHsM8tw8WK0fs0fxNKAscfwQl7nRY4j6Cd8qDX1Q7GSyfGV1oqufo77HOxN4twKLENyaV2XwsNFDOhKXs0f3zLa+ZHA3MUPnOulqb8HUdMrHW2Vk9s+1OWNg84bzHLJO65j0ieo6UgO6QIiUW4fbNfMcjbE2bi4C/CLAGDgOvK/H8JWo99cfNGdMfe0IF7fAPymwLtLeFiJHxYtr4ufd3IbZn+ZBDOujnyOOmZxEIEoHzGlnQm+s73cTePqTIKQ3yd5QYYIbKMe+V2guwasgS0Rw9fZ4sAv9Dbbezp1Y4dYg5q90KzxDGczYWKnlTsTC5EFblt9bW2RIk6aMC11D+h/fvHNLwHZPytjMOvYqQgO6YIgSmzUUgXQhQ6VqECYfp+ddUbjNmfVyHQjTUvy5BjGrD1fTlSJVMRYzC+DRazxjz0ljewU3Z4XCT8qR+2zbH4ua99p65Cp+PJchvds+26/vlWbomMfLOV88iIAI7E2BM65MjC5AuvY3dgGyzdKkc936ZPQx3Mlo5JCIQbwJcbPwKc9w6KFetMM81zoT6JpSsqRvrbBvmrZe+rLNP4TFCNYxeVIx1ewUK3XhY1N44uGinrnER4rfzqnZ6z3vBBFz0MDlVRbk9JHqOE4Edd1pxalDNiIAI+JfAFvjyf2dKuS2AOwiVsp3XCHf0+6hO2TspcN2RfIC1DD2pD6O88TMm6zm8o7eVQRlsZadDSetb1MY4kdHnn4qh3Ip3MNJfIpDJBK7rl2vDcHP8PfwuMbkJLR6TNtQ7CR20sJPJV0b0574I89D7ULTmo3wTYyxZW421Cpn23xNmfFxzUlvvpfM8fVOd3YxyF42F7v+fbnInvZIwkxfd//k2M63uh8R1dCc+tlOWjWqfZZ1xHIkIJIKAFLhEUG3U5usIfP0YE9JAfLG/00PpYRvh0cs4E6Bl7TWuHmLCOaVrlh2IScSTYmSMm/h1vePy6L3nPdMnvz+uUVrNGnhBOh/z9W9RpJQKGbfj6jmzz/H9jrjLysLrIsxg+0FJayi01D07prDhW/pbBEQgDQmwrus83DhznotU8Tq2c5ZNObLYzkBc3AzcbP9pcbVNgUva0/jt2F1SlDTEqFOKgAAVKxbAPqBR7OVrsJRdjTjr3QmVOVyyO891mM9yMMHVMMc/hPFpLHVF5Yxuv7Tg9cUcx+M21OMu6pVjrN3G+U4iAskisOPOLllHzMDjPPRFDYJYax1LhBS4DLwAknDKVNqeQdbG51fX2vtf1W1X0Iqy8nZS4DAPIW13jlO/Zj9YxXpjMuqS18q6QCOjYrY7+TnS+UtEQAREoDEBWt4HvbXFuSGefESxjYyiXuO+sFpMPLzIfoTMlI+j1haz0x7wTqk9grpYtOJLRIAE6ML//Kpax52RBbW5mFh62h47KWJUshiLzWd6fuyJFYU+eGZZGs53nZA9sj3+bjjl/Xtlrd2OmmxU3vj+jciAfDPi3ZqbF9mnhtkl+VoiAskgIAUuCZRplXgFx1kYymKUhEPqEBlCgMH/dyyoso/X1xsTijQUuohk09G/kfx+8I5MWI0+0ksREAERiJhAQysZC3pHo8DxoLzp/isUtkORgfYK1MiileSMyeWIyc2xu1EzrmGCpIg7qR0CS2B9zTb718oaexELlFTaGgpC2qDs19lBDTxNju2cbVtObdsi5YvGtl8gBvP/Frj13ViY/m+jCuwkFZlviFl/+5CAFLgkDAqLeVOYMIK32LveUjsf6z8RiIjAmYgZeRarhg2FhXJ/hMK4DJpmohCJCIiACCSaAF3HqMQxERKtcbHKuchqOao94+IqnPilh5fUIB17vT2FG+uGyZViPY729zcBJhthghtaZBvLCVCw9ofrJK2zjZOR0LW/JULF8Oyp5U7mSG7Pdp49sNBoDZaIgN8JSIFLwgj1Df0Y0M2N5v+euMmWiECsBE7vluMocLx5ugL+95fhQTcRiQiIgAgkm0AfuGRTgWNK9XgIY48mwaXy+tlV9gBi4uYiIcXY90vtFri2XYfMtS1xbYtHP9RG6ggU4w71NYSfeELlnRmSvw2lLdb6aaxHyuLcTOZFYXjLo6hnWNBS7c/rlJ5FIEUEpMAlAXzfBpYQZv+TApcE6Gl0CHpGPrKk2r6H1NolcO/wxJnEkM74KGS72vGu96meRUAERCB5BBhr9MZaeJrAhTJewmLJ9w3Lt+OR5OSiTyqc2lo3fF6F+Kc6exw321qwihdpf7SzARaxhooZXWZvHZSPrMn1iN3OdbI8xtpTekH9Ae6SN8+pdGqRUl/7HcIKru2bG2vT2l8EkkpAy/VJwN0NAbMMnqXMRsFiiQi0lMAbyGA66t1SJx7kiWU7u5FwBfpoKW8tRantREAEEkigf2ihci4WKUNJ/OJ2tBPhLjfz6BI7Fa7hlI/W19kIJDi5H5Y53pBLgk1gCSy3pyMD6ThYWBuPJzM83jkkPy7KG61tR08os1/MdpU33puxoLyUt2BfP5naeylwSRr5wfCtpsySApck4sE+zFfw/eeEduKH5U6aZJ7NW42Ct4N9huq9CIhAOhHw5rhy5FhnUe54C9O4v3hQoT0GyxtLmDBp00+QsfKID8riEncX7/6qveYJcAx/OqvSBiCD6X+RoITut29i0TIRwgXQ4VD6maWZcjIWA6YfXWyHdpAjWiJ4q83EE5ACl3jGzhEGo4AxZTZqlkhEYHcE/rG8xoa+7U5o3G4Irp2XxxY6j93tp89EQAREIFUE+DvlSSI9Tc5DgpOZuPFm7TjKBBRspjWOWQTpbi4JBgFaUVkm4p6F1Y4rI5XyO+DKeETH+JaMWAar2wkfltmFcMHdjKymTPn/4Ih8+y8WAzqgzptEBIJKQApckkaOhSaZ4chbpUzSYXWYABGg//9xE8vs3GkVxuxbLIbLCe2To4qNLkQSERABEfArAd6Ae/HdnyfY04TH+d+4IqfkAI/LBGE/g1vcge+V2qebtEjq12uE/eJY/QBz3KHjyxyLG1UoFsFefHwJktPkRlwEvqlzpTJ/76JqLIaWwqrnWt0OgbVtOubTHyIRikQEgk5AtuMkjeD58OPmQyIC4Qhswcpgl1c3b19BZjmAV8cVmme5DbeP3hMBERABPxFgCnYmoWhYFy6R/eOcelyXLLsSNePogkfljUocS6n8emCeFcHaIvEPAY4PFym5WElhzbV/jSl0Yrnj2ctJyDB55fRKmxHyeOJ1cPugPCdTs7KXxpO02kolAVngUklfxxaBEAFml/wNbjh4u8FyAAuPK5HypqtDBEQgUARGtWtjvVE2J5mZ2JmI4gUojs9CEeiKvz3Ly+C3Sp3Cz4ECmOadpdpGN0bKOXvl2LITSuKqvK2F58oFcJU85P2y7coba6LOPqbYyWIp5c1Br//ShIAscGkykDqN4BO4fr88O6azW5w0+GejMxABERCB5BFgQWeWVPklygz8BWVXVqDm6reRCOp4/KbeNzzfUSyT1xsdKRwBhpLcMzTfeqLou5dRNNx2kb5XjZw5f4S75O3zqqwUSXQoe+MY96IERTyPE2m/tL0IJJKALHCJpKu2RaAJAgysbpypjda3/THBSURABERABCInwHi4P0FZ+/Dw4u2/pa8jq+EQZDm8eU6VE38VeavaI1oC4cpJsJ5bvJQqqmrPrKixgW9ucUoDUHnLwxR6E4q9fw6rW7yOE+35az8RSCQBKXCJpNuo7feQvvaHn1bYpdMrGn2il5lEYMrGetsPE87BqHnTWInLJA46VxEQgfQjsAqWr/99WWuLE1BKoKW0RsOV8+Mjip0i4IyzooXmt7DODEFCi1fRN0niCUxHvFuHVzYb73sSIe+grM4Y1Eg9e2qFLcWCKOU7PbJtzjEldgsUOBYBl4hAOhOQApfE0WVq5b8urbF/rajdpVhlEruhQ6WQwNuYdI5FIdFazDf015+hjGkpHA0dWgREIN4ERuKm+uSPyu25lTXxbjqi9nj/TmvP3GNL7AcoPcDbeRaMPhV9Y33NRGfKjKizabYxa60difp8jHf75qRyWx9KWhKP0/wYCUpYjPtYJEP5JDR/jt0zyyYeXmRPjy6MS8HvePRTbYhAoglIgUs04QbtDw0V894CMz9d6CSZReD5VbV22qQyx0e/HVaF3zq4yBi3IREBERCBdCEwLOQG/tkWf8xxnVAA/FEU/x5/WJF5c/AbcKtk7TjWBluuuTiul97La2qhIJcZ73Moz4wpsD3jUG+NytopUL7HIUGJZ9UbUNzGSWAzAWN7UHuldIjrQKox3xOQApfEIRqIHxtP5pWqVo3HIhOeaXk9a0q5VWHYmSltAlYLj0TAvUQEREAE0omAV/pkboJrwUXKbBysNNOOLLYHECPXEUods1U+sazGcWe/HCnnpchFSnTX7Z8Ez9OROIYuq8wOypprTCITi0xFyAGtpqNh2X0t5P7KBCWPQSlnQffTusXWfix9074ikEoCUuCSSJ+ThrcSNa/UH6uTSTz9jD3UfciOxdhH3jD0KWqNAPsi48qhRAREQATSjUD/0G/b/LJ6C5fEIpXnS7fKS1GmZQHcKm/s79aJq8FUzKyV/RCXzBT0c7W4GtUQ3b2w2uHHMec8996hOyye0TQ44es6OwGWPNb18+IWWR+VCvg8jN95cItVmFs0ZLVPuhCQApfkkfQmN1ngkgw+RYd78Itqu/qzSufoI+Ba9MFhxfLRT9FY6LAiIAKJJ9C/2L2toLeBl1wi8UeN7Aisu8lC34tQb/O6frlWiELPjEumBWkI6sfR4uO56UXWcmZufQ+Ut+tmufPcMISKvA/ljUpcpEKnS1rZDhtfZocjhu7NtW4ClJ5Q3JhddAHGiwp4TuRNR9oVbS8Cviegr0GSh2hAaHKbtVkWuCSjT8nhhpS0cW4OqLy9iZi3zrDCSkRABEQgXQk09C7wuzWLXjF3DM63JceXOKnn2yNWi0oELT5MlDEcWSsfXlJj5aF4rnQds1jOqwxsHsBCJWUksn++C+WNYQKRCK2gVJ6HgTfj3CaudxU3FoV/eP8CR3G7DIpbbmTNRtIFbSsCgSOgr0OSh4w38pTPNvvPvSTJKDLicId0yHKSlVB5482BRAREQATSmQDDBLrDYkIJSpZd9pmp55dCkbsPxZ+pOFBmIY7vMpT96fHaFrtyRqUzbzsf6L/tBIpgvXznEDch1xuY51i2oaWyAdkp75hfZb1fd91XvcygtOL9Y1SBk0H0wl45sri1FKi2yygCyqKQ5OH2MnRVICBqAWIEPJfKJHdDh0sigTHtFe+WRNw6lAiIQIoJ8Aac9eBYCyxIQldKlh6gtYeufH+CZeltuPExo+JD+JuPUbAynQ+l4sweOcbC4RJzwgKeHVPYYhS0zN6/qMaeWl5jvBfy5IiOWXZ9vzw7trNuTT0mehaBpgjoW9IUmQS9PxQudcchK9OgktaWpwjcBFFOXbOMm2iH1dzhoZIRqeuJjiwCIiACqSEwHJ4mLOa9AXXAgiitoZed3DXbeSws22qPIMkJXfy+hsWIWRGnbqy0axDbfAq2OXevHCgc2QbdL2OESldBhPcv9EJ9FSUGHgJLKsXelZENY+d3oAxf3SfXPA+ljAGpExWBGAhIgYsBXjS7coXvtXEtX6mK5hjaJzUEWKj9W0ihzHiJv48qtDN6KL1xakZCRxUBEUglgZ/2zbWfh5KDpLIf8Th2XyTjuHNIvt02KN/+u7rWHl1Wbe+sq3NKwjy7stb4YCzdGd1hleuZbSwqnW66XCUUNp4TF50nb6i3se+X2j1D8+3HULqakylQeP8JS9u/Udh9bbWntpmTkfuSfXLt8t45TsmB5trR5yIgAjsTkAK3Mw+9EoGoCKyp2uoEX2/GinMJlPS9QzEUUTWmnURABEQgwATS0bWQmQ+5KMfHSriH/gNKyVPLa52yA19BMWHGYT72Qo2yb3fndjk2Gu6WQRV6NrLg+f2Lq+1dKKytWrWysQgHmIH4fcqv51Y5NdhYk62h0NI2ESUA/gtr20tQeBtnIqWV7XK4qJ4FZTc/Qitew+PobxHIdAJS4DL9CtD5x0yAFjemnWYhWLqDPHdgYaAn7piBqAEREAERSGMCrEf2s/3ynMcniPN7ekWN/WtFra3GQh7nAdZE44PKDQtNn9Il25jQivNDUOTns6vsvkVVRoXMkW3bbDwUMwrdRV8bV7S9JM6S8q32FpS8N6HwvYswAi5kNpROsFCe2TPHzoG76f6hRG4NP9ffIiACkROQAhc5M+0hAtsJcJXyrCkV9mkoWP+h4QV2VCd9rbYD0h8iIAIikMYEDoBCcsAe+XYnyhFMQPr7f8Ol8oVVNbYOVrllUObuW1TtPBg+cSAsWIdCkaMyNwbWOb/GwTNL9h+hvHF+CycsgvTuV7X2Z8SzfQCFrbGVjfswE+k3oLx+Ew+es4xt4UjqPRGInoDuNKNnF/WeG7E6df60CifF8tNjCuyg9hqGqGGmeMerZlY6NYPYjV/2z3Oyk6W4Szq8CIiACKScAK0ytNiUwoTzI2R2THdh4pPDoKjwwVIEE3Duz62qtZfhSkiXS3pqMHaODwqtcYOR1IwWKefRLsuG+iS52eNI2NIGLpP1sLqFk614+8bPq3b6iOczFvcyxyGD5HGwODITabrFAu50wnohAikmIM0hBQPQFitxdDPgDzrTLEuBS8EgxOGQDyA2gGmlKd+De8itA/Pi0KqaEAEREIHgE3gR8U/Xzaq0dki1nwkKXMMRo7XpcKTE5+NPw/ON9c2YoZjzPi1WXMSthRmL8z8fj4Z25n59i9pAsWvtKHcsO0Tlji6biRSqaSz78AWUbj5egdJZQy1tN0LljIW7eY5M/z8OyVtYE04iAiKQHAJS4JLDeaejcKWOq1Mfwd0iKIVOdzoBvUAGsm12F2IcKFxxffSAAlERAREQAREIEfBinais0MWuV6NkF5kEahAsbXxcCUsk9aL5qAE7DdkZpyCj47SNdTYTLovVUOjosjgPNdL4oPXOEyZQKYZyVAJlmEmy+Oy9LsZdnPee98zPqH4xFm0THnz2Hny9xXuNRWTv/abcJb0+NHzOQn+YQfJ+WBolIiACqSEgBS413G0IfsypwDH1vCR4BBi78P6hRXbp9Ep7fGSBcYKViIAIiIAIuASGNqiFOQsKSiYrcA2vCS7gDihu4zzO2cv9hNY4KnWzwWnWlq3GGDQqdbSKUWrwtB416PhIhtASyCM34UHpvH8eEpJIREAEUkdAClyK2A9p697xz8aPNX+S5XiQooGI4bBMF62afjEA1K4iIAJpS6B9TiunvhczM1KBY9FrSXgCXjwcY+LObLBJGSxkG6C0sSD6Rj6HHuuh0Xnv87nhZxugDVaF1oVpiWuHcaAb6x54bo9n77X33B6rj97nfOb7e+D5wk/K7emVdVbXyJUyCxroBXtnO+6TDbqqP0VABJJMQApckoF7h+MPNYVxcIvLtlofFAuViIAIiIAIiEC6EBgCKxwVuM/kaRLVkDKmjI+9ItybFj1a+mhJi1Ye3r8Q2TJr7PZ5VU42TbazL+qbMlkXY74lIiACqSUgBS5F/FnMkj+wXNyiD3yfIv0gpmgoWnzYJ5CZqxAzIgu5SkRABERABHZPYDjmORaD/hTxXpLkEYil3txcxN/RxZNhARf2ynEeTGxCXXAfKHASERABfxDQtzFF48BVtf74kaRM1eSWolFo+WEZk3D59Ao7c0q53TJ35/TJLW9FW4qACIhA5hAYhSyFlMVQAOjqJ/E3AWbKHPxWqZ0xudy+bjBetLxJefP32Kl3mUdAClwKx5wpeCleEegUdkWH3g2BSqTnOg91+5gljHKOgrddEPpfBERABHZDwJvjuMknWqjcDanUf8QEKd+fWuF0hNkxJSIgAv4mIBfKFI7P93rkONkoG05yKeyODt0EgZ/OqnKygvHjFw8qtN5yI2mClN4WAREQgR0EeqJ+GX8vu+S1NtSFlviYwDlQ3r5EvCLj5v42qsA6IJmJRAREwL8EpMClcGyO6ZxlfEj8S+AlFDT9S6hYN4vRnqpMav4dLPVMBETAdwQWHFfiuz6pQzsTeGBxtROryHd/NzjfqW268xZ6JQIi4DcCcqH024ioP74hwNXIiz6pcMo8sAjr7wbn+aZv6ogIiIAIiIAIxEqA9eZ+OqvSaeaoTll2bd/cWJvU/iIgAkkgIAUuCZB1iOARYHbQ702pcAqn5iFU8V9jCiw/lpzMwUOgHouACIiACKQxAZYxouskC4V3zm1lT40qTOOz1amJQHoRkALng/FEjgwnS5cPuqIuhAg8tbzGxn9d57y6a0i+k1ZZcERABERABEQgXQhch/juz1Gjj9FujxxQ4Chx6XJuOg8RSHcCCsBK8Qg/v6rWzoebHjXpDae0dWrDpbhLOjwInIVCpSzvsLJyq126r1xKdFGIgAiIQLQEHllSY2+vq7WjO2Xbxfuo5mm0HOO9X0dY3ai8XdUn107qovqm8ear9kQgkQSkwCWSbgva7pLXyujGQGGtnL5FMoq2AFvCN2ER0z8Nz7faUOmAhB9QBxABERCBNCXw4ura7UkypMD5Z5B/PTDPSVgydk+3pJF/eqaeiIAINEdA2kJzhBL8+dC2bZwVMB6GwcQSfxHI1jfEXwOi3oiACASOwIg9XAVhhuY4343dkUhckqf4bt+NizokAs0R0O1pc4QS/HlxVivrHbK6qaB3gmE30/yCsq2yuDXDSB+LgAiIQKQEhmOhkrIYv7GlIY+TSNvQ9iIgAiIgAjsISIHbwSJlf41s53qyfrzBTZqRso5k8IG31G6z4yaW2bj3S21+qfwmM/hS0KmLgAjEmYBngWOwwCeILZakhsAShGkcOr7MZiNxiUQERCDYBKTA+WD8xrZ3Vyenbqg3LU6mZkB+8lmlLa/YatPh4rNRgW+pGQQdVQREIC0J9IGXCRNmUCZpoTIlY8zSOBcgYdqH6+vs6AllVsn01xIREIHAEpAC54OhO2hP1wJXgR/UGZu0MpbsIXllTa09uazGOez1/fLswPbK7ZPsMdDxREAE0puA97v60XrNcakY6Qe+qLYPQqVxbh+Ur7qmqRgEHVME4khAClwcYUbb1DDEBxQhFo7yEVbHJMkjsBGuk5d8WuEckBlAbx6Ql7yD60giIAIikCEExoYWKidhjpPtJ7mDPq+03n4ys9I56HGds+2CXirlkNwR0NFEIP4EpMDFn2nELTIB1JiQG+U0WeAi5hfLDtfPqrS11e7txN9HFVquvhGx4NS+IiACIhCWwLhQqnoums1RDFZYRol4k7PbpdNd5Y33Gg+gPI5EBEQg+ATkK+aTMaRLQ+5Qs0HFqseSrCF5Y22tPbbUdZ382X55NrKd2CeLvY4jAiKQWQSYrOuUrtl2EBYr2+W4HieZRSA1Z3v/omqbEHKd/MuIAtunUKuUqRkJHVUE4ktAClx8eUbdmpSHqNFFtWMZssVcOcNdlRxU0sZ+JdfJqDhqJxEQARFoCQF6N/znoMKWbKpt4kRgReVWu2lOldPaCV2y7Xy5TsaJrJoRgdQT0FJM6sdAPUgBAWbiWlO1zVpjIfjBEbB+6puQglHQIUVABERABBJF4NJPK42LlYWIsX8I85xEBEQgfQjIApc+Y6kziYAAA7lnH1Ns47+qs4NDwfUR7K5NRUAEREAERMDXBO4Zlm/1M7fZN7tlW898rVL6erDUORGIkIAUuAiBJXLzKpQRmIwip4vLtipLVCJBh9ruVdDaeu2tbFxJQK1DiIAIiMB2AixBxjpkXvbl7R/oj7gS6IfMyq+PK4prm2pMBETAHwS0JOOPcXB68c8VtXbkB2V2+YwKFdn00bioKyIgAiIgAvEhcCGKSXd4ebP9fkF1fBpUKyIgAiKQgQSkwPlo0MeG0izXbjX7ROUE4j4ynyN19XtwmZSIgAiIgAikhkAV5rctiMtSzdPE8N+CMg0SERCB9CcgBc5HY7wfSgjske2mV56yod5HPQt+V6gUnzu1wo6eUGZXhQqaBv+sdAYiIAIiECwCB3o1TxEusFW6RlwHb0PNNhv8dqldACvnulB907geQI2JgAj4hoAUON8MhRlVN6+cgFYn4zsw96IWzozNrlJ8eEeFfsaXrloTAREQgZYRGI16cBRmR/y8VAuVLaPWsq2un11pq1A64B/La2wlniUiIALpS0AKnM/G9rAO7uQ2HoU3tToZn8FZVrHVbpnr1nw7EbVwmJFLIgIiIAIikHwCI/ZoY/ltXE8TZgGWxIfApA119vjSGqexS/bJtf3BWSICIpC+BKTA+Wxsj+zkKnB0hZgZshj5rIuB686P4TJZhYXeYtTC+SPSKktEQAREQARSQyAHdx1evPe7UuDiMgg1MLYxOQyF5QJ+NzgvLu2qEREQAf8SkALns7EZCfcSFt2kTESxaUlsBF5YVWuvrKl1GvnNoDzbt1CXfGxEtbcIiIAIxEbgyJAb+wR4migMLjaW3PsPC6psfqnrMvnYAQUqzxA7UrUgAr4noLtZnw0RdbcxoSDvD6XAxTQ6pYixuPoz13XyALiTXL5vbkztaWcREAEREIHYCRwcChWgp8lcZAeWRE9gcflW++28KqeBM3vmmOfFE32L2lMERCAIBKTA+XCUxu2ZZV3yWlt3PCTRE7gWyhsDuVtDKX5wRIGFwi6ib1B7ioAIiIAIxExgJBbU6EpJmayMyy6IKP6n9fLiTyusGsY3ZrC+Z6hCBKLAqF1EIJAElI7Ph8P28365dssA+bDHMjRMAMNaQ5TLYHnzsnvG0qb2FQEREAERiJ1AHlbT6Oo3sKSNDW2rZBvREn39y1rzEsH8fki+dcp1wy+ibU/7iYAIBIeAFDgfjhUnN0lsBGh1e2Z0oV3dp96GtJUlMzaa2lsEREAE4kvgLLj7SWIjcAKyKr82rtD+uaLWLuolnrHR1N4iECwCUuCCNV7qbYQEvHjCCHfT5iIgAiIgAiLgewLHdc42PiQiIAKZRUCmicwab52tCIiACIiACIiACIiACIhAgAlIgfPp4DGD4q/mVNmB75XaDNWDa/Eo3YZsXF8gK5dEBERABETA3wQYpsxyOU+vcAtQ+7u3/ugda74xOZdEBEQgswlIgfPp+OcjDu6+RdU2dWO9vYFAZUnzBJ5DzTcqvUPe3uJwa34PbSECIiACIpAqAncvrLbDxpfZFTMqLZRzKlVdCcxx75hfZQPfKrU7F1QHps/qqAiIQPwJSIGLP9O4tMh6cEd1ckMU31yngt7NQaXF8ppQzbehyGzGum8SERABERAB/xI4JjTHba7dhnICmueaG6lFZVuNClw55rvZqp/XHC59LgJpTUAKnI+H11PgPsbExjovkqYJ3Ph5la2CWwkTeD6Amm/MQikRAREQARHwL4HhWGjrGEp9/95XUuCaG6nLZrg139qh5ttdKBsgEQERyFwCUuB8PPaHdXAtcFX1Zh8jTkASnsCnm+rtoS9cd5Ire+fa/rK+hQeld0VABETARwS4znZIaJ57XwrcbkfmGcQJvhvyxvnd4Pztiu9ud9KHIiACaUtACpyPh5ZFTrvnu0P0iuLgwo4UC3Zf+mmF1eO5W15r+/VAFUAPC0pvioAIiIAPCRzZ0V2o/AiLlGUKhAs7QhvhYuqFCBzUPssu2kc138KC0psikEEEpMD5fLBPRqFOyitrlMgk3FDR8vYJLHCU+4bnWzGDByUiIAIiIAKBIHBSaI5jmMCba+VpEm7QGCKwtnqbZeOO7cER+aZZLhwlvScCmUVACpzPx/ukru7q5AIELy9RevydRmt11Vb7JSY2yvEoZPrNbipmuhMgvRABERABnxPYq6C1DWvrJp16VZ4mu4zWJMTAP7zEDRG4qk+uDQ2x2mVDvSECIpBRBKTA+Xy4D0d8QE5olN5SNsqdRouZy/oWtbYCZC55AKuSEhEQAREQgeAROK6zu1D5tua4XQbv/kU1xlCBvaHo3txfIQK7ANIbIpChBNxfzQw9+SCcdiFcAn+2X571KWxtJ3eVhanhmA0obmOTjyh2Cp33wuQmEQEREAERCB6BY+FB8delNXYkygpUIKCZi3ISl8DfRhXYqHZtbEBJa+P9gEQEREAESEAKXACug1sGaNWtqWFiuQBlnWyKjt4XAREQAf8TYMblNSe1Neknu44VmVzdN3fXD/SOCIhARhOQApfRw6+TFwEREAEREIHUEuBCnHwoUjsGOroIiECwCOg3M1jjlfG9nbqx3n46q9LKlW46468FARABERCBdCTA2qZ0JZWIgAiIQFMEpMA1RcaH7zNpx1PL3YBmH3Yv4V1iIPdl0yvsnoXVduKH5Qk/ng4gAiIgAiKQfAIsKZCpsqFmG+a3Mhv2dql9jAyUEhEQAREIR0AulOGo+PC9RSgjMPTtLcaJrQeKex8RKn7qw64mrEt3QXGbHqr5dm0/xQQkDLQaFgEREIEUEHhxda3dOb/K9shpZf8bV5SCHqT+kD+fXWlfoebbJizYqq5p6sdDPRABvxKQBc6vI9OoX32QLr9rnjtc/8Ekl2kyc3O93Tyn0jnt01Dv7VRl5My0S0DnKwIikOYE1mGFcgrc5N9FOQEqMJkmr6EO3qPIxkm5GjXfBpW49fEyjYPOVwREoHkCUuCaZ+SbLU4JKS2vrMksBY6ukxd/UmE1sD52zm1lfxlR4JsxUUdEQAREQATiQ4ALc0yUzxDnN9Zm1jxHhfUizHMUKm6/UvZph4X+EwERCE9AClx4Lr589xuwPFGWVmzNKN/4/4Pr5Cch18kHoLx1hBInEQEREAERSC8C9DIZiZpnlGdXZpYCdz2Sc62F62Q27spY+y1PtfDS6+LW2YhAnAlIgYsz0EQ2dyhq5XQLuVH+K0MmtyXlW+3WuVUOVhYy/2ZIiU0kZ7UtAiIgAiKQGgLf6ZHjHPh/sMBtyRA3yve+qtvuOvkTuE4ObyvXydRcfTqqCASHgBS44IyVsVbO6d1dK1ymxMFdMaPSKpFOuRDVTO8flh+g0VJXRUAEREAEIiXwnR6uG2VVvdmriAlLd2FowHnTXNdJepf8eqDmuXQfc52fCMSDgBS4eFBMYhunhyxQy+FGOSkDUgyfv3eOdUBGsl8jHmCvAl2uSbzUdCgREAERSDoBZlke3d61QL2QAQm75pbWI77bTdjy2AEFlqtpLunXnA4oAkEkoJ+KgI3aIXCj7IkJjvJYKFtVwE4hou6egdXYOceW2E/6qmxAROC0sQiIgAgElMC3urtulEzY9TXqoqWzDIO75KyjS+whxHef2MX1sEnn89W5iYAIxIeAFLj4cExaK3SjPBdWqcHIUpUpKYb3hAVOaUuSdonpQCIgAiKQUgLn7JXjJPNgNsrxiA9Ld6Hr5CX7uEprup+rzk8ERCA+BFTIOz4ck9oK0wvfOjAvqcdM5sE4aSPkTSICIiACIpCBBDpBoXn+wEJkpMxySsdkIAKdsgiIgAjsloAscLvF488P0zm7MGP7+r2xxf62zC1m6s8RUK9EQAREQAQSSeAkuBOy7mc6CouVP6k5Lh2HVuckAkkjIAUuaah1oJYQuPjTClsGJe7KmZW2ugrpuSQiIAIiIAIikCYEqpBV+byp5XYBinb/EPOdRAREQASiISAFLhpqPtqnFjoOs1ilgzz0RbW9vc6Nd/jDkLztNe/S4dx0DiIgAiIgAiJwzWdVtqBsqxPX7dW8ExUREAERiJSAFLhIifloe2bo6g13w2MnlBsVuSALJ7TrZrkFuw/eMwsB3co6GeTxVN9FQAREIB4E3sGi3ikfldvzq4JfE+5dnMsjS6sdLExGdlQnpSGIxzWiNkQgEwlIgQvwqHdFOYFVlVsdV8NXAlzwtBrK53cnlzsFu9tlt7KnxxQo62SAr0t1XQREQATiReDmOVX2Gua3+xa5ik+82k12OyyHQLdJlnzrW9Ta7h2qgt3JHgMdTwTSiYAUuACP5gF7tDE+KH9dEtykHz+bVWmfbXbdQB/ev0CukwG+JtV1ERABEYgngSt6u+n1J66vs4Xw1AiqXDG9wlZgwZUZlp8YWWAlWKyUiIAIiEC0BKTARUvOJ/tdFHI1fH1trX26KXixcBO+rrMHEftG+V7PHDu9uwqZ+uTSUjdEQAREIOUEvtkt29qGlJ17FgbTCvfMihp7LuQCelWfXDuwvVwnU35hqQMiEHACUuACPoDnwY++O1wpKfcvDt7kdsf8akNSLutV0NruGy6XkoBfjuq+CIiACMSVQD7q5ly+rxsT/fiyavuqGhNGgIRWt/Omudkm94fHzG8HaZ4L0PCpqyLgWwJS4Hw7NC3rWC5G8JJ9XBeTZ1fW2tqATW7/OajQfgAl9HG4lDD+TSICIiACIiACDQnQapWDua4GHpSPhZKANPzcz3/3xALrtf3yrBC+k8+MKbRs3XX5ebjUNxEIDAH9lARmqJru6MVwo+QqZSVMWX9Y4GZybHprf33CyezRAwrs0A5yKfHXyKg3IiACIuAPAh1R0Ptb3d2FynuRzKSCbhsBktsH5dmso4utd6FuuQI0bOqqCPiagH5NfD08LetcZ0xuF4escI8gmcnG2mBNbi07S20lAiIgAiKQqQR+sV+uk514HbxMHl0avKRdeyNMQCICIiAC8SKgX5R4kUxxO9f0zXUCvX/UO9fJcpXi7jR5eE6+P5tdaSwdIBEBERABERCBlhAYVNLGTkNCE8rcLf6eQJZWbLXSOi2ktmRctY0IiEB0BOS3Fh033+1FP/sVJ5Q4fva+61yoQ1TavvVxuX2EdNCT1tfb+MOKVO/Nr4OlfomACIiAzwjcOjDPuFg5bk//3rpQcTsNhcepvz13YIENKHZL/fgMpbojAiIQcAL+/RUMONhUdJ9B0n6WH8+ocJQ39vF7PbOlvPl5sNQ3ERABEfAZAVrh/Cy0uZ0ztcJmb3FL+swv3SoFzs8Dpr6JQIAJyIUywIMXpK7/34Jq+2sobuFSpITmQyICIiACIiAC6ULgl59X2ctrap3TuWVAnn0j5PKZLuen8xABEfAPASlw/hmLuPbkAxTI/j5WArf6wA3/eRQw/Tni3iiHd8yye4aqDk5cB1uNiYAIiEAGEpgDS9eScn/EwzGxyu/nu1mgT+2abTdCgZOIgAiIQKIISIFLFNkUtjttY70d8UGZPb2iJuXZut77qs7OnVZu1CP7IxbguQMLnXo+KcSjQ4uACIiACAScADMuj3qv1H4QKpKdytN5Y22tXT7dLdY9sl0b+8foAoUIpHJAdGwRyAACUuDScJA5gRzY3g1vvAJxZ6kq7v3ppnr7xqRyq0I4AEsdvDquUMW60/B60ymJgAiIQLIJbMWyIOeWiUiK9VgKywrw+KcjOReTlrBUwH8PKrQC1GWViIAIiEAiCUiBSyTdFLb9yP75lovRZb3TH37qrgwmuzsfb6izMsxq7bJb2VuHFFkv1cFJ9hDoeCIgAiKQlgQu2SfXxrR3k5qwNM2aquS7UlZigv3u5Irti5SvYZGyS55uq9LygtNJiYDPCOiXxmcDEq/uDES2rt8McmPNGFR936LqeDXd4nYuR6KSe4fl20tjC83v2cNafFLaUAREQAREIOUEaON69IACy4MOt6Fmm13wSfJjvvNhaXsCfegED5NXxhU5YQIpB6MOiIAIZAQBKXBpPMxX98m1Izu5rpTXY4VyAhKbJFtYWHysj2v2JJuHjicCIiACIhAfAqyxdntoofLNtXV22zw3iUh8Wm9ZK8d0zrLFx5fY/nv4u8RBy85GW4mACASFgBS4oIxUFP1sjSXKf44qtO4o8l0L7xL66c8rdevTRNFcs7u8j4Qli32SEazZzmoDERABERCBwBO4CguVXrr+W+dW2b9Xumn8E3ViW2p3Te2smLdE0Va7IiACTRGQAtcUmTR5vyNcOxhUXYQi33QzuWqmm84/3qd398JqO/7DMvt/9s4EPqoiXftP9s7K4kRWQQQRRoKCqKCjBtxgxKAIo1fREb3KzOgIjjPDh9+VmdGrXh294q74XXFBR6+OI4gDbhBBBVkdFgkIIpE9ypJ0kk7SSb6nztJ9ej+ddJZOv/Uj9Fnq1PKvOlX1Vr31nsu/cOJIkA4u1vFJeEKgNQk0NgYO2lozfolLCAiB0ARepBqjUtNXb+mNtHqsJhNbwr28uxYnLSnHalp6FicEhIAQaEsCIsC1EP3vS7/XQm4PA79hVO146+xsjOe3adRvLJ0yUqK+N/eHTdXaKl8V+80DbbCZPJZ5krCEgD+BdWvX4pvt3/hflnMhkNAEvv32W+z6dlebM+hEQ1nvca91TxoQOYsWmId2iq06ozIGpj5XoPbZqQnKX9EwWCJN6bz68iv45KOP27ycJQEtS+DgoUPYtavt3+eWzWXHCV3fINVx8iM5CUHgEurpq79YOmU++WZ2aDucuvUvtR/h0wtycFy6mFCOJWcJSwgIASHQHgmUlZWhrrF9tPfKhP9nhTnoQSEuPYZT06p/u35NpWfV7QRuSXiXWi3tI9etUytWrVyJQYMH48KLL2qdCCWWNiFQfvQYfkxRWlqntEn8Eml0BGLYzEUXsfhuewJqX9xjVH2sVB+wicJtZ4d26WdOXPCpUxPe1F67GdyHsO7CXBHeouAoXoWAEBACQiB2BJQQ5y+8VbB/U+b+o3VVfObP3FM37JMKj/A2uXcavr4kF33kkzjR4hT/QkAIxJhAbJdkYpw4Ca5lCajO6b+2ufDX7S7cRmuR1/dJj9gxqQ3i13E2ssHoD0/KTsYLw7NQmC9VqWVLS0IXAkJACAiBaAlMW1+NNUfc+PNgB37ROx1pNqatH+XE5iPsFw/V6B2dUtF8+vRM/NsJ6dFGL/6FgBAQAi1CQEbdLYI1PgJV1rTU6tlBdlKzv3Zpf0oNcniXFPSnYKbu/7Jvus9+gkuphplHgyjqOfWJgJmnOLQPhsdHjiWVQkAICAEhkCgElLGR/91Tq+1Xu4F72NTfHdQWueAnqRiYk6x9dFvZ3OpGY19W942z3iO8KaHtrwUOTTXT6keOhYAQEAJtSUAEuLak38ZxP8kZxWknsXPaXoM3vq+F0qTcys8MqD/TqU8QWDeEq5nIf/KDpafmJWuWLU1/8isEhED8E6h312P9+vU486wz4z8zkoOEJ3AWJyPVvuz/2OLCcuM7qE/sqIH6s7raKzuD3+T2uFmcmKxmN/j7gRkooHVLcUJACMQ/gYaGBriqXcjKzor/zDAHNpQJOkQ+JRMhCAxh5/TyiCzsu6wT5tEU83VUo1SdXi5X2bpzM3itqStpef7srikivFl4yKEQ6CgEUlJTUFVViYkTJmDpx5/YzJYL275chKfuvwc3TZ6KNzY7ted2LnsFN42djBe+LLMZjngTArEncO5xqVh2fg6+KMzVtgooIyT+rrRKN8RlXld76VS/KMKbSUR+hUD8E0hOTsabb76Bp598Ck6n3k9FzlX77d9kBS5y6SWED2U58gaqS6o/cUJACCQugQsKC/H1li249d//HacOGYLpM2ZgzEUXhgbiPoQNa/Yjw7EHy9cUY/8HazCsbCkumzpfe8a57SBuOTs/9PNyRwi0AgE18Xh210w8cVqm9qmbHZUNUJ/ByeB+gO4Oy/JbK6RFohACQqBtCNw4dSqmsW+74Nz/h5v4+8upNyInJyd0Ytpx/5bE75QZ5ihCpz+aO8qscNkhmXFdufsH3Ooain8N3Mv9YtI5RFOHxK8QaG8E7v9iFxa7u+Gz8zuG6oUdvv/1wAP44vPPNa+2BDnXBtw0aCKWa0+MwAsr/4bR+W64Ux2QmUI7xOPPz6i5xdpnBNZOuyD+Ei8ptk3gtl/9WvuMwG+n32H7GfEYfwR+8vx6XH1cNZ6edG78JT6KFFdUVGBi0QTtm3edOnWyJ8i1w/4t5gLck48/ri1PRsGyQ3ptyMxFecEYdF69oEPmTzIlBBKJQM1xJ6CuWz/kfK2LJ4mQdzW3p/YMmHN8SZyIuvOu3+E3t98eIvtOvDK5APeuAcY++SmeurxPCH/xd3nnjp2468474y/hLZziXYedmkXi/seFmcFu4TRI8C1P4ODBg8hIT0fnLl1aPjKJoc0IfF3mRNcMGvfJ6/gTlTU1Nfh2507U1+s2H5Qgd/sdv8XUm28Owb/99W8xnxj97fTpUH/iTAKPmAfyKwSEgBCICwLKmMmUa6/FmtWroQS3iy+5BL+dMR2D+THf0C4HBRcUAlSjHNSva2hvcXin63FdccMvfxmHKZckCwEhIASEgD+B4mXL8M327drlzKws/OKaqzHhyiv9vVnO21//FnMBzpJbORQCQkAICIE4JPCf992LtWvW4JJLL7UhuBkZLFuGyY8Uayclm/cCQ06Jw5wHT3IXrjxMnHRV8JtyVQgIASEgBOKGwGcrVuCDJUugBLcp10/BLdOmoWvXCJOO7bB/S44b4pJQISAEhIAQaHEC7/z97zh44CAW/vN9PPP8cxFW3czk7McDZ96Esb+9HcN5ackHW/i/G8teeQOlbtOP/AoBISAEhIAQaDsC35eWYtYfZ3Lf28349LMVmDlrVmThDe2zf4v5Hri2KxaJWQgIASEgBJpDQKlO7i7djZNOOslWMDsXPYr7i4EBPz6FF497HjseOQdPjS3AnJIRuPKy7/GPqhnYPO8aOGyFJp6EgBAQAkJACLQMAbWn+70FC3HeBefbENqA9t6/yQpczOpJ+/1WRMyyKAEJgQQh4CrbhkWvPIU/3DYVN93zDrQvxrh24pV7bsMvbnsBHdXOrvoOnF3hTVWF6u8+wvK3Kbw578bKRy7hlRxcfG0hf9fiH+uK8MELIrwRhjghIASEgBBoYwLqO3ATrrzClvCmktre+zdZgYtVhXKX4o3nPkBFzRd46MlinPzbFzFnuPdbSMPvfQ//e8OQWMUm4QgBIdCCBPZ/9gb+/m0F1s9+gGbxT8ELnzyOlReOxYtanIV4t2QehsiyErUkXSgrq0Buj3zLKpsL+/dXIJ/XZJN1C1bSNglaTVR+jI8+/hLrv9qDS/70JK4ZkgP10fb7H3oPo/7yjHzzr03KJXaRqsmrjxd/hE+/XIcfu16OJ+6biBw1eXX/f2PR4dPx9NO3QL7qGDvebRWSlLMN8u28f5P+1UYZ2vKS2gfX3H4L4BqBlRTglj95Ey6D+hbSN55vIdkKRzwJASHQ5gR6/Owa3P4zYDMnZJZTR/AWCm8n//ZVlNz1M8osbjhEeNPLiN94y+/hD8OBHgHX2rxIJQGxINCOP2obi+xJGMCRbRvwHTLw4/scx3Dvz5obT7VMXlXh4KMU4PxfeQEXdwSknG0UWTvv32QFzkYZRuel/X0rIrr0i28hIARMAs7NL+D08Q/w9Cos/e4RdJwvm5k5lF8h0AQC7fCjtk3IhTwShsDmF6biCrXBlU5NXr3nmbySeX8NSgf5T8o5fgtS9sDFvOyMb0Uw3GDfQir78hWMO3Ekxo0ciZse/VDfWxPzNEiAQkAIxIJAzolDNauKGHQKghkZ3r95EW6f/Hts0DbJxSJGCUMIxAEBx8koPFNP59gnH8XoHhzUc7baM7R3bsYDk0finLHq7x5sOBIHeZIk+hA4cdQ5xvlVeJ7Cmypbh8NTwto9af98kMXlSdhydqp931Mx4MR+GMd+btHmjrr7Oy6LDiLAxbrc/L8VYQnftfMdjLr6T/jlko+xeNU/MODJabjk0S8tPuRQCAiB9kRg2ePXYL1KUMlX+M5lTZkLHz56G64a/1ssWbPbekOOhUACEAg3UUmT20Mux4oLHscXS1bh6atKMHnYPShNACodKYvhJ6+k/esoZR26nI/gqYsuwt8co/Hwvbfg2Jq/Y8b4y/HhfvkuTHspexHgYloS4b4V4cK7/+cuYPSDuGJQDmPtgVvm3YJDT07HMpmdjGkpSGBCIBYEypY9gFte+Dl+fb36IPU/sfkQf0qX4Y1laijqwCV3PY159xbyWJwQSDACYSYqS997lMZ+TsFfrjtbgzLs+ru5ij0ff35jW4JBiu/shp68UvmS9i++S9eb+lDl7Cp5G6+f8SQW/98bMPGGu/Hhor/woYPYfqDC+7ActSkBEeBigF99K+Km3z+KB6aegxcnPY+n7pqG8wcx4GV/oxnyn+GWZcDxNDy+ZQ11yc8Z4rHWltvnJHo6iC3fiQQXg2KQIIRA8wm4d+LRqbfh0afuwaipL+CZNU/jtonjtXBffuj3GHf+TZx78SpT1tWI7mTzoUsI8UUg3EQlUH5gM9B9PE7uYuSK6pbj2R+W7D0aX9lM4NSGn7zygpH2z8siHo/ClXNqt0vxxkN636fyljNouL6dIB4z2kHTLAJcDArW1rciXD9AzT/m1tR5YnT0GqK9EOVHfXSzPPflQAgIgVYm4C7Hx8v+iWcfmY8Zb67GJbSX7RhciPOZjG/e/zvOm/sprtFW0Fs5XRKdEGhjArYmKlOd2PwFe7rOGUizpjcXOPTRRtnzbWXS3o6jnLxqb8mX9NgkYLOcU7v0QR+lLGY4Z0kxtxOcgnM9MzPmHfltKwK+O1LbKhVxHu+QX72LlVf5fgvplBuexYqLLd9CCkpaF+b2HamKcwKSfCHQQQg4huEfG1aDbzPyuxi2sh1D8Iy6ltYF+TlBX+QOknnJhhAITUCfqNyG5Wfyo+3z1EfboX20fc7sYn60/RZ88Jn6aLsTFftDhVED7/RlKD9yvc0IGJNX31BjyJy8Qq6avHoUyzl5dZNMXrVZ0cQ04iaVcxmeGP8ormQdGGYR6mKaLgksagIyGokaWZAHbH0rIg2q3jszLM9XHMUenp7fr5vlohwKASHQlgQcXawfpdZTEuxaW6ZR4hYCrU3A1kQle7nTxnPP6CK/1KltM2eeClOr0u+unLYHAjJ51R5KoeXT0IRyXnY/jRL99g0svkQ+pNPyBWQ/BlGhtM+qeT4dJ2JUd2D9Ie8+AOeeLVB2EXrmiRzdPLjytBAQAkJACLQoAW2i0n9yQ320Pd/7+QAmoFMe9SVLtuGgx1hdBfaUcP93t84tmjwJvPkE1ESVR/PACE67JpoHzYfbjkKIppw38HuAzzoeweK7dKNErrJSlMmun3ZRmiLAtVox5ODSe6cALzyDzUbl/+K1R/mxuLsxur+hqtVqaZGIhIAQiAWBtAxdnyRNXuFY4JQwOgCBUy6fTqNdf8ebq/RvRjm/fJ1WKbvhj1cXdIDcSRasBKT9s9LoeMfb3vk9Jt+/H9dQdlu2bBmWffgKbjjzIRyWNYd2UdhJjXTtIiUJkQg3lj06Hrc82QM3TdqPF98egnc3P4IholOcEKUvmexIBNxY/cbjeOSlp7CeqwvnT7odv7rrNpzVQyS5jlTKkpemETiy4QWceeUDuPKWq/CPF/j9KBoEuv1sWgQS10EISPvXQQoyZDZcJW9gyNhZAffPv/c9vHjDkIDrcqH1CYgA1/rM4Szbj8PV/LRAnx6eTwq0QTIkSiEgBISAEBACLULA7SzDPnZ0mV17ivGfFiEsgQoBIZDIBESAS+TSl7wLASEgBISAEBACQkAICAEhEFcEZA9cXBWXJFYICAEhIASEgBAQAkJACAiBRCYgAlwil77kXQgIASEgBISAEBACQkAICIG4IiACXFwVlyRWCAgBISAEhIAQEAJCQAgIgUQmIAJcIpe+5F0ICAEhIASEgBAQAkJACAiBuCIgAlxcFZckVggIASEgBISAEBACQkAICIFEJiACXCKXvuRdCAgBISAEhIAQEAJCQAgIgbgiIAJcXBWXJFYICAEhIASEgBAQAkJACAiBRCYgAlwil77kXQgIASFCC+Q8AABAAElEQVQgBISAEBACQkAICIG4IiACXFwVlyRWCAgBISAEhIAQEAJCQAgIgUQmIAJcIpe+5F0ICAEhIASEgBAQAkJACAiBuCIgAlxcFZckVggIASEgBISAEBACQkAICIFEJiACXCKXvuRdCAgBISAEhIAQEAJCQAgIgbgiIAJcXBWXJFYICAEhIASEgBAQAkJACAiBRCYgAlwil77kXQgIASEgBISAEBACQkAICIG4IiACXFwVlyRWCAgBISAEhIAQEAJCQAgIgUQmIAJcIpe+5F0ICAEhIASEgBAQAkJACAiBuCIgAlxcFZckVggIASEgBISAEBACQkAICIFEJiACXCKXvuRdCAgBISAEhIAQEAJCQAgIgbgiIAJcXBWXJFYICAEhIASEgBAQAkJACAiBRCYgAlwil77kXQgIASEgBISAEBACQkAICIG4IiACXFwVlyRWCAgBISAEhIAQEAJCQAgIgUQmIAJcIpe+5F0ICAEhIASEgBAQAkJACAiBuCIgAlxcFZckVggIASEgBISAEBACQkAICIFEJiACXCKXvuRdCAgBISAEhIAQEAJCQAgIgbgiIAJcXBWXJFYICAEhIASEgBAQAkJACAiBRCYgAlwil77kXQgIASEgBISAEBACQkAICIG4IiACXFwVlyRWCAgBISAEhIAQEAJCQAgIgUQmIAJcIpe+5F0ICAEhIASEgBAQAkJACAiBuCIgAlxcFZckVggIASEgBISAEBACQkAICIFEJiACXCKXvuRdCAgBISAEhIAQEAJCQAgIgbgiIAJcXBWXJFYICAEhIASEgBAQAkJACAiBRCYgAlwil77kvXkEXPuxYUMp3FGE4tq/GRt2OqN4QrwKASEgBISAEGhFAn59m+tIKT5/5w2sLnWFTYT0b2HxyE0hEFMCIsDFFKcEligEnCWLMG7QOZj8xBdRCXCH1r6EyRcW4J53NicKKsmnEBACQkAIxAkBa9+2a9lTGHdiPwwZdgF++btZWPFjddhcSP8WFo/cFAIxJZAa09AkMCGQAAScm1/B6eP/BEx6FF89MhGOKPLc5/JHsLLLiRg15XLsdb6DF28YFsXT4lUICAEhIASEQMsQCOjbnKW48/8exG/un69FmBEhWunfIgCS20IghgRkBS6GMCWoBCCwfxkmK+Ft0F1YSeEtpwlZzv/Z7Xj/v36O5bMn4oFl+5sQgjwiBISAEBACQiCGBIL0bak5fXDJ1KtxfhTRSP8WBSzxKgSaQUAEuGbAk0cTjcB+PHrlTfgG3fDMvF8hvxnZP+WaP2PGIODFqVOxrCyaXXTNiFQeFQJCQAgIASEQQCBM3+auC/Ad6YL0b5EIyX0h0HwCIsA1n6GEkCAEdr7zn3j2AHD8pHsxpkcI7WO3E6Ulm7F5wwas/nIDSo+EEs7ycdXvppDcNtzy54UIvzU8QQBLNoWAEBACQqDVCdjq25iqjLRM/n8E29i/bd7Mfm5nWYi0Sv8WAoxcFgIxIyACXMxQSkAdm8B+vPnwP7UsXjX5TAQT33YuewHjBhRgzNjLceuvJ+LaqydizLCT8dSynUHR9Dj/aoxVd95/GB+XhhL0gj4qF4WAEBACQkAIxIBA5L7NjKR0/f/i9hOH47IrJ+KK8ZfjigvPwoCpL2B/kO5L+jeTmvwKgZYhIAJcy3CVUDsYAffOlXiRq2/ACIw5tUtA7tz7F+HSqQ9QvfIUPLP8G3yxahdWvnm35m/O1Ouw7EjAI4DjRJx1prp+EK8s3BTEg1wSAkJACAgBIdByBCL1bdaY/zb7T1jSfQSuvP4qHG/eWPYAzrvlFQR8HEf6N5OQ/AqBFiEgAlyLYJVAOxqB3f/6wpOlYDsCXAe+M+7nonNXfX0u/4xRxubvg9jyXTAJDqgxnlq/bpuoUXoIy4EQEAJCQAi0BoFIfZs1Dccry8ur3sJf73sEX6x5w2vcZNmf8E5JgAgn/ZsVnhwLgRgTEAEuxkAluI5JoPrH3XrGBl2AfkFMT+aceCbGdu+G4ZOuwsnG/SM7vkN4G5M5GHHBCD3c/RUI/4WdjslVciUEhIAQEAJtRyBS32ZN2bXXXeK1vJx/Np5Z9BfP7UUff+M51g+kf/MDIqdCIKYEgm3liWkEEpgQ6BgEDKksNwNqG3eA63I2nlq1Sru888t3cM/0u7BEU7kM8OlzIS3DKw2m+dyREyEgBISAEBACLU0gQt/mE72v/omDe76H8/56Hz/eE+nfvCzkSAjEmoCswMWaqITXsQlU1IRcKSvbvAi3j+yHS6++C7j5VazZ8I5XxaRjU5HcCQEhIASEQDwTCNO3hcyWozfOHhTyrtwQAkKgBQmIANeCcCXoDkig5FPsClT1x5ENL2DU+N9y1e0UPLxoPZ665WfowqW6IF5DQvGd2wzpTW4IASEgBISAEIgtgRB9W/hIUpFheKgI7xHSv0UAJLeFQJQERICLEph4T0wCJ444x5PxQFVHJ9574AH9/qCr8PMhppXKNO9+Ac/T1gMXNn9RrF/okRtcNdPqXY6FgBAQAkJACMSQQPi+LUJErr1YXqL7uezcE/08S//mB0ROhUBMCYgAF1OcElhHJZCal+vJWrCZRNOaJI6W8TOnuiv713oYfRsvBIp9oDLmD4aVkysvPwcOTwxyIASEgBAQAkKg5QlE6tusKdA/5O29Urr8A33/26C7cN0wc+LSvC/9m0lCfoVASxAQAa4lqEqYHY6Ao/8V+M/RKltr8cqiwA9zm2okOPACzhs5GTdNHolRV/8JhwwSc2ZNwoATJ2O1Vaey7Cu8r0l4p+CK0X06HDPJkBAQAkJACLRvApH6NpV6s9ua9+j/w+bSMrjcLmz78CmMufUp3v05Xn/1V/AX3yD9W/sueEld3BMQAS7ui1Ay0DoEHBh/l24yeclLiz2rbHrcOfjFoy9q1ri08wNrsfz7M/DMko/x8CQjdSXbMPy3v8FQr9FJ7PzkbX74Gzj++pk4N6D3M56THyEgBISAEBACLUYgXN/GSB3DcN/cuzC8O3Bo2aO44vyzMGTAYFx266MYfv1fsLTkaZyVH2jQXPq3FiswCVgIaASSGumEhRAQAnYIuLHs/vG45YVtmPmPTbhlmEUa0x53oWw/FShTc5Gfb97Tr7kdXdCji0VJ0rUZtw+6HEs4e/kuO8Ahllt2UiJ+hIAQEAJCQAjEhkCkvk2PxeU8gooKF6rr6pDZtSfycwIFN82n9G+xKRYJRQiEISACXBg4cksIBBLYj0fHnoNnS5ojeDnxxm0F+I/3gf9csgnXDDKFvcDY5IoQEAJCQAgIgZYnEIu+TaVS+reWLyuJQQgAokIptUAIREWgB+56dwn+Df/EFYUPYJu5OcB2GE58eP9FmvA2883VIrzZ5iYehYAQEAJCoOUINLdvUymT/q3lykdCFgK+BGQFzpeHnAkBewTcpXjhlgvw0Na78dWqWyJ8LsAb5OYXxuKK+3PxzCfzcEl/WXnzkpEjISAEhIAQaHMCTezbVLqlf2vz0pMEJBABEeASqLAlq7En4HK54XCE2AcQLDpa73KlOuSTAcHYyDUhIASEgBBoFwSi7ttUqqV/axdlJ4lIDAIiwCVGOUsuhYAQEAJCQAgIASEgBISAEOgABGQPXAcoRMmCEBACQkAICAEhIASEgBAQAolBQAS4xChnyaUQEAJCQAgIASEgBISAEBACHYCACHAdoBAlC0JACAgBISAEhIAQEAJCQAgkBgER4BKjnCWXQkAICAEhIASEgBAQAkJACHQAAiLAdYBClCwIASEgBISAEBACQkAICAEhkBgERIBLjHKWXAoBISAEhIAQEAJCQAgIASHQAQiIANcBClGyIASEgBAQAkJACAgBISAEhEBiEBABLjHKWXIpBISAEBACQkAICAEhIASEQAcgIAJcByhEyYIQEAJCQAgIASEgBISAEBACiUFABLjEKGfJpRAQAkJACAgBISAEhIAQEAIdgIAIcB2gECULQkAICAEhIASEgBAQAkJACCQGARHgEqOcJZdCQAgIASEgBISAEBACQkAIdAACIsB1gEKULAgBISAEhIAQEAJCQAgIASGQGAREgEuMcpZcCgEhIASEgBAQAkJACAgBIdABCIgA1wEKUbIgBISAEBACQkAICAEhIASEQGIQEAEuMcpZcikEhIAQEAJCQAgIASEgBIRAByAgAlwHKETJghAQAkJACAgBISAEhIAQEAKJQUAEuMQoZ8mlEBACQkAICAEhIASEgBAQAh2AgAhwHaAQJQtCQAgIASEgBISAEBACQkAIJAYBEeASo5wll0JACAgBISAEhIAQEAJCQAh0AAIiwHWAQpQsCAEhIASEgBAQAkJACAgBIZAYBESAS4xyllwKASEgBISAEBACQkAICAEh0AEIiADXAQpRsiAEhIAQEAJCQAgIASEgBIRAYhAQAS4xyllyKQSEgBAQAkJACAgBISAEhEAHICACXAcoRMmCEBACQkAICAEhIASEgBAQAolBQAS4xChnyaUQEAJCQAgIASEgBISAEBACHYCACHAdoBAlC0JACAgBISAEhIAQEAJCQAgkBgER4BKjnCWXQkAICAEhIASEgBAQAkJACHQAAiLAdYBClCwIASEgBISAEBACQkAICAEhkBgERIBLjHKWXAoBISAEhIAQEAJCQAgIASHQAQiIAGejEF01jXCG+XMzDNdhF+5cfAxDF5XjpT31NkIVL1ERaPAtA8Xc6txu733rdTlm3ayux86yOmziX0mZG/uqG+MaS8mOKkxYcBRJ76i/Y3jpYJzlp6Eezy8tx/X8m/CRE5v8K3Ncl04UiY9LDiy7Ym/ZlbTzskvIfqmF6lU8sCzd48Lb22pwxMZr6C6vxdubq7HisP32M9JYSBsntfN3wgaaIF4asfNgHUpt9J07tzkxmuPAt8vsc3Wr8Q376bLKeuwrV7/2nw1MbCOWrq3A6MUJ3LcEQumQV1I7ZK5imqlGvPTRMfy6NlSgSVh5WScc3ejCnGrlpxFTv6rBpN5ZyAn1SDxcd7vx/BoXDiUnIcMnvY042pCMm8/MQv9QtaehAZt21+Dd3W6sZYNXXs/GKCUZV56Qjut/moEuTZg2cB6oQu6qOk9KivpkYcGIdM/5xq8qcEZpg3Y+77xOuDE/yXMvUQ+OlLnw17U1eDBYp5ObgYqLM+OujpZsrsDg7dYJEqN+IY7Ku64e/zzagIVGxZylshPqXerIlTceOdSw7A7HT9kVd7R+yc770EL1qr2zdB91oe9qF5CZjsOnRAaVmpWEBdtrMH+7G1uLcjEoUhtUU4tx71ehOELQBT2ysHGUt2+O4D0ubpdsZL+zg+OLlDRUTMgO229WVTWguLYBV9YpISxyv+Q8yLHN50EGmBwzzTs9Gzf2TYma0fYD9UxDMigPJmbfEjWx+Hwg0isbn7mKcaodYd8f/QXNzlC/zZk1iXGimx1cA/653+0ZZPoGl4wiNgyhBLhN6yswtNSfBRuU7dWYvr0OO67IQf9ohbgU34ZwYWk1lg5Ox5hsPWVpljIqt9lw+uYp+rMjZTV4oaQW88vqMWpwDp4f3H5epxUbKnD+Lqug45u/wryUsJ2Qr291Vo+lHAy+udeNudXJ2HoFO/xoyzAw0OiuNNThMR/hLQlFHCdk+NWN6AJtA9+sq3mWaDvWUMeSsUiH8cghztLc3H6pPbdxIatXs8oodDvXXJYh0xuTG414dz2FNwoMi8/NQhc7Yaam4b+HpWL+Bjfu/7oOrw5NC/8U29kxmcnorXVz7I/dDZivJgcpaEzJ5aPsbsq5+nb9Se2nHwyfoSjumn1di/Y1ybi3TypOSGnEyr11mEshcOq6CnzfkIt7+rFSR+HMMWvC9i1RsIpnrx3wTWvZ4ijMTMHpmd44fuBqVGe+W4OG52DB1y6U1Cdj3OD4W9nw5kg/ch0JJbyp+40I1zD0O4EdQak+o1TABm+TWoHzODce3sbVvWYLO424kCuEdYWONlu8OLinBjPL9FW/fi5rHj2ZbZODfTucAcLblK5pGPeTZFS4uIJQ6saFvaJ99Rvw+I46Q6BvhHcttHWzWOWJLgnLx3XCeZZ30XNLDuKTQHRjlLbJIzUS4smd18x+qb22cS1XBqHbueaybLk0M+TKGtx7lL+dM3CRdXYoQqT5/TIxi5N9D+5w4c9D0sJPrFLgu2ecV8hzl1Vh/opaFPXJxKvDvNcjRBmXtwcNycOh3vVIzYl24jOK7Gam4g8jsuDgIzcOA6asLcf51CqavaUGd/aLc42uKDCIV/sEoh3F2Q+5g/q8hh3itG6BnbjL6cZ+zkB1QgPWHapHgWfGpBErNldh7vduqK1xeTlpmDUgGct5XkNGx+c7MG1AKkp3VeG5Aw1Q41HzmhKUlm6owudqYo17vM48NRtjuybBSdW4x9Tmi9RkXDE0A9vWV2Iy9a3nnZuHG1Xaquvw0lcuvPyjLlyoGbLbTsvCpJ72R0icXPO4h87Ixe96cfDPlS2lq43kZOT76lV6/KqDnOPS8Rrz+LOTM9AnU83U1WHawkrMNXxtL7cE7vNklCfcdzj/YIae51CPhmXRiCUbKrHGpdLYiHMLsjGmcxLclbX47/W1qOHbcUL3TNyoypL7Kl76shrfcyaumkJ74XHA73d587HrgAsPr6xBJ6M8teRQ3Wrh19V4i+oM2rZICrPjemVg6pAM5BszekcOuvAUVVjUzOm5gwh1TzXu26vCTcLp+en4w5kO9DRn/0Ll0XqdrP+y0boJIRmfjMnV8mV6mzbCPNJ/1b6Jl7fXYmmVLoT2zknF1MEOjOmm1xfX0Rr8lbO7psqfqpdPfVmJ3kzjtaYqbVjOZnyNWLWtGvMoQG7nntI88jiVguUNQzMxKIIg5iqvwS0fV2O+GRR/3/nKiWJHGv4wLEPr9CLlg4XI8q5meTeiU9cMTOrsxq9X1aCc6qTvjclEnSqLbxW7ZEzme7V5YxWeVu8Q39sxA7Nwz+A0lPA9fX6HG1+p9Gel4k9nZ2O4sQps+x0ONcBy12P9d7V4f4+v6vE1Jztw84A0y0RF0zlq+GzG0xrtjKU4cfTHWjyxxYV/aPWQ70p/B+7gKrsa0GjOZrpV/bRTz1RZPlZSB3NR93Q2av7vm/NwDR6jSrz+blANvE8y/mWmpwm/durowrVV+BdnSDKy03BNj0Y8RjXor1TfwXb8+ijbcVd1YL9kt81Re01/EamNi/jeh3vnMrhXx5LX3sBz62qwku8W2DZcc3KmX70ncBttaqhiKTtci4++rcWnRxq09kf5G3hcGm4fmgU2/YjUzvUKwtKMK3K5Ana5m2FG87uzlHuc+cC8ggyfdqKEWxkW8t5O1qcq1qGCHhn4zZB0i/ZFCm4enIIHt9bjY44h+gcZ24RKh8vs/nwmaOm7xo3XN9Vi0KmZ6LS3Cn/+ph4DT8rEPaekImJ6jGe70/9ZqOW7V6u9n1lpSbiSE+NjjT7Jkyb6f5tjnQXGmOKEn6TjztMcev/KPnvh5hoc9ni2HJDFoP6ZGJmnj+XKDtZgHvtAxUm54eynrzvFwoltz7rSGjhVv9HbMo5i/X99Yw0+5Z41xffCgZkYyrrbJMfn1S4cs707b3AGCqlpVMxrKlku7ll8gxpMOd0dvmmoYRq+rkU6xx4+aeMz/m7n7mr8DzP5PeNS48LJLKMif6b+D8l5uyWQ1EjXblPXLhLGPXA0TjJV298GPD6yE+7oGfiCrl97jHuwdJSF3J+1TNufVY8nFldguvFssOyYftdztsXcw2VeUwOR5xZ59989PjKPcSfDGpc1THX/prQanLOiRmvMrffU8YzB2XiMg1A7Ttf5Vm85UMjG7E4KNsd3TsPpfNnNBsZOOMqPkwLAdUurPQLAvcOiVwkIqSeeTp308dnYtaEcQ43BhsnJWVYdgUWqT9lOGZCtqZGoFaxephDEGc06Du5xtBppS5XIrVwK7kmvx31B1NYLelH//+x0Ctmh41YCwvJL83AeBw2hylKPh/+ncz/DeJsqMfTuz+k51tdpQeqrHn4j3l5Rrgn/nvgsB1M46/fqMOZlX6XP/kOvF33/55Dy0Hn11rlGvM69pNdVeJ82j14r7IRrOTERzoVMA8v/8PhMfLKiImI+wD0co4Pt4TAY77K8w8HSUsB+e5P+Slhup3j2j9h+h4934/qFnL3WQknGusvyMJyy+87N5Riw3RwVWaLgYQE75/XnqdXm5nFUodqLJ3TdjFk74661cPDNr3lW0NWB1YUOrc2xl247fMLV+1SWZ462H2jfrkr02mCM6MwE+fx6y87nctCTcHFytt1410LWUUuYZvtmuRTy0Nq+mP2K9VrQB7X3wYFXaYhhehPbOM97H+6duyQVExeF31NV2CMTH43ShRK7bSp86pVRRml1uP7dSp8JIG/euRdsTB7GVPnus7beV/vc0zcF6+NtlisDs8fdflvvTR/TsPQYJh/1rY8h20z2aRXs08w9+i7uwcrkHqwp/dj/RbGSZvY1/vvRg8Wr6t57PeuC9yOW9AR71ptP3zGMi3v+xi11aQKOvtfMGMqmp2LHWG7TqK/FULb3SrAN5h46Kw9/7J2MFcZKV4CfFLYFl+ltgZmuQvbvy9i/K6eM2pxV7AoZvt331OSo9i5WjPOutHnGIeRTzfJyG/2wNQ0qHYFpM8es1vrAyeqVFRi3X+9frH3ZvUNzcA8XEcTFH4Fo5vbjL3ctkOLpa8ppYYjWJheov6O4/ssaqDn7NMusiznBXrKx0ld4S+fKjV+aTL/WPVzmNeXV1GW2PmaNy3rdVV+PeyzCW1F+Gub18s4WzdlaDS442HJ1llm14r01mMCZ8VGfVyDznXK8fjD4INM3YGX8RbcUmGsR3go6p+OXTdiUaw27KD8VU8wLtXV4Zl89svzl0ga3DRZJOO9EL59/HdZH5xutVkSPurGbcR35wTtyL+iehpNCrEBOPp7h+cWtOpcZXa2vWgPOX14FJ8MNVZZm9lBbiwVRWFks5wZqj2MHdHlI4Y0D+a1OH6GnIDcFUyy6sfPVapOK21K3PWGrA3aUPVPscGZnR4HWK7wlYVafdMzKVUJbCs7m5EBEFyoNvP79Vn0F2gwjdD7AVcMgzqjrkcoiUHhTYdXrq+E8iuYdDpIK9CcT5VT6H++XjocsdWYTV93fpYpUszkyfDvxqHSE4hHLdkbFY3UF3GNjdZs4SJq7T6/TdtJth08prcQpjQXdJePxgem41dMMuDGTs/5KCJjpJ7wVKm2CJjr771qIOmqJd/q/XFBKGXactQzNfsV6LWgYWpvDFb8o2riQfQ25hnznqI4acC/dl3Hxfq66q7KKok0NmqfkNFzXVd1hW9yD/WK/NEzxlHkjJnCV1R2qjVHtHPsXKzeTpe1yZczW54OmMcq23hqGU/XrKSnobikzXRPGgd1UNW+c2BnVnAgpUg9xQnWhxfKko3Oqdn1PrflOWENuwrGVI9ktHpmNd4ZzNUvTzImQHuuzuWnYeGkn1NHAyoIeerswZ2sVOJyg4+T4p7rwNmNAFuomMo/096zqU2rd+B339CEjDYsKc7BD+8vF3ouyca9Z5pz4m0LhrWx3paamqOrFc9Q0UpyUcHurFoUbgz9zaeM7sw/k1nHD1eOvpvCWm44dZGxNp+krql9aodxV2YAyWqFcsdmJscYk8iz2BdqkucHGmwYj9FDXLZGX7a7ShTfWkZWXdsbGCZ2x+4w0FNDPbGqaJKwlZAujeDz07S3jMQetnWYO9orZ0Kl9XWpAN59m2YMsKjBV9fjQsIqokljIGfSK8XlYNo5L1jFO8xSukK07Nxvj6uswxwybDdSzvHYjVbxe62xebMDqH+010ruoZhLcNeA6CnJLK4PftV6l1luA6/eTVFALqVkur1MG/kgVTdPN5IBmS51vx3/kQI0tFn176Y2YCmvTsXqaX67HckvnpspxS3kjvv/RK8D9OwfaN17MRrCfNw1qFlI1/mqz8ZF9lrjZMSwY0wmPFeZh96mWWS6qXnxWbubA/KW640Wd0chZOK0DMS4fMnRVXDUNOFId+k95O2CqzapnOWFgDjTMGLy/DXh/pzdPqn6uvzgXr/48B7M8nRTwNK2U5XRj3i7L8grNXEFceRnTyZXP3EOWvIapc27NsIwZexKG98zAAxez06UxlP5ejKaHgF+VhopzLdKlmYZxDhTbzEdAoOzM3jqDK6bnOKD24Pu6FGws6ozDZ1nj5AzwwGyWsxooeH0f8OgSea816SjPgcOX5uKTszMxLJfGAjr51ul9FM6by1FLl414gqW/JdoZazyFPRzYOC4PjZdmWuoa8I99bt2bjXRH5tOAd6nSZbqHzsjGHUOy8F8jvSPfhQfc+I5GBLzqukmYR+2GZRyk7aC6WfTO/rvmH3ZRL6r2sl1ZN8ASL/ue4H2O/9N2zkO1OY3h2zib7WtACsK8c2q1tXo8B8IX+Zb/y7vrmtGmelNw0SjuYxqXg9v7pqKrI5nGIrz34GxAY5h2Lnif1fRyVVoY4dp6S8psHFIlVAk1HMj7tPcUYK4d6tC2MSgT9YdTU8Hhh+Z+sO7ZJgf1XDHHMnY+P6CHYOd/rgBxJWwspV/N8rTd9GhBs/29MJuqrUlITU1B0ahcvKa1udwqQhVAFw2IzVSvMVetHhyarquN0t+/n6m31wt/cHOSIwl9uqaiv/aXAvf+GszWXn1qwIzORk9qM7yvBD26WVyFmmZMLOdwxevpMQ5NuAHVbqkhGeCcVLmcrV2lBsaFtMjNyR09nRYhMeCpSBfqMfSDchz/MQ2QcVuFWjksonG0BzzbcSI9H+q+N5/PjcwB5WnN9embjdna2LAB2zjGERd/BCwjyvhLfJukmI2kmrXQHYU4Wp/0X/zR7lFX/xOL+sk1AzN0lQU2OFdmUp0wjFqlGbqtX4b3LAd8Sh1iPff3eBxXpnqpKXs/t4VCCnpGLvYiqrUdZttGmy2o4P6+9zdVY6phsEOpdn7MDX9jrIMKv3jUjNYlg9Lx+NFG7GLHMEezVgUs5L6K63kvosWrgPC8FzhBhYJh7OR3GCoxFIYm7PLeV0e7DmottX4xDItUdi6TU6gGobzXN2Azv/WyUn/K8/+q/XUY4vkuSzJGdw8vceyiVUqPy0zDJYYA3ad/BqZscRsDw0Zs56Chl8cjG+s+3Hem9cBpGMWOdq5RnIsZ3h971eNqqoN496FZHjQOlUrIVQ7LoJ/C3mHeM1VlfJ7g3gH/+qnViuRU3EDB9EFlMplOF2qBLtbBDq+bYo1dzjm0rlVATX5dnaUBk1epIWgSHjo1C388JegbpKIP67Q0RJUP33JTndmkEHs+ivqxA1dAuNo6hXsx5msp4R6kQXpaC7sxrIpQkxxhkx36JuvxU8srMdvyGvt7zukUA4424vGPVw2UWqKd8caThHtPN5SzszNwWx+aNzcmwDyDUhvpjsjHr77MpJW3meu8qdCOarkX8ZBlQMN3+BpjI2p/7kecwhVfvT74PRfq1C9O1ReEftesL1oyZp2u+/1pD17fYbQrTN9ODirD7UMOlRT/62HbnDCaEnbfexzvG6PPO8d9RV6XhDln6qqyaunvtl4sf20vsC5cRNOmjs3yhmo92vptFYZuNSYDrDeMY+3NtuLndbOdC+Jd2+sVTRtqDaOp3K1heI451tiiTvzSri5t2laJh7nPc74VtbrRGo5GOX6qVXRvZLbTw73Rg32aa467jDa3nMJntdonqVx1LTIXcKBiaFEo1UDNcbJLNaPmdg+1Mt+Xfa9yj5+VrW1fUHui1VhC9UPnK80Zi0vNS8WFPN/EsQ6VcAJcnTEhqbaX+FpjTsHFHB/MNupuwIPhLnByY97AVKTT0Nh/7dIFuPKj9VwBTNXbi3DPhr2nPrWje/jV58fwNA/1ftg7VtinCfTe87DByc12Q8Dv9Wo36Wq3CXn8TLUPrf1U9CIOMM0Bup1hsNpoa8tRvaWLMSnt4N63G89LhcuyH2+lWpEKK8BxkzBVGwYZkU38khaVjEZtPi1UPkGTxbZMHQdLrNZYp+PPA1P4DRsajGHbq6u3qXLRG3b7LKwNbgPmbqlFsYqTq1dT2MDPpxC+6FsXVprCOFlEa0AzSPuvYrDttAEscQcs2PmHwA6vWz5hmFYZ2PS/vJtqtWEGYv5BqHN9TtK8E76u2+bMQfmiYW709VFLa8TMLZU4mpKLByLUJTM10fyGz0cyzjwuTN6MAYFZnzzxqveHrSY/NRVjR5WgTyi8mfWMoRfRvG0eX1hVBz2u2RxtxuOJUD9osXbGE08SaLPD47J9x1O8bjPdkfic4Iki7AEn831cc99hn8AsJ+HrqFeAsBqVUo+HFSws4Tf10CM0hwjAUlQhfOhGM3xvhnvnkpQBRY/LjpDBaMvjyJ5KX+GNBhxmdALm8Jt+LeEilWuoOCNxD/pcRgrOZX31n9xbz33hZxj7wmf0SsfltDx8YBdV2T3qw36hkb+dcvV7KuRpUfdUjwClPEWTnqJOyQFCizJkYro9xnYHdX6rUjW3AB/FMUAV9dk9eaFhr+ncWqJcEfea3mEaIeFLxe6eLgnc2ubrklNwmlqtpBR42Ed7RPdmxp/np/Kr7kaqu3oIQf5PT8E1NNSihM5rB9Zg9Ac0YLLfheWVGZ7PJWlP+bVNEQfxnChZY/YhjONCDhhHWap9FYXhnha2QVIml9opgYhl307T3YbJUgKCtyEJmRC+ECdZbn72PS0xdmOvxA9krwwzw64eWXiAKiPsorvQipKmGmEJJ+DQM9AEsqyrL0rFjB9J68kH6pTlSPVLv3mcWbLjXOwhHVavTPc2sxFgAL2p2qCcZrGR5vw3UYVxMq15KYtGbqprHGIDSC05j+tsqG7oF0KsWnp82zvoT9WnWdtpAtkzmDZm5fh4NCyGnMiM7lWZa8R8rhgqV0B9/duyOXPJWe9NXMkyndq7ZcViXrf+/oQfSPU4Pqu2DOawj3HzIznzPTeS0NPqz3M9xEFGOt67zNMlBfWUyjrnoOnMIq4YmZ357HVOqgrl4Eaz01JPsj64OICx1s8S1SF203O27QcvR5Vwi7agN16jE4mGcx9ukm/s24D1u2lFdSNXtYxyW8lZxqDTx97YQh+lNSMfKtpIhRk65rB3onqHVUg+K/ZJeItqt5O4crtw6VFfAY5em8Uxinh8MthC7Yw3jga8SlXY4aeoilWPxZYZbG3iIop0h+Vzkm+7XMRJpme5D9ZNK7T6GFD98mXd5/1gBdTeFI7/aOAPzkNW1Upv6sMeNaeOhg247W7af+8tnYZKbsh3rgFvf8fy1yZy6rHMr/yb26buoiVg0ylVzfWFNAhEw1RzPIapzLt+v36DZZ+7LViuwfpVn7h9TqgqrwRe1lOzr1Gg39aEN7YlVN+fZBiJKuGeUvgLcBzA7+HjRV1SPZPBPsE39cSLnCFEkR76XrjXDScNaJmT0yoJ+44a/TC1oPqpvmpHLQ2sZeF5w6iI8hPouBd/mWEBm1oELzFMj6NKKRV5yI2Ww7m1pMCqjUHjOy9r4zTu01R7X/3UKM34VTvvpKjoTWcj1tGaeJMceXkmJjgRNbMr9/hxO8d73JM/RmsX9VAXcj++2gNrri4eMrmEipT5PJf5nF/NT+9wm8R5lnFZqEfkenwQYE8lrkUIcNP05fnegfz80iqMXurEtCVec/rWeNOsMyBU+ZtY7MSdHzjxoNVTBMFR7efyugbMWl+N1dQF333MjRXfVOOV/ZxpsfPy8oPJtyw8iqEfVeAJfsbgpQ1OjOZnAOZ4A8eE3npcyxnHTM5izq+ox4RVLk2Hfu1GWnF8nwZemIfnuUH2vmJaiDRU8ixBxOAwBXfyQ6TBXDQscmhK+la/QMZzZXOEUlvyceozAN5r1lUY9WHxaczvEja4fbhJ3qtm68YArqysoKn+24qtvUAKzrJjvMMSfw7VdcP9cVuHtifgPy37A5VQOnV1BZJoUe7ulaxTS8uR9O4xzD2U4lM/51At7Ilt3Ny+ltYcDSFWRa02/GuE2bl4VwAbcOOyCty31oXjfL4nF6bOlbswmgZwnthWh6wuaTjXf8bTks+oDqnyaX3PIuYjqsCj8xyLd1iPsRFb99diFY3MTLBoQWsfLI8pxzDxhMl6NO9WmGACbs3Z4sR9bG/upuXemZZx/5Xdve9cs/mwXb7UYvF04Q5lVrsWO9h+bTlYi6doxv4o9cYH6F8rNtLIvSnvs+7SKNV1qywJC8hBiAtR1VHL5EmI4Frzcqg2riXqwIPsN56goa37PnL6WL8cR62CWLapmyjorOUepvs+s7THZhUL0c4pg1MBLqpyDXg67IVg/WroB5JwYo4aazTimLkSZapVcszQ2zCVrz7n87ynH/aOTVzOehTz6ZOyW3A4GEV6tHzSoMtrFmNiygLpbRy/KHc19zA6aOxI9bHF/EzB8xZ/mgeL/LSe37ibqrT1lUXJS/0tfCZhoNEHT11TBa/JgkYsXG1Yt+SKFXc+BDgzfqXC+cwur6Raxs8AmRbLAx6K8oKmNs1nPuGkkY+r4GdszEUAxn+/oRrq48fnxFs/lPE0wyaUx4f/6r7nhhy0ewLBR7/tPtnxkcAxI2iwZLF331IxlamL/ZLe3Vg1G9Q/HQVcbtN1k9kwHQ70e4xGLMKtVKRyk/9y7h04f6/e0GnxWRW4U+rwB274jaS66CozZpk5qJnOP3+nTF6r1QHVYRzw2wytZto+MuKfzzzMP+z/NPCasWcv8E70V/KZlse3BJq7jooFP1BKmxyY6xksJ+Ei6sSnctO1d/8T08a9MNqMnZHME9TH3DytfiPmMr8Hvq3D2BEOzO1Ti1HmvYo6nL/atxF+bmQW+jAcs7zD5dwrOIXz5b1XMJRWuyorMMEwGazdqW3Ag5bzNQfduMOnfjZi+hazVzDC4ozlbHPmz1TTMarDJtaLTRWNuKwgj3WuNmKdq9iv6nMDijlAw1ZvWtXRmOPM0ZPvdbtnvu9ZmHxwEBEtS1Znn2fM4btvaeoptf8O+4apPe3Hdzatrc32A7CbM62lWhvSDI4240GYbwNF9W755cH/1Lc8GjF7l0nY8Mlv9N1krB5ramJG/WsOn7Hca1Wo1JO0KFScHMjv8qasBw0BjeztwIKutL7rab8aMN0z+PX69Uut94bfke06SnUnXyZ+ARmnduMN/nTkq2YawrVxtvoav/cnfMx8d7dahCrlmRb+fqOpgKfYblPVY2b61bFyJyjVcrM95l7KUZ/7vcFqvzC71xy/98Pbzjm8Knl6kNr/tsvV8ky4Qz3dwfrVcE8BQ9VkI/eav88PfGmrmOy7xqVzJYvt/qglFXjt5FR8WlLj+Rarq847lviK36RV7tweLTgcjCI9Zk5/xYnHf+7gZF9GA2aqj+wqRz3biZyAUcqZZh+r/L2xNRVXdknCAQqjD7Ig3+Ie/vFcpzJVSEEL3fd/Ug4qwWiunIbofknDRDcO51567i2fz0nzvu+V0/ov1UypjfOg0RW+dnYW8vmEvwCv2sA5PWpwIYXKmRQSP9+dihHs32bHUCW3p2qDKZxt4nhsZ4OD3+jLwCxq1zzITmkUP201i2W+UutX9TxZ//e3UqvGJEWLaXuhopa2EeowixOv3Tl+W8M6Mz9L/1RSC5a+NWlyHEMCLTjlEsNUtpugqPbmo6YYImHmeJQD4AU0bTuPA/0CZfyEf8ok7K3mfT4+nCbxNZfJPUJnUIizBslNwItP9a6qHTaEJR/1FUtY6tHzzu6EjXymyBqOcVxIXTg7dhdSOQN9axDdbnA26q2zaKnQo4aQhELL90MKj0ulul0SzmQjWOiXLpWEQu4fW0nVsGstK5NBkhnxku9MYTJuPdt3isw8i4bFCBrZ8DiaPh6mLDUpq11kZrpbT/RV6cinFSfTvLHpx/wdOSIPWyksF5oXjN8Clukn5+Xx22z6q+djWjoIM/XYKJqVj84l0WpXHvaOdGBGCNPnJyj9C1U/x2XjOYu5ej0emtrul4nDtIbpFfZT8BtaawxWr2xxVvU/IBPKiEm2Zrkz4FY0F+zmw0+t2T8Ka1l0N+s/1aRO9eDnPi3j+CdZ3qZTfZBcc7bf4SR2nv6OfPmdN2vboD60OstSNj+qCZxmc7QZD5PX0u2MUkU3ORTSaMFz5tftDTRT+NHhQxeb36uymW47fKie9NGl2XjcwtZTGnzeoe154TtE1bO3DPPl5n1lifM1z7VGHPKb8zD9BfzaraMWJgFhmBdYL5RZ+6idUXet9TyY4QsVrtnmhGvjbL33Ed45ax6KaHnV6vTy934Xy26baq1XZnj5fTOxuI/nRdYuT6F1wiLPJa5eKZmGQEK1c2ZY2q/5nO1y9fuMgPm8T6Am92D9qp9Hv9OeJ6RrbfPsEl0LRjGYcjYN7ih/NHpz3RYlvKXgNaO/3mkOBPi5jKeVYEsLwhdok7J+Ads59cuLUuXXnM91m+kx4ivMp9EkCmoLaUnNFN6m9KKVXpr4N1UHVX1Yx+/aqn6lmKtS0/nBciW8KQuflF39LPZyewTzvJCCuvorNlXCuTVhHvu5h9TnB2jEbDrVMjXhjWOdxer7pP5jFUuexrCPNevUQk7eKuGtgB/6Xsn9/cplsAzsuFTaG9CcJWx1nspPLumfPeBePU2yT8HdVP3VypTC14Oa8JaCT9jPa9cszwfslGHf9HeuQGr5VM/Syu70vRTeOBNUxPIy5Fo9HfJ/3BCQD3m3cFGV7K5FHjcQm4Yf/T9GGvCxR+5PKqN1wjoOJI6nSoNFrIg6pUeoKqKWx1UDkZmRDE3FLopQ1L6QI9qqHx9KTkZ+CGHAxXgqGnjf2BdnRuFkQ1lt7L/L5MxmTnMyYwbaxN/msggXrYsrO+w/NEZdlDlhP89HKpUlKf1+KIZ+j8T0VH1+4DD3OWjfKWM5Bkujm36OsLxVx59L9ZTQdYX1k9+qUS5YmUbirMxZs1rQ0UhOM+u3CsXf2c+H/5MxPG/mO2zWl1xKi+ZgxT91seBoJx7/eIOdRyrzYM+Euubku6LGKpm0ImIaUfL3ayfddvm42UAe0SzaKTPgynBT4KBLq1PKD4X5WLy/7aKO+kONcB6xjWtKX0PhwfpB+41FeRhMnc1DbB/Clb9KqlkHwvVLwbLkYR+mP9OfC9/OhQ07Yhsa7OnAa6H61UCf+pUVXx7TNCF8xxR6PuqYpq5sb/3bk5KNFRjMfd73Dstt/kRaqIT5XA+fHvOj1kXcL72AHxVX5azmSMLXB45T2Ce5mcdQ77BPEkKc6Lx5M2Ld8A3AbB/UmK1nS6qheqI1GHJRsis/Cudfph5vIQ7UeKCCfX1Tx4UhgpXLbUBABLgWhe7Gne84tb1j6gO1p3HmY74yp+9xKdhh8ztYnkfkQAgIASEgBIRAvBPwE+BWXpYHy+f44j13rZ9+Gt6YoH1qJhV7J+ZoBszCJqKyht8d47YNrr4d5jc9vdoWYZ9q0ZseAY7fVV0wQq2jiRMCQiAUAf/FglD+5HoTCLjKaj2GP5QlQ//9Ts+dxQ9A+mqNNCEWeUQICAEhIASEQJwRiGp/XJzlrS2SS3XAN8el4BAtQve0Ez/VP5eMSUVaDle77fhvDT/GVjf/PYytEbXEIQTijYAIcC1YYg7qAC0fDLxDXeWvqsyVtySMooXDm0/NRH8f0/otmBAJWggIASEgBIRAeyLAvXw/5x7wERyFVLupnmrZw9OekhlPaXFw/3ofu+MKbq3oyW9NtieXmpXCfb8p6NtZZrbbU7lIWtonAVGhbJ/lIqkSAkJACAgBISAEhIAQEAJCQAgEEJBpjgAkckEICAEhIASEgBAQAkJACAgBIdA+CYgA1z7LRVIlBISAEBACQkAICAEhIASEgBAIICACXAASuSAEhIAQEAJCQAgIASEgBISAEGifBESAa5/lIqkSAkJACAgBISAEhIAQEAJCQAgEEBABLgCJXBACQkAICAEhIASEgBAQAkJACLRPAiLAtc9ykVQJASEgBISAEBACQkAICAEhIAQCCIgAF4BELggBISAEhIAQEAJCQAgIASEgBNonARHg2me5SKqEgBAQAkJACAgBISAEhIAQEAIBBESAC0AiF4SAEBACQkAICAEhIASEgBAQAu2TgAhw7aZcGrF0bQVGL3Zik7vdJKpZCXGX12DaomO4e2tds8KJ7uFGrNjoxNB3jiKJf0OXVsMZXQAt6ttV6camsnq4WjSWlgncbtpbo9xbIw4vxWDvZiN2HqxDaXWj11urHrV1/K2R2WDcmxNvO2JWU48lW6uxoqyhORlq+rMN9Vj4ZYWnnZy20beNLt3jwtvbanCk6TFYnmzE+h3VDK/WEl6wa5ZH2sHhzm1OjF5UjrfLonzHpWyDlHfTC9RaF+21+7GoW43Yd9SNkrI6/rlRVmNNfztqR6zJivlxI0rLarFqnzsuxysxx9EOAxQBrh0VyvYD9SiubkBlfTtKVDOS4nK6Mbe2EVsqo+wAmxHnegrB5++gkMQwClKATWSZ2ozwYvqouw63fEDhckUF5u5rPSYxyUMUaW+Ncm+NOKzc/N/Nko0VGPB5Jfp+WNUmEwRtHb+VTUse+3NvTlztidmSlRUYt7UGX/vKTc3JXhTPNuL1TyowYW8928kkFPDJ3rneoYD7qAt9V7sw+dtYdURJyKqqw+QtVbhjs5nhYNeiyEIreK2qakBxbQP21UXXVkvZxq5s/euivXa/efGX7avGhHeOoddSJwavqOSfE8e/fxTTjLrbntqRFn0NaurwyxVVGLWqGt+10TxTi+avAwTubbU7QGbiPQsOChzKpes/cfX/voMuPMzGrsS6epiS1Lp5oJDxWKne0jx+Vi42TuiMxosz4WjdVOixuTnDvrESD28zByxtkYiWj7PFyz0Ux1auWwHvptlytnI6PCXazPiDlpsn8PZzEMDdTtJC1ZlmMrMTtR0/7sPVGHeYE0z5DkzraSbKzpOx8eM+WoPrKlRYKVh5aSdsnNgZ9/QzOh804t31Sj8gCYvPzUKX2ESJQUOzcS+jmL+92qNhEuxajKJrs2CkbHX0sSnbIHXRZnvb1PiVwHj8qhosZDYKclMxb2AGHu+hvxv9OxvviPnK2kxLm1XGZkbs4gpkseLQIx2DzDw3M0x5PLYEpFhiyzNBQ2vEwjUuzKRqYF1b1igz7vR03NrbHJC0TZG4j9Rg3I46LK6yxJ+ahnmX5WL3RXm4o2crC7eWZDTpMGjaW77cg3JsUgZi+9CgIXk4NCYXh8dmISe2QdsKrXnxt3y52cpEC3kKVWeaxyx2iV2+pVYLbHZBm0wtYfcefVJpxqlZGJntl6/KGtx7lNc6Z4DNVAxdCm4+VelCNODFb8xZvmDXYhhlGwQlZRvDsm1WXWxa3dq4Q383C3tkYv3FObhxSCbuGJWLxis64Xe99QFGe2lHWrp6f3dQL8vfnRSPSwotTad9hN9utMvaB47gqSjdXc2BeCpuPjkJzyyvwif1KXhodDYGKXo1brz9lQsLyvWVnxN+ko47T3Mg3xQmeP/1TbXoflImzkItHvuqFtupmZKVloQrB2dibLfQgoarsg4f7qzFsh8aUFVPNY60FEw9nZ1uZ//BfyM2cY/B3/bU40eVjOQkDO+Wjl8MTvfMoO5kHv5nZx2+V1oxKcmYfGominzibsQq7sl4c389lMzROy8VVwx0oCDPPy7etDrOdi/82oXPNW0bzpj9qwrreH9Q/0wMMfzlpSfBebQWL26qwRaOHY7LTsUNQzMxKNMaEI8jsfTzbj11ldfije21+Je6WO/Gy5urAcY1joOkfd9UY7UrCVcUZKKPpcbv3FUNakZ4rqvzj10p+OUpKfhwTTXeYplmkdUF/R24tq/lQSNiLc6ttVhpqIgel52CcSc70NfFtJTog6Qff6jB61S9qE1JxTUsj8M/Uqj7gen6qcMnLWUHazCP6WcRaW54rwxcd0q6j3AQbfqMZPr8uKvr8L9MW60jFVOYHjNX+9SelwMNOGtgJkZ6ypz7CclxQ53OLtWadsSw3H1S6D0p3ecKydH0ZbduRa7/Zog2f1nv15XWwNk1A5OMyYKoyqcZdV1LYVPjD/O+muUeiVWo9jDte75PFcm4aUgaVm+uwryD6v1JQu8uafiVtU00ENup8/6lEalNDFdnHP7MjLb5JLbD/Y+58ADfix+48nQC26eb2T6xCfN11Wzrt7jwUXkj22PgZwMcGJdRj8X7GnCaz3vj+5jPWUMd3lR7qnIzMLazeUd/z77me3YR26j+xkuptS873aipT8K4033bLvPJqH65723J1zVY/r3eV83Z68JpNSkYY2mLdpbWaern8woyPG2D83ANXqM65XH5rOt9zf5K7y/+5WpEblfVPprXQ6eo50kOzOD+5Dnf1eK+wala2xbsWugQzDuNKNnNVRKmVbWXqiwKemTgN0Ms7WXUZVuH1zfW4FO25Sq8C1meQ6NdYZGyjUHZmmUMBKuL5l3V7qv3469rXRxPUWWS46nLWGZFPb31sCl1i0MszQ3MTfHUf+0Cx1RmXwn/doQe9LZfjRGTMX8Nx4hOpXabjKlnZGNM1ySofXwvc0J3D1+9gPbQqKv2xoiRx2l22tXIfVU9PtzFxKak4bJuagwYOV6Nk/zXqgSSGulaNca4i6wRT9AQx3R9YsZIfRLWXdYJP612YdxSl7bMrFROVCXXXHoqdozN0Tpi575K5K4yRuXG09afGYOz8djgNF5qxEuLj2FqdTLDzsPwDMa7gPFqgpH1CeC18zrh2nxDsOKA/O4PK/FggL8U7LgiF/2TG6Hp5O/XO21zX5gK8d6hObhngGqWGvH20mOYrGZeLW7K4By8yo42nAuVv3vPysOdaS7kfu4DzhJUCjZyNYrjBM25qLoQiaXl4YDDUOlYTpZbPirHr2uTsJJlNtKIT+VZL1fzeiOeYzn/OkRypwzIxqtDVTnpbtNm7mXbbs42mldBoSgbBVsrMdN7yThKw+GJWXhTi8OMU7+1Ym05zjdUP30eo9C39bIcfaKA6Y0mfT7hWE6Uikga66xSn9Lrh7pp1j2gsFcWlp1tzLhxBnToB1R5ot+tV+Sg+J+Kj572IT8Gr9fRlrslaX6HDXj4nfIQHLORdrDKZt2yU//9og44NfmY7yZg1jcvL/vl09y6rpLX1PjN5/yzqMrtnt5JttqK4O1hLj7je+bbTlpjYV0uMusyYLfOR9cmNoavM0ZbbJZZKBZ6qv3ap8Nsn4rNtt6aL/34oZF5+KMNdUgX1Sczi2tQ1CcLC0aYM9vck/bRMU2tccpAtjMUgEF18DsXVmIOg1d+/06/4VviwDQFXHHXYujCKk1A895LwnK2i+dp7aLZD3jrufLnKqtC5grVMLIdKMrV2qOSzRUYrGYiOUhdeWle4EqeejDAWd6jIvZxWoaCXQt40OdCyHLjqmHFmExNMAzpRwspsGzPYtmqfdPB3OMs2zukbIOhsVwLVo7BrlkeCXsYvC46w7b7wK18f55X74/moo+/ZGM5Bu9QY6VkvMXl6UkWgdAINMq2NxkP9UrCTO439XG56ai4WNfeCF9XAesYMdI4zW67GnkskUpjcNWo7OHAWI41I8Xrkzc5aTUC5jpRq0UYjxHleSd1MIuzrlupOjWcM69PfKp36DMGZKFuYic0snN7NpeCVa0bvzN3p1tn8XLTsJF7Durob0EPHf2crVWgocQgjjNKp2ZgwchcVHOPQiPDX9xLf+Y6rvjpVgwb8FKxIbylpOCT83JRd0VnHL4oG8vP4kwuvZftrsI4Jbzx/spLO2v7wnafkaZtXJ+9kZ25kkG4WfVVJbxRYNh4mR7XVj5//8mRhww5x2fh8KXZeMiYrX7tXKqVXZSL27v7Vq0CrlTsLeqMQ+c5MEXLbT3+w2TE1RxbLINQMi/lDymybAAAQABJREFUdM/CoUIHitSF9DRs5aBiL9NxZkYS9H00SQF7C/Vy9V4399soYfw1cq+7Is/DfD5XONcb8prqREzh7dZ+mTjEAVAdByRbz8jEn09Kw2/G5WHHMKMT4aDiEAXVvZfq+0n801K2u9IQ3pLw3BlU1WBZq0HIrSofXEkc/JkLpphoN33q0VAutXMaHtfGjfX48qgx4VBdi38YdbD4QC32GQ/v26/PxhcaOvDWtMem3EOlUl1PDsvR+mS4umWr/lsDs3tsvNfWtsFe+TS/rmtJbGL84crNLitrnr3tYRK815PwOPc8VbAtOnRuhv5Oshb/Yo1uyi2aOu9bHJHaxAh1xp+ZpW1WdeiQajtDtE9/XaG39QWd07GDbaS1DVdptKsM6TYMYow4ztKpsL2ZeLo+szR/ew3fPwp0y3ThTe2TM4U3Z5lLs+qrWdddVIGF0VpHTE3H6kJjBott5I5xndh252KUZ1KLEwOqiNhXdLdcc+Rn4rVclct6vPIdLehSoNOFN+6TG2MIb1yVeGlFuWb5N4kGIO7bXOtpt9STukvCUE01pRFULglzzbwX/DfnuHS8xn54N9Ov2stqs93n3r6Fh402LZqyNYU3DqoVE/+yDZ6KwKvNKVs1ibZpRxWmcRLk+d1+g/3AqAKvtGTZMrYjXIV9uLgc01a6Qhhtik3ZWjMWrC5a74Pv4la/8dTc7RxPVZq+gqXJvBf8d9BPMzFLu9WAyatopXVxBV7fVedbl/3bEfq3tv0LCvNQN457PrUxUYMmvGntC8c/u89I18ZeqKjFawcD6yrCjREjjNOiaVet6Q0+1knCeUOzKLxxHBch3uAk5WprEPAdZbdGjHEcx5R+WXhgqAODOiezE6vBTNXOZqbjwaHG7GhqCv79TH1WdeEP/qZXOet3IVdnsrkUT39F1KvWO8VGzDP15vzY9B+gqwQ4GmjSlup8J3c3Ov2aRqjxtosd+lRt4M1Z0LG5GJPPZX+WaJe8NJzXWwlfjXjfEJKeG5njmSXt0zcbszX1nQZsozqQx9U3oEwzi56EQb0zfFT8PH78D1KT0IUqR8dr15MxiAOTLhzJdfGR/VLwj/Mz0ZPX8jkgeWiofrOcFr6Ui56l9pjvf1RxyM9LhrZtgw1s7+xk9GQ67A6srIHdylW0aznzlpqcjLFn65vvFUt90MGZwfX6Mp2aGX9+WAbyKSSmEvygvhnoz4FPTmYyemXpK6RFBJGfkYKeLPdA5y2fWVwNnWaoIeVQ6Ht6DNVX1QOHa0HNHh8XPn0+XoOcpGC0MRHwKc0DK7dvb522aVs7odD4hbESu5Yqucpd01ev09qJ+V8Myt0MKtSvPY7h6paXr636HyohUV4PVz4xqesR0hMufoQst+hZWdtDa5KmcELrjgFpyGFblN8tE2+ep9efTftraeTIG080dd4MP1KbaK/OmKGZv3odUmOVLkHaJyfVm2drrwL9jcnS3nG9Dc/GLKscZgYX5vdwhd7mHZ/h2/U6GO88TUhyoxcFIM3ICAWKTylQqtZSrdzlUoicyxXwx/ul4rjaekygwLTQeFfDROl7S6ni0xXkpKBvpmq7ky0rew2gjREKcBTGNV/mf0rA1MvwQVpf1VfjgOc4yaWrgdbj4fcrMJWfRJjRKx2zMhsxmwPp2zwWJ81wtF0APGnEhiM6B3VHV1vzveZ9IshRRhquZT/ch+l3VtfjcGoqxhkTiD9QpdPX2Shb7QGuLl7IsmWYZtkqoyvRuKaWLRrcuJvaNkM31mIu68cb3EveJNciZas0GI6ha3E1Zh5uwFzu0fDI3n6JDFaOwa75PRbiNFRdNL2zvAqzMCjCeCrq+LnX+wFqLr1m7IHZxPp13YZKpC2uBLWZI7oZp+agqCvfqcw0/GG42W8adZAvcp++WZhjaE/VGOXlDdTmGDHoOK1p7WrYvsKbMP0oaLz+nuS8NQn49iKtGXMcxnVhT3NpHqimEKU5rl5ksvFVs6Lqb/inxmibJoiNRQ3dX9c0DPahTfPN3fQL5QGdjv6Iu7IWT3DWK+ldmrT9mGbL1xlNJzsWlRIzDYW9HBbVQP1Z/f9GlBt9wa8+ZwdhpFHNkJrqkvtU3BQwztU6qwZcSFXK0R85sbSp3ycK0vcUcj+XWg00XVfDZHUxv6+ivjNk5gN2WZoBtchvEqacqAuYevDJOEFrh80Bhsk0Cb8/1WygAxPiaesDGmmr3wajfJJw/vG+o4VU7kG8UPPaCBqDsrhI6bN4DXF4cm+9Hs/d79ZmFot3qQhSsNhQEV3AvSXU4cL72mx2Ci7oHkz49Au8CeXuF0LQU0/WQ3AMX7fMsgLC1v+gMTf1Yvjyafm6Hj7+gFx5yi16Vtb20BruhD7edlJdd3AP3BTNQyOONTSlzntDj9QmKp+R6ow3NP2okEJHuPapzlg1K+rDdszn4WQMDN0E+Pg0T344qgsuNRRifF0SruFEoNdRDZ8ChW4FshHvrFP9SjI+UQaQhuXgvZHKbyP+g/uKo3F7D+oFflpXvz0+KhB+v2yL+vVtitQVqFW4eZY9gbM4UDUtaO6jdoKazJyltgOczUnOS3NwL5M3d7sLJV45TQsnVv9t2laJ6xccRS5XSHp97MSvfTpbbyx2y1a1I76W9lJwsZ8WiTfU4EdNK1uGxQnaaq56vsXyL+Spr/AcPK5gV1uibJU2Sjr/Zg3IwAyjXvi+3cFSEoNrYeqiFjrHUwMsYwqVTs94ip8uapZLTsG156lVtFx8om0xYWjcqjJguVcbJnj4yZjYx/vyODiBXKg8ZqbAGOppj+XnhOhPI40Rw47TmtKu2uwrwsarZUn+ayMC1pFqGyUhXqJNxlCL8ZA9hz0jH9zKGRfrtNQodqxVnPqxNnRFnawznXqe1cbbkK6mFlM/qMJ85YENwHMnpuO0rAbMYkdebDx0kDNiyqkNvUEd1VrWmHu60lNwIc3ljbJ0qFUUQntqaUjGHy/PxUlfVmIy1S2LK2g+lrO79w7LtZiXDhqDrYte1Srdu2eAxZlexWhXlCxtRdpkT0ngpHRoR6a6ETn6sxZw6CdC33E3eMLi1jNfx07kNDVg4sDksM93iCKkzzeUoGeO/DTMQA3msJy3cpKAYyBanUvDRSelYAo/6DufK3L3cz/UXF4uyG+6CeFI5R40cVFeDBuH7fofZaRhvYcvn2jbjbBRBb0ZPv6gj6iLUbPybQ+94SaD9pp8Hd+nn5hXmlTnjYdttIlmNNH8+ref/u3THqOdjSbMUH5POI4wuN81w1DDsvr7zrLyUqCERbMd4n449Y6qd5Eai5rL6akEKvYR/NDwPmSgpzWgMMe7jRXAM38SpOs3BmrKhHqA4yrRSo+QlIR/86jXN0KfAErGpJONBjGZBrC4yj97Vz0+PdCIQUEs7uYFyX+wawHp4IX1G8pxhjKwQKdW/C7vlYoDNEB1XRCV0khla/Y9/v5U2NlWeVpdiOCaVLYqTK76PDae7GgE5VWuwpVHiCfU7diXrR7TmFF5GMMxzUt7OVngHfaESgZVqQPHI8GuhQxA3QhXF3m7qFPgBES48VTU8TOOVI67xlAzpqJbNc75vAabaIhtY40DA1X6QjifsQPHVr1D+At2OfIYMSX0OO2ElhxLhInX8/mRYDmSay1NIEgr3tJRdozw+3UjOpqcVRvinzeNPgTJmtO4tnCvG85hFitZvL7PmI1VKiv+rvS7Gk14K6CFr9XU8ddVAevQW5uJ1X33VlYkd9Aa4IE6rmSleSxOesKiasm5HEzNr+ZG9YtzjY3qnru+BxQYJrGhbuRA7u01uiA3m/n7A/d4NUUN0TfwEGdGZ2CXZYhQbF5uwEaqiw43jb/QnLWmLmTzaY83Mh2mCVYN+OxQA4bb2Nzuedb/wBLWuh8bOYNoqQccrL6sDZjYCVCtR822x86l4vIeSZhDYf1vm/V6NourJqmsA/x0HuZzye9lbSoe+Pd+zZVSg6TaxiAgyFPRXVJxUFXZdv2PLvQm+26dut6E5NluKyLVQ74XrMvDrYP26gZ8YiQpjftszfcn2jpvp01sQs5DD0qNeuptZ9mGcz3C+9mIBhyKsi5nZulSWYmatFJ9iOGO7OEHgzWjIPqFTaUu7ByepgtxnMDZw8v9lE6qxZn7oGkMFT0te9YsXvwOG7CZZaNWK4Z1sbQ1Hl9UQVdCC9XGaEBUU4HVb9XjuQ8qtQkd/bwRL25z0/iWnv5yJfHScBc1Oz2uO1f4QCFLX2n0xnVU0zbxFf6DXfMEFHDA/kkT3pLwFvcaTaKFP+VKaGQGQQS4kAKHUW7m+6j6UCf7UG/ZNmIdrfJG45pUttYIuBLXdNcyZRtNeoKVY7Br9sIMVRf1pwPLK/h4qunxe1OZwy0zpoEbcz7cezd2R7bGiCHHaY4mt6u2chAy3hYcH9pKWGJ78u0REptFVLl3cJ+T2qNUvLcKzxt7hTwBBGv3a7lp1eLPWVaN2/brDfbVQUzUH6vS76lO2xSgSja79BU5IyK130PbJ0XVw//DmTvPzDHvc6KbLgknasv1jTifnz+gtWsfp/vRL2kbhtUhB72TNKuYPK7xUwPVvQb9Xx9McJ+YXxxBPftdjJql3/ORTvW0AZ8Y3z9S/tdvqMKDkR4Mej8JA42V2OmrKsF/Ps5aBuqGqcLq48lz4g1rKk0Pew1R8jtdqw2Ld1w5VfvqYu2GnaBGW414ULOOlYyiE3TVj3O0UVgDZmsqtNwvF0GNqDnlHk2ewnMMFVKy7fofKoRYX2/pum43vYHlZr+tiBTH9C3VKPN44p5RfiNSGwBxlfen3C9qvj/R1nk7baInWh40rc5YQ9CPc0xVKLbh91ja2U38VMLMKEd0Du59U232t5aGUlmGvWC1rh7/Fg1RmQZD/oem+5VzHtE/qOsrjCThVEN4sS4U7SurxXqqSfq3Q1pAbreukUF1vb7+q6SaB28dOGbZ6LRkhaGiyL25u8/VY5uz1eUxdmT2T9apnkyHV2jTgtb+a8QWzXBSEjp5PAe75n0i4MhUrWPf1tv83AlXKJ/fYXY8weINCMVzwXwflfr+M1wxNF3Znmpjf7l5JfJvU8o2cqheH21Rtt7YIx0FK8fAa+qTFPcVO/F6REMtweuiJxUsL5/x1EHveOp6z3gqMH7P8yEOyvbVYJXfinupsVdcqTDbmygJEXikyzbGiOHGaU1tVyMlS90PF6+d58VPyxAQAc4GV1MAsHpNzXNgbh8d369WV2j7xp5YW4m7tT1rR/G2aQ3L8pDyN4FWIx9eWcEN6VySV/fYKU40OmJrPP2UxQ+6haVVuHNtNV5fa5pt5kXuB9IWZ5iGl/rpaZhLC1ZptEx235dO3EmT1GnvVWr7y8aOMCwz0upRL+6lu5tqkk/Qz/WLjiKNG5NVR6+siuW+fxTXr6jES9ywe72xj6/guNTAVT2VqCBO78QpKH5YjjuXVuDtYLOh5nPeflLTPG0KSzOoyL9J+Lmh7jN/VxVGL3Xibu7zO8PSWZthWPmb19Sv//Uxw2lcRvNQj1EfHMU0DnAeXkGLVdxj+N/qQy90ypiMckrAv764gn6qQS2oAKfCmqKu1tah73vleIKWQe/m5yQmGPxe456SfOMp/3SYgYW6bt4P9tulu7kviXc5sDaM4KFnz3Qjb7yudPIts+rBwmlOuQcLz/9aMI7mqra/X+3cr27Zqf9Bw/G7aIdxKD/W6y1Z163xWJMf7HqwcrPLKlh41viUhbXjF5TjPraH0/jZjMlGW/jW6bomQVPrvK02kQmJus74JJ4nfnUImRl4dqA+wTFHtbPc8zya+6+GWlbM/IMIda6swI7nzYV7DWuvXGm/jZ/1UH2BMhc+iYaoxg3UpZsH+c25fbzuoMERbaJOT4IRNAenBlePDMmwrltRhTM+r8Az+wJXc1xH6vUJwKwUw+iUEZTlZ2gPFUkD3tc+GApsotGScVpbRKMRNETVp1sGHtJkODf+J0gbagZl7hs0z7VfDroXq46LDPqaI49g13we8juhAZNxWvwNGLWEFgK3VWPa+7rFTuXTVWcKcn7Pmad+ZavexznURlBu5gbVPzspYJTj+NUequaTEX+bUrYRAzU9tKOyNZPk8xusHINcW/pVNWYfdkNZ0lb738M5/7ro71cfT+l9b65ScVQeqLE03hhPKaE8oL75B+JzTkMg66sxiuU/dHE57l7pxDT2xX036LMZMwbTcI6Pf+9JxDbR6zXsUbgxYvhxWhKa2q5aExQsH+HjtT4tx61NwGxGWzveuIrvJyFWQEaOyMM6rlZpK3HcTzSdxh8e1GZvkqlo4+sKuX/hWTYsCw/XYSY/lq3cFBofOTzGuwRNuxUel9PN4TFhP4c6MteV1mNGvwzdNC2tN/5oTLEOH5aHjaemoVA9Sctks6mqOaeCnXdKI9hOcv9cBv5OE/YPqc8baCsudZhOP/PZPxVRR1sLJiVZe34+91NMpcnc+UxeET/auuTsEBlXcfm4JEwakaEPMmipaM7Reuyj2o85kPLfFO+ghUbFrID7AnONcKJh6RO1jZM+/Iab+QmGYqoHPshZ4Ftp4fMTQ/g1g7DyN6+p356aCiNnBA31J2SkYwHNBD9krMTNpTGWmdy/ojqQGmNmXW36f8voSOZTXWqu36yeJ3yGNW+cUT5kN51qqw+qQQ5X3hYXWr73x0u20+cJPMwB911MMNJ/b/90zyovOEC6WrNQCjxE9UlLlQwSWPPLPUigPpdCcbRdt+zUf58Yg5+EYm+t26H8+NefmNZ1y6DebvxqZT7Y+2qrrSCeUO2hTi4Zz1EAKWRdns32cK4aB3PFZwGNApjqbur9aUqdt9smhqoznpI1mNmuQ3zw/7d3PkBSVXe+//ZM90z3/OOPjn8GBEdQITijgIlQLIpoSnkmg2vpbp7i7rJ5T8xuSvTVrpapldrCipbZ2kSsStZQLyG7AUtX1gQSCzWCE9EHoqKZkQwSCEIYXBidGeZf/59+33P/dN/uvt19+x80+DsF07dvn3vO73zOn3t+5/zOObOuauTRIDVYodYbcwCtk4cHr+Nh3+uMBux82xmneIyWC1o4qIE/7va6mRYZm98e00wTl/C8pX8xLB8mTfdirZIxGkYnlTQ3251Wfh1K2ZxBV8ItswI0xZ8ajyldgYsYJnodXP+mPxv3HL9o4Y5NanBqzf4A+j73o50m+qq8bOPRObO0xoDrZOforcKawyFtcEvr9PHdo8wuTXfMsp7PvNe9n9v888tTLB9mu2J3z/Rv/8mNF64zjqJhnPfsC5JfNY8V0EM8ZKzxyydv1RqvbcbmE1v50lzDtlpt+77L2NSplul35vLPW2fh0tcZylun8tnlo9291klGl5Nl2nYS2BKhtSymKnvr5tdhA99fKr/Uu1c5rT+1xFxuwsEHm/JmCd7mkscOcAMz1Tfpptn3k9zka722KzfbtLnqvF6z1BqPOmh7bSKJ30rtXeXsI+bqpxXYrsYF4kXqu0r7LVe81gDk+rQSkIO8S4I7hgF23CNs6N1qm26aCZnOPHiyo7UeW3g22MBoVJs989FUcVJqDTYfsnwGaDJCqwN4uKiXOlUWF0OfoTyoLe2tMpgPBWgSOcxtvN3cct9HUx6v0Zaavw9w7YMyq1TbKDuRzXwu/skOQt8IA/AwfrUdc/yHfC4ys8wnFDu/Kv393LjFQ/maNaXMzld+91T+UHendYULjTZMR8z8Zv415AASIH+t/8HjC0olX36pKdB3SfI9e9z5cMwUUq7yn+m58t0vX1l3JHOWfMufVeLQ3C6en9jG3SaP0wzcw45n8lb1yZIVUuadtomlKDPJ0qZ+i+Khl4Z52HbywdepvtK++4O4kVMDnTyCZpiDN4l1V2k+jRs8O5DWFatDnAXjFufabolDAbS/zpk7zjiE2WlNNC08G5SzByfbeLD41JQGPlPwKfd3vnMK1/fG4PQAa/Pw43U8DP4BLU7KsGMIKwer0MXzMduUcDRzXMWDyddzDWTv8gZ90xW7eymyZP6qv+/CfOdO5s4RmRTSzM+n/xLh+2GA74cwy2xL0m4U6X4z3sk7by0h8aD15TxofYjH07wRP+Td8jtnRk933iZiN+p3lGX2ayll1i4f7e4Zgak+kK/e2RE/ucriAO2k/VSkfHy/Jh1dlCX+RJoyX6njKajD0WVvvzKH4PyXfPuITvpphbSruSR2Em+uMOT30hJItPulDfcLFpqq5JbhGLvUG9ugK3/61tB2ntLvedkwObO75jloOWRQNvreLErgJO66VJTTzmIrMgytwSw2DPtUqPQ7Y2n/vN1dlT/ZmDYwT3J30PSQveRfio6InZxlvVeSfM8uYT4cM4WUq/xneq589x20G+WLXBt0aE7dxtOIrxhWYWVxpOqag/3QCynzTtvEUpQZE786RHtzfxWWc7Za6yhys6fn3hqh8kbH2fJLsrSrZhjxT84K/2trkGbcITxxuBZP5NzJjTM7nP5a3RXB7O2jnBly44Xdutnlhjm1FuWNm3n0jHLtlhtHithcafE1NBGn6ffq3WO48w5D2YoLn34x63Ka6dO0dPWeESpmbMH+xPNJeT6dOt5GU974yE6u8V3PTzVz0mIEYXcvPfRMd3K/7zI9mem+m2U2+yBppict9/POW8uzOS7PRN5aRbIzr1O/2+Wj3T0zrJx9JdMjP3OVRe3MWYt/8zJb/KafbJ8NfBc7fW9nCyev3xz2EZ300wppV3PJ6iTeXGHI76UlIApcaXmmh6bP7he8NXB6gHJHCAgBIVB5BAJaWxeDspo819yBPwaxkrNS2DeGNs7QdBudLTVCb12n6jTd83hES2/rOHxc3+bEtcxswK6xYSw8GMbCt/U1OesYxt/Ed9VVocTwySgPA76tDsbybCdBp/uhKdYLy6pxMsyZqPRf0+9wJnHToii+znVId+0Z037voEnoJsvuzHO5HfuROS5Ma0rMCtrdSw/87LuTb94mUmgcoG5bJM5Q3iaE0034jf6M5Tbs8tHunvUZx9f5lkUj4JLF71jQIjxKH7EIeF/sR8WEssz5HxgMYu2HIUyf6sMqw06/zFFK8EJACAiB00wghh3cAOlXI1X49sI6zDjHhgYDQyE83xPEL7g7q35OlwsLeZ7iX3Ed3Kxci3lKmBOamR/N4JXJWC6T7BJG6ywomuQOKLszmoArE3pxQkAI5CYgfcTcjMSHPQFR4Oy5yF0hIASEgBAQAkJACAgBISAEhEDFEUjYM1ScaCKQEBACQkAICAEhIASEgBAQAkJACFgJiAJnpSHXQkAICAEhIASEgBAQAkJACAiBCiYgClwFZ46IJgSEgBAQAkJACAgBISAEhIAQsBIQBc5KQ66FgBAQAkJACAgBISAEhIAQEAIVTEAUuArOHBFNCAgBISAEhIAQEAJCQAgIASFgJSAKnJWGXAsBISAEhIAQEAJCQAgIASEgBCqYgChwFZw5IpoQEAJCQAgIASEgBISAEBACQsBKQBQ4Kw25FgJCQAgIASEgBISAEBACQkAIVDABUeAqOHNENCEgBISAEBACQkAICAEhIASEgJWAKHBWGlmuA8EY+kaj6BuK4jj/j0SyeM76Uww73hvGjdtG0F1wGFkjOIt//KKyKUe6yxGmKloxHDoRxlF/7CwuZ9lFjwwFserXp/CdnnB2jw5/DYxG0N0XRcCh/9PprdRpdSZ7DDu7RtD+0iBc/N++w48RZw+eJl/nfhm3B1muNsM+tkq8W7F1NRjFKz1+7OwbPyPY+k4EtDZR1VfXS8PoDlrEKLFskaEQNn/EtPZb3zEx7D3ox+aPQxiwRJ3XZYnlzCtuej4nGOabaPFfVgKiwOXEG8PPtg3C9/IpXPDqMC54fRhT+L9x6yDu3TmGQ9aGLGdYuocD/x1Fp38c1AfFpRD4orIpR7rLEeb+rmHMfHsU018bq7BOd0pBKuJrgKMz60Mx7Bu1diAKDDASxv9+lcrKzmGsP16C8AoUI9NjJU1rpkhS7u/lANb1B6nU8n5bNdDNdtCd4udMfv0ilPFMfMvRZmSKq+LuV3BdfWXXMJb1BPH70owp5YU+0OfHBW8HtDYR1S6gpgrn1SaCKLVs7joXthwI4vrOEeyPD3K7UDcWxl37xvDAR4VBKLWcCQK5r84VhrlTKj5OJwFR4BzQNkfOl0x049mZNXiqmb0Ouo19Icx8ZRTHHYRh9eLVH0eN9eYX7Po4R/S+t3PU0kDrAL6obMqR7nKECbPFUC/yAlymfC8gqPI9UmDaEOEoedcovvdxYR2M8iVID9mWfaFpLVRYdpJ/cFSfRVj3lUZ0LZ+I2Fd98BYaXjHPZcqvIst4MSLl+6xtnjoIJNNzZWkzHMhzLnjJxLTYtEX6/VjWz8GOZi9WtZiFs9hQnT//2r6Q5nlFax1iyycg9rV6tBiPl0U2twffn6uGdKL4rkVjndVej7XsO2084M/beqkscjpHiHOBYR7JFa+nicDpbw1OU8JKGY3ZufjGnHqsaq/Dw4sbEb7Zhw4VSTSMzRU4sl7K9Jc+rBi2vhvAIzQrC0sJTMKrvyqTblXUl1lXNeHk0kb031qHhrwlO7fzPTIQxLKDYWwbs4BhZ2TDbY04cnMTHmgpTOm1hFbEZYWwN+t7TQ3um2qMZBWRqmIetc0vBlhcGS9GonyfLTRPC30uX/nOMv9F1dXyMX3TUKDWtJk9kdPJNYKXNVPGanx3bvqQc7lka2714VEmc+PBAA7FrUar8c05SrEbx0//EJ+acwSjXHI6ihznBkNnaRVfp5NAJVmunM50FxRXMKpMoPROmLupFv9wcQBbP1X3dNOo3bRR3xNw4fY2H6ZZyB467MfLg0i7nyrEoSN+/ORQGH9SppXVVbhrDpXEC512cmLIJ/6RwRA20SRjr59xVblww9RadMz0JDrlwQg2fxjAliG99bzk/Bo8dLUXzWYHjGlW8b3waRSqvzq1yY3br/CirSlHJ5Wj3lt/H8DbmvloDL/83Rje5/OzZviwoIkXphsfx27awb9wcpzhU75WL+5utUBV/nLKaAaW4ZPPP9cdwkWX+fAVhPCDD0M4QLnqPC78+Wwfbk1iH8P+I0FsPRoGswhj9Nd2cS3+7qqaJGYqvFnMtwm9Y/jnP0RxBcP+x6nAa4dCeOMzpkWVIU81Vl5ThwUT01nVK64fjeGH5FrH2ZGpkzz4JrmnDbyOR7GDHH+l8aHMvmr8JWW2CzORegdpSHi2v2L+vX80iJHJtbjT6ICr8v16oBp/fWU1XnvXjxdZZupYfm+YwTybbuRZ1nzXOWQt/0ZepbJ97EoPtPo1XIW/vcqDPWS34YSKX2d3f1KZ1ZPUdyKIDQdCWj6qO/Om1OKeKy35aJPywGg4ax4ePR7A8/v1mbfPPwviOZr5hKrd+MbsGvR/TqXuM2DZl7x6u2Ck5TLm14xTATzB5z5jGb+k3o1vtvOeL0UAP+vivgB+MxTTyt2fzfRiWW0U246P4+orVL1JL0dJIWRhf5XhsanGBdUm/JSLW/YxGedRlr+iLLNSZSmizgW4tuV5cv+dijMawb+zfoNxLWPH9PgfnLWdjsqaJfFanD0h7DLMYc+rr8ayy72YHqAsGfLLa1PGVZBOyk2+8llETbnMUVez5GnW8pD1OYsIOdrfo3xXbRtjeb3chR+9OYbt0Wo8dWM9Zqnq7rCMZK3vFlEyXZaj3p8spK5mZarqZoHvSpXw8TBe6OM7o7EWt040SXANKevO78Mu3My+xgyjidXK+qEIglEXll2T3Acxn8znU63ZeulPEezSHhrH811juMzS7pdXNiprs6vxZE8UrzP9My7U27iWy7x4kOtnn/4khMdnuxPv3mwJE4bFM8zGV347YwRcMbozFvtZEbFaA3cKK9nXeHbRBKwyGhI1vf/4lmGsYUd+0+IJuLuZv3Pjg2+FXNh12wQsiNuIx/AM76+O3zfDq8L7tzVhnuYvBs0++1NdWTLXhSg8a9sb8NjMFMXFllvMYfzACG3aG3emLt6rxsHbGzGDClpgMIBlOwLo1OLRX0DaZY0bB29t4Asjhs07TuEuKqVWt2J2A37ORjWbGzk+isbdekfX6m/tV5rw2FRXnLX1N/N6xcx6/Lzdo33NLaP5VObPTLKYTzw4ux4/mK3Hl9HvxFoML/VpLxI7P0um+fDnvX6s1hRWM2T9Uy83Ol+zjEHp62l+q9HFWZw2o0ypjSdWvu7HxuTgtG+PUuYnNJnTy5mdfNpDljTYBJl0ywxjyZQ6vHGdGpE1y12St/gXM8/M5+I/GBdmvucq/3bPL5lGGa71GPUrNWTzuxs9HQ16x5K3dr43hOsNEz7Th/ZJZavnNt3fyIkxNL4dQgfD33KtnsZntrAOp+WLWfdj+N5LQ3gkKUD1xYP+O+rwQkq7YJeWxKPJeR3oZ13sNOtiwpd59RRHPR5O0+7NX/XPTPEp9g95Alpak58wv6XIkrNdMJ+z/8wkx5tsB/f9ZshR26m3sfbhm2XN/LX7I649PJA+Ur+CdaStZzRDftXDY7RRiTLurNw4rQumfNk+M7GCUVeRtR2Nj7KlRZEpXLMextuhtCeBBF/znWb15OL7bAK+5M/17lDPlOZ9p79XrTJYr/Ov94n8S7zDM/HSY9LrR+vn2d9phb4rVRwBmk/6OoOWtkjdjeG535zCPcPMkyv4TuTAFWia/NDWUTzNX1W79V9st7K/iVU42V33B6fQfjile3gxzSgX6jNx5ZYtwHbYx3Z4RSvTOFd/D6u062WU/acO9p8cJLLccmajeK4wzJZG+e3MEcjc0p85mSo25r39EQz4ozjKEfzHuYukUt7Ajt+SZn10SF8/4Epb29akTaKl3zcT2ndkDMuU8lZdjV23TNTWhRyZ70EbPazhqJfT3Sqdxn/giK5AKQUldsdE+G+px5sL6jTlTWkPz/xW7zA+OLMO4Tto897RiH9rZBpDEfwfZZMeDOPnSnlj2rtu4xoW+un5ig/fvTx3a9pwQR36Gd9Txsj+pkU0x7u5Ed++KLUourBhAU1VGfe2KfpvG7kL1V6tP+ZARhNutk/r+p9GD7pumaDFt+ViPb6ne8bADfI013BeDTZx5uPIMvJQzJZ4dRPaQc7KmbtlWcOjsrttQT1eooZ+25xabGFa/HxOsTLTcw9nOM31lXExWabWza2H//aJOLnIiIN5cs9eU+GO4vtvGMrbxBocMfi/2arP1D5Jmbm/jq1zlAbbJy03jTTqZVq/b66bUbPTm1Se3d4UT6OZZ9ny3VH5t2WrdyQSsriwjuskhjV2nFHWxIvgL97V2fUdGTWUNxeend+o5aNSvu9T/jgjNPutAI1d7JwrRx5W4e+WNeGg2clgJ/skFe7eW+owicGl1UtLWto4on2S8vYv9mKFFnUU/xRf9xHFv+zU62Ib8/og81rVB7N8Ku9OjKqysdeiNP4oWXo7WO4yyJKzXbAGZnPdcFEdTpr1psaDnlua0Mu6/+VaVzoj4/nUttNJWVOPKiXcVN7uoznWSSoXYXb4eub78M+XebLml7ZRA8Mwy1U+5capfEbyMn7kqqtO8zQ1AufPZWt/E2xU+I+yXeyhWfU8zgo7KSOO6nuq4DbfzfxR7U6p6n0hdTUr0yLelSrJkbCuQF17ntUSx4U7rtFH8zZys4/jSqF7Q1fe1Do5U3kb6UvsHNn+62FsVTN5ebi2uU3YMlF/QA0kD7ON6/+y3uaqu+WWzcs9B1QbfowbSiWcC+2aGVAMNIpw5IqRUymM3QfHsIoDTD8+YjOCl0OCcjJ0IlupGOZIpvx8hgik9prPkBhnR7TrOWo7edswpr/txxptG/UqHPx6Q3xBb2GpiOFlo8P27IIGsM+vuWnT67FGazzH8TFNp8rhPhsd13YS9NZ7sLhFf0EE+oJ4RLVTvho82W6M4rmr8b+MhnvrZxEEXLrCiug4+jQOLsyiCabVbDSjvG4XJtE86wLNQxVm8cU0iW/iSSm6n1Iu/4YyuRn3rdfV41FNPL3RdiRjRgHsfuBI6k0cla93afF1LGzEpkblL4YNyl5SuVoP7m6nCZyPpmZU4vvdbiwzlNDPAqn5w9FBzlTe2uLBJNawGTNpCsu0eMdjPIJiHJdfZLyMeTSFoR/qcfDvfRxRfaDVAy+fa77QixcW6y/M7k9DmiI/wsEDLX84vnpkaR2mae9xFxbPZcd+sj6b95ODGVbS5ZWGuEiOL+5jnt2t8qyqSsszteBcMdRetBnzPd/yn8zWKtwKDjg8oMyANXa+JHb7I4l4HmVnZNV0PQ8aqGz9cClNf1VA/SF0mXqyNWBe58rDBl8VpnD3NOU6WJiba6vRwvKU3VXjF9f7NLPkSex4PdWuV4KhkD4Tr/JaGyTitOwvmNczmNeqPnQsNOtD9tDjv2ZkH/fBC12WForQbCNLSeocTbWbm6qgWUpTiZ1aX4UW1n0nSqhVUnWdtayxzG3eq9cBNRvx47m1zA9Vt9neTK/VODrPr8LKTXb5UlNj8z1XXXWUpzbhOnwuW/trDVVtbPEE28VZE6vgrIwkeJbqfVfOep9Ia5a66oRpIe9KRt4/rLcFF9Qmd9W8rKMbtHdUBFNe0mfj0FiD33LwRbUiatapkYM/62n5s45LD84LRbF851DGwb1EOpOv+jWdxYWrz6e5Its463u67LKxiVZtRWcfB84tYnEFAl0MHwzobCw/2V4WKifGI/gOLS/au0JYz3x4nmv2C3HlYOhYthIxLCTd8kz5CaR0m8sf4dkcw4opNbiL601+dyyENcOq0x7DH3iA0QytR1JoymLgsXKau//tU/ghr9T22uZaO3V1XFMQcnUGlU9n7hK1iybNyDYe5UzO0QDWcgT12+212myBn0qF5vwh+LZQedHW/enbfWv3x8bh5zbCixjEVr6UbqIp5ZJGNx7jmq6liQVyzgRRvlTa00ohRxgvtd6swhVKj6GyqBrtq6gIaS6bjPTguGM42YPZSe9HF9ou5A022kMW5az7Y+4wyHUzG3O14z43vmQRPzIawo+4acvq/pQXDhmahiF6goCvTk2+4+UauBVcn7dRKUKMN2yMyLY1u9MGDuYomfm2GDL8mGFaPx2nwfqQo2sXVqTk2SWWPFvMl3+Si+e7w/JPVppLYWsNc/m0zOwGWY71eubC9ReYgelPu7l+8yZedpPxoP0UHJzkYfxRo85YZbO7XsL2RJksm25yo/5F77BQWzPysYNa+gzTk/Zp1oekm86/xNknHlnCdYBZZXHSLjA4x3UuEXUBV7nKGuJ5/Q9zEjMGqRE5yy+2AVp9d1Bu9EkRRpNLPkumpwpl+Z5XXbXJU0tQmS9tn8ve/i7mIJbpbuIglekcvTtYx0r9vitZvY/nn5mixGeuuqpm2uPOypQDOcW8Kz8b1N8ZQXKz9gnU9Tc4wLqSJoa64/KGm/QZf9Uveel9NRJVhe3cPGkp+yd/eyHNwneH8E9c49qxOEtCjdC0DyowPL1AC6fVZseqMyqbVc4c14XJyUDZz/DTKurFOdX4IZW4grp5ZWFYItlycJOfK5+ApZtZ+cKeaQn/7FK1qYgLHdx8YMk7XEvTO46H9wVx60KHDaJdArgA+l2zDa6pxk1sKBda+vlj7Di1cFONUrpmzu71evx4hKZlG9nZXEPTxDVHI+jl9sCf68NFWnT3TWZHw2KmsJAvhjEOf3k4Wv/w1xtx2TujuIumn53DEXRydG8tZ4EeM0z5ipPXBQ7OZ3THHMmY8fG0HzomVKXpkGojE6vb+8EQ5h/WM+ZBdry/PsWN/+bmHffYmKV0XOROdGSDIax8dUxfr8aNRp69tAZX143jUb5gO60RaNdVuCz1RUkO51v8nTCUwNYGznRZ7qvLKZOVYhLF52ZnO+X3fNKQ8qiDr9nzLGMATsu/USeS2CYFSnapG25Y2TEefTM3F2fKkh5kP6caV6tnOR3ab6f85pWHKWFn+ao2DrG6uELB2SnVLT6WqvBbPZf4OmGOpgecKsvhEte54sTPUdYseU3jguJcZLyAcpNDPgcSlbeu5hLAqfxVaLdsxOSoXXZa33OJGP+9jPU+HgdngnLUVYvXlMvi3pWXnMdGjIOttRazazOCTywzQm1qkMd8Z3I9HA2FeOxAjaa8Kf8NLT5s8PFd1BemyWVt2uCfGWbS50hU38CE/ZLU/cOUv9MmG7tXdtW4yYZJkvzGl4LkVM9yV9IffI0xcxOUn1OBG7ILPNe9cjAsRLYiGeZKpvx+Zgik9gHPjBRnSazWXSgXc3e5tt4Auj8N4ygbxGnxNIyjiyaP84x1cWrLWx5bktnRFG8RO48b/S68+dVGOB0cyxygs/hb2KD/fLkPTx3341u7uY4rxF32qIzceSGLBE3w1AL+H2ubVGSIiZ3eOxc2IcYX8uZ3dUVuDZ/7R643KfcofKtTGTOInnp7a28EI9wi2ao7HTdGPvX1MEyjpry58OKSJtypmSoC+7nBBGwUOG1W0Yjk6CdUknndNtmLPUu8BpswpmojpKmSjOPdkyw71u3meeD7dsMb36OYqnbGPMidPD8Lc/0cTS0tQXz4id7tPk/ZEKa5PNOQ9nyZbjgs/yMnjPjV6LatG8dbn2dhR9PDuZqSNo736a8tvhkRA6OC9u9aHaVZn5pdSDGjzC8PbYWzv5kpLcb9eF7/N8snV9Ymyuc4TmZ61j6mwu8a8ZS6ztkL5Kztsn/Wcpdlyszrt7hL67wcm7xYnky/tISVs9xosyTpQeR/p0Lrao6EOCsjsZK/70pW77PlX6b6lum+lVUR70pfnd6W71cDKOq9Z7iBY6OYrbZMNlw3LWkOzfPoShwHoY7xfmvKe0Bfbz0ObiKMFgdjzgOcKlXWQEto7ZFoe8wYucqi3LJxIFKlQ5mkW+Mf1KxikgcPElKlXxUkpzUY0+LHes/hdVkYWuPOJVuJGFqjlOvKIWDX06sc6SpZkiYPvqbJF8XvjaEZc0OK7ccS01Z7PxjDk1nT4cKlDWokPobruR0zdwZPchwAduycxh9hpTZH2JUid6+xUPkk73tp6qbWA3VyG/wfH0u8IDQhLLKMmJ1cdozvNHZqRJDmlQ6l1WWlWaAlTIePOpbRaXgI8UgFS1rVLp1/rx0PAfyl2gY/yNkbLTB28M0t2znK+eODpvDJMynWeE+N6eae6mVqKlv7PwroM3JWj8b1/fv86IvfH6dyzEEC9X2iB2qJlFqHoK3XGg7hmcOJ/FG7FT7KGWHllhkHzWtfzD9FpMEMohSf6fleuvK/Ookd10FZ2H2Ja0iuMGYLVr47pga1Dcfzm/YYuzxSQ1brzFJdvnlomoilhpPv9wZOiy1RD7F8PsYRYLPOdvOohEfMWfs8Ak1n7/xhp+2C8xCTfTptu5KfyvTNFc/r1btHwX9JzuRo3syeX4mw8i03Zvh5f+ZRVwvN00Kfy5YWZ2WkdPXdlKVc9d4M3+lnJqbFvCu9bLdUe/9Hy4sywt1gb9ij9zFe5Jm0+nrtKH7yR/19MDJAixgldOL1wC8uzDEGHq1Gxcf7Qth7IhpvW9RjpjtmzPAtTNpAxfyV5tJlli3A2atORndZkjlODPsGdXPSCca0XIT1ZS+XtXBFiK0rRE7bgDLcPN0MM4hhe9sZQ+4K+84wbtwyhM3mhmy2ocnNSiMgCpyDHDE7F8leq40zt2J4lTM4qoH8H5ezh0238fAYbtwxgu9wfdh8Sydb+5F/UsO79Vpjt0F2yqf88hS+Q9PEZ94Zwb2/HoSn02/buJphJT6dxh/Df1IuDyvr96hcfo+mj/pxAC5cyx033E1erJ+mF4v797BS/2YEz7w3iu90DsH1y0Gtggf6aE//8iDu3TmKn30wint/q2tzbee5tXV0CZkyX+nKDJXW14bw0I5hbDZmslLZmCFY7zuR0XzO6adK6/JOrnGj0b86YkFXmmpxh3rpcUOBZdpbbxwLXxnGcx/7seplfdcvFX4gHNcG0qJrVbtC0G09OoaH3vPjufeGEyOnNF9Ne+ewDFzALekfZxlY9WvmjdGgvniNvjgdzJ+fter588gHw7h31xh+9t4It5o2lBBuyvGAsUGHlVkxaUhLVMqNpHgsv9ndt8v30pR/RqzYsVw/zvK6ilv3W9mpeJfO8+k7PXK2efqvhvAMd3j9Do8IWW6UvU3X1YGngaQ5p3nIPTI0pwY/7u0cxqqdftCSybmzdLi07pmvFv92hTKLBZ7mTmgeLqi/ccsgd1e0eHQeujGAkF7nbIOwRKFkKUedS8TrtO1KbzvNMFLLmsrrDu3HKBa+Osi8GGFbN4z2lwbx/WN6fbXLLy5pTnP5lJtUOczAMt03f0/6zKO9satPSWFl+JLpuUxypt5P/a6icVpGSlbfzbSVqd6bwdt+ptQP5ceOabHvSjcH7tRA8dbeEE0f6Wgt8Pc84ke9n9RGM3dysG7ZFbom8yTPilR+vDSv1wb59KZDPUVHxcd4l8THfhjWPTvHMP/tYfzouLGuXPes+e82Ngm5gksM7FxZZWOEH/IMOuUWXay/Q7UvXPe+Tb00yWW6IVZX9wjm7xnD9O1j2qZsmj/Ln0LktDye/fIMMMwuUPKvjhhynd4veqkssz/SwA15xJ09BOxr5tkj/2mRlHscaC51cP5aY73X9hN6QzON55SZW8R3cjeEJzlSdB93INxudLhNYc3wzO9gR+2/uOX4U2qrfja0T/aGsZpK4Ua2tB1ci5U6Yhx/LuXCafwNyrSCG5A8cjiER/pUZ6YKG77SgKXGDpgLrm3C+5xV02biuL5tNQ+vflJbj1NFQy666ios4cdG2tOvPKxv6tHRXItXrkslpDzbORfuvLZWf8lQjqcHozhurD1KY2M83qItnOforWG2kVNGu2gz3FvCtQL/RkVta38Yj/AAbeVWTPGin1vM6y9lbkpwnbHNO3fzuofrHtdzHeCmmXrBOGTsFOY2181ZXpwN3EnSLBNP03blnqNRPNhai7XKnI+7DX5uZq4KiruIvT+fprk0u13DMrBevWm5iHrL4oTZJu9gHrd37jLyZyN3p1zJ9YvKPUjzVbUtvi4z121Y3ntqgMFJGrSAnPyxpDE5nsTDqXmmZLDNdwfl345tIiZ1VYVn2ZFZwvK0huXVll1tDTYsM+oZ/a2mye+TqjPAmbdtS9RZjvrLy+zYM4s15zQPvc0+vGiMcm+kydP6DGvYUsPXY2HHi7tYqjrXxg5To3Fz1lWNPJ6gBivUGhy+YDt5SO86HrC9zvBwvtfpC9eefT6ylLLOmWk2P522XY7LGvN6yzIeV2LMuq7nTnaPcEZBdXyDxmxGzvwyy7jDcqPS4lg+M+G2n07rqn2e2gaZdDPzc07lPz9DU++ojDio70niZv1SunpvF43z+pGBadHvSlq4qAFVHnOymVYim98e47uHZo0Xe/EvhuXLpOlerFVlNRpGJ5U0N9+Rrfw6lLT9vqlgcudXM+/UTrDxRKcqcHw9aeOyNFWclKmNKaNskRB+qMwkeNzIDYaFkBK1ez+Xe/DzKbb15uvNY65PNOtrPE3mRf5ymk/m/DwDDHPKZHpwyDBirtPzefBnBe3UYkYon6ebgBzkXQbiAZoS9tMc0eOpQrNlxy4nUalnh7nluZtbbvtooqC2k8/XOYk/QtvMAcqoOtWTaKJgNobJccUwwM5OhH7caqtkbsVtdepMPGXiqbY2n2S+FKwecl3TfrtvhAGQ0yRyspchVyDZZcz2dPzAZh4UuoVneA1wm0fVn/dlTA/lJY8weUwmM1NRyhaH+VuAZh79fCF6uCsZdd3sjlCP0/TSw5dD5rxhEIof18gp5+MGKSlLHrT76X8KT0N6WAXeyZLv+Zf/xMGuXTx/rm3cGbsAy66md/PIA6d11GkejpjliHndUFihzgE2iodeGuahvTxSgYdg86hB5y4Le+eBFF7ncsXhpO3KFUbq7yrfOA5FHd+FRps2NZ/8KqTcpMrj/LvDulponhb6nKMEOCsj+dd3M/LTV+/NGB19ZmBa1LvSH8SNnHbq5NE+wxyAsq4Hs5eJ5/Hx3LfVoWr03N6IWaoPMRRA++ucueNa7PASw5pDe3icB2MP4WRbEx6eWkBno0yy7e+ipQrXeidtjMZlC6t4WPl6nj/buzz5+KYBnvs4eXcM/cvr7a2A8pbTQpaK0PKtYxjikSRv8ID0dHe6GVokyCKbU4ZHPx7B9H0RPNreiCdmZtSCLZHKZaUQKEv3olISd6bkUDbX8VGuPIVQz3rz6ZDZhO8kfnUmEtcm53BKgchcoSdRaSjKaedCFRmGpoAWGQZnNpRTaU3aDjotcTzHKguPNO+WG151LpjTfGXetDgZCVP88pankGcsCSnFZZZ8L6b8h5Wtn6p7Dth5WXbzUcBVsp3mYQPzJHcnyxlIdRjv5v4qLJ9Ro5/BxE2DnntrhMobHWcOL3FapszosrA3veT+zN4u5H4+sw8nbVfmp+1/UfmWrU3NJ78KKTf2Ujm567CuFpqnhT7nRHSH7XIx9d0Uo9z13ozH0WcGpkW9Kzlj+a+tQS7HCOGJw7V4IudOz5xxmuXG6q4IZm8fxa52N17YrZtdbphTmzRQup9n267080zRQjf6KYdso0H8BZU3Nfv2bUtad3Ltspp9XDe/LnkXTR6WvpbHKTw4pzHz+ztvOR3ltubp9DN0IJtjhjG89Uc1ulWNb15WZD/KgVjipbQEcnbhSxudhCYEKoiAsY6hoO2BKygZX3RRAlo+xnha3rnnDvwxiJW9HGDYN4Y2zsh2G4MNauY805q9c4+CpEgIpBM4l+t9amrn8Yie3tZx+Li+zYlrmdmAXWPDWHgwjIVv6xuerGMYfxPfHVuFEsMno9Xouq0OxrJ3J0Gn+Sm5bJxpfGWpGx6m1TqgOre9AUfmuDCtKXmmMECLh1auB3zgyuxs8pUzkVCXfgacbfBnhmFO2Rwz5LFY17Ns0RKlUB0+IYtcnW4CYkJ5uolLfBVDIDAYxNoPQ5g+1YdVxnq2ihFOBHFIIIYd3EjnVyNV+PbCOsw4x4akAkMhPN8TxC+4VlUfaHBhYbMHf8V1cLPUOkpxQuALSeDcrvelytIIl2QMcEmGr2zm3IVLWsmyFZ4qeVIInD4CosCdPtYSkxAQAkJACAgBISAEhIAQEAJCoCgCyXPRRQUlDwsBISAEhIAQEAJCQAgIASEgBIRAOQmIAldOuhK2EBACQkAICAEhIASEgBAQAkKghAREgSshTAlKCAgBISAEhIAQEAJCQAgIASFQTgKiwJWTroQtBISAEBACQkAICAEhIASEgBAoIQFR4EoIU4ISAkJACAgBISAEhIAQEAJCQAiUk4AocOWkK2ELASEgBISAEBACQkAICAEhIARKSEAUuBLClKCEgBAQAkJACAgBISAEhIAQEALlJCAKXDnpSthCQAgIASEgBISAEBACQkAICIESEhAFroQwJSghIASEgBAQAkJACAgBISAEhEA5CYgCV066+YQdCePx35zCvTv9GMnnOfo9eiyAzR8HMZDncyXxPh7F1neG0f7SIFz8v6ornBRsaWWLYe9BP9MaSkprZCiEzR/5sbM/lhS3fBECQkAICAEhIASEgBAQAucaAVHgKiVHozG8NxzDxlMxJKtA2QWMDAYwfU8Ad/0xmt1jWX6N4bntw1jeG0U3XGhjHFMbE0Wq9LK5UDcWxl37xvDARwlK7joXthwI4vrOEeyPlCWhEqgQEAJCQAgIASEgBISAEKgIAonedkWI8wUWohpoUsnnp8cxhhh+uTdA3y5sW1SHSY6fK43HyGAQ9wyrsKqx65YJ6LpjIh5rZQI0Vx7ZZrXXYy2j2HjAj25TWXN78P25bsYaxXd/n1DsDEHkQwgIASEgBISAEBACQkAInDMERIGroKwcyleW0SDWDvKhibW4WdP+8g2gOP9HjunK0iRhlD4AAAs2SURBVINz6rCgPiWssslWjW/OUcraOH76B1ODA5pbfXiUdzceDODQeIos8lUICAEhIASEgBAQAkJACJwjBFRPWFwOAoHRMF47FMIbn41jjKaO8FRj5TVUWia64k8eOuzH64Fq/PWV1XjtXT9eHBpHXXUVbpjhxd3T0zHvp///OBLB52GG1+DBw7OrcVE8NGcXh46GaboIbGirhRnDSH8Qm2hOeV5zLe6cnpgN293jx+8CMTROVvKY953Fk+aL695e+X0Qb/5J15Se7g3g6mA1ln7Ji2mGIOWUreUyLx7sGsHTn4Tw+Gw3GjQBqdiR4ZM9UbzeF8OMCxN5kya/3BACQkAICAEhIASEgBAQAmcpAbPff5aKfzrEjmH966NYnbTEbBzrd5zCpsUTcHezUhRi+M2+IL4VAu7vscpEf++PYNupevy83TSMjGHrziEsp5IRd8NBrP80/s3hRQwffKqEqkJ7U0JZcUejuP8oBTkaRc+URsxiDu//aAQLD+h+d11RpPKmpKMC9/CBkKY8asIOhrFyMII3rzQVuDLLVlWNq32M2R/BAU7CzTNK8ZTJKm1RvHU8glUXmrw1CeWPEBACQkAICAEhIASEgBA4JwiICWXObHThtjm12LKgEX6u8YrdMQHbpujY7vkwALUCTTlvXC9yYRP9hm9vivvbyJ0T9xrWfscPjxrKmwvr5jYgzDB7F3nRoQej9A/HbiRIr9WcuatNPOJt9mFTo/oexX98EkWgbwyzNeWN6+SWNtHUMYbdH4/i3l+f0naNbN8yhGcOhpEwRkyElfHKXYM9S4xIazw4uGwC+m9pxEKLHIXJBvSdCODxHUOabK6XTmHVO34cTzOJdKG9WeVBDJwcjTvvRLfG8VjIohzHf5ULISAEhIAQEAJCQAgIASFw9hMQBc5BHs6Y6UNHSzW84zEcp2nk5RcZ2lowBn/K8/fNrsfd9OuuqsKt1+kbbiQUjRheM7ZJvO+KejzQ6tZMH1su9OL/aptwpASW9es4uI8HFTiXvvlJ3K8Ld1xTo317smsYvp2cjaN7lkrlrROBQx8NY+G+MH5H8861FzMd0XGs7hrF3/fkpcLxOV1JamuoxnSfC5Pqq+JmnGp9WiGyIRLCTW8HsGYwhkcvduO+Gs5+9gYx5dWxtKMVaMVKx5m+AYt2x3tqKWBnXyTpmAHlU5wQEAJCQAgIASEgBISAEDgXCIgJpYNcjIyG8KN3A1jdb1EW1HNUGJIN9VxYcakVaRUuUbqUX1c0FvtiGNJm2Kqw8nKrP27CcZGHs0cRbNUUEwdCBaPYZ8iQ6lvNwm3whbDS0C4fndOAVS26rj7j8jpspyK3dKoe/2PcbOTGV/1Yzw1J/jW+niw1xPTvvSf0qcKrabaYnBL6LVA2cDfJn8314ZLWWjRrUY5jIWfjlHnmR5xtXGCZ4UuXSO4IASEgBISAEBACQkAICIFzn4DMwOXK4yAVIc4AacqbrxrPzvZh1/xaLLF9zgVORGV2kXG8q0+IoSZVUfOkzqRlDkb7pbYai1LDMB8Zj2BXfGrQhf9pVRZr3XHlTfNe78GfKyUzOJ7X+XNHhnVl9svnp6lvQKGy8TiEeXHlTUlXhQXn60D1OUVN4qQ/TZyBTHNU9JIV6zQfckMICAEhIASEgBAQAkJACJyVBLKpG2dlgkot9NFPgtjIQNu4e6N/WSNWza7FAu4qObWQiNxuLFKbb9DE8N3Pk9dpBT6PaPE4XwNXhSZtdi+KE0kTg1E8++oo1sfli+GnH2cxj/SH8QulVNZWQRMt/ly2i3F8pMnvwtxJNgoUFa+SyEYTyd3JiYsLNcgdNbUNXCw7gYImrcd4t2OSuTNl3LtcCAEhIASEgBAQAkJACAiBc4KAKHA5svHUmK5otTZUwWv43f9RQFe2cjyb/rMLlzboCs/9747haFzxiuL5LstuHOkP2twxw4rhlOXRV3aO4Ftq9o1nwx1ZpM9bPd0TwHGbENStHR8G0cnPddyoxUyfuh+hGeTeYyEcjc/kqbuGi0T0mURuoDLdVusrjWwDx/xYyYPC2y6uxbwk88kY9nGdnDrAfIJlqi0wEtXScpkxDaqOVHi8cwTPHcljZxgzjfIpBISAEBACQkAICAEhIAQqkIAocDkypbVFNxHcenQMD73nx3PvDRu7OvJBbuRh6jfmbpSpwaXev3WeF23KUyiM6b8cwuPvjGD5lmEqKsaMXCazyNSA+b1dbULC2byX/6QrKN3ctGSZdjxBNXqu92HahbV4StPhIvjJ4XQlZi/93/TpOBUkH/7OWCNnRtPVPYL5e8YwfXv6BiKBgaiuwNZV4wLzgZTPYmUL9Ptxwx41NViN//xykvbGNYUhbNOUVA+mW0rwh3/SZxoXcQMU5XZ86Mea/gjUbqED2h35IwSEgBAQAkJACAgBISAEzm4Clu7v2Z2QcknfwB0izWMDnj4axD08X+1BrtNaq2aeQuOg5aPmmnSdIU2MFu7QqGaKLq0zUNfX4v8t8eI+TVEbx5peblwSdWHD/Dqss53NSgsyfqOFO6So4wfW7A+g73M/2g8qJU0dF6Cf/6aUnxVzdMHWHA7FjzxQAezvGcZ85d9Xg99y//9U8T01hmmkjUIZ4W6cynVw/Zt11k67afwpRrbIYADLOoM8Z45pudlMSyL07v1BbOXXp67wJOTmDpY/VFOaPNbgBm7SolzrJIM52eeJVg9A/goBISAEhIAQEAJCQAgIgQoj4IrRVZhMFSlOgCaFtMiDhxt0NKdMCBUq8MBoFH6lQ3Emi8u2CnI73zmF63tjWLegCQ+kzKJlCrCbRwm082y4tolU3pbWYVIGjwMnxjB5dwz9y+sz+snwqHa7ENkC/Up5C9AUsgrbb24Cj65LdpEwVm3lGr9qN3qXN6DF+HU/ZxNnUyFdO7cRj7UmtE7F2FfPIyCSQ5FvQkAICAEhIASEgBAQAkLgrCQgCtxZmW0WoblL5vKXxzgjRYXmjoRCY/GRdKnMJrWZN95dMaUGN9HEcoimoAEqTN+4hmaXpiIZDOOhl0eBOY34wZUJhSgpsFxf8pQtMhTAV19XyhtdjRubplXhM3UoN5Xcq66sw1JuWLJzFxXWT6mwfoUK61Rjho1HIbTzKIRuzr71f60wZTNXUuR3ISAEhIAQEAJCQAgIASFQCQREgauEXChShgCn8U6GXZjWlMsidhzP/noI39KXlmmKUSLqKrx/W1N8sxA1E7b+RDUemG3ZJSTh2fGVc9mAkeNjaNythFPmm8kTw+YM4whn1PppcpqUVuOAdQ8PFW82FVDHEopHISAEhIAQEAJCQAgIASFw9hAQBe7sySuRVAgIASEgBISAEBACQkAICIEvOIFcUzZfcDySfCEgBISAEBACQkAICAEhIASEQOUQEAWucvJCJBECQkAICAEhIASEgBAQAkJACGQlIApcVjzyoxAQAkJACAgBISAEhIAQEAJCoHIIiAJXOXkhkggBISAEhIAQEAJCQAgIASEgBLISEAUuKx75UQgIASEgBISAEBACQkAICAEhUDkERIGrnLwQSYSAEBACQkAICAEhIASEgBAQAlkJiAKXFY/8KASEgBAQAkJACAgBISAEhIAQqBwCosBVTl6IJEJACAgBISAEhIAQEAJCQAgIgawERIHLikd+FAJCQAgIASEgBISAEBACQkAIVA4BUeAqJy9EEiEgBISAEBACQkAICAEhIASEQFYCosBlxSM/CgEhIASEgBAQAkJACAgBISAEKoeAKHCVkxciiRAQAkJACAgBISAEhIAQEAJCICsBUeCy4pEfhYAQEAJCQAgIASEgBISAEBAClUPg/wME2XMbsRTSBAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(filename='Images/07_1.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def trapezoid_rule(f,x0,x1,mf2):\n",
    "    # f is a sympy function and mf2 is the maximum of f''\n",
    "    y0=f.subs(x,x0)\n",
    "    y1=f.subs(x,x1)\n",
    "    h=x1-x0\n",
    "    ti=h*(y0+y1)/2\n",
    "    te=h**3*mf2/12\n",
    "    return ti, te\n",
    "\n",
    "def simpson_rule(f,x0,x1,x2,mf4):\n",
    "    # x0,x1,x2 should be equidistant\n",
    "    # f is a sympy function and mf4 is the maximum of f''''\n",
    "    y0=f.subs(x,x0)\n",
    "    y1=f.subs(x,x1)\n",
    "    y2=f.subs(x,x2)\n",
    "    h=x1-x0\n",
    "    si=h*(y0+4*y1+y2)/3\n",
    "    se=h**5*mf4/90\n",
    "    return si, se"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <span style=\"color:#19bfc2\">EXAMPLE 5.6</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-size:large;\">Apply the Trapezoid Rule and Simpson’s Rule to approximate\n",
    "\n",
    "<span style=\"font-size:large;\">$$\\int_1^2 \\ln x \\, dx$$\n",
    "\n",
    "<span style=\"font-size:large;\">and find an upper bound for the error in your approximations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = lambda x: np.log(x)\n",
    "x0=1\n",
    "x1=2\n",
    "x = np.linspace(x0,x1,100) #p+1)\n",
    "ti=r'$y = \\int_1^2 \\ln x \\, dx$'\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "# Move left y-axis and bottim x-axis to centre, passing through (0,0)\n",
    "# ax.spines['left'].set_position('center')\n",
    "ax.spines['bottom'].set_position('zero') \n",
    "# Eliminate upper and right axes\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "# Show ticks in the left and lower axes only\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "\n",
    "pl=plt.plot(x,f(x))\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y') \n",
    "plt.title(ti)\n",
    "\n",
    "y0 = f(x0); y1 = f(x1);\n",
    "plt.fill_between([x0,x1],[y0,y1],edgecolor='b',alpha=0.2)\n",
    "\n",
    "plt.plot([x0,x0],[0,y0],'b',alpha=0.2)\n",
    "plt.plot([x1,x1],[0,y1],'b',alpha=0.2)\n",
    "\n",
    "# plt.xlim([0.9,2.2]); plt.ylim([0,0.8]);\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Trapezoid rule approximation is 0.3466\n",
      "Trapezoid rule magnitude of error is 0.0833333333333333\n",
      "Exact integral is 0.386294\n"
     ]
    }
   ],
   "source": [
    "x = sp.Symbol('x', real=True)\n",
    "f = sp.ln(x)\n",
    "x0=1\n",
    "x1=2\n",
    "d2f=f.diff(x,2)\n",
    "mf2=abs(d2f).subs(x,x0)\n",
    "te,ti=trapezoid_rule(f,x0,x1,mf2)\n",
    "print(\"Trapezoid rule approximation is\",te.evalf(4))\n",
    "print(\"Trapezoid rule magnitude of error is\",ti.evalf())\n",
    "t1=sp.Integral(f,(x,x0,x1))\n",
    "t2=sp.integrate(f,(x,x0,x1)) \n",
    "print(\"Exact integral is\",t2.evalf(6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = lambda x: np.log(x)\n",
    "x = np.linspace(1,2,100)\n",
    "x0=1\n",
    "x1=2\n",
    "ti=r'$y = \\int_1^2 \\ln x \\, dx$'\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "# Move left y-axis and bottim x-axis to centre, passing through (0,0)\n",
    "# ax.spines['left'].set_position('center')\n",
    "ax.spines['bottom'].set_position('zero') \n",
    "# Eliminate upper and right axes\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "# Show ticks in the left and lower axes only\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "pl=plt.plot(x,f(x))\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y') \n",
    "plt.title(ti)\n",
    "\n",
    "x0 = 1; x1 = 1.5; x2 = 2\n",
    "y0 = f(x0); y1 = f(x1); y2 = f(x2)\n",
    "plt.fill_between([x0,x1,x2],[y0,y1,y2],edgecolor='b',alpha=0.2)\n",
    "\n",
    "plt.plot([x0,x0],[0,y0],'b',alpha=0.2)\n",
    "plt.plot([x1,x1],[0,y1],'b',alpha=0.2)\n",
    "plt.plot([x2,x2],[0,y2],'b',alpha=0.2)\n",
    "\n",
    "# plt.xlim([0.9,2.2]); plt.ylim([0,0.8]);\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simpson's rule approximation is 0.3858\n",
      "Simpson's rule magnitude of error is 0.00208333333333333\n",
      "Exact integral is 0.386294\n"
     ]
    }
   ],
   "source": [
    "x = sp.Symbol('x', real=True)\n",
    "f = sp.ln(x)\n",
    "x0=1\n",
    "x1=1.5\n",
    "x2=2\n",
    "d4f=f.diff(x,4)\n",
    "mf4=abs(d4f).subs(x,x0)\n",
    "se,si=simpson_rule(f,x0,x1,x2,mf4)\n",
    "print(\"Simpson's rule approximation is\",se.evalf(4))\n",
    "print(\"Simpson's rule magnitude of error is\",si.evalf())\n",
    "t1=sp.Integral(f,(x,x0,x2))\n",
    "t2=sp.integrate(f,(x,x0,x2)) \n",
    "print(\"Exact integral is\",t2.evalf(6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  5.2.3 Composite Newton-Cotes formulas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The composite Newton-Cotes formulas is simply the sum of the corresponding approximations on adjacent subintervals, called **panels**, formed by a sequence of equidistant points. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(filename='Images/07_2.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Composite Trapezoid Rule"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-size:large;\">\n",
    "$$\\int_a^b f(x) \\, dx = \\frac{h}{2} \\Big(y_0 + y_m + 2 \\sum_{i = 1}^{m - 1} y_i\\Big) - \\frac{(b - a)h^2}{12} f''(c),$$</span>\n",
    "\n",
    "<span style=\"font-size:large;\">where $x_i = a + ih$ with $h = (b - a)/m, y_i = f(x_i)$, for $i = 0, \\ldots, m$ (in particular, $x_0 = a$ and $x_{m} = b$) and $c$ is between $a$ and $b$.</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Composite Simpson's Rule"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-size:large;\">\n",
    "$$\\int_a^b f(x) \\, dx = \\frac{h}{3} \\Big[y_0 + y_{2m} + \n",
    "4 \\sum_{i = 1}^{m} y_{2i - 1} +\n",
    "2 \\sum_{i = 1}^{m - 1} y_{2i}\\Big] - \\frac{(b - a)h^4}{180} f^{\\textrm{(iv)}}(c),$$</span>\n",
    "\n",
    "<span style=\"font-size:large;\">where $x_i = a + ih$ with $h = (b - a)/(2m), y_i = f(x_i)$, for $i = 0, \\ldots, 2m$ (in particular, $x_0 = a$ and $x_{2m} = b$) and $c$ is between $a$ and $b$.</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def composite_trapezoid_rule(f,a,b,p,mf2):\n",
    "    # f is a sympy function and mf2 is the maximum of f''\n",
    "    h=(b-a)/p\n",
    "    X=[]\n",
    "    Y=[]\n",
    "    for i in range(p+1):\n",
    "        X.append(a+i*h)\n",
    "        Y.append(f.subs(x,a+i*h))\n",
    "    Z=Y[1:p]\n",
    "    ti=h*(Y[0]+Y[-1]+2*sum(Z))/2\n",
    "    te=(b-a)*h**2*mf2/12\n",
    "    return ti, te\n",
    "\n",
    "def composite_simpson_rule(f,a,b,p,mf4):\n",
    "    # [a,b] should be divided in p equidistant panels\n",
    "    # f is a sympy function and mf4 is the maximum of f''''\n",
    "    h=(b-a)/(2*p)\n",
    "    X=[]\n",
    "    Y=[]\n",
    "    for i in range(2*p+1):\n",
    "        X.append(a+i*h)\n",
    "        Y.append(f.subs(x,a+i*h))\n",
    "    Z1=Y[1:2*p:2]\n",
    "    Z2=Y[2:2*p:2]\n",
    "    si=h*(Y[0]+Y[-1]+4*sum(Z1)+2*sum(Z2))/3\n",
    "    se=(b-a)*h**4*mf4/180\n",
    "    return si, se"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <span style=\"color:#19bfc2\">EXAMPLE 5.8</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-size:large;\">Carry out four-panel approximations of\n",
    "\n",
    "<span style=\"font-size:large;\">$$\\int_1^2 \\ln x \\, dx$$\n",
    "\n",
    "<span style=\"font-size:large;\">using the composite Trapezoid Rule and composite Simpson’s Rule."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = lambda x: np.log(x)\n",
    "a=1\n",
    "b=2\n",
    "p=4\n",
    "x = np.linspace(a,b,p+1)\n",
    "y = f(x)\n",
    "ti=r'$y = \\int_1^2 \\ln x \\, dx$'\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "# Move left y-axis and bottim x-axis to centre, passing through (0,0)\n",
    "# ax.spines['left'].set_position('center')\n",
    "ax.spines['bottom'].set_position('zero') \n",
    "# Eliminate upper and right axes\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "# Show ticks in the left and lower axes only\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "pl=plt.plot(x,y)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y') \n",
    "plt.title(ti)\n",
    "\n",
    "for i in range(p):\n",
    "    xs = [x[i],x[i],x[i+1],x[i+1]]\n",
    "    ys = [0,f(x[i]),f(x[i+1]),0]\n",
    "    plt.fill(xs,ys,'b',edgecolor='b',alpha=0.2)\n",
    "\n",
    "# plt.xlim([0.9,2.2]); plt.ylim([0,0.8]);\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Composite trapezoid rule approximation is 0.3837\n",
      "Composite trapezoid rule magnitude of error is 0.00520833333333333\n",
      "Exact integral is 0.386294\n"
     ]
    }
   ],
   "source": [
    "x = sp.Symbol('x', real=True)\n",
    "f = sp.ln(x)\n",
    "a=1\n",
    "b=2\n",
    "p=4\n",
    "d2f=f.diff(x,2)\n",
    "mf2=abs(d2f).subs(x,a)\n",
    "te,ti=composite_trapezoid_rule(f,a,b,p,mf2)\n",
    "print(\"Composite trapezoid rule approximation is\",te.evalf(4))\n",
    "print(\"Composite trapezoid rule magnitude of error is\",ti.evalf())\n",
    "t1=sp.Integral(f,(x,a,b))\n",
    "t2=sp.integrate(f,(x,a,b)) \n",
    "print(\"Exact integral is\",t2.evalf(6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = lambda x: np.log(x)\n",
    "a=1\n",
    "b=2\n",
    "p=8\n",
    "x = np.linspace(a,b,p+1)\n",
    "y = f(x)\n",
    "ti=r'$y = \\int_1^2 \\ln x \\, dx$'\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "# Move left y-axis and bottim x-axis to centre, passing through (0,0)\n",
    "# ax.spines['left'].set_position('center')\n",
    "ax.spines['bottom'].set_position('zero') \n",
    "# Eliminate upper and right axes\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "# Show ticks in the left and lower axes only\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "pl=plt.plot(x,y)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y') \n",
    "plt.title(ti)\n",
    "\n",
    "for i in range(p):\n",
    "    xs = [x[i],x[i],x[i+1],x[i+1]]\n",
    "    ys = [0,f(x[i]),f(x[i+1]),0]\n",
    "    plt.fill(xs,ys,'b',edgecolor='b',alpha=0.2)\n",
    "\n",
    "# plt.xlim([0.9,2.2]); plt.ylim([0,0.8]);\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Composite Simpson's rule approximation is 0.386292\n",
      "Composite Simpson's rule magnitude of error is 8.13802083333333e-6\n",
      "Exact integral is 0.386294\n"
     ]
    }
   ],
   "source": [
    "x = sp.Symbol('x', real=True)\n",
    "f = sp.ln(x)\n",
    "a=1\n",
    "b=2\n",
    "p=4\n",
    "d4f=f.diff(x,4)\n",
    "mf4=abs(d4f).subs(x,a)\n",
    "se,si=composite_simpson_rule(f,a,b,p,mf4)\n",
    "print(\"Composite Simpson's rule approximation is\",se.evalf(6))\n",
    "print(\"Composite Simpson's rule magnitude of error is\",si.evalf())\n",
    "t1=sp.Integral(f,(x,a,b))\n",
    "t2=sp.integrate(f,(x,a,b)) \n",
    "print(\"Exact integral is\",t2.evalf(6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <span style=\"color:#19bfc2\">EXAMPLE 5.9</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-size:large;\">Find the number of panels $m$ necessary for the composite Simpson’s Rule to approximate\n",
    "􏰋\n",
    "<span style=\"font-size:large;\">$$\\int_0^\\pi \\sin^2 \\, dx$$\n",
    "        \n",
    "<span style=\"font-size:large;\">within six correct decimal places."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "37 panels are sufficient\n"
     ]
    }
   ],
   "source": [
    "x = sp.Symbol('x', real=True)\n",
    "f = sp.sin(x)**2\n",
    "a=0\n",
    "b=sp.pi\n",
    "d4f=f.diff(x,4)\n",
    "mf4=abs(d4f).subs(x,a)\n",
    "mf4\n",
    "for m in range(1,100):\n",
    "    si,se=composite_simpson_rule(f,a,b,m,mf4)\n",
    "    if se.evalf() < 0.5*10**(-6):\n",
    "        print(m, \"panels are sufficient\")\n",
    "        break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  5.2.4 Open Newton-Cotes methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some integrands that have a removable singularity at an interval endpoint may be more easily handled with an **open Newton–Cotes Method**, which does not use values from the endpoints. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Midpoint Rule"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-size:large;\">\n",
    "$$\\int_{x_0}^{x_1} f(x) \\, dx = h f(w) + \\frac{h^3}{24} f''(c),$$</span>\n",
    "\n",
    "<span style=\"font-size:large;\">where $h = x_1 - x_0, w$ is the midpoint $x_0 + h/2$ and $c$ is between $x_0$ and $x_1$.</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Composite Midpoint Rule"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-size:large;\">\n",
    "$$\\int_{x_0}^{x_1} f(x) \\, dx = h \\sum_{i = 1}^m f(w_i) + \\frac{(b - a) h^2}{24} f''(c),$$</span>\n",
    "\n",
    "<span style=\"font-size:large;\">where $h = (b - a)/m$, the $w_i$ are the midpoints of the $m$ equal subintervals of $[a,b]$ and $c$ is between $a$ and $b$.</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def midpoint_rule(f,x0,x1,mf2):\n",
    "    # f is a sympy function and mf2 is the maximum of f''\n",
    "    y0=f.subs(x,x0)\n",
    "    y1=f.subs(x,x1)\n",
    "    h=x1-x0\n",
    "    w=x0+h/2\n",
    "    mi=h*f(w)\n",
    "    me=h**3*mf2/24\n",
    "    return mi, me\n",
    "\n",
    "def composite_midpoint_rule(f,a,b,p,mf2):\n",
    "    # f is a sympy function and mf2 is the maximum of f''\n",
    "    h=(b-a)/(2*p)\n",
    "    X=[]\n",
    "    Y=[]\n",
    "    for i in range(2*p+1):\n",
    "        X.append(a+i*h)\n",
    "        Y.append(f.subs(x,a+i*h))\n",
    "    Z=Y[1:2*p+1]\n",
    "    mi=h*sum(Z)\n",
    "    me=(b-a)*h**2*mf2/24\n",
    "    return mi, me"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <span style=\"color:#19bfc2\">EXAMPLE 5.10</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-size:large;\">Approximate $\\int_0^1 \\frac{\\sin}{x} \\, dx$ by using the Composite Midpoint Rule with $m = 10$ panels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = lambda x: np.sin(x)/x #sp.sin(x)/x\n",
    "a=0.1\n",
    "b=1\n",
    "p=10\n",
    "x = np.linspace(a,b,p+1)\n",
    "y = f(x)\n",
    "ti=r'$\\int_0^1 \\frac{\\sin}{x} \\, dx$'\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "# Move left y-axis and bottim x-axis to centre, passing through (0,0)\n",
    "# ax.spines['left'].set_position('center')\n",
    "ax.spines['bottom'].set_position('zero') \n",
    "# Eliminate upper and right axes\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "# Show ticks in the left and lower axes only\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "pl=plt.plot(x,y)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y') \n",
    "plt.title(ti)\n",
    "\n",
    "for i in range(p):\n",
    "    xs = [x[i],x[i],x[i+1],x[i+1]]\n",
    "    ys = [0,f(x[i]),f(x[i+1]),0]\n",
    "    plt.fill(xs,ys,'b',edgecolor='b',alpha=0.2)\n",
    "\n",
    "# plt.xlim([0.9,2.2]); plt.ylim([0,0.8]);\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Composite midpoint rule approximation is 0.93209913\n",
      "Composite midpoint rule magnitude of error is 3.36899267778294e-5\n",
      "Exact integral is 0.93608313\n"
     ]
    }
   ],
   "source": [
    "x = sp.Symbol('x', real=True)\n",
    "f = sp.sin(x)/x\n",
    "a=0.01\n",
    "b=1\n",
    "p=10\n",
    "d2f=f.diff(x,2)\n",
    "mf2=abs(d2f).subs(x,a)\n",
    "mi,me=composite_midpoint_rule(f,a,b,p,mf2)\n",
    "mi\n",
    "print(\"Composite midpoint rule approximation is\",mi.evalf(8))\n",
    "print(\"Composite midpoint rule magnitude of error is\",me.evalf())\n",
    "t1=sp.Integral(f,(x,a,b))\n",
    "t2=sp.integrate(f,(x,a,b)) \n",
    "print(\"Exact integral is\",t2.evalf(8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.5 Gaussian Quadrature"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The set of nonzero functions $\\{p_0, \\ldots, p_n\\}$ on the interval $[a,b]$ is **orthogonal** on $[a,b]$ if\n",
    "\n",
    "$$(p_i,p_j) = \\int_a^b p_j(x) p_k(x) \\, dx = \\left\\{ \\begin{array}{ll}\n",
    "0, & \\mbox{ if } j \\neq k,\\\\\n",
    "\\neq 0, & \\mbox{ if } j = k \\end{array} \\right. $$\n",
    "\n",
    "<span style=\"font-size:large;\">*Theorem*. If $\\{p_0, \\ldots, p_n\\}$ is an orthogonal set of polynomials on the interval $[a,b]$, where $\\textrm{deg}\\,p_i = i$, then $\\{p_0, \\ldots, p_n\\}$ is a basis for the vector space of degree at most $n$ polynomials on $[a,b]$.\n",
    "    \n",
    "<span style=\"font-size:large;\">*Theorem*. If $\\{p_0, \\ldots, p_n\\}$ is an orthogonal set of polynomials on $[a,b]$ and if $\\textrm{deg}\\,p_i = i$, then $p_i$ has $i$ distinct roots in the interval $(a,b)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <span style=\"color:#19bfc2\">EXAMPLE 5.13</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-size:large;\">Find a set of three orthogonal polynomials on the interval $[−1, 1]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Start with $p_0(x) = 1$ and $p_1(x) = x$, since $(p_0,p_1) = \\int_{-1}^{1} 1 \\cdot x\\,dx =0$. Next, take $p_2(x) = x^2 +c$ and find $c$ so that $(p_2,p_0) = 0$, i.e., $\\int_{-1}^1 1 \\cdot (x^2 + c)\\,dx =  $ $2/3 + 2c = 0$, which implies that $c = -1/3$. Moreover, $(p_1,p_2) = \\int_{-1}^1 (x^3 - x/3)\\,dx = 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <span style=\"color:#19bfc2\">EXAMPLE 5.14</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-size:large;\">Show that the set of **Legendre polynomials**\n",
    "    \n",
    "<span style=\"font-size:large;\">$$p_i(x) = \\frac{1}{2^i i!} \\frac{d^i}{dx^i} [(x^2 - 1)^i],$$\n",
    "\n",
    "<span style=\"font-size:large;\">for $0 \\leq i \\leq n$, is orthogonal on $[-1,1]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(filename='Images/07_3.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gaussian Quadrature"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-size:large;\">$$\\int_{-1}^1 f(x)\\,dx \\approx \\sum_{i = 1}^n c_i f(x_i),$$\n",
    "    \n",
    "<span style=\"font-size:large;\">where $x_i, i = 1, \\ldots n$, are the roots of the degree $n$ Legendre polynomial and the coefficients $c_i$ are\n",
    "    \n",
    "<span style=\"font-size:large;\">$$c_i = \\int_{-1}^1 \\prod_{k = 1, k \\neq i}^n \\frac{x - x_i}{x_k - x_i} \\, dx, \\,\\,\\, i = 1, \\ldots, n.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <span style=\"color:#19bfc2\">EXAMPLE 5.15</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-size:large;\">Approximate the integral\n",
    "    \n",
    "<span style=\"font-size:large;\">$$\\int_{-1}^1 e^{-\\frac{x^2}{2}} \\, dx,$$\n",
    "    \n",
    "<span style=\"font-size:large;\">using Gaussian Quadrature."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exact integral is 1.71124878378430\n",
      "The Gaussian Quadrature approximation for 2 is 1.69296344978123\n",
      "The Gaussian Quadrature approximation for 3 is 1.71202024520191\n",
      "The Gaussian Quadrature approximation for 4 is 1.71122450459949\n"
     ]
    }
   ],
   "source": [
    "x = sp.Symbol('x', real=True)\n",
    "f = sp.exp(-x**2/2)\n",
    "a=-1\n",
    "b=1\n",
    "\n",
    "t1=sp.Integral(f,(x,a,b))\n",
    "t2=sp.integrate(f,(x,a,b)) \n",
    "print(\"Exact integral is\",t2.evalf(15))\n",
    "\n",
    "f = sp.lambdify(x,f,'numpy')\n",
    "for n in [2,3,4]:\n",
    "    x,w = np.polynomial.legendre.leggauss(n)\n",
    "    gauss = sum(w*f(x))\n",
    "    print(\"The Gaussian Quadrature approximation for {} is {:.14f}\".format(n,gauss))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-size:large;\">*Theorem*. The Gaussian Quadrature Method, using the degree $n$ Legendre polynomial on $[-1,1]$ has degree of precision $2n - 1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-size:large;\">To approximate integrals on a general interval $[a, b]$, the problem needs to be translated back to $[−1,1]$. Using the substitution $t =$ $(2x − a − b)/(b − a)$, we find it easy to check that\n",
    "\n",
    "<span style=\"font-size:large;\">$$\\int_a^b f(x)\\,dx = \\int_{-1}^1 f\\Big(\\frac{(b - a) t + b + a}{2}\\Big)\\frac{b - a}{2}\\,dt.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <span style=\"color:#19bfc2\">EXAMPLE 5.16</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-size:large;\">Approximate the integral\n",
    "    \n",
    "<span style=\"font-size:large;\">$$\\int_1^2 \\ln x \\, dx,$$\n",
    "    \n",
    "<span style=\"font-size:large;\">using Gaussian Quadrature."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exact integral is 0.38629436111989\n",
      "The Gaussian Quadrature approximation for 2 is 0.38659494411674\n",
      "The Gaussian Quadrature approximation for 3 is 0.38630042158401\n",
      "The Gaussian Quadrature approximation for 4 is 0.38629449693871\n"
     ]
    }
   ],
   "source": [
    "x = sp.Symbol('x', real=True)\n",
    "f = sp.log(x)\n",
    "a=1\n",
    "b=2\n",
    "\n",
    "t1=sp.Integral(f,(x,a,b))\n",
    "t2=sp.integrate(f,(x,a,b)) \n",
    "print(\"Exact integral is\",t2.evalf(14))\n",
    "\n",
    "f = sp.lambdify(x,f,'numpy')\n",
    "for n in [2,3,4]:\n",
    "    x,w = np.polynomial.legendre.leggauss(n)\n",
    "    t = ((b - a)*x + b + a)/2\n",
    "    gauss = sum(w*f(t))*(b - a)/2\n",
    "    print(\"The Gaussian Quadrature approximation for {} is {:.14f}\".format(n,gauss))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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