{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden"
   },
   "source": [
    "# The Laplace Transform\n",
    "\n",
    "*This Jupyter notebook is part of a [collection of notebooks](../index.ipynb) in the bachelors module Signals and Systems, Communications Engineering, Universität Rostock. Please direct questions and suggestions to [Sascha.Spors@uni-rostock.de](mailto:Sascha.Spors@uni-rostock.de).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Theorems\n",
    "\n",
    "The theorems of the Laplace transformation relate basic time-domain operations to their equivalents in the Laplace domain. They are of use for the computation of Laplace transforms of signals composed from modified [standard signals](../continuous_signals/standard_signals.ipynb) and for the computation of the response of systems to an input signal. The theorems allow further to predict the consequences of modifying a signal or system by certain operations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Temporal Scaling Theorem\n",
    "\n",
    "A signal $x(t)$ is given for which the Laplace transform $X(s) = \\mathcal{L} \\{ x(t) \\}$ exists. The Laplace transform of the [temporally scaled signal](../continuous_signals/operations.ipynb#Temporal-Scaling) $x(a t)$ with $a \\in \\mathbb{R} \\setminus \\{0\\}$ reads\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathcal{L} \\{ x(a t) \\} = \\frac{1}{|a|} \\cdot X \\left( \\frac{s}{a} \\right)\n",
    "\\end{equation}\n",
    "\n",
    "The Laplace transformation of a temporally scaled signal is given by weighting the inversely scaled Laplace transform of the unscaled signal with $\\frac{1}{|a|}$. The scaling of the Laplace transform can be interpreted as a scaling of the complex $s$-plane. The region of convergence (ROC) of the temporally scaled signal $x(a t)$ is consequently the inversely scaled ROC of the unscaled signal $x(t)$\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{ROC} \\{ x(a t) \\} = \\left\\{ s: \\frac{s}{a} \\in \\text{ROC} \\{ x(t) \\} \\right\\}\n",
    "\\end{equation}\n",
    "\n",
    "Above relation is known as scaling theorem of the Laplace transform. The scaling theorem can be proven by introducing the scaled signal $x(a t)$ into the definition of the Laplace transformation\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathcal{L} \\{ x(a t) \\} = \\int_{-\\infty}^{\\infty} x(a t) \\, e^{- s t} \\; dt = \\frac{1}{|a|} \\int_{-\\infty}^{\\infty} x(t') \\, e^{-\\frac{s}{a} t'} \\; dt' = \\frac{1}{|a|} \\cdot X \\left( \\frac{s}{a} \\right)\n",
    "\\end{equation}\n",
    "\n",
    "where the substitution $t' = a t$ was used. Note that a negative value of $a$ would result in a reversal of the integration limits. In this case a second reversal of the integration limits together with the sign of the integration element $d t'= a \\, dt$ was consolidated into the absolute value of $a$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Convolution Theorem\n",
    "\n",
    "The convolution theorem states that the Laplace transform of the convolution of two signals $x(t)$ and $y(t)$ is equal to the scalar multiplication of their Laplace transforms $X(s)$ and $Y(s)$\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathcal{L} \\{ x(t) * y(t) \\} = X(s) \\cdot Y(s)\n",
    "\\end{equation}\n",
    "\n",
    "under the assumption that both Laplace transforms $X(s) = \\mathcal{L} \\{ x(t) \\}$ and $Y(s) = \\mathcal{L} \\{ y(t) \\}$ exist, respectively. The ROC of the convolution $x(t) * y(t)$ includes at least the intersection of the ROCs of $x(t)$ and $y(t)$\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{ROC} \\{ x(t) * y(t) \\} \\supseteq \\text{ROC} \\{ x(t) \\} \\cap \\text{ROC} \\{ y(t) \\}\n",
    "\\end{equation}\n",
    "\n",
    "\n",
    "The theorem can be proven by introducing the [definition of the convolution](../systems_time_domain/convolution.ipynb) into the [definition of the Laplace transform](definition.ipynb) and changing the order of integration\n",
    "\n",
    "\\begin{align}\n",
    "\\mathcal{L} \\{ x(t) * y(t) \\} &= \\int_{-\\infty}^{\\infty} \\left( \\int_{-\\infty}^{\\infty} x(\\tau) \\cdot y(t-\\tau) \\; d \\tau \\right) e^{-s t} \\; dt \\\\\n",
    "&= \\int_{-\\infty}^{\\infty} \\left( \\int_{-\\infty}^{\\infty} y(t-\\tau) \\, e^{-s t} \\; dt \\right) x(\\tau) \\; d\\tau \\\\\n",
    "&= Y(s) \\cdot \\int_{-\\infty}^{\\infty} x(\\tau) \\, e^{-s \\tau} \\; d \\tau \\\\\n",
    "&= Y(s) \\cdot X(s)\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "\n",
    "The convolution theorem is very useful in the context of linear time-invariant (LTI) systems. The output signal $y(t)$ of an LTI system is given as the convolution of the input signal $x(t)$ with the impulse response $h(t)$. The signals can be represented either in the time or Laplace domain. This leads to the following equivalent representations of an LTI system in the time and Laplace domain, respectively\n",
    "\n",
    "![Representation of an LTI system in the time- and Laplace-domain](LTI_system_Laplace_domain.png)\n",
    "\n",
    "Calculation of the system response by transforming the problem into the Laplace domain can be beneficial since this replaces the evaluation of the convolution integral by a scalar multiplication. In many cases this procedure simplifies the calculation of the system response significantly. A prominent example is the [analysis of a passive electrical network](network_analysis.ipynb). The convolution theorem can also be useful to derive an unknown Laplace transform. The key is here to express the signal as convolution of two other signals for which the Laplace transforms are known. This is illustrated by the following example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example - Transformation of two convolved signals**\n",
    "\n",
    "The Laplace transform of the convolution of a causal cosine signal $\\epsilon(t) \\cdot \\cos(\\omega_0 t)$ with a causal sine signal $\\epsilon(t) \\cdot \\sin(\\omega_0 t)$ is derived by the convolution theorem\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathcal{L} \\{ \\epsilon(t) \\cdot ( \\cos(\\omega_0 t) * \\sin(\\omega_0 t) \\} \n",
    "= \\frac{s}{s^2 + \\omega_0^2} \\cdot \\frac{\\omega_0}{s^2 + \\omega_0^2}\n",
    "= \\frac{\\omega_0 s}{(s^2 + \\omega_0^2)^2}\n",
    "\\end{equation}\n",
    "\n",
    "where the [Laplace transforms of the causal cosine and sine signals](properties.ipynb#Transformation-of-the-cosine-and-sine-signal) were used. The ROC of the causal cosine and sine signal is $\\Re \\{ s \\} > 0$. The ROC for their convolution is also $\\Re \\{ s \\} > 0$, since no poles and zeros cancel out. Above Laplace transform has one zero $s_{00} = 0$, and two poles of second degree $s_{\\infty 0} = s_{\\infty 1} = j \\omega_0$ and $s_{\\infty 2} = s_{\\infty 3} = - j \\omega_0$.\n",
    "\n",
    "This example is evaluated numerically in the following. First the convolution of the causal cosine and sine signal is computed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$$\\frac{t \\sin{\\left (\\omega_{0} t \\right )}}{2}$$"
      ],
      "text/plain": [
       "t⋅sin(ω₀⋅t)\n",
       "───────────\n",
       "     2     "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import sympy as sym\n",
    "sym.init_printing()\n",
    "\n",
    "t, tau = sym.symbols('t tau', real=True)\n",
    "s = sym.symbols('s', complex=True)\n",
    "w0 = sym.symbols('omega0', positive=True)\n",
    "\n",
    "x = sym.integrate(sym.cos(w0*tau) * sym.sin(w0*(t-tau)), (tau, 0, t))\n",
    "x = sym.simplify(x)\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the sake of illustration let's plot the signal for $\\omega_0 = 1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 614.4x460.8 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sym.plot(x.subs(w0, 1), (t, 0, 50), xlabel=r'$t$', ylabel=r'$x(t)$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Laplace transform is computed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left ( \\frac{\\omega_{0} s}{\\left(\\omega_{0}^{2} + s^{2}\\right)^{2}}, \\quad 0\\right )$$"
      ],
      "text/plain": [
       "⎛    ω₀⋅s      ⎞\n",
       "⎜───────────, 0⎟\n",
       "⎜          2   ⎟\n",
       "⎜⎛  2    2⎞    ⎟\n",
       "⎝⎝ω₀  + s ⎠    ⎠"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X, a, cond = sym.laplace_transform(x, t, s)\n",
    "X, a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which exists for $\\Re \\{ s \\} > 0$. Its zeros are given as"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left \\{ 0 : 1\\right \\}$$"
      ],
      "text/plain": [
       "{0: 1}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sym.roots(sym.numer(X), s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and its poles as"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left \\{ - i \\omega_{0} : 2, \\quad i \\omega_{0} : 2\\right \\}$$"
      ],
      "text/plain": [
       "{-ⅈ⋅ω₀: 2, ⅈ⋅ω₀: 2}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sym.roots(sym.denom(X), s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Temporal Shift Theorem\n",
    "\n",
    "The [temporal shift of a signal](../continuous_signals/operations.ipynb#Temporal-Shift) $x(t - \\tau)$ for $\\tau \\in \\mathbb{R}$ can be expressed by the convolution of the signal $x(t)$ with a shifted Dirac impulse\n",
    "\n",
    "\\begin{equation}\n",
    "x(t - \\tau) = x(t) * \\delta(t - \\tau)\n",
    "\\end{equation}\n",
    "\n",
    "This follows from the sifting property of the Dirac impulse. Applying a two-sided Laplace transform to the left- and right-hand side and exploiting the convolution theorem yields\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathcal{L} \\{ x(t - \\tau) \\} = X(s) \\cdot e^{- s \\tau}\n",
    "\\end{equation}\n",
    "\n",
    "where $X(s) = \\mathcal{L} \\{ x(t) \\}$ is assumed to exist. Note that $\\mathcal{L} \\{ \\delta(t - \\tau) \\} = e^{- s \\tau}$ can be derived from the definition of the two-sided Laplace transform together with the sifting property of the Dirac impulse. The Laplace transform of a shifted signal is given by multiplying the Laplace transform of the original signal with $e^{- s \\tau}$. The ROC does not change\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{ROC} \\{ x(t-\\tau) \\} = \\text{ROC} \\{ x(t) \\}\n",
    "\\end{equation}\n",
    "\n",
    "This result is known as shift theorem of the Laplace transform. For a causal signal $x(t)$ and $\\tau > 0$ the shift theorem of the one-sided Laplace transform is equal to the shift theorem of the two-sided transform."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Transformation of the rectangular signal\n",
    "\n",
    "The Laplace transform of the [rectangular signal](../continuous_signals/standard_signals.ipynb#Rectangular-Signal) $x(t) = \\text{rect}(t)$ is derived by expressing it by the Heaviside signal\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{rect}(t) = \\epsilon \\left(t + \\frac{1}{2} \\right) - \\epsilon \\left(t - \\frac{1}{2} \\right)\n",
    "\\end{equation}\n",
    "\n",
    "Applying the shift theorem to the [transform of the Heaviside signal](definition.ipynb#Transformation-of-the-Heaviside-Signal) and exploiting the linearity of the Laplace transform yields\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathcal{L} \\{ \\text{rect}(t) \\} = \\frac{1}{s} e^{s \\frac{1}{2}} - \\frac{1}{s} e^{- s \\frac{1}{2}} = \\frac{\\sinh \\left( \\frac{s}{2} \\right) }{\\frac{s}{2}}\n",
    "\\end{equation}\n",
    "\n",
    "where $\\sinh(\\cdot)$ denotes the [hyperbolic sine function](https://en.wikipedia.org/wiki/Hyperbolic_function#Sinh). The ROC of the Heaviside signal is given as $\\Re \\{ s \\} > 0$. Applying [l'Hopitals rule](https://en.wikipedia.org/wiki/L'H%C3%B4pital's_rule), the pole at $s=0$ can be disregarded leading to\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{ROC} \\{ \\text{rect}(t) \\} = \\mathbb{C}\n",
    "\\end{equation}\n",
    "\n",
    "For illustration, the magnitude of the Laplace transform $|X(s)|$ is plotted in the $s$-plane, as well as $X(\\sigma)$ and $X(j \\omega)$ for the real and imaginary part of the complex frequency $s = \\sigma + j \\omega$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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CjLKaxEvP8gw2Pt7JyGF/WkDDAIylGVYBeag3fgmePYJdfJo7PWHDyB/hVmB+8/IfkVf2d/0GMPgIg3j4BguicMcWfokePiwcNzNjG+ZMUy5Z8O/rksZLFLnqXy6H8YtElbBbVIhI/vNyBE8fwSFTsK8C1FJRZkizlqS4RjqwxiAJp/0+1u6wsEl0KH/xv7ZCDMRP8xCFmRuf/jd4+gg28mkOH89OEx0YKCpV2TsRbvD3/cZXOLZcJAAV/BNDUGXkCyDET7nDHft68loTGOEzUpNS5Ox8vJc+TPsNvpoGoY5qpq7kdnyal+jhI1inpwGSNKcFnE7eWMYMbCcDYOOv6y/0zexaAvDO/I88GZP9pG/B00dw1J4WhgbKbLwjJxbwxOEYdgQLcCS1If1+qfIg0dH8tC/CKImmzjBUm+m8DUzw8BEs1NMgUwJdo2Zzwh/g8logMkRe/rp+4oNur4DDIy4OCFbneQOE6OkjWCguoAl6c6z4HSCLBQITziugTBv268AXyr0JlnWHf/MWigtYmIs0smzPeRw68bHjcxf2XkAmPPBdcHyMAqWj3wQpfPgwxs3oZxWeg0MjxnmakMF0MlMEGONl1ovhgAi4+njxhlitGgQ1MmkYquA7XggrevgwQgv3Vg8hps5IitkX973j94gA2b1+/TBp4Bj1NMENtoiC5FrA8OkjWKmnaVLYUp5cIiac3JnL0lp86Oqv7I1gcLgMo9SDkJsYBUbycsLxU6kwDCiZCo+XokAlDOOtbbxWEebZIWJ5a8U1xJvgrMPYEpeknM7ymb3noNdgbXdABe+68hpTHCbvoznB8ynCGyCI6HZ/2pkhqaAmZhQS6+GfftqZ6OkjWCp6OsaQEr0Bqfcco92Kiw8R/aW9j2EqlvFz9mKolAHpdOPo6KGULGahDilTg9kMdSlZXw9nfNh87Ph5jZMxXPzFXAyz9NpvOx0/ffj+gm6EiYjVsoGPCepbq9wtUEBPaeq3Z4M7y7F7+fTCZCWEenRfFNJyOT9ltuDhI9hEqWwwRYx+AJakDkN6LjnIR4f+nt8wELfO8ElKoxqSBz4rNwwMn0pmw58bpRveA3s6ylLZvm56tIkBZtwBspxLyr01UMKrxMjdeZaxMIKPvaJLvUME/LKL0gCBFVorBr1wPpRsFGLXYNc/ozTJdHqcTwB6O/2JKQpXlCZ6+vAvAdbvwKLhsNJqHwP/sqks4TxOSnz4gvbrgKLtuztzvR8WxnSWjOVOOl+dflzvFz99WPAWtmcmsooGuIUNNg7iHMrwmPlMZpeI+nUjpaIyRn0Wg4Z15uV/I2wdbPwOEO3dBN4QigFMZtFOnrxctpUBuPYvzv2CZRr+TIy08z+Y01gu5xE/fQRHjUeQKRuT9gOn7H0wqaDbEWRq89kIpvD7Hb9jen1wNHfo0F93Ujo0Lws/Du4+pVN2JIL+/r7vcG7ePnJ/GTfA19AyUXgd2sjA67nbvkeFBi5MaaH2OdLC0AdOPCGtMPHZlO0YspOAFXwewMPgOyw5CRCl+jGPmyaFTx/Bm0jIT3SkAq5w99IzQvDvv/geJfoEcadvp7SM26RIuru08VJFpGCP0vvHl0FCL3BNNuZ9vjPRSDYwwNX+1fk0gUmhXib9G4Qfrf0SaIiePvyNVCICC3SGlFGYtEMBwYiZBBt/w+falGuA86NsDSKDa4Pjp9KhMyslBJQnyxzOpUR/3fh4IyPAfS/hWcWC+DbmcZmqexvp8OkjMMY00v2d9S9TyUyJWM1sMQwzeCa9BX6jKYwR2+5PEnca/MQXb5KrOizRRdXjp49gM5UsAWeI9xK8rsxrM4cbcKdg8zf4Odcgq/qsAqJ1rRXO6bn8XADBfAO+Q8/HW2c7OwyUpjLKEvS/ns34rEW8YAcN9rZSCR1MGxXEzu0sY+niLn/y931PxOGLtVPA4cDlsB/D0XQYvmLb6DOUwDrePC43sx4ZlNk8Go7XvJF0/FSVuwXIfxg27sTcdan5X/c93scAeb9Og79uIreWJ6swiGLwuiSq2B/f8Cd30+/Le2TjF0z4K3Y9C47/tbnx04dv51isRVaFTSfmxEdnwCa+B+txGFI4ZC47LreKXgK7+Cn1jjTNfhzF4h4Z619v6xI+fQRW5GmouB5ijgdrL0CiZV0idO1bnT3hkK8XQeEQFh8dTdW3OSv7PSYo/sX5JHMrpnqm3u2OwoCMTzIXPX0Ep42nkFU1iUq2UYB2wCWvyIdL8oLTebPhlKptXwHjNUG3sKzxYsPhU97hzPM96eVwnesE0mwr6frL3Q7vqsupt9wS9zrwmgC84FbScrMsOgk4Yevga4lyeTTh3YW/osuzA8V4l+FpsAS2aJ7Z3rvD/CSpHQG68e/ODjnBO2l0IsyenywtpTwF7qIa1YiE+udyT0Tu6119WowNu5vGwjYVblJOLiKh/t3ekdTLmzAO1uSxejAdpa+YUm7zsCwhGF6s7LhiWy4LDajV5x2Jc7e/e/oI3kRRuRNXNZ9iFzj1d1TOZaH+i78ud3gnTTFNQJosbHNcySURw/OO5Y6Ucm+NFI87eYaG5UhOcmllrkUMz13THeG4bHvNWHjJrDiq8iDeqYxPWcT7duAYz9I9DZhkFi6ruBbbO6ZscQBwfMu4Q87yLMnToi8s0WHZDz77rOctPLvkKTA8n3rWtE9mKYeFtTK7rdwGJnz68H0ZXVy1o8ZrfbDQi17LFhCXE9+GyWsHv5qVToe+7/WkSu8mKNoKc2vLxyzdc8xlXQJ6HNyc10OF+J+NZNGqAJhM15X07l2c+CZErHRHVqW3Ugq2ppGLCeAsZ2Zl/9tHxD6Ddd0htX01xIpV43JaYwzAJ+xZW/EGn30GhntHtJDOqDJJmnSywYCou4q78fFGRrT01aRKbxMVbKUTsPgaw7ytSNMN+ae36TuicY6Ve1ojotGsKpiA8yB/bivk4ZK7wCre1o8EFG+QmDjIN8j1k6SHDx+Bl3gaYseRsNpOFv9h/cSCA9jv+xR7u8CQqi8KrgPt+UF0q5YcOBc4VpWaO/4UG8yc5zdWd0c8Ena7t07sADIGZ9tXtap37uNzHDC2X6qe7IolAzvUmXq53y98+AjsgOLh/LQlGoKcVwXNAvId2Y3XZR7voinpdZbMVm+kLEAsVblnEfUOLuaOcKR313gHM5ke3Q/vGlycUphj7ujfzfsOsnzb7hnIo4Ggc356gPjpw79tT0MUYPjUdXlFSmdltN2FCJm4t3OHjOLtpRJzR29j5VgwzqXUlYjcBnt/vSF+2XKquUHDWFYFK1ovGD7kFT7eO7b5VKU7z86qXPeudnhVfS3mN7EMM+/gZey+Ri0M1yzfECR6+gguq0L2+bB+WgS1IEp5SckR+/Yv98tuwDHFbF5zWH8NmgzcoSZM/2G9btghK11Oo5/S8XzT/Xk/ZlPmaBbKZQ1DGvf9iJ6qrpel42dXIBasS+16On4N95PLkZk0zyZDbx8x8w40g/sN2TWL7wCeMUyGAF7O9/qFT5W1CadfqmqazwZPc67a2a9vHr9JQCt36FDeVVVq+DiYOGiwkWXZXRnMvjrgX+yXE5vdjVTtOzNnuiol8Q+SsHikDvj7vkGMd30FfUizZhGUrnHmcTePc6ywgMu+A9+yo/IJNtBKKUi3YAL7qm3zDmZ40CLWtiPz2tlKhewL7bWxqpLm0EEL2a2/8zt8sOdsnwY8AR/ZZ8+MILbepKUAvQau+fVgi+8qlBWEwzC48WAGpfdRxRgCecX3LHt6G3zZSYXrWetnSdTWMxLm4+0jZt/Bzr8eDR9M0mpZdBUIK+Ur6/XLvYkvQsR6Xy7dce3w00olAW5nXXmY6Vz9lkN5wLPbe1ovfN1Gheoz1mxV0+H4rSYVIf/2t31HNJz9Qxte2XjZbFf1mLvx8U5GvO9ljOWiKaKswgwa+n/+HDvfDESfmU2UmuWtHGzZVM45vkFfO4JpnjOjk2MLZXjvbp+Icwib9/YRigSB79sRrPJsnRJuTkvrIcErbPysFwlEFt807umv8fUyKOkBqJF17FbvhxXMVycInyP7l2eHl/O82dOgOzyg9XJh5jfbU5iXiyiA6/0+VzCfRoVYMmNFssz8+xTzoqePwNw9H6vdEyVdEp+Gl2zycr4KEpnHHQF7wI40+ebkix1boxp41/zE5iTipjvKkL3TpqQHnnqiY4B39rytV6a6y+KD07kjZuUZFGUVNCprXehpcNU+vtFBXPvziVWndZpJMHQmvgPusvnHhVWjpw/fnijzhhHuJAGoHOloEoYiIcm3PztCBt51eFphccswR0XoLpV0XNF5X2fwr8+GoJrr1dRPHzjHDudhXGuoJDpPxmxM/qPOhjfp8xsvuEPU8q6DMjPgFuaU6agszVEaX8CUg+tzvWFim1wuDm64Vc6Cmx+3O4mf4g1pR0qxFnywIjgHXe1eXBMUmxRfHttR7guyw96yyo/Hd1ndmtgNsnTaXvaHgs+Z4m6BWhNoJDsyM7w3UaUCGJax8Mw+uGlIlYnkBv/FN7hj1+0+DePBbiYquYntiLH4woQRVvTd9I78h5PNKI7VQugAsk1lJbJ/2ft4LyMZYkcGibeXqvXobBKgAju6G2WDB3qDu/M7OiJ9eQk1RGrcLqUT4srXecWYXa7sv/SO0D1gJvujG/eFy1GCs7vn8SYGFHpPZsYXPKDMDByyeZ6GB2ChkyqeQqnGxw+vZ4j7/lbZc+DQifmiZBhYHd3fUKzx/fOG7BsXsyhBEh+YT4n1hfkqymeOBE0f42xQpl1/q/y0VO0DT5GFLuEjEkR897ynK9fX26quXHX2uWYV1bycSKSIBJd7T4ZGakYw2LDgEBb0b3d4WyOZ5PWeV1/WSC2vAPFsPhMwU8NZUJ5rSJT9Nd1ARVw8+rT5TjiT9ZAHHuXiIsWqZseQwHvkprLeCL/ehLMP63bJvq1mTmppNV+iR/xU+QnAbgdTL6tpsEmU2Nn1eBsjevp6dqlzS5W9BCvbkgwa25Nfvbc8Gh9d6h0Iy0NST+MV2OrTfoqPV2ftmJ34uGtHZNjzFMqOrLlY/26YZHjCKwLsS12BY9nT1OzrVVV+B8cksCv8yR7s+ZhqbBCpDP7V3pBi5boyZcCmDjJWjTo2GBGR3kjODFzfDhzjARZlQHFgTtJxGxzQcAXSXTUuADh7Mjy+7qYyPNifl4URp0LfKzwckORg9+8MD6PvVJ0rxwBYEsdxv2H8VDketLYkYbCIJC11pXh8tY6xvYu48w7p0jF5qhaEG0lZmXscFbJurC/VRCZyR91+t3tiOQfFdKVaVhYFYZnFVA+2OqkriyJgyQG/32EMPaOnbMnC2UmasADf3BRMD/Q430beluaFBsHeSqnSY7L9QDVoN3GqknhbwEH9hd3RV8CGonDV2Noch6HVvtJQvm59vJUBu99RuO+tlOo94LOb8F1ruGii5RFRdhd2Axx0YR/hIGzFzByDxZ/3BD9tR63g3BU8VSRkJBzH8g1M3OHtPK+mjF2st4VkwISAR1dCgi+pBz5wT6LRV4+hRKPccqmyd5ziIVoU0TzfwexozXAwmZAxP858nQNg7urS//XuhHchEkl28E3nLqjgY4xiSdYng/yldvFNn4YGV2cHmvFQi9IF6+jdPBeZal1tfEIx00c5rwfav0L7pxE0pq3wrROHLSTgobePmOgFVGBH8MZDBCqb5lwna3fU3hmyPCQORWKSjyDWG9K6WYB/sG7AwFRhENReMH74sOGIHObK/eJYOzoIdQl2EFiMqPzoxZ5EnrN2S8OmgDGq8ozcax3f00geeVHvcC+pao3G2c+sxBwc+rp6WkRCiHupX2frnhFWllEGjD5XRkRhO5K3j5jGuzZ7Q5KbB/SUqQ/8PtmM7uDArab5TrGI6QPDHWzY20eVG3WWuEvAgP/p6Zqg4rNkf9/3pEGduGtJAhDsWVlBQ+faxNfAV5c2wBcPpqjUgbGdUzAlsXfylU/pS/0urHm12MY3wepPjRvY7nMJLHhlEvkqjW+ydxB176Cp/ySOmVossD37ldnhsvfgVG5IIXNxMvFz488XBKBwke2iwtWU3Dn2yLYXv7B+7sPqPQlGXy2dEozwvQZnMbF8F0ZUBtBn74Fh3KFHeyBKWYIVO8baFMKUnNRuMNIxfch1q9H4utNQ04TfNAMyWDe11OjwqdKf8jnJZqi39FRyvWY7fjU7kR2JVJsd6+fBvKcRMtxBxjr4c66HMcyY2PmwcEMSo+vMVEoAiDisgDzzfp5T2UWRjOk7v5czkb9aEnU/xYqVlTKZAItVLxCxusDy7Ai5eqZYvZ/ZrLGpsuIEML6TsDztKLDcL1eytMHRGwCcq2tzuRpaHCQtif1RzmFZu1NRwUg68kW5HR7Yc7V0wZzHnaul0x0sDjktUTEUqQPX/HrBq2OJldoGXNfXcW/p8sA+aYoM945CFm8nlXCCOyxoCKOcrWX0Ryxt+Ru/o1oOLo5jGQ/r9DDh+64pV19PZnzSIs3wF5n3x50dvZVSWsyBI1WUSceOYKv1QqB8+Cu7J/EObq1YgWjhZ3fJqK7zi91ZwJjvLU7VtJ+TdRZmR5hld29x+FRZWQWXgdENalWtKibn7Xy8k5HitQNlee5ijfoDoT0WLxuy0TH99L3Lp4n5eedJ76gpp4NjSFYrutZtytFHzN+Do/lyaladbFlfCQaoWgxYxWOlZn3Z+HgnI1FkB4rx0IpqRfKotUr4xtE91L4nkKcDcLOh6t9jHMSBAHMJ7yAcDbOXJbJVmr50GmNjSQP793zDUDZQJRfRK0Ma+07pxrA7DumSUQMB02UAO6QO7yood4esxMJrLGjA2kjqiCQQ/+rsyb77AgmUfHcwhKqTCWAoHBNyeB9BvI5jHFunFtoVvn6Vb43BwQBvHzEB9U3jjmCrB5g1KKJ3y3TJoHTMRHr7+EaCc+H1LfLCuvJzQQ3LkI47ASAvlTd8uprbziMvYaqVzry3Z2AZY1MX6F47pA6PUT5Nuzg4kcl+3LHMRUQzUEB8/rlDKfLuqRJ3ABWtSQgb1jKEYNfUFZD8O72DhXhsgyyEyRo4lYfYBsyFpQmFwaWAndxBEJxrmY18TKWU1HFlvn/zlCCwEUwVtvLjmTslBfrYMMR6fjBlB0t3dlE1XpOVymZDclsD7SP27u35joxFVqji/PHqdsABdrZ/ewZXOryikaT0uuPwbfAaJUpDLZRSwK7aPUr0K/cMTPYOcOWBKNXHUfq3fTzeOZe7Xwnuvnrugq49WYtfXKySFg/gQOuQxC5wLa85mIE2E7jk1TfMcUQaIoPjNOdce9T6KsKL5DPfcW2I4zp3TeVjEz9J+jz2iKr3SEiP+vhXc0PLEhdHKrMZJ4vEwRDjmVcD0EghDXDnBh/gYnG8YbW5K1UvzpZbajEMswp8Os1aUcA4rPdMhNx3pBza9FwrZuKHZFOZn4F9iw1WJBu8Hi/1DdYaSNtrrtLmOBZwZcYF0Ni1bzu8vOfNyXGAuQGluvKpM85YUuJrFOXwvf+GW+KhtafRPk5tZR4rft5aqhLdI/roo7sdrsozJ6qOgcNoa+eBdes9kdanF6752ZAT2bAMZ2NxqDX0SLgd10xalmTPYuocDlfpV6dmXyb1BfL7DbHnVTc2NbuoCT+6vWn4VA3EOSK9SuDEUmZNC3LfPH6TSEDd0dvH85vKe8VdrE0WD7ZF7TZ9hhY42ddrGL2NVMpmydneg73A0pmUNRyJuP6+70h6zRZZrCrPLdRNVaLq7Xu8j4F6ugHOubBNdYwgErlrezNrZdXvIIrE+DBvR3cfZy+Vcojv0Xu9JKAuTh2ppMHe70gM8lCfplV17qCWCq669avGw5UhA5S4I60UQK6m41iVz3C1a06BdzrD0xYIvDt653iQQKktwCNkcyZAlGN1qguxvAshNjTPcQ+bUucyHZqmQNbemroahDqkfzh3oC3P566x0iclGEMnPV8tXgI6Gfno1xM3mecLrDNsKCrDYaLdHoyNYWmkcLyeuEmhInMuCJW70Wn7VqHq15sTXoVIAPxUzH462Nc7Z0rtOyfvrSLJsx7lSu1zdTT/WO6IaHjETbUJFbeTYJoYYBxdNzUSIn2etyd78wtcUfZmouOXRJfxn5oKFDJ5D95sKIX3aCXZJtl7J9wRpC+naj5xXAvIXBGvTHNNrwxo6Aay5JIikiWGuZsNeScpgv05r2JVP1Dkk6jX+yL5hu6azZ0GN54n83OwoU9DI8O4o/rEu6xKjwR3O4emc/SDp/btI9JL/au9IzmXla8H7elRbLDdUDcV1zTGti5SUne0vvLggNKrMvNVmlkNHNPSrx57HkUJ0MMOMO2BZtXS5hOGN+tsAtMrcBAFFAKQvcMMephUowUBGWZSkx7gplyutu2uqhtg2B2exFM3nial4Y7T/drPSz+7TJ4vyAViyIb8Efe6Kg3xTM2m0sM5zDzPu1rMFV3d633hLK6tNN1RBaVav0Sj+CFxFgxsM6tqTUTZDcBusYe/YjzlBpi2OBLXHK8B8eW0lFZO08htlKXC+wzAt953gOiFHooHnYd5qEK70tdkWtc8xuYuEmL3JOl+xSxK0k0cgjHXVWhXeDzioT7GeT25wLsISrDCOxl4OhlQaUOqYKQW+vdmA9hy/YWyC3Du6MF5COH6y1FWmMYHia5/2RF88FCzKhVASq1BMWFzmmkKNkeKsIuyN6ygC/sIB2HTCseWC/YNfBPFb4K4TgATN7gRz56oI3lP7SCRx3+mecuTLoAIrM8GP+z6W/phmBBc/lNHjRm0OoKhHOf75w1WxqUe9MPsjN3m2jIQfRWVNyrvgICLkTBp5jumssKoLjBSuS6+Uy4C8wf4rtxBFJsJgNTr0WTXaClTijx97RNzzevV29eXW3wjtyMfmMkR1br6AwrBuh/zqoj96sdivxQpMTtiHPA/VOarNURoOLNrvAIXSHVy1kmawyfePuLoTBAT2cG+PWz5NDp90gvox6NMFTeHrNyFop/+4Od9JL2V0giSRiR6WoZvgyvWaYvCH/7C3mGOF+bg4njDJtmcexzvmY9yjZj5uvXxVkZhkT05wV/BkXKC2UiAOJw+EvZMnewjQhSAqdcjWd5WagYJVt46PDBDNbEu6O0jDn/4W7+jt4cHjpTzktn2Ux61cAxMW9EMH436YOqOcsBomUgLWKUwRqu3pQ4fqnXG4OCsZvN1Mu7TOoLe0YyPWhQT2ZCU6WAPzQdo/bSDlgqzzOvZltLogtEAq7x+RXyfpsyzBOBTtZN41gWafGEtcoE7IoHeXdAYl3Yky4M/KW5JiwiDM8HVuWMIoJJzLdYKExQa9RVECJ+uOS49m28FEsbCHmde/R++ns34rEVRhx2BLGepNCkFl6FmTd7BDZ7K8A7jC/7S7gDGHgBWBWBjSFI+t5VjmelIWfPx8gYR0qU45GaA35WeWdehwVapKWcUAfEp0QZX54JnlWnD+FnMytK5W0rS5CMN3wfbG/CWy2NVAAP7CeQkwMV/+/YRS38B7RW3cM2W0s/we50ZNGSGYA06SZEA5Vu5Ox6alPNREk27QfOGT70CouFTAnf2Fe3JOuJ35rhpbqWL52N8Hgh7dzwAy8YP5sBDS4quLH2+Dnr8dM0sYjfvYsOw0+cwEc/IxUYrih9sqKd3XadmYbRCS42fk76N2s8lePlQxXe1r0dtPauqkTvAu8YfgJJYnXxcZQ5+IMi3whusrUfmsYDwVxO4osuWdS6ULSAHj+E2JrW+wKIrVTrg/jtAp7djSq3JoOZWmVJpKNoaYRig+QCM7kmH//qJanlHlLa0N4C9toScSODx+cYOJcwzeEquAUylcebaZnqgq12vJ5G55vGXK2LZqzi3VvsNn3h8JqpHDx/BVVCtCAiwhr8AwMMMSwOIgizB1bnjATYqCOuSy1wlISPdSbjx0zVTCd60aWT8IPebq6nIV/MYm7sofrBDqXNUiqcpb2Ah51hOFn9AaWaBgBeIGht68rnmWG3+G5aFjdMTu442jYSJL7dvvneATgdcqt6L1zZfCKKvHIZAnAyw6MuN0dy7oGqOwqIt5QvyBCgJKYqz+Fdnw/K5wFLVwvCOdeik4X7UNREmiBIEQHTDFXHBOQEnR+aMthAkmGZJAudRoMUH8xca7HUYnoIrU9U8W3YvMxg/JBY8OW+XbTyYWcbCHmEtDyOGmM+P/e6RLjxfoaIqeLnGMCx/pWPpNdMrEDVc37IDJ3gmQ2kNOeVh+4ut5s7Ze0TeOcAPd72OMRK619xPRd7xEdcdjp+ueVnnsDgIUxMGb8Nq2/HVvcTuIpL1d9wRh3yp4InTxZt+DDw7FD2OtHGfq13xHm/d1WKP/WbsQ8gdSipXIozL+n0QtaFuzrWpKmkp+MoKs3Xs76lwTxQGck3whrYCLjInYi9sKXSm1a82jyVXU+WEf7I8HRZS9WytigMkfzv7n7a3dV26xh3UOTNnsyc2T1612uH9DCDADs7oWSyVs8yOizsMpMw+8ym5OuCSgYXbUL/qoQ6VpeHH1rXbxI6c2zX+w1d1fJSygzR6wPJpNJDdErrekPPPbS8jMunj0B3BKMuQ5D5xJBknDVoPY9bWsJVVGRZ0SuPs9Woy5cYhg+DVjoio9yZqxIYTi0WxzrowdyMrcBfF+fw331Ha59g7VRPkWSWrEiHgbF7VBE6IIDKPr8d6MquRbeahAbJDbdzdjY83MgoN3doekSuPPgyavQEOfb/bM0QP1Z1hnvNcSXUnyLyK+lwMEPv0SArcUBjpHjT1iZtp2DRO+FgwuLLGbURRSP9gbrCCLndQhTg+JAmAAz92WcFIfQ+oxo7yYc91KYMHNukY+nlhMYxcXQRxfCi6IRrF9snwXbx9udntm6vo68vliS9DFLv6BJw/n7fhHTa12hu8/M3ic8RrAlVBmC84mxscncsOeQaJIdhTTw6QRVzqx+WHLwIyuSPf3DtTT5vFNJkkXO3nqQD1iPb4goaPsncoPx6oUtXNrGwHZj8HySoSBkJFyAdhd5DjtfGEo9r4TXZmakzoWHVfX+5OfBmimMgvdvDH/Si9y6BmgCOrRSdz8RnJUflrEMn1L88ONOjxQ5Uu0WG3FZxjRfCVEOjLki6f3JHB52EWFQYBQtciyoRT8Jla7gUIA4yz45Z45EghhDobayrt57ww52K/vofxydQnK/5xR0r3sKnd3ki6PQxM5WtwRBTf8s/mLdLXIeEpwyvoovZ8Z5zHT685lAdJ3mESHYzmVbv09XrH9zUS9XfgGY++qYAOzEwpxkPDd64COl879eneXTeCdZJ83NgqxlTGq0Y8fkjMCpN8sIMX6z3wDZrMjAtlY2gaCJavCzO+wEHSCcyU2jhFc/GBQwpuo73rvAFWQpXmeZ7fCCI7itg9e6LKFraJTXLG+IojXz0f/fibb392QFbPcCi35oT9Kfo5Z9JJ4whhhA9lPwMdw07XwYgrt5HBpM/spODhwzcnagrYVYrESqnWVwPeKEQYWJ/XtS0PtKjsBhTLmiWwKimZ7fmINa8A5GywMR43Ug02EFAhQDb8iROpzKQo+OFzqR3qpaMQPU2MtBe8Pu9QY6VQ0/QFpR1xQO/AP20a2GS/kGxXtZWFFCJJzofZO5p+UaqdRBAMARXY4vo5aPSP3V/szqKgw44j6FEjVW8mQNcVOAO0WDlmUXTBp1KvZ+Q4pkSTZAFp1GEsn8agP+L4amB4dhQ4e65CVUsZt4TxPvwndjet6WtR+M13LRtusIvqVRUEjDuXLel4WcGVQBMOSMAGfd8FzYowtcSDbj8/+5lSWdzX930+yN6whC7iU+0ccExNykLDwi4r7QteAT68cCDW2e5mAftOKhniOVtAMH5KJMj0o8qsFWpCZ8/dElxdhBgiPj+ivaOPzKAJ5I0x2TSp9bxrGGNDFymxr6czfTUkGi/Kyq1DDQdwedtdFOYGFX27s4NpelBFRTCztMM8MKsI+zivHq0uAw2gzYbMYPc6KhXnnHiVaeALJi+Va06n55kD5PpqKo7PNvB6/aD1JbvizysMsdokdI6Co7ZuxUJ4UZujEpGTHak4zno8beYWHMXJbAI6BGBa9YsJ2aePbDZYPxeMqrQ5w7CfsnP1KFeOd6S1+uB1R8s+WrFMyGDDb2pKaq7dyaCbHc2Tndr4S28fcdAuCDfuqF/34IBKiTLMuK1tZe7+8mVRbDuAD6+H59jikX1NWVnVgPpaWcWAXxc2XqgonPdpB388bd7dStVTsgHf0MSUhCugpmhhWMzf+h1yh0OJnqZesIt+EyUqLK4yThmqID6F2hFcOthfvJKE5WLhA9Urensf72UQjHq1BYVPN1TQyyKrq2KknEV9x0Kx2qcnG5pBuZhA025xdKvqlurM5Zp168fdXQTxmTR+WJcnmATOgGMIeLA32JU0Hj19BDdB5agczT6v6Zx9tKu7ph+z82/OjsjNoNo1hkafw+cdn7OWvxzM8KQFgZ7X2/DAnsLhcsZghbXG3bRRjx58jeFopL5+upCfD4rz9lGllJxI3FXYBz9erznubrQp2PYNGacuX1NoEw6nr5/jwh+LrwUAMeB3L1sYj62pCrCnbNXN+HEvq1Y2lOBccrfBf7h8XJU9vZ7Wt8tgU+tNiDSQ4Fz6fgdsXhjDUfEFcGlxcIpVXw11NHBvdXhNo/jODozlYSnVluUEdNHs59Rxu1TdKKTtY69foL51e+AUA5vygrWe8xeoHzx9+FdVpbw4pskCHEAFBUdUgeEgVuff7JeLFhw/pknGljVZ5cemQZmPMBYb+b0NUptrL5RmmQFduvaR/bHULjJkUC4B3SBkuZxcc1ZwzGzDGD4409V+25e3fAa/I6DpLYiKPuC9rFCM2X+npotH6lZAQDdYQJdQqsa4pDz1Y9hn5QKGAnXAP28xvxl0wkHHjTIMkNodTQofqqzsZNO5asoU/m9fSpZnGGNLF0n/vzB1E6lgQLuN7MQJG/MXph48fQSGRNWrqXSLndtMuim6G0XpXLPzOoD2JRdKMViQQspntahgRurN0ylTzpyVkp/Y4rrGCs0OD+xRDZXlcd5pW9I34Mu40qFdBT2gJnfJEcNL/Oh6VuWhdlbVrJKj6KFKjrC9nRa6sUMCPFxdJUdfkWuMRQNZ+NN//HxOq+crNGwZC2LFT6Z8tyvoEcXZfd/y+YY/m3Lmc/GniXtYVs77tSq2fjXjizTCgLvvSNtxbqpqaxMM76nGikBbU6VFfhTMv9c7arY8JKWyUHjmZPvIyqdc+zUewY+z+8hrhwtxwLyKBns2vm7pD7gJ/Soa9CVMH/xvKO12yZDi1YA83ZycTSc6R1uyrgtuAvJ0d6fLSfys0/+bHbGK6dWdLnyqsjdcIS6E/Wc5tcm++4vdWRTgeV3Q9/iQ6qnA/sYSzs5D6xfKby572tHKxdswZY3BleV15tlQXVNYIvDlg9cdwUznA5WlD4xlPg7kCZhOJD1gxz423CEifMXKGm0zm7UOpis5z6vVdaQs+NB6QzMm1xCrsBtHtTF/BMbtHgsYxhFdw73B/rmeVkOMW8llCJJkrKDAfJim4Hvm1zGCC+ZVs1osnpCs1VceEnkj8deH/ncYhDPp+SaE8abzsW/iZVzipw+bo8OZqgw/w8RiYaoalsHl4w7yUjD+QJujBNkoxBRETnbUynlvoko0uFEbxIHzz6aWp4otogiJ/+b3Gv501jznrLCcOqsqhU7QcgLdlY1XKghLbCjlcxdKlVR5FGJqE1hheg7l4UcCur+wtxA9ptmRcogS0dhdg23ih6pFg4vh2Ad2fqWJOa9RwV8dc+xofeF6g87moj1VDOd02Phf6mbAj2rkE2QqBODwWj7bFVPA27kSn+c9aTl8iOUD106gNBSg4PxhZZNyUl32FLIhP6fm9Xw2l+ySA3cWxdPsmfo2cPCVjjDe8desOB8OpJamqcAROb7DhC9MSidMahysB8hSj1PT5fxrHV7TKKbzMvpzubgqmXEZ+0p/GIMFAm8fsXoecPcdcTjPjKhGLtNEHCbbwp4fYulB/CawOr/IMDYZC78zzNThhLEU55ZhgqePAKuo2f/k0Ol1pHBt1GY6iG/6yGYHQvDImmr4ALjSwpyg6/MaG+KpgwG1ezVfzNcKnqZKVdCotHTv1rsGRkfili8t7ICAHtRT4xdAaLX5gJsoWX2GwxSUABruiGR6N0EFcjnz3tqcpMqi6rePODziX5w70jV7pufnAqiRI3D83fglfvrQfJABLjSs1GhiqYQBPcsYm7ooMLZBh3HFAuWMkYgajIbdw8VRqCHknr64sCOpzftEZcxma9tsP+7pWHfYJ58+N345EOx9moouYKtHl7o1M93Q28c34pFLjTeECb17oNI97FUbGro8GIm6qmdcdd+/Ni8n5LtuQvMVYI3m6l6Cr6N8gyB+6HuVDUEGRwYiPOAF7DlptlTDP5SOESm/gWy0QwB0pAzNG5uwOVNRP/DfrBhDpAsG0scd5BqW4pdL1/GvoFX5Ms7hw4fNmgAkzExSB2Bu4CVrNoVnE2MjFwXF7hgI3LH1CsexLAvB90tg++apyh7PytFHb/zwShlglT1+ZU0RC4pCJi9HGBwZQ4XVBUu2IpKlDnmIOLDkyx47uJvD0VS3TALf9WPg5anCRj9yHTC6HQFMz8SpnvBkToYEM1iMIynSEcVFXJP4suNwIZQ6UeGS2qVhRgHe/7g6UbmZJwHkusX7MtWVDhtXljzP4TNLvA+fPqzldGFpDq8dxaGzyHe41zq+ppHY/2mfT9N9Dg4NMCZOa/lpn6OnD99NaGIB2PbVWgp2WB3+o9Bh5FZ2OBCPSark8WRJjFpuwGykeiXsenEHn3e+zH89EkQLk/ASJ8mo/bisUemBrOpTptflcV/FwOsZooEXlYrBml2NYxswH1gk+3lmq/ZW8zeqx44Aq2dJVE8IL8viJX0ilaK3j1jYDyzPhjQnF8QTOjcCpiWXwS7muzOrh6gDyP+6fOAT3acpUq00g8/KoGtqIBoqWy4x3qEfeDhe9SrYW06OtZ+zjPvtI5YVfNS/IwDn7JjyUAvQNE8gXXO6SpNDWuJypjvAQADBV+E0FgN5Jwv5rwBD+FTN+Bo2j5VYZ6N3GUozYQlUVUufEy9ex6l87CjwEIRM7jfs04DAyWagptHDX6T7DcOnj+BNnjYtq2HVjtM0M3iKUqUURMq+/+Z3RWZqFijigFCh0HFrRPFD1WPCYFvP3MYtPtqxyjG/INcYi0aC9WeiogZCA01kAwTEyvnWD8Knj2CdnjaJivbNyqSJRxeljaVLf13vEJLhLotnnVqjE3/8jiGFT9UuEIbFmsOfkwX1vZfVL/Dr2YzPWhR0ehkJuohPbbLAjNtct5L1bm8f3yTI+ADxLrl9YVQJhzjmkUR7aH20gC5AjAFfFHTaUTfqMV6l8yZcR+v/dzB9s+UrI8IXt3yGvCPY72ECFQcD9THgaZ14YUYUcAsFdB9DvFy67GJmzcsBvj7GCm2k5TDCHAAfYu/I2PZopSr7KS1zAfHzE1/xUA1wkObhsdANSN+l5eqMgF/OSv5SuC0KLwUM/lPj/fkASc8WP20UWqPJELUFs1LXtUg8D0z3HScs05DeCXyxCgb7eVcTRg/VqbKBNmb1nuxt1tXQ1TPcsSGOwoovh1ldwY8oldA02UayxzItm+IxQfgmEAg/E8V+OjzS28anjWmrA59xpQYd+VAQJBJ/3W2/i/U4aZiX8siCA/Aw83Zw8dPHGorC7Wb1znmuIKa77fE2BiGTHUqRt05PG7xUsaqnbDCs3ZAfCxUkf11fbozl+ggVi54VeG6dJ441UqvCQD33XcoO4+cpBjR+zCZtua+xQbwrV1K7r2F6CsPrOpEvt6ieGlCqH2suFDM9pORHCr8nz9xBwmMOCwNylJ/CgKPfWUTxU/UvbIQvQ9UdpTHj6Onem/AeRKr6hu31MIAmSE18iIElLJjlxnx8Exv2IcOt4veiLCbgujU+o9fPUobw6cMGn+DnhSNHcbI6F1Kz9DzcGuPQSPZ/HeA7QF6d41o5FxcvJ7PY3z7i1Ccf9u+IrzpiELEzm6vVZoUTnFl+foYqXW3BF49eFykdpUV1XLhHdSqnmb+hMpBIvPSVmdfDv95iqEgA/yit+RAw2aszTaQb+brMDo3S82FPm5jGRP1VWsn5jyb5hNpl4PN+WcAfjvX19VzqvNlQXjGik9i8STJvfU/5rDZmC+6ldykfkfx7mRf8qSrpZ6apYqjGfhQyL/FTJgF2HrVJL0YEB9xmo3FcZSaWWvxcwi1lAi4FUrE8bkWdKj5OtWjGdRgf9inT5w2Wg1VmB/cQVvW+wP6zRyDlPk2W71WTVdm8Iq0oYaTuB8rvjhQ2D0WpWBmuoaV6BU5nEozyo0sB6tpTBfJVxFAVCON3a7/oijXKLxL3fc3jDhQOqRekK1WR/JNMbQUKw6fqS9ngKnKzqp2JJ1lVPh6siZFKFFjcAAD/mIWrFQJHgRT9bGJNRN7C0JzP2l8G964hftq8Pljxduj94O4lRYWCUWC47f0Cqqpy2dTwjzSipeemqb1xAMantjt05GSdT1aHelKC1ZIJQJz5jOSkfZahFqahuuyr9js0FO9N1BJn0DtkI33YjEWmI20lePMdMN3B44TpvGK4rqsZXiuK20Z5BgF831FsgpeCDeXJPfN7zZr67W18vJFR4GhHQw1vI9UTZ7CQRMnJnHG9Zs4G6kqw8Tvaqg3N8LGwBOcq9dVX7cuyxgsVRT3uOFVW30jwvWNNNiLlvQJV4VPSsINanFlUGMvBMgplU3n0LKZbQWhrQzazR7jU/pKjN6z8lW0Fm9q4hYlMPkF7HQn7J009XThS+FSFOOMgkusieco/mDvcqKfnUOex5gBKUOFp7DprnvgdSD87cJznMFWKUPFyQy8HEoMD+fbxjXrmO9jXc109PKmGBmfuta52+oCNcsF+5CWCn3eYzyIoBPfnmkv2KaJEz9RXF6TRajQLszDxnsr18qBdDNWikOAdInip4yAOllUJn5NCJiDU2zMwi7Gdi4IKO0J8zjVVw5Sh6SU24SsN6SUxA/ev9atA0xc71bAC+9iqst9g76rE2Ci6EYijGwCMq+monvc8YRdXP3OGkqT1RPKyrwHtKSf6KuuonAiGux6rXThMcLuS41yVypeBduQDeaIdX/DkqInc9fPOPBgJT5FO5Yt8LxtB9zKoKclgooB8M+zAsOqRkAUFl+eOVfUiW5f4iJakHORrK1YVPlVjyUFKmtUp0pb2GZif2JxEwa0NnbdcVUddP/JIzWSCkxNa3j7iBIhAAtrBQhy6QZDFqSI49+sOT84nePuIk1x8drIjZ9iDAyo5qRRfil4EiyaUEKlAPnp4nYe4uiflUI4RxJ3U2AnQpVPNW3Bz4I2bdegpwPlkgN/opDtav3m6k+qxEtN+mh3Ak+ExCU9BIMHXqV4/gr4xUWONgYUbujk4/ocIR4gQfeOzAUi7mE+tNbAs0y4P4RMowTUsyg21uRDxdaTgSWPqikNUk+ZK7hlJ0nsYRvWltNcj9q54/LQYwGArrSkNbJxJuUBRKMHXmu+A7gsD6SoVQlsRTupIWUzY8y2xr/DDv3dLiCSwXLj0ai9obmj1hAifqjtxO+lCbHrbhAsWz3RJQAzqo/jqDqbuUXJ1v4S3tYHDDCcnMKFruq6fBOZT+DsoNFNWRw9s4bFW6WJL4UOGhAZ8MO7jabGcAuuvukVXAgkljSCC9GrI1LdzT2sXTi8wVOc3lX0UOj7fKL4ekvQ1Z7WtODqIty41VQI1zvMDRYFC/XoipLMcqimCux+Hwu/N3N9HSN4j2LChZMLVWtS0IqVzLmdwcviO+gsGcY6v2sxd7wmPbTGoCjQmoeDo17uFD9XUdMBB8KN4EUpPSV2dHWsYmbcoaLQBmboQlNCUFqYeSWRssAPJ1XHQzc9wEesO+Y/VpfZ5dF447LIpcGoJH9L7Qpr9zFcrA08VDOTq15MMK94Ot6ybPM4hpHcO6Ze3jl8jCpe8HkbzVkk5fGmmsi4oHMuRriG1virjruoO7dQTMVTPi691rsYEOPrsovjxjabqix47ms2czOtIqvE/RTCewcbHOxmF7HagZg8dqxsJzOOx1JRhpVZmnP3Ilw+mX3Yc7klTpg1O16iSWDonFUnnCySP4GS+jqo8//+0JutUfWz1GHlKWQKq7/ECuPBysburoKkYldQx248HVnZcmaKuJBgIbhtQiyuTqldPweayAzxFCwrygi1RZN2XVTeAZlfjo/aHA1UA5QWOsbKCLqFm6UuCO8TJLwqV+swUwKVj9e/NlPzfPr7JbvEVrT2VgAf/sqaZZLahLasS8ItdjO2cH89+XXv27YgSRWArs0l5ZLHHqTmlkdoR2J07APzC6Ehy7swbR2yHG7ne0OWbMX+MAsYblCHPpqnICT/OWTSx4TyuWdyRHOOj/j31sjxr7AYOTkv1acxVL/v1bEaHLUgJeP0G+2dNMdZkPUYm5xedGpYa8U3/XG6IzrjqgDr+wiy3KjWB4FGmOMyP9NWEl5OFXYFU1dqsKmDBKU/iqHkNOQyCNoGgeoeAe7tyvKtKcfAP213pGT5Vv24KUezjyksLf6sgq8vsYrIWhY1fT4b0TprE+9TqADAFmrG24TKBEbTxDuadoPPjZrVwrgl+lne3czHWxAz3Toe3NApov5iG62q3ambV5zmKpqmDlGYFAKOocKD17rAt3mY9bYADbgFI0Rx41VyOS/r2THaAWl/P//PjL9ScJztinFP06GBEw/DL5EC0OQwewP5wDvF38Zod+oanY1Df4DRcbqb9nMKNgF6U9+TrHjv4m8fT1PII2y0IWMlN0xpcGsQMfV73qsLhRw+eiqSlpJ/jqMGyq/NSGJFzow2XdeaMLdPNmD8jZT7XS/r75ilV58ocWuszS9ZBP2YZJq4aHcrLfj3Dr3fkp70kXTMs7TS1g90/Z2VCS8ri4d7Fjmz2Hdn/+chIKqSzdYu+HHgy06pD9ex2bIijVIANLY9cDVftovB6xzWPec6izvphQM7XfPeUAn41u6oFrLjf9iaAKsAYU3scSTM+st4QPveiCOoaRUtG43iwQ3iaksGjkKEfdbiDb5kNaC3okpcK3uZ1Cr95qo7sTE6ibFYt/jiVAeNCrxhKRcG6DfF9514+bYoDgBnnd81u8zp6W2Kav/G+f7432Np8E1gcxRS1XMeod9PL8OnDtybicDgN4JRvk4pCqatRRfDanu3ZEZ3x1Fy1gchwsE39XWGC1wUOgjaB+LtBJHLlFnUEKw2U9lwiUV/RtzCpw5dnrgtSj7nGbgPtrvgzHMO6IPFT9dyv5/JZILxVEoInLcRSQRSIvUP7L4wupQxzMKef/pj7O8bqZvDVu8TeIsgF2BFocBRT1eIzzasIZGVZlzj64Ourr8u8jhZJBkwvhSUWE+8HfK9kXl/9DaTLl2uNXaFADXU76zgO+znuwLnaCHkpd4Gq8IthNmRyEHvb8vRW7l7n8dNHIDWrWx7YGYcHm8srVz1nFFD3lekNR88F8upkdXJkpda1UW8QA4kirz7w35HA60ktqtc+raTF9oygXgctkM59YebVEJLP1NRSF4DlaFpXeAwh1DAdJmB2L99e19mrxKzm1Lp+DqxUxYQiYhegwjsBAaRzmNev4CnmHvDL1wmMn6qTBqA8bzj9CFzDVBGXa7VDKxxkLNzg5ecjyTyUIvhM4gR7xFEYrBmXztyoUxnU6Wz7Ne+BWg6m2ZBW54pBanRk03FkeODL0hBIDmJfgXi0A5s6X/0ZL1RwLgPQeodAZiuiZg1szU7YuBTA+KHaiffGZeUBwtufC7x4kD+G8FG85PUiW1+swvpN6rtSVFiz2Cn2mojFWKCJrIxxwSpWzZUOxK0N3SBcqqtWPYdMp7XemXXIQof6pU+NN3SL6pyTXpkNZ5ktLHnNq0oPZoL1mxbY5QuqHC/KQPHzeu5dJkh+s6qtafmlRVrE2uXw6SMQrJ6SHguwkulVwC2tqOVCoGAG+tanzpa0jTj+TRO0WvtFaIueqtQ2Y6FIHphSAvtyllVq+3Vp46UKco/2lHJ93UvVcrEBfFmpI3AO6r0U5nj4e//Jghlm510taqqQjn5XqYQPVYwOsEyQwpg0vvYxrmL0rwsbLlSU2nMHkqZpkXn0ltRzCZDsyjAOH6ohBFh5PTXGFYZvrDCS551DdxtFnTYUgbj7qDIkOh1KgYn5pTB3imQGMfZg318mIi4bV0+mygwE/RznKpWrXMuNIAbs/daitTJAG2XKlcGaXHPxwofk6Hi/WtOSkHOFcTUS/JW7x1w8kq03qJQuX+PyHUAP5Vw9tOBkutxZmIPi8LsdNMmjQ2oIBhudmujuaV2NDUZHARyfPr0YKfSkKvVLAeTpSX0h+lE1ZzvWpn1p686RANzli5gd5umCpSh3G4noofqEZEoT6hMNiJVtb32TGNu4IKvntsw/nkjmK82rn1U+bcQnDgBc8poeGIaXfGV6h0j5VQpSEX/HqThl+/D+5bwSxT3pMlCOXuWYvglW8Rau5aUnA/OteK+feeLb6z3ljV8pheob4QBnVefoRgVLFDiSPnxqvMG6uGKBGiWnshI3GXjOPUlEiLJjfHFhNRRyFbunTVOGCbCaKv41UD91fwzkR1ffuzMxXhi93NmJ1tKlivUOV8dU13iExiDKutrBYx3C+rRhPgNWABs2G2e+pNWrJzhcAb99NVHJvWuqH4Kr72ddaTM9a7xtlH3jXc3XA0CuWCIRil3Kpkkr+H+Wlhgsqa8YvM5tfDF29bs7izWgZFuHwcSPt484MOmLtzu6LDhSp1oYgEaXtkrlZkmSsyNp3pdGdzT6KGyvkwkLNZiO1XdP/0rHdzTKuroDVD8dCV0So8HsLdGSpeH1ax7HF+knlnKieNbrlsW/pErzzzxmxfIqsKHlTphykjOCO33Hv9k6hiuE/xL5A1u5FLLwoUZJzJmJNSl5Fbqvq8/MV8YYU8AoWv5yDpCrdK4+eTiJpp0c7KmkPh5h5MUXRje0p+CAWKDOOizMiEVcZVjurYmvQZT08mqDD5/DqMlWxstUUaxJHKyeo0FoI+A8n/j8p4Mk/IugPENi26PSX2E9sMdvH1FeQXBt9lQpfvX1qlKsaqrMnwPeV3VkDEmjDzxfjlG5HJrcurBDwkz6PG6B4GWYWOBz7g0ZQK5UrEZH5KNtrKjE6GKwUXQjkJZfviIuEFe7XoCT80pdPUYxTxZGnwPg/voOeyKTeghhf029s8T9Ui3XIoyd+prUju4Kgx3aiIxw6CbzEZ+BYYwNXZSvsaHMyUOcT5vPNDg+xX7M2th1T6N77WP+HVE+T8lRe4+KbTKVfahzxJXy7YdefOXnwgiwCLaFdRzN7gJ70paru0L8lPJiZit5DhKFgwWsOjWPw1UdYyHRz5f9RYL6cStTP17GOFpjI5tzKl424dfE9qcmLDMn5ODSHodCL0F87VUFz1NyyM15MDnbXpJNLqvMKZL2fOXnXr6ZrQIMmzNWNpc1LlnLFz59+IGop0UVifCHLerBkQXGhKLgZBC3us5f596b5V31JEDx7AGo8xc/1UCJCWvPBamZGc5j5Wh66DVGo1Hgd4eE58ksqiZPsC2nYBPod1P36lDc82SZ1zPBXTIulezgRoG624zEuvQN3zT61P11COhCPaW4YtNZjsasUP6Fq/mSm5zhAsNXQ3u+TLz6f8E4Wz+vQimhCihHQV1fVb4736RqVWBs5b3mthuSWK1vwqcah9AyK6TN2nKa+ikG7BDjmOm6oaLXO5BURhqIS+gUxmTmyWq89EeIIUYAUa7Qy7jPVVhU4s5O12khePaA1t0MpNRAkXm9A4SvUV19tWpjSTjPJK6z6G8Y0vA1rQ12z6WRagyVOSJbmJXeQi4sFL192vl6Bp+H5lSDBeCZDqVLH32oqXBIiwNWt2EFXZah9pE4GbOVJfebHP4Rx0wDVrKh0s7TWlZ7KIClqY4yGfsmSxcJq4E28/I1dokuF5CJ+s3mctmApnGKvkUx+4AYb6jiZfI2++2cJqYBheTWVx+mr9YxNnhRusaO/m6Ow3/ajCuAO07wBWA+5qgyJ+Hl8anT64baI7pqpNHg1Va2B4DqZZAj6dwlxrcCDccp+bHOfCUSHpeIGj9Vp32garKJSuLVz6yBRB5sjWFooFlvCIG7SsvqlQJAUFbPtnKMOyHdE1d9XWYH/nOAnrJIcULZTwk/ZoxiXFE2N7DkwsKXFWiXhatQG1ilnHOx8Lw63kSqVsDaN+gHLo3kG55wYN2aHHJyCAVHQ/ehruDTztebBLg0QxIqtjdhySeTQhguNTMSWB2XlGzoJORyNNWIHSrGNY52GrD+iGl7wOlebaXmYym10ci4j70s3AmnKyQQ6ZY+9tqRQOU5BL4hu0aDocshnIfdqo8YHQboa0eVJ/vdDlMjCxPV2ax8NdL46ppjVxvFxW6NrRULIOBUN81jAZy/i8njp6RxjAbhFAwTx0Y9jKH77C6ga5EgdytEuZnGB2ik6fKVIw6vGxw/ffhS0FN62eyVb2c9l1qbkogi3c2Xju4Ekx/O4vE/j+83mY5iUbiDTVqSTCCwLXveGNU86ZOKEpgjXXBDKblLKlUGWODLTLRlCeeRVTIUCkc+CX01jc+XM1Y7jdo0Y7zxanf15Am0QV/92LB+Lh1SuzJCnkV74LxyUqZtFP7y6dPrV+QAaoLRbum0MwX3ecjEdBt5wa9myUwMAmqiVpBcH+SM75B5PdlgNdQALWpl7VrG6Xz7+Ebi8mWGlx2dy9iI85NNcpzaswGzJ5kyCoAFDO+2MrUpkgAwpYocso9rj+On3OODzaKZiHXiDyeaCttib+vjrYxyY1/fYv+wPW2UfG1n4pSigwNtW1JX6ahIJjicLyfSe9juaSO8JhYTC8t2I6d1AviI8UNAQHckOw0s52nixWmST8tKVHQ2Pt7IKK/xdUnQ38inzbqHtew2Dxh3oRAOvn18UyHjb/ytR4OV6vAbTzUwBc5y6dHhU/ViH0lyKJgG2CXd79MnySHpDdTrDSV3rmx1NSSB99W84gLTuGYVBFprIHPtSCmq+PjDivlOFm7muvqWeWczPmxBgt6eZNkvvFzJsqVYESJ+zClPSxXyY0w+i39d7PBvwtMmZtdpc4moaphDefuIS4yCi7MByriylZou9MrPt59PXE5NAI3iEYHMdcdbAYX10adYR+3zHj0XPlRHHHxQmcqRBFGq1hbR51AxJ4qisxtW0GW+6gtBXbktQAAzXa66IVdLD5jyyzFDT1dbfSHgSKcqSNJp7Yw+vlHSXR1uQ8+UxuyLYSl3Gd6drReVtOhZntCSRDmOO4IinuPnBnMuqdW/8efY9TW/LZRCfKHh9aQ215o8beozXEXhixxm3mXtomqZwPhsCNq48uRqHQCwnyXiwm+o9DSSggM1c0NWlif+KTCHPcIOUuU7OHJM6ac+QPSlwg1VA652qrL3BM+2tNOaxopfhmqwr7VuaD7jqpOqC8SlrNZLlV2rsMJSfQM1OFAz79B/MwiaWdSjzlCp3WQufMig1+TXbfzmHCeSxxq/6dqe2JhEeYQbdF9XOlDrLfjcvrzCvAa4hfFEX2nY0NnANSZPm4jbOOzutEMFe1jr1UbXrwdyjc+FE8DRzLqZ+zM61IiChRPChwT6B3eY7RxJF1tja0eTLB0lMxYn3eTCLa0rXGlNhZVsxmNOATen8o68fXyj9/tS3IYT6Aob6n6UcNf7WFlgeUHpMODpCyE7st8du6sGSOxilCxgBzo8hFRD9+zz+Ndrf5ioPgYRc+3sNtc1QsNFsDEijQK11/qlnJT83EmC7B3YA2utX/yUVpDtsip79JPRJiqIdoVd6xhbOzdh6tazQFOkWFV6QtLyOcctm4dPH4F+/zQdvPNlu+nmbBup7o2Bnh7p/XdYpCszB9swZUZwcC9B5pun6rHLjCq2LgJ0qazYsgV0VYZQN4jCKK9bGd8YP20gKUy3aZBGlpqS2cKyL992v1566yv46jE0CwBYtT3DC6Zx50C7MR1X8X9dc/MP1fMBb0xtefAuwN5gw7Ix9pxIizoRB38OzNst3y4K6rxafevqGqofAOCGN+GPJ62nIGkQ1HZVkA0+xOW86q1R0ywLluAyH6tHYhQw8TnyhtihG15Q+6MTHJrlADhRoCLtTiP3Ik5BNGIDUHCFF9XODxzU1Xm9m8j09vFNzM4Xal5PAPDcKr1we6eOODQ0Gv+55qhGMkjAkjfUX7ji6eqxwbaAh7YeZ0N9cMKIky+23jl4SacLtzM1FQk0il4rBy98SkcMv14L8QG9PRjpUJsS10EHDjdK2HutPMT1FE8bWclG00NNN3H6ZP6CusjIsdyb++M5TL5stSrok43a4WaB8y6QECnpgcy1IQPKY2zqzpQ5YrYKRh+W5fURxxMDhve5vT9uc+qpGsqPYYQOhha7d+KEqJ1ugK59DWRHSMTThLjBmfV52vjDBqI05QdGOqarIW1ooOeqLqogxWeMoZy6BtMhQxyJXIFKsyPD0lNdVMNXGNxQTV5ajaJCFcnXaO6g3CEoX+9EoorTfWUXxU/VxJtEl16/MWaZ1EXKZ1AxIwqCeHfIoZdTDLLXU60Gev2MOYRPHzbTOqdqs8dIzQ42izT77Nnt2BRHCV0bBDeXlKtRB5a35Llkg9Y0WCYK5wQk/vUyZsdqKEsw4QTi6xBnp5Q1NTfEDj6FfzmN1hVdVAPJTmRZYTau/3mNSXZlzECkedUFe772aYPlesJ118+TxbzMBweVaa5r3uHgPDCvIn/cmZQF5kGhTo0MiiRMH/t/KoG6oI0NKQ1AMaXyajAZP6V9oQI1MhMS4eb52UXpix59j/l4oB3uoEneeef1oPydeF6tMxks47jyxFz6FGDrV9usuWxSFRgM3FnPJqYKKAkwCpK41PP1q+vRIF5dtjssd+Sg99XlOdRXfdp0nT4QjDXKcvkJcuQ7dzZ+qi42FDwonuBDUqtS8n2nEjuJKMJ9izA/nETnSy0qTz/YSEsyWx/YU0kwkfzmSzO3BoOHliEL7r1UFo5zXxJM9PARfN7TFBXARUpbFGDwfYrpLL4uE4mDr6fduUrBqk+HX21KdoPZPI2mhcpWoCy8nrLjLwkXkOYPMKla3ticbP5qS0gbCS50WESdrRFT/0ba2tCExeVCaiLCzv959Swtx6mRAGEIwudOO3RKTytQoXXLo1lbAZbowc+IZgbykS8tvNjCwQUCT5ub1UsGz10BfPx/GnMUlC65uGGHTM7h79mG3DG4BnyvEjQX94c4PlLVXy7D9Yiu0jlyBijIXA44sa4+AxFkdWnxLXCcHKpGQwcfbfoUXHm+k2bDp49AyFhl1tZN2wTHPo7VITAStXzd4+XUfJeGrwLcBJCoqm6O6BPxiHSZgLZvSCx3ebjqCzNIWlXPRFDeLJ4bCgs+b385H8th4argq/3s663zAKy6cl5cVSFg7Xvy2b4ceKWzAUIcSZIenGpa+lCAWQNOtyEdxuW4apUAG3GssYE9tdUsM1LOA068w795TEhV4K2lqaa5FiMXvA+kQZ84bZCwXJ6rIs3BNOJihwrYuZ5XkaYnHPms+A6k/3zKG/w9mBvT2eAQOMrrrKvDzldkHSPlKPK+gQK7h54bjAUcLEGxn+PM9isrx2fGPq/bkVQ5bR1G1WA5LK4kNhhBKodMoeMosrlgdFw04pYa3CC11lMTVecS0XBMPuethk8fwYs8rSN7x+ewHJ2GiBbEMEJYuOS/+J0xNqw8D7e/rEJ5bMOlsIUPH9YaE76CR5NyQqdBtoQxb13DdYqy5HdUuX7l4ipdaYfl6FL9AeYxAxgo+z5xv/kbvgk/FLyw6IKC3qTrdsRPH8EePm3QSAe2sL0CRoD/UlVIUA4UbPmdCDPkxOAgupwsjlu/E2HCpxrG3uDQyCfy8ghKB3Q2Pd7FKEP5MoCZYV18cmO7QgUpqeAuAxg/xQueVOxO5qRxSkzB+VZGr6tshUqVnxS3JaPXlVtUpg5TOLlULNvvIBiSWwJlNZBnNsTRXTL0tPFynWxDn1jgZTSzNCgY8bnThuIu7zI8bZoRoNeZZc9stqsuSVRS5V+eDVEkl4yr0QmcFidmceuBENoUSY9CDz55v8PoP50j1PA/h1k1MsWJrdMKupc7vq1RDvAtIpy6BkDiXZX8GefhsoPx00ewl08b/DTY+0XaFBbuVJwrKgryt36HUJ6xPmyDpHRXvJQ6orkEPmbkkbB+t0oYU7G2I61uijgal5IQPtQ43QrjxyYvzCpNNhLjGWx9vJVRguNtqH866ahw9BiPkTU+SLX1q9XOF/gaw9Eo7HmDrB8PtfclXXUiwE096ReoY/SpA+hLrJEAvCOT6IvgokSigvVsxj8bMI8EjZB/uvrM6yq0J+eqyUQ72rHuNJM7V6JipJ778u+9uUcz3wrSd5hiUBnQuTc3fPpwN+tpoq01H6km5rKrkdHuWPz19fOXowyuUKoWDgMn79A0lXwNK4nUc19X3QAP3OOkTEX4COOSrOZmQ2g7ZgGzC9SPDe7X0wrUfgB4dpzyshW2Wxg/ks4DbeHVJie+D3va0LtR2TlTUSFcLaVIRLVovs/boXF4apB6nLA5aFdaS8N3FBCN4oe+eLQh3d0TdFf/C+BCwiheHFyKLqE3ijz4AvCGGIgr6a7idLIrBTXgxE7JVYFCHSjAG3J5XUV3lbYmXBJVw+PsjvPO+XM1al8B3pFIZDFSvNkbvf/ZOQ/y7RkAmxioRImhL0fTPatGIwj8DmZ5KK8Ah7eJI0X6pS9vbcj2dFVxFY522jJp8+C96byS/lyNP1DR7/VL1ap+T6xus3dIDLBdCxg+fQSSKaVULiHfRZ/I0TTqvBfp/J7EukGpdOnu00bMDSY9yF+wFll2MCgk8Nnx60bG9xdPG9KH7a1pmTvsnkShqNww8C8b4iGOpqaiszaMjFp70SwEHQYRXQXuTjZpbaWTMLfxTekkxyUUxU81TJeRe8I65pfgAkgocg1PbEiizMbXe8T4coEaTDROg5IilPux0taiKE4gL2y4wq5mpeJl7FSpStDFr/fjKl52oySBxnUH1OHTDQNQlrJ9BGoZd0A9fKqu6qzVtkIyWDJ4wjpWF5sv/DMmlFH8/fWgtX9bnzblbx6zGlQg+lyoKqxH8y/3zdMBNPgKMPDpsMU6bPLTIurhU64gFRDwMPzlcb4bcFRKgqeAxIpGJMDuuCcesOc9yWSNlQKftMgyrhF7vgznE4E7KleYqWBibj5Ws5Ur4hA/pNYBe9YHu8nTuDTwyiZL41mg2KJEaXA7KJ0jHCipsiZ2/zMDDvw9VAQXMb1AaNgRFvY+UYmzFErYdiqdNtVohQ0jGOZy0R2W0OFGqlHn/AMbVD849kpbHIv9PpfaEHZwV0TFNanT3RoC5Ty4Kz/MJcs+jt2wwy6qetq8tZmYYWp3kp3nBbb8hFoXgu2w0p41fto4x0mrNoy5FVBQVaIHRV+B9b4lrdwsZzKTd8mT5XnXtsZPH4G4pgpwLBoHyTBWAgCTxIkDHTMS4zYoqp58xRdkOgIHXtuLw/Qc55Uj66uFvtx1B/5/PP7MXxLVLzO0Sfh0spzsoJLz8Y1e6EnBL6uqrrixqm/7sEgJW91SaleZra8WBlrIhuReVzpQeSE8TZO2UVKZ857P60khgdLwuqrqfd4qbQWNsjxTLAjFdpWwRmKSK9XcJgao4rCtxHe2mAdTAW/CHj59BMR8Ve/hOhUtSAMxOc3ZhlKNT+Q3iEYuMV/le7j6RiDZ96IlNbaLpIaAyN/lcT/vWVls1pbxiDot9nko/clDYDGiitKldqQ/OeT3aT3dOzjnwjEAAKqSigI6LlXekADqMktV0AOB5yx2UdiT4e0jFoR9Hvp6o6JCqpQIpnD4Mxy2ps+7HC8mbVGM9vUb4sMBzcBNTDs3Hbcz0UrSkF+WFqGHDQX+LjFXfWseZSwNqGZm39pVjbQ4n8hvANIuaSOZa3wTjoWzmlomqV9Tu1wxJCB5G8JLHiJ92mgpvJKgfuOtLApj+ollLn7dAfM9QqT8WXCM1tRBsZWV6x6g/4A+vSyau4RSyZ+cxDoVCyyWJ7jkcZ/e+QR0Qw29tyAqr7FDppSonsYK8IcSg0+fbjnmOPqa/zemakDOco8JjJ8+bO7fCTpCU0zhu2SQHnNxnuuLXVmQabHBxLiUd1UIs4hHJoZzk64CYVcqDBjynRhTlTREodYimQBxgEpXZkz4lBmCnWE/zrKl+IZNSlk1rp7QFQtXfqbhlkIWz11ojiYILZNGLRzIvH65kah4yXcvd/pYHRp1hmO9+gzAtlzpY9HDh7WRHSDqlisEOgHqnkxTZdkHi5uGNVthBaGU8yhzOsgIvre4n+oDg00pasjW6g0U4qcPa0KJg5foFCyKrzol/8XjFwmSWu8sWk7M5BoNFVpUS9Je+xs+fATr9LQu9BxASeU0k2XUvhK1o8Ruf13v4OtMGsXL6SJaIRyTK/YaPXxY8zos6WkRkJP+RuMq3VUNVylKJnyZyLl86Cqjgj0UMzPbKT7k88+APr3M072PUw0a3HU9lI1DYzFEMyP66dPjDSzOw/KqAsdeWRyCSA9AamH8SMF0sf8OnchbEdWPwppZZz1AKibYqJwrFEB8Ar+hisoja0/rQg7id1JxYUuBo49xJTq5KrpP7jZoge6KqM4avsTOJgs+cPGFsiIJzpeQPlM/s1k4Hk2VCRw0nBeGCZ+q4yzsgdFxeFpQjapekB6/i/laFIHaUOXgWuKnDYKBQ+Rdp6OwVlEa3eCXZwSGe4dW6W2ZOhFgfSy99zytB5sasoUysK+ybpADXVFo1ZKyvkkDtA/gv/OuJXVlLl9EutcwkeKxEiln5bnjPl7TPr95+gjWhHrvYR0U6Rm4a4S2Kur3deBISr/d8E/nN1hFN+wCEw6Yf5JP5cC77jl2uFHK913nxToXrhFT4cQ2juOupIqfPoLr8LSpQ3OuyjLOJscBU8ZiUKHhX587+g8PaCZunt1siuV/3cP4wqdql3WwEuI0yzHABabaZXkkKiRFQbLAnYPCReIeUqi5skyuuHD4UFPVGymjiY8zA/SolaG37/E+RhlxO3iIRzg00BWrLqjFhIkiwxsXCPkE5dVMWl+1WhXhTCUUtmMu+Lwrwj2hOlC5NpBhV7VSwTVAAhOliKoafH+9cmY9oTUQuTbkTriqlVoaJi09PxH3d6zB737ylityvVxJ6toRDcliPxBqe2czIiJGHlYH+XZnQ5alqwup0ouNMYetqkE+iZWRiOnLSDv0LEf3Uy487HipGljCjvHa3kjn8nXCOzMGOy4hcmXxEqutvBj/kaapV6DrY1hNT9MM0advFWMrF6XrbbgariipFN8OfnZoLQDD+rxSfF2J1dcwXzZ+np6mRgQdmNiqZnhXDzVdCQV+X3674dXBpH1eaQAlY5L4G7eQHz99BJdU87s4SMbgEgE/PleXNyp/8C/1jmjh1CWgNMqZzzipSjH3TmZ81KI8rg11BK6j1Yg2GMfBxmcMklP/V1QhSE0OHPONsM5sbJcFaoKhMCRXMOSbp2pYlJL8gY39SAsCusgrhFJRCO91puQfN014wg9MX2avzNOylj/i7OngeL5+jT3dZZWDg92fwio4appcHcnogUzzcssdV9R4Wpv5idcuqzgK266+o1EkJxBBbi2aXeqp11tLRsotgKOXDwkfUswf7+RwdBfYUTDRqYi/JzHEkkGk/b/e0cGXJVUKxElwh84Z6M8YV+t0Vyj0ZcwdapH3gaqm4kw3kruD/CxfymSkw/lK5uuCqicYrFIlkt/DUvKwlEWxwVAH9gWG1zvG+Cuigs1pk+CoC1gppoasBDJcIGR+pnDTEplOdV7zaZiucqVwR081CZKOEPyO4gGuyNT0GtcBxg4tSqPZkHji0g11lsMrNAPSDAimU1Ywypdx2ckOrcjbM9U0A2uRRtKLZL7rVdPs63C+1LoBKriMUkWbJ4uOpvkLONypJvmh3u8y0A19lVyHqyloB5xHs5XCOlWV1YT1D75/vrnmmS23hLEJdZXAx1yOLnz4CHZMBf9sv77UQMpuUwX/vkoYKa2vtz3xVY1V0Yfzv8pYD5wICaqB0BqIIBsyGD3Sq3KlUulhdKKGTUL9iDWQgCTvUGM81qtCkVaatdFkvlUGPrhyiFwW75PkDXKCSy2JtsY7UxpWI5hxtHIo/SSg8T4VfRmrurRDI5RgZ9RuKlPzXPPiotx9n6XsuCIO+b0qSgGxdBXoWVXwE+qEPlm+6VIuxjcqNmLIU3Smkyy6FD7VpLsMoDIZysKSJNy+a9LdVw8de9wo22eDmfbMscag4aYb92VWe2LOzMc39Q++9b4FoyTRvmFTFKCmj7/yn+Kn6lA/+mFJCAT2s1pYyeehMbGMYo0bzqBL3FZNZLLMLh42AFcNXosEG5/n3Tbmp01oXd6mQiogqTMpV4gpMCq3CMUun+fdB3AqGANbkpcyVPvVGOibpw//pGmMkgUgstD0afkzH1FqbXQwN+RPuJBUzXdOeNtjDaWBMRnXcHI/LcCFsHeK+ZgmSPY6VN2Kr1BuvhQ/JSWugG1jMJoBMJLIa+2KuFQ55r5+ntyGNO7CG5QrvQigCwBhm9cMm6+2MbZ1URDv5QQjFzGvWr4jFU1xxw/VwSsWanyA/XpzNN/dasgE1famn1eKhfK3UWay6553EGJP21CtDdwJMwtNym3tUKeYUGrwtZANoocrHqxZaMz7aKbyMW9XuTqRWhOIDa/L5/6aqN4rj8qsVtrBPMYqfQzEhkCt2dCEx4X1qhVp3DONmj96m1mEMyKiPg14PT3BXRJVHJ7U/bIRUewlVc+Pb7i8r9e8jKZd1qFKhw7ftaTcWleaSUSjfJJy35EfD8NweeWqR2MgVjof7tbq4RDqcT4PfTl7woas4f8oTSLBnxmZOwT2+SH0EKD6cyp9Ikr+dbNa79cbx2prwqXVG6S7RWT89BG8iBohJ9wjYnpWKIHcrTTfIH06ePE7za0pgZcTq6regQUEV5pb+PQRnHjeELbRYZ6duvYWdod5+wi1kEjtutH+T+eCw92D+5wWCwaOZx2J8ri9rQ+3MkqYuhO0yqkyGja0X6+AP3NlaIVPH8FWqld4GixLeSMB6aknddMMM7z9rd+gybjKgQpaEvC+Ta9jOGtWObRQCvGVhjsKe3WZPTgtU6uU7obN8VONVmdOH2FmJfXtw5J4/M2PdzNKm9pBiT3qoaly8FvplGMAvBjHNVXOr9NwqcpnuqrBlX5YuFlVo1dBS/xQHa8752qxDoUZE70pkcJjyjHzDSJmLxcTuFdB3eoPanRKVoRJWzckyrD1b86GfHNXHFpVzTDfXRIGkM+qqgnk1kBLui8IFtxWBm575Tkx4ee6IOFTjTzu2dpzVXbsz3U1wvPuTXwPgryaHQ2COuUJxnO5e3QncsQuz4t5W5QycJcDsfuyUV0YtZXKcU9M+Obpwz9raqrP1nbcyQxmjlOw0raD9NXgbG4o6qtMlE9X4ukJmq4mUN7Wh1sZ5a3suCOednWVDU/QMnVDgEfpnwmVnuDqal0bRDeX+mqqAxiCiS+8rJyncXWVc9MbA6q8oSTNPWzqWg8YPgmPYbBBNtS/MMxxDA7nhgiiKwGqdJil3qu1GKftaYRmFJQIJMMNNQWuxKY+VZkFoqKWFQBUgZooSSWQ5DYoHy4k0Hw5BtQNQuhb2tWMM6l9CLEhH8VTsVSdi8PRzX3hAuHma9JdpFoHqtedz5MknBbsYlu96dMt8MdPH8GFUOt/dsBl+UUmXO4W04rTCf37syOGQ2HI8pdIROBWjuOaUvrViMdmOcq+eDlhxhVgVOHX2djAdjLNeQUaAlnTl2s22GpP3yAjmdQVpilViSt8KgIR6UmBHnIT9yYc0Jj0Yxx9WoXJIu7hU812mHg9JokBCWdr37L6jHwFOjFwiWJSO5QtT0hVjeQ4u81SIuwGqb5awfuaoa+7bsiXcXVUviBpp+KctIPk1NcsRl8Z9nXXDdqHuyYqksSnWFd12JNc2TXm7SNWDX3d9baDktcmqw8E/j7bX0fPHr6tU4d4epcuAIolnenq4Ovmsga28d7fPC0IknOZy5NxRsm1v+HTRyACriLsyVIVO1EwH1mhhkhXD0TD9YYZ62qRYPxGT6bCaK6NveE3T8mKG+e12PQIylMZpN3W0GXLIf2NgmYvB5lc/UWFIwdLZrNBHJzDVc0cicK+XPMZo6tK3U4ApNpDUMYrZzB+qkGCzIDgerDA3wjlM3B+sTOLEhvu+/HDEUb+dVQBbIVpaho4NgDsVOcQSpq+6L+hRNeFfJqihQtFTneawl2XaBSk9AcIcQMSdLmR+nNX5nye9vNJbqTurlEups+lNiyhK8GsGmLAESrrnAzDKLp6OkShCVeyeb2bm1WEFIZM3iZtRl5TjKptMe72mNbTf14TCvBChFE8dHXFQXhdcH8TGMSEeU88yr+83M/bFFAVwtU59XETB0yyqvPK4VtQgDiKrQDT9oGw/ihL4ce94b01WuOpYLZzeTMoc1kXmBp21Mz20njlz5kPzoq+WvNgSVcksAfXoq00VWc14/UhF8B5Vr0cWw7n33Zw+/n0SneF1ug2mPEy34Ad6GeKmrCA9tZBIzAZa7FWB+F6vtwYyMUnmkgAS8RLSn/aiGPtNYLU3wDOvJr7RDmUnD1l26yWLwnm637HO0gHmA6rVbVm+kc5frOxp8bqJIbOuXOwYRfpiB8+/P1bYzXxc3wny4U4D02Na8zMBn7Ejwe29VSGbLDbGyibK7Cob1vlCKduTgsLOdQ5JMwm8wWZe/V+3MHc8Ad8PfYWh4pHsq9KPpAaLCrX41hD4yIL6F3wVzveEf/gZSrHVwDZYT/Pu/Lij143egX3eL4u95kMn1Iy6GgIak0IdG9JePCZtYUFbkOa3MHE6D2ZqL64vKr72Y/tMC/PF1FtRRSwCcToWwmiXUpMPCnSogAX2l37GD3UCENmCTMvpLMpdSZTfPrIOUbCUdrbp0X52YxA5+yv4uqZ6TxAOiiJCYL4eMW9J68XVvMbF562wgM9CMf6yoH+clWC4x8d0g2mzlW7VTG/OqxZHxpNrvuIA+mBOv6LqbMQQRpqe1Bg/G9QHD58+B5BSSX9sIasfZL4qm07DyZjBVjJwfE1OPzf+I9PdHJYtT5PjcXUMlx2vcFJ8PDhni71MyG/xLkclfkjp1LYA6jnnsXXSysYjQSKUtEGhdqu2IF7GOMD5lvNX29rtnQWLO60KBqNU749WPj04S/T6vYz58EfZ9yP3JWcG+E9d1FfvxamceKYJJG8VFtdQV5/PSK3wG2gZG1GmuDBCpF+5WKn8ZjUc7HRTXCkx51NFz99+DdAqTj4PN4ANu9ss6olSC/UK0h+Bzlum7oY/n15PQ+H2nFmL/uiipxhUepncCzjc+bvwy8x3lNjaEjHi1EH9kW63EX8VHN+YG7MTcIoYId0/lwxPBa3g6yTX7i2+XnKkqbplMRKrU+uHTx9+BdBTSkHq/gO2sPKLANdhAA4u9fm9aoFP3622nFg27uGjPeszqJx4NwPt73MzFwGpilT+GHi8TthswHUV/VlUO7jErbXiyp8Hv2MZYn+zrjgKeeKjWlqasyc+9otEoPbMeCc66Z0bE+10yzAOmpjmYkG1a3uxVFFXKDyvR4b9/nq8xuFwl8qchC40WyNBniGzKjtqPF29/IZymItWRVoU3kMLN5I3239BhfnEZxnLAQEC0W8iveW2Mjbhd3+TabajxOyzeTCEqemT4TNqXevFccnRL7W8vCwbl0yKYn6bxM0fhjTYGYh/HOyBWwsfjnkgl3fF/sy/3v+ysW76Sipnar1ha+vV77uN08fvrNQX+gJG1iJHGCrp9qLBpDa9ywbaJF3EZ6h9omvkgAvimatAWszfTq+NxtqZrz8AaYVYPHgCVYJDPixGuOEGSV+vsG9fl1hUZyGbPngmRM77/ULnz58pKdEU+aZwQB22gsgfTUl7+/2RybhxMhwZiPGhRsurwuIn7Gs4lsR8pLWjrzaHzTY2d/2+fnxWAv3nD1jBRmvPZgJbZPWcj0XsfRP5YZqFDc9RP0tsChlIabBfdcxC7Jd/GySe/0I/nnA8CZGNWCG8KWu9QufPlwjop748IBHe+sDRpABWjtlPinxLc7r+ZuHzcuYaX3rkyRXVdOexY4tMME944ddXcmxpH38pgoAR5Pv0HpWLA9u8y70CB/y/QZXgYeMmTXwVKNfU1q/SmyxZhalHG/oFUfJriplkDm3uMdKsseBP3BnmCZVmGbGEcFLiverkPzSlQ2Nzty9eX6zlz4K4JmAg7QrfEwm3f8GQme2ybZjNtfMds41uA9h+PQRxJU1+6qBhKwcEHDuw2agxwXVfhz63uSZ1AeYa6TkQpY/rj2OHj6CrRQ6OEajJaYNh11bOCAo4wp2fkMdiovnnt9oLb6vsP6Zo86pGY/Mx/4NycwKOuLMlKmMdazadYvDhwrpwp1MkkyYWaqf7WpY/fXuxHchqvy5bfSPh4y6zuwZhtM6v29jN2SOHgftHVc9nuP67rf7ca9WWkGWD1Yb68Z2jS0vI9jgFPB2TGSCib7iLq5u6etJn/7tp5OlvNdQsIPVJvCzAK1AdZchDrR896XvOsGfDlj2bqh871l6t5+DrK1y+LA4L7jQr/cdYtVJPSx5jm3JKrDwkPt1Njzew4hHbajvcLPO1LqJaojFfU/W0DR1FIhydf0stVu96i1LoTqq2AWMR7uTwsOnj0Cn0vxdHIxrBA6u5Rxq/+F3Cwl0rR3ppF5iq7oongTv3XIZsHCHnFiUqevnwW4wfd5FFf3odIa4qDDZzVj9RxSf9m/1erkCp2851TjRpaundyuXOvnNUyZrcqAlnd8b0+YAw5qiC24SZ5yV6bc+2VOhBcRCmoabUCvLOHX+XJcXu7CoaO/ldEjvODEbkiHsw4KTWBrOKlPKXpTkHCSKf2ZUDevEmgA6LQiYOSr6kobipw+XBz2NbSdq8J08CPhkjV+NKLvLml7tw0DgXNi3tFm9UsEdVTzatdqxGY7I1J3un6q0FY6y0f4xUXW9YPz0EWRVq4dsqbzqZsyI2WVEgiT7IAl7R/aNY0UknY6UeZyGceKFP92sHNfibADNMBVsL2KgObM4oyjy4VLimOJaxSc+xvpxkXVwEfbIVs5hV3HqWkhKUlg6abeDPZU6hdLBZhpjqYG+mnUDqylcx8bJygMC7LiHJcZPHz6G0qi6TP4+DSvB8MxVvh1UdfuQ674azcTQzDQlgyb4fneOS/jwEXDYZ6x8B8yH34E1HJxfcdIDjzJ/A1xAbBWOxBedy0Xcwkb89BFYWjWOndQtVMbZWDJkuCDMX/fLTzbkMHvk5xlmjmDjcXI5MXuyf7ZVQ4dU6TPFSn1XcYzTEvY4EeHOsYqeKomZLc6oXlTmq8O5t5XG/MUfx/41KKTeEDSyzMheiyazwO8tXuQ6ldhJROboviE/bGvrmq1nbOV88YdvxzFhvNcnc+xn/23C0Atp4I6LUNRysDPMyVSiWYtEtSB7zXEnG2rs3CID9R0H7Gq5qsT3rHMVH0SlT35Rwv2GPxyO44een9bVrWHHu7w/MJeGzsXd4fxQ9V1HiUfGu/GHVlrBYNnVqqMMnz4CJ6EpetQjaW3ZnrNwlc2IRP0YXKeyIabgpi9rwgugkS0te+QBBK968qgS3k93/iWfzoqIgcGHFayVAnPwmU/nP3y4t0A5EaxaTZWW+cRNl24bpNm5d2ZDPIvqLFzFkgA6A/951dd9NYixgfPx2S+UPCdJ3p2pXiLd87yHOIZPH74te36je/sYgPp5UV2idcRMBjZ/8W0pTRXRkcnYIp0XJYofqsqkM4MoWyUduHWZYxWafPV4oQuLqs5fN4D/H2tfkB67jvM69yqygv5sy5alPR3tf9oEKauSW0ANyvoH73VHt28cW6JAEATd1twe3ytrF5oj17jaxBcTCBkbBRc7UmHLTXdXy/9Gzntg9nV3tgjPkgyv3chZri48e2yOhVd/mWjStpumJ48cT/NUc0JKxPBT07pD9CQWqBsrni5a2QXYuptjkVZgz2M2ugeONd+VSrkW489zrtU5FTh1QIj+07j+T+r5VBvtjEIvE1qHSbvFQkj3vBHysP9luLGrjlkuzB6Y/tuJMwm3kXNY0Sh89V4TWsPUNUnlJvA0J+LtETEmoFjasUU4PNI+3BlZK6VopnguRGSELYjcCj/B44y8x/IcGJ79kx5riuCdQBhQXVf7IJjL2JcOn3Ax1zgfFq1x9+Hv2XCx2A31OyPKObuA2eDYtd7GltvNROrVRaCnGLpqr/vcwyYSuCzuNWUwJNDW80Ivf1Ptg2rTv/21dhNdzK3Z5Zt9gao1uungRejddGkDIXijKrW6cAAVQsSKIpIFZkv41j50lcvvOdiaUOigt2WTl6tIzJwgt78d09l3nJTyZ8zM1wM5qSqpaS2kOAUALW7JHn8laJNJ095QY7GNskdem5L95aUXEt7RqkafHPvM6Lrnh6Bpvathw1zOwz1aoMvaUzo/HJqBm78ffk5lA01L0vjHBCdsUeL0/BQ+k/mP0OpJK4Uh3v10Lbu9KbsJ8p56p0IudpRxlaxH6lpSReJzfmZCo9H7Y4QI54LFkGuf7Q31ergoAIuHnkE2ExQcJnTIj2yzeq59BLSCh5btisM+syGdAkfLrDnoGQII8pZC34zJgauDYwsnRzTscl0Ef6WjSPS13zngCgRh6+k7Br0AvYjPtqPeYSpBfuWT2Z2u7d/ZJbhoGh39qHJ1HFwfo54z+gyu+9i+5Zk6cVQOLxOc3ehl1TTpyBNvHDAMQwC8SLBmt3D7O/J9TaixVh108KDRqYQGApDJgEUgZNWGzFt7JnDN9IpoH6Tg9lcccGr1S+9Y0xE7U1wpv9hc1znYv2zzJPLwkYKDzOWLCwNQYUyxQqDrlamtdimL6tqiaOtpdRwZQoWj0+nJAnqzgwUXt7yiLNyNAg5kkaRkCGjGzhPFpfZBhkcvSAg1LFvCJeqtWpic8jsvfKDgYnE0WjiLPd/hwm8Hxkd/DqrsYlF3bO4vPQtRG4O72BVDINYNAdK/EAu6OogqnDfSrpqPqEDkbg8CZ8Y761KLi0iucHFick858G0tilUoWvyIKbNKnou9Tl74vhwWjL3vOwM63wePry2cU2q6w6Gi+Qq6oopmSEQUyUBNcHGg6t7mHqz4gCXECBtMWEP1K7xchRp4QmsfbWCJgV0bDJbCenA7unWw6OgU7S7PC3hIYrdti6mwtqN6UxXNdHTmwmPgL2D09Tgifv003SJisGw9ihdLEN/s31k+3FbPHVhIeIuojGl6wJrwbdzW7UY/VA9Hg+HzpiqXWVlYPMMR2/6QFM7fNCDqAKe2wx34MDDMaZAteBGw6Xdg1ouLqIo0raQQtxeuDVDZ6MdJQMnn/qdz5IG5O72U24dLnFIjfgVX1HX9AQ3A/bG7fWBiRxuUYpyYQXc/1/ar93Ndo29JtdPRfqYZyrz3cknzHM9eG6SeV3ZwFdBRJIq8uPKqolRPRC0RyEGn2/Z+GYrI1YWix3DFWnNFnRrPk/rRFV2cFGlO0AfQOntzC3m77rw+AGYaeDbq78KKXtTlnzPtjFGH/6TdX2u+1vj5XmoUerRFOWfgJyiPWAiOhNVOAJSn0PYea13Pnq8yMSEP2EPx+/1YC0S4EzeH120gx9yPF5z/k2XrrFmYQd2PZ2EzIm+6Oo2OESJ3s5JeXXgYa5oQFkkz0Oluxx+8cjpBsm9/pr5sQBuAxPvZey7q6/HU4iJwMcLK+T8MNoFIJvkMnLj7pbExhdGPFb8MmTTZ73NhX9n3jkKivfM+f1IAmeeIFEAvraAoPFTYJYZCQxNgQV/+HDtOMY/bgXwNC96k13ZeXRpgGaYBQ0wKsyuwTxwSDJlI7iYkHbRvJWYTwiHN0ZMhumx3cUwzEE3Eos9lQksQeVNxekuu2O8gQM/13O7DS5ht/lYHokL3jd+m5YzYAVRxAyq1GJvvKjAcivuhnnFvqARCkSJxWRzOLyZcIXn9M0rlQeijxGDTCh6BPUEVo0rfk/rVkuI/DncIU/jVF/CHp9z2f/lOOfRqMJ21rrjCoI6AT3nMNKPaAa0FUOZLj506DBBj8+fDi1BQqQTqY8daH1SVpEwog1rqaoDg8NsN07QMBscD8ogmNyfdzM8JF8KsNKnNx5fLdbeT7wlon67MaZiB59fTGQH7MIZ08XJW+9HwOJGrC48hQbJX22Jwczz8KUanPy1MkYjzgvMlFIsGu4pjunwe6wvOq9WFQ7uwaV0tgEGCfmHAZb9ghQiY4sAZBmPvWUUYK9rWQZHAPm9JNa+34J34OtAUZELRGMVzjI1JveU93VI8do71wVQAYoJ5DdteIbaEw4sBI9v7JaG18eefrOjxzTgBrjBk13QzA/6W3F8qZDFr+oADnxfGeJNozHqG9HiPoQV5z1vMClBtfbyp9HU0vvZWZGl/c3hu/5C9JfzYvnOKmRmYOY06TPaycU5p/VBNfprn0ia4mDWOGl+JxptSfTbbvw8NubxpbgIYpWryFg6xG2BqMOO4cO5Rq9RpVqjPJyg+MHrFgssVtyqAWngr0jxE5xX81p6QTVIo2T5AT8rl+TNl14cjLpX92PY/HOmXiJkfxxg0fqAImT1FL7udm+jxUr1fvCt3vL79iimrR7c4O51xuN+fXF142o3zax/boAlmpNl7sqC+Rdqt/PpFmj7BfIrdE2F9YTdv2ry3p0JZFGQyr1jyW2Wc4K/NPVH/AZtRYtidba0o7NJbWd+y6ji9wOj3Tt9v8Cm8vtcL/skWjzd00d8dcrR7hGGt0T/qqYmhW5S9wrtpy2VM8JarUT+AiTgyIRfYW/i6fYPf2TXJlykjqFHXxWRpx5o9b/Q2pJvm06sLjxVNVgk4XRZS5gOzySD3tiTg+I2rnqh9KW/XPohjeE7r+KxmPPcB8cZVf4+tOCxRdiLU7qPL/4O3l3Qa/MNqr9xftv9h3ZCg3OueirTNQDcOKKuHx84ItF2veTO8JUlRHkru69/nufGeetHdN5ig761vQdNaLmlwE2TkuV31Ll8h3Nk5stcBJ4nIMDjDxvP2xzypvbCSV9/Wq91N9shBU7FHlk+hkpTHBQ4qLm5SkF/QTQTfXLza1e6xPvYD2MdwW1zS5wGy8Dco+H7iL9PFtg+aaP4giO62TxEiEAHgQfhnAt0DQ162xULQuFqWG0oQtO2HKYfgJumGHN/2q/GHvESF0tXp9kIIhjtKL/sePSJiohovaL1KQwjScffcvYPrmI2nV7tTq9OMp4uYUjh5ou5juSKe7jB4WUE5/vz7YBHIbdEGnocqxKNajPY6vcXihvNqcaH7v+kmC3sKy0HKFfkQRiCe9cN5mSBjhCzFKXZnE7NlRkft3N57tNHxQ8GvGV5JBHaG15ld+LhKMKHKTsCw2aNKEgpSJwge0KgAUiI4TYs3Rwh9RfalOFBkfRbqXaBsZ9v27e/79rLN6K8lpXC9snTiHrypFxeuamyySUAEN7jBwLQSqjE4JhyIEr/P7rcWhfSM3i63h899t89p/7vcJ2oJ70d+pIeGOx+Rw1oUi2sL6cMNR/VqN0lPSH1//KKwkBelPxJydAhRtlQT1Cy0C7OF8xtwYrQLrnaBRHOmMpDjTZsTqCrG1zZ3oEHiiV7h+j+QvFdn+qj/FCN3J6Th5MQ1fT5FAQ3nHPMAc0B8+4/bHzOOJyQuufmjscaCLQJORZklpw4IREWB4oTHrWe22wwrwHjP3WMRv/3Dstxc59qc6vqtrv7a/5kpppqznhsKkQd+vMO4JxQPgjql+qqB9fbNuz922zmOi899BandsZ5cXTjV3WTf+YXyJRC339D3UBDOi0/gHyk2abr3zcKvbfvsPBSQwtGb0gWWuU/uE/tndj9051h722CT4Um95i5oEdaj/Dp5WI1kZcemm7fs8dOJwG6wxA7L1TceK1KO+2wrkbba/dK9Q098zn6fydVI0oCTANIcl6auzqT3nL65hN/Tc5cQ1hYPdgDxD585sJTdI2NeOTf/4W30QyD8vXX75srjc41OB7tTrjgbFEVrVCzi5K9uau/N2GDY44Y+9scfY/PJ1YXSjM3Th82vQgt0+IY9CWct1pyRfFw0oErkpttuOOJ0dH+5zQJI6uM6/xTqv8xwXcNbTp86DuIdTUH+UfntpKE9SwVmhGSuYoW6tQI1r9hG4Mdqt2lQM8OF6PVxrx7tHmkxYHbLfj7xAu3Sj3lMalCt6DaZUdEgoCl4W7gHb6FeKD7+75+uk1OINUN6S1LZOBsYPWn/pVwQw679DHBFLk98J4jjNpzFjDYS2HyggTJ3tcMGfckODHNCKBHMsWAjOZ0w4ortDW+QQ6U3mJ7ruqcIfVhdRNkMHiZOGLvJJTRI6xa9YHLGGq+yDbRyk9kbhkTGI6z3nOsPq4tAJd3T0cB+ClRib753Y0o3T4piJmiU2JcM+ZkdmWJRyd7ZmlDB66UBSoXT7z7B+IrCzvahnxb3wlp7/3KxP7fexB+DqfcH3uyZwxwMViJx7e+DgNSri19WNbvNOm5Ui9NRr6dgS4In5TT2uGwANYMFLe9Txt0BS+leL3071vqgKoQzipLfTgtgNbz2QSFPK2d+xA33Ajce6L+00DqnY9LHYllmgK+L8vF+HNGxRpGgRHY8Yf51es8tHHLqUdd4VfZbb2ygVxd+TKNkatsCje8V1lm1RkVXlBP4oR7IBYNaHLKfd2ElnenefHp1Ef36zR2tkJ13gU/1APBP2WKJ5v5R0EUA8Sv1KOku2d57Ty4uQorcPrTNcfTp5DKaCbEnUbL+6w/yPfPN4Ekoqw1aZdtikDNvUDf8/JPyDA5mnn9aN46Eh+QVRVhLIUJWLba6htMEfc8pbUBBkJDEIWRtMYKwiYioQ5w66iP0ZdfEG9zMewcnrzlbcnER1GHTVKNQTOGkbJuzpQAY9jfVP3N00TXt+aJlBzkeJudfzbpqdeFBJBojkt1glspCE5mOY+jjKTNJQ854eziBDkhsR4d7nm2du6SrVxfxPpoWnHFZiCMXy6ABMLybDFMQf58QdAfZb7aDv18RSfI6oItejfMLgxDIFyBk2I9zjAh9l+FoXY0yM+xPiPfvMcQdu70OWW1Pd7rgw2pvfNl3zLjbQDla0pjv1pf3lol/H+ZPU7vK8Y3Xw4kB+/9ToM9f5Su5uAiI3H07zwpCw9tMoA67bRO4lzGH1C++pfN5+xrVqgPn8uVep1YXyqw0pz5Bw9lr9REyBv/vedfEfYXRMBM4A2aY0NwQBwM/7xvWwlFwA9JYhxosPC4gUPTetB8BZGkpgz/1xzvuQRUC7c/g6N/J+Cb9OgpKf5dnmxgQb/gs/Fo5dz+hsEYqaM39cy1FBK9lP7VNt6V7HgXz4KXlthl9JYS3iKIzJk7DTih7F0TAFtFuwlmOwYHvKfIxg0TBNaY11eHLJVcXH5tUMGsFDlz2qexARkxhWZxOy5SR1wSOea2wXSpbmOmgHhgUM0MzGp3wxOXP3vPfbCcRvq1+cR2DTNOrC7/+o6fJ+wMTvq/9w0E6So6NgoXH1kCw4Uhh/GKPCcVGdIMJbpbLLvqYkh3NAHj8I+c/FfuvJ6RYSENZvnZonDAxwJ+OfysNpRn0/n12D39Btqc88AIBDEGBXFx4HTSU6Stw/4UAUuET7cEN33O1D7rjOtvtvYaGjzecTOCpNrRc7EfyqinATPAsO8xcDiAOjEq2kNFNVzk/yWmPCSQuy8pCWr0XpIpeT7kuTDz9p9VLNIcbOArWFJ7+9yZcKIs7iuJLi9AgN92HS5NZh00ldGz26Ojo/Ctz+N4HjX2+ULWmgkIkXpBdobWDdUFK0o89g/xGqD0gW/QZmemMWVpsK8rNpRLOp25U1LSmhfmV5SOluxPbVeKFd2WhJTxuhjZujRT72BGJYnOhkatr4+RqhDtIhUu01hhesYu0X2Uk49cxmsX0CV5UbIuF1tu2I+aHAL4UoOWff5JQ4xtyQhsik9dCdWvxHjdTDX3SccbUVj6ARspxX70kV3y+ctZ0X6XbSM3k6iLuyCZvVC6T8h1nWAHdWhaQYOz/R3b7Peu9+Szq3G3Q4PO3d9r27TzrE6pA16OATJPXcAjERd7ZxYqZLJHUCit5kexOKKmx0hkqagfgZXG+BZdHSSGNk2NfealtQobBoGb0N1tIRgXOgMwJq5p+dTG6lOPSXxDq21kjTOrTdB9uAcbBua0ubckxZYkLgya42dAEu2lfnQtpbsLgHPdLvYISFen4hLfHom/zRiV7TcAlBezeeQ9h5kwkj9XPg7K/Gh80gMtjvaAG8KjC8bi66Oi9OEMQjIFXlsNuCL6IgBfGx+IBWU6pc0Sep0yR7lEStslWPlHXwwdG9QUKrwMjh11T/lu792QE3htLEcXc/dwNbTlNByVokBe8q5NSGhMqGitqOYaFwsXckoY13h697fT1JbbDiw7d/NLC+D4X0qS8vQwC1eLCac9wxN6PDVwfjMgyvJGcuuO+gYwjnWEgl0BLV8SxbJdRyjlyW0oHaX6HG87NIM1Inhj+dimV7PxytmvgCA8loQyiSeVzDQZ36mphg3nUzQuzFzo1wylJumlyY68Jp5ZdD81d/898XeFgnmx3dO5JMFX0MnmlGdFCsMYpQrdXPusgLuTqwlXngQjsleCo2o/tjlkj5im2hWrUn2tuIR9Phn5KXF6YjuloT9wB8q5jV+OUK4NJPtqH3mrOVOAfysVebPbuHMwJ/8uZfdvvT0Bn8zljAF0WGYH2bMemuw2NsUEcoj7WN9B+rvahuTXD+MRjJN7Wvu7pHp8FFIMaUEL9wy+kKe3WrJzSlElXQZ/X5WhlDW1VtDSL4st4fRaIIl7Yldff0DoIDL26iBfVdPtyXkEGbeGzafdDCXWSeK+PBQQ0YwzrM7vI1hSpOXKcSDWEPb5IMJ+y3dxSB91pKC5vtcuCQed7o4ueKcgteB6/Pioyb7oNUhwDQEbcMaBMIQff/pLxD6a6GmazuINyHqLrGYC/CRgoYR1PCqZoz+yzevnAk9djLTFkBDLzy4VvyKwzZq78/JM8PadSZ5QLduRIO5LAEwN9a2/VeH9m+RSCLppRvyWV2ubW3W5Mv6HZEX0jIf0V/t+0rjuB/6HhrenudGD2C93HfmCqYYlQ/vBw+Ji3ZfsrLFENWx4XMPFhp73eVvy0jkA344QMnPIoTdvYgVPZgBNiYx6faJdfCdp3I6wZHg4j1GzPhp61DT04XSov6DQKnicIve3uxh7seBOKC384Eb0kPmVwdkKvOhXZNS3KE6oybDwD4Ql55YmsvdQ/rmzHFkPPztGXDvubO8PVq4ug0tsH6p3LBv2uPiFWc6BsuXE6/ujhvnTCoM1KGD2TMDDWW+RAkkGb5QUNOqpGNzdNAKOYZGNJNUTQSMHW3pXL7hF5NSgqZkKOS6iA5jwFhIJ26XuWuefjxiRMbMOJg/HucjTJXZ66/ITS7brvM73aG6yg1rFTV5CeXmu5eofVuwRSSxqVJ/OENhwq3m661ZCjOrxBsPG4A9F7bFvgP7Kp75nv9/uruaNXxggOn227r3DI9TAiipT0tnvuaUfYz2gbxs7L3utsl/4aDyG6TRlV2p/sxDhwxA27sS7HSgbFhlHwh9V4bZjobThw37w6fIUdKrVC+yetzfzVJfSC/MCryGJe/k3/fG/BQkFT+9A2j2JqQrsRWK26uZZNg6wJrnZ2Y5Y1pyM66BAsojdXlClUPd5zlNLnQ9hLvs7171CrM4fOwg5pDBsFVrkjs16NsobtH0vMvDxrr+cKWzsWsXUMVnnTY1jFyJ7mlLO9PsS+snlI7+Qtp3QpM/Q4x6XfpOlvKJRveNN2JLYU4MI+1V8Vv2XFYWuPWVXBA2z7fX4/rC7uMZDABiQv5RwW4aKBKWO3loxzADsbe+txwSpjL+rJ86uj/tv55Kx60Vx4nDB00zGz4f2zz1PjBuW01vESYXxt6IkaWnYq2BXB9t9Dn0SrHap6oew/Z/Dy5PbqdpQgFnBvAJru9yxeVuPlV93YeUfoo07vb/BkzP4Nd/+IXl28ETMZUoDk/cSm8maGJnak2mHKO2MkHOkKavsoN0MG75I745CrizgBzW8C223g18Fw2618RHiTtln8xIyb7fvZH4ii9kmR/OCTHvfZ5bUAeaHQC2iOkoVJViBlgS3IBXCAyvNle9DNoPmYLi1xeVwxZZl31DZyOTFM8HJTyhhapooKNE8fVIbnpiArLBxEc6vPMu9UhlzF17UsDaaxtTsn3z0QlJbUPCNN7Ke0uFB/CfhOHNh0yaVzIYPpnu3M+137UQwF5L6H2zgEHH2HbUMAqRYX4XoPN3zwdqv7s+3gsnL3rVETBoRL/kiK7Is56LR7pcv04C9+J0VydaFi3/ahz5XnPi7NsJsu9dKaAYvf7VVQWR2RL257b/DKL4s2tbiI99Hcmt32/gluJcG24ez+JtLifaUTGsb9W0OebFdDTP1ACegaIki5uvBKS7g9YbvuoWZJl6W9UakSA9d4YWZcIRWiUnzBVLb+BffR7KJXF3FVNMcjBgP8TdkWsBcY836lg5a4Wl66jK/dW6nCp+lGf17Fxes0dInRrp6s2p/wp8S2YwovQBSMUSLO7WOagFxcvP0HqpI1zBoOu6PCOYZiB40GlBnECDHfToRd9+CykocG5K81SkSUBZUXM7vHJwjUmQ9li0FuiOPZH263m8I/rhwIJ3wrx8v73r2VJuHtg4kIIGACDkOEWetRbikTy9nH8bCd0k9mqRHkLCLcAVqvLoJGbh+ambkwDnHP/qEVrxxb17ZG/WMg/O2oeC/E3/2N7rJ5dNL+PWHXGbiCFI8zc5JohNjQECa4S0gH9mPvEyu4WoinJWPzfW1JzqX8cPVCfbx4yyFAqD2Xz4viM2619H884beTVKgpf/PhPHbqUY7f3Sxur4FS1IyflXn4TxAGUU6iaQ5D9BoEWD1CMYTod/0ZZ/HEjY+R880vlePAXrXth8pBVIaUxJQy+ROcbVhFsmm70Wpfdz+7K6gFmK0rwXkBc2itv5wUAeIOWb/HX3s1uQbhR1MJeduxy3FKsx8T8zfZEWl41Q7odUWx+eiVaa78f5EuQUkZeo8GXLv01vu7ysWFywfDDs3yb8xGxAfGmYjhQkgAsqWaPjzR3l443fA/pD/bcWKy8w+kOAa5/Avu9boLCR9Ww60o24HY9x+Msj7h95i7XdG7EcU/ZSyh5pk8zscZZRsiYQtgQNXIxy1hqbdGmNXeKME7Id5R0N4clOC3oCJ6eDGiy/aUwZwA+b/oPr8S7AjirTpy2sZlqxYXzlpEo+mFIX8VO8+2lCUT/pYEO045jpdLW3aIhFw7xqg6bXSbtInFiMQobCHFP22rGVaNbjWK7zVeFy4BE+wmiOSxaX/gC92lbpRpMQ6EXNxkQiE54SZjpb7mlGhCs6x/LUvJz+seY8H8T2hhcAJIppLfplqZBVuBfXrgn9o9pYPv3V+x1/clBIY3w+PuqkDSdlwMzJ9BNSoxDgWnT/NHbq3cfMKSoVG0MCJkn5YY+9UpBzUJK+bnKJmnYk07wlzxZ6SAp5DFxWfnqdtQaTp3sIb6zgukB4iV/nX16rLUCvu65D02sHgue8/ASWakMx1Otv4SyyXLnvEo6xE0qCHBISKVi2GIAXWa3eTen7xfoe7fEH3rlt1o4Di3tYtauDiSKmAGO7Ce8XJyunqFwG7y+8LQq/bqQNpGNcr7RDxtbvJdSPT3DhWn3LdU79s+yORx/6XVDVrReGWv8R5qle2YwMXDoAFckP4M73lga8y+YnMPSnsq+CU6GDzWMfGQ6XLpNx832lUdJNm3CSHmCbrsfji9GqVnkDZ2MADRKnjPXnl+25Byj4kK//i4dU0h+7VT1Od77OPbqsVFfMImBfx2n13e2+TwxLZmPT988MdaQyY9ah/053x/4RazfPI6Q8hn90v+YzvxpCZOit8RkoEGDJZgCkIGHusRmUx74ZXyX7nZt5PDmYa6eZcIhGWnj5Gxqy161NVAECq4Htsuhynhho6QCBplDGCQi4tA6s3f0GWYxPedfal12wMjS587juwneDux0BFmwfbg3ix/QhLaUTKXXPM4MxgB/K9/4JhomNe/nb2G+yr7sBqtVpbwgtIA7WD/5jNAPFVBaF2D8l8cMW+NZ9ihztvjdsC132OeXI2CuB0MWK9USGf3LTSGLBTK4KbI0xnlKlaXik5EO6CoW7q8++iSPTWRmJexJnieMFfg5vM87HfsV3VmEWpNh5xqKgjzEB4v71ufanYztA+tDwbz7N/hP4fUFVeMvkleYpbLG5idRvOtZS9puNqpxRC3YnSlHRSoPc6ypQChNO2Vaaxqhn4xA8nPpIHn6iEERszpNRRHrS401wl1sA+VcQtC0HP5Fgcz+QPPjCbUIOkF2jSgU9I0IRx6aYOr6/Nsu+ccpLvl16/ucLW6cA6leSpr0RCIwOKh4YEU51PRVZRxmZB/U11AkxJqgUv8nSUkyt4akS3Y/Onz+x5Osc/YJKqT8ir+1cfZfTBmkL2Q9gHYKYEaL0o/rqKRekWUwE8Q0CcAHFRh/eGEKJxWNyZgUbbZQ9af4Q9ZgPfgOt4pKFp64UTuBCzKWvyjTpB8Q8J5FSPuz14mYBQ99wOYYDnBQF10NBlGQJUOTkbJ8HQ0LolGBAYBx5lwhR92/ZECFdupHMpWvbqILqSmu5ZEXxW6nzI8jg4ncqsd/T/DQTPanR1mbltvGSnoo+yyebkaFSpUflxCvWMP1picK8QUSuUIBjdH9xoArmW+6c+cPDszXkWx35z9W+J1H3eSq1cXIQZo2lVHiGhcZJXQl/wTE+EO1It+YarvLdzp394+vCveYuAU23oW1yftbn3yxwrt+yGhVCgKGz5nlA+vMaOzF7cpwCcdlq2FpaM3Yj18oxmoDRWcAad1+NypxdBoWrqGghb+YwVo2vsmfEtEdGohyMrnAtwKtJdgrOCka8/XRF1Wnxx20uaU1AgEaB/Qu5LNccgwMqLvBq9Tq/bm41DsbihHdEyee/GIpkaqCGP3CdkkzX3ahw4mix2rnfY4vGCtIxkRb3uGxIFoGZp2aw+/PlyIYFYP8CI/WvowwU6O1jCaNN2DCPN0/nu3fA+77FPFY8IFQtWWTXvsiBIaPmsqxc/NiX9lOtc/V9z3E01pztB0jiF1m7wOPJ7wCq3AiSbYSH/W4dn2YXUR6qL2QY3E269BkNtF5HeznZfTEPAfz8B1df2W/cMptDRHPbYh85erFqItB7cthKsWwrNrPzPeIC1r6ToVLeWMx0v2LZDSXpGGId6hFTueTi9G6RS1R0CYCiBw3n3FrN/4n+wfVgNNnqdGpADevOUG1VAL3QUX9NqngCknPFouf6rfM+iyV7AG0Xhq7zbIZlouU3cyucAnlF8o3908whl+cXPS5Nuyu6FKa1zOj0/oDaMigfahBYJzF8hOkwHLM2b9WVTZ/9OW+K0gg2VpzfVVxZ7ADnnBY9Qjrl7RcEdTugltJQyOtw/onTeXdrR6gNW092433x8zgO/HHDDaMW41dNYkd9izO63rf4V+iZOUAxRc2V+P/fgMxYCF3DxAgVxdhH1780k8diJgOIGkG0aFe0zuURN9qN37BCcFitfaB3wn9GkCTb9QwebR9rTPHpEEzT2DUJOriyAD2gdTFq6OxyE78oroj0Bv5z7/qXQ8mRlK4kLTYUTJ1AS/P4G5YtRyxD9LxeDWYrH3QNabe/hjbBsnokfTwRY5BcY1BDOQKpBZ7zqQqy4cWUHjZtcup2Iho3ThyHs2LNNbAXHGET5LnFH/X3qAg/a+n2C1aA+HBilUVp1gsx3mJVQBkPhtTK/u35HZTfeyYdozVBcvHw+9GGUEGOlhwiEO3277KveGv/fyka4Hqfbyp2+OewHBIyiDi8PhwfvAcY6Ulw4e195BE0g/mts22RhkCR5ivYdE7Ly9u76LUPnCBV8PpGMAoOur7UvaPYxs1gBY8GmiE4bChRkiVyJnbdIDv/rf6hybodOElxrCea5+faxfZkEsUkm7Pc/dOXyDimc0ravyByswPBb1M2VN8ARw7rQPBWWNV6//6SlwTIYzYcexFxEuCpYt2FWBX3cg575tOphimFeNxoG1qzmOZDmPfiLvwqleXLiwIeov9gJgg4BE0nJhey29AsNmxgsdxOPmUkqXtA8KZZpMIBrv+PHuIOC6yvWn+/D79kjeiYYONcuyNyDhaAErIJIRdwE0y+HZ9w7aowYoVp1rg4P8dj4oDaNNh12lsxII9Zee6lufT5ZThDK9FpQM7ARbnFn79C9RzqcJyDNymVGM7YMdJVpG7JVG4zDY5Ih2gpKcUBmiVEA4pBpYvWAcl07s2nzGGeWex4I5mMDr0eS06WRWdBkiKS4YhX160Q0z3/6A5Afjw1kTV5MtX/XAp8fGtX/AoGq3nqW9a0+7+/jggBazyAqy395G4OYe//RIMz5oYHzdB1NCWUxtOgQrnRUH1hMSSFqrbR8MEjgFj0MEI0bQv9lD9nb91j6sOQztMPf3DKYC/HnffnrV0iCMQcpXCf7BPvXu1CilmyV/zHKpX1XTPbRIOFZbmIiUfYAWvbq4vQSyXfS3gCf2KXZNKEy1YlTZWz7GewyuR+G+Jp+mjMoW0sV4Ot5IRLH9+LBfD4zg/u2wdTjRa3Q6QQWUeo+gYy4Q2u59YL7vDQ1ZMtZ0ZxCEpAdGIMa8eMN9QfwJFPG8LlkxyiOapey2sHQcyKhxVkPSFOIgjSwNeiY8iP2R/ZatoK17liZXww/ydEhSkWvDV+Yn3CANw0J0VlH32fvIA9HOwRXP41L73nKePUaLSVbXicEFBtYtFJ597KBoc6IPPSEXYnWf5vY5R/EXXLxdq486EhaCtEg0AYsy7i5Umhb/4f9oB6TeI6JE1suJvnEkanCxiN998hwEj/eRkKuLqMm3D0M/DB/a/QhHts1RfS818xr+OBUP3KF35NrAdRU+Z3ktt9HOfw+L3P5ClTNBH0yaW+LdGYBH2mk/3i3W9NmCYu4QbYWZcCiYrrE54LSlw684i7glUrEK77EdQyygE7Uj1PVTFLSOeGJ/g1fKDPnk8EK17fOaJaBWFx44ojp/YXcWuG5YFrD1TkjRWUfDzOOmdVqWaNrkR+j0QOcZZNnAX2Qfu/7XPw7dtd5ZYIC99PHMr2nrejVa/g3TQlqKniSLd11aTYlmTRyrDp4B9L62Dq5Q2uKW+LH/hH6XaNtgh1meT1VWeJwFUZ9C+BdiGEmCF3B0tuxX+GDRgTra13Bk4V9NqWXgp30AS6p0zymX18n9eqoa4VAiQbNDudt5tt9s0HrvdXhRt6KMyzgY23aFo+3epy14qbifC7W4CHUoVKP28iz6QbmHgZfZM91/fNazFpM+ZUWrD9i8kORARgN2KIfi513qobSXFToIkIfBq9Q+5/npm8OdsMdwuR2k63l4OBb1MPrE9K+bYvrD7oTmCvNij7V6Z8Nh11tAANEyyW+QF5WcvXqS7QyHMCClowzGQq4uIsFvWpMnWGMnQNPpIT37kMa/hlMPesAYpIwulwv2dQkUqUWgrq9Q9QNadpkAoVhufftQwjLIURFcYu9pgrRzjWXiT+VS9Kw1eTRVQ0EFh1E2HAyEznM9fpvDfO1yC1rQHgLp6e6hdXMFOmdu1EFmx35C0yYli0MAXMsJ7OkzP7Y+oVf7tlJy+bHbFNviYUJgJ9xQnaN5uCWGXIZrCnlB7dUV+f3EXBYI2ofAoUQEHAs+FQvwWkXTTnWeZOfTLW0clNTgCERtY9yyNR9xW1naG0K3FziWi4ugm9oHGTd6wQ6wOD6SwbLYLvvmiGuoaL607jTgu6fNxXgWMKDScSaFAWYNgQVl9bRlk4aqJiObaP+Jh3Z1Pfj5CjXVn5ssUtbjrJ4eYv+87jG+tvDrvrnkzN5xst3vrI09aqRevJmOg4P+ZI+m4dgvt5hmf+i+Vvub9xR2ytR375800lPTc4bnz9dj3upmeUKOHAb9ezk5bqeUqCQ5aW1hhlyA6QJAVUCXhGppHMF9j9/HxwtIHcFjPoC1ALQPHQO89RFR8bArFoEJdIBlJ38Zxu97cYkeJYrKOJHVrzm7/uLTqlmXXL0yIV8kPGeY6lQ7R6i0OFDu9KICpZQVnYCNSUdwlGqPDYaaXvmHsqL0bceYM9o+/HKZWp3ohx2Xd+mBXxgoRa8uPKUOrermQwwu4ELLmwKfUzaZp98D3309AJldje3DVSrEA4K8mCCjZelDi+HlpyWpB97HECsIATrPNZ63n1UnuI8Q5dgNtLm9mYitAs8z8D9FBU894qEQSK7zvGKK5GaXqMcHrijQnvKDWSzVb4MdA6wdjljwuffeh9WFqxabMvu1t5psd+Ix0GmDJp9PGsfHhjCUCm4fWry5DADHyqDWgdeacUjOv6NRthrTgSyn2VxrdEJOto+7TK0uQvfStE6G978BLaCKXOLBjxVzgn+/wO9dORh6bBpr8l4Vx9aW4h0l/kyLiPskiQq93pt2QhDNDDjPe3HE5p94zX8dAJ/0KBFM3LswEtrVwOBUH1j+T3cuUQA9o1T7XpNt7o2M/vA9UnJDMuet42bOdryCez/cA09RVGmSz6i0fWVRMHSXNGWTSZiA1P3pHpl424W0lxO1AfvdCNqh46bNmv9k86Uy/Z7Q+E2rxu2DcbIBA9tZOL0bBjrbjz9VmSewKzTgNq3TErQs8mBLLzCCAbsR5EqaRIgyCBymWHbXYbLS5TniPeGQk1acxX2lkfY7L8iz+jDc8+a61VK8ObtqfRabPdiF6+x+c++1SF1bVFqv5/ojPt+r+Rwqe8FwVMC9ekCD4xhFzbMS88CeFlk4A9W0yhcBcg3M5WWrrQxxLYPZj2lbSs+GG/qawW96ZadsMRdFuhdyMvduSbfw4A0gF+T1jpCh2YyOdLUWZQJDG7h0YxplaBmYnFDLA1X3+uO6I5vM0nx+HLoOytFNbEr04ek5dHySy/iu388rpdGq6eimdATirM/on3oHJ81vPOiqi3MVhv1y+MGIrioOZX4puj3WrpZk3flP3X4pusXqQtPGqPBtuEYTKuFrKmvgOt5jwHPMCdwPuwDCIDMb6LfYYdHigDA+BmlxRRwtcYxj8eUIbt6ugjYWSyx9XHr4DZ35iro7fOYNsJTIMS1OrvFj3t3yvJDBChZN2tFgyGfJdY2ns0/Zp8yI+sbYdkd1c/g19UmaFq3O+/V9WF0o0xN9cRaJ8OcYaPb5svfkDEqoMV5oyPLyGTbipVdR7Avdveh6MTzYoN2y6In2hdMv5eb9vt54cUEkase2dGNdrtWjWqDx2rZA57u9gBAXrQeo0/7a5OrCn6J5pnh5wlqq335desTltfSRX5xeNPisGOjgrB0wyJgKIFcX/pWiaW+19wueDlXfawsRj8B8nCR9KosqYdcJetqZnM2nMtO6gawEMGrr93v72nGf6RCbVi1e/7MTgkwKGR1ugrtsQFptRiH++4lytE8a/dPVcAgUzzEAFTdECMrYAF3dV/2cNKswiQS3b//hPFAj7kKGt1MsDyYvUI5Pm8OwbKvrenW14rqOIyFXF3ouo53LLgBIMcrlLj3+YYXcnB/iCdki5W7aB+MKrvgEnNsMfSH/taBtoDb/Map7YAZHc4GmcwclwRAU/cAAX1sR8pE2zecT5gu2IN7Sb+/qiqnQYsyhmIDzuPucibWDsbB7+KyOPHf0a8Trow6yXNk9+JTN4thPCE27/r7gsu98ily1kAyTcJit/6B1AgU+d3yhNJUknkQEf6qz4KJKiC0vT7KusO6EAXhk1XTsphRhPq1R2U1U7Yt0r/xqRzpeHVc8CfFiRdlxQwcwUgD7vjX9LSh/z8Izerp9oLN5t2rYK+4ww/JEoFz1zxSe78kU23qbbcTih9Nw74G4J8pO6qWyTzBBLUBVAQAD9u42WNb6z5NFjEhaqZesVhG8St4AjohuMWPnQInj1dsgFhd6dTWvo5Ts/wV0imUb0SOgGh7oRTeAwJe2tfYXW8iCsBZ3vx3e7M9G0IG67wUVPqSWx9XNb+w4dVcDEEddaylXF37UmjyYXAZdgZKByiCWs43zZwwfLsOYx2aZah+Jdb169vXqQidhNB++VnBaN89jDUlHz68e4sYnZzzvWiUsSS8L2DlaXVkLPUc4dotmVs6pzBCnEBlKyAXP4vPSHHr4f/qnxgVxzcqEfIxxOOEE4haPJ9I0GOadt6sgbXJgjM+MUhkpijWfQoR5HNELaNtsC8pfmNLQCtqAxtgIgTnOFFYQ6RxlWr260KPW5LnkEugIJigogOlI55X/HFcYl/kb2fbuP5Jf5uFq0W6uC1jquIJlz/7tmshMxYVGLr85nQzkDuhCsnTAIQO+T3sp+60jow0O9MYYb+17z3VahmhawAt3i7Kv3iYDyZhFzvqhbDGjNEb4kBgoUuG1veEAGhjsflWKAqUVsxFL9qhqYlhXFGDPhMuqxxK5unBiLvosUAKxPQbq3V5Y9EIryofSeL+yHL+kMEVmD2B+nYPD1qsLFa81x0YWg2wzIDwAsXYLMPtncgHPX5DprqXrKyndMggUL7/garLLqPvK7AMO69WFW6s3HyllCSI+FY6yJQmhSRGDqbgR+4AmGFwEOH6lNcoj5ZVIyMVF5PRNd30K6Q4uWAPnK6Tc+Lvsp39cVaFYd6radnK32zawMFQLctWlvTuig7ssrocnRY1jPQngREo5o/TEXkf7oHzihXXAP9Tnryg9oRjzR3D0tZaRFTfDG287V3ce8WSixkgE5WDGa6ETRKAsTESvit0Ptmdt068+U/yfjIOcRR508YO5gOyTtA+fUCgFqLJghhcOvooBrDUm157rGr15lFaRRAnjxedU7sj9FGMcLrhLgUraILjzT8v1UbScN0PHw/Q6TVtDQnaEhtneL5CdGtX6ngkWedSVucXYjVL8yXcU7M5yxZQOMbyDmzhPIGYpCmofUJMQWXC+dugYvx4ywcB3U0hdtPRUWLtZpA8aHP2Ff4oC8ErwLqgzh9QENOygKdTiQrW8TTul5f+hhpVC4mtY8Yz7Vkh/JzQNsMS6z0bYN6gLMZXdoGL3gxKdrDQNf9okRTKJ5pNh7REM0PkEQlSxQy/Be6d43vGqZ2/OePn40d5ZmV+VHrkaUMBhS3FZjiU/XYUi4r92BaOqn+fid1r5bx88b2DXu0UFY8PZPENfKZQCI+p9OVgCciKUJ4qHMLtaT3c+5PcTz3dZbvy7iLf6kVxtQ7thS0IL1ai5y9WFEyZhW27HIOPa8vTiCjabt7BwduXV05i8/S7bLXiGHgHN0DdVIVcXoVVvUtou+rR87ortH2QdGV0S8Leect0Ca27eaAGe3+7O9Tqj9P6G6yVSF5jmca80a4WKwvu5XkD7lkSjYz4+rEonWePU80Ya7nwHRzw4nhzIj8BkQN8dwjva3CKd8sZ5LTWY4W3tnElOd6evXlyEnwweD6943/wguy/+FcZ8zN9P28+8lDKRs64+Lx1bzLDQHe8+rC6cmgipcTJEZTsvn94FcM9hfU85OIsx4NMawyIs+ezGXpgHdX9avbqIQ9g+NFfybgqoU9Cct4cK2bKF7Q+Zl6+aQ+WUopBzwjl6zByXqz4LwS5UBBUcEaDwKOBtrl61oOJD2HOv5yhlFFVgTGgBYTd+cz2DvYGtdFV4jncnGkMoOhgv7ms3eoSOehrghEebIVSUzRt9nfIF0YLV0+uVm+A2H+hipwS1HX9Ta0w+lXNhhGfuOK7J4osnrkdcVFH66KdVLS58Z0VfVDl3TBL1SbDlFrBxtRvdhhOyHVp7bU4k7iAj9z5Q1BnKf3KOp6rV3s0zdv96obqs5+WKk3SOQo9eDGPXFXo1ez5I19BVE5j9XVaudeKq0ea5SIZz7O2D6DR7Wcf3ZBTKzttJhWWXT1vgaaLXVFqomu9QSF73M4VYoWJA6N+Ryt/OlSKJV1gyb2gvvsB7ARbGw4keYJql+aNxYq25Y6htYoC1CwYZrqP/pwgcWowYmXKqKaz0zj30Djue5k6V5arXzS3sI1paBIXWxlvCWIwVYVPwxBPEc1Sb0j5oWXhLKUKZfcXkDHJxRcgfR+UHqlIWO+MB626JQcxnS178/KckiTTQTij+sipv+ACi/g3aoGAyYuelldcDqwnfdiflzN7IXOBZsPltba+mR4MPq9GtYYmW/eAH8i3LqM9wPqUdirrjUNmjPM5amLgglP1oSVtLZC3r1llK4dfKpAgT2tSoQA5tEfijcP785yjdeW2BTwPRgrrXEwZrardHCcxjX+PWk3xYXQSYbrqVWchbowxXd3RYXAHfzr8n9+uyyHsyEj0v9i0tRUUB1h56D7NJFaZpteR5PYkUjsKeYLcUDjmmYY58enD+py1uRKFpQtmBKVuD2s+4LD2wwEQ5uCxhhUJ1sDNaXghhFF7ZlpEmg4UZ5xl2AZ598lYYSi9NUDLTviXI/C1QXM51INCdUHz4AaVj1WSf03MXJYb92gesKEqctBDxq4vu27ko7FptbgpfAcd8Cu+WgXY8ced6SXoJDyppT2c4waSthizoLOPU6tVlgclBPmDqieAHBsjzA1pAVCVBys8+N4zDUbP3CgZjhSSkpqtrcd+An0RznErsT3ZZTnYhStjvPjyebXZr3bzvh9W4KXCVGJjd8SbytUUopn5o/6S/mfPnCErnD667A1FwEo4ilEc0cNiKRzv03HRFsGo3ZfzIc0u2Ar1+cgGJy32jQEjJYMnvig06SudoL8BHtFDp+wsDZsfD6dVFyFWalrcIfUaMQ4l5uH5X7DGz7Fc5yWG5ncjLB2gCZW6/yklideFqpKa0S7u7tsK30lv6MLz6/JGtYjOq+29ZYPMJKYaP0VMB7bBtpTOkm1zRyYv+I9jZx/nxtvIUQjnMsr9r53JxEWitfWhe4sIlb7e2iI/6CdKPc/s7QQv2hq6V244Y7GlwBjdSZwjl6kIJ6JD5GS4xbP+DUR0glUrPrCnqI3T145ZhWgls2sekIn5uflF4GS513ldUDgcd8GDAEjtu7cPxVLVXVqudY81GaJnmDfK7s8xA6XZSr+ueAs6a7CmJ84tIisETuN+7jck+StR6deFgJMZSrNk5SjTIA8REpVwIdyl0GXVC218uHU2wnP5xUUYaPJdeXYT8pn1wOTvxN6xez97smY6B6Zla57l/UvTBrY4+TmDf6t+WIhgFSsT999iMgPbiYuiDIZWCRrboN7TT0Xt02ZAI3bt725ucu8sLLBisWwyBxHibeD69iKhsz2dJqsEkAHZAu1D6iYMorU8YoT3hOiOAKSaiIPZuMbvGEruolIvOEw6vJojBqDlh8zGFRzJYcESh1ZB1ifGFatwhNzOcoQ0nCWy4oGKMqj04xrLs6LLyvFZIxmm6O5hav8fBxZaQuJz4h29GSq8unJdvksZXTYc43KlCM+bAYl33PwYsj8ojrAzSPihwgJcODGzzTB2U721ZxFLh170bJa4djjzh+2dwqI57V60uXJzWtBMBqO68Qp6DYSPFgnS0JHIt2+MKCaPAwnXPrlQknMAEm5cZ/kmUyuoaExoT2N0ahX40lYZo5NhvrlZI2fhNPKDoGbbEACFxL2yw7r+hqFx1R8BrN0CV8Vkv+4/nPUxzhxkl5k5ZsLzWbspOSti8FPPc5oQ9g+s3q71NDJ+EeG57yTeJKoE/8IQ+JyYDap6CwSVx929n5zxF1F0R1jAbDA1Nl0XrzozSPO6xywnGw6/uBYc9Y/+g64ZZLi6za0oWzfDCYF+vx2GL2sXxJGaC9HArKv/0W0/wEPG+KVSe4Fhv0CMadMkBUZueU1YT1IcsBQwlvT0wCFMYhrrDVU+radSjZYIZlTxSsguz7AtNUeePD8vew9lZ9cXyAt8M5QZTaDQ/lQkMXu1m+jUSQz1Liys6Zrivkcyweddt2lZ3Qdpst10RNVTnLk0jn1PuDE80jT9UFYhT8Y9rUfTXhZI+4f+688F5T5+QDgq8SDUyWguMfiQNmka8PSokgT2jlatOu8Md44oZuwVzP6+g3d/zSJka8tj93MaBRN1w6Fgz5PqQxUGmE69OaQZojH7q44DbwTbWiThaUMk9o8P5LT6rmCsy8oGXop9vXWt2DiLB0mNo+9Tiwim6EMoceYVCJLsP+nXcQhkanymhN4OSJbi2+cAgw5lwp8UMDK9qe8QVSgvK1T62IWKZ9K1Psw/sZFmx45GGkSlrNaF59ww5KQHjYXlux66PvrAjeN7W4URkyoH7hOuViTqiaQPR/yxdvlHWszOv1NeJSkBmSKxJho/EP8NTyTJr2Ktm8Fae4FPhNWcDJsB0FsrCes3CPN4ACCf7H9yzu1mZlse913EoJUqGp7MPB2ZCvLJCsbjw/gJcXAWZANI17C1UIm7sQRIL0Y3wvAjAyP6mmyBRb4KwzcmmAz2B5UNtYMTgHLYlF+zAtr7nb0j3YXURhZmmCzmiROemNrYb0aJdMBL1SH/4nJyicnNc29ZfUoG6vsMmuboIqRMkUAmNFGsNwLLuhzPn3EhWK6Oet9RbOLB9410DINRLTd7/Su5deZcKDPMU03FT6eam5RUlg9MbRauFVzfwk+bnwoR6VI6LEw6o56933Bi7Ty4uokuqfeiq4g0aUUSxs2x/zwV7wL9UnYWZ7AXhkuA+4OHE5d8hXtSrUf8sJaHkhcABH4l+ON4V4lrzraSOj6uzVO3atDpWdKV5YLa/B+IjgAFDYtffUsDmHcEbtpIT6wfc6Ie0ki8uXCcWJahr9ywOsAi51j1WnvaJUVXZXUP50iKehqumw5uqrNBKzPNkkRte4uQeiHSHj+pG44GPBfz3wT6eGmS+8p0nk73/m1E3ny+aLp9qBjndlsKTVrZ20vz7YVszQSTRvgkkCmyMtkK7qO/2TVqrpfhlXBV7jEVAU/rhsfd068V+VcjVRQSwpjvShCgWGBuyGgxgAkJOR02zJFDvMD3GAe2gjS9kHPaqr/M20WfKKIbpZxR2WAGnaeFExZm1s1+cWLH/ut9yVMa3PHcQgWzernZUhw2brDhsXtFmvIViIijlPKOoQ3jMsIezZ90wDNuycYPkkWyLLJfXegaz87V1LdcktA92DZZ32bEF9+To2b59+ZEahhkuDiS1jpEiKNtuzhQeV+2jRVUzEU3EB79To8vwss0ZKY79X773nV5dRJRoH6T2XIyFgwt5NWBAwXTo9fgDQx9geOp+CdMumOft2Z2kN0RKCID/ab9n4ZY5nrBsvWRYw1EC5PVwFdOri9BlQ699/A/zaZI/SM6gOfEg1MVdy7hfOrfkLR7gErxh4VzdkefWuanVmMl7wgPrx4U9OR3dohhznu3uQ3CE8OGeyEtKjrT68lxbyZ7Be3RXXP/JGdG0r27HwUuO/Hmfa6CK61s8Q1wRTO2X5KjfvSdsMgkT4XtGXwqhNEP3aZEQ06azG4VFiqhCNS9Qjf2Wsr8d+5f0tnl7/HzHZL3qPhPXiZPiYgQE3itsJt52odpZnGN+fhJosbep0jCk49VCiUFg26gFzEf9kRLfCR1b1IewuaHvnjEQwiMJXPAcVGpjYOZb+LwIxcBPk1hJFn94bWqGnPed7AQFWtHHiuESIDtBaIVrJ1f5Umr01fIfgpwLvcgeymDG9+r5V6uL0Cy1Dxon3ozq4w4NvuBlA05vdjH/kY5Z+unsum3sHNyO/cWvMpRaXWjQjc7rDVapO7hbi4f1HGNP36UCPEQ/pgJYBTtGTxhMs+PS5yanUMWK5kte7x6pxfee3cxlBeYrIHdsH5yRPl9bDGvgXjLaleUxw82y1/AC3lFGjxKO/Xnb7QVM1VA0173dEmBp4y28dhT9P9ihT3fK+GE1LMXtl5SUfiKMgKBy+Mm5EeGjIDi1AY8tKERf+3qFvAnb7b7J9KpbYWUUzwpG1OyHGyc0er+pO4tSuYOc/XaCIo2tIQPEB+6iiXLsL40Ts8dQhfi7YSvB4hCfzq449621ELve6vsPq5FX2O63FP4HZHuClU7qbMB7R/c/2aGtGrwmVGlZotp8eKY9as2egNn7KHFrKRUNLd6Oq/bbmSfUXbK59bDBT3tpXQfScaY0MOZulK+S3u7ZKmiWMPuHVPd2NNCrC78W4jazPYVIjiws5Y4/lZaBXiKPKxdUUdR8AMwBwdn+E6aIdooCzqlBMlyBNAGoMJ1C83HT5452zvixCyD+SVDPVQ0zJPiEsAvPBdzRYN6hQd7zcVsuMGk+pfdm3LbMcg0S/A2ROh1hUoD+2DA1o5J9bdE2mmhLuIiDyO59sgccnXoXrVxduBS7qaQBmzVfGcOPAe3spszXHbGZcvuVOn4/ioLw7KDfC5hTKBOw32zTxRQA0RHPWfnHLcjIW8DZ4q9H44EXQ8kdLO5VkZ0/N/4hXF34T6fLTyAIeQv+MR5WdJhxZu/1bCXw77kiO0WCeFrCOR5OrS486Ia7DDoI9iiJVcza9qBLVRc8Qk9Q9DB5TDQy2nsGJoAOptpFdmsVmDkEF9NMqFgwFBw+toaiYGWKwZfZ4O/tY0tkSBwyj7ZtAywe/uEuFyhuu91E9eKyXLB0s9+7eR/2unf5OGOlJM9Eiwq/SsdH9IbVtHfpySsGq7VFyE+abgK05Od0tS3en4WmT2KVcUF8PV2Euug1N+C2hPSChRjIi2T3s8sWpI83d90bD/jtCG/aBoj2wNM9ZTEvASZGtgXjfqDenrpt8PkL5CWxpuVFCM8gEVypcFkQ9DDDSaFXtPt6NgvjMsOvakMWdOBCstuyuCpFonlapHpOolCFWHMi8aiYwgXBAARR/g3tCBvkBfAsOO0WlrYf2afyvGv2cgERLHQANaCMcaaCXLryJhXx5zFJwe6qsGxJ9pSXm+Xlq3MAoh5PL7bnelmCem9+Aq6jQAR78RbRf1JGyzHyYxU0YzabT1nPq1s6ZbSFX6nG1A4hjqY86PM2Y1YPbB/qh1wDiKBs/1pY+G9Ou6R1isspbE7Q4ur2PhUd/mc0GVniDGmEwRbbnWW/552SQhktZzxvlKHaxObT6aFq65SPgZByhGZRDbnnWsaX7PO7kexoVbu8693viSvSL/Y61Svi7NkrsfnWZZF9PG+htNe9O65FpdUrOKLASL/zjGIdSeCjHwDXqL2IjAFrHuf+6ZuM1vAmpPsM7DZ3SgL8OxHgEOfDy0uJeRgyntE0RlBE05hDsZ+8EnXT19+b/bLY1D7EMkFqUxJ8jgcKyVCR62MHVLu1sJdWjAEODxTa6cbT2QnHgjEOqNdtaIxevSsHIuLjnldHHQwoPfG8CdUyKgPBtscQpMC+hMEICX4qoHHa4rm9HQlo3o5tYMQ2nlMAlp5dt1ECKd7x6DcS1uLFBlDuKVjpFdXGnrCqxUUIrppkskDzA5sgIwOis+MVUich0JrgAMC0w6EUK8nFg5AUFTeo+Kd6QITSeAZTQsqZMcepIgb6zHdDeFc35hZtR7T4OYMpeYfiAOiOVbZIrwperj+FKi5S4D7BTYl9quY7zCIFdmRxs4Wy36oOlozR3p7nlTp2JwUdfB6YXtdF1/eIENEOrSp4v2rrXzoYkwS5ebW862QuZIJ2zcX4QV5y58Wx59QmC2vhU2BRq0RrpCUZZb19CmjxiQbB5z3FSOWQy3mTsAGr6sbZNMmWiTNj+Sa07eLPvzAD3XbfarvMdezsSlPXFOUE+mPlbLEGJ7BkT94A/XwIoz/Xh9XFQSVyC8slUHVLSHNKV5v+t1VGt76oGvKELkpWgWs+3NruYUwtgL2+5fExH0wAeF6vuzNqVBcPz5rX1T+cpeep9DD3YXURyv2mlf5Ck+sTCC2rRBUZE6jtP21/b9ivtc6MFglvseNwphNCw1LSmK9GJdCURHnMvFKTruZzVAyiY+hT15FUZ8nVOBbh6TUuioQ/DndBr1xe+7gm+NIiKtPNndcNWK4p/BAsVp8eWKWDu6hkvz5sZIErBj14cpPrbdSuFxeaC8ahPaLQiYNg0PxOZmiZmCaODzuxaO9e+9Drx1tf3HTHAg/EefB+wGv7fWQxtxO/+bKUbvUvGM4/8Xx6dRHdcU1304luRJCbGeOvDk8dbecex99+p2+JV3KV4oY97YO72sO+lv3DfeS0KinSi3cGNUHgZXzewy6wiBsbLpT4irxqx8HokOjAOtkzrKOkW497n1i5uHBxPzT/UMamfLN3W3wn7gqpewGedxbb3wofqXL+xGyr4/BJOgwaiOteIJm7MTZ7rh2Q1oXgsbejL1YuhrxkXTEE6AegFp1YQfYLFkQ2zFLM8Fy8TssvTRdrgP12EOGwiS4Y7/AjlePjSJTqnRB2BaUgv9DBN8oRcnUR+t/2QS/M23NxZuHFuPvkqQ2U2x86cd29tGVZ+OFydYMh2xipq1cXzi2BckoYdm9nG2QPahndRkk0fTIm6nGwY6KDGJlh4XSLnBne8Ns915d2GlOJwqipfz1kktbPm6RDsOeh1c+9AGz4Ko4Fr7fPKLwSXjrsxex+QHX8WmNMqL8mkUDyeuwEazbCGoJLREm/4imgkUM7fEyq564olGKcIfcjBbnmQ9VhOmQQBKW5q54x6EmpAGn57ikqplX9plUboDrxxzrzfh0pnFcFIf9Y+M9gCGJdAfuDyXUw5bYHjM5OXi3mmGUo1bYoOlg0OEqI0eq13l9Vry5c0Nd0z9D5vwtamc1dqO1rpuP60fq/CeeVJV3NjdhP+3/ivFrMOGIGgNKy0RRtnFevhbhcqK7BgNkWHeS/XPUWMfReRbHOrlUD69EiZhECKqXi72Lz48qrsrzk+LxFzHur7T9j9grSmy74f3ta9QS8RvBYh8AwbzT/n57K+kVpSUwUmmjtjuPjCYpSxoOEkt5AnF3e+LHhgJxuspBeGLTsOYOTeE9Te40uQbmGuqrh55cjx7uqg6e0L7XQd8Z/bLN7Vy6ue9uVULHEcLx/oopNz8Xz1ldc2IfFpNNDVTqvcOqkGYVMExg7OqckTK6aJm8mxbOrWvGE5ldgN7vKfPQtmsRT7xv+T1RRkYLTtBOSaXZrBhNx2pc8wo7W7pEA5qqyw+7Y5xZxbNc3zBG1jYgDCwR+boe76vNaJz0hzzMGUnwLO/jV8ivokW2vgZbz4gjXNPNK3YSSHIPYMXzST1DCj1cIgOMxRB2RVnRGBeLrebH4YscOKrVi2MEWDWrscKgtz6mKEUEwNshvbnsHZ4BaDFLuEUSuLiIkBHLLyFdr/Pzsc4l03xAv1U3oA6e9o+gpzXh9eYvJe1fwT/9EU4zuNf0lQvjWK5ml88jy7f7He9hdjnFAL+DpPO8t4cn/LcuxG8pLIQX2IH5XGZa4T+2H1UUUOJouiAiRYXQM2Xm1n9u1A3+H38aEBTvV3d/sf+sPY6cN/8Gf8MPqbXSKztMfuIdYDCuBzmnbpG6D5HPxnvpgsbiLtGv1HKxE7IdL+D2Em1RjeZR+Wk7nKsjmoy6zXcHuCu7kYb/+1chMoZocIpivh+1xuUuTiR66DI+KcmGM+rLLsU8r4PKYCYkhyRn62bANkL2ja93RqtSPBivysARjhJXvx9ewQmvz8dKw9Nmd+7hu/CQTDFqWncExETYJJFM02eYSvy+nCHrCd4JyT0/lzEzTgj1nvwKjmzImF+7YfjGisKBGhXG1Fh3tYjziTHCG+2lPH/yqVlivoVPPLtHkrnAMHqgrXyQedyHiiUMni+/tw32gShSspDEj6SfYPCxOs4W5gpNagV9ug1NaFaNAfkIYec+gwwPztETHnijDqAZ1N6eRuACA59szBGFE0hdSxHrY9nIBWlljuoCQiQn93/NeUsK/NR80aOcNRm324mB+EJVpodTlbN19ux74Gz0rrWvtM8wwaDmuV726CI/Q5i6+B7gfYF2Q43n3ebrSDVh4ik6QSTIU0rwuZhkZ9BHgaHJdw2FA1LEpZHlcEqY9fOjtQ4vy2lUZmK57huPL+m4cozv+xset0IMg+pf17L17+830y8VF+OU1t3k9VzhL/2BvWpxcQ58r7WK5v96AdgaqfbjVeqQc4Og1OFEuLkLs0tx8OxsQ6j/PgLthyi08vLk2ZgKRyIjLsCGycFZhAYJSfCm3CxHLwnlZbOy8c+tJYbdA8M213VtPri7C/6D5qMG6GkYKnUI1XOO9Z3pkIfdLmJB2UxOz5r6Mlj/uALpoaj0w1A5PovwdhenZDPUfKcjF9Do3dLjw49WCZ4ABIQrk5bunZDG9pJpnD5b2I86WDQ+f11AlCODHlM9PzWporbDJAjX+EpAYZ5AboBDzrbdnDO6QwmyR8Cfbng6DLTyUMcFOrxoC3fHYlga4cb5lhpeHZQZMJdiknPgvYzhLH53SxP7O/U497mOhVxdR328y/8M33FAzjbeN0UTrbUrIXvdjgTi5WENucuIS8LTQ/kOfYC8qs/wanpHKviPhGOmIoGBXgEtx7btdnSshtTIOmx/DPJZOR/sr7Jg2H616woQggDCtRrHUe4JfCNO7RFOdYQY45KNQbhsr5hCp7hiqjnns3UQNrpo7Wl6bXVFhVGYfr+a4DJQzJjfEmsEtMq1o+6At5WJr7Lsd3mvIJbPfufnvOLGv7fUZLQISxRuCLOnBjxNurqsXAAh84UXaGcQxYYhBHFvSc6IeB2oF/vmhXuO9gJxOfgGAb0edYqQreHkX/tkmdM+1AoVmgXLTrtLNqcd/ShBAinwv2unbYZ3kAbzh2qCRnWq/969u3cv1E/xhZ3SXkmS/uVd5zv7nI8YBtIbCRAhPKDXwNJBwNNEk+tDFH14/HnXiryf+ujnPifu2QNu97Udv0vnvFuT7ilfSHiuuWNoSQ84sAmASDAhfO7NB/Ys6KK00Pu98ZXu+YfBgwmO6/ZKlzWuUH7iMgp6PGSeBsDfNp4GiNBrBzjbd2vushRaWcj13sQlmuthCBUmBt7jCo6e/tw+r0eF/2P1sAQCuEHCt2e4W//duLN1fpYpTo1iMsSV4VWeOsg2YzVErVoveSGdPXcICHG6VfiWw86G2PWeTH7e9MJAbE5LsrrJczL/Tdt7wkgspOCSeUY0gZQdkqxj0cKUoO5R0lhhCJExheJFiQq81CQ0xbsUyrRMSiQzf9yMmvgsFNhdUPMaYrEUDLJ2dHsNQe+4803m4Po47dumWjrtL0najVzGhEXXaZgPx3C/8D6tRoLM3VlZ44aIp0z5PlK95mUF1T/LTPV6fBeggGc6a7ox+G0SdXF2El1pzt1m7TtExixdrHzfyPOlaK7zXbpD+wFaatks13V4lGsC8Tcv+eS/42PmwKPXHiyDBQRS/GjdltAfv9dWeI1cXLhNuup2kYPrlfm7ePmypQhSelKp4ROSvja9pMbDJ0iFIV9BN5ce1Axa4gm+if83z+g678xuGwR8pY+ykS5lgKIw7n4vIKD6YgAQY9xC6jsvuO8waRp5Y6z46dEnRnTIVjwsAFOJGlfiyDwYFAuLhugXTILtPhR5qQu8QY0diZKLtNFiLZZgAbfcwUVZpZEzKKGF/beoLAUKtdjH5Rs51cx0gAy4KjHC28Q51FiLc/9O2FqYngL/Lxz0k9sPqwhu52oe+L95I6v1jYAEtdleInK+1/FFNHNU1ByvK886bQ0g1NB1ydeHiDdARaK7L8J7JaHxEGu/EA2cpuNTjOU5hMcMHENmhxKQT2EPa00SZnwugeICZQG4ynBl3GCTo9gI8wuzbtfcrjIkCKCidcFRZkt/c5PiCoPEKiYzFoKhX8+o2pwQeyyYIpRVGOmigQnoF+ifvMddUpba0fjeBnWNMF0REmPgFjzGPcRYewm1INbAxXux+OPvvvt8tz4vTeHpBqj+cXl2ESK196F6C3cua3b8E/UEGnKLGw0VtAzddR/gLr363rb5Hh85Jr1ogxvOuGN4InZ1vSARiEp5VyKXVoCniNVYnjDmJxcLN6nXCgsJjRDShaaNVxQnEK0MgkVMgBY54i7nq623fT+sUFK88RiZUvYlm+h0JoI+vQLzBQEvfdmqwHhd7PiXF2G0Qk5EsN7oicNjVFG4DQodCb44Z3daEYWo+HRdb1X4fytH2JWNzKXk25aPGV8XxxfdCutTluOttFfphdRHSDUg64OuyY1QfvuueU4Q17XFKpR63ADDQO5p4nDkFlLO//LYi0KuLKMI0XbQRgnCg/nqimecHIfSwIPvXDfZbqoJ60yDTBhNwwNzN3cCOW/AvXc6pl82ETgVadW4fqtQHRr6c3r4FiacBwEhkOS0/I+69JQ/NLYYMQICdAklWMCPc8YioXNBU4zmhzfSI8e4sITf04VIPQ33r3l8dlXpQ9eKMTJbgzBgcZn8BVFu4R9YjTH1lzZ2h0gnkJ2M5QX7abWa7bvUf2+uNdyQ77SknOiEqsyQGCBSMXIIxB5IYJImp10soMGWF2SE4SSXMkOzL98kReTBPH1YXISxpHxoRMn47qDyEPwCq4EXFEZ/gEkejadPRV/GilEed00v5fvf3WY657iVcS1Z8yp5aU60MQwrPWympjiMaZBHKQ7ABPi+HnQmTRAvRxyh6fukdTmVp2HnoZavoxbVkrOQaA0GBHk5gmPTjI0M7LBEU5ARlMcsEY1SNPRAYzQteGWffdKKUQUuiz8zh2NXYPlylis7jFe4JKS3LIcLQyTA/5LMZXi+pI2TK5vF8YwZPQQiJ5qbWsAKtXjxLK8g/R8K8YMvpixlSLLKJYtTKnt2UGhTjGmV1pc+itbMXb/ftaG6KN6JCUWOem0+KWs8uS+RnmAtRJ8A6BkNichMujjXhu2KeVVQ/Bf3OQcuEE8HYHJA8kC7bltx81+3bGr7IqoGMcj+P2TF2SwVhbG8zI2XE2UjhZSpq3fxKm5HPksS1+bg5+585MLcNlTC5z48rV43xNPdx7yntvobEHiABf4QnY+U8MKThnx5JKLq1J2w7ltY0N/GpK/rWEIjtLHaqXXG1NAkabEAOhf/mbdSOLMt+V43l4iKupbj8a+hmXeZ/eA3in277EFWpR1csa9BBu72l1pezpHgpB+7O+IBqtDNt6HkZ7Hw9KYHVSsKkG35lKQhHZOV+iYk0g1dWJoBhlr8ANyGWYaC8/9jS2Xg4jqY4C38zPBVOiMgW7J16yLBPMLLYD6uLqOC3DxV/LstFSlTPHUkYgFQBhfc75GEqmBe+LPB6Sm0Ix+Jmf316deFF8iZL6hum79UNzRZ2olDR2n+0QGDC3mMoLgZg1QvJaYZr3rrG1HrBqzDIN6OySJj1GAUHRGS7HhR6OrtruCo4Uh5+Rvnu/UKNkWbYU3ZDWHTFuPfzHo3Ainr8+p1wUzCcFBl2xUxAjyjoZRwJNi0SUFQ1g90hNE7zicd1t2sq+9MZUAoUJ/qzOOnzXAtAE9Am01UoJe3l2X+pyLtzoHlxvCcAY5bZNHdULRZuYR8JsdoZ2aqqE9A0aEJBgGrsWkyztE3lfPbhcjtHcnoqJtfk3VpZfCtv+i9ddboCHPaD8WE1KgIW2XdXuNYrb3c5gBFJUkBLBbe/CrSY++oHMgZIni4Mu+uzanERZdim5WFb5PlAmnbfHeiyjNuCl20nkMYMewAL2D4zyGTv1fE72nH81ucQgfKhr6vsa59ChoNjjHO11xQXw4GwGaw/pwg4ah6llBT2r8dlb3b06Ja7lCJXF8Gntg/8a4H9c9qjDxY81nnXCRgvNKGDl/YSIwHCeMtS8IRIHjDxwkOfmqwgeo9n5N0kwUbebbHDbgVMCTstpy61j77kUmmejvenQxueg0wDRW6jYCnDfgMCvRiMxWZ4wC723dM+3+FNBgtpBUWto+b0ZpEsu/mMtQKnk+wacbtqa/RmccUKz8knIHmqUGta0Sa0u10ZhzqHi3BtW8yaL8Zym/AXP3KGT6XnNnvffZzko6zyuHntvYZQd7+unmBDl9BvXrm6iJI7UIu9jezZB8Ijuixc0iENtUSJfka9kSDjGDFmqTaGhrlhUoqpnLIMSXH0hPdHpSjNBzjYjV2dI0CblkX0MB4TcyCocmUCZCb5WLTi2QnFFIG8Y7xUPJwkhGj2dr88WFV5ATu5Z+lfYw+5uIjCYvsgHoP4IjlTtG/eurd/KkTOyHFJ2hPN2qtdeqcnknZGwhhF1jVokvTcFoVd5+3D9S/4NFEWempMQeuK0We5G1goXkG0D1vTPXuPaBt4FfJ+dbYV4lwe5UyBSdI5XFH06iK8bZrbE9nDwYUNXXeWPSAx+vfB5oh74Txv7qUvJEDfvvos7gKp5xbSBFl8odKQGbXktzsqZgMYwCvwALYNCSl2fENRYKZlq/Ftw9YWxpg1xKgHCuH906rFRbjGNHcnsgv98PusQKwT4/6ky5FwmRk3xno6TDqTQcl4BsuHR64rVxdhWQArgwxWGY2N2GMAzjGwW/rgcIuDGVLkd06guStrzd5cmzE3OSZ0yAoMJRD6s11QrTieuwwEeQCxDXCjgQ+ri+Bb2wd+livwkPdeuA2R0fuW2vZZFUgCTOIBa0YEwTtdc5cFiLokRzEzPCBIaSC8oaHvxOc68OelGo2WIj2nhYQJ9y3LuKNd2kIMrFMNrdgFmqLtglNXPD33h+NMYcxxtIOKCjf+fHu0gENCoc15xceGOoT0wJcBHPTgA7WXRb5gzkXuwKsoE2AuRQ/NWcz18H55F5yWyzs1tZCXF+8mcP4Mk0WL2LYeKyoMALG1pNtgklQpOICb0WjPgk37EJwEr/hOQk55dywbiJ4dv2rtlQIL7aWP4RS0GM0dRsfp1xPXqYKkecHLdmS2ZyqeL0RAxc6Dl5sP30EO8UkyNiG9YjWl8NRZD58H4mZvW2+TEIVZXoGacGpp4zWgxoZq2wGa3D6ybY6wapRuSqJRe8JlyTik5iO3bEdAR5mRPNvpCgZO6GQo4zSDNiT8IOpNMKQ5MGgLT2evL4ZgKZExZROHZvKqOXSRKXIoWEHcLsUfVhcO+qPetO07CiV2fdshXztxw88L12fNqCS+453od14hvHEXRANpgVlVfZGjowk1WAZsYn6HgU7nKDP25REiRHEH0yrFDPj9DrTDCcu+GXYBwq69ot7xx0lYDsvnmMS9AQ/kftCk2dV5RlvkcQUnrVJCQnGOF5ewo3FTbSHIsRODmU/9xcnVhV/20dRhHxxvCEnsdUbDs6DAKDK4n82Qb7RZX0dP61ZM3IxHk4sLr+o2XQM+ceAxWB6kdLnW3lXJNR6DSfp6dhJn0Jpm3ECh2z1z+XVg+3XvTTyceppwzbIMINrZ7LRmHGM0L2w9mohMlaULE3Ydg0mhJIb54VV+TnuL51oDPYlchoOq+9NWGC3h4jyPXh4899sFQC8uogDcpFoIsBICeNSFfRTcsd6iBFYvHghli3k/pyGePkjyrHfp9cPqIhrWmlvAIJqU3RGKIeMwRNZWMrzBbYI0gW7qJs+ASIgE+zoB41ExYvMZP7AhujrG23JAOTkqiGsXn3dmU+zdJFBHGQm2km6zmzEr50eKZWZ02pELKgYCnOu+GY60H6dc0t2MSLhrQXA+ZjJpBa55NzMwLkaDJwtkm11RfkhVU7So2I3yjbfzoOMFjpex+a8bqHxYXUShpml5yYbZSiV7GrF7v0S+ewTYNTMjvSB5RExmWdGgfzjfc6Qa+b+QA/CsY4LuhNFOMdUG0xsvzynte65RR1LyRUpSzSh+EagexgD2FziyhPuwvZjgTkRNjAL7mwfO/leC6c3HHrP2rvVGBB9WF1Gtb7q6L3S6rhIwEL7VH2xP+yv/zvB8UMAhwaJ3Uxp2L24wZfdYkDiyrkPLYhOKEFRY12LIBFqaDr81LPp2CbsYVSF0eBOSIJZjx2xszG1aU0C7a4tBbUoBSjPyCZcube1oPiUBo8L34q8vwX/J35OctsBbQSaYjpCkJzo+9mxnGZh0s6/b1dmC6KMZ0oRmHlZtiMYAzMBYHbYDJAYZqpJyWpt4fOtS3UZzV0cDC5t/8QxAs0d1TrlDcp3HU8sRSkUAr2Ci3Bmm3Fe6IiSrnJyWDsaW+9olm8awSCLT4ZbhxSn/NEoBjKbilewZly2hZKP33qcveOJlT1mGzRMriHECd4770xu7E+5PFnCdRbN3Z2cimCdFj1Iu6BYoVnsn+Ha21QG2PcQNt5EPq1HSNBwKcxqgzHSV0qeMk3qE1C1SneOcWEdS7ZC2gxXOP4brdh/e8fNPcwY0L59BXZDfF52LhvBLD9DHXuIpOMlHCY0R6io+P8KZbfd+z2MOZY91cnXhyWrzJAyX5bb7jw2/HXvQAEoTyKt9M9RrBGxGB7llXWjwg4HNbll4gE1R7KPQ9LmbHLmXwsq4FlzqKEbYP3xEeYxGaE4sv0Lx1xOLyD0fgnZIoPb6YwlQuQUjiqniqGBGUkayrzCoBu+47RGJI0tVtRaeqs1QNpFLs/lY+AvKe5/Pdazdj5XSBIL0nvDiGPiNOVT2CNcZ5UNoZm7HOCZq4FD5MW6iWv/mDlP2ivY1VE1XMcgWhJ1wqhK9ARPas1gBLIKdoU6ggeLOgTc8wemuePUQqtlWC7hHWasZuhyS84cZ6o7zewZoqVs4x6jyMmUIbv3Cg6nULEluOqcW2irk5sdmtz5+Du88O79/hgN924BP+aOm+aYgpc4jJhXaIUm97kIp3QnhmCCRENSluiP6W0T0dP3nnwQGFLWMIvJ6XmFhl6tfpidsdkYRWa4uHIYHO2uxCJLt4mbsR76N+OhhobXlGaoectFHk7E9HRqFsr/xEjUUWufjoGCOl8cbNg8vj30D54XfV+FLFV0xgnKkSH4G7HzfRtGyY6FlxU6smL5e/byKLIOD0ef9TiwKtA9RgyYZLCP5nSdu7g2/Fez1H3dRLDcm/rC60Du9T2mH4jHhp+Vaw5VLsnm0UDCjW4dEqPYhoCkgT4tUI5oU92GFr6aHNPzb7hloenHh+LLF/BqUEezHMDnFXIaffyo942B0dMh+b2HMSkhNF5wKejgxIR6X34mYFz/npfmXsOLLsYCM+wr1p4U0TCq3H5fqZNw/mWNwpuyV6FgY97N4OnqzhOj1WeXiwlKXmApY7bBWdyGEa1AOconjZMpE3efh+yGZtI7dPggoLogbVrc4xHDS/aif6t4TIDujl6Lv2ZAuWqOA1PJZolqiGFBKRo3W4rL1jsOKQBTKjnIX8PTqIgp17YMO4ETJPXWHIjQhXp8KezM4RRJgo0UMu6B6XcQA6H43iDGmkddWRsazH72w6am99wmhKtZTHrm6iEps82a+vbqmwLliAPHo/VM9gbxyOyNjfM+pww11t48Nfw7srLoftzEGra3QDHwCbUdQXPO5fxZLNnupyPEtlPQeRF65YJDv/rJ7Ovx3nsW7MaBKMFxy37N6dRHdQs37vQ7bSha+gMghZYisVfaN8e6icdPW6rtr3Y4wAEjHBj+YftXK1YUmDy0mYBYkiaf3wPT+TY76aKIx3t2t1bnWHJIYu2NGb51eXUQfU/OOquNyUwy/+vd1jZGsqjNL9D1NcFYiSXzTGX+1fzgfuEowKQNzW36kUGXGkSVsTkwL2HELezU+Xee23tMCqFaAcj8TGicpomz+llJGg3V8rNTnPymtimCSx7n4enomvQM6FbBaFKqY8Ggh7jpu5pqmubQ29bjDh8G20M7ai/HedNvycBwL0CQQFiGSJ+SLJEaEDt9eIO5ZBON87VEdUzkuzSPn2He8/b6w70jY/J7ao9TeLyxKJPMEfByJbbt6daTU6LTejyGl0KuLqAw39yIyuH5FWMOYgm5dpCyNeCH51SeA/z0SL3sNXtvc60vsrlcXnn+1mO5gZ93iyIkhSlenjQUrxZK1CS+P6k1aWCbapVBwcVaoCGpctMp6ketTJoRjxsCGxWKyaHLV0InfpnGimsz52nHXXhEqTozZjBe0Dk77w+oiGnma9wafF24q1DV3jOvxtyRbjHnfzwx95Xs+2Hw6RHF7c8zPCIxO+RVeYJmA3Jk4trkD64k2p913ncHwElb3yslViGlnFPAICm4+GMsOBbqv7HDCui7qAaqwxzDzBP0Oyx/Chs/+YQvWXqy17LtPU+DlKZ5tDI7s65FBLBVtH1LXy0+Wxw3DVHeDAyfUZuD2d4TeYm6XnVfbPYjFFk/6PSuuX4bnX2z7987e5BD2IV8XRBwwarCsab1neLIUnBKiEy4Kqqxr7hkGnRUm2ByemVxxnUrvMa7Em3HNkvu0uel0BtdjX9w9zWooiXimRi/fCR5KjG+KfrcEndAZ2YPdrsEjctaRs1MvejH5vCJDWPX0Sh2aKcaABbm68N8XorbkN0b2aB2DJyVappTojIY3AsOjQ8COYLV/3O5ge7a9D777783GGdEJVz/tkGneq2sZtBfccfenvd9hqudXdNQ8b19gIbTJgMvzR1HAmJHvkNCKQGyv0q705D+GsLkL7nimwfOgOY3Hb78vGo8PMBNgbDI6Me6+Y0rnsTRowu3PmIhwV7a/AM0gLu2wxNRjiVIwUN5iRrcRqVAHP2F40I4LmpDyARfNzk+sGWML0ZaZ0Db2I7UfM1AdgW8txojYqyi4C65y6yVF2YxjveGzsB4OOXa4svjRTNt6f1a5uHAmJE7rYbHL3pvdFdDflX5a2dvk6oA5ne7/xRq9zcgupdXdrXDpdXUHp3p4cWAUUewFeN3rOpBkrOHAetdQ1OIiSiXtQ6mp/A8FF/SnQJdY3RhAl1Ym3P0sVQ3LHztGKDogfpQcenZZmaKJ7egh+9YCkBbqmi6/7q5igWQNMmM8Z9+Q/G1PYLNpLae5vv8oZ/ZrEx2ilkOHkaPoExC1n8cNAQwOhV5xx+iCMM20MJ7ufJqgFkE1ju7j6nwwBpqv3XnagFZ/eXJx4Rx5k4z6jhwI5O6PT6fecjh4qb0wIRdjWVfz+TrYYrbxkSzYcYw8VkEDmqPNyCdI4hA+EJYrY+Km/Wb7bSUM10QGSdOMGRQAyfUBUKDEwxQhB0SGKqNXRxQvODPwXMPzXxQeszMrPJoyZvUemLQbQh2e2lIyagSTcsXtmVFc8i2/7Xco/rC6cJQb44xP+2IpqiSY1ZWieqLqyLyqMuFEECQS/mt5L4edTLTCWuDqVgaCQKa4ZQZkJwcQx7VCXILIDYNuyyrd1lxgZQ7kB3rqxv+73eOhwcrnOA9yceGYI0inbC/RkHc5ESLLTTkxTEVLUXM6Kf/7InBSD0ghjs2rv3YxFT8QksOjKcawRclOJSW4d8WWX/NQFsnFhQPtplD5DpHpiWHuGHJQYTZ997eT62Sc1jNF/dcwRzjYW4paRoYtVxchXW/uNWGHAXJkL4tgtJOzwdKzgkvdZ0A7knMhFbuwG5GHZBD7pQz3MVaz4BnaeH9H8oGY51XWnmyVfYwF0KsLL4C16BneViQeCBWnvcmIurL1mBfMZrhAEforOnjONfklBnB17evdwUPoKM6VvWDd19OzyK8L2Z1hvP1wExtvyj86yUThHuXKfl3/TsVtFsfcsvC4nDYb179YXTiODJXsBrSRMP4PR2e9u9jp5ftfrmwEu/X0XWXBbA3b6/XCdN8e7OTqQi/0ew5K3a8EPW66ulWXSiApsz1DvMtSvKZTQoxRwkftFsR20uqtYnxn0CaInmjNtbk1DDx50+aMomWMXQ2oHGZ4iXYGIibQN5pkiwUUO0r2Y9zpHZgLGE+B8gRyh/2+8BqBqYYlhJjbmSx19mgiUAtPMp7Li0my33y63mnZmoU9//G29gnjoixAqYEJ1ViyoZve/gotcwr5saidgd/WDa7ducF+vMJjIso6otpDofIEBMASLiCA3VkW/yng6nr3h1GKlmZnMwA72eOAngbTkLWd+LGhJJRa/mlEynD8jGjHav3NLTmK4XrAFjjG2buO7SWtPbg24Fd78bdjY9ilHuIJ2NEBi8Ny5biioZLfvYLxmaFTJJ8LH9e+NJwQq9em0dwV1X5ODPB0Y0ZbG7naQ9gOf13Dupan2TvcgrQTeRolkke3YvaC5mHAcu/GWMNNQS8ugqtsmtu0eGeYAANJdwsutaZuNMdRwwwZAIFrobm3HQ58iozB4FSgFIGtKLPy+B5jmQ3uMQsNWy0A4fbNLPyHbYKguHkeNGpPNfmvT+taHACfdmqO++H06kIT+/iu2S6j3cdCVldH9M9qSAqnvqIHcF977YmWVka8wyQ4j2hIhf3Xn3mMWdariyCsm+sOcykR1yrsyFMYAgr5ouC37we0NZduWAyIKk7KwyNdLy5CHd5cQY+qNaZ4HZgbVvb9nrzClfhcTT4qFdt2RZzduxflBevxXqlQi4tgoZtmrd3iJF978ql9sEDrvR78lA9V+1miTyJB2xRXVhpHQ68ufOc0uc92B3MWEH8qBibkXG4S/p16eY6hCFjq09s39HMDLBm4vtJtgsIYbg6tJvAUFFDizZ2YtAZLfmx1i9+lHwFV+uF07QsJRLK/njEg4LDM4Z49qhcXzkc0N1E2mAKPN8yxtbt1zNWhDAFjL16n9nAYkjfc6H4ySx0tZHp14UrT5s0btbiLLb6bZYP3UB3aAiJ0qaNBEKYEeClb8CWnk+v96eTiwqnBpplE+4BwRMSZ3bDzylZ+dGFqQkLLMtdoIa9rRi+e/QO4WiNxFYkkTXMntGex3xc2Lbb57Sv6oT2PvIcIhYN6nua+rrPN65ln/JE4lmjzGdeZWl2E7g/krIcgeyy/F+wwhwmG9CEROsHndVlyDJt7xcJ32/4pjM5B71rtVBjB9ILWe46i3rND5IwnPlDewmvBXm00nyoymeaSr3LF6mZTFupjWvFh/+yvsXFqdeF5TIhQ7aJAuwvE6mW9deMClFLGcYZUkTAmzefuYHTCtkUKvUVBTjHJnF951T2/tmxlhzBMMy/L2yzI2akpmN8dFTKRqtE8fIYBz3uWFexngQETMLNh6t0HXyrQTEtnM8rZ5FXEXKjLkL59KPuxba7uSMHZFZ7izmhpIxlW93A39L1m0NSY8NDlEiLFpVz3BABA9aZAAPjte/IyD9CQD0P4p1tTuDz1uQyVpclNZtUG26F/SUFer3sq3Vybk5HDlwJtb34Ysan8EVLdhy+FXF0o4m4anmf7GsjzXC912DldP9VGxz1rVyJeTF7XbY1u2P0cWaNaXEStrkW7lf2KfXcgV+0jBsBTbVuitvc8sSAZRNjcVDjsJ+AqtFuNydSsUMDzjRmXBaElms+xh8w62iST/VURPxQZT0mMXxggrtITiTt+vwWgYVCtVxeOOUIpY4cVbL2dbGTVHaGI+5eyjjN0d+zAtQ8HVCVrvFrweOcRjB5aFHsDGC1iPzU0tUdOJjAzR/QDB3w/koT9vvB9qHbNFf99Bh/2LsMS8IAi+pfIyNJJPAj+fY7SDXVf483J1YVjtpDz7vglbptoN/Lhlo7qmuO04xDypJg5Yu/f/nz8/t028lDyyNWF359dz5vX7apoCYctUUzY5eiF8skTBAsMose0uat6Bpfh5HvHE06Kcjz/Ap9fGyyzbRTulHABs2TEfmywpuSQBHJoxTHpC6acW1xVLkV29nUfNUa9uogidvMWTruj7CR7vghL0VCjqFZQXvR+pYu741+7VAOTWA54lpfeQ60unM6Jocr21s8YoACDnJ4Z0jxSkD8zmj7I54pRFW4N4+VqO0Jb9NqrVJLh5iGs+H5ED+VU2wcO9kSksXjrNmqnnbPrriwTTPiYv2PJYXMf9gIv4q67Oq6eMwpaj6aSM6qMZCfFnHb74EhREa23tY8xEuCA0hePawJUaAeOB9IIt+cAALT/QemtbKL1TQjzJkQVWjwBPvauEHD0eHLcFteYl0G1b7TYMkPiTpBwSNwtShgiwo9X9CKEiJwTjxQ2jxvj3GLrGwJew6HVEO2gK+TqwjFlqLVCI2nRxb7ndt0JLIMHnAB6nPhQOImQYmEuYSBvLy8ZIA//CVFFE7WCx21HlJNumsLOmDOSzxJd8QCB+UdXqSZ4LDECJ0KyvZpi8aHucGW7wqLNXnc+8PkrMIIznrJE+ivmfWncTvKvGD9SrgvRBj+2ANvnjHBqj2drj0MeVZ9AlXJCiImj4HUw+8SXvzjZ/s7VKkOxvUc9DPx4iesUaUhXbKvFhX+SJr+fbX6LIVA6WJ5o4DjGFwlyY2D370dFs1yh20HaL7ncADAjJ+lcIkX0lD97ySq+9jJm2VcIZuw2x41k36xkA12RMnLYzHO1GepFkrmGVmuzHQcPEfvytuGj9UNlkjTPHbX3K2hEQ17nHr1i1/kqvsvVRfBb7QMfhvKj/dfkGhvbEXaOfmSFbwLVQ1KwGC5TMY7aHQ7L3odSSgKIJmwzeqLfk9TOgNqZxf5Hf/7Z97+K0JSQn9GeQjZ6KBhXA2rFN/qOqv3td0cTDppNvp6uOOy1Q+0B167T9KsYJRYXDnebG4payLL/HdolD0jqUqckCG7hxNmM5g/yKmJkgOUwKLrYjy948seYQMoR8ERthikaSaXah8wLKM5BMrS75fKbS9PxM+RQ7N/cPjyJAH6Cd5yjJ3/D6KEnN8BrUBMR2TuxYw44Zx4pov/VneJf0J6i+I1/YLztiHdydeG0RLii4L8cMZZldTT1TySTgsMYSU/KXjRBs158RotV+Q4penXhqUKIPy2fhh+WHQaoMAZZx9ABpR1n8Dwk7Q8TSHfNj15Ye579niVD6R9KEryynuz5gqWDYa18JkT0kfao1UUUdlo0dVSDKcCftuN9KsC/D60hvA40OsrX+GjHemHSi4t2oEjqLeVydeHYsX2AmtWi72FXvl34vlv6iHUBHEaV+6i+9+3fk3sd+9pHkVstLhxUdm0vPNwONHcacI3cVdzAlFMe33ZPQUfYpRLVE9sUY9qXXl2ENKZ5fyJOE3JJjHxIlmz6x5V9jlxKM6Mk9R4nYmSqpdaXPV+GbWyp8WnVLUwpqgkNeSw/jG5B+09rCgn7USAJ+ifZPZ5NTui1YGlEKBjsCW1feG3zsA1ZOxPL0BVPOiZoyVgaEcIUNMqhxGRY095LFGRVSkSTjhlNg+/ALQa85+zi8MuyhrLt5z3gnd4ilJ6a0GfBPlWotSBryP6p7N32OUEK/VHYPKj37+cIUwKpfSCcCt48zjKava4t566d5cDwOddDMrBofFtPf1bMtju7gkcxQDRdGyAZAQwhF9rskO6gUfYGyXJ1oSJZKN43hBHIup15Pe1AerxTSnghqp1RbiSbKbot1mpn8sKP0UexRVbLk12aeDzmySgcD9Nlv14358PqZnexI1BJyHPedgZ8Jzg95LO7BcAA5KB4g0/hNAsH9ROgAH0dMf7bHgODQgER7H9xxt5Teh9Rz3iJ8i9Hmpir6kDO4nAeD6gWF1GVbd5st9fNTbLhbGOhpN5ztGnTnqjiPndLe88ZQsoIum9z5tACWL6ljAT7cfZxNJellGOgfGfCrn0MwuNLCye32gcurMK8GOQHlHGYh7B/qhW8MIoaev/zcXXhiC0GRJfTTlBBiyKwdCi2xf1LWZZXE/LuLnL5PNfNSxIWRPKYbCBXF6FXbN6bYBAcAxAQjhOyJt9aosOBqhsH7X6ANgM0ggm4f75tG2mjXl04LRcfF7M8z/OnHn6d9rITrKjsK27IktJmp3uTZZYZbABJXkPsvlk8dL9YS5a28KXkHIHIdF+32PcGruT3hc4Nw8XsiGfoOLZu6a2SDcZgTFBsM3weuoq0YYyZl21z7rMMFeijaH6Gjozg85D0IKc+4wrbriN1DpalGhzMDybgyjfiPYOMOI+aBxMgVxe6mZvc+QCbK24Cy/dPWDfVVy8X4Q1m8DwkL4yuLUtkUKiHvs7+Bcc9IY3SPzSLnNAsyKiHzs8aysOQvM0nb+53OYVGGVoqGLXtnF1GZJD1Wu/y9XZ/Wr26CHamaTYnbRhltKM6uuHP2UtAY3H1zegZZPlK0/lNAjismIsKzgQCpW5Ay+nmGYotEitCKwgW+PIfI2pcpdeeGKbn6eRzuzSSQ8csRtS4MTi7GqrKa5/ARGEVpW1n0DzvqWE0+NhFsuFasJ9eR4nUUJA/PJGcoyh/+0yhKDconlD+KhCzlpiOJrJcmqdNEEPRvdz03le5mii1PK/mkas95EbrWRNMsuwXW4iNlgWBSjnrOIMie08MQ7KN9AVAYIOgM43hGZQ4o2nkBHBM5SfNuydP/DUWBqE0Q6Od1/NUF6aQq7y6fJI3elrU3GOAq53LazyhXF2EJrB5X1HGTNM92JQK0wAH6qI9SWgIJ7RxsXwmZvcW+2Rph4DN7rOz3l7aNBZS9nFoBFL2CZqGHXtpx+6wAQj06kKz1K6ghcfD9VMwwugavRYUJdByxoTdx4pPLaTY4FuqkwEWcHvOrxTdvFY1Q53CQGTToBMzltDufniibqFuv8qPLlZNEFmwfCK0AgYRYKmEHwNn7Z2yYxiBZx8zlFHv+URMPDwM0yUPZpZCpJI7lU1TI5p9zFAyMDqkafoEQzQSkDd0BSihrHdGzoDhjOoFuahan/FtHym77iS7BdQ/HW4o2fJCLJHn2D/t17/9C84XXuFrC83/Q1m+Yzi1K9ntMlhH3Y7k44IteN4CT7Z4CLaObbVf7j9eU9pvwRbFVxQ0z+BTSJIYvSBp85FXcOG1vO68e0EYzUIzylHghgkynqNmVOnBbhrQv+8xvbpQOB4+OBa78+EjMy+cnztFZBcIo0R/5Txf2pLSPRR6LbtA0VSUfQhkvygU8KMM0PMuELKHQnWMAAyH9oK4g2Hc/2S+QRH9BLKC/bpoUUlQn/uvs9BY+zh3wWHQZOhxLYCmCeEjnAzB+T1vd8KZu9hI1jB4CWiOsvcNpMc8vMPOtu0EeI4mbxr7p9gzjugngCf6OvqETXvb6QzAvK5REBNCH1EAGhXk711xKUfTNKeDW9U+HYwC8D/dcIF8KGeMisoaZjL5yl0wtto/fSMAvboIfUzztiIwuXhyyJ1XQ9O+0WR7EtfTzHDWIMlCDNoo57pCw4Y56ds98ogFakqyzOjxIUE2xBV7qmCFMaq67GfsPgFaeC4+OORv55MwWjNg+46tBEeGc1ujAIAoZOjeZ5nsAAk5Cj6cbx7nwo5h9n0VleLTLvthEikXF1HobN7XYW8lRy3K4HGNbg/VHcLLos+7oxiYbRL72n85y1lKVGGPs7eHCF5ohmaG5DUxtPcslh95jpABXPdOiDHQx7OgGTUfktjEADWLGfZB8VNDh+fNwNIUjWZBz9t7SGYfrPZhL9xeHISnPWWgx4RXCmYoFthmaXpvKXDAOcfhNAdjGwdu9lX6TVVv888PqwsPBE3HDaCRvHpDi/0P7UX2MMMpgwliHrbLm5t6w4r78pEvK6i12hlsCktpIvS8HkCS0tBTgFDCsPsL8osYS8WvNc6Xjdv/wD/maoS09fbxMhQVanERlEzTFA4mVMDxb3e2wCBIibmgAs3MEH4SlBmTmPJmSZv/2P6sPfSnglShmHSOZvZtGzUfmgGEb2fIfpyRscaoVJ5u8FzoKTdBculoYDiKPVh4oYObiJyQchY8856R/5MXET0CuE9gwL+BDg/KWtICNEv71XjkOYNFwMtttKE4r78aj8Tqwl9GyLQtPCMigKkxTJJyL5jQ5JvSPaOyvYFNRe26bpEQHuUadJheXSjj0PWol89mq34F9noEvdg4vT2jAkDQbZQ9LajaQ4F7syDRvRZU9KME3guWfD80jXyoUGcdliiGB+Uaw5v+SQDPOZVxvVpgRYi47N/nQeOwB7luxKlXFyHDau73vK4FfSKY7WW3/xYUk1LRUtnW2HY1jEbtsKS+sWBOdW87ubrwtCr68cu1u2Eh+uCuI93TIOl2ZGzZAE/fzzqguXHTuTQmVBaDJNVNswzinJEkcnw/oz7xjn1jjtWFCS1+LVl63XkmAeM5Uh4I4AozL4O8V8zlW/EH3BBAri68ztRcW5qxv6OymOyJznsgBNWoirrUjE5Q8kJiwuuFsSueI+APjAE4CvHRLGiIeWC84zdoL4S5F8VNQOnVRUDaphHwafFtc2OLjN1Wox9PAK6X2CgQuf3Li8fdA8XomwTQq4uoYTdvc7Ir3Z7rB12U9iavHBVi1S7Fa97PWxjI92puImsAYPfPZf/sWu9xZAxZcTg/ofjEroEoattxxagEA5yppi1GQ6mbjrI+r+4Un1CBgUNnDIZOw6JPLy4iBwzzSvvIoFpwBWywcY4DyhlRwSdPIAIYRo/Wd2j+7YqxH8PlIlp5BT9AAf0QBDwYZvGWZYUewOJMtkCObpSCBge/t8QtR6nGGeUKssube9znciBXwihe5EReplOwmWYbM+4Lso9ijJo9nQOSqAxFYFMqBsrDz/D7Im8jBkbnjJl0+PGBUZzhRkbzIZFyDEJ2c0kxPlDQEHYljWxbLi5CrAMRzwlOA34vm/evHVd0okptPhf3PM996PuIwYfwkszuBvT/1q5dV5YcOfr8imPuGpKqiiw+XAGSv8AYMuRJkCFcGot19fHKyCTZF9ORZXQT4wwO+55TzSIzIyJfsufltJi2Q4kom3zFej4epEZVhv6gSmSVEpr2WD3kQczDObDwhfM+b+5ONsRGC+WoDULRqk28tLkLh3pwRrkjjEIYl4W2L6F1su0CtMQdzNRdbguZOrWjMJ9A7/6A1DNQVLaaQLkJpg87aumLnt2GjnQPVN4s94udOYuBScFDmU0nfKtOf0eOTZnSbBEAVhUP1uuYp44rpTtCoORbd3+PHHjgSMo7whWE51idpVwVeeUQ5cTRJ5XqHFTPSdGOMos3iWQEeuT23gnFF+kCaZ3Hi75yEirYIWmTrbDiXrmiN4qdtWI8awanB5gpG3rVzuAiHwjuWsbpcZbVc8ldDNx0Wc/+rGFfgX4X5gbP0d8ULVOJ5XuxnYBwCxYnIW/yzwp6jB21DAjHbB/XpnYIAQT7WrV7barmyI8hMNnL8wQChpR3qNnvJ8gaQIgBxsZgeGu2GcseFuX8bEMaBeXH3afT2Dl5WFOEbnEc8SF88TWwI2HrrtngYhbRO+W0xPBmsRwvq9wJc883K7hNYS/ConYh5diXNYTBXQ1cj7McTyjMx4kCJ3SjjksGI9aPickru/jTuXPUK/YHL1rQx0seTl641gBYKzRHbXnxCXnT6kdvDfpjTPX1ohPOYuDH3MaUo52TwBn0Y4tm51yOQfnZ661q0nqR23dMND4lY38xOOk5IBOmfwNKycO1Ix029turFHDSeb5vd0P3o4+56Ic8hA6SqSWbos05hsPQViZAVfsPojt6dygXGpkA3mLglN4yAeS8QRSraMAPYe3nl3tRuMy9o8MX8ZjWpB9tseShC95greUakJy4Ni5GfV9lRF6Tza/CFAorb87itJJ1RnOYDyWOG2q0KLXrPhOs6LaFX6N9vITstOknGO3YoGUT0GtZCujGIJgU2ZFZEMAscKNIj0LkHcls5G3Z5ArBJgIeQUhjPevIqadgj5PaFYH6ouMy4aMW+bya7GTBLAr83WtGPulFpkre9xo2eVGWBwDDjxeVkPopD/fzy0NUFL8v/3o0S+BsuFr62mKdrTweVoPD96DXnag8aOhhl9o/a6tdy5B1dDyqHu9ghwT7WjLbkYruB25syjYunZNGDpSX1il/zIa0yLW/DYDcqw7aXw0cVvQHFNKwwelO2i5Kq/b9mM9CAAj4q5cX6GwN0eV0TMTurwYnRtc1MbI1ZJIo8ryagFabBsnTK3lEb0+TgD+fdMvzEOwBE4Emz5hWYDiJgypKNDYEABj1s4i27DAmbEDfEgN+5+HqqZmhItlCAKWpaiMfM0d6I+10DXh3VwM1rtbpG3pq1upcOablmq2+KS6gvHuRnWzz5QVCVpvmLq99kv+H1cBNxJg1gyGwJ4zgHFzlhZF5XODbrKf3I2RJTwfGMxcdutPqZRoix6EOil8H7rJkOggQSfcF+QzT0PmrwQm4IhB7o/7iBlfVFmKw/QrMvfx7HqDdkEdB6XH32bTsppzcpvXwt5yKfPmq+w79+h3nWp9v2Q25m9Bq0H+lzWHH9B5TwWeHCMsgY/chJurDT62kRQAM/QruuXtEtf3Nz2rbqRNR62bXsrXf/KyzGvhxt7Q2uBjxX0ijE1hpCcYenqckbUNQkX3t7u+SB14ccXtD/jMTRUaAQhhv1H69txzOFXmqliONhv6HnOI2+/QxBXmHWEwohKVRyEtTi3hBsrLxgB4y5YRjR2s0cpws+U6bRdzGAwVgm+PihIOTyQWRr6JAKaUhwCLNuS4Nyl0NzlvpD2+xokkDenmdhzbhjdfKyiei1Q5plrwvywjAH9HZ6AAD5yyNpfiK0Y496VlvSN3Ss+ReIM0UP65oxjACEpTqMly/oIrNfkAKg13L+9W5wFsLXLUZWYElocwW4+TyWS1q7d1kKoauKMWdLR9WtvMw8VpNzghTuKuBgzZrpV1vpauQ+QXxjbI27uWo9LPg5+czLNkNtLwnNCaWN5/R3B5qrT6FA0uZQPC9JEtOtyV4yFUQB4NpngU2b6iHBPpxqrGhmQIjet2lheLE5CoI4JMfN8yAPeOcJkzg1qKLqVmbE9nnNDIk7rgUY3c1cFHEop3Rjlw70X6lxFlQzO4J10IXBMjGFuQuX5bHUV4Vge5icGxn920t+rEK4ARpPWHOhOLmhwDBOna1aUadUPyoJi3Ji1mt7/3V4GTpQHDHVSiKUcSL5XZVy47xUredrJ492Ttvp92yd+RcIOcCTZgENKU0RFiK/CgtWgavWXqEADEbRi5QGlPNh8FzV4MTDuuaWIrJw/LUpzKuFg1regmqTvhshQSyvsKIAVom56gGOUIC3mLgFN+CZHLQmkAawVJJfHQ8h19gl4brjssiH8aqL4RJ1IpcsHXTIrurgdtYC2sLLgEzFy+CnjX3HGfEvAgXCr5vYUAYX3f5oZg9MUpntjrxWy5OmaiKMaUdpR/kpFtaFpJ+ZQ+EzKTLmhc5kJTzoSVrf9GpkvBUa3yLce+pomA9CSC6ZyCKHUauTn3f04OQB8sIiOUEyJcfF7F3I85JwShnGnuyY97wpWXHxKz1Q/ep2KbVoa5THkTR6DIl+ONFTs45Qpt3XbFFvhQcamrtvMQ0QwiH2S/yLw5zZFQ1oyL8i0ic1g8YrqOamW3Lh3mLgb4ii2bDKKDxlZweMSEjxYMjKkou1iU9LbVPrlE0xHsIelmFnu5q4BfPUoqQZyEfF9Inr2cUYntIlDLHJd59PmOO4W9rKIuuXHJqhAUVWDi7ps7tpZrUeLqIGgHsTsmpaEeCZN0d9OkeVoMT8++aKCwWOANUye7JbsTDZip4Ccc8R2AhY1P4bwA1w8CCNie4cxeDA8q6D+LSpWGEhLEbYm7lpFY/vLKcazYuWFAtqdBIfsVKpfBXgxMv6ZqRI1AB1QeQZsWstGYQxMvsYfGVl637vMf3+1XsYyx1xFhl+XF9dROhcM+hQgvXXcZmCqKatj115T49rAZmwGySAeINmFmuD5cv4zZeZMoJE+zJpXizFJZLIQ95YKa33JgqtD4PQs3wFGe4O3RPBnq6D5IS7EnFxdewiZzqRYeYULpU908HfjEgaVGyox3QDcBm5Psdc8wNNYdUvHile3w4JIXx5O7TajR2yunSNOkq4KmW+BDG2JEo83YNLVEGzebQRQzPWcf741iUMrQdATx2WvrD6fKwC5fhV9Wi7Lcl/uUrm094JS24i4FrcSOWIpADbu5AuFUu1CuWoqEc9FOX7xVtLLij3/4Go3QkwHneyqnlzZ8v7OktBg6Arfc9kH3WvBwE7kcE24FXDC7vyER5g7/W31tuzt3wU7kmMQ9BmOF4DpVXCOWwCB1uWBnpErhTI4TirgYuKJnKnoSNy263isTm8VK9l8112pcpLvYA9W5xnqozLlPsrQbntHT/dOHwlxv9dnUczW2atSdYfZ9y/2YhLDULPVPEhwotjU2zG365oJlz2+8VWXLAbTwKiv3ldcuP83HEKw19iaAWzjaWqft8oCbTaSxul9FsM6KREzJEh72gJ5EKoRO2X6XoJSxokaxPkWdnG3ctOFH/rum4QhcUOGUcSPB6heZOWq+TJbBw3ccjoAgQsmi7HCwYauEWLcnlmyPvKR6gMtRSsuNhukjBXAd9b/LwK6HdXQ1cB7G2RXKfi5woNOtEuc85TAZ52VTAe6mwn3dpJQfcBvIIcGxVZ03cQsWuewhLFA9QEP+iOrdlDtXhOk+h0atHi7cYuGGwvCJ4BSFWQpsFCwtkGHIhxciUey8V8TSiets4ZtBoEL4pI7qrgfO77rJBdCFAok7SmkGBE9aw28N/L1Hn8yFVhNZbQ8VWMm52RebHvToqsrPIFbxVISMgQt3mldOolbjxTUaFjLsaHL/TXTeV0DVZIErWvRb+VuJTXGUpnXoHoWUKYrYU3XqsaUv+auDkwPT1U77GrSl0slyu2T2RbCoXVvYkKLxdQxueITtcjqLBEOi+U2ZibpeB+PVmP22VyehJ99lMQobz2bQNsLw/ecY2bwUjlDtyE96wpbVWRvXXpb0filDfoR46EJki0R2dxsjfs07jSNHLmudSLkwJ+/nlIRYHwO9JAXizr5YCIGQNNavQ4wQGlDlOm7lerlhMdJKSnXUd8qTdnZp82bF3D6vBict1zT8sckHQCAYIJWZ7W34eI4/jrUubTuXOqEyog2nl16V1V4NDS6110Z0jSnwhMpXjOIZs54hSTILfodqR42QDAorwFtkcebh4TMfg4QMKl5ei/cVEFALZLPCEcI1sWKkCP2fQ2rHSXPDZkf9MLKxNfRCsj+aQYDA3JhUOeY7iF0qDFlC5LcZ/y3NbAkxqx1Lt/NXgOMn+4FRvXLETXdlkIwWWJauD4shmRyMKcphsUkARJivn8MZU5bOO4Cb3chyaTssiR1ipjdjf01KwoMMOw+IuBkdU7xrXLybgIo9CcEodBYpOfoAjwu8oq2C+sj/41qxCZLZmfAWt9x+02i+JIzVio3V2SShhwZysC+1OdfvcGAZX4ncEBNj37v42OdbaER2XpP35iA/mSS2YJ44UeQTlRi+7VzCPWkRKedf21aZa/4VME42LXWoMxva5q4EbM+sWjIL60gAW0Bq0zVkjDCxw6rYhz52yq/7AxuDj5F9UvUtFaPc9Q3wMv74a3n08XZOpOJaNUiBQq5yIMuyhHZ+IHMBPCo+1dvIP6uP3EXiCi60kSvyokDbNQ4D6Zxqxg1Mpiv4+BY995+5uEa55SsiGRFBXnOvouuTopStP+/NBZO86jhWnIAlBtg6VO8eZzSY7r5tLfDvSF4gPtUEQ9RSIfIISHrifejsdGENp5bc1UeQMWVEUfLIgoltv7mWtxTg4dZjReLKEEBD2o+IIWMl9BmLVZ3tYDU6GQtc+togQwTvJR85TQLn1t3WSLZ2MhhW1qM2O1XmM7P8cZ/zTXwxcxbGYxaE9mdGF+hLfNHNP6VEk8uOGlij0nvWHeylAAH0aZItODFcszRoFcIFoSe+fTh8hAo7p7nKKquVHQhvKM1LH9pNKaDtqocgpt1qohl4EN7iWbENrcyYqRc2UsO2IuL85dGtNKU+AHqLyelupI6PIgSxUKlgKKLp14rWJIR82Vv7qfDZ/NXAaaLq7YAK4r5pQJh3vqbvTl82kvcUZr1O7xMl3hWSAs6/dPwZndFcDt6rWf1x2CyNPxcKIzZP3qsaW4ylOJRdn/HzCB+N6/YEaFnnfEHYGPooTT3Gc9Zuaoj5KrmbRVOeEIRa/qSnOauDH3Gq0WtMTlLHd92gbyx0bZ5Jr94rF0m8kY5m4fqzaz4fVwI1Uf7BpxTpF3poaInsd0xySygj6UrePQ/PX5dPRDFpq6VzqtrsaOEuw2EAWBJI15S8CbrRh2diF4SrLdLOpRd0g2fei/yPHNE5K9rAanKgi3OyFCQCY7CqGQjY5r+nBPG+QByG/7p9FyUB/IA/Vuvucmh9bLzHC83Iwgv5bVsUXbWXfALrFuA857lnbExdhsXFN9XwHVw6c31P48fb3LOR4Ri2kQWsxsbNjiIHj5ij0+1ruofR+9KiQOyo3HbKOnIrxDl0dg4u33we6iR+wrqigtlXd8CG3YTV8YG6YkvDl0r4aqv1nK2vhWvEr7TCecMPBq0l2HB0lGzs68hDwYT20ZC/kssISxnRZ82TPEnJ1ZU/Rx9spt4ie4PJTJzyJkx7pp46T48hv2uO7ZoWYFXNoFDLBYg9z8rAanBgKYiuaBVNkq7VVJIqnbOC8kxXixFw2pERTU9p903sDoVedxYf9zinds7yBiH5f535SR94fHH/TKZjRwqgRKPd6UOa/1GjZl+7+Hnmm0FFG5/m7zqbiV0W3BG2+r8297Pi5i8ExsXi+IjYmoaRGDC06+qRVcUeVeUdaXiY5WrrChZYRajyuBilg2GR3NXBTZpHRAzNGkmaexCudsxE/s9Uc4e8Inb07AetE1iqqbWEOM0yPCbTcHHLmtsG00JcF04LRgHL45GUVHQhwr3YyPJzLwy4bisuZsbXYHizLqdxBePFVZuo9dXaMfyz1WOeCwSkLXVgDWyZN81cD13BMA0U7KZhDtLeXq51mtzToK6ozZrvdxZcfd3QkI7+4+8+BUTxR625O+eJl1PlwRfelvX88bIay0/7AZhume+IAoKscKnnt7TrAf2nI6bIMngQJ1naozA7MD6uBKk0WHBA7G+WPCEbX2N8sVaVvnQt9r5SBz1umEj5hKQMRud4q+CeMCp5D5gi+d9jHkkI/7oJP1BzT32V/kbnb0I5aNmleALajVOhbYih+qTr64xzp2XdenRf81cBPdHePvzjThgRE69NQS105cUw5XfT2rta88E7DbNzXVLn9xcDZvvU4luMugK1Cvo1ow/nL30+qpX1fpUKOkCUKxJTgl+/xwqa8w8Az5ZM7RB/2PvrD+xOHr22wT/HQEfOc7wfheyUK5KJnPhbZIAsmosnHTBRwVwPnNNZhBkQk6mAgwfOYWPLLfd9UCtoTR35znBZHludJRgexdWWmajNoxTnlwlBftV98w2wWg5f3fSFjXDyavDMLoXjYirHx7yst3k+5RfJig3APLhjROS4Ods1QCyeUO3KQCZw0Bf6oetDkJApRuI85EIWeRMrFFzo5LEc7lzzKKeX9rGoLfzU4dKr79AtTEI7b/D9qZy+7Ew5ceLFGCxJnMevKYG+02pnu318Nji3orum40WcaztBaWyDmnh/05Q1dUijy6T5SutXxwXwguzLn67Sh9A5P3xM8ewMjFjy75drIjQfqODSO/8v3JBS67Cj3JffRgkBIJbLUbLCS6xoUkRlDzjl2hPbebKyF9uSqo9S+AECk0b7VM4WU7G6IEVAVYhTBnwecHwhlQ991O3meWsAF3HXyvuhPTs6SRajurOMogT/wP3O+DDPYFMMsNfSLwczERVkACNUa6YK9Fpszao65ueZawXi4u6ErFd6e/FVNfxKAtHr0PawGHufpmjUBdoCGZRVfqxzWx8DNvuBxoR0xgndj1X3jBsODisSqRwzpmQaSHYHt+7IpcpSsHV6OAuu0SEvgQ1yYidoaihR2xC/eTJjFL+RTqAGXy5nRLCQOxERtDUV/3wuN7H30h/fnmRoukC7B4sjZBJ1qSiKyAWcOjbsYOEm12hrBh6prHlpWOuiFeLgq+D1qi7pYca8fVIIlVnw8G4cwQatHxnTFrOWo8t0uc7TOQ3Mevhh3O6wK79Bpl/r3r5V95C0G5zv3hz3C9OoTHvE8cX7P83zSz5ZYIV7QKtwRBLBHOFexubcYKNcymUfQHKrnMR1VaMllKhTfUc7E9wTO3jy7Bc5SKhgSL3Y5it9ssxKOeBDOiF6deqK+Ogx8M35zYnN+ZqsebzU40Lb7UPi+cKwSBkPI9lbx2+ONc8j/dS8hemL6wwkTTyowSVNHYFNKMh9HpaENrpaG8LrmTiCFHTcGrcdLtoG8XgqGE/GbDygXWhN4akR7GcWbaoftAf3V4OA268OYKmrb8dwCjDBT5JcfN3CCQksa+LxRPmV/3SWLd9TvgwfUYFubLYU4Y9pRLEqojvUThPSM4X5yf+U6t9lRkMFTTox2dDwgnN902gvz24sWHgt2WXnSzCRSrWpJerP8WP66iZ2p1VeJt7sa6K3r/h29YeUxQ1xsERLAajmmN2EC4LwcVeCEQpKEQgG9n61OcvuwGpzT3jXQniEAAhHLdRQUbJEAN2DPo2o7ikYJurRGoOIwhHWCsja0506DLTIYyHnvntje22G3Ln5VbiKuRtWAUZpd/CiApszt+4xkQrpMhhcOXGTH0Q0SNT1Th6f3hSpqe4LKb8jcosoZ+DiivBe1peecb8WwAtcMduhm7MZ1/4ZiDhPyAzFKpMp5rNe9+ry962x7pPg/oyRT4mXrcFmE3+rQqdWon71yysp3SPHknFsPOnG4ssVidaJ4gtXTnd1kzir3KPFvJsJavKGy9NTsCdn5YkNKvfNIeeV6r58OuaQgsvug89YWCQpek+Z8JGubx6HDhiJ5CjK6D0rQQeBIwsKMyZ6WeunoHDvKkggmsb5RDSe9AHzcqtHpGeNmmiOYHcWExBp033jc2nsW3ueMGfNJ7hFF4NRkwgG0zzCHf6lzECdfpzfzF4MjR8xK5YR3d2KylkC3ZJ0OOIJ2hNI9waA3L9BtZoXYcjn6pWCbLlNRPGPI+OUOJZ4cJlPi5ZYAOWRtkN+sOsmxhRQgfC3EMxNrza1aUV0OmC1NAO9ZQgqtvq7CZGKECSto3iqWsKHTgiDEWV4r1x7zbdG0rmD6yumrQTuqawlfMMlMPeqFp4asPh7DeWoquCxRSoy29YNoRxtVb+i5MlQpdzXwr90fdkmuB8oJo/ZManLDR1YoV7F2ZOcxS99dv5BRdRAxKiIDhKZRpenop8six2Jlg6nOMQfxXvzMXw3ON+8POyXeNx7oAQDmliDuzxQbpsYsTfSuyTKOTxO075Jfs5q8xcBRuWmiwsiABxrq01dxNz+VnPPukFbYe+kP79FxJI4OvqNMicC3Poa6IC0IjfqaoBUbl+s4Ek4+ljrw+QBCemq6f8pQQy/nMSVlHxGZQ0+a3/cpcIQ3dC2cL6cOxNKebne29jPOoeTE8vs40LsDtTAQALQc2Ywp4Kkds5cU83SceoxHy7keGkEB39OsAEFyVxvP9rAaODKyVlLtPjBv4kRh91VtlLWvtnAt8uv6Mwog+wPgRMq2GM2qxRFH1M7Fvhb+bccXQl76A9fJKOs8ipXCYxyi9YV3KMmOKiXCJiw8KuAyySYLAm4RUu8gshQAUu7xfaEIMwXdNx3awr9G7UEJHToPn+EIHcskfzUB5g1eWjToaCfOpFwZpD6OAC631JyWr4shlsvG9sVzDC2760Kj/mrgpMEaINSaEAaBJWxx1N06lpDrLePphDBEbW4gQD1d1mS4HPNiPKwGJ6iCYAuOXj7wtiquQzpmlwie70BjMPP5kCOi4Z4iXz8bfj9mMOhhNTiGDIav4dTCPJ5oZIlkAAsGOUEiR2beU2nzdhtNTpb7ikb9SFa4SzTb4rgTSt4WGkWCuyoANVsC94luuRONuqvBuXT94ZKiqEbwgw3hFZt5xGmXmaDwvaJM8JEpyoe4BPk47gwoohFt585QWr5DUSZO3hRl9FG4LtibI9dkKoVnbyj53cGEmDvqD+7LRtNb6hE8a52v/J04TYf7xUgd6sr7g+svmP8OpGjEDi2iHxTJDYo38wQmecuS+D2cSXm4kVrjnUmK8Peoym+WwlRloeFA+BlN53K2uU3emaQwdVk9RI/VwOXTomQZDnAYPW8xcGBicjze8pERdrrRj3Y2WGWmkMOYiZXlIGmAW27AqWKKvMA2EzAeVoNDCkcBX8N3kDsjPy42XNjH0FSMfFGgolVcBX0dlWzX+yovDuStBseY9gfjK9taS0T/Vy3oECBQHtTcJYvK+dJe0nfLYxr3OTfQXwzckJkoKhYX4fKi7VfGHHbnunCYtSHATOxVd40bajBv7XCJAodDLtyTLLRDFn076SaLipcBSUdUWyzbqNx3rjKFCBs4JP3W3d0k57o4ksseaeXNhpm0ciM/K1pviHkrnOPIvfB4uiocTLMFK06m9ioR+j9p0MNqcMyEdRxIgPtAyjdSMuIoC3YQqkPNV+3j5/N1qT3oD/YDLRm0w5AOqztQTvhAzndkyDNf3h98vxiRgnJelfEw+WBeX4Zw1vWtNkPnErg7bmhaBXMPq4F7MCubLyXi36GSO8do6qNzr7m/20N03wxGt57+8nk5ach5u45mm+fcG44U5gWRzdHmOOjop9DzQE/A8XQPq8E58NYiCW8UTRgasGIe80M8iskZ3EJUp0HieGJuhm5QqiuU668G/rr6qwW3YqSjwLnoPjm7So32hrRHeqi7ewfQHiwW6Pyw2uL6slVAcEc47+4XjSapVei+FcFNqZjdp1J+lltTZzCX3fV5AJPqSDhrA38eaIc2uOTDauAOa2SeCf5ASR1oo+DOOiUBbrg5HlwH8IsZqMSMGKSX2wFEk9FpSE7ubHBBzyU1OhukFnZyun/Q5K9XYfLwNhjULtt6rrYX72hihwMmv7g/PIf32imsGc/X8PpwMwWvapD0RNRkhF78xeCcpq4TYYUzIu0fA+swkse2z7OKDmzYYWDYxev+RcUIFgw4v5UAXfdhrfi5PdogRbJf3N3HyJgk1iqG2FfgITFe+cEuzvcrzkQliybAUZGoQKKVVvCwGpwDZVKkQOATieaIhgohtbEd3pt37M4OD8y+e3/Yq4JULP18lf+NtVk7JedKfX9H2O/tD8/h7KxztfX5/vbz9/D3IFv080/HD5hOk2P3A+N2QLL4+a8e/vWPcGALxbLLy/njv8O//Duasf/88T/hL//3158//jfoUHMhxsCH9oFrfuA/9AMVVAYNg6/1ifUr/vMv43fkeuZ05Ov9l/xDP5GR6yivj/6Sv/JfMh7w3/4If5P//h9zdyUHCmVuZHN0cmVhbQplbmRvYmoKMTEgMCBvYmoKNzAwNDUKZW5kb2JqCjE2IDAgb2JqCjw8IC9CQm94IFsgLTEwMTYgLTM1MSAxNjYwIDEwNjggXSAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDMzMgovU3VidHlwZSAvRm9ybSAvVHlwZSAvWE9iamVjdCA+PgpzdHJlYW0KeJxNkktuazEMQ+d3FdpAAetvr6dAR3n7n74j3w4KJKBiSyRF50mTCPn3qC1RS/k8miXqLXpclDtzvfj9WJz3ZNPrS9xCdM2N95Iu8XOkXELXwPcT8f7eKXxSNxKH8wwoSyUTiX0ums7ErTIkw8QwkGbiSMF14O+GbAT2iznit9ol05Hwz0xu5aaspPDweWphCau5W7LsRfpQ3MPZMh0R9NvssWc6XLw4ISPXc9Hy3kxlzHCqDRs+zrWCZVjDXL7YxyMvEhDdU9lpWbCk2E1UCYEwcUtOyvfmpm5THDKbleSmr63SmryVrZJ2yKKlf4MaRMbfyhv0IKhkZiwHkr2ggrSGmBceJIB+q6KviajySF93E1TxVJ8ndYJRiZ4+WPxcRBHtqRybxX/IFTav2W3bGxkMVSw5GjVPqflWirti/Z617c+Kn+fnP7Yqe/EKZW5kc3RyZWFtCmVuZG9iagoxNyAwIG9iago8PCAvQkJveCBbIC0xMDE2IC0zNTEgMTY2MCAxMDY4IF0gL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA1MzIKL1N1YnR5cGUgL0Zvcm0gL1R5cGUgL1hPYmplY3QgPj4Kc3RyZWFtCnicPZNLbiYxCIT3fQpfYCQDBtvniTSrP/ffzld0MosWtHm6qvyU1/hjMb6fvHesHHlq2LTXZoyvp717OPHhUSN3Dq9SpHyEz5ErRqw90nZbIvM9WdTEmjRWpmrixnC6fV6PSa9nsUbsGscoiLE0OeYdmnV7RffV9uuxfdqzYCu2zTd9m6qTE79tjlah2k6Ms4Zt3DmxqSbygiybfWELG7u7pwkI44cju1vm63EuiuPLFfWKN9vprXK/DOCmbc9VBC8tuV97FCi3lItfMZVDt8ozHOSKfnZOW7Yoe09id4ZZ/dTcpImPA1e6MSY0Ts6sQXQBo9LXOmoEZcu4eUHDzB4hy3ADck4/DMv2zEXCHRcErHmEQpBcwApcMikscLQC0YJksus0pJRvZ2fabW6mAbKMQi/yxKgyRPFbEyhD94y8o6QnaitVs+qMPbVeuqrgGt63KruvUCpFdMK3Qb9Ydkc17XhQtoUbuLf1bJmgYVjdgCBWtEd6d+NPii14XtLzfxzKZnvlAo9NF0DdrmFiILsShCn2iIADESTnfHVnq6btnL0bUCuXLcy4k0GnApvhhrA/z5laDOf3gfJKWj2XpxroK8+7QUJCW98/rytSmAm9OFKfNLhQhqhbvLJEHoqyB9skeizmp3Qmu9/7si+TlVFZXVPViqCySu8LFNBfrtcS8fOeqKOQVGZL8Hfzz/P3H4io1HUKZW5kc3RyZWFtCmVuZG9iagoxOCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDkzID4+CnN0cmVhbQp4nD2NOw7AMAhDd07BBSqFTwK5T9Upvf9al34W9GRje2TnxpsrbjTj0Mm7kFgUnqQvLbKh7GOAeuarfZFFDrKUch1lUKoaOUu2Fve3lvCsLdIJYypI/pHjAuJdG/cKZW5kc3RyZWFtCmVuZG9iagoxOSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDMyNSA+PgpzdHJlYW0KeJw1krlxQzEQQ/NfxTbgGe7Fox55HNn9p36g7EADiOSCAD473Ia524en9RjWc9inP5em289TO61q2vdTfax6WyUrExzLarW9ntxuxS+7wLaMefH1xNqXRXFiLQvnxHR2fDNdbb5YibyYRzOXzbQYKOW2mAdFv2pp6ccCpXR21rmIg7Etx8Fl4ixO4E770gZ7cqYKhp4yBHGFvkM7YsHZbJP0Jqjuy6IUC86onkBRKIfnMi+h+lv2IeskHcbiVqUxZPlAE1+EJt0pQ83pB2sIcfGkgw0w4BcYmnH/n2VrkL0NR9hpRhV0TvOMN96BywidOVChZkXMJSncRKoYqUctmK/gBMbyXZHsx5GfM+kTiwAzgqUQENXofx/c23krcuREakoKPrxeju4XytGbqctu5rij+5ZdmpFSgMP+n9rr+foFmDF5uwplbmRzdHJlYW0KZW5kb2JqCjE0IDAgb2JqCjw8IC9CYXNlRm9udCAvRGVqYVZ1U2Fucy1PYmxpcXVlIC9DaGFyUHJvY3MgMTUgMCBSCi9FbmNvZGluZyA8PCAvRGlmZmVyZW5jZXMgWyA4OCAvWCAxMTUgL3MgXSAvVHlwZSAvRW5jb2RpbmcgPj4gL0ZpcnN0Q2hhciAwCi9Gb250QkJveCBbIC0xMDE2IC0zNTEgMTY2MCAxMDY4IF0gL0ZvbnREZXNjcmlwdG9yIDEzIDAgUgovRm9udE1hdHJpeCBbIDAuMDAxIDAgMCAwLjAwMSAwIDAgXSAvTGFzdENoYXIgMjU1IC9OYW1lIC9EZWphVnVTYW5zLU9ibGlxdWUKL1N1YnR5cGUgL1R5cGUzIC9UeXBlIC9Gb250IC9XaWR0aHMgMTIgMCBSID4+CmVuZG9iagoxMyAwIG9iago8PCAvQXNjZW50IDkyOSAvQ2FwSGVpZ2h0IDAgL0Rlc2NlbnQgLTIzNiAvRmxhZ3MgOTYKL0ZvbnRCQm94IFsgLTEwMTYgLTM1MSAxNjYwIDEwNjggXSAvRm9udE5hbWUgL0RlamFWdVNhbnMtT2JsaXF1ZQovSXRhbGljQW5nbGUgMCAvTWF4V2lkdGggMTM1MCAvU3RlbVYgMCAvVHlwZSAvRm9udERlc2NyaXB0b3IgL1hIZWlnaHQgMCA+PgplbmRvYmoKMTIgMCBvYmoKWyA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMAo2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDMxOCA0MDEgNDYwIDgzOCA2MzYKOTUwIDc4MCAyNzUgMzkwIDM5MCA1MDAgODM4IDMxOCAzNjEgMzE4IDMzNyA2MzYgNjM2IDYzNiA2MzYgNjM2IDYzNiA2MzYgNjM2CjYzNiA2MzYgMzM3IDMzNyA4MzggODM4IDgzOCA1MzEgMTAwMCA2ODQgNjg2IDY5OCA3NzAgNjMyIDU3NSA3NzUgNzUyIDI5NQoyOTUgNjU2IDU1NyA4NjMgNzQ4IDc4NyA2MDMgNzg3IDY5NSA2MzUgNjExIDczMiA2ODQgOTg5IDY4NSA2MTEgNjg1IDM5MCAzMzcKMzkwIDgzOCA1MDAgNTAwIDYxMyA2MzUgNTUwIDYzNSA2MTUgMzUyIDYzNSA2MzQgMjc4IDI3OCA1NzkgMjc4IDk3NCA2MzQgNjEyCjYzNSA2MzUgNDExIDUyMSAzOTIgNjM0IDU5MiA4MTggNTkyIDU5MiA1MjUgNjM2IDMzNyA2MzYgODM4IDYwMCA2MzYgNjAwIDMxOAozNTIgNTE4IDEwMDAgNTAwIDUwMCA1MDAgMTM1MCA2MzUgNDAwIDEwNzAgNjAwIDY4NSA2MDAgNjAwIDMxOCAzMTggNTE4IDUxOAo1OTAgNTAwIDEwMDAgNTAwIDEwMDAgNTIxIDQwMCAxMDI4IDYwMCA1MjUgNjExIDMxOCA0MDEgNjM2IDYzNiA2MzYgNjM2IDMzNwo1MDAgNTAwIDEwMDAgNDcxIDYxNyA4MzggMzYxIDEwMDAgNTAwIDUwMCA4MzggNDAxIDQwMSA1MDAgNjM2IDYzNiAzMTggNTAwCjQwMSA0NzEgNjE3IDk2OSA5NjkgOTY5IDUzMSA2ODQgNjg0IDY4NCA2ODQgNjg0IDY4NCA5NzQgNjk4IDYzMiA2MzIgNjMyIDYzMgoyOTUgMjk1IDI5NSAyOTUgNzc1IDc0OCA3ODcgNzg3IDc4NyA3ODcgNzg3IDgzOCA3ODcgNzMyIDczMiA3MzIgNzMyIDYxMSA2MDgKNjMwIDYxMyA2MTMgNjEzIDYxMyA2MTMgNjEzIDk5NSA1NTAgNjE1IDYxNSA2MTUgNjE1IDI3OCAyNzggMjc4IDI3OCA2MTIgNjM0CjYxMiA2MTIgNjEyIDYxMiA2MTIgODM4IDYxMiA2MzQgNjM0IDYzNCA2MzQgNTkyIDYzNSA1OTIgXQplbmRvYmoKMTUgMCBvYmoKPDwgL1ggMTggMCBSIC9zIDE5IDAgUiA+PgplbmRvYmoKMjQgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA1NCA+PgpzdHJlYW0KeJwzNjZXMFAwNDJX0DUyNlUwMjRQMDczUUgx5IIxc8EssGwOF1whhAmSz4GrzOFKAwBMkA8VCmVuZHN0cmVhbQplbmRvYmoKMjUgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyNzkgPj4Kc3RyZWFtCnicPVI7ksUgDOtzCl+AGfAXzpOdrbL3b1eCvFdkrERGkh3SUroMDWkjVWIMqezyMy7CtlT+DiL7XD6/0NY60JyHo4uNCaAp96WrA3YVrZIWvusoMgTmENhommhOUXAKCbV92nCQh/oA6zIidr0vBiV6NrKtQ/Yg9hOpGVJBOfCOhFCEh82+Y/g4cTztzRNgTp4MOCN79TNOKV05YTkUMDK3wy2w3tdnX89GuYi85gdhDiLHInJiUxMMkkCxHF6OdPDUU6M2A+RRXDBRx2yxwM+9Zz7oMaRT6JHt2FwupF5k8IX52aHwYD+3AAYqqrWdBjtYvb+OY72GDb+P4VrkjtuKLRygTRcOxDvBEVnv7y15rt9/B3JuBgplbmRzdHJlYW0KZW5kb2JqCjI2IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMjc2ID4+CnN0cmVhbQp4nD1SS47oMAjb5xRcIFL4Jj1PR7Pqu//22bSaFRZgY0jKS5aopUwtk1SVXUt+dHTuMvk3NK9Gz7D15sxD5kmxODK3yj0M5JlbrNBrb9SrCwCxSO7UEtslxpZLxZJkh6ztEHdk0OHFKtnM+NrCDjdrjkdSFypepwcF+Yww8E7Mfb6JZSE0Vxltt8BBDxaoAz0wCxO5IuPdaxM9jXgLoKwPmb+ILjfUXI9sTIBTuNoL3qmU1jEPFYmiHOxGGr2fo+Y4ocPbPWI59nIJRwbe4mjHe/BFiJ5GVkSsfsizEfmGDalIj5jKG+puH3r8ja3YaH92JknB11/W20w10rng1Fyt1l+DR2jw3qjh8/dLnvH7HyEmbhIKZW5kc3RyZWFtCmVuZG9iagoyNyAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDI0NyA+PgpzdHJlYW0KeJxNUbttRDEM698UXOAA62t5ngtSXfZvQ8kIkMIgoS8ppyUW9sZLDOEHWw++5JFVQ38ePzHsMyw9yeTUP+a5yVQUvhWqm5hQF2Lh/WgEvBZ0LyIrygffj2UMc8734KMQl2AmNGCsb0kmF9W8M2TCiaGOw0GbVBh3TRQsrhXNM8jtVjeyOrMgbHglE+LGAEQE2ReQzWCjjLGVkMVyHqgKkgVaYNfpG1GLgiuU1gl0otbEuszgq+f2djdDL/LgqLp4fQzrS7DC6KV7LHyuQh/M9Ew7d0kjvfCmExFmDwVSmZ2RlTo9Yn23QP+fZSv4+8nP8/0LFShcKgplbmRzdHJlYW0KZW5kb2J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   "source": [
    "sigma, omega = sym.symbols('sigma omega')\n",
    "X = sym.sinh(s/2)*2/s\n",
    "\n",
    "sym.plotting.plot3d(abs(X.subs(s, sigma+sym.I*omega)), (sigma, -5, 5), (omega, -20, 20),\n",
    "                    xlabel=r'$\\Re\\{s\\}$', ylabel=r'$\\Im\\{s\\}$', title=r'$|X(s)|$')\n",
    "\n",
    "sym.plot(X.subs(s, sigma) , (sigma, -5, 5), xlabel=r'$\\Re\\{s\\}$', ylabel=r'$X(s)$', ylim=(0, 3))\n",
    "\n",
    "sym.plot(X.subs(s, sym.I*omega) , (omega, -20, 20), xlabel=r'$\\Im\\{s\\}$', ylabel=r'$X(s)$');"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "* Derive the Laplace transform $X(s) = \\mathcal{L} \\{ x(t) \\}$ of the causal rectangular signal $x(t) = \\text{rect} (a t - \\frac{1}{2 a})$\n",
    "* Derive the Laplace transform of the [triangular signal](../fourier_transform/theorems.ipynb#Transformation-of-the-triangular-signal) $x(t) = \\Lambda(a t)$ with $a \\in \\mathbb{R} \\setminus \\{0\\}$"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Differentiation Theorem\n",
    "\n",
    "Derivatives of signals are the fundamental operations of differential equations. Ordinary differential equations (ODEs) with constant coefficients play an important role in the theory of linear time-invariant (LTI) systems. Consequently, the representation of the derivative of a signal in the Laplace domain is of special interest."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Two-sided transform\n",
    "\n",
    "A differentiable signal $x(t)$ whose temporal derivative $\\frac{d x(t)}{dt}$ exists is given. Using the [derivation property of the Dirac impulse](../continuous_signals/standard_signals.ipynb#Dirac-Impulse), the derivative of the signal can be expressed by the convolution\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{d x(t)}{dt} = \\frac{d \\delta(t)}{dt} * x(t)\n",
    "\\end{equation}\n",
    "\n",
    "Applying a two-sided Laplace transformation to the left- and right-hand side together with the [convolution theorem](#Convolution-Theorem) yields the Laplace transform of the derivative of $x(t)$\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathcal{L} \\left\\{ \\frac{d x(t)}{dt} \\right\\} = s \\cdot X(s)\n",
    "\\end{equation}\n",
    "\n",
    "where $X(s) = \\mathcal{L} \\{ x(t) \\}$. The two-sided Laplace transform $\\mathcal{L} \\{ \\frac{d \\delta(t)}{dt} \\} = s$ can be derived by applying the definition of the Laplace transform together with the derivation property of the Dirac impulse. The ROC is given as a superset of the ROC for $x(t)$\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{ROC} \\left\\{ \\frac{d x(t)}{dt} \\right\\} \\supseteq \\text{ROC} \\{ x(t) \\}\n",
    "\\end{equation}\n",
    "\n",
    "due to the zero at $s=0$ which may cancel out a pole.\n",
    "\n",
    "Above result is known as differentiation theorem of the two-sided Laplace transform. It states that the differentiation of a signal in the time domain is equivalent to a multiplication of its spectrum by $s$."
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### One-sided transform\n",
    "\n",
    "Many practical signals and systems are causal, hence $x(t) = 0$ for $t < 0$. A causal signal is potentially discontinuous for $t=0$. The direct application of above result for the two-sided Laplace transform is not possible since it assumes that the signal is differentiable for every time instant $t$. The potential discontinuity at $t=0$ has to be considered explicitly for the derivation of the differentiation theorem for the one-sided Laplace transform [[Girod et al.](index.ipynb#Literature)]\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathcal{L} \\left\\{ \\frac{d x(t)}{dt} \\right\\} = s \\cdot X(s) - x(0+)\n",
    "\\end{equation}\n",
    "\n",
    "where $x(0+) := \\lim_{\\epsilon \\to 0} x(0+\\epsilon)$ denotes the right sided limit value of $x(t)$ for $t=0$. The ROC is given as a superset of the ROC of $x(t)$\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{ROC} \\left\\{ \\frac{d x(t)}{dt} \\right\\} \\supseteq \\text{ROC} \\{ x(t) \\}\n",
    "\\end{equation}\n",
    "\n",
    "due to the zero at $s=0$ which may cancel out a pole. The one-sided Laplace transform of a causal signal is equal to its two-sided transform. Above result holds therefore also for the two-sided transform of a causal signal.\n",
    "\n",
    "The main application of the differentiation theorem is the transformation and solution of differential equations under consideration of initial values. Another application area is the derivation of transforms of signals which can be expressed as derivatives of other signals."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Integration Theorem\n",
    "\n",
    "An integrable signal $x(t)$ for which the integral $\\int_{-\\infty}^{t} x(\\tau) \\; d\\tau$ exists is given. The integration can be represented as convolution with the rectangular signal $\\epsilon(t)$\n",
    "\n",
    "\\begin{equation}\n",
    "\\int_{-\\infty}^{t} x(\\tau) \\; d\\tau = \\int_{-\\infty}^{\\infty} x(\\tau) \\cdot \\epsilon(t - \\tau) \\; d\\tau = \\epsilon(t) * x(t)\n",
    "\\end{equation}\n",
    "\n",
    "as illustrated below\n",
    "\n",
    "![Representation of an integration as convolution](integration_as_convolution.png)\n",
    "\n",
    "Two-sided Laplace transformation of the left- and right-hand side of above equation, application of the convolution theorem and using the Laplace transform of the Heaviside signal $\\epsilon(t)$ yields\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathcal{L} \\left\\{ \\int_{-\\infty}^{t} x(\\tau) \\; d\\tau \\right\\} \n",
    "= \\frac{1}{s} \\cdot X(s)\n",
    "\\end{equation}\n",
    "\n",
    "The ROC is given as a superset of the intersection of the ROC of $x(t)$ and the right $s$-half-plane\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{ROC} \\left\\{ \\int_{-\\infty}^{t} x(\\tau) \\; d\\tau \\right\\} \\supseteq \\text{ROC} \\{ x(t) \\} \\cap \\{s : \\Re \\{ s \\} > 0\\}\n",
    "\\end{equation}\n",
    "\n",
    "due to the pole at $s=0$. This integration theorem holds also for the one-sided Laplace transform."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Transformation of the ramp signal\n",
    "\n",
    "The Laplace transform of the causal [ramp signal](https://en.wikipedia.org/wiki/Ramp_function) $t \\cdot \\epsilon(t)$ is derived by applying the integration theorem. The ramp signal can be expressed as integration over the Heaviside signal\n",
    "\n",
    "\\begin{equation}\n",
    "t \\cdot \\epsilon(t) = \\int_{-\\infty}^{t} \\tau \\cdot \\epsilon(\\tau) \\; d \\tau\n",
    "\\end{equation}\n",
    "\n",
    "Laplace transformation of the left- and right-hand side and application of the integration theorem together with the Laplace transform of the Heaviside signal yields\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathcal{L} \\{ t \\cdot \\epsilon(t) \\} = \\frac{1}{s^2}\n",
    "\\end{equation}\n",
    "\n",
    "with\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{ROC} \\{ t \\cdot \\epsilon(t) \\} = \\{s : \\Re \\{ s \\} > 0\\}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "* Derive the Laplace transform $X(s) = \\mathcal{L} \\{ x(t) \\}$ of the signal $x(t) = t^n \\cdot \\epsilon(t)$ with $n \\geq 0$ by repeated application of the integration theorem.\n",
    "* Compare your result to the numerical result below. Note that $\\Gamma(n+1) = n!$ for $n \\in \\mathbb{N}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
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    {
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      "text/latex": [
       "$$\\left ( \\frac{s^{- n} n!}{s}, \\quad 0, \\quad - n < 1\\right )$$"
      ],
      "text/plain": [
       "⎛ -n              ⎞\n",
       "⎜s  ⋅n!           ⎟\n",
       "⎜──────, 0, -n < 1⎟\n",
       "⎝  s              ⎠"
      ]
     },
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     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = sym.symbols('n', integer=True)\n",
    "\n",
    "X, a, cond = sym.laplace_transform(t**n, t, s)\n",
    "X, a, cond"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Modulation Theorem\n",
    "\n",
    "The complex modulation of a signal $x(t)$ is defined as $e^{s_0 t} \\cdot x(t)$ with $s_0 \\in \\mathbb{C}$. The Laplace transform of a modulated signal is derived by introducing it into the definition of the two-sided Laplace transform\n",
    "\n",
    "\\begin{align}\n",
    "\\mathcal{L} \\left\\{ e^{s_0 t} \\cdot x(t) \\right\\} &=\n",
    "\\int_{-\\infty}^{\\infty} e^{s_0 t} x(t) \\, e^{-s t} \\; dt =\n",
    "\\int_{-\\infty}^{\\infty} x(t) \\, e^{- (s - s_0) t} \\; dt \\\\\n",
    "&= X(s-s_0)\n",
    "\\end{align}\n",
    "\n",
    "where $X(s) = \\mathcal{L} \\{ x(t) \\}$. Modulation of the signal $x(t)$ leads to a translation of the $s$-plane into the direction given by the complex value $s_0$. Consequently, the ROC is also shifted \n",
    "\n",
    "\\begin{equation}\n",
    "\\text{ROC} \\{ e^{s_0 t} \\cdot x(t) \\} = \\{s: s - \\Re \\{ s_0 \\} \\in \\text{ROC} \\{ x(t) \\} \\}\n",
    "\\end{equation}\n",
    "\n",
    "This relation is known as modulation theorem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example - Transformation of $t^n e^{-s_0 t} \\epsilon(t)$**\n",
    "\n",
    "The Laplace transform of the signal $t^n \\cdot \\epsilon(t)$ \n",
    "\n",
    "\\begin{equation}\n",
    "\\mathcal{L} \\{ t^n \\cdot \\epsilon(t) \\} = \\frac{n!}{s^{n+1}}\n",
    "\\end{equation}\n",
    "\n",
    "for $\\Re \\{ s \\} > 0$ was derived in the previous example. This result can be extended to the class of signals $t^n e^{-s_0 t} \\epsilon(t)$ with $s_0 \\in \\mathbb{C}$ using the modulation theorem\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathcal{L} \\{ t^n e^{-s_0 t} \\epsilon(t) \\} = \\frac{n!}{(s + s_0)^{n+1}} \\qquad \\text{for } \\Re \\{ s \\} > \\Re \\{ - s_0 \\}.\n",
    "\\end{equation}"
   ]
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   "source": [
    "**Copyright**\n",
    "\n",
    "The notebooks are provided as [Open Educational Resource](https://de.wikipedia.org/wiki/Open_Educational_Resources). Feel free to use the notebooks for your own educational purposes. The text is licensed under [Creative Commons Attribution 4.0](https://creativecommons.org/licenses/by/4.0/), the code of the IPython examples under the [MIT license](https://opensource.org/licenses/MIT). Please attribute the work as follows: *Lecture Notes on Signals and Systems* by Sascha Spors."
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