{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Course**: BIO-341 [_Dynamical systems in biology_](https://moodle.epfl.ch/course/info.php?id=14291)\n",
    "\n",
    "**Professor**: _Julian Shillcock_ & _Felix Naef_\n",
    "\n",
    "SSV, BA5, 2025\n",
    "\n",
    "Note that this document is primarily aimed at being consulted as a Jupyter notebook, the PDF rendering being not optimal.\n",
    "\n",
    "In the solution code will be provided for all the plots required. This is only to have good looking plots and to help you familiarize yourself with python and jupyter notebooks.\n",
    "\n",
    "**You are expected to solve everything using paper and pencil, unless clearly stated otherwise, as the exam will be with paper and pencil.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/8w/hhwzbx0d6zg_2q5hrl31_yn00000gq/T/ipykernel_99967/3074590393.py:8: DeprecationWarning: `set_matplotlib_formats` is deprecated since IPython 7.23, directly use `matplotlib_inline.backend_inline.set_matplotlib_formats()`\n",
      "  set_matplotlib_formats('png', 'pdf')\n"
     ]
    }
   ],
   "source": [
    "#import important libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from ipywidgets import interact\n",
    "from scipy.integrate import odeint\n",
    "from IPython.display import set_matplotlib_formats\n",
    "from matplotlib.markers import MarkerStyle\n",
    "set_matplotlib_formats('png', 'pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Allee effect"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The goal of this exercise is to understand the stability properties\n",
    "of 1-dimensional first order ODEs and to study a model of population growth.\n",
    "\n",
    "A fixed point $x^{*}$ of a 1-dimensional ODE $\\dot{x}=F(x)$ satisfies\n",
    "the condition $F(x^{*})=0$.\n",
    "\n",
    "\n",
    "* A fixed point $x^{*}$ is (linearly) $\\underline{stable}$ if $F'(x^{*})<0$.\n",
    "\n",
    "* A fixed point $x^{*}$ is (linearly) $\\underline{unstable}$ if $F'(x^{*})>0$.\n",
    "\n",
    "* A fixed point $x^{*}$ is (linearly) $\\underline{semi-stable}$ if $F'(x^{*})=0$ and $F''(x^{*})\\neq 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stability of fixed points in 1-dimensional systems (paper and pencil)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Analyze the 1-dimensional systems (a, b, c) below graphically:\n",
    "\n",
    "* Sketch the derivative $\\dot{x}=F(x)$ in function of $x$. \n",
    "* Mark all fixed points and determine their stability. When possible, calculate the fixed points explicitly. \n",
    "* Sketch the solutions $x(t)$ for two initial conditions leading to different qualitative behavior (for example one solution that flows to a fixed point and one that goes to infinity). \n",
    "\n",
    "(a) $\\dot{x}=2x-x^{2}$  \n",
    "(b) $\\dot{x}=\\cos(2x)+1-x$  \n",
    "(c) $\\dot{x}=x^{2}-8x+16$\n",
    "\n",
    "**Hint**: In the second equation, $F(x)$ is written as the difference of two functions, \\textit{i.e.} $F(x)=g(x)-h(x)$. In order to find the fixed point(s), plot $g(x)$ and $h(x)$ individually and look for intersections. You might want to use trigonometric identities."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> (a) The fixed points satisfy $2x-x^{2}=0\\Rightarrow x\\left(2-x\\right)=0\\Rightarrow x=0$ or $x=2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "image/png": 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T8O0/V3DpVg4AUw+/iV0D8VzPxuwZR1QH8fzBOojxPmVpszB1+1RcSL8Ad407lg1chgCHgFp5biIiejAswjUcNVWE43J7RGT1CnQGfL3jMh76MhKrDpt6v3Vt7Io1z3bB6mcj0LWJW70pwAGATCrBkDbe+PulHlj0RHu08HZAns6ABZHX0PuLXfj54A0YjPx9hYjIGjiqHPF9v+8R4hyClIIUTNk2BXE5cWLHIiIiIgtgEY6IrJYgCPjrVAL6fhmJb/65gkK9EZ0CXfDbtAj8OrULOge7ih3RoqRSCQaGemPzi93x/ZMd0MTDDhn5evz3j7MY8u1eRF1LFTsiERFVgrPaGUv6LUGQYxBu5d/CpK2TEJ0VLXYsIiIiqmEswhGRVbqYlI1HFx3AzFUnkJBViEZOGswfH4Y1z3VBx0AXsePVKqlUggGtvPD3Sz3w7tCWcFDLcTEpB+OXHML0n48h6fb8cUREVHe5alyxtP9SNHZsjOT8ZEzaOgmXMy6LHYuIiBqo3bt3o0OHDlCr1QgODsaiRYss/pwffvghunbtChsbGzg5OVXqGEEQ8O6778LHxwcajQa9e/fGuXPnLBv0AbAIR0RWRW8w4pudVzB03j4cvZEBjUKGWf2a4p9Xe+GRNj71athpVSlkUkzqFoTd/+mDpyICIJUAf59NQr+vdmPNkVhwClAiorrN3cYdPw78Ec1dmiO9MB2Tt03GubS6+0WCiIjqp+joaAwePBg9evTAiRMn8NZbb2HmzJlYt26dRZ9Xp9Ph0UcfxfTp0yt9zGeffYavvvoK8+fPx5EjR+Dl5YV+/fohJyfHgkmrj0U4IrIaZ+OzMGz+fny98zL0BgEPt/DEv7N7YWbfEKgVMrHj1RnOtkq8PzwUW17qgXZ+TsjRFuH1dWfw1I+HEZ9ZIHY8IiKqgIvaBT/0/wGt3VojS5uFZ7Y9gxPJJ8SORURE9URKSgq8vLzw0UcfmbcdOnQISqUS27dvBwAsWrQI/v7+mDt3Llq0aIFnnnkGkydPxhdffGHRbO+99x5eeeUVtG7dulLtBUHA3Llz8fbbb2PUqFEIDQ3FTz/9hPz8fPz6668WzVpdLMIRUZ2nKzLiy+2XMPy7/biQmA1nGwW+GdcOS57qAG9Hjdjx6qzmXg5YN70r3hrcHCq5FHuvpKL/V7vxy6Eb7BVHRFSHOaocsbjfYrT3aI9cfS6e3f4sdsftFjsWERHdjyAAujxxLpU8v3d3d8ePP/6Id999F0ePHkVubi6eeOIJzJgxA/379wcAHDhwwHy72IABA3D06FHo9fpyH9vOzq7Cy6BBg6r/Z1uG6OhoJCUllcqqUqnQq1cvREVF1ehz1RS52AGIiCoSl56PF1adwKm4TADA4NZeeG9YKNztVeIGsxIyqQTP9myMh1t44rXfT+PojQy8veEsdl9Kwedj2sLRRiF2RCIiKoOd0g6L+i3CK5GvYH/8fszcNRPvdHkHo5uOFjsaERGVR58PfOQjznO/lQAobSvVdPDgwZg6dSomTJiAjh07Qq1W45NPPjHvT0pKgqenZ6ljPD09UVRUhNTUVHh7e5f5uCdPnqzweTWamu1AkZSUZM52J09PT9y4caNGn6umsAhHRHXW32cS8dq608gpLIKDWo6PR7XBkDZlf+BTxYLd7bDmuQgs2x+Nz7Zewvbzt3Du272YNz4M7f2dxY5HRERl0Mg1mPfQPLwb9S7+uvYX3j3wLpILkjGtzbQGPQcqERE9uC+++AKhoaFYu3Ytjh49CrVaXWr/3f/PFI+kqej/nyZNmtR80EooK2td/X+SRTgiqnMK9QZ8tOUCVhww/XrR3t8J3z4eBl9nG5GTWTeZVIJnegSjc5ArXlh1HDfS8vHYogOYPaAZnu0RDKm0bv5HRUTUkCmkCvxft/+Dp40nlpxZggUnFyA5Pxlvd34bcilP5YmI6hSFjalHmljPXQXXr19HQkICjEYjbty4gTZt2pj3eXl5mXuZFUtOToZcLoerq2u5j2lnZ1fhc/bo0QN///13lXJWxMvLC4CpR9ydvfOSk5Pv6R1XV/B/biKqU+LS8zHt52M4l5ANAJjWqzFe7d8UChmnsKwprX0dsenF7nhrw1lsPJWAT/6+iEPX0zB3XBgcNRyeSkRU10gkEsxsPxPuNu74+NDH+P3y77iVdwuf9fwMdsqKv/AQEVEtkkgqPSRUTDqdDhMmTMDYsWPRvHlzTJkyBWfOnDEXriIiIrBx48ZSx2zfvh3h4eFQKMr/vlDbw1GDgoLg5eWFHTt2ICwsDIDpte3evRuffvppjT5XTeG3WiKqMw5Hp2P4d/txLiEbLrZKLH+6I94Y1JwFOAuwVyvw7bh2+GRUa6jkUuy6lIKRC/bjekqu2NGIiKgcjzd/HF/1/goqmQp74/fiyb+fRFxOnNixiIjIyrz99tvIysrCt99+i9deew0tWrTAlClTzPunTZuGGzduYNasWbhw4QJ+/PFHLF26FLNnz67wcZs0aVLhpVGjRhUeHxsbi5MnTyI2NhYGgwEnT57EyZMnkZtb8h2lefPm2LBhAwDTj1Qvv/wyPvroI2zYsAFnz57FpEmTYGNjg/Hjxz/An5Dl8JstEdUJqw/HYsIPB5Gep0NoIwdserE7ejfzEDtWvSaRSDCukz/WTe8KH0c1rqfkYcR3+7HncorY0YiIqBwPBzyM5QOXw13jjquZVzFh8wQcu3VM7FhERGQlIiMjMXfuXKxcuRIODg6QSqVYuXIl9u3bh4ULFwIw9TDbsmULIiMj0a5dO3zwwQf49ttvMXq0ZRcHeueddxAWFoY5c+YgNzcXYWFhCAsLw9GjR81tLl26hKysLPP91157DS+//DJmzJiB8PBwxMfHY/v27bC3t7do1uqSCEIl17ElAEB2djYcHR2RlZUFBwcHseMQWb0igxH/t/kClkfFAACGtPHGF2PaQqOUiRusgUnJ0eK5lUdxPDYTUgnw3yEt8XS3wDo7oSmRteH5g3WwpvfpVt4tzNw1E+fTzkMuleOdLu9gZMhIsWMRETUohYWFiI6ORlBQ0D0LG1D9UtF7XZXzB/aEIyLR5GqL8PTyI+YC3Kx+TTH/8TAW4ETgbq/Cqme7YEwHXxgF4P1N5/HWhjMoMhjFjkZERGXwtPXE8oHL0T+gP4qMRXgn6h18dOgj6A16saMRERFROViEIyJRpORoMW7xAey9kgqNQoaFE9pjZt8Q9rwSkUouw+dj2uC/Q1pAKgFWHY7DtJ+Po1BvEDsaERGVQSPX4PNen2N62+kAgFUXV+HpbU8jKS/pPkcSERGRGFiEI6JaF5uWjzGLonA2Phuutkqsea4LBrX2vv+BZHESiQTP9AjGoic6QCWXYueFW3hy6SFk5bNnBRFRXSSVSDGj3QzMe2ge7BX2OJVyCmM3jcWhxENiRyMiIqK7sAhHRLXqbHwWRi2Mwo20fPg6a/D79K5o4+skdiy6S/9WXlg5pTPs1XIcicnAo99HISmrUOxYRERUjt5+vbHmkTVo5twM6YXpeHbHs/jhzA8wCpxWgIiIqK5gEY6Iak3UtVSMW3wQqblatPB2wPrpXRHkZit2LCpHpyAX/DYtAh72Kly+lYvRC6NwNTn3/gcSEZEo/Bz88PPgnzG88XAYBSO+Of4Npu+cjtSCVLGjEREREViEI6JasvtyCiYtO4JcbRE6B7lgzXNd4OHAFYTquuZeDlg3vSuC3WwRn1mAcYsP4FJSjtixiIioHGq5Gh90+wBzIuZALVMjKiEKo/8ajT0394gdjYiIqMFjEY6ILG7XpWRMXXEUuiIjHm7hiZ8md4KDWiF2LKokPxcb/D69K1r5OCA1V4fHlxzExaRssWMREVE5JBIJxjQdg9WPrEZT56ZIL0zH8/88j08PfwqdQSd2PCIiogaLRTgisqh/LtzCcyuOQVdkxIBWnlgwoT3UCpnYsaiKXGyV+OWZzmjdyBHpeTo8vvggziewEEdEVJc1dmqMX4f8igktJgAAfr7wM8ZvHo+rGVdFTkZERNQwsQhHRBaz8/wtTPv5GHQGIwaFemH++PZQyvmxY62cbJT4eUpntPV1REa+HuN/OIhzCVlixyIiogqoZCq80ekNfNf3O7ioXXAp4xIe2/QYfjjzA4qMRWLHIyIialD4bZiILGLH+VuY/ssx6A0ChrT2xrePh0Eh40eOtXO0UWDFlM5o5+eEzHw9xi85hLPxLMQREdV1PX17Yt2wdejl2wt6ox7fHP8GT/39FK5nXhc7GhERUYPBb8REVOP2XUnF878ch94g4JE23vhmXDsW4OoRR40CK6Z0Qpi/E7IK9Hjqx8NcNZWIyAq4adww76F5+LD7h7BX2ONM6hk8uvFRLDu7DAajQex4RERUh+zevRsdOnSAWq1GcHAwFi1aZPHnHDZsGPz9/aFWq+Ht7Y0nn3wSCQkJFR4jCALeffdd+Pj4QKPRoHfv3jh37pzFs1YXvxUTUY06HpuBZ1cehc5gxMBWXpg7th3kLMDVOw5qBVZM7oQ2vqY54p5cegg3M/LFjkVERPchkUgwrPEwbBi+Ad0bdYfOqMNXx77CE1uewMX0i2LHIyKiOiA6OhqDBw9Gjx49cOLECbz11luYOXMm1q1bZ9Hn7dOnD9auXYtLly5h3bp1uHbtGsaMGVPhMZ999hm++uorzJ8/H0eOHIGXlxf69euHnJwci2atLn4zJqIaczEpG08vO4J8nQE9QtzwzeMswNVn9moFlj/dCU087JCYVYgnlx5GSo5W7FhERFQJnraeWNB3Ad7v+j7sFHY4m3YW4zaNw+dHPke+nj+qEBHVVykpKfDy8sJHH31k3nbo0CEolUps374dALBo0SL4+/tj7ty5aNGiBZ555hlMnjwZX3zxhUWzvfLKK+jSpQsCAgLQtWtXvPHGGzh48CD0en2Z7QVBwNy5c/H2229j1KhRCA0NxU8//YT8/Hz8+uuvFs1aXfx2TEQ1IjYtH08uPYysAj3C/J2w6IkOUMm5Cmp952KrxMopndDISYPo1Dw89aPp7wAREdV9EokEI0NG4s8Rf2JA4AAYBANWnF+B4X8Ox7+x/4odj4jI6giCgHx9vigXQRAqldHd3R0//vgj3n33XRw9ehS5ubl44oknMGPGDPTv3x8AcODAAfPtYgMGDMDRo0fLLYgBgJ2dXYWXQYMGVfrPMj09Hb/88gu6du0KhUJRZpvo6GgkJSWVyqpSqdCrVy9ERUVV+rlqk1zsAERk/W5lF2LC0oNIydGimac9lk3qCFsVP14aCm9HDX5+pjMeXXQAFxKzMWX5EayY0gk2Sv4dICKyBh42Hvii1xcY0WQE/u/g/yE+Nx4v7XoJffz64I1Ob8DHzkfsiEREVqGgqACdf+0synMfGn8INgqbSrUdPHgwpk6digkTJqBjx45Qq9X45JNPzPuTkpLg6elZ6hhPT08UFRUhNTUV3t7eZT7uyZMnK3xejUZz32yvv/465s+fj/z8fHTp0gWbNm0qt21SUpI5291Zb9y4cd/nEgN7whHRA8nVFmHSsiOISy9AgKsNVk7pBCcbpdixqJYFudlixeROcFDLcfRGBmauOgmDsXK/xhERUd3QvVF3bBi+Ac+0fgZyiRy74nZh2B/DMP/EfA5RJSKqZ7744gsUFRVh7dq1+OWXX6BWq0vtl0gkpe4X97S7e/udmjRpUuGlUaNG9831n//8BydOnMD27dshk8nw1FNP3beXX1lZK8opJnZTIKJqKzIY8fwvx3EhMRtudkqsnNwZHg7q+x9I9VJLHwf8OKkjxv9wCDsv3MIHm87j3WGtxI5FRERVoJFr8FL7lzAkaAg+PPQhjt46iu9Pf48NVzfglQ6vYEjQkDr7xYaISGwauQaHxh8S7bmr4vr160hISIDRaMSNGzfQpk0b8z4vLy9zL7NiycnJkMvlcHV1Lfcx7ezsKnzOHj164O+//66wjZubG9zc3NC0aVO0aNECfn5+OHjwICIiIu5p6+XlBcDUI+7O3nnJycn39I6rK1iEI6JqEQQBc/46h92XU6BWSPHDxI7wd61c92eqv8IDXfDVY23xwq8nsDwqBv4uNpjcPUjsWEREVEVNnJvgxwE/YmfsTnx59EvE58bjzb1vYtXFVXij4xto7d5a7IhERHWORCKp9JBQMel0OkyYMAFjx45F8+bNMWXKFJw5c8ZcuIqIiMDGjRtLHbN9+3aEh4eXOz8bUDPDUe9U3ANOqy178begoCB4eXlhx44dCAsLA2B6bbt378ann35apeeqLSzCEVG1LN5zHb8cioVEAnwzLgzt/JzEjkR1xCNtfHAzowCf/H0RH2w+D19nDfq38hI7FhERVZFEIkG/gH7o6dsTK8+vxOLTi3E65TTGbxmPgYED8ULYCwhwCBA7JhERVdHbb7+NrKwsfPvtt7Czs8Pff/+NKVOmmOdfmzZtGubPn49Zs2Zh6tSpOHDgAJYuXYpVq1ZV+LhNmjSpdqbDhw/j8OHD6N69O5ydnXH9+nW88847aNy4calecM2bN8fHH3+MkSNHQiKR4OWXX8ZHH32EkJAQhISE4KOPPoKNjQ3Gjx9f7SyWxDnhiKjKNp9OxMd/XwQA/G9ISwxggYXu8lzPYIzv7A9BAGauPoFTcZliRyIiompSyVR4pvUz2DRyE4Y1HgYJJNgasxXD/xiO9w+8j+T8ZLEjEhFRJUVGRmLu3LlYuXIlHBwcIJVKsXLlSuzbtw8LFy4EYOphtmXLFkRGRqJdu3b44IMP8O2332L06NEWy6XRaLB+/Xr07dsXzZo1w+TJkxEaGordu3dDpVKZ2126dAlZWVnm+6+99hpefvllzJgxA+Hh4YiPj8f27dthb29vsawPQiJUdh1bAgBkZ2fD0dERWVlZcHBwEDsOUa07HpuBcYsPQldkxKSugZzzi8pVZDBiyk9HsftyCtzslPjj+W7wda773fOJLIHnD9aB71PlXEq/hG9PfIs9N/cAANQyNSa0mICnQ5+Go8pR5HRERLWnsLAQ0dHRCAoKumdhA6pfKnqvq3L+wJ5wRFRpSVmFeG7lMeiKjHi4hSf+90hLsSNRHSaXSfHdhPZo4e2A1Fwdnlt5DAU6g9ixiIjoATVzaYbv+n6H5QOXo517OxQaCrH07FIMWj8Ii08vRo4uR+yIREREdRKLcERUKYV6A577+RhScrRo5mmPb8a1g0zK1dGoYnYqOX6YGA5XWyXOJWTjtXWn77vEOBERWYcOnh2wYtAKzHtoHpo4NUGOLgfzTszDgHUDsODkAmRps+7/IERERA0Ii3BEdF+CIOC/f5zFqbhMOGoUWPxUB9iquK4LVU4jJw0WTGgPuVSCjacS8P2e62JHIiKiGiKRSNDbrzd+H/o7Pu3xKYIdg5Gjy8HCUwsxcN1AfHv8W2QWZoodk4iIqE5gEY6I7mt5VAx+P3YTUgnw3fj2CHC1FTsSWZnOwa6YM9Q0fPnTrRcReYmTeBMR1ScyqQyDgwdjw/AN+KLXFwhxDkGuPhdLzizBgHUD8OXRL5GUlyR2TCIiIlGxCEdEFdp/NRX/t/kCAOCtwS3QPcRN5ERkrZ7oEoDHO/lBEIAXV53A9ZRcsSMREVENk0qkGBA4AL8P/R1z+8xFC5cWyC/Kx/JzyzFo3SC8tfctXEq/JHZMIiIiUbAIR0TlikvPxwu/HofBKGBUWCNM6R4kdiSyYhKJBO8NC0WHAGfkFBbh2ZXHkKstEjsWERFZgFQiRV//vljzyBp81/c7dPTqiCKhCBuvb8SYjWPw7PZnERUfxXlCiahe4GdZ/VdT7zGLcERUJl2RES/8ehwZ+Xq08XXER6NaQyLhQgz0YJRyKRY+0R5eDmpcTc7Fm+vP8KSFiKgek0gk6OnbEz8O+BGrh6zGwMCBkEqkOJB4AM/tfA6jN47G+ivrUVBUIHZUIqIqUygUAID8/HyRk5ClFb/Hxe95dUkEfvupkuzsbDg6OiIrKwsODg5ixyGymHf/OoflUTFw1CiweWZ3+DrbiB2J6pFjN9Ix9vuDKDIK+L8RoXiiS4DYkYgsiucP1oHvU+2Iz43Hz+d/xror68zFNwelA0Y0GYGxzcbC38Ff5IRERJWXmJiIzMxMeHh4wMbGhh0X6hlBEJCfn4/k5GQ4OTnB29v7njZVOX9gEa6KeHJGDcHm04l4/tfjAIClE8PRt4WnyImoPlqy5zo+3HIBSpkU66Z3RWtfR7EjEVkMzx+sA9+n2pWlzcL6K+ux5tIaxOfGm7d3a9QN45qNQ49GPSCTykRMSER0f4IgICkpCZmZmWJHIQtycnKCl5dXmUVWFuEsiCdnVN9Fp+Zh6Lx9yNUWYVqvxnhjUHOxI1E9JQgCnl15DDvO34KfiwabXuwBR82Dde8mqqt4/mAd+D6Jw2A0YH/Cfqy6uAr74/dDgOnriY+tD0aEjMCIxiPgbXdvzwMiorrEYDBAr9eLHYMsQKFQQCYr/0chFuEsiCdnVJ8V6g0YuSAKFxKz0SnQBb9O7Qy5jFNHkuVk5esxZN5e3MwoQP+Wnvj+yQ7swk/1Es8frAPfJ/HFZcdh7eW12HB1A7K0WQAACSSI8InAyJCReMjvIShlSpFTEhERlWARzoJ4ckb12ZvrT2PV4Ti42iqxeWYPeDmqxY5EDcDpm5kYs/AAdAYj/jukBZ7pESx2JKIax/MH68D3qe4oLCrEjhs78MfVP3A46bB5u6PKEUOChmBUyCg0c2kmYkIiIiITFuEsiCdnVF9tOp2AF349AYkEWDG5E3qEuIsdiRqQFQdi8M6f5yCXSrBhRjfOD0f1Ds8frAPfp7opLicOf1z9A39e/RO38m+Zt4c4h2Bw0GAMDhoMHzsfERMSEVFDxiKcBfHkjOqj+MwCDJy7BzmFRXihTxPMHsBflql2CYKAGb8cx99nkxDsZotNM7vDRikXOxZRjeH5g3Xg+1S3GYwGHEw8iPVX1mNX3C7ojSVzL7X3aI/BQYPRP7A/nNXOIqYkIqKGhkU4C+LJGdU3BqOAxxcfxOGYdLTzc8Jv0yKg4DxwJILMfB0Gzt2LpOxCjOvoh09GtxE7ElGN4fmDdeD7ZD2ytFnYeWMntkRvwZGkI+bFHOQSOSJ8IjAoaBB6+/WGvdJe5KRERFTfVeX8weq/aS9YsABBQUFQq9Xo0KED9u7dW27byMhISCSSey4XL16sxcREdcui3ddwOCYdtkoZvhnXjgU4Eo2TjRJfjW0LiQRYfSQOW88mih2JiIjqKEeVI0Y3HY2lA5Zix5gdmB0+Gy1dW6JIKMLe+L14a99b6LmmJ6bvnI71V9YjvTBd7MhERESw6rE+a9aswcsvv4wFCxagW7du+P777zFo0CCcP38e/v7+5R536dKlUtVJd3fOfUUN08m4THy94zIA4L3hoQhwtRU5ETV0XRu74bmejbFo9zW8sf4M2vk5c4EQIiKqkKetJya2moiJrSYiOisaW6K3YHvMdlzPuo598fuwL34fpBIpOnh2wMP+D6Ovf1942nqKHZuIiBogqx6O2rlzZ7Rv3x4LFy40b2vRogVGjBiBjz/++J72kZGR6NOnDzIyMuDk5FSt5+QwBaov8rRFGPztXtxIy8cjbbwx7/EwSCQSsWMRQVdkxOiFUTgTn4WujV3x85TOkEr5d5OsG88frAPfp/rleuZ17IzdiZ03duJC+oVS+9q4tUEvv17o6dsTzZyb8RyIiIiqrUEMR9XpdDh27Bj69+9fanv//v0RFRVV4bFhYWHw9vZG3759sWvXrgrbarVaZGdnl7oQ1Qfv/nUON9Ly4eOoxocjWvPkk+oMpVyKuePaQaOQIepaGpbsvS52JCIiskLBTsF4ts2zWDt0Lf4e9Tdmh89GmEcYJJDgdOppzDsxD49ufBQP//4w3o16F//G/ot8fb7YsYmIqB6z2uGoqampMBgM8PQs3ZXc09MTSUlJZR7j7e2NxYsXo0OHDtBqtVi5ciX69u2LyMhI9OzZs8xjPv74Y7z33ns1np9ITDvO38Jvx25CKgG+HtsOjjYKsSMRldLY3Q5zhrbEG+vP4Mvtl9G7mQeaeXFybSIiqh5fe1/zkNWU/BTsituFvTf34lDSISTnJ2PdlXVYd2UdFFIFOnp1RE/fnujq0xWBDoH8oZKIiGqM1Q5HTUhIQKNGjRAVFYWIiAjz9g8//BArV66s9GILQ4cOhUQiwV9//VXmfq1WC61Wa76fnZ0NPz8/DlMgq5WRp0O/r/cgNVeL53oG483BLcSORFQmQRAwdcVR7LyQjNBGDtgwoxsXDiGrxWGO1oHvU8OjNWhxJOkI9tzcgz039yA+N77Ufi9bL0R4R6CLdxd09u4MV42rSEmJiKiuqsr5g9X2hHNzc4NMJrun11tycvI9veMq0qVLF/z888/l7lepVFCpVNXOSVTXvPPXOaTmahHiYYdX+jUVOw5RuSQSCT4a2RpHYvbgbHw2Fuy6hpceDhE7FhER1SMqmQrdG3VH90bd8WanNxGdFY09N/dgb/xenEg+gaS8JGy4ugEbrm4AADRzboYInwhEeEcgzDMMGrlG5FdARETWxGqLcEqlEh06dMCOHTswcuRI8/YdO3Zg+PDhlX6cEydOwNvb2xIRieqcLWcSsfFUAmRSCb54tC3UCpnYkYgq5OGgxvvDW+Gl1Scx798reLilB1r5OIodi4iI6iGJRIJgp2AEOwVjUugk5OvzcSL5BA4kHMDBxIO4lHHJfFl+bjnkUjlau7VGuGc4Onh2QDuPdrBVcKV5IiIqn9UW4QBg1qxZePLJJxEeHo6IiAgsXrwYsbGxmDZtGgDgzTffRHx8PFasWAEAmDt3LgIDA9GqVSvodDr8/PPPWLduHdatWyfmyyCqFam5Wvz3j7MAgOm9GqOtn5O4gYgqaVhbH/x9JglbzyXh1bWn8NcL3aGUc1gqERFZlo3CBt0adUO3Rt0AAKkFqTiceBgHEg/gQMIB3Mq/hRPJJ3Ai+QSWnFkCmUSG5i7NzUW59p7t4ajiD0dERFTCqotwY8eORVpaGt5//30kJiYiNDQUW7ZsQUBAAAAgMTERsbGx5vY6nQ6zZ89GfHw8NBoNWrVqhc2bN2Pw4MFivQSiWiEIAv73x1mk5+nQ3MseM/tySB9ZD4lEgv8bGYrDMem4mJSDef9ewav9m4kdi4iIGhg3jRsGBw/G4ODBEAQBN3Nu4uitozh66yiO3TqG+Nx4nEs7h3Np5/DT+Z8AAE2cmqCdRzu0cWuDth5tEegQCKmEPyQRETVUVrswg1g4YS9Zoz9PxuOl1Schl0rwx/PdENqIv8qS9dl8OhHP/3ocMqkE66d3ZW9Osio8f7AOfJ/oQSTlJZkLcsduHUN0VvQ9beyV9mjj1gZt3NugrXtbhLqFsrccEZGVq8r5A4twVcSTM7I2qbla9PtqNzLy9Xj54RC8/DAXYyDr9cKvx7HpdCKaedpj44sclkrWg+cP1oHvE9Wk1IJUnEw+idMpp3Eq5RTOp51HoaHwnnZBjkFo49YGrdxaoYVLCzRzacYFH4iIrEiDWB2ViCrng03nkZGvR3Mvezzfp4nYcYgeyPvDQxF1LQ2XbuXg+93X8CKHVhMRUR3lpnHDwwEP4+GAhwEAeqMeVzKu4FTKKZxOOY3TKacRmxOL6KxoRGdF489rfwIApBIpgh2D0dK1JVq6tkQLlxZo7tIcNgobMV8OERHVAPaEqyL+QkrWZNelZDy97AikEmDDjG4cvkf1QvHwaqVMii0v9UATDzuxIxHdF88frAPfJ6ptGYUZOJN6BqdTTuN82nmcTzuPtMK0e9pJIEGgY6C5KBfiFIKmLk3hqnaFRCIRITkRERVjTzgiQp62CP/dYFoN9eluQSzAUb0xrK0P1h+Px+7LKXhr/RmsfrYLpFJ+ASEiIuvjrHZGT9+e6Onb07wtOT8Z59PO40LaBVNhLv08kvOTzT3mNl/fXHK8yhkhziFo6twUIc4hCHEKQWOnxuw1R0RUR7EIR1RPfbn9MuIzC+DrrMGr/TkPHNUfEokEH44MRf+v9+BwTDpWH4nD+M7+YsciIiKqER42HvCw8UBvv97mbakFqeai3KWMS7iScQWxObHI0GbgcNJhHE46bG4rgQR+9n4IcQ5BE6cmCHYMRpBjEAIdAznXHBGRyFiEI6qHTsZlYlmUaUWuD0e2ho2S/9SpfvF1tsGr/Zvhg03n8fGWC+jbwgOeDmqxYxEREVmEm8YNPXx7oIdvD/O2wqJCXMu6hisZV3A54zKuZFzBlYwrSCtMQ2xOLGJzYvFP7D+lHsfH1gdBjkHmS3GBzkXtwmGtRES1gN/MieoZvcGIN9adhiAAI8MaoVdTd7EjEVnEpK6B+OtkPE7dzMKcP89h0ZMdxI5ERERUa9RyNVq5tkIr11altqcVpOFKpqkgdy3zmnkYa4Y2Awl5CUjIS8D+hP2ljnFUOSLIwdRbzt/eH34OfqZrez/YK+1r82UREdVrLMIR1TOL91zHxaQcONso8N8hLcSOQ2QxMqkEn4xug6Hz9mHruSRsPZuEgaFeYsciIiISlavGFa4aV3Tx7lJqe0Zhhrkgdz3ruvk6ITcBWdosnEw5iZMpJ+95PGeVM/wc/OBnX1KY83cwXTurnNmDjoioCliEI6pH4tLz8e0/VwAA/3ukJVztVCInIrKsFt4OeLZnMBZEXsP7G8+hR4gbbFX8r42IiOhuzmpnOKud0d6zfanthUWFuJF9A9FZ0biRfQOxObGIy4lDbHYs0grTkKHNQEZKBk6nnL7nMe0Udmhk1wjedt6ma1vTtY+dD3xsfeCocmSRjojoDvymQlSPvLfxHLRFRkQEu2JkWCOx4xDVihcfCsFfpxJwM6MA3/57BW8OYg9QIiKiylLL1Wjm0gzNXJrdsy9Pn4ebOTdNc8xl3y7O3S7SJeUlIVefi0sZl3Ap41KZj20jtzEV5G4X5Ypve9t6w9PGE24aN8ikMku/RCKiOoNFOKJ6Yuf5W9h5IRlyqQTvD2/FXx2pwdAoZXh3aCs8s+Iolu6Nxpj2vgjx5Pw1RERED8pWYVtuga6wqBDxufGIz41HYm4i4vNM1wm5CYjPjUdaYRryi/JxNfMqrmZeLfPxZRIZXDWu8LLxgqetJzxsPOBp42m63HFfKVNa+qUSEdUKFuGI6oECnQHvbjwHAJjSI4gFCGpwHm7piYdbeGDnhWT878+zWDW1CwvRREREFqSWq9HYqTEaOzUuc39hUSES8xLNBbqE3ATzJSk/CSn5KTAIBiTnJyM5PxlILf+5XNQu5oKcm8YNbho3uGpczbfd1Kb7NgobC71aIqKawSIcUT2wIPIqbmYUwMdRjZkPhYgdh0gUc4a2wr6rqTh4PR1/nUrA8HYckk1ERCQWtVyNIMcgBDkGlbnfYDQgrTANyfnJuJV3C0n5Sabb+bfM227l34LWoEV6YTrSC9NxMf1ihc9pI7cpu0hXvE3tap4bTyPXWOJlExFViEU4Iit3PSUX3+++DgB4Z2hLTkpPDZafiw1e6NMEX2y/jA82XUCf5h5wUCvEjkVERERlkEll8LDxgIeNB0LdQstsIwgCsnXZSMpLMhfnUgtSkVqQirSCNPPt1IJUFBoKkV+Ub5q/Lif2vs+vkWvgpHIyF+WcVXdd33HbRe0Ce6U9pBJpTf8xEFEDw2/rRFZMEATM+escdAYjejV1x4BWXmJHIhLV1J7BWH88HtdT8/DV9st4d1grsSMRERFRNUkkEjiqHOGocixzXrpigiAgvyi/VFGurEJdWkEa0rXpKDIWoaCoAAVFBUjMS6xUFplEBkeVI1zULnBQOsBB5QBHpWOF1w5KB9gr7SGX8ms3EZnw04DIim05k4S9V1KhlEvx3jAuxkCkksvw3vBWeHLpYaw4EINHw33RysdR7FhERERkQRKJBLYKW9gqbBHgEFBhW0EQkKfPQ0ZhBjK0GWVf33E7szATOfocGASDeVhsVdkp7OCocjQX7xyUDub79kp72CpsYaewM9+2V9rDTmFnuijtWMQjqkf4r5nIShXoDPhoywUAwLRejRHoZityIqK6oUeIO4a09sbmM4l4b+N5rHmWizQQERGRiUQigZ3SVNzyg1+ljtEb9MjUZiK9MB0Z2gxka7ORpcsqdZ2ty75ne54+DwCQq89Frj4X8YivVmaNXFNuoa5U0U5pum8jtzFdK2xgI7cxX6vlag6pJRIZi3BEVmrxnuuIzyxAIycNpvcqe1UqoobqrSEt8M/FWzgcnY4tZ5IwpI232JGIiIjISilkCrjbuMPdxr1Kx+mNeuTocpClzUK2Lvue62xttqlAp8stfX37dqGhEADMQ2dTCypYQraSNHJNqcJcVa41cg1UMhXUcjU0Mg3UcrXpIlNDLpXzR0+iSmARjsgKJWQWYOHuqwCANwc3h0YpEzkRUd3SyEmDab0aY+7OK/hoywX0beEBtYL/ToiIiKj2KKQKuKhd4KJ2qdbxeoMeefo85Ohzyi3U5ehzkKcztcnT5yFXl4uCogLkF+UjX59vvhYgACgp6KUVptXkS4VMIjMX5NRydamC3Z1FO5VMBY1cU6qt+fr2baVMCZVMBZVMBYVMYb6tlCmhlJr2sehH1opFOCIr9MnfF1GoN6JToAuGtGYPH6KyPNezMdYeiUN8ZgEW77mOmX1DxI5EREREVGkKmQJOMic4qZ0e6HEEQTCtHntHUa6gqAB5+rx7inV37jffL8pHnj4PhUWF0Bq0KCgqQGFRIQoNhTAKRgCAQTAgT59nHoJraRJIKizSFRfy7t6vkqmglCpLbsuUUEgVUMgUpus7L3dsk0vlZW6/875cKudwX7ovFuGIrMyRmHT8dSoBEgnwztCW/AWIqBwapQxvDG6BmatOYEHkVYzp4AsfJ43YsYjIQj7++GOsX78eFy9ehEajQdeuXfHpp5+iWbPyV1QkImoIJBIJNHINNHINXOFaY48rCAL0Rj0KDYWmolxRoalAd/t+qYLd7aLdndfFbbVFWhQYStrpjDroDKaL1qA1X+uN+pLnhqmwWGgoRA5yauw1PSi5RA6F7K6iXQWFu+LinVwqh0wiu+d2Wdvut18mlUEhUUAmlZW7Xy659zGL79+5XyqRQiaR8TtnDWIRjsiKGI0C3tt4DgAwrqMfQhtx1Ueiigxt440VUTE4eiMDn269iG/GhYkdiYgsZPfu3Xj++efRsWNHFBUV4e2330b//v1x/vx52Npy8SIiopomkUhMvc9kSjgoHSz+fEbBCL1Rby7M3V2ku3Ob1qiF3mBqW1774gJikbEIeoMeeuNdl9vbioxFpe4XX3QGnXmYb7EioQhFRUUW/7OobRJIIJPITEW528W94gKd+Vpa+n5Z28z7pGUcX9k2t7fLJaYi4Z3bituYi4eQQCY1XUslUjzk/xA8bDxE/bNkEY7Iivx+7CbOxmfDXiXHq/35yz7R/UgkEswZ2grDvtuHP08m4KmIAHQIqN68LERUt23durXU/WXLlsHDwwPHjh1Dz549q/RYeXl5kMnunUdSJpNBrVaXalceqVQKjUZTrbb5+fkQBKHMthKJBDY2NtVqW1BQAKPRWG6OO4uVVWlbWFgIg8FQI21tbGzMPS60Wm2FX2ar0laj0UAqNQ0T0+l00Ov1NdJWrVab/65Upa1er4dOpyu3rUqlglwur3LboqIiaLXactsqlUooFIoqtzUYDCgsLCy3rUKhgFKprHJbo9GIgoKCGmkrl8uhUqkAmHpo5efn10jbqvy752dE2W1r+jNCJTO9d1qtFkWSonKrGrXxGVFQWIB8bb65MFdkLCpV1JMqpTBKjNAb9MgvzEeBrqCksGcoKfAVGYsgVUghSAUYBAMKtYXQ6rQoMhbBIBhgMBrMt4uMRZDIJTBITdu1Oi30Or2pACgUwWA0bS9ua5QbIUgE03MV6aHT6krtNwgG6AU9DEYDJDIJJHLTn5lgECAUlfzdMaD0+1KqrVGAoC/77xkAQAZI5VJx20qBJo80gYeNR41/RlSJQFWSlZUlABCysrLEjkINTHaBTujwwQ4h4PVNwpI918SOQ2RVXvvtlBDw+iZh6Ly9gsFgFDsONUA8f6h9V65cEQAIZ86cKbdNYWGhkJWVZb7ExcUJAMq9DB48uNTxNjY25bbt1atXqbZubm7ltg0PDy/VNiAgoNy2LVu2LNW2ZcuW5bYNCAgo1TY8PLzctm5ubqXa9urVq9y2NjY2pdoOHjy4wj+3O40ZM6bCtrm5uea2EydOrLBtcnKyue2MGTMqbBsdHW1uO3v27Arbnj171tx2zpw5FbY9fPiwue1nn31WYdtdu3aZ286fP7/Ctps2bTK3XbZsWYVt165da267du3aCtsuW7bM3HbTpk0Vtp0/f7657a5duyps+9lnn5nbHj58uMK2c+bMMbc9e/ZshW1nz55tbhsdHV1h2xkzZpjbJicnV9h24sSJ5ra5ubkVth0zZkypv8MVteVnhOnCz4iSi7V9RixdulTQFmmFPF2esHZDxW3f/exd4XL6ZeFi2kVh2R8VZ5j29jTh3xv/Cjtjdgrf/vFthW1HzhgprDi3Qlh+drnw/ob3K2zbc0JP4aODHwkfHPhAeHndyxW2bTO8jXAtw/Q9uqY/I6pynseecERWYkHkNaTmahHsZounIgLFjkNkVWYPaIbNZxJx+mYWNpyIx+gOvmJHIiILEgQBs2bNQvfu3REaGlpuu48//hjvvfdeLSYjIiKqu6RSqXmIsY3CpsK2bjZuCHE2LXyW6JhYYdtgx2D08e8DAHBIrnjochv3Nniy5ZMAgHM4h3fwTrltO3l3wpud3wQAxMTEYC7mltu2e6PuCHYKrvC5a4NEEMrpm0plys7OhqOjI7KysuDgYPlx70QAkJBZgD5fREJbZMQPT4Xj4ZaeYkcisjoLI6/h060X4eOoxr+ze0OtqGLXcaIHwPOH2vX8889j8+bN2LdvH3x9yy+6a7XaUsPxsrOz4efnh4SEhDLfJw41K7sth6NyOCqHo1a9LT8jqteWnxEm/Iyoelu5VGr6dy+V1vhnhE6nq/R5HotwVcSTaBLDrLUnsf54PDoHuWD1s124Og1RNRTqDXjoi0gkZBXitYHNMKN3E7EjUQPC84fa8+KLL+KPP/7Anj17EBQUVKVj+T4RERFZiNEAFBUCRVrTtb6g5Lb5UrzvzvsF999uvtYBBq3pvkFXepuxCJi8HfDvXOMvrSrnDxyOSlTHnY03DZ8DgLeHtGABjqia1AoZZg9ohllrT2HBrmsYG+4HVzuV2LGIqIYIgoAXX3wRGzZsQGRkZJULcERERA2S0WAqiOkLAH3e7et8QJdfctt8Kbi9Pf+u9ncdU1bhzFh+L8BaYyi/Z19tYRGOqA4TBAEf/30BggAMa+uDNr5OYkcismoj2jXC0n3ROJeQjW//uYL3hpc/VxQRWZfnn38ev/76K/7880/Y29sjKSkJAODo6FhqGBcREZFVEgRT7y5tLqArvuQB2pw7bt+97677ury7CmsFpgJZbZPKAbkGkKsAuRpQqE3XclUF29V3XFSA4o52xdcypem2TAXIlXddqwG1+L3cWYQjqsMiL6dg/9U0KGVS/GdAM7HjEFk9qVSCtwa3wIQfDuGXQ7GY2DUQwe52YsciohqwcOFCAEDv3r1LbV+2bBkmTZpU+4GIiIgAwGgEdDlAYTagzb7rOqv0/VKFtTzT/TsLacby57WrEXINoLQBFDamIpfijtulttvevtYAStu72qpN1/cUzm4X1WQqQNZwS1EN95UT1XFFBiM+3nIBADCxawD8XCpenYaIKqdbEzf0aeaOXZdS8NnWS1j0ZAexIxFRDeA0x0REZBFFWqAgEyjMBAoyTBdz4SyrjMLaXde6nJrPJNcAKjtTAUxpb7q+332lLaC0K794JlcDtxecIMthEY6ojvr92E1cvpULR40CL/QJETsOUb3y5uAW2H05BVvPJeFITDo6BrqIHYmIiIiILEUQTEWx4iJaQebtYlrmvdvuLrjpy18Zs0pkSkDlYBoSWera8Y779vcvrClsG3RPMmvHd46oDsrXFeGrHZcBAC8+1ASONgqRExHVL0097fFYuB9WH4nDh5svYMOMrlz0hIiIiMgaCIJpaGZ+GpCXZrrOT719//Z1fnrJtvx0U1FNMD7Ak0pMxTKNE6B2Mt1WOwAqxzKKande37Ffoa6Z109WjUU4ojpo2f4YJOdo4euswZMRAWLHIaqXZvVrij9PJuBkXCa2nbuFgaFeYkciIiIiangEwTQHWl4KkHsLyE2+XUBLv6Oollq66FbdVS7lGlMhTeNsKqZpnG9fnMrYfsd+lQMgldXUK6YGjEU4ojomM1+HRbuvAQBm928GlZwf9kSW4OGgxpTuQZi/6yq+3H4J/Vp6QiZlbzgiIiKiGqHNBfKSTUW13GRTgc1caLt9Xby/Oit0ytWAjRtg6wrYuJpu29y+bd52+6J2MhXVFFwtm8TFIhxRHbNo93XkFBahuZc9hrX1ETsOUb02tWcwVh68gSvJudhwIh5jOviKHYmIiIio7iqeWy0nCchOAHISTZfs29d3Ftn0eVV7bKU9YOcO2HoAtrcLasXX5gKbS8k2pa1lXiORBbEIR1SHJGcXYnlUNABTLzgpe+UQWZSjRoHpvRvjk78v4usdlzG0rTd7nxIREVHDVKQDcpPKL7AV365KcU1hA9h5mAprdsUXT8DW3XRdvM3WA1DaWO61EdURLMIR1SHf/nsFhXoj2vs7oW8LD7HjEDUIEyMC8eO+aMRnFmDVoVhM6hYkdiQiIiKimmU0moZ+Zt0EsuJuX98suZ+dYOrFVllqR8Deu+TicPv67iKbys5yr4nICrEIR1RH3EjLw+rDcQCA1wY250qNRLVEo5RhZt8Q/PePs5i/6yoeDfeDrYr/PRIREZEV0eWVU2Ar3hYPGPX3fxyZErD3uqO45nP7vk9Joc3ei0NBiaqJ3zKI6oivd1xGkVFAz6bu6BLsKnYcogZlbEc/LNl7HTfS8rFsfzReeChE7EhEREREJYp0pmJa5g0gIwbIuH2decN0uyD9/o8hkZqKaY6+d138TMU2Bx/TXGvsDEBkMSzCEdUBF5Oy8eepBADAawOaiZyGqOFRyKSY1a8pXlp9Et/vuY4nugTAyUYpdiwiIiJqKATBtEpomUW2GCA7HhCMFT+GyrHsAlvxbXtvQMYSAJGY+C+QqA74YtslCAIwpLU3Qhs5ih2HqEEa2sYHCyOv4WJSDhbuvoY3B7UQOxIRERHVJ4JgWvQg/RqQdhVIuwakXzddZ8QARQUVHy/XAM4BgFMA4Bx4+3L7vpOfaZ42IqrTWIQjEtmJ2AzsvJAMmVSCWf2bih2HqMGSSiX4z4BmmPLTUfwUFYMp3YPgYa8WOxYRERFZE0EA8lJvF9qu3VFwu24quFW4sqgEcGhUusDmHFhSdLPz4FBRIivHIhyRyL7eeQUAMDKsERq7c/UgIjE91NwDYf5OOBGbiUWR1/HO0JZiRyIiIqK6qEhrKrKlXgJSLgOpl28X3K4D2qzyj5NIASd/wKUx4NoYcG1iuu0SZBoyKlfV3msgolrHIhyRiI7dSMeeyymQSyWYyYngiUQnkUjwysNN8dSPh/HzoRt4rlcwPB3YG46IiKjBKswGUq/cLrZdMhXbUi6Zho8KhnIOkpgKai7BpiKba+OSoptTACDnvLNEDRWLcEQi+nqHqRfcmA6+8He1ETkNEQFAjxA3hAc44+iNDCyMvIZ3h7USOxIRERFZWl4akHweSLlYUmhLvQLkJJR/jMoBcGsKuDczXRcX3JyDAAV/xCOie7EIRySSw9Hp2Hc1FXKpBM/3aSJ2HCK6TSKR4JV+TTHhh0P49XAsnusVDG9HjdixiIiIqCbo8k2FtuQLpqLbrXOm69xb5R9j53lHsa0Z4N7UdG3vxTnaiKhKWIQjsrCYmBgsXrwYv//+O1JSUqBQKNCkSRMoB/wHgBKPhvvBz4W94Ijqkq6NXdEp0AWHY9KxYNc1vD+8FdLS0pCbmws7Ozu4urpCwpNuIiKiustoANKjgeRzwK3zJdcZ0YBgLPsYpwDAo0Xp3m1uTQGNU61GJ6L6i0U4IgspLCzEjBkzsHz5cjg4OODxxx9HUFAQ9Ho9dpyKQUyBEoKhCI0yTwNoLXZcIrpDcW+4x5ccxK8HY/Dr/ybh+tlj5v2NGzfGiy++iIkTJ8LJyUm8oERERARoc0w92hJPA0mngKSzpuGkRQVlt7dxBTxaAp6tSq7dmwMqLpJGRJbFIhyRBWi1WjzyyCPYv38/5s2bh0mTJsHW1hYAIAgCTi0+iJjodPgUROPFKa9AUpCJ559/XuTURHSn7KtHobt5DkrfVsjx6QzcUYS7fv06XnnlFbz99ttYt24dBgwYIGJSIiKiBiQ3xVRoSzwNJJ02XadfByDc21auATyaAx6tAM+WJQU3W3cOIyUiUVh9EW7BggX4/PPPkZiYiFatWmHu3Lno0aNHue13796NWbNm4dy5c/Dx8cFrr72GadOm1WJiagj+85//YN++fdi2bRt69epVat+Ba2k4HJ0OpUyKdf/3LD5X3MCLL76Itm3bonv37iIlJqI7bdu2DUOGDIGyUUt4PP4x7Nr0Q9bB32DITgFgKqYDQEFBAYYMGYLNmzezEEdERFSTBMG0Amlxoa34Ojep7Pb2PoB3G8CrDeDV2lRscw4EpLLaTE1EVCGrLsKtWbMGL7/8MhYsWIBu3brh+++/x6BBg3D+/Hn4+/vf0z46OhqDBw/G1KlT8fPPP2P//v2YMWMG3N3dMXr0aBFeAdVHGRkZWLJkCf773//eU4ATBAFf77wMAHi8kx98nGzw5ZdfYufOnfjqq69YhCOqAzIzMzF69GgIgoCC2DMoiDkJTWA7OEaMRfq2+aXaGo1GSKVSjB49Gjdv3uTQVCIiourKTgDijwMJx29fnwAKM8toKDGtQlpccCu+tnWr7cRERFVm1UW4r776ClOmTMEzzzwDAJg7dy62bduGhQsX4uOPP76n/aJFi+Dv74+5c+cCAFq0aIGjR4/iiy++YBGOaszy5cthMBgwderUe/YdvJ6OIzEZUMqlmN7btCKqVCrFjBkz8MILLyAuLg5+fn61HZmI7vDTTz8hPz/f3Nsta98v0AS2g13rvsiKWgNDTkqp9kajEfn5+VixYgVmzpwpRmQiIiLrkp9+u9h2oqToVlYPN5nStFCCVxvAu63p2rMV524jIqtltUU4nU6HY8eO4Y033ii1vX///oiKiirzmAMHDqB///6ltg0YMABLly6FXq+HQqGofIC8PEBWRtdmmQxQq0u3K49UCmg01Wubn2/qol0WiQSwsale24ICwFjOakEAcHtesyq3LSwEDIaaaWtjUzKHg1YLFBXVTFuNxvTnDAA6HaDXV6vtvxs3YljfvvC0szO9p2q1+e/Kgu3nodEVYnyYH7zkBvN7/sTIkZg9YwZ2bN2KycXFO73e9NjlUakAubzqbYuKTH8W5VEqgeJ/C1VpazCY3rvyKBSm9lVtazSa/q7VRFu53PRnAZj+TeTn10zbqvy752dE2W3ryGeEoNfjh2++gY0glMwsE38BkqtHIGncAQ6dRyNj5yIoANz5P4ZEELBk7ly8OHmyadXUqnye3PEZUaW2/Iww3baWzwgiooZKlwcknLyjh9tx0zDTu0lkpoKbTxjQqD3g0940h5tcWduJiYgsR7BS8fHxAgBh//79pbZ/+OGHQtOmTcs8JiQkRPjwww9Lbdu/f78AQEhISCjzmMLCQiErK8t8iYuLEwAIWaZT7nsvgweXfgAbm7LbAYLQq1fptm5u5bcNDy/dNiCg/LYtW5Zu27Jl+W0DAkq3DQ8vv62bW+m2vXqV39bGpnTbwYPLb3v3X8MxYypum5tb0nbixIrbJieXtJ0xo+K20dElbWfPrrjt2bMlbefMqbjt4cOCIAjC0Zg04cPeT1fYdvW0aSWPO39+xY+7aVNJ22XLKm67dm1J27VrK267bFlJ202bKm47f35J2127Km772WclbQ8frrjtnDklbc+erbjt7NklbaOjK247Y0ZJ2+TkittOnFjSNje34rZjxgilVNSWnxGmixV+RnSbtlTwf3W9ILN1Fj6r6DGBan1GCIJg+ndSUdtdu0ra8jPCxEo+I7KysgQAQlZWlkB1F98nogdkNApC2nVBOLlaEDbNEoSF3QXhXWdBmONw7+WbMEH4fYogRH0nCDcOCII2T+z0RETVUpXzB6vtCVdMcteqNoIg3LPtfu3L2l7s448/xnvvvfeAKYmA+f9eRch92qiKe1UQUZ2jTbwCSfPusO80Etj1o9hxiIiIxKfLN83ddvMwEHfEdJ2Xcm87ex9T77biHm4+7QCNc63HJSISm0QorkJZGZ1OBxsbG/z2228YOXKkeftLL72EkydPYvfu3fcc07NnT4SFheGbb74xb9uwYQMee+wx5OfnlzkcVavVQnvHUJvs7Gz4+fkhKyEBDg4O9wbjULOy29aRoWa1MRz15ZdfxqZNm3DhwgXT3ym1GmeTcvHIvH1QGfXY8UJX+Lvalnq4yMhIDHnkEfz977/o2aePaSOHmpluW8tQMw5HNbHyz4jUpCQEBAaW2VQIDIPH2A9g1BUieeHTkBXm3NMm9sYNuLq6cjhqWW0b+GdEtk4HR0dHZGVllX3+QHVCdnY23yei8ggCkBkL3DwCxB0G4g4Bt84Cxrv+n5UqTPO3+XUG/DoCvp0Ax0biZCYiqgVVOX+w2p5wSqUSHTp0wI4dO0oV4Xbs2IHhw4eXeUxERAQ2btxYatv27dsRHh5e7nxwKpWq7N5JtralvxSWpzJtqtP2zi/FNdn2zi/xNdn2zqJDTbZVqUq+BNVkW6Wy5EtbFds+/cIL+OaHH/DXP/+YF/yY9+8VAMDgDoHw9/e45yHmL1uGwJYt0aN375KNCkXJl9f7qUpbubzky3ZNtpXJKv93uCptpVLLtJVILNMWqBtt+RlhUsXPCFd/f3g3bozr16/jnt+oYk5Am3gFKu8QaDqOQObeleZdEokEwcHBcPHzKynqFXuAz5MK8TPCxFo+IyoqghIR1UVGI5ByEYiNAm5EATcOADkJ97az8wL8Opkuvp1MBThFFf6vJiJqQKy2CAcAs2bNwpNPPonw8HBERERg8eLFiI2NxbRp0wAAb775JuLj47FixQoAwLRp0zB//nzMmjULU6dOxYEDB7B06VKsWrVKzJdB9Uzbtm3RrVs3/O9//0Pfvn1xq1CGbeduQSIBnu/T+J72//77L/744w988803FQ6lJiLLk0gkePHFF/HKK6+UuT/rwBp4jPov7DsMRfbh9TBqS3onzpw5k/+GiYjIehn0QOLpkqJb7AGgIKN0G6kc8Gpt6uXm29FUeHMs4wcoIiIqk1UX4caOHYu0tDS8//77SExMRGhoKLZs2YKAgAAAQGJiImJjY83tg4KCsGXLFrzyyiv47rvv4OPjg2+//dbcW4mopixZsgRdu3bFgAED0HbaXADA4FBvNPGwL9Vu+/btGDNmDB566CE8++yzIiQlortNnDgRb7/9NgoKCmC8azhtwZVD0CVHQ+kRBPsOQ5EVtRpSqRQajQZPPfWUSImJiIiqQV8AxB+73cttv2lON/1dU18obEzFtoCupkujcEBZhR70RERUitXOCScWzhVClXXs2DE88vhkKEf8HyRSKT7uZY8+YU2h1+uxf/9+LFiwAHv37sWgQYOwdu1a2NnZiR2ZiG7btm0bhgwZAkEQ7inE2TTvAffhr8NQkI3E76cCRYXYsmUL+vfvL1JasgY8f7AOfJ+oXtMXmOZyi94DxOwzFeCMd81DqnYC/CNKim7ebQFZJaczICJqoBrEnHBEdV2HDh0w+n+LselcKoSbpzF+8Ful9vfu3Rtr1qzBqFGjIK/snEpEVCsGDBiAzZs3Y/To0ci/PeF+8W9W+Zf2Q59+EwoXXzh3HIZf/jeJBTgiIqp7inRAwnFT0S16j6kAZ7hrMR1779JFN/cWJQsLERFRjeM3fyILic8swNYLaQCAdR9MRdELfZCSkgKlUong4GCEhISInJCIKjJgwADcvHkTK1aswLfffotr166ZdghGqK5FwujyBPz7T0LPPn3FDUpERAQARgOQeOp2T7e9poUU7h5eau8NBPUCgnqYim7OQZzPjYioFrEIR2QhS/dGo8gooGtjV4QHuQFBbmJHIqIqcnJywsyZM/Hiiy8iPT0dOTk5sLe3h72jE3p/HomErEKsPx6P8Z39xY5KREQNjSAAyRdKerrF7AO0WaXb2LgCgT2AoJ6m4ptrYxbdiIhExCIckQVk5Omw+ohpUZBpve5dEZWIrItEIoGrqytcXV3N257pEYz3N53H4j3XMLajH2RSfqkhIiILy00GrkcC1/41XXJvld6vcgACu5cU3jxacngpEVEdwiIckQWsOHAD+ToDWvk4oEcIe8AR1UfjOvnh23+vICYtH1vPJmFIG2+xIxERUX1TpAViDwLX/jEV3ZLOlN4v1wABEbd7uvUEvNoCMn7FIyKqq/gJTVTD8nVFWB4VDcDUC07CLv9E9ZKNUo6JEYH45p8rWLT7Gga39uK/dyIiejCCAKRcKunpFrMPKCoo3carDdD4IdPFvwsgV4mTlYiIqoxFOKIatvZIHDLy9fB3scGgUC+x4xCRBU3sGojv91zDmfgs7L+ahu7s+UpERFWVnw5c33W78LYLyI4vvd/Os6ToFtwHsHMXJycRET0wFuGIapDeYMSSvaZecFN7BkMu4xwcRPWZi60S4zr6Y3lUDBbtvsYiHBER3Z8gALfOAVe2AVd2AHGHAMFYsl+uNq1cWlx482jJxRSIiOoJFuGIatCm0wmIzyyAm50Sj3bwFTsOEdWCZ3oEYeXBG9h3NRVnbmahta+j2JGIiKiu0eYC0buBK9tNhbe7e7u5twCa9DUV3QK6AgqNODmJiMiiWIQjqiGCIGBR5HUAwNPdgqBWyERORES1wdfZBsPa+mDDiXgs2n0N301oL3YkIiKqC9KuAZe3mQpvN/YDBl3JPrkGCO4FhPQHQvoBTv7i5SQiolrDIhxRDdl1KRmXbuXATiXHE10CxI5DRLXouV7B2HAiHlvOJiI6NQ9BbrZiRyIiotpWpDUV2y5vNw01Tb9eer9zIBAywFR4C+wOKNSixCQiIvGwCEdUQxbtNp1oje/sD0eNQuQ0RFSbmns54KHmHvj3YjKW7L2Oj0a2FjsSERHVhoIM0/DSi5uBq/8AupySfVIFEBBhKrw1HQC4NuHcbkREDRyLcEQ14PTNTByOTodcKsHT3QLFjkNEIni2ZzD+vZiMdcdu4tV+TeFqpxI7EhERWUJGDHDpb1Ph7UYUIBhK9tl53h5i2h8I7g2oHcRKSUREdRCLcEQ1oHhF1KFtfeDtyIl0iRqizkEuaN3IEWfis/DzwVi89HCI2JGIiKgmGI1A4onbhbctQPK50vvdWwDNBwPNhgA+YYBUKk5OIiKq81iEI3pA8ZkF2HImEYBplUQiapgkEgme6RGEl1afxMqDMXiuVzAXaCEislZFWiB6j6m32+WtQE5iyT6JzLSCabNBpotLsHg5iYjIqrAIR/SAlu2LhsEooGtjV7TycRQ7DhGJaHBrb3z690UkZBXijxPxGNeJq90REVkNbY5pNdMLG4GrOwFdbsk+pR3QpC/QbLBpqKmNi3g5iYjIarEIR/QAsgv1WH0kDgAwtQd/BSVq6BQyKZ7uFoQPt1zAD/ui8Vi4H6RSTsJNRFRn5aebhple2Ahc+xcwaEv22Xvf7u02GAjswdVMiYjogbEIR/QA1hyOQ662CE087NCrqbvYcYioDhjbyQ/f/HMFV5NzsftyCvo09xA7EhER3Sk3Gbi4CTj/FxCzFzAWlexzaQy0HAa0GAp4c343IiKqWSzCEVWT3mDEsv2mBRme6R7E3i5EBABwUCswrqMfftgXjSV7r7MIR0RUF2TdNPV2O/8XEHsAgFCyz6PV7cLbMMCjBSDhOR0REVkGi3BE1bTlTCISsgrhZqfEiLBGYschojrk6e5BWBYVg6hraTiXkMX5IomIxJB2Dbjwl6n4Fn+s9D6f9iWFN9fG4uQjIqIGh0U4omoQBAE/7DX1gnuySyBXQCSiUho5aTC4tTc2nkrAD3uj8fXYdmJHIiJqGNKvA+c2mC5JZ+7YIQH8I0yFt+aPAE5+okUkIqKGi0U4omo4FJ2OM/FZUMmleKILVz8kontN7RGEjacSsPFUAl4b2AzejhqxIxER1U+Zsaai29n1QOLJku0SGRDU0zS/W/NHAHtP0SISEREBLMIRVcvSfaZecKM7+MLVTiVyGiKqi9r4OqFTkAsOR6djxYEbeH1gc7EjERHVH1nxwPk/TIW3+KMl24sLb61GmopvNi6iRSQiIrobi3BEVRSblo+dF24BACZ3CxI5DRHVZVO6B+FwdDpWHY7FzIdCoFFy6DoRUbXlJAHn/zQV3uIO3rFDAgR2NxXeWg4HbN1Ei0hERFQRFuGIquinAzEQBKBnU3c08bATOw4R1WEPt/CEn4sGcekF+ONkPB7vxOHrRERVkpsCXPgTOLsBuLEfJaua3p7jrbjwxqGmRERkBViEI6qCXG0R1h6JAwA83S1Q3DBEVOfJpBJMjAjE/22+gGX7ozGuox8kEonYsYiI6raCDNOKpmd+B2L2AoKxZJ9vJ1PhrdUIwMFHtIhERETVwSIcURWsO3YTOdoiBLvZoleIu9hxiMgKPBruh692XMblW7mIupaGbk04TIqI6B76AuDyNuDMb8CV7YBBV7LPp31J4c2JPYqJiMh6sQhHVElGo4DlUTEAgEndAiGVsjcLEd2fo0aBMR18seLADSzbH80iHBFRMUMRELMHOP2bqeebLqdkn0dLoPUYoNUowIVz8BIRUf3AIhxRJe2+koLo1DzYq+QY1d5X7DhEZEUmdg3EigM38M/FZNxIy0OAq63YkYiIxCEIQPxx4Mxa0wILeckl+xz9TIW31o8Cnq3Ey0hERGQhLMIRVdKy/TEAgMc6+sFOxX86RFR5jd3t0KupO3ZfTsFPUTfwztCWYkciIqpdKZdNQ03P/AZkRJds17iYhpq2fhTw6wxIpeJlJCIisjBWEogq4WpyLvZcToFEAkyMCBQ7DhFZoae7BWL35RT8djQOs/o3ZTGfiOq/7ATg7DpT4S3xVMl2hQ3QfIip8Nb4IUCmEC8jERFRLeI3AKJKWB5l+sX24Rae8He1ETkNEVmjniHuCHa3xfWUPPx+NA6TunGOIyKqhwqzgPN/AqfXAjH7AAim7VI50LivqfDWbBCgshM1JhERkRhYhCO6j6x8PdYdiwdg6slCRFQdUqkET3cNxP/+PIefDtzAUxFc4IWI6glDEXDtX+DUKuDSFqCosGSff4RpnreWIwBbLkxDREQNG4twRPfx27E4FOgNaO5lj4hgV7HjEJEVG9XeF59tu4To1DzsvpyCPs09xI5ERFQ9ggAknQZOrQbO/F56gQW3ZkDbsUDoGMA5QLyMREREdQyLcEQVMBoFrDx4A4BpdUOJhL1WiKj6bFVyPBbuh6X7orHiQAyLcERkfbITTHO8nVoNJJ8v2W7jahpq2nYc4N0O4DkTERHRPViEI6rA7ispuJGWD3u1HMPb+Ygdh4jqgSe6BGDpvmhEXk5BbFo+55kkorpPlwdc2GQabno9EuZ53mQq0/xubR8HmvTlAgtERET3wSIcUQVWHjD1gnu0gx9slPznQkQPLsjNFj2bumPP5RT8fOgG3hrcQuxIRET3MhqAmL2mHm/n/wL0eSX7/CNMPd5ajgA0TmIlJCIisjqsKhCVIy49H7sumeY3eTKC85kQUc15qksA9lxOwdqjcZjVrynUCpnYkYiITJIvAqdXm1Y3zY4v2e4cZCq8tXkMcAkWLx8REZEVYxGOqBw/H7wBQQB6NnVHkJut2HGIqB7p09wDjZw0iM8swF+nEvBYuJ/YkYioIctNAc6uMw03TTxZsl3tCLQaZRpu6teJ87wRERE9IBbhiMpQqDdgzdE4AKYeK0RENUkmleCJLgH4dOtFrDgQg0c7+HLhFyKqXUU64Mo24OSvwJXtgLHItF0qB0L6m3q9hQwAFGpxcxIREdUjLMIRleGvUwnIzNejkZOGqxcSkUWM7eiHr3dextn4bJyIy0R7f2exIxFRQ5B0xlR4O70GyE8r2e7T3tTjLXQUYOsmXj4iIqJ6jEU4orsIgmBekOGJLgGQSdk7hYhqnoutEo+08cb64/FYeeAGi3BEZDn56cCZ34ATPwNJp0u223maery1HQ94NBcvHxERUQPBIhzRXU7GZeJMfBaUcinGduQ8TURkOU9FBGL98XhsPp2It4e0gJudSuxIRFRfGIqAa/8AJ38BLv0NGHSm7VIF0GwQEPYE0LgvIOPXASIiotrC/3WJ7lLcC+6RNt5wsVWKnIaI6rN2fk5o4+uI0zezsOZIHJ7v00TsSERk7VIumQpvp9YAuUkl273amApvrR8FbFzEy0dERNSAsQhHdIe0XC02nU4EYOqhQkRkaU92CcB/fj+NXw/F4rmewZDLpGJHIiJrU5hlWt30xC9A/NGS7TauQJuxQLvxgFdr8fIRERERABbhiEr57dhN6AxGtPF1RDs/J7HjEFEDMLStDz7ccgHxmQWIvJSCh1t6ih2JiKyB0QhER5oWWbiwESgqNG2XyEyrm4ZNMK1uKmevfiIiorqCRTii24xGAasOxwIAnugcIHIaImoo1AoZHu3giyV7o/Hr4VgW4YioYunXTYW3k6uA7Jsl291bmApvbcYCdlzZnYiIqC5iEY7otv3XUnEjLR/2KjkeaestdhwiakAe7+SPJXujsetSMm5m5MPX2UbsSERUl2hzgfN/mIabxkaVbFc7AqFjTMU3n/aAhCu6ExER1WUswhHd9ushUy+4Ue0bwUbJfxpEVHuC3e3QtbEroq6lYc2ROLzav5nYkYhIbIIA3Nhv6vV27g9An3d7hwRo/JCp8NZsCKBQi5mSiIiIqoCVBiIAydmF2H7+FgBgPIeiEpEIxnf2R9S1NKw+EoeZfUOg4AINRA1TZhxwapVphdOMmJLtLo1vDzcdBzg2Ei0eERERVR+LcEQA1h6Ng8EoIDzAGc287MWOQ0QNUP+WXnCzUyIlR4t/LtzCwFAOiyeqqj179uDzzz/HsWPHkJiYiA0bNmDEiBFix7o/XT5wcZOp8HZ9NwDBtF1pB7QaCYQ9Afh15nBTIiIiK2e1P7NnZGTgySefhKOjIxwdHfHkk08iMzOzwmMmTZoEiURS6tKlS5faCUx1lsEoYNXhOACmnihERGJQyqV4NNwPAPDL7eHxRFQ1eXl5aNu2LebPny92lPsTBCDuCLDxJeDLZsD6qcD1SAACENgDGPk9MPsyMHw+4N+FBTgiIqJ6wGp7wo0fPx43b97E1q1bAQDPPvssnnzySWzcuLHC4wYOHIhly5aZ7yuVXLa9odtzOQXxmQVwslFgcGv2PCEi8Tze0R+Ldl/D3iupuJGWhwBXW7EjEVmVQYMGYdCgQWLHqFh2InB6tWmut9TLJdud/IF2E4C24wDnQNHiERERkeVYZRHuwoUL2Lp1Kw4ePIjOnTsDAJYsWYKIiAhcunQJzZqVP6G1SqWCl5dXbUUlK/DLoRsAgNHtfaFWyEROQ0QNmb+rDXqEuGPP5RT8ejgWbw5qIXYkonpNq9VCq9Wa72dnZ1vuyRJOALs+Aq7uBASjaZtcA7QcbprrLaA7ILXaQSpERERUCVb5P/2BAwfg6OhoLsABQJcuXeDo6IioqKgKjgQiIyPh4eGBpk2bYurUqUhOTq6wvVarRXZ2dqkL1R8JmQX496Lp7wCHohJRXTDh9mfR70dvQltkEDkNUf328ccfm6c2cXR0hJ+fn+WezGgErmw3FeD8ugDD5pmGm476HgjqyQIcERFRA2CV/9snJSXBw8Pjnu0eHh5ISkoq97hBgwbhl19+wb///osvv/wSR44cwUMPPVTqF9C71erJGdW61UfiYBSALsEuaOxuJ3YcIiL0be4BTwcV0vJ02HbulthxiOq1N998E1lZWeZLXFyc5Z6sUXug3wfAC8eAKduA9k8BagfLPR8RERHVOXWqCPfuu+/es3DC3ZejR48CACRlTE4rCEKZ24uNHTsWQ4YMQWhoKIYOHYq///4bly9fxubNm8s9plZPzqhWFRmMWHvE9H5O6BwgchoiIhO5TIqxHU294X69PVyeiCxDpVLBwcGh1MViJBKg20zArYnlnoOIiIjqtDo1J9wLL7yAcePGVdgmMDAQp0+fxq1b9/YOSElJgaenZ6Wfz9vbGwEBAbhy5Uq5bVQqFVQqVaUfk6xH5KUUJGUXwtVWiQGtOE8gEdUd4zr6Yf6/V3Dwejqup+QimD11iYiIiIisXp0qwrm5ucHNze2+7SIiIpCVlYXDhw+jU6dOAIBDhw4hKysLXbt2rfTzpaWlIS4uDt7eXBGzIVp9uxfc6A6+UMrrVKdQImrgfJw06NXUHbsupWDt0Zt4Y1BzsSMRWYXc3FxcvXrVfD86OhonT56Ei4sL/P059ysRERGJyyorDy1atMDAgQMxdepUHDx4EAcPHsTUqVPxyCOPlFoZtXnz5tiwYQMA00nZ7NmzceDAAcTExCAyMhJDhw6Fm5sbRo4cKdZLIZHcyi7ErkumBRkeC+c8f0RU9xQPSf392E3oDUaR0xBZh6NHjyIsLAxhYWEAgFmzZiEsLAzvvPOOyMmIiIiI6lhPuKr45ZdfMHPmTPTv3x8AMGzYMMyfP79Um0uXLiErKwsAIJPJcObMGaxYsQKZmZnw9vZGnz59sGbNGtjb29d6fhLX78duwmAU0DHQGU08OMyLiOqevi084GanQmquFv9cSMbAUA6bJ7qf3r17QxAEsWMQERERlclqi3AuLi74+eefK2xz50mYRqPBtm3bLB2LrIDRKGDN7aGoxT1NiIjqGoVMijEdfLFo9zWsORLLIhwRERERkZWzyuGoRA/i4PU0xKbnw14lx5DWnA+QiOqusR1Nw+V3X05BQmaByGmIiIiIiOhBsAhHDU7xggzDw3ygUcpETkNEVL4gN1t0DnKBUTANoyciIiIiIuvFIhw1KBl5Omw9mwQAGMehqERkBcZ1MvWGW3MkDkYj57oiIiIiIrJWLMJRg/LHyXjoDEa08nFAaCNHseMQEd3XoFBvOKjliM8swP5rqWLHISIiIiKiamIRjhoMQRCw+rBpKOq42/MsERHVdWqFDCPDGgGA+TOMiIiIiIisD4tw1GCcjMvEpVs5UCukGNaukdhxiIgqrXgl5+3nk5CWqxU5DRERERERVQeLcNRgrLm9IMPg1t5w1ChETkNEVHktfRzQxtcReoOADSfixY5DRERERETVwCIcNQh52iJsPJUAABgbzqGoRGR9iheTWX0kDoLABRqIiIiIiKwNi3DUIGw5k4g8nQFBbrboFOQidhwioiob2tYbaoUUV5NzcTIuU+w4RERERERURSzCUYPw27GbAIAxHXwhkUhETkNEVHX2agUGhXoDKPlMIyIiIiIi68EiHNV7N9LycDg6HVIJMKo9F2QgIuv1aAdfAMDGUwko1BtETkNERERERFXBIhzVe7/f7jHSPcQd3o4akdMQEVVfl2BX+DprkFNYhG3nksSOQ0REREREVcAiHNVrBqOAdbeLcMU9SIiIrJVUKsHo9qbPst+OckgqEREREZE1YRGO6rWoa6lIyCqEg1qOfi09xY5DRPTAxtz+QWH/tVTEZxaInIaIiIiIiCqLRTiq14p7igxv1whqhUzkNERED87PxQYRwa4QBJh7+hIRERERUd3HIhzVW1kFevOcSY+GcygqEdUfxZ9pvx+7CaNREDkNERERERFVBotwVG9tPJUAbZERzTzt0bqRo9hxiIhqzKBQb9ip5IhNz8fhmHSx4xARERERUSWwCEf11m9H4wCYeoxIJBKR0xAR1RyNUoZH2ngD4AINRERERETWgkU4qpcu38rBqZtZkEslGBHWSOw4REQ1rnhI6pYzicjVFomchoiIiIiI7odFOKqXinvB9WnuATc7lchpiIhqXnt/ZwS726JAb8CW04lixyEiIiIiovtgEY7qnSKDERtOJAAAHu3ABRmIqH6SSCQY06FkgQYiIiIiIqrbWISjemfv1VSk5mrhYqtEn+YeYschIrKYUWG+kEiAwzHpiEvPFzsOERERERFVgEU4qnfWH48HAAxr6wOFjH/Fiaj+8nJUo3sTNwDAhhPxIqchIiIiIqKKsEJB9Up2oR7bzyUBAEa351BUIqr/RrU3LT6z/vhNCIIgchoiIiIiIioPi3BUr2w5nQhtkREhHnYIbeQgdhwiIosb0MoLNkoZYtLycTw2Q+w4RERERERUDhbhqF4pHoo6qr0vJBKJyGmIiCzPRinHoFBvAMC64xySSkRERERUV7EIR/VGbFo+DsekQyIBRoT5iB2HiKjWjL49JHXTqQQU6g0ipyEiIiIiorKwCEf1RvGk5N0au8HbUSNyGiKi2tMl2BU+jmpkFxbh34vJYschIiIiIqIysAhH9YIgCFh/4iaAkknKiYgaCqlUghFhJQs0EBERERFR3fNARbicnJyaykH0QI7HZuBGWj5slDIMaOUldhwiolpX/ANE5KUUpOZqRU5DRERERER3e6AiXI8ePZCUlFRTWYiqrXgy8oGhXrBVyUVOQ0RU+5p42KOtryOKjAI2nkoQOw4REREREd3lgYpw4eHh6Ny5My5evFhq+4kTJzB48OAHCkZUWYV6Azbd/sI5ur2vyGmIiMQz6vZn4HqukkpEREREVOdUugh37tw5FBUVldr2ww8/YPLkyejevTv27duHy5cv47HHHkN4eDhUKlWNhyUqyz8XkpFdWAQfRzUigl3FjkNEJJqhbX2gkElwJj4Ll29xyggiIiIiorqk0kW4Ll26IDY29p7tc+bMwauvvop+/fohNDQUBQUFOHLkCDZs2FCjQYnKs+H2ggzDwxpBKpWInIaISDwutkr0aeYBAFjHBRqIiIiIiOqUShfhzp8/j4CAgFLbEhMTMXPmTHzwwQdo2bIlFAoFxo0bh/bt29d4UKKypOfpEHkpBQAwKoyrohIRjbz9WbjxZAKMRkHkNEREREREVKzSRTg/Pz/IZLJS24KDg7F371789ttvOHbsGNavX48ZM2bg008/rfGgRGXZfCYRRUYBLb0dEOJpL3YcAtC7d2/ExMSIHYNqGN9X69GnuQfs1XIkZBXicEy62HGIiIiIiOi2B1qYYdmyZThx4gSGDBkCABgwYAB27dqFb775BjNmzKiRgEQV+fOEafLxkewFJ6r9+/djy5YtpbbFx8djwYIFIiWimsD31TqpFTIMDvUGAPx5kgs0EBERERHVFQ9UhBs3btw929q3b4+oqChERkY+yEMT3Vdcej6O3siARGKajJzE4+/vj59//hkTJkxAZmYmlixZglGjRt0zhF0shYWFmDNnDpo2bQq1Wg0fHx9MnjwZN29a35xZkyZNgkQiqZXP2Lr6vubn5+OPP/7AlClT0KZNGzg4OMDW1hZt27bF+++/j9zcXFHz1QXDw0yfiZtPJ0JbZBA5DRERERERAQ9YhCtPYGAg9u/fb4mHJjIr7uHRtbErvBzVIqdp2Pz8/PDrr7+iY8eOOHXqFP79919ERkaae8mKqbCwEH379jUXZ4YPHw4/Pz8sW7YM7du3x7Vr18SOWGfV1ff1119/xciRI/Hjjz/CaDRi4MCB6NGjB6KjozFnzhx07NgRycnJomYUW5cgV3g5qJFdWIRdF1PEjkNERERERLBQEQ4AnJ2dLfXQRBAEARtuD0Ud3o5DUcUWHx+PJ598EkeOHEHbtm3x0EMPoU+fPti2bZvY0fDRRx8hKioKERERuHz5MtasWYNDhw7hyy+/REpKCiZPnix2xDqrrr6vSqUS06dPx+XLl3H27FmsXbsWW7duxaVLlxAWFoaLFy/i5ZdfFjWj2KRSCYa3M/WG45BUIiIiIqK6wWJFOCJLOpeQjWspeVDKpRgY6iV2nAYvOjoa48aNwy+//AInJydMnToVv//+O65evSpqLr1ej3nz5gEAvvvuO9jZ2Zn3zZo1C23atMGePXtw7NgxsSLWaXX1fX3qqaewYMEChISElNru7e2N7777DgCwfv166HQ6MeLVGcU/UPxzIRlZBXqR0xAREREREYtwZJX+uN0Lrl8LTzioFSKnqT/Gjx8PiUSCDz/88J59+/btg1qthoeHxz1DOLt3737PEEVfX188//zzFs17P/v27UNmZiYaN26MsLCwe/aPGTMGALBx48ZKPd7mzZsxefJktGjRotQ8ZB999BG0Wu097WNiYiCRSNC7d28UFBTgjTfeQEBAAFQqFZo0aYJPP/0UgiCU+Vzr1q1Dp06doNFo4OnpiaeeegoJCQlVePUl6tv7WpG2bdsCALRaLdLS0kROI64W3vZo6mkHncGIrWcTxY5DRERERNTgPXARbv/+/eYvn3feJrIUg1HAX6dMxYji4VZUM95//33I5XJ8+eWXyM7ONm+/dOkShg8fDplMhs2bN6Nx48blPkZkZCQCAwNrIe39nTp1CoBpwZiyFG8vbnc/U6ZMwW+//QZHR0fzPGRxcXF4++23MXjwYBgMZU+Ar9Pp0L9/fyxevBgtWrRAnz59EB8fjzfeeAP/+9//7mk/f/58jBkzBsePH0fXrl3Ru3dv7Ny5E126dKlWYam+va8VuX79OgBAoVDAxcVF5DTikkgkGHF75eg/TlSvgEtERERERDXngYtwgwYNQnx8/D23iSzlwLU0JOdo4WSjQO9mHmLHqVeaNGmCp59+GhkZGfjmm28AALdu3cKgQYOQlZWFtWvXomPHjhZ57t69e0MikVTpcr8VQmNjYwGYem+VpXh7cbv7WbRoEZKSknDw4EHzPGQ3btzAI488gn///Re//PJLmccdOHAAEokEly9fxtatW7F161bs3bsXcrkcX3/9danVPGNiYjB79myoVCrs3LkT//zzD9asWYOrV6+iefPm2LRpU6Wy3qm+va8VKX59AwcOhEqlqqFXYb2G3V45+mB0GhKzCkROQw2JXq9HXFwcLl26hPT0dLHjEBEREdUJ8gd9gDuHUpU3rIqoJv1xe5Lxwa29oZRzRHVNe+edd7By5Up89dVXmDJlCoYPH47o6GgsWbLEoqtiDhw4sMo9rby8Kp4PsLi4ZWNjU+Z+W1vbUu3uZ8SIEfdss7e3x9dff41Nmzbhzz//xFNPPXVPG6lUih9++AFubm7mbeHh4Rg0aBA2btyIo0ePonfv3gCAH3/8EVqtFlOnTjVvK34N8+bNQ4sWLar1WVuf3tfybNmyBUuXLoVCocAHH3xQrceob3ydbdAp0AWHY9Lx18kEPNer/N6ORA8qNzcXv/zyC1atWoXDhw+XGh3h6+uL/v3749lnn7VY0Z+IiIiornvgIhxRbSrUG7D1bBIAYARXRbUIX19fTJ8+HV9//TXatm2L1NRUzJkzB88884xFn/eNN96o8ccsLlZJJJIK91fFlStXsGXLFly9ehV5eXkwGo3mx7ly5UqZxwQGBqJp06b3bC/elphYMl/Xvn37AACPPfbYPe2bNWuGsLAwHD9+vMq569P7WpYLFy7giSeegCAI+Pzzz81zwxEwPMwHh2PS8QeLcGRBX3/9NT788EMEBgZi2LBheOONN9CoUSNoNBqkp6fj7Nmz2Lt3L/r164cuXbpg3rx59yyuQkRERFTfsQhHVmXnhVvI1RahkZMG4QHOYsept2bNmoW5c+ciNTUVkyZNwrvvvit2pGqxt7cHAOTl5ZW5Pz8/HwBKrZpaHkEQMHv2bHz99dflFu9ycnLK3F7ecNji572zt0jx4gv+/v5lHuPv71+tIhxQf97Xu928eRMDBw5ERkYGZs2ahZdeeknsSHXKkNbeePevc7iQmI1LSTlo5mUvdiSqh6KiorBr1y60bt26zP2dOnXC5MmTsWjRIixduhS7d+9mEY6IiIgaHBbhyKr8dbJkQQaptOzeTfRgBEHArFmzzIUmubx2PiY++eQTXLx4sUrHvPHGG2jevHm5+4sLWTdv3ixzf/H28gped1qzZg2++uor+Pr6Yu7cuYiIiIC7uzsUCgV0Oh1UKlW5xbnyeuKV5X6996qrPr2vd0pNTUW/fv0QGxuLp59+Gl988UV1YtZrTjZK9G7mgR3nb+GvU/H4j1fl/myJquK3336rVDuVSoUZM2ZYOA0RERFR3cQiHFmNrAI9Ii+lAACGcVVUi5k1axZ+++03DB06FIcOHcLy5cvx2muvWbzHwtatW7F79+4qHTNp0qQKizXFQxLL6zlWvL1Nmzb3fa4NGzYAABYuXIhHHnmk1L7iFTlrgo+PDy5fvowbN26U+Wde2UUk7laf3tdiOTk5GDRoEC5evIhRo0ZhyZIlNV68rC+GtfXBjvO3sPFUImb3b8Y/J7KoiIgIbNu2DQ4ODmJHISIiIqpTOKs9WY1t55KgMxjR1NMOzb14Ym8JX331FebOnYvOnTtjzZo1eP3111FUVIR33nnH4s8dGRkJQRCqdLlz4YKydOvWDY6Ojrh27RpOnDhxz/7ff/8dAO4pqpUlIyMDAODn53fPvrVr11biFVZO9+7dAZTdq+Ty5cs4efJklR+zvr2vgGkI7/Dhw3H06FEMGDAAq1atgkwms/jrsVYPt/CEjVKG2PR8nIzLFDsO1XOHDh1CYWHhPduzs7Pxn//8R4RERERERHWD1RbhPvzwQ3Tt2hU2NjZwcnKq1DGCIODdd9+Fj48PNBoNevfujXPnzlk2KNWYjadMQ1GHtmEvOEtYu3YtZs+ejSZNmmDjxo3QaDSYPn06vLy8sGbNGpw+fVrsiFWmVCrxwgsvAABeeOGFUnPDffXVVzh9+jS6d+9eqZX6ihdRWLx4calhp3v37sXnn39eY5mffvppKJVKrFixAnv37jVvLygowEsvvQSj0Vilx6uP76vBYMDjjz+OXbt2oUePHli/fj2USqXYseo0jVKGfi09AQAbTyXepzVR9YwaNQqffPIJJBIJkpOT79mfl5eHr776SoRkRERERHXDAxfh3nrrLbi4uNxz29J0Oh0effRRTJ8+vdLHfPbZZ/jqq68wf/58HDlyBF5eXujXr1+5k6lT3ZGaq0XUtTQAwNC2LMLVtN27d+Opp56Cm5sbtm7dCnd3dwCARqPBG2+8AUEQ8Pbbb4ucsnr++9//onPnzoiKikJISAjGjh2LLl264NVXX4WrqyuWLVtWqceZOXMmbG1tsWDBAoSGhuLxxx9Hz5490atXL0ybNq3G8gYHB+PTTz9FYWEh+vTpg4cffhjjxo1DkyZNcPbs2Ur12itWX9/X+fPnm4cHu7m5YcaMGZg0adI9l9TUVJGT1i3FP2BsOp0Ag7HqKwMT3U9AQAA2bdoEQRDQtm1beHh4oF+/fpg9ezZWrFiBL7/8Et7e3mLHJCIiIhKPYOWWLVsmODo63red0WgUvLy8hE8++cS8rbCwUHB0dBQWLVpU6efLysoSAAhZWVnViUvV9FNUtBDw+iZh2Ly9Ykepd86dOyc4OTkJNjY2wqFDh+7ZX1BQIDRq1EgAIERFRYmQ8MHl5+cL//vf/4TGjRsLSqVS8PT0FCZOnCjExsZW6XHOnz8vDB06VPDw8BBsbGyEsLAwYfHixYIgCAIAISAgoFT76OhoAYDQq1evMh9vzpw5AgBh2bJl9+xbu3at0KFDB0GlUglubm7C+PHjhZs3bwoTJ04UAAi7du2qMGt9fl+L/9zud4mOjhY7ap2i1RuENu9uEwJe3yTsv5oidpwGpyGdPyiVSuHw4cPCH3/8IcyZM0cYPny4EBwcLAQGBgq//PKL2PEq1JDeJyIiIqoZVTl/kAhCOcv5WYnly5fj5ZdfRmZmZoXtrl+/jsaNG+P48eMICwszbx8+fDicnJzw008/lXmcVquFVqs138/Ozoafnx+ysrI44XAtGrMwCkdvZOC/Q1rgmR7BYschIrJKb6w7jdVH4vB4Jz98POr+C5JQzcnOzoajo2ODOH8oKiqqtRWYa1pDep+IiIioZlTl/MFq54SrqqSkJACAp6dnqe2enp7mfWX5+OOP4ejoaL6UNSk7WVZ8ZgGO3siARAI8wvngiIiqbdjt4fx/n02Crqhq8wsSVeTOlZsrU4CLj4+3ZBwiIiKiOqlOFeHeffddSCSSCi9Hjx59oOeQSCSl7guCcM+2O7355pvIysoyX+Li4h7o+anqNt1ekKFToAu8HNUipyEisl6dg13hbq9CZr4e+66miB2H6pGOHTti6tSpOHz4cLltsrKysGTJEoSGhmL9+vW1mI6IiIiobnjgsQJ6vR5JSUnIz8+Hu7v7Ay3M8MILL2DcuHEVtgkMDKzWY3t5eQEw9Yi7c1Lg5OTke3rH3UmlUkGlUlXrOalm/FW8KioXZCAieiAyqQRDWntjeVQM/jqZgIeal///H1FVXLhwAR999BEGDhwIhUKB8PBw+Pj4QK1WIyMjA+fPn8e5c+cQHh6Ozz//HIMGDRI7MhEREVGtq1YRLjc3F7/88gtWrVqFw4cPl5ozzdfXF/3798ezzz6Ljh07Vulx3dzc4ObmVp1I9xUUFAQvLy/s2LHDPCecTqfD7t278emnn1rkOenBXUvJxbmEbMilEgxuzRXViIge1LB2PlgeFYMd52+hQGeARikTOxLVAy4uLvjiiy/wf//3f9iyZQv27t2LmJgYFBQUwM3NDRMmTMCAAQMQGhoqdlQiIiIi0VS5CPf111/jww8/RGBgIIYNG4Y33ngDjRo1gkajQXp6Os6ePYu9e/eiX79+6NKlC+bNm4eQkJAaDx4bG4v09HTExsbCYDDg5MmTAIAmTZrAzs4OANC8eXN8/PHHGDlyJCQSCV5++WV89NFHCAkJQUhICD766CPY2Nhg/PjxNZ6PasbG273guoe4wcVWKXIaIiLrF+bnBF9nDW5mFODfi8kY0oY/cFDNUavV6NevH0aNGiV2FCIiIqI6p8pFuKioKOzatQutW7cuc3+nTp0wefJkLFq0CEuXLsXu3bstUoR75513Sq1oWty7bdeuXejduzcA4NKlS8jKyjK3ee2111BQUIAZM2YgIyMDnTt3xvbt22Fvb1/j+ejBCYJgHoo6jENRiYhqhEQiwdC2PlgYeQ1/nYpnEY5qXI8ePbB161bzVCBEREREZCIRBEGo7sE5OTkNroDFpetrz7mELAz5dh9UcimO/vdh2KsVYkciIqoXLiRmY9A3e6G8/fnqwM9Xi2tI5w/PPPMMduzYgW3btqF58+bm7SdOnMDbb7+NLVu2iJiuYg3pfSIiIqKaUZXzhwdaHbVHjx5ISkp6kIcgKtem04kAgD7NPFiAIyKqQc297BHiYQddkRE7zt0SOw7VMz/88AMmT56M7t27Y9++fbh8+TIee+wxhIeHc7ErIiIiatAeqAgXHh6Ozp074+LFi6W2nzhxAoMHD36gYNSwCYKATae5KioRkSVIJBI80sb02br5TKLIaag+mjNnDl599VX069cPoaGhKCgowJEjR7BhwwaxoxERERGJ5oGKcPylkyzlTHwW4tILoFHI0Ke5u9hxiIjqnSFtTPN17b2Sgqx8vchpqD5JTEzEzJkz8cEHH6Bly5ZQKBQYN24c2rdvL3Y0IiIiIlFVeWGGu82ZMwdKpRL9+vWDwWDAgAEDcOTIEZ5o0QPZfHso6kMtPGCjfOC/pkREdJcmHvZo7mWPi0k52H4+CY+G+4kdieqJ4OBgNG/eHL/99huGDBmCbdu24bHHHsP/t3fn8VGW9/7/37Nn38kCCWEnBgSRKIsoi4qgtlaPKMeWyqn21Frbr/V4Wq2/HvB8v9alVmtr69JatK1a2yO0PXWDyqrsCrLvAQIhCQnZt0lm7t8fyYxESMg2uWcmr+fjMQ8yd65JPreXM3PnPddy4sQJ/fCHPzS7PAAAANP0aCQcn3QiEFqmoraEcDdezK59ABAoN7S+xvpec4HesGTJEm3btk033HCDJOm6667TqlWr9Nxzz+nee+81uToAAADz9CiEGzZsmNatW6e//OUv+uSTT7R06VLde++9evLJJ3urPvRD2wsqdLKiXlFOm2bmpJpdDgCErRvGtYRwHx8qVXmt2+RqEC7mz59/zrFLL71U69ev1+rVq/u+IAAAgCDRoxCOTzoRCL6pqNdclKYIh83kagAgfA0bEKPcjDg1ew0t38Nu5wisIUOG6OOPPza7DAAAANP0KITjk070Nq/X0LutO/X5RmgAAALH91rLlFT0hcTERLNLAAAAME2PQrj28EknumtbQYUKKxsU7bRp+ih2RQWAQPOtC7f+cJnKahpNrgYAAAAIX10O4Y4fP96pdr5POk+ePNnVX4F+zDcV9dpcpqICQF8YkhKtsYPi5PEa+mB3sdnlAAAAAGGryyHcZZddpm9+85vavHlzu20qKyv1m9/8RmPHjtXSpUt7VCD6j7Onot44bqDJ1QBA/+F7zX1nZ6HJlQAAAADhy97VB+zdu1c/+clPNGfOHDkcDuXl5WngwIGKiIhQeXm59uzZo927dysvL08//elPNXfu3EDUjTD0yfFyFVU1KNZl15WjUswuBwD6jRsuztAT7+3ThsNlOl3dqAGxLrNLAgAAAMJOl0fCJSUlafHixSosLNQLL7ygUaNGqbS0VAcPHpQkffWrX9Unn3yijz/+mAAOXeKfijomTS47U1EBoK9kJUVpfGa8vIb0/m52SQUAAAACocsj4aSW9d5OnTqlW265Rbfccktv14R+yNNmKiq7ogJAX7thXIY+O1Gpd3YUasHkbLPLAQAAAMJOt3ZH9Xg88nq9/vtXXHGFiotZzBndt/XoGZVUNyouwq5pI9gVFQD62g2t68Jtyj+jkuoGk6sBAAAAwk+3Qrgv2rFjh2pra3vjR6Gfem9Xy/Sn2WPS5bT3yv+WAIAuGJQQqUuyEmQYYpdUAAAAIABIO2A6r9fQe7tapqJef3G6ydUAQP/lew1+r3V5AAAAAAC9p9sh3BtvvKFPP/1UTU1NkiSLxdJrRaF/2VZQruKqRsW67LpiBLuiAoBZ5o5tWZNz45EyldU0mlwNAAAAEF66FcJNmzZNixYtUl5enmJiYlRXV6dHHnlEL7zwgjZt2qSGBtaSQee9u7NlKuo1ueyKCgBmykqK0sWDWnZJXb6HKakAAABAb+pWCLd27VpVVlZq//79eu211/Qf//EfKi4u1iOPPKIpU6YoLi5O48aN6+1aEYYMw/BPe5o7lqmoAGC2ua1TUt9lSipC1K9//WsNHTpUERERmjhxotatW2d2SQAAAJIke08ePHLkSI0cOVLz58/3H8vPz9fWrVu1bdu2HheH8PfZiUoVVjYo2mnTVaPYFRUAzDZ3bIaeen+/NhwuU0WdWwlRTrNLAjrtrbfe0v33369f//rXuuKKK/TSSy9p7ty52rNnjwYPHmx2eQAAoJ/rUQh3PkOHDtXQoUM1b9683v7RCEO+DRlm5qQqwsFUVAAw29CUaOWkx2pfUbVW7CnWvLwss0sCOu2ZZ57RXXfdpbvvvluS9POf/1wffPCBXnjhBT3++OOd/jm1tbWy2c69LrHZbIqIiGjTrj1Wq1WRkZHdaltXVyfDMM7b1mKxKCoqqltt6+vr5fV6260jOjq6W20bGhrk8Xh6pW1UVJR/renGxkY1Nzf3StvIyEhZrS2TgNxut39d6562jYiI8P+/0pW2TU1Ncrvd7bZ1uVyy2+1dbtvc3KzGxvbX9HQ6nXI4HF1u6/F4OlxyyOFwyOl0drmt1+tVfX19r7S12+1yuVySWmbb1NXV9UrbrjzveY04f1teI3iNCPfXiC4x0CWVlZWGJKOystLsUkKe1+s1rnxypZH9w38Y7+woNLscAECr5/55wMj+4T+Mf1uy2exSwgbXD4HX2Nho2Gw2Y+nSpW2Of+973zOuuuqq8z6moaHBqKys9N8KCgoMSe3err/++jaPj4qKarft9OnT27RNSUlpt21eXl6bttnZ2e22zc3NbdM2Nze33bbZ2dlt2ubl5bXbNiUlpU3b6dOnt9s2KiqqTdvrr7++w/9uZ7v11ls7bFtTU+Nve+edd3bYtqSkxN/23nvv7bBtfn6+v+2DDz7YYdtdu3b52y5atKjDtps3f/46+dRTT3XYdtWqVf62zz//fIdt//GPf/jbLlmypMO2f/7zn/1t//znP3fYdsmSJf62//jHPzps+/zzz/vbrlq1qsO2Tz31lL/t5s2bO2y7aNEif9tdu3Z12PbBBx/0t83Pz++w7b333utvW1JS0mHbO++809+2pqamw7a33nprm/+HO2rLa0TLjdeIz2+8RrTcwv01oivXed3eHRXoqd2FVTp+pk4RDqtmjGYqKgAEi+tb14Vbd/C0qhra/8QWCCalpaXyeDxKS0trczwtLU1FRUXnfczjjz+u+Ph4/y0rK3AjP9sZiCJJqm5o0toDp7X+cKm2HD0jt6f90SUer6GKOreqG5rU0NT+aBEAABB8LIbR0SUBvqiqqkrx8fGqrKxUXFyc2eWEtJ9+sE+/WnVYc8em64WvTTS7HADAWa59Zo0OltTo2dvH6+YJmWaXE/K4fgi8wsJCDRo0SOvXr9eUKVP8xx977DH94Q9/0L59+855TGNjY5upNlVVVcrKylJhYeF5+6knU83W7zuh+S9vOn9ji0VWh8t/19vU0PL5+nnbSlZHxDlt7VaL7DaL7FarbDZLy32rVa7ISDlsVtmsFlma3bJbJZvVIkdrW7vNIpvVIrvNquioaDlsFjntVqm1rctulcNmld1qldNu9X8/NiZGDptVjta2NotXTptNDptFjtbHOG0t/ybEx7Y8zmaVt9ktqwzZrRb/NLGzMdWsBVPNut6W6agtmI7avba8RrTgNaLrbW02m9xud6ev83p9TTigMwzD0Ls7Wz6VnntxhsnVAAC+aO7FGTr44UG9u7OIEA4hISUlRTab7ZxRbyUlJeeMjvNxuVz+i+yzRUdHt/mjsD2daeOTmpSgOZdkq9lrqMnjlcdrqNljqMnb8nWTx1Bz6/Emb6SaPYaavS3H/F97vWrytP1j2hfIeSW5JbkNSWf/ndnQ/h8k56rqQtuesVjkD+p84Z7DZpXLbpXLbpPL0fJ1hMPmPxbhaP2e3SqXw6oIf7tOfK+x4ayfbVNUlOO8IeAXOZ1O/x94vdnW4XD4/3jtzbZ2u93/x3ZvtrXZbJ3+/70rba1Wa0DaWiyWgLSVuva8D1Tbs4Oz3mx7dtDXm23PDiZ7s217r+E9bRuo5z2vEV1vGyqvER2FoF9ECAdT7C+uVn5prZx2q2blpJpdDgDgC66/OF2/+PCg1hw4rZrGZsW4uGRAcHM6nZo4caJWrFihm2++2X98xYoVuummm0ysrMWI1Bi9/PW8Hv8cwzDkNaQmj1fNXkOe1iCv2XNWuNca1nlaA7/m1sCv2ettE+41eQ15Wtv6vu9u9srtafm3ydPyPd+xJt+/Hq/czYb/WJPn88f4vt901vfdrd8/ezCOYailfbNXan+gRUA57VZFtAZ9UU6b/99Ip02RDrsinTZFOVrvO22K/GI7x9nH7Yp0WhXptPvbuezWTgV9AID+gytqmMI3Cm76qAH8YQcAQWh0WqyGpUTrSGmtVu4r0ZfHDzS7JOCCHnjgAS1YsEB5eXmaMmWKXn75ZR0/flz33HOP2aX1GovFIptFsllDa1d5wzD8I/7cZwVzvhCv8aygr6HZq8YmjxqbvWpo/bfl5lFDU8u/jW3+/cL3zn5c0+ffa2j2tAkCfSFgVUP7U9R6wmJRS1DXGtbFuOyKbr3FuGyKdvq+PuuYq/1j0U67bFZCPQAIZaQfMMV7O09J+nzxbwBAcLFYLJp7cbp+teqw3tt5ihAOIeH2229XWVmZ/vu//1unTp3S2LFj9e677yo7O9vs0vo9i6V1zTqbFOk0J0A0jJZRgGcHew1NHjU0eVTv9qjO7VF969f1TS33G5o8qnM3q97tVX1T83nbnd2+vsnTMrpPLaP96lrbq/3lvrok0mE7J5yLi7ArLsKhuEiHYv1f2xUb4fB/HRfR+r1Ihxw29uYDALMQwqHPHSqp0cGSGjlsFl190fnXaAEAmG/u2Az9atVhrdpfonq3x7Q/nIGuuPfee3XvvfeaXQaCkMVi8a89FxvA39PsaRnNV+duVoPbq7qmZtU2toR5tY3Nqmn0tP7bcv/sY7XuZlU3nH28WbVujzzeliF89U0tQV9pTffri3TYzgrpWoK5s0O6+EiHEiIdSohyKjGq7b9OOwEeAPQEIRz63Ae7W6aiXjEiRXERnVtAEgDQ98YMjFNmYqROlNdrzYHTmjOW0csAcCF2m1UxNmuvLbliGIYam73+0K7l38+DvJrGZlXVN6mqoUnVDb6vm1Xd0KSq+mZVNTSpqr5Jte6WHSd9QV5xVdcX44t22pQQ5VRClEOJUU7FRzmU6Ps6suXfxOiWwC4h0qHkaJfiIu2sjQcArQjh0Ofe39USws0Zwx9zABDMLBaL5oxJ128/ytcHu4sI4QDABBaLRRGOlg0hUmI6t7vj+TR7vK2BXWsw1xrSVTe0hHa+IK+yvkkVdU2qqHOroq5J5XVuVdY3yWtItW6Pat31OlnR+V13HTaLkqKdSo52KTnGqZQYl5KjnUqO8d1vPdZ6PMLBqGsA4YsQDn3qZEW9dp6slNUiXZPLVFQACHZzxraEcB/uLZa72ctUJAAIUXabtXUUm7PLj/V6DVU3NKu8zq3y1nCuot6t8trWsK6+SeWtwZ3/+3VNqmlsVpPHUHFVY6dH3sW47EqOcfqDugGxLqXFRigtzqXUOJdSYyOUFheh5GinrGxUASDEEMKhT33QOgoub0hSjz7JAwD0jUsHJyolxqXSmkZtPFKmq0YNMLskAEAfs1otio9yKD7KoSGK7vTjGpo8OlPrVlmNW6W1jSqrcausplFltW6V1rTe9x93y906Wq+msVnHyuo6/Nk2q0UDYlxKi3NpQGtIlxYXodTY1n9b7ydFEdYBCB6EcOhT7+9mKioAhBKr1aLZY9L0xqbjen93ESEcAKDTIhw2DUyI1MCEyAu2NQxD1Y3N/qCutKYlqDtd3aiS6gYVV33+b2lNozxeQ0VVDSqqapBU2e7PddqtyoiP0MD4SGUkRGhQQqQy4iM1MCHCX1tvrd8HABfCqw36TGlNo7YcPSNJuo51hQAgZMwZk643Nh3X8t3F+r83jZWNEQUAgF5msVgUF9GyU+vQlI5H2zV7vCqtcftDueKqBpVUN6qkqsH/dXFVo8pqG+Vu9upYWV2HI+viIuz+QC4jviWcy0yMVFZSlAYnRSk52snmEgB6BSEc+sw/9xTLMKSLB8VrUCc+DQMABIfJw5IVG2FXaU2jth0vV96QJLNLAgD0Y3abVenxEUqPj+iwXZPHq+KqBhVWNKiwol6FlfUqrKjXqYoGnaxo+bqqobnlVlStfUXV5/05UU6bshKj/KFcVlKkBrd+nZkYpUgnm0kA6BxCOPQZ/1RURsEBQEhx2q265qI0Ldt2Uu/vKiKEAwCEBIfNqszElqCsPTWNzTpVUa/CyobWgK5eJysadKK8TgVn6nSqqkF1bo/2F1drf/H5Q7oBsS5/KDc0JVpDU6I1bEDLv1FO/uQG8DleEdAnqhqa9PGhUknSdawHBwAh57ox6S0h3O4iPXLDRUzLAQCEhRiXXSPTYjUyLfa8329s9uhkeb0Kyut1/ExLMHe8rM7/dXVjs05Xt6xd98mx8nMenxEfcVYwF6NhrQHdoIRI2W3sOA70N4Rw6BOr9pWoyWNo+IBojUiNMbscAEAXTR81QBEOq06U12t3YZXGDoo3uyQAAALOZbe1hGcDzv0bxjAMVdY36fiZllDuWFmd8ktrdeR0jfJLa1Ve16RTlQ06Vdmg9YfL2jzWYbMoOzlawwdEa1RrCDgqLUbDUmLktBPOAeGKEA594gOmogJASIt02jR91AB9sLtYy3cXEcIBAPo9i8WihCinEqKcGpeZcM73y2vdOlJaq/zSWuWX1rQGdC33G5u9OlRSo0MlNfpgd7H/MTarRUNTojUqLUYjU2M1qjWcG5ISLQcj54CQRwiHgGto8mjVvtOSpDljMkyuBgDQXXPGpuuD3cV6f3eRHpg92uxyAAAIaonRTk2MdmpidmKb416voVNVDTpyukYHi2t0sKRaB4prdKC4WtUNzf5wTiryP8Zhs2hYSowuyojVmIHxyh0Yp9yMOCVGO/v4rAD0BCEcAm7tgdOqb/JoUEKkxg6KM7scAEA3zcpJk91q0YHiGh0+XaPh55maAwAAOma1WjQoIVKDEiJ15cgB/uOGYaioqkEHimt0sLhaB4qr/V/XnrU5xF+3F/ofMzA+QrmtodyY1mAuMzGStVuBIEUIh4Dz7Yo6e0wabwYAEMLiIx2aMjxZ6w6W6oPdRbp3xgizSwIAIGxYLBZlxEcqIz5S00e1DedOVtRrf1G19hRWac+pKu0urNLxM3Utu7pWNuifez+f0hoXYVfuwDiNz0zQ+KyW28D4CP4WA4IAIRwCqsnj1Yd7SySxKyoAhIM5Y9NbQrhdhHAAAPQFi8WizMQoZSZG6eqL0vzHqxqatLc1lNtT2BLMHSypVlVDszYeOaONR87426bEuHRJVrw/mBuXGa+EKKayAn2NEA4BtSX/jCrrm5QU7dRlQ5LMLgcA0EPXXpSmR5bt0mcnKlVc1aC0uAizSwIAoF+Ki3Bo0rBkTRqW7D/mbvbqYEm1dp+s0mcnKvTZiQrtO1Wt0ppG/XNvif7ZOkBCkoYkR2l8VoImZicqLztJo9NjZbMyWg4IJEI4BNTyPS3Doq/OSeUFHQDCQGpchCYMTtC24xVasadYX5ucbXZJAACgldNu1ZiB8RozMF63XZYlqWWjvN2FVfqsoCWU+6ygQkfL6vy3v7WuMRfrsuvS7ERdNiRReUOSND4zQZFOm5mnA4QdQjgEjGEYWtEaws1mKioAhI3ZuenadrxCywnhAAAIehEOmyZmJ7bZpbW81q0dJyu17Xi5PjlWrk+Plau6sVlrDpzWmgOnJUl2q0VjB8X7Q7nJQ5MVH+Uw6zSAsEAIh4DZc6pKJyvqFeGwatqIFLPLAQD0kmtz0/Tk+/u04XCpqhuaFBvBBTkAAKEkMdqp6aMG+DeAaPZ4ta+oWluPntGWY+XaevSMiqsatb2gQtsLKvSbdfmyWKSxA+M1dUSypg5P0WVDEhXlJFIAuoJnDAJm+e6WUXBXjRzAMGYACCMjUmM0bEC0jpyu1er9p/Wl8QPNLgkAAPSA3WbV2EHxGjsoXguvGCrDMHSivF5bj53R5vxybc4v0+HTtdp5slI7T1bqpTVH5LBZdElWgqYMT9HU4cmaMDhBLjt/9wEdCdkQ7rHHHtM777yj7du3y+l0qqKi4oKPWbhwoV577bU2xyZNmqSNGzcGqMr+bTlTUQEgbM3OTdeLaw5r+Z5iQjgAAMKMxWJRVlKUspKidPOETElScVWDNhwu08eHSrX+cJlOVtRry9FybTlarl98eFARDqumDEvWjNGpmjF6gLKTo00+CyD4hGwI53a7NW/ePE2ZMkWvvPJKpx83Z84cLVmyxH/f6WRb5kAoOFOnvaeqZLVIs3JSzS4HANDLrs1N04trDmv1vhK5m71y2q1mlwQAAAIoLS5CX5kwSF+ZMEiGYajgTL3WH24J5NYfLlNpTaNW7T+tVftb1pQbmhKt6aMGaMboAZo8LFkRDkbJASEbwj366KOSpFdffbVLj3O5XEpPZ2RWoPk2ZLhsSJKSogk6ASDcTMhKUEqMS6U1jdp4pExXta4pAwAAwp/FYtHg5CgNTh6s+ZcPlmEY2ldUrTUHTmv1/hJtPVqu/NJa5ZfW6tX1R+WyWzV5WLJm5aTq2tw0DUyINPsUAFOEbAjXXatXr1ZqaqoSEhI0ffp0PfbYY0pNbX+kVmNjoxobG/33q6qq+qLMkLd8T5EkpqICQLiyWi26NjdNb24+ruV7igjhAADoxywWiy7KiNNFGXG6Z/pwVTc06eNDZVpzoESr95/WqcoG/86ri/6+WxcPitfs3DTNHpOuUWkxslgsZp8C0Cf6VQg3d+5czZs3T9nZ2crPz9ePf/xjzZo1S5988olcLtd5H/P444/7R92hc8pr3dpytFySNDs3zeRqAACBMrs1hPvnnhL995cNWa1cQAMAACk2wqE5Y9M1Z2y6DMPQgeIard5fon/uLdbWY+X+DR5+tuKAspOjNDs3TdeNSdeEwYmycT2BMBZUIdzixYsvGHht2bJFeXl53fr5t99+u//rsWPHKi8vT9nZ2XrnnXd0yy23nPcxDz/8sB544AH//aqqKmVlZXXr9/cXK/eVyOM1lJMeq6ykKLPLAQAEyJThyYp22lRU1aCdJys1PivB7JIAAECQsVgsGp0eq9HpsfrW9OEqrWnUh3uLtXx3sdYdKtWxsjr9Zl2+frMuXykxLl1/cbpuHDdQedmJfMCHsBNUIdx9992n+fPnd9hmyJAhvfb7MjIylJ2drYMHD7bbxuVytTtKDufHVFQA6B8iHDbNGJ2qd3ae0vI9RYRwAADgglJiXLr9ssG6/bLBqm1s1toDp7V8T7E+3Fus0ppG/X7DMf1+wzGlx0XoxnEZunH8QI3PjGfKKsJCUIVwKSkpSklJ6bPfV1ZWpoKCAmVkZPTZ7wx3DU0erT1QKompqADQH1ybm6Z3dp7Sij3F+s/rcswuBwAAhJBol11zL87Q3Isz1OTxav3hMv3vZ4X6YFeRiqoa9NuP8vXbj/KVlRSpG8cN1E2XDFROepzZZQPdZjW7gO46fvy4tm/fruPHj8vj8Wj79u3avn27ampq/G1ycnK0bNkySVJNTY0efPBBbdiwQUePHtXq1av1pS99SSkpKbr55pvNOo2w89HBUtU3eTQwPkJjBvLiCADhbuboVNmtFh0ortHR0lqzywEAACHKYbNq+qgBenreeG398TX6zdfz9OXxAxXltKngTL1eWH1Yc36+Tjf8Yp2WfJyvsprGC/9QIMgE1Ui4rviv//ovvfbaa/77EyZMkCStWrVKM2bMkCTt379flZWVkiSbzaadO3fq97//vSoqKpSRkaGZM2fqrbfeUmxsbJ/XH65W7CmW1DIyguHCABD+4qMcmjQsSR8fKtPyPUX696uGm10SAAAIcS67Tdfmpuna3DTVuz1aua9Ef//spFbuK9HuwirtLtyjx97Zq5k5qbp1YqZmjk6V0x6yY4zQj1gMwzDMLiKUVFVVKT4+XpWVlYqLY6TX2TxeQ5c/9k+V1br1x7smadrIvptaDAAwz2vrj2rR33fr8iFJ+vM9U8wuJyhx/RAa6CcACG7ltW79/bNCvf3pCe04Uek/nhTt1E2XDNQdlw/WyDQG2aBvdeX6gagYvWZ7QYXKat2KjbBr0rAks8sBAPSRqy9KlSRtPXZG5bVuk6sBAADhKjHaqTunDtHf75um5d+/St+6apgGxLp0ptatJR8f1bXPrtVtL23Q37afVGOzx+xygXMQwqHXfLi3ZSrqjNGpctj4XwsA+ovMxChdlBEnryGt2l9idjkAAKAfGJUWq4evv0gbHpqlJQsv0+zcNFkt0ub8M/o/f9quKY+v1OPv7dWxMtasRfAgKUGv+WdrCHdN64gIAED/4Xvt970XAAAA9AW7zaqZOal6+et5+vihWbr/mpFKj4vQmVq3XlpzRNN/uloLXtmkVftK5PWyGhfMRQiHXnG8rE4Himtks1o0YxQhHAD0N9dclCZJWnuglOkfAADAFBnxkbr/mlH66Icz9fKCiZo+aoAsFmndwVL926tbdM2za/THjcdU7+ZaBeYghEOv8I18uHxIkuKjHCZXAwDoaxcPildqrEs1jc3adOSM2eUAAIB+zG6zavaYdL32jcu15sGZ+uaVQxXrsuvI6Vr9f3/dpSlPfKin3t+n4qoGs0tFP0MIh17hC+GuZioqAPRLVqvF/x7AlFQAABAsBidH6ZEbcrXhR1frv27MVVZSpCrqmvTr1Yc17cmVeuCt7TpQXG12megnCOHQY5X1Tdqc3zLq4drcNJOrAQCYxTcl9cO9JTIM1lwBAADBI8Zl1zemDdXqB2fqxa9N1GVDEtXkMbR020nNfnatvvWHrdpxosLsMhHm7GYXgNC35sBpNXsNjUyNUXZytNnlAABMcsWIFEU4rDpZUa+9p6qVOzDO7JIAAADasFktmjM2XXPGpuuzggq9sPqw3t9dpA92F+uD3cW6cmSK7ps5QpOGJZtdKsIQI+HQY//c45uKyig4AOjPIhw2TRsxQJL0IVNSAQBAkBuflaAXF0zUiu9fpVsmDJLNatG6g6W6/eWNmvfieq0/VGp2iQgzhHDokSaPV6v2l0iSrs1lPTgA6O987wWsCwcAAELFyLRYPXP7JVr94Ax9ddJgOW1WbTlarjt+u0l3/GajPj1ebnaJCBOEcOiRLUfPqLqhWUnRTl2SlWh2OQAAk83KSZPFIn12opIdxwAAQEjJSorSYzdfrHU/nKmFU4fIabNq/eEy3fLr9frGq1u062Sl2SUixBHCoUf+uadlFNysnFTZrBaTqwEAmG1ArEvjMxMkSSv3lZhbDAAAQDekxUVo8ZfHaOWD03V7XpZsVotW7ivRjb/8SPe+/omOnK4xu0SEKEI4dJthGP7pRtewHhwAoJVvp2zfmqEAAAChKDMxSk/eOk4rvn+Vvjx+oCwW6d2dRZr97Fot/vtulde6zS4RIYYQDt12qKRGx8/UyWmz6sqRKWaXAwAIEldf1LIu3EeHSlXv9phcDQAAQM8MGxCjX/zrBL33f67UrJxUNXsNvbr+qKb/dJV+s/aIGpu53kHnEMKh21a0joKbOiJZ0S67ydUAAILF6LRYZSZGqrHZq3UHT5tdDgAAQK/ISY/T7xZeptfvnqSLMuJU1dCsx97dq2ufWat3d56SYRhml4ggRwiHblu5t2Wtn6uZigoAOIvFYvEvU+DbQRsAACBcXDEiRf/47jQ99S/jlBrr0vEzdbr39U/11d9u0qGSarPLQxAjhEO3nKl1+7dpvjon1eRqAADBxjcl9cO9JXwqDAAAwo7NatFtl2Vp1YMz9L2rR8plb9lJde5z6/TEe/tU5242u0QEIUI4dMuaAyXyGlJOeqwGJkSaXQ4AIMhcPjRJUU6bSqobtbuwyuxyAAAAAiLaZdcD147Siu9P19U5qWryGHpxzWFd87M1en8XU1TRFiEcuuVD/1RURsEBAM7lstv8m/b43jMAAADC1eDkKL2y8DL95ut5GpQQqcLKBt3zx0/1b69u0YnyOrPLQ5AghEOXNXm8WnugZaHtWTmsBwcAOL+rW98jVrIuHAAA6CeuzU3TPx+Yru/OGiGnzarV+09r9rNr9dr6o/J6GRXX3xHCocs+OVauqoZmJUU7dUlWgtnlAACC1IycAZKkzwoqdLq60eRqAAAA+kak06b/mD1a791/pS4bkqg6t0eL/r5bt7+8QYdP15hdHkxECIcuW7mvZUTDjFEDZLNaTK4GABCsUmMjNC4zXhK7pAIAgP5n+IAYvfXvU/TfN41RlNOmLUfLNfe5dXph9WE1e7xmlwcTEMKhy3wh3CzWgwMAXMCs1h20V7IuHAAA6IesVou+PmWIln//Kl05MkXuZq+efH+fbntpg46V1ZpdHvoYIRy65FhZrQ6V1MhmtejKkQPMLgcAEOR8Idy6g6fV2OwxuRoAAABzZCZG6fffuFw/vXWcYl12fXq8Qtc/t05/3lLADqr9CCEcusQ3Cu6yIYmKj3SYXA0AINiNHRivAbEu1bo92pJfbnY5AAAAprFYLJqXl6X37r9Slw9NUq3box+8vUPf+sMnOlPrNrs89AFCOHSJL4S7ml1RAQCdYLVaNGt0y2i4D/cVm1wNAACA+TITo/TmNyfrobk5ctgsWr6nWLOfXas1B06bXRoCjBAOnVbT2KxNR85IYj04AEDn+d4zPtxbwnQLAAAASTarRfdMH66/fucKjUyNUWlNoxYu2ayfLd8vj5frpXBFCIdO++hgqdwer7KTozQsJdrscgAAIWLaiBQ5bVYdP1Onw6dZgBgAAMBnzMB4/e93p+mrkwbLMKRfrjykr/52o0qqGswuDQFACIdOW9k6jWhWTqosFovJ1QAAQkW0y65Jw5IkSav2sUsqAADA2SIcNj1288V6bv4linbatPHIGV3/i4+0/lCp2aWhlxHCoVO8XkOr9rfMT2c9OABAV12dw7pwAAAAHbnpkkH6+3enKSc9VqU1jfraK5v0yw8Pysv01LBBCIdO2VVYqdPVjYp22nT50CSzywEAhJhZrR/gbDlarsr6JpOrAQAACE7DB8Ro2b1X6La8THkN6WcrDuje1z9VbWOz2aWhFxDCoVN8u6JOG5kip53/bQAAXTM4OUojUmPk8Rpay85fAAAA7Yp02vTUreP11L+Mk9Nm1fu7i3TLr9freFmd2aWhh0hT0ClMRQUA9NSs1impq/cTwgEAAFzIbZdl6c1/n6wBsS7tL67Wl3/FOnGhjhAOF1Ra06gdJyokSdNHDzC3GABAyJrR+h6y5kAJa5sAAAB0wsTsRP3vfdM0PjNeFXVNWvC7zXpt/VGzy0I3EcLhgtYeOC3DkMYMjFNaXITZ5QAAQlRedpJiXHaV1ri1q7DS7HIAAABCQnp8hN761hTdPGGQPF5Di/6+W//vH3v4UDMEEcLhgnxTUWeOTjW5EgBAKHParZo2IkWStGofU1IBAAA6K8Jh0zO3jdd/XjdakvTbj/J135ufqqHJY3Jl6ApCOHSo2eP1L6A9M4epqACAnvG9l6zaX2JyJQAAAKHFYrHoOzNH6Ln5l8hhs+jdnUX66m836Uyt2+zS0EmEcOjQ9oIKVdY3KSHKoUuyEs0uBwAQ4ma0jqr+7ESFymoaTa4GAAAg9Nx0ySD9/huTFBdh1yfHyvUvL6zXsbJas8tCJxDCoUO+kQpXjRwgm9VicjUAgFCXFheh3Iw4GYa09iBTUgEAALpjyvBkvf3tqRqUEKn80lrNe3GD9hdVm10WLoAQDh3yrdnDVFQAQG/xT0llXTgAAIBuG5kWq2X3TlVOeqxKqht1+8sb9FlBhdlloQOEcGhXUWWD9pyqksXSMhIOAIDe4JuSuubAaXnY1QsAAKDbUuMi9Na/T9GEwQmqqGvSHb/ZqA2Hy8wuC+0ghEO71hxomYo6LjNByTEuk6sBAISLCVkJiouwq7K+SdsLys0uBwAAIKTFRzn0x7smaerwZNW6PVq4ZLNW7is2uyycByEc2uWfijqaUXAAgN5jt1l11SimpAIAAPSWaJddv1t4ma65KE2NzV79++8/0Xs7T5ldFr6AEA7n5W726qNDpZKkma3ThgAA6C2+9xbfBkAAAADomQiHTS987VLddMlANXsNfffNbXp/V5HZZeEshHA4r63HzqimsVnJ0U5dPCje7HIAAGFmeuso692FVSquajC5GgAAgPDgsFn1zG2X6OYJg9TsNXTfG59q+W6CuGBBCIfzWr2/ZXrQ9NEDZLVaTK4GABBuUmJcGp/Z8iHPmv1MSQUAAOgtNqtFT88bry+PbxkR9503PtU/97BGXDAghMN5rW6dHsRUVABAoPh2SV19gCmpAAAAvclmteiZ28brxnEZavIYuvf1T7VqH9dcZiOEwzlOlNfpQHGNrBbpqpFsygAACIyZOS0h3LoDpWryeE2uBgAAILzYbVb9/PZLdMPFGXJ7vLrnj59oc/4Zs8vq1wjhcA7fVNRLBycqPsphcjUAgHA1blC8kqOdqm5s1taj5WaXAwAAEHbsNqt+Pv8SXXNRqhqbvbrr1S3aXVhpdln9FiEczrHmQEsI5xuhAABAIFitFl01qmXE9dqDrAuHnnnsscc0depURUVFKSEhwexyAAAIGg6bVc/fcakuH5Kk6sZm3fm7zcovrTW7rH4pJEO4o0eP6q677tLQoUMVGRmp4cOHa9GiRXK73R0+zjAMLV68WAMHDlRkZKRmzJih3bt391HVocHd7NX6Q6WSpOmjmIoKAAgs33sNmzOgp9xut+bNm6dvf/vbZpcCAEDQiXDY9NuFebooI06lNW4teGUTO9SbICRDuH379snr9eqll17S7t279eyzz+rFF1/Uj370ow4f99RTT+mZZ57R888/ry1btig9PV3XXnutqqur+6jy4Lf12BnVuj1KiXEqNyPO7HIAAGHuypEpslikPaeqVMKFIHrg0Ucf1fe//31dfPHFZpcCAEBQiotw6PffuFxDkqN0orxeX39lsyrrm8wuq18JyRBuzpw5WrJkiWbPnq1hw4bpy1/+sh588EEtXbq03ccYhqGf//zneuSRR3TLLbdo7Nixeu2111RXV6c33nijD6sPbr6pqFeNHCCr1WJyNQCAcJcc49LFg+Ilff4eBPSVxsZGVVVVtbkBABDOBsS69Ie7Jik11qX9xdX6zuufskFWHwrJEO58KisrlZSU1O738/PzVVRUpNmzZ/uPuVwuTZ8+XevXr++LEkOCbzrQ9NFMRQUA9I0ZvimphHDoY48//rji4+P9t6ysLLNLAgAg4LKSovS7hZcpymnTR4dK9eO/7pJhGGaX1S+ERQh3+PBh/fKXv9Q999zTbpuioiJJUlpaWpvjaWlp/u+dT3/6hLS4qkH7iqplsUhXjiSEAwD0Dd8HP+sOlsrj5QIQn1u8eLEsFkuHt61bt3b75z/88MOqrKz03woKCnqxegAAgtfYQfH65b9OkNUi/WlLgV5ae8TskvqFoArhunOhVVhYqDlz5mjevHm6++67L/g7LJa2UywNwzjn2Nn60yekvlFw4zITlBTtNLkaAEB/MT4zQXERdlXWN+mzExVml4Mgct9992nv3r0d3saOHdvtn+9yuRQXF9fmBgBAf3H1RWn6rxtzJUlPvLdP7+48ZXJF4c9udgFnu++++zR//vwO2wwZMsT/dWFhoWbOnKkpU6bo5Zdf7vBx6enpklpGxGVkZPiPl5SUnDM67mwPP/ywHnjgAf/9qqqqsA3ifNOA2BUVANCX7Darrhw5QO/sPKU1+0/r0sGJZpeEIJGSkqKUlBSzywAAIGwtvGKojpbV6dX1R/X9t7ZrYEKkLslKMLussBVUIVxXLrROnjypmTNnauLEiVqyZIms1o4H9Q0dOlTp6elasWKFJkyYIKllK/s1a9boySefbPdxLpdLLper8ycRopo9Xq07SAgHADDH9FGtIdyB0/r+taPMLgch6Pjx4zpz5oyOHz8uj8ej7du3S5JGjBihmJgYc4sDACCI/fjGXBWcqdOH+0p0zx8+0d+/e4VSYyPMLissBdV01M4qLCzUjBkzlJWVpaefflqnT59WUVHROWu75eTkaNmyZZJapqHef//9+slPfqJly5Zp165dWrhwoaKionTHHXeYcRpB5bMTFapqaFZ8pIPUGwDQ53zrwn12okJnat0mV4NQ9F//9V+aMGGCFi1apJqaGk2YMEETJkzo0ZpxAAD0BzarRT+ff4mGD4hWUVWDvvP6p3I3s2NqIIRkCLd8+XIdOnRIK1euVGZmpjIyMvy3s+3fv1+VlZX++z/4wQ90//33695771VeXp5Onjyp5cuXKzY2tq9PIej41oO7cmSKbNb218gDACAQ0uIilJMeK8OQf2Q20BWvvvqqDMM45zZjxgyzSwMAIOjFRjj0m6/nKdZl15aj5fq//9hjdklhKSRDuIULF573IuuLW+oahqGFCxf671ssFi1evFinTp1SQ0OD1qxZ06PFfMPJataDAwCYzDcazrdGKQAAAPrOsAExeu5fL5HFIv1h4zH9eQu7hve2kAzh0LtKaxq140TLiEFCOACAWXzvQWsPlMrrNS7QGgAAAL1tVk6aHrimZX3e/++vu7SDnet7FSEc9NHBUklSbkacUuNYfBEAYI687CRFO20qrWnUnlNVZpcDAADQL31n5ghdNyZNbo9X33njU1XWN5ldUtgghIN/2o9vGhAAAGZw2q2aOqJll3SmpAIAAJjDarXoqVvHKyspUgVn6vXD/9lxzvJf6B5CuH7O6zW0lvXgAABBwvde5NswCAAAAH0vPtKhX91xqRw2i97fXaTfbzhmdklhgRCun9tVWKmyWrdiXHZdOjjR7HIAAP2cL4T75Hi5qhqY+gAAAGCWcZkJ+tH1F0mSHntnL+vD9QJCuH5uXet6cFOGJ8tp538HAIC5spKiNCwlWh6voQ2Hy8wuBwAAoF9bOHVIm/XhqvmQtEdIXfo535o7VzEVFQAQJK7y75LKlFQAAAAzWSwt68NlJrasD/fo/+4xu6SQRgjXj9U0NuvTY+WSpOkjCeEAAMHhypEtmzOsPXiaRYABAABMFh/p0LO3XyKrRfqfT07o/V2nzC4pZBHC9WMbDpep2WsoOzlKg5OjzC4HAABJ0uRhyXLYLCo4U69jZXVmlwMAANDvXTYkSfdMHy5JenjpTpVUNZhcUWgihOvHfNN8rmIUHAAgiES77MrLTpLUMhoOAAAA5rv/mlEaOyhO5XVN+s//2cGMhW4ghOvH1rX+YeOb9gMAQLC4clTrlNQDpSZXAgAAAEly2q36+e2XyGW3as2B0/rDxmNmlxRyCOH6qeNldTpaVie71aIpw5PNLgcAgDZ8o7Q3HC6Vu9lrcjUAAACQpBGpsXp4bo4k6Sfv7tWxslqTKwothHD9lG96z6XZiYqNcJhcDQAAbeVmxCk52qlat0efHi83uxwAAAC0unPqEE0dnqyGJq8eensn01K7gBCun/p8PTimogIAgo/VavEvl7COdeEAAACChsVi0RO3jFOkw6YNR8r05uYCs0sKGYRw/VCTx6sNh8skSVeNYlMGAEBwurJ1SirrwgEAAASXwclRevC60ZJapqWeqqw3uaLQQAjXD20vqFB1Y7MSoxwaMzDe7HIAADgv30i4XYWVKqtpNLkaAAAAnG3h1CGaMDhBNY3NemTZLqaldgIhXD+0rnUq6rSRA2SzWkyuBgCA80uNi1BOeqwMQ/roEKPhAAAAgonNatFT/zJOTptVK/eV6G/bC80uKegRwvVDaw62/CHDenAAgGA3fRRTUgEAAILVyLRYfXfWCEnS//3HHlXWNZlcUXAjhOtnKurc2nGiQtLna+0AABCsfO9V6w6eZooDAABAELpnxnCNTI1RWa1bP12+z+xyghohXD/z0aFSGYY0Oi1W6fERZpcDAECH8oYkKsJhVUl1o/YXV5tdDgAAAL7AYbPqv28aK0l6fdNx/8AfnIsQrp9Z27oe3JVMRQUAhIAIh02ThiZLktYxJRUAACAoTRmerK9cMlCGIf34r7vk8TKD4XwI4foRwzC0zrce3CimogIAQoPvPWvtwdMmVwIAAID2/OiGixTrsuuzE5X605bjZpcTlAjh+pHDp2t0qrJBTrtVlw9NMrscAAA6xbeR0Kb8M2po8phcDQAAAM4nNTZCD8weJUl66v39KqtpNLmi4EMI14/4RsFdPiRJEQ6bydUAANA5I1JjlBbnkrvZqy1Hz5hdDgAAANqxYHK2cjPiVFnfpJ9+sN/scoIOIVw/8lFrCDeN9eAAACHEYrFo2oiWKam+9zIAAAAEH7vNqv++aYwk6a2tBdpTWGVyRcGFEK6faPJ4tfFImSRp2ghCOABAaPFtKLSOEA4AACCo5Q1J0g3jMmQY0v97Z48Mg00afAjh+oltxytU6/YoOdqp3Iw4s8sBAKBLrmj9AGnPqSqVsr4IAABAUHtoTo6cdqvWHy7Th3tLzC4naBDC9RMfte4oN3VEiqxWi8nVAADQNQNiXcpJj5UkfXyI0XAAAADBLCspSt+4Yqgk6Sfv7lWTx2tyRcGBEK6fWNf6B8uVTEUFAIQo35RU1oUDAAAIft+ZOVwpMU4dKa3VHzceM7ucoEAI1w9U1jfps4IKSWzKAAAIXdNGtm7OcKiUtUUAAACCXGyEQw9cO1qS9NyHB1VZ32RyReYjhOsHNhwuk9eQhg2I1sCESLPLAQCgWy4fkiSnzapTlQ06fLrW7HIAAABwAbflZWpkaowq6pr0m7VHzC7HdIRw/cBHh1rWg2MqKgAglEU6bcobkijp87VOAQAAELzsNqv+Y3bLaLjffZyv09X9e4MtQrh+wLd2jm8aDwAAocq3rMJHbM4AAAAQEq4bk6bxWQmqc3v0q1WHzC7HVIRwYa7gTJ2OltXJZrVo8rAks8sBAKBHrhzR8oHSxiNn2GULAAAgBFgsFv3gupbRcK9vOqaCM3UmV2QeQrgw5xspMCErQbERDpOrAQCgZ8YMjFNilEM1jc3a3rrpEAAAAILbFSNSdMWIZDV5DP38nwfNLsc0hHBhbl3rmjnsigoACAdWq0VTW9c4XXeQKakAAACh4j+vy5EkLdt2QgeLq02uxhyEcGHM4zX08aEySdKVhHAAgDDh22iIzRkAAABCxyVZCbpuTJq8hvSLlf1zbThCuDC262SlKuubFOuya3xmgtnlAADQK3yjuz87UamqhiaTqwEAAEBn/Z+rR0mS/rGjUIdKakyupu8RwoUx33pwk4cny26jqwEA4SEzMUrDUqLl8RracLjM7HIAAADQSbkD4zQ7N02GoX65UyrJTBjzrQfHVFQAQLjxjYb7iHXhAAAAQsr3rh4pSfrb9pPKL601uZq+RQgXpurdHn16rEJSyy4kAACEk2mt720fHyKEAwAACCVjB8Xr6pxUefvhaDhCuDC15egZuT1eZcRHaFhKtNnlAADQqyYNS5bVIh0prVVhRb3Z5QAAAKALvts6Gm7ZtpM6XlZncjV9hxAuTPlGBlwxIkUWi8XkagAA6F3xkQ6Na910iNFwAAAAoeWSrARNHzVAHq+hX6/uP6PhCOHC1MeHfSFcssmVAAAQGL73uPVszgAAABByvnf1CEnS0k9PqqSqweRq+gYhXBgqr3Vrd2GVJOmK4awHBwAIT741Tz86VCrDMEyuBgAAAF0xMTtJedmJcnu8WrL+qNnl9AlCuDC04UiZDEMamRqj1LgIs8sBACAgLh2cKJfdqtPVjTpUUmN2OQAAAOiif79qmCTpjxuPqaax2eRqAo8QLgx9dNZ6cAAAhKsIh02XD02S9Pl7HwAAAELHNReladiAaFU3NOtPm4+bXU7AEcKFofWEcACAfmJq67ILHx9iXTgAAIBQY7Va9O9XtoyG+91H+WryeE2uKLAI4cLMifI6HS2rk81q0aRhSWaXAwBAQE1r/cBp05EyNYf5RRsAAEA4+sqEQUqJcamwskH/2FFodjkBRQgXZta3jgQYlxmvuAiHydUAABBYuQPjFB/pUHVjs3acrDS7HAAAAHRRhMOmf7tiiCTppTVHwnrDLUK4MPPx4ZapqNOYigoA6AdsVoumDk+WJH18kHXhAAAAQtHXJmUrymnTvqJqbTgcvsuMhGQId/ToUd11110aOnSoIiMjNXz4cC1atEhut7vDxy1cuFAWi6XNbfLkyX1UdeAZhuFfE4f14AAA/YXvPY/NGQAAAEJTfJRD/3JppiTp1fVHzS0mgOxmF9Ad+/btk9fr1UsvvaQRI0Zo165d+uY3v6na2lo9/fTTHT52zpw5WrJkif++0+kMdLl95kBxjUprGhXhsGrC4ASzywEAoE/4QrhtxytU525WlDMkL28AAAD6tTunZusPG4/pn3uLdaK8TpmJUWaX1OtC8ip1zpw5mjNnjv/+sGHDtH//fr3wwgsXDOFcLpfS09MDXaIpfCMALh+aLJfdZnI1AAD0jSHJURqUEKmTFfXacrRc00cNMLskAAAAdNGI1FhNG5Gijw6V6g8bj+nhuReZXVKvC8npqOdTWVmppKQL7wa6evVqpaamatSoUfrmN7+pkpKSDts3NjaqqqqqzS1YrW8N4a5oXRsHAID+wGL5fF249UxJBQAACFl3Th0iSXprS4EamjzmFhMAYRHCHT58WL/85S91zz33dNhu7ty5ev3117Vy5Ur97Gc/05YtWzRr1iw1Nja2+5jHH39c8fHx/ltWVlZvl98rmjxebTzCenAAgP5p2kjWhQMAAAh1s3JSlZkYqYq6Jv1t+0mzy+l1QRXCLV68+JyNE75427p1a5vHFBYWas6cOZo3b57uvvvuDn/+7bffrhtuuEFjx47Vl770Jb333ns6cOCA3nnnnXYf8/DDD6uystJ/Kygo6JVz7W07TlSo1u1RYpRDuRlxZpcDAECfmtI6Em7PqSqdqe14oyYAAAAEJ5vVoq9PyZYkLfn4qAzDMLmi3hVUa8Ldd999mj9/fodthgwZ4v+6sLBQM2fO1JQpU/Tyyy93+fdlZGQoOztbBw8ebLeNy+WSy+Xq8s/uax8dbBkFN3V4iqxWi8nVAADQt1JjIzQ6LVb7i1u2tb9hXIbZJQEAAKAbbsvL0jMrDmhfUbU255/RpGHhs+RWUIVwKSkpSknp3FTKkydPaubMmZo4caKWLFkiq7Xrg/rKyspUUFCgjIzQv1D/+HDL9JupI8Lnf04AALpi6ohk7S+u1seHSwnhAAAAQlRClFM3TxikNzcX6PVNx8MqhAuq6aidVVhYqBkzZigrK0tPP/20Tp8+raKiIhUVFbVpl5OTo2XLlkmSampq9OCDD2rDhg06evSoVq9erS996UtKSUnRzTffbMZp9Jp6t0fbjpdLkq4YznpwAID+yfceuOFwmcmVAAAAoCf+9fLBkqT3dxWpPIyWGgmqkXCdtXz5ch06dEiHDh1SZmZmm++dPV94//79qqyslCTZbDbt3LlTv//971VRUaGMjAzNnDlTb731lmJjY/u0/t629dgZNXkMDYyPUHZylNnlAABgisuHJclqkfJLa1VYUa+BCZFmlwQAAIBuuHhQvHIz4rTnVJWWbjupu6YNNbukXhGSI+EWLlwowzDOezubYRhauHChJCkyMlIffPCBSkpK5Ha7dezYMb366qtBu9tpV6xv/cR/yvAUWSysBwcA6J/iIhy6ODNBEqPhAAAAQpnFYtG/Xt6S1/xp8/Gw2aAhJEM4tOUL4aYOD5950gAAdIfvvXA9IRwAAEBIu2nCIEU4rDpYUqNPW5fgCnWEcCGuqqFJO09USJKmEMIBAPo5Xwi34XBp2HxiCgAA0B/FRTh0w8UDJUl/2lxgcjW9gxAuxG0+ckZeQxqaEs3aNwCAfi8vO0lOm1WFlQ06VlZndjkAAADoAd+U1H/sOKXqhiaTq+k5QrgQ9/HhUklMRQUAQJIinTZNGJwg6fP3SAAAAISmidmJGpEao/omj/62vdDscnqMEC7EbfCvB5diciUAAAQH33si68IBAACENovFovmXtYyGe2tL6E9JJYQLYaU1jdpXVC1JmjwsyeRqAAAIDlNHtIwO33i4TF4v68IBAACEslsuzZTdatHOk5U6WFxtdjk9QggXwjYeafmEPyc9VskxLpOrAQAgOIzPTFCkw6ayWrcOlIT2hRoAAEB/lxTt1IzRqZKkpdtOmlxNzxDChbD1TEUFAOAcTrtVlw1tGSG+/hBTUgEAAELdLZcOkiT9ddvJkJ7pQAgXwj5fD45NGQAAOJvvvZF14QAAAELfrJxUxUXYdaqywT8rMBQRwoWowop65ZfWymqRLmc9OAAA2vCFcJuOlKnZ4zW5GgAAAPREhMOmG8YNlBTaU1IJ4UKUbxTcxZkJiotwmFwNAADBZczAeMVG2FXd2KzdhVVmlwMAAIAe8k1JfW/nKdW7PSZX0z2EcCFqPVNRAQBol81q0eRhTEkFAAAIF3nZicpKilSt26Ple4rMLqdbCOFCkGEY2nC4VBIhHAAA7fl8XbhSkysBAABAT1ksFt08IVOStPTT0JySSggXgo6W1amwskEOm0V52awHBwDA+fh2D99y9Iwam0NzygIAAAA+d/OElimp6w6eVkl1g8nVdB0hXAjyfaI/YXCiIp02k6sBACA4jUqLUUqMUw1NXm0/XmF2OQAAAOihoSnRuiQrQV5Dem9n6E1JJYQLQawHBwDAhVksrAsHAAAQbm4clyFJ+seOQpMr6TpCuBBjGIY2HWn5Q2LKMEI4AAA6MqX1A6uNRwjhAAAAwsENrSHclqPlKqoMrSmphHAh5lBJjUpr3HLZrbpkcILZ5QAAENR8H1htO16hhibWhQMAAAh1GfGRystOlCS9s/OUydV0DSFciNnQ+kl+3pBEueysBwcAQEeGpkQrLc4lt8erT4+Vm10OAuTo0aO66667NHToUEVGRmr48OFatGiR3G632aUBAIAA8E1JfSfEpqQSwoUY33SayUOZigoAwIWcvS4cU1LD1759++T1evXSSy9p9+7devbZZ/Xiiy/qRz/6kdmlAQCAAJh7cYYsFunT4xU6WVFvdjmdRggXQrxeQxuPnJH0+Ro3AACgY74pqRsI4cLWnDlztGTJEs2ePVvDhg3Tl7/8ZT344INaunSp2aUBAIAASIuL0OVDkiRJ7+4InSmphHAh5EBJtc7UuhXpsGlcZoLZ5QAAEBJ8H1xtL6hQvZt14fqLyspKJSUlddimsbFRVVVVbW4AACA0hOIuqYRwIWTj4c/Xg3Pa6ToAADpjcFKUMuIj1OQx9AnrwvULhw8f1i9/+Uvdc889HbZ7/PHHFR8f779lZWX1UYUAAKCn5ozNkNUifXaiUgVn6swup1NIckKIbxqNb20bAABwYRaL5awpqaUmV4OuWLx4sSwWS4e3rVu3tnlMYWGh5syZo3nz5unuu+/u8Oc//PDDqqys9N8KCgoCeToAAKAXDYh1Ka91SuqKPcUmV9M5drMLQOd4vYY25bMeHAAA3TF5eLKWbjupDYdZFy6U3HfffZo/f36HbYYMGeL/urCwUDNnztSUKVP08ssvX/Dnu1wuuVyunpYJAABMct2YdG3OP6MPdhfpG9OGml3OBRHChYh9RdWqqGtStNOmiwfFm10OAAAhxTcSbseJStU2NivaxSVQKEhJSVFKSkqn2p48eVIzZ87UxIkTtWTJElmtTPgAACDczc5N0//9xx5tOXpGZ2rdSop2ml1Sh7g6CRG+qah5Q5LksNFtAAB0RVZSlAYlRKrZa2gr68KFncLCQs2YMUNZWVl6+umndfr0aRUVFamoqMjs0gAAQABlJUUpNyNOXkP6597gn5JKmhMifNNnmIoKAED3+N5DmZIafpYvX65Dhw5p5cqVyszMVEZGhv8GAADC2+wxaZKk5bsJ4dALPF5Dm/NbQzg2ZQAAoFt876EbjxDChZuFCxfKMIzz3gAAQHi7bky6JGndwdOqczebXE3HCOFCwN5TVapqaFaMy64xA+PMLgcAgJA0uXUk3M6TlappDO4LNAAAAHROTnqsspIi1djs1doDp80up0OEcCHAN23m8qFJsrMeHAAA3TIoIVKDk6Lk8Rra0rrjOAAAAEKbxWLRdbkto+E+CPIpqSQ6IcA3bYapqAAA9AxTUgEAAMLP7NYpqR/uLVazx2tyNe0jhAtyzR6vNrd+Wj+ZEA4AgB6ZPDxJ0ue7jgMAACD0TcxOVGKUQ1UNzfrkWLnZ5bSLEC7I7S6sUnVjs+Ii7MplPTgAAHpkyrAUSdKuk5WqamgyuRoAAAD0BpvVoumjBkiSVu4vMbma9hHCBTnfdJnLhybLZrWYXA0AAKEtPT5CQ1Oi5TXEunAAAABhZGZOqiRp9b7g3ZyBEC7IbfJPRU0yuRIAAMKD7z11EyEcAABA2Jg+aoCsFml/cbVOVtSbXc55EcIFsbN3b2M9OAAAesekoWzOAAAAEG4Sopy6dHCiJGnlvuCckkoIF8T2tK4HFxth10UZrAcHAEBvmNQ6Em7XyUpVsy4cAABA2Ph8SiohHLrIvx7ckCTWgwMAoJdkxEcqOzlKXkPaGsS7ZwEAAKBrZo5uCeE+PlyqhiaPydWcixAuiG3KbwnhJrEeHAAAvWrS0Jb3VqakAgAAhI+LMmKVER+hhiavNgThdR4hXJDyeA1tZj04AAACwvfeuukImzMAAACEC4vFohmjg3dKKiFckNp7qkpVDc2KcdmVy3pwAAD0qkmtIdzOk5WqbWw2uRoAAAD0lpmjB0iSVu0/bXIl5yKEC1KbWkfB5Q1JlN1GNwEA0JsGJUQqMzFSHq/BunAAAABhZOqIFNmtFh0/U6djZbVml9MG6U6Q8q1Rw1RUAAAC4/MpqcG3XggAAAC6J8Zl16WDEyVJ6w6WmlxNW4RwQcjrNbTlaMtION/C0QAAoHexOQMAAEB4mjYyRZL0ESEcLmR/cbUq6poU5bRp7KB4s8sBACAs+UbC7ThRqTo368IBAACEC18It/5wqTxew+RqPkcIF4R8n8jnDUmSg/XgAAAIiMzESA1KiFSz19CnxyrMLgcAAAC9ZNygeMVF2FXV0KwdJyrMLsePhCcIbTrCVFQAAALNYrEwJRUAACAM2W1WTR0efFNSCeGCjNdraFM+mzIAANAX/Jsz5BPCAQAAhBPflNRg2pyBEC7IHCypUXldkyIdNo3LZD04AAACadKwlpFwnxVUqt7tMbkaAAAA9JYrW0O4T4+Xq6YxONb/DdkQ7stf/rIGDx6siIgIZWRkaMGCBSosLOzwMYZhaPHixRo4cKAiIyM1Y8YM7d69u48q7hzfJ/ETsxNZDw4AgAAbnBSl9LgIuT1ebTtebnY5AAAA6CXZydHKSmpZ/3dTkCw9ErIpz8yZM/XnP/9Z+/fv19tvv63Dhw/r1ltv7fAxTz31lJ555hk9//zz2rJli9LT03Xttdequrq6j6q+MN+aNJOHsR4cAACBZrFY/O+5G/PPmFwNAAAAetO0EQMkBc+U1JAN4b7//e9r8uTJys7O1tSpU/XQQw9p48aNampqOm97wzD085//XI888ohuueUWjR07Vq+99prq6ur0xhtv9HH152cYxuebMrAeHAAAfcL3nhssn5ACAACgd/impH58iBCu15w5c0avv/66pk6dKofDcd42+fn5Kioq0uzZs/3HXC6Xpk+frvXr17f7sxsbG1V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      "text/plain": [
       "<Figure size 1500x700 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''simulation of the system for (a)'''\n",
    "\n",
    "#define F(x)\n",
    "def F(x, t = 0):\n",
    "    #t plays no role as the system is autonomous but is needed for odeint\n",
    "    return 2*x-x**2\n",
    "\n",
    "#show F(x)\n",
    "x = np.linspace(-1,3,100)\n",
    "y = F(x)\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize = (15,7))\n",
    "ax1.plot(x,y)\n",
    "ax1.axhline(y = 0, color = 'red', ls = '--')\n",
    "ax1.scatter(x=0,y=0, marker='o', s = 100, color = 'black', facecolors='none')\n",
    "ax1.scatter(x=2,y=0, marker='o', s = 100, color = 'black')\n",
    "ax1.text(x = 0.3, y= -1, s = r'$x^*=0$' + ' and ' + r'$x^*=2$', size = 15)\n",
    "ax1.set_xlabel(r'$x$')\n",
    "ax1.set_ylabel(r'$F(x)=\\dot{x}$')\n",
    "\n",
    "#simulate F(x) in time\n",
    "tspan = np.linspace(0,2,1000)\n",
    "l_x0 = [-0.02, 1., 3.]\n",
    "for x0 in l_x0:\n",
    "    X = odeint(F, x0, tspan)\n",
    "    ax2.plot(tspan, X, label = 'x0 = ' + str(x0))\n",
    "ax2.axhline(y = 0., color = 'black', ls = '--')\n",
    "ax2.axhline(y = 2., color = 'black', ls = '--')\n",
    "ax2.set_xlabel(r'$t$')\n",
    "ax2.set_ylabel(r'$x(t)$')\n",
    "\n",
    "ax2.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">(b) As suggested in the hint, $g\\left(x\\right)=\\cos\\left(2x\\right)+1=2\\cos^{2}x$ and $h\\left(x\\right)=x$, which intersect at $x\\approx0.86$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12ca29bd0>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/pdf": 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",
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# show the intersection of cos(2x) with 1-x\n",
    "x = np.linspace(0,1,100)\n",
    "y1 = np.cos(2*x)\n",
    "y2 = x-1\n",
    "\n",
    "plt.plot(x,y1, label = 'cos(2x)')\n",
    "plt.plot(x,y2, label = '-(1-x)')\n",
    "plt.legend()\n",
    "# plt.set_xlabel(r'$x$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8570957470689922"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# find numerically zero of F(x)\n",
    "from scipy.optimize import fsolve\n",
    "x0 = fsolve(F, 0.)\n",
    "x0[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/pdf": 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",
      "image/png": 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pZ1w/IyODq6++Gm9vb77++uszHoKxYsUKbDYb8fHxZGVlnXbI5/Hjx/H09FQBXURERERKMGs/vLT74H/l5eV1xg9759qXPrWffODAAQoLC4vbIp5y/Pjx4n7hcGHtXM63b32mzwh//UBrs9lYsmQJq1evZvHixcyYMYOJEyeydu1aoqKiqF27Nlu2bDnjfcfHx9OnTx+6dOnCu+++W+K2sWPHlrju4+Nz2rwLfV7+PkL/ySefpE6dOowZM6Z43t9HwJ3Liy++yOOPP37G28732UZERKSsVIV65Cn79+8nPj4eh8PBwYMHadOmTfFtoaGhJCYmllg+KSkJFxcXAgMDz3qfl9LO5f333ycnJwfgtFrl9u3bueKKKxg+fDhPP/30ObdREapVEd1isVzw4ZwVrXHjxnh4ePDLL7+UGOkB0KJFCz788EOysrKKR8T89ttvWK1WmjRpUrxcdHQ00dHRjB8/ni5duvDZZ5/RuXNnoqOjSUxMJDU1tXjkCThHoPfv3x83Nze+++67M45EWb16Na+99hoLFizgqaeeYvTo0Xz44Yclltm6dSuXXXZZWT4dIiIiIlINVIX98POJjo4uMar5lC+++IKvvvqKZcuWcfvtt/PSSy/xwgsvlFhm69atREdHF1+/kHYurVu3xuFwsHz58jOeQLNFixbMnz+/RDF99erV+Pj4UKdOHcD5/Hfr1o1u3brx7LPPUq9ePb7++mvGjh1LdHQ0b7/99mnF+Li4OPr06UP79u2ZO3fuWds1Dhky5IzzL+Z5+fsIfR8fH2rVqnXRI9iCg4MJDg4+bX5pPtuIiIiUlaqyH5Sfn8/gwYO5/fbbadasGUOHDmXLli3F+yRdunRhwYIFJdZZvHgxHTp0OGs/dLi0di6n9mX+btu2bVxxxRXcd999vPLKK+e8/4pS+X/D1Yy7uztPPvkk48aNw9XVlW7dupGcnMy2bdsYPHgwzz33HPfddx/PP/88ycnJjB49mnvuuYeQkBBiY2N59913uf766wkPD2fXrl3s3r2be++9F3Du+AcFBfHbb79x7bXXAs4R6P369SM7O5tPPvmE9PR00tPTAedJBWw2GxkZGdxzzz2MHj2aAQMGEBkZSYcOHbj22mu59dZbi7OvXLnytBMMiIiIiIhUB/3792f8+PElBqQcOXKEhx9+mClTptC9e3fmzZvHNddcw4ABA+jcuXPxuitXruSll14qvn4h7Vzq16/PfffdxwMPPFB8YtGDBw+SlJTEbbfdxsiRI5k2bRqjR49m1KhR7Nq1i+eee46xY8ditVpZu3Ytv/zyC/369SM4OJi1a9eSnJxcfO6kPn36kJWVxbZt22jVqhXgHIHeu3dvIiMjmTp1KsnJycV5QkNDz5v5Yp+XC3X8+HEOHTpEfHw8ALt27SrOeLacpf1sIyIiUtNMnDiRtLQ0pk+fjre3Nz/++CNDhw7l+++/B5xt0mbOnMnYsWMZPnw4a9asYc6cOXz++efnvN9LaedyJtu2baNPnz7069ePsWPHFo+Ot9lsJY5wq3BGJZaWlmYARlpa2mm35eTkGNu3bzdycnJMSHZpioqKjJdfftmoV6+eYbfbjcjISGPSpEmGYRjGn3/+afTp08dwd3c3atWqZQwfPtzIyMgwDMMwEhMTjUGDBhlhYWGGq6urUa9ePePZZ581ioqKiu/7qaeeMu64447i60uXLjWAM15iY2MNwzCM+++/32jdurWRm5tbvN6bb75p1KpVyzhy5IhhGIZx5MgRw263G4cPHz7r46rKvxMRkYtxrvcpKR09hyJVT1Xe57vvvvuMG2644ay3d+7c2Zg9e7ZhGIbhcDiMvn37Gv379zccDkfxMo899pjRsGHD4n301atXG/7+/kZ2dvZF58rJyTEee+yx4v38Ro0aGR988EHx7cuWLTM6duxouLq6GqGhocaTTz5pFBQUGIZhGNu3bzf69+9vBAUFGW5ubkaTJk2MGTNmlLj/O+64w3jqqaeKr8+dO/esnxHOpyyfl/vuu8947rnnznr72XKea53SfLb5u3O9pvU+VTb0PIpIdVFV94OWLl1quLi4GCtXriyed/DgQcPPz8+YNWtW8bxly5YZ0dHRhqurq1G/fn3j7bffrvCszz333Bnf/+vVq3fR91kW7/UWwzjZUK8cTJ48ma+++oqdO3fi4eFB165dmTJlCk2bNi3V+unp6fj5+ZGWlnZaD7vc3FxiY2OJioo654lyapqjR4/SsmVLNmzYQL169crsfp944gnS0tJO65X4V/qdiEhNc673KSkdPYciVU913udbuHAhjz/+OFu3bj1re5O/u/XWW4mOjmbChAnlnO7ibdmyhSuvvJK9e/eWeoT8paoKz8sp53pNV7f3qYv9jL58+XLGjh3Ltm3bCA8PZ9y4cYwYMaLU261uz6OI1FzVeT+oOiuL9/rS7RlepOXLl/PII4/w+++/s2TJEgoLC+nXrx9ZWVnludkaLSQkhDlz5nDo0KEyvd/g4OBLOhRTRERERKSyGzhwIA899BBxcXGlWj4vL4+2bdvy2GOPlXOyS9O6dWtee+01Dhw4UCHbqyrPS010MZ/RY2NjGThwID169GDTpk1MmDCBMWPGMH/+/ApMLiIiYq5yHYn+d8nJyQQHB7N8+XJ69ux53uU1Er1q0e9ERKoEw4C/nFjtUmhU1aXTcyhS9WifT6qbmjQS/e9K8xn9ySef5LvvvmPHjh3F80aMGMHmzZtZs2ZNqbZTls+jYRhgGFhKebSIiEhZ0n5Q1VTpR6L/XVpaGgC1atU64+15eXnFJ7786wkwRUREysT27+DD6yD1oNlJpBxsPJTK4//ZzIxf9pgdRUREpEo432d0gDVr1tCvX78S8/r378/69espKCg44zrl9dnekZdHwlNPkTLzrTK5PxERkdKqsCK6YRiMHTuW7t27F58V/u8mT56Mn59f8aVu3boVFU9ERKq7zGT4/lE4sBJiPjU7jZSDpPRc/rvhCAu3JpodRUREpNIrzWd0gMTEREJCQkrMCwkJobCwkJSUlDOuU16f7bNWrSLt2+9ImTWL9J8Wl8l9ioiIlEaFFdFHjRrFn3/+yeeff37WZcaPH09aWlrx5fDhwxUVT0REqjPDcBbQs49BSCvo8bjZiaQcXBYZAMCuxHQycs88Mk5Eyk4FdoUUKVc19bVcms/op1j+1grv1HP29/mnlNdne5++fal1370AxI8fT+6uXWVyvyIiIudTIUX00aNH891337F06VIiIiLOupybmxu+vr4lLiIiIpfszy9g5/dgtcONs8HF1exEUg6Cfd2JCPDAYcDmw2lmxxGptux2OwDZ2dkmJxEpG6dey6de2zVBaT+jA4SGhpKYWPIor6SkJFxcXAgMDDzjOuX52T74iSfw6toFIzubIyMfoTA1tczuW0RE5GxcyvPODcNg9OjRfP311yxbtoyoqKjy3JyIiMjp0o7AwnHO6d5PQWhrc/NIuWpfL4AjqTlsOJhK98a1zY4jUi3ZbDb8/f1JSkoCwNPT86yjUUUqM8MwyM7OJikpCX9/f2w2m9mRyt3FfEbv0qULCxYsKDFv8eLFdOjQwZQvHiwuLtR5/XVib72NgsOHiXv0MSLffw9LDfoSREREKl65FtEfeeQRPvvsM7799lt8fHyKv7328/PDw8OjPDctIiLibOPy7SjIS4M6HaDbo2YnknJ2WWQA38bEs/GQRqWJlKfQ0FCA4kK6SFXm7+9f/Jqu7krzGX38+PHExcXx0UcfATBixAhmzpzJ2LFjGT58OGvWrGHOnDmlagNTXmz+/tSd9RYHbr+D7LVrOTrlNUKfnmhaHhERqf7KtYj+9ttvA9C7d+8S8+fOncuQIUPKc9MiIiKw/gPYvxRc3J1tXGzl+rYnlUD7es6+6BsPpeJwGFitGh0rUh4sFgthYWEEBwdTUKBzEEjVZbfba8QI9FNK8xk9ISGBQ4cOFd8WFRXFwoULeeyxx3jrrbcIDw9n+vTp3HzzzRUV+4zcGjcm/LUpHBk1mtRPPsG9WVP8b7nF1EwiIlJ9lXs7FymdXbt20atXL/bs2YOPj0+5bef777/nmWeeYcOGDVitFXZeWRGRind8Pyx+xjl95fNQu7GpcaRiNAv1wcNuIyO3kL3JmTQJKb/3VBFxtnapSQVIkaquNJ/R582bd9q8Xr16sXHjxnJIdGl8rryS2qNHkTJjJgkvvIhrg4Z4XhZtdiwRkSpr+fLljB07lm3bthEeHs64ceMYMWJEuW4zNTWVMWPG8N133wFw/fXXM2PGDPz9/c+6jmEYvPDCC7z77rukpqZy+eWX89Zbb9GyZctyy6kqaiUxceJEHnnkkeICem5uLkOGDKF169a4uLgwaNCgMtnOtddei8Vi4bPPPiuT+xMRqZQcRfDNSCjIgvo9oNNDZieSCuJis9K2rh8AGw+qpYuIiEh1V/vhh/Hp1w8KCjgyZgwFfzsJqoiIlE5sbCwDBw6kR48ebNq0iQkTJjBmzBjmz59frtu96667iImJYdGiRSxatIiYmBjuueeec67z2muv8frrrzNz5kzWrVtHaGgoV111FRkZGeWWU0X0SuDIkSN899133H///cXzioqK8PDwYMyYMVx55ZVlur3777+fGTNmlOl9iohUKr/PgkNrwNUbbngLdORNjXKqpcsGFdFFRESqPYvVSvjkSbg1aUJRSgpHRo3GkZtrdiwRkUolOTmZ0NBQJk2aVDxv7dq1uLq6snjxYgBmz55NZGQk06ZNo3nz5gwbNowHHniAqVOnlluuHTt2sGjRIt5//326dOlCly5deO+99/j+++/ZtWvXGdcxDINp06YxceJEbrrpJlq1asWHH35IdnZ2uQ4aVlWhEvjyyy9p27YtERERxfO8vLx4++23GT58eKlPcpObm0vLli158MEHi+fFxsbi5+fHe++9Vzzv+uuv548//mD//v1l9yBERCqLpJ3wy0vO6f6TIKCeuXmkwhUX0XVyURERkRrB6uVFxKy3sPn5kbt1KwnPPqv2siIifxEUFMQHH3zA888/z/r168nMzOTuu+9m5MiR9OvXD4A1a9YUT5/Sv39/1q9ff85z4Hh7e5/zMmDAgLOuu2bNGvz8/Lj88suL53Xu3Bk/Pz9Wr159xnViY2NJTEwskdXNzY1evXqddZ2yUL3OsGYYUJBtzrbtnmC5uJOXrVixgg4dOlxyBHd3dz799FMuv/xyBg4cyHXXXcc999xDnz59GD58ePFy9erVIzg4mJUrV9KgQYNL3q6ISKVRVADfjICiPGjcDy671+xEYoLous4i+v7kLFKz8gnwcjU5kYiIiJQ314gI6rw5jUNDh5H+3QLcm7cg8P4hZscSkZqgitQjBw4cyPDhwxk8eDAdO3bE3d2dV199tfj2xMREQkJCSqwTEhJCYWEhKSkphIWFnfF+Y2JizrldDw+Ps96WmJhIcHDwafODg4NJPEt7rlPzz5T14MGD58xyKapXEb0gGyaFm7PtCfHg6nVRqx44cID27duXSYx27drx8ssvM3z4cO6880727dvHN998c9pyderU4cCBA2WyTRGRSmPl6xC/Cdz94brpF/3lplRtAV6uNAjyYn9yFpsOp3JFs5DzryQiIiJVnlfnzoQ89RRHX3mFpH/9C7fGjfHu3s3sWCJS3VWheuTUqVNp1aoVX375JevXr8fd3b3E7Za/fYY+dVTP3+f/VaNGjS4g8OnOdN+GYZxzm2darzTrXAq1c6lgn376aYlDGlauXElOTs5pL9rzOXToUIn7+WtPo3/+8580bdqUGTNmMHfuXGrXrn3a+h4eHmRnm/QtmYhIeYiPgRWvOaev+Tf4nvlbcqkZ2keqL7qIiEhNFHD3YPxuvgkcDuLGjiVfg8dERIrt37+f+Ph4HA7HaaO2Q0NDTxv9nZSUhIuLC4GBgWe9z0tp5xIaGsrRo0dPm5+cnHzaSPO/rgOcMevZ1ikL1Wskut3T+Q2MWdsuheuvv75En586depQu3ZtUlMv7EN+eHh4icMlatWqVTydlJTErl27sNls7Nmzh6uvvvq09Y8fP05QUNAFbVNEpNIqyIWvR4CjEFoMglY3m51ITHZZvQD+s+GIiugiIiI1jMViIfS558jfu4+czZs5/Mgo6n/xf9i8vc2OJiLVVRWoRwLk5+czePBgbr/9dpo1a8bQoUPZsmVLceG5S5cuLFiwoMQ6ixcvpkOHDtjt9rPe76W0c+nSpQtpaWn88ccfdOrUCXCe8DQtLY2uXbuecZ2oqChCQ0NZsmQJ0dHRxY9t+fLlTJky5ZxZLkX1KqJbLBfdUqWi+Pj44OPjU2JedHQ027dvv6D7cXFxOevhEg888ACtWrVi+PDhDB06lL59+9KiRYvi23Nzc9m3b1/xC01EpMpbNgmSd4BXEFzzutq4SPHJRTcfTqOwyIGLTQffiYiI1BRWV1fqzJjOgVtvI3/fPuKfGEfEWzOxWLU/ICLloArUIwEmTpxIWloa06dPx9vbmx9//JGhQ4fy/fffAzBixAhmzpzJ2LFjGT58OGvWrGHOnDl8/vnn57zfS2nn0rx5c66++mqGDx/OO++8A8CDDz7ItddeS9OmTYuXa9asGZMnT+bGG2/EYrHw6KOPMmnSJBo3bkzjxo2ZNGkSnp6e3HXXXRed5Xz0DlIJ9O/fnzVr1lBUVFRi/vbt24mJieH48eOkpaURExNz3m933nrrLdasWcNHH33EXXfdxS233MLgwYPJz88vXub333/Hzc2NLl26lMfDERGpWIfWwm/TndPXTQevsx9mJjVHoyBvfNxdyCkoYmdihtlxREREpILZg4OJmDkDi6srmUuXkjJzptmRRERMs2zZMqZNm8bHH3+Mr68vVquVjz/+mFWrVvH2228DzhHeCxcuZNmyZbRr146XXnqJ6dOnc/PN5Xuk96effkrr1q3p168f/fr1o02bNnz88cclltm1axdpaWnF18eNG8ejjz7KyJEj6dChA3FxcSxevPi0gctlyWKc6hBfCaWnp+Pn50daWhq+vr4lbsvNzSU2NpaoqKgL7ide2RQVFVGvXj3mzJlD//79i+fXr1//jGeVPduvbOfOnVx22WXMmTOHO++8E3A+h23btuW2224rPqThoYcewmKxMHv27DJ9HNXpdyIiVUR+FszuDsf3Q7vBMGhWhW7+XO9TUjrl+Rze+8EfrNidzAvXt+S+rvXL9L5FRKRm0Ht92TDzeTzxzTckPDUegDrT38S3X78K3b6IVC+qfVVN5/q9lfY9qnq1c6mibDYbEyZM4PXXXy9RRD9wgSdAadas2WknC/X19SU2Nrb4enJyMv/9739Zv379JWUWEakUljznLKD7RsDVk81OI5VM+8gAVuxOZv3BVBXRRUREaij/QYPI27GD4x9+RPxT43GtVx/3pk3MjiUiIlWM2rlUEg8++CA9e/YkI6N8DzmPjY1l1qxZREVFlet2RETK3b6lsO495/QNM8Hdz9w8Uul0rO/si74u9vhZj+ISERGR6i/4iSfw7NIZIzubI6NGUXTihNmRRESkilERvZJwcXFh4sSJ5dq7B6BTp07cfvvt5boNEZFyl5sG345yTnccDg37mJtHKqXoyABcrBYS03M5kppjdhwRERExicXFhTqvv449IoKCw4eJGzsWo7DQ7FgiIlKFqIguIiJVz6LxkH4EAqLgqhfMTiOVlIerjVZ1nEco/BF73OQ0IiIiYiaXgAAi3noLi6cnWavXkDT132ZHEhGRKkRFdBERqVp2LoSYTwEL3DgbXL3MTiSV2OVRtQBYd0BFdBERkZrOvWkTwic7z6NzfN48TnzzjbmBRESkyqjyRXT1OK089LsQkXKXdQwWjHFOdx0NkZ3NzSOVXsf6ziK6RqKLiIgIgG//fgQ+PAKAxGefI2fLFpMTiYhIVVBli+h2ux2A7Oxsk5PIKfn5+QDYbDaTk4hItWQY8MNjkJUMQc2hz0SzE0kV0OHkyUX3p2SRnJFnchoRERGpDIJGj8a7Tx+M/HyOjBpNYXKy2ZFERKSSczE7wMWy2Wz4+/uTlJQEgKenJxaLxeRUNZfD4SA5ORlPT09cXKrsy0pEKrOt82H7t2B1gRvfBru72YmkCvD3dKVZqA87EzNYf+A4A1qHmR1JRERETGaxWgn/12scuO128vfv58g/HqXevLlYXF3NjiYiIpVUla52hoaGAhQX0sVcVquVyMhIfZkhImUvPQF++KdzuucTEB5tbh6pUjrWr8XOxAzWxqqILiIiIk42b28i3prJgdtuJ2fjRhJffoWwF3XCehERObMqXUS3WCyEhYURHBxMQUGB2XFqPFdXV6zWKtshSEQqK8Nw9kHPPQFh7aDHP81OJFVMx6hafPz7QZ1cVEREREpwi4qiztR/cXjEw5z48kvcWzQn4I47zI4lIiKVUJUuop9is9nUh1tEpLra+BHsWQw2N7hxNtjsZieSKqbTyZOL7khIJz23AF93vYZERETEybtXL4Iee4zk118n8eVXcGvUCM8OHcyOJSJiiuXLlzN27Fi2bdtGeHg448aNY8SIEeW6zVdeeYUffviBmJgYXF1dOXHixHnXMQyDF154gXfffZfU1FQuv/xy3nrrLVq2bFluOTVsWEREKq/Ug/DTBOf0FU9DcHNz80iVFOrnTmQtTxwGbDiYanYcERERqWQChw/Dd+AAKCzkyJh/UBAfb3YkEZEKFxsby8CBA+nRowebNm1iwoQJjBkzhvnz55frdvPz87n11lt5+OGHS73Oa6+9xuuvv87MmTNZt24doaGhXHXVVWRkZJRbThXRRUSkcnI44NtHID8TIrtAl0fMTiRVWKco52j0dbFq6SIiIiIlWSwWwl55BbfmzSk6fpwjo0bjyMkxO5aISJlJTk4mNDSUSZMmFc9bu3Ytrq6uLF68GIDZs2cTGRnJtGnTaN68OcOGDeOBBx5g6tSp5ZrthRde4LHHHqN169alWt4wDKZNm8bEiRO56aabaNWqFR9++CHZ2dl89tln5ZazWrRzERGRauiPd+DASrB7waBZYFXbLrl4nerX4r8bjqgveg2RnlvA6r0pLN+dzIaDqTgMcLVZcXWx4uPuQq8mQVzXNpwQX3ezo4qISCVh9fCg7swZxN5yK7nbt5PwzLOE/+s1LBaL2dFERC5ZUFAQH3zwAYMGDaJfv340a9aMu+++m5EjR9KvXz8A1qxZUzx9Sv/+/ZkzZw4FBQXY7Wdui+nt7X3Obffo0YMff/yxbB4IzhHziYmJJbK6ubnRq1cvVq9ezUMPPVRm2/orFdFFRKTySdkDPz/vnO73EtRqYGocqfo6nhyJvvlwGrkFRbjb9aVMdfTb3hRm/LqH9QdSKXQYZ11u5Z4UXlm4g64NAxnUrg6Doutgt+kATRGRms5epw51pk3j0AMPkP7997g3b07g0AfMjiUilZxhGOQUmnP0ioeLR6m/7Bs4cCDDhw9n8ODBdOzYEXd3d1599dXi2xMTEwkJCSmxTkhICIWFhaSkpBAWFnbG+42JiTl3Rg+PUuUrrcTExOJsfxUSEsLBgwfLdFt/pSK6iIhULkWF8PUIKMyFBn2ggz64yKWrH+hJkI8byRl5bD58gssbBJodScpQbEoWr/ywg593HC2e1yDIi15NgujWsDaebjbyCx3kFzpISMtlweZ41h9M5be9x/ht7zE++f0gb9zejgZB5x5FIyIi1Z/X5Z0IGT+eoy+/TNK//41bkyZ49+hudiwRqcRyCnO4/LPLTdn22rvW4mn3LPXyU6dOpVWrVnz55ZesX78ed/eSR2b+vSBvGMYZ5/9Vo0aNLiBx2TlT1vI8ekhFdBERqVxWvwlx68HND254C3QIrZQBi8VCp/q1+GFLAn/EHlcRvZrILSji34t3MW/1AQqKDGxWC/d0rsfQ7lHUrXX2DxP3da3P4ePZfLc5nneW72PzkTQGTl/J09e0YPDlkTp0X0SkhgsYfBe5O7aTNv8r4v75T6L+8yWu9eqZHUtE5JLt37+f+Ph4HA4HBw8epE2bNsW3hYaGFo/yPiUpKQkXFxcCA8/++ami27mEhoYCzhHpfx0dn5SUdNro9LKkIrqIiFQeiVtg6WTn9MDXwK+OuXmkWrm8gbOI/nvsMUbT2Ow4comSMnJ58KMNxBw+AUDvpkE8fU1zGgX7lGr9urU8eaRPI266rA6P/2czv+09xtPfbOWXHUd5885ofN3P3PNRRESqP4vFQuhzz5G/dx85mzdz+JFHqP9/X2Dz9jI7mohUQh4uHqy9a61p2y6t/Px8Bg8ezO23306zZs0YOnQoW7ZsKS48d+nShQULFpRYZ/HixXTo0OGs/dCh4tu5REVFERoaypIlS4iOjgacj2358uVMmTKlTLf1Vyqii4hI5VCY72zj4iiAZtdCm9vNTiTVTNeGztET6w+kqi96Fbc1Lo0HP1pPfFoufh52/n1rW65scXGjTsL8PPj4gcuZu/oAUxbtZOmuZB6Yu46PhnbC01W7yiIiNZXV1ZU606dz4JZbyN+7j/inniRi+nQsVp1DQ0RKslgsF9RSxSwTJ04kLS2N6dOn4+3tzY8//sjQoUP5/vvvARgxYgQzZ85k7NixDB8+nDVr1jBnzhw+//zzc97vpbZzOXToEMePH+fQoUMUFRUVF+UbNWpUPMq9WbNmTJ48mRtvvBGLxcKjjz7KpEmTaNy4MY0bN2bSpEl4enpy1113XVKWc9F/fxERqRyWT4GjW8EzEK6dpjYuUuYaBnkT5ONGXqGDTYdOmB1HLtKirYncOnsN8Wm5NAjy4ptHul10Af0Uq9XC0O5RzB/RFR93F9YfTOWhjzeQW1BURqlFRKQqsocEEzFzBha7ncyffyFl1ttmRxIRuSjLli1j2rRpfPzxx/j6+mK1Wvn4449ZtWoVb7/t/N8WFRXFwoULWbZsGe3ateOll15i+vTp3HzzzeWa7dlnnyU6OprnnnuOzMxMoqOjiY6OZv369cXL7Nq1i7S0tOLr48aN49FHH2XkyJF06NCBuLg4Fi9ejI9P6Y5KvRgW41SH+EooPT0dPz8/0tLS8PX1NTuOiIiUlyPrYc5VYDjgto+hxfVmJyoVvU9duop+Dv/xf5v4NiaeMVc0Ymy/puW+PSlb38bE8egXMRgG9Ghcm5l3XYafR9m2XdlwMJV75qwlO7+IK5uH8Pbdl2G3adyJSE2l9/qyUdWfxxNffU3ChAkA1JkxHd+rrjI5kYiYJTc3l9jYWKKiok47KadUXuf6vZX2PUqfCERExFz52fD1Q84Cepvbq0wBXaqmUy1dVu87ZnISuVC/7DjK2C83YxhwZ6e6zB3SscwL6ADt6wXw/r0dcHWx8vOOo/zzy804HJV2zImIiFQA/5tuJOCeewBIePIp8vbsMTmRiIhUNBXRRUTEXL+8CMf2gk8YDCi/k4CIAHRtWBuAmMMnyMorNDmNlNbv+48x8tONFDkMboyuwyuDWuNSjqPDuzaqzey7L8PFauG7zfG8v2p/uW1LRESqhpBxT+B5+eU4srM5/Mgoik6cMDuSiIhUIBXRRUTEPLErYO3J3pLXzwSPAHPzSLVXt5YnEQEeFDoM1h04bnYcKYU/j5xg2IfrySt0cGXzYF67pQ1Wa/mfM+GKZiG8cENLAP710y62xaedZw0REanOLHY7daa9gb1OHQoOHSLun49jFOoLeRGRmkJFdBERMUduOnzziHO6/f3Q+Epz80iNcaqlyxq1dKn0jqRmM2TuOjLzCuncoBYz76rY/uR3dYrkqhYhFBQZ/OP/YnSiURGRGs4lIICIt2Zi8fAg67ffSHr9DbMjiYhIBVERXUREzLF4IqQdAv960O8ls9NIDXKqpYv6olduuQVFPPzJRo5n5dMy3Jf37+uIu91WoRksFguv3tSaIB839iZlMnnhjgrdvoiIVD7uzZoRPukVAI5/8AFpCxaYnEhERCqCiugiIlLxdv8EGz8CLDBoFrj5mJ1IapAuJ0eib41PIy27wOQ0cjbPfbuNLXFpBHjaeeee9ni7uZiSI9Dbjam3tgXgwzUHWbozyZQcIiJSefgOGEDggw8CkPD0M+Rs3WZyIhERKW8qoouISMXKPg7fjXZOdx4J9bubm0dqnBBfdxoGeWEY8HusRqNXRv/3xyG+WH8YqwWm3xlNRICnqXl6NQliSNf6ADzx38368kVERAj6xxi8evXEyMvjyKhRFKakmB1JRETKkYroIiJSsRY+AZlHoXYT6PuM2WnkLyZPnkzHjh3x8fEhODiYQYMGsWvXrvOut3z5ctq3b4+7uzsNGjRg9uzZFZD20pxq6aK+6JXP5sMnePZb54i+f/ZrSo/GQSYncnpqQDMaBnmRkpnPzKV7zI4jIiIms9hs1Jk6FdeoKAoTEznyj0cx8vPNjiUiIuVERXQREak4276Grf8Fiw0GzQa7h9mJ5C+WL1/OI488wu+//86SJUsoLCykX79+ZGVlnXWd2NhYBg4cSI8ePdi0aRMTJkxgzJgxzJ8/vwKTX7hTJxddvU+jxiqTtJwCRn66kfwiB1e1COHhXg3NjlTM3W7jmWtbADBv9QEOHjv734WIiNQMNh8fIt56C6u3NzkbNpA4aZLZkUREpJyoiC4iIhUj4yh8P9Y53f0xiGhvbh45zaJFixgyZAgtW7akbdu2zJ07l0OHDrFhw4azrjN79mwiIyOZNm0azZs3Z9iwYTzwwANMnTq1ApNfuM4NnEX03UczSc7IMzmNnPLCgm3EncghspYn/76tLVarxexIJfRuGkzPJkEUFBm8+uNOs+OIiEgl4NYgivCp/wKLhRP/9wWpX3xpdiQRESkHKqKLiEj5Mwz4/lHIOQ4hraHXk2YnklJIS0sDoFatWmddZs2aNfTr16/EvP79+7N+/XoKCk7vG52Xl0d6enqJixkCvFxpEeYLwJr9aulSGSzamsBXG+OwWuCN29vi6243O9IZTRzYHKsFftyayB+xx82OIyIilYBP794E/eMfACS+/DLZ5xiAICJSmVV0q84DBw4wdOhQoqKi8PDwoGHDhjz33HPkn6c9lmEYPP/884SHh+Ph4UHv3r3Ztq18T/KsIrqIiJS/mM9g10Kw2uHG2eDianYiOQ/DMBg7dizdu3enVatWZ10uMTGRkJCQEvNCQkIoLCwk5Qwn2Jo8eTJ+fn7Fl7p165Z59tI61dJl1Z5k0zKIU3JGHhO+3grAiF4NaV/v7F/cmK1pqA93dIoE4OUftuNwGCYnEhGRyiDwoQfxufpqKCjgyOgx5B+JMzuSiMgFMaNV586dO3E4HLzzzjts27aNN954g9mzZzNhwoRzrvfaa6/x+uuvM3PmTNatW0doaChXXXUVGRkZ5ZZVRXQRESlfJw7Doqec030mQOjZC7JSeYwaNYo///yTzz///LzLWiwlW24YhnHG+QDjx48nLS2t+HL48OGyCXwRejZxnrByxe6U4sxS8QzDYPxXf3I8K5/mYb48emUTsyOd12NXNsHbzYU/j6Tx7WYVSURExLnfEz7pFdxaNKfo+HGOPDyCosxMs2OJiACQnJxMaGgok/5y7oa1a9fi6urK4sWLAXNadV599dXMnTuXfv360aBBA66//noef/xxvvrqq7OuYxgG06ZNY+LEidx00020atWKDz/8kOzsbD777LNyy6oiuoiIlB+HA74bBXnpENERuv3D7ERSCqNHj+a7775j6dKlREREnHPZ0NBQEhMTS8xLSkrCxcWFwMDA05Z3c3PD19e3xMUsnaJq4W63kpiey+6j+pBrlv9sOMLPO5JwtVl54/a2uLpU/t3TIB83RvZxnvT0tUW7yCssMjmRiIhUBlZPT+rOmoVLUBB5e/YSN3YsRmGh2bFEpJwZhoEjO9uUS2kHAwUFBfHBBx/w/PPPs379ejIzM7n77rsZOXJkcXvOC23VeYq3t/c5LwMGDLig5zMtLe2cLUVjY2NJTEwskdXNzY1evXqxevXqC9rWhXApt3sWERFZPwf2LwMXDxg0G6w2sxPJORiGwejRo/n6669ZtmwZUVFR512nS5cuLFiwoMS8xYsX06FDB+z2ytnT+hR3u43LowJZvjuZ5buTaBrqY3akGudoei4vLdgOwD/7NaFZqHlfqlyoB7pF8dHqgySk5fL1xrjiFi8iIlKz2UNDiZg1i4P33EPWipUcfXUKoU9PNDuWiJQjIyeHXZe1N2XbTTduwOLpWaplBw4cyPDhwxk8eDAdO3bE3d2dV199tfj287XqDAsLO+P9xsTEnHO7Hh4epcoHsG/fPmbMmMG///3vsy5zahDXmbIePHiw1Nu6UJV/qI+IiFRNx/bBkmed01e9ALUbmZtHzuuRRx7hk08+4bPPPsPHx4fExEQSExPJyckpXmb8+PHce++9xddHjBjBwYMHGTt2LDt27OCDDz5gzpw5PP7442Y8hAvW6y8tXaTivbBgGxl5hbSr68+wHg3MjnNB3O02hvVwftH07or9FKk3uoiInOTRuhXhr00BIPWTTzj+6acmJxIRcZo6dSqFhYV8+eWXfPrpp7i7u5e4/UJadZ7SqFGjc17q1KlTqmzx8fFcffXV3HrrrQwbNuy8y58p67lyXiqNRBcRkbLnKIJvHoaCbIjqCR2Hm51ISuHtt98GoHfv3iXmz507lyFDhgCQkJDAoUOHim+Liopi4cKFPPbYY7z11luEh4czffp0br755oqKfUl6NQ2C7+GP2ONk5xfi6apdo4ryy46jLNySiM1qYfJNrbFZy2+Ht7zc0SmS6b/sYX9KFou3JTKg9ZlH54iISM3j268f+WPHkvz66xydNBnXyHp49+hudiwRKQcWDw+abtxg2rYvxP79+4mPj8fhcHDw4EHatGlTfNuFtuo8xdvb+5zb7NGjBz/++OM5l4mPj6dPnz506dKFd99995zLhoaGAs4R6X8dHZ+UlHTa6PSypE+KIiJS9lbPgMNrwdUHbngLrDrwqSooTT+9efPmnTavV69ebNy4sRwSlb8Gtb2o4+9B3Ikcft9/jCuald9Ol/xPVl4hz367DYBhPaJoHlZ12rj8lbebC/d1rc+MX/cye/k+rm4VWq6jX0REpGoJHD6M/P37SfvmG+Iee4z6//c5bo10dKZIdWOxWErdUsVM+fn5DB48mNtvv51mzZoxdOhQtmzZUlx4vthWnZfaziUuLo4+ffrQvn175s6di/U89YOoqChCQ0NZsmQJ0dHRxY9t+fLlTJky5ZzrXgpVNUREpGwd3Q5LX3FOXz0Z/NUnWCovi8XiHI2OWrpUpDeW7CbuRA4RAR482reJ2XEuyX1d6+PmYmXzkTTW7D9mdhwREalELBYLoS++gEeH9jgyMzk84mEKjx83O5aI1FATJ04kLS2N6dOnM27cOJo3b87QoUOLb7/YVp2X0s4lPj6e3r17U7duXaZOnUpycnJxW9G/atasGV9//TXg/N/66KOPMmnSJL7++mu2bt3KkCFD8PT05K677rqEZ+jcVEQXEZGyU1QAXz8ERfnQuD9E3212IpHzOtUXffnuZJOT1Axb49L44LdYAF4a1AoP16p9wuHa3m7c1qEuAG8v22dyGhERqWysrq5EzJiBPTKSgiNHOPLIKBx5eWbHEpEaZtmyZUybNo2PP/4YX19frFYrH3/8MatWrSpu63mqVeeyZcto164dL730Urm36ly8eDF79+7l119/JSIigrCwsOLLX+3atYu0tLTi6+PGjePRRx9l5MiRdOjQgbi4OBYvXoyPj0+5ZbUYpTl22yTp6en4+fmRlpaGr2/VPMxXRKRGWToJlk8BjwAY+Tv4hJqdqFzpferSVYbnMCO3gOgXl1DoMFjxRB8iAyv/oZhVlcNhcOOs39h8JI1r24Qx867LzI5UJg4dy6b31KU4DPh+dHda1fEzO5KIlJHK8D5VHeh5hLz9+zlw+x04MjLwvf46wqdMUQswkSooNzeX2NhYoqKiTjspp1Re5/q9lfY9SiPRRUSkbMRthBVTndPX/LvaF9Cl+vBxt3NZvQAAlu/RaPTy9J8Nh9l8JA1vNxeeva6F2XHKTGSgJ9e2CQfgnRX7TU4jIiKVkVuDBkS8OQ1sNtK/W0DKzLfMjiQiIhdARXQREbl0Bbnw9QgwiqDljdCq/A73EikPxS1ddqmIXl7Scgp4bdEuAB69sjHBPtVr5M5DvRoAsHBLAkfTc01OIyIilZFX166EPvcsAClvvcWJ+fNNTiQiIqWlIrqIiFy6X1+ClF3gFQzXvG52GpELdqqIvmZfCvmFDpPTVE9v/ryHY1n5NAzy4t4u9c2OU+ZahvvRoV4ARQ6D/6w/bHYcERGppAJuu43Ahx4CIOHZ58hcucrkRCIiUhoqoouIyKU5uBrWnDwc9frp4FnL3DwiF6FFmC+1vV3Jyi9i/cHjZsepdvYczeDDNQcAeP76lri6VM9d0Ds7RQLw+R+HcTgq7WmHRETEZEGP/gPf66+DoiLi/vEPcnfsMDuSiIicR/X8BCMiIhUjLxO+eRgwoN3d0HSA2YlELorVaqHnydHov+5IMjlN9WIYBs8v2EaRw6BfixB6NA4yO1K5uaZNGL7uLsSdyGHl3hSz44iISCVlsVgIf/llPC+/HEd2NocffIiC+HizY4mIyDmoiC4iIhdvyTOQegD86sLVk81OI3JJrmoeAsCSHUcxDI0iLis/bUvkt73HcHWx8vQ11edkomfibrdx02URAHy+9pDJaUREpDKzuLoSMWM6bo0bUZiczOGHHqIoPd3sWCJSSvq8ULWUxe9LRXQREbk4e3+G9R84p2+YCe6+5uYRuUQ9mwTh6mLl4LFs9iRlmh2nWsgtKOKVhc5D1Ef0bEBkoKfJicrfqZYuP+84SpJOMCoiIudg8/Wl7rvv4hIcTN6evRwZNRpHfr7ZsUTkHOx2OwDZ2dkmJ5ELcer3der3dzFcyiqMiIjUIDkn4NvRzulOD0KD3mamESkTXm4udGsYyNJdySzZfpQmIT5mR6ryPlx9gMPHcwjxdWNE74Zmx6kQTUN9aF8vgA0HU/nPhiM80qeR2ZFERKQSs4eFUffddzg4+G6y//iDhAkTCf/Xa1gsFrOjicgZ2Gw2/P39SUpytoD09PTU32slZhgG2dnZJCUl4e/vj81mu+j7UhFdREQu3I9PQkY81GoIV75gdhqRMnNVi1CW7kpm8fajKn5eopTMPGb+uheAJ/o3w9O15ux23tkpkg0HU/m/dYd4uFdDrFZ9sBKRymHFihX861//YsOGDSQkJPD1118zaNCgsy6/bNky+vTpc9r8HTt20KxZs3JMWrO4N2tGnelvcvihEaR//z32sFCC//lPs2OJyFmEhoYCFBfSpfLz9/cv/r1drJrzaUZERMrGjgXw5/+BxQo3zgbX6t+eQWqOK5sHM+Fr2Hz4BEfTcwnxdTc7UpU17efdZOQV0qqOLzdF1zE7ToW6pnUYLyzYxuHjOfy2L6Van0xVRKqWrKws2rZty/3338/NN99c6vV27dqFr+//WvcFBen/Wlnz7taNsBdfJGHCBI699z62WoEE3j/E7FgicgYWi4WwsDCCg4MpKCgwO46ch91uv6QR6KeoiC4iIqWXlQILHnVOd/sH1O1kahyRshbs6067uv7EHD7BzzuOMvjyemZHqpJ2H83gs5Mn1nz6mhY1biS2h6uNmy+LYN7qA3y29pCK6CJSaQwYMIABAwZc8HrBwcH4+/uXfSApwf+mGyk8lkLyv18nacoUbAH++J/jSAERMZfNZiuT4qxUDTqxqIiIlI5hwPePQnYKBLeA3uPNTiRSLq5qEQLAku1HTU5SdU1auAOHAf1bhtC5QaDZcUxxe8e6APyyI4m0HI1QEpGqLTo6mrCwMPr27cvSpUvPu3xeXh7p6eklLlI6gcOGUWvIEAASJj5Nxq/nf75FRKT8qYguIiKls+U/zlYuVhe48R1wcTM7kUi56HeyiL567zEy8wpNTlP1LN+dzLJdydhtFp4a0NzsOKZpHuZL0xAf8osc/LQ10ew4IiIXJSwsjHfffZf58+fz1Vdf0bRpU/r27cuKFSvOud7kyZPx8/MrvtStW7eCEld9FouF4HFP4HfDDVBURNxjj5G9YYPZsUREajwV0UVE5PzS42Hh487pXk9BWBtz84iUo0bB3tQP9CS/yMGK3clmx6lSihwGk37YAcA9nesTVdvL5ETmur5dOADfbo4zOYmIyMVp2rQpw4cP57LLLqNLly7MmjWLa665hqlTp55zvfHjx5OWllZ8OXz4cAUlrh4sVithL7+Ed+/eGHl5HB7xMLm7dpkdS0SkRlMRXUREzs0w4LvRkJsG4ZdB98fMTiRSriwWi1q6XKT/bjjMrqMZ+HnYGdO3kdlxTHd9W2cRfc2+YySl55qcRkSkbHTu3Jk9e/accxk3Nzd8fX1LXOTCWOx26rzxOh7t2+PIyODQsGHk68sIERHTqIguIiLntvFD2Psz2Nzgxtlg0zmppfq7qkUoAL/uTKKgyGFymqohO7+Qfy/eDcDoKxrh7+lqciLz1a3lSXSkPw4Dvv8zwew4IiJlYtOmTYSFhZkdo0awenhQ9+1ZuDVpQlFyCoeGDqMwWUfJiYiYQUV0ERE5u9QD8NNE53TfZyGoqalxRCpK+3oB1PJyJS2ngD9ij5sdp0p4b0UsSRl51K3lwT1d6pkdp9I4NRr9u83xJicREYHMzExiYmKIiYkBIDY2lpiYGA4dOgQ427Dce++9xctPmzaNb775hj179rBt2zbGjx/P/PnzGTVqlBnxaySbry91338Pe0QEBYcOOQvpqalmxxIRqXFURBcRkTNzOOCbkZCfCZFdofNIsxOJVBib1VJ8glGNID6/pIxc3lmxD4Bx/Zvh5mIzOVHlcU2bMKwWiDl8gkPHss2OIyI13Pr164mOjiY6OhqAsWPHEh0dzbPPPgtAQkJCcUEdID8/n8cff5w2bdrQo0cPVq1axQ8//MBNN91kSv6ayh4cTOSc93EJCiJv924ODxtOUUaG2bFERGoUFdFFROTM1s6Gg7+B3QsGzQKr3jKkZrnu5AjiH7cmkF+oli7nMu3nPWTnF9Gurj/XttEh/n8V7ONO14a1AfhOJxgVEZP17t0bwzBOu8ybNw+AefPmsWzZsuLlx40bx969e8nJyeH48eOsXLmSgQMHmhO+hnOtV4/IuR9gCwggd9s2Dj/4EI6sLLNjiYjUGKqIiIjI6ZJ3wy8vOKf7vwy1oszNI2KCzg0Cqe3txonsAn7bm2J2nEprz9EM/u8P56jFidc0x2KxmJyo8jnV0uXbmHgMwzA5jYiIVFVujRoR+cEcrL6+5GzaxOGHR+LIyTE7lohIjaAiuoiIlFRUCN+MgMJcaNgX2t9vdiIRU9isluJR1epnfXav/rgThwH9W4bQsX4ts+NUSv1bheJqs7InKZOdiTr8XkRELp578+ZEvv8eVi8vsv/4gyOjx+DIzzc7lohItaciuoiIlPTbGxC3Adz94IaZoFGlUoNd19ZZRF+8LZHcgiKT01Q+q/el8MvOJFysFp68upnZcSotPw87vZsGAfpCRkRELp1HmzbUffcdLB4eZK1aRdxjYzEKCsyOJSJSramILiIi/5PwJyyb4pweOBV8w83NI2Ky6LoB1PH3ICu/iKU7k8yOU6k4HAaTFu4AYPDlkTQI8jY5UeV2fTvn/9Mf/kxQSxcREblknu3bU3fWW1hcXcn85Rfixo3DKCw0O5aISLWlIrqIiDgV5sHXI8BRAM2uhda3mp1IxHRWq4Vr26qly5l8uzmOrXHp+Li5MKZvY7PjVHq9mwbj6mLl0PFsdh/NNDuOiIhUA15duhAxYzrY7WT8uIh4FdJFRMqNiugiIuK07FVI2gaeteHaaWrjInLSdW2cI4h/3ZlERq4OlQbILSjiX4t2AfBwn4YEeruZnKjy83ZzoXuj2gAs2Z5ochoREakuvHv1ImLaG2C3k77wR+L++bhau4iIlAMV0UVEBA7/Ab9Nc05fNw28g8xMI1KptAz3pUFtL/IKHfy846jZcSqFub8dID4tl3A/dx7oFmV2nCqjX4sQABZv1+tIRETKjk/fvkS8+SYWu52Mn34ibuxYDJ1sVESkTKmILiJS0+VnwzcPg+GANndA8+vMTiRSqVgsFq5r6xyN/l2MWrocy8xj1tK9ADzevynudpvJiaqOvs1DsFjgzyNpxJ/IMTuOiIhUIz5X9CFi5gwsrq5kLPmZI/94FIcK6SIiZUZFdBGRmu6XF+DYXvAJhwGvmp1GpFK67mRf9JV7UjieVbM/kL75yx4y8gppGe7LoHZ1zI5TpQT5uNE+MgBARzWIiEiZ8+7Vi4i3Tp5sdOlSjowejSMvz+xYIiLVgoroIiI12f7lsHa2c/qGGeARYG4ekUqqUbAPLcN9KXQYfLMpzuw4ptlzNINP1x4CYOI1zbFade6EC3XVyZYuS9TSRUREyoF3j+7Unf02Fjc3spav4Mgjo3Dk5podS0SkylMRXUSkpspNh28fcU63vx8aXWluHpFK7vaOdQH4Yt1hDMMwOY05Ji3cQZHD4KoWIXRtWNvsOFVSv5ahAKzZd4y0HJ34TUREyp5X167UfWc2Fg8Pslat4vDwBynKzDQ7lohIlaYiuohITfXTeEg7DP71oN/LZqcRqfRuaFcHNxcru45msOnwCbPjVLgVu5NZuisZF6uFCQObmx2nyoqq7UXjYG8KHQbLdiWZHUdERKopr86diXz3HaxeXmSvW8ehIfdTmJpqdiwRkSpLRXQRkZpo1yLY9AlggUFvg5u32YlEKj0/DzvXtHb2Rv+/Pw6ZnKZiFRY5ePmH7QDc26U+UbW9TE5UtfVr6WzpsnibWrqIiEj58ezYkcgPP8Tm70/u1q0cvPseChITzY4lIlIlqYguIlLTZB+HBWOc010egfrdzM0jUoXc0SkSgAWbE8jIrTmtOL5Yf5jdRzPx97Tzj76NzY5T5fVr4WzpsmxXEnmFRSanERGR6syjVUvqffoJLqGh5O/bx8G7BpN/8KDZsUREqhwV0UVEapof/gmZR6F2E7jiabPTiFQpHesH0DDIi5yCIhZsTjA7ToVIzy3g9cW7AXi0b2P8PO0mJ6r6WtfxI9TXnaz8IlbvO2Z2HBERqebcGjak/qefYK8XSUF8PAcG303url1mxxIRqVJURBcRqUm2zodtX4HFBje+A3YPsxOJVCkWi4U7OjpHo//fuprR0mXGL3s4lpVPgyAvBneuZ3acasFqtXBli2BALV1ERKRi2OvUof6nn+LWrBlFKSkcvOdestetMzuWiEiVoSK6iEhNkXHUOQodoOfjUOcyc/OIVFE3XVYHu83Cn0fS2BafZnaccrU3KYO5vx0A4JlrW2C3adexrPRt7uyLvnxXEoZhmJxGRERqApfatan30Yd4REfjSE/n0ANDSV+0yOxYIiJVgj4JiYjUBIbh7IOekwqhbaDH42YnEqmyAr3dintaf7HusMlpyo9hGDz/3XYKHQZXNg+mT9NgsyNVK10aBOLmYiU+LZe9SZlmxxERkRrC5utL5Adz8L6yL0ZBAXGPPsaxufP0ha6IyHmoiC4iUhPEfAq7F4HN1dnGxcXV7EQiVdodneoC8PWmOLLzC01OUz5+2pbIqr0puLpYeebaFmbHqXbc7TYubxAIwLJdySanERGRmsTq4UHEm28SMHgwAElTpnB08mSMIp3sWkTkbFREFxGp7k4chkXjndN9JkKIimEil6pbw9rUC/QkI7eQ/244YnacMpeTX8RL3+8A4KGeDagX6GVyouqpd5MgAJbvVhFdREQqlsVmI+TpiQQ/8QQAqR99TNxjY3Hk5pqcTESkclIRXUSkOnM44NuRkJcOdS+HrqPNTiRSLVitFoZ2jwLgvZX7KSxymJyobM1evo+4EzmE+7kzsncjs+NUW72aOovof8Qer7ZHNIiISOVlsVgIHPoA4f+eisVuJ2PxYg7d/wCFx46ZHU1EpNJREV1EpDpb9z7ErgC7Jwx6G6w2sxOJVBu3tq9LgKedw8dzWLQt0ew4ZebQsWzeXr4PgInXtMDDVf83ykuD2l5EBHiQX+RgzT4VLERExBx+11xD3TnvY/X1JWfTJg7cehu5u3aZHUtEpFJREV1EpLpK2QtLnnVOX/UiBDY0N49INePhauPeLvUBeGf5/mpxQi7DMJj4zRbyCx10bRjIwNahZkeq1iwWC72bqqWLiIiYz6tTJ+r/3//hWq8eBfHxHLjzLjJ++cXsWCIilYaK6CIi1ZGjCL4ZAYU50KA3dBhqdiKRauneLvVwt1vZEpfGmv1VfyTxd5vjWbnHeTLRlwe1wmKxmB2p2uvVJBhQEV1ERMzn1iCK+l/8H55dOmNkZ3Nk1GhS3nm3WgwUEBG5VCqii4hUR7+9CUfWgZsvXD8TrPp3L1IeAr3duLV9XQDeXbHf5DSXJjUrnxcXbAdgdJ9GNAjyNjlRzdClYSB2m4WDx7KJTckyO46IiNRwNn9/It99l4C77gLDIPmNN4h/8kkceXlmRxMRMZWqKiIi1c3RbbB0knP66lfBv665eUSquWE9orBaYNmuZHYmppsd56JNWriDY1n5NA725qFeav9UUbzdXOhQrxYAy3clmZxGREQELHY7oc8+Q+hzz4LNRvp3Czh49z0UxMebHU1ExDQqoouIVCeF+fDVQ+AogCYDoN1dZicSqfbqBXoxoFUYUHVHo6/el8J/NhwB4NWbW+Pqol3EiqS+6CIiUhkF3HknkXPex+bnR+6WLcTedDNZq1ebHUtExBT6hCQiUp2seA2ObgGPWnDdm6B+xiIV4sGeDQD4Liae/cmZJqe5MLkFRUz8eisAd3eOpP3JUdFScXqdLKKv2X+M3IIik9OIiIj8j1fnztSfPx/3Fi0oOnGCQ8OGkzL7HQyHw+xoIiIVSkV0EZHq4sgGWPm6c/ra18EnxNw8IjVI27r+XNEsmEKHwWuLdpkd54JMWbST2JQsgn3cGHd1M7Pj1EhNQ3wI9XUnt8DBH7HHzY4jIiJSgmtEHep9/hl+t9wMDgfJ06ZxZNRoitKrbhs7EZELpSK6iEh1UJAD34wAowha3QwtbzQ7kUiNM35AM6wWWLQtkfUHqkYhdNWeFOb+dgCAKbe0wdfdbm6gGspisdCriVq6iIhI5WV1cyP85ZcJfelFLK6uZP76K7G33Erujh1mRxMRqRAqoouIVAe/vAQpu8E7BAZONTuNSI3UOMSH2zs6T+T7ysIdGIZhcqJzS8su4PH/bAacbVz6NA02OVHN1r1xbQBW7ztmchIREZGzC7j1Vup99hn28HAKDh3iwG23c/zjTyr9fo+IyKUq1yL6ihUruO666wgPD8disfDNN9+U5+ZERGqmA6vg91nO6etngKf6GYuY5bErm+DpamPToRMs3JJodpxzeubbrSSm5xJV24sJA5ubHafG69IwEIAdCekcy8wzOY2IiMjZebRqSf35/8W7Tx+MggKOvvIKR0Y+QmFqqtnRRETKTbkW0bOysmjbti0zZ84sz82IiNRceRnwzUjAgMvuhSb9zU4kUqMF+7ozvIfzJKOv/bST/MLKedKtb2Pi+G5zPDarhTdub4enq4vZkWq82t5uNAv1AeD3/VWjHZCIiNRcLgEBRMx6i5CJE7HY7WQuXUrsDYPIWvuH2dFERMpFuRbRBwwYwMsvv8xNN91UnpsREam5Fj8NJw6CXyT0e8XsNCICPNizAbW93Th4LJtPfj9odpzTHDyWxTPfbAVg9BWNaFfX39xAUuzUaPTf9qWYnEREROT8LBYLte65m/r/+RLXqCgKk5I4NGQISW++iVFYaHY8EZEypZ7oIiJV1Z6fYcM85/Sgt8Dd19Q4IuLk5ebCY1c1BmDaz7tJTMs1OdH/ZOcX8tDHG0jPLSQ60p9H+jQyO5L8RbeGzr7oa9QXXUREqhD3Zs2Imv9f/G65GQyDY2/P5sCdd5G3b5/Z0UREykylOnY3Ly+PvLz/9YBMT083MY1I6RxJzWbR1kQWbztKfFoOeYUO8k9eImt50q1Rbbo3DqRTVCDebpXqT06qspxU+G6Uc/ryERDV09w8IlLC7R3q8uW6w2w+ksYT/93MRw90wmKxmJrJMAyenL+FnYkZ1PZ24+3B7bHbNJ6iMunUoBZWC8SmZBF/Iodwfw+zI4mIiJSK1dOT8JdfxrtrVxKef4HcLVuIvfEmgh59lFr33YvFZjM7oojIJalUn5wmT56Mn59f8aVu3bpmRxI5o8IiBx+vOcD1M1fRfcpSXv5hB38cOM6R1BySM/JIyykgp6CIXUcz+OC3WB6Yt552LyxmzOebOHw82+z4Uh0sHAcZCRDYCPo+Z3YaEfkbF5uV129vh5uLlZV7Uvi4ErR1mbMqlgWb43GxWnj77ssI9XM3O5L8ja+7nTYR/gCs1mh0ERGpgnwHDqTBgu/w6tkDIz+fpNde4+B995F/6JDZ0URELkmlKqKPHz+etLS04svhw4fNjiRymk2HUrlu5m888+02/jyShtUCl0fV4oXrW/LVyK4sHNODn8f2YtnjvXnrrsu4s1MkkbU8KXQYfLc5nr6vL+fVH3eSnltg9kORqmr7t7DlS7BYYdBscPU0O5FUEytWrOC6664jPDwci8XCN998c87lly1bhsViOe2yc+fOiglcyTUM8mb8gGYATFq4g/3JmaZlWb03hUkLdwDwzLUt6Fi/lmlZ5Ny6nuyLvnqv+qKLiEjVZA8Joe477xD60otYPT3JWb+B/YNuJPXzzzEclfOk6yIi51Opeku4ubnh5uZmdgyRM0rLLuC1n3by2R+HMAzw97Qz5orGXN8unNreZ37d1q/txTVtwgDYGpfGpIU7WL3vGLOX7+PL9Yd58YaWXNsmvCIfhlR1mcnw/WPO6W6PQt2OpsaR6iUrK4u2bdty//33c/PNN5d6vV27duHr+7+e/EFBQeURr0q6t0t9ft6RxKq9KTz25Wbmj+iCSwW3UNmVmMHIzzbiMODmyyK4t0u9Ct2+XJhujWoza9k+Vu87hmEYprcBEhERuRgWi4WAW2/Fq0tXEiZMIPuPP0h84UXSfviBsBdewK1hQ7MjiohckHL9FJeZmUlMTAwxMTEAxMbGEhMTwyEdxiNVzL7kTAZOX8mna50F9Jsvi+CXsb14oHvUWQvof9eqjh+fDruc9+/tQIMgL45n5TPqs028+fMeDMMo50cg1YJhwPePQvYxCGkFvZ8yO1GV8+eREwz7cD3Z+YVmR6mUBgwYwMsvv8xNN910QesFBwcTGhpafLGp52Uxq9XCv25tg4+7C5sPn2DGr3srdPv7kzMZ/P5aTmQX0K6uP6/c2EpF2Uqufb0AXG1WEtNz2Z+SZXYcERGRS+IaUYfIeXMJmTABy19GpSfPmIkjP9/seCIipVauRfT169cTHR1NdHQ0AGPHjiU6Oppnn322PDcrUqY2HUrllrdXE3cih3qBnnw+vDP/vq0tgaUsnv+VxWLhyhYh/PRoT4Z1jwLgjZ9389gXMeQWFJV1dKlu/vwCdn4PVjvcOBtcdOTOhVh/4DiD31vLzzuO8u/Fu82OU61ER0cTFhZG3759Wbp06TmXzcvLIz09vcSlugvz8+ClG1oB8OYve/jP+oppV3f4eDaD319LSmYezcN8+fD+Trjb9QVHZedut3FZPX9ALV1ERKR6sFit1Lr3Hhou+A7vXr2goICUt94i9oZBZK9bZ3Y8EZFSKdcieu/evTEM47TLvHnzynOzImVm6a4k7npvLanZBbSN8OOrh7vS5WSv0ktht1l5+toWTLqxNTarhW9i4hn8/lqOZeaVQWqpltLinCcTBej9JIS2NjdPFbN6bwr3zPmDjLxCOkXV4rGrmpgdqVoICwvj3XffZf78+Xz11Vc0bdqUvn37smLFirOuU1NPIj4oug4P9mwAwFNfbWHxtsRy3d7R9FzunrOWhLRcGgZ58fHQTvh52st1m1J2ujWsDejkoiIiUr3Y69QhYvbb1HnjdWy1a5MfG8vBe+4l/umnKTx+3Ox4IiLnVKlOLCpSmXwbE8fwD9eTU1BEzyZBfDa880WNPj+Xuy6P5MP7O+Hj7sKGg6kMmbuOrDy1mZC/MQz4bhTkpUGd9tDtMbMTVSlLdyVx/7x15BQU0aNxbT68vxPebpXqlCBVVtOmTRk+fDiXXXYZXbp0YdasWVxzzTVMnTr1rOvU5JOIjx/QjFvaR1DkMBj1+SZ+318+BdI9RzO4/Z01HDyWTd1aHnw6rHOpW49J5dC1kfML+zX7j+FwqOWbiIhUHxaLBd8BA2j4w/f433YbAGn/nc++/ldz/KOPMQr1eVhEKicV0UXO4Le9Kfzzy80UOgxujK7DnPs64FVORbfujWvz1cNdqeXlypa4NEZ+upGCIp2xXP5i/Qew71dwcYdBs8GmAnBp/brzKA9+tJ68QgdXNg/h/fs64OGqdhblqXPnzuzZs+est7u5ueHr61viUlNYLBZevak1VzYPIb/QwfAP1/PnkRNluo3F2xK5cdZqDhzLpo6/B58N60yon3uZbkPKX5sIf7xcbZzILmB7QvVveSQiIjWPzc+PsBdfoN5nn+LWvDmOjAyOTppE7I03kvX772bHExE5jYroIn+zNymThz/ZQKHD4IZ24fz71rbYbeX7p9I4xIc593XA3W5l+e5kJny1RScbFafj+2HxM87pvs9BkNqQlNbuoxmM/mwTBUUG17QO4+27L8PNRQX08rZp0ybCwsLMjlFpudiszLwrmk5RtcjIK+TW2Wv45PeDl/w/3+EwePPnPTz48QYy8wq5PKoW343qRt1anmWUXCqS3WalU1QtANaopYuIiFRjnpddRtR//0Po889j8/cnb89eDg25nyNj/kH+kTiz44mIFFMRXeQvjmflM/TDdaTnFtK+XgBTbm6D1WqpkG1HRwbw1l2XYbXAfzYc4Y2fzz6SU2oIRxF8MxIKsqBed7h8hNmJqoy07AIe/Gg9WflFdG5Qi2l3tCv3L8Oqg8zMTGJiYoiJiQEgNjaWmJgYDh06BDhbsdx7773Fy0+bNo1vvvmGPXv2sG3bNsaPH8/8+fMZNWqUGfGrDHe7jffv60DvpkHkFTp4+putjPx0I2nZBRd1f9vi07jng7W88bPzhLn3danHJ8MuL/MWZFKxTp2DZW2sesSKiEj1ZrHZCLjjdhou+pGAwYPBaiVj8WL2DxjA0SmvUXTihNkRRURURBc5Ja+wiBEfb+DgsWwiAjx45572uNsrdtRq3+YhvDzIecLI6b/s4auNRyp0+1LJ/D4LDq0BV28Y9BZY9S+7NJz9pjcWt7N4667LVEAvpfXr1xMdHU10dDQAY8eOJTo6mmeffRaAhISE4oI6QH5+Po8//jht2rShR48erFq1ih9++IGbbrrJlPxVia+7nQ/u68jT1zTHbrPw49ZEBk5fybcxceQWFJXqPg4fz+axL2K4dsYqftt7DFeblSk3t+aFG1rpNV8NdKzvHIm+7sBx9UUXEZEawebvT+gzTxP19Vd4du6MUVDA8blz2duvP8fefx9Hbq7ZEUWkBrMYlbhnRHp6On5+fqSlpdWonqlijglfb+GztYfwcXNh/siuNAnxMS3L1J92MXPpXrxcbfwwpgf1a3uZlkVMkrQT3ukJRXlw3ZvQfojZiaqMyQt38M6K/bjbrcx/uCstw/3KbVt6n7p0eg7hzyMnGP35Jg4eywbAz8POjdF1uKV9BA2CvPCw27BYLDgcBruTMliz7xi/7z/G0p3J5J88h8Z1bcN5ol9TIgPVvqW6KChy0Ob5xeQUFLHo0R40C62Zfx8iZtP7VNnQ8ygXyjAMslauJGnqv8nb7TzaziUsjKDRo/G74XosNrVpFJGyUdr3KJ2dTgRYsv0on609hMUCM+6KNrWADvDYVU3448Bx/og9zj++iOG/I7poVGFNUlQAXz/kLKA3ugouu8/sRFXGwi0JvLNiPwD/uqVtuRbQRcpKmwh/vh/dnfdXxvKf9YeJT8tl3uoDzFt9AACb1YKPuwsOh0F6bmGJdbs2DOSpAc1oE+Ff8cGlXNltVtrXC2DV3hTWxR5XEV1ERGoUi8WCd8+eeHXrRtp3C0h+800KExJImDCBYx/MIWjkSHz691cxXUQqjKpyUuMdy8xj/Fd/AjC8RwN6Nw02OZGzYDLt9nb4uruw+fAJpp3scys1xMrXISEG3P3h+hlgqZi+/FVdckYeE7/eAsBDPRtwXdtwkxOJlJ6Pu53HrmrCyievYN79HRnYOhRXF+duWpHD4ER2Aem5hXjYbfRoXJtxVzfl20e68emwy1VAr8ZOnVxUfdFFRKSmsths+N84iIaLfiT48X9i9fUlf+8+4sb+k/033ED6woUYDofZMUWkBtBIdKnRDMNg/FdbSMnMp2mID2OvamJ2pGLh/h68enMbRn66kVnL9tGjcRCdGwSaHUvKW3wMrHjNOT1wKviGmRqnqjAMg2e+2UpqdgHNw3z5Z7+mZkcSuSg2q4XeTYPp3TQYwzDIzi8iI7eQjNwCCooMGgV7FxfXpfo71Rf9j9jjGIaBRV+qiohIDWV1dydw2DD8b7+d4x9/zPF5HxYX011nzSLokUecI9N1HikRKSf67yI12n83HGHx9qPYbRbeuL1dhZ9I9HwGtg7j9g51MQx47IsYTmTnmx1JylNBLnw9AhyF0Px6aH2L2YmqjAV/JrBoWyIuVgtTb22jIqNUCxaLBS83F0L93Gkc4kOLcF+9tmuY6Eh/7DYLSRl5xT3zRUREajKbjw9BI0fS6Ocl1B49CquPj7OY/thY9l97HSfmz8eRr8/NIlL29ElMaqzDx7N5YcF2wNmDvEV45ew1+ux1LYiq7UVCWi6v/rjT7DhSnpZNguQd4BUE176hNi6llJyRx3PfbgVg1BWN1AddRKoNd7uNtifb9fxxQC1dRERETrH5+hL0yCM0+uVnao86WUzfv5+EiU+zr++VHHv/fYoyMsyOKSLViIroUiMZhsHEb7aSmVdIh3oBPNSzodmRzsrLzYV/3dIGgP9bd5iNh1JNTiTl4tBa+G26c/raaeBV29Q4VYVhGDz9zRZSswtoEebLI30amR1JRKRMneqL/of6oouIiJzG5utL0KhHaLT0V4KfeAKX4GAKk5NJmvpv9vbuw9F//YuCo0fNjiki1YCK6FIjLdl+lBW7k3G1WfnXrW2xWSv3iN8O9WtxS/sIAJ75ZiuFRTpxSrWSnwVfPwQY0PZOaH6t2YmqjB+3JvLTtqMn27i0xW7T25qIVC8dVUQXERE5L5u3N4FDH6DRz0sImzQJ10YNcWRlcXzOB+zteyVxY8eSvWEDhmGYHVVEqihVG6TGyS0o4qUfnG1chvWIIqq2l8mJSuepAc3wdXdhW3w6n/x+0Ow4UpaWPAepseBbB65+1ew0VUZuQRGv/LADgJG9G1balkwiIpeifb0ArBY4dDybhLQcs+OIiIhUahZXV/xvupEG331HxNuz8OzQAQoLSV/4IwcH303sTTdz4r//xZGj91QRuTAqokuN8+6K/Rw+nkOor3uVav1Q29uNcVc3A+Dfi3eTlJFrciIpE/uWwrr3nNM3zAQPf1PjVCXvr9xP3Ikcwv3cebh31flbFhG5EL7u9uIvCTUaXUREpHQsVis+ffpQ75OPifr6K/xvvQWLuzt5O3aQ8PQz7Ondh6NTXiNv/36zo4pIFaEiutQoR1KzmbVsLwATrmmOl5uLyYkuzJ2dImkT4UdGXiGTTo7AlSosNw2+HeWc7jgMGl5hbp4q5Gh6LrOW7QPgyQHN8HC1mZxIRKT8dKofCMA6nVxURETkgrk3b07YSy/ReNlSgp94AntEBI60NI7Pncv+gddw4K7BnJj/FY6sLLOjikglpiK61CiTF+4kt8DB5VG1uK5NmNlxLpjNauHlQa2wWOCbmHiNSKvqFo2H9CMQEAVXvWh2miplyqKdZOcXcVmkP9e3DTc7johIueoUFQBoJLqIiMilsPn7Ezj0ARr+tIiIWbPw7t0brFZyNm4kYeJE9vToSfzTT5O9aZN6p4vIaVRElxpj9b4UftiSgNUCz1/fEoulcp9M9GzaRPhzR8dIwFlI1Jt7FbVzIcR8CljgxtngWjV681cGmw+f4KuNcQA8d13V/VsWESmtjvWdJxfdfTST41n5JqcRERGp2iw2Gz5X9KHu7LdptHQpQY89hr1eJI7sbNL+O5+Dd97F/gEDSZ75FnmxsWbHFZFKQkV0qREMw+DVH3cCcHfnejQPq9onIHz0ysa4261sOJjKLzuSzI4jFyrrGCz4h3O662iI7GxunirEMAxe/N55YuCbLqtD27r+5gYSEakAgd5uNAr2BtTSRUQuzYoVK7juuusIDw/HYrHwzTffnHed5cuX0759e9zd3WnQoAGzZ88u/6AiFcQeEkzthx6k4aJF1Pv4I/xuuAGLuzv5Bw6QMnMm+wcMJPaWWzk2dx4FR4+aHVdETKQiutQIi7cf5c8jaXi62hjTt7HZcS5ZiK87Q7pGAfCvn3ZR5NBo9CrDMOCHxyArCYKaQ5+JZieqUn7cmsiGg6l42G08efJEuyIiNUHH+s6WLhsPppqcRESqsqysLNq2bcvMmTNLtXxsbCwDBw6kR48ebNq0iQkTJjBmzBjmz59fzklFKpbFYsGzY0fCp7xK41UrCZ/yKl49eoDNRu7WrSRNmcLe3n04eN8QUv/v/yhI0mA2kZqmap1VUeQiOBwGry/eDcAD3aKo7e1mcqKy8XCvhny29iC7jmbw3eY4boyOMDuSlMbW+bD9W7C6wI1vg93d7ERVRpHD4I0lzr/l4T0bEOKr505Eao729Wrx+R+H2aAiuohcggEDBjBgwIBSLz979mwiIyOZNm0aAM2bN2f9+vVMnTqVm2++uZxSipjL5u2N3w034HfDDRQeO0b6okWk/7CQnI0byV67luy1a+GFF/Fo1w6fK6/E56orcY2MNDu2iJQzjUSXam/Bn/HsOpqBj7sLw3s0MDtOmfHztDOid0MA/r14N/mFDpMTyXmlJ8AP/3RO93wCwqPNzVPF/LAlgT1Jmfi6uzC0e5TZcUREKlT7es6R6H/GpZFXWGRyGhGpKdasWUO/fv1KzOvfvz/r16+noKDgrOvl5eWRnp5e4lIWCh2F3Pfjfbyx4Q3WJ66nwHH2DCJlwSUwkFqDB1P/s09p+PPPBP1zLO5t2oBhkLNpE0n/+hf7+vVn//U3kDx9Bjlbt2E49NlcpDrSSHSp1gqLHEz7eQ8AD/VsgJ+n3eREZev+rlHM++0AR1Jz+PyPQ9zXtb7ZkeRsDAMWjIHcExDWDnr80+xEVUqRw+DNn0+OQu/RAD+P6vW3LCJyPvUDPanl5crxrHy2xadzWWSA2ZFEpAZITEwkJCSkxLyQkBAKCwtJSUkhLCzsjOtNnjyZF154oczzbEnZwsakjWxM2sgHWz/Ax+5D1zpd6VGnB93qdKO2R+0y36bIKa4Rdag9fDi1hw+nIDGRjF9+IePnn8n+Yx15u3eTt3s3KbNmYQsMxLt7d7x69sC7Wzds/v5mRxeRMqAiulRr8zceITYli1pertzfrfqNXPU42eP96W+2MuPXPdzSPgIvN/1ZV0qbPoY9i8HmBje+AzYVgS/Egs3x7EvOwt/TzpBu9c2OIyJS4SwWC5dFBvDzjqNsPJiqIrqIVBiLxVLiumEYZ5z/V+PHj2fs2LHF19PT06lbt+4lZ2nk34gpPaawMm4lq+JWcSLvBD8d+ImfDvwEQMvAlnSv053Lwy6nbVBbXG2ul7xNkTOxh4ZSa/Bgag0eTNGJE2QsW0bmL7+Q9dtqio4dI+3bb0n79luwWvFo0wbvXj3x6t4d9xYtsNhsZscXkYugaptUW3mFRUz/ZS8AI3s3rLbF5ds71uW9lfs5eCybz/84xLBq1LKm2kg9CIsmOKeveBqCdULMC1FY5ODNX5xHlAzv0QAfd30BISI1U/t6ziL6hoOpDOthdhoRqQlCQ0NJTEwsMS8pKQkXFxcCAwPPup6bmxtubmV/LiofVx8GNhjIwAYDKXIUsfXYVlYeWcnKuJVsP7adbce2se3YNt758x3cbe5EB0fTKawTncM607xWc2xWFS+l7Nn8/fEfNAj/QYMw8vPJ3riJzBUryFq5grw9e8mJiSEnJobkN6dj9fHBs2NHvC7vhGfnzrg1bozFqk7LIlVB9awqigBfrj9C3IkcQnzduLtzPbPjlBu7zcrI3g15cv4W3lu5n3u61MPNRTuHlYbDAd8+AvkZENkFujxidqIq55uY+OIjStSySERqslN90dcfTMUwjHOOAhURKQtdunRhwYIFJeYtXryYDh06YLebO7DBZrXRNqgtbYPaMip6FCk5Kaw8spI18WtYm7iW47nHWZOwhjUJa3iTN/Gx+9A+tD2dQjsRHRxN01pNsVs1OEPKlsXVFa/Ol+PV+XIY9wQF8fFkrlxF5soVZP++FkdGBpm//krmr78CYAsIwLNTJzwv74RXx464NmyoorpIJaUiulRLhUUO3lm+D4CRvRvhbq/eReUboyOY9vMeEtJy+WpjHHd20pnBK40/3oUDK8HuCYNmgUa/XJCCIgczfv3feQ28q+kRJSIipdEmwg8Xq4XkjDyOpOZQt5an2ZFEpIrJzMxk7969xddjY2OJiYmhVq1aREZGMn78eOLi4vjoo48AGDFiBDNnzmTs2LEMHz6cNWvWMGfOHD7//HOzHsJZ1faozY2Nb+TGxjdiGAb7TuxjbeJa1iasZX3iejIKMlh2eBnLDi8DwMPFg1a1W9EuqB3RwdG0DW6Lr6uvmQ9BqiF7eDgBt99GwO23YRQVkbt9B9lrfydr7R9kb9hAUWoqGT/9RMZPzpZEVh8fPNq1wyO6HZ7R0Xi0aYPVy8vkRyEioCK6VFM/bEngSGoOgV6u3Nbh0nvvVXauLlaG9WjAS99vZ/byfdzaPgIXm769Nl3KHvj5Oed0v5egllrtXKjv/4zn4LFsanu7ck+X6ntEiYhIabjbbbSs48fmwyfYeChVRXQRuWDr16+nT58+xddP9S2/7777mDdvHgkJCRw6dKj49qioKBYuXMhjjz3GW2+9RXh4ONOnT+fmm2+u8OwXwmKx0CigEY0CGjG4+WCKHEXsPL6T3xN+Z2PSRmKSYkjPT2dd4jrWJa5zroOFhv4NaRfcjlaBrWhZuyUN/RtqtLqUGYvNhkfrVni0bkXgsGEYBQXkbNlK9h9ryfp9LTl//okjI4OslSvJWrnSuZLViluzpni2i8ajbRvcW7XCtX599VUXMYHFOHVWkEooPT0dPz8/0tLS8PXVN8JSOoZhMHD6KnYkpPPPq5owum9jsyNViOz8Qrq9+iup2QW8eUc7bmhXx+xINVtRIXzQH+LWQ4M+cM/XoMPuL4hhGAx4cyU7EzN4on9THunTyOxIp9H71KXTcyhyYV5csJ0Pfovl3i71ePGGVmbHEan29D5VNirb8+gwHMSmxbIpaRObkjYRkxTDoYxDpy3nanWlWa1mtAhsQcvaLWkZ2JIGfg3UW13KhVFYSO6uXeRsiiFn0yZyNm2iID7+tOUsnp64t2iOR8uWuJ+8qLAucvFK+x6lkehS7SzfncyOhHQ8XW01auSqp6sLD3SL4t9LdjNr6T6uaxOO1aqirWlWv+ksoLv5wQ0zVUC/CCv2pLAzMQNPVxt3X15z/pZFRM6lfb0APvgtlg0HU82OIiJSZVktVhr6N6Shf0NuaXILACk5KWxO2syfKX+y7dg2tqdsJ6Mggz9T/uTPlD9hl3NdDxcPGvs3pnGA89IkoAlNAprg5+Zn4iOS6sDi4oJHy5Z4tGwJdw8GoCAxkZyYGLI3biR3y1Zyd+7EyM4mZ/0GctZvKF7X6umJW4vmuDdpiluTJicvjbF5e5v1cESqHRXRpdp5e5mzF/pdnSLx93Q1OU3FurdLfd5ZsZ9dRzP4dWcSV7YIMTtSzZS4FZZOdk4PmAJ+EebmqaLeXeH8W76jYyR+njqMVkQE4LJ6/gDsSEgnK68QL50rQkSkTNT2qE3fen3pW68v4BytfiTjCNuObWNbyjZnYf3YdrILs/9XWP+LYM9gmgQ0KS6sN/JvRD3feni4eJjxcKSasIeGYr/6anyvvhoAo6iI/P37ydm2jdyt28jdto3cnTtxnKGwDs6e7P8rqjsL627162NxrVm1EpGyoL1uqVY2Hkplbexx7DYLQ3tEmR2nwvl52hncOZJ3lu/nrWV76ds8GItGQFeswnz4egQ4CqDpNdD2DrMTVUlb49L4be8xbFYLD3Svb3YcEZFKI8zPgzr+HsSdyGHz4RN0bVTb7EgiItWS1WIl0jeSSN9IBkQNAKDIUcTBjIPsTt3N7uO72XNiD3tS9xCXGUdSdhJJ2UmsiltV4n7CvMKI8ouivm9950+/+kT5RhHsqc9qcuEsNhtujRvj1rgxDBoEONvA5O3fT+727eTt3kPe7t3k7d5NYVISBfHxFMTHk7ls2f/uxGbDHlEHt/pRuEadutTHLSoKW+3ael2KnIWK6FKtzD45Cn1QuzqE+dXMb/yHdo9i7m8H2HToBOsPptKxfi2zI9Usy6fA0S3gGQjXTVMbl4v0zor9AFzXJoyIAJ04T0Tkry6rF0DciRw2HExVEV1EpALZrDYa+DWggV8Drq5/dfH8zPxM9p7Y6yyup+5mT+oe9qXtIy0vjYSsBBKyElgdv7rEfXm6eFLfrz6RPpFE+EQQ4R3h/OkTQYhnCC5WlWukdCwuLrg3aYJ7kyYl5hedOEHu7t3k7dlTorjuyMqi4OAhCg4eguXLS6xj9fbGtX59Z2G9bl3sERG41o3AHhGBS0gIFqu1Ih+aSKWi/8pSbexNymTx9qMAPNSrgclpzBPs486N7erwxfrDzP0tVkX0inRkPax63Tl97RvgHWxunirq8PFsFm5JAODBng1NTiMiUvm0j/RnweZ4NhxSX3QRkcrA29WbdsHtaBfcrsT81NxUDqQfIDYtlti0WA6kHSA2PZYjGUfILsxm+7HtbD+2/bT7c7G4EOoVWlxUj/COoI53HUK9Qgn1CqW2R20V2eW8bP7+eHXqhFenTsXzDMOgMCmZ/NhY8g/Ekh8bS15sLPmxByg4cgRHZia5W7eSu3Xrafdnsdux16mDPSICe90IXCMisEfUxR4ejj00BFtgoIrsUq3pv65UG3N/iwXgqhYhNAr2MTmNue7vXp8v1h9m0dZEjqRmayRvRSjIcbZxMRzQ+jZocYPZiaqsOatiKXIY9GhcmxbhZz8ztohITdW+nvML8o0HU3E4DJ1IXESkkgpwDyDAPYDo4OgS8wuKCjiccbi4oH4k4whHMp0/4zLjKHAUOK9nHoGE0+/XarES5BFUXFQP8Qwpng71DCXEK4Ra7rVUaJfTWCwW7CHB2EOC8ep8eYnbHHl55B88SH7sAfIPOIvqBXFHyD98hIKEBIyCAvIPOG87I7sde3AwLmGh2ENCcQkNwR4advJnKPbQUBXapUrTf1SpFtKyC/hqYxwAD3Sreb3Q/65ZqC9dGwayet8xPl5zkPEDm5sdqfr7+QU4tgd8wmDga2anqbLSsgv4Yt1hAB7sWXOPKBEROZdmYT542G2k5xayNzmTJiE1e/CAiEhVY7fZaeDfgAb+p+/vOgwHSdlJJQrrhzMOk5iVSGJWIknZSRQahRzNPsrR7KNsTt58xm1YsBDgHkBtj9pnvQR6BFLbozY+dh/1wRasbm5nbAsDzr7rBYlH/1JYP0zBkTgKDh+mICGBwuRkKCigIC6Ogrg4cs62EZsNl8BAXGrXxlY7EJfaQbjUrn3yEoitdm3nvKDaWL299bqUSkVFdKkW/rPhMDkFRTQL9aFzA7UvAeeXCav3HePzPw7xjysb4+mqP/dyE7sS1r7tnL5+BngEmJunCvty/f/+lrurz6+IyBnZbVba1vXj9/3H2XQoVUV0EZFqxGqxFo8q70CH024vchRxLPcYR7OOkpidWFxcT8xK5Gj2URKzEknOScZhODiee5zjucfZnbr7nNt0tboWj5r3c/MjwC0Afzf/ktfd/Z3zTk57uNTMc5DVVBYXF1wj6uAaUQe4/LTbjYICCpOTKUg8SmFigvPn0UQKEhIpOJpIYUKis9BeVERhUhKFSUnn36arq7PYHhDgvPj7Oy8Bzp8up+b95Tarh16XUn5UVZMqr8hh8OGaAwDc17W+vqk86YpmwdQL9OTgsWzmb4zjns71zI5UPeVlwLcjndPth0Djq0yNU5UVOQw+/v0gAEP0tywick7t6gbw+/7jxBw+we0dI82OIyIiFcRmtRHsGUywZzCtaX3GZYocRZzIO0FKTsppl2M5x0jJ/d/1jPwM8h35xSPbS8vd5o6vmy++rr74uPr872J3/vz7/FPXvV298XH1wW61l9VTIpWAxW539kYPDweiz7iMUVBA4bFjFKYcozAlmaJjxyhMTqEwxXkpSvnftCMzEyM/n4L4eAri40ufw939f8V2b2+svr7YfHyw+vhg8/XB6n3yp48vNh9v50/fk7d7e2NxdS2jZ0SqIxXRpcr7dWcSh4/n4OdhZ1C7OmbHqTSsVgv3danPi99vZ95vsQzuFKmeqeXhp4lw4hD4R0K/l81OU6Ut353EoePZ+Lq7cIP+lkVEzqldXX8ANh06YWoOERGpfGxWG4EegQR6BNKUpudcNq8oj5ScFE7knuBE3glS81I5kev8mZaXRmpuavH8tNw0UvNSKXAUkFuUS252LknZ5x9RfCbuNnc87Z542b3wdPHE037y4uK8eNm9im/3cPE4bd6p5dxd3HFzccPd5o7datdAnErMYrcX90Y/H0duLoUpxyhKSabwxAmKUk9QdOLkJTW1xM/CE6kUnUiDggKM3FwKExMpTEy8uIweHli9vbB5emHx8sTq6YnVy8v509MTq6cXVq+TPz3/drvXX6Y9PLC4u2N1d8fiotJrdaHfpFR5H64+AMAdneri4WozN0wlc2uHCF5fspt9yVms3JtCryZBZkeqXnYvho0fAhYY9Da46XD6S/Hhauco9Ns76m9ZROR8ThXRdx/NICuvEC837daLiMiFc7O5Uce7DnW8SzeIxTAMsguzSc11FtkzCjLIyD/7JT0/vcQyWQVZAM4ifFEux3OPl9ljsVqsuNnc8HDxwM3mVmLa3cUdd9v/Cu5nuu5qdcXV5ordZv/ftNVe4udf59ttJedZLTphZlmxurs7W8dElP516cjK+ktxPQ1HZgZF6Rn/+5mRTlFGJo70dIoyMnBkZDh/pqfjyM523k9ODkU5ORSRUnYPxsUFq5vb/4rq7u5/ue6Gxd3D+dPNHYu7G1Z3D+fP4uvuWFzdsLi6YnG1O3/a7VhdXYunLWeaPnVdJ3ItM9rbliptz9EMVu1NwWpB7UrOwMfdzq0dIpj72wE+WBWrInpZyj4O3412TnceCfW7m5uniotNyWL57mQsFrhbf8siIucV6udOqK87iem5bIlLo3ODQLMjiYicV1ZWFjbb6YMlbDYb7u7uJZY7G6vVisdf+h5fyLLZ2dkYhnHGZS0WC56enhe1bE5ODg6H46w5vLy8LmrZ3NxcioqKymRZT0/P4lHaeXl5FBYWXtKyAdYAAjwC8KjlgfVkkS4/P5+CgoKz3q+HhwcGBpkFmRzLPEZ6Tjo5BTlkF2Y7LwX/+1lgLSDPyCOrIIuMnAwycjLILswmpzDHudzJZfMd+RguBharBYfhIDs3m6yis78mLC4WLDbnYzMKDYyiM/+OT1u2yMAoPMeyNgt2u7Ow7mK44OJwKS68u1id0y5WF2xWG652V1xdnfOtDiuWQgs2qw2b1YaLxQUXq/Nis9hwdXXF3c0dm8WGzbBhFBjFy1mt1v/dr8WGm6sbHu4e2Cw2MKAwrxCrxYrNYsNqPfkT50+7qx13N3esFisWw0J+br7z9r8tD5S4XwsW8nLy/recxeq8j5OvFxcXF9zc3JzPmWGQfbI4fSYX8ndfqmUtFggIwBoYiPcF/o8wCgtxZGaSkZREUXo6jtxcHFlZOHJycGRl48jJxsjOwb2wEEd2No7sbLJOnKAoO9u5THY2juwsHNnOaXJy8DhVvC4sJDs/H0dGxllzeP6l0J3rcHD2/xAll81zODj7X/3JZV1csLi6km+z4bC7YLW7Yjk5z+LqnMbugqerG1a7HVxs5FusOCwW5202KxYXOxabDYvdBWwueHp4YLW7gIsL+Q6DIqsVi4vNuS2b7eR6Niwudjw9PbG52sHFhQKHQaHhAKsNi83q/OliK77u4eGJ7eQ2CooKKXAYzuVsNueXAafWs9nw8PTExcMDq4fHef/3uLu7F7/3FBQUkJ+fX+L2c71G/kpFdKnS5p0chX5VixAiAjzPvXANNaRrfeatPsDy3cnEpmQRVdvr/CvJ+f04DjITIbAx9H3G7DRV3sdrnKPQ+zQNpl6gXqMiIqXRrq4/i7YlEnP4hIroIlIlhIeHn3H+wIED+eGHH4qvBwcHn7X41qtXL5YtW1Z8vX79+qSknHnUaIcOHVi3bl3x9RYtWnDw4MEzLtuiRQu2bdtWfL1jx45s3779jMvWq1ePAwcOFF/v2bMn69evP+OytWvXJjk5ufj6gAEDWL58+RmX9fT0LFHMufnmm1m4cOEZlwVKFPnvuece/vvf/5512czMzOKi+0MPPcSHH3541mWTkpIICnIOwBo7diyzZs0667KxsbHUr18fgIkTJzJ16tSzLrt161ZatmyJn5sfb0x+gxdeeOGsy/7xxx907NQRgH/961+MGzfurMsu+XkJnXp0Iq8wj3fefodnHj/757N/vv1PmndrTl5RHiu+XsEXL35x1mW7PdWN0C6hFDgKOLTyEDGvx5x12TpD6xDQI4DCwkIyYjI4OO3MrzOAsLvDCLzS+b6duSOTA1MOnHXZkNtCCBro/F1k78/+f/buO76q+v7j+Ovem70DIQvCXmFPBRQcKMgQwW2ttXUideJo0f6q1VZrtRatA627WqsWUEAUUUERUJQ9wh4hmyRkJze5957fHycJIAQTSHJyb97Px+M+cu6933vvm5Bvxud+z+fL3kf31jm23SXtiJsWB0BFegW7H9pd59iYi2KIv9psq1J5qJKd99e9+Wyb89uQ+Ctz7rqKXGy/c3vdY89uQ7fp3bDb7BhOgzU3rKlzbOyIWAbeO7B2Bf+Sy5fUOTZuaByjHx6NDRs2m425l8/F7Txx+TiufxyTnppUO/adK9+horDixBl6xfKLl36BzWbDho1Xr36VouyiE46N6RzDzW/fDJhvpL1y3Qfk7j/x957I+Ejufe92HJVuHFVunr/rbdL2nHjPgfDQQF753RX4VbpxVLr543++YkvaiZ83yGHnqwtHYXd5sLvc3LNxOysPF55wLMC2Xr3B5cJwubg/PZ3PS+ou5P/Yo2dtgf7BzAw+Kjrx5wHg227daVPdpuax7CzeKyioc+zSrl1p72/2mn8qJ4c3Dtd99snHnbvQo/pNmOdzD/FiXl6dY9/v2ImeY4Yy6N9zefbZZ0/6PWLZsmWce+65ALzyyivcfvvtdY49GRXRxWsVllcxb106AL8e1cXiNC1Xp7ahnNOzHct3HOK/a1KZNTHZ6kjeb+tHsPlDsDlg2svgrx3AT0ep08WHaw8C8KuRWoUuIlJfgzpWF9HVF11ERFoxP4cfEQEREADRQdEnHXte0nlM6j8JgJANIbxP3UX0u4bcxRVTrgDgw6oPuZIr6xw768xZXH755VR6Kvk8+HNumn1TnWOn9ZjGhNETcHlcbLRv5BEeqXPs8PjhjO4zGpfHRaorlZd5uc6xHcI6MCBuAG6Pm/zSfHZTdxE9LCCM+NB4PB4PpYH1W4VbHx7DQ7mr3DyuOtl6aqhwVZBZmlmv5y2tKmV7/pHivceo+7mLK4tZk3WkeF/lqXuFcnFlMV+kflF7vSZ7XWMX7l14zPW6lFWV8cGBj2uv53nqLkiX2V38peOG2ut7Q+teve90GNxydUHt9f3PuOFwncO58S4Hfm7wd8HWN2ywqe6xL0yyE+Sw4zBgx6c2qDsynw61ERVgw+6Bg2tsUFD32JQONgoDwO6BgjJOmrcgFPKDzLHOelSsMwp2MujnhzUam1HX+UktQFFREZGRkRQWFhIREWF1HGlh3li5jz8t3EavuHA+u3u0NhA5iaXbsrn57R9pExrA6lnnE+inftOnrCQHXjgTyvNhzP1w/h+sTuT13v3+AA/N30LntiF8de+5XrUBrn5OnT59DkVO3Xd787j6le+IjwjiuwfHWh1HxCfp51TjqPk8ZmRknPDzqHYuJx7bktu51AgOblg7l/qOPbr9wum2ajhaYGAgftUraBsy1uVy4XQ66xwbEBCAv79/g8e63W4qKk68ShrA39+fgICABo/1eDyUl9ddEG7IWD8/P/wD/PEYHtweN8Wlxeax4cbjqf5oePAYHuwOO34BfngMDy6Pq3YeGYaBB495jFE7NiAwAI/hwcCgrKSs9j4D45hjbOb/hwfzdcrLys37qp8Xw8DjdmG4K8DjIsDfwHBV4nE7KS8uwnBX4nFXYtRcPC48Hhc2jwt/f/B4XBgeFxXlFXjcLvC4MDxuDI8LDA8Y5v2B/mB4XBiGG2dFFYa7Zowbjh5vA/9A82vdAJyVRu33EwNb7e0132ECAu0Y1X8GV1Z68FTfcfSYmscFBtrN221QVWXg8RhHjTnCwHZMhkqXgXHU2J8+v1+ADWx2sIGrysBdx/PWjK35HlEzts6vH387tuq/8d0uA9dPxh59zd/fBkeNdbuN41675kH+Dht9orrwm19/ddrfI4qKikhMTPzZn/VaiS5eyTAM3luTCsC1IzqqgP4zzuvVjoTIIDILK/hsSxaXDKrf5hzyE4YBC+8yC+jx/WFM3acLSf0YhsHb1RuKXjeys1cV0EVErNa/fSR2G2QVVZBVWEF8ZNDPP0hExEKhoaHHFH5PNq4hz1lfRxe+G3Ps0YX6xhx79BsLjTk2MDCwtm91Y44NCAioLcxaNdbf37+2QN2YY/38/GoL6o051uFw1PtruCFj7XZ7o4+12+z42f0IjKzf1wMAUUcdGwZUlUFlKVSWmB/LSsBZcuT60ff99LiqDFwVUFUBrvLjP55kdbolfvq+hM0BDn+w+4HdAfbqY4e/eV/N9UC/6jF+1bcd/bgTXbdXP95hfrTZq4+P+njM/bYTjHVUP89JnuuYsT+9zX78eGzma9nsR32sud3+k9ttddx+ovG2I7c7zPl7ut8jTvYG5NFURBevtPbAYXZmlxDkb2fqYBWEf46fw85Vw5OY/cUu3v0+VUX0U7Xxv7BjsfmDatrL4Fe/b9JSt7UHDrMju5ggfzuXD+1gdRwREa8SGuhHz7hwtmcVs+HgYS6KTLA6koiIiPgij8csaDuLoKIQKmo+FlbfVnDktp+OcRYdKYSfeF1xI7OZLVf9gur+6BdoXhyBZiHWLxAcAebFr/o2R/VtfgFH7qu9/0Rjj3qemiJ4bbHbr7pQLN5MRXTxSv+pXoV+8YBEIoLq985xa3f18I7886vdrNmXz67sYnrEhVsdybsUpsGnvzOPz3sQ4vpam8dHvLfG7IV+8YBEIoM1l0VEGmpwxyi2ZxWz/mABF/VTEV1ERER+hrsKyg9DWR6U5ZtnWh9znH/87RUFjbvSOyAMAkKPuoQd9fFE94WAf0h1ITwI/IJP/NE/xCxiq2AtTUBFdPE6hWVVfLLJ3HzimjM7WpzGe8RHBjG2dyyfb8vmP2tSefhiFYHrzTDg49+CsxA6DIdRd1qdyCcUllfxyeYMAK4+Q3NZRORUDEqK4r01B7W5qIiISGvmroLSQ1CSDSU1H7OPui3nyMVZeOqvY/eHoMjqS4T5MTDiqNuOvn7U/YFHFcf9gs3WISJeRkV08Trz16fhdHnoHR/O4KQoq+N4lV+c2ZHPt2Uzd20av7uoN0H+2mC0Xn58DfYuN3/YT50DDn3rbAwLNqRTUeWhZ1wYQzpGWR1HRMQrDUqKBmBzeiFuj4FDe0uIiIj4lopCKMqAwnQoSjePi9KqP2aaRfLy/AY+qQ2CoyGkDQS3gZC21cfVt4W0rb695jjaLIj7BWmVt7RaqgSJVzEMo7aVyy/O1IaiDTWmRzs6RAeTdricRZsy1YO6PvL2wOf/Zx5f+CeI6W5tHh9hbg5stnK5erjmsojIqeoeG0ZogIPSSjc7s4tJToiwOpKIiIjUl8djFsELDsDh/XD4ABSmVhfMM8xLZXH9nsvuB6HtICwWwuIgNLb6OPbY20JjzIK4XYvqRBpCRXTxKutSj2woqs0xG85ut/GLMzvyt8928O73B1RE/zkeN3w0w9wFvPNoGH6z1Yl8xub0QrZlFhHgZ+fSIZrLIiKnymG3MaBDFKv35rHhYIGK6CIiIi1NZRnk74XD+8wi+eH9R4rmBangqvj55wiOhoj21ZdE82NkewhPgPB4szgeHK02KSJNSEV08Sr/+V6bEJ6uK4Ym8cznO1mfWsDO7GJ6aoPRuq1+Hg5+BwHhcMkL+oWkEb1XfUbJhH7xRIUEWJxGRMS7DepYXURPLeAa7TEhIiLS/AzDbLWSuwvydld/3GV+LDx48sfaHGZBPLozRHUyL5HtjyqaJ5i9xEVaOcMwyCl2siu7hN05xcRHBnNRv/hme30V0cVrFJZXsWiTuQmhNhQ9de3CAzm/eoPRD388yEOT+lgdqWXKSYGv/mweX/Q4RHeyNo8PKXW6WLChekPR4ZrLIiKna1D1HjEbDhZYmkNERMTn1RTLs7dBzlbI3gqHdpiF86qyuh8XFAVtupqF8ujO5t+XNUXzyA7g0CJBkaMdKnayPauI7ZnF7MguZndOCXtySih2umrHjO0dqyK6yIks2JiB0+WhV5w2FD1dVw5L4vNt2cxbl84DF/XG36EV1sdwV8H8W8FdCT3GweDrrE7kUxZuzKC00k2XmFBGdG1jdRwREa9X83vRzpxiSpwuwgL1K76IiMhpc5aYRfKaYnlN4byi8MTjbQ5o0wXa9oCY6kvNcUhbbcgpcgIVVW5255SwPauY7ZlF5sesInJLKk843m6DTm1D6dYurNnrCfoNW7zG/340T4G6YlgHbUJ4ms7t1Y524YEcKnby1fYcxvdtvnfuvMKKv0PmRnO1wJR/6pedRvbeD+Zcvmp4kuayiEgjiI0IIjEyiIzCCjanFTKyW1urI4mIiHiXylLI2gwZ6yFjg/kxdydgHD/W5jAL43F9IbYPxCZDTE9zZblWlIvUqdLlYUdWMRvTCtiUVsCmtEJ25ZTg9hw/z2w26NI2lF7x4fSKD6dHbDjdY8PoHBNCoJ81m+KqiC5eYWd2MRvTCvGz25g2WJsQni4/h7mZ48tf7+XDH9NURD9axnr45inzeNLfzU1apNHszC5m48EC/Ow2LhuijW1FRBrLgA5RZBRmsTm9QEV0ERGRk3G7IHsLpP1QXTRfD4e2g+E5fmx4wpFieVxf8xLTE/wCmz+3iBfxeAx2Hyphw0GzYL45rZCUzGIq3cfPs8hgf5ITwukdH1H7sUdcGCEBLats3bLSiNThf2vTADi/dyxtw/TDqjFcMTSJl7/ey7IdOeQUVxAbHmR1JOtVVcD86eBxQd9p0P9yqxP5nLnVc/m83rG0C9dcFhFpLP07RPLZ1iw2ptVxirmIiEhrVVFkFswPfg+p30H6WqgsOX5cWBwkDoHEwZA4CBIGQXhcc6cV8UoVVW42pRXyw/58ftyfz9oDhymqcB03LirEn/7tIxnQIZIBHaLo3z6ShMggrzhLXUV0afGq3B7mrUsH4PKhWrnaWLrHhjGkYxTrUguYvy6dW8/pZnUk6y37i7kCITQWJv7d6jQ+x+X2MG+95rKISFMY2CEKgM0qoouISGtXmgf7V8D+b82iec7W41eZB0ZAh+HQfmh10XwwRCRYk1fECxVXVLFmXz5r9uXzw/58NqcXUuU+ti1LsL+DAR0iGZhkFssHdogiqU2wVxTMT0RFdGnxvt5xiNwSJzFhAZzXO9bqOD7lymFJrEst4IMfD3LLmK5e+42sURxYDav+aR5f/CyE6lT4xrZiVy6Hip20CQ3gvF6ayyIijal/+0gAUvPLOFxaSXRogMWJREREmomz2Px7bt/X5iVr8/FjojpBxxGQdAYkjTD7mNut6ass4o0qqtysSz3Mqt15rNyTy6a0wuN6mbcLD2R452iGdWrDsM7RJCdE4O+wW5S48amILi3eh2vNTQinDmrvU5OvJZg0IIE/LdzGnkOlrEstYGinaKsjWcNZAh9NBwwYdC30nmh1Ip/0v3VmK5cpAxMJ8NNcFhFpTJEh/nRuG8L+vDI2pxcypmc7qyOJiIg0DY/H7GO+63PYu8xsz+L5SduI2D7QeTR0GgVJZ2qVuUgDGYbB9qxilu84xMrdufywPx+n69gzOjq3DWFkt7YM69SG4Z3bePUq8/pQEV1atLwSJ1+m5ABwxbAki9P4nvAgfyb2T2DuujQ+/PFg6y2iL/0jHN4PER3goiesTuOTCsuqWLo1G1ArFxGRpjKgQxT788rYlFagIrqIiPiW8sOw5yvY+Tns/gLKco+9P7ozdDkHuowxL2E681WkocoqXazancdXO3JYvj2HjMKKY+5vFx7IWd3aMqp7DGd1j6F9VLBFSa2hIrq0aB9tyMDlMRjQIZJe8eFWx/FJVwzrwNx1aSzalMkjU/oS5N/KTmnb/SX8+Jp5PPUFCIq0No+PWrApg0q3h97x4fRNjLA6joiITxrQIZIFGzO0uaiIiPiG/L2wbQHs/MzcFPTovuaBEdDtPOh+gVk8j+5kXU4RL5ZVWMHn27L4MiWH1XvzqDxqtXmgn52zuscwpodZNO8eG+bTK81/joro0mIZhsGHP5qtXK7QytUmc0bnNnSIDibtcDmfb8tmysBEqyM1n/IC+Ph28/iMW6DruVam8Wn/W2u2crl8aIdW/UNXRKQpDdDmoiIi4s0MA3JSIGUhpCyA7C3H3t8uGXpcCD3Gmf3NHf7W5BTxcmmHy/hsSxaLN2eyLrXgmPvaRwVzfu9Yzu8dy8hubVvfQsuTUBFdWqxtmUVszyomwGFnysD2VsfxWXa7jWmD2/PPr3Yzf11a6yqif/Z7KM6ANl3hgkesTuOzdmUXs/FgAX52G1MHay6LiDSVvokR2G2QVVRBTlEFsRFBVkcSERE5OcMwNwLdOt8snOftPnKfzQFdRkPvydBzPER1tC6niJfbn1vK4i2ZfLYli00/WXAxtFM0F/aJ4/zesfRo5avNT0ZFdGmx5q9LB+CCPrFEhugd5qZUU0T/Zlcuh4qdtAsPtDpS00tZBBvfA5sdps6BgFCrE/msmg1Fz+0VS0xYK/jaEhGxSGigH91jw9iZXcKmtEIu6KMiuoiItFAFqbD5Q9j0ARzafuR2RwB0Ox+Sp0CvCRDSxrqMIl4ur8TJok2ZzF+fzoaDBbW3221wRpc2TOiXwPi+8cRH6nfG+lARXVokt8fg440ZAEwdpJWrTa1ruzAGJUWx4WABCzZmcOPZXayO1LRKc2HhXebxqDuh45nW5vFhbo9R+4bY5UM1l1u6b775hqeeeoq1a9eSmZnJ/PnzmTp16kkf8/XXXzNz5ky2bt1KYmIiDzzwANOnT2+ewCJynAEdoqqL6AVc0CfO6jgiIiJHlB+GbR+bhfMDK4/c7giEnuOgz1SzVUuQ9lASOVUVVW6Wbsvmo/XpfL3zEC6PAYDDbmNUt7ZM6JfAuL5xWuB2ClRElxZp5W5zRXR0iD/n9tKu2s3hsiHt2XCwgHnr0ny7iG4YsOhuczf3dslw3oNWJ/Jpq/fkkVPsJCrEn/N7q5jT0pWWljJw4EB+85vfcNlll/3s+H379jFx4kRuvvlm3nnnHVauXMmMGTNo165dvR4vIo1vQIdI/rc2TZuLiohIy+DxwP4VsO4ts9e5u7L6Dht0PhsGXAV9pkBQpKUxRbyZYRhsSivkvTWpLNqUSYnTVXvfgA6RTB3UnosHJraOrgNNSEV0aZHmrzdXrk4ekEiAn93iNK3D5AGJPLpoG1szitiRVUyv+HCrIzWNzR+av7zZ/eDSl8FPP0SaUs1cntQ/QXPZC0yYMIEJEybUe/ycOXPo2LEjs2fPBiA5OZkff/yRp59+WkV0EYvUbi6aXohhGOppKSIi1ijOhg3vwLp/w+F9R26P6wcDroR+l0OkzlQVOR1FFVV8vCGD975PZVtmUe3t7aOCmTa4PVMHt6d7bJiFCX2LiujS4pQ6XXy2JQuAaUP0Q7W5RIcGcF6vWD7fls289WnMmpBsdaTGV5QBi+8zj8/5HSQMtDaPjyuvdPPZlkzA7Lsvvmf16tWMGzfumNvGjx/Pa6+9RlVVFf7+x+9n4XQ6cTqdtdeLioqOGyMipy45IRx/h4380krSDpeT1CbE6kgiItJaGAbsXQ4/vAo7PwNP9WrYgHAYcAUMuR4SB1mZUMQnbDxYwLvfH2DhxkzKq9wABPjZmdgvnqvP6MgZndtgt2shRWNTEV1anM+3ZVFe5aZz2xAGJ0VZHadVuXRIez6v7p31wPjeOHzpm65hwII7oKIQEgfD2fdYncjnLU3JprTSTYfoYIZ2irY6jjSBrKws4uKObdMTFxeHy+UiNzeXhISE4x7zxBNP8Kc//am5Ioq0OoF+DnrFh7MlvYjN6YUqoouISNOrLINN78P3L8OhlCO3dzgDhl4PfadBQKh1+UR8gMvt4bOtWbz+7T7WpRbU3t49NoxrzujIpYPbEx0aYF3AVkBFdGlx5lVvQjh1cHudgtzMzusdS2SwP9lFTlbvyePsHjFWR2o8a9+E3V+Ym9ZMnQOO41fISuOavy4NMFehay77rp/+3xqGccLba8yaNYuZM2fWXi8qKiIpKanpAoq0QgM6RLElvYiNaQVM7H/8m1kiIiKNojDNXHW+9k1z01AA/1AY9AsYdgPE9bE0nogvKCyr4r0fUnl71X4yCisA8HfYmNQ/gWtHdGJYp2j9vd1MVESXFiWnqIKVu3MBtX+wQqCfg8kDEnj3+1TmrUvznSJ6/j5Y8pB5PPaPENvb2jytQG6Jk292mXN5quayz4qPjycrK+uY23JycvDz86Nt27YnfExgYCCBgdqLQKQpDWgfyX+ATQe1uaiIiDSB7K2w4hnYOh8Ms5UEUR3hjFth8C8hOMrSeCK+4GB+Ga98s5f/rU2rbdnSNjSAa0d04pcjOhIbHmRxwtZHRXRpUT7ekIHHgKGdounUVqd7WeHSIe159/tUlmzNorzSTXCAw+pIp8fjgY9/C1Wl0HEUjLjN6kStwqKNGbg9BgM7RNKtnTYy8VUjR45k4cKFx9z2+eefM2zYsBP2QxeR5lGzueiW9EI8HkM9MUVEpHEc/AFW/B12fnrkts6j4czp0GsC2L38b0eRFmB3TjEvLt/DxxvMv6kBeseHc8PZXZgyMJEgf80zq6iILi3K/PVmKxetQrfOkI7RdIgOJu1wOV+kZHPxwESrI52e71+CAyvN0wqnvqhf7JrJ/A0ZgFahe5uSkhJ2795de33fvn1s2LCBNm3a0LFjR2bNmkV6ejpvv/02ANOnT+f5559n5syZ3HzzzaxevZrXXnuN9957z6p/gogAPePCCPSzU+x0sS+vVG9miojIqTMM2LvMXHm+f0X1jTboc4m5z5Q2ChVpFFvSC3lh2W4+25pFdYdMRveI4bZzujGyW1u1bGkBVESXFmNndjHbMotqezuJNWw2G5cMSuSFZeY7n15dRD+0E76o3sBw/J+hTRdr87QSew+VsPFgAQ67jckDvPjrpxX68ccfOe+882qv1/Quv/7663nzzTfJzMwkNTW19v4uXbqwePFi7rnnHl544QUSExN57rnnuOyyy5o9u4gc4eewk5wQwYaDBWxJL1QRXURETs3er+GrP0PaGvO63Q8GXg1n3Q0xPSyNJuIrtqQX8szSnXy1Paf2tnF94vjted0ZmBRlXTA5joro0mIsqF65ek7PWO0obLGpg9rzwrI9fL0zh4KySqJCvPD/w+2C+beC2wndxsLQ31idqNX4qHouj+4RQ7tw9b72Jueee27txqAn8uabbx532znnnMO6deuaMJWInIr+7SNri+iXDNJZQSIi0gAHf4CvHoV935jX/YJg6K9h5O0QpQ3hRRrD7pwS/rF0J59szgTAboMpAxO57dzu9IoPtzidnIiK6NIiGIbBxxvNVi6XDNLKVav1iAsnOSGClMwiFm/O4hdndrQ6UsN9+w/IWAdBkTDln6BTn5qFYRh8vMGcy1NVtBERsUz/9pEAbEkvsjiJiIh4jcxN5srzXUvM63Z/s3g+5j4Ij7c0moivSDtcxrNf7GLuujQ8hlmqmDIwkbsv6EmXGO0N2JKpiC4twvqDBRzMLyckwMEFyXFWxxFg6qBEUjKL+HhDuvcV0TM3wdd/NY8nPAWRKuY2l41phRzIKyPY38G4vprLIiJW6VdTRM8oxDAM9dEUEZG6FabDl3+CTe+b120OGPQLOOcBiPKyvwVFWqiCskqe+3I3//5uP1Vu8+zfC/vEce+4nvSOj7A4ndSHiujSItS0chnfN57gAG382BJcPDCRJz7dzpr9+WQUlJMYFWx1pPpxOWH+dPC4IPliGHCl1YlalZq5fGGfOEIC9CNGRMQqPeLCCPCzU1zh4kBeGZ21sklERH7KWQIrn4VV/wRXuXlbv8vh3FkQ093abCI+osrt4d3vDjD7y10UlFUBcFb3ttw3rheDO0ZbnE4aQhUOsZzL7WHRJrPwNsWbN7H0MYlRwZzRpQ1r9uWzcGMGt57TzepI9bP8CcjZCiExMOkfauPSjNweg4WayyIiLYK/w05yfDgb0wrZklGoIrqIiBzhccPG9+DLx6Aky7yt4ygY/xdoP8TabCI+wjAMlu3I4S+fpLDnUCkAveLC+cPkZEb3aGdxOjkVKqKL5VbtySO3pJLoEH/O7hFjdRw5ytRB7VmzL5+PN3hJEf3gGnMlBcDFsyFMP5ia03d78zhU7CQy2J8xPfW5FxGxWr/2kWxMK2RzeiGTB+jNTRERAdLXwqKZkLnBvB7dGS58zDyLVwuQRBrF3kMlPLJwG9/sPARA29AAZo7ryVXDkvBz2C1OJ6dKRXSx3MfV7R8mDUjAX99MWpSJ/eN5eMEWtmUWsSu7mB5xLXiH6Moys42L4YEBV5m/BEqzqmnlMrF/PAF+mssiIlar7YueXmhxEhERsVz5YXPl+Y+vAwYERpg9z8+4BfwCrU4n4hMqqty8uHwPc5bvodLtwd9h44azuvDb87sTEeRvdTw5TSqii6Uqqtws2WqePnbJIG3+2NJEhQRwTs9YvkjJ5uMNGdw3vpfVker2xSOQvwfCE2HCk1anaXWcLjeLt2QCMGWg5rKISEvQv7aIXqTNRUVEWivDgI3/hc//AGW55m0DroZxj0FYrLXZRHzINzsP8cePt7A/rwyAc3q2409T+qqlng9REV0s9dX2HEqcLtpHBTNUGyq0SJcMSuSLlGwWbMzg3nE9W+Yf4Hu/hjUvm8eX/BOC9bXU3L7ecYjiChdxEYGc0aWN1XFERAToGReOv8NGYXkVaYfLSWoTYnUkERFpTrm7YeFdcOBb83pML5j0d+gy2tpcIj4kp6iCRxdtY9Emc1FZXEQgD1/clwn94ltm/UROmYroYqmPN6QDcPHAROx2fXNpicYmxxLs7yA1v4xNaYUMTIqyOtKxKorg49+ax0N/A90vsDZPK/XxRrOVy8UDEnFoLouItAgBfnZ6xYezJb2IzemFKqKLiLQWHjd89yJ89WdwVYB/iNm6ZcRvwS/A6nQiPsEwDOavT+eRBVspqnBht8GvR3Xhngt7EK7WLT5JRXSxTFFFFcu2m5ssTBmoza5aqpAAPy7sE8eCjRks2JjR8oroS2ZB4UGI6gTj/mx1mlapxOniy5RsQG2ZRERamv7tI9mSXsSW9EIm9k+wOo6IiDS1QzvMRUZpP5jXu54HFz8L0Z2szSXiQ3KKKnhw/ma+SMkBoF/7CP566YDa/WjEN2nnN7HM51uzqXR76B4bRnJCC96wUri4+k2ORZsy8HgMi9McZcdnsP4dwAZTX4LAMKsTtUpLt2VRUeWhS0wo/dpHWB1HRESOUvPH3GZtLioi4tvcLljxDMwZbRbQAyNgyj/huvkqoIs0EsMwmLcujQue+ZovUnLwd9i4f3wv5s84SwX0VkAr0cUyC6vbP0wZmKg+US3cmJ4xRAT5kV3kZM3+fEZ0bWt1JCjLh4V3mscjZkDns6zN04ot2FDdykVzWUSkxTmyuWihNhcVEfFV+Xth3i1HVp/3GAeTZ0OkzhIVaSy5JU5+P3dT7erz/u0jefqKgfSK16LQ1kIr0cUS+aWVfLvb3Bl88gCdWtzSBfo5uKhfPHDkzQ/LfXIvlGSbm+OM/T+r07Rah0srWbHLnMtqyyQi0vL0jAvHz27jcFkVGYUVVscREZHGZBiw4T9HrT6PhKlz4BcfqIAu0oi+3nmIi2av+Mnq81EqoLcyKqKLJT7dkonbY9CvfQRd26kFhzeYMtD8JWzx5kyq3B5rw2yZC1vngc0B014C/2Br87RiS7Zm4fIYJCdE0D1Wc1lEpKUJ8nfQM878A29zmlq6iIjpxRdfpEuXLgQFBTF06FBWrFhR59jly5djs9mOu2zfvr0ZE8txyg/D/26Aj26DyhLodBbcthIGXQM660ikUThdbh5btI3rX19DbomTnnFhLLj9bH57Xnf8HCqptjb6HxdL1KxmvniAVq56ixFd2xATFsDhsipWVp9FYInibHMVOsDoe6H9UOuyCAs31bRy0RklIiIt1dEtXURE3n//fe6++24eeugh1q9fz+jRo5kwYQKpqaknfdyOHTvIzMysvfTo0aOZEstxDqyCl842FxbZ/WDsH+H6hRCVZHUyEZ+xK7uYqS+s4rVv9wFw/chOLLj9bJITtA9Ya6UiujS77KIKvt+XD8BktX/wGn4OO5P6m4XSBVa1dDEMsw96+WGIHwBj7rcmhwCQU1zB6j15gN4QExFpyWo2fd6SoSK6iMAzzzzDjTfeyE033URycjKzZ88mKSmJl1566aSPi42NJT4+vvbicDiaKbHU8njg29nw5mQoSoM2XeHGz83FRXb9f4g0lnnr0rj4+W9JySyiTWgAr10/jD9d0o8gf82z1kxFdGl2izZlYhgwrFM07aPUhsObXFz9psfnW7OpqHI3f4AN78LOz8ARANPmgF9A82eQWp9uzsJjwKCkKJLahFgdR0RE6tDvJ5uLikjrVVlZydq1axk3btwxt48bN45Vq1ad9LGDBw8mISGBsWPHsmzZspOOdTqdFBUVHXOR01R+GP77C/jiYTDcMOAquHWFzswVaUQVVW4enL+ZmR9spKLKw9ndY/jsrtGMTY6zOpq0ACqiS7OrbeWiVeheZ0jHaBIjgyhxuli+I6d5X7wgFT79vXl83oMQ17d5X1+Oo7ksIuIdkhMicNht5JZUkl3ktDqOiFgoNzcXt9tNXNyxBaG4uDiysrJO+JiEhAReeeUV5s6dy7x58+jVqxdjx47lm2++qfN1nnjiCSIjI2svSUlqM3JaMtbDy2Ng56fgCISLn4VpL0Og9iQSaSwH88u4Ys5q/vN9KjYb3DW2B2/dcAaxEUFWR5MWws/qANK6HMwvY8PBAuw2mNA/3uo40kB2u42LByby8jd7Wbgxk4v6NVMfbI8HPv4tVBZDhzNg1J3N87pSp/SCcn48cBibjdo2PyIi0jIF+Tvo3i6MHdnFbM0oJD5SfwyKtHa2n2w8aRjGcbfV6NWrF7169aq9PnLkSA4ePMjTTz/NmDFjTviYWbNmMXPmzNrrRUVFKqSfqh/fgE8fAHclRHeGK96CxEFWpxLxKcu253D3+xsoLK8iKsSf2VcN4txesVbHkhZGK9GlWdVsQjiyW1tiw/UHnDeaXN37+svt2ZQ6Xc3zoj+8Cvu+Ab9gs42L+v1Z7pPquTy8cxsVY0REvEDfRLMv+tYMtVQQac1iYmJwOBzHrTrPyck5bnX6yYwYMYJdu3bVeX9gYCARERHHXKSB3FXwyb2w6G6zgN57MtzytQroIo3IMAxeWLabG976gcLyKgYmRfHJnaNVQJcTUhFdmtXCjZmANiH0Zv3aR9C5bQgVVR6+3N4MLV3y9sDSP5rHFz4Kbbs1/WvKz1q0qXouq5WLiIhX6FNdRN+Srs1FRVqzgIAAhg4dytKlS4+5fenSpYwaNarez7N+/XoSEnQ2YpMpzYN/TzMXE2GD8/8PrnoHgqOsTibiMyqq3Nz13w08tWQHhgHXntmRD24dob37pE5q5yLNZndOCSmZRfjZbVzUT61cvJXNZmPygESeX7abhRszmNKURVSPG+ZPB1c5dDkHht/UdK8l9bY/t5RNaYU47DYmaC6LiHiFvonm5qJaiS4iM2fO5LrrrmPYsGGMHDmSV155hdTUVKZPnw6YrVjS09N5++23AZg9ezadO3emb9++VFZW8s477zB37lzmzp1r5T/Dd2VvhfeuNveECgiDy16FXhOsTiXiU7IKK7jl3z+yKa0QP7uNR6b05ZcjOlkdS1o4FdGl2Syqbv8wukcMUSEBFqeR03HxQLOI/vWOQxRVVBER5N80L7TqOUhbAwHhcMkLYNfJMy1BzVwe1a0tMWGBFqcREZH6qFmJnl5QTkFZpX4XE2nFrrrqKvLy8nj00UfJzMykX79+LF68mE6dzAJSZmYmqampteMrKyu57777SE9PJzg4mL59+/LJJ58wceJEq/4Jvmv7JzD3ZqgqhegucM17EJtsdSoRn7LhYAG3vP0jOcVOokP8efHaoYzs1tbqWOIFVESXZmEYBgs3moW3yWrl4vV6xYfTIzaMXTklfL41m8uHdmj8F8neCsseN48n/BWitBFRS6G2TCIi3icy2J+ObUJIzS9jW0YRo7rHWB1JRCw0Y8YMZsyYccL73nzzzWOuP/DAAzzwwAPNkKqV+24OfPZ7wDDPwr3iTQhpY3UqEZ/y6eZM7np/A5UuD73iwvnXr4bRsW2I1bHES2hZpzSL7VnF7DlUSoCfnQv71n/DGmm5at4MqVmV3KhclTD/VnMDnZ4TYNC1jf8ackp2ZRezI7sYf4eN8X3VykVExJvUbC66JUN90UVEWgyPBz57ED77HWDA0N/AL+epgC7SyF7/dh8z/rOOSpeHsb1jmTtjlAro0iAqokuzqCm0ntuzXdO1/pBmNXmguZHQt7tyOVxa2bhP/s1TkLUZgqPh4mfBZmvc55dTtrB6Q9ExPdoRGaK5LCLiTWqK6OqLLiLSQlSVw4fXw3cvmNcv+BNM/gc41DRApLF4PAaPLdrGo4u2YRhw3YhOvPKrYYQFap5Jw6iILk3OMAwWVRfeJjflJpTSrLq1C6NPQgQuj8FnW7Ma74nT18KKv5vHk56BcJ250FKYc7m6LVP1mygiIuI9+rbX5qIiIi1GaR68fQmkLABHAFz2Gpx9txYQiTSiiio3d7y3nte+3QfA7yf05tFL+uKwa55JwzV5Ef3FF1+kS5cuBAUFMXToUFasWNHULyktzOb0Qg7klRHkb2ds71ir40gjunhgI7d0qSqH+dPBcEO/y6DfpY3zvNIotmUWsbe6LdMFyXpzQ0TE29SsRN97qISySpfFaUREWrGCg/D6eDj4PQRFwnUfQf/LrU4l4lMKy6v41Wtr+GRzJv4OG89ePYjp53TDpjeq5BQ1aRH9/fff5+677+ahhx5i/fr1jB49mgkTJhyz07f4vppV6GOT4wjV6TI+ZfIAczXy6j15HCp2nv4TfvVnyN0JYXEw8enTfz5pVDVz+bxe7QhXWyYREa8TGx5Eu/BAPAakZBZbHUdEpHXK3Q2vXwR5uyAyCW5cCp3PsjqViE/JLXFyzSvfsWZ/PuFBfrx1wxlcMqi91bHEyzVpEf2ZZ57hxhtv5KabbiI5OZnZs2eTlJTESy+91JQvKy2Ix2PwSXXh7eIBav/ga5LahDAwKQqPAZ9uyTy9JzuwClZX9wKc8k9tpNPCHNPKZYDaMomIeKua1ejbtLmoiEjzy9xorkAvSoO2PeCGz6BdL6tTifiUjIJyrnx5Ndsyi4gJC+SDW0cyqluM1bHEBzRZEb2yspK1a9cybty4Y24fN24cq1ataqqXlRZm/cHDpBeUExrg4NxeauXii2reHFm08TSK6M4Ss40LBgy+DnqOb5xw0mg2pRVyML+cYH8HY5M1l0VEvJU2FxURsciB1fDmZCjLhYSBZgE9soPVqUR8yr7cUq6Ys5q9h0ppHxXMh9NHkpwQYXUs8RFNVkTPzc3F7XYTF3ds39y4uDiysk68CaHT6aSoqOiYi3i3hdWF1XF94wnyd1icRprCpOoi+g8H8sksLD+1J/n8D1BwwDydcfzjjZhOGsvCjeYq9LHJsYQEqC2TiIi36pdobi66RSvRRUSaz64v4N/TwFkEHUfB9QshVCtjRRrT9qwirpizmvSCcrrGhPLh9JF0iQm1Opb4kCbfWPSnDfsNw6izif8TTzxBZGRk7SUpKamp40kTcnsMFm82i+iT1crFZyVEBjO8czSGQW3rngbZ/QWsfcM8nvoiBOld4pbG4zH4pHYuq5WLiIg361tdRN+ZVUKV22NxGhGRVmDHZ/Dfa8BVDj3GwS/nmpuJikij2ZxWyFUvf0duiZM+CRF8MH0kiVHBVscSH9NkRfSYmBgcDsdxq85zcnKOW51eY9asWRQWFtZeDh482FTxpBms2ZdPTrGTiCA/RvdoZ3UcaUI1hdVFDS2ilx+Gj+8wj8+cDl3GNHIyaQzrUg+TWVhBWKAf5/bSXBYR8WZJbYIJD/Kj0u1hV3aJ1XFERHzbjs/g/V+CuxKSp8BV70JAiNWpRHzK5rRCrn31OwrLqxjSMYr3bhlBTFig1bHEBzVZET0gIIChQ4eydOnSY25funQpo0aNOuFjAgMDiYiIOOYi3qtmE8KL+sUT4NfkJz2IhSb0j8dugw0HCziYX1b/B376OyjOgDbdYOzDTRdQTkvNmyMX9olTWyYRES9ns9nok1DTF10tXUREmsyOT80CuqcK+kyFy18HvwCrU4n4lJoCelGFi2Gdonn7xjOJDPa3Opb4qCatbM6cOZNXX32V119/nZSUFO655x5SU1OZPn16U76stAAut4dPt5hnIaj9g++LDQ9iRNe2ALVtP37WtgWw6X2w2WHaHK3IaKHcR7VyuXig2jKJiPiCfu3NNgLaXFREpIlsXwzvX2cW0PtOg8teA4cKeyKN6acF9DdvOIOwQO3fJU2nSb+6rrrqKvLy8nj00UfJzMykX79+LF68mE6dOjXly0oLsGpPHvmllbQJDWBUt7ZWx5FmMHlAIqv25LFwYwbTz+l28sElh2DRPebxWXdB0hlNH1BOyff78jhU7CQy2J+zu6uVi4iIL+ibqJXoIiJNZvti+OBX1QX0S+HSf4FDhT2RxqQCulihyXtszJgxg/379+N0Olm7di1jxqjncWtwdCsXP4daubQGF/WLx2G3sTWjiH25pXUPNAxYdDeU5UJsXzh3VrNllIZbuNFchX5RX7VlEhHxFTWbi27LKMLjMSxOIyLiQ3Z/caSA3u8yFdBFmsDWjCMF9KEqoEszUkVEGl2ly8Nn1a1cLlYrl1ajTWgAZ3ePAWDRxoy6B276ALYvAru/2cbFTxt+tFRVbg+fbalp5aK5LCLiK7q1CyXAz05ppZvUhuxlIiIidTuwCv5b0wP9Epj2igroIo1sz6ESfvXamtoC+lsqoEszUhFdGt2KXYcoqnDRLjyQM7q0sTqONKPJA8ye2TUbUR6nMB0+vd88Pvd3kDCgmZLJqVi5O5fDZVW0DQ1gRFfNZRERX+HnsNM7PhyAbZnqiy4ictrS18G7V4KrHHqMg0tfVQFdpJGlHS7jl69+T15pJf3aR/DGb4argC7NSkV0aXQ1BdRJ/RNw2G0Wp5HmNK5vPAEOOzuyi9mZXXzsnYYBC+6AikJoPxTOuseakFJvNXN5Yv8EtWUSEfExfRLMvujbtLmoiMjpyUmBdy6DymLodDZc+Tb4BVidSsSnHCp28stXvyezsIJu7UJ56zdnEBGkzXqleakqIo2qosrN0m3ZAFw8MMHiNNLcIoP9GdOzjpYua9+APV+CXxBMnaOVGS2c0+VmyVazLVPNGQYiIuI7+lRvLqqV6CIipyFvD7x9CZTnmwuFfvFf8A+2OpWITyksq+K6175nf14ZHaKDefemEbQNU1tYaX4qokujWr4jhxKni8TIIAYnRVsdRyxQ0zt74aZMDKN6s7L8vbDkD+bx2IehXU+L0kl9fbMzl+IKF3ERgQzvrFYuIiK+RivRRUROU3EW/HsqlGRDbF+49n8QGG51KhGfUup08es317A9q5h24YG8c+OZxEcGWR1LWikV0aVRLaxp5TIgAbtaubRKFyTHEeRvZ19uKVszisDjho9+C1Wl5umNZ063OqLUw6JN5pkEk/onai6LiPig3gkR2GyQVVRBXonT6jgiIt6logjevRwKUiG6C1w3H0K08ESkMbncHm7/zzrWpxYQFeLPOzeeSeeYUKtjSSumIro0mlKniy9Talq5JFqcRqwSGujH2N5xACzcmAHfvQSpqyAgDKa+AHZ922npyivVlklExNeFBfrRua35h6hauoiINICrEj64DrI2Q2g7uG4ehMdZnUrEpxiGwUPzt7BsxyGC/O28/uvh9IrXmR5iLVWzpNF8kZJNRZWHzm1D6N8+0uo4YqGawuuWDWswvnzUvHHcnyG6s3WhpN6W7cihrNJNh+hgBiVFWR1HRESaiFq6iIg0kMcDH/8W9i4H/1D4xQfQpqvVqUR8zrNf7uL9Hw9it8Hz1wxhSEe1CxbrqYgujWZh9UaSFw9MxGZT+4fW7NxesUQFwgMVs7G5ndD9Qhj6a6tjST0t2GDO5ckDNJdFRHyZNhcVEWmgLx+BzR+AzQFXvg3th1idSMTnvP9DKrO/2AXAY1P7cUEfnekhLYOK6NIoCsuq+HrnIUCtXASC/B38td1SBtr3Uu4Ihyn/BBVjvUJxRRVf7cgBYIrmsoiIT9NKdBGRBvhuDqx81jye8k/ocYG1eUR80LLtOTw4fwsAt5/XnWvP7GRxIpEjVESXRrFkaxZVboPe8eH0jFOfqlYvYwPj8v4NwJ+NG3GHxVscSOrr863ZVLo8dGsXSnKC5rKIiC/rW70Sfc+hEiqq3BanERFpwVIWwWe/N4/P/z8YfK21eUR80Ka0Ama8uw63x+CyIR24d1xPqyOJHENFdGkUC45q5SKtXFUFzJ+O3XCxlDN5t2w43+/NszqV1FPNXJ4ysL1auYiI+Lh24YHEhAXgMWBHVrHVcUREWqbMjTDvZsCAYTfA6HutTiTiczIKyrnhzR8pr3IzukcMf72sv/4elRZHRXQ5bYeKnazakwvA5AEJFqcRyy1/HA6lQGg7vu/zEGBj4aYMq1NJPeSXVvLtbnMu12wOKyIivstms5Fc3dJlq1q6iIgcrygT/nM1VJVBt/NhwlNqUynSyEqdLm5860dyS5z0jg/npV8Oxd+hcqW0PPqqlNP26ZZMPAYMTIqiU9tQq+OIlVK/h5XPmceTZ3P+kL4AfLoli0qXx8JgUh+LN2fi9hj0ax9B13ZhVscREZFmcGRz0UKLk4iItDCVZfDe1VCcATG94Io3weFndSoRn+LxGNzz/gZSMouICQvg1euHERaoeSYtk4roctoW1rRy0Sr01q2yFD66DTBg4DWQPJkzu7YlJiyQgrIqVuw6ZHVC+Rm1bZkGqC2TiEhroc1FRUROwOOB+bdC5gYIbgO/eB+CIq1OJeJznvp8B59vyybAYefl64bRITrE6kgidVIRXU5LekE5P+w/jM0Gk1V4a92+eATy90BEe7jorwA47LbaFj81BVppmTILy/lhfz4Ak7W3gYhIq1Gzuej2rGLcHsPiNCIiLcSyv0DKAnAEwNX/gTZdrE4k4nPmrk3jpeV7APjb5QMY2ina4kQiJ6ciupyWT6p7XZ/RuQ3xkUEWpxHL7F0Oa14xj6f8E4Kjau+6ZJBZkF26LZuySlfzZ5N6+WRTJoYBwzpF0z4q2Oo4IiLSTLrEhBHkb6es0s2BvFKr44iIWG/j+7DiafP44ueg00hr84j4oB/25zNr3mYAbj+vO1MHt7c4kcjPUxFdTsvHG6rbP2jlautVUQgf324eD7sRuo895u5BSVF0bBNCWaWbL1JyLAgo9VHTlmnKIM1lEZHWxGG30Tu+pi+6WrqISCuXvg4W3GEenz0TBl1jbR4RH5ReUM70f6+l0u1hQr94Zl7Y0+pIIvWiIrqcst05xWzNKMLPbmNSf/VDb7U+exAKD0J0F7jw0ePuttlsTKl+k2XBhvTmTif1cCCvlI1phdhtMFFzWUSk1anZXHSr+qKLSGtWcgjevw7cTug5Ac7/P6sTificiio30/+9lrzSSvomRvD3Kwdit9usjiVSLyqiyylbUL0K/Zye7YgODbA4jVhix6ew4R3ABlNfgsCwEw6raeny9c5DFJRVNmNAqY+aM0rO6h5DTFigxWlERKS51WwuqiK6iLRa7ir48NdQlAZtu8OlL4Nd5RKRxmQYBg/N38Lm9ELahAbw8nVDCQnwszqWSL3pp4KcEsMw+GiD2j+0amX5sOBO83jU7SftFdgjLpzkhAiq3AafbslqpoBSH+ZcNs8QuGSQ+tCJiLRGNSvRU9TORURaq8//Dw58CwHh5kaiQZFWJxLxOf/+7gBz16Vht8Hz1wymQ3SI1ZFEGkRFdDklGw4WkJpfRkiAgwv7xFkdR6zwyUwozYF2veG8P/zs8JqWLh+rpUuLsjWjiL2HSgn0szO+r+aywIsvvkiXLl0ICgpi6NChrFixos6xy5cvx2azHXfZvn17MyYWkdPVOz4cmw0OFTs5VOy0Oo6ISPPa+F/4/iXzeNocaNfL2jwiPmjNvnweXbgNgFkTkhnVPcbiRCINpyK6nJKa9g/j+sTp9JvWaMtc2DofbA7zF03/oJ99yMUDzV7b3+/LJ7OwvKkTSj19tN58U+OC5DjCg/wtTiNWe//997n77rt56KGHWL9+PaNHj2bChAmkpqae9HE7duwgMzOz9tKjR49mSiwijSEkwI8ubUMBrUYXkVYmYz0svMs8HvMAJE+2No+ID8oqrGDGu+tweQwuHpjITaO7WB1J5JSoiC4N5nJ7WLQpE1D7h1apOAs+udc8HnM/JA6u18M6RIcwvHM0hgGLNmY2YUCpL7fHYMFG8w2xS9SWSYBnnnmGG2+8kZtuuonk5GRmz55NUlISL7300kkfFxsbS3x8fO3F4XA0U2IRaSzJCWrpIiKtTGmeuZGoqwJ6XgTnzrI6kYjPcbrcTH9nLbklTnrHh/PkZf2x2bSRqHgnFdGlwVbtySO3xEl0iD9n99ApOK2KYZh90MsPQ8JAGHNfgx4+pfpNl483qqVLS/D93jxyip1EBPlxTq92VscRi1VWVrJ27VrGjRt3zO3jxo1j1apVJ33s4MGDSUhIYOzYsSxbtqwpY4pIE1FfdBFpVTwemHczFB6ENt1gmjYSFWkKjy3axoaDBUQG+2sjUfF6+ikhDVbTymXSgAT8HfoSalXWvwO7loAjwPxF09Gw9h8T+8XjsNvYkl7E7pySJgop9VWzoeikAQkE+mnlcEtQXFxs2Wvn5ubidruJizu2N35cXBxZWSfeEDghIYFXXnmFuXPnMm/ePHr16sXYsWP55ptv6nwdp9NJUVHRMRcRsV5yQjgA21REF5HW4Nu/w54vwS8IrnwbgqOsTiTicz7ekM4736Vis8GzVw+iU3XrOBFvpQqoNEhFlZslW81iilq5tDKHD8Bn1ac4nv8HiE1u8FO0DQtkTPXZC9pg1FoVVW4+3ay53NKMHj26zoJ1c/np6ZWGYdR5ymWvXr24+eabGTJkCCNHjuTFF19k0qRJPP3003U+/xNPPEFkZGTtJSkpqVHzi8ip6ZMQCcCeQ6VUVLktTiMi0oT2fQPLHjePJ/0d4vtZm0fEB+3OKWHWvM0A3H5ed87tFWtxIpHTpyK6NMhX23MocbpoHxXM0I7RVseR5uLxwMe/hcpiSBoBI28/5aeaOtgs2M5fn47HYzRWQmmg5TtyKHa6SIgM4ozObayOI9WGDRvGmWeeyfbt24+5ff369UycOLFJXzsmJgaHw3FcET8nJ+e41eknM2LECHbt2lXn/bNmzaKwsLD2cvDgwVPOLCKNJy4ikOgQf9weg13ZOltMRHxUcRb870YwPDDoWhj8S6sTific8ko3v313HWWVbkZ2bcvdF/S0OpJIo1ARXRpk3jpz9fCUQYnY7doMotVY8wrsXwH+ITD1RbCfeuuPcX3iCQ1wkHa4nLWphxsxpDTER+vNtkxTBmouW2Xr1q24XK5jbnv11Ve54YYbOPvss/n222/ZuXMnV155JcOGDSMwMLBJ8wQEBDB06FCWLl16zO1Lly5l1KhR9X6e9evXk5CQUOf9gYGBREREHHMREevZbDb1RRcR3+Z2mQX00hyI7QsT6z5zTkRO3cMLtrAju5iYsECevWYQDv29KT5CHf2l3vJLK1m+IweASwer/UOrkbsbvnjEPB73GLTtdlpPFxzg4KJ+Ccxdl8b89ekM1yroZldYXsVX1XNZrVysM2LECDZu3EjXrl2Puf3hhx8mICCACy+8ELfbzfjx4/nhhx8YMmRIk2eaOXMm1113HcOGDWPkyJG88sorpKamMn36dMBcRZ6ens7bb78NwOzZs+ncuTN9+/alsrKSd955h7lz5zJ37twmzyoijS85PoKVu/PUF11EfNPyx+HAtxAQBle+BQEhVicS8Tn/W5vGBz+mYbfBc9cMIjY8yOpIIo1GRXSpt0WbMnB5DPq1j6BHXLjVcaQ5uF3w0XRwlUPX82DYjY3ytJcOac/cdWl8simThy/uo00tm9mnmzOpdHnoERtWu5GcNL9t27aRmJh4zG2ZmZk88cQTvPrqq/Tp04ft27dz9dVXN0sBHeCqq64iLy+PRx99lMzMTPr168fixYvp1KlTbb7U1NTa8ZWVldx3332kp6cTHBxM3759+eSTT5q89YyINI2alegqoouIz9n5Oaz4u3k85TmI6WFtHhEftCOrmD98ZPZBv+eCnozqFmNxIpHGpSK61Nvc6lYu0wZ3sDiJNJtVz0LaDxAYCZc8D3VsLthQI7q2JS4ikOwiJ8u2H+KifvGN8rxSPzVtmS4d0qHODSOl6Z1oQ82uXbvSu3dvPvzwQyZNmsSSJUu48sorSUtL43e/+12z5JoxYwYzZsw44X1vvvnmMdcfeOABHnjggWZIJSLNITnhSDuXk20qLCLiVYoyYP6t5vHwm6HfZdbmEfFBpU4XM95dS0WVhzE92/Hb87pbHUmk0aknutTLnkMlbDxYgMNuY8rAxJ9/gHi/rC2w7AnzeMKTENl4b5447DamDqrZYDSt0Z5Xfl5qXhlr9udjs8HUwZrLLc0bb7zB+vXrmTRpEgDjx49n2bJlPPvss3UWtkVEGku3dmH4O2wUV7hIO1xudRwRkdPnccO8W6A8HxIGwvi/WJ1IxCc9vGArew6VEh8RxD+uHKh9t8QnqYgu9fLRenPl6ugeMbQLb9rN7aQFcFXC/OngqYJek2Dg1Y3+ElOr++ov236IgrLKRn9+ObH51XP5rG4xJEQGW5xGfurqq4+fa0OGDGHVqlUsX768+QOJSKsS4GenR6zZ5kstXUTEJ3z7D9i/AvxD4fI3wE9/y4o0tgUbM/jfWrMP+rNXD6JtmOaZ+CYV0eVneTxGbeFtmjYUbR2+fhKyN0NIW7h4dqO1cTlackIEvePDqXR7+GRzZqM/vxzPMAzmVa/8v3SI5rI36dy5MytXrrQ6hoi0Ake3dBER8WoH18Cyx83jSU9D227W5hHxQQfzy3hontkH/fbze3Bm17YWJxJpOiqiy8/68cBh0g6XExbox7g+6l3t89LWwrfPmMeTnoGw2CZ7qZo3ZWrOdJCmtS61gAN5ZYQEOBjfV3PZ20RHR1sdQURagZrNRVVEFxGvVlEIc28Eww39r4CB11idSMTnuNwe7vrveoqdLoZ2iubO89UHXXybiujys2p6Vk/oF09wgMPiNNKkqsrNTXcMD/S7HPpObdKXmzIoEZsNfth/mNS8siZ9LYF568y5fFG/eEIDta+0iIgcLzlB7VxExMsZBiy8GwpSIaqTuTBIGyWLNLpnv9zFutQCwoP8mH3VIPwcKjGKb9NXuJxURZWbRZvMVhvT1P7B9335KOTtgrB4mPhUk79cQmQwZ3ePAeB/67TBaFNyutws3JgBwGVDGm+TWBER8S19qtu5HMwvp6iiyuI0IiKnYMO7sHUe2P3g8tchKMLqRCI+57u9eTy/bDcAj0/rT1KbEIsTiTQ9FdHlpL5MyaG4wkViZBAjuqi3lU/btwK+e9E8nvJPCGnTLC97+VCzoDt3bRoej9Esr9kafZWSQ1GFi4TIIEaoT12LtnLlSpxO53HHIiLNISokgMTIIAC2ZxZbnEZEpIFyd8Hi+83j8x6CDsOszSPigwrKKrnn/Q0YBlwxtAMXD0y0OpJIs1ARXU7qw7UHAZg6uD12u06B81nOYvh4hnk85HroOa7ZXnpcn3jCA/1ILyjnu315zfa6rc3cdWbf+amD2+PQXG7RJkyYQHp6+nHHIiLNRX3RRcQruZzwvxugqgy6nANn3W11IhGfYxgGv5u7iczCCrrGhPLIlL5WRxJpNiqiS52yCiv4ZuchAK4YlmRxGmlSSx6q7hnYEcb/pVlfOjjAweTqd67/t1YtXZpCXomT5TtyALh0sNoytXSGYZzwWESkuSRXt3TZlqEiuoh4kWWPQ9YmCG4D014Gu8odIo3tvTUHWbI1G3+HjeeuGay9tqRV0U8VqdO89Wl4DBjeOZouMaFWx5GmsmsprHvLPL7kRQgMb/YINS1dPt2cRYnT1eyv7+vmr0/H5TEY0CGSHnHN//8rIiLepaaInpKlIrqIeIkDq2Dls+bxlH9CRIK1eUR80P7cUh5btA2A+8f3ol/7SIsTiTQvFdHlhAzD4MMfzVXBWoXuw8ry4ePbzeMzb4Muoy2JMaRjFF3bhVJe5WZx9Ua20jgMw+CDH822TFdqLouISD3UbC66I6sYl9tjcRoRkZ9RUQTzbwUMGPRLSJ5sdSIRn+Nye5j5wQbKq9yM7NqWm87uanUkkWanIrqc0NoDh9mXW0pIgINJ/fUuvs/69AEoyYK2PeCChy2LYbPZalejq6VL49qYVsjO7BIC/exMGaQNX0RE5Od1bBNCaIADp8vD/rxSq+OIiJzckllHWlNe9ITVaUR80pyv97AutYDwQD+evnKg9syTVklFdDmhmlXoE/snqMeVr9r6EWz+EGx2mDYH/IMtjXPp4A7YbbBmfz77c/UHe2OpWYU+sX8CEUH+FqcRERFvYLfb6BVvtv/alllscRoRkZNIWQTr3wFsZh/0oAirE4n4nC3phcz+YhcAj0zpS/soa2sHIlZREV2OU1bpYtGmDEDtH3xWSQ4susc8PnsmdBhmbR4gPjKI0T3aATB3nVajN4bySjcLN5hz+YphHSxOIyIi3kSbi4pIi1eSAwvvNI/Pugs6jbI2j4gPqqhyc8/7G3B5DC7qG8+lQ9pbHUnEMiqiy3EWb86itNJN57YhDO8cbXUcaWyGAQvvhvJ8iOsP5/zO6kS1alq6zF2bhttjWJzG+326JZNip4uObUIY0aWt1XFERMSL1G4umqkiuogvevHFF+nSpQtBQUEMHTqUFStWnHT8119/zdChQwkKCqJr167MmTOnmZLWwTBgwR1Qlgdx/eC8B63NI+Kjnlqyg105JcSEBfL4pf2x2dTGRVovFdHlOB9Wt3+4fGgHfYP0RRv/Czs+Abu/2cbFL8DqRLUu7BNHZLA/GYUVrNh1yOo4Xq+mlcsVQzuoZ50XefDBB2nTps1xxyIizUlFdBHf9f7773P33Xfz0EMPsX79ekaPHs2ECRNITU094fh9+/YxceJERo8ezfr163nwwQe58847mTt3bjMnP8q6t2DnZ+AIgEtfAb9A67KI+KhVe3J57dt9APzt8v60CW05tQMRK6iILsc4kFfK9/vysdngsqFq/+BzCtPMzUQBzv09xPezNs9PBPk7ak8Pe2/NiX+Jl/o5kFfKd3s1l73RrFmziIqKOu5YRKQ59Y4Px2aDnGIneSVOq+OI+JyRI0dSVGTNm1TPPPMMN954IzfddBPJycnMnj2bpKQkXnrppROOnzNnDh07dmT27NkkJydz0003ccMNN/D00083c/Jq+Xvhs+qV52P/CHF9rckh4sOKKqq474ONAFxzRkfO7x1ncSIR66mILsf47w/mytUxPdqREKnNInyKYcDHvwVnEXQYDmfdbXWiE7rmjI4AfJGSQ05RhcVpvFfN5sBjerQjURu/iIhIA4UG+tGpTQgAKdpcVKTRff/991RUHP+7blFREffff3+TvW5lZSVr165l3Lhxx9w+btw4Vq1adcLHrF69+rjx48eP58cff6SqquqEj3E6nRQVFR1zaRRuF8y7FapKodPZMOK3jfO8InKMRxZsJaOwgk5tQ/jDpGSr44i0CCqiS61Kl6e2lUtNIVN8yA+vwt7l4BcMU+eAw8/qRCfUMy6coZ2icXsMPlyrDUZPhcvt4X/VnzttDiwiIqdKLV1EGt+ll17KX//6V2w2Gzk5OcfdX1payjPPPNNkr5+bm4vb7SYu7thVpXFxcWRlZZ3wMVlZWScc73K5yM3NPeFjnnjiCSIjI2svSUmN9Dvpjk8gbQ0EhMO0l8CukoZIY/tsSybz1qVjt8EzVw4kNLBl1g5EmptmgtRaui2b3JJKYsMDGZsca3UcaUx5e2DpH83jCx6BmO6Wxvk515zRkbUHDvPfH1K57Zxu6ufdQMt2HCKrqILoEH8u6KO5LCIipyY5IYJPt2SpiC7SiDp16sSiRYswDIOBAwfStm1bBg4cyMCBAxkwYACbNm0iISGhyXP8dO8rwzBOuh/Wicaf6PYas2bNYubMmbXXi4qKGqeQnjwFLv0X2OwQpYVfIo0tr8TJQ/O3ADD9nG4M7aT9mURqqIgutf6z5gAAVw1Pwt+hd/R9hscNH82AqjLoPBrOuMXqRD9rUv8E/rRwKwfzy1m5J5fRPdpZHcmrvPu9OZevHJZEoJ/D4jTSUFVVVWRlZVFWVka7du20saiIWKZmJfo2FdFFGs0//vEPAAIDA/n222/JyMhg/fr1bNiwgfnz5+PxePjb3/7WZK8fExODw+E4btV5Tk7OcavNa8THx59wvJ+fH23btj3hYwIDAwkMbILNPm02GHBl4z+viADwxwVbySutpFdcOHdd0MPqOCItioroAsD+3FJW7s7DZjOL6OJDVj8PB78zT3m85AWvOOUxOMDBtMHteXv1Af675qCK6A1wML+Mr3ceAtSWyZuUlJTw7rvv8t5777FmzRqcziOb+HXo0IFx48Zxyy23MHz4cAtTikhr0yfRLKLvOVRCpctDgF/L/x1CxFuUlpbi52f+OX7JJZc02+sGBAQwdOhQli5dyrRp02pvX7p0aZ05Ro4cycKFC4+57fPPP2fYsGH4+/s3aV4RaT6LN2fyyaZMHHYbT18xUAuyRH5CvwkLAO+tSQXg3J7t6BAdYnEaaTQ5KfDVn83jix6H6E7W5mmAq4ebBeAlW7M4VOz8mdFS4z9rUjEMGN0jhs4xoVbHkXr4xz/+QefOnfnXv/7F+eefz7x589iwYQM7duxg9erVPPzww7hcLi688EIuuugidu3aZXVkEWklEiODiAjyo8ptsDunxOo4Ij6lpoBuhZkzZ/Lqq6/y+uuvk5KSwj333ENqairTp08HzFYsv/rVr2rHT58+nQMHDjBz5kxSUlJ4/fXXee2117jvvvus+ieISCPLK3Hyfx+ZbVxuO6cb/TtEWpxIpOXRSnTB6XLXbuD4izO9p8gqP8NdBfNvBXcl9BgPg6+zOlGD9EmMYFBSFBsOFjB3XRrTz+lmdaQWr9Ll4YMfzM2Br9Vc9hqrVq1i2bJl9O/f/4T3n3HGGdxwww3MmTOH1157ja+//poePXRqpYg0PZvNRnJCBN/vyycls6h2ZbqIeLerrrqKvLw8Hn30UTIzM+nXrx+LFy+mUyfz98fMzExSU1Nrx3fp0oXFixdzzz338MILL5CYmMhzzz3HZZddZtU/QUQa2dFtXO4Y27L3UBOxiorowpKt2eSXVhIfEcR5vdQ2w2d88zRkboSgKJjynNk/0Mtcc0YSGw4W8N81qdwyuqs2GP0ZS7ZmkVdaSVyENgf2Jh9++GHtcXFxMeHh4SccFxgYyIwZM5orlogIwDFFdBHxHTNmzKjz94o333zzuNvOOecc1q1b18SpRMQKauMiUj9q5yL85/sjG4r6aUNR35CxHr55yjye/AyEx1ub5xRdPDCR8CA/9ueV8fWuQ1bHafHerZ3LHbU5sJcaPXr0cRt3iYhYqY82FxUREfFZauMiUn+qsrRyu3OK+W5vPnYbXH2GNhT1CVUVMH86GG7oOw36ee9pliEBflwx1Py6fGvVfmvDtHBHz+VrNJe91rBhwzjzzDPZvn37MbevX7+eiRMnWpRKRFqz5OoiekpmEYZhWJxGREREGpPauIjUn4rordyb1YXJsclxJEQGWxtGGseyP8Oh7RAaCxP/bnWa0/arkZ2w2WD5jkPsyy21Ok6L9e73Zt9KzWXv9uqrr3LDDTdw9tln8+2337Jz506uvPJKhg0bRmBgoNXxRKQV6hEXhsNu43BZFdlF2uhbRETEV6iNi0jDqIjeihWWVzF3bToAvzmrs7VhpHEcWA2rnjePpzwHoW2tzdMIOseEcm5Ps1f/26v3WxumhSp1uphbvTnwtWd2tDiNnK6HH36Ye++9lwsvvJB+/fpRXl7ODz/8wPz5862OJiKtUJC/g64xoQDqiy4iIuIj1MZFpOFURG/FPvjhIOVVbnrHhzOyq/cXW1s9Zwl8NB0wYNAvodcEqxM1mutHdQbgfz+mUep0WRumBZq7Lo2iChed24Ywpoc2B/ZmmZmZ3HnnnTz22GP06dMHf39/rr76aoYMGWJ1NBFpxZLVF11ERMSnqI2LSMOpiN5KuT0Gb1Wv6v31qM7YbDZrA8npW/pHOLwfIpPgosetTtOoxvRoR5eYUIqdLuatT7c6Tovi8Ri8sXI/AL85qwt2u+ayN+vatSsrVqzgww8/ZO3atcybN48ZM2bw5JNPWh1NRFqxo/uii4iIiHdTGxeRU6Mieiv1RUo2aYfLiQrxZ+rg9lbHkdO1+0v48TXz+JLnIci3TsWy2238amQnAN5etV8bmx1l2Y4c9uWWEh7kx+VDO1gdR07TG2+8wfr165k0aRIA48ePZ9myZTz77LPMmDHD4nQi0lolJ4QDKqKLiIh4u8OllfzxY7VxETkVKqK3Um9Wr1y95oyOBPnrXUevVl4AC+4wj8+4Bbqea2WaJnPZ0A6EBDjYlVPCqj15VsdpMV5fuQ8w53JooJ/FaeR0XX311cfdNmTIEFatWsXy5cubP5CICNCneiX6vtxSKqrcFqcRERGRU/XnT1LILamke2yY2riINJCK6K1QSmYRq/fm4bDbuG5EJ6vjyOn67PdQlA5tusIFj1idpslEBPlz2RBzpXVN+5LWbntWESt352G3UbtSX3xT586dWblypdUxRKSVahceSNvQADwG7MgqtjqOiIiInIJvdh5i7ro0bDZ48rIBauMi0kCtpoju8Rgs2ZpFRkG51VEs99aq/QBc1DeexKhga8PI6UlZBBvfA5sdps6BgFCrEzWpmg1Gv9yeze6cEmvDtACvf2uuQp/QL4EO0SEWp5FTlZqaWq9x0dHRAKSna18AEWleNpuNPonqiy4iIuKtSp0uZs3bDMD1IzsztFO0xYlEvE+rKaLPmreZW/+9ln+t2Gt1FEvllTiZX70x42/O6mxtGDk9pbmw6G7zeNSd0PFMS+M0h+6xYVyQHIdhwKutfC7nljj5aEMGADec3dnaMHJahg8fzs0338yaNWvqHFNYWMi//vUv+vXrx7x585oxnYiISZuLioiIeK+nP99BekE57aOCuX98L6vjiHilVtNAd/LABN7/8SD/XXOQO87vQZvQAKsjWeKNlftxujwM7BCpdx69mWHAonug9BC0S4bzHrQ6UbO57dyufJGSzbx16cy8sCexEUFWR7LEu9+lUlk9l4d01Fz2ZikpKTz++ONcdNFF+Pv7M2zYMBITEwkKCuLw4cNs27aNrVu3MmzYMJ566ikmTJhgdWQRaYVqNhfdpiK6iIiIV1mXepg3qzsSPH5pf+2lJXKKWs1K9LO7x9C/fSTlVW7erN6Ir7UprqjirdX7Abjt3O7YbDZrA8mp2/w/SFkAdj+YNgf8Aq1O1GyGdmrDsE7RVLo9vN5Ke6OXV7r593f7Abjh7C6ay16uTZs2PPLII2RkZPDSSy/Rs2dPcnNz2bVrFwDXXnsta9euZeXKlSqgi4hlalaib88sxjAMi9OIiIhIfThdbn73v00YBlw6pD3n9GxndSQRr9Vq3n6y2Wzcdm43Zry7jrdWH+CWc7oR1sreffvP96kUV7jo1i6UcX3irI4jp6ooExbfax6PeQASB1kaxwq3ntONH9/+kXe/O8CM87oREeRvdaRm9d8fUsktqaRDdDAT+ydYHUcaQXR0NJmZmVx66aVceumlVscRETlOt3ZhBDjsFDtdpB0uJ6mN9uIQERFp6V5ctoddOSW0DQ3g/yb1sTqOiFdrNSvRAcb3jadrTCiF5VW89339NnLzFRVVbl6t3oRw+jndsNu1ctUrGQYsuB0qCiFxMIyeaXUiS4ztHUv32DCKna5WN5crXR5e+cbsBz/9nG74O1rVt3Gf5Xa78Xg8tdfPOusssrOzLUwkInIsf4ed7rFhgFq6iIiIeIMdWcW8uHw3AI9M6Ut0K21rLNJYWlX1xWG3Mf2cbgC8+u1enC63xYmaz9x1aRwqdpIQGcQlg9pbHUdO1bq3YPcX4AiEqXPA0bpWYNew223cMqYrAK+v3Neq5vK8dWlkFlYQGx7I5UM7WB1HmsimTZsoLS21OoaIyDG0uaiIiIh3cHsMfjd3E1VugwuS45g8QGcwi5yuVlVEB5g6uD3xEUFkFzmZvy7d6jjNwuX28PLX5srVm0d3JcCv1f23+4bD+2HJQ+bx2D9CbG9L41jtkkGJxEUEkl3k5OP1GVbHaRYut4eXvt4DwC1juhLk77A4kYiItCY1m4uqiC4iItKyvblqPxsOFhAe6Mefp/bTPloijaDVVVMD/OzcNLoLAC9/sxe3x/c3Rlq8JYvU/DKiQ/y5+owkq+PIqfB44KPfQmUJdBwFI26zOpHlAv0c3Hi2OZdfXL4bl9vzM4/wfp9szuRAnjmXf3FmR6vjSCP7z3/+w7p166iqqgLQL7oi0uL0qV2JXmxxEhEREanLwfwynl6yA4DfT+xNfGSQxYlEfEOrK6IDXHNGR6JC/NmXW8rizZlWx2lSHo/BS8vNlau/HtWFkIDWtZmqz/h+Dhz4FvxDYeqLYNcKZIBrz+xEm9AA9ueVMW+9b59Z4vEYvLDM7Gd3w1may77m7LPP5uGHH2bYsGGEhYVRVlbGQw89xEsvvcT3339PRUWF1RFFRGrbuaTml1FcUWVxGhEREfkpwzCYNW8z5VVuzuzShmuGa/GVSGNplUX00EA/fjPKXME6+4udPr2C9dMtWaRkFhEa4OD6UZ2sjiOn4tBO+PJP5vG4x6BNF2vztCChgX5MP8fsjf7cl7uodPnuXF6aks3O7BLCA/341ajOVseRRvbNN99QWFjIjh07eOutt7j33nvJzs7moYceYuTIkURERDBgwACrY4pIKxcdGkB8hLmabUeWVqOLiIi0NP9bm8a3u3MJ9LPz18sGYLfr7FaRxtIqi+gAN5zdmagQf/YcKmW+j65gdbk9/H2peQrPTaO7EhWinZi9jtsFH00HVwV0Ox+G3WB1ohbnuhGdaRceSNrhcj748aDVcZqEx2Pw3Je7ALhuZCcig1vnhrKtQY8ePbj66qv529/+xpdffkl+fj579uzh3XffZfLkyVbHExFRX3QREZEW6lCxkz9/kgLA3Rf0pEtMqMWJRHxLqy2ihwf5M+PcbgDM/mIXTpfb4kSNb966dPYeKiU6xL+2D7x4mZX/gPS1EBgJU54H9Ug+TnCAo3YuP//VbiqqfG8uL9yUwdaMIsIC/bhpdFer40gz69KlC1dccQWPP/641VFERGpbumxTX3QREZEW5ZEFWyksr6Jf+whuVg1IpNG12iI6wK9GdiYuIpD0gnLe+z7V6jiNyulyM/uLnQDMOLc74UFauep1MjfB8ifN44lPQWR7a/O0YNec0ZGEyCCyiip4b41vzeVKl4e/f27O5VvHdKVNqM4oERER6yTXbi6qlegiIiItxZKtWXyyOROH3caTlw3Az9Gqy30iTaJVz6ogfwd3nN8DgOeX7aas0mVxosbzn+9TySisID4iiOtGqhe613E54aPbwFMFvSfDgCutTtSiBfk7uP387gC8sGwP5ZW+sxr9vTWppOaXERMWyI1aTSAiIharKaJvzyrC7TEsTiMiIiKF5VX830dbALhlTFf6JkZanEjEN7XqIjrAVcOT6NgmhNySSt5Yud/qOI2i1OnihWW7AbhzbA+C/B0WJ5IGW/5XyN4CIW1h8my1camHK4Ym0SE6mNwSJ2+v3m91nEZR4nTxz6/MXuh3XdCDkAA/ixOJiEhr1yUmlCB/OxVVHvbnlVodR0REpNX766cp5BQ76RoTyl1je1gdR8Rntfoiur/DzswLewLw8td7KCyrsjjR6Xtz1X5ySyrp1DaEK4Z1sDqONNTBH2DlbPN48mwIa2dlGq8R4Gfn7gvMufz8V7vJLXFanOj0vbpiL7kllXRuG8LVw5OsjiMiIoLDbqNXnDYXFRERaQlW7cnlvTUHAXji0v5aRCnShFp9ER3g4oGJ9IoLp6jCxbNf7rI6zmnJKargpeV7AJh5YU/81QfLu1SWwUfTwfDAgKugzxSrE3mVSwe3p3/7SIqdLp5essPqOKclt8TJv77ZC8D943trLouISIuhvugiIiLWK690M2veZgCuPbMjZ3Zta3EiEd+mqgzmipoHJyUD8Nbq/WzP8t4/CJ74dDslThcDk6K4eECi1XGkob78E+TthvAEmPCk1Wm8jt1u45EpfQB4/8eDbE4rtDjRqXv2i12UVroZ0CGSif3jrY4jIiJS60gRvdjiJCIiIq3X7C92ciCvjITIIH4/obfVcUR8noro1c7p2Y7xfeNwewz++PFWDMP7Nkpasy+f+evTsdngsUv6Yrerj7ZX2fcNfD/HPJ7yPARHW5vHSw3t1IZLBiViGPCnhd45lzelFfDO9wcAmDUhGZt64ouISAvSJ1Er0UVERKy0Ka2Af60wz1z+89R+hAf5W5xIxPepiH6U/5vchyB/O2v25bNgY4bVcRrE5fbwx4/N3ZivHt6RAR2irA0kDVNRBB/91jwe+hvocYG1ebzc7yf0JtjfwY8HDnvdXHZ7DB6cvxnDgGmD2zOym07JExGRlqV3vNkTPbOwgsOllRanERERaV2q3B5+N3czHsNsTzw2Oc7qSCKtgoroR+kQHcLt53UH4C+fpFBc4T2bjP77uwNszyomKsSfB8b3sjqONNSSB6EwFaI6wbjHrE7j9RIig/nted0AeGLxdsoqXRYnqr9/r97PlvQiIoL8eHBistVxREREjhMe5E9Sm2BAq9FFRESa2yvf7CUls4ioEH8evriP1XFEWg0V0X/i5jFd6dw2hJxiJ895ySajh4qdPPP5TgDuH9+L6NAAixNJg+xcAuv/Ddhg6ksQGG51Ip9w0+iudIgOJquogme/8I65nF1UwdPVc/mBi3rTLjzQ4kQiIiIn1qe6L/oPuzPZv38/ubm5XtlCTURExJvsOVTCs9W1qj9O7kNMmP5mFGkuKqL/RKCfg4en9AXg9ZX7vWJ1zeOLUyh2uujfPpKrh3e0Oo40RFk+LLjDPB75W+h8lrV5fEiQv4NHLjbn8r9W7GXtgXyLE/28xxZto8TpYlBSFL84Q3NZRERapoKCAgoPbAPgsX++QZcuXWjXrh09evTg2WefpaCgwNqAIiIiPsjjMZg1bzOVLg+je8QwbXB7qyOJtCoqop/Aeb1iazcZvef9DVRUua2OVKdPNmUyf306dhs8NrUfDm0m6l0W3wcl2RDTE87/g9VpfM4FfeK4dEh7PAbc+8HGFt3WZfmOHBZtysRug79M66eNgUVEpEVasmQJHTp0YOHb5mboAbFdau/bu3cv99xzDx06dGDJkiVWRRQREfFJ7/2Qypp9+YQEOHh8Wn9sNv3NKNKcVESvw1+m9ScmLIDtWcU8vWSH1XFOKKuwggfnbwZgxrndGZQUZW0gaZgt82DLXLA5YNoc8A+2OpFPevjivsRHBLE/r4y/fdYy53JuiZP7/7cJgF+P6kLfxEiLE0lr9uKLL9KlSxeCgoIYOnQoK1asOOn4r7/+mqFDhxIUFETXrl2ZM2dOMyUVkea2ZMkSJk2aRHl5Oc7sPQD4xySB3Q8AwzAwDIPy8nImTZqkQrqIiEgjySqs4K+LtwNw37heJLUJsTiRSOujInodYsICefKyAQC8+u0+Vu7OtTjRsTweg3s/3EBheRUDOkRy1wU9rI4kDVGcDZ/cax6PvhfaD7U2jw+LDPbnb5ebc/nNVftZ1QLn8n0fbuRQsZOecWHcr42BxULvv/8+d999Nw899BDr169n9OjRTJgwgdTU1BOO37dvHxMnTmT06NGsX7+eBx98kDvvvJO5c+c2c3IRaWoFBQVcdtllGIaBx+PBXZSDp6IEm8Mf/7ZJx4z1eDwYhsFll12m1i4iIiKnyTAM/vDRFoqrW39eP6qz1ZFEWiUV0U9ibHIc155p9iW+94ONFJRVWpzoiNdX7mPl7jyC/R3MvmoQ/g79V3oNw4CFd0F5PsQPgDH3W53I543p2a52Lt//v00UV1RZnOiI11fuY/mOQwT62fnnNUMIDnBYHUlasWeeeYYbb7yRm266ieTkZGbPnk1SUhIvvfTSCcfPmTOHjh07Mnv2bJKTk7npppu44YYbePrpp5s5uYg0tbfeeouysjI8Hk/tbZWH9gPHtnSp4fF4KCsr4+23326uiCIiIj5p8eYsvkjJxt9h48nLBqiNr4hF/KwO0NL9YVIfVu/NY++hUh6av4XnfzHY8r5T27OKattS/GFyMl3bhVmaRxpow39g56fgCDDbuPgFWJ2oVXhwYjLf7DrEwfxyZn6wkZd/OdTyvuOb0wp58jPzlLz/m9yHXvHhluaR1q2yspK1a9fy+9///pjbx40bx6pVq074mNWrVzNu3Lhjbhs/fjyvvfYaVVVV+Pv71z9AaSk4TvAmksMBQUHHjquL3Q7Bwac2tqzMfJPzRGw2CAk5tbHl5XBU0fE4oaGnNraiAtwn2bOlIWNDQszcAE4nuE6yf0RDxgYHm59ngMpKqDrJG5gNGRsUdORrpSFjq6rM8XUJDAQ/v4aPdbnMz0VdAgKgZi40ZKzbbf7f1cXf3xzf0LEej/m11oCxhmHw6rPPEmIYHPOVn7kLkvoRENuF0q3w0xPLbYbBv2bP5o4bbsDm729+3sCcP2VldWdoyLzX94gTj9X3iIaPrWven+zrRESkiRWUVfLwgi0A3HZud/3NKGIhLV/+GcEB5kpvP7uNTzZn8uqKfZbmyStxcuu/11Lp9jC2dyy/OKOjpXmkgQoOwmfVBarzHoS4vtbmaUVCA/147urBBPjZWbotm2eW7rQ0T4nTxR3vraPKbTChX3ztSnkRq+Tm5uJ2u4mLizvm9ri4OLKysk74mKysrBOOd7lc5OaeuHWS0+mkqKjomAsAiYkQFnb85bLLjn2C2NgTjwsLgwkTjh3buXPdY8eMOXZsnz51jx0+/Nixw4fXPbZPn2PHjhlT99jOnY8dO2FC3WNjY48de9lldY8N+8mb69ddd/KxRxczb7315GOP/n+dOfPkY49uA/TQQycfm5JyZOzjj5987Lp1R8Y+++zJxx7d0/+VV04+9uj+3e++e/Kx8+cfGTt//snHvvvukbFLlpx87CuvHBm7YsXJxz777JGx69adfOzjjx8Zm5Jy8rEPPXRkbGoqhIVhCw9n8759lAClR10e3WR+zvxjuxDzk/tKgRJg87592MLDza+tGmVlJ89w3XUc42Rj9T3CvOh7xJFLY3+PSExERMQqf/kkhdySSrrHhvHb87pZHUekVVMRvR4GdIjiwYnJAPxlcQqLN2dakqOiys3Nb//IgbwyOkQH8+TlAyxfFS8N4PHAx78FZxF0OANG3Wl1olZncMdo/nppfwCeX7abjzekW5Kj0uVhxrvr2J9XRvuoYP56qeaytBw//Vo0DOOkX58nGn+i22s88cQTREZG1l6SkpJOOE5EWj5PeTFw4nYuIiIicnq+3ZXLh2vTsNngycv6E+in1p8iVrIZRl3nGlqvqKiIyMhICgsLiYiIsDSLYRj8aeE23ly1nwA/O+/dfCZDO7Vpttf3eAzueG89n2zOJCLIj3kzRtE9VqfxeJU1/4LF94FfMNy2EtrqXWSr/PXT7cz5eg8BfnY+uHUkg5Kimu21PR6Dez7YwMcbMgj2d/DeLSOa9fWlcbWkn1Onq7KykpCQED788EOmTZtWe/tdd93Fhg0b+Prrr497zJgxYxg8eDDPHrUidv78+Vx55ZWUlZWdsJ2L0+nEeVQ7i6KiIpKSkijMyDjx51CtGk48Vq0aGj5W7VzM41No55Kbm0unn66KBtwOf+Jm/g+b3UHa878isDT/hE+ZeuAAbePi1M7lRGP1PcI8bsHfI4qKiohMTPSJn/VW8qXfmUSaQ1mli/Gzv+FgfjnXj+zEny7pZ3UkEZ9V359R6oleTzabjf+b3Ie0w2V8kZLDzW+vZd5to+gcE/rzD24Ef1uyg082Z+LvsPHydcNUQPc2eXtg6R/N4wsfVQHdYveP78Wu7GK+3J7DLW//yNzbRpHU5qedXBufYRj8+ZMUPt6QgZ/dxku/HKICurQYAQEBDB06lKVLlx5TRF+6dCmXXHLJCR8zcuRIFi5ceMxtn3/+OcOGDauzH3pgYCCBNYW0o4WGHlvUqUt9xpzK2JAGfA9oyNiji3CNOfboomFjjg0MPFLobMyxAQFHCrNWjfX3P1Kgbsyxfn5HCuqNOdbhqP/XcEPG2u0NHts2JISEbt3Yu3cvx6y/cVdRlZ9GQEwn/OO6Urb32CK6zWaja9eutElKOlJYNe9ourms7xEmfY9o+Ni65v3J3mAQEWki/1i6k4P55SRGBnH/Rb2tjiMiqJ1LgzjsNp67ZjD920eSX1rJr99YQ9rhk6yiaSSvfLOHOV/vAeDJywYwslvbJn9NaUQeN8yfDlVl0GUMDL/J6kStnsNuY/bVg+gZF0ZOsZMr5qxmd05xk7/uS1/v4fWV5r4KT18xkHN7xf7MI0Sa18yZM3n11Vd5/fXXSUlJ4Z577iE1NZXp06cDMGvWLH71q1/Vjp8+fToHDhxg5syZpKSk8Prrr/Paa69x3333WfVPEJEmYLPZuOOOO054X1WO+XOtrpYud955p1qWiYiINMDGgwW89q358/Uv0/oTFqj1ryItgYroDRQS4Mdrvx5G+6hg9ueVMe3FVWxJL2yS13J7DP60cCuPL94OwD0X9OTSIR2a5LWkCa16DtLWQEA4XPLikVNRxVLhQf78+8Yz6REbRlZRBVfMWc2mtIImeS2Px+DZL3bxt892APCHSclMHdy+SV5L5HRcddVVzJ49m0cffZRBgwbxzTffsHjxYjp16gRAZmYmqUdtBNelSxcWL17M8uXLGTRoEI899hjPPfccl/10oz8R8XrXX389ISEh2H/ye0xlHUV0u91OSEjIMW+8iYiIyMlVuT38bu4mPAZcMiiR83pr4ZVIS6Ge6Kcoo6CcG978ge1ZxYQEOHjh2iGc14irSiuq3Nz13/Us2ZoNwIMTe3Pz6K5ayeNtsrfBK+eAuxIueQEG/9LqRPITh6vPKtmYVkhYoB//+tWwRj3bo6zSxX0fbmTx5iwAbj+vO/eN79Vozy/Wask/p7yFPoci3mPJkiVMmjQJwzDwVPfmDuoyhLgrH6Uq7yAZr94GmAV0m83G4sWLGTdunJWRRU6bfk41Dn0eRernhWW7eWrJDqJD/Pli5jm0DatnWywROWX1/RmlJbGnKDEqmA+mj+Ts7jGUVbq56a0feXv1fhrjPYmswgqu+dd3LNmaTYDDzj+vGcwtY7qpgO5tXJUw/1azgN5zAgy61upEcgLRoQG8e/MIRnZtS4nTxfVvrOGl5XtwuU+ycVc9pR0u47KXVrN4cxb+DhtPXtZfBXQREfFa48eP55NPPiE4OBibzYbNZqMyZy8Afm3aYw8IwmazERwcrAK6iIhIA+05VMKzX+4C4I8X91EBXaSFadIi+l/+8hdGjRpFSEgIUVFRTflSlogI8uf1Xw/nsiEdcHsM/vjxVi6fs/qU27s4XW5eXL6b8/++nPWpBUQG+/POTWdy8cDERk4uzeKbpyBrEwRHw8XPHruhlrQoYYF+vPGb4VzUN55Kl4cnP9vO1BdXsjXj1OZyldvDv787wJTnV5KSWURMWADv3TyCq4Z3bOTkIiIizWv8+PGkpaUxe/Zsunbtiqe0AHfpYWw2O50HjmL27Nmkp6ergC4iItIAHo/BrLmbqXR5OKdnO6YOUvtPkZamSdu5PPzww0RFRZGWlsZrr71GQUFBgx7vLad8GYbBqyv28Y8vdlJW6cZmg2vO6MjMC3sSU493Dj0eg+U7c3hsUQr7cksBGNIxiqeuGEi3dmFNHV+aQvpaePVCMNxw+RvQ71KrE0k9GIbB3HXpPLZoG4XlVTjsNn4zqjPXjuhEl5jQn328x2OwcFMGzyzdyYE8c9PhvokRvPIrcx8F8T3e8nOqJdPnUMR7GYZBfn4+09/bzA9ppfxlaj+uHdHJ6lgijUo/pxqHPo8iJ/fOdwf4w0dbCAlw8Pk9Y+gQHWJ1JJFWo74/o5p0i98//elPALz55ptN+TKWs9ls3DymK5MHJvDE4u0s2JjBf75P5b9rUhnaKZrze8dxfu9YOrU98k3QWeXhu315fJWSw1c7cjhU7ASgXXggsyb0Ztrg9mrf4q2qymH+bWYBve+lKqB7EZvNxuVDOzCmZwyPLNjK4s1ZvPrtPl79dh8DO0RyyaD2jOkZQ2RwAOFBfgT5O8guqmDNvnx+3J/Pit257D1kvhEWExbInWO7c/XwjgT4qXOWiIj4HpvNRtu2bRnSLY4f0vaSklVkdSQRERGvk1lYzl8/3Q7A/eN7qYAu0kI1aRG9oZxOJ06ns/Z6UZF3/SKeEBnMc9cM5pcjOvGXxSlsPFjAD/sP88P+wzz52faTPjY0wMG1Izpxx/ndCQ/yb6bE0iS++jPk7oCwOJj0d6vTyCmIDQ/ixWuH8mVKNm+vPsCKXYfYmFbIxrRj27sEOOxU/qR3enigH7ee05XfnNWF0MAW9S1WRESkSfRJMFfsbMvwrt/dRURErGYYBv/30RZKnC4Gd4ziVyM7Wx1JROrQoio8TzzxRO3qdW92Rpc2fPzbs0g7XMayHYf4KiWbVXvycLqOLbYltQlmbO84xibHckaXNgT6OSxKLI1m/0pY/YJ5POWfENLG2jxyWsYmxzE2OY5DxU4WbcpgwcYMdmeXUOx0AVDp9mC3QXJCBMM7t2F45zac3T2GyBC9ESYiIq1HTRF9e1YxHo+B3a6zKUVEROpjwcYMvkjJwd9h48nLBuDQz1CRFqvBRfRHHnnkZwvdP/zwA8OGDWtwmFmzZjFz5sza60VFRSQlJTX4eVqKDtEhXDeiE9eN6ESV23NMEd0GhAQ41LLFlzhL4KPbAAMGXwc9x1udSBpJu/BAfnNWF35zVhfA7H1eUumiuMJFRJCfzh4REZFWrUtMKIF+dsoq3RzIL6vXPiIiIiKt3aFiJ48s2ArAHef3oGdcuMWJRORkGlxEv/3227n66qtPOqZz586nFCYwMJDAwJ/fiNMb+Tvs+DvUF9mnff4HKDgAkUkw/nGr00gTstttRAT5E6HiuYiICH4OO73jw9mYVsi2jCIV0UVEROrhkQVbOVxWRXJCBLed283qOCLyMxpcRI+JiSEmJqYpsoh4r91fwNo3zOOpL0KQdpwXERGR1qNPYoRZRM8sZNKABKvjiIiItGifbs7kk82ZOOw2nrp8gBZdiniBJu2JnpqaSn5+PqmpqbjdbjZs2ABA9+7dCQsLa8qXFmk+5Yfh4zvM4zNuhS5jrM0jIiIi0sy0uaiIiEj9HC6t5P8+3gLAbed0o1/7SIsTiUh9NGkR/Y9//CNvvfVW7fXBgwcDsGzZMs4999ymfGmR5vPp76A4A9p0gwsesTqNiIiISLPrk1hdRM9UEV1ERORkHl20jdySSrrHhnHH2O5WxxGRemrS80XefPNNDMM47qICuviMbQtg0/tgs8O0lyEgxOpEIiIiIs2uV3wENhtkFznJLXFaHUdERKRF+jIlm/nr07Hb4KnLBxDo57A6kojUk5ouiZyqkkOw6B7z+Ky7IWm4pXFERERErBIW6EfntuaGoilajS4iInKcwvIqHpy/GYCbRndlcMdoixOJSEOoiC5yKgwDFt0NZbkQ2xfO/b3ViUREREQspb7oIiIidfvLJ9vILnLSJSaUmRf2tDqOiDSQiugip2LTB7B9Edj9YNoc8Au0OpGIiIiIpdQXXURE5MS+2XmID35Mw2aDv10+gCB/tXER8TYqoos0VGE6LL7fPD7395AwwNo8IiIiIi2AVqKLtHyHDx/muuuuIzIyksjISK677joKCgpO+phf//rX2Gy2Yy4jRoxonsAiPqDE6WLWPLONy/UjOzO8cxuLE4nIqfCzOoCIVzEMWHAHOAshcQicdY/ViURERERahJqV6HsOlVBR5dYqO5EW6Be/+AVpaWl89tlnANxyyy1cd911LFy48KSPu+iii3jjjTdqrwcEBDRpThFf8tdPU0gvKCepTTD3j+9ldRwROUUqoos0xNo3YM+X4BcE014Gh6aQiIiICEBseCBtQwPIK61kR1YxA5OirI4kIkdJSUnhs88+47vvvuPMM88E4F//+hcjR45kx44d9OpVd3EvMDCQ+Pj45ooq4jNW78njne9SAfjrpQMIDVQNQcRbqZ2LSH3l74MlfzCPxz4M7bQRiIiIiEgNm82mvugiLdjq1auJjIysLaADjBgxgsjISFatWnXSxy5fvpzY2Fh69uzJzTffTE5OzknHO51OioqKjrmItDZllS5+N3cTANec0ZGzusdYnEhEToeK6CL14fHARzOgqhQ6nQ1nTrc6kYiIiEiLU9MXPUVFdJEWJysri9jY2ONuj42NJSsrq87HTZgwgXfffZevvvqKv//97/zwww+cf/75OJ3OOh/zxBNP1PZdj4yMJCkpqVH+DSLe5MlPt5OaX0ZCZBCzJva2Oo6InCYV0UXq47sXIXUV+IfC1BfArqkjIiIi8lO1K9G1uahIs3nkkUeO2/jzp5cff/wRMM8Y+SnDME54e42rrrqKSZMm0a9fPy6++GI+/fRTdu7cySeffFLnY2bNmkVhYWHt5eDBg6f/DxXxIqt25/LW6gMAPHnZACKC/C1OJCKnS82YRH7OoR3w5aPm8fi/QHRnS+OIiIiItFRHr0T3eAzs9roLcyLSOG6//Xauvvrqk47p3LkzmzZtIjs7+7j7Dh06RFxcXL1fLyEhgU6dOrFr1646xwQGBhIYGFjv5xTxJcUVVdz/P7ONyy/O7MiYnu0sTiQijUFFdJGTcVfB/FvB7YTuF8DQX1udSERERKTF6hITSqCfndJKN6n5ZXSOCbU6kojPi4mJISbm53stjxw5ksLCQtasWcMZZ5wBwPfff09hYSGjRo2q9+vl5eVx8OBBEhISTjmziC/7yycppBeUk9QmmAcnJlsdR0QaiXpSiJzMt/+AjPUQFAlT/gknOc1RREREpLXzc9jpHR8OwFa1dBFpUZKTk7nooou4+eab+e677/juu++4+eabmTx5Mr169aod17t3b+bPnw9ASUkJ9913H6tXr2b//v0sX76ciy++mJiYGKZNm2bVP0WkxVq2PYf//mC2L3rq8oGEBWrtqoivUBFdpC6ZG+HrJ83jiX+HiERr84iIiIh4gdq+6JmFFicRkZ9699136d+/P+PGjWPcuHEMGDCAf//738eM2bFjB4WF5vx1OBxs3ryZSy65hJ49e3L99dfTs2dPVq9eTXh4uBX/BJEWq6Cskt/NNdu43HBWF0Z0bWtxIhFpTHpLTOREXE6YPx08LkieAv0vtzqRiIiIiFeo6YuulegiLU+bNm145513TjrGMIza4+DgYJYsWdLUsUR8wiMLtpJT7KRru1AeuKjXzz9ARLyKVqKLnMiyxyFnG4S2g8n/UBsXERERkXrqkxgJqIguIiKtx2dbMvloQwZ2G/z9ioEE+TusjiQijUxFdJGfSv0eVj1nHk+eDaE/v0mPiIiIiJiSE8Kx2eBQsZOc4gqr44iIiDSp3BInD83fAsD0c7oxuGO0xYlEpCmoiC5ytMpS+Gg6GB4YeA0kT7Y6kYiIiIhXCQnwo2tMKKDV6CIi4tsMw+AP87eQV1pJ7/hw7rqgh9WRRKSJqIgucrQvHoH8vRCeCBf91eo0IiIiIl6pb3VLl20qoouIiA9bsDGDz7Zm4We38fcrBxLopzYuIr5KRXSRGnuXw5pXzONLnofgKCvTiIiIiHitvok1m4sWWpxERESkaWQXVfDHj7cCcOfYHrVvIIuIb1IRXQSgohA+vt08HnYjdB9rbR4RERERL9ZXm4uKiIgP83gM7vtwI4XlVfRvH8lt53azOpKINDEV0UUAPnsQCg9CdGe48FGr04iIiIh4tT7VK9EP5JVRXFFlcRoREZHG9fbq/azYlUugn51/XDUQf4fKayK+TrNcZMensOEdwAZTX4LAMKsTiYiIiHi1NqEBJEQGAZCSWWxxGhERkcazM7uYJz7dDsBDk5LpHhtucSIRaQ4qokvrVpoHC+40j0fdDp1GWZtHRERExEeoL7qIiPiaSpeHu/+7AafLwzk923HdiE5WRxKRZqIiurRui++F0hyI6QXn/cHqNCIiIiI+o4/6oouIiI95ZulOtmUWER3iz1OXD8Bms1kdSUSaiYro0nptmQtb54PNAdPmgH+Q1YlEREREfMaRlegqoouIiPf7bm8eL3+zB4AnLh1AbIRqCCKtiYro0joVZ8En95rHY+6H9kOszSMiIiLiY2qK6Luyi3G63BanEREROXVFFVXc+8FGDAOuHNaBi/rFWx1JRJqZiujS+hiG2Qe9/DDED4Ax91mdSERERMTntI8KJjLYH5fHYFd2idVxRERETtnDH28lvaCcjm1C+OPFfa2OIyIWUBFdWp/178CuJeAIgGkvg8Pf6kQiIiIiPsdms9EnQZuLioiId1u4MYP569Ox2+AfVw0iLNDP6kgiYgEV0aV1KUiFz2aZx+f/AeL6WJtHRERExIepL7qIiHizzMJyHpq/GYDbz+vO0E7RFicSEauoiC6th8cDH82AymJIOhNG3m51IhERERGf1re9WUTfpiK6iIh4GY/H4L4PN1JU4WJgh0juGNvD6kgiYiEV0aX1+OFfsH8F+IfA1JfA7rA6kYiIiIhP65sYCUBKZhEej2FxGhERkfp7ZcVeVu7OI9jfwT+uGoS/QyU0kdZM3wGkdcjdDUsfNo8vfBTadrM2j4iIiEgr0DUmlEA/O6WVbvbnlVodR0REpF42HCzg6SU7AHhkSh+6tguzOJGIWE1FdPF9bhd8NB1c5dD1XBh2o9WJRERERFoFP4ed3tWbi25RSxcREfECxRVV3Pneelweg0kDErhyWJLVkUSkBVARXXzfqucg7QcIjIBLXgC7vuxFREREmku/2s1FCy1OIiIicnKGYfDQ/C2k5pfRPiqYx6f1x2azWR1LRFoAVRPFt2VtgWWPm8cTnoTIDtbmEREREWll+rc3+6JvSVcRXUREWra569JZsDEDh93Gc9cMJjLY3+pIItJCqIguvstVCfOng6cKek2EgddYnUhERESk1elXW0QvwjC0uaiIiLRMew+V8MePtwAw88KeDO0UbXEiEWlJVEQX3/X1k5C9GYLbwOTZoFOwRERERJpdj7gw/B02CsurSDtcbnUcERGR4zhdbu54bz1llW5Gdm3L9HO6WR1JRFoYFdHFN6WthW+fMY8nPwPhcdbmEREREWmlAv0c9IwLB9QXXUREWqa/fbaDrRlFRIf4M/vqQTjsWoQnIsdSEV18T1U5fDQdDA/0uxz6TrM6kYiIiEir1i/xSEsXERGRlmTZ9hxe+3YfAE9fMZC4iCCLE4lIS6QiuvieLx+D3J0QFg8Tn7I6jYiIiEir1699BABbtBJdRERakJyiCu77cCMAvx7VmbHJOotdRE5MRXTxDQGH5wAAYKlJREFULfu/he9eNI+n/BNC2libR0RERESO2ly0UJuLiohIi+D2GNz53/XklVbSJyGCWRN7Wx1JRFowFdHFdziL4aMZgAFDfgU9x1mdSERERESA5IQIHHYbuSWVZBc5rY4jIiLC7C928t3efEIDHPzzF4MJ9HNYHUlEWjAV0cV3fP4HKDgAkR1h3F+sTiMiIiIi1YL8HXRvFwaYq9FFRESs9PXOQzy/bDcAT1w2gG7VP6NEROqiIrr4hl1fwNo3zeOpL0BQhKVxRERERORYfdUXXUREWoDMwnLueX8DhgHXntmRKQMTrY4kIl5ARXTxfuWHYcHt5vGZt0GXMdbmEREREZHj9Eus6YteZHESERFprarcHu58bz35pZX0TYzg/yb3sTqSiHgJFdHF+y1+AIozoW0PuOBhq9OIiIiIyAn072AW0bdqJbqIiFjk6c938MP+w4QH+vHitUMI8lcfdBGpHxXRxbtt+xg2fwA2O0ybA/7BVicSERERkRNITojAZoPMwgpyS7S5qIiINK8vU7J5+eu9APzt8gF0ahtqcSIR8SYqoov3KsmBRfeYx2ffAx2GWZtHREREROoUFuhHlxizYKHNRUVEpDmlHS5j5gcbAfj1qM5M6J9gcSIR8TYqoot3MgxYeDeU/X979x0eVZm/f/ye9ARSCCGNBEIPSJHeBUQRRIquIBYECyso7qLLD8EG+BWxgQULqEhwbViIsNJdKSrFBAi9QyAEQiipkJ7z+yOSNUJCEjI5M8n7dV1zXSdnzplzz0nOPJPPPPM856WAllKvyWYnAgC7lpSUpJEjR8rb21ve3t4aOXKkkpOTS9xn9OjRslgsRW5dunSpnMAA7NLlcdH3nGJcdABA5cjOzdf4L7crJSNHbUK89eztzc2OBMAOUUSHfdrxtXRgmeTgLN05T3JyMTsRANi1++67TzExMVq5cqVWrlypmJgYjRw58pr79e/fX6dPny68LV++vBLSArBXLet6SaInOgCg8ry6Yr9i4pLl5eak9+5rJxcnSmEAys7J7ABAmaWclFY8U7DcZ4oU2NLcPABg5/bt26eVK1dq8+bN6ty5syTp448/VteuXXXgwAE1a9as2H1dXV0VGBhYWVEB2LnLPdF3M7koAKASLN1xSp/+dkySNGv4jQr19TA5EQB7xcdvsC+GIS0ZL2WlSHU7SN3+aXYiALB7mzZtkre3d2EBXZK6dOkib29vbdy4scR9161bJ39/fzVt2lRjxoxRYmJiidtnZWUpNTW1yA1A9XFD3YIietyFDCVfyjY5DQCgKjuQkKZnvtspSRrXu5FubRFgciIA9owiOuxL9Hzp6FrJyV26c67kyJcpAOB6JSQkyN/f/4r1/v7+SkhIKHa/AQMG6IsvvtDPP/+sWbNmKSoqSjfffLOysrKK3WfmzJmF4657e3srNDS0Qp4DAPvg7e6sen/0AmRcdACAtaRm5mjs51uVkZOnHo39NLFf8d+sBIDSoIgO+3HhqLT6hYLlW6ZJfk1MjQMAtm7atGlXTPz511t0dLQkyWKxXLG/YRhXXX/ZPffco4EDB6ply5YaNGiQVqxYoYMHD2rZsmXF7jNlyhSlpKQU3uLi4q7/iQKwK61CCnqj7zzJkC4AgIqXn2/oX9/s0LFzF1XXx13v3ttWjg7Fv6cFgNKgGy/sQ36eFDlOyrkkhfWUOv3d7EQAYPPGjx+vESNGlLhNWFiYdu7cqTNnzlxx39mzZxUQUPqvvQYFBal+/fo6dOhQsdu4urrK1dW11I8JoOppXddby3ae1q74ZLOjAACqoA/XH9GavWfk4uigD+5vJ98aLmZHAlAFUESHfdj0vhS3WXLxlIa8LznwJQoAuBY/Pz/5+fldc7uuXbsqJSVFv//+uzp16iRJ2rJli1JSUtStW7dSH+/8+fOKi4tTUFBQuTMDqProiQ4AsJYNB8/qzdUHJEkvDblBbUJ9zA0EoMqgEgnbl7hP+vn/Cpb7vyLVqm9uHgCoYpo3b67+/ftrzJgx2rx5szZv3qwxY8bojjvuULNm/xs/Mjw8XJGRkZKk9PR0TZw4UZs2bVJsbKzWrVunQYMGyc/PT3feeadZTwWAHWj5x+SiJ5MydOEik4sCACpG3IVL+sfX22UY0oiOoRrRqZ7ZkQBUIRTRYdvycqTIx6S8bKlJP6ntSLMTAUCV9MUXX6hVq1bq16+f+vXrp9atW+vf//53kW0OHDiglJSCnqOOjo7atWuXhgwZoqZNm2rUqFFq2rSpNm3aJE9PTzOeAgA74eXmrIZ+NSRJu+LpjQ4AuH6ZOXka98VWJV/KUesQb00bfIPZkQBUMQznAtu24U3p9A7JzUca9K5UwgR3AIDy8/X11eeff17iNoZhFC67u7tr1apV1o4FoIpqFeKto+cuatfJZPVqWsfsOAAAO2YYhl74Ybd2x6fKt4aLPnygvdycHc2OBaCKoSc6bNep7dKGNwqWB86SvBhjFwAAoCpoVZdx0QEAFePfm4/r260n5WCR5tzbVnV93M2OBKAKoogO25STKUWOlYw8qcUQqeXfzE4EAACACtI6xEcSw7kAAK7PpiPnNf0/eyVJk/qHq3tjP5MTAaiqKKLDNq2dIZ3dL9Xwlwa+xTAuAAAAVcgNwV6yWKTTKZlKTMs0Ow4AwA7FXbikx7/Yqrx8Q0NvDNZjNzU0OxKAKowiOmzP8U3SxjkFy4PekWrUNjcPAAAAKlQNVyc1rlNTkrSb3ugAgDK6mJWrMZ9FK+lSjlrV9darf2stC53vAFgRRXTYlqx06Yexkgzpxvul8NvNTgQAAAAraBXCuOgAgLLLzzc08dsd2p+QJr+arvroQSYSBWB9FNFhW36aKiXFSl4hUv+ZZqcBAACAlbT+Y3LRXRTRAQBlMOfnw1qxO0Eujg6aN7KdgryZSBSA9VFEh+048rMU9UnB8pD3JDdvc/MAAADAalr9MbnozvgUGYZhbhgAgF1YuTtBb/10UJL08tCWal/f1+REAKoLiuiwDRnJ0pLxBcsdH5Ua9TE1DgAAAKyrRZCXHB0sOpuWpTOpWWbHAQDYuP0JqXr6mxhJ0uhuYRreMdTcQACqFYrosA0rp0ip8ZJvQ+nWl8xOAwAAACtzd3FUE/+CyUV3nkw2NwwAwKYlXczWmM+idSk7T90a1dZzA5ubHQlANUMRHebbv0za8aVkcZCGzpVcapidCAAAAJWg9R+Ti+6KZ1x0AMDV5eTl64kvtynuQoZCfd31/n3t5OxIOQtA5eJVB+a6eE76zz8Llrs9KdXrbG4eAAAAVJrCcdGZXBQAcBWGYejFJbu18ch5ebg46uMHO6hWDRezYwGohiiiwzyGIS17Wrp4VqrTXOr9rNmJAAAAUIla1/1fT3QmFwUA/NX8X4/pq9/jZLFI745oq/BAL7MjAaimKKLDPLu/l/YukRycpDvnSs5uZicCAABAJQoP8pSzo0UXLmbrZFKG2XEAADZkzd4zmrF8nyTpudub65YWASYnAlCdUUSHOVJPS8v+VbB80yQp+EZT4wAAAKDyuTo5qnlQQa/CHUwuCgD4w55TKfrn19tlGNJ9nevpkR4NzI4EoJqjiI7KZxjS0ielzGQp6Eap59NmJwIAAIBJ2vwxLvqOuGRTcwAAbENiaqYeXRitS9l56tHYT9MH3yCLxWJ2LADVHEV0VL5tn0mH10iOrtKd8yRHZ7MTAQAAwCRtQn0kSTvimFwUsLYZM2aoW7du8vDwkI+PT6n2MQxD06ZNU3BwsNzd3dW7d2/t2bPHukFRbWVk5+nRz6J1OiVTjerU0Pv3t5OzI6UrAObjlQiVKylWWvXHBKJ9X5D8w02NAwAAAHPd+EcRfVd8inLz8s0NA1Rx2dnZGjZsmMaNG1fqfV5//XXNnj1b7733nqKiohQYGKhbb71VaWlpVkyK6ig/39DT38Ro58kU1fJw1qejO8rbnU53AGwDRXRUnvx86YcnpOx0qV43qcvjZicCAACAyRr61ZCnq5MycvJ08Ey62XGAKm369Ol66qmn1KpVq1JtbxiG3n77bT333HO666671LJlSy1cuFCXLl3Sl19+aeW0qG5mrTmgFbsT5Oxo0byRHVS/dg2zIwFAIYroqDy/z5OO/yo515CGvi85OJqdCAAAACZzcLCodai3JCYXBWzNsWPHlJCQoH79+hWuc3V1Va9evbRx48Zi98vKylJqamqRG1CS77ae1Ptrj0iSXr2rtTo18DU5EQAURREdlePsQemnaQXL/f5P8m1oahwAAADYDiYXBWxTQkKCJCkgIKDI+oCAgML7rmbmzJny9vYuvIWGhlo1J+zbxiPnNGXxTknSE30a6W/tQ0xOBABXoogO68vLlX4YK+VmSo1uljo8bHYiAAAA2JDLk4vGUEQHymzatGmyWCwl3qKjo6/rGBaLpcjPhmFcse7PpkyZopSUlMJbXFzcdR0fVdfBM2l67N9blZNnaGCrIP3r1mZmRwKAq3IyOwCqgd/eluK3Sq7e0uD3pBLebAEAAKD6aftHEf3gmTRdzMpVDVf+TQFKa/z48RoxYkSJ24SFhZXrsQMDAyUV9EgPCgoqXJ+YmHhF7/Q/c3V1laura7mOierjTGqmRn/6u9Iyc9UxrJZmDW8jBwfqBQBsE+9OYV0Ju6R1rxYs3/665F3X3DwAAACwOf5ebgrydtPplEztjk9R54a1zY4E2A0/Pz/5+flZ5bEbNGigwMBArVmzRm3btpUkZWdna/369XrttdesckxUD+lZuXpoQZROpWSqYZ0a+vjBDnJzZt40ALaL4VxgPblZUuRYKT9HCr9Dan2P2YkAAABgowrHRWdyUcBqTpw4oZiYGJ04cUJ5eXmKiYlRTEyM0tPTC7cJDw9XZGSkpIJhXCZMmKBXXnlFkZGR2r17t0aPHi0PDw/dd999Zj0N2LmcvHw9/sU27T2dKr+aLooY3Uk+Hi5mxwKAEtETHdaz/jXpzG7Jo7Z0x9sM4wIAAIBitQn10co9CdoRl2J2FKDKevHFF7Vw4cLCny/3Ll+7dq169+4tSTpw4IBSUv53HU6aNEkZGRl6/PHHlZSUpM6dO2v16tXy9PSs1OyoGgzD0As/7NaGg2fl7uyo+aM6ql5tD7NjAcA1UUSHdcRFSb++VbB8x9tSzTqmxgEAAIBtu5HJRQGri4iIUERERInbGIZR5GeLxaJp06Zp2rRp1guGauO9nw/r66g4OVikOfe2LZxYGgBsHcO5oOJlX5J+GCsZ+VKr4VKLwWYnAgAAgI1rFeIti0WKT85QYlqm2XEAABXs+60nNWvNQUnS9ME36JYWxU9OCwC2hiI6Kt5/X5LOH5Y8gwomEwUAAACuoaark5r415Qk7WRIFwCoUn47fE7PfL9TkvRYr4Ya2TXM3EAAUEYU0VGxjm2QtnxYsDz4Pcm9lrl5AAAAYDeYXBQAqp4DCWka+++tys03NKhNsJ65LdzsSABQZhTRUXEyU6UfnihYbj9aanKLqXEAAABgX9owLjoAVCmnkjM0esHvSsvKVacGvnpzWGs5OFjMjgUAZUYRHRVn9XNSygnJp77U72Wz0wAAAMDO/Hly0fx8o+SNAQA2LflSth789HedTslUY/+a+mhke7k6OZodCwDKhSI6KsbBVdK2zyRZpKEfSK6eZicCAACAnWkW6Ck3ZwelZebq6Ll0s+MAAMopIztPD0dE6XBiuoK83fTZw53k4+FidiwAKDeK6Lh+ly5IS58sWO7yuBTWw9w8AAAAsEvOjg5q/ce46NuOJ5uaBQBQPjl5+Xriy23adiJZ3u7OWvhwJwX7uJsdCwCuC0V0XL/l/09KPyP5NZX6vmB2GgAAANixdvUKJqbfdiLJ5CQAgLIyDENTFu/Sz/sT5ebsoE9Hd1DTAL6pDsD+UUTH9dkTKe3+TrI4SkPnSs58ugwAAIDya1fPRxJFdACwR6+vOqDvtp6Uo4NF793bTu3r+5odCQAqBEV0lF/aGenHpwuWez4thbQ3Nw8AAADsXrv6BT3RDyWmKzUzx+Q0AIDSmv/rMX247ogkaeZdrXRLiwCTEwFAxaGIjvIxDOk//5QyLkiBraSbJpmdCAAAAFWAX01X1fP1kGFIMSeSzY4DACiFJTHx+r8f90qSJvVvpuEdQk1OBAAViyI6yifmS+ngCsnBWbpznuTELNsAAACoGAzpAgD2Y8PBs5r47Q5J0kPdwzSuVyOTEwFAxaOIjrJLjpNWTi5Y7vOsFHCDuXkAAABQpVwe0mUbPdEBwKbtiEvW2M+3KifP0OA2wXphYAtZLBazYwFAhaOIjrLJz5eWPC5lpUohHaXu/zQ7EQAAAKqYdvUKiujbTyQpP98wOQ0A4GqOnbuohyKidCk7Tz0a++nNYW3k4EABHUDVRBEdZRP1iXRsg+TkXjCMi4Oj2YkAAABQxYQHesrN2UFpmbk6cjbd7DgAgL9ITM3Ug59u0YWL2WpV11tzR7aXixMlJgBVF69wKL3zR6Q1LxYs3zpdqs04ZwAAAKh4To4Oah3iI4lx0QHA1iRdzNYD87co7kKGwmp7aMFDHVXT1cnsWABgVRTRUTr5eVLkWCk3Q2pwk9RxjNmJAAAAUIVdHtJl2/Fkc4MAAAqlZ+VqdESUDp5JV4CXq/79SGf51XQ1OxYAWJ3ViuixsbF65JFH1KBBA7m7u6tRo0aaOnWqsrOzrXVIWNPGOdLJ3yUXT2nI+5IDn78AAADAetrV85FET3QAsBWZOXkaszBaO+KSVcvDWZ8/0lmhvh5mxwKASmG1Suj+/fuVn5+vefPmac+ePXrrrbc0d+5cPfvss9Y6JKzlzB5p7YyC5QGvSj71zM0DAABsWu/evRUbG2t2DNi5dvULeqIfSkxXSkaOyWkAoHrLycvX+C+3a9PR86rp6qSFD3dSkwBPs2MBQKWxWhG9f//+WrBggfr166eGDRtq8ODBmjhxohYvXmytQ8IacrMLhnHJy5aa9pduvN/sRAAAwAb99ttvWr58eZF18fHx+uCDD0xKBHvnV9NV9f7o4RgTl2xuGACoxvLzDU36bqd+2ndGrk4O+mRUh8J5KwCguqjUMTlSUlLk6+tbmYfE9frlTSlhp+ReSxr0rmSxmJ0IAADYoHr16unzzz/X/fffr+TkZH388ce66667VL9+fbOjSZIyMzM1depUNW3aVG5ubgoODtbDDz+skydPlvmxNm/erL/97W8KDAyUs7OzfH191bdvX3333Xcl7peQkKCnnnpKTZs2lbu7u3x9fdW+fXtNmjSpvE+ryisc0uU4Q7oAgBkMw9C0/+xR5PZ4OTlY9OED7dSlYW2zYwFApau0IvqRI0c0Z84cjR07tthtsrKylJqaWuQGE8VvlTa8WbA8cJbkGWBuHgAAYLNCQ0P15ZdfqmPHjtqxY4d+/vlnrVu3TgMHDjQ7mjIzM9W3b1+99NJLSk9P15AhQxQaGqoFCxaoXbt2OnLkSKkf69tvv1X37t21ePFihYaG6m9/+5tatmypdevWadiwYZo8efJV99u0aZOaN2+ut99+W87Ozho8eLC6dOmi8+fPa/bs2RX1VKucy0O6MC46AJhj1uqD+mzTcVks0qzhbXRzOHUBANVTmYvo06ZNk8ViKfEWHR1dZJ9Tp06pf//+GjZsmB599NFiH3vmzJny9vYuvIWGhpb9GaFi5GRIkeMkI0+64S6p5d/MTgQAAGxYfHy8Ro4cqaioKLVp00Y333yz+vTpo1WrVpkdTa+88oo2btyorl276uDBg1q0aJG2bNmiWbNm6ezZs3r44YdL9Ti5ubl64oknlJ+fr6+//lpRUVH6+uuvtWHDBv36669yc3PT66+/fkVR/tSpU7r99tuVlZWlxYsXa8+ePVq0aJGWL1+u2NhYbdy40RpPu0poV6+giB5zIll5+YbJaQCgepm3/ojeW3tYkvTy0JYacmNdkxMBgHkshmGU6d3ouXPndO7cuRK3CQsLk5ubm6SCfxr69Omjzp07KyIiQg4Oxdfts7KylJWVVfhzamqqQkNDlZKSIi8vr7LExPVa9Zy06T2pZoD0+GbJg2F4AOCvUlNT5e3tTTt1HTiHVcevv/6qlJQUDRw4UL1791ZERIScnJy0ZMkSPfHEE6blysnJkb+/v5KTk7Vt2za1bdu2yP1t2rTRzp07FR0drfbt25f4WLt371arVq0UHh6uffv2XXH/0KFDtWTJEi1atEjDhw8vXP/ggw/q3//+t+bMmaPx48dXzBOrJnLz8nXjS2uUnpWr5f/oqRbBvE6gctFOVQzOo/356vcTmrJ4lyTpmf7hGte7kcmJAMA6SttGlbknup+fn8LDw0u8XS6gx8fHq3fv3mrXrp0WLFhQYgFdklxdXeXl5VXkBhMc3yhter9gedC7FNABAKhG7rvvPlksFs2YMeOK+y73tvb397+it3WPHj2uGLolJCTE1AK6VJA5OTlZjRo1uqKALkl33323JOk///nPNR/L1dW1VMf88xxASUlJ+uabb+Tt7V3iNzJxdU6ODmr7x7joUbEXzA0DANXEf3ac0rORBQX0cb0bUUAHAFlxTPRTp06pd+/eCg0N1ZtvvqmzZ88qISFBCQkJ1jokKkJWuvTDOEmG1PYBqVl/sxMBAIBK9NJLL8nJyUmzZs0qMj/NgQMHNGTIEDk6OmrZsmVq1Kj4f6jXrVunsLCwcmfIy8vTwYMHdfDgQWVnZxe7XVpams6cOVPiY+3YsUOS1K5du6vef3n95e1K0rBhQzVs2FD79+/XN998U+S+TZs2adWqVWrQoIFuuummwvW//fabsrKy1KNHDzk7O+u7777ThAkT9MQTT2jOnDnXzA+pU1jBhxIU0QHA+tbuT9RTi2JkGNL9netp0m3NzI4EADbBakX01atX6/Dhw/r5558VEhKioKCgwhts2JoXpKRYyTtUum2m2WkAAEAla9y4sR566CElJSXpnXfekSSdOXNGAwYMUEpKir755ht17NjRKse+dOmSnn/+efn7+6tZs2Zq1qyZfH19NXz4cEVGRiojI0NSwdjkkZGRatu27VWHVfmzEydOSCroFX81l9df3q4kjo6OioiIkLe3t+655x517NhRI0aMUK9evdSjRw/deOONWr16tVxcXAr32bNnjyQpICBAPXv21LBhw/TOO+/ogw8+0D/+8Q81atRI33777bVPTjXW4U9F9DKORAkAKIMtR89r7OdblZtvaMiNwfq/IS1lsVjMjgUANsFqRfTRo0fLMIyr3mCjDv8kRX9asDzkfcmN4XQAAKiOXnzxRbm5uWn27Nk6deqU7rjjDh07dkxz5869YsiWijRkyBDNmDFD4eHhmjhxov7+978rKChI3377re666y55e3srLCxMtWrV0l133SVJJfaIl6T09HRJkoeHx1Xvr1GjRpHtrqVnz55av369GjRooOjoaC1atEgbNmxQjRo1dMsttyg4OLjI9klJSZKkzz77TDt37tT8+fN19uxZHTt2TE8//bQuXryoBx54QDt37izV8aujG0N95Oxo0ZnULMVdyDA7DgBUSbtOpuiRhdHKys1X33B/vTmsjRwcKKADwGVWK6LDzmQkSUueLFju9JjUsJe5eQAAgGlCQkI0btw4JScnq02bNoqOjtbUqVOtPqa3h4eHfvrpJ/3222964403NG/ePB06dEi//vqrHn30UQUFBen06dOqW7eupk+frpiYGIWGhpb4mJc7cBTXk66sHTy++uorde7cWfXq1dOWLVuUnp6ugwcP6t5779XLL7+sW265RTk5OYXb5+XlSSroPT979mw9/PDD8vPzU1hYmGbNmqW7775b2dnZev3118uUozpxd3FUy7rekhjSBQCs4dCZND346RalZ+WqS0NfvX9/Ozk7Ui4CgD/jVREFVkyW0k5Jvo2kW6aZnQYAAJjs6aeflsVi0blz5zR69GhNmzbN6sdctGiR+vbtK6lgfp34+Hjl5+ere/fu+vjjj3X8+HFlZWVp//79evHFF+Xk5KTz58+X+Jienp6SpIsXL171/kuXLkmSatasec18hw4d0qhRo1SnTh0tW7ZMnTp1Uo0aNdSkSRPNmzdPgwYN0qZNm7RgwYIrju/g4KBRo0Zd8ZgPP/ywpIJx5FE8xkUHAOuIu3BJI+f/rqRLOWoT4q1PRnWUm7Oj2bEAwOZQRIe07z/Szq8li4N051zJ5epfdwYAANWDYRh6+umnC3tpOzk5VdqxZ8yYoZCQENWtW1chISGqXbu27r//fi1dulSZmZmSCnp3//jjj2rfvr127dpV4uPVq1dPknTy5Mmr3n95/eXtSvL1118rJydH/fv3LxwG5s+GDx8uqWhB/PIEq4GBgXJ1db1in8v3JyYmXvP41VlHiugAUOESUzP1wPwtSkjNVBP/mop4qJNqulZemw8A9oQienWXflb6z4SC5e4TpNBOZqYBAAA24Omnn9a3336rQYMGyd/fXxERETp06JDVjzt48GA9//zzql+/viZOnKgxY8bI19dXX375pYYMGSIvL6/CMdEHDRqk7OxsNW7cuMTHbNOmjSRp27ZtV73/8vrWrVtfM9/lgruX19Xnjbm8/sKF/xV627ZtK6lgbPSrDR1zuSd9aXrCV2ft69eSJB05e1Hn07NMTgMA9i/5UrZGzv9dx89fUqivuz5/tLNq1XC59o4AUE1RRK/ODEP6cYJ06Zzkf4PUe7LZiQAAgMlmz56tt99+W507d9aiRYv0zDPPKDc3Vy+++KLVj+3m5qY1a9YUjon+0Ucf6ciRI/rtt9/02GOPKTg4WAkJCQoODtb06dO1fft2hYSElPiY3bt3l7e3t44cOaLt27dfcf93330nSbrjjjuumS8wMFCSFB0dfdX7o6KiJP2vd7kktWrVSg0aNFBGRoa2bNlyxT6Xe623a9fumsevzmrVcFHTgIIPGqKPJ5mcBgDs28WsXI1eEKUDZ9Lk7+mqLx7pogAvN7NjAYBNo4hene38Rtr/o+TgVDCMi9OVXzEGAFQPM2bMULdu3eTh4SEfH59S7WMYhqZNm6bg4GC5u7urd+/e2rNnj3WDwqq++eYbTZw4UY0bN9Z//vMfubu7a9y4cQoMDNSiRYu0c+dOqx5/0aJFuuWWW65Y361bN82dO1exsbHKzMwsHBO9NL23XVxcNH78eEnS+PHji4yNPnv2bO3cuVM9evRQx44di+z34IMPKjw8XJGRkYXrhgwZIknasGGDPvzwwyLbb968WW+99ZYk6e677y5y3zPPPCNJ+sc//qFz584Vrt+6datmzZolSRo7duw1n0t11+HykC7HGNIFAMorMydPf/93tGLikuXj4ax/P9JZ9WozpCsAXAtF9OoqJV5a/v8KlntNloKu/RVmAEDVlZ2drWHDhmncuHGl3uf111/X7Nmz9d577ykqKkqBgYG69dZblZaWZsWksJb169frwQcflJ+fn1auXKk6depIktzd3TV58mQZhqHnnnvOqhnc3d2t8rjPP/+8OnfurI0bN6pJkya655571KVLF/3rX/9S7dq1i0wEetmJEyd04MABpaSkFK5r166dJk6cKEl6/PHH1bJlSw0fPlw9evRQ9+7ddfHiRf3973+/4oOAMWPGaNiwYYqKilKzZs00aNAg9enTR926dVNycrLGjBlzReEdVyqcXJSe6ABQLrl5+Xryq+367fB51XBxVMRDndQs0NPsWABgFyiiV0eGIS19UspKkYLbST2eMjsRAMBk06dP11NPPaVWrVqVanvDMPT222/rueee01133aWWLVtq4cKFunTpkr788ksrp0VF27t3r4YOHSpHR0f9+OOPatSoUZH7H3vsMdWtW1c//vijNm3aZFLK8nNzc9PatWv1wgsvyMPDQz/88INiY2M1atQobd++/Zrjqv/ZG2+8ocWLF6tfv35KSEhQZGSk9u7dq169eumLL77QvHnzrtjHwcFBX3/9td5//33Vr19fP//8s6KiotShQwd99tln+uijjyry6VZZHcIKxkXfE5+iS9m5JqcBAPuSn29o0nc7tWbvGbk4OejjUR10Y6iP2bEAwG5YjKvNcGQjUlNT5e3trZSUlGIncEI5RC8oGAvdyU167BepTlOzEwGAXaqK7VRERIQmTJig5OTkErc7evSoGjVqpG3bthVOnCgVDHfh4+OjhQsXXnW/rKwsZWX9b1LA1NRUhYaGVqlzCMB6us38r06lZOrLRzurW2M/s+OgGqiKbb0ZOI/mMgxD05bu0cJNx+XoYNG8B9rrlhYBZscCAJtQ2jaKnujVTVKstPr5guW+L1JABwCUS0JCgiQpIKDoP2ABAQGF913NzJkz5e3tXXgLDQ21ak4AVcvlcdF/j2VcdAAordlrDmrhpuOyWKTZw9tQQAeAcnAyOwAqUX6+9MPjUna6VL+H1Ln0494CAOzPtGnTNH369BK3uTykRHlZLJYiPxuGccW6P5syZYqefvrpwp8v90QHgNLo2MBXS3ecUhRF9GohL9/QlmPntXrPGZ1Nz1JWTp4ycvKUnZuvZoGe6tPMX10b1ZaHC//WAsX5aMMRzfn5sCTppSEtNeTGuiYnAgD7xLuN6mTLh9Lx3ySXmtLQ9yUHvogAAFXZ+PHjNWLEiBK3CQsLK9djBwYGSirokR4UFFS4PjEx8Yre6X/m6uoqV1fXch0TADo3KOiJvvV4krJy8+Tq5GhyIljDzpPJWrwtXst2ndbZtKyrbhMVm6TPN5+Qi5ODOjfw1ZieDXVT0zqVnBSwbV/9fkKvLN8vSZrUv5lGdqlvciIAsF8U0auLswekn/7ojXjbDKlWmKlxAADW5+fnJz8/64wZ3KBBAwUGBmrNmjWFY6JnZ2dr/fr1eu2116xyTABo4l9TfjVddC49WzviUtTpj6I6qoYLF7M1Y9k+fb/tZOE6b3dn9b8hUM2DPOXm7Ch3l4IPTqJjk7T2QKJOJmXol0Pn9MuhcxrcJlgv3NFCdTz5sBb4cecpPRu5S5L0WK+Gerx36SfRBgBciSJ6dZCXK0WOlfKypMa3SO1GmZ0IAGBjTpw4oQsXLujEiRPKy8tTTEyMJKlx48aqWbOmJCk8PFwzZ87UnXfeKYvFogkTJuiVV15RkyZN1KRJE73yyivy8PDQfffdZ+IzAVCVWSwWdW5YW8t2ntamI+cpolcRhmHou60n9cryfUq6lCOLRRrUOlhD2warR+M6cnG68hu0Q26sK8MwdOTsRX2++bg+2xSrpTtOad2BRE25vbnu6RAqB4fihxcDqrK1BxL11KIYGYZ0b6d6mtw/3OxIAGD3KKJXB7++JZ3aJrl5S4PnSCWMVQsAqJ5efPFFLVy4sPDny73L165dq969e0uSDhw4oJSUlMJtJk2apIyMDD3++ONKSkpS586dtXr1anl6elZqdgDVS9fLRfSj5/RPNTE7Dq5T8qVsjf9yu349fE6SFB7oqVfuaqV29Wpdc1+LxaLG/jU1bfANuqtdXU1ZvEt7TqVqyuJd2njkvObc29ba8QGb8/uxCxr3+Vbl5Bka1CZYLw9tWeJ8NQCA0qGIXtWd3imtf7Vg+fZZklewuXkAADYpIiJCERERJW5jGEaRny0Wi6ZNm6Zp06ZZLxgA/EXXRrUlSdtOJCszJ09uzoyLbq/iLlzS6AW/68jZi3JzdtBTtzTVwz0ayNmx7HM3tQ7x0ZInuitiY6xmrzmoQa2Drr0TUMXsjk/RIxFRyszJV59mdTR7eBs58o0MAKgQFNGrstwsKfIxKT9Xaj5YanW32YkAAACA69LQr4b8PV2VmJalbSeS1K2RdeZ+gHXtjk/RQxFROpuWpSBvNy14qKPCA72u6zGdHB30aM+GGtq2rvxqMi46qpcjZ9M16tPflZaVq04NfPXB/e3L9YEUAODqeEWtytbNlBL3SjXqSHe8xTAuAAAAsHsWi6WwN/rmI+dNToPy2HDwrO6Zt0ln07IUHuipxY93u+4C+p9RQEd1E5+coZGfbNH5i9lqWddL80d1KJyEFwBQMSiiV1Untki/vVOwfMfbUg166AAAAKBq6NrwjyL60QsmJ0FZbT56Xo8ujNbF7Dx1a1Rb34ztqiBvd7NjAXbrbFqWRn6yRadSMtWoTg0tfKiTPN2czY4FAFUORfSqKPui9MNYyciX2twrNb/D7EQAAABAhbncE317XJIysvNMToPS2p+QqjGfRSs7L1/9WgQo4qFO8qLYB5RbSkaOHvz0dx09d1F1fdz1+aOdVZtvYgCAVVBEr4p+mi5dOCp51ZX6v2p2GgAAAKBC1fP1ULC3m3LyDG09nmR2HJRCfHJGwXjNmbnqFOard+9tKxcn/h0FyisjO0+PRERp3+lU+dV01eePduZbHQBgRbxrqWqOrpN+n1ewPHiO5O5jZhoAAACgwlksFnX5ozf6pqPnTE6Da0m6mK0H52/RmdQsNQ2oqY8f7CA3Z8ZrBsorOzdfj32+VdHHk+Tl5qTPHu6kBn41zI4FAFUaRfSqJDNFWjK+YLnDI1LjvubmAQAAAKzk8rjom5hc1Kbl5OXrsX9v1ZGzFxXk7aaIhzrJ24MhXIDyyss39NSiGG04eFbuzo5a8FBHtQiuuIl5AQBXRxG9Kln1rJQSJ9UKk259yew0AAAAgNVcHhd958kUXczKNTkNivPGqgP6PfaCPF2dtPDhTgr2YbgJoLwMw9Czi3dp2a7Tcna06KMH26t9fV+zYwFAtUARvao4sELa/rkkizT0Q8m1ptmJAAAAAKsJqeWhUF935eYbioq9YHYcXMXqPQn6aMNRSdIbw1qraYCnyYkA+2UYhl5Zvk+LouPkYJHeHdFWPZvUMTsWAFQbFNGrgksXpKX/KFjuNl6q383cPAAAAEAl6NLg8rjoDOlia06cv6R/fbtDkvRw9wbq3zLI5ESAfXt/7WF9/MsxSdKrd7XWgFZcUwBQmSiiVwXLnpYuJkp+zaQ+z5udBgAAAKgU3RoXFNF/O8zkorYkKzdPT3y5TWmZuWpbz0eTB4SbHQmwa59titWbqw9Kkp4f2FzDO4aanAgAqh+K6PZu9/fSnkjJ4ijdOVdydjM7EQAAAFApujf2kyTtOZWq8+lZJqfBZTOX79eu+BT5eDjrvfvaycWJfzuB8loSE68Xl+yRJP3j5sZ6tGdDkxMBQPXEuxl7lpYgLftXwfJNE6W67czNAwAAAFQif083NQ/ykmFIv9Ib3Sb8euicIjbGSpLeGn6j6jKRKFBu6w+e1b++KRgWaVTX+nrq1qYmJwKA6osiur0yjIJx0DOSpMDW0k3/z+xEAAAAQKW7qUlBb/QNBymimy0tM0fPfL9TkjSyS331Cfc3ORFgv2LikjXu863KzTc0uE2wpg66QRaLxexYAFBtUUS3V9s/lw6tkhxdpDvnSY7OZicCAAAAKt1NTetIkn45dFaGYZicpnqbsWyf4pMzVM/Xg3HQgetwODFdDy34XZey89SziZ/eHNZGDg4U0AHATBTR7VHScWnllILlm5+XAlqYmwcAAAAwSfv6teTm7KDEtCwdPJNudpxqa92BRH0dFSdJeuPu1qrh6mRyIsA+nU7J0IPztyjpUo7ahHhr7gPtmVcAAGwAr8T2Jj9fWvKElJ0mhXaRuo43OxEAAABgGjdnR3VpWFuStOHgWZPTVE8pGTma/P0uSdJD3cPU+Y/fB2zPjBkz1K1bN3l4eMjHx6dU+4wePVoWi6XIrUuXLtYNWk0lX8rWg/N/16mUTDX0q6FPR3fkAykAsBEU0e1N1MdS7C+Ss4c09APJwdHsRAAAAICpejYpGNJlwyGK6GaYsWyvElIz1cCvhibdxjAutiw7O1vDhg3TuHHjyrRf//79dfr06cLb8uXLrZSw+srIztPDEVE6lJiuAC9XffZIJ9Wu6Wp2LADAH/hI056cOyytmVqwfOtLUu1G5uYBAAAAbMDlyUV/P3ZBmTl5cnOmo0ll2XL0vL6JPimpYBgXdxfOvS2bPn26JCkiIqJM+7m6uiowMNAKiSBJOXn5evyLrdp2Illebk767OHOCqnlYXYsAMCf0BPdXuTlSj+MlXIzpIa9pQ6PmJ0IAAAAsAmN/WsqyNtNWbn5+v3YBbPjVBvZufl6/ofdkqR7O9VThzBfkxPBWtatWyd/f381bdpUY8aMUWJiYonbZ2VlKTU1tcgNV5efb+iZ73dq7YGzcnVy0KejO6pZoKfZsQAAf0ER3V5sfFc6GSW5eklD3pcc+NUBAAAAkmSxWNTzj97ojIteeT759agOJaardg0XPdO/mdlxYCUDBgzQF198oZ9//lmzZs1SVFSUbr75ZmVlZRW7z8yZM+Xt7V14Cw0NrcTE9uXVlfu1eFu8HB0s+uD+dnwYBQA2ikqsPTizR1r7SsHygNck7xBz8wAAAAA25vK46L8cOmdykuoh7sIlvfvfQ5Kk5wY2l4+Hi8mJqq9p06ZdMfHnX2/R0dHlfvx77rlHAwcOVMuWLTVo0CCtWLFCBw8e1LJly4rdZ8qUKUpJSSm8xcXFlfv4VdnHG47qow1HJUmv3tVKfZsHmJwIAFAcxkS3dbnZ0uLHpPwcqdntUpt7zU4EAAAA2Jwejf1ksUgHzqQpISVTgd5uZkeqsgzD0ItLdiszJ19dGvrqzrZ1zY5UrY0fP14jRowocZuwsLAKO15QUJDq16+vQ4cOFbuNq6urXF2ZFLMkS3ec0ozl+yRJkweEa1gHeusDgC2jiG7rNrwundkluftKd7wtWSxmJwIAAABsTq0aLmpd11s7Tqbol0NnKUhZ0ao9CVp74KycHS16eWgrWfgfxVR+fn7y8/OrtOOdP39ecXFxCgoKqrRjVjWbj57XxG92SJJGdwvTYzc1NDkRAOBaGM7Flp3cKv0yu2D5jrckT77aBQAAABTn8pAu6xgX3WoysvP0fz8W9J597KZGauxf0+REKIsTJ04oJiZGJ06cUF5enmJiYhQTE6P09PTCbcLDwxUZGSlJSk9P18SJE7Vp0ybFxsZq3bp1GjRokPz8/HTnnXea9TTs2qEzafr7Z9HKzstX/xsC9cIdLfggCgDsAD3RbVVOhvTDWMnIk1reLd0w1OxEAAAAgE27ubm/3lt7WBsOnFV2br5cnOgzVNHmbTii+OQMBXu76Yk+jc2OgzJ68cUXtXDhwsKf27ZtK0lau3atevfuLUk6cOCAUlJSJEmOjo7atWuXPvvsMyUnJysoKEh9+vTRokWL5OnpWen57d2Z1EyNXhCl1Mxcta9fS2+PuFGODhTQAcAeUES3Vf/9P+ncQalmoHT7G2anAQAAAGzejSE+8qvponPp2YqKvaDujStviIvqID45Q3PXH5EkTbm9udxdHE1OhLKKiIhQREREidsYhlG47O7urlWrVlk5VfWQnpWrhxZEKT45Qw39aujjBzvIzZlrCADsBV0zbFHsr9LmDwqWB8+RPHzNzQMAAADYAQcHi/o085ckrdl7xuQ0Vc/M5fuUmZOvTg18dUdrxsMGSisnL1/jPt+qvadT5VfTRREPdZJvDRezYwEAyoAiuq3JSpN+GCfJkNqOlJr2MzsRAAAAYDduaVEwj9B/958p0qMW12fL0fP6cedpOVikqYMYwxkoLcMwNGXxLv1y6JzcnR316eiOqlfbw+xYAIAyoohua1Y/LyWfkLzrSbe9YnYaAAAAwK70bOInFycHxV3I0KHE9GvvgGvKyzc07T97JUkjOtXTDcHeJicC7MfbPx3Sd1tPysEivX9/W7UO8TE7EgCgHCii25JDP0lbIwqWh34guXmZGgcAAACwNx4uTureqLYkhnSpKIui4rTvdKq83Jw0sV8zs+MAduPb6Di9899DkqSXh7bSzeEBJicCAJQXRXRbkZEkLR1fsNx5nNSgp7l5AAAAADvVt/kfQ7rso4h+vdIyczR7zQFJ0oRbmjKOM1BKm4+e17ORuyRJT/RppPs61zM5EQDgelBEtxXLJ0lpp6XajaW+L5qdBgAAALBbfZsXTC66PS5Z59KzTE5j3+auP6Jz6dlq4FdDD3Spb3YcwC4cO3dRYz/fqpw8QwNbB+lft/INDgCwdxTRbcHepdKubySLg3TnPMmFSUYAAACA8grydlfLul4yDOnn/Ylmx7Fb8ckZ+uSXY5KkKQPC5eLEv4/AtSRfytbDEVFKvpSjG0N9NGtYGzk4MBEvANg73gWZLT1R+nFCwXL3CVJIBzPTAAAAAFVC33CGdLleb6zcr6zcfHVu4KtbWzCWM3At2bn5Gvv5Vh07d1F1fdz18YMd5ObsaHYsAEAFoIhuJsOQfnxKunReCmgp9Z5sdiIAAACgSrhc9N1w8Jwyc/JMTmN/dsQl64eYU5Kk5we2kMVCT1qgJIZh6Pkfdmnz0Quq6eqk+aM7qI6nq9mxAAAVhCK6mXYukvb/KDk4S3fOlZxoYAEAAICKcEOwlwK93JSRk6dNR8+bHceuGIahl5ftlSTd1bauWoV4m5wIsH3zNhzVN9En5WCR5tzXVuGBXmZHAgBUIIroZkmJL5hMVCrogR7Yytw8AAAAQBVisVgKJxhdvSfB5DT2ZdWeBEXFJsnN2UETb2NCROBaVu4+rVdX7JckTR10g/o08zc5EQCgolFEN4NhSEvHS1kpUt32BWOhAwAAAKhQt7cKkiSt3J2gnLx8k9PYh+zc/MJi4KM9GirYx93kRIBt2x2fogmLYiRJo7rW16huYabmAQBYB0V0M0R/Kh35WXJyk4bOlRydzE4EAAAAVDmdG/iqdg0XJV3K0aYjDOlSGl9uOa7Y85fkV9NFY3s3MjsOYNPOpmVpzGfRyszJV6+mdfTCHS3MjgQAsBKK6JXtwlFp9QsFy32nSnWampsHAAAAqKKcHB3Uv2WgJGnZztMmp7F9qZk5eue/hyRJE25pqpqudPYBipOdm69xn2/V6ZRMNaxTQ3PuaysnR0osAFBV8QpfmfLzpB8el3IuSvV7SJ3Hmp0IAAAAqNIGtv5jSJc9CcrOZUiXkny47oiSLuWoUZ0aGtEx1Ow4gM0yDENTl+5W9PEkebo66eMHO8jLzdnsWAAAK6KIXpk2fyCd2CS51JSGvi85cPoBAAAAa+rcoLb8aroqJSNHvx05Z3YcmxWfnKFPfz0mSZo8oDk9aoESfL7lhL76PU4Wi/TuvW3VqE5NsyMBAKyMd0aVJXGf9N//K1i+7RWpVpipcQAAAIDqwNHBottbMaTLtcxadUBZufnq1MBXtzT3NzsOYLM2Hz2v6Uv3SJIm3RauPuFcLwBQHVBErwx5OVLkWCkvS2p8q9TuQbMTAQAAANXGwFYFQ7qsYkiXq9odn6LImHhJ0nO3N5fFYjE5EWCbTiZd0uNfbFNuvqHBbYI1tldDsyMBACoJRfTK8Mss6XSM5OYjDZ4j8aYUAAAAqDQdwnzl7+mqtMxc/Xr4rNlxbIphGHpl+T4ZhjS4TbDahPqYHQmwSZeyczXms626cDFbLet66bW/teYDJwCoRiiiW9up7dKGNwqWB86SvILMzQMAAABUMwVDuhS8D/9xB0O6/Nm6A2e18ch5uTg66P/d1szsOIBNMgxDk7/fpX2nU+VX00XzRnaQu4uj2bEAAJWIIro15WRKkeOk/FypxVCp5d/MTgQAAABUS3e0Liiir9l7Rpk5eSansQ25efl6Zfk+SdJD3cMU6uthciLANi3cGKulO07J0cGiD+5vr7o+7mZHAgBUMoro1rTuFensPqlGHWngbIZxAQAAAEzSrl4tBXq5KS0rVxsOMqSLJH0TfVKHEtPl4+Gsx/s0NjsOYJO2Hr+gl5cVfNg0ZUC4OjXwNTkRAMAMFNGt5cRm6bd3C5YHvSvVqG1uHgAAAKAac3CwaFCbgt7o3287aXIa86Vn5Wr2moOSpH/2bSJvd2eTEwG252xaVuFEogNbB+mRHg3MjgQAMAlFdGvIvihFjpVkSG3uk8JvNzsRAAAAUO3d3T5UkvTffYk6l55lchpzfbT+iM6lZymstofu71zf7DiAzcnNy9eTX23TmdQsNapTg4lEAaCao4huDWumSknHJK+60oBXzU4DAAAAQFKzQE+1CfFWbr6hH7bHmx3HNAkpmfrol6OSpMkDwuXixL+FwF+9sfqANh+9oBoujpo3sr1qujqZHQkAYCLeLVW0I2ulqI8Lloe8L7l5m5sHAAAAQKFhHQp6oy+KipNhGCanMcfrq/YrMydfHerX0m03BJodB7A5K3cnaN76gg+aXr+7jRr7e5qcCABgNoroFSkzRVryRMFyx0elRn3MzQMAAACgiEFtguXq5KBDienacTLF7DiVbkdcshZvK+iF/8IdLRieAviLY+cuauK3OyRJj/RooIGtg0xOBACwBRTRK9KKyVJqvFSrgXTrS2anAQAAAPAX3u7OGtCyoPf1t9FxJqepXIZh6KUf90qS7mpXV21CfcwNBNiYzJw8PfHFNqVn5apjWC1NHhBudiQAgI2giF5R9i+TdnwpySLdOVdyqWF2IgAAAABXMfyPIV2WxpxSRnaeyWkqz487T2vr8SS5Oztq0m0UB4G/mrl8n/aeTpVvDRfNubednB0pmQAACtAiVISL56X//LNgufs/pHpdzM0DAAAAoFhdGtZWSC13pWXlatWeBLPjVIrMnDy9umK/JGlc70YK9HYzORFgW1buTtDCTcclSbOGt+EaAQAUQRH9ehmGtOwp6eJZqU5zqfezZicCAAAAUAIHB4vubh8iSfqmmgzpMv/XY4pPzlCwt5vG9GxodhzApsRduKRJ3xWMg/7YTQ3Vp5m/yYkAALaGIvr12v29tHeJ5OBUMIyLM59WAwAAALbu7vYhslikjUfO68T5S2bHsaozqZl6f+1hSdIzA8Ll7uJociLAduTk5evJr7YrNTNXbev5aOJtzcyOBACwQRTRr0fqaWnZvwqWb5okBd9oahwAAMprxowZ6tatmzw8POTj41OqfUaPHi2LxVLk1qULQ5oBsA8htTzUo7GfJOnzLcdNTmNdM5bt06XsPLWr56PBbYLNjgPYlDdXHVBMXLK83Jz07oi2jIMOALgqWofyMgxp6ZNSZrIUdKPU82mzEwEAUG7Z2dkaNmyYxo0bV6b9+vfvr9OnTxfeli9fbqWEAFDxRncLkyR9teWE0rNyzQ1jJZuOnNfSHadksUgvDWkpi8VidiTAZqw9kKh5G45Kkl6/u7VCfT1MTgQAsFVOZgewW9s+kw6vkRxdpTvnSY7OZicCAKDcpk+fLkmKiIgo036urq4KDAy0QiIAsL4+zfzV0K+Gjp67qG+j4/RQ9wZmR6pQOXn5mrp0tyTp/s711LKut8mJANtxNi1LE78pGAd9VNf66t8yyOREAABbRk/08kg6Lq36YwLRvi9I/uHm5gEAwCTr1q2Tv7+/mjZtqjFjxigxMbHE7bOyspSamlrkBgBmcXCw6KEeBYXzT387prx8w+REFWvhxlgdPJOuWh7OmtiPcZ6BywzD0DPf79T5i9kKD/TUlNubmx0JAGDjKKKXVX6+9MPjUna6VK+r1OVxsxMBAGCKAQMG6IsvvtDPP/+sWbNmKSoqSjfffLOysrKK3WfmzJny9vYuvIWGhlZiYgC40t/a1ZWPh7PiLmRozd4zZsepMImpmXr7p0OSpEn9w+Xj4WJyIsB2fL7lhH7enygXJwe9PeJGuTkz2S4AoGQU0cvq93nS8V8l5xrS0A8kBxpbAIBtmjZt2hUTf/71Fh0dXe7Hv+eeezRw4EC1bNlSgwYN0ooVK3Tw4EEtW7as2H2mTJmilJSUwltcXFy5jw8AFcHDxUn3d64nSZr/61GT01ScmSv2Kz0rV21CvHVPBz6wBC47nJiuGcv2SpKe6R+u8EAvkxMBAOwBY6KXxdmD0k/TCpb7/Z/k29DUOAAAlGT8+PEaMWJEiduEhYVV2PGCgoJUv359HTp0qNhtXF1d5erqWmHHBICK8GDXMH204aiiYpO0Iy5ZbUJ9zI50XX47fE6R2+MLJxN1cGAyUUCSsnPzNWHRdmXm5KtHYz899MfkwgAAXAtF9NLKy5V+GCvlZkoN+0gdHjY7EQAAJfLz85Ofn1+lHe/8+fOKi4tTUBATcwGwLwFebhrUOliLt8dr/q/H9O69bc2OVG4Z2XmasniXJOmBzvXt/gMBoCK9/dNB7Y5PlY+Hs2YNb8MHTACAUmM4l9L67S0pfqvk6i0NeV+y0NgCAKqOEydOKCYmRidOnFBeXp5iYmIUExOj9PT0wm3Cw8MVGRkpSUpPT9fEiRO1adMmxcbGat26dRo0aJD8/Px05513mvU0AKDcHv5jgtFlu07rZNIlk9OU31s/HdSJC5cU5O2mSf2ZTBS4bMvR8/pw/RFJ0sw7WynAy83kRAAAe0IRvTRO75TWvVawPOA1ybuuuXkAAKhgL774otq2baupU6cqPT1dbdu2Vdu2bYuMmX7gwAGlpKRIkhwdHbVr1y4NGTJETZs21ahRo9S0aVNt2rRJnp6eZj0NACi3lnW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      "text/plain": [
       "<Figure size 1500x700 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''simulation of the system for (b)'''\n",
    "\n",
    "#define F(x)\n",
    "def F(x, t = 0):\n",
    "    # t plays no role as the system is autonomous but is needed for odeint\n",
    "    return np.cos(2*x)+1-x\n",
    "\n",
    "fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize = (15,7))\n",
    "\n",
    "#show the intersection of cos(2x) with 1-x\n",
    "x = np.linspace(-2,3,100)\n",
    "y1 = np.cos(2*x)\n",
    "y2 = -(1-x)\n",
    "\n",
    "ax1.plot(x,y1, label = 'cos(2x)')\n",
    "ax1.plot(x,y2, label = '-(1-x)')\n",
    "ax1.legend()\n",
    "ax1.set_xlabel(r'$x$')\n",
    "\n",
    "\n",
    "#show F(x)\n",
    "y = F(x)\n",
    "ax2.plot(x,y, label = 'F(x)=cos(2*x)+1-x')\n",
    "ax2.axhline(y = 0, color = 'red', ls = '--')\n",
    "ax2.scatter(x=0.86,y=0, marker='o', s = 100, color = 'black')\n",
    "ax2.text(x = -1., y= -1, s = r'$x^* \\approx 0.86$', size = 15)\n",
    "ax2.set_xlabel(r'$x$')\n",
    "ax2.set_ylabel(r'$F(x)=\\dot{x}$')\n",
    "ax2.legend()\n",
    "\n",
    "#simulate F(x) in time\n",
    "tspan = np.linspace(0,2,1000)\n",
    "l_x0 = [-2, 0., 1., 2.]\n",
    "for x0 in l_x0:\n",
    "    X = odeint(F, x0, tspan)\n",
    "    ax3.plot(tspan,X, label = 'x0 = ' + str(x0))\n",
    "ax3.axhline(y = 0.86, color = 'black', ls = '--')\n",
    "ax3.legend()\n",
    "ax3.set_ylabel(r'$t$')\n",
    "ax3.set_xlabel(r'$x(t)$')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">(c) There is only one fixed point at $x = 4$ that is semi-stable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/pdf": 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",
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      "text/plain": [
       "<Figure size 1500x700 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''simulation of the system for (c)'''\n",
    "\n",
    "#define F(x)\n",
    "def F(x, t = 0):\n",
    "    #t plays no role as the system is autonomous but is needed for odeint\n",
    "    return x**2-8*x+16\n",
    "\n",
    "#show F(x)\n",
    "x = np.linspace(1,7,100)\n",
    "y = F(x)\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize = (15,7))\n",
    "ax1.plot(x,y)\n",
    "ax1.axhline(y = 0, color = 'red', ls = '--')\n",
    "ax1.scatter(x=4,y=0, marker= MarkerStyle('o', fillstyle = 'left'), s = 200, color='black')\n",
    "\n",
    "ax1.text(x = 3.5, y= 2.5, s = r'$x^*=4$', size = 15)\n",
    "ax1.set_xlabel(r'$x$')\n",
    "ax1.set_ylabel(r'$F(x)=\\dot{x}$')\n",
    "\n",
    "#simulate F(x) in time\n",
    "tspan = np.linspace(0,4,1000)\n",
    "l_x0 = [3., 4.2]\n",
    "for x0 in l_x0:\n",
    "    X = odeint(F, x0, tspan)\n",
    "    ax2.plot(tspan,X, label = 'x0 = ' + str(x0))\n",
    "ax2.axhline(y = 4., color = 'black', ls = '--')\n",
    "ax2.set_ylabel(r'$t$')\n",
    "ax2.set_xlabel(r'$x(t)$')\n",
    "\n",
    "ax2.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Allee effect (paper and pencil)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The classical view of population dynamics states that due to competition\n",
    "\tfor resources, a population will experience a reduced growth rate\n",
    "\twhen the number of individuals is large. But this is not necessarily\n",
    "\tsufficient to describe the dynamics of some populations. Indeed, for\n",
    "\tcertain species, it has been observed that the growth rate of the population\n",
    "\tcan be null or even negative for a low number of individuals. This\n",
    "\tis called the Allee effect and can be explained, for instance, by\n",
    "\tthe fact that it is hard to find mates when the population density\n",
    "\tis too low. The effect leads to distinct dynamics for\n",
    "\tthe population size.\n",
    "\t\n",
    "\n",
    "Let us consider the model with $a,b>0,\\,r>0$, and the number of individuals $N(t)\\geq0$:\n",
    "\n",
    "\\begin{equation}\n",
    "\\dot{N}=rN-\\frac N a(N-b)^{2}\n",
    "\\end{equation}\n",
    "\t\n",
    "As $N$ can be factorized in this equation, it is convenient to study\n",
    "\tthe *relative growth rate* $g(N) = \\dot{N}/N$. In order to get an Allee\n",
    "\teffect, **1)** the relative growth rate needs to reach a maximum\n",
    "\tat an intermediate population size and **2)** it has to be negative\n",
    "\tat small population sizes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1) Sketch the relative growth rate. \n",
    "- Which kind of function is it?\n",
    "- What is the maximum relative growth rate and for which number of individuals it is realised?\n",
    "- For which values of the parameters $a,b,r$ we have an Allee effect as described above?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Answer:*\n",
    "- The model is given by $\\frac{\\dot{N}}{N}=g(N)$, where $g(N)=r-\\frac 1 a (N-b)^{2}$ is the relative growth rate. $g(N)$ is a concave parabola, it has the maximum at $b$ and it crosses the $N$-axis at $b\\pm\\sqrt{ar}$.\n",
    "- The **maximum growth rate per capita** is realised for $b$ number of individuals and it is equal to $r$.\n",
    "- The Allee effect is present when the population number is low (but stil positive) and the growth rate is decrasing.  \n",
    "   We basically want a combination of parameter that has g(N) negative for small positive values of N\n",
    "   (population going extinct at low values). We obtain this behaviour by getting $g(0) = r-b^2/a$ (the parabola's intercept)\n",
    "   and setting it < 0 \n",
    "   the parabola crosses the $N$-axis at positive values of $N$, which is realised for $b \\gt \\sqrt{ar}$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2) Study the qualitative behavior of the solution using the  procedure:\n",
    "\n",
    "* Sketch $\\frac{\\dot{N}}{N}$ in function of $N$ and the one-dimensional vector field on the $N$-axis. Which are the fixed points of this equation? Are they stable or unstable?\n",
    "* Now, let's go back to the full equation (1). Represent $\\dot{N}$ in function of $N$ for different conditions satisfying or not the Allee effect.\n",
    "* Discuss the existence and stability of the fixed points, and how it relates to the presence/absence of the Allee effect.\n",
    "* Discuss how the number of fixed points changes as a function of $a$. Plot the fixed points as a function of $a$. Which kind of trajectories do we have in the $N-t$ plane depending on whether $a$ is smaller or bigger than $b^2/r$?\n",
    "* Can you think of other causes that would lead to an Allee Effect ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> As said previously, $g(N)$ is a concave parabola that intersects the x-axis in $N^{*}=b\\pm\\sqrt{ar}$. These are the two fixed points. The graph below shows an example for $r$ = 10, $a$ = 500 and $b$ = 100."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/pdf": 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",
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#define g(N)\n",
    "def g(r, a, N, b):\n",
    "    return r-(N-b)**2/a\n",
    "\n",
    "#define parameters\n",
    "r = 10\n",
    "a = 500\n",
    "b = 100\n",
    "\n",
    "#plot g(N)\n",
    "N = np.linspace(0,200,100)#np.linspace(0,7,100)\n",
    "\n",
    "#plot g(N)\n",
    "plt.plot(N, g(r,a,N,b))\n",
    "plt.axhline(y = 0, color = 'red', ls = '--')\n",
    "plt.axvline(x = b+(a*r)**0.5, color = 'black', ls = '--')\n",
    "plt.axvline(x = b-(a*r)**0.5, color = 'black', ls = '--')\n",
    "plt.axvline(x=0, c='gray')\n",
    "plt.xlabel('N')\n",
    "plt.ylabel('g(N)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">$\\dot{N}$ is a cubic function (see figure below) that has 2 or 3 fixed points for $N\\geq0$, depending on the parameters $a$ and $b$. The fixed points are either $N^{*}=0$ and $N^{*}=b+\\sqrt{ar}$, or $N^{*}=0$ and $N^{*}=b\\pm\\sqrt{ar}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">In the case $a > b^2/r$, $N^{*}=0$ is an unstable fixed point and $N^{*}=b+\\sqrt{ar}$ a stable one. If $a < b^2/r$, then $N^{*}=0$ is a stable fixed point, $N^{*}=b-\\sqrt{ar}$ an unstable one and $N^{*}=b+\\sqrt{ar}$ is stable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/pdf": 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",
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def Ndot(r, N, a, b):\n",
    "    return r*N-N*(N-b)**2/a\n",
    "\n",
    "#plot g(N)\n",
    "N = np.linspace(0,200,200)\n",
    "\n",
    "#define parameters in an easy way\n",
    "b = 100\n",
    "r = 10\n",
    "\n",
    "#plot g(N) for r>ab**2 and r<ab**2\n",
    "a = b**2/r \n",
    "N = np.linspace(0,200,200)\n",
    "plt.plot(N, Ndot(r,N,a,b))\n",
    "plt.scatter(x=b-np.sqrt(a*r),y=0, marker='o', s = 100, color = 'black', facecolors='none')\n",
    "plt.scatter(x=b+np.sqrt(a*r),y=0, marker='o', s = 100, color = 'black')\n",
    "#plt.text(x = 0.5, y = 4., s = r'$r>ab^2$, 2 fixed points for $N \\geq 0$')\n",
    "\n",
    "a = 100\n",
    "N = np.linspace(0,150,200)\n",
    "plt.plot(N, Ndot(r,N,a,b))\n",
    "plt.axhline(y = 0, color = 'red', ls = '--')\n",
    "plt.scatter(x=b-np.sqrt(a*r),y=0, marker='o', s = 100, color = 'black', facecolors='none')\n",
    "plt.scatter(x=b+np.sqrt(a*r),y=0, marker='o', s = 100, color = 'black')\n",
    "#plt.scatter(x=b+(r/a)**0.5,y=0, marker='o', s = 100, color = 'black')\n",
    "#plt.text(x = -0.25, y =-1.5, s = r'$r<ab^2$, 3 fixed points for $N \\geq 0$')\n",
    "\n",
    "\n",
    "plt.scatter(x=0,y=0, marker='*', s = 100, color = 'black')\n",
    "#plt.ylim([-2,8])\n",
    "plt.xlabel('N')\n",
    "plt.ylabel(r'$\\dot{N}$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">For larger $a$, the unstable fixed point $N^{*}=b-\\sqrt{ar}$ approaches the stable fixed point in 0 until it collapses into one single unstable fixed point, which occurs when $a=b^2/r$. Afterwards, only two fixed points remain: a stable one $N^{*}=b+\\sqrt{ar}$ and an unstable one at 0. This case corresponds to the behavior of the population qualitatively similar to the logistic growth. See figure below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/pdf": 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",
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#define r domain\n",
    "a = np.linspace(0,5000,5000)\n",
    "\n",
    "#define parameters in an easy way\n",
    "r = 10\n",
    "b = 100\n",
    "\n",
    "#plot N* depending on r\n",
    "plt.plot(a, [x if x>=0 else np.nan for x in b-np.sqrt(a*r)], color = 'red')\n",
    "plt.text(x = 2000, y = 300, s = 'stable: ' + r'$b+\\sqrt{ar}$', color= 'green')\n",
    "\n",
    "plt.text(x = -200., y = 100, s = r'$b$', color= 'black')\n",
    "\n",
    "plt.plot(a, b+np.sqrt(a*r), color = 'green')\n",
    "plt.text(x = 500, y = 50, s = 'unstable ' + r'$b-\\sqrt{ar}$', color= 'red')\n",
    "\n",
    "plt.plot([0, b**2/r], [0,0], color = 'green')\n",
    "plt.text(x = 10, y = 10, s = 'stable', color= 'green')\n",
    "\n",
    "plt.plot([b**2/r, 5000], [0,0], color = 'red')\n",
    "plt.text(x = 3000, y = 10, s = 'unstable', color= 'red')\n",
    "\n",
    "plt.xlabel('a')\n",
    "plt.ylabel(r'$N^{*}$')\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">At low population densities for a small $a$, i.e. $a<b^{2}/r$, we have an unstable fixed point at $N=b-\\sqrt{ar}$. Initial populations below this unstable fixed point will reach the stable fixed point at 0. This represents a critical population size below which the population risks extinction. This situation is unlike the logistic growth (see Course Chap 1), where the trajectories always grow or decay to the only stable fixed point at $N=K$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">The general idea of the Allee effect is that for small populations, the growth rate of the population can be low and even negative. This can be due to a difficulty in finding mates, which can lead to consanguinity, but also to less efficient hunting strategies in small groups. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Formation of a dimer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The formation of a dimer $C$ from its subunits $A$ and $B$ can be described by the following reversible chemical reaction :\n",
    "\n",
    "$$\n",
    "A_{F}+B_{F}\\overset{k_1}{\\longrightarrow}C\n",
    "$$\n",
    "\n",
    "$$\n",
    "C\\overset{k_{-1}}{\\longrightarrow}A_{F}+B_{F}\n",
    "$$\n",
    "\t\n",
    "The total concentrations of the proteins $A$ and $B$ are constant ; they are denoted by $A_{T}$ and $B_{T}$ , and by $A_{F}$ and $B_{F}$ for the concentrations of the free (non-bound) forms.\n",
    "\n",
    "* Express the conservation of $A_{T}$ in function of $A_{F}$ and $C$.\n",
    "* Write the equation describing the temporal evolution of the concentration of the complex $C$ by using the total concentrations of $A_{T}$ and $B_{T}$ and the kinetic constants $k_{1}$ and $k_{-1}$.\n",
    "* Describe the type of this dynamical system (order, linearity, etc.).\n",
    "* Calculate the **equilibrium** concentration of the complex, in other words what is the value of the **stable** fixed point for $C$. Express the result in function of $A_{T}$ and $B_{T}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">The total concentration of $A_{T}$ can be described as a sum of the free, non-bound form and the complexed form $C$: $A_{T}=A_{F}+C$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">The equation for the temporal evolution of $C$ reads:\n",
    "$$\n",
    "\\frac{dC}{dt}=k_{1}A_{F}B_{F}-k_{-1}C=k_{1}(A_{T}-C)(B_{T}-C)-k_{-1}C\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">The equation in point 2 represents a 1st order, non-linear ODE, due to the quadratic term in $C$. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">Setting the time derivative to zero (steady state) and solving the quadratic equation $k_{1}(A_{T}-C)(B_{T}-C)-k_{-1}C=0$ for C leads to:\n",
    "$$\n",
    "C=\\frac{k_{1}B_{T}+k_{1}A_{T}+k_{-1}\\pm\\sqrt{(-k_{1}B_{T}-k_{1}A_{T}-k_{-1})^{2}-4k_{1}^{2}A_{T}B_{T}}}{2k_{1}}\n",
    "$$\n",
    "Only the solution with the minus in front of the root is a stable fixed point. The latter observation can be deduced by noticing that the quadratic form corresponds to a convex parabola, therefore the first fixed point (the solution with minus) is stable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scatchard plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Scatchard plots** were historically used in molecular biology to estimate the affinity (equilibrium constant) of DNA-binding proteins for DNA. Imagine that $A$ is your protein of interest and $B$ the amount of DNA that you can vary over a  broad range. Assume that you can measure the steady state amount (the values at the fixed point) of DNA bound to the protein (which is equivalent to the complex $C$ in the above reaction), and the amount of free (unbound) DNA.  \n",
    " **Note**: in practice this can be done using electrophoretic mobility shift assays (EMSA) but you do not need to know such techniques to solve the problem here.  \n",
    " \n",
    "* Show that one can determine the dissociation constant $K_{d}=k_{-1}/k_{1}$ by linear regression, _i.e._ show that there is a linear relationship between the ratio $C/B_{F}$ and the bound fraction $C$.\n",
    "* Set the necessary parameters and use Python to do a Scatchard plot\n",
    "    * Start by plottig the linear relation between $C/B_{F}$ and $C$.\n",
    "    * Add labels to your plot \n",
    "    * Add lines for the axis\n",
    "    * Write what you are plotting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">If you set $dC/dt$ to 0 and solve for $C$ you get $C=\\frac{k_{1}}{k_{-1}}A_{F}B_{F}$, which can be rearranged into $\\frac{C}{B_{F}}=\\frac{A_{T}-C}{K_{d}}$ with $K_{d}=\\frac{k_{-1}}{k_1}$. This is the Scatchard equation, since by measuring now $C$ (=bound DNA-protein-complex) and $B_{F}$ (=free DNA) and then plotting the ratio $C/B_{F}$ versus $C$ you can determine the dissociation constant $K_{d}$ from the slope."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/pdf": 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",
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "C = np.linspace(-2,6,100)\n",
    "A_T = 4\n",
    "K_d = 3\n",
    "\n",
    "#plot C/B_F\n",
    "plt.plot(C, (A_T-C)/K_d)\n",
    "plt.xlabel(r'$C$')\n",
    "plt.ylabel(r'$C/B_F$')\n",
    "plt.axvline(0, c = 'black')\n",
    "plt.axhline(0, c = 'black')\n",
    "plt.text(0.5, 1.5, r'$\\frac{C}{B_{F}}=\\frac{A_{T}-C}{K_{d}}$', size = 15)\n",
    "plt.text(2.5,0.6, 'slope = ' + r'$-1/K_d$', size = 12)\n",
    "plt.show()\n"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.5"
  },
  "title": "Exercise 2: The Allee effect"
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
