lectures/lecture-13/lecture-13.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Lecture 13:  Sparse direct solvers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Recap of the previous part\n",
    "\n",
    "- Distributed memory for huge dense matrices\n",
    "- Sparse matrix formats (COO, CSR, CSC)\n",
    "- Matrix-by-vector product\n",
    "- Inefficiency of sparse matrix processing\n",
    "- Approaches to reduce cache misses"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Plan for this week: how to solve large sparse linear systems\n",
    "\n",
    "- Direct methods (start today and continue in the next lecture)\n",
    "    - LU decomposition\n",
    "    - Number of reordering techniques to minimize fill-in\n",
    "- Krylov methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Plan for today\n",
    "\n",
    "Sparse direct solvers: \n",
    "\n",
    "- LU decomposition of sparse matrices\n",
    "- fill-in of $L$ and $U$ factors\n",
    "- nested dissection\n",
    "- spectral clustering in details"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Direct methods for sparse matrix: LU decomposition\n",
    "\n",
    "- Why sparse linear systems can be solved faster, what is the technique? \n",
    "\n",
    "- In the LU factorization of the matrix $A$ the factors $L$ and $U$ can be also sparse:\n",
    "\n",
    "$$A = L U$$\n",
    "\n",
    "- And solving linear systems with **sparse** triangular matrices is very easy.  \n",
    "\n",
    "<span style=\"color:red\"> Note that the inverse matrix to sparse matrix is not sparse! </span>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-2.  1.  0.  0.  0.  0.  0.]\n",
      " [ 1. -2.  1.  0.  0.  0.  0.]\n",
      " [ 0.  1. -2.  1.  0.  0.  0.]\n",
      " [ 0.  0.  1. -2.  1.  0.  0.]\n",
      " [ 0.  0.  0.  1. -2.  1.  0.]\n",
      " [ 0.  0.  0.  0.  1. -2.  1.]\n",
      " [ 0.  0.  0.  0.  0.  1. -2.]]\n",
      "[[-0.875 -0.75  -0.625 -0.5   -0.375 -0.25  -0.125]\n",
      " [-0.75  -1.5   -1.25  -1.    -0.75  -0.5   -0.25 ]\n",
      " [-0.625 -1.25  -1.875 -1.5   -1.125 -0.75  -0.375]\n",
      " [-0.5   -1.    -1.5   -2.    -1.5   -1.    -0.5  ]\n",
      " [-0.375 -0.75  -1.125 -1.5   -1.875 -1.25  -0.625]\n",
      " [-0.25  -0.5   -0.75  -1.    -1.25  -1.5   -0.75 ]\n",
      " [-0.125 -0.25  -0.375 -0.5   -0.625 -0.75  -0.875]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([1.75000000e+00, 1.65849874e-17, 1.12884010e-34])"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy.sparse as spsp\n",
    "n = 7\n",
    "ex = np.ones(n);\n",
    "a = spsp.spdiags(np.vstack((ex,  -2*ex, ex)), [-1, 0, 1], n, n, 'csr'); \n",
    "b = np.array(np.linalg.inv(a.toarray()))\n",
    "print(a.toarray())\n",
    "print(b)\n",
    "np.linalg.svd(b[:3, 4:])[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## And the factors...\n",
    "\n",
    "$L$ and $U$ are typically sparse. In the tridiagonal case they are even bidiagonal!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.          0.          0.          0.          0.          0.\n",
      "   0.        ]\n",
      " [-0.5         1.          0.          0.          0.          0.\n",
      "   0.        ]\n",
      " [ 0.         -0.66666667  1.          0.          0.          0.\n",
      "   0.        ]\n",
      " [ 0.          0.         -0.75        1.          0.          0.\n",
      "   0.        ]\n",
      " [ 0.          0.          0.         -0.8         1.          0.\n",
      "   0.        ]\n",
      " [ 0.          0.          0.          0.         -0.83333333  1.\n",
      "   0.        ]\n",
      " [ 0.          0.          0.          0.          0.         -0.85714286\n",
      "   1.        ]]\n"
     ]
    }
   ],
   "source": [
    "from scipy.sparse.linalg import splu\n",
    "T = splu(a.tocsc(), permc_spec=\"NATURAL\")\n",
    "print(T.L.toarray())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Interesting to note that ```splu``` without ```permc_spec``` will produce permutations which will not yield the bidiagonal factor:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.          0.          0.          0.          0.          0.\n",
      "   0.        ]\n",
      " [-0.5         1.          0.          0.          0.          0.\n",
      "   0.        ]\n",
      " [ 0.         -0.66666667  1.          0.          0.          0.\n",
      "   0.        ]\n",
      " [ 0.          0.         -0.75        1.          0.          0.\n",
      "   0.        ]\n",
      " [ 0.          0.          0.          0.          1.          0.\n",
      "   0.        ]\n",
      " [ 0.          0.          0.         -0.8        -0.5         1.\n",
      "   0.        ]\n",
      " [ 0.          0.          0.          0.         -0.5        -0.71428571\n",
      "   1.        ]]\n",
      "[0 1 2 3 5 4 6]\n"
     ]
    }
   ],
   "source": [
    "from scipy.sparse.linalg import splu\n",
    "T = splu(a.tocsc())\n",
    "print(T.L.todense())\n",
    "print(T.perm_c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 2D-case\n",
    "From a matrix that comes as a discretization of  a two-dimensional problem \n",
    "everything is much worse:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x1192c9850>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy as sp\n",
    "import scipy.sparse as spsp\n",
    "import scipy.sparse.linalg\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "n = 20\n",
    "ex = np.ones(n);\n",
    "lp1 = sp.sparse.spdiags(np.vstack((ex,  -2*ex, ex)), [-1, 0, 1], n, n, 'csr'); \n",
    "e = sp.sparse.eye(n)\n",
    "A = sp.sparse.kron(lp1, e) + sp.sparse.kron(e, lp1)\n",
    "A = spsp.csc_matrix(A)\n",
    "T = spsp.linalg.splu(A)\n",
    "plt.spy(T.L, marker='.', color='k', markersize=8)\n",
    "#plt.spy(A, marker='.', color='k', markersize=8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "For correct permutation in 2D case the number of nonzeros in  $L$ factor grows as $\\mathcal{O}(N \\log N)$. But  complexity is $\\mathcal{O}(N^{3/2})$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Main challenge: how to make factors $L$ and $U$ as sparse as possible?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Main tool to analyze factors sparsity: graph theory\n",
    "\n",
    "- The number of nonzeros in LU decomposition has a deep connection to the graph theory.\n",
    "\n",
    "- ``networkx package`` can be used to visualize graphs, given only the adjacency matrix. \n",
    "\n",
    "- It may even recover to some extend the graph structure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EDNNe2Lt3L6SkpAQ2bn1lZGTUmGimpaVxHkM7z/8nMDAQw4cPR3JyMtTV1cUdTq06deqEmTNn4u+//xZ3KJSAvH//HlFRUYiNjUVMTAxiYmKQlpaG0tLSKqUubdu2RZ8+faCrq8v5T0tLC5KS9IYWRVG1owmlCBwOScaewCS+x1lhpQGJ58FYtGgRBg0aBC8vLygrK//8iWKQl5eH58+fV0k0ExIS8Pr162bdef7lyxcoKyvj9OnTmDlzprjDqdHLly+hrq6Oq1evVimJoBqfgoICeHl54dSpU3j8+DGAb018lYli165dISMjg7CwMOjq6oLJZCIjIwNxcXGIiYlBamoqgG+/qzNmzMDMmTPRo0cPcb4kiqIaKJpQiohH2Fts9ItHOZvwVFMpwWRAksnAltG94WD4rRHnwYMHGDduHFq0aIFr167BwMBAWGELXE2d5wkJCUhOTq6z81xLSwsqKipNItG0srJCUVERHjx4wPdYhaXleJNZiLJyNlpIMqGmJAc5af6uJK1btw7Hjh3Dhw8fICMjw3eMlOh9+PABW7Zsgbu7OwoKCmBlZYXp06fD2NgYqqqqXP8e5eTkIDo6Gl5eXrhw4QJyc3MxdOhQrFmzBpaWlkJ+FRRFNSY0oRShd1lFWOcdi/spGWCAgKD2N3UJJgMVbILB6u2w3VanWs1kWloaxo4di+joaJw8eRJTp04VdvhCVVPneUJCAp4/f17ldlyvXr04Wxs11s5zLy8vjB8/HnFxcejduzfPz09Oz8fFp28R8uIz3mYVVdlAnwFAVVEW5prKmGSkip4deGve+vr1K1RUVGBvb49Dhw7xHBslXoQQnDlzBsuWLYO0tDTmzp2LGTNmQE1Nje+xi4qKcPXqVRw9ehRPnjzBjBkzsHfvXigoKPAfOEVRjR5NKMUgOT0fTjvOIo3dGkSuXfWEQEkW5hrKmDxQtc5u7pKSEsyfPx+urq5YuHBhg6mrFKTaOs8TExMbbed5WVkZunTpAjs7Oxw/fpzr533/gaTyA0dtfvaBpDaXLl3CxIkTERMTAx0dHa5jo8Tv3bt3cHJyQlBQEKZNm4Z9+/ZBUVFR4PMQQnD69GksX74csrKyOHnyJH7//XeBz0NRVONCE0oxMTQ0RO/evXHkhAtftywJITh27BgWL14MExMTXL58ucHWVQpSY+8837t3L1auXIlHjx5h4MCBP308vyUTm0f3hqNh3XuXZmdnQ1tbG4aGhvDz8+N6Dkr83rx5AzMzM1RUVODUqVMYMWKE0Od8//495s6di4CAAJw5cwbTpk0T+pwURTVcNKEUg69fv6JVq1bYvXs3Fi1aJJAx79+/j3HjxkFaWhre3t7Q19cXyLiNUWPoPC8vL4exsTGKiooQGRlZ53GMgmzqWmDes9bvOzk54cqVK0hISEDnzp35no8SjdTUVJiamkJSUhKhoaHo0qWLyOZms9mYM2cOTp8+jXPnzmHKlCkim5uiqIaFJpRiEBMTAz09Pdy7dw+DBw8W2LhpaWmws7NDTExMk6irFLSaOs8TExPx6tUrsXSex8bGQl9fH/Pnz8e+fftqHF/Q207tstPhNHd9z9vbG3Z2djh58iScnZ0FNh8lXJ8/f4aRkRGYTCZCQ0OhoqIi8hjYbDZmz54NV1dXeHl5YezYsSKPgaIo8aMJpRicO3cO06dPR25uLlq3bi3QsUtKSjBv3jycOXMGixYtwp49e5pcXaWgFRcXIykpqdoWR6LoPD906BAWLVqE9evXY+vWrVXGEvTG+AAgLclE8FLTKjWV/v7+sLOzw5gxY3D58uUm0UnfXDg6OiI4OBiRkZFQVf35cazCwmaz4eDggNu3byMxMREdOnQQWywURYkHTSjFYMmSJbhx4waSkvi/jVkTQgiOHj2KJUuWwMTEBF5eXmjfvr1Q5mrKeO08/z7R7N69O9ed53v27MHKlSvx559/YvPmzZyEbsrpp0I7utPNyQgAEBAQADs7O4waNQqenp70w0cj4uvrCxsbG1y8eBETJ04UdzjIyMiAlpYWzMzM4OXlJe5wKIoSMZpQisGQIUPwyy+/wNPTU6jz3Lt3D/b29rSuUsC47TzX0NCotsVRbZ3nu3fvxurVqzFu3DgcPnwYeZCF5YF7QnsNN+Ybw+PkAezYsQO//fYbPD09G2RHPFWzvLw89OrVC/3798f169cbzFVlDw8PTJgwAd7e3rCxsRF3OBRFiRBNKEWMzWajbdu2WLduHdasWSP0+d69e4exY8ciNjYWJ0+epEXzQsRv53lAQADmz58PNpsNyzUnEZYjI9Crk5WYDID58gFSr+3B+vXrsX79enplspE5evQoFi1ahJcvX6Jr167iDoeDEAILCwuUlJTg0aNH4g6HoigRogmliKWkpKBnz564desWrKysRDJnSUkJ/vjjD5w9exaLFy/GP//8QxMIEeO287x79+748OED8kyXQUqhk9DiYRZlwsepL3R1dYU2ByUchBD069cP3bp1g7e3t7jDqebq1asYN24cYmNj0adPH3GHQ1GUiPB3RhvFs8jISABAv379RDZny5Yt4erqCn19fSxduhTR0dG4fPkyrasUoXbt2mHw4MHVuvpr6jwvI0xItv1FqPEQWSX00NQW6hyUcISHhyM6Oho7duwQdyg1Gj16NDp06IBTp07h4MGD4g6HoigRoVcoRWzt2rVwc3OrcmVKlO7du4dx48ZBRkYG3t7e6N+/v1jioGoX/yEXow7xf873zwQs/BW9O7UR+jyUYK1atQoXLlzAu3fvGuyRoytWrMDFixfx8eNHcYdCUZSIMMUdQHPDYrHEmsQNGTIEERERUFZWhomJCS5cuCC2WKialQlwm6CGMA8lWCwWCwMHDmywySQADBo0CJ8+fcKnT5/EHQpFUSJCE0oRIoQgMjJSpLe7a6KiooL79+/DwcEBU6ZMwdKlSzn7LVLi10JSNL+Wd0NuIy4uDqWlpSKZj+IfIQQsFgt9+/YVdyh1qowvKipKrHFQFCU6tIZShD58+IAvX76IPaEEvtVVnjlzpkpdpaenJ62rbADUlOTAACDMWhRCCJY5TwH5WgIJCQn06NGj2l6avXr1EvuZ51RVHz58QGZmJvT09MQdSp3U1NTQunVrREVFieRccYqixI8mlCLEYrEAiLYhpy4MBgMLFy6Erq4u7O3tYWBgQOsqGwA5aUmoKsoiNatIaHOotZNDxId31TrPf6zv7dq1a5VEU9RnnlNVZWdnA0CDP4mGyWRCWVmZEy9FUU0fTShFKDIyEoqKimI9Iq0mpqamiIiIgK2tLUxMTODi4oJJkyaJO6xmzVxTGW5PU4WyD6UEkwFzDWWeOs99fX2xf/9+sZx5TlEURTV8NKEUIRaLhX79+jXIP7iVdZVz587F5MmTERERgd27d0NSkv6IiMMkI1WcffxGKGNXsAkmD6z9Q03r1q0xYMAADBgwoMrXazrz/M6dOzh+/LjQzzynKIqiGjaaLYgQi8WCvb29uMOolYyMDM6ePQt9fX0sW7aMU1fZrl07cYfW7PTs0AqD1dsJ7SxvdeVWPD9XRkYGenp61er3vn79ipcvX1ZJNMPDw3HhwgUUFxcDEMyZ5xQ4x2NW/rs2ZEVFRfQABYpqRmhCKSKZmZlITU1t8PWJDAYDixYtgp6eXpW6yoZS99mcbLfVwbD9dwWWUBJCwCAE2211BDJeJSkpKfTq1Qu9evWq8nU2m43U1NRqpwP5+PjUeOb594lmz549IS0tLdA4m4Ju3bpBWloasbGxMDc3F3c4tcrMzMSHDx/Qu3dvcYdCUZSI0IRSRCq3z2gsiZmpqSnCw8NhZ2fHqaucOHGiuMNqVlQUZbF5dG+suRYrkPEYDAbSAw5iZ+5/2L9/P+dql7AwmUx069YN3bp1w6hRozhfJ4Tg48eP1RLNO3fuVDnznHaeVyclJYU+ffo0+O14oqOjAaDBb29EUZTg0IRSRFgsFmRlZdGzZ09xh8I1VVVV3L9/H3PmzMGkSZMQHh5O6ypFzNFQFRkFpdgTmMT3WCutNCGpNhYLFy5ETEwMrly5IpZuYQaDgU6dOqFTp04YNmxYle9Vnnn+faL5s85zLS0taGlpQUFBQdQvRSz69u2L8PBwcYdRp8jISMjKykJDQ0PcoVAUJSL06EURmThxIlJTU/Hw4UNxh8IzQggOHTqEZcuWwdTUlNZVioFH2Fts9ItHOZvwdAtcgsmAJJOBLaN7w8HwWyPOw4cPMXbsWEhKSuLatWvVmm8aosrO8x+3OXr16hWn87xjx47VEk1tbe0m13nu6ekJR0dHPH/+HJqamuIOp0YDBgyAsrIy/P39xR0KRVEiQhNKEdHS0oKFhQUOHz4s7lDqLTQ0FPb29pCTk4OPjw+9nSVi77KKsM47FvdTMiDBZNSZWFZ+f7B6O2y31YGKomyV779//x5jx45FVFQUjh07hhkzZgg7fKGo7Dz/MdFMTk7G169fAQAKCgo1JpqNtfO8tLQUnTt3xvTp07Fnzx6+xyssLcebzEKUlbPRQpIJNSU5yEnX/y5E5fGyvr6+GD16NN/xURTVONCEUgQKCgrQunVrnDp1Ck5OTuIOhy9v376Fra0tEhMTaV2lmCSn5+PC01S4/vcEEm07AvhfUsQAoKokC3MNZUweqFpnN3dpaSkWLFgAFxcXzJ8/H/v3728yXbmVnec/JprPnz/ndEjLyclxbpd/n2h269atwZd1LF++HOfOncP79+/r1byUnJ6Pi0/fIuTFZ7zNKqpyKhMDgKqiLMw1lTHJSBU9O/C2I8C8efPg6+uL1NTUBv/vSFGU4NCEUgQePXoEExOTBnGOtyAUFxdj9uzZuHDhApYvX46dO3fSPxwilpSUBE1NTfjduIXuekb1vrpECMGJEyewcOFCGBsbw8vLq8GfwsKPys7zHxPNhIQETud5ixYtoKmpWS3RbEid50lJSdDW1sbmzZuxfv16rp8nyKvcNXnx4gX09PSwdu1abNy4keu4KIpq/GhCKQJHjhzB0qVLUVBQIPTOWlEhhODff//F8uXLYWZmBk9PTygpKYk7rGbDw8MDEyZMwJcvXwRSz/rgwQOMGzcOUlJSuHbtGgwNDQUQZeNRW+d5QkJCtc7zHxNNcXWer1mzBvv370dUVBS0tLR++nh+63A3j+4NR8PaN8Rns9kYMmQI0tPTER0dDVnZnyegFEU1HTShFAEnJydERkZyzvJuSkJCQjB+/HjIy8vD29ub1lWKyOrVq3Hp0iW8fftWYGN+X1d5/PhxTJ8+XWBjN2Y1dZ4nJCRU6zyv6YQgYXaeFxcXo2/fvlBSUsL9+/fr3CD+cEiyQHYKWGGlgQXmNe9UcfjwYSxcuBChoaEwNTXley6KohoXmlCKQP/+/dGvXz+cPn1a3KEIRWpqKmxtbfH8+XOcPn0aEyZMEHdITZ6VlRVkZGTg6+sr0HFLS0sxf/58nD59GgsWLMC+ffuaTF2loHHbeV5TotmhQweBNAQ9ePAApqammDJlCk6fPl1jUukR9lZge5kCwC47Hc6OAZWuX7+OsWPHwtnZGUeOHBHYXBRFNR40oRSysrIyyMvLY9++fViwYIG4wxEaWlcpOoQQtG/fHgsXLhRKnRohBMePH8eiRYswaNAgeHl5QVlZWeDzNFXcdp7XduY5k8nkaT4PDw9MmjQJU6dOxenTp6s8/11WEYbtv4vScrbAXp+0JBPBS005NZX+/v6ws7PD6NGjcenSJfoBhKKaKZpQClnlFhoPHjyAiYmJuMMRKkIIDh48iBUrVsDc3BweHh60rlII3r17B1VVVaFvy/J9XaW3tzcMDAyENldzwG3neeWZ57x0nru7u2PKlClwdHTEsWPH0Lp1awDAlNNPhXYe/PmZA3DhwgXMmjULo0aNgqenJ00mKaoZowmlkLm6umLWrFnIy8uDvLy8uMMRiZCQENjb26NVq1bw8fGBnp6euENqUvz8/DBmzBi8ffsWKioqQp0rLS0NY8eORXR0NE6cOIFp06YJdb7mqLbO88TEROTm5gLgrvPc09MTTk5OUFRUxIkTJ6De/1dYHrgntLjVky7h9rWLmDp1Kk6dOtVkGg4piqofmlAK2cKFCxEUFITnz5+LOxSR+r6u0tXVFY6OjuIOqcnYtGkTjhw5gs+fP4tkY+6SkhLMnz8frq6uWLhwIfbu3UuvRIlAZed5TYnm58+fAVTvPG/fvj0uX76MJ0+ewHj+PnxqrQEBXpz8X2zsCrBfhOLITDO6eTlFUQBoQsk1QgjS09MRExPD+e/z58/Iz8/Ho0ePoKOjg19++QVKSkrQ0dGBrq4udHV14eDggK5du+LSpUvifgkiV1RUhNmzZ+PixYtYsWIFduzY0aDrKgsLCxEfH4+YmBjExsYiIyMDnz9/RnBwMMaMGQN5eXkoKytz1lZbWxstW7YUeZxjxoxBcXExAgMDRTYnIQTHjh3D4sWLYWJigsuXL9O6SjHKzMysMdF89+4d5zGd5pyClMIvQotBRaEl7q+yENr4FEU1Lg33r3sDQAhBWFgYXFxc4Ovry7kqICsrCx0dHXTu3Blt2rQBAHTv3h1SUlJ4+/YtAgICOJskA9+u8FRupdEYj3qrL1lZWbi5uUFfXx8rV65EVFRUg6urjIuLw+nTpxEQEICUlBQQQsBkMtGzZ0907NgRJSUlAIDc3FxkZ2fj6dOn2L9/P4BvV4c0NDRgY2MDJycn9OjRQyQxs1gskXfSMxgMzJs3Dzo6Ohg3bhwMDAxw7do1WlcpJkpKSvj111/x66+/Vvl6fn4+nj9/DlZsIrYnKQo1hrTsEhSWlvN1TCNFUU0HvUJZg8LCQpw+fRouLi6IjY2FiooKJk2aBENDQ+jq6qJ79+51dmISQvD27VvcuHED8+bNQ+fOnfH+/Xuoq6vDyckJc+bMEer+dA3RnTt3MH78eLRu3Rre3t5irassLi6Gu7s7XFxc8OTJE7Rv3x7jx4+Hvr4+58qjjIxMrc8vKCjgXMl89uwZrly5gpycHJibm2PWrFmwt7cX2i3hjIwMtG/fHh4eHnBwcBDKHD+TlpYGOzs7xMTE4OTJk5g6dapY4qBqF/8hF6MOPRD6PAELf0XvTm2EPg9FUQ0fb/tTNAN37tyBrq4uli9fDg0NDfz33394/fo1duzYATs7O6irq/90Ww8Gg4GuXbuibdu2AICoqCjcvXsXxsbG2Lx5M7S1teHt7S2CV9NwDB06FOHh4WjTpg2MjY3h4eEhljju378PPT09ODs7o02bNrhy5QrS0tJw+PBhzJgxA/r6+nUmkwAgLy8PIyMjODs749SpU/jw4QPc3NxQUVGBSZMmYcCAAYiKihJK/JWb44vzCM8uXbrg3r17mDhxIqZNm4bFixdztsOhGoYyAW4T1BDmoSiq4aMJ5f/Ly8vDnDlzYGFhgS5duiAhIQFXrlzBiBEj6jyBoi4sFguqqqpo164dhgwZgvPnzyMlJQWGhoaws7PD+PHjObfRmwM1NTU8fPgQtra2mDBhAlatWoWKigqRzJ2fn48FCxZgyJAhaN++PeLj43Hz5k2MHTuW7+5UGRkZTJ48GXfv3sWzZ89QUVEBQ0NDbNiwAaWlpQJ6Bd+wWCzIy8tDXV1doOPyqmXLljh9+jQOHz6Mo0ePwtLSsln9LDd0LSRF89Yuqnkoimr46LsBgC9fvsDExATu7u44cuQIQkJC0LNnzceL8YLFYlW7ktS5c2f4+vrC3d0dd+7cgaGhIV6/fs33XI2FrKwsLly4gL1792Lv3r2wtrZGVlaWUOdMT0+HkZERzpw5g4MHD+LevXtcnX1cH4aGhggPD8eff/6J3bt3w8zMrEo9Lb8iIyPRt29fnje/FgYGg4H58+fj9u3bSExMhIGBASIiIsQdFgVATUkOwq7WZvz/PBRFUQBNKPHlyxcMHToUX758wbNnzzBv3jyB/LEmhCAyMrLGW5MMBgMTJkxAVFQUWrRoAXNzc7x584bvORsLBoOBZcuWITAwEJGRkTAwMEBMTIxQ5kpPT4e5uTlycnIQERGBRYsW1fuKM7datGiBv/76Cw8fPsTz588xfPhwgSWVNX1IEbchQ4YgPDwcHTt2hImJCc6fPy/ukJo9OWlJqP7/STbCoqokSxtyKIriaNYJZVZWFiwsLPDlyxeEhIQI9KrVu3fvkJWVhf79+9f6mC5duiAkJASSkpIwMzOrsuVHc2BhYVGlrtLT01Og41d+WMjJyUFoaCh69eol0PF/xtDQEEFBQUhMTMSIESOQn5/P13j5+flITk5ucAklAKioqODevXuYMGECpk2bhiVLltC6SjEz11SGBFM41yklmAyYa9BtoyiK+p9mnVAuXLgQaWlpuHPnjsBvgXLbPFGZVLLZbEyfPh3Nrem+sq5yzJgxcHR0xOrVqwVSV0kIwaxZszgfFjQ0NAQQLe8MDAwQFBSE2NhYrFy5kq+xoqOjQQip80OKOLVs2RKurq44dOgQjhw5AisrK3z58kXcYTVbk4xUBXrk4vcq2ASTB6oKZWyKohqnZptQ+vv7w93dHQcPHoS2trbAx4+MjES7du3QuXPnnz5WRUUFp0+fxp07d3D69GmBx9LQycrK4uLFi9izZw/27NmDkSNH8l1XefnyZfj5+eH48ePQ1NQUUKT1Y2hoiF27duHEiRMIDQ2t9zgsFgstWrQQys+roDAYDCxYsAC3b99GfHw89PX1aV2lmPTs0AqD1dsJ/CqlBJOBwertoK7cSqDjUhTVuDXLfSjz8vKgra0NHR0d3LhxQyibjY8ePRqlpaW4desW18+ZOXMmrl69ioSEBK4S0aYoODgYDg4OaNu2Lby9vaGrq8vzGBkZGdDW1saQIUNw5coVIUTJOzabDTMzM3z48AExMTGQleW9vm3mzJmIjo5uNAnau3fvYGdnh7i4OJw8eRJTpkwRd0jNzrusIgzbfxelAtrehxACCbARtNQUPTrQ/ScpivqfZnmF8sSJE8jIyMCJEyeEdnJNfZonKs9I3rt3r1BiagyGDRuG8PBwtGrVCsbGxrh8+TLPY+zfvx8lJSU4fPiwECKsHyaTCRcXF6SmpsLFxaVeY0RGRjbY2901UVFRwf379+Hg4ICpU6di6dKlKC8vF3dYzYqKoiw2j+4tsPEYDAayAo9h2thR+PTpk8DGpSiq8Wt2CSUhBKdOncK4ceOgqiqcGqAvX74gLS2N54RSQUEBM2bMwPnz5zlH/jVH3bp1w6NHjzB69Gg4ODhgzZo1XNdVfv36Fa6urpg6dSo6duwo5Eh5o6GhgTFjxuDUqVM818qWlpYiPj6+QTbk1KVly5Y4c+YM/v33Xxw6dAiWlpa0rlLEHA1VscJKMDXEK600cePwn3j58iUMDAzw9OlTgYxLUVTj1+wSyrt37yI5ORmzZ88W2hyVDTn1uZrk7OyMzMzMZneSzo9kZWXh7u6Of/75B//88w9GjRrFVV2lv78/Pn36BGdnZxFEybvZs2cjLi4OT5484el58fHxKC8vb3QJJfDtqtbChQs5dZUGBgaIjIwUd1jNygLznthppwNpSSbPNZUSTAakJZnYZaeD+ebqGDRoECIiIqCiooIhQ4bA1dVVSFFTFNWYNLuE0s3NDRoaGhg8eLDQ5mCxWGjVqhV69OjB83M1NDQ4p+o0dwwGAytWrMDNmzcRFhYGQ0NDxMbG1vmcc+fOYcCAAWI9K7wuw4YNg5qaGs6dO8fT8yIjI8FkMutVU9pQmJqaIiIiAsrKyjAxMcGFCxfEHVKz4mioiuClphjUXQkAwETdV8krE89B3ZUQvNQUDob/u6PTqVMnhIaGYtq0aXBycsL8+fNRVlYmvOApimrwml1CGRYWBnNzc6HVTgLf/vjr6enVe4P0ynOvm2G/VI0sLS0RHh4OeXl5DBw4sM66yqdPn8LKykqE0fGGyWRi2LBhPN8qZLFY0NTUhJxc4z6ZpHK/SgcHB0yZMgXLli2jdZUipKIoCzcnIwQtGQINZjrYuenVTtRhAOiqJIspRl0RvHQI3JyMoFLDJunS0tI4efIkjh8/jlOnTsHCwgLp6ekieR0URTU8zeqYg5KSEiQkJGD+/PlCnYfFYsHa2rrez+/Xrx8yMjLw/v17dOnSRYCRNV6VdZVOTk5wcHBAZGQktm3bVuXUm0+fPuHTp0/o27ev+ALlQt++fXHu3DmUlZVxfY54bacuNUYyMjI4c+YM+vfvj2XLliEqKgqenp5o3769uENrNnp2aAWpGB9of/2Kq77+eJNZiLJyNlpIMqGmJMfTCThz5sxBnz59MG7cOOjr6+PatWsYMGCAEKOnKKohalZXKOPj41FRUSHUhCMvL4/v00wq46usxaS+kZOTw6VLl7B79+4a6yqjoqIA/HwzeXHr168fvn79ioSEBK4eX1FRgZiYmEbV4f0zDAYDixYtwu3btxEXFwcDAwP68y5iLBYL/fv3h5y0JHp3aoN+qgro3alNvY5TNDEx4dRVDh48mNZVUlQz1KwSyg8fPgD4djqLsERHRwPgL6lRUVEBk8nkxEv9D4PBwMqVK3Hz5k08e/asSl3l27dvAQh3fQWhsrY2NTWVq8cnJSWhqKiowSfK9WFqaorw8HC0b98eJiYmcHd3F3dIzcLnz5/x/v17gf5MVdZVTp06FU5OTliwYAE9fpOimpFmlVBWEmb9pCBOM2EwGEKNsSn4vq7S2NgYXl5eAL7929W3dlVUeI2vsiO6od/Kry9VVVXcv38f9vb2mDRpEq2rFAFuj4blVWVd5bFjx3Dy5ElaV0lRzUjD/svbCLFYLOjo6EBKSkrcoTR53bt3x6NHj/Dbb79h/PjxTXarJRaLBTU1NSgqKoo7FKGRkZHB2bNncfDgQfz7778YPnw4MjIyxB1Wk8VisdC6dWt0795d4GMzGAzMnTsXISEhSEpKgr6+Pp49eybweSiKaliaVUJZedVPmFc/BNE8UVFRATabTa9ScqGyrnLXrl24desWCCHIzMwUd1h14naT9kr1OXWpMaqsqwwODkZMTAytqxSiyMhI9O3bV6hX8yvrKrt06YIhQ4bgzJkzQpuLoijxa1YJZWXt2osXL4QyfmlpKRISEvj+45+cnAxCCNTV1QUUWdPGYDCwatUqbNu2DcC323hxcXFijqp2ycnJAL51rv8MIaRJdXhzw8zMDBEREVBSUqJ1lUIiqg8pnTt3xt27dzF58mTMnDmT1lVSVBPWrLYN0tDQgIyMDFgsFszNzQU+flxcHMrLy/nuxq28KtNUa+aExcnJCevWrQODwcDAgQNx9uxZjBs3TtxhVVNZZ/v582cEBATg48ePyM7ORq9evSAjI4Pu3btDTU0NTCYTqampyMnJaVId3txQVVXFgwcPMGfOHEyaNAkRERHYtWsXJCUbx1tWUVERXr58iaKiImRkZIDNZkNZWRkyMjLo0aOHWPcTzcvLQ0pKish+pqSlpXHq1Cno6+tj0aJFiImJgZeXFzp06CCS+SmKEo3G8e4sIBISEtDV1RXabTRBnWbCYrGgqqrapGvmhEFZWRmdOnXC+PHj8fbtW9jb22Pt2rXYunVrlf0qRa20tBT+/v54+PAhYmJi8PDhQ5SVlcHS0rLW58jLy0NHRwetWrUCwN3VzKZGRkYG586dg76+PpYvX47o6Gh4eHigXbt24g6tioqKCty+fRtPnz5FTEwMYmJiOHcZasJgMKCurg4dHR3o6urCyMgIw4YNE1myLI7ttRgMBv744w/o6Ohg3LhxMDAwwLVr12BoaCiyGCiKEq5mlVAC3+p63NzceNpUmluVp5nIylY/VYJbhBD4+/vDxMREgJE1H4MGDcLt27cREREBfX19rF27FlFRUbh48SIUFBREGktCQgJcXFxw/vx5ZGZmokePHtDV1UWLFi1gbm6O/fv3o3Xr1pCWlgYhBF+/fkVRURGSk5M5iUlgYCAAQF9fH+PGjcOsWbMwZMiQZlNfy2AwsHjxYujq6mL8+PEwMDCAj49Pg7h6/+bNG7i6usLV1RXv37+HoqIi9PT0YG1tjdWrV6NXr16Ql5eHhIQECCFgs9koLCzE8+fPOet76NAhbNq0Cb/88gtmzJiBmTNn1uvIVl6wWCxIS0ujV69eQp2nJr/++isiIiIwduxYDB48GMePH8f06dNFHgdFUUJAmpm4uDgCgHh5eQlkvIKSryTufQ6JTM0i+sPGEMfJ0/ga78GDBwQACQ4OFkh8zY2/vz8BQMLDwwkhhNy6dYsoKCiQHj16kNjYWJ7G+n5t497nkIKSr1w9LyUlhVhaWhIApF27dmT58uUkISGhxvh+ZtSoUcTc3Jzs3LmTqKurEwBES0uLhIaG8vRamoI3b96Q/v37ExkZGeLu7i62OF69ekV+//13wmAwSKtWrcjcuXNJWFgYYbPZPI/FZrNJZGQkmTdvHmnTpg0BQKytrUlKSooQIv9m2rRpxMDAQGjjc6OkpITMnDmTACALFy4kZWVlYo2Hoij+NbuEkhBCTExMiKWlZb2fn/Qpj2z0jSNDdt8hamv8Sdcq/10nQ3bfIRt940jSpzyex546dSrp0aMHqaioqHd8zVl5eTnp0qULmT17NudrKSkpREdHh8jJyZErV67U+fy61lZtjX+da1teXk727t1LZGRkSLdu3YiHhwcpLS2t8pjRo0eT/v37c/16OnXqRNauXUsI+ZZ8hIaGEhMTEwKA/PHHHyQvj/efscasqKiITJ48mQAgy5cvJ1+/cpfkC0JFRQX5999/iZycHFFVVSWurq6koKBAYOMXFhaSc+fOETU1NSIjI0P27dtHysvLBTZ+JR0dnSq/H+LCZrPJkSNHiKSkJBkyZAhJT08Xd0gURfGBQUgthT5NmJubG6ZOnYonT57AyMiI6+e9yyrCOu9Y3E/JgASTgQp27f90ld8frN4O2211oKL489vgycnJ0NHRwebNm7F69Wqu46Kq2rx5M3bv3o3ExESoqqoCAAoKCjBz5kx4eXlh3bp12LJlS5W6Sn7X9vPnz7CxscGTJ0+waNEibNu2rVrjRWxsLPr27YsjR45g7ty5P30d6enp6NixIy5fvgx7e3vO19lsNo4ePYo1a9ZAUVERPj4+zapphxCCgwcPYsWKFTAzM4OnpyeUlJSEOuenT59gb2+PBw8eYN68edi5cyenvlXQCgoKsH79ehw6dAhGRka4cuUKOnfuLJCxS0pKIC8vj8OHD3P1MygKDx48wLhx4yAlJQVvb28YGBiIOySKouqhWSaU5eXlMDY2RlFRESIjIyEtLf3T53iEvcVGv3iUs0mdycaPJJgMSDIZ2Dy6NxwNVWt9HJvNhrm5OdLS0hAbG8tXHWZzl5ubC21tbejp6SEgIIBTb0gIwe7du7F27VqMGDEC7u7uaNu2Ld9ru8JcFf8udkRGRgauXLlSY/1rfX7mbt68CWtra6SkpNRYV/fmzRuMHz8eKSkpuH37drPaWggAQkJCMH78eMjLy8PHxwd6enpCmSc9PR3m5ubIycnBpUuXYGpqKpR5fvTw4UM4OjpCVlYWISEh6NSpE99jhoeHw9DQkOcP08KWlpaGsWPHIjo6GidOnMC0adPEHRJFUTxqVvtQVpKUlISrqyuSk5M5exfW5XBIMtZci0VpOZunhAMAKtgEpeVsrLkWi8MhybU+7sSJE7h37x5cXFxoMsmnNm3a4Pjx4/jvv/+q7GHIYDCwevVq/Pfff3j8+DEMDQ3xp8dDvtd2W9AbZP0yACEhIbU2Ux08eBARERE4ffo0V8kk8L/TTGrr8FZTU0NQUBB69uyJYcOGcbp3mwtzc3OEh4dDQUEBxsbG8PDwEPgc6enpGDp0KHJychAaGiqyZBL41kAYGhqKoqIimJub4+PHj3yPGRkZydntoiHp0qUL7t69i0mTJmH69OlYtGgR3a+SohqZZplQAoCOjg7WrVuHHTt2wNfXt9bHeYS9xZ7AJIHMuScwCZ5hb6t9/f79+1ixYgWcnZ2Fsj9mc/T777/D0dERCxYsQHR0dJXvDR8+HOHh4WD2HAy36ByBzCelb4fo/Jo/CNy9excbNmzA4sWLMXDgQK7H5OY0kzZt2uDWrVvo0aMHLC0tm925yV27dsXDhw8xduxYTJgwAStXrhTYSVhlZWWwtrZGdnY2QkJCoKGhIZBxedGjRw+EhISgsLAQVlZWKCkp4Ws8FovF2e+0oWnZsiVcXFxw5MgRHDt2DJaWlvj8+bO4w6IoikvNNqEEgA0bNsDW1hb29vbw8/Or9v13WUXY6Bcv0Dn/8ovHu6wizv9/8OABrK2tYWRkhAMHDgh0rubu2LFjUFdXh4WFRbWksoXCL4C+PSDAio8f1xYA7t27h5EjR+LXX3/F9u3beRqP29NM2rZti4CAAADAwoULeZqjKZCRkcH58+exb98+7N+/H9bW1gI5fnPnzp2IjY1FQEAANDU1BRBp/airq+PmzZt48eIF/v77b77GaujHeDIYDMybNw937txBYmIiDAwMEB4eLu6wKIriQrNOKCUlJXHx4kWMHj0a48aNw5UrV6p8f513LMp5vA36M+VsgnXesQC+1YBZW1vD0NAQ169fp7e6Baxt27YIDAyEmpoaLCwsqmxoz1lbAe7n+P3aAkBoaChGjhwJY2Nj+Pr68nRVKDc3Fy9fvuS62aZ9+/Y4dOgQvLy84O3tzXPsjR2DwcDSpUsRGBgIFosFQ0PDah8ieBEXF4e///4bq1evbhAJWJ8+fbBhwwbs3Lmz3qUN5eXliI6ObhQNXIMHD0ZERAQ6duyIX3/9FefPnxd3SBRF/USzTigBQEpKCpcuXeJcqZw6dSoyMzORnJ6P+ykZPNfV/UwFm+B+SgZmLF4LCwsLGBkZwd/fX6xHsTVlCgoKCAoKgpqaGoyMjLB161YkvM8W6trGpn7B8uXLYWFhgYEDB8LPz4/nDwv1Oc3EwcEBv//+OxYsWICysjKe5msqhg4divDwcLRp04avusp58+ahR48e+PPPPwUcYf2tWbMG2tramDNnTq2n8NTlxYsXKCkpaRAJMje6dOmCe/fuYeLEiZg2bRoWL15M6yopqgFr9gkl8C2p9PDwwJkzZ3D9+nVoa2tj44VgSDCFdBoJuwIBSXnYt28fbt26RZNJIVNQUMCDBw+wcuVKbN68GTYr9kBYS8tkAKOX/4OjR49i586duHnzZr2uPNfnNBMGg4Fdu3bhw4cPddYFN3Vqamp4+PAhbG1tMWHCBKxatYqnusqoqCjcv38f27dv57qBShRatGiBnTt34tmzZ/W6DVx5hb4hnDLErZYtW+L06dM4fPgwjh49SusqKaoBa5bbBtXl48ePmDdvHp51GAkpBf636ahNp9ZSeLTWSmjjUzVjsVgYeyYWbDnh7VsoWZyFG/OM+GrimDZtGhITE/Hs2TOenzt48GC0bNkSQUFB9Z6/KSCEYP/+/Vi5ciUsLCzg4eEBRUXFnz5v/vz58Pb2RmpqKqSkpEQQKfcqKirQrVs3DB8+HKdOneLpucuWLYOvry9evnwppOiE6969e7C3t4e0tDS8vb2hr68v7pAoivoOvUL5g19++QXnL10WajIJAB/zvqKwVDDdqBT3emrrgAgxmQSAChlFdO7ana8xIiMj631r0tnZGcHBwY02cRAUBoOBZcuWISgoCJGRkTAwMEBMTEydzykqKsKFCxcwc+bMBpdMAoCEhARmzZqFS5cuIT8/n6fnNvSGnJ8ZMmQIwsPDOXWVbm5u4g6Joqjv0ISyBm9/6NQVBgLgTWah0OehqkrNLISwL8nzu7bFxcVITEys9x//sWPHgslk4s6dO/WOoSn5sa7S09Oz1sc+fvwYeXl5mDBhgggj5M3EiRNRWFiIBw8ecP0cQkijTygBQEVFBffu3YOjoyOmTp2KJUuW0LpKimogaEJZg7JydpOah/qfxrC2cXFxqKioqHc3rpycHHr16tXsNjqvS2Vd5ZgxY+Do6IjVq1ejoqKi2uOioqIgKyvLU+2qqPXo0QOtW7fmaX1fv36N3NzcRtHh/TMtW7aEq6srDh06hCNHjsDKygpfvnwRd1gU1exJijuAhqiFpGjy7H17dmOgZhdoa2tDS0sLHTp04BwTSAmHqNZ2058bYNjzF2hpaUFbWxvq6upc30KtPM1ER0en3vP369evyjZJFCArK4uLFy/CwMAAK1euRFRUFC5dulSlrpLFYkFXV7fKOe8NDYPBQN++fXla38rHNvYrlJUYDAYWLFgAXV1djBs3DgYGBvD29m4SCTNFNVY0oayBmpIcGIBwb40Sgsi7t+B5PI5zy0ZBQYGTgHz/vyoqKnWelkJxT1Rrm/EmEfv9PZCVlQXg256nPXv2rLa+mpqa1fanFMRpJjo6Orh+/TpfL6Mpqqyr1NPTg4ODAwwNDeHt7c05ijAuLq5BnXFdGz09PQQHB3P9eBaLhY4dO6Jjx45CjEr0hgwZgoiICNjZ2cHExASnTp3C5MmTxR0WRTVLNKGsgZy0JFQVZZEqxFrKru3kcDc6El+/fsWrV6+QkJCAxMREJCQkIDIyEhcvXkRxcfG3eP7/FuaPiWb37t0hKUmXkBciW9u7d0AIwZcvXzjrWrnGp0+f5pzLzGAw0K1btyrrev/+fb6uTgLfrsbR2rLaWVhYIDw8HDY2NjA2NsaZM2cwfvx4lJaWQl5eXtzh/ZS8vDxPxzBGRkY22at3lXWVf/zxB6ZMmYKIiAj8888/9L2RokSM/sbVwlxTGW5PUwW++TUASDAZMNdQBvBtD0xNTU1oamrC1taW8xg2m423b99WSTQTExPh5+eH3NxcAN/2pdPQ0KiWaGpoaDSo/fMaGlGtLYPBgLKyMpSVlWFqalrlcTk5OUhMTKyytl5eXnjz5g0AICEhAQ8ePKjxinX79u0FHndzpKamhkePHmHWrFlwcHBAZGSkuEMSGhaLBScnJ3GHITQyMjI4c+YM9PX1sXTpUkRFReHy5cv0d4WiRIgmlLWYZKSKs4/fCGXsCjbB5IGqdT6GyWRCTU0NampqGDlyJOfrhBB8+vSpWqIZGhrK2fCXyWSiR48e1RKRXr16NYqrL8Im7rUFvh0LaWxsDGNj4ypff/bsGYyMjLBu3ToAQGJiIm7duoUjR45wmkjatWtXbW21tbXRqVMnWoPLo8q6Sn19faxatQoyMjI8XflrDD5+/IhPnz41mfrJ2jAYDCxcuBC6urqwt7endZUUJWJ0Y/M6TDn9FI9eZQr0SpYEk4FB3ZXg5iT4Oq3MzMxqV70SEhLw7t07zmNUVVVrTEYUFBQEHk9DJpS1ZQCDerTja23d3NwwdepUZGdno23btpyvl5WVITk5udravnjxAqWlpQCA1q1bQ0tLC1paWnj79i2ioqIQFhaGrl27Nugmk4YiODgYI0aMgIyMDB49esR32YEwzZkzB0+ePOHqvPIbN25g1KhRePXqFbp16yaC6MTv3bt3sLW1RXx8PFxcXDBp0iRxh0RRTR5NKOvwLqsIw/bfRamAtpohhKCFBAN3lptDRZH34/jqKz8/H8+fP6+WjLx69Qps9rfX1qFDhyoJZlPvPBfG2jLY5TgzrjvMB+jWe5ylS5fCz8+P603JKyoq8Pr162prGxkZybmi2bJlS/Tq1avahwheOs+bCwcHB/j5+YHJZHLqKhsiIyMjaGpq4vz58z997LZt27Bnzx5kZWU1yd/l2hQXF2Pu3Lk4f/48li5dit27d9O6SooSIppQ/oRH2FusuRYrsPGy/juEDROHYuXKlWJ/cy8pKUFSUlK1ZCQpKalZdJ4Lem1bRHnh08NrcHNzw5gxY+o1hpmZGdq1a4crV67wFUvnzp1hZ2eH33//vcraJiQk1KvzvLk4cuQIli5dChsbG3h5eWH16tXYtm1bg7jCW1JSgsTERLBYLMyePZvTlFdaWopXr14BADQ0NKCgoIA+ffpAV1cXOjo62LdvHwoKChASEiLmVyB6hBAcOnQIy5Ytg6mpKTw9PdGuXTtxh1UjNpuN1NRUxMTEICYmBrGxsfj06ROKiooQEREBVVVVqKqqQklJCTo6OtDV1YWuri7U1dUbxM8nRdGEkguHQ5KxJzCJ73GWD+uJj7fPYseOHXBwcMDp06chJycngAgFq6bO88pb6U2t81xQa7vSShNTDTpg2rRp8Pb2xl9//YWNGzfylHSz2WwoKChg9erVnBrK+khNTYWamhq8vLwwbty4Kt/7sfP8+//98OEDgJo7zyv/t3Xr1vWOqzF49OgRTExM8PjxYzx48ACrV6+GpaUl3N3duToHXNAqKioQGBgIFxcXXL9+vUrn/q+//goDAwO0bNkSfn5+MDc3R8uWLZGRkYHY2FjEx8dzyiGUlZWxceNGTJw4sUopRXNx9+5d2NvbQ1ZWFt7e3g2mnpQQgvv378PFxQW+vr7Iy8sDACgqKkJXVxddunRBixYt4OrqigkTJkBKSgqfPn1CbGwsZ6eIli1bwsrKCs7OzhgxYkSjev+lmhaaUHLJI+wtNvrFo5xNeKq7k2AyIMlkYMvo3nAw/NasceXKFUyfPh09evSAt7c3unfn79xnUamt8zwhIaFRd54Lcm3ZbDZ27NiBP//8E7/99hvc3NzQpk2bWscoLC3Hm8xClJWz8fnTB1j/aoAA32uwtrau9+vZtGkT9u7diw8fPqBVq1ZcP6+mzvOEhARO5znw7cpnU+48Ly8vR9euXWFjY4MjR44gKCgIjo6OaNu2LXx8fHiuq/x+fVtIMqGmJAc56Z//wc/NzcX+/ftx+vRppKWlQUdHBzNmzICxsTHc3Nzg5eWFtLQ0tGjRos7XEhERgYEDB6J///6Ijo6GlJQU7O3tsWLFCs7em83F27dvYWdnh4SEBLi4uGDixIliiyU/Px/Hjx+Hi4sLkpKS0KNHD0yZMgUDBgyArq4uVw12X758QWxsLCIiIuDu7o6oqCh06tQJM2bMwMKFC9GhQwcRvRqK+oYmlDx4l1WEdd6xuJ+SAQYICGr/hZdgMlDBJhis3g7bbXWq1UzGxcXBxsYGWVlZ8PT0hKWlpbDDF5raOs8TEhIaTef592tbuXa1YYKADQYMushh/4QBNdbDBgQEYNKkSejYsSN8fHyqHOWXnJ6Pi0/fIuTFZ7zNKqqyyTohBF3atoSl9i+YZKSKnh24TwiBb1e0KncGOHHiBE/PrU1hYSFevHhRbW1TUlKqdJ7/mGg21s7zP//8E//++y8+fPgAOTk5vH79GjY2Nnj58iXOnj1b7arvj+paXwYAVUVZmGsq17q+AQEBmDNnDrKzszFp0iQ4OzvDwMAADAYDJSUl6NSpE5ydnbFr166fvpbQ0FCYm5sjLi4OioqKOHfuHE6ePIl3795h7dq1WL9+fYP9oCcMxcXFmDNnDtzc3MRWVxkYGAhnZ2ekp6dj3LhxmDVrFoYMGcJ3CVFkZCRcXFxw8eJFSEhI4ODBg5g8eXKj+/2jGi+aUNZDcno+nHaexbuK1oBcu+p/MJRkYa6hjMkDVaGuXHtCkJ2djYkTJyIwMBA7d+7EihUrmtwvf307z7W0tMRyi7EyGbh0NxqlUq2B79ajcm1/7a6AI0sd8cdEW+zYsaPWsZKSkmBjY4O0tDRcuHAB/X4dxnXS+rMPJLXx8fGBra0twsPDoa+vz/Xrrg9uOs9btWpV464CDbnz/M2bN+jevTtOnDgBZ2dnAN+SaicnJ3h6emLt2rXYunVrtfh5+VBS0/pmZWVh8eLFuHDhAkaMGIETJ05AVbXqFlTnz5/HtGnTkJSUhJ49e/70tezbtw8bNmxAXl4eJ3EqKyvD9u3bsW3bNmhoaODMmTMYMGAAr/9MjZa46iqzs7OxfPlynDlzBhYWFjh16pRQuu4zMjKwZMkSXLx4EdbW1jhx4gRUVFQEPg9F/YgmlPU0YMAA9OrVC8dOudbrllaliooK/Pnnn9ixYwccHR3h4uLSIOsqBa0+neeV/yuKzvPu3bvjd9txmL18fY1ru379euzZswdRUVHQ0tKq83VOmzYNQS8LoTxyAcCUqNdt9c2je8PRsO79LQsKCqCjo4Pu3bvj9u3bXM8haLV1nicmJqKgoABAw+88Hz9+PO7evYvExETOBxtCCPbs2YM1a9bAysoK7u7unO22+C2bWG6min8XO+D9+/c4cOAApk6dWu1nPCcnB71794aBgQF8fX25Gn/KlClITk7GkydPqn0vNjYWM2fORGxsLHx9fTF8+HCu424KQkNDYW9vDzk5Ofj4+KBv375Cmys9PR3m5uZ4//499u3bh5kzZwr9Pczf3x9z5sxBeXk5QkJCoK2tLdT5KIomlPXw9etXtGrVCjt37sSSJUsEMub3dZU+Pj7NZr+4H3HTed62bdsaE01BdZ5nZ2dDUVERFy5cqHX/uuLiYvTt2xdKSkq4f/9+nVfbDt1Owt7g5G9bC/HxR2SFlQYWmNd+VWrJkiU4efIkYmNj0aNHj3rPIyyEEKSlpVVb24bYef7x40doa2tj9OjROHfuXJXvBQUFwcHBAYqKivDx8UHoF2mBNHaVR3oj+OCKKuUR33N2doanpyfi4+O5vuLUp08fDB48GMeOHavx+6WlpRg7diyCg4Ph5+cHKyuresffGL19+xa2trZITEwUWl1lZTKZk5OD0NBQaGhoCHyO2nz58gUWFhb4/PkzQkJC6vzwS1H8ogllPcTGxkJXVxehoaHVjtTjR1xcHMaMGYOcnBx4enpi2LBhAhu7sSsvL8fLly+rJSPPnz9HUdG3c7llZWU5t8u/T0Z47TwPCQnB0KFDER8fX+en+vv372PIkCHYtWsXVq1aVeNjBL010S47HU4D0Pfu3LmDYcOGYc+ePVi2bJnA5hOFhtp5fubMGcycORO+vr4YPXp0le+9evUKNjY2eN9SDa0s5ghsztrW9+bNm7C2tsbx48cxZw538xUVFaFVq1Y4fvw459Z9TUpLS2FnZ4c7d+7g5s2bAn1PawyKi4sxe/ZsXLhwAcuWLcOuXbsEVleZmZmJIUOGIDs7GyEhIdDU1BTIuLz48uULhg4dii9fvuD+/ftclUpQVH3QhLIeKuuYcnJy6uzgrY+srCxMnDgRQUFB2LVrF5YvX97k6ioFqbLzvKarXj92nv+YjNTWeV5Zd5afn//TOr9169Zhx44dOHbsGObOnVvle4LePB0ApCWZCF5qWqWm8sGDBxgxYgSMjY1x8+bNBlubWB85OTl4/vw5Z01F2XlOCIGtrS1u3boFf39/WFhYVPn+i7QMjDj0EGyGhMB+R2ta37t372LkyJEwNTWFv78/11fhnz59ioEDByIsLAwGBgZ1PrakpATW1tZ4+fIl4uLimvz2UD8ihODff//F8uXLYWZmBg8PD4HUVU6cOBG3bt3Co0ePxJJMVvr8+TN+/fVXKCoq4uHDh03qPYJqOGhCWQ9Lly7F9evXkZKSIpTxKyoqsGHDBuzcuRMTJkyAi4sLZGVFd7JOU1DZeV7TVa/09HQA/+s8/zEZ2bt3L968eYPHjx9zNc/SpUtx8OBBnDhxArNnz+Z8TxRHdz58+BAjRoyAoaEh/P39m83Piag6z0tKSmBra4u7d+/C398fQ4cO5XxPFOt77949WFtbY9CgQfDz8+Pptv/x48exYMECFBQUoGXLlj99/Js3b9CnTx9MnToVR48erfdraMxCQkIwfvx4yMvLw9vbm6+6yuvXr2P06NFwc3PD5MmTBRdkPT18+BCDBw/Gvn37BFaqRVHfowllPZiamkJZWRleXl5CncfLywvTp09Hz5494e3t3WzrKgUtKyurxkTz7du3nMfIy8vDxMSk2lWvmjrPCSFYsmQJ/v33XyxZsgR///03PhSwYXngntBeQ+DiwQi66oZVq1ZhwIAB8Pf3bxbNXD8jjM7zkpIS2NjY4N69e9izZw/mzp2Ll18Khbq+QUuGIMT3EpYuXYqBAwfi+vXrPH9YmD17Np4+fcrVed+VDh8+jIULF+Lu3bsYMmQIr2E3CampqbC1tcXz589x+vRpTJgwgecxcnNz0bt3b+jq6iIgIKDB3GVatGgRTp8+jdjY2Eaz/zHVeNCEkkeCOs2EW7GxsbCxsaF1lSJQUFCAqKgoDBkyBMOHD0eLFi2QmJiIly9fVuk8r+n2aocOHbB//35s2LABnTp1gvmKowhJqxDo1atKEgxA5n044s9vwpw5c7B3716aTP4Ev53nFRUVWLJkCU6cOIEhQ4ag36ztuP48V2jrK/cxErFn/8LMmTNx6NChel15NjQ0RO/evXH27Fmun8NmszFgwAC0a9cON2/e5HnOpuL7usrly5dj586dPNVV7t27F+vWrUNycnK1rZ/EqaCgABoaGhgzZkytjVoUVV80oeTRy5cvoa6ujv/++w8jRowQyZxZWVmYMGECgoODsXv3bixbtqzBfOJtairrzr7fx7GkpATJycnVEpEXL15U6TzX0tJC586dERkZiRLLNZBS6CS8QPO/4Ow4NZiZmQlvjmaA185zWVlZBAYGQspuGyTb/iK8wPI/49SYLvU+8KByJ4pdu3Zh8eLFPD33zJkzcHJywsuXL5v1XRFCCA4ePIgVK1bA3NwcHh4eUFJS4up5vXr1gr6+Ptzd3UUQKW/++usvHDhwAB8+fGgQh0pQTQdNKHnk5eWF8ePH49OnTyI92qqiogLr16/Hrl27aF2lEB07dgyLFi1CQUHBT08QKS8v55x5XqXzPOU12v1xXqhJPwNA3KbhPO15SnGvrs7zjxnZUFl6uUGvb0xMDPT09HDv3j0MHjyYp+cWFhaiU6dOWLhwIf7+++96zd+UfF9X6ePjAz09vToff/fuXZiZmSEkJKRBfuBLTU1Ft27dcOrUKTg5OYk7HKoJoQklj9atW4ezZ89ytjMRtcuXL2PGjBm0rlJI6lN39qO4tBz8duShAKOqWcDCX9G7k2B3GaB+7smLNDierf/PB7f4Wd9z585h+vTpyM3NrVfH9ty5cxEUFISXL1/Wa/6m5vu6SldXVzg6Otb62NmzZyMkJARJSUkN9k7SiBEjUFpaipCQEHGHQjUh/O8C3cywWCz0799fbPOPHz8ejx8/Rl5eHgwMDMR6IkpTFBkZyff6fhVCXV1NygS4HRHFPWkZ0dSr8rO+LBYL6urq9d7+Z/DgwXj16hVycnLqHUNT0rVrVzx48AB2dnaYMGECVq5cifLy8hofGxYWBjMzswabTAKAubk5IiIiOLXhFCUINKHkASEEkZGR6Nevn1jj0NXVRXh4OAwMDGBlZYV9+/aBXmjm39evXxEbG8v3+raQFM2vVUJcDKfOjxIdUa3vl/SPnC2QeMXvB6PK7XKioqLqPUZTIysrCzc3N+zbtw/79++HtbU1MjMzqzymrKwM8fHxQj3GURD69u2L/Px8vHr1StyhUE0ILcDiwcePH/H582exJ5QAoKioiBs3bmDdunVYvnw5IiIicOrUKVpXyYfExESUlZXxvb5qSnJgABBmik8IwRSbESBfS2rtPO/YsWODvkrSWIlqfUeY6ENaAjyfec5msxEVFYWRI0fWe35NTU20bNkSLBarQdYBiguDwcDSpUuhp6eH8ePHw9DQEN7e3py6yoSEBHz9+rVRJJTA/65kU5Qg0ISSBywWCwDEesv7exISEti1axf69++PmTNnIiEhAd7e3lBTUxN3aI1SZGQkAPD9x0BOWhKqirJIzSoSQFQ166okC/+IZ1UaRu7du4dTp05V6zz/MdFUVVUVyJnnzZUo1rdLW2mc8vetsr63bt3i6szz9+/fIz8/n68PRpKSkujYsSMyMjIE9ZKalKFDhyI8PBy2trYwNjbm1FV++vQJABrUVkE16dChA6SlpTnxUpQg0ISSB5GRkVBQUEDXrl3FHUoVDg4O0NLSgo2NDQwMDHD58uUqJ3pQ3GGxWOjZsydatWrF91jmmspwe5oqtH0Kh2p2gI5Ob+jo6FT53ved55WJSFRUFC5dulTlzPNevXpVSzR79OghsDOMmzqhri+TAUvtTrCy6g0rKyvO12vrPHd1da1y5rmysjKAbye1fPjwod5nntOr23VTU1PDw4cP4ezsjAkTJiAyMpJzDnpj+LdrDDFSjQv968EDFouFvn37NshfRF1dXYSFhWHChAmwtLTEP//8g6VLlzbIWBsqFoslsHKGSUaqOPv4jUDG+lEFAbqUvAbQu9r3JCUloaGhAQ0NDdjY2HC+zmaz8e7du2pb4Pj7+3MaL1q0aIGePXtWO6qwtjPPmzOhri+bYPLA6le4KpNFZWVlTuJS6fszz0+cOIGcnBwEBATgyJEjnMcI68zz5kxWVhYXLlyAvr4+Vq5cieDgYHGHRFFiQxNKHrBYLIwdO1bcYdRKSUmpSl1lZGQkTp48SesqucBms8FisTBq1CiBjNezQysMVm8n+LOeGYBM/jvMdpyHT0lbsG7dOq5uXzOZTHTt2hVdu3aFtbU15+uEEKSnp1fb1PvevXs/PfO8V69ezXZjZKGt7/+f5a2uzNtV8rZt22LgwIEYOHAgPD09YWlpievXr9d45vmtW7dw5MiROs8819LSQmlpaY1HUVJVMRgMLFu2DHp6erC1tQXwbR/QLl26iDmy2rHZbJSXl9PSF0qg6D6UXMrKyoKSkhIuXLiASZMmiTucn/L09MTMmTOhoaEBHx+fBnebvqFJTk6GhoYGbt26VeU2Iz/eZRVh2P67KBXQ9j6EELSQYCB4qSnOHtmLTZs2wdbWFufOnRPIbfofcXPmuaqqao3JSE1nnjc1gl5fEIIWkkzcXmYGFcX6fQgkhKBDhw6YO3cutmzZUuvjuDnzHAB69OiBwYMHc3XmOQXcu3cPpqamkJaWxvnz5zF+/Hhxh1QjYbzfURRNKLl0584dWFhYID4+Htra2uIOhyvR0dGwsbFBfn4+rav8icuXL8PBwQGfP38W6C1Aj7C3WHMtVmDjZf13COsnmGPVqlXw8/PDlClT0KVLF/j4+EBDQ0Ng89SloKCAc3v1+4SEmzPPm1rnuaDXt+D2Cbism1mlXIEX79+/R5cuXeDt7V2vMSrPPPf09MSGDRswZswYfPjwgeszz2vrPG8uCCFo27Yt1NTUEBMTg1WrVmH79u0NLgGvPPEtPT2dU3NLUfyit7y5xGKxICMjA01NTXGHwjU9PT2Eh4fD0dERVlZW+Oeff7BkyZIm9QddUCIjI9GlSxeB15M5Gqoio6AUewKT+B5r+bCeSJcwwJo1axAREQFXV1c8e/YMNjY2GDBgAC5evCiwW/Z1kZeXh4GBAQwMDKp8vaYzz5t657kg13eRmRoep0jD1tYWf/75JzZt2sTzv0nlTgX1rQWWkJCAuro6ZGRkICMjg6tXr0JCQqLWM8+57TyXkZGpVzyNDYPBQN++fdGhQwdMmzYNK1eu5DTFNaSr9iwWC506daLJJCVQ9AollyZNmoRXr17h8ePH4g6FZ+Xl5Vi3bh3++ecfTJo0idZV1mD48OGQlpaGn5+fUMb3CHuLjX7xKGcTnmruJJgMSDIZ2DK6NxwMvzVqXLt2DVOnTkX37t3h7e2Ndu3aYcqUKfD398eWLdzXVYpKTZ3niYmJSExMbDKd54JaX0IIdu7cifXr12PkyJG4cOEC2rZty/V4W7ZswYEDB5CZmcnXB8dff/0VsrKyCAwMrPNxdZ15/n3nebdu3Wr8IFHfk3wasg0bNuDIkSN4//49Hj16BAcHB7Rt2xbe3t7Q1dUVd3gghEBHRwd9+vSBh4eHuMOhmhCaUHJJW1sbZmZmOHr0qLhDqTcPDw/MnDkTvXr1gre3N62r/H+VdWd//PEHNm/eLLR53mUVYZ13LO6nZECCyagz8aj8/mD1dthuq1Otpi4+Ph42NjbIzMzEpUuXYGlpiS1btmDz5s2ws7PD2bNnhVJXKUi1dZ4nJCTU2XmupaUFDQ0NtGzZUrwv4Ae8rC9hV4DBlKh1ff/77z9MnDgR7du3h6+vL7S0tGodq7C0HG8yC1FWzsaaVSvwNesD7gT+V+/XkZCQgN69e+Py5cuwt7ev9zjfd55/v76vX7/mPKYpdp6/fPkS6urqOHfuHKZOnYrXr1/D1tYWycnJOHPmDM91ld+vbwtJJtSU5CAnXf8PWY8ePYKJiQkCAwNhaWlZ73Eo6kc0oeRCYWEhWrdujRMnTmDWrFniDocvlXWVBQUFuHz5MszNzcUdktilpaVBRUUFPj4+GDNmjNDnS07Px4WnqXD97wkk2nYE8L8rSQwAqkqyMNdQxuSBqnV2+2ZnZ2PSpEm4desWduzYgZUrV8LX1xdTp07lvJ6ePXsK/fUIWm2d54mJiY2i8zw5PR9nH77E2VthkFL8BTWtL0mLw5tgN7yOflxrfV1KSgpsbGzw9u1bnD9/vkpNZHJ6Pi4+fYuQF5/xNquo6qk9hKCrkhzMNZUxyUgVPTvw9sFi6dKluHjxItLS0tCiRQuensuNmjrPExISkJKS8tPO886dOzeKkh1LS0sUFxfjwYMHAICioiLMmjULly5dwurVq7Ft27Y66yrrWl8GAFVF2Xqv7/Tp03Hv3j2kpKQ0qDsZVONHE0ouPH78GIMGDUJ4eDj09fXFHQ7fMjMz4eDggNDQUOzZsweLFy9uFG/SwnL9+nWMHj0aqampIjvhorLL0jfgJnr0HVjvqw8VFRX466+/sH37dowfPx6urq54+/YtbGxskJ6eDnd3d76O4GtoGkvneeV7xsOn4WjTRb3a+kZGRkJfXx/Hjx/HnDlzah0nPz8fM2bMwNWrV/Hnn3/CadEqbPCNF8hV7pqkpqaiT58+WLBgAXbs2FGv115f3HSet2rVqtq6NsTO8ytXrsDe3h63b9/mNEMSQrBv3z6sWrUKlpaWcHd3r/YzKci7GDVJSkqCrq4uNm7ciLVr1/L3IinqBzSh5MLRo0exePFiFBQUNJkNnsvLy7F27Vrs2bMHkydPxsmTJ5tN4fyPtmzZgoMHDyIjI0NkibWnpyccHR0F1lV+9epVTJs2Dd27d4ePjw+UlJQwefJkBAQE4O+//8batWub9IeGhtZ5fuTIESxduhQFBQW1XuVzdnaGp6cnEhIS6tyzkBCCHTt2YMfle2g3/A8wJSRRwcO7dmWd5ubRveFoWPsHJkIIrK2tER8fj/j4+AZT31jZeV7TB4mG2nnOZrNhbm6OtLQ0xMTEQE5OjvO94OBgTl2lj48P57Qrfutwf7a+bDYbZmZmeP/+PWJjY2kdPSVwNKHkgrOzM8LCwhAVFSXuUATu0qVLcHJygpaWFry9vRv8GbTCYGNjg8LCQgQFBYlszjVr1uDChQtIS0sT2JhxcXGwsbFBVlYWPDw8MGzYMGzevBlbtmxpNHWVglZT53liYiJevHgh1M7zWbNmISIiAiwWq9bH5OTkQFtbG/3798f169frTGoPhyRjT2ASCCF8Jb8rrDSwwLzmMojz589j2rRp8Pf3F8luAfyqrfM8ISGhQXSeJycnQ1dXF/PmzcPevXurfO/169ewsbFBSkoKzp49i/R2fQWyU0Bd63vs2DHMmzcPd+7coaVOlFDQhJILBgYG0NHRwZkzZ8QdilBERUXB1tYWBQUF8PLygpmZmbhDEqmuXbvCwcEBu3fvFtmcwuoqz87OxsSJExEYGFilrnLKlClQVVVttHWVgibsznN9fX307dsXp0+frvNxvr6+sLGxwdq1a7Ft27Yak0VB73W5y06Hs2NApfv378Pa2ho2Nja4cOGCwOYSh4bUef7PP/9g9erVOH/+PCZPnlzle4WFhZg1axb8E7KgNHKRwOasaX3v3r0La2trzt0oihIGmlD+xNevXyEvL489e/Zg4cKF4g5HaDIyMuDo6IjQ0FDs3bsXixYtatK3SCtlZmaiXbt2cHd3x4QJE0QyJyEEysrKmDdvnlC6yisqKvDnn39ix44dcHBwwOnTp6vUVV66dKnK8YvU/wii87ysrAzy8vLYt28fFixY8NM59+3bh+XLl2P9+vXYunVrld87gZ/GA0BakongpaacmrsHDx5gxIgRMDIywvXr15v0rVBRd56z2WzMmjUL586dg5ubGyZOnFjl+28zC2G+5w7KCUNg77c/ru/du3cxcuRIDBo0CH5+fs22tIkSvoa/wZuYJSQkoKysrN4bBTcW7dq1w82bN7FmzRosWbIEEREROHHiRJN/86m8JSnK9X3//j0yMjKENqeEhAS2b9+O/v37Y/r06Rg0aBC8vb3x7NkzTJ48GaNGjWoWdZX1wcuZ54mJiThx4kS1zvNOnTrh69ev+PTpE8LDw3/aeb5s2TIQQrBixQqUlpZi+/btnLq/dd6xKBfgWeEAUM4mWOcdCzcnI9y8eRP29vYYMGBAk08mgapnnn+PnzPP6+o8ZzKZcHFxASEEU6ZMQUlJCWbMmMF5/HqfOIApAYYA1/j79Q0MDIStrS2MjY3h6+vb5N/PKfGiVyh/4uzZs5g5cyZyc3ObTf2Zu7s7Zs2aBW1tbVy7dq1J11X+888/2Lx5M3Jzc0XWJSrKrvLKusrs7Gx4eHjAwsICmzZtwtatWzF27FicPXtW7NvsNHaVneeVyUhQUBDi4uKqPIabzvP9+/dj5cqV0NHRgaurK+Q7qcPywD2hxT0wMwiepw5i+PDhuHr1apXGEeobbjvPf1zbHzvPKyoqMHfuXLi4uGDMmDE4duwYCpjyQl3fX3NDcPHYXgwfPhzXrl1r8h8WKPGjCeVPLFq0CLdu3cKLFy/EHYpIsVgs2NraoqioCJcvX26ydZUTJ05EamoqHj58KLI5N2/ejH///VdkXeXZ2dmYMGECgoKCsHPnTqxYsQI+Pj6YOnUqunbtCh8fH6irqws9juZi4cKFCAoKQnh4OM+d55KSkjh06BBevHiBoSuP4SWjE08d3dwi7AqUxgVhyxgdODs70yvVPKpv53laWhp27NiB0tJSDFt9ApH58jx1dHOLsCtQEhuIjb9pY+7cuXS/SUokmlVCWVZWhhcvXiAmJgYxMTH4/Pkz8vPzcfXqVYwaNQrt2rVDu3btoKurC11dXWhpaWHYsGHo3LlzszyiKiMjAw4ODrh79y727duHhQsXNug/PJVdnzExMYiLi0NGRgYyMzNx5swZzJ8/H7KysujQoQNnfTt06IBevXph2LBhOHz4sMjirNxYPjg4WGRzfl9X6ejoCBcXF6SmpsLGxgZfvnzBpUuXMGLECJHFU195eXmIi4tDXFwccnJy8OnTJ/j7+2Pq1Klo2bIlOnXqBF1dXWhqaopluxjg27GFKioquHTpUo3f56bzvGXLllCcdghSCr8ILc7ObVrg4Rp6UoogcdN5LiEhAXl5ecg5/gMphU5Ci6Vz6xZ4uJauLyU6Tb6G8s2bN3B1dYWfnx8SEhI4b9hdu3ZFp06dOAnSx48fkZ2djXv37nG2eJCQkAAhBIMHD0ZSUhI0NDTE9jrEoV27drh16xZWr16NxYsXIyIiAsePH29QdTifPn3C+fPnERAQgJiYGE7jROvWrdGhQwfk5+cDAIKCgsBms/HhwwdOF2/79u3x5csXGBgYICcnh6czk/nBYrHg4OAgkrkq1VRX6ePjw6mrHDlyJLZt24Y1a9Y0qA8N2dnZuHjxIoKDgxETE8NpnpCQkEDr1q2RnZ0NADh06BBKSkqQl5cH4FvjjJaWFvT09DBu3DhYW1uL5ExwNpuNqKioOk9catmyJXR0dDj7D1b6vvM8OuEFzuR1FGqsH3LLUFhaztcxflRVDAYDKioqUFFRgZWVFefrP3aexyYm4Yas8D4sAMCHPLq+lGg1ySuU5eXluHbtGlxcXBAcHAx5eXmMHTsWhoaG0NXVRZ8+fepMHvLz8xEXF4egoCBs3LgRrVq1Qn5+PoYMGYJZs2Zh/PjxTWaDc265u7vDyckJvXv3hre3N1RUVMQWS0VFBW7dugUXFxdcv34dkpKSsLa2hr6+Pufqo6qqao2JEZvNxqtXrxATE4OAgAC4urpCQkICUlJSsLe3x6xZszB48GChJVXi6Cr/UVxcHMaMGYOcnBx4enpi6NCh2LhxI/7++2+MGzcOZ86cEWtdJSEE9+7dg4uLC65cuYLy8nKYmpqiX79+nPXt1atXjb+D2dnZiIuL49yFePz4MWJjY9GpUyfMmDEDM2fORPfu3YUW+4sXL9CrVy8EBQVh2LBh9R4n/kMuRh16IMDIahaw8Ff07tRG6PNQVdH1pZqiJvfRJSYmBjNnzkRERARMTEzg6uoKe3t7ngrOW7VqBWNjY85xbgkJCbh//z5cXFwwdepU7Ny5E66urjAyMhLWy2hwJk6cCC0tLdja2kJfXx9eXl4wNTUVeRzx8fFwcnLC06dPoaenhwMHDmDixIlQUFDg6vlMJhPq6upQV1fHhw8fICUlhZSUFLi7u8PFxQVubm4YMWIETpw4IZSGGXF0lf+oT58+CAsLw8SJEzF8+HDs2rULW7ZsQb9+/TBt2jQYGxvDx8cHPXr0EHlsL168gJOTEx4+fIiePXti8+bNmDp1Kjp25O5qnYKCAgYPHozBgwdzvhYZGQkXFxccOnQI27dvx4IFC7B9+3ahJM2CWt8yAW4T1BDmoaqi60s1RU2mUresrAwbN26Evr4+SkpK8PjxYzx48ADTp0+vd/cii8VCly5d0KVLF0yYMAG3b99GVFQUZGVlMWjQICxfvpxz+7Q56NevH8LDw6GjowMLCwscOnQIorrA/fXrV/z999/o378/cnJyEBoaChaLhfnz53OdTP6IxWKhT58+UFVVxZo1a5CUlARvb2/ExsaiT58+OH78OKd5QlBYLBbk5OTEvrm4oqIiAgICsGrVKqxcuRKTJk3CiBEj8PTpU5SWlsLAwAA3b94UWTzl5eXYtWsX9PT0kJ6ezmmEW7VqFdfJZG369++Po0eP4uPHj9izZw9cXFygo6MjlBpWFosFVVVVKCkp8TVOC0nRvDWLah6qKrq+VFPUJH7a8vPzMXToUGzfvh3r1q1DREREtX3G6iMyMhL9+/ev8jU9PT08fvwYO3fuxNGjRzFo0CBkZGTwPVdjUVlXuWjRIixatAgzZsxASUmJUOfMzc2FqakpNm3ahOXLlyMqKgqmpqZ835ZmsVhVriQxmUzY2NggPj4ejo6O+OOPP2BnZ4eysjJ+X0KVOfX09ES2RVFdJCQksGPHDly+fBm+vr4YNGgQZGRk8OzZMwwaNAgjR47Ezp07hf6hIScnB6ampli3bh0WLVqEmJgYWFlZCbzsQFZWFsuWLUNsbCy6desGS0tLrF27VqCvLzIyUiBXn9WU5CDsSlbG/89DiR5dX6opavQJZX5+PkaMGIG4uDjcv38fmzdvFkh9IyGkWsJRSVJSEitXrkRYWBg+fvyIYcOGITMzk+85GwtJSUns27cPFy5cgKenJwYPHox3794JZa68vDyMGDECiYmJePDgAbZv346WLVvyPW5ZWRni4uJqXN82bdrg5MmT8PPzw3///Qd7e3uBJZWCSjgEyd7eHo8fP0Z+fj4MDAwQHh4OPz8/rFu3DmvXroWDgwNnKxRBy8nJgZWVFWd9d+/eLfSmrx49eiA4OBi7d+/Gzp07sWbNGoEklXW9Z/BKTloSqorC3TdQVUmWNmyICV1fqilq1AllQUEBrK2tERcXh8DAQIFclazEzWkmffr0wZ07d/DhwwdYWFhwtoVoLiZNmoSHDx/i8+fP0NfXx927dwU6fmUy+fz5cwQFBQl0fePj4/H169dqV6C/9/vvv8PHxwc3b97E+PHj+U4qCwoKkJSUVOec4qKrq4uwsDAYGBhg+PDhOHDgALZu3YqrV6/ixo0bMDY2xsuXLwU6Z25uLoYPH46UlBTcvn0bxsbGAh2/LkwmEytXrsSBAwewe/dugVypTEtLQ2ZmpsA+MJhrKkOCKZzrWEwQmGsoC2VsijvCXF8JJoOuLyVyjTqhXLFiBaKiohAYGIgBAwYIdOzIyEgA+Okf/969eyMkJATv3r3D3LlzBRpDY9C/f3+Eh4ejT58+nP0cBXULccGCBYiPj0dgYCAMDAwEMmYlFosFBoMBXV3dOh9nbW0Nb29v3LhxA1u2bOFrzpiYGBBCGtwVykqKioq4ceMGVq5ciRUrVlSpqywpKYGhoSFu3bolkLkIIZgxYwaSkpIQHBwstn+TxYsXY9++fdi1axfc3Nz4Govb9wxuTTJSFcqm1wDABgN5kQECrxGmuCfM9a1gE0we2HRPOKMapkabUIaGhuLEiRPYvXu3ULqtWSwWlJSU0KVLl58+tnfv3jhy5Ai8vLzg7e0t8Fgauvbt2yMwMBALFy7EwoULMXPmTL7rKm/cuAE3NzccPHgQhoaGAor0fyIjI6GhocFVp+/IkSOxfv167Nq1C9HR0XzNKSUlhd69e9d7DGGTkJDAzp074enpCV9fX5iYmEBOTg5hYWEYOHAgRo4ciV27dvH9oeHq1avw9vbGqVOnxH7FdunSpZg0aRKWLFnCOZe7PlgsFtq1a4fOnTsLJK6eHVphsHo7gV/FkmAy0ImZi/2bV8POzo6zdyclWsJc38Hq7aCu3DyOCqYajka5D2VRURH09PTQsWNH3L17VyjHStnY2KCwsBBBQUFcPZ4QgjFjxiAsLAwJCQn17jxu7C5cuABnZ2f06dMH165dq9d+lXl5eejTpw+0tbXx33//CWVPSBMTE3Tt2hXu7u5cPb6srAwGBgaQkpLC06dP67VJtpOTE1gsFudKVkMXExMDGxsb5OXlwdPTE2ZmZvjrr7+wfft22Nvbfztvuh5b72RmZkJbWxsmJia4evVqg9hIPSMjA1paWjAzM4OXl1e9xhgzZgyKi4sRGBgosLjeZRVh2P67KBXQ9i+EEEgyCEJWDEXM4xBMmjQJnTp1go+PDzQ1NQUyB8U9YayvFBMIWTEUKkKu0aSoHzXKK5QuLi548+YNXFxchHZGaU0d3nVhMBg4duwY8vPzceDAAaHE1BhMnjyZU1dpYGCAe/fu8TzGwYMHkZmZiRMnTggl2aioqEB0dDRPt1lbtGiB06dPg8Vi4eLFi/WaV1ANG6Kiq6uL8PBw6Ovrw8rKCgcPHsTff/+NK1eu4MaNGxg0aBBevXrF87jbt29HaWkpjhw50iCSSeDb7gWHDh3ClStX6vUzC/D+nsENFUVZbB4tuCvaDAYDn28cwvK502FmZoZnz54BAAYMGAB/f3+BzUNxRxjrmx7wL07s246KigqBjUtR3Gh0CSUhBCdPnoSNjY3QPlFnZmbi3bt3PP/x79y5MyZNmgRXV9dm/ctcWVepra0NCwsLHDlyhOtbpBUVFTh16hQmTZqErl27CiW+5ORkFBYW8ry+hoaGsLS0xMmTJ3mes66u8oassq5yxYoVWL58OSZPngxra2s8ffoUxcXFMDAw4OmKXElJCc6ePYvZs2fjl1+Ee/QcrxwcHNCzZ0+cOHGC5+dmZGQgLS1NKOvraKiKFVaCOfZ1pZUm3DbPw82bN2FsbAwJCQk8ffoUZmZm+P3337FlyxZaVyliglzfFVYa2DDRAtu3b8fo0aM5R9FSlCg0uoTyyZMniI+Px+zZs4U2Bz+nXcyePRtpaWki3RS6IWrfvj2CgoKwYMECLFiwAE5OTlzVVd66dQvv3r2Ds7Oz0GLjZ32dnZ3x6NEjxMXF8fQ8brrKGyoJCQns2rULHh4e8PHx4dRVPnv2DAMHDoS1tTV2797N1YeGa9euISsrC7NmzRJB5LxhMBiYPXs2rl69yvM2YMI+AWmBeU/stNOBtCST55o7CSYD0pJM7LLTwXxzddjY2HA2sDc0NMSjR4/g7e2NzZs3Y+PGjRg7diytqxQxQa3vAvOeWL16NW7cuIFHjx5hwIABSEhIEFLUFFVVo0soz549i27dusHCwkJoc0RGRkJeXr5ep5no6+ujf//+OHPmjBAia1wkJSWxf/9+nD9/HpcuXcKQIUOQlpZW53NcXV2hp6cn8K7u7/Fzmsno0aOhrKzM8/py21XekDk4OODRo0fIzc2FgYEBWCwWrl+/jtWrV2P16tVwdHREYWFhnWOcPn0aZmZm0NAQzBUZQZs2bRrYbDbPZQ2V7xnq6upCiuzblazgpaYY1P3bzy0TdSfwlYnJoO5KCF5qCgfD/3X9amtr49mzZzAxMcHIkSOxe/du/Pnnn/Dz88OdO3cwcOBAJCUlCe21UNX9uL4MPtZ3xIgRCAsLg7S0NIyMjJplsygleo0uoXzy5AksLS2FVjsJ/O80k/rOYWVlhadPnwo4qsZrypQpePDgAT59+gR9fX3cv3+/1sc+fvwYo0aNEmptHT+bi7do0QKWlpZ4/Pgxz3Ny21XekOnp6SEsLAz9+/eHpaUlDh48iG3btsHLywsBAQF11lWWl5fj0aNHGD16tIij5l779u0xaNAgPHjwgKfnsVgs9O3bV6jvS8C3mjs3JyMELRkCTYnPYOemVztxhQGgq5Isphh1RfDSIXBzMqqxQaNt27bw8/PDhg0bOBvYm5ub49mzZ2Cz2TA0NKR1lSL2/fp2LU0FoyCj3uurrq6Ox48fY8SIEbCzs8Off/5Jyxko4SKNSElJCZGUlCRHjx4V6jyamppkwYIF9X6+h4cHAUC+fPkiwKgav8+fPxMzMzMiKSlJjhw5QthsdpXvp6enEwDEy8tLaDGw2WyiqKhINm/eXO8x9uzZQ2RlZUl5eTnXzxk0aBCZMGFCvedsaL5+/UpWrlxJAJBJkyaRwsJCEhsbS3r06EEUFBRIYGBgtefExcURACQkJET0AfNg8eLFRF1dnafnaGhokIULFwopopr9/vvvxNLSkhSUfCVx73NIZGoWiXufQwpKvvI81rVr14i8vDzp06cPSUlJITk5OWT06NGEwWCQLVu2kIqKCiG8AqouxsbGZOLEiXyvL5vNJjt27CAMBoOMGjWKZGdnCydgqtlrVAllREQEAUAeP34stDny8/MJg8Egrq6u9R7jxYsXBAAJCgoSYGRNQ1lZGVm8eDEBQGbMmEGKi4s537t58yYBQJKTk4U2f2pqKgFA/Pz86j1GcHAwAUASExO5enx5eTmRk5Mju3fvrvecDdWlS5eIjIwM6devH3nz5g3JysoiI0aMIEwmk+zatavKhwY3NzcCoMH/QTt79iwBQHJzc7l6fF5eHgFAzpw5I9zAftClSxeyevVqgY0XHx9PevbsSdq2bUtu3rxJKioqyKZNmwgAYmNjQ/Ly8gQ2F1W38vJyIisrS/755x+BjXnjxg3Stm1b0rNnTxIfHy+wcSmqUqO65Z2amgrg21m8whIdHc33aSaVdVRv3rwRUFRNh5SUFA4cOIDz58/D3d0dpqamnLrK169fQ0JCAt27dxfa/JV7QPKzvpW7C3C7ZU59u8obA0dHRzx+/BjZ2dnQ19cHi8WCv78/p65ywoQJnLrKlJQUdOzYEW3bthVv0D+hpaUFAFwfNVm52b0o1/fLly8C7yqvrKscNGgQRo4ciX/++Qd//fUXfH19cfv2bRgZGdG6ShFJSkpCUVGRQJv4rK2tERYWhhYtWsDIyAg+Pj4CG5uigEZYQwlA6PWTUlJS0NbWrvcYwq6jagqmTJmChw8f4uPHj9DX18eDBw9ACAGTyRT6+rZv356v00wqNzUnXG6FJOwOYHHT09NDeHg4+vXrBysrKxw6dIhTV+nv749Bgwbh9evXYLPZkJKSEne4P1UZI7f1ZiwWCy1atODrPYNXwvqZatu2La5fv45169ZhzZo1cHBwwNChQzl1lQMGDEBAQIBA56Sqq1zfvn37CnRcdXV1PHnyBMOHD4etrS3++usvWldJCQzNfH4QGRkJHR0dtGjRQtyhNHn6+voIDw+HlpYWzM3NcffuXaHPWbm5uCg31Oanq7yxUFJSwn///Ydly5Zh6dKlmDp1KkaNGoUnT56gsLAQBgYG9doEvTGofM8QZbLMYrGE1lXOZDKxdetWXL16Ff/99x8GDRrEOSFqyJAh+P333/H333/TRESIWCwWunbtCkVFRYGPLS8vDy8vL2zbtg1///03xowZg9zcXIHPQzU/jTKhFOam4YI4zaQ5b2rOK2VlZQQFBWHevHnw9PREeXk5iouLhTYfPx3elXj9QyqME1QaIklJSezevRuXLl3C1atXYWJiglatWiEsLAyGhoa4ePEi8vLy+D4HXNh4jU8cJyCJoqvczs4OT548QXFxMQwNDfHkyRP4+Pjgr7/+wp9//olx48YhPz9faPM3Z8J+z2AwGFi3bh0CAgLw4MEDDBgwAImJiUKbj2oeGlVCWXlyCre1TbwqLS1FfHw8338cUlJSAABqamoCiKrpk5KSwsGDB7F48WIQQmBsbIz3798LfJ4vX77g/fv3fL9RV15p69Kly08fSwhpdEcu8svR0RGPHj1CdnY2DAwMEBUVhYCAAFhZWSE3NxcODg4/3a9SnN6+fQsA6Nix408fK6j3DF4J4oMRN3r37o2wsDAYGxtj5MiR2LNnDzZu3AgfHx8EBwdj4MCBSE5OFnoczYko3zMq6yqlpKRoXSXFt0aVUPbu3RuSkpKIiooSyviCOs2kMj5B1780dcuXLwcApKWlceoqBUlQdWdRUVFo0aIFJCQkwGKxEBoaihs3biAiIgIJCQkoKiriPPbdu3fIyspqVgkl8O1nPzw8HHp6erC0tMShQ4fw119/AQCuX78OExMTvH79WsxR1qyyzlZaWhrv3r1DYmIiEhMT8e7dO2RmZla5ghkXF4fy8nKRXoHOz89HcnKyyOas3K9y7dq1nA3shw0bhqdPn6K8vByGhoa4ceOGSGIRJDabjeLiYmRnZyM3NxelpaUN4ur527dvkZ2dLbL3jMr9Ki0tLWldJcUXSXEHwAtpaWloa2tzEgNBE9RpJiwWC126dEG7du0EFFnz0KVLFygqKsLJyQlPnjyBubk5/v33X8ydO1cgNY+RkZFo1aoVz7sEEELw+PFjPHz4EDExMbhx4wbKysqgo6NT4+MZDAZ69uwJXV1dTl1dbY9typSUlHDz5k2sXbsWS5cuhaOjI+dW29mzZ2FgYABPT08MGzZM3KEiNjYWT58+RUxMDNzd3ZGbm4v27dvX+FgFBQXo6upCV1cXubm5Ij8BSRxd5RISEvj777/Rv39/TJ06FcbGxvDx8cGzZ88wefJk/Pbbb9i6dSvWrVsn0vpkbr158wbh4eGIiYnh/FfTBxoJCQloampy1ldXVxcDBgyo9WdBGCp3ohDlh5RWrVrhypUr2LFjBzZs2AAWi4ULFy6gTZs2IouBavwaVUIJAMbGxrh58ybYbLbA64dYLBY0NTUhJydX7zEIIbh16xaMjY0FGFnzwGAwMGDAADx+/Bi3b9/G8uXLMW/ePERERODIkSOQlpbma3xe687S09Nx/vx5uLi4ICkpCXJycujTpw++fv0KExMTbN26Fa1bt4akpCTKysogISGBoqIiJCUlcf5oPXnyBAAwcOBATJ8+HU5OTvU60rOxkpSUxD///IP+/fvDyckJ0tLSiI6ORlhYGCZMmIDhw4dj165dWL58ucgTkZycHLi7u8PFxQUsFgtMJhM9e/ZEQUEBTExMsHDhQsjLy6OsrAzAt1OSCgoK8Pz5c8TExCAoKAgvXrwAIQS//vorZs2ahYkTJwp9W6TIyEiRd5VXsrOzg6amJmxsbGBgYAAPDw/4+vpi8+bN2LBhAyIjI3H27Fm0atVK5LH9qKioCF5eXnBxceHc7ejQoQN0dXVhZ2cHDQ0NyMnJIT09Ha1atULLli2Rl5eHhIQEzgfHvLw8SEhI4LfffoOzszOGDx/O2eVBWFgsFpSVlfHLL78IdZ4fVX7Y69u3LyZOnMi5Bd6rVy+RxkE1YmLZ/ZIPjx8/JgDIrVu3BDLe96cQGAyzIQ6TpvI1XlhYGAFAAgICBBJfc+Pu7k4AkOfPnxNCvm0yLS0tTYyMjEhaWhpPY/14woR6r95k0aJFP31eeno6mTJlCpGUlCTS0tJk4sSJJCQkhFRUVJDAwEACgDx8+JCrGH777TdibGxMFi5cSNq2bUsAkGHDhpGEhASeXktTwGKxOP8G169fJ+Xl5WT16tUEAJkwYQIpLCzkabz6niCSkZFBnJ2dScuWLYmEhAQZM2YM8fPzI0VFReTy5csEANcbPw8YMICYmpqSMWPGEAkJCSIjI0OcnZ1JRkYGT6+FF9OnTyf6+vpCG58bWVlZxNrausoG9t7e3kReXp5oa2uTpKQkscWWmZlJFi5cSFq3bs35fbt06RL59OkTT+Ow2Wzy+vVrcuTIEdK3b18CgHTu3Jls376dlJaWCin6b+8Zw4cPF9r43EhKSiLa2tqkVatWxMfHR6yxUI1Ho0so2Ww20dHRIWPHjq33GEmf8shG3zgyZPcdorbGn3St8t91MmT3HbLRN44kfeL9ZAhnZ2eioqLC07F81P8UFxcTJSUlsnz5cs7Xnj17Rrp06UI6duxIHjx4UOfz61pb1dXXSd8/fWpdWzabTS5evEiUlJSIkpIS2b9/P8nMzKzymHHjxpHevXtXOzayNp07dyZr1qwhhBBSVFRELly4QDQ0NEiLFi3I9u3bSVlZGVfjNBWxsbGEwWAQBoNBDhw4QNhsNvH09CSysrJET0+PvHr1qs7n17W+amv86/zdZbPZ5PLly0RZWZkoKCiQ7du3kw8fPlR5zLBhw4iJiQlXr6XyNJM9e/YQQgj58OED2b59O1FQUCDKyspCO0JUT0+PzJo1Syhj86K8vJysW7eOACAODg6koKCAJCQkEA0NDdKmTRty48YNkcd07do10qFDB9KmTRuyfv168vLlS4GMy2azSXh4OJk9ezaRkJAgOjo6JCwsTCBj/6hTp05k7dq1QhmbF3l5ecTOzo4AIH/99Rc9fpP6qUaXUBJCyKFDh4ikpCTPV3neZhaSyS5PSNc1/qT7uoAfEsmq/1V+f7LLE/I2k7srJ2/fviWysrJk06ZN9XlZ1P9btmwZUVRUrJLMffr0iQwZMoRISUmRY8eOVUvo+F3b3NxcMnr0aM4fx/T09GpxpaSkECkpKXLgwAGuXsfnz58JAOLp6Vnl60VFRWTVqlWEyWSSfv36CeyPXmNhY2NDFBUVCQAydepUUlRURKKjo0n37t2JoqJijUeW8ru+OTk5nD+OdnZ25OPHj9XmiI2NJQDIuXPnuHodCQkJBAC5fft2la9//PiR2NracubKycmpx79SzUpKSoikpCQ5cuSIwMbkl5eXF5GTkyO6urrk5cuXJCcnh/z222+EwWCQbdu2cf3hix/Z2dlk/PjxBAD5/fffeb6bwQsWi0X69etHmEwmWb16Nfn6lfez02uTnp5OAJDLly8LbEx+VFRUkL///pswGAzy+++/C/RnmWp6GIQ0gLY2HhUXF0NPTw/t27fHvXv3ICEh8dPneIS9xUa/eJSzCSrY3L9kCSYDkkwGNo/uDUdD1VofRwjBb7/9hqioKCQkJNBiZj58/PgR2traGD16NM6dO8f5+tevX7Fs2TIcPnwYs2bNwuHDhyEtLc332q616oGTq6cjISEBZ8+ehY2NTbXHstlsWFhYIDU1FbGxsVzV2QYGBmL48OFISkqqsW4yPDwcEyZMQGlpKUJDQ4V65GRDEhkZiQEDBsDOzg7+/v7Q1tbGtWvXIC8vjwkTJiA4OBi7d+/GsmXLwGAw+F7fNZbdcWLVNLx48QKnTp3CuHHjqj22oqICJiYmyM3NRVRUFFf1uhcvXsTkyZORlZUFBQWFKt8jhODKlSuYPXs2evXqhVu3bqF169Zcx16biIgIGBgY4PHjxxg4cCDf4wlKXFwcbGxskJWVBU9PT1hYWGDTpk3YunUrxo4di7Nnz0JeXl4oc+fk5MDS0hIpKSk4evQop/lLmL5+/co5mtLBwQHnzp0TSG3lrVu3MGLECCQnJwtl0/r6CggIwKRJk9CxY0daV0nVqlFtG1RJRkYGp0+fxqNHj3D06NGfPv5wSDLWXItFaTmbpz9IAFDBJigtZ2PNtVgcDql9vzV3d3fcuHEDx48fp8kkn3755Rfs27cP58+fx82bNzlfl5KSwqFDh3DmzBm4ubnBzMwM230j+V7bTTeS8bKlOoKCgmpMJgHAxcUFoaGhOHXqFNdNWz/rKjcwMEBoaCikpaVhbm7eYLfREbT+/ftjxYoV8PX1hZubGzIyMmBgYIDY2FjcuHEDK1aswIoVKzB58mTsu5XA9/pu/i8Fb+Q0ERwcXGMyCQD//vsvnj17htOnT3Pd/MVisaCmplYtmQS+NTjY29sjKCgIiYmJGDFiBPLy8niKv7Y5mUymSLvKudGnTx+EhYXByMgII0aMwN69e7F582Z4e3vj1q1bGDhwIGd/XkHKzc2FlZUVXr58iTt37mDChAkiae6SkpLCunXr4OHhAU9PT0yfPl0gB1pERkaidevWDe7D5ahRoxAWFgYmk4kBAwbAz89P3CFRDVCjTCgBYPDgwZg3bx7WrFmDR48e1fo4j7C32BOYJJA59wQmwTPsbbWvx8TEYOHChXB0dMTvv/8ukLmau+nTp8PS0hKzZs3Cmzdvqn3v/v37SJNWxcknHwUyn4yRA16hQ43fY7FYWLFiBZycnGBhYcH1mNx0lXfu3BkhISGQkpKChYWFQJKOxmDjxo1QU1PDjh07EBoaCh0dHVhYWODIkSPYuXMnPDw8cDM5D/+GCibJbjlgPFLYNW/9EhERgfXr12PhwoUYNGgQ12Nys7m4gYEBgoKCkJCQgNGjR/OddERGRkJTUxOysrJ8jSMMCgoK8Pf3x+rVq7Fq1SpMnDgRlpaWePr0KcrKymBoaIj//vtPYPOVlZXB2toaKSkpuH37tlj2eh03bhwuXboEDw8P/PHHH3yPJ4oTkOqrZ8+eePr0KYYNG4YxY8Zg06ZNdL9KqoqG91PLg927d8PAwAAjRozA48ePq33/XVYRNvrFC3TOv/zi8S7rfxtXx8bGwsLCAt26dePqainFHQaDgTNnzqBly5YwNzdHampqle937NEbsr9OAwRYsfHj2gLfNjEfNmwYevXqhX379vE0HrenXXTp0gVBQUH4/Pkz1qxZw9McjZWMjAzc3d2RnJyMyZMn48qVK1i8eDEWL16M6dOno/9gSyhZzRX6+kZGRmLYsGHQ1dXFtm3buB6L/P9pJtzsFWhoaAhfX1/cu3cPhw4d4jnu73E7p7hISEhg+/bt8PLywvXr1zFo0CDIyMjg2bNnMDExwahRo7B9+3aBbCC+e/duPHv2DP/9959YDw6wt7fH8ePHcerUKQQEBPA1VkM/Vatyv8qtW7diy5YtsLW1bTYfgqmfa9QJpZycHAICAtC3b18MHz4cDx8+rPL9dd6xKOfxNtnPlLMJ1nnHAvi2wfDQoUOhoqKCoKCgGm99UfVXefWOyWTCzMysypXKdd6xKCcABHh76/u1Bb4lkxYWFujevTsCAwN5qoHLy8vj6TSTbt26YefOnTh27Bju3r3Lc+yNkb6+PgIDAxEbG4vRo0dj06ZNuHjxIi5fvoyRG91QwYZQ15fFYmHYsGHQ0NDArVu3eKrxS01NRU5ODtd//E1NTTF//nysX7+ec3QnryoqKhAdHd2gE45K48aNw5MnT1BYWAgDAwOEh4fDz88P69evx/r162Fvb4+CgoJ6j5+QkICtW7di1apVMDIyEmDk9ePk5IThw4dj7ty59U6wcnNzkZKS0qA/MAAAk8nEhg0bcP36dYSGhmLAgAF4/vy5uMOiGoBGnVACgLy8PG7cuIF+/frB1NQU69atQ0lJCZLT83E/JYPnuqufqWAT3E/JwMqtezFgwACoqKggODgYioqKAp2H+kZFRQUhISFgMBjo27cvXF1dkfQpT6hr+/xDDnbv3o2BAweiW7duCAwM5Hmz6vqcZjJv3jyYmJhg9uzZAqnHagyMjIxw69YtREdHo3///ujSpQs8/7uLr+3UUSHgdsHK9X3xMRf79++HiYkJ1NXVcevWLZ7rnitPM+FlfXfs2IH27dtj/vz5PM1V6cWLFyguLm4UCSXwv7pKQ0NDDB8+HPv27cOWLVtw9epVzuEP9amrJITA2dkZampqnOM8xY3BYODEiRPIzs7G+vXr6zWGOE5A4getq6R+1OgTSuBbUhkcHIxNmzZhz5496NevH/7xeQIJppCKs9kVcL2fjKVLl+Lhw4c0mRQyVVVVhIeHY8yYMXBycsL49YcgIaSlZTIA25X7sHbtWsyfPx/37t2r15VnFosFaWlpaGlpcT83k4k9e/YgKSkJQUFBPM/ZWA0cOBBhYWHo0KEDTE1Nsc8vTLjru2ofli9fDmdnZ9y5c6deJ9uwWCx06NCBp9NM5OXlsWPHDty8ebNeV3QEdRa9KCkoKCAgIACrVq3CypUrMWnSJIwYMQJPnz5FaWkpDA0NqzTecePJkyd49OgR9u/fj5YtWwopct517doVa9euhYuLC7Kzs3l+fuV7RmPqoNbQ0MCTJ09gYWGBMWPGYPPmzbSushlrEgkl8K3rrvIM0tatWyOA9UbgV7A4mBLoOcQGO3fuhIyMjHDmoKpQVFTEuXPncOPGDWTLdBL41atKbAKUKPbAw4cPsXfv3no3P0RGRkJHR4dzlje3jIyMoKuri5MnT9Zr3sZKU1OTU2P4srilUNe3qG033L9/HwcPHqz3VjaVtW68dhTb2dlBSUkJp06dqtectXWVN2QSEhLYsWMHLl++DF9f3yp1lYMGDcLIkSOxc+dOrusqT506BTU1NYwYMULIkfPOyckJ5eXluHjxIs/PjYyMhK6uLs/vGeLWunVrXL16FVu2bMHmzZtpXWUz1mQSykq9e/dGYMg9SCkI9xzU9MIKFJaWC3UOqrrBQy3BbKUs3Enk20GnnwFfQ9S3uJ7BYGD27Nnw8/PDx4+C6WBvLJhMJqY7z4Vk245CnYch3x59Dfiru+Omw7sm0tLSmD59Os6dO4eSkhKRzNlQ2Nvb48mTJ8jPz+fUVV6/fh3r16/H2rVr4eDg8NO6ytzcXHh4eMDZ2blBdkJ37NgRY8aMwcmTJ3luPGroDTl1YTKZ+PPPP+Hn54fQ0FAYGRnhxYsX4g6LErGG9xspAGk5JQCEuxcZAfAms1Coc1DVpWYWQtg78fO7tiUlJUhISKj3H4cJEyagoqICwcHB9Y6hsWoM65ueno6PHz/Wu3liypQpyMzMxJMnT7h+Di9d5Q2Zjo4OwsLCYGBggOHDh2P//v2cusobN27A2NgYL1++rPX5gYGBKC4uxtSpU0UYNW+mTZuG2NjYOl/Hj/h9z2gofvvtNzx79gz/x95Zh0W1fX/4HcACUbFBxQQBBQMwUK9gxxUBA+yOa3deu7sTsAsL7GtiJzAICgrYXZgICMz5/eGP+YqEMEGe93nu43Nnztl7HZdzztr7rM9aALVq1eLIkSMZbJFIepItA8ofsemTw5Fe84j8j6zg2zt37hAbG6vww79w4cJUqFBBnjOXk8gK/lU2l7FKlSrkzZs3Tf5Nq6o8M1O4cGGOHz/O2LFjGTNmTIK8yqioKKysrJLNq/Tz86NUqVKULl06na1OPfGq87T4NzAwkLi4uCy/YICf6Ss3btzAzs4Oe3t7Zs6cKeZV5hCyZUCZWyt9Lmv7ls14enpy7949YmJi0mXOnE56+XbtqpVs2rSJ69ev8/nz5zSdG9/NxNzcXOH5q1evjr+/v8LnZ1XSy7979+zixIkTPHnyJM0Pu/huJuXLl1dobi0tLSwsLNLkX0VU5ZkZTU1N5s+fj4eHB4cOHaJevXro6Ohw69atFPMq/f39M/3fQfHixTEwMEiTf6VSKZqamkrdMzITBQoU4ODBg8yYMYNp06bh5OQk5lXmAJRvPpoJKVdEBwmo99WZILBl9SKWvXsN/BQFGRkZYWZmhqmpKWZmZpiZmWFsbJyplIhZnfTy7ZlDu3FfEiJ/oBkYGMj9+qt/ixVL3H1FKpViYmKiVDeTatWqKV0EOyuSXv5dOWcK87/8VOJqa2tjamqayL8VKlRIsj9zfK6bMjl81atXl78aTA2KqMqzAh07dsTExARHR0esrKzw8PDg8OHDTJs2jYkTJ+Ln58emTZvk4qnbt2/Tu3fvDLb6z6R1QRh/z8hOIk8NDQ2mTp1KjRo16Nq1K7Vr18bLy4vKlStntGkiaiJbBpQ6ebQwLKzNk9+6YqiSskV1OP/mJW/evCE4OJigoCD5n66urrx+/TPQ1NDQoEKFCokeViYmJujq6qrNvuxKevn2Qsg9vn//zv379xP49/Tp06xbt47Y2J+CrCJFiiTwq6mpKdeuXVN6F0VXVzfNoo3sQHr59+HH9zx9+jTB7zY4OJgjR47Id6Rz586NsbFxot+un58f9vb2StlQqFAhIiJSn8epqKo8K2BhYcGtW7fo1KkTzZo1Y9GiRcyaNYsaNWrQo0cPbGxs8PT0pGLFinz9+pUiRYpktMl/pEiRIolaxqaEn59ftnjdnRRt2rTh5s2bODg4UKtWLXbu3Mnff/+d0WaJqIFsGVAC2FUuzvYbT9RSOkhTQ4KdcXEkEgklS5akZMmS2NnZJTjm48ePiQLNPXv2JGghWKZMmUQPK1NT0yxxw8xI0sO38HPnqkaNGomCwx8/fhAWFpbAvzdu3GDbtm3yIDA4OJjQ0NBE/i1Xrhyampoqtzs7kR7+1dDQoFy5cpQrV45WrVrJvxcEgdevXycKNNetW8fbt2/lx+3evZtHjx4l8K+JiYnCZYj+hJ+fHz179lTL2JmB+LzKSZMmMXr0aHx9fXF1deXGjRs4ODhgbW3N7t27M9pMtRAbG0tAQAAuLi4ZbYraiM+r7NatG23atGHmzJlMnjw5Uyr1RRQn2waUXWobsuXaY7WMHScT6FrHMMVj9PT0sLGxwcbGJsHn37594/79+wkeWMePH2flypXyXK7ixYsnGWjq6+tnyx2KtJLRvs2dO7f8lXe7du3+d25cHKdPn6Zly5b06NGDHz9+EBQUxMGDB/n69SsAefPmpXLlyon8W6lSJXLnzq2Wa8pqZKR/JRIJ+vr66Ovr07hx4wTfffjwgV27djFs2DCaNm3Ku3fv2LlzJ8+ePZMfY2homOh3a2pqqlTzA2VV5VkFTU1NFixYQM2aNenduzdBQUF4enpy8+ZNunTpQqtWrdDS0lJJH/DMxP3794mKisr0uaHKUqBAATw9PZk9ezZTp07Fz8+Pbdu2iW/qshHZNqA0KqFLg0pFufrwg0p3OjQ1JNhUKEKl4or9CPLnz4+lpSWWlpYJPo+OjiY0NDRBoHn58mXc3d358eMHAAULFkwy0CxbtmyOWullVt9qamry4cMHABYsWCDvwCIIAi9evEi0Y3369Gn58VpaWlSqVEnu1zt37pA3b16+f/+uVC5mViSz+rdIkSLExcWRN29eNm/eLM+v/Pr1K/fu3Uv06nzFihXyRWKJEiUS/G6DgoLInTs3giD8cZGYFTvkKIOzszOmpqY4ODhgZWXF3r17OXLkCFOmTGHevHls2rSJAQMGoKOjk9GmJsu3b9/IkydPqo6NF1xVr15djRZlDuLzKqtXr54gr9LY2DijTRNRARIhuy33fuFZ+HeaLLtAtKpKkQgCubUknB1lR5nC6fOQj42N5dGjR4lewQUHB8tzsPLly4eJiUmiQLNixYpZrutCalG1bwVBQCKL5UDv6lialFN4nNGjR+Pp6cnDhw9Tdfy7d+8SBZrBwcG8ePEC+LljVq5cuSQXEmntP52VUPlvF8ijpcGZkQ2V+u12796de/fupUpQExUVRUhISCL/hoSEyKtCFCpUKJFfzczMKFOmjHyROHfuXBYuXMjHjx9z1BuK8PBwXFxcOHv2LIsWLWLkyJFUrVqV+/fvY2ZmhpeXFxUqVMhoM5OkUqVK2Nvbs3Tp0j8eO2rUKA4dOpSmupXZgXv37uHg4MCrV6/EvMpsQrYOKAH23HrKhIOBKhvvy5l1rB7Zmc6dO6tsTEWQyWQ8e/YsyWAkvo9sUspzU1NTKleunC2U56r2bezVrQhhVzhw4AB16tRRaIxGjRqhp6fHgQMHlLKldOnSNG7cGFtb2wS+ffTokULK86yIqv27wMkcZ+uU0xn+hLm5OfXq1WP9+vVpPlcQBN68ecOtW7dwcnKibNmyAHz58oV3794lOFZLSwtDQ0OqVq0qDzQOHjyYrPI8uxIbG8ukSZNYtGgRXbp0oWDBghw9epRcuXIRHh7Onj17aNasWUabKSciIoIbN27QuHFjmjRpQpEiRYiIiODo0aM0bNiQEiVKUKRIEczNzbGwsMDc3Jy2bdtSpEgR9u/fn9HmpzufP3+me/fuHDlyhJkzZzJp0qRM/bYtLi6Ohw8fEhAQQEBAAO/fv+fDhw94eHjQo0cP8ufPT/HixbGwsMDCwoJy5cpl6utRNdk+oARY7R3K4lMhSo8zwq4CvtvnsmPHDkaNGsWCBQsy3c09/qGVVKD5q/K8fPnyiQKRrKg8V5VvxzarTDvT/LRr1w4fHx/WrFlD37590zSGIAgULlyYMWPGMHnyZIVtefnyJaVKlcLDw4OOHTsm+O779++EhIQk8G1QUBBhYWEpKs/NzMwoVapUltvhUta/8a+URzSqyIimJkrZEhkZia6uLmvWrGHAgAGpPs/f3x83Nzf279/Pmzdv5J+bmppibm5O3rx52bZtG61bt0ZTU5Nnz54RFhYmz7v9lVy5ciWZg2tsbJzqV6xZEQ8PD3r37k3RokV5+vQpjx494p9//uHUqVPMmzePsWPHZti/7ZCQENzd3fHy8iI0NFS+4CtXrpx8AXDq1Cnq169P3rx5efXqFffv35f/XiUSCbVq1WLdunU5Jq3hV2QyGbNmzWL69Ok4OjqydevWTPUcevbsGZs3b+bYsWPcuXOH799/VqAoXrw4+vr6REZGEhISgoWFBQAvXryQpzLp6upibm6Ovb09PXr0oGRJ9baVzWhyREAJP3c7ph2+S6xMSFNelqaGBC0NCTPtq+BsbYggCKxcuZLRo0dja2vLnj17KFq0qBotVx1JKc+Dg4OzvPJcVb6Fnwru4cOHs379egYOHMiKFStSFMtERMfy+EMEP2JlvH/zmub1anLU60AC5XBamT9/PjNnzuTly5fyPMw/kZTyPCgoSJ7wDz9vbknVW8zsynNl/CsRZHw4uQ5jrfccOHAgzR1WfvVv6L1gXP5uzPXLF6hVq1aK50VHR7NlyxZcXV3x9fVFX1+frl27UrduXf777z/27dvHixcvUqw7+PbtW65fv07btm0xNDTk6dOnFChQgIoVK5I3b14ePHggV55raGhQsWLFRL9bdSrP05vbt2/z999/8/z5c0aMGMHixYvleZXOzs64u7unW17ljx8/8PDwwM3NjYsXL6Knp0fHjh2pVasWR48e5ebNmzx58iTZ31V0dDT37t3jzJkzjBkzhsKFCxMeHk7NmjXp168f3bp1y9Q5ourg8OHDdO3aldKlS2d4XmVsbCyHDx/Gzc2N//77D21tbdq2bYulpaV8Z7lEiRJJnhtfKSJ+F/PWrVscOXKE2NhY2rRpQ9++fWnRokW23LnMMQEl/MzLmuQZyKWw92hqSFJ8OMV/36BSUeY6mifKu/L29qZjx47kz58fT0/PLJ1QnZTyPDg4mLCwsCyjPE+LbyUICEiobViAxc6WSebUubm5MXjwYKytrdm/f3+ClWXom6/svPEU7/tveRr+PUERbkEQKF0oD03NDOhS2xCjEmlbactkMoyMjGjQoAFbtmxJ07lJERcXx+PHj5NcSMTvgOXJkwcTE5NMrTxPk38FGYJEg3oVCjO/XTXePgrG0dGRHz9+sH//furXr5/iXH/yr2FhbRqblEjWvzdu3KB3797cu3eP1q1b069fP1q2bImWlhY/fvygdOnSdO7cmeXLl//xui9cuICtrS2BgYHExsbi7u7Ojh07iIuLY/HixTg5OSUSBAUFBaldeZ5RfPjwARMTE96/f8/SpUsZMWIEBw4coGfPnlSsWBFPT8805VX+umDIraVBuSI66ORJ+a2Tr68vvXv3JiAggEaNGtG3b18cHR3JmzcvX79+xcDAgNGjRzN9+vQ/zn/gwAHat2/Ps2fPkEqluLm5cezYMQwNDXF1dU1UaSC7E59X+fr1a3bu3Enr1q3T3QZ/f3969+6NVCqldu3a9O3bF2dnZ6V2TT9+/MiuXbtwdXXl9u3b1K9fH3d392wnRspRAWU88gdGyFuefkj4wJAAhkW0sTMuTtc6hikqQp88eYKjoyP37t3D3d2dTp06qd329CQp5XlwcDD379/PtMrzeN/uvhBAdC5d+CXYjfdtHcMCrB7RkanD+zN+/Phkx7p+/TpOTk5IJBIOHjyIgZG5yhYkyXHy5ElatGjBlStXEpWcUiXJKc+DgoKSVZ7H/1m5cuUMU57H+3fHOSmxeQsl6V+LopqsH9OFXeuW0qFDB+Dnbl/Hjh25cuUKK1as4J9//km0EFJ2wRkZGcnUqVNZunQpNWrUYNOmTfLXYPHs27ePjh07cufOHapUqfLH612+fDkTJ07k69ev8vSaT58+MWbMGNzd3bGzs8PNzS1REJWU8jwoKIiHDx8mqzyP/7NEiRKZYpGYHIcOHcLBwQGALl26sHHjRh4+fIiDgwPh4eF4eHjQtGnTZM9PacEgAQwLa2NXuXiiBUNUVBTTp09n8eLFVK1alU2bNiUq5eTq6srAgQN59OgRhoZ/ztedPHkymzdv5uXLl/LPwsLC6Nu3LxcuXKBv374sXrw4Wwvwfufz589069aNo0ePpmteZXR0NHPmzGHevHmYmJjg6uqqcC59cgiCwLlz5xgwYAAvXrxg5syZjBw5MtOlzilKjgwof0WRFeqvREZG0r9/f3bs2MHo0aOZP39+tvnHkRxZQXlesWJFWrd1YsCYf5P07cCBA9m9ezd3795N8TXoq1evaN++PXejClG0+T8IEg2FXqvPsK+Cyx8EIdHR0dSoUYMCBQpw7dq1DHuoZ3bluSAI6OnpMXLsBNr3+idJ/zZt2pRHjx4REBAgD35jYmIYM2YMK1eupE+fPqxZs0aed6hs2sSEphVxndATPz8/Zs6cyahRoxLdByIiIrCwsKBChQqcPn06VeN3796d+/fvc+PGjUTfnT59mn79+vH582fOnDmTqBRZUqhKeZ6RxMXFUblyZXLnzi0vLu/p6UmBAgXo1KkTp0+fZv78+YwZMybBb0iZBUMBzRiaN2+OVCpl6tSpjBs3LtF97PPnz1SpUoVatWpx8ODBVF1Lq1atkEgkHDt2LMHnMpmMjRs3MnbsWPT19Tl//jwGBgZp+FvK2shkMmbOnMmMGTNwcnJiy5Ytas2r/PTpk9y/kyZNYtKkSWp9O/P9+3emTJnC8uXLsbOz4/Dhw9miPFyODyhVgSAIrFixgjFjxmBra4uHh0emzjlUFzKZjOfPnyfa8Upv5fmnT5/Q09Nj27ZtdOvWLdljzMzMsLS05PDhwykGbytO32PZuQepqhmYEmOaGTPEzijZ76dOncr8+fPx8/OjatWqCs+jLj5//sy9e/cSBZrprTx/+PAhFStW5MSJE7Ro0SLJY0JDQ7GwsGDQoEEsWbIkwXdbt25lwIABVK9enQMHDuAZ8l0lwq7IG3s5umAI1tbWSX4/atQo1q1bR0BAAEZGyf87+JU/qco/f/5M8+bNCQkJ4cyZMwoXP4+NjeXBgweJAs179+7JRQhp7XmuTs6ePUuTJk34999/2bFjB9++fWPv3r389ddf/Pvvv8yfPx8XFxfc3NzQ0dFResGQ9+5hnnrv4dSpU8n6d8CAAezatYu7d++mancSQF9fnz59+jB79uwkvw8LC6NRo0bky5cPb2/vHBVUAnh5edG9e3fKlCmDl5dXqn83aeHTp080a9aMBw8ecPLkSaysrFQ+R3KcP3+ev//+mzp16mSLoFIMKFXIuXPn6NixI7q6unh5eVGtWrWMNilToKjyPP7hldaV6fnz57GzsyMwMDDFwMzLy0uuKuzevXuSx6RX6RpfX1/q1KnD5MmTU5V7lZlISnke33pSHcrz/fv306FDB16/fp1sYjzAokWLmDBhApcuXUqUPuDj44OjoyOycnXIVb9nmq85OZLz75UrV2jQoAELFy5kzJgxqRortaryz58/06xZM0JDQ/H29lbpfUcmkyXZ8zwoKOiPPc/VrTzv27cve/fu5dKlS4wePZrz58+zePFihg8fzv79++nZsyeVKlWi/VRX3H3e/XnA5BAEkEjoVCU/87o2TPKQc+fO0bhxY9asWcOgQYNSNeyrV68wMDDgwIEDODk5JXvcgwcPsLW1RVtbmwsXLmR7pfDvBAcH4+DgwJs3b9i1a5dSgsff+fW3c/bs2QxR2V+8eJFWrVpRt25dDh8+nKJQL7MjBpQq5te8yk2bNmXr/qyqIDXK89KlS8t3ulKjPF+2bBmTJk1KkHeWHD179mTnzp3s37+ftm3bJvguvYprxyf3V6hQgcuXL2caIYyy/PjxgwcPHiTasVZWeZ5U3llSxMbG0rBhQ+7du8fZs2cTCeekoc9wcvVFpqGlsvSCpPwrlUpp3LgxpqamXLhwIdW7ebdu3aJWrVrcvHkz2V2xeD59+oStrS0/fvxAKpWqvYRQcj3Pg4KCEinPf/etqpTnnz59wsLCAh0dHU6fPs2KFStYvHgxXbt2ZePGjYSFhWE/cgGCtepy25NaMPj6+tKkSRNq1KjBmTNnUp0WcPz4cVq3bs3Dhw8pX758iseGhYXRoEEDatSowbFjxzJ1jqs6+Pz5M127duXYsWPMmjWLSZMmqeTvoGvXrhw9epRz585laGvTixcv0rx5cwYMGJAqsV5mRQwo1cD379/p378/O3fuZMyYMcybNy/b51WqGmWU5xMmTEg27+x3YmNj6dy5M15eXuzfvx97e3v5d93cb6it/d/2PrUBCAwMpFGjRhgaGnLmzBn09PRUNldmRVnluYODAxoaGhw9evSPc3369ImmTZvy8OFDzp07l2D3Lj386+/vT+PGjalYsSKnTp1KdRkogA0bNjB48GC+ffuWqnSQwMBALC0tmTBhAjNnzlT0EpTmw4cP8pxqdSvPQ0NDsbW1pUCBApw/f55z587Rp08fTE1NWbPVgx4eIUTHyBKIt5Th9wWDn58fTZo0wdjYmJMnT6Yph3jOnDksXryY8PDwVAVHR44cwd7enu3bt9O1a1eFryGrIpPJmDFjBjNnzlRJXuWxY8f4+++/U3xDlZ4sXbqUMWPGcOXKFerWrZvR5iiEGFCqCUEQWLZsGWPHjqVRo0bs2bMnR+ZVqprUKM81NDQoWrQof//9d6qU5zExMXTq1InDhw8zb948RowYwcP332m6/KLaruPMyL/wv3iSgQMHyoPJrFjGRZWkVnkuCMLPV5nt26dKef7x40e5SGfz5s3Y29sT+uar2v1799o5evfuLRfhpCWYhJ/CsStXrhAYmPqUi+nTpzNnzhx8fHwyXcqNupTnoaGhNGzYkIIFC7Jnzx4EQcDR0ZGY+gPJXaYqKlwvJFgwnDhxgi5dumBkZMSpU6fSLEhr164dHz9+5Ny5c6k+p3Pnzpw8eZKgoKAU0z2yM15eXnTr1g1DQ0OF8yq/fPlClSpVqFKlCidOnMgUO75xcXHY2Njw9evXdHnLoA7EgFLNxOdVFihQAE9Pz0x3k88uxCvPpVIpnTp1wtramri4uFQrzwHGjRvHihUrsLa2ptY/izge+k2lu1fxaEqgyMcgbq0fh4ODA+7u7jk+mPwT8crza9euMWHCBCwsLPjw4UOqlecfP36kW7duHDt2jE6dOlGm7Sj2B7xVm3+Lfb7HjbVjaN26Ndu3b1do57l27dqYmJiwdevWVJ/z48cPqlatSrVq1di3b1+a58wIVKE8DwkJoV27dty7d4+JEyfSrEMPuu66pzabrd4c58DmtbRo0YLdu3enebEAUKFCBRwdHROJxlLi3bt3GBsb069fPxYuXJjmObMLv+ZV7t69m5YtW6bp/NmzZzN37lyCg4PlLVAzA3fu3KF69eqsWrWKf/75J6PNSTNiQJkOPH78GEdHR+7fvy/mVaqZmzdvUrt2bXneWVLK8/g/k1Ke58+fn1OnTiFpMwMtPX212Sn7/IbFtvnp0KFDplgdZxXi884ePXpEuXLl0qQ8NzU15du3bxw8eJCCXZahUVB9Ozyyz6+ZVy8vnTt3Vsi/sbGx6OrqynfM00J8xYnnz59n6V2stCrPjY2NuXv3LgcOHKCc01jiKtggQ/W/LUEWx4+7Z5jfwZLu3bsr5N+PHz9SuHBhhV5fjxw5kp07d/L8+fNsk2+tCL/mVc6ePZuJEyemyhdxcXFUrFiRJk2a4Obmlg6Wpg0HBweePHmCn59flns2iAFlOvH9+3f69evHrl27GDt2LPPmzcvU7e6yKuvXr2fIkCF/zDsTBIG3b98mWeLoTfhnyozcq9YfswS4M715mmqeivzcWVi6dCkfPnxI0T8pKc/jNHJlev/euXMHc3Nzzp8/T8OGSSuLkyM8PBwDAwNmzpzJuHHjFJo/MxOvPE8qNSJeeW4wwJVcalwQli6Yh8sTmih8vre3N40aNUp1gftfCQoKokqVKuzdu1deuD+nIpPJmD59OrNmzaJdu3Zs2bLlj4Kv//77j5YtW3Ljxo0/tlDNCOIXzbdu3UrXEkaqQAwo05Ff8yobN27Mnj17xFedKmbAgAFcu3aNgIAAhce4fu85Lltvq9CqpDk2tD5VDHJOBwxVoEje2a/8+PGDU7eCGHL0hYotS4wy/t2+fTvdu3fn06dPChWL79q1q7yXcE4hXnnuG3CXIeejQA27k/Eou2BYunQp//77L1++fFFIsFmvXj309PRSJUzLCXh6etK9e3fKli2Ll5cXlSpVSvZYZ2dn7t27h7+/f6bcAYyLi6N8+fK0adOGNWvWZLQ5aSLj2x7kICQSCaNGjeLUqVP4+flhZWWVo2746YFUKlW6llgebR0VWZMyP1RYjiinIJVKlSrvkTt3bkqVSZ+cKWX86+fnR8WKFRXuPGRnZ8fdu3flr4ZzAhKJBH19fcqbW6POYBJAAB5/iFD4fKlUioWFhcLVP5o2bcrNmzcR94N+4ujoyI0bN/jx4wfW1tacOHEi2WOvXbtGy5YtM2UwCaCpqUmzZs24du1aRpuSZsSAMgNo3LgxPj4+FCxYkLp16+Lh4ZHRJmULYmJiCAgIUDqgzK2VPj+L929ey9WtIn/m48ePPHr0KMv4Vxb7Q+FzlV0YVa9eHZlMliMXrOm1UFOmPq2fn59S/q1Rowbv3r37Yy3WnISZmRk3b96kXr16tG7dmnnz5iUKuD98+MCzZ88S1aTNbFSvXp07d+7IK5dkFcQErgyiXLlyXLlyhb59++Li4oKfnx9z584V8yqV4N69e0RHRytdoLZcER0k/NyFUBeCINC8Xk3yakkytOd5VsLf3x9A6YAyvfxby7Q8ZUuVTHPPc5lMhlQqZcKECQrPX6VKFTQ1NZFKpdSpU0fhcbIi6bVgaNrIFpMS+dPc8/z79+/cu3cvzWKrX4kPiPz9/SlVqpTC42Q3ChUqxOHDh5k2bRqTJk3Cz8+PzZs3y/MqVXUPUTc1atQgJiaG4ODgLFUZRgwoMxBtbW127tyJpaUl48aNw9/fn927d4t5lQoilUoBlF596uTRwrCwNk/C1fe6sHTBPGw47JlAWHD8+PF07Xme1ZBKpeTLl4/KlSsrNU56+Fc/vybT16+R+/fgwYN/7HluampKsWLFePToEV++fFHqoZc3b1709fV59eqVqi4py5AeCwYQGNarE2H37iKVStm9e3eqe54HBgYik8mU8q+hoSGampo8ffpUVReUbdDQ0GDWrFnUqFGDHj16ULduXTw9PalUqRKPHj0CSDHHMjMQX1vz0aNHYkApknokEgmjR4+mWrVqODs7Y21tjaenJxYWFhltWpYjPu+sQIECSo9lV7k42288UVudwqZVDGjRogotWrSQf56c8tzV1VUtPc+zGn5+flSrVk0lu/hq9a+GhBYWhvSyT1gbLynl+ZkzZ1i3bl2CnufFihUDfrZe1NDQwNTUlNKlS6c55yuz5oipm/RYMJQtosO0Mf/bQU5OeX7kyJFEPc9z586NRCIhODiYPHnyKNTzXCKRpLrFY07FyckJExMTHBwcsLa2Zvfu3fLvMvubwHj7slqOrBhQZhKaNGmCj48Pjo6O1K1bl82bN9OxY8eMNitLoaxg41e61DZky7XHKhnrd+IEqKbzJdHnEomEEiVKUKJECezs7BJ8l1TPcw8PjyR7nv++M5JdOjRJpdI0l9BJDrX6VybQtY5hos+1tbWpXr16oh3033ue7969Gy0tLebOnZug5/nvqRF/6nmek1H3gsHOuHiCzzQ0NChXrhzlypVLUGQ7Xnn+62/X09MTTU1Nebs/dfc8z8nE51V26dKFVq1a4ejomNEmZWvEgDITUb58ea5evUqfPn1wdnbGz8+POXPmiA+MVCCTyfD391cq7+xXjEro0qBSUdX3epaA5ocHdGrdjvXr19OzZ89Unaenp4eNjQ02NjYJPk+q5/mJEydYtWqVXPBTrFgxeQDy60NLX18/y+xixeedjRw5UiXjqc2//9+ar1Lx1O8W586dW77LDHDlyhXKly/PoUOHePLkSYIaqfGvz1PT8zwmJibH7mJlxIIhKeKV5/r6+jRq1Aj42XyhWbNmLF26NNEicdeuXQleYxsaGiaZGlGoUCFkMlmW+f1mJL/mVc6ZMwf42XpRFW+y1EVWFWuKAWUmQ1tbm127dmFpacn48ePx9/dn165dYl7lH1BF3tnvzHU0p8myCyoLOARBQFNDwvEZ3VkgC6RXr174+fmxZMkShQU4+fPnx9LSEktLywSfJ9Xz/PLly7i7u8uVgwULFkzyYZVcz/OMJCAgQOm8s99RtX8RBDQlEuY6mis1jFQqpV+/fmhqalKhQgUqVKjA33///cs0Sfc8P336tLznuYaGBjKZjKNHjxIbG5uqnufZicy0YPiV+EoUXbt2pXDhwtSrV4969eolOObbt2+Juj8dPXqUFStWyAONIkWKEBcXx7Fjx4iLi0tVz/OcjKamJrNnz0YikTB79mysrKw4ceKEvO1uZuPBgwfAzwVFVkIsbJ6JOX36NC4uLhQqVAgvLy/MzZV7UGVn9u3bR8eOHXn9+rVK283tufWUCQcDVTbe59NrWT2yM507d2bDhg0MHToUGxsb9u3bR/Hixf88gJLE9zz/vYNManueZ5TyfN26dQwbNoxv376lOd8sJVTt39grW9m3YCR169ZV6PxXr15hYGDAwYMHFXo9F9/z3MvLi2XLllGnTh2ePXuW6p7n2Yln4d9psuyCUuV9fiePlgZnRjakTGHFgvKAgACqVavGxYsXadCgQZrOjYqKki8SDxw4wL59+zAxMeHBgwep7nme03nz5g0lS5akZMmSREVFsWfPHpo3b57RZiVi/fr1DB06lK9fv2YpEaa4Q5mJadq0KT4+Pjg4OFCnTh22bNmS41ttJYdUKsXAwEDlvYtdrA15/y2axadClB5rhF0F/F8Vo2vXrvj6+rJw4UKqVq1K+/btsbS0xNPTU+2ttrS0tDAyMsLIyIi2bdvKP0+u53lmUZ5LpVKqVKmi0mASVOvfgXUNOHb5FQ0bNmTNmjX069cvzWP4+fkBipc1KVasGMWKFUMqlZI3b14uXbqElpZWkj3P06I8z4q7XmUKazPDvopKFwwz7asoHEzC/ypRKKLczZs3L+bm5pibmxMQEIC+vj7BwcHExsby8OHDBKkRaVWe5xRKlCiBvr4+nTp1Ijg4mFatWjF37lzGjRuXqf6NS6VSTE1Ns1QwCeIOZZYgIiKCPn364OHhwYQJE5g9e7aYV/kbLVu2RFNTU22tyPbcesq0w3eJlQlpeoWmqSFBS0PCTPsqOFsbIggCq1evZuTIkTRs2BAPDw+io6Np164d/v7+bNiwgR49eqjlGhQhKeV5/J/pqTy3srLC3NyczZs3q2S831GVf3/8+MGIESNYt24dAwYMYOXKleTOnTvV46W2V/mfaNKkCXFxcXh7e6d4XEo9z39VnicVaCqiPM8IVnuHKrVgEAQBiURCv9olmexg+ecTUmD48OEcP36c0NBQpcapWbMm5cuX58CBA8kek5zyPDg4mE+fPgH/U57/7l9FlOdZBScnJ54/f861a9eYOnUqc+fOpUOHDmzatClTiKBkMhnGxsbY2dnh6uqa0eakCTGgzCIIgsDixYuZMGECTZs2FfMqf0EQBEqWLMmAAQOYOXOm2uZ5Fv6dSZ6BXAp7j6aGJMXAI/77BpWKMtfRPNGuxoULF+jQoQPa2tp4enpiZmbG4MGDcXd3Z+jQoUrlVaYXSSnPg4ODVa48j4mJIX/+/CxatIhhw4ap41KAtPlXkMUh0dBM1r/u7u4MGjQIKysr9u/fj76+frJjRUTH8vhDBD9iZUyaMI6od8/wPv2fwtcRFhaGkZER27dvp2vXrgqN8bvyPP7Pe/fuZUnluTILBk0Eoq/uICroHPv27eOvv/5K09y/+vefAf0oXTAP+/fsTOslyPH19cXKyoojR44kyK1NLUkpz+P/fPPmDZC9leeHDh3CwcEBqVRK9erVOXDgAD169KBChQp4enqmKa/yV9/m1tKgXBEdhfu7x3P27FmaNGnC5cuXE+XXZnbEgDKLcfr0aZydndHT0xPzKv+fly9fUqpUKYXzztJK6Juv7LzxFO+Qtzz98D1BAWUJYFhEGzvj4nStY5hi8v7Tp09xcnIiKCgINzc3OnXqxPr16xk2bBj16tVj79696ZJXqWqSUp4HBwcTFhaWSHn++wMrKeW5MnlnihD65itbrjxgy8lb5Cqsz699oeP9G/3Qj08+Rwi+4Z3sLt2NGzdwcnJCEAQOHDiQIK9S/m/o/luehif8N4QgULaIDnaVi9OltiFGJdK2yzthwgQ2btzIixcvyJcvX5rO/RNxcXFy5fnvAUlqlOdp2a1VNQkWDJKf5buSRRYHvywY8sZF0LFjRy5fvsyyZcsYPHhwiruzKfoXgbKFFffvgAEDOH78OI8ePVL56+rw8PAkA83UKM+zygZHbGwshoaGODo6smbNGgDu3LmDg4MD4eHh7N69O8W8ypR8KwEMC2sr7FsAZ2dnAgMDuXv3bpZ4A/ArYkCZBXn48CGOjo48ePCALVu20L59+4w2KUM5duwYf//9N48ePaJcuXLpOreyK9TIyEgGDhzItm3bGDVqFAsWLOD69eu0b9+e3Llzc/DgQbXnVaYXSSnPg4ODuX//forK87t37zJu3Di+fPmSbsXbr1+/Tt26dbl0/SZ6ZYwT+dfb25tGjRqxf/9+2rVrl+w4r1+/pn379ty8eZO1a9fS3Kmzyna5k+LNmzeYmprSvXt3li9frsilK4QgCLx8+TJRiaOgoCC58lxTUxMjI6NE/k1v5Xnom6/M9rjAmbuvyF3YIMkFYfHYdxxaMoYbpw7J81ljY2MZO3Ysy5cvp2fPnqxbty5Rjpsq32IkxbNnzzA1NWXMmDFMnz5dgatXjKSU58HBwTx48EC+SCxRokSCnerMrDz/999/WblyJSEhIZQsWRL4+calc+fOnDp1innz5jF27NgEdqvbt/Dz7YKZmRkLFixQWYm09EQMKLMov+ZVTpw4kVmzZmW610zpxaxZs1i2bJnSeWcZhSAIrFq1ilGjRmFra8uePXuIioqiXbt23L59m40bN8qLIGdHUqM8l0gkVK9ePd2U52vXrmX48OHJqsoFQcDR0ZHr168THByMnp5esmPF51Vuv/KAYi0HI9HUUihPc4Z9FVysUy4j0rFjR7y9vQkODqZo0aKpnkOdxCvPf/dvRirPZ86cyYoVK3jy4jVPwr8nWjDExMRgZWWFhoYGN2/eTPBvbPv27fTv3x9zc3MOHjxI6dKlAeXzcP/kX0EQaN26NQEBAdy9ezdTqPJ/VZ7/vkjMzMrzDx8+YGpqyl9//cX+/fvln8fFxTFlyhTmzZtHx44d2bRpEzo6Omr3LfzMnWzUqBFPnz4lMDAQHR0dha8voxADyiyMIAgsWrSIiRMn0qxZM3bt2pXigy274uTkxOfPnzl79mxGm6IU58+fp0OHDujo6ODl5YWJiQmDBw9m06ZNDBs2jMWLF2f6vEpVEq88b9WqFbly5cLKykr+0FK38rxfv37cvHmT27dvJ3vMy5cvMTMzw9HR8Y9ioXhhSLzAQ1HGNDNmiJ1Rkt95enri5OTE7t27cXFxUXiO9CIp5XlwcHC6KM8dHR35+vUrZ86cSfYYX19fatWqxezZs5k4cWKi7xwdHYmOjmb//v3cji2pkkoBKfl3x44ddOvWjcOHD9OmTRul51InvyrPf18kZhbl+d69e3F2dk7yLcP+/fvp2bMnFSpUoP00Nzb5vFN6vpR8C7BhwwYGDhzImTNnaNy4sdLzZQRiQJkNOHXqFC4uLhQuXBgvLy+qVq2a0SalK+XLl6ddu3YsXrw4o01RmqdPn+Lo6EhwcLA8r3LdunUMHz48S+dVKopMJqNgwYL8+++/jB8/Hkgf5XlqVeVubm7069ePNWvWMGjQoCSPUXWtywVO5jj/tttx+/ZtGjVqRL169Th06FCW3KmPJz2U5+XKlaNjx44sXLgwxePGjx/P8uXLOXr0KE2bNk3w3bt37+jYsSN+n/Oi13yI4hf8G0n5VyqV0qhRI1q2bMmuXbtUNld6I5PJePbsWZK/3fRWnguCgJOTE1euXOHSpUtUrlw5wfd37tzBfuR8ZFadVDZnUr6FnwsUOzs7nJ2ds5yy+1fEgDKb8PDhQxwcHHj48CFbt25NMa8rOxEeHk6RIkXYuXMnnTt3zmhzVEJkZCQDBgxg+/btjB49mvnz53Pt2jXat29Pnjx58PT0TNQZJ7sSGhqKsbExJ0+epFmzZn88Pl55/vvDKi3K87SoygVBYNSoUSxfvpx169YxcODABN+nR3HtgIAAGjVqRNmyZTlz5ky2fUuhqPLc1NSU8uXLy1OCPnz4QNGiRdm1axedOqUcLERHR+Pk5MS5c+c4cuQITZo0SfD9w7efabL0AnFoqCyI/92//v7+NG7cmIoVK3Lq1CkKFSqkknkyE4Ig8ObNmyQDTXUqz9+9e4etrS0fP37E29s7QVAp/+3GxIGafAs/a882adIEY2NjTp06lalbQv4JMaDMRkRERNC7d2/27t2bY/Iqz507R+PGjQkKCpL3Qs4OCILAypUrGT16NLa2tnh4eBAZGYmTkxMBAQHZPq8yHg8PD1xcXHj79i3FihVTeJy0KM+LFSvG/v37Wbp0Kc7Ozn/seS4IAiNHjmTFihWsWLGCoUOHyo/v5n5Dbe3/tvepjY+PDy1btqRMmTKcOXMmyyhtVUlqleeVK1fGzMyMPHnysHXrVo4cOUKzZs3+qDyPiorC0dGR8+fP4+XllUABrG7/+vr60qxZMypUqMDp06ezZTD5J+KV57/7VlXK8zdv3tCoUSM+fvzIuXPnMDExAdTvW/i5M9m0aVOMjIw4depUpsiLVQYxoMxm/JpX2bx5c3bu3JltdywAlixZwtSpU/ny5Uu2DJ69vb3p2LEj+fPnx9PTExMTEwYNGsTmzZsZPnw4ixYtytZ5lRMmTGDnzp08e/ZMLeMnpTy/evUqz58/lx8Trzz//YH1a89zQRAYPXo0y5Yto3nz5mzcuJHoPHo0XX5RLXYD/C2Rsn7hdGrUqMHJkydzZDCZEr8qz38NRnx8fOR5fKlVnkdFReHk5MSJEycYMmQI8+bN41WEoFb/OuQKZM28KXL/Zuf7uCLEK89/DzSTU57/+mfJkiUTLBLjg8rHjx8zd+5cmnfsSYuVl9Vm+4mhNhzYtIZZs2ZRrVq1bLPzLAaU2ZRf8yoPHTpElSpVMtoktdClSxcePXrE1atXM9oUtfHkyROcnJwIDg7G3d0dFxcX1q5dy4gRI6hfvz579+5VavcuM9O8eXPy5MnD4cOH023O4cOHc+LECY4dO5bmnudv3rxh9uzZfP78maYTNnI7oiBx6rjFyuL45n+C4fUNGD9+fIbWd8xqdO7cmbCwMBYvXpwm5XnlypW5dOkSs2bNolixYtiNWcvFV6h0B0vO//t3UO1iTJ48Odt2rVEH8crz3wPNkJAQeXmyQoUKJSpxZGhoyNq1a1m7di1m3aYRWdoadbhWQwK5Hl/jwd75jB07lmnTpmW5FovJIQaU2ZgHDx7g6OiYpfIqo6KiCA4OJjAwkA8fPvDp0yf2799Pt27dyJs3LyVLlsTc3BxjY2Ny5cqFmZkZdnZ28gK12ZXIyEj69+/Pjh07GDNmDPPmzePq1at06NCBvHnz4unpSc2aNTPazD8ik8l48uQJd+7c4dOnT3z8+JFr167RrFkz8uTJg4GBARYWFhQuXBhBEChevDiDBg1ixowZ6WZjgwYNMDAwwMPDI0n7k+p5/qvyXEtLi/z586PtvJBcegZqs1M/vxbXJidfgFkkaUxNTWncuDGrV69O9F1qlOfFixcnJiaGfB0XqNm/mlyb3EJt4+c04pXnv/9u7927J18kamtrU7p0ab43GodmoZJqs0Uj4j37elTNdrnwOacrfA6kYsWKXL16ld69e9O+fXsmTZrEzJkzM9Wr4e/fv7N//35OnDhBQEAA9+/fJy4uDoD8+fPz7ds3AObNm0dsbKz8VVXu3LkxMTEhODiYRo0aERMTk61f/ebLl49t27ZhaWnJmDFj8Pf3Z8+ePfj4+NCuXTvq1auHq6urwq321MWPHz84cuQIZ86cISAggMDAQHle26/s2bMnwf+XKlWKypUr8/79+3R9FSSTyfD390+2pZ2GhgaGhoYYGhrSosX/Hva/K88Dgu7zX/7k2y2qgtffYomIjlW61VtOIiIigvv37zNmzJgkvy9YsCC1a9emdu3aCT7/XXkeEBSCfyF1+zdO9K8K0dLSwtjYGGNjY9q2bSv/PF55Hh9gBt4LxbtgCbXaIugUxaRqNbXOkRGIO5Q5AEEQWLhwIRMnTqRFixbs2rUrw/M1/Pz8cHNzY+fOnXz58oU6depgaWmJhYUFFhYWVK1aNUnlXnh4OIGBgQQEBHD69GmOHDkCQMmSJenZsyd9+vShUqVK6X056cqveZVeXl5UrlyZf/75hy1btjBixAgWLVqULnXcUuLevXu4u7uzdetW3r17h6mpKTVq1JD719zcnKJFi5I7d240NDSIi4sjKiqKJ0+eEBAQIPevj48PADVr1qRv37507txZrYnraVWVJ8fdl59pvUp9OVjxHBtanyoGWTuRPz25evUq9erVw8/PT94BRxFE/2ZfRN8qjrj0yQFIJBLGjx9P9erVcXFxwdraGi8vrwzJq3zx4gUDBw7k6NGjGBgYMHToUHr37k2FChVSdX7hwoVp2LAhDRs2RFNTkxMnTnD16lW2b9/O+vXrmT9/Pn379mXx4sVZXjGXHHZ2dvj4+ODo6EjdunXZtGkTmzZtwtLSkpEjR+Lv759heZWvXr1iyJAhHDx4kMKFC9O9e3f69Onzx9qompqa6OjoyHOaXFxcyJMnj7y9qLu7O0OHDmXMmDFMnTqV0aNHqyVo9vPzA1Aq2AD4ocIyQZlhnuyCVColV65cSt/7RP9mX0TfKk7G9D0SyRCaN2+Oj48PefPmpU6dOhw8eDDd5hYEATc3N8zMzPD19cXDw4MnT54we/bsVAeTvyOVSqlSpQrW1tasXLmSly9fsnr1ajw8PKhSpQpHjx5V8VVkHsqWLcvly5dxcnKiU6dOjB8/noEDB3L27Fnu3r2LlZWVPDhKDwRBYMuWLZiZmXH58mW2bt3Ky5cvWbZsmcKF9qVSKZaWltjb23Po0CGePn3KgAEDmDRpEnXq1CEwUHXFwn+ds3Tp0koH47m10ufWml7zZBfi7xnKiphE/2ZfRN8qTva7IpEUqVixIteuXaNFixa0a9eOf//9V56zqC6ioqJo27Yt/fr1o3379ty9e5eOHTsqvcPk5+eXQIiSL18+Bg8ezN27d7GwsKBNmzYMGTJEXkIiu6Gtrc327dtZunQpS5cupWXLllSpUgVfX1+KFy9OvXr12Llzp9rtiIyMpG3btvTq1Ys2bdoQFBRE9+7dlVamSqXSBDuFBgYGLF26lKtXrxIZGUnNmjVZu3atsuanOKeilCuig7p71Uj+fx6R1PP7PUNRRP9mX0TfKo4YUOZA8ufPz969e5k3bx5z587F3t5e3vZK1URFReHg4MCZM2c4evQo7u7uKqmnFhMTw507d5J8+JcpU4Zjx46xbt061q5dyz///JNtg0qJRMLIkSM5deoUUqkUa2trwsPDuXjxIs7OznTt2pVRo0bJW9apmvhg8uzZsxw6dIht27bJO84ow4cPH3j69GmS/q1duzZ+fn78888/DB48OEm1riIIgqB0bl08Onm0MPylG4Y6MCyiLQo20sCPHz+SvWekFdG/2RfRt4ojBpQ5FIlEwoQJEzh+/DhXr16lVq1aBAUFqXSO+A4TFy5c4OjRo7Ru3VplYwcFBfHjx49kHw4SiYSBAweyadMmXF1dGTx4cLYNKgEaNWqEj48PBQsWpG7duhw+fJjNmzezcuVKVq5cSbNmzXj37p1K54yMjMTBwYErV65w7Ngx7O3tVTa2VCoFSHY3KU+ePKxYsYLRo0czdOhQlZSNevHiBe/fv1dZ+SW7ysXR1FDPXoeGBOyMc05Pd1UQFBRETEyMSgJKUK9/NTUkon8zENG3iiEGlDmcFi1acOvWLXLnzk3t2rXx9PRU2dijRo3i/PnzHDlyhEaNGqlsXPj56koikVCtWsqlF3r27Imbmxvr169n5cqVKrUhs1GuXDmuXLmCo6MjLi4ujB8/nkGDBnH27Fnu3LmDlZWVPFBTBYMGDeLSpUscO3YMW1tblY0LPwNKHR0djIyMkj1GIpGwaNEiRo0axZAhQzh+/LjSc4Lygpx4utQ2VE/Ra0AmgPZLX7WMnV1J7T0jtajTv3Eyga51DNUytsifEX2rGGJAKUKlSpW4fv06LVq0wMnJiSlTpii9m3fx4kXWrVvHwoULadKkiYos/R9SqRQjIyN0dXX/eGzv3r0ZMmQIkydP5uHDhyq3JTOhra3Njh07WLJkCUuWLKFly5aYm5vj6+tLsWLFqFevHrt27VJ6nv/++48tW7awevVqlQeT8PPhX61aNXlrw+SQSCQsXryY5s2bM2DAAL58+aLUnEWKFKFMmTIKj/ErRiV0aVCpqMp3OjQ1JBT58Zbx//RgyJAhxMTEqHT87IpUKsXY2DjJcmSKoE7/NqhUlErF/3xvE1EPom8VQwwoRYD/5VXOnTuXOXPmKJVXGRkZSd++falXrx6DBw9WraH/T1rFE/PmzaNo0aL079+f7F56VSKRMGrUKE6fPo2fnx9WVlZ8/PiRS5cu0aFDB7p06aJUXuXXr18ZMGAATZo0oVevXiq2/idSqTTVr54lEgkbNmzg48ePTJgwQak5a9SokaDHr7LMdTRHS4UPJUEQkAgyvCY7s379ejZu3Ejjxo158+aNyubIrqhKcPUr6vCvBgJzHc1VNqaIYqjatwBaGpJs7VsxoBSRI5FImDhxIseOHePKlSsK51WuWrWKJ0+e4Obm9scdJkWI72aSlly3/Pnzs3HjRs6ePYuXl5fKbcqM/J5XeeTIEbZs2cKKFStYuXIlzZs35/3792ked8GCBbx//56NGzeqNPiK59u3b4SEhKTp4V+2bFnmz5/PunXruH37tkLzqiPgKFNYmxn2qqv3KpFIeHNsJUtmTqJ37954e3sTGhqKpaUlt27dUtk82Y24uLg03zNSgzr8++7Eao7v266yMUUUQ9W+BZhpX4Uyahb8ZCRiQCmSiJYtWybIq0xLACaTydiwYQMuLi6YmJioxb6wsDC+ffuW5od/8+bNqVOnDhs2bFCLXZmR+LzKtm3b4uzszIQJExg8eDBnz54lMDAwzXmVP378wNXVlb59+1K+fHm12Hz79m0EQUizfwcOHIiBgYFC/o1XlaujH7qLtSFjmhmrZKwxzYyZ18+eNWvW0KxZM4yNjfH19aVMmTI0aNCALVu2qGSe7EZYWBgREREqXzCAav07snElutpUZODAgfTv35/o6GiVjCuiGKr07dhmlXG2zp65k/GIAaVIklSqVIlr167RvHlzHB0dmTp1aqryKr29vXn48CH9+/dXm23KiCf69+/PqVOnePz4sYqtyrxoa2uzc+dOlixZwuLFi2nVqhXm5ub4+PhQtGjRNOVVHjlyhLdv39KvXz+12atoNxMtLS369OnDjh07iIiISPOcoDpBzu8MsTNivpM5ebQ00pyXpakhIY+WBguczBliZ8SQIUMSFLB//fo158+fp1u3bvTq1YuhQ4eKeZW/kVX8O7xJZVavXs2mTZvYunUrtra2vHz5Ui02i6QOVfl2sF32bgkMYkApkgK6urrs27ePOXPmMHv2bNq2bcvnz59TPMfNzQ1TU1NsbGzUZpefnx9lypShaNGiaT63Y8eO6OrqsnnzZjVYlnmJz6s8efIkPj4+WFtb8/nzZy5dukT79u3p0qULo0eP/mNepaurK3Xr1lW4+01qkEqlVK1aVaFuJn369OHbt2/s3bs3zXP+SVWuLC7WhpwZ2RCbCj/rdP7p4RT/vU2FIpwZ2TDB7sZff/2VoID9vn372LhxI+vWrWPDhg1iXuVv+Pn5YWhoqJIaqcnxu381SDlXOyX/9urVi0uXLvHs2TMsLS25evWq2uwW+TOq/O1mZ8SAUiRFJBIJkyZN4tixY1y+fJlatWoRHByc7PGXLl3CwcFBLbl18SiT66ajo0PTpk25dOmSiq3KGjRp0gQfHx90dXWpU6cOR44cYevWraxYsYIVK1bQokWLZPMq4+LiuHjxIu3atVOrjcoUFy9btizW1tZ4e3unec7q1aurJef3V8oU1mZ7n9qcHvEX3WqXpWwR7URdOSRA2SLadKtdljMj/2J7n9pJ5l2VKVOGS5cu4ezsTLdu3Rg1ahR9+/bF29ubkJAQrKysxLzK/0cd+bFJ8at/y/54Ct/eKezfWrVq4ePjQ6VKlbC1tc1RqTqZkd9/u3livsBvAs/U+jbbIoiIpJLQ0FChSpUqgq6uruDp6Zno+7dv3wqAsHfvXrXZIJPJhKJFiwrTpk1TeIzZs2cLhQoVEmQymeoMy2JEREQInTp1EgBh/PjxQmxsrODt7S0ULVpUKFu2rCCVShOdExQUJADCuXPn1GZXdHS0kCtXLmH16tUKjzFgwADB3Nw8TedUrlxZGDJkiMJzKsO3qBjhzotPgt+TcOHOi0/Ct6iYNJ0vk8mElStXCpqamoKdnZ3w9u1b4fnz50Lt2rWFPHnyCFu2bFGT5VkDmUwmFClSRJg+fXq6zmtjYyO4uLgo7d/o6Ghh0KBBAiD069dPiIqKUpPFImnB2NhY+GfoCKV8m90QA0qRNPHlyxfByclJAISpU6cKcXFx8u9OnjwpAEJISIja5n/69KkACIcOHVJ4jKNHjwqA8OjRI9UZlgWRyWTC4sWLBQ0NDaF58+bChw8fhMePHws1a9YU8uXLJ+zatSvB8Tt37hQAITw8XG02+fn5CYBw5coVhcdYv369oKmpKURGRqbq+K9fvwoSiURwd3dXeM7MwPnz54VixYoJhoaGgq+vrxAVFSX06dNHAIShQ4cKP378yGgTM4QnT54IgHD48OF0mzM2NlbQ0dERFi5cqLIx3d3dhdy5cwt169YVXrx4obJxRdLOly9fBIlEImzatCmjTclUiK+8RdKErq4u+/fvZ86cOcyaNQsHBwd5XmVoaChaWlpUrFhRbfOrIrne1NQUgJCQEJXYlFWRSCSMHj2akydPcuvWLaytrfny5QuXL1+mXbt2dO7cmTFjxsjzKu/fv4++vr5KerEnR3w3EwsLC4XHqFKlCnFxcTx48CBVx8erytWh8E5PGjZsmKCA/f79+3F1dWXt2rWsW7eOJk2a8Pbt24w2M91RtyAnKdShKu/duzcXL17kyZMnWFpacu3aNZWNLZI2sss9Q9WIAaVImonPqzx69CgXL16kdu3a3Lt3D5lMhpaWllrz0KRSKUWKFKF06dIKjxEv9sjOvb3TQnxeZf78+albty5Hjx5l27ZtLF++nOXLl9OiRQs+fPhAbGwsefPmVastUqmUypUrK9XNJN7G1BZuj1eVm5mZKTxnZiE+r7Jjx4507dqV0aNH069fP7y9vbl//z6Wlpb4+PhktJnpilQqpWjRopQqVSrd5vTz8wNUH8TWrl0bX19fKlasSMOGDdm4caNKxxdJHVKplNy5c2eLe4YqEQNKEYVp1aoVt27dQlNTk1q1ahEQEKD2Of38/KhZs6ZaRT85kfLly3P16lXatGlDx44dmTRpEkOGDOH06dPcvn0bKyurdFENp5d44vc5FVWVZ0by5cuXqIC9iYkJvr6+lCpVivr167Nt27aMNjPdyIh7hlQqVZuqvGTJkpw7d46+ffsyYMAABgwYINarTGfi7xm5cuXKaFMyFWJAKaIURkZGXL9+nSZNmuDm5kZMTIxad/5UEXAI2bz1oqLo6Oiwa9cuFi1axMKFC2ndujXVq1fHx8cHPT09tm7dyrdv39Q2f3w3k/T2b3zAkZ2QSCQMGzYsQQH7t2/fcuHCBbp06UKPHj0YNmxYjqhXmVGLFHXOmTt3btauXYubmxtbtmzBzs6OV69eqW0+kYRkx3uGKhADShGlic+rdHZ2Ji4ujlatWv2xXqUivH//nmfPnil9o3727BkAJUqUUIVZ2QqJRMKYMWP477//uHnzJtbW1nz9+pUrV65gYWHBu3fvUlWvUhFCQ0P5/v270jfq+ELQqdkd+vHjB3fv3k33gCO9aNiwYYIC9gcOHMDNzY01a9awbt06mjZtmq3zKt+9e8fz58/T1b+CIChV+iot9OnThwsXLoh5lelIdHR0tr5nKIMYUIqoBA0NDWbOnAn8rEUZn1epSuKT65UNOBTtxJKTaNq0KT4+Pujo6FCnTh2OHTvGwoULAVi+fDktW7bkw4cPKp1TVeIJf39/ec5cXFwcERERfP/+nbi4uETH3r17l5iYmGz9cDA0NExQwH7MmDH0798fb29v7t27h5WVFb6+vhltplpQ1T0jLTx79ozw8PB0m7NOnTr4+vpSoUIFGjZsiKura7rMm1O5e/cusbGx2fqeoShaGW2ASPahUqVK6OjoMHjwYI4cOUKtWrXYsWMH9vb2KhlfKpWSP39+KlVSroWVv78/VapUyTY5c+qiQoUKXL16lT59+tChQwdGjBgBwMSJE1m/fj1WVlZ4eXlRrVo1lcwX382kcOHCaT739evX+Pr6EhAQgKurK5GRkeTJkyfRK93cuXNjZGSEhYUFFhYW8teEqrqGzEq+fPnYunUrVlZWjBo1itu3b7Nnzx58fHxo164d9erVY+PGjXTv3j2jTU2Sr1+/EhgYSEBAAAEBAdy+fZuHDx8SGRkpfxuip6eHjo4Opqamcv/6+vqSP39+tVae+J2MUJXH51WOGDGC/v374+vry8qVK8V7nBrw8/NDQ0NDqUoU2RUxoBRRGRoaGlhaWnL37l1u3LhBjx49aNu2LdOnT2fKlClKq7+lUinVqlVTahxBELh48SINGjRQypacgo6ODrt378bS0pIJEyaQL18+Xr16ha+vL46OjtStW5dNmzbh4uKi9FxSqTRNuzoxMTEcPXoUV1dX/vvvPwRBQFdXl6ioKKpWrUqvXr3Inz8/79+/R1NTEz09Pb5+/cq9e/cICAjg6NGjfP36FQAXFxf69etHq1at0NLKnrfF+LxKCwsLOnToIF8QXLhwgUGDBtGjRw98fX1ZvHhxphAbyGQyzpw5g6urK4cOHSImJgYtLS15wNisWTO0tbUJCgqiePHiFClShC9fvhAUFISXlxdLliwBQFNTk2HDhtG3b1+qV6+udrv9/PzSXVUO/8urrFmzJoMHDyYwMJD9+/ejr6+frnZkd+IrUejo6GS0KZmPDKyBKZINWb9+vaChoSE8e/ZMiIuLE2bNmiVIJBLB3t5e+Pz5c5rG+r3DhJFpVWHo0KFK2XfhwgW1d3vJrpw8eVLImzevoKGhIdy6dUuIiIgQunTpIgDC2LFjhZiYtHWJSODf55+EwsX1hRkzZvzxvIiICGHKlClC8eLFBUCoXbu2sHHjRuHx48eCp6enACTZ6ed3ZDKZULNmTcHKykqwtLQUAEFfX1+YPn268P379zRdS1bjyZMn8gL2O3fuFGQymbBmzRpBS0tLaNiwofDmzZsMs+379+/CnDlzhLJlywqAUKVKFWHZsmXC7du3hejo6FSP8+XLF6F06dKClZWVoK+vLwCCpaWlsG3bNrV2yWrTpo3QrFkztY2fGq5duybo6+sL+vr6wrVr1zLUluxG3bp1hc6dO2e0GZkSMaAUUSmfP38WdHR0EgQGR48eFQoUKCBUrlxZCA4OTvH8kNdfhGmH7gh/LTwnlJtwVCj7y3+G448I1ad4CdMO3RFCXn9RyL4uXboIlSpVytFtF5Xh3LlzAiDkzp1b2L9/vyCTyYSlS5cKmpqaQpMmTYT379+neP6f/Gs57UiK/vX29hYqVqwo5M2bVxg6dKhw+/btBN+3bt1asLKyStW1xMbGCtra2sKiRYsEQfjZpWfQoEFC7ty5BWNjY+Hy5cupGier8v37d6Fr164CIIwePVqIiYkRLl68KBQvXlwoU6aM4OPjk+42Xbp0STA2NhZy584t9OnTR7h27ZrCv9XPnz8LgLB582YhJiZGOHTokNC6dWsBEJo0aSI8fPhQxdb/pHTp0sL48ePVMnZaePnypWBjYyPkzp1bcHV1zWhzsgXx94zFixdntCmZElGUI6JSChQoQKdOndi4cSPfv38HoHXr1ty6dQsNDQ1q1arFkSNHEp33LPw73dxv0HT5RbbfeMKT8O/8XvxFIpHwMUaL7Tee0HT5Rbq53+BZ+PdU2/b8+XP2799P//79xTqWCmJnZ4etrS358+enffv2TJ48mWHDhnHq1CmkUinW1tbcvn070Xmp9e/7aEmS/o2KimLQoEHY2dmhr6/P7du3WblyZYI8pgcPHnDixAn69++fqmuJV5XH57rVqFGDNWvWIJVKKVy4MA0aNGD48OHZtsZfvnz5EhWwNzMzw9fXl5IlS1K/fn22b9+eLrZERkYybNgw/vrrLwoXLoxUKsXNzY06deoo/FuN/3dYo0YNtLS0sLe35+jRo5w4cYL79+9jbm7O6tWrVVpGLCNU5cmhr6+Pt7c3vXv3pl+/fvzzzz/8+PEjo83K0oSEhCS4Z4gkRAwoRVTOuHHj+PDhA1OnTpV/ZmxszPXr12ncuDH29vbMnDlTXq9yz62nNFl2gasPf6qG42Qp3+Djv7/68ANNll1gz62nf7RJEAT++ecf9PT06Nevn6KXJgJMmTKF8PBwnJycWLBgAW3atKFGjRr4+PhQsGBBbGxs8PDwkB+vrH+3X32Ag4MDW7ZsYdWqVVy4cAFjY+ME5wiCwIABAyhTpgydO3dO1XUkJ54wMzPj8uXLLFmyhA0bNtChQ4dsG1RKJBKGDx+eoID9+/fvuXjxIi4uLnTv3p0RI0aotV5lZGQk9vb2uLq6smTJEi5fvqySDiTJdTNp0aIFd+7coXv37gwdOpTx48erLKjMCFV5SuTOnZt169axceNG3N3dadSoEa9fv85os7Is8f5Nj1zcrIgYUIqoHCMjI2bMmMGyZcu4efOm/PMCBQpw4MABZs6cyfTp03FycmLxiTtMOBhIdKzsj4HG78TJBKJjZUw4GMhq79AUj92zZw9Hjx5l3bp1FCpUSJHLEvl/GjVqRJ8+fTh9+jTbtm3j+vXr1KpVi4iICK5cuYKDgwMuLi6MGzeOlWdDlPbvlCP38IksytGjRxkyZEiSoix3d3fOnj3Lxo0bU50s7+fnR9myZZNUlWtqajJy5Ei8vLw4deoUHTt2zNa7O3Z2dvIC9jY2Nnh6erJp0yZWr17NmjVraNasGe/evVP5vJGRkbRt25arV69y4sQJRo4ciaampkrGlkqlmJubJykwKlCgAGvXrmXFihUsWrSICRMmqCSolEql6OrqpquqPDX069ePCxcu8PDhQywtLblx40ZGm5Ql8fPzo1y5cgpVosgJiAGliFoYNWoUNWrUoEePHgnqFWpoaDBlyhQOHz7MldcCqy8+Ucl8i0+F4JHMTmVYWBjDhg2jQ4cOODg4qGS+nM7ixYvR1dVly5YtXLlyhXz58lG7dm1OnDjBjh07WLJkCetPB7D0TMqBfmrJb9OJd7pJl4sKCQlh9OjR9OrVi2bNmqV6zNR0M2nRogWenp78999/dO3aNVt3WSpbtixXrlyhXbt2dO7cmbFjxzJgwADOnj1LUFAQVlZW8h7VqiAuLo527dpx+fJljh07hq2trcrGBlJVXHzYsGEsX76chQsXMmPGDJXMqWwlCnVRt25dfH19KVeuHH/99Rfu7u4ZbVKWIyO6LmUlMt+/epFsgZaWFjt27ODDhw80adKE8PDwBN9Xs2mEXpMBoMIH9NTDdxPlVIaFhWFra0uRIkVYs2aNyubK6RQqVIitW7dy8eJFJk2axMWLF2nVqhXt27dnypQpOHXrR4lWQ1UagCXl35CQEGxtbSlVqpS8TExqEAQh1Q+Hli1bsnPnTvbt28fOnTvTbHdWIj6vctmyZfIC9lWqVMHHx4fixYtTr149duzYoZK51qxZw4kTJ/Dy8lJ5MBkdHU1QUFCqXj0PHz6cmTNnMnPmTK5fv67UvGktfZXexOdV9urVi759+zJo0KBsvfOuStJyz8ipiAGliNowMTHh7NmzPH/+PFFQOckzkDgBUKE4JlYmMMkzUP7/Dx48wM7ODh0dHby9vSlWrJjK5hKBJk2acPDgQY4dO0bv3r3ZsWMH8+fPZ+7cubSesQOZgErFT7/7NzQ0FDs7OwoVKoS3tzd6enqpHuvp06dp6mbSvn17XFxcGD58eLZuVQg/fTZixAhOnz6NVCrFysqK8PBwLl26hIuLC926dWPkyJFKtd98/PgxEydOZPDgwWnaVU4td+7cSVM3k4kTJ2JlZUWfPn0Uzpf98uULoaGhmT7gyJ07N+vXr2fDhg24ubmJeZWp5MmTJ3z8+DFTLxgyGjGgFFEr5ubmnD17lqdPn1KjRg1OnTpF6JuvXAp7n+acuj8RJxO4FPae0Ddf2bZtG9bW1mhra+Pt7S0W91UTrVu35uDBgxw9ehRbW1vatm2L+/7jROga/lwwqJBf/bt7927q1q1LgQIFOHfuXJr7sivSzWTlypXyYCsnYGdnh6+vL3p6etStWxcvLy82bdrEqlWrWL16NU2bNlU4r3LAgAEULVqUefPmqdjqn6S1m4mWlhabNm0iNDRUYZt+VZVnBfr37y/Pq7SyshLzKv9ARnRAymqIAaWI2rGwsODWrVtUqlSJ5s2b02vuJjTVVLVHUwIdJ6+iR48etGzZkitXrmBgYKCeyUQA+Pvvv/H29ubDhw9Ur16dA7ffoKFG/3aaspbOnTvTuHFjLl68SMmSJdM8jlQqpVixYmn6t1GsWDFmzZqFh4cHz549S/OcWZGyZcty+fJlnJyc6NSpE+PGjWPgwIGcPXuWu3fvKpRX6efnx6lTp1i6dCm6urpqsVsqlWJiYoK2tnaqz6latSrDhw9nxYoV8pJnaZ0zKVV5ZqZu3br4+PhgaGjIX3/9xaZNmzLapEyLVCqlePHi4uZECogBpUi6UL58eXkbtScx+VW+exVPnADhefQ5cuQIO3fupGjRouqZSCQB9erVw9/fn+HDhyN9E4OKN5/lxAnwNlcxPD098fDwUDiNwc/Pj5o1a6b5lXzXrl3R1tbOUQ9ebW1ttm/fztKlS1m2bJk8r9LX11eeV5mW3FJXV1dKlSpF27Zt1Wazorlu//zzD58+fWL//v0KzZmcqjwzY2BggLe3Nz179qRPnz5iXmUyKHrPyEmIAaVIuiGRSHDp1hOtgmnfUUoLGgWKY9e0hVrnEElMvnz5mDJzDrn01LuC1yxQgqYt/1ZqDEUDDl1dXTp37oybmxtxcXFK2ZCVkEgkjBw5MkEB+/DwcC5evIizszNdu3Zl1KhRf8yr/PbtGzt37qRPnz5q65keFxfH7du3FfJvhQoVaNq0KRs3bkzzualRlWdW8uTJw4YNG+R5lY0bNxbzKn9DFOT8GTGgFElXnnyISNQhRdUIwOMPEWqeRSQpnqTD37uy/n337h0vXrxQ+OHQo0cPnj9/zq1btxS2IavSqFEjeQH7unXrcujQITZv3szKlStZuXIlzZs35/3798mef/LkSb5+/UqvXr3UZuP9+/eJjIxUWDzRq1cvrly5wosXL1J9TlpU5ZmZ/v37c/78ecLCwrCyskpQRzgn8+bNG16+fCkGlH9ADChF0pUfsbJsNY9IQrKCf5XtZmJpaYmWlpZ8nJxGuXLluHLlCo6OjnTq1Inx48czaNAgzp49S2BgIFZWVsn+3fj5+WFgYEC5cuXUZp+y3Uzq1auXYJzUkFZVeWbGxsYGX19fypQpQ4MGDXJUekdyZLYOSJkVMaAUSVdya6XPP7l9e3Zz8uRJnj59mq2LUWc20su/3mdPExAQQFRUVJrP9fPzQ1dXlwoVKig0d548eTAzM8Pf31+h87MD2tra8gL2S5YsoWXLlpibm+Pj40PRokWpV68eu3btSnSev7+/2tvWxXczSUsZqV8pU6YMenp6afJvWlXlmR0DAwPOnz9Pjx496NOnD0OGDFFr+83MjlQqpUCBApQvXz6jTcnUqCeJRUQkGcoV0UEC6n3tLQgsnz2ZeV8/AZA/f35MTEwwMzPD1NRU/meFChVU1uZN5Cfp4V9BEBgzoAdCTBQaGhpUqFAhkW9NTEySVRBLpVKqV6+uVDeT6tWr5+iAEn7mVY4aNYpq1arh7OyMlZUVXl5eXLp0iYEDB9KlSxd8fHxYuHChPF/S39+fnj17qtUuZXPdJBIJNWrUSNMOpSKq8sxOnjx52LhxI5aWlgwdOpSAgAD27duX5hJd2QFV3DNyAmJAKZKu6OTRwrCwNk/C016WI7WULarDg4/vefLkCcHBwQQFBcn/9PLy4suXL8DPG6axsTFmZmYJAhIjIyNy586tNvuyM+nh33JFdfB/81Lu03j/7t69m6dP/9d+s0yZMokCTVNTU6RSKa1atVLKhqJFi8r/HeV0GjdujI+PD46OjtStW5fNmzezZcsWLC0tGTVqFLdv38bDw4OiRYvy8eNHhco8pZb4biajR49WapySJUvy6tWrVB+fnQUbAwYMoGrVqrRv3x5LS0sOHjxIrVq1MtqsdMXPz482bdpktBmZHjGgFEl37CoXZ/uNJyovbA6gqSHBzrg4mpqaVKhQgQoVKtC6dWv594Ig8PLly0SB5rlz5+RFmjU1NalUqVKCQMTMzIzKlSujo6OjcpuzG+nhXz09PWxsbLCxsUnw/bdv37h3714C/x47doyVK1cik/0v7/LkyZMMGjQogX9LliwplgRRkPi8yr59++Ls7Iyvry9z587FwsKCDh06yHcv1c3jx4/59OlTugZ38ary9u3bp9uc6U29evXw9fXFycmJv/76i3Xr1qlVWJWZ+Pz5Mw8ePMi2CwZVIgaUIulOl9qGbLn2WC1jx8kEutYxTPZ7iURCqVKlKFWqFE2aNEnw3fv37xMFmtu2beP58+fyY8qVK5co0DQ1NaVQoUJquZ6sSEb6N3/+/FhZWWFlZZXg8+joaEJCQjh48CDTp0/H0NCQS5cu4e7uLq+5V7BgwUR+NTMzw9DQUHzVlQq0tbXZuXMnlpaWjBs3Dn9/f3bv3o2vry+Ojo7Y2NiovdRSRnQzUVZVnlUwMDDgwoULDBkyhN69e+Pr68uyZcuyXN3NtJLVOiBlJGJAKZLuGJXQpUGlolx9+EGlu1iaGhJsKhShUnHFum8ULVqUBg0a0KBBgwSff/nyhXv37iV6db506VK54EdfXz/JQLN48eI5btcrM/o3T548mJub4+3tTZ48eTh69Ci5cuUiNjaWhw8fJlhIxL+ijYj4WZpIW1sbExOTBH59/vy5mBaRBBKJhNGjR8vzKq2trfH09OTy5csMGDCA7du3s2/fPv755x+11KGUSqWUKFFC6W4mkZGRqQ6UlFWVZyV+zascNmxYjsir9PPzI2/evJiamma0KZkeiSBKYEUygGfh32my7ALRKiozIwgCGkIcx4fUxbRMcZWM+SciIyMJCQlJEGgGBwcTEhIiL/BcuHDhJAPNMmXKZOtAU9X+BcijpcGZkQ0pU1hx4UPPnj25e/fuH2tIymQynj17lmjHOigoiE+fPgE/g6ekdjSNjY3JmzevwjZmFx49eoSjoyOhoaFs3ryZDh06UL58eZ4+fUqjRo3Ys2ePyjtZtW7dGplMxokTJ5Qax8jIiL///ptly5b98djRo0dz8OBBHj16pNScWY0rV67Qrl07cuXKxcGDB7G2ts5ok9RCjx49CA4OFmtypgIxoBTJMPbcesqEg4EqG+/buQ2U+PYALy8vjIyMVDZuWomJieHBgwcJBCNBQUHcu3dPXuYmJyjPVe3fBU7mOFsn/7o7NVSrVo3atWsr1AkF/peDW6lSJVq0aEGpUqXkPo7vLBKvPP890ExJeZ5d+f79O3379mX37t2MHz+ejx8/cubMGb58+UL+/Pnx9PRU6c6egYEBPXv2ZO7cuQqdLwgC9+/fx9TUlPbt21O6dGkiIiJwdXWlW7duFC5cmKJFi2Jubk61atUoW7YsjRs3Rk9PjwMHDqjsOrIKL168oF27dvj7+7N+/Xq1K/hVwZcvX7hz5w6BgYG8f/+eT58+sW3bNvr164e2tjYlSpTAwsKCKlWqoK2tjbm5OTY2NmzYsCGjTc/0iAGlSIay2juUxadClB5nbLPKNCoZg4ODA2/evGH37t20bNlSBRaqjri4uCSV58HBwUkqz38NSIyMjMiTJ08GX0HaUda/giD8fI3a1JihjZRbJERFRaGrq8uqVasYOHCgwuMEBQVRpUoVzpw5Q+PGjeWff/z4MZHyPCgoKFXK8yJFiih1bZkZQRBYunQp48aNw8TEhPv373Pnzh26dOlCcHAw7u7udOrUSel5Xr9+jb6+Pvv27UuTQOb9+/ds376dQ4cOERAQwMePHwHQ0dGRv0kIDg6mbNmyaGtr8/r1a/kxurq6fP/+HTs7O7Zu3YqBgYHS15HViI6OZvDgwbi7uzNkyBCWLl2aqfIqv3z5wp49ezh+/DgBAQHynWRNTU0KFy7Mly9fiI6Olu+Wh4eHI5PJkEgkVKxYkbCwMHr16sWaNWvIly9fRl5KpkcMKEUynD23njLt8F1iZUKacu40NSRoaUiYaV9FvnP1+fNnunbtyrFjx5g9ezYTJ07M9K+Wk1OeBwcHJ1CeV6xYMVGJo6ygPFfGv8jieHtiNXaGedi+fTsFCxZU2A4fHx+sra25fv06tWvXVnicqVOnsnz5cl69epWqv/uklOdBQUE8ePBArjwvXrx4kq/Ps5Py/PTp03To0IHPnz8zb948hg8fTv/+/dmxYwejR49m/vz5SuVVnjhxglatWhEWFkbFihVTPFYQBM6ePYubmxuenp4IgkDLli2pVasW165d48aNG7x8+TLJwCj+9xoQEMD58+dZuHAhefLkITY2ltatW9O3b19atWqVbd40pAZBEFi/fj3Dhg3DxsaGffv2Ubx4+qQeJWfPtWvXcHNzw8PDg6ioKBo2bIilpSUWFhZYWFhgYmKS5CL9+/fvBAUFERAQwOnTp9mzZw8AhQoVomvXrvTt25dq1aql9yVlCcSAUiRT8Cz8O5M8A7kU9h5NDUmKgUf89w0qFWWuo3minDqZTMaMGTOYOXMmTk5ObNmyJcu+akxKeR4cHJzllOdp8S+CDCQa1K9UhHmOFgReP0/nzp0pWbIkXl5emJiYpHreiOhYHn+I4EesjKOHvZgxZghfwt8pXIA6NjaWsmXLYm9vz7p16xQaI5545fnv/g0JCcm2yvNHjx5hbm5OZGQke/bsoX379qxcuZLRo0dja2uLh4dHmnZrf/Xv9q2bcV8+n4/vXqf4d/Pw4UP69u2Lt7c3pqam9OvXj65du1KsWDG+f/9OqVKl+Oeff1L12vzgwYO0a9eO4OBgvL29cXNzw8/PD2trazZt2kTVqlVTfS3ZgcuXL9O+fXty5cqFp6dnomoL6cGTJ0/o378/p06doly5cvTp04eePXtSunTpNI+1YcMGBg8ejFQqZdeuXWzevJk3b97g7OzMqlWrKFasmBquIOsiBpQimYrQN1/ZeeMp3iFvefrhe4KOKxLAsIg2dsbF6VrH8I9qXy8vL7p164ahoSGHDh2iUqVKarU9PUlKeR4cHMzDhw8ztfI83r87zkmJzVsIfrEj3r8mBeLYNKkXR3e60bx585/nhYbi4ODAs2fP2LFjB/b29n+cw/v+W56GJ/w3hCBQtogOdpWL06W2IUYl0rbQOHz4MG3btsXPz09tZUSSUp7H5+CmpDw3MzOjYsWKalFPq5LNmzfTu3dvACZMmMDs2bO5ePEiHTt2JH/+/Hh5eaW4A6Sof+Pi4li1ahWTJ0+mWLFirFu3jhYtWiT4LWzbto0ePXrw4MGDVLXmnDJlCq6urvL8WfgZVPXv35+wsDD+/fdfJkyYkKMqArx48QInJydu377Nhg0b6NGjR7rMK5PJWLduHRMmTKBQoUKsWrUKe3t7pRZeAwcO5MqVKwQG/swFj4mJYdeuXfLC+atWrcLFxSXbvEVQFjGgFMm0/Lr7kFtLg3JFdNDJk7aHZXBwMA4ODrx9+5Zdu3ZlurxKVZMVlOeCIFC4cGGGjRpLxz6DE/lXEASsrKwQBIEbN27IXzt+/fqVHj164OnpybRp05g6dWqCh4Uqd7mTIjo6GktLSwoWLMiVK1eU/4tII6lRnufKlQtjY+NMrTyPioqiXLlyFC9enLt379K0aVN27drF169fcXR05N69e2zatAkXF5cE5ynj32LaGjg5OXHixAmGDBnCvHnzyJ8/f4Jzvn//joWFBUZGRqlWiSenKo+KimL27NnMnz+fWrVqceLECaXSNbIaUVFRDB48mE2bNjF06FCWLFmi1rzKyMhInJyc+O+//xg4cCALFiygQIECSo9bu3ZtKleuzLZt2xJ8/vbtW4YOHcrevXvp1q0bmzZtyvQLufRADChFsj1ZMa9S1fyqPP81IAkODk535fmjR4+oUKECx44dS7YFoo+PD7Vr12bOnDlMmDBB/rlMJmPevHlMmTKFNm3asG3bNgoWLKh0Hu4M+yq4/EFBPn36dObMmYOvry8WFhapnkPdCILAmzdvkkyNyKzK87179+Ls7MyUKVNYvXo1enp6eHl5UalSJXle5ZgxY5g3bx5aWlpK+1fv4WkCPNfj5eVFs2bNkjx27NixrF69mtu3b2NsbJyq8Q0MDOjVqxdz5sxJ8vsbN27QokULTExMOHnypEqCnKyCIAisW7eO4cOHU69ePfbu3auWvMrIyEjs7e25evUqBw8elL/VUJbY2Fh0dXWZO3cuI0eOTPKYnTt30qNHD5ydndm6dWuODyrFgFIkRyCTyZg+fTqzZs2iXbt2bNmyJdEORU5EJpPx5MmTRMpkdSrPDxw4QPv27Xn58mWKBajHjRvHypUrkUqliYoKHzt2jC5dulCyZEmcZ25mqzQ8zXb8zphmxgyxS1pJHhAQgJWVFRMmTGDmzJlKz5Ve/Ko8//XPJ0+eyI8pU6aM3K/ppTwXBAEnJyeuXbvG8ePH6dWrFw8ePGDLli20a9eOFStWMGbMGOzs7Gg6YglrLz9TZjKQSHCsqMWyvkkHGzdv3qRu3brMmzePcePGpWrY1KrKfX19adKkSY4MKgEuXbpE+/btyZMnDwcPHlRpXmVkZCRt27blypUrHDt2DFtbW5WNfefOHczNzTl//jwNGzZM9rj9+/fj4uKCs7Mz27Zty1FirN8RA0qRHIWnpyfdu3enbNmy8h0RkcSoU3n+77//4u7uzqtXr1K0Ib6dXWRkJOfPn6dcuXIJvg8JCeHvYXP5UaOD0tcbT1K1LsPCwrC1taVw4cLcunUrS5Zv+p1v375x//79RAuJ9FSev3z5kqpVq2JqasqBAwcYMWIEHh4eTJw4kVmzZnHhwgU6T1lD3r96Kz1XPEn5NyQkBFtbW0qVKsW1a9dSvcuUFlW5j48PjRs3pm3btolen+YEnj9/jpOTEwEBAWzcuJHu3burZNxBgwaxZcsWjh07hp2dnUrGjGf79u10796dT58+/TFdYd++fbi4uDBz5kwmT56sUjuyEmJAKZLjCAoKwsHBgXfv3rF7925atGiR0SZlKZRVnrdu3RpBEDh+/Pgf53r27Bm2trbIZDLOnz9P2bJl//ddfDeemLgE4h5l+L0bz4MHD7C1tUVHRwdvb2+lW/pldtJbeX7z5k2aNm2Kubk5x48fZ/369UycOJFmzZqxaO0mnNyl/IiVqc2/oaGh2NraUrBgQby9vdPUQnDu3LksXLiQjx8/pirAjhcjHT9+PNvncidFVFQUgwYNYvPmzQwbNozFixcrlVd58eJFGjZsyKpVqxgyZIgKLf3JyJEjOXz4MA8ePEjV8RMnTmTp0qX4+/vn2DaNYkApkiP59OkTXbt25fjx4/I8vZyWV6lqUqs8//DhA+bm5vTu3TtVyvNfg8q9e/fKW7x1c7+htn7h2/vU5tq1azg7O5MvXz7Onz+f7YPJlFCn8vzGjRs0a9aMqlWr4uHhQVBQEC4uLhRoOxkNfRNU6N4E/r116xaOjo7o6uri7e1NyZIl0zRWhw4dePfuHefPn0/V8YIg0Lx5c+7du8fdu3ezbCkzZVBVXmVkZCTVqlWjePHiXLx4US0ltGxtbSlWrBj79u1L1fFRUVFUq1aNIkWKcOnSpRz56lsMKEVyLDKZjGnTpjF79mzat2/P5s2bxbxKNfCr8vzWrVssW7aM0qVL8/r161Qrz58+fYqjoyP+/v6MHj2abkPG0WbdDbXZ3Dj6KpuXz6NWrVocOHCAUqVKqW2urIyqlOc3btzA0dGRiIgIFi1aRMWa9elzQH29sZvH3sRt6Wxq1KjBkSNHFFosVKxYEXt7+1T1+47n8ePHmJmZMWnSJP799980z5ld+DWv0tPTE0tLyzSdv3jxYiZPnkxAQACVK1dWuX0ymQw9PT3Gjx/PpEmTUn3e5cuXadCgATt37qRz584qtyuzIwaUIjmegwcP0qNHD8qVK4eXl9cf86FEFCc+7+zBgweUKVMmTcpzY2Nj7t+/j4eHB6XsR0ClBshQw66yLI7vt08yoVlFhg8fniN3GpRFEeW5oaEh//33H0eOHMG850y+6ddU6e6kHFkcEbf/Y4xdWUaPHq2QMvfz588UKlSIbdu20a1btzSd26dPH86ePcvDhw+zZHF6VfHs2TPatWuX5rxKQRAwNjamTp06bN++XS22PXjwgEqVKimUntCoUSN5ik5OQwwoRUQQ8yrTizlz5rBo0aIU885Sozw3GOBKLj31vYI2KJCLqxOTLi8johypUZ6XGuCKljr9q5uLq5MU9++FCxewtbUlMDAwzd1wbty4QZ06dfjvv/9UVuImqxIVFcU///zDli1bGD58OIsWLfpjXuW5c+do3LgxFy9epEGDBmqxa//+/XTo0IHXr1+nKa8WYM+ePXTq1Ing4OA0dfXKDogBpYjI//Pp0ye6dOnCiRMnmDt3LuPHjxfzKlVM+/bt+fDhA97e3mk+N155Lg0MYsiFaFDH7uT/IwHuTG+e5kL6IooTrzyXBgYx+74emdm/y5YtY9KkSXz9+jXNO5yCIFC9enVMTEzw8PBQaP7shCAIrF27lhEjRlC/fn327t2bYkvDLl264OfnR1BQkNruz5MnT2bz5s28fPkyzedGR0dTqlQpevfuzcKFC9VgXeYl5+63i4j8RqFChTh8+DCTJk1i4sSJODs78+3bt4w2K1shlUoVblkokUgoVaoU5S1qoc5gA0AAHn+IUOscIgnJnz8/lpaW1G1mT2b3r1QqxcLCQqHX5RKJhJYtW3Lt2jWF589OSCQSBg8ezNmzZ7l79y5WVlb4+fkle/yVK1do06aNWhf7yrRWzZMnD82bN8+QbloZjRhQioj8gqamJrNnz+bAgQMcP34cGxubVJeNEEmZT58+8fDhQ6V7YP+IlanIopSJTqd5RBKSXv5VZh5lFkYA1atX59mzZ3z48EHhMbIbf/31F76+vhQvXpx69eqxY8eORMeEh4fz5MkTpe8hf0IqlVKzZk2Fz69Rowa3b98mLi5OhVZlfsSAUkQkCZycnLhx4waRkZFYW1tz8uTJjDYpy+Pv7w+g1I0aILdW+ty2mjdpRP369enfvz/Lli3j5MmTPH36FDFLSL2kl387u3SkQ4cOTJs2jT179hAQECAXg6VEZGQkwcHBSgcc8L/fhMhPypQpw6VLl3BxcaFbt26MHDlSXgkC4Pbt28DPgFxdvHr1ijdv3ii9YIiIiMhxmxFigpCISDJUqVKFW7du0blzZ1q1asXcuXMZN26cmFepIFKplLx58ypd5qNcER0k/HxtqT4EBnfvSGjwHXx8fNi+fXu69zzPqaSXfxvWNCMkKJCNGzemqed5YGAgcXFxSgUc8R26Hj58SOPGjZW/nGxE3rx52bRpE5aWlowYMQJ/f395XmVYWBgSiSTVvdYVIf51uzL+jS9sHhoaqlZbMxtiQCkikgKFChXiyJEjTJ06lQkTJuDn58emTZtSbC0okjR+fn4K5539ik4eLQwLa/Mk/LuKLEtM2SI6TB8zUf7/vyrPf1Ume3l5qa3neU4lvfy7ft4K+f8npTzfs2dPkj3PY2NjkUgkfPnyhQ8fPijU81xTUxOJRCLudieDRCJhyJAhmJub06FDB6ysrPD09EQmk6GhoaHWhZtUKqVQoUKJWr2mhXilenwb05yCGFCKiPwBTU1N5syZQ82aNenRowd169bFy8uLChUqZLRpWQqpVKqyMh92lYuz/cYTlXbJiUdTQ4KdccLuHRoaGpQvX57y5cvTunVr+efJ9Tw/d+5ckj3Pfw00TUxMxIVJMqS3f/X09LCxscHGxibB57/2PI/37fnz5xEEgSZNmgA/e54nVZRfX19ffJuhJA0bNsTX1xcnJyfq1atHp06d1D5nfH6s6Lu0IwaUIiKppF27dlSuXBkHBwesrKzYs2cPzZqJtQpTw/fv3wkODmbYsGEqGa9LbUO2XHuskrF+J04m0LWOYaqOjVeelypVSh5gxJNUz/Pt27cn6HletmzZBIHIrz3PczKZxb/xyvNfO7nUqlULY2NjJkyYkMC3ly9fxt3dPUHP86QCzbJly4q7k2mgTJkyXLx4kX/++YfNmzcjkUiIiYlRqg94Svj5+eHk5KTUGDnVt2JAKSKSBqpWrSrPq2zZsiXz5s1j7Nix4mr2DwQGBiKTyVSmzjQqoUuDSkVV38tbAjYVi1KpuPJ9losWLUqDBg0S7com1fP80KFDLFu2LEHP86SCkZR6nmcn1Obf/+/lrah/Y2NjCQwMpHPnzlStWjVRUfPY2FgePXqUwLcBAQF4eHjIe57ny5eP8uXLAz9L4BQrVgxTU1MqVqyotiApq5MvXz42b95Mrly5cHNzw9bWFi8vrxTrVSrCx48fefz4sdLCwfhUCUVaemZlxMLmIiIKEBcXx5QpU5g3bx4dO3YU8yr/wPr16xkyZAjfvn2T929Wlmfh32my7ILKyvsIgoBEFstWZyMaWlZRyZhp4dee57/ubIaEhKS653l2QtX+BcijpcGZkQ0pU1hbofPv3LmDubk5Fy5c4K+//kr1eTKZjOfPn8t9euzYMc6ePUvBggX5/Pkz8DPvzsjIKJFvK1eurLLfTFbn6dOnlC1blgIFClCoUCG8vLxUWkLI29ubRo0acffuXczMzBQeZ8OGDQwePFil97usgLhDKSKiAJqamsydO5eaNWvSs2dPbGxs8PT0FPMqk0EqlWJmZqbSm2uZwtrMsK/ChIOBKhlPIpGgdfsgbTceZufOnQlyJdODfPnyUa1aNapVq5bg85iYmEQ9z3OC8lzV/gWYaV9F4WAS/qcATmvZGg0NDQwNDTE0NKRFixaEh4dz584dXr16xdu3bxMtIlxdXRMoz8uXL5/It6ampnLleU6hTJky6Onp0atXLy5cuEC9evVwc3Ojc+fOKhnfz8+PfPnyKV2JQiqVYmpqmqOCSRADShERpWjfvj0mJibyvEoPDw+aNm2a0WZlOpQtBJ0cLtaGvP8WzeJTIUqPNbZZZbpOWEX37p9p06YNM2fOZNKkSWhoZGy53ly5cmFiYpKoL3BOUJ6rwr+CIPxUDf9liLN16nInk0MqlVKxYkUKFCig1Dhnzpyhdu3aSCQSSpQoQYkSJbCzs0twTLzy/Fffenh4JFCely5dOpFvzczMFFKeZwUkEgnW1tZIpVIuXbrEwIED6dKlCz4+PixcuFDpChLxHZCUWYQJgsD58+epW7euUrZkMBAdOgAANoNJREFURcRX3iIiKuDjx4906tSJ06dPi3mVvxETE4Ouri4LFixg+PDhapljz62nTDt8l1iZkKacO00NCVoaEmbaV5EHGzKZjFmzZjF9+nQcHR3ZunVrltoJEgSBV69eERQUlCjYzKrKc2X8q4HA53OuFPoQhJeXV5pfZUZEx/L4QwQ/YmUMGjgAA10tDnjsSuslyAkMDMTCwoIDBw4oJP6IV57/LvgKCwuTl6kpVqxYkoFmdlCeb9++ne7duxMWFkaFChVYtWoVo0aNomHDhnh4eFC0aNFUj/Wrb3NradChhS229euydu1ahe27dOkSf/31F2fPnqVRo0YKj5MVEQNKEREV8WtepbOzM+7u7pny4ZzexD9A05p3llaehX9nkmcgl8Leo6khSTHwiP++QaWizHU0T/I16KFDh+jWrRtlypTBy8sLIyMjtdmeXiSlPA8ODs4SyvME/pVAXEpPLlkcaGjK/Rsd/hIHBweePHnC9u3bcXBwSHGu0Ddf2XnjKd733/I0/PtvRdYFyhbWwa5ycbrUNsSoRNoWG8OGDWPv3r08e/ZMpSKc6OhoQkNDE/n2/v37iZTnvweaZcuWzfCd+NQSGRmJgYEBAwcOZN68eQCcP3+eDh06oKOjg5eXV4opCSn5VhAECueKo611JYV8C9C9e3euXbvG/fv3s8zfqaoQA0oRERWzf/9+evbsScWKFfHy8pIrOnMq27Zto0ePHnz+/FnpV4WpQf7ACHnL0w8JHxgSwLCINnbGxelax/CPat979+7h4ODA69ev2bVrF61atVKr7RlFUsrz4OBgHj58mOmU56FvvjLb4yJn7r4kd2GDJP1b6PsLTq+dSuCV01SsWBGAr1+/0qtXLw4cOMCUKVOYPn16oge+qhclv/P27VuMjY0ZOHAg8+fPV+Ty00xSyvP4V+m/Ks+TysHNrMrz4cOHs3v3bkJDQylYsCDwU7Dj6OhIcHBwknmV6vYtwPPnzzEyMmLGjBmMGzdO8QvMoogBpYiIGrhz5w5t27bl06dP7NmzJ0fnVY4YMYJjx44RGhqa7nP//kqrXBEddPKkLc/q8+fPdO3alWPHjjFr1iwmTZqU5V8bppbMqjyfNWsWy5Yt4+nLNzwJ/57Iv9++fcPc3JwKFSpw5swZuR2CIDBv3jz+/fdfWrVqxY4dO+Q7r8qmTcywr4LLH3I0XVxcOHPmDEFBQRQvXjzFY9XN78rzX//8+PEjkHmV58+ePcPMzIwuXbqwfv16+eeRkZEMGDCA7du3M2rUKBYsWICWlla6+FYQBNq0aYOfnx9BQUEZvqOfEYgBpYiImggPD6dz586cPn2a+fPnM2bMmBwTiPxKw4YNKVGiBHv37s1oUxRGJpMxY8YMZs6ciZOTE1u2bMlSeZWqJinlefyuV3ooz52cnPj06RPnzp1L9pjTp0/TrFkzXF1d6du3b4LvTpw4QadOnShevDiHDh3i7GstlQi7xjQzZohd0qkRhw4dwsHBgZ07d6pMlawOBEFIUnkeFBSUqZTna9euZfDgwXh7e2Nra5vA/pUrVzJ69GhsbW1pOmIJ6648T36gVJKSbwF27dpFly5d8PLyom3btkrPlxURA0oRETUSFxfHv//+y/z583FxccHNzS1H5VXKZDL09PSYMGECEydO/PMJmRwvLy+6d++erfIqVUlyyvOgoCCVKs/Lly9Pu3btWLx4cYrH9e7dmwMHDnD+/PlEVQZCQ0NxcHDgbf5K6DTqr9gFJ8ECJ/NEavKwsDDq16+PlZUVR44cybILy6SU50FBQRmiPJfJZNja2vLs2TOuXr2aqIi4t7c3naesJk+D3iqbMynfAoSEhGBjY0OTJk3Ys2ePyubLaogBpYhIOrBv3z569uyJkZERnp6eOSavMiwsDCMjI/777z+aN2+e0eaohODgYBwcHHjz5g27d++mZcuWGW1SpkeVyvPw8HCKFCnCjh076NKlS4rzfv78mSZNmvDw4UPOnj2bSKwR/OwtrVZfQybRVFmQ93vx9AcPHmBra4uOjg4XLlygRIkSKpknMxEREcG9e/cSBZoPHjwgLi4OUI/y/PHjxzRo0AAdHR28vb0TBJXPwr/TeOl5fsTKQE2+hZ/BpK2tLXp6ely4cCFNKvPshhhQioikEwEBATg6OvLp0yc8PDwS9X7Ojuzbt4+OHTvy5s2bDM8ZUyW/5lXOnj2biRMnZtldp4wmrcpziUTCkiVLuHbtGnXq1Pnj+B8/fqRp06Y8evQoUVDZzf2G2to7bu9Tm7CwMOzs7NDW1ub8+fM5rhVfvPL8d//+qjwvUKBAkoFmapXnYWFh2Nraoqury7lz5+R/x+r2Lfzc5ba1taVgwYJ4e3tny8VCWhADShGRdCQ8PJxOnTpx5swZFixYwOjRo7N1IDJp0iS2bt3KixcvMtoUlSOTyZg+fTqzZs2iXbt2bNmyhfz582e0WdmG5JTnDx48kB+TWuV5fFB5584dZsyYwejRo3n0IZKmyy+qzf4++i9ZOHkU+vr6nD9/HgMDA7XNldWIV54ntZD4XXn+u3+TUp7HB3ZxcXGsWbMGi/rN1Orb0yP+4sIRD0aPHo2BgQHe3t6ULFlSbfNlFcSAUkQknYmLi2Py5MksWLCATp064ebmhra24u3gMjMtWrQgV65cHDlyJKNNURteXl5069aNsmXL4uXlRaVKlTLapGyNi4sLwcHBTJgwIU3K8/Lly+Pq6srSpUupUaMGtQct4b8HESrdwZIjyPjie5QOFWDhwoXy0jYiKROvPP890ExKef67f/Pnz8/o0aM5dOgQ1gMX8kHPLOVapQqiKYH8r6UEbJ5Cz549Wbp0KXp6eqqfKAsiBpQiIhnE3r176dWrV5bLq4yIiCA4OJjPnz8TERFBSEgIVatWJU+ePJQuXVqu4hUEgZIlSzJgwABmzpyZ0Warlfi8yrdv37Jr1y4xr1KNmJmZYWtrm6ibSXLK83v37hEZGQn8VJ6XLl2a169fo+28kFx66ts1LJ5Pws2p2bNuaXoTrzxPakfz1atXwM+2jOXLl6dQoUK8qTUIrULq2zEUvr5lYxuDbJMXrirEXt4iIhlEx44dE/UBz2x5lYIgcPXqVc6ePUtAQAABAQGEhYWR0jpUW1ubqlWrUqlSJd6+fUvZsmXT0eKMwdTUlJs3b9KlSxdat24t5lWqiYiICO7fv8+oUaMSfZeWnueB90J5W0i9+YzvIgUiomPTXPdUJDG/9jz/tUQQ/Exn+DU1IvBeKO8LqjeXUUO3OPVtG6t1jqyIuEMpIpLB/JpXuXDhQkaNGpXhgci7d+/Yvn07bm5uBAcHU7hwYapVq4aFhQUWFhZUrVqVYsWKycu8xMXFERUVxePHj+WB5+XLl3n48CEaGhq0bt2avn370qpVK7S0su8DVsyrVC/Xrl3DxsYGHx8fLC0tFR7n7svPtF51WYWWJc2xofWpYiC+7k5PRN9mHNn3zi4ikkUoXLgwx48fZ9KkSYwZMwY/Pz9cXV0zJK/yy5cvTJgwATc3NyQSCY6OjqxatQo7O7tUKS6NjIzkXYFmzZrF0qVLmTNnDu7u7rRt2xYDAwMWLVpEp06dMjxoVgcaGhrMnDmTGjVq0L17d+rWrYunp6eYV6kipFIpWlpaVK1aValxfsTKVGRR5phH5H+Ivs04clbnchGRTIqmpiYLFixgz549eHl5Ua9ePR4/fpyuNpw4cYIqVaqwbds2Zs2axYsXL9izZw+NGzdOVTD5O1KplJo1azJo0CB8fX3x8/OjXr16dOnSBXt7+2yp/I7H0dGRGzduEB0djbW1Nf/9919Gm5QtkEqlVKlSJdUF0JMjt1b6PPrSax6R/yH6NuMQ/0ZERDIRzs7OXL16lc+fP2NlZcXZs2fVPmdsbCz9+vWjVatWmJqacufOHcaPH690gV4/Pz9q1qwp//8aNWqwd+9ePD098fHxwczMDE9PT2XNz7SYmZlx8+ZNbGxsaNWqFfPmzUsx91Tkz/j5+SXqeKMI5YrooO79ccn/zyOSvoi+zTjEgFJEJJNRrVo1bt26Rc2aNWnWrBlLly5VWyASGxtLly5d2LJlC66urpw8eZJy5copPW54eDhPnjxJ8uHv4OBAUFAQTZs2pUOHDhw4cEDp+TIrhQoV4siRI0yePJlJkybRsWNHvn37ltFmZUliYmK4c+eOSgJKnTxaGBZWb0qJYRFtUZCTAYi+zTjEgFJEJBNSpEgRjh8/zujRoxk9ejTdunXj+/fvKp0jNjaWrl27cvDgQfbt20ffvn1Vltfo7+8PkOzDX09Pjz179tCxY0dcXFw4ePCgSubNjGhoaDBr1iwOHDjAf//9R926dRMU5xZJHUFBQfz48SPBrrcy2FUujqaGevayNDUk2Blnn85QWQ3RtxmDGFCKiGRStLS0WLhwIbt37+bgwYMqz6scM2YMBw4cYO/evTg4OKhsXPj5alJbWxtjY+Nkj9HS0mLbtm20b98eZ2dnrl+/rlIbMhtOTk7cuHGDqKgorKysxLzKNOLn54dEIqFatWoqGa9LbUP1FDUH4mQCXesYqmVskT8j+jZjEANKEZFMjouLC9euXePTp09YWVlx7tw5pce8fPkyK1asYNGiRTg6OqrAyoRIpVKqVauGpqZmisdpaWmxfft2atasSe/evYmOjla5LZkJMzMzbt26Jc+rnD9/vphXmUqkUilGRkbo6uqqZDyjEro0qFRU5TtZmhoSGlQqSqXiqrFTJO2Ivs0YxIBSRCQLUK1aNXx8fKhRowZNmzZl2bJlCgciUVFR9OnTh7p16zJ06FAVW/oTqVSa6lw3LS0t3N3dCQsLY86cOWqxJzNRqFAhDh8+zKRJk5g4cSLOzs5iXmUqSMu/qdQy19EcLVUGHYKApuTnuCIZi8p9C2hpSETfpoAYUIqIZBGKFCnCiRMnGDVqFKNGjVI4r3LJkiU8fvwYNze3P+4gKkJERAT37t1LU65b1apVmTRpEvPmzSMsLEzlNmU2NDU1mT17NgcOHOD48ePY2NiIeZUpIJPJ8Pf3V3lAWaawNjPsq6huQImEj2c24H9F/dUZRFJG5b4FZtpXoYyaBT9ZGTGgFBHJQmhpabFo0SJ27drFwYMHqV+/Pk+ePEn1+bGxsaxbt46ePXtiZmamFhsDAgIQBCHND//x48ejq6uLq6urWuzKjMTnVUZGRmJtbc3Jkycz2qRMSVhYGN++fVOZIOdXXKwNGdMs+VzftDC0YVnqlZRgb2/PzJkzkcnE4tcZiSp9O7ZZZZytxdzJlBADShGRLEinTp24evUqHz9+xNLSMtV5lSdOnODFixcMGDBAbbbFdzOpUiVtuwP58uWje/fubN68mR8/fqjJusxHlSpVuHnzJnXq1KFVq1YsWLBAzKv8DalUCiRfNUBZhtgZMd/JnDxaGmnOu9PUkJBHS4MFTuaMblGVgwcPMmPGDKZNm4aTkxNfvnxRi80iqUNVvh1sJ3a7+hNiQCkikkWpXr06Pj4+VK9enWbNmrF8+fI/BiKurq5YWlqqZacnHj8/P6pWrapQN5N+/frx7t07Dh8+rAbLMi96enocOXKECRMmMGHCBFxcXIiIiMhoszINUqmU0qVLK11sPyVcrA05M7IhNhWKAPwx+Ij/3qZCEc6MbCjfvdLQ0GDq1KkcPnwYb29vateuzf3799Vmt8ifUZVvRVJGIohLYRGRLE1sbCwTJ05k8eLFdO3alY0bN5IvX75Ex8XFxVGgQAGmT5/O2LFj1WaPpaUl1apVY9OmTQqdb2FhQd26ddmwYYOKLcsaHDhwgB49elChQgW8vLyoUKFCRpuU4TRr1ox8+fJx6NChdJkv9M1Xdt54infIW55++M6vD0kJPwtb2xkXp2sdwxQVv/fv38fBwYGXL1+yc+dO/v77b7XbLpIy8b7dczGAKC1d+KX2blp8K5IEgoiISLZg586dQr58+YQaNWoIjx8/TvR9cHCwAAhnz55Vmw3R0dFC7ty5hZUrVyo8Ro8ePQRra2sVWpX1CAwMFCpWrCjo6ekJJ0+ezGhzMhSZTCYULVpUmDZtWobM/y0qRrjz4pPg9yRcuPPik/AtKiZN53/+/Fmwt7cXAGHGjBlCXFycmiwVSQuVK1cWBgweppRvRRIivvIWEckmdO7cmatXrxIeHo6VlRXe3t4Jvo/PQ6tevbrabFBFN5Pq1asTGBhIbGysCi3LWlStWpVbt25Ru3ZtWrZsycKFC3NsXuWLFy94//692vIn/4ROHi2qGBSkhqEeVQwKprnlXoECBfD09GT69OlMmzaNdu3aiXmVGcy3b98ICQmhVs1qSvlWJCFiQCkiko2Iz6u0sLCgadOmCfIqg4KCMDAwoHDhwmqbXyqVKt3NxMLCgqioKB4+fKhCy7Ieenp6HD16lPHjxzN+/Hg6deqUI/Mq/fz8ANSa96tuNDQ0mDZtGocOHeLs2bPUqVOHkJCQjDYrx3L79m2FKlGIpIwYUIqIZDOKFi3KyZMnGT58OCNHjqRHjx5ERkby48cPtLXVW0MtvptJ/vz5FR4j3sacpPRODk1NTebOncu+ffs4evQoNjY2OS7QlkqlFClShNKlS2e0KUpjb2/PzZs3kclkWFtbc/To0Yw2KUcilUrJlStXmitRiKSMGFCKiGRDtLS0WLJkCTt37mT//v3Ur18/XV6z+fn5ZemdpMxK+/btuX79OhEREVhZWXH69OmMNindiO+QI5GotutJRmFiYsKNGzdo2LAh9vb2zJ49W6xXmc5IpVKqVq1K7ty5M9qUbIUYUIqIZGM6d+7MlStX+PDhA1u3biUyMlJtc8lkMm7fvi2+RlIT8XmVtWrVokWLFixatChH5FVmx0VKwYIF8fLyYurUqUyZMoX27dvz9evXjDYrx+Dn5yfep9SAGFCKiGRzatSogY+PD/r6+rx48SJV9SoVIb6bibI36nfv3gE/e16LJERPT49jx44xfvx4xo0bR+fOnbN1XuWHDx949uxZtnz4a2hoMH36dLy8vDhz5gy1a9cW8yrTgR8/fnD37t1s+W8qoxEDShGRHEDRokVZtmwZACNHjqRnz54q362MF08oe6OOz5krVaqUKszKdsTnVe7du5fDhw9jY2PDo0ePMtostaDuDjmZgbZt28rzKmvVqsWxY8cy2qRszd27d4mJicl2u96ZATGgFBHJIVhZWQEwYsQI9u7dS4MGDXj69KnKxpdKpZQpU0bpbib+/v5Ur1492+TMqYsOHTpw/fp1vn37lunzKmUyGQ8fPsTLy4uZM2fSoUMHatasiZmZGRKJBIlEQtWqValTpw49e/Zk6dKlnDlzhosXL5I/f36MjIwy+hLUSnxeZYMGDWjTpo2YV6lG4itRWFhYZLQp2Q6x6JKISA5BX1+f4sWLkzt3bq5evYqjoyNWVlbs3bsXW1tbpcePF08og0wm48aNG3Tu3Flpe3IC5ubm3Lp1i86dO9OiRQsWLFjA6NGjM00wHhAQgJubGzt37iQ8PByAIkWKYGFhgbW1Ndra2uTLl48yZcpQtmxZvnz5QlBQEHv37pXvoOfNm5cFCxbQs2dP9PX1M/Jy1ErBggU5dOgQM2bMYMqUKUilUrZs2YKurtitRZX4+flhbGysVCUKkWTI0LLqIiIi6cqgQYMEfX19ISYmRnj37p1gZ2cnaGpqCitWrBBkMlmaxkrQQeT5J6FICQNh+vTpStn333//CYBw/fp1pcbJacTGxgoTJkwQAKFTp05CREREhtri7u4uWFtbC4BQokQJYdy4ccKJEyeEFy9epOrfWWxsrBASEiIYGBgIlStXFvLlyydoamoK9vb2au30lFnw9PQUdHV1BTMzMyEkJCSjzclW2NjYCJ06dcpoM7IlYi9vEZEcxO3bt6levTpeXl60bduW2NhYxo0bx7Jly+jevTvr169Psg94PPIex/ff8jQ8YY9jQRAolhf+rlmeLrUNMSqR9p2Vdu3aERYWhr+/f6bZZctK7N27l169emFkZISnpyfly5dP1/mDg4Pp3bs3169fp1WrVvTr14/WrVuTK1euNI/17ds3ChQogLu7O46OjuzevZuNGzfi7+8vfy2up6enhqvIHAQHB+Pg4MCbN2/YtWsXrVq1ymiTsjxxcXEULFiQadOmMXbs2Iw2J9sh5lCKiOQgqlWrhrW1NWvWrAF+1qtcunQp27dvl+dVPnv2LNF5z8K/0839Bk2XX2T7jSc8+S2YBJBIJLyPlrD9xhOaLr9IN/cbPAv/nmrbnj9/zuHDh+nXr58YTCpIx44duXbtGl+/fsXKyoozZ86ky7yxsbHMnTuX6tWrEx4ezqVLlzh27BgODg4KBZOQsJtJoUKF+Oeff/Dz88PNzQ1PT0/MzMzw8vJS7YVkIkxNTbl58yYNGjTg77//Zs6cOTmiTJQ6CQ0NJSIiQhTkqAkxoBQRyWGMGzeO06dPc/DgQflnXbt25cqVK7x79w5LS0suXLgg/27Prac0WXaBqw8/ABAnS/mhFv/91YcfaLLsAntu/Vn4IwgCQ4YMoUiRInTr1k2RyxL5fywsLLh16xZWVlY0b96cxYsXqzUQiYmJoXPnzkydOpWRI0fi7+9P/fr1lR43vpuJmZmZ/DOJREKfPn24e/cutWrVwtHRkRUrVig9V2YlPq/y33//5d9//xXrVSpJTqgakJGIAaWISA6jXbt2tG3blkGDBvHx40f55zVr1sTHx4cqVarQuHFjVq1axapzoUw4GEh0rOyPgeTvxMkEomNlTDgYyGrv0BSP3bdvH4cOHWLt2rUULFhQoesS+R+FCxfm+PHjjB07lrFjx9KlSxe+f0/9bnFqiY2NpWvXrnh6enLgwAHmz5+fYspEWvDz88Pc3DzJbialSpXCy8uLsWPHMmLECFatWqWSOTMjGhoazJw5E09PT06dOkWdOnUIDU359ySSNFKpFENDQwoXLpzRpmRLxBxKEZEcyMuXLzEzM6NVq1bs3LkzwSvm2NhYxo4di9u5IIq0GqayORc4meNsbZjo8xcvXlCjRg3++usv9u/fr7L5RH7i4eFB7969VZ5XKQgCXbp0Yd++fezduxdHR0eVjBtPjRo1sLS0xM3NLUUbxo0bx+LFi1m3bh0DBw5UqQ2ZjV/zKnfv3k3Lli0z2qQsRZMmTdDV1cXT0zOjTcmWiDuUIiI5EAMDA9avX8/u3bsZMmRIgleiWlpajJoyhxKth6r0VenUw3cT5VS+fPkSOzs78ubNy+rVq1U2l8j/cHZ25tq1a3z58kWleZVbtmxh9+7d7Ny5U+XBZHR0dKq6mUgkEhYuXMigQYMYPnw4wcHBKrUjsxGfV1m/fn1at27N3LlzxbzKVCIIgkpKm4kkjxhQiojkUFxcXHB1dWXt2rUMHZoweJzkGYgg0VCpOCZWJjDJM1D+//HBZGRkJOfPn6dkyZIqm0skIRYWFvj4+MjzKpcsWaJUIPLq1StGjRpF9+7d6dixowot/UlauplIJBIWL15MuXLl6NOnD3FxcSq3JzNRsGBBDh8+zL///svkyZPp0KED3759y2izMj3Pnj0jPDxcDCjViBhQiojkYPr27cvGjRtZs2YN7du3582bN4S++cqlsPdpzpn8E3EygUth7wl7+5WzZ89iY2PD9+/fOX/+PBUqVFDpXCKJic+rHDNmDGPGjKFr164K51UOHjyY3Llzs3TpUhVb+X/t3X1czXf/B/DXuZmohSm5JAmlcoiSX2xzkYsMD5Rdl4qirdkudmfCyOy6hqHL3X67cV1CNrZL5eaYm2iYYuZH6Uh3UnOTK0xKk9rVcU7n94fVHIXq+/1Wznk9//HQOefz+ZxpnVff7/v9+dzX0NNM2rRpg40bN+LkyZM1OxiYsuq6yl27diExMRGDBg1Cfn5+cy+rRas+GpYd3tJhoCQyc9OnT8eOHTtw/Phx9O7dG4u2fAeFXJptexQy4JVlmzFixAh0794dx48fR8+ePSWZi2pTKBSIiopCbGwsdu/ejRdeeAGXL19u0BiZmZlQq9VYtWoVbGxsJFmnRqOBq6srrKys6v2aIUOGIDw8HMuXL8e9e/ckWVdLExAQgFOnTkGr1WLgwIE4ePBgcy+pxdJoNOjYsSPs7e2beykmi4GSiPDyyy8jOzsbL730Eo7/VCL61clqegNwudIS//znP3HkyBE4OTlJMg89XmBgIH788Uf88ssv8Pb2xpEjR+r92g0bNsDOzg6BgYGSrS8tLa1RV5Lefvtt3LhxA/v27ZNgVS1T7969cfr0abzwwgsYM2YMli9fzrrKOlTXT3KPW+kwUBIRAMDW1hbrY77CM89Je16ysn1nhL7yGuRy/vhpTv369UNKSgq8vLzg5+eHNWvWPDGI/Prrr9iyZQteeeWVOrfzEYNer0d6enqjat369esHHx8fREdHS7Cylqt9+/bYs2cPFi5ciMjISEyaNIl1lQ9p7C8pVH/8iU5ENa4UlwOQ9jd4A4DLxeWSzkH1Y2Njg4SEBERERCAiIgKhoaGPratMTExEaWkpwsPDJVtTXl4eKioqGt08ER4ejsTERBQXF4u8spZNLpdjyZIl2LlzJw4ePIjBgwezrvI3RUVFNduTkXQYKImohlZXZVLz0JMplUr84x//wLZt27Br167H1lWmpqbiD3/4A1xcXCRbT3XzRGM//P/4xz/CYDDg7NmzIq7q6TFx4kScOnUKlZWVrKv8DU/IaRoMlERUo5WyaX4kZGWk49atW00yF9VPUFAQTp48idLSUnh7e+P777+v9ZyzZ89K/qGs0WjQrVu3Rp9m4uzsDCsrq5oQYY6q6yqff/55jBkzBitWrDDrusq0tDRYW1uzAVBiDJREVMPJxkriG973NxieGjAaHTt2hJ2dHYYOHYoZM2bg008/xeHDh1FYWGjWH37NqV+/fkhNTYWnpyf8/Pywdu1ao38LjUaD/v37S7oGoZtPKxQKeHh4mHWgBH6vq4yMjMSCBQsQGBhotnWV1d+3rNuWlrK5F0BELYeVhRKOHSxxpUT8c5+rdbOxxP60FOTk5CA7Oxs5OTk4ceIEYmJioNVqAQBt27aFu7s7evfubfSnk5MTPxQkZmNjgwMHDmDBggWYPXs2zpw5g+joaFhaWqKoqAhdunSRbG6DwYC0tDS89957gsZxcHDAzZs3RVrV00uhUGDp0qXw8vLC1KlTMXjwYOzevdvsrtRpNBoeU9kEGCiJyIivqx22nroiydZBCrkMw107oU8fFfr06WP0mE6nw6VLl4yCZkZGBuLj41Fefr+Jp02bNnB1da0VNJ2dnfHMM8+Ivl5zpVQqsXLlSnh5eSE8PBzZ2dk15x9Lue1KQUEBbt++Lfi2OreGMTZx4kS4urrC398fAwcOxLZt2zBq1KjmXlaTuHPnDvLy8rBw4cLmXorJY6AkIiNTfBzx5cnLkoytrzIgZJBjnY8plUq4uLjAxcUF48ePr/m6wWDA1atXjYJmdnY2Dhw4gNu3bxu99uGg6erqijZt2kjyXsxBcHAw3N3dERAQAG9vb8lLEdg8IR2VSoWUlBRMnjwZY8aMwbJlyzBv3jyTD9/p6ekA+D3VFBgoiciISydrDHG2xY8Xi0W9SqmQy/B8Dxs421k36HUymQyOjo5wdHQ0uqpiMBhw8+bNWkFz06ZNuH79es1ru3fvXitouru7o23btqK9N1PWv39/pKamIjAwEEeOHMGhQ4cwY8YMSYJIWloa7OzsBJ9motVqoVAoRFqV6Wjfvj327t2LDz/8EPPnz8eZM2cQExODZ599trmXJhmNRgMLCwu4u7s391JMnszA6nciesjVkgqMWJuMShG397FQynH4vaHo2sFStDEfpbS0tFbQzMnJMdoOp0uXLujdu3etsGlrayv5+p5GOp0O9vb2KCoqQkhICKKjo0W/+jtu3Djcu3dP8FY3rq6uGD16ND755BNxFmaCdu7ciWnTpqFHjx7YvXs3evTo0dxLkkRYWBiysrKQkpLS3EsxeQyURFSn2JQCzN+VIdp4URP7InBg3be7m0p5eTlyc3NrBc38/Hzo9XoAQMeOHetsCLK3tzf524NPMm3aNPzwww+4fv063NzcoFar0a1bN9HGd3BwQGhoKJYvX97oMe7evYu2bdsiJiYGYWFhoq3NFGVlZcHf3x/FxcWIjY2Fn59fcy/piaqqqnDlyhVkZGSguLgYZWVlSExMxLhx49C6dWt06tQJHh4eNf+/muvpSc2Bt7yJqE5BAx1x624lVn13QfBYc/1cmz1MAoCVlRW8vLxqHcFWWVmJ/Px8o6D5448/YvPmzaisrATAznPgfh1afHw8jh8/jj//+c/w9vZGfHw8fH19BY998+ZNFBYWCj4eLz09HQaDQfLtjUyBSqXC6dOnMWXKFIwePRrLly/H3LlzW9QvTjqdDgcOHEBCQgLOnTuHjIwMlJWV1XpeQkKC0d87dOiAPn36ICMjA8OHD4fBYGhR78sU8QolET1WbEoB/rYnC7oqQ4NqKhVyGZRyGRaPV7WIMNkYer0ely5dqnVFMzs72yw7zzUaDby8vLBv3z74+PggMDAQycnJWL16Nd555x1BH9iJiYl46aWXkJeXB2dn50aPM3fuXGzevBnXrl2T7LxxU6PX67Fo0SIsX74ckyZNQkxMDKysrJp1TT/99BNiYmKwefPmmiviAwYMgIeHBzw8PNC3b1906tQJSuXv18Xu3buHwsJCnDt3DufOnUNycjIOHz4M4P6G9+Hh4Zg2bRo6d+7cXG/LpDFQEtETXS2pQKQ6A8fzb0Ehlz02WFY/PsTZFssC+jZJzWRTMxgM+M9//lNn0CwpKQFgup3nAwYMgIODA7799lvodDq8//77WLNmDUJDQ7F+/foGvbfySh0uF5dDq6vCN1u/QvSaj1Fa9HOjr/hWVlbCwcEBU6dOxerVqxs1hjnbsWMHwsLCmrWusri4GLNnz8aWLVvQrl07hISEIDw8vFFd2hs2bMAbb7yBgwcP4uuvv8b27dtx7949zJo1C4sXL4alpen9bGpODJREVG95P5fhm1MFOHrhJgqKK/DgDw8ZAEcbS/j2skPIIMcGd3ObAoPBgKKiojqDpql0nq9fvx4zZ85EQUFBzSbn//73v/Haa6/B3d0darUajo6PviJd8z2UexMFJcbfQzAY0M3GCr6udpji4wiXTg37HoqLi0NQUBBycnLg5ubWiHdHmZmZ8Pf3R0lJCeLi4jBy5Mgmm3vnzp2YOXMmtFotVqxYgdDQUEGhb+bMmUhOTkZWVhaA+81669atw+LFi9G1a1ds3LgRQ4cOFWv5Zo+Bkoga5cGrS62UcjjZWMHKgmXZj1Ldef5w0Kyr8/zhWs2W1Hl+584dODg4IDg4GOvXr6/5ukajQUBAAMrLy7F9+3YMGzbM6HVSX+XWarUYMGAAbGxskJSU1Ni3RwBu376N4OBgHDp0qEnqKu/du4fw8HBs3boV/v7+WLdunSi3pQcNGgQXFxds3brV6Ou5ubkIDw/HiRMnsGDBAnz88cesrxQBAyURUTOqT+e5ra1tnUGzuTrP161bhzfffBNHjx41Co63bt2qqatcs2YN3n77bchkMsF1uB+NVyHoCXW4ixcvxpIlS5Camop+/fo19q3Rbx6sqwwMDMSmTZskqavU6XSYPHky1Go1Nm/ejClTpojyPa3X62FtbY2lS5di9uzZtR6vqqrCypUrMX/+fERERGDlypUMlQIxUBIRtUBarRZ5eXm1gmZubm6tzvOHg6bUnedVVVUYOnQobty4gfT0dKPbkjqdDvPmzcPatWsxdepU9J8yH/979KLgOef49cJbvi51PpaVlQVPT0/MmzcPS5cuFTwX/a66rrJnz57YvXs3unfvLtrYOp0OU6ZMwa5du7B9+3b4+/uLNnZ2djZUKhW+//77x+5C8Nlnn+Gdd97B3LlzERUVxVApAAMlEdFT5FGd5zk5Obh79y4AoHXr1nBzc6sVNMXsPL9w4QL69euHUaNGIT4+vlZH9TfffIO3125D25EzRJkPqHsv08LCQvj6+kKpVCItLQ2tW7cWbT66LzMzExMmTEBpaSliY2NFq6ucP38+Vq9ejfj4eAQEBIgyZrWvv/4aoaGhuH37Ntq3b//Y53766ad499138a9//QtvvPGGqOswJwyUREQmoCGd5w8HzcZ2nickJCAgIABjx45FXFycUVi9WlKBP60+ikq9ePv/PXza0rVr1+Dr64tff/0VSUlJJnvaS0tQUlKCyZMn49ChQ1ixYgXmzJkj6N81NTUVPj4+WLJkCSIjI0Vc6X0RERFQq9W4eLF+V8enT5+OuLg4ZGVloWvXrqKvxxwwUBIRmbCGdJ7XtXH7kzrP9+/fXxMqv/rqq5rnh246Jdl58FvDfZCfn4+xY8eioqICycnJDJNNQK/X44MPPsCKFSsQFBSEjRs3NqquUqvVwtvbGwqFAqdPn5Zkv9bhw4fjueeew86dO+v1/NLSUqhUKnh6emLv3r289d0IDJRERGaqvp3ndQXNjh071jxn3759CA4ORvv27bF+/Xq4DBiCkZ8ck2zdU9pfxNqP3oe9vT0SExPRs2dPyeai2rZv346wsDC4uLhArVY3uK7y888/x6xZs5CSktKo/SWfxGAwoEOHDpgzZw4WLlxY79ft2bMHEyZMwL59+zB27FjR12XqGCiJiMhIdef5w0Hz4c7zBwOmjY0NNm7ciOTkZAx+aw1+tu4FvRSfLlV6lKUlYFpfSyxZsqTZT3QxVxkZGfD390dpaSni4uIwYsSIer3OYDCgT58+UKlUiI+Pl2Rtly5dQo8ePbB//36MGTOmQa/19vZG586dsXfvXknWZsoYKImIqF6qO88fDpoPdp63bt0aNtM+g/I56Y6362Qlx6kPRks2PtVPSUkJgoODcfjwYURFRSEiIuKJt4pPnDiBF198EYcOHap3CG2oXbt24eWXX8a1a9cavJ9ldHQ0ZsyYgStXrsDBwUGS9ZkqBkoiIhKkuvM8JycHZ7POY1OpOyBhDZoMQObfR3Ej/RZAr9dj4cKFiIqKQnBwMDZu3PjY021eeeUVHDt2DHl5eZJtbfXBBx9g06ZNNTXCDVFWVobOnTvj/fffx6JFiyRYnemSbqMyIiIyCwqFAs7Ozhg3bhwmTn1d0jAJAAYAl4vLJZ2D6kehUGDFihWIi4vDt99+i+effx6XLl165POTkpIQEBAg6T6pGo2m0bWZ1tbW8PPz42lLjcBASUREotHqqkxqHqqfSZMm4eTJk7hz5w68vb1x+PDhWs+5ffs2Ll++LEkjzoOEBEoA8PT0xNmzZ8EbuA3DQElERKJppWyaj5V333qzZjPqY8eOoaioqEnmpUfz8PBAamoqvL29MWrUKKxevdoolJ09exYAJA2UN27cwPXr1+Hl5dXoMTw9PVFSUoKrV6+KuDLTxwIUIiISjZONFWS4f1taOgY894wOiYmJ+OKLLx7ZeV79Z5cuXbivYBPp0KEDEhISEBkZiTlz5iAtLQ0bNmyApaUlcnNzIZfL0atXL8nm12g0AISFVpVKBQA4f/48HB0ff4Y8/Y6BkoiIRGNloYRjB0tcKamQbI5uNlb4duf9LWfq6jw/efIkvvzyy5rOc2tr6zqDppOTExQKhWTrNFcKhQJRUVHw8vLCq6++iuzsbKjVauj1eiiVSiiV0kUPjUaDdu3aCTpz3MLCAsD9s8ap/hgoiYhIVL6udth66oqop+RUU8hl8O1lV/P3Vq1aQaVS1VxVqvZg53l10MzKysKOHTuMzjx3dXU1Cppin3luzgIDA+Hu7g5/f394e3tj8uTJks9ZXT/JK9JNj4GSiIhENcXHEV+evCzJ2PoqA0IGPfk2ZHXneXX3ebXqM88f3kszMTFRsjPPzZmHhwdSUlIQHByMzz//HHK5HAaDeOe7PywtLQ0TJkwQNAabcRqHgZKIiETl0skaQ5xtJTvL29nOutFjyGQydO3aFV27doWfn1/N16vPPH84aMbExODatWs1r23smefmzMbGBgkJCZg4cSL27t2Lv/zlL9iyZctj96tsjF9++QUXL14U3PRT/e/94PGi9GTc2JyIiER3taQCI9Ymo1LE7X0slHIcfm8ounYQN4g8SWlpKc6fP28UNHNycoz2W6zPmefmLjc3F25ubrCwsIC7uzvUajWcnJxEGz85ORnDhg1DZmZmrRKIhoiOjsbMmTNRVlbGK9INwEBJRESSiE0pwPxdGaKNFzWxLwIHtpyu24qKCuTm5hoFzSedeW7Oned6vR7t2rXD66+/DrVajbKyMsTHx2P48OGijL927VpERkairKxMUOPPzJkzcezYMWRmZoqyLnPBW95ERCSJoIGOuHW3Equ+uyB4rLl+ri0qTAKApaUlPD09a91iZed53RQKBTw9PfHTTz8hNTUVQUFB8PPzw8qVKzFr1izBAVuj0cDDw0NQmDQYDPjhhx8E7WNprhgoiYhIMm/5usD2WQv8bU8WdFWGBtVUKuQyKOUyLB6vanFh8nHYef5oQUFBmDVrFrRaLQ4cOIDIyEjMnj0bZ86cQXR0dIPqKssrdbhcXA6trgqtlHKkncvCkMH/I2h9qampyMjIQFRUlKBxzBFveRMRkeSullQgUp2B4/m3oJDLHhssqx8f4myLZQF9m7xmsqk9qvM8Ozvb5DrPS0tLYW9vj0WLFmHBggUAgNjYWLz66qtwc3ODWq1Gt27dHvn6vJ/L8M2pAhzNvYmCkgqjDfQNBgOee0YP/4HOmOLjCJdODW/emj59Or777jtcvHjRZK8US4WBkoiImkxNILhwEwXFxoFABsDRxhK+vewQMshRUDe3KXhU53lOTs5T3XkeFhaGpKQknD9/Hq1btwYApKenw9/fH3fv3kV8fDx8fX2NXtMUv5AUFRWhe/fumDdvHj788MPGv0EzxUBJRETN4uFblk42VrCyYCVWfTzNnefZ2dno378/5s2bh6VLl9Z8vbi4GIGBgUhKSsKqVavw7rvvQiaTITalQFDJxEfjVQiqR8nE5MmTkZiYiJycHNjZ2T3x+WSMgZKIiMhE1NV5npOTg7y8vBbVeb548WIsWbIEKSkp6N+/f83XdTodFixYgFWrViEkJAReoZH436MXBc83x68X3vJ1eeTje/fuxfjx47F161aEhIQIns8cMVASERGZOK1Wi/z8/Fo1mrm5uc3Sea7VajFgwAAoFAocO3as1u35bdu24c0136DtiBmizfmobacKCwvh4+MDDw8P7N+/3+y2cxILAyUREZGZqqvzvPrPx3Weu7u7w9nZGa1atWr03Onp6Rg6dChUKhUOHjwIa+vfa2avllTgT2uOQqszACIFvLo2xi8sLISvry8qKytx4sQJODg4iDKXOWKgJCIiIiP17Tx3dnau2dqoMZ3nKSkpGDFiBPr06WMUKkM3nZLs6M6t4T4A7h+xOGzYMPz3v/9FUlISevToIdpc5oiBkoiIiOpFis7z06dPY+TIkbC3t0dMTAxse/TByE+OSfYeDr/3R+ScSsJf//pXyOVyJCUloWfPnpLNZy4YKImIiEgwIZ3nRUVFCAsLQ2pqKoZFfIErzzhCL0E6UcgAuzu5+L8vIjB69GhER0fzNrdIGCiJiIhIMvXtPHdzc4NOp8PVfuFQPtdZsvXof7mBZYNbISQkhA04ImKgJCIioiZXZ+f5hZ9QOvJDSYOeDEDm30dxz1ORMVASERFRi5B17ReM/ewHyefZ//aLUNm3k3wecyJv7gUQERERAYBWV2VS85gTBkoiIiJqEVopmyaWNNU85oT/RYmIiKhFcLKxgtRtMrLf5iFxMVASERFRi2BloYTjAyfZSMHRxpINORJgoCQiIqIWw9fVDgq5NNcpFXIZfHvZSTK2uWOgJCIiohZjio+jqEcuPkhfZUDIIEdJxjZ3DJRERETUYrh0ssYQZ1vRr1Iq5DIMcbaFs521qOPSfQyURERE1KIsC+gLpciBUimXYVlAX1HHpN8xUBIREVGL0rWDJT4arxJ1zMXjVegqccOPOWOgJCIiohYnaKAj5vj1EmWsuX6uCBzI2kkp8ehFIiIiarFiUwrwtz1Z0FUZGtSso5DLoJTLsHi8imGyCTBQEhERUYt2taQCkeoMHM+/BYVc9thgWf34EGdbLAvoy9vcTYSBkoiIiJ4KeT+X4ZtTBTh64SYKiivwYICR4f6m5b697BAyyJHd3E2MgZKIiIieOuWVOlwuLodWV4VWSjmcbKx4Ak4zYqAkIiIiIkHY5U1EREREgjBQEhEREZEgDJREREREJAgDJREREREJwkBJRERERIIwUBIRERGRIAyURERERCQIAyURERERCcJASURERESCMFASERERkSAMlEREREQkCAMlEREREQnCQElEREREgjBQEhEREZEgDJREREREJAgDJREREREJwkBJRERERIIwUBIRERGRIAyURERERCQIAyURERERCcJASURERESCMFASERERkSAMlEREREQkCAMlEREREQnCQElEREREgjBQEhEREZEgDJREREREJAgDJREREREJwkBJRERERIIwUBIRERGRIAyURERERCQIAyURERERCcJASURERESCMFASERERkSAMlEREREQkCAMlEREREQny/7+wMfoeEm5QAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "import scipy as sp\n",
    "n = 3\n",
    "ex = np.ones(n);\n",
    "lp1 = sp.sparse.spdiags(np.vstack((ex,  -2*ex, ex)), [-1, 0, 1], n, n, 'csr'); \n",
    "e = sp.sparse.eye(n)\n",
    "A = sp.sparse.kron(sp.sparse.kron(lp1, e), e) + sp.sparse.kron(sp.sparse.kron(e, lp1), e) + sp.sparse.kron(sp.sparse.kron(e, e), lp1)\n",
    "A = spsp.csc_matrix(A)\n",
    "G = nx.Graph(A)\n",
    "nx.draw(G, pos=nx.spectral_layout(G))#, node_size=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## What is fill-in?\n",
    "\n",
    "- The fill-in of a matrix are those entries which change from an initial zero to a nonzero value during the execution of an algorithm.\n",
    "\n",
    "- The fill-in is different for different permutations. So, before factorization we need to find reordering which produces the smallest fill-in.\n",
    "\n",
    "**Example**\n",
    "\n",
    "$$A = \\begin{bmatrix} * & * & * & * & *\\\\ * & * & 0 & 0 & 0 \\\\ * & 0  & * & 0 & 0 \\\\ * & 0 & 0& * & 0 \\\\ * & 0 & 0& 0 & * \\end{bmatrix} $$\n",
    "\n",
    "If we eliminate elements from the top to the bottom, then we will obtain dense matrix.\n",
    "However, we could maintain sparsity if elimination was done from the bottom to the top."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Example of dense factors after LU \n",
    "\n",
    "Given matrix $A=A^*>0$ we calculate its Cholesky decomposition $A = LL^*$.\n",
    "\n",
    "Factor $L$ can be dense even if $A$ is sparse:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix} * & * & * & * \\\\ * & * &  &  \\\\ * &  & * &  \\\\ * &  &  & * \\end{bmatrix} = \n",
    "\\begin{bmatrix} * &  &  &  \\\\ * & * &  &  \\\\ * & * & * &  \\\\ * & * & * & * \\end{bmatrix}\n",
    "\\begin{bmatrix} * & * & * & * \\\\  & * & * & * \\\\  &  & * & * \\\\  &  &  & * \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "How to make factors sparse, i.e. to minimize the **fill-in**?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Why permutations can reduce fill-in? Here the example...\n",
    "\n",
    "We need to find a permutation of indices so that factors are sparse, i.e. we build Cholesky factorisation of $PAP^\\top$, where $P$ is a permutation matrix.\n",
    "\n",
    "For the example from the previous slide\n",
    "\n",
    "$$\n",
    "P \\begin{bmatrix} * & * & * & * \\\\ * & * &  &  \\\\ * &  & * &  \\\\ * &  &  & * \\end{bmatrix} P^\\top = \n",
    "\\begin{bmatrix} * &  &  & *  \\\\  & * &  & * \\\\  &  & * & * \\\\ * & * & * & * \\end{bmatrix} = \n",
    "\\begin{bmatrix} * &  &  &  \\\\  & * &  &  \\\\  &  & * &  \\\\ * & * & * & * \\end{bmatrix}\n",
    "\\begin{bmatrix} * &  &  & *  \\\\  & * &  & * \\\\  &  & * & * \\\\  & &  & * \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "where\n",
    "\n",
    "$$\n",
    "P = \\begin{bmatrix}  &  &  & 1 \\\\  &  & 1 &  \\\\  & 1 &  &  \\\\ 1 &  &  &  \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "- Arrowhead form of the matrix gives sparse factors in LU decomposition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original matrix\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L factor\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "U factor\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Column permutation: [0 1 2 3]\n",
      "Row permutation: [1 3 2 0]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy.sparse as spsp\n",
    "import scipy.sparse.linalg as spsplin\n",
    "import scipy.linalg as splin\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "A = spsp.coo_matrix((np.random.randn(10), ([0, 0, 0, 0, 1, 1, 2, 2, 3, 3], \n",
    "                                           [0, 1, 2, 3, 0, 1, 0, 2, 0, 3])))\n",
    "print(\"Original matrix\")\n",
    "plt.spy(A)\n",
    "plt.show()\n",
    "lu = spsplin.splu(A.tocsc(), permc_spec=\"NATURAL\")\n",
    "print(\"L factor\")\n",
    "plt.spy(lu.L)\n",
    "plt.show()\n",
    "print(\"U factor\")\n",
    "plt.spy(lu.U)\n",
    "plt.show()\n",
    "print(\"Column permutation:\", lu.perm_c)\n",
    "print(\"Row permutation:\", lu.perm_r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Block version of appropriate sparsity pattern (arrowhead structure)\n",
    "\n",
    "$$\n",
    "PAP^\\top = \\begin{bmatrix} A_{11} &  & A_{13} \\\\  & A_{22} & A_{23} \\\\ A_{31} & A_{32} & A_{33}\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "then\n",
    "\n",
    "$$\n",
    "PAP^\\top = \\begin{bmatrix} A_{11} & 0 & 0 \\\\ 0 & A_{22} & 0 \\\\ A_{31} & A_{32} & A_{33} - A_{31}A_{11}^{-1} A_{13} - A_{32}A_{22}^{-1}A_{23} \\end{bmatrix} \\begin{bmatrix}  I & 0 & A_{11}^{-1}A_{13} \\\\ 0 & I & A_{22}^{-1}A_{23} \\\\ 0 & 0 & I\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "- Block $ A_{33} - A_{31}A_{11}^{-1} A_{13} - A_{32}A_{22}^{-1}A_{23}$ is Schur complement for block diagonal matrix $\\begin{bmatrix} A_{11} & 0 \\\\ 0 & A_{22} \\end{bmatrix}$\n",
    "- We reduce problem to solving smaller linear systems with $A_{11}$ and $A_{22}$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## What we can do to minimize fill-in?\n",
    "\n",
    "- Reordering the rows and the columns of the sparse matrix in order to reduce the number of nonzeros in $L$ and $U$ factors is called **fill-in** minimization.\n",
    "\n",
    "- Unfortunately, [this paper](http://i.stanford.edu/pub/cstr/reports/cs/tr/75/531/CS-TR-75-531.pdf) by Rose and Tarjan in 1975 proves that fill-in minimization problem is **NP-complete**.\n",
    "\n",
    "- But, many heuristics exist:\n",
    "\n",
    "    - **Markowitz pivoting** - order by the product of nonzeros in column and row and stability constraint\n",
    "    - **Minimum degree ordering** - order by the degree of the vertex\n",
    "    - **Cuthill–McKee algorithm** (and reverse Cuthill-McKee) - reorder to minimize the bandwidth (does not exploit graph representation).\n",
    "    - **Nested dissection**: split the graph into two with minimal number of vertices on the separator (set of vertices removed after we separate the graph into two distinct connected graphs). <br> Complexity of the algorithm depends on the size of the graph separator. For 1D Laplacian separator contains only 1 vertex, in 2D - $\\sqrt{N}$ vertices."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### How can we find permutation?\n",
    "\n",
    "- Key idea comes from graph theory\n",
    "- Sparse matrix can be treated as an **adjacency matrix** of a certain graph:\n",
    "the vertices $(i, j)$ are connected, if the corresponding matrix element is non-zero.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Example\n",
    "\n",
    "Graphs of $\\begin{bmatrix} * & * & * & * \\\\ * & * &  &  \\\\ * &  & * &  \\\\ * &  &  & * \\end{bmatrix}$ and $\\begin{bmatrix} * &  &  & *  \\\\  & * &  & * \\\\  &  & * & * \\\\ * & * & * & * \\end{bmatrix}$ have the following form:\n",
    "\n",
    "<img src=\"graph_dense.png\" width=300 align=\"center\"> and <img src=\"graph_sparse.png\" width=300 align=\"center\">\n",
    "\n",
    "* Why the second ordering is better than the first one?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Fill-in upper bound minimization: Markowitz pivoting\n",
    "\n",
    "- General purpose approach to ordering the elements of sparse matrix that will be eliminated\n",
    "- The Markowitz merit for every non-zero element with indices $(i, j)$ is computed as $(r_i - 1)(c_j - 1)$, where $r_i$ is number of nonzeros elements in the $i$-th row and $c_j$ is a number of non-zero elements in the $j$-th column\n",
    "- This value is an upper abound on the fill-in after eliminating the $(i, j)$ element. **Why?**\n",
    "- We can order elements with respect to these values, select the one with minimum value, eliminate it and update matrix. What about stability?\n",
    "- Then re-compute these values and repeat the procedure\n",
    "- This method gives us the permutations of rows and columns and sparse factors\n",
    "- Main drawback is efficient supporting number of nnz in every row and column after matrix update without complete re-calculating\n",
    "- More details can be found in book [Direct Methods for Sparse Matrices by I. S. Duff, A. M. Erisman, and J. K. Reid](https://oxford.universitypressscholarship.com/view/10.1093/acprof:oso/9780198508380.001.0001/acprof-9780198508380)\n",
    "- De facto standard approach in solving Linear programming (LP) problems and their MILP modifications"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## What if consider only neighbours? We get minimal degree ordering!\n",
    "\n",
    "- The idea is to eliminate rows and/or columns with fewer non-zeros, update fill-in and then repeat. How it relates to Markowitz pivoting?\n",
    "\n",
    "- Efficient implementation is an issue (adding/removing elements).\n",
    "\n",
    "- Current champion is \"approximate minimal degree\" by Amestoy, Davis, Duff.\n",
    "\n",
    "- It is **suboptimal** even for 2D PDE problems\n",
    "\n",
    "- SciPy sparse package [uses](https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.sparse.linalg.splu.html) minimal ordering approach for different matrices ($A^{\\top}A$, $A + A^{\\top}$) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## But in these methods we ignore the knowledge of good structure for sparse LU! Let's exploit it explicitly in the method!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## How to formalize reduction to block arrowhead form?\n",
    "\n",
    "**Definition.** A **separator** in a graph $G$ is a set $S$ of vertices whose removal leaves at\n",
    "least two connected components.\n",
    "\n",
    "Separator $S$ gives the following ordering for an $N$-vertex graph $G$:\n",
    "- Find a separator $S$, whose removal leaves connected components\n",
    "$T_1$, $T_2$, $\\ldots$, $T_k$\n",
    "- Number the vertices of $S$ from $N − |S| + 1$ to $N$\n",
    "- Recursively, number the vertices of each component: $T_1$ from $1$ to\n",
    "$|T_1|$, $T_2$ from $|T_1| + 1$ to $|T_1| + |T_2|$, etc\n",
    "- If a component is small enough, enumeration in this component is arbitrarily"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Separator and block arrowhead structure: example\n",
    "\n",
    "Separator for the 2D Laplacian matrix \n",
    "\n",
    "$$\n",
    " A_{2D} = I \\otimes A_{1D} + A_{1D} \\otimes I, \\quad A_{1D} = \\mathrm{tridiag}(-1, 2, -1),\n",
    "$$\n",
    "\n",
    "is as follows\n",
    "\n",
    "<img src='separator.png' width=300> </img>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Once we have enumerated first indices in $\\alpha$, then in $\\beta$ and separators indices in $\\sigma$ we get the following matrix\n",
    "\n",
    "$$\n",
    "PAP^\\top = \\begin{bmatrix} A_{\\alpha\\alpha} &  & A_{\\alpha\\sigma} \\\\  & A_{\\beta\\beta} & A_{\\beta\\sigma} \\\\ A_{\\sigma\\alpha} & A_{\\sigma\\beta} & A_{\\sigma\\sigma}\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "which has arrowhrad structure.\n",
    "\n",
    "- Thus, the problem of finding **permutation** was reduced to the problem of finding **graph separator**!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The method of recursive reduction to block arrowhead structure – Nested dissection\n",
    "\n",
    "- For blocks $A_{\\alpha\\alpha}$, $A_{\\beta\\beta}$ we continue splitting recursively.\n",
    "\n",
    "- When the recursion is done, we need to eliminate blocks $A_{\\sigma\\alpha}$ and $A_{\\sigma\\beta}$. \n",
    "\n",
    "- This makes block in the position of $A_{\\sigma\\sigma}\\in\\mathbb{R}^{n\\times n}$ dense.\n",
    "\n",
    "Calculation of Cholesky of this block costs $\\mathcal{O}(n^3) = \\mathcal{O}(N^{3/2})$, where $N = n^2$ is the total number of nodes.\n",
    "\n",
    "So, the complexity is $\\mathcal{O}(N^{3/2})$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Packages for nested dissection\n",
    "\n",
    "- MUltifrontal Massively Parallel sparse direct Solver ([MUMPS](http://mumps.enseeiht.fr/))\n",
    "- [Pardiso](https://www.pardiso-project.org/)\n",
    "- [Umfpack as part of SuiteSparse](http://faculty.cse.tamu.edu/davis/suitesparse.html)\n",
    "\n",
    "All of them have interfaces for C/C++, Fortran and Matlab "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Nested dissection summary\n",
    "\n",
    "- Enumeration: find a separator.\n",
    "- Divide-and-conquer paradigm\n",
    "- Recursively process two subsets of vertices after separation\n",
    "- In theory, nested dissection gives optimal complexity. \n",
    "- In practice, it beats others only for very large problems."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Separators in practice\n",
    "\n",
    "- Computing separators is not a **trivial task**.\n",
    "\n",
    "- Graph partitioning heuristics has been an active research area for many years, often motivated by partitioning for parallel computation.\n",
    "\n",
    "Existing approaches:\n",
    "\n",
    "- Spectral partitioning (uses eigenvectors of Laplacian matrix of graph) - more details below\n",
    "- Geometric partitioning (for meshes with specified vertex coordinates) [review and analysis](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.31.4886&rep=rep1&type=pdf)\n",
    "- Iterative-swapping ([(Kernighan-Lin, 1970)](http://xilinx.asia/_hdl/4/eda.ee.ucla.edu/EE201A-04Spring/kl.pdf), [(Fiduccia-Matheysses, 1982](https://dl.acm.org/citation.cfm?id=809204))\n",
    "- Breadth-first search [(Lipton, Tarjan 1979)](http://www.cs.princeton.edu/courses/archive/fall06/cos528/handouts/sepplanar.pdf)\n",
    "- Multilevel recursive bisection (heuristic, currently most practical) ([review](https://people.csail.mit.edu/jshun/6886-s18/lectures/lecture13-1.pdf) and [paper](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.499.4130&rep=rep1&type=pdf)). Package for such kind of partitioning is called METIS, written in C, and available [here](http://glaros.dtc.umn.edu/gkhome/views/metis)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## One of the ways to construct separators – spectral graph partitioning\n",
    "\n",
    "- The idea of spectral partitioning goes back to Miroslav Fiedler, who studied connectivity of graphs ([paper](https://dml.cz/bitstream/handle/10338.dmlcz/101168/CzechMathJ_23-1973-2_11.pdf)).\n",
    "\n",
    "- We need to split the vertices into two sets.\n",
    "\n",
    "- Consider +1/-1 labeling of vertices and **the cost**\n",
    "\n",
    "$$E_c(x) = \\sum_{j} \\sum_{i \\in N(j)} (x_i - x_j)^2, \\quad N(j) \\text{ denotes set of neighbours of a node } j. $$\n",
    "\n",
    "- We need a balanced partition, thus \n",
    "\n",
    "$$\\sum_i x_i =  0 \\quad \\Longleftrightarrow \\quad x^\\top e = 0, \\quad e = \\begin{bmatrix}1 & \\dots & 1\\end{bmatrix}^\\top,$$\n",
    "\n",
    "and since we have +1/-1 labels, we have\n",
    "\n",
    "$$\\sum_i x^2_i = n \\quad \\Longleftrightarrow \\quad \\|x\\|_2^2 = n.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Graph Laplacian\n",
    "\n",
    "Cost $E_c$ can be written as (check why)\n",
    "\n",
    "$$E_c = (Lx, x)$$\n",
    "\n",
    "where $L$ is the **graph Laplacian**, which is defined as a symmetric matrix with\n",
    "\n",
    "$$L_{ii} = \\mbox{degree of node $i$},$$\n",
    "\n",
    "$$L_{ij} = -1, \\quad \\mbox{if $i \\ne j$  and there is an edge},$$\n",
    "\n",
    "and $0$ otherwise.\n",
    "\n",
    "- Rows of $L$ sum to zero, thus there is an eigenvalue $0$ and gives trivial eigenvector of all ones.\n",
    "- Eigenvalues are non-negative (why?)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Partitioning as an optimization problem\n",
    "\n",
    "- Minimization of $E_c$ with the mentioned constraints leads to a partitioning that tries to minimize number of edges in a separator, while keeping the partition balanced. \n",
    "\n",
    "- We now relax the integer quadratic programming to the continuous quadratic programming\n",
    "\n",
    "$$E_c(x) = (Lx, x)\\to \\min_{\\substack{x^\\top e =0, \\\\ \\|x\\|_2^2 = n}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## From Fiedler vector to separator\n",
    "\n",
    "- The solution to the minimization problem is given by the eigenvector (called Fiedler vector) corresponding  to the second smallest eigenvalue of the graph Laplacian. Indeed,\n",
    "\n",
    "$$\n",
    "    \\min_{\\substack{x^\\top e =0, \\\\ \\|x\\|_2^2 = n}} (Lx, x) = n \\cdot \\min_{{x^\\top e =0}} \\frac{(Lx, x)}{(x, x)} = n \\cdot \\min_{{x^\\top e =0}} R(x), \\quad R(x) \\text{ is the Rayleigh quotient}\n",
    "$$\n",
    "\n",
    "- Since $e$ is the eigenvector, corresponding to the smallest eigenvalue, on the space $x^\\top e =0$ we get the second minimal eigevalue.\n",
    "\n",
    "- The sign $x_i$ indicates the partitioning.\n",
    "\n",
    "- In computations, we need to find out, how to find this second minimal eigenvalue –– we at least know about power method, but it finds the largest. We will discuss iterative methods for eigenvalue problems later in our course.\n",
    "\n",
    "- This is the main goal of the iterative methods for large-scale linear problems, and can be achieved via few matrix-by-vector products."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of vertices = 34\n",
      "Number of edges = 78\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import networkx as nx\n",
    "kn = nx.read_gml('karate.gml')\n",
    "print(\"Number of vertices = {}\".format(kn.number_of_nodes()))\n",
    "print(\"Number of edges = {}\".format(kn.number_of_edges()))\n",
    "nx.draw_networkx(kn, node_color=\"red\") #Draw the graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<class 'networkx.utils.decorators.argmap'> compilation 21:4: FutureWarning: laplacian_matrix will return a scipy.sparse array instead of a matrix in Networkx 3.0.\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAGzCAYAAADAAAv4AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjYuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8o6BhiAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAW90lEQVR4nO3dW4xeVfk/8OftgemRgqUI2FKgCISY1GgUPFTJj2iJNdFqCjUkdOiNVFuUxKrxokVuGhpIJIAoIVY81AsKRMDQ0PKHSAIGEowgatAeMHBh6Am1hx/Qvv+L2vXrMFN893RW99p7Pp+kCX1nv3s/e+3Z8+2s/a6HTrfb7QYARMSYugsAoBxCAYBEKACQCAUAEqEAQCIUAEiEAgCJUAAgEQoAJEKBxti+fXt0Op245ZZbhvX+J598MjqdTjz55JMjW9g7dDqduPHGG7Ps+8gY/PSnP82yfxAKDLJt27ZYvnx5XHDBBTFp0qSYNGlSXHzxxfH1r389XnjhhbrLAzIaV3cBlOWRRx6Jq666KsaNGxdXX311zJ07N8aMGRN/+ctf4oEHHoi77rortm3bFrNnz6671FFp9uzZsX///hg/fnzdpdBSQoFky5YtsXjx4pg9e3Y8/vjjceaZZw74+s033xw//OEPY8yYd/8Fc+/evTF58uScpY5anU4nJkyYUHcZtJjpI5K1a9fG3r17Y926dYMCISJi3Lhxcf3118esWbPSa/39/TFlypTYsmVLfO5zn4upU6fG1VdfHRERTz31VCxatCjOPvvs6Ovri1mzZsUNN9wQ+/fvH7DfI/vYunVrzJ8/PyZPnhxnnXVW3HTTTXGsJr533313zJkzJ/r6+uIjH/lIPPfcc8M655w1HvHKK6/E1772tbjwwgtj4sSJMX369Fi0aFFs37590LZ79uyJG264Ic4555zo6+uLmTNnxjXXXBM7duyIiKGfKbzwwgvR398f5513XkyYMCHOOOOMWLp0aezcuXPAvm+88cbodDrxt7/9Lfr7++OUU06JadOmxbXXXhv79u0b1vjRPn5TIHnkkUfi/PPPj0suuaTS+95+++2YP39+fPKTn4xbbrklJk2aFBER9913X+zbty+WLVsW06dPj2effTZuv/32ePXVV+O+++4bsI+DBw/GFVdcEZdeemmsXbs2Nm7cGKtXr4633347brrppgHbrl+/Pv71r3/FV7/61eh0OrF27dr40pe+FFu3bq08rZKrxqM999xz8fTTT8fixYtj5syZsX379rjrrrvisssuiz/96U9pvP7973/HvHnz4s9//nMsXbo0PvShD8WOHTvioYceildffTVOO+20Ife/adOm2Lp1a1x77bVxxhlnxEsvvRR33313vPTSS/G73/0uOp3OgO2vvPLKOPfcc2PNmjXx/PPPxz333BOnn3563HzzzZXGjpbqQrfbfeONN7oR0f3iF7846Gu7d+/uvv766+nPvn370teWLFnSjYjud7/73UHvO3q7I9asWdPtdDrdV155ZdA+VqxYkV47dOhQd8GCBd2TTjqp+/rrr3e73W5327Zt3YjoTp8+vbtr16607a9//etuRHQffvjhdz3HJ554ohsR3SeeeCJbjd1utxsR3dWrV7/rMZ555pluRHR/9rOfpddWrVrVjYjuAw88MGj7Q4cODRiDdevWvev+f/WrX3Ujovvb3/42vbZ69epuRHSXLl06YNuFCxd2p0+fPmgfjE6mj4iIiH/+858RETFlypRBX7vssstixowZ6c+dd945aJtly5YNem3ixInpv/fu3Rs7duyIj3/849HtduP3v//9oO2XL1+e/rvT6cTy5cvjzTffjM2bNw/Y7qqrropTTz01/X3evHkREbF169b/dponrMZjHeOtt96KnTt3xvnnnx+nnHJKPP/88+lr999/f8ydOzcWLlw4aB/v/Nf+sfZ/4MCB2LFjR1x66aUREQP2f8R111034O/z5s2LnTt3pu8BRjehQERETJ06NSIOT2G8049//OPYtGlT/OIXvxjyvePGjYuZM2cOev3vf/979Pf3x3ve856YMmVKzJgxIz796U9HRMQbb7wxYNsxY8bEeeedN+C1Cy64ICJi0Nz72WefPeDvRwJi9+7dxzq9Y8pV49H2798fq1atilmzZkVfX1+cdtppMWPGjNizZ8+AY2zZsiU+8IEPVD6HXbt2xTe+8Y1473vfGxMnTowZM2bEueeeO+Q5RIzs+NE+nikQERHTpk2LM888M/74xz8O+tqRZwzH+sHX19c36BNJBw8ejM985jOxa9eu+M53vhMXXXRRTJ48OV577bXo7++PQ4cODbvWsWPHDvl6t+L/WTZnjUdbsWJFrFu3Lr75zW/Gxz72sZg2bVp0Op1YvHjxiBzjyiuvjKeffjpWrlwZH/zgB2PKlClx6NChuOKKK4bc/0iNH+0kFEgWLFgQ99xzTzz77LPx0Y9+9Lj29eKLL8bLL78c9957b1xzzTXp9U2bNg25/aFDh2Lr1q3pX94RES+//HJERJxzzjnHVUvdNW7YsCGWLFkSt956a3rtwIEDsWfPngHbzZkzZ8hQfje7d++Oxx9/PL7//e/HqlWr0ut//etfK+0HjjB9RPLtb387Jk2aFEuXLo1//OMfg75e5V+SR/41evR7ut1u3Hbbbcd8zx133DFg2zvuuCPGjx8fl19+ec/HreJE1Th27NhBY3f77bfHwYMHB7z25S9/Of7whz/Egw8+OGgfxxr7oc4hIuIHP/jBMeuBd+M3BZL3v//9sX79+vjKV74SF154YVrR3O12Y9u2bbF+/foYM2bMkM8P3umiiy6KOXPmxLe+9a147bXX4uSTT47777//mPPWEyZMiI0bN8aSJUvikksuiUcffTR+85vfxPe+972YMWPGSJ/qCa3x85//fPz85z+PadOmxcUXXxzPPPNMbN68OaZPnz5gu5UrV8aGDRti0aJFsXTp0vjwhz8cu3btioceeih+9KMfxdy5cwft++STT45PfepTsXbt2njrrbfife97Xzz22GOxbdu24xscRi2hwABf+MIX4sUXX4xbb701HnvssfjJT34SnU4nZs+eHQsWLIjrrrtuyB9O7zR+/Ph4+OGH4/rrr481a9bEhAkTYuHChbF8+fIh3z927NjYuHFjLFu2LFauXBlTp06N1atXD5gSGWknqsbbbrstxo4dG7/85S/jwIED8YlPfCI2b94c8+fPH7DdlClT4qmnnorVq1fHgw8+GPfee2+cfvrpcfnll79rEK9fvz5WrFgRd955Z3S73fjsZz8bjz76aJx11lnDGxhGtU7X0yVq1t/fHxs2bBjyk0+laEKNMBI8UwAgEQoAJEIBgMQzBQASvykAkAgFABKhAEAiFABIhAIAiVAAIBEKACRCAYBEKACQCAUAEqEAQCIUAEiEAgCJUAAgEQoAJEIBgEQoAJAIBQASoQBAIhQASIQCAIlQACARCgAkQgGARCgAkAgFABKhAEAiFABIxlV9w2t79sfuvW8Oev3UySfF+06ZaNvj2LbKPquo+7yqblu3Eq5DCfslj9KvV6VQeG3P/vifW56M/3370KCv9Y0bE//vW5elk7JttW2r7LOKus+r6rZ1K+E6lLBf8mjC9ao0fbR775tDnkxExP++fWhA+tm22rZV9llF3edVddu6lXAdStgveTThenmmAEAiFABIhAIAiVAAIKkUCqdOPin6xg39lr5xY+LUySfZdpjbVtlnFXWfV9Vt61bCdShhv+TRhOvV6Xa73SpvKOFz7G3dtoTPsZewbd1KuA4l7Jc8Sr9elUMBgPbyTAGApPVtLkrQtHpzaNIYNG2ap0lj22ZtuQ6tbnNRgqbVm0OTxqBp7SiaNLZt1qbr0Oo2FyVoWr05NGkMmtaOoklj22Ztug6eKQCQCAUAEqEAQCIUAEha3eaiBE2rN4cmjUHT2lE0aWzbrE3XofVtLkrQtHpzaNIYNG09QZPGts3ach20uQAg8UwBgESbixMgR5fUto4BDEdb7506atXmIrNe6zUG5dRLs7T13qmrVm0uMuu1XmMAw9PWe6euWj1TACARCgAkQgGARCgAkGhzkVmv9RoDGJ623jt11arNxQlgnULz6qVZ2nrv1FGrNhcAJFY0nwBNq7dXbb5mMFpZ0ZxZ0+rtVZuvGYxmVjRn1rR6e9XmawajmY+kApAIBQASoQBAIhQASKxozqxp9faqzdcMRjMrmk+AptXbqzZfMxitrGgGIPFMAYAka5uLEuSqt0nj0KRagXpla3NRglz1NmkcmlQrUL9sbS5KkKveJo1Dk2oF6ueZAgCJUAAgEQoAJEIBgCRbm4sS5Kq3SePQpFqB+mVtc1EC6xSaVStQL20uAEg8UwAgaX2biyra2vWzSbXmYgygN61uc1FFlXNr0jg0qdZcjAH0rtVtLqqocm5NGocm1ZqLMYDeeaYAQCIUAEiEAgCJUAAgaXWbiyqqnFuTxqFJteZiDKB3rW9zUYV1Cu1lDKA32lwAkHimAEDS+jYXuaaEmjYOo53rBb1pdZuLXK0rmjYOo53rBb1rdZuLXK0rmjYOo53rBb3zTAGARCgAkAgFABKhAEDS6jYXuVpXNG0cRjvXC3rX+jYX1ikQ4XpBr7S5ACDxTAGAJGubixK2LUHT6gVGr2xtLkrYtgRNqxcY3bK1uShh2xI0rV5gdPNMAYBEKACQCAUAEqEAQJKtzUUJ25agafUCo1vWNhclbFuCptULjF7aXACQeKYAQJK1zUUJ+20SYwDNleP+rWNaPVubixL22yTGAJorx/1bV/ufbG0uSthvkxgDaK4c929d7X88UwAgEQoAJEIBgEQoAJBka3NRwn6bxBhAc+W4f+tq/5O1zUUJ+20SYwDN1ZZ1CtpcAJB4pgBAUrnNRS6mTqoxXsDRamlzkYsWD9UYL+BotbW5yEWLh2qMF3A0bS4AyEIoAJAIBQASoQBAUkQoaPFQjfECjlZrm4tcfO6+GuMFHE2bCwBGXBHTRwCUofKK5qZNW9TRZbA0bT0vYORVCoWmtVeoUm/Tzq1XbT0vII9K00dNa69Qpd6mnVuv2npeQB6eKQCQCAUAEqEAQCIUAEgqhULT2itUqbdp59artp4XkEflFc1N+8y7dQrtPS9g5GlzAUDS+hXNVOP6wujW6hXNVOP6Aq1e0Uw1ri/gI6kAJEIBgEQoAJAIBQCSVq9ophrXF2j9imaqcX1hdLOiGYDEMwUAkka2uSihBlwHaKPGtbkooQZcB2irxrW5KKEGXAdoK88UAEiEAgCJUAAgEQoAJI1rc1FCDbgO0FaNbHNRQg24DtBG2lwAkHimAECStc1FCdtSBtcM8hqpeyxbm4sStqUMrhnkNZL3WLY2FyVsSxlcM8hrJO8xzxQASIQCAIlQACARCgAk2dpclLAtZXDNIK+RvMeytrkoYVvK4JpBXiN1j2lzAUDimQIASeU2F5CbqSY4rI5pdaFAUbTEgMPqav9j+oiiaIkBh9XV/kcoAJAIBQASoQBAIhQASIQCRdESAw6rq/2PFc0UxzoFOKyOdQpCAYDE9BEAiRXNNJZpJtpOmwvokXYYtJ02F1CBdhi0nTYXANROKACQCAUAEqEAQCIUaCTtMGg7bS6gIusUaDttLgColekjABIrmo9Sx69qnBiuF/RGKPxHXUvKyc/1gt6ZPvqPupaUk5/rBb0TCgAkQgGARCgAkAgFABKh8B91LSknP9cLemdF81GsU2gv1wt6IxQASEwfAZBUXtFsioW2833LaFYpFLSCoO183zLaVZo+0gqCtvN9y2jnmQIAiVAAIBEKACRCAYCkUihoBUHb+b5ltKu8otk6BdrO9y2jmTYXACSeKQCQVG5zAfwfU03kVMd0vVCAYdISg5zqaitk+giGSUsMcqqrrZBQACARCgAkQgGARCgAkAgFGCYtMciprrZCVjTDcbBOgZzqWKcgFABIKi9e0xAPhsf9QE61rGiua4UdNJ37gZxqW9Fc1wo7aDr3AzlZ0QxAFkIBgEQoAJAIBQCSSqFQ1wo7aDr3AznVuqLZOgUYHvcDOVnRDMCI80wBgMT/oxkKZKqJiHqm64UCFEZLDCLqaytk+ggKoyUGEfW1FRIKACRCAYBEKACQCAUAEqEAhdESg4j62gpZ0QwFsk6BiHrWKQgFABLTRwAklVc065IKZXGfMZIqhUJdy66BobnPGGmVpo/qWnYNDM19xkjzTAGARCgAkAgFABKhAEBSKRTqWnYNDM19xkirvKLZOgUoi/uMkaTNBQCJZwoAJJXbXADNZaqpWeqYrhcKMEpoidEsdbUVMn0Eo4SWGM1SV1shoQBAIhQASIQCAIlQACARCjBKaInRLHW1FbKiGUYR6xSapY51CkIBgMT0EQCJFc3AILmmmew33/G1uQCyyNUOw37zHV+bCyCbXO0w7Dff8bW5ACALoQBAIhQASIQCAIlQAAbI1Q7DfvMdX5sLIKumfe6/afvNcXxtLgAYcaaPAEisaAaOSx1THMdTQ91Kr1UoAMNWVyuG4dZQtybUavoIGLa6WjEMt4a6NaFWoQBAIhQASIQCAIlQACARCsCw1dWKYbg11K0JtVrRDBwX6xSqKb1WoQBAYvoIgMSKZmCQXFNCpU+dnAilj4FQAAbI1bqiCS0ecmvCGJg+AgbI1bqiCS0ecmvCGAgFABKhAEAiFABIhAIAiVAABsjVuqIJLR5ya8IYWNEMDGKdQj6lj4FQACCxeA0oUgn/oi6hhl6NVK1CAShOCSt/S6ihVyNZqwfNQHFKWPlbQg29GslahQIAiVAAIBEKACRCAYBEKADFKWHlbwk19Goka7V4DShSCWsESqihVyNVq1AAIDF9BEBSzIrmJv2aBm3XtCZ3JdRQt1a1uWjScnJouyr3Ywn3bgk11K11bS6atJwc2q7K/VjCvVtCDXXT5gKALIQCAIlQACARCgAkRYRCk5aTQ9tVuR9LuHdLqKFurWxz4XPGUA7rFJpHmwsARlwR00cAlKGIFc0Rfv0DToy6f9bkOr42FwAV1f2zJtfxtbkAGIa6f9bkOr42FwBkIRQASIQCAIlQACApIhQsUwdOhLp/1uQ6vjYXAMNU98+a0tcpFBMKANSviOkjAMpQxIpmoCx1T7GoofrxW9XmAihH3a0g1FD9+K1rcwGUo+5WEGqofnxtLgDIQigAkAgFABKhAEAiFIAB6m4FoYbqx29lmwugHHV/Pl8N1Y+vzQUAI870EQBJ1hXNdf/q1TTGC5orx/3bqjYXdS8RbxrjBc2V4/5tXZuLupeIN43xgubKcf9qcwFA7YQCAIlQACARCgAk2UKh7iXiTWO8oLly3L+tbHPhc/fVGC9orrasU9DmAoDEMwUAksormk1xAEerY4rjeNRdQ67xqqXNhVYMwNHqasVwIuqt+/iNaHOhFQNwtLpaMQxX3TXkGi9tLgDIQigAkAgFABKhAEBSKRS0YgCOVlcrhuGqu4Zc41Vrm4u6P+MLlMU6hXzH1+YCgFp5pgBAUrnNRS51/0pXAmNwWK/jUMJ45aqh7v2WMLYlyDF9U/r0URGhUPfS8xIYg8N6HYcSxitXDXXvt4SxLUGONhOta3ORS91Lz0tgDA7rdRxKGK9cNdS93xLGtgQ52kxocwFAowgFABKhAEAiFABIigiFupeel8AYHNbrOJQwXrlqqHu/JYxtCXK0mWhlm4tcfC7aGBzRpM/S172eINd+SxjbEozGdQrFhAIA9Sti+giAMhSxopnDmtZtsoq6fw3PpfSpgOHWa2zzbVv38f8boVCIupa0nwh1twvIpQktC4ZTr7HNt23dx++F6aNC1LWk/USou11ALk1oWTCceo1tvm3rPn4vhAIAiVAAIBEKACRCAYBEKBSiriXtJ0Ld7QJyaULLguHUa2zzbVv38XthRXNBSvgcey51f947l9I/cz7ceo1tvm3rPv5/IxQASEwfAZAIBQASoQBAIhQASIQCAIlQACARCgAkQgGARCgAkPx/vIRdvyWm9sMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The 2 smallest eigenvalues = [-3.37640596e-15  4.68525227e-01]\n"
     ]
    }
   ],
   "source": [
    "import scipy.sparse.linalg as spsplin\n",
    "Laplacian = nx.laplacian_matrix(kn).asfptype()\n",
    "plt.spy(Laplacian, markersize=5)\n",
    "plt.title(\"Graph laplacian\")\n",
    "plt.axis(\"off\")\n",
    "plt.show()\n",
    "eigval, eigvec = spsplin.eigsh(Laplacian, k=2, which=\"SM\")\n",
    "print(\"The 2 smallest eigenvalues =\", eigval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sum of elements in Fiedler vector = 2.4702462297909733e-15\n"
     ]
    }
   ],
   "source": [
    "#plt.scatter(np.arange(len(eigvec[:, 1])), np.sign(eigvec[:, 1]))\n",
    "plt.scatter(np.arange(len(eigvec[:, 1])), eigvec[:, 1])\n",
    "\n",
    "plt.show()\n",
    "print(\"Sum of elements in Fiedler vector = {}\".format(np.sum(eigvec[:, 1].real)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw_networkx(kn, node_color=np.sign(eigvec[:, 1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Summary on demo\n",
    "\n",
    "- Here we call SciPy sparse function to find fixed number of eigenvalues (and eigenvectors) that are smallest (other options are possible)\n",
    "- Details of the underlying method we will discuss soon\n",
    "- Fiedler vector gives simple separation of the graph\n",
    "- To separate graph on more than two parts you should use eigenvectors of laplacian as feature vectors and run some clustering algorithm, e.g. $k$-means"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## From Fiedler vector to separator\n",
    "\n",
    "- Elements of eigenvector $v$ corresponding to the second smallest eigenvalue of the Laplacian indicate the partitioning of vertices\n",
    "- If we select some small positive $\\tau >0$, then we can split the vertices in three groups\n",
    "    - $v_i < -\\tau$\n",
    "    - $v_i \\in [-\\tau, \\tau]$\n",
    "    - $v_i > \\tau$\n",
    "- After that the separator is composed with the vertices corresponding to elements of $v$ such that $v_i \\in [-\\tau, \\tau]$ \n",
    "- The size of separator can be tuned by the magnitude of $\\tau$\n",
    "- The distribution of elements in $v$ is important to identify the size of separator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Fiedler vector and algebraic connectivity of a graph\n",
    "\n",
    "**Definition.** The algebraic connectivity of a graph is the second-smallest eigenvalue of the Laplacian matrix.\n",
    "\n",
    "**Claim.** The algebraic connectivity of a graph is greater than 0 if and only if a graph is a connected graph."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Practical problems\n",
    "\n",
    "Computing bisection recursively is expensive. \n",
    "\n",
    "As an alternative, one typically computes **multilevel bisection** that consists of 3 phases.\n",
    "\n",
    "- Graph coarsening: From a given graph, we join vertices into larger nodes, and get sequences of graphs $G_1, \\ldots, G_m$. \n",
    "- At the coarse level, we do high-quality bisection\n",
    "- Then, we do **uncoarsening**: we propagate the splitting from $G_k$ to $G_{k-1}$ and improve the quality of the split by local optimization algorithms (refinement). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Practical problems (2)\n",
    "\n",
    "- Once the permutation has been computed, we need to implement the elimination, making use of efficient computational kernels. \n",
    "\n",
    "- If in the elemination we will be able to get the elements into **blocks**, we will be able to use BLAS-3 computations. \n",
    "\n",
    "- It is done by **supernodal** data structures: \n",
    "\n",
    "- If adjacent rows have the same sparsity structure, they can be stored in **blocks**:\n",
    "\n",
    "- Also, we can use such structure in efficient computations!\n",
    "\n",
    "[Details in this survey](https://arxiv.org/pdf/1907.05309.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Take home message\n",
    "\n",
    "- Sparse matrices & graphs ordering\n",
    "- Ordering is important for LU fill-in: more details in the next lecture\n",
    "- Markowitz pivoting and minimal degree ordering\n",
    "- Orderings from SciPy sparse package\n",
    "- Separators and how do they help in fill-in minimization\n",
    "- Nested dissection idea\n",
    "- Fiedler vector and spectral bipartitioning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Plan for the next lecture\n",
    "\n",
    "- Basic iterative methods for solving large linear systems\n",
    "- Convergence \n",
    "- Acceleration"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Questions?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
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       "        line-height: 110%;\n",
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       "    .warning{\n",
       "        color: rgb( 240, 20, 20 )\n",
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       "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
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       "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
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      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.core.display import HTML\n",
    "def css_styling():\n",
    "    styles = open(\"./styles/custom.css\", \"r\").read()\n",
    "    return HTML(styles)\n",
    "css_styling()"
   ]
  }
 ],
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