05-Distances-Timeseries.ipynb

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   "source": [
    "# Distances and Timeseries"
   ]
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    "%matplotlib inline\n",
    "%config InlineBackend.figure_format='retina'\n",
    "# import libraries\n",
    "import numpy as np\n",
    "import matplotlib as mp\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import slideUtilities as sl\n",
    "import laUtilities as ut\n",
    "from importlib import reload\n",
    "from datetime import datetime\n",
    "from IPython.display import Image\n",
    "from IPython.display import display_html\n",
    "from IPython.display import display\n",
    "from IPython.display import Math\n",
    "from IPython.display import Latex\n",
    "from IPython.display import HTML\n",
    "print('')"
   ]
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    "%Set up useful MathJax (Latex) macros.\n",
    "%See http://docs.mathjax.org/en/latest/tex.html#defining-tex-macros\n",
    "%These are for use in the slideshow\n",
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    "$\\newcommand{\\vp}{{\\mathbf p}}$"
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    "\\newcommand{\\mat}[1]{\\left[\\begin{array}#1\\end{array}\\right]}\n",
    "\\newcommand{\\vx}{{\\mathbf x}}\n",
    "\\newcommand{\\hx}{\\hat{\\mathbf x}}\n",
    "\\newcommand{\\vbt}{{\\mathbf\\beta}}\n",
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   "source": [
    "Today we will start building some tools for making comparisons of data objects, with particular attention to timeseries."
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "Working with data, we can encounter a wide variety of different data objects:\n",
    "\n",
    "* Records of users\n",
    "* Graphs\n",
    "* Images\n",
    "* Videos\n",
    "* Text (webpages, books)\n",
    "* Strings (DNA sequences)\n",
    "* Timeseries\n",
    "* ...\n",
    "\n",
    "How can we compare them?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "## Feature space representation"
   ]
  },
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   "source": [
    "Usually a data object consists of a set of attributes.\n",
    "\n",
    "These are also commonly called __features.__\n",
    "\n",
    "* (\"J. Smith\", 25, \\$ 200,000)\n",
    "* (\"M. Jones\", 47, \\$ 45,000)"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "If all d dimensions are real-valued then we can visualize each data object as a point in a vector space.\n",
    " \n",
    "* (25, USD 200,000) $\\rightarrow \\mat{{c}25\\\\200000}$.\n",
    "\n",
    "Likewise If all features are binary then we can think of each data object as a binary vector in vector space.\n",
    "\n",
    "The space is called __feature space.__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "We then are naturally interested in how __similar__ or __dissimilar__ two objects are."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "fragment"
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   },
   "source": [
    "A dissimilarity function takes two objects as input, and returns a large value when then two objects are not very similar."
   ]
  },
  {
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   "source": [
    "Often we put restrictions on the dissimilarity function.\n",
    "\n",
    "One of the most common is that it be a __metric.__"
   ]
  },
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   "source": [
    "The dissimilarity $d(x, y)$ between two objects $x$ and $y$ is a\n",
    "__metric__ if\n",
    "\n",
    "* $d(i, j) = 0 \\leftrightarrow i == j\\;\\;\\;\\;\\;\\;\\;\\;$ (identity of indiscernables)\n",
    "* $d(i, j) = d(j, i)\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;$ (symmetry)\n",
    "* $d(i, j) \\leq d(i, h)+d(h, j)\\;\\;$ (triangle inequality)"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "A metric is also commonly called a __distance__.\n",
    "\n",
    "Sometimes we will use \"distance\" informally, ie, to refer to a dissimilarity function even if we are not sure it is a metric.   We'll try to say \"dissimilarity\" in those cases though."
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "Why is it important or valuable for a dissimilarity to be a metric?"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "The additional constraints allow us to reason about and more easily visualize the data.\n",
    "\n",
    "The main way this happens is through the triangle inequality.   "
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "The triangle inequality basically says, if two objects are \"close\" to another object, then they are \"close\" to each other.  \n",
    "\n",
    "This is not always the case for real data, but when it is true, it can really help."
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "Definitions of distance or dissimilarity functions are usually\n",
    "diferent for real, boolean, categorical, and ordinal\n",
    "variables.\n",
    "\n",
    "Weights may be associated with diferent variables\n",
    "based on applications and data semantics."
   ]
  },
  {
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   "source": [
    "## Matrix representation"
   ]
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   "source": [
    "Very often we will manage data conveniently in matrix form.\n",
    "\n",
    "The standard way of doing this is:\n",
    "\n",
    "$$ \\mbox{$m$ data objects}\\left\\{\\begin{array}{c}\\;\\\\\\;\\\\\\;\\\\\\;\\\\\\;\\end{array}\\right.\\;\\;\\overbrace{\\left[\\begin{array}{ccccc}\n",
    "\\begin{array}{c}x_{11}\\\\\\vdots\\\\x_{i1}\\\\\\vdots\\\\x_{m1}\\end{array}&\n",
    "\\begin{array}{c}\\dots\\\\\\ddots\\\\\\dots\\\\\\ddots\\\\\\dots\\end{array}&\n",
    "\\begin{array}{c}x_{1j}\\\\\\vdots\\\\x_{ij}\\\\\\vdots\\\\x_{mj}\\end{array}&\n",
    "\\begin{array}{c}\\dots\\\\\\ddots\\\\\\dots\\\\\\ddots\\\\\\dots\\end{array}&\n",
    "\\begin{array}{c}x_{1n}\\\\\\vdots\\\\x_{in}\\\\\\vdots\\\\x_{mn}\\end{array}\n",
    "\\end{array}\\right]}^\\mbox{$n$ features} $$\n",
    "\n",
    "Where we typically use symbols $m$ for number of rows (objects) and $n$ for number of columns (features).\n"
   ]
  },
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   "source": [
    "When we are working with distances, the matrix representation is:\n",
    "\n",
    "$$ \\mbox{$m$ data objects}\\left\\{\\begin{array}{c}\\;\\\\\\;\\\\\\;\\\\\\;\\end{array}\\right.\\;\\;\n",
    "\\overbrace{\\left[\\begin{array}{cccc}\n",
    "\\begin{array}{c}0\\\\d(1,2)\\\\d(1,3)\\\\\\vdots\\\\d(1,m)\\end{array} &\n",
    "\\begin{array}{c}\\;\\\\0\\\\d(2,3)\\\\\\vdots\\\\d(2,m)\\end{array} &\n",
    "\\begin{array}{c}\\;\\\\\\;\\\\\\ddots\\\\\\vdots\\\\\\dots\\end{array} &\n",
    "\\begin{array}{c}\\;\\\\\\;\\\\\\;\\\\\\;\\\\0\\end{array} \\\\\n",
    "\\end{array}\\right]}^\\mbox{$m$ data objects} $$\n"
   ]
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   "source": [
    "## Norms"
   ]
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   "source": [
    "Assume some function $p(\\vv)$ which measures the \"size\" of the vector $\\vv$.\n",
    "\n",
    "$p()$ is called a __norm__ if:\n",
    "\n",
    "* $p(a\\vv) = |a|\\; p(\\vv)\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;$ (absolute scaling)\n",
    "* $p(\\vu + \\vv) \\leq p(\\vu) + p(\\vv)\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;$  (subadditivity)\n",
    "* $p(\\vv) = 0 \\leftrightarrow \\vv$ is the zero vector $\\;\\;\\;\\;$(separates points)"
   ]
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   "source": [
    "Norms are important for this reason, among others:\n",
    "    \n",
    "__Every norm defines a corresponding metric.__\n",
    "\n",
    "That is, if $p()$ is a norm, then $d(\\vx, \\vy) = p(\\vx-\\vy)$ is a metric."
   ]
  },
  {
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   "source": [
    "## Useful Norms"
   ]
  },
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   "source": [
    "__$\\ell_p$__ Norm, where $p \\geq 1.$\n",
    "\n",
    "Defines the _Minkowski distance._\n",
    "\n",
    "$$ L_p(\\vx, \\vy) = \\left(\\sum_{i=1}^d |x_i - y_i|^p\\right)^{\\frac{1}{p}} $$"
   ]
  },
  {
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   "source": [
    "A special case of this isthe $\\ell_2$ norm that we've already studied, which defines the __Euclidean__ norm.\n",
    "\n",
    "It is equal to the euclidean distance between the vectors.\n",
    "\n",
    "$$ L_2(\\vx, \\vy) = \\sqrt{\\sum_{i=1}^d (x_i - y_i)^2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "Another important special case is the $\\ell_1$ norm.\n",
    "\n",
    "This defines the __Manhattan__ distance, or (for binary vectors), the __Hamming__ distance:\n",
    "\n",
    "$$ L_1(\\vx, \\vy) = \\sum_{i=1} |x_i - y_i| $$"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "If we take the limit of the $\\ell_p$ norm as $p$ gets large ($\\lim_{p\\rightarrow \\infty}L_p$) we get the $\\ell_\\infty$ norm.  \n",
    "\n",
    "The value of the $\\ell_\\infty$ norm is simply the __largest element__ in a vector.\n",
    "\n",
    "What is the metric that this norm induces?"
   ]
  },
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   "source": [
    "Another related idea is the $\\ell_0$ \"norm,\" which is not a norm, but is in a sense what we get from the $p$-norm for $p = 0$.\n",
    "\n",
    "Note that this is __not__ a norm, but it gets called that anyway.   \n",
    "\n",
    "This \"norm\" simply counts the number of __nonzero__ elements in a vector.\n",
    "\n",
    "This is called the vector's __sparsity.__"
   ]
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   "source": [
    "sl.hide_code_in_slideshow()\n",
    "display(Image(\"figs/L5-Vector-Norms.png\", width=150))"
   ]
  },
  {
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    "<a href=\"http://creativecommons.org/licenses/by-sa/3.0/\" title=\"Creative Commons Attribution-Share Alike 3.0\">CC BY-SA 3.0</a>, <a href=\"https://commons.wikimedia.org/w/index.php?curid=678101\">https://commons.wikimedia.org/w/index.php?curid=678101</a>"
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  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Similarity and Dissimilarity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We've already seen that the inner product of two vectors can be used to compute the __cosine of the angle__ between them:\n",
    "\n",
    "$$ \\cos(\\vx, \\vy) = \\frac{\\vx^T\\vy}{\\Vert\\vx\\Vert \\Vert\\vy\\Vert} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Note that this value is __large__ when $\\vx \\approx \\vy.$  So it is a __similarity__ function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We often find that we have a similarity function and need to convert it to a dissimilarity function.   Two straightforward ways of doing that are:\n",
    "\n",
    "$$d(x,y) = 1/s(x,y)$$\n",
    "\n",
    "$$d(x,y) = k - s(x,y)$$\n",
    "\n",
    "For some properly chosen $k$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "For cosine similarity, one often uses:\n",
    "    \n",
    "$$ d(\\vx, \\vy) = 1 - \\cos(\\vx, \\vy)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Note however that this is __not a metric!__\n",
    "\n",
    "However if we recover the actual angle beween $\\vx$ and $\\vy$, that is a metric."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Bit vectors and Sets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "When working with bit vectors, the $\\ell_1$ metric is commonly used and called the __Hamming__ distance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
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9HwAgd1GoAgAAAPzEqWU/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\nxKLDW9ebT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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {
      "image/png": {
       "width": 550
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "display(Image(\"figs/L5-hamming-1.png\", width=550))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This has a natural interpretation: \"how well do the two vectors match?\"\n",
    "\n",
    "Or: \"What is the smallest number of bit flips that will convert one vector into the other?\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"cbe734565269623a\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#cbe734565269623a\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ce3YcKtO8Rqe+/W2R9BUaaF4YM8tW57poHpP0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\n+UPFh+WWxnULXR96LvItS+KWucXHjd33bLzSNcx1rmmPlS8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ZAgCQ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\nXX/tQY/5erF6iMOc0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NJUPs93juH4TGePPOm4pi6UJgYAAAMo6ADwC5fiT+vA2k817O8m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\niofXdhsPXPWj9lwynWXGnFjQTzUHr8j6h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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {
      "image/png": {
       "width": 550
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "display(Image(\"figs/L5-hamming-2.png\", width=550))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "In other cases, the Hamming distance is not a very appropriate metric.\n",
    "\n",
    "Consider the case in which the bit vector is being used to represent a set.\n",
    "\n",
    "In that case, Hamming distance measures the __size of the set difference.__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "For example, consider two documents.   We will use bit vectors to represent the sets of words in each document.\n",
    "\n",
    "* Case 1: both documents are large, almost identical, but differ in 10 words.\n",
    "* Case 2: both documents are small, disjoint, have 5 words each."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The situation can be represented as this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"632824a9e6112e8b\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#632824a9e6112e8b\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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+vHP7nkf++P2o9SWNExMTeO75F0qGxdtV4CDDIhFVyjSRikQwOz9fcQEb03Sg\nYHqQNzwwZa2/iq6fCYkXDOBiiaKamupAV/9xuNxBu7tKm8ihZBFwzcLvmi1ruqrL6cShWw5h/759\nUNX6H3EnqmcMjPXIHMfvPrMVv1I0GujGnz+Uws+1rL3q2BtvHcMd4++Wd3LPU0idrN2RxrHxcbzw\nwgswjOK7FAHgPk1iBzcUJqJK5HNYmJvHQmTB8rWlFFOqyBteFAxvU4TEYhJvmcDbJWbqLoXG2+Fy\nt9jdUdpkiiigxT2DgHOmrK05An4/jhw5gp07B+zuOlHTYmCsN8k38TPPnMBfWb3GbnsL8tht67t+\n4U20f/cEIuWeH/4rzN77j9Fh9/flY8bGxvDCiy+WDIuPaBK9DItEVA4hUVhMYHZ+DvF4ovzHSYG8\n4UPe8MKQDrCgFvCeKfGjEqFRUTX09B2Hy8PQ2AwUoSPomkHANQNFrL7mNxxux23HjqGnp8furhM1\nHQbGOjI/+efoeP2flTj6MJ749NP4tHu9XyWO33+yBf+qkhlWrq/hvU/8Gm6tkTXqo6NX8eJLL8I0\ni3+0BYBHNaCH921EtBpDR3whgvn5eeTy5RXuAJZGE3O6HwXDW5cVTjfbB4bEqyUGlhRFQ3f/7XB7\nQnZ3k6pEgQG/exYtrqmygmN/fx9uO3YMoVDI7q4TNQ0GxroQx9OnfgGPjPxd6VNcf4LoY7+4IdVL\n33vrKI6Mn6rwUQ/jT+9+HL/Qae8nwyOjo3jppZcsw6KCpbDYzbBIRCvJZDA3P49INArTLH/aqW64\nkTP80E0XOJq4stOmxCulRhoVFd39xxkam4wCEz7XLELuyVWDoxAC+/btxdEjR+BwNOMUb6LqYmCs\nccnYC/g3rzyAP131w+0v49oXvo7eDfia339B4NNlz0m90dFtP8QPjj1iyxTVpWqoz1pOQ1UAfEpb\n2muRiKiIkMhFFzE7P4dksvy9E6UUKBh+5Jp2beLanTUlXlphemrv1pPccqMJCegIeaYRcE2vWhzH\n5/PijhMnsHXrVru7TdTQGBhrVW4Ef/XeL+Nnrn2/zAc8jG8/8kN83r/2gjcAMHX1a+h959+us/MP\n47eP/D5+acfeqhXEmZ+fxw9++EMUCsX7LKoAPsmwSERWhEQ2EsPUzDSy2VzZDzNNB7KGD7rhg+Ro\n4pqdMyVeLFUIR3OhZ9tJOBweu7tJNtBEHiHPBHzOhVXP3bZtK04cPw6fz2d3t4kaEgNjjUnEz+G7\n538PP3Ptv67h0YfxB8e/g1/s6694u4tsegjfPP0rFQTUMqgP4X/d8x/wc9tvxy7P5u2ltLi4iCe/\n/33Lmz0VwKc1IMz7OSK63hqDYsHwIGf4YZhOcNrpxrhoSjxXIjQ6nD5s2XoHFK1GFslT1TnVFFo9\nE3Br8RXPczg0HDlyBPv37YNgUTuiDcXAWBN0fDD4x/jylX+Fp9MbcDn1IfzTzk9hvy+AgZ7P4x90\nhovPMWfw/PALOJcaxncW/gbPxS9s7lN0/SS+1PEg7t3xU9b9WaN0Oo0nnnzScgqZAuAzGtDO9w0i\n+tAagqKUCvLL006l1Ox+Bg3pginxfInQ6HIH0bP1BBSF3/vmJeHR4gh5x+BUVq7KFw63486TJ9He\n3m53p4kaBgNjTVjAf3w8jK+ubzaptZ63IE9abLWRewXiiXuq/1RL9WcNcrkcvv+DHyAajVkef5Rb\nZxDRh9YQFA3TiZzhQ8HwgqOJm2+lLTc83jC6+49BiM14o6T6YSLonkbIPbni+kZFETh862EcOnQz\nRxuJNgADY42IRt/Hu/EM2twh+BxeeB1eODQNXsUDhwIAGhzL1dk1RYNuLq3VkyhANwSEmUfKyELX\nC4jpi0gV0khlozC9h3Fvh/UI46ujp5Fx+uF3eBFQfPA6HHCoH35dFQ7lx1OAHOqPP9nVlj/l/bAP\nAFAwPvzvPAqmDr2gIyUzKBQKSBspJAspJPQUnJ4S/amQrut46qmnMTM7a3n8Pk1igG8SRLSGoLg0\n7TSwPO2UqmcpML5XojCtP9CLjt5bGAAIDiWHNu/oqtNUu7o6ce8998DvZ/EkovVgYKS6I6XEc88/\nj7Gxccvjt6vAQX4ITdTc1hQUvcjqAVY7tZHE0tTUiyVCY0vrdrR37be7m1QTJHzOCNo8V1fchsPp\ndOCOE3dg584BuztMVLcYGKnuvPPuuzh9+ozlsYMKcLsmAclPoImaEoNi3TMh8QNDYtS0fh3v6L4Z\ngVC/3d2kGqEIHa2ecfid8yuet3NgAHfccQJOJ2cOEFWKgZHqypUrV/DiSy9bHtulSNyjgWGRqEkV\n4nFcm5xEJpst73wGxZqlQ+K7usSUxeu5EAK9/Sfg8rba3U2qIW41gbDvClSl9MbVfr8P995zD7q6\nuuzuLlFdYWCkujG/sIAnn/w+DKN46kmfIvEJhkWi5pTJYGLyGhKJZFmnMyjWh6yU+LYBRCzuUlTN\nib5td0F1uO3uJtUQBQbavFdX3LtRCIFjx47i5oMH7e4uUd1gYKS6kMlk8N3vfQ+pVPG+I60C+AlN\nglUMiZpMoYDZqSlEIhGU80bGoFh/EpB4XAcyFv+Dl7bbuAOKotrdTaoxXmcE7Z4RKMIsec7AwA7c\ndeed0DRu10K0GgZGqnmGYeCHP3zKsiKqSwBfVJf+JqImYRqIzsxidm4OpmmuejqDYn2bNCW+YwBW\n/6f9gV50brnV7i5SDdJEHu2+K3BriZLntLW14sEHHkAgELC7u0Q1jYGRat6rr76GoeFhy2Of1YAw\nwyJRc5ASqYUFTE1Po6Drq57OoNg4zpoSL5UohNkW3oNQeKfdXaSaJBF0T6PVPVHyDJfLhfvvuxe9\nvb12d5aoZjEwUk27cOEiXn/jDctjd6rAHm6fQdQU9FQC4+MTZVU+1U0XMoUWmJLVEBvHUmA8W2JA\nuafvNnj8HXZ3kmqUS02iw3e5ZEEcIQRuO3YMBw8esLurRDWJgZFqViQSwfeeeAKGUXyHsFcFTqrc\nPoOo4RUKmL52DdFYbNVTTdOBjN4C3WQhlEZkLldOvWbxuq9qTmzZfjc0zWV3N6lGKaKADt/lFaeo\n7tq5E3feeRKqynWxRNdjYKSapOs6vvu97yEWWyw61imAxxwMi0QNTUoszs1iZnoGxirrFKVUkNFb\nUDC8YPGrxpaREt/QgbjFMY83jJ6tt9vdRappEm2ecQRcMyXP6O3twYMPPACHg1PZiT7EwEg16bXX\nfoTBoaGido8A/pEmIXhTSNSwyp5+KgVyRgA5PQDJ14SmMS8lvqkDVqtY2zv2oKWd6xlpZT7nHNq9\nVyFK1FcOt7fjE594GG43ZysQAQyMVINGRkfxwgsvWh77nAa0876QqDFVMP00r/uRNfyQkiXxm9E5\nU+JFiyI4Qgj0bL0Dbk/I7i5SjVttXWMwGMAjn/gEK6gSAWDJEKopyWQSP3rtR5bHjqgMi0QNSUrE\nZ2cxdOHCqmHRMJ1I5jqR0UMMi03sgALsUoo/75ZSYm7qPUhj9Sq61Nxyhh+Tif3IGT7L4/F4Ak8+\n+X0sLCzY3VUi2zEwUs2QUuKll15GLl/8aV+nAG5VORhO1HAyaVwdGsK1yckV1ypKqSBdaEUy3wGD\n1U8JAvcqAkGLI4V8BnPTZ+3uINUBUzowm9iDjN5ieTydyeAHP/whpqam7O4qka0YGKlmvP/++5iZ\nnS1qdwrgEQ0sckPUSKSJyNQkLg4NIZ3JrHhqXvcjketCwfCBRW3oQ24h8JBmfSOTTEwiuXjN7i5S\nHTChYja5G8l8u+XxfL6Ap595Bteu8eeJmhcDI9WESCSCD06ftjx2nyLBWmVEjcNMpTBycRAzM7NY\naRX9DdNPwTL3VKxHCBwr8aMRmT0PU199304iQGAhvQPxXI/lUcMw8exzz2OSI43UpBgYyXZSSrz2\nox/BNIvvHPeqQJ/CEQWihmCamL82gaHhYWRzpW/kOf2UKnFMAbaI4vcP3Shgfua83d2juiEQzfQh\nkum3PGoYBp599jlMT0/b3VGiqmNgJNudP38ec3PzRe1BAZxUuG6RqBHoiQSuXLyIubl5rPRbnTO8\nnH5KFREQeEgTcFv8uCQTU0gnZiu/KDWtRK4b82nrrVl0Xcczzz5ruXyGqJExMJKtEokE3j31nuWx\nB1SAN4xEdc4wMDs2huHLly0LWn3IlCqS+Q5kC22cfkoV80PgZIk7mvnZszBNVk2l8qXybZhL7rI8\nVijoeOaZZzA3N2d3N4mqhoGRbPWj11+Hrhe/ke9XgTZmRaK6ZqaSuDI4iIVIZMXz8noAyVw3DNNl\nd5epju1VgD6rqamFLCJzg3Z3j+pMWm/FXImRxny+gKeefhrz3HKDmgQDI9nm0uXLuHZtsqjdI4AT\nnIpKVL+kRHRqCkPDl1YeVTQdSOY7kdFbIDmbgNZJQOBeTcBqd8549Cpy6ajdXaQ6k863YT49YHks\nny/gqaeeRjwet7ubRJuOgZFskc1m8eabb1keu49TUYnqVz6Lq8NDmJ6ZWXmtoh5EIt8Jw2RRG9o4\nIQjcXmJG89zMaUhpVnZBanqpfDvm09stj+VyOTz9zDPI5ViNlxobAyPZ4t1TpyxfYAcUiR6OLhLV\npfTCPAYvDiGdLr2vomE6kch1IqsHwQ+GaDPcogAdFlNT87kU4pFRu7tHdSiV78BCZpvlsXg8gWef\new6GYdjdTaJNw8BIVReNRjE0NFzU7hTAvSoAyZtIorqi65gcuYKr4xMwzdIjODk9iGS+Aya3yqBN\npEDgflVY3uBEFy7B1PMVX5MometEJLPV8tjMzCxeffU1u7tItGkYGKnq3nr7bUiL3bpPqhKCIw5E\ndaUQj+PSxYtYXCy9juejCqgcVaQq6RACt1jc4ZimjsjCcOUXJAKQyHUhnuuxPHb5yhWcKlH1naje\nMTBSVU1MTFgWugkLYIA/jUT1QywVtrl05QoKeuktCwqGF8lcJyugUtXdpiwVUfu4RGwM+VzS7u5R\nnYpmtiBdaLM89v4HH+DSpUt2d5Fow/EWnapGSom33n7H8tidnIpKVD/0AiaGL2N6ZqbkKVIKpPLt\nSHNfRbKJQwjcbnGXI6VEZPai3d2juiWwkNqBnOGzPPrqa69hZnbW7k4SbSgGRqqaoaEhxGKxovbt\nikQ7syJRXTCSSVy6OIhEsvQIjW66kMh3QTc9dneXmtwBxXpP33RqFtkU99CjtTGhYDa5GwWLmROm\nKfHiiy8im83a3U2iDcPASFVRKBRw6r3iuf0CwEmFaZGoHizOzmD40qUVp6BmCi1I5cOQUqvgykSb\nQ0AszWCxMD973nI9PVE5TOnAXPImmLL4ByyVSuPlV16xu4tEG4aBkari7NmzyGSKP207oABu5kWi\n2mYsVUGdnJwqubeiKVUkc53IGwGwsA3Vkq0C2KpYbbORQCo+uYYrEi0pmG7MJXdZHpuYuIbTp0/b\n3UWiDcHASJsun8/j3PnzRe1OAdyu8tNdoloms2lcGRxasQpqwfAsFbbhdhlUk0TJmSyxyCWOMtK6\nZI0gItl+y2PvnnoP09PTdneRaN0YGGnTXbhwEfl8oaj9qAJwJIKodmUiEQwNDiOXL71vXabQwsI2\nVPPahcB+izuefC6FdII39LQ+iWwX0oVQUbuUEi+++BIymYzdXSRaFwZG2lS6ruPc+XNF7W4B7OPo\nIlFtEhKRyUmMjo3BLDH6IqWCZL6DU1CpbhxTrW96ogvcBoHWS2A+vQOGWTzLIp3J4KWXXuZINtU1\nBkbaVIODg8hmc0XttyrgNhpEtcg0MHl5ZMWy8B9WQeXeilRPAhDYaznKmEA6wW0QaH2k1DCX2mm5\nzntyagrnL1ywu4tEa8bASJvGMAycOXO2qN0lgP0KP2kjqjn5HEaGhrEYL71eMacHl6ugcgoq1Z/D\nJX5so5Fhu7tGDSBn+BHNbLU89u67p5BIJOzuItGaMDDSphkeHkbaYt7+zVy7SFRzjGQCw4NDJfcO\nk1IglQ8jqwfB31+qVyEI3GTx45vLLCKdmrO7e9QAErlOpAutRe26ruPV116zu3tEa8LASJvCNE2c\nPnOmqN0B4BBHF4lqSnphHsOXL0M3DMvjplSRzHdCN912d5Vo3Y6WGGVc5FpG2hACC+nt0KWj6MjU\n1DQuXrxodweJKsbASJvi6tgYkslUUftBFeDoBFGNEBLzExO4Oj6BUvUYdNOFZK4TpsXND1E9ahMC\nOy0+uMyko8hl42u4ItGNTKkhmtpmeeztd95BMpm0u4tEFWFgpE0xeHGwqE0FcCtHF4lqg2li8vII\n5ubnS56S1/1L6xW5ZQY1mKMl9mVMRMfs7ho1iLTeilShrai9UODUVKo/DIy04RYXFzE5NVXUvkcF\nBEcXiexn6Bi7fGnF4jbpQggZPQTOCKBG1CEE+kTxB5jJxDWYpm5396hBRNLbYFoUCJucnMLwMAst\nUf1gYKQNd3Fw0LL9AH/aiOyXz2NkaBipVNrysJQCyXwHCobf7p4Sbar9FgPnpmkguXjN7q5RgzCl\nhoXMdstj7757CoVCwe4uEpWFt/C0oXRdx6Xh4sIBnQII2N05omaXyeDS0BCyuZzlYdN0IJnv5P6K\n1BQGhIDXoj0eu2p316iBpPOtllVT05kMPjh92u7uEZWFgZE21MjICHL5fFH7QZVrF4nsZCQTGLo0\njIJuPd3OMF1I5sMsbkNNQ4WwHGXM55LIpKN2d48ahsBCehukLL7lPnfuHPdmpLrAwEgbymo6qksA\n2/mTRmSbXCyGS5evwDBMy+MFw4Mki9tQE9pf4r0pEeUoI20cUzoQy/UWtRuGiXfefdfu7hGtirfx\ntGEWFhYwN1dccXGvACBZOIPIDon5OYyMjsIssW9GXvcjXWgDi9tQMwpAYLtF9e5UcgqGkV/DFYms\nxbNdMExnUfvIyChmZmbs7h7RihgYacOMjIxYtrPYDZE9YjPTmJi4hlITwjOFFlZCpaZ30GKLDSkl\n0olpu7tGDUVBJNtveeTNt96yu3NEK+KtPG2YkZHRorZeAbh5L0pUddGpKUxNlb7hTRdakTdYiopo\nqwCsagIn4wyMtLHS+VZk9eLX3fn5BVy+fMXu7hGVxMBIG2J+fh6JZLKofTeL3RBVXWRyEtOlpjhJ\ngVQ+jILhs7ubRDVBQGCnxd1QJj0PU+e0VNpIAtGM9SjjB6c/gJS8Z6LaxMBIG8JqdBEAdnJ0kaiq\nFq5dw8zsrOUxKQWShQ7optvubhLVlN0l7oZSnJZKGyxv+JDMtxe1x2KLGL3KYktUmxgYaUOMjBav\nX9yiSHBtFFH1zE9MYHZuzvKYlMryHovOCq9K1Pg6BRC0aE8mpuzuGjWgWHaLZfsHH3xgd9eILDEw\n0rrNzs4imUwVte/mTxdR1cyNj2Nuft7y2FJY7OAei0QlCAjssthVJpNegKnn7O4eNZilfW+LRxkj\nkSjGxsbs7h5REd7S07qNjI4WtQkAAxxcJNp8QmJm7CrmFxYsDzMsEpWn1BKKJKel0iaIZ3st29/n\nKCPVIAZGWrerFnPu+zgdlagqZkbHEIlELY+ZUkUy38mwSFSGTgG0WLSnkpyWShuvYLqRKrQVtc/P\nL+DatWt2d4/oBgyMtC7xeNxyOuou/mQRbbr5iQlEoqXDYirfAVNqdneTqE4I7LSYlppNR2Gaht2d\nowa0mOmxbP/g9Gm7u0Z0A97W07pMTk5atm/j4CLRpopMTZZcs2ia2vI0VIZFokpss2iTUiKbidjd\nNWpABdOLdKG1qH16egbREh8GEtmBgZHW5ZpFYGwTgMLpqESbZnF2BjMz1ltnmKYDyUIYkmGRqGJd\nCuCw2Aovm1qo/GJEZVjMWo8yDg4O2d01oo8wMNKaSSkxPVVcDKCfWZFo06Tm5zE5ab2mypQqwyLR\nOqgQ6FWLE2MmPbeGqxGtLm/4kNN9Re2XLl+Crut2d48IAAMjrcP8/Dxy+XxRex9/qog2RTYaxdjE\nhOUxKRWk8h2QUq3wqkR0vX6l+FPPXDYBU8+v4WpEq0vku4ra8vkCrlwZWcPViDYeb+1pzaxGOQSA\nLiErvxgRrSi/uIjRsauWx368dQZHFonWq69EeyY9X9F1iMqVybfCtPiw7+LgRbu7RgSAgZHWYXKq\neP1itwC4nQbRxtJTCYyMjkJafBYjpUAyH+bWGUQbpF0AXov2DNcx0iYxsfSh38fNzy+U3GOXqJoY\nGGlNTNPE7Gzxmo5+/kQRbaxsBleujMC0TIsCqUIHTOm0u5dEDURYvpdlWCmVNlEy12HZfvECRxnJ\nfry9pzWJxWIwjOJ9qXo5uEi0cQoFXL58BYZhWh5OFdphmAyLRBtti8V7WSGfgmmyCAltjoLpRlYP\nFrWPXh21vN8iqiYGRlqT+XnrKRJtXL9ItDFME1evXEG+ULA8nMq3QzfddveSqCF1lPjwM5eN2901\namAJi2mp+XzBcgszompiYKQ1mV8oXvzfwvWLRBtDSEyOjiKdyVgeThdaoZseu3tJ1LDaBGBVbzif\nXbS7a9TAsvkQpCy+NR8dHbW7a9TkGBhpTRYsFmF3MisSbYj5iWtYjFuPZOT0IAqGr8IrElElFAiE\nLWbM5DIMjLR5TChI66Gi9vGxcU5LJVsxMFLFTNNEJBItamdgJFq/xPwc5uasy/cXDC+yesDuLhI1\nhQ5R/KaWzzMw0uZKF9qK2nL5vOVWZkTVwsBIFStV8IaBkWh9cvFFXJu4ZnnMMF1IF1rBad9E1WH1\nnpbPsfANba5svgVSFv/wjV4dtbtr1MQYGKlipQretLLgDdHaZdIYHb0Kq98i09SQyreBYZGoekoX\nvknY3TVqYCYUZPTWovaxq2MwTXMNVyRaPwZGqtjiYvGUHBa8IVoHQ8flkRHLmwEpFaQK7ZCWJTiI\naLOUKnyj5xkYaXOlSkxLnZritFSyBwMjVSyRKH6z5HYaRGskJCZGR5HPW2yfIYFUIQxTOuzuJVHT\nUSAQtGgv5DMVX4uoEtl80HJaKgMj2YWBkSqWSBYHxiBHF4nWJDo5jUQiaXksVWiHYTrt7iJR0woq\nxR+G6oW03d2iBmdCRdYo/rhikoGRbMLASBWzGmEM8CeJqGL5xRimZ2Ysj+X0IPdaJLKZ1YehhULK\n7m5RE8joxYFxYSGCXC5nd9eoCfE2nyqSy+Usp8612N0xonqTz2J0bMzykG64uX0GUQ2wem8zCpyS\nSpsvVyh+D5BSYnp62u6uURNiYKSKJJLWU+eCFV6HqKmZBkaujMIwiovcmFLl9hlENSKgFP8e6kYB\nhlFYw9WIypc3vDBlcdmlqSkGRqo+BkaqiNV0VADwKCx6Q1Su6bFxZLPZ4gNSIJUPsyIqUY0Iwvq9\nTecoI206gazOdYxUGxgYqSJWgdEjAEiOhhCVIz47i2gsZnksrbeyIipRDSm13ELPcx0jbb6MxdKE\nWCyGdJqFl6i6GBipIlajIlxpRVQemU5hcmrS8lhe96NgeO3uIhFdxyEE3BafhxpG3u6uURPIFaw/\nspidnbO7a9RkGBipIlbVuVzcg5FodYaBkdGrkBa/LobpQkZn6SiiWuSy+J01uYaRqqBguizXMUYi\nEbu7Rk2GgZEqks8Xf6rqZnEOolXNTEwgZ/H7I6WCFIvcENUsqw9FTVO3u1vUFARyhq+odSGyYHfH\nqMkwMFJFLEcY7e4UUY3LRCKIRKOWx1KFdkip2d1FIirBZTUl1eSUVKqOglVgXOAII1UXAyNVxGqE\n0cWBEaLS8jmMT0xYHsrpQRgmP3IhqmVWv6GmwRFGqo6cxdr2dDptXWmbaJMwMFJFOMJIVAEhMX51\nDIZZvN+iYTqR1VkyiqjWuSymi3MNI1VLQbcuhsZ1jFRNDIxUEesRRha9IbKyOD2LZKq4/L6UAulC\nG7hukaj2Wc2iMTkllaqkYLogLbYum1/gOkaqHgZGKpuUEoVC8TQcF296iYrIdBpT09YbLGf0Vphc\nt0hUF9wWbQanpFLVCOTN4lFGjjBSNTEwUtlMi2l1AKBWeB2ihidNjI5Zb6FRMDzcb5GojiiWn4ly\nZg1VT97iPSO+GLe7W9REGBiJiDZYdHoG2Wzxel9TqsgUQnZ3j4iI6kjBKB7nTiSTdneLmggDIxHR\nRspmMDM7Y3koXWiD5Jg8ERFVwJDF5QVzuRwKBRZfoupgYCQi2ihCYmxs3HIqal73cwsNIiKqmG44\nLdutiqoRbQYGRiKiDZKYnUcqnS5qN6WKrN5id/eIiKgO6SU+bEwmOC2VqoOBkYhoI+TzmJwqURW1\n0ArJasJERLQGplQtt9ZIch0jVQkDIxHRBrg2Pm5ZSbhgeKGb7jVckYiICAAEChbrGFMpBkaqDgZG\nKpsQ1iMkLC5OzS4djSCeSBS1S6kgw6moRHVN8k2OaoDVGnhWSqVqYWCksimKAlUt/pHJ8d2Umpmh\n49rENctDGT0EKVkVlaie5SzaFEWzu1vUZAzTUdSWy+bWcCWiyjEwUkVcTovSzoJrs6h5zU9NQzeM\nonbdcKNgeOzuHhGtU87iM1FFdVR+IaJ1MGXxhxT5fN7ublGTYGCkijhdxaWd8xxgpGaVzWB+fr64\nXQpk9BDAQjdEdc8yMAoGRqouw2K2Sr7AwEjVwcBIFbEcYWRgpCY1ce2a5RrejB60/DSYiOpPThT/\nlqscYaQqs1rewBFGqhYGRqqI01k8wpjjIAo1ofziIhIWe2CZpgN5w29394hog3BKKtUCqw8hC4WC\n3d2iJsHASBVxuaxGGDnESE1GmpiYLFXopgWcikrUOHIW+98pCgMjVZdpFt+yG4YJw2INPdFGY2Ck\niliNMGYlb46pucTn5pHLFU8F0g0391wkajBWdShVlVPOqbpKVdzmtFSqBgZGqojLouhNyu5OEVWT\nXsD0zLTlIe65SNRYTEhkLdoV1VnxtYjWw4R1YOS0VKoGBkaqiN9fvDYrIQEITkul5jA3NQ3DMIva\n87ofpuQ0NaJGEgdgWrSrDq/dXaMmU2qE0TDNCq9EVDkGRqpIIBAoapMACpyWSs0gm8XCwkJRs5QC\nWT2whgsSUS1LlPgs1OngHqtUbdbBkHdfVA0MjFQRq8AIlH5TJWok0zPTlttoZPUWyBLThYiofsUt\nfuGFUKA6uFaZqqtUMBSCkZE2HwMjVcTr9UJVi39sFsHESA0um0EsGitqXtpGw2d374hoE8Qt2hxO\nji5S7WBgpGpgYKSKCCEs1zHGOSWVGtz09IzlxyIZPQhOCiJqTHGLbaM0jR8QkR34wTzZh4GRKmY1\nLTXO1zFqZJkMorFYUbNhOriNBlEDs3pvc3D9ItmhxOeSHGGkamBgpIoF/MWBMcbASA1satp6G40s\nRxeJGphEzOL3W3OyQioRNRcGRqpYMFgcGBe4tQY1KJlNI7a4WNRumE6OLhI1sASAvOUII6ekElFz\nYWCkirW3txe1mQDSJkdaqPFMTXJ0kagZzZZYm+9yB+3uGjUhBYZlu6qyQjdtPgZGqlhbW5tl+ywX\nZFODkek0FuPFdRKXRhdddnePiDbRnEXBG1VzcUsNsoUirAOjy8X3Itp8DIxUMafTiZaW4k9YZznC\nSA1mZm7Wsp2ji0SNzyowulwtdneLmpSi6kVtmqZxhJGqgoGR1sRqWuosBxipkeh5xCwro3J0kajx\nScspqZyOSnZRRHFgdLmcdneLmgQDI61JuD1c1MbCN9RIIrPzsBhgQFYPgKOLRI0tASBr8fvPwEh2\nUS2mpHI6KlULAyOtSThcPMJogIVvqEGYBhYWFoqbpcrKqERNoHTBm5DdXaMmJSxHGBkYqToYGGlN\nShW+mWLhG2oAiUgEulH8aW6Oo4tETWHGtCp442TBG7KN1Qij08kpqVQdDIy0Jk6nE6FQqKh93LS7\nZ0TrJCTmZueKmqUUKBjcf42oGYxbfPbp9rTa3S1qYpZrGJ0cYaTqYGCkNevt7Slqm5CC6xipruVj\ni8jl80XtOcMPydFFooaXlhLzFm9jHk975Rcj2iCqUvy+5HYzMFJ1MDDSmvX29ha15SUQl7yppvo1\nMzdn2Z7n6CJRU5go8Zmn2xeu7EJEG0ZCU3JFrYFAwO6OUZNgYKQ16+nuhqIUh8MJTkulepXNIplM\nFTUXDA+k1OzuHRFVgdV0VE1zweny2901alKaKEBY1IhgYKRqYWCkNXM4HOjo6ChqHzc5JZXq00Jk\nwbI9Z/BNmag5SMsPPT3ejsovRbRBVIvRRQDw+/khBlUHAyOti9W01CmuY6R6JCWikWhRs2E6YZis\nREfUDKISSFq0e3xcv0j20dTi9YtCCAZGqhoGRloXq8BoApjhfoxUZ/LxOAp6cRW6vOG1u2tEVCXj\nXL9INchhMcLo83mhKLyNp+rgTxqtS0c4DIejeG3XFQ4wUp1ZiEQs2wuGx+6uEVGVXLFYUuF0+aFp\nrEZJ9lGVbFEb1y9SNTEw0rooioK+LX1F7VdMcFoq1Q9dx2J8sai5YHggodrdOyKqghQkrllU+fb6\nuuzuGjU5zWJLDU5HpWpiYKR1275je1FbTnJaKtWPRDQCafH5BrfSIGoel0tU+PYFeyq7ENGGknCq\n6aJWjjBSNTEw0rr19/VB04qnpV7mACPViYWF4umoUirQTU5DI2oWlyymozqcPrjcQbu7Rk1ME3ko\nwihqb2tttbtr1EQYGGndNE3D1q39Re2clkp1IZNGJlu8PiRn+ABwlJyoGSQhlyp8f4w/wNFFspfV\n6CIAtLezci9VDwMjbYgd27cXteUlMM1pqVTjorFFy/YCq6MSNY1LnI5KNcqpFQdGt9sFn49LJqh6\nGBhpQ2zZssWyWuqwuYaLEVVRbLE4MBqmE6Z02N01IqqSS5bVUX1wurhOjOxlNcLY1tZmd7eoyTAw\n0obQNA1b+7cWtV8xAYDTUqlG5bPIWkxHzXMrDaKmEZESMxbTUX1+ji6S/ZxqqqgtzOmoVGUMjLRh\ndgzsKGozAAxJTkul2rRYYjqqbrrt7hoRVcm5ktNRe+3uGjU5RRSgKoWido4wUrUxMNKG6duyBV5P\n8cjMWRa/oRplFRhN08HpqERNQofERYu3J7cnBKeL+9yRvVwseEM1goGRNoyiKLjpppuK2mMmEGXx\nG6o1hQJS6eI344LJ6ahEzWLYXCrQ9nHB0NbKL0a0wVxasqjN4dDQ0tJid9eoyTAw0obas+cmCFEc\nDs+w+A3VmNRiqeqonI5K1BwkzloUu9FUB7zcToNqgEtLFLV1hDvs7hY1IQZG2lA+nw/9/X1F7ZdN\nQLL4DdWQ6GKsqM2UKgxORyVqCrMSmLXaezHYB0VR7e4eNTkFhmVg7O7ptrtr1IQYGGnD7d2zp6hN\nArjAaalUK0wTqWRx5Tnd8ADgzylRMyhV7CbYyumoZD+nlrR8N+rp4eg3VR8DI224vr4+BALFe1ex\n+A3VCj2VgimLfxbzXL9I1BQyUmLIIjB6vGFoTm6ITvbzOIpHFzVNQ0c4bHfXqAkxMNKm2LOnuPhN\nUgKjXMtINSCeLH4jhgQM02l314ioCj6QgG7RHgz12901IgCAS4sXtXV1dUJReOtO1cefOtoUN+3e\nDVUtXgPyjiE4yki2SyaLK8/p0gVORyVqfFkpcdoiLWoON7yBLru7R7S0flEtXjbR0831i2QPBkba\nFG6323KUMS6BCcPu3lFTMw2kLbbTMEyX3T0joio4I4GCxWdDodYBCMHbIrKf1XYaANcvkn34ykib\n5uaDB6GqxT9i75gcZST7FJIpWCxfRIGBkajhFaTEaYulEarmhJ/TUalGeBzF2z45HBra29vt7ho1\nKQZG2jQ+nw+7du0qao9IYIoVU8kmCYvpqJCC6xeJmsBZCWQtPjAKtQ5wKw2qERJeR7Sotbu7m+sX\nyTb8yaNNdejmm6EoxeHwHQMcZSRbJBLFBW906QTXLxI1Nh0S71ssidBUBwLcSoNqhFNNQ1XyRe1b\nt/JnlOzDwEibKhAIYGDHQFH7nARmOMpI1WYayGQyRc0Fw213z4hok503gbRFe7B1OxRFs7t7RAAA\nj7N4dFEIga39nDJN9mFgpE136NDNEKI4HL7OUUaqMjOTgdVPnCG5fpGokWWlxNsWaxcVRUOgdbvd\n3SP6iM9iOmpnZwc8Hu4TTPZhYKRNFwqFsH3btqL2iASucF9GqqJUOmPZbpgOu7tGRJvolGm9drGl\ndRtUlb//VBscShYOJVvUbnUPRVRNDIxUFYcP32q5lvENQwDgKCNVRzpTPCHNNB3g+kWixhWHdWVU\nRdUQbNthd/eIPmI1HRXg+kWyHwMjVUUoFMKem/YUtWcl8AHXMlKVWK1fNCRHF4ga2euGhNX2v63t\nu6GqrI5MtcPriBS1tbe3IRAI2N01anIMjFQ1hw/fCqez+Ob8PWOpeh3RpjJNZLPFU310TkclalhT\nUuKSxYeSDqcXwVZO86PaoSo5uNTiWTDbOB2VagADI1WN2+3GoUOHitpNAK8bHGWkzSWzWUiLzyUM\nyREGokYkIfGaYf1hZHvHXgjBWyCqHQHnvGX7Nk5HpRrAV0uqqgP79yPg9xe1D5tA3O7OUUOzmo4K\nAKbJcvpEjWjYBGZk8YeRHm8rvIFuu7tHdB0Jv0VgbG0NobW11e7OETEwUnWpqopjx45aHntRB7fZ\noE2Tsip4I1VIqHZ3jYg2WFZKvGZYH2vr2G9394hu4NYSUJV8UfvuXbvt7hoRAAZGssGOHTvQ2dlR\n1D4vgfOcmkqbJJfNFbUZJqejEjWi100gbdEeCG6By9Nid/eIbmA1uqgoAjt3DtjdNSIADIxkk+O3\n3w4hisPhWwaQ4yAjbYJ8vvjTW0NyOipRo5kwJc5bbaOhqGjr2FP5BYk2kQIDXmdxddT+/n54PB67\nu0cEgIGRbNLR0YF9e/cWtZsAXjDAqam0saS0DIym5HRUokaiQ+LFUlNRwzdBdbjt7iLRDbyuBQiL\nSvG7d+2yu2tEH2FgJNscPXoEPp+3qH1SAlfMNVyQqJRC3nLjFsk9GIkaytsmsGjR7vaEEGjdbnf3\niIpYTUf1eNzo6+uzu2tEH2FgJNs4HA6cvOOk5bEfGQKSezPSBtELect2jjASNY45KfG+xeiiEALh\n7kOWyyCI7ORQ0nCpqaL2nTt3QlF4i061gz+NZKv+/j4MDOwoas9L4CVOTaUNks8yMBI1MhMSLxgS\nVpNTQm074XT5K74m0WYLumcs23fvZnVUqi0MjGS7E8ePw+VyFbVfMQVGODWVNkA2X1whdSkscsSB\nqBG8ZQJzFnsuOl0+hMJcC0a1RxE6fM6FovaOjjBaQyG7u0d0AwZGsp3b7cbx47dbHntZF8hykJHW\nKZ+zKnjDCqlEjWBcSrxbotBNR9chCMFbHao9ftesZbGbA/u5TyjVHr6KUk3YtXMntmzpLWo3ADzN\nqam0ToVCoahNcjoqUd3LSIlndetjwdZtcHlb7e4ikQUTAddsUavP58X27dvt7hxREQZGqhl333UX\n3O7iqanzEnhX59RBWjvdKB5+MBgYieqahMRzpkTa4pjT5UNbx96Kr0lUDT5nFJoo/iBz3759LHZD\nNYk/lVQzvF4v7r7rbstjH5jADAcZaY0MvXgIQkq+/BHVszMmcNUs/jBRCAUdPUegKPxQiGqRRNA1\nVdSqaRr23HST3Z0jssQ7Jqop/f192L9/n+Wx5wxwqw1aE8NihFGy4A1R3ZqXEj8qsW6xvXMfXO6A\n3V0ksuTWEnCqmaL2m3bvtiwASFQLGBip5tx27Bja29uK2rMSeFoH1zNSZUwTpiz+meEaRqL6VJAS\nT+tLa9w/zhfoQrB1m91dJCop6CreSkMIUfLDcqJawMBINUdVVdx3773QtOIqltekwCmuZ6RKGNbD\nEJIvf0R1R0LiWVMianFM01wId99sdxeJSnKqKXgcsaL2/v4+BINBu7tHVBLvmKgmtbS04MTx45bH\n3jeBqyZHGalMhnUJRSn5wQNRvXnLXNqj10pnz61QVafdXSQqKeSetGw/eOCA3V0jWhEDI9Wsm27a\njR07tlsee8EQiNvdQaoLhs4RRqJGcEmaeKfEusXW9l1w+9rt7iJRSS41aTm62NXZie7ubru7R7Qi\n3jFRTbvrzjvR2hoqajcBPKkDJovg0Cp0s8QdJtcwEtWNeSnxXInlCF5vB0Lh3XZ3kWhFLR7r0cXD\nRw7b3TWiVTEwUk1zOBx46MEHLSuHZSTwfV2wCA6tSEjrnw/+1BDVh4yU+IEOWE0udzh96NhyK4Tg\nFHOqXS41AY+2WNTe3d2F3p4eu7tHtCoGRqp5gUAA999/HxSl+IZgVgKvGgyNVJrkjwZR3TIh8ZQh\nLZcgKIqGri1HoaoOu7tJtKJQidHFI4c5ukj1gYGR6kJvTw9uv/12y2NDBnDe4KfLRESNReIlY6k6\ntpWO3sNwuvx2d5JoRW41AbdW/JFHb09Pw65dTCRnMZ1OIGPq67/Yx5k6MoU4IslrGMtkK3qokYtg\nOp2Abq6/D9lcBOOJa0hv/DOsSdr6L0FUHfv37UM0EsXg0FDRsTcMwCsktnNaEhFRQ3jTBM6XuLFr\n79gDn7/D7i4SrUKixXPN8kjDrl0svIngUydubFMVQDsAqGEAIRzQfjz1RyCIjuXhq1nz+mAdw7kP\n1y0b84B+FoC8cQPWnrcgT95WXr/kWXz+ezfjiQ9vE1UN0PYt9wlF/Srdj3OA8eELkxvf+2wGjzXB\nJAcGRqorJ04cRywWw8zsbNGxF3SBT2pANzMj3aDUnFT+oBDVqtOmLFkR1R/oRUv7Tru7SLQqj7YI\nt5Yoat+ypRddnZ12d29zqCH8ew/wnzLXtRkmYJz56J/nNuLruB7AvwyHyz9fd+KW4E14IrE86GDo\nN/RpTf0KfgUDTXIrIaTkCh+qL5lMBt974gkkk6miYyqAzzqAVrs7STUjG41i5OrVovbFbJ/dXSMi\nC0OmxDMlwqLLHUTP1jugKKxyTLXORG/wLBxKrujIZx77NDo6GnuEXC9EMDj9I3x79E/x72ef2JiL\nur6EPzrwi/ipvn0IO9Y45lWIYyR2Bs+N/gX+p7H/c02X+Ad7X8Hv7bkLPU007MbASHUpGovh+9//\nAXK54hdipwB+UgW8TfKpD62MgZGofoxJubxlUjGH04MtW09C0VwVX5eo2gKuabR5xova+/v78PBD\nD9ndveoyZ/Di6f8d91/+gzVf4tePXMZv7hjY2H4VRvC7zw/gV5Jlnq/+Mp578PfwQKD5SsA03zOm\nhtAaCuHhhx6EphV/vJOXwHcMoGB3J6nG8bMyoloys7x9hlVYVDUXevqOMyxSXVCEjpC7eO2iogjc\nfluZa+4aidKF+279feQe+AHuWMPDf/LQ+MaHRQBw7MD//MgY/pdy0pDrazj7uT9oyrAIMDBSHevs\n7MT991lvt5GRwHd1gKGAFMX6ZY4D0ES1IyIlnjCs91pUFA3dfbdBc3rt7iZRWUKeCSii+KOPffv2\noaWlxe7u2cbZ+ihefeD/ruxB6lfw27s3c0ZQP/75ri+scs6XcerRX8OBJr5xYGCkutbf34e77rrL\n8tiiBL6jCzA0NjdVLbHWSRiVXYiINkVUSnxXB7IWL9VCCHT1HYPLHbS7m0RlcSppBJxzRe1utwu3\n3nKL3d2zndL6D3Bm+8PlP8DYkBI5K1KdXSscfRhPfvLrONxE6xWtMDBS3du1c2fJKR4LEvh7XUAy\nNDYtVS01wsifCSK7RaTE3+tAqsTxrt7D8Hjb7O4mUZkkWr3jlkeOHD4Ml4tTqgHg4KGvlT81VT0G\n3yb3Z3j62yWPfeXk4/gUJzcwMFJjOHjwAA7dfNDyWIShsbmVGGEUYr079xLRekSkxHd0lNz4uqP7\nILyBxtzYnBqTV4vBrcWL2ltbQ9izZ4/d3asdjiP4L+WOMmqeze2LOYj/a27K+tjAe/hqT/NOIb4e\nAyM1jGPHjuGm3bstj0Ul8C1dwGRobD6lAiN/FohssyAl/t4oHRbbwnsQCG21u5tEZVNgIFRidPH4\n8eMQookXwFk4ePDfo6y5A7m/wKvpck5cm8Vr/wN/afW/xvV7uHb4Vnu+OTWIgZEayp13nsTu3bss\njy0yNDYnhSOMRLVkXkp8x1gqTmalLbwbofBOu7tJVJEWz6Tlnovbtm1Fb0+P3d2rPa678XddXWWc\n+B5+99rEJnVCxwuD/5tFuxt/fvcvo9fGb0+tYWCkhiKEwN133YU9N91keTy+HBp1hsbmIYRlpVQB\nBkaiaptbNSzuQSi8u7KLEtnMpSYRdE0Xtauq0pzbaJTpgUPl7cv48ugr2JRBxvTr+IlFi/bd7+Dn\nWhiRrsfvBjWkO+88ib17rdcLxCXwbV0gb3cnqWqsKqUqHGEkqqopKfFdw7oaKgC0d+zlyCLVIRNt\n3lHLI4cOHUIgELC7gzVLCf4EnixnXmr8t/DUJiTGK6O/a9H6VVw8dMDm70ztYWCkhnXyjjuwf98+\ny2MJCXxDB+IVXpPqk9PhKG4UeuUXIqI1ubK8N27JsNi5Dy3tm7AxN9EmC7qn4VQzRe2hUAiHbr7Z\n7u7VOA2P3lrOvozv4ScvbfT2GuP47xe/VdT65eP/M1ieqBgDIzW0EyeO48CB/ZbHshL4dgGY4ezU\nhud0OovaVO7DSFQVZ0yJH+gSpT6iCXfuR0vbDru7SVQxh5JFyD1Z1C6EwF13niy9DzB9RGn9CXy7\nnEKkw/8dgxv4dVMz38B//Pj9X/Cv8ZU+VkW1wsBIDe/47bfj5oPWW24YAL6vA1ckU2MjswqMChgY\niTaThMQbpsTLK/yqhbsOINi23e6uEq2BRJt31LLi9r69e9HZ2Wl3B+uEhs8d/ssyzvv/4XcnFss4\nrxw6nj7/qx9rc+M/3/4PwS0XrTEwUlO47bZjOHzrLZbHJIAXdYEPTACCwbERuawCo9ABFj8i2hQG\nJJ4zgHdLhEUhBDq6b0awdZvdXSVaE79rDm4tUdzu9+Ho0SN2d6+uiPYv4C/8q5/3Jxe+vzHFb9Iv\n4ycjH2vr/A5+iYVuSuJ3hprG4cOHcefJO0ruhfSuAfzIEAyNDchqhBGCW2sQbYaClHjSkBgs8esl\nFBWdW44hEOq3u6tEa6KJPNrc1nsu3nHiDjis1s3TCjz4x7f80eqnxf8Z/u/F9b9vnxn6zY+1HMa3\njn7C7m9CTWNgpKayZ88ePPjgA9A0zfL4RQN4Rgc48tRYHFaBEYDCdYxEGyoJiW8bEuOm9QdzquZE\nb/8J+PwddneVaI0k2n1XLD9w3DkwgP7+Prs7WJcc3T+D33OvdlYWP3/ujXV+pUH81qVnb2zq+UP8\nBOeiroiBkZrO1v5+fPLRR+B2uyyPj5sC39ZFyWp+VIec1p/2KqyUSrRhJqXE4wVgTlqHRYfTiy1b\nT8LlYVEJql9B97TlVFS324Xjx2+3u3t1LIifvfk3Vj9t6qt4ZR37oi1c/Sv85Q0vUYfxrVtP2v3k\nax4DIzWljo4OPPbpTyMYtN4fKSqBx3VgmqGxMSgqNK24Wp3KwEi0ASTOmBLf0VFyfZHbE8KWrSeh\nOfkxPtUvp5JCyD1heezE8eNwu1cdIqMVtGz9Z/iKWO2sZ3DPxaE1foU4vnX2P93Y1PnbHF0sAwMj\nNa1gMIjHPv1pdHSELY8XsFRB9SyL4TQEj9tT1KaKdXxMSUQwIPGCAbxsAKVWFvkCXejuPw5Fc1Z0\nbaJaosBcmopqcWxgYAcGBriP6Pp14Zdu/hernzb8Bzi3htsyM/pd/EL2+hY3/vzQvXY/6brAwEhN\nze1245OPPrrimoO3DOAFrmusex6vRWBUGBiJ1ioJiW/rEudXqEERbN2Kzt4jUBTuR0f1LeQdg1PN\nFrX7fF7cceKE3d1rGN27/yX+yaq3W3+I/8+ViXIud4NXz/3rGxta/wd+ipVRy8LvEjU9TdPw0IMP\n4pZbDpU8Z4TrGuuex1McGIUwIVj4hqhiH65XnCmxXlEIgXDXAYS7DpasTE1UL7xaFAHnnOWxe+6+\nGy6Xq8IrUml78L/u+eKqZ/39mf8To5VcNvcKfmJm9oamrx18lPsulomBkQhLNzdHjxzB/fffV7KC\nKtc11jevRWAEAFUU7O4aUR1Zfb2iqjnR3X+CeyxSQ9BEHu2+EctjBw8eQE9Pj91dbDh7bvo3aFvt\nJOM/4usTi2Vfc3Do93HD1oveP8E/6/TZ/VTrBgMj0XV2bN+Ozzz2aQQC1sVwPlzX+K4BrmusNy43\nFIuRDoWBkagsOSnxtC5XXK/o8rSgb9td8Hhb7e4u0QZY2kLDagumcHs7jh45YncHG5PrOL7fu/pr\nyJ+c+VvEyrrgCH5/8Bs3tPzSzf8I3NynfAyMRB/T2tqKz37mMfT1bSl5zgcm8L2CAFfA1REh4PYU\nV7DTuI6RaFWzUuJxHRiWpaeXBkJ96N16B1QHK0VSY2j1TFhuoeFwaLjvvnuhqlybu1mOH/jz1U9K\n/xL+ZH719/DIlT/CH1//0qV+Df++j9v7VIKBkciCy+XCww89hEOHbi55zpwE/q4ATJgcaawXXk/x\nagUWviEqTULifVPimzpQavLXh+sVO7oPQQjeVlBj8DojCLqmLY+dOH4cwWDQ7i42tuCn8TdlZLp/\ne/p7WHme0AL+69nfvqHlZ2/9WfTa/fzqDF/ZiUoQQuDY0aMrrmssAHjaEHjVBFhFtfb5LCqlKsKA\nwv0YiYqkIPE9Q+K1Faagcr0iNSKHkkbYY71ucWBgB3bv3m13F5uAhi8c+sPVT4v+DP5qsXSp5tTM\nf8evX58o1a/gq9u77X5ydYeBkWgVO7Zvx2c/8xja2krPpx8ygMd1gfKXX5MdvAG/Zbuq5OzuGlFN\nuSKBv9WBcbP0FFSPrw1btt/N9YrUUBQY6PBfghDFISQUCuGuO++0u4tNw9H5j/A1x2pnZfHz514q\ncSyDb7z/qze0fP7mX8J2u59YHWJgJCpDKBTCY5/+NPbt3VvynIQEvlUATptgQZxa5XTD4Sh+93Ew\nMBIBAApS4gVD4ge6XHEbobbwTejuOw5N43YC1EiWitxYvSc4nQ48+MD9JWcc0WZox/908F+vftrU\nv8aTxVtkwox+Ez+XvL7ly/jaTo4urgUDI1GZNE3DHXecwAP33w+X02l5jgTwjgF8pyCQqOzyVCUB\ni1FGTcmCU4qp2Y1Jib/WgfOlZ3dBc7jRs/UOhMK7uL8iNZygewpeR8zy2D13342WFhZKqba2gS/h\nX6z69vweHrvwflHrC6f/yQ3/vufQ/xt77H5CdYqBkahC27dvw+c+91l0d3eVPGdBAt8oAO9ztLHm\nBP3FW6YIYXIdIzWtrJR4zpD4ng4kVzjPH+jhFFRqWG5tEa3ua5bHbrnlELZu3Wp3F5vUDvzLPV9c\n/bQr/w3nrr/dSj+Ph+avP+GX8Ue7++x+MnWLgZFoDfx+Pz756KM4euQIFMX6U3YJ4JQBfLMgytwn\niKrBE7Rex6hxWio1ocsS+BsduLjCqKKiqOjsOYTOLYehqqsuKCKqOw4lhw7fZctjW7b04sjhw3Z3\nsantuenfoG3Vs/4QX59Y+Ohf7539X244ev+BX8VBu59IHWNgJFojIQRuueUQHvv0pxEMBkqet7i8\ntvEdA+C0xxqgOeFyFU8p5jpGaiZpKfGUYeKHukR6hfNcnhb0bb8b/hZ+Mk+NSRE6OvyDUIRRdCzg\n9+O+e+/l9Gu7uY7j273tq572lxefXno9K5zCl8ZPXXfkl/EHe3bY/SzqGgMj0TqFw2F8/nOfw4ED\n+1d8UzltLlVSnWdmtF3AYlqqpmQhGOip4UkMmhJ/YwCXVqiAKoSC9o496N16EprTW8H1ieqJiQ7f\nJcsPDFVVxQMP3A+Xi4WdasE9B/7z6ifFfwvPF4Dx4f8dr1//2EO/hgPM/OsipJS8QyLaILOzs3j1\ntdcQi628wcZuBbhTlVDAVzA75BcXcXmkeI+tVL4duulZwxWJal9ESrxqyhW3ygAAtyeEcPctcLp8\ndneZaBNJhH1X4HNELI/efded3G+xpmTwt8968dOr7F/26MBfYtvEP8Gf5j9s+TIufuHrLHazTgyM\nRBvMMAy8/8EHOHPmDEyz9K+XA8AxFdinSkAyOFaVaWLo7FkY5o0LtwqGB+nC6tNeiOpJQUq8bQIf\nmMAKSxUhFBXt4T0ItG7jFDxqeCH3NbS4Jy2PHbr5II4dO2Z3F+ljUjO/A/+rv1r6BBXAx2YW33No\nHC+x2M26cUoq0QZTVRVHjxzBZx57DO3tpZdpFwC8vlwUZ5Yf21SXoliWR3dwew1qIBISF02J/6ED\n760SFj3eMPq3341g23aGRWp4PudCybC4Y/t2hsUa5ev6x/jKSi9PRctQv4r/wrC4ITjCSLSJTNPE\nmTNn8f4H78MwzBXP3aFI3KkKOMu8Nq1PfjGGyyOjRe2clkqNYE5KvGxITK8ye0FRNLR37kMg1G93\nl4mqwq3G0RkYtFwQ0tnZgUcfeQSaptndTSphevhL6Dn9x2Wd+9mjU/jO9m67u9wQGBiJqiAWi+G1\nH/0IMzOzK56nADisArdwmurm47RUakAZKfGmCZwzVz/XF+hCuPMAVIfb7m4TVYVDyaI7cN66Imog\ngM889mm43fx9qGnyLD7zzZvxxGq3SOrXcO3zv4Zeu/vbIBgYiaro8uUrePudd5BOp1c8zy+A21WJ\n7QoYHDfR9NVRRKOxG9qkFIjnegEWJKI6okPijAmcMoHsKu/qDqcP4c4D8PjDdnebqGo0kUd34AJU\nJV90zOV04tOf/hRCoZDd3aQyvPfWURy5YduMYr90Yh7/eQs//N0oDIxEVVYoFPDBBx/g3Pnzq05T\nbRXACRXoUTjiuBlysRiujI4WtacLrSgYrBBJtc+ExAUTeNsAUqucqygqWtt3L69TZAkDah6KKKA7\ncHF5nfqNVFXBJx5+GD09PXZ3k8qV/A7EU58vfdz1J5h97BfRYXc/GwgDI5FNFhcX8eZbb2Fi4tqq\n53YK4KQKtDEzbqwS01IN04lkvtPu3hGVJCFxWUq8qQvEyjg/ENyC1s690DTuKUfNRUBHd2AQTtV6\nZs89d9+FXbt22d1NqkgGf/eUF/8oaX30P9ydxH/s5Ie+G4mBkchmY2NjePOtt5FIJFY9t1+ROKEK\nBMq4LpVnbmIc8/MLRe2JXCdMyRJEVGskxiXwhiExW8asA5c7gHDnQbi8rXZ3nKjqFBjo9A/CpVmP\nvx++9RYcPnzY7m7SGixO/iZCr/+74gPBbyL18E/Ca3cHGwwDI1EN0HUdZ8+dw+nTZ6Dr+qrn71Qk\nTigCLo44rl8mjQuDQ0XNed2PjB6yu3dEH5mREm+YEhPm6r/4mupAa3gP/KF+bpNBTcpEp38YHi1u\neXT/vn04ceK43Z2ktbIsfuPGnz+Uws+1cMr9RmNgJKoh6XQaH3xwGoNDgzDNlX81BYBdCnBUAby8\nH1yXseEhpFI3TleSUiCR64aEanf3qKlJTErglClxtYygqCgqWlp3INQ2AKFyawBqVhIdvsvwOqKW\nR3ft2ol77r7b7k7SeuReQfsT9yByfVvP85An77e7Zw2J7yZENcTr9eKOO07g4MEDOHXqPVy+cqXk\nuRLAsLn0Z4cicUQVaCn/S9F1OtrDSKXGbmgTQkJTMygYfru7R01JYkwC7xgSU1Jgtaq9QggEQ9vQ\n2r4TCtcpUlOTaPeOlAyL27dtw9133WV3J2mdpq5958awiIfx7GGGxc3CEUaiGhaJRPDuu6cwPjFR\n1vlbhMQxVaCdVVUrY5oYPncOunHj3lyG6VgufsPvJVXHh8VsThnAXJm/w4HgFrSGd0NzctUONTuJ\nNu9VBJxzlke3bOnFQw8+CFXlzJH6Fsd/fbIFv3B90dvdg5CHbrK7Yw2LgZGoDkxPT+Pdd09hZna2\nrPM7BXBMBboZHMu2cO0aZueKbzJS+TB0kxs50+YyITFkAqcMIFrmY3yBLrSGb4LTxTJYRKuFxa7O\nTjzyyCegaZxcV+9SM78D/6u/el3Ll3HxC1/HHrs71sAYGInqyNj4OE6dOoVIpLxbyjYB3KJK7FDA\n4LiabBYXLl4sajZMF5J57uZEmyMrJS5K4AMDSJb5GI+3FW3hvax8SvQRiXbvKPzOecuj7e1t+OSj\nj8LpZOXr+reAr383jF8v/LjlX9w2jz/a2m53xxoaAyNRHRobH8fp06cxOztX1vkuARxQlv447O58\nDZu8cgWL8eKKesl8BwyT68Jo4yxIiTMmMGgCq9dFXuL1daK1fSeDItENJMLeEficC5ZHQ6EWfOqT\nn4TbzZkijWDh6n9A+J3/9OOG4F8j9fBPcxuNTcbASFTHpqam8MHp05icnCr7MQOKxCFFoI3TVYuY\nqRQGh4eL2nXThRRHGWmdJCRGpMAZw8REBb97/kAPWtp3wuUO2v0UiGqMRNh3BT5HxPJoMBjApz75\nSXi9jBONYRBf+sZe/PFHL59u/PUnM/hp/u/ddAyMRA1gbm4Op8+cwdWrY2U/pk0Ah1SJAU5XvcHE\npUtIJIsnBybznTBMTmeiymWlxAUJnDWAeJmPEULA37IFLa074XT57H4KRDXIRIfvSslqqKFQCx59\n5BGGxQZy9t1P4ObRZ37csPss5KEDdnerKTAwEjWQaCyGM6fP4PKVKyj3V9slgL0C2Mf9HAEARjKJ\noUuXitp1w41UIWx396huSExJ4KIJDFUw7VQIBcGWfgTbB+BweOx+EkQ1ylzeZzFmebS1NYRHH3kE\nHg9/h6rCnMFTZ34Hj45/HdCVpTbfL+J/2/az+MXdxxHegHsLM/441Gd+6scN6lcw8vmvYrvdz71J\nMDASNaBEIoELFy9ieGgYuXy+7Md1CGC/KrFTAM28lcT48DCSqVRRezLXCUNylJFKS0Fi0AQuGECs\ngsdpmgvB0FYEQ1u5jyLRChSYCPsvwaMtWh5vb2/DI5/4BNcsVkvyVXzmh3fjiZK3DA/jbx94Av+w\ndT3vnTP4+ne7byh087W7k/i1Ts6+qBYGRqIGpus6Ll++jHPnLyAWi5X9OAXAgALsV4BwE6511BNx\nDF++UtxuupDKh9HMYZqKGZAYkRIXTeCqWdnPhtsTQkvrdngD3RBCsfupENU0Rejo9A/BpaYsj4fD\n7XjkE5+Ay8UPXarCHMQ//dZe/OWqL3u/jLM/+Qc4sMa3zjfeOoY7xt/9cUPfq5DH77T72TcVBkai\nJjE1NYXzFy5gbGy87OmqAOAXwB5lacpqM42tXR0aRDqdKWpP5duhm5zmRBJzH045lUC2gndSIQT8\ngS0Itm2Dy91i9xMhqguayKMzMAiHkrU83tnZgU88/DC3zqiiojWFK1jr1heLY7+J0Nv/7rqWL+Ps\nT359zeGT1oaBkajJJBIJXLw4iKHhYeRyuYoe2ymAXQqwswm25yg1ymhKFYlcNzjK2IwkIhK4JIHL\nJhCp8N1Tc7gRbPlw2ilvaonK5VTS6PQPQVUKlse7ujrxiYcfhsPR6O9MtWQEX/72AH7LLPP0be9B\nHru1si8R/wHEM5+6oek3703i18OcilptDIxETUrXdYyMjGBoeBgzM7MVP75TALsVYKcioTVoeCq1\nL2Om0IK8EbC7e1QlUSlxSQKX1hASgaX9EwMtW+ANdHHaKVGF3GocHf5hKMI6mfT29OChhx6Epml2\nd7W55N5E+xMnECn3/EoDY+EU/ul3jt443XXgLORhVkW1A3+7iJqUpmnYvXs3du/ejXg8juFLl3Dp\n0iWkUumyHj8rgVkDeM0Q6BLAbhXYJSSUBgqPvX29iF+I4+Mfq7m1OAqmF1KqdneRNklUSlxeHkmc\nX0NIdDh9CLb0wR/cAtXB4htEa+F1RhH2XoaA9S/hwMAO3H3XXVBVvhZXnQLsAfD6ZlzbHMSXn/hY\nWAz+GaIMi7bhCCMRfURKicnJSQwND2NsbAyGUe5ckx/rEcB2BdgmAG8DFMyZvzaBubn5ova87kdG\nD9ndPdogEhKzEhiVwOgaQ6KiqPAHeuEP9cPtCdn9lIjqWsA1gzZP6b2FDxzYj+O33253N5tXhSOM\n9x+4guf37lj9xMJZfPmJmz821fXn8cbn/gzHOcxlGwZGIrKUy+Vw5coIhoeHMb+wsKZr+AWwTQG2\nC6CrXsOjoWP4/AXohlF0iNts1LeclBiHxFVT4KoEMmt8N/R42xFo6YM30A1F4UgH0fpItHquIeia\nKnnGbbcdw80HD9rd0SY3gi99YwB/XNbb+hfx8mcex92rvF2a8efxuacf/NgWHW78+UMp/FwLp/Pb\niYGRiFYVi8UwMjqKkZHRirbnuJ4KYIsisUMBtgpRV0VzEvNzmJi4VtRumg4k8p1gAZx6sVS05qoE\nrpoSU1Kg8jH0JS5PC/z+HniDPXA4WDWXaCMoMNDuuwKvI2Z9XBG46667sGvnTru7SgBefrUL95ZR\nA+Fnj07hL7Z3r3jO5Stfx673fr2o/SsnY/hqD6tJ242BkYgqEo3FMDoygpHRUcRii2u+TpsA+gSw\nRQF6hERNhy4pMTJ4EdlscVXZnB5EVg/a3UMqIQWJayZwTQITJhBfx7Vc7iD8gV74At3QnF67nxpR\nQ9FEDh3+YTjVjOVxh0PDA/ffjy1bttjdVVqWj/w3uF74f61y1sN45rNP4yHLT4l1XJt5Dr/z7qP4\nbYv/7b922xS+trUbZD8GRiJas2g0ipGRUYyMjmBxcT234kBYAFuWA2R3DQZII5nE0KVLlscSuU6Y\nnJpaE9JS4hokJk2BayYQXef1lkJiD3yBHoZEok3iUhPo9A9DEYblcY/HjYcffhjh9sr38aPN9eyr\n3Xh4Zmblk9SH8JOhXTBVL7Y429ChuhHJvI/fn/0fJR/yW8fn8W/6+P+7VjAwEtGGiEQiuDo2hvHx\ncczPr23N4/U6rguQXTUSIOcnJjA3X1wAxzAdSHJqqi1SkJiSSwFxQgLRdb6jCSHg9rTB6+vgSCJR\nFficc2j3jpZ89QwGA3jkE59AIMCtjGqSOYIvf6eC/RhX9UX8/UN/hc+18EPYWsLASEQbLpPJYGJi\nAhMT13Bt8hry+cK6rxkUSxVYu5SlPSCDwoYiOqaByxcvWj4fTk3dfDokZk1gBsCslJg2BZIbcF1N\ndcDj64TX3wmvrwNCZSk+os0n0eqZQNA1XfKM3t4e3H/ffXC5XHZ3llZSGMJ/eGYP/lNmndfpeRwj\nd3wR2/nZa81hYCSiTWWaJmZmZjA+MYGJiYl1rXu8noKlaazdAugUEl1CwFWFSqx6IoHhy5ctjyVy\nXTBlPZXzqV1yuUDNrARmlv9EJNZcpObjXO4gvL5OePydcLlbIATvUIiqRYGBsP8yPFrp94P9+/bh\n9ttvg6KwOmZ90PHB4P+BW8/+WuUPbf0N/ODwP8ejrSG7nwSVwMBIRFWVSCQwMXEN09PTmJqesiwk\ns1YOLIXINgUIC4k2IdCKjZ/OOjc+brnViLk8NVVyamoFJNISWAAQMYEIgHkpEZEC+gZ+Fc3hhsfT\nDo+3DW5/JzSNIxZEdnAoaXT4L8OhZC2PK4rAiePHsXfvXru7SmuSwfDkm3jq2tP4+9jreC71IvDR\n0lQ34LoJcB3GzwQP4YH2k7h7y2Hs8vD1uNYxMBKRraLRKCanpjA9PY3pqWnk8vkN/xp+AbQJibAQ\naINEuyLgW0+QNJanphaKp6YWDC/ShbYqfxfrgURWLlUpjUhgXgIRSMxLseb9D1eiaq6lgOhrg8fb\nDs3ps/sbQNT0fM4FtHtGIIT1L73L5cID99+Hnp4eu7tKRNdhYCSimiGlRCQSwfT0NCanpjAzM7Mh\n6x9LcQsgCKBFLP0JCokWCLQICUVgxemthXgcl65csTyWLoRQMPw2fzerz4REEkDcBBaxFA7jUiIu\ngRgE8pv4bqNqTng87XB72+D2huF0MSAS1Q4T7d4x+J1zJc8IhUJ4+KEHWdyGqAYxMBJRzZJSIra4\niLnZOczNz2F+fh6RSBTVeNlSsBQiA0IiBIHAcqhsAeAREhDAwsQkZucsboAkkMg33lYbcnmUMAkg\nDvFRGIxDYtEUSGDj1hiuRAgBl7sFLncILncL3J5WVjMlqlGqkkOn7xKcarrkOf19fbj33nvgdDbW\nayZRo2BgJKK6ous6FhYWMDc3j7m5pSCZTKZs6YsTEmPDwzDSabgh4RICbgAuAA5oKOQ64BIKnMBS\nu1j6W7V1jaOEDiALICeX/mSFQF7KpTYA2eX2nJDL/y2QEdjUEcKVOJw+uN0huDwhuNwhON0BCMFC\nGES1zqNFEfZdgSJKf5R06NDNOHrkCAtPEdUwBkYiqnvpdBoLCxFEY1FEI1FEY1EsLi7CMDZ/vCuf\nz2NwcBAFo3jD6YLhQbrQio+vldSwFBzdAnBBwi0AxyaFyDwkchLIQCyFP1xXf6DGCKHA6fLD6Q7C\n6QzA5QrC4Q5CVVl5lqi+rL5lhsvpxN333I2t/f12d5aIVsHASEQNyTRNLMbjiEYiiMZiiEQiiEaj\nmzIaGV9hPePS/oxck/NxDqcPTlcATmcATpcfLncQqsPLUQaiOqeJPNp9V+DWEiXPCYfbcf9993G9\nIlGdYGAkoqZSKBQQj8eRSCSRSCaQSPz4TzKZhGmu7SVxcmoS0zOzlscyhVbkjeZaYyeEgMPphab5\n4HB4oDm9cDh80JxeaA4PFEW1u4tEtMG8zgjaPSMrTkHdt3cvbr/9NqgqXwOI6gUDIxHRMiklkskk\nEsnkDUEyEV/6e+UtPySGL11CosQIZiofhm421l5TquaEw+GFpnnhcHrhcHigOn1wOrxQHW67u0dE\nVSKgo907Bp9zoeQ5mqbhrjtPYmBgwO7uElGFGBiJiMqUy+WQSCaRy2aRy+WQz+eRy+WRy+eWjsUT\nePPtt5BOZ6AbBnRd/3FFVymQzHfCkJrdT8OSUFSoqgOK4oCqalBUJxTVAVVxLrc5lv6tOiFUJxxO\nDxSlNp8LEVWPS02gw3cFqlL6A7VQKIQH7r8PoVDI7u4S0RowMBIRbaBIJIInv/99FAo6gKW1lMZy\neMwWNMzEt0HXTZhGAaZZgGEWYOoFmObmlKJRFA2K5oCqfBj4HFAUJ4R6fQh0sOooEVXIRKtnEkHX\n1Ipn7RwYwJ13noSm8QMmonrFwEhEtMGuXbuGZ5591nI9ZFYPYCZ5E5Z2eiQiqj8OJYt232W4Vthb\n0el04I4Td2DnTk5BJap3DIxERJtgcHAQr/3odctj6UIIc6mdYGgkovoi4XfNos09DiFK3z52dXXi\n3nvugd/vt7vDRLQBGBiJiDbJ22+/gzNnz1oeSxdal0Mjt5EgotrnULJo846uuF2GoggcOXwYN998\nM7fIIWogDIxERJvohRdexMjoqOWxVKEN86kBMDQSUe2SCLqnEXJfg0DpW8aWliDuvfdehNvb7e4w\nEW0wrkAmItpEd999F9KZNGYs9mj0OSKAV2A+vQMMjURUa5xKGm2+kRXXKgLA3r17cPttt7GwDVGD\n4ggjEdEmKxQKeOrppzE7O2d5PJkPYyG9HQyNRFQbTITcU2hxT654lsfjxp133omt/f12d5iINhED\nIxFRFeTzefzwqacwP2+9sXUy34GF9DYwNBKRnVxqEm3eETjV7Irn7RwYwPHjt8PtdtvdZSLaZAyM\nRERVksvl8MOnnsLCQsTy+FIhnAGweioRVZuAjlbPJAKumRXP83q9OHnyDo4qEjURBkYioirK5XL4\n/g9+gGg0Znk8qwcxl9wFE6rdXSWipiDhc0bQ5hmHIgornrlnz0247dgxOJ1OuztNRFXEwEhEVGWZ\nTAY/+OEPEYstWh7PGx7MJPfAlA67u0pEDcyppNHqHVtxqwwACAQCuOvOk+jp6bG7y0RkAwZGIiIb\npNNp/PCppxGLxSyPF0wX5pJ7UDBddneViBpMudNPhRDYv38fjh45wgqoRE2MgZGIyCa5XA7PPvec\n5ZYbAGBKFTPJPcgbPru7SkQNofzpp6FQCHfdeRKdnZ12d5qIbMbASERkI13X8eJLL2FsbNzyuJQC\n85kBpPNtdneViOqYU0mh1Tu+6vRTh0PD4VsPY//+fVAUFuAiIgZGIiLbSSnxox+9jsGhoZLnxHM9\niGa2gNtuEFElNJFHi2cCfufCqucODOzA7bfdBq/Xa3e3iaiGMDASEdWIU6few/sffFDyeEZvwXxq\nAKbkWiIiWpkCAwHPFFpc0xBY+VYvFArhjhPHWdSGiCwxMBIR1ZALFy7ijTffRKmX5oLpwnxyF/Im\nRwCIyIqE3zWHVvcEFGGseCannxJRORgYiYhqzNj4OF5++WXk89ZFKaRUltc1ttrdVSKqGRIeLYZW\n7wQcSnbVszn9lIjKxcBIRFSDFhcX8exzz2FxMV7ynHiue3ldI0cGiJqZS00i5JlYtaANALS3t+H2\n227j9FMiKhsDIxFRjcrn83jp5ZcxPj5R+hzDg/nUAAqcokrUdFxqEi2eSXi0xVXP9fm8OHr0KHbt\n3Gl3t4mozjAwEhHVuPfeew/vvV+6GI6EQDTTj0SuE6yiStT4KgmKTqcDhw4dwv59+6BpLJhFRJVj\nYCQiqgNjY2N46eWXUSjoJc9ZqqK6A6Z02N1dItoElQRFRRHYu2cvbr31Frjdbru7TkR1jIGRiKhO\nxGIxvPDii4hGYyXPMaWK+dQAMnrI7u4S0QapJCgCwPZt23Ds2FEEg0G7u05EDYCBkYiojui6jnfe\nfRfnz19Y8bxkvh3RzFbu2UhUx5xqCiH3JDyOWFnnd3V14tjRo+jq6rK760TUQBgYiYjq0MTEBF59\n9TWkM5mS55hSRSSzDal8G7i2kah+rCUoHjl8mJVPiWhTMDASEdWpbDaLV197DWNj4yufpwcRSW9D\nweQ6JqJa5lKTaHFPMSgSUU1hYCQiqnODg4N48623oeulC+JICMSzvYhlu8F9G4lqiQmvM4agcxou\nLVXWIxgUiaiaGBiJiBrA4uIiXn7lFczNza94XsF0I5LahqzBYhhEdlJEAUHXLHyuOWiiUNZjGBSJ\nyA4MjEREDUJKiYsXB/HuqXeRz698A5ouhBDL9HOaKlFVSbjUJALuWfgckbIfxaBIRHZiYCQiajDp\ndBpvvvkWRkZHVz03ke9ALLOFezcSbSIFJryuBQScs3Cq6bIfx6BIRLWAgZGIqEGNjY/jjTfeQDK5\n8rooKRXEcj1IZrthcn0j0YZRlRyCrjn4nbNQhFH243p6unHrLbcwKBJRTWBgJCJqYLqu49R77+Hc\nufNY7eXeMB2IZrcglQ+D23AQrZWEW0sg4JqBt8xqpwCgaRp27hzA/n370NraaveTICL6CAMjEVET\nWFhYwFtvv42pqelVzy2Ybixme7l/I1EFFBjwueYRcM3CoWTLflwwGMC+vXuxa9cuuFwuu58GEVER\nBkYioiYyNj6Od955B7HY4qrnFkwX4rluJHNhcCsOImsOJYuAaxZ+5xyEMMt+XH9fH/bt24u+vj67\nnwIR0YoYGImImoyUEkNDQ3jvvfeRzmRWPd8wnVjMdSOV6+AaRyIAitDhdUbgc0Tg1hJlP87pdGD3\n7t3Yt3cvgkFubUNE9YGBkYioSRUKBZw9exZnzp6Druurnm9KFYu5HiSznTCh2t19oqoS0OF1RuFz\nRuHRVh+hv15rawj79+3Dzp07oWma3U+FiKgiDIxERE0unU7jvffex/ClYZjm6m8JplSQyncgkevk\nPo7U0BQYcDsX4XMswONYhED5t0yKIrBt6zbs27cX3d3ddj8VIqI1Y2AkIiIAQCKRwJmzZzE8PAzD\nKG8tVkYPIpHtQkZvAQvkUGMw4dHi8LkW4NWiEKKy2yS324U9e/Zg75498Pl8dj8ZIqJ1Y2AkIqIb\npNNpnDl7FoODQ2VNVQWW1jnG851I5jpgSk65o3oj4dbi8Dkj8DoiUCooXvOhcLgd+/fvx47t26Gq\nnLJNRI2DgZGIiCxls1mcPXcOFy9eRD5fKOsxEgKpfBuSuQ7kDD846ki1S8KtJuF1LcDniEARRsVX\n8Pm8GNgxgB0DOxBub7f7CRERbQoGRiIiWlEul8OFixdx7tx55HK5sh9XMF1I59uRyrdzrSPVCAmX\nmloqXuNYgKqU90HI9TweN3Zs34EdAzvQ1dlp9xMiItp0DIxERFQWXdcxMjKCCxcuYn5hoaLH5gwv\nUvkwUvk2mNJh91OhJqIIHW5HHB5tER4tDlXJV3wNl8uF7du2YcfADvR0d0MIjpwTUfNgYCQioorN\nzc3hwoWLGBkdKbtAzocyeguS+TCy+RZuz0EbToEJp5aExxGHW1uEU02v6ToOh4ZtW7dhx44d2LKl\nF4rCPUiJqDkxMBIR0Zpls1kMDQ3h4uAgkslURY+VUiCjtyBdaEOm0MJiObRGEk4lDbczDrcWh1tL\nVLT9xfVUVcXW/n7s2LEDfX1buGciEREYGImIaANIKTE2NobBoSFcuzaJtby1ZPUg0oUWZAutKJgu\nu58S1TBN5OF2LsKtLU01XUvBmg8pisCWLVswsGMAW7f2w+HglGkiousxMBIR0YbKZDK4MjKCy5cv\nY36+srWOHyqYbmQKIWTyLcgafgCcDtjMFBhwaXF4HAm4HYtwKNl1XU8IgZ6ebgzsGMC2bVvhcvED\nCiKiUhgYiYho08RiMVy+cgWXL1+ueMrqhyQEcnoAGT2AXCGInOEDt+tobIrQ4VRTcGtJuB2LcKlr\n+9m5nsfjRm9PL7Zs6cWWLVvg8XjsfppERHWBgZGIiKpiZmYGly5fxujIKHL5yitVfkhKBVkjgKwe\nQK4QYICsc0vhMA2nloJLTcGhpuFQyt++pRRN09Dd3fVRSGxtbbX7qRIR1SUGRiIiqirTNDE1NYWr\nY2MYuzqGdCazvutJBTkjgLzuQ073IWf4uHVHjRJCh2sTwuHStQXa29uwZcsW9Pb0oLOzE6rKKrxE\nROvFwEhERLaam5vD1bExjI+PIxqNbcg1DdOJnOFDzvAir/uQN3yswlpVcnnkMLMcDtNwqKkNC4cf\nCgQC6O3tQW9vL3p7ergWkYhoEzAwEhFRzUgkEpiYuIbxiXFMTU1VvMfjSgqmCwXDi7zpgW64UTDc\n0A0394JcFwmHkoOmZOHQMnAoGTjULBxKBorYuP93H3I5nUvhcDkkBgIBu78BREQNj4GRiIhqkq7r\nmJ2bw/TUNKampjA3PwfT3Pi3LMN0Im96UDA8S6FS96BgupdHJLk2UoEBTclBVfLQ1Bw0JQ9NyUFT\nM3Ao2U39Dmmaho6O8EfrENvb2yEE/58QEVUTAyMREdUFXdcxMzODqemlADk/v7Cm/R7LJQHopguG\n6YRhOlGQS38bxvK/TSckVNRvqFyaNqqKAlShQ1F1qCIPh5KHquSWQqGS25SRQiuapqG9vQ3t7e0I\nh8MIt7ejpaWFAZGIyGYMjEREVJfy+TxmZmYxMzuD+fl5LMwvrKv66lpIKWBKBwypwpQOmFKFKTXo\nUoMpNZimCtNcapdQACkgoS49bvnfJhSsLXSaUIQJBSaEMKEIHUKYEDAhlOV/w4S6fExVClDE0h9N\nKaxrs/v10jQN7W1taA+3I9zejvZwGCGGQyKimsTASEREDSMej2N+fh5z8/NLIXIhAl3X7e5WWaRU\nIG8Ijtf9Syy9VQvU31u2qqpob29DuD2McLgd7e3tCIVCDIdERHWCgZGIiBqWlBKxWGwpPEYiiMVi\nWFxcRCqVtrtrDcfldCIUCqGlpQUtoRaEWkIIhVrg9/sZDomI6hgDIxERNZ1CoYDFxUXEFhc/CpGx\nWAyJRGJTCus0CodDg8/nR8DvRyAYQOuHAbGlBR6Px+7uERHRJmBgJCIiWmaaJhKJBFKpFJLJFFKp\nJFKpNJKpJFKpFFKpdN1McV0Ll8uFgN8Pn98Hv98Pv2/pb59/KSRyn0MioubDwEhERFSBXC6HZDKJ\nVDqNbCaLXD6HXC6HXHb573wO2WwWuVweuVwOhlH94jJCCDgcGjTNAYdDg8vlgtvthsftgdvjhtvl\ngtvtgcfjhtv94z+Kotj97SUiohrDwEhERLSJdF1HPp+HaZrQdR2GYaz4B1gKfBACAgJL/1n8b0VR\n4HA4oGla0d+aptn9tImIqEEwMBIREREREZElzj0hIiIiIiIiSwyMREREREREZImBkYiIiIiIiCwx\nMBIREREREZElBkYiIiIiIiKyxMBIRERERERElhgYiYiIiIiIyBIDIxEREREREVliYCQiIiIiIiJL\nDIxERERERERkiYGRiIiIiIiILDEwEhERERERkSUGRiIiIiIiIrLEwEhERERERESWGBiJiIiIiIjI\nEgMjERERERERWWJgJCIiIiIiIksMjERERERERGSJgZGO/O1ZAAAAPklEQVSIiIiIiIgsMTASERER\nERGRJQZGIiIiIiIissTASERERERERJYYGImIiIiIiMgSAyMRERERERFZ+v8DcdGVQYv9v5wAAAAl\ndEVYdGRhdGU6Y3JlYXRlADIwMTYtMDktMThUMTE6NTE6NTgtMDQ6MDDeRgdYAAAAJXRFWHRkYXRl\nOm1vZGlmeQAyMDE2LTA5LTE4VDExOjUxOjU3LTA0OjAwWVPPDQAAABd0RVh0dGlmZjphbHBoYQB1\nbmFzc29jaWF0ZWSMKAOzAAAAD3RFWHR0aWZmOmVuZGlhbgBtc2JUdX10AAAAFHRFWHR0aWZmOnBo\nb3RvbWV0cmljAFJHQrMgSd8AAAAWdEVYdHRpZmY6cm93cy1wZXItc3RyaXAAMzaaI+VyAAAAAElF\nTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {
      "image/png": {
       "width": 550
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "display(Image(\"figs/L5-jaccard-1.png\", width=550))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "What matters is not just the size of the set difference, but the size of the intersection as well.\n",
    "\n",
    "This leads to the _Jaccard_ similarity:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$JSim(\\vx, \\vy) = \\frac{|\\vx \\cap \\vy|}{|\\vx \\cup \\vy|}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This takes on values from 0 to 1, so a natural dissimilarity metric is $1 - JSim().$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "In fact, this is a __metric!__:\n",
    "\n",
    "$$JDist(\\vx, \\vy) = 1- \\frac{|\\vx \\cap \\vy|}{|\\vx \\cup \\vy|}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Consider our two cases:\n",
    "    \n",
    "Case 1: (very large almost identical documents)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"e4be14fe986ffdeb\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#e4be14fe986ffdeb\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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cdQmBoFvh7E65LGZmZxGdjaJoGEt+uSVVFM0gQ1qdkJCISSwIcVNSoPKVTeXpniACwQ74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\nTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {
      "image/png": {
       "width": 550
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "display(Image(\"figs/L5-jaccard-2.png\", width=550))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Here $JSim(\\vx, \\vy)$ is almost 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Case 2: (small disjoint documents)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"349c78e49d78407f\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#349c78e49d78407f\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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1+G3/oNU+J94xZAoBBIDjykoTr9n7GQFxRCxuf3/6oaGhNJy9Wf9p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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {
      "image/png": {
       "width": 550
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "display(Image(\"figs/L5-jaccard-3.png\", width=550))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Here $JSim(\\vx, \\vy)$ is 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Time Series"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "A time series is a sequence of real numbers, representing the measurements of a real variable at (equal) time intervals.\n",
    "\n",
    "* Stock prices\n",
    "* Volume of sales over time\n",
    "* Daily temperature readings\n",
    "\n",
    "A time series database is a large collection of time series."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Similarity of Time Series"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "How should we measure the \"similarity\" of two timeseries?\n",
    "\n",
    "We will assume they are the same length.\n",
    "\n",
    "Examples:\n",
    "\n",
    "* Find companies with similar stock price movements over a time interval\n",
    "* Find similar DNA sequences\n",
    "* Find users with similar credit usage patterns\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Two Problems:\n",
    "\n",
    "1. Defining a meaningful similarity (or distance) function.\n",
    "2. Finding an efficient algorithm to compute it.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Norm-based Similarity Measures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We could just view each sequence as a vector.\n",
    "\n",
    "Then we could use a $p$-norm, eg $\\ell_1, \\ell_2,$ or $\\ell_p$ to measure similarity."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Advantages:\n",
    "    \n",
    "1. Easy to compute - linear in the length of the time series (O(n)).\n",
    "2. It is a metric.\n",
    "\n",
    "Disadvantage:\n",
    "\n",
    "1. May not be __meaningful!__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"5e589107c3bb0d77\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#5e589107c3bb0d77\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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NnqnQ3k4M/sr+a8PeDUu3Lp2xfsbcjXP3/LVHCQYdKU63mvtHgeXOO5N/2mnFsMF0VMdo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\n0sfoMT2YAOxSe4n2hAHxIN1OVGZsIYP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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {
      "image/png": {
       "width": 550
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "display(Image(\"figs/L5-ts-euclidean.png\", width=550))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "It is clear that ts1 and ts2 are \"more similar.\"   \n",
    "\n",
    "However, according to Euclidean distance: d(ts1, ts2) = 26.9, while d(ts1, ts3) = 23.2.\n",
    "\n",
    "Not good!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Feature Engineering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "In general, there may be different aspects of a timeseries that are important in different settings.\n",
    "\n",
    "The first step therefore is to ask yourself \"what is important about timeseries in my application?\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This is an example of __feature engineering.__\n",
    "\n",
    "Namely, the art of computing some derived measure from your data object that makes its important properties usable in a subsequent step."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "A reasonable approach may then to be:\n",
    "    \n",
    "* extract the relevant features\n",
    "* use a simple method (eg, a norm) to define similarity over those features.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "In the case above, one might think of using \n",
    "\n",
    "* Fourier coefficients (to capture periodicity)\n",
    "* Histograms\n",
    "* Or something else!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Dynamic Time Warping"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "One case that arises often is something like the following:  \"bump hunting\"\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"69825f16c5bf2153\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#69825f16c5bf2153\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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T7sjquLuGtuKO566EQCDE5u6P6PU/PvQqLKtakdWxEQj5CIks5QmvfHU/3t76H/zh2Z/i\ni/ZX4fG68dkPL2PaMp7toSVFIBDAVQ8dhN/862gceK0El96zAVaHKdvDimAmThreusb98aONl9D/\n/qz9lWwPlUAgLHHcXlfCz6++70fZHiIA4JUvHgUAWihRbOv7krH9G188Dp/fl9Uxf9X+Tsy6VcvW\nQyAImj7UaVfFfP6f9+7M6pi9Pi9+dd+J2KL/JEIoAcC8y57VsREI+QoRS3lCx1DohnLPa7/Efa//\nCtc9diJ++eAmeH2ebA8vBodrDiMGPQDglS8fwJUPHIjByQ4MTnWgf7KDbvf98Ff44zO5FSkz2aZi\n1hWrS3HrT1/CL0/8ByQiKQDg866X8MdnzsGfnv1ZzlqJ//eTv+PXDx2GKfNwtodCIBB4xuf34f1t\nLyVsM2TszfYwU0pN+8OTF+PLH97O6rjf3/ZCws/LChoZ12/t/iRrY37ts39h3MR8vX/kzT/gvpdu\ngMvjhMlqSLJnAmHpQsRSnlBb2kYvj80M4IXP7wUADBt7cNC1Uny0PXcqiHt9HvziHxtx1l/acPvT\nP8HfXrwY3/Z9hJ/8bRVe+fL+mPafd74Bhyt3cuuHpzoi/r2qbi88fnU3NEodAEAsDoolu3Meb337\nGN785lG8/tWD2R42gOC8gD88eRYuuGsP3PDoCbj7tSvxdc+7eObjv2R7aAQCgUf+8vQV2ONCbmnM\ndz53dVbHur3nc9Y2q+v3gFwiiVj34baXszZmt8eFLzrejVgnFkW2UctLGLf967NXZG3c09apuJ99\nsP0VPPzmbdj7EgUO/lU5Hnn9tqyNk0DIJ4hYyhMCSFwO66YnT8v2EGl6xrahd+IHAMDbWyPtbF/8\n4h+M22zv/RC5UPLLNj+LrQMfRq4MBKBWFtH/lOwUS+G8tvmf2R46AOC+13+F/21/Cl2j3+KTsDTB\nD7Y/le2hEQgEnvj8+7fw1Ad3R6y7+Nib6WVR1J398Xf/llVr8c2d77G2ue28p3DE+h9HrHvxs39i\n1jaTlTF/vD10/VxRuw4n7Xc+/nF57HEct+fPYtaNzwxkZcwA0D/ezrnt618+jhc/ehBjxuyNl0DI\nB4hYyhP6x7/L9hA40z7I/hYxmmsfPR7PffzXbA8dX3e+Cb8/cl3fZGSOvUwSO+m4d2IHzLbspjW4\nPU68/OUDjJ+1Va/HE+/fDv0osbglEPKdt75+MmbdvmuOxnM3fYfTN12KP5wb+3LkHy/fkLXxWh2x\nRgk/OfSqiH+XFFaiXFcb0+7sP+yRlTG/9+3z9PJNP30EN/zkIey58uCYdhccdSv+/ZtP8cjVH2P/\nNUcDACwOC4Ym9VkZdzJp+YMGPW598iJc+NdNsNhza+4wgZBLELGU47y39Ukcfr0MO4a+ZG1721Nn\n58TcmR0Dn7G22X/V8TEpFx/t+G+2h46u0dhisydsuCzi3zKJgnHb+1/LbqpLolTGr/Tv4KG3r8d5\nd+2Og64V4Nw7dsGMld0inUAg5B7vbX02Zp1IJEZL7Vpcc9a9OGKvM3DUnmdEfD5uGsYz79+T7aHj\n37/5FP/57Vc4/9jfoaZ4GQDgsN1PhlKuwmkH/QKHrIs0pBidGcSooT/j4xyfHgQAqJVqLK9fl7Dt\nri37Yre2/XHkXqFz/tKnD2d8zNv0n+K9bS/GrL/nstdx5PrT8aN9z8PxG8+J+XzMNIznPvgHhz0Q\nCEsTIpZymG973sctT/8Y8+6QAPrZAbeiWFLL2P6dbU/g7pcv49r9gtE1toW1zW9O/RcO3/3ciHXt\nI5tZnZ0WkkAggM/ag5OlFVIpfvWj+3HyPpfhxwdfH9FOJBRj31Unx2y/YzB7k3oBwOf3cmon8AvR\nN7EDm7vewuBkR9YdpwgEAncmTSNweSL/1lfW7Iqm6tUR684+7Grs3rIfGiuW0+v+/MzlmDRl1+yl\nrW4dVjfuBZVCgysOeQh/POVN/PmiYBSnSF2Kv1zyAq45PTLFkMmVbqEZ2Dl3dcOKIzhvc9BuJ0Or\n1AIAXv3in3B5nBkd8+/+fQ693FK1Gmq5CucdeR32XXs0br/gadz404dx88/+jTMPujxmW/McMXwg\nEOJBxFIO8/h7t8SsqyxYidN2vxW7N23Czw/7Pa479d8Rn7/y9UNZjxi43JH2pBqFGqfsGznhVS5R\nokwbK/rO/NOyrLn7dY1swZhpEACwac0ZOH7DRbj8hLtpY4dwzjviD/jLz9/A7T99CW3VuwEATLaJ\nrIq9jkH26CMA7Ft6OXSSWvzx+Z/jJ39bhRsePR4+HzehRSAQsstn370e8e/L93kET/5uG8RRNeuW\n1++Gf/7mEzx+/eaI9b2j32f7EGg6OjqwdvUuMetP3P98XPGjP9H/3tz1fkbHZZwdh93pAAAsq+Re\nl0gqkeGAXU4AAJhts/iq/X8ZHbfL46CXH7jiY3xyzxwu/VGsicO6lv1i1jlctoyOlUDIJ4hYymG2\n9TNFKgQo1lThzos+xE8PvQlyhvkzr3+d+fA/E2saNuLO89/Fg5dtxYkbL0WBXAGNuBgH158PqUSO\nEzZeguU1u0dsY7BM4Lv+7ERoOoe+opc3rT0pYVuBQIC9lh+FfVefgPWthwEAnG43vu54Iytjtzkt\n+Oc718esP3TXM3D83heipWoXHLyWuYDu551v4MvO17IybgKBkBxfdoSiLI261Vizem3C9gVyNf5y\nYcgtdVsPe5o03/zQ/3XMuomJCQQCAVRVVcV8JpPIcc6R19D/ttgza/LQPx5yRG2sXJnUtsvrQil7\nRvNoxsbs9/vpGoF16lXweOK/dNyleWPMOuNsftVsJBAyCRFLOco8w1ue2pImVO3M8abYe+Ux2LPl\nEFQUhaI0j/zvd/iq881sHwKEEGD31kNQXdqMmtIWvHDDFG445XmsrjwcAKBWFuGByzbj1z+KNCXY\n0p35lAsAGDCEbpBNlbvGbUcVJKQ4fPdQnag3tmTHFe+lz+7FgKELAKBVaqBSFKBKV48rTrwXvzrp\nATxy5Xb87uxn8cL1I4zbT2TRvYlAIHDD6Z7H111BO+u60ibsUXgmVqxgj3w0l4VeSr2zOfPOmP5A\n0DVHLALEouBc1Y6ODqxcmViIqJVqAMDW3sy+QGsfCEXj1MrCpLZtqgqlQ1odsxkbs9lmhG+nOZFS\noknYtrSwCqeuuh6n7RtK29dHFQsmEAghiFjKUR58M/RWTavU4M1bZ/HEb3ogEkWaIsilSvz1gnfx\n3HXDWFYWyk3/+of34PXmVmqVUqZGdWlzhNgQCoU4Zu8LcOGRf6TXbdZnRywNTQUtV+VSKUoLazhv\nV1++Aqtq9wQAfNH1FoanujI+9v6JHdCIi1ElX4mHLt+Ol2+awZO/6Y1JISwtrIFMrEhxLwQCIZtM\nmUbo9LDigipUV1ejoKCAdbu+ngFUahsAAHanJaNj7htrx8h00KBh/zXH06UX2tvbsWrVqoTb7tFy\nIADA6/Nj2pK59PLwMhaFqpKktlUptPTyvMue1LbpYDSHIkNKsZa1fZl6Gc7Y9CtceMxNAIDpOSMm\nTSOs2xEISxEilnKQQCCAT74POcNtXH4CVHJtTEQjmjsu/IBedo6pYTJlxwrUH0jOMEAgEOCsg67F\nni2HAAAGpnZkfMyBQIDeb2PZWtZzHc3xe19EL38/mPk0l5m5cWglNWjUbERl8TJIxTKIRMwFKwvk\nsTdS67yZbRcEAiGHkAeKWMUGRWdnJ3Sa5B76+cIQloq2YWUwZXlychJ+v58xBS+cg9adSC9/tPWl\nrIw/WapKQ9kfY9OZc/GbtoTEkkLCLpYoVjWsp5c7BtjNmQiEpQgRSznIwOQPmN7pTLNu2X649vRH\nOW1XrKnEHs0HAQDcXmdWHtrHpvtgcQTfXBbINUltS1ly+/zIeIFaj88Ni8MKAKjUNSW9fUlYJCoQ\n8Ce9fbrMzAXfusrESta25bo67LfmZDoaBgA9Y6T+EoGQT5jNZk4peEajEW63G1KZLCvjHJnqoZf3\n2imWuESVAGCPFaG6Rt0j+VFrsFBVDKVUDgAYM/ZlbL9G8xi9XJCEWAo3VDJZJzM2XgIhnyBiKQcZ\nMXTTy0fveV5SUY7j976YXjZn4cL30hf30suHrvtxUtvq1JX0ct945qNLFPEiMokIr71km5/N+Jin\nrcH0CalEztpWKBDh9AOuxv2Xf43GiuCcgW4Odu8EAiF3UGvUUCrZX450dHRgxYoVkIqDYmnWYcno\ny6hhYy8AQCQEKksa6DGxzVcCgkYPFAFk9gVaOlSXNAMARqYzJ5YMs6lFluLVDSQQCCGIWMpxxCJp\nUu1VisKsjndb34cAgvOsDtjllKS23bDiaHr5s/aXs3ocyVJT2kovDxo6M7rvebedrsUlFbOLpXDa\nqvYAAMzMGbNuOU8gEBJjmw/NNyorLee0TWdnJ1auXInyolD0eyaDL9JGDEGxVKVbBrFIjMnJSfh8\nPlRXV2dsDJmmWBP8bsw2U8bmLRnD0vCUUu5iiUAgsEPEEoE3AoEAxmaC5gaN5bvQrkdc2b31UEjE\nwZ/kN1kyeUiVwoJSaBRB56ahqY40e0sOU9jEZ2mS5g0t1bvSy0NTmRV5BAIhOcLn/6xo2oW1vdls\nxtzcHGpra1FZ3ECvn5geytiYO4e/AQAoZCoA3KNK+UyxtoJedrodafTEHfu8lV6Wi9hNPwgEAneI\nWFrE+DM8d8Zin4bDFSzKWl3SkvT2MokC5ZRjk2suo2NPF4FAgIayoGXsoPH7jKa5mGyht8QyDml4\n4SikKnrZ689OMWACgcCN0bA5ME017POVOjs7sXz5cgiFQlTp6un14zODGRuz0TIFAKguCRofcJ2v\nBESWaTBZpzI25vC6Tsma/QCgUx4zSXiaokDA/dGuXBcqOzI4pc/4uAmEfICIpZwk/oM224W7SB1K\nzTDbjRkd9dh0L71cVZy8SQKX48tl6sqDb0vtznmY5jKX5jITln6RbGSJQCDkD6PGkLtadUkja3tq\nvhIQ6dI2Pj2YlfFPTU0llYJHRaMAwGLJnOV5eDRIqyrO3AnKAk3Vq6CWB8/zpGk428MhEHISIpZy\nkPAHbXVUnRw2yotCbw9nrJmtyD0eJpZqipszuu9coCYsmjZhylyR1/Dfi1TKHlnKZ0FKICxlqPk/\nQgFQWVKfsK3VasXMzAyWLQuKpJqy0Ausb7o/zMr429vbk0rBk0nkKJAHTSxc/szVLJqYCaYpioRA\nWRH3mnv5yor64NzVrqFvsz0UAiEnIWIpBxkPe9Cu1C1LatsCuYaeOzOdYbFkshvo5WLt4p28Gw+p\nKJR6kUn7cLfPTS8LBaKU+/H7k6uPRSAQMsvARHBOaHlhLeuc0K6uLrS2tkIkCl4TKnR1WFW3OwCg\nZ2x7VsafynwlrSJYH2rWZkhqu3QYmw7egyuLGiASpn5NzSTh5h/Jsnzn72LMNJxWPwTCYoWIpRxk\nMkwslRXVJb19RVHwDeKMZSzpbflCmETOdOR2wRuTx+vM6Lwft2eeXk7WmCKfKS0M5auPTfek0ROB\nQFhIXB4nJmeDJQJqy9jTnMNT8Cj23Fm3yGgxYGA8s4YuLpcLHo8HNTXJRWokCEaWpucy9/JvwhRM\nd6wuZU91zAXcHhc+bw+aIsklEgiQXPbAyoY96OUvf8gvcyUCIRMQsZSDjJuDYqlUU5HSRNHKogYA\ngMk2BY/XnfT22USnCs65KvavxZYtmav9M2UO5WqXavM17SJ5cdlYuZZe7pvIXm0rAoGQmLe/fIpe\nbqtdl7Ct3W7H5OQkmpoiRdWqZaFC1N/3fZnR8c/NWZOOKnm9XgTcwZdXLo83I1EP85wRTk/Q7IYy\npch1fuj/ml4+ZLfTkjJ4AIDVy/ailz/Y+mK2D4dAyDmIWMpBxk3BN/xVutRMEignOgGA/onvs304\nSaFTVwEIRpZ8fm/G9jtlHqSXK4rqU+8ozyjWVEKr1AAAeie+y/ZwCARCHF746CF6+cT9zk/Ytru7\nG01NTZBIIqPkCmnIUtrtdS74mL0+LySi4GOGy+FPWiz19/dDpyqj/z09u/DGOeHmF1XFqYml8qJQ\nxD4TEbwPtoUEztEbzk56++ow84+vu95d8PESCPkGEUs5hm1+FnZn0ImnUpdaCsDaZfvSy9v7Psj2\nISWFThOqTzHvztyE3ilzqO5Ixc7IXL7gTOM8CQQCNFfuBgDon9wGH5m3RCDkJJTdt0gILKtKbBvO\nlIIHAMIMz78ZnOiCxxecv6mRlCedgtfe3o5ltWEFvycXXniEW5RrC5IzWKLYd22owPrWnk8WdLyB\nQADvf/s8AKBMW4G9Vh6aUj9rGoJRR1JCgkCIhYilHOOHwS/o5VTtt9c2HUAvb+3NL7FUrKncuSTA\nvDNztZYmwsRSeR5Flnw+L97d9h/631JxcnWWAKCpalcAgNvrR/fIN9k+JAKBEAU13wcAallq2Dmd\nToyMjKClJbZd+FzS/omFFx69Y6Fo9bq2fZJy4vT5fNDr9Thm/7PodT2jC58qHF6fsFBdklIfK+p3\nh1oZNFra0vX+go531NCHydngfK5iTUXKbqfJ1ugjEJYSRCzlGO988xi9vO+q4xnbsBkfqORaSCXB\nejudo19lbOwer4teTjZnmqJYFRZZymBh2vDIUlmY6UGqZMqcYnv/xxiZDhaqXFO/L+RSZdJ9bFge\negv60Y7nMjJuAoHAne7ubkjE3Ixn9Ho9GhoaIJPFzndd0bA7xDvT4vSjC5922z0c2seBex+Z1Lb9\n/f0oKSnBrm0baPvw7/q+SKqPbCEUCrFXWzDC8/3Al/D7F84dNVzcbVh1eNr9zbsyl9FBIOQLRCzl\nGJ91vgAAaChrQ1PVLin3I6Jc5XyulPtIlqGp0JvK6pLUomLF2ip62eG2ZWzs1JwlnaoE0hTfsKkU\nhfTyxEx/Sn0ky2ftL9PLey4/KqU+dm3ahAJ5UFxv6/soI+MmEAjc6ejogBfcruWdnZ2MKXgAoFYW\nYuPKoGjZ2vspDOaFdUz9Vv8xvby8ZXXSx7xy5UoIhUKsadgAANjR9/mCv4iSiKT0cjqlGNY2bQQA\nzLtdGNxp+Z7LFKqCUTSvz4/+sY5sD4dAyCmIWMoxXJ7gnJGGspV5Vzy0bzKYIqFTlUBbkFr6QrG6\nkl62zc9mbOzmnTWiKIOJVNilMfPpj190vBoct6oY1SWpFQIWicQoLAhG9Hz+/HJPJBAWOy6XCwMD\nA5hzzgIAREJx3LZutxv9/f1oa2uL2+bAXYMZC4EAsGOBIzXUfMrigrKkU/C6urpoQwhqrtWc04ZZ\n2/SCjtlgHqGXq0tStw5f0xhymNvRv3DOg3OOWV76OXj3k+nlt75+csHGSyDkI0Qs5SxpCqWdNyaX\nZx5e38JP2PT5vBgyBJ33GivWptxPdUkzdmaJwGgZXfBxR5NqfSgAqCxehorCYDHeb/vezUgq3tRs\n0PJ8ec1eeSeuCQQCO93d3dCUyODfeTlZ27Qhbtve3l7U1NRAoVDEbXPAuhPo5c6hbxd07D3j7QAQ\n48rHxsDAAIqLi6HVagEATVWr6M9GDX0LOmb9znlRAgANlctT7qepOhRJ049sX7Dxnvt/G9LvBMCm\ndaG0/+/6Pluw8RII+QgRS4sU2c45S14f8F3fx2n2xs7odA88vuDdPLx2T7JIJXK0VQUL5Blmhxc0\n13shWNd0SHDslomI2k0LjUjITyHdDNYBJhAIHGhvb8e8JFSQdXmCGkuJUvAoitSlKNcGI/gLKZbm\nHLO0bXihqjipbakUPIqNq4+gl79sX9iiqdRcLpVYB4lYmnI/4aUvXJ6FsWn3+/202yAAyMOs4ZNF\nLlVCLgker5/cCAiECIhYyiH4jEQUyLX08ic/LHyROSrCAQB1Ja1p9ASsrN8AAQTw+FwYNix8rncg\nEIDDNYsyWQsUIk1afa1p2Egvdw5nzlwjXeSS4E12wtwDtzdz89wIBEJ8XC4XBgcHoVCHzBp2bdmP\nsa3X60VPTw+WL2ePhgiFwVt/zwKaPLy35Tn6Qf6IPc/ivJ3f749IwQOA3ds20SYPH21/ecHG7PP7\n8G3PpwAArbgyrb7k0gLaTOO9b55dkPFGR9kO3ePU9MYsUaS1PYGwWCFiKYcYMXTTy5qC5N7ERSOT\nKKBVBucNbe1dWOtSABEhCZEovSjH8po96OWByYUvqmu2TcHisGKl5kjUFq1Jq68VdXvTyx3DX6fR\nEzser5tOzQGQVhrehhXHAAAcLhc2d725oOMmEAjc6OrqQn19PcQcnPD6+/tRVlYGlUrF2pYy4HH5\nFq4w7Tdh5g7H7nMO5+0GBwdRWFiIwsJCep1ELMUujfsAAHrGty9Yavk3XR/SyxpJWRo9AXKpAhtX\nBiNiVuccZsLqN/FFz1jISv3+X76Dhsq2NHoDBDvnhu3o/5z3sRII+QwRSznE5u636OXdmw9Oqy+B\nQIDGyqCb3pBRj3nXwjrLeX38GQOolUUAgAACMM0tfMX2gYkf6OUqHbeK7fGigA0VqyCTBG84vePb\nFnTc9776y7DxpFdM9tB1oTe/X3S8vqDjJhAI3Ghvb8eqVaswY2W/DnZ2dkZEY7LNls73AAC7Nu0N\nnYa78KCOOZp9VgfdPr0+YGhSvyBj/t+WZ+jlckV6wgMADtktZJrw4bf8Z3js6AsZR4TPkUqVdc3B\nqGUAxEKcQAiHiKUcYsdAaFLl7q2pVeEOp6EslLveM7awD+7hYy/Rpu4oBwDL6/YCZXCxRb+w+ekA\n0D8RejtXVZyaoxyFSCiCSh6s+u5ZwHS2QCCAd7c/Tv9bJkm+vlI4tWWhBwOn27Fg4yYQCNxwOp0Y\nGhpCW1sb+idCVs7qgsKYtn6/H93d3azzlaKZc8zhq/Z3eR/7yFQvjHNBh9Fdm/bjvB1TCh5Fc3Uo\n6t839kPM59OWSdzzwrV4/fPHkApenxcvfvYI/W+ttCKlfsI5YN0JlNcSPv2e/5dQI4YeerlEm17a\nIABsWHnYznPhx7fdH/E+XgIhXyFiKYegaiKJRYBGqUu7v/qK0A2nZ2zrgo3b7/fj3W3/AQBolRrs\n1nxIWv0VqcpQog7eqL7pfQcuz/yCjR0A+sJS/SqLuUWWEiEVK6AW6eC1yxbMEW/aMgbbfOjN3/Eb\nL1nQc0QgEDJLd3c3Ghoa4PTa8V1/cB5NQ1kLKovrY9pSqWuUexwbIlHIfvyp9+7kfexdw6H7TTJR\npaGhIWg0GhQVFcV81lQTipz0jsWmZ7/55X/wr7f/jBsfPQdbuz9JeszvhkWVjt94Di/nQVNQhKay\noMj7uut/vBs9UAVpS7XJWbPHY++worZf/PA2r2MlEPIZIpbyjGQuiBplaN7TvHvhQup949/BuDNN\n5MBdzkzLQYiisjiYU+/2+qEfXViht0UfvCmIRVKoFemL1HVNB6FQWgOtvwEDkz+k3R8TvRPb6eUr\nj78buzYdkHpnUQQC+eVASCAsRqh0tC++fxPenVm2Jx1wEWPbZFPwwtPDRo38F9CeNITKPpQX1XLe\nLtoFLxx1WNHv9sHNMZ//841b6OWf/zX56+FH21+ll3986K8A8GO6VF20c36Yx4tt+k/T7i8cKsLW\nWJl+Ch4A1JQ1oXLn9/XB1hcyUv6CQMgHiFjKIfL1wvRd/0f08p6th6feURhF6nJ6eSAsTY5vukY2\n00JPqyzm5e3cfqtPoJc//eGlBRl3/0TozWpT1a5p9ycSiqFVBt9K900unEMWgUBgJzwF771v/wsA\nEAqAI/eOdZULBALo6upKKgXv5AMvph+KB6a68TbPRUiHRgfpZa6RJb/fn1D0SSUytOyst/RFR7CO\n3TddH+G43zZh3fkCzDkj5+WuO1+An962J5xu9swEn9+HL9uDc4ZX1u2G5hp+xAcAFIcVOr/474dh\n3fkCXPvgaTjqNzV4+dNHEm4777Kjd5TZ5MjpnseYKXieGyv5m6tG2bRPWSagHyH3AgIBIGIpZwgE\nAhgydgIAJKL0IzPRfNW5cJP2t/eHXI/WLOOen56IQlUpvdw/xRydcXuc6B75Bu40Uhve3RZ6SFAp\ni1LuJ5zdWw6lHQEX6rxbHSZ6WadOP7deIBBgt6bgPLlBQ3dGjDUIBAIzXV1daGhogEwmw2c/BK8h\n/gBQrCmPaTsyMgKFQoHi4uQcVK858156+bf//DG+6/0CHq8bPn96ZjEAsLXnIwCAWCjEmiZuRVOH\nh4ehUqkSHodhNhSxuviOQ3D+3w7EyHT8yNiOwS3Y0snuBrul8wNabDXvNErgq8h3eWFsZO2db57D\nhHkMv3/8vITbnvH7XXHK79diwyUyvPfN83j988fwq3+cgD8/+Qvc+dyvaBNaPsWSTh0StwttDEUg\n5AtELOUI3+jfxdjMAABgv1Wn8N7/jqEvMRxmTc4nYzPBWg8VRbXQpml5TqGUaSDeWWi1P05k6W//\nvRDn370e1/372JSicpOmIbz8ZfCBQSoWokCeXo0lCrlUiWXlwTz19pEtmLUZeek3nLHp0MTe0sIa\nXvrcvfkgenlrTwbs5gkEAiPhjnBUraLDdj+ZsS2XQrRMHLDrcVhZtxv973P+vA/2vFiGPS4UY935\nAhz32yZ0D29Pul/9wA8YsASjIavq9oRMIue0XaIUPAq7a45e/rrrA8Y2j14TaXt9+b3Hsu57W09o\njtP+uxyX9DEnYk3dflhbFf8los/vw9CkHq9//ij+++F9GJ4MXtvf2fwMhoy9AACnx41fP3gqbnz0\nHHyw/RU889E/8NzH99N9lBXxcw8AgKqwOXHbej5Lo6elzQffvohHXr8Ne14kwrrzBXjo1d9ne0iE\nNCBiKUd4+Yv76OVT9vslL31W6Boi/j0wsTA1iwII3swpccMHAoGAji6NTMeKPLvTire2Bt3gNve8\nhze+fjjpfXz2w4ugip9fdOTfIBKKk+4jHq3Vu9PL3+j/x1u/FIOGoDtWZVEdZCkUEmQSl7u3hBwY\nP9rxPO9jJhAI7MzPz2N4eBhtbW0RKVg6dTlj+3Qswy849ndxPxuZ7sdvHzotaXfMu567ll4+ZD23\nF3+BQIDTcTxx3bdxP6tQ1+Pecz/BLs0bcc9lkRH9g64swrHXLsPT792FwYkuOjXvq/b/4YTrWvDQ\nG39I6fxxQSKW4aTdr8bX9zmxaW2scNvjQjFOuLENNz76M9z21KU4/sZW/OLvR+Dah8/gvI8KXR1v\n49297UB6+aNtie3O3R5XxP/zhUAgAK/PuyB9f9P1Efa6SIxfPXAS7n3lBvplx/2v3YztUeLT43Wj\nd/T7vJ2CsZQgYikHMM1N4vPOVwAAbdW7oa12jzR7DCIVy3HJUX+m//38p3fA7+d38r7P58WkORhZ\nalDsy2vfRQXBdICZOSNmrBMAgG29H+KB13+DI2+MdH36vxcuxC/u3YhtvR9y7v+LnSlyQgFw+B4/\n5XXs4UL1lqd/jDtevBijxh78573b8NH259Lq2+vzYHQm+PaxoYy/9Ivq0ma0Va8DAHze+QpsTguv\n54RAyCQWuwljxgHeHchSIRAIYHiyBxa7ibVtd3c3li1bBplMhrv++xt6/f67xD5oj4+PQygUory8\nnLVfJjauPgL1pfHLJQxM6bHh0gI8/Nqt+Kr93YTj39r9CT7a9gq+7gsVtT5508WcxkGlEpaUlCRs\n11a3K16/vR/XnH43Nq09FofvcSpaqlbhhI0/wwFlF2HNqmBtwb1XHRbhaGe2zWJ0ZhD/9+wvceJN\nK7DhUiX2v0KDi/9+OB29WWikEhnuvOxV7L/maNa2n7cnVzIj3N0wXWrLm7FxZfDF2Y7BLXSki4L6\ne/ri+7dxwBVqrDtfgH0uU+J/m59Naj9ftb+L469rxlX3Hk8Ll97R7xesdEUgEMDQpB6DE93Y7QIh\nDvplIY69dhkM5jHe9mGcHcf5fzsQbh9zKuvP/m8/rDtfgHXnCzAy1Ytf338STvn9WvzpSeJmm+vw\n9xdGSJltPR/Av/PFwpG78/vQftRe5+HxD2+Bbd6OHUNf4sXP7sLJ+1/JW/89Y9vgcAXfKlUIdk+z\nt0gqixvp5V/8YyOu/NEDuPqfR0S0aVMfhEH7F3D5ndgx9CVufuJkvHjjFOvNw+1xYlt/MI1jTf0+\ndCFcvpBH1T16+csH8PKXD9D/frZ2fVybcp/Pi9uf+Qn8fh+O33gJmqt2gdfngXluCj5/8KZCad76\n8kixlO4bqj3bjkD32Db4/MDkzCCaq3fh9bwQCHzx6Xev42/PXgm314VLjr8F++5yLPx+H97/5nm8\nvfkpbO37IqL9gbsch7VNG+H2OCEQCHD8vj9HWVE1/QJJKIx8d/jSxw/B6XHi2H3OweycESWFldjS\n+QGe+/AfGJ8ZxNWn/R0Olw1rGvdGWVF1xLZdQ1vxt2evhMVugs/vRf9kF/3Z2mV74Zi9z8am3U5E\n9/A2OJw2PPnenTDPGXDD2Q+jp30SK1Ytx3UPnYHP2oNOnZVF1dhj+YEx5yDVFDwKiViKl2/vwdbu\nT3Dzo+dA5i9Erym2Jt99r95EL6+oXYfW2l1QqauHUCjEfa8yR6f2aNoEuZRb1DteIVomqkuX4fSD\nL8PpB19GrxscHMQ777wDjSaYSi0WSXDzz/6NWds0Pt7BPG90zjHHuF4AfuYq0f1FzX266/LXMWro\nw9Pv342nPribdftTD7gY15x5L3pGd2BoYBhWoxsG0XY8/OZtAIDGiuVoqFzO65hP2Pc8fNERrL/1\n6Y7XcXrZ5Ria6MaEaQhX/eNYlGqrMWYaptt7fX5c8/DpcLrs0KpLIBFJ8fkPb+HTHa/j3COvxQn7\nnw8gGHUBgD2Wb8LFfw/WdBo29mH9RaGslAK5Eo9fswWP/e//sL33M/z0sF/DZDNiVcN6bFgdNJCy\nzVshk8ghEAggFrFntLg9Lux1SWQ66JzTjjmnHYf/pgaPXP0x1rXuxzhPze/3Y2iyGw2VyyEQCDA0\nqUdlcT2EQhHGjQOoLmuESCjCvS9eh0fe+iPnc3zcDS308nMfP4CywhrMWCchEooxauzDifudj/13\nZU8hJWQGIpZygPA6QnzU+QlHo9Th7gs/w7l/D0YM7n7tKgwZu2GcHcbKug3Ye8XRkEuUqCtP7WK7\nte+DlLZjIxAIRIilMdNgjFACgHrlXqirq8O77Y8CAMx2Ez7Y/gwO3f3HCfufd9vpFLy6stQfNuJR\nVlSLQnU5EOdF7KzdGPe73t7/Md7d/jQA4P0diaNQ9TyPXSYOPdx4fW7ez8tSxTQ3CbFIis++fwm1\nZcuxZtk+2R5S3jNjnaKjAjc++jPW9h9+9yo+/C5kD33fq7/DXy58Htf98zQUqcrw40N/hRP2Ow+z\nc9MYMfTilicuBAD837NXMPZ3yV2h69GP9j0PVcUN8PjcmLVN49mP7os7jh0DX2PHwNe4/elfxHx2\n4Z2HoFReD+NHQxHrTzvwcsaSDJ2dnTjxxBPTPpe7te2PZ278AXfddRcuPPk6vPL5I7RQi9nnyDZ0\njrAXOV+xbB2nfVMpeGeffXbK4+/u7kZra2vM+jt/8Soefu0W3P/azZz6EQqA1trQC6KFSo+qKWvC\nr8+4C+cceQ3GjANoq9sVN/75l3h/5J8R7V6+tRv1FcHjaqvbFa5ZIaxGPS458Q+45MQ/wOvzcBIL\nybJhdei3/dfnr8KT792JCfMIvS5cKIXzu8d/HrPu9/+5AL//zwXYuPJQWoDttfwgxMPudOCk34eE\n861PhuzyD9/jVLzzTeQ9saa4AS/+oTtuyZJAIID/bX464fH+/K8HoLKoGuceeT027XYiBAIBXv3s\nX1ArCnHbU8Goj1gkhNfHPTNHKAA+vsuC6dlxjBh6WefO3fvKDRH//mjHa7jujHtxykGXYsw4gAKF\nBoUqfuaEE5KHiKUcQD8euvHo1OlX4Y6muXpXLCtbjgFD8O3mK189CADYpv8Yb336LMbm23HjaY/j\n0D2Su1l5vG689lUwWiJcgITOIlViy9n1zQejXrkcRxxxJX4Y/wAT5uAF/P9eOAe7NB6AYWMXVtbv\nDaVMTW8TCATw5tf/jHDBEwoWJht17bJ9sWq3etzz+mVweSLD8r+4fwM2th2H3ontGDMNoqa4EVef\n9DA6hr/CQ29fz3kffBlqUJRpQxOFv+19H8vr1i/IuVkKBAIBvPvtf3D/m1djZi7S5OPP576GDSuO\nyfYQ85rj9z2X1U2MjV8/GJxTY7BM4o7//hp3/PfXKfXz4mf/TGk7JozOoZh1ZxwSK9iMRiPcbjeq\nq6u5dMtKT08Pli1bhkPWn4xD1p+M3tEf8Pf/Xp10SphSqsSetcfiguNu5tR+dHQUMpkMpaWlnNoz\n0d3djZNPjjXAEAgEuOC43+GC44LRL6/XiytvOB9CEfCJ4VG63Sn7X4iLjr8FAQQYHQcXitLCKpQW\nBq3Fq9Ur8eFfzHh/+zP4ov0dHLvxp7RQCj+ecBZCKAGAShFpdhQulFKFEkpAfHMONqKFEgCMzgxi\nz4tlOOvgK3DZSX/C+988D4vdhB8dcCGEAiHO+P2u6JvsjNlOrVRHRBcnzGO47alLaHEUTTJC6dwj\nrsFlJ/2JPpcNlctx4TE34cHXb+HcBwDc/vQv8FXne/hg+8sAgN+cdhdOO+gXMVFwwsJDxFKW8fl9\n+PSHFwAAOlUxWqp3S7NHZn56yO9w81ORE0ZV4go0qw7E2Hw7bn32JwCA/Xc5mZNhQCAQwIfbn6Hr\nPBy528+AKX7HLBAI8Piv2nHhPesw73ZDIZVi3h2Mdpx14DW48Kg/4YknnoBQKMSfz30LP/lb8G2U\ny+PDybdHTnhtrFiJI/c4F0qpCn958aK4++N3/EIct/FiHLfxYtzyxBl477tQhXiP14+P219Gi2p/\nFIjMGJ3pxy8fOjhuXyvUh6Df/glc/shoD9/53futPQmyl8+Hy+PDG5sfxpkHXhP3vGzufgcdQ19B\nIpZi31UnoL48uShXIBDAtz3vobq4mfeIKhdGDHq89vVDWFG7Hpt2OZX37//1rx6K+1u75l/H4uHL\nt2Biph8bVh0LsVCCu165DCKhGJcc8zdeCjsvdgQCAX512MOYsHYjoHDC5/fB5/dCIS1A5/C3KNVW\n4bD1p2FotAd3vXYNb/utKKyF1WGEw514LpRYFHzhs2mXE7HvmqOxcc0REApE+Lb7I3y47SVs+/Y7\nBNRWdI/Fr2WzpnofHLX2fEglspjPOjo60krBi6arqwvLl4cyDJprVuPeXwajSy6PEx6vC59sfxUy\ncQEef/5B7DAHjWvUSjX+fsnrGBjTo/3rYTTVtWHt2rUxD9zx4OKCl4jp6Wl4vV5UVVWxtu3u7kax\nvB5qtRpf3TyPvz59BQQCAX59xt058TcXCARw0qaLcNKmi9LvLE3qSpswbOyL+7lUJMLpB/0SbbW7\n4LbHLoFYKIPVM0N/fvC6E/H+NvY6g38+/xlc8/DpAIBzj7gW/3r7TymN98n378KT799F/1unKUfn\n0LcxQunuX7yG/XYJvqiamBnC7x44H1sG301qX4lQSGS0UArnouN/j/3WHoM33n8eLeW745ZXT+fU\nHyWUAODNr/4TkX5KyBw5K5a2934Ei30a+645ESKhKOIz4+woHnjjN/im5x3Ul63ENac+iuqSJgQC\nAQgEAvj8vphtmGBqZ3dasaXrbdSUtrHO1/D5vBAIhBAIBPhg29P4/dNnYVnZchy/98U4cq+fQyEt\niBr3GAoUmohIx1Mf/Ikuirpx5QkL9sbgoHWnY1nFatz85KkYmOpkbHPrsz8Bdoqm9c0H46YfPwOL\nfQblRXWQiuUYn+nH9wOf4vbnYlNejtrzXHz42lbex91QsRLv3BacExUIBDA3b8aosQcr6/eKaffu\n7Q4cep2SsZ/+yQ784/WrGT+zO60Lcs7DueHMJ7GsYjX++9kdMIdNkq5R7gaTexB2X6yZwin7XoG9\n2o7A618/jGL73rj0tD/g3rcvRddoyBGquYpbqgtXCuQaHLT2x3jr28cwOtOP9qEvsbphI33+n/vk\nDrg9TtSVtuHGJ0JOVw++dR1euH6EtjH3+/34tuc9+Pxe7L3iKMZ9Pf3R/+GBN6/deayXo616d9z+\n3E9x7qG34OxDbsC824avOt7A8to9UVXSyPnvOhGf/fAyrnssNm2p6q1r8NQ1/bz8/U3MDOCOFy7E\n1z2Jb8Dn3x2K2h205hR88H3QgbC1ah0O3+MceizUdY0QS6mmFsuqVmCffeKnNU5WTcIyLMZJp56A\nYm05Xv/8Udz/2k0w29jNFijU8gKsqF8PjbseF59xE6qqK/HCRw/g6853oVYWobasGXVlzSjX1aGr\nsxOOOQ/OP5v5oWb9ioNQpWmDavYVXHJJ8C221+fB+osiH9ZPPeAiaK1rsM965pSlzs5OHHnkkbyc\nR4/Hg/7+fhx7LHOqkEwih0wix1EbzsaOHTtw+K4/xZ+P+Cc6BrZg45ojIJcq4TAKIVlVhvb2dpx0\n0kmc993R0YEzzzwz5bHHS8Fj4ptvvgEAyOXB47n+Jw/GbbvU/+ZuO+9J/OWpK7Bj6Gt63RF7nIaV\nDetxyoGXQCQU0QJz+4cj8Pv9uOGGG+Dxuun1XUPbcMYf4r8AfvK6LVi5bA/ssfxA+PxelBZWoVxb\nhz8+G9/w4A8/ewzWCT/GLJ148sv/i9uOyU2wTFuBjWtCfzOVxfW48Ig/4qiRS7DPpj2xvecz3Pr4\nuZhz2gEALVWr0TMerPMoEghw5sG/xBmHXIFvuz7EbU9eiFJtNX512t9RV9YC/eh3+GLr+yiTxv8t\nrlq2HtZVXszOzuKXP/oz/v5i5Euc+654G+99+19Mm6bwScdrEZ8duttJOP+Ym5b87zJb5KRY6p/4\nHpc/GJrMut/K49FctQsmzUN469vHItqaBz7DGX9uhlgggEgggcvvhkpRgGtO+jcO2OUUdAx9hWFD\nFw5ed2bEm6N/vnU9nv/sr/jZIbdi3uPAvMuGgYkd2Nz7Ll3o7cA1J2POMYPfnPIvlBbVwu11QiEt\ngMszj989fhK+6HorZuwDhi78/dUr8I83fokqXQvEIin6JiOLqt590UfQKHV49H8346MfgtacQgHw\n4wOvW9DzuqxyNR67Omg57fV5cNXdxwAe5rZbet/HsTdzT4so0VQD4F8shSMQCKBR6mKEEoVMosD9\nl36Bqx7eREegAKBUugxl8hVot77JuF1dWXLztbherMLz3YVCIc4+5Hqcfcj1+K7vE7zy5f0wzU2g\nUb0G38++ErPtI1dsRUtNUAjtufwIPP7446gpbcH9v/gKQ4ZOWO0z8Pm9aKjgzw2P4sg9zqH/zt7+\n5lHMu2z4qutN2Bxm2q6diZNuCxZfLJArYHeG5uGdvv9VOHjXM6FTl+PPz/0MlbpGXHbC3bRQAoDn\nP7sbMqEU1fK1+Of/bkL36BZ0j30Dg2UCBXIlKouaYXOa8edz30JtaSs2d70F/dg2+PxelBfW4sg9\nf84qpGxOC6NQAoBx0xA2XSPChUf+EcftfWGM4YfX58EW/Tv4ouN1HLj2VAwbOvFd/ydYVb8BdpcV\n3/a8i+W1e6KpYi1ue+6cmP5P3/8qlGlrMGjoxKsMNveUUAKAPz7/c/zx+cjc/2PWn4tfn/JPcqNM\nEalIgZqy4BzIUw66FKccdCmmLRP4uv1drF9xMBwWD/733ts44LC9UaytwOaOd7Fb2yYUqUshEUlp\n4XrHHXdAV6SDXKrAWYddibMOizXLGddb0dyaOIV4cHAQDQ0N9L/FIgkOX3sW3tkRSg9eWbsXerZM\no6YmtoaO2WzG3NwcamtrwQcDAwOoqKiAUqlkbdvV1YUVK1agQleLCl1o/+3t7Whra0NVVRXkcm61\nlUZHRyGRSFJ28wOCYmm//diLoQcCAQwPB1O1JZKFSV9LtO98Y3XjXvj9j5/BBx98gHPPPTdhW6lU\nCpvNhkAgEPGctbx+HW4463786ZmLoVWUYJ32ZJx40vF4/qP7cOJ+52PlsqDzr04T+ns5cdN5+PjD\nz3Dcscfh2kdC0Ze3/jxEW6R//fXXUMtK8M2Dt+OL79/C3S9eg97xDtZjuumn/4q5TxQWFuL7779H\naWEVDl1/Kg5dfyoGxjtRpCmj5wg53Q78/Y67cdGxl0OpVOKYfc7BMfucE9HPsqoVWF6+Ae+9917C\nMcjlcjidTvz0xN/gRwdcgKvvOxFWuxl3/OIVVBbXY8PqwzE8PAyZqwTv9v0bUpEIPz/qRjqVlJAd\nclIs1ZS04NYfP49XvrwPfcPd8Exq8O+OxLmeNYrdUSZrxWbzU7DN23HjE6cCT4Q+v/25n+HANSdD\nAAHqy1fg8Q9uBwDc92ZseoZYIESBqAQffv9fAMCpfwqlCGmVWlgc7JbKHl8AQ0Y9AKBQXIE53yR8\nO6+Xlz+wCRKRAB5f6AK6T+tJME06UFXC2jUn2B6qxCIJrjj+XmzevBmC8nFatEUjBLBcfRg65uLX\nCjp+7wuzkkbFxKqGDXjuujH4/F6Mz/Tjw++ew5fffoASRT0QFUC6/acvomN4M07c5xep7SxFdmna\nH7s07Q8AeP7553HrT1/Eh12P4YXP/w6BALj06L/TQikakUiMxso1Czq+tY37Q6cqhsk2g1e/fpjx\n4Z5CKpRAJlBjzhd6Sx8ulADgmU/uwDOf3BGx7pWvH4rpq0BUhhb1IRiZ34FPw96q2Z0O9O4sTPzT\nv61mHMedL1+Ea095HAevO5MxOjQxM4C//Dd2fotSpEKFfA367V8CAB5867d48K3fYlnZcqys24A3\nvvl3zDbUnD8g0oBj+wBzAce/nfcO1rcdRv+7UtuEpz/4C6zeGSSiUFwBtaQMI/M78PqWf6GxYjX2\nXnEMHn/vVtSUtOCMA6/JidShfKVEW4mjNwYj6V1TXVApNWir2xUAcNSG2PmbPp8PdruddlyLx+Tk\nJNauXZuwzeDgINati/wbX1V4OEZrutE+Gox+KH3laGsrZryWd3R0YPny5bxlInR1daGtrY21ncfj\nQV9fH445JnK+ndlshtVqhdls5tRP+HGkk4LncDgwNTWFZcvY7z9jY2O082GmxRIX8vlFCHU+TSYT\niosj59GetOkiHLPPOZBJ5PjLX/6C1fUbsfGyI+L3JZZg3bID0VaxFy457vfoG2/H5T/6c0QtqaKi\nIvT09EAkFGG/XY7BfrscA6d7Hufcvje6x2KL2F9y3C04/9gbGfdXWFiI2dnZiHXLqiLTW+VSJd0u\n0QsFpr6iocQSAKiVhXjwauZyJ60lG/F/1/5rIb4uQgrkpFiSSuSQSmQYM/VBIy+FQqTjpd8Pv/8v\ndJKaiLe4TBRK6rFaeyw+MsbaeoYLpWJpHTTicgw4tqBArsDercehsXINtva+h2/7PqLbrS/+CbbM\nPI5Z7yS9LlwoScVCHLv7pejq6sLq1cwPgwt3nuW45fQXMG0Zx+h0D3b0f4LpuXG8/OUDaK3aFVOm\nQbRqDokRSwqpFH89731UFDXQqVcAfylD6byJ0xYEFadOXYHVDRtx5KpedHd342dnXYxz7gg+xNxy\n1rPYd/WJ2Hd1+k5S6VKkKsMvjrsT5xz6O4hEkpj0zUwjFAqhUZbAYp+Bj+VraNLuA62gDl+ZHufW\nOQOlmgo6FZULtYpdIRZIMODYQq/z+AK49ZmzceszZ+Ov572Npz/8E9SKItx41jOYd9tw2p8aY/q5\n4IjbsLH5FPzvvbfgNIxj3BSaWD9g6KINUZJhU+ll+G72BZg94wCA564dQEVxQ0Sbjc2nwjoswYeT\nd6BMW4dZuxHD07G1XrTSKpTLVmBkPnjzv/u1q3D3a1fRn3+w4xk8fMU2Iph4wOVysUZDLBYLVCpV\nQoHi9/thNBpRUVGRsM3w8HCEi53D4cDo6Ch+dfqdePSdP2Lf1UdhZHAibsSks7MTmzZt4uXYA4EA\n9Ho99t2XvU5ef38/KisrYx4Y29vbsXz5cnR1deHAAw9k7Yeio6MDp5/Obe4GE3q9Ho2NjRCL2R9l\n2tvb6ftTJifI8y2CcjFKRZ3/ycnJGLEEBNM4AaC8vBxTU1OsLxwqKiowNTWF84+9ifFzJlEilyrw\nzM3f4d0tz+E3D50WGptIiP3Wxq9tpdVqMTc3B7/fn/B3odVqYbFYEs6NU6vVcDgc8Pl8EImYMx3k\ncjlcrvwq4kvIUbEEABtWHosNK4/F+Pg4Pv7kI/z07B0QCISoKWmBP+CD1+dBgVyDeZcND755LVwm\nIWSBUmw2J+73wPJf4cXRKxHvcvOzQ27Cupqj8cHH7wI7DaxK1GUokBfCYBlEW/WewehUxSpsqD0D\nszM2HHLIIREPLGcfcj3mHGY43Q4o5Co8+/SzuOf0L/CnF09D+8iWiP395ODrcdr+v4LFZMdoX+I3\nzQtJibYKJdoq7Np0AADgqh/dDwBwOp146OEHUVfSjDM2XYOj90rPfSqbNFauwQvXj8A0N8lb4V8+\nUSkKsz0EmhM3XIreLVb8b/KWGFOJ357yCEy2Key9/Gj4bHL09OhxRts5UMrUaB/8AnJpASp0y1BV\n3ITfP3EK2ke2QClUwul3INpP6OeH/R4/PfQmvPDpXRgeHUI5doeg4jS8vyN+gcMCcTHqi1fBaZmi\nHRDDCbeYP7j9Fby/PdY2lkpznJiYgE5dgcd/0oX3tj6JKcsI+sa3Y3v/B7DOh5yS1CIdlJISTDn1\nCc+bSCAFdtZp+dHGS2KEEhB8eKoqacJzPx8FALQPfomL/7Expl1r9R6wTNvj7mv/1ScRocQRtgdM\np9MJmUyWsM3s7CwKCwsTtjGZTCgoKEjY18TEBLRabYTg6OrqQlNTE9a17Yt1bW/Abrfjns33MEZM\nrFYrZmZmOEVTuDA6OgqlUgmdjv2lZLy6Th0dHVi7di1GR0dZzxHF2NgYRCJRQmHJRjLzlTo6OuiH\n4XgPstHkojDJRajzOTw8nLBeVkVFBSYnJ9HS0pKwv4qKCoyNxS8WmyiCc9DuJ+HOS17G4LgefVsN\nuOHaW2mxxoRYLIZSqYTVak342+USNRIKhVCr1bBYLHH/nsIjS4T8IWfFUsQgRZKY1CPKsU0hU+GX\nJ96Lzs5OjIyM4CenTWDGMoGO4S/xt5cuxara9Thj0zX4YPuz0I8HJ8bLJVLUla3CYet+jB0Dn6K+\nYhX2W3UiKnQN0BYUY2xsDHVlbXjxrDGY56bQVLUL4xuHjo4OzJmdjA8samURPe9BIVNBKVNhfdsR\nMWLp7IOvh0yigMUU/6EomwiFQohFEjxxTU/6nSXJQqQllBbWRETCliJczuuJ+16Ghzoewr2XfI1x\nczcEEGCvFUchgECEQYler4dQKMK65uDb5GgRev/lm3Hx3Xui3LUvtpufh1wtgtNtg8k2g/1WHo+f\nHBJMjThpvyswOTmJjz/+GL857RFYHdPQj2+BxRGZO3nzmU9D7W2C2+3G9fvcBafbgXteuQKvbWa2\nbr7xiVNj1m1a/aOYNEepRI6j9grNE/L7/fjHa1dix8Cn+OkhN0InasOnm9+BVdmB0w64GrWlrRAI\nBAgEAvhg29NQytXYa/nReO6553DRT34NlVaBAjk3N7CV9XvjyuPvxp2vXA4AkEulePLX/ZiesOKH\nru345b6/w5n/F/lA+PDl36Ctlt8i0EsZp9PJGlniIpYmJydZH/6j5ysBwajHbruFJsJ3d3ejqamJ\nMWLS2dmJ1tZWzg/8bHBNwfP7/dDr9TGRI7PZDIvFAqvVmtEUPK/Xi/7+/piUQCZmZmbgcDjoyBJf\n5y7T5GqqnlAohFAoxPj4eMJ25eXl0Ov1rP2Vl5fj22+/jfu5VCqFVCrF3Nwc1Gp1xGcioQib1h0P\nrANu234bBAH2KCIlhBL9fVORJTaodumIpVz9npcyeSGWkkGnroBOXYGWmnU4eq/z6ToE+68NuvPc\nc889eOV3s5DLgmLrlAOuitsXFW3hizMPvBYuzzye/viv9DouNt0EQjYQCASoLW1FW/2uafXz61Me\nweuvvIVrDvk3Nqw7BE63A0NTnWipXsd4U1BIC/DXC96F3+/D3168CK9vfgSVRXX411Xfo0CuwZYt\noRcOcqkSvz7lYVx98kMYmPwBd710KbYNfMo4DpEQuPH0p+lrQSKEQiEuOz5kQ9vV1YX68hU44ojI\nCf0CgQAH7xbr5MVVKFF9nLjvZThu4yX4ZMd/UV3SgtLCakxPWKFR6lBT2oL3/+jCR9ufhcE6ik1r\nT0V1SVNa38lSgsuDh9PphEqlStiGT7EUPl+JSsE77bRQ6lBXVxfWrGGem9jZ2Ym9996bt/PT3d3N\nqbDt0NAQCgsLodVqI9ZT86f0en1SBXI7Ojpw6qmncm7PdB7LyspQUMCettzV1QWxWAyBQAC3252z\ndWryNZIlEokgFAoxPT2dsF1FRQU+/fRT1v7Ky8sxPT2dMDWuqKgIs7OzMWIpHK1WC7PZzGogwiVq\nVFhYSBuEpNMXiSzlJ7l5xeCJeAXbspW6Ipcq8bPDfo/CgkIAwJXH35OtU8MZ8oYjf8jV76qxcg3K\ni+rRUBFMz5BLlWir3T3hA0vw7a8YvzjuTvzh7P/SQilR+8bKNfjrBe/hyN2Ck/aVIlXEBe7yY+/B\nQetOX7BCjukiEopw4K6nobUm1mpXIpbi0D3OxlkH/ZYIpQWAS2TJYrGkLZb8fj9GRkZQX19Pr+vs\n7ERTUxOk0uB9ye12Y2hoiDFVyW63Y3JyEk1N/PwGpqen4XK5ONUo6uzsjKjDRNHR0YGamhrO/QDB\nVEQAqKxMvQh7d3c350hWZ2cnXC4XJBIJ5zlLuXo9zUWEQiECgQDcbjfm5+fjtispKYHFYoHH40nY\nn1QqhUajSSi+uAoctjbJ9MUlssTWl0wmg9vtzlthvFRZ1GIpF5FLlXjgF9/izgvewwn7XJpSH5n+\nI8vGHzW5kBAAQClTY/+1J3GO1EjEUvz2jMfwt/PewYaSC1EoCaZcHrbrmThkt7OyfTiEHIWLwQMf\nkaWJiQloNJqIaEh7e3vEPI/e3l7U1NQwjodKz+PLzY1KweMiDCjL8OhzYjabYbfb0drayllgpJuC\nBwRTgLmIJZvNBoPBAIVCAb/fz8kMgm8W+/2MEktyuRyTk/HNekQiEYqLi2EwGFj7LC8vT9gXF4FD\nRZ/Y4NKXVqvl1Bdbup5QKIREIiEmD3nGkhNLufC2qKqkEbu3HJwTYyEQ8g0ufzfr2w5DS/U6/PHc\nN/HJXwK44awnY2onEQgUfBg82Gw2+Hy+mDS1cIaGhiKiSna7HWNjYxEmBV1dXYwRHCAoMpgMFlKl\nu7s77r7CGRsbg1QqRWlpZO298BS8ZOYrtbe3pyWWJiYmIBKJYsYT7xgLCwshEongdrvpCF6ukc/P\nA0KhEH6/HyKRCFNTUwnbUiYPbFCOePEoLCyE2ZzY0YvPyFJBQQG8Xi+ryEnWPpyQHyw5sQQs/rc8\n2YTPc5vPNw9C9hEJxShScS+sTFi8cHHDSxRZ8vl8sNlsCS2PUzF36OrqQnNzMx0p8vl86OnpYRQe\nTqcTIyMjrE5iXLHZbDAajTFmE0zES8Frb29Hc3Mzpqam0NjYyNoPdZ78fj+qq6tTHnsyLnjd3d0Q\nCASYn5+HQCBgFcW5Ti4+vwgEAojFYni9XlYhxBYx4tou02l4ADeTBy5tZDIZq1jKxe95KbMkxRIX\nyA81yFITLOR7JxCWHmxiyWq1QqVSJXRR4zJfaXh4OEKcRKfgDQ0NQafTMYoyvV6PhoYG3h729Xp9\nXMe9aBKl4DmdTs61joDMpuC53W4MDg7CbDZDJBJBpVJlvCDtUrmHSiQSOJ1OViHEFjEKb5eoLy4p\ndsmIIKrWUrr9abVaWK3WhH2RyFL+QcTSEmapXMQXgkyLKvJdEQipweVvh23OEh/zlSYnJ6FWq+n5\nSna7HePj4xGRokym4CXaVzhGoxFutzvGvIFKwYsXCYtHumLJarXCbDajrq6OtW1vby9KS0uhUCig\n1WqhUCiSEku59vIsl+8DMpkMEokE09PT8Pl8cdtRhWnZzq1Wq4Xf74fNZov7udVqTdgPl1Q9ILLW\nEtuY2KJGYrEYCoUi7rgBIpbyESKWCEuCXLvpEZghZiKEbMA2Z2l2djbhXCSAXSxFp+B1dnZGpOAB\n8QWM2+3GwMBAUqIkEVTEhUtKHzWm6Af1jo4OtLW1ob+/n3Nq4NTUFDweD2pqUq91p9fr0dzczKlW\nUldXF9RqNVQqFRQKBaRSacYjS8mQz9ciqVRKvwxI5GKnVCohk8k4iZhEqXgSiQRyuRxzc3Nxty8o\nKIDf7+ckTDKZ1scmlnJZFC9VlpxYytaPkO0imMt/HPl8Ac8Wufx9JkOufve5Oi4+x7ZYfkO5DmVj\nnOghmi2y5Ha7YbFYUFJSErdNtFiKTsEbHx+HRCJhNC2gHPIUCn7q8vX19cV13IuGab6SxWKByWQC\nEHyg5VLrCOAnBY+rZTg1/8vj8dCFaCUSCWeDB/L3lxwSiQQKhQJqtZrXVLxcMnngWpiWi1gibnj5\nxZITS3xCLqaRkPORP+Sy2CAQMgmXGktsYslgMKCkpCRutCN6vpLdbsfExASam5vpNonS4jo7O3lP\nweMiOCwWC2ZnZ2NMIKioUrIueOmKJaoGVfh5iwdVRHd8fBx2ux0+n48WTJlmKVxvpVIpZDIZZDIZ\nqxDiavKQyXlLfEaW2EQVScPLP4hYIuQ9S+FGxJVcPRf5LqTzffxLnUR/F3yIpWTnK3V0dHBOwfN6\nvejp6eE0v4gLfr+fc39dXV1obW2NKeJKWX/r9XrO4zIajXC5XGml4PX19aG6uppTRKy7uxu1tbWQ\nyWSw2Wy0G16upuHl+zWGSnEUCAS8RZYy7YjHh9Mdl30SsZR/ELFESEiupi0SCAQCH3ApSGuxWNIS\nS2wpeCaTCQ6Hg1FI9Pf3o6ysDCqVipfjHR4ehlarZZ2DBcRPwZuZmYFcLodUKkVxcTGn/VIGFenc\nU7im4AFBoSeXy1FaWoqSkhLMzs4iEAjkrFjiSq7eGyUSCcRiMTweD2/24aWlpTCbzfB6vYyfZ9o+\nXK1Ww+FwxB0PBYksLT6WpFjK1YtNrpLM+SLnlkAg5BJsD+ds5g5+vx9zc3MJxQWbWBoaGqLFks1m\nw+TkZEwKXltbG+NYOzs7057nEw7XFDyHw4GJiQk0NTVFrA93wUsm2pVuIVoqIsZl7FTRWpPJBKVS\nidLSUgQCAXi9XmIdvkBIpVIIBALaBS6R8YJOp4PD4WAVDGKxGDqdDgaDgfFzrnOWuJhJcBFLQqEQ\narWa1TWPj8gSeZbKLZakWMpnlsqFd6kdK4FAyA5caiwVFBQknI9kMBhQXl4e9/Ph4WHU19cDCIqf\nlpYWTil4fr8f3d3dvM5X6u7u5iRyuru70djYGCMuqHlHyUR5pqenMT8/z8nuOx5jY2MoKChAUVER\na1tKEA4NDcHv90OlUkGr1cLpdHI2eABy74E1l++J1Hm1WCysc42EQiHKysrSrrfEd60ltvpIXPtj\nS+kjkaX8g4glBnL5gkQgEAgE/mATS2zzlUwmEwoKCuL2MTU1hYKCAjqNLjoFz263w2AwYNmyZTHb\nDg4OorCwkFPKHBeo+jaJomAUTIVoLRYLpqenodPpYLPZOM8/ykYKHlUXanZ2FnK5HIWFhXA6nTmd\nhpdr4iwZJBIJ3G43pFIpdDodb6l4ieY3cSkmy1UsUbWWEkXEqH2yzVuSSqUQi8Ww2+2MnxOxlH8s\nObFEhFBykPNFyDXIb5LAJ+kWpE1mvhJTCl53dzeampogFotjts1WCh5Vh6m1tTVmPG1tbejt7UVL\nS0uM8UM8MmkZbjabYbPZ4PF4UFdXB4PBAIFAkBdiKZ+RSqVwOp0oLCxEQUEBa9SID5MHkUiEgoKC\nhGlxSqUSADA/P8+6r0zNgZLJZKTOUp6x5MQSkN9vb7IB1/NF/sAJuQb5WycA7G54bAVp+RJLHR0d\naGlpiRBG8VLwAoEA75bhXFPwenp6GOswpZKCNzMzA5vNllYKnslkwvz8PKqrqzkdY2trK4aHh1FW\nVga5XA673Z60WCL3s+QIF0tSqTQjkSUg87WWuLjmAYkjUCSylH8sSbFEyH3IQy6BQMgEXNLw2Mwd\n2OYrUWIpOgWPqhvU0tISs+3IyAiUSiVntzk2rFYrzGYzJ9HClIJntVphNBpRXV2NsbGxGOOHeFAp\neFyjUEx0d3ejpaWFk4ChxOfQ0BBkMhkqKipgsVigVqvp4rSZhsv9LN/FmUQiocWSz+eDxWKhCz4z\nUV5eDqPRyDpHqKCgABKJJK6IybQjnlarTbsvUpQ2/yBiaYlDREn24fodkO+KQEgeLm54C5WGFz5f\naW5uDlNTUxEpeL29vYwRHGBhUvBaWlpYxYLP52N0nevs7ERrayv6+/tRV1fH2SiBjxQ8rsVvKQe/\n0tJSuFwuOBwOlJeXY3Z2FjKZjFN9plwnV+8DVGSJMkooLi6O62IHBFPR1Go1ZmZmWPtOFIXKx8K0\nIpEIIpGICKY8Ii/E0lJ5mOR7/Hz0l+zbLj6PIdNv2rjuj2u7fP89cmWpHCefLJVrWj6Qzpwlm80G\nn88X9/PwFDxKbHBJwaPaZyMFb2BgAKWlpVCr1RHrqagY136A4Pwhq9VKOwGmwvz8PMbHx9HY2Mja\nVq/XY9myZRgbG0NdXR2mpqZQUVGRVbGU7xEjrkgkErhcLlpMsDniAfyk4nEVOHzZh2s0GlZTCS59\nkehSfpEXYolPsnHhWir7zFXIuUgNvs8b24N/rv+dLIVUmqVIojlLbDWWEqXgAZFiKToFL14EBwDG\nx8chFAoT9p3sMY6MjHBKnWMSaXNzczAajWhoaEBvb2+M8UM82tvbsXz58rRS8Hp7e1FfX88pkkWJ\nz+HhYVos6XQ6eL1eCIXCpMVSrr2syOXri1AohEQigVKp5CyWuJo8JOor02l4XF3z0q21lGu/vaXO\nkhNLQP7/CPN9/HySyzePTMN3ZIxAWAokSsObm5uDUqlkdKoDEqfgBQIBer7S3NwcDAZDhFgZGhqC\nTqeDRqOJ2ZbvqBIlOBIZWQBBccgU7ero6EBraytGR0dRXFwcE3WKRyZd8DweDwYGBtDa2oqhoSFU\nVlbC4XBAIBDQNZZyPQ0v3+/tcrkcMpkMFosF5eXlrEKIa2QpUTsuUSMuqXoA91pLXOzD2doQk4f8\nYkmKJQKBQCAsHdjc8OI9RKc7X0mpVEKlUtFiI5kUvGxYho+OjkKlUkGn00WsT8UFb3Z2FrOzs4z1\no7ji8/nQ19fHKZLV39+PyspKAKAfUsvLy2GxWGgnvFwXS/mOXC6H3++HWCyGRqOh63rFg0v0CQCK\ni4ths9kY09a0Wi3sdjt8Pl/c7fmutcSlP6VSCb/fH1cQEbGUXxCxREhItqIQ+f6GjUAg5AcLJZYS\npeAB8cWSwWCA2+3mZJPNBZ/Ph97eXk4ip7OzM2ZMlDFFU1NTUmKpo6Mj7RS8oaEhFBUVcYpkhafg\n1dTUwGAw0POVUokskQh88lACIFycJor6FBYWwuv1xi3eSiEUClFaWsoYqRIKhVCr1axRHKFQCIfD\nwXoMXB3xFtI+nPz2co8lJ5bIjzA1yHwNAoGQjyS6Lvn9fng8nrjpaYnEksfjgcViQWlpKePnlFii\nLLfDDQrGx8chkUgYt+U7BW9wcBAlJSWcBUf0viljiunpaQgEAs7zqDLpguf3+6HX62nL8Pr6eno+\nGfUdZjOytFTun5RpASU4+EzFy6V5S3z0RSJL+cWSE0uE/GEx3DwICwOJPBL4wOVyQSqVxr3WJBJL\nU1NTKC4uZrTiDgQCGBoaQkNDQ96k4FEPotGRsnAXPK7GDhaLBTMzM2ml4AHc5yuNjIxApVKhsLCQ\nFkvhTnjZFkt8ksvXPplMRkeWFsLkIZEjHpfCtHw54nGNLBGxtHggYolAIBAIS5J0aixxma+kVquT\nSsEzmUyYm5tDbW0tb8fI1ep7IVLw0ikAazAY4Pf7455jpvPpcrkwPT2NyspKGI1GlJWVLTqxlMuE\np+HxbR++2GotUcKSkB8QsUQgEAiEJQkXsZTINpxtvpLVasX09HSEC57JZILD4UBNTU3MdpRgSWee\nTziJ0v2iSZSC53A4YDabOddLyqQLHtV2+fLlGBkZQWVlJWZnZ6HRaCCVSrMulvjMkMj1bAtKLGm1\nWs5peFxNHsrLy2kBHQ0X8cLVEY9ElghMLEmxlMth7FyFnDMCgZCvxLt+JSpI6/f7YbVaU4osUWKp\no6MDbW1tEREWKi2O6cGX7/lKXFPwTCYTbDZbjICjRI9er0dzczOnSBElELkUkU0E17Q/g8EAn8+H\nysrKmBQ8t9sNt9sNlUqVkljK9H0v3++z0ZElnU4Hh8ORUBSUlZXBZDLB6/Wy9q1SqWAymWI+y/Sc\nJZlMBrFYzGpMkarBA5D/v4XFxpIUSwQCgUAgJCpIOzc3B4VCwVhjye/3025r0YTPV0omBc9qtfIy\nzyccril41JjCI1o2mw2Tk5Nobm5OOgWvtbU1rRQ8m82G6elp2k2Qy9gBxJg7WCwWaDQaCAQCkoaX\nAcLFksVioQ1BEkWOxGIxioqKYDQaWfuP1xfXOUuZrrVEIkuLByKW4sBV1RP1H0k2zgef+1wq3/tS\nOc5sHONSOGf5RKLUpUQP0FR9HibMZjOUSiXjtgaDga6xEh1hsdvtMBgMjIKISnlLR2REj5EpWsQE\n03ylzs5OtLS0wO/3Y3h4GM3NzZz2y0cKXk9PDxobG+MWAw6HEkterxeTk5Oora2NMXcA2FMuo8l0\nyluup9hxgRIAlFW33W7nNCeJaypevHZqtRpOpxMejyfuttmotaRSqeByuRjHRazD84ucF0tcfzR8\nt8v348zVfS7E+HIR8rtduPHn8j5zdfwEZlKtsURFLpgYHBxEfX09Ywped3d3XBHAdwoelcbGNv/J\nZrPBaDTGCDhK9PT19aG6upqT0Jibm4PBYIiYo5Xq2LlEsqxWK8xmM+rq6jA2NoaSkhJIpdIY23Ag\nebHEJ9l4oZcNwgUAFV3i4naXriOeUCiERqNJGOmhUudsNhvrfvhK6xMIBHHHRdmsE/KDnBdLhKVJ\nLt8QCATC4iAdscQ2XymZFDy73Y7Jycm0RQaXfTG1a2lpiRBwdrsdExMTSafgUdExLhGheHg8HgwM\nDKClpYXz2EUiEZ2CZ7PZ4PP5aJOBXBBLS4VosbQQjniJ7MMzOW8pXZMHkoaXXyxJsUQexJOHnDMC\ngbDYSGTwkIpYouYrFRcXw2QyRaTgud1uDA0NMZoWdHV1oampCRKJhJfjmp+fx8TEBCeTBSZR1dnZ\nSRs6cC0MC/CTgjcwMICKigoolUrWtuFzsqLNHYBQKqXb7YZQKExLxKXKUooQM4mlsrIyTE9Pw+fz\nxd2Oa2SpqKgILpcLDocj5rNMO+Klax9OxFJ+sSTFEoFAIBCWDvFe9iQyeEhFLBkMBsjlcgwPD8ek\n4PX29sZNZ+M7BU+v12PZsmWs4svpdGJkZCQmikNFxUZHR6FWq+Oeh3DCDSHSgasLntPpxOjoKJqb\nm+H3+zE6Ohph7gCErN9TjSrl2kvCXBdeTGJJKpVCo9FgZmYm7nYqlQpCoZBTpCYTJg+ZiCyJxWII\nBIKE86wIuQMRSwTeyPULOWHxkGsPMYT8hC0Nj6nGkt1uh8fjQVFRUcxnqaTgxRMs6cDVMrynpwf1\n9fWQSqURx0el4HHth9pndDpfsgQCAej1ek7pg+Fjn5iYgFarhUKhiBCy2a6xlMrx5zPh83DCRQKX\nVLxkTB6YolC5XJg2FUe8fP8tLDaWnFgiD/TJQ84ZgUDIV1JxwwsEAnFrLLGZO1B1Y8INE3w+H3p6\nehhFgF6vR0NDQ9wIV7J4vV709/dzis4wRbSoFDyJRJLUfKX29va0U/AmJiYglUpRXFzM2pbJMhwA\npqamUF5eDq/Xi/n5edopLVmxRO57ySMSiSASieByuSLEBFdHPK4mD/EiS5kUS0qlEj6fj9WkgTK6\nYIKk4uUPS04sAUSxpwI5ZwQCYbERb87S3NwcZDIZYxob23wlh8OB5cuXR6TgDQ0NoaioCBqNJma7\njo4OXlPw+vv7UVFRgYKCgoTtPB4P+vr6YkQVNe9oenoabrcbVVVVrPsMj0alA1dx5vV6I8ZOiSWv\n1wuz2YzS0lLMzs5Co9FAKBRmPbK0lO6flAAIT1PjIoSSMXlIRyyxpeoB3GstcU3XI7WW8p9FJZZy\n+YKUq/WHcrXGTC5/l3yzlI410+T7uc338ec68eYsJaqxxDZfqa+vj3MKntvtxsDAAOfoDRe4ps71\n9/ejsrIyQlTZ7XaMjY2hpaWFFi5cIix8GVRwFUsDAwMoLS2FSqVCIBDA8PAw6uvrYTAYoNPpIBaL\nI77DbIslLiyWSBaViqdQKAAADoeDcxoel8hSWVkZZmZmYgwjqJpGbrc77rZUlIftusq11hKXeUsa\njQZ2u53R4CKeWFosv4XFxKISS3zB9w+V/PDzA1L/Zukd51I4RkJ84j1Ep2LuMDg4iMrKSpjNZjQ0\nNER8Fu7aFk5vby9qamroB8t0SWbOD1MKXldXV0opeB0dHTECMVksFgusVitqa2tZ24afT4PBAIVC\nAbVaTafgAZFzzrIplvi+xuT6CxQmkweNRoNAIJBQfBQXF8NqtSYUOwAgkUhQVFQEo9EYsV4gELBG\neqRSKWQyWUZrLYlEIqhUKlit1pjPZDIZiSzlCUtOLJGHo+QhRWkJBEI+E+8BM14aXjyx5PF4MDs7\ni9LS0pjPhoaGIBAIYlLwxsfHIRaLUVZWFrMN3yl4o6OjUCgU0Ol0Cdv5/X5GUUUZU9jtdkxNTcUU\nqmXC4XBgdHQ0bYOK7u5uNDc3sxbRDQQCEWKJiioBYDR3AFIXS7kuTHIRJrEEsKfZiUQilJSUcIou\npZuKl2lHvHipeCQNL39YcmKJQCDkN0REE/jA4/FAIBAwurfFE0vhaV7RDA0NwWg0MqbgMUVovF4v\nent7OUWBuBIvgsU01sLCwgi3P4fDQafg9fT0oLGxkZOzXaZT8MbGxiCXy2kTiKGhIdTV1QFATGQp\nn9LwFgvRYimZeUvJmDwwtcu0WEqmL1JrKb8hYolAIBAIi5Z44jqVGkuJ5iuJRCLMzc3FRGPizVfq\n7+9HeXk5VCoVb8cab1/RdHZ2xi1Em0oKXroueC6XCyMjI5wMIqKPMdwJj8/IUi6+lMnFMUWTamSJ\na5tE7XK11hKJLOU/S1IskdB68nA5Z/lwIScQCAQgtRpLieYrqVQqrFixIiKNzGQyweFwoKamJmYb\nvlPwpqen4XK5OLnXdXV1xeybEj3JWI/Pz89jZGSEU9tE9PX1oba2lpN9enikzmQyQSAQQKfTYXZ2\nFhKJhDasyCWDB67PHIvh2SSeWOLT5CFeX1xrLXFxxMt2ZGkx/BYWE0tSLBFyH3KhIBAIC0miGkvx\n3PASiSWHw8GYgtfa2hozD8fn80Gv1/Mqlri6142NjUEikUTMuwqfd0RFvJRKJes+u7q60NjYGFHU\nNp2xs0EJwurqagDxU/B8Ph/sdjvUajWA7IulpUQ8sUTZuXs8nrjblpeXY2pqivX+r1arIRQKY0wT\nMp2Gp1KpMD8/D6/Xm7AdiSzlP3khlnLVdjtbkLEtnnHxfQzZsILnc59L5Q1svo9/MRDP3MFut0Mq\nlcYIgEAgAIPBwCiWBgYG4HK5OLvgMc0ZSheuluFMUSVq3pFUKs14Cp7f70dPTw+n6FS0IIyXgmex\nWKBSqWijjXxww1ssmRnxxJJIJEJxcTEMBkPcbRUKBRQKBUwmE+t+mFLxuAgcLtEngFutJaFQCI1G\nw5qKF29cxDo8f8gLscSFbFyQcvkHzWVsuX4R5/MYcpVsjD9Xz9lisOxfKteXfINJnMabsxRvvpLZ\nbIZcLo+x+aYe/lauXBkRQbLb7ZicnERjY2NMX52dnWmLjHBsNhuMRiMn9zqm+UqU6EnGetzpdGJ4\neDjtFLyRkRGo1eq4Vu3hsM1XYjJ3oMaaij17Lr7UyMUxhRMuAKhzPj8/D2DhU/EKCgrg8/kSRmso\nEcRXrSWuc5uY9knVpCLkPotGLBEWlly/QBMIBEIyJFtjKVEKHoCYFDy9Xo+mpqYYR7lAIMBY4ygd\n4u0rGqPRCLfbTaexAZHzjsbHxyGTyWinuUR0d3ejoaGB0zwjtn64RLKiBaHVaoXL5aLTCaemphjN\nHahjJGl4mSG6dlB4ChoXIcTV5CFeX/FS3igkEgnkcjmrCOLSF9WGLbIUb58kDS9/WJJiiTz4EwgE\nwtKGL7Gk1+vh9/tjUvDiOdONjIxAqVRyEiRcSSYFb/ny5RFRy/B5R5kuREudPy77pOowUal11Hwl\ngUAAl8uFubk5+pxGzzmLl3JJ4J9oAZCsIx7XyFK8vriaPOSCfTgRS/nDkhRLBAKBQFgaJLIO50Ms\nDQ0Noa2tLSIFz+12Y3BwkLFQK98peG63G0NDQ5yKwjKl4FGFaAHuUR6Xy4XBwcG0U/BmZmaScvAL\nH1t4Cp7BYEBpaSn9HYS7GbpcLohEoohCwVzIxTTYXBxTNInEEiWEEr2w5hpZKikpgdVqhdvtjljP\nVeDw5YiXjn04EUv5AxFLBFayMbeJRP8IBMJCEi/akIxYMhqN8Pv9WLduXcT6vr4+VFdXM86T4TsF\nr6+vD1VVVaxzciwWC8xmMy0wgMgUPLPZDJvNxmhzHk13dzfq6+vTjtZ0d3ejtbWV9d7hcrkwPDwc\nIQjjmTsAuVeQdqkY1wDMYokSE0qlEjKZLKEA0el0mJ+fp+c5xUMkEqGkpCTGMCKfCtNKJBIEAgFG\nN73F8FtYTCw5sZQPb2ZyEfKHS8gVyN8wgQ8SGTxEu9Q5HA643W4UFRVFrG9vb4dAIIgQIED8FLzx\n8XEIhULaiIAPuBaipWzMwyMs0Sl4LS0tMTbnTPDhggdwj2T19vaipqaGFj0OhwNWq5UWSLkulpYS\n0aYF0WKCLXIkEAhoC3E24jnisUWNuDrikcK0BIolJ5YA8uCfL5CHYgKBsFDEe4hmqrEU7rQWTkdH\nB2prayMEht/vjzsPh++oEmW7zUVwMO07XPQkk4I3MDDAeW5TPBwOByYnJzk5+EVbsA8PD6OmpoY+\n79E1lmw2Gy1480UsLZb7nVgshkAgoNPjogUHF0e8dEweMj1nSavVYm5uLqHFeKK+iFjKD5akWGJj\nsVy0CAQCgRDfOjz6Idpms0EsFsdEnOLNV5qensZuu+0WsW5oaAhFRUWMNZT4ishQDA8PQ6PRsNpu\nOxwOTExMoKmpiV43Pz9PW387nU6Mj49HfB4PvV6Purq6lKy4w+np6UFDQwMkEknCdj6fL0YQhqfg\n+f1+GAwGWizNzc2hoKCAlxpLfLxY5ft5Ih9e9sartQRwM3BIxz6c79Q5tlpLIpGIs8U4UwQq2j0Q\nIM+guQgRSwRWyB8ugUBYbDDNWUpmvlJPTw8CgUCMI1y8tDiDwQCv1xth250u8YreMrVrbGyMECbd\n3d1YtmwZZDIZenp6UF9fH1OIlwm+BB9XF7yhoSHodDpoNJqIdZRYMplMUCqV9HcZnUaZL5GlxUR4\nKp5SqYTf76cFAZeoEdfIEpWuFy4go2s7McGl4CwQjJIpFAreai2RyFL+suTEUi4/+HN5Y5TL4ycQ\nEpEPb0TJcS4+ErnhRUeQmFLwAGax9M0336C4uDhmjk88scTkRJcuyViGR6fgpeKC53a70d/fn/Zx\n+Hw+9PX1cXLTiz5Gl8uF6elpWnSG11cCmAvSErGUWRI54ul0OjgcjoQCoby8HNPT0/D5fAn3o1Ao\noFAoYuYosc1bogrOWq1W1mPha96SXC6HSCSCw+FIeK4IucmiEkvZeEjJZZcbss+F64tLu0z/NoiQ\nTg3yPS1NmB6imSJLXq8XZrOZLn5KMTQ0FCMaJiYmIBKJUFZWFrM/vi3DqTfqlZWVCdsx2Zg7nU46\nBc/n86G3t5eTcOnp6UFNTU3aKXiDg4MoKSmBSqVibRsdPRsZGUFlZSVdgDeRuQN1rKmIpVz8O83F\nMTERLQDCoypCoRBlZWUJ0+ykUik0Gg1mZmZY98UUhcrVWkvEPjx/yXmxlC8Xh8VOPr8t5/s3lI3f\nZK7uM9//PvN9/ITU8Pv98Hg8MZElJrFkMBig0+noh3MgVB9o9913j2gbL6pkMpkwNzeH2tpa3o4h\nWSe5cIHT1dVFp+ANDQ2huLgYarWatS++CtFyHfv4+HiM+AxPwQMizR2A3Iws5fJL1YUgUWQJ4N/k\nIZV5S9lwxGPqK55YWiy/hcVCzoulbEF+qAQCgbA4cblckMlkMWKZSSwxpeBt3rwZEokkxkqcLQWP\niy03V7im4DGl/4XPO+Laj8fjQW9vLy+phFznKzHNyYoWS9HfT3QqZS6IpaUGm1jiIoSSMXmIbpdP\ntZairdYJucmSFEtECOU+5DsiEAh8EX09SVRjiYttOGUZHk6ioq58W4ZbrdaYArNMUE5y4YLD6XRi\naGiIFitchUtPTw+qq6uhVCrTGvvk5CQEAgFjqmI00eLT6/VicnKSPvcOhwMulytCtOZiZIkLiynK\nnagwLcDdEY+ryUMqtZb4tg8naXiLmyUplgjJsZgu4oTFARHThHRIVGMp2vI7OnIxPT2N+fl5Rhe8\ntra2mOiR1WrFzMwMp3pCXKEKyIYXmGViYGAApaWlESl23d3daGhogEwmo4ULlyK5fLrgcZkfxSQ+\nR0dHUVpaSrv2Rafg+f1+WK1W3tzwiHV4anCJLBmNxoRudFzT8HQ6Hebn5yPc77IRWeKahscUWSLW\n4bkPEUsETmTDqY9cMAgEQrowXUeYHqDtdjuEQmHE+kAgEOO21t7eDoFAECN+EqXgtba2sgqbZOAr\nBY/r3CEqBY+P6BjXfXZ1daG1tTVCfA4PDydMwZubm4NCoYiYX5YvkaXFRHTtoGjBIZVKoVarMT09\nHbcPrVYLv98Pm82WcF+U2A+PVBUVFbGKFy7RJ6odm824VCqFVCplHSuJLOUvS04skQdwAoFAWNpw\nrbFkNpshk8kiUs927NgBqVQakfplt9sxOTmJxsbGmH3xnYLndDoxMjKC5ubmhO38fj+6u7sj9u10\nOjE4OEiLFa7Cpa+vD5WVlSgoKEhr7HNzc5iZmWFNHwSYxefQ0BDq6urof7OZO1DHTMRSZokWAAUF\nBfB6vRFzc/g0eYhuJ5PJIBKJYLfb426j1Wphs9lY7cm51lriYvKQjMEDIbdYcmIJyI8wNoFAIBAW\nBqY5S1zMHaanp2G329HU1BTRTq/Xo6mpKSKiAYREVHT7dOjt7UVdXR3jnKtwRkdHoVQqodPpIsZZ\nX18PuVxOz3sKFx/xaG9v5y0Fr7m5mTXK5nA4YsSn3+/H6OhoUuYOALEOzwZMAoDJEY/LvKWFMnkQ\niURQqVS81Vri0qagoAA+ny9CNBKxlB8sSbFESI5kLtBEiGYXcv7zA/I9ZRemB2imB+3oh/H29nYo\nlUrOKXhdXV1oamqCRCLhbezx9hUNU0QrvBAtV+Hi9XrR09OT0RQ8vV6PxsbGiPM2MTEBrVZLW6D7\nfD7MzMxEGEUwCV6mKGKusliuC1zEEldHvHTswzNt8sBl3lJ0Kh4RS/kBEUs5Qq6/Mcr0RXyx3DRy\nlUyf31z/fZPjXNwwueFxScNjEkvz8/NoaGig1zEVfaXgOwWPKiDLdc5P+L5dLlfKKXjl5eWcCsgm\nwuPxYGhoiDV9kBo7m2X49PQ0tFpthKCanZ2NMHdwuVwQiUS8zhdLhaV2P2MSANEigc80vLKyMkxP\nT0ek1OVqYdpok4fo+V0US+03k+vkhVji80ezFAptJsNS+YNcDMeZq8fA57j4NhLJ1XO2VMafq3Cd\nsxQuloxGI+x2e0x9pb6+PlRXV0cUfQVCc4uYRFSqDA4OciogOzk5iUAgECH0uru76RQ8t9vNWbjw\n5YLX39+PysrKmPMUjcfjwcDAQIxjHlt9JSB/bcOBxfXcwSWyxMXAobS0FGazGV6vN+H+pFIpNBoN\nZmZm4u6PiVyILMlkMvh8Pta5U4TskhdiiQvZeIDius9sXAQXw4U308I2G30thu9pKUC+p/wlnhse\n25yl6Bo+7e3tKCsr45yCF27RzRdMRVqZiI4qAZGip7e3FzU1NaxCwuv1Qq/X8yKWkjWTCBdVgUCA\n0Qkv2vKcb7FErMNTg4tYAtgjR2KxGDqdDgaDgXWf0ZEqrmKJqyPeQhamjY4ukftN7rFoxBJh4SAP\n/gQCYTHBJQ2PehinrmuUZXj4A7vf749b1JXvFDwgdctwl8uFgYEBeh1X4dLf3x9TpykVAoEA5+K3\nTOLTYDBAoVBEjCPa0j0QCMBqteZtZGkxQaVGejweeh2TSOCSipdqcdp8mbMEkHlL+QARSwQCgUBY\nUkQ/RDscDggEgoh14WleBoMBLpcLBoMhYr7S0NAQioqKYgrZut1uDAwMcBIHXBkfH4dYLI4wNGCC\nKuZaW1tLr9Pr9airq4NcLoff70dPTw+nsfGVgjc2NgaFQhHhzMcEJT7Z5isBsWl4NpsNMpksYg4T\nEUvZg60wLbCwjniUOEsUieMyr4nqi63WklKphN/vZxU9xD48PyFiKQ/JhzA8gbCQkL8BQjpEP0Qz\nzVcKj1x0dHSgsbERIpEo4oE/XgoelebGNj8nGbim4HV2dqKtrS2imGu4C97IyAg0Gk3M8Ubj8/nQ\n3d2d0RS8eGOLFktUzZvwSFO0uQOQnljKxUyJXBxTPORyeYRFtkqlgsfjgdvtptdxMXBItdaSVCqF\nTCZLOCdKo9HAbrfzWmuJS7pedAQq+lwRco8lJ5by6WKTS3B9OOXrIZY8DBMIBL6Ivp5EGzywmTu0\nt7ejoKAgJroRTyx1dHRkNQUv2gUvPMrFVbgMDAygpKQEGo0m7bF3d3fHGDbEO0am88k0X4nN3AHI\nv8jSYrrvcXHEowwcwtP1ouEaWaIMI8IFDVv6nFAohFqt5pQ+x3XeEltfKpUK8/PzEaYVJLKU+yw5\nsUQgEAiEpU20wUP0g7bX64XJZEJZWRkMBgPcbjcsFktECt7ExAREIlFMWpzX60Vvby+nKBBXzGYz\n5ubmIlLrmLDZbDAajREmFFQKHhXl4iqW+CpEOzs7C7vdjpqaGta2TGLJZDJBIBBEOBDmm1haTCKI\nK1xMHsRiMYqLi2E0GuP2U1BQAIlEwildjikVL9PzltjaCIVCaDSaCFHFdK6W4m8mlyFiKYcgfxyR\nkCjg4oL8vgnZIJ4bXvhDdHRBWqPRiKKiIojFYlo0DA0NRYileFGQ/v5+lJWVpV2XKBwqMhOeWsdE\nV1cXmpubIRaL6XXh846MRiM8Hg+qqqoS9sN3Cl5LSwvr2KempmLszoFgCl5dXV1M22gnPKaiwrki\nlriw2O53fDnicW3D1I5rrSU+HfFIYdrFyZIUS+ShLTkW20V8sUK+p/yAfE/Zxe12QygURggKJie8\n8BS8mpoaCAQCTvOV+DJFCCfevpjahafgud1u9Pf3R7jgcUmHGxwcZDSuSAWukax4aYZczB2AhYks\n5eKzQi6OiQkuaXgAd0e8VE0eMl1rKZW+iFjKfZakWCIkT75coAnskId1wlKGS0Fa6mF8amoKHo8H\nTqczIqpEOc5Fp5b5fD7o9Xpe5yvNz89jYmICTU1NCdtRRXDDC83q9XrU1tYmnYLHl+BzOp0YGxtj\nHTsQXxBGiyWPxwOLxYKSkpKIdnwbPPDFUr3eco0scRFCXCNLqdRaSsYRj6/IUnS76HO1VH8zuQwR\nS4uYTAsc8gdOyATkd0ZIBy4FaSmxRKXgDQ4OxqTgRTvOAcEH+8LCQl4iMhR6vR4NDQ0Rltjx2tXX\n10ccW7josdvtMfOZmPD7/ejq6uJFLPX29qKurg5SqTRhO4vFgtnZ2ZgIktVqhcvlipgXZjAYUFxc\nDJFIFNNHPqfhLTaiC60CC28fXlJSEmEYkenIEte+SBpe/rHkxBLXBy2+3d9IZCY/4PN7Wgzf+WI4\nBr6OcSmci8VK+HcX/QA9Pz8PABE235RteEdHB1atWhUT3YgXBens7MypFLy+vj56W71ej8bGxoj0\nQyYGBweh1WojDBVShWvaX7w5WUzzlZhS8Gw2G8RicYwIJtbh2SNeZCk68qJUKiGRSBLOGyouLsbc\n3ByrvXa0YQS1v0T1kZIRS2y1llQqFVwuV0J3P6bzwCQsCblFzoulhbg4sD305NMFKR24Hme+n49s\n/Iby4RhybVx8H2OunrOlMv5chanGUngkyGw2QyqVYm5uDh6PB0qlEkDwgQ0IRmgmJyfR2NgY0W8g\nEIix7U4Xr9eL/v5+VsHh8XjQ19cX0a6npwc1NTX0+DOdguf3+9Hb28t5vhKXFDyAu7kDkH+RpcX0\nQoZJLMUTE2yRI6FQiNLSUs7zlqhUPLFYDKVSmbA+klqthsPhiLDyZoJLrSWBQBDjdMcEiSzlHzkv\nlgiRZOsBajFdxAkEwtIh+prJVmMpPAVv1apVGBwcjHhg1+v1aGpqionQjIyMQKlU0qKKD/r7+1Fe\nXo6CggLWdpWVlRHtwgvRejweDAwMoKWlJWE/fKbgDQ8Po7CwkLVOU6J5TemYO1B954JYWor3TyYB\nIBAIFtzkIXp+E5daSxqNhleTBy5iyWaz0cVwiXV47kPEEiEnIRcKQiLI74OQKmw1lpjEEhfLcL6j\nSkAwGsQlBa+zszOiXXQK3sDAACoqKugoUzyGh4ehUqkiXP/SGTuXqBI11yp6XpPD4YDVao0QRoFA\ngDGyxGTuADCbeeQqiy2SHC9astD24dl2xOPSRiQSoaCggI5SkchS7kPEEoFAIBCWDExpeNFiSS6X\nw+fzobq6OkIsud1uDA4OMkZo+J6vFAgEOAkOv98PvV4fIZaiU/Di2XJHEx6NSpdkLMPjpeDV1tZG\nzGOanZ2FTCaLEX1MkSWXywWRSBRjBJEMufhSJhfHxEQyYolPk4dUCtPy6YjHJbJEtaP6ImIp91ly\nYmmxvb3JBMmcMz4v5OS7Sp58uZEuZsh3kNuwFaSdnJyE2WzGypUrYTKZEAgE6NS6vr4+VFdXR5hB\nAMD4+DiEQmFMxCMdRkdHoVAoWNP6hoaGoNVqI44hfN5RIBCAXq/nJLr4EnxGoxFerxeVlZUJ21Fz\nspjGNjw8zCkFD4hfYyn6e8oGS/U+loxY0ul0sNvtCQVDeXk5DAZDQoMFINYwgmthWq5iiU0IpdKX\nTCaDx+Ohj22p/mZymSUnloDcfJghfxyExQz5fROySfg1P9Gcpfn5eTidTvT19eVVCl74vj0eD3p7\ne+l1Y2NjkMvlrKJrZGQEBQUFvMy50uv1nFzwBgYGUFZWxjgni8kJjykFD2A2eJifn8+bFLzFSDyx\nxDRniYuBg1wuh1KphMlkYt13eHQpVwvThrcTCASQyWSsbn+E7LEkxRKBsNTJxRcGBEImSDRnaXJy\nEoWFhfD7/TEpeH6/Hz09PYxRkIWyDOeaxhYulnp6elBdXR3hgsdFdPHlgkftk+vYmdq5XC5MT0+j\nuro6Yn2ykaV0xFIuvuDJxTHFQyqVwu/3x7jMxRMcfKbihc9v4iqW2FL1kumLj8K0hNyCiCUCJ8jD\nNSFXyKcHBkL2if69hD9EO51O+P1+WlhMTk5CKBTS83bC3djiFZw1GAxwu90xD/bpMDMzA5fLxdrn\n2NgYJBIJSktL6XXR8464CJdAIEDXlEoXu92Oqakp1uK31JwsJiE3MjKCysrKGMdBJrHkcDggFApj\nhFGuOOElw2K7z8artRRPLHFxxEvW5EGr1WJubo52nmMimWKyVqs14fek0WginO4S9UXsw/OHJSeW\nFsOD1mK7oC7VYyQQCJkn/CGaydzBarVi1apVMJlM8Pv9KCkpAZDZFLyuri60tray3q+io0pUCh41\nTrPZDLvdziq6RkZGoFAo6GNNh56eHk7FbxPNyWKyDHc6nXA4HDHFcuM54eWjWFpsyOXymNQytVrN\nWGuJqyNesrWWRCIRVCoVrFZr3PbxxhSNRCKBXC5PWGsp2ukuHtECjYil3GZRiSXygB2CqyhcDIYM\nXI4hl38bXMeWy8fAF3wfY76fs3wffy4SPmcpWiyNjIxAKBSiqqoq5oE9XhRkocRSKpbhVAoeNQeo\nu7sbra2tEY5yTGQrBS/eMcYrRltWVhZzLLleYwng9ne8GF7kRhOv1hJT4dby8nIYjcaEBg5cI0s6\nnQ42m40WamyRo3j1n5jga95SdJQq+lyRa39usajEUqbhenHL94tgtsbPZb98ji1X+8oWi+EY+DrG\npXAulgrhc5bCoxJerxezs7NYvXo1AETMV5qYmIBQKERZWVlEXyaTCXNzczFGBOlgs9lgMBhY09iM\nRmNM+l+06EkmBY8PsUS527EVv6XGxiSWvF4vJicnUVtbG7F+cnKSs7kDwI9YysUH1lwcUzySccST\nyWRQq9WYmZmJ219hYSFcLhccDkfC/VJ/q9kyeeAyb0kqlUIqlcJmsyU8V4TcYEmKpXy62OQKJPpB\nIBDylfDrUrw0PKPRCABYtWolHI65CLGUKAVv+fLlrJGbZNDr9WhqamJNY6PGRAn5aBe8+fl5jI+P\no6mpKWE/Y2NjkEqlMUIwFQYHB+O624UzPT0Nl8uFqqqqmM9GR0dRWloaU6R2amqKs7kDkDuRpaX8\noiUZsQSwp+IJBIKUUvG4GDhkwxEv2j6cOldL+TeTqyxJscQF8tBPiAe5kBEI+Ynf74fH44mILBUW\nFuL7HZ/hqSduh8PWj3vvvgC/uvIgDPS9BokkuF2uWYZ7vR68+frd0He9iU8/fhEA0Nvbi8rKSlqo\n9PT0oL6+HhLqIOKQrUK0bW1tjNdSphQ8IDknPCB3xNJSJlwAhJMJk4d8cMQjhWnzByKWcggi0AiL\nGfL7DkHOReYIfyB3uVyQyWT0OiqF61+PXI+eni8wO/s9ZmcNCAT8cLst0Hd9A7PZDJvNhpqamoh+\nrVYrZmZmWNPlksHtdmNwcJA1jW3Hji9gNvejq+tLPPnkbTAaR1NKwQP4tT1fqPlKfr8fRqORMfq1\nUAYPufhSLBfHlIhkI0tcrMG5GEFE98V3YdqF6IuIpdyGiCUCK9m4QJOHyeTJtxvpYoR8B7lNvBpL\n8/M2xvY+nxcdHe3QqDzo7v4m4rPOzk60trZCJBLxNr6+vj5UVVVBoVAkbNff1xPx73vuugyff/oY\nli2r3zluH/r6+liFy9jYGEQiEeNcoGSZmJiAWCyOsDFnYm5uDtPT04wi0+/3Y2xsLGYO2MzMDNRq\ndcR3R7GYIkuL7b6XTGFagHtkiWutJYPBAL/fz0m8cBFUAPc0vGRrLRGxlNssObFEHmZSY7FdxAkE\nwtIj/AHa5XLB6/Wyzq/57JMXsW3bC7jrzosxOTlIr89WCh4AjIyMRvzbYBiGwzGG0ZEOAMG5QyUl\nJVCpVAn7yYYLXnd3N5qbmxlF5sTEBLRabYxYjGfu4HQ6EQgE6DpZ0Z/lm1habCQbWdJqtfB6vbTp\nARNlZWWYmZlhrWMkk8mgUqkwMzMDjUYDu90eUyCXy5iYxshWa4kSS2zPTSQNL39YcmIJIA/+CwXf\nQpQIW0I8yN8wIRUS1ViK135g4GP632MjwYiO3W7HxMQEq3lCMvj9fuj1elbB4XA4YDabGD8b6N+B\ne+66DA/c9wvU1VWy7jNbYimZFDwgeXMHILfEErEOj0StVmN+fp5RvLBFjiQSCbRaLaanp1n3T/Ul\nFAqhVqsTRntUKhU8Hg/cbnfCPrnUWop2uotHdGQpvCYVucflFktSLOUzi/GCSsgs+f4byvfxEzIP\n9eCRrFjS67+P+Pf09BiA4Jyb5uZmVvOEZBgZGYFGo2EdU3d3N8rLKxg/e+edx9De/gXm5gwI+GYT\n9jM+Pg6BQIDKSnZRxYbVasXs7GyM3Xc0LpcLw8PDcedk8WXuABDr8FwgnlgSCoXQaDQLbvIQ3o5L\nmh2ftZa4mDyQyFL+QMQSgRXycEogEBYD8QrSCgTMt8KtW1+P+LfBMAxg4QrRcjVHqKutYW330kt3\n4G9/OR822yzj53xGlfR6fdzUunB6e3tRU1PDOPcoEAhgeHg4bmSJKQ0vnrlDIBCI+K75xO0mD7Rc\nSSQA4okJLgYOXE0ewm3GM+2Ix0V4KRQKCAQCOBwOIpZynCUnljJd6HSpkU9vvQgEwuIn/HrOVJB2\ndLQHgYCfblNVvT9aW9cz9mUwjMDpdGJkZIRT4dVkSOQQR0G55fn9Nk599vRsxc03ncT4WTZS8BId\no8FggEKhgFqtjlhvt9vh8XgYI0jxIksulwsSiYTX+leff/oybrn5VFz+i31w7W+OhNfr4bTdUn6e\nYBNLqTricTV5iK61lGuFacPbhZ+rpfybyVXyQiyl+wDu9/swNTUIr9eDuTkTnn/mdjz/zO2w29l/\nyNk8hkAggL6+bdi+9V24XI6ktyckD59ibzEIRy7HkO/HSQouLx2i0/AG+7/CH245nf58xYq9oVBW\n4ZJf/I1xe4NhGB0dP6ChoYExOpIqlGsXW0ocFZnp6fmWc9822yz8fn/EusnJSQQCAcaisMnidrsx\nPDyM5ubmhO18Ph96e3uTnq8ULwUPCFm/R8NHCl74A6vX68Grr96P8fE+AMDsrBV6Iv0AAFrSSURB\nVAEvvXB32ucunTElYs46iu6uzfD7fXj/3afwv7cfhcXCPseHb1IRS6WlpTCZTAnNGLim4RUWFsLj\n8cBut3OKGvHtiMfVMGJ2dhYymQxut5vcZ3KUnBdLXC8Oidr997k/4e47f4bf3XAYbDYzpqYGsX37\nu3j7zQeyfXgJ6evbhn89fBWef+52/OPuC2NueOmSzNuLfP4DXoi3NHydDz5+34sFYhCyuMafi0SL\nJb3+i4jPFYoSNDQ0QC4vwLJlG2K2t1im8cjDv0BlpY7XcXFNwevs7ERFRSF6e7cDAFpa1uH+B7/B\niSdeFtHutNN+E/Hv0VF9xL/b29t5iyr19fWhurqaVZwMDg5Cp9PFRI4oEpk7xLM2z4RtuF6/Fb//\n3ckxYuP995+C3+9LsVdm+LivDAz8gMGB/+GpJ2/Gxx8+j+ef/xtefPEe3HDdcXC55nkdLxupiCWx\nWAydTgeDwRC3X+o3lMhkgYJKxctGraVkIktCoRASiSTC5IGQO+S8WOKD77a/Ry8HAl4AwQuSy+kI\nW597YsA4NUQvz8yM4ocdH2FsrCeNHgkEwkKTi9cSQpDweSwWiwUOR+TDjEqzDA0NDfD7/fAFmOsF\n+XwefPj+Q7yOi0sKns/nQ09PDyzmPnrdPvucAIFAgIMPPQuVlcG6RTpdAw48+DRceOFf6Ha3/+Es\n+HyhN/W55oIHIO58pUSRpUyIpaeeCBb9ZeK7bY/gs0+e52U/fPHKS/fSy88+G/oNeDwudLZ/ldGx\nyGQy+Hw+RpvvRIKDaypeMiYPmU7DSzayBBCTh1xmSYilcMzTn8DrDd0gPR43/vPY9fjTbSdjbEyf\nRs/pweUt8rPP3IqPP3wCVutM1saZ7jFwhTxwLi5IlCQEOReZJ9wNj0p38Xg8UCo1dJsDDzwNBsMs\nGhoaMDQ0hJKSSpx33u3Ya6+jcOCBp0X0NzU1yFuk32q1wmw2MwqFcAYGBlBaWhqRgrfrbgcBAMRi\nCX59zb+xYuVxOPGkqwEAhbqyiO2fePzWnWOfgtfrRXV1ddpj9/v96OnpQWtrK2vbRIJwZmYGAoEA\nRUVFMZ/Fq7GUqE4WX2LJYpmOqK3FxIcf/gcjI4mfHTJpHZ4oevTAA1djeLgL9//jKphn+pLoNXVk\nMllShWkBbkIoGZOHyclJqNVqOJ1OeDzx55rxWWsp2chS9Lkiz0C5xZITS9G88+YD6Or8AjabCd9u\nfiPbw+GEx+PE8HAHuju+zMgfFHm4IxAIiwHqIZoyd5ibC9YrqqhoxuFHXgCPx4PS0lL6wX6PPQ/H\nz35+K0457WrU1EQaOgwPd/EypkRFWsPp7OzE8uXL4fUG68CUlFRDLg8VYxWJpLA7JFi7djcAQH39\nShx0UGg+1ldfvQGXa57XqNLY2BgKCgoYRU444+PjkEgkKC1ljtbFS8Hzer0wmUwoKyuL+SyeEx7A\nn1j639uPcGp3261npL0vrrDd86XSxMd9+x/OwnfffYze3nfgdNoXfLzR9YMoNBoNHA4H49wkLkIo\nGZOHqakpCASCuHblFAUFBfD5fKzRHS61lhQKBQKBAObnE6c+kshSfrDkxZJev4Ve7u3bRi/nqqp3\nOcfR3fEcHrzvUjz++HXY9u07GdlvNs4HEWkLR67+vgkEvol2w6PEkkajxvx80FVOp6vA4OAg/cAe\nnTImFArx2+ufwJln/pZe9/WXr3McQWLY0tOAYASnu7sbK1asiDtPpq+vD7W1tbTxhFAoxKmn/xrL\nlwed/QKBALxed9Zc8BK1i5eCZzQaodPpIBaLYz6LZ+4A8CeWtm9/n3Pb/zx2C2eHvIXC5ZpHT8+2\nmPXhv9twPnz/8QUfU6JaS/EKxfKZhldWVoaZmRl4vd6crLUU3g8RS7nLkhBLGk28t1k/YGYmlIts\nt5nz5CEydLMc6P+OOOURlhz58XdKyDWoOUuzs7NQKEIFZUtKgmKpoaEBExMTEAqFMdEMkUiM/Q44\nia7J9MUXr8Ljcac9Hi5OcqOjo1AqldDpdHC7g2/pxeLIgrjxBEl1dajvLz9/Gy6XCzU17HWauMCH\nZTgQjCzV1dXFrE/F3AHgd85SPH7yk5tQVBQa2+efv4JfXXkgtnz9dkS7TL70m54eYxTT+286Geec\n8/uY9f392xd8TKmYPBQUFEAikSQUIyUlJbBYLAnT6oCgYURRURGMRiMngZNpRzyVSgWPxwO3202f\nK/KiOPdYEmIpnPr6NaiuDl7cbTZTxGdOpw1Wa+btNePh93lZ22zd+jZu+d3ReP/dR7M93EWJ0TiC\n/739MLZ8nR8pmgQCIT7UnKWgVW/o9qfVFmNoaAgNDQ0JH+wFAgGWLVsNIPgWP90XVT09Pairq2O1\nIe/q6qKL4M7PB1N/VKpC+nO/34/e3l5G4bJmlwPo5bfe+idWrlzJy8OYyWTC/Pw869wnk8kEu90e\nV6BZrVa4XC7GVLtUzB0AfsSSz5fYlUytKcYf//wm/XsAgr+JRx65Hv3936d9fplg+96MhtDLXyqt\nc/36wwEAe288BscddzH23PMIFBcHLeodDgvvjn7RxJuzBCSOvLCl4olEIhQXFyd0zaOgIlW5WmuJ\nElUkspS7LGqx5HI58MG7j8JqNQIAautW4YKL78ZpZ94EsUjCuI1hciDbw6bp7eNeS+OD9x+jb6IU\nmba3XmzMzIzj73/7CT7+6Cm8/NJfcfedPycRDQIhjwlPwxMKQgYNYrECbrcbZWVlrFGQurrQZ+m6\ni3FJwQNC85V8Pi8cjlixNDw8DI1GwziHZ/ny9VixYi8AgN1ugkjEraAtl7G3tray3h+o6FO8ArHx\nokpAfHMHYOHnLM07Qi9OTz/9N/jzX97BfQ9sxmmn/RonnfRLrFy1NwDg8MPPidn24w+fTWmf6d5f\nHn8sFD0668e34Kabn8fPfn4rve6oY87DuefdhoMOOhMA4PW6F0zYUaQSWQK4peJxNXnIliNeMn1R\nhWmJdXhusqjF0lefv4T333+M/rdYFMx7Li6uwgGbzmTc5ovPX4TDYc320GE2T0Lf/TUAQCZTYdOB\nP0ZtbWSeeXFJbcS/hwYW7qKXaZGQC6Lk/Xf/HfHvqal+jI7wM6l7oTCbp/Dov67B9PQovvzsRfzp\ntpPx5OM3wenk5wGJQMhHAoEA3G43hEIhxGJxMLIkDc2DMZlMqK+vh9lshs1mS5imtteGo+nlcGvm\nZKGswNnS2KgCspWVlbDZZun1anXIVIFNdJ12Rqju0oyxl5dzqtfr03bBA+KbOwDBNLxsRZYMU6G5\nP2t3PQBabQmEQhEOPPh0HHr42RDtfJ6oqFoWs+3XX7+V8ZpGACKeXYpLqlBV1QihMNY4pK5hBb38\n1//7OaamhhdsTOmIJb5MHqhaS1wK02bTPpxElnKXRSWWoh+wd+z4MOLfy5eHigyu3/s4xj70+q/x\n5uv/SHmffPHdtlBtqOOOuxyHHv5zHHH0RfQ6oVCMK3/1GH50Uugm2NvLPRK1UOPPhsjhe5/TxhHc\ndcfPIupzUbz95gNwu/m9mPE1frvdgmnDEHr0m3HnX8/GO+/8E3NzM+jo+BTvvvMvXse8UCyG3yMZ\nf24SXmNpdnYWCmXISW52do5OwUsUBQGAZctWo6Vlt519zkfUL0qGoaEhFBcXxy3SShGeghcullSq\nSLGUSHQplaF9fPTR8ymPmWJ+fh7j4+NoampK2M5ut2NychLLli2L2yaeWLJYLBCJRFCpVIzbLaTB\nw+TkIJzOYImO5uZdodNVxG1bWsosrD//9OWk9sl3Bke8udoAUFUV+b3dfNOPeN13OKmKJa6OeMlE\nlrgWpmUTVGxjD2/D1T6ciKXcZlGJpWhUYW/eZDIV9tjrGPrfarUO++x7CuN242PdqKoqZ+2fK6lc\nBL/f8REAQCyWYcXqfQEADQ1rcMKJV0OuUGPffU+GQCDArrsdRr85+vKLF9HV8UXS+8pVMp3+R+3v\n04+fhcEwyNhmcHAHpqYG8NUXL+bU2AHAYBhCIGy/Hk/ozeZXX76UdF0YLseQ7ymaXMfP93ESEZQ5\nqO8uvMaS2+2GIuxh2jg9zTpfKZxddtkfQLDQZ6oW4mwOcRRUCh6AqMiSLjh2oxFerxeVlZVx+4i2\nk07X9ry3txf19fWQSCQJ2+n1ejQ2NsZt53A4YLVaGaNHicwdPB4PXC5XXCGVrliaGOunl5uadknY\nloowRfPNNyGnWj7/3uP1Ff0SL5HgLyjQxPQ5PT3G2xjDSVUsFRcXw2azJUxLoyJGbOdXpVJBJBLB\n5/PRZgrx4LPWUjLOelQaHqmzlJssarFkt4UU/bnn/QVyeWTxuiOPvhg//dn/4Te/fQ6r12yi1/v9\nDiikc1x3syDMzAQvXHV1KyGTKej16/c6Gtff+DIOP+pCANQkx9CbrSef+B3MZvawdDLk+wNxsgwM\n7kj4ucsxim1b38TMAt1cUsXC8r0//u9r8e9Hfo3BwR0wmcazPdyUyeXfYy6PbalDPUBbLBZotVrY\nHSFzBq/HA5VKhampKTQ2NrL21dSyjl7uY7Bq5gKX+UpUWmBtbTDl2mYNvfGm5ixxcaSTywsi6jil\nGx3n0wWvtraW8cGezdxBq9XG/Xvj0w2vqqqZtc1xx12M4uIqnH/+n1BbGzwvg4MdtDV9JpiYCM23\n3n33I+JG3ShuvuWFiH9PTgwuyLgSiSW1Wg273Q6fL9ZkgnKkTJRmp1QqacMWNihhxSZglDsjzmz1\nkbjUWlKpVPTLmUSQNLzcZ3GLJfssAKC6ZjlqamMv2AKBAK1t66HVluKY4y5DXd0q+rNvvnkzJ5S9\nWCyNWRd9Y/n5BXeguiZ4fH6/F4P932V72HmL3W7BzPRIwjYORx98Pgfuv+/SpKM1C4nZPJHw856e\nLejt+QYejxv/e+vhnPh9EwiZItzcobCwEJbZkPAoKSlBd3c3GhsbGWv6RFNXtxwSSdDBrq9vB2v7\naCYmJiASiRgd4MLp7OyMSAucmwsTSzszJ7gKl5NPvoqX8+jz+dDX18c6X8ntdmNwcDBhu0TzlVJ1\nwgMyYx0ezlHHnIfb/vgadl9/KPbd90QAgN/vQ1fH5oy9QJkcD0XDDjrkNFaHxYqKBtz2x1CtsKnJ\noQUZVyIBQKVZxktV4zpvKVmTh0zNW6IK4XKptRQeWSIv3XKPRSuWAoEAHDvFkqqgkLW9Wq3DhZfc\ni9WrgzarExO9Kc0B4nP8XFGrdTj4oJ/Q//b5slMYbzH8gW//9t2En5900jX08rzDgv+99VBOGIIA\ngMVijFlXWFiBc34eOwnd5Z5Hd+eX2R4ygZAxwmssRT/klJaWck7BA4KpV/X1wXlE/f3Ji6VkUvCo\n+UoAYLOFi6VC2Gw2GI1GNDQ0ZOw8Dg0NQafTsc616u/vR1VVFRQKRcK+Epk7pOKEFwgEIuanZZrw\nFDerdYbXvhPdY8N/h+XldVy6g05XQb+QnZoaXJDzwRYtYZu3xMURj6vJQzLzljJpH65Wq+FwOCAW\ni0lkKUdZtGLJ5XLAu1M0FHAQSxQb9j2JXs7W/B+fzwuvN5inG51rHg+lOnSMfb1beR/TUnHDc3sS\nh95X73IATjvtRvrfn376LP74h5Pw9ZevZmW8FH6/H7Y5U8z6Qw45By0te2DVqv3odTZLOzxuMyYn\n+5PZBYGQtwQCgYgaS4WFhZieDj1gFRUVYXBwEC0tLZz7pOrrWCzTMJnY32yHwyUFjxJC4eYI4WJJ\nrS6i5wRxiYZptSX08pwl9Yd4vlzwXC4XZmZmUFVVFfOZ2+2G1WpFSUkJ47aJzB1cLhckEknCOTsL\nSUHYXOlkSee+Z7eHHsgVChWnbQQCAS3ARkd7FuR8pCOW+I4sZaPWEpd5S0KhEGq1Gm63m4ilHGXR\niiV7hGtQIeftyssb6GWX056VsYdHKgoKtJy2qalZjvLy4E31++8/hsdDvPpTgYpGAoBYJMEhh56L\nysrgA1RRUSXEYhnWrjsIjY2hOQt+vxdvvvEPzDGIlUwxNzcD387igs0te6CoqBJlZQ1YvcsmAMDp\nZ/0Op59+Ey69/CF4vbMIBNyYGOfHQjgbkBRCQrJEp+HNzITN2xNKUF1dnTAKEo1CEYqsGAwjnLeb\nnZ2F1Wql5yHFo6urC83NzRFCyGoNXWNUqkLOKXgAUNcQKj0xMzPBaRsmuOzT7/dDr9cnbDcyMoLK\nykpGoTc1NYWSkpK4gmehbcOXEoWFQde8/v4dC1KglotYSlSY1mAwJEx351prqaSkBFarFSqVKmcd\n8ZxOJ6mzlKMsWrFkC3voTSayJBKJIRAET0tHxxe820RzIVwsKTmKJYFAgAM2nQUACAR8MJuTe9PJ\nF3w+xGY6rc/v98NkCj5ENDfvgZv/8A4OPPhsXHDx3Tj1tBtw7vl/pW/excWRb0O9Xje2bnkro+MN\n56svXqKXm5p2w5VX/weXX/kvel6FUCjCml0PRFVVC3S64Nh/+OFjeDzulPZHIOQL4W54lFhSKBSw\nWIJzNMRiGex2IecUPAqlMpRulcx1r6urC62trayRj3DLcArKvKeiogGAkHVOUDjFxZV0psJ4ii9K\nqAfXeHOJKKgiuYnmFaVaXwnIbbEUbsgUHu1hI1tp7OvWHUgvf7ftI977TyeyJJPJoFKpYDLFfxGp\n0+ngcDhYIzJCoRAlJSXw+Xw5W2vJarVCJBKxGkIQMs+iFUteb+jHJpFyf1solSrQ1haszO1y2TDQ\ntz3jY7dHCD3uIf21ux6EwsJgjrfDNhjXVjVZFsNcJC7Y7bPwB4JvsGpq2ujjlkrl2GXdwbTIAICS\nkti3wl999UrWIh6ffPw0vSyVyCESieJ+b1XVoYer2289MSsvBAiETBM+Z2lqahgeT/CllE5Xjb6+\nfs4RmnThkoLndDoxMjKC5uaQE5vH48bwcCcAoLFxDfr7+1FZWck5GiYQCFBZGcw+CHdOS3bsfLjg\nAambOwC5LZbq61fQ5TyotMlMWId7vaG5ysncs/fdPzT14LXXHuT9fMhkMng8nrjRITbBwZZmx8U1\nL7wvp9PJKl64zGviMnaqDdfIEmXy4HK5SPZEjrFoxVI67LN/qP7S2Fh3xvfvCLM8L1ByiywBwQuk\nVhsMqc+a2zE51sHbmJbCH2645fradYckbFtaGjuB1mo1ov37T7J9GCgpTZzes3znywAAcLsd+PiD\nJ7I9ZAJhwXE6nRCLxXC5XDAYRun1TU27o7CwMK5hAJ9QxVzZ7Ml7enpQX18f4Wg2PNxFWyw3Nu6S\nVApeiOBD9NRUas5nXPfJJgg9Hg8mJyfjpiImMnfwer2Yn59fsBpL6SISiVFcXLnzOIYztl/KKbGs\nrI4Wa1woK6tFy04r/GQiYVwRCASQyWQp1VoCuM1J4mryUFFRAZPJBL/fn3K0Kxw+ay2F24eTVLzc\nIy/EUqYf1GtqlkMgCF5sRna+ycvkcTrCLlgF6uRu4MowcfXlVy9nbOy5DpffEGWqUV6+LGLuGhPl\nYRXQpWGRy08/eTbjx0C9sfP7XPC4ZlBTtyJhP2t2PSji393dX6d13rj+feaq4OZ7XLl6nEsdp9MJ\nn88HjUYDw2SoRprLFUg6BS9Venp60NDQAKlUmrBdeCFaiu7OzfRySVkN65wgJoLpe4DLNR9hQ84F\nu92O6Z3FexNBFQlNFBkaGxtDaWkp43kIBAIJxZLFYoFGo4mbxsiHWBKGFZpNJbOCOs8GwzCvmRnx\n+vL7/RgZCb7YratL/rdMFd5NxayEC4lS8TQaDWw2G2OtJYDbnCSuJg9UX2xiSC6XQygUwhFWi40J\nLrWWNBpN3FpS4VBjImIpN8kLscQFPi9IUqkclZXBh+HhkY64Dz8CgYC3B6Pw8dsdYa42SUSWAODQ\nI86jl33exBbiXM9ZMu0y/aC4ECmCEgn7jbawsAyHHnouGhrW4qJL76NTN0dHO5MyeuDjO7BapwEA\nXu8sdDpRTPHlaMRiCS665D7639PToznxgL8Qv8dcJN/Hn29Q1yWn0wm3273TCS/0YGUwmlJKwZPL\nlfSya56bGRAXy3CPx4O+vr6YduElIex2FxQKBXQ6XVJjLikJpRJPJ1lUm3LeCy9um+oxJkrBM5vN\nUCgUcdMLM1FjKfwY1dripLcvKwtmHkxPj3Mu5ZHO/XNoqINOp65jeVnGRFNzyLBI3/VN6icuDlxq\nLVmtzCU4+HbEMxgMnGst8WHywHZ84f2Ep+ERcoucF0vZemCo3XnBcc7PwWBYmGJt8Yics5ScWCov\nb4BcoU5qG0JqbDr4bJx/0V0oL29A2/IN9PpePf83m0QYjaFUj13WHsRpm9q6Fdhzr+MAAB6PkxZc\nBMJihXKaCqbOhKyzxRJF3ChGIhoaV9PLXF6QeL1e9Pezz42i5iIVFMR/6TE4OJiSwCspqaGXZ4zj\nSW3L93ylujrmWkDpzFcCgt9zMq6GTBjD3A251iwKp7w8KAQDAT/M5qkFn7PU3xuqsRT+u+RKS+s6\nOnWvo4P/+ntsAiCR4CgsLITX64XdHv+FRFlZGYxGI2uReLlcDqVSCYVCkXP24RqNBnNzc5DJZEQs\n5SA5L5ayRbg1dKYffsPT8JRJRpYWilyIPOQydQ2r6GXTTHJvbNNlNixtorikmvN24SYV09OjnLcj\nEPIRp9OJ+fl5SCQSiESh61lr68qU+ispqaadUw0G9rkpAwMDKCsrSyiCgNhCtBQWS+iFxuDgUEpi\nqbg0FFmKsE5nwePxYGBggLUOlcVigcViiRs1AgCfz4exsbEFMXcAgvPC0o0sUd+nWCxFUVHyQtrp\nDKVvzc/PJb19svT2bgMQjGIsW7Yq6e3l8gJoNMEIml7/Le/jSzRnCWAXE2ypeDKZDGq1GjMz7PXD\nqBcjuVaYViwWQ6lUQigUErGUgyxasRTwpVcvoKllN/pG2NOzJaNjp9LwpFIFJBJp0tuLhMF8a+Jy\nljlEIvaikAuFP+y3LpbKOG9XGiaWZpKoE0Mg5CMulws2mw1+vx/hpX3WrNk1pf7EYgl0uuBDPRfD\nBC4RF6o+EVM7287agWKxFH6/BDU1NUiWkrCXKUYj97/5gYEBVFRUQKlUJmzX1dWFlpaWhLboExMT\n0Gq1caM/ieYrAZlJw6PqZul0lSllt4TfDzLxorGv7zsAQH39KrpcRLKodxbTXYjnhnTswwHuJg9c\nU/E8Hk9GHfGSMXkAQMRSDrJoxdLIcMgJLrxyOVcUCjWqq4Nv7oaH2jM69tmdrmwFqtQqgVM3RKNx\nJG8jQvk67nxCpQ3Ndxgd7cr2cAiEBSMQCMDj8WBubg7z8/PweoMPbgKBEE1N3OoUMUGlaO3Y8WlE\nah/T/rmksQ0NDTE68wUCAfqBuLi4Fm1ty1N6iC8sLKOXk5nIz5cLHnWMiSJPXCJLiZwL+RBLlJCM\nrqeXCgtt8GA0jtK/vYICTbJd0rDNdU2HdArTAkGBw+Z2x6UNEBRVNpsto7WWkrEP9/v9RCzlIItW\nLLW3fwogOFm/qWX3lPooUBUCAOcJmnzgdNowPR28UFdVNqXUR1lZ8EbkctkwN8celmaDTEhPjkDA\nn34nGaCiohGFhcGHkh07PoTTacv2kAiEBSEQCEAmk2F2dhZWqxVut2Pnej9rcdhEhEdq7vjrBXHb\njY2NQaFQoLg4sVlAvOjT1NQQ7V7ncvlSrgklFArph2JKfHE5d1yc9+bn5zE2NoampsT3rURiaX5+\nHvPz8ygqiv+i0GKxLGhkyWabxfR0MEVRkeH5v6m8JPT7Q5kF1dXNSW8fjcPBf9pgupElLlGjZCJL\ns7OzOTdniWrn8XhInaUcZFGKJbvdgomJYIXy1tY9Uw5L8wnXH/7YWA+9XF2Tmp1tWVkDvWzMsDkF\nn+ST+CooKKSXLUmaJaR7UQwvwEyljnJBKBRhjz2OBBA0eRjg+PCUC5AbCSFZZDIZ5ufnMT09DY8n\n+Dej1Zal1Wdj41p6eXJyMG47Lg5xQPz5SuET1wMBBWudpkRQ11WXax4fvv8Ma/uJiQlIpVJWocfF\nFj0QCGBkZCSuWKJS8OJd+30+H+x2OzSa+BGUdMWS3W6lBYhanZzbYD5TVRX6Tc3OGnntO12xVFZW\nBpPJBK/XG7cNV0e8oqIiuFwuCASChNbgfNZaSiay5Ha7SWQpB1mUYsliMdDLFZWp31SywWhYXSe2\nejnxKCkL3YgMGSyKt5RRKjWQy4NFEmeStORNF+rFABDpdsWF1hWhArW9PZFGJvkkVgkENiQSCV3I\n1O8PPtiIxenNNVy1Zp+If8crQsolPW1sbAwSiQSlpaUJ22m1GkgkkpTHTBUgBYAdO9iLaCfjgsfW\nzmAwQKFQQK1mjtiwpeBZLBao1eqE0cBsF6UFIq+d46OZL2yfCi1hGTj9vfy+OGMTS1qtFnNzc3Hd\n7MRiMXQ6HYzG+CKOi2seEPxuKKOVRGJIJpNBLBbDZkucccGl1pJWq4XFYmF9yVdYWAin05nwXBGy\nw6IUSzZryMZVrU5+vlI2oVLwAKCyIjWhF+6IZjYlZw8bjyXxJj+NQxQIBCguDp73mQy74Y2N6QEA\nGk1p0m9CKyub6ahYT09mXR8JhExAPbgGU9DkUKvVEItFEZ+lCjUpnmKgb0dMm5mZGTidTlRXJ3aq\n7OrqYowqRcMW4WHjokv+Ri8PDXWwtucilrxeL2NtqGi4zFdiM3dINF8JSF8ssdWR4kLbivV0Pzt2\nfMApNTvbL6cam0NR0v7+HWn0FAubWBKJRCgoKEhYi4jvVDyxWJyxeUuUoGITXlqtFna7nUSWcpBF\nKZbCa15E38xSIZM6IVyUiFNwwgMArTb0ZtJsZp/wyEa2L+KZwO/3w+8LhvhlcmVKfVAi1WYzZcyJ\n0OWah8EwCACork5+orpQKERzyx4AgJmZUZhMExkZN4GQaQQCAf0fn/NQb77lBXp5cDDWDKirqwut\nra2s19HOzs640af5+dBDVnFxeqlhQqEIxx9/KYDg/JSpBNkHFosFVqsVtbW1Cfvs7+9HeXk5qy06\nm1iamppijSwlmq/k9/vhdrshk6Weeh+etp/q80N1dTM2bjweAGAyjcNi4e8FWvSLS75eZFLOjgAw\nOqrnbbwAu1gC2Of1cC1Oy8XkoaKiAoFAIOcc8QoLC4lYylEWp1gKmzOi0qT+Fk4mC1qb+nxuuFyO\nlPvJNGKxBBpNUDCZzdwdj3KJTEey5uZm6Ld/VIQoWUqKayL6ywThLnY1NalN+m5pWU8v9/duzci4\nCYRMEwgE4PV6YbPZEAgEb33JFv1mIjyay1S7iEsK3vT0NFwuV9zo0+efvkgvl5Ymbxkeey5CkY5E\nL9S6u7tZrcABbrboQGKx5PP5MD09jbKy+PPI2GzDXS4XpFJpWqYd4+P99HLDstRqcAHAfgecRC9b\nzIMp98PGyFDoHlBaWptGT8F0cgDw+bxp9RMNF7HExT6cTQhxjSyVl5fD6XTmXK0lqVQKiURC0vBy\nkLwQS1wfnKl2c7ZQaDWdCZrZKNrp5+kiVVQUfEtkNvMTKUj2O8gkfOyTesgRQIBiXWp2sbowkWWz\nmXk/F0z9DQ2E0iXqlq1Jqd/G5rACzCQVLy58fp9LIq01x6DMAZxOJ3y+4LyGioqGtPtVKAroqFH0\n92q32zE1NYVly5Yl7IOKKsWLPvWGzSHZsM+xaY+ZeigGgBlj/KgHFxc8yi2PTSzNzMxAKBTGdbqb\nmZmBRqNJaBCRiRpLUxMD9HJFZX3K/dTWhs6b3c6PYQLT7+O77z6il6Pn0CULJTIHB9nTM5OBD7HE\nRQhxNXkoLy+Hw+HIqH04V0e8wsJCElnKQfJCLCXLXFi9C1WKtYoAoLSkjl6eMcSKpYWw1B4fD07W\nLygogkSS+kW/aGdI3em0RaRw5BN8pf9x6ccc9kZYl2JkKTx9I95EVb6PcWjoBwDB1JqaFN0TtdpS\n2hVsOklzimzYyudqXwvRH4E/KJcpqRTw+4MvpSorl6XZa/BvT7WzzER0raXu7m40NTWxGknEc8ED\nAItlGgZDMFVuzz2PgVSavnlBaXnoReDAwPeMbVwuF0ZGRlitwEdHR6FQKKDTJX4xOTQ0hLq6urif\ns81XAjJTY+mNN/4JIFj8V6erTLkfgUBARy65lpNI5SVKe/uX9HJhYWnS24dDWY/7/V5enxu4iqVE\nkReVSgWxWJy2ax4QnEOkVqsxPZ3YubawsJBVUFHt+IpSFRUVQSAQkBdqOcbiFEtzVIG2wohK2slS\nXBZKdzBOL7yrnM/nhdEYtPpetmxtWg9eVGQJAGZn05+3tNiZmQmJYV1JamIpG4zvtJqvrGxO6yEq\nnb8TAiEfcDqdkEqlmLOG3FLLyurS6DGEZme6tzXMXAjgloJnsVhgNpvjpqf1dH9LL++yy768jHf5\n8vW0wNu+/SPGtKu+vj7U1NSwzv/hIwUPYHfC+//27jwsquoN4Ph3GBj2TUUQ1BD3VBS3XEtxyTSX\nTC3TzMrSds0229P6mZZZWantubSoWVqpWW65hbvgjrKIgOzLsA7D3N8fIwMjA4wwKNr7eR4fZ+5y\n7rl3BrjvPee8B2q/ZenkiTDTmOemTdvUqDsflD48ycm5iF5v+/ka8/K0pqCma9dBNS6vY8d+gLEV\ndsYzt9msno6Ojuh0ukofIloTTFTVFc/e3h5vb+9Ks+aVaNSoUaUZ7Kytk7XbWZs+3NPTE7VaLcFS\nHXNjBkuXuuG5udVsIGzZNMxbt3xX64Pfi4pKm14DA4NrUBJ4lMkCmJebWav1vhGkl21ZqsHTxKut\n5A+ws8vVnTxRiOtFyQ2rXq+nuLgYtV3pE243j5onAILSYCkzM5nDB7cSF3eGzMw0YmJiaNmyZaX7\nliSAqCgL28mTYabXZTOW1YRabW+anDYnJ5Pc3PJZyK4kZbgtgqWqkjsYDAZycnJqtWXp3NnDpte3\n3np3tcspUXYYwC8/f1zj8i5Xdoxc/frV6z5eVnAn8wCpJHlQTdnZ2aHRaCrtXmZNwGFtVzxrkjz4\n+/ujUqkqzVBXEuBUFbhYM9fSlXTDs7Ozk2Cpjrkhg6WCS09aXGp4A+no6IJKVfoHbOWy12q13mV/\nOMpOclodqjJPxI5FVD2XRqVl/Qe6FhUUGMcwqNUONunmcr0pmcy27AS3QtxI7OzsKC4uxte39Ibc\n0bF6mS8v5+FRelO8dOnzvDNnPC+9MJiECxs4eXw3BQV5HDm83eJkn1WlDC+bXKgm3covd/PNPSpc\nZzAYiIyMrDJYSklJoaioCH//ym/Us7Ky0Ol0lSZvqKobXnZ2Nq6urpWm9q5psFT2b3CTm6rXrbms\n8RNmmV7v2vULhYX5FW5r7d/ZsnVMSy19gGuLYKlBA/MyKqvvlbJmrqXs7OxKW5+sGZN0JUke1Gp1\npQGMRqPB0dHRJnMtXUnLkqh7bshgqUTJDWBNBAV1NL2+ePHctT4lqznYl3ad2Be23iydenVc7acc\n1+qpiq3iQmv7qNcVJa2oqakX0Ols9wdSiGutbPIFlUqFj4/t597zqCDralFRHp9//iLLv3uLJYtn\nsnDBVLPfbXl5eSQkJFQ4LqiwMJ8DB/4CjGMibTEHkCWXPySJi4vDw8Ojyhu3ktanqm70z58/X+l4\npZIJSSs7XlVd8KDmwdLl3ShrqlWrztxxx0OA8bOMOFqzB5eXS08rDZbq1bdNj4gJE142vS55iGgL\nVQVL9vb2uLi4VBpwWNNqZG2SBz8/P/R6/VVL8uDk5IRKpSIvL6/KcgwGg7Qs1TE3dLBkCyEhg83e\nWztw/1pr2743Ts6lLWtxVkw+WFP/hRaoymjKJORIvHD2WlfnijRpakyRqyjFxF8aByXEjcRgMKDR\naMjPz7R52Z6elQdgBw/+DUBSUqzZXExnzpwhKCgIg0FPVpb5YPOiIh2zXrzD9L5jx9uws7NdsFS2\nNezll4YRHX3MrF51qQseXJ1gqSRoVKlUZvMO1YSfX2kSEUvdHa/E5X9jc8t0sXezwZySYN51cO/u\nNTYpE2wz11L9+vXRarWVduezthueh4cHKpWqym2v9rglLy8v9Hq9BEt1jARLVQgOGWj2PjU17lpX\nySqOji48NOV90/u4OMvBUl3+gbRl8FXVeep0BWizT2AwVD8DUGDzjnh6GruRnD2732wMWu2xzefX\n9KbS+UTiYo9f0b62TCtfl7+P14JcD+tlZCSx/LvZbNrwtcXrpigKaSn/sGfPetMyh2pO/H251m1v\nsXrbY+E7SUm5QHGxnpMnT9KiRRAvvTCEl164g3W/fAoYM+B99sl08vJKn7IPHznNpterX+i9pnFL\nAGF7/zA9DDx9+jStWlU+ybVWqyU1NZXAwMAqj2VNcoeaZsKDmgdLZ88eASAgoCXOzm7VLqcsD8/S\nVsfjx/eYXicnx2EwFFe4X8lnkZ+fQ0ZGstm6+PizbNrwNWfOlM6Lp9FUfyLesoI73WoK/hMSIsnN\nTa5hiUa2SB9uZ2eHj49PpQGOm5sbdnZ2Vnd5q6oV6mqnD3d2Ns7vKb/765YbJgVW2a4WJTeptngK\np1aruXvMi/y8Zh4AKUnnadiw+nMvVMbW3Z/8/IKwt9eg1+u4EHeq3PprkfbZ1mxRN0VRSEqOQa/X\n4ufXttrlaDRODBj4AGt/ng9Abm7Vv6xrIjMzyfSdcXJ0rVFZ/gGlN0bJSTG1Wm8hasO+fzeye/c6\nAMLCNtC6dTeG3vkIHh71UJRiCvISyM4uvTFq2bIz/v7Nq3s4M35+lv8mBAUFExUVbrbsjz++NKWn\n9m3Uj4QLW00ZzTZu/JqdO9eSk5Npts+gQZPw9bXt3x03Ny8mT36LJUueA2D79lVs376K4cOfpLCw\n0OI4JJ2ugMjIwzRp0oozZ6Jp0aJFlV0Dc3Nzyc7OrrTlKCkpqcoU5VlZWTRuXPmEvDUJls6fP0VK\nijErasuWIdUqwxKfhqVp2sPD/2Hl8rfZt+9PixPdn4tsiYuLC+fOHbVYlrt7fQoLCzl6+Eub1e9y\ndnZq7pvwCos/mwFAVoZtMgHbIliC0pajyrp1lmxTVXDt4+NDcnLlwaCXlxeJiVUn9/Ly8iIhIaHK\nbawJ4pycnCgqsn32RFF9N1zLUlZWMnq9MViyxYBHAMcyN6JFRbUzs3Jubpbp5trOTk2TwHY1LlOt\ntjcNCC4orFnf47o8KW1NZWenUpBvfILbqFFQjcpq3ban6XVeLQdLx8pMRtimTc/qFwRmc3oZroPx\nVtfj90zUrtOn95teJyZGs337Kg7u3wxATvZJsrKOmNar1WqmP7vYZscuO8daWbfdNrbS/ZIStxMZ\nechs2eWBkodHfe4c8WitXDNLk5j+9tsnOGmyLSZ7+W3dYhZ99CSzXryDX9e+T6420qz7niXnz5+n\nSZMmlWb4srZlqba64el0BSxcMNX0vkPwrTa7xg0a+JtNULtz5y8WAyWAxMTICgMlME6LotNZ7v3g\n5VVx8owr1SG4t6llLSkpvIalGTk5OVU52ao1wYQtkzw0bty4yuQN12JiWicnJ/kbV8fccMFSSlKs\n6XXDhoE2KdO1TF/gnBzbDgAtcSHuNCVdqkIHPIC3t2/NCjS5lDa3SLKcVSQpIcr02s+vZk+a3dy8\nTN+72k6UcPKksUuHWq2hbfuazdxetoVOZ8MMSEJcLe4WxmxER0dQWFhIbm60aVnjxq14c/baWp9b\nbMyY6YR0CcXd3Rt7++p39xs3biaOjs61UkcHBw2TJ79VbnlExO9s3vSd2TKDwcBff60AjPPwpKZG\nsnfvGubNfcDUfc2S2NhY/P19eW/eQzw2tSt7dq1Hpyt96FhUVERGRgY+PpVPqFpVsGQwFJOdnVat\nYCkxMdpsEta2N1vfrdIaz7/4NV26DKx5QRXo3XtkjbP/lmVnp6Z1664AFBXlc/jgVovbFRfr2ffv\nRlKTz5jN1ZWRkcS2LT+yc8fP/Pj9u8TGnkSttuNY+Fb2h22qMBAoG3Dk5GRy4vi/Zt+VnJxM6tf3\ntip9uDXBUmBgIHl5mXyx9EV2bFttcRtvb++rPteSq6sriqKQn5/DyRNhZtdAXBs3TDe8EklJpX8U\nffwCbVJm2QGPNc0qV5HEhNOm1x2C+9ms3AYNGpOZeZHk5Biys1Px8LB9Jqjr3YmTu0yvfW3QLcfe\nQQPk2Wg0UcVK5tjw82uGk1PN+ter1fb4+DQlJeU80THhFBcX16g8IWpbfPxZtv79IVlZyezY1oaM\njPLjGPbt28S+fZtM7wMCWvDq6z/Uet0efXQeIV0GoFKpeHf+JvT6IlPAs+ufX1ix4m2z7e+7bxZe\n3r58vvR509xpTz61iPYdetV6XXv0upPCwnx++OFds+W//baUuLjTdOjQF99GgWza8HWFZaxc/g4d\nOvRm8+blBAS04NFp8/H1vQm9vogtf32KVlvaPWnZsrdYu/Yjnn3uC/z9g0hJSaF+/frY21d8O2Iw\nGMjOzq6wW1VCQhQrl7/NuXNHOXzwG3r0GEZSUiyBge24c8RUXF3L75efn8POHWtYu3aR2fKxY2fa\nvOu5RuPEI1Pnof7yFSIidtGwYRM8PX2IiztNRkYSXbsOxtu7IQkJUTRp0opRo58iLu40Tk6uuLh4\n8MPKuRw4YGwltbNTlxvr1LXb7TatL0DPXiM4cmQ7AEeObKNT5/58+/VrhIVtRKNxKncDf+rUHxWW\ntX17aSBy4MDPfPXVK0ya9Dq9+ow0287Ly4uLF6M5FrGbNas/4OLFmAqupzcxMX0IDLTcbd7Pz48d\nO3aYLcvJyWT71h/ZuvUnQkL607nrIFb/9D6pyTGkJhuTsHTpNsg0WXOJsnMoWfpeXLgQiV5fREBA\nSzIzU1n14/t4ejbg9jsml9vWmpal4mI9Rbo0iosL+fLzWRw/vofevUdy/wOv2/wzFta74YKl1NQL\nptc+Pk1qUFKpsnNb5GgzalBSxRLiIwF/3NzqUb9B4xqXV6JDcH/Onj0AwLHwHfTqc+UT7dXlMUs1\nlZmZzP59vwOg0Tjj79/CJuUaDDoKchPJz8+x2UDhsvR6HVqtMXuWt7dtsja1btODlJTzFORr+far\n57F37FjzQoWoJfXq+VFQYOw+e/586ZhMX9+bqF+/ESdO/Ftun8kPza61+kya9AbLlr2Fu7s3nTqH\nmn5vqtX2Zq1YfW69iy1bVpKYGE3XroOZ8uhc07oXXvqW/WEbCe7Uz6bjZqpyW/+x3NZ/LN989Sph\nYRtNy48c2W66Ya5MYmIUiYnGFvr4+LO88dpoJk16nYyMFLNAqUROTiaz3xzLgw/OxsGxkakLXlZW\nKscjdgOYbqSzs9PJyEhDrS5i4YJHSU6OMz20bNOmG926DWH58jlm5f/7r/HGPTr6GNu2/WRaHhp6\nL65ujcnJyWDe3Acs3ox36Tao1q7zQ1PesXrbsl33pjw61/Q9KSjIJS9Pi4dHfbb8tRKAVq272Lyu\nrdt0Nb0OC9tAWNgG03tbtHQsWzabv/5aQY8ewwjpMgAXF3d+X7+IqLO/88mi9ZXuq9Nl8O7/JrLo\n0z0c2LeZ7757k2bN2hMcfCvBnW7Dz68Z2dnZ6HQ6NBoNCQnnmP3mONP+u3evM41vLEurzcDOTk1S\nUixRZ8Pp2n0wnp4NTHMoeXh4mG0fH3+Wt2ffC8DM578kM/0gW7caW7Q6hvTD77IH9iUtS3l5Wn5e\nvRCtNoPxE14y9SRKT7/I0sXPERt7Ent7D5ISs031lWDp2rrhgqVifWlTsGMNB72XluOMRuOMTpdP\nfPxpIo5uJzAoGJ2uwGZjeTIzU3D3CiAgoJVNg5PWbUsnHkyIP2OzcuuSmvTtTU8vHbjZtetQm0xS\n6dswkIT4M+TkZLLht0+5e9yLNj/nrDKTW3p52abLZuu2vdi1cxUAUVGHad6q/XXfb/paZOC73q/Z\n9cLZ2Y277nqaH3+cZ7a8e/chNGgQUC5YCg291+wG1NZ69LoTP/9mNGjgj51d5T3cZz7/JUlJsTRr\n1t5sedOmbWjatOaToVbXgw+/TUjngSxZPLPS7dq06Y5G40i7dr3LtUiVWLasfGDaunVXTp8+YHr/\nzTfGG8DAwM5Me/SdKve/3KlT+zl1an+V25XYuvXHStf7+zfHy8vHytKuDScnV1MWQ0utF7Y8To8e\nw0yBZ21ITIzil18WsW3bjzRv3tGUYt9aTz1R2vIaHX2M6OhjbN++ildf/xE70ln+3RzuGDa50lbR\nst56Y4zZ+59//pCnnvnE1MXOw8ODwsJ8vv36daKiws3S/S94b4rZvhcTY8oFS66uruTmpvHs9H6m\nZeHh//DZkv3odAW8/NIw03K93jzN/DdfvcqDD5u3SIurp84HS3WlVcPNvR7pafGkpJznxx+Mfbwd\nnfxxdm5Ci6B6tGzdndMn9xLQpA2enlf+y7ZkElN7eweb1rtsalilljuG1ZXPqrr1slWL3uA7HuXc\nucNkZ6cQHr6VocOfqHHr0uXnkJFZ2uXIVi1LzZoFX7ak6u+LLTMq1uXsjLY8Zl0+z+tNv9BxZGen\nsmHDV2WW3Vtuu6lT5xPSZUCt1sXOzo6goA5Wbevm5lWuu09d0SmkH3PeWcf78x8uN/dT166D6NZ9\nKB07lSZAcHJy5ZtvXquy3EceeZcu3Qax5LOZ5VqrYmIOVbn/lbLUVawijRu3wtXVg3797rH9Bb2O\njbv3+QqDpYCAFjz59Md4e/vyw8q5xMaepF27nnTuOoiAAMs9NHJzszm4fzPffz/XbHlmZkqVgdKY\nMdMJHXgf3379ulnX2stlZaXy/Ezj+LDYWNi/fwPVZTAUE30uHC8vLzIyMmjatCn7wzZx+PDWKvdN\nS02gsDCfc2ePUpCfQ05OJq3adCUpsfx5/rz6gyrHNYaFbWTsPc/V2d8bN7o6HyzVFe5uxmDJkuXL\nXqFDcH8iwrfRsGEgT03/qsoni2UdPvCn6bWtWsMsKapB0/nVflp+tY6nKzNDua0mfPTwqE/vPnez\nccMS9Hodx8J30O2WYTUvuIzM9NLBq142SgaiUqkYMOABtmwxDuyWFhJxPRgx6nFUKhU7dqxh6NAp\nuLoau8r06zeO7dtXERDQotYDpRuNj09j3p2/icemlnbF8vMLZMqj5VuRbuk5FFDYs2c97dv34ciR\nbeUyuo0dO9PUvW3a4wuIjj7GvLkPVLt+9vYO9O07mrw8LXq9Dh+fxnTuOqhcq1xiYjQ//TDv0piS\nFmRnp3H48DbAOJFw//73MGToQ9f6ctdZLi7uTJ36HkuXPg8Yk6g88dTHBAbebLbd+AmzrCrP1dWD\nW/uN4dZ+Y8p1+SwrKKgDrq6ejB4zHS8vHzQaJ1NX1oemvMPdY2ewZtUHHD68Fb2+iJCQUKsCGEvu\nuusp9uxZT1KZ5GBlnT9/kqAWg9n1z0/Exe7l99+/sKrc1asXsHr1Aqu23bLFunGUWVmpEixdIzdc\nsJSfr615IRaUTfJgSUS48RdwcnIMsbHHLDylNw7I9/b2Nbspj4o6ypo172Jv7wVA5253YEt2dvam\nLoTHj+/kz42fc/sdtZOGFq6/G+y4uJOm1341TBteVsvWt7BxwxIA0mphIuPcnNKxc24e9WtQkjkX\nl9KB0AUF1Z+gV4irafjIxxg+8jGzZWPvmUmXboPx97fdz/V/iUql4s3ZP7P6J+OA9UmT36xw21t6\nDuOWnsYHQseP7y63vnffUWbvmzVrz5LPD7L6pwVs2fK9afmgQRO5e+wMtNoMiooK+fH7ebi5eXL7\nHQ/SoEHAFWcwbNSoGdOfXXKtL+V1LaRLKAsWbsXZ2f2KHgJX5cGH32bsPc9xNvKIWbfPYcOmlPtZ\nvpynZwMefuR/ZstycjI5dODvcq1WZY0f/xK39S+fzr912278unYRDg6ORETsMluXmpqAm9txIiL+\nJCKifJmdOvWjTZvuHDmyjYSEKLKz06w6/0mTXufixRg2b15mtrxePb9LmR3Tuf32SVy8GEt0dAQT\n73+9whY7Ufuum2ApPv4MJyL+oVuP4RbHaBQX64mOOsrFhNJf1LbsxlKvXiOrt404soWGDW9Co3E2\nzRB/aP8mwsJW4u/figcemoebmxdabTqb/jDO9WEwFODuarAYZNWEWq2mT99xbL3UWvDPjh/o3mOk\nDVOT156r0Q0pNsY4R4harcE/oKXNyi0770p8mbFiBQW5qFR2VqUCLijIubSti9n+sVHh5JQJlmz5\nByw4ZADbt3+PVptKYWHepYDJu8blCnG1qdX2VzVJwo3Izy+Qp5755Ir26dQp1DSOqFev4QweMhkn\nJ8tjQcfeM5O+t93NxcQY2rXvZfp7WZIG/vEnF17rSyDAYjZBW3Bz86JDcB+GDn2YhIRzBAV1YODg\nSdUu69Z+Y4iMPMT+/X+WWx8aeq/FQAkgMLCdKahOSDjHxYRoDhzYzKFDW7hw4QwXLpiP9/bxacys\nV1aYpWvvF2rswvnJx09z7NhuKtOmTTdTApO8vGx27frVtK5r18HcdffT5OVpTa3k4tq7boKltavn\nc/HiObZvX8mgwQ8T0KQNLVsauwgoisLxiB0UlJknoVPIIDSa6s3kbUkDn/KzRdup7LB3KH+MsLD1\nhIWtR6Nx5sWXV1FUVMixcOMPb0LCGb76fAaKopCSUtrsazAUcP8DlQ+qra5+ofebgiWA9+fdi5eX\nL6PHvlHpfrm5WTg5ud6wYye02nRiY42Piho3bl2juVAu5+bmjUbjgk6XR1TUYT5dNJVePUezZo2x\nG0vLVt05H3scF9eOXIz/FycnBa02jaSk6HJpYdu3v420TFe2/v0dx49tqk51rObi4kHfvuPYsOEz\nAOJiT9CokW2yStrS9daCKcR/Rb/QcYR0CcXDo75Vfzv8/ALLDYQX/x1qtT0jRj1us/IefuR/jL3n\nOVxdPUhPv8jfm5fTrFkHevS606r9/f2b439pCpFDh7aUWz98+FS69xha4bxWjz3xAU88VjpP16JP\n95KXl01szElOnthL1+6307x5aabZiZNeo/+A8Wzb8gNqtT239huDSqWSQKmOuW6CpYsXz5le/7X5\nK+zs7Hn5tbU4O7vz16YviAjfjrPLTQAEBgYzeswLNj1+fQtpyD08PPD39yc12fI+Ol0+c94cjotr\nCwzFpeOFkpNjym3b/ZYRtZJiGoytSyNHzmDdutKndJmZSWz8Ywme3pZTju4P+51ff1mAr28Qrh5d\nObBvAw69b6dhw6bWHrbO++3Xj0yBSUngbSsajRMDBk4ydcVLiD9jCpQAIs/sA0Ctvog2O7Vc5puy\njh0zzheReMHyelsleCjRsk132PAZxcX5nDt3iO49bD+HhxDixuXpKfP5iWvHw8M4bMLHp7HV46ku\n17Zdj3LL3przC76+ld8DqdX2LFi4jQsXztC8eUfs7R3w9GxAcMe+BHfsa3GfgIAWTJxUdZIUce3Y\nrv9OLbG3t6dBg/K/eA0GPYWFeWi16ezcWTrhWUDjNkx+eL7NZ2dvaCFYGjZiCoOG3IWzswf29o60\naWt5AsG83LMUF1c8/sPH5yZCB1Z/sKs1OnYeWC6BQUryeZKTY8tN5lhcrOfvv74BICkpitSkMxw6\nuIGPPniA4xH/VHiMkqeIcXEn+X75Gxw6sImcnMxaPa+aOBd1GABHRzd63zquhqWV1+fWe5gwcU6l\n2+TlRVUaKFWle/fhODvbbuZ2AB+fpnh6+pKZtovjx/7mwoXTFW5bVKSjqKiwXEtPWmo8p47v4cyp\nMM7HHsdgMGAwGIiMPEBmZlJVVTDJycko19JWW06f2Mvuf1ZfteNdqeLiYvJyq579XQghRM04O7sx\nduxMnJ3d6NbtdpZ8frDKQKmEq6sHrVt3tXl2Y3Ht1NmWpT9++5SM9ETU9g706jOGf7aV3+a9d81T\nxLq6ezNt2js2HcNRwuWyPrsPPDif5s2N/eGfe/F7dLoCPDzqG28IT4WxbNnLZtvfcssIbgudyBdL\nniEjwzi3j52dPa++sR6NxqnWu7o5Orrw6hu/8fHCB003q3p9Nplpe3h/3lYmPzgPP/8WODm5snnT\nl+TkpJv2zc4+Ynr9/co3eO7FHziw7w/Udmo6dxuKl1dDwNg1avPGLzh2zNjl8PhxY2B1+5BHuLXf\nfVdU36q6WUVGHmDDb5+i0TRDr+9CxJFtqO0dcPesT5MmbSss8+LFKE4d380///yITpcPQMtWXW3a\nZbOsm9v34b4Js1m79j0c7B0xGIrJzTWON3J19aZly65kZaWgUqkYMmwaLi4enD1zgIZ+zfDwaMCH\nCyah1+sqLL9V61usrYrVVCoVvXrfxcYNS1AUAyeO/UPjxq2Jjg7n7Jn9aByciD1/nNOn9qJx9MXV\ntTmvzlpMz553kZObaUp2UpZX/d5EHPkJnc7YDDtw0EP07jsGjab82C1jAFbAsaPbWbduId71/Klf\nz980ubKTUxN8/TuSmtKOBtWYeDo6Opy9u9YQFBRCYPMe5OdrmT/3HrKyjHVzc/OmY+eBV1xuQUGO\naQoAMD400Gic8fUNrPZnoSgKWm067u71WPXDHI4d28HIkTPo3nNEzT5kIYQQlRow6D4GDLqyexdx\nY1IpdbTz//JvX+HUqT3llrdrd6vpJvxyr735R4UDSW3h04+nkpBwhtZtejJp8v8q3XbRh1NMXQff\nnPOnaeBqenoCG377DFdXT4YOf9Kqgf62lpmZxNdfPEda2oWaFwbcPeZFQrrczkcfzScjdY/FlpIO\nwf0ZNfpZUlIy2L9/P6NHjwZAr9dRXKwvNxnsmjVraNBAQ7EujaKiQk6c3IO/fwv69B1H/QYBvP1W\n5TeLXl6+dOo0kKAWIdipvTly5Cga+wT27F5TbtsJE2dzc/u+1FWKoqBSqbh4MYq8PC2NGjVn88bP\nyc/XMuaeWTYda1UiIyOJ9+eVPoy4c/jTbP7zS3S6PJseZ/rMZTg7u+Pm5kV6ejq//baerPSdJCVF\nVbiPnZ0zdnaO6PWZvPTKz7i5eRMXd5Kjh/6iR+/RuLp44OLqydq1a+natStNmxqfBhYXF/PxwgdJ\nLZed0A4oDXI6dhzAuPGvAsZxewBJSWkcO3aMESMsf+/S0xNY8umTOLp0YMiQUdjbFbLsu1k4ODjx\nzLPfmHWVTEhIYPfu3YwdaxxsbDAY0GrTcHHxNP2eAIiOPsP6Xz8nJfkw/fpPYNvW5aZ177y7DSGE\nEELUvjobLCUmnmPJJ4+hLy4yW/7G7A188N4ktNrLJ8sbyl1jnq/VOhUU5HDy2G5atO5WZSrxK9n2\nWjAYDCz68GGL46fK8q7nT25OJr16j2b7thUVbte58xBi4orIzthfabeyfv2nkZahJzVpO4mJZyvc\nrl79vmi1JynSpVJTarUrDg71KCiwnML71Td+q7XxYtcrRVFY9OGUSoMWW2rV+hbatevPpk0/kZ8X\nXePyxt/3JpHn0mnVKghXVzsCAzsQExPBF0uetmp/T8+GBAS05ty5QxQW5tK+w0hc3YPMgiWDoZh9\ne9fj7e3Hn39+SVJSFB6eIeTnxVJUVNoyO+mBubRuW9r/vWywlJFxkffnjTete/6lH/Hy8iUvL5t3\nZo+ssH6PTPuYwEDrJkAVQgghRPXV2WAJ4MC+Dfyy9j3T+x4972L4yKfZvPFzduwoncRr2uOf0aRp\n2+oc4j9NURRW/fg24UfLT+bWuHFbgjuG0qvP3RgMBtRqNadP7C3XvbCsej4DTMHS9JnLyMpK4Zsv\nzTP8aTQ+uLi3JjNtF5XROPqiL8rCYKj+RLrWCOl8O2PGvVSrx7hepaXG88H7EytcP2jQQ3Tqcjvb\ntyzj4MFNGAzFDBg4mS7dhlJQkIurqyeKouDuXo/s7DSKi/UkxkeyaePSardqTpg4B602nfXrqk4p\n7OMXSlb6MXS6ZJo160h09FErjmCZo6MfwSHjGDXqLtOyrX99a5rAtzIPTXmf5i1KE6lERUVy8OAR\nWrWox6qf3jbb1sPDh5kvrGDp4qdIiD9TYZne3o2Y8dxy1GrbTKQshBBCCMvqdLAE8M/27/lz0xc4\nO3vwwqwf0WicycpKYf5c44D8Xr3uZtiIJ691Na9r52OPs3Rx6TWsVz+Amc9bbkXaH/Y7f/75JQ72\nGkaMfIYVy181rfNucCvZmYd59fVVpjFAUVFHOXroLw4c+KNGdbS3d7yUVaYhBkMxzYI6EhgYTPvg\nfqhUYGenJiUljuhzR1j36wd4ePjg5ORKenoien2hqZzg4FDGjX8VlUqFwVBcLumFMHfi2E5Wrnjd\n9L5bt2EMHzW9XAKVK72W58+f4OsvZlJUZDkYdnBwpqgonzFjXsKzni/5uVpubt/HNLYvJyeTjb9/\nxpEjfwHg6OhKYWGuWRkuLkEUFqZQXFz1RNVBQSEkJERWOBGvo6MfHTqNZfjw4cTHn8FOZccXS6dT\nXKyrsmwHByc6hQzk6JGt6HR5ODh441WvEylJlrvSubnVMxszWJEnnv4Cf3+ZpFAIIYSoTXU+WAJI\nS0vA1dUTJydX07IzJ8M4E7mPvrfdi6enz7Wu4nUvMvIAK5e9RlFRAS++vBoPj4pTvxYX61Gp7LgQ\nd9IsyAK49dZ7uX3o1HL7pKZeYOH795stu+mmDjw45T1OHt+Ni5sXv6/7CJ2ukJCQgTS9qT0tWnUD\nlBpnNjQYilEUY+KCkn/COgaDgcjT+3D3bICvbzObtmQUFRVy6vge4i6cZPeu0oyW7dr15b77Z1tV\nRkZGEvb2Dri71yMnJ4OII9v4/fdFle7TrFlHHpyyALVaTVZWCgCenj5kZCSxctmr6HQF5Vq+HB39\naNV2GA28C9lWQXdULy8/3D3qE3f++BVfi8DAYGJiwqusd2rqBbTaNO6bMJt2HeruODshhBDiRnFd\nBEvi6rjS1oGcnAzee3e8qeWmVetbmDR5boXBiMFgYMfWFRgUA1263YGXl6/ZekVRUBSDtPb8xxQW\n5rP4k2mkpJynSdN2TJw0Bzc372qXl56ewIL5Eyyu8/UN4qnpX1byHS1GpbIjOjqc/WHrSUmOIzEx\nEgeHejg6+pKTc9Jse0dHV0bf/Tye3g1p3LgNKpWK4mI9ycmxfPLRFKvq+9AjH9C8eQhHDv7F6tXm\niWMemvI+dmoHigrzadGqGzpdPlptOj7VyAIohBBCiCsnwZKokZiYCHKy02nbrrfN57YS/x0Gg4Hc\n3Ezc3Lxt0vKn0xUQfmQLTQM7cOrELrb8vYxmQR25Z/yrVzQvVVGRjrffGm4xfXuTJjczZNhjBAa2\nt7hv2e7CAMOHP42d2p7zscc4fHgz3vX8uf+Bd8xSi587d5jww38THr4db28/HntysVmGPCGEEEJc\nXRIsCSFueMXFxdXuQrjs25c5fWqv6b1G48yTT39B/QYBVe4bG3uciCNb6NHrriuaE6q4WI+dnVq6\njAohhBDXmARLQghRifT0RD5cMJniYh2+vs14/KkltTK3lRBCCCHqHgmWhBCiChcvRnMx/izBIaEy\npk4IIYT4D5FgSQghhBBCCCEssLvWFRBCCCGEEEKIukiCJSGEEEIIIYSwQIIlIYQQQgghhLBAgiUh\nhBBCCCGEsECCJSGEEEIIIYSwQIIlIYQQQgghhLBAgiUhhBBCCCGEsECCJSGEEEIIIYSwQIIlIYQQ\nQgghhLBAgiUhhBBCCCGEsECCJSGEEEIIIYSwQIIlIYQQQgghhLBAgiUhhBBCCCGEsECCJSGEEEII\nIYSwQIIlIYQQQgghhLBAgiUhhBBCCCGEsECCJSGEEEIIIYSwQIIlIYQQQgghhLBAgiUhhBBCCCGE\nsECCJSGEEEIIIYSwQIIlIYQQQgghhLBAgiUhhBBCCCGEsECCJSGEEEIIIYSwQIIlIYQQQgghhLBA\ngiUhhBBCCCGEsECCJSGEEEIIIYSwQIIlIYQQQgghhLBAgiUhhBBCCCGEsECCJSGEEEIIIYSwQIIl\nIYQQQgghhLBAgiUhhBBCCCGEsECCJSGEEEIIIYSwQIIlIYQQQgghhLBAgiUhhBBCCCGEsECCJSGE\nEEIIIYSwQIIlIYQQQgghhLBAgiUhhBBCCCGEsECCJSGEEELUSfqCAgpM//TXujrVoOXIppUsXbqU\n5X8e45qfgV5f5nqW/su/5hWryflcXnl9LZ6TnhObVvLH4cQK1x/ftJoVv4WRVsPjHN+0mr9OpQJ6\ntBkZZFfw/U8/tLFufLduYBIsCSGEEKLuyf6Xbq7OODtf+td8cQ1vQK+2AjbO8CDkjolMmzaNSR9s\nI+ua1kfL6gcdSq9nmX8uH+671her+udzW5nvRfZBnnBywLn+eA5pi2vhmPn8c+9E7twSZ3l19lGm\n3zmO+3+OwqWGx9l57zgG/x4F2Qe4tUE9PBccsrhl/M7pTJq88Rp/t25s9te6AkIIIYQQ5Xh0YsO5\ng3z7cBdebvUtUf+7h/rXuk5XougMX34CU9bH8sXwpte6NgBoc4DOM/jlw7vwKCq6tFSHc0Cza121\n6p+PlyMOAEUxvHtbVz5TQlkXuYbe3upaOaamK7R2shwKaU/s5O9i+Pq10Tjb4DhtnRzAuTGLflmH\nXbuWFrdz8WgJTT2N10DUCgmWhBBCCFEHOdEo8GaaqqBV5y4083YC9Bz4fgG7aEujuN9Z+udZbrpj\nBvOe7MH+Re+wYFM4gaGP8OpL4wmyh/SDq/lsxR7OREeTjTute49i2lN308zJeIQLO1fyzoIvOaX1\npN/IO3DOyqLThGcYHOQI2WdZ/u6bvP9HBF5BPbj/6ReZ0j8I0BO5aTkfLFnGSRrTsUs3ht03icHN\nvcrUvYCdC19hrR7Gb/2O9/6FNg89hf/OpextOoqRnqf4ZuNF7n1uKi2yD7J47kI+3xqBV9AApr3+\nMuNDGlzxuVIUw0/vLiWlzyM82T/I4hV1BPDpyJ19+5a7AazsWqUfXM3He+zo1/QCH320Dn2TUGbN\nfYamZ9fwylvLSQ/owaNvvMzw5m4AGJIrP6eddKRV9g4WrArDudUdvDH3Wbp7q03HGXZzNp/8bznn\nCeC+t+bzSJ9GFZ+PyhGNomXluGbMighmxekNjPA3Bkrp4ev43+sfsjlGRfsed/DE60/T29/R+Nn/\nu5J33v2SPdHptL3zCV577lHaeWNW/7XbEgga2p+WXuDSbQJP9vcBIC0xgt+/WckHy83rf2T9DLj9\nW+5triZy0zdVfEeMcs/9w+JPPueP8Bz8g2+m/5AHmHy7f+kGDt445URzOLETvZp7g5LBjs8X8eFP\n29G37EiTyD/Aa0Tp51jRORck8Mfni/jy1zCKA1rSuc8gHrhvDM3cr/XP+XVAEUIIIYSok7KVrwag\ntF10yOw9oNDpfmXahPbG16CgCVVmPDLC+PrtnYqiKErEvFYKmlDl6dnzlLenTzCue2yNkqcoSvqO\nucb3oVOV+e/OUkbbG8t591CGouSdUB53RMFllDL3m2+Udx5ppwDKvLAMJXnDCwqg9Jw+R1n60Wxl\noBqFt8Muq3e+8ses4cbyO45SJtw/XVkfk1pad4xl743913hcl1HK3K+XKDNHcOk4KVd8rkrWXqWT\nHQrvhVV4LVeMQqHrHOVoTLwSczZGiYk5q5w9G6NkVXGtwj8aZjr2o49OLK0HKPc986jxuPVmKKeL\nFEVJ22vdObmMUl5+6dJxBi9VUi87zn3TpxvLUQcr6+L1FZ/PXXOUL94yXuslhzJK1+5daCxr4svK\nNys+UiZrUPCcqhzKV5Skv980rhv1svLt1/OMn6HnVOVYvqIoWQeM26qDlRfnzVOevXTdjd/BS8e0\nUP80Q75yeN1qZXdMgZXfEeNnNlBt/A5+uGSJ8tpIFHznKGmGst/7bOWrEBTeO6QoSpHy96w2prLn\nvDTBeO0HL1WyKjvnvHzl14nGc3pq3hJl0SxjvV8My1BE1SRYEkIIIUQdVUGwNO17JUtRFMWQrnwQ\ngsKkpUpckaIoSr6yaiIK3T9WUhVFKSoqKlNWvvLPW60Vun+spBmSlc9CUHjgWyW1ZHXeAWWg2hgs\nxa64V8H9fiUsv7Qen4Wg8Nh65fCHfRR85ygXS1YZ0pULyfnlq647qoy2R1kYUVBa91EoDJyj7IvP\nVhRFUc5+PV5BE6psTC4pK1n5LBSFu79V8g1Xdq6K7oLy85KPlJ8PpVR4LU03+pf925Jd8bVKVRTl\n5OJhCp5TlV2X6hn+YR8FdbCy8qRWURRFyfj7TQVNqLIz2/pzKrnu4YuHmfYtPc6l4CjyJ1OQavF8\nJpaeQ7+yQaIh3XjMx9YoprNK+lsBlDcPnFTmdkJh9NLSz/7CBqWTHcrw708pZ1cY618aoOWbBy6V\n1L9EuJXfkbwDxuBmruk7oigJZ2NM16nsMdsuOqQYoo3X477vT5m2P7m4j0L3pUpWJec8e/cuZbKm\n7M+RoujT45W0IkVYQRI8CCGEEOK60qpzBzwAVPZ41oNWfXrR2B7AiQ69hwHGcSz22ki+nDERlUqF\nSuXMrW+chsaOaLTn+TsC+vbuYjYOykNl/D82Kh60y3l4aCihoaGEho7k8cPAL6cobtAEkl7Db8Ak\n3l36PTuO5RPg41S+kvoishUoLMovXaaFVuNG0c3fHSjgTPgP0O8eevlcWq/yof/YPrArjsQrPFcc\nAhg99WlGhzSo/OINnMOR+GTi4+OJj48hJiaenu4VXyvjWJgsuKUzHS7Vs3HIQHAMokWgsdudo09D\nADRXcE4l171Fr2GX9i17nEvjjQLaMNoelAoG5BTmAMHBdLKD7S89wvenCy9d5yj+/gdYPIbBocbP\ncJD/QADUeRfZEgH33jew9LP3D+YeVzibpiXmmLH+/fxLxjwVlTtuxfU3crHyO+Ls15pOdjCry1Ce\nnr+UX7ceQtP8JpxUls+3IM2YyuKuXi3KrbOr5JwNTjfRty+cfKozd057m6/XbOK0viH1ZDCOVeQy\nCSGEEOK6oi4squS9MS+YSklh8YCbefx4KO+s3spd3YJI+O5+Bu6uqFSHS/vlcPHMTug8g9dfGIy7\nDnTACy9Mx+DYio79p7G7qA3vf/cGs6YtB2Dk54f49ZGQK6x7Eekx5dfrs4GidIr01p/rFbFrSDN/\nH2MAVsKaa5VZ+tLJq6GxokVA2RhAqd45mcks+8YYcFbEEaDVS2zb1oyHfXsy4ZZnaBu3hJJPYvCc\nb5nR1RedTofmhReYqYOAAEcOlwtGXGjYAuyUQtIvVHCcCj+D8ppPWGrddyTgDjbtWcX8Tz7jgxen\nsQig23yiwqZZLtgB0ITStF7FySssnbNfkwYErzqK4f1P+HTeazy81LjtirMFTGjuiKictCwJIYQQ\noo5ywBEwVCPXl0p7jrXh0OeTz3h5TH/a3nQTvk5JkAmKswt+ajgUG2/avigpnigDKCo3Y4vNuTw6\nDhnCkBFDGDFiCEOGjGBo/zagd6fX5NdZu01ByYtkbidY9+WuaqQ1d6drvz5w4BSpZZYmJ+6CFs1o\ncMWPswtIiI0lWVvFjDsqx/JXs5JrdWUX3dbnZIVsLXb1evDtzoWQtZTOkz8nw9mLIAfYXNCUIUOG\nMGLECIZc+iw7NPHCTw0/RpepYUEUf0SAQeVi/Oz37uKU9tI6JZvk9Curkt7q74ge31vGsmD5NhSl\niBOrnoajm0jQVlK4bit7Y3LKLVacPSs8504+kOMRzJT/fc7hYoXcyF/pZAcb9sXUwgdy45FgSQgh\nhBB1j15L9KHdHNkDWVEHOXgqwTTx5kkrdlfcG9FJA7s2ruffU6fYs3o2HV48A41BcWjLtPnDyH1n\nCH2mvsI700eiaTaUIwbjvs0H3gtZS2k9+m3+jjhHVEQYK2bdRof393Hyszvp/sp3HDwVS3RkJKdP\nAH1b4WnlaZWte9P+D0L6Qu555QdOxp5jz8rZDPgQ+k7pTz2V9ecKQPYRhgUF4rv0UOXbJe/lxzXr\nWbNmjfHf99+z4ay6wmt1pWx6TlYqAtx7TCd88XhYO5W7P0pk0gfD4J1Qxr73M6fOnePwznU830nF\nmxGNeHh2X3j+Fl5df5jUhFN8NX0Sa/Xwyh030+K2e0G7nFtuncTbs2cQYt+YZw+DT5l+dlXV39rv\nSP7BT1B1eZZfwiKIjT1LxKEjYO+BQwXPBpxb9mayBqZPfp0NhyLY8c0s2j6269J3ukWF5/z2zp3c\n5qjig593cS42lsjjpzhigJbNfW38SdyYpBueEEIIIeqevOM82n0gfxcDCyfTdffHpP07GYC+jiV3\nkw64l8sq7QleoKhu4vnfFvL+wBn0/OUF0IQyUA1/X9qqw9M/sMPxVd767Hc2Bw3g4w9f4unp7xpL\nbTGRi3uLeLzvQwz65TVTybM3+VHP0I39z0ym6/8uLRz4MvteHGjxhso4Bsp8TWndwTn4ISJ/jaPl\nqPu4+VJ5A+es58dH2gNaq8/VuNqBTvbg4VFFK9zhpTw0dqnZopvfP8S2Sq6V2XFK2HtYfH9l53R5\nWeWP41HB+B0TN0wtZR2mLWXV4aOMe74v2w7G8deHbzFo+hjWvHBpg5CpbKrvTOfnf+anxDHcM7Iz\n71xa9d6mc5e6pE3k4l4VL7w8j1VrGzD6q2/oNe1Btuksf4aWrkW9ltZ9R5zqt2Z0+AxG91hoXKAJ\n5eMtH9HdGY5ZOlfnYOb9tZBvb5vBsC4LQW0cr3XEdP4/8Ffhs+XOeXOjm6h3XzueGNOXmZcW3z1/\nE09190JUTaUoilLzYoQQQggh6qACLSnaAty8fXC2N1+e7+Rumjw0Yd3TBIw7zs6LW+jjXbKRnowM\nLfb29ji7u5e52S0gIyMfsMfb2wYT1RRkkKLVo9i709Dbqebl2fpaXefnlJEP9vYOuLub10ObkYJW\nD27ePniYzreA7AInPEo2Tf+Xu317UvTVKdZPan0lB7b6O6LVZqDXg5O7t3XX/dLn5GhW76rPWV+g\nRZuvR+3sjoeTtJdYS4IlIYQQQvzn5P/7Li49ZzF84qMEKHtYsvIYPLuGvAV3mwIo8R+U/S8h3j05\n0u9+ZnRQWPjRCnC/n7D4ZXSXCVz/kyRYEkIIIcR/jiE5nBXf/srpxHhS81wIvnM89w/vjkfNixbX\ns6IUdqz8np1nYohLy8OrRT+mTBlLS29pifmvkmBJCCGEEEIIISyQbHhCCCGEEEIIYYEES/8V+Sd5\nfUAHQkND6eg8gG9O5dS8TAvOrn4JVccBDOjfke4zfya/5kX+Z8i1E0IIIYSoW/4PTI63DKYOJqQA\nAAAuelRYdGNyZWF0ZS1kYXRlAAB42jMyMDTTNbDUNTIIMbSwMjK1MjTXNTCxMjAAAEIvBRq9hg+5\nAAAALnpUWHRtb2RpZnktZGF0ZQAAeNozMjA00zWw1DUyCDG0sDIytTI01zUwsTIwAABCLwUa3774\nRgAAAB56VFh0dGlmZjphbHBoYQAAeNpLLC7OT85MLElNAQAW7QQh+9VbpAAAAB96VFh0dGlmZjpy\nb3dzLXBlci1zdHJpcAAAeNoztgAAAKAAbNMr3oEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {
      "image/png": {
       "width": 550
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "display(Image(\"figs/L5-DTW-1.png\", width=550))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Both timeseries have the same key characteristics: four bumps.\n",
    "\n",
    "But a one-one match (ala Euclidean distance) will not detect this."
   ]
  },
  {
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   "source": [
    "A solution to this is called __dynamic time warping.__\n",
    "\n",
    "The basic idea is to allow acceleration or deceleration of signals along the time dimension."
   ]
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    "Classic applications:\n",
    "    \n",
    "* Speech recognition\n",
    "* Signature recognition"
   ]
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    "Specifically: \n",
    "\n",
    "* Consider $X = x_1, x_2, \\dots, x_n$ and $Y = y_1, y_2, \\dots, y_n$.\n",
    "* We are allowed to extend each sequence by repeating elements to form $X'$ and $Y'$.\n",
    "* We then calculate, eg, Euclidean distance between the extended sequnces $X'$ and $Y'$"
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   "source": [
    "There is a simple way to visualize this algorithm.\n",
    "\n",
    "Consider a matrix $M$ where $M_{ij} = |x_i - y_j|$ (or some other error measure)."
   ]
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    "$M$ measures the amount of error we get if we match $x_i$ with $y_j$. \n",
    "\n",
    "So we seek a __path through $M$ that minimizes the total error.__\n",
    "\n",
    "We need to start in the lower left and work our way up via a continuous path."
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    "Basic restrictions on path:\n",
    "    \n",
    "* Montonicity\n",
    "    * path should not go down or to the left\n",
    "* Continuity\n",
    "    * No elements may be skipped in sequence"
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    "This can be solved via dynamic programming.  However, the algorithm is still quadratic in $n$.\n",
    "\n",
    "Hence, we may choose to put a restriction on the amount that the path can deviate from the diagonal."
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   "source": [
    "The basic algorithm looks like this:"
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    "`D[0, 0] = 0\n",
    "for i in range(n):\n",
    "    for j in range (m):\n",
    "        D[i,j] = M[i,j] + min( D[i-1, j],  # insertion\n",
    "                               D[i, j-1],  # deletion\n",
    "                               D[i-1, j-1]) # match`"
   ]
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   "source": [
    "Unfortunately, the algorithm is still quadratic in $n$ $(O(nm))$.\n",
    "\n",
    "Hence, we may choose to put a restriction on the amount that the path can deviate from the diagonal.\n",
    "\n",
    "This is implemented by not allowing the path to pass through locations where $|i - j| > w$.\n",
    "\n",
    "Then the algorithm is $O(nw)$."
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   "source": [
    "## A related notion"
   ]
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   "source": [
    "A closely related idea concerns strings.\n",
    "\n",
    "(Strings are just sequences, like timeseries)."
   ]
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   "cell_type": "markdown",
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    "Given two strings, one way to define a 'distance' between them as the minimum number of edit operations that are needed to transform one string into the other.\n",
    "\n",
    "Edit operations are insertion, deletion, and substitution of single characters.\n",
    "\n",
    "This is called __edit distance__ or __Levenshtein distance.__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "A very similar dynamic programming algorithm can be used to find this distance."
   ]
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