{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Active Contours using Parameteric Curves"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This tour explores image segmentation using parametric active contours.\n",
    "$\\newcommand{\\dotp}[2]{\\langle #1, #2 \\rangle}$\n",
    "$\\newcommand{\\qandq}{\\quad\\text{and}\\quad}$\n",
    "$\\newcommand{\\qwhereq}{\\quad\\text{where}\\quad}$\n",
    "$\\newcommand{\\qifq}{ \\quad \\text{if} \\quad }$\n",
    "$\\newcommand{\\ZZ}{\\mathbb{Z}}$\n",
    "$\\newcommand{\\RR}{\\mathbb{R}}$\n",
    "$\\newcommand{\\CC}{\\mathbb{C}}$\n",
    "$\\newcommand{\\pa}[1]{\\left(#1\\right)}$\n",
    "$\\newcommand{\\si}{\\sigma}$\n",
    "$\\newcommand{\\Nn}{\\mathcal{N}}$\n",
    "$\\newcommand{\\Bb}{\\mathcal{B}}$\n",
    "$\\newcommand{\\EE}{\\mathbb{E}}$\n",
    "$\\newcommand{\\norm}[1]{\\|#1\\|}$\n",
    "$\\newcommand{\\abs}[1]{\\left|#1\\right|}$\n",
    "$\\newcommand{\\choice}[1]{ \\left\\{  \\begin{array}{l} #1 \\end{array} \\right. }$\n",
    "$\\newcommand{\\al}{\\alpha}$\n",
    "$\\newcommand{\\la}{\\lambda}$\n",
    "$\\newcommand{\\ga}{\\gamma}$\n",
    "$\\newcommand{\\Ga}{\\Gamma}$\n",
    "$\\newcommand{\\La}{\\Lambda}$\n",
    "$\\newcommand{\\si}{\\sigma}$\n",
    "$\\newcommand{\\Si}{\\Sigma}$\n",
    "$\\newcommand{\\be}{\\beta}$\n",
    "$\\newcommand{\\de}{\\delta}$\n",
    "$\\newcommand{\\De}{\\Delta}$\n",
    "$\\newcommand{\\phi}{\\varphi}$\n",
    "$\\newcommand{\\th}{\\theta}$\n",
    "$\\newcommand{\\om}{\\omega}$\n",
    "$\\newcommand{\\Om}{\\Omega}$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "*Important:* Please read the [installation page](http://gpeyre.github.io/numerical-tours/installation_python/) for details about how to install the toolboxes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: Method definition ndgrid(AbstractArray{T<:Any, 1}) in module NtToolBox at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:3 overwritten at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:3.\n",
      "WARNING: Method definition ndgrid(AbstractArray{#T<:Any, 1}, AbstractArray{#T<:Any, 1}) in module NtToolBox at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:6 overwritten at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:6.\n",
      "WARNING: Method definition ndgrid_fill(Any, Any, Any, Any) in module NtToolBox at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:13 overwritten at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:13.\n",
      "WARNING: Method definition ndgrid(AbstractArray{#T<:Any, 1}...) in module NtToolBox at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:19 overwritten at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:19.\n",
      "WARNING: Method definition meshgrid(AbstractArray{T<:Any, 1}) in module NtToolBox at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:33 overwritten at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:33.\n",
      "WARNING: Method definition meshgrid(AbstractArray{#T<:Any, 1}, AbstractArray{#T<:Any, 1}) in module NtToolBox at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:36 overwritten at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:36.\n",
      "WARNING: Method definition meshgrid(AbstractArray{#T<:Any, 1}, AbstractArray{#T<:Any, 1}, AbstractArray{#T<:Any, 1}) in module NtToolBox at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:44 overwritten at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:44.\n"
     ]
    }
   ],
   "source": [
    "using PyPlot\n",
    "using NtToolBox\n",
    "# using Autoreload\n",
    "# arequire(\"NtToolBox\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Parameteric Curves\n",
    "-------------------\n",
    "\n",
    "In this tours, the active contours are represented using parametric\n",
    "curve $ \\ga : [0,1] \\rightarrow \\RR^2 $. \n",
    "\n",
    "\n",
    "This curve is discretized using a piewise linear curve with \n",
    "$p$ segments, and is stored as a complex vector of points in the plane\n",
    "$\\ga \\in \\CC^p$.\n",
    "\n",
    "Initial polygon."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "gamma0 = [.78, .14, .42, .18, .32, .16, .75, .83, .57, .68, .46, .40, .72, .79, .91, .90] + 1im*[.87, .82, .75, .63, .34, .17, .08, .46, .50, .25, .27, .57, .73, .57, .75, .79];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display the initial curve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x316902cd0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(0.1015,0.9485,0.040499999999999994,0.9095)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "periodize = gamma -> [gamma; [gamma[1]]]\n",
    "function cplot(gamma, s = \"b\", lw = 1) \n",
    "    plot(real(periodize(gamma)), imag(periodize(gamma)), s, linewidth = lw)\n",
    "    axis(\"equal\")\n",
    "    axis(\"off\")\n",
    "end\n",
    "cplot(gamma0, \"b.-\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Number of points of the discrete curve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "p = 256;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Shortcut to re-sample a curve according to arc length."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "ArgumentError: Module Dierckx not found in current path.\nRun `Pkg.add(\"Dierckx\")` to install the Dierckx package.",
     "output_type": "error",
     "traceback": [
      "ArgumentError: Module Dierckx not found in current path.\nRun `Pkg.add(\"Dierckx\")` to install the Dierckx package.",
      "",
      " in require(::Symbol) at ./loading.jl:365",
      " in require(::Symbol) at /Applications/Julia-0.5.app/Contents/Resources/julia/lib/julia/sys.dylib:?"
     ]
    }
   ],
   "source": [
    "using Dierckx\n",
    "curvabs = gamma -> [0; cumsum(1e-5 .+ abs(gamma[1:end - 1] - gamma[2:end]) )]\n",
    "resample11 = (gamma, d) -> evaluate(Spline1D(d./d[end], real(gamma), k=1), (0:p-1)./p)\n",
    "resample12 = (gamma, d) -> evaluate(Spline1D(d./d[end], imag(gamma), k=1), (0:p-1)./p)\n",
    "resample = gamma -> resample11( [gamma; gamma[1]], curvabs( [gamma; gamma[1]] ) ) + 1im*resample12( [gamma; gamma[1]], curvabs( [gamma; gamma[1]] ) );\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Initial curve $ \\ga_1(t)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "UndefVarError: resample not defined",
     "output_type": "error",
     "traceback": [
      "UndefVarError: resample not defined",
      ""
     ]
    }
   ],
   "source": [
    "gamma1 = resample(gamma0);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display the initial curve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "UndefVarError: gamma1 not defined",
     "output_type": "error",
     "traceback": [
      "UndefVarError: gamma1 not defined",
      ""
     ]
    }
   ],
   "source": [
    "cplot(gamma1, \"k\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Shortcut for forward and backward finite differences."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "BwdDiff = c -> c - [c[end]; c[1:end - 1]]\n",
    "FwdDiff = c -> [c[2:end]; c[1]] - c\n",
    "dotp = (c1, c2) -> real(c1.*conj(c2));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The tangent to the curve is computed as\n",
    "$$ t_\\ga(s) = \\frac{\\ga'(t)}{\\norm{\\ga'(t)}} $$\n",
    "and the normal is $ n_\\ga(t) = t_\\ga(t)^\\bot. $\n",
    "\n",
    "Shortcut to compute the tangent and the normal to a curve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "normalize = v -> v./max(abs(v), 1e-10)\n",
    "tangent = gamma -> normalize( FwdDiff(gamma) )\n",
    "normal = gamma -> -1im*tangent(gamma);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Move the curve in the normal direction, by computing $ \\ga_1(t) \\pm \\delta n_{\\ga_1}(t) $."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "UndefVarError: gamma1 not defined",
     "output_type": "error",
     "traceback": [
      "UndefVarError: gamma1 not defined",
      ""
     ]
    }
   ],
   "source": [
    "delta = .03\n",
    "gamma2 = gamma1 .+ delta .* normal(gamma1)\n",
    "gamma3 = gamma1 .- delta .* normal(gamma1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display the curves."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "UndefVarError: gamma1 not defined",
     "output_type": "error",
     "traceback": [
      "UndefVarError: gamma1 not defined",
      ""
     ]
    }
   ],
   "source": [
    "cplot(gamma1, \"k\")\n",
    "cplot(gamma2, \"r--\")\n",
    "cplot(gamma3, \"b--\")\n",
    "axis(\"tight\") \n",
    "axis(\"off\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Evolution by Mean Curvature"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "A curve evolution is a series of curves $ s \\mapsto \\ga_s $ indexed by\n",
    "an evolution parameter $s \\geq 0$. The intial curve $\\ga_0$ for\n",
    "$s=0$ is evolved, usually by minizing some energy $E(\\ga)$ in a gradient descent\n",
    "$$ \\frac{\\partial \\ga_s}{\\partial s} = \\nabla E(\\ga_s). $$\n",
    "\n",
    "\n",
    "Note that the gradient of an energy is defined with respect to the\n",
    "curve-dependent inner product\n",
    "$$ \\dotp{a}{b} = \\int_0^1 \\dotp{a(t)}{b(t)} \\norm{\\ga'(t)} d t.  $$\n",
    "The set of curves can thus be thought as being a Riemannian surface.\n",
    "\n",
    "\n",
    "The simplest evolution is the mean curvature evolution.\n",
    "It corresponds to minimization of the curve length\n",
    "$$ E(\\ga) = \\int_0^1 \\norm{\\ga'(t)} d t $$\n",
    "\n",
    "\n",
    "The gradient of the length is \n",
    "$$ \\nabla E(\\ga)(t) = -\\kappa_\\ga(t) n_\\ga(t)  $$\n",
    "where $ \\kappa_\\ga $ is the curvature, defined as\n",
    "$$ \\kappa_\\ga(t) = \\frac{1}{\\norm{\\ga'(t)}} \\dotp{ t_\\ga'(t) }{ n_\\ga(t) } . $$\n",
    "\n",
    "\n",
    "\n",
    "Shortcut for normal times curvature $ \\kappa_\\ga(t) n_\\ga(t) $."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "normalC = gamma -> BwdDiff(tangent(gamma)) ./ abs( FwdDiff(gamma) );"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Time step for the evolution.\n",
    "It should be very small because we use an explicit time stepping and the\n",
    "curve has strong curvature."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "dt = 0.001 / 100;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Number of iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Tmax = 3.0 / 100\n",
    "niter = round(Tmax/dt);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Initialize the curve for $s=0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "UndefVarError: gamma1 not defined",
     "output_type": "error",
     "traceback": [
      "UndefVarError: gamma1 not defined",
      ""
     ]
    }
   ],
   "source": [
    "gamma = gamma1;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Evolution of the curve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "MethodError: no method matching endof(::Base.Math.#gamma)\u001b[0m\nClosest candidates are:\n  endof(\u001b[1m\u001b[31m::SimpleVector\u001b[0m) at essentials.jl:169\n  endof(\u001b[1m\u001b[31m::Char\u001b[0m) at char.jl:18\n  endof(\u001b[1m\u001b[31m::String\u001b[0m) at strings/string.jl:37\n  ...\u001b[0m",
     "output_type": "error",
     "traceback": [
      "MethodError: no method matching endof(::Base.Math.#gamma)\u001b[0m\nClosest candidates are:\n  endof(\u001b[1m\u001b[31m::SimpleVector\u001b[0m) at essentials.jl:169\n  endof(\u001b[1m\u001b[31m::Char\u001b[0m) at char.jl:18\n  endof(\u001b[1m\u001b[31m::String\u001b[0m) at strings/string.jl:37\n  ...\u001b[0m",
      "",
      " in (::##5#6)(::Function) at ./In[8]:2",
      " in (::##11#12)(::Function) at ./In[9]:2",
      " in (::##15#16)(::Function) at ./In[12]:1"
     ]
    }
   ],
   "source": [
    "gamma = gamma .+ dt .* normalC(gamma);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "To stabilize the evolution, it is important to re-sample the curve so\n",
    "that it is unit-speed parametrized. You do not need to do it every time\n",
    "step though (to speed up)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "UndefVarError: resample not defined",
     "output_type": "error",
     "traceback": [
      "UndefVarError: resample not defined",
      ""
     ]
    }
   ],
   "source": [
    "gamma = resample(gamma);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "**Exercise 1:** Perform the curve evolution.\n",
    "You need to resample it a few times."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "LoadError: UndefVarError: gamma1 not defined\nwhile loading /Users/gpeyre/Dropbox/github/numerical-tours/julia/NtSolutions/segmentation_2_snakes_param/exo1.jl, in expression starting on line 1",
     "output_type": "error",
     "traceback": [
      "LoadError: UndefVarError: gamma1 not defined\nwhile loading /Users/gpeyre/Dropbox/github/numerical-tours/julia/NtSolutions/segmentation_2_snakes_param/exo1.jl, in expression starting on line 1",
      "",
      " in include_from_node1(::String) at ./loading.jl:488",
      " in include_from_node1(::String) at /Applications/Julia-0.5.app/Contents/Resources/julia/lib/julia/sys.dylib:?"
     ]
    }
   ],
   "source": [
    "include(\"NtSolutions/segmentation_2_snakes_param/exo1.jl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Geodesic Active Contours"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Geodesic active contours minimize a weighted length\n",
    "$$ E(\\ga) = \\int_0^1 W(\\ga(t)) \\norm{\\ga'(t)} d t, $$\n",
    "where $W(x)>0$ is the geodesic metric, that should be small in areas\n",
    "where the image should be segmented."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Size of the image $n$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "n = 200;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Create a synthetic weight $W(x)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "nbumps = 40\n",
    "theta = rand(nbumps,1).*(2*pi)\n",
    "r = .6*n/2\n",
    "a = [.62*n,.6*n]\n",
    "x = round( a[1] + r*cos(theta) )\n",
    "y = round( a[2] + r*sin(theta) )\n",
    "W = zeros(n, n)\n",
    "for i in 1:nbumps\n",
    "    W[Int(x[i]), Int(y[i])] = 1\n",
    "end\n",
    "W = gaussian_blur(W, 6.0)\n",
    "W = rescale( -min(W, .05), .3,1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display the metric $W$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x320e4ccd0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "imageplot(W)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Pre-compute the gradient $\\nabla W(x)$ of the metric."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "G = grad(W)\n",
    "G = G[:,:,1] .+ 1im*G[:, :, 2];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display the image of the magnitude $\\norm{\\nabla W(x)}$ of the gradient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x3266d5d50>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "imageplot(abs(G))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Shortcut to evaluate the gradient and the potential along a curve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "EvalG = gamma -> NtToolBox.bilinear_interpolate(G, imag(gamma), real(gamma))\n",
    "EvalW = gamma -> NtToolBox.bilinear_interpolate(W, imag(gamma), real(gamma));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Create a circular curve $\\ga_0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "r = .98*n/2 # radius\n",
    "p = 128 # number of points on the curve\n",
    "theta = transpose( linspace(0, 2*pi, p + 1) )\n",
    "theta = theta[1 : end - 1]\n",
    "gamma0 = n/2 * (1 + 1im) +  r*(cos(theta) + 1im*sin(theta));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Initialize the curve at time $t=0$ with a circle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: imported binding for gamma overwritten in module Main\n"
     ]
    }
   ],
   "source": [
    "gamma = gamma0;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "For this experiment, the time step should be larger, because the\n",
    "curve is in $[0,n-1] \\times [0,n-1]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "dt = 1;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Number of iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Tmax = 5000\n",
    "niter = round(Tmax/ dt);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display the curve on the background."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x321348d10>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(-0.5,199.5,199.5,-0.5)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lw = 2\n",
    "clf\n",
    "imageplot(transpose(W))\n",
    "cplot(gamma, \"r\", lw)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The gradient of the energy is\n",
    "$$ \\nabla E(\\ga) = -W(\\ga(t)) \\kappa_\\ga(t) n_\\ga(t) + \\dotp{\\nabla W(\\ga(t))}{ n_\\ga(t) } n_\\ga(t). $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Pointwise innerproduct on the curve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "dotp = (c1,c2) -> real(c1.*conj(c2));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Evolution of the curve according to this gradient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "MethodError: Cannot `convert` an object of type Array{Float64,1} to an object of type Int64\nThis may have arisen from a call to the constructor Int64(...),\nsince type constructors fall back to convert methods.",
     "output_type": "error",
     "traceback": [
      "MethodError: Cannot `convert` an object of type Array{Float64,1} to an object of type Int64\nThis may have arisen from a call to the constructor Int64(...),\nsince type constructors fall back to convert methods.",
      "",
      " in bilinear_interpolate(::Array{Float64,2}, ::Array{Float64,1}, ::Array{Float64,1}) at /Users/gpeyre/.julia/v0.5/NtToolBox/src/signal.jl:414",
      " in (::##19#20)(::Array{Complex{Float64},1}) at ./In[24]:2"
     ]
    }
   ],
   "source": [
    "N = normal(gamma)\n",
    "g = - EvalW(gamma) .* normalC(gamma) + dotp(EvalG(gamma), N) .* N\n",
    "gamma = (gamma - dt*g);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "To avoid the curve from being poorly sampled, it is important to\n",
    "re-sample it evenly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "UndefVarError: resample not defined",
     "output_type": "error",
     "traceback": [
      "UndefVarError: resample not defined",
      ""
     ]
    }
   ],
   "source": [
    "gamma = resample(gamma);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "**Exercise 2:** Perform the curve evolution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "LoadError: MethodError: Cannot `convert` an object of type Array{Float64,1} to an object of type Int64\nThis may have arisen from a call to the constructor Int64(...),\nsince type constructors fall back to convert methods.\nwhile loading /Users/gpeyre/Dropbox/github/numerical-tours/julia/NtSolutions/segmentation_2_snakes_param/exo2.jl, in expression starting on line 7",
     "output_type": "error",
     "traceback": [
      "LoadError: MethodError: Cannot `convert` an object of type Array{Float64,1} to an object of type Int64\nThis may have arisen from a call to the constructor Int64(...),\nsince type constructors fall back to convert methods.\nwhile loading /Users/gpeyre/Dropbox/github/numerical-tours/julia/NtSolutions/segmentation_2_snakes_param/exo2.jl, in expression starting on line 7",
      "",
      " in bilinear_interpolate(::Array{Float64,2}, ::Array{Float64,1}, ::Array{Float64,1}) at /Users/gpeyre/.julia/v0.5/NtToolBox/src/signal.jl:414",
      " in (::##19#20)(::Array{Complex{Float64},1}) at ./In[24]:2",
      " in macro expansion; at /Users/gpeyre/Dropbox/github/numerical-tours/julia/NtSolutions/segmentation_2_snakes_param/exo2.jl:9 [inlined]",
      " in anonymous at ./<missing>:?",
      " in include_from_node1(::String) at ./loading.jl:488",
      " in include_from_node1(::String) at /Applications/Julia-0.5.app/Contents/Resources/julia/lib/julia/sys.dylib:?"
     ]
    }
   ],
   "source": [
    "include(\"NtSolutions/segmentation_2_snakes_param/exo2.jl\")\n",
    "\n",
    "\n",
    "# gamma = copy(gamma0);\n",
    "# displist = round(linspace(0, niter, 10))\n",
    "# k = 1;\n",
    "# clf; \n",
    "# imageplot(transpose(W));\n",
    "# track  = gamma\n",
    "# for i in 0 : niter\n",
    "#     N = normal(gamma);\n",
    "#     g = EvalW(gamma) .* normalC(gamma) - dotp(EvalG(gamma), N) .* N;\n",
    "#     gamma = resample( (gamma + dt*g)); \n",
    "#     if i == displist[k]   \n",
    "#         lw = 1\n",
    "#         if (i == 0) | (i == niter)\n",
    "#             lw = 4\n",
    "#         end\n",
    "#         cplot(gamma, \"r\", lw);\n",
    "#         k = k + 1;\n",
    "#         axis(\"equal\"); axis(\"off\");\n",
    "#     end\n",
    "# end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Medical Image Segmentation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "One can use a gradient-based metric to perform edge detection in medical\n",
    "images.\n",
    "\n",
    "Load an image $f$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "n = 256\n",
    "name = \"NtToolBox/src/data/cortex.png\"\n",
    "f = load_image(name, n);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x326c034d0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "imageplot(f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "An edge detector metric can be defined as a decreasing function of the\n",
    "gradient magnitude.\n",
    "$$ W(x) = \\psi( d \\star h_a(x) )\n",
    "      \\qwhereq d(x) = \\norm{\\nabla f(x)}. $$\n",
    "where $h_a$ is a blurring kernel of width $a>0$.\n",
    "\n",
    "Compute the magnitude of the gradient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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m+f5NTk4aSQlCx+XzefzoRz+64Fz09fXRq3O73UwsaTQa9LwCgQBWVlbeMjXm8Xjo4WmqsNPpkC7V3muz2YTX6zW0GHWqu1CAtVrtgl6YjFU8OZ/Px2el501USuQ5xGIxzrXuZu31eploMjIyglarRQ9tYGCAxdWBQIDp9efOnWNPM53VafH+h6UNLd7XiEQiOHToEABn4ZRFJ5PJkA7btm0b07pF3V2y5qrVKunFRCJBmkinvVerVaytrVGaaP/+/cxg63a7NJhaMknOLwZHi9wC56WkNn9FvF4vqblYLMbzyO8AhxYT6arN8Hq9NF59fX2GZJVcf2Njw1C2fyuQc+g0/l6vRwPV19fHOSiXy/B6vZx7t9vN430+Hw38ZkOolThcLhfvPZVK8ed6vW7E3LRh6e/vN56JloeSzcnY2BhGRkZ4jsXFRZ57eHiYz63dbjNONjc3R0No8f6HpQ0tLCwsLK4ovL73t4XFRUQ4HDb6bq2srDCIv7S0ZNBAUmsk2WyifTc8PExPZWNjg3TTzp076TF0u12MjIzQ82q1WtyBdzod7t7lsxpCoQUCAaMH2BtB6wcC51mAUqnE3+vaqwsdr2ky3d5EvA4Zx9vBG1Fn2tsSD0auL16Q1lLU3ppWEtmMXq/H+/F4PIZWoy5+1q1tVldXmZgRDoeZ/JHNZnnM3NwcgsEg352hoSG+I3NzcxQNHhkZYXF5tVrF8vLyL3x+FpcHrPGyuCQQ6imdTmP37t2Ml8zNzdF4DQ0NGSrwYmAikQhGR0e50GnVhZWVFS6o2iBFo1G43W4aj4WFBUNwV8dxZGGT30km4VuBlpiSxVorbLwZxGBms1karFwuxwX5UqJSqdBYBYNBFItFzslmw6eNmsx7s9lEr9cz7lXmulKp0PDqdPhEImHQeZFIxHgPJFXe6/WSVna5XFhcXDRUQkRdpdFoMCbZ7XaZ0h8IBNBsNplpanH5wtKGFhYWFhZbDjZhw+Kiw+12M5h+++23I5lMUtKpVCqRBnK73dxld7tdUoPVahW1Wo07+1arxcQBnRUHnE+SEKpRi8cKtITT+xFCeZXLZdKoUsN0qSD0oMvlesfFvm6326AKhQLM5XL0vAKBgNG7TCeNuFwuI1FGasE6nQ7W1tbolQHnvWXdrqVWqzHbcf/+/cjlcnjyyScBOPSkbavy/sU7MT+WNrS4aBB6J5FI4PDhwwAc6mhubo6Zd4ODgzQkui9VPB7nIrO2tmbEvHQh7maRVlnshTIUKlHHUSRO8n6FpPen02lDaPdS4pelN38ZdLtdzrXH4+Hz0in5kskpBqdardLgFYtF3ne9XjdU8n0+Hz+nKUVNfabTaW5uZmZmMD09jVtvvRWAo3QiJRVvlOpvsTVhjZfFRYHH42ENz44dO5ja/tprr+HMmTM0ZrOzs0b6tHhobrebwqtDQ0PY2Ngw2pBs9rgEog4hC5n8P5lMsj7o/Q7xRHV7lq0GbRh0B2rZ0MhntOq/eFTBYJDH6KQZOYd45LosoVKpGCn0EguTzZLEUvfs2cN35+TJkzaR4zKCjXlZWFhYWGw5WM/L4qJgcHCQun7btm3D8ePHATi74gMHDtBDCoVC3Al3Oh2mvfv9fnpu2WwWw8PD3IHXajUjNV1DqEbZncsxgUDgfR3nEvj9fuzduxcAcPToUezatet1fwfM2FQkEuH9avURwLlvoe3y+Ty9k4tJE74ZxLvx+/0cWyAQQCwW43vQ7Xb5rDZ7WkIXS4bjwsICACejVLy1gYEBXqdQKOD06dM8xuv1kl4OBAJMye/1enj11Vd5fYutDWu8LN4RxODs3LmTC+qpU6fY+2nPnj04d+4cFyi/38+FtF6v03jt2bMHJ0+eBOBILi0sLHDh1b2s3gg+nw/dbpeJCFo14lKrj0uCQbvd5r3pFHr5t4amNyXm5fV6ea5AIGCko2tV9263y/T+zV2e2+22UQoghsDtdvNcm2WxLjZk0xCLxQyJL11DBpzfeLRaLcbCwuGwkZIfDAZ53zptPhaLGQLL8vvFxUUMDw/zvfJ6vaz9S6VS7DTwfo+DWrw5LG1oYWFhYbHlYD0vi7eNUCiEnTt3AnB2zELVnDx5ku3s2+022u02Pa9KpcIdd7lcZsLGysoKKaFsNmtoELpcrjf1vOr1OjweD3fjejd/KREKhQwKSuv96Z83Q7wlXSBdKBRIs4VCITQaDX6u3W4b55P71PcoWobyuUajwbG53W5De/FSQq6vMwc3j028RMD0Knu9HpM/IpEI29YAjscpXl2v1+O709fXRzoyGAxibW2NLIDWl9y1axdb3qyvr9vkjS0Oa7ws3ja2bdvG3k3ZbJYiu8lkknTi7OysIaeUy+W4iIoqBuAYMjnXiRMn4Ha7SQX1er03jVHUajX4fD7SVLVa7XU01cWEFq+VxVXXO+nPACZtqA1bvV7nmD0eD6lSycCTc7TbbWMOZD59Pp9R26azMmOxmNErTObjUtOGAlHikLFpiSm/30/joedN9xOT1Ho5JhAI8JhKpcLPjY2NMduwXC6jWCyyhCIcDlNtY/v27di9ezcAp+GpUIsWWxOWNrSwsLCw2HKwnpfFW4bseO+66y52C3755ZdJ40xOThpej6bGdu7cSU+lVCrR09ixYwdOnDjBz/n9fkOP8M2SLoSe1Eke4oVo+uxiQc7dbrcNZRDtYW2mOiV5IhqNsqg3Eomwf1U8HmfNF+BQW5oyEw+t1+sZ3qvMTa/XQ6PRoGfVaDQMfcc3qpW7lNDUnFa68Pv9Rl83mcNms2m0dAkGg9R7LJVKr+uCDTjv1/79+wE4yiTBYJDJKdu3b+fnlpeXcf311wMA7r77bvznf/4nAJt5uFVh5aEs3jJ+67d+C4Cj9v6v//qvAJxFVBZhiV8AwJEjR3DVVVcxjvFGLee1hJP8TveieqvQVNTFkED6ZRAOhxm3SyaTvJ96vY5kMkkaNJvNUikinU5T2qher2Nubg6As9AGAgHOhahNAM7CrbP45FwejweJRIKxx1qtRvpMi+Tm8/n3hXCtGCWv18v3Q8uCiRqL0MmFQoGfq1QqvLdoNMoYq8RKRR5qYmKCBcter5d09qFDh3Ds2DEAwIMPPnjJ79XiwrD9vCwsLCwsrihYz8vil4LM94033oiPfOQjAID//u//Jn3l9/v5mVarxaLRwcFBbGxs0BvTbUs0tafbm7xRQfI7gfbwLga0tJF4NIVCgdRpNBrlfTQaDcTjccRiMQDOfQuVWiqV2BpEZxG+WYG11hKUc/X19SEcDpOeTKVSTEpYXl6mJxsMBukBX4q5fqsYGhoiVdjpdOg5ptNpI/lC19GVSiV6n36/n1JgO3fupCcKmBmt6XSaBc+33347n8eRI0dw9uzZd8U7tzDxTsyPNV4WbwqXy0Xq5Y//+I/x8MMPA3AWBlFEFwVwwMkwlEVYFkcxTo1Gg4bE4/EY8Qah1d5JI8YLQafQN5vNt2XAtGp6KBTiYuv3+2mYNR3o9XqplvHBD34Q7XYbS0tLAJz5EdquWCy+LYV3odK0pmAgEEAoFKJh09mcjUaDxdCtVovak41GA+fOneN53qsFXDZB4XCYRkneHTHkgUDAMMyCQqHA+RT9Q9kU7dmzh7RsJBKhkZudnaWyydLSEp577jnGCq0Re/dgjZfFJUUoFMI111wDAJiensa3v/1tAMCtt97Kl29ubo67Wq2iIRJB2njIouTxeLi41ut1o6njxUQkEuE5o9EojWOj0fiFtT5iTL1er/G+1Wo1Gqw9e/awEWI6naaaQ39/P72z48ePo1AoGLVZslBqg5fNZumxVioVbNu2DQcPHgQAHDx4EPv27eO5T506BcCZ94ceegiAEyN87bXXaAiazSY9r16vx0VcJ3y43W7Mzc1xcxGLxfi3TqdDD63ZbBobkrezbLhcLhqmQCDAOdAbmFQqRcMq15ax6ZKLaDRKjyoej3Pj1O124XK5+LzW1tYY5xoeHuYzmZ2dpSHcu3cvXnrpJXrAVn3+3YONeVlYWFhYXFGwqfIWvxB+vx+xWIw0zalTp4wsL/EAVldXSbf4fD7uXsXT0dSY7L6lcBUwe3bp+NfFgMvlohdVq9V+YWq00KPBYJCxJCmABpzd/3XXXYdbbrkFgLNz1Ons4n2eOXMGL730EgBn99/r9eiVDQwMMN4Si8XoXVUqFSpCTE1N4c4776SnUK/X8eMf/xiAo0YiO9ZUKkXViEAggD179tDTCIfDpNwymQxpy5deeskoQ9AF3Zqy9fv99Iy9Xu/rdsni3WjdxDeCxPNk7vUzCIfDhhclz8rtdhvFyM1mk+9epVKhZ5ZMJpm5OD8/j3K5zHnz+/308DqdDmnusbExZna2222EQiG+g9bz2hqwxsviFyISiSCVSnEBmZmZwdVXXw3AWdSFamm1WqzVabVajLsEAgHDSPl8PqOOR34WNXA578VEq9UyOvrKWER1QovCalUPWZC1Usbhw4dxww03kCo8ffo0jUI+n+d8LCwsYHp6GgBw9dVXo1AocLFcW1sjZbV9+3YuqIcPH2Y88a677sJVV11F1ZJnnnkGjz32GACnJk6M6dLSEhfuZrOJiYkJPqtIJEJjHIvFaDBDoRDOnTsH4HxTSLnHXq/H2Njo6KghbqypU03N/bIUfq/Xu2DdWTAYpOHw+XykciXtXe5HJ/jE43HSrcVikTHAWCzGTtyAY3R1kofcWzwep9p8sVhENBrlM8nn8++qCr/F24OlDS0sLCwsthys52VxQchuWihD2bH29fVRH+7JJ59k9pbur9TtdpnQIB2NZVfb6XQuqLfXbDbprV1sNBoNUns+n4+790gkAq/XywSFZDKJs2fPAnBEXOVzy8vL9Db/4i/+Aq1WC//wD/8AADh27BhuuOEGAE5BrHhb9Xodzz33HACnFf3ExIRBuwmtNTg4iB/+8IcAgA9/+MOkEO+99158/etfx7/9278BcBQh/vzP/xwA8Oyzz+LIkSMAnOchSQwulwuNRoMqHZlMhjTk+vo6JicnAQCf+tSnWNS7tLSEhx56CE899RQAJ3PvwIEDABzKTTyYcDhMmk48KE0pvlmGnqZXAed56zmQv507d844r7SGkfHIOxYKhTAyMgLA8cjkeKE6hfL1+XwGDSnPd2pqiqLSr7zyCiYnJ3kP5XLZKKa3eH/iisk2DAQChrjpFr3tdw1ifG666SYMDg7i6NGjAIBrr72WvZCOHj1q1NDIgpHJZEjTyUInFM36+jrpxWAwyHiEfp5iKC8WkskkF2FNV/l8Pvj9fo4nFApxATtx4gQ+9rGPAXAMhyzoMzMzuP/++3HnnXcCcGKAYki04K1WcV9aWsLo6KihEC+xqM997nN45ZVXAAC/8Ru/gRdeeAEAsG/fPjzxxBO49tprATiZd6IEsbS0RJqtVCrxWQn1qmOPEmeLxWIGLSu02KFDh3DPPffQsK2vr5O6vP/++41mn7Kgu91ulMvlX6qkQd4Pqe+7UP3a5OQkKU1tFAHHsMjGR5cS6LrCfD5PYd5IJIK5uTluqqR8AIDRpHJwcBCf/OQnAQAPPfQQJiYmuDasrq6ymerljotd//hWYbMNLSwsLCyuKFz2npfObNvc6dbijXHHHXcAcLyj+fl57l4PHz6Mr33tawCcuZUd7+LiIuc6EonQu1ldXUU8Hqd3oAVZpWcVAHocFxNCSwUCASZSHDx4EDfffDMAsJ5Ixrp9+3bqM46Pj7Nl/IMPPshMv/379yOXy1GQuFAokMrqdDr0bvx+P+cjGAyi2+3yc81mk8kGt9xyC2ux4vE4duzYAcChZD/2sY+x+Pbxxx9nndfMzAzf/1qtxnO53W50u12jPk3ed6/XS++mr6+PnnA4HDbqufbv349PfepTnKvHH38cAPC1r32Nz8jv96NerxtelNxrKBTi/SQSCXq8kvEp3prX6yXtl0gkeH0tdJzNZtHf388arsHBQXpHa2trnANd81UoFIyWM61Wi/OumRePx0O6NxgMIpPJ0OOLRCKkF+U5X47weDycw/cfTz24AAAgAElEQVSqMNsWKVtcVGzfvh3XXXcdAEctvtvtUhLq3LlzeOSRRwCAGXeAk6Isi6iWTBoeHsa+fftITzzxxBN8Yfv6+riAHTly5JKlKE9MTOC+++4DAHz605/mOPP5PAqFAhfY06dPM/Zz4sQJZuql02nez9raGhc2wInv6Z5bWvld4Ha7EQgEaEg6nQ6vOT4+bmRpyiYhn89jamoKi4uLABx6UijAUCjEDMd0Ok1j4XK50Ol0jAxOGUen0+HCHQ6HuZkIhUIYGBhgxmI4HOZiH4/H8aEPfQiAQy/++7//OwDg5z//OQKBAM9RqVRIfUajUcbZgsGgEb/yer2kVgcHB3mv3W6XNF+1WuV9jo2Noa+vjwvr3Nwc51B3LQgEAqQ3M5kMIpGIIUGme6/Jz7lcjgZ8amoKx44d47Obnp4mBS50ucWlgaUNLSwsLCyuKNhsQ4vXYWpqinRJpVLBNddcw+LbRx99lMH92dlZg6ISWqper3OXH4lEMDQ0RPorn88zyysYDDI5QwfpfxGEGnsj6DogSar4wAc+wN//0R/9kVEs3Gq16A1obyIej5PKymQy3JV7vV50u13SVLqHl8/n49g6nQ5/L+1RdNabzJXf7ydV+cILL5CGDQaDmJ2dZYJBr9ejh1UqlUiJlkolQ1w3GAzyHlqtlpEkIse0222ObXV1Faurq+ylFgqFWAi8e/du/L//9/8AAJ/4xCdw8uRJAE42XrvdJgUYiUR4vna7zYxJr9dL72Z8fBzDw8P0mFZWVvCTn/wEgJMkopNo5J0QL0rO3ev1eA+1Wo3ea71e59y2Wi24XC56s71ej+Msl8tGdqvMbblcNkR7M5kM33G/329kSVq8f2CNlwUhC2o0GsUzzzwDwKF31tfX2ftoamqKi2gwGCTFlM/nuTD4fD7GZ6anp/HQQw8xs2vXrl00ZPV63WhI+Ivwyxi3cDhM+uvmm29mTOb73/8+aalsNssYyquvvmpw/W63G+vr6wBeL+Ar9xaLxZBIJAwRV536Lz97PB4avHa7jWg0arSw17S3UIOJRIKU5srKCiYnJ7nw6s/r9PhUKmUYxXq9zntqNpv8m8/n4/3o5qAulwvdbtcQUNaFvGLAZ2ZmeM9SOCzPTmcL6iaiupB5bm4Ox48f57+vu+46/Mqv/AoAJ6YohkPPtcvlQrlcpjEeGRnhOHu9nmEwtcHWG4XNNKourJbf5/N5hMNh3sPGxgabVqZSKcZLLd5fsMbLghgaGgLg1EWJ5JDL5cLCwgJ3ou12mwtDs9k0aqb0Ii5ot9uYnp42zi2xrWazSaP1Zt1s34wbTyQS2LFjBxMePB4PZmZmADiLkd49i4GQBB59ba2qcaGFzu/3o1gsGiUXMh/AeTFfURYBHGORTCa503e73UbtksSIdLp2tVpFIBBg7Zvb7WYMLpVKGZ6SQERpL2Q8tFiyjr9JTEh7N4JcLsfnMzs7yxIJ6dgs5ygUCjTUHo+Hmxvt1WazWayvrxtCyFKKcODAAf5+bW2NxlcMq8xJLpejwfR4PIZ3pee92WwaRl/eUa/Xy2cfCoV4b9KyR4xXJpOhkRwYGODGx6rNv79gY14WFhYWFlsO1vOyICR1fHl5mXGYxcVF5HI5HDp0CICjFrFt2zYAjvisQCsh1Go17lY7nQ61/QBnZy07Xq1192bZo2/keYlnsmPHDlx//fWMsTz55JPMCtSFr1orT36vFSpkN681EHULkE6nA4/HY3hoQll5vV56BloNolqtIhQKGanlsosPhUI897Zt2+iFHThwALlcjp5VJBJhvMfr9TJup2M6cj8yl9ojdLlcxn3L9TfPv/7b2toarz8/P096s7+/3/BuZmZmOG9ut9uIb8r5U6kUdu7cyVihjjl94AMfMChJoSpFd1LOHQ6HOb9aVUPrFK6trWF1ddWgDeWYSCTCdy8ejxsxs263S8+r2+0ym3NiYoLxX12EbvHewxqvSwy90L3fIdTeM888wxqYfD6PdDrNxWDnzp1UPNCK341Gg7+PRqOkZyRe8D//8z8AHMN2IUPkcrloiD7/+c9jcnKS8krHjh2jQK2mzwYGBvAHf/AHABxppZ/85Cf4x3/8R/5NFvhGo8EF2ev1ctHTsRLAWdyE0my1WvybpkQ7nQ6azaahCCHGz+12GwZD5iMcDqPZbPLcWqHd5/NxUdyzZw/7ee3atQurq6t8DrfccgvFdJ9//nnjGci9eTweJBIJ0mSlUokGxuPxGGoKYhDK5TK63S4No8TN5FlJfLBUKvGYTqeDdrvN862urvIefD4fz5VMJvnu12o1lMtlxtNuueUWbn4OHDiAX//1X+f9yHP/2c9+BpfLZaj2i8HT49ExwFarhXQ6zX8PDg7yZ7/fb4gYyzMIh8PI5XI838TEBN+3m266iRS6ULUW7w9Y2tDCwsLCYsvBel6XCDpjaitgeHiYdM3g4CB3xULbPP/88wCc4Lzcm+7BFQgESBFpemzv3r1vqGk3NDREzcBYLMYMr4GBAXz605/GvffeC8DZZcvYyuUylR5GRkZYKP2Nb3wD3/3ud1n0XKlUeM1sNkv6q7+/n5RosVhEsVhk6v7w8DBee+01AA79JN6j7jzs9XqRTCbpacRiMWbvlctlzon0QQMcWkprHTabTYO2k3kbGxvjee+66y7UajVD9UEot/HxcVJzHo+Hnqj24uRv4gk2Gg0mPvh8PkN4uVKp8B40bVir1XgP+j3O5/Pw+/28biAQMLINxfNaXl7mHLZaLUOw+ciRI9Rt/MY3vsH+aLfffjs++9nPAnC8s29961s8RzKZ5HswNDREj0xnVe7ZswelUonJOoVCgfddq9UoWjw8PMx76na7OH78ODNNo9Eo72FtbY2MhPW83l+wxusSYatQhYL+/n7GNDwej5EerBs4avV3vaC53W7GeFwuF+uVGo0GXnzxReNaUgd011134e677wbgUEdyvr/5m7/BX//1X/Oa8/PzNJ7RaJTZbF/84hfxox/9iL+/5ZZbuLidOXOG9Fk4HGacbmlpiYtzNBpFp9Ph+TR1pDPYer2eIXO0bds2I2tN40J1Xvl8Hj6fj4ut7iGma5Ty+Tw+/vGPc8yPP/441d8HBgZ4LZ3yrTM+Q6EQSqWSIYosFKCW5dr8GZ0BuJn2E2OorxmNRtFoNEgBhsNhjsHv9/M9WltbM1L19TzqEoPDhw/j+9//PgCnfEFUPX7t134NX/7yl/HNb34TAPD1r3/daJop1Knf72evtIGBAWSzWRpWv9/P572+vs77qdfrfI+TySRisRjfg4WFBWzfvh2AIwz80Y9+lPMmlKbFew9LG1pYWFhYbDlYz+sKh+xkR0dHuZOemZnh7lsKWHVnZNnJ1ut17ri73S49i1Qqxd8/++yzxvWuvvpqBuc/8IEPMJHjd3/3d7mTPnToEHbu3EnqstVqsVOuz+djEsGzzz7LYzY2NrCxsWEUTeuAvHhEOruvUqmwNgowk0ni8bjRn0wnYmivCgAz3TQd2Gw2Df1Aj8dzwSSLRqNBqnNhYYF9w+bn5zE1NYVrrrkGgLPrf/TRRwE4VJjuTybeRCKRgNvtptevBZJLpRLvIRKJGF7gZm9avEqtEbi5rkoXNrdaLfT19fHexPv1+XxGQky73ab3mEqleHypVCL9m0wmmbTyjW98A3feeSd+53d+B4BDKX7lK18B4GS9yvGBQIB1iCsrK4aHl8lkXqeDCDjvh3illUoF27ZtYzJINpslDdrf38/7kfu3eH/AGq8rHELvpVIpxj3Gx8eZKgw4C6yWR9JK1LI4aikiTR1JerIsnH/yJ3/Cn++//34aot///d+nuOvp06fxgx/8gMZUmhICDj0pi9HPf/5zFiVnMhm0221KG4XDYRbV6uLSbrfLWFiv10MgEDDEdGVBLJfLpNY0PSoq7LIodzodnq/T6XBBDIfDnM96vY5kMslsQ11I7PV6+fvXXnuN8ZWHH37YKEZ++eWXuXjGYjFDpUTur1gsotls0lB3u11jPHI/1WrVoAp1mUOr1TI6L8i96+LyYDAIl8vFeQsEAjR43W7XKCPQRnZz+YAY3ZWVFRqbcrnM2J7P58ODDz6Il156CYDT42zv3r0AnHiazEGr1eJcN5tN435ErFjmWjYQxWKRc722tmZIezWbTZ57ZGSElOTU1BTfdy2xZfHewNKGFhYWFhZbDtbzuoLh8XhIt+iuuOFw2KCLXC4XKZVAIGDIKcluvl6vG7SSLjQFwCB8f38//u///g+Aozn4xS9+EQDw1FNPUU+xWCwaWXO6TisYDBqadlqKqFgs0lMIBoOGtyj34/P5OKZarQafz8fduE5+qNfrRtKN/Cz9qnQNmZ4r3T9Od4QOhUJGvZKmsgT1ep2JMrOzs3C5XLy/5eVlesm6b1in0zE8QxEO3oxut2tkOOq+VpoG1XVV9XrdmGtNEfv9fkNvUs6nC7U9Ho8hihsIBOh5acHbWq3GY7xeL72o+fl5bN++HS+//DKPEW/p2muv5RxubGzwOs1m0ygc1/JfuuZS91e70Dst8y4JIICZhZjP5w3v1eLdhzVeVyDkSx8MBrkIP//884y9VKtVQ18OgJFJKF90bUh080Wdli06eqJjt7i4SDXxj370o1yofvSjH3EsssBo2k7Go/sz6YJawFmQxOgFg0EjNV0XqmodPP1/r9driLjKPPV6PUOdXRfolstlQxhXawTKHMgxcj86tVs3SCwUClQmWV9fR39/PxdRr9drNLPUOoUyh7LR0IZR9xrT86bpL00Fa8HbVqtl3JvMZ7VaNfqYtVotHtNsNrnAdzodjlloQ63kIVRjo9EwsjblmYrCx+HDhwE4tOquXbsAOBSeGKhHHnmEhjAajaJarXJDogvCNY2pe4tJ0bWmS4XO3rFjB59bpVLhO1qr1azxeo9hjdcVCFms+/v7+cXe2NhgOrl4JMD5FhMCrSYeiUS4uKbTaX5Od6Vtt9vYsWMHfvM3fxMA8IUvfIGLzsDAAL7zne8AcOpzJL4TjUaNrrvaI9IehKRfy8/hcJgeolbP0Iaj0+nwXCLiKouWz+dj7EUbIr2IN5tNpFIpxrn0eDYL+ErQX+JFOsFBvNRGo0Hj0263WYMmcSntKWgDrssA5Hg9H5vv2+fzGfct3oQYMpnrbrdrKGnoBpby3shiL/cTDAaNOdwcf5K5qVQqRusSkcISBRI5Rntnx44do8c5MDDApJVPf/rTuOeeewA4rVu+/OUv8571//UcauOpPeF2u42VlRUj3V/GkMvlmCx09uxZbvDy+Tzfla1WFnO5wMa8LCwsLCy2HKzndQVCKJXR0VGqVezbt4+qBFpQNRQKGZ6Xy+Uy4hOyE3W5XNyJtlotg1J59NFH8cQTTwBwYjf79+8H4Ijnys7+5MmT3GFvbGwYahX6+vF43BBx1aoR8Xicu2fgPGVWq9WMjEPxyIQClXHrrDndE0rTcMFg0MimjMfjRjxOimNjsRjH6XK5DGpMp4zL2AEzDhQKhYzyA+3RxGIx0lq6J5p4RHo88jcAzBbUtG44HDYKlTdn0Omia930cvPnxFvTHm8wGOSYQ6EQQqEQz+H1eum9bhYs1uceGhqit/Wnf/qnzDz8j//4DyOFXs77ve99D6dPnzbuR9O38k7E43FmprbbbWQyGeO68h05d+4cbr/9dgBODE5ibvF4nOOWd8bi3YU1XlcYvF4va3KGhoZw6tQpAI6iuVBJiUSCi06j0UCz2eSirJMScrmcscALfeLxeLh4fOc730G5XGZ9zg033ICnnnoKgCO3oxsaivCsiMteKLZWLBaNNPPNC4fQX6VSife5ubZLPtPr9eDxeLjYSyxHIAudGAU51/LyshEnE1pJG4pKpcLPJBIJJhIApgH2er2s7XK73Yx5pdNp7N69m/N+7NgxJtd0Oh3etxYa7nQ66OvrM1L0ZdyBQMBIWpG5kQ2Apol1qrsYWS1VJb3KdImApifl+oFAwKgzSyaTpEVXV1dZ5rC+vs5zNRoNbhakfEPGraW8HnjgATzwwAMAnNIOUcFIJBL4q7/6K441FosZqh7yTIrFIuWgYrGYkajidrtZ97a4uMi5np6e5ji9Xi8NtjVe7w0sbWhhYWFhseXg6m3RSrutInj7fsPExASLQD0eD6mTWCxGCrHVahm70kAgYOjvacFZeQ7JZJI73OXlZapo3H///ZiensZ9993Hf4uH1dfXZyRf6EJkXUirqTCdDac7AkciESN9u9VqkdKcn583MvW0yG673ea4NUVaKBTonQDgZzweD3q9HumjXq/HMVSrVUMDUTy8UCiEer1OUdhoNMrjr7nmGs7H6uoq6aqFhQXceOON9LwKhQKTUY4cOcJEGS2O7PP5jOSScrlML0ZTkvV6nc9d+pPJ33Q2qZ4raQUjc6AzFHWX6nA4bGQuynxEo1EEg0F6nFdddRWvc+7cOUMtQ3trg4OD9Lbuvvtu/PjHPwYAHD9+nM90cHAQX/jCFwAAt956K77yla/gG9/4BgBwzuX5COLxOOdadBrlui6Xi/Ou38OPfOQjVIyJRCJ8D1977TXep8VbwzsxP5Y2vMKQSCT4ZTx9+jQztr71rW/htttuAwA8/fTTBiWi6TC9OOoeXMVikYvD8PAwF4+//du/xWc+8xk8/fTTAJx4lhyjM/D04io0joxTp1zrVPBqtcqxiXiwrjGSBT6bzXLMWtYIcAyLTgcXgxMMBmkser2eEdPx+XxUINF1Y5py1FScKO4LvVQoFEjRalps9+7dzPiMxWJYXFzk5zKZDGvAhHqTOdANFl0uFxdlHesLBAK8B03xbqbmtOK83rRcqJ+XfE7Pga6P6/V6jH81Gg2USiVuKBYXFw0aUp69fjbpdBp9fX2kS48fP47jx49zDHJ8uVzGT3/6UwDOZuDAgQPsUDAzM8PnEI1G+Yw2NjY4Tp2hKueW8YyMjPAZ6FihlkzTWaoW7x4sbWhhYWFhseVgPa8rCOFwGB6Ph8oP/f397F+VTCYZaPd6vUbL+F6vR48mFovRg9A7c9HvA5zi41dffRUA8Pd///f4wz/8Q+6YpeU6cD5hQq6pz6WLSwGzP5oc73a7ueOVIl7dLVgoL5/PZ9Ti6MJquXfAoUTlmHK5TG9PK3S0223EYjFDUUKoO10z1ul0jJoxrfkXCATokejkgFKpxGezsrKCVCrFc2xsbLC779TUFOcqFovRAwmHw4bgbDAY5D3oQmJ9XnnmMh5dfKxFfnUBtyR5aOUKXQena/I03SrqJIDjuQh9renncDhMWjoSiaDVarGlTrfbJd1ZqVToMQEOlQoAjz32mFFY3O12mWWp1VS0RmYgEEC1WjU8NA2Zm6WlJd5nsVjk8ZFIxCZtvAewxusKwvDwMFqtFr/0u3bt4oIYj8e5cG6OJ2raLhQKGTSioF6vs7ngddddh3/5l38BANxzzz04deoUs+i0koEu6tWLo6i9a4OllT50OrxWe9dKGHoRBc4bP52KLT27dJakQNNi+ryyUGsVdr2oy2KtjYq0nJfFXiuG9Ho9Po9Go0FqUHphycLbbrcZv9FUoS689fl8CIVCvK7L5eIc6I2ClkMqFAqIxWKGGokYPy1qqzcNEneU624uYtfPQz8nbdAjkYhRGC0GS2JjgPNO5fN5GpxoNMrPAeeLg9vtNinrY8eO4dChQ6Qnz5w5Q9pP05PtdpvXF6Fl/S5qBRShS9fW1ji2XC7HTUsqlcLq6uoFZbksLh0sbWhhYWFhseVgPa8rAOIpjY6OYm5ujjvGaDTKos/p6WnK9XS7XWPXrItYa7UaqRtdFzU4OIjh4WEAjtfxv//7vwAcOaivfvWrHEOj0TA8Ik3nybmkAFTLBMkxWrhV1/BId2JNZWkBXi3Uqr0wnaSxmVrUnpIuhtY1PtVqlbt+8WKA80WuwPnaM+0VCqLRqCFuLBJZiUQCZ86coTecSCQMb0+y4ZrNJj036Rsmz25z3zFBs9k0aqm0F6VlsTbr/enCX50443K5DKFg3TtNy1tparler5OKTSQSfHe0VmMmk0E0GuWzbzQafPeSySSf6eLiIj8jgsZjY2Mcg5bskuLuQCBgvDvBYNAQTtZet/a8hOqUpCLAka2yGYfvPqzxugIgadnJZBLPPfcceyL1ej2D35fFpNPp8Pd+v9/oC6Xb1o+MjLBn1tjYGBfhU6dO4Y477gAAvPjiixgaGqJ6x+joqFEULLRYpVIxYjc6BVwrgAeDQaMxpvzcaDQMVQy9aGsxXl1w7ff70ev1WBbQ19dnxKkuRDtqTUHAWTjlmFQqxd/rmJ1Qe7LYakMwPz/PBT2bzdLoSRGwnGPzwigp51qto1gsIp1OGzSmpuZk7HquZWw6VqezJOWd0GLC1WrV6Jnldrs57m63a/TMkrHJfMo5Go0Gi5SnpqZogE+fPs3PHDp0CMVi0Sg5kHNHIhGOWeJo8vP6+jp2794NwNmUaYp2YmICgBNDlHMVCgXjHalWq8Y7JnMQjUZ5TDAY5HWTyST6+/uxsLAAi3cPlja0sLCwsNhysJ7XFQBpKfHjH/8Y1157LWmuEydOMAng7Nmzxu5Zdt/NZhPVapVew+DgICmZQCBAeSktU3Tu3Dl6WrlcDvl8ngW/s7OzPHcsFmPNUl9fH72JUqmEdrtt0FSbe0kB570T4HzQXddsaS9K1xTJTl6yE8UTy+fz9Ph04oFWWo9Go4hGo4Zmn9yD7ja8vr5uZLzJ/cq5dU2ReBCxWIw/Dw4OIpvNXlC6Kh6PMyFBa0j6fD40m01mvmlZLT22UChkHKd7gElWIACjK7OmzyTxQteNXUiBXyfTtNttNJtNvkdTU1N8j06ePEk6b3x8nF5PtVrF4uIi36uBgQHOoWg/AqYnmcvlcPToUXr+9913HwuLH3zwQdKwtVqN7U2CwSByuZxBCcrnGo0GPeNqtWrUJWoq/aqrrrKe17sMa7wuc0iGIeCI766srBhfTE2N6QVMjEKr1YLf7zeKR0Vk97777mNvrsnJSYyOjgJwDKEsMjMzMzwH4FCYsug1m01SL7lczugJlUgk+DkZB2AaLJ1pJ8ZT02uavtI0pC6y1q09dNq7NhZa1aPb7WJ9fd3QExRD1mq1jH5Ruu1JKBQyYiy6cafc2+7du5n9mU6nUalUDJpMt5yRY5aWlhgvkr5lMgbdzkYXEuuiWjFwsvhrMeBQKMQNRa/XM2jlSCTCd0cX9WoDrPuoifGT+4nH4zhz5gwAh3bTBkuMgBQ8a7ULof0CgQAzM6vVKuczFovhe9/7Hsd922234dChQwCc9+W73/0u50bo4tHRUWSzWY41nU7zfPl83qCc5TPJZJK/n5mZwe23347Z2VkA4DO0uLSwxusyx8GDB+kdDQwMYGNjw1i45Ausd9+BQMBo6qhjFfF4HDfddBMAJ0azb98+AM6OWXb2Tz75JG6++WYAzgIUjUbpDejU8v7+fgwMDAAwU9Olp5MYqVqtRmOoY0m6PqjZbBpJBD6fz6jvEQOj5Zxk8dU1bTIfOp280+lwLMlkEqVSyUhEkIU7GAwacS25z76+PsRiMZw9exaAEyvUmwFZ0G+44QYmbHzwgx/E4cOHqaj+/PPPU3Vfe7IHDx40ZI86nQ49S12PpufK6/VynLpEQT6n43rao5Lr9Ho9o15PvF55jpKaLvFSuY5O4JidnTVS4i+UJCJNJeUct99+O721Y8eO4fnnnwfglHyIt+j3++H3+9mVu1KpsIFlMpmkJ9vf3893slgsIhqN8plks1mOp1Ao0PPq7+9nUtPIyAifQTabhcvlogdujde7AxvzsrCwsLDYcrCe12UKiYlI7AR4ffGv7rek0511IW+j0UCj0SCddubMGZ77ueeew+c+9zl+TuJc8XicXk80GjV205q+q9Vq9BI0lSWpyjLOUCjEbLREImG06dCxI+1BaKUI4Hx7E4/HY1BZmjaVcWyGFovtdDoIh8NGPE2nrcv9ADBS8BuNBrM+O50OKa8PfehDnLdkMokPf/jDAJwsRlElARxBZdE9LBaLRksUmWtpVyMeQC6Xo1cobUxkzFpJJBgM8t86ltRoNPju+Hw+g1rUsbpWq2XQrQKdqi8eqk69161TdOdtmTcpi9Btd5588kkAjvizUIipVIpZr8Fg0OgQvry8zOeTTqfpRYkWJuDEWP1+P9+lbrdrZIAKtb1t2zbOZyaT4fMcHh7GqVOnjHR/7VlbXBpY43UZwu1244YbbgDgLGASixL1coFWXQiHw6QKw+GwoRbQ6/WM2iRZLAEn8A44yR/C+Y+OjnJxFpUH3ZZdFtFSqcSFSat0C8Wl5Z10SrxOhNAKEBq6p5imqzwej3G82+2+YCPGRqNhGHM5vlwuG1RhPB43aC6tji60mChvSELA+vo6F9RQKMTfN5tNKqi/+uqr2Lt3r5EAIs/x+PHjnBtNYYpBkbmKxWKGQocco+v4gsGgESf0+/083+bfi2HyeDwG/auTW6TeTuZAIOr9Ot6oDasYLF2Tp6lqwDFEQsmFw2FeR5qXyvEDAwM8Zm5ujga40+kYCUoyT0KJamUS3QRU3q18Ps9j1tfXOZ9jY2OYmZnB9u3bOTZrvC49LG1oYWFhYbHlYD2vywiyc4xEIpiengYA/OAHP8BHPvIRAE7xsLT0AMw28V6vl9TcZqUJnRGXTqe5Sx4ZGeFONpPJMN15enqamWTtdtvQQmy324bGniQrbG6fobsXu91u7uI3a+rp3bL8HTA9L+B8JqXOUBQvUHb4rVbL0LfTRbhyD9KjStNc4pHoVHDxTuTaqVSK4ykUCqS8yuUyEzHkHIDT7yoajVLgOJfL8fhkMsldf7VaZZIJYHouwWCQY6jX6xyz/lk0/cRz0eoStVrN0EbUHaxlXuQc8qx0en40GjUSPnS7FJ1GL/Mo8yb3thkiIi3jETqvUCjQ0wkGg1hdXeX773K5+IOa/VUAACAASURBVLl6vW70opN3b2Njw3gvtYqL9h5zuRzT6/1+/+vOq9vMSEavxaWDNV6XEWShGR0dNWI30qZ+dXUVvV6PBmfbtm38ws3Pzxv1PfKllXR6+aJLS3vASb2Xz2UyGWZf+f1+Uk4Sl7qQeobP5zPS0eX66XQaxWKRi4OuHYrH4waFqRXQN6vHa6V0WXQ0hdloNAwDqBfNarXKhU6nmUs8Q0tPyTXD4TCNXDweN2q0gPMK7uFwmH9bWFjAJz7xCQDOovnYY4/xGWQyGWbX3XTTTZzTtbU1Hj82NsYYpEgrCf2r69u0ALGeT+nzJce4XC4+Hz03ej5EOkun1MvYxsbGDPUO+YzeCACOsdJyV7rvmDw3qaXSwsUyv7ofl5Z6isViOHPmDClW4Hy/rkqlwnNLJiNwPiNWbzY05avnQ+bN7/cz83Bubg4HDhzgvycmJphZanHpYGlDCwsLC4stB+t5XUaQIPWBAwfw0EMP8eejR48CcILMu3bt4o5zdXWVO97R0VGjc/HmBAjxqkZGRhg0/+hHP0oPb2BggDvptbU17opHRkaMBI9IJMLdc7vdpnel+0MB5+u25HPitXS7XYO20mobWhlEZ49JxqRAPKFQKIRQKMRza/0+n8/HYyQbDXAyyxKJBHf62pPTfa2kmBkArr76aszPzxsZijoTUQpin3nmGXrJiUQCTz31FAt2z5w5w/no7++n9xyPx1kbJq1r5Fnl83lDDFiuH41GDS8sk8kYCSRyHa2s4nK5OB+tVotKI3Jd8coGBgb4vJeXl/kZUeGQ6/b19dF71fOuaUfRNZTsyVqtZiibyOd0XznJ+FxZWQHgZAtKO55bb73VqE0TSCalzFW73abuYjab5bPXhcxa3Hh+fh4f//jHMTc3B8BhJPbv3w/Aoeo1U2Bx8WCN12UCEQcFnIVGFxn/13/9F4DzlJ186fv7+5nddvToUX5JdSq1y+WC3+83lB+E+vmzP/szUl65XI6xm0wmQ2HU5eVlQ7BWx6xarRYNZqVS4cIUj8eNhU6LAbfbbaYx6yLcbDZrUGNyLZkbWUDy+byRbVgsFrlAa8X8UqnE46WJJ3BerUMWaP23zSn111xzDQAnrlWr1YysPFnUBwYGaMiOHDmCz372s3wep06dMuJHYpRWV1extLQEwCmFkDEHg0GjyFhLafl8Pv6sKcBOp4ORkREu3PV6ncZdU89S8gCcpwm1yohuLCnPdMeOHXw+5XLZaABZr9d53/39/byHbrf7uvdAygJCoRDHVC6XSedNTk4y3rqwsGD0CtMUdiaTodrGs88+awhMZ7NZHjM8PMz3X5c4LCwscEMiZQkyljNnznBDsb6+zvnQz/xSQzdivRJgaUMLCwsLiy0H63ldJhgcHKTn9eqrr+LOO+8E4LQk0R7I7OysoRMo0lGRSIS7X92GolKpoFqtkro5evQoJaGeeOIJ3HfffQCARx99lK3YE4kEr7G+vo7BwcEL1t3oHkq9Xo/eQKPRMLK/dGKHLmbWO3m5H62Dp70OuZ9EIsH5qFarRpfmgYEBBvdbrZYRtBe6KBwOGwkt7Xab86b7jmlppNnZWSSTSaNAV7yJyclJXufjH/84adSzZ88axbu6z1U8Huf1l5eXWaA7NDSEQqFgFAzrzFLxfkulEq8vmaTaqxLPVtcBNptNXt/r9cLj8dC7AGBk3umsPXm+m3U0m82mIVQs59bajMFgEKOjo0Z2qcyh7ujdbDZJEw4ODqJUKvHfo6OjZBdefvll3HbbbQCA/fv346mnnuJ4er0e6fRAIEDPa3MLHl34Ltf3+/04cuQIPvOZzwBw5NEmJycBmOzApaz90tmtVwqs8bpM4HK5aDDOnDlDbcHHHnuMlf/ZbBatVouLtzYEPp+PRcapVAqLi4sAHAoiEAgYDRxPnjwJAPjnf/5nHDx4EICzQEsqs6SBA46xKJfLVIvQIr1yPsBZJGTRLRaLRvzI6/UaorDa4MnC4na7jeJS/XO1WjViP1r1IRqNGiofsgDEYjEu8DpVfzM1OTQ0xCwz3QdqaGiINN/OnTvR6XRINd55552cg1qthr/7u78DAHzpS1+i2sYnP/lJnD17loXlOjZWr9d5b6Ojo6QQs9msoQQfj8eN/mJy/UAgwHuQeZXnW6lUjBie1jnUheIul4vn08oZcn7AEQ2Wd1LoarlePB7n37Sav+4HJiLMupRBx4/k51wuR0MotK6kqodCIf6tXC7zHb3mmmvwwx/+EIBDE5bLZT57XcysFT+kTEIgzzAYDKJYLHJTpgWltRrLpTReVwpVqGGN1xaHfFGkHQbgxCckBgCcV0qQRAy9e5QFpFgscqEqFAqGhJQW5gVA9Y6dO3cawfkLxRn8fr8RR9G7Z92tWMeOxGPQNVN6sdfp9XJN6QCsDZt4EI1GgwtYoVDgMXqRBM6Lx8o1ZUHVsk+SLq3nVBCJRHhMp9NhuvT6+jruvfdeqo5oD2BgYICyT51Oh2KzqVQKlUqF569UKpwf8aABJ16k0/M3tzrRXZy1OLJOdtDCuG6320iI0Qrxm+vr5Dno2JpW7Oj1eoZR0g05q9UqPVZtjLXslJxD7kkbLr0B6nQ6RifndrvN61YqFT7T8fFxdg6/7777WIYgn5dxl0olztvmtjACqUUEzscvX3zxRQDA9u3baSS1CLLEoS0uDmzMy8LCwsJiy8F6Xlsc0lLE7XYz7rB9+3bSfgBeFzvSO0idTi6eSLPZ5G5SF6LKue655x4Azm5aUvJffPFFFss2m01SKLJb1/EJnRKvRVdl5ytahFphQ44Xykog4/P7/cZ96fuu1+uGeK5uOKlVH6Q5JWDGe7xer7H7195rp9MxYh/yc71eZ2ZaLBZDLBbjWLXGX6VSIcWbyWQYT5yZmXmdZqAc39fXR89axwbdbjeSySTjR9qj0c099dyIZ6wLdPX5xLOv1WpGLE0/Ax3L0tRgOBzm3EqhulZK0YXSMuZgMGg8N11CUa/XjULyC3nwUpit9RmFHRgbGyPl7XK5mA7/8ssvIxAI8H0DQC9Vxzt12x6twCL3Ic/7wIEDeOWVVwA42bm6yHnzO2rx9mGN1xaHGK9iscjYx8GDB6m+7Xa7DarG6/UaSuwCXe+kezw1m02Ew2Geo6+vj+nx//RP/8RzfOxjH+OXd35+3qD5YrEYr7m+vs7FSce1Wq0WF4xIJGIkG+gUaa0kr+NPIl+k4xZ64RQaSBvver1upLAXi0Uujpt7Wcn9yJj14q3jYQKPx4PrrruOczg/P8/r7N27l4bk5MmT7Pr7pS99CX/5l38J4Lwauk6s0L2xdJq2PCuhR4Wi1Q0+dap8u92mMZfxycZFx+b8fr8hv6Xr7uSzcq8a8qx08oXQjFppRVOVQiHqeivZtOj+ZHJuEfoVaOMr9XuAU3Mom7pisUgqeXZ2Ftdeey0AJ8FCd5fWySm6hEMn8Wj1EjHEEuNMp9OG7JpW5bCCvRcPlja0sLCwsNhysJ7XFofsBJeWloxiW9lFjoyM8OdIJGIU6YZCIUM1QXalOllCuszKLvvWW2+lh/XAAw/gV3/1VwE4KfRClXQ6HaYnx2IxQ2mhv7/faEGiPRrxBiqVClKplLHTl112u93mTjYcDpPWkm7Hcm7d6kSnK8diMSPZQqcYu91uBtVzudwFBW6bzSZyuZxBPV6oENXr9TJzMBQK4cUXX+TOvNFo0DPQ9NmBAwfwyCOP8Phjx44x5TuVSvH4ubk5g3rVfah0XymPx2MIxMqz1l5Gr9d7XTscSYEvFAqGZqCm9jSd1+l0DOpQzq0pQPHgtSakKF9oD1wXp/v9fkOdJRgMGu+yzGGn02GJg3ir2pMTrK+vs3D8sccew+/93u8BcCjvF1980VATEdrb7XZfsOedHnO1WsX4+Dj1FB977DEjC1bms91uUzHF4p3DGq8tjEgkYmToyeIvNAngZDgJjTQ+Pm6k+2oKIxgMGguFnLevrw/RaJSZVPfccw++853vAHAUFB544AEATvNErVyhF5N0Os0x+Xw+I44iv9c0Vl9fH9xuN8etlel1u/Zer8friFq+GJloNMpzaxpUDBZwXlJKq6jLONrt9gUpHpEFEuNVKpUMKkwvgLKAeb1e7Nu3jwt8qVQy4igixnvgwAHWBwGOtJDEZbxer2GItCyXxHF8Ph92795Nuah0Om0o9WshXJmDaDSKjY0Nfk6XTwQCAdJ+Gxsb3Nx0u12USiUjfqVV94WC1BSt1Nrp8ofNMT35vaZ1fT4f7zUSiXDeGo2G8X5ohZD+/n5j4yNjKxQKrIX85je/id/+7d8G4GTPvvrqq7zvSCTCa+r+c+l0mtfRdLP0v5Pns337ds7VsWPHeI/JZNIar4sISxtaWFhYWGw5WM9rC2PHjh1GKwvZ8Z47d467yFarxXoWt9uNZrNp0Do6w0qLo8puM5FIGOfesWMHfvaznwFwdp+SJKKLMXUiiNCUF/JI0uk09RB1y3nAoe00VSg7YS2Eq9tYiFqHUDzA+d18u902asa0Qke326V2nS6I1TVbm2ukdAF0KBQifaY7KWtvr1qtolarcWfu9XqNGimhWKempqghOTs7i0gkQvUM7XVEIhHWhp08eZLz0dfXh8XFRc6prtfTnZD1uVqtliF2rO8hHo+TmnO73YYySigUYiJFKBQyisAv1B9NMjE1XSl0mk7C0YK3ksghNKh4fAB4bYEuTs/lcsZcyXhGR0eZEXvbbbfh2WefBQDs3r0bIyMj9OL1GHSBvIxb/q+zKrPZLOdnfn4eN954I4+RMe/atQt79uwBAHrHFm8f1nhtYezbt89QCZAFPpvN8guvizRPnTplpHPr1GmdPdVoNIyYV7VaxfXXXw/AyW6T2Nbg4CC/5Nls1sgi1G3UPR7PBWNehUKBi3OlUjHiE71ej/ejZXn04lgul410ZX0dndY8PDzMYwqFgpG1F4vFDPFbUcvo9XqG4K3Qiaurq0bmXaFQ4PH6mnqeRQhXzrGZLpP5ePbZZ7m45nI57Nixg4bN7XZzsSyXy1y8y+UyzyeZh6Ju3m63SdFqhQwtqzU2NoZWq0WKVVRYZA6EZhPhY5k3nfLtcrn4juk+Xa1Wi1R0o9Ewipl1TzH9vmgKMh6PGxmXo6OjNNo6pqlVU2Qe5HzpdJoF6t1ul+9uMpnE448/DsAxZHv37qXxOXv2LBU26vU6vwuVSoXn1XSinF82B8FgkEXKwWCQMeJEImHQ4xbvDJY2tLCwsLDYcrCe1xaFZG7JLtfn83GXG4vFmKXm8/m4I9zcMkF7Crrw1OVycccuEkV79+4F4HhvQkOWSiVDSkh3yZWxeDwedDodegq6nb0uWO50Otz9+/1+I6Df6XSMYLpQTDpTr9VqoVarcQy6nfzKygopKu3hSSaZbg+ij9cCsTLP4mnJPdRqNSPTTu6n1WqRak2lUgYVqzP1er0ed/apVIoCyIlEAisrK4aEldy3plfD4TA9E0k+Ec+l0+mQstJdiD0eDz1zwPFUdIaf3I8UccvP2vvVQrtut9uo0RP6zev1GmPR9KSu0Ws0GkZCjfwsHrO8yy+88ALfiVAoxHc0Go3SQ0yn00gkErzvTqdDLyiTyXCcd9xxB37+858DAD7/+c9jamqK71+1WuU9dLtdw3vVmZ0yTunQrCljyaScnp7mM81kMrjppps4Zp0gZfHWYY3XFkUqlUI2myW1pYt8db8pvehISrOOKcgCrVN/pTmfnDcajTIL7mc/+xmpLZ05pSnITqfD2JMUuuqFTxYtrTjQaDQYY5JFQC/wWiNPIHqGci5peAiYWWZ6QdSZdhKTkc9lMhkuyMlk0li4Ne2ZzWaNmJUep1yn2+0aiiEul+uCxczaEJZKJVJ+fr8fa2trhnaj/pw2sho6w09Trz6fjwY8kUhwDBJv0qn/OmYphlUL+zabTSMOuVkPUcdOddNN3dBSMvQA532V38diMaO3l26oGQqFaFTy+TyNSiQS4VxvbGwgEAjQeJTLZRp73detWq2Sgnz66acxPT3Nd3xtbQ3PPfcc51CumUqluCHqdrtGxqgukPf7/fwudjodvju5XI7HW+P1zmGN1xbFwMAANjY2jFiM7DZ9Ph+/JLJzB5yFqd1uGyoSWphXPquP6XQ6Ro3RyZMnqUyQz+cZG9h8jCyuXq/XWGw3C8fqxola+kfH3fRir721YDBIw1OpVIy0d7lXwFlMdDxOL+7hcJhjyOfzXGgkUUXmU8YyPDyMarVqeLNaEUKO0SUJLpfLEDfe3HFZFrHFxUWOJR6Ps4klYEooaaOvZbG0Cof8TeZdtzrp6+vjgiwq8roFiNyPbtSpEyTE6xAjp+u8qtWq4S3qVHm328370XMg8yPzLl6UFlGW+5Px+P1+Q11Fdx0AzidJxGIxvqNyHOAYEnmnH374YYyNjXFTtn//frYKKpVKNHhaNk3HPTudjhFz0zJYpVKJczs8PMz77+/vp0dp8fZgY14WFhYWFlsO1vPaohgeHsbMzAyz0QqFglEEK7vFoaEhowWIx+Mx6Aod79EqC5ICPzw8jPHxce4yS6USvadUKmXsjDU1J7vNYrFIUVb5m6DZbNJz1D2mIpEIhoaGDMFc3TLjQiKyohYiY9MeUbvd5r15vV6jjYzWKdSNKnXmo44NTk1NIRKJ4OjRoxyDPkbGrBsa1ut1rK2t8fmIDqOMW+v1ye8rlYoxNh3L0vEvvcsXClS8EL/fb3iPUvC8a9cuo5B9ZWWFafya/tJxOvmb/F/fa7Va5XNIpVK8H91wUrQmxXPxeDwcp26PogvN+/r6kM1mKULc19dn6HTq/mRTU1O8Nx37rNfrvNdCocBec/V6nZ7o0tIS1tfXSasODg4ypX11dZXXX1tbY1lFJBLh58vlMrxeL8bHxwE4qfJynysrK/ToBgYGKJg9Pj7OzEeLtwdrvLYYZJEYGRnBK6+8wi/m+vo6F7RYLEY+P5lM4syZMwCcL2wsFmOwPplM8os1MzPDL5ZeuK+99locPHgQDz/8MABHBULiMq1Wi4YgFotx0ZHkCcBZkLViQbvdNmJeulmhpsjW1taMpoiyQMviJZ+TRaJSqRg9njwej1EDJ5/rdruGOoVOXNBdgLPZLGk63UNsenoad999N5twfu973+O86YW+1Wox1qLFWWUOdHq7GDmduCDq+Vpt4kJiwLVajXOSSCSQyWT47DOZDOM4N998MxXrH3nkESo/rK+vIxKJGA0XZR737NnD+15eXjYoSZ2woGOCoVCIi30oFDLUTFqtFudUS1TpjUutVuN9xuNxdlOWOdBxSDE+Ho+HCjBPP/20obihG5YKFQs47758RhRgZNy5XI4xq9XVVdKLxWKRPdlCoRCN1/DwMFZXV3HvvfcCcFLtv/3tb3PM8l57vV6qoRw4cAADAwMszbB467C0oYWFhYXFloP1vLYYZCc9Pz+PyclJ0nvVapU7+FAoZBRcinclNI3sHmu1GouEG40Gd5Lz8/M4fPgw/j977xpj11mdj69zv1/nzPjM2DO2x46TOAmOa5OEgIKSAAVBoU2KSluBqqpqKxVEhVSVii9VER/4VKkqVau2QgX9KkoKSDSGQhMKhNxKEkKcOLE9vs5k7nPu5+xzP/8PR8+aZ22fqO3/92X8Y68vHs+cs/e73733+671rGc9S0TkzjvvFBGR73//+yIyjjyWlpZEZOzpw5Pe3t5WzzwQCOjP6KrsLibG5xgKY+rxcDg0qhywaDSqZInt7W1THgBxXpGxNw/iwGg0MjCbu+0JvPlSqaS0ZvxdZOylI3L693//d+n3+/K+971PREQWFhbkm9/8poiIPP300zrm4XCoEFWj0TDsRyhuYJzM7gM8ChUOZlOymC+OhQgMdvToUZ3Hv/7rv1ZYeX19XR577DEREfmXf/kXjWZ6vZ7pWcUKLO9617uMZiCz6bj3WTQa1XGACCIyfqaYlME2GAz0PNymp9Vq3dDvjYvaOaLH85rNZnVulpaWZGZmxsCGXNaAccRiMdOuZTAYyB133KFziuv4/ve/L88999wN1+A4jp5zcXFRPvjBD8rZs2dFZPyOAl7c2trS82xvbysZpdlsaqTs2f8/8zavm8ywuK6vr8v8/LxCHczwExED6YA2DKoyXvpgMKh0dyjOi4yZUH/8x3+s5/n+97+vi+DVq1d1ceHW8JlMxtCtseiWSiVJJpOmQSLTzGGxWMzU6jDNulKpaE6GIbdisWgUNWKxmP6f+1Jx/ypAQCLjxeTChQu6QfOGyQoZjUZDF5mdnR35x3/8R11sT58+rerkp0+f1oXu/Pnzes2BQMAo3nPbelZRnyQgzDkvzGkikTA1aEzZPnnypHzyk58UkXFN3he/+EUREXnmmWf0c4uLi8p0g8wTjs3yWax+zxR4QJrcpwr3JJPJKOTmZiQyJZ+lo5hl2uv1TINU7s2FORLZFfoVGTtbqEPcv3+/lEolAy8zPR1Wr9fl6NGjIjKGA7/yla9oTvDWW2+VRx99VEREPvWpT+k7961vfUvY4CidPXtWHnjgAYWPE4nExHxgrVZTRxIqHnAEPfvfmwcbeuaZZ555dtOZF3ndRBaJROTgwYMiMk6gt1ot9XKTyaR6m27lCfbYp6en9f/1el2hNS52/fM//3P1Kp988klxHEdhkNdff90U4iIiYviK4a7p6Wm54447lHXGrUYYLmNlh3a7LRsbG+rJ9no9Q2rANXMCnIu1MQdcW8YRFddiTU1NaTQWCoV0Prjou1KpmO7C4XBY/vmf/1lExgKr6BFVKBS0e7Lf75dnnnlGRMaRbCaT0bExK5JFYCORiN43FHNz8S/moFKpaJRQLpflwQcfFBGRQ4cOyUc+8hH5u7/7OxEZ91vDXPPzcf36dVNfV6lU9NjhcFgj81qtpvctkUjoHAC25LYhuJ50Oq1EmdnZWUN66Xa7euxyuaxdwFlvkpVAEEmzyDQX2OOZKxaLpsB9dnZWI0uOfAaDwURB5evXr0sqldJn+Qc/+IHAHnnkERU6vu2224ygLiK/y5cvyzPPPKP925rNpj7/gLPxeVzbuXPn5J3vfOfEOjrP/mfmbV43gXE/IabA84seCoXMS4IXMxQK6QKEfBEWAxYw9fv9ugjec8898tWvflVExjDhiRMn9DzT09O6MDSbTYVi4vG46emElxdKFcwW5D5QGGe73dYNE/kEsMkcx9G/McPRcRzTO4oXUVZwYNo8LyzD4VBSqZRRW+eGj1iEm82maeSI+RIZw4P43K233qoL3enTp3Wez507p9eI+8lq61wSwBJOUHzHWFlBBXDxww8/rHDr7bffLmfOnJGnnnpK5xdzBVUMXAPmgOE7kRvb1mODchzHzDvPKdP4WbCW5wkQKHc0wHkYCubnOJFImIaU4XBYn4lut6t5qevXr+tcx+Nx4xCk02kjSIxjs8KF4zhGbDiTySiN/dSpU5ofvOuuuxQ+RgkIrv/q1at6rShwxnxiA+dCfAhms8Pm2f/OPNjQM88888yzm868yOsmsmQyqSzCTCYjV65cMf2a4PnV63XjeQKaQCEyvFREXSLjPl3vfve7RWTsiaIOCH214HUvLCyox1ypVPTY8XhcP8PssVwuJ+VyWb1R9oRZ2sgtw1MoFPR43D5jbm5O4R1uBwJG4yTh11AopOep1WrGS89kMkpUyWazCj+yN8+Ro4itcWq1WnL58mUdN677oYcekne84x36fURfuB543Ozxc2SADsLMyOOaKUh0nT59WqGs9fV1OXPmjEYk3HPLcRxzDTiPWyORIy83uw5RKQgeGPdgMFA4UGQXQnbLhOGeidiO2AyP4m/4l4vKEV3jeIg4y+WyikUvLy/L7OysXLt2TUTGXY3xjHLfsH6/b4hMIrvsUhxTZCwGDCj41KlTGpG1221Tr3jt2jWFci9cuKBoB0ugiYjOUzgcllQqpcgBt/fx7H9m3uZ1Exherkgkor2BFhYWZH19XR94zpeMRiMtvuViXdDq2QBjfOhDH9IGej/+8Y91swkEAqa5ZTAYVEpxLBbTl9Tn8+nP+XxeF4KlpSV5+umnlXo/GAyU4bi0tGQETPEiRyIRue222/S6NzY2dHF6//vfrwvLl7/8ZT3P1NTUDcw7ZqZhAVlbWzOKFM1mU2HDubk5o77Bivecc+N8GvfjunTpkpYeFItFefvb3y4iY8fg8ccf1yaebno7ixNz/sstloyF/zd/8zflkUceEZFxzu3JJ58UEZGf/OQnUq/XdQNeWVkxyibYyHhjh74lw5UsuMvK75gbHAsL8XA4NGUJzJ5k6Nbv9xsVGNzfbDarz1c2m1V1i1tuuUVqtZpuRNFoVMsP0um0btJnz55VB+TOO++UwWCgueF+v2/EjnEfA4GAbn6HDx827NRqtaqO1M9+9jOFKn/jN35DnYZSqaTPms/nk0qlonOdz+f1uuPxuM5HuVzWezMzMyPpdFohyc3NTW/z+l+at3ndRJZOp/VFPnbsmNkwRHapu/l8XqnDTz75pP7ebalUSn75l39ZRMaJadC8/+qv/kpfvnw+L/1+X8+7ubmpL/0dd9yhC9Dly5dN64lbb71VRKzckMi4BgZ/q9VqSsrY3NzUcx45ckQWFhbke9/7noiMvVUsGs8884xS0y9fvqzHBj0ZGzQ6EYtYWaD9+/cbmaatra2JEkjcAJMX9OFwKNlsVhdOzvH4fD6d6y9/+csaJT/wwAPyp3/6p9oO4+tf/7qqnnCbjXQ6rd9HtMcbK8oXPvaxj8mf/dmfichY4QPPQCqVEsdxjEDzJNFg/n0wGJRMJqNzlclkTI4I18Ddo1OplFH0L5fLhvCDzXx6elo3TLTWwd/Q9kZknKt75zvfqfMBB+CJJ56QYrGoZRqs1MISUA899JBRJllaWtIoqFgsmmaSeN5wHSLjXPLc3Jx+rtPpaC3k0tKSPP/88yIi8uu//uvynve8BzxmWAAAIABJREFUR0TG79oLL7wgIqJ5MDiW6OqNcbJDAifhgx/8oESjUaXhc22kZ/8z83JennnmmWee3XTmG92ksaq7Yv//ZYPn9sADD2gu6sSJE/LEE08ou63b7SqGf/LkSaWQt1ot1eG7fPmy6Sl07Ngx+fznP6+f+8u//EsRGbfmAJyXy+WkWCxqkS+38Lh06ZJGIAxxZbNZjejuu+8+efrpp+W73/2uiIy9UkCaCwsLCu9MTU0ZKvmZM2fkV37lV0RkLGJ69epVERH5/Oc/L3/7t38rIuN8BCC4r3zlK5JOpzXCKpVK6j2L7LZs2draMpFFuVxW+OvWW29VyGptbU0jydXVVUOx3tnZMYKzXLQNY2r71NSU/M7v/I4cO3ZMjw0tvvPnz2t08p73vEd//ta3viWj0UijtXe84x16Hz/72c8qrLtv3z5lfzKbD3PNZQHcSJEjyXa7rfdh3759Gllfv35d4bidnR0T9eTzeYXTWPEjl8sp2/G+++7TPFksFhO/36//P3TokB77+vXr+ryeO3dONRgffvhhabfb8rOf/Uw/h2tl4WO/36/32ufzST6fN801mYbPfeZgaHmDsc3Pz+tzkM1mNV8Zj8fl4x//uIiMI/szZ87oveImqXNzc6bAnUWlESF+5CMfkWvXrumz98QTT2jEzPfw/3X7v9l+vM1rjxvXs7z3ve/VzWtmZkaee+45rTFaWlrSz6G2SkTkM5/5jC4Sn/vc5+TChQsK0fz2b/+21tp88Ytf1AZ83LcIAqj4XCqV0pcrmUzqIs4dZ/P5vOaovva1r8nS0pLpg4QFutFo6M/T09O6aM7OzkqhUNB73G63FZq5ePGiLrQMs5w4cUIGg4Fu4K+//rp+h2vd0um02WyYbj83N6cQFVOcNzc3dXGsVCpG7b1Wq+mCxK9SIpEwnaVjsZh88IMfFJExTIb52Nra0pyMiGhu8Ac/+IGcPHlSnZOtrS350pe+JCK2g0CtVjNNHZnU4IaiGLKDYZPF/UomkzofzWZTobGZmRldXHFPYNPT0+rccEficrmsm000GpWDBw/q/AYCAZ3fRqMhH/rQh/SeYD6effZZee2113RTKZfLRnDXrd6B62GhYSb7sPLL7OysHvfKlSvm+eVuB+9617tULf6HP/yhOmXFYlGv7Zvf/KYsLS0ZsWU4UUxewn0UEbn77rtlfX1d1fAvXLigzxjm5RfB/m+2Hw829Mwzzzzz7KazX2jCBitF7FULBoOmLxQinXa7LYVCQb01LvSMRqNy1113iYjIJz/5SfnsZz+rvz9w4ICK+wYCAfmbv/kbERmz1pA8npub08+k02mjXQfRXIwNXnYwGFRv9+LFi/LDH/5QRER+/vOfSzQaVa+de2OJ7EYB7XZbXn/9dREZRzr79+9XVY90Om1alyAZn81mFX773ve+Z8oA0um06bTL52GPHRqCIuOIBrR3pn6LiImuWq2WJvdZf3A0Ghk4Dmw0eN9oK/Paa6/p9cRiMZ3rL33pS+qxI8IEQ/FHP/qRjikSiSisy4XZ0K7kfme4V0yc8fl8Gl3lcjmlpOP+sCYjopN+v6/nQXTH0TSIEN1u10CDIA7BMPdnz56VT3/60yIyFhD+1Kc+pfPhZjgCduNr5WsTEZ13zAHuKUfAw+FQn4N6va7vDggsYLHGYjGNkK5cuaIMwWPHjsmLL74oIuMSBYZKueA4Go0aQg/GycXgjuPIwsKCQvDMiPXsf2a/sJvXzQI7hsNhXSTa7bahQcfjcX34E4mEkUBaXl4WkTE2z40PFxcXVRy0VCqppE0+n9djRyIRZRd2Oh1pt9u6EIvs1uywAng4HFZ4pNFo6MsLVXneMCYZ9+Pa2toSx3EUAsxkMgrjbG5u6sJ74cIFrbsBPMQ070nMNBa/hTIExh2NRnXh5h5g8XhcN9JgMChbW1v6HXeNEuaJqfYQ0sXfLl26pAoZ8/PzypDsdrvy8ssvi8gYinvhhRc01xeJRIzCBZ5f3jxBTefeaRgnL46dTsc0AXUcx1DluTZsUp+tVqtlaPD9fl+fvc3NTd3ILl26pM5WPB6XRCKhjsdoNFJ48NChQzrvpVJJN45YLGY2U4YK8X+MGYbNizesSTV1nU7nBlV5/J8FhFmUWUT0fszNzel7dPDgQXnqqaf0WhcWFhTO39zcVGbp8vKyznOpVJK5uTnNq3Kpi2f/M/NgQ88888wzz246+4Xd6m8WnkosFjN6e0jonz17Vqanp41ILcMOgL9ERL38N998U+6//371Kjc3N9WTPXbsmP5cq9U0Ge04jrTbbfVKmVWIVvX4PXvCXKQ5iTQgMvaSMWaOgILBoHS7XZO45poijI097NFoZFq0sJcej8dNny8Wd3WPG/AmHzuVShnFhNFopLVIuA6cc1LNWKvVknw+r1HyYDDQyJRbexQKBWW2HT16VK5cuaL3LpVKKUTLhASGPf1+v6m/Go1GRpWDC4bxDKC78CSNSVZ96Ha7Bvbq9/sK0YZCIcP8wz3e3t7W+Uwmk5JMJjWCjcVi8uyzz+p3eC5Z74/vVzgcNp2UOeLC9UDXk6NMjqwxZj4nro0FfBEhhcNhvVeO4+izt76+rmxLwL54N7vdrkbJc3NzpuYLURyK3TE/+Xxex+T3+/d0KmOv2C/s5iWytzcwbvyHF+GNN94wLLP5+XnDsuKHHy9JKpXShXZtbc3QiNfW1hTGOXTokPYWWl5eVuiHFwiR8YuNsfn9ftOsEAtIJBIxECargff7fZMXmjT+aDRqFuF2u22aC6JwNh6P61hAWWc1fSxUqVRKF9doNKpjQV6KBYUB7TGMycoMmUxG/H6/aYjJ8k58PbhObF4Mt2Lca2trWrSNaxIZL3Sbm5sGzoN1u10j2MubJ4sdsyxWv9/XRTSZTGr+DOxRLNDValVzPyyCPBgMzHWys9Ttds04eawYCyTLsFiPRiNVWikWi4YdyEXk3FGAOwIw/DscDg3Mx05EKBQyor/MVmTYk2G7cDis0DSrzW9sbOh939raUtbrsWPHJJPJqIzU2tqawvFHjhzRz41GI3VGkEPEvE9PT+t1h0IhA9N7Ntk82NAzzzzzzLObzn6hI6+9bCwpAw9xbm5OPbpsNivD4VC96eFwqASDVCql9UGhUEiT8wcOHJBcLqfe5/LysnYR9vl8ytxzHEfrusrlsiEL4Hci4yiGoTnugMttR6LRqGldAi+bW3MEAgGF1YLBoEQiEYVLs9msRnKpVEq9d2Z4wStn7xXeN9ftiOy2qkd3YpYWwnym02llozGUdvToUSkUChrVcU8zjFtkt7ZLZByp7OzsGJIEa+zhHvz0pz/VGrz//M//lHa7rfPOEl/8M/cJA9yEY4dCIYVeo9GoGQ809VAcDmkjruXK5/MaUfn9fp0bRCkMs+HeRaNRvVf1et3oOLLQ8LVr1/Rz586d02ciHo/rswc2K9etYdztdlvHmk6njbBwOBxWMsX29rbeK9ah5O9ks1kJBAKm2zbGEI1GFd5E3y+Rcb0f5jadTsvb3vY27czMffZWVlb0O/Pz83rcXq8n3W7XFDDzs+xFXv+9eZvXHjXQ1n0+n8IrR44cUWhvampKVlZWlHLdaDQUTjt79qy+5NlsVhe7u+++W4bDoUKCb7zxhpw+fVpExvkwfD+dTutLBWFRXijwkjMFvtVq6ULFDDhsSsgPBAIBXRA5P8SLa7/fl1wuZ9iCGNvq6qpeGxcLA27CRsQ/R6NRo97BIsMsKluv1w0Uhe/UajX9OZ/PG409zkWJiDknC9Q6jmMWUSxO1WpVCoWCiIwLZ5mdx+wzFgfmwlvMC4z7qkFPEHONYtvjx48rk/Pll182+dHRaKTnKZfL+hwCKsRn3MLHvCnA0ICS/8/Fzfjb3XffbToiwLmASj+rz+N5CwaDet98Pp86EMlkUkKhkP4fPcFExhsOvtNqtXSzSSaTksvlDDSNsg1syiLjzQfPW6PRUEYvGmuirOHKlSum5x1g4dtuu00dspWVFRkOh6aJKpxPvk7P3tq8zWuPGhaBdrutXvHi4qL+jPwGvD9WkWi320pDHo1GSgL4+Mc/bjoRx2IxXSimpqb0ZQYuD4tEInrsUCik0UCtVjPUdESITE3vdDpaSyRimwj2+339fSQS0cgtn8+Lz+fThZfJG5wf4TYf6IzLGxPmsNPpmNYt2Myj0ajp+syeMOfmML8i40WrUCjooiOyq4hQq9V0bPl8Xje1TCYj9XpdP8cCrblcThfEWCymi1Y2mzX1dZ1ORzcLRLO4v3zNTHWPRqOmASW+s7Ozow7R8vKyeXa43Qtyj7hGFioOBAKGBINnYm1tzeQ7+TOc43zwwQd1Ds6cOaPfP3DggIm8otGoOmyDwUDJEa1WSzeWzc1NI/k1HA41p8fq76Dri4h84AMf0A3utddek62tLX3eotGoRm7Hjx/Xz+3s7OgcrK2t6aa/s7MjJ06ckG984xsiMlZQwXXeeuut6gAMBgPdvBqNhnQ6HZXCWlpa0jlIp9MTI27PrHk5L88888wzz2468yKvPWjhcNjkDThqQTSQTCZNLyoWZQ0EAuphDgYDzX/BWwUTcTQaaRuUhx9+WNuO/PznP1dIBG3icWwWeEUBMs4DY2hw//79sr29rbk6ZomxJ8w5FOgKwkuNx+MKwwSDQfW+L126ZFh33J4ETDWRcdTAOSpEMGiq6Pba8X0YQ4jXrl0zmo6ZTEY1GbvdroGZcFw0eGSlFMwhRzD4G74DBRD8nyOst2LK1ut1w5qD159MJvU8m5ub+pl0Oi2pVMq0LsHP3OKFG30OBgPpdDoa9SYSCR3P9PS0Ru4zMzOGmdput+XRRx8VkTH8+9Of/lRERP7kT/5EEYWlpSUVHS6XyzIcDvUaarWaPpeFQkGjK7/fr/OOCBVjCAQCGiUvLCzI/fffLyLjSBD3tFQqyb333qvX0+v1NALmiHN1dVWp/ocPH9bi8ldeeUX+6I/+SAWj77jjDm2dsry8rNe2ubmpUZzIOOJ78MEHda446vcKlv9782ZoD1oulzN1N1jge72eLnqosWJ6PCfQAZm98cYb8tGPflRExi/8+vq62eRQ/X/o0CHdMP1+v/4MKjZ3Y+baKj4nxsw1RRsbG6amptFoTITjOp2OkSyamZlRmK3dbqvM0NmzZ/Wct99+uybTm82mhEIh89JPUlHnTQBq4oCVWMqHpYSY/FGv12V9fV3PE4vFFObimqJqtaqLK6jb2Ij6/b7JrXGzUUCNUMTga8C4udeYe5Hj54Dr7fr9vulIzNdcKpV084HqCI7NHbm5Rorp3OVy2TyHCwsLIjLe6LHJdzodOXXqlI73K1/5inzuc58TEZFvf/vbKgrdarWMzFIikTDqKnBoms2mjhkKJrgfjuPod4rFouZbc7mcbmrPPfecfOITnxCRsRP07LPP6n1wHEfzkIFAQCW7+v2+3p/5+XnNvW5sbMji4qK8//3vFxGRr371qyp0/Oabb5q5xXtUKBSkWCxqHvKZZ55Rkd5EImHEmj2bbB5s6Jlnnnnm2U1nXuS1By2Xy5liWSSPuRWG4zjS6/UU4mF23WAwUA+v3+8rI/HAgQPy0ksvKUNtZ2dHo5u1tTWNIAqFgkYJOzs7RteO20/0ej09DxurW4CFCI+bGYL4P8YJBtzm5qYcPnxYPWaGhWZmZtT73b9/v3q4juNIo9HQsfl8Po0amJLfbrcNnR4QGIxZkogKOaILhUJSKpX0/8ViUX+ORqP6s+M4hgjChbvc1Ri6ejwXImPvm0sh+Dusw8dwLaJiJnbAAoGAIdrgvoOROEkFhedAZBdKnfR5hiFxf5gFuLi4KEePHlXB5oceekgZfc8///zE84PgAKiQ732z2VQIbzAYaJS7s7Mj3W5XtQWZbbuysqLfv+222zSSRGEz3we8V6PRSH+u1Wr6fK2urmpEFolE5L/+67/k5MmTIiLyf/7P/zGF+Kz2gWvb2dkxhd7T09NmrgE5g1zl2Y3mbV570DKZjNYYjUYj3SBKpZJ5KVhZoN/vm75OvBBi8yoUCtJoNBSr59qW1dVVfXn27dunGxmUFbjGh2Edzt2wFBFTtJm5x8xF3jiy2axu0v1+Xy5fvqz/n5+f1/OXSiWFV7a2tvQz5XLZMO94M2fKNm9EyN9hrIFAwIj2sjPAyg6O4+gimM1mFe5kZRFmHuJ4vGGxhNOkDQLzyb23ML8smMv3GQxUVpfA9/mZYGknzgG6r5vZgTwH7s/1+32jsMH0fTBYjxw5Ij6fzzRM/Y//+A8RGW94LJfFKinhcFhLOxYWFvTnVCqlc729va0/h0IhOXjwoOZ52+22KsxcuXJFVTDS6bQeq16vG5ktlqQajUbqOI1GI31frly5otd8+PBheeKJJ+S9732viIyfCcwb17nFYjHzHnEOb2ZmRnNjPp9P83R4Vz270TzY0DPPPPPMs5vOvMhrDxoTMbLZrIkAGBJiuIY7FDPBQEQ0sRyNRmV7e1ujoIMHDxrtO0AUfr9fIRkoWsArrFQq6iUnEgn1LDmaYLZWNBrViEBkV+sQn4OXzon+48ePy+///u/r57a2tnQOzpw5o8n0b3/72/LII4/otfj9ftO5F3Ows7NjSC8MtXGNEtclNZvNifAmCAGTNPLckRKguVQqZZQ8ksmkmXeGLXEsJrKIjO8vYNR6vT6x0Ju/L2LZnGgvIrILsfK1caTB7Ws4cnDXqeHcnU5HiRkc+c3Pz6t2ps/nk8cff1x+7/d+T0TGTDtEr/1+XxmbrGYCiBpzX61WdTxQmMF84JzHjx+XRx99VFv6PPHEExqVHT9+XN544w0RGUdrrAjDGoiI+ETEwJaFQkHvwebmprZH2bdvn3znO9/RbtCLi4vKro3H4wqdZrNZnSeweH/2s5+JyDgSxJinpqYUkgyHw6bQ27Nd8zavPWjb29u6aG1ubuoDz9AGXmq8tNyM0u/3m0X07rvvFpFxG/NOp6M03mKxqAtIOBzWxeCZZ57RPkNQlODqf3xuZWVFIRmmUodCIVOY2W63lVWVSCR0zO12WzfcVqulvbkuXLggmUxGocv5+XndsHw+nwqdHj16VGGobrdrFmHuMcXUcre6eigUUgjNXeg9SfiVmzKKjBcnLpTGPE1PT+smj82AN3Q+NuaAG2VCtYJZngxdMh2e8458DSxIHAwGdcNqtVqmeBlSRfgclyzgOQyHw2Yj63a7ujHimkXG+VpsPtxYMhgMyqlTp9RBWl1dVaeBc7csJba9vS21Ws0UBmMOKpWKkfLCYn/33XfL66+/rnDbI488opvuuXPndFMpl8uGUcslC7yR8XsVCoWMuDE+X61WJZvNKtQ/Pz8vP/nJT/RnbHjBYFCfgXg8bnKkLKLMrER0WPDsRvNgQ88888wzz2468yKvPWgMGzIpgqMG1CFxJ2Ou08J3stmsen7f+c53ZP/+/RqVXb58WaV3AoGAFnDec889Com89tprMjc3px7i9va2nvPDH/6w1t1cuHBBJYfW19dNS/VgMKheKbcKQa0Ljsu1LdC1w/EQNRSLRS2yLhaLGoVBgxHRDsNfHI0wsQSQHdciYQ4RkWBuuTA7FAoZrxtMN67DY499NBoZ+SsmtIjswnEMAaIWi0kW8MAzmYz+zJJWfr9f4vG4kaUCwWA4HOo9xXVgPty1bhwBwDgKwz1kOTDAfiKic7ixsWEINJVKRSE4lshikV0mJYGUgYiv2+2aWjlYsVhUyHljY0MOHz4si4uLIjLWbjx//ryIjAuGcazBYKBjC4fDpgUOX/dgMFAIPRQK6bPHOpjr6+syOzur79Lc3JzOOzNlp6enTWRfrVaVLevz+QwjFzC9Jw/11uZtXnvQpqamFI6Lx+O6+aytrekiAdUL3qS4CSDYVqlUSl/4Z599Vk6fPq2FyS+++KJpJolj5/N5XQx2dnbkzTffVGWEf/iHf5Bf+7VfE5FxPuFd73qXiIzZUnjJa7WaqiScP3/eqI4Hg0Ed88bGhubjuPHhwYMHZd++fbq4lEolhZtYAYLp9bVaTarVqi6CqVTK5C1w/l6vpwsLIBnAVNxwsVAo6Dkdx1FojBl4IrZpJRcI41wYJ98rdjpY6WFxcVHvzczMjKG9+/1+I1CLa8Mc4XoY2mOYORwOm35crDnYaDQMyxLj4U4FbrFlKPKLjBd1bIzFYlHP2W63dcyj0UgSiYQ+i51ORx2Xffv2qbPDEBnuC183b9q4hnK5rHDgcDiUV199Vd8fx3F0PPF4XB2N4XBomkzy/OBcIuNNCpA3Owp8/Y1GQzY3N40KDD8jfFycf2NjQyKRiD7/L7/8st7rSCRinBvPJpu3ee0hw8ITCoV0sd23b5+pNwKFFsoVWIi5Tiufz5s6EZAi2u22NBoN9cz5JfP7/fLCCy+IyHjhxKZ05MgRGQwGmlN45JFHlCRx9uxZVdJmle+pqSndyK5evaovqsh4QWLSCbctQQS0vr4u6+vr+gIz4WM0GmmE1m639TpBophE7e73+/ozt26BnBTml5UaWGmC84doJInogMsAQOYQsWrkvPDjupmwwd10senHYjFTVsDK+G6JLs6TsfV6vRs6V2NsuCaQHTj3gsiJNxJuyIkaQxi3MWm1Wuo4lUolnQ/HcUzucTAY6IbFLUhYWHhlZUVqtZpG96zqwdT/er1u8oaBQECfi3Q6PZEc02q1jCoH36PBYKBOERM2+v2+kWPjshV381Pk8zhCCwQCelzk2fid58iWnRDPJpuX8/LMM8888+ymMy/y2kPGjSXdeRmRsccNLDyRSKg3i8/BG+eIKpVKqbfn9/tv8Jr53Iicrly5ojmDeDwuhUJBvv3tb4vI2IN+7LHHRGSs2wZ4kVmInU5Hzwl6MyJEzpV0u12F5pgN5/P5xHEc0/4d3mu1WjU0dYbCuH17OBw2ORUYi92C1o055bwUwz6ca0RfLfbm3XAafg/vGVRsbhqJ77PWImsjttttZVCKWPp2t9vVaI2VN1qtlokSRcSMm4VnYVAZYb1KRBdcisF0dES1iDxYVeOWW27RHN7m5qaBFhkuTaVSho3J0TieHZFx5MMUfy4HgTEzFPCqOyrCPeH7BhQDqiusiAJ4D+PD7xHRsVpGq9WSQCBgIE3MdavVMrAn63/i3CLj95lLB/j8nk02b/PaQ4aXp9PpGGFeTlgjYTw3NyfdbtdQoVmRHAsyVDVExotrs9nUl6nf7ytUVyqVTFNGCJgWi0VJpVKajO73+yYfh4WFFS3a7baBKqempnScDNMxCQB/wzh5sebNPBqN6iLBNVtYHLn/FUNELCDs3rze6l4wpMoqHO7Fn7/DP/PGyhBpIBAw48Z94425VquZ3BarWED1BN/n2i7eqHkzDAaDCmVxLg3j59o73uQYUnV398X1DIdD0wsLuR/eWPE53LtAIKDw4urqqj5v4XBYn8lAICC1Wk0393q9ruNlhQ+G2eBcYHOHEg0M34lEIjcQM1hyC1Ally8w2YdLCty5TjeUy5A3n9Pv9+s4+XPsEHGnA8+sebChZ5555plnN515kdcetG63a4pT4XnF43EDQQQCARMdMOyICG1mZsZER+xN+3w+I9YK75Vbc2QyGYlGo0rAWF1dNQW2GE8sFlNvsVaraZHz9PS0ZDIZ9UzZi3T3uIKhSBPjGY1GJpmNCIS9UpQHTNIwTCaThqHojpAYwsG1MfwWDAYVLkomk6YbNeYP18ZwI+s7MgTIpQwchW1uburvy+Wy8fTZ3HqEzEzj6KjRaCj8lEgkjNAxR7JcpByLxfTaG42G6UnGhcw897VaTSE4/s6+ffsMo4/hyeFwqLqUDGXPzc1p5HXt2jWpVCrm3sNYeJlbxIAEAeiShXHj8biBtjk64tKMXC5nOlXj2eGSCYY6o9GowuKYQ9YwxPMFnU8eJ0PlDKfDotGoR5d/C/M2rz1keBlTqZSp88ICv7q6atQU6vW6Lk5MDWcBUahX41i5XE5ZXhAkFRm/cNyQEGNBU0jUo7RaLVUv6Pf7qqQRiURMfyeMy+fzSSaTUVgItUj4GfDM1taWkedheJChPlY/CIVCJsflOI5pjskQDy+83PKeF36/369zzefhmiQwFLGZJ5NJvR5WDGFjeAvGQrL4me/v2tqagbL8fr+BvDg3585z4X7XajW9D5lMRuea1SHgGDDrDX/LZDIGssbPjuOYDbDX6+kzVa1WzVyzfBhDeMyk5A1vOBzqsVZXV00pQiqV0vvN9Y/ValWPBZgcGxbLkVWrVZNHZRi3Xq/r5h6LxXTz4wanPH6fz6fPOyBZfIcdC24MG4vF9L3EGDFXrCzCkKibQerZrnmwoWeeeeaZZzedeZHXHjJ4xhwNZDIZ9ezZC8tkMuI4jvEE4Ym2Wi1VnqjX61oIWSqVlIAhMq6nYpUBHL9YLCrhYm1tTUKhkCbXGYJbXFzUscbjcRPpwHOENiLgI/4+PiuyK+ArMmavlUolU3MF4xopETFJbiZScNEpEza4+7N7rlOplI5tZmZG/9ZoNDQaSSQS0mg0FO7pdrta3O3WGeQx87lYm7Db7eq4k8mkHjcWixlWImsg8piZAQcvH5/r9XoaDTiOo1Hy9PS0qk4Eg0FJp9N6fZVKRSOQTqejhIJgMGgg3+FwaKA6RDQQnMVn3GQSjmC5zxXqvLrdrkZeIBThOWDGY6lU0rlKJpM6n8vLy6YgnKNpFrlm0srOzo7E43H9v7tnHeYzEAjou8M92lqtlgSDQX1nEomEEWHG3GKuMRf9fl+/g/cZYwMs7ekavrV5m9ceMoaPAEk0Gg19eRh2qtVqBm6pVCqad+h2u/pSoJ28yHhT4AWaVRvm5uZMPg1jaTQasrKyoi/d8ePHdaF54YUX5PTp0yIyfoFxznK5bCC//fv3yz333KPnxGLdbrf1Jd3a2jK5p1wuZ15gXBvnM7rdrtkYmPHIG5yIpYfzwhYKhQxIJ4gFAAAgAElEQVQjDxtRJBLR6+l2u7roAubjUgRW6OBjYdHEvDJcioWKj8XsS3yWlfpxD5j2HggEzAaH5pIiY8gX9zGdTut4CoWCbl4o6sV4stmsnmd7e9sIEuM8yOMwO5bnB9fj3uA4DykiZqPG/WUFFbAtMb+NRkNZtFw0zZvKYDCQer2u9xGlABjnpEaq+XzeFAm3Wi2TI4Wx8wjBaZHxxoOx4HN4LlndpdvtqsD0tWvXpN/va0nKYDAwuWguQmcVFc92zYMNPfPMM888u+nMi7z2kMF7Gw6HCtN1u10lOySTSVMw6e7h5W41DwPzEPp/LHEDD6/ZbGpEw3VN0WhUhsOhvPLKKzq2u+66S0REjh07phDP8vKyeuzpdFrP2Wq15Ny5czq2bDZrIix0s+WCWEBP8IxZVicYDKqXzVAW2m9wkS++z8KzXDyMpD2ixFqtZjo7c2QB+KxWq5m+XSdOnNC5WltbU+mqZDKp96Ber0sgEFA4juWyQqGQHvvw4cM3iNDyfYRNTU3pPWS4FGxS7uyMzzUaDb0HMzMzeh4QDbg9Cer4uMA9l8vp/e10OuY5SqfTptsw5r1arZriYy7snZubk1dffVVExtEJellVKhU9LvrPcSE+jCNBRJz4fSKR0HEzVMnPy9TUlNFg3NjYMPV/sHA4rNHSzs6OogGIJPF5bv/iJiUxLMyRZzKZ1PEkk0kTTWMO3bV1nu2at3ntIUNOAkwzESsmylTq6enpia3ZRcRoHvr9flV0T6VS0mq1TB4Dmx82G5ExZo/z1Ot1SaVS+qKfPXtWN6z5+Xl9MZnSn0wm9Ry9Xk+2trb0peU8HRcZcyNIwGJc3MlCtAzH8ULHhaOZTMZsWPg9b1bIu/AcYt76/b6BvNzFqYC5isWi9iErlUo6HobzkOvAvHEBdLfbVcq4yK6+JRci43jIGzITk4V9oazCFH2MBzCzyBg2xAYH2j3n0QBFM4OuVqvpPU0kEhIIBEwjVG6aCZgrEAgYwV8uC2DIOB6Pm75smJtkMmlUOdzHw3WnUilVevH5fHL16lW9p7lcziiDYMNZW1szGo5uJwHn5D5d2KTwHd6Yc7mcfi6Xy+nzUq/Xjc4l3rNkMin9fl8d02w2q/ekVqvJkSNH9Jo9m2ze5rWHjOuS8DIzHdxN6xYR430yfRqLTrFYNBI0ImI8dXyOvT1+yZvNpqkX8vl8WsPV6XT0mCzdwwtor9eTbDarC1qz2Zw45nA4bFpC8IbD+Y1QKGTqv7jLtFt+Z9LPPDYs2pzE51wdU6R5vrvdrqFVc5NHVhlhire7XQq3aOHF3n2PWaWD819uEgvmptPpGHIKdwvGBpNMJnX8b775plF0YMUPvlc874gmWAWGSRowzuMg6sFz1W63jSgzkxWYgs/1VMFgUJ9XXIeIJWJAIJqp7pzn4hZCHMmxAgruBa4Bx+52uzp+LsWIRCLqzMC4cSgcL67XCgQCRkmH6w05l8uRmmfWvJyXZ5555plnN5152/oeMvbkWIwXHq/P51PvrNfrGWiKPfN0Oq2eJ6tyJJNJ44kin4Xv888YC5oy8jEQnaysrBgB0UmFs/DqWXOQjZtrcmEm0425aJPVFEajkck7MDWbozr8DT+7ISJuOsnaeaymwIw1zAPmitmPfF24H4DFuI0KjjccDhWO6/f7GvWwKoN7DrhhJJ8HAsbw1rksAO1wRMawIcoyVlZWJBKJGFYhPjc7O2uaP3IEwhERt4/hz6FhqogozIi/cSF8o9HQCJ4Lyt0lBrFYTPOdPp9Pf56ZmVGkYmFhQYrFopw7d07vF8bAaiisWRgOhzWHDOPoj589LirG+GZnZyWVSmk0y88Oq9gwPBmLxW4o4eDol6Npzyabt3ntIWNIYlKinnMgICQgb5DL5W4QWxXZ3bDwc6lUMmKryPGgmyyOzcfil54hq2QyacRJ8R3+PjY/hnVgnEviOiaRMakBf2NIk/Mem5ubpvstq2dwop5zMjyPEPzlmiv+GyyRSOjiDriLoVzkohgGEhFTn+f3+5W+zcSQ4XBoIFVWaXBDWQx5sZQQ5iYYDJp7Hw6HjbI9iBh33XWXNoJ85ZVXJBAIGEgLf4vH40pAGQ6HujgzGQXziY2gXC7rdXc6HaMQwjlWlvliFXdW9UATUxy71Wrps8vyYYlEQvugnTp1yjg1hUJB59BxHKXaZ7NZvQeBQEAymYzOPUOCuA6R3XwkjoV3595775VwOKz1lExvZ/Fr7iCA3CmrxWCcnOOdVDfo2dg82NAzzzzzzLObzrzIaw8ZvEp3IpcpuAznochW5MZ+TYgmoFYhsgvnwctldQf+jshu1IA2FgzxcIsKjtDchbwiu14oJ+55zPD4U6mU6gX2+32jTNBsNtUr5XYXwWBQz4NiW0REXBzKxAE2RF6Tug3n83nTr4kJMI1GQ2655Ra9J5OiZFyTyDjSymazWhbA3Zf5GgKBgBFhdrfsQOTGBAm+b1zYjmPjb4FAQKnpH/jAB+To0aMiIvLSSy9Jp9MxahU4Tr1e13uazWYNS5ShWI5YGdrmCDEajUo0GjXQGJ7LAwcOaER07do1E7GiNAHXw7AdjtXpdOT222/XsV2/fl3nanV1VZ+JeDyu0VImkzEiyJ1Ox9Dbee6h6zkYDPQ5OH36tNx2220iMi4Zef755+X48eMiYsWAd3Z2DIuWmZMiYhikeF62t7f174CnPbvRvM1rDxke+EajoQ8y/i8iRtUAOS8ssEyZ9vv9mgNotVpKwQdLjnNWgIJarZa+zKy2gb5SzH7C5+LxuJ6TRW6Z2Ybf4XpY1UNk9+XsdrsKKSH/gIWT1QuY1s2bJH6PhYI36Ugkoj2moFgPGwwGRtUCP0NVH3ONxaxarcqRI0f0el555RU9Nl8X16OBDs25NV7EYUwzn5mZMYugz+fTeahUKnpPmRHY7/elUCiYEgH+G56j7e1tZcfNz8/LhQsXdAz9ft84JNxrjBmkDBO7WZIsuMs5WncjVMwPy2oFg0EdWzKZlGQyaZRWuGEkU9AxzlKpJNVqVTf3eDyuc+o4jub6WMwXAsj8jHPNI1QwHnroITlw4IDO4dWrV0VE5MyZM7K8vCz33XefiIi8/e1v1w2vXC6bnml4JqvVqoHAmeFbKBR0nhiy98yaBxt65plnnnl205kXee0Ri0Qi6r1ubW0p7NFqtYy2GTyy6elpI14biUSMigW84kajIYcPHxaRsarAfffdpx58uVzWJP7FixdleXlZz8EMOtQ2iYjp7cUafY7jmLFwfdBoNNLjsQCvu4cRQ43tdttEb8x0Y7YkRwOsNsGtNXK5nHq8zWZToRrAhgzhMTGD26swNIeCWJFx9MpRB5NZWIePxWv7/b6pv2JxYhZxjUQiRkGEySAcwXBBO2sbsn4firhFRH7605/Ke9/7XhEZq3q88cYbhqDAUCxDc/wZbhPj9/s1Uh0OhxMjTETvPL+4p0zKYIHcarUqS0tLOm+5XM7Ux0H5YnZ2ViHI1dVVGY1GCi27NS5ZQYWfcYZsM5mM3H///SIi8qu/+quqdnPu3Dn5+7//exEZIxLQ9bzvvvvkt37rtzT6Gw6HSt7Y2dkxHcHxXkNJBOfEs4LxYD7d7W482zVv89oj1u/3FSJgqIAptKPRSP/WbDYlFosZFQruW7SysiIiIu9+97vl3nvvFZHxBrW1tWXUN2699VYREXnf+96n8Ncrr7xiYC13zotzYwy9MHOQm0Iy9Z/p5AwBshoE8iZcOsA5QGw2TBMHlZyp84BEWZzVXXDc6/UM/Zqp9nw9nHfJZDK6UC0tLZmcJOdKsACl02mpVCpmrAy5YTxcLBwMBiWbzZrCb1ax4HljYxYf7ouIVXG/ePGinDhxQkTG+aZoNGrEcPG5SqVi2IK8CLuVWliNhB0NZoxizkXGzziO7d7McVxscBjP1taW3lOIQ4uI/PznP5f5+XkRGecql5eXTY817uHFiiPMRo1Go7rhHDp0SO644w4RGd/fL3zhCyIi8o53vEMeeOAB/T6g+R/+8Ifyne98RyHw8+fP68baaDRMMTe/F7hOzCE7JzCPKv/W5sGGnnnmmWee3XTmRV57xFKplEIqlUpFoTmGEFgyCQQNeHKcNGdY6/bbb9f2F8ViURYXF9X7XFlZkccff1xExp4s6w9yRNfv9815WM+QYSE2hpQY9nO3fuBEPUdxXDTd7/cNS4v7LuFYo9HIMDMZ9kPxLsbDrLlwOKwRDXcU5uiGvd99+/ZJNpvV+ieuTeNokQuE3RqUDMMGAgFDamAmKAsk8zHcBAmez3q9bjryckSDCCQejyvz8Zd+6Zdu0JHEd2KxmCGMsD4kXx//zFEUF3fjvjE5hgtxObLm6JdJNIVCQd8LEdHIhYWF0ZsLY8BciIyfay545vs7Nzen0Zzf75fXX39dRMZR1fve9z4RGbMOz549KyLjKBCwdKfTkVAopN9/8cUX5c4779Q5wL3mcUWjURVSFrE6o5MgYc9uNG/z2iOG3JCIhWh4MWDVCFDDAXn1ej0jCotFZ2pqSs6cOSMi480rm83qi55KpRRuKZfL5mVkhWsWvOUXixdXLrJ0Q27MYOPFmuEzVjhAUS8X8sJ4g+KFFsabBMObWBhQYoCxcO8yhhd5PLwJoOgVIqwMs2EDxTxxSQAXHDO8yLR5ZhSyOgjGz3Ayb+ZuZ4AXPN4geOEErHzPPfdIPp/XnJHjOMru43saCARMU0bWgXwrBRW3qCwzVRnmZqUYd/6Q54QFo2u1muaJisWivi+dTsc4RaPRyIwJc8jPyezsrExPT+tzsbKyosd+5JFHlDl4+fJldQR3dnbUOeJGrCJj0V/AsrFYzOSCuUibNy9mhvLzNglK9Gxs3ua1R4xfZsa//X6/biScjIe0DLw9Ts73+30j2/TYY4+JyDi6euqpp/TFLRaLep5Go6GLVqFQUFVriMqC7v3qq6/qeOr1uun+jBcTnWXxe84l4frwL2/YbpmmSdJIXGuDa+XP4Nh+v99EHRw94ViJREJGo5HJTXGnX6Zlw0nI5XI30LTdmyHOiRwItwvBWFmZBIszzwGOh3Ez+aHf75vyAa6lYukpjlIxJhgir263K4cPH9YxcndtjvYSiYQuwiCgcF4J3+d55ro7rkvDHPBGz3lI3uSDwaCp/8N38vm8Pvuc+2XiEAzvBZOaHMdRSv7Jkyel2+1qtLW+vi7vec97RGQcaSPaeu6555Tsw/m80WhkhKmZiMENUkOhkM4TS5FhDrgLgZto4tmN5uW8PPPMM888u+nMi7z2iDGbbHZ21lC+J3nZ8CK5Kh9RUK1WUxbhxsaGRlTwEPGdZrNptA2haec4jjz11FMiMs6fHTx4UE6ePCkiIvfff79CJy+++KLmHVqtlnrMrH7g8/lMOw1u887tXhhSgSeOv7lzRJyX4oiO6eDD4VCvG8KrIrZFBcbGdHKeZ25iCC9/cXFRer2eKWLGfYOKBIyFazlackNEuB40bMTcMLzIkCbni7iMAuxLjto5skUkyBDmpUuXJJvNKtOu2WzqXKXTadPXjVmeDAVz3rDb7WpEMxwOjdoHN4DE3zF/3HCS85PuIl0uK2BomvUl3WxYzoPCDhw4IKdOnRKR8bN76dIlefe73y0iY0QCzNtvfOMbWoyczWZNUT+zLUejkYEE8bxMT0/rc4jx4TvRaFTHzbCuO7L2bLJ5m9cesUqlonmHXq+nP6fTaSMfxF2Aw+GwEebF565evSqf+MQnRGRM9UVea2lpSXq9nnmJsdAUCgVd3FjRHbDaj3/8YxEZ04hxvFQqpb9niMnv9+s50DeJ6264rorp8Uxn9/l8SkXmBQ8NNXFsXii5LxTLUPV6PdNEEAsiaus4v8A9xPj7LJP08ssv64IWi8UMMQTnaTQautBVq1Uj98R1Y1wrx12eR6ORzMzMqEPiOI7OYblcVqcjmUyaDYrJNqw4AoKAyNi5gQPz0ksvyd13321ypDhPvV43/clYRDYejxvRX1a0YDo4fu84jjSbTVO7x/POhBF8Z2ZmxkhXra2t6TPKsDLnPTG3eP44X8swZjQaleeee05ERI4cOSL33Xef1jw+9dRT8sYbb+j9xb1iuaxwOKz3Bo0p4QCcP3/eSGTh/u7bt888X6VSybzPDDtinJcvXxbPJpsHG3rmmWeeeXbTmRd57RFjBQbHcQwbiiE4bpXQarU0imCttmAwqIXJf/EXf6E6eFAfwOcqlYpJqMPjZhZgIpGQWCymMEi9Xte29+FwWM/f7/dNWw0mbDCsxBqIfG2sjhGPxyWbzaqOHHvzq6urRgkB0Wa1WjUCvu5CYHyOC3+r1aqEw2H15uv1uhEkxnhmZ2eVwNJoNOT555/XyIUJBkzdZ5Yok0owHmZmwoPP5XLqpe/s7Egul5tYcBwIBJS0wpCUuzM0n7PVahkGKe4Vum5jDnw+n8719evXTaSAZwWEFW6hg0iw2WwqWYi1DKGswjAnPtfpdExPMty3ZrMpGxsb+n8oiIjssvUwhzw2Lo3gqDmVShl9SDxfgUBAfvKTnyiJhTUZGQKPRCL6jnBvLogzM7sU88ERJhvYmlzQzfcR3/E6Kb+1eTOzR4wfWM4nMNWXFbvRzwvYfC6X089NT09rTmZnZ0ePVavVDDQVj8cVnmT5IaaJg6KNxZ/hIhZ75RbraMUuMl40eXESEcOg48aF+EwikZDhcKjQTbvd1s2TWW5+v18pzcgdYRFgtXVWN+fFBBsPFlg3BIjzMKR64cIF2d7eNvRt7gPFNXA4FliDXF/G6vUHDx4UkfHGDKgUkkkYAyvEcy6o1Wop3IXjYUNjBRNeQNkJ6vV6sra2pvnORCKh6hClUkm/H41G9V4BgmT4mRtIcqcCnBelD7j3buo9rN/v67yh3IBZeQxV4vv8bGUyGbNJ8nPV7/e1xCGRSOi78+qrr5oNKxKJ6P11s2T5OXKzIjHvXObB/fC4LnM0Gsns7KwRHeYeeDBPYeOtzYMNPfPMM888u+nMi7z2iHG0xX27RHa9PyYUoOYLEQ63ITl69Kh6v244gutJIpGIwkeckG80GqY3WKPRMLVMTGTgQlVEZ71ez3j/rAziLj5mdiDDMOxxp1IpAxEh2uM+W2CVsaoFogvHcfT33W7XtAzp9XqmQy7mptlsqlIJSCEiY/YmXwN7/VyrxxEe15xhDgGZQVsQ34GxniOOwUK2mLdIJKLEEIyBmZU8Phw/nU5rQXoikZCrV6/q/ExNTSmMGY/HNbLlAnlAi/x/zAfDZ61Wy5BzWCkF98I97/zsQyx3UrsVdzE6xoIaK8ypG63AsRzHMfVsLMzLz4jIbusWhsUxPpFd/U/MaTKZlK2tLREZR6mIpDqdjj6TpVLJFDezBmMoFDJC1p5NNm/z2iPGbDTHcRSmCgQC+pIxdRo0caYYYxEuFAoKP8ViMX3pmMmF/7NyBqtisyyRu4gUP3PRJy+S7gaN4XDYiNfCWEkgFAqZJohv1XOLlc4dx7kBDmPokgubeUGHgYmGsUejUf1+KpXSRTwQCOgivry8bBbYSQswrsddgI2FK5PJqLp4NpudSOXGhoDFnyn9TLXn3/v9fmm1WsZxYQFfHJ8bbWIe4WwkEgkdWzqd1t/zBgUIdFJxNlPd2QGDLBdLR02S7OJ8IHKVfI+5DGCSAspoNJJYLGYgeJauYkiTFer5ejjvh3kUsV0MeLMD/MyF65yL5HlgGNCtsAFjtiRyZ57daB5s6Jlnnnnm2U1nXuS1R4yljSKRiIkQJhWditxYwwLvLZlMamLa7/dPlCfC/1kUFp5nLBZTLxu/Z/0+9uwBf7G0EfdtQp+uSd2gmfkYDocN5MbJfiaDiIiBhFgslq+Bz5PNZjV65T5SmHPANRx5hcNhhYsCgYDR/uPIksfF0QTXIYmM7ylIJ/l8Xj3qYDCo5JpOp2PEiLm7L7NRk8nkRCgZ0R7XtGEOOTpCF26ck+vwksmkRpzZbNbIIeH7INrg/zyHXBSMv/H8AOYeDoemqJfbreDZy+fzEo/HdWy9Xs8U+XLUz+8Onz+ZTOp9cLP78H0wCrkGjeFsRF6pVGpitAjtSoYamcTD42R9Sf5OMBg0Eeek+fPMmjcze8Sq1apZCBmi4YeZhWNTqZTRlGPdOGgRss4gNpRJOZ5cLmdySQyVcLFpNBrV8yQSCYVHer2eKTJmKnkkEtHNg6EXZudxHimdTpt8DdPOeXHM5/MKiaKgFt9Bzyn8PEmRHYseM+/AtDt58qRuMKVSSecwl8vJzs6OgT9ZuYLhOFZnX1hY0DmZmpoyeUMcmxmJYHhiga9UKuYe4Jy4DyK7hbPYfLa3t43YMudLOdfC1PtWqzWxwDcWiylrDs8kPtdut3Xek8mkzjvT4qFmwhsB5mMwGOgm6fP5NMc4MzMjpVJJN0YWUWZ4kQuBIbyMMTSbTQNj8rOP62HHD2PgEgW3piO+g3sF8WBmQrIjxu8sxpVMJsVxHKOYz33dMAfufm2e7Zq3ee0RYyKEiBiCwiTB3mQyaWpiuN0EK5CXy2WZnZ0VkV0PFy8QFLhFxvR6vDAs8ttqtYzYKy8mW1tbhtgB8/v9uhimUinjmXPeg8kSjUZD69FqtZrs27dPv8PCr9FodKKXjs2bPeZJyu2swg7hWozn+PHjWuvjjvYwzu3tbQkGgyZS4QiCDedMp9NSLBb1/+VyWe9Bo9HQ/CSiOhh7/RzpJJNJc9953qPRqJHcQmRcr9eNygm+h3vAOS/MD495a2vL5C352eFonOeaSw9AnMDGyg4Wi/6m02kjX7a4uKjnPXfunMkPcvTobvjISAGXmnBkjPmIxWIm58ubFEe2nU5Hx4Zji+yScyaVjXD0zCUS9XpdUqmU6aDMFHk8k8Vi0ZCQPNs1L+flmWeeeebZTWde5LVHbHp62sAthw4dEhGLrXNhKKr4J1GUmXabz+c1Url69aqkUimNyrjRHxfETk9PG+YUtyBhmC0WixkaMo4VDofVK+10Ohq9idhoiaGZSCSiXnGxWJRKpaJ5u0AgYNh9gPOgkCEyZvAxRNPv93WuuAkgixkj54ZrOH78uOrTvfjii3Lt2jX9PgvEcoTszkkgQotGowpBFotFUzzc6XQ0z7W2tmagTlZ2QJQiMo6A8Z3BYKDXkM/njXKGG2bCWOPxuM7v1tbWDUW4+FypVFI9vUgkosdut9uG/s3PQbvdNooQuL+cfwJ8jEiDIxhmb7bbbb1O5MUQmcbjcaMiw9eNuQW7kBEKbm3DpRVAF3AdDM/zPHL0yO8bR7+sn7m2tmYiQS7G5pwms3X53vPcuhuZerZr3ua1R4xrqfbv368vbCqV0ge5VqvpIuPupMyqAslk0ihAAI6DpBQ2pkajoYuO4zi6eXKOB99jOSOMs9Pp6GLA/aZ6vZ4uvCBrYGyhUMiotXMvK86Lzc3NmRyAe9PGHEAlIRKJSKfTMY3/8DnHcQy8yaSOdrstt9xyi4iIXLx4UTskB4NBVb7Y2dkxxAWu+3I32uSml4cPHxaRcT7jypUrCpNx77NAIKBjzmazuuENh0OjbF8sFnWxbbfbSiC5ePGiyZPlcjlDr2YyB+a62WwamjfXwQ2HQxUdLhaLOjeO4+hcI3/GGy3McRyTw2PKuc/n05o0hvAYamRSBu4D14oxPIlnj7sTtNttSSaTOj9cMsG98ThP1m63jcPFJSSQm8LcuGn8IqI5XRw7kUgY2J/hRYaBeTPmukBW22CY3TNrHmzomWeeeebZTWde5LWHjD1MhiTgOVarVS0gBXV5UjfawWCg8JfjOOrtbm9vS7VaVSgnEomoV8n9xLjYF94iF8viPLlczjAMWbMQx4J3DNiNk86DwUA9ZGZLDodDQ2pgkgYLwtbrddOChOeg3++bCA8eL3c4RmE05ocT7fl8XpaWlkTEChgzvR/HYwYauv4ePHhQ5+P111+Xzc1Nvb56va7nvOWWWwzUid93u13Z3t7Wa93Z2TEiubjO2dlZU6xbKpVuUObAv4gMstms6XWGrtzu+1upVDRCnJ6e1gh+Y2PDqHwkEglzfziC5nvNcwX2oYgtX4hEIgbmg4At5p5hToZbcT3RaFQcx9Hx8He4lKHVapm5ERETQXOExUXOHOXCNjY2JJlM6vzm83l9xlqtlj7H8Xhcf9/v9yWdTpvoFXNdr9f1edvY2DBRqWe75m1ee8TC4bAKrLbbbVPHwwKkjH8PBgOjZM0CvG9729tExOYdKpXKDZRgpq0zdMT1Rdz4r1AoaC4ITEKR8SbJ+Q2GTTqdjlGH4A2PNxu82I7jSCaTUaYcL0DMjHNT0zk/2Ov1TK+wSe3nMQ7kYWZnZ7VX2c7OzkRlEjDoeCPBcWKxmOZyMpmMLuJgnGGjzmazZhHDBsU1X7wJuK1SqRg2G8YSDAal0WiYfA8vyPhcIpFQCBP0fLd8lchYKBjQ6czMjFHc5zlxMzOZhcgbM7MS0efN/Tlm5KHekJmRk87JzxtyXvwssnOB83PzR3zerXKBz2E8zWZTf890+GQyKYlEQufqyJEj5p3jDgtc14XfiYw3Ni49YIYjX79nu+bBhp555plnnt105kVee8RYe46JGG5VDfZqOSGOmiWRceSCCCKdTiuEAsUFriXiyItJDcx8wvlwPFaHYOiHGYbwHEEs4fOwl86QjLvjLTxNZj5ywTO+x8fhuWIvG+fnnxFBINqZnZ1VaGxlZcW0NGEiSLPZ1Otm1lkikTCalNz7yXEcPXYikdBxlstlve8zMzMaBaIXFmBRJsQ4jqPnX19f198fPHhQcrmcsgJZlYPrCKPRqEbCiOa5hgtzycXqyWTyBj1HhuP4/uDvrCWI82CumAjBRcIMk0Pjj1uVsP4jroejabRR4doobl0Cc9d8saAxw/EcIfLzztcmIvL+979fkYITJ07I2bNnRWT87LLiCbMIWenErajDc8oC057tmrd57RHjgl2mli3uiCQAACAASURBVDMkIrL7kKN/FRQU8vm82RS4SSQefjD6OH/FEj9YeMvlso4FCxtDNFiEI5GILvyxWMwsbiyDw7Ajb568MVer1RsgTSw6mUzGbMD4mVlzyNVw/oep8jBeXPFdhgexADGMxJsXcnOQeuKcYjabNU0ROccVDAbl2LFjIjLOY4DRl81m1RmIRqMKKx05ckS2trZMIS2L8WIOp6amdHHMZrPS7Xa10Jo3WTfdH/cQ/da4OSWMN9l4PG6KuzkvyiUcmD8RWzzs7pSQyWRMUS6eI352wEzFMWKxmIHbeMPisotCoWCo/+x4MDSO+ZiZmTECwO12W+eDVT263a7eX5Fdp8rv98uDDz4oX/jCF0RE5A//8A9leXlZz8ObD2DlRqOhLEcY7mk4HDYqJ/wZz3bNgw0988wzzzy76cyLvPaI1Wo1UwODiGp6etpAiPDS0fmVizvhtReLRfXY/X6/MhSPHj0q7XZbPWhOOjN0FIlEboBk4IkuLy8bJiQ87WazqcQDhqhA0GDpHWajcc0WrjkajUqpVDLadfiZi6m5Pgh/Y2IHxskRDcNSKFpFlDk1NaX1XAxVci1XvV43napnZ2fl9ttvF5ExgQXnr1QqSsAplUpy6tQpvb6lpSUTdaAgfXl5We677z49z5EjR/Q7HNlmMhklXDiOozWBIERgrllMF2MVGUdoeNa2trak1+sZrUS+bpyHSTcsoixiiTN+v9/cay4qDoVCBjlg1ADGTEo83xzNMsOQ273g51QqJZFIRO9jMpnUe18qlfRY2WxWz3vu3DlJJpOyf/9+ERGZn5/Xz21tbWldHwsJhMNhfa+mpqZkfn5e72kkEtF7kkgkzLuIuUkmkwaF4EJvt+wZIyqe7Zq3ee0hu3DhgoiInD592qhLoNh1Y2NDN4utrS3Z3t5WanapVDI5o5deeklERPbt26cQ1fr6umEvudWrsdiGw2F9EVG8jE1mZmZGN4xqtar5FVaSDwaD+pJDJxH/z+fzZmNjtQ18363hxkW5Pp9PNy/u24QcAiAWVohn6DQUChltx2g0OjHXx0W93W7XMODC4bDO++233y7FYlFExnAr4KKrV6+q03Hw4EFxHEeVK+LxuBFxxdxOT08rY+1f//VfZWZmRjd6FmEGDClimYtuQVlW1SiXy3L+/Hm9B9i8YrGY7Nu3zzDduMEo5qparZr71mq19BpGo5Eu9szIYygcTD9e/DFv7XbbsFOZGj8YDMx94I3NnRvD7x3HUVi3Xq/rhlcsFg0UjA1ucXHRsP0uXbpk+nZh3iuViuaSe72evPbaayIisrm5Kd/61rfkD/7gD3Suf/SjH+l9wziTyaQ+H9j4uFSFtTDdhd+e3Wje5rUHbXp6Wh9uKAaIWG8VLzJj87zwPvXUUyIicv36dfUC8WLjheGme5yX8vl86i2CfIFFaGtryzRsZJVuLAysFoKWFNw6BYuB4ziqKMHUZbSO4AaYOCfnJqampgwVu9fraQTA9TWBQGBi9+ZkMmkW1FqtZjY5eNxMholEIjI/P6+LWCAQkIsXL4rIWO0CKhSJRMIk4bnBJi9MgUBAVldX9fcvv/yyiIxVVpiMUalUdN6azaZeZzqdNqoTfr9f8yoshxQKhXSxrtVqGu3F4/EbxspzjXpBt5wSR3UcmXJrDz4WcrScf11ZWdE5YCFdrrGCEoWIFZxm1RXOg4IEgfckEonouOv1uumizULWhUJBP5dOp/WdK5VKep3r6+saicZiMX0+Tp48Kffee69ec7FYNPlrzq0i1zgcDiWZTOo4jx8/rmSdtbU1eec73yki43IFdwdnz8bm5bw888wzzzy76cyLvPaQwYNeW1tTL5sFUTudjmkvzjCXyC5bKZFI6HeCwaDRH3QX9cI4OoKHLjK5nxdgLi6mZPYXFzlDRYAp9yxei+Oyh4tIgAuOmX7Nxdjunl/cPoahT3yu1WoZRiLnnriIlBUpOE8GGjY88PPnzyscyCojrEDBKiIi4/vIOY1Lly6JyBgufuWVV0REFFLD9WxubppyA1xDtVo1Rc7uXm2sNIGItVaryZUrV0RkHL2ygkkymTQaihjPysqKaWXDSiPc0oSfSZRJiOwWAjO9HudhKJvHCZ1ERCScz2PaOqtbJBIJabVaCrsz85Bzn+4C/2azaVRhcM/cESZ+7nQ6+ky8+OKLMhqNNGpOJBI6B41GY2IJSbVa1Rwk/obxMHOY76dn1rzNaw8ZvzzAuf1+v25YnI9ADQ/XGzGpgaWieDGIxWJGLBUWDAYVwmAKO5QROA/FnW05ac4SQ/yScs8rbkCJ8+JYGH+tVpNgMGgWa070Y564sSVvWrgGGOf2WCgVihwYG8MzXHvENWhQscAGv7m5qZ9jhQ9edHDfcAyeXyycImKkqtDJGfe+Xq8bajrn87j0oN/vK7TG88zQZ6/XUygZyiYsWMs9p7jEAWNpNBoSCARuUCrBzyxwy7VT7ASwowCZLtwfPh734+LmmPx9lnOq1WoSiUQUnmOyEdetcRcGEEn4OeFNDtfTbrdvqHsUGW9wKysr6sSsr6+b/nMMVeKeuAWIK5WKqVXEO+Z1Un5r82BDzzzzzDPPbjrztvU9ZKxswCoQzP5iUoXf75/Ivkqn0+q5ZbNZwwrjLrqsLTgYDDRJzZEZe8/4ziRtQowB50cye21tzURoOKaIhQNFbJ8s1s7jiIavkwkrk5QiEBGxCCyLqyKixDG2trYUyuLeYOyR+/1+qVarCksxJMnXyN+Bx81MN24fg+8j4sR3+HNMZGACCxcLI5rgCIvJOTy3YAeiOJxb7fDzMqlrNSDdSWNjSNPdzRpjxN94PKzE4S5iZ8IFFym7BXVFdmFPHM9xHKMxic+yGDD6bPFzzVAhQ8uTCsUxv9yGCNfHY2s0GvqOuZ99nqNut2sYl55NNm/z2kM2SYCT80d+v9+oqDN0w9/P5/PKemPm4vb2tslTiewusiwlxNRcbBbMAJsk8ROLxQyEx73JRERzRJDvEbEKHzwWLEy8KbBcFYsGY6GFMgM+x2oInE9g2BKbHc6zs7NzAxOQ/8WxmPkXjUZvgFjxOf6+W7aKj4mx1Wo1hTDdYrnxeHyiujrnMeGYuHOH7rGxA4AeZMxYZIMTAiUOkfEGxxCY+zu8ebGAMfec4+fILX+G42ITwDGmpqZM81PMVafT0TEg/8aNXXH8SCRinmNW3uBjcC6WVTn4/XPncYvFoubmDh48aDZgZlKywLNbzQQOJ2/MnOP2zJoHG3rmmWeeeXbTmRd57UFzd5mFhUIhjQx2dnaMGgGzp1ggNhgMyoc//GEREXnqqafk1VdfNcfmRDefiyEzbqeBcYiM4UGGZLgfGSKTWq0m0WhUiQisG8ckBp/Pp+ePxWJGbJWjT2asMeTmhvgikYiJvGBca4TohgkbGDd3yuW2GNVq1USvoVBI1TZY1QPjw9g4euVaM65vq1QqJipkr5+NCSQM7SEaANOUO2CHQiGNUt3tSxiu7ff7yrQbjUZK7IjH4zc8A9yeBObuXMzwXSwWM0oeLHiL54iL0FHkjIiEx5pIJEwdHpMyqtXqxMiHa9CGw6EeFy148LywsgieRZGxEgqe41AopNdSKBTkkUce0blaXFyciKJwp+1EImFg/3379ulzlEwmdcz4nWc3mrd57SHDC+xmZbGyNzPieKHhDaZWq8nDDz8sIiKPPfaYUtt/93d/V/7t3/5NXn31VRGxArzMtlpYWDALLxe7Mh7faDTMYsKQDl7kQqFgIB53AfOkxRlSV5NgLt4ceEMAHMnFsrBsNqvf73Q6JrcRDAa1qFdEjBAuxuw4joGbWq2WKbbFIsqsTIZ+APMx1MebD28CUO7odDpm3kREx1kqlXRjdRzH5ERZDoznrdfr6T2MRqNmk2anJRwOm+aHbiV5/MwbID+vXBCOMeCcnNviBqHhcFg3Ar5eCANjrnkzZycokUgY1quIbezK94Fzb5CHQlE+5iQYDOoGeujQIbnjjjv0PMh1slp8Pp9XpqHI+HnjjZlhXXaustms0uUBR4uM5b9wfzmv5pk1b2Y888wzzzy76cyLvPaoIVpqNpsGaoD3nEgkxHEcU0MCb+/xxx9X+aLPfOYz8rWvfU1ExtHAkSNHJkrf5HI5rV1iggE8XHiim5ubGp2w8GqlUtGfk8mkHDhwQEREi0zhPXNBK0dBrD/Y7XYlk8mYdvCISlkD0S2+2263TX0cR6kcbbHMEdcvJZNJ9aa5IJULngeDgWQyGdNrbFJ9WyAQ0HslMo7kmBnJ48F1Q9dQZAx/8XmZ2ekmunD0LCJ63kKhoDAXQ7mVSsVoETJkOxqN9JyZTEbPUy6XTXTFRcpMPuDolyMwjH8Sm7PRaOh4GFoLBoOGGMIweTqdNsxFzAHawHCUyTVsmGuWigLRBbVh8/PzcvToUREZR7tPPvmkiIyfKcwnt5d588035eLFi/Loo4+KyPj9427fXMzN8Pf6+rpGiI7jmOthkWzPJpu3ee0hw8vEcByLqyaTSdWDQ5t5Vl5nhQ68cAsLC6qc8fLLL0u/39cFZHZ21izQeLG3trb05W82m+Y7+XxeX9xGo2G087h1OTaReDxuBGa5OJMVw0V2N5i5uTmjVM6baTabNawsHKvVaonf7zfCvKwez4rdDE0xiy8YDOrCu729rTAdqzlAeJYZoHxsnDMejxuNQFa/YFgKfxcZL8jXr18XkbHCRqlUMveBr4d1ErnoOhQKKcOz0WjItWvXRMTmQd1sRx4rjoN/Aa2lUinTo4pzkqwm4nZCmDLe6/XMvHHPOMxhOBzWufH7/VIul83c4967KfU8n8ycZfiYoWhuvjo7OyuFQkG/0+l05Hvf+56ObXFxUUTs+7e+vq4Q78zMjCSTSXnhhRd0nKywwTlm7sO2vLysSir9ft+8M3A0OGfmmTVv89qDxi8Zb1DxeFwXs3w+L91uV18gJhjMzMzI66+/LiIi//RP/6Tiqj/4wQ9kenrayOXA/H7/WwqtBoNBQwHn6GZSnVckEjG1VO5EP1PiEY0Mh0PNHVWrVel0OkYhnVuNYPNxS01xvVGlUjHXB+O6HQgVczQLskMqldLzxGIxU0/HeT/OZblzXlhQUV+EeZuamjILGi/wWJwPHDhg1Ph5Hvle9/t90yiT83fVatUQFDg6wv2MRqOm1UggEDCq/cjxZDIZPT+3P8G1wvieYr5gbjIHRxq4Bqa2wxnhej3OG/L34cSgCSnmx734s7OHz5TLZUNY4nYnhUJBy04uXLhgkA4o0mxtbUmj0ZATJ06IiMhtt92mThlHrJyDxLnhUDBVPxaL6bPiETbe2rycl2eeeeaZZzedeZHXHjTO13AlPjO+AOkAW/f7/eqtMW0+FAqpF5jP541GHsNF6LeEYyHySiQSEo1GJxZncvEwe44+n88oLrTbbROdTKIxs1ArYFMu/uXojfNS7P1z5MXwIMOJ3NrecRzTcgZ5JhGrY8eQDiIvprRzdAFjOj206jj/xAKv3GaeozB3ThNRJrMsuah3ZmZGRqORPhOpVMrAqpgPN8OQi8oZ1s1kMhqFMRu13W4b2jo3GOXoCP/H/eGInp8x/o67LMP9vHHE6aahi4yfDVbY4NyciMgkDUcUqzPkDGPotlar6TjdOcg777xT5/fQoUMGxmTDOaEag0h5c3NTz8v98DyFjbc2b/Pag+buacSisAyVJBIJk7/BC1uv1w3BAC9/Op2WTCaji3UqldKNjXt7ra6uan4DxAUcz606jkXYnVfiOhf3JsOKBby4MVw0Go100WC6NOYE52EBVc7DsELHaDQyKgcMMYEYg+vh77CMFedK+D7wOd2qC0xocBxH55pzde12W8fAm3QkEjEwJBNyOEcEtXaR8YLMmyTo9iJWTZ8bL4ZCIUMACQaDpt4I887QIDYb/I5rodyyRyxj5e6AwL3kuHM3zy0LDdfr9RuaW+IcTI3nMgXcC3yO7w83+mQJKK4BY5icoWzOYaZSKVlYWJBz586JyJjwgTwzS3zxWPCs4dqq1aoZgycP9d+bBxt65plnnnl205kXee1BQ5sKkbGXzBR0GLTz4K2B0SYy9ljvvvtuERH52Mc+pv2iZmZmpFgsGg1CRAMsyDozM6NU+1qtJhsbG5q4v+2224wyAVN/+fww0M9RtMzeL1OXmRWG4lxcGzP6GOLiQleGC2FMcMDPzWZT55OhI3wOf+M+aIiCcJ5UKmVaVrB3zG1L3CLBrAnJiiBMFGAo7tChQzo/6+vrptcYvp/P5w1js1KpaHfqWq1moiCed44wE4mEKUqHra2tGeIOR2dMdXf3lWOlCj4P3/toNKqlGe7IjeeDIWuGnBmKdmtHMiQJiBPHw3wyqWRra8tEX/wsggCCMXMXbhCM0BMN92dqakojL2YLs67n2tqaHh9zxWxQbhHj2WTzNq89aLlczizGgJWY2u6mbDN+/tGPflRfkk9/+tNGOaNcLutGtLGxoZBIJBKR6elpPQ+gwUQiIXNzc/oyhcNhOXnypIiM5abwks7NzSncVKlUjGJCvV7Xa2BqN7+YnPuBoCwvYjheo9EwiyYvrm62H8xNZ3crbGDhTiaTBtZhGIdhKYaPWL4IEByMN45MJmNEdyfVbIXDYbnnnntEZLy4tlotnZNUKjVRASKXy5meW+l0WhmTnKOJxWI6V47jmLooNH0Usc5Sp9PR83BvsWazaerTAoGAgbPZoXHDXgyDYgx8T0V2F3TINjFky1JRvDG64VXMG+ee+v2+2TDxmdFoZHrlYY4xB3ivGo2GXjPLeq2trUkymbxh08P3uQ6QWYj4u8hYQJtzpMz+5LnxbNc82NAzzzzzzLObzrzIaw9aKpXSOpM333xTPfb5+XmF88rlssRiMfWyI5GIRj7NZlMeeughERF5+umn5dSpUyIi8vWvf93Us/h8PlMP8+abb4qITR6nUilJpVLqwfp8Pvnud78rIiK33nqrQmtXrlwxSgjwUDudjhZ5iohcv35dIRsWGoa+nMhuESyimOFwqN9pNps6FigiiIyjPbdiB8N0kyAmfAYRQL1eN7U2bs0/nD+dThsvG/BRp9NRz34wGGi0WalUJJVKmRYiHDHD+15aWpJbbrlFRMbss2azqeSL/fv3G1IDNPEcxzH6ltPT06a4m715/J6jBq65Exmz63CtuVzOtBbBdwAZMnEGx47H4waSY2Ypw7RcpOxmDXJfuE6nY7QJJ/UK47YpQBLwXHKdGCJTHAv3ClE7M2wxBwyxTk1NKQKws7Oj0ZPjOKZdy8bGhs6nm/jD1zo9Pa1R3WuvvaYoBgsqM0TsmTVv89qDdvXqVQPjYHErl8tGpikej5uGgLCVlf+PvTcNsuuqrsfXm+ex+3WrB6m7NQ+2bAkJ22B5LCaDCQ6JAzgDQ0KKkKQSPiQUVRSVUAVFVX6ESlEEU+RDqBAMIRgwHmSDBzzKs2zNUktqDT336zfPw//D/e+lfdoy2DEGtX3WFz31e+/ec8+97+yz19577TM0akeOHMHo6CgAh9vXNIT0MQJMo5DL5Yz28/rHtLi4SKOxsLCAiy++GIDzQxQ68syZMzSEfr8fs7OzLPQMhUIGzaWpMN3HSQvJaiM3MDBgKC7I93U8SI4ni5amwvx+/0saBcq1pdNpQ7JIK96LYU2lUgadqNO6ddzP4/FwbKlU6iVZjjrjUsaczWZpiEKhEGZnZxm/SiQSNAoul4sxE91bTGhPHas7n8q9zsSUzcz56LBYLGYIzMpiPTQ0hEAgwPEsLi7yPPK8AC+V2AoEAoYcknxfz6cWGpZYoza62pBpw6sLqyuVCt+LxWIvyXyVMesYcjAYNGTDtPGSTeHU1JQRPxNDGAgEDCmw6elpzpVW89ebFsB5lvWcyvkrlYpxzVZl4/ywtKGFhYWFxbKD9bwuQFQqFZw8eRKAGbBtNpvUQjt69ChcLhephlwuZ+wqZbeos6UAsx+WDmwvpdZkt1ev141kjmQySSorEAjgqaee4jll91mtVrkrdbvdmJyc5Dh1hiJwLhFCFxKLSOn52nH4fD56calUigFw2aHrbEF5T2em6WPpFi4yH7r2R3b51WqVHlAqlcLU1JRRyKsLbzUFqXsyLe14rQPyAl17tHHjRszMzLCvlMfj4XWHw2He30ajYUhC6SzAcDhsJFVoD15neS4tIpf35ufnDS9Onj2Rk1paTCzn1JmZOmFCP3uJRILebLFYfEkSjaDRaBjdh3VdlNb/lOdVis7FqyuVSoYnpzP/5LXca13bpeljLYytqWS5B5lMxmiNk8vlyHzoRBCttwk4NOQTTzwBwOkBJt50Npu13tYrgDVeFyB8Pp+xiIqxmJmZwcaNGwE4P6p8Pm+kP8vCkM1mjbiDpsl0Iaz+Ier4iG4sKX2G9EIu1JZWbdCLps7+EkOmxXg1taf7MGmaTmetaaXyVqtFQ+p2uzkWGYcsorIoy9zoDEcZi8/nMxZLl8tlFHfLwq2bA8rCIjHJ+fl5oymiTn3Wgr+ibyjzo4t3ZUGuVqsG/dVqtYwsR72g6QxFnXavdTH1/dFUoX5WAGdR1/E4LSAs34nH49zojI+PI5PJGArrQn/J8eXa5LiSJi6bGr1Z0s+bjvFI/y6Zk3A4zPvj8/l4Tj0HkoEr/49EIjTuWuVeZ3kuLCwYosyapu50OtQPzWazRs89ubbR0VGUSiUjXimGUJQ0ZJy6cB2AMTZ5XnSTWFuk/PKwxusChF6AQqGQodKta5fq9bohOSQLVTabNWpO5EeaSCQwOztrBNp1TON8tVIisyTGMJ/Pczw6piH/B5wdppY/isVi/NHr3adeUOv1uqGCoYPz2iPR6hbZbJbXIqr65+u4rAWN9dhE9UHXY+l0clk0fT4f51ZiJdqY6sQSvSHQBkofWytA6MQD4FwtXygUQrlcpqGWFH3gnOcDOM+BbhdTq9WMdi3ifUYiES6YzWaTMU2REtP1cuczrC6XiwkOmUzGUCbRc1Cv13nOfD5veIEej+e8jUx1eYHeREksTrz2Wq3GjUIoFDKaZmplFZfLZdRzyZwGg0EaFd3WRuZAd84+30ZDxid/FwSDQZw4cYIK/GfOnHkJWyBjk7+nUinU63V+R8e5zqfIYfFS2JiXhYWFhcWyg/W8LkA0Gg3ueIPBoNEDSV7HYjFks1mD6pAdeKlUYgbayMgIvYb+/n725wJMjTyd1agpFaFqZCerW6k3Gg1STLrpno6FSKaizsLTO2t9Tk1B6liJptwqlQp3svF43NBW1PEa3XRSt2GJRqPGd0KhkJGirwVe5Vha8SAejyMSiRjH096jXMNSVQ79OT1XWvMvEAgYvb30ePS9B8D4k9frZdq8zK14dVpYV+v1TU5OvkTw99d5gtVqlZ7BwMCAIQRdKpUMD03fA+316FYySwvAtdeh73W73Sa7MDc3x+dtdHSUfcv27t1reNb1ep3vNRoN/hZ0+YVW64hEIsZvQc4rcyqIxWLnbZ4aDAbh8XhIAU5NTfF7OvOx2WxyzoaHh5HP5zk/uVzOOOf5CvktTFjjdQEikUgY8QAJDHc6HQZ1JRVdNzyURadcLvP9NWvW4P777wfgqGBoPr7T6Riq4Vq9YKlauyw2yWSS49GUio5bRCIRvs7n81ixYgUD2FptIxaLMRECOFejI/EROY/P5+OPvFgs8jtzc3NcxCW1XKAV87X4rabc5Nq1nJE2JPI5bfwikQh6e3t5PcPDwzxvpVLh4hyJRIw51MeWOQYcoySL6+joKI2fGElNfUpfNp1eHwgEuLjL4iyxoJmZGY5H04nasEtPM4FOH6/VaryPrVaLFFc2mzUaUGqlfl3+oA2uKOTrOist8CzQhl02GjKG3/u938P3vvc9AM5G7PLLLwfg1D/ec889AJz7qwWrdU+zUChEA5PL5Yxr02n0mprW8UH9HOpuBJFIBGNjY/z/+Pi4kVIv0DJafr8f8/PzBvWpa/80NW9xflja0MLCwsJi2cF6XhcgPB4PC4EXFxe5s9+wYQMTJ7Zu3YoXXniBu1zt7bhcLrYrv/zyyzE5OQnAScdd2sdIdx6W18FgkAF92f1LVp8WrJVjAOcywwDH05Dd/8UXX4yTJ08aKdKyQ9Vp97VaDUeOHOE1p1Ip7tJrtRrPn0qlmDKeTCaNxBAd+C8Wi4bKh06H14oHWokjk8lwrgcGBujlynkBZ5dfr9c5Bz09PVizZg0Ahz4TAWKdrCBZlVqPUOatUqlwd93T00O6q1AoYHh42BCyle+cPHmS3me5XOb99fv9LBSX72glDd3Lamnm3fnoRZfLZaTKy7X5/X4kk0nOqe59pjUHdeKDJFjoLFjx+HTij/ZAUqkU/H4/haVvuukmXHbZZQCAe+65h9ezdetWXH311QCABx54ALVaje/19PQYhfj69yLX2dvbC5/PZ6TKC9OgPa/Z2VlmmUajUYyMjABwPNHrrruOCS3ZbJbn11SlTq5xu91Gt26t9KITlCxeHtZ4XYDIZrNMz9UNBTUvvmHDBhQKBUxMTABwFp3zVfLHYjHccMMN/L4WqdW1UJ1Ohz9YTYnIQiSLdzAY5CKm+3FpeZ12u02KaXJyEh6Px6CLdPxLxpJMJrF27VoADvWj+19piZ9arWYseqdOnQLgLJSpVMoQvJV5C4VCpM/0PMnY5Vrdbjcz27R0lsvl4mZi7dq1RgZYsVjkgtbf34/NmzfzOzLObDaLYrFoCObKOfv7+7Fz504AjoE4dOgQ56BcLmN+fp7zI7EtreQxPT1t1Kt5vV5SY7qpoVCXgGMg5H7OzMwgEAjwvXq9btBkWiRX5m1hYcHoBadrlzRcLpfRLDUSiRixNvleNBo1NkSCvr4+Q9l+amqKxr2vrw8PPvggvy9z8973vhd79uzBiRMnOI+6EanMTbvdNp79crlspK/ruK78fWhoiJvCa6+9luN65JFH8OlPfxq33norAOeeOEGx5gAAIABJREFUynXr2K0Wn06lUjh+/Dil0/L5vHFOi18PSxtaWFhYWCw7WM/rAoTsugHHO9HCr7KjvOiii5BMJul5BQIB7vIWFxe5Qzx06BDFfPft28cdsBxPdoKiewg4O3Ndv1UqlUgD6ow4vVsFYCQoCIUiyRfiAaxZs4a731arhYMHDwIAxsbGjDqxQqFA2k73GtOeRTgc5uuZmRkUi0VeW6VSMYRftYeod/nRaNRoD6LpL/F+tUbgPffcg56eHv6/UCiQxgwGg/TCRkZG6CVs2LABtVoN+/btA+DoTWpNR/FS9+zZg3e9610AgKeeegpDQ0PcweudeavVol5lNBrlsQS6hkvfH03nSTJMJBJBu93mbl/oLH0cmQ+tF6j7VGkdSK/XS5pMPytL1UySyaTRQVrXQmkq2+PxGG1dhBYNBAJUobn//vuZzNLX14fh4WE+v/l8nt6eTsrQtZQrVqwwNAw1lex2u+kxB4NBvPvd7wbgsAF79uwB4LQgOnv2LI4ePQrA8VLFU9fak+Vy2WhP9PTTTxv3TdP5tr7r18MarwsUQhf5/X7+kOLxOKv4y+Uy+vr6+MBrhYtEIsEF6OjRo7j++usBOBRTIpHgAl8sFkm7SWo24CwwYgjb7Taq1aqRFaVVKHR6/PkUAjwej0FP6niLllA6e/asIVG0uLjI6/H5fIackSyaQ0NDHGdPT48hq6Oz/RYXF3l+UdXQcyuxDr2I6p5mOmuut7cX3W6X1KnL5aLBcrlcvLaDBw/SMLfbbfT19XFsWty3t7cXDz30EK9NDN6pU6dw5swZLqjr169nPK7b7RpzrWnYSCTCay2Xy9w0VCoV0pi6/bzQdzpeqrPeZLHXdLP0ZNOqKZoylnNqlRRRGRG6VNOq2sjJueT73W4X1157LQDHUIuBOHLkCFatWsVzStxPNiA6o1agSw9SqRQNoWzMdCxUp61LfHHdunU0uHfeeSfGxsYAOBuvH//4x5zDUqnEGK2O4blcLm4kK5UKwuGwUbZijderg6UNLSwsLCyWHazndYFCt/iQHV2tVuMucHFxEcPDw0Z7EB1oF9puYWGBxwqHw6jVakYhrlBoWocuEokY7Uh0QF+3iygWi8ZuVZ9fe2Tdbteg+nTmn9ZTXKo5eL4C3XK5zM95vV5SquLtyY5XvA/A1FrURbjSYkPmSrf5KJfLRq2PfEdoNp2koDPGdDdorY9XKBRI+WpvOhAIcKx6DgqFgtHCvtVq0RsPBAJGV2N9rX6/3xiDrvMST6fRaBj3QHf7Bc7pJi4tjNbdqHXhtu527Ha7DVFnXZSsu31ryjsWi/H89XrdqPdLp9P0Uo8dO4YDBw4AMGnZWq3GsZRKJbRaLc7PUnknoYh9Ph8zXUulktGupd1uk+oTWSvAoSSFqgwEAvSiZmdnsW/fPs5bOp3mvdJajS6XC+vXrwfg9L/r7+/n86azYJfOu8X5YY3XBQpZALT6QalUYnxkfn4eK1euJP1TLBb5wA8ODpJGmZmZ4YK+cuVKvPDCC8yo09lf7XbbWIxkoRL1cPkBRqNRYxHT9IrWTBSIJp9Qa+FwmAtau9026EWtOqELQrXKfa1WY2aZ1nOU/8t3yuUyY1ZaoLbb7Rop9e122xCSlWsQ2glwFl6tZaiNrsvlMig8uVc6JpROp7F+/Xoj9igLt06ljkajpAZLpZIRm6vVajSyPT09XFzn5+e5uEtxuSzQummmVpCoVqtchEVRXvf60vStTvfXIr+dTocUmk7JbzabNJ46XiWGWQxGX18fr0cb3Hq9bhii9evX81pfeOEFxrY2bNjA82ezWdK4+l7LGM63QUqn00bcUmKzgPObk+vu7e3lOfXmaP369RzzkSNHjHPqIn9dBuDxeEh13nXXXdi6dSuNsVb211m4Fi8Pa7wuUOiutZoLlx/8/Pw8SqUSDZFOcY5EIkYSgnD7mzdvxuHDh43OsLoZnqhy6AC+BP11g0H5oer4kZaN0inWgUAAtVqNCQbJZJLnn5iYMFQ5BKKcIdfWaDS4uPb29hpej1aEkPiQjFOrkWtjJJAAvlZbl2NroVTtHUWjUcTjce6Yc7mcEQPUAsY6LrZ+/Xps374dAHDDDTfw2GfPnsWTTz4JALjyyivx2GOPAXAMppZdcrvdNH4ilgw4adnHjh0D4Gw6pqenjRYgMj+Dg4OsR9u8eTPvz4kTJ4y6Nd35V86r/wUcT6nb7WJ4eBiAk3wg39ceiN/vf0n5hnwumUxix44dAICnn36amxudSOHz+ZDJZGi8pqamOIedTocbtDNnztBAyXcErVaLv5l8Ps9nRG+oVq1ahbm5OeO8cr+3bNnCeq6HH34Yb33rWwE4910Sio4dOwaXy8Vrbbfb9DBnZ2cNFRydYNTb28t71Ww2DTFgXYdncX7YmJeFhYWFxbKD9bwucNTrdXoNug2FZEsJjVgqlcjz6yLYYDBIauIjH/kIrrjiCvziF78A4Oz0pT/YM888w1iDz+fjDlHHRwCHPhKard1uczff19dHL6pYLJIWq1arePe7382MsQcffBB79+4FYBbeTk5Oclcej8cNCs3n81FZodFo4IUXXgDg7KR1ZtpSGlL3mNLZbHIer9drxOCWzruOVchrEYfVFKmeDzlWoVDgTjwUCuH06dM8b6vVYqba1q1bSSUFAgGqjEi/Ni3+KjqOrVaL9FVfXx//LkoZ4kFMTU3R+zt69Cifgw996EOMvUxMTLD5p0A3bNTUrTwfmUwGq1atYjq43++nt1Ov17F//36OWXuyWpi3Uqkw7VwLBQ8PDxuxz76+Pj4vK1eupBd09uxZnD59mueU30g0GkWtVqM33Gg06A0HAgFm68ZiMd4P8Zh1uxPtLb397W8HANx99930/Pbt28fzT05OGjRop9PhdWuaOh6P8/no7e01GsXqgnKbafjKYI3XBQ5NmenU2pUrV2JycpILXyKR4MIwOztLo5bP5/kDmZ2dxY4dO/jjePHFF/G5z30OAHD11Vfjv//7vwE4ySBa7FX3+tJJEuFwmPVksViMsYEVK1YYUkQjIyO48847AQA/+tGPqCqQTCZJ/egF7OKLL8bMzAwNzsUXX8zF8eGHH+YioRMnlv7wpbeVnkeZJ5kb+byW75H5jcVixmIki3in00EulzOU03UsSCdi6HqlRCJBQ9Jut/m62Wzi93//9wE4GwgZ28LCAhYXF2mYPB6PUeMkC68WI3a73YhGo3xevF4v51or4W/ZsoXf012DBfpe6zICMQiSRCFzescdd+CjH/0oAMfoyud0t2VJepHjPf/883jb294GwEm+kI7cuuuBJFWIwent7WVNXbVa5fPRbDa52SoWi5idnT1vc0uXy8UNTSKR4GZvxYoVRllAMBjk868lnLZu3crnsFAo8H4Eg0FjE9TpdAxFF4m9rl69mhuITCaD/fv3Gx0jztc53OLlYWlDCwsLC4tlB+t5LQPoflHiDQwMDCAcDpPK0Vp8s7OzBsUor3fv3o0PfvCDFDHt7+/H97//fX5GAtjXXnstvaCFhQXSN4Cz+5Udai6XY7LAs88+y53swMAAtmzZwte33XYbd5g33ngjE0NOnz5NjykYDHL80WgU8/PzuPLKKwE4FKkUUx89etRI/dcacuL1AGavsWQySU+lXC4bWWW69Uk+n+eud2BggF6Q9k4kMK9bkuhkFsFSodVsNmuILcsY9u7di127dgEA7r33XlxyySUAHM+i1WrRo5A+VXJsOX+tVjNoJr/fz2vQ7Th0icCJEyfw7LPP8pqBc+nxuoN1JBKhF6e7Ry+Fx+MhjRmNRumBa9pWygXEg11cXKRCxYoVKwxFGdG4PHbsGKanp3kds7OzRksgSeTQ3qbb7TZEjIFznowuwJZrBZz7pmm/SqXCc6ZSKfz85z8HALztbW8jhbl//36mw0vXbt1iRZ7Lvr4+Q0lEiqy3bduGffv28fnXGogWrwzWeC0j6AZ4U1NTyGQy/DFHo1EudNlslotRX18fqZpyuYxDhw7RsGzZsoUxltOnT3Mx2L9/P3/IjUYDwWCQi06pVOKPPp1OM7alYzIA8Mtf/hKAY+y2b99OqvH06dNGby9Z8HVfqgMHDmD79u1ckA4dOsTFVs4rY9GZfvV6nYt6MpnksScnJ410eK0ermuudLah7le1tDasUqnQkAQCAaNPlsxNt9tlhqU00NSLpbyOxWKcW11TVC6XEY/Hed5Go8F7Wi6XeQ2hUMig2U6fPm0opWjaTjY6CwsL3AyIHJOOHcpc6T5oovQv36nVakbsUASF9XzIezLOSqViZNQJBTg4OGhQZTIf9Xod+/bto1HQVLCm08vlMhf/arVqZEx6PB6+V6vVjE3I0uatMr+BQID1lKlUipT3zTffjK985SsAzJ5dHo8Hs7Oz/I78dgDnOZRrzuVyjHUGAgHMz8/zGDrGavHKYGlDCwsLC4tlB+t5LSOUSiV6V7rOCDAD5cFgkO83m02jP9PExAQ9nGAwyN2rVPwDzq5W11hpr0HTe/r78XicO8darcYd5saNGxEOh3H8+HEATn2L7mkknsGKFSuMAt94PM6kgtOnT/MaPB6PUQOzNOCtPQ0dnNfitULndTodVKtV7vS9Xi+Pp7UitbBvMBg0WrRIF14Zg3gJugZOqMnzFZ6PjIzwPKtXrza6O+uiZ8DU3pPXuvBWCqi1F6V7rMnrarVKT8fn86HRaBhF6TI/ukeax+PhPPn9fkN8uVarMXmhp6fnJbqWem7kPIlEwrhW3bdM61jm83mOIRwO81q1p6aTbiSj8XxqFX6/n78LXUMnCR8yb5lMBu94xzsAODT1TTfdBMCprRSaXHu1Uowtv4upqSnOgU6yOnPmDGvbJiYmjF5h1WrVqmq8SljjtYzQarW4sAjlJj9a3UAvFApx4dZN7aRJpRipkZERxlgOHz7MH+ZVV11l0Fe6aFMWSBmDGDlNJw4ODjJuIUZIjJdWbdBxupUrV+Lw4cMAgGuuucZowjkzM8OFX/c30+nboVDIOLYWn9UZZ8A54yUCs1rZ4HzweDxcUEulEnp6enhsHUPTzRf1scLhsHGtWjpqeHjYaNwpElLSsPJ8KeyVSoWLo852bLVaCAaDRsGufK7ZbBpGSStnLIXeEOj+aDJmKQmQDUW73SaFGAwGjUVYZ/35/X4avFgsxk2UFlEOhUIcpyir6E2A3HttmLWorVC8OlVdU9MynsXFRdLPxWIRyWSSafhaveO+++6j0v/DDz9M46eFqIPBIDcBMtfyfHS7Xc6THovQtvq5snh1sLShhYWFhcWyg/W8lilk9ys7PGmxADg7WUmK0H9vNBrIZrOGDJQUit5999244oorADiZXBJ8DofDCIfDrG/p6emhh5XL5ehhJZNJBvS1sO+jjz6K/fv3G+1NNM0lu92BgQEWt15yySW49957SUU1Gg1Do0+339Bej8/n43m0V6o1IUulEnfp8Xgc4XCYu95KpWKMU2s4ilcr1JXuwquz/bRclpbr6u/v5xxGIhHuuHt6epi4sGvXLrz44osAQNFlXQytPS+tZyjnF51G3ZdNXutkn0ajYXgqSyXIxIPQGZuaEm02m6jVakbyhECSHwAnWUe+EwwGUa1WjZ5ZUqAei8WMz2ntSbfbbdQcavpWe6VagDiVStEj10k44v3J/IpHtGXLFvT39zNL0uv14u677wYA/PVf/zXPcfvtt5NpmJ2dNTpyh8NhZlwCMDxzmY9IJMIMxVqthna7bRzDFie/OljjtcygaTGtJLC4uMjFVtqnA85iIlmAs7OziEQizBA8cuQIi0svu+wyqm3s37+f6gGBQACdTsdIS5aU+r6+PoN6kR9vLpejIZqZmYHH42GsTovfhkIhXHPNNQCc7K1bbrkFgPPD37Nnj9FCXismCDQVl0gkDPV3ObdAFiqdEu12u43GhQ8//DAX1Hq9TqqyWq3y+z09PYb+no4lyTHlGmQBW1hYwMzMjKFaLp/LZrN4+OGHAQA33XQTFzM5lizCHo+HG4J6vU4DnkwmDd3GcDhsNAvVpRR6sdcFvm6327gegY7tJZNJGmwxXjrjUu7PzMyMcW1iLPr6+rB582bqIQ4MDDCu9Oijjxp0osyby+VCNBrlPdfF8lpxX8YqY4lGozR4mqrT8+bxePDnf/7n/P4zzzyDxx9/HIDzW5Cswh07dnCDl0wm+UzpOLCULujmnYJqtWpsDOT7EkOU35U1XK8e1ngtM+iaounpaRqccDjM2MnmzZuxbds2AMATTzzBRVi8Cfn/Y489Rg/tbW97G43atddei927dwMAjaAYn1KpRE/h8OHDXMCi0aihJq53yI1Gg2OLRqP01tatW8fFZGpqCh//+McBAN/61reMXXKtVjN2/WKM4/E4YxOikKDjYaJiAZyL7eiFLRQKYWhoiN7fzMwMY3NLvRZtPLXx0Z1/df1VvV6nZzI2NobR0VHG9J599lkuqB6PxxB01Qvd4uIiF3KdHNNut41ECN2Ko1qtct60l6uV21utlhELfbl2HC6XyzAKMm/NZtNoTROPx7mJ6Xa7hoGQZyWZTGL16tUsHxgZGSEDcNttt1F2qa+vj0ZamAUZa19fH4+n1fN1d4OhoSGk02k+rzo9PhwOUxZr586d+PGPfwzA6e69fv16xoIBUELtX/7lXyhHplU9dKeFnp4eQ+kkGAzyeiYnJ/m70uUXtVoN0WiUMTSLVw8b87KwsLCwWHawntcyg3gwPp/P0GeLRCLcoZ4+fZq7SK0fmEgk0Gw2uYNfXFzET3/6UwDA+973PjzxxBMAgLVr1+L6668H4HhnJ0+eNNKfdcGu7CSr1SrPLz28AMdja7VapBp37drF19VqFd/85jcBAF/+8pfx0EMPAXC8Rb1L1YWv/f39hgeiacR8Ps+d7Pr165nRtbi4SA3IaDTK151OB3fddRc+//nP89jiDXi9Xu6sQ6EQPZDFxUV4vV7DIxVvS8oKAGeXL+OcnJzEli1bsHnzZo5baNl8Ps9YmMTt5H4GAgHOgcTnZNza8xIkk0ksLCzwGnTBsc481AXP0qtM3tNp9F6vl1ThmjVreCzpmaWVKyRLsr+/n9RgIBAw2pl885vfZIF8vV5n/Gf79u30aKanpxkXm52dRaPRoFc3OTnJcWrvU8c6x8bGMDc3x6J2nYXb39/P5/Lxxx+n4O7Jkyfhdrv5XEajURZdP/DAA0arFPEKI5EIj9tqtVCpVOgJXnnlleyXpuO1lUrF0E+0GoavDdZ4LTPIYpBMJqlaAJh1XqdOneIC3dPTg/HxcQAwFkP5/2233QbAMSrC7d9xxx2M/Vx66aVwu92k09LptJGYobvRyqKTz+cNemRgYIAp+S6Xi/TZ6dOnDbkgid1IjZOgXq8bEju6nk0WaknkkM+lUikuDjrJRILrwLl6Nll08vm8Ue+kx6BjT51Oh8fQXXd13KJYLHKeqtUq9u7di4svvhiAWc81MTFhyD7JIu73+5FMJnnspQZT5tfr9RrJJIuLi5wDvcDrbgAypzIfWpRW18oB56TFNm3aRDWWffv2odVqMXlBxzQDgQBjeDrlfMOGDXjLW95i0JOywTp16tR5m0lKarw8Y5OTkzQw8/PzRm8w+R3IcWSutSCxpkQ3bdpEo3jVVVfhP//zP3HvvfcCcGoO9SZGzqNjr+l0mgZTaEGR/9J04PDwsLHpkGuLx+NGgofFq4elDS0sLCwslh2s57WMUSwWDepGK19IIkYmk2Em1+LiorET1e1SfvKTn+DDH/4wAGcnLa1Oent7cdlll9E7OXLkCOmwYDDIwmatprA0+279+vWkt5555hlSnZoa1Aof0uFZvAO9Y5YeXICzw5Wd8Pz8PBKJBGmubrdLb6BQKBhaj0I9zc3NYcuWLUb/K01L6QQHXcjc6XSMsWmvTmg/Te0JrSbj8fv9fD06Osrv626+5XLZSMbodru8Nl08rBMSlo5Hp9frOSwUCsZz02q1DKpQK4GINxEKhegpyFjk2NVq1ejoLeefnJzkc+j3++Hz+fgs6uQITW/K/4Fz/dr02GTetTcuJQJyznK5bHTylnnT6h0nTpzgvRofH0cmk2HrFWEG5FrlczphQ//2ZB7lmrQHnslkDLUa8Z69Xu9LWtFYvDpY47VMIT9wnQYsP7JEIkHjs3r1av54stks6vU6F/+enh5Sfffeey8uv/xyAI7Cxbe+9S0AjoHR2YsLCwuk0FqtlhE7EegUZsmSEyM5NDREOi2Xy3Gcp06dwtDQEMdcr9eNmiAxnrFYzGj+qOWP6vW60UfpfH26+vv7ScWdPHkSH/jAB7igSDwLMGlDvTh2u13DEOiaJD2ecDhsKE2Uy2WeR6eza1rq1KlTXGjL5bIhVyVq6TIfuuZLxinXdb74ZKvV4nm0akWn03mJoLBck9frJWVXr9dfUrogc7J03nUsSD8LAPgcdLvdl03j17Sh2+3m9bndbkOKS6DlsqrVKprNJp/LYrFICq+3txcXXXQR51fijldccQUOHTrE+SsWi3zetJiwxAdljLqP28DAAMeWSCQ4bzMzM4xpDg8PG5mHVg7qtcHShhYWFhYWyw7W81qmECFQ2b2Vy2XuhCORCHfC5XKZO79Tp04ZGXEej4de2fHjx/HAAw8AAP7wD/8QV111FQBHeSOdTrPr7eLiIos53W43vSjA7JukW1LMzMxQsWN0dJS711KpxISN8fFx1n+tWbMGALgzzuVyRtadQNcnyflll16r1YyeW3LMVCpFb29ubg5DQ0N47rnnADhe3dIeVALZiS+lerQAr1yv3ANdlFwul0mZaT3ESCRCCvHEiROsYTty5IhB/3q9Xs5VPp832p7Ijl/oQPGsdRZepVKh55XJZAyVE1235vV6jQJo8QTn5+fpwfj9fqOPWaVSoRcVCARIn+keVUK9ircSCoUMr1CuQdfHeTweo4+Zy+Uy6NrzecbNZtPoaaYzVQOBAFU07rzzTqpnrFq1Ck888QTnulQq8Vr1vdUtarQ+ZCgUwsqVK1nrVavVmFXZ7XY5Nu252WSN1w5rvJYx4vE4f6S6bX25XOYiODExgbe85S0AnB/p6dOnuTgsLCww42rFihW46667ADjtzt///vcDAC6//HLce++9pFQ+8pGPMJPrhz/8IVOkdYxIZ8MVi0WcPXuWWWDZbNZQWZB05f379+PRRx8F4KgajI6OcgHQkkWFQoHG5uDBg1xAOp0OUqmUEc/TNKrQnj6fjw0BR0dHDcX7eDzOOYxEIjx2qVSi8erp6cHCwoJBL+peYTLOhYUF4zp1m3itTtFsNnmdhUKBjUKfe+45DA8PG8WvQkXlcjnDaMu81+t1lMtljluEbYFzfdlkDmRDMzMzg1QqRapPy0vFYjGOeX5+3qDzPB6PIekkxq+vr48bgFqtxjFL3zIxBplMhs/OyZMnuZjr5ppSAC6GJJlM0khKKYHcA/mMZEFqRRgZdzqdNuhrKfD/2te+hscff9zY7OiGnPL3ZrNpFL7L+TOZDPr6+kirPvvss3ze3vrWt5L+Pnr06MuKP1u8elja0MLCwsJi2cF6XssUpVIJw8PDpHXq9TopvEqlgpUrVwJwdrKyIwyFQojH46ynKhaL3OWOjo6ytuULX/gCdd927dqFT37yk3jmmWcAOMWdsmP9+Mc/ziLj+fl57iqz2axRS+V2u41kAdkVLyws4NJLLwXgBLOFJty9ezcikQgpzUAgQG9iYWGBBaBy7fKZRqPBXW6z2eT74XCYu+R77rmHu2dpPy90kWg/AqaQra7b6enpQSKR4HkAGPSR1CHJWAGHihsZGTEkpmQOstksKc077riDdO3/+3//D+vXr6cnt1TPUKBbg4jenhalldfhcNioexPJo76+PuRyOXoX8Xjc8JbEE33hhReMzsk6A7Ovr4/Hnpqaoufl8XhYiJxIJNDb22t4fPv27QPgeMlaFkvmMxwOG7V7WmT65bL1JDtRGIVarcZnbGxsDD/4wQ8AAP/6r/+K559/HgCwZ88eIxlEZyh2Oh0eSzJrZZzCbuzcuRPPPfccad10Oo0nn3wSgNNSReZGZ2VavHZY47WMMT09TSpIt0WvVCo0UKlUikYhk8lgzZo1NFKTk5NcRCVWADhZWd///vcBONTcVVddRTornU6zsPm9730vPvWpTwFwVDHEwPn9fsY9pqen2WsLcIycjK3VatHIDg8P0/iOj4/D4/Fwsdf9r9rtNhfAfD5vZO1pvbnZ2Vku6hdddBGNz969e2l8BwcHMT09zSzAZrNpZNrprD3dMj6TyRjFw7KIasPs9/sNJftDhw4ZhdY6zVoXl8viPDs7iw0bNvCeBINBLo5amzCRSJByE7pL04OCVqvF+SgUCjxuq9XC6Ogoi8i18ZWxA06Jg4w/GAwazSQTiQQOHjwIwImJappP6NHJyUmcOXOG11qv13k9PT09Rk8yMaSFQgErVqwwOifomJeOmUncMBQK4cyZM7z2zZs3c+Py6KOP4nOf+xzv1de//nUAjlHR2ZzdbpebE4/Hw3itNpYjIyM08i+++KJhmCqVCg27zgKORqP8jVq8dlja0MLCwsJi2cF6XssYhULB2F3LbrzT6bDQcmBggLvVs2fPIp1Oc4fYbDa5w1xcXOSx8vk8WzdUKhUcOXKEO/APf/jDpIXuuOMOFnauW7eOit3AuWD23Nwc9u/fb7RP15llkvm3du1aJoLMz8+jUCjQcwFgUJ1Cn8ViMY6rWq0abUhCoRB348ViEd/97ncBODt28fb6+/tx8uTJ87YD0TSSz+ejR1KpVBAMBpmMMTk5ye/pGjRdpNzb24tyuczjzc3N0QNJJBJGZ2nxOvx+v1GEnc/nOR+ixSf3UBdG635YWrG80WhwPmZmZugZDA4OYufOnfQq9u3bR13AaDRqdOoeGxsD4HiImUyG81gqlXh/NGWni6SDweBLerGJ91lOpq3rAAAgAElEQVQqlfhMdrtdelRSIC3PVSAQoJessx+1qvzi4iJ6e3spj9Zut9kj7QMf+AC9qK9+9auk030+H9xut5HlqOve5NnVGp2afq9UKujp6aEeYjgcNu6J1vm0eoa/OVjjtYzR6XT4Y9BGTFpWAE7mofD32WwWHo+HC3wqleKCqnsvSVwHcAxktVrFrbfeCsCJja1evRqAYyAkplGtVhlD6HQ62LlzJ4BzFIzORJSFstVqMdNv7dq1XFji8biRvaWbIurMMi1GXK1WjYVC06Dj4+NcjLZt28brn5ubewmVJYt6o9EwlB3k+7FYDCdPnuQCHQ6H2aaj2WySCtPtRFKpFHp7e3k8EUgGHMMqMbx4PM75FEMkBieXy5GKzeVyRmxOFt1ms4l0Os15y2QyfA7ks4BjGMWIXH311SgUCnjqqacAOHEdSSePRqO8htOnT5OuPXbsGLxeL2M+x48f5yYoHo8blJkuItdj0Au5x+NhbA04lz25efNmdLtdUpKJRILv9fX1GcXZsqEKBALYuXMnr+/uu+/GtddeC8DZrHzjG98A4Gw6tJ6jbrYphduAs/GQwuJAIMA5mJ6e5txK+YUY87m5OY6n2+1yDrrdrnE/LF4brPFa5pCFXILbgGOw5EeuOwcHg0EUCgUunLKoyud07ZD8kEOhEGq1Gt976KGHcNNNNwFwYhrC+8/OznK3Oz8/z3T2a6+91qitajabXLS0IsXCwgJf+/1+1Ot1Lmi6R5Xb7ebn6vW6oeDQ6XR4bVpRotvtcmFJp9P8TD6fx8LCAnfQunuyrt+Sxp+AYxDOnj3L+dVqGaVSiZ6GHpc0yhToRaxQKNDgRiIRo67I5/PRaJfLZb4uFApGDZX2GPP5PO9ppVLhXOtU/WazyR5mfX192Lt3L70LHWPSKf3hcJj3Q0o0dD8v3ftMq3fosemygnw+zw3SwsKCES8SUeje3l7kcjkeY35+3ogByrxHo1HOzapVqzA2Nob7778fgNOnTmKp+/btIyPRbrf57C4sLFA5Re6dHFsn5qRSKUNqTTY0pVIJo6OjRg2iLiHRXrLFbw425mVhYWFhsexgPa9lDtnNdTod7j5DoRB3v8VikV5AOBw2Mql8Ph/1BOfm5uiBSAdbOVa32+VO9PHHH2fsQ3s3hUKBu/mVK1eyLca2bdtw8OBBQyXhfHGhubk5XovX6zWyEpvNJj2iwcFB7nh1/EuOp1OuJR4WDAY5Nr/fzzHPzc0hl8sZ3on2vMT71AoQ1WoV0WiU16PFXv1+v6G9J+cpFovGtXa7XV5DMBjkbl6oQjmnFjvW72llFZ0qL6oXWjBXKFEtatvpdOgl12o1HDhwgPGlZDJpFITL39PptOHlZ7NZlgKsXLmSXky5XDayL7VosS5s1nqX8Xicz246nWaMy+VyIZfL8XNacDccDhup6ULjbtmyBdlsltmT4XCY8du9e/fSC9M0uYxT5lHHvOQZlPGIF+h2u+ktbty4EaFQyMj8lXHqe63nw+K1wxqvNwj0wp1Op7kgasoLMBXNs9ksEy7GxsaMBn5yrHg8jt7eXi5I09PTpGT8fj8bWH7uc58zZJ3knNVqlSn08h0t4aTjcWJUV6xYYSyitVqNhigcDnNx1mnVkiavGwfKGHbs2MHrnJmZ4aI7OTlpUKQul4tzo+lJAEayhY4V1mo1LrxyvUvHViwWjdRuAIYhkviIjmWJcrw2xrKhWBo3lEU4mUwiFosxqUGnvWtF9MHBQUpxidqIUF6dTsdI9BDjF4vFeH+8Xi8mJiZ4nh07dmDr1q0AgKeeesqIZWkaVKfrR6NRQ/JLXl9yySWMud1+++1GFwAAxjMh42w0GowHPv3009i2bRv+5E/+BADws5/9DI888ggAk17VvfCkb9ivo/VqtRqN/vbt22m8fD4f7rnnHnzkIx/heOS6/X4/n0kdU7V47bC0oYWFhYXFsoP1vN4g0K0x+vv7uWOuVCr0LJaKyyYSCUxOTgJwioRl9/zCCy8YBZnhcJi71lQqRXWG6667Dp/+9KcBOGn4Dz74IADg4Ycfxmc+8xkATgFnLBbjeWKxGD2IpZlpkiXn8XiwYsUKBu6np6eNHbdAFxJLkofW9du+fTsAp0hZ6J+9e/ca2YGhUMjwBGWXrL0EnWigKTrA8ZZ0lpqcv91u83Wj0YDH4zEC+nLd1WqVNOyBAwdINeruxnKtQo01m02DnpQ5GRgYwOHDhzlvCwsLhvaleGJbtmzhddx1113YtGkTvVEt3Dw4OGh0Kxav0OfzYcOGDZyrQqFAr3vjxo1Uzjh69KhRSFypVDhv1WqV11cul3HNNdfw2oQBuPHGG9HX18ci7NnZWSZcaGrO6/WSaUilUviHf/gHKmncfvvtLMpPJBJG0opcp26vcj4IJfpXf/VX2Lx5MwDnN7J7925e22c/+1keZ/fu3Qa9KecU2tbiNwNrvN4g6Ha7XNByuZwR65BFs9lsGgt8o9FgPMDn83ERDYVCpPpkQZdFR0v56IXyuuuuw5/+6Z8CcFKnpbZmaGgIO3bswJ49ezg2rUIhC6BukqlrrwAzc+/s2bOkiHp7e7lo1Wo1hEIhQyxWFuupqSmmO2tRXYnByOKiY1bNZtNo5KjrkxYXFxlvWarSL3PtcrloMCUupZX2dR82oaLGxsb4d4lPyncCgYChiiELYSqV4v30er1YtWoV732hUKDx0X3cYrEYfvaznwFweqfJueR6ZA5mZmZo/FauXGncn4mJCd6XxcVF0rK7du3ic3To0CGWAZw6dQput5vz1mw2+ez4/X4+L5FIhHG2Y8eO4bbbbuP9zmQyjFnNzMzw2KOjo9wcvf/978ehQ4eMfnRi9Kenp5nq7vV6eX9+lfFKp9OUSkun0/jiF78IwNl4icFNp9N4/PHHce+99wJwjJ3uoWebTr4+sLShhYWFhcWyg/W83kDQbd5lN9lut0nHuVwudDodo1BS6J7Dhw/TuwoGg9z9ZrNZlEol7u7T6bSRASdZhadOncKGDRsAAFdddRXplUceeQSXXXYZz/fzn/+ciQNut9vIgBMPRmqIdLKCFMQGAgEjieDUqVMAwHYb4kV5vV5eQ6lUMlpuyPibzSY8Hg8/p+cwn8/TA9Fek9B5uuWGQFNhyWTSaJWiC3Z1TZ6mTteuXcukiMHBQeM75XKZnxMRYsDxqGRsJ06cwLp16+iRBINB1nz5/X4maZw4cYL3M5fLIZfLGdmUMgZdWH327FmMjo5yzD09PSyo9vv91L48cOAA5zoYDNLby2QyCAaDLEr3eDz0lnRrn3w+z7+LdqfQkNr7SyaTfN6y2Sz+7u/+DgDwR3/0R/j7v/97Q0RYnrH+/n6OTfct04kccr/kGX3f+97H5/L222/HRz/6UX5ufHwcgJMUks1mjWdEno+lx7b4zcEarzcohBLRwq2RSAStVotGyuPxUFF9cHCQFOLatWuZrnzixAlMT08zM6vdbpOO83q9XOgOHz7MWMXs7Cw+9rGPAXAWtqmpKabkv/3tb6dQsKbwANMQLC4uGhlb8rmBgQG2ct+3b5+R6acVwDUtNTExQXrR6/XSwElauSyWoVCI2YLRaNTIEtMUok6Z1o0hNW3Z7XY5Zq/Xi4WFBYOeksW62WwyBtff30+JoVQqhWw2y89VKhVDDFiMQrvdNtQ29OdWrVrF7Em/38+sxueff57U3sTEBBKJBI2u3kR4vV6+Hh8f5z1cs2YNAoEANxRDQ0PMQA2FQnyOSqUSzx+LxRAIBEjf6uap7XabBkaXB6TTaczPz/M+ptNpGqyZmRlSjTfffDM3S3/zN3+Dw4cPc8PWbrcNQWOdti7PisTEZLMUjUaZan/y5EkcOHAAgPO8CJ0+Pj7OwvtKpYJQKGRkK+qMTYvXB5Y2tLCwsLBYdrCe1xsUupjyfMkFgEMR6dbwsks+ePAgd+axWAzlcpk740ajQbqov7+fO3btwdx///3skHzJJZfgnnvuoXcSjUZ57HA4zF1vqVQyhHC1XFW9Xucuefv27RzzgQMH6CFOT09jbm6O31m1ahWTJxYWFuihVSoV7uyl/5WmJ4WSdLvdRoKFFqjVrVcA8HO1Wo10U6FQoEfUbreNflp+v98oMpbvR6NRegypVAoLCwtGRp5OzND6juJpAY6noNuLaEhXZl1D1+12DY9Ey2LVajV+rtFoMNPP6/UaxdVnz54l/ZzP55mN2ul0+PdQKIRwOGxk4cmxo9GooX0or4vFolF0vW3bNlKIp0+fxvXXXw/AYQpEePm+++5DKpUyuj5r8WY5tt/v53MskGcsk8nwWTxz5gw91tWrV/M72WyW90oSa3T2pcXrD2u83uCoVCqGrh5wjh5xu91cYGu1GlUoNE0YCASQTqdJp2l19FqtxoVFU0xnz57FL37xCwDAO9/5Tmzbtg333HMPvy8ZX4ODgzQk09PTRhakHBNwDKjEa3p7e5mivHr1ahrmRCKBRqNBujSTyfB4QpvKmIVyc7lcaDQaxvzogmWtdafT5pfq4MnrWq1mZATKPLXbbaMo1uVycaHTor+6Zf3SAl99To/HY+hTyoIqfcfEUOtSAt2kEoBBdcr7Mjb5vlbvcLvdpPxisRh6e3tJHx8/ftwwlFptQxt5j8fD4zUaDd5fKcgGHDpPK8UEg0F2G5iammKM89prr+XzOj4+jvvuu4/zMTc3x41LvV43KFEt8KxT11OpFK8nHA7TYOXzeUPrURff62t2uVz8LVnx3d8OrPF6g6NSqXDB8Hq9aLfbhvGS9/TufWBggLvHYDCIVCrFhebAgQP8vnD9gFnjFAwGmcgRi8Xwjne8A5/4xCcAOEFviSFcdtll2LRpEwDgyJEjjGEUi0VEo1GmGw8ODjLWoRfgSy65hHGHWCxmJBukUikai1wuZ3QUlmuW0gFZdAKBgLGIC7R6iY7RATBiHZIQI8eShU4SAHSNmsxVJBKhwUwkEhyzpOfL+Vqt1kvOLd/XnqOW3/L7/YYaiRZE1l2mdXKMKKzL52TMWiRY2sBInOlTn/oUDduTTz5pGGPt5S5N95d7og2cbiyZzWZx3XXX0RDdeeed+Nu//VsAzjMm4rd33303r2dxcRGxWOwlsk4yHwL9vIfDYaxcuZJec7lcppFctWoV/64lviTZR+asUCgYJQoWrz9szMvCwsLCYtnBel5vAsguNBaLwe12G/Sc3lnrjELZPVYqFdRqNcapUqkUHn30UQDnCoMBx9PQCh5y3Ntvvx2lUgm33HILAOArX/kK9fR+8IMfMI5y6aWX8hzigWlxYKFofvrTn1K3bu/evfxOsVhEqVRi2nt/fz+vU6eca8pOYly6DEAon0qlwh1/IBAw2rC0Wi16eJo66unp4S49EAhwPicnJ+Hz+egd6J5kfX19/PvY2Bi9iXg8bvRB01mimloTSlKux+/305PTMaZqtUpPJxaLGeUOWjex0Wjw3pdKJV5fPB6n5yJZkELH+v1+3gedMamP2+12MTw8zBjl+Pg453R+fp7eXigUYtH2Jz/5SZTLZXp1jz/+OO68804AwHe+8x1qK2YyGcbzpJ+Zbq+jhaA1hSxYvXo1fD4fjzczM2O00JF7PTU1RY9NZ2Wm02l4PB4je9Li9Yc1Xm8iFItFhEIhLlyBQMCg04SCCwQCVDJot9uoVCqkUVauXGnISMli7/P5DLFZodL8fj8eeugh1h7t3LmTzQE///nPM1X/C1/4AhfkzZs3I5/P873x8XGef2xsDHv37gXgpPFLzOvgwYMolUrYtm0bAGdBke9Uq1UjbV0Ma6PRQLfb5bVqNf5ms8mU70wmw3TtTCaD6elpLsqaIioUCkxiSCQShqJFvV6nwSqXyzxnsVjEddddB8BJYReqdPXq1Zibm6Px0LV7rVaLBqvZbHJBFapR01mykApFCjiGROZNqEkt9Cv3VCf45HI5GvN0Om3IV915550UpV23bh2fowMHDnAOvV4vNm3ahCuvvBKA84yJqHM4HGY92tatWxkzu++++3DzzTfjk5/8JABH/Pmxxx7jtcqze/z48ZeI34oqhxZ1XhqL0s/bnj17mDyUyWR4bVNTUzyPbpgZCoU4z8ViEb29vbxui98OLG1oYWFhYbHsYD2vNxl0C49YLMbd9OLiInfp3W7XaKvu9XpJqYRCIe5qt2/fzsLkWq3GHaou1pXdqnherVaLntPmzZvxl3/5lwCAL33pS/jnf/5nAGDas3gamsq64oorSDVu2rSJenJjY2NYu3Ytvaqnn36a7eP9fj939jr9XPQU5TszMzOcG5/Px+usVCqkMjdt2oR4PG6I+cr3ddq7boshWZDi+SQSCQrhbt++HZdeeikA4N/+7d/oWXz1q19l6jbgeCcyp7oliqavpKWLjEeSMWQMuvOwzuScmZkhNVYqlXgNWvMQOJeRqPt6CaRz9rve9S5Sg8ePH+dnJyYmsGfPHnzwgx/kdQvNNjIywjE/9thjTM751re+hfn5efzBH/wBACeLUZ7RSqXC6+l2u/TS5foEuVzuvIK4mUwG73znOwE46fBnz55ltqH0sJN5k3MGAgF+pl6vk4JMp9PW6/odwNVdpt3RdDaYxf8NbrebKgm5XI4Lot/v5w82HA4jFouRytGp5ZFIhAvD+Pg4Y2s6M63ZbBqLoFZdCAQCpBA/9rGPcUG977778OUvf5ljGB4epqrGpZdein//93/n3zVNF4lEjBohWRC1kkexWDQURqrVqhFb0w0FdUq9FswNBoNcIE+cOEFD3+12ef5EImE0mYxEIsYcDA8PA3AyLsWQfehDH8IVV1wBALjhhhtw8803c0PwyCOP4I//+I8BAL/4xS+Ysenz+biIut1ulEolUo87duyg8Th79iyzDQcHBzn+bDaLM2fO8DyVSsWI2ch8hEIhUqe5XA5zc3PcXGgDesstt/D5+O53v8vN0apVqxCJRPj/4eFhKnb84Ac/4LHe8573MN40MTGBb3zjGyytOHTokNF3TL7j9/uNjEsArDnU0M1XL7roIiqbPP/88xgaGuJzCZzrXlAul3l/wuEwqUcdB9V0osWrw2sxP5Y2tLCwsLBYdrC04ZsYWshWJ1nUajWjZYcW5vV4PEZ/JKG2+vr6uPteXFzkrjQYDKJcLnPH3NPTQ2+tXq/jf//3fwE43si73vUuAE7Q/hOf+AQzyGKxGDPygHOB9iNHjjB5RNqMyM54enqa3mIikTAoTbmWWq1mZInpJASdCCEqFIDjqSQSCXb7TafT/Jx4NoDZX00EiMWLicVifH3y5Em+vuOOO/D1r3+dc3P06FF6Ozt37sSxY8cAON6n6EMePXrUEKt1u91MBtG1VIVCgZSX7gGWy+WMmiifz2d4MVpTUuZT6gWFytUF6jrDUGv9pVIpvOc97+G4/+d//of91t7//vfzc0eOHCFtLO1zhH7t7++nl6uzPHVbG+BczzV5T8adTqfJNJw4cYJU38jICLrdLq9HFzYXCgWjVk1ea3bC4ncDa7ze5NDq6Hqx1YoS7Xabn+vp6aEhmp6e5sKvMxS9Xi8XTRGylYXM6/Uaad5yrIcffpiL+A033IDh4WHSRfV6HUeOHAEAXH755fz7/Pw8zy9jlmsIBoOGwZVFp16vG0bG5/MZMRH5jhT8yvdlPqQ5orwnFB1gFjPX63WOrdlsGurmiUSClNfi4iKuuuoqAE7GpFBUnU4HR48e5VyNjY3h5z//OQDgpptuovE8c+aMUXC7tE+WVovXsSDZGOhYEWAWQ7fbbfbpikajhnBtqVQylFB0KYEes5QuTExMYP/+/di4cSMAh16U2NihQ4ewf/9+AE4Gq5QLDA0NIZvNcuNSrVZpyHTJg573druNTqfDZymVSpEO9Hq9NH7T09OMgyaTSczOznLjozdvupdbsVjka933zOJ3A0sbWlhYWFgsO1jP600O3ZpDaoeq1aqhiaf7bnW7XaMzs+jqpdNp/j0SiTCJYGFhwfCCGo2G4dXJ7rVSqbD4ORaLYWhoiHTPyZMnSZmFQiF6HdPT00bvqVAoZOjiyXu1Ws2gtQQ+nw9ut5s7bl3n5ff7z6sRKOK5QlOl02l6Btob0Of0eDwIh8NGQozewQvN1tfXx/ms1Wo4e/YsvVmdtDIxMUG69Pjx40b3Z7/fT80/3ZMsGo3SG2m325ybQqFAgWLA8TTEY8zn8xTWrVar9PAksUV7vbrViG6pIt9fvXo17rzzTnqq11xzDb3MX/7yl3j66ac5h0Jvzs3N8RmQYwv0fdT1aK1WCz6fj/MmxwIclkGuW2sRulwuVCoVo+u0LjaXZ0LrTeqO5Ba/G1jjZQHAWQCEjovH48xS63Q6qNfr/GGXy2XSMGvXruWCdurUKS7og4ODxgKqe1lpBQiNVqvF2Mt//dd/oa+vjzRXOBymBmI+n8c//dM/AXAM3re//W0AjtpGJpNhplo0GqUB9Xg8HM/U1BTT3k+cOIFSqUTjoRekSCRCY64XaimolfkYGxtjk8bx8XGe0+fzcaEOBoOYm5szFlxZXAcGBmgkR0ZGXlKEKyUGw8PDVCn5j//4D9JvX/jCF/Dkk08CcDYDmUyGKf6333471SmGh4eNImdBIBBAq9XiYu31ermh2bp1K4uKjx07xrF4PB5kMhkaYL3w9/f30+C43W7GRKVH1r/8y78AcBQyJMY0NDTEuS6VSnyOYrEY2u220RRUb6JkPkOhEO9PrVZDKpWi0czlcsw8bLfbjHmFQiGjFGOpar88e1pLs6enh4XvFr972FT53wLE07jQd2qyiAYCAS7oYqxkQdPK6el0mjGNSqVC49Nut2lspqamcPLkSWPHqzs2a1V6uac+nw/lctloIihYtWoV66Le97734S1veQvP+eKLL+LBBx8EADzzzDOsTVuzZo2hwCDHXb16NTZs2MAF8fnnn+c4/X4/Pcl2u00v4ejRozh58iQN1sUXX0xjXCwW+TndEbjRaGDTpk2sb/vABz5ACaSDBw+yXGB4eBhf/vKXea26SWMwGMRXv/pVAM6CfMcddwBwjKkYY4/Hg6uvvpr/3717N+/j8PAwjZrH46GE08zMDJLJJGNBIyMj2LVrFwCncajc9+9973t8fvv6+oxu0Norq9fr3Nz8xV/8BY30xMQEHnroIdx1112cH7mv1WrVaD+jkyKSyaRRI6jjpbouUTAyMoJLL72UtYCTk5P01Ht7ezkHExMTrE2TJBUZTyAQMMoAJL1+fHz8JW1mLF4bbKq8hYWFhcWbCtbzep3h8Xg41uW0a5NYQavVMlLIvV6v0XtJPIhIJGII8+r7k0wmWVQ7OTlpeFhac1BnuS2li/Tx5JwAuKvevn071q1bR5qqVqsxhrZv3z56AM888wy/v3HjRsRiMXpiQ0ND9JIrlQo9p8OHD7MJ4szMDHp6ekh59fX1kZK86KKLSFe5XC5873vfA+AUCK9atQo33ngjAMfT+NGPfgTAURm59dZbAQBf/OIX8Z3vfAeA2aBRxvPhD38YAHD99dezHUm1WsWXvvQlAI5nceutt9LzyeVyjNFEIhFm99144430Xqenp43CZp/Px3n/5S9/yb5s8XicXrY0rNRKHDKnu3btokjvbbfdRk9rdnYWiUSCtGq5XDZ6iYn3uvS4jUbDUHsR6BY8Xq8XO3bsAOBkcj777LPMuNRZtKVSiR6n/i0Gg0FEIhGjMFk81kAgwPNb/ObxWsyPNV4W54UsJqKWIYZlcXGRdFooFOIPXgvcJhIJxlAmJiYwOjrKhebw4cOkF5caczEc0lhSFjcdJ+vt7eXnFhYWSKv19PSgVqsx5vXud7+blGKz2SSV9sADD9D4Cl0k9OLU1BRpP1371O12jQB+KBSikdSUVzwep9Fft24dDceuXbtwySWX4Cc/+QkA4Nvf/jb+7M/+DIBDIQrV+ZnPfMaQ7tL1Ss1mk6ndnU6H4/zsZz+Lr33tawCc+Nfu3bspiyWGCXB6n11zzTWcTzHGPT09aLVaeP755wE4Gw2hDVeuXElDNj8/T6PU29vLWi+ZH4mt3XvvvYzBzc/P83caCATYGw441xNMxiBUtBYwdrvdv9JwCAW4bds20r0HDhzApZdeyuvW0ldLhXnFwAUCAczOzhr96IQu1TEvi988LG1oYWFhYfGmgvW8LH4t3G43M8hcLhd3solEwhBKlUcpFApRXLVWqyGXyzHBoVQqkXLLZrM8loZQZnI8oS4BxzMQz8/r9Rr9tzwej9HmXc45PDxMak+LEUciEXpUcjzxyiYmJpgoMD8/b/S4qlQqhkciHlImk8Hq1asBOBTi/fffzzk4cOAA/vEf/5HXJynxpVKJXs8jjzzCsXg8HsMDaLVapO0GBgbotW7bto0U14YNG5DJZPidyclJtiTJ5/P0Rm655RbOh9vtRqPR4HhmZ2dZuKzLJzqdDjX8xsfHcfLkSRY6VyoVeoL9/f2GxqV45q1Wy0jG0DqS1WqVdOKvK/yV53B0dJT3cXZ2luPfuHEjpqenWVrxchgeHuY43W630R6oWq0ahewWrx8sbWjxukPTdrIgaepIC7p2Oh0aDolziPHRaeetVouLnlZ60HVg8q/ORpP6nEQiweO2221DAVyrSwSDQaZIB4NBLoAS75LFPx6PG80TtVSUXLMYaRljLpcjtaXV9HO5HONAzz//PD7+8Y/TAD7xxBOMvXg8HmZm7t69m8Y4HA6j2WwacyCG0efzUVS2p6eHIr/xeBwjIyM0csFgkPNTqVSoXKFVOKLRKCqVCsc2Pz9PQ9ButxkLq1QqpFcXFxdRqVR47FarZdwfMQJ+v99YnEKhEI2C1A/K9/XfXw79/f2kCn0+H43P5OQkY431eh2nT582KEKtlCLxQB1bkx5v8rzo67F4fWFpQwsLCwuLNxVskbLFK4LWyJMds8vlMjLixOvodrv0qKTgU3b2MzMzxq5fjlWr1YzeUxpaZ7DT6fD9cmlV2fAAAA6zSURBVLlsJAToBJJ6vU4PrVQq4fjx4wAcb0KyC0OhkFGMHIvFuDNPpVL00ILBICku0WqUYySTSSZSNBoNXrdupbF582asXr0a3//+9wEAL774Ij0nr9fLxJJYLEavxeVyGcom4okBjpcqCSPNZpO6jx6PB1NTU/TEhoaG6Elq7+qZZ57h9cTjcdTrdc5bsVik16KTcIrFouGJ6pqrZrNp6A/qv4uHKvdZ/tV6jL8KHo+H92HFihU83vz8PD3BdevW8dk7c+aM8VzIPMq5tRqJ3GvpRWe9reUFSxtavGrIYhCLxfg6n88zBqHTk+v1Ovr6+rgATU1NMXYyNDREQ1ar1Zix9qsa+7ndbkN+SBZ3v9+PaDRKo6Kfj7m5OWawRSIRvid0oNCYWu09n89zcevt7aWBEiMiYxgaGiKV1Ww2Gbup1WpMtb/66qsxNzfHwuJAIMBjB4NBZkg+99xzNGqyuAs1pw1bMpmkAe90OlyQXS7XS4yCLPYSa5LXuj9bs9k0KDyZK4/HY1DBcn8rlQpcLheP3Ww2jdihPpbMk1azAEBD+qvg8XgQjUZJq3q9XpZcBINBlkn09PSw08G+ffvgcrkMaS5Z4trtNudB05sXunjAGxmWNrSwsLCweFPBel4Wrwmyg9fB+UajQbpJJI4keWFgYICfm5+fNwpQhQrzeDw4ffo0PTDxBJZCt/gAHMpKU4BCmU1NTRlCw0KRSXaiLobWLVV0wocukJ2bm+O52+02j5dIJOhFveUtb2FGHwD88Ic/NASAtRSXeCW5XM6om6tUKrz2VqtFak56igGO1yOfEa9QvItWq8Xr6Xa7vFdSZAycq2eTeQsEAkaNn+4GLR6Kz+cz5Jn09+V9wKzDezXejVznmjVrMDY2xozU5557jsXZqVSKc3X69GkjuzAej3N+q9WqkQQjz97LPVMWv13YbEOL3zm0ankoFCKlJPEHWQQzmQwX3lAoROqmXC5zMert7cXg4CCNx8LCAik4yYRbilAoBJfLRQqwWCzSGGrdRC38KtSXNkSy8MviLtA/E9123u12GwXN+vtCIcZiMfh8PoOmkuOHQiGDOhUDUyqVkM1meV6tWK9Tufv7+43Muk6nwzF0u12ja4AgGo3y/vj9fuM8brfbiEPqz2mNTq2OEg6HfyXV+3KQeR8ZGeFmJxqN8ri1Wg3PPfcc31u5ciWzUmdnZ2nUWq2WUf5QqVSMeyrzI8+gxYUDa7wsLgjIohcIBLh7DoVCqNfr3JnPzc3RwPT09HCx1u1Izpw5g06nY3TAFS8KgCHbpBtJvhwCgYAh+ySvpVOwjMflchkxL/FadHxH0uF1jZK8p+MrlUqFhkOaWWqjIMZEp4+Hw2HGgkQSS8bQbrep3uFyuTifWuVcXxfwyuTIAoGAkXijDetrhdRP6euRedP3Xjd/LBQKNEo+nw8rVqyg8Tpx4gSTNDqdDucgnU7Tg0+lUkzlt7jwYWNeFhYWFhZvKljPy+J1RSaToVoE4MR1dOaZeCCRSITaeT6fD4VCgTRPrVajNxCPx1lw3Gw2mV0nsQ3dUPB80I0TXS4XOp2Okc6tmxrqz8nz9ko8PTmWfr3UCxJvT7wK+Zt4EK80lfz1hm4N8kohdG0qleJ8SgNOfTyZyzNnzpDm0/G4druNVCpFj/ORRx5hlqYus8jn8/TwstnsshLAfrPD0oYWFyw8Hg/i8biROq/jKIJ2u824haSCi2HTYq31ep1NM1utFuMjQn8JdHNLqbd6Jfh1z9Vv6uci59GND/Xxzyeb9duGNsCdTseoqRMqFHAMjhiVeDzODUShUDDqqpbG4+R4ukRBdxPw+Xyo1+u8j4FAgHNVLpc5R5lMhs/Xy8VELS5MWNrQwsLCwuJNBauwYfG6ot1uo1KpcGet+0XpAmGdlt3tduH1eo2dvSRsuN1uZu2VSiUj4023TvH7/cxq7HQ6hhchu/RWq4V2u83/a+/C4/GQvtKUmShs/Dpqyu1283uSwbdUZUIg9FmtVmMSgpxHK0VolRF9LN2aRARw5f8vR/ctTe7QfdV0ga8uUpbPBINBo8eaTmgpFAqkPhuNhqEfGAqFeH0ej8fwvLWAr07JLxQKPEY6nWbCRqvVorfncrlsgsabEJY2tPitQIyPVn7XMat4PM57KsZOvqMXuWq1amTgiSGUuiP5bG9vryHCqhd7WehEkkqMx1JKUx9bC896PB4eY6lxkPPohV8yGrXaxVIDJt/RyuZut9uIx8l32u22MU4tKVUulzkHuomoHqc2HGIkxaiEw2FuNJYK+8p98/l8RhyvVqsZYr5i5CTOJefUKh/AueaS5XKZBk/fq1AohNnZWcbQkskkn5dgMGhkKL4SxQ6LCw+WNrSwsLCweFPBel4Wv3VIDVg8HueOv9Fo0APSRc2AswMXClCL/GpKyefzwefz0aPQvbAmJydJhSUSCYNqTCQS1C1st9ssLNao1+v0osLhMFwuF72dTqdjdFk+H7VXLBbRbDYNb0fTdIJyuWx0F9bQ9VdaOcPv9/O4Umcm16CpTaHtZA4l2WFhYQGRSIReUKvVoneTy+X4nUgkwvmcmppCMBhkgk06naaCSqfTYR80fQ+l7YnuoaVr714O8XicLV4mJiawbt06AE6X6PPdK4vlBZttaLEs4XK5uEhrKq3ZbBoxHvmbfE7oxEAgYDz8YsDkPTEEtVrNoMJk0ctmsyiXy0ZKvCz4brebRk33Lctms4hEIkZ2nXynWq0aqvbawAUCARofTVV2u12OORgMGgLCMnbAMe7yOZfLRWPTaDRoVGKxGFqtFueq2+0a1Kv8PZ/PM2svGo2i0+nQqGh6UCul1Ot1FhWvWrXKULnPZrM4evQov/9qsXLlSuN6NQ2qi5EzmQyee+45AFZM940CSxtaWFhYWLypYD0viwsCgUCAnk4gEECxWKSHFAwGjXb0WrxWvATxmrSWn3gXWgJKWqcAjteUSCS4+zt16hQpM+356U7OIuQrtUydTsfoD6almeRYSzPrvF6vQReK53by5EkWLVerVSQSCXqMWjS4WCzSo1qxYgXnA3CoR5kT7THqerJAIMCxlUoltFotY9zaQxPPWHetnp6eRj6fp4f0q6ATWLxer5H0Id7W/Pw8z+n3+/mder2OYDDIsdri4zceLG1o8YZCIBBAOBzmQqcX/mKxSCorHA5zcZ6bm0Oz2TR+DC+nDqHTw+PxuJEJKeeKRqOk6XQ6fa1WM4qK9f+18nqr1WJcqVwus/GlnFf3mNLqIzLWaDRqUIJut5sxpmAwSIN19uxZvg4EAojH44wJaqrR6/XyWJp2DIVChnHX9K3b7eYGwu/3Y2Zmhvfg5bIsdTq8nnuZG23wxIDHYjHOjc7SdLvdmJ6etmnwb2BY42XxhoTetev6J20gZEFvNBovadOhO/8KQqGQEVur1+tcyPVPQXfgBWAkS2jDGg6HmZggTRqXnkcWbjm+dCKWa5M2KrrL88LCgpHqrlufaEV3n89HI+nxeJDJZChcrKFV6bVE1tJrFbFiwPF8lkppAec8R10PtrR2Tv6+ND1eoKW4tDHUNWP6/BZvTNiYl4WFhYXFmwrW87K44KG9Ad1uRbcj0cXLAAwFiE6nY6Spa1pMp51rz0neF8jPRJQmtPqHZA7q2JFugSIeoe6Hpduo6EJe8Uaq1aqhkKG9Sk3z6YJpaa9yPlUN7V1pelOUQOT6tOagVhkBYFCL2ivUafxa81DPm0B7WFqgeaknqD9r8cbFazE/Vh7K4oJHt9sl9ed2u/ladyGWhU6rYmj5It3gUP4eDAYN5Yuli7o2htrg6SaP8q+cRxs8bWwCgQDjPTphw+v1csw6tnO+zZlW6BC6VNe6SW2bGMCXowZ1DZpQfuej7TQdqONknU4HzWbTqH3T/cC0oddzqKnHX4Vlup+2+C3D0oYWFhYWFssOlja0WHbQXpD2dJZScOLR6A6+SzMFtbivzmqs1+s8tk6Q8Hg8qNVqTJVf2pZFXmsvQ3dQBhzPSXs04ilpfb5oNGpQhS6Xi+OLxWI8VrPZZIFxNBo1EjO0R6VT4L1eLwuOvV7vSzIAZTxLk2Pkc5JhKddVLpeNdH0Li1cKm21oYfH/Q2fNaWgKUStahEIh/r9SqTBzT9d26fiVpLnLYh0Oh2kgJOMRONfzCnAW/kAgYCzwWgleaqm0MLBQbkIlLu19JueMxWLGtWlFCn2epcK8cp5QKIRKpXJeytLlcnHMnU6HqiKRSAT5fJ5iuhYW/1fYbEMLCwsLizcVrOdl8aaHbkEv9KJWp/D7/UZR79TUFD0S7REtrQuT74uHp2lBXTys29lLwXQ0GkW9Xjc8Qa1HKMc+c+aMoU6hE0B0fZvOXJRrAc7Vf8l4tLixvu5iscisykKhYDMBLX4jsLShhcUFDp0+rqHjdjrt3cLizQBLG1pYWFhYvKlgPS8LCwsLi98JrOdlYWFhYfGmgjVeFhYWFhbLDtZ4WVhYWFgsO1jjZWFhYWGx7GCNl4WFhYXFsoM1XhYWFhYWyw7WeFlYWFhYLDtY42VhYWFhsexgjZeFhYWFxbKDNV4WFhYWFssO1nhZWFhYWCw7WONlYWFhYbHsYI2XhYWFhcWyg/d3PYD/K5apGL6FhYWFxW8A1vOysLCwsFh2sMbLwsLCwmLZwRovCwsLC4tlB2u8LCwsLCyWHazxsrCwsLBYdrDGy8LCwsJi2cEaLwsLCwuLZQdrvCwsLCwslh2s8bKwsLCwWHawxsvCwsLCYtnBGi8LCwsLi2UHa7wsLCwsLJYdrPGysLCwsFh2sMbLwsLCwmLZwRovCwsLC4tlB2u8LCwsLCyWHazxsrCwsLBYdrDGy8LCwsJi2cEaLwsLCwuLZQdrvCwsLCwslh2s8bKwsLCwWHawxsvCwsLCYtnBGi8LCwsLi2UHa7wsLCwsLJYdrPGysLCwsFh2sMbLwsLCwmLZwRovCwsLC4tlB2u8LCwsLCyWHf6/9uqABAAAAEDQ/9ftCPSE8gJgR14A7MgLgB15AbAjLwB2ApN3DwebulW0AAAAAElFTkSuQmCC",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x320fae150>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = grad(f)\n",
    "d0 = sqrt(sum(G.^2, 3))\n",
    "imageplot(d0[:, :, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Blur it by $h_a$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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IBE4O4XkFvgqcBMsrXE5EHg6HWSIyx3+YstL39TXLtFnezsV4VQnIir4SJfm1caQ/AqUj+X8ew3q9ntXuA1arVSYn11jWsZiOR08y/Vaibr1zfw34PvK58b6YMsT32AtTyT/2W6J1+f31ep0Un7jvXCsRdLYqTdULC8/rtBDGK/AqeL2gUD3DLC/71Gq1spJHm80mE0/gtZaA4liU5n3hexxo5/PC5OxNnH81lLbzjqmTIW+jpY1gvDiPab1e22KxyPLBNH6E194xzHLjxVJ5Nhx/xpB7wg5edHhGlY/nGWCt9K/wFiF6P1gows9Et9vNnj1OQ/inFjWBvw5BGwYCgUDg5BCeV+BFqCQe1TP6/X4SaQyHw0Qh1uv1bCW+XC4TrTObzbKiqextYZvVapVRhex5qbScPS/tSux5QX/Vqtqrr6jH5Pd4DFnmra95nBuNRuaZskiEE3z5nI55Xvzdkmjlj0DFIJ7aEJ6Wd0/4ehTqkbPnxWIW9uLY8+LxaLVa6Xn1CjSXBC2Bt4kwXoEXwcowbiZ5dXWVJPH9fj/RiTxJocgujJeWavKqaKAoLce5vAmMt+EKHWbPMmts81eOBcestH9WadLTOBdXTmf5Nxs4/MP1eZXodeIuGa8SpfpHFZcKTQtQQM7uUX18DXo9vA3nk1UqlfSaK9mb5fEspmibzWZWCJljqrwoivjXaSBow0AgEAicHMLzChwFPAbO59LqGWaWvC6AlYOLxSKrLcgeFYsveCXM31OFoicU0HqIrG77K2ggFWiwF8VVJEpFcdlD41b33W43eWHaGoSTwJkS1bYnmgum+Ut4zZ6b0pt8H/4q8Qa/j2tjuhXga9DctpJ4Q5Wm7AkrsI9ms5lV6OBnlJ/FEG+cBsJ4BVzwxMtxrvPzc7u+vjazfTIyJPFmlsUQtDcXJxmDNuRitRzbQMyL91eidHSiZOPlxTCOJRUfGws1RExFwRCxIavVaul9xLK0VBK24SaRPAY82TPdxdX0ebIulULCdXIjSDZ+GG+cg2d8XjtWem+UnmRKkM+bjRQbMv2sVBlEz8E7V2502Ww2076ggPWK9kb86+0iaMNAIBAInBzC8wq40BJQaHFyeXmZaEOUfjLLe2NxB+DpdGrz+Tx5W+xRadkmrUX4NSWd8D6rHL3VOa/kXxJyeLlc8KjgiXa73fSaC8Tya7QG4W7QLE7BNXAZLC57hf3B22JvjcUxZoe0G8CClmazme5PrVaz+Xye9SHz+oaVXnvg72EMsY3SiPx9PX8INrS1i3dtKI6sdQrr9Xp2PXwf+ZlmFSw/eyHeeLsI4xU4gCeNh8JwOBym15iczSyrRTibzWw8HpvZvpfWbDZzq7ozHcjJrZhAv6YqBgwXT5al2AlTiKXJSalCLkDc7XbTxDcYDNJ4tNvtTEXIFJU2msREyRXvMQ7YptFoZMnM2F+j0cjiW5xwzPEw7S+G43AMcjabWb1eT2pQTV/weoBpvOm1k7suOkoJx2xgSigVYQYV7dVd5PcrlUrWBWEwGGTPLCcw8zMVeDsI4xU4AEvjG42GdTodGwwGZravqsFVHzDRLRaL1Dl4PB7bdDo1s/3kqE0VS8V4S17Ua1e/pe+otJzjGaV4mIoIYKi73a4Nh8PkfV5eXibRCosvGo1GFpfisUKnaLyG0eeUgvV6ncbebG8kueQWpyLwNk9PT5l4gQUtOCY354RUH/dUK094rWi0Osexsdf74FXJx3jjnDnl4pjcn8Hf4TwzNj7s/XIpLowzxrfVarlx2TBebwsR8woEAoHAySE8r0ACr1A5Kbnb7abqGSyJ32w2adU/mUwyz4vjB6WqGBp/ek2bjz+CEpWmHl0p+bher6frv7i4sJubG3v//n36Gyt2blPP6j5QcUzHwdPpdDrZOTGF2Gq1Mm+Ax4opQMTcttvtQd1E3i/fK3jGk8nEms1m8kTm83kWd/MaenLhXB1H9U5KKQY6vp56E+fAXlWJwlOa0KOmmf41s0z9iefcbE//sjfrpRgEvj3CeAXMLDckTJN1Oh3r9XppcivFbqbTaZoQF4tFJr1mcACei8UyNptNRiv9kQmjFLOCeALva4zFk7o3Go3Un+z9+/f2/v37RBuyUWGajaXXmPjxGcdb2u12oh1BzZo9l4fi8lcY6/F4nJXO4vQAnoT53NgQ9fv97L7xwmM2m2UGi40cvoOx9TpS6/3WMlr8jHEfM49u1dialsJi8D1g48WxVKR94Pgw+mdnZ9lCgWOXHAMM8cbbQtCGgUAgEDg5fPee17GkzcAzSsV3e72e9fv9jDb0PC+lmwCmigAvMVl7cf1Z6pBFGryy73Q6mQqQ+2lxkjG/7na7ydN6//69DYfD5JWt1+tMOQivZT6fJ69lPp/bcrnM6u1Brci04WAwSOPearXs7Ows7Y+9rclkYvf392a295S4u3C3283qPXJyMx8H3h4oSNBkUIfiOKPRyMzM7u7u7O7uLu1nOp0mGvFYBRStnMHjizFstVpZWgF7i/r8sILUe0bYA8M+eNxxTE0ubzQaSTXa6/XSGCiLEMrDt4Pv3ngB3oMeD2Aek/CK756fn1u/389KGDE1xv2R1GiZPcfPeALiWAnvi2MTf8R4scGq1WrpnHu9XqLkhsNheg1jwZQVU4qY3NrtdrZNpVJJE/d4PE6G5OHhITNeHJdilSVX3e92u1l8hVVwHNtig/Xp0yf78uVLeh/jDiqMYzdsmPl68J1Op2PD4TCLp8FIjsfjdJzff//dfv3117SvWq2Wyet5gi/J3rWsFhsvr7K+d3+910znKW3JZbXYSHMqg5ZA6/f7mTHnRVkoD98OgjYMBAKBwMnhu/a8NK/ELFZMCg6oc4dkeBr9fj/L7VLPy6OOVCDBK2uz53vAIgL2Mvg7rwXEADhOq9VK13BxcZHUgR8+fEivr66urNfrpRV3rVbLkqY5KRfA6v3h4cHMzD5//pzotMfHx3Q9LBTQ/bDnxZRZvV5PFCRq70Ek8eXLF/v8+bOZ7b0geGGTySR5BthHiY6DIEH7sA0Gg+SJ9Xq9dO/evXtnNzc3ZpbXsURh4cfHRzPLvRP2MNXT4ueiVqu5dK2ZHYg0WBXI3+GiwniO2TvCNtgfq2NZYYljcA4YrrXT6WTVYbi24vcwl3xtnc+3hO/aeDFO7cb8E2DjzpMJS+Pb7XY2sWy320zpxpJkjllhAu33+3Z+fp72zSWQ2FgtFgu3aCufa+kazJ7Va9woEwWEf/rpJ/vll1/MzOxf//qXffjwwcz2Ro1puvV6neJULPdX5eDj42MyWPf39ykuNJ/PDwwWwCpLrmjebDazOA32hbJGmGxvb2+TwRqNRpnh4NJIaiBY0cdxzPPzczPbG6+Li4vsb7wGpYjtgaenpxRfM8sVijzB6yKGz4fLQDF9rJ0GWFKvVfc5zsaJ1Vrw2Su/NR6P07mcnZ1Zo9HIVJusPMSzu1gssnSH7wmnOD8GbRgIBAKBk8N37Xm9pnjojw4OqHuKPJQY4oRb7sflBeq59cT5+Xnm4XAZKRZ4mNkB3VMK3PN3uEcWctLM9r3G3r17Z2Z7qhD0V7fbTfuFl8AlrkAH3t3dpdfc/XmxWNh4PE518LgU1mq1Oqq0YxUdMB6Ps8RmjA3+hud1f3+fjjmZTLJu1Kry1PYtZnne2ng8Tp7b7e1tqu1ntve80B376uoqeVdmz94XaGUcp9vtZt4foOo+Li7Mna6n02kaaxZ/wJP0ivFq2SimEDUpvtSrDOdydnZmnU4nExVxniOe3dlslsb6e6ENT/kavmvjZXbaN+fvRklOrjEqrmvHdfm08jugSj+mDc0sTfbr9dpVcmHS40ndq1SuNQdhKM32MRrQX81mMx3n9vY2TdyoEYjJcj6fp0l0NBplibsc21NJPPZditWAnuXPeTyxr1qtdlCXD58xNadxHUCTenFsjBXTvaBE6/W63d3dZZQixvDdu3eJNmy321lDUST24rNScWMYHBQZ5hgctnl4eMjSL3isuVajyuY5lqWxSk8VyPUlz87Ossr6lUoli32yMpPVqF71+phjvg2+e+MVOIRXfFYD/Ww4MLmb7ScXziMqVezmWIsG5L0qFFwyiQ0njsOiBxyHc3PQqgUGq91up+/xZK3xEI6XsJR6Op2m11zaCRNgKUbD3pZXConHH+BYoeYxccxIPVU+H2xTKtXEOUrcpRrH5DQJxN0eHx+T8er1eulec5wN27Cowos3QVTBeV6cb8dSfZbasxjFG7OXxrT0HR43MAgcA2MvE97nZDLJyp55LV0C/xwi5hUIBAKBk0N4Xj8wSrQhJ4qy14O/vZYmpR5KaBSIVa7SXzgOS7Qhr2f5M1NJ2KbdbidF4fX1dVb5YrVaJXrw8fEx69Wk/apYMclemLYA4WvzvC2VhrM3wuo4M8u8Mk5RgCcJ2T48j1arldGY7Mnx9ZQ8r5JnguvlOCbTixjDbrebFeTd7Xbp+jabTaLcuPalNnXkVi7dbjejfPneg8IEdcsxsNI94OvkuosYf4UmzvNYcd1FbpXS6XSyxOwo2PttEcbrB4RXsJYn27Ozs2LjQS63ow0j+TswUI+Pj9lnXOao1WqlMkm9Xi/LPTo/P0+Tznw+T8ZnsVik8z8/P0+ijOvr66yp4pcvXxL9NZ1O0yQ8m82yyV4D/1xWyOtbhcnRk/VrhQ+moUr3gBcNw+Ew6w3GlOZsNkvXcHd3lxl2jhtyDy8Vj3hV+7UhJ3cl5ty76XSaGQF+dpbLZVYhg40Xj6Hmt4Hi7fV6yWCdn5+nBcloNLLRaJTuPbpym+WydU1D4EWILjL4e1rVwysaXKlU0jM6Ho8z4dH3Kps/FQRtGAgEAoGTQ3hefzPeWgb7sVYh3IqCV9+qgGPBBa8+PZqPaR9sz4nEkLDf3Nyk5OHr62s7Pz9P++O6fpPJJK2m+/1+knV3Op2s+O1ut8sUgSwt97xFHRuMg34PK3RPCcnQArXe8czytILhcJg8yeFweOB54Xu73S4rnstJyXwf+BqY1uXXHp3IdBh3YmbPi3u+rVarRH0yFccUJGhGPC8stmk0Gsm7ubi4SJ7Xer22x8fH5EF/+fIl1Vq8u7vLRDhAvV7P/uZrUMEIKx/Ze9P2QBBs9Pv9zAvkqiJv4bf9oyGM1z+At/Zgc26XVxyVlVgwUJpHY5bTQiqVx/vz+dzW63WaNHq9Xpqg//Wvf9m///1vM9tXwYBEu91uW7VazSYnzg8CuEoD4kOetFx7MpXwNR0INOcI/7Ox0PwiruDA++H4CmjDy8vLjH49OztLBosXGkoHcmxN41+s4itdG++Pr2e322VUKVNz/JppS80DZEqRiz/z+8PhMMvV++mnn5LB+PXXX5PBYbpXx7p0f/jaWf3KlT7McmPEi4ter5cpD1XS/9Z+5987gjYMBAKBwMkhPK+/GW9tNaYKQ1B4XEnALFefLZfLzLtQtR7v2yz3zsz2Y4DjXF9fJ2/rf//3fxNVOBgM0moY+V9IGL69vc1agOBcOE8MLTrwvfv7+6TOY+Wgp1Dj8/Q8FU10PVb9wysW633m0Xna6Ze/h/uA68ZrVr3Bu+N9e16HquNUKVqCXjPTxEyzcS1BflZYxToejxMdWK1WD75nthetDAaDRCly/qEqGbnAM183e4U6HqyW5IofrLBlerHb7SblIVcLgbf71n7r3zvCeP1AAK3k9e3inl1c2QExLo4lvSY5k5Vg9Xo90WE///xzKpJ7dXWVtVvHZDYajezu7s5ub2/NbG+8YMg4ORaNMnGc9XqdKKbb29tkvDg25yX6MrwJTONIDE7K5TFh6pW/a5YbD14MzGazVH3k7OzMlstlup67u7tkmFmBxwYclSb4vD25/DFptxo/b2x0f9wzi/fNalQA5zqfz5N6EtdhZlncEvvDMzoYDBLlzCWyOGEYvdP4fqu6FPvFs4RYJy8iYLDYsDebzaxZqC40onPFP4ugDQOBQCBwcgjP6wcCKEOsGNvtdtb6nBN8AaxcOfDO9FFJtQbUarVMpPHhw4eU32NmyTsODEhZAAAgAElEQVSaTCapX9Vvv/1mv//+e/K8Hh4eMvEGjs+le5rNZpajNJvNsoTSY54XqywBFSvwqlrHANCg/bEkYYCVmePxOF3z4+Nj5nnd3t6mz0ajkXtt8BY9AYlZTvuVvAMdA4bmh/GYeAm7Oh6cPLxcLtO9Z2Uol66Cx49nh+/3u3fv0rjxMcAaaAkwvGaqE8+0CjbMLP0W0LvMLKfZvVYpke/1zyKM1w8ArTKOHx23g0fhVLO8OjpoLW/SZ3mxvuaqETc3N/bzzz+b2Z4qhLGYz+dZs0W0mf/vf/9rnz59Sj2ztJYeNw3k88f5mtmBwfWoI41dvaY+nid/ZxVfKRGYVXyqhMPE/fDwcCA1h/HiHl7j8dhtAqp0X0lh6KG0jV4H/i/FyY6NIcec1ut1WpAwTc1FjzmtwWyfToFnFKkEZrlCEvvm6u/e+TC1CDk9jyOeUa67yHQiG696vW6r1Spow38YYbx+AKggAD867rTLEmv+YSOG4k2CnDejVQ4Q2L65ubFffvnFPn78aGb7uAUmloeHhxTH+e233+y///2vme07Bd/d3aXJmgUXOJZZHrRvNpsHFce9lTC/V/KgFKWYFsbAK3SsngmPG0+2HBubzWaZ9J87/2qMx1tMvGSg2Pjod3lc+Bq969Ft2Nvyvudtw01NtTgylw87OzvLvCB47a1WK+UINpvNLM+MFyvH0iS03BQ/87xA4oLRXG0eXth0Os1idSGb/2cQMa9AIBAInBzC8/rOwSthxLu46aRX4NUrSutV5ajVapnnxSrGy8tLMzP7+PGj/ec//7GffvopHYcl8L/99puZWRbjGo/HNpvNsiRYr6Egt8yA6u+lRGOlxVSB5iX48vV7+8cYqhdWopG0ZQxX61C1Y8nj9TxGVc15lJ/3msdN42R8fH3tyf31fPScSwWF+Xscc202m6lR5mAwSNtzn613795lvbjYq1ssFplU3gO8Xz5fPMuz2Sx5WPqMc5+vWq3mNmYN/H0I4/UDgCtqNJvNrI8SVxrw5MW6D+05pfs2208yiHH95z//sY8fPyYacTQapVJPv//+ezJet7e3Kb6DvLJSzMmjnrxuux7UWOn/XhrAsYmZq5NzDp23DY8VN3+EaIYrrXOeEfbH18b3ig2elq4qQQsLe7RfKRcMhqu0/9J48fgoxaslyMyec/dY1IPtlstlGrfz8/NUJgwpE1wajGlDjpPx8fV+c7V9xBfr9Xp239V4lSjjwN+DoA0DgUAgcHIIz+s7h/aYYs+LV4vaDuQ1xWvZG6jVakn5d3V1lQQaHz9+tG63mzwkVhX++uuv9vvvv5vZnirUpFNPYMArfk4khoT+pY6+npwd+1CvjSXU2iHZo04VuprHPhqNRvJE+/1+1hZGVZPshWB7VuoxPakeF9cZxDnouagCsuRRaXWKYx4Fe7YqVOHjcs84ryoInkkuTozvVSqV5JFtNpvkeV1cXNgvv/ySqOnHx8cszYKLRJeuTyX98LwajYZLLTabzYz+fSkRPvDXIIzXdwqeqNh4cVFXs7yorOYL4X3No+FJEhNQvV5PNM7NzU0yXqisAarwv//9r/2///f/zGyvMIQcHpURcAyVgJeMD86ZjbCZHcRWvB5kmFx1Wx6/0tiWaEqvBJTuT6vUw2A1m81EG2JfMPqofG52GGvE+1zponTe2EbLOXnje+w1/68LmtJrzbnSMcP3dGxhcKbTaVb5BeO2XC7TcW5ubuzi4iLlhn369ClVblksFtmigK9DY6q8KOLmnBwbZAqR++FxxY+gDf8+BG0YCAQCgZNDeF7fKTx1YKPRsGazeZDQafbcUsQsL/aq+VLazgP7brfbSRV2eXmZqLCnpycbjUaJKvy///u/JNLgXC4t5Ms0ZskD0EA/50yp58WddT0FnYfSZypa4e971Ksea7VapfPhnC1u/YIxwD3hyhPcokbVpHpOTLeyt8Wvt9utS31q4m5JiVk6ppfkrN2YdRtu08OejNmeWsY2rA7kljtQAeJZHA6Hic5+eHhIFCA/B2AXSt42U4j4Difyw/vl8deE7sBfjzBe3yE0FsW0FNMbu91zm3d+rcVMvSRb3Xen00kTxvn5efohz2Yzu729TQnInz59ShTidDrNjCeAifJY3I2/a2YHcSue3JQG9faj8GJj2D8bbTWS3mSPa+ESSojDTKfTpCjkahvYhpt6omgvLy74HHCfPFqVx4bjZ5homX711Iq6aFCq76UFgTcGfD5KbeM1jwEbXT0+0izQ0BMGazAYpOfy8fExWwDw4gj74f8BfI9pQ15AQGmL+8j97AJ/H4I2DAQCgcDJITyv7xC8quWk5G63m/VEYpqNc2O8gDPTOkzRQDXX6XSSYKPVaiWPajKZ2KdPn1LR3dFolAXdvSRc/Ztfc78oL9nW6y92rDWIeg1eoJ09T3hd2svJA3sqXAIJ42j2nMdltqelmErjPDYum8T3xxsf9kJZzFGCJg/z+fM1lO5RSaSh39FtVa1ndihMMXv2HlerVXqWWUm52WySV/r4+GjD4TDl0V1dXdn19bWZ5SW2eDzgpfNxNQ8N3/MUqI1Gw9rtdlZcGNtHwvLfhzBe3xG8OFez2UwUSrvdtnq9nv0AORmTK1qwIk/rFrIxZHoGhuzs7Lll/ePjo3358iWjCjlR1FM+KkrvexJ6j+rTseEYkVKQqqTDNqr0e815636xz81mkyY6yL3N9veAJ02WiXNszOuTxdeo+9DzVGVdierT2B5Tp2rQS8nZqnrl5xLPEdfYZGrQS/RlI8eUMcvp1+t1pnyFYfN6hZk9FwDmBGo+NlOdOH9+XavV7OnpKSsu7MVYw4j9tQjaMBAIBAInh/C8viPwypuFFFiFttttazQaWVsKpqIQGF+v19kqUWu6cfdlqAo7nU5aFa/X67Ta/fz580GuDdNaOE+zQ/HFMcpJ8VISbYnWMrOMKvRWyUopqTLPS7BlkYhHc7IXhlU6lx9Sr7BUJZ89Faa3FCog0ZqVHjTn6hiV+lJpJHhneEbY82q325nnpvfAU7s2m830Pj9Ts9nM5vN5qj5/dXWVnQePEXuSLPDhMdEOyXjNSckQwOD3s1gsst9S5Hz9PQjj9Z1A1Vte7TxMFly0lOXxTHVojMRTGDJt2O/3s2aWkMDf3t5mkng1Xnz++uNmBVyp6oNK6D3jc2zS0Ot8zUTDkz/HDbXppcrZvbihjifuUb1ez+hF7mm2Xq8P6FKclxo4z7AydMI+FrNS+fexBYGOIcvKdQzUSHNCOX+uBY15EYZxn8/n9vj4mEnl0Tplu90mledsNkvPvipRtYYkjyGfM1OYjUYjOwcch5WhIZv/axHG6zsBewcc5zo/P0/eUa1Wy/j41Wrl5nZpdQgGqgmY7X+02He3203HXywWKZbz8PBgj4+P6W9Mxma5R8cToFbJ4NUvf86TNeJA3nkfk3Ifi3l5uTowXNp3S89H961ycMR4+v1+qkLy7t27FDdsNpu22WxSseKHh4fkzc7n86wXlnpUpS7PpdfH4lSlceL/PTGHHofTFvA/nkO9txzb44LP2jzUu9fw+vG8cTxtMBjYxcWFme1/F17KBs6B7yO/Zm+aRVEsj+92u+n48/ncTQcJ/HlEzCsQCAQCJ4fwvE4cHqXS6XQS539xcZEoFCTBsreiychmh9UU+H9WIlar1bSqZfXXcrlMasPpdJp5CrzC1biavl+iCgFdpZeSmUu0lncMvm4eWy0Wq3/jdWl77YMGerDf76eish8+fEiebKPRsOVymdU69K5BPYbS97y0Ag86Vl5iMp4Pb3xKx8U2XK0C+9Nr4Jgd03GbzSZRp2bPXhA/k+v12mazWaKpmR2oVCpZLztWODL9q+B4Hj9vTIVy93BubVOv19M5B2341yKM14mD4yj4wfR6vdQM8vLyMlGI8/ncarVaNql7/bx0EjazA/GBWT4Z1Gq1jILknBemJ19TeQATw0v5U8fiPa/JN9KJ5FjMjMdBRQkvVe+A8eJ7xXEuUFnX19dpoVGpVLKFBk/2XAGF45M4DseVvColx3K2+Nq9mGJp3Hg/x+JkOO/FYuGW8tLnq1KpJOPGdPRisSga1slkkmK+kLGb7Q2ZUn04NzWaTAtz2SfOi+R7wEWVW61WOr5Wm/fELIE/hqANA4FAIHByCM/rhHFMYYjV/GAwyLrzsly51WpllAy8JV4hqwiCt2+328mrY3qE6R1W4CnUo/GqPHjX/BoJPXs6pWRbVSjqPkoiBG49UhKJaGK3Fm7l1AOMYa/XS69xDzhxlj0q7ftllheo1XPzihgfu0YeH36Pt2FZv1en0GsX49HP+j2WzfN5z2az5GVypRU+N9Qf5A7UQLfbzeTxXCVFz5PPTalPnL+qFbG/TqeTfotcPUQrowT+HMJ4nTBYYcgNDllh2G63sx8p54AxB79er9OPmCcJbOdNtsPhMMXWqtVqpiT0cnz0fZ70lFbzFF68P2+/HuWkr1U5eIwa8yZn7KskO8fYavFeXmho/hRPtFwEdjweu6o1vU5sj9JQWqECY1hSHJZiMRq3864Xx+XOBZ5RgBFi+tmjWXVxUqlU0jYcO/WuweyZXi2Vu+L8Nl4Y8DOy2+0O7p1eDxuv5XKZxdB4Uddut5NKlEtaHSvXFXgdgjYMBAKBwMkhPK8TBValXpFcTnblIPNyubTdbpdWkKxk48A2CwKQmMn1DOFtXV9fJ6XcdrtNCkOtPsB5TaXqFN71eSICpfW0IzDAK2n2nMwOxQt6XBzvmFqRV+nsgXBbDPbC2KvzWpKY5dTtdDq1+/v71OpjNBolKpZr9Gl/LD1PprR41X+MctVrxHjod3l82fPS68a1qaiGx4Df4/2yV8jeDp8Tnzuqw3j3m8+TPdZGo5GSwrE/9mY1/xDnwhU1NptNVqsRzEev13NrK0bB3j+PMF4nCkzcHL8CVdFqtdIPjpV/aKPOKi9vAuLqB6BgeHLCcS4vL5M6brlcph8vT2CNRiO9b5b3UWKZucYZ+O9jP3SvQgT2wbSQt82x1yVFnb5fUhG2Wq0Dehbb1uv1LBkZ94AXDePx2O7v7+3Lly/pby6c7B0fRlaNAcaAX5doK6ZEdV86iXv0rR6Hx41pM100eOWl8JqPq+pXhZ4b04O9Xi8ZlWazme5Bu922ZrOZ7ZOr1+P4/Nvh85/P57ZYLNL+OP6ssnkY35DN/3kEbRgIBAKBk0N4XicGXpUyTcXeDq+sN5uNPTw8mNm+xNBkMsk8r1KeFx9PxQbc1oJVb55AAuozzfcxOyxeqyt7zjUr1Rw8ltDM8IQdXs3EknijRLmpCpDvh5Y1wnatViuVhOr3++l7LNhYLpdZjTwtYQR4npGXvKv3ENDE5hKN6inyPE9Vx8e71x7YY2KqU8U2pX3gOGhvwvlc8KIWi0XyvJhmh+fFlCT/lgDNr+PCwNPpNDESrDBstVoZI6G97P5K7+sYc/A9IozXiQLGiw0JXqOShtn+h4WK7seMFz/42s6ewX9zJXpQJ2aH3D7HOjRhmeMWniJQj6sJqfp5SUbP2+s4eoa1RGlCNefVZOTXvLDABMpJ5EhlGA6HaRLlyQ37KkndS+AxKdWoPEbJlq7Hg8aA9LX2FVNjyueAe6/nz+pJPaanSOWqMWY5RctJ30wbtlqtrM8dP68qleckZaBSqdhsNksxX96GjScnRnsLkb8KP4LhMgvjdXLQmA4LBDjOhdeTySQVd51MJjabzdxKAiwiUAPB3la9Xk+r0qen5wZ8fJzZbJblfHGgnY2XyvEVnmF7KRZWmoC8SQ/XVpJps9egnlepmgaDJ7But5tW/cPhMBmvfr+feb/qSXneEo8NzskDjwHHGrW81bH402uP7xki9fB0zNSrwftaTZ6P5S2q2EhzqoHZ3mDxooqL57LAqdFoZMIZFix577OXdnZ2ZvP5PBkvFeTwb4dz4P7quNePYrSAiHkFAoFA4OQQnteJQT0veEFaWUEVhmbPPbs42dVT56kEvdFoZNU7uMUKPKzxeJx5eDgmqCKWOzOlWKL5+D3l8o/FTryYldJS3ndwrXxsz4sDncjnVJLkc2yN29Twqr/ZbGbxJr0fnmrO7HiSK3shXEGFW3McW6Ufq76Bz0tJxnpPleLl6/NoX34mtZXIsfPROCmnhzCFDo+pUqmke9Dr9bJkftTjxPdwD7ieoVKWq9UqYxuYVmalriaUvzZmGzhEGK8TAtNakMlzJQAvOM5NJrWiBE+ATNcwHQnjhYaWw+EwiQ3q9XraN3P+2m9K5eRsVDzj+dLEWirk6n0XxwG8osPHDBjO7Rg4zuVJvnFcFlKwZJr7limly2IQjpPwNnrNXs8s7temi5aSISkBxkLpV++61SiV4preMbFI4OfSuyde3A7gfKzlcpmNIYzXYDCwXq+XYlPz+TwzUjgWxCB6zceugQtms8AJ/b9KseXAywjaMBAIBAInh/C8Tgy8ytcqDkyZcEKreli8SmavxFu9Qi3Fq1RQiJvN5qBjstmeqmTPq1qtZhU/8FlJtq6UFIOrJ3ir95K6rkQn8nWrZ+ut8rF9aaUPsNezWCxsPB6nbbi1R7PZzBJi8Z31ep3RSuyhKXWqnrQn0vAKLPO5l6jUY2P4EuWl96ZE/+r2fE5Mu5mVq3KoYIS/51HWZs+e1+XlpV1dXSVV7nQ6zehWoJR6wMfT62Fqv91uZ7J93GPsL7yvr0MYrxMC/2CQU1QyXsy/A/iReaWN9DhMV3GuSqvVSscZj8epfNHnz5/T68fHxyyuxkpINrg6gWnljZeKuOrrktHj93XSVZpLc7jwHsZMaTpWoFWr1fS6UqkcyKHx92QyyZolgpJtt9uJrsVE6cXT9L5pWkLJEOnCh6/Ruw+lhcEx+Tzj2IR8zPip2vGlor/edfK1ejTzbrdLz+FwOLTr6+v0/Go1E6+klV4n9mm2H0vcx0qlklVdwe8IeWU81mG8vg5BGwYCgUDg5BCe1wnAEzWgZqC3EmVFoSaqHstJ8oLu9Xo98/Cq1WpW9eH33383M7NPnz7Z3d1deh9AnURO2AXYu1qv14lOVJWZ5hF51+PRea+9ZvZCOA9H+0qZHVJPu90u87BYlMG1IpfL5YEIxmy/Gufrxcpcez+xt6R0IJ+bquA8mou9X5wTnzeuW4UuLGJQb/WYavTY+wB7dextaoUKr1XJsWOxqpA7KbPwp9/v29XVld3c3JjZnjnAM87PpXe+Zs9qQ2yDsTXL8y+bzWbysheLRSYgYQVreGCvQxivE4LKbrmHkJaEYs6eqZLX/DCYNoTykIvMwjjd3d2lwrG3t7epDNViscjO08yyZGqGlyyLeJFXiuclGsqLX2mSs8aR2Mh4yaVMO2Ey43Pjkk68L752jkNCaYbr5iRWAAaK6VammHjS44olpQoUZ2fPvca4WDKk+lw5wpPUa4ytlC7gKQ35tbdAUlqOOyW02223saPXYw3jpHQlLxR4fDFug8EgUYdm++caMUmtFuNJ5XFvIcnn54U7N1QqlYx+bzabGb1fivMGfARtGAgEAoGTQ3heJwCmDbmWobbd8Dwvr/wP79dbCWt+EReZNbO0WpxMJsnbGo/HKc9rtVpl1FNpBb/dbrOeSFxCinOeSh7jMaWhCjH0uvF/yfPitjBc1me1WlmlUskSv7mUkOdd8dhhfNnj5FwsToiFIs3ssDQRlz9iulUpPeyPCzd7SdJ8DqwUZUqS72FJ6KLvqffnKTj5dbVaTeMFypA7TXvCHe43B2qRvXhgu90mj4qVf+122zqdTupNd319nZ5rLoistSWZkmVPjulnpaW5L95sNsto/6ANvw5hvN44VDmFH3Kz2cyK8Wry8bEKDEyhedSa9u9iOTdTTFw3jic9pfyYMtPEXZ6QVd7/knxb8VpKlOkmVWx6FeJ5kbDb7Ww+n2eydb1WvOY0ADaGSu3hujnFYL1e22w2c8cX8RKzfUItXmuDSn5eWq1W6r3W7/eT8arX69k58HjwNXAvKxyPx9RLMcBnes26DX+Pq7l0Op0sfqRSdaagWd3H8ni+No4j8nX2+33r9/sp+f7m5sbu7+/NbB//4tqIvCgrJaTrM+HFVGE8cQ5cdzFk869DGK8TAE8MOqHib3SQ9bblHxwHuktNGjkmgiaX7D2wwdHcIkBFBKWg9zGJdknC7p0zDHEp5lUSo/C1sgfAngqv0mu1WirkquellRl4nNAaRrfh783n8/QZPC8us4VJmCc6zhVCDpzXXRtxHbP9ZM1GgeNmGo9jY8GeRWmsNeeJx71UiYMNES+Ums1mMZbLscKzs+fOx7gub1HE19NsNpORHI/H1ul00t+Xl5d2eXlpZvv4F2K8XJWef2vKTnDlGx4D9uzVeGkqROBlRMwrEAgEAieH8LzeOFTizCtUjsUwJcJVKBjHvBNeFeuKvd/vp1Wp0jBMT7KHpwnHJWi8A+8di2d5smocy0soLVGiiKmwFwIgRcDsWdlpZlkxV+wDK+6Hh4ckl+b4yG63s+Vymc4NnhjOx/Mq4WmxqtBracL32iuiDG+L27C0Wq2sXt9isTjwJDBufB/hgXjnW0oK9tSkug0/h0zXwlPhc/NiWZw6wM+mWV5kl2Ons9ksXc94PLbz8/NUOLnX66X4193dXSo4zZ41//bwe8H2rAxVD5O3abfbWa3DUuWYgI8wXm8caryYUtFK8i8ZL8QjShQPXnc6nTTpXV5e2nA4TBOKxmE4zsLxNxzD6xjr/Zi9CVErhWPfvB/NxfJoHf4eNweEcIHjWZ7x41hYu922breb9j8cDlMs6cuXLylWwoF+xMJ4rEp5URq39MaAz40n+3a7nRmsi4uL9Pr8/DxbgEBco/QkqGWMFe4pG1ycvzc+WllfY0Gah4ZtvDHwJnDPeLFMHcf04q9K8WIMHh8f7fHxMVs8wRBdXFykslGTySSTtuO5GQwGdnV1lZ6DarWaDONsNnOvw6MavXSDQBlBGwYCgUDg5BCe1xuF552okILpiWNVKEoVNrSKBPZ9cXFh79+/NzOzDx8+2Pn5edputVplrU+8hFZv5e0pszS5lMF0o7YK8YrVYp8qZwaYKtS+WlhBM/XK16NUabVazboiY8U9GAzs8+fPZranm1C/EOPEieOeh6j1/vgc+FpVRQgK8/z8PKsUwd5ArVZL3sj9/X2iwkajUeYlnp2dZVJ19sI0KdirRqLevHrNPKb8LDL9De8G7XO8e8ICHy6CjGN4CkP2CheLRUYb3t/fZ88IxvTm5ibJ67lPHSfid7tdu7q6SiIPFqBst9u0zXa7zcZJW6R4v5GgD8sI4/XGwT8ENl6YTLi6gjfBe+WUvArY9Xo9/WDfv39vHz9+NLP9j7fRaCSDtVgsUlyHVW9MVfIEhkmXjZR+hm3YqPGExHELrUTAxkt/6Dzxa+6Q2XPckGXWTNsx7YcJDMfGPTk/P0+GvtPppDHs9XrJkN3f39vj42PattTU8Ficj2NjjUYjGWCUNsK9ev/+ffobNKHZnr4CpclFlMfjcRbzYiOFv3G9/JoXG5orx1C606ME2RAxPcm937CvUr6fxli9qvD893K5TM8xxgWfDYfDNHYXFxdZY1f8Dri8FIrvcrUbjg/yuWns1cslDNrwdQjaMBAIBAInh/C83ijYC2GFIVaE9Xo9W9VxBQSlWrz9Apx3ghX7x48f7eeffzazvTfB3o5SNJ5KTNtYaHFVLzCtVNN6vc6C3qyOY28POFaQV5Ou2YPQ9iBMj2JsOREYQXse9/PzczPb00fH2nfgHNlLVhEDQ71ZpgohxHj37l1G8V5eXqbvLZfLJDa4u7vLKE2uQ8nFeLmWIHvG7CVwzhrOjSlN9vpVOFTK3fPoQBQ3Zg/HK0TN9w0eq/f8MxW9Xq+T54U8RKYEUeeQPdvJZJKeSVaCLpdLm06nadyq1Wp6XjjPjPPRcC1eblhU23gdwni9QWhVDS+BEz+ClxIaVRrP23CvoeFwaB8+fDAzs59//jlNjogf8D44eZdpNp7cmKbjJF9VSXo9uzAxeDSVJuh6FS2OjSeOpeOA/3lSZlUlJq3NZpMpLheLRYoxDYfDLG6oikJeAJRiXqXFRb1eT5PjcDhMx/zw4YP99NNP6ZjNZjOd66dPn+zTp09mtqcKYci4agTGj4vXegsnNVCahMuf8bhi/1yySa9NY59cRYZl/RzjZWWoTvaqhNTj4Xssode0D1ZwgqL98OFDGtv5fJ7oxuVymeKb2BbfY+OlBp8Xo/y70ColAR9BGwYCgUDg5BCe1xuFt/plagF5Td42LPJQhRervKrVaqaqwgr+8vIybY+Cu1xwFtuYWVqVMq3FwWsVRXB/IzPLAuuqLuRt4NEw5Tafzw8K5PI+AF7xcikkj7rBa/aINptN5mkxjbhYLFIQfzabZXQT1GdI3PU8PFZsqufI97HT6aQk4/fv36d79eHDh6R8rFQqNh6Pk7f166+/pn5r3OaDqVdsx2IDTRLGuZQSkZkOU8EG54mZ5cVsPUqSxSi9Xs/a7XY6B07UVjWqerWeipU9PKUzuR7hcrnMikwjMf36+jpRjbPZLH1/Op3aeDxO51Ov17M8M2Yt2KtkepETlpkGjYTlMsJ4vVHww8sKJQb/aM0sox34x8k029PTU/qexrnevXtnZpapC0ejkc1ms2zC57b1PKGx8eJagCUVoKojmSKrVCpZVQuv3t50Ok0T8nQ6zaqwezX/MGb4DowIJg1MKDhvnvj4nDnewQmy8/k8jRNTr1dXV5lBB5Vqtq/KwQnCjErluf/TYDBI9+enn35KtGGn00nnMh6P7e7uLhms3377LVFb4/E4nZsadqWm2ZB56kAYfX4ueQHgUbSNRiOLnfIxmRJlmq7X62XVT1j2zveRqTnc95divlzhXRuuNhqNjIbEc420AxyTDTKnkGjcj+PCGCfUC8W96PV62fl4VUECOcJ4vXFoDg2Agq7M+wZ3ay0AACAASURBVLPwwGuVgskdn71//97+9a9/mdl+QsSksVwuU5PJu7u7rHqBmWWrZC8mwlUsIHvnFbdXnooNBeIebDA4RoRtZrNZijWMx2ObTqeZyIO74eq4Abwa5niPypjZs9AK+OyFcd4b9nV5eWk3NzeZvB0T4f39fSYCAGBwsc3l5WUyXizKmM/nSXxxf39vt7e3qaO1elueN4pFB4wHi2u4KK4WftY4FcdBj3k3LPf3jHm73T4whFxklz11jiXxMXVRp+eAbTjOx0KVbrebFmhszLVKCRvMu7u7LP7KBpxjwexJcxftbrebLfi8CjmBHDFCgUAgEDg5hOf1BqFqKV7hsrqPPRKuSddqtVIcpNlspu1Ba4GO+/jxY/K8Li8v075Ho1FSpoHLx+pTpcvHirQCHDNiSb/GUbTdixff22w26Xq4qK7Kt5lWYgqRvQ+MJ1dKYFoLK+FOp5MlafOqX4/jJR/vdjt79+5d8rba7XaS1z88PGSeF9/farWaVvqDwSB5A5VKJW3z5cuXFOO6v7+30WiUvC2me7W/mNbL9HpocSsb7iGGa8Q+mCZut9tZRRjcU20/wx6WxtYAKF2ZHuQEeW5eqkns3jOGfeL+KrXIv5/Sc4nfFddPREwYHjA/o3xNmkzNbV24BQ8nLHPifNCHOcJ4vUGUJnX+keOH4BWS7fV6mXwbxgqTGf7+8OFDoqKq1WpGP4GO4wZ8+J4n6dWSNjzhPDw8pAmVc6S09BVXQ+92u1lOG6CSeB4njfVxvhAmGhVi8ATCAhAITcz2EzrGDFJ9poiYWmPjyLTndrvN4lQQX/R6vcwocEFjpYxxzNFolGjd33//PeVvgTplsQDH/TxBD+ToXh7edrvNSoHBcICC5OaafB9YrIPX6FbMOXFcAYTFElzRAtfE12d22EFay5R5paeUysP9hWHm+4Bt+P6s1+t0PYPBIKWWIG8O54Nx0mNyqSgU7OVYckkoE/ARtGEgEAgETg7heb0heMV4taZcqX0EPjfbr55BUV1dXaVVPgLe8CIuLi6yVico1jqbzTIqRbP/AS2UyjQMVtLj8dhGo1Ha92KxcIUD7HlB0IBr4MoVTMkgYRjHQWsLs2f1odl+Nc8rcwCUDPY9m82Sh8gpBtzPC/tSEYhZOVEa1CJW5JeXl2l/fH9Zgg5aCceZTqfJM767u0ue1+3tbaJ44Y14ibwqjmGPqNfrpfNhoQxXnWCvFN4zjsNFf1erlVvMF6IQVhLC22M68PHxMV0PPHZ4W5PJJH2PxTGcIqFgL0al8uyR1Wq19Pxxrcdms5n1buMxxJih8zLGhylJpQrxnclkcvCb4fQYPreotuHjhzZeb/WhYOPFEl42Xt45cxyDlXJcRf3s7CyToHMZG2+yx0SNz5jG4FwbrZDB1M/j46OremMJO+dydbvdg7b1+Iyvc7PZJGN1f3+fxY+8HDAF8mmY7uECvBj3SqWSJjbEtZgWZQqRSwHB2CCHCGP98PCQDHOn00mGhCueaIms0WiUZO/8Gnl4GI9S9Q5cr1kuTUcuFQzo09NTltOmqQhmlhprYv9KLXtjg0UCnr1Go5G24QombJgRv2OD5d1TXURh/DGmrKz0KET83rj6O8dBOY8O3+n1eulYvV7PLi4u0nPU6XQyyphjY1yAmCX1fH/U4AZ8xMgEAoFA4OTwQ3tebw3eapFzjFiFWKJJzPJqAazug9qLVWu82uSgOedLabsVXtl7lBmvNlGBgmkl9rwA9hZBFcGjGAwGacXO1M96vU50JHpUsaqxVPdQi7jie4vFIqPtOO8G9wCKRC/3iGk69rTgveB7k8kk3QNWEbIaD92OQaFBSYjtX+qpxtdpdphEjvFEfhEXJMZ5QzCBsWGvh2nVkiiB7+FiscgUsdvtNvP64aU+Pj6m1w8PDwfPjidG8XqGMQXP1Jz3u1GhD7MQ0+k0eblPT0/peobDYZasf3V1lVVNwdiw9/zw8JDGE561l8xcog2j2kaOH9p4vaUHgR/SUkmoSqVyYCxUko3P8CNnSTEMIVNEfHxsv1qtEh2HCcSboLX0FKCVwbUqvScn5xgKS7rxN6uyeBtMBuPxOGvTzvvRyYzB14Nj4LxhFLiwMCZ9pn94EmUjz9+ZTqfZhMYJ1Hgf9C6O//DwkCi0h4eHdE9Ytq4KRx4jfqY4cbzX66WJt9PpZAVvmTqdzWaZuk8XA9g3j5Uq/VihaPZMjW02m0RdsqpR45NeySy9No3D6vf4OWCDywaCk6aZ0uRebpvNJnvN6t7Ly8t0PSrjx7jzuWBc+LfAFPpL6SiBoA0DgUAgcIL4oT2vtwbtsmqWJyyaPa/mIRzQYrb4jJNoS0VqtewSl5HCChMiCK9Ls5fTpNDVsQap+XueV4Tr8Upk8Yof+VdeWSBv37x/9pCYDoR3w9fZ7XazZGYVbAB8jfDIuIYhzoc9RaYnQTtihc6CiZJYAdfKwX5WoMLb6vf7SYTQarVst9ul47C6jyk7pp9xHL5W79rVE2W6kss+4ZpwzvBUOB/QA3vmnneFbT1Gg0taoSAzl4fC+GiRXdwvLlA9HA4zGpG9V6YQ+Rng3yvO00vurtVqRz3RHxlhvN4IeNJReTz3g2IVINfY48mDC9b2er00MWHS5XgUT05s/JR29NR6/GNio6HXUqI+tNeSJs7y5MLHBHSiwrEVJaOo26uR10roOJdWq5Um4cFgkCW3eoYd++DKFKzC42RoptKwT7O8eodWVvES1XENGMNer5cUjufn58lAQF2I54XVi6vVyi1w641xqQoELwb4GpjyZum+Z3z4GF6NS4++9qhTVrSyyhOUIddaZKqPFwq4L9zTDfFRPL+cRsHxVr5ObMvjxsf3KtqgZmIYsD3CeL0B4AfmFTrl8jC8WoNn4BkfrV6NiWkwGGT5MdPp1I29HIsLlaS7PLHohKPxBf3MLC+Pg1UwV9nmVTagK+mSh8XbqZfABphjimaWGSUcv9lsZufa6/XSRMRVzyEn5+OwQeKx4qK2HDc5llNX8jR4TLnaBZeAwns4DnLkzPael1flXlf9+ro0oWqVfs4v43Y6nALC48TPvOZz8aJO89m08DCOCY+K88xwDvz780pK8bE5HYTb9/B44TPPM0cumFdAm5/9RqORnsOIfeWImFcgEAgETg7heb0R8OqTZeNeGxSzZ/6dV39MlWDlxitpSNixj8fHR9fzYs8PtEWpPxK/X1qZ8/dK8nimauCBsFSdV+Ycq2KVXK1Wc2NzWsnAo56wP6/iAdc/BL0Er6HVaiU6TgvzaqULT7LNidqsBEVhYr7/JWrOU1Vi3NjT4TY1OE8oClnSzjEW9nj1GXiJumTPGCkaTF3CE+TrWS6XB14le5LcZBXQNI5SWkC/30/96/r9fhob/I48WlbVrRyTZA9Rq2pgDLlyDbfswXVyGgwnfbPnxfHeiHs9I4zXG4BSHVxRvVQpHUaIjRkHplmqy3Qgy33RaNIsN4w86TWbzYOSTl7MSGlDLjB7jO5gYQrHI7rdrluNQakbHBMVNXgC4vNlg1eK36hh5JgKxgmUJnfE5UA/LxRA96jRYeOlNBgLWzRW+BrjpZM9U7FcSBfnBuPF1CfHpVR4wv97snOVfLM8fzAYJNqu3W5nZbkwwXNHAxhSnI+OD4OfPY1tcU4dqrZwyTFQk/hd8G9Jq3Jgv9qpoJR/+OXLl5QnxqkcMFwc28Z48kKuVJotELRhIBAIBE4Q4Xm9AWBF6dGGpVqCkIlzcVJP1KAtKp6enrLKDwjUq/KPa9+pt+N1jOVVMQMene4f27ASjPsmdTqdTM7Nq2SAvUpUgGCPi1fsJYEDzlFfawI4V53QXlQe9cn0m3qex44PeOITz8v11JY8ptza3qtuAY+1lPSs6k78z3RniTZkD6jf72cFgJkdeHx8TN2fv3z5kryW1WqVeZ+abF5qdQLP3SxvvcIeM4tz1ut1Vs2E0xfUO8LYdDqdrAYkJ7iv1+vkxd3f36d+a+iNZ7b/XaKuJM7Ho4+ZMse9fas1Wf9phPH6hvCKg5rlEyLDU155VJIW9sUPudPpZJMT045KW4Jq4R+b2WFTQi/G40mdvUlHCwizMo5bsaMKBM6HDRYmIDVebExV8q3j7k2OjKen5xJSq9XKZrNZmnRY0s9VGlixhsneiwkqVVmKx3nn5I01aDOMKZ8bx/CYVub4zTEVoRpZ7z5zXIpLkcF4MXXJRYdhvEajUXofsUamzZiq9BY+nU4n60jQarUOcgPN9kYb1zOZTGw8HmelsNiQ8D0FWKH5+Pho4/E4fY9TTbjE1ng8TsdE3zTuacb3nn8jUW3DR9CGgUAgEDg5hOf1BqB0gNJvJYqIoXkqWAUy/YZ29tqaHcfwCgCjwytWiJycyZ5X6TXOXXsnmeW5XUxx4Zy56y63z+DKC9j/YDBI7dh5THEOJVUkjxvvj1/z2INy45p9fA1ecvkxqIrP68Xlwavxh7H1aMxms5muk4v5wvN6iYLy6Emv5xw/U5xbBoEGU3WcGM0VKbzEexzHoyfr9Xry8C4uLuz6+jo987VaLROncE1BvD8ajQ6Ut/wb5OcI1zydTpO3eH5+br1eL4lBmCFhkZUWuK5Wq5mXCbDyV7uVB54RxuuN4iWZt9nhxMvyYJadc6NBNRK8b1ZwsdpRG/VxuRxsz9U++DuYHDlplGktbsTIExvvjysWlNR0oBq5t5WXKMrUE/bBhpXHl1V3ACYmb4Ll89HGoaXE4lJZL1B5XlKuLnT4tdKvuG+NRiO715zcrupLT+GoE2fpPvKChGnUSqVyUEme5fnedaLfGtOquvDAWOM6z8/P7eLiIhkzHuvxeJyV28JrLerMqRGaHM4J/oiR3d7eWq/Xy4oOvwQYTy8BuaSIPZaE/yMiaMNAIBAInBzC83ojeI2yTGkkTgI1M5eO41UxKAzOT2GainNosD3OjUsYeRQT0zAcpEYOEVN9ntqQc48mk0mmBkMCMl83xoZXueqJet1oVRXJ23DRYF0Js/hCvSWmRplKK+WQKY3p0UpaCsnzOPA+PoM3pDUizfbPhFcUVmlUHh8Wt3jCEC8ZWXtj4dpQoJbzydhLZvGFsguquPVea+FmLmANag5dvc0s69A8n8+L9Tv52rVnHY55d3eXlZvS8l/ec4hnAOPDXro+HwEfYbzeEDxKgI2K/qg1UZMLjbLxwg8OP140+0MDR+ybqUZVzfEPk4/r9dyazWYZXbTb7dKkxdehva+YiuMK3FBmYYz0us321NN0Oi3SYZ5Rw75eSgJVdSLX3+OJRiti8PUyFYRkcVyrt69jEviSQhLXxnSa1n7U42BC9hYk3nW/5jOADRSeAa6QgXt1dnaWnhdeKOE82WB4hmS5XKbjjEajjPZbrVZZUj4rCr0GqR48KpmBKvSgKqvV6tH94fpLyer8fOFv/j+wRxivNwAVbHjGQQGjwB4Jx5V4Jcqlau7v71ODw8+fP6eVKBuvwWCQxBKtVuvAe8M5aUsVvM8xNy1zpHE7bmIIQBCBc9O0AS+NAMaOhRQqGjE7nGhLE8Ixj8yLCeEzb5WNicrzvNQLOibOeU21DTXO/BrwKo6UDJMHfL8Ui2IDo54WLxT4ODBe9Xo985pYdo59mh16N1iQoVIG9s0FdGezWRZz0wLAeo34TGOeCkjtYSRbrZZ7T3mct9vtwXMcxunrEDGvQCAQCJwcwvN6QyjRhvxaPR1PlcRQOu/h4SHVWru7u0vezXa7TYotr8ivt+JdLpfuSpTjQKC1eH9c449XuHwtWlmgBPXoPG9LK1J4EnjvOJ4XpN/RSg+ed6SeCtN0fM6sYkRs0luNq3KRz5fpSVWt6T681yXoMdVb4+N4VJhZHhtjST0zBajpiOMoVcj314vbrVarg4armhaAbY7Fk/Te4fhe7BFVSuD18+9Sx/Y1DVx532aHif6BPcJ4vVF4+UYqnVZ49MZ2u03Gaz6fZ5WtuZq47psl32dnZ1l8gJtZevko2+02C8bz/jSGwRM300NmVjRePIm+5oet5Y60mgTTg8coQfyvcTJve5VYlyYqnoSXy2XaHjEZPlfP4Ghcj0UspYodHC+FsSgZyWMoGVBvsgfdzLmEpbxCnKf2wdImnIDGTvlzzTn0nh1A43h6HDV4fC4au/xaClAXVUDkeZURtGEgEAgETg7heb0RHFtVHVvBezJi9i60bQrTKNqTCKjVask7Q204rIxRQxCveRsWcnAVDqaFzJ5Xx2dnz91jucguVuwqg9frZMDr8QQKx2TqvAJnZacm/2rRVFbxlWrP6Xl6K2imdbneHnpMlapNeIBKDftgscNut3MTibWOpnqbr/EeVbyhaQW8Pd/HUv86vlat51nyTvhc+Liluo3HEn5VMOV5VJ6XxtuwN87PCl4rvX2MwtRjeekLPyLCeH1DqPTZK6HE/DlPJnjND7b+iPF/yeCV6DiWHqOiO9N+/GP2JiqujgFFJBsCzovCa6Yjsb9STg+jVEqLoU0mS8ZL6SvvfmAC8ib/l/otecbQLC8WizHEIoHH0YtvehOwqvWwPa6HiwnX63U3RonXGufysNs9V+xgdSs+A3QRw2Ndiol6pcawjVK53niokSrdAwU3P/V+S8cMVim2x1VO8H02+nyO3lgHbZgjaMNAIBAInBzC83oDwIrfa4PA3glXInjNPvG/BuqZ5iol1YL2m06nVq/Xs/1xoJ3fZ49MV5LcR4nBhWy1npwnSiglxx6j1Y4F073x0fMxs4N7w4nAx3Lx+Bgl2hDntlwu07VCsMGiBU9AotVCsE+znDbcbDZJTepV3uBtPVpKPVQVabAHXRqLp6cnty8bH2u322XqQO4fp2pbzovk1j2l3Du+B16uoEfDvZR7h/3y74ppWS6OzNcMpa6XK6fe549OD5YQxusbQumqUhylRIWZWUZDeD8EVZkpRePt8+kpb1iplcq5BxErw2DwVP7txTlwnaUSTqXJvmS8gFKy7DElmEdflRLFMZ48cfLEX5LXawyN42yqqsO4HTtvjyLGeLAxxD1ZrVapQHOr1cqSgmu1WhZfLBlZfr8klWdpuxoYvkY2Urzw4cTm+XyeGXRNGObz0+atJePu3WucD987r+oJ0+R8TaCRYbB4ccC/F6Zn8Rt9yXh9bUrDj4SgDQOBQCBwcgjP6xtBhRbVajWj0Jia43wkXpFxqSa8d+w1VpFe3pjWbGMvQGvkcQ1FHH+5XGaBeu48zDQi90piWktXpTxGfN0l2lQ9HqUdvZUs9s3QvCRci67SOSDvXQ9TQri/LwllWO2ouUMlj0MTYtmT47YjTOc1Go3kDdTrdbdWpEI9YfaWcL743/O8mMrE+XBvLYA9+Nlslgl5NOm65B2XFJ/HBCclb+uYyhLHqdfr1mq1kmfb6XTSObM4ptlsZvSmeqnAsWMGnhHG6xuCJwNWsDUajWS8zPIft1ZPKBmsYxJ6r1EeV5s3O6R5PMqLVXj84+f9YiLyCsTyRMWFUkHPvERfKU1XmgCOTUYqlddYnY4hx7rM9vcK31utVhlNV1LH4bjY72smKr5W3Zd+j1WfGFOm37j2JNSkXi+qEmWttO6xhQJT1PzsaZoFtuHuBDh/zzByLEt/O6Uit/qM6th6z4hS0xwzwyKu3W5bv99PDTB7vV66Bk6r0PgbjoX/PXq8RJkHwnh9U6hQgLvR4jUHufE3/i8JGXTfDJ6gNYfGW0mr8eL3uIvwdrtNK+nlcplNmuy5qETcOz4mPc9gMjSnSPGSF+ZJknl/XnwD58OTJacYYFLm0lk8aQEl6X5JHHDMwJUmuKenp+w+4HxqtVrWYdlr38LnyNeN99XjKz2Xeg/YA8dnLEoqxQBxfN4GxqPb7WaepEr1+Xn3ngmcs2ek1GPmdjPdbtfM9g0wLy8v7fLyMv2N3wJ3sPYqmRz7DWMbT3ASiJhXIBAIBE4Q4Xm9AXhqQ17lluizEtXACjheOWIV58nodSXKq2+OnZjlDQa5aSWrxDiWxdy+rsq92n3qpXhycMXXeCql7yo1B6gHxu3teaXPtCHTdOp58bVqBRTAo4V5+2MUk+dFcWWVSqWS9W7juJcq+rxxgDTdi5XpuTE8711f63HYO+aYYL1eT95Wr9dL8aZGo2HL5TKLsXG8z/MWNTWD7xenT/C49Xo9u7i4MDOz6+tru7m5sXfv3qUxRcFrjokeo6/1GdHfLF6H5/WMMF5vAJ40/DUPKT/waqS8fCUtbcT0pBdXA7bbbeLwWeI8n8+zJoIsFNBmizwBAaXANN7niRfXwxO6Fp7VseHxYEPytXEEpovq9bo1m800cVar1YMYDc5ZJ8OSAfeMl5ZCes3zgcnNE/GwkTw7e24u2ul0rN1up15ULJzRhYJK03lMvVghG7KXJl6ukMHH1XQB7KPZbGYCCbxGTiLuiZc/iNd6vmw0OTWEKWJQhcPh0H766SczM/v48aN9+PDBrq+v0zmgZx5Tsrw48uhqL6VEK7gEdfiMoA0DgUAgcHIIz+sb4lig3VMRejQDB3PZO8DKjb0rrFahiprNZmlVW6lU0mpVxRPsHbCSsFarJTqxJMTAavc10mNGKQlWFYCex4XzKVGvWqXB82jUc8N4YgzhedVqNVfd53lNHi2r6k8cE+ICT3hTEufoeWM/ZnuPir1nFjt0u91Ecy0WC1derukKpXEvebZ4Xr0ixtq77ZhAoaQwxDOubW10W1yPdsfmfdfr9eTJ9Xo96/V6aazw27m4uLD379+b2d7zury8tMFgkPaHc+NjlopiAzwGXK2j1H3auw8/EsJ4fSMco640F8uTCit0cuMfOSiiarWaKaE4l6nZbCZDxGpBlOjhHxpXRvAKoqok+WtL3BwzSqWJW6lXpWC43NZrSkUp8D5iLVyomGN9XAhXt/UoK61Gosf0aOFSSoB37pzH51XbAOUGY8ay9WNxKYbSYd5ii59pvTY1ZEp7cm6UR0PyJA4DwUbCi5kxcC4wgN1u187Pz83M7Orqyq6urszM7PLyMhmyXq+XvjMYDA5KqHm/C6VAPTUl/vdKxQVtmCNow0AgEAicHMLzeoM4lotVEigwmDJrNBppla3b1Ov1tJJ8eHiwh4cHM9vXMxyPx2b2TLN53grTiYyXaELP61RvolSpQbflFa6uSr3cMu9ceX+lVS2vhJvNZvp7tVql3mez2Syj5rAvzZljD+SY6ERVo7yNl7eGa2DPic8THvd8Pk/0F6ptsOfliXdUjapjyMcsPZuaGMzH8OpDevvzhAx8zev1Ous5x1QuP0fqxfHv5OrqKlGCP/30k93c3JjZPn+LKTxW2vL4ViqVA9pdX8MT5WekpHR9rejlR0MYr28IjQd4KjE1HKpW4offm+w5NvD09GTtdjsppjh5mAuLsrwX2zFv71X5LqkIj6kA9YeoP/JSrA/QROYSnabHL6F0PvwZxxDN9oYAk9ZisXATbHFuvCDhSdQzXlC8afNCfI+3KSW68iTKk+tkMkmUF2T/XGWeKTfPSHqVXY4ZUw+6UGDaj2OV2iTVK16N72J7rtbClPfT05NLzUFFOBwOzczs3bt39uHDh/Qakvh2u52Os1qtkkJzuVzadDpNC756vZ4Wgkole/FEvOb487EFV2CPGKFAIBAInBzC8/qGUGWcp7LiFbt6Opxfw0IERqnwLI7DtBSrErESV1qQa9JxiR9dVXpeoF53afWtnhd/VtoXjsPnw16pl2uDY+g+dJyYIkLeD/Yxn8+z4rceNQhvhD9j78ITcsAzYO/iGP3E73s5cdVqNZ3ndDpNXhg8SU669trxqLLtGB1W8rz4fmtpL62pyCg9o17ZNDAD7AFrThX2iXsKrwvlnS4uLjJaFee5Xq/TGD4+Pia6eLfbWavVSp5bu91O4zubzVwRj46vR5vr+4EcYbzeADzZu0etqQqRqQ+GxhNYXTidTtOPTukVnqgwmZlZNrnxZL1YLLIEXW8CUyPEk+Br5d8l8I9cDWHJeHnHKcXTPOq11WqliuDeGBybjI5VVzDLk2MR7+LPMAmWJjTs10srgGrULL+HnU4nVUU32xsFjt0co6++ZoL1FipMP3txUByfa36ykeVz40WdUu28Xy8WDMMF49PtdrOC0xiP9Xptd3d3Zmb25cuXlF6w2Wys1WqlJOVer5eOM5/P3c4AfJ34jH8zL6k3A2G83gxKE6fi2AToSY9Xq1X6wS0WCxuNRllOD1eE4MkRk0Sr1bKnp6ds4gPXPx6P0744T4wN4UtxK++1Xj8bvNfEwnSs+PNSeSzvb46JcBX2er2ernW5XKbXJSPteZI6QevxMWnDaK7X66xSRMlweB4S/meDy95itVpNeWudTif7zPNa8KzxQsor4KyeveZgsbfkbWN2GOdS466AwMkzGFzMt91up7ysi4sLGw6HmbeFa2PPaTwe2+fPn81sb7wQ43p6erJOp5M1AUVcWWOf3jjqeLzGww1EzCsQCAQCJ4jwvN4AEA8peVUlOpGl4h7lZJZ7Xg8PD3Z7e5tWjFxLz1v1m+1pJG46udlsEu14d3eXvnd/f++u8s0OaSEPnsydYy+8L15VH/NQS95JqdCpngNThUgp6HQ6dnZ2dtDyRa/TizV6Mn6+b+pZPD09pXPQWok4JisKvWvl97naBvdR63Q6WcFZ9rz42ljOfmzsAWUDlOI+lk6BMfDoYLM8ZsbjATYBf/N5cswMPbjM9knGvV4vo8q5wDJ+L6PRKP2WRqNR+h2ARgYN2Wq1kierz7Gmb/Bvm6+xlDoQeEYYr28IDbpzPhcH9AE2VpgY+IfBkyBPeuDsb29v7dOnT4nq2+126cfMldI5jwmUGQfHuWIHS5Q9qoYnP/3smARe6SLexjuOxpW8cca+eeLQskc80WkJJYwH9y5jKTRPlEqPadyN85W4gza/r6kAGAele3mi9gQpfA5meYfl2WyWiTQ6nU66Vpb+87hjnF5D5fI1l0QJ7TM7NAAAIABJREFUHNdRg8jlyPBdXIPmvpntxSgae+T7zSXUOE+Mfyfr9Tq9nk6n6ffCNPlsNktjg9w/r4CwLk7YWJXyuRjH4sc/OoI2DAQCgcDJITyvbwheUXEljfV6nVaVTCcq9cIrN/Yo2PPa7Z5r700mE3t4eEg0yHa7Td/jBEylWpiG5NUrCxmazWamCtOKHJ4EXaHnz4VXvcRVrRWnvag8YQZfi3pJvBrmmpDdbjdRQmiBwopNrqrBKIkXlJbFcdgDgndW8tZYMFIq9qqr9lLCMnvdTJGyh+dV9fA8AvUevDQA3UafCa1Igs+Z7iwV4EVFDY9a1tQDjNt0Os06Tc/n83R/VV2L15wm4l0fK1U9+hvPg6e8LSFUhznCeL0BKN3j5UsBGlPhbbw4ymazSRMdqkFg4tIq19yPiwvzrlarbIIFuHrB2dlzVXs2siUqj68Fr9lwaB+j0gQAYEL16Mljqi6ltvA9bnbY7XbT5L7dbm0ymSTF5Xw+L7atL12f7psbKWIbbhyJbbz7y/3ElstlFv9Rms4r0gvjxbFTnE+3282eFV2QcMUQHVNvrEuUcek1junFfHV8eXvNNQOYgsR1me2N0tPTUxbH5PJS/Bvh1wB6m/F48DmW0jT4PY05B15GjFIgEAgETg7heb1xlCiCUhFPs1zgsNlsshUlt0Xn1TTTlkyPQG3Ite9wHA5yM2VXyl3ic9RrU1rtWK1HppVY5KJ17Hgl6yXu4jNPscn0GSetrtfrrI4dCzY2m43rxem+2+122jeUbvgO9gVvxhN2aIsXHmsWN5TEG9vtNj0D0+k0o3w7nU6ia7lvmXogTNmy56X3u5SzpJ8x1It7SYSD4/L//D4/O0zxYgwqlUrmVamC1KNeWZSBsfDo7D9C8alQx6O3A2G83hT+zEOpDzzAxmu9Xh/0N/IMAU+OmDQ9Rdxut8t+8MeqGpTUkwyNj3hFTDnmxX2bMLlqiaXSsfT8zPImhP1+PyWxdjqddM3T6dRms1kmpebyPyqBxnhyFQve9/n5eaIkmeKFIeYYDYyKp0rEcbC9jikbGKbPFouFjcfjzDCy6hTjMZ/Ps9JgJdVnCcfiNSWForeAKSkUdbIvJUNje46fYX+l7g1sNEqqWTZ+vEA8ZsiPjYEu5PQ6A0EbBgKBQOAEEZ7XGwBWVLx69GoWekmuXsIt02RKE7K3pZ6NR0Vi5ccCAVbEsQhAy/zwtfAq+TUr9VItQKWrtGNziR70jokVLq6t0+kkj2g4HKbX7XY7E7NonpV3nqwORB09TorlfTMNy4pA9byYKmRlJ96Hh+x18dUCy0wRV6vVTNnJuX+gDbnYrJc8DJS8bB7zY++x8EfbnjA7UHqG9LfE3+XnhY+LZ9KjQfl7JSEFtmXPCx4w18E8ljjP+1flcCmp/kdHGK83Ao+rNzukDfBjBp3hPfBmllFrqobjbTxqTl+bWTYhepOjqq10Eue/PerQu5aXJjpNOC5NWqqA4+1ZEt/v91NxVq51V6/XM+OlCdneooLTFdAyHgZrMBgko8BUny40dEHACwiPxkVskovXssxbe4LhOPP5PO2v1WplylJWRXISr9KQev3ePeDPS4aAFxOoHM9S+ZJ6sRRrLMX9eBuuZnEM/HxpTJXHgSlEptY5Jovx8+LBvEB8enrKVLdBHT4jjNc3hCceMDv0bnhC1ImfH2z+0XqxARVC6PG9HDJ4NN4EpcbLq2qAH1up+v0x4+U1G+TvcQ6cjo3uuzRJcHVxjkX1er00oXOgH7E1bwWvEy+EGMPh0C4uLtLfMA7YH3di5liaTm6e58WvG42GPT09ZUWE8XoymaR9e5JvGLlWq5XGg+N0vV4vba/Xz96nLh50si8ZL89jZZELvoPzPebBa/6V91s4dg56Hd5rvhZ9vlW8wcaLBTl8Drw/vm7PeAX2iJhXIBAIBE4O4Xm9AagiT5NyuU4hrzzZ8ypVwWCJNWIinMDsKZmYTjyWOK0yZG/1/VK/Mc870l5WOCccB+/vdrusTYjXuFH3repC9ry63W7yNM7OzpKnMZvN7P7+3sz29e2Wy2V2rXyv2FMBBXl5eWmDwSAr/ApPjvurccKznivfE/acmDaEx86UIj8HXM8QgJfASctcYBbX0263E4U4m80ydal6WJ4K0PN+PQqQaT4uvou/SxSg3m9vf6pQLClf1avzzpOfT8QAS8yHqn3xvsrgvQK++hsI2vAZYbzeCHTCZ87bK77Lkzi2Z3oREyVyWMz2k858Pk8TZ61WcxscehUKSjRKyXgdC257rz2U6BqlXLzv6zae8QI9w2IFjDVLqR8fH1M18cfHR1ssFhltxjEnTPCDwcAuLi7Sa/RFM9sbLsSPWPzBFBHTZTiGV9qoUqkcTK78HDBFqTQv9sOxNi6NxMa82Wyma0Ms6iUJt447o2SwlCpV2k8FOnpt2N4zOCV5vXeO3vUci1E1m023sLVK8LWb9ktikEAZMWKBQCAQODmE53VCKHkWAFZvjUYjtbXgyheTySStms1yGa/W5QN4pYpjeKtP9QRLCcfHKCKcP1eqwDF5e0/VhVXta6ox8LkrRQtw3zIuZgzVHtNHXDmDk48h0Gg2m/b09JTVmGTxBK4VHiCPE1+P162Yx3a73WZSeb5XXBmFhQ9QT+Jv9QpxnfV6PVMxcmFcvT9eErxKxPU+ebQ0ey34mz2XkhRfn8OXFIrwqEoUpwcWVcDj5jQLeKl4bnDOfHymfNXb9JS7pRqhPyrCeL0R8MTLE7nZYZVthhfnajQa6YfEDz9a2Hs/GLNyFQSeBDX3hiXBpRhGaQLhiY7pQOQ3lfK8vDQATMAvVdhgmk3B48FxIFYBolcUjwdL4lkOj9hRpVLJir1y+SEzK05gbCT5nLlU03q9zu67Vt/w5PXtdjurjMJV2LnKBzd1bLVa6Trr9bpLQeI8S8bLk5fzdvifX7+mwobimOHxDBQWMJ7Ct7QvpuZ7vZ5dX1/bu3fvzMzs6uoq7Wuz2bhxXxzXoyw1DaG0sDymuPwRELRhIBAIBE4O4Xl9Q+hqkz0PXXEqdMXGnhcXleUkSQSSPRWfJizrcTh/iVeSTBt69IZ6XrrvY+IPrvhRog2Z9tTjlJKhS8dRMQnXTYSgAd/l3Cp4WIPBICU2dzqdTNWpyeJevtGxe16qhsKeFzxWT7ABrxvAGHLukfeZ1/KGj6HnpwIJT62K770kUoCnxfReCepFeepHpQzVQy3lTHoeGSdwX15e2i+//GIfP340M7Pr6+v0vKBTNbZXRS0rRfW6zXK25Uf2sjyE8XoDwI+8VNiWf2S8DT43yzl4Ti7d7XYZ3aNtybmVeWmiYcPIUns+Pm+jTSGxD++1pwI0O5wES3iNKrIUw1Djpfv16C+z55QDs70izysphYRhs8OCyCon5/tbUuep0WVaib+jdCTH5riKBgBaiuON3nOGfeD/kqKvBKULtRp+Sc6u9B5/5tGLSA15KWGfaUJU1ffKUrHRZgPHSejX19f2P//zP/bzzz+b2Z42fHh4MDOzz58/p9+f10DTu9/HDG7gGUEbBgKBQODkEJ7XN0JJuGB2mFzKK/ZSy3ezw9Ut3uPVLnsNrG5jCk49DU2g9lbM9XrdVZzpteq5lVaTmqDKScq8vQbDS/Skeg2ACk08Kksps3q9ntScg8HAzs/PzWwfuOdEZO2j5inlWEjRbDYzxSjTlSxU4XFgRZ56zpVKJaP9WLCh+V/4bL1eF6kspVU9j0Y9BfV+SyXQ+DyZVVDxBHte/CxwcWKltr1x599Yo9HIetYheR3f498L7i8Xcb65ubF///vfdnNzY2Z7pSmOw/dUS56p9+nRoyUvLBDG65tCjRf/aLkqhkezqeHSWBDkzrvdLivOysVNGWyUjsW++LVOTjwx6Q/RSw7FcQGeZFh9WZKGK9WoE5p3DA9cKcKjyZiGrVar1m63U2zr/Pw8xT64gC9LzlGNgpWRgNc7zeywnxcb1pLxxWuOYXlJ6GaWJuFGo2G9Xi8dB8aSv4Nz5pidd1zvOEoXe4sg/h4rEtV46bXzazZeGr/CPWU626MD2UhxlRJ+36s4gsWA17BVoedfurbSe2HAnhHG6w0AP35ejfOPkfl8zUXiIrXc5gKc+2azsdvbWzMzG41GNplM0qTKUuhjMR7sH5+x4fRkvDqp6IrZ+5F6q/rSD9UrZloycHjtxeYgx+fJja8Hq+9ut3sw2XMOF/bNHain02mSxmvwnSdofp/HAWPA+VgsINEUAQYXf2XRCAuC4Dm2Wi07OztLEy97+vx6uVweSOhLz8QxL+yYxP4l6KLHixt6snfehs+T73ulUknjpoKU0vXAqKlnzZ2qtUEqn4v+7cW/vNhieGJ7RMwrEAgEAieH8Ly+EXQFpbQSy5V59aytyr1kxvV6bY+Pj2a2XyWjLt9oNLLxeJwqR2hSr0ev8PniM4bXOt3MlxfrcRiapF1Kej5GT7L3eEwBx9QVV+lYLBbJw9rtnov+gh4ysxTvgle23W6TJzsej1NFhdlslo2Vt9LW47ASdLPZpMaXZs/JxGa5dF/HXT1oTmZmLw5eVKfTsVar5fZre3p6ynqNwatEexWlEbENn4uq6EpUsBf/VW+tRMUxBamePsYB/3tMgTINfE/0+KzYxHjsdruDosuj0cjM9h44xtBTnHoK39J1/uieliKM1zdEyXjxpMVxD550NCbCYLqJKzvM5/OD0kRsFHj7EqXz9PSUTcpMO3LBXI1tsJEtvS51RVa6xqMgNW5Y+qGzUVMDwU0ZOX7GNBLiGVzIFhTtw8NDWhhw5XnN4+Lzbjabbqxzt9vZYrFwS0pxhQ5PXOMZfR5fXDf21W630+TLcn1NV1DjxfTkS7J5nNdrJmZ+fUzgw3Ey3lYpZ17U8fPKVDJvw6IVHBfb4JjNZjON4dnZmXW73fTZer1Oxms2m2UiK+4KoQIcNdp8PfjOa9ISfhQEbRgIBAKBk0N4Xm8AGpxfLpeZEAOrQASG8T4H5FmGy0mWLI3nVbVZuUWEt5JVOTY+4xW3tyr2lH7sAShVyOdV8ry88/QSjl9a5aPLLTwKLqKqLUkAnDNW3ZPJJK2yx+NxohDZG1GPgak59n7R2dnMkoCAnwn2ur2akthvaXx4G74Hi8UiE2xwJQ6mknFt0+k0q4dYonh1zF8j1mGoelQpPG87jwL06HjP81JhjdmhkII9MtwrMCLwjNljVmELnxung3h0Kb7zGir8R0QYrzcAPJRMb3A/IKYjtAoHHuZSeSguwoomgvwDwg9by+GUfjBKEQH8g/MqtXv7Kxko3udr3vPO08sxKl0PJp2Hh4c0vlrUlnOfdrtdmpwmk4lNJhMz21N7XEbq2KTsSeBrtVp2P5lmUgqPX5fG6FjFEjZk3LuMuw7wWHOhYjyHpXt67LpLhs07f7z+/+2deVdjx67FxeDZYOgxucP7/l/rvUzd6QYMHjHQvD9Yu/pXQmVIbm6C09pr9WoD9jl16hyXStLWVlSO0WKaKqzNDUq0QfKbLR/G4xxEjV37/X4lwjwej6smnnqfryt8Dnxo228S0oA9IMOGiUQikdg5pOf1QkAvhMl1v6sUfGjN7CvDr9/vF9UHFlZ6MdDpdFo8CO5E/S6dYaYovCdErDB5jtt24/rfh4SeYhtG3hX/RgZddG16LS9ktVqV3bfai5jVXu3BwUFVxyNv1qwOAW7zRnyNl+Z2s9lUrLlW6JGEGB5bu/xITYQhOL+zZ2iN7FaGIOmhyvOKPHB/fR4tb7r1HLW8MJJo/Hz4HliRt+WPy3vMIuVer1fCgyxMHo1GdnJyYmZm3333nf3zn/8sPw+Hw8L25XMUPZ/RXHuSRhSe1fu+ZaTx+gvhF7docWFc3H/xmQ9j/mh/f7+EDU9PT6svFaVvBoNBYcf5LwZzHWSnsVjW07T55dMXzi/CREusV9cfhRc9VT6aS70vajIZ5en0M4t/aUi8UKtCU2Y1g41zQGUHjstfgzdK/j38mxa61iLmF0TmOL3ShFfmjwqOmffjPfWlDLzu1mbLX6tH9HkfcmuFEL0IL6/BGyx/PLOvJQpU4Nfr8XhcGSy9Hg6Hdnp6amZm7969s9evXxfVFZ83bIXE/b2KQOO7LRT9LSLDholEIpHYOaTn9UIQherM4vYhBD0Aha/0v9nDblE7QjHYtCvtdruFaUcZG+5cPZNKtWL+/J5EwDBOywPx1+R3yNF88H2+xo2hMS8g3Donx8Tz3N7eVufxnlfkxbS8K86HP54XiFW9la6F5/ESSByPfu9FnSONPz4rChnS04884qi4t8WmbL2H2OaBtSIN3tuMSCu6N4xitMKo9Kz7/X4hXPA7MxqNihfGECJfy8NliDXqBceQe8TCjUgm/lqSsPEVabxeAPwXzqtYEAyZMWx3c3MTKj1sNpvy5dvff+jppC/pZDIpi6VX6GCYkL2O/JeuldfxLMKIKcfj8cvvQyhemUCIQkrbFoXo836BjM7jC0jNYq3HVk7FG1HPWosaRur+svCbx4uMgo7LY0SbAxpC6fpFhohGlrqA24yKDxv6EO1zNxTR8X1+j4bAh6w9XV6gIWM/Lxqv4XBYvhfUFr27u6tyxPr8YDAon9XfqLSijR/D0mKT6l75guVIuSaNVo00Xi8A+lJyQYwMmK/697F+7faurq6KJNTp6WkRYb28vLT5fF6+gL6eJfJaZPAIfpmiHSLfE1HlI5CSrEVXn+F1b/Pi/O9apJendvTRebyxiGp3/C6f18Yc3OHhYbVr10Kppoj8DFUc/Hzpf9b0eYIAr2ebiHJ0POb6vnz5EuYQn5pDv1Hxxmzb57fdpy9fvlRj9sSU6Dx+LN4Li8bja+r4TDICIWOk1xS/jqS8fG7O359IhNkb5W8dmfNKJBKJxM4hPa8XAu/FPBUi8JqBZl93a+v1uoQtptNp2dHNZjObz+clz6U+UxxDdP5W0zx6a/f391VIxR8rolV7xphvY9GiNUfel1dJeCo86D+v17wH/Hwr39JiUuqaeJ30aCImo8+F8Rh+rNG8KWxIb8mzCvU6ytN5eO++xdojPGuW4VZ6S5EHHI1nW36S7+EzGYUr/fH8eThXNzc3oTAANSUPDg7K963X69l4PK5yYzyfj5D4uTF7rPMZtbzJIuUaabz+Qjy1cJjVSuOinZt9Tc4zjEGSRKQg7utz9DmdL8pZ6bXGQ6p9JAqs87RyXtE16nq8UWx9Vu/zJBGf6I5CYf46Cb/otXI5retpXZ8WMOYro9AbDVGn07H7+/sqf9XKD+oz3W63eh/nh+r5zG9uC716mnbr+lq/95uM1tzz91EekwYnGhvDtduux/+Nx2I5CPN7Zl83hdzssRZMz7vG2e12qwal3IhEhiwCNx2tOq9vHRk2TCQSicTOIT2vvxB+58pQkkIPg8EgFNZdr9fVLswXH2vnp904z0mPIApFkaAhb4a7fnp/rTCO1+SLdulPeSMRS4y7T4YQPWOTO+GWwsc20kALPmTW8gp9KCsKi3LcAj2vvb29Sv1DngHHTc8r0tF7zg4+IjzoM8I28gWvKQrH8T2RKgafQ38OzyTk/W6d03trPJ5AgpTvpGz29T7c399XhAuBoV+RjeRh9Xq98v3r9/tVuxl+L1rw5K1kG8ZI4/VCwC82q/3H43F5+KMvMsOLet9oNCoMQzLW1KaeQrJk5EVSNRoPDRvpyhH29/cffeFb4adoQX9qcRV8GKm1CG7LE7QMaxS+0ngjI+HP6Y/VMlg+jKt7IIq2noPRaFQ+c319Xd0Dz3Bs5S6j62tdvz7P/lOCDHFrDlrHowH3m5VoE6Tz8rqeWsB9qNHfx4iqzxyTzvNUrtFfv38P72PE3vTHY/649YzrdRqxB2TYMJFIJBI7h/S8Xgi858UQoHbfDOep/oR1QL7eRxBhYzab2cXFhZ2dnZnZQzsP7qxZtMlQJdUEuOOkh+jrYQTtKOlpMBlODUSGR6KaJI2TRcz0IKgDqd/p/2hXG/0c/Y1zo/BQKwS4LbnOa+IckRAgj9nsYe4078PhsKqdi5ip3mvxnrnQEhDWz9tIGjp/p9N5pPzgP0MvTHNIz8vfO70vIm/o55ZH5ckxDNlGbEPvpft5pIfF8USem8gw+i5S7zLyJAVGNLyn91uYx98q0ni9ILTi/gznaTFTWCkKb3AxWa/XpWByOp3a2dmZffr0ycxq46Xj69gKQfb7/cqA0rDx3NtyLz5MFhVgc6H1n/G5scjgSNYoWtxa8Itky7DxHsh4RSFWhtk2m82jgtRWqI6LHjcAXCx7vV6VL6ECCpmDPizFn2k4eCyvEM/raTE2CebTotILfcbLVQm+KaM3hLwPPn8r+NKBlvGK4EONPh/XCo9Smm29XhcljeVyWZWj8Hlv5cl4Hm7wMufVRoYNE4lEIrFzSM/rL4Svq2IxpEJ96/U6DJNph0kWHouU5W0dHBxUbe6vrq5KryF6XpT/8dp7o9Go6hLLVvXaFa5Wq6oNOuVtfLHscxhjhPfKInjvKZJnaqFVexTt+L3n5Xf29ACew+67v78vx2J9nN7XYueREeg9WYYKGeLlPRC0y49ChGQU8lkTE1Kg0K8nGPBYXivR1xLqM/S4+T/DbE8VpD/H8/agxxeFeP15+Iyv1+syB4vFopCilstl1V1bUP2mDz+a1fNJzzpDiDXSeL0A6AvLh1cGh23ZWwugWW28VqtV6dPV6XQe6azxi0HjFS3Wit/TMHoqvX6v86zX60qPzTcH9DkWf23+b56WTcPkwzs0Yq3Q0bZz+tyJn49WgbEfF4/Phda/t0U518IWlQXwWeGxveH2ob5II9IzFFsbCuYaI6Ydw4YcB8cf5Z70+eieaMwMYUd9smjAn1IOaanjt/rm+Q0mx+mLvjUGMnrZrNTPje+Xxg2rFxbYdk3fKtJ4vRBwx+lV3UnKaDWtM/u6c2P8XcfW5/m/r5uJSBV+UWGTRp/jiephPFoGxs9FaxH1JAAvwRTlKvxiGxENOD6zdg2aztO6Dy2K9XPmg/V9/X6/Wiy3UbeZN/G5R79A6vpJ1PGeYDQf3vAcHh5WxoN/o0GM5vOpueF9o1rFZDIpEQASfDabTdk4XV9fVws+z3V3d1dtBP33Ipof3/DUy10R+lklKXotI0cKvpfy4kaSuU96xUmTr5E5r0QikUjsHNLzegHw7CqfI9IuLGLa0QtiA0l5Qf1+/1HfIjLn6G1xPD7+H+1kqQfnd7tRrsZsu0fEHbIPtUUhQO6Ku93uoxBPS72jVSDM87QaRoptGYUOOU/MMUW7dOaPxORkX6jBYFB9hl4DWaeeTcgQp5/7iBEYMe2e8ozNtof6ovuj47b0MKPzqxTj+PjYzMxevXpVXrMUZLPZFCHq2WxWqZHwnlAb1JdV+HmJ8rIan8bmW9nob2zeyhA6n0nl78jsZB4zynOl11UjjdcLQrRQMJZOtettop4Me/ALooZ7WizX63W1wLY6AhMMnXilcoa4+CWlkTo4OKhqyBjW4nXyC6xj6jMRYcTX3/CzLVUDf60+VEgjr4Wq2+1av98Pw5C++7InF3AR0t/6/b6Nx2MzMzs6OiqL8/HxsW02m2oToTH437dCc57UoE2Qr/Pyob6nyi9EumltAqLcVqTK0drg+M2W5uTNmzc2mUzM7MG4My8rEtLFxYVdXl6WnK/CiBo34TeN3DwRLSKT7tt4PLbRaFT+Np/Pw+7JhL6X0XPkn5U0WjEybJhIJBKJnUN6Xi8Q23Zk9DQo9NlifzGMJMFeJcBXq1WV9Ob5/G4vojVHLDqd03sw1HqL2t6b1f3ISBG+u7ur2H5sE9LyvDztnHPjd9o8tsbJjsTytswelC663W4Y7rm7uytz671S30VX4x0MBnZ6empmD56FXh8dHdlqtaq8UV13p9Opwso+xBvdH0+u8ey8FoMy8kbkqUVhLsKHAL1XSC+VXjtDtMPhsKiOTCaT4nnx/phZpULjCTY8ZxQ+jrx1H+rWsXUejuX4+NjG43EZD+e61YLIhw3NYi83va420ni9QDyHiSV5Hi6QUQ3M3t5eCbP1+/1K5brT6YSUa37hRNf2+RedM6JYR2PWF1t1Y2YPhoBt72VAO53OowWWISay67xR5c/RAsLFXYsw55RhITL/lIuS8eJcRbk50tzv7u6q2h39b/YQcnrz5o2Z1cZLbEOGLqNwa3RtNCocpy9f8GMWfDhNr/lMbGMOtsoNfIkDj8fQLp8Vbrao9MIxHxwclPujuWYNll7T2PlnxbNbPeNR4zk6OjKzB4N1cnJiZl/Fs3lOhg2jEhTlVFslImnInkaGDROJRCKxc0jP64XA11lFHpHZ1x2nQldRTdXd3V1Vc+ULI1s7+EhMlCFInT8KS3mmn+/4rDGw11Gv16ta1jO06L1Hhp+4e+V7/C41Yo9Fx/V6c2a1t0UWYLfbfaSewfnVLr3b7ZbXuk8iESyXyzKG4XBYdvAnJyclFHVwcFDV1On4+pvu4f39V409jSvyPjnOCK2auiisGIUYIyKRr7vzhI0W81C/Hw6HlbfFcC3ZrZ4hybnvdrtVkTDDk1EoXO/jvGiuh8NhuT8nJyclgiACj2rNlstlVdvF+WBIlGxfj/SynkYarxcCz+JjCIK0YE+1ZSU+jR+pujIWCocw7h7lHbggagFjbolhJb/Y6fcCW9Trfy7qzGuxMJuCpq2CZdLZ7+/vrdPpVGUF+pvv1eTHHC0gPlykEKKOSWZmFOLhQqXXDJPp8170mGExr4jhDYNZfQ95TRqj5oOF73y+9PNT99EvphGzUeP2xb8CNwctcWNe22AwqKTJuNhTKYbn0nMUhUW5CeKmJSoX4fzq+0M26Hg8ru7Vcrm0y8tLMzO7uroqG5Wbm5sqt8rvAan7rZxjoo2csUQikUjsHNLzegHQjp1ECHohUS2VduYkL+hvatFg9iASymS2Wd2tVztBeg1e5+05Ban+90zfRLbjAAAgAElEQVTUdzqdsnsdjUbFi7m//9rag4WdEiaOPA0dX7/zosWRPBTDfH6s/NkTHKLrlNfU8lQiIofCWlF3Xb5m+EtzznvPdimRd6v5oEfBa6M3rxDX4eFhVdTrGYp83nw9WdTehCHjiIGozwyHw/IctKS2FGJm5IHzwfPwOr22ZsT28yzEzWYT1suxnuv4+Lh4XoPBoLzn5ubGZrNZ6ZN3dXVV6YnSG2cI9ODgoPIeo+9Yhg/bSOP1QuCLQCNtQza5E32cX0J9mRkiWiwWhSElQ6IvkL6UZg8LiIzH/v5+FWLyC2VEE2doT+cxs1Jkqi/90dFR+Rvb2ZMhJiNNgxEtlJ72vs2ARoWz3vCSvUl2IA2MD0XyMwQXe+U3SL0XKLxsZo/CqLwP/FtEu9e8s99alOei8PN0Oq3O6w24Lycw+1ooznCnziPjode+l5WufTQaleevxQKUwkYkxksDw++LdD0jJXeft+PnaaiZU5xMJvb69Wsze2CD6jlmM87VamUXFxdlLmezWTUHkSqHFDn0jPnvUhqtp5HG64XAEzYi2i1fc5Eye1zn5b/MZg+GYzQalfN0Op3ilVGJnu1NtHOMdqX+SxapYIiQIDo4z+9JBNzl+9qwyMP0c7bNmHKB55zxeDRE19fXZYEnSUXtQFoUdOYa9XmVKLCRqIzBaDQqXikXROV0WsSQbYl+/Y15P98NW/daCyjHHd0fT2Y5OTkpm6LRaFTmdb1eF6mm5XJZjit5Kz2zo9GoEFVYekCDJ4+dxj4qRfDCvFSO4Wd47/13x3uZurZXr17Zd999Z2YPxkskjbu7u3Kd8/ncLi8vi8oHCRs8L/O92gRGXnsaruchc16JRCKR2Dmk5/WCEHkAanRn9rB7VpjBs8yoKsBcCXNmh4eHNhwOi7fF3NhyuazCHvIavOdFqjrHTO+m1+uV8Mh4PK4o4Ht7exVlPArtyTOJ+jjd3d1Vu2yGVFmQ6sVNBR9K8z/T8xHIhPRKESz49bkojVltPZj3Y8hMv6e4sK6HHgTbeZAlymthIax+p/dp1z8YDMqxVqtVU6vRrO4vpvsxmUzszZs3JZw2HA7LOReLRTkPn9Gbm5sqR9vr9UoIrt/vVyFvCumqKFzXQgaq7slqtSpekPJdXt1En4ko/z402ul0yv158+aNff/992b24IVpDubzefm+LJdLm81m5blu3Td6XmLtMlwbhYUzhNhGGq8XCCa9SQlmh+Ver/eI2ssYfqQwb/YQOtQXkHVii8XCzs/PzewhD8Iv4pcvXypJpqjG6P7+vgorKbwyHo/t6OiofGmXy2UxjLzOL1/qTs6SBjJ7WBx1bfy8D29qrDqe0CKZ8DXnntet37WU/X3+KSIHHB4e2mKxKHOyXq/L+2S4eDydn2FDXzMVXZtChtyscB64iOpzvuklr8EbSb8hUdiPnQsoWUbDoVBnVOfV7XZDgWgv5svFnuHJy8vL0vxRklq+1MPPAXOFAjdPulenp6f26tWr8prPoZ6J+Xxui8Wiyk9G9Pher1ed03dMbvXwSsTIsGEikUgkdg7peb0gcJcV0ebX63XVQ8iHsHgchg1J2z04OCghvH6/X943m82qnafCJjc3N49o3vTw6AVFbK3BYFDGrOuKdOd0bI2LoTUWH5PNRi9MnlKrQHbbDjbShNS5/Hx6kgcZeS0P7/Dw8FHJAwkbDAXrGGoFH3l19CZYnK6wGr2gSKB5b2+vzOFqtaoKwsk2JGPTF22TSMHQq/c0xEiUR8hx895HRcpfvnwp86Cf9SxfXV2VSMHV1VXxvHw7HYbd+BxT0UUhPJJb5HmJ5KTr5ryxKJkiyt7bJVFHuLu7s+vr63I97LjMe5CeVxtpvF4gtqlt6Iu8Xq8fhfAIhr+0wIvC6yncZg+GIKJVaxGOWF4Mp5H2vre3V/We4qK8Wq2qLyzDSmSiSexU59GiMZ/Py0K1XC7LsTy9vqUA4dmRZA7y7z4c6NX7W8bLyxRxbGRjMlzUqlfy+Q4u/AyXejo6w4ua08ViUULBg8GgbIguLi6qkBeNJI/l2Z9+PII3plTC5xyQpRmpnuja2I+LFP+rq6tiPGSANW9eUUVgSFLXymvT80YlDYa8NY9mZmdnZ/b582czewhbslbO54i9kdQ4yQSmMW/VESZqZNgwkUgkEjuH9LxeKJ7DPNRuNgKLbbVbnE6nNp1OS9uN0WhUeRAt5pPZ11CO18RjqITHore4t/e13Qm73JJIQpLH0dFRaQliVodo+HmGWljbZBZ3pda8+r95vUK9j7VcniwReWicJzLtFLKjrh817shKpAoKw3a8Ru+B+zmIVEZ6vV4hODBcrJAXj+HHrdfeg2A4ms9L1MpG9XEMabLwm/PKZ3c2m1VkDDJV5YWRoaj75j0ujpv3T2MZjUbF23r79m1hGJ6enpbQ5+3tbWEYfvr0qQpb+hAv54q6iz4EGinpZM3X85DG64XDhxD1Jb2+vm4WKfP1zc3NozwBGx7qi+mFUj2lmAsAFTYi1Qg2ClTYk+Eesg11/qOjo6o/kpmVxXY2m1UFoTLg3mhwsfWitlzQfSiMxuupvENLtYJ/1/lplLrdbsXAZFiKrEqyDXu9XrlWjU9/e47x4nVvNpsyHjYhXS6XlfHxoU8aG/ZeY5iLzDsvCaVj+f5k4/G43OfRaFQVh/P54sZlsViUZ8dft3/+I0apVznh/aCSxr/+9a+KHq9nez6fF4N1dnZWxiVFD6/cEt03zbu+ExTWJvM2MrKJGhk2TCQSicTOIT2vF4pIAokhRIXsfIsUs8cSTtwhK3Ro9hAeoQcQiZlGYRiGgsjEotchiDBCkgUlriTD8+7du8KCHAwGNp/Pq3Hr8ww1UitPoSeGa+ixkkxC1pwEUs3sEfsr8ryi4mDuuDk3lMhSvZvZw05ftUP0fsfjcSVU7FvdR0w9H7r12o+tTtm+iD3a4fN6GN70ntd8Pi8eBEkZlDBTmFvXyvqp4+Pj8vmDg4PiXalfG0lBJDhELUz0DDB8zHAt51rP2/Hxsb169apImP3jH/+w9+/fl/ujsc1ms621kEJUyK7x8/7S80qG4W9HGq8dQKR/pkUrKrpkvoW5rOvra5vNZkWDbbVaVUKpkdq7GH0sIn1K+JWKFMvl0haLRRXq0+fH43FZMN6+fVsWE7OHBVGLmP88Q1m+PxQXjaholAZXvaKoDiHDTjq6X0w8NZxzEOW1PPV/NBpVahlanDm3MlwMoUWK6tHYIlV5H35uFVZrHDqWD33q79RxZPG8NAz1PhmLwWBQsfhev35d7r0afGo8um9ittLoCj68SSakDKXuA4vndQ9OT09LmPD09NSOj4/L8/f69euy0aAO5NnZWVGOn81mVf6KVHufH4xyycpftwqT04A9jTReLxyRgoJec9fNPBV3vNyhip5L8oM+f3p6WtQe7u7uiuG4vLy06+vr8gVu0bK92jyle0jyYFfiyWRS8lyTyaQYFe1I5QWxhoYLgxe7pZdCQsH19XUZ52g0KovUZDKx8XhcPndxcVHml/VFNH66B1EXYJ9z44LKhpYksMzn83INJycnjxo0khhC4xXdA69I4RFJQPm6OE+P15i9gLBvfhq1P2HOTDkm5VtPT0/L/fY5q8jIRtcqUP1DMlz6udvtVteg5+3t27fFeJ2cnFR1a51Op6rn+uGHH8zM7P/+7/8KPX6xWFT3gd8/Ku5TdJhqNzJcWdv1+5E5r0QikUjsHNLz2gEwbOjFOyNWElth6HP6n+yt8/PzEkJ8+/ZtCZXc3NyUHJNyZNplzufzKu/UChuSCSYqstnDzlihGxYi02tarVZFL87MqoZ9FLIdDocVW5LhPF8oql0x27O8evXKhsNhFeYSq7HX65U54PyK/h3tjnl/GPqRR8Q8DEO5UciNnpuH9zr4e38/onxcdDyOjUoT8pKpNCHPMVKU4LG8eDTzV+v1uipYplILqfFU/6CHRg/Th2gp5EyVD9Lh6fWfnJzYwcFBuScMU3/+/Nn+93//18zMfvjhh5LzIgtUY2E+TXN1cHAQelfypCNR5wwbPg9pvHYALeO1TdGcCwgVCtbrdTFYnz59sg8fPpiZ2fv376s6K4VUJHpKIoNe+/qaqKHh4eFhRUqgwVHi36wmYihkF4UKpdBuVocNFVJiWCkSRz05OSlEgVevXtlgMCiL4HK5rEJ7nH/OLRfRVokCpa8ULqJaegQaDhm7SIzXyxwx5Kff+fO0xHxFJY9UOfr9ftnQHB8fl/smwWAutlE4zwtMU6rs4OCg3HN2ClgsFuX5nM1mVcjY57mic+p6OI/M2zEHJ8MskWsZ0IuLi2KkPnz4YD/99JOZmX38+LFs/Ly0VbfbrcLhek01FeaSfT4v6fG/HRk2TCQSicTOIT2vFw6GEOjdKOzAVh3cjQu+/xZDgmdnZ/bzzz+b2YPnpXBev98v4ZV3795V6gHcLc7n86q4tEUo8O3PORYmxn1ojkn4aPes/zkusv30eSb0j46OynUOh8OqJUnLI/KeFwtfCf6epBXRounVscUMmWm+3CFSu6DX0VKS0BgEeie8PxTh1fs8xd+sZkjqeeBnGa6lt+W9I7JQybiUd7JcLovnpYL2qISDY+dYyDDV/xrbYDB4FLnQ6+vr63Lejx8/2i+//GJmD57Xp0+fzOwhCqHn1St0sOiZ5KNOp1PGtL+/X3njLBbPUOFvRxqvHUBEd9aXL+qd5OtfWJ9DiZrLy8sSNvzxxx9LDuDdu3dloT09PbX7+/tKYFWLzufPn+3i4uLR+Rne0eLcUu9g7RLpzeoZpXGzRxUXe4aeKLLLUKOacJrVBkusTNKVI3V1jSH6n/BGjQKzq9WqMtwaDxtBbqPk83o6nU5znC0wLMXF3ocYWQvFxqXsAabPt0KFVJHgfLHujAxQGnrW9M1msyq35ssXoo2CXut6OL/j8ThsUPrly5dSRmL28Fx//PixvKaShmcY6n8vb6Zwa7fbrQR7lcfVuTinGTb8bciwYSKRSCR2Dul57RAYWtBO7anW4T5hrX5HZg/JcRVd/vzzz4WkoYJSsweCw3A4LGHE8XhceQ1e0cFDO27ueFlHRK9Q6Ha71S653+9X7MWWVhwT9fQW1U5e1+brwaL+Yt7rYgGqD5PxfZEgq8YnQgDDg/1+/1G4lOfkvaP3ywJZL6LM8fA6I8/LE10YMqbuovdyNa8aT0TW4fxonCQ60DNljzayDTebTeiR+PChV6FhCFieNuvzqF7iWbgXFxelWJ3sWnpdnF+RiPiM6ZwsmL6+vq6Yrckw/M+QxmuH8NQDHuUAmF/p9XoV622z2ZQv7IcPH0LB3slkYr1ez969e2dmD+oDKvKlOoXZ1/DRcrms2IZUY2D4zIcAuej1er2yiGrcZg+hGy1ut7e3lUAtjczt7W1VqMpQIeeLTDcJrOpvDH3S4B4cHFSLMkFWpHJHPhfJxfrm5qZanBle5TGY6+McUsHBM05bIG3f97LydHL2VKOILK+LuRyzuokn4Q263kd6PMV3veySP1YE/34v2RXlXufzuX3+/Nl+/fVXM3vIBUfST3xGmRsUPZ8KJEKLUajNpg/fJp6PDBsmEolEYueQnteOIUrw6veRrA5rcMSKYtEnmYc//vijmdXsPnlASkafnJyU191ut/JOtKudTqdVbYtZXdRJSSJ6R/RMKGJ6e3tbeV7ambOr8s3NTeVRkFjCMB+9NXmy2mVTDNgXOdOjYmdo38+L7/MeJhmC9LboRTA02PK82I7ekyVaIru6RxoPC5Gp+efZmGQYsnszvUTOry9Q916Y7vfNzU25D/P5vBAYKNwsvUBKkLU8Xl+kT69I4Tzqdx4cHBSP++zszH755ZfieanjuM4TsVB9YTQJLZ7YoeuhKIBColFRe+J5SOO1A+BCxy8vhXkZ55ciuVnNNtSX2iuKmz3QkkUPZkhFi7iONx6Pq7ySxkOW2tnZWTEwUpDQgkZKvKeMC2o0qAWEJQGr1arq7aUFSHPRCvWRpu71IbWg8JyesRkdS+/jAu2LjPWa5+XCTY1ALpRiFzLnpfN64VmGSr1h5FyTucjSgclkUkLB4/G43EeqTlCHT9epY+zv71cbIqrAC+v12nq9XtX3jWobbGzJZ4qhPq8aE4XjlHdknziFQUejUaX5qZD5Tz/9ZD///HPRLRTLUccmoq4BMqpU2Y9CxFdXVyWXphKADBf+fmTYMJFIJBI7h/S8dgg+NKhQWYRI21AJc+0+GdZZr9dl50kZG3lOOsa///3vqieTOs7e3t6W456enlYJ+Ol0WuR22BXZ149pJ6vuz9Q2JDGDOnjUBdzWl4phLUEJeI61xSyLOgpH88wQF+ug6Hlx3un9qlZNY+a52CmA3pYnQfj6M84HxyMCi+SyFCokE5Mq6GxZr/HoOdjf36/uAz0qPnvr9bo6Pp9lzreuUzV59AR1PV4XUJDXpetj3y7JQJk9hLbFtP3pp5/sw4cPxRNjCyA/p3wOfL0iC5hZdE3pK0YkfLeCxG9DGq8dA4uUb25utoqt6v0sRPW9qLiAyFiQWaYvH0Nj3333XRkDWYn68u7t7VXiuTqO2UPoRF/mu7u7YrCodKECbC6cOjZblXDhlzFvqTFEYT8ZRYUNF4tF2ByQQroKxXERjvpn+VAW25uwWPfm5qYymFw0SZWnwoaOofNEDDv9z+dDY+71elUO8+joqBybBb8cG0OACj/rnu3t7ZUNABl5DPfqfWQoCgyXirln9lUM2NPLzWqFDM6NhJ+pW0jjp2f86uqqFCJ/+PDBLi4uKhYr7x3nj6FgljVw46IGrGYPmzUyF6kL6vPWid+GNF47BF/bwjzXUztws69N//il08JAQ0Digu9YK+q72cNCoc90u91SG+ZlmpbLZeWtaEHcbDaVFBGvzXf7pVHhLp07cU8QICmBu3S9Vk0Rc15R/RQp+Fo0o/n1ixHJI60+Wxyz9xwpHeWVSaKyCF1zdB5P7ZbxkrI/lS9I449UW5TPY76S/asir9/Xonm6vjYUw+Gw6nDMe9fy0CiKK0/Sb4bMHjY+8vo/ffpUCBoyXLz3nDcaLBJoSLvv9/uV3JVAA87c77auEInnIXNeiUQikdg5pOe1o9COO+qkTPYXQ4vKMVHgleEv5i0U9lCxbhTee/36dSWOq90v82qHh4c2nU6r3TiZaQqpXF5eVuEuCv3SA6BHxUJiqXgwRBrpHLK/0mazsel0WtGXo7AjFUJ8npFhMq92wfAsPRLu5v3nGa7ynhfvW0QZ12f4Pv5N92c8HhcvWS1h6HnxOdB5vAfC8zAMOR6Pq1wl75sPb/LzbL0ipZfxeGx7e3uV+gbniqoganPz/fff27t378pzuV6vi/4m2X5nZ2fltcLFpOhH0YnBYFAV6LNPGDUUGZ5kyNnrj2bY8D9DGq8dgw8dcrGMwhbMHXlJIxoyLshcdDabjc1ms5IfYG3XcrksCw2VtNnyXuSASAaK6haXl5dlXKLzR0oNPjzKvEeLDu57iGkxnM1mdnFxUUJJrM/xdTc0pP48XgJJ0Lz7RpmsG2MexRsb39iRYbpIbd73APP1Y1FjSdHhGc7iM0VquM/3UB5JxsfXvekz2hhwgacAsOjsb968KUovg8GgOtZms6nmiGMT4eT169f23Xfflc3WxcVFMV7L5bKQMmazWdmgSVmF+TneH83VmzdvSiNT9jeTTBrzojpnS7Q4Ddd/jgwbJhKJRGLnkJ7XDoM7Oe6YqQBBD0KhLHoALfYUi3XX63UJsVC5Qscwe9g9a4fa6/XK7+/u7irPh58nm22xWFQqDAx9anwam8CQDIuyNR55A+PxuPx9s9kUVpkEWPWzOgT7edPP+jxFaul5EWQUqkUHvVvu7CMvTGGxyPPyVHlf2BwxIekdiaSh89DrIEHHU/9ZlOu9OrJL6VGp/EIsU80JQ8uDwaA8O2xZ0+v1HnkrOi9b6PBeq+Ca3wuF8Bgi9sxSeowMFY5GI3v79q2ZPZSJiGl7fHxczTND7VdXV1W7lug7Ks8rva/fjzReOwqf87i9vQ1rjGisPAuNCgq+bkfQgqMFgIodzFW8evWqfJkVwtH7X79+XXISk8mkhOmYy1qv1xUrjHU0zG0xfMUQnUJSHIPGRibjer0uoSMZroge3zJeOgaFh1lD5sO6+r2nwXMDQRag5tZLIzFvR8ao/z03Drz3lEmiQoiX4mJtF69FTFWzr2FL5m8oL8XeaXp9fn5ul5eXZYEnU5ZG4Pb2tlJNYV6XcmJeTJgh6/v7+0r2TM0kuVFZr9ePmH/C4eFhVQf3/v17MzP7xz/+UQSq2Q3g+vraFotFVc9FSrzPc/m5Tfw+ZNgwkUgkEjuH9Lx2GGRw+bqoqNbHf4atLCgkq3CNjstWIYvFoqhlcDc/GAyquhd5PUdHR/b27dsSbjk/P6+YjNyJcyfsQ5r0TnQeEgoU/mK4R2OgkO1isSiho/l8Xnl8fjcchV71mvVlUaE4CQ26N5xrsvg072yroRBZVLsXqXfwNYkMDM3Rs/bt6OVZr9frSkSZuoIMzfrQIQugKYLsvU39jWHim5ubcn6G3zzxhKHTXq9XvKPJZFI8v/39fZvNZqVD+C+//FKFLlkw7Dt/6xooVHxyclI6ejPcKsUQHff8/LwodrD7MpVJWj33Er8Pabx2HF6o16zdjl4LIsNMWgxub2/L4tTpdKo82e3tbaVwoS8mQ3tkrN3e3tq//vUvM3tYqCeTSTFel5eXVb5IrCx+ySVyGuUgWGBLOroKo3U9DBt2u91wcdYCFhmvlsCtjD+LbSNDwnCi8l8KT3Y6nWpB42e8gnrUbFRzonMKUZG0DBYZn1TRkNwW+63ReLFQm8LAnGsy7bxiiMbZ6/VsOBxWzxGFl/WZ5XL5qDxAG6Tj4+OqqF0GZjQalY3ObDaz+XxeOiT88MMPleAu7z3vO8sSmIOjkPBqtaqed4W/z8/Pyz8ze1R+wU1ZFiX/cciwYSKRSCR2Dul57ThaxaoRSYMFvmZWhdl8iweGgdgO4+bmpiS9zb7WP1GAlAKu7969s/39/RJ6+f7778tn2Lri8vKyeEdqF0GPRO87Pj4uO3GyEaWPR8+LBdVsR9KS6OF8+XnzRAzvzZo91h9sHdOz+9gCpOV5+RCcP7be49mHZCgynEfNQpI0GE6jN29mj6SRoq7It7e35fnwrUX4jJGlSa+UZBR5a/yZxdD0jhRqXC6X9uuvv9pPP/1kZg+6hfKI5vN55RV6z54sSY2T5I8vX76USMFmsynelTwteWKLxaLy9Dmf6XH9cUjj9TdBRIk3e1zUSzBP5lW6fd8i5pmogUi2IBcGMsgmk0kxOGJrmT2EABXaOzs7KwvD5eVlFbryVGgtMl6YmDR8qR6Y1RT4iK4czZUX0vVhQ/+zXreKl82sYkl6dXs/ft4D/RwV/3LMPu/H93kRZs+Ai7QSfb8pHUtNMjW/Xp+RxsurnDD0qM0O54jqFoeHhzYej0vR8unpaSlmHgwGZTwUwv38+bP98ssvpaiegrs00gzhKbyqzU6/3y/Hvrm5qbQv9ZnValWOO5/PbbFYlGeWKiX+e5XG649DGq+/ESKlB3ow8sgYt6dyhLwBejCShuIXkF1mSWtmfoRCrWZWUeq1gJ2cnJQams+fPxeh1E+fPtnV1VUZ23A4LJ7b0dFROSbp1hqnrm0wGJRFnLtfT2dv1b1tM/g+F9VakLx3FtGkSYQgqcKsLgvgffP1X4JKCuhRRGokPn/mVTp4PG5OmFciWUfH4OfMauOnDZC8JYrU8vNUtDg9PbX3798XqvrJyUmZn/v7r217ZrNZocN/+PDBPn36VDZCNCo+v0l5qsFgUK6HeS7/GXY60LOvTgetWrk0WP8dZM4rkUgkEjuH9Lz+RmgVyPqcC/+P+kox5KUdP7UBtUumR0Plis+fPz8Kwfz73/82s6/9o8weQogK95yfn1eFzGdnZ2Vnu7+/X3bFDK350B6Zf8yV+DCZ4PUDeWzfWoQeCfUiyVpjqM/30iJ8WJZ5HDHoOp1O8XDMano9c5JU1NCYGVKkKLNvS8JjRUxV32JGHsx8Prder1c8aJYv8Lr9/LGcgvPe7/crpRSFCb/77jv7/vvvy3PR7/eLd0ORXXrtnz9/tul0WuVfIy+I0QUVUzMfF3mPbM3DRqgqRN4WmtYcJv44pPH6G8Lnvzwi48VGeWwSqS85Fbz5efZ+0sJCIV/mcPS/QoVHR0dloWJeTDkVJse5oEYismaPxWOplK7PeOV2LqKsdfNhOhoIlgWQWu67L/M8nvRBCjkNvV7LYGtOOO+sB/OhRf5PA+zDVzSsvj9ZFBJliHm9Xtt8Pi9j8IaMAsI0FgyLspRhPp+X56Pf7xex5/fv39ubN2+q3KXKND59+mS//PJLea0aq9lsVpVdbOuxpk3DaDSq5pH3yqvA+DILzQ3nJ+u5/hxk2DCRSCQSO4f0vP6m8L2TCO7QyapSCI+eRafTqTwxaiCa1SoU9HQU0jGzqsh5uVyW83z//fdV7yZ9XooPHE+LjMIdNv+nXh9FWKNiX09oMatp6/v7+9X169z6TKursfd6o3YevtjX3xt5YuPxuNJtlEc2m82qECLH6K/Bn5tgkTE9W36G47++vi5hYnqPpMNT2UTPje73wcFBFYLTfHY6ncIoFEFD7zs/Py8U+J9++ql49ywKVijbPw86J8kxCtEOBoMqVOjbwjBEzEJ8elr8ORmGfw7SeP3NQSq3wAWSCxnrbrggMmTFeqFerxfWmUlSyuxhwbm7uysL0GKxKIZtOp2WXNjbt2+LIZ1MJnZ6elqOQQHhg4ODMHQjpp3GQyNJZYXb29tmDsL/TANDdt/h4WFFAefx2Eq+VRvGY+/t7ZXFcT6fl7m5vr629Xpd5no4HBajRMNxdXVVFmQqePhxa+78mLVRUciYIdb7+/tK2USbFrI4NW7VOFFCaf/1j6EAABLXSURBVDgcVl0HGCYeDodlDGLraZ7YkYDKFT///LP9/PPPZmb28ePHMldR/VYrVEjRYIUNdT9p8PS8Mc8VhQp1ToYXvcBz4r+DDBsmEolEYueQntffHBEDMfK86LVQuFW9wfg+1sFwZy5w53lzc2OXl5cVwUG79Ol0WhLw//M//1OFlE5OTsoxGFK8v78vn/FJcl7jZrOpyCRRO5JWL65t8D2zDg8PQxUMajNqXCRSyBu4vb0t8/Hhw4eizKCwJ1uvULRXntJ0Oq0UR8jM7PV6VX+wFsvUExF0TpIajo6OKjIJPVhqJd7f31cCwJqP0WhUidySDbparSqxZPbcmk6nhYzx66+/lnqui4uLaq68PiXDpSST6Bp8d2+Gym9ubiomYVRw7D2vqPCb40n88Ujj9Q3AGzAWE7eMF1lqzAV5JXH22dLfGF5RSIUqB1R41wI0n89LCPHNmze2v79vk8nEzB4WGjL5uOgwB0VjpnPp/Vq0vIGRgr2ujaHCSDrLK450u92KVu17jHGuyM4jLVuLo5pjmj2EPb98+VIM0Xg8riSy9Bkp42ts9/f3VS6HOU0yP8mmY8mDxqfPa0NxenpayW3R4PHaut1uOT8VR6TUrmvgZof5yfPz80J7n06n1ZxcXl5WoULmMfmMM9fHcCeNV7fbfSScLOPFMKbvdtAyXi16fOK/hwwbJhKJRGLnkJ7XNwRPrvA7SRa08jMMiXAHT8+HNT2dTqeqjeHOmjtZSuzQC/vnP/9pk8mkKnylUDC9IzHTlDAnw5DeUbT7Xq1WjxL7LW/L14Kx2FZg8fFyuawEig8PD4sXdXR0VGqcKGNFxud0OrUvX76U61NrGbO6BQjPOZ1O7fb2turBRa8hYlUqJOwJOmYPbD+1sjk9Pa30LUmI2dvbK9czHo/LOD3RpdvtludisViUsZ2dnRUW4Y8//lhYhJeXlzabzcpz4fuOkVhCQWPONWvLfB0fCUoMD/LYnrnoSRqaj2x38ucjjdc3BrIPFes3syp85gt0zWqD53XxzOqCWOZUlFdiMTQVzdlHSovh5eWlvXr1qiyIw+GwGJzXr1+XBf34+PgRxZuUfOWSJJxq9rXfk5mVRpRR8TANWUQtZ5hM76OR9E0dyXQ7PT0tAsVv374teSCNT+On8ZtMJuU8k8mkzAGbbl5cXNhqtSpzwjlgiJeF2TJ+ZN7p2GwienR0VCmW0Hjd399XeoS6nm63W+X2VqtV1aSRiiwyWB8/fizF6cvlshK55Zwyp0jjq82JxtPr9aoNVqQ4IsNFYd0oBBiFCvX7DBX++Ujj9Q3D7ySp1MCdud6r9zGXRBUJqlD41hc+uR29ptf06dOnsiiPRqOym99sNmXhJwFAdGfmgpT4l+qCfk9aNhc0zgeNNBc2nx+ip0IFdH7m/v6+Ij+8evUqNF7r9bqqj7u+vi5Gl54Kc3j9fr+SxJpOp8Uo0LNkY0oK6p6cnFQSSv1+v1zD69evy2vV+5l9zZORpCGv7PT0tFwnn4/NZlMpr0jGyewhz8WOAjKKyp2y6zOJO7pubhpGo5GNRqMyP8x/6R6b1W1Y1ut1pcrRalDqCUK+1Ukarz8XmfNKJBKJxM4hPa8/Ab6x4V8Nv5s0e+xtsUEisdlsqpwT2YosgvV6eww7ygtimI877OVyaefn58VDoOfF3Nj79++LaOvR0VElEHtwcFBej0ajspsn7V79pRRW0pjMHnbjOs/V1VXxDOQtcg6p2kCPk3qKbAdyfHxcroe5Pe74dX55A4PBoFDG2RqE7WI0v2zsyJyTvKi3b98Wr1Z0dt5vjZOF0bw/Nzc3NhgMqtAa24tQKUVe4NnZmX38+LHoEdLzoprKarV6lEuid05PkvPOMQ+Hw0etXcweNwH1dPhWnsvnxra9J/HnIY3Xn4iX9oAz/0WKN40XFQ/MauPFpLevbSGhodvtVlT1iDDCxeP6+rpqXNjv90vuhkn76XRaCfuye3K/36/yIFRZ0DklKKsFmlJAFItdrVaVaoXv+8VOvyRi0HAMBoOKpq1r63Q65bovLy/t8+fPZva1OaeOTaLM3d1dyR1NJpPq3vX7/cpIUr1etHcqtUslJeqY7I265kavtfjz3l1cXJQNCY2+lDKi8CAJElSqUBiX18f8YqSWoTBqpATPfKvPWXlJp6hmK8pzmb287/W3ggwbJhKJRGLnkJ7Xn4CXvDOj50SqLz0vhkW63W6VqKfnxJ05+zPx/8FgULEVmZxnSGZvb6+EFzudTkiXPj8/ryjaStabPYQRVSzLNh2k92v3HoX6yCLU3zSW9XpdroHhSVLoGXLTefQ3zavZg4cnL+rHH38s2n2//vprRd4g+eL6+rro/b1//754dLoWeaPdbrfShxSL8M2bN8ULk/dCL8p7JGY100+hW4UE5/N5uY+LxaJ4ybPZrFzbbDarGIotb4skHq8IQ6KKF9bVPdzb23vEOo20MD3oSXliRuRtZajwr0car4SZPRbw9cZLYP7O7Gu4kf2zvHRQp9Mpn6MiBRUtuMiIBk1KPUM/MmpXV1dVmJA1XGzsSKp9r9erVCuOjo4qOSVen4zN8fFxJTDrF0E2VdRnqBav/mTCer2uJJAoPKuwoViDDH/ReOnz0+m05M9OT09tPB6HOTiOk3JM19fXjxpNUqRX94A5QDE5WYogo0QDxVyWWJqR8norHKcxR7mt0WhU1fHpvonGT5Ym1TIiFRmdt2VMI4OVhuuvR4YNE4lEIrFzSM8rUUBv6Tk7zPv7+6oIlYl1zzZkDZiYcp1Op/q9vDCpclDVI6oHW6/XlV4gw3b0wqglSK07eV700PQ3Fl2zpsh7M9Tvo+AuQ6/39/cV4eHi4qJ4W1KR0O8ZRvUt7FkkLO/o8vKy6n91cnJSrofCvByPV0ZhCxt6Uazlur6+rtRQWPjt38fXZA7Si/dagCQ/8JnxnjI7S5NQQpYmPa/lclmxPiOVEc0pn7eom3TWcr0spPFKPIIX8m21tycTkYWgkZwUlThIYyazTYuRQk8MFZLxxbHpM+v1uhKI5fFoGL2IrKjVZlYVt9Lg+WPpOLpu/Y59x7waw2KxKPkfsu4Y1mIuTQsrNwQyKizGvry8fMS6ixiXfu7IGCXLUou/7h0LhFlG4CWUouLdKEfUyrFS0YVSYMPhsBhjhgp5XZxrCT9HrMJW+Fusxm3jTrw8ZNgwkUgkEjuH9LwSIVrelw+HsfcT9fI8e8x3IjarxXzpESnkF4Wl6D34GpyDg4PyPp5HYxK8F8ZQo8KG3vNiqJPeQUvMl2Et1XJRDknXRq9yvV5XoT0SWlh8zDDf4eFh8eIkPBsJCvOe0tPx94vhTV/v5CW+Iu/EawEyHOg1JCNvnHJbaqMiz7Lb7Vbj5nioS8ixEa1nV55XEjN2C2m8ElvhF53WAmBWi/RSiFfv1f9aXFnsy1yYch1Uf4/a1PuCZ6/VSBHWKFwlVRCGEWlwaJQYNqRR8AsvGYZ6vb+/b5vNpqKWyxBpHBqbFmEupLw+swcDw9wNwVwdX3t4o9aig0fGJ1rYo9f+2fFjYxE574HvBsAyB85BxECV8YrG43NurZBm5rZ2A2m8Es+Cz8WYxQuaQLKDl9iRQeMC7/NS9G5IxPAq496QcRGmNFVrQfbnocRVlIeRsYrU9L0Svc83URaLJQZ8n1dQpxcUgRuIp8g1rQ7a/GxrEefn9bkW+YHq9Z7MQoUMGqxoQ6PnQGNgDo733tcYehmniPYeETHSYO0WMueVSCQSiZ1Del6J3wS/09+mymH2WFyVuSjP/GPIjiCjjwXPCseZffVmqM4QNRHka3kTzJt5j0SvvTcR9fjy3povgvWhQD8H7IMmD5M07wg+d9MK8RLe82qFFqPP8dr4M6+75bEyrMrr5vs8C5A5Tt8LjkXF+r3ewxxpxCLcFjVI7AbSeCV+MzyZw6xuDujDd7e3t5XBinJEvV6vIkWQzNESQfWhORpG5nF8nZhXuo/IBv5cRGuxj0JnLbTqr7wIbGTwWqFboUWSaI2zZcxooCOCBfN+URiVx1C/N37GGyq9j+UB/BsNkTdQpPR7qbGosaTmJ7G7yLBhIpFIJHYO6Xklfje818Dfey+MxAx6XpHWnae56zhmj5UZdH6GFf1nfOjIqydEmo4Ry9JfezQf28BwWtS1mhAT0hMq+Hc/Tl0LPa8o3MiQpsJ8EW2d72O/NoUASU5pdStugZ4xW5j4cK//TKsLN0OIJHakQsbfF2m8En8InsqFRYbJi/4KCi9F4atWTZHeF4WluIBFr1syRTxPdL2/ZW5opLaFzzhPHKtHZPCi64nYgpHx4oaixbhssUEJGhX9zHlgSDDaNESh0sgw8l5547UtVJj4+yDDholEIpHYOaTnlfjD0CpebTHiSAJgXZbCQ1GYzR9f8EW7nun2HPiQVXQ9EsilVxAVDEfhrxYjL9IxbLEL/fXytTybiHHpQ3ueoNFiHzK8ydeHh4dNUkrkvXoShmdjRt6091g572QYsvZPrNNkEv79kcYr8V+BL2p+Ku/AhVWLFhf4KLfmP+cX6Og9DNP5Y3kaveAXWb+4+7GbPW6qSGPUUr4gwzKi7BOt3zMs63uOPUd5g9fgrzPKhen6WDBM5QvOgZ/TVujUh2uppk8ZK56HzMNWODrx90KGDROJRCKxc0jPK/FfhZeH2iY/RIkg7y1FyfsI2oF7wgfJBr7mLPJCvIdF+FBWFNL0vaKiQmcPH1rb5mXSe2yxIlte6bY5bHktJFuIEMGf6XlFckx+XuhNS6arNRaGX6MWLZTbSoLGt4M0Xon/OnzOKFKo52Ioo0KDw78JXmHc5zoiLT8vuEt2Hce6TXmC7//y5Uv1voi5+FTYMDJKUXhVx47CnfqfRsaH6SLj1TKkPJ8/j8J3EW29VVjtjZff0ERjU/6uRYmPxITTcH07SOOV+FPQ8rai+i2v4ODzOL5Ls9njhoJekaLleXkvj2jlxnz+iIhkqDzl3RuS6HpkhFrEAy98rHPSKHgF/Wj8GsNzDBjn1s911PDxKe+Vua2WJ+pFdlsGK43Wt4fMeSUSiURi55CeV+JPR0SL5u5dIUOy0SjoSmUH0sxbLd91DJ2b5/QqEC0Nwcj78r9vFTZHeSRPO/fXI4/KF/nqM/LcfPjNz2l0PQyJPleY14d4t4kdPxet8/pnotVrLL2tbxtpvBJ/Gbgg+jDS/v5+WbgPDg7KAtbpdCoj52vDWkK2bExJGr8Pc0WhqOcK7m4L7fm/69p4nZGSCMfTInz4kGxkvHwIb5uqfEQGiY7LkG8rz+Xn5CmDE4WVW8otiW8bGTZMJBKJxM4hPa/Ei0DkhZGZ5oV+zWr6t/c6PNuwpf7xVOgqel/LQ9O59H+L8OHZl9Frf92tY3MsTyHyJD1ZxY87ItdEHmVLH9Kfu+Uxtej+6W0lWkjjlXhx0IIVLaLeeG0L47VqivRaubUoBMfXUWgtyttxnJFRiD7vz+N/Fy3YrVDnc7HNsEbvjcbRYopuU3HfZnyeY9QSCSLDholEIpHYOaTnlXixiEKAPrz4HO2//f39ylsjEaRVZ8WfPWHjOV4Ca5cY2nzO9UY/+9dPhen0c/Q3hlspiKzriwqG6fGqcPipbsW/x9NKJJ6LvfsdfYqeQ+9N/P2wjfm37edIKso3YvQhxEihw+yx8XhqnNvCm9GxhRZb0BdnbzNekQH0/bz8tfq/+WtWmDBS1XhumDCRMPvPnpEMGyYSiURi55CeV+JvgecQN/TaexlRzdO2z7SEhp9zztbfPbaxJ/37Ig3B1s/+nH5srTnwdV4teaYdXU4SfxH+k+clc16JvwWem19phQVbf/Ovo2M+ZSBax9j2ex33t+TJovf+nrE9VT4QGdZE4s9GGq/EN4WnKOrCcz37bQv3c47xnDqz33v+1t+3kU62jS3zWYmXhMx5JRKJRGLnkDmvROIvxH/qeSUSu4zMeSUSO4o0UonE70OGDROJRCKxc0jjlUgkEomdQxqvRCKRSOwc0nglEolEYueQxiuRSCQSO4c0XolEIpHYOaTxSiQSicTOIY1XIpFIJHYOO1uknMWdiUQi8e0iPa9EIpFI7BzSeCUSiURi55DGK5FIJBI7hzReiUQikdg5pPFKJBKJxM4hjVcikUgkdg5pvBKJRCKxc0jjlUgkEomdQxqvRCKRSOwc0nglEolEYueQxiuRSCQSO4c0XolEIpHYOaTxSiQSicTOIY1XIpFIJHYOabwSiUQisXNI45VIJBKJnUMar0QikUjsHNJ4JRKJRGLnkMYrkUgkEjuHNF6JRCKR2Dmk8UokEonEziGNVyKRSCR2Dmm8EolEIrFzSOOVSCQSiZ1DGq9EIpFI7BzSeCUSiURi55DGK5FIJBI7hzReiUQikdg5pPFKJBKJxM4hjVcikUgkdg5pvBKJRCKxc0jjlUgkEomdQxqvRCKRSOwc/h/8H5oOA20OxgAAAABJRU5ErkJggg==",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x326fa3550>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 2\n",
    "d = gaussian_blur(d0, a)\n",
    "imageplot(d[:, :, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "256"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "f = copy(d0)\n",
    "\n",
    "n = maximum(size(f))\n",
    "# t = [collect(0:n/2); collect(-n/2:-2)]\n",
    "# (Y, X) = meshgrid(t, t)\n",
    "# h = exp( -(X.^2 + Y.^2)./(2.0*float(sigma)^2) )\n",
    "# h = h./sum(h)\n",
    "# real(plan_ifft((plan_fft(f)*f).*(plan_fft(h)*h))*((plan_fft(f)*f).*(plan_fft(h)*h)))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Compute a decreasing function of the gradient to define $W$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "d = min(d, .4)\n",
    "W = rescale(-d, .8, 1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x326febb10>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "imageplot(W[:, :, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Number of points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "p = 128;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "**Exercise 3:** Create an initial circle $\\gamma_0$ of $p$ points. When plotting the image, you need to transpose it to have axis coherent with the cplot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "LoadError: transpose not implemented for Array{Float32,3}. Consider adding parentheses, e.g. A*(B*C.') instead of A*B*C' to avoid explicit calculation of the transposed matrix.\nwhile loading /Users/gpeyre/Dropbox/github/numerical-tours/julia/NtSolutions/segmentation_2_snakes_param/exo3.jl, in expression starting on line 8",
     "output_type": "error",
     "traceback": [
      "LoadError: transpose not implemented for Array{Float32,3}. Consider adding parentheses, e.g. A*(B*C.') instead of A*B*C' to avoid explicit calculation of the transposed matrix.\nwhile loading /Users/gpeyre/Dropbox/github/numerical-tours/julia/NtSolutions/segmentation_2_snakes_param/exo3.jl, in expression starting on line 8",
      "",
      " in transpose(::Array{Float32,3}) at ./abstractarraymath.jl:10",
      " in include_from_node1(::String) at ./loading.jl:488",
      " in include_from_node1(::String) at /Applications/Julia-0.5.app/Contents/Resources/julia/lib/julia/sys.dylib:?"
     ]
    }
   ],
   "source": [
    "include(\"NtSolutions/segmentation_2_snakes_param/exo3.jl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Step size."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "dt = 2;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Number of iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Tmax = 9000\n",
    "niter = round(Tmax/ dt);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "**Exercise 4:** Perform the curve evolution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "LoadError: transpose not implemented for Array{Float32,3}. Consider adding parentheses, e.g. A*(B*C.') instead of A*B*C' to avoid explicit calculation of the transposed matrix.\nwhile loading /Users/gpeyre/Dropbox/github/numerical-tours/julia/NtSolutions/segmentation_2_snakes_param/exo4.jl, in expression starting on line 10",
     "output_type": "error",
     "traceback": [
      "LoadError: transpose not implemented for Array{Float32,3}. Consider adding parentheses, e.g. A*(B*C.') instead of A*B*C' to avoid explicit calculation of the transposed matrix.\nwhile loading /Users/gpeyre/Dropbox/github/numerical-tours/julia/NtSolutions/segmentation_2_snakes_param/exo4.jl, in expression starting on line 10",
      "",
      " in transpose(::Array{Float32,3}) at ./abstractarraymath.jl:10",
      " in include_from_node1(::String) at ./loading.jl:488",
      " in include_from_node1(::String) at /Applications/Julia-0.5.app/Contents/Resources/julia/lib/julia/sys.dylib:?"
     ]
    }
   ],
   "source": [
    "include(\"NtSolutions/segmentation_2_snakes_param/exo4.jl\")\n",
    "\n",
    "# G = grad(W);\n",
    "# G = G[:, :, 1] + 1im*G[:, :, 2]\n",
    "# EvalG = gamma -> NtToolBox.bilinear_interpolate(G, imag(gamma), real(gamma))\n",
    "# EvalW = gamma -> NtToolBox.bilinear_interpolate(W, imag(gamma), real(gamma))\n",
    "# #\n",
    "# gamma = gamma0\n",
    "# displist = round(linspace(0, niter, 10))\n",
    "# k = 1;\n",
    "# clf\n",
    "# imageplot(transpose(f))\n",
    "# for i in 0 : niter - 1\n",
    "#     n = normal(gamma)\n",
    "#     g = EvalW(gamma) .* normalC(gamma) - dotp(EvalG(gamma), n) .* n\n",
    "#     gamma = resample( gamma + dt*g )\n",
    "#     if i == displist[k]  \n",
    "#         lw = 1;    \n",
    "#         if (i == 0) | (i == niter)\n",
    "#             lw = 4;\n",
    "#         end\n",
    "#         cplot(gamma, \"r\", lw);\n",
    "#         k = k + 1;\n",
    "#         axis(\"equal\"); axis(\"off\");\n",
    "#     end\n",
    "# end\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Evolution of a Non-closed Curve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "It is possible to perform the evolution of a non-closed curve by adding\n",
    "boundary constraint\n",
    "$$ \\ga(0)=x_0 \\qandq \\ga(1)=x_1. $$\n",
    "\n",
    "\n",
    "In this case, the algorithm find a local minimizer of the geodesic\n",
    "distance between the two points.\n",
    "\n",
    "\n",
    "Note that a much more efficient way to solve this problem is to use the\n",
    "Fast Marching algorithm to find the global minimizer of the geodesic\n",
    "length.\n",
    "\n",
    "\n",
    "Load an image $f$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "n = 256\n",
    "f = load_image(name, n)\n",
    "f = f[45:105, 60:120]\n",
    "n = size(f)[1];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x3287fee90>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "imageplot(f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "**Exercise 5:** Compute an edge attracting criterion $W(x)>0$, that is small in area of strong\n",
    "gradient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "LoadError: UndefVarError: ff not defined\nwhile loading /Users/gpeyre/Dropbox/github/numerical-tours/julia/NtSolutions/segmentation_2_snakes_param/exo5.jl, in expression starting on line 1",
     "output_type": "error",
     "traceback": [
      "LoadError: UndefVarError: ff not defined\nwhile loading /Users/gpeyre/Dropbox/github/numerical-tours/julia/NtSolutions/segmentation_2_snakes_param/exo5.jl, in expression starting on line 1",
      "",
      " in include_from_node1(::String) at ./loading.jl:488",
      " in include_from_node1(::String) at /Applications/Julia-0.5.app/Contents/Resources/julia/lib/julia/sys.dylib:?"
     ]
    }
   ],
   "source": [
    "include(\"NtSolutions/segmentation_2_snakes_param/exo5.jl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Start and end points $x_0$ and $x_1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "x0 = 4 + 55*1im\n",
    "x1 = 53 + 4*1im;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Initial curve $\\ga_0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "p = 128\n",
    "t = transpose(linspace(0, 1, p))\n",
    "gamma0 = t*x1 + (1 - t)*x0;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Initialize the evolution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "gamma = gamma0;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "transpose not implemented for Array{Float64,3}. Consider adding parentheses, e.g. A*(B*C.') instead of A*B*C' to avoid explicit calculation of the transposed matrix.",
     "output_type": "error",
     "traceback": [
      "transpose not implemented for Array{Float64,3}. Consider adding parentheses, e.g. A*(B*C.') instead of A*B*C' to avoid explicit calculation of the transposed matrix.",
      "",
      " in transpose(::Array{Float64,3}) at ./abstractarraymath.jl:10"
     ]
    }
   ],
   "source": [
    "clf\n",
    "imageplot(transpose(W))\n",
    "cplot(gamma[:],\"r\", 2)\n",
    "plot(real(gamma[1]), imag(gamma[1]), \"b.\", markersize = 20)\n",
    "plot(real(gamma[end]), imag(gamma[end]), \"b.\", markersize = 20);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Re-sampling for non-periodic curves."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "ArgumentError: Module Dierckx not found in current path.\nRun `Pkg.add(\"Dierckx\")` to install the Dierckx package.",
     "output_type": "error",
     "traceback": [
      "ArgumentError: Module Dierckx not found in current path.\nRun `Pkg.add(\"Dierckx\")` to install the Dierckx package.",
      "",
      " in require(::Symbol) at ./loading.jl:365",
      " in require(::Symbol) at /Applications/Julia-0.5.app/Contents/Resources/julia/lib/julia/sys.dylib:?"
     ]
    }
   ],
   "source": [
    "using Dierckx\n",
    "curvabs = gamma -> [0; cumsum(1e-5 .+ abs(gamma[1 : end - 1] - gamma[2 : end]) )]\n",
    "resample11 = (gamma, d) -> evaluate(Spline1D(d./d[end], real(gamma), k=1), (0:p-1)./p)\n",
    "resample12 = (gamma, d) -> evaluate(Spline1D(d./d[end], imag(gamma), k=1), (0:p-1)./p)\n",
    "resample = gamma -> resample11( [gamma; gamma[1]], curvabs( [gamma; gamma[1]] ) ) + 1im*resample12( [gamma; gamma[1]], curvabs( [gamma; gamma[1]] ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Time step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "dt = 1/10;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Number of iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Tmax = 2000*4/ 7\n",
    "niter = round(Tmax/ dt);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "**Exercise 6:** Perform the curve evolution.\n",
    "Be careful to impose the boundary conditions at each step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "LoadError: MethodError: Cannot `convert` an object of type Array{Float64,1} to an object of type Int64\nThis may have arisen from a call to the constructor Int64(...),\nsince type constructors fall back to convert methods.\nwhile loading /Users/gpeyre/Dropbox/github/numerical-tours/julia/NtSolutions/segmentation_2_snakes_param/exo6.jl, in expression starting on line 11",
     "output_type": "error",
     "traceback": [
      "LoadError: MethodError: Cannot `convert` an object of type Array{Float64,1} to an object of type Int64\nThis may have arisen from a call to the constructor Int64(...),\nsince type constructors fall back to convert methods.\nwhile loading /Users/gpeyre/Dropbox/github/numerical-tours/julia/NtSolutions/segmentation_2_snakes_param/exo6.jl, in expression starting on line 11",
      "",
      " in bilinear_interpolate(::Array{Float64,3}, ::Array{Float64,1}, ::Array{Float64,1}) at /Users/gpeyre/.julia/v0.5/NtToolBox/src/signal.jl:414",
      " in (::##29#30)(::Array{Complex{Float64},1}) at /Users/gpeyre/Dropbox/github/numerical-tours/julia/NtSolutions/segmentation_2_snakes_param/exo6.jl:4",
      " in macro expansion; at /Users/gpeyre/Dropbox/github/numerical-tours/julia/NtSolutions/segmentation_2_snakes_param/exo6.jl:13 [inlined]",
      " in anonymous at ./<missing>:?",
      " in include_from_node1(::String) at ./loading.jl:488",
      " in include_from_node1(::String) at /Applications/Julia-0.5.app/Contents/Resources/julia/lib/julia/sys.dylib:?"
     ]
    }
   ],
   "source": [
    "include(\"NtSolutions/segmentation_2_snakes_param/exo6.jl\")\n",
    "\n",
    "\n",
    "# G = grad(W);\n",
    "# G = G[:, :, 1] + 1im*G[:, :, 2]\n",
    "# EvalG = gamma -> NtToolBox.bilinear_interpolate(G, imag(gamma), real(gamma))\n",
    "# EvalW = gamma -> NtToolBox.bilinear_interpolate(W, imag(gamma), real(gamma))\n",
    "# #\n",
    "# gamma = gamma0[:];\n",
    "# displist = round(linspace(0, niter, 10))\n",
    "# k = 1;\n",
    "# clf\n",
    "# imageplot(transpose(f))\n",
    "# for i in 0 : niter\n",
    "#     N = normal(gamma)\n",
    "#     g = EvalW(gamma) .* normalC(gamma) - dotp(EvalG(gamma), N) .* N\n",
    "#     gamma = gamma + dt*g\n",
    "#     gamma = resample( gamma )\n",
    "#     # impose start/end point\n",
    "#     gamma[1] = x0\n",
    "#     gamma[end] = x1\n",
    "#     if i == displist[k]   \n",
    "#         lw = 1;    \n",
    "#         if (i == 0) | (i == niter)\n",
    "#             lw = 4;\n",
    "#         end\n",
    "#         cplot(gamma, \"r\", lw);\n",
    "#         k = k + 1;\n",
    "#         axis(\"equal\"); axis(\"off\");\n",
    "#         plot(real(gamma[1]), imag(gamma[1]), \"b.\", markersize = 20)\n",
    "#         plot(real(gamma[end]), imag(gamma[end]), \"b.\", markersize = 20);\n",
    "#     end\n",
    "# end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": []
  }
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