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    "Inpainting using Sparse Regularization\n",
    "======================================\n",
    "\n",
    "*Important:* Please read the [installation page](http://gpeyre.github.io/numerical-tours/installation_python/) for details about how to install the toolboxes.\n",
    "$\\newcommand{\\dotp}[2]{\\langle #1, #2 \\rangle}$\n",
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    "$\\newcommand{\\umax}[1]{\\underset{#1}{\\max}\\;}$\n",
    "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n",
    "$\\newcommand{\\uargmin}[1]{\\underset{#1}{argmin}\\;}$\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",
    "$\\newcommand{\\pa}[1]{\\left(#1\\right)}$\n",
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    "$\\newcommand{\\qandq}{\\quad\\text{and}\\quad}$\n",
    "$\\newcommand{\\qwhereq}{\\quad\\text{where}\\quad}$\n",
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    "$\\newcommand{\\qarrq}{ \\quad \\Longrightarrow \\quad }$\n",
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    "$\\newcommand{\\Zz}{\\mathcal{Z}}$\n",
    "$\\newcommand{\\Ww}{\\mathcal{W}}$\n",
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    "$\\newcommand{\\Om}{\\Omega}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This numerical tour explores the use of\n",
    "sparse energies to regularize the image inpaiting problem."
   ]
  },
  {
   "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": [
    "Here we consider inpainting of damaged observation without noise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Sparse Regularization\n",
    "---------------------\n",
    "This tour consider measurements $y=\\Phi f_0 + w$\n",
    "where $\\Phi$ is a masking operator\n",
    "and $w$ is an additive noise.\n",
    "\n",
    "\n",
    "This tour is focused on using sparsity to recover an image from the\n",
    "measurements $y$. It considers a synthesis-based regularization, that\n",
    "compute a sparse set of coefficients $ (a_m^{\\star})_m $\n",
    "in a frame $\\Psi = (\\psi_m)_m$ that solves\n",
    "$$a^{\\star} \\in \\text{argmin}_a \\: \\frac{1}{2}\\|y-\\Phi \\Psi a\\|^2 + \\lambda J(a)$$\n",
    "\n",
    "\n",
    "where $\\lambda$ should be adapted to the noise level $\\|w\\|$.\n",
    "Since in this tour we consider damaged observation without noise, i.e.\n",
    "$w=0$, we use either a very small value of $\\lambda$, or we decay its\n",
    "value through the iterations of the recovery process.\n",
    "\n",
    "\n",
    "Here we use the notation\n",
    "$$\\Psi a = \\sum_m a_m \\psi_m$$\n",
    "to indicate the reconstruction operator, and $J(a)$ is the $\\ell^1$\n",
    "sparsity prior\n",
    "$$J(a)=\\sum_m \\|a_m\\|.$$\n",
    "\n",
    "\n",
    "Missing Pixels and Inpainting\n",
    "-----------------------------\n",
    "Inpainting corresponds to filling holes in images.\n",
    "This corresponds to a linear ill posed inverse problem.\n",
    "\n",
    "\n",
    "You might want to do first the numerical tour _Variational image inpaiting_\n",
    "that use Sobolev and TV priors to performs the inpainting.\n",
    "\n",
    "\n",
    "First we load the image to be inpainted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "n = 128\n",
    "f0 = load_image(\"NtToolBox/src/data/lena.png\")\n",
    "f0 = rescale(f0[256 - Base.div(n, 2) + 1 : 256 + Base.div(n, 2), 256 - Base.div(n, 2) + 1 : 256 + Base.div(n, 2)]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x322130210>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.text.Text object at 0x322157a10>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "figure(figsize = (6, 6))\n",
    "imageplot(f0, L\"Image $f_0$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Amount of removed pixels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "rho = .7;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Then we construct a mask $\\Omega$ made of random pixel locations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Omega = zeros(n, n)\n",
    "sel = randperm(n^2)\n",
    "Omega[sel[1:Int(round(rho*n^2))]] = 1;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The damaging operator put to zeros the pixel locations $x$ for which $\\Omega(x)=1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Phi = (f, Omega) -> f.*(1 - Omega);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The damaged observations reads $y = \\Phi f_0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "y = Phi(f0, Omega);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display the observations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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 0x322b45e50>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.text.Text object at 0x322b35b10>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "figure(figsize = (6, 6))\n",
    "imageplot(y, \"Observations y\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Soft Thresholding in a Basis\n",
    "----------------------------\n",
    "The soft thresholding operator is at the heart of $\\ell^1$ minimization\n",
    "schemes. It can be applied to coefficients $a$, or to an image $f$\n",
    "in an ortho-basis.\n",
    "\n",
    "\n",
    "The soft thresholding is a 1-D functional that shrinks the value of\n",
    "coefficients.\n",
    "$$ s_T(u)=\\max(0,1-T/|u|)u $$\n",
    "\n",
    "\n",
    "Define a shortcut for this soft thresholding 1-D functional."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "SoftThresh = (x,T) -> x.*max( 0, 1 - T./max(abs(x), 1e-10) );"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display a curve of the 1D soft thresholding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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 0x32363ced0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = linspace(-1, 1, 1000)\n",
    "\n",
    "figure(figsize = (7, 5))\n",
    "plot(x, SoftThresh(x, .5))\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Note that the function SoftThresh can also be applied to vector which defines an\n",
    "operator on coefficients:\n",
    "$$ S_T(a) = ( s_T(a_m) )_m. $$\n",
    "\n",
    "\n",
    "In the next section, we use an orthogonal wavelet basis $\\Psi$.\n",
    "\n",
    "\n",
    "We set the parameters of the wavelet transform."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Jmax = log2(n) - 1\n",
    "Jmin = (Jmax - 3);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Shortcut for $\\Psi$ and $\\Psi^*$ in the orthogonal case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Psi = a -> NtToolBox.perform_wavelet_transf(a, Jmin, -1, \"9-7\", 0, 0)\n",
    "PsiS = f -> NtToolBox.perform_wavelet_transf(f, Jmin, +1, \"9-7\", 0, 0);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The soft thresholding opterator in the basis $\\Psi$ is defined as\n",
    "$$S_T^\\Psi(f) = \\sum_m s_T( \\langle f,\\psi_m \\rangle ) \\psi_m $$\n",
    "\n",
    "\n",
    "It thus corresponds to applying the transform $\\Psi^*$, thresholding\n",
    "the coefficients using $S_T$ and then undoing the transform using\n",
    "$\\Psi$.\n",
    "$$ S_T^\\Psi(f) = \\Psi \\circ S_T \\circ \\Psi^*$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "SoftThreshPsi = (f, T) -> Psi(SoftThresh(PsiS(f), T));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This soft thresholding corresponds to a denoising operator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x327546c90>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize = (6, 6))\n",
    "imageplot(clamP(SoftThreshPsi(f0, 0.1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Inpainting using Orthogonal Wavelet Sparsity\n",
    "--------------------------------------------\n",
    "If $\\Psi$ is an orthogonal basis, a change of variable shows that the\n",
    "synthesis prior is also an analysis prior, that reads\n",
    "$$f^{\\star} \\in \\text{argmin}_f \\: E(f) = \\frac{1}{2}\\|y-\\Phi f\\|^2 + \\lambda \\sum_m \\|\\langle f,\\psi_m \\rangle\\|. $$\n",
    "\n",
    "\n",
    "To solve this non-smooth optimization problem, one can use\n",
    "forward-backward splitting, also known as iterative soft thresholding.\n",
    "\n",
    "\n",
    "It computes a series of images $f^{(\\ell)}$ defined as\n",
    "$$ f^{(\\ell+1)} = S_{\\tau\\lambda}^{\\Psi}( f^{(\\ell)} - \\tau \\Phi^{*} (\\Phi f^{(\\ell)} - y)  ) $$\n",
    "\n",
    "\n",
    "Set up the value of the threshold."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "lambd = .03;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "In our setting, we have $ \\Phi^* = \\Phi $ which is an operator of norm\n",
    "1.\n",
    "\n",
    "\n",
    "For $f^{(\\ell)}$ to converge to a solution of the problem, the gradient\n",
    "step size should be chosen as\n",
    "$$\\tau < \\frac{2}{\\|\\Phi^* \\Phi\\|} = 2$$\n",
    "\n",
    "\n",
    "In the following we use:\n",
    "$$\\tau = 1$$\n",
    "\n",
    "\n",
    "Since we use $ \\tau=1 $ and $ \\Phi = \\Phi^* = \\text{diag}(1-\\Omega) $,  the gradient descent step\n",
    "is a projection on the inpainting constraint\n",
    "$$ C = \\{ f \\backslash \\forall \\Omega(x)=0, f(x)=y(x) \\} $$\n",
    "One thus has\n",
    "$$ f - \\tau \\Phi^{*} (\\Phi f - y)  = \\text{Proj}_C(f) $$\n",
    "\n",
    "\n",
    "For the sake of simplicity, we define a shortcut for this projection\n",
    "operator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "ProjC = (f, Omega) -> Omega.*f + (1 - Omega).*y;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Each iteration of the forward-backward (iterative thresholding) algorithm\n",
    "thus reads:\n",
    "$$ f^{(\\ell+1)} = S_{\\lambda}^\\Psi( \\text{Proj}_C(f^{(\\ell)}) ). $$\n",
    "\n",
    "\n",
    "Initialize the iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "fSpars = y;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "First step: gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "fSpars = ProjC(fSpars, Omega);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Second step: denoise the solution by thresholding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "fSpars = SoftThreshPsi(fSpars, lambd);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "__Exercise 1__\n",
    "\n",
    "Perform the iterative soft thresholding.\n",
    "Monitor the decay of the energy $E$ you are minimizing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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 0x3276ed550>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "include(\"NtSolutions/inverse_5_inpainting_sparsity/exo1.jl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "## Insert your code here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display the result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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 0x32755a950>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize = (6, 6))\n",
    "imageplot(clamP(fSpars))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "__Exercise 2__\n",
    "\n",
    "Since there is no noise, one should in theory take $\\lambda\n",
    "\\rightarrow 0$.\n",
    "To do this, decay the value of $\\lambda$ through the iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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uv/32OOaYYworVVe8+OKL8c1vfjNOOeWUeOmll2LJkiWxZMmSePnll6PVasWSJUv+LA6b68I06fBs3n78kWC6zZ577hkREU8//XTx98cee6zTsQsWLIh3vvOdVXTBL3/5yzjxxBPjvPPOi6OPPjoOOeSQ2G+//eKFF15oqw+DBg2KU089Na6++upYvHhxbLPNNmn8elPGtxNOOCFeeumluPbaa2PatGnRv3//Ls2k6xuO28svvxxPP/10FaVw6623xurVq+Oyyy6Lz372s3HEEUfEwQcfXMgH64M/RVa8YcOGxZtvvhmLFy8u/r5w4cL1fq2IrtemcuaZZ8aWW27Z1v8x77LLLvH3f//38cMf/jCWLVvWePyHP/zhGDRoUON/n/3sZ7vdh3a44oorotVqdVtqeP755+Pll1+Oc889N0aMGFH99x//8R+xdu3aGDFiRHziE5/o8vf9+/ePTTbZpPYdMH/+/G73+/XXX4+IPz4D5i8Lyw2mE7fcckuVfU5ZZzocM2ZM8feZM2cWnuNPPPFEXHPNNfG+972v+j/OPn36dPq/zO9+97udQvm64o033oiXX345tthii+pvAwYMiMGDB8d//dd/dfm7dR7wXX2M7LLLLrHLLrvEJZdcEnfffXeceOKJf7YwrB/96Edx8sknV//Hd/HFF8frr79emYnXjZ2O26uvvhoXXXTReu3HusQ5L7zwQrc8+LvDlClT4ktf+lJcdNFFccEFF1R/fysZO1esWBHPPfdcJ9381Vdfjf/8z/+MDTbYIJUz1lkTpk6dGrvuumu3r/vFL34xLr/88jj//PPjwgsvTI8977zzuiXlDB48uNvXb4ef/exnMXTo0Nhvv/1q21988cV4+umnY9CgQbHFFlvEgAED4qqrrup03P/9v/83Zs6cGVdccUUMGjSoy+v16dMnpkyZEldffXUsW7askqHmzp0bN9xwQ7f7vS7ZVTvzYv48+CPBdOL000+PtWvXxlFHHRVjx46NV199Ne6666648sorY/jw4XHyyScXx0+YMCGmTJlShEBGRPF/bEcccUT85Cc/iS222CLGjRsXM2fOjJtuuim22WabbvVpzZo1MWTIkDj66KNj1113jX79+sVNN90U99xzT5x33nld/m6TTTaJcePGxZVXXhmjR4+OrbfeOiZMmFCEdp5wwgnx+c9/PiLiLUkN7fLqq6/GQQcdFMcee2zMnz8/Lrroothvv/3iyCOPjIiIv/mbv4mtttoqTjzxxDjjjDOio6MjfvKTn6x3k/46Hf2MM86IKVOmRJ8+feK44457y+f8yEc+EhdeeGGsXr26CoFclzWQH6AdHR0xefLkNH32k08+GXvttVe8973vjYMOOigGDhwYzz77bFxxxRUxe/bsOPPMM2PbbbdN+7XON2H27Nndzio4bty4OOyww+KSSy6Jr3zlK+maXZ8+CUuXLq3CUu+9996IiPjmN78ZEX+01HzsYx8rjn/kkUfioYcein/6p3/q0jp01VVXxcknnxyXXnppnHTSSfHOd74zPvShD3U67uqrr45Zs2bVtpGvfe1rcf3118f+++8fp556arz++uvx3e9+N8aPHx8PPfRQp+OXL18eP/3pTyMiKp+nH/7wh7HtttvaH+EvkbctrsL8xXLddde1Pv7xj7fGjh3b6tevX2ujjTZq7bjjjq3TTz+9U8bFiGiddtpprZ/+9KetnXbaqbXxxhu3dt9999Ytt9xSHPf888+3Tj755Na2227b6tevX2vKlCmtefPmtYYNG1aEg60LD7znnnuK3//Xf/1X6wtf+EJr1113bW222WatTTfdtLXrrru2LrroouI4hgK2Wq3WXXfd1Zo4cWJro402qg2/e/rpp1t9+vRpjR49uttj1FUIZF2o3OTJk1uTJ0/u9NsZM2a0PvGJT7S22mqrVr9+/VrHH398a/Xq1cVv77zzztbee+/d2mSTTVqDBw+uwlEjohjjrkIgv/3tb3fqD8fg9ddfb51++umt/v37tzo6OoqwNR67LgRy5cqVjePx+9//vnXaaae1tt5669amm27a+sAHPtCaN29eKyJa3/rWt6rj1qxZ04qI1nHHHdepr8pLL73U+s53vtOaMmVKa8iQIa13vOMdrc0226y1zz77tP71X/+19eabb1bHaggkWXcP3cm4uI5bb731z565c9091P2n62kd//RP/9SKiNZDDz3U5TnXzVNTiG87IZCtVqs1Y8aM6hkbOXJk6wc/+EGXGRf1PjbYYIPWgAEDWh/96EdbCxcu7Pb1zJ+Pjlbrz+hpZP7q6OjoiNNOOy2+973vvd1d6TGrVq2KQYMGxVlnnRVf+cpX/uTXu+yyy+Lkk0+Oe+65p9LS/7vw4IMPxu677x4//elPK918+vTpccQRR8Ts2bPjXe9619vcQ2OMYsdF89+eyy67LN54441O5lvz1qiLeb/wwgtjgw02iPe85z3V32655ZY47rjj/IFgzF8g9kkw/225+eab49FHH42zzz47PvShDxV7H5i3zrnnnhv33XdfHHjggbHhhhvGddddF9ddd1184hOfiB122KE6rjvppY0xbw/+SDD/bfn6178ed911V+y7775vyeve1PM3f/M3ceONN8Y3vvGNePnll2Po0KExderU+NKXvvR2d80Y003sk2CMMcaYWuyTYIwxxpha/JFgjDHGmFr8kWCMMcaYWnqt4yKz7OmGM0yru/nmm3fZtnbt2qKu6Xv79etXtGn63zVr1hRt3KEvc/XgebfbbruqzG2Qn3zyyao8cODAou2RRx4p6itXrqzKzCa3atWqqrx69eqijal4dbzW7b1Qd81vfOMbRdvXv/71oq7bLfO+VqxYUZWZ339dHvd1ZDvwcaMhzTTHudYxYNY8pof+wx/+UJUZ9fDEE09U5QMOOKBoGzZsWJfn1XOyjePM1L7nnHNOVeZ48LeadZC7Werc//73vy/adt9996KuIYlMfa1rbe7cuUXbRhttVNT12WB6bB2/ddtLr4PPiW5oxT0a3uquluvgvhiaAprpoOfMmVOVud05s5IqG2+8cVHXceamXe9+97uLum5gxfX96quvVmVuIMX6qFGjqjI3U9M1zOeC7zVdFzyWz7GuC7Zp33lfddk51/Haa68Vbfps8BrZu59rNnuP8FnQvm+wQfn/3axnKd91bHnPHHfdvIv/9qxLRV/HutT57WBLgjHGGGNq8UeCMcYYY2rxR4Ixxhhjaum1PgnUkFSzoe6juhV9EKgZqQ5K7fC5556rPWfdNVV7pYb8zDPPFPVbbrmlKnOrW9WeFi1aVLRRv9QtXVU3jyjHZ+utty7aOJY6Jqq3RZT+C/PmzeuyLSJi9uzZVXnhwoVdXoNjRy2Rc5Sh98nzKJmWGZHf54gRI6oy/QFmzZpV1HfaaaeqrHMZEXHTTTdV5XW7/K2Dvg2qlbOvHB/1feAaVv2Z2iV1UH1W6Eugda6Rl19+uair/w59B3RMOF9M66yaN+dP1zCfiyZdXZkyZUpRV98e+vmov5D68dSha5zvIF0jd999d5fXiCjvm8+N3jd9dfhsqq8K3wf6W84Jx1bXHseZ60n7zjWj88fzcH3redmmv+UYNJ1X0TXC32V+UFxbmd8IfUH0OhxnnlfHMusPx7kn2JJgjDHGmFr8kWCMMcaYWnqt3EBTlpotaUZS0wzNZ1lYGs2m2fVpstdwO4Zy7bvvvkVdwwEHDBhQtD388MNVmeZOomGGNEGpSZFmLo6BjhfD5NTsfeuttxZtDLfT36oUElGaoLNxjijnhOOemRRpslPTH9toAtZ1wt0JNfyP13/ggQeKupr7OAa77bZbVVYJI6JzWGh2X6zrfNLcqfKIht5GdJ5rNXUzhE7nj+ZYhmRlc6113gf7w3Wq6PrmcayrNEDJZciQIUVdzf9777130abhZFz7lEr02eW7QtcQw+s05DEiYosttqjKWWggn3G+g/QdyXHX+aNElkk1PA/7p1AG0+etSV7U6/DYTCZg3/W3/HdB+8774phkkgvfD/pu5drT/mWyDvvH9aTvnKZ/M7qDLQnGGGOMqcUfCcYYY4ypxR8JxhhjjKml1/okZCk3qUGqhkSNiGlYVY+jPqghkNTbqLGpdshwth/96EdFXVOvMkRMNVv1XahDtaim/ikM31q+fHm3rsFxpv6tuiy1OoV6G8N2NOSP18zWAbU6rVOf5Hjp3DNkVe+FqbLpW6BzxnWga03XVkRnH4msr1k4J0MX1S+Ca//QQw8t6uoXQY39tttu67J/mhY6otReqcMuWbKkKnPeqctqH+jfkfmbcH3pfXNOHnvssaKu/ijU+fUZ1xTkEZ3X5bPPPluV6Weg4cqcS9Z1XTA1tfq4aN/q+p75C+j7kvOeheJRq8/C+DL/gKZnM0tfrLQTuphp/oRzq/3hNYj6CGTn4RhkdfY1exZ6gi0JxhhjjKnFHwnGGGOMqaXXyg0MNdOsZQz7ULMOzbg0tWtmMg11iyhNwjStMwuemp0effTRoo1m3Xvuuacq0zyk58l2Q+RvKZXorofZToURpZk5y7iWhX3yt7yG/pamUJ5XTZ40rWVjwmuqOZTzx9A87QPXjM4JTaxjxowp6jfccEOXfVfzOk3t2W5ynBPWVVqijKGm9pEjRxZt1157bVHX8NuJEycWbfqM0bRNGUPDJ7lGaHpXOAa6pgcPHly0ZeGalITULH/ggQcWbb/61a+KumZA5TrYYYcdqjLXmj7TEeV6Y99VishMxxGleZ9yg+6oSbN3trNiNs7sD9daJiPyOdZ3R/a7TIpgexbmyHvOMkLymtpXtjXtLqlQHs12l8zCS4meh3OUhbf2BFsSjDHGGFOLPxKMMcYYU4s/EowxxhhTS6/1Sdh+++2Luup6y5YtK9pUox03blzRdscddxT1BQsWVGXuyDh27NiqTH2SKWQzzY3+FKoh8Tyq1zeF6eixTBOrOpqmb65Dw9QyvY1wTHQMGIKpaWLpQ8IwOZ1b+lrwmqrrZeldeV/cJU919Wx3Qo7l448/3uV1uDOnhrsyVJHXVN8Z+k/QB0BTe3O8tO/0B6B+qWPC9azXoF/P0KFDi7rucEkdXTV2+srQt+Doo4+uyj/4wQ+Ktl122aUqU/N/8MEHi7qOAX1KuE51bXJHRtX9GZLJ1NR77bVXVaZfhvaBc5mFLvKa2e6fmW7dFHqqcF1mIX9N6cO7ItvVNKK8t+y+sl1gm/qj6z3zD8p+V3cNfR9k4a5clyR7z2X+FD3BlgRjjDHG1OKPBGOMMcbU4o8EY4wxxtTS0VofosXbwDe/+c2iTh1bueuuu6oyt4LN4tOpbar2Sn2Zuplq1aqpR3TW4NUPgRqyapRZqtCIUkOmHqc6tm7dG9FZn89yBFBrVaijrV69uipTm9OxZRw7009rvoqm7YOzLVTVD4Kx/bqFMuu8L9UOFy5cWLRlOijHQOck2844otwKmX4QPFa3gObjnaXn5trT/mpOgIiI4cOHV+X777+/aGP/VMvn+tl5552rMvV3arbz5s2ryhMmTCjaHnnkkapM/47999+/qGvaaKaQ1vuKKMdErxERcdBBB1Vl+itwvPSZ4zX1nUN9mWtY84Lw3aXvCr5juFW0kqVBZn84tnqdJh+E7P2lxzal1VbdP8t90LTltN43n3Gdd/pdZOPFNdt0L0q2jTTf0VrP0trz+pMmTery+l1hS4IxxhhjavFHgjHGGGNq6bUhkEzHq2FFNCVrSmKalSgFqCkpM+tSili0aFFRV7MzTX+8pkogNMeqCYr3nIXw8DxqZqa5k6l72T9F+5CZz3mdLE0szXdZKCXPQ7OcjntmFqQZl2OiYXKcP5V1KDsxvC0zJet5eI3M7My+7rnnnkVd5YYZM2YUbToG2a54EeV83n777UXbj3/84y77rinSI8rnkZKCSkv77rtv0UYZSseEMo+u4fHjxxdtDKXcb7/9qjLNrzyv7nb55S9/uWg7//zzq7KGhEZ0lq9UTuJ7Re+TYY2cE33mVKqJiJg/f35VZgg0JUb3SB5gAAAgAElEQVQdS74TM1lAZS+eN9utkX2nTJA9J1l/2JalWuax+kxlYaBZqnxeh2OZhcJnZKmoI8r3HN9l2j8+bz3qy1s+gzHGGGP+KvFHgjHGGGNq8UeCMcYYY2rptT4Jqr9FlBpcFk5G7YnpeFUPZ7idXpOplaklZpoRwzBV82Koi/aH5yGqz6umHlHqcdkWyhGl/wL1Nx1bhvtRN9Pf0l9Br0n9lGFW2nfOX6Y70odD74s6OtPhanpurhHtL/uehWTymqqV8555Ta1T79a+RkTcfffdVVlTiUeUc0at/plnninqqvNruF9EuXU0Q1bpn5OFfb3rXe+qygwf41bWmm5dUz1HlD4B9LHZY489irr2l+ehP87BBx9clb/1rW8VbeoLQj8azqeuE641Dbts0qL1Pjlf6ntFv6zHHnusqKtWzfBIfc/w3cDnWJ8pPpuZHp+le2/yJcjCHPW3TVs667OapV6mT0I7WQPa2ao5S8WcnYdtmd9YT7AlwRhjjDG1+CPBGGOMMbX0WrmBIT3Lly+vyjQ3qnmPISE062qWQGagU3MVz0Pz/ogRI6oyzXA0q6qswf5oeBTN1XrP7DtNV2pao8mQ4ZJ6L5RcdKc+7nhIGUVDtGg6vvbaa6sy55IZBLNdKynBZKFUunMo54/H6vhxLBcvXlyVdSfHiM4mVpVcKN3o+qI0QtlCM/rp2orobCLXEERdExHlWHMMuE7VlEwJQc2YNLVzvFTWYFijzjVlFD5TM2fOrMrcoVVhiCjN6fr8ccfYj3zkI0X91ltvrcrcpVLnmvPHZ1VlAq41vU+G9HK3W323ce3re45ZMJkBUuc2mz+uZ/ZP12lTSK2a6TNJgdfke1jnj2OpfeD4cH1nZGZ6vr91vJrM+3os5Y8sk2Q7O1FmoaY9wZYEY4wxxtTijwRjjDHG1OKPBGOMMcbU0mt9EqgFqyZI7VA1UabRzUJ8qDNqGBM1IepUek3dxTAi18Opv6seR52TqaFVf6Zvg2qH9EGgbq06Fv0XtO/UIDnuc+fOrcqa3jaiDBllCB39ILLQIPZBtVaGJ+pYMo0u51rrS5cuLdp0fBhGSFR3pAapY0utl3qqjgF9Ntg/DXdjaK6uRQ2Zi+isp+o1OUfZboQMPVOfAK4nXftZXyNKfwqO+0knnVSVqcPSt0HHlmM5a9asoq6+NDyv9ofPJnfb1PPwGVc9nj4IDz/8cFHfdddduzyPjhdTY3OXSm3nnOg6pV8B33NZOGKmz2eplumvwPPyWVV0jrgus3TKWZgj+8rz6DWzcPKI8h3EdZn5L7UzXnovnNueYEuCMcYYY2rxR4IxxhhjavFHgjHGGGNq6bU+CdSbVSunZqU6GrUnxghnsbR6zWwLV9IUA5+lKNU2aqLMB6Ht9DvQOuOOiZ6H6V21P4zX533uvvvuVZlar6at5Rywf6rPcayybW55Ht3mlj4A1Lh1bOkjoeelRktfAtXjuWZ0zTbpuTon9EGgf45ek2tE1x5zBOh8RZR+JNyWWK/JPA26VTXPu9tuuxVtWT6KK6+8sqhramiuJ82/kD0XEeXcc76Y6lj9K5h/QVNeZ2m0IyJuvvnmqvzhD3+4aFPfAs6J+iBERDz44INVmVtiL1mypCrzvvisqm8Wc1foM8ZnKHvPUWOnHp/5AOgc8RnP0iBn/WlKca2/za6RbSMdUb6fuIZ5L/pbvjsyPwheM/t3QX/Ld2tPsCXBGGOMMbX4I8EYY4wxtfRauYE7qakJkeFIai5iG00+bFfUZM8QFZqZ1ARE0x/lBg2lys7L0LJVq1YVdTVxchc6vQZNV5lZjmFyeixT49JENm7cuKrMUC7tD9MyZ7u+0XyXSTUcZ+37o48+WrTR3Khm58wUyb5SclHTP/uja41zy7quJ6bj5nyqiZjhrXovlAmGDh1a1FWCoYSga4/jwzWju1Ryx0q9Jq/PnSd/97vfVeVjjjmmaNM1RPMrn2l9TrKdSyNKiYpzq2G0XAeUrz760Y9WZYZha3+bTOQasrlw4cKiTdNa873Gtafh01kIZBY2GFG+WzkGmXTL82h/+b7kfOqzwTlRaTALG2zqj9LUnyz1cZY2uh35I3tnc65V9mFK8p5gS4IxxhhjavFHgjHGGGNq8UeCMcYYY2rptT4J1MpUl6HGphop9RvWVUfLUj9nv4sodTOmYaaWr/oTU9FSU1aotareO2rUqKJNx4R9ZciYarZZSA/DCHmfmh44C3NsSkGq7U1bn+qxTE2rIX3HHnts0UbNVjV3ricdP/pEUI/vqm8R5b3QL4Njq3PNcSbaX55X+8DU1EzzO3r06KpMHxftH++ZYXO6hqgha/gdn7fMX4garWqvXPv0vdD7VJ+DiM5bRd9yyy1VmWmj+VuFmnK23nWLdYZgMqxQfRL4HKt2Tp8WrlNtz0IVeR/ZFs/U7rPwyWxrdpL5abTj55O9ozP/Bf6O/cnGnc+fwnvW8zSFzWs9S+Ge+Wx1F1sSjDHGGFOLPxKMMcYYU4s/EowxxhhTS6/1SaA2pvoudWvVbzJtjsdS+9W2prh21YW4/evtt99e1DXdK1MAZ1ArUz2OOrrqgbwGY2l5L4reF+cgS0G6ww47dLs/WdrTJo1Nc1k8/fTTRdvBBx9clW+99daibc899yzqqoczxa72Idv6OCL3X9BrUL/N4tw5lhofH1Gmbc78avg7pgTWtMNM851tt5z5L3DNaLpgXp/+ODq21JCzuH/67kyaNKnL/tx7771FXdcF0xerls81TJ1YfQu4nrS/9HPgfWpqePr5aH+4DvlM6/rKNP+mXAP6W67hLL0y39H6zFN/51hq36nrt5OGWK/J+8zec+yPvp8y34GIco7470uWVj/zDaH/ks4J57Yn2JJgjDHGmFr8kWCMMcaYWnqt3EDUVJOlsGQbw//UHJvtEEkzEsPA5s6dW5Vp9j700EOL+jXXXFOVudOcmgkpL9AkreY+htBkaZmz1MK8TzUBU0Yh2j+aF9UMTlNolpaZJk2GiKnpjTtYLl68uCrT5Dtv3ryiruFuNCWrGZXmTt6LmhQ5t3PmzKnKDItdsWJFdAVNiFkqaO6WmoVrcV1q+mCutSeffLIqc06406P+lvOlzwbDf7kOdPwYjqjnZUgfzcO6RhiOSOmEa0jR1Muck2xXz2xHP7ZlzyrHJ5MJM5mV58lCILP+NO1kmu3YqPPAOeHzp88u7zkb5yz1ciZfN81tNgZce3psJtdmkiuvw2cq28WzJ9iSYIwxxpha/JFgjDHGmFr8kWCMMcaYWnqtT0KW4pb6qepA1Mapg+qWuNTqVOulv0K2He2ECROKthkzZhT1YcOGRVdo/6h3MYQmC81THZY6XqaNMTxSt+hmuBbDdjINUn1BqJdm26s2pcNWDZn+FDr32TbbvA7HS8eS/gAcd/0t71P1+MmTJxdt3GpYdcdMh+V1uC6zECyGUul1eM3hw4dXZfpl0AdHr0mNVsMlOe/0B9Cx5tbV+pxwXXIN63k4fxwD7S/nT9uaQg61ne8gfc9wfWehb2zL/AwyXb3J70Bh33VMeM3sPNl5M7+eiPIZa0rprmQppdnXzCehKU2zwvWk88tr6nrK+hpRPnPZezfzU+kutiQYY4wxphZ/JBhjjDGmll4rNzzwwANFXU2TahKPKKUBhovQVKqmSYbeqPmaZiSGmml/aH7lb7Pwza6Oi+hsSlJzFc1Tat5niBjNqHodmuw1lJK7BrJ/agZj5r999tmnKt91111FG+cky16pGfsiytBBjruObWb2jsh3HNSwIs4lzddqmly0aFHR9nd/93dVOdvxMKIcdx5Lc2OWGTQzsdKMyjFR1MxL6Y3mfu0vx0t/S7Mtx0B3rWRfu+pbRG4G51rLfpuFuzZdU+eEx+p5mkJq1Qyd7brYFI6o/ct2S2RfeZ5sDFjv6ncR7WV5zGjnt9mxmYSQ9Z3/9mTPNXeI1HGn3MCx1HbKafpMcY30BFsSjDHGGFOLPxKMMcYYU4s/EowxxhhTS6/1SdAd6iJKzY++BFkYGrUnTTebhTHttNNORRu1H00hq+mAI/LwFmqtqkVR8yeqf2UpbbPxiSjHKAuPYhghtTHVV1VPjohYsGBBVR41alTRRq1Ox5b+FPRR0FA4avXaH84714WOEdtU+2XII+dIx4RhlrobaLYzYESenpupxVWTpE9JFibHa+pYUmvVOeHvMp8EhrMpWXppnpfXVLLdSCPKMeA6oIas98lx1+s0hS52N2Vy0zOua5jXzN4V7eyaq2Th5BHtpUHWvmcpm6m/txNy2NU5636n7VkYOMeAZGnjuYaz0MrMH41t+lzz3aHvT24X0BNsSTDGGGNMLf5IMMYYY0wt/kgwxhhjTC291ieBaWtVt8q0Q8Yh05cg04xUB/3xj3/c5e8iIgYPHlyVp0yZUrSp30NEnqoz21q0p/HW1PXpo6DXocaW6fGZBkn69+9flenbkKUH5jkfeuihoq7naidOu5246Ha25FXoH6D3yfwd2VaxzF+Q+VPwPAMHDqzKQ4cOLdouvPDCon788cd32b8sPp4a7s4771yVuQW2jnsWCx5R+pjQx0XnnfkxuHW1rlvm7+BzrD4U1OP1WL5HOCfad46P1pvi2jPdWueEY8drNvk+dPc89CNR2vFf0Dr7lq0LHpv5v2RbvnPcMz+2zNehyRdF1wF9CbR/fAfSv0rr7Ls+G7rde0TEuHHjol1sSTDGGGNMLf5IMMYYY0wtvVZuyELEaA7SkBCaf7Jd4GgeVhlDU+pG5LsIMm0tTUBDhgypyjRtZWGNPFavw9CbbPc4yg/ZWLaTslVTVfOaGlJHE7SaxCPKuV6yZEnRxnBJlSN4X9qHLOyTZLsuUv7Iwpqy81DW4XjpeSmncQx0zTC1sY7l3Llzi7bjjjuuqGuYarazIsOs2D/tA9ewrgOah/lsqolVd6GMKOXH0aNHF200M+t5uYZp1u1u6mXOX5Yqm6bkLBSPZM+x1jkH2XOcSW28Z96njmWT3KhjSZkgk52IXofyh16T887+6JhkoeeE75VsR0beZyYxbr755l32Z9CgQUVd/83gv1N639kOw93FlgRjjDHG1OKPBGOMMcbU4o8EY4wxxtTSa30SsnCkLBUttTn6NqhOlPkAMBUudWH1O2DII7VX7XumhWnYYERnzU1DX6iNqRZGbZwaqd4nNW29ZpY+OaLUDseMGVO0aejinnvuWbTdf//9RV11NY57FsqVpeBu0j0z/VQ1yGwdRpTrjdpvtlUt9V31N2lKf5tpm7oumA6b60n9ENhXPZY+JAzR1HqWkpx+NJwj9XGhNq73zDnIxpljmaXRzXwS+M6hbp2RhdBlZKG5HIMsTXM76YCz8GTeM8dEoX9A5i+UhQPqmogofRSyZyiifD9kc8vz8L70nTRy5Miijf5nei98t3Y3bTX7R3QesnDt7mJLgjHGGGNq8UeCMcYYY2rptXIDzc5qVslCzQhN5FmWQEV3yKs7j5pgaYKi2UvrNKOq+SwLs4wozWA0n6nEQSliiy22KOpqBmN427x586oyTdm8r2effbYq02SoYWpPPfVU0bbHHnsUdZVraBLPwrcy0y3Nde3s2qdzzeOyDHDZ2qI0koURZiZ7XpOZCXVOuJ7YP10XXDMqIdBET3OsrovtttuuaFNzMc2vXE/6W64DlRu4JjKZh+PO57i72fQyCTEilx+yDIKcW+1PJjuxrWlXyK7g9fle0f40ZUrMJD7tbxbaHVGGXfI9rO8ZnochtVmWx2znR11rEeVzxP7w+dPr8F2fZZYlmYyp953929ddbEkwxhhjTC3+SDDGGGNMLf5IMMYYY0wtvdYnIdt1jWGNqgM1hQZlO5WppkZtlZqj6k3UqXis9j0L2+Pv6Eug7dzdTjVc6t3UxvQ8TIOsWma2c1pExN/+7d9W5RtuuKFo07HkboTZLoe77rpr0caw0KVLl9aWI8r7YugU14yShZpR22WqVfpiKDq31ECpM6ouS22VddX22fdtt922KtOXQFMkR5RrnKFc2h/2nWOrc509b/RlYGjsY489VpV5XxqumWnG7AOfBaLzQH0+C5Pj/Gl/eU1dl5xLjq0+qxyDnvokZOF/Tf4d2fuAZCmluzouonPfdZ3w+dd3Lf1EsjlpZwz4btXnhO/kzMck8+9o8gXRdyKvofeVhUp2F1sSjDHGGFOLPxKMMcYYU4s/EowxxhhTS6/1SWCeBNVzqC9nukwW557F9WY6UETpA8Bj6Xeg12mK21aovSqMs1UdL9PYI0rdkyl3NWUyfRnY9x//+MdV+aCDDiraVNPmNsTUYXUsly1bVrQ9/PDDRV3Hi3H3qnWuWrWqaON4ZX4i6nfA+cm2Keexme5JbVrjrZtyOuh40h9Gt5zlNTjXWmdeAj0v1zd9HTLUZ4Pb4aoPQkQ5BprvIaKcI/ru0C8k0/UzP6R20mjzWNXHOT7aHz5TWTpeXlOfm6b8HUqWR6IdTTvzkWAf+Ex11xeMv3366aeLNvU/4Xmy917mX9Xkc6Pt9INgH3SsOe56n+3k+mjnPD3BlgRjjDHG1OKPBGOMMcbU0mvlBpqOMvNwthtZZi6mmVLNTMuXLy/ahgwZUtTVBMXUxtkulYQm4ew8amZ+8cUXizY10/OeaYrUdp5HJQ5eP9t1bf78+UXbBz7wgarMXR85lnrNESNGdNnXiHL+aKZcvXp1Vaa8wGO7a57l3GVpdLMdI2mWZBrkFStWVGWmeqWZfs6cOVV5ypQpXfaHa4vpb3W8OLfaB0oaw4cPL+o6R7ymjh93Fc2kG7ZlJnuai/VeaI6lKVnDFbOUzU07fGp/OZZZWzsh2lpvZ/e/LLSzSZrU/tLUzvewtvO90k7/ujon+9MUVqz9y3b85e/474K+BzlfmWzQThvfT3qf2fytD2xJMMYYY0wt/kgwxhhjTC3+SDDGGGNMLb3WJyHbZjMLI2wK28v0StWbmOpVtzPmNTUVbkTnFLeqabE/WYpdaqTaB+qVmuJ20aJFkaHn5Xn0vhmGyjA5DUWjX8ZVV11VlYcNG1a0sa6hcAwfy7Rp+kxoHxgCmfkgkCydcjvapvod8PqDBw8u6qrzM63vggULivoBBxxQlRkOqOs7SyUeUYYZZn49uu13ROc50dS5TKOrzwLT3fJZUOhTkunx7Lvqu9SXObb6LLQThpZt3535K3Dssi2Lm1LMZ+h1eA1ta0oPrD4BPA/HUn1KOH/a96ZwUu1DOz5bPDbbBjw7L9F12vSOVjL/JZKld25ae28VWxKMMcYYU4s/EowxxhhTS6+VGzKTHc1eag6ieZEmTf0tzZ96DYZKZVnmnnrqqaLOEL9Zs2ZVZWZRVLMc+8psYxoKR9P/gw8+WJUZRsjMhGoGp7lM75uZLbl7o0Lzvu44yP5873vfK+oXXnhhVWboKU3ket8MI+SYKJRONJw0M6NmYY0Ruek2Mw/THKu7y91zzz1FG9eFjgmlG5Ut5s2bV7RxvHRM+NyohMb1wx1SVebhc6Pri+NMOURN25T7tH/sD8+j494UPqbzx/NonXPJdanm6yzUk2PAdaBrmNJEtrNiFjKetdHsTrlB3wHZ+JBs903eB4/V/vIaur64IyPXcCY3ZNcgumaytRZRzidlAp3PTGrjNbN/77hGeoItCcYYY4ypxR8JxhhjjKnFHwnGGGOMqeWv0ieBOpDqak076CnZzoBsy7SoLLUxz0tUt+J56BOgfaK/goZAUhOdO3duUR8/fnxVpk9CpldyTrQ/WQjdLbfcUtSPOuqoov7MM89UZWqi1J9Vh2S64L333rsqX3/99UUbfRJUc6fmp7tAct55bLYjm44P1yXrek2Gk+r4RJTa69ixY4u2xYsXV2WuA64vnTP6Eqh/wI477pj2Xe+bqZ+z9LJ8xrQPHAP1ceF5+IzrHDXtOJjNkfodNIUK6n23k2KXfjQ6lutDb65Dr6mpuSMiRo0aVdT1HcRnkX5aOga6ngnHgO8gvU6Wmppw7WW+ajrOWfgh+8c1wrnOUl5nvgSZ/wL7k62nnmBLgjHGGGNq8UeCMcYYY2rxR4Ixxhhjaum1PgnUc1T74fahqr0yvpp6k+o51IX0mtTbMi2Tejdj/ceMGdPlNfVYanPUmzTOnf3TvmsOgIjO+mCWipb5DhTq1jom1Jc15S9T9TLGXPXCxx9/vGhjSmK9DvXchx56qCozjfanP/3pon7xxRdX5UyPz7TCiM7rQtH5o5ZJfwr1F5g0aVLRpr4WEaVPiebgiCjXAa/J+1Ttl2tGfT84BlynOieZRsqx4vxlOUM0lp5tWX4M+pDQzyZLi5zlSci0cY67XiPbtj2ifJdla4vXz3J08PlXfxxeg748Rx55ZFV+5JFHijamn9f8GczfkeUMYR+6mwcgS3Mckfuq6XnXZ9rjLO1/d9vYP65Z9SXie7cn2JJgjDHGmFr8kWCMMcaYWv5q5IYsxaaaSpl6luY8NSFmZiWag2nWUfMnTUfbb799UVdzkZrhI8r7ZBghJQVNI81wJD0PzXc0M+ux7Kua2hkyl4WT8poqMdAczLAr3QVy/vz5RdvSpUuLupotGZ6o48OQJ4aB6pzwPHov2Q56JEubyzauU11fTDd7+OGHF3Xt+/Tp04s2nU+mw+Z9ZiFiWRhaU0pZRc+rYYwRndeXnpcmcp2TTIpkndfgferapEk8WweZqTszHXMs+RwzbLUrmkzi2ofM1M/U3QceeGCX7ZoWPqJz+K2+v3gfOl5N6cuzd5meh3PAdann5b8D7YQRZtIE6e4uw9ma5W+Ztjoby55gS4IxxhhjavFHgjHGGGNq8UeCMcYYY2rptT4JWYhP5h9AvZLhI/rbbFtU/o66mepCTMPMraO1Tg1JdbQBAwYUbVl4Fv0XVGtlyuadd965qOsYcbtsHUtN8RvRObxUj83SYXO+GMKqGjzTwnIsszFR/Zn9oS+Izic1v0zP5bpU3wLq3aqDcgzobzJw4MCqTH+Y2267rajrOtlhhx26PA/DGhmKqvPJlLbtbFmcpUzX9Z2FTkaUz0a2NTO1Zz6rGsbLZ2rJkiVFXZ8N3le2lTZ9JrLQ3Ez/ZjiwQk07W/scL+0v/V90rnlffB9k2viKFSuKus5LtkU35491rhMlG8umeldwHfLfBR139q0dX5UspJZkaZkzv4yeYEuCMcYYY2rxR4Ixxhhjaum1cgNRkwtNLNkOhER/m2WryjI1RpQmcp6HuzeqaZJhYHoemnwzeE01W2pGNbZFlCGRHDsdH4YqDh48uKirpJDt1kZzIuUGNb1TuqHpXU2nNI2q3MAQrEWLFhV1Hb+muc7a1PyYhe0R7nK47777VuVbb721aJszZ05RnzBhQlXef//9izaVEGiG59jqPFCm03XRlHVSn03es5qzaa7urlmZ/WN/eF69T8pVXMMqzXGdangi1xOfPx1rPlNZlleaq9UknZm9m3bU1Gchk0o4B+28gxheqs8xw20zE3m2G2+T1KVkZvls90bOAZ8F7R+P5ZrpbpbMdjIukkwq7Qm2JBhjjDGmFn8kGGOMMaYWfyQYY4wxppa/Gp8E1YWo66uuRk2Nmo1q3AyPynazo86o2lSWQprnpdakWid/l+1OloVD0SeC96JjRD1QtTHu5EZNW30buPOljgnHh3Oi/bv00kuLNo67hqVxfNT3oikcSn/bXf0vorOGq/fCEEP1N/nABz5QtO26665F/corr6zKZ5xxRtG2bNmyoq4aM/VmnU/2lcdmIVk6Z9Rds9BFaqs6f5lWz+tk1+AzTp8b9bVg2mPOtY5RltY305rZJ673LBSPbXqdrK9c+/SH0WeT74PuhtdFlGP5zDPPFG0abtt0XqWdVMKZP0yTP0C2LrNrtNP3zJcgm9smP58sRHJ9pGJWbEkwxhhjTC3+SDDGGGNMLf5IMMYYY0wtvdYngfqSar+M39cYZW6LzGNVn6O2Qx8FJdsel3pglgeAeqXG/TdpyAo1LB0vapBZ36mjq+a/4447Fm3Ud7V/+jv2gePD3Ac6RzzPpz71qaI+a9asqvz4448XbaqZ0meDY5vpepkPCXMP6Hm49nSbXfoVvOtd7yrq//AP/1CVua01dU9dX0yVrXPCMcj8T9im58m0XkKtVceLuSGoaeszzmvq/PH5oq9M5mNC9NlgbL/2h+NDzVjHmsdmW0VnGne2nTDXBM+j88ccD5nfA9Fnd7vttivamnyoumprR9fPztO03XJ2n5mPSXYf7WzRTXTNcP1kviHZeDktszHGGGP+ZPgjwRhjjDG19Fq5gai5kaajLD0wzcNZyk8NY2oypWVhhDTha+pX7hCnJk7uDEiTWBYWozuyaehdXd81hJShi5rmlzLBE088UdT1OgxD03HnHNAMvmDBgqo8fPjwoo279mkqWO7smJl8sx31aLLP0p7S9KdzxtC8E088sSofc8wxRZvec0S542Y2X+SFF17osm3cuHFFnTKP3jfNpLoum1Lj6nhl4WSUfLIQtsz8yueCoZV63kweiijvk3Ot8gifW5rwu5tyl2OX1bMwOd4H50j72855SCa9ZbJKO+GIWT1bB5Rusx2A2Vd9/jNZl7QTWk16KhNkEsb6wJYEY4wxxtTijwRjjDHG1OKPBGOMMcbU0mt9Eqhba/gdddgsxS51ftWmeB7V8bJtY3lNhgZR+1Utltur6nmprWZafubbwLYs5e7QoUOLNg2/GzVqVNG2xx57dHlNjrvep4Z51vVv/vz5VXnvvfcu2lSrjyi1YK4RvU9qhQxP1GM513os+8pjVc/kNe64446qzO2feeyBBx5YlbfeeuuijetA02UPGTKkaNN1yfXNa2qYahZy2LSVbqZFq57KEEOiY5v5SDRtyZ1tS8y6rgOOj/oo8J4znbidEMwMjruu6WyL94hy7vnuylK68zxZ+DTvMwvby7Ztbmcs9bz0M8i2nOY96zOV3QfrTUHB7cMAACAASURBVD4Jes1sC/qmMNDsWGV9rDVbEowxxhhTiz8SjDHGGFOLPxKMMcYYU0uv9Umg/j1z5syqPGHChKJt1apVVZn6G1O4qmaUxfJSg2QMvJ6H+iBRbXPw4MFFm6YkZtraLEY/SyuabXkbUd7b888/X7RpTL7mXojonO5ZcxpwDPQa1AN5X3rs0qVLizb2T49lamP1X+B56CeiKbiz+5o4cWLRNmjQoKK+5557VuXp06cXbSNHjqzK9EV573vfW9TnzJlTlbfddtuijetC1/iTTz5ZtGmKYuYlyFLTtqNFE9VPOdeq82fpgSNKnZhrRP1a2LcsFTThNdW/gf4nmvujaVtifcYyzb9Ji87IjuUa1lwtmqclolwXTflEsvwUJFsz2ncel+W9YcptHdumLZ6zrb7b8Q/IdP92tpXOfBuy32b94TPeE2xJMMYYY0wt/kgwxhhjTC29Vm5Q82tExNixY6syTcdq0qRpiOYYTS1Mk6Yey9/RLKcmTYZk0fSupq4ddtihaFO5gamNmS40C4FUsxzTMmchawyTUzP8Y489VrSNGDGiqN97771VmamN9bxZ6uCIciy5syPlIt0lUsMGI0p5hHPA+dRx59xmYakPPfRQUT/88MOrMncR3W233aoyTdCUCXbaaaeqzDXCVNUaIqnho7wO74t0N1SwycychSBTZunqdxGlWZXzpW1cExzbLCSTY6L9y0Ki+UxlO0/yOc7Gsp3wvyxslxKLSrDsezvmc61zvngv2qcsTXuTxKLhrpR5ta3pPNkukN0N22W9SeLoLk1hl5ncoPDfsJ5gS4IxxhhjavFHgjHGGGNq8UeCMcYYY2rptT4J1LhVl2GYo2ph1N+p3Xf1u4g8JIyoDkp9ieln9bwMR9RwN/aHerjqpwx5yrZFpX6qY8kUwBpqOmXKlKLtqquuKuqa0pnpr9V/gamfOSfLli2rygy7pHb/wx/+sCqfd955RZv6GRBqdwxFVXR86BfCtadbPlNH1/tk2/bbb1/UtZ2hgtdff31RV/8czp/OfVP62yzFbRayxrqOLf0D9Fng77hmVH/Owr7ok8S06Pq8UatftGhRUdcwWj63mT8Fn+Ms7FH7zt9xTPQ8mX8AQ4P5jOv7i9fM/AyysL0mnwSdPz43Op9N78vubjlNsjWT9b3JPyCjHZ+E7Nh20n7ru4Jz2xNsSTDGGGNMLf5IMMYYY0wtvVZuYJiTkoVH0UzDHQgVmvraMR2pibUp7FKvQzOhmrZocqKJXM1yNKNqneehiVxN7dxlUU3Z06ZNK9qYCVD7w2tqKOMzzzxTtHF8VFqiNDFw4MCifuqpp1blffbZp2hTCYbjQ+lGr5NlgKMZXjNSRkTcddddVZkhorr2GIbGOdH+Tpo0qWijjNLdddq0Q5y2c7xUKslM0BF5qKX2nXOw8847F3V9drmeNMyYpnWeN8v8x3HXNczMlvoOovRAeUHrNJHrvWSm/4hyTjh/eg1KNVnYNdHzUhbIdl1sWnc6tpy/LAw0kx/aCTnMZINsPJqyjWam/+zZYH+yLI9ZFlGutewaPcGWBGOMMcbU4o8EY4wxxtTijwRjjDHG1NJrfRKYIlW1PGqSqqcyNe6zzz7b5Xmp56i22qSFqeZG/Y3HqgZPfUm18SVLlnTZH9az8CzqW5qiNaIMVWJfNRyRfiFMtaq7y9HXQjVthvQxjbX2l/fMUFhNdUztXs+jvgIREaecckpRv/nmm6uy7tYYUfpecB1Q+913332rso5dRLkuGarI+9K+0weB4a6ahjzbxY9zy2NV+9V05RHluqSOnumgbFOfEqZaHzVqVFG/4oorqjJTU6tPB++D/dMx4LNAfxhd03w2ta3JX0j1ZvYnCyfl3Oq7jc+bnodtHBN9dnlfWV8zf44m35QsJXimx7MP+n7I0uE39YdzpqiPQlNa5nZSOOu6aEqL3tU1eN7Mh6MpZXp3sCXBGGOMMbX4I8EYY4wxtfgjwRhjjDG19FqfBOY3UH2HeqD6GVDfYgpg1XCytKft5Eyg5kctTPVD3RI4ovRDoK5Pn4Bse2qF2hy3W9Uxovar/guZPsn+qU4eUepm7Ct1NNWbOX+sz507tyoztXL//v2r8sc//vGibfr06UX9gx/8YFXmfKluTc2ROuPy5cur8ujRo4s29UNgDD7j03VM6EOSrdOmlMkKx1J9RbguNbcFcyhwDPSanFt9jpmKmul4VZ+n5q5aPfVb+olkKYCZd4Njrej4NKVh1jnhetLfci6Z70DPy+dY56HJZ0rniM+fru+3sp0415q+Z3hsNgb0E2FdyXLiZMfyPrOtmLNcFk0pnHVM2smvkPlB8DlpZzv47mBLgjHGGGNq8UeCMcYYY2rptXID06eqmZCphPfee++qfO+99xZtTIerpkmafBWanGhG1RA2hl3ShKmmU4YuZhICzXkaMkZpIus762oOfe6557rsD83MNLXpeZ566qkur9kUiqeSEPvDvp911llV+ec//3nRttdee1VlppD+H//jf0RXcB1kZm+iZnCOl0oRt99+e9HGEEg19/M8DJ9Ust0HuWazXU95HpWP2jHrZqZkmmYffvjhoq7rn+GkutNjJndElCZ8SpOU3rRPDD3V83Id8D6171laX45lFj6dtTVJgXodmqv1t02yahZSSzLTtz5jXGu8F33m20nLzLHNdsLMZJSm3VN7eqw+C1yXWTgnj/UukMYYY4z5s+CPBGOMMcbU4o8EY4wxxtTS0WoSFP9CYcrdHXfcsSo/+OCDRZvqz9TGqTeptkh/hex3RHUi6pzUElW3pj6o2u/SpUuLNoaM6b1R/9Nr8r5WrFhR1FXjZviY9jULG4oow9uo5+pvGdLE8crCORk6qGFp73vf+4o23XqYWzrT70DHiHOiYZYMoSX6W4azTZgwoSpzLBniq2ObpfXlsVna4WzLcta53jN/Bfo66G/ZVw1PZgpiht9q/cc//nHRNnHixC6vz7nOQt/o85Jtyatz1JRKWJ+jbKvopmdKf0stWvvKNZv5n2T+C03/PGRpf9sJIdcx4DmzbZOza/A82brM1nfTu76dUMYsxD4bg4wsxTX7runUu4stCcYYY4ypxR8JxhhjjKml14ZA0jSpIWM0w2UZqGgG11AqttG8r9BErnWamRmeqHIIzftqjqV5isdmmcg0ZJRjRxOUZnmkOV9NrDTRMwRS+85jdY64C2SWoZJSDedITdKUKTT0NJvLiIjf/va3VVmlrIhyDXHHUZoJ1ezLcdY2zWAY0dlcrfNHE2I7uy7qedlGs7POWbZjXpM5Vq+ZjQ+vT2lQJaDhw4cXbdnaz/reJN3ob7OdHbM5iCjDVrMMeZl0xDrPk5mZM1k12zGySZLS8WNbNia8z0zyyMIcOT7t7MiYkYWlZudpkkqy8zC0WcnCyzO5b314E9iSYIwxxpha/JFgjDHGmFr8kWCMMcaYWnqtT4KGj0VEPPDAA1WZO7mpjk79m+lvNQSKqZ9V+6EeSJ8E1ZBUm48o0ydHlNpv5pNAfZDHqq5HDUu1c56HaaJ1TDheqldmWmZExLPPPluVd9ttt6JNNXiGEWYpr5vSsKq/B8ddUxs/9NBDRds+++xT1NVngSGj6tPRlAJYfTqojWvoKe8rC2simY8C10Gmo2eaezv6N8+bhW/qeLGN/jCabp2pztX/JNP82T/OSeaTwGP1PJnvAPuQ7RRIXTrT3DOtvClFsu7QmoXbZXNZ14f1QTt+GVx7Okdvpe/ZM5S9g5qumflTZGskO0+WUjrzx+kutiQYY4wxphZ/JBhjjDGmFn8kGGOMMaaWXuuTQP1UNVxq9RlMw6r+AVlMN9PmEu0D9WXWVf9miuQshpraWJZyV3X0bKtaHku/jP79+1dljgHn5Etf+lJVPvvss4s21V6ZQyHbupqw79q/p59+umjT+WMMvuaGYB+Y5nvPPfesyhznbDtvjqUey3vM4q05Plk8epYumNfkvWT5DzIdlufNthPWOq+f6bJZmmGOD/OCaDuP5bOZ6bu69prmT9cefSTUP6Apb0NTPoaurp/lyyCZ5p+NF9c+13vmT9HV9evo7hjwPZdtv5z5GTT5XWRpxzOyuW3yg9D5zfJBOE+CMcYYY/5k+CPBGGOMMbX0WrmBpq1sdzQ13WRhgxGl2TAze/F3DAfUa2YhKhFlqFd2Ht6Xmil5bBaW1rQ7mvaX5lfdUY/m4fe+971F/ac//WlVZmrjbAc93qdC8xn7rtIN01/ffvvtVZkhtNxhU9fJuHHjijY1FzMtc2bSZF91t01CcyNDUZXMJNyOyZ7z0JRuuavfZXJWFrbH32XPaia9cQ74TGk7ZQI+UyqLZe8VjjMlBT0P3wd63iykj79txwSdzSX73s4OhNo/jh3HIJOdujouor1QT5V1KDPpjrokM+83hSNmkhTDcbP503qWpppk42O5wRhjjDF/MvyRYIwxxpha/JFgjDHGmFp6rU8Cw2s0LXKWbpZaT6bPU89RbbMd7akpZG358uVVuR2tjn3QMWF44i677FKVGWZJrU7TJDNl8p133lmVv/zlLxdtV199dVHXMaEurKmf6TuQpRLmvHPcda7pTzFy5MiqzLFkKKxqyDo/ZOeddy7qGh4ZUeqyTN2t64L+HfRB0DBRjmWWLjjTorNtfyM6j19XNOmemQ6bhS5S09Yx4jV1XXDNZqGebKOOrXUeq33nOuR8ZqGnOs5NY57Nrb67msKI9djsndiUbjrzcWlnS3M9tp3fcY1k/cl8CzJdv530zjxPO2s462s721Ur3X2GM2xJMMYYY0wt/kgwxhhjTC29Vm7gDn+rV6+uyllYI01QNAsqNNUwxEfJzEE0OTEToJoG2fcsI10GQ/pOOOGEqszsh9tuu21R1/uk2Ut3RPzKV75StO2///5FXfuuuz7yGjT1Z6FBnAP2XftLGWWHHXaoysy4yJ0e1dw/adKkok138eRcUubRuc2yHzK8Lst+2BSamO0GmpmZmfmyq+tH5Bn7SLaLp0onfN4oG2ThiCrlcJy5ZlRCoKyThSBzh8bsd5l0w/vMJIRMUshC8XiNLJtlU4h2V9dnH9rJTMi+a3+znS95HcoomdzYJBt01da0e2T2jLMPWfbY7vaH9aw/lhuMMcYY8yfDHwnGGGOMqcUfCcYYY4yppdf6JDBlq2o9WRs1GmqbqstSP9JU0NTxqFfqb6kZMRQuC4HMdo/jsQMHDqzKU6ZMKdqmTp1aW46I+M1vflPUV61aVZV1V8WIiPe85z1V+Z577inaHn/88aKuY7LddtsVbTp+/fr1K9qyHfQGDBhQtNHvQI/lnGT6N/VKDRlVH4SI0r+CWjTnVtdTFiZLsl3pmvqeheqqNs2+0ych0zP1mk279mW7HOqaZl91HUaU6cuZDnvWrFm154zovJ50XQwdOrRoo4/JsmXLqjLnT8Mus/mK6H4IJK9BMn+BLGwvS3XeTgp33leWDr+d1ML626YdELtLptUTrvV2dqnMwuY515mvQ3b9bD1ltOM71BW2JBhjjDGmFn8kGGOMMaYWfyQYY4wxppa/Gp8E1a24jbTSlKpToZ7U3S1KI0qNq8knQePBNV0xz8NYfqI+AjfccEPR9oUvfKEqn3/++UUbNb8xY8ZU5Tlz5hRts2fPrsrUHBmPnm2Brfo3/RUyzU/PGdF5u2XV3HlfmsMgi3mPKNMr85rz58+vyvTZyHwkmPI3y1mQ5frgmmVuBl1D1PV1bLnW2tGQs7wNrOucML+J1tlXroslS5ZU5Z122qloW7BgQZfXJw8//HBVZprvQYMGFXWOkZLFo2fbLWfrm74WWerszGeE7xyu9+6mHW4aSz1P07s1y5OQpbHPxjJLBd2UFyHLT5P5JLB/emyTb4peJ8sH0Y5PQnZNvnd7gi0JxhhjjKnFHwnGGGOMqaXXyg003So0rWWSQju7mql5Lws7iyjNSpQXaL7W69Dkqub0phDIXXfdtSrTVKtmXZpUeV499iMf+UjR9u///u9VmSFzHBM1kTP9rZp8KVPsuOOORX2fffapyhqSFhGx1VZbFXWVmmiyU7Mcx4ApgBctWlSVs/TcXGuUnXQsKUVk4YiZKZnyAs/bXbmNZkqGsGWhXTrXTPnLNNv6rLKvuoY4JwxH1DVDGWzhwoVdXoOSgcp2fBb5XtF2yo9Z2HWWnjebW8oxDA/W9ZVJVHw2s11FOX9a5zOdSQFcT9mY8Fi9L641rsvsPDon7YRO8h2ov+W/A5kUwbbst1k6bI579m9Ylra6SVbtDrYkGGOMMaYWfyQYY4wxphZ/JBhjjDGmll7rk0ANV3U0atyqaWW+A4SaUZbiknqlaonUxqijK9tvv31Rf+SRR6oydUbq36rXz5s3r8tjNX1zXf90223qp6rnMnyMGqSeh+OuaY8nTJhQtFGbHjlyZFXmfVGzVe2V/dFtpbnFNNPzZlvp8poK71Pnmr4CGu7Ga3BdqlbOMDmeV+870625Znnsiy++WJW5DrKtfQcPHhxdcccddxT14cOHV2X60agPQkQ599Ra1R+HPkDU43UNcwy4LnQMqN3rfWfppuvqivpw8Pr0kdDnOJuTpq2i9T2TaffZVtUR5XPCcedvVSvPwsKzEFHC+cv8aDKyZ6HJJ6Gdrb6z82T/vrSTXlnHL1t33cWWBGOMMcbU4o8EY4wxxtTijwRjjDHG1NJrfRKoh6umlMXV0l8h2yY104yonzJlsp6HWyirxh5RxnXfdNNNRZvq87yvTO/i+GisOPvOePQddtihKnM7aNUyNTad14gotXFqpKop6/UiOueKUH+B3XbbrWhjjLBekz4JmkKZaX2pW2sugixWvCmVcRazrOflfNG3Qa+ZpfXmeXlNXUOZ30NEOX702ejqehGd9V2N/ae2qmtP9f+Iztq0pgvP+pptixxRPquZP0dEeS+Z/t2UN0XvjW3qZ8C1T3Q+sxTgXM98xhRq7pqbhf5T1Lh1vLjWOJbaP/pTZVtFN/VXybZi5vxlqaAzfwb6d+ixvAbHK/Mpya6f5U3Icv00jWV3sCXBGGOMMbX4I8EYY4wxtfRauYGmLTWv0dyoIWtNZl01P9Icq+fV8L66uh47YsSItO9qdho7dmzRpmFfNE8xJFLbaerTazKtL2UDTYu88847F22/+tWvqnJTGla9JsddzZg0H06ePLmoq1wzZMiQoo3jrqbArD8cO6bD1f7RtK3XoOmRZssszXcWZsU1nKXK5W91rLM0upmkQWg21TGh3ME5ev7557u8xsqVK6sy1xNDTTXM8ZlnninaVLagyZeSwqRJk6ry7373u6KNUo6ei1Klridek2tGz8trKLwvwvDgrq6xfPnyoo3mfZXeMlmVEhDfiTpnWRh4RLmGsjHgOBO9ZrZbItdsJiFkOyk2pcPX3/I9l+0C2Y7EkYWTZrQTOtnltd/yGYwxxhjzV4k/EowxxhhTiz8SjDHGGFNLr/VJGDBgQFFXrYf6smrT1M2o9ajOqHppRKlTM8SI/gIrVqyoytTNly5dWtSPPfbYqszwxPvvv78qU3umzjhx4sSq/NRTTxVtel/UaNl31QsXL15ctOkYUPPP0k/zvlTn++1vf1u0UZfVcMVs29+IUsvn+OgaYd+Z6jhLlavj07Q1rNbpi6Lj1aRP6pxxK2aGqamPAMcrCxHL1jR14jvvvLMqH3jggUUbw2Z1rOm/oPfdNJY6t1n6W4Zrsv7Vr361Kn/uc58r2jiW2r/58+cXbbpOqd2zf+rbQ58gheuS61v9SJ544omibffdd6/KTGk9bNiwon7NNddU5fHjxxdtes9cs/TlUb8Dzi19XtRXRX0iIsotufks8J2t6yDT/LMtlCPKOeI7UK/BMWD/1A+Bvih8bvS3XN9Zmu92tqvW++Y7sCfYkmCMMcaYWvyRYIwxxphaeq3ckJkFabJTExRNRzQPaZ2mtcxMyExp2j+aHimVaFjh+9///qJNZQOaxGlKVtPf7Nmzu7wmd4Gk6U9NnDSj6jUp6zBsT89LueG9731vVaZpjXIDzesK14Ga7BiClWWo1DC9iM5jreh5afaj2TLLsKa/5dgx7ErXXpM5VuePx2YZ+2gu1ix9c+fOLdp0p8fp06cXbVyX2nc+b9qfLDQ4opRD1DzN8zK8btasWUX961//elWmNKIyYURuHtbMhHxOyF577VWVKSHo+4prlM+YzhnloSeffLIq77fffkUb71PniHKfrm9KbQz51XcJJQ2Gfut5uQ70/cnxyXaFzKQIwvNkO73q2uOzyHWZ/ZuRhWhm8kcTvJeuzkPJpyfYkmCMMcaYWvyRYIwxxpha/JFgjDHGmFp6rU/CL37xi6Ku4TXU3FWjob8C9SbVcBhCk+2ulflIMOSQKVPVZ4Ka1sknn1yVGU5z1VVXFfVly5ZVZWqJquNx10fVSyMibr/99qpMDVL717RTmY617uAXUWqQ9OeYMGFCUVftlSE97IOOJVOkah8YlkqdUccr262N12DaWtXZszTWXIccE22ndk+075lfDUN8OZY699Tjn3322S77zvOqjwD7k+1SR/8A9YOghqzPPHVpPgvq50Nd/4gjjijql19+eVWm5q7pwj/zmc8UbXzm1WdBn6+I0heEvjBc7/oOoC+RrlP69XC9K1zDOic6zxGd00LrOyd7/iNKH47sect2yYwo1xufN/VRyFItR5TrvZ1dH7MUyfSRYP+yHSyzvpNsF0iFfe8JtiQYY4wxphZ/JBhjjDGmFn8kGGOMMaaWjlZ395z8C+PjH/94UVetlelKFcYdU0dT7S4bGupk1JBUN6N+St8C1WkzTYs6J8+jsc88j2pT1APpI6Eabpb+lnkjeJ+arle3540oU9zyvqjjaUpbxqOrzhlRzuf2229ftKk2zljsdnwSsnTF1NwzDVLHj+tStd6IfFtp5jvQ/nGd6jpg35kLQbdmfvTRR4s23V6c64BrT+vMl6H5KZruS8m0e/okcP70mtS/mV9Ef3vccccVbd///verMtOXMw+A9ilL1cvcAvSvYn4IReeBzwlzR6iOzTXC+euqr+wPx5m+M+pDwVwx+hxzbnlefRayXANsa2crZr1G1tZ0LOs691nq5SZ/Lz0v2/S89DfZcccdo11sSTDGGGNMLf5IMMYYY0wtvTYEkil3NayJoUG66yJTxi5YsKCoq3kmSwfKXRYZBqbmIJoIaWbKdqlU07+GeUZ0NuHfdtttVZmmPjVns69MSaySC0OeNFUvzaa8ppr0eV8ajjhjxoyiLUu5O27cuKKNoV577LFHVWY65yzVMuda5y8zL9IsyLHV++a8qwm4nd3/eE2mU9ZQPfZd1wHHjrLB7373u6rM8dEwx6Yd6tQcSrO8rmnOF8eE9a6uyXA/mtr1meKaHT58eFHfc889q/L73ve+ok1DkC+55JKijWtN3yuUXLSuYx7Redx1/iiVZOuS60DJ5o9rlhKQHps9QxHlOqCJXOUY9p196Or6hP3JQgXbSZGche1m8mJEnuZbaRrLrE3rXPs9wZYEY4wxxtTijwRjjDHG1OKPBGOMMcbU0mt9EqghacgP/Q5GjhxZlRnixBA61XepL6uexDTM1CC1f9SMsxAjojos9dz77ruvqA8dOrQqU9PS87A/1Cv1t9Qg9T4ZmpRprRwvnQeGeVGPVw353nvvLdre/e53F3UdI64Dva8mzU/vLfNJ4FzyvLpmuJ409DNLYRtRpmluCrPUtUefG50HpsrmeX79619XZYbmqR8L/YOykFGmbF60aFFV5vrhsZpOPAvx4/jQ70DXBcN/dbvliIj//M//rMrnn39+0fad73ynKtOvh2ma1YeJIdraPw07jSj9qSIilixZUpWZXn2nnXaqyllIL2Gbrm+u5yztOMc5mwe+v3X+6OuUvZ/Yd32O2daOD0A7fhDqo5ClbG4i85nItrkm2pallO8utiQYY4wxphZ/JBhjjDGmll4rN9CsoyZpmsgz0zZDGdWsk4WWMEsZTfjaTjNcFjaXmeEIz6uhgjStaaY9mvNp6tZrambEiNIE/P73v79oYzYvnQea5XW8mBmRx6rJ9Zhjjina7r777qKuZvrM3MhxpllOx4umPT2WpnaanXU98Zran2wuI0qZh2Zcoudl/3SOaPaeOXNmUVezb5aplDJKttsezbh6Hj6LHINMutExYQZPzp9mluQuhzRta2ge5Q9dp4899ljRds455xR1nT8Nq4yIuOGGG6ry/vvvX7TxmiqHMCTzzjvvrMoMI+b6UtmJ49zdbKM8L+eWmS/1mc9CMvk+yvrAZyoz2WdhhFkIe7aeI8r1xTHI/g3JQkR5z92VF0g2Ht3FlgRjjDHG1OKPBGOMMcbU4o8EY4wxxtTSa3eBPOWUU4q6hoitWbOmaNMdxxgCuWLFiqKuGm42NNTNqH+rVkcNmfqualNMtaq6Z9NuZKqrsU1TVdMnQccuokzPO3r06KJt/PjxVVlDrurqmvaXqXJ1TOh3wfHSlLbUWtV3ICIPs9Lxa9qxTvV4+puo3wPXQaZfUqPV33IMMs2W40P/GF3DXDPTp0+vynPmzCnauA40ZTL718661GeDmq2u2Wz31ohyzphCWn2SGMbIkDp9xqjn0h9G54zrW8M39frsa0Tps8BraEgmfRCYFl39d+h7ke0QSbJjdf44l00+Chl6LH+na5jzxWdcj+V5snTqWQgk50Svweuznu2oyf7pvXHtZaGnRJ+jbA1zLL0LpDHGGGPWG/5IMMYYY0wt/kgwxhhjTC29Nk/CwoULi7qmjX388ceLtlGjRlVl6je69XFEGTdNPUn1yUwLiyi1aPoZZNu4UmfU8zZtoaraPf0yNH6fuhn7pxo8dTyN92baY271q+fl+Oh5qY9mY0s9Pos1pnaYxX9naVk5BroOsrh/wjbtO9vYH71v+rRwTDifiq4vpiTea6+9irrmTci2Taeem8Xds6/quQLyQAAAIABJREFUk8AcExx3nTM+J/pb9ofHqn8F5y9LQ8yttbV/9E3h86fPLrVyPZbX53k0Zwh9JNSnQ32QIjq/566++uqqfNRRRxVt2r/MVyeiHNsmfwW9t0yPZ1u2rTTHS6/ZpOvrnPGdmKVlzvKmNKWx1ncrfcOyfAtE116WYp75H3qCLQnGGGOMqcUfCcYYY4yppdfKDTTDqelUQx4jIu6///6qPGzYsKKN4W1qQmfYnqaNVdN+RGfTqJqLGD5Gc5X+lm1qMm8yZamZl6Z2lQJo8uUOjWqaZMiMhtfRpMldKXWMMpmA4WMZWahSRGn6yyQOjh2lHK3TbKomvCykr64PSmZ+pfk6SwGsoYo8F8+j/eHc3n777UVdnwWGCquZmffIa2qd60D7mkk1vA7XgUosfBY5J/pbSjNZem7KPPosZObziFJS4/ioVNKUclv7zudNn6OmEO1ly5ZV5Xe9611Fm44Xd9vk+Oh7mM8i35HtjLvCsdVnM9sFkvOe7SaZpXfmezers6+8T5UY2L9sN0neZ7Z9QDY+PcGWBGOMMcbU4o8EY4wxxtTijwRjjDHG1NJrfRLoS6Da2eDBg4s21Wyo1Y0cObKoa7pX6rAa/sfrZ/ob9dMs5S5DjPTYpm1RVffM0qlSp5o3b15R33XXXasytxrebbfdqvIDDzxQtDEdrqYv5nbQY8eOrcpMV5z5C2QpWiM6j7WSbf/K+VO9MAvlappbbefaY98Vph1++umnq/Jhhx1WtH3rW98q6uPGjavKHC/1j2GoIvuu659rT3/L++B8Zj4Set6mLXmzdaA+EpzLLKSWPiXZs0ntV+eW/aGWr8fSR0mfW53niM4hiDp+HGcN0WR/uJ60nWNw/fXXV2X6ZTHsUtca/cQWLFhQ1PX9ybBnXU/U8fkOynxB2gkjzHwSlKa08bpmsrBd9o/rqbvbyvOaRNda0xh0B1sSjDHGGFOLPxKMMcYYU0uvlRu4Y5yG4zHzn5rsaH5hJjI1+SxZsqRoU5MPTazMFpeZlTKzZRYCRfMwzXtqZs3MXmyjOW/MmDFVmVkVN9tss9pz1vVdf0sJSM2mAwcOLNoYGpTt2peFObF/Ovd6H3XomslCp0iWXTMLHyO8ps7RTTfdVLQxo6CaobPQRZrEObZ6bDu7VJJMMtN6k5ymzw3vuZ1QLz0Pf8fzah+y3QD5HuFcq4zAd5eGVlIqybIN8l2m64n3cc899xT1Y489tiqrvBBRSop8NrlTqL67+B6hpKB94n3p+5TnycL/+PxrG8cnC2/N5AZKPuyP3ktTmHrWlj0L2XuP/cmyMfYEWxKMMcYYU4s/EowxxhhTiz8SjDHGGFNLr/VJYCpf1cOp9agGSU2NOvo555xTlYcPH160HXzwwVX50UcfLdqoo6ney3Su2a6Cmf5GbSzbuZD+C9rGcCi9r4gyBHL06NFF27XXXluVJ02aVLQxBFLDRDWldUQZEslQriztaRY2xDrbVPdsSrWqmiDDHLNQpcwPgnOr52WoGX1cNJxswoQJRdu+++5b1KdNm1aVVV+OKMPkuEYYfpfp/DoP9G3g7nbqp0GdOAtZzfRchlKq/s31xPvMnjf6HWgYL+dW/aA4J//v//2/oq6pz/X5iijTbPOe+dzo+4p91RBD7pK7xx57FHVdX5wTbeNYMmRcr5OlIGf/Ms09S1dMOF76jDfp+npvWTgyx4f3mf02Symd7aya+UjwWD4Luk4ZUt8TbEkwxhhjTC3+SDDGGGNMLf5IMMYYY0wtfzU+CZm2qboiNbUvfelLXf6Oepz6BOy8885FG1MUq96Uxc5HlJoX9S89D2PVGQut2hjzG6h+SW2VMd6PPPJIVZ49e3aXxzJen9r4oEGDqrLmXogoY7qphVNrzfwMSOa/oOPT5NuQbWGcxTNTI9XfUv9WjZbbP2fblI8YMaJo4zo95JBDqvIVV1xRtOnYcotwXlN1/syXgD4I1JT1vtlXHb+mFMn622x7cfog8L70OWbfmadAfQC4NfoBBxxQle++++6ijfkFdK71fcS2pUuXFm30Sdhuu+2qMt95uqb333//oo05OebMmVOV6Xul80C9ff78+UVdx4fvFY6lvq/4jGdkqc+51rTvXD+8ph7bjo8ExyR7J/Hdkb2fMh8g9k/vhXOr1+Ba6wm2JBhjjDGmFn8kGGOMMaaWXis30AynphuGCqqZkuGIhx56aFHX3QkpE2jYI8NOst3IaNZ96KGHirqGT1FC0OtkoXjsL01/anZiWOP48eOLuppVKTfMnTu3KusOcBGdzWVqxmTfdXwYPkpzsZpjs/NElGa5LB02+5qFHPE8Os5NYald/Y7H0jT77LPPFvU999yzKv/qV78q2vbbb7+ivmjRoi77p+PHMMsszS/vS82dbGPKaw2RzHalbNr9L9vdTs9LKZCSgt4XpQiGSOvzSJlHU43zPcIwY03xvnz58qJNx2vHHXcs2igbXHfdddEVOpacW74PzjjjjKqcyX18H3EsVZLiOzEzgxM16fN5W1+yRbYjYiZ18RrtpADPyJ6pLEU665SWdV3eeOONRZtKkd3FlgRjjDHG1OKPBGOMMcbU4o8EY4wxxtTSa30SGA6oOla21TBDsKj1qEZJzUj1SupS1M1UJ2KIEX0S1F+AeqXeC++L2p3qjtQgM9+GefPmFXXVEqkrqm7G648aNaqo6zbFWV8ZqqQ+CO2ic8Y50j6wP1kIVJY+ldoz9UE9D9eaXpPhder7ERExbNiwqjxx4sSi7de//nVR13ujP4ymyqb+zjHRZ4xhX/R1ULi+VMvX9NIR+TjTJ0HD7fi86VguXry4aKM+r/0ZMmRI0UZ/GN3WOQvt3Gef/9/emf3uVZXt/37/AJlaKLQMpbRQGQplEqmIQxyQAxIPROOBiXFISDzwLzCeGg/QxESNBybGRKIQoxIlMomIODAjQydKKaVlKIOcv7+znWt9up5rPfuLb/J7zPU52jtrP3utvfba+9m5r3v4YNPGudQ0zUzprinKmT758ccfb/Y1pTPDJTWsUUMlq45Pz61aNe+Xzi1Dl/le0Xcr54c+CvrucCHrXFt8bnQM7jkepTbW39IHwIVHjs67qI+qds3wvadzwnTKnEt9jnkefa7X4oNAYkkIIYQQQpd8JIQQQgihy8rKDTQPqcmF5hc1HVGmYGY0NWlqKFlVawaj+YdmZw1rojmfaIgYzXBq2qLJl6Y/NecxDE3Py5AeHqsmVx572mmnTdsMNdO2qnaOGHqqZjhel5rSqloTnQtrrGpN1i5jpsuENkLXEM35NAGrjMB1qRU1uQ6/+c1vNvs//elPp23KKGqurmrnmnN57NixheNxIZqcZ50/rhENwaqq+tOf/jRtf/jDH27aVN6jqZ/PlM6tZvOsaqUujofmYTVfs41ykZrQGS7pwm0Jw4UVlQkeeOCBpo0hhzt37py2KauoJMVniveW603Ra2FoICUF97yRZaunjs7jJCo3du47yVP32Qff0U7mpWyga9OFZBK+r/SZ57rU7J+UJvncLEMsCSGEEELoko+EEEIIIXTJR0IIIYQQuqysT4LT46lJqp5DPYnhNaqDUm9WPZdQR9OwK6aQZtjVa6+9Nm278Bpel/pPVLUhY04rZ4gRz6tpWhmOqBo7NeO9e/cuHM/In2LR76panw1336va+WObjoH3a45vg877I4880rRxvnQ8XGsaCsv0u7fffnuzrzo//Qy4DnSN0xdE773zf6lq549rRjVbjodhjl/4whem7b///e9Nm4bbMWyPuvkHPvCBaZuhuarLsvIdz6vra+RPoc8q0xc77ZyhzHpe9qEVZLmerrnmmmZ/x44d0zbD2+66665pm/eS/h7q68BnU6EWzjXjUhRzbtWfgedVvyhX9bGq1fKdL9GoWqPzO1jW74Hj4XxwDC7ltf6WffIZ0/k6ePBg0/bQQw9N27pe1kosCSGEEELoko+EEEIIIXTJR0IIIYQQuqysT8IoLllRfYmaEfMdqL7E2GLuL+qD53Ux5lVt3L3zSaDezdS0qvkxN8O3vvWtafuHP/xh08YSuDp2plpWfZf9u7l18cLU7Y4ePdrsU5N0farPAnV0vbf0baC+rPeBPhJ6HsYhP/jgg83+oUOHpm1q5ZpXgjk51q9f3+w7PZfapuqZHLsey3l1sevsQ+8fU0rTd0c1U5eemzlMeJ16j+iHoX4rXBNce6rn8jx8xrdt2zZtM0Wx3j9N31xVddZZZ9UiqDd/4xvfWDgevp+Yh0NRHw6dj6rjS4/rWuR7Rf1Y+CzSv0PXjEttXNX6QfDZ1HXBZ9GlRXfvS/Y/8i1Q9FqYG2LkF+XG4PwXdF3S/4WpxfVaOL6vf/3r07aWBK+q+vWvf71wrIuIJSGEEEIIXfKREEIIIYQuKys30IzqzF66TzMXQ0sUmr1031UYrGpNQDTLs081cbp00zSXcV/NnxdddFHTpml9b7jhhqaNIZpqFnThZG6eq1pTKedLx87f0fyp4W2jUEq9DzQd0+zs0DAsnkfHs3///oX9V7VmeoYq6bUwtSqvS/e5flyVPMoWakrmdTlZhyGHeizDbTkeNZ3S/Kr3hKZ1DQ2uas2xTCWu64v3mamNNfUyU4nv2bOn2deqjOxT7x+v+cCBA82+mvt5b/UZY1poonIEpQlNuUvzNO+1vi85Ht5Phc+qvue4fvisqgTC8bjUxmutwsi1NqdipF7LKGTcVaUk7rw6t5SLOD59NlhVVNfQL37xCzueZYglIYQQQghd8pEQQgghhC75SAghhBBCl5X1SaDe5HQqp3/PCaFRDZDhWi49MPugj4JqnQxnUY2LKXaZtlbTvTL1s9PNqNmqv4cL96E2znCpa6+9dtrWVKFVVZs3b562eR2cL5dG14UfEaZ7dX2qnsrwMdX86GuhZVqrqq688sppmymJVfvlXHKNqD8MNXf6HbjwLbeGmWZbfSjYp/bBuaN2r+GAGlJYVXXvvfdO21dddVXTRl3/yJEj0zbvpc4X5476rvp/aP9VVb/73e+a/dtuu23a3rVrV9Om75Xzzz+/afvLX/7S7GvabYbJaolnl4K4qr02lghXnZolgV1qcT7jLkx2Tnlj+kzpM8U+XRlpV9bdhTm68s9V7buDY13WX2HUJ9+12u7SO3N+XMl3ounxmdZ7LcSSEEIIIYQu+UgIIYQQQpd8JIQQQgihy8r6JLjUnaMcBorTv3geV+Zz2RSfVcfHCKu+6nwA6GdAXVa18i1btjRtHK/CuGiN22Ysr8479UCOXcdHvwM9L++l09HZB++R3k/qjDrekU+L6vXs84knnljYB8f+/ve/f9r+/e9/v3Ds1JeZu0L9TbjWmDNEz8sSwXqd1DWdhktNVHV03j/ea13vOndVVR/96EenbfoO0N9E1zD9c9Qvg2miGa+vc/nFL36xafv+97/f7GuZa+bv0HnW9NtVVRdffHGzr88CfRvU92PdunVNG3NFqN8P2/S3vGbmoNB769IOOx8pwja370pMj/IiuJw4Os+jNMx6bfS50d/yd3zv6rtslMdFx8450OeIzzTzXuizwj60BL3LfbIssSSEEEIIoUs+EkIIIYTQZWXlBpp81CREM5OaXGieoinJmdM1RIx90OSj4Vo0m9KEr6YljkePpQmKKZN17DTH6nXTzEyzpY6B16XhbaNqe2qyd+E+NGkSF3bFNp0vminVXMzfuVTHHJ+as3/72982baya+cILL3THVtXeP64nl56XIYY09+t649rTdcBnyKUhpzldJSCaWHmdznyt88zfMWWyri+uPZUbGGL4uc99rtnXe83qjR/60IeafR2vk7ooE/B+6ruDz+azzz47bWvYMMda5Z8pvQ/uPVLVmqvZh74vmfqZ909lDD5vXHvaj5M/OFbHHCmCuGdBx+6qo1bNk7r1ty4FP+eOz6bKD+xTQ9oZdn311VfXXGJJCCGEEEKXfCSEEEIIoUs+EkIIIYTQZWV9ElyqTuLKolKbdql7VT+lVuf0L6bNdT4TbFN9jlo0Q71Up3r99debNtVBqUEypexNN900bWuZX/6WWhh9JrRP6ox6nZxznlfv0cinRH/rwpGo+VEjVQ2QaZnV34ThbM8991yz/9hjj03bDA1UmNKaqbL1WpwfRtXy5WiptbIctAsn0/NSp6bmrr4gfG503kc+N5pqmH41qrHv2LGjaeOa0fBgpi92ZZN5nc4HgGtaz8NwV/Vb4dpnuLS+g5ymzfMwFE7fD+xD7wNTXPM8LmTcvUt5r93706XOdz4JozBnd6x7TlzYNXGhnnymnG8Dcf9p+tz8+c9/btrikxBCCCGE/xj5SAghhBBCl5WVG2jec3KDmr34O5p5tUqdmpWrWtMbTWmsoKf90JTlspgx9E3Ni1q9rup42eDGG2+cth9//PGmbevWrdO2ZpzrjUfNnzTDq2mLJjEX/uOy+fF3NJ/peWjacxngOHY1sbIPmsg1LJRtKkWwUiFlDBey5kz2HJ+2M0Omk2tcJVPKCzQt6/zRHKxjd1lCOT5KCAr7oDyjEoPLpsfxUHZaNLaq4+dA551rWJ8/rktnandhoKxKSXlGr4V9uFBhzome10m3IwlB2907uKq9RzyPk1znVEvUaxmdR8fOe+uuy72DmDVUK6ASJ1GNZFUNB969e3fTpnIWZee1EEtCCCGEELrkIyGEEEIIXfKREEIIIYQuK+uT4EJxqBmpDspUr9SUVWdkmmHtg2kyWWVRNb9RiJjqoLwu1YXZRn1Xw1127ty5cOwMa6TuqFo19VxXyY26mWrTrqLmyCfBpdV2VTw5748++ui0zTS6vJ/qj8IQMT0vx84+dQ1xrHpvGd5KVK9kn9RBtU/qqa6NY9DxOX8K569Q1aZ0Zh96XdSpOZcu5a4ey/BRavW6z/vOZ1PniP4BLsUux67asPqpVLW+F/Qz4jrVMGcX4jcKEafvheJCX9mnPpsujLBq+cqPfM+56o1O1+e7y/kScGzOj4X3SPtkWDrvtUvBr+ehvxDXk841w3hffvnlaZvvrrUQS0IIIYQQuuQjIYQQQghd8pEQQgghhC4r65PgdGzqaKqJ7tmzx55XNUr2oX4Ho/Kh+lvqQkyDrGl/zz333KZN9SYXX13ValpsUw2SeuTNN9/c7B88eHDa5nXpeUe5KnSf51Go/zlNclRCVX1MmCL5mmuumbZ/8IMfNG28R9u3b+/2X+W1VerxeqzLfcD15FJ3M/+DSxPr/EbOOeecpu1f//pXs6/6Kn0JNL8Ix8578pnPfGbafuaZZ5o2TdnM+WEZZ/Unog575plnTtvUxqkL63Ux9wifDV2b9P1QXwKnGVe1Pi5c7xs2bJi2mbKZa0+vxaULZh/Or4b6t46HZeT1flW1+jzH6nwSnJ8B1wGvU58FXpfuOz8owrHqdXHt8zw6Jy5HSJX3Z3KpqfleUV8V+qapT47L17EssSSEEEIIoUs+EkIIIYTQ5b9GbnCVuDSNLdMeM8WtShM0GaopaRSmo2ZBnuf5559v9q+//vppmxXsLrroommbaaL37dvX7L/77rvTNs1wmopZq+BVHZ+6U8fOsC81x9LE6lIL05TmKugRNZlxPAxZ07k+++yzm7Zbb7112qY5n2Fzug4YNqtzwLG7FLJOJnAhvWQU1uTSYWv6cD4zl1xySbOv64JpxzWUi/edplGthMk0tXpvafqnGVWlLie10dROE7DOO83pvBY1JXOt6fqipEETvs4f5+DFF1+ctvUZrjo+pE7XP58FnT++H3U9V7Vzwiq1GmZJeYFrT+eac+fWMOG1KHOqJep4RuZ8fTbZh7su3lt9rrn2nSTrKtHyueX8qNzAipquDMFaiCUhhBBCCF3ykRBCCCGELvlICCGEEEKXlfVJYKiS6qvUfhVqT1p+tqrVgqgLqdZDPdeVg6YfBEPPNOxRwyGr2hSb1LCosamGyzA0Dde64IILmra9e/c2+6rlcS5V42If1L9UI9UQtSrv38G51HlnCB21ae3zvvvua9r0uuhn4HR1Nz6Ga7m0tXNCsFzpWlcSuMqnm9V9PkPUWjX0y/kAuXK9Va0/DOdA553PptO/GZam64C6MH0UNJSR65s+SnoupnDXcuwMXeYzptfy5JNPNm36fmAZd/fMc340LJQlpxl2rXNAfwodD9+PczRurhkXEu38DIgrB+2ejTl+bC71M/009Dl64YUXmrYrrrii2dfrdinleV3O94Jhjjre+CSEEEII4f+MfCSEEEIIocv//K+zufx/zNatW5t9vQwXMkMTOVHzo8sYRlMtzZ8u89fll1/e7F988cXTNk2+GvZIEzTNjRdeeOG0zXAtnS+aRlWK4Bg4X9onw8cYRqhmS5pNNYSHpkeGZGqoJ824t99+e7OvVQ4pcejYWcmNsoVbM9rmqiNWtffMSRM0k7rQKbe+uc81o9BM6aoKujkYVeZcNkxuVEVQ54Rr312ny87qKr2yT2ZDVHmPUgT3VQpgCKSGPfKe8N7qeDjPGmbJ6pEaZlnl5St9/ueY812VRZ6L877ouB66Fl0WU75z3D7bdM26dxf7ZHg515PKWZwDfSfxf4DhwSoDjZ4b5VOf+tTCtkXEkhBCCCGELvlICCGEEEKXfCSEEEIIocvKhkBSg1Q9jJqM6nyujechLuyL+0wpq5x33nnNvmpcDMlSvZIaFkMrNYXrJz7xiaZNr/OVV15p2qgdaj9MB6r6HH0QqHvqedx8UF+mv4BqraxUuHv37mZfx0Q/A4Xpb1lVUMdETVI1wFF6bl0XPNalkKUPgAsV5L6Ol+vZpWx1FeNc9T/659AvQ0PsXBXPUcU6VynQ+Ui46oSj51/vNXVhrYRJGEqpY6Avjz7HXJcubM9VCmXFSqbu1bl0KdM5Py618cgHQM9F3xQdH9+B1Nx1Tpz+zt9xvvS37jyjipq6/vnu4nOjcG71/nF+3DNO/wX9LcezFmJJCCGEEEKXfCSEEEIIoUs+EkIIIYTQZWV9EqjVqb5DTUs1P+rxI3132f6pw2oZWerLTAms+hJ9AFSnoq7I3Awax/3www83bRs2bJi2WRrWpZ+mrq/X/de//rVp++QnP9nsO21MdT5qvTxW9dzf/OY3TRtTyuq957yr7wfvAdeMat7UDvV+cR1wLl2eBD3vqPyz/naUatWlZdbrpC+BK3PNOVB/E+cfUOX1ZlcynGOfE6PvzuP8F5w2zdwjuk+fFj6bOgaOVX0b+B7hsdSqFbcueB59z3Dt6VhH70NtH43VHavrgP4U9AlQnP/JKH2582PTfb5HXJp2+o05nxfeL33vufwYVe0zx+dY532UF2gZYkkIIYQQQpd8JIQQQgihy8rKDTT5ODOhC4Vzv3N9sn+mWn322Wen7RtvvLFpo7lfTUlMSawhfQx5VEmjqq0guW3btoV9uPS7Va0pi2FMagajGZDyg4Z60gx3+PDhaXv79u1NGyth6j7DfWieVVOpqybnKqdVtXPC69Q1wz5cWCHXms4zzdMu1THHTnP/ot9V+UqULn0xZR3XJ8fuUkq7uXRjdzIhf+cq6o3M6WqK5zXrc+xChQnnR58N/o5SgK4TmvP1uvk7HqvncSGGro19juQil1Ja1zTfFe7YOeuAc+Iq0br+2afee4bFbt68udnXOXBSCefSrQuX/tqFYC5LLAkhhBBC6JKPhBBCCCF0yUdCCCGEELqsrE8CNVKXrtSFljj91JUB1lTBVceHmlx22WXTNrVMLX1MqMfpeTdu3Ni0uZLPqvlXea2OuqP26UqofvzjH2/aqPmpD8UDDzzQtKkmyrK6hw4davY1bJUamwtB5Lw7TdSlV3Ylw+ekSHY6/iiFrPbpQimJS7k7mgMdA8OsXHiZS91LXAikC81z6YK5Zp02znnmc6x6s/PZ4Hk4t+7+OS3a3RPi/FY4di1BT38KnUuGrDq/g5F/jrtO9Rsbhb7qnHA+9LqdLwPP4/wO6M/BffWTYnl6F/rt1ohba1Xt/Dl/Cte2LLEkhBBCCKFLPhJCCCGE0GVl5QZnSmKbmsxG5mE1z9A8pRnWrrvuuqaNld1UGmCI38svv9zsv/TSS9O2y6JIuYFZ3rQKI8P21GQ3qv7nKrupOZZ9MCOkmsxortaQ0bvvvrtpY2Y7lXZohuMYdN+ZnblGnOxEU5/KTs6ESdiHHjvKoujWtzN1O5MvcdkiaYbXuR3JCzp/lBCc6d/JM64KLHEmcp6HfTqTtB47MpE72cnJBDyPk8H0WIZL8zr1PvB9pPD5cut9JDe4DIdOSiK6Tig767Ppnje281g9j1sTVb4iI8PdVarg3M6RFN17RsczmstliCUhhBBCCF3ykRBCCCGELvlICCGEEEKXlfVJoNaimqmrfDeqsqbt7777btO2ZcuWaVvTLldVffCDH2z2VTdjGBF1NA2TYQiNVm+kTkUtUUOZqOsvmxq3qp0TrZxYtXwqU55369atTdsdd9wxbf/hD39o2uiXof4LvH8cg7azzfkkOE3b+b+M0jsvW3GQ94Tavd57l861yoeI6bW46ojc59qbM5fOj8WlC58T/ufWN31TdHzOz4D7DH1z98RVxnT+MKPKhdrO+6fnGVVW1Sqoc9Y399XXaE6KcldZ1VWP5Hidz5RLjc3zcjz67ue9pb+HS6tNXx491vkLcP3wP2RZfybn17MssSSEEEIIoUs+EkIIIYTQJR8JIYQQQuiysj4JTF+sWjTT+qrOrzkJqo7Xv1X7oZ6jepOWQa46Pg/Axz72sWn7ueeea9qoAarmfvDgwabtyiuvnLapPVGn0vMyZ4GLr6ZuplqZ8+9g/6408z333NPsa24EzqUr303Nz5VYduNxPghVXuPW83LunG7t4uM5l7x/qilzrbmSwRw7fTocy+YeGJVbdyWe1feCz/ScMu7L3q8RLj238+Fw/i9VPkeArgv6bBDVynl/dF3Qp4XpzF25ZZfy113nKAfCwpw8AAAgAElEQVTNss+jy68wB3ddVe1ccn5cuWW+g/S89P3gs7oszrdphK6vU045ZU39N2N5z2cIIYQQwn8l+UgIIYQQQpeVlRuY/lJNrieffHLT9vrrr0/bGvpTdbx5SE1bp556atOmprZLLrmkaduxY0ezryGSrLJG87C2OxP+6DxqoqLpVk2aNJHThKgV2Xjs22+/PW2PUrY+9dRT07aGPFa15jOGFBE1n9H0SLOqq7K26Jy9Y101UP0t5Q4nN7hQLle5tKq99y7tMdtdumBXWY77XAc6By5skH26dMWcuzkygTJKce3aXZuTEEbpnfW6ndzHOeC7zM2JmraPHTvWtPHdoe9PF2rq0pVX+cqOxJnMdQ54Hlch1a3ZOe8KtmmffM+5qpl8TkZzsixO+uaa0WthWui1EEtCCCGEELrkIyGEEEIIXfKREEIIIYQuK+uT4NKeOo2Gmj9DRE4//fRpW30ZqlrNj6EtTF+sqZdZRpo6tmrybNNQuAMHDjRtLBXtQhedvwLnwJWKfuihh6btSy+9tGljyec333xz2nZ6JP1LeG9d+WeXLphz4NKnOlza45GOru2uPK5bz1Xz/Cs0zJEaqbYxHNKVHnbraTR2F+Ln0qm7EEjq1PrbOemdOR6XOpv3wPla0D/HrX+dS65Lt2bYp/oS8bo4dhfmqGt2ThjjKORQr4Xz48qJO1yK8tEz5MJm9X9CS9Wzrapq06ZN0zbvCcfnUjG7NPfu/vGe6P/Ck08+2bRdffXVC/tYRCwJIYQQQuiSj4QQQgghdFlZuYGmGTXHMHzMmaCYTUtNRzz28ssvn7YpC1BS0FBBmqsY8qfnOvHEE5s2rea2cePGpo3nVVOlM8uPwnLUJEZz1dGjR7vHVR2fVVFlDF6zmuVYsY5zq2ZxXpfLAMc2HS9lAp7XZQlUE7nLoljl1577HVGzJe+fkzhGlfnWivYxkhv0PvBYJ5HxPK5CoquKN8dk76QlHuuqSTpTtzuWc+BC6jhWNdO70Ff+1skEoxDIZdt4Xj5vOvbR/XNz6czwLpTShbeqjFN1vNSsmRv5jqY0odftwjfdmuV5WPFXz3P++efXeyWWhBBCCCF0yUdCCCGEELrkIyGEEEIIXVbWJ4G4VLmqGVFHd2FW55577sJjqUu9+uqrzf4FF1wwbV977bVNG30JFOpmGrbnQt247/Rc6pysOKgal85dVRva+fjjjzdtDLvat2/ftM25VKgrMhWt09F5nU7z02NHYXL6W6dJvhctWve5LjmXLlzLpWmeU0HPacFOP3VtxIUu0l+B61SfBR6r949z6XwJXMhj1fL6/CjNt65LrjX9LX1l3HriPLvKjm6dOr8et2Z7Y3DHLjueORVaeay+n/g/QPS5dsfSH8CFMfL+jUJRFfdfxPNqePmFF17YtGml4927dzdtCYEMIYQQwn+MfCSEEEIIoUs+EkIIIYTQZWV9EpxvAdP8qobFlMRMAaraD/Ub1eqpmx88eLDZ1/wCqh9VHZ8zYNeuXdO2i9N2sbK93yqqy/KaGcur6ahV4+N5HnnkkaaNmpqmB2WKa81Pwfmgjqe+FqO4f702p1uPNFtdB/T90DkY5R1w+rfT46kT63WxzWncLtWr00Crltebne/HqE+dA7axJK/C59j5SNC3weVbGPkoKC4FuCsHzefP3SOXA4M4/wmub22fk9rY9UnmlF/X/VHuCudbpPPF9yP/F1z6cr0n7v5UtdfJe8t16srDuzwufD/o+3P//v1Nm+Zq0Lw2ayWWhBBCCCF0yUdCCCGEELqsrNwwp3KZCzXbuXNns6+m7kcffbRp+/KXvzxta3hf1fFmJTWvX3fddU0bzfs6JoYjqrmfbTTH6nVSJlDTGqtH/vjHP272P/KRj0zbNHOp6e/BBx9s2nhPdLwbNmxYOHaGk9L0p6FKTKPNOXHVHZc1HVe168mFpbnwMUKzqQuH4jqdE07mTMDOzMznZlnz8MjEqtfiwjXZh0uj68L/5sgoLh0v9xkKu2wfVe17hX3q/DlZoGr5UEGXzpnncXKDCw3meUYSngvRdOuS8+VSZes8j8KcnelfcSG03B9VfdTx8b2i4+M78ciRIwvPw+dNx+vCNZclloQQQgghdMlHQgghhBC65CMhhBBCCF1W1ieBqBZEfUn1by1fXFX19NNPN/uXXnrptP2lL32padN0ygwtYfriK6+8ctqmHk9tU3V0lrlWbWoUbqfXTb8HDTOkn8Fdd93V7KtPAn0bDh8+PG1v2bJlYVuV1+dVR2OIITU2nZ9RaWbV4FzoEueS8+VS0zpN2zFKcauMdFnF+RLMCX0blWpedJ5RmJ7qp/QZ0fPQt4F6qo6Hbe7ZcOmmufZ4Xt2nTuzgvKtOzPlZ6zpwoYKuFDPP6+4z547nnZMKetHv2A+fcaLn5drT59iFR7JPNwejVP7uWXAh2lxP+r/A9xHDwvVYtrl7shZiSQghhBBCl3wkhBBCCKFLPhJCCCGE0GVlfRKOHTvW7KsWxFh63adPAv0FVA/X1MpVrfZE3Yz6vPooPPzww03b9ddfX4vgeV2f1K1Uf1q/fn3TdujQoWmbMbfU3G677bZp+84771zY54knnti0MW+D+gRQm1NdltfB61QddFS2dVmdcaTVqc7nNMhRWds5OrHiUtqOYrFdumC9JyMfCRcD71IAE22fk/9hjp7qylpzfJpbg75ExMXSO/8OF1vvcijwd9zX58bp8aO0zPpbp5vP8W1gny4FvstzM8KtN313jPJ3uOd4Tol192w6HwU+C7ouOe8uRwdzYrj+10IsCSGEEELoko+EEEIIIXRZWbnh7bffbva1KiPlBjXxMMSQ5iE9D6uGqbmK5nxWhTz99NOnbZo0WTHytNNOm7ZpHlITPsMRaa7SMEeGxajc8MADDzRtlFz++Mc/LjyPM9E5mYDms/e9733d7d55nLl6ThU6Z4an5KHmUJe2dtSnq76p10lz65z0zi500YVvumqI/K2TG0amWZe2VplTcdDdE84H17A+j6NU0C6lu8I1y9BKl+Z7juyk+y7FNU3Q7lkgbn5cGnKaxN1z4sJ25+Dmx4UGvpc+XcjvKLRa/0N4rP43cU24+8nr0vvA/6m1EEtCCCGEELrkIyGEEEIIXfKREEIIIYQuK+uToPp7VavvUAfatGnTtM1QxQsuuKDZ37p167T9wgsvNG2adph617p165r9Z555ZtrWFM298anOR81P9SZqfvSZUG3/5Zdfbtp0vugjQb1L00/zOjVMh23UZV2YlTJK5+pCKZcti1w11uAV1RkZ2rlsmCXb5/gyuHC7OelveazOwWjszifBzaUb3yhcUuGz4H47J4TO+TbMCX1TRmWJl02DzDZel/OLcPeE49Fnns+tS4vs0qBTq3dpo+eUN3d+B+65GYU1utTreh5X2ruq9T9x11zVvvv5XnFj53mdn9acsunLEEtCCCGEELrkIyGEEEIIXf5r5AY1xdN8rlkWKTds3ry52d+3b9+07TIB0tS/d+/eZv+qq66atmkydJkJaVZS0xHPwzBQrSp2//33N207duzonrPqePOZygjO7EVTGsO+dL54rDO5zpEbnInTmUZHFeK03WU4ZBtDPZetpEjmSAouHNBVgRxlY3OZ5JyM4sbOeXfnmRO255gjRczJOulkFL6DdOwu6yQlPBf65iQp4ubShS6OTPYuk6QLV3ZZQueEpRK3Zp3E4bKqjiQEvUe8X6OQyEV9cs1yf9l7NMoougyxJIQQQgihSz4SQgghhNAlHwkhhBBC6LKyPgkaplfV6tbU/DU88ayzzmramMJ52Sp57IOpjTWFsoZgVh2vE6mWz+qWeh72cfnllzf7X/nKV6btr371q03bz3/+82mb4VCvvvpqs+9Sfq41RMyF0LEPVpfUY0dhVk63dn4GztfB6egMF3P65RwNmeNxYWnEaeVzQhddiJibH45Vr4VrT9uo53Lf+VPoeV0KaZ6HY6dPgGrIzr+Dv+N59ZnnHOjzz9TrzueF78A51STdc+zWj1uXfK8x3bpeG+dA53mUsnlZv4NRSulFv6vy7wr3Phj5cGjqZbZpeLlu98Zw9OjRaZv+CnreVIEMIYQQwv8Z+UgIIYQQQpd8JIQQQgihy8r6JDBHwBlnnDFtM0Wy5g+gXsr0xcumDqXepqWhq1rtidoY/SBUq2PMsp6Hmtpbb73V7H/3u9+dtj/72c82bVoylNoh/SBUD5vjSzAnBajeh5Hmp/PHuXQlljlfej9d3HFVq+9SG1dd2MVMs92l3GUbxz5HT3WarcNp924dzIlrZ04OLZ07yjmxbAruOSmSXdlftrv3AePfOV96nexDn3++n7ie9Ld6To5hlHLbrQttc/kxuK/vqqrj33N6rHvGOT9zypS7dMXuOXG+RaN8C84ngdei5+Ka0WNHPiWa+4fMWQfLEEtCCCGEELrkIyGEEEIIXVZWbnBmXq3kWNWmcKZJjCFHaqqhqU9N0AxrZJ+vv/76tD0y2alZlamN1TzLsZ588snN/k9+8pOFfRw8eHDapvmV0omOgWY4V4XOmTCdGZXhPi4caSQTuPAtvS72yXut8075yskELuSI16X3fWQW1D5d2uqq9lqc5OJMtVXtvR6F+CkuTbObn5F0o2NwUhfHSolD551tc6qVLmv25j6fBb23bqxVrRw551l0KcpduulRSJ9bI3zX6nXT1D6nsqrOgbsnozTfrk3HOgrJ1DXNeed16rFsc1LJaaed1uxrO59xHZ9bI8sSS0IIIYQQuuQjIYQQQghd8pEQQgghhC4r65Nw6qmnNvuXXXbZtM3Uyxr+50K5qo7X0RTVsan1vPbaa82+alojDVn3qZVrP0yfrGWtq9prYelq1eeosTMNso6dPgAutJM4/wAN3xqletb5oUbL+7dsiVenl1a1+irDbXUM1BVdqWinn46uy5U7duflOnXpnZ0viNPc56TRdWGWbKM+754p7WMUjqjnYR8O52cw8k1xfjXOl2dOyellz8nzcqz6W+eDwH2GPHLsLi2zHjvq04VPu3eJ81Fw/wujVPC6hly68Ko2HJ/h7uozxd/9+9//bvb1/el8gNaaRl+JJSGEEEIIXfKREEIIIYQuKys30OSjphpWS1STy5EjR5o2Fw7oqtDRBMYwQgdNWzp2SgpqklJJparqoYceavZ/+ctfTtuUY/S8DKWkqVuzee3fv79po0lRmZP5b1lTNuHYmXXOmUq1bZTRUM2GNOe50DeXndGFk41ClVyImJOznBmV5k5WNtU1/eabbzZtukZc6CSh3KG/5Tp0GQ7Jstn8eCxx5tn3kr1ured1EpALQx1l/tPnmPKMW5fuWeB5iN5fjmeOBLRsKKN7H3E8XHs6njkZPEcho65KpcL3N+dE5VKGnur4RvdkGWJJCCGEEEKXfCSEEEIIoUs+EkIIIYTQZWV9Em6++eZmXzUkhiOqTuzCqqpajZtpj9XXgVqd01NHVc1U/+axuk/t90c/+lGzr2EyThemxkadX8fuNGSmkKY25nR9Nx6X2pThmtTVXZ/OJ4GhSy48UdfQSKd2KVtduCbHo/vunhBXXZJ6KfvUNcSqcy6czc2J803h7+gjoeNxfga8X3wWdOyj8Da3ZhYd1xvfsqmO54STujGwf16nC/XW+XIVPbnPsXHe9X3B95w7j3uOyZyU0vq/wPG4SrjOT2SUCtpV0XWVHd07ke9dF+a8FmJJCCGEEEKXfCSEEEIIoUs+EkIIIYTQZWV9ErZt29bsqzZNvwNX/tnFy/NYLf980003NW1PPPFEs6/6EjUi7r/zzjvTNnM8bNmyZdr+9re/3bRRs1X9i1q96la8rvPOO6/ZV72SepzOLfU355fh0hfzd9Tf9DoZr69lwAn1VKcdunLeo7wSDtenQv8Ol26W65ua5LKpWLkOnd797rvvNvtrLcnrUgAT5x/gcmCM7q3Tv50vCNfwsqWr2Y/Tyl3ug95vF7VRY3fXxbFrG383J3U3WbZs8Zzyxm6+RrlQnD+MW2vsU39LXw+m2ddzsW3Pnj3T9qFDh5o2loo+/fTTp22+D/Q6XWn2ZYklIYQQQghd8pEQQgghhC4rKzew0uMbb7wxbTO1scOFLjHl7+bNm6dtpkSm/KEmM2emrKo6fPjwtK1VwqraSo/s41e/+lWzr+ZjmsTV7ESzm/ZfVXXmmWdO2zTn67XQXEZcGKGrVEjTu/Y5qjTHuV3UxuNc1UUnh4xCzZzp1JkCKQXonIxSrTqJQ02j7MOl8nUm/FGoma43ZwZ38hBxz60zB/NY4qocjip1Ki4lsJNKXJjsqA83Hpfq2KXVnpOWmYxCIhUnubg17MITudY4B/r+mrP2XCgl39/sU1OdU5o499xzp+2LLrqoaVNJuqrq2LFj07aTclWuXiuxJIQQQgihSz4SQgghhNAlHwkhhBBC6LKyPgmuzK3T36hvUZ9XPwTqOVdcccW0zZAwjkd1Kurm1LQ0tFJTK1e12tOBAweaNupxqsG5NMNsc6GL1BFV/6LvgEstTH1Q4T2gVqf3hPfWpdV1eqULi+v9dtk2V1aWPgBOR3dpa9nG++A0W1funM+GtruxO92c4+U8uxSyXBeuRLeOYeSDoONh/1xPy66D0XrSueT90/HxmvnumOMv4NqcX4tLbey0+9HcuRBJ5+fjxsdjdb5G4a06f25dcp7dmh2Fb+p8OV+QOe8DpqrXkO1lw6EdsSSEEEIIoUs+EkIIIYTQZWXlBoaEqEmaJjqFoW801WimRJqONCOWZrzqnceNlRw9enRhn1rRUsM8q443e6kJkWZLNW0503FVa6KiKVvPq+E8vfOoNODGQ9Maw4ic+dGZQ122uJF5WH/rzKajKpB6P10WvpHZe9lqklXLV9zkWnPho8SFLjpcOJuTpPhbd0/YhwupG5mH59zrRb+rat9JTpLiczKniqDev5GZWe8fpVLFrVnujzJdOlnKyQ1OCuTY58iErsKnvrucnMfzjCrauvun0jIlV8rb+r5gtWKdkznP5iJiSQghhBBCl3wkhBBCCKFLPhJCCCGE0GVlfRJeeumlZl9TbLowIurdPFb1nF27djVtqkXt37+/adu7d2+zf+GFF07bO3bsaNruvffeZl+1xCNHjjRt6odwzz33NG2bNm1q9jUdNbU61bCodzO9ss4X9Tj1/VBfiqrjfRQ0LJV9qP8Eq1mOqhwqTiN1OF24yvsvuPC/OWlq3VidnsvfOd1xjo7uNGPn50N/Ch7r/Dv0WOevwPPwml2IqKt2OSdEbNkKjL3x6XM0Chl16G/5TKluzXsw5/7pu4PPBZkz7y781vXjngW+n1xYsavUyT50PFyXfLdyDArHoOHm/C/SNlaeZTi+vnv5nOi8j+7fMsSSEEIIIYQu+UgIIYQQQpd8JIQQQgihy8r6JFC3Vr3J6VTUgVgO2rF79+5pm6mMqRlt37592qZWt3Xr1mb/jjvumLYPHjzYtGns7CimW7UoalpOK2ecrfpBuPLBGzdubNpcyVKiGuCoBK8rS0z/imXTu7pYZ57XxeRzPKOUsovG4NIMs3009kV9cH9UylfbXZ4L3nfn3+FSEhOOx5UT1vs1SqPrUuM6vwhXEnvkb6LXzfFp2yh/h76v+Iwro7wb2qdL8802lzeB9935ABDnc+N8cHhOl5repY12Y+Nac+uJ8Lyadp9zqz5dfCfr/0BV1QknnLCwTf/j5vgkLSKWhBBCCCF0yUdCCCGEELqsrNxw3nnnNfua+pgpLdV8RrmBpqOTTjpp2taUyFVtGNGZZ5658HdVVd/73vem7aeeeqppoylJUzrTdPvmm29O26MwKzU/OnMsU0hruumqqp07d3bPWdXOLcdKU62r2qfzPjLZa7tLn1rVShfORM4+XApnV1VwJAEp7p4QnlePnVMlz51nlALY4cJAXXVCN/ZRGl/dp0zozMyuIuNIunHmWic7EWdO12eB7y6GB+vYXfrp0T1x5nVXHXGtFVB77YvOy/vH8E0NiXbSkguTZTv/B9y9dfea7yNK3+75e+utt6ZtSgjr1q1r9nX9879H58RVRF6WWBJCCCGE0CUfCSGEEELoko+EEEIIIXRZWZ+EZ555ptlX7Yc6noaWOC2zquqMM86YtlUjqmp1PJZtZqrOW265Zdq+8847m7YDBw40+88///y0zVTHmmqV/hSuxKuGyBCOnWmjlw0jJC4c0Wl19G2Yk86VuLSsCvVAp+/OSac8Kpe7CKebV/lwUrJsn6M0yK7N+SS4eXf+AiPfFB0DtXtlFIq3rM9Gb3/Reciymn9V+1zzWaBP0JyS4a5P53OzbEpytnOunB+Ee6ZG61ffiTzWpUhe1r+E+6OwVL1OPqfu3cZ08+p3wPc39zUFP/0VnG/aWoglIYQQQghd8pEQQgghhC75SAghhBBCl5X1SXB6ILUxzaHA+NPPf/7zzf4rr7wybbMUq2pI69evb9oYq/rkk09O24899ljT9vjjjzf76kNBPwjNk0CNj7qs6oXUxvRYnoe61dlnnz1tHzp0qGlTLYzzQ18Ql7LVpbt1fgennHJKs8/r1H6oJer46Isyp9yy81eYUwbY+X648sb073CpxefkPnDjmxNn7zRuxrwvm0Ohanl9daQh69xy/Tj/Cqdbj3wbFvVf1b6T+AxxvlwKZ4Vt7FPHyz7cmuE90Hs9WiMuFfucdarP+Jzy3Wtl5Lszx29L54DvIB0vfRnoa6H3k+8DHQ/9HtZCLAkhhBBC6JKPhBBCCCF0WVm5gaZuNb84cyd/9/DDDzf7n/70pxee58iRI9P2/fff37T985//XHgsTX0a8lhVtXnz5mmbZiYdA8euFcV6/ShqChyZNNWcR7OgmlFdtUbC8E3FmTDZJ+UiXrOa12iG19AgFypFnKQwSgG81rS+zlzN++XkhjmmUXedTgLiWJ20NOpzUf9zzjMK2+Mz5o511UCVOWGXrrLjKI2uM6Hr+LhGnGTGseq1jFIbuz5ctcQ5MgHP6yRFVzHWjXfOdbn2OZUnKTe4dOFcXwrXjM77nCrHi4glIYQQQghd8pEQQgghhC75SAghhBBCl5X1SXBhO9Rvdu3aNW1v3LixadOUzVVtCCLTJ6uufuqppzZtGjrJY//xj380bdTDDx8+vHDsqpFqOGSV1wA5PxrWSA1r06ZNzb6mPXXpU53myHbqwE73pI6nczBKp+y0fMeckFqnHc7B6eij61RcaJ77Hductul04tEc6Hy58t0jXJ/uvjsfhTkpt908O38gHstnU8fH8zAtsxuPK33swp4ZJqd9cu5YZl7flyNfFHeP3LzPSSmt+6MU6cumiabvAM+jfluj9aznom+YviPpS+Decy7M0fkyLEssCSGEEELoko+EEEIIIXRZWbmBplGVDZgNUbMNPvDAA03bDTfc0OyrTKAyQFVranMyRVXV9u3bp+277767aaOZUM1VzqzLPmm2VBmDJnyVKniel19+udnXkEyavVy4D++JmsFGYWmO/4TJjH3OqTjIaptzzrMsLmsax8NQWJpDl5Vc5sg8zozqzPBVrbl4TlicC9/k/DgTNHGhb2sN1+R5nLzGY3VuOc/uGXPzPspOqfPHUGp9f77wwgtNG2VWF3I4J3Rxjlyk68mFGPK94WQed57R86THct65r+9Tzo/e29E7T+8f39F6nvcih059veczhBBCCOG/knwkhBBCCKFLPhJCCCGE0GVlfRKotWjYDkNCnEbz0EMPNfvr1q2btjUUsKrVGc8666ym7aqrrmr2f/azn03b1LSoV+p4XdgQf0ctWn0bqL+pFkxNmzrjhg0bpu2//e1vTdt55503bT/99NMLf1fltUMdO6+Z90+vhWFD1OP02LWmIOZ4XXjUqILlslUOR9UI52juDqd/u5AxF7rIOeC6dPqq9km/jDmVQxcdxz44Pq61OX4Hbi5H93NRn6NU1O4Z1zXrqlnyvCeccELT9tJLL03bp512WtPGd5CrPMuxO98UB4911Tf1ftLXgqHnLmxe/08Y9snx6P6caqCuUqdL2cyxu/Xu/MSWJZaEEEIIIXTJR0IIIYQQuuQjIYQQQghdVtYnYZR2VHn11Ven7Xfeeadpe+2115r9PXv2TNvUsFTfYQ4F5h445ZRTpm1q/jqeqtb3YY42Tt8CzQdBvVJTL7sSylWtr4HmTKhqS2CffPLJC/tnPy4OmVomx6M6GjU2/lbb6b+w1lh/l7OArDXN7yilrcsn4ObWHTsnd4XztRjh/DJcLoa15pwgc3w4XKy/K4ntYvlH49F769p4XpcLwfm0EL5LNS8I/RWOHj3a7Ot7j/lE+Gzq8+jmx+WRqfL5DfT553uOOr9Lla1j5e+4Ll3ZbeeTwPPyP0RhHh7N5+NyhoxKjy9DLAkhhBBC6JKPhBBCCCF0WVm5gWYwNfPs27evaXPhf9u2bVvYB0No1NTGqo9vvPFGs+8qqdFMSFOXouYiDc+sOt4EddJJJ03bvC41QdHMxX2XOlQlmFHFM70uNY9xPCPzoo6HJjmOXcfHNh3DHNO2M/m6cKheP4sYmZnVbDmqfOmqJbpKcy7cjuNx4X8uJIuyikpUbFtrymt3v6ra5+Ttt99u2jiXej/dHIzG4EJGneTiQhddG3EymJMmmJb5nHPOafY1pTvfT+494+aAY3XHupTkrupjVbu+uUbcc+Keca5RF4rupFK+L90zTlza+LUQS0IIIYQQuuQjIYQQQghd8pEQQgghhC4r65PA8DbVppguWMP4+DtqP/fee++0Tf+FM844Y9o+ePBg08bQINW0XPpNjkFLOle1uhVDA4mGID311FNNm4ZhMiST+pZqcEzDqilKqQcyjbWGSLq0opwf6njaD8Ms6Zui94zz5cIjXZpmF544J/TNhVKOdH3nw+HCE51PCeF8uT6df8CcEsYa3sq1Rh1W58hp7KM03+prxHXAkDEdr/MzGDzFaiUAAAKYSURBVIVZOm1Y55J98F2hzwbbnOY/J7RT9zdu3Ni08T2n/h28fxyf9sl7onM5Kres42PYpfY5Kketc+nCW9k/3wfazueLz6bz5dE5GfWp+3xf6m/1/qyVWBJCCCGE0CUfCSGEEELosrJyg1YjrGrNOvfdd1/Tdv7550/brNb4ne98p9n/2te+Nm2/+OKLTZuacWj2ZjXJW265Zdq+9dZbmzaaONUUuGXLlqZNM0JS/mDYpe67bGw0QZ199tnNvmalPHbsWNPmMngxVEjNuuvXr2/a1CxI0zUlBDXhOdNoVZsR8vTTT1841pEEpOY8J5U4k29vfMviqoGOjnU48znXha4DhmuttX+y1hAtZ04fmXydNOHM/cuGs/bGt6h/js+1sd2FxfE6uC41fJpZZ2+66aZp+/7772/aXEXPUaigSgOUJnR9uYqjVe07SDPbVh1/LcociUyPpSSt75iqVs5275EqHy7pcCGaZNnKs8sSS0IIIYQQuuQjIYQQQghd8pEQQgghhC7/87//ibyNIYQQQvivI5aEEEIIIXTJR0IIIYQQuuQjIYQQQghd8pEQQgghhC75SAghhBBCl3wkhBBCCKFLPhJCCCGE0CUfCSGEEELoko+EEEIIIXTJR0IIIYQQuuQjIYQQQghd8pEQQgghhC75SAghhBBCl3wkhBBCCKFLPhJCCCGE0CUfCSGEEELoko+EEEIIIXTJR0IIIYQQuuQjIYQQQghd8pEQQgghhC75SAghhBBCl3wkhBBCCKFLPhJCCCGE0CUfCSGEEELoko+EEEIIIXTJR0IIIYQQuuQjIYQQQghd8pEQQgghhC75SAghhBBCl3wkhBBCCKFLPhJCCCGE0CUfCSGEEELoko+EEEIIIXT5f1TWsTirblYsAAAAAElFTkSuQmCC",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x322e3f050>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.text.Text object at 0x3274c57d0>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "include(\"NtSolutions/inverse_5_inpainting_sparsity/exo2.jl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "## Insert your code here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Inpainting using Translation Invariant Wavelet Sparsity\n",
    "-------------------------------------------------------\n",
    "Orthogonal sparsity performs a poor regularization because of the lack of\n",
    "translation invariance. This regularization is enhanced by considering\n",
    "$\\Psi$ as a redundant tight frame of translation invariant wavelets.\n",
    "\n",
    "\n",
    "One thus looks for optimal coefficients $a^\\star$ that solves\n",
    "$$a^{\\star} \\in \\text{argmin}_a \\: E(a) = \\frac{1}{2}\\|y-\\Phi \\Psi a\\|^2 + \\lambda J(a)$$\n",
    "\n",
    "\n",
    "*Important*: The operator $\\Psi^*$ is the forward translation invariant wavelet transform.\n",
    "It computes the inner product with the unit norm wavelet atoms:\n",
    "$$ (\\Psi^* f)_m = \\langle f,\\psi_m \\rangle \\quad \\text{with} \\quad \\|\\psi_m\\|=1. $$\n",
    "\n",
    "\n",
    "The reconstruction operator $\\Xi$ satisfies $ \\Xi \\Psi^* f = f $, and\n",
    "is the pseudo inverse of the analysis operator $ \\Xi = (\\Psi^*)^+ $.\n",
    "\n",
    "\n",
    "For our algorithm, we will need to use $\\Psi$ and not $\\Xi$. Lukily,\n",
    "for the wavelet transform, one has\n",
    "$$ \\Xi = \\Psi \\text{diag(U)} f $$\n",
    "where $U_m$ account for the redundancy of the scale of the atom\n",
    "$\\psi_m$.\n",
    "\n",
    "\n",
    "Compute the scaling factor (inverse of the redundancy)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "128×128×13 Array{Float64,3}:\n",
       "[:, :, 1] =\n",
       " 0.00390625  0.00390625  0.00390625  …  0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625  …  0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625  …  0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " ⋮                                   ⋱  ⋮                                 \n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625  …  0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625  …  0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       "\n",
       "[:, :, 2] =\n",
       " 0.00390625  0.00390625  0.00390625  …  0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625  …  0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625  …  0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " ⋮                                   ⋱  ⋮                                 \n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625  …  0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625  …  0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       "\n",
       "[:, :, 3] =\n",
       " 0.00390625  0.00390625  0.00390625  …  0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625  …  0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625  …  0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " ⋮                                   ⋱  ⋮                                 \n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625  …  0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625  …  0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       " 0.00390625  0.00390625  0.00390625     0.00390625  0.00390625  0.00390625\n",
       "\n",
       "...\n",
       "\n",
       "[:, :, 11] =\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " ⋮                             ⋮     ⋱                    ⋮               \n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       "\n",
       "[:, :, 12] =\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " ⋮                             ⋮     ⋱                    ⋮               \n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       "\n",
       "[:, :, 13] =\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " ⋮                             ⋮     ⋱                    ⋮               \n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25  …  0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25\n",
       " 0.25  0.25  0.25  0.25  0.25  0.25     0.25  0.25  0.25  0.25  0.25  0.25"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "J = Jmax - Jmin + 1;\n",
    "\n",
    "u = reshape([4^(-J); 4.^(-floor(J+2/3:-1/3:1))], (1, 1, 13))\n",
    "\n",
    "U = repeat(u, inner = [n, n, 1])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Choose a value of the regularization parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "lambd = .01;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Shortcut for the wavelet transform and the reconstruction.\n",
    "\n",
    "\n",
    "\n",
    "*Important:* Scilab users have to create files |Xi.m|, |PsiS.m| and |Psi.m| to implement this\n",
    "function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Xi = a -> NtToolBox.perform_wavelet_transf(a, Jmin, -1, \"9-7\", 0, 1)\n",
    "PsiS = f -> NtToolBox.perform_wavelet_transf(f, Jmin, + 1, \"9-7\", 0, 1)\n",
    "Psi = a -> Xi(a./U);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The forward-backward algorithm now compute a series of wavelet\n",
    "coefficients $a^{(\\ell)}$ computed as\n",
    "$$a^{(\\ell+1)} = S_{\\tau\\lambda}( a^{(\\ell)} + \\Psi^*\\Phi( y - \\Phi\\Psi a^{(\\ell)} )  ). $$\n",
    "\n",
    "\n",
    "The soft thresholding is defined as:\n",
    "$$\\forall m, \\quad S_T(a)_m = \\max(0, 1-T/\\|a_m\\|)a_m. $$\n",
    "\n",
    "\n",
    "The step size should satisfy:\n",
    "$$\\tau < \\frac{2}{\\|\\Psi\\Phi \\|} \\leq 2 \\min( u ). $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "tau = 1.9*minimum(u);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Initialize the wavelet coefficients with those of the previous reconstruction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "a = U.*PsiS(fSpars) ;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "fTI = Psi(a)\n",
    "a = a + tau.*PsiS(Phi(y-Phi(fTI, Omega), Omega));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Soft threshold."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "a = SoftThresh(a, lambd*tau);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "__Exercise 3__\n",
    "\n",
    "Perform the iterative soft thresholding. Monitor the decay of the\n",
    "energy $E$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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8+dq1a1d3ywsZOa0tXp+VuUyuBAAAhAqLcRYPFLRYLPrLX/6i+fPnS/K1dmVkZOjOO+/Uf/zHf0iSnE6nUlNT9cILL+jqq6/u8Dzf/e53VVdXp7feesu/7qKLLtJ5552np556qku1uFwuORwOOZ1O2e32nn6lgDla06gLH1wnq0Xa9YvZiokMN7skAAAQID3NHQEd41VYWKjy8nLl5eX51zkcDk2bNk35+fmdHpefn9/uGEmaPXv2aY9xu91yuVztllCSEh+llHibvIa0m1YvAACgAAev8vJySVJqamq79ampqf5tnR3X3WOWL18uh8PhXzIzM8+i8t4xcYhDkrSrhOAFAAD68F2NS5culdPp9C/FxcVml3SK8f7g5TS5EgAAEAoCGrzS0tIkSRUVFe3WV1RU+Ld1dlx3j7HZbLLb7e2WUDMhw1fTrlJavAAAQICDV3Z2ttLS0rRu3Tr/OpfLpc2bNys3N7fT43Jzc9sdI0lr16497TF9wYTWFq/9FTVqbPaYXA0AADBbt2+1q62t1YEDB/zvCwsLVVBQoKSkJGVlZWnx4sV64IEHNHr0aGVnZ2vZsmXKyMjw3/koSQsXLtSQIUO0fPlySdJtt92mmTNn6uGHH9bcuXO1cuVKbdu2TU8//XQAvqJ50h1RSoqNVGVdk/aW12hSZoLZJQEAABN1O3ht27ZNs2bN8r+/4447JEmLFi3SCy+8oCVLlqiurk4/+tGPVF1drRkzZuidd95RVFSU/5iioiJZrScb26ZPn65XXnlF99xzj372s59p9OjRWrVqlSZMmHA23810FotF4zPs+uf+49pV6iR4AQAwwJ3VPF6hJNTm8Wrz0Dt79Pv1n+uaC7O0/FsTzS4HAAAEQEjM44VTtY3z+uRItcmVAAAAsxG8etnkLF/34p7yGjU0McAeAICBjODVy9Id0UqzR8njNbST+bwAABjQCF5B0Nbqtb2oyuRKAACAmQheQXAyeDHOCwCAgYzgFQSTsxIlSR8XVamf3EQKAAB6gOAVBBMyHAqzWnS0xq1SZ6PZ5QAAAJMQvIIgOjJMY9PjJTHOCwCAgYzgFSSTM33djYzzAgBg4CJ4BcmUYb4B9tsO0+IFAMBARfAKkguGJ0mSPi1xqs7dYnI1AADADASvIBmaGKMhCdFq8Rp0NwIAMEARvILowmxfq9eWwhMmVwIAAMxA8AqituC1ubDS5EoAAIAZCF5B1Ba8thdXy93CA7MBABhoCF5BNCI5VslxNjW1eLWjmAdmAwAw0BC8gshisWga47wAABiwCF5B1tbdmH+Q4AUAwEBD8Aqyi0cNkiRtPVSlxmbGeQEAMJAQvIJs5OA4pdp947y2HuLuRgAABhKCV5BZLBbNGDVYkrRp/3GTqwEAAMFE8DLBV0YnS5I2HSB4AQAwkBC8THDxKF/w+rTUpRO1bpOrAQAAwULwMsHgeJty0uIlSR98zt2NAAAMFAQvk/i7G/cfM7kSAAAQLAQvk8wYfXKAvWEYJlcDAACCgeBlkguHJykyzKpSZ6M+P1ZndjkAACAICF4miY4M07QRvlns399TYXI1AAAgGAheJro0J0WS9N7uoyZXAgAAgoHgZaJLx6ZKkj46XKXq+iaTqwEAAL2N4GWizKQYjUmNl8draMM+7m4EAKC/I3iZ7Ktj6W4EAGCgIHiZLK81eK3fe1TNHq/J1QAAgN5E8DLZeZmJSoqNVE1ji7YdqjK7HAAA0IsIXiYLs1p0yRjfZKrv7WZaCQAA+jOCVwi4bJzv7sZ3dpUziz0AAP0YwSsEXDImRTGRYSqpbtAnR5xmlwMAAHoJwSsEREWEaVbrZKpv7ywzuRoAANBbCF4hYu7EdEnS6p1ldDcCANBPEbxCxKwxKYqOCNORqgbtKnGZXQ4AAOgFBK8QER0Zplk5vrsbV9PdCABAv0TwCiFfb+1ufJvuRgAA+qVeCV41NTVavHixhg0bpujoaE2fPl1bt27tdP/169fLYrGcspSXl/dGeSHrqzkpioqwqqiynrsbAQDoh3oleN1www1au3atXnrpJe3cuVOXXXaZ8vLyVFJSctrj9u7dq7KyMv+SkpLSG+WFrJjIcF02Lk2S9Jftp/+tAABA3xPw4NXQ0KDXX39dDz30kP7t3/5No0aN0n333adRo0bpySefPO2xKSkpSktL8y9W68DrCf3mlCGSpL/uKOXZjQAA9DMBTzYtLS3yeDyKiopqtz46OlqbNm067bHnnXee0tPT9bWvfU0ffPDBafd1u91yuVztlv7gK6OSlRxnU2VdkzbsPWZ2OQAAIIACHrzi4+OVm5ur+++/X6WlpfJ4PFqxYoXy8/NVVtbx3Xrp6el66qmn9Prrr+v1119XZmamLrnkEn388cedfs7y5cvlcDj8S2ZmZqC/iinCw6z6xqQMSXQ3AgDQ31iMXrh97vPPP9f111+vjRs3KiwsTFOmTNE555yjjz76SLt37+7SOWbOnKmsrCy99NJLHW53u91yu93+9y6XS5mZmXI6nbLb7QH5HmbZVeLUFY9vUmS4VVt/nidHdITZJQEAgC9wuVxyOBzdzh29Mohq5MiR2rBhg2pra1VcXKwtW7aoublZI0aM6PI5LrzwQh04cKDT7TabTXa7vd3SX4zPsOuc1Dg1tXh5hBAAAP1Ir45ej42NVXp6uqqqqrRmzRpdeeWVXT62oKBA6enpvVhd6LJYLPrWlKGSpFe3FZtcDQAACJTw3jjpmjVrZBiGxowZowMHDuiuu+5STk6OrrvuOknS0qVLVVJSohdffFGS9Oijjyo7O1vjx49XY2OjnnnmGb3//vt69913e6O8PuGqKUP1X2v2antRtfaUu5ST1n9a9AAAGKh6pcXL6XTq5ptvVk5OjhYuXKgZM2ZozZo1iojwjVUqKytTUVGRf/+mpibdeeedmjhxombOnKkdO3bovffe06WXXtob5fUJg+Nt+tq4VEnSyi20egEA0B/0yuB6M/R0kFso27DvmBY9t0X2qHBt+XmeoiLCzC4JAAAoxAbXIzC+MipZQxKi5WpsYZA9AAD9AMErhFmtFl1zoW9+sj9tKTrD3gAAINQRvELcd87PVJjVoq2HqrS7rH/Mzg8AwEBF8ApxqfYoXT7e9+DsFz44ZG4xAADgrBC8+oDrLh4uSVpVUKLKuiZziwEAAD1G8OoDpg5L1MQhDrlbvIz1AgCgDyN49QEWi8Xf6vVS/mE1e7zmFgQAAHqE4NVHzD03XclxNpW7GvXOrnKzywEAAD1A8OojbOFh+t5FWZKk5z8oNLkaAADQEwSvPmTBtGGKDLPq46JqbT1UaXY5AACgmwhefcjgeJuumjpUkvT7fxwwuRoAANBdBK8+5saZI2S1SP/Ye0yfljrNLgcAAHQDwauPGTYoVlecmyFJenL95yZXAwAAuoPg1Qf95JKRkqS3d5ap8HidydUAAICuInj1QWPT7fpqToq8hvSHDbR6AQDQVxC8+qibWlu9Xv/4iIor602uBgAAdAXBq486f3iSZoxKVrPH0GPr9ptdDgAA6AKCVx92x2XnSPK1eh08VmtyNQAA4EwIXn3YlKxEXdo61uvR92j1AgAg1BG8+ri2Vq+/fVKqPeUuk6sBAACnQ/Dq48ZnODR3YroMQ3r43X1mlwMAAE6D4NUP3P610bJapLWfVWhLIc9wBAAgVBG8+oFRKfH67gVZkqQHV38mr9cwuSIAANARglc/ccfXzlFsZJh2HHHqrztKzS4HAAB0gODVTwyOt+mmWaMkSQ+9s0eNzR6TKwIAAF9G8OpHfjAjWxmOKJU6G/XspkKzywEAAF9C8OpHoiLCdNflYyRJT/zjgMqcDSZXBAAAvojg1c9cOWmIpg5LVH2TRw+8tdvscgAAwBcQvPoZq9WiB+ZPUJjVotU7y7Rh3zGzSwIAAK0IXv3Q2HS7FuUOlyT9vzd3MdAeAIAQQfDqp27/2milxNt06ES9/rDhoNnlAAAAEbz6rfioCC27Ypwk6Yn1B3ToeJ3JFQEAAIJXP3bFuen6yuhkNbV4dffrnzCjPQAAJiN49WMWi0W//OZExUSGaXNhpVZsPmx2SQAADGgEr34uMylGP52TI0n61d/3qLiy3uSKAAAYuAheA8D3pg3TtOwk1Td5tOTPdDkCAGAWgtcAYLVa9NC3z1VUhFX5B0/o5S1FZpcEAMCARPAaIIYNitWS2b4ux1+u3q3Pj9WaXBEAAAMPwWsAuXb6cE0fOUgNzR7dtnK7mlq8ZpcEAMCAQvAaQKxWix75P+cpMSZCu0pcevjdvWaXBADAgELwGmDSHFH69VXnSpL+sPGgNu0/bnJFAAAMHL0SvGpqarR48WINGzZM0dHRmj59urZu3XraY9avX68pU6bIZrNp1KhReuGFF3qjNEi6bHyavndRliTpjlcLdLzWbXJFAAAMDL0SvG644QatXbtWL730knbu3KnLLrtMeXl5Kikp6XD/wsJCzZ07V7NmzVJBQYEWL16sG264QWvWrOmN8iDp518fp9EpcTpa49atf9quFg/jvQAA6G0WwzACOqlTQ0OD4uPj9eabb2ru3Ln+9VOnTtWcOXP0wAMPnHLM3XffrdWrV2vXrl3+dVdffbWqq6v1zjvvdOlzXS6XHA6HnE6n7Hb72X+RAeDA0Rp943cfqL7Jo5suGakll+eYXRIAAH1CT3NHwFu8Wlpa5PF4FBUV1W59dHS0Nm3a1OEx+fn5ysvLa7du9uzZys/PD3R5+IJRKfH+8V6/X/+53v203OSKAADo3wIevOLj45Wbm6v7779fpaWl8ng8WrFihfLz81VWVtbhMeXl5UpNTW23LjU1VS6XSw0NDR0e43a75XK52i3ovnmTMnTdxcMlSXe+ukOHjteZWxAAAP1Yr4zxeumll2QYhoYMGSKbzabHHntM11xzjazWwH3c8uXL5XA4/EtmZmbAzj3Q/OzrY3X+sETVuFt044qPVN/UYnZJAAD0S70SvEaOHKkNGzaotrZWxcXF2rJli5qbmzVixIgO909LS1NFRUW7dRUVFbLb7YqOju7wmKVLl8rpdPqX4uLigH+PgSIizKonFkxRcpxNe8prtHhlAc9zBACgF/TqPF6xsbFKT09XVVWV1qxZoyuvvLLD/XJzc7Vu3bp269auXavc3NxOz22z2WS329st6LlUe5T+8P0pigyz6t3PKvQbJlcFACDgeiV4rVmzRu+8844KCwu1du1azZo1Szk5Obruuusk+VqrFi5c6N//xhtv1MGDB7VkyRLt2bNHv//97/Xqq6/q9ttv743y0Impw5L00Ld9g+2fXP+5/vzREZMrAgCgf+mV4OV0OnXzzTcrJydHCxcu1IwZM7RmzRpFRERIksrKylRUVOTfPzs7W6tXr9batWs1adIkPfzww3rmmWc0e/bs3igPpzF/8hDdMmuUJGnpG59oS2GlyRUBANB/BHweL7Mwj1fgeL2GbvnTx3p7Z7kSYyL0559M18jBcWaXBQBAyAiZebzQ91mtFj38nfN07lCHquqbtfDZLapwNZpdFgAAfR7BCx2KjgzTc9deoOzkWJVUN2jhs1vkrG82uywAAPo0ghc6lRxn04vXX6jB8TbtrajRDS9uVWOzx+yyAADoswheOK3MpBi9eP2Fio8K19ZDVbrllY/VzAO1AQDoEYIXzmhsul3PLrpAtnCr3tt9VLet3K4WwhcAAN1G8EKXXJidpKe+N1WRYVa9vbNct7+6g/AFAEA3EbzQZbNyUvT7BVMUEWbR33aU6q4/fyIPjxYCAKDLCF7olrxxqXr8mikKt1r0l+0lWvLnT3iuIwAAXUTwQrddPiFNj10zWWFWi17/+Ij+4zW6HQEA6AqCF3rk6xPT9eh3z1OY1aI3tpfolle2y93CVBMAAJwOwQs9Nm9Shp5cMEWRYVa982m5fvjiR2poInwBANAZghfOymXj0/TctRcoOiJMG/cd08LnNsvVyAz3AAB0hOCFszZjdLJW3HByktX/+z//0tEanu0IAMCXEbwQEFOHJelPP7xIg2IjtavvsOSqAAAftklEQVTEpW/9/kMdOFprdlkAAIQUghcCZsIQh964abqGD4rRkaoGXfXkh9pSWGl2WQAAhAyCFwJq2KBYvf6T6ZqclSBnQ7O+98xmvfVJqdllAQAQEgheCLhBcTa9csNFumxcqpo8Xt3yynb97v39MgwmWgUADGwEL/SK6MgwPfm9qbp2+nBJ0n+9u0+3/Gm76ptazC0MAAATEbzQa8KsFt33jfH65TcnKtxq0epPyvTtJ/NVUt1gdmkAAJiC4IVe93+nZemV1jsePytz6RuPb2LQPQBgQCJ4ISguzE7Sm7dcrHHpdp2oa9KCZ/6l5z8oZNwXAGBAIXghaIYmxujPP8nV3HPT1ewx9Iu/faZbXtmuGma6BwAMEAQvBFVMZLh+d81k3XvFON+4r51lmvf4Jn1W6jK7NAAAeh3BC0FnsVh0/YxsvXpjrjIcUTp0ol7f/P0HWrmliK5HAEC/RvCCaaZkJWr1rV/RrDGD5W7x6qdv7NQtr2xXdX2T2aUBANArCF4wVWJspJ5ddIGWXD7G3/V4+aP/1AcHjptdGgAAAUfwgumsVotuumSUXv/JdI1IjlW5q1ELntmsB976TI3NHrPLAwAgYAheCBmTMhP01q0ztGBaliTpmU2Fmv/EB9pdxsB7AED/QPBCSImJDNeD35yoZxedr0GxkdpTXqN5j2/SI2v3yd1C6xcAoG8jeCEkXTo2VWtu/zfNHp+qFq+hx9bt1xWPbdL2oiqzSwMAoMcIXghZyXE2PfW9qfr9gilKjovU/qO1+taTH+r+tz7jYdsAgD6J4IWQZrFY9PWJ6Vp7+0x9a8oQGYb07KZCzX50o/6x56jZ5QEA0C0EL/QJibGReuT/nKfnr7tAGY4oFVc26LoXtupHL27Tkap6s8sDAKBLCF7oU2aNSdG7d8zUj/5thMKtFr37WYXyHtmg368/oKYWr9nlAQBwWhajnzyjxeVyyeFwyOl0ym63m10OgmBfRY3uWbVLWworJUkjB8fqP6+coItHJZtcGQCgv+tp7iB4oU8zDEOrCkr04Oo9Ol7rliTljU3V0q/naOTgOJOrAwD0VwQvgteA5mxo1n+v3aeX/nVYHq+hcKtF37tomG67dLQSYyPNLg8A0M8QvAhekHTgaK1+9ffdem+3745He1S4/v2ro7Vw+jDZwsNMrg4A0F8QvAhe+IIPDhzXA6t3+x83lJUUozsvO0fzzs2Q1WoxuToAQF9H8CJ44Us8XkOvf3xE/7Vmr47W+MZ/5aTF687LxihvbIosFgIYAKBnCF4EL3Sizt2i5z8o1B82HlRNo2/G+0mZCVoyewx3QAIAeoTgRfDCGTjrm/WHjZ/r+Q8OqaHZ98Dt3BGDdOdl5+j84UkmVwcA6Et6mjsCPoGqx+PRsmXLlJ2drejoaI0cOVL333+/Tpfv1q9fL4vFcspSXl4e6PIwgDliIrTk8hxtXDJL1108XJFhVuUfPKFvP5Wva57+lz48cPy0/3cKAMDZCg/0CX/961/rySef1B//+EeNHz9e27Zt03XXXSeHw6Fbb731tMfu3bu3XWpMSUkJdHmABsfb9P/mjdcNXxmh372/X3/+6IjyD55Q/sETmpyVoH//6ijNGsMYMABA4AW8q/GKK65Qamqqnn32Wf+6q666StHR0VqxYkWHx6xfv16zZs1SVVWVEhISevS5dDWip0qrG/T0xoP605YiuVsfOzQu3a5//+oozR6fxl2QAIBThExX4/Tp07Vu3Trt27dPkrRjxw5t2rRJc+bMOeOx5513ntLT0/W1r31NH3zwwWn3dbvdcrlc7RagJzISonXfN8Zr091f1Y9njlBsZJg+K3PpJy9/rLz/3qCXNx9WY+uYMAAAzkbAW7y8Xq9+9rOf6aGHHlJYWJg8Ho8efPBBLV26tNNj9u7dq/Xr1+v888+X2+3WM888o5deekmbN2/WlClTOjzmvvvu0y9+8YtT1tPihbNVVdek5z88pBc+KJSr9S7IpNhIff+iYfp+7jAlx9lMrhAAYLaQuatx5cqVuuuuu/Sb3/xG48ePV0FBgRYvXqxHHnlEixYt6vJ5Zs6cqaysLL300ksdbne73XK73f73LpdLmZmZBC8ETK27Ra9uLdZzHxTqSFWDJCky3KqrpgzRD2aM0KgUngUJAANVyASvzMxM3X333brlllv86x544AGtWLFCe/bs6fJ57rrrLm3atEn5+fld2p8xXugtLR6v1nxaoaf/eVA7iqv962eeM1gLc4fpkjEpCmMcGAAMKD3NHQG/q7G+vl7h4e1PGxYWJq/X263zFBQUKD09PZClAT0SHmbV3HPT9fWJadp2uEpPbzyo93ZXaMO+Y9qw75iGJkZrwbRh+u4FmUrigdwAgNMIePCaN2+eHnjgAWVmZmr8+PHavn27HnnkEV1//fX+fZYuXaqSkhK9+OKLkqRHH31U2dnZGj9+vBobG/XMM8/o/fff17vvvhvo8oAes1gsumB4ki4YnqTDJ+q04l+H9eq2IzpS1aBfv7NH//3ePl1xbrq+f9EwnZeZwHQUAIBTBDx4Pf7441q2bJluuukmHT16VBkZGfrxj3+se++9179PWVmZioqK/O+bmpp05513qqSkRDExMTr33HP13nvvadasWYEuDwiIYYNi9fO543TnZWP01x2lein/sHaWOPXGxyV64+MSjU2367vnD9X8yUOUEEMrGADAh0cGAQFgGIZ2HHHqxfxDeuuTMjW1zgcWGWbVZeNT9d0LMnXxyGTmBAOAfiJkBtebheCFUFFd36Q3C0r1v1uL9VnZyfnlhiRE69tTh+rbU4cqMynGxAoBAGeL4EXwQgjaVeLU/24t1qqCEtW0zgkmSRcOT9KVkzM0d2I6XZEA0AcRvAheCGGNzR6t+bRc/7u1WPkHT6jtX11EmEWXjEnRNycP0VdzUhQVEWZuoQCALiF4EbzQR5Q5G/TXglKtKijV7i90RcbbwnX5hDTNnzxEF40YxNxgABDCCF4EL/RBe8trtKqgRG9uL1Gps9G/PjkuUrPHp+nrE9M1LTtJ4WEBf6wqAOAsELwIXujDvF5DWw9ValVBid7eWS5nQ7N/W1JspGaPT9WcCenKHTlIEYQwADAdwYvghX6i2ePVh5+f0N93lmnNp+Wqqj8ZwhJiInTZuFRdPiFN00cmMyYMAExC8CJ4oR9q9ni1+WClVreGsMq6Jv+26IgwfWV0svLGpeqrOSlKjrOZWCkADCwEL4IX+rkWj1dbCiv19q4yvffZUZW7To4Js1ikKVmJyhubqq+NS9HIwXE8sggAehHBi+CFAcQwDH1a6tJ7uyv03u4K7Spxtds+fFCMZuWkaOY5g3XRiEF0SQJAgBG8CF4YwEqrG7Ruz1Gt212hDw+cUJPH699mC7dq2ohBmnnOYM08Z7BGDo6lNQwAzhLBi+AFSJJq3S3atP+4Nuw7pg17j7abpkLyPbpo5hhfCJs+cpDioyJMqhQA+i6CF8ELOIVhGDpwtNYXwvYd0+aDle1aw8KtFk3JStT0UYN08ahkTRqaoMhwpqsAgDMheBG8gDOqb2rR5oOV/iBWeLyu3faYyDBdMDxJ00f6gtjYdDsz6ANABwheBC+g2w6fqNMHB07og8+PK//zE+2mq5AkR3SELhqRpItHJWv6yEHcLQkArQheBC/grHi9hvZW1OjDz08o//Pj2nywUjXulnb7JMfZdGF2oi4YnqQLhifRIgZgwCJ4EbyAgGrxeLWzxKkPPz+hDz8/rm2HquRu8bbbJ94WrqnDfUHswuwknTvUIVs4U1cA6P8IXgQvoFe5Wzz65IhTWwortaWwUh8drlLtl1rEIsOtOm9ogi7MTtIF2UmanJUgO3dNAuiHCF4ELyCoPF5Du8tc2nrIF8S2HqrU8dr2Y8QsFml0SpwmZyZqyrAETc5K1KjBcbLSPQmgjyN4EbwAUxmGocLjdb4WsUO+IFZc2XDKfvG2cJ2XlaDJmb4gdl5mghJjI02oGAB6juBF8AJCzrEat7YXVWl7cbW2F1VpR7FTDc2eU/YbkRyr8zITNGGIQ+cOdWhchl0xkeEmVAwAXUPwIngBIa/F49XeihptL6puXap08EtziUmS1SKNSonzBbEhDk0c6tC4dIeiIxm4DyA0ELwIXkCfVFXXpILiau04Uq1dJU59csSpozXuU/azWqTRKfH+VrEJQxwamx5PyxgAUxC8CF5Av1HhatTOI07tLHH6wliJU8c6CGMWizR8UKzGpsdrbJpd4zLsGptuV7ojioleAfQqghfBC+jXKlyN+qQ1jO08Uq1dpa4Ow5jkm3F/bHq8xqb7gti4dLtGp8YxxxiAgCF4EbyAAedYjVu7y1xfWGr0+bFatXhP/Z+1cKtFIwfHaWx6vEanxuuc1HiNSY3X0MRoprcA0G0EL4IXAPkmet1fUesPYrvLXPqszCVnQ3OH+0dHhGlUSpzOSY3XOamtr2nxyqC7EsBpELwIXgA6YRiGypyN2l3m0p7yGu2vqNHeilp9fqxWTV96DFKbOFu4RqXEaUxqvEa3BbLUeKXabQQyAAQvgheA7mrxeFVUWa99FTXaV1Hb+lqjg8fqOuyulKTYyDCNGBynEYNjNSI5TiNTfK/ZybFMdwEMIAQvgheAAGn2eHXoeJ32tgYyXwtZjQ6fqJenk0BmsUgZjmiNGByrkYPjNLL1dcTgOFrJgH6I4EXwAtDLmlp8LWQHj9Xq82N1ra+1Oni8TtX1HY8hk3ytZMOTYzV8UKyGDYo5+Zocq5R4QhnQF/U0dzDzIAB0UWS4VaNS4jQqJe6UbZV1Tb4QdqxWB4/Vtf5dp8OV9apr8ujTUpc+LXWdclx0RJiGDYr5QiCL1fBBMRqWHKt0exR3XAL9DC1eANCL2lrJDh2v06ETdTp8ot7/eqSqXp30XEryBb2spBgNHxSjrKRYDU2MVmZSjDKTopWZGKNYG//tDJiFFi8ACEGnayVravGqpLrBF8SO1+nQiXodbg1lxVX1amrx6sDRWh04WtvhuRNjInxBLDFGQ5OiNTQxRpmt4WxIQrSiIhjsD4QaghcAmCQy3Krs5FhlJ8dKY9pva/F4VeZs1KETvkBWdKJOR6oaVFxVr+LKBjkbmlVV36yqet/zLTuSare1C2OZiTEamhitIYnRSnNEMZM/YAK6GgGgD3I1NutIpS+IHalqUHGlr+uyuHVdfZPnjOdIjrNpSEKU0h3RykiIVkZCVOur7+/kWBtjzIBO0NUIAAOIPSpC4zIiNC7j1P/BNwxDVfXNrWGsrZWsXsVVDTpSVa+y6kY1NHt0vNat47Vu7eikxSwyzKo0R9TJQPaFgDYkIVrpCdGKY5wZ0C38iwGAfsZisSgpNlJJsZGalJlwynbDMFRd36yS6gaVVjeozNmo0uoGlXzh7wpXo5paJ5gtqqzv9LNiI8OU6ohSmt23pNijlGa3Kc0RpVS7bxkcb1NEmLU3vzLQZxC8AGCAsVgsSoyNVGJspCYMcXS4T7PHqwpXY7tQVlrdoLLqRv/frsYW1TV5dPBYnQ4eqzvN5/m6NdPsUUq125TaGtJSW8NZW2izR4czpxn6PYIXAOAUEWFWDU2M0dDEmE73qXO3qMLVqHJXo+/V6VZF29+uRlU4G3W0xq0Wr6FjNW4dq3FrZ0nnn2kLt2pwvE2D421KaX0dHBfV/n28TclxNkWG04KGvongBQDokVhbeOtzK0+dKqON12voRF1TazDzBbKjrcGs3OVWhbNRFTWNqq5vlrvFqyNVDTpS1XDGz06IifhCOGsLa1H+cNa2PiEmglY0hBSCFwCg11itFn8Q6qxbU5Iamz06VuPW0daWsWM1jb7XWveX1vta0Krrm1Vd36x9FR3PcdYmIsyiwXE2JcfbNCg2UoPi2l4jlRRr06C4yHbrmfsMvS3gwcvj8ei+++7TihUrVF5eroyMDF177bW65557TvtfHevXr9cdd9yhTz/9VJmZmbrnnnt07bXXBro8AEAIiooIa52Vv/OuTcnXguZsaNaxWreOutw6VtvoD2TtAlqtW9X1zWr2GCp1NqrU2dilOmIjw5QUF6lBsTYlx/luUDglrPn/jmQuNHRbwIPXr3/9az355JP64x//qPHjx2vbtm267rrr5HA4dOutt3Z4TGFhoebOnasbb7xRL7/8statW6cbbrhB6enpmj17dqBLBAD0UVbryRsDzkmNP+2+7haPTtQ26WiNW8dr3Kqsa9LxOrdO1Db5/q71rWt73+Txqq7Jo7rKBhVXnrm7U5LibeH+EJYUG6mEmEglxkT4aoxpW06+T4iJ4A7PAS7gE6heccUVSk1N1bPPPutfd9VVVyk6OlorVqzo8Ji7775bq1ev1q5du/zrrr76alVXV+udd97p0ucygSoAoKcMw1CNu6U1hLl1vDWMnah160RrODvRGtpO1Pm2eU73oM3TiLeFtwaxCCXEtAW2CCXFRCqhdX1STGuIi41QYgxdoKEoZCZQnT59up5++mnt27dP55xzjnbs2KFNmzbpkUce6fSY/Px85eXltVs3e/ZsLV68uNNj3G633G63/73L5Tr74gEAA5LFYpE9KkL2qAjfI5zOwOs15Gps9oeyyjq3quqbVVnXpOr6JlXWNau6vklV9U2tj3ZqkrOhWYYh1bhbVONuUVFl1+uLjgjzBzVHdMTJJcb3ao+OUMIX10efXB/G0wdCSsCD109/+lO5XC7l5OQoLCxMHo9HDz74oBYsWNDpMeXl5UpNTW23LjU1VS6XSw0NDYqOjj7lmOXLl+sXv/hFoMsHAOCMrFaLElpbpUYO7toxntbxaVX1J8PZF//2vTapujWotYU2j9dQQ7NHDU5Pl8eqfVG8LVz2L4SxhJj2wezLYY3Q1rsCHrxeffVVvfzyy3rllVc0fvx4FRQUaPHixcrIyNCiRYsC9jlLly7VHXfc4X/vcrmUmZkZsPMDABBIYdaTTxToqrYu0Ko6Xwirbm05czX47up0Npy6uFpf61qf19nWwlZS3bVxa18UbwtXfFS44qMiWl9P/m2PjvC/t0d9eT/fa1xkOM/7/JKAB6+77rpLd999t66++mpJ0sSJE3X48GEtX7680+CVlpamioqKdusqKipkt9s7bO2SJJvNJpvNFtjiAQAIIV/sAh02qHvHNrV45WrsOJQ565tV3UlgczY0+x+y3hba1IOWNl/9UlxkZ4GtfVBrC29xtgjF2cJ9S5TvtT9NmBvw4FVfX6/w8PanDQsLk9fr7fSY3Nxcvf322+3WrV27Vrm5uYEuDwCAASEy3KrkON9M/93V1OL1hbHGZtU0tqjmS6+uDtZ9+e8mj7fdmLaehre27+IPY18IZG1/x9vCFdvB+6GJ0aed4NcMAQ9e8+bN0wMPPKDMzEyNHz9e27dv1yOPPKLrr7/ev8/SpUtVUlKiF198UZJ044036ne/+52WLFmi66+/Xu+//75effVVrV69OtDlAQCAM4j8wuObeqqx2XNKGPMFudOHt7rWoFbnbvG3vDW1eFXZ4hsD1x3fnjpU//WdST3+Dr0h4MHr8ccf17Jly3TTTTfp6NGjysjI0I9//GPde++9/n3KyspUVFTkf5+dna3Vq1fr9ttv129/+1sNHTpUzzzzDHN4AQDQR0VFhCkqIuyswltL69xqte4W1Ta2+F79fze3BjWPat3NqnX7gltta2iraWxR5mmeNWqWgM/jZRbm8QIAAMHS09zRf0arAQAAhDiCFwAAQJAQvAAAAIKE4AUAABAkBC8AAIAgIXgBAAAECcELAAAgSAheAAAAQULwAgAACBKCFwAAQJAQvAAAAIKE4AUAABAkBC8AAIAgIXgBAAAESbjZBQSKYRiSJJfLZXIlAACgv2vLG235o6v6TfCqqamRJGVmZppcCQAAGChqamrkcDi6vL/F6G5UC1Fer1elpaWKj4+XxWIJ+PldLpcyMzNVXFwsu90e8POj67gWoYNrETq4FqGB6xA6evtaGIahmpoaZWRkyGrt+sitftPiZbVaNXTo0F7/HLvdzj+mEMG1CB1ci9DBtQgNXIfQ0ZvXojstXW0YXA8AABAkBC8AAIAgCbvvvvvuM7uIviIsLEyXXHKJwsP7TQ9tn8W1CB1ci9DBtQgNXIfQEYrXot8MrgcAAAh1dDUCAAAECcELAAAgSAheAAAAQULwAgAACBKCVxc98cQTGj58uKKiojRt2jRt2bLF7JL6leXLl+uCCy5QfHy8UlJSNH/+fO3du7fdPoZh6N5771V6erqio6OVl5en/fv3t9unsbFRN998swYNGqS4uDhdddVVqqioCOZX6Vd+9atfyWKxaPHixf51XIfgKSkp0fe+9z0NGjRI0dHRmjhxorZt2+bfzrUIDo/Ho2XLlik7O1vR0dEaOXKk7r///nbP6ONa9I6NGzdq3rx5ysjIkMVi0apVq9ptD9TvXllZqQULFshutyshIUE/+MEPVFtb2ztfysAZrVy50oiMjDSee+4549NPPzV++MMfGgkJCUZFRYXZpfUbs2fPNp5//nlj165dRkFBgfH1r3/dyMrKMmpra/37/OpXvzIcDoexatUqY8eOHcY3vvENIzs722hoaPDvc+ONNxqZmZnGunXrjG3bthkXXXSRMX36dDO+Up+3ZcsWY/jw4ca5555r3Hbbbf71XIfgqKysNIYNG2Zce+21xubNm42DBw8aa9asMQ4cOODfh2sRHA8++KAxaNAg46233jIKCwuN1157zYiLizN++9vf+vfhWvSOt99+2/j5z39uvPHGG4Yk4y9/+Uu77YH63S+//HJj0qRJxr/+9S/jn//8pzFq1Cjjmmuu6ZXvRPDqggsvvNC4+eab/e89Ho+RkZFhLF++3MSq+rejR48akowNGzYYhmEYXq/XSEtLM37zm9/496murjZsNpvxpz/9yf8+IiLCeO211/z77N6925Bk5OfnB/cL9HE1NTXG6NGjjbVr1xozZ870By+uQ/DcfffdxowZMzrdzrUInrlz5xrXX399u3Xf+ta3jAULFhiGwbUIli8Hr0D97p999pkhydi6dat/n7///e+GxWIxSkpKAv496Go8g6amJn300UfKy8vzr7NarcrLy1N+fr6JlfVvTqdTkpSUlCRJKiwsVHl5ebvr4HA4NG3aNP91+Oijj9Tc3Nxun5ycHGVlZXGtuunmm2/W3Llz2/2WEtchmP7617/q/PPP13e+8x2lpKRo8uTJ+p//+R//dq5F8EyfPl3r1q3Tvn37JEk7duzQpk2bNGfOHElcC7ME6nfPz89XQkKCzj//fP8+eXl5slqt2rx5c8DrDp2pXEPU8ePH5fF4lJqa2m59amqq9uzZY1JV/ZvX69XixYt18cUXa8KECZKk8vJySerwOrRtKy8vV2RkpBISEjrdB2e2cuVKffzxx9q6desp27gOwXPw4EE9+eSTuuOOO/Szn/1MW7du1a233qrIyEgtWrSIaxFEP/3pT+VyuZSTk6OwsDB5PB49+OCDWrBggST+XZglUL97eXm5UlJS2m0PDw9XUlJSr1wbghdCzs0336xdu3Zp06ZNZpcy4BQXF+u2227T2rVrFRUVZXY5A5rX69X555+vX/7yl5KkyZMna9euXXrqqae0aNEik6sbWF599VW9/PLLeuWVVzR+/HgVFBRo8eLFysjI4Fqg2+hqPIPk5GSFhYWdcgdERUWF0tLSTKqq/7rlllv01ltv6R//+IeGDh3qX9/2W5/uOqSlpampqUnV1dWd7oPT++ijj3T06FFNmTJF4eHhCg8P14YNG/TYY48pPDzc/1+WXIfel56ernHjxrVbN3bsWBUVFUni30Qw3XXXXbr77rt19dVXa+LEifr+97+v22+/XcuXL5fEtTBLoH73tLQ0HT16tN32lpYWVVZW9sq1IXidQWRkpKZOnap169b513m9Xq1bt065ubkmVta/GIahW265RX/5y1/0/vvvKzs7u9327OxspaWltbsOLpdLmzdv9l+HqVOnKiIiot0+e/fuVVFREdeqiy699FLt3LlTBQUF/uX888/XggULVFBQoBEjRnAdguTiiy8+ZUqVffv2adiwYZL4NxFM9fX1pzxkOSwsTF6vVxLXwiyB+t1zc3NVXV2tjz76yL/P+++/L6/Xq2nTpgW+8IAP1++HVq5cadhsNuOFF14wPvvsM+NHP/qRkZCQYJSXl5tdWr/xk5/8xHA4HMb69euNsrIy/1JfX+/f51e/+pWRkJBgvPnmm8Ynn3xiXHnllR3eNpyVlWW8//77xrZt24zc3FwjNzfXjK/Ub3zxrkbD4DoEy5YtW4zw8HDjwQcfNPbv32+8/PLLRkxMjLFixQr/PlyL4Fi0aJExZMgQ/3QSb7zxhpGcnGwsWbLEvw/XonfU1NQY27dvN7Zv325IMh555BFj+/btxuHDhw3DCNzvfvnllxuTJ082Nm/ebGzatMkYPXo000mY7fHHHzeysrKMyMhI48ILLzT+9a9/mV1SvyKpw+X555/37+P1eo1ly5YZqamphs1mMy699FJj79697c7T0NBg3HTTTUZiYqIRExNjfPOb3zTKysqC/G36ly8HL65D8Pztb38zJkyYYNhsNiMnJ8d4+umn223nWgSHy+UybrvtNiMrK8uIiooyRowYYfz85z833G63fx+uRe/4xz/+0eH/b1i0aJFhGIH73U+cOGFcc801RlxcnGG3243rrrvOqKmp6ZXvZDGML0y9CwAAgF7DGC8AAIAgIXgBAAAECcELAAAgSAheAAAAQULwAgAACBKCFwAAQJAQvAAAAIKE4AUAABAkBC8AAIAgIXgBAAAECcELAAAgSAheAAAAQfL/AdXMjvBp/z8OAAAAAElFTkSuQmCC",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x322213dd0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "include(\"NtSolutions/inverse_5_inpainting_sparsity/exo3.jl\")\n",
    "\n",
    "# niter = 1000\n",
    "# a = U.*PsiS(fSpars)\n",
    "# E = []\n",
    "# for i in 1 : niter\n",
    "#     fTI = Psi(a)\n",
    "#     d = y - Phi(fTI, Omega)\n",
    "#     E = [E; 1/2.*vecnorm(d )^2 + lambd*sum(abs(a))]\n",
    "#     # step \n",
    "#     a = SoftThresh(a + tau.*PsiS(Phi(d, Omega)), lambd*tau)\n",
    "# end\n",
    "\n",
    "# figure(figsize = (7, 5))    \n",
    "# plot(E)\n",
    "# show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "## Insert your code here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Perform the reconstruction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "fTI = Psi(a);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display the result."
   ]
  },
  {
   "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 0x322e9a850>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize = (6, 6))\n",
    "imageplot(clamP(fTI))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "__Exercise 4__\n",
    "\n",
    "Perform the iteration with a decaying value of $\\lambda$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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xyy67xP333x+nnnpqXH311XHDDTdUun9XQh5XZX/+FNf9c9LuWj/xxBPjrbfeKvww6th2221j9913jwMOOCCuuuqqmDBhQnzmM5+JV155pbFPr732WixfvrxL/3WVl156KT7+8Y/Hiy++GNdee22HUM6VHyVPPfVUh98+9dRTsd566zV+5IwfPz7mzJkTc+bMidtvvz2WLVsWRx11VDz33HMxZsyYLve1u/Tr1y8+/OEPxz333FP5NJn3FlsSTOXIxJfHww8/3OHchQsXxgc/+MEquuDSSy+NadOmxbe//e3qnNdff70tj+WIP77AjjnmmDjmmGPimWeeiW222SZOO+20+PjHP157vnrq13HYYYfFt7/97bj66qvjmmuuif79+8eUKVPa6lN3efjhh2O33Xaryq+88ko89dRTsddee0XEHxP0rFixIi6//PLYeeedq/Mee+yxVdqPpjHqDsOGDYt33nknHnvsscJi8sgjj6zytt4LOlvryqhRo+Kzn/1s/OhHP4oPf/jDXbpu79694/TTT4/ddtstvve97zVaIS666KI44ogjunTtrnygvf7667HvvvvGwoUL48Ybb6y1kgwePDj69+8fd999d4e6dvIO9OrVq3CInD59erzzzjux++67p78bNmxY/OY3v4lXXnmlsCYsWLCgS+2uZGXipldeeSXWXHPNtn5r2seWhL8ibr755toXzkqtnGa/u+66q/AreOKJJ+LKK6+MPffcs/o/zt69e3e45ne/+90OoXyd8fbbb3cwr2+44YYxaNCgWrPoSlZ6VHf2MbLFFlvEFltsET/5yU/isssui4MPPvhPFjZ1zjnnxJtvvlmVzz777HjrrbeqD56VY6fj9sYbb8QPfvCDVdqPlS/Qdj/YMlZ+aLGvf2kZO9td6+Skk06KN998M84888wut7nrrrvGtttuG2eddVZlvu+MVemT8Pbbb8enPvWpuOuuu+KSSy6J7bffvtNzDzjggPjv//7veOKJJ6q//eY3v4mFCxfGQQcdVJw7f/78ePzxx9O2X3vttTj55JNj4MCB8elPfzo9d6+99oq33norzj777KLv7ayd559/PmbMmBEDBgyoDWU1qx5bEv6KOP744+PVV1+N/fffPzbbbLN44403YsaMGXHRRRfF8OHDO/yfzYQJE2LKlClFCGREVJkOIyL22WefuOCCC2LttdeOcePGxV133RU33nhjrL/++l3q08svvxwbb7xxHHjggbHllltGv3794sYbb4zZs2cX1gmyxhprxLhx4+Kiiy6KMWPGxHrrrRcTJkwowt0OO+yw+Od//ueIiHclNbTLG2+8ER/96Edj6tSpsWDBgvjBD34QO+64Y+y3334R8ce49nXXXTemTZsWJ5xwQvTq1SsuuOCCVW7SX+l0esIJJ8SUKVOid+/eHWLcu3PNAw44IM4666xYsWJFFQK5MgXwe2G9UA4//PD42c9+Fo899li6p0W7a52stCb87Gc/a6t/X/rSl+Kggw6K888/v4MTqLIqfRK++MUvxlVXXRX77rtvPP/88/GLX/yiqNe1/+UvfzkuueSS2G233eIf/uEf4pVXXolvfetbsfnmm3cYk7Fjx8Yuu+xSpD6fOnVqDBo0KMaNGxe///3v46c//Wk8+uij8etf/7rR32ffffeNHXbYIf71X/81Fi9eHOPGjYvLL7889cG59NJLo1+/ftFqtWLZsmVx7rnnxgsvvBA//OEP3/O1Zv5//kxRFebPwDXXXNM68sgjW5tttlmrX79+rdVXX701evTo1vHHH98hC11EtI499tjWL37xi9Ymm2zS6tOnT2vrrbfuEK72wgsvtI444ojWBhts0OrXr19rypQprfnz57eGDRvWmjZtWnVeZ1nq/vCHP7S+9KUvtbbccsvWhz70odaaa67Z2nLLLVs/+MEPivMYCthqtVozZsxoTZw4sbX66qvXht899dRTrd69e7fGjBnT5THqLASyLhRvl112ae2yyy4dfnvrrbe2Pve5z7XWXXfdVr9+/VqHHHJIa8WKFcVv77zzztZ2223XWmONNVqDBg2qQvQCIYGdhUB+61vf6tAfjsFbb73VOv7441v9+/dv9erVqwin47mdZbirG4//+Z//aR177LGt9dZbr7Xmmmu29t1339b8+fNbEdE644wzOvSrM7oTAnnAAQe01lhjjdpMiko7a72z+X344YdbvXv37nLGxVar1Xr77bdbo0aNao0aNapDqO97xS677NJWCOWcOXNae+65Z+uDH/xga5111mkdcsghreXLl3c4LyKK9d1qtVrf/OY3W5tttlmrb9++rXXXXbe13377te69994u93XFihWtQw89tLXWWmu11l577dahhx7auvfee7sUArnmmmu2tt9++9bFF1/c5fbMu6dXq9WDPZLMe0avXr3i2GOPje9973t/7q50m+eeey4GDhwYX/nKV+Lkk09+z9s7//zz44gjjojZs2fXJqx5P3PffffF1ltvHb/4xS/ikEMOec/a2WijjeKwww7rUsIpY8y7xz4J5n3L+eefH2+//XYceuihf+6uvK+oi4c/66yz4gMf+EDhiLmqmTt3brz22mvxL//yL+9ZG8aYEvskmPcdN910Uzz00ENx2mmnxf/6X/8r1a5N+5x55pnxu9/9LnbbbbdYbbXV4pprrolrrrkmPve5z8WQIUPes3bHjx/fIaeEMea9xR8J5n3HqaeeGjNmzIgddtjhL87r/v3A3/7t38YNN9wQX//61+OVV16JoUOHximnnBInnnjin7trxphVjH0SjDHGGFOLfRKMMcYYU4s/EowxxhhTiz8SjDHGGFNLj3VcZDY+3ZiG6XfXWmutTuteffXVoqwpbLlbmaYJfvnll4s6el1nrh687kYbbVQdc7vkJ598sjoeMGBAUTdnzpyi/Oyzz1bHzGn+3HPPVccrVqwo6tZZZ52irOO1co+Guja//vWvF3WnnnpqUdZtmXlfunEN9yxYmZt9JSu3sa2DGxJpFjbOtY4BM0IyjbSm1WV0hKa03XXXXYu6YcOGdXpdpurVOo4zd3M8/fTTq2OOB3+ru+YxC57OPTfI2XrrrYvy5ptvXh0zRbautXnz5hV1q6++elHWZ4MponX8Vm5DvRI+J7rxFfdeeLe7X65Et9+OiGIPBO6HMHfu3OqY26JnGR25iZKOMzf34t4RS5YsqY65vt94443qmFkMWR41alR1zE3XdA3zueB7TdcFz+VzrOuCddp33hczK2pZ059HlM8G28je/Vyz2XuEz4L2/QMfKP+/m+UsNbyOLe+Z465b0fPfnpUp6+vYZpttOq3rDFsSjDHGGFOLPxKMMcYYU4s/EowxxhhTS4/1SaCGpJoNdR/VreiDQM1IdVBqh88//3ztNevaVO2VGvLTTz9dlG+++ebqePTo0UWdak+LFi0q6qhf6q5yqptHlOOz3nrrFXUcSx0T1dsiSv+F+fPnd1oXEXH//fdXx4888kinbXDsqCVyjjL0PnkdJdMyI/L7HDFiRHVMf4BZs2YV5U022aQ61rmMiLjxxhur47vvvruoo2+DauXsK8dHfR+4hlV/pnZJHVSfFfoSaJlr5JVXXinK6r9D3wEdE84X0z+r5s350zXM56JJV1dWboW9EvXtoZ+P+gupH08dusb5DtI1MnPmzE7biCjvm8+N3jd9dfhsqq8K3wf6W84Jx1bXHseZ60n7zjWj88frcH3rdVmnv+UYNF1X0TXC32V+UFxbmd8IfUG0HY4zr6tjmfWH49wdbEkwxhhjTC3+SDDGGGNMLT1WbqApS82WNCOpaYbmsywsjWbTrH2a7DXcjqFcO+ywQ1HWcMANN9ywqHvwwQerY5o7iYYZ0gSlJkWauTgGOl4Mk1Oz9y233FLUMdxOf6tSSERpgs7GOaKcE457ZlKkyU5Nf6yjCVjXiYaoRZThf2z/3nvvLcpq7uMYbLXVVtWxShgRHcNCs/tiWeeT5k6VRzT0NqLjXKupmyF0On80xzIkK5trLfM+2B+uU0XXN89jWaUBSi4bb7xxUVbz/3bbbVfUaTgZ1z6lEn12+a7QNcTwOg15jIhYe+21q+MsNJDPON9B+o7kuOv8USLLpBpeh/1TKIPp89YkL2o7PDeTCdh3/S3/XdC+8744JpnkwveDvlu59rR/mazD/nE96Tun6d+MrmBLgjHGGGNq8UeCMcYYY2rxR4IxxhhjaumxPglZyk1qkKohUSNiGlbV46gPaggk9TZqbKodMpztnHPOKcqaepUhYqrZqu9CHapFNfVPYfjW0qVLu9QGx5n6t+qy1OoU6m0M29GQP7aZrQNqdVqmPsnx0rlnyKreC1Nl07dA54zrQNearq2Ijj4SWV+zcE6GLqpfBNf+nnvuWZTVL4Ia+2233dZp/zQtdESpvVKHXbx4cXXMeacuq32gf0fmb8L1pffNOXn44YeLsvqjUOfXZ1xTkEd0XJfPPPNMdUw/Aw1X5lyyrOuCqanVx0X7Vtf3zF9A35ec9ywUj1p9FsaX+Qc0PZtZ+mKlndDFTPMnnFvtD9sg6iOQXYdjkJXZ1+xZ6A62JBhjjDGmFn8kGGOMMaaWHis3MNRMs5Yx7EPNOjTj0tSumck01C2iNAnTtM4seGp2euihh4o6mnVnz55dHdM8pNfJdkPkbymV6K6H2U6FEaWZOcu4loV98rdsQ39LUyivqyZPmtayMWGbag7l/DE0T/vANaNzQhPrpptuWpSvu+66Tvuu5nWa2rPd5DgnLKu0RBlDTe0jR44s6q6++uqirOG3EydOLOr0GaNpmzKGhk9yjdD0rnAMdE0PGjSoqMvCNSkJqVl+t912K+ouv/zyoqwZULkOhgwZUh1zrekzHVGuN/ZdpYjMdBxRmvcpN+iOmjR7ZzsrZuPM/nCtZTIin2N9d2S/y6QI1mdhjrznLCMk29S+sq5pd0mF8mi2u2QWXkr0OpyjLLy1O9iSYIwxxpha/JFgjDHGmFr8kWCMMcaYWnqsT8LgwYOLsup6jz/+eFGnGu24ceOKujvuuKMoL1y4sDrmjoybbbZZdUx9kilkM82N/hSqIfE6qtc3henouUwTqzqapm+uQ8PUMr2NcEx0DBiCqWli6UPCMDmdW/pasE3V9bL0rrwv7pKnunq2OyHH8tFHH+20He7MqeGuDFVkm+o7Q/8J+gBoam+Ol/ad/gDUL3VMuJ61Dfr1DB06tCjrDpfU0VVjp68MfQsOPPDA6viHP/xhUbfFFltUx9T877vvvqKsY0CfEq5TXZvckVF1f4ZkMjX1tttuWx3TL0P7wLnMQhfZZrb7Z6ZbN4WeKlyXWchfU/rwzsh2NY0o7y27r2wX2Kb+6HrP/IOy39W1oe+DLNyV65Jk77nMn6I72JJgjDHGmFr8kWCMMcaYWvyRYIwxxphaerVWhWjxZ+Df/u3fijJ1bGXGjBnVMbeCzeLTqW2q9kp9mbqZatWqqUd01ODVD4EasmqUWarQiFJDph6nOrZu3RvRUZ/PcgRQa1Woo61YsaI6pjanY8s4dqaf1nwVTdsHZ1uoqh8EY/t1C2WWeV+qHT7yyCNFXaaDcgx0TrLtjCPKrZDpB8FzdQtoPt5Zem6uPe2v5gSIiBg+fHh1fM899xR17J9q+Vw/Y8eOrY6pv1OznT9/fnU8YcKEom7OnDnVMf07dtppp6KsaaOZQlrvK6IcE20jIuKjH/1odUx/BY6XPnNsU9851Je5hjUvCN9d+q7gO4ZbRStZGmT2h2Or7TT5IGTvLz23Ka226v5Z7oOmLaf1vvmM67zT7yIbL67ZpntRsm2k+Y7WcpbWnu1Pnjy50/Y7w5YEY4wxxtTijwRjjDHG1NJjQyCZjlfDimhK1pTENCtRClBTUmbWpRSxaNGioqxmZ5r+2KZKIDTHqgmK95yF8PA6amamuZOpe9k/RfuQmc/ZTpYmlua7LJSS16FZTsc9MwvSjMsx0TA5zp/KOpSdGN6WmZL1OmwjMzuzr5MmTSrKKjfceuutRZ2OQbYrXkQ5n7dEDCLgAAAgAElEQVTffntRd+6553bad02RHlE+j5QUVFraYYcdijrKUDomlHl0DY8fP76oYyjljjvuWB3T/Mrr6m6XJ510UlH3ne98pzrWkNCIjvKVykl8r+h9MqyRc6LPnEo1ERELFiyojhkCTYlRx5LvxEwWUNmL1812a2TfKRNkz0nWH9ZlqZZ5rj5TWRholiqf7XAss1D4jCwVdUT5nuO7TPvH561bfXnXVzDGGGPM+xJ/JBhjjDGmFn8kGGOMMaaWHuuToPpbRKnBZeFk1J6Yjlf1cIbbaZtMrUwtMdOMGIapmhdDXbQ/vA5RfV419YhSj8u2UI4o/Reov+nYMtyPupn+lv4K2ib1U4ZZad85f5nuSB8OvS/q6EyHq+m5uUa0v+x7FpLJNlUr5z2zTS1T79a+RkTMnDmzOtZU4hHlnFGrf/rpp4uy6vwa7hdRbh3NkFX652RhX5tvvnl1zPAxbmWt6dY11XNE6RNAH5ttttmmKGt/eR364+y+++7V8RlnnFHUqS8I/Wg4n7pOuNY07LJJi9b75Hyp7xX9sh5++OGirFo1wyP1PcN3A59jfab4bGZ6fJbuvcmXIAtz1N82bemsz2qWepk+Ce1kDWhnq+YsFXN2HdZlfmPdwZYEY4wxxtTijwRjjDHG1NJj5QaG9CxdurQ6prlRzXsMCaFZV7MEMgOdmqt4HZr3R4wYUR3TDEezqsoa7I+GR9FcrffMvtN0paY1mgwZLqn3QslFd+rjjoeUUTREi6bjq6++ujrmXDKDYLZrJSWYLJRKdw7l/PFcHT+O5WOPPVYd606OER1NrCq5ULrR9UVphLKFZvTTtRXR0USuIYi6JiLKseYYcJ2qKZkSgpoxaWrneKmswbBGnWvKKHym7rrrruqYO7QqDBGlOV2fP+4Ye8ABBxTlW265pTrmLpU615w/PqsqE3Ct6X0ypJe73eq7jWtf33PMgskMkDq32fxxPbN/uk6bQmrVTJ9JCmyT72GdP46l9oHjw/WdkZnp+f7W8Woy7+u5lD+yTJLt7ESZhZp2B1sSjDHGGFOLPxKMMcYYU4s/EowxxhhTS4/1SaAWrJogtUPVRJlGNwvxoc6oYUzUhKhTaZu6i2FErodTf1c9jjonU0Or/kzfBtUO6YNA3Vp1LPovaN+pQXLc582bVx1retuIMmSUIXT0g8hCg9gH1VoZnqhjyTS6nGstL1mypKjT8WEYIVHdkRqkji21XuqpOgb02WD/NNyNobm6FjVkLqKjnqptco6y3QgZeqY+AVxPuvazvkaU/hQc98MPP7w6pg5L3wYdW47lrFmzirL60vC62h8+m9xtU6/DZ1z1ePogPPjgg0V5yy237PQ6Ol5Mjc1dKrWec6LrlH4FfM9l4YiZPp+lWqa/Aq/LZ1XROeK6zNIpZ2GO7Cuvo21m4eQR5TuI6zLzX2pnvPReOLfdwZYEY4wxxtTijwRjjDHG1OKPBGOMMcbU0mN9Eqg3q1ZOzUp1NGpPjBHOYmm1zWwLV9IUA5+lKNU6aqLMB6H19DvQMuOOiV6H6V21P4zX531uvfXW1TG1Xk1byzlg/1Sf41hl29zyOrrNLX0AqHHr2NJHQq9LjZa+BKrHc83omm3Sc3VO6INA/xxtk2tE1x5zBOh8RZR+JNyWWNtkngbdqprX3WqrrYq6LB/FRRddVJQ1NTTXk+ZfyJ6LiHLuOV9Mdaz+Fcy/oCmvszTaERE33XRTdfzJT36yqFPfAs6J+iBERNx3333VMbfEXrx4cXXM++Kzqr5ZzF2hzxifoew9R42denzmA6BzxGc8S4Oc9acpxbX+Nmsj20Y6onw/cQ3zXvS3fHdkfhBsM/t3QX/Ld2t3sCXBGGOMMbX4I8EYY4wxtfRYuYE7qakJkeFIai5iHU0+rFfUZM8QFZqZ1ARE0x/lBg2lyq7L0LLnnnuuKKuJk7vQaRs0XWVmOYbJ6blMjUsT2bhx46pjhnJpf5iWOdv1jea7TKrhOGvfH3rooaKO5kY1O2emSPaVkoua/tkfXWucW5Z1PTEdN+dTTcQMb9V7oUwwdOjQoqwSDCUEXXscH64Z3aWSO1Zqm2yfO0/+9re/rY4POuigok7XEM2vfKb1Ocl2Lo0oJSrOrYbRch1Qvvr0pz9dHTMMW/vbZCLXkM1HHnmkqNO01nyvce1p+HQWApmFDUaU71aOQSbd8jraX74vOZ/6bHBOVBrMwgab+qM09SdLfZyljW5H/sje2ZxrlX2Ykrw72JJgjDHGmFr8kWCMMcaYWvyRYIwxxphaeqxPArUy1WWosalGSv2GZdXRstTP2e8iSt2MaZip5av+xFS01JQVaq2q944aNaqo0zFhXxkyppptFtLDMELep6YHzsIcm1KQan3T1qd6LlPTakjf1KlTizpqtqq5cz3p+NEngnp8Z32LKO+FfhkcW51rjjPR/vK62gempmaa3zFjxlTH9HHR/vGeGTana4gasobf8XnL/IWo0ar2yrVP3wu9T/U5iOi4VfTNN99cHTNtNH+rUFPO1rtusc4QTIYVqk8Cn2PVzunTwnWq9VmoIu8j2+KZ2n0WPpltzU4yP412/Hyyd3Tmv8DfsT/ZuPP5U3jPep2msHktZyncM5+trmJLgjHGGGNq8UeCMcYYY2rxR4IxxhhjaumxPgnUxlTfpW6t+k2mzfFcar9a1xTXrroQt3+9/fbbi7Kme2UK4AxqZarHUUdXPZBtMJaW96LofXEOshSkQ4YM6XJ/srSnTRqb5rJ46qmnirrdd9+9Or7llluKukmTJhVl1cOZYlf7kG19HJH7L2gb1G+zOHeOpcbHR5RpmzO/Gv6OKYE17TDTfGfbLWf+C1wzmi6Y7dMfR8eWGnIW90/fncmTJ3fan7vvvrso67pg+mLV8rmGqROrbwHXk/aXfg68T00NTz8f7Q/XIZ9pXV+Z5t+Ua0B/yzWcpVfmO1qfeervHEvtO3X9dtIQa5u8z+w9x/7o+ynzHYgo54j/vmRp9TPfEPov6ZxwbruDLQnGGGOMqcUfCcYYY4yppcfKDURNNVkKS9Yx/E/NsdkOkTQjMQxs3rx51THN3nvuuWdRvvLKK6tj7jSnZkLKCzRJq7mPITRZWuYstTDvU03AlFGI9o/mRTWD0xSapWWmSZMhYmp64w6Wjz32WHVMk+/8+fOLsoa70ZSsZlSaO3kvalLk3M6dO7c6Zljs8uXLozNoQsxSQXO31Cxci+tS0wdzrT355JPVMeeEOz3qbzlf+mww/JfrQMeP4Yh6XYb00Tysa4ThiJROuIYUTb3MOcl29cx29GNd9qxyfDKZMJNZeZ0sBDLrT9NOptmOjToPnBM+f/rs8p6zcc5SL2fyddPcZmPAtafnZnJtJrmyHT5T2S6e3cGWBGOMMcbU4o8EY4wxxtTijwRjjDHG1NJjfRKyFLfUT1UHojZOHVS3xKVWp1ov/RWy7WgnTJhQ1N16661FediwYdEZ2j/qXQyhyULzVIeljpdpYwyP1C26Ga7FsJ1Mg1RfEOql2faqTemwVUOmP4XOfbbNNtvheOlY0h+A466/5X2qHr/LLrsUddxqWHXHTIdlO1yXWQgWQ6m0HbY5fPjw6ph+GfTB0Tap0Wq4JOed/gA61ty6Wp8TrkuuYb0O549joP3l/GldU8ih1vMdpO8Zru8s9I11mZ9Bpqs3+R0o7LuOCdvMrpNdN/PriSifsaaU7kqWUpp9zXwSmtI0K1xPOr9sU9dT1teI8pnL3ruZn0pXsSXBGGOMMbX4I8EYY4wxtfRYueHee+8tymqaVJN4RCkNMFyEplI1TTL0Rs3XNCMx1Ez7Q/Mrf5uFb3Z2XkRHU5Kaq2ieUvM+Q8RoRtV2aLLXUEruGsj+qRmMmf+233776njGjBlFHecky16pGfsiytBBjruObWb2jsh3HNSwIs4lzddqmly0aFFR95nPfKY6znY8jCjHnefS3JhlBs1MrDSjckwUNfNSeqO5X/vL8dLf0mzLMdBdK9nXzvoWkZvBuday32bhrk1t6pzwXL1OU0itmqGzXRebwhG1f9luiewrr5ONAcud/S6ivSyPGe38Njs3kxCyvvPfnuy55g6ROu6UGziWWk85TZ8prpHuYEuCMcYYY2rxR4IxxhhjavFHgjHGGGNq6bE+CbpDXUSp+dGXIAtDo/ak6WazMKZNNtmkqKP2oylkNR1wRB7eQq1VtShq/kT1ryylbTY+EeUYZeFRDCOkNqb6qurJERELFy6sjkeNGlXUUavTsaU/BX0UNBSOWr32h/POdaFjxDrVfhnyyDnSMWGYpe4Gmu0MGJGn52ZqcdUk6VOShcmxTR1Laq06J/xd5pPAcDYlSy/N67JNJduNNKIcA64Dash6nxx3bacpdLGrKZObnnFdw2wze1e0s2uukoWTR7SXBln7nqVspv7eTshhZ9es+53WZ2HgHAOSpY3nGs5CKzN/NNbpc813h74/uV1Ad7AlwRhjjDG1+CPBGGOMMbX4I8EYY4wxtfRYnwSmrVXdKtMOGYdMX4JMM1Id9Nxzz+30dxERgwYNqo6nTJlS1KnfQ0SeqjPbWrS78dbU9emjoO1QY8v0+EyDJP3796+O6duQpQfmNR944IGirNdqJ067nbjodrbkVegfoPfJ/B3ZVrHMX5D5U/A6AwYMqI6HDh1a1J111llF+ZBDDum0f1l8PDXcsWPHVsfcAlvHPYsFjyh9TOjjovPO/BjculrXLfN38DlWHwrq8Xou3yOcE+07x0fLTXHtmW6tc8KxY5tNvg9dvQ79SJR2/Be0zL5l64LnZv4v2ZbvHPfMjy3zdWjyRdF1QF8C7R/fgfSv0jL7rs+GbvceETFu3LhoF1sSjDHGGFOLPxKMMcYYU0uPlRuyEDGagzQkhOafbBc4modVxtCUuhH5LoJMW0sT0MYbb1wd07SVhTXyXG2HoTfZ7nGUH7KxbCdlq6aqZpsaUkcTtJrEI8q5Xrx4cVHHcEmVI3hf2ocs7JNkuy5S/sjCmrLrUNbheOl1KadxDHTNMLWxjuW8efOKuoMPPrgoa5hqtrMiw6zYP+0D17CuA5qH+WyqiVV3oYwo5ccxY8YUdTQz63W5hmnW7WrqZc5fliqbpuQsFI9kz7GWOQfZc5xJbbxn3qeOZZPcqGNJmSCTnYi2Q/lD2+S8sz86JlnoOeF7JduRkfeZSYxrrbVWp/0ZOHBgUdZ/M/jvlN53tsNwV7ElwRhjjDG1+CPBGGOMMbX4I8EYY4wxtfRYn4QsHClLRUttjr4NqhNlPgBMhUtdWP0OGPJI7VX7nmlhGjYY0VFz09AXamOqhVEbp0aq90lNW9vM0idHlNrhpptuWtRp6OKkSZOKunvuuacoq67Gcc9CubIU3E26Z6afqgaZrcOIcr1R+822qqW+q/4mTelvM21T1wXTYXM9qR8C+6rn0oeEIZpazlKS04+Gc6Q+LtTG9Z45B9k4cyyzNLqZTwLfOdStM7IQuowsNJdjkKVpbicdcBaezHvmmCj0D8j8hbJwQF0TEaWPQvYMRZTvh2xueR3el76TRo4cWdTR/0zvhe/WrqatZv+IzkMWrt1VbEkwxhhjTC3+SDDGGGNMLT1WbqDZWc0qWagZoYk8yxKo6A55dddREyxNUDR7aZlmVDWfZWGWEaUZjOYzlTgoRay99tpFWc1gDG+bP39+dUxTNu/rmWeeqY5pMtQwtWXLlhV122yzTVFWuYYm8Sx8KzPd0lzXzq59Otc8L8sAl60tSiNZGGFmsmebzEyoc8L1xP7puuCaUQmBJnqaY3VdbLTRRkWdmotpfuV60t9yHajcwDWRyTwcdz7HXc2ml0mIEbn8kGUQ5NxqfzLZiXVNu0J2Btvne0X705QpMZP4tL9ZaHdEGXbJ97C+Z3gdhtRmWR6znR91rUWUzxH7w+dP2+G7PsssSzIZU+87+7evq9iSYIwxxpha/JFgjDHGmFr8kWCMMcaYWnqsT0K26xrDGlUHagoNynYqU02N2io1R9WbqFPxXO17FrbH39GXQOu5u51quNS7qY3pdZgGWbXMbOe0iIhPfepT1fF1111X1OlYcjfCbJfDLbfcsqhjWOiSJUtqjyPK+2LoFNeMkoWaUdtlqlX6Yig6t9RAqTOqLkttlWXV9tn3DTbYoDqmL4GmSI4o1zhDubQ/7DvHVuc6e97oy8DQ2Icffrg65n1puGamGbMPfBaIzgP1+SxMjvOn/WWbui45lxxbfVY5Bt31ScjC/5r8O7L3AclSSnd2XkTHvus64fOv71r6iWRz0s4Y8N2qzwnfyZmPSebf0eQLou9EtqH3lYVKdhVbEowxxhhTiz8SjDHGGFOLPxKMMcYYU0uP9UlgngTVc6gvZ7pMFueexfVmOlBE6QPAc+l3oO00xW0r1F4Vxtmqjpdp7BGl7smUu5oymb4M7Pu5555bHX/0ox8t6lTT5jbE1GF1LB9//PGi7sEHHyzKOl6Mu1et87nnnivqOF6Zn4j6HXB+sm3KeW6me1Kb1njrppwOOp70h9EtZ9kG51rLzEug1+X6pq9DhvpscDtc9UGIKMdA8z1ElHNE3x36hWS6fuaH1E4abZ6r+jjHR/vDZypLx8s29blpyt+hZHkk2tG0Mx8J9oHPVFd9wfjbp556qqhT/xNeJ3vvZf5VTT43Wk8/CPZBx5rjrvfZTq6Pdq7THWxJMMYYY0wt/kgwxhhjTC09Vm6g6SgzD2e7kWXmYpop1cy0dOnSom7jjTcuymqCYmrjbJdKQpNwdh01M7/00ktFnZrpec80RWo9r6MSB9vPdl1bsGBBUbfvvvtWx9z1kWOpbY4YMaLTvkaU80cz5YoVK6pjygs8t6vmWc5dlkY32zGSZkmmQV6+fHl1zFSvNNPPnTu3Op4yZUqn/eHaYvpbHS/OrfaBksbw4cOLss4R29Tx466imXTDusxkT3Ox3gvNsTQla7hilrK5aYdP7S/HMqtrJ0Rby+3s/peFdjZJk9pfmtr5HtZ6vlfa6V9n12R/msKKtX/Zjr/8Hf9d0Pcg5yuTDdqp4/tJ7zObv1WBLQnGGGOMqcUfCcYYY4ypxR8JxhhjjKmlx/okZNtsZmGETWF7mV6pehNTvep2xmxTU+FGdExxq5oW+5Ol2KVGqn2gXqkpbhctWhQZel1eR++bYagMk9NQNPplXHHFFdXxsGHDijqWNRSO4WOZNk2fCe0DQyAzHwSSpVNuR9tUvwO2P2jQoKKsOj/T+i5cuLAo77rrrtUxwwF1fWepxCPKMMPMr0e3/Y7oOCeaOpdpdPVZYLpbPgsKfUoyPZ59V32X+jLHVp+FdsLQsu27M38Fjl22ZXFTivkMbYdtaF1TemD1CeB1OJbqU8L50743hZNqH9rx2eK52Tbg2XWJrtOmd7SS+S+RLL1z09p7t9iSYIwxxpha/JFgjDHGmFp6rNyQmexo9lJzEM2LNGnqb2n+1DYYKpVlmVu2bFlRZojfrFmzqmNmUVSzHPvKbGMaCkfT/3333VcdM4yQmQnVDE5zmd43M1ty90aF5n3dcZD9+d73vleUzzrrrOqYoac0ket9M4yQY6JQOtFw0syMmoU1RuSm28w8THOs7i43e/bsoo7rQseE0o3KFvPnzy/qOF46JnxuVELj+uEOqSrz8LnR9cVxphyipm3Kfdo/9ofX0XFvCh/T+eN1tMy55LpU83UW6skx4DrQNUxpIttZMQsZz+podqfcoO+AbHxItvsm74Pnan/Zhq4v7sjINZzJDVkbRNdMttYiyvmkTKDzmUltbDP7945rpDvYkmCMMcaYWvyRYIwxxpha/JFgjDHGmFrelz4J1IFUV2vaQU/JdgZkXaZFZamNeV2iuhWvQ58A7RP9FTQEkprovHnzivL48eOrY/okZHol50T7k4XQ3XzzzUV5//33L8pPP/10dUxNlPqz6pBMF7zddttVx9dee21RR58E1dyp+ekukJx3npvtyKbjw3XJsrbJcFIdn4hSe91ss82Kuscee6w65jrg+tI5oy+B+geMHj067bveN1M/Z+ll+YxpHzgG6uPC6/AZ1zlq2nEwmyP1O2gKFdT7bifFLv1odCxXhd5ch7apqbkjIkaNGlWU9R3EZ5F+WjoGup4Jx4DvIG0nS01NuPYyXzUd5yz8kP3jGuFcZymvM1+CzH+B/cnWU3ewJcEYY4wxtfgjwRhjjDG1+CPBGGOMMbX0WJ8E6jmq/XD7UNVeGV9NvUn1HOpC2ib1tkzLpN7NWP9NN9200zb1XGpz1Js0zp39075rDoCIjvpgloqW+Q4U6tY6JtSXNeUvU/Uyxlz1wkcffbSoY0pibYd67gMPPFAdM4320UcfXZTPPvvs6jjT4zOtMKLjulB0/qhl0p9C/QUmT55c1KmvRUTpU6I5OCLKdcA2eZ+q/XLNqO8Hx4DrVOck00g5Vpy/LGeIxtKzLsuPQR8S+tlkaZGzPAmZNs5x1zaybdsjyndZtrbYfpajg8+/+uOwDfry7LffftXxnDlzijqmn9f8GczfkeUMYR+6mgcgS3Mckfuq6XVXZdrjLO1/V+vYP65Z9SXie7c72JJgjDHGmFr8kWCMMcaYWt43ckOWYlNNpUw9S3OemhAzsxLNwTTrqPmTpqPBgwcXZTUXqRk+orxPhhFSUtA00gxH0uvQfEczs57LvqqpnSFzWTgp21SJgeZghl3pLpALFiwo6pYsWVKU1WzJ8EQdH4Y8MQxU54TX0XvJdtAjWdpc1nGd6vpiutm99967KGvfp0+fXtTpfDIdNu8zCxHLwtCaUsoqel0NY4zouL70ujSR65xkUiTLbIP3qWuTJvFsHWSm7sx0zLHkc8yw1c5oMolrHzJTP1N377bbbp3Wa1r4iI7ht/r+4n3oeDWlL8/eZXodzgHXpV6X/w60E0aYSROkq7sMZ2uWv2Xa6mwsu4MtCcYYY4ypxR8JxhhjjKnFHwnGGGOMqaXH+iRkIT6ZfwD1SoaP6G+zbVH5O+pmqgsxDTO3jtYyNSTV0TbccMOiLgvPov+Caq1M2Tx27NiirGPE7bJ1LDXFb0TH8FI9N0uHzfliCKtq8EwLy7HMxkT1Z/aHviA6n9T8Mj2X61J9C6h3qw7KMaC/yYABA6pj+sPcdtttRVnXyZAhQzq9DsMaGYqq88mUtu1sWZylTNf1nYVORpTPRrY1M7VnPqsaxstnavHixUVZnw3eV7aVNn0mstDcTP9mOLBCTTtb+xwv7S/9X3SueV98H2Ta+PLly4uyzku2RTfnj2WuEyUby6ZyZ3Ad8t8FHXf2rR1flSyklmRpmTO/jO5gS4IxxhhjavFHgjHGGGNq6bFyA1GTC00s2Q6ERH+bZavKMjVGlCZyXoe7N6ppkmFgeh2afDPYppotNaMa6yLKkEiOnY4PQxUHDRpUlFVSyHZrozmRcoOa3ind0PSuplOaRlVuYAjWokWLirKOX9NcZ3VqfszC9gh3Odxhhx2q41tuuaWomzt3blGeMGFCdbzTTjsVdSoh0AzPsdV5oEyn66Ip66Q+m7xnNWfTXN1VszL7x/7wunqflKu4hlWa4zrV8ESuJz5/OtZ8prIsrzRXq0k6M3s37aipz0ImlXAO2nkHMbxUn2OG22Ym8mw33iapS8nM8tnujZwDPgvaP57LNdPVLJntZFwkmVTaHWxJMMYYY0wt/kgwxhhjTC3+SDDGGGNMLe8bnwTVhajrq65GTY2ajWrcDI/KdrOjzqjaVJZCmtel1qRaJ3+X7U6WhUPRJ4L3omNEPVC1Me7kRk1bfRu486WOCceHc6L9O++884o6jruGpXF81PeiKRxKf9tV/S+io4ar98IQQ/U32XfffYu6LbfcsihfdNFF1fEJJ5xQ1D3++ONFWTVm6s06n+wrz81CsnTOqLtmoYvUVnX+Mq2e7WRt8Bmnz436WjDtMedaxyhL65tpzewT13sWisc6bSfrK9c+/WH02eT7oKvhdRHlWD799NNFnYbbNl1XaSeVcOYP0+QPkK3LrI12+p75EmRz2+Tnk4VIropUzIotCcYYY4ypxR8JxhhjjKnFHwnGGGOMqaXH+iRQX1Ltl/H7GqPMbZF5rupz1Hboo6Bk2+NSD8zyAFCv1Lj/Jg1ZoYal40UNMus7dXTV/EePHl3UUd/V/unv2AeOD3Mf6BzxOl/4wheK8qxZs6rjRx99tKhTzZQ+GxzbTNfLfEiYe0Cvw7Wn2+zSr2DzzTcvyn/3d39XHXNba+qeur6YKlvnhGOQ+Z+wTq+Tab2EWquOF3NDUNPWZ5xt6vzx+aKvTOZjQvTZYGy/9ofjQ81Yx5rnZltFZxp3tp0w1wSvo/PHHA+Z3wPRZ3ejjTYq6pp8qDqra0fXz67TtN1ydp+Zj0l2H+1s0U10zXD9ZL4h2Xg5LbMxxhhj3jP8kWCMMcaYWnqs3EDU3EjTUZYemObhLOWnhjE1mdKyMEKa8DX1K3eIUxMndwakSSwLi9Ed2TT0rq7vGkLK0EVN80uZ4IknnijK2g7D0HTcOQc0gy9cuLA6Hj58eFHHXfs0FSx3dsxMvtmOejTZZ2lPafrTOWNo3rRp06rjgw46qKjTe44od9zM5ou8+OKLndaNGzeuKFPm0fummVTXZVNqXB2vLJyMkk8WwpaZX/lcMLRSr5vJQxHlfXKuVR7hc0sTfldT7nLssnIWJsf74Bxpf9u5Dsmkt0xWaSccMStn64DSbbYDMPuqz38m65J2QqtJd2WCTMJYFdiSYIwxxpha/JFgjDHGmFr8kWCMMcaYWnqsTwJ1aw2/ow6bpdilzq/aFK+jOl62bSzbZGgQtV/VYrm9ql6X2mqm5We+DazLUu4OHTq0qNPwu1GjRhV122yzTadtctz1PjXMs65/CxYsqI632267ok61+ohSC+Ya0fukVsjwRD2Xc63nsq88V/VMtnHHHXdUx9z+mefutttu1fF6661X1HEdaLrsjTfeuKjTdUpppi8AACAASURBVMn1zTY1TDULOWzaSjfTolVPZYgh0bHNfCSatuTOtiVmWdcBx0d9FHjPmU7cTghmBsdd13S2xXtEOfd8d2Up3XmdLHya95mF7WXbNrczlnpd+hlkW07znvWZyu6D5SafBG0z24K+KQw0O1dZFWvNlgRjjDHG1OKPBGOMMcbU4o8EY4wxxtTSY30SqH/fdddd1fGECROKuueee646pv7GFK6qGWWxvNQgGQOv16E+SFTbHDRoUFGnKYmZtjaL0c/SimZb3kaU9/bCCy8UdRqTr7kXIjqme9acBhwDbYN6IO9Lz12yZElRx/7puUxtrP4LvA79RDQFd3ZfEydOLOoGDhxYlCdNmlQdT58+vagbOXJkdUxflI985CNFee7cudXxBhtsUNRxXegaf/LJJ4s6TVHMvARZatp2tGii+innWnX+LD1wRKkTc42oXwv7lqWCJmxT/Rvof6K5P5q2JdZnLNP8m7TojOxcrmHN1aJ5WiLKddGUTyTLT0GyNaN953lZ3hum3NaxbdriOdvqux3/gEz3b2db6cy3Iftt1h8+493BlgRjjDHG1OKPBGOMMcbU0mPlBjW/RkRsttlm1TFNx2rSpGmI5hhNLUyTpp7L39EspyZNhmTR9K6mriFDhhR1KjcwtTHThWYhkGqWY1rmLGSNYXJqhn/44YeLuhEjRhTlu+++uzpmamO9bpY6OKIcS+7sSLlId4nUsMGIUh7hHHA+ddw5t1lY6gMPPFCU99577+qYu4hutdVW1TFN0JQJNtlkk+qYa4SpqjVEUsNH2Q7vi3Q1VLDJzJyFIFNm6ex3EaVZlfOldVwTHNssJJNjov3LQqL5TGU7T/I5zsaynfC/LGyXEotKsOx7O+ZzLXO+eC/apyxNe5PEouGulHm1ruk62S6QXQ3bZblJ4ugqTWGXmdyg8N+w7mBLgjHGGGNq8UeCMcYYY2rxR4IxxhhjaumxPgnUuFWXYZijamHU36ndd/a7iDwkjKgOSn2J6Wf1ugxH1HA39od6uOqnDHnKtkWlfqpjyRTAGmo6ZcqUou6KK64oyprSmemv1X+BqZ85J48//nh1zLBLavc/+tGPquNvf/vbRZ36GRBqdwxFVXR86BfCtadbPlNH1/tk3eDBg4uy1jNU8Nprry3K6p/D+dO5b0p/m6W4zULWWNaxpX+APgv8HdeM6s9Z2Bd9kpgWXZ83avWLFi0qyhpGy+c286fgc5yFPWrf+TuOiV4n8w9gaDCfcX1/sc3MzyAL22vySdD543Oj89n0vuzqltMkWzNZ35v8AzLa8UnIzm0n7be+Kzi33cGWBGOMMcbU4o8EY4wxxtTSY+UGhjkpWXgUzTTcgVChqa8d05GaWJvCLrUdmgnVtEWTE03kapajGVXLvA5N5Gpq5y6Lasq+8MILizpmAtT+sE0NZXz66aeLOo6PSkuUJgYMGFCUjznmmOp4++23L+pUguH4ULrRdrIMcDTDa0bKiIgZM2ZUxwwR1bXHMDTOifZ38uTJRR1llK6u06Yd4rSe46VSSWaCjshDLbXvnIOxY8cWZX12uZ40zJimdV43y/zHcdc1zMyW+g6i9EB5Qcs0keu9ZKb/iHJOOH/aBqWaLOya6HUpC2S7LjatOx1bzl8WBprJD+2EHGayQTYeTdlGM9N/9mywP1mWxyyLKNda1kZ3sCXBGGOMMbX4I8EYY4wxtfgjwRhjjDG19FifBKZIVS2PmqTqqUyN+8wzz3R6Xeo5qq02aWGquVF/47mqwVNfUm188eLFnfaH5Sw8i/qWpmiNKEOV2FcNR6RfCFOt6u5y9LVQTZshfUxjrf3lPTMUVlMdU7vX66ivQETEUUcdVZRvuumm6lh3a4wofS+4Dqj97rDDDtWxjl1EuS4Zqsj70r7TB4HhrpqGPNvFj3PLc1X71XTlEeW6pI6e6aCsU58SplofNWpUUf7lL39ZHTM1tfp08D7YPx0DPgv0h9E1zWdT65r8hVRvZn+ycFLOrb7b+LzpdVjHMdFnl/eV9TXz52jyTclSgmd6PPug74csHX5TfzhnivooNKVlbieFs66LprTonbXB62Y+HE0p07uCLQnGGGOMqcUfCcYYY4ypxR8JxhhjjKmlx/okML+B6jvUA9XPgPoWUwCrhpOlPW0nZwI1P2phqh/qlsARpR8CdX36BGTbUyvU5rjdqo4RtV/1X8j0SfZPdfKIUjdjX6mjqd7M+WN53rx51TFTK/fv3786PvLII4u66dOnF+VPfOIT1THnS3Vrao7UGZcuXVodjxkzpqhTPwTG4DM+XceEPiTZOm1KmaxwLNVXhOtSc1swhwLHQNvk3OpzzFTUTMer+jw1d9Xqqd/STyRLAcy8GxxrRcenKQ2zzgnXk/6Wc8l8B3pdPsc6D00+UzpHfP50fb+b7cS51vQ9w3OzMaCfCMtKlhMnO5f3mW3FnOWyaErhrGPSTn6FzA+Cz0k728F3BVsSjDHGGFOLPxKMMcYYU0uPlRuYPlXNhEwlvN1221XHd999d1HHdLhqmqTJV6HJiWZUDWFj2CVNmGo6ZehiJiHQnKchY5Qmsr6zrObQ559/vtP+0MxMU5teZ9myZZ222RSKp5IQ+8O+f+UrX6mOL7744qJu2223rY6ZQvrv//7vozO4DjKzN1EzOMdLpYjbb7+9qGMIpJr7eR2GTyrZ7oNcs9mup7yOykftmHUzUzJNsw8++GBR1vXPcFLd6TGTOyJKEz6lSUpv2ieGnup1uQ54n9r3LK0vxzILn87qmqRAbYfmav1tk6yahdSSzPStzxjXGu9Fn/l20jJzbLOdMDMZpWn31O6eq88C12UWzslzvQukMcYYY/4k+CPBGGOMMbX4I8EYY4wxtfRqNQmKf6Ew5e7o0aOr4/vuu6+oU/2Z2jj1JtUW6a+Q/Y6oTkSdk1qi6tbUB1X7XbJkSVHHkDG9N+p/2ibva/ny5UVZNW6Gj2lfs7ChiDK8jXqu/pYhTRyvLJyToYMalvaxj32sqNOth7mlM/0OdIw4JxpmyRBaor9lONuECROqY44lQ3x1bLO0vjw3SzucbVnOMtd75q9AXwf9Lfuq4clMQczwWy2fe+65Rd3EiRM7bZ9znYW+0ecl25JX56gplbA+R9lW0U3PlP6WWrT2lWs28z/J/Bea/nnI0v62E0KuY8BrZtsmZ23wOtm6zNZ307u+nVDGLMQ+G4OMLMU1+67p1LuKLQnGGGOMqcUfCcYYY4yppceGQNI0qSFjNMNlGahoBtdQKtbRvK/QRK5lmpkZnqhyCM37ao6leYrnZpnINGSUY0cTlGZ5pDlfTaw00TMEUvvOc3WOuAtklqGSUg3nSE3SlCk09DSby4iI66+/vjpWKSuiXEPccZRmQjX7cpy1TjMYRnQ0V+v80YTYzq6Lel3W0eysc5btmNdkjtU2s/Fh+5QGVQIaPnx4UZet/azvTdKN/jbb2TGbg4gybDXLkJdJRyzzOpmZOZNVsx0jmyQpHT/WZWPC+8wkjyzMkePTzo6MGVlYanadJqkkuw5Dm5UsvDyT+1aFN4EtCcYYY4ypxR8JxhhjjKnFHwnGGGOMqaXH+iRo+FhExL333lsdcyc31dGpfzP9rYZAMfWzaj/UA+mToBqSavMRZfrkiFL7zXwSqA/yXNX1qGGpds7rME20jgnHS/XKTMuMiHjmmWeq46222qqoUw2eYYRZyuumNKzq78Fx19TGDzzwQFG3/fbbF2X1WWDIqPp0NKUAVp8OauMaesr7ysKaSOajwHWQ6eiZ5t6O/s3rZuGbOl6soz+MpltnqnP1P8k0f/aPc5L5JPBcvU7mO8A+ZDsFUpfONPdMK29Kkaw7tGbhdtlc1vVhVdCOXwbXns7Ru+l79gxl76CmNjN/imyNZNfJUkpn/jhdxZYEY4wxxtTijwRjjDHG1OKPBGOMMcbU0mN9EqifqoZLrT6DaVjVPyCL6WbaXKJ9oL7MsurfTJGcxVBTG8tS7qqOnm1Vy3Ppl9G/f//qmGPAOTnxxBOr49NOO62oU+2VORSyrasJ+679e+qpp4o6nT/G4GtuCPaBab4nTZpUHXOcs+28OZZ6Lu8xi7fm+GTx6Fm6YLbJe8nyH2Q6LK+bbSesZbaf6bJZmmGOD/OCaD3P5bOZ6bu69prmT9cefSTUP6Apb0NTPobO2s/yZZBM88/Gi2uf6z3zp+is/Tq6OgZ8z2XbL2d+Bk1+F1na8Yxsbpv8IHR+s3wQzpNgjDHGmPcMfyQYY4wxppYeKzfQtJXtjqammyxsMKI0G2ZmL/6O4YDaZhaiElGGemXX4X2pmZLnZmFpTbujaX9pftUd9Wge/shHPlKUf/GLX1THTG2c7aDH+1RoPmPfVbph+uvbb7+9OmYILXfY1HUybty4ok7NxUzLnJk02VfdbZPQ3MhQVCUzCbdjsuc8NKVb7ux3mZyVhe3xd9mzmklvnAM+U1pPmYDPlMpi2XuF40xJQa/D94FeNwvp42/bMUFnc8m+t7MDofaPY8cxyGSnzs6LaC/UU2Udyky6oy7JzPtN4YiZJMVw3Gz+tJylqSbZ+FhuMMYYY8x7hj8SjDHGGFOLPxKMMcYYU0uP9UlgeI2mRc7SzVLryfR56jmqbbajPTWFrC1durQ6bkerYx90TBieuMUWW1THDLOkVqdpkpky+c4776yOTzrppKLuV7/6VVHWMaEurKmf6TuQpRLmvHPcda7pTzFy5MjqmGPJUFjVkHV+yNixY4uyhkdGlLosU3fruqB/B30QNEyUY5mlC8606Gzb34iO49cZTbpnpsNmoYvUtHWM2KauC67ZLNSTddSxtcxzte9ch5zPLPRUx7lpzLO51XdXUxixnpu9E5vSTWc+Lu1saa7ntvM7rpGsP5lvQabrt5PemddpZw1nfW1nu2qlq89whi0JxhhjjKnFHwnGGGOMqaXHyg3c4W/FihXVcRbWSBMUzYIKTTUM8VEycxBNTswEqKZB9j3LSJfBkL7DDjusOmb2ww022KAo633S7KU7Ip588slF3U477VSUte+66yPboKk/Cw3iHLDv2l/KKEOGDKmOmXGROz2quX/y5MlFne7iybmkzKNzm2U/ZHhdlv2wKTQx2w00MzMz82Vn7UfkGftItounSid83igbZOGIKuVwnLlmVEKgrJOFIHOHxux3mXTD+8wkhExSyELx2EaWzbIpRLuz9tmHdjITsu/a32znS7ZDGSWTG5tkg87qmnaPzJ5x9iHLHtvV/rCc9cdygzHGGGPeM/yRYIwxxpha/JFgjDHGmFp6rE8CU7aq1pPVUaOhtqm6LPUjTQVNHY96pf6WmhFD4bIQyGz3OJ47YMCA6njKlClF3SmnnFJ7HBHx3//930X5ueeeq451V8WIiJ133rk6nj17dlH36KOPFmUdk4022qio0/Hr169fUZftoLfhhhsWdfQ70HM5J5n+Tb1SQ0bVByGi9K+gFs251fWUhcmSbFe6pr5nobqqTbPv9EnI9Exts2nXvmyXQ13T7Kuuw4gyfTnTYc+aNav2mhEd15Oui6FDhxZ19DF5/PHHq2POn4ZdZvMV0fUQSLZBMn+BLGwvS3XeTgp33leWDr+d1ML626YdELtKptUTrvV2dqnMwuY515mvQ9Z+tp4y2vEd6gxbEowxxhhTiz8SjDHGGFOLPxKMMcYYU8v7xidBdStuI600pepUqCd1dYvSiFLjavJJ0HhwTVfM6zCWn6iPwHXXXVfUfelLX6qOv/Od7xR11Pw23XTT6nju3LlF3f33318dU3NkPHq2Bbbq3/RXyDQ/vWZEx+2WVXPnfWkOgyzmPaJMr8w2FyxYUB3TZyPzkWDK3yxnQZbrg2uWuRl0DVHX17HlWmtHQ87yNrCsc8L8JlpmX7kuFi9eXB1vsskmRd3ChQs7bZ88+OCD1THTfA8cOLAoc4yULB492245W9/0tchSZ2c+I3zncL13Ne1w01jqdZrerVmehCyNfTaWWSroprwIWX6azCeB/dNzm3xTtJ0sH0Q7PglZm3zvdgdbEowxxhhTiz8SjDHGGFNLj5UbaLpVaFrLJIV2djVT814WdhZRmpUoL9B8re3Q5Krm9KYQyC233LI6pqlWzbo0qfK6eu4BBxxQ1P3sZz+rjhkyxzFREznT36rJlzLF6NGji/L2229fHWtIWkTEuuuuW5RVaqLJTs1yHAOmAF60aFF1nKXn5lqj7KRjSSkiC0fMTMmUF3jdrsptNFMyhC0L7dK5ZspfptnWZ5V91TXEOWE4oq4ZymCPPPJIp21QMlDZjs8i3ytaT/kxC7vO0vNmc0s5huHBur4yiYrPZrarKOdPy3ymMymA6ykbE56r98W1xnWZXUfnpJ3QSb4D9bf8dyCTIliX/TZLh81xz/4Ny9JWN8mqXcGWBGOMMcbU4o8EY4wxxtTijwRjjDHG1NJjfRKo4aqORo1bNa3Md4BQM8pSXFKvVC2R2hh1dGXw4MFFec6cOdUxdUbq36rXz58/v9NzNX1zXf90223qp6rnMnyMGqReh+OuaY8nTJhQ1FGbHjlyZHXM+6Jmq9or+6PbSnOLaabnzbbSZZsK71Pnmr4CGu7GNrguVStnmByvq/ed6dZcszz3pZdeqo65DrKtfQcNGhSdcccddxTl4cOHV8f0o1EfhIhy7qm1qj8OfYCox+sa5hhwXegYULvX+87STdeVFfXhYPv0kdDnOJuTpq2i9T2TaffZVtUR5XPCcedvVSvPwsKzEFHC+cv8aDKyZ6HJJ6Gdrb6z62T/vrSTXlnHL1t3XcWWBGOMMcbU4o8EY4wxxtTijwRjjDHG1NJjfRKoh6umlMXV0l8h2yY104yonzJlsl6HWyirxh5RxnXfeOONRZ3q87yvTO/i+GisOPvOePQhQ4ZUx9wOWrVMjU1nGxGlNk6NVDVlbS+iY64I9RfYaqutijrGCGub9EnQFMpM60vdWnMRZLHiTamMs5hlvS7ni74N2maW1pvXZZu6hjK/h4hy/Oiz0Vl7ER31XY39p7aqa0/1/4iO2rSmC8/6mm2LHFE+q5k/R0R5L5n+3ZQ3Re+NdepnwLVPdD6zFOBcz3zGFGrumpuF/lPUuHW8uNY4lto/+lNlW0U39VfJtmLm/GWpoDN/Bvp36Llsg+OV+ZRk7Wd5E7JcP01j2RVsSTDGGGNMLf5IMMYYY0wtPVZuoGlLzWs0N2rIWpNZV82PNMfqdTW8r66s544YMSLtu5qdNttss6JOw75onmJIpNbT1KdtMq0vZQNNizx27Nii7vLLL6+Om9KwapscdzVj0ny4yy67FGWVazbeeOOijuOupsCsPxw7psPV/tG0rW3Q9EizZZbmOwuz4hrOUuXytzrWWRrdTNIgNJvqmFDu4By98MILnbbx7LPPVsdcTww11TDHp59+uqhT2YImX0oKkydPro5/+9vfFnWUcvRalCp1PbFNrhm9LttQeF+E4cGdtbF06dKijuZ9ld4yWZUSEN+JOmdZGHhEuYayMeA4E20z2y2RazaTELKdFJvS4etv+Z7LdoFsR+LIwkkz2gmd7LTtd30FY4wxxrwv8UeCMcYYY2rxR4IxxhhjaumxPgkbbrhhUVath/qyatPUzaj1qM6oemlEqVMzxIj+AsuXL6+OqZsvWbKkKE+dOrU6ZnjiPffcUx1Te6bOOHHixOp42bJlRZ3eFzVa9l31wscee6yo0zGg5p+ln+Z9qc53/fXXF3XUZTVcMdv2N6LU8jk+ukbYd6Y6zlLl6vg0bQ2rZfqi6Hg16ZM6Z9yKmWFq6iPA8cpCxLI1TZ34zjvvrI532223oo5hszrW9F/Q+24aS53bLP0twzVZ/upXv1od/9M//VNRx7HU/i1YsKCo03VK7Z79U98e+gQpXJdc3+pH8sQTTxR1W2+9dXXMlNbDhg0ryldeeWV1PH78+KJO75lrlr486nfAuaXPi/qqqE9ERLklN58FvrN1HWSaf7aFckQ5R3wHahscA/ZP/RDoi8LnRn/L9Z2l+W5nu2q9b74Du4MtCcYYY4ypxR8JxhhjjKmlx8oNmVmQJjs1QdF0RPOQlmlay8yEzJSm/aPpkVKJhhV+/OMfL+pUNqBJnKZkNf3df//9nbbJXSBp+lMTJ82o2iZlHYbt6XUpN3zkIx+pjmlao9xA87rCdaAmO4ZgZRkqNUwvouNYK3pdmv1otswyrOlvOXYMu9K112SO1fnjuVnGPpqLNUvfvHnzijrd6XH69OlFHdel9p3Pm/YnCw2OKOUQNU/zugyvmzVrVlE+9dRTq2NKIyoTRuTmYc1MyOeEbLvtttUxJQR9X3GN8hnTOaM89OSTT1bHO+64Y1HH+9Q5otyn65tSG0N+9V1CSYOh33pdrgN9f3J8sl0hMymC8DrZTq+69vgscl1m/2ZkIZqZ/NEE76Wz61Dy6Q62JBhjjDGmFn8kGGOMMaYWfyQYY4wxppYe65NwySWXFGUNr6HmrhoN/RWoN6mGwxCabHetzEeCIYdMmao+E9S0jjjiiOqY4TRXXHFFUX788cerY2qJquNx10fVSyMibr/99uqYGqT2r2mnMh1r3cEvotQg6c8xYcKEoqzaK0N62AcdS6ZI1T4wLJU6o45Xtlsb22DaWtXZszTWXIccE62ndk+075lfDUN8OZY699Tjn3nmmU77zuuqjwD7k+1SR/8A9YOghqzPPHVpPgvq50Ndf5999inKP//5z6tjau6aLvy4444r6vjMq8+CPl8RpS8IfWG43vUdQF8iXaf06+F6V7iGdU50niM6poXWd072/EeUPhzZ85btkhlRrjc+b+qjkKVajijXezu7PmYpkukjwf5lO1hmfSfZLpAK+94dbEkwxhhjTC3+SDDGGGNMLf5IMMYYY0wtvVpd3XPyL4wjjzyyKKvWynSlCuOOqaOpdpcNDXUyakiqm1E/pW+B6rSZpkWdk9fR2GdeR7Up6oH0kVANN0t/y7wRvE9N16vb80aUKW55X9TxNKUt49FV54wo53Pw4MFFnWrjjMVuxychS1dMzT3TIHX8uC5V643It5VmvgPtH9eprgP2nbkQdGvmhx56qKjT7cW5Drj2tMx8GZqfoum+lEy7p08C50/bpP7N/CL624MPPrio+/73v18dM3058wBon7JUvcwtQP8q5odQdB74nDB3hOrYXCOcv876yv5wnOk7oz4UzBWjzzHnltfVZyHLNcC6drZi1jayuqZzWda5z1IvN/l76XVZp9elv8no0aOjXWxJMMYYY0wt/kgwxhhjTC09NgSSKXc1rImhQbrrIlPGLly4sCireSZLB8pdFhkGpuYgmghpZsp2qVTTv4Z5RnQ04d92223VMU19as5mX5mSWCUXhjxpql6aTdmmmvR5XxqOeOuttxZ1WcrdcePGFXUM9dpmm22qY6ZzzlItc651/jLzIs2CHFu9b867moDb2f2PbTKdsobqse+6Djh2lA1++9vfVsccHw1zbNqhTs2hNMvrmuZ8cUxY7qxNhvvR1K7PFNfs8OHDi/KkSZOq44997GNFnYYg/+QnPynquNb0vULJRcs65hEdx13nj1JJti65DpRs/rhmKQHpudkzFFGuA5rIVY5h39mHzton7E8WKthOiuQsbDeTFyPyNN9K01hmdVrm2u8OtiQYY4wxphZ/JBhjjDGmFn8kGGOMMaaWHuuTQA1JQ37odzBy5MjqmCFODKFTfZf6supJTMNMDVL7R804CzEiqsNSz/3d735XlIcOHVodU9PS67A/1Cv1t9Qg9T4ZmpRprRwvnQeGeVGPVw357rvvLuo+/OEPF2UdI64Dva8mzU/vLfNJ4FzyurpmuJ409DNLYRtRpmluCrPUtUefG50Hpsrmda666qrqmKF56sdC/6AsZJQpmxctWlQdc/3wXE0nnoX4cXzod6DrguG/ut1yRMRvfvOb6vg73/lOUfef//mf1TH9epimWX2YGKKt/dOw04jSnyoiYvHixdUx06tvsskm1XEW0ktYp+ub6zlLO85xzuaB72+dP/o6Ze8n9l2fY9a14wPQjh+E+ihkKZubyHwmsm2uidZlKeW7ii0JxhhjjKnFHwnGGGOMqaXHyg0066hJmibyzLTNUEY162ShJcxSRhO+1tMMl4XNZWY4wutqqCBNa5ppj+Z8mrq1Tc2MGFGagD/+8Y8XdczmpfNAs7yOFzMj8lw1uR500EFF3cyZM4uymukzcyPHmWY5HS+a9vRcmtppdtb1xDa1P9lcRpQyD824RK/L/ukc0ex91113FWU1+2aZSimjZLvt0Yyr1+GzyDHIpBsdE2bw5PxpZknuckjTtobmUf7Qdfrwww8XdaeffnpR1vnTsMqIiOuuu6463mmnnYo6tqlyCEMy77zzzuqYYcRcXyo7cZy7mm2U1+XcMvOlPvNZSCbfR1kf+ExlJvssjDALYc/Wc0S5vjgG2b8hWYgo77mr8gLJxqOr2JJgjDHGmFr8kWCMMcaYWvyRYIwxxphaeuwukEcddVRR1hCxl19+uajTHccYArl8+fKirBpuNjTUzah/q1ZHDZn6rmpTTLWqumfTbmSqq7FOU1XTJ0HHLqJMzztmzJiibvz48dWxhlzVlTXtL1Pl6pjQ74LjpSltqbWq70BEHmal49e0Y53q8fQ3Ub8HroNMv6RGq7/lGGSaLceH/jG6hrlmpk+fXh3PnTu3qOM60JTJ7F8761KfDWq2umaz3VsjyjljCmn1SWIYI0Pq9Bmjnkt/GJ0zrm8N39T22deI0meBbWhIJn0QmBZd/Xfoe5HtEEmyc3X+OJdNPgoZei5/p2uY88VnXM/ldbJ06lkIJOdE22D7LGc7arJ/em9ce1noKdHnKFvDHEvvAmmMMcaYVYY/EowxxhhTiz8SjDHGGFNLj82T8MgjjxRlTRv76KOPFnWjRo2qjqnf6NbHEWXcNPUk1SczLSyi1KLpZ5Bt40qdUa/bBPq4mgAAIABJREFUtIWqavf0y9D4fepm7J9q8NTxNN6baY+51a9el+Oj16U+mo0t9fgs1pjaYRb/naVl5RjoOsji/gnrtO+sY3/0vunTwjHhfCq6vpiSeNttty3Kmjch2zadem4Wd8++qk8Cc0xw3HXO+Jzob9kfnqv+FZy/LA0xt9bW/tE3hc+fPrvUyvVcts/raM4Q+kioT4f6IEV0fM/96le/qo7333//ok77l/nqRJRj2+SvoPeW6fGsy7aV5nhpm026vs4Z34lZWuYsb0pTGmt9t9I3LMu3QHTtZSnmmf+hO9iSYIwxxpha/JFgjDHGmFp6rNxAM5yaTjXkMSLinnvuqY6HDRtW1DG8TU3oDNvTtLFq2o/oaBpVcxHDx2iu0t+yTk3mTaYsNfPS1K5SAE2+3KFRTZMMmdHwOpo0uSuljlEmEzB8LCMLVYooTX+ZxMGxo5SjZZpN1YSXhfTV9UHJzK80X2cpgDVUkdfidbQ/nNvbb7+9KOuzwFBhNTPzHtmmlrkOtK+ZVMN2uA5UYuGzyDnR31KaydJzU+bRZyEzn0eUkhrHR6WSppTb2nc+b/ocNYVoP/7449Xx5ptvXtTpeHG3TY6Pvof5LPId2c64KxxbfTazXSA579lukll6Z753szL7yvtUiYH9y3aT5H1m2wdk49MdbEkwxhhjTC3+SDDGGGNMLf5IMMYYY0wtPdYngb4Eqp0NGjSoqFPNhlrdyJEji7Kme6UOq+F/bD/T36ifZil3GWKk5zZti6q6Z5ZOlTrV/Pnzi/KWW25ZHXOr4a222qo6vvfee4s6psPV9MXcDnqzzTarjpmuOPMXyFK0RnQcayXb/pXzp3phFsrVNLdaz7XHvitMO/zUU09Vx3vttVdRd8YZZxTlcePGVcccL/WPYagi+67rn2tPf8v74HxmPhJ63aYtebN1oD4SnMsspJY+JdmzSe1X55b9oZav59JHSZ9bneeIjiGIOn4cZw3RZH+4nrSeY3DttddWx/TLYtilrjX6iS1cuLAo6/uTYc+6nqjj8x2U+YK0E0aY+SQoTWnjdc1kYbvsH9dTV7eVZ5tE11rTGHQFWxKMMcYYU4s/EowxxhhTS4+VG7hjnIbjMfOfmuxofmEmMjX5LF68uKhTkw9NrMwWl5mVMrNlFgJF8zDNe2pmzcxerKM5b9NNN62OmVXxQx/6UO016/quv6UEpGbTAQMGFHUMDcp27cvCnNg/nXu9jzp0zWShUyTLrpmFjxG2qXN04403FnXMKKhm6Cx0kSZxjq2e284ulSSTzLTcJKfpc8N7bifUS6/D3/G62odsN0C+RzjXKiPw3aWhlZRKsmyDfJfpeuJ9zJ49uyhPnTq1OlZ5IaKUFPlscqdQfXfxPUJJQfvE+9L3Ka+Thf/x+dc6jk8W3prJDZR82B+9l6Yw9awuexay9x77k2Vj7A62JBhjjDGmFn8kGGOMMaYWfyQYY4wxppYe65PAVL6qh1PrUQ2Smhp19NNPP706Hj58eFG3++67V8cPPfRQUUcdTfVepnPNdhXM9DdqY9nOhfRf0DqGQ+l9RZQhkGPGjCnqrr766up48uTJRR1DIDVMVFNaR5QhkQzlytKeZmFDLLNOdc+mVKuqCTLMMQtVyvwgOLd6XYaa0cdFw8kmTJhQ1O2www5F+cILL6yOVV+OKMPkuEYYfpfp/DoP9G3g7nbqp0GdOAtZzfRchlKq/s31xPvMnjf6HWgYL+dW/aA4J7/+9a+LsqY+1+crokyzzXvmc6PvK/ZVQwy5S+4222xTlHV9cU60jmPJkHFtJ0tBzv5lmnuWrphwvPQZb9L19d6ycGSOD+8z+22WUjrbWTXzkeC5fBZ0nTKkvjvYkmCMMcaYWvyRYIwxxpha/JFgjDHGmFreNz4JmbapuiI1tRNPPLHT31GPU5+AsWPHFnVMUax6UxY7H1FqXtS/9DqMVWcstGpjzG+g+iW1VcZ4z5kzpzq+//77Oz2X8frUxgcOHFgda+6FiDKmm1o4tdbMz4Bk/gs6Pk2+DdkWxlk8MzVS/S31b9Vouf1ztk35iBEjijqu0z322KM6/uUvf1nU6dhyi3C2qTp/5ktAHwRqynrf7KuOX1OKZP1ttr04fRB4X/ocs+/MU6A+ANwafdddd62OZ86cWdQxv4DOtb6PWLdkyZKijj4JG220UXXMd56u6Z122qmoY06OuXPnVsf0vdJ5oN6+YMGCoqzjw/cKx1LfV3zGM7LU51xr2neuH7ap57bjI8Exyd5JfHdk76fMB4j903vh3GobXGvdwZYEY4wxxtTijwRjjDHG1NJj5Qaa4dR0w1BBNVMyHHHPPfcsyro7IWUCDXtk2Em2GxnNug888EBR1vApSgjaThaKx/7S9KdmJ4Y1jh8/viirWZVyw7x586pj3QEuoqO5TM2Y7LuOD8NHaS5Wc2x2nYjSLJelw2Zfs5AjXkfHuSkstbPf8VyaZp955pmiPGnSpOr48ssvL+p23HHHorxo0aJO+6fjxzDLLM0v70vNnaxjymsNkcx2pWza/S/b3U6vSymQkoLeF6UIhkjr80iZR1ON8z3CMGNN8b506dKiTsdr9OjRRR1lg2uuuSY6Q8eSc8v3wQknnFAdZ3If30ccS5Wk+E7MzOBETfp83laVbJHtiJhJXWyjnRTgGdkzlaVIZ5nSsq7LG264oahTKbKr2JJgjDHGmFr8kWCMMcaYWvyRYIwxxphaeqxPAsMBVcfKthpmCBa1HtUoqRmpXkldirqZ6kQMMaJPgvoLUK/Ue+F9UbtT3ZEaZObbMH/+/KKsWiJ1RdXN2P6oUaOKsm5TnPWVoUrqg9AuOmecI+0D+5OFQGXpU6k9Ux/U63CtaZsMr1Pfj4iIYcOGVccTJ04s6q666qr/r70z+d2kKtv//f4BMnVDQ3cDTdNAy9DQTDKIOMSRBYkL0bgwMQ4JiQv/AuPWuEATEzUuTIyJRCFGJUpkEhFxYEaGnmmappuhGWT//naV63z6PNd56otv8nvM9VlV5dRT59SpU/VU7usemn29NvrDaKps6u+cE33GGPZFXweF60u1fE0vXeXnmT4JGm7H503ncv/+/U0b9Xkdz+bNm5s2+sNoWWcX2nnttdc2bZxLTdPMlO6aopzpk5944olmX1M6M1xSwxo1VLLq+PTcqlXzfuncMnSZ7xV9t3J+6KOg7w4Xss61xedGx+Ce41FqY/0tfQBceOTovIv6qGrXDN97OidMp8y51OeY59Hnei0+CCSWhBBCCCF0yUdCCCGEELqsrNxA85CaXGh+UdMRZQpmRlOTpoaSVbVmMJp/aHbWsCaa84mGiNEMp6Ytmnxp+lNzHsPQ9LwM6eGxanLlsaeddtq0zVAzbatq54ihp2qG43WpKa2qNdG5sMaq1mTtMma6TGgjdA3RnE8TsMoIXJdaUZPr8Jvf/Gaz/9Of/nTapoyi5uqqdq45l8eOHVs4HheiyXnW+eMa0RCsqqo//elP0/aHPvShpk3lPZr6+Uzp3Go2z6pW6uJ4aB5W8zXbKBepCZ3hki7cljBcWFGZ4MEHH2zaGHK4c+fOaZuyikpSfKZ4b7neFL0WhgZSUnDPG1m2euroPE6icmPnvpM8dZ998B3tZF7KBro2XUgm4ftKn3muS83+SWmSz80yxJIQQgghhC75SAghhBBCl3wkhBBCCKHLyvokOD2emqTqOdSTGF6jOij1ZtVzCXU0DbtiCmmGXb322mvTtguv4XWp/0RVGzLmtHKGGPG8mqaV4YiqsVMz3rNnz8LxjPwpFv2uqvXZcPe9qp0/tukYeL/m+DbovD/66KNNG+dLx8O1pqGwTL97xx13NPuq89PPgOtA1zh9QfTeO/+Xqnb+uGZUs+V4GOb4hS98Ydr++9//3rRpuB3D9qibf+ADH5i2GZqruiwr3/G8ur5G/hT6rDJ9sdPOGcqs52UfWkGW6+maa65p9nfs2DFtM7zt7rvvnrZ5L+nvob4OfDYVauFcMy5FMedW/Rl4XvWLclUfq1ot3/kSjao1Or+DZf0eOB7OB8fgUl7rb9knnzGdr4MHDzZtDz/88LSt62WtxJIQQgghhC75SAghhBBCl3wkhBBCCKHLyvokjOKSFdWXqBkx34HqS4wt5v6iPnheF2Ne1cbdO58E6t1MTauaH3MzfOtb35q2f/jDHzZtLIGrY2eqZdV32b+bWxcvTN3u6NGjzT41Sden+ixQR9d7S98G6st6H+gjoedhHPJDDz3U7B86dGjaplaueSWYk2P9+vXNvtNzqW2qnsmx67GcVxe7zj70/jGlNH13VDN16bmZw4TXqfeIfhjqt8I1wbWnei7Pw2f8vPPOm7aZoljvn6Zvrqo688wzaxHUm7/xjW8sHA/fT8zDoagPh85H1fGlx3Ut8r2ifix8FunfoWvGpTauav0g+GzquuCz6NKiu/cl+x/5Fih6LcwNMfKLcmNw/gu6Lun/wtTiei0c39e//vVpW0uCV1X9+te/XjjWRcSSEEIIIYQu+UgIIYQQQpeVlRtoRnVmL92nmYuhJQrNXrrvKgxWtSYgmuXZp5o4Xbppmsu4r+bPiy66qGnTtL6f/vSnmzaGaKpZ0IWTuXmuak2lnC8dO39H86eGt41CKfU+0HRMs7NDw7B4Hh3Pvn37FvZf1ZrpGaqk18LUqrwu3ef6cVXyKFuoKZnX5WQdhhzqsQy35XjUdErzq94TmtY1NLiqNccylbiuL95npjbW1MtMJb579+5mX6sysk+9f7zmAwcONPtq7ue91WeMaaGJyhGUJjTlLs3TvNf6vuR4eD8VPqv6nuP64bOqEgjH41Ibr7UKI9fanIqRei2jkHFXlZK48+rcUi7i+PTZYFVRXUO/+MUv7HiWIZaEEEIIIXTJR0IIIYQQuuQjIYQQQghdVtYngXqT06mc/j0nhEY1QIZrufTA7IM+Cqp1MpxFNS6m2GXaWk33ytTPTjejZqv+Hi7ch9o4w6Wuu+66aVtThVZVbdmyZdrmdXC+XBpdF35EmO7V9al6KsPHVPOjr4WWaa2quvLKK6dtpiRW7ZdzyTWi/jDU3Ol34MK33Bpmmm31oWCf2gfnjtq9hgNqSGFV1X333TdtX3XVVU0bdf0jR45M27yXOl+cO+q76v+h/VdV/e53v2v2b7/99mn7+uuvb9r0vXL++ec3bX/5y1+afU27zTBZLfHsUhBXtdfGEuGqU7MksEstzmfchcnOKW9Mnyl9ptinKyPtyrq7MEdX/rmqfXdwrMv6K4z65LtW2116Z86PK/lOND0+03qvhVgSQgghhNAlHwkhhBBC6JKPhBBCCCF0WVmfBJe6c5TDQHH6F8/jynwum+Kz6vgYYdVXnQ8A/Qyoy6pWvnXr1qaN41UYF61x24zl1XmnHsix6/jod6Dn5b10Ojr74D3S+0mdUcc78mlRvZ59Pvnkkwv74Njf//73T9u///3vF46d+jJzV6i/Cdcac4boeVkiWK+TuqbTcKmJqo7O+8d7retd566q6iMf+ci0Td8B+pvoGqZ/jvplME004/V1Lr/4xS82bd///vebfS1zzfwdOs+afruq6uKLL2729Vmgb4P6fqxbt65pY64I9fthm/6W18wcFHpvXdph5yNF2Ob2XYnpUV4ElxNH53mUhlmvjT43+lv+ju9dfZeN8rjo2DkH+hzxmWbeC31W2IeWoHe5T5YlloQQQgghdMlHQgghhBC6rKzcQJOPmoRoZlKTC81TNCU5c7qGiLEPmnw0XItmU5rw1bTE8eixNEExZbKOneZYvW6amWm21DHwujS8bVRtT032LtyHJk3iwq7YpvNFM6Wai/k7l+qY41Nz9m9/+9umjVUz9+/f3x1bVXv/uJ5cel6GGNLcr+uNa0/XAZ8hl4ac5nSVgGhi5XU687XOM3/HlMm6vrj2VG5giOHnPve5Zl/vNas3fvCDH2z2dbxO6qJMwPup7w4+m88999y0rWHDHGuVf6b0Prj3SFVrrmYf+r5k6mfeP5Ux+Lxx7Wk/Tv7gWB1zpAjingUdu6uOWjVP6tbfuhT8nDs+myo/sE8NaWfY9dVXX11ziSUhhBBCCF3ykRBCCCGELvlICCGEEEKXlfVJcKk6iSuLSm3ape5V/ZRandO/mDbX+UywTfU5atEM9VKd6vXXX2/aVAelBsmUsjfffPO0rWV++VtqYfSZ0D6pM+p1cs55Xr1HI58S/a0LR6LmR41UNUCmZVZ/E4azPf/8883+448/Pm0zNFBhSmumytZrcX4YVcuXo6XWynLQLpxMz0udmpq7+oLwudF5H/ncaKph+tWoxr5jx46mjWtGw4OZvtiVTeZ1Oh8Armk9D8Nd1W+Fa5/h0voOcpo2z8NQOH0/sA+9D0xxzfO4kHH3LuW9du9Plzrf+SSMwpzdse45cWHXxIV68plyvg3E/afpc/PnP/+5aYtPQgghhBD+Y+QjIYQQQghdVlZuoHnPyQ1q9uLvaObVKnVqVq5qTW80pbGCnvZDU5bLYsbQNzUvavW6quNlg5tuumnafuKJJ5q2bdu2Tduaca43HjV/0gyvpi2axFz4j8vmx9/RfKbnoWnPZYDj2NXEyj5oItewULapFMFKhZQxXMiaM9lzfNrODJlOrnGVTCkv0LSs80dzsI7dZQnl+CghKOyD8oxKDC6bHsdD2WnR2KqOnwOdd65hff64Lp2p3YWBsiol5Rm9FvbhQoU5J3peJ92OJARtd+/gqvYe8TxOcp1TLVGvZXQeHTvvrbsu9w5i1lCtgEqcRDWSVTUceNeuXU2bylmUnddCLAkhhBBC6JKPhBBCCCF0yUdCCCGEELqsrE+CC8WhZqQ6KFO9UlNWnZFphrUPpslklUXV/EYhYqqD8rpUF2Yb9V0Nd9m5c+fCsTOskbqjatXUc10lN+pmqk27ipojnwSXVttV8eS8P/bYY9M20+jyfqo/CkPE9LwcO/vUNcSx6r1leCtRvZJ9UgfVPqmnujaOQcfn/Cmcv0JVm9KZfeh1UafmXLqUu3osw0ep1es+7zufTZ0j+ge4FLscu2rD6qdS1fpe0M+I61TDnF2I3yhEnL4Xigt9ZZ/6bLowwqrlKz/yPeeqNzpdn+8u50vAsTk/Ft4j7ZNh6bzXLgW/nof+QlxPOtcM43355Zenbb671kIsCSGEEELoko+EEEIIIXTJR0IIIYQQuqysT4LTsamjqSa6e/due17VKNmH+h2Myofqb6kLMQ2ypv0955xzmjbVm1x8dVWrabFNNUjqkbfcckuzf/DgwWmb16XnHeWq0H2eR6H+5zTJUQlV9TFhiuRrrrlm2v7BD37QtPEebd++vdt/lddWqcfrsS73AdeTS93N/A8uTazzGzn77LObtn/961/Nvuqr9CXQ/CIcO+/JZz7zmWn72Wefbdo0ZTPnh2Wc1Z+IOuzmzZunbWrj1IX1uph7hM+Grk36fqgvgdOMq1ofF673DRs2TNtM2cy1p9fi0gWzD+dXQ/1bx8My8nq/qlp9nmN1PgnOz4DrgNepzwKvS/edHxThWPW6uPZ5Hp0TlyOkyvszudTUfK+orwp909Qnx+XrWJZYEkIIIYTQJR8JIYQQQujyXyM3uEpcmsaWaY+Z4lalCZoM1ZQ0CtNRsyDP88ILLzT7N95447TNCnYXXXTRtM000Xv37m3233333WmbZjhNxaxV8KqOT92pY2fYl5pjaWJ1qYVpSnMV9IiazDgehqzpXJ911llN22233TZt05zPsDldBwyb1Tng2F0KWScTuJBeMgprcumwNX04n5lLLrmk2dd1wbTjGsrF+07TqFbCZJpavbc0/dOMqlKXk9poaqcJWOed5nRei5qSudZ0fVHSoAlf549z8OKLL07b+gxXHR9Sp+ufz4LOH9+Pup6r2jlhlVoNs6S8wLWnc825c2uY8FqUOdUSdTwjc74+m+zDXRfvrT7XXPtOknWVaPnccn5UbmBFTVeGYC3EkhBCCCGELvlICCGEEEKXfCSEEEIIocvK+iQwVEn1VWq/CrUnLT9b1WpB1IVU66Ge68pB0w+CoWca9qjhkFVtik1qWNTYVMNlGJqGa11wwQVN2549e5p91fI4l6pxsQ/qX6qRaohalffv4FzqvDOEjtq09nn//fc3bXpd9DNwurobH8O1XNraOSFYrnStKwlc5dPN6j6fIWqtGvrlfIBcud6q1h+Gc6DzzmfT6d8MS9N1QF2YPgoaysj1TR8lPRdTuGs5doYu8xnTa3nqqaeaNn0/sIy7e+Y5PxoWypLTDLvWOaA/hY6H78c5GjfXjAuJdn4GxJWDds/GHD82l/qZfhr6HO3fv79pu+KKK5p9vW6XUp7X5XwvGOao441PQgghhBD+z8hHQgghhBC6/M//OpvL/8ds27at2dfLcCEzNJETNT+6jGE01dL86TJ/XX755c3+xRdfPG3T5KthjzRB09x44YUXTtsM19L5omlUpQiOgfOlfTJ8jGGEarak2VRDeGh6ZEimhnrSjHvHHXc0+1rlkBKHjp2V3ChbuDWjba46YlV7z5w0QTOpC51y65v7XDMKzZSuqqCbg1FlzmXD5EZVBHVOuPbddbrsrK7SK/tkNkSV9yhFcF+lAIZAatgj7wnvrY6H86xhlqweqWGWVV6+0ud/jjnfVVnkuTjvi47roWvRZTHlO8fts03XrHt3sU+Gl3M9qZzFOdB3Ev8HGB6sMtDouVE++clPLmxbRCwJIYQQQuiSj4QQQgghdMlHQgghhBC6rGwIJDVI1cOoyajO59p4HuLCvrjPlLLKueee2+yrxsWQLNUrqWExtFJTuH784x9v2vQ6X3nllaaN2qH2w3Sgqs/RB4G6p57HzQf1ZfoLqNbKSoW7du1q9nVM9DNQmP6WVQV1TNQkVQMcpefWdcFjXQpZ+gC4UEHu63i5nl3KVlcxzlX/o38O/TI0xM5V8RxVrHOVAp2PhKtOOHr+9V5TF9ZKmIShlDoG+vLoc8x16cL2XKVQVqxk6l6dS5cynfPjUhuPfAD0XPRN0fHxHUjNXefE6e/8HedLf+vOM6qoqeuf7y4+NwrnVu8f58c94/Rf0N9yPGshloQQQgghdMlHQgghhBC65CMhhBBCCF1W1ieBWp3qO9S0VPOjHj/Sd5ftnzqslpGlvsyUwKov0QdAdSrqiszNoHHcjzzySNO2YcOGaZulYV36aer6et1//etfm7ZPfOITzb7TxlTno9bLY1XP/c1vftO0MaWs3nvOu/p+8B5wzajmTe1Q7xfXAefS5UnQ847KP+tvR6lWXVpmvU76Ergy15wD9Tdx/gFVXm92JcM59jkx+u48zn/BadPMPaL79Gnhs6lj4FjVt4HvER5LrVpx64Ln0fcM156OdfQ+1PbRWN2xug7oT0GfAMX5n4zSlzs/Nt3ne8SlaaffmPN54f3S957Lj1HVPnN8jnXeR3mBliGWhBBCCCF0yUdCCCGEELqsrNxAk48zE7pQOPc71yf7Z6rV5557btq+6aabmjaa+9WUxJTEGtLHkEeVNKraCpLnnXfewj5c+t2q1pTFMCY1g9EMSPlBQz1phjt8+PC0vX379qaNlTB1n+E+NM+qqdRVk3OV06raOeF16pphHy6skGtN55nmaZfqmGOnuX/R76p8JUqXvpiyjuuTY3cppd1curE7mZC/cxX1RuZ0NcXzmvU5dqHChPOjzwZ/RylA1wnN+Xrd/B2P1fO4EEPXxj5HcpFLKa1rmu8Kd+ycdcA5cZVoXf/sU+89w2K3bNnS7OscOKmEc+nWhUt/7UIwlyWWhBBCCCF0yUdCCCGEELrkIyGEEEIIXVbWJ4EaqUtX6kJLnH7qygBrquCq40NNLrvssmmbWqaWPibU4/S8GzdubNpcyWfV/Ku8VkfdUft0JVQ/9rGPNW3U/NSH4sEHH2zaVBNlWd1Dhw41+xq2So3NhSBy3p0m6tIru5Lhc1IkOx1/lEJW+3ShlMSl3B3NgY6BYVYuvMyl7iUuBNKF5rl0wVyzThvnPPM5Vr3Z+WzwPJxbd/+cFu3uCXF+Kxy7lqCnP4XOJUNWnd/ByD/HXaf6jY1CX3VOOB963c6Xgedxfgf05+C++kmxPL0L/XZrxK21qnb+nD+Fa1uWWBJCCCGE0CUfCSGEEELosrJygzMlsU1NZiPzsJpnaJ7SDGs33HBD08bKbioNMMTv5ZdfbvZfeumladtlUaTcwCxvWoWRYXtqshtV/3OV3dQcyz6YEVJNZjRXa8joPffc07Qxs51KOzTDcQy678zOXCNOdqKpT2UnZ8Ik7EOPHWVRdOvbmbqdyZe4bJE0w+vcjuQFnT9KCM707+QZVwWWOBM5z8M+nUlajx2ZyJ3s5GQCnsfJYHosw6V5nXof+D5S+Hy59T6SG1yGQyclEV0nlJ312XTPG9t5rJ7HrYkqX5GR4e4qVXBu50iK7j2j4xnN5TLEkhBCCCGELvlICCGEEEKXfCSEEEIIocvK+iRQa1HN1FW+G1VZ0/Z33323adu6deu0rWmXq6quvfbaZl91M4YRUUfTMBmG0Gj1RupU1BI1lIm6/rKpcavaOdHKiVXLpzLlebdt29a03XnnndP2H/7wh6aNfhnqv8D7xzFoO9ucT4LTtJ3/yyi987IVB3lPqN3rvXfpXKt8iJhei6uOyH2uvTlz6fxYXLrwOeF/bn3TN0XH5/wMuM/QN3dPXGVM5w8zqlyo7bx/ep5RZVWtgjpnfXNffY3mpCh3lVVd9UiO1/lMudTYPC/Ho+9+3lv6e7i02vTl0WOdvwDXD/9DlvVncn49yxJLQgghhBC65CMhhBBCCF3ykRBCCCGELivrk8D0xapFM62v6vyak6DqeP1btR/qOao3aRnkquPzAHz0ox+dtp9//vmmjRqgau4HDx5s2q688sppm9oTdSo9L3MWuPhq6maqlTn/DvbvSjPfe++9zb7mRuBcuvLd1PxciWUwPVgyAAAgAElEQVQ3HueDUOU1bj0v587p1i4+nnPJ+6eaMteaKxnMsdOnw7Fs7oFRuXVX4ll9L/hMzynjvuz9GuHSczsfDuf/UuVzBOi6oM8GUa2c90fXBX1amM7clVt2KX/ddY5y0Cz7PLr8CnNw11XVziXnx5Vb5jtIz0vfDz6ry+J8m0bo+jrllFPW1H8zlvd8hhBCCCH8V5KPhBBCCCF0WVm5gekv1eR68sknN22vv/76tK2hP1XHm4fUtHXqqac2bWpqu+SSS5q2HTt2NPsaIskqazQPa7sz4Y/OoyYqmm7VpEkTOU2IWpGNx7799tvT9ihl69NPPz1ta8hjVWs+Y0gRUfMZTY80q7oqa4vO2TvWVQPV31LucHKDC+VylUur2nvv0h6z3aULdpXluM91oHPgwgbZp0tXzLmbIxMooxTXrt21OQlhlN5Zr9vJfZwDvsvcnKhp+9ixY00b3x36/nShpi5deZWv7EicyVzngOdxFVLdmp3zrmCb9sn3nKuayedkNCfL4qRvrhm9FqaFXguxJIQQQgihSz4SQgghhNAlHwkhhBBC6LKyPgku7anTaKj5M0Tk9NNPn7bVl6Gq1fwY2sL0xZp6mWWkqWOrJs82DYU7cOBA08ZS0S500fkrcA5cqeiHH3542r700kubNpZ8fvPNN6dtp0fSv4T31pV/dumCOQcufarDpT0e6eja7srjuvVcNc+/QsMcqZFqG8MhXelht55GY3chfi6duguBpE6tv52T3pnjcamzeQ+crwX9c9z617nkunRrhn2qLxGvi2N3YY66ZueEMY5CDvVaOD+unLjDpSgfPUMubFb/J7RUPduqqjZt2jRt855wfC4Vs0tz7+4f74n+Lzz11FNN29VXX72wj0XEkhBCCCGELvlICCGEEEKXlZUbaJpRcwzDx5wJitm01HTEYy+//PJpm7IAJQUNFaS5iiF/eq4TTzyxadNqbhs3bmzaeF41VTqz/CgsR01iNFcdPXq0e1zV8VkVVcbgNatZjhXrOLdqFud1uQxwbNPxUibgeV2WQDWRuyyKVX7tud8RNVvy/jmJY1SZb61oHyO5Qe8Dj3USGc/jKiS6qnhzTPZOWuKxrpqkM3W7YzkHLqSOY1UzvQt95W+dTDAKgVy2jefl86ZjH90/N5fODO9CKV14q8o4VcdLzZq5ke9oShN63S58061ZnocVf/U8559/fr1XYkkIIYQQQpd8JIQQQgihSz4SQgghhNBlZX0SiEuVq5oRdXQXZnXOOecsPJa61KuvvtrsX3DBBdP2dddd17TRl0ChbqZhey7UjftOz6XOyYqDqnHp3FW1oZ1PPPFE08awq717907bnEuFuiJT0TodndfpND89dhQmp791muR70aJ1n+uSc+nCtVya5jkV9JwW7PRT10Zc6CL9FbhO9VngsXr/OJfOl8CFPFYtr8+P0nzruuRa09/SV8atJ86zq+zo1qnz63FrtjcGd+yy45lToZXH6vuJ/wNEn2t3LP0BXBgj798oFFVx/0U8r4aXX3jhhU2bVjretWtX05YQyBBCCCH8x8hHQgghhBC65CMhhBBCCF1W1ifB+RYwza9qWExJzBSgqv1Qv1Gtnrr5wYMHm33NL6D6UdXxOQOuv/76advFabtY2d5vFdVlec2M5dV01Krx8TyPPvpo00ZNTdODMsW15qfgfFDHU1+LUdy/XpvTrUeara4D+n7oHIzyDjj92+nx1In1utjmNG6X6tVpoFXL683O92PUp84B21iSV+Fz7Hwk6Nvg8i2MfBQUlwLclYPm8+fukcuBQZz/BNe3ts9Jbez6JHPKr+v+KHeF8y3S+eL7kf8LLn253hN3f6ra6+S95Tp15eFdHhe+H/T9uW/fvqZNczVoXpu1EktCCCGEELrkIyGEEEIIXVZWbphTucyFmu3cubPZV1P3Y4891rR9+ctfnrY1vK/qeLOSmtdvuOGGpo3mfR0TwxHV3M82mmP1OikTqGmN1SN//OMfN/sf/vCHp22audT099BDDzVtvCc63g0bNiwcO8NJafrTUCWm0eacuOqOy5qOq9r15MLSXPgYodnUhUNxnc4JJ3MmYGdm5nOzrHl4ZGLVa3HhmuzDpdF14X9zZBSXjpf7DIVdto+q9r3CPnX+nCxQtXyooEvnzPM4ucGFBvM8IwnPhWi6dcn5cqmydZ5HYc7O9K+4EFruj6o+6vj4XtHx8Z145MiRhefh86bjdeGayxJLQgghhBC65CMhhBBCCF3ykRBCCCGELivrk0BUC6K+pPq3li+uqnrmmWea/UsvvXTa/tKXvtS0aTplhpYwffGVV145bVOPp7apOjrLXKs2NQq30+um34OGGdLP4O6772721SeBvg2HDx+etrdu3bqwrcrr86qjMcSQGpvOz6g0s2pwLnSJc8n5cqlpnabtGKW4VUa6rOJ8CeaEvo1KNS86zyhMT/VT+ozoeejbQD1Vx8M292y4dNNcezyv7lMndnDeVSfm/Kx1HbhQQVeKmed195lzx/POSQW96Hfsh8840fNy7elz7MIj2aebg1Eqf/csuBBtrif9X+D7iGHheizb3D1ZC7EkhBBCCKFLPhJCCCGE0CUfCSGEEELosrI+CceOHWv2VQtiLL3u0yeB/gKqh2tq5apWe6JuRn1efRQeeeSRpu3GG2+sRfC8rk/qVqo/rV+/vmk7dOjQtM2YW2put99++7R91113LezzxBNPbNqYt0F9AqjNqS7L6+B1qg46Ktu6rM440upU53Ma5Kis7RydWHEpbUex2C5dsN6TkY+Ei4F3KYCJts/J/zBHT3VlrTk+za1BXyLiYumdf4eLrXc5FPg77utz4/T4UVpm/a3Tzef4NrBPlwLf5bkZ4dabvjtG+TvcczynxLp7Np2PAp8FXZecd5ejgzkxXP9rIZaEEEIIIXTJR0IIIYQQuqys3PD22283+1qVkXKDmngYYkjzkJ6HVcPUXEVzPqtCnn766dM2TZqsGHnaaadN2zQPqQmf4Yg0V2mYI8NiVG548MEHmzZKLn/84x8XnseZ6JxMQPPZ+973vu527zzOXD2nCp0zw1PyUHOoS1s76tNV39TrpLl1TnpnF7rowjddNUT+1skNI9OsS1urzKk46O4J54NrWJ/HUSpol9Jd4ZplaKVL8z1HdtJ9l+KaJmj3LBA3Py4NOU3i7jlxYbtzcPPjQgPfS58u5HcUWq3/ITxW/5u4Jtz95HXpfeD/1FqIJSGEEEIIXfKREEIIIYQu+UgIIYQQQpeV9UlQ/b2q1XeoA23atGnaZqjiBRdc0Oxv27Zt2t6/f3/TpmmHqXetW7eu2X/22WenbU3R3Buf6nzU/FRvouZHnwnV9l9++eWmTeeLPhLUuzT9NK9Tw3TYRl3WhVkpo3SuLpRy2bLIVWMNXlGdkaGdy4ZZsn2OL4MLt5uT/pbH6hyMxu58EtxcuvGNwiUVPgvut3NC6Jxvw5zQN2VUlnjZNMhs43U5vwh3Tzgefeb53Lq0yC4NOrV6lzZ6Tnlz53fgnptRWKNLva7ncaW9q1r/E3fNVe27n+8VN3ae1/lpzSmbvgyxJIQQQgihSz4SQgghhNDlv0ZuUFM8zeeaZZFyw5YtW5r9vXv3TtsuEyBN/Xv27Gn2r7rqqmmbJkOXmZBmJTUd8TwMA9WqYg888EDTtmPHju45q443n6mM4MxeNKUx7Evni8c6k+scucGZOJ1pdFQhTttdhkO2MdRz2UqKZI6k4MIBXRXIUTY2l0nOyShu7Jx3d545YXuOOVLEnKyTTkbhO0jH7rJOUsJzoW9OkiJuLl3o4shk7zJJunBllyV0TlgqcWvWSRwuq+pIQtB7xPs1Colc1CfXLPeXvUejjKLLEEtCCCGEELrkIyGEEEIIXfKREEIIIYQuK+uToGF6Va1uTc1fwxPPPPPMpo0pnJetksc+mNpYUyhrCGbV8TqRavmsbqnnYR+XX355s/+Vr3xl2v7qV7/atP385z+fthkO9eqrrzb7LuXnWkPEXAgd+2B1ST12FGbldGvnZ+B8HZyOznAxp1/O0ZA5HheWRpxWPid00YWIufnhWPVauPa0jXou950/hZ7XpZDmeTh2+gSohuz8O/g7nlefec6BPv9Mve58XvgOnFNN0j3Hbv24dcn3GtOt67VxDnSeRymbl/U7GKWUXvS7Kv+ucO+DkQ+Hpl5mm4aX63ZvDEePHp226a+g500VyBBCCCH8n5GPhBBCCCF0yUdCCCGEELqsrE8CcwScccYZ0zZTJGv+AOqlTF+8bOpQ6m1aGrqq1Z6ojdEPQrU6xizreaipvfXWW83+d7/73Wn7s5/9bNOmJUOpHdIPQvWwOb4Ec1KA6n0YaX46f5xLV2KZ86X308UdV7X6LrVx1YVdzDTbXcpdtnHsc/RUp9k6nHbv1sGcuHbm5NDSuaOcE8um4J6TItmV/WW7ex8w/p3zpdfJPvT55/uJ60l/q+fkGEYpt9260DaXH4P7+q6qOv49p8e6Z5zzM6dMuUtX7J4T51s0yrfgfBJ4LXourhk9duRTorl/yJx1sAyxJIQQQgihSz4SQgghhNBlZeUGZ+bVSo5VbQpnmsQYcqSmGpr61ATNsEb2+frrr0/bI5OdmlWZ2ljNsxzrySef3Oz/5Cc/WdjHwYMHp22aXymd6BhohnNV6JwJ05lRGe7jwpFGMoEL39LrYp+81zrvlK+cTOBCjnhdet9HZkHt06WtrmqvxUkuzlRb1d7rUYif4tI0u/kZSTc6Bid1cayUOHTe2TanWumyZm/u81nQe+vGWtXKkXOeRZei3KWbHoX0uTXCd61eN03tcyqr6hy4ezJK8+3adKyjkExd05x3XqceyzYnlZx22mnNvrbzGdfxuTWyLLEkhBBCCKFLPhJCCCGE0CUfCSGEEELosrI+Caeeemqzf9lll03bTL2s4X8ulKvqeB1NUR2bWs9rr73W7KumNdKQdZ9aufbD9Mla1rqqvRaWrlZ9jho70yDr2OkD4EI7ifMP0PCtUapnnR9qtLx/y5Z4dXppVauvMtxWx0Bd0ZWKdvrp6LpcuWN3Xq5Tl97Z+YI4zX1OGl0XZsk26vPumdI+RuGIeh724XB+BiPfFOdX43x55pScXvacPC/Hqr91PgjcZ8gjx+7SMuuxoz5d+LR7lzgfBfe/MEoFr2vIpQuvasPxGe6uPlP83b///e9mX9+fzgdorWn0lVgSQgghhNAlHwkhhBBC6LKycgNNPmqqYbVENbkcOXKkaXPhgK4KHU1gDCN00LSlY6ekoCYplVSqqh5++OFm/5e//OW0TTlGz8tQSpq6NZvXvn37mjaaFJU5mf+WNWUTjp1Z55ypVNtGGQ3VbEhzngt9c9kZXTjZKFTJhYg5OcuZUWnuZGVTXdNvvvlm06ZrxIVOEsod+luuQ5fhkCybzY/HEmeefS/Z69Z6XicBuTDUUeY/fY4pz7h16Z4Fnofo/eV45khAy4YyuvcRx8O1p+OZk8FzFDLqqlQqfH9zTlQuZeipjm90T5YhloQQQgghdMlHQgghhBC65CMhhBBCCF1W1ifhlltuafZVQ2I4ourELqyqqtW4mfZYfR2o1Tk9dVTVTPVvHqv71H5/9KMfNfsaJuN0YWps1Pl17E5DZgppamNO13fjcalNGa5JXd316XwSGLrkwhN1DY10apey1YVrcjy67+4JcdUlqZeyT11DrDrnwtncnDjfFP6OPhI6HudnwPvFZ0HHPgpvc2tm0XG98S2b6nhOOKkbA/vndbpQb50vV9GT+xwb513fF3zPufO455jMSSmt/wscj6uE6/xERqmgXRVdV9nRvRP53nVhzmshloQQQgghdMlHQgghhBC65CMhhBBCCF1W1ifhvPPOa/ZVm6bfgSv/7OLleayWf7755pubtieffLLZV32JGhH333nnnWmbOR62bt06bX/7299u2qjZqv5FrV51K17Xueee2+yrXkk9TueW+pvzy3Dpi/k76m96nYzX1zLghHqq0w5dOe9RXgmH61Ohf4dLN8v1TU1y2VSsXIdO73733Xeb/bWW5HUpgInzD3A5MEb31unfzheEa3jZ0tXsx2nlLvdB77eL2qixu+vi2LWNv5uTupssW7Z4TnljN1+jXCjOH8atNfapv6WvB9Ps67nYtnv37mn70KFDTRtLRZ9++unTNt8Hep2uNPuyxJIQQgghhC75SAghhBBCl5WVG1jp8Y033pi2mdrY4UKXmPJ3y5Yt0zZTIlP+UJOZM1NWVR0+fHja1iphVW2lR/bxq1/9qtlX8zFN4mp2otlN+6+q2rx587RNc75eC81lxIURukqFNL1rn6NKc5zbRW08zlVddHLIKNTMmU6dKZBSgM7JKNWqkzjUNMo+XCpfZ8IfhZrpenNmcCcPEffcOnMwjyWuyuGoUqfiUgI7qcSFyY76cONxqY5dWu05aZnJKCRScZKLW8MuPJFrjXOg7685a8+FUvL9zT411TmliXPOOWfavuiii5o2laSrqo4dOzZtOylX5eq1EktCCCGEELrkIyGEEEIIXfKREEIIIYQuK+uT4MrcOv2N+hb1efVDoJ5zxRVXTNsMCeN4VKeibk5NS0MrNbVyVas9HThwoGmjHqcanEszzDYXukgdUfUv+g641MLUBxXeA2p1ek94b11aXadXurC43m+XbXNlZekD4HR0l7aWbbwPTrN15c75bGi7G7vTzTlezrNLIct14Up06xhGPgg6HvbP9bTsOhitJ51L3j8dH6+Z7445/gKuzfm1uNTGTrsfzZ0LkXR+Pm58PFbnaxTeqvPn1iXn2a3ZUfimzpfzBZnzPmCqeg3ZXjYc2hFLQgghhBC65CMhhBBCCF1WVm5gSIiapGmiUxj6RlONZkqk6UgzYmnGq9553FjJ0aNHF/apFS01zLPqeLOXmhBptlTTljMdV7UmKpqy9bwaztM7j0oDbjw0rTGMyJkfnTnUZYsbmYf1t85sOqoCqffTZeEbmb2XrSZZtXzFTa41Fz5KXOiiw4WzOUmKv3X3hH24kLqReXjOvV70u6r2neQkKT4nc6oI6v0bmZn1/lEqVdya5f4o06WTpZzc4KRAjn2OTOgqfOq7y8l5PM+ooq27fyotU3KlvK3vC1Yr1jmZ82wuIpaEEEIIIXTJR0IIIYQQuuQjIYQQQghdVtYn4aWXXmr2NcWmCyOi3s1jVc+5/vrrmzbVovbt29e07dmzp9m/8MILp+0dO3Y0bffdd1+zr1rikSNHmjb1Q7j33nubtk2bNjX7mo6aWp1qWNS7mV5Z54t6nPp+qC9F1fE+ChqWyj7Uf4LVLEdVDhWnkTqcLlzl/Rdc+N+cNLVurE7P5e+c7jhHR3easfPzoT8Fj3X+HXqs81fgeXjNLkTUVbucEyK2bAXG3vj0ORqFjDr0t3ymVLfmPZhz//TdweeCzJl3F37r+nHPAt9PLqzYVepkHzoerku+WzkGhWPQcHP+F2kbK88yHF/fvXxOdN5H928ZYkkIIYQQQpd8JIQQQgihSz4SQgghhNBlZX0SqFur3uR0KupALAft2LVr17TNVMbUjLZv3z5tU6vbtm1bs3/nnXdO2wcPHmzaNHZ2FNOtWhQ1LaeVM85W/SBc+eCNGzc2ba5kKVENcFSC15Ulpn/FsuldXawzz+ti8jmeUUrZRWNwaYbZPhr7oj64Pyrlq+0uzwXvu/PvcCmJCcfjygnr/Rql0XWpcZ1fhCuJPfI30evm+LRtlL9D31d8xpVR3g3t06X5ZpvLm8D77nwAiPO5cT44PKdLTe/SRruxca259UR4Xk27z7lVny6+k/V/oKrqhBNOWNim/3FzfJIWEUtCCCGEELrkIyGEEEIIXVZWbjj33HObfU19zJSWaj6j3EDT0UknnTRta0rkqjaMaPPmzQt/V1X1ve99b9p++umnmzaakjSlM023b7755rQ9CrNS86MzxzKFtKabrqrauXNn95xV7dxyrDTVuqp9Ou8jk722u/SpVa104Uzk7MOlcHZVBUcSkOLuCeF59dg5VfLceUYpgB0uDNRVJ3RjH6Xx1X3KhM7M7CoyjqQbZ651shNx5nR9FvjuYniwjt2lnx7dE2ded9UR11oBtde+6Ly8fwzf1JBoJy25MFm283/A3Vt3r/k+ovTtnr+33npr2qaEsG7dumZf1z//e3ROXEXkZYklIYQQQghd8pEQQgghhC75SAghhBBCl5X1SXj22WebfdV+qONpaInTMquqzjjjjGlbNaKqVsdj2Wam6rz11lun7bvuuqtpO3DgQLP/wgsvTNtMdaypVulP4Uq8aogM4diZNnrZMELiwhGdVkffhjnpXIlLy6pQD3T67px0yqNyuYtwunmVDycly/Y5SoPs2pxPgpt35y8w8k3RMVC7V0aheMv6bPT2F52HLKv5V7XPNZ8F+gTNKRnu+nQ+N8umJGc758r5QbhnarR+9Z3IY12K5GX9S7g/CkvV6+Rz6t5tTDevfgd8f3NfU/DTX8H5pq2FWBJCCCGE0CUfCSGEEELoko+EEEIIIXRZWZ8EpwdSG9McCow//fznP9/sv/LKK9M2S7GqhrR+/fqmjbGqTz311LT9+OOPN21PPPFEs68+FPSD0DwJ1Pioy6peSG1Mj+V5qFudddZZ0/ahQ4eaNtXCOD/0BXEpW126W+d3cMoppzT7vE7th1qijo++KHPKLTt/hTllgJ3vhytvTP8Ol1p8Tu4DN745cfZO42bM+7I5FKqW11dHGrLOLdeP869wuvXIt2FR/1XtO4nPEOfLpXBW2MY+dbzsw60Z3gO916M14lKxz1mn+ozPKd+9Vka+O3P8tnQO+A7S8dKXgb4Wej/5PtDx0O9hLcSSEEIIIYQu+UgIIYQQQpeVlRto6lbzizN38nePPPJIs/+pT31q4XmOHDkybT/wwANN2z//+c+Fx9LUpyGPVVVbtmyZtmlm0jFw7FpRrNePoqbAkUlTzXk0C6oZ1VVrJAzfVJwJk31SLuI1q3mNZngNDXKhUsRJCqMUwGtN6+vM1bxfTm6YYxp11+kkII7VSUujPhf1P+c8o7A9PmPuWFcNVJkTdukqO47S6DoTuo6Pa8RJZhyrXssotbHrw1VLnCMT8LxOUnQVY91451yXa59TeZJyg0sXzvWlcM3ovM+pcryIWBJCCCGE0CUfCSGEEELoko+EEEIIIXRZWZ8EF7ZD/eb666+ftjdu3Ni0acrmqjYEkemTVVc/9dRTmzYNneSx//jHP5o26uGHDx9eOHbVSDUcssprgJwfDWukhrVp06ZmX9OeuvSpTnNkO3Vgp3tSx9M5GKVTdlq+Y05IrdMO5+B09NF1Ki40z/2ObU7bdDrxaA50vlz57hGuT3ffnY/CnJTbbp6dPxCP5bOp4+N5mJbZjceVPnZhzwyT0z45dywzr+/LkS+Ku0du3ueklNb9UYr0ZdNE03eA51G/rdF61nPRN0zfkfQlcO85F+bofBmWJZaEEEIIIXTJR0IIIYQQuqys3EDTqMoGzIao2QYffPDBpu3Tn/50s68ygcoAVa2pzckUVVXbt2+ftu+5556mjWZCNVc5sy77pNlSZQya8FWq4HlefvnlZl9DMmn2cuE+vCdqBhuFpTn+EyYz9jmn4iCrbc45z7K4rGkcD0NhaQ5dVnKZI/M4M6ozw1e15uI5YXEufJPz40zQxIW+rTVck+dx8hqP1bnlPLtnzM37KDulzh9DqfX9uX///qaNMqsLOZwTujhHLtL15EIM+d5wMo87z+h50mM579zX9ynnR+/t6J2n94/vaD3Pe5FDp77e8xlCCCGE8F9JPhJCCCGE0CUfCSGEEELosrI+CdRaNGyHISFOo3n44Yeb/XXr1k3bGgpY1eqMZ555ZtN21VVXNfs/+9nPpm1qWtQrdbwubIi/oxatvg3U31QLpqZNnXHDhg3T9t/+9rem7dxzz522n3nmmYW/q/LaoY6d18z7p9fCsCHqcXrsWlMQc7wuPGpUwXLZKoejaoRzNHeH079dyJgLXeQccF06fVX7pF/GnMqhi45jHxwf19ocvwM3l6P7uajPUSpq94zrmnXVLHneE044oWl76aWXpu3TTjutaeM7yFWe5didb4qDx7rqm3o/6WvB0HMXNq//Jwz75Hh0f041UFep06Vs5tjdend+YssSS0IIIYQQuuQjIYQQQghd8pEQQgghhC4r65MwSjuqvPrqq9P2O++807S99tprzf7u3bunbWpYqu8whwJzD5xyyinTNjV/HU9V6/swRxunb4Hmg6BeqamXXQnlqtbXQHMmVLUlsE8++eSF/bMfF4dMLZPjUR2NGht/q+30X1hrrL/LWUDWmuZ3lNLW5RNwc+uOnZO7wvlajHB+GS4Xw1pzTpA5Phwu1t+VxHax/KPx6L11bTyvy4XgfFoI36WaF4T+CkePHm329b3HfCJ8NvV5dPPj8shU+fwG+vzzPUed36XK1rHyd1yXruy280ngefkfojAPj+bzcTlDRqXHlyGWhBBCCCF0yUdCCCGEELqsrNxAM5iaefbu3du0ufC/8847b2EfDKFRUxurPr7xxhvNvqukRjMhTV2Kmos0PLPqeBPUSSedNG3zutQERTMX913qUJVgRhXP9LrUPMbxjMyLOh6a5Dh2HR/bdAxzTNvO5OvCoXr9LGJkZlaz5ajypauW6CrNuXA7jseF/7mQLMoqKlGxba0pr939qmqfk7fffrtp41zq/XRzMBqDCxl1kosLXXRtxMlgTppgWuazzz672deU7nw/ufeMmwOO1R3rUpK7qo9V7frmGnHPiXvGuUZdKLqTSvm+dM84cWnj10IsCSGEEELoko+EEEIIIXTJR0IIIYQQuqysTwLD21SbYrpgDePj76j93HfffdM2/RfOOOOMafvgwYNNG0ODVNNy6Tc5Bi3pXNXqVgwNJBqC9PTTTzdtGobJkEzqW9XslT8AAAL1SURBVKrBMQ2rpiilHsg01hoi6dKKcn6o42k/DLOkb4reM86XC490aZpdeOKc0DcXSjnS9Z0PhwtPdD4lhPPl+nT+AXNKGGt4K9cadVidI6exj9J8q68R1wFDxnS8zs9gFGbptGGdS/bBd4U+G2xzmv+c0E7d37hxY9PG95z6d/D+cXzaJ++JzuWo3LKOj2GX2ueoHLXOpQtvZf98H2g7ny8+m86XR+dk1Kfu832pv9X7s1ZiSQghhBBCl3wkhBBCCKHLysoNWo2wqjXr3H///U3b+eefP22zWuN3vvOdZv9rX/vatP3iiy82bWrGodmb1SRvvfXWafu2225r2mjiVFPg1q1bmzbNCEn5g2GXuu+ysdEEddZZZzX7mpXy2LFjTZvL4MVQITXrrl+/vmlTsyBN15QQ1ITnTKNVbUbI008/feFYRxKQmvOcVOJMvr3xLYurBjo61uHM51wXug4YrrXW/slaQ7ScOX1k8nXShDP3LxvO2hvfov45PtfGdhcWx+vgutTwaWadvfnmm6ftBx54oGlzFT1HoYIqDVCa0PXlKo5Wte8gzWxbdfy1KHMkMj2WkrS+Y6paOdu9R6p8uKTDhWiSZSvPLkssCSGEEELoko+EEEIIIXTJR0IIIYQQuvzP//4n8jaGEEII4b+OWBJCCCGE0CUfCSGEEELoko+EEEIIIXTJR0IIIYQQuuQjIYQQQghd8pEQQgghhC75SAghhBBCl3wkhBBCCKFLPhJCCCGE0CUfCSGEEELoko+EEEIIIXTJR0IIIYQQuuQjIYQQQghd8pEQQgghhC75SAghhBBCl3wkhBBCCKFLPhJCCCGE0CUfCSGEEELoko+EEEIIIXTJR0IIIYQQuuQjIYQQQghd8pEQQgghhC75SAghhBBCl3wkhBBCCKFLPhJCCCGE0CUfCSGEEELoko+EEEIIIXTJR0IIIYQQuuQjIYQQQghd8pEQQgghhC75SAghhBBCl3wkhBBCCKFLPhJCCCGE0OX/AQrf+bbRT7s9AAAAAElFTkSuQmCC",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x322db5190>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.text.Text object at 0x322ed0e10>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "include(\"NtSolutions/inverse_5_inpainting_sparsity/exo4.jl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "## Insert your code here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Inpainting using Iterative Hard Thresholding\n",
    "--------------------------------------------\n",
    "To improve the sparsity of the solution, it is possible to replace the\n",
    "soft thresholding by a hard threshdoling. In this case, the resulting\n",
    "algorihtm does not perform anymore a variational minimization of an\n",
    "energy.\n",
    "\n",
    "\n",
    "The hard thresholding is defined as $h_T(x)=0$ if $-T < x < T$\n",
    "and $h_T(x)=x$ otherwise. It thus defines a thresholding operator of\n",
    "wavelet coefficients as $H_T(a)_m = h_T(a_m)$.\n",
    "\n",
    "\n",
    "Define a shortcut for this vectorialized hard thresholding\n",
    "\n",
    "\n",
    "\n",
    "*Important:* Scilab users have to create a file |HardThresh.m| to implement this\n",
    "function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(::#19) (generic function with 1 method)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HardThresh = (x, t) -> x.*(abs(x) .> t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Display a curve of the 1-D Hard thresholding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "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 0x322677810>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = linspace(-1, 1, 1000)\n",
    "\n",
    "figure(figsize = (7, 5))\n",
    "plot(x, HardThresh(x, .5))\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The hard thresholding in the translation invariant wavelet basis $\\Psi$\n",
    "reads\n",
    "$$ H_T^\\Psi(f) = \\Xi \\circ H_T \\circ \\Psi^* (f) $$\n",
    "where $\\Xi = (\\Phi^*)^+$ is the reconstruction operator.\n",
    "\n",
    "\n",
    "We follow the MCA paradigm of Jean-Luc Starck, that alternates between a\n",
    "gradient descent step and a hard thresholding denoising, using a decaying\n",
    "threshold.\n",
    "$$f^{(\\ell+1)} = H_{\\tau\\lambda_\\ell}^\\Psi( f^{(\\ell)} - \\tau \\Phi^*(\\Phi f^{(\\ell)} - y)  ). $$\n",
    "\n",
    "\n",
    "Number of iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "500"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "niter = 500"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "List of thresholds. One must start by a large enough initial threshold."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "500-element LinSpace{Float64}:\n",
       " 1.0,0.997996,0.995992,0.993988,…,0.00601202,0.00400802,0.00200401,0.0"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lambda_list = linspace(1, 0, niter)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Initialization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "128×128 Array{Float64,2}:\n",
       " 0.0       0.0       0.0       0.0       …  0.0       0.802956  0.802956\n",
       " 0.571429  0.566503  0.591133  0.610838     0.0       0.807882  0.0     \n",
       " 0.0       0.0       0.0       0.591133     0.0       0.0       0.827586\n",
       " 0.561576  0.0       0.566503  0.586207     0.0       0.0       0.0     \n",
       " 0.369458  0.0       0.0       0.551724     0.0       0.0       0.0     \n",
       " 0.0       0.0       0.310345  0.0       …  0.0       0.0       0.0     \n",
       " 0.517241  0.0       0.0       0.325123     0.82266   0.0       0.0     \n",
       " 0.546798  0.0       0.53202   0.0          0.82266   0.0       0.832512\n",
       " 0.0       0.44335   0.0       0.0          0.0       0.842365  0.0     \n",
       " 0.0       0.0       0.216749  0.0          0.812808  0.0       0.82266 \n",
       " 0.0       0.0       0.0       0.0       …  0.0       0.827586  0.0     \n",
       " 0.0       0.0       0.0       0.0          0.0       0.812808  0.0     \n",
       " 0.0       0.0       0.472906  0.369458     0.0       0.0       0.0     \n",
       " ⋮                                       ⋱  ⋮                           \n",
       " 0.0       0.482759  0.0       0.472906     0.0       0.0       0.0     \n",
       " 0.605911  0.0       0.0       0.507389     0.0       0.0       0.0     \n",
       " 0.0       0.472906  0.0       0.0          0.977012  0.0       0.891626\n",
       " 0.0       0.477833  0.0       0.507389     0.0       0.945813  0.0     \n",
       " 0.0       0.0       0.0       0.0       …  0.0       0.0       0.0     \n",
       " 0.0       0.0       0.522168  0.0          0.0       0.0       0.0     \n",
       " 0.0       0.0       0.0       0.689655     0.985222  0.960591  0.0     \n",
       " 0.0       0.0       0.625616  0.0          0.990148  0.0       0.0     \n",
       " 0.458128  0.458128  0.625616  0.0          1.0       0.0       0.916256\n",
       " 0.0       0.0       0.0       0.0       …  1.0       0.0       0.91133 \n",
       " 0.551724  0.0       0.0       0.0          0.97537   0.0       0.0     \n",
       " 0.689655  0.674877  0.0       0.0          0.0       0.0       0.0     "
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fHard = y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "fHard = ProjC(fHard, Omega);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Hard threshold (here $\\lambda=\\lambda_0$) is used)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "fHard = Xi(HardThresh(PsiS(fHard), tau*lambda_list[1]));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "__Exercise 5__\n",
    "\n",
    "Perform the iteration with a decaying value of $\\lambda$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "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 0x327694710>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.text.Text object at 0x32754f390>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "include(\"NtSolutions/inverse_5_inpainting_sparsity/exo5.jl\")\n",
    "\n",
    "# lambda_list = linspace(1, 0, niter)\n",
    "# fHard = y\n",
    "\n",
    "# for i in 1 : niter\n",
    "#     fHard = Xi(HardThresh(PsiS(ProjC(fHard, Omega)), lambda_list[i]))\n",
    "# end\n",
    "\n",
    "    \n",
    "# figure(figsize = (6, 6))\n",
    "# imageplot(clamP(fSpars), @sprintf(\"Inpainting hard thresh., SNR = %.1f dB\", snr(f0, fHard)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "## Insert your code here."
   ]
  }
 ],
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