{"nbformat_minor": 0, "worksheets": [{"cells": [{"source": ["Reconstruction from Partial Tomography Measurements\n", "===================================================\n", "\n*Important:* Please read the [installation page](http://gpeyre.github.io/numerical-tours/installation_matlab/) for details about how to install the toolboxes.\n", "$\\newcommand{\\dotp}[2]{\\langle #1, #2 \\rangle}$\n", "$\\newcommand{\\enscond}[2]{\\lbrace #1, #2 \\rbrace}$\n", "$\\newcommand{\\pd}[2]{ \\frac{ \\partial #1}{\\partial #2} }$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\umax}[1]{\\underset{#1}{\\max}\\;}$\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", "$\\newcommand{\\diag}[1]{{diag}\\left( #1 \\right)}$\n", "$\\newcommand{\\qandq}{\\quad\\text{and}\\quad}$\n", "$\\newcommand{\\qwhereq}{\\quad\\text{where}\\quad}$\n", "$\\newcommand{\\qifq}{ \\quad \\text{if} \\quad }$\n", "$\\newcommand{\\qarrq}{ \\quad \\Longrightarrow \\quad }$\n", "$\\newcommand{\\ZZ}{\\mathbb{Z}}$\n", "$\\newcommand{\\CC}{\\mathbb{C}}$\n", "$\\newcommand{\\RR}{\\mathbb{R}}$\n", "$\\newcommand{\\EE}{\\mathbb{E}}$\n", "$\\newcommand{\\Zz}{\\mathcal{Z}}$\n", "$\\newcommand{\\Ww}{\\mathcal{W}}$\n", "$\\newcommand{\\Vv}{\\mathcal{V}}$\n", "$\\newcommand{\\Nn}{\\mathcal{N}}$\n", "$\\newcommand{\\NN}{\\mathcal{N}}$\n", "$\\newcommand{\\Hh}{\\mathcal{H}}$\n", "$\\newcommand{\\Bb}{\\mathcal{B}}$\n", "$\\newcommand{\\Ee}{\\mathcal{E}}$\n", "$\\newcommand{\\Cc}{\\mathcal{C}}$\n", "$\\newcommand{\\Gg}{\\mathcal{G}}$\n", "$\\newcommand{\\Ss}{\\mathcal{S}}$\n", "$\\newcommand{\\Pp}{\\mathcal{P}}$\n", "$\\newcommand{\\Ff}{\\mathcal{F}}$\n", "$\\newcommand{\\Xx}{\\mathcal{X}}$\n", "$\\newcommand{\\Mm}{\\mathcal{M}}$\n", "$\\newcommand{\\Ii}{\\mathcal{I}}$\n", "$\\newcommand{\\Dd}{\\mathcal{D}}$\n", "$\\newcommand{\\Ll}{\\mathcal{L}}$\n", "$\\newcommand{\\Tt}{\\mathcal{T}}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\al}{\\alpha}$\n", "$\\newcommand{\\la}{\\lambda}$\n", "$\\newcommand{\\ga}{\\gamma}$\n", "$\\newcommand{\\Ga}{\\Gamma}$\n", "$\\newcommand{\\La}{\\Lambda}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\Si}{\\Sigma}$\n", "$\\newcommand{\\be}{\\beta}$\n", "$\\newcommand{\\de}{\\delta}$\n", "$\\newcommand{\\De}{\\Delta}$\n", "$\\newcommand{\\phi}{\\varphi}$\n", "$\\newcommand{\\th}{\\theta}$\n", "$\\newcommand{\\om}{\\omega}$\n", "$\\newcommand{\\Om}{\\Omega}$\n"], "metadata": {}, "cell_type": "markdown"}, {"source": ["This numerical tour explores the reconstruction from tomographic\n", "measurement with TV regularization."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 2, "cell_type": "code", "language": "python", "metadata": {}, "input": ["addpath('toolbox_signal')\n", "addpath('toolbox_general')\n", "addpath('solutions/inverse_8_tomography')"]}, {"source": ["Width $n$ of the image."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 3, "cell_type": "code", "language": "python", "metadata": {}, "input": ["n = 128;"]}, {"source": ["We first load an image."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 4, "cell_type": "code", "language": "python", "metadata": {}, "input": ["name = 'phantom';\n", "f0 = load_image(name, n);"]}, {"source": ["Rotation over the Spacial Domain\n", "--------------------------------\n", "Given an image $f$, its rotation is defined by rotating the pixels\n", "locations\n", "$$ R_\\th(f) = f(R_{-\\th}(x) $$\n", "where we have use the same notation $R_\\th$ for the 2-D linear operator defined by the matrix\n", "$$ R_\\th =\n", " \\begin{pmatrix}$\n", " \\cos(t) & -\\sin(t) \\\\\n", " \\sin(t) & \\cos(t)\n", " \\end{pmatrix}$\n", " $$\n", "\n", "\n", "Computing rotation $R_\\th(f)$ over a discrete grid requires\n", "interpolation."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 5, "cell_type": "code", "language": "python", "metadata": {}, "input": ["t = linspace(-1,1,n);\n", "[Y,X] = meshgrid(t,t);\n", "rotation = @(f,t)interp2(Y,X,f, sin(t)*X + cos(t)*Y, cos(t)*X - sin(t)*Y, 'cubic', 0);"]}, {"source": ["Rotation Over the Fourier Domain\n", "--------------------------------\n", "A difficulty with spine-based rotation is that the corresponding operator\n", "is not exactly orthogonal.\n", "\n", "\n", "In particular, one does not have $R_{-\\th} = R_{\\th}^{-1}$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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GuLp7UXxtXngVYROeae3VsWNHDU877TQFTiSoBMlr1qlTpypwx2RWYOliBQYA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\nRBViWVVGFaIdf/zxCtq0aRM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"output_type": "display_data"}], "prompt_number": 6, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "imageplot(abs(rotation(rotation(f0,.2),-.2)-f0));"]}, {"source": ["To circunvent this problem, one can define the rotation using a\n", "Fourier-domain interpolation (a.k.a. Shannon). This is easily performed\n", "by decomposing a rotation as a series of shears which can themselves be\n", "implemented as diagonal operator over the Fourier domain.\n", "\n", "\n", "X-aligned and Y-aligned shear matrices are defined as\n", "$$\n", " S_a^x =\n", " \\begin{pmatrix}$\n", " 1 & a \\\\\n", " 0 & 1\n", " \\end{pmatrix}$\n", " \\qandq\n", " S_a^y =\n", " \\begin{pmatrix}$\n", " 1 & 0 \\\\\n", " a & 1\n", " \\end{pmatrix}$\n", "$$\n", "\n", "\n", "One has the following decomposition of a rotation matrix as a product of\n", "shears matrices :\n", "$$ R_\\th = S_{-\\tan(t/2)}^x \\circ S_{\\sin(t)}^y \\circ S_{-\\tan(t/2)}^y. $$\n", "\n", "\n", "If we consider continuous functions defined over the plane $x \\in \\RR^2$ and\n", "define the Fourier transform along the X-direction as\n", "$$ \\hat f(\\om,x_2) = \\int f(x_1,x_2) e^{-i \\om x_1} d x_2 $$\n", "one can compute the shear transformed function\n", "$$ f_a(x) = f( S_{-a}(x) ) $$\n", "as a diagonal operator over the Fourier domain\n", "$$ \\hat f_a(\\om,x_2) = e^{i \\om x_2} \\hat f(\\om,x_2). $$\n", "\n", "\n", "By analogy, we define the shear transform of a discrete image as a\n", "diagonal operator over the Fourier domain.\n", "_Remark:_ to ensure that the transform is reald-valued,\n", "one should be careful about\n", "how to handle the highest frequency $n/2$,\n", "otherwise the transform would be complex-valued.\n", "Note also that this is an orthogonal transform (the eigenvalues have unit\n", "modulus)."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 7, "cell_type": "code", "language": "python", "metadata": {}, "input": ["t = [0:n/2-1 0 -n/2+1:-1]';\n", "[Y,X] = meshgrid(t,t);\n", "shearx = @(f,a)real( ifft( fft(f) .* exp(-a*2i*pi*X.*Y/n) ) );\n", "shearx = @(f,a)fftshift(shearx(fftshift(f),a));\n", "sheary = @(f,a)shearx(f',a)';"]}, {"source": ["__Exercise 1__\n", "\n", "Display the effect of shearing $S_a^x$ for several values of shear $a$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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eT2iiwUtQ0cVJHFjIpWPIPMThfD6fVSIUCiH9PRQKISGeFRH7VPNQUPVlGEY4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AiC0JFIABMEQRA6EglggiAIQkciAUwQBEHoSCSACYIgCB2JBDBBEAShI5EAJgiCIHQkEsAEQRCE\njkQCmCAIgtCRSAATBEEQOhIJYIIgCEJHIgFMEARB6EgkgAmCIAgdiQQwQRAEoSORACYIgiB0JBLA\nBEEQhI5EApggCILQkUgAEwRBEDoSCWCCIAhCRyIBTBAEQehIJIAJgiAIHYkEMEEQBKEjkQAmCIIg\ndCQSwARBEISORAKYIAiC0JFIABMEQRA6EglggiAIQkciAUwQBEHoSCSACYIgCB2JBDBBEAShI5EA\nJgiCIHQkEsAEQRCEjkQCmCAIgtCRSAATBEEQOhIJYIIgCEJHIgFMEARB6EgkgAmCIAgdiQQwQRAE\noSORACYIgiB0JBLABEEQhI5EApggCILQkUgAEwRBEDoSCWCCIAhCR/L/u0xYMc0Q8QUAAAAASUVO\nRK5CYII=\n", "output_type": "display_data"}], "prompt_number": 8, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo1()"]}, {"collapsed": false, "outputs": [], "prompt_number": 9, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["By analogy to the continuous setting, we define a discrete rotation by\n", "decomposing it using a series of shear."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 10, "cell_type": "code", "language": "python", "metadata": {}, "input": ["rotation = @(f,t)shearx( sheary( shearx(f,-tan(t/2)) ,sin(t)) ,-tan(t/2));"]}, {"source": ["__Exercise 2__\n", "\n", "Display the effect of rotations $R_\\th$ for several values of angles $\\th$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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oNdDUTFrbGaw9VFW12+1YBuSRUJoQEW7Cpz71qU9/+tO/+93vLrnkEvHe4naJ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mQyGRzPYgNvDXtrc3Pz1q1buQ0YEf31r3/dv3//7373u7/+9a9EtHTp0q6urqqqqq1bt86dOxe2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lBm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\nRK5CYII=\n", "output_type": "display_data"}], "prompt_number": 11, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo2()"]}, {"collapsed": false, "outputs": [], "prompt_number": 12, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["To avoid issues when using large angles, we replace a rotation of angle\n", "$\\th$ by 4 rotations of angle $\\th/4$. Note that this makes\n", "computation slower."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 13, "cell_type": "code", "language": "python", "metadata": {}, "input": ["rotation = @(f,t)rotation(rotation(f,t/2),t/2);\n", "rotation = @(f,t)rotation(rotation(f,t/2),t/2);"]}, {"source": ["__Exercise 3__\n", "\n", "Display the effect of rotations $R_\\th$ for several values of angles $\\th$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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zBLZR4HK5WJoJgFSzp5ZR+E2whmrPMgk9jnDbbbd96UtfEpF8Pj8xMfFv/s2/\nueeee2ZnZ2n4lXGLdLfbjUQi5XKZSEiboPP5/I4dOxYWFnDccLlclUolGAw6nc5oNEpAJiJkFBnq\nqCzo9XprtdpoNGq1WrRncdrdbpeEG2UwFn2/3z8cDsPhcDabhRR5cjweT7VaDQaDtVpN/TKgomAw\n6HA4arWa3+9XdTu6zeXl5YMHD6JjrFQq99xzz/ve9z5Y6vTJKXbTXhkHu/rc2huWlbo0/rPPdNYD\nkvU9fXLNpoQhsDPCeV1n1zl7gfMXh12Ye2vwY0A/GoKVNa21ymc6EoxUGPtcdtllzzzzzJ//+Z+/\n+93vFpF6vR4KhX7iJ37CsixqSBwnFAo1m81UKnXs2LFLL730+PHjIsJQrnQ6PRgMcLJQpyVUHvgT\n0jLM6XU6HZyZcMEQETT02GFks1nLsniGQ6EQNMCITmU1Wo/dbrfH46F7TMZjzCzLWhN9+nw+erTb\n7XY8HmeiSiaTKRQKsVis2WxGIhGEJ/fff7+MvUUmJydzuZwGT7CdDqXUW63Ck1dqZF7zAY1GIyI5\nbk65XA4Gg9rqsLlhRBzrBZvGdOMMsdWudyMCtR56P5JXanfkdrt7vZ7dbEJjCNbiZ555RkRuvvnm\nRqPRaDRCodChQ4dWVlacTufi4iJ+hjrgsVwuT01NnThxgkZmdICFQmE4HIZCoUKhQG+yy+WanJxM\npVKLi4toN5rNZrPZ7HQ6iEcqlQrzIQl0otFosVis1WrT09OhUCidTqfTaeatwKPoNXK5HEfDtqpQ\nKMzNzXU6nU6nE4lE0FD4/X5UG7SgqWTR5/PlcrlUKpVKpQqFAv3U/X6/0Wg8//zzzz///B/+4R+K\nyNe//nURoRGNuycig8EAkYiSmfYgc5/t3xVEhGgY6Qefy5r5ztVqldh3TUJyE8MQmIGBgYHBhoQh\nsIuM85fjOrdS+PMkrBeT5VvHcLvdhDjaaUTooCI3nauiwy3D4XC73c5kMiLyL/7Fv/D5fMFgMBgM\nfvvb337LW96yY8cOhBhqUlUulzOZjB6cwMLj8WSz2ampqVqt5vF4cO+tVqvI+VqtFiUxusHY3+v1\nViqVdDrd7XbdYxQKhUQiQfFpMBhgBBUMBmk+CwQCJ06c2L179+7du2u1GnIPt9udSCSOHz/Oaa+u\nrmqtLpVKnTx58uTJkxMTE8ViMRKJEPcwb5Mok7yfXkggELj77rtrtdrrX//6q666yul0JhKJXq+n\n3Qh6q1HnqzqDMIv0poz/j3C3KZjxuViW1W63GfIZiUQ4gsDqiJAAACAASURBVL2lbNPDENi6wNbM\np23Nq95AUGU2Cy5VLu33gsyo9LCU0zsVCoWWl5f37t375JNPojUQkaNHj8bj8dXV1WQy2Ww2NSsI\n8bhcrlarFY/HX3zxxRdffDEej9OzTB+00+kk++f3+8PhsMfjQeweDodp+aLeg/IeKiWpiL6x2Ww6\nnU6/3w9zRCIRmszwpCeF6PP5BoMBM8OGw2E8HocM0PHDyvjZT01N5XK5ycnJpaWlVCpVLBYDgQD8\nCpFwN3DMikQiuVzuv/yX/yIi3/rWt4bDYbFYjEajNMlxe3XYit/v9/v9/X6fEWgiQpmNjT6fT+16\n1RwSokKv0Wg0dFzABXtCLjq20KWuN5y/Xg3+m52Pw57zY4Kt84Vxg0JVdmJjNYpeLNmI4NkOndx4\n440i8txzz7Hxr//6rweDwfT09NLSksPhQH2OAL3T6aRSqXa7Xa/X9+3bt2/fPtqBB4MB/WEwEDWn\ner3OUBKKUijsGa1CwQyKtSwLr2GE8rSaURvrdDp+vz8ejzPihNOLRCKNRmN5eTkSifT7/cFg0G63\n2+12rVaLxWKEg91uF2ok7gmHw/V6HSXkzMwMJo3RaJRWZa0IWpb1ve9978EHH4zH47//+79/3XXX\nVSqVSqWiZS2Hw9HpdKBwzEGQdeg3A+1WlnFVTLUkfCL8ibKc0+m02/tuehgCMzAw+GcAObHm8q+I\nIMzTOVXaMYYy8DWveY2IXHXVVRjGr66uYpJ74MCBdruN3iEUCnU6nYmJiSeffHL//v2lUonFPZlM\nEqm4XC4Egep/j2Z9OBzW6/VEIkEExqQxHJtoh0IrzxhowjW/3+8cIxAIMEPL6XQyS2xpaSmTyQSD\nQZJ4pVIJvwy0+NPT09lsFi951CK1Wg1tPcyt3ON2u3HaLZVKHBm9/s033/z2t7/93//7f/+d73yH\npGWv1yMQJOnHYVWXMRqN6HdGPkMKl8ALalRPEH7FGIWdR6OR5h43PYyM/oxwPqTeG0I9vwbnwyMR\nPf15EtObx/tsQKeU2BTz/GBvTpJxajGTyeAlv3379oWFhUsvvRQh4tNPPy0iP/3TP71//36Xy1Uu\nlwk7WGSXl5c9Hs/c3Nyjjz567bXXvvDCCyJCoYgsn9/v73Q6O3bsEJFyuRyJRGq1Wjwex+qQs2Ja\nJlGLztjEiYOWZx4DroXIZjAYVKvVXC6HicZoNCJw7Ha7R44c0TswNzc3NTWljh4ql1djDtwU4Wwa\nnAeDAWElF7iyshKJRBKJxNNPP/0bv/Eb/+7f/btvfvObInLTTTdBQmuaju2W/1gdylhbf/pAy5Ft\njugabJEn332xT2CL4mwer8cee0x/ftWrXnUuTufiQ8vXBusHdisjWAr2UtNeVlgtAvEqVvmPfOQj\n/MoUlYmJCTqxMpkMw1bILr7+9a9/6qmnstns3NzcyZMnWfT7/T7NYbVaDe2G+t4Oh8NAIMD0YeIq\nEWF8MzUwbBU5PVQV6jSI9IOwyefzVavVyclJGILamMfj4esUDdpcSzgcphQHSXMEIh6iIqIuLhaa\nqdfr4XAYr6wDBw4cOXJkNBolEomvf/3rt912G8nVN73pTQ888IB6GKrFFL/Cpo1Gw/6fQtnLPjvU\nvpKoKeUWGccsJoVoYGBgYLBBYQjsIuNHzR/awy9+Bef0pC4ojBZx3QJHIs0TikgymRyNRqqjsw8F\nVlE4Geyf+Imf4Nfl5eXl5eVCoeD1eomfyuVyq9W64oorrrjiiscff3xmZgafJAwGaW1OJBL5fN7p\ndIZCIa1ddbtdnNdpRkaOWK/XU6mU0+msVCo49qJvFJF2u41mkgRgoVAoFAoYPHa7XeQhSBOTyWS5\nXH788cfJQBJ+cYTnn3/+kUceSSQShFYEfyIyHA6DwSD2UQiyUCGiH3E4HBMTExMTEwsLC7FYzOfz\nWZZ14sSJT3ziExz505/+tIhwM2U8nVlvJoZYastL1CVj7yj7pGzAO3Itan6/FWBSiBsJP4So+NOm\nySgarAf0ej2qOwgERARRO07tuNnqtK1qtcpaPD8/f9VVV0Fjjz/++MGDB0Xk8ssvZ6TWsWPH9u3b\nt7S0RJprdna2UqngzISWXcbzwPAkrFar27dv5x2j0SgEhtSQeSsiks/nIQkmh+E7hb0hWT6GaZFv\n9Hg83W4XyuTlIvLiiy/u3Lnz2WeflbGbPn9Sif/y8rLf7+duNJtN9azCGJ6MH36MFKgQMYpIPB5v\nt9uo7aempv7u7/7uySefFJGrr776jjvu+B//439gIElGVER4OXIM/SAoPUJdugN/YiM8p8YoJH63\nArYKUa8rnL/66oYOxbbODIiNAr/fT8NsKBRCWSBjN0IZT/xCE0F5ScOCPXv2RCIRHG8XFhYWFhZC\noRA6i2g0msvl3G43bVL1eh2lXyKRUB0dKnm6gylT0VbcarV0MhbjNEEkEhER9JDD4ZAjY2OvTu0a\nxmEZ7PF4arXa5ORkNpvNZrOXXXbZU089peIUEUEPKeP/raj/iUfxf8IdmPAI4T63iHf0eDwEgo1G\no9frxePxwWBAwHfXXXfdddddIvKJT3wilUqhlqS4qNIMTLZUi6/O+jJueVaHfs5WR4zykh/uoLiZ\nYAjsouFHGlx55nnCjchhJou4PqHrIL1f/FssFlk9SceVSiW/34/+UL+CML4ykUh8+MMfvuyyyy67\n7DLCL5q9pqamSqUS63uxWAyHw7TuYrGB17uIuN3uaDS6sLCgqcJwOKwaPJx8UcyjLiEE6XQ6HEql\ngHjAD4dDyBiDj0AggKUh1IjUnsCFSAhRu4w95iuVyvLyMkTl8Xjwv2DACvNQOOBoNBoMBh6PB4dG\nGrz8fj+++H6/P5lMHjx48ODBg/fee28ikfiN3/gNGScMYUflMEQi3H87V0FjZAudTqd9fCUbUfNf\nkAfk4sMQmIGBwctDJXBEFbg0iW2hZLHGP0lEYIhkMvkLv/ALIpLNZg8cOHDq1KlTp05NTExks1mv\n1xsMBhcXF7dt23bs2LFjx44dOHCA3gy32x2LxehujsfjUFqn00kmk263m56qer1Ooy4GuAxupj2L\n4ZacCTsjoaSrrFKpRKNRwjVGUOL4Xq/XiXtKpVK/3ye845K5FpgPVs7n84RlKAZ5RzrJCBYDgQBD\nk+mV5jSot9FPXalU2u02jlaf/exnReTXf/3XX/va19rHqajXBn7HbNRWZXlp/gbRo4wrlKMxts5Q\nZkNgFxoXIEt2IWUdj9lwTg5osojrB6PRiHScvNSMA7Cl1+tBNtpBXCgUmCEyPT19zTXXEFhgk0Hd\nKJ1Onzx58sCBAwcOHHj66aczmQy5vkqlonbv9Xo9Go3ioEGVSEQsyyK86HQ6pBmJzGj5gsba7Tan\nwRnCLsFgUI0T2+32xMREtVp1u90Oh2PHjh07duywLAu/D7hNa2N2FXuv11Preq/XWyqV6B8QEfqs\nqQWiHGm32+p5yIiWUqkUjUZh1l6vt7i4CIfdfvvtMpaEEC/ieqV1RxEho4j5PWel2ULA9WoMx25b\nAYbALg4uQNLsfHPY6aR1Nu9osojrEJZl0eClHn1iM+Jjcff5fP1+PxQKDQaDXbt27dq1S8YRQ7FY\n/M53vjM7Ozs7O5vL5XD8G41GTCKm+DQ9PT0YDAqFQiQSYQdSgtgYtlqtWCzmcDjI3bXbbXJ0xEC9\nXg/m4FQZ30ysQ8dYv9/n+xBNbIREzDoREa/X2263tdY1MzNDsGVZlo4fg7C1+LSysrKyslIul51O\nJwW8WCyGawZJRfKQiF+o5zEzjEJdu90ul8ukSV0u1913353L5d773vf+zM/8DAPJkIe0Wi2fz6eh\nldvt5lo0damRloho1lG5VieibQUYAjMwMDAw2JAwBLYJsbS0RF3h3AZhdh+pjSgVMfhRoaNJWq0W\n6TW1mtUCGMMe6/W6eslblnXzzTfjPfHtb3+bLN/U1BQ5ukQisbq6qjaGlmVls9l9+/adOnWKiZSV\nSoWCWSgUCofDhUKBeIvUnHrhe71e4ir1B0FM4XQ66ffChgOXKcuyCGL6/T5VKzT3gUCAGM7hcJw6\ndQqFCFfNe9nvhkoqcrkcU5sZmIkEQ1UY3Ci9SwRVXq+X04jFYpxeIBAoFApkEX/3d39X/e87nQ55\nTt6LQ1EYQ06CYZXq7OkVW2MotXXy8IbADH40bPS+aYMzh67FusWe19KNFGC0+fcXf/EX6av9gz/4\nA8uyrrzyyiuvvPLRRx/ds2dPPp/vdrvhcLharbLo00Scz+dDoRDFJ3T2ExMT5Pcikcj8/DxTRYbD\nIe1io9GIpmY150VemM/ng8Egp8epYlsFi7DoY0jPPDCEiJCfjFOFXLW9kMZ16SVnMhnki5ANMhZU\n+xQCyR9yGggIaWujDYALJ0l4//33P/HEE9deey2FRtBsNmkp043IQWlQ044xAFetmaJi+sAM1hHO\nhjDOLdn8s0cz3LaZoMoCsS3fMlYhYkTr9/tZT7U/7M/+7M8effRRETlw4MDhw4dRIe7fv39xcTGV\nSiGXwFpeZ3/QvIV6XkSglsFggKDD7XYTmcFVsI7b7Q6FQkwgczqdo9GoXC5Ho1HM4On3wo+DU0V8\nTwswAye73S4vpO6lF8ie0I9lWdogrJKKlZUVCnU0gdXrdaQuhJiMR5GxpIK+MQ0ElVpKpVIikSiX\ny1/5yleeeeaZEydOsB39CKyp9pKQMWU8Lsf+McGR9o2mBmZwXsDXpQsjWDi3zvHnw4d+DbQxbusk\nQNY5GFCiM0p0oCV/xa6i1Wph6F4ul9n+pje96dWvfrWI7N+//6d+6qcInkqlks/n63Q6TLzUFBlB\nmN/vX11dzWQyOv6q1WqFw+Hl5WWkFhAVGg1GX66srNBZRWRGRpHJJmzESh8nDpJsRGB42OscE1Qq\nqpUXEViN0JM5k1AdHdYej2d1dbXdbiPf93q9NJ8hjOSNiP/gS6fTaVkW7vWEemQU6a32+/133333\nZZdd9nu/93u8OwyHclJENGsKv3Y6HR0CIDZnfe0u0GE3WwSGwDY/zlVUZKKrrQZWRl0xiQDIARLc\nVCqVcDi8srJiWZZKtx944IH//b//t4jcd999Tz75JAwRDodVNIhwTuMhEWHRZ4jXcDj0+Xz0VEWj\nUQZ9sY4zcysYDOZyuR07djSbTeIklPTNZpO0G2xHuYsBK5yYxnw0I0NspArJzokIkj8RgQx4UwI4\nGQdVInL48GFmrBBXaT1PA1M6B3gVbEerNXTY7XZ9Pt+JEyeuuOKKUql0ww03vO9975ubm5ubm1te\nXoa6kEqyM+JJEWGGC+0EGFaRGuUC1+R7twIMgW0A/NgOh+cqbFpaWjLstTWhcm1WVWpIMATKAmaL\ndLtdxAUulyuVSr3uda/rdDq/8iu/cs0110BarOY0EbMiszRjWdtqtTDGJTo5dOhQoVB49tlnX3jh\nhaeffvr73//+8ePHjx8/ns1mGYZCGxYtaG63OxgMYuNEspGEHs1SRDxoHDgHAqbRaER8hjwkEAhg\nCAIBQEK9Xo+4EyKX8XhJ/sokMLqkaV+rVCrBYBClu4hoPzVuHejjg8Eg7saTk5NOp3NxcXFubm73\n7t3xePy222677bbbZKwWoXmAT4HZoSKCZIb7RrAFPXN6a2qTWwFb62q3IJaWlqamph577LGLzoIG\nGw7aLdvtdhuNBlMW1SGCvl0ISURw9RWR1dXV55577vrrr//ud7977NgxPHlx6KhWqxxEu8owW0J/\nWCwW9WE7duyY/TSy2Sw/F4vFG2+8EXmhjPOWsCBdYhCJiBAPhUIh3DdCoVCz2ZTxKo8NfL1eh56b\nzSbt0sSCvV6Pkl65XEb7p4OnRYSOaTi4XC5j8ygi8CjJRgQmnPNgMMCrvlwuDwaDyclJETl8+PDM\nzAxmVIuLiyLyW7/1WyLy+c9/fmVlBVmKDufElDIcDhNZik0SqZ6Qa4aOnp8nYt3BRGAGBgYGBhsS\nhsA2P84mhDof/WQGGwWDwUBLRDpomOCJ+El15yKCMB0D3KNHj4rIt7/9bYaYAJwMy+UyKUeOSZxE\nKk8fVGzvkT+ITdRD5vDv//7vs9nssWPHFhcXyRbitOR0OsPh8OrqKhtHoxE+UhwQ6SNCEmKpUqnE\ndBhsNXbv3s2bMp25XC4zLEZPQEtNxEPFYtHr9aJm1GyhjqumzIbkHXk9SvpCoWBPe5IGfPbZZ7/4\nxS9ycMqHBIupVMo+ooFr0SiQoFBjWW0qQM1xPp+LdQRDYFsCL1vEmn4pTn+JSR4aQDNaldGKF5oF\n5O/8K2PFgcPh+Mmf/EkRoe0JhR5H8Hq94XC43W5HIhH0jcgC6c8VEYpJjPWip1jGUxydTicCxWKx\nePz48cXFxcOHD/OU0i+MNX46naZ1mvMJBAKUu1QxT5swJTflUdQoMu4WQJqvXu9rdOpkSo8ePVqv\n1+2DuyiPUTDrdDpU0ZhPFolEEBDivIXTPPew3W7Pzc196lOf4iCkE3HkwrPK6XQiV0EGieSSneE2\nTlJlliaFaHAecbFM/5bG4NfTGUu3rKGuCxx+GVPE9QOWY22eZR3XgICFu1qtYpUrIkRao9Hok5/8\npIjcdttt6XQahuh2u/F4PJ/PEzcUi0VM2YlC6vV6Pp8XkVKpVCqV0NlDGHb1hIoacPi1LGt+fn5+\nfv7xxx8PhUIOhyMUCpXLZe0URgqI2D0ej8/MzMzMzMRisenp6cXFRfQgHJDZKCKizWHI/Ihm6EVT\ngZ/T6eSFFLfw3mVP2Kvb7cZiMbwN/X4/nWHEbVB1u90Oh8PamgYjfv7zn//85z/PNc7Pz0Oxds9D\nGVsncz5Qmt1uGCC/PF/PxDrDVrnO9YCL3t6EiQb8pFVxRTabXT9R10W/VwZiUwqwdrO4M6ZEp0p6\nPB70HSKCOnFiYuKOO+4QkTvvvHNhYQEKjMfjL7zwwuWXX46PFKp3EmXo5lm4kcsTP0EG+OHaz0rV\nHyq7b7Vajz766AsvvEAsyDvW63WoxefzpVIpRk3S14XgHpmi2j4x0xmxIuSHWAPO4A7ohBTonHZs\n+uRcLhem+PTGdTodMpblchlpomVZyCw1qCLf2Gw2aYD7oz/6oz/6oz96y1ve8vM///PKTOpoxf8I\nTljDOAZDKw1zZDj1gjwgFx+GwLYusi/FOTnmj611NFiH0G4te9SFFROzIrGZoBNLRKampvBz+uhH\nPyoiX/3qV2+66abFxcXFxUWPx5NKpY4dO5ZKpZaWlhhl4nA4aDdWAlMDJ7SLcBWdWIRxTNuCPldX\nV/nKhWFHsVjMZrMLCwu0qbHWcxAlGDqXGRPDX9XZvV6v4+KBoJGddcYKjcnaZ+3z+Xq9XqVSIdjS\nNGkkEsnn8+l02l4RVBE/rpK8Hf3XIhIOh1988cW9e/decskll1xyiYh85CMfEZF6vR4KhfQd4TM6\nmmn/4lbAtWRK1ZufbwZbAYbAtihOj7ReNvYy8o2tDLWT4FfN5sEHdPKKCB3HIkKHk9fr/fCHP8z2\nAwcO6KwsbA/b7XY8HtfQp9VqhUKhQqHAah4KhQjmSqUSuTgRwTiYmInVXFmEE3vhhRfq9Xqz2Xzu\nueeWlpaY2sX5UzTq9XrlMYrFYqlUoiMNOwyui6ZpHRGp4K9kC1W9QsUuFovReQZXMSwGeT0sSCKU\nkhukqE3Z1Pmq1Sr3p1qtHj169OjRo91u9zWveQ1DwvhaICIkZrkznJ4OG4OGuSE6hHPrJDAMgRkY\nGBgYbEgYAtsYeNWrXnWusnMaVGnItX5KXwbrCgwFJvcl49iLkZJMlURHJyL0DsdiMfJpX/3qV9n/\nG9/4BiGOesmTb2w2mxps9Xq9RCKRTCZFRAWEKgRXJ0OdG0KWjxCHHzweT7PZrFarzWYzl8sdPHjw\n4MGDhw4dyufz5XL5hRdeOHz4sNPp5DlH+07eEnsnnA9dLtfevXtlXPnT2hghjurpdUKmiCwuLtJX\nQFBFNpW5LVwvwhOn04k9B3OWuS5O2+v1ojCklOVyuX7u535Oxv9Jp6am2Jk3rdfr5G/FZrpBpVDN\nEsVWudwKMAS2pfFDqMuMTTGQcRlMi0CDwUAFAuT3WJGhH5Jm6XT6L/7iL/74j//Ysqz3vve9Oq/E\n4/GQSYvFYn6/H49Ej8fT7/fb7XYmk1E/e9Z6hAywCMyhUnhd7tkfBSDb6SobDAbLy8v/9E//9OST\nT6ZSqVardezYMe0Dq1arZPmgYST7WDcFg0HYAikjb8rAFNVkqrw+n88Xi0Wkj3jhI8fXO6OKeb/f\nj9RF7SUtyyqVSlgydjqdcDhMuSubzeJNJSLQLXbGIoLxP/dfDRX1bvAZrcl/bnoYKykDA4NXBKs5\negEajFjKxdbFPBgMCoVCJBJBTN9oNLZv3/7+97+/3W5/4xvf4DiUebCSwvyX0A3awGA3nU4TyeH4\nh7hcXirch8xwWtKTxJxQxi5KKiJHLnjy5MlEIkHbmYxF8Fi8E7rpC3u9HvuICAdEBsn7qqkxwnqH\nwzE5OYkoUYMhr9fLnEz8FWUsfKcMVi6XaYDjnJPJJOFmOBw+ceLElVdeKSLz8/PRaPRv//Zv4/F4\no9Eg3goGg41Go9VqYajIx8GN4swHgwH9eXrO5+NhWIcwEZjBOYORIG4y6Nd53CtY01ViTpaPjfiy\nI//z+XwLCwvf/OY3fT7fz/7szxKWQUJEDH6/PxQKqVsuicFWqzU1NZVOpxnOAnudLkZQ60ICEbtZ\nvozdKKAc9mw0GidPnvz+978fjUZJuxHHEEKR4sPwnmFj6sNrfztCsV6vh1iDgGk0Gi0tLVWrVecY\nql0ks8qUS84ECWU4HGYgJ6pLPA+hn5mZmSNHjhw5ciQcDi8sLBw+fFjnmXEVXC+yQ+0Do6sBSqZD\ngNSl6QMzWI8452UwA4MfAp17AknAWIRHeKITeeDLruMlWfTf+c53NpvNX/u1X7v++uuvv/76+fl5\nAg5E8NlslhqYWksMBoNWq6Uyet6Lf3U5hlBJu2l8pkAtaS+YiQh7tlqtpaUlaIa2Lfx/ZVzWQgQ/\nGo0uv/xysQ2EZB8CRBnnSGXswW9ZVjKZ1J9pZIY/dHgYl8Cv1WqVNGOlUnG5XGgLedXq6uq+ffv2\n7dv35JNP/uZv/iYp2WKxqJNrmPgs46iL5KR6cxD8caUq0N8KMARm8DIwDGcgNuYgUqGFWURYKKkh\nyThe0UWfX9/0pjcFAoH777//qaeeeuqpp/bv37+0tBQKhSKRSKFQ2Lt378rKysrKivrZE/poFUeN\nJ3QWl4y7oFQKQfpOe36hLnvQRrEK7nnxxRepJ6Flx1xKGZp5ZoxZicfjKCzgBjKBmE7xdlwgXFss\nFtPpNDUwzg1q1IoU9Eac5PP5Go0GUpdms+nxeHADcTqdsVgMV5Hrr7/+gQceaLfbf/VXf6W3mpoZ\nk1nE5spIAEftUDeeTu2bGIbADAwMXh4aRsiYUWApFThoXCLjXKKIUAmjtnTTTTdlMplMJvPcc8/N\nzMzUarV6vR6NRufn5xOJRCKRQJ5Hy7DX652cnJycnERVISKBQMCuqVNiWEOZEJj2q2nvGsGQNpM9\n9NBDDz300PHjx4nA6NkiLOt2u7VajV6uUqlEwpDAi84qsY33xNWQ6JMBzVwLE08ajQZ/5QjRaJR6\nGMexD7rkAiE5imdIXTwez+zs7MmTJ0WEGzIcDum04yZrhhNvFNyz9P6r4dZWgCEwAwMDA4MNCaNC\n3NKg0eTsm8CMfGOzwu6FIWN7X77s44uh0naVxkWj0X6/f999991+++1f+MIXPvOZz4jIBz/4wXw+\nH4lEmDkSjUY5MjUqj8cTCoVKpVIikZBxNuy5557TEZRq+6RadkR3GoqpBk9s8khNMKIyJyNaKpUY\nnTwYDHbu3KkJt06nUyqVLMuKxWJa69LMof3IgGYvj8ejgkniSI0aSWai0fB4PKr1UFdDEanVaolE\nAnE8SdRCoRAKhZ566inc3fTIKysrYtOwqPOWjEeJ6h3Q2uRWgInANhjOoY5D2ySxsDsnhzXYTKCc\nQ2HJnkbTHRjhwc9MPQ6FQpVKhVfdcsstIvLggw8++OCDJ06cSCQStVrN4/GUSiWSgbitU9dhenKh\nUCgUCqlUKhAIIGTw+/3Y17K+63gtSJTeKTR4agpF8YkTo/NaB46QWjx58qTD4QiHw71ejyPQah2J\nRCzL2rNnD+wl4yYBu2GujKnR5XKFQiHIg2sJBAL0MqOzgNfdbrf2k9F8pkZc9Jy53W4UiZx/IpEo\nFouNRuOuu+563etexw3hDsi4KIhqRvkb4Qa+/uR7tV1608MQ2BbF6YylW35UBYcJvzYrWP1ZfFWF\nqENAtIUWKZ2MfTRisVi9Xh+NRgsLCyKSSqVSqVQmk2HBbbVa09PTRCr2YV3EVYjuisWix+OBwFqt\nFiPEYAUZxzR0g3GeWgPTiVz2sxVb0Qg0m81HHnmkWCw6nU7ekUiLJi2n07lv3z725OXK06rsQDaJ\ns6LP50OWWalUfD4fKk2dhEIjM0W1SCRSq9XY2eVy1ev1YDCI62M8HufgCwsLu3fv5j8jBiKcJBp9\nndiCjJ4pLTL2O6bqdvqAlU0MQ2AbD4YwDC4MNBCBw9aM+lV/dP6ksUW5XMYj6pd/+Zdzudx73vOe\n97znPVddddX8/HwoFHK5XEtLS8w0wUUJCsTeiUUfW6ZUKsU6XqvVeEcNLNQqnkUfZQeTxqAuRA0c\nmYVexlOM9fyhW6XGZrMJjTGjRFut8XniJcoQBHzM5+z3+3RJkyDlTXXoDKeEYr5SqaTTabuDPnKS\nYDC4sLDAO6Kz37dvX6fTCQQCZEFRefT7/V6vFw6HVTwpItC/jCWanK2ZyGxw7rGlvhmdJcy9Wldg\nGgjf8TU5xrqJlp3GXp0kqTbqH/vYx/SH/fv3l8vlXq83MzNDXBUOh2u1WjAYhDwY4UixCqP6VCrF\nk6DhGtUddkNZTi6RCEnF9wgIoTRV0tu7stxu9/HjEUmXugAAIABJREFUx3WUl8/ng2na7XalUpmZ\nmdm1axdjkYFerI7gGg6HyWQSxlKTKopz9Xo9lUoVi0WCPI/HUygUYrEYxBaNRqPRaLVaJe8nIpVK\nZW5ujmQmUsYPfvCDXq/3zW9+M++eTCY7nU4qlRKRWq2mEkcRoeuLBKOymkkhGmxynOE4lX8WJhzc\nCoAA1vjs8SuxSK1WI3um8odIJCIiX/ziFw8fPnz48OGFhYWHH36YiKpQKMi4fBWJRIrFIjYZjOOC\nKohvgsHg3NycjAeFEGzJ2FpXVRuEHdpJpnYYatLBniz6ECEL/RNPPEFbcalUWlxcpNva5/MtLy/D\nr6rIsBOn/hoIBLxer7ovcmL1ej2dTs/Pz8/Nzc3NzZXLZXYjy0cUxZhNqlZU406dOqV1vuFw+OCD\nDy4vL6sRF/S8urrKZ0G9jQwqd5tbx5HtIeOmhyEwAwMDA4MNCUNgGxLnJO5ZeinO/oAGmxV2915M\nJdDU8WWfjJwON0FVWK1WvV7vrl279u/fv3///tFodODAgUKhgOwQX3bsoyKRSKfTqdVq/IBrMEeg\nNjY3N0c8RNIM5T2nRAKw3+97PB6mR+JzSFWMk+d8KMuJCA3FRCrNZvOJJ5544okn6vW6ZVmZTGZ1\nddXhcLjdbhJ909PTnANKfXWjJ+4JBoNqk0E+E7kHecJSqVQqlYLBIKb7vKPqL5jngvdHs9lE5KLC\nQofDkclk7rzzTpKWpVJJxlOqSd4SkqrziApYuBtGRm9wvnDo0KGLfQrnDOcjf7iZ7s+mAW1GWkxS\nkE8js2dZFrUxhn7RFpbNZo8dO3bs2LEbbrjhxhtvXF5ezmQypVKJ0VYulysQCPBzLBbDrJ2kYjAY\nZJKWz+ebm5vbvn379u3bRQQtA4bCIqKuFiqaF5FgMEibFzUznHDr9brmJ1n04V38G3O5XD6fp8IH\nfS4uLi4uLqbTaTST2rgGvF7v7t27VbdC4pRL1sIeIhGIU8eYQXhwHraQHKFer0NsxWIxEomEQqF+\nv/+FL3wBRt+5c6eI0H6Al4dW4+AqNaU0NTCDjYGzJw9jeGhw5qCkxCJuN0Oi9BIKhbQPCS0GCu92\nu33rrbfeeuutIvLxj398ampqaWkpFotFo1EKNtgsYW84Go/KjEajtVqN5X4wGFQqFTrMpqam9LBQ\nqXKSvdalk1MgXVq17EEJBKAmiiIyPz+/sLCAJfHy8nI0GqUiBRNfcsklzHnhNIbDYTAYnJiY0KFi\nkBCFNxnHiMRwvFBEUHAw8LPT6UCfKAyj0ah6JFqW5XA4Hn744eFw+LGPfQxOOn78uIhEo1G179Jq\nnDKWttZtqZFghsAMfkwY+camh0YYMu7etXcxa16RIcvBYFBHarHIkjR7+OGHH3744fvvv9/n8/3q\nr/4q81Oy2SzrNYELk5Gj0SjetYQm6Di8Xi8eE91ud2pqanJy0u72qzEHYRMsxTljWog6nxjRbsWr\nY5d1tLGIHDlyhG6wer3OzqVSaXZ21u/3X3XVVcgL6/V6PB6fnp6m34vJKfAurdyMetG3wx24UqlE\nIhFSpmxnDGY4HCZGJNPIUGm32/2qV73Ksqz77ruPoHZyclJE0HauGbisulAlY0T25/XBWD8wBLaB\ncREpxLDXVgD1LSIVnRIiY9rQMfb9ft/r9cJblmWxrFOM0Q7i97///SJy2223hcPhYDCIaQXJQIyd\nXC7X8vKyzlihlNXtdvG50H6vSy+9dGJiQk6TBVIeIxCBTnDQp2Ma1R9nQijJudForKFMvV7HEYOh\nZX6/n0Zj3uuKK6647rrrrrvuum3btqVSKUpQsAV3iayg+upCjS6Xi6kozWaz3+/HYjHeEWt5mNLv\n91NjsywrkUjU6/Uf/OAH3//+9//1v/7Xes4yJmkYS6txRMCWZfFNglM188AMzgu2zjejs4G5S+sE\nTEqkM5fOJ6KfNbUWYh104VCO7kP9ye/3Z7PZT37yk0888cTRo0eRURDNOJ3OUCjUbrc7nc7ExATp\nNTQa2Dsx6ATNQiAQyGazU1NT0WiULmA9ExmnE0ejESwo4weJo9GtTLCi56zZNrUoXFpawmtDo0na\nk6EidBn8EI/H6fdaXl5mDidjqVFnaJzU6XSYB21ZltfrLRQK3BAtH5J4hMb8fv+RI0f27dvX7/fn\n5ua0g5s8JMf0+Xw6WlOHQcNwSsZrorRNDENgGxuvetWrLnAwdOHf0eBiQQMUNfNVm1p7p9HLqhDV\nPJdUoYg899xzV1999RVXXOH1etvtNot+o9EgWorFYktLS6rsIPhrNBp0NKtmgRJRIpHYsWPHaAwy\nllqWgxoJa5gBrb66UBEBE5JFvQTim9nZWXqTiWbQZaCVaDabUGM4HMY+sd/vN5vNWCxGMxlJVLaj\n2gAwOrM0k8kkJToqefCox+OB2wqFwmte85pvfetbb3vb25gQxukx05LDIrbUxjgCSnZTOt86ZTBD\nYAYGBgYGGxKGwC4CzrlS/McLiV7pVT/kaOc19jp06JDR0K8rIA2g2YgAhS/7+k2f0IeEGBESMnpM\nIgjF8vl8Pp93uVyXXXaZiPyn//SfXnzxxWg0msvlcrlcOBxm6nEulyP6QdDRbDYxyXW73RSxer0e\ng5tLpdL09PS2bdumpqZwCiYKIcmpigz1P5SXRiRqpcGf1ji4nzp1iktDGU/uMR6P5/P5bdu2LS8v\nLy8vo4FkgoxlWdjskmOk+KdBHufT7/fRVcbj8dXVVVT+KOwx0KrVatpM9uKLL+7duxezkl/5lV+h\nr4BcIm+KvQghKY6LetWqydw62FpXa3A2MJnDLYg12UIdQ8yiTy9zq9UKhUII3KEc5ngxmpmdB4PB\nZz/72Uql8ta3vvX6669HPc884nq9jp1SpVJh0e/3+8lksl6v4y5YqVR0506nE41GV1ZWcLXfvXv3\n7t270+m0KiR1BUdVgVZijQ0xzWQy7gFAc8HIrmq1uri4mEql0EPST9btduPxOG1h6XQasqE9uVKp\n4OeL5MTj8ViWVSqVYrEYWT74DIPjarUaiUTY2e5BRTWLc2Oy8/e//30R+fznP480ka8CMKvaaOn0\nLxl3tim2Do1tlevc9Di37LLmaKbutTWh+gj9gQjD7peBDK9er3s8HhZ95QbiM3aenJzM5/Mf/ehH\nReSjH/1ouVym3FWtVjOZDF1fmAKjLMeNEPKLx+Os4xAhdIIlPISHylzlDPAoP3s8HiJCbDK4EIIz\naINQRkR6vR4seOrUKTqpg8FguVyORqOITYh1qMx1u91EItFqtZLJZLlc1oJZv9+v1+uTk5O5XC4e\nj8fj8VarRV0QJaRWCqmWUaKjTa07Rq/Xe+Mb3ygif/mXf8ltJ4IkIqTFTdsboC4+BZ0jAyVvBRgC\nu9A4fxK7c85hinN42H8WRoK4fqDf60+fpSI2CSIyCrQPjCMRkeFwCNuxcy6Xczgcn/vc555//vlL\nL730/e9/PwZmExMT2Ww2Ho+32+1IJEKOTkRisZhqGiuVCkqQSqWSSqVgO2hJFfNvectbyFtalgWP\nIkSE1dS4HWIjoCFM1BCTP/GvXgspRL/fz7tAxtFo1OPxlMtly7JWV1cTiQSnisgiHA6vrKykUimU\nHXAnryUwgu3osatUKphxaMxEJHrNNdeIyE033cRGRkXTcIaMRcU1p39qr7R9U8IQ2MXBeSr2bNw4\nyVS/1jN06JfYJNr2QZfEOtrPK6fNkGSMsoh88IMfFJH3vve9ExMTExMTaNAxWEKVzgiVRqOB9i+Z\nTGp0EggEVlZWNPQplUqkFi3LOnr06IEDB6644goUjzImLf61l7VEBFkgNMaRmQdGfDMxMaGdZ+12\nG8ND+AZ7jkqlQlHQ5/NRzVInDmjbLqN3jOdZE2xp8xbiRuwfh8Oh7o9t1Xe/+10RwT1LRGZmZjhP\n4k6tTfJXLftpwdKoEA02OTYu1RlcSGhvrLYwi00soPJ0pTcZ2+baNRQyJhK32/2tb33r7rvv3rZt\n27ve9a53vetdjOBi5KM2h9GZ6/f7e73e8vKyJsdEhI2qX19dXV1dXQ0EAsFgkF7g6enpHTt27Nix\ngxPmDO0OWOQqfT6fOobodbndbp/Pl8/nh8MhYVw4HC6Xy36/H4aDIdxuNy8slUq9Xo/4DOtFiG0w\nGHAJeFnxju12m4ylHpkRl2QyVe5PvzamG5C9iCwuLmJNomPYlKvIW9J4oOlQ0wdmYGBgYGCwrmEI\n7CLgvGaoL0rh6pzAnhUxWA9QwycZP7RrnDj4FesKreIg6JBxFlHDAj3Ub/3Wb4nIhz70oQ996EOz\ns7PdbjcWi62srGgUgkciecVMJqOOG/y1Xq/Pzs4Wi0Wfz0eij5hMPQB37ty5c+fO7du3JxIJPSu1\nkuKHNfJ65OyUuBwOhx65Wq3SeswO5PEsy0LXnkgk3G43L1GgFuGe4IWIlQnHZOAyhS4RQQPi9/tR\nbHIzV1dXP/GJT5AwpHUakyqar+m55uAMZPH7/c1mM5FIkCNNpVJmoKXBhsfFaucy2DTAWJYUohKA\n2NzoMcNFX6fzqBCIyziLCCtAJDROPfvss5/97Gc51K//+q8Xi8V2ux2NRtVad2VlJRQKIdJbWlpq\ntVrUujBud7vdi4uL09PTKysrbG+326FQSCtDWFpEo9Err7zyiiuu2LVrl56MjEfD4MakRxYR3DGo\nS8k4Ter3+8vlcjAYxF+D04MtSGPiYqyeIJTKuEXkFekDo3bV6XTUtDcajbpcrlwuNzU1tbKysn37\n9nK5jL1vp9PZu3fv3/zN3zCKLBAIdLtd6mF6blyLw2ZkXKlUOOfV1dU1BchNDMfW4eqzwTmPDPS2\nX3vttef2yKdjzdiUdcheKDjOR/hlHu+zAfUeEWFIB+I3dWCye/uydtvvNhbyGuKovJvhJvF4/NSp\nUyISCATe9773HTx4MJPJrKyspNNpESGioitr165dS0tLOuaxVCohu4fPkGxUKhX8EqPRaLlcxu13\nZWVFjRy73W69XkffyME5K2Z3iQg0wxlOTU3t2bNndXVVRBj7ws52R2D84xmPQju2jOV/alLFrdPx\nXVTF6vV6IpEQETi4Vqv5fL5arYYDMmeSTqfvv//+9773vV/60pdgLMgSFb6I2IXy3E8uRN1+Zcs8\n+YbAzgjnb229AAS2/nHo0KHzlDw0j/fZwOFwoFagYVnGDod23mKxZknlQ8TqUMasYHesxz8XxwoU\nCn/4h3/42GOPvfvd7/b5fPF4PJvNikgsFiuVSpOTk61Wq1QqpdNpuIfMIR3BaOg5T3qBSeXRNSwi\nqNsxaQyFQiqsb7fbjzzyCFJG5Igiotxw1VVXYWMI9cLBRFc407MzeorhcNhsNuPxuHYT81qEiByc\n/mjsRSB14qdgMFgsFuPx+NLS0oEDB5555plLL71URJ5++ul3vOMdv//7v0/+EDWHjL8Q8Ikwt0XG\nA1b4CNiBnVGHnt+HY33AENgZ4bwGB1ucw85f+CWGwM4O0WiU2kwgEKBrSsYrqdgiMBZQ/VVEKAJ1\nu11IS8aBAjwRiUS05PP0009ffvnld95555e//OVUKqX2TtFo9Nlnn7388ssXFhZmZmZgDkJAHOVx\nAKFtC/8qWAoloYi02211WiJhWCwWRSSdTtPChQIemmE3r9dLJKfm9HoVeAprPITNMS1c2IXI2OAD\nNiVJKCIcTUSCwWA+n5+bm2M65eTkJMOXHQ4HfWNETouLiw899JDH4yFniNa/0+kQ3q2JdPV7A5Hf\nFozATA3MwMDg5VGtVgmYUJCLCC1ZCBzUgm8Ne1ETguTslSeduqKLu4jceeedIvKrv/qru3btqlar\ne/bs2bNnz9GjR3u93uTk5MrKSjAYzGaz2reLH+BoNMKMCmf3wWCA55Pb7abFuFwuO53OcDjMbkSK\nOkIzHA6jthgOh8xNjkQibrfb7/cXi0VoCVZAsoECnm7rdrutLMXsTQZSM8qS8SgoNWgJQBLS7XYb\njUY8Hl9YWJienp6eni4UCslkstlsVqvVnTt3VqtVZPd79+5dXV3dtm3bT/7kT4pturSMe+mYVcYW\nnWapvlnY7V+wJ+Siw0RgZ4Tzp44bjUYmAjuvt/c8HXkrwF4DIyhBssHnpffWnkXU1xJ7abimcQPb\ntfgUDAYbjcY999yzf//+yy677LWvfa2I0EGsdhh6Go1Gg8ArHo8Xi8VYLEYOjaSiZVnaiSwiy8vL\nUBFDTHK5XCqVEpFarcb2arWKgIJ3JLzT4WSEPhgz8ldGtIiI2+2GQanMKVsTgSE4RG8i40AwGo1W\nKpVQKKQVOIZtYlh84sSJHTt2kD696qqrvva1r7VaLWbNUDArFovYU2kKkRtCZ7TmPwGZ2y3y5JsI\nzMDAwMBgQ8IQ2MXHVnZR2srXviFA7o4MoToh2S3qscnAIEMl6YRZNE4xEGQ0GhFMII7Q1CIbP/ax\nj4VCoa985SvYvefzeYZYEtygVq/X6yQJQ6FQoVDIZDL5fD6RSCQSiVwul8lkUIiEQqFsNpvNZmOx\nGJ1hiC+mp6cxJ0wmk7x7LBbL5/MYJDqdTozkW61Wr9dLpVJkC3nH4XBYr9fT6TTK+F6v12w2/X4/\nDoexWEyHLCPZoM5HJpPD4ihP5Q8tPp0D3W63Wq1u27ZNZ0DfcMMNIvKJT3yCulqxWCwWi263O5fL\nBYNB2s5SqZR+LiJC+KUKSYpzF/IhuYgwKcQzwnltsN3KWcTzmj8Uk0I8O+hHAyEh5VBBh/1X+3Rj\nGbOUXRqHiEMTiZpCFJFYLFYul//zf/7Pv/3bv33y5EkRueGGG1DPkxXEUVdEqCGl0+l2u00piBQi\nfdCxWKzRaLhcLkTthUIBNWMsFkOpodwZCoUajYbX64V6RYSJXKQrfT7f6uoqMj8SfZTHVlZWVMRB\n5rPf709PTzNKRkROnjxJ51aj0bDTCTew0WjgR8yfSJA2m81t27Y9/vjjV199NV/mjhw58vTTT//s\nz/4sdv5qgpVOp1dWVlA5asu2jJ9w9lTJqGyZJ99EYOsCWzMQ2ZpXvYFgN6qQ8Td9lSOiWWg2m7ik\n65KKlS18hvLb4XAg4cPrz+v11mo1IjMRabVaHo/nk5/85Pe+971t27Zt27btlltuefTRR3VaGEbv\n/X6fOhaRFkEMwgfs6jHedblchD5Us9BxuG2gJYvOa8uyCHECgYDf7+dUEe6zc7lcxquwXC4nk0lC\nT6fTWSwWB4MBoyYdDketVqvVahMTEwSpEAn6i2AwyBgUpB/NZhPFR6VS4fJXV1f37NnTbrdnZmZm\nZmaSyeR9990nIrOzs0Ry7AZ7qeBTrUm47QyRUaOQC/qUXFSYCOyMcL4tjrZmEHa+wy/ZMt9DzxPw\npRURepjUute+z5r+ZQWZN11hXS4XonaCFbtqUfH2t7/9nnvuEZFCofDud797eXnZ5/PV6/VYLEby\njT5lj8dDOKi6dtqBm82m1+vtdrsET41Gw+l0wnORSIQRXzIWpPCOg8FAm8MQ5RPYMa5MRJDmi0gg\nEKhUKujUSUtGo9FsNptKpbD6FZFWq7WwsECqMBqNapqUa6czLBKJ0CKdSqUgThFpNpuNRuNf/at/\nJSKf+9znpqamcrmcjANfGduCaP+16mXsHWBrPogt8uSbCGy9YKuFI1vtejcidMXkZxR0+p2DJd4+\nB5l0nw6sgsDwnULwTRsvEnwOQrUGwd7f/M3ffOADH/jABz7QarVuv/32xx9/nDipXC4T+pTLZepM\n6P2YfVwqlWCvSCTS6/UikQhWUphLQUj4dxCgkMEjF+fz+QjXcJCCMJAXIq9nWKXD4SA5qXJ54rDp\n6enl5eVOp8NB3G436cpoNAp9ar8z7WIulwsNJFHgcDgMBoOFQmH//v2j0eimm2666aablpeXc7lc\nMpkU20gaLOq5yUgZCRDVa18b18QWN28FmAjsjHABTGa3WhB2AcIv2TLfQ88T8Ipds5FWJH6Ghwin\n1pTBqBLRnCSneUNobCFj2beIXHLJJc8//7weOZfLffzjH/8//+f/XHXVVdTG0GW0Wi28g1G3y9jp\ninV8MBhQAyuXy5FIpFKpRKNRamb6dqQWidvY6PF46vV6v99PpVLMX9b+a7rBnE5nMpkkEET9sW3b\nNo/Hs7i4SPqOc1YjY8ppnBtToZPJJGU5MrH9fh8TXr/f/+KLL37uc597xzveISJf/epX3/Wud6mA\nhSOTZVUjLrtDh4wLYHobRYS+5h//g984MAR2RrhgS+3/Y+/Nw+Qqq/zxU/u+di29prMnJDGsshlR\nUGBEYljGZyZIDAgjcQHEBUdEvyjCoOI4g4OCYERAUEDwAUQGBmQnskQIIYZsnd7XWrqqa99+f3ye\ne36nb3Wclh6SVPr9/JGncvvWrXvf+77v2T7nnNkgw9j2UgLsIAfr9ZA3zD+EKYDeWvgvfyZRlokD\nNjgZMoMLSkGehUKhsbGxtra2/v5+IgoEAkSUSCQuvvji22677ZVXXvnCF76AfCkiQkEms9mMtOVM\nJsNNolGHAnQPzl1DXjMYgJx2jdRmVFPkWF25XEZ3yqGhITgVAYTBmpubwQ2BSZTNZvv6+mBQougG\nbg8NOVEUOJlMok4j6vPWarV0Oh0MBmGoYZSKxWI+n+/o6BgdHX344YdxfNWqVbFYDKdB+JFWhhGj\nChmG22M9QEoviLpZMvOVC1FBQUFBoSGhLLBpYf/0qTrgRlhLSwsRDQ4Ovnc/sT/NL1IW2MyA7lP4\njIiLrmqUzvbS1e2Fa4srE/I1QV5nMyIQCCQSCRRIlDVqe3p6Ojo6rrzyyo0bNx577LFE1N/f7/f7\nkTtVqVSi0Sh70lAFCpYZjnAJKK/Xm8lk2KsGywlUPbR1JiLUthgaGpo/f/7Y2BjnbCHg1NzcDI4f\nzJ1arTY2NsatVWDnERGcjaiC4fP5YrEYEUUikXg8bjQaEZzz+XyY+alUyuFwuN3uN998c/ny5c89\n99xHPvIRInr66aeZbUjaBIZRJf2ukjHPx/kgnvH/fD4chFACbFo4BAQYhBMDUkpKLD5BCTAFQFaj\np320TUGsC//Kfbz+aoiHIVMKCWSkkfLNZnOlUuHLwq+4aNGiCy+88OKLLx4dHb3ooouIKBaLBQKB\noaGhJUuW5PP5sbExhIhMJtP4+HhHR8fAwEAkEoHkQGaxx+MZHh5G8AzylWNIcDly6zKXywV+Pwon\nQu7CH+jxeCClcLcoYOhyuRBgMxqN6E4Jr2AwGMxms9x7BQWobDbbyMhIS0sL7o2IfD4fsrM//vGP\n33TTTUQUiUSIKJVK2Ww2VMaqbwKAf1n8IxAoS3aRJs9mycxXAmxa2D+7Lb1nJep10gsYHBzczwLs\nPS08PyXU9J4JdInMOjtAKv7Q+plhj+qF3AqLROkNHSQBxOFwwFDDW8OfNm7ceOGFF2LmrF+/3uv1\nNjU1bdmyxe12+3w+ZvY7nc7h4eFoNIoWkUSUSCQ8Hs/Y2FhLS0smk8H947KwC1HnECE6nIk4UygU\ngkAiTeharVYQHSHAyuVyc3Pz2NhYNBpNJBKgPhIRZGQikbDZbEwRRM4WssRGRkbQkJOIhoaGli5d\nunnz5nPOOeemm2566KGHzjnnHB4WiFiOQSLQiErKuEmkBKDOL47o4mGzZOYrATYtHJA99z2VYfvf\nAtv/0ouUAJsZ+GXB6oLlxHwBk8mETldMNMAHps7LS3GpCE5g4pq24PixMUTa9h0Oh8fGxiKRyPnn\nn3/FFVcQ0bXXXnvbbbcdddRRJpMpGAz29PSwnQR2n81mMxqN2NYdDkcmk0FhKpPJFAgEuHclfqVY\nLCLLmD9D3MZiMafTycnIqKwB2j3EhtlsHhkZQZkPu93OVUUwAqgdxeneUvagSDFG1eVybd++/dpr\nr/3CF76wadOmE044AeRJ3A+Ggu0qbkCDwYfTlTTRxW9ENm/TpesdqlACbFo4BATYdPCexsCUAGs4\n8MvSVZqH1QJGouS/ScDNxUx3SC/wwtG1i7/FQTXpB2OAfb5+/XoiuuOOO95+++3LL79827Zt6FfZ\n1tZGRKVSKZFIoEQ9anOQVjJqeHi4paWlUqkkk0lIOwhds9lsMpm4oxgiZLBgIMkggVwuFyc4m0wm\ndBRDQhju2eVy9fb2os49Hgr0SIfDwcxJlJ6CCzGTyWBOut1ug8FwwQUXXHDBBWefffYzzzyDPpwM\n9s2S5slES5opNQMZU5xVLEQlwKaF/bzt0kFA6Pi/xQGRXqQE2MzgdDrZp8dbJ3+Az4pFEcfGOEsJ\nOynXRUSOM4egMBmQuSUDaaTROpYsWfLOO+/MmTOnp6cH93PllVd+4xvf2L59+z333IOMsb6+PiIq\nFArz58/v6urq7OwcHx/HL8KNhmtmMhn0dyYieCzhP2SnJfdSqVQqxWIR7b5II3egkBVpCddwCRKR\n2WyOx+Pz589HZAvnmM1mp9NpNBrRHgVMk0ql0tzc3Nvb63A44G988803H3/88RNOOOG888679957\neczReIUNUyaesAIBWYWLwCxjwc8BM5o1M1/R6BUUFBQUGhLKApsW9r/pQIeQEXagzC+aNXroewRd\nDIwm6/gM5nxzMIxpfqgmRZq/kTRzgYM6OBNWDl+HSYkoVM8lGWGO4DqrV69+9NFHV69eTUTxeDyd\nTqNaI/KOiWh8fBzml9lsDgaDAwMDoJOAVVGpVGw2Wz6f51RoeBQNBgPiWHAhohaJ1WpFXSgYiJlM\nBt1bzGYzStfD5vP5fLAv+/r67HY7WIWIlpVKJRRItFqt3d3duP/vfOc7b7755tVXX71p0ybcDO4E\npi2I+3hw3aCxySWJ9dJKUzEwhUk4IJsvNb4M28+k+Xqo6T0TgLlARCjcXiwWZb0oOLhwnCUWEaFp\ncv3VcA73VcGUgEyCAJOBMZSNR0tiRJ6IaN68eV1dXRdffPH69esXLlz4yCOP3HLLLUTU398/f/78\ncrmczWYXLFiwbds2ImptbeU2zSMjI5FIRHZmgrK7AAAgAElEQVTPAquCCR1wdRoMBpvNlsvl4F0k\noomJiWAwCFpHNpsFz8LlcsXjcTzCxMQEqiwSUbFYrFaruVxuzpw5uVwOMS23242qHyi92NPTA9L8\nJz7xiRtvvPFrX/uaHG0igiSTnayJqFarsWOWBxy3B90Co6pIHApT40Dtv9TIMuyASy9SAmxmYC44\n7Cep79PkUuj1X0Rxpnw+L3OTp/wJCC2czKX/5E+wkVQqlRAiIqLf//73a9asQfTonnvuSSQS8Xg8\nHA5v3bp15cqVRDQyMmK1Wm02WyKR6OjoSCQSMF8CgQCnBDgcDkSz/H4/hGsikQA9hMsTT0xMoEsL\npz/39va2t7fDMjObzalUChYYKgIbDIaRkRHkMuO2rVYrWBg7d+486qijHn/8cRzv6Ojo6+tbtGjR\nzp07Of7HdM1isahjxkOGYUzYFJaiDgPFNSHf/YtvHCgBNi0cwC2YDigv8V3jALoNJdT0ngl0eWB8\nUBbG5fr0aLlCRNg60SFMnoltt1arIfsK34Irj+l/2MRxWfyX/WZEFIlERkZG0KALJQ1xPhGdf/75\nzz777KJFi9AlkoiQ2rx169ajjz765ZdfXrRoEc7Ed9HDjKVjrVZDLjM8mZA3RJRKpSKRSCqVgrTD\nlefMmTMyMkIaT8RqtbKIHR8fr9VqHo+Hu1wODQ2Fw2FkgJ1++unf+c537rvvPiL69Kc/za1BSZD7\nUf9QZz/BGYuB5cw50jLPdF9RLEQFPQ4SAUYNIsMOBtsLUNN7JkBNI9Jk0pTAdsk+QCKCSLNarYVC\nAX1DSHMVAtIPKQ0O2keMjYi4bAd70qLRKCjyRHT66af/8pe/zGQyxxxzTE9Pz9KlS4kIZH2v1zs0\nNDRv3rzx8XHkTrlcLm76Jct2QPKhoxh6cuJ34T9EVhmkGmw7ZJ5BCOGGK5VKKBTK5XIej+ett96K\nRqNEFA6HY7HYypUrv/71ry9fvpy0Jfz666/D7+fxeNDoEk8q683rgn8gT0rrCmYrZDzXvydNsr6r\nd95gUAJsWjioNuKDXIYdPNKLlACbGWQMrP6vupwkFkvSsJCAGWE2mwuFAif/yrgXizEuYw+LjW0L\nTuCFI7G1tRVUdSL61Kc+tX79+lNPPfXee+998skniWhgYKCvr48JFBA5eKhMJlMul30+H1o8ExGq\nJtpsNq4egh9CTQ2r1To2NhYIBOC9bGtry+fzyOhC3SzQRsbGxqxW68TERDabPfzww/Fcr7/++qWX\nXnr11VcT0RtvvPGtb33r0UcfJSKv14tq9BhGaWhOmVonu1ZaLBZM7HK5jNGW3ZmRsjZlct6hByXA\npoWDYS8GDvKQ2EHiOWSo6T0T8HuUJAvpTtT1AGPAQ4gtldti6c5hxgF2cHYbktZMmaUjd2hkjmK5\nXMaOD/na1taGhmGvvfaax+NZvHgxEa1bt25oaOiNN95YunQpHIOQSel0urm5GfnFHo8H8TYUsuLK\nvKlUCvZTsVjEQfTqxA2k0+lqtYoqiAgN4tc7Ojri8XgoFPL7/W+88QZ+rqOj44UXXvD7/evWrbv/\n/vvRS5q0IpB2ux2EEYhzEtKLGZg0ubiJ1A9YqpGWq0eTuZqHPFQemIKCgoJCQ0JZYNPCwWNS0EFs\nhB1s5hfNGj30PQLHYOC2Qs3cbDYrS9TLFC5YACjLVD/yXNUXkRtdV0wSrRqZkuDxeDKZjOzeIksm\nSrebyWRqbW3t7e19//vff//99xNRZ2dnuVzu6uq65pprHnvsscWLF+OLixcv/utf/+r1evP5PJfA\nd7vdeC5U2Whpadm7dy/uGVaa3W6PxWLBYBC34XK5kP6VyWTsdjvqYmQymVKpZDAYdu3a1dHR8b3v\nfY+Izj333N/+9rf/8i//AhsrFAohK4A7fPL4sGVmNpthbzHlEpA1+3kwdb1GcabqyKwwCQfVpkwH\nGS+Rg150EA+UwrsAisqT1t0Y7EGj0QgfV31VQwkdO2NfpfyYx4g3JYusQ1gySQS3AUmJfit8cQTD\nwFpsb29Hfam5c+euXbv2+uuvL5VKN95440svvbR7924i6u7ubm9vB3UQPb2IKJFIIFs5n8+Hw+Gu\nrq4lS5aQ5i0EWQNSnIiGhobwdYfDARkPOTo+Pn722Wc/9dRTZ5999nXXXffiiy8S0dVXX/3MM8+Q\nlubMKQcYEJPJ5HA4CoWCzEHGeDInk4iMRqPD4ahUKvl8nlszkybpuewkLqKq0SvocbDty3TQ0DoO\nZulFSoDNDJKFyOlHFouF87S4oaVkDeyLcw+DCWJJBs84hMMWCVMN0dMLPVxIMzhKpRJ4Fqici4tg\nW8cVZCjom9/85sknn4xekcBLL7303//9388///z4+Hg+n4dE6ejoKBaLMGIKhUIgEBgdHSWiXC7n\n8/nsdnsymfR4PDCeOjs7iSgej+ORh4aGTjzxRCL67Gc/e/rppxNRX1/ft771rTvuuAO/2N7eHo/H\nEbiy2Wx4XlSRJy06aLFYILyTyaQcNE6Mw1AjMKYbKEgsFucYilky85UAmxYOwq0ZOIBi7KBiG+4L\nanrPBHDZkcaM58HUcevxJymTTCYTdudCoYB8XukKk9Bl7ErnJJsUfGU+jSUcu93kyTiYTqd5ozca\njccee+y6deuI6DOf+QzqxG/atOnVV1/dvHkzEb3yyiujo6PhcBgMSbRxIaJIJNLd3W00GlEgA3K0\nVCpt3br1H//xH7dv3+52uzds2IBi+biTyy677O6772YRzhYhCvNzhhYeCv82NzcPDQ3xmODpYGXq\nKqFQXWcA0GSkJxaYJTNfCbBp4WDeo2n/ijFpclFDjYzC3wtdIrMsPE9TjS2LHxgBcku1Wq3wQyLB\nWfZfxibOX8GV8YuQQCzAYIVwWzK0pqy/Z1yZP6DUhfReWq3WwcFBBLQYu3btuueee1577bUVK1a0\ntLTcfvvtRJRKpU477bTNmzefdNJJe/bsaW9vJ6JoNGq327/61a+SJiZxhW9/+9u33norcpybm5tx\nz6Ojo+ibbDQac7mcTgbLNijSfaorPgn5BKqkLNPF7kRpdKpEZgU9DvJtGtC9yv9zSdZYogtQ03sm\ngJuOiKrVqq5WLImIlE735++iYhP3A9OdwHtufeGJ+suyYMNBNq10Hk78aCAQIKJEIsE/gXgSbMFQ\nKLR79+45c+acffbZPp/vzjvvJKJPfvKTF1xwwbJly6Ych2w2C6uOce+9965du/bFF18855xzjj76\naJQ9fPnllzE4oVCILSoU/IW9yP5P3cM6nU7J5uBwo+RlkHAYcikpcEZIm+fyvcySPDBFo1dQUFBQ\naEgoC2xaaAhrA6h/oTM0xRrR8GKo6T0ToJkIaR4t2V+RtLb3MmEZf2U3lzShkNqMhpawn+RF2Npg\nG4LNMkm6A+pDYoCsy06CJOnxeJBTzOCKHvU47bTTzj777Ntvv33evHlEdOGFF/r9/ltvvfWKK65Y\nv379FVdcQUQ333yzblEANpvNbrcj2mcymTj4B9MQdpW8YZ3/kI1d2FVywNEpplQqTVk6mSYX78Cw\nzJKZrwTYtNBYuzbjb7zcKaXalMsSOPRGQOF/hXzp7NYjMapMTdTVkwX/njPDiEgGvUjIHnwL+zXv\nzmihIuUTk/Fk9xbd1SAPJB+E6SEQmZAocOLl8/nOzs7u7m5ubbx48eI9e/ZM0/NmNptRHRHXhDiE\nrAWBxWw2MwmeRJUsSHEMHSJ5KGolSS6Qr/WSm38a9VCICBlgpEW/ZFVlKSkPYSgBNi006PbNeNdv\nedY+uAIRcX3YKetFse3FgwyjClnM9bw4iCXszjpOHWJU0rzgtpOo+8fkEXlB3uKnzEjDyTIEJcFR\nNF0DF6/XC846BFs6nc7n88FgENR/jEb91TgUh6xn3AYf5MZpIHPyYMqiUGB5EBFyA/hPfHsmkwmj\nSpMpHvUjg2GcJTNfCbBpodH38VkLNb1nAp72EBX4V9ekCidwPUMSTapwPkroguZQD3Ye1peol6fp\nLDA2WfgXIQLRE4u/K7d1LjBfqVR8Ph9sJi4H3N7ePjw8jEwvnSCUCcUAhE2hUEBWFpq80GRvJ2cg\noFUmTaUEcGMUn8/HTTtJK1Vss9ngTpRDja+wXSu1BB3NUllgCv8/lABrUKjpPROgfwdpEoV3z/oi\n9LLKkcViqa8EAQKeyWQyGo3YlGtaq0zegnWlgSE50N9E0hFBsZMBJA6q8XZPRCDy4REcDofObGIn\nZFNTExGhqQqJ8h+4iNlsTqfTONnlckEqyEIk0xlGTveGXOHcNT6OtAE2qrLZLEtNbgfKPyfHXzd0\nEGw1DdO5t0aHEmDTghJgDQo1vWcC3bRnWYUN1Gw2oxQ66Bs6wcaSQHa0qgf3XOamYkQk3YYSfyOR\nGVYLbCApwFhChMNhFNdwuVzVahXCQNpMsjmLfBYdVYSIUEcKPk+LxYJQFtUZW9L7x0R/3fBifsqi\njvxfFKqX7apJ0yT4v/Le+J7xQ7Nk5isBNi0oAdagUNN7JuBpr0sl5lgX78hyx+f4jU6kYUe2Wq1I\nq8I5fGWWjqSZOJyqPGVsTHr2puTmgUgCvoPBYEC1QNJ4j1Pes0yURnpyqVTill0olkhEEB4GgwGt\nlqVkku5HSXhhb6HBYOAImRxS0gQedAJdZEsauPUXhxjTZXDPkpmv8sAUFBQUFBoSygKbFpQF1qBQ\n03smkNXopb3C1G3ZixJ0DNJ6r7AzEF61+nAR20NTXlnHLAe4dYjNZmMfIBGxkYRi+bgN2DeyVTGe\nBdX0uZwVO/rmzp3b29sre2bKn663Ak0mU7FYdDqdlUoFfjz27MmMAl2oTP4JhEyTyeT1ehOJBA+I\nwWBA9SmQ8qmu7GR97RKqo2jOkpmvBNi0oARYg0JN75mg3oUoIaUXExRJS7Sqv5rNZjOZTOitJfd0\nmbDFHcUQGAPZT+ch5KpR/EMy1sWnWSwW/NXtdu+rlDD7IVn2oG0K357f7zcajfF4XNf7mJ9IFx7j\naBYyl4kok8nImvE0ucE0iyKQ7PHF+lryTH6RaXPyNbHzkAQ7ZspHPsSgBJiCgoKCQkNCxcAUFBQU\nFBoSSoApKCgoKDQklABTUFBQUGhIKAGmoKCgoNCQUAJMQUFBQaEhoQSYgoKCgkJDQgkwBQUFBYWG\nhBJgCgoKCgoNCSXAFBQUFBQaEkqAKSgoKCg0JJQAU1BQUFBoSCgBpqCgoKDQkFACTEFBQUGhIaEE\nmIKCgoJCQ0IJMAUFBQWFhoQSYAoKCgoKDQklwBQUFBQUGhJKgCkoKCgoNCSUAFNQUFBQaEgoAaag\noKCg0JBQAkxBQUFBoSGhBJiCgoKCQkNCCTAFBQUFhYaEEmAKCgoKCg0JJcAUFBQUFBoSSoApKCgo\nKDQklABTUFBQUGhIKAGmoKCgoNCQUAJMQUFBQaEhoQSYgoKCgkJDQgkwBQUFBYWGhBJgCgoKCgoN\nCSXAFBQUFBQaEkqAKSgoKCg0JJQAU1BQUFBoSCgBpqCgoKDQkFACTEFBQUGhIaEEmIKCgoJCQ0IJ\nMAUFBQWFhoQSYAoKCgoKDQklwBQUFBQUGhLmA30DCvsPBoMBH2q12t8+7W+foKBw8ONdz/ZpflHh\nYIASYLMFWJZYk/sSUbx0FRQaGu96tk/niwoHD5QAm0X4X1cjr9v9cjsKCu8hZjLbpRhTOJihBNgs\nglyrunWr1qrCIYZ3Pdv5r8oCO/ihBNgsglqZCrMHarbPBigBNosgV7KywBQObajZPhugdJNZBMVC\nVJg9+Htnu/wwnS8qHAxQW5WCgoKCQkNCJTIrKCgoKDQklABTUFBQUGhIKAGmoKCgoNCQUAJMQUFB\nQaEhoQSYgoKCgkJDQgkwBQUFBYWGhBJgCgoKCgoNCVWJY1pAbiOnOhqNxmq1SkQmk6lardbn0pnN\n5nK5TEQOhyOXyzkcDiLK5XJ2uz2fz095/Wkm5Fmt1mKxaLFYSqWS2WyuVCpEVKvVfD7f+Pg4EVks\nFhysVqs4DRe3WCw+n4+IUqlUsVh0uVyFQgE3abVa8VD5fN5gMFitVo/HMzY2hl+02WyFQsFkMlUq\nFYvFgq/UajW73V6r1QqFgsvlwkNVKhW32z0xMeFyuTKZDK6JO8FxHjd+aqPRWNPAx00mk8FgqFQq\ntVoNv4vjGEw5/nhYfMaY68qwqjTHmcBgMJjNZiLCSycivA6ezzjIs91msxFRoVAgIo/Hk06nichi\nseBS5XK5Wq0aDAaDwcDTAJPToAEn8xpxOp3ZbBaTBEcsFkuxWJR3iBsolUpEJNcXJr/JZCIiTF2c\nQ9oi4p8golKpZDQacefyr3wdfnxczWg0mkwmHDcajbhtfB2jobsIFpH8wLfKa5kHmceZf9pqtdZq\nNXyW92M2m+12+8TEBN4UH6dZM/NVIvO0gKUl54dc2CaTiQUb/lqtVll+YO8mse1arVasZyKqVCpY\nuryJ85XNZjOuo/u5evB0592cb5tntnzRZrO5VqtVKhWsIiw/rHaWFnwmpALLEjwjr15sMbodjYi8\nXm8qleIr02TxT0RutzuVSsnfwkXy+TzfKlY7aw9SUOneTn3/C8haORoKfy9YQyKx8/L4Y9pjwGu1\nGmYCEdnt9nK5XC6X6yckAzOThJqlO2HKg4DRaDSbzcViUacP1U8MeZznttPpLJfLxWKxfrZLQBgX\ni8VarQZpxNfn37XZbOVyuX6IpOzklc5fZB3LarVWq1UMFD+sbtDkwmdtjzccnMYjj5Nx/izZ2JUL\nUUFBQUGhIaEssGlB15qBBw2q0JQ6Jnx67MQj4e6QvgV5TalRSheEzsGIa0LtgolTrVYrlQr7LnAa\n64y4FFuHOuOpXtU1m80+ny8Wi/GdwJTRaaz4utlsNhgMuAKsLvYdSdhsNiizup+b8mTd47PfhjVc\nPohBY4OgUqngOPy60lWl8C7A0x5jC/dyoVDAHJPTGKa89N86HI5CoQADizQDut63xia+XCNEVKlU\nrFYrPAc2mw2vNZfLmUwmvG4sCtgceN34XafTiUmCg+w2wATGlfmJSPNwwjCC26NcLsuZJm+YH1za\nSbqliiettw7Z269zV7BjnC/O651vUrpG5ZXZ9oLXnU09naP1EIYSYNOCwWDAViudafIELDYICYvF\nwrNtysCM2WxmKYJgDwkHCDsNOABQrVZxEGuDf1pOXxzUCVdsOvgvbpuEJOC7worCdqMraSo9crhh\nt9tNRHCKYu3VB/ZwHC5QIoKM4XgYzgkGg/F4nDQlwOFw4Lfy+bwMkEghxCEW3fjLJ+WbxxfV9J4J\nsC0SEXubafIGit0fW7nBYMALyufz7DaXkkB3ZbxBXE0Ga3Vn1k9pXFMnIXQXJ20m1OsxUvZMGZPW\nRciwxHQalW65QfZA3PJB6T/nx+RIGwnRhQiFFDn8uyzt9uVThWhkgYeDfOSQhxJg04IMBvBcJC32\ny45p3Tn1Jg6zG3TAdwOBwMTEBJ/8N5gdoVAokUhUq1WPx0NE6XTa6XTiygaDATImnU5LMgWvYXzm\nBcmriGGz2Ww2GwJUMjgsH9Dv9yeTSRnKBlgT1xmUPAjy5+q/LkejXqLr3ghpmxSkl9xKOMKhpvdM\nUN+tWLKW5O4vP7PRg5eLXdVms2WzWafTWSqVdIExvGjELHnrh2ODVR+81kKhwKEjDjPjPmG46IgM\nVBd5JU2F4tmFK7MRz1+X2hIbN7zqbTZbqVSSCh+JST5lNI5nPq9ZEt4FErJKcsTwJ16t/BPS9UJ1\nIUO2Uw95KAE2LRgMBrgm4KTSCSoiYvYdEWUyGal8UZ01g9Uut1qr1YrJzSIHU5bXJC6I9WwwGLxe\nL8wXCZ1zRvIGpWKo65NUq9Ug8PL5PDaLKRVbrEnp8ZPXqSdx4HwZVcYYZjIZ8L4Q/ZbuHd4y+KCU\ncPg5DJ1Of8e/2CDYzoOerqb3TMACTLof5AkwKfAqp9y+90WU0LUs+Rt8CqnzyQ0dorF+m5ZbOeYA\nu69xcEq9St6YXCwcI2B/pjxZpwtKmEwmJnGwySVVMRaBOM50LSIKBAKJRKJ+nerujTQer84pKgf2\n0EdNYRrg4cL+yPsyaZravoDzrVYrxFUoFJJ/Ap+KT7Pb7SSmPqSCPFle2Wq14nx8DgQCpDF6GQhQ\nkcYVZrCrAXxIPg4x6Xa7+Tp8kB/Z6/V6vV7SfImg5vPX2dVJk/V3aJ2kKby6X9QBQ4pfgQzDDfM9\n8EEsYD5u0sBDeqAnTmOD2e38avBfzEZ5HHNVnszThqeu0+nEDJETm1+37qDRaHS5XLgIZgIgv261\nWnFxvHGojySWmwSmKwlTDB/49ng18V/liuOFbzabWZvkv/Jiqb8OaXMej8lLD5D/9Xg8vEwwbnKf\n4YmNf+12O/8QX0RuKQd67uwnzJbnnCHsdrvZbIYYwESUE4instPplKJCt4okjYKXE4MFoVED/gvJ\nxGvDZDJhclMdePZPeWUpaLHL4PZ4k+L1Xw8sCXl9XvxUt/UAuLhZAwnxI3+Oo4ZE5Ha7MSy6TVBe\n0GKxRKNRPkFeUz4OljQ8UQrvGjzNMM4YYd4uTSaT0Wi02WzyNJyJySZfH47b7XaWBDoxg8/1sqep\nqYk/S1LJlLMd67R+ErLIkWuQxArFlXWyTV6WJs9zHgQpukisC5PJBFVPrjuLxcKbRr17FnA4HFKq\nwZ8v/ypP5vuUV0Ny2IGeO/sJikavoKCgoNCYONAStDFg0GoE0GRlh11wU+pTBo03j//qlD55GlsM\nUn90Op1spkzpQiQiv9/v9/uJqKWlBVcwGAwOh8PhcMBcI1EpAJCfXS6X7s7xi2yNQWGUXhHpVnI4\nHPUeyCm9gjRZi2fAEyUvgt/ie+ar8RDJ2yDNO6rzAskQi8K7BgmjioT6Lw/ye9yXC076KvZ1Mgnz\njl80X4HdFTiHvdbS2+Hz+filY26wRc7zhy+os7fwVybr68w16T/AlWESWa1WaYwyY7PeISEtV51R\nK7cIHig4aXWXkh4a6b/hBWWxWKT9eqDnzn7CbHnOGcJiseic17yGMQUxezCPsQDY5UXCMYKTTSaT\n3W7XBRjqr48j4XCYhCfB5/PxJs5zGksaS1S3eLAk+Gq8BqQfEs8iIw3yNvj2pBRnVzsWGz+IXJC8\nv/CikvcgFyc2BZ2Q1g0IH/F6vbrdU15Q7oA0a5bxewTeKPfltcYr5tfBs1QXc2XUKzc4X84lRL/4\nheLfepEJvc3lcrGyBUWwXlfjSLAEr0Sd/iTjTPI6Uz4+CVVPXpaI3G43Vr1cF3hYvmcpU0nsElIb\nw0GOe/EPSee8brRtNtvscZ6rFT4t8OSQGpxcBrppjZWDacrTi2WJ7mSn01mv5AIgfdRfH/YWEbW3\nt7e3txORz+eT3AcShJFoNMp3pdtBTCYTNgI+gePArA8ytYQmK63YL3h96nRJPofHCqOhuwH5LakT\nSNYGDErdd/k+cY4urs4q9oGeOI0NZgPJ91U/gVm8TamQ8b7MhsiUNrrO7mlubq4/hyYLPDnNgsEg\n/yhmBdNM+N6kMJDhLuaYkFja/Fe+W8TSWCWV+iIugsevF/b17hMSK70+Gqd7OtL0Y3z2eDxS7vL2\n4vF45Pgf6LmznzBbnnOGkA4N5g3qaEjYdmFd0eTdtl5yWK1WLDNe57qpjwXJJ/NcN5lMEEjSjaDz\nUsrfxZ/8fr+8Wwgtpoe4NMiLsNjgizOHxWaz6UQ4q958ssVikR4nKajYwyPFP1uTckBoqrh6vQ92\nymcHDvTEaWzwMMqZLw9iJoANyMcxt/kE+RU5k+vZPTw3eLHg/Hp7TlJFdBNA55zUeQ7k47AzUHcP\nciJhEtrtdnkFOVfl0pbCDxRK+S0IPOk+Qf6M7tlxESx/o9HIy5CEx56/xZ5GNt2MRiNex4GeO/sJ\naoVPC5zSMeUE2pd7gSa79bCWpnR/QZYwGxiyBM5DiXo+UiQSiUQisLqCwSCWh8/n8/l87HtkWYjj\n+Ix17vf7peeQhRCvGZw/Jc8QX9SFx+S90WTf6b5GyTiZkA3oQl802fblg8zS1iUe4IPL5TrQE6ex\nQZo1wyIEgkeGfOTbkZQ5nSCRXji5a0v2OV9Q5+dg4LVKgwmon4o0ld0Dp4JO0ZFxI+kPZPnKByE/\n2OUgNUi2wOqNS10GCE22U0mIJV1MgTRFUz5s/WLhm9eJ+QM9d/YTZstzzhBGkZNh1Jjf0m0FIwM0\nel14rB5YEsy/YKKwXG8saTiWhp9ra2sjIrgN5Yrl8yXtWGqybG/BNjIajTzjW1pamAOCIzLDjLSE\nG2lsSZ8+QxfimlIz5TgHtkI5gDxuui1GrmqDFpzXxbqmvBOTVi5d4d0BVoKkKujeCz6A0S5TGjhz\nQ+dz5hklSfAul4vTyPggrzhMbE5QkYITkWmpu0ieOs8Ttgh1N69zZur8K7rzpWyTSpUud5OvTHVJ\nNVTnKnc4HHxj0oWIAcRjsjqLJaPbUnTeCx4Wq9V6oOfOfoISYNPCvhKB2TKjqcA7LyuDbIHV+7uk\nXw6QFph08QGRSMRkMsHDsGTJEqyH5cuXE9HChQsXLlwIieX3+6Xo0hEd/X4/byVYiqxX8i+yibav\nHGTpX8UHXlE8AvV6KJ8w5WjgR+s9onyQJbr0c+qi3DRr9ND3CPwG2dmlG3yavHuyIUJiUXDkaUpT\nm7+O/Cf+OTkNZGjToHGm5EUg5HQygDTFi4QnEHaenCfSSVDPjdSxn9ihhw1Bdxv7ShSb0vfAd2s2\nmz0ej91ur8+Bk/FpvqxOWNJk7/psYyGqPDAFBQUFhcbEgZagjQGMlS66W69pWgTqh1qnfkIfhH+D\ndSg2gDo6OojIZrNJpSwcDttsNqfTycTCv43Ozk6+bTakTCaT2+32er0wsFgFlmWudDCbzTiNb4+j\nZfKhpF8I3ifJfuZnxEF2BuoKhUDrhMIOlZYrdOCG5YBIyxgn6yoXHOiJ09iYkvsg/4uXq6ufwrOa\nhOeNbQUuxsFvymQy1ZPROZ4kK1Po+Laku7sAACAASURBVJC6+2EziycYT8t6Gwhcc5oK9f4Ao1YQ\nTt4GOxV07hleI9KFiAdk/zku6PV6+SY5skiTM8wkiaMekhUiHZtms/lAz539BFXMd1owmUyymjvG\njkRhUMM+KsdbRQ1Q+EZkc1gdUMTTpBWobm1tHRgYoH00zXI6nWvXrkXPhccff/zMM8/88Ic//OST\nT0aj0U2bNhGR3+8fHh7evn37cccd9+yzz3Z2dnZ3d8t7RgFip9MJH2N/f384HB4dHUUnM3lL8lsM\n2X8W6xAlTXW1U0l0i0C9XX5As1aGHOW9ueYpf7ZqLWtJK+Zdfxskek9I4Ew1vWcCqZ1wvXl2g3O3\n+/rObSSWCfxyKEJPdZXa5VrgtHpMS3Sb4+5fpBWo5V9kGYYpJAsKA3JioFkdaSEiFAjmX8cP4Z6N\nRiMmJ2l9ZNAbiFsCGbQWSPxzEFTow4B63zz3HA4HmozzrJbPQlrsQDZG55FBCX8MPo7j4rz/1DSi\njRxS/He2zPz9JysbGaTxf3SZHySiAuyeZlOAB5l1MYvFAguD/4p8F9gumNltbW1tbW2sk4ZCIcnL\nuOyyyz796U+Pjo4ODg7WarVSqQQBGYvFarXa3r17+Z4zmUytVtu8eXOtVnviiSfGxsYeeOCBBx54\n4O67737ppZfw0zDRJEASkQUYWQHEI8DPjl1JFz2WqiiWJeuPUgWWfA2DoNfLYqZUl9pFIoQmdWTJ\nHaA6HJDZcsigfjxlFFNGjORMQBIhCT49g+0w3fky6YI0K5zJ67rADxGBhUST2RNsEjE9ijTzrp4Z\n7/f7DQK6x5zSOJOkeY4lWywWHR2Rh4VXvbTSJMdERt0ksVZG1nV1THS3yu4KquN2Hui5s5+gVvi0\nICeNQVDhmUpXP9d5SvFawgdMZVnEnTSr32q16vI3b775ZtzA5s2bN2/e3N/fz7cEiTU6Ojo6Oooj\nmUwGwqxYLMIG+hvo6enBOR/96EfXrVu3bt269evX40dxD8FgMBgMcpF7/EmuVV5yvDiZN6VbZvtK\nstGNKn/QZSlIP6QORq1mAdMOcZwF8HsxGWYPpGwwak25puQRANJ/y6+M8x0Nk/PTAek8dLlcrMTU\nJxHyQd7fIcYgDvEnmT2pu7jNZmPNqb5utdz9pXDFRNI58Vi88dKGolbvLZdX3lfbCjl7daMqU1zY\n1qTJmqIs8SOF8YGeO/sJyoU4LRi0qhPwX6EJEBEVi0V4BmC2Y39Hy6tMJsMt7HTtslpaWgYHB9nC\n8Pl8IyMj/Fsf+tCHiOiEE05YuXLl2rVrU6mU1+uF8wFroFwu53I5j8dzzz33nHfeeUT0pz/9KRKJ\n3Hbbbclk8rjjjoOr8GMf+1hfX99dd90VDAY/+MEPPvnkkxs2bCCi00477dlnn/3Qhz6UTCZ1NKef\n//znoVDI6/V+7nOf27VrFw7CgcnNNplYPzExYRDtiEizStnn43K50JaXx7A2uX0tjydcN9A0MUrs\n2zFN7n5r1JqHTemDZbMY72JiYkJN75mg3jQxTG5GZTabS6USJj/76/BfrAuHw4GpK7ts1yY34Ebw\nuL7RK+YD/JayCaTL5YIjGlOINE8aOocFAgF8pVgswqkYCATk+gIgF2u1ms75VqvV2KlIWh+72uQG\nnph+WBcmk8lut/PNo9GreXJ/L4fDUSqV+Ie47528eYNovAkvDhyeTKbVTXjI4Gw2WxMN1YyTWwj9\nL2/3kIASYNMCs725o7lVa+Sq68rKgH/caDR6PB5sysVi0el0VioVCDxMTe5je+6551566aVHHnmk\nVLsymYzUFvv6+t58881EIvHoo4++8soryWTy+OOPJ6JCofD0008vX768t7d33rx5/f39RJRMJles\nWGG327ds2XLCCSc888wzJ554IhG1t7fv3bt35cqVXV1dbW1tGzdufPTRR4moubn5mGOO4d/6r//6\nLyK69NJLw+GwxWJBNK6+Ca+U3BMTExgcGUVjyNihHNj6oTNrzTBl/MNms3GvZ/n1aDQ6NDSkC37g\nNNOs6Uv7HkGaxeZ9NDuWsbGa1k+5vsu2zWarVCqQB6y4EFEwGERrVigcFq16IcQPLs4X9Pv96XSa\nt/L29va+vj4i8vl8ExMT+2qJSUSHHXbYX//6V7gWYrGY3W7XBZUxb/EI0Wh0eHgYthe6SKfTabvd\nPjExwWorvmXRusVK+cpqK1uKPAllO3JsJizOZWyY70oX/Abbq1arcSNmvg3dgNe/rEMVikavoKCg\noNCQUBbYtMC5nKxAMaA9QQmCtcQUqWKxOKU2GgqFxsbG8Lm9vd3v9x911FG/+tWviCgej0M5hVJp\ntVo3bdq0ZcuWbdu2EdFjjz22YMGC559//qijjjIajR0dHW+88QYROZ3OJUuWZLPZsbGx1tbWHTt2\nENHq1as3bty4ePFin88HywzHXS7X4OBga2srEfX29nZ0dECvnJiY+MlPfvI///M/LpfrG9/4Bm5v\nYGAAZ5588skvvPBCuVwG295oNI6MjLCViXtmRRIkLpPJVE+7ktzFSqWCL0rClaRUSWoiafQz/Bx7\neEjo/uxahDoP/tjM3vysBligNNksIC0eU61W4TZkXpxMLMFX2K+ItwYvHwmmOF4Qk13ZCjEYDHPm\nzOnu7manHBGVy2Wr1epyuQqFQj3v1Gw2L1u2bGRkJBKJEFF/f7/ZbB4eHr7hhhu+/vWv7+sZcZ8D\nAwMdHR07d+5ctGjRddddd/XVV095MvfuARsQJiN7Mo1Go8vlYq4jFj5iurVaDdsCJ4ew11FHrMUX\nm5qaYrEY/2KhUMAvSvcmbp43cJiDfHuzZGNXAmxaMJvNvIaxXTLLlj3Xchbiv2DuwgNOWmCmVCrJ\nTbmrq2vu3Ln4/Pbbb6OUBnDhhRfu3Lmzu7vbaDTCzfLxj3/8+eefX7169aZNm6xWa39/P2pw5PP5\nkZGRZDJ5xBFH/OUvf1m5ciURPfPMM2eeeebQ0FA8Hvd4PGazGa4ev9/v8/l6enocDofb7U6lUpC7\n27dv9/l8cD6sXLnyyiuvJCL8yplnnklETzzxxCWXXLJ3717cHvYmCGN2rbAvvp7szk4kGdsgwYpm\nGrEMIfBfp4x7cVmTUqkEqcbCD7enpvdMIF2I9f5YLAR+QToyN7vL+LXyEagXOE2y8PmEefPmdXV1\nyTMxRQOBAHyGROR0Oj/xiU9AgfP7/d3d3Z/+9KdvuOGG+qcYGBhwu90QAKRlKMKfn8/n66tvENHQ\n0BA8+UNDQ3a7fffu3e3t7bfeeuv3v/99eRrm+aJFi3bu3CmPY1HoIt9Op7NWq/F/wWpmsSS9i4DL\n5crn85KvD/Ffn1TD+oS8q1ky85UAmxbAEiyVStJzTdquimXG5GCODONfDhJg/mHFPvLII0cffTQR\ntbS05HK5WCyG8oaww4jo3nvvHRsbGx0dnTt3LghURLRjxw6v15tOp8vl8vz580GUJ6KxsbEFCxaY\nzea+vj6v14uVA4b9rl27Vq1atWvXLrBFiGh4eLhQKDQ3NyNkNT4+jt2htbU1Ho9XKhWr1bpjx44F\nCxYQ0datW5uamtasWXPVVVchexqxsbvuuuuII474zW9+k0qlrFYrlhm88zwsFouFk+RY0vNoyHXI\nYW0Sqqs00SQgmXS7A3jD5XKZj+Mdqek9E7AAw56oM7hheFWrVfAO2NOAGV6f3kfiNTG3kC+o81Ug\n4WR0dJTzF4FFixYde+yxr7322gUXXPCv//qvuhv+y1/+AsWRNPn65z//+atf/Wpzc3MymURttmQy\n6fV6IXpNJhMrUiDcp9Npi8VyxBFHvP3220R0+eWXn3vuufL6RGQ2m/fs2ROJRH7605/efffdJIpH\nZzIZv98/ODhIgrplsVi8Xi8sKrfbjV/E5iD3E5npz8mjMrrGY8s5bfgvq9S4Ar47S2a+EmDTgkxk\nJmGQ1UR+Yn06rcPhqFQqsEuIKBwODw0NnXfeeWvXroVNQ5oTj4jGx8d/97vfXXfddZjoK1asGB4e\nXrx48eDg4NjYGLcWC4fDcHfs3r2bS5/Z7fZkMjk+Pt7S0lKr1Xp7e4motbW1XC43Nzfv2bMH2crY\nCJYsWZJIJBwOx8jIiN/vR4oxEfX390ej0UKh4Ha7LRYLHsrn85XLZWigH/3oR7/zne+Anbhw4UIi\nisVin/vc5+6//35+ZMTk67mC2LkgxqT3TyrgcrSNRiOLMXbF1Bu7GHzwj+XC5rTTvxHYV/hfgbdG\nRFarFdm49aQbSX+QNATJ8SGN9c5eYkmrAzEB8xDeiL1790qLJBwOn3POOUQ0MjLS3Nz805/+FMff\neeed4eFhIkqlUitXrrzvvvu++93vzps3DzMqm812dHQkEgmbzYa+BJAccLVhKhaLRTDv4/F4NBrt\n7u4GB6pYLGL+OxyO4447bnBw0Gq1RiIRLLeLLroI5Cki2rhx4+GHHw53xdNPP42DgUAgHA7DY89M\nE2R0JZNJJtZLy1XSo3RjiyFyOp06Ti9pbnksNF5uGLpZsrErATYtSBYippqOAuvz+ZLJJBfMxpJm\n3ZO9KDiNiCqVCrQqENn37t175plngk8MRl8ymbTZbGNjYxaLZe7cudiX8/n86OhoOBzGDUSjUcgq\nv9+fz+dbWloSiUQ6nYZfsb+/P5vN2mw20JwQEyKiYrGYTqc9Hg8qaAwODiKdOZ/P+3y+/v5+v98/\nMjKCWNfg4GAoFILUyefzLpcLAuzoo4++/PLLP/axjxHRCy+8cMEFFxDR7t27iai5uXloaAjLEjZf\nqVSSop2zXqAqWq1WkNMwSryM6xUC1t+nLL0B6qOUjiTqHSi8C+ho9KxYsKDSub/YOQzzup6z6nA4\nQC8kkRfFywTpJSTUmnvvvfeWW2659NJLpRk0PDz8+9///uSTT37ooYf+4z/+g4iampri8XhrayuS\nKbHEQqFQT09PS0sLHBW5XA5rLZ1O+/3+RCLR2to6NDSE5Ya7Qt0ck8nU1NTEIas9e/aEw+FEIuH3\n+19//XUiWrZs2bHHHptMJpubm88777wPfvCDuLEHHnigvb39+uuvf+SRR0jLp4Q3Mp/P44L8jKRx\n7klTzgxaneJKpcL7DPN7SXDl7XY75r80dnV00Fky85UAmxaQ8KSLchER4i4Gg6FUKvGuilmFVX3M\nMce89tprEAbf/OY3582bt2bNmt27d3d2dnIkdv369V1dXclkEskfWGaxWCwQCCBRenBwEDtyc3Mz\niAmFQsHr9Q4ODiJenUqlnE5nIpEwGo3hcBgyJhgMNjc39/b2trS0jIyMIPpNRGNjY0uXLt2zZw+K\n3ESjUVDkHQ5HLBbr7OyMxWJYsUTU1NSUTCbtdjs0WY/Hw5JjYmLi9NNP/8pXvgILkoj+7d/+7T//\n8z+hFMM/w0q0y+VCRErnKdK5mIjIbrfDqGImfT29WL4Fjs3IJDP4VTgpTeHdgVOPZUxFZzTDf87s\nDAYrbWziRCIR5GN5vd5MJiNfqN/vn5iY4JcViURWr179yU9+8vTTT8cRBJn++Mc/nnLKKXfdddev\nf/1rzF443qEG4QoQAEQEYWk0GvP5PKYxmPEjIyMejwehaLfbzTwjXBC2ZqFQwDPCGwm/vc1mQ9eh\neDze19fn9/vfeuut448/3u12I3ezUChs2LAhFArddNNNXq/3lltuIaI///nPmPNg55No+zA2Ngaf\ngUwh4DgFidXBDDKwXfgVYJPBzqMzjmfJxq4E2LSA/ZfzdlnZwQdJ2SCipUuXbt++3ev15nI5bNZr\n1qwhot///vfymj/+8Y+J6PXXX3/11VcNBkNTU1M2m/X5fENDQ0TU3t4ei8WQZeL3+2HbxePx0dHR\n9vb2RCIRCASwKRARXIJE5HA4EokEDhYKhcHBwZaWlrGxMb/fj/wzInK73T09Pc3NzZC7nP/IqZEk\nLBiTyZTJZHw+H7TvoaGhefPmEVFPT08wGIRv87Of/ewXv/hFnF8oFNatW/fQQw/BgwdhXCqVZNgZ\ntwqXFGm7JMxE0pRNXbYQaZ5D9g1CULGCjz1CMj6Qf6Om90wA5x5pw8vWLSfUQ7BxOBPHkaWEd1cf\n8kS9Tf4Jl8tlt9vhNl+0aBFcc2vWrDn33HORBLlly5Zdu3Zt2bKFiG6//fZ0Or106VJEzkKhELxz\nTqczlUo1NTVBAmGeQwb4fL5YLOZwOMrlMhajz+eDgwQyDyZOoVDAnDdrHcw5qWtiYiKXy0HGcFL2\nnDlzMplMOByOxWIGgwGZl/39/UccccRFF130/ve//7jjjoN19Zvf/Obhhx/+4x//CBk/f/78PXv2\nkJbUxaU+bTYbbg9FEorFIs6X4WEWbBx15oKikGQy63mWzHyVB6agoKCg0JBQFti0gMJIzCHk0DQX\ndJ8yK6VcLp966qlz58790Y9+REQej2fLli0rV6586aWXXnzxxZtuuomI/H6/1Wr1eDzxeJy9BESU\nTCaNRmMgEEDICtqZyWRasmTJ1q1bOzs79+7du2DBAmhzgUAAfnPEpWHKpNNpkDKgpsEvRxrbKpvN\nFgoFWZ8NJpHdbocxBFOmWq2iqj2+6/P5oPPOnTt3fHwcgauurq7DDz+ciC699NIzzjiDiJ5++umr\nr7765ZdflgPidrtRpJGPcMaYdPTZ7fZqtcrcqnoSB4n69xxWZA1Ulq7X1bJS+HvBqUWyYAQJfh27\ntsxms81mk15EuL9kCXZkR4Ce6vP5kAqJK5966qnHHHPMRz/60VNOOQVf7+vru++++z74wQ/efvvt\nv/vd78CANZlMixcvfu211+bOnZvJZBKJBOpcgzHEkWkYIghopVKpaDQ6MTGBXEMiSqVSoLBLZlap\nVPL7/dlsFjyLarUK+t/o6GgkEoEf0ufz4fGj0ehbb70ViURgY2GREtGqVasee+yxSqWSy+W+973v\nPffcc0T0q1/9qre3949//OPtt9/+6quvmkwmPMvIyAhP+zlz5vT09OjSSwA+CFsWKWX1RWfwmU1k\nlLL7P5oFBzWUAJsWsFNzoEtGp2X1THjM4UhEM5S//vWvS5cuxQnj4+MgNUQikZaWFpwMXzz8XVgh\nuGChUAiHwz09PahpzfVD9+7d29raivo6XNHK6XQiUmUwGDweD7YGxBVSqVRbWxsYhlhm+Xwe5a+4\nphynGMOdiAAAy7ZkMtnS0lIul0Eqw+aFNBcQMTweD1ZyoVA48cQTr7rqKrBIfvjDH951111E9NZb\nb4HZwb9Ck3OQzaLv7ZQtJxiyFwwJfyO+zg0vOMdWTe+ZwKC1X+CNHhFKnjBIv4PznLUHdhJC4HEM\nbEoe6ZlnnnncccetXr0aOtBDDz1ERBaL5dFHH73jjjsikYjdbo9Go5gPyWSyVqshcJXL5drb2xFU\nAysYPUdsNhu8fxCZ8C7WajVUhCIip9Ppdrvj8TimIuZ5pVIB4ymTyXR0dIBJS0Sgv4PjXi6X8YDF\nYrGtrQ3NfdxudywWw+MMDg62tbW1t7cPDw9bLBYocKtXr/7Yxz72uc99Lp1O33HHHT/5yU8Qz8Mo\n8boIh8PYNwqFArKYZVgRIwaKL1OZ+B3R5JUyq9qpKAE2LXA5vkKhIJefzFXSJWcQ0YYNG372s5+N\nj4/L5iM/+MEPfvWrX4HpR0RNTU2YbVh43KHOZrNB+zMYDMlkkknn4LWn02nE2HBNECBRYoOTxsBE\nikQiPT09c+bM6e3thVKJn6hWqyg6zHUEsPgnJib8fj+znCHnUHTD6XTys3COF7Rs7gSG8qb/9E//\n9OUvf9nhcGAjQ0wO9ehI6IlTDnKtVuNSiswPJiLOj+aQNb4yZW1fWMa6KJrC3wtWzjDmsuQKEWEH\nR91CqHSctMSlnGVhQMSTTjzxxJdeeunCCy+EYnfsscd++MMfxq+kUqlLLrmEiJ544olAILBixYrd\nu3d3dHTs2rULAVo2qd1uN1Q9/Bd8Qo/HAzIhVEMEvTBtYPDBt4G0y46OjvHxcafTiRIBgUAARL5a\nrTY0NBSJRCA8QE10uVxg3oONheUwPj7u9/uHhoai0SgWBYzL3bt3oyAAUgJGR0dfeOGFtWvXnnzy\nyevWrbPb7Sjzcdddd/X09GAwQZLCICAJGuPJijJvKTKmSESZTIZrsUpNmgOBhzyUAJsWeI8mja4t\nLQDQYZ1Op670wJ49e+bOncu1bZ599tl33nnn1ltvnZiY4PbHyNhwOBzJZBJcCXgjS6VSIBDIZDIT\nExOBQAArJJ1OgxAcCARAU8Y09fv9uVwOUWX433Ab6XQafhvS+g8RUaFQQAwcN4xuTKTV0YAwSKfT\nMBZTqRR6NeGyoGORVm7VYDDAWQE5ajQacXBiYqK9vf2yyy4766yziOjss88GgcVut4NmQqLYMZJY\nOaWUU7u4L6Iu64sm1xTGCVarFb+uS9ebJSVN3yPwnijLK7OlBY1N5pZwjy6XywWjnLRiSNlslqvO\nH3/88Q8++CAYfcCWLVs2b978yCOPgKzR1NRkt9v37NmzePHid955Z/78+ZjSIyMj8+fPHxsbg+XE\neRoDAwORSAQT2+v1wqbx+/2FQgH1LHK5nM/ng37p8XhsNhvMMovFgqkLcZjJZNxuN3ewJM2JimR/\nOPOJKBQKIX0bnoNSqYRf7Ojo6O7uPuyww1BxGPJp3rx58+bNe/311/fu3XvWWWedccYZ69atI6Jq\ntbpq1Sq32/3UU0/B5II7NBaLwcaS9exJ6MqY8Kzt6ZznpK2sWbKxKwE2Lcg8MJpc0A/c93qz4Lrr\nrrvqqqv27t3LlaJWrFixc+fO448/HioqVDxQp5BQmUwmS6USRKPZbIZ6FY1G2V2OfEzUZTdr7YyJ\nKJVKeTwexMDS6TQUZNDDUqlUMBgcHx+3WCzY9LlxEepZFAoFlnBYIdVqNRAIwAby+XyZTAY0J9Rm\nxMlIHgBHERsTEcViMRT4MJvNqVRqYmIC3V6+//3vb9q06aKLLkJFR5b9U9anJyK73Q53DUZVErF4\n5JkIR5pxhkuxuTar0jnfI3DKLfQA1jawCmT5DJAMQTpF6cJyubx8+fK3334bLsTx8fFKpbJo0aL7\n7ruvUqmgDA0RPfDAA/l8/vnnn//5z39+yimnIKa7aNGivXv3trW19fb2LliwoK+vDxOsqampq6sL\nBTWMRmMmk8FMttlsuVyuWq2iNBosLQjUbDaLBnXcZBlehGKxKKugwRMO3QsyCSoj1EpoQg6HA7cx\nPj4OnQlLA7KThLI1NDTEeTJjY2MDAwMnnnji2NhYNpvt6urCs//hD39wOBwDAwMLFiyQcS/OP0Gg\njpm6XLBD+hvwmStS8vHZo7opATYtMJ+YvVusV2JLhRHGC3jFihVvvfUWu7/+/d//nYjuuOOOZcuW\nvfLKK62trYVCgVeI3W63Wq1wGLL9hBxGVCMNhULs5SMihL7y+bzX64UJiA+odODxeCDAUMatqgGf\niQiyE0YP1gMU50qlgiBftVqVnSNQwy2fz6MlGKevMRfZZDJB3Z4zZ87u3bsjkUg6nYbTEvRiq9X6\nwAMPrFq16ktf+tLNN9+sq7DldrthdGJ3gK+GpurWAc0A3kudz1DaAaTtp5D07+W8OMQhE5nrC0Yg\nAx18B5jsWBqwzHBw8eLFKEhBRFgUfEG0BX/ssceuu+66Y445xmAwBINBVNoMh8N9fX2LFy/u7++3\n2WzVapX5F6FQCLIqk8m0tLSAfw8KCdQvFPwlIrCrrFYrqn0mEgmIUnjbOKDFNHoYYS6XixMGSPM0\n5PN5p9M5NjbGDV3dbvf4+HhTU1OtVkOAmYjg8OCmzIh1feADHxgYGEilUgaDoaWlpVKpIO3yyCOP\nhF9x165dl19++cDAAMo/cj2qVCoF9zhpKQGIxHOOI45LjwWrerOnBo2i0SsoKCgoNCSUBTYtwNSQ\n1aEAGO+gEkk+6x133LF+/XpEg41GI2rMg187d+7cZDKJ4DARQaVCtvLo6CiTfaH6gYsoK1uDagjf\ndzwehyEozax8Pg+1tLOzE+5BRLbYVQjbi1lVZrMZoTv0g4eXH1QR0hw10Ciz2SwHzNASularoUIV\nHhwMfoTxxsfH29vbEed4+umnL7roIlQKz2azqAP5pz/9CexhjBiHqUEeQ5K1nJy6kq88INL7L4tE\nzKqCOu8RUJxCHsGoMlmDmXL1lThAnUAXbyK6+OKLf/jDH8KpQERvv/32NddcQ0QPPPDAunXrent7\nY7EY/HhEVKlUPB5PX19fU1OTwWDAZCMi9HZAj3KHw9Hf34/ocrVajcfjgUAgm80GAgFQh6LRKHx9\naAfBYTmEvnCTLpcL4atAIACbBj4VkBJxAlzZuVwuFArB4cHeOazQ+fPnw3AMBAKcAZLL5ZDy/8Yb\nb0QikWAwmEgkstmsxWLhWNeePXtOP/30Bx98EKcdeeSRuCw3l5F1p9j2hW+c5z/+C3uX6VHKhagw\nCVjJ7KdiB2Aul0O6Sa1W47LZZ5999oMPPphKpSASzj///E2bNhHRggULcrkckpbA98PFQUcGBQMc\ndyJCXQkEmRDKIqKmpqbx8XGQfSFLIO1isRhcK3BawqExODgIvx+YgcxvxALLZDIOhwNJPHCtYM3Y\nbDaHwzE4OAjRWKlUEAaHyEQ/FCJCG3VkDoCORUTj4+Mej2dkZKS9vb1Wqw0MDECcLF++fNu2bR/+\n8IfPO++800477de//jURnX/++UTkcrnMZnM2m4X3krRSICQSXHTN3bkNru4dYdnz7oAlrab3TMCZ\nUtAMsIdyGJJnPoZaVkRE2UyItLVr1xLRrbfeCiH0yCOP9Pf333fffSj3fuqpp77++uujo6NHH330\nwMAAyE0oyAnVRObzgWeIXKjBwcHly5fDTRcIBDAr4D1jz2cul2tqakIaJYpxEFEwGBweHkZgmIhA\nA0FapMViAX/PYrGA94jgMfhNqVQKqx5plE6nE5GFeDyO+Q/CcDAYROCNSzKWSiUw7OEDh9K2YsWK\nTCYzPDz8/ve/f9WqVRs2bADttSuQEwAAIABJREFU/gMf+ABSBfDITI9CLcdkMikVZdn6XFfia5bM\nfCXApgWDwYB1W9+gEvNJ5jJv2bLlfe97H+gbTz311Je//GUYWxAkiFehiB8RoUguKlUPDg4Gg0FZ\n2x7ECoSCSCM+mEwm0Bxg0hERcjDL5TLKhkIDbWpq8vv9Y2NjWGnYeogIIQG/3x+Px8FR5EAaCqHW\narVQKMRVc3AD4EmCds8DwikEzPIHxwSx8UgkgttDy5VCoYDugh/4wAeI6I033vjMZz4zZcNJu92O\n8PvfaG6JZ4HxyjnmbLRhM509kYD3CHgRpOUscx0jbJTgzmFFcGsVfJGF2RlnnPGHP/yBL/jUU09d\nc801L7744gknnICTIUtaWlr27NmDxEQiQkIk1ET0GeAyY6hj63A4kKQB3atYLMJPALYwz/OWlpbu\n7u5QKARWEcfGvF4vsjktFgto9B6PByY+RF0mk8E8x9pB9SxOHYHGhlwxm83GnHVwIEEd4v4yCOBh\nlEZHRzkB9M033zzssMP6+vqam5uhgCLx+YknnkAFSI/Hk8/nebdhswx11GTNa9LUPo5bkxJgChIs\nwGSZMvwJ+iYWM/rdXXnllagZT0Rr1qx56623mDEMqcNxV9KazIIcgVazTB8HbwqEOngFg8Eg3JjI\nycddEVGpVMrlcpFIZGhoyOFwwK8Sj8dZH4SltX37diICHXHBggUg47a2tmJZ5vP58fHxzs7ORCKB\nBBoicjqdyG5BzVCOkMMmw6XQpZM0eojb7cYCg1AhIqvVCq+gxWJ57rnnTj31VCJ64okncrncZz/7\n2cceeyyfz7P41/Xr01U5kckuJHhfshk0H6/vwajwd4FHGx4IVtRgtTCbSVeGBqvj/PPP/9KXvuTz\n+dB5h4hee+21Sy65BAY9WqoS0fz585E4lUgkUP+TiNxudzqdbmlp6e/vd7vd/BKNRiMcCeC1s04G\nN/7w8DCSOiDtiCiVSjU3N6PLHew/IuLEKVCTYDyB8Qv5Bx0RggFTETKMu1/CJnO5XCaTCaV1sZah\nJhoMBrZBiahWq4Ein0ql5s2b9/bbb2P0PB5PJpPB48BhgFTuX/ziFy+88AIq3HNfZnzAFoFh5zvB\nHcoeofjrLOlFrgTYtAAnOHZJaYRBnmH2tLS0oD9sJBLp6+trb2+/5ZZbfvzjH/v9fqxArPx0Oo2k\nJVwBCiM8itycgoiQX4wj+XweMmlkZARkPJCU7HY7pi88HolEAq284JFvaWmBXwXb0Pbt26VgYD06\nGAzi4qFQyGg09vX1gQyJrQFrjCu64r+kMd1JSzqBOA+Hw8jFQbF8EpYZL785c+Y89dRTRPSDH/zg\n4osvJqJTTjnlT3/6Exc5RX4PEXF3dhn/wwbBJinoYWjdiYeFyORyHiqReSYwGAy6iie1Wi0QCOC9\nVCoVdmHNnTt379698+fPJ6I9e/Z885vf/N73vicv9dvf/vbOO+989dVXm5ubUbEabxCvz263Q12D\nkcE/AU4s23bQ5LxeLw6irxgRlctlSBTO9yDNfAQ9EsFaTlNDwFjXRhWZiLgfrvxrtVph87ndbr4N\nuDHRuweZLZj/SJcEvZ7XptVqhVmWTqedTieKb2FIUacNfdXj8Thy4K644orrr7/+Zz/72eOPP/7w\nww/LMYQR1traOjg4yPs2NhPE3uQTzZKNXQmwaUHyiYkItghp8SS0F3r00Uc//vGPExEqX+Tz+dNO\nOw2foQ1hP8WEQziaiGw2WyKRwE4BFyWuXCgUAoFAf38/mvJh5bhcLjCDkYCCdBbcDxqmIGYGgy+V\nSiGiBj/hm2++iZtn85HdPpj3Pp+vvb0ddaGYp44nRQgtnU6DIk9azzPU5vB6vdiM+vr6wuFwsVj0\neDzDw8PIISMiJIqFQqFNmzYtXryYM4cikcgtt9zy5JNPXnbZZXAlERFcOpBV2Mgkq77ehctvBIEH\n/CKYILMnnfM9giRxsFeQVR+2lRctWrRz5050DsLJP/rRj7785S/v3r17wYIFqA714IMP3n333WvX\nru3q6orH4+FwGKLxnXfeaW9vRzJJLBZD0iTXwqjVarLpSblcRrokctGYVNXU1AT9DzEw2EPwlxiN\nRuSEsJ8AcWKDwYCnYLcbDmINMpcqk8lg4kFCsHIJwVYul5H9yXUxOEaLPnxEZLFY0MAlHA53dXVF\nIhFUenO73Vj7zc3NPT09RqNx1apVRLRx48brr7/+G9/4BhHdeeedl156KWn1BEql0rJly7Zt28au\nXXhT2djCQenAPOShBNi0AK0Nc0UGYywWC1h8q1evfvjhh6GNlkqlUCj0+c9//pFHHlm+fHlPTw9W\nFJwGOAENivAZyb+QE/DXEZHZbB4fH+/o6Ojr6+vs7IQAczqd4JLAKccxMHgtRkdHUQIY7zSTyTQ1\nNVksFrRr2rp1K7RaFHYDy1FXSNdms82ZMycQCHBzB7TLQ940Ct7AMQIpNTY21tnZuWPHDvTuQ9IY\nupQhrRUbnNfrHRgYMBqNhx12WFdXF9fb7e7uXrx48YsvvkhERx55JNuvKLKFrjSwOEmUN5QyDBsN\nXFjcMpGI0AgbBJP3eGocymC9jSvJQmOTlSfRKXjFihVbt27FyRdddNFtt92G7+7YsQOk076+vk98\n4hNojjVnzpyhoSHYSfPmzctms6jYybMLbI54PN7S0oL6ajWt2RuchyDxwuoire1qoVDAEoNMMpvN\nqFaDdEBO8IfbDWcGg0FMNsgVn8+HeF42m+WSm5hU+EUuFpPL5WCuwTEORx8SqFFcDRFcIioWi9Fo\nFFnM0WgUFEqcxr3aIQ5RaO3YY4997rnnvva1r11yySXhcBhS7cUXX2QnYT13F2RFuZbhg31vJ8fB\nAZUHpqCgoKDQkFAW2LQAHRBGDyx0qH4cpHn11VeXL1+OViPt7e0vvvjit7/97Z6eHqSGQPUDiw9c\nJlR4IiJUWgPbiohMJhN78O12eyAQgJKFv8JjAN0wmUyCOkVEFosFfyqXy5lMBrkj8+bN6+/vLxaL\nfr9/YGCAtTauZg2VTRJ22SETCATgFQEVAt1YZN/LRCLh9XqTyST+C3UbbBGHwwENNx6P46/5fL65\nuTmdTo+Ojvr9fiiqw8PDixcvfvXVV3/4wx/+8z//880338xdMZmLgWI/shgB7lmaZfIrujwwFOB5\n72bFIQ+2wOBGAyGovrgJE+T+3//7f0SEBC8ieuqpp84666zW1lYiOumkkx566KGjjz56eHjY6/X2\n9/ejotKmTZtAI0IxJLy+trY28NfhwZM1bbEM0X+Sa4EiywqxK+4ExH4OMGPZskcmJadO8uzCwoTL\ngWtoIfIKE5/7NiDhEnYYZiPcoZlMhgvWgP2EocNiR4FseFBIa3qCPEt4L3HxpqamkZGRiYmJCy+8\n8Oqrr77zzjuJaP369UQE3gpqCsMPicIfMIu5PAeOzJKNXQmwaQGOArQaQeCai2micM7vfve7c845\nB7MqGAyuXr36+eefP+WUU3bu3MlVdJGhgg7iVqsVJ4fD4XQ63dTUNDo6ChcZtz4CjxbLBk4zRIPh\nxPf5fPl8Hgsbnne49Zkesm3bNr/fD1eJxWLZvHkzPAxczBATnUQZeG5kfOKJJzJHAxyqRCKB/rNY\n20g0RkvcSCSCwBVOgL8FlGKsYbRlCgaDWLpIHY1EIgMDA3Pnzt29e/cnP/nJDRs2YCp+5CMfGRgY\ngMArFouIN5AWpWAOJ/wzOIJblXQ4FoFqes8EBoNBtv5CUiCmE2kqBWeLf+1rX/vBD37A3/3lL395\n4403NjU1IZj02muvHXbYYaDboPLn8PAwaSlc2PGZlBGLxSqVCsqEIqEKbjfUS8O/TqczkUiwkHjn\nnXdYWeH5jP+6XC6Hw9HR0cGhOxCg4Bvn/uAImsJnyIRD0tYFki+lgxqkCSwZ+Os8Hg8YkkidZuIJ\nfPUIxUF84iJcmRo3gBTGLVu2HH744blcbvfu3VdeeeVXvvIVImL1zufzIWlSMubhyZSJ5KofmMIk\nIGjMY8X7I1ILiejZZ5896aST+PwNGza8+eabiUQClQmhn6Kgtc/nGx0dBTOKiCYmJnw+38jISDAY\nBFGis7OTiLi/ERdrJyJofNAroS1i0qOmBhRDruTmdDqHh4dReA29NFl3ZmOL22SQthNxyipSSltb\nW5FDww0pEHVzu93JZJJ7Y+L2uNIo8mO4HjnMUJSbQ/Y0ESF2iJybrq6uBQsWgALwk5/85LLLLuOR\nlBkLfHFdjFo2CeOcNiSSq1qIMwFbYIg7giDKVXFl9PTqq6++9tprsZ+Oj4+Hw+Grrrrqpz/96ZIl\nS7C5R6NRm8329ttvL168GHRZCLCFCxe+9dZbnZ2dqPaLqzU1NSFxGD/KNUVhMOF1x+PxgYEB5i/A\nO0KT69iyRS6ZDsDChQu9Xi+MOSLCZQ0GA/LD4EUgTc8D95VVw3K5DPIhaSIE8jUWi4F/D9nGDCZo\nlsxX5K/gCryx4P5bWlqGh4fz+Xw0Gt22bdtXv/pVIrryyit/9rOfff7zn8cNSF2NuzihZAFpBKtZ\nsrGbD/QNNAaQCELa1GEBhj36mmuuOemkk7Zv3w5vidfrLRQKfX19hx9+OGgInLMcj8ex6UNi4WAq\nlQqHw3DORCIRzDz03HM4HC6XKxaLwUdRq9Wi0eiePXtQDpi9IqgfWq1WoUhi5cB6e9/73jc8PFws\nFtEYDCdj0WLqM9ccCxhEjGw2izq8yWSys7MTZYKRv4KT0+k0KvegFgl7OOGfrNVq4+PjoVAIg4Zm\n02azORgMcsoXaqpC3P7DP/zDY489BjbHqlWrzjjjjJdffhklGGKxmOxUC28SRDURgfmCrhmZTIZF\nHZa0jjuq8C6AXZuNBum/ikajqDQ9NjZ22mmnkWb0hMPhu++++7HHHluyZAmTlbLZ7I4dOw477LBY\nLIbtFYmSO3bsQImKUqk0d+5cWOfpdBp1qsLh8ODgIPoKkVZfrVKpQH9CbiIuztKUpReTelDOg58I\nwnj37t2ysvuyZctAoPf7/ZlMJh6PM9UC7CF4JjDPwTME3QMOdtx2S0tLKpUCp79areIKqLyDRZdM\nJtkQRLdV+C2hoWJVdnV1oSGfw+Hw+/2/+MUv8CyXXXbZ6OjoDTfckMvlWHoh1QQda7mjGCeTzAYo\nC2xa4ERmmqzNgXy1YcOGH//4x5zddeedd1533XVwgiMIhAlnMBhCodDQ0JDNZguFQqg7hcbkYP05\nnc5IJIKlCBccnG8oMUWa2yEQCBQKBfB34czBPOaLyN53BoNhcHCwWCyWy2UU75GMMvYZ8pNCvWV9\nFmvs8MMPB8O4Uqkg8RPmFLYPtIfm7yKVDQU+mH4JexG1FbjqPDwtcEt6PB6UBXr66adXrlz5qU99\n6p577sFewzX+cYe6zFldf1Ede1hN75mA6X8AV0PXnfb5z3/+5ptv7u3t7ejoIKLvfve7d955J/Kf\nBgYG5syZQ5p9D8tp/vz5AwMD2GQhA4aHh9E8Bf7zcrmMOdPV1TVv3jzY+qSFb+H627179/j4OHvS\nmCEpy6/Up2zK4/WzZdmyZWazGanT+BPiZ9BZQd8l4Wy3Wq3I7sIMhDIH5ycnuhERroBJ3tPTw/Wo\n+D6hGeA46MSdnZ1PPvnkpz71KWh16XT6/vvvP+mkkyKRCKQ1N3CBDwPPwh3h29raEI8/5KFYiNMF\nZgyq3UB5JCJQh8HWHRsb6+vr6+vru/baa4nI5/Ohi3kul3O73W6322g0dnd3o3tQb2+vz+dDOA1B\nI4SOkcyECoEoZtHS0hKPxwuFAvJakHyDqlF+vx+1CWCUcNYLNotEIgHJtHDhwmAw6HA4Fi5cuHDh\nQshCeDmYzcF9ldBUCcomgGpviPaBnptOp6vVqs/ng0hDrItLYKBsB+IcyNHO5/PofOj3+xHHxg0P\nDw9ns9lFixZlMpnm5mY8y0MPPdTb2/vFL34xGo1WKpX58+cnk0nwX2BoQnr5/X4INoRYsPh5P8JB\nrGeFdw1YydipSYS7LBYLOnQT0Q033HDzzTe/8847kF5ElM/n4/H48uXL4/H40qVLYRnD8Mpms01N\nTQMDA5CFPFVCoVCtVkPpXlhjIyMj/f39y5cvR1kyIJ/PFwoFRLDQ1o67ouBfECV4PrOGR5qvD0C9\nKC6/SZqhuW3btr1797700kv4CShbWCnIvzQJoDE61jh+Ef7DWq3W398P/woRcRHFfD4/ODiIVEuP\nxwMlmCvysAsBeQLd3d1nnXXWk08+GQqFQqHQsmXLnn/+eSK64oorMplMoVCIRqPRaJRdEbhIKpWC\n7wHuk9kAZYFNCzKjk4sfElE2mz3llFOeeuopKHQ4Yc2aNcPDwzCeOjs7k8kkfNOckozEXqwosJig\nNqKQAaYgd4lEVj9+DtULubJwJpPB8XK5HAgERkZG0J4c/hZUPi2VSul0urW1ta+vD/v7n//8Z+7k\nhBuuD2nUw+l0Njc3+/1+jpCzHppOp7Fc4RVBHA7RbK6UCkcTc2GIqFKphMPh7u5uhLXBhySiWCyW\nTqcHBga4oA5UeGZRoipKTWv0Bx0ZzcnYHcqcLjW9ZwLpg2UTR9eu/umnnz755JOJqFKp3HjjjUS0\ncePGtra2rq6uQCCAWUpEra2t8CSjZRfLGHTVgrIFHgcRZbNZuONAfIBiR1pH74mJCSyZPXv26Cot\nQYDp6o1herAHhfOvZeJUfUIk/rtgwYKmpqZSqQQTCnLCYDCgtC5oHRxwwsOiem8+n+eCMlAHMScR\nxiatizooKvBzQhTBh8FsL2hpO3b8f+y9eXSkd3Xmf1UlVUkq1b6ptFerW73a3U27aQ9gN554AdsM\nJBlPAscGs5wEQkiHJBybEDAOnIRhJg4hYYvBJgnjGLCdQDAYE8B23HbstN2L7e6WuqXWLtW+LypV\nqX5/fM57542anKPgkPlh1fePPupS6a23qr7Lvc99nudOBAKBI0eO3HrrrR/96Ec/9alP6e1NTk5q\nM0JzE9qLE+VX5GhlYK3RGq3RGq3xczlaB9iGBsUkUiJt4UpA96Mf/UiM9GVubm5ubi6bzYJTR6PR\n6enptbW1wcHBwcHBM2fOuN1uIiNFBYn1gNfW1tZAFGEJE09hd728vLy8vOx2uxHHYGPj9XoBOtrb\n2+PxuMvlslqthUKBXKRYLKIVw6ve7XZrER6xi5hyL7VMJD0CghMDmiMEXl5eptpM4Xptbc1isUCm\nB7vgVulsu7q66vP5YBtjz9HZ2YmdDzF1oVCYn58ndcMBgdvr7e1ta2v78pe/vG/fviuvvLK/v392\ndpb0CxUdsbBCW5THVaPDIFJujZc5tIrj8XhWV1cpieHt1NPTY7Va77rrrquuugpOh9Vq5ZtKJBJt\nbW1er1fdNCKRyNzcHLkFsFu9Xk+lUqlUCiaIy+UKh8PNZpMJ43A4pqencSCEVcg8bzQacBfVsYnF\ngkEiDElmAgO/3XXegGpGSiKoeKAYPcGhJjIbFxYWnn/++WKxGAgEQE3gxMNTZ7lBiyXHgqyL6gCU\nmyQym82qkbff7/f7/SyTQqHQ09MDcsArAiHm8/mRkZF6vQ5+HgwGvV7vO9/5zlgs9olPfIL+giIy\nOTmppK18Pq+Fxk3iIyUtCHGDQ0EJbRynHIeDBw/+6Ec/ojUXNIRrrrkmHA53dnbOzMyMjo5ihi0i\nQCWAJwpeJxKJcDg8MzOze/du2hex3mgGkclkWDZgcViiMU3ZwaE2hEIh9hfM4LnVRqPR3d3NsQfK\nBw4zMTExPz9vdgbSo0vVzRd/AvC1RkdHKYd0dXVxY+Ymk1QpUJ5hT4wamvWPzVVbWxtg7PDw8MLC\nAvK1dDq9ffv28fFxEQkEAk6n87nnnvv2t799xRVX6CcPTHRx40RuGIBISQdNo6nKOqP01vh3jXU0\nzjajm6XaFNE5CDnE7bff/sADD4jI2NjY1NQU5ILh4WGCj0AggGIPCq7b7SZUokMKGzcMBTEUuxwG\nRHhqIY1DGHQPSmtigpfRUZgNiMXgiajvFCJoMYlhzD8r+GwWWtnt9pGREafTScCnSjjVw2kdDuoW\nIgEmP+aKLpcrk8mYCSZUkcvlssoSeEV0ci6Xa3l5mZoxN9BsNsvl8sc+9rH//t//+9vf/va/+Zu/\nEaMfmGKk2hTCrPl5ZY9WBrahoTx4wjcN8USkq6sL8aMYTY33799P76toNEo0SvyoRSDKsNRsOQaC\nwSDqmVwuR5SHfxrsRxiAQO1tRsNiojZyO6zbisWi1+utVqtcoVAoMK25Qy0n+Hw+tS7kUlgS6Oml\ni1N/UEsLAHePx2Oz2fAj1sMYHj/RK7sAZBDC5Fwuh8iso6ODKxw/ftzn85FNhsPhiYmJaDQK5QxS\n2X333Sciv//7v+9yuVwuF1E2R6MYuxL6PF3AmJTDFlOZdmv81APxQ3t7O58586FQKDDP77nnnksu\nuYTKq4jkcrlKpVKpVEgFhoaG0I3AWaCMBOk0GAzScIuWC0zCSCRCUGWz2dLptN1un5ubo1irDQeK\nxWK5XMYbl+XQ29vb29vr8/m4N8pjxWKRH7S/My0jWHHmapMYE0lPL85sTbZQNK6srExPT09OTmYy\nGcSdaGPK5TLc2u7u7u7ubtohicjy8jLnK36klUplcXGRQ4h8iww1FosR+KJuJCWlJEw3GTGWYbFY\nTKVS0Wj0pptuSqfTf/3Xf7179+7du3fncjk6CHKTLGQlNG6G0crANjSY1mqRnslk+vv7RWRhYWHX\nrl0vvPACidS3vvUtEXnLW96CqDmRSKDbVQ0TYRQUYR70er3T09ORSKSrqwvrDbhzyWTS5XLhW4/b\nvYiEQiF+QF+pan8xHJ7w6cCrqV6vo5ImCWsz7Lfr9frs7Ozc3BwZm5i8AFQpbO5CYjWavNBKhrN8\n586doIXAiQTObGQcIVgPsIOwMaE+zmazHJ9Wq5VdhuNKNxH+HRsbe/DBB9///vf/2Z/9GQ2lJicn\ne3t7YSerH4/Gs+vajbacOP5DhjkDGxgYmJ+f5yhi6k5NTUWjUWzDbr/99m9961vI6oEBJiYmLr30\n0ng8zuyCQ0tOzDeubKBGowH3IZlMQqOHpGO32z0ez9LSEjRdEVGCu91uxw1A58zExAQ2S8oGMmdg\nAGtqIqMxlphQdBX1/8QWPEwwrhyNRjVnIqYkJbXb7XSbJG7TFBNxZ6FQgHXJMiEjNDt6NI3WMPV6\n3ePxzM7O9vX1Ac8ODw8Xi8VYLLZ169Zbbrnl5ptv/tVf/VUR+frXv07QCZrCwqe7xSZpJNQ6wDY0\n1kGIBPsisrq6+md/9me/9Vu/Rfpy/PhxEfnkJz85Ozu7vLy8e/fumZkZNWUHNw8EAouLi8FgkKOI\nchfp0cDAAEpkEWG9gYcQ4omItqBlm8ZUnhujKS25ERIQv99PrYsYs1gswmiamZmhMHDs2LF1DgXa\nB1JXO6ZN1LTkXwtr9uzZAzjJOuS3IELcjzaLomK3srLS1dXFgS1GIyifz8eha7PZ+EC2b99+7Nix\n3t5erCBvu+02TvS3vvWt4+PjgJAc3iLS3t6uFDUxacLIdDdVMeBnMXTaB4PBRCKB8l3nzPT0NK4x\nIvKrv/qrzzzzzMDAgBien0CFKo4ExNNjDD2yGAkQbjVqpNLR0eF2u8nG6LnF40RslIj6+vry+fzk\n5KSIeDweNMvPPvustoQ1typeN4iBzJN53SNMMzEiJIBrM33xsssuqxvDbrfrMqQZHqCoEtwBQq1G\nJzAGUR2QO+p+lra63mDPT+6bzWYbjUY0Gj1//nyz2fzRj35E35nXve51zz77LCe6mRq6ecDz1gG2\noUFx5SeWYS6//PKnn376/PnzW7duvffee0XkXe961/XXX59IJOgYq4ahHBtq+Mb8ps8eaiqn06np\nGl4DlKapVIkI/rlU4NTJVIwmszTStNvt5D3sESi9eAmNQM+ePevxeKamporForaOpVnlusBNFwbl\nbrIcXnFgYCAYDGLCxiuqPYcY/sLql0E3FgBS4nQOIT3wVFdQKpWi0SiB58zMzKFDh/7hH/5BRG67\n7bZPf/rT0Wj0woULFxfq+ILwLxCTd19rer+cof5JHBvaa+3HP/6xiBw+fJinffazn/3TP/3TwcFB\nTUQymQxxG/JkEQHcdrlcQNyKE1DlrVQq4HJMhmAwqKQGi8WivhisJqYTUB4pEfqNTCbTbDbPnj3L\nDNR1hHciKmMRMQtINA8TU9ZuXgXmn/UJnHP79+8HxMYlQD8u7dLHMd/R0dHT08MSJkdUZJ5MFL9g\nu92u0R5UFLSSWtLu7u6en58HmfyDP/iDX/qlX+JTzWazO3fuPHPmjNra9fX1LS4ubpKZ36qBtUZr\ntEZrtMbP5WhlYBsaEGRzuZyGOWaAIpVKkf5DDfra1762uLhI9Vvt/sQg4y0vLw8PD58/f54iLYUi\nCrB+v58agxhmviBvNGjgQYoHcGepS4vB0IN2aLFYuCs83LAbKBaLfr+fNisulyudTmcymUgkMjk5\neeHCBXPWpTJthSBwx9EqNw8ybfr7+yH7qnkVsTAOv9rYAtI8SZiZ9RsOh+H3JxIJnBJFJJ1OU5wL\nhUI+n+8f//EfccDq7++/4YYbfvjDH2qOJUaHT17XjKLo/bem98sZ+nVrcTQQCMTjcUWM+e2rXvWq\nYrE4PDwMj3THjh0Ik0ERcYXWNGVlZQV9BV+W3W5Heo/eg4QPoiDeNLi0kNvRJRKxPBl83WiMDsXX\n6/XOzs4yn8+fP2+2DdS3w5TQzNL8w8WeZMDpcKmw1BGjurZr1y6n01ksFlGPiOFoRXek9vZ2Ph9W\nBKUynqmJrBjsMAi05tZIXEELafF4PBKJxOPxaDQ6OTnZ09PzhS98QUQ+97nPwXUSU1Mb/nCTzPzW\nAbahYbPZEKOASyiEZbPZtm7d+tJLL01PT4+MjHzkIx8RkW9/+9vgjZlMhjKvuv9Ra8WHl9nGDK7V\navj29vT0qMcEUImIYBuZjYbMAAAgAElEQVQqIihO6C1LXZon0JicgpmepkxiQD8MnODi12o1nGYw\nFFhcXMT7g01f35ouMCRiIB5mknGtVhsYGPD7/VA8xCiYORwOanXUS0SkVCqFw2E8D/P5PDsaFjtd\nXV0UC6empogJQKssFgumkU6n821ve5uIvP/973/mmWcuv/xys6mdbjraY0WhRYor5sJAa/x7h7Ly\nms0mgi0+/H/5l38Rkcsuu2xqamrLli1vfvOb5+bmCFxEJJVKtbW19fb2zszMRKNRjG5h6mISwVcP\nXwOs2O12B4NB6AwiUq1WMaqoVCr0agBaJD6D0Ajrldtj2jscDoJFrpnP551O5/Hjx7URD1NFV7F5\n6ERSnFBZQvrIOuDa6/X29/fzjtQjEdBvbW0tm81yz0Sx0JrgQPIpcWSWy2X8RxC98YGEw2Fcv/kr\nXmt+fn7btm3/8i//cuDAgeeff55gVAwUkcXLAs/lcpunnUrLjX5DAzWlyizq9Tq7cDKZHB0dFRHK\n1yy/F1988eabb/7+979/6aWXJpNJ5XN3dHQsLy9Ho9F4PJ5MJnU5oYCZm5vDA5dFQvqCyqparTK5\ntW8CbHIl4wUCgWq1ihGiUiowmoIET+WcdYhnPCTgvr4+q9WKrTBEEngf6lgPCR7DOjElNFxqfn6+\nXC5feuml9APr6empVCqZTMbn83EnvEen07m0tASBOBQKod3Bcaqnp6e/v//UqVPbtm1jTYZCoamp\nqXA4TJP4Wq32+7//+yLi8XhogYhbsfqWgvirEEf7hGkxvzV+6gERRkRQEBPj/93f/d1ll10mIrVa\nbcuWLXBwCoVCIBCgigO9IpVK0eCDr4YaT7lchmrkcDi0YBYMBonzlJtjs9lSqRRRYDKZDIVC3E+h\nUCCOhLKoLvX5fB7GB+uC5xOf7d27lwX40ksvMaVZKVoxJZXnOIESqR0PxAjU0Iro5OcJmUwGBYse\n8xpNWq3WcDhMhEocSQHMbrf7fL5EIiEibrc7nU4PDw+fO3cOb1WSRT7krq4uIjBWFlHd+Pj4jh07\nlpaWent7H3nkERF5wxveoHleW1sbn79iMJthtDKwDQ00JYjAzOoiZpu2FAJCefe7300yBEkhGo0C\ngm3fvj2fz0Ph9Xq97OPaIZBS9tatW1nwVLyx1XA4HCwGWjDjDSpGxCeGdBGaPieTiKCaUiqjhoQu\nl+vs2bPsTWCS6K+Z/TrWGSTqStZHwCc7Ojr27NmjIS3HpEIx7EdQsESElIslBxA0Ozs7MDCAeJMw\nluCABrsWi8Xj8bDgDx8+/PnPf/43f/M3v/SlL0F6FmPNEz5zWTPtsLOzc10XqNb4dw0zhNhmdC3Q\nHSORSASDwQ984AMnTpzIZrPhcBh+Ke2E/H4/Ds7Aa9DHcdHNZrO4QouI3+/XKWE12rwx9xwOx+Li\nYigUyuVy2hzS5XIR/LlcLghQYsw6jkbMrEWku7ubjuQ4XyuJY3x8HE29GDC7mPpF8Ab/LTK9Wd1s\ntVr37NmDoIXfVioVFHJra2uJRIIaAV4bWD4Szqozcnt7eyqVGh4eRm9DvEVaCSkXVEaMri4weFGI\nkr9+6UtfuuOOO775zW8ODQ3Nzs5yEMIXXbecX6mjdYBtaMAvQrELvqGVsHK5/P3vf59+SKdPnxaR\nN73pTQMDA9PT0/v27XvhhRe0KW0qlero6AD9o5wmIpVKRVvS+f3+WCz2qle9SkQWFxcxWOJgY5kR\n6obDYeT3iuBT6MInVMF0i8XCH5JOBQIBbuPkyZPkeUp0ZL9IJpOzs7PU5NRqgRAVgE4FYWKUoETE\n4XAMDAwQ80IwU5qlxu+I3rgTTk0RATxxOp3Ly8terzefz8NOBGlUcbdZ3UIc8F/+y3959tln9eR2\nu93ZbHZkZGR6elpbVfEWzMYHrfFTjHVOHCTNR48ePXTokBjw2sjIiGpp1aUF12mNq0Qkm836fL5c\nLtfR0QGewW6LmL27uxuqIfPK4XDQDA/0Wwz/tlwux+oTQ7bI/o61B1g3enkRAfFOp9Nw/3RdlMtl\naPfNZnN2dpY4UiMzTbZYFLxHCnJaCWaEw+FQKOR0OrF/E4MKi3BTXYzZOliMTqeTO+E2XC4Xdtti\nuLWJiMvlwpcAQi/1NgBYqJvFYjESiTz22GNiLMNLLrmEthiMTVUDa7EQNzrYMetGsy4eBMiiJBCP\nx48ePXr06FEMn0ZHRx977LH9+/fn8/lyuVwul8PhMMyOQqEwODhIVxGXyxWLxXp7e8HNfT7fhQsX\nLly4MDQ0RDWYQ4grsF+DUTD1EUJ2dHQkEglIvbhfwxVGMZ3L5WhWwj3v3LmTdi3JZNLn86XTaSwA\n/H7/zp07qbGpFyIcX7JGljSVCRGhoUapVJqYmIjH4/F4nHXOCyFkxhpARNxuN+rUSqXCeu7v7y+V\nShTGiQy4ckdHh9frJd7P5/M7duw4efLkyZMnDx06RJQQjUbX1tb6+/v7+/s1B52envZ6vZxeYnhX\nbpI1/LMbdrvd6/USQEDsbjQanF4iQpRz6aWXNpvNSCTSaDTwi5mbm6PDDulXLpfL5XJ9fX25XK6n\npwdsvKenh/OgVCphIuPxeCBBgBmEw2ESMs4PLDDa29vxWtMWdExdr9erunW0zPV6HX0IRylwHLMR\nAycRsVgsoVDo8ssvv/zyy3fv3r1//340yKCLlAyQEjabTRWuiUg0Gt26devIyIgimbwipBKa0yqs\ngj0HGmdcQrgNq9WKQaJqyMjeWFwul2t2dpbmZBzeLpeLVYkXyYEDBw4cOIBEYWpqSkTwBxCjwcV/\n1hz5fzxai3xDA4UKQBlJCaEfp0gwGKQz8sTEhIi8/vWvj0aj586du/HGGx966KGDBw8CgqnpkTnB\nd7lca2tryWRyaGgIV1POSK/XS0mMp6mLj8fjyefzwINEfyICZ4kdRI0T8dpBmKJeOyKysLBQLpfx\n+8F9ilfE6adUKs3Ozuruz7vW+FSZfgql8sxdu3Zxz5VKRdNBRD9i2MGxH/X09GjrWDp28sxcLqe2\nHQChMMG06L26uvrcc881m83vfve7N9xwg81oh0hjC213qQ4p3Hlrer+cwfcoRlCvTa10rxSRyy+/\nPJ1O488LaEaARehTLpfJtGZmZiKRCLkFxitIcfmOKBFx0ogI5KNms+nz+eLxuBpScAOwc8EDmAaN\nRoNGeuZCGgZmHo9nenra3E6FlYKxk2o0wavVTW1tbY3TolKptLe3K3jOGeZyuXhrgJasOxEBFyWq\ni0QinCuhUIiwjMROYQlaw5B3kmaxWGA722y27u5uQmG9jfb29mq1GggEKpUKE/7o0aO4DHu9XjYZ\nMaoSm2TmtzKw1miN1miN1vi5HK0MbEMDBFwFUlRc9Le7du167LHHgsEgvR7e8pa3+Hy++fl5alS0\nmhQRv98PA4oIkbrRCy+8sHv37uXlZUrcYihUnE6n1+slMNTuJwS2BI9EuHoPUBbN8SBIHe1O4Afy\nTPK8U6dOQeJSJ0O3293e3k60ePLkScUJuQfK5pTlxZCpEQ5Xq1VC8t7eXtzKIWvQGEJE7Ha7lrIJ\nk0Wks7MTXgnYFG9KRMjSisWi2vBD+h8aGrLb7YcPH7799tvNCIlmh6qDYbQysJc/YBuJCIIQcm6d\njYyrrrpKWUI8gaSf7wijFhHx+/2FQgFquM1m6+3t5XFoFICKShy1Wq1cJBaLhcNh3Ht5HH0h8KMS\n3FdXV+GMwOVhPlCR6uzsnJiYwPOMQjINfXj17u5uUhmv16tOoQgf9RMAPMcgSsVhNGGnm6U6vZE4\ngkPWajVqdYD8aN3YClj4Foulr68P6m+j0UgkEkp85y2srq6q+0lvb+/S0pLf78/lcmwCoCz/9E//\nBIuEd0o+SjlZ4fRX9mhlYBsa9XqdGQP6oacXjXmuv/76YDA4OTlJn+9du3Y9+uijQ0ND+Xx++/bt\nL774YigUCoVCUBBZCUAxS0tL27Ztm56e7unpQYoLzkYbZby32fEB8ZF6cFYFg0FzabqnpycUCmF+\nr2sGDggFIdpbYIS/uro6MDCgOi23281lKaQVi8WDBw+ydLFZ483CNFHSMIgHy54SHQ3JstkscE0k\nEsEXXETA/SHW8yGAilDcttvtNWNQPMNxB3+ggYGBgYGBdDr96KOPcg8HDx70+Xwqd4P9oURNhSL/\nEyfIK3NQymI3V/ItMQ0MWxGJx+OwIahvdXV10ZKYAhJVXpqJKB6ez+cBfj0eD+IKZh2HB12bIe6H\nw2F6DTPP4UcgDYYrxPOpdTWbTbfbvbKy4nA4mGkUkPbv39/T0+NwOCiyUnhzOBwIUejOhUIrHA4P\nDw97vV50n3AmqdLxXvihUChgdlWpVHAnKBQKNH9AD2C1WgnXcrkcZTw1H8DXsVgs0mCBil0mk6E9\nGKUKTkScTln4tNOjXtDd3Y37Ynt7+8mTJ0WEdgHVapW2fB6PB2bKZhitDGxDgy1b/R0ikYgKCe12\n+9DQENUvxj333PP5z3+e9jyLi4s7d+4km1laWtq+ffvc3BxepaRrbrcbhh4SFm2jMD8/jyNqW1tb\nMBhUCRpxHBYDiD1FBGoybYdKpRLUEioTiEPNDYpqtVqz2VxcXMR3EdoVd06i1t7ens1mOQ80rMZ0\nAI9wEeEYxkFAw9WRkZG+vj4kmalUCpMFEcGAXx2NCZBRYa+trWHLTTmB20bIDJfE5/PBkfmFX/iF\nVCqVyWROnDjxvve974tf/KIYJrNiuPeKsc9Sp2yxEF/mMGe6WgNOp9OkZSKyurp6+PBh8p58Pg8f\nAUtMaHhqFmOxWJjzXq93ZWVldHR0cXFRRHw+H/NfRBqNBq+ovu8k4srg7+rqwjyaZyrXjowNAxcz\nkkGTBw6ShtEME/tBgj+9st1uX0eCADUpl8t+v5+3nMvlWFkUbpvNJgtQOxDxWmperGymWq1GzoSW\ngIO/VqsNDw+Dr+RyOfOdAFcQAeiVqXzncjn9kEUkHA5/5zvf8fl8FPPUFWHzzPzWAbahoXhIs9kM\nhUJMbhEZHByECPSVr3zlne98J08bHx9/9atfvWPHjmw2e+DAgR/+8IcwCxwOx9LSEs2QdLaRcLCD\nI/zkG2GVErIpkgPFg5TF4XAsLCxw5aWlpS1btiwvLxM5sonDx4U0sbCwEA6HeZwSMfCmmXGLTQYx\noNPp5MnVanV5eZm9Roz6sBg8dTE0WORA27ZtI261WCz0JDS7ipC8Yr0jBstfk04xuJ20BIQrnEgk\nVlZWDh48KCLQYSYmJo4fP55Kpfbv38+T6VIB+CkiakYghvz8Zz87XrFDwwLV9mFzrmdSV1fXwYMH\ntWcCERL9SgqFQigUWl5eVokFMQqpBj5hYhDB2azbjT6xCB9tNhvGuCB4Ykw/gDuwR56vdtVwfzSq\n8/v9SAZnZmZgQIjI/Pw8wAOvyAyJRCJcAebIwsICazmZTPKWwTNYs+VyGeMb7Quj9m9Wq9Xj8SST\nSafTqUob2qOgogGHEBFctsEzuY7muCRnTqdTaSPkgtCJU6kUoZ6IJBKJ8fFxBKNqf0X0tkk29tYB\ntqGhSnsVi7D84vE4AVqz2Xz88cdpAzY5OfnRj3703Llzbrf7hz/84Tve8Y4nnnhCRKLR6Pz8fDQa\nnZ2dRasrIri6wdxlC9BiFUvUbK1dLBb37dtXKpUKhcLU1JTH41GvKU4FlFWsdlRl6kZPxwoxmopx\nwLC81cYiGAwiT65Wq5xPbUZ315mZGf5cMzAxSInK76LHRE9PD8G4Ov2Ab7ANmd8gSSrUZ0JOEUEu\ng10QAiMC57Gxsba2tvPnz//2b//2Bz7wgfvvv19E3vrWt4oILkdjY2OaB6t3fmt6v5xhzsCoPJG+\n64O1Wu3gwYN8p1pYYlJ1dnbit0mEB3fO4XCkUin6latBKIVbUijmOYj32toaxxVGayKi/FvONu02\nokRBIiSyt2q1OjQ01NHRAbOfzjsiEovFqGBxavLgwMAA4Af8VavVym03m03OZmQeZGCFQgEYn5QI\nEEVEOLQANtfW1rhnpddztiUSCTXF37lzJ2tnbm4unU5rMMqHo9xdEQFRB5+n3EA84ff7H330USqO\nbUYPMPaTnyjEfuWNlpXUhgYkDrAFtmOSMLp78Bxd2KOjo2NjY3/7t3/7tre97dChQy+88ILZoG95\neVlpC/wVPYSgeGgUhg60UqlcuHCBwg8jHo9D3CciY61S1hKRVCqlGZimVhCgh4eHuU6j0SAL7Orq\nAqkD6xgbG8P4x2azeb1eUhmQxkajMTAwoIxk7oTDVf8VA5zRGFnNfFGqgrRoaYqSHjGpy+VaWFjQ\nLHNpaWlkZATYJ51OX3rppSJy7NgxxEanTp0SEdpJ9PT02Gy2WCw2PDw8MTHR0dFBEkBIYeYatMZP\nMQYGBkBoAc1EhNifycYEI1AAeWa3DQaDy8vL/Jc+2mLkWNls1ul0ptPpkZERJmckEkmn09AWVlZW\nuD4lVQhBTBLNwJhXq6urWB2yTVM0Ii1TlhBVIkBIertglEMTZKIrPAZFxOVy4V/ldrs7OzsBKrnt\nEydOkAChhhSRPXv20B3GYrGA0jPPiQuhy7e1tWmEiiuxiMzMzAwNDREadnV10XFJRKrVqvqYDA0N\noQ/TLuQiouI29HPK3tJtxIwZtm2abpbSInG0Rmu0Rmu0xs/paEGIGxoWi4XEC5mhWhYxXv3qVz/7\n7LM333wz7VRE5Atf+ML3vve96enpWCy2e/duItPJycloNJrJZFwuVyKRIHkCHqnX6yBmOEnzeDKZ\nTCQS2ptRjBqA8sUdDgdXrlaruDGBHqgnTT6fJ0Na13l5aGgIYnFbW9vY2Njs7KyI9Pb2YnMAUgTC\nk8vlaE4oIt3d3UtLSyD7S0tLilp0dHSAfoRCIR6BYIJJgRjxI4hoqVQiftSKfVtbWzab3bp1qzrp\nrRlNC5EBaEmPdC2Xyz311FN8AoODg+avSUt0AwMDRNat6f1yhhlChC9DQUiBdBHZsWOH0+lkdfBN\ngR5THNL6EIJ0pvHKysrWrVuZkCidoS2orxIWHiATSiwSw3IX1g8EInOqoU5vIApUpPr7+2Ox2NLS\nkpa7qPU6nU7MBgH6EokEfdJJBIvFogr2EZbgc88bx+PNbrcXi8VgMBgOhxFrx+Nxyr2Q5lkU8Xic\nJLW7u7urq4vuzCKCwZvX68VYDuKiiJB1sQwpY4tIs9lE79zd3T03Nzc6OooBdyQSefTRR9kxtNxA\nOW2TzPzWAbahob1FqNbAIxKRUCikvvKvec1rjh49yuPnzp3buXPn7t27L7/88q997WvYGxaLRTB6\nOLJqckqHpGKxCJ8YVCGZTFL7WdcsnFWkOLh6kv5E5yR2gabRAAl4DQ8OvVogEMATATENxx4IiYhk\ns1kKBijVfD4fazibzbJOOJBYq6lUis0LthjELT43zh6WMdsc3cuIBmBhKU0AFzvwn2AwSKzg9/sn\nJyf7+/tTqdSTTz75wgsviMh1112HGz0fy7pm2ZuHi/UzGkriUDjabCKTz+cbjcaVV15JxxOtyMIy\nX1pawvaMvg1w0IlanE4nZCgRgVyOX5SIcJxwCMGDT6fTkOPFkEjyJzqRxNi7daUoOA/lnQkM5V1E\nqLA2m82JiQlKs7xT9RFW/zMG2jXuUEmPmIBwA/R8EJEtW7bQCQ8KIjEWZWl4j5xYGkqiIrhw4QKf\nqvr2Uhvu6upS0RiKl0Qi0d/fj7SGA+zGG2/82Mc+Bn9Sw1yW8CbZ2FsH2IbGOk8dlpmIaHRGivPt\nb39bRN70pjdduHDh3nvvfeihh6anp6+//nqsNuEQKrGYilRfXx9NIrAWzGQy6supfvC0ARMRwkDt\nz6IRKPdA+KmKYGWrr3PQ56ijkMDFdbnu2bPH7/eHw+FisYiUJJ1OUz8gd9Tm7qoYpXuLwvrkTFyT\nZS8GC5HKvO5olEPQhHk8HvReInL+/PmBgQH8IclTlffYaDRCodBTTz31sY997MiRI1yZdYsD5MrK\nihpys521pvfLGSqxoBxVKBRQqTM3/H5/uVw+dOiQ1WrFykjrRuzvUG05NkiqCASxkIYGBWkQZq9a\nAfh8PlQQ9XqdepU6BFL3heCghk/UrjiBzF5lDoejo6Pj+PHjTqezWq2eP39ejEW0zhqNNwufSP8r\nIjCYeERjRKUIsbJ0BfX19XHeaKQrImtra7FYzOfzwbZVM2u8DXt7ezOZTDabxVJAXwj+sDpd4VqA\n5THPYbE8/PDDjUaD+yHjFCM0bPUDa43/O9QggBNIMzD4b+CKIjI8PMzj0Wj0Ix/5yKlTpyKRyPHj\nx9n0RQTULplMbt++XQu/OGjkcrl0Oq3h7TpSrJ4xLDxtPmk+mRAsr2vhaOa7s79wD+wILGAwPXom\nwV0cGBhg+aHwF5GzZ886HA5aPXFlbg9lj7INgUAhB2vEyjHT1tZWKBT8fj/8l1AotLi4ODAwwBlm\ns9kIKkOhUDabdbvduNRj9sHLpdNpPit2IhG56qqrfvzjH/f39y8sLACoQjpQ4nVrvJxh3s2ZRXyh\n+vjk5CRbJ52GtPEjIRftTlTjhRzK5XI5nU79guiQsri46Pf7E4mEitA5AqHvg5CLCEosTi8xaat9\nPh+8ia6uroWFBZZhrVZLp9OTk5Pz8/PcmEryzQtZBWesLPKtNaMtnxjlA4jpnBDwKXgJc3tM1CbR\naBTfbXaJSqUyOjoKuRF7Do5/JJXpdJryAVQmEdEGQ1arNZ/Pw6VCskYvFZAJVfKAT6Cb5va0odJm\nGC0Sx4YG9jksA3hNWEfHYjFs42HKfehDH/rQhz7En9jt9kgkcvTo0b1798ZisVgs5vF4IET19/ef\nPXsWh4KOjg5VGTscDio3IrK6ukoJgVCUB8HixGhfRPRH0kPXBtaYzRgiAsmQcBU4hSWqVF0RwRef\nMzKZTJ49e/Yf//EfT506derUqXg8fuLEic7OzsHBQShbvCLRqN1u93g8lOUowkH94rJqLk65gvtH\nWG2324H4gY844QKBAGRrDmYkrmK4eKBLbWtrGxkZeeCBB/hAXv/614tIJpOh6gCOZLfbN5Uh989u\nYHfU19enTjR9fX3VahVnmWw2e8kll/yv//W/6EqMR0a5XCZzolLFrzCzsFqt4XC4VCoRwzEbUXpg\nRQ9/ndNFae7Q37mIGKxdEQGOY25w/BDnDQ4Ozs/Pz8/Px+Px559/fnFxUTnoavvE/OSCemXCO6Bs\n1o6I0PcZ7RqItKZWYoi76RvO0ZtMJpeXl+EK8mBnZ2cymaSIxcei1vjElDjWWywWBNfonWE8Ammw\nruv1+sjIyOrqKgq57u5uIgNCRjpXqJ2N3uErfrQgxA0NdkM2bo4xpjhgOm7ompkdOXLk9ttv7+3t\n/c53vnPkyJGBgQEeByek+0MwGMTiD6MBmqr09PScOXOGb4Q1Yy5WidFxGFyFOq3F6GWuuY75C7Va\nrXqcYC4nRkdmtfag/C4mlRu/VThCROiBGwqFurq6eDJ4CEZBtK4QEZqjYwHOOcSraGmdsxYANpvN\n0twIEFJpIzyfIkcqlRodHUWoAIRYKpUCgcDi4uIzzzwjIktLS/v37+f6fr8/lUrxHklGVSLdGj/d\nUF9BPlsevP7667/5zW+KSFdXV1tbWy6XO3DgQF9f38LCArgW9VFICtpMQEQ4P4AHgSJFBFekQCBg\nFiwjAuOknJ2d5dgTESj4Pp8P+IHtXkQws49EIqdPn25vb6dB69raGum4QuhaMBZjtivxQQtIHC1i\n5JosKJa2PocBNEJDIh4Bynvta1+LRxQJHzgnMRzVBy3U2Wy2YDC4uLjI6jCLuCn9auWCjzqZTGLK\n02500Xz66acB283VX/DYTbKxtzKwDQ0AffBrfB/Yc+mLymGmVjTf/OY3+ZnQbGJiIhgMIr0Kh8ND\nQ0Pt7e1zc3NkJ3gkclmfz0fKpRYVYpS1QS2o9Gh1RwvO6yYr3KrOzk419qWQQIAsBvpHLZ06drup\n1TIrRE3w4JXEYrG5ublqtYrXBl3KcBe12WyYztHVAsXrysoK14R/KAY4Q4RLfR51J8/x+XzcBusc\nJ9+RkZHjx49v27Zt27ZtxWIRz0YR2bNnD7aTkUgEbZnT6YRCQjbZ1tYGhvmfMjtesYPJZrfbqSpx\nPn33u98l/OdBm81Glh8MBvHiw8wln887HI7u7m6iK8SCWPpaLJZUKkVAAzQHIbDZbGJjSP7R09OD\n1wypFbpmRFpYVASDQRYLRaMTJ06cP39+eXmZJmGg8ViDthmtlpXQpC2E9M1qjsXTNPXRMh6zt62t\nTUFREYGUi6EiU31ubk5N4Dj/wG9IjIBVeeP1en1xcZGYmF0FFzf8Eok+Ozs7yQJXVlaGhoa4FD3Z\nidXOnTtnNZpnMpLJJMtkM4zWAdYardEardEaP5ejdYBtaKiZDY5HCjEvLy8T+4vI+fPnCVeLxeKx\nY8dE5Jprrrn55psvvfTS6enp6enp0dHRp59+ulwuA3cQoE1PTw8ODhaLxc7OzsXFRRU2Ab9ofxMe\nJM6C8kAUaTWGGBYydFuoVCp0rYUJrR0fxMgXxfADpRc7sbaIaBGCWFgMLGV1dRWre0zEHQ5HPB7P\n5XL4hXOFRqMB1lGr1bDe0IqUwjgkTNgkkupxh+l0mtumMYfP58tms8ViccuWLXNzcySs1WoVzgsY\nkYjcf//9OOtD3eYTg06m5JTWeDkD3I8KFgXa17zmNfyKaXnixAn68uDCTFEH8mqtVsNQA9ZrpVLB\nq8JqtXYZo729PZ/Pl0qlbDYLZUMtCmu1GmiY1WqlnoS7CmXjlZUVTTvm5+fPnj2bTCZtNtv8/Dxz\nAExSmfdiysDUblQMuILEi7dpfjKwIf2UgTrIJqnmkhuJ0RjaYrFs374dwBMeCisCHSS+nThc84fV\nalW7kONmUqlU6DKxsrJChZjFwiIql8uUKgqFwuHDhw8fPjwxMXHFFVco/5DcDq3kf/ZE+X80WjWw\nDQ0zI8AMN6tAGM6vgjUAACAASURBVDWSPicYDD788MO40F533XVPP/20iLz2ta8FA1lcXNRTB0/3\nlZUVDpK1tTX4RYiLtUqsskozP0pLWWKA+Mqt4EFl4nGfCqSIsaSRv+jjivKvk4giTOG9cyqMjo4C\n1sPi1eoajHlILolEAohViSS8Fm9cRPhbPMvVaxWRgLalSKfTkMpmZ2eHhoYWFha2bNnyzDPPfPaz\nnxWRXbt27du3j1NQZapi8Ec2j5zzZzRUw8Cc13l49dVXi8gPfvCDxcXFvr6+f/iHf7jjjju0nlSr\n1QKBAE1DBgYGlpeXRQR7aNU7E6aIiNvt7ujogIng8Xj4El0uV3t7Oy3C/X5/NpvlHNJC0erqaiQS\neeGFF1h0TFfiOXUYWCegFJONJ6vPzODV98ildI2b617g8GL48GqrvO7ubjBGt9sdjUahGipuia5L\nRKrVKuioFtH1lK1WqyDqIkIz5YGBgYmJiWg0ytvxeDxLS0tbt26lItjW1vbDH/5QRGZnZ4eHh813\nKyKNRiMQCGiD5lf2aNHoNzSYrGbpLrOwUqngysFCQuGEg8Zzzz138ODBWCz2oQ996Otf/7qIfPOb\n3xwdHUXjTKGbKzDhkslkW1ub2+0mvWPlVKtVqsRm3jC1JTPVQkzGFmI6t0SEahBRnp58ZmWYGoZC\nRORX1APEsEnVC6px4nPPPTc8POzxeLAu1Y6d8KSLxWIulxscHNTNC0YZZhxU73Egpfn6hQsXfD6f\npmg8h7DX6/XCdgkEAktLS+xQ7e3t11xzDQ8ODQ1x2EMT5SJsT/rhtMZPN6xWK9Xc5eVltCI7duw4\ne/bsmTNnzE8bGxtbWlrq7+9nf3e73YlEYm1tbevWrSdPntyyZYuI4OKBRCwQCKRSqb6+PhFJJpPs\n7NVqdWZmRq1brFYrJWGEzBqoYX4tIidOnMBUV0RwBli3ZavNtDKbmMasLGj6ZqUH9EgY88qMZ1Ih\nT9ZVwELjvKRzAuEgnEMgGfXIRpfJmc3WoeJIEjKytGw2y0UCgUC5XJ6fnw+Hw7lcjoUfj8e3b9/+\n5JNPXnXVVQ8//DBGoHwIej9KIuvu7t4k3SyllYFtcCgLcW1tDScnpcwxTc3mUtpv5Qtf+MJ73/te\nEXnnO98pIhMTEy6Xq1qtgpYwNZvNJnQ7li5aUX5IpVKxWMysRIYNryHhujyJoU8223CY1Srmp5kt\npvQP17GtxIjsgOb05AsGgzt27NAuXyKitk9Wq7W7uzsWiyErRs6STCb7+/svXLiwbds2Eblw4cLA\nwAA+JjDT1Fl/dXUVU9RsNuv3+zVW6O7upqI+PDz8yU9+UkR27drV3t6utXHMhESkWq22MrCXP+gp\nKgaVTqfQtddeKyLf//73RWR6enpkZOTv/u7v/vAP/1DTXxhJxHBTU1MiEolEICtxHU3EoZsjT1b3\nCtCzSCRCl1TgODEaKDebzUqlsrCwQA9J892qdFKMRi1iMAnXLZaLJ7kZWTGzec3YBvMcCLFhtIR2\nOp0g/2SQNETW+axAIob9JG1iKCwBElVIICLgFplMZnh4+NSpU/v27RORCxcudHZ24r/T09Nz6NAh\nArhrrrlG25ebCbebR8jcOsA2NAjB9BhQhhu6WsAQTctWV1dBFH/jN37jzjvvDAQC99xzj4i8973v\n3bp1K0mVXgrsC8SsWq2CmIvRZRXvwWQyqQxg1uE6b8N13F/z6OjogNBs7gVjpuepqZX69/A4uAdH\noPmyepY3Go2xsTH84MHcKYDZ7XZsBXSTArRpGs7liuRQ/ULOiYpFRFwuF9K3arXa398/NTVFszGo\nhnNzc1u2bHnqqafIumZnZ1/96ldzY7wv3RZbB9jLH+u0dDC/CVlE5Bd/8RcfeughxCEnT5785V/+\nZb5Zn88Xj8dtNht8dz1jLBYLVhoUscjOI5EIKmaIiFxB15pK9fXkWFlZ0QqoHjmAe8R2OoeZcpRO\neVDnhvl8UiGzGGeVurXxuKZQ6z4chUzb29vxims0GhTIeUXeOLp+pRqKQV9Ej4xgwO12T01N0cmW\nZ1osllgstn37djoERSIRmh9BxD927JheBC8FaMO8KVwrN8nMb0GIGxpM62q1iurWjL9ls1ntoUXo\nRyNmq9X6+c9/vlwu33vvvW95y1tE5Nlnn71w4QK6SxqJiZGdQNlQqE1E6vU6TR2DwWCtVgN2I9oC\n5RBTnGjOyfRfLqjbjU5ohT6U166RtTlEXQeY9Pb20iODw4+rTU1N7dmzZ3V1Va1GVBDNTqfGxJg9\n1mq1YDCobJFYLMYb6ezsxDdPjCMTa1cIwXyqpVJpZWUF3Onaa6+lutbR0YE+QfnQ6rmgJ2Vr/NRD\n43q1slxZWWHHFBFgho6OjkKhsHfv3t/93d/92te+JiK5XC4SiSAQzmQyQ0NDIoIzL0l5oVBAziUi\nyWTS5XI1m02v11ur1ZiKahNVq9UQyHP2LC4uptNpaq7FYlGTDHMehlhTDBhZZYtqHMpaxo0X314x\nVlbDaI/J6SKmU4oDVVETqBxOp7O3t7dpNO6h4TIvigWiiOBRokbD+mTeGrFaPB7fsmULSxWxs9vt\n7uvrw4xGDC9KzAdIf//n//yfIhIIBGKxmKoCeIOJRELX4yt+tFiIrdEardEarfFzOVoQ4oaGmsbq\nfzWaA80z/5ZQC4O+7du3P/LII9i9nz9//oorrigWi4cOHdJ2KiRkMBpIv7TbCHbUPp8vFotp20wd\neE4rgVBDxXWDJIxgk7iMZM6MovCKa2tr5naa/ABkoXClZmBqY7pv3z6LxcJLQ26mO8ya0Y5ZROx2\nO/JMguLR0VFuo6Ojo1QqAT9SIeCGKTHa7Xb1bBQRq9VKP1+o9gT7jz/++JEjR1DOEsxqEsmttqb3\nyxkKTZOKae6lgN6RI0c+85nPJBKJYDA4MTGBs1cgEOjs7Mxms8FgUJG0qampAwcOJJNJTYYU9MZs\niQIn3xcTBt58sVj0+Xww+GdmZsz8I3AzMSTG6H/N96+52jqHGgXklViobVy4oLmk1NHRgXrafBHI\nh/39/cqiFBGHw0EZOBAIUOcWo38mCwS1sjrjwDOiQw1AuoiEQiGbzba4uOjz+RKJxNatW0Xk/Pnz\noVCIDg9PPPHEuXPnxsbGuBM+EDJIVpzb7aZS+B85Ff7/OloH2IYGDCJm8DpzdzH2SjgOYgL06Epl\nburx4Q9/uFarffGLX7z22mv/+Z//WUTwNwP4hjGo3UYAxzEwZYWgwI/FYvwXpEVfUZ2uFEhUcrmY\nTizdO3jEXLvWMpJyGrl5qF+1Ws1cG+A6fr//kksuoQoI5gMBurOz02azaU0ewkgul3M6nWD9VP7W\n1tZQgClTH8cN6Gcul0tVd/A26/X6tm3byuXyww8/LCLT09N79+5tNpsANdAHxOQ43preL2c4nU6O\nBMx5VUrBhLHZbDRSEZFYLBYOhz/3uc+JyH333Vcul5m6xWIRJG3btm1PP/00vAxqpVzE6/UuLy9v\n2bIlmUx2dHSosRNqJ9QXjUaDg5NjzGq1Mi01WDFzlDSSM4d0TAamNOacyqTXEHAdiQmVmFkwgx5O\nr7xnzx5kjqlUCrISLVFYJlCTuAKG1JyCSLXEFCNiI5lMJqPRqIjMzMw0Go1QKIThFpHr4OBgvV6P\nx+O/93u/9773ve9Tn/rUhz/8YTG4Y9zPun1pk8z81gG2oaGuMLr7a55EEZtDSD9M86kwNjb2wQ9+\nUERgJD7zzDO33nqrw+GgtNNoNEgdyOoUZ0e6SF2N7UBEstlsKBQqFovZbHZ5eVnrWxr6/cQ7Z8Wq\nLIbFzBth0lMrQpIl/9pBUUx+9mIKUfWyO3fuJFsSEdoPptNpCPRWq5WcD5WPNkJjr8EXB1cq/El5\nCVZjtVodHBxcWlpyOBykjLgQORyO8fHxV73qVT/4wQ9E5I1vfOMjjzzCXSnRS0SIbSns/4dNgs03\noOSIYYqIK3wmk1Fuvc/nO3LkyEc/+lGOAegV+/fvP3DgAP3AwA9EJBaLbdu2DQ4e9mPM/1wu5/f7\nl5eXASE47UqlEkxUBPjT09MqsjRv1toFos3oEGRmNokIJHXYDWaMRJ+pOZxGmapcNs//YrHI0uae\n/X5/IBDQsFIbGFUqFe4ZHzi9Ny0A2+12bYlC25dwOJxMJpnbim14PJ58Pg8Fl9Oura1teXn5hhtu\n+PM///Njx44dPHhw3fmK97HVaLq0jnj1Ch4tEsdGh3p6sio04lO+AGJkEcnlcqr67O3tnZiYeN/7\n3icio6Oj11xzjcvluuqqq/7+7/8eXBH/WbfbvbS0FAgElKpECzst/zJTXS4X+4LH43E6nbSaFWMe\ncybp2mOp40khpkI3oSg7DqVsVg5hKU4ZsPhERHt9sVloesdlu7q6PB4PFEcx6s+BQABKVaVS0U4u\nZKhdXV1E1iISj8dLpRI7EX1pOYCJ0Ht6emZmZvCXox80apuOjo5wOHzVVVcRmT7yyCMsXRFRG3v5\nSSTp1vjpRsPooSwi7e3t9BOHQCgihULhjjvuGBwcfOc73zk1NYVA4kMf+tD9998/ODgYi8WmpqYQ\nR+7evbtcLkM4dLvdyktCNeX3+2kMRj6HyWFbWxshEbQLEanX63zXzWYTM1+zNl87BPFf1S/iUGOG\nl829/fRtsiiUx8HjtGbVCGn37t1irKxEIkErS2X50xEG/hFd7kQENQjqt0KhoOytcrkcDofj8Tja\nksHBQeU0Liws2Gy2HTt2kI2J0XqNuOGRRx4RQ7BfKpXQicLRZWVtqsnfysA2NLSco8tAzyq5aMas\ny2AwAhaRO+6449Zbbw2Hw81m83/8j/9x+vRpEYlEIrVabW5ubtu2bbOzs3iucxFdTkD8YhQMOES1\nPiEi4+PjHo8nnU4D+JhhNI4cOIdmqr2ZMcxFVL5mNVoiiYGwa3Jpblu+urp6ySWX4E+v8SlW99iL\nNAxDbmBJnMidTicf3enTp/VpVNGorNjtdphpdrsdYJDjORwOLy0t0eXvySef5MnwjAkszBAKXxMO\nqv/hk2HzDLZ+/RnHI50z4FcjIyOVSkWPNMY999zz7ne/+x3veMfjjz++Y8cOETl27NjQ0BCpBieW\nmstg+jU7Ozs6Oqq1okwmQ/iyuLioPYbMwaKYvDaAGWmppf3qxNTDAUTE3GBh3aV08rS1tWkXBTEO\nOY/HEwgEQD7FOD6Z22RRQOUsfLzcvF4vqwlhjN/vR6atL0RBC0kZlm98hlu2bEkkEoODg0899dS+\nffu42+Xl5T/6oz+66aabbrvttk9/+tOaQSp2qlUMMViUm6QPQ+sA29Bgsl7clMHcYEUFYVaj4zj2\nNrA59FKzs7ODg4M33XTT5OSkiMzNzY2MjEDN56hTBJ80Ti0DeFHoJKoIYZpSLatWq6VSaXx8HODO\nbBYnphoYmjPt4Kw4jPmtmeFQFrmilCySSCTS399PEyav10voh5aLtpaYRnKUIivGPUQMHMZqNJ+k\nqUp3dzcfYyaT2bJly9TUFP4L3d3dmuw2m81AIHD69Oknn3yS4/+GG24YGxubmJiAX2BGOM2ud63x\n0w2N28yYW71eVwiRgMbj8dx222233347LUmHh4ePHj36gQ98IJvNApGJyI4dO9Lp9NTU1JYtW2CZ\ns+nTiTEUChEn8WB3d3dPT8/S0lIkEkkkEmfOnNGYTOF6wjLFrvVY7e7uZp2u60Vgthowo+j6BCI8\nnTD63i+99NJisTg0NIRDvBg9yfiXGh5lXUpc6g9AkgR8QjjldDpnZ2cpmHGdcrkMytrT00PN7MKF\nCygHtmzZsri4SEj6C7/wC1/60pd+8IMfwKHXN6uBGvuAfhqyaWZ+6wDb0ICgAUAH2MUuTPKhcZAe\nAMxgVRfipiMiU1NT3/jGN2666SYRmZ6eFhEaN4dCoYWFBZ/Pl8/n4SxQDOOsUm4C4iqPx5PJZPr6\n+iYnJ7kyHfMsFot55Vit1rNnz2p3BhFRFqIuXbXI4vaaRrdAEVEVixhHckdHx65du7SzBslW09SF\nnUoDvqW0zeVjgZcYDAb5L5Epp11vby8rVot/7e3thUKBW1VVEJ8qt7e2tvbUU0/hpvOjH/1I77ZQ\nKGgSqaSsVg3s5QzSERGp1+scAOaUnVYpRCcrKytf/epX3/GOd4jhjvbxj3/8u9/9rs/nY3Y999xz\nBw4cIOHI5/OaiHi93pWVlXQ6jVUY6dr8/Dx9whqNxuLiIji5GPs10QkHjEq+1AlTc251olmnRFZQ\ngbmq1r1mEKWrqws4tK2tTfvMJZNJ4NBcLsdta6jKMqFBknr+ctphH8VHRCDIK2LwGAgEpqent23b\ntry8zMETCAQsFguoo8fjIcg7cuTIb/7mbx45cuSzn/0sX4Se6HrPNFcSQwq9STb2lg6sNVqjNVqj\nNX4uRysD29Ag0CPMNyPpCiGCYjeNziOKZdEJAmhRjBDy2muv/eQnP4lX/Rve8IYXX3zRYrFccskl\nZ8+e1QbEEPmwiRsaGgKcweiTi6P9Av2z2WzaBE/rFvV6PRQKEb1iwkT8ODs7Sx/kTCZjxg8ZVqvV\n6/Uq2OL1evv6+si6RkZGNKEhtoVhj1JHDJY/CI86yotIs9l0Op3hcHh1dVUjTTQApVKJtofqbkz5\nEIlYT0/PuqRwfn7+M5/5zJve9KaPf/zjInLnnXeqma+amYopEm9N75czENiJkQqbC7H6IAgzqO+n\nPvUpEbntttv487vuuuu2227D6ysUCmEAnUgk3G43lCgROXfu3ODgoNVqLRQKfr+f6UrPkXw+D83h\n7NmzutzM/DpNB83UQb3ndYxEEcHVIpPJXNyImeFyubZu3QqZUBl9kOBxXFOXHKalw+FIp9Ner1d9\nexOJBJUthb65GQx3KpWKx+NhLY+MjKysrGQymVAolEwmIS6JSDabzefzY2NjmUwmFov98R//sYi8\n9a1vJf3SWzWjhexLSuIAX90k3VxbB9iGBqtCbWkajYbCcRf75CqwsE4XvHXr1rNnz7J4/v7v//7N\nb36ziMzNzR09evTuu++empoaHh6enZ2FnTg/Pw9bicoT87XZbCpAJyaEp9lsqo2N2f4nn887nU70\nWL29vfwVZHSLxVIoFLq6utLpNAj+uXPnhoaGEOg0Gg0cgGKxGA54mUwGnhhvvFQqYVpIyyXeKdgp\nNEIxQD/e/tatW8FIY7EYHxeQLBWLfD7vcrnYMlKpVG9vLyTM1dVVahUi4na7z5w584Y3vOHLX/5y\nR0cHopmFhQX2EWWCmcXam8fS9Gc0zFJ0rTMp8YFtnc0aKS6P33333TfeeGNvb+/q6uqXv/zlj33s\nYyISDAZ7e3tjsZjL5bLZbBcuXMAMjEkLGW95eRnmHnWjjo6OVCoViURyuRwEfbzcEGmVSiWtzJlZ\n7xpHmu/WvEhV4qLoqIi43e7du3dnMhmqblCTxKBg0JMazhF/2NXVVSwWETh2dHRoNZcXhZekdSm1\nJGb9clDV63WWXrVahWyplqqRSOTkyZNdXV3/+3//b3aJd73rXffeey8vkclkYB6KsS+xKvP5vArM\nZdOEbq0DbEODCa3dttb1GRJTH0gRUX0VhrZmxSUkpZWVlSuuuOKqq64SkTvvvFNEbrzxxoWFBbzO\nmJoYtFPXQcssItA6OJZgiCilUIsBVMhFBIIGPrno1bg9j8dDlQIqI5apIoIpvsViCQaDyWSSJ6Nr\nIb/EtkAjVqVLNIx+evAGOU6oUvC40+l0OBzc+fLyMocxfQtXVlYsFovT6dSTBkVzuVz2+/3xeDwS\niZD/cbWvfvWre/bs+cM//MM77rhDjOoa+4LFYjG7RGp7+J/RlNgMQ/uBretLwjBLCW02GxJAEbnp\nppu+8Y1vwNdIJpN/+Zd/KSKf//znh4eH6/X6yspKtVrduXPnSy+9JCJ8yzt37oRwz0pRL2AcFFWP\nPzU1per4dQMSvLnkqfkZt61d60jTg8Hgli1bUqmUtqyDMEWbSsT4YvjxV6tVnOZZZe3t7dlsFh9C\nl8sFIV5EcrkcxzlpojbJo15VLBb7+vrm5+cJDc+ePbtv376ZmZlarYZVP3fr9/tfeumlvXv3/tZv\n/daNN9544403igiyfSzCObbNgZr8JOr8Jpn5rQNsQwPsYl3PAjFIEMweZUbwg1n/ywBmkX892+69\n995bb731oYce+spXvnL06NGdO3eyBZN2IONVLK5QKADoEdbhAiwGr9fcu1lEOHiob7OWVPuFzy96\nUoUcIUQ1Go1EIjEwMMBm5Ha7adbA+a2Nm8UwL1gX3ioLmdORvaa/v58bSyQS9XpdER7UzS6XK5lM\nejwes62q0+lks3O5XIhYo9FoZ2fnww8/PD09HY1GFQ5ie1IslOQPwdDF3kKt8e8amoHxIfNFWywW\nIp5arcYkV/AWjDqTydx777233HIL4BvZ+Sc+8YkvfOEL0WjU4XAkk0m6LYtIPp8PhUIXLlzweDxY\nsIvI7t27S6XS3NxcMBhkDpCdRCKRl156yWq1LiwsEIcRqzENWINWo6Uyv1XvabfbDbahZr42m62z\ns5N26rjCawMUuLVimFNzNiuEKAarC2EiiIWIQDlOJBKsO1YQGSSPFAoFn8+n8xly8pYtWyYmJtra\n2nbt2iUiR48efe1rX3vFFVf87u/+7t133/1rv/ZrvCIznPtUaKdpapakJI5NJSBpHWAbGutW8rpQ\nlOxE3ejVGpFYaR3GSGA4MjICC/H973//X/zFX/CrBx988JOf/KQ6uKM45uBkOoZCoXPnzoXDYbI6\nMg8xAmT6OFiNVrOgDeooqC7dYhgQoPdS/hWrtLOzEx48C5ijBfYU/xL0cSBxeuk+AjkTKMPsO1Uq\nldSSUdM14lkUPGJqd6s52eTk5N69e0+dOrV3714ROX369MrKyvz8/Lvf/e577rnHXANQAYO5DNay\nknr5QyeMhm7rHEH14704XPvFX/zFG2+88V3vehcBWVdX1+/93u89/PDDa2trY2Njc3NznBZADqFQ\niGZgsGqfffbZYDBIVy22ZlYQQJzNZsP5MJFIALPPzs5OTU3Z7fZQKDQ0NKTqSTE8WWAb6tthzoP1\nYWkhIo1Gg5jPYrHg5SgGsbBQKLjdboVSmFoKgYCxc1mQdmpj2BW+8MILfX19xGS4nuqnl81mt23b\n9txzz42Ojnq93scff1xEDh06dOutt77tbW8TkZtvvvn//J//IyLbt28fHx+PRqPrPFGJD7Ct4rzU\nsUlmfusA29Bgq8UIR9MsfqUUXvMgGtJ4TfVP9FO/+Pp/+qd/+tu//dsi8qY3venFF18Ukd7e3rW1\nNdI7YjcuS3l5aWlpaGhoaWkJRU42m+UEZVNgoUKCYKVxsmrpAqeAnp4ekjbeC7pOjjT1YHU6nSsr\nK2p/oPkTW4AWP7RirLlXpVJxu92cdmrqwSnFZoT8C/+qUCg0NzcHcR8aSKlUCofDpVIpkUjs2bNH\nRH784x//1V/9VTQaveyyy8w9zDinaTyvFo6gSS0a/cscuuOLSTOrxV0egWWubepEBDcWcimt9YpI\nNpv9yEc+8tBDDzkcjp6eHkCw+fn53bt3nz59Gg0JXytYIjqztrY2JUSAJRD6QPFQMRk+nHosidG0\nj4TMDK+BScIP0gor7p0AhqVSiTOMTwCQAIYUHwgeNKurq263G4iVBYJgmaSNJikiMjg4uLa2Btoh\nhkpEROx2O+bUlP0mJycvu+wyETly5Mh111334IMP/s3f/M23vvUt5cvQ5UuMqqGaEphd68yquJaQ\nuTX+70DkaD7DzM3xeILCa6yif6tgBlEQZ08RiUQiMK8GBwdPnjw5Pj7+iU98QkSmp6fX1taoezsc\nDmb/2toatBFOTZwReFxN2GBziKFHJvZcWVlRUB5ClBi5jsL91OTJ1ajViUHloj+yGD2WxMBUtYGk\nJoK8x0KhgFqFO2HRhkKhWCxGLYFPiT5hlUoFMIpjfmFhIRQKofeKx+NXXnklnX937tz5xBNPXHfd\ndY8++qhqwzlBNfw0WzNw9m8SLtbPaKiZLwnWOs7quvanZkcxERkeHl5cXFxdXX3ggQdE5Jd/+ZdF\n5MUXX8xkMvfdd9/jjz/O3Ojq6lpYWBgZGUmn0yMjI6j7WTjYL6VSqdXVVYIb6srVahWXZ7xmxODE\nItNUS3vWptVqRSav6TgMplgshjyL+YxOn2PS4/HQPZKLACdwemkVeXl5ORQKTU9PA4dwCtIdEFzd\n7XYDS8Tj8UqlMjAwwPGcy+UGBgZEJJ1OA4309fUtLS15vV7KuldfffXOnTuV7UWKmUqluNV1ma7Z\nnYBQVR/cJBt7SwfWGq3RGq3RGj+Xo5WBbWhoIwY0/IofKll23dAsrWHqX/5vmdwoZe7kyZOXXnop\nDz700EN33nknMVez2VSCA2QNCOJ0nRARnE+r1arD4cCrWwwSB7eBy62if6AcMDjAErkIDt9YFSvh\nijJ1vV7H2kBdtUBRqM8p0AH8iK7L5XJpcRtLQwiKRM1ra2sej2dubg7mSL1eBwmhYJDP5wcHB4lS\nx8fHReTs2bOPP/74LbfconYbYmqK1jQ6omkZkrSsNb1fzjBDiNq4gMRdRBwOR6FQwKjeTHFyOByV\nSkWTM5poP/DAA3v37iUpEZH/+l//K8ADvZuhe4yPj19++eUigjttf3//8ePHd+zYUSqVNKlqb2/H\nU9jr9cKkFxHKUS6XC6oFt6Fqk+7ubmRSwAmNRqNQKGzbto3pAYQA/Oh2u+v1Om+KRUTzBLWE5+ZB\nL5PJZF9fX6FQoBkQV8YNx2q1JpNJ8rlIJNLZ2bm4uGi32yHKarEqEAi0tbVNT093dHQ88cQTZGbX\nX3/99773vYsJzDogqnDb3JuqvsytGDYJ9tA6wDY0mE+4+Zk7p3BQqd01W7PZY0aN0cxXAwNUg/l8\nPq9+g29961vvvvtufebtt9/+ne98B6clHlldXe3q6kIL0mw22cppdofFlDoTAtyzetFTI/jt6+uD\n7KvYptrwWo+P5wAAIABJREFU0EjQYrGAqIgIKAckeBWf8S8HJDCOKs/gKwK3qn8PJXeIIdlsVlvD\nUBLzeDy43imUn8/nt23bduzYsb17954/f/6//bf/JiIf/OAHX/Oa1ywsLKgURkTYsBQFFZNrpZn8\n0ho/3dBS0LoJbNYbsQTUV1NEcrkcYOO+fftOnDihf7WwsACHFn7Qe97zHhH5yle+8sY3vnF6ejoQ\nCIRCoaNHj4rItm3bCoVCPp+PRqPpdFpbNLBqHA6HKuW5MbVm93g8KprkNtCTUU7mcbvd3tHRgeO7\n6jcw6qV7g8ZzItJoNCgDM8eo2yHPgE6SSqVGR0fx4QWTTKVSjUZjYGCAlZJMJvP5/PDwcLlcRjHJ\nLjEyMvLEE0+MjY297nWv+5Vf+ZV9+/bt27dPRE6ePNnT02OxWBBHUkUGkKfcaGYqsRb4WeFQvpFN\nsrG3DrANDe0/AndWfWlZFRfLwtQygC1eRRtkSHr4iWEKbB6Ql37nd37n13/91xuNxtatW61Wa39/\nv4hkMpmurq5SqdTX1zczM+N0OrWpGDQnfQkxLLrFqPpWKhVoxHNzc5A1VlZWnE4nJyIXx4AOwRa3\nR6zXbDaz2Wx3d7e5YGb+QLRIrtsHGaFykavVqnrGq84ULVoikfD5fMiDxKhA8KIIv3bu3Ckid955\n58c//nE1v1/n7soGqskZNQ+Osf/QibC5hmYzDLXEND+o80T7UZEnIXsXESTnFy5c2L59+8DAwP33\n3w/b/rnnnuPJuACT64BAvPDCC2NjY3jgplKpoaEhtbikz1Z3dzdxlZpZUzOzWCycWGKooV0uFw0n\nsbARkXQ67XA4Ojs7u7q6UqmUriAWAphEqVTCcndlZQXjbGrMzPlqtcopCG9FfXZ8Pt/U1NTevXvj\n8Xij0SBefNWrXsUTVJtPPe+pp55685vf/NWvfhUSx+joKBobc7/QRqOxTt2lZXhumzdrblorRm+z\nTTLzWwfYhob1X/dBVzKxdjGgcqsnk5I4xETf0kdo5EpspZ2I19bWzOCYiFxxxRV/8Rd/MTc399nP\nfhbV58DAANLjUqnk9/tpNSQGO7FcLrPMlPGBaBr6Rr1eJ1jjD+F9ZLNZLigivb290C7QTXORTCbj\n8XhSqVQ0Gk0kEkr/YzGrk6maCwBoIB4Qo1EZGlLAQ5vNpjYZHDA9PT3YkLOvqQlvtVp9+9vf/uEP\nf5gGSG984xttNlsoFJqfnzc7izM0/DQnB7JpyMQ/o7EOLddu3fqI4uRimuf6w65du06fPn2x7SxQ\nOd9gIBCYnJx85JFHzpw58/3vf59jw263Ly0twWYkzeI2MKomMoMQwWHQbDaRWCFh5MoIPMAVcrkc\nyLYYDGFgiXq9TioPG5BIq7u7G5BDRKxWK2YcLCumk6Z0xK/0TBCjoWU2m11ZWQmHw5xM4+Pj3d3d\nbCDRaPTEiRN4ax08ePDKK68cGxt7+OGHv/KVrzz22GN8OOpXB5jBRYArWC/mrwBAFQCWjFCMphmb\nZOa3DrANDcXN9OPSxgosg3/rY9SgVQzkAbOln/g0EeEkEJFarVar1W655Za//uu/rlQqX/3qV0Xk\nT/7kT6xWKwSnTCaDxbsYyrN8Po+NIXlPNpulg0OxWGw0GkSvYuDm/AmKK2Z8NpuFEwiuwk3iyhEI\nBObn5yEKciZRUQCfDIfDQCi4vWnJTeNEKIXgigTFYgCtEBRpuURwsLS0tHv37pmZmaGhoe9973si\ncuDAARF5/vnnCRcujkwBrAAtFfrfVEDKz2iodlAPKopDCvYq1ZYNXZNy8qF6vT48PIz1X29vLx2c\n0+n04cOHC4UCcYn2FhkfH//ABz5AvXNtbW379u3BYPCf//mfR0ZGzpw5Q2aWzWZB8gGutbsxdWIy\nP+1OhzyrXC7X63W3282hxWtZrdbOzk7uk9OO6lepVIpEIvF43Gq1ag0M+iUxGVdAIE8f2sXFRT0y\nV1dXA4FAIpHYvn37iy++yHJzu90sf4vF8uSTT77+9a+/7777+EBEJBqNogdtb2/no1haWtKy4k9E\nd3C0Mk/sdZkx8M8mEZC0DrANDXM1+2I/Dm2FrCUfc0utdW2HxNj91RcD0EAVV/wVCz4QCNx11123\n3HILf5jJZD74wQ8eO3aM8kC1WgWlAdJ0Op3pdNrv97O/YGmDy9zKygoyfl7RYrF4PJ5SqYSaklOT\nhcFvUbSI0Tae5nsah4px/PDSKiro6Ogol8tqpQEEJAamAcLpdDq1dqL+Tz09PbFYjA9kYGDg3Llz\n+Xz+wQcfvPLKK9WMQGNSM5lbOQUklLR4FhGOz9YB9jKHmRCh/YJBF8TA1TWSWCfYt1qtxDfmnJjm\nbSQZ6NNvuOGGX/mVX+F8evrpp5FMrK6u/tEf/ZHdbj906BCKYGppNputu7sb3S4qMepJEJfIhyqV\nCicBYAY6ZVRc/MxRB2aIvpP3RXfjeDzucDi6uro0QSyXy8xwIjAxlltHR8fMzMzu3buff/757du3\ni0ilUqHuSyC1detWEZmamgqFQo899thNN9107bXXvuc97+GjuOuuu+67774zZ87s2LFjeXlZcUg9\n+83WaP9Wt2W+joutEn4i++MVOVo0+tZojdZojdb4uRytDGxDQ93o+VezK7gG65oXmO2m1gHWPK7d\nVOUntT8mhzDLFV/96ld/8YtfFJH9+/eLyHe/+90vfelLp0+ftlqtABEkHKlUKhQKpVIp4kQcP/EL\nr9fralsANYvIzuPxALyIgbMTa3d3dxPAUv0WEUgfuPiIkVZiE0ftTUSSySSFNMzrfD4fKSlQYSqV\nCgQCaklATSKXy8E5jkaj5FXc6nve855rr70WbyE+KKJReFkul4vPUJvL6L/qUCBG5vezmRGbYuBY\nISIgZuu6LojJ8b1p6hip3VzNi8LpdILXURgzuzq97nWvu+66666++mo49CLywAMPPP/889dee+3t\nt9++tLTU1tYGF9/r9aZSqXK5vLKyEgqF8vm8pv7khVyWteN2u+lCyeREZay3R8VLTWTwgYNtSBsH\nEAgSMiaqEndtNluxWITxxA5AKe78+fORSARKkcViYT6Pj4//0i/90nXXXff2t7+9Vqt95jOf+frX\nvy4i5G1ApmLUC8UgcWjFS2UhYuTB8KrMnS4uZsxvHg+a1gG2oaFEOzPnTUyzB0hBZV48QXVgbMG6\nmSLAMrdTYos37wL8Cc/Umtk73vGOz33ucyzIT3/60w8//DDMJaRUbO4wrEQE/JATiIK21thrtVo4\nHK5UKmwBvAWv18tzYPpRSCsWi/AsWO3t7e0sS2ohYPHUpcTg1tNgpaOjQ0FLivDIg0SEuvTCwgJw\nUG9vbzqdttvtFNL6+/uffPJJEbniiiuefPJJqMNi+BxSANMFbI4PzP1r9AtqTe+XM7SriHJwmCrq\nuGHePc1yEf38MYgSQ/toNpJgGuCZWavVbrjhht27d99www0icuWVV/Kcb33rWy+++OIzzzxz/vx5\nEYnH493d3fv375+fn6e+xVqAzbG6ugq5g/mfy+UoIyEFURVmV1cXpA94Tyw0bWvAO1LLNKqA8Xjc\n7/cTI4rRq6+vry+ZTNIMjzrfnj17qtUqZr7nzp27+eabReTw4cNvf/vb5+bm/vZv//ZP/uRP4vE4\niwJTYz6icrmswYEW17X/O5+SsueZ5+vIShdP/k0y81sH2IYGnjRm5iGPX9zFQP41O2tdGVZrCeZh\nLqpd7DinsLsYvQQ/8pGP/MEf/IGIxOPxj370oyJy6tSpYrGIS1OtVmNh+P1+t9s9NzcXCoXK5XKt\nVoNGv7S05HK55ufnXS4XfEhevVAo0N8Imokyhv1+/+Lios/nK5VKtVqNyBRePnU7nHV4RUSUdOfC\n70eMJjLsMvV6nSNwcHCwXq8Xi0Ukz+3t7fSkeO9733v99dffc8897373u+Vf+/OaU1V2Lm0Kxa+U\ndKBfSmt6v5yheZKS3JAxmduUmJ9vbnRpbtImIjBskVvZbDYt+YhIe3u7dsO6+uqrReT1r3/91Vdf\nfejQIZ7wwAMP/NVf/ZWIHD58+OTJk9/4xjewqw+Hw8wlZfEg89fDkmUIcKJtVxcXFz0eD3adPT09\nqrVHiMkZbG6t2Ww2/X5/oVAoFot4DR8/fnzv3r1PP/30/v374e6Tpy4tLY2Pj7/lLW95//vf//Wv\nf/0zn/mMiBw9evSf/umf7rrrLqyH9fZqtZqquNgltMHCxWzncDiMtyTLYd02onJMcyq2SWZ+6wDb\n0IDgYMYGlRzMbNNGXzx/nZmvWfLFXqD+pDwOG5DVaDV1fCb/UHs3NQ7u6+u7//77r7jiCq7w4IMP\n3n333S+++KLNZrvkkksgceRyuUqlol0EOzo6SNf8fn9bW5vb7WZ/SSQSNLagsk1qCAYiRnHb7XZj\nQdLT06NCKxFZp/2s1WrZbLa/vz8Wi0Wj0YmJCbYM2o+B/7hcLrY5jPL6+/u7u7uTyeRVV13Fgh8f\nHz9w4IBZ5a0ftbKttC2ZrnDlv/GBtLX6gf1HDLNqghOIrVO/EVA7aG96Vvn9fvVAGRgYmJ+f53Hz\nDgsdQ0QQclwc6v1/7V1bbFRV918z0+lce5u29GYpWAtEwD5gNKiJlWI+SXwgRoPhSRJMxAfFAC8G\nn/RBNCrGJ6MlJiJGMEEJL/pgSERuAqYpCkEtIZSUloZC6Z2W+R5+Ob//mn2mpH/7KTnO+j2Q6bDn\nnH32WXuv+1pPPvnk1q1bf/jhh23btkFmAj788MMTJ04sWLDg0KFDSGMXr7ELrB2ILMecGVCO0CHs\nnZqamqtXryL/HR0SRARxsEjVQrFs1MVAa5UbN25AT2IYVGlpKdLIkMEGcm1vb//oo49SqVRlZeXp\n06cROdzR0QE9D+yKTVvYbw9CJzNDYEKkIMtaiGikwo6a2J6sf+hEihVOK1djYLMCNgbzYJhs6JSo\nd+CUkmLSRt5QIsltLEs2phsl6LNbRNatW7djxw4RaWpqEpF9+/bt3bv366+/hqsM1eghmiEoH/Lj\n0NAQwhcR5g6+Il6JmunpaXBrLc1Fo9HBwUHIueRJiDmsqqqCNoYHqampOX/+/L333nvmzJnly5ez\nxi6uUF1d3dfXh+OvsrKyoqLi8OHDzc3NP/7448TEBJ79tdde27Vr1/Lly7u6unBHpsLo18GmnfDh\nIWoLDkVRPgAj77mA1m9k5fvbWtL+hvhPXfeEtl9QMtKKk8kkqr3o98JmQMPDw1SsqWSsWbPm9ddf\nP3jwoIi8+uqr6B4uIh0dHfv378f4UCjU3d2NclAwA4rIzZs3FyxYgDBINDqHgAgHGCIGWa24rKwM\nHcPBw5jy1dPT88ADD/T19VVVVY2MjOAKJSUl58+fz2azzz777JYtW5AfKSKPPPJIZ2fn5s2b29vb\nYRrB08GAj8XhHmcwLerrI9FFvH6bXH/tHcfiO8xJS9WYBlzyBUL5xsBmBdSiZrAAv9ex8vAki8i0\n1wmMw3QuJysXsImJeKbFsNfiVkSg8YD0xevTSD5BbQ97dfv27WvXrj137ty6det2796NKf3222/f\nfffd+Pg4THPT09PopIdyA0hn7u/vZ0l7dCRJp9PoToJNwuzO+vp6iIE4VhBSUVJSgnQ0FAq5ePEi\nVDeIsSMjI7gyS/WjKS3MJv39/devX//1118zmUwmk/n4449feuklEQHD1uHaJFEckf40Br4I/Xbg\nny+QinB/E2hCBHdh0gJ4ErIU/KIbWRcalNDpRUENrjUEPjCrHXSFKycSieHhYbQN0/voxRdf3LRp\n05dffvnOO+84N/3888/ffvvtFStWXL58GTururr66NGjxcXFCItHWqSIlJWV9fb21tfXQ4Fj+SXw\nLVaNAtWhLx368FVUVDz//PMismHDhu7u7uXLl0Nw3Lt3Lypg9fX17d27Fz+EnCcilD6xbtgFnDb6\nKjhRMAzW0OoaGTO2ku66oAU43qtAwpeMgc0KICayKx2FyLZYkmsqdOoUiBcJ4ncbwFZA7Ue7zUNe\nN3QW68xms2SEVJ6Ip556asuWLXAkiMiBAwc+++yzI0eOTE1NtbS0sFruzZs3e3p6EokEOt7SITwx\nMcG2TNhOCIXKZDJ//vlnJpNh11c0Q0LaWSgUgg+subm5v7+/sbHx6NGjra2tFy9ehM4HaRde9N7e\n3scee0xEVq5c+fTTT9fW1nZ2dj7zzDMoGYdpk0Xhg2benBirc2nN2FlV9Ej731BAQSIUCrHFFKwO\nuvsUBoAmJycnWbhPvBgfPRIvLp1OFxcX69aL2ukbj8d5Bb7oUCiESmOitJMNGzZs3br13LlzqL54\n7dq15557zj///fv3v/nmm5WVlQMDAzU1NXBrIXMfmVJIfsfgiYkJlMBAeTOoUOvXr+/q6mpqaiop\nKRkYGFiyZAkv3tHRsXPnzoceemjXrl38MhaLwYKqCQ/GQ54SmDPKv4lSxTSdS65/XctzgLaWw97g\n2IEK5GC3PDCDwWAwBBKmgc0KTikpp/Cz5IuM9/9cl6GikgH3NYot0SAgKkaZ9e95BR2LTHtjXV3d\n6OgoRLn//Oc/IvLWW2+hx+uhQ4c6Ojpqa2tRUPHQoUPNzc2NjY1DQ0MTExMw+ovI0NDQfffd19XV\ntXjx4kuXLsGJPTw8XFZW1tfXV19fn0gkzpw5AyH0ypUriDxGTfqs1+1ibGzs5s2bbW1thw8fXrZs\nWVdXl3g+kkgkMjg4+MEHHyC8UES+/fbbX3755Ysvvvjjjz9Yqg7uOr2GzupRJ8Cf7F2p9VeUZET6\nzv+KBgoQbNsBWnUKns3krYG9EVuD6oV+iejtwBLyqHnP0mUigtbDThyjiMTj8dLSUl0vlHjjjTfW\nr1/f19dXW1sLs8SKFSvOnj2LEu8zYXp6mj2dr127Vl9fPzExgapRCDUi3nvvvX379mHOPT0999xz\nz+HDh/E45eXlKOMJMmZRGJZM06eBjmpBn1in1gbOFq6bQ+1OcDJt6Xg12gJUIAe7MbBZAVVoEXeL\nfasJy7GrSG5kPA2AtGvpviT+9dffa1uliPCMZuAWDXriJUqjfo+IzJs3b+3atf39/Y8++ujWrVvF\nK66zZ8+e3bt3w3aXTCabm5sZyzsyMoJq9ExMQaRWJpO5cePGpUuXVq9efeTIEREBk5s/f/7o6OjY\n2FhjY6OInD9//vHHHz937lxPTw9KT8Fa8uCDD86fP3/9+vUNDQ3IkhaRhx566Oeff8Yj610t3mbm\nOjCIQ68qvPfY/9rYgo3NUBcj77kA4YWSa87SBAxXLmLrnbBblkGiQAa7Imo4+bP3kMIP0tXWMFje\n4DCj3JZIJBAZz4JnMz3CJ598sm7duqtXrzY1NaHqYHNzMzI68HTaLicimzZt+uabb2pqamDnRPDF\nokWLTp486Vw5kUjgiZy60ogndAyq2vUF+mcuQd6ChwSb58E7jrVyksqxL3gdHDgFQvnGwGYFUDkY\nlZOEwXqmSIESr2iv/+f0ZqEWIpNpGD4Hny0zo9l4TB8feU3eKDZKJ7ATdy4i8+bN27FjxwsvvCAi\nv//+e0tLi4gMDg5u2rRp37598JmdPn163rx5qVTqwoULCxcuZJW5xsbG7u7uJUuWTExMDAwM4C6V\nlZVTU1MIKURfShGpqak5duzY0qVLV6xY0dLSsmzZsieeeEI8o/+pU6e++uqrzs7O77//XkTS6TQC\nkZE/gKXDIg8NDen0L73OiKZxMhYQw818BvH0V8cNY/j/gonMBBaZDkh86S+6QU5TVlZGnqTHZDIZ\niE3YFIjOFU8uRLFpyoUU45yTmgPAM6C1VFRUQHepq6u7fPmynrwWOtnnCE+BJIHW1tbOzk79E80q\nYLQQkRs3bqBUKWbS0NAA0TCrakk7z4Jv0uk0y3Ui8QuLwKwPyc2iEV+9HgZwYRjL+jgooE54WcMs\ngGNRPJNd2IPuN0GEVf9W0FkymYTYFY1GKfHRPuP/ub4mSzeFve6CnAwjnQBevLS0FEdMLBarrq6m\nMaS1tbW1tTUSibS3t1+4cGHPnj1XrlzhM549e3ZwcPDAgQNLlizZtm1bXV1dXV1dW1vbwoULW1pa\nKisra2pqUqnUxo0bN27cmEqlWlpa1qxZ8/LLLy9atGjVqlWrVq16//33T5w44V896H9EcXExllGv\nlRaEKaKK59nmSAIp2FgKFLjyvwgj7zlCUyn+dSgzGo3iexzWqVQKmjHkDOddwPAI1UcTAz6ASkkJ\nGIx/SfDMfyoqKoJURFLnFRyw7AW/QbEoPhFq6OgpNTQ0oAwVLsg0AA7AYOQd48EBzASSk56z+Laq\neESun477Qi+4Bu/FReOX3Aj8r7tNO/8QTAObFUKhEMQ9nXXB/4USIB6zgUyka/RhGK1/IoLC6uKZ\nUHRCLutOQdWDwkE5y8lzBL1ms1kYzbDDnYwTPgI+OG98+/btCK/PZDLvvvvu7du3h4aGysvLUZnt\n/vvvP378+MMPPzw8PPzTTz+tXLmS5wUUNWehuru7Dx482NHRkUql2traYG88duwYBNVsNjswMMAF\nQfMX5sbCPEihGOnb0DXFs+w7CeN8ND8ZY6RFIc4FDhOCpkW1zFlzGrh0DglrwOOdhr0O5mRF7HQq\n6j1Cl6KCxdhX/EvC1uoRyQaWPdyRt4MGw53lJAvy6UCETqlS9AODXwoPiDZjupgZi2jQb8eGLCwT\nI16PSnzWzwJ+T5MM15ZsVc9TL29eysfGsTB6w/8Bm1azBJoj8hbTBEDcOsFTD/bH3Ot4DRgBtEVR\nvHQQ/DwUCpWWluogBYcXIooB/SH1yIULF164cKGiooLdWAj8V1tbG0o0iUhra+v4+Pjq1auPHz/+\nyiuvnDp1CpJve3v7zp07T548uXnz5tOnT3/66aci0tvbq11ZRCgUQi+VmZYIn7VfmjngNIY4e5VS\n6u3bt3VlI64qrmDkPRfQB4ZmJVnPms1FBsU6mXngK6jiQQaDLKhbt26Vl5frnHTCH6wkKkaJCc7g\nbbFYLOz1tMPFMQFteebeCXvt0fE9O0ayMhy+pw8vk8ncunWLjYqcq4nyGqDvCR/BX/lJPE+hv+mJ\n+EyvNMyCqnUSiObE/C2nR+N5AZaSsjB6g8FgMAQT/4SdMvgQJalpqzeBTuf4zApytEfDYYPP8Xi8\nqKiIJnXHVq4vjs+Q4HhlUV2bcbV4PE5TD2vJ0PjAG3F64lnk6V5qampqampCTdW8RKIdAPAZ5B0m\nIg0NDYlEArU/otFoZWUlMp1FJJVK1dXV8bcwP+KOdKXoe3FlnGnkdXU44G/vNuEEG+IRGBcW4YX8\nUzvGaFtG8Qt8RvSgA7zuIg/afwnShf2NFyeh6ptKriuI2wR1N/gTUgJ9TuKpg+Lby7AuaMCrRFcc\nnXyEMzek0+Az/XOakhFwL2qTotaUXpw7f9a3kFyPO/cmsssLAbbDZwWSi44vEBVh4dC93tioqxSJ\nRBxanwnwY2sXrt7edCxrLsgNqZFKpUDN8XgcGxW7ETsQexW2e31rDGOj90wmU11dXVFREQqFFi9e\nHPJQUVERDodra2vjCoh3x+KgQLBeEGzjcDjMU4BngcMRMVvGpGiW6YTAwNHFlu36pKB30PCXwfPd\n4VuaRJ0DnXCEIdRa85OcBrcVRsL0rQdgB+Et5+VqmqWJt1tZmVrHODiDNXtLp9OxWKykpMThvo4I\nqxmJZvNILSDFch2i0aheKx2rIt4GwS1gOdcOyPLycvzpSHV8BMgB+BxW5Sv/9SiU55wjNJUz7AfE\nxCAl5GYWFxdja7FVueQCzAYkzo1KEhcV96WjHPXegwOAhMtbMO5RC3eiIpQ0fUuurlNUVOSoZTOB\n4m1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"output_type": "display_data"}], "prompt_number": 14, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo3()"]}, {"collapsed": false, "outputs": [], "prompt_number": 15, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["We check that this discrete rotation operator is exactly invertible,\n", "$R_{\\th}^{-1} = R_{-\\th}$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "text": ["Error (should be 0): 1.3e-14.\n"], "output_type": "display_data"}], "prompt_number": 16, "cell_type": "code", "language": "python", "metadata": {}, "input": ["theta = .2;\n", "e = norm( rotation(rotation(f0,theta),-theta)-f0 );\n", "disp(['Error (should be 0): ' num2str(e, 2) '.']);"]}, {"source": ["We check that the inverse is also the adjoint operator,\n", "$R_{\\th}^{-1} = R_{\\th}^* = R_{-\\th}$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "text": ["Error (should be 0): -1.3e-12.\n"], "output_type": "display_data"}], "prompt_number": 17, "cell_type": "code", "language": "python", "metadata": {}, "input": ["theta = .1;\n", "a = randn(n); b = randn(n);\n", "dotp = @(a,b)sum(a(:).*b(:));\n", "e = dotp(a,rotation(b,theta)) - dotp(b,rotation(a,-theta));\n", "disp(['Error (should be 0): ' num2str(e, 2) '.']);"]}, {"source": ["Partial Radon Operator\n", "----------------------\n", "The Radon transform is defined, for an angle $\\th \\in [-\\pi/2,\\pi/2)$\n", "as an integration along all lines of angle $\\th$. It can thus be\n", "defined equivalently by 1-D vertical integration of the image rotated by\n", "an angle $\\th$. We use here a simple sum to replace the continuous\n", "integration:\n", "$$ \\Phi_\\th(f)(x_1) = \\sum_{x_2} R_\\th(f)(x_1,x_2). $$\n", "\n", "\n", "The radon transform is defined as the collection of projections for\n", "several angles, $\\{ \\th_i \\}_{i=1}^{m}$, usually equi-spaced in\n", "$[-\\pi/2,\\pi/2)$.\n", "$$ \\Phi(f) = \\{ \\Phi_{\\th_i}(f) \\}_{i=1}^m \\in \\RR^{n \\times m}. $$\n", "\n", "\n", "For $y = \\{y_{i}\\}_{i=1}^m \\in \\RR^{n \\times m}$, where $y_i \\in \\RR^n$, the adjoint of the Radon transform is\n", "$$ \\Phi^*(y) = \\sum_i R_{-\\th_i}(U(y_i)), $$\n", "where $ U : \\RR^n \\rightarrow \\RR^{n \\times n} $ replicates the vector\n", "along the lines, $U(v)(x_1,x_2)=v(x_1)$.\n", "\n", "\n", "Number of angles for the partial tomography."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 18, "cell_type": "code", "language": "python", "metadata": {}, "input": ["m = 64;"]}, {"source": ["List of angles."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 19, "cell_type": "code", "language": "python", "metadata": {}, "input": ["tlist = linspace(-pi/2,pi/2, m+1); tlist(end) = [];"]}, {"source": ["Define the operators $\\Phi$ and $\\Phi^*$"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 20, "cell_type": "code", "language": "python", "metadata": {}, "input": ["Phi = @(f)perform_radon_transform(f, tlist, +1, rotation);\n", "PhiS = @(R)perform_radon_transform(R, tlist, -1, rotation);"]}, {"source": ["Display a Radon transform."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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pYhoj8xzFLIPTAUmNRunAessTNLee95YODEikSc9aSwkoNqTnlpWqVP1qsUza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\n8QATEZEp+T+m+TxdIvXYZwAAAABJRU5ErkJggg==\n", "output_type": "display_data"}], "prompt_number": 21, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "imageplot(Phi(f0));"]}, {"source": ["Check that $\\Phi^*$ is indeed the adjoint of $\\Phi$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "text": ["Error (should be 0): 3.5e-12.\n"], "output_type": "display_data"}], "prompt_number": 22, "cell_type": "code", "language": "python", "metadata": {}, "input": ["a = randn(n,m); b = randn(n);\n", "e = dotp(a,Phi(b)) - dotp(PhiS(a),b);\n", "disp(['Error (should be 0): ' num2str(e, 2) '.']);"]}, {"source": ["Partial Tomography Pseudo-Inversion\n", "-----------------------------------\n", "We consider here a coarse sub-sampling of the Radon transform."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 23, "cell_type": "code", "language": "python", "metadata": {}, "input": ["m = 16;\n", "tlist = linspace(-pi/2,pi/2, m+1); tlist(end) = [];\n", "Phi = @(f)perform_radon_transform(f, tlist, +1, rotation);\n", "PhiS = @(R)perform_radon_transform(R, tlist, -1, rotation);"]}, {"source": ["We use noiseless measurements $y=\\Phi f_0$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 24, "cell_type": "code", "language": "python", "metadata": {}, "input": ["y = Phi(f0);"]}, {"source": ["Display the corresponing 1-D projections."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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AmYHqr584gOn3dvtyy1aX0RDykCuELmhpHtXKvJ4Nz620iAs0mE1pD0KGKczH\nhPWT6riz89iQQQU1ykML23vfM/PsirHvfHgEnYmnhizr1lXeDspa29u+uv07ttetvIjvx3GMGR3H\nstmtpuZ+epZeKNlFKXDUSljIqtwIKnF8Ew0LGBGJiIiobsnABzRsYxZzIjzCSo8ijZJIe9YC8zzU\nJyxKPFCmW2mcraR5BmetBGIaApTZcHiEOKy7kFs81tG8EPBYt2L6WflJsTYbNIaMMWGSZ6ZGmErX\nPC4jTYFVw4io427s3WXG0AB9vXrBtbYIvYoxT8a+70jKOUO6dgmqromq/7n80xsF/uO76mGRJdtX\nsKp1Ow9n/jzz0DPvO7zNH6NhAdtYttNMOfuodqHLYPPXe++tFaZQRgwPo21UJo3gmi9Kafi44VjO\nIDg7tCSOX4/gaJiK6n+1tm9ZvWnj8L2w/sDM3PfWimNyXHE0pYF1ZUJQeX06FRisN7PFrk0bmDKq\n5lw+ZNLdrHHI03nei9I1lNDU3ghrm87S2eQxuUiFXOnm86v4mQiOY8ulvsZth8olGhYwRW2vlQ1k\nyscObJ18tFWXyIse+eRmHOSNmefPnjExG8yRTUlpWmA3ENuue1pffF4jfP37tt3xpSH48TinFyEN\nJXpS+UGmGJCVVARr7fww8iEv1riytuvWziV771Zv1QsLZmfEIpZ/PC408RCvJhUOho+sMhpv8mpY\ngwfhFZVacXevBIysdyC6lhsOles0LGDJc3j1gWxirxuHDVeXl4ovfAypGPwPitpnSuy5Hkdq0W+s\nhiPm3+RTs2XFy6SQ1TDvTQOHaurkEq3eVkMyT7h+SjII8qHK+67veShQMnpirdh3wgSu5GN2WNXs\nHmY202y8I7R5M3tVUL8US5VHPh9Af7dwoTvTsIDRZi/iPal+q7WHZBEKX/Dc1TB4Dh0FlavF78P2\nNBpr87W6jZgQygS15KYhio3hC6fNQ4QWQ+bmc9752SWhql5hZi7sLY120eS2p2PHJYPL7jiOczQs\nBjRmruCjIhsnCePT2dgKiwViUlvRO40PqCN1Bq0KmIlTeJPssPznCw9srcjF3+K73J/LS9NWAwKJ\nyHG9AA8NFsOYEzodAhxPEsLKY942OI7l6WbnWP1yxiLvzo2drpZns6l0Qvx11WDVfRQFOGha6bEg\nN7/mL8bzGmLx42WcdV15Zx2r9WywJaFKd6oojHlsFGgRplQoenVWIXGQ2G1CxQZDEh3vbw4nW+YS\nL0eygFYFbL6y1ZbrNiemCYslja7Q6Dvv5w3Us7dYStHJ1TOmTy8AACAASURBVEFWza/se54GFH3F\nOZEHcSDfeTa8VPDwXIriEdPM5bEVof7wN5nsGxrfm4+VZXAXs1ZPLl6sJtimX5fytfO/Pj25y5bB\nlKWJwhvLYON7Tcwty9Wr2Lg6OXj6ETx0EC0ibFMSfbn9dLdj7K7Wzxye9vRf23Wa10FbLsVy5DC4\nCa0K2OcZa769zKwlpg6v+Svqpquufs1xNHSdyPqMrPP+Wte5q2VSrn5HVXuIhoPriJnGnbLi+HIM\n9Hz1K42w1QjvlP2dzw/uZkWtz+6PDNl4lpz3fqS+tTFVWYUqj7Ad/YouVB2MRQB6zHp2RIPbQOu+\ndN5z32vqxdKli4WkT8txTnky4BAgYM85r/1PFSv2aZCCLtskr10cgofKT0TkKHTe65c2SY5h7rxX\ns0zI8P4YBa3c+GJww9SVE0eQg6LmVqLIqh5FZt4VCVY4eX52mT1+EQYTufKnZ/5DY4j+nnyh9HmO\nXvEhVyx2HghuPo2ItyZMqjyrAyPFo+od1xd729vpMt58Me8D3/rXDO5bTaEuBwK2m71ZzIl1+00H\nRA3fiNW9nZubOzp0quGlrr8kJ/NssHyYHoLOJ98Z77veV2pB7eLJ6vSyRJV/2R/LnC9yDCXRJ/lt\n8YPeK2ZRXaLIDYWNvGPAvX4Kb0dzjEN5buFy5eFcZ3281ppkxQajbm1neAL0mdT6mczRbhNryYY8\nBT5Z9jpbmqvy54UNbAcCdiXGRPtg11fCUSBn06/FGo/jWclEdmRD770MGkbOmhBywds+RliZJFdt\nja1aUaaUiVNLiK6URdbCSKMlsLjjQ9JRVwbQpYWZm/OOi0zrrRw7iDOb1NzgKemCryg614oDJHRe\nmNqsjPVf3nMblhfkZknl3woE7HPoCnP+PUmBUjTYT2Pv86yBbD7yFoJRjK0pmrEaE5h/rv6QVO0q\n5iXnX3hzMVDEgMZPzZJXNKxFeVsku6Zr6hWctbLXS7HXpZHbsmUcx86+r6phk3ChGwsP/IcFELDL\niCnGg5ZUI6OKaab2HU44sslbYpjTvHi+RlXVs3e8aqkD2TH691RtnsWDPa/Lbi0FfnogH065/QTv\nmQK7jK1Nw2ttASxLf35+/avTghTroQ9/7o3USN1J6erpw5/HB8mDzB/Jg+QxeExRt/7GQMAuYwxr\n3L+cEPcwpENpzSSywfCGCMaDzJMxu+v5pmstftcH2OhZHKbJ1fG0uu+i2mHpTizSq2/DrRR0i3pt\nn8Ssm2WTmoQxOjRC2+5XCsHXzJAth1S92uKFRPTxWXlyb7UYds+H+QNAwD6KtgKZTOhkbA6SM//a\naACuWJu35kvpUMabzntxzoQwL+SRijaRMck5uUOBzue5kfAYp8nF65PrOexorotp3t1oTYT3+6qM\nu9qwDBYDyvUTN056pnGAW0j6ke5X771O6Xrve1vpwkPqbw8u74KZbLi80uCK/IxZ+bmGTU/T/I2P\n07V1n7/HEX00ELAXeW0QXBkE5tkhKk6SxQHT0GpkFCEhIupt33GXKsrnX7z8o9Xmu2Gqd15TNefp\nsKnTZErD37Aklgd3zG2vd9RrbyRh4e+6WybZEpMk5QXVfEFQjTf0kPmNTgWm850np0KctNWCcg0z\ns/G916Y8qbeD/lq12zgMehA4lYq21uZP29KD97LV9bk5040X8M4AAraJ45+KlaJKtdnx+ip3dN8P\nPsn8O6ZDhsgVRUl3UhZFPGiflN2+3Og80KC5MFgjL6a+69KtGGFpmC6G3Y2j8JYIDj3stGWRAjFW\nFLOW2NFCGQHNSiQ36TqU6L2PVQJc0Ez/YvYw6a3a96kl3vyLIl7o7/QGI9/Rf+7DQMCO4eWHz3iz\nUjLKdt3oxGAmZ4tvsvFxqacYMnIjLPob761eiSUNe6ptB5RKaXMtYV5M/eD9W1s8otPWBy6WNGOT\nwofmC0uFVhFR19m+5/xd419rd7pMEctKVuormqev+cr6su99qnTjfcdDhzzrRqdcstLm62Ebja3P\nBMzDi1gFAnYBL3gh9Ds2V69xVwsGljyaka5Enhi2wnwDLe2x0oppnXuqVwpkOBhjyuVYfXnuJcuG\n51QXY1Jha8g3rn3IZM+pmprq2fz+Gub1Vgwlwc1bwnrfpfncZGIXHA3qm+eTqUIblb7pQ1X1xlfP\nbgsv10BY557P7WeAgN0CcW7e5k7I9D2PCWFZ8nLcIA00tRm4LpatlMC/MztMCo2CGQae+Zgi844t\nn2WvgzE3BVINJJvV9FuStErcivoJ538Y0sbjpSsOINaI5sLdqhWfU/cDNhyooh8bzzH9/DSJPq1U\nkYvpIqq7KpnJFazGVvXKWCve90TR38gUJiuRw0rzsPGT46Hcy5ou3ubv2su+axStnwMBu4L5s760\nHpbGcWeFdqtRng39ZbyworcSl3h/OLZ6sf2x/XxnFzE8gqpUmBpC8xqYY/+E/MXZ6P/CvCFvNUCZ\n42HeODtpmF6TProQOW2QD/red7HOr1hLjlwIYVzZiqEishxb/zdYkClWiMwdC27c7oBOBAJ2Detx\nzPO/lgs8zxJ74/ftS6mol8ibrZvejU5cNbPyv24PRLSzjiS5Z+x1v+Ls8j0tp6SDfvX6pDan6/ZB\nb/tksgz5i3HZrPzQaaBsJe2vlnZCs7IyxcFYK0Wgr1a+pzwucUbF2z+7emd76BHcsQIErBGKwI1Z\nZ5Y6z8p+t8Xi2lj2u8jaqvqW+fKtUok/gYy5iWp+EZHhYaFrg6m7JMlLb00tvooAwuoCWH6/UhnP\nLac1Z1I1dHgUArG2XI2Z77OAjvVlsPE4X/V2wDH4DhCwjzNb3tk18b9V/v8lLKamHtHGaYtT8TO5\nXCct+C9RvXqWnC4XrYywMU9xtWa88SZVQQvBLEV8TPe7MNeY+hXSiqBh1oD7dcKsTo1VGzJ3JC4E\nJcZPTwUhV6dK4DNAwK7EeEN233QS6vX+HvIx5+CijssclSt23rpdMr8ixpDI7m4mRLQw+uvpOxdv\nIRt2fzN7a2McxIMoi3DR4h1bjkrL3sf5hwjzkDopuvpVuUHFN+41wWqx8ksTQMAuY68UoaLoU/LK\n4k1TRCIsbVOJNVgyCURiwlPVrzd9W5TzZ5OF+drMutW4ZHWtpVRrOMdM1UwIeX7kkjw4svMaH1as\nrtsVHZzH41k3wnb58F/lq/oYnAkE7AlXuezEy5sR8L9pq6V6iWsxMuc4frYPOp8vKKXLS/OU5E8w\nBO/l0jl3S8YjLPpJVh9hFzO3eu+Temn9+AIhs5QUaLW5sxW9Ee7PGW8cr+ULy2OMjarMAeh0VQNz\nIGBXsl1jXtPR39QwoiE5bOO2nypqfMm0OjYaThldtYqCE47T9rzoxljJM2Xezx7pSm6Jdguammhd\nZ40hYqeSTMN+i2gL/XEegqG3YDQfg1MNC4+Ql7CaGGF3WOtaqJj140DA2uB3pegNSiMsqxh4hxHp\nM8zlqr6KlqpGHhoVXp14zc2vjbONtLdJQthCBnHV95iWwXJSG1han2RUr8zsSTrvuXo++8l6TfwI\nELC78wUrOlcRy0ykf5fX5DiIp4s05fbJghn0KYWupG3YxE5yr8ezzK6qfuhbRmetIsu4QCiT3tvR\n624mZ0qztGgiSgVEjIkrc0lQ9WjVZi2NsPf4TFhpa2Xj3gUCdl80O2c+gb19Wfl7IBLdSvNityJk\njFBZX3xvQff7s6JGsQZgPqS+XRJYx/o0TG91GxhjQiAuF8A2seGARSoaRsP3yHgTLNHmhcl6Uzql\nVrH+zZBRZDGvAwF7haVxoZox806iIjyHZ7E88Im1vffbc5mHUuzMhu8Qx1G1MPOYoDxQ8+Cg/BQZ\nmLkNrCPKxvHy65CMwp2P+mLs4tQsK18n6m3vePKXFNmv9bKslWBrRtg9WH9yfs1hAwEDv0s+1u+y\na9MgEgvrDf8+Flv4mvCYv2jT56N/vqvt/sPSMjAm9dMaX9P2lSR9z/NS1EdR8VKI1F8fiFnVfyZe\nDRmbqqSbGB6BDReVHsHdgICBb6aYp0/mpzVTZdcC2Qu29ScDEQs1Ut06xKavTvO1ITjN06QCx5iL\nwLMdbZ01xFjKlwJxtUimMaMjse9Z2z2XwSMu0LAepuliNNiOtzLCcrQL2tVHcRkQsCZBQam9qN+s\nUiW5qK84k6+VdlxvhjUfYrGlKvV731gYYdvfqJex8MJVDyzuPJU3dDZQlPz8Af5AGZR4JBLzK0SG\nGy1CxsQUNOdcGBdCd8wzshZ0EzluP1zo/kDANnFIt19wCWnyriPmWsnEPcNNVb2s2LLpyGnkKzQf\nsw9WZk5FlMyGfe37Tm2Zsa3c3MlH5Q5PESKyXaevMAUS0XW7QlYvNMKe2vqTOsW/tBIGAQPfT1nf\nIQ1zGo6YB99NGzoX/STz1+/mUCoO8gWzJn9L1f7I1UvDHIY/GEOi7bDzjekhIsRDx8tAnMT97Ebh\nS0Ib23uK8GzZT0vdR7fhUK/Edz64fZGEzwp1Hc8niz7fDQgY+EUqU/VkEAwj0Hrizsp8/GOrXEuh\nHCKV/t2VzYaLULT7Ko5/TI1akoThQ+fDdDId4qU9NOjx5YUxJVkt6UbPG2ZWycJO+cmWIaCM76n8\nu/oAALiGOPwtb1A0k0zD3JsZqRrHkfJnD2wHpQepbRtF7Ngi5A1TRw+1KL+kP8hghBm1W70hKgPi\nrVhrLfc9G3Y0hC0aY/5ixYiPLYAt0WUdrpnZGDKBO+/Ja98yYcM0HLteYRm2H83w6JDsP3zwAAIG\nfhfxQj5bz0842wf/2j6tWDbhYwV9Cpumy1ZuUnGotbd7Md6EwcuXSKKliuU4ytLcuOy46/+M8RQe\nwf0Z4o5q2btWLkvHXTLUirTruLGQMZaFaXqyKrSGuSOyo6kaG/EYs9V6m7MyfSlyFfKpzzpv2qYN\nAQEDoESEDA8lYgd1Sz7DfML+4baTVXILxs7/upDXuxFtFJmGQh09DTMxd94Li/FGF7T4wUTke1/f\nzzCexor4G9p3beHNMXrLvfOdD4/gyBkKYi1N62+J6ATCVl3Knfe07fF4reKGtZamMfTihR6/EsFB\nWAMDIBadqgVupQKKKmNb2nS9wDvB9LoWs77NehCBeJk3llTyITVvoJUwhjruUo2Pjjv356LP7SF1\no2QoME/n+A9XjI+NRok2aI4nawz3g2PQWWOITKVeVBU7Leny8pNzoJP5+4CAAUBUC+vQUnnr71oK\n5dgex5FKeFQVovpi/teNx7O4h1X9YzbETmtSpDFUM2c77/ueQzDe9x13bIYIw8eiHOZ8pgv2a1ix\nIqSdMJmCIaHggh26iw1xqnpN2LBYqznave2ttYPrNS5GglOBgAFQZ1b+d+sbn2aDzetx5MWoJsUV\nt0y9XXjLCHOxLruaHcmX5ZgcU3gEFyrrNKpeuYk2V6NRTaft2VLtrWcndiUi5JxQcCGYeIn+hiJV\nQ0UPZkNDsSnDTDYQxevZey/WinPnZY+tu6/X8h2/CAjYGj+yEAqUsu4UswkhxSMkDdgeRf0CeWXF\nVNOoaoS941kad+iCIxseQRsNJ/TJD5Y0vH4SJzLYXtZKPYj/sbg09Zkh9ajvrEh0ovrOkwsp9U1n\nNvHiu8BsAjmxlth53/vO01TOP7ZK+mYP9xaBgH0ItEVogqRho4g4N8pViI6v9M8w7ypdfwZq8CUj\nbAgtib/aLCgxruQZTm2IHdlArGZE8ptphxE27ChMUraDYza57SUuNtYq3IaLedAn5y8v8ZY5smBM\nj7kQVpwTZhOs6hm/+EFgPxCw3ahz4OqjAGdRDnYiWigv/ZtsbK1csdqxYn6l8HdmM1fW8Y3TQuvx\nrP+Mug2LyVYgp+O1tjPOCyGKtboMFn/V5ls1LndmvH8AepXY8NPGxx/rS/DjQMD2cbcCQuAM5hpW\n6Yo5pSIVq+tSu8rSF17EqnrpDnNDXyMt5mswYz7ysE99r3ihh2h3x/wjmNn7zlEw3vQ9i9SVIL9i\nzsmXlQ7Vq8GGwyNQZkZObo0LulmwpUn6yicO9wghiCsgDwyAOvmIPA7ZtbwqsdZ4ny+qfyadeZ7o\nOrw+JqgxG6JoHgViRzZEue169R/OiAXjmWWQvkEFu0mpCTNcCBeo88sHyWn7Cytiv2x+WbFjel1w\nuUcxBVKqT5VDrEWisGE77mb3gvqW+U01kjNmL37ZDGIBWGAAVEjds+rWxjbb6UAjbNzntin5KKVW\nvO9zI8z7bmmdJgQztieexrn13qv5lduC+quViRexTsvjqe+9tTYGZwayYpmNo6Droy6QcwKf4SVA\nwADYiVTyw2SatarkEpVCF1/7zPXmYVtaiyXl876npHDDSthzNXX2abUkZmY2uVRNlLJlDcvR2Mvg\niAOJc8FR6nOWY8VyVqPr2Lj2O5SAuQPNC1hKizcZR3/EsfsD7bOzQ4b6+uZhqEuyMckFS8oXHLN5\nbUWEmTW8u+us2ljGUCDWoIwVNArRGCri7NV/uPSub5GqSMxnsJaGsB19PQ9mWcmpGAv2b9Cw9VX2\n9XnG5WEyn6fhNbC5UH3VwvHPeLHvz8bSqLoSln4dKs1vLcBaMH+Lhr9vfHvuaRxGvc5a630/jaMk\n3/lhjadT44yyBTAt0C5CxlfymdKnWCvem9fOtAm0xqPmJ6ROAsEEJrLkbNcReccUaJipLMhM1DC7\nlucOttOwBSYihWKdYX4BsIv5DHp9TJ/PqZdkYLvttX09Rqs7arCivpJsSz2R+TwquSurfrNvJeWV\nU54BJlajDX3vO++fyNK2oalIyfidK/waDQvYHJW0QsPMlKuODXwbNS/i05ywqguoWCrbYsQUEfOT\nPz2L8igOXMMTmI33vfddcoUxs0Zt1A+AQvEpVR/p11Oxy4eLm6YReRmtLayWITuX5obK7xGwJf+h\nTPnwUYEf5IVkwZTFNf9T/uI82Wv801BHcakAVe+99316YwhDzdmeicgN4QZpgWfdh+0qnVt+FRFL\njpk77x0FDlHDYuoYGw5ERDyTpdpUxqY/7ZoN6E18n+aGyi8RsGvnC++7/hFT1BxLq/FvFuaoG1Vs\naKjB+OTtS7aXC4HGtS+RmHWrA5+Om0V9jfzdkyVA82IgyXewZGganzVeIaJU6tcFu7pw+XJgKqCv\nETD1HCpXzR2QM/+DlB1YpmNRNbq96kVMYYpb1sOyhGWT91tZLC41bYZS/FWEeu/zDpNdt9xiGLFF\nNQyJPMj8ETkbjTAiRyHatbUrxhyL3Oc3HWXq9tK8gCW5asvyBW1RFqpXi0REHqOGJfUqyrc/ZV7b\nqcBayd2So8i5kJcsSk7I5Etkw899E9ph8kHySB2tFpa+oF4LpAqQqvqqW9o1jaaTBjYsXoqG1FWr\nbj0SBw4bpXkBA+BaVNuMiQ0P1wWjGJVS4V1KdlJtBV/D3/XnInNLy+6lPl5pOq/qlVaqhtLyksfh\nW2u1QyNpj6tp164SYwxJbCgDIVugt33Srb5n9dDqNXcUNqbx6VramYf5PUDAAHgLY0i8xDzfWpGO\nRLKKVKUGybFF0Ec1IlGzjwM5XWBTsy8fDUcrzQVHNtpVZISMpcl8PxkEOrzqrtRtuI5WM24kPO0a\nxEtvY05C7OCsmXZE5CylKh52mLUMpZbZ7O97md2J/Kn7qblFw4nMAFzCJKIhrr6KEJm/WJrCGBKx\nMRc4WwZL8YEUxUzUX5e7mOZVgNM2sZNLICLS1lOkHReHHvbpLWpXWSI2QeMIfOeJPBnjuy44z8EQ\nBfoz9CCyQawlZmutsdTx+KHjDrM+Xj81Pr7AvNyGJoOrd7Hz3niv5hWWzN8HFtiVVItJg+ZQwYgj\nV80Iy9NgxxeTMs3XzIwxphKRqC131RrLd+g773vPzDyNJEo+yRRm3dueKC6eFe0lY/X6vi9NAWN+\nsNXvO1SLtvjeW0fe990sSBWFgF8GAgbA2yTrZNCw3L1TnWhbsVqdSAmOrEQZ0yKw+XJa/EEkPIKW\nji32Fv2KZtg6k6VCO8VLLIrInQlhPoUqKhzCYfgy5o/M3xiJmu6C931c4po+JPPn4cn+QxBrqZmc\n41OAgAGwicVKrEVvsLSZs4bZmLoGxEJNmX6UK2GBVMN626tJp9aVFav9O8Z32aC+ykDsO29Cbf0/\nMLFLObYUXO+9OFeo17iYR0TGkDFCxvz9YpXYc2EXbe7pw6G3QwN2tgey/rJTFwIGwA42VfXVCHuK\nYRTFXzVqo1IYN18JI0cuxJ08hCkUU3LdrbVWM4c0DNKK5b7vvF8a+5JP0lrRmILV03jShBqsE2xZ\nRMqQaFJz7J2WG8pYSngJCBgA5yBCRLbrcmegShczG29coOAmqdCqPbGWrpaGohCItYlivm/bdWRM\nqYKD83A9EU0j31IAfXUDpBm9j7VSlI/S663TCG2GOW9JYwzlPUXneN9NEuR/OzAUAnZ30orG3pbk\n4A70tk/WWDK88lspXthwno+ccH/Od35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"output_type": "display_data"}], "prompt_number": 25, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "plot(y); axis tight;"]}, {"source": ["The pseudo inverse reconstruction is defined as\n", "$$ \\Phi^+ y = \\Phi^* ( \\Phi\\Phi^* )^{-1} y. $$\n", "It is the minimum $L^2$ norm reconstruction\n", "$$ \\Phi^+ y = \\uargmin{ f} \\norm{y-\\Phi f}^2. $$\n", "\n", "\n", "_Remark:_ When $m$ tends to infinity (continuous set of angles), the Radon transform is not\n", "sub-sampled and $ \\Phi \\Phi^* $ is a filtering. For $y(r,\\th)$ a\n", "continuous set of Radon coefficients,\n", "$$ (\\Phi\\Phi^*) y(r,\\th) = \\int y(s,\\th) h(r-s) d s\n", " \\qwhereq \\hat h(\\om) = 1/\\abs{\\om}. $$\n", "When $m$ is large enough, it is common to approximate\n", "$\\Phi^+$ using\n", "$$ \\Phi^+ R = \\Phi^*( g \\star y ) $$\n", "where $g$ is a 1-D filter with $\\hat g(\\om) = \\abs{\\om}$\n", "and $\\star$ is the convolution along the first coordinate of the Radon coefficients.\n", "\n", "\n", "This is *not* the case in our setting, so that $ \\Phi \\Phi^* $ is\n", "actually difficult to invert, and it is thus computaitonaly difficult to compute\n", "the exact pseudo inverse $\\Phi^+ = \\Phi^* (\\Phi \\Phi^*)^{-1} $."], "metadata": {}, "cell_type": "markdown"}, {"source": ["__Exercise 4__\n", "\n", "Compute the pseudo inverse reconstruction using a conjugate gradient\n", "descent (function |cgs|)."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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LGRTNfUzkO9QYaSnIPmsi3wtTDsdKE0uTDSwIdAs6yZxySH5ENuqSnIWzDi5H99xzjxIy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\nrpYAAAAASUVORK5CYII=\n", "output_type": "display_data"}], "prompt_number": 26, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo4()"]}, {"collapsed": false, "outputs": [], "prompt_number": 27, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Partial Tomography Total Variation Inversion\n", "--------------------------------------------\n", "We consider the following reconstruction\n", "$$ \\umin{\\Phi f = y} J(f) \\qwhereq J(f)=\\norm{\\nabla f}_1$$\n", "where the $\\ell^1$ norm of a vector field $(u_i)_i$ is defined as\n", "$$ J(f) = \\sum_i \\norm{u_i}. $$\n", "\n", "\n", "*WORK in PROGRESS*"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 28, "cell_type": "code", "language": "python", "metadata": {}, "input": ["return;"]}, {"source": ["This problem is rewritten as\n", "$$ \\umin{f} F(K(f)) + G(f) $$\n", "where $G=0$, $Kf = (\\Phi f, \\nabla f)$\n", "and $F(u,v)=i_{\\{y\\}}(u) + \\norm{v}_1.$\n", "\n", "\n", "The primal-dual algorithm reads:\n", "$$ g_{k+1} = \\text{Prox}_{\\sigma F^*}( g_k + \\sigma K(\\tilde f_k) $$\n", "$$ f_{k+1} = \\text{Prox}_{\\tau G}( f_k-\\tau K^*(g_k) ) $$\n", "$$ \\tilde f_{k+1} = f_{k+1} + \\theta (f_{k+1} - f_k) $$\n", "\n", "\n", "One has\n", "$$ \\text{Prox}_{\\la F}(u,v) = \\pa{ y, \\text{Prox}_{\\la \\norm{\\cdot}_1}(v) } $$\n", "where\n", "$$ \\text{Prox}_{\\la \\norm{\\cdot}_1}(v)_k = \\max\\pa{0,1-\\frac{\\la}{\\norm{v_k}}} v_k $$"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 29, "cell_type": "code", "language": "python", "metadata": {}, "input": ["Amplitude = @(u)sqrt(sum(u.^2,3));\n", "F1 = @(u)sum(sum(Amplitude(u)));\n", "u = @(z)reshape(z(1:n*m),n,m);\n", "v = @(z)reshape(z(n*m+1:end),n,n,2);"]}, {"collapsed": false, "outputs": [], "prompt_number": 30, "cell_type": "code", "language": "python", "metadata": {}, "input": ["ProxF1 = @(u,lambda)max(0,1-lambda./repmat(Amplitude(u), [1 1 2])).*u;\n", "ProxF = @(z,lambda)[y(:); reshape(ProxF1(v(z),lambda),n*n*2,1) ];\n", "ProxFS = @(y,sigma)y-sigma*ProxF(y/sigma,1/sigma);\n", "ProxG = @(x,lambda)x;\n", "K = @(f)[reshape(Phi(f),n*m,1); reshape(grad(f), n*n*2,1)];\n", "KS = @(z)PhiS(u(z)) - div(v(z));"]}, {"source": ["We set parameters for the algorithm.\n", "Note that in our case, $L=\\norm{K}^2=n m$.\n", "One should has $L \\sigma \\tau < 1$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 31, "cell_type": "code", "language": "python", "metadata": {}, "input": ["L = n*m;\n", "sigma = 10;\n", "tau = .9/(L*sigma);\n", "theta = 1;"]}, {"collapsed": false, "outputs": [], "prompt_number": 32, "cell_type": "code", "language": "python", "metadata": {}, "input": ["f = fL2;"]}, {"source": ["zeros(n);"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["g = K(f)*0;\n", "f1 = f;"]}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["niter = 100;\n", "E = []; C = []; F = [];\n", "for i=1:niter \n", " % update\n", " fold = f;\n", " g = ProxFS( g+sigma*K(f1), sigma);\n", " f = ProxG( f-tau*KS(g), tau);\n", " f1 = f + theta * (f-fold);\n", " % monitor the decay of the energy\n", " E(i) = F1(grad(f));\n", " F(i) = norm(y-Phi(f), 'fro');\n", " C(i) = snr(f0,f);\n", "end\n", "clf;\n", "h = plot(E);\n", "set(h, 'LineWidth', 2);\n", "axis('tight');"]}], "metadata": {}}], "nbformat": 3, "metadata": {"kernelspec": {"name": "matlab_kernel", "language": "matlab", "display_name": "Matlab"}, "language_info": {"mimetype": "text/x-matlab", "name": "matlab", "file_extension": ".m", "help_links": [{"url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md", "text": "MetaKernel Magics"}]}}}