{ "cells": [ { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "Introduction\n", "============\n", "\n", "In most presentations of Riemannian geometry, e.g. @o1983semi and\n", "[Wikipedia](https://en.wikipedia.org/wiki/Fundamental_theorem_of_Riemannian_geometry),\n", "the fundamental theorem of Riemannian geometry (\"the miracle of\n", "Riemannian geometry\") is given: that for any semi-Riemannian manifold\n", "there is a unique torsion-free metric connection. I assume partly\n", "because of this and partly because the major application of Riemannian\n", "geometry is General Relativity, connections with torsion are given\n", "little if any attention.\n", "\n", "It turns out we are all very familiar with a connection with torsion:\n", "the Mercator projection. Some mathematical physics texts,\n", "e.g. @Nakahara2003, allude to this but leave the details to the\n", "reader. Moreover, this connection respects the metric induced from\n", "Euclidean space.\n", "\n", "We use [SageManifolds](http://sagemanifolds.obspm.fr) to assist with\n", "the calculations. We hint at how this might be done more slickly in\n", "[Haskell](https://www.haskell.org).\n", "\n", "Colophon\n", "--------\n", "\n", "This is written as an [Jupyter](http://jupyter.org) notebook. In\n", "theory, it should be possible to run it assuming you have installed at\n", "least sage and Haskell. To publish it, I used\n", "\n", " jupyter-nbconvert --to markdown Mercator.ipynb\n", " pandoc -s Mercator.md -t markdown+lhs -o Mercator.lhs \\\n", " --filter pandoc-citeproc --bibliography DiffGeom.bib\n", " BlogLiteratelyD --wplatex Mercator.lhs > Mercator.html\n", "\n", "Not brilliant but good enough." ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "A Cartographic Aside\n", "--------------------" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "/Applications/SageMath/local/lib/python2.7/site-packages/traitlets/traitlets.py:770: DeprecationWarning: A parent of InlineBackend._config_changed has adopted the new @observe(change) API\n", " clsname, change_or_name), DeprecationWarning)\n" ] } ], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "import matplotlib\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "import cartopy\n", "import cartopy.crs as ccrs\n", "from cartopy.mpl.ticker import LongitudeFormatter, LatitudeFormatter" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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C3749efLkKVOnTiAxMaGA0hcvZd03d/PmTe7de0iHDn1xd/fE2Hg6Hz9+5PLl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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8, 8))\n", "\n", "ax = plt.axes(projection=cartopy.crs.Mercator())\n", "\n", "ax.gridlines()\n", "\n", "ax.add_feature(cartopy.feature.LAND)\n", "ax.add_feature(cartopy.feature.COASTLINE)\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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37/nw4RMfPnzC2fk8mpq5i9J0cHBmyxZb3NweStnqgmX58kXY2Z0iOTmZZ89eULZsuTTn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Sh1yu2SrEAgQFV1EMePH6dPH41SsyM+Pg5Pz3tERUXx/XsUb9++Zf/+g+zZswlt7YHF2ndAQCDD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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8, 8))\n", "\n", "bx = plt.axes(projection=cartopy.crs.NorthPolarStereo())\n", "\n", "bx.set_extent([-180, 180, 90, 50], ccrs.PlateCarree())\n", "\n", "bx.gridlines()\n", "\n", "bx.add_feature(cartopy.feature.LAND)\n", "bx.add_feature(cartopy.feature.COASTLINE)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "Colophon\n", "--------\n", "\n", "This is written as an [Jupyter](http://jupyter.org) notebook. In\n", "theory, it should be possible to run it assuming you have installed at\n", "least sage and Haskell. To publish it, I used\n", "\n", " jupyter-nbconvert --to markdown Mercator.ipynb\n", " pandoc -s Mercator.md -t markdown+lhs -o Mercator.lhs \\\n", " --filter pandoc-citeproc --bibliography DiffGeom.bib\n", " BlogLiteratelyD --wplatex Mercator.lhs > Mercator.html\n", "\n", "Not brilliant but good enough." ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "Some commands to jupyter to display things nicely." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "viewer3D = 'tachyon'" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "Warming Up With SageManifolds\n", "=============================" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "Let us try a simple exercise: finding the connection coefficients of\n", "the Levi-Civita connection for the Euclidean metric on $\\mathbb{R}^2$\n", "in polar co-ordinates.\n", "\n", "Define the manifold." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "N = Manifold(2, 'N',r'\\mathcal{N}', start_index=1)" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "Define a chart and frame with Cartesian co-ordinates." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "ChartCartesianN. = N.chart()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "FrameCartesianN = ChartCartesianN.frame()" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "Define a chart and frame with polar co-ordinates." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "ChartPolarN. = N.chart()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "FramePolarN = ChartPolarN.frame()" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "The standard transformation from Cartesian to polar co-ordinates." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "cartesianToPolar = ChartCartesianN.transition_map(ChartPolarN, (sqrt(x^2 + y^2), arctan(y/x)))" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Change of coordinates from Chart (N, (x, y)) to Chart (N, (r, theta))\n" ] } ], "source": [ "print(cartesianToPolar)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\left\\{\\begin{array}{lcl} r & = & \\sqrt{x^{2} + y^{2}} \\\\ \\theta & = & \\arctan\\left(\\frac{y}{x}\\right) \\end{array}\\right.\n" ] } ], "source": [ "print(latex(cartesianToPolar.display()))" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Check of the inverse coordinate transformation:\n", " x == x\n", " y == y\n", " r == abs(r)\n", " theta == arctan(sin(theta)/cos(theta))\n" ] } ], "source": [ "cartesianToPolar.set_inverse(r * cos(theta), r * sin(theta))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "Now we define the metric to make the manifold Euclidean." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "g_e = N.metric('g_e')" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "g_e[1,1], g_e[2,2] = 1, 1" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "We can display this in Cartesian co-ordinates." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "g_e = \\mathrm{d} x\\otimes \\mathrm{d} x+\\mathrm{d} y\\otimes \\mathrm{d} y\n" ] } ], "source": [ "print(latex(g_e.display(FrameCartesianN)))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "And we can display it in polar co-ordinates" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "g_e = \\mathrm{d} r\\otimes \\mathrm{d} r + \\left( x^{2} + y^{2} \\right) \\mathrm{d} \\theta\\otimes \\mathrm{d} \\theta\n" ] } ], "source": [ "print(latex(g_e.display(FramePolarN)))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "Next let us compute the Levi-Civita connection from this metric." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "nab_e = g_e.connection()\n" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\nabla_{g_e}\n" ] } ], "source": [ "print(latex(nab_e))\n" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "If we use Cartesian co-ordinates, we expect that $\\Gamma^k_{ij} = 0,\n", "\\forall i,j,k$. Only non-zero entries get printed." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "print(latex(nab_e.display(FrameCartesianN)))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "Just to be sure, we can print out all the entries." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\left[\\left[\\left[0, 0\\right], \\left[0, 0\\right]\\right], \\left[\\left[0, 0\\right], \\left[0, 0\\right]\\right]\\right]\n" ] } ], "source": [ "print(latex(nab_e[:]))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "In polar co-ordinates, we get" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\begin{array}{lcl} \\Gamma_{ \\phantom{\\, r } \\, \\theta \\, \\theta }^{ \\, r \\phantom{\\, \\theta } \\phantom{\\, \\theta } } & = & -\\sqrt{x^{2} + y^{2}} \\\\ \\Gamma_{ \\phantom{\\, \\theta } \\, r \\, \\theta }^{ \\, \\theta \\phantom{\\, r } \\phantom{\\, \\theta } } & = & \\frac{1}{\\sqrt{x^{2} + y^{2}}} \\\\ \\Gamma_{ \\phantom{\\, \\theta } \\, \\theta \\, r }^{ \\, \\theta \\phantom{\\, \\theta } \\phantom{\\, r } } & = & \\frac{1}{\\sqrt{x^{2} + y^{2}}} \\end{array}\n" ] } ], "source": [ "print(latex(nab_e.display(FramePolarN)))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "Which we can rew-rewrite as\n", "\n", "\n", "\\begin{aligned}\n", "\\Gamma^r_{\\theta,\\theta} &= -r \\\\\n", "\\Gamma^\\theta_{r,\\theta} &= 1/r \\\\\n", "\\Gamma^\\theta_{\\theta,r} &= 1/r\n", "\\end{aligned}\n", "\n", "\n", "with all other entries being 0." ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "The Sphere\n", "==========\n", "\n", "We define a 2 dimensional manifold. We call it the 2-dimensional\n", "(unit) sphere but it we are going to remove a meridian to allow us to define\n", "the desired connection with torsion on it." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "S2 = Manifold(2, 'S^2', latex_name=r'\\mathbb{S}^2', start_index=1)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\mathbb{S}^2\n" ] } ], "source": [ "print(latex(S2))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "To start off with we cover the manifold with two charts." ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\left(\\mathbb{S}^2,({\\theta}, {\\phi})\\right)\n" ] } ], "source": [ "polar. = S2.chart(r'th:(0,pi):\\theta ph:(0,2*pi):\\phi'); print(latex(polar))" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\left(\\mathbb{S}^2,({\\xi}, {\\zeta})\\right)\n" ] } ], "source": [ "mercator. = S2.chart(r'xi:(-oo,oo):\\xi ze:(0,2*pi):\\zeta'); print(latex(mercator))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "We can now check that we have two charts." ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\left[\\left(\\mathbb{S}^2,({\\theta}, {\\phi})\\right), \\left(\\mathbb{S}^2,({\\xi}, {\\zeta})\\right)\\right]\n" ] } ], "source": [ "print(latex(S2.atlas()))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "We can then define co-ordinate frames." ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\left(\\mathbb{S}^2 ,\\left(\\frac{\\partial}{\\partial {\\theta} },\\frac{\\partial}{\\partial {\\phi} }\\right)\\right)\n" ] } ], "source": [ "epolar = polar.frame(); print(latex(epolar))" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\left(\\mathbb{S}^2 ,\\left(\\frac{\\partial}{\\partial {\\xi} },\\frac{\\partial}{\\partial {\\zeta} }\\right)\\right)\n" ] } ], "source": [ "emercator = mercator.frame(); print(latex(emercator))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "And define a transition map and its inverse from one frame to the other checking that they really are inverses." ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "xy_to_uv = polar.transition_map(mercator, (log(tan(th/2)), ph))" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Check of the inverse coordinate transformation:\n", " th == 2*arctan(sin(1/2*th)/cos(1/2*th))\n", " ph == ph\n", " xi == xi\n", " ze == ze\n" ] } ], "source": [ "xy_to_uv.set_inverse(2*arctan(exp(xi)), ze)" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "We can define the metric which is the pullback of the Euclidean metric on $\\mathbb{R}^3$." ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "g = S2.metric('g')" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "g[1,1], g[2,2] = 1, (sin(th))^2" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "And then calculate the Levi-Civita connection defined by it." ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "nab_g = g.connection()" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\begin{array}{lcl} \\Gamma_{ \\phantom{\\, {\\theta} } \\, {\\phi} \\, {\\phi} }^{ \\, {\\theta} \\phantom{\\, {\\phi} } \\phantom{\\, {\\phi} } } & = & -\\cos\\left({\\theta}\\right) \\sin\\left({\\theta}\\right) \\\\ \\Gamma_{ \\phantom{\\, {\\phi} } \\, {\\theta} \\, {\\phi} }^{ \\, {\\phi} \\phantom{\\, {\\theta} } \\phantom{\\, {\\phi} } } & = & \\frac{\\cos\\left({\\theta}\\right)}{\\sin\\left({\\theta}\\right)} \\\\ \\Gamma_{ \\phantom{\\, {\\phi} } \\, {\\phi} \\, {\\theta} }^{ \\, {\\phi} \\phantom{\\, {\\phi} } \\phantom{\\, {\\theta} } } & = & \\frac{\\cos\\left({\\theta}\\right)}{\\sin\\left({\\theta}\\right)} \\end{array}\n" ] } ], "source": [ "print(latex(nab_g.display()))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "We know the [geodesics](https://en.wikipedia.org/wiki/Geodesic) defined by this connection are the great circles." ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "We can check that this connection respects the metric." ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\nabla_{g} g = 0\n" ] } ], "source": [ "print(latex(nab_g(g).display()))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "And that it has no torsion." ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0\n" ] } ], "source": [ "print(latex(nab_g.torsion().display()))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "## A New Connection\n", "\n", "Let us now define an orthonormal frame." ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "ch_basis = S2.automorphism_field()\n", "ch_basis[1,1], ch_basis[2,2] = 1, 1/sin(th)" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "e = S2.default_frame().new_frame(ch_basis, 'e')" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\left(\\mathbb{S}^2, \\left(e_1,e_2\\right)\\right)\n" ] } ], "source": [ "print(latex(e))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "We can calculate the dual 1-forms." ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\left(\\mathbb{S}^2, \\left(e^1,e^2\\right)\\right)\n" ] } ], "source": [ "dX = S2.coframes()[2] ; print(latex(dX))" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\left(e^1, e^2\\right)\n" ] } ], "source": [ "print(latex((dX[1], dX[2])))" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\left(\\left[1, 0\\right], \\left[0, \\sin\\left({\\theta}\\right)\\right]\\right)\n" ] } ], "source": [ "print(latex((dX[1][:], dX[2][:])))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "In this case it is trivial to check that the frame and coframe really are orthonormal but we let sage do it anyway." ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\left(\\left(1, 0\\right), \\left(0, 1\\right)\\right)\n" ] } ], "source": [ "print(latex(((dX[1](e[1]).expr(), dX[1](e[2]).expr()), (dX[2](e[1]).expr(), dX[2](e[2]).expr()))))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "Let us define two vectors to be parallel if their angles to a given meridian are the same. For this to be true we must have a connection $\\nabla$ with $\\nabla e_1 = \\nabla e_2 = 0$." ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "nab = S2.affine_connection('nabla', latex_name=r'\\nabla')" ] }, { "cell_type": "code", "execution_count": 115, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\nabla\n" ] } ], "source": [ "nab.add_coef(e); print(latex(nab))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "Displaying the connection only gives the non-zero components." ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "print(latex(nab.display(e)))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "For safety, let us check all the components explicitly." ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\left[\\left[\\left[0, 0\\right], \\left[0, 0\\right]\\right], \\left[\\left[0, 0\\right], \\left[0, 0\\right]\\right]\\right]\n" ] } ], "source": [ "print(latex(nab[e,:]))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "Of course the components are *not* non-zero in other frames." ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\begin{array}{lcl} \\Gamma_{ \\phantom{\\, {\\phi} } \\, {\\phi} \\, {\\theta} }^{ \\, {\\phi} \\phantom{\\, {\\phi} } \\phantom{\\, {\\theta} } } & = & \\frac{\\cos\\left({\\theta}\\right)}{\\sin\\left({\\theta}\\right)} \\end{array}\n" ] } ], "source": [ "print(latex(nab.display(epolar)))" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\begin{array}{lcl} \\Gamma_{ \\phantom{\\, {\\xi} } \\, {\\xi} \\, {\\xi} }^{ \\, {\\xi} \\phantom{\\, {\\xi} } \\phantom{\\, {\\xi} } } & = & 2 \\, \\cos\\left(\\frac{1}{2} \\, {\\theta}\\right)^{2} - 1 \\\\ \\Gamma_{ \\phantom{\\, {\\zeta} } \\, {\\zeta} \\, {\\xi} }^{ \\, {\\zeta} \\phantom{\\, {\\zeta} } \\phantom{\\, {\\xi} } } & = & \\frac{2 \\, \\cos\\left(\\frac{1}{2} \\, {\\theta}\\right) \\cos\\left({\\theta}\\right) \\sin\\left(\\frac{1}{2} \\, {\\theta}\\right)}{\\sin\\left({\\theta}\\right)} \\end{array}\n" ] } ], "source": [ "print(latex(nab.display(emercator)))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "This connection also respects the metric $g$." ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\nabla g = 0\n" ] } ], "source": [ "print(latex(nab(g).display()))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "Thus, since the Levi-Civita connection is unique, it *must* have torsion." ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\frac{\\cos\\left({\\theta}\\right)}{\\sin\\left({\\theta}\\right)} e_2\\otimes e^1\\otimes e^2 -\\frac{\\cos\\left({\\theta}\\right)}{\\sin\\left({\\theta}\\right)} e_2\\otimes e^2\\otimes e^1\n" ] } ], "source": [ "print(latex(nab.torsion().display(e)))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "The equations for geodesics are\n", "$$\n", "\\ddot{\\gamma}^k + \\Gamma_{ \\phantom{\\, {k} } \\, {i} \\, {j} }^{ \\, {k} \\phantom{\\, {i} } \\phantom{\\, {j} } }\\dot{\\gamma}^i\\dot{\\gamma}^j = 0\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "Explicitly for both variables in the polar co-ordinates chart." ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "\n", "\\begin{aligned}\n", "\\ddot{\\gamma}^\\phi & + \\frac{\\cos\\theta}{\\sin\\theta}\\dot{\\gamma}^\\phi\\dot{\\gamma}^\\theta &= 0 \\\\\n", "\\ddot{\\gamma}^\\theta & &= 0\n", "\\end{aligned}\n", "" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "We can check that $\\gamma^\\phi(t) = \\alpha\\log\\tan t/2$ and $\\gamma^\\theta(t) = t$ are solutions although sage needs a bit of prompting to help it." ] }, { "cell_type": "code", "execution_count": 71, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "t = var('t'); a = var('a')" ] }, { "cell_type": "code", "execution_count": 73, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\frac{a}{2 \\, \\cos\\left(\\frac{1}{2} \\, t\\right) \\sin\\left(\\frac{1}{2} \\, t\\right)}\n" ] } ], "source": [ "print(latex(diff(a * log(tan(t/2)),t).simplify_full()))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "We can simplify this further by recalling the trignometric identity." ] }, { "cell_type": "code", "execution_count": 74, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2 \\, \\cos\\left(t\\right) \\sin\\left(t\\right)\n" ] } ], "source": [ "print(latex(sin(2 * t).trig_expand()))" ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-\\frac{a \\cos\\left(t\\right)}{\\sin\\left(t\\right)^{2}}\n" ] } ], "source": [ "print(latex(diff (a / sin(t), t)))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "In the mercator co-ordinates chart this is\n", "\n", "\n", "\\begin{aligned}\n", "\\gamma^\\xi(t) &= \\alpha\\log\\tan t/2 \\\\ \n", "\\gamma^\\zeta(t) &= \\log\\tan t/2\n", "\\end{aligned}\n", "\n", "\n", "In other words: straight lines." ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "Reparametersing with $s = \\alpha\\log\\tan t/2$ we obtain\n", "\n", "\n", "\\begin{aligned}\n", "\\gamma^\\phi(s) &= s \\\\\n", "\\gamma^\\theta(s) &= 2\\arctan e^\\frac{s}{\\alpha}\n", "\\end{aligned}\n", "" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "Let us draw such a curve." ] }, { "cell_type": "code", "execution_count": 77, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Real number line R\n" ] } ], "source": [ "R. = RealLine() ; print(R)" ] }, { "cell_type": "code", "execution_count": 78, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1\n" ] } ], "source": [ "print(dim(R))" ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "c = S2.curve({polar: [2*atan(exp(-t/10)), t]}, (t, -oo, +oo), name='c')" ] }, { "cell_type": "code", "execution_count": 80, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\begin{array}{llcl} c:& \\RR & \\longrightarrow & \\mathbb{S}^2 \\\\ & t & \\longmapsto & \\left({\\theta}, {\\phi}\\right) = \\left(2 \\, \\arctan\\left(e^{\\left(-\\frac{1}{10} \\, t\\right)}\\right), t\\right) \\\\ & t & \\longmapsto & \\left({\\xi}, {\\zeta}\\right) = \\left(-\\frac{1}{10} \\, t, t\\right) \\end{array}\n" ] } ], "source": [ "print(latex(c.display()))" ] }, { "cell_type": "code", "execution_count": 116, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\mathrm{Hom}\\left(\\RR,\\mathbb{S}^2\\right)\n" ] } ], "source": [ "print(latex(c.parent()))" ] }, { "cell_type": "code", "execution_count": 82, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/plain": [ "Graphics object consisting of 1 graphics primitive", "image/png", 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UfmYmnDxpO5E4hIpeJJD06AFTpkBWFtx+O5w6ZTuROECY7QAicobUVDN006sX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\nIiIOp6IXEXG4/we9CUJvGgDcZgAAAABJRU5ErkJggg==\n" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c.plot(chart=polar, aspect_ratio=0.1)" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "It's not totally clear this is curved so let's try with another example." ] }, { "cell_type": "code", "execution_count": 83, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "d = S2.curve({polar: [2*atan(exp(-t)), t]}, (t, -oo, +oo), name='d')" ] }, { "cell_type": "code", "execution_count": 84, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\begin{array}{llcl} d:& \\RR & \\longrightarrow & \\mathbb{S}^2 \\\\ & t & \\longmapsto & \\left({\\theta}, {\\phi}\\right) = \\left(2 \\, \\arctan\\left(e^{\\left(-t\\right)}\\right), t\\right) \\\\ & t & \\longmapsto & \\left({\\xi}, {\\zeta}\\right) = \\left(-t, t\\right) \\end{array}\n" ] } ], "source": [ "print(latex(d.display()))" ] }, { "cell_type": "code", "execution_count": 85, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/plain": [ "Graphics object consisting of 1 graphics primitive", "image/png", 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] }, "execution_count": 85, "metadata": {}, "output_type": "execute_result" } ], "source": [ "d.plot(chart=polar, aspect_ratio=0.2)" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "Now it's clear that a *straight* line is curved in polar co-ordinates." ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "But of course in Mercator co-ordinates, it is a straight line. This explains its popularity with mariners: if you draw a straight line on your chart and follow that bearing or [rhumb line](https://en.wikipedia.org/wiki/Rhumb_line) using a compass you will arrive at the end of the straight line. Of course, it is not the shortest path; great circles are but is much easier to navigate." ] }, { "cell_type": "code", "execution_count": 86, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/plain": [ "Graphics object consisting of 1 graphics primitive", "image/png", 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] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" } ], "source": [ "d.plot(chart=mercator, aspect_ratio=1.0)" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "We can draw these curves on the sphere itself not just on its charts." ] }, { "cell_type": "code", "execution_count": 88, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "R3 = Manifold(3, 'R^3', r'\\mathbb{R}^3', start_index=1)" ] }, { "cell_type": "code", "execution_count": 90, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\left(\\mathbb{R}^3,(X, Y, Z)\\right)\n" ] } ], "source": [ "cart. = R3.chart(); print(latex(cart))" ] }, { "cell_type": "code", "execution_count": 91, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "Phi = S2.diff_map(R3, {\n", " (polar, cart): [sin(th) * cos(ph), sin(th) * sin(ph), cos(th)],\n", " (mercator, cart): [cos(ze) / cosh(xi), sin(ze) / cosh(xi),\n", " sinh(xi) / cosh(xi)]\n", "},\n", " name='Phi', latex_name=r'\\Phi')" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "We can either plot using polar co-ordinates." ] }, { "cell_type": "code", "execution_count": 92, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "graph_polar = polar.plot(chart=cart, mapping=Phi, nb_values=25, color='blue')\n" ] }, { "cell_type": "code", "execution_count": 93, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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ZW1CwHaZBbfyqqGikXBNJ1rhjx45Ej7YQCouLW4Z7A/NTnvVAgXb+RCNEtVJ6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\nxRDZmnC0EMZcgq0il6ER9kEOd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"text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(graph_polar, viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "Or using Mercator co-ordinates. In either case we get the sphere (minus the prime meridian)." ] }, { "cell_type": "code", "execution_count": 94, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "graph_mercator = mercator.plot(chart=cart, mapping=Phi, nb_values=25, color='red')" ] }, { "cell_type": "code", "execution_count": 95, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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S+jo+4yNet2KnEJ1wwMevcp+6xLYbYTG87jptobqTaowxzW3npP0+adKkSZMm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\nw8Pl5eW5H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"text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(graph_mercator, viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "We can plot the curve with an angle to the meridian of $\\pi/2 - \\arctan 1/10$" ] }, { "cell_type": "code", "execution_count": 96, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "graph_c = c.plot(mapping=Phi, max_range=40, plot_points=200, thickness=2)" ] }, { "cell_type": "code", "execution_count": 97, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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+Db7ik08mRUX1mDWrh81Gq1Y/Pu7nZ4+b9a9+d/6+Q6+1YFmB1h7awSUgQcIx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\nx+/N5MM0NRTymzvmYYFCoWZ4GB7v/m33eZwx7n8JlO+nXDpgPPwEmqu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A/XnNYu90HPPu\nDZoM44SMe7dd+tJ+cXfTCkpIJhIqclikNfcpkS5yNLlS71kIhxUmw2bb1ppwYhSMg8chAIfjfs/F\ntm5D6F23HfClwUxzem7LDlW1rM3Q6nduKjucBvRvWRr30895F7kd7vlnJmpsp0inxU0k3oQRjtPZ\nyQhiaQbctrc7TkO3febC4UQgMEtVbVsNY2s0ugvGwytwj8gfIpEl3Vyvahi3JJN5WP5AoBryuzaG\ncY1hXAMB1z3eg0lk5BTXdYPBQEan6qTnbcinxu66h2GH6+bhNHqhwP7MM8/kDjqOQsvAgfNPxLh3\nu5kcPbH8KCWFyRcRE+kSEekq+1XwWpE1sBI2ZtvuePxR+CVcBbfTH7bCxu6322XnP4Hfw8RCUVMY\nBU+Wo+d+xrifGpwGn3sWvm7eBgvOYb5peqZZmx43zXFwbzQaf+sthX3Hjqmqisw0jFmlLOu6LXAw\nmTwMzY6zMxpNwAKRmcHgapgFzztObVZdaxaOHctP5sKmSKRLeNbz/FqnF3IXnCzit2QaA5FUnU4R\nBIOLYE8kksefLU0HvgvySgjAQ9A0cOCkEzHu3YYcRBJZ5ElelO4vJxJq2wkIwAjPO87M2PYekexC\n0HDY99ZrRY4WyYOcadsBeAC+wn2ZzUC6hWVNhpvhKZiQJRCdBlgw1LK6/xD6Gs7QMqcGp5nnXlVZ\neQ4Xw86P8vvc5nbwe7g3GFzid0UQyW6cVBzQ6rrLYRdMMozVnnc8/UZkLUyD8bad564/Y1reZXdH\nIge006Ncn7ctwwKR2dAKB2A31BtGiaxKILCpkB6vYWRrTHaLvNkyyaQfUH3yRIx7KR2rM5m0QugR\nGZJ5VTrs4XmJzDPYtttgDTSXKCtfFa66Hn7HQNj9Hkr9clnWLBhrWR1wD+wpoBx5GdxZdrTM6UH8\nnjHupx4jTLM/18AeGGWac3InwGiIwmYI9FAVyk9Wew2abDv/vb/IazAFZtr24QJ9J/KYJ2iBepEj\nWZccjUbrRJbBSJgEOyBhGOp535Pu7WAahrHRMPLP70Vzn44c9sp15wwePB82VVTMPDHjXlBXJ2NO\nN1HKbon7oosvhtUiz/rCjSLLYL7foalHB0Y4rNPD+rT8N8T/ielPwfoSrodnTDPdHSyWt5oBrocn\nfeX3MsLpYWHK0rjr6fLp+wgAPAVtuU0P0oAH4WHD+HVPF4coxEs5EuBVqIZprnvI85IZ46szp3me\nX5e4PRLJtr/LDSMGu+EgzBXZ6rq7IhH/KccpljKfs5PNIvnDg92GDXMxeHAofcMgcshx1POSMAlW\nwqaKCnPw4CPpFPbMRHbHeUOLhnALcRFd53RDdIi80dMk9zRs+zC02fYueBnqIAZ1vVhN5JHUggp7\nxsEL8Bh0FP67gRfh9a4jeY4x+A0814vf2qnF6UH8lqtxPz0+fR+ebffnPmj4TSC/PFMs5itSPVRZ\n2YPmPseOKSwVaSpRcsBHIqGwAKphrq/T67rtjtPsuhugChpExsK2YDDDnfc8Xyhrb4YYehY6OlSk\ndMGyva6bP4EkGGyMRjtfOpnc57otjrPRVziAbY6jsF3kWLrwSEQHDpzrG+j0vpJJdZxlsKGiYviv\nfnVDt/vxL3cchSbYBnsgASuhOe13FzoDoLW4b+4n+/cCntchsg6aIQbr/MFw2Bf/Kqm4LGOTnV5F\nPK5w+G578wMwDp6H7flceJgKC+DJroP7THNFzsx74elSAg99CmdomVOJ0+PT9/Gs45zDD2FkNFyV\nd0IsprA5GBwPo8PhYq3mfCSTB1y3wW+ZFg6XWv2fiY4O/2x4HRbCi/AqvBiNblPVZPIg7I1E9uxK\nJmsdZwFshq3QrWdeOl0OG1z3OOORTO5VVc9rCwYbUqX+G2CXYRzsNafhONWQuPLK+3tNy6TzOz1P\nRY76pt9xfJ2WVemDBFZ0Z9xLPfNS8+OwApr9bhxwGLJNqm3vF2ku3YW37cnpx7Dbt+d1tj0WXoJn\n4a4MESqY7Ge/pAVkUuProNo0j4f6LWsdPBiLlRR46FNoz9v+ptzwjlOgVXYy0NDQ0N7efqp3cXLw\nXsNoowL+WmtfzjvhYx+rs+3zXffrsO+yy8YWX+2GG+o/8pFFAwb8q+oFwGWXtUJjT7fUrx8TJmxx\nHF+g8e/gbPiXCy+s79dv1vjx26D5X4zk1AsvZPToAdAG/aNRLryw+JpNTaX/vt4POn588sMf3tav\n344LLzx4wQVtL7980DDeHwy2RyL9k8kPq763sfHv7r+/+7UikUjuoONcCM2NjUbJW8rGhz/c+eDS\nS6mpeef996M64P77qal5n+d9trZ2RyTSeMEFy+BgTQ033NCRd5EbbpjqOPu7fa1kkgsuWNuvX7xf\nv921tX+TSHxe9YOq59bUIPIGnJs1f/Tos2tqPgj06zezX79Xii/ueV1+FOmUhPzU6NFXqv6tSD84\nD57u1+/d/W7o1+/VePy7551HOJwQGZR5YSj0SdP85OLFdekR2/4kVJx3HlBOX9UXX3zxb/82vwxq\nmeFUny69x+lEu8NQGHkTZ2eNJxIKL0BjVZU/bb3IVHgchuZdJxJJwtSuKx/M6m9ZCoLBZYZRJ3Ig\ntUhLIuGz7fOgGlbC1A8w5gtcP1YuK3HNUrxsz1O4Fg4Yxlp/flY01HVX5MuM7zE8rwmSIvf12nP3\naZ9u4Thv+ulGIhtEHoaAyMg0h1OE0Pc8FdkjcgSaYW+hGCdMLB6uTCQU5hbx4nO6rzyb62g32LfD\ngzDrSnneb91nWVtN86XMOaGQwu5YTOFmf8Sylvo+PqwtI2HI04byPWPc+wSgCkb8nE9ljYvMBC+d\nlQHJYHBTMOjBWNveeCyDrU0m9znOoixZEr8XtsiDtp2/DWYWksmDweASw9jiOC2Zdsd1m4PBFlVt\niUah8eNMuJJfnUsEFsAKeF2kM45XxFplPZVM7nXdxrQkl2G0Os6uSKTdcTYWETnp6NB005ISkTfP\nXWQk7BOZciK0TInT8pISItsdR2Fe+pBobVXbbrVthXrY4Tds6jZpxfO0lNZa4bDC3NzxeDxPqmtW\nFlA4/AY8BQuH8PXbIACjTfNC/pC7mh89TmsiwdN+EmTel+6zOG0MyxnjfuqRTL4BW/vzm4v4jmYU\n88Eo01waDmsglUTTtVH9I5niM/CSYcyJRLZkrgwNhnEoEonCA93tYY/rbjWM5TlCAKqqHR3qeaqJ\nxH2cB20/5gOZHrUvhAIroB7WwUyRqOMsikazMwUdZ1s02tjR4Ud6VaQtGNziul2ibcb/Z++9w+O4\nznv/D5N7bx7+4ktbdInLynHMyLmmr+0kTrKvXG4SJaGdKHFiZyHLtizZKqb7nqEsx5ISUTapakGk\nJJoSVahK7g4oUuy9F4BNJAg2sO7uACAIFoBg7+/vj7M7mK1YQLEJQPg+evgsZs+cObur+c573vJ9\nQ1NLJFdcvtxldfiC5O44s2CbyDO/aXLX4mKcjnMRlmR0G60efXuXfOWqKnIGOg/DWBhzCWYGj8Tj\nBck94afJGFMLa0VaVfWXJv5l3nk3TIZXYHTevh+aMi++BbdCjf0zHO5a4euVRb/lfuXRZ8i9srIF\n6v+cz8AjGti+wmRVDYXqfTnfNWuySjThRWOaLl7UUGipSG5UTVWhxd6ltgCqBGBeCSPxucq53+Nz\n2+Gf+UVp3eA1a9RxGmALbIPNsFbkCMyEp2AibLBK69XVZ6qrCwcSQ6HtoVCp/HGfQcpEcXI/OGzY\nr7tN7iXyVvNGHvWfBK6rIgegHg7DMWgWSYvUa4caz7rys9ShATZ0Navd5+4iFWoLRS5oOt9xHSzI\nfvfFBxj4MoyHKGSbI7vs/7+x2AmY4DcPiEZ7Db/3jVCqRS8m99OnT/eBEmFVFZkeCnk3wUDu/rvQ\n7arqeW3wtKquWXMyx4zNSa6ASnglFHoh///JNWs6tEdEzhW7/x97TI1RxzlfbHlTKyrmhEJJ2AOw\npZhOZD48z+bO18MWSFrhclgPcxxnj+NUV1V51dVJVfW8DscCHKqoKJVXU0Jmq3y4rgc7QqH73gK5\nFyg3yxsz13Fs2OMkNMFx2O84KnLOZtOX8Nobk64wKG3Iu67CtG7UuIrUGbOroChxPK7QDPOKFbjC\nG58l+kP4IUQC9ns0ujeTSDMTXvSFKmMx7S0+9z5jMmrvzZYBdu7c2Vf6qf5Pkav/SmQgB3Y3/m7t\nlCl33jkxFNoFXH31/4Lfqalpt+MuX2bt2ov+aVVVqVBoSCg0oLHx926/fXnOpHfe6YnYbp1UVOwW\nyb3q1VdPGzBg7Z13MmYMjz/+P/OXdbyhYdGIEVdPmTK0sfEIHK7WUOiYn01RGtdee/LDH747FLok\n8j7P+5OqqovV1R8MhQiFflfkI1OmXBoz5v033PA7n/3s5QEDkh/+8OYRIxgx4tK11x6Atpqac0BV\n1e4icx8rZwE+VLXIO783aFDhJJZOcegQ8Hv2dUMDwIgRXHtt+4ABrQMGtAwYcHzAgPYBA9rg45kz\nTqh+UPV/q/7R449TU/O/Hn+ctWu54YailxgzBtVPeR5jxnDtta0Fx3geN9xAKvWVsWO79p0ANTWf\nXLv2rMh78t8aO/YQHBL5jOpnipxddyl8wzhV4H0w1xh71JghN95IMsm6de3hMDDAHl+7lq9/PdHV\nFV4R7Ny580ov4b8PV/rp8pbQN7xjMMVxUhdTqa/zh/DYQ2YyDLdvOU5TKJTwR3reEdjueWczJ1Y5\nTp2qVlc3wcu2KYcPkb1Bgy4U6jB4q6rqYRmUUoU84Lou7IQEeJHIMncj7Oi0JtNx2iORsyJHKysL\nNAN0nBqRfZqdAyOyo6KiAepDoX2QgMPQDAlogF1QC4thvbVzPU9FZnZDGzIHIqOhQWRSp5a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36kozAz+EzKiNLsggPQDmdESjXVE8liYWNOiTT4qr+adtDnbvUsSkj4GjOzmDEOC2FrTjK7qoos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\nc492dIuCyCM3Nzc3N1cre5SjxV1Tqe+6RDKS0KvVNFrcNQBJSUlFRUVa3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"text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(graph_polar + graph_c, viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "And we can plot the curve at angle of $\\pi/4$ to the meridian." ] }, { "cell_type": "code", "execution_count": 98, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "graph_d = d.plot(mapping=Phi, max_range=40, plot_points=200, thickness=2, color=\"green\")" ] }, { "cell_type": "code", "execution_count": 99, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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HR79mt1+ckHDkMj7vwLo/sbIzSMgBDyxHL2KQh6VwKfQHi8t1rTm+1KRp6xMS\njkEfburO9cUEIGfW/ik+9VTyzJldZszoYrPRrNlPywMC7PEz/tH7rj+07bYaLMvQ2kBruAQkSDgG\neXQp4chVFHeEfRAAl0ARlGHpKu79NoF2uK4kfzm9L6HjJoSFa8vZ04KW7UnsAEEklNJVkCChLZ7L\nQEJzuBRaQgsIgC/g72CB5nACjkMpSJhDn3f4Fgql7FfvJ6lpsxMSOkAQuKTUaiz/DoLi4wWgadsT\nEo7CcdgLUoiu8fE31FjTk5BwBA7DrJcYvww9G3sPnFnZg9QtQZooJCQEGDdu3JndrU8MXzJ566hy\nNk5ezLaayMjIM75nJSxsIdjgLXgNXtD1Q1ZrSQcS3+f2dRALo2ASvARd+CskwzFdl/AB/FvTal/9\ni4mRUGi17pdS6l/qPFFPtR3WQV7dksTElJrXM2EZbPjpifHj1wuxHFZCCgzn7o/4Uzl4oAxKoBRK\n4SCUQCGk0L4I8mEH7IJtEArZsA92gzncqQQOV+3BnP+lAo5ABawjSPBRLmyHdbD31Oq5PFnFXtfQ\n5wmvV62z0ez9IsQPQtQe36frEtyQBUtgmK7Pr/PsARjdh2GD4RX4sk4xlLrM2npZWdnZ2LmPNLhL\nLzbLyLN2/mJ+cyriz5Tjx6XV+iLYYDYYMAmywN2Tf9lgNMyB92AsfABW/gMHaiUMjLVaJ1U/tFpT\n4XB1fz5rfysDwMYJecJcUlkpIdluL4yLO1S3PC6X1PUFul4oRHG9BR4k4h5iTCA6LEmBTZAF22EX\n5EMe7IZU2sB322l/GA6BBzzwMVTAMfDAKrpAVAbtSqAYisEFuyAZUmABXa5nAiy7iXca+eiE2Fqd\n3XWeijYb1h0OCTMhChY0tB+HQ8J++FbXk80GrOqUdzjK4XVYbWHac/Aq/Jlbs7MbKdQFLTk5+Sxl\nejUV7lJK+Ys7zDSRmfLJycln9VX8mzk0CZ6DxPvuixRiCux9kP9UXQzlUSz3Yn0LxsE/uaITDfUz\neU+IeUKsghKIh1XVT4mXBP1h4MmfotstIdVur90xPi6uqGpXNngPEsEFB8ED+bDHMKRhSLdbut3S\nMCR8r2kr3G75/PNvnLKjEyc2BQdfwX/hvxH2EfttNul0lmvaVhhjtR6y2fKFSBNCugphSrCYfLK3\nvEtKKW/jP8UucxKC/RAFEbAIcsAGz4JNiDHmQKfqQNf1fEjQ9SO13o7D4TbPP3T9ECwTIhfcp1xa\nqOcz3GMeFB0Ol66nwQKYLsQYGC7ELii/nBnP0t6AnkwV4kRj+7rwnJsKn0911PZmuJ8aQJxJAAAg\nAElEQVSbQ1xycvLZOwXzb/ACfCPEQkiE70GH0ePptQ1Gw6N0nK/rvxcj4OWX6TIW3oGyBgbY2O0r\nYC18IsQMh0Pq+vGfXuWPMBAGkluQa7XGwC6Iq6yUQnggvaqqvUPTyjStLCxsI4yC1LqjomrStKWw\n0Px706ZN9b21mRARHZ17uk9geqPP2iAMltZaLkSylFLXpRB7IRJehkzYoOvrT918HKwQItN86HBI\n2CfEvkZfcTEcggPVS1wuCa/DECHGQAa4ezDagNZEgOpCI+W5inWTT4219MNmmXqZEa/aapoO/q3r\nxQ5HOSRCMriu4HF4Ox2krps1WSkl/AAlT4rUEBgH79R3FcflklBqtcbGxEj4Ar6CCTExUkoZG5vD\n78AGve+yWn8w266FqDS7sNfswWLKyZGwzm5PO13h51anf2VlZX0rrIT/2e2rTrefrxt99iWXS+p6\neeM17qqVl0MK/A1Gw0ewDmJggpS1ptmRsKORMaiQLkQh7IUVVUvecjgOmqdSFt6H8tYkL9dDdH0d\nhOj6aT4rf1VeXh4SEnJme8Kclu+0yUjvhrtXOoRW93wqKKg97FsxadpIiNV1WeI6FsjTkHElS2Zx\n80PcC6f8rwI5QpzMpiKHw8z3zTWizuGQsALKjlfV1A1jNugQBjPgIy62c19btLuxTD/ttcDc3DKY\nZxi7G1/NMNw1a9OjR4+uuw6Mh9Mf6Q0jC75o6FldP9lKLsQ2XT/Q0Go1XvRj+B6WCXHA/NDgK12f\nDy9AAmyHFQ6HhCVQKEQ91xuklLoe43AUyZNnBuaB890az87/Ex1fhGCQ2Qd0PQ5CLsDpCkJCQkJC\nQs7966pw/4m3zmKGDBny73//e/LkyVu21DNg/UKmaSPh1R/Cvo0Q9mt4D/b3ZLgNtut6wpLs6nDX\n9Qo4CBtrbvu1EO/AOHParZOtyYVWa6rVusxuD6u6KmszM9FsmIbZMAOWwul/CfA9LNe0MadbbUbN\nRpvg4OD61hnSxEm4YEZDTxnGAqfTXbXaEl2vf7CFrh+FhbBZiHIhsuCni0DwbZ2V4yAYpkIG7Ks7\n1ZqUEvQaf38Nn9ZaYTD8Fd6BCD1N11fC8KacW/iBlJQUb8W6D/JyuHv3QDd06NDHHnssJSVl1apV\nXiyG7wAbPP0Kd96FDvstxA/ixnKHY8OMGVUrvOVySSiEInjb4Til5XtnXJwBY2AMtGEOlEO0EGW6\nLoODc6SU0dEp8EnNTRwOyW39+P1v6DAJlmhafEON6ZqWCBut1o+q87RelZUSvo+N/akpZty4cQ28\n01l1l9e35kTDKGzoWU3bV2PNnzo+OhxS1/dBOmTDFiFOOU2EreYfNS+91tWvXz7sh3RIFmJz9ZoO\nh1vXq9tkPoB4yK+54WAYB5/DE7wkhIQp8Jl/19/Ly8unTZs2bVrtefbPJd8Zm2q6oMNdSrllyxa7\n3X7fffc99thj5eXl3i2Md8FzYLuZv9xMFOyy8m6Y3b4nLu7Udd6Db4KDD2raMvg8Lu5kn7ucHBkd\nnWO3f3MDfV6gzTh4F7Y5Mmq9RGxsTvVkKdJsi79kLQ+DHU0f4nZLw6iANZAAKzQtyWo9GUiGkQMZ\n0dG7NO00TahOp6xujG70zY5sYrhLKWF+Q09p2q4aq4XBIlgOO2EXNHiHDSG2Q5ZZTog/3atvh53y\nZHN8NDwrxBjzYxRigTnXjcsl4adfbyhMhg+xtGOCEOVQAavhs0aKdF7zkdq6T3WVkV4Pdx851pmN\nMykpKSkpKRdmxMM0sF3JP65kDuQ+ah22P/eUniRxcWWwBRZAaFjYak1bL6U8cULGxEghdoAb0u32\nSKv1kyv4IRTeh3frXFyFn1pUDEPCLuPjb3gYnkIbrdVa2TDMq7UbwOyuEx0WVtpIzprlgVnBwad0\nfrXb7fW9XwfMbLzLTY2VZ2naKcOL3G5pGIfcbvMyaSbkwm7I17QM+MFZzzSUtQmxALKF2NHIQKca\nBciseUFC17cLMRN0mFqz3QbKYP/T3DIB/gcyO1vX55t93qGo6sL46a8NnC/MRpiUlBRvF+Qkr1dV\na/FyuEvfO9yFhIS88cYbO3bs8HZBzhFNWwaTqnr1pUGcENm1OpgEB28yx/FIKeE1CIG5sB6ShPip\nU6PVmgm5I3X5DzAb39+uke+xsaWw0vzbMPIg3+2WlbKSR+Ep3LLBoIUYiDMMCfGQCpthK2yApbDG\n6ZSGcbIXud2+BJbExp7s7e50Sk0rufXWl222PKt1ndW6T9Mk7NQ0CT/CNMiFHKu1ALZarXshXdN+\ntFr3wwZNO2QY8Zq2ABbAck3brmkHYDFkwX4ohT2QAgmaVmoYNT/PHYZRT/+cunTdZV5EbcrKQmTX\nbIIXIgocup4kpQQnzHe55DzH8Re4SqfXP3iourmnenZi+ABeh0TY3pRX9GUej8enYt3kU/0gpS+E\nu699IlLKefPmSSkff/xxX/v1nHG6vhf+ej1DYQ64YFrdVgKrNRHKgoOz4uIKnE6zq3UojK5ZZ3S5\nJCTXrF2+AeNgLkTCGHDHxUl5smsjOKEgNlZKKcNmhfEYPIU2qnbN3eR0Sk07ObGt2232g9wBqZAJ\n5vhTF+yGXMivCt9UMGcWyII0SIK1kAQpMA/SYD2kQBRsg2zYCebkY/mQA4VQAYchD8rgIMTDIlii\naeVSSsPI1rRCt1uCW9NcsBf2Q4GmFcFeWAarDGNrE7+Cpt98Q4hsKISNup4Fsx0OqeulNZ7N+Bt8\nBF/BdSyruc+qNpxx8BfIgDV17xByvjBj3RcaYWopLS31tXqq98Pd185lqu3Zs0dK+dxzz913333e\nLstZ4XAUg20YPSFYiBJdl1B7vA+kw16rdQlsgM3BwTmw2OGQMFaI2TVW2wa1O6XPgiWwCOZAJISD\nlBIWwN7qhgtnkpNHTqm5x8UdiI7eYbWuMwypaatgqznno2Es0LQEiLXbC6Ss59ZOUkpYbS43a+5u\nt9S0grZtVwQH79G03YYhNU3abMedTgmZMNMc1Kppm2BNTIx0OqXbLYOD6xnZpGmJDbzi9/UtnA8/\nwHCwQQTs1LTD5oGhgZ1kCVFUzxN1uFxm/6LFVT0pf5paZ7wQ78JX8CZXQxzsqT7WOhw5YMvOlvCM\nwyGhFNKg9hUR3xcSErJhw4bTr+cNP+sOq+eG98PdR5rdG/Hdd995/UL8GWfeCKInA+EpGC2lFKKk\nzgqFsB++0PVjwcF50dGu3NwiWGV2WhdihhALdL3IvJdpvSZDFMyHxTAfpsHnkO9cVb2CM8nJE/AU\n3DoAtkEBbNQ0M5c3QoKmFUopc3PLpJSxsdJma7DJ2O2WdefRlQ0OYloPS5rY5i6l1LS5sKzeF60X\nLKvZVmNyOg8ZxgJNG2N2CRUixhyrBVGwufGxqfLkNzID5kEW7JNSVt9CttDhCIUp8FVVO5ium91s\nDplVeHje4XDBcHlyXvh9MPd8GcK6YcMGX451kw9WUr0f7j74oTTEPB+cPr2xIem+Lzd3v5TyAS63\n8ia8255B8J7DIYX4KTd1/SgUQ3StbcPCUoKDXbm5Jzt0wyqYCFGneUXDGA+9eGcqnc2KfASM0UaC\nm2tfNptl3LL2mB1N212rdhkWVhoWtq2hV9G0OMOoZ0KVBsL9Y4gODk5tvOSnbrKwvoXzG7p8Cuvq\n5ntdTqeECIiBZCGyGjpMwgwhXLp+zHxYPYKpFTNX6PrHMAG+recKtnkH8C+E+BpegNAaT5XCQqin\nn6jvMGPd4zkPbjjlg83L3g936ZOfSyOmT59uNvn5/jlHvRbMiLWBlTdhfXceEOIreL+62qjrByCx\nocGimralekoAu30z7JZSwiQhGrsq6HTKR7S54H6agQtgCSypivj2t2PW3OtuArVz3GZrMNljYiTE\n1puzzvqWwiiYFx2dX/ephmjaJk2rXXl0u2VD/e6dTgmxTdy5eRiAZFgvxA4hyuBbh8Ot6wkwE9YJ\nsavWJh35x+cQAYvBHPhU755dLrMpLAam1Ax3KSXshVifrb/7fm29Jl9rcJc+Eu7nUeXddODAgbS0\ntJCQkNDQ0NOv7UtG6DM1egXyBexfpM+WUup6jHnDOVgEieaMAvWqrJTVg3Gs1mlwODr6oPnQbl8C\nX9pscdHRm8LCMqKjc63WcLPxwW4PgyWwX9OSD+XmLg0O/gbmwBL4Hl7pQOAfuexx5n8ZJk+crHdH\nR2fAFk2rfTUbljf0vuz2H5vSp7DGrpLqbS5vdJMJmlZnshspDaPBqXo1bWe9m9S3803VBRMiT0oZ\nE3Mc5kE8fA/rhSh0OE42wlQ4HBGwzKztwzI6bgBZ72BWKeXJfN8DM+EDsDkcP60J+2B2rdD3riNH\njoSGhh45UnseTV/mm9VTnwh33/xommjDhg3Tp08fOnSotwtyeroe/ySX9+SvsDPDsdpcKMQnMEGI\nQiHMu1Y0WJm127fY7TFSSiHcVmtRWNhPzTjR0a7g4LUwC76D6ZBW3RgdHb0VCuDUBpCcnDWaNh3u\n1eAZrn+E2TAZvtA0KaXVuk7Tjp2o08TSSCd3WBUcnFXvU3Vr7rm5B2FjE6cfOPVV6jkeNN72AisM\n4/T3gKy+UaqUEj6FpbBBiBrfhUuOhCmwBFZBEqRCKqyETmwyRzmd7iVmmFP6CPER2ByOgqrlJbDQ\nF+rvGzZsCA0NPY9q69V88Gqq9JFw9wPDhw8PDQ2dPn262cfGB+n6/KEEwkIofocgcyE8C8FCTHI4\nJGxpZAaSuLg8WBccnAgxcLJrx4kTEuaZN4y22U6YKWoYOyECZmjaAikl5GraNk2r/5jxUCAMhWGM\nvIZFMAveo9U7XBnMzXVXhpjc+ubojY0thoQZM+rvXd7AxGGhsLgpo41q0rQUwzhea2HjO3G7Tz8G\nVUppGEfdbqlp6bAOkiGv+lYk3wqxQIhoiIUNkAapkAgZerjBg4+IdJgMe4Q4Ted6eA8Ww37zoTlh\nmRDfSykhFxIdjqOnLedZEhoaet7V1ms6x3NPNpGvhLsPtlj9AqGhoQMHDuzXr5+3C1JbievYA1hh\nM+wby3XSfVzXyyAKJtpsX8BE2G23N9Zbw2pdDt9DCuRVVkpdXwDbYWtwcHZY2D6zN0tNhnEYvoPV\nEKlpXxlGg5cuDYfBX7h8IG92ZTE8wp8yIBVWQQwsMAdbut3Hnc6HqGesqZTSZtsEMQ3tv96vA0Y0\n0sjTELdbwhrz7xOGccAw1hvhQ/iXS9PWQpqmFRpGjKZNPbX5uy1fNd5k5HRKc0xWdRvOEqe8m5AV\nmjYPVkICbICNEAsLoeZ8NLpeKkQarIX5QjR4BuxySfjc5ZKwu2azmxCfwMcOx2FwN+UgdMZNnz79\nvGvbrMs32x68doPsWiIjI5955hlvl+IM2LdvX1FRUVRUFBAaGtq8eXNvlwjgsYCW63m7mBdDaf8J\nr5YwUNOO5+UB11itxfHxC+32oOjowY3sISBgAgyCBPDAXClnNv6KM2fmP/VUudXa3GrdFh9fCVit\nlX37BtjtXe32PrV3PjCAtlBBB8eUWF5uBi1BQjOohAqogKNQBgUA2JzOlPz82197rapsK53OB+6+\nm65dmTkzb/360r59u+zaVTFz5sGuXZstW/Zl797d8/Ie6ts3YP36dlbriZz4FQep9NDO0NzH6OaI\nPxxuHP8hr337WS9eZO1+J7tu1Pr0gDmzZnWA66AcPoFD8DF0Z/ktpK8kuALaQgA0gxMQAIVQCVTd\nobsZHIdyWEWPN3AG8n2wtjjU6Vw86IVH1/+Qk8OgQavi49tDawhoxZbD8kkgLTi4M6yYNOkquBSy\nuOlmNgPthbjGMBg0qIFvJ1nXLwoPd8MRmFP32wkICJPy9aq/XbrebdKkms9OhA3wKayW8k+Nf7Nn\nSlpa2uzZs8eMGXNuXu6sKisra9WqlbdLUZuvhLsP3TL8TDh06NCWLVumTJnStm3bFi1aTJw40YuF\nGW9M+Xf4by1U3kRwaw72CZ4yYcLd0dEH//znbDgIfYSYC63i4xsM94AAA94MDt5vtzfv2/f6076i\nlNx994G8vOMTJhy127sEBDwTFvbhrl2dJ01aDpXQ2m6/SNM69u3bqm/frkDAowEEwrbfkvSJ233L\nNeS4Bw26WtO2T5oEWKBZVVaaSXoMyqEMsuAgV3Zi7zz+VEDfAO3v8fG7rmRnEKvc/O4WVlbQ5hLm\nuPAInuzHZ+0gEAIghs4v8PXjLJtK+AmwQAUcB0vVWzgBF1Wl9iE4AcHwKtzHjMs5voIhrbU/5Man\nzuIP7Sjrzn4rieG89zhfdITddL6O3Wu4cQDLzR2O59VIBlv5+hhPFGCBq3/D6tbsvo15d5DVDE8L\nCIBWcBy6QnNoBntp148tDm30oPVfN/6BO51HBg1qAWgaCQlbHY5egwevhs90/ZlJk57QtDma9uCk\nSW1rfKFx0F3KK6uXaNr3CQnFkCTlpLr7P7NGjRoF+Ees46vJDg10nzr3fPO85tebPHmyOeuk0ZQ+\nz2fa/tzcO+kFC2CfDaxo1ZP0ulwSEuBk73IYqeunnJW7XBJWQyLMh6xGLrTWEhe3HTZWt+3KquHv\nJqdTwnKbbQ+sgET4zGbbPj48n96Clj/yNDMSZ5jzkdlsMx/WprTj9W48/ym3OghcD+mwE3KqbnW9\nC+YQtIYrMmA1zIAI+B7WwHLIhVLYBDZIBQ8UQDnshcUEwoqJaEc07bCmxYM0jNzg4G12+zHDSAkO\nbnB4kpQ1bwArpdS0U66ymNsZhvnpbWxHWDvm9iDqXqbcx0cT6fI/uqyG5Kr3sgdyoBgOQgmMhTRY\nB0tgKRbYBGlfcm0M/Auegf26nlc9eOmUL2tmVfHSq2cH0/X58E/4rs5byIJtUPsO4/B3WCTEWWkj\nraioiIqKCg0NraioOBv79xafzS5fCfcLwXPPPdevX7+333773NwhpCg391NNs/Al7NV4eLnjp1bv\nuLidsABO6cUBI83E0PU8iNO0jODgzJgYCdmQW7fvSkM0bTkURkf/dL8kuz2s4ZXjIQniYSmkcPFs\nOrwEk2Cc1To/Jqa6e6S0Whebx8ejhrFB05ZCHCRAZ77+Lw/sgjzIh2zYCpmQAHNhMUyACFgKi+Eb\nmAdrNO05HnyKR3Y6T7kSEBsWJmNjpZQbo2uP3qrmdks4pe9jdWf2rYYhnc4iw4iCv/DHt/ndQq5M\ngQxwQREkc8UX/P4QlEFJ1b8DcAj2wW7YBF+COedkPGyB8VwPOx5j8iyC1lXdlNz89xcIgYKqi+A1\nhwVArtksr+vbYJbDISFK10+cOuFMCiyv9RvIzpbwWfUF8zPIjPXU1J8xaux84ZtXU6VPhfvhw6fv\nMXa+S01NNX/l+/fvP/3av86HQtzArfDWk9bBG2JO6YcgxB4orXWHUvg3vGu1hmva/LAwl5QyLi4f\nXEIchtVNfFHDKIKCsLCf0iEmprTWJOzmXGA2m4QtsEzTHJr2LWznqonc349rJ0MqbIU02Ox0Sk3b\nZRi5VuuPD2nTpdsznLtn0HoPFMK7XA7J/fn7D5AK22FH1fS75n21t0AKlMIBKIL9cLBqUoUEOu2B\nbZAPLkiEbNgFW6rmxk2G7bAUVsMSSIBkWAXT4WuuLzGMMCyzYBWshY2QBC7IrrqVycGqyngJlMJB\nGMtjsDmODpshHmLA7EcZbyz+Dc7rmHYZSw2jnnMGyOjAf6ufWKLrn8E8WAiLYS5EgY1hNS+0wm6Y\nXWvwsMMhYaGuF0opzdkUhJC16u/wOnx8BvM9NTXVX2PdpGrup+ezn9HZYEb8We0n8B9NszDAwiB5\n/JTee5o2F0qio/eaD6Oj3cHByZCk60eFmAWjzOW6fsycDqzpExxKKc2JfKvl5u4Hm822wGabAjbY\nDJlOp3Q6Zc1TAZgNO6SUPAXPwROBOQfljBnyJt4NZIqFyBqNMVmQBRlWVsFSWAaLPjHWzZghg4PT\n54QtXzM+9jttyEQ6zaWVk87BdJtOywrYTusjUAHlUACVYCV6Plel0DqG7gWQwuUuLnPTNobfOOi+\nlj4DeLM/H97Fd/0J/yejV3GXB8rAA+VwEJ7gkyIohVI4DGVVIX4I8mEfuGEVFGualOZkZidg/Y8N\ndJ3UtHzDOCilhLFg07QxTqfbMFKklE5nObxhGAn1bOZwTIMFsBDmwgL4Chbpk+BDmFnvfJO6vh+i\nYLwQh6WUsLlm/xl4LTtbwriatwP8ZcwfeVTUaWanON/5bK3Uh8LdZ89uzp6Kiorhw4efpa6TNizw\nZk8eqrlQiCNQbrWebEnQ9fmQVrN7u8NRAeOllEJIM5RgTBMn2NK0A5pW82Ee/B2et9vnOJ2NHSGg\n6k6kj8AwGAYPkQUpYIO1UAZLCcpyejY7PU6nhETDkFbrTlgE2yAJ9oNZm98HhZADe6vytgjSYRts\ngK2wF7JgF8RBDmyBA1ACebAfyuEwHKmK6z29+B/su5FZi7nrIJTBIbDx/sf0fwvyzSnhIUvTpGHk\navVPXHzqm6099abJ6XTX/ZzdbgkxkAaToL5wr+Zyvc/NM6EXA+C/QUz6iNuhtKH+70IshTVm+gtR\nXl1Vh5ellLr+A8TBLxybY8Z6WlraL9v8PBIZefrbrHuLCnfvi42NHT58+Jmt4MDzA7HA2324u3qh\nru+BwxDrdB62WheATdfX1rftGJgKH1c9bNIUOppWAbs07Qhsg32aVlm9t0a2OuF0atr2Hny5iPa7\nYGk7+DM8B0NJb4FL03KcTvNeGHUvSMfF7agOytxceeKEzKkz1D8nR7Ztm5yTIw1D5uRIqzXdZvMY\nhjkr5A+QmpMjo6Pzw8IKcnMro6NLzZOc48drne3U/YiWBzFZSind7h+ccrTxMxrZYGW9F9fNCYcb\noWnFsBdWaNp39d4lHJbCV7BKiJ3mHD6/ZSQc6oEzCr4Rwn1qTV7Xy2EdfCNEMuwyb9RnzhwppYSn\nYW8Tv/1q5vnohRDrJl9OLR8K94iICN8cxXsOHD9+fOrUqTabbciQIW+++eav3BtsFCL8AS6H0Q9w\nlblQ17dBCETAWlil6w1WpYUog50w1jB2GkZ244njdktN+x/Mgr0NFOazutsUGcZmyIZhDIG92VxR\nDh5wwW/7wDPwF3j8lB9n3UCMjZVw+hBpYOKw1bB2/PjTbt3QPk8z60AjDKP2bJc1njrNtpp2sHoi\nB02bBMmatrc6sWGGEKcO4XU4/iamQEl/XlhcdSV2cY3JJ82S6PpecMBGIfbAT2kFSVCg67U71dR1\n9OjRUaNGRUVFXTixblI196a6YMO9JpvNNmrUqISERs/BGwYbzdbSvlwLIU59VNVycwqR1IYnmDq5\neXWaw+cQbhj1zNnidEpI0rQ8q3WZpi2FwoZ3mCRzchLt9s12e83OHulQCpB6F2MrDKPmKP6TLe9P\n40z/aaGm7Y2LO+Uqn6YlNWVQZQPhngIxmrbqtJs3/L5ODjqt9xLo6bZdZs5TX2f56W+gAWtrviG3\nW2paBoTDj7C03k2EyIKCu/jPF/AXsIED5sLn0B+bdJ1cTdfNPqxf1NjwICyG4uzsBsuTlpY2atSo\nUaNGXWix/v/snXmcVNW177/Jve95yXt2bkzM5MnN4E1uws10k5izjMnFmIQkLzG5iVVqglNwRGPO\nOXFCDWACBsUuNYoTOCJag6IMMskM3UUz0zTQNFNVnW6abrppZhCxe70/TldRXVNXA4ldyO/Dh0/1\nqX127XOqztpr//Zav9X70buMe29e4/wjsXv3br/f379///Ie+pawENZ5rtwP+CjcKXwmGPQs+1zT\n3FaYRTXNA4bRlJJrj0a3wkh4CkZFo3G/f5nIWlgXj6vPt8Ork9fRobAzt3RMR0c5H/wJj2yB3XAY\nGpKWPWzbWlFxgfF4zvB5fgy/hd9hXG+4TZ2uqGFki0RWQA5aKQOjR4/O8RGsgjfD4S4HXbd7FzWt\nh85ZIxQqSvcx6/QcphC6L+sYjyu0pJTrRaqgwnP5TXMFLIFF2fO3abZCg3c8Hgz64BWYDtNgglfi\nIxb7m2n+wLwH7k//kcAay1LYm9mjqqp6Zv3tt981UZpTKIBTxr23o/jnB66F9SmO+9f0gds/xm+h\nyRMm9KIj8sGyNHs7EHyhkEIIXoIxIhOzGrip7dB0/E3EB/XQCpu92O1QSFUPJaW/AoEqmBEO58hn\nqayt5EK4Cq6gXduTH5RZ1hnWBAJbVL3Y9KPwlgHeP9tWw3gObg6FEiLeJLcF9iULq86HamiEndAM\ntZAQiRrGJpgJD8DvRYbb9uREQm17sm1PDoUSoVAikVAYL9Kq2vlBPQXcBrdlHSwqXlCkCTaKVMOq\njLUL1CRfzDLNpelWHjZ4+vtHEQzOMM1xcBX44A/wSX7/79iwHYZb1iRVNc2OrVsVmlI9e3j55ZeH\nDBlS3LWetOi1cTIeepdxP4V88DjNAibeNB+HuvSAiovoA4Ohxufbr6rt7ZpecjMDsZhm22jbngU+\nkV0e7RAKKbwocrTanIgLuzPOejSZFPpneIZv5PtEw5idba9T8P/Fz8UwEHtiJw8NGxIJTSS8MHkV\nqYVVkIAG2AVNIl3Mempzdfr0zlfRqFex71Ai4S1xcggIR6N564F4Hdr2Qm8YiYRCFWwSOQBxaIH5\nUOfVZS0G8ELWke4XIl55blgLObiSjP3PWExhtmW9nXy3NsNGq6qBPGuNecw0f8mnYKSf//wED8FB\nuM40h8diComtWxV2b916lIQp6gpPdvRyZ7TXGfdePhm+u/AerUGDBmUcP3LE88tWGkanX1xuP+mD\nPtwBD3hHgkE1zUbNhVhM4aWUIykSg3WhkIIvm032+2fARJF5tl0HyVTbeHyDSBTCEIVGmJwnxMVD\ne7tCXT4FdsfZ6h8wkR9+gqvgSvji1bAPEl7Qiwd48XgEHcCXytc/jk46dSVTnntqRvEWDSIq4pnU\nVbatIju6nv4q1HY9Usi4i3jrjBrb7ojHFRqz74BIW84NANOshVdN8w3YkUHaBAOuRO4AACAASURB\nVIOdyU8f4Ob/y8g/wx/5cBkLTFMtawb4YNLUqWpZd0Hfiy664hQJk8Ip494z9PL71Rvw7LPP3n77\n7QMHDqysrGxubo5G6+B52AKPew0s69AZPNiHVX24Be72DqYLvGQAtsLKpD06IJIq43BN/lMeg+Xw\nKoxYJbIBdkAz3NNVrUgkN1fr98+DbR0d6rqtXgijZwphF2wzjPrycrXve4ZLYCBcjNu8O0PUF1YV\nSYYksgIkKys9p3taUefnB0zwSnKLHOnJWTFYk8yKXZ9xFdmmWcTTZtiYcTNFaqAxo308Xmh3NxZT\nuA+aMoT7vSUUPHYgpsss6x64jrNhWzCowWA1yOmnX2BZd5nmqJxZUafQO3HKuJcwbrjhhiFDhvTr\nNwRmwzXJRfTrlrUPFl/Dt3/Od+FW03xBVbPVozyIdMBc8MEfMwwN3Jrvo2EDLLsMH7wEb8DE2zl/\nlv1kVrM10WhDrtNd2+6AwYZxvWFcn098RoYIV8JV8NM+6ZNTIlFUYIkHx3Fy9CzNMEskLwlTDERW\ni/RgDzYbtu2FGz5n2wpbYIHnjLe3eyTYKtjs5e7mGcAOyKytmq8uSgrBoEKDaU5OqciZZjOMSHn0\ne4LBP8HP+S6Un3H6Vy6+6FK41LI2W9YSGFkgcuY9hd7PMfQ64977b1mvQiy2D/779NP/A84EgQtj\nMQ0G9WMsvBcehsvNG2CYaeZY71dUeHGTO2x7T87Oczr7zcuXwwzY64Nr4Tp4xJ4jMg0mwWx4DsKu\nu9tTF/B68PsDtj1ZZLiXVQ+LC7Dt6QgtD3EJXAWXY99TnTawSbCumB5UtbIys0p1R4caRlWB+h7F\nwyOmRI5d5hDqRDrnP5EoVMA6iMFMWOetDAqeXp1hzUXyFiNMO8vL6f2d9wXBLZbVhTIabVmfgg9w\nNrwx0LzsSGwP3A03wtDMXdn3Knq/G9rrjPuyZctO2ffiYVmL4AG/fzZ8Dc584IGHH3hgEuz8Kr/+\nC/wNNlgW3Ao3Z5wIlTAHCvGn2bzHK3AZZ8L+87HLYUog0+O27UNQBfNhETwKD8AI29ZQqD3FjkCs\n+AuUPwkDYCD8z9HfKgRFijUx4YyAR1XXfUtEYa7Pl+n29hQwFe7sES2T1cNYWCnSAnFwRbrwKl6Q\nEawpMH9Ac/o3JfJQcZ/bCttVFYbCBNPsvBXBYHDIkCHBYFCPHFlkWaczt4yNvwXBgD/AbVBboBzj\newenjPuxoDcnffUqxGIKd8EdsM40h6vqokWLTz/911/60i9+aZqD4WHQiopYTOGvweAB7dxWrYdl\nMAfcArS1SAQ2qWqV4yQcpwbqoYY+8JhIXlpXZKzIcNtW2260bW8KicIbIrXeZ4lsLkJ/pQv4NVwJ\nV6Yb95pspYF8qKnJjA+JRtugFhZlmf0eQ2QMWMUPxkM8nhJ83w7boF5ku2fTRQ7lO8vTJxBpFWkU\neSkU6vwWbLsDjnJfxRNW0AxBb2MZnoa+Z50lv/td1+36WAwWlbHsRvgZfWAQ5M5OeK+h95upU8a9\nVBGN1sHFMAJGw8gkDRIXmenz3fC5srLPwU9gnOP4/QG4CUaY5iRYHgg0RiLrYLffn6vadBJD7CM3\nGte+DpugFbbBLpFf8iO4P6NlKORx6Dk8fagLh9WLDoR5sAxWwTiRWPGx4XbQ5lIYCJegnYR7D7jy\n9iyZmGi0BTbB3OM37omEwoJupytvsxrWwBIvrF5ERd5OvetFuCeTAYpCKJQQGSMSTZZg7cyKyg52\nzAcYDpEhQ+KqetZZ3x8ypNw0/2Sas3K1bPpPHrAAHBgO49OFJN+DWL78eCUz/wHojca99693egPA\nB5fDffC3SCSqqoYxP1WCZ0V5+TXwXTinb1/oC/fBKBj+zjveuYmUsFc2ZgcCatvToRF2wDZQ294f\nDl/jfwHaRFa47n6/P2YYtZ5RK+C3GkYX3gPmwHrb9gQj18IaqIAqkXiqE9fd67qZOlz8Gi8s0p5k\nh8N6nEbZdffCIlhy/MZdVaE2YynjRdmLzIW1UAdN4HqUS/5ONtl2+7FJ1sAbIqugMwiyGL0dVTXN\nN+Des846D/77yJEjF130XIpsgactq8sVWdZ+aPLz9c9ygfClMxjkhb2/Z1ESDmhvNO4lMSu+u6ip\n2QU+GAqjvCCH9nbNKLBwOzwAn+DzcP6PfvSbqVPnnX76XTAS5sGOHJ267ii4R+Q6aIFt0C6ylHQy\nZD1sgq2wpchxpu9lhsONsNG2O2kHz5obRmV5uefVVkMtbIJVsEpkg8ic1OlyyaX8pjMsEmaI1GrR\nmDgxM6s2EKiHxVBtGIuL7ycnEgn1IhphMmyFRjgI+0QUtqfnUhUGzAVXVW37GE0mLISdYMHobt1/\n03zxrLP6WdYt1dXVMNQz6+mB/5ZVA9enwmm0s6xHDH7/eX7xM043+MN72XkvCQe0Nxr3U+gW4IMr\nYBg4ySP1XWKQg8Gn4BG4kjNERjY3N5eXl/t8vjPPPAd+kTorHXWwFHzwOqhtf4UuIc0iLuyz7XdS\nyjPFQORA6rVtq8jBAo0TCQ2H1edrStI4m2ELxJNVlTZDA2yBRSIrRNaEw+o4e8Ph3eFw3pqfgUBd\nv34j0y1sIqGO42nFrzCMKr9/s+NEI5Gt0ejeQEBdV8PheHpjb6HgDUmkGVqgEZpgP7TBfmiGjV5+\n7PEAthyDjEHXHppFWuJxFVkL82BBSoImBcsKw7e+9KWfTJ06N+3EfbACrs1qPCk9Ygr2w8QLuOA3\n4ANoHm69R733U8b92FESq553C/AX8MFo0xznPZCWpV7kgwe//81rzOcegqfgIZjkS38+74Evwdnl\n5c94qi01InFogja4wxOB6Wy5JRTy6AIV2QL7eqp9qNqFP+nRLmgK0WiTqvr9GzltEuaFfP+7sJHT\nKmERbIF62AGt0OKJEEAr7IQd0ATrYTnUwkpYCjtgJdQm2aatsCRZOO8+uBvuhlHwJFQn9xp2eaWW\nRDpgs8hh2ATroBEWw0B4U8SFVcfP8MA0WH089j0eV2gVmRUKtaUdmWXbB5If8Xn4ajCYuV4JBj37\nPjjPwB7yXPhYTGGqaY5XVR8YDIfduvW9GNtWEgaqlxr3kpgY3y3AVXCnqprmE8HgNlWFPY7TGRpo\nGC9ZlsZiutqyHoGn4GE4GAxqZ85Lg6qWl78EX4PPnQ2/gGUwOzOzNJ6uUCiyB3LHwhdGKlRSZFlO\nfbECiESi0Wid4zwfiUT9/koR5bsGLOKST/Dzj4uoYWz2POtodL+mUf8pUj4c1spKvfHGNZ7r7Wkz\niMQNowmmwF99vgmBwMZweH84fCgc3uk4Na7b44j1cNjbKV3lfS60Qr1IHEbBFT3qCtYcp/Nu2wrx\nUGhX+sG2NoVz4StwXr4TTVMhL0llmsNN8wFVhVGp+uA/4FN9mDT1PZmzeuDAge4bvdvopca9JCbG\ndwWWtdwwrl+7tlFVwRG5JxU2LjIepljWUfMUNE3Pvt8J8bhC5ybqcJGf8UHwQ78+fKiffM87bttT\n4PZ4XG17d4pkiMf12Cx7KKR+f2eIHjxXjNsejR5JJNTv32gY18NDXt5TIqF+/0SReHTNaljP1XAZ\n4S3FusqBrGD8QGCDyES4xTDG9OSC8qJwuVHbXi2yMhkt44nM5BZehqoMtZljGsyO9Bmib99+8CX4\nH0+ZAHxe1GyuEwsFsJtmGP4IT0CjRwBeAtfy8b48epwDLjmUiuvZS437gQMHSmJu/AfDezjLyxeq\n6tCh0+APcJ+3r2VZu32+7dmn+Pn5o/ATzoG3hti7VfWgbU+Ex0HjcceZBuVlZQIfKyv7TP/+l3tn\neTq33mtoPrYMTNvWQKBFO0P9ci/5AwGPW08YRoPf31AgEsYwro9ENsJyroCBGIOMYxhS8kPXwjZY\n5fcvOuZO0gFj0ncXukVSSGcDrIJK2054MpOaS9m4pxBpgLZ33tGKimhZ2dfgq9nyNbY9OX2z1EMw\nqJA3yl5VTTMIf4bZpnlYVS+FW8Gm7DgHXHI4ZdyPF6ec92yI3JNyu8Bnmq/AU5a1y7IO5quvJNIS\nkB9C4np+NQoehFWwEmpEVNUwJsIKkfnwWN++gwcOvHXo0KFr1qzx+e5Nnh6HY59lA4FWVRVpT9mX\nJHfRAG1+/17HaXDdzE2/PBcyPBKpgxh+GAhXIkOLyoYaOHBgxpFIpFFkJ6zLEiY4RsCqnAK8xSOR\nUJHt8DDMheMdFpwDX4HrRPLq0qiqaW6ESFfN9+oCzjuMVlW4F9aa5jsjTdMBP18oXCb35EOpmKbe\na9xLZXr8R6Jr6MLv4FUYAn/Lp9VnWer3rzWMin9j7qPwFJTDKzDGjoqshqr0AA+RBfA3wxju891T\nVvYFkR+EQpUQP2YWWORNv3+dYbwAm6FRpM0wtgYCiWg3cin5ehseCBw2jK2BYIDfwmXwK5wnc4T9\nZMDv92cccd3DInNh/TFs8OYETDt+jzvZ1R+gQWReKOQJA1yeWkIVA9u+pazsa+CHqUVugJvmYrjO\nM/Hwl2zNyGSzF2G899qyNsCh7/DdP8AwgOOt+ltCKKFA7d5r3EtlevyHAXwpJysWU6iDZXC3aY7L\nf8oiv385HPwRv/8rPAZj4C7+9XyuzGmyRV6Fl2EC3Cjih2+XlV2zZs2aHo0zkfCSJ4cna+otMIyN\nHUV554Ug8leYYdsaCAfoD+fCb+C87n/A/fr1yzgSCMwWGQIzT5Rxt22FVSekN9t+E2ozvp1QKOFp\nrhUo6TdmTKSs7OtwvUiliAs1PZpvgsFDEIEVprktW10gFlN4NvWnZa2A6bDVExKDGy2rULbzyYQS\ncjp7r3EvoRnyH4OubvtE2AlvWtZiGJb/lFmw+ovMWAJV8DA8CU/BAxT63kVehldgEoz9r//6Wf/+\n/QcMGDB48OBDh3ITsq7bGghMcZznbXsy+FISviJ3iYzOnTDVc8CQlAK7/1Y/58L34LvIzeLuKGRZ\nslUhA4ElhnG3V9rphEBkOEw8zjh3D7Y92bY1H8lj2ytEWqFSpNmrJNXWtq+s7BvwDfiNbXdm9sKO\neFxhX0+HZFkKYU9TKB1wr2W1dj1yO7zVjyuGgqpCz4r9li5KyC71XuOuJXUf/94wzeHpO2AwFzYk\nX98dDOYWd+zDGNj+Sz7/G/p8ggtUdWTSvg/vxr6vAhdC8HpZ2dOGca9t/3HQoEEXXnhhqo3r7o5G\nm0TWGsZM8Nl2pqUMhfZ4pbBPCOC3cHvqT+dJh1+DDbfA1UTX5eV6OrJWDR0dahg3wJoTIj8QDnsl\nog72NNYzJ0Ihr5ZIXeGJJx5XuB/6wTfBZ9sb0t8V6dCk5k+PPt0LooUX0+OjLGuZaWY+iXALzPsk\n05PG/R7TzJtKdjKhhAI9erVxP8XMpAC/SXs9HDLcqKHZp1zGd6ChH3c4xldHOEfDAd8QeRLGwuT8\nWiewBJqj0X3RaKNhvAIz4dXTTnvszDN/0q/fBWef/WU40zAGi7xR2AZB/QkxoKoKgzLcQ+dph+vg\nDrDhd3l/ydmqkB0dKjIC1uULSewREgkNhxOqed3tHsGjRGxbU5N3rja3wLfAtO2x3hHbVlhh24c8\nnj2tGOFOkV15uskBy2r19m+CQYVUQa4cWzqxmH6ecyF2Mb8u43K4/T2i837KuJ8YlBC99XeFYQwG\nXyQSdd1W+C3sCAS6eEkw3DBGHf27vX0oZecx8gKeXmAYB90u7lsiGi2Hp+AJ+JthzM8KA1dVOJC9\nHQeTYSZE4BzD+LbPN6DwsG37SE/VfQsAakQy6QLnaYeb4Da4Ha7K/WPO1nOPRvdUVirUGMaKnKf0\nCGlRjD3bnMiJFNueoXrvVf2GwfBj+K9p03Kog4VCatv74DaRR7wjtv1OykYXCdM8lBzAXpgOAdOs\nytnyAs74PLcYzDL4H7gVZp/0RfhKyLLrKePe+9HRoTDQsiapqmkOh9dgd0ab8vKN8NdAYIGqRvz+\nIPyRn8CRR+28cdyTRZ6Ax2FEmuSAB1gGR6vH2XZLKKQwx7Y1Emlsb1eYAovhZ2Vl3/T5rqqszJ3Z\nCGtPFCcTjW6F1Tk1iu0pNr+HwXAbMirHZOLzjUy99nJW/f5VsBaW+HwNnuUXWQ8LA4EdnpnuERef\nVoSk+vivN9WbSKeKr8g7MBaeLCvr17fvz8vLH++2E3gcpsJCkZgnIFE8TLOT4gsGFZab5hp4zrIy\nq5rEYvo1fnsFnMVM01xpmmNhkmlm/jJPMpSWRerVxl1Lbar8e8DvD8Agy5pums/CINhpGNXZzSxr\nGYx8yBo/C2bzEdiaQd1kY7LIGHgS/tqVf4e9Hlcr0gLL85kG22637bdhOJxfVvZfAwdmpinBnhPF\nyUQitbDFi5rPBhecwU1wB9wGV8LHn/SkZmxb4cBpp63ylJBFRnR0aCBwMBBQWO5Fgvr9u/z+Bsfp\njAf3wvDT9cK8g7atsFdEIQ7roMU7GA6rbVd4tIxISwEh5SIxYEDzgAG1oZAXXllfVjatb99b+vf/\no23fli1Mnw/pqr+wsEcJxqbZrp3hMc/AG6Z5RFUta2O2fb+Abw2Eu+FcboXBMLLbn1yp45RxP5Eo\nrbv59wDcAUPgr37/czAb2hwn10K7o6MPN8PI5zkLKgwj1n1Fi3j8geT+6ktJAkUkDntgk8iuIgOl\nEwmFcfBL+CaYtj3VthdAPSw/fuPuONWBgOv3V0KT48RhBzRCKzSIPG7bU0RGOM7zdsTmRrgN/ghX\nd/lVb9qUSeZoJ0m95IQsLMJhFRme7HMdLIelIvs9IckiITI9kVBYDC3QIqLTpysM8vmuHjp06NCh\nOfZUCiBDwwB2wRqRDcWkLHh6zhD0YpNgf9pbz5jmjNSfZ/DkVTAELsYHk+BmWHlyMzOlFeJxyrj3\ndnTGpvO43z8b9kFtNJoZkjg7ELgPfNCHuz/CPbAzEjkAGyKR7suhDYen4Un4M4gsgbdShYF6Ctfd\nA1857bT/gm/CIHjMMCoM48VIZLPr7i2mh2i02XFqHOd5v7/VMFpgrc/nZerPg+3dBstzAwyG27Fn\nHjWr2Zy7qop0wLITFJl+1C9OL3eX1sC7hLUiHbbdydEnEipSKbIT4rAT2kTaRQ54+wqhUGjo0KGG\ncT4ci/pNtt6AV8ojFNJUPb98gCcgnPZnTXpOk2nONc3Z3us7rZYB8BhcgOUVCofnTuLyqiWnidLb\njft7PGAGfDADbolEljvOeqiGzNXxOJEJMBJ8sK1yC4yFh6LRBGyKRLr3vRPR6MNJ+/5jbviR1Goy\nZuPYsHbtWr//Nfj5aad9HS6AO2EdLIMZMCcS2RoIbI5Gt6uq6+6ORGr8/iYRFzbDdpFdfv/TgcCU\nrnvACqtE1nb70XbIZhDcBrd21uTTPN6WiEJMJIcaT0+R7p4XqP2d1F2YBTWwDXbAVmiCmEjnJJNI\n6E03zb3mmmuGDh0aCoUSCT02oiN7GFDv2V9VrxBrVb77CZMzvO+MIjCWlTDNqap6C4yG12G+9SA8\npJ1kzvHWHO+1KC23XXu/cS+tqfLEor3dSxV5ERzHedMLe8gIOJtumguhBoYmeXOohQd8vtndFkqO\nRKKBwEaRdbfJVQ/C0zAWXhVZF4nAKtctVFijMKBRZMXQodPgykGDBvl8vwsEZgwd6u3E1iQl0dfC\na1AJS0UqHGduILA6Gs1d4wm2iLTlfCsDgcpAyn/nelT1xhtvzG7mugo17olIq+xq3CtTNH04rCIJ\nqIatsAN2wVsiOYLBEwk1jCvgbDjzvPN+btsVaR1Gj0H+ITu83bbfyWbe4RU42rvIGzAH5mU1W5pR\ndGmGZZXDeJgCwc449xFeG6g6WZ33U8b9xOM967yXl8+GUaZZCT6Y5CWYHH1ygsEgLIIaWJF8+GCL\nR7WLTIWHC3QeCrWIDDeMlV7+ZkDkHs6aQp8FMAWu4xcTnGHHNmzHmQfbI5FW11WRelX1+a4eOPDm\nsrIfgC0yzTAWJhLq99eK1MIaWA91EIN6WGYYNX5/wnE2+/1L/f7XOzo0GlVoKZ6/dtXl90n+/VLG\nvjg2u43ITqh2nNixXWMK4bCKxD35AWiBeLJI0yERhcZihl1TUzN06NAxY54pKxs4erROn64ih2Cj\nbSdEKo7Bec85H0CLSI4cYwiKTIRXYYHmidaHo7Kgj5jmXyEIb8C9fEZVLWsOjIYmVQ0Gm2BETwdc\nEig5irgEjHvJ3dMTBfB5hZbgTmiIRPZblqaWzJNgOawBTSrOhEIK+9JOfwEezNPzGr8/kF6HWmTK\n13h0PkRhMSyAN2GJSE3P9xxhgcgOx1kHs2E3rA4EtKNDR49+qV+/fv369fP7/fPmzcs4y6O/RRqT\noSlede7NcCcMhy2wRGQ3VIjUJxLquuo4nQ5yNNrquhqNHqX1jQvPQz7BDz7JNfCToz/yFGsvorDc\ncQ4UcN5dVx1nv+OoyAHbVpHd0JKs4rQPGuAQtIALe5KRMwo9IPLD4bC3X+pFwmTrBos8CjthYY+2\nB3Ky6qGQQo7VWCik8LrIOhinqjkXfJalnv9wFzwPE+F12GLdCY+YZgRuM815pnkwWYv1zh6MtXRw\n9913v9tD6BlKwLiX3GroRAGWegK/pjndsvaqdtYSGgVzYQ1Unn121/Yruqo8tldUKDzmufCu2+H3\nR2GJYayORrvE23R0KMTLy1XjcQ2FIh5XAhUwHcZD8YHfImugAWoMI+44TSJN2W1s277jjjscx1m7\ntnsaXTvpgmWwyO/fIVILqw1jO2yBxmRFU6+uXgJaYTdsgTZogOXQBMuhGrZAAmqhDVzYCdthO9RA\nHez2VIhhN+yB/fAWtEIc2mCHSHs4rK7bGSWpaQHpGdNfzj3VbHjeesZmL8zJdfmrYW7y9SGR7bbd\nTUxkvi1TkQPpTn08rvAqLExrsDi9AlfXsW3/OQM9KuaNoxzgYzAERib/bFVVuN6yuqEESw4rVpyA\nfLd/MErAuL83afdg8Oi2GAwzzVdVFRoe5kPzoQaWdg1Ot+3MjS+ROlUNhfaLvAZjbHu7yPxoNAdz\n3d6u0CWa5Ub6T4N5sASWwEJ4FUbDuDwpp+GwQq1hbIYq2Oe6h5JjyHuB4XDY5/MNGzZs06ZNha08\nDAmHNbUfmI1AoD4a3R+JtKRMpesmNzC/5PD9q7jAx3eu4EMTXFcDgT0iTYbhwhaRRDisTveywYUg\n0oWFgEy1gwykzHp2GE/GN+ghkVBoyTqyACq8rzgb+ZZboZCmMuBsuwkWZreEiTDRNCd2ORqLwbIv\n8uQ0eDXthwdNphmGJyxrhqrCBstSy1oHf849gpLFKeP+d0HJRSCdEMBfPLolGFS4Bv68N6YfZekq\nqAbNCieGFsM4KvFaXq6GkVBV294CCw1jEjxjGLnFgaEh4yFPkbMTYBoshqWwGKZDBGaIVEcilZXq\n8z0OQcfRFMsCtekGvbClO3To0LBhw4YNG+bz+XIGLCY7sRyn0DxRGFwLg+EOGEhgXkBVo9GDhlEH\nNcVE4HQLkbe6jnaNSO64T4+ECYfD2XI3yXNzhOSrKkzMuZ/shVTCivQLKbwBCzFYAHNEcq8wvMob\nljU5pUI6BJ6EgfwKDg3ny+mNTXMjPBwMakrTLbmtevvWEyC004tQcpyMloRx1/ceM+M4z3uxZaoK\nmyoqFP7yE/o+DVW5LLthVGW43qpqGMsNY41hrPDIaC8ADl607UyZ7+w4ivJyTQnlboxE5vr9UyEK\nS6EKZsNk+B2/2BvuUkeisrJLzovmt1YZ2LRpk2fls02863ZyuMds3K++52quTcZHXkN0fVRVDaMS\nNvp8+7s9vVtkTGAim7Pd4XA4nPPqMpDvGkWaupWICYUUqkIhhbxqaLa9A1bBpgKh7imbHovpD/j3\nkTAOPIfdNNsyfnrBYDs8kzzxylhMYVcspnC9aU4pPODSwvjx49/tIfQYpWHc32sBMz7f46Y5S1V9\nvjZvqQ53wlAftGbtALruftgRCHThYf3+1RB13UwpYL9/GrwIT4tM8I7Aer8/U3J9wIDGiRMzjqmP\nKybBHFgKy6ASpsMYWJc0ZuGwZuje9LQ+UcoIpnR6HWeVV381Xe6mp4gsjhh3GdwBd8CNOHc+ITIC\n4vmMbY9CJDNI6kRCMwxxxhUVQIHd6+L3aaEKqjLMt223wgxYadv7YWdB4945V+0MBh8Eb+n22lGS\nfU/Xxnd1rdLngyWmqaZ5P9xX5IBLAqeM+98L7zXPHQaYZrWqQoMXIXM2d8HwnRU51rqh0Dvpbns0\n2gDzbVuhIruxB9veAWHDeMow/pThaycbdHkNq9IX+0GYn3Tkl0AFjIcnxAcbRbr0ljP2rlt4Jv7C\nCy8cN25c//4VcKtqIWbcM5uRSDQarYtEouGwGwhEDeN6n+9xkRFlZb8xjOv53Ne4Dm6H22EgfOH/\nQSVsdBz1/sEuEXUcFTks8g40w0rYBPVQDU0eO+84KrJPJD0rNTt+fKWqDkui+AsXyZtbINJW5K62\n5/6HQgqLbXtPKKQwG9alDLptF0pS895y4Nnk3uls88eWdSApXbc9FYwbDO6G8em+fDAYh9ug0bK2\neLtEp/AuojSM+3vNc/eWxrGYmqZaVu01nBcGuNvvz8GnwrZAoEVVo9E6kbvgZu94t8kvtt0CCyCc\n04+D+bAprxJWR0c8EJhrGIthOSyHi/DBnpnyq3QF97PPXlnE5ebG3LlzHccpK/tW//5XrVixSuRJ\nx5kdjbZoZ5DilGQZP5/IiHDYDYdd8DnO8559V9Vo1FXV/v2vct1W123t0A55XLgN7oBfnQ6VPd1K\ndd2jTn047MVTtsBa2AsbRUaIPCbyMHxb5BLbvq2nl1zAfIfDCuuK6QQ6025FlsESWA8zM34MsD+f\n8/5LvjESXoZpMC0t0DYWU/BZ1tLUZAYvB4Oakd9kWbOg2TTnwz3FjLYkUIqEu5aKcdfSXBYdG4LB\nOFzf0aFeIPvpPPEQvA4/5L/h/ozGjlPrPWyBwEZ4MhQ6mk9fTGFl2DtoUpieNAAAIABJREFU0DJ4\nBZ627R3aGTnzPNSKVLmudssl7A8EJsNsMCn/KKuWwFyIwFwRVT2eahgdHdqv3xDoD9+Cj8G/ww+n\nT2+MRFZ6FrbIuqyjR49OvXaedfDDHXA9UCdyAiRqU0S56+qwYcMGDrwZvgmjRXZ5qjgib3tKk92i\nu8onRWUzwVR4HTaINKUsuFeFNfWTgFU5+f2ltv0kTIDpMCGrVpdlTYbroN6yFJ63rB2qOaYceAJq\nClR/LDmcMu5/X5RiKNKxwbImweWOMw+aIHwDn30FxsFnmAqPWFaXAA/DaBTxApbnZvhi2RkxGfD5\naj0eIJFQn68CpsBUeAzuSCQ6lQ6LBzR/heeqPFFEmA+vQzl9NoSL3VhL0iM+qBLZpqqO0wDbPVNu\nGD/2+a4dNmzYjBkzjufH4KrLQDDPgjo+fQIqf3pWsqamJkXCiMSyKXIvQB7isMoL08xuUBgQL5xS\nJrIKVoq8lW/Ssm1XZJVtT7btPdls0j0wDibBG3A4/yeZ5npYbVn7tNOdz5y/g8FD0AT3njQKkSVq\nfErGuJfo5HkMgIvD4XWOsxZav8KlY2ECvGBe7uWFw4hAYJ7X0u9fCfthak4GpjAt095+lHi17XaR\nt7zHWWQdzITJ8Lfix5zaSp3l978MFbA8uek6B56DNx0n29P27J1Iu0iDYWyJRnM44+mh3x0dunbt\n2mHDhl122WXdRp6kkM16B8Y/wdf6wHJOn8jA430E+vb9VQa3LrKtmOKlSbXINbattv12tyVYw+Ec\ngfCJhNr2AVgGWyEqskDk5W4/Gi6HbbatGgqtsW0NhZ6HMEyDGVD4p2NZW+AVy+ocSapyUzpMs+2k\nKcx08OCxiyy9uygZ416ik+cxAK5wnJBhVFuWzrLuCSZjFaDJdfc7zhtpCYHLYf0LLxzO2U+3wgHg\nLatrM57lRMLbjpsFk+F1kcrc53fpKlOn4DVYCEu8ohiwAF6EBtsud970+d42jK1+f5uIGwgUCkYU\nqUtlcqX47kOHDk2cOHHYsGH9+/e/+uqro9G8pbE9ZGdIua7K94ZDHV/8E7fBNcf4FAwbNsxxbhW5\nPvstT2ilR4CVsFFEPVngPG3S5SUe8UqtwlGh9kRCRZZ0/2Gh0MVc+WVmPMaXl0IdxGEyvAC7Qnlr\nt6qqab4J000zDkvgCc0lUqadHv2Ok0ZBrETte8kY9/cIIpEl4BN5FJpqQvOf9BICYzFVTVVMNs1X\nYKRtL4E9EyceydeVYdTme0tVYT1sKFD2E7YkrbyX81JRmd/IQ24KKG4PnQkVsAJWQGVSR3BxrsKt\nubqdJ3J06sqmifv16+fz+caNG1cgKGXw4MwSUaoKC2EbX7G5He6Em3C12PhHb/XgIR/vX6QIQTpS\nkUWJhIrsgZUirRlWHhJQA8thK9Rnz98iW/O53Vtsu9G2p8JMqIZNsBGGMNCFLbAS1LYLV9O2rHqY\nlBzJQXgQHsxXFhzGFKjxXUIoXc6glIz7e2FPNRR6G66ANwwjdr9hhOF1qI1EHKe6PI0fhlEQ7Y6B\nzX08HleRBugmSDGjkJNtewZxIbyZSGg43JSya9nh7Wmn1P8rq2oDgQhUwFJYCZXwMkyGCfAE7HCc\nvWvXanPzrqzwcpiTfsxxcow5Eol4Jn7w4MF+vz+7QU7J33BYYYXz1CSugNvhDrih+2eho6MjIx3J\n0znIBvQ4eDfffCAShzfhTdgCTdAIeX3zLpY9HtdQ6EEYD1OhBjZAHBqgHrbCI/wSYhoKabwNxotM\nKxhof79Xm8mDaWow6BV3zMECBYONMBqe7P6yez1OGfd/BEr3LhcPeAUug8aKCr0fJsB4w1BV1z2U\nqo5kmmtEpsDTIq/n6+fgwdyxzCLDYU4xhZYKEAtQCVWwBF5L1qBoVNVAYI3jbIe56bqAR2niykoN\nBGbBUhgCe6AF6iEGy2EBLII5MNUwtLLSo2BSUX0efL68yxRVdRwnZ1x5TqfecY7yCVzVWV+ba1E9\nmsI0GZbDWpGX4SaRq0T6Qv+yssf69n3HcapFNBxeKzJXpM0TqOxyi1anFzItBtlB7rbt3eo41It4\n9Hoz7Cqw9fojSYySG6IiU2EyVEFdMla/ATZD3CsFG4+r6rTQvvRZWWQZ5Oa4THMOvJZ+JBjsTCuD\nO1JJrSnEYt4veclJQLuXLiF8yrj3LsBMuAvabPM3z8KrsD0a1c5nabOqwivxuIo0w1woDwRqXTf3\nUjqdDE0kVGSByFjtTG/JTdOnw7YL7atFoy0iVSJ1EAUXwjADFuUSomrMOFIpMgYaoAl2JGUY98Au\nrzQqbILNEOQ/oO1KLt7tOOq6d/ifukA2dzvsFGeScq5zuvMiCnVTw6qqP/gPuAxug8Hwe575BHvh\nMLwN++E+OA/OhZ9BDbTATq8sHrR5dbihGZpgJ2yD6+Bp+CQvfoyJ9VAPK2ElVMBKqIUVoLbd4JHr\ntq22PRZGyW8Nbr3xxuoBAw6IvAW7vfrdue7nXFgj0paeGTtJZJbI0zAfVsF62Jr00Dcla6N02Ha2\nXCQ0dS02shJeyZDcgYk52XPYEwy2e5Ydbuj6lmWadbDGsk4GZqZEUUrGvUS3NYpHJOJpt0RNUy+H\n12BOmmEyzVaYZlm7VRX2+/2eb1s+aFDVoVwUS4rxFHFhseN0+nu2rdlCNNnoNjIvEllpGHOhAnYZ\nRjUsgmpYDdUiW1OOXkbOajqOeMGPgcAWw4h5DirsgjbYA7fy0z4sX8WHm+FeeAJWQwVMgDcMY6/j\naDRalYe7D4fDV199tScf/53vfGf2jBnN0aiq1jvOFMdpcpwmgE03cuNhOAxT/wUGJu371cz6qajq\nxLFjhw0bdpvjZEs+pHAf3zwSXul9pDqOuu4ix9kTDvdnGMR3y//bAuuShUiawYVGaIJ1fOApPnE+\nP/0ydyT5qjao/xgbbuWai/nTCM7M9714BM48+6/D+fjjsBBWJ73ybdAALmyCHUkPvQBEmtIjcDzt\ngVBIRZaLzLHtOpjkFfHIBiyFhZZ1RFWDwfZ0Jx0ejsUUdsIDhQfQy1HSVHApGXct8XtdDCAMIw0u\nubtrFonPtxiWiExR1UhkW8o6RyI18Dg86LqZ0ivQ4vPVwVLDqOx6vN7v716nJZHQfDuoImvA5/fP\nVVXDmJRSI4lGYyJVfv8KkVrDWAvrYAXMhAlFZvGoqrquK7ICvsw90LwNWuFPcD/shb2wE5phG2yG\nVTAXlkDEMBKOk2JUjkSjlY5zr2F8Gb4N58ED8BIcBB+shlaAtcNkQrqODAPhFvgDfJm+0nfYsGHd\nKs7nFKzv7C0r52hm+EiSxZoLMWiG3Z57Dkv3J1Qra5+HebAQlsFKiMJU6LDtjnBYVd8Oh/34Yc+f\n+PZqqIUtUA/bIA4xTzG0h3X50rl+kY6042Phze6qaR9KZaha1gbTfEM7ZQmeVlXT7IBASTMzJc0W\nlJhxL+l73S0saxLcCMPO4LpByeqUquq6+2CcYXQ+tIZRe/bZRw3H9Om7QiGFgJdtnwIsyQ6qi0Ti\nxXAyHjI4Ab+/BpZm1abIW2O6slIdp84w1sNqWAyboR6WwESY7DidSTT5A06W/1zmJSIR7eh4zu+/\n/+yzF/KhBCRgB+yEPUlzvwd2QCPEoTrJ4E+BcbAA/gY/AhO+wBln8RGf/PoC2SCisAmWeAoEntst\nMp0vwqfgU3A2Zed+VrsTESsgYADNyW7rYV2SztkOu7K/l9w7mYnEBBgDr8GzMBdWwgaAPd/gmUZo\nhHUQF9kpoqq3yUtQAYt7ZN6hOtUetmjnlnut108+dYpk+4auDvuIYPAIDDXNqKqa5laYnykNX1Io\naYNzyrj3Ipjmw7AABsPwp9LcdtNcDFNEOmPOsnMLVVVkFjzlvY7HFebDouxmsCEQKDbnPsXai2yH\npTkNWb4gyHQ4zkFVDQTWBwKNgYDnulZDLSRgK8Qh5DiHRBpFOjcho9E2WCFdSfYPUj0RZsE8iMOC\nZEjg1iST4/3bDftgBzSBF+e3HIJwJXyO0z7BaR/io324Adz0gKL+/e/r33+A9LuAj8PvYTDchNwr\nnoGGtuS00ukxe3cDXtRkDH447AWYbgMXdsEB2PGvrPgsMz7H82vDmaTiymQt7Zki98s9u217Bngb\nsytElor8FebBYtiY5NC3QwL+xLXn88Rqr9x42jWkZohQSGFR8SY+tRAUidn2HpjXtaTX4/nSlS1L\nTbOLnL1pvpxSqzbNathV6sxM6eJ9qkrp4NChQ3369Hm3R/H3wvve9xR8tQ9vHOID1/Pik7rhlVfW\nXnxx9YAB/3n++Wf++c8d9fWfCoe59NKDqh/I14PI2SI/fOghgHCYSy45+u7FF0975ZVzEokz/+3f\nihzPDpEz4fDixf+Ss4Hr8ulP71f9vwU6qa/nwQfxxpMT5567+txzv/7QQzF4Hyj8L+iAD8BhaHWc\nrz300EzDOOPLDbdt4yuf5gM7OBhg/qfY/q/srONDLby1S8794qc+fGjx4u85zuRbbtkH34f/Df8M\n/+xdCByG98Nb8AJMgA44yOn/zuEXwy8+V1VVt3fvW3v29PngBy+qr3//d/7z5fsfav7ohzceOef9\n798yym99VM43L9l8BrVfkCuqqprgdHgf/B/4F3gbzoB2eB+0/YwpX6eyhU8c5p9fwP91Nt/HdWfR\n9k/wNpwGH4B98EEA3p8c2BH4EByA/wX/BP8b/gk6IAIXwvtBwZOp/ITIIbiWO+dVffsF/vurbFLQ\nJFsV46xbtaHrNzjTtn9g2//86U8X/qJ3hkIfFuEzn5ks8t3Fi8/IaOA4Cxcvfl9V1fcyjsfjfPaz\nB1T/T+qIbddWVW2tqvpZ8l0X5qteUejjeytWrlz5jW98490exXHg3Z5deobx48efrNuqphmEseB+\njV/04fdTg16c2f3TpqmqDhiwHzZ0dGgolDf1NB5XiMBz8Jh2Lq67CLUbxuqcAr/ZsO227KTTbMD8\nblUAXPdY6mwYxsuw88OEvsELUAM7Ps5NMAHqoRV2JmtV74A6aIINsBtqYQFUwaY+VHycBedwy6X8\n9pOMPoeXzmL6t3nhVzz6K55+Ef4HBM4GE66AGxhQB9thI8ShFd7km2exBQ6fxUY4BPuhCVqEqRb3\n2txlMfQiHnqAizZz5iE4CIfgbTgIh0EInMU6z3a/0/X/1L8j8Da0wyE4DAfh7WQPb8HfYJ23vsja\nrzi6JZ5IbBOZB8u8vWxYBJO7Mu8iDSJuAUdepAU2wawC33g8rqaZubMKEzJUdOAZeNSr/audWVdP\nlSjtXrpBkB5KzLhr6d/xfDCMUfA4JIZwxuf5Edzj8z2VHmHmPSFwMCcHKrJIJBUeMwFehDEisfQ2\nECuQkpo8dzHEI5EdHR0qkohE8nI4rtsGB4pJNS0yFz8cVsdpPQPrYr7/EcZCbA0faYN62O44B1xX\nZF002hCNtkQiDY6z1nXV72+8+urdM2boZZe9Ew6ryEHHUZ9PYZtIwjDiUAe7oM6LRBdRcM9g7YdY\neQ5Tf8e3vgFRmEffWjgC7fAOvJ38/wh44TSH4AC8AwfhQLKQ9m7YlQzibIJmSMAu2Ast0IcgtMzi\nQ41QBfWwFo6IPMg5o7gwxLe2wJt8pFZ+FOarr9vrNBzWTZu82q+HCkgQdN7SDdnTaoVcdMS2Z8Oq\n5N7DEk+7Ih5PhFb9WFbBjOyukj7BBhhaxFf5XHp1jlhMYWMqUNKyNnqCYnBtsn0iJz1YEij18I3S\nM+4nK+0Ow+HND7PgUXjCGQrD4U+JxNH6Sra93bYP59R9hekZFj8QqIKnIdC1WaGsVNtWWBaJHLUp\n4XDegBlVDQRqiyHcVRV2RaM51luwyec7ABt8PnUcXRQ+fC1n+Dr3DMdB8za/vykSSbV3nEORSI/X\nbTklxu5ywhA3jYfPN4xyiMB6kS2g4XCLyHrYI7JZ5LU+hD7OXecw8L8Z+1E6hSuTHbaEu2oW5Miw\nLbS9YdsqshdqYW2xoURJiOTQ7O3idycSGgp5UTfVUA0VMBXu5Hs/kze9JkkFoRrbVmgtUp8ZXjDN\nZ5OvE7DUu0zLqjLNpWnNvPj3FVBnmtN7dnm9A6XuR5aecS/16TQnAoEpcC9sO48ht0Cr68JfMmrZ\nwABoyVhcx+MK8wYOzKfvMQ5ehzGqKtKRL07GMGoNY0skkmOftgDrYhjriuRbHKfzcyORNr9/nchW\nWO84+0XaVXV5ILDE798KTbASfJCATzLT788cj+NsDAS6j9AvbkgKMZGJhSsldeoD3wp3wo059GcK\ns1JQX8xgRFwRhTjU2baKdK9yEw5nbmUXmh7i8Y0ic2EFrIaH6fNpBsOLsBoqk2M4AoXEiNJhmlM9\n4sU0PfJwXyzWGdueQjAYh3shUWQd3VM44Thl3HsFRO6Cv0D9SL78iAgELKs5I8wAqqFLMmo8roZx\nfSSSV8bEK64msgjGQIUkXTYPkUitYcwzjLxpn5FIbUqUMQPRaB0kipTdhRpogk2BgIp0LjH2um6F\nyBzYCHu8/HiRqkDAC43MKEzqwXGeL+rzioDjKKzr23dRMWXwuCaZ33QTzvSjMUP5hGWOnpij5G0O\nZDDdtn3IthVWdFe7Y1fXP4ty/n8tr8CbUPM1Lr2Ij9wil3vH4/GiUttSsKxp4PN2d6AaXreszO0c\nuNZLq0o3+qWCk2Bvr/SMu5b+cikbIndBOWwbB+XlWwzjVVU1jAfTSy/BKmhJ/RmPq2E8X7gaUTjc\nWak5FPKewNfKy49UVu523VbHmQDTu7XO+XzzQGAt7AwEMuXFu366ihyGFa57NB68w3VV1WNClsLr\nMNcwFgUCGZwG7M1pFntUurrw2KDBMIoy7qrK5XAb3Am/P+q/d1ulL+UXd9csr4RkIqEiB0Was98S\n6SJHky31noFQSGEybLZtXRxKjIRx8CT44GDcq7nY1u0Wetdh+zxpMNOcll2yQ1UtazM0e5WbSg4n\nAf1bksb95HPeRe6C+7/ARI21iHRa3ETibRjuOJ2VjCCWYsBte7vj1HZbZy4USvh8M1XVttUwtkaj\nrfAKvAb3i/wlElnazfmqhnGH6+Zg+X2+Ssjt2hjG9YZxPfgCgaM1mERGTAkEAn6/L1X5FNxwuC6X\nGnsgcBB2BAI5OI2iS3QcxXPPPZd90HEUmvr2nV98AWuuhNthMNiE42FV9Sq1FkCWnlienosIYfJE\nxES67Ih0lf3Ke67IGlgFGzNtdzz+OFwL18Bd9IGtsLH74XYZ+WXwZ5iYb9cURsLYUvTcTxn3dwcn\nwX3PwPfNO2HBGcw3zbBpVqWOm+Y4GBWNxt95R2FPe7uqqsgMw5hZTLeBQBPsd92D0Og4LdFoAhaI\nzPD7q2EmvOg4VRl5rRlob89N5sKmSKTL9mw47OU6jc/o8C3XfcwwvJJMYyCSzNMpAL9/EeyKRHL4\ns8XpwHdBTgkBeAQa+vadVLxxV1UZJZ3+u42rrsiIbtpLIoM8yYni/eVEQm07AT4YHg4fZWZse5dI\nZiJoKOR561UiRwrEQc6wbR88DN/mgfRiIN3CsibD7fAMTMgQiE4BLBhiWd3fhN6GU7TMu4OTzHOv\nKC8/gwug5dP8Obu4HfwZRvn9S72qCCKZhZMKA5oDgRXQCpMMozocPhp+I7IOpsIrtp1j1Z/WLGe3\nOyORfdrpUW7ILsvQHI2+ZBizoBn2wU5YaxhFsio+36Z8ZeoMI1NjslvkjJZxXW9DdWyPjLuqcgXc\nCnfBDfDTPt23T2PS8qFHZEj6Waltj3A4kT4H23YbrIHGImXlK0IVN8Kf6As7P0SxD5dlzYSnLasD\n7oddeZQjL4V7So6WOTmI31PG/d3HcNPsw/WwC0aa5uzsBvAQRGEz+HqoCuUFq70JDbade+0v8iZM\ngRm2fTBP3Ykc5gmaYK3I4YxTtkYi0wxjOYyASbADEoah4fAvJAe3kw+GsdEwcrc/huI+HVnsVSAw\nu3//+bCprGxGT427qspDwi1wF9zc/ePT7S5lt8R9wc6XQLXI855wo8hymO9VaOrRhBEK6bSQPis/\nhfi/M+0Z2FDE+fCcaaaqg8VyZjPAjTDWU34vIZwcFqYkjbueLHffgw/gGWjLLnqQAvwNRhvGzT3t\nHKIQL2ZKgNehEqYGAgfS2WSoTm8WDnt5idsjkaP2d3M0WhcIrDCMGOyE/TBXZGsg0JqMUnecQiHz\nWSPZLJJ7e7DbbcNs9O8fTC0YRA44jobDLkyCVbCprMzs3/+wF7+e+ufNWI7zlubZwpUHhVvgTvgD\nzhuFzHO3RIfIWz0Nck/Btg9Cm223wqtQAzGoOYbeRB5LdqiwaxyMhyegI//vBl6COV2P5JjG4A/w\nwjF8a+8uTg7it1SN+8lx9z2EbbsPD0DtH3y55ZliMU+R6pHy8h4U92lvV1gm0lCk5ICHREJhAVTC\nXE+nNxA45DiNgUAdVECtyNOwze/vdOcT0egcv98TytoNKpKTUu/oUJHiBct2BwK5A0j8/vpotPOj\nXXdPINDkOBs9hQPY5jgK20XavVF4Kal9+871DHRqXK6rjrMc6srKht100x+7HY93uuMoNMA22MXp\n07jgV/wR7oRBuOq6eZgtaC7sm3vB/seAcLhDZD00QgzWewdDIU/8q6jksrRBdnoV8bjCwfvszQ/D\nOHgRtudy4eENWABjux7cY5ors1qOgmeL2XjoVThFy7ybODnuvofnHecMLoER0VBFzgaxmMJmv/8V\neCgUKlRqzoPr7gsEar2SaaFQsdn/6ejo8OaGObAQXoLX4aVodJuquu5+2B2J7Gp13SrHWQCbYSt0\n65kXT5dDXSBwVEnYdXerajjc5vfXJlP966DVMPYfM6fhOJWQuPrqB4+Blukclb7FDwUH7oS+8CMD\nfI4zRWQE+FITCazszrgXO+cl28dhJTR61TjgIGSaVNveK9JYvAtv25NTr2GnZ89r/j97Zx4mR3md\n+5/u9b2Jrh3Zlo0dm8bBVnBi2TFxnKQPBCc2SWTHON7SEzCrkcAYY7u/EmCDwIAtgQEziEUsQuwg\ndVcLCWm07/uM9n0ZoaW7azSSRsuMVrSAdO4fX3dN9To9Y8eaGfQ+PDw9VV99VdWteut8Z3mPMc/D\nKHgZ7g+IUEGNzX7xBWSy2zfConC4NdQfjW6Ex5PJigIPnQrHira/6Wr4X2dAq+wPgU2bNh07duxM\nX8UfBh8JhZrpBf9HF79RdMCnP73OmD7V1V+Dg1dc8Xz52QYOXP+pTy0499y/Vr0IuOKKJmho7yX1\n6MGYMdscxwo0vh/+DP7q4ovX9+gxbfToRtj5VyFv4sUXM3ToudAMPWtrufji8nPu2FH57/Ux0NGj\nvfPOa+zRY8/FFx+56KLmN944Egp9rKrqWCLR0/POU/1IQ8P7H3207bkSiUThRse5GHY2NIQqvqR8\nnMefyInZ7IZpcAFcuIMb33j00W/V1d3luo8uXjwxkWi46KLlcKSujoEDTxedZODAiY5zqM1zeR4X\nXbShR49Ujx77Fy/+v+n0l1Q/oXpOXR0ix+GcvPFDh/5ZXd0ngB49pvboMbb85K6b86dIRhLyC0OH\nDlD9U5EecD682KPHB3sM7NHjzVTqP88/n3g8LfIvwQNjsc+Fw59bsmSdv8WYz0Gv888HutKjOnLk\nyD/90+IyqF0MZ/rt0nF0J7c7/AqG3Maf5W1PpxVeh4aFC+2wepGJ8Cz8qug8iYQHE3NnPpLX37IS\nVFUtD4XWiRzOTrK7unp9VdV8mAOLYBVM/DjP/R0/eV6uqHDOSqxs11X4MRwOhTbY8XnR0OrqlcUy\n49sN190BnsjvOmy5W7ePqrr1LgPhHhgEBndbjlfKcU7adCORzSLDICIyxPfjl8kecl0VaRE5ATvh\nQKkYJ4wrH65MpxVml7HiC7qvvFxoaG8yg+BxmDZAXrOt+6LR7eHwqOCYWExhfzKp8Au7JRpdZm18\n2NCFhCG7jcv3LLl3CsBCGPxDvpC3XWQquH63I/CqqrZUVbnwvDFvnQp4az3voOMsyJMlsb2wRR43\npngbzDx43pGqqqWh0DbH2R3knerqnVVVu1V1d20tNHyGMQO45RwSMA9WwiyRTByvDFvl7fK8A9XV\nDZYiHUdDoSbH2ZdIHHOct8qInJw+rX7TkgpRNM9dZAgcFJnQcbdM7u3wE7gbfgVRnJociYKiTgmR\nXY6jMMd/STQ1qTFNxiishz22YVObSSuuq5W01orHFWYXbk+liqS65nXXisePwwswvz9fuxMiMDQc\nvpjfFM5mo8e+JhK8aJMgi56606LbEMtZcj/z8LzjsL0nP/8q39JAMR/8NhxeFo9rJJtEk9uo/qmg\n+AyMCoVmJhLbgjPDplDoaCJRC4+1dQ0t1dXbQ6EVBUIAdu8J11VNp3/H+dB8JR8PWtRWCAVWwnrY\nCFNFah1nQW1tfgc+x2msrW04fdpGelWkuapqW3V1TrQtFBpTJrni9Ol2q8MXJXfHmQDrRZ79Q5G7\nqvJjuBN+Bb9AhrReZSkxTsd5F2ZldRutHv3BdvnKVVXkGLQdhrEw5hTUBLfE40XJPemnyRizGhaL\nNKvqb0z823zwThgFr8KQgnU/NGY/XAP9oc7+GQ63r/D1zOKs5X7m0W3Ivbq6Cer/ji/DQxpYvsIo\nVQ2F6n0530WLcko04SVjGt99V0Oh2SL5UTVVhSb7lNoCqDKAKWWMxBHVk3/MP22Ab/Hr8rrBixap\n4zTAGlgPq2CxyD6ogSfhRVhmldZra4/V1hYPJIZCG0Khkn1ZNcAgFaI0ue/u1++pDpN70bxVroQ7\n4FeZKqfsyP3+m8B1VWQn1MNeOAC7RDJd+rRVjWdJ5Vnq0ADL2pvV7nN3iQq16SLvaCbfcQlMy937\n0v30fAWehijkmiOb7b/fWOwwDPebB0SjXYbfu0co1aILk/vbb7/dDUqEVVVkXCjkXQ09ufNfQzeo\nque1wDOqumjRkTwzNi+5Aqrh1VDohcJ/k4sWtWqPiJwo9fw/8oga63/eAAAgAElEQVQao45zstTl\njamqmhQKpWALwJpSOpGF8DybO18PayBlhcthKUxynC2OU5tIeLW1KVX1vFbHAuypqiqXV1NGZqty\nuK4HG0Ohe34Pci9SbqZWJfiH53DJlfzT92AyPV+DI3AEGuEQbHccFTlhs+nLCDEYk6kwKG/Iu67C\n2A7UuIqsNWZzUVHieFxhF0wpVeAKb15M9Ba4BSIB+z0a3ZpNpKmBl3yhylhMu4rPvduYjNqlyb3b\nZEOKTIpE9AmR3lx3HjetSiSqqqpDIaOqnncSWnwj99QpDTbrcN1UKDQuFHoNXr/qqjkF06Z9u6y6\nel1hPUooNMZfOBfFQc+b7jhLIQnLobZWQ6F5IkVk34vd1GG4IxR6Q6TZ844nEltraw+GQutDoRUi\nG0Kh+mzP5+2QhMWOo47zrkgjbA6FkqrquqXkSopY4mVQWKGqGXLf1rfv3R0j96Ym9aWy/Cx4kQOw\nH3Zn23Q3Q5JzJ8GRPC+2RSUR5nTa9vQo7qeyvJ9Oa8cSyUXWiBQxVEWaYE1ej8Yg4Nfh8CJVvQV+\nApOy8gLJpIbDNnP3tXD4JV9DIhpte+3YSdBtfDLapcldu8svAaMdJ/1uOv0D/gIe+a0ZBTfZXY7T\naJnOwvP2wQbPO549MOE4a1W1trYRXrFNOXyIbA0adKFQq8GbSNTDHCinCrnTdV3YBEnwIpE57nLY\nWEofyofjHIxEjovsr64u0gzQcepEtmluDozIxqqqBqgPhbZBEvbCLkhCA2yG1TATllo71/NUpKYD\n2pB5EBkCDSIj2yR322nEqhaLtIB1qmyBA7AXDmZ7pq63DhYfXP5RbofbgC38+fDCmdtblG/bw+Zu\nuVMz5N7uUgZVhRvj8bTIYN/vJ7IQ6oxR2F5mNQCpaLQe7hwc/pqBK3Ky4A/B85opznjGbuxC2jIr\nVxZxb3ZRnCX3MwzP2wdjq6p2LUskhsKHicJvIpFVdm9V1SbHyTHKRCaHQm943tuh0PyqqpxHvapq\nFrwUCr3pebaPZY7Eq81r9LwjItOheLWUxSHPm1FVNR+SsBpOZBkLauFg0YZ51dVrYWUolE4kWoI+\nlmL3W2anJhI74XBtrTpOfYDNjziOwhrYA9PgTmiCndAEe2AXpMGDOlgOK2EvTIdpMMNx9N57Feoc\nR0WOiDSJtEAt1EEz3AZh2AS7ba9WOAq74BAcgaPZnqlH4CDsFTnu6xNUEteVB4VfQs8RfGA9P8bd\nlPNS6kDfcM34YWaK7FRVuN5u7Ci535D98LzIJBjjO/1ETpYh92wOzH3JpEbhGng4HM5OtT8c3qSq\n0egk++5R1VhMw+GKmlKdcZwl906EbhAAgYVVVTtW1667k14P82fwsN+qGJaJ5HRKqq6eEIk8DRHX\nLdK9zHHmQwzeEInlqZq4ro1VLnGcNrqpjQqFrJt8pcgxLygyMy9vTs97W2QxzHOcnYlERYqPRXvA\nBq6/Hg56XhuhlIKsysz/RZpsYqX9P+yEdCSy2zIyeK6rIqdEPJHjsC8Umt2r16W9eo0oIZpQ7gIq\nHO+Mcuh1KyRtliQRsnc6wXHWlD+2PGCAyODsZ68DkjK+wQ6TRQ75hraWyKLxj/IPDIcHz4yt+LH1\nvCeT0ehyaHX/wU3hcI2qQtsaD50B3YBMgujy5N7VkUjUwvpIZJeqXs3nnoMPc1s47DfoKKrIOP7d\nd8vNWVU1ORRaCNNEXve8ZlX1vH0ik2BTdXXJWGWz542vqpoE222zzQLpdJFNvoWYSCRDofWh0IZE\nYpfntaM9Wyi03PNKqqmEQlOg3aK+pWApvl+/I1mnisIex1Fohp9CulevyyAMx+Ag7BQ5ImJfA/vs\neH+ePLRL9sDzFPYzCH4Ft+E2VdToo02ITNFMq6YDIgWNONqCMSqyEp6HjYHEx0ZjMiY2FI+x5wlz\nQuQmGAB9+Rd4FGbbmGo0Ol5VbbaupfjOj27gCQiiy5N7NwirwiLLuV/i2qfgeYDfum46kUgWumXj\ncc1T4ysxZwOMhTdDodHV1fPgikceWQSR2triTvPaROI+WAATYUkx6koklkEKFlZXTwiFbhfZXErb\nqzzK90EV2VaJsyJ4gZ6nsMc6TGCLiO0/l3HpqOqIEUVmcF2F5b16vek4t7d5OpGjdrbsCmAjNNsm\nGJXY746jcJgb4RdwN9wB/eFDl7Z9ZBtX1frZGIX9lRvvIgmYBusL82GMaRJZpFq8NioeL1JXFUK+\nw0dh5PfD48LhTBjWporCHbHYIXi60is7ozhL7p0L3eD3gE3V1UlV/QDDfgvPw3/wcRgGD+f1rBCZ\nChMqsdHgiG2iJLICZsDwUOjpqqqJVVWjCwffFAr5re+K9r1T1URiO+yF34oMarO9XxkkErWRSMm3\ngsju8nTpOApJaIJt1srumHaY45yCvX37TuxYtgxkfGV+hS00ieyxksJF6ps4rNYFfxvcDXfDz1t7\nsXYAhcWrcNx1FSKuWzKrNTtyLmws01EPnjWmBZpSBUHxoE8m95AHLuCmH8D3w+OykgP3qGosdhxu\ngyLx5E6I7uRw125A7t3ATeZnrXw29MBd8DxcDReEHoK5tjLQorp6icgGVTXmdKSk8Ls/51HNmPnX\nu+4JY07BFBhTVTXP83Ly6iZWVc2ABbCqqmpfiXBndXVjKFQPB0T2hUI3/R73aq9tW+ldjUGydpx3\nPE9hG3hBb0Cwd2hHr2EybBep7ii5l0zHtO54kdNQDyPvvXdqdfWuoNY5P4dBcBcY3J0dzPuBSQVb\nvIAUZZE3dLaIbLuqwqry88fjCpuKFa/OLiT3aHRrT579Fh+JQG+eyIZbR2smZ+anMKHz57kfO3as\nG5BJEGfJ/cwDYuHwAlWFyK30HA4/g5mJKfAKPGLHeN4RGFVb25w9pFwNp+sqeCKrQ6HWQptEYlMo\nNBEmQ0119fLJiXlTqqrmwTZIh0J7sl018pBINImkHGenyAZrfoZCNxVtmV05QqH9nlf8V4MDIlth\nvIiW6WEERYLJ7YLrWls71lFyb0cWo+NsgX02l9++PfneR/kF/Ap+CZd35BkMivRmL2l7cNED4405\nrplEyVpYFkxjrcT3ZYzChoKz5K+6otFVMD4crv4ePSPQk2dhTzQ63j8d3AF1nb9HdncqX7Lo8uTe\nDQB3JJMaDg+ORsdfygXD4EZ4xrkHFsHwqqrE6dNqTI0xc/xDRMp3Pd0A+yKRonpVG2EqTILxX+fH\ndXxwTQllUMdZXFW1papqRyKxR9W6d3aoqsig6uoJv8/9Vlc3VVfnk7t1l8OBCr3YlaNoEZPIAWjq\n1avdPVQ7BtjoX/NVVx2n51IuvowoDII74CdsOdWO11WpluV5jhpj3oVFsD2vUqnC0Gs8bpPWX/K3\niKzOOzYcngrT7eeeXBYB4W+gOfj2hYdh41ly/+OjO5B7V4+phsMPhsMTbADqHC79HdwOl/H/YFcs\npvBEKPRIKJSTTPbII1qqA9rp0xoKraiqKm721ta2/JDoBD50A9f+Oa/BrFBotOPMq61tTUP2vCNV\nVethWSLR6sARqbN5LNXVE0Tu/33u9/Rp9eOTIipy2vcGQUXlr+1KWywkd+s5gbdCIff39LlXPD7P\n3aSqWj2lmlvgLrgbfokMrjTvvagAg+uqL/sjshrSvv4XzBBZEDi88q4pLcbshVezf+aYFOHwJJgf\n3BJChL+CAxdwX2CSV2D9WXL/46M7kPvPftbuzqKdCvAj+I0l92h0/H0wGC7k2zbvMBY7Cc9UVeVo\nZycSO6CxsFyotnYvvATNiUTxRmvDQ6ElsAOs/ZZINFZVbYS5MEdkSiKRFJkUCq2ort7qea3N+Tyv\nBXZXVx/KXvC42toOJixCHcyD4pnsNlRQCcoXQwVRKBxmE+Fhd9++t3WA3DsQwrVBVwv7VvPR554+\nGS3JO5Dqivi9qOntugp7YBY0Qr65I7LKmJbs54quOZVqfdcas09Vg6k1IvPD4fwVRCyWupBvQvoy\nPma3hMNvwnOV6xGdxR8Q3YHcuzqi0XXwu3D4t6oaDm//EZ+8Fy6lr633gYjISBgRibwZPEqkJZHI\nMc89T2FiJFIPh2tri1juE0TGwnxwObdwry3phDfh8UWLjhfsbS1fqqqqESmWM1EatqQTNmZ7TxcZ\n4zgHK2/3+vuQu70G2CUS/+OQu0iLf5TjrMvfe79we1ZL8mboeZnrlixKso1tcydvgm2QgmaRchUQ\nIuvaJbvme1dSKYUfBeZZVUpRoCf/CfusmlgyqfAC3Nf52+x1szwZi7PkfuYBQ+FeW6udTOr7WRuF\nC/kG7E0mM5lnqZTCM8a0FpcuWqShUKtns7Z2J4yurW1xnBVFw33zq6tfhwXgJRKFlpTI9FBobSLh\nVVXNC4XmwjKYLjLNPxcc9m35RGJHKFQy4yV32oUibxQW64vsKVYZtC9v4V8GUFLWqk1k3TJNodAT\nHSD3DijbOI4GFDrzq8PU8vuPsu0+fgIhERkiMkQkP+/FL/GFN2AJNNjvNp0uF4IOHD5NpJz4RO7g\n+f4PB5F4PJVKqchbIiVVl+E6aL6UL94J0eiaWMxSfEX/Ws4gukFGdSG6Cbl3aX9ZNLoVfhKNZvKO\nz2Hi3XABt0AzXO0Pi8dVZE7Q1e5LqtbW7oDRicROVa2qWleUImtCobmwxnFUtapqX1VVxsleXb0a\n5oq05sZ53kHPO+I4b0EdLINJMA3Wel6rQ9w/dSmIvF2+pr/Q/rUKAeWnDVxAx41Bm5wOR/v2/UUH\nyN2XKa8cnqeQsanLGP7cQqaQ9ZeYGUYzlD3V98MYk4b54EHKCgLnXlg5JThVNSZjK4hUpHxg1dBU\nVWSwMTVwP8wRaSNXCnZdwO1foQ+8nt3ye6VX/RFwltw7L7o0ucM6uN1vqwRNP+djIR78C2L/FX4l\nODIeV2gtuAxYVW9EImuzn9f4vU99jBWZA/NCoYZsyiPsSyS2VlXNgEVFfTgWiUSyqmotLIVlMDMU\nmuE4s2trd4qsq64uYjt7nsLivLS8Enedn2Yncrpyo/j3XOlb5Zm+fTuSLVO5RygIG0Fp+2u5AX4M\n34EvQ19UFWpgFKyCJmgUKem5ggXli1SDXi9wS8XkfYhstYaCyMMwDBYYs65oEVPuWXZcyLd78rPz\neEAzbvfOTu5n3TKdF136t4GRMAMGZRsdtHyPL8G6D7Nak/k63amUwmu+xpPI2/BC7mzpSCSnRrE2\nkZgKc6A5UH0q0giLHKexApWug7BJJFVdfQDmwWrYAItgepCqrOxi5excOBKSlbuzRSoNvZY6NRzp\n23dEJfIDeegoub+jlQUzJfJ9el9Dz5dgMeyGfbDHmEyra5GWUgwOM8rML7I5LxIbj6tI8ZYjgTn3\nxuNHYKJvsBdtQRUYH4G1MAJG3chnfwXRaLILSf52J3QTcu/qgPnwC7JNhy/kWx/j2X7c+7sSSegi\n84xpisdPwLA8+wsa8myrCEyC+tznHuaJVBpbg8Y8QjFGYQmsg7UwFybCdNdtny5BHpWXKYhv89hC\n2AQVEZ06VeEtaBJRSEIa0tAETXAJhEWOw2qR07ATVsIKeE3kBZEhnqcQ8dvgadal0wHYZnulFhyu\nqyLzHUdhO2yHJj4ygU/W8I+3MOAc17NaY63dOUSShTkzxpSv/Cri+DamPh4vtwaCFpgRbDsVjx8u\noxUD98J2WB4JPz0A7gMYEo3+HoIVZ9FRdB9y77rGezKptig8HJ5sjfePcOlD8CJUlyB3zbhoRsKN\nQSqPx/OzCRcbE4GVAWb3tZ/ak+9c3BUA663IiesqbIQ1sAYmidRXYt7mmZntao7qumodFLbsU8S2\n+FhrHf1BCq6uXlB4uOMorO3b9+eVuGV8Bcessk19Vh2+oT1+pP1QE3wnZUVpNsNOOAjHRHIyYfgR\nDIK74TbMbCPfyRF+MOaoSIOv+qtlWzKVkfA1pqaUMQ7TYV1eMruqikwrJScQDg+GJCxS1VQs9muA\nBzp5knu3dLhrdyL3Lu52r9NMl7JpqhoOL4zS82l6Plqa3FUVboY4tGZfxOP5wauHcrtcwlT74Pnj\nK7u8/MxIy+mQ73/1PHWcd0SsBboZ5om8Bc8X5fo8Nq8kASabUtkEu/M6H1UOx5kAV8C+SOTO9vrc\nRfJrCxxHYZvIAWgU2VeU7seNOwCNsBZWwlxogn3QYgeXuQt3t4uTyYLnhiL/GEQGw9X+K6HUa1gk\n/xcsnCf3z6VQB3WFC8HsiR4t3BiNajj8W3gWhiWTmorFrqCnL6HRaTFy5MgzfQn/I+g+5N6lX78+\nS1ozJxrd9EVumgDj4bkS/A6Zf5FWlds+gcbsDQpsPQFTIJ2lcJiZt5avsJ4laOO7bqNv6FVyuOep\nyEFogLdgK6x3HIVpebU8qprXClxbm9sdtjrEebxZtLlzhYCHYG+vXi+2n9xPln+jwGxYDQmYnm0g\nZVtjH7daxO2FmWj4ebaQ9RbMxCIlTK6rMFdVYWdRj3yhFk0e4vG0/VmNqYdpIm9nbyclkiwcD0Ng\naMHGCDwNUyDRm9sMRCCYAnAWf0x0H3Lvum4ZDRR2x2LvwMPwa9g8AsbCBBgFG3NZ2ZiaeHxf4PBq\nGCcyGybck2nipBG4HuZkD4QfFj728XjbxrvI5kAm9YaOvR40p1/SAZET0AB7oBFSMAvmwVHHedvz\n1HGWiqwUaSM/2nE6LnEjotDct++E9pJ7XhGQ66rtGC6ShOWwH9LQDIehOev3Xwb3wpyOqROravqU\n8lMyhay3I/cX/9LhSthW+IOWD4H6iMd3woOwNtC7Q2FT4fosO21Own40uhDugomwNRbTv+L7D0Bv\nroJyCv5n8T+H7kPuXRpBrZJweDwMsby2PxodDxPgJUgFaFXk2dzDI/F4k11K9+kzS1VrjIkEHDJl\nHu+gMlSJASuMUVhZtOq9Y41AA5NP1YxnYxWcgPpsa2zrQ38LlsJsx1GYCWMdRx0n6TgNqgo3VeKW\nKZQesgsCaAiF3AEDbi56lOuq4+x0nBbH2et5KrILamAzHIbd2b7YR+EgHLTK8uW/CivNKLKjA/FY\nkXfTh9Td7XJHpt2HDCvF78thXUH0u+1GSMa8C7NFDgX9LdAA02xAqBDJpEaj0/w/w+HnYaw9andS\nb4Bn4MP8sJM73LurT0a7Gbl3XflfeCIWy2QURKMb4EnYYmNWDdHoBJgMb8Aj2MTnMXmH+y0UYC68\nCTGhz2V8wG6FSJnc5HS6zeS2lUX1wf3DjUlWco9F4TgTICIyxAqsF+zN/N91FdKwB/bCDpgHd0EL\nHIAWaMzW9TTCJlgK9bA6mwOThjWwFLbBZvBgDWyDE3ANCCyFvdCc/f9hOAYtcBxa4G3rTvFbs3YM\nUBssLoO1IqkKZ4MH7AczwRCFu+BOGIC7Lf9FAatEdooMNqYuc4hp09teD6uDugXwvGY7rMbjWkY9\nPxx+LHCUX0Kx7qXoc7fCcwBPVnSHZw5d2p1bHt2K3L/97W+f6UvoIOBXvoEDw2IxazRlRUhSqddh\nCkyA39C7uXiAKx2Pn4C3Vy/ST/EAjIHhNfH9MKjNs5ey7Czv+31TS198Rav+PDiOiix0nP2+2kx5\nkfpC+I30/D9V1aYt9ut3RORVz1ORk/52kYO9em3t1WsFbIW1sBdeiURurNyU7lj81gKWFi3KFTkg\nUjzFxUJkSNASd7e78phk+N1gakzu4EbrVEmnVaQ+nda8lqe5gzfDmsIM1HhcYZStMjPmWPkspnB4\nsKrC0zA5e6feV7nsIbiczwWbbndOnCX3roGXXnrpTF9CB5FMKjxsP8MwVYXh8FhwzEiYAOPgiWIh\nVmNU5C04MOMedxY8xmdhBkwwpu1KTmNmFPK7yGCbQVEqu65j8DyFHUGas15smxTY3tmKWr7r168v\nFAsL7u3bd6rIZlgtcle7fO4d9kE5zgQYXapQ0/PUdT2IlBBqL/LulKclkyV5K/J0XgXDgcDn4jVK\nqZT1g20quldV4WmReZpxu5dLmYUr4amgYCQ0fJ2vPAl9+AF0sNXUHw1n3TJn8T8O39cJz6rafOoR\n8GBwzON8aBKMhxdgVYELHLbBvu9yxQIYKVdDTSplH85p8Fj5wGnecw4R101rJg2jjRJWzY0ZFIVN\nYRQ5Vmj8WoIWOdghZ3T+ljK07mPqVIXFsL9fvyFue87aYaqCiOtq0ZbTebB6Yf6f6XTx1hyqaqaa\nTEfWQcij4o/3ZX9EDhpjzfDWNlvG2HyeNpS8YKExO43ZHI+3kZUEL0IsHN4Y2NJ0DX/zPMBznby7\nXtd15FaC7kbuXTfb3SaWJZMaje5SVai3nTqCY+JxfRHGw2R4BY7nErYxB+HoIvgRX/ograI0qZTt\n3jAdcpRqgkinM24N11VY7G933fz8kKIoJVFrKzzb9NuIPGkz/duLoKe4aMelUnBdhb3/+38P++Y3\nv1nJeNuftDeXBjduHD8+b0ApOM4E19WgbHJbl/eOFY8MEn0h0prOaEneCVE/eO7L7mdepOm0ikyB\nGkjChgrEYfZmy9yGiSwqTFH1EQ6vh7mQ01ABGp+Gv+efobIyijOHLp1i1ya6G7l3XQ8a/FpVfUvH\nOkPgZXhe5E0NLM9ni4zPhliXBez3yXGF3S4fPI+Hi9rpIhthOowsuhcOWgGTIFy30q5shQzueW1w\nU/BYSHdISneCqq5fv75CZvdc1yYRXcr5cKgnt5xjXz5/0P/yiN5xFrquF+yUVCFgONSKtBGKoD/c\nnilk5fNfynZDPGl/ZZFpsBA8WF1xzdrOwOdXSgVdrJRYMqkQCabEQPoX/GUfBsCcis535tCNfTKq\n+r84i86BcPgckTGLF2/ObjgAqF4HH1+8eL/jrPRHfq2u7n0iJ+H90PDYY5MuushuH3RFNegkvvfk\nuNsvv7zIKerqPqf679DziivqevQYe9FFM/xdngesuOgiPvWpvEPITt8GXPdRz8t8Hjhw4sCBE4G6\nursqOdZxroM/qeg0uXjhhVENDW9//vOf79GjR6kxEwcObEgkqnr0qOrRY2Dr93IcTr9Dn7zBzfT2\nPx/j/dc5zt+K/K3IdY7zWfn+34p8sk+fXw0b9iG4RCThuqNcd7Tnjc7+/8vwQ1h9+eXrevSY06PH\n4h49Tg4c+MWhl//3f5936UXAqXbdnciPVC8S+fMePZYlEiWH6QsqnxQOw5/CV1Pwv4DFi1c99li6\nR4+34Cvp9D+pnqd64WOPbUyn2zjpRRdtS6U+EbiGLxT9aXr0qIlGb1G95IorhkSj1yxenLm1z/a4\nDk6/jyPb+Ap8rF33+8fH97///TN9Cf+TONNvlz8wuq7lrqowFG7Pft6S/dACD8FzxuRkNWw35nWY\nCmPgGZgvci/fgLVQV4kj0RiFqTAruwCfparFJMKXVW5QixwVOShSMnOuDNobtnVdd/369f36PZjn\nxPc8XeXOVNUITHCcoEE9wXEGyaXPONWXiQM/gJ29et1fXf2E56nr7hOZ47rat+8IGDlgQAOsAk9E\nYa/j2Hjvyj59Nha/mkI4Tj2shyRsh4FwKX8JB26SXw+pOCwbXDO5rsKkMoq+ZqShCi74DhyFNdBQ\nNBACcZFJpSaJx9OFC7U8t0w8fgrGWaHHZFKj0fGq6idlXcC3P8wcGATjOnmGe7dHdyN37cpBErgf\nhmQ/Z6g8GlV4CZ6Elwu9pTGYAuPhXoDNVmugX79Km9WpKsyARSKr4nHLIA25e7eJlHS5BiFyvEz2\nRQWXUaR7VGXn1W/I4k/z9G2EHoCH4U6IwBAYALabUeFRtuNoJDK08oCq76wQUUhbxm8TvbnUdQap\n573sPAU7hf8YADUwGsZBGZHJoomhVtKnKNJphYmwA/ZybpxvXZzW4q8CkYWl/DNFoyPQIrIsewG7\nrCvGIhwebD/DALulJ6NgJYzu/Bnu3dvhrt2S3Luu8Q4OPGQ/h8NqH5tkUmFtKqUiLrwYj+c3yRwB\nk+EW6M0z9slvV8aefc6NsSw/CeYE2aYS/RZY5Tcn6nCyYIX9HEaM2A3LRd49l9f/gXuv5bJJUAtJ\nOAYnoBkqIV2RnbBV5MnKUyGLhnyzyo41cE/RAENu0mej66o6zkZYBinYAVthDSyGKbAvy9x70+W+\nSZGtdqDNpYENsAmSIidVFeYRvp+7YCBmdvFXgTEHCg0FY2ry5MOyl90CT6RSakxjXhsm/2UQjc4Z\nHzsegZ7EYT0Mg+dK3kDnQNcligpxltw7EWCmL6EXDh8KlDU9aSkYHoPXjclZbteKjIfHoCeLPkM8\nW5XadjNSkQV5ZmA6rSK7rRygyDZjNuUJCBfMsBLW525p87TFAe+UOlZkly3u/wDLzuc3t/KV+bAG\nDsDbcBx2W0KvuHjU89RxTsMhEbc8uTc3Nw8fPjx7hYvKjPRnFlkD830J+Nw35Z4iZVDGrIY0pCAF\nW2ElLLRGfWmIbIRZsAtyZIfTaYVVfGAJt8NdMAiuKSU8l0++pYV/DxhzCEYXdA7o73+OxVK9MRHo\nSQJqk8lMRm9nRtdd4leIbkjuXXq1BaNsTiQsD5D7s0G/p8hSkYzE9gyRuVADN9Ab1tzIlaPgmT59\nvtSnZF1ids6aUg5ckdOwPJ1WqIWdpXp6iBQ5Pp1WX1CwcniewglYFdxoO+H16rXxI4x5hk+uhV1w\nEE7AYdgFKqKue4Pkt+urBI6j0Nyvn1Oh5d63b9Rx8mXNyyDbg3u1yCl/Y9txhXR6g8hGsFlN4woo\n3nUV1sFOm5JjAyfBASIKq+xrkp/BL+Eu+ClmfBETHq717fcyzjc4ACthvDFbgtttbapFMqmX8olL\n+Ti8oapwXzTakdDLWfwBcZbcOxdgrdXCjkbVj1nFYhoOa3AdLbJCpG6+GTQD5sPVXKaq4H2PgVPh\nDXgc/k1KGiYwta2appOaMQM9mAcrYAmMsZa+6x4uo0XVMeMdWkSS2dBl0rdwt4isg4Nw0prnBaZv\nx8ReYCq0tMvnLvJ8u1LpNbB+ct1DEIFNIm0rGIgcWOqqun6gJ3AAACAASURBVO5YiPHh83gYRsJO\n2O83Y8o9S8bith55Y1pLE2SYcCfcBU4p+/0BLSsgI7LZL5gLNmAKh5fkjbyMnjDcpj9CdScvX+rS\nLFEhuiG5a1decMFcuBWetPyuqtFoTSyWUs2PpF0qNRCP8vcP82mRtaoK6ZskMRamwXh4Eu4r5nGt\nROZXVaHJmP3BlGeRrbAKNsBSkWPGnCxt+1d4u/74etifJ3d+U69eSdgFJ9qarr2SL56njtMA+/r1\ni1ZS0RrE6dOnKzxEZEuBYP0SaBTZ0ZYi/GrXVRgPu2H/R1gFu+/gP2vNg6UPudOY3f6PFSwqTms6\nozV2O3yjyPMOo4pGVkTGw2yRPbApmzI/1lJ2NLoFfpszOpnszc0wGdZHo5mijc6Ms+TeVdF13e6x\n2LvR6BQYBnfZ5BO4zu6CSDyeEwX7EEPhdV+zF+rtQzgWpkINPA3v5FexNokUV3DNA+yEMcGenMbs\nsZ3tNOMfqLexQJGlInme97YFbbIjT8MOmGpFw60ZvaBfv6EQgVSl0dFTbY4JwnU9kaGQDoV+VqHl\nXliv3ybFQ37epHWnZD+vhIXBt6NIGl4FD/bDtpw3Wjo9FabDepETJbNrZoms0cx6K8cMNxMNA+HH\n8FXkN/lvSpHVxuRn5oAL67IGe2YdEI+fzGpjrM4/fTIJb/yEf/wgS2B652/QcZbcuyq6rghBMqnh\n8BPh8JvwuE0gCQam4Mbg4BEQ5iZ4U2R+KqVByfcYTIMpEAPfoSMy0ph2OMThLZ9iYFZRVskmbKyx\nORsiO41RkVT5ulbPU5Gj/oTWA66q9c6gJbAb6gvqPMtAZHnbg3IB82BXJDKoYnJfVbixvBVfuN6A\nVcFXlchcGA9bYQccgL3glfnedhkzHaZBbcHUIiPte0JkDNxftA03/WAA3ICZ0noO21DXmFZNAmPS\nsEKkVSkh2P4Q7ksmNRxuFajIbh95Od8dxJdte/Ggmk3nxFly76roum4ZVbUL3mQykx0YDs/yd4nM\naTXeUym/HYcxB+G5HD30Y8fqRCbCNBjV2rKjuEZg6StZYPOwoaInIZ224pTvwgZ4CzbBBCvMG3RE\nFPK26yrsngVNFVvrQVQochA8ncgBOPjFL94WiVSkV1zeM1Sho8aWEYik4TAcgH2w3xgV2V55y/K1\nIrOgxuZNZi1/+FHgUseVEunlvzL8zhX+P4k92Q9DjakXeatVaNo/KuC0gV8XdncJh2efz8NPw418\nE7bkCSKdxZlC9yR37cr8Dk/ClZpxhj6Yl1LmR89qjbkHDge8LrAIngu6YepEJsNUGA0/pXd7r0Sk\nGRrzkh0rhzEqctgYhUbYDvUwCxYWGtrn8XpvXn4Q1jrOpdK2AH0eSlcClUSfPg2w4+KLL6v8FG0N\ncH2Kd12FMfC046jIEdgKx+BtaIEjpfp6G3MSVlV0I+n0GzALRsKtkCdnployOqqqfBsGwI1wBfz9\n1wOHxGBLCdGh1nSpcHhUMANSVaPRFEybCc/Bh1kIc2BUBfdwFv/j6Lbk3nU9M/CYZXBYAMPzarhF\nBsfjx1X1RZGRsCewjAdPZD2MFVm+bl2m/85bxoyFGfAmNFSoAdZ6rqRIo8iwjt1IOq2u66mqyBDH\nmaEZ98syWAYNkIa9sAo2wnpoENlmWU+k7YzyPLTL1vc87dNnPRwYMODnlbhlykxuUx5dV0X2wFqw\nVvlR2Gvjw8HpRZrLTGXDG66rMN+YivIIfWWFvBwaaBHJN8Bb934Xrocb4L8xDz5upe2NUWO2irxQ\n7MJ8DeHXwuHBwQxIuB9mP8C/LINfEobt8HI0eqhwkk6F7q0X5qPbkntXjqmetskG4fAJmBKN5i/V\noUZVj8fjCdiZQ+5vZWudJsDoJ5/M8PtA+sRhOtTAYxWrCVlPuuvaxMd2s232kh61afuFeJmP/obL\nX+Q/HnaOixyBXbANUrAKdsJ22ASLHEdFtjmOOs7JMjxcphGg9QuJqMhez1PYCIthCTTBVXAJREQW\n2i56Ik2Oc8rytd/R23EycvOOo7AYWmAbnIQT8DYchkP2cHtUr14LRowoou7rOKdLqf7mLT5ct6Ka\nKVUdyLk/hAjUBCjeVkWILCqpBf+q4dPn0suBN+k5x98O9+eNTKVag8lZmyOyKLawJhrtzc0wcwof\nWwCq+kHugi3weCWXfWbxXnC4azcm965ruasqPBaNTg2Hd0AdPBONJoN74/HTsHKeqXZhbsAZ7FtY\nmslcngjjVFVktaqOhBkwEZ6pjN+NUViTDdO1+xZcV2GOMUUcGinHSUILnMzOC01Bk9ZxTsIWS6b2\nPxHr22mB/bADUvAWDIe7IA1NsAw2QUrkmMgxmJ2N8Y6EepgGDbAMpsAiWAmr4W24Fq6CxZCCnbAT\nDsIh2AfH4RAcgYOwH3bDnmzP7ll5UYQ8WF2gwvIoz8sRoM89pEgKE1xfXgrf97pHYCzMgRjsiq/z\nveTGHCrhaRkNy/h/M/jXf+Y65FeSHb+6UJbAJjIZUxOLtajq+mj05/S8gK/BhBf560zGriq8BCPD\n4YJEmrM4Q+i25N51fe6a8cxcHw7XwdZodD28GA7nxEJF9D5I5DI1JPPmiccVZsFE+8SOhukwFV6G\nk6Vz3X3KgJUiJ7KTVyQflh280F9RBHMthoushH2wJfcFA0152ZNttgpyXYUR8DysgyWwLfAmOOU4\nCodEDjmOwlFo7tNnj3WSOI6KnIQmOBEKfUPkJrsxaK3nIfji8TyFesdRSIscaTPF3nXddevW+fMU\n/RoLZfRzv4qniu71+6v4OGbMHIhwLSwLHJ6TuBKPK0wReccYTb1zlCuyIdbv+yHW4blnnwY7UimF\nibXR6G/gAejJ7bBgerh/7sjlMKmT1y5pF2eGdqHbkrt25cVXODwFboVBviAXPB+N5hDJfTAaZudY\n7vlu1lRKjTkejytMgmmf58YYzIBpMBLeLcbvQaIJRtKMUZHjbV550WE3yKTjxmyAu2AaFDIobMnb\nViZGCotE3s0b0F6fu+Mo7HCc2yspOi3P4I6jsMG35Ys2rrL87jhatGdhm9k+IpsL8oveKfr9bDVm\nphkFh37JX/02+wYVma2qIgths5+97oP/hgHQH75nM6+WGzPX32vrXT/A2Gv48qvwJvTmZpiSd95w\n+EnYARPK30hnQNd12LYX3Zncu/SvCEPhyqABCy/4ZlE8fuIJGA1Tc8g9mTeJ7XGc/bwNJsLr1Xx0\nElTDDJgu0hJ41o05Gnzy89THRMoZmKoKdYUDDhqzGvZAmZZOsL6QqoK+IJuOWUx9oHVAu/gdlkCq\nEnKvvPzVde06qb7Ua0nkIchXY4aKrtt1FUYHpio5Mp1WaL6Ljz8L1fI9kUUwGtaKvCOSLHqgDBau\nh/5wBan97wZ9QfG4wuJXYBrcDRfwA6j1m7kH7uLZNvvodhK8R6KpepbcOy1gGFwFb/nZMsmkwovh\n8ARV7cllj8Jo0FTwkHW5+jPTRfLXLvG4wuyf8K8/52+tBuEymAnLRWpMQiRPzH1NHk+V4hQrRli4\nfWa/fnVQD6fN78rebKqQEGG+63oidZU0cdUKshWDcByFXf36XdvmSNjcrmmzR60UWeW6OR2x02mF\nFt9Lo+3pYmghssmYlqJfdRCw62Gz7DMMgcWwTeSwyCqRmWUEnPkmXAsD4Ar41IXW2FfVnoz5GLUL\noZrevRkYDreoajSaoywUjdoY/tJ23MmZw1ly7w7oum4ZVY1GN8GDMDkvFRJeg6E9ucz63D9Da9xY\n5EiQ3Pv0mVFqcljyRR6cDvXZVkGbYTWMgRk5S4EizTMLyaho1HTplCnVIjYrRVVFdonsyR/UeqKc\nJYLr2ghqfZudtXMnaVt63p8fZsDuAQPalh+AdqhOOk7+OkBkiMiT9i0b7JFtz1u42GoTMBHGlxmQ\nTivsgs2w7Ys88VRrCdvrMKbMgfEtca7J2O/85RePxeMRgBnnE7+F82CK78oPZkOqKiyssMytM+Cs\nz/0szjzgcRgSDhduj/Xk9qs5dzR8lcE+2xrTqhwZj+vNN5dkpVQqw9HDTd0YznmNv9kCSUjCOlgH\n4+Ep+XrRBhp5xibkZyWtW7du3bp16rrzrS55FmU8CVZFx/MUVgSrK/2+VJWgXZY7zIfd/fpdU4FE\nTH7rwdIX4Nm8/kIYc8KYZdA/t/f02nvvrXRyH9Y5ZszBYmc5CotgK3g2njJaZDg8DLbfC7xafnIz\nxvADvnoBL8BYeIiesLUnr8CcbFKMqmoslrLd9VQVpsBzMLm9N3JG8N4x2/UsuXdywAO+1FTu9lHn\nEnX4nKYUGiynG6NQnx3wSvmZUymVrCawSBpqv8FD/8FtdXx4Mb1ScA1/Dwfv4BuFrOk3ezNmXnD7\nqVOnMoaw686BVQU5l6VMTiuV1THxXh/33ntqxYpKBzvOcTjUr9+QNn3ulb8zrHxuGaTTCodsgVIw\nIBx01LR1ilaFL5vhqqrGHINF0GglZdLpnEXMUBgOgeBqkV5LrUilfvk+aqAWVsEvOQd2wOq85aPf\nXS8aXQExmF5+MdF50KVdte1FNyf3rv6ijkYbYV1eelk0uvbO6KaePAnPL4mnNVvcKLLJ6iMas0ak\nbQeofStYueDslrmwCpZ/gsf+ne/D/qf5ylpYCi5szymYaixZZZNOz4PlxbLpjdmd54b2PIWZQe3J\ngou8us0bCQxuI4Ey97zpfv3uL0/u0LZT3qJCCQQ4qJl1Q8UvotZjc2IPIutgmu3WV9AjaZe/hnvZ\nPPI4DG11zpT0dMVEXoWZsBRWwY18tDcPFv1KY7GUlaGG12ASLOv8GZAWXZ0Q2oVuTu5d3b8Wi70D\nU/IcmrGYzo3tv4xeIW6El60+uzEq0izSoqrGVHrXsKQwH1Jkq0gDzIWmf+LuS7hyMR+07d8WwBqR\nR/iQSJOfsp1neC6A9aXrpEQyngHXVV+1pkwSfSlHR4nbqbSCxnEUUiJ3lXfL5Mlwlh1ZkTKlfY3B\nEtfN/D8Ppax4keZsQVk9zIRm2AZrinquINMiNZVSkcFTjfE15lQVXswb/248/pCNq8NqiPHxf+Jf\nIJERh7jwW3njk0mNxRqj0RZ4GSbYKqcuga5OCO1CNyf3bgC4P896gkj/8I394TI+aMxeGBuPq8hx\nmG8jk8a01c6tdao3i7p9snt3iGyFFbAY3Gu5ZCq9JsAaqIXn4Sd8cc2UnJTnGKyFo2VTQGB1niPb\n2rOlIJKvNl565kqDnyJvws5I5EflLfdKUvstKvEpua5CizGt4Qdbx1tI8XlhXmNszW0KdsGu/ET1\nAmPc7+cnkomIRGAA3JfREN0QDLzHRMbBIlgDK+FFicB4WMkHH4JxkOQ6iOQQRSyWgh/DCzAdXstr\n9XcWnQRnyb2zIxodbzWy/S3wU82KRmW3jIZnYQ4kjak0acRa/apaVP5bVa3GumbcuDNgA6zpycRP\n8NCzfPh+PjAOZgUkhefAhrL57KoKt8PsPDor45ZRVZFkhXdUnmFd1/M8dZwJIkPgVmju2/faXr2M\n46jjTHDdfCFiKwpWCUSOVZIOb8wpOFQYWHZdhXkFGzffc88BWARJaLZx1FJ1BlZGNPBnSzyuMDa4\n8XfwHNguXLaZxmiRkVmhhpWg8fh53Aoz7A9oq1L5yGiuhR/C5cFa6AjcB6OSSYXteR75Tov3lMNd\n3wvk3qUTIi3gUXjad2vCo6p6dYDcVRUSMAY8KBsxy0JkqjHB3s1FaCMvQ9GY4/fccxQWQj1sgtU9\neeFSfngN574Bk+EVOFKa2UUaYV1W2CBnIV+e3FVVpKLmpZ6nIkMsg0NEZAjc6zhLRV51nDm+EJjn\nqUgS9kciN/XrN1gDlUrZ4tUkHBRR2ChyUKQNjcbKQ8FwpHTl7WjNvEcXQiMsgwNW4KzNaY2pCXa1\nhd1FM50eyyrH9efDT8NYWAZrIC2iqsa8A2uCRj2Mjk06Fn0zyg/herjSNyb6294A0WjSj+F3fryn\nHO76XiD3bvC6hnvhWV9vz5L7CLg117WdSinMhqcqmzNHdDseL9o5qJXxjXm7V69pp06dyh2wFuph\nA8y8gCsv5Ou30PsGGFmkVVBjgbWeDnxug9zzNMQLJn/KdRVmijwNIysxomEq7Ovf/6dl3DLQ2m8o\nq1pzUqRJJEenU+Ro2+drnbOIi0kkDSvBg31wGHb535X9IivRJQ6u2EotxdYZ8whUw5swB9ZCi8iL\ncq3ILFgAywsCs63fAFfB9dCPZJPCNGutw9xgimQnRzew89qF7k/u3SCEEo3Og1XwXDg8TVXhyYfD\n/z0SXiySazgbJreZzhyPp+PxfFPdGBXJ8VkHpQpFShZqXsWf9+W+3kyFlM2V781jMKU3t9a7M6+V\nOwqr1VXVmIXGLNCMrVpcCNfH6dN61VU5TgbPU5GDhaWtFdr4jqPQFIkMLUvuJW1Sx1HYCLUiO2BL\nJWdUVXjYttEw5oiNJ8Me2G8zbfw1j9+QNq/E6dSpU3kv14L5X9ZMylNxcr8LXoA5sBrWwhT57ue4\nCZbCcngor0Ov5v4DiL4a5R/g4wIz+dBTqhoOT22zVvYsziC6P7lr1+f3ZFKhDsbBq9HoFnjE4cOv\nwQsF5C5yOJWyGgOTRFaUooJSyc6plOau7ptUtaWlXHK0df33h34y6GpxJsrVl3LHx5gH9bAN1sIK\nWJhNf8851nWbsydqOwIs4veySPpFT4Wo0EsOM6HJcX5RxiiuxNkCa0SOwJIygQbXVZHtMAU2QIvt\nymS1z0pPOw6Kz3jq1KkyefEwBSYX+T7j8YdhBiyH9TAffsFfwmx4yxgVeb5Q6TeZ1Lxge/iSB2Ea\nfzGI64jGo/zfkeFwfhPws+g8eE+Qe5fWdreAByGZTCq8Co8PIJSAkUUs9+XZbpwzYSJML+yILTK7\n8EkO7E372SnQkE6/U6b9wn1wL1zfGtfNWujGvMD5r9LnafrdS78v88wnmA9bwIM0zIfFEDfmkNUa\nC8oCF4XrWvf3oQra3bUxIHupG6A5EvlRqQEV6oXZ14xmKsiWwIs2qGCMwhuwHvbDIdtVRWR3m3dq\nITIYInB9qQFFTXhIi9TCMBE9HI9rPD4cXoC5sAhcWAur4EE+CXHYAAtV1ZgakScLZ4vF8tcuMJFz\n/4sryYRYP9HBFl1nBF3dwusAzpJ710Asdhy2xmK2ZeWLn+fKN+ClIj73N0Qy5rBIC0zv02ceTAv6\nUqHIkxyELUBduHAjJO3zXxSzRVbC7oB73TbI1gwX12r66FqR2bAJGqGG8z3ozy3/zm8/z0jYBTuh\nERrgoMgRkV3ptBqzK53W6uqkndN1VWS44+zSihMT2+R3z1ORFDT17/+zUmO+J/npK4UQScICkSao\ng0bYCe9ACzTnNkD0XedaprupD2N2itSqqsiy8iUL99xzz9q1mRq0J+Tnj8nP54j0ZPAnmL8etkET\n7IODcABmQpTLLuYeqP832XoHn3kUenFZqWUZTPRFBZJJhbm872W+ABfBd+GHRO8vqxHaydANYm/t\nxVly7zKAEeHwO5px3b4Y5W8WFOjOwLhgIootblJVmANjbG9Skbb9pCInRE5BqpS3odGYVVBbsHRw\nXYW5eZ037I4FWZbfAWlYDYP5u8f54Oe5FVpEjsLmPn0OwhrYAXugCfbAdlgFa0UaRRpE2raoYXoF\nN7gVDv5T3797vX//h3j/acfpx2d+xEdj9B7GJY/yz1/gl//BgG/IG45zAqaLrIYaeAt2wF44DG/D\nAXg7r1Gq/z0Yo8ac1kDSUTrdNrnn6SqLrC1ebJxOazy+w5iXYSEszX63O+E7/PYfePEA7M22j6qX\nr22Ef+EnkPZ/0KkiI+AbpdumwxZws58n87Eb+DL8I1wC532HDzxf/kY6G85a7t0T3eN3hYFWVCsW\nOwFPwdO/C19XMGZ0UHhLVW++2WY2qzEnYBqMNaZRS8A3AzWzDthfNLH6VZHZsLpYGWo6rbCsXKa7\nMbWQhEZohK1wA38HTdW2SXNTk+sqLPXXA8aoyLu2Ox3sgmbYAfuhGVpgCtwNB6EJdkE9pKERNsEa\nmAPbRfbDKpgBa6EOpsBGWAlNcD3cCquhPmvgHoWjcAhOwhHbYO/vmfEPTL2f6z9B3WN8526+/kv+\n7QtcXolaL0z0RWC0QEKg4LspuvHQ8bSq6oMwEt4gE9DYDDusoIzt4goHYTt8kjH9+Vmdec3KyBmz\nG0bDLr+plsXtErkKIpAq1rPFJrDT+1swnP8zjr/+Al+ELxG+5t/o9Qt4tqvoDbyX8Z4gd+0uizKY\nZx8qeOaz3BsO59jgqZTCsLwUi3HjFPaI7M/O8BLUwgyRHG2TIK1biCyAFVBXeBljYEsxjUeRRYHu\nekXkgnNgzHpIwQ3cBE1zOWctjAWHLze65QpNjcmk1hS6xe2WKqn7HI/czo03c++5LL+ZIf/A+E+y\nCvbA7ru57POMFHkHmvr2/U6/fqMKi5VyWn9kc1mOi+wAD/bDPtgFe2AlpEU2FrXeM9/JYNdNQ8R1\n96fT5b4Wkc1BcrdvyFdhUjYKuj2bLHkoS+V7YB9sBk2lNJXSeHyOMbAUJhuTNOYwLIDthewNkVRK\nNZWKwOBiPyXve9ZqG/C+yfT5Z8LElsQ0Q/qPhcP5TdvPohPivULu3cN4D4enQEMyqfBolL/5EMOC\n6o82TAqbCg1AkdP2CRdZphnJkZ0wyZhDIr9+9938rs2plM0E3wQ78qWj4vEaOFhwDtc9EiyzNEaL\n1tHkY9iwuT956Ou8ks56bLbCEhgDy0T2GzPP8qbrNhmzxRhVvYQ7S87mujWwFppt49Si9aCqmnEo\nN/ft+58l9rbhcN/iqmde3wRLYQYMh5fgFng893TwhP85nVaRUaUCqtPd49/lplHy3RdhOiyDjfAW\nNMFBOJy1zQ9kwxSHRG7jK5fkFqZmTzodxsMc2CqX7CjS8PqcC+V716SOp+58xPT+NBd8HPO4MU+b\nlKZSmqIv4WvCvO83sJ4/qeHCj/Kp/wxM/ijM6HJm+3utfMnivULu3cNyV1VYFIspRG6j7yP0hEcg\nY5hZ680YFSki1SKiebpajzxyqFevOTDdt4UDg5eoqsihrD5Bq3fmUZhSxNW+v6jcYBnhmtxhe1+S\n22dDPTTCLngDDsMBaIF9sD3rw1kHy2FJ1tH8EjwLL8NL8ChMgtdgKTxcLE80cLU26aipf//izTra\n9NrD7Tl/p9OaTt+UzQp9GFTV73+be+CeQWa1qloNhKUiY2EW1MJ22AHNcAAOZG9/P2yFd0Q2y9dG\n8Gl/nviKGs75phl6Z+p4ygwzZoShb1/5ygyRA5DkT2fxqZ/yz/D/2Tvz+Kaq9P+/UVSCClpcR1wR\nFcYRwdH76Czfn4zijIzODHYUBAUdFWZGzXEZR6GuLeq4FsUFUXGh5Eb2fd+3FujG0rI3Yd8KsrZs\nnt8fNwlpkpYKhbTNeb948WqTm5uTNPmc5z7nOZ+nNdwBd8If4U64E+6AW6F51L8/wd+gHdwG9V+A\nZZa1Gt4It+spKtIwpJIWadWKWvP1/1kkirjXjjVVHfiC+aHzNcin8BwurTV4LGuM273QtrVSu8sz\nR4QvQwG3HXat7vNpmA5jQ1EeDNOB6Ht18JbtzmO/hmExSjBHx3zGcJOs8oBJoWXGXK/+G8+uFekK\nxbAH9kMJHIQDcAAOwkHYDwehBDzwP9gBm4OC6Ic1sAIKYCHkg9MNajYMhYmQKZLO+U25H7afwwUd\n5Q9/oItb3npLunSRrjqs5qc8KjCqLFFqCuRAFvSHn4Izx0Gvd55SD8sHsL0XjRw7F2eo22En7A3G\n5s4i8lKYeQarXlW9P1b2Ytuv/Wqwoh08TKBZ0hPwJNwITV00voF638JKcPJGq/lVB9rBfXA3/AX+\nH7QI0/FWcCvyvFx2A0ktuPhKuBVJEc8Kj/vL97nkcciBPMsa7HwMwv5S34fvWa1BmMjdUDOA/vAx\nJD8MH8Mn7hFaa8taCH2CmZnY6gPfOFoXnYfRWosUwHzIhO8d5bdtLbI+7AB9M6nDg+ZTYacdqCuk\nvESzUjpoNbMl7OCoNVy/38nMbBUpFSmCdbAQ1sFEZ9Mn7IFS2B/8fz8cCM4BpVAKu2AfFAevBp6i\nBey4nF/2hoWwBAphDsyDH2AYDIIMWKvU+xDIpztj9fubc5Qd9/dz21D4AgaDDZNhGiyFq+kBm3fB\nXtgDu2EbbIMVML8+qZfzwK9pfgdJ90MH+Ad0g3/Ck/A0uIP//wv+DU/CXTfiehqyYKNta99G7dM+\ne/waWOXborXW6hWPb/curfUhrdvc/Wx0G8KpSj1WNpUU3Gk1Cwqhi9t9pLbH49EwqcYlZHRtScke\nAwkk7rXJWQK+hidb0DQZuuJyUiIwXGSujrLlCnvUFwsXLhSpKJr2+Zyk7QKYB5MjYthXcI2B9WW6\ndgwoz6owRERvoOADvwy7t4zjSgXD2+f1+pUqgI0wmUahssFuJL/IvRYfae+yvSJa63mwGIpgGWyC\ndcFFyBIogTewYMdVXHQfHApeDYQmg31QEqyecYox14IflsAymAN5MBmmwzDIEtFe7xQR7fWuUap3\ncCPoQlgDO2EH7II9cAtpsG4Z+ODR2+h5FY06ce7DNOwCTwVF3PnhSXgCuqKmKTVV+bVfTVRaa+qP\np1EPn0+L5MLaUEussm/skfk4WCi1VUR/8cWBV155JfzICUp1ht22rYPtnCyrRAeupSZAd7d7X9hp\np4d6qNYsjLjXfmpT3s2ypkCfK3jkCUiG5rSA5KIiDa/DcCiI1YLjFaUCBde2Xe4EIDLN+UGpEpFC\nyIVxoXRNXxgDLfksdJ7KlANqrceO1U2aBPbEOwbCobv8fh3yFnaIaNMaYpZSjqn5rEBSe5aIX2Rn\nzMlApHzrY++k63gYCh9o03aiyBaRxZALW2FLsMTSuRoIBf4Hg3OA88MBOASlsC1YO1kM6+BT2BxM\nKO2DPbAL1sNSyIYbSAPfOY+CG56Ep+BxpLf4tV+N97IQKwAAIABJREFUPcr7qNRqmA1LnF2+oRaJ\nUYf9WNYRaGrEBLBw4cJQRm6iUl3gL1wlssSy9jpeYEVFgY2pbndgId3tXuO0wLaso/i7VU9q0xf/\nZ5FA4l5r0u4OkNEY96uc9TAkQxL3gccJ4S1rRbij06pVq7TWtr0vyvMvRuVGeI7F59OQp9RBWAgL\n4Idb6NaWzlpr2GTbGsZGn6HCMe/0emPIbkRtvtba6430Lp+g1BuwPOhPK7IDllfetCscv99ZGFyX\nnByj0dIEb9hx+kgp5GJI5f/tEimCDbAV/GFFLM6mpq6wFjbB0LOxL+H+O2nxCI2egicZ1laa8igs\nnQ5d6l86bmTotVeU6fD7NUyDKY6bslLOxFxuqzyldoX6W2mtoV+sKnZ96NAh27Z7Jj97EW/BxHBD\ndujpiDt8pQPZmHHQpwa5P0ZQmy7ZfxZG3Gsqbvcu6NOQ1z+i4XOQallQFOqgBhNhVPPmR+wYwx3B\nQoho6Bx+S9QEcERiz2Tkb+gFhbAUJsOIynRqLft0cyAnOo0TEbkHBxysHff7x4m8Asnwgjws8qnI\nt8ETxmgyF3aG2Nu1/H4Ng2CrUi9EPaTcIki/X4vsibjxLVV0XrNbX72Q564ntQlN/0azLjRyw4vw\nHGqO8m45Uo3j9WpY2Y9f/FB2RRqGRpzWtrVIZjC1syrijxLt6Fn2gVoHJuYNMf04Hdq08cBkWKGL\njiTWIdlZjfd4DoHHcR2wrLmVb3FVDTHinhDUMn2H2fD9uaQOgQ/B5/FAmmWl6oBb4UoYCZ/Pnn1I\nB6vgY50kOeQuIvJe1L1HdORdGAdF9mYdSOysgDwYqdR+XQmcZVGttYgWKVNOV565LiQ/I20d48nW\nJEFyxBTl92uRGJNW8OE/lH/XeFgfHblXGBSX+dW7wuv1e+U94Sl4AVLgJeQ74Tn8Orb4er0a1mq/\n/hQGQvi1ichYv995V0fBWlhr2xo88GrMJQ14t5zX9a1IvshWJ+0mMiTm3x0GweqWqGR47JJLdCAb\n42T2crTWljUYujr1/h6Prrlhe0lJicm5JwS1TNx1QN/7N+VfI+B/AP+BNyyrq2XtDe5aWg6TlNpM\nMFEejeNB6PPFkLaQ66H2+TrD88GQUyQ1WDyigzv7l8IspQ5qrWN+m8JP7vX6w/2qyivv+R88B2nw\nV+6OWbyvdYxoOuyucpM20B+KH330yQoGGY7frzk3XY1UapSiMyh4CVLgBeQb4c93c9MruEbB1PKe\nUQfMIQJR5Huc3ZuGX6mxtq1hubPbNHzxALrDi+W/tIkx43fIj4j0lSqzlcy2NSxyDngGkmG8233n\nnW9D8syZy93u3Za1T2sNnzu1MUVF2rJqkkFYBAkbtutEE/fat7Ti8TgFjt/dy1+HQhouy/ra4/FB\nSqhAZcwYp8RteMz0awgRDR9G3Ag5Tug3Vqnwreoin4cfppQP0ps0mQnLoAhWQh6MD0WdMa0o4b/B\nH2IsftqwAmZx0Y0Mq9joMbxeMwKlYhR9aq1hKKyKiNy93h/LtUh8GJ4MRugvwvN493qdCN3v12VF\nOUa3aK9XQ2+YLnLY69UiTj/qnVDsYoFTEho+r8Qsg4kgeqhK7YsuJFVqS/D4SZB3ZLbWeopSydCC\npvB+cPBT7rwz3bLGwIzgLUd3YavOJGaFu0NiiXutBDZCX8j4DQ//AA9Yz2ut3e5xsDL8MJFRMEJk\nSXn5GZ9Pw5gITRHZ7ASb34uMC/rYQowvTMeOZXI4fr8W2Q4+WAWLYI6zMBlOSBaj24TOAh/04u6p\nwUxOBVSggzCtnNuHOm32wneohjt8OXh9XrrBi9AdngV3jO9LLLOHwlBhksgMmAE5sAU2wjqRwLro\nHn+wy3lwDoRv4Qco91qk7EtILvvrSpgMy6MO+yxoJlEUMbt/ZFnJ0NUKTBLBnjBfwryXXx6rtYaB\nNaX5dXkYcTfUYB55ZDGs8Xg0DH2E//cm9Z3b3W4NR1r22LYOpnEnhTvShHBaODl7SkMTgMgSmKK1\nTodxR5pylPuFETkUtfoXSI9APiyDNbAMsmCQ369FsmBauNnZFJFpUARd6B5+nvDXEk15OyedwUfg\n92sYE10tA4OPHKP9dIUX4OmG3N65/OcNiKnXu9tZVBBZBAMhE1bCHtgcui5R6qeImaAH/A++O/LG\njhIpv5FKWULLD46vvg5YBpVp4mHbGpbCupg9vh91ppagfsMUmAKZTrQOn599duyNx4YagRH3GozH\n48nPz9cBHR+otaPdn8xzd9eBjM1K8G3apLXW8G5IdpXSMDUihA/P4YoE5FJknYjWPt+woOuASIy0\nQ9nzlAkqY5ZL+v2BsD3YUmIlrIBc8N5B+7/TpREZ0amYCvQ9+rIg+ErLNM3w+zUsENkIAyG/efM/\nt2kzyXms3x9oIasyFE8EMjDywV2QFXP8SmmRBcGNTZtgY3ADbKmTVIHPITl8ORSGRGfGhop44Bs4\nizla65jzbkyUGgFvwpow04gpIRFXahnMhBXlLQNYVmonSIb0YFcAyIYZljUJPoMXnFR76DNWE0nY\npVSHhBP32rHAEv19g2kez8EF7lTwnsOrwRsXu90aNmitRQZHqLnIGpip1J7gr5+E3+vzadgusgx8\na5QaHXQdEMmpoEtf2HgW+P0ahlfm5UC+yMYzmXcVX0IOFMPWYCn5j5AHmSKbRPaH+tjFOkmZID0Y\nR2sIOEuGm8a46AXjLmtw2ZUN3NqvlSqGIdR7n1uv4letsLrwtz9Q73OlNOTCYpENsAL2wmYoDTrI\n/+icMHpIXq8f/uv36/B1bFgac9mjO7+w4XvQWtt2uXVN0YiU+RjAWJFFSv0Ei2B90PQtconYtn3O\njclhkbtl7XKmAfgenoMyNUiemmg7kNg5GZ2A4l7TC2b27YvsiRoCvtdaP4nViC/usEbpQEQ/T2sN\n60XylIr0eHGMJGGuyMro1VSttchW2PCp4wTp82mtYUAlh6qUhjkVr+IGRz7J69W7vRNHQQbnR9wb\n7GqknYS100ADdkAxFEMPGAoboBj84IPCoE3AXFgL82E85AQvDhZBLuyGTWDBENjg9FQKbindGdxh\nWgq7G1Aosi+0aTZohlO+7XCgzjLgg+8UOAZvXxoxDYTK0qeJDILPAztvj9LkyKlrsu0f4Yuyz7sY\nlkeUHkWl5pNDafRkaE3jc/kM8pwLFOgM75a3N63GRfEmcjfUDPLz8+fMmVPBAW73Frd7y2K3+0uS\nIAMGFBXp0LKqZZXJKUcgsgJmiyyM1dihoDMPjg3GlW3alNtVNeqB7+gw/arwyEVNeLkfTIWe0veo\nhSKwLNaNebAKpjgxu9+vL2Hgv3nsz3z5Vz6/j8+FYe3obTHwZr6DTFh3yqlXctGvuLk7993N3/64\nFgbBg5xbDEtIWgX58C38iTazvTleb0CYlRpRgZ2Os15admBfijjrkyvL3r42/DzzRQbCLJE7yilO\nd7BtrdSs4Bl6+HxOr6UJsNq5RIsaT2C9NKLUdbinsCl3wlRYBJOcSnboClMrXkQ9cOBARXdXJ2rH\nZfoxk4jiXhOD90p+o6Dv7dYAN653uew3/BuGwbjQDhT4RORg+Y99X6kfYTYMU+qIk5dI4Uv8/iMa\nw+4mTWZXcsBKjRB5P+zkOyqsaVnbkrTJsFpEBwoHY+xZLfuQI/uelNKQ7+TcnSsVrfVKkSXgg2JI\n5tVw0f1CZcMkyOfMJO5HBoi0GR+Rsu8qyW3lGb/X6+QukkFo/Kl6v5N8VJ6yiyyGH8vZc/SNDlsz\nKM8P5yv4ArrS0ul2G4FSGhaFdF+pQhgJK6HY59NK7Y1+h32+wLorJNt2mRnDskbC/CZ83s1KhTla\na7d7JXxvWRU1AgxRIxI1JnI3VGtefvnln3U8fCe0fAne5dI/0Qm+DRmwWNYUJ44up49EIDvs8+mg\nK+RMn0+DR3inL2itldoBlbowhxjGAErpmLOLUro5w6ZHbspfVHEID0udftzhN5Z6x7zMdYthq9MJ\nT0RrDWMiH3v+X2EdDepLO+eA6N1bzx75xev1wApYCl5cs2MJ81Gd6yENimBsdGh/BJ/vY3gLV0Rm\nRqlD8E5I1m1bw2RYF9qFoAPXB5EVpcGJKfLVWdZ6yG3LBV35BQwrKtJu9yQYaFmxG0WVx8svv1xt\nA/kED9t1Yop7TYzcfxbgvYb7v4JBoKzukA9DPR7t8QSUQKkfo3e7QGrUiutGyIVRsPCf3Ky1hs91\noJYmt+J1P6fyJBqlNCyMCG9h9AXMjl6X9Ho1rChvB5PICigIf9BAmA9boCdtN4Rprd+vlTpSK+md\n7eXKy2Bxgwsaaa293q2ULbuM2a/jfAZOgwJYAj+ETN4DI6nMnqMJsOyo9sjvwxdwIYGts0qtVWq+\nU8hk2042fxVsdZ6ubFVSpM9PMDVf5u/kdOCzLN//cXUytOIvkA/d4Ptj9hjIy4vdHCa+1Pqv+VFJ\nRHGv/hdreXl5x3nZC7bQ8mv4EhZ58mAojLGsEZYV8CSxbR/0VupIm+zwVEzU2fIgC7JCxmQ6GKvG\nXC9ValvF0q+UDs0ufVSvNjyUVP7G/XJcywN1OCLrtNaHvN634W0YIPJfgEeijg/oILdBK/i1wHTH\n3zy6jFIk8q2A+SFd3qHUcBgNY0Qqs6Jg24EettHml9H0hC+hszwDjt3noz5fqFY98n0oa+FQxmxd\nqRERMbvbvQnGWdZPRUX6UuRJaMu5MB6mQt/jd4+pnhKfyCSiuGdnZx/9oDhx4MCBqrrOhW9ac9nH\nMMmyYL5lzbesxaGGqw6hqjgdyzUs7FSru/CnlnSCYbAS5ogUOfItoh2Xq7LHfxLzPNGcydLeIv/H\ni1BQ8ZEieWFuNmXyDELjQFVfmeMj2kUN1Vqr4Yqn4YkkzvoWVj/66FNaa6VKyz7ww9DaafCW9dER\n9xgYD/3kqQrGrNSPsCysWqbwqJF7GvyNy5O4H9JhBawPxenRHJmx+D7ksWPbgTSUz6dDYTsMh0Wh\ngOFd6AYtuANyYURV+YIdOHDASHz1IRHFXVfXS7aq/WK43Vvgy7ac0w2es95x9lK63XtgcniHHa01\nPCEyQCS1XGcVJv2Bbu8D/NO5RaQk2J9urMgm+Co8F++sH1aGfiq1C8DA8BYT5eEYnEUM8rDX+w94\njQtTVZmFBK9Xh9tVegeX0hEUKPylGkZDjlL/8Xq9Ikdqb0QWiJSZ+8Pt0cMOK+kkiwfDeJgfOwV/\nAPzhoiwyD2bHXCl1sO2fRMa6GAZbYAesPmrBe9jEvNkpkIcZtv1TcAyZQT+4ReGv4r8wBu7hUpgK\n4x3rx6rFSHx1wIh7teAEfRksa56Lr1twWxcahgI3eMyyCmBQWe9ADRMhdnrb59NJ9EmGxkQKmc/n\nlFcvg7nwCTzlSHAlRxhY75N3YRk8rdRRqnFElodnJxYpNReWgPb7ldIi28sefETu1WDFY8inorVe\n5Z3VjP/CvA5t2qhHP2zMG6HDQq6NwV8jI22niVXorcsVGQvzIvP7MbJVIkUiB6It5m1bgw1FsBX2\n3C5bHudPL3CZUz1ZMWGR+3JYGDEZQBqMdPIwIQrd7iHwGlfCKJhXyV1mx0B8F1rNaqpOWHGvPpmZ\nKszDxMSyZsK3jXlIuNNxBLSsVOfbbllFMDCkCJs2aXgIPlDqcPR5YMWz8HcuLu+JlNIieyEHVsNc\nkTyljhKM+/36Ln7zMWj/T07k7vRTLW/fE0wOPRCS+8jts6EgLBsT0dFbaw2Bjkfn38O/rqQ/LIK1\n8Bq3w8rrqTcTtkIhDIW3uWxgUKaV0lDGdF5r7Wx2jUiteGE8fAavqzUVLJnCCNvWtu237Z1K7XDO\nD7the8Tr7Qb34SrvKqrsOV/0+TR4RYqj7poDKyIWbjZ4PMNgGpzH2zAHJp4Eo/YBAyq7660KqX3+\nr8dAgop7dVhTzcvL27+/Um0ujpO+7sHgTeJpF8OdWrdQ2YzHo2FGmzaB7ZRKjXBKLES+su0ybxEs\nfZNrvuPoHxiR2batIR+Wgh8WK7U/pl6LDHVz3deg/To85+73a5HSiC6A0K+Mbvr9PSAXPKpMKaRt\na5EdYU8xswvXPnAtLe9lL6wgaSsslQ4wGFa34tTTeULbdiF8wa83gh9mQFtcHcoGziL55S2HbvNr\nxS+/gQ3lV8wotQ3miGyBtbAF1sCC8lI0ztXMUa9+4EPI9vk0fB1W/F4ishfWwuNud9l8S1GRDRmc\nDSNgIYyxrMgdyyeI/fv3n+RETXX4gsedBBV3He8/f0pKysl8ule5FL6CDx0NdbtHlG2bOReyYLTI\nO7Yd2MMSkV0RWXoN/QZXQtwjdFwpLeIPGmwtdpRXqXyfT0N/NxcOAu0/DKuiT6WUhs1OHiZi2bO7\ns4Jq20rp6MfCIpHZHWT0u1w0qR48AI+wBO6VKcEDxkI2NAk+kV/kx/1KfcfFryLJ8GqYE28FlY6w\nDCZdxBPp8GbYm+MkZ2AprIbNsAuKYCOMhqcrTqY74t5WYj+lUiOU0iL9RX4IjmGGDuTH5jh7u5y2\nShEP/ALu43EYDvkwNaYh2gll//79ubm5Rz/uuDE5GYfEFfd4ZWZOsqw7jLCsN7nmPL6D4U7v7Ogv\nv8hKmAV2uPQ4Eq/UCJFlsHhw0GGmApSKTP462LazDJsHa2AjbIb1sAAmwDewosItrP0iMh6DypbH\niETmx9vy1xmwCu6/Hh7Br/dofaS9HwyEBdAs+Ou04A9D/X79sDzcjaSp8BHnv68iMx46kBfqFRqP\nyJQW/AXGwxQohlIRZ0hbbVvDc/CvUE78qCG5I+4vqUirCae0Cf4THGqy1tq2SyEPZoWvBBQVabe7\njPNXOsAnsALGQ3Z82+ad6ESNEXeHxBX3kx+5n5ywpTyeh0dp5USsTZrMbdLk6ZgWIiKrYU6E9aNI\nKrwEywbBl0cL3pUqqlj/fT4nql0LQ3/Dc7fy2d2yEjJhjWOQAvkiPqWcLfVbtdbg0YFAfhss7yGv\nD4TXyo7E79cih0WWKrX3Il4fDlkAY7gH7oOkD7TWb0iP5So1X3X/mJugqAWnLLTt4WqIDtiBFYYm\nGOjbngdGwYskhZ0/G7zgC6buf4QfYQ/8CKtglyvYt8jZ9+/U9ig1wumlF3ozK34Dc5T6BLRvd/D9\n3CMy2rGRCSdYAr9YJLJWEtqHfp7hyVa4mtADsmEQzK4ODVH3799/4nKSRtwdjLifDOIr6w57srJm\nwkJowxNQCOlJtI4+TKnl0F8pDbPBGy4osCCJ93rCArsi7zDb3hxtP1keH8EQ+DutRXY425F0cNdS\nMPjdCNthI2yAAsiHdQ0Zcw2fwzTIF+mvtVZqv9+vldqhVAkM/hN/GsY5P6jRfr/m1ktpYfk36fu4\n4yX++Aa3evg/4WkY9QvO+yud2/P3R/ldQ76CxU67EhgHmVDo9E6CDbARSmC/yMGYW7faigpY0ASv\ndSIOgCXBVxejb0Y4+Up9DR/Iv+E7+MC2YzSPFdkP22FL9Kqv2z0xFLbD29Abxjenj8XfYfbPNRg4\noZygRI0Rdwcj7iecuFQLlEehZeUG9H0c9H/PHWO3EXzg/GDbGrJhjhMYimxpyvPBrpvJIpF2BSFi\n9m6OwHnsf+B78NuOK+86WK2UFinT01nkiFG7o/sWfa5jXFD9/yeyGrbDdtgEu2EbFMNmKIYNsB02\nww7YBdtgB+yDhTAffgsZsA52wo4kJrnIc0x6YQzMhk8b81HTYCYkJkqNcAS9La5kmG3H9PwqCgXX\nSu2u8GxLh6uXeoDQONa9+6EIVsNsHch0bY04BjpqrS0rH4Y5bpGf0eIJbochMKmCp44XAwYMSHDj\n9RNE4or7SaA6BOwxKNJeGsEomAYTkqKsyT0eLTI1/BaRbTAT+sLyFtweSnaHdhU5vvAhKiPuSo2w\nbX9gZ6nPZ9taJGBE7vM5a7D94QOltEhBmUjZ7x8QbG0RAXSBzm05X/hd6FkaN7i+qet24U8uuoEb\nusBDSbwAKxrQsCU05beQ3FWSncHcLt2d0Nu2/X5/jO2vzl3Oaw+9UqWyOtAoBcaXYysWEvfoGdG2\nne7VGc409gI8EvmMe5ydwM5jlSoMpu8nRpzKsr6HPjAUbChsxJwZcB+/gx/c7lJdjcnNzS0trYIR\nmrA9REKL+4krhq3mkciOIn0TL5zLIBgCU2GsstqFHwCPxXygyDbIdPF1VKNUn1JTQipfyU1MPp8e\noVRy0CneWemNxtlmKZIOT8MjqarfM5AM0RXl4Q2GQhNP67quZKA51G0bckmEF2HZKVzwO05JBhdt\nIbk1ScngVUdmO5FUF21DtYlOAr2c5eKf3lSZvWFo7FlngvMo533z+bTIFhgCn4vMVGpG+MHO06Wq\nHK21Y1oc3tVWBxswKTUv1BLEwbLehlkwGma5mNWDX02HZO6AETWlz3VpaelxhkSmwj1EQov7idin\nWs1lPRwYAjkw4lf0huku3i3yBBoiW1ZqRLmFg8+nYfht9IR8x3sg2m7MtjUMUUqLrD+ac2Rqqkgy\n+G1bax3TiFhHlZeMsAsd+XPR1lHw8H8vKa/QuC2uoJNi4OLA1RSaQwMhqQV123LhzTAbrmjKdY/D\nndwOb13FK0/D3TwkMkKpESJLREZdxsP/hq6VWEaer5QNMVzVtbOA8a6zGVVkh0hGee/MLHsp5MIE\nWB/TkkxkuMh0rbXTNVdr7fGsgWToCN/CKMsqsawfk6EHrvv5PcyoKcruUFpampKScswSbyL3EEbc\nq4yMjIwapOwOlrUIFj3PXV/TDKbCxF9xx0j3G0VFGrrGfAhkP09SMufrgI4vhayIFk4+n4YuPp9W\naiN8Bp8rtVCp+VGn6jpBqX9BasB1famORXR5iTMljIiSUZGPtNaPw9O4HK8VkSW30L4XXNriFm7s\nQfsk/n4VDzSl1b0wAn75W84fCP8gGaZewvO9cfVXR7bbKFV0Ac/1A0+F4u7zaej5X0keBl2ln1JO\nXekqWAqbRPY5FyVKzazAnU1kLcyALY1YNL783oSO1btt74Asy+rjTGlu92oYCOucSpgnIRmuo1v0\nJtWaQmlp6bFlaaqbs0gcSWhx1xW2JK08ubm51TS9XgksazEU3MuTM6EN3WF6El/dwj2X8HfLGhp9\nvMiaprgjLBht23GnWg2jRFbHzMw41YG27Q/YyUgqJA+3C511yH7qA8gux0B4csQtxbbdCb6Kimzh\nY611B+4ZDAPkL5Atol+XAd/RwAONeJmzv+DsPjR+DT6CkQ0452VYAh3o5qLns7gmwRdcbNsaHhP5\nAAZfyGfv43qdlpADK2E1rIEC8IkccBZ1ldp/Fh98CCNhQjDxUnZg83SspQhIh4mwBXYqpf+PF3tw\n16LyTYSVmgaPiaTCQOjt8fjcbr9lFcNSp5uS1ro7vMwFMBVyaqiyh1MlifjEJNHF/Tjn+YyMjLhs\nSqpaLGsezIOPXiepN00upC/MuYTXLqan2x25+dPn05DdlrOKYylx0INwCSyEGRV3x1ZqEfTrKgM+\nhecAvDABhsN8WAn5MEtkM/hF5jlrkkpp2HS7LH+P87+Hm+gOS0BBV6U09IcFd4nfC72g2B6hteNk\nsOhDGmfCTPiQKx6m6UX0hMG3wIdcBpNcfHUbDw+D3twQ7k4DA3bb9shyMukhRKZ0ly794GCsnIxS\nS51zwv+CNf7DYC1sgyP99rbZ9ncwDmJ75Gst8hH8G5KdTqcej4bBsB5yQ8n3T6zWf6QD5EX37qjR\n1Lhr4uqAEfdjF/fa9IFzuw/AEuhyl/Xyasv6kmtb0AfmXcu/zicNVlrW8tDBkNWYF5+Dogo2lQZy\n+ithDSwGT7izbgiReVrrSSKj4DpedCr8Yp2qvy5rbNAXRsHoGMH7t1rrf3HHPJgKL3G11lpkwwWM\nupIeS7ngGyyb8/5GF5jZjDPgVe3b/SDNpsIqmCV3aa1FiuEZSL6MB/vAUBruOsor7TZVqWeCiwdR\n934H2SKrYRuUOMF+NK/BcFhW9j7b9oXaboR5QPaFKbDZshx3oMBV4+tW8lX0Oo+RE2t+wB6Toy6W\nmpxMOIku7sdmQlBbF21gInzl8RRrrefBBBq1oC/MgSwYBtkwU2utVImL8cnQDfqUH9LCF6Gfg5uD\nlkIBFIqsCxbzfewc0AfO4/NQC+kIRMZEyqZtT4DxsCUou7a9xym5gdFK6VXqXZuzM+FrXL1wHbIn\n1ud/Wmv45j1lQ28YdmGDK56V27/DNRmKAEYrdTA4+D4j7MKncM2BB+gKM+GziIpPB2e/UkS5pG1r\nkeUwF4phOWSFNjGVR1/I4Jy/y/dKbRQZBt3Cm+QpNcLj8Xs8GobDjFC+xbK2BgfcDxbCsjnWvRU/\nUU2ngqDKiHs4iS7uP5faKushYDwMsqzPtNba45kOL/DHFnwAc2A0eN1uDXmwxEV6Y+Q1+KYcfff5\nNMTYwKWUFtkJm2A9OIY2ox6WkdfyeISdejgRPTS01nvtkb/j4QnwMVzKc07FpA4I6wJH6B+i/TRc\nn9CsAOZAkXppGMwXuZx/wcAbODUT9sEtvBY25j4wRamCVJGP4O3gq7NtvyPuYaH04yKfwTNKbYeR\nLj6GrbANfoQDzhKCbWuYCc+IfBcauW0f1lortc7n0yI/NEb+QdJIeIMLYm4NE/HAf2AjLIe8UPUL\nDBgV8OgfA0tG0GJQJZzdagElJSUxo3gj7uEkxEehSsjJyalNeZgKgGEw1e0OFLd8D/kwgEtb8M6F\njIRJbvd+GAB5kNYWl+30YYrlSSAS6X4VjVIHYI7IQciE5eCH+ZAnssK2j3R2VWq54zNj2xpGQ55j\nAzAapji/lHkJ38IMGKx9+i5ugrGTOS8P19Mkl8JK6ls8AVObc4bIN9q2fT4tMsrn00pNVmr6cLuw\nEzwILWha9uXMCOb9s2ERbIWDsB1238DU22WnY2AgslVkE2TBQsiAaZAMmTBDZIeIz8m8h64DDvgO\nfQX/LUeXLasY8i1rp9basoaHnGH+ZI3qyI2DTAWwAAAdR0lEQVQNGQZLuvLyAi7ISQxlD1FSUhKu\n5sbmN4LE+jTEpDKzfYLIegjLyocZMDN0+b/KshbDEnibP8B0mAOztNa2XdyapJdgILSjKQwQ8Sul\nnY4fSuU56fKKgb7BH2ZczdNu2sBI8MNGWAbFsAm2wWLIgwJYBgHD2yS6NSc1mccsHtFaiyyCvOBO\nzu1gw2fOke3lndtl8hb1+lPyL0iH6SJ3B70V90AqvA4fi2xtyoNJDIUsmAR+2BX8tw92OZOKSAG8\nuc+n3+CCBZBZjrAqtVupQxW//LnqpZeC9aDhD4Rs2B7qkOd2Z8EgrfV8t/tLeJw/QPbFzHmZB7Tb\nrauDH1g8yMnJcWS9+nTgqSYYcT/KZ6LW52EqAMbDWMsKJItXul+aA4WwEAbR6K88DgUwH/o25p5B\nMAYy1UtbgrmRYJ59udOdGVbBdJgPi8NKX0aLpML3MBlGwuiL+OBLeEK8TpI9qnPeMsfrxrY1FIEN\n3WE1bII1sAk2wRbYBuvCvIV9sDM4SWyHHTAPJsHvg4/dA3tg+4Vkw9oLyH2rbKs8mB7eGNa2f4L3\ntNafw3yYV1Fi6uuK3+R+6o1keDh4huDOso1QbFlroXtYEubrh/jLD9YdrekAQ2Htnby/0mpbyb9m\n7aZ///7JyZVt7pggGHEvt9Td5O90QN+nwFzLytdaN6Ltd7hyoADmwR30gBGQD5kw6H4efYdrok9i\n22UWV6Px+bRSG5Tao1QpzM+A8eVXBMIwkTFhJ98o8hl8+al6rzW/ak3z1vxSuF34Q1OeGW7ribbW\nWis1R6mVoaeDr2F8cvLjb6kJT/KrNK4ZA/NhIzxCh1CwH/EqlNoL3yq1EQYX2RNtWOSYA5SDyJSK\n20+LpLbl7Bbc4WIQzIOtsC7slXYL+/nzC/kmmU4wCVbeiOcxHqngzImGCdujMeIeA/NBCaeoSMMU\nGA9jLGsBdL6C1r1JyoUPuQGm9nEP01rD+zAflsF0x/wkHJE+th2j60U4SmVBKsxtS4P34UsYKhKz\nuNBZ0gz9H3Fvd7m9Kbf9npb/gRehD7wJvcAL/UErNUXkWVrWpdfNMBUKaPBv7toHRUEzX6W2lNcD\nD4aJTPgtTftBDiSh1tux5Rv+Af8VKbeRrG0Xu/gasmAj+MOLLS0r0AbL5/F0BngFxkMWbPkd6Y/T\n+V6rqOI3M6EwcVhMjLhrHabmxnWoPIqKNEyCCTAHMiD5LZKmw3PcC7M/oUkPXJfTugW/bEHnJDJg\nBayCmSFxjinEEYikOrtvRij1ULAkJTVGMfuz8C48LfJV9El8Pi2ybqfqOVlkS2B99sy3absX9sFu\nmMYFf+UJmPgbmAra54O3tW971LN8UfbXfiHH+R8gC57mVvgG0uGFcF+BUIdC+C56brJtZ713I2y5\niEzYMMtTxp+nqEi7aNvduj0Z/kPDh7gbhsLSRnjupRPkJ2p2PTZG2cvDiLvWwc+HCdgrxuNxulhM\ngrEwE3rrIn3Q7b6FlBa8nwdT4B8kNaVFMrTmmha0S8ILy2ANLFRKwxsV71nVWsMkpQKJsg9gAHwA\nT8NYEaXWQLbIkSsAkU0wuezDe0d70STxz6n24UB5is/3leoLfaHXK6+8EjomppOXSCo8KpIv0l8k\nQ2t9yLY9kAerorY1hfuXiaQqNQrGOr1EbFvDAtgApbC0MV8+wN/nw3NRyfqX3COExm54kiub8QTk\nQ2EjxsI4yLask9FRvQZhlL0CjLhrrXVubu7MmTPjPYqagdt9ACbBMBgDs6D/B+7ZLjIWQiHMBw+0\npenT8A18EQy6fb6Qy9haWKTUgQpUHqZBT+fnVDUF+i+BeTCknA6uSmmnBhEyYp42OscCn8LYcHEn\nWOoewufT8CgkO13r8kQmgNOYO9qzLPhEIx3DMhgL/WAcrITNMA7WwNdN+e1bsBBach+0h0fgfkh2\n0daZFN+BV7ihBW/BelgBkyALZkNRLTCKqVrMdXbFGHEPUCUOYomD270fZsBImAYLYdrdPD3D2X4K\nk+AdXH2gD3wcFZyKLIWFsBKWwjyRHbatldrl3KtUPkyFJ2AIQeP49erNebAIFsBXsUpTlJoPGbAK\n5kXoO7wcfTx8AN+Fi7sO6rtta6X88AE8obX22faz0BmExq1J6gT7Yk0gIqNgKsyEItgJP0KhSBmf\ny864ZsF8eKPsS3jIeqgtrkfBza0XMhA2XsOARnwC38JEWAVFMf4GiY2paj8qRtzLYDIzPwsYZVlL\noS8MhvEw9346ZcGYYH9PR+vHwnKR6aGWE76Sl1QmvCEyUMQP44NOYZtgNYyBuTDMth1jrHFHns+2\ns2AJTCvrwQv/VOqn0K8+n4b3oAuMFxkH6dHhPrwK3yr1fNgtj8I/4CHb9jnHO8bCoX+PcD08sdun\ntdYiC0X2QaZIUbBycW94uyWtNZTx1EyGWfANPBY28lTLSobGPJtEGmy+gILrGXLAM8OyMmAMzLes\nY/3b1GpMNqYy1NFaYwgjJyenVatW8R5FjUFkVVbWHlgJZ8JpUP9m5tzNe4+zCagHp8EpcBCAXbAV\n9sMeGMh157F0PE9s4OJ5vtcuvzxwQr+f9u0XZ2Yicn1m5g7QUAobRPaJ/F6n376EG1ux8CL8P3Hm\nRazK4Yp97PvMNxUgdJYjpxpi2+2uuOJLmAcNAdgBDeA82N28+bQxY+a2b5+m1EMPPHA5UKdO592+\nbwel90pPHwl713JHCc2bsGIxraERnA+nwFmwE2bBbXAI1mt9S8Tb4vXuTU9fP3fuNcC8Z555Nz39\nMqgD7xUVccUVwFJ79J0dhq3jcUiChh35rL/nXuRGlb6gV69MuMLj+bOIc6yhDOYbWkmMuMcgIyOj\nY8eO8R5FTcK26dAhGzbCHrjQsi6ApG1ZM25k0aN8dRmbkqAe1IU6UAf2QynshN2wC0qhFP5u2zzw\ngHPCOnXGaH136PzPPHMYTk1Pz4YkkSszM525ZCmMg3/DHjgE5zdg/C5+IdICzlDqnPR0X2bmcKX+\nLVL3gQeoUydPpIHIVZmZczIzp8CZjRuPSU4ekJ6+Hc6GU+FUOB32w5lwEOrATpFLlULkyMTxzDNz\n0tPnwD7YonXvmG9InTof+3xPXX45n9WpMyV440CtgYel+/dZN8Mv4aI/88VVFLzlvrp+enegTp0p\nUARnat3+BP2lajrmu1l5jLjHxnyGjgGlSnv1Wgi74HTLOj0zUwjo/kI40ImPWjLmXM5tysrLoU4w\nkNagYTeUwnbYDwWc3Y2PJ9qd73gg8iluvTUtMzNfpEVmZoHWA4Atfp5v//X6zA+X8ygcgjOLubGE\nq138CDtcFEOd+vjXcQ8ccnHQRV4JTUvYdDpb4f2rafMomzK5VZiXya2d+OwbWmyjzkz9dczX6AzA\ntvump/fOzMwHbPs9J+oP4fXuat9+clv++09WTIJMroczlnNPCbeV8Es459dMe4zeezj4nJ4IKLUp\nMzMpK2sPbND6+qr+s9QezLfy5xHntFA1xiyxHhsej7asLU7bjfDunW63hkLwwZw/8uAbXNMf1zSY\nB2tgM+yAPfAjbIfGdDmPb5fAZOgHq5yqG5/voO+Q08waOoukRlc9vg2zRZIhib+kcJOTLh8Os2Ap\nzIbNsAgu4b8w8LcwH4pgqbMhNmjlBUdy585tTum6UiNCHrwhnLum2dnZ9gTnFssa3oTX/sRvGtMB\nRsEKKHYx8RdM70ZKDhdoj0drvbPIqS7NhvWWFdkUxRCBybP/XIy4V4T5PB0zRUXashaADYPDJd6y\nBsEk+BaKwA85V/NBe5q/bXXSWmuPZyautTCLBjDxSf62Bxx34LVQAAXwBa6VAa3fK7IVZjh1kOGr\nprYd7BNl26ki2rZnwKLQiq7W0L1Bg7Tny6loDLUJdCrWRVJt26d9gXqe/batfb51So0QGSryOjwC\nbXEJN7Tgby7ehYEwHrbB9vd44l0ensk170ABDMLlvDlut4aNlrXLsmJb2BvCMVWPx4BJyxyFlJSU\ntLS0eI+iBiOyPitrB2xyu+9ITw/dmJaVlQ9/aMySRmzP5y04CMVu9y2wq1evV69m40ratGLtU3x+\nG5vOhjPhFDgFDsBh+Axuh9NgLklzuLSYfVtosp1662mq1D3p6SN9vnfKLq+WoU6d1xo3vrhNm/xX\nXvn08svZ5z+clj7oj9L04fb/uZbiZPLn0ngW1zzJlPrQDBpCMdSBtbALFkAJZx1kzwruLeaWYi4v\n4TK4Fk6BlbeQ+wZfHGL/71laCuugmHMGctFMHimkNdSH0+EUra86OX+Cmo7JxhwbRtyPTk5OTmFh\nofl4HQ8+H1deORmaAJZFZuYVgG37O3R43kXJrcw9nWvP5dR5PL+fbev4f3AqbIIdsBZKJ3qevkPY\nlZ62rtfLZ0ASjIK98BAAu+EUKIZ94Id1sJWkoVyzlfpbSAKuYF0J9RtTvIrGV1BcTP1t3FiH+mfx\nxWdsqQcNYSdcBucE1wD2wGmwGtbCOBrfzLoJXL+PuvmklHA2XAQXw2E4FfQ9vHY264U1X3LTOi7P\nsUZfnpmZa29s1WE5HAguJDvJdO3xnN/eLJdWGqPsx4wR90pRUlJSWFhoCrCOnzp1hlnWbVlZfmhk\nWadkZfWFzVAfzoFD9zD9QebkQAOumkrDtTRdwQsudpZwDZwOu6BuEpsPsu98PNeQ81/WN2ZTIwDq\nwU9wCA7BDjgMu2E+/ALqw8WBVD6HoRha88qpHLyBt97HtZrLbmarzWXF+Ndz0zrOyOchF+vrs30d\nN8D1cAH8BPVcFMPmm1l4D70WcdVB5tVlSwk0gRvhM26fQfvNRU+8mb6tV6/h8Gv4BZwBxdDA42mU\nmUno2sVQGcx18/FgxP1nYIKIKkQpevWaDRdDXdgIW+EAnNqYyY3IuZccFyW3cO4d9LuccS9YuQeo\nP5FHijk9Kysb/g+WwKVwI1wAp7Tjk1vIPpf1f2V+XagLp4GG/9DiTfLrAXAq1AHged5MpwEUwygX\nb5RwSXAYwFmWVdcZXmYmIqSnf0DWgs7WNedmvT4YGkIDWAvAFXAxPOvxwFnezG3te22A66AlnAln\nwEFwWdaZtm3K1Y8Fo+zHiRH3n4f5wFUtSpGZuSsrqxj2w2GoD8WwCq6GTU3pV0yD7fz5Nnq/z9RB\n4A9Wiys1slev74KncVnWrVAMjTMzuzg3/SiyE4ZmHexoNfwpa6oPLLcbkTcy22/ncK9e75999hki\nORMmfBsajM8XUOH9vsNnXHHqv+pc+mvWnQWboBiycQEXUtLWss6GOzMz8fHn9guvlht69VoCw+Aq\n+A2cAfvc7itFMOmXY8YEUsePEfefjdH3E4HPR3o6vXplwcXwIzSC/dAAlsBPsC2J6Y3Y24gZjVkN\nXAHXwUFcW3CdT0khruvYXkzSNurXY19/bmxP3tlW25U0ekYl/0pkSHr6/UqNylyxPXPgL6X1LR0m\nnH32YZHFzZv/IzRJNGfdVup3YK6Lks2wJzi27Zx/BQ2+5h8Xc+a1rJ1GFzgNGsBZsAXmwEG41rJu\nA5Qymn685ObmtmzZMt6jqPEYcT8WzAboE4rPh5OezsoqAmA/LIRLoDGcAbNcTCihWxLZsPcuBl3M\nxp2cdiqn7Ob0h8jfhKsULqfkElgEv4BT4ByYDOfAODgTvuXtBqxqSN9boC5n7eGwi5ISGq3jV43Y\nvpzbGpOTT3cXh7ZzLTSEhlACGvbBabAWzocBcNjt7ibyCyPoVYUJnqoKI+7HiNH3k4NtA3To4Afn\n30/gg4ugBZwCl8JauBBOhd3QEE6FHXCO42fjYkUjxq3jLy5OL+FCF6tLuAB+hHmwHqZBd7gVToXT\n4ACcBTvgDDgMB+Es2AelsA8ugMOQZFlnOIYEYJLpVYyJ2asQI+7HjkkLxgXbRoQrryyG3VAP9sAa\nOAv2wLlwCHbDYTgL6kA9qAOH4ABcDn7YBHVhBwyBdfAPuBOy4ApoBBvgdKgP58PpUBd+Kio631lc\nNVJ+QjFfqKrFiPtxkZOT07x583r16sV7IImObZOZSa9e60BbVlJW1g5noxDUhUNQF/ZBHTgdNLjg\nQzgNRsJoWG9ZzbOythcVJWVmAiZpHgdMNqbKMeJ+vJgPZc1Fqf+kp78b7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"text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(graph_polar + graph_c + graph_d, viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "# Appendix A: Conformal Equivalence" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "@Agricola2004 shows that the geodesics of the Levi-Civita connection of a conformally equivalent metric are the geodesics of a connection with vectorial torsion. Let's put some but not all the flesh on the bones." ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "The **Koszul formula** (see e.g. [@o1983semi]) characterizes the\n", "Levi-Civita connection $\\nabla$\n", "\n", "\n", "\\begin{align}\n", "2 \\langle \\nabla_X Y, Z\\rangle & = X \\langle Y,Z\\rangle + Y \\langle Z,X\\rangle - Z \\langle X,Y\\rangle \\\\\n", "&- \\langle X,[Y,Z]\\rangle + \\langle Y,[Z,X]\\rangle + \\langle Z,[X,Y]\\rangle\n", "\\end{align}\n", "\n", "\n", "Being more explicit about the metric, this can be re-written as\n", "\n", "\n", "\\begin{align}\n", "2 g(\\nabla^g_X Y, Z) & = X g(Y,Z) + Y g(Z,X) - Z g(X,Y) \\\\\n", "&- g(X,[Y,Z]) + g(Y,[Z,X]) + g(Z,[X,Y])\n", "\\end{align}\n", "" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "Let $\\nabla^\\tilde{g}$ be the Levi-Civita connection for the metric\n", "$\\tilde{g} = e^{2\\sigma}g$ where $\\sigma \\in C^\\infty M$. Following\n", "[Gadea2010] and substituting into the Koszul formula and then applying\n", "the product rule\n", "\n", "\n", "\\begin{align}\n", "2 e^{2 \\sigma} g(\\nabla^\\tilde{g}_X Y, Z) & = X e^{2 \\sigma} g(Y,Z) + Y e^{2 \\sigma} g(Z,X) - Z e^{2 \\sigma} g(X,Y) \\\\\n", "& + e^{2 \\sigma} g([X,Y],Z]) - e^{2 \\sigma} g([Y,Z],X) + e^{2 \\sigma} g([Z,X],Y) \\\\\n", "& = 2 e^{2\\sigma}[g(\\nabla^{g}_X Y, Z) + X\\sigma g(Y,Z) + Y\\sigma g(Z,X) - Z\\sigma g(X,Y)] \\\\\n", "& = 2 e^{2\\sigma}[g(\\nabla^{g}_X Y + X\\sigma Y + Y\\sigma X - g(X,Y) \\operatorname{grad}\\sigma, Z)]\n", "\\end{align}\n", "" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "Where as usual the vector field, $\\operatorname{grad}\\phi$ for $\\phi\n", "\\in C^\\infty M$, is defined via $g(\\operatorname{grad}\\phi, X) =\n", "\\mathrm{d}\\phi(X) = X\\phi$." ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "Let's try an example." ] }, { "cell_type": "code", "execution_count": 101, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "nab_tilde = S2.affine_connection('nabla_t', r'\\tilde_{\\nabla}')" ] }, { "cell_type": "code", "execution_count": 102, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "f = S2.scalar_field(-ln(sin(th)), name='f')" ] }, { "cell_type": "code", "execution_count": 103, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "for i in S2.irange():\n", " for j in S2.irange():\n", " for k in S2.irange():\n", " nab_tilde.add_coef()[k,i,j] = \\\n", " nab_g(polar.frame()[i])(polar.frame()[j])(polar.coframe()[k]) + \\\n", " polar.frame()[i](f) * polar.frame()[j](polar.coframe()[k]) + \\\n", " polar.frame()[j](f) * polar.frame()[i](polar.coframe()[k]) + \\\n", " g(polar.frame()[i], polar.frame()[j]) * \\\n", " polar.frame()[1](polar.coframe()[k]) * cos(th) / sin(th)\n" ] }, { "cell_type": "code", "execution_count": 104, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\begin{array}{lcl} \\Gamma_{ \\phantom{\\, {\\theta} } \\, {\\theta} \\, {\\theta} }^{ \\, {\\theta} \\phantom{\\, {\\theta} } \\phantom{\\, {\\theta} } } & = & -\\frac{\\cos\\left({\\theta}\\right)}{\\sin\\left({\\theta}\\right)} \\end{array}\n" ] } ], "source": [ "print(latex(nab_tilde.display()))" ] }, { "cell_type": "code", "execution_count": 105, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0\n" ] } ], "source": [ "print(latex(nab_tilde.torsion().display()))" ] }, { "cell_type": "code", "execution_count": 106, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "g_tilde = exp(2 * f) * g" ] }, { "cell_type": "code", "execution_count": 108, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\mathcal{T}^{(0,2)}\\left(\\mathbb{S}^2\\right)\n" ] } ], "source": [ "print(latex(g_tilde.parent()))" ] }, { "cell_type": "code", "execution_count": 110, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\left(\\begin{array}{rr}\n", "\\frac{1}{\\sin\\left({\\theta}\\right)^{2}} & 0 \\\\\n", "0 & 1\n", "\\end{array}\\right)\n" ] } ], "source": [ "print(latex(g_tilde[:]))" ] }, { "cell_type": "code", "execution_count": 111, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "nab_g_tilde = g_tilde.connection()" ] }, { "cell_type": "code", "execution_count": 112, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\begin{array}{lcl} \\Gamma_{ \\phantom{\\, {\\theta} } \\, {\\theta} \\, {\\theta} }^{ \\, {\\theta} \\phantom{\\, {\\theta} } \\phantom{\\, {\\theta} } } & = & -\\frac{\\cos\\left({\\theta}\\right)}{\\sin\\left({\\theta}\\right)} \\end{array}\n" ] } ], "source": [ "print(latex(nab_g_tilde.display()))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "It's not clear (to me at any rate) what the solutions are to the geodesic equations despite the guarantees of @Agricola2004. But let's try a different chart." ] }, { "cell_type": "code", "execution_count": 113, "metadata": { "autoscroll": "json-false", "collapsed": false, "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\left[\\left[\\left[0, 0\\right], \\left[0, 0\\right]\\right], \\left[\\left[0, 0\\right], \\left[0, 0\\right]\\right]\\right]\n" ] } ], "source": [ "print(latex(nab_g_tilde[emercator,:]))" ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "In this chart, the geodesics are clearly straight lines as we would hope." ] }, { "cell_type": "markdown", "metadata": { "ein.tags": [ "worksheet-0" ], "slideshow": { "slide_type": "-" } }, "source": [ "References\n", "==========" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 7.3", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" }, "name": "Vectorial.ipynb" }, "nbformat": 4, "nbformat_minor": 0 }