{ "cells": [ { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "2P62Q8mYxqOT" }, "source": [ "# Plotting Spacial Hypersurface Embedding for Schwarzschild Space-Time" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "colab": {}, "colab_type": "code", "id": "KLMjfPh1xnFQ" }, "outputs": [], "source": [ "from einsteinpy.hypersurface import SchwarzschildEmbedding\n", "from astropy import units as u" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "CnZmT-pMunhw" }, "source": [ "Declaring embedding object with specified mass of the body and plotting the embedding hypersurface for Schwarzschild spacetime" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 330 }, "colab_type": "code", "id": "kWlPvx7euNMQ", "outputId": "6abe8a00-3cc5-4d68-87ac-17da5a03fcdc" }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWQAAADuCAYAAAAOR30qAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvIxREBQAAIABJREFUeJzsvUmoZVl23/1be5/mdu9Fn5mV1WVlZanKqU9IVXI5yzODsREaSAiMJFsgYzA2HtW0wOChSWEwyLKkgbCkGnjiBiwPZDAIGxsblyRLX8nyB6Iq+yYyMiMyXnOb0+29vsHe+9xzX/TxIl5FRp1/kRUR997T3nv+e+3/+q+1RVUZMWLEiBE/eJgf9AmMGDFixIiAkZBHjBgx4gnBSMgjRowY8YRgJOQRI0aMeEIwEvKIESNGPCEYCXnEiBEjnhCMhDxixIgRTwhGQh4xYsSIJwQjIY8YMWLEE4LsAT8/lvWNGDFixIND7udDY4Q8YsSIEU8IRkIeMWLEiCcEIyGPGDFixBOCkZBHjBgx4gnBSMgjRowY8YRgJOQRI0aMeEIwEvKIESNGPCEYCXnEiBEjnhCMhDxixIgRTwhGQh4xYsSIJwQjIY8YMWLEE4KRkEeMGDHiCcGDNhcaMeKuUFWccwBYaxG5r54qI0aMYCTkEY8I3nucc3RdR13X/esigrW2/88YgzEGERnJesSIExgJecSp4L2n67o+KhaRnnBVQ7fWRNRDpM9Za8mybCTqESMASQ/NfWLshzwCVUVVadsW7z1AT6SqStM09yTVtI+Tv7+RqEc8pbivH+9IyCPuG6raR8QniXj4mfsh5Lsd43ZEDUGTBsiyjDzPR6Ie8UnCff1IR8lixD1xkogTCT4OIrzTftM5vPHGGywWCy5fvty/N9SnT+rUI0Z8kjAS8og7Ijkmuq5DVR8rEd8L6biJbFO0nIjaOdefY0L63O0SiiNGPIkYCXnELVBVqqqiaRqKouiJ8EnE3SLqpHOflFBGoh7xpGIk5BE9VLV3TFy7do3VasVLL730wPt5EojtbkQN0HUdbdvuvDcS9YgfNEZCHtETcbKmJe/wAyZ8zwynOa9EridJ9k5Eff36dfb395nNZjuuj7HoZcTjwEjIP8QYFnPAblRpjOmdFE8SHhcJ3omob9y4wWw2u0VLV9W7RtQjWY94GIyE/EOI2xVznCQQEXloQj6ZXPskIxHvSQ39fopesiwbiXrEA2Ek5B8S3K2Y43YwxjyVksWjwr2kD+/9Tgl5+uxY9DLibhgJ+SnH/RRz3A6nlSweV5R81sT1oNdxJ6JO+0oyUdM0O+8NpY8UVY9E/cOHkZCfUpy2mONhI+RhCfWIXdyr6MU5x40bN6iqik9/+tMAt9WoR+fH04uRkJ8yqCp1XVPXde8hfphI6zQa8uPEWZP9Wejhw+8nSUvJ5TIWvfxwYSTkpwTDqrrr169z48YNvvKVrzz0/h5Wsqiqirfffps8z5nP58znc/I8f+jzOIkLFy70VXpngfl8fqbHGxLvWPTyw4eRkD/hGBZzpIc5y7JTR7cPGomu12tef/11jo+Pef7553HOcf36dT744IOeJM6fP09Zlkyn04eu/jOZPVOCvHjpEjY7u8fEe3/P+zIWvTy9GAn5E4rbFXOkB/lReIjvdx/r9Zr333+ftm35/Oc/z2KxoG3bW6bYTdNgrKVpGlbrNc45vHcYY7GZwYihmJQYDQPKHa8bzlRK8epx6rBntNrZaSSSBy16gfA9t23LZDKhKIqRqH/AGAn5E4a7FXMkPApCvleEXFUVy+US7z2f/synmZSTuz7ERVEAkE2n/WuqSuMaPNA1LcfHxzjvUfWIETKbUxYFWGFiiqirerozJAunDtUzHAC8f+QzgHsR9RtvvMGVK1fY398fi15+wBgJ+ROC+ynmSLDWPpII+cqVK7e8vt5sWK6WqFfme3MW03n/nvJgDbNFhDIrw3ZZyXyWdqS0bUOlHa1raeuOo+6I5XrDfDrBWINHMUaY2QmcksDuRi8ORVTw8XOPm4oWi8Uj1dzvhvT78d6T53k/MxmLXn5wGAn5CcaDFnMkGGN64n5YGGOYTCf9v5ebFdc/+ojJdBqSdbMFAB5ll/p3Kfl2w8KdSLv/rAimKJlR7rx/8aJyvDxE1dN2gSwOuiNUwyBkMBSzkkKgyGbIbYhauftS68ou6ar3oHcebG73TZyGuL0o2RkRcn/ME7r1WPTyg8NIyE8gHraYI+FRSRbOe47XS46XS0SEi+cvMtvfAxSHHxBUfFDTv0RgIHfc6UxOvu7ZJcstCcb9C3gjqFj2Z/s7H/R1xabb0LWOumvp3BKvkBkTIs4sY24Mtpjhzd3uo+wQqlNwIreQ8d1I/eR7J492t20ze/aP5P0kEmEsejkLjIT8BOFRrczxsITcb6HK8WZJ61qOV0v25nPK+RyP0m1pd/D/J7bn9iTsb9liCwUcdyMrxQFdDFe74X4EmJTklLsxtYKvalpq6tZx0K5pj45QgRyDlAV5ZphIhi1niAkRvxlQqFOHBxRF2A4au9cn/XkPB5XbXYsM7oCceF0IEbK74xD2eOCcO7VufT9FL8PXqqoC4Ny5c2PRywAjIT8BGHqI/8//+T+89NJLvTXsYXC/drLtYx9lB1U+PrxJVW2wNgNruHjlSnw/RMS7hLQlZd2JkrXf73CqH7bdjaaHcP1Wt6dtB3jV2xAi/bntbCfAtCSjJJuG9238sG4qWq3ZdJ66WdMeHaJAZi0mz5nkloIcp9CJYOI9Gh57eJc9t0b423OUfrvbkfVORO49nfhb9vU4cb8R8sPgTkR9dHRE13VMp9Ox6GWAkZB/gLjdEkkpojjNj88Yw+c+97nbvpcIcxvnKqpwvD5iebQkyzIu719EZgUfXH0fRXfEiQ7tiaInYt3u+26EmaJgGby2e256y+dvOXdN+7mVsjvu/oPu01MCzEosJYvh/hVkU+N9zbJxrNuK2rVcu/4BRZajxjIvLRkFdjrF9xy2O1vwg8PI4DU/OL8oRN1Cuk4Vq76/V2k/J/f3KPE4CflOcM6R5/ktkfkPe9HLSMg/ANyumCM9ENbaUyfkYBuxDnXYIRl7FDwcr45YLo8p8oLLFy7DJMOhGBSnW4nCRyb0BGIzuj3OkBqdDrTkwdmEfdwaRabXE1piFHtiHynZJskBwK2ErQxI9zYY3tUkHQwHBxUwsxKhZC++3l39gPOXn0XrGr9esWoNvlvijw8AJcss5CULK4gpYVqCyAniHA5oAUOJI52LIZLjbT43/Lvc5r3TINnczhLOOcqyvOX1H/ail5GQzxB3K+ZIeGSELCGKvB0Z45WDowPWR0smsxmXLz6LKU0vSniUTkO02+kwAt6SoR+wofb/F7YZ4mSk7G7z2iDI3iEo0t8HEbi6QOnOB0I6qWHf7REcWtfSQDX8fB9hy/bYTsEZQWYT/GzCXE7scFOhrua4cTT1TcyhIgKZzZE8Y5YZMlOi0xIr0s8Q0vcxJGZLuH/it7OSYSR9UvIYRtBnYcl7lHhQ3fphi15+9Vd/lW9961tnZiU8LUZCPgPcTzFHwmkI2fd/hsSQ25EbFHVweHzIcr1kVk649NzzmCJJDX67j5g085r+2x5DdUvMQ7KMmwHQ6YAcdJc0Ow3EMyTdBNFdSWN4TenzrvOQGTK/S0jKrUQ+lAuEbdJw+FkFROLfNTg50O37nQ4GBA2f3bHFTSeITCiB5MgWBV1v8L5h2Th8d8jxjQ2LvMDYnCzPmWZCZifopMCLYOP5OTxezU7Scnh9gZTlFh17GD1/Esi567q7VmTeL+5F1P/+3/97/vE//senPs5ZYSTkx4gHKeZIeBhC7iWI/s+gw/WJOAfHh4csqxWTsuTKlecgTxFwkB+G+q1POq0P//kTrJqkgSz+Q4dvsCXdHb1h8FenuwSyk/jT3X/ric+5zgc3RPzQNtrc3e5OhJx+8Dr4Grxuo+HkiOsJ0CveByL2hHvVX85A79B0nEjuMpsiTPuIeh63JRL1cdOh3SHuoKPqGvZnc4zN6VpHV7bh2iRJGVtZKJCxDiLm3eh5eN3C/cka8/n83h96xHgUzo67YVhp+kmSLkZCfsR42GKOhAexrG2JWHf+rgQicZ1ydHSTg8Nj9vbPceWZZ8FGMvMpkt7KD0l6SATcrivciRA4kZv3IZpUQkSYzkcA9beRHnSrk9YK5a5VuYdTyOJ7t4uUnXqMD8dneIy4r0ROJyPmRJg+Ea7uSh5poMhke55B9hG8QuPDOfcR+2Dnad9WtuSu8eS8bpN5XsBEol7I9rrOe2C9xmvL2jkOlxu6o3UgVGsoignzHKyd4ssCI1HHP3HvlK12bdjKGveKmi9cvHDmbU0fNyEPMRLyDyFOW8yRcD8R8kki1vi/RES+VRrnufrB+5SzGc997jN4CfJFIt8UiXrVnchvSHBdbtkZGwbRq9ckX8QHPcoN9eEhR6tVINvMMs0ycpshmSGbzjGYXhpIZD6cjquCu817w2tXv0v6t7s/t4PTQLJpnyclDx+PLUAnUUKJx1LdRtUq20EItsRnB9H1cDToB4J4j1LdTDoHEWA+wwiYTc3i3AVkkqMOZLXCScdB3UFX4bxDROi8Yz5bMM8NmZ1ii5z0UzPxqm5nszsZNasqWZbtuHzOAl3XPXZCPotjPGqMhHxKJCK+du0a0+m09w8/7Khsrb0lOZGwTcyl/8K/++iv8Xx04xqdC+m8S89+KkTEkYhb4sM4iIITEQ2lg/RMZjan9lAMo9m4jQU2HvK4YXV0yNF6zf50xsVnn6dVyPC01QrXeLRquHm0wnsl6xzTxQwRi5lm5FmYMpu43+pENKrIjjwhXnBebqtDOw9idl/vT92DM7te4q0UEAeleINSLjMNAE7Bm92BIm23IpxvL8Wc0KEdQQrpJRTZRueJrBNJO684YzA+DA7Z3hwL7Mk2yvWdwmaNw7OsWrzb0HmPlRDNz6dTytxSmhJTFBjZknO69n5f3vc6zVmSsnPukWjId8Ph4SHnzp17rMd41BgJ+SFx0kP80UcfcfnyZWaz2b03vgustX0V0xApKt5GxtpHeL7qODi+Sd3UTGdzzp3b46Or14LLIpGHbh0Q/eOmKaEX/tspatBIQn4b3fUyRNyB89AdH3K4XrM3nXHpmU/1ckaY/hvycg8Njd5InTEq59B2ha/BHVcctkucKhMbomnNPDKdkkm4l8PBwosgIft1SyQswFphdhs+6QcaHZDxgOR6IndxAEhwgnrBDq+f4dvaR89CjLB1ez4Vgaz72cXgXjaEAS3NGAzxnovQ+SCfpESi6lbf9lawe3NyIGerHWun0KyoOmVTVRx1a1Q7nFem5YRJnmPynLnNsVkRKwNTpiHeEw0HNI95xZjTeu3vB0dHR5w/f/6xHuNRYyTkB8TtijlS96tH8QO21rK3t7fzWihZPilRgN+0fHxwg9p37C0WLC5d3MoSKiEhNSAAr9tkXCLVpKU2fksO4Y1Ifh5qtu+liLo6PORgs+TcdMGVZz7Vb5OIzzhBh5Gq7z9CScbGnqOcByKZxtc7rXFtjVvVVLWyaY8AmOYZkGGmBm0EFUEH2kMi2nRu/g7PuVFQuz2PtI0AaxfOg3h/+13EQck5MMNtJZFzIGuNWkCabQhRHlFFU7Q/1J3TeUuMkON35LyiKluJZPCdeNlKI34wCCQy95mQZQvSMJbkCd95cBvq1tFsNqy7Y5q6pZjk5DbHece6rsisociK8DvTR9MT5W543IR8cHAwRshPK+5WzAGBSE+2KnwYTCaTXrJI5Jui4lSd1q0bPl4e0DYNe7Mpe+evoETPMOEBrrqaLs1TU8Sm2yQTDKQKjZqsbIkKQKKY2+mWBKrDQw6rDfuTGc8+82k2LpKHDkwHPpDfqoPZQFdN+rUgOAfegvFb0rZMsHaCXZzDCszi9Xe6oXMdbumomobGd1TNhsJkSJaTTYXMTBAK1EuUHQYXQiTJ2+jO/fgTpxs+np8O7oV2EpJ9bkuSSbZQNETXlhC5x32kaFZUAuHG70HSF5Gi9Z3XwTul8UJOJG3ZvtfPUqLEIZHQjUIr8TtKx4+DikPCAgDZnGkZXBkSr9F0LZumom1b1tWGuqqwxmCNCf2rPZRlibX2E+PjHWKULJ5C3E8xBzy6go48z6nqKuqLW71YUbp1xYfXr6OZcG5vj+zypVjEoT2xpiRdnpW0zpEb23uLAfBhGl2wjXhVoybsdt0PRkJ0KAqroyOO6g175ZRnrnyqd1MUCn5QNqeD/Ro3ILb+hsYo2Q2kiKEHDWIYmM5DyJmTGWAPtIOyscymCzpd03lPe+ho9IBaPdZ1+GyGTDOyDAozQyQP5+C25zj8U+I/vBvY3mT7oVUnzPrckA6iY6hVKGNWr99vjJRbD7mJ/TzcgFgRNgoTG+5hOIkgfTiVkEiN5CopEtYwU8kG55Xkjy6dzIDA0ywh9Q7ZOjC0d32QZWTeYLOMc+cuYM+F8bvVlq5xtF1L07Zce+cdbt68ubNO4uNYL/FR4/DwcJQsnhY8SDEHQJZlt/SIfRi0XRs9xNv/2vWam8dHdN5x/twe7C8wOnBNqNIOWC9Mdw3Oe4zaPiDzGh/wO0TJxm8f5LCBYX1wk2VVMZ+WPHPpufDWIBJUFdSBMfSRcjglRRxRthjctxgZdgrZkKQiCWmUCE5GsT3nOBMTexare+QCfhEixjmw6jpys6Z10B511P4GLUqOIFaR2ZzcQC4zjGQ98dlYNTKUOyTqDjoQjzWWRaf712oY3LZqhPbM3CrkPQ2GeyEx7C58fyui3zgSpgPrBG+1j4B7KSh9NhFvfL/TKCml7zNJIEk7iWfQR8wkl44EL3rT7MwccsnJy5xpGVT//SihNU3DarVitVpx7do1VqsVXdeR5zmLxWKHqO+WsDur3hkjIT8FeJhiDgiEvF6vT318ay1N2+FRNpslN28e4Zzj4oVzmPk0RF6xei5VzaWkXIr0NBIv3lP7kPhJrznAKmwikcAgokVYdTAxsLl5yLKq2Z/OuXz5edSBHzgb1CfCgpWHRSSrcBPB+0CCVQtFii4HoWmmW/IIN3o7WFi2pNwfL23qQt+1VKyhwz8BdRmF3afIQPf7XeNdw9qtUKc0xx0bdx0nSoGFMoe8BrsgM7OoL8QI1EGepIp43UNTb+l2ZZBE2BBmD9txUnti9SohEk8DloIQtGbaKui+LnwmRbw12pNu0p4hSBXJ4ywDzdlLKsUO+xhGzMFpEe6sU49kpifodK9vZxYrioKiKLhw4cL2qqLnfrlcslqtuHr1KqvVCuccRVH0BL1YLJjNZmRZdmYe5IODAz772c8+9uM8SoyEDKcu5oBHJ1lYY+m04/2r7yEiXDi/B7NJT7qeEDm1qrHCjj6p1Wgg32S/cj4WUURWSNKFB4xLEZtso1oP7uAjPqo75os5i8mEfLEAH6rB6g6KGNhIjBxFYBL14J6kfYiivYRpezGI8oZYO5hnJBWAmOBHFdZteO/kNnjCGnfZVlohXpemYw+KRpK8YKRg5gvMBDRPx1S6rsb5hsZBvaxYuRWKkouFeUbbeVy3JpPpYPTYHluHbDyI9LvoJuvfHhD1RmFug7yUHBn9YKYZPmZiexKNkTo2fLciu9GzSbKQbqPndC9TqbfRLWmHopKQuvSbFmzWWyhTMnDoYb4bRISiKLh48SIXL14c3B/diajff//9nqjTbPLq1as9YT8Ogh5dFp8wPKpiDjh9Uk9VuXl4EPRjVS7Oz2P3Z3h83+Snt0VFBm3ZRpVRdGYD5BoeK+89Vge+3j6KDgS7aWEiYZ/V4QGrasNsb858/gxTgeXmRu9TTYk/GOwnaswodA3YWObm4msKTPw2utxebPgjSxkoBteQSCbqyEOSQ4ndiXwUwQdSwWAgGDo6hn96DyZ9RVEmMGaCNRNsu489l85bcd2GVju8h/b4iI07BIQst8g0JxMDFJRZOQift39s4mCzsz5qZLgy6c2yjUjFBF83JgvXMKjyqJySR0tekjcwUHsoRXFJComzjE62EobG34hLEfNg1x7FZxZ810fIEBr0x5/TQ3eUExHKsqQsy1uI+ubNm7z11lu0bct7773HOq5CXpblLRH1aYj66OhoTOp9EpCsa845/vzP/5wf/dEfPfWSMmkq9jDncv36deq6xuYZi9mcdtmR789oos8ieYTbKBKmqNj7baFHkBwIpAQ4MRjv8RqmzsHWJn0PCI2ktzw+YF1vmO4tuLR4PhwnerTUEdk1bJMruC7Yv5LtLBFz42A2aJQsg2g5KgC3FJcUUbdNpDEkUDsg6/49CfvFud0k2kD6MImQB9P67c2OBBnfU2XrfkhkL9GJYGdkCnW3ZO/ic9E+GKLl1nta38HmgLXPsSKYMkPKnEIEayfMtNjenwjvoHWQ7yTzIsk6KD1UKqiT/osNA27UoU34vZj4+VDIEt+TMGOqiIU8SVYZRsz97CZa5SQlgSV24QsyUzq1x6HyigjWWmaz2U7PblWlrus+on733XdZrVZ475lMJjv69P0S9aghP+G4nYf48PDwkfghHzRCVlU+/PBD3njjDRaLBV/4wheYz+c0eNqDG73VrYs6g49k3EFvXxMCeVq2EWamIdJSFZwTCh/0wiQhQODY9eEBm6pisj/h0uL58Oyq9Pph3YCKwTsfbGQqiAQpYSZbiSEk2GASzymFZRojYzFwvIHFiWS8EKPrQQJPBtFkGUlnh9EcwVrWdYjbathiBkTbDfajA7LWRObx3OM14MK2Nkb7fXOgdEzfDGQJQ2YXZDbsrzEXmReA7+i6dZA9tIWDDW3XkGc5zHIkzyksZGaG8xl5HARSYs4TBsyJDXdGNV6nCI0OnRWKxqq7jcLUht+F+DgjMmBV+0rFNEh3cR/qQ6ScZJzwHYR2oQ4lC0p2JORbm+c/KtyupFlEmEwmTCYTLl261L+elntKRP3xxx+zXq9vIeoUUQ+ThYeHhzt69ycBPxSEfKdiDuCRmdPvN0JWVT744APefPNNzp07x4//+I8znYaShJ5Hum5gVdNepvCEh6ojJObSU1dpmMEnQiwU1t6EDmVR67XAsgM9OmBTV0zPzbm4+BQ42eqYbKNY0VjYkSot4uulA0mWtKRfRgZrN1AUxKTeVr/MBwS5I0sYqNcwKbfRbjoXFyPAFOEZHwPfDsRty/RSdC3pH7GKLyGRsWokeDMg26RXr2ExGwwMOz+JEI2n15JEIhIlFwdCRp7t98S5Vjg/Ae8bOlfRdkrdtGw2G1zb4IoCmQcPdWEEm80wzoaBL8kuSVaII6SPs5YUORe6/e2qCTeg6mBq4iyIGDFH+aK/V/F3luQLp0rmXH9daWISv8agP/No8SBJPRHpWxJcvny5f31I1Mvlkhs3brBer3vt+j/8h//AzZs3uXr1Kp/61KeCr/o+cHBwwN//+3+fP//zP0dE+O3f/m2+/OUv8wu/8Au8+eabvPDCC/ybf/NvuHDhAqrKN7/5TX7/93+f2WzG7/7u7/K1r33toe5JwlNNyPfrIT65ptfD4F4Rsveeq1ev8tZbb3HhwgW++tWvMplMbvtZyfOoHcdtNbTJTKyVvMFpqm18TPaQOE/w1Igv8S6Q8ubwJpvliumlc1xePN8n8YzAsoWFDdvFZ5lcYCMhstaBFGEz2KwgnXovmwC+I1o6IkkOonZxA8mCbYTdtYQkWzpEZAGJkV/y2vbE6xU6E/7UbUSb/m5SJHzyniqYjB2pA5H+/vXyyFCzhnBBO/8OSEm7dI19JC6Qm3AOhoLCFhTxKdsI7E+UzjU4X9N2jqrpcM0Sr0qeWWrvqdojcmOBKbkx25E6Hm/thalNsxANvT1iFOxFQ8JWJMymjJJ2IRpdGRK+Uw/4zuPLok/qeYQ8Rskn1z15VHgUfSzuRtQ3btzga1/7Gv/9v/93/sW/+Bd873vf4+tf/zq/8Ru/cc/9fvOb3+Snfuqn+Hf/7t/RNA3r9Zp/+k//KX/9r/91vvWtb/Hqq6/y6quv8iu/8iv8p//0n/je977H9773Pb7zne/wj/7RP+I73/nOqa7rqSTk2xHxvRrCn/YHYoy5bVMW7z3vvfceb7/9NpcvX+Ynf/Inb7t0DaSiOsV1DkHC8kmDB77XfjUkdFJxh7BN3Emq0zUTXNOxqm+yqWqm5xZcnH+WTdJY48OtKkyVfgWOFGkqoK4BnSIZO6RoU7JKt4WAqlBa0EZZrm+Ca8DkWMkoipzNesKkkN55kPY1y7WvcAP66xVgs4HplC0ZxgOJy7ZrHEXHQXJn4Ln9Ok6JaAlEEwYE7SUaOak7J4LFB/JPxzeBxKsNzOf00bgMyDkb2OQSSUPUjp1gTYk1ZZBlCli1sFcovtuwOTzAtx3VpqLbXIdpEch5lmOyjNxklDIJMxgXo2QDtddQaOKCdCEojcIk6sNGlDYNWFHiUQPeO5B8EBmHm+B5fOTwOG1vIsLly5f523/7b/Obv/mb/Ot//a/vu2HS0dER/+2//Td+93d/F9ja/H7v936P//pf/ysAf/fv/l3+2l/7a/zKr/wKv/d7v8cv//IvIyJ84xvf4ODgoI/IHxZPFSE/aDEHBKnhUa1eMIRzjnfffZd3332XZ555hq9//ev3NW0yCE5Dt7aUyEsBWpOizUTKum0SXyDBliaxqfyy4nCzYe/KJS7OL8X12oLW2zrIrPT8YwQ2NUzjPDXZx/AFjRMmMeqFQHrWB+nADFwEqspqdZO2WjOZLMjLGW3jcV1HVW+o3Xs06zmZyYCCIocsnwEZON1KAWwHGY113r2UQIiQxQni/Q5/pj8t2ovlw2++15kJg16/v0FUPSz/7oVWlyFu2yA+SSql0A8k/XkIrNfCdMGOMyQNWDaRdpQkVIP8MwPEB8dH0RlmxUU6gdkCsB6nazqv+LqhXt2ksRlGhCzLkamFzFDaCZq6OMXk4GSgMXsjQZ4wg3Py4DB9NzsrW9nicZZtpNWmHzeGz//9zIBff/11rly5wt/7e3+P7373u/zkT/4kv/qrv8q1a9d6kv3Upz7Fhx9+CMB7772343P+zGc+w3vvvTcS8sMWc8CWkB8Vuq7jnXfe6b+YV1555YHIXhC0cds+xBoYSFV1AAAgAElEQVS7ug0i4zwRh4/c46WP8JYHH7OpaiZlyf5in5y98Lm0jcTS3D60DYfJAdcmz2s8F7VoVweyGsgAFthUymQaXl+uDmibNZNiTj59nmkJrlOyQvrIdKZXEPF07Yq2VdqqZbNe0XlHgcWaAskseZZhzRQErNn2uuj7Dzsfemz44DbYscQRCNvo7vkCrA6U+Z70+m9/vwVKgG577RounmoTXhf10ekhSFzd1cbeFSqD5FeSeLvBMeItWG6E+TxskxwOqrBa07/u0F7zbnqPtkHMgtxE//D5S8HDjMPpmhZFl2sqv6HxnswYssJCIVSTktxMyKylcjCxcVVzQqe5kHcIMoVEQh42tFceDzGfRevNh+km13Udf/Inf8Kv/dqv8corr/DNb36TV1999Y6fv13UfVrp8xNNyEnAP42HOM/zO/YffhB0XUdd1/yv//W/+PSnP803vvGNh/rRZQirw2OMgzbN6nxs8KMhkZT8x0ag6kIjms3Rx6w3NZP9gkuL59l0K9y6IQfaFoqYcVIXNMRqA2W25TNrYL2B2YT+RdMJ3ue0DWSp/2Q6TwvLwwOabs0kW7B/LvS3cC6s3ScaFemod3tCFJzbee8ySDLD5shh8yWu9bTVmmN/iFeYacu63CezkGUzjLVIjKbF+z6aBnoJJrRmM7syBoFUURPdJFvdGRNmBEaBWCSTot3e0xw720uyRMh2iSqJ+kogMCHPw4CAl21ULcIsC9quJ5GxIAamWST2+EUbA74OFkKNlsEUvbcuOjEURCy57AXiXuyjBPeL0lLrCjy445q6XdK5jiIz6KTA5BkytWTZHDHb/stZlMNUtmT8uGrpzqJS7+jo6JauiffCZz7zGT7zmc/wyiuvAPC3/tbf4tVXX+XZZ5/tpYirV6/yzDPP9J9/5513+u3fffddnn/++VOd9yeakIfTkdM0hD9NhNw0DW+99RYffvghIsIrr7xy6oYrNhKPtSEqSj7VELlB50JE673gjj/m6OiY2cWLXJpeQlSoovUr6LwSqrTcIAlFnD6zTaLhAzn4JkR/ae5qVOgqJZ8mjVZZLo+ouhUTJlw891yY6sYkW4ay2ShFvAXpWzEK67Uy2/a4RCJJmylMzF5fCDLXEBZvWofoGt/AZnWTTSxgMIDxjqyckJlJ3xYzWNsU47aSRN9hTsPrGkm4l0hislHM4PeTZg15uBbjQyVnmlWs1jBfyM5ggAqd1+29S9EuQtcpWR703dTzwxA08rIkiuqJ0qGuCfcpDggqYfZS5PQ+cySMExPYFowIdJozseeRnBACJ6eMbeho8FUDH29YyhFGlaracEEU29RoOaGcTVGzXSzgceAsVvI4ODh4YA/yc889x2c/+1n+4i/+gi9/+cv8wR/8AS+//DIvv/wy3/72t/nWt77Ft7/9bX72Z38WgJ/5mZ/hX/7Lf8kv/uIv8p3vfIdz586dSq6ATzghw+l7tuZ5/lCEXNc1b775JtevX+dzn/scf/Wv/lX+9//+3w99HkNYa8m8p8ViCI2DMgnVX7mGB2V17QNWHmZ7e5x/9oW4zFDImOXAygnqAwFZC5sqaMTexYfNBLvXdELvzQVo26AzqiNop16ZzJW2gXp9SNWumGRzLu09i+8UGwtVQkScuGibqJNBxUdh/bZ5e5RLVJRJp0gW5vt9tCihd0Nh571zY09hUy2h7pCN4ruKw+6YVj25GKZZDgrtbEGWmV5CCIlQH5y1ScONiT0RME4RmwZ3+ii4cAQ7RbKFpdcLoJNtws6HUrm2S0UZQ00kavZCGJW6lIhTMghJ2IHcIp0wm+l2LSkJ9sDWD+yD0R7XOJjm9H5wE50f9INM+M3McsFTUEpBPVUmezA10IoiH16lsDm+qjh2DfV7b4EPRSpDj+9kMnlkFtGziJAftijk137t1/ilX/olmqbhxRdf5Hd+53fw3vPzP//z/Kt/9a/43Oc+x7/9t/8WgJ/+6Z/m93//93nppZeYzWb8zu/8zqnP+xNPyKfFg2rIVVXxxhtvcPPmTT7/+c/zpS99qbfSpWj7tBGyMQbnHBNT0HoNpEwg4vWH1zhynsV8zrw4x4SQbe+XNIpTb3E2EEic7pYWmg3kqeRYo2TRgjXaNx8qMmgrJctCBKvOs14eUVXXKbOLXNp/LmqtIQJsa08e13FKfuAyc7vVcrHU24hifCg+SNY0UWjxZCrBY8x2uzKJ30h/fsbHOfxkj+nUhIQYQSpp2g7dLGmXhxx0DarCJLMUuUHqEpeVobwb+qQaouQmeLV7GSOGmz4aqsX7KH8EkrRpACFq/hJGtIlXJHXlF4gVNZSEpF2/RqCBtoYsA7o4GGi41+LqPqEpAmqEegN5xk7lYtuE6HorycDKwaxfVhvaLrb4dCBW2HhlFnXk1oe+JCIC5/bJ7AUuWiifeZapF/xmw3K55Pj4mA8++IDNZoMxZqdibrFYUBTFAxP1k7x800/8xE/wx3/8x7e8/gd/8Ae3vCYi/Pqv//pDnd+dMBLyfbbN3Gw2vP766xwdHfHCCy/wla985ZYf4iNrMBT3s0dGYxydU7p33+G6F/YXM/ZnF8l9aPLeeshSb4oOJiYQc46hctWukzRqpVvLmlJXYCf0VgBR8NHU7OuG42bDfr7g4v7ng7zQl+eFz25wFN7EJFpgDOPDVH9abgk2NOyBZuMoCtNXsYiEqLKpg86ZPp86uFWbjum0b44cEnrOQdYhfhtlWYFpZmgXc3JrWUSicp2ncR00S5aHa5ouZC5nWYbNDFQzygs2yh4SM27h3PKoC4gPqa6UcDMSnB6YQLippaZFkC7aQiSEqptWmZQx1FWCju01lFCL9D5rEehaRXwWEpcxvJculoNn9JbGVBadEp4qgaB33DBdIP5kBWw95DY4LdQHPVyM4NoWUdMn8CzC1BiIpDuEc471es1yueTmzZu8++67oeTf2p32m4vF4q5ByVlpyJ+0sml4Cgj51FnNLGO1Wt3x/dVqxeuvv85qteILX/gCL7/88h2P+bD9LE4iEXJd13z45pvcuHGDZ154gef2LpAr1G0oqbUifQSMQimh3eXEEqbRPqOpQ3QlGtpgbpYwnWgfDRa54irI4sOsqjSbQ47rFROTsW9m7C32QZVVrcxT6zYfEmVzDRnH3p0Ro+HcOMRvvWZpKu2d64s6th2FwDcu9pXQPnlmBMS6eKyoN+OD7mL91oER71sYaPyOM8AYyMRSnZ9zMbP9dTetx7ct2nzMxwcWbTsky1hkAraENqc8ZzHeIT4eyMBm7ZlObWzNuXX1rCvPZGKiFJOyllEWTzYZEQSHytYzLhL86+oFvw72F/FxkS4VNp0yGXYKMrBZS/Bna9y3iY6UeCNUoXahcVRq8Wll2/ekcTDLg22ynJZksROdFTh3F19FWl7sZLKs67q+Yu6jjz7ijTfeoOu6W9pvpq5uzrnH3g/5k7haCDwFhHxa3EmyWC6XvPbaa1RVxYsvvsjly5fvSf6PahknVeWtt96iqipeeOEFfuRHfoR364q6Cw9TaUCbtIR88h+Hc8tjAGnEbGWDKF0ISlFsp8tCcAR0MepdrY6oNktKW7I3exbxa9qmDZ5fhZlxITKMyafUA2JVdcwnIUpO7grjXXAgJAN0jAJzcZhEcFFDFoUsiwSrIPi+8s3idwpHxHchanUdErN5QpiGB1dHrHiQOFinyF98b0cTCXINNqMqFlwxIZvoVWlbBdfQrA85bjKkqzm4cYNpLmDngUgcfXIuCcl57kLELgYZLA9i1WPUoNvu9MHzPZH4/YToWxVMofgqFKIkh0ih4Z4Sl6bSNujGwVEikaCDOybNfJoWyr7ZdSTn2K60csI8UzKFhYebXUNHIO+LD2lyy7KMc+fO7RDgyT7J7733Xt8sKM0279SD4lHg4OCAZ5999pHu8yzwiSfkRxEhD0n06OiI1157ja7rePHFF7l48eIDeZpPEyHXdc0bb7zBBx98wHPPPcdXv/rV/tifLkredDWNAdcquRWyLpTpeoGqhakNUZKrQWwg5MKEUufpJBQJhKblGqPLkLRr6mMOPz5gks24sPcsNkaq6yODUQ/Oh6WABNZrxywuo2wExHtmmUOc9kUcqp4MT105JkWa6qeo14eRJBJu0JIV6RySmV7fhjjz1w7R3rqAeBca4vguTOtjyJta54u2CKnTWpq/K+LaoPvGCF6i/iDO960rLYLNBSkKTLHPvs348MZN9uZznPPQrFk3S461QI0wzQy5LaAoQwVf1l8QGGFTecrSBp0YF5elEnKj4CxiQk9iEaVuwaZF/7wDMWwaZVpIWPlaFPFK1QnTgr73dNsQPpOkCRcXBIiST9+0yAcP+zyHPcLnjnNofcVUYGYFw+mepSHu1ic5ORJWq1XfgwJgOp3uRNPT6fShn++joyN+5Ed+5JFcy1niE0/Ip0Ui5IODA1577TUAXnzxxYfqEvWwEXIi4o8//pgXXniBsixvSZYYYyjy8CC1JvSAyAnP7qVc8DkcxgVLbA7rlQSdVqHMlbaCvAjuh8Iq1Ubx/phqvaIkZ3/xPGURnBmhe1iwFEjnMc73CbBJrAsW3SaejEBbtxTR8yUaquhs1oUklwNC+QE5Sr3pKCd2QKZBitDkQFCPSeWunUOsbNtrxh7FpnOoMX0k2Xdp8x4xYVDUwT026oIWnD4fFAEMLaI5Mc4m6MjhxgqC8S05SpEbyKZks4JcMpz3dBp7QVw/Ylkqx+pBMuY5mHyGwWJyEPFRdjdUjaecmFjII31HvFKg6+K9d4riKE3YJiUZmwamJeAHvVfSAKZRk+gIpe4+JPWyPETz8ylcAioXouQuU1pVNgcbnvvC3aWKR4nUT+by5cs7PShS5Jykj2EicTab7WjUZVnek6g/iZ3e4Ckg5NNGyMvlko8//hhV5aWXXjqV7vSgSb26rnn99de5efMmL7zwAl/+8pcREd55553b7uczxZS33Ialg05Cw6EsruaRCZybwaaBPAdaOFh2vfYq0YqmXtlUx1THh4GI95+JGrOyWndBI44JtzxT3FEH+z54hn3wAK83LdPCYFQRDR5d7fzABqaoc8FqFv1tvcNAQYzDpLXqAPDkCk29oZyUsQIqbJAZt2MNw3fxv+g9j5EiGgnVEXRa1d14T13YLhJv2hb1iIknsg2oEeni4q1dKCrpQhFSUU5AHBbIjOALQ32x5JksJLGcQtuFULVpjzhehRHAZhmz3CI6w0lGloWqDwNUa2Uys2E5JcKgUrUwLQVcKKlJ5fI429/ndatMJ9s1/zZrmM6kX85qMYW9Gf1qM6smFBW5zId1BgXoWi4/NsfxrbhTBd3QwTFESiSuVqtbEonDaHo+n++0Jvgk9kKGp4CQHwapI9Trr79OURSUZXnqtnlw/46NoXXuC1/4wi2ODWvtHffz+emU73UbNg66qJluvJAbIRMhz0KgdPEiTMo9cgPrpWKtcnzzmM4tyck5t/cpWlVKq/guiLczE/6eDAfWKyoV4oIIrdGZMbGuL76AQOa5ieXFLiTlRB25V5q2pYxeuz5p5zu0k6DzpqoUVcg61FnECBqtZtZD060pbbBsiO9Q3yHGIF5ImycTtKhDfWiTNHzsQw8J1zekD7GwiZY2F8vLY29g7yjzPJyD80ETVgXjQ5RtpG9MJCYsBCAxe5YBWSZUXtmf7rNvDOpD+XvXeMStWR86Wg1GxjLPyG1GJXPwbZiNuI7SCHgb3CxeWFcwnQrqXehT7YOVMXXEc114fzZRpnOhriArQy8Up7BuwIliRGlEsUQd/YzxoJa3eyUSV6sVH330EW+++SZtGxYI/u3f/u2+s+KXvvSl+67Ye+GFF9jb2wt1AFnGH//xH/Pxxx+fWetN+CEjZFXts8DT6ZSXX36ZxWLB//yf//OR7P9eC53ei4gTrLV3LXb50t6U/+s2dB00quQom0ooSsGIYCU1kukwhXLuwoqjj2vOX8yo6mfIJZCo9Z668qGsWhUryqZ2QUf1imiHl4yqbpnmgollb5kIVd0wybKo1QaNuVqvmJYl1bqm3tSUuQ3WK2vCdbaBZDNj6LqK3A5/fsFKZjKHdooxgrpQSixaoWrDVN078C3SZWBiJKyCGu3bc8qOWBEgXhHrgyeXmNnDI9LFlpxBhxYFrTe9BCCxTE5ilze0i8nLoNU0dU2eZb3MEA4mmNjTM2nkuRic9ZSTCRMJNjP10Kx8kC2qQ46qFlWPrI9YTPbQicXYGSa3gTzjCuKYsMhrbgwqsD8PVYV2YUKr1UqRQqijjbtqwozDGaWWEGlnFj43MXx411/0o8ejsrzdLpEIwRX1sz/7s/yzf/bP+I//8T/yz//5P+fFF1/k29/+9n3t97/8l/+yI6W8+uqrZ9Z6E54CQr4fyUJVuXbtGm+88QZ7e3v82I/9GLPZ7JGfy50ki/sl4oRUGHI3/Oj5Kd/9aINaOK5hYZXVOkxhOyO0TrA0ZPWHGBEWFy/gVdgThxGBtadulM2xi70fwkM7yaCp2tAqUxXvHAVd8MeqkvzANkWFPjXECc6HDz+8SWknlEUO3lFVLUdHh6AOMSXz3IaCCDxMZttCEKJunRo7p8t30Tlh2pjEC5JFEcLxYEkzEntcSJQmTNrhIEoOToVAaIK4QOI5gmq7+31YRcThXSwMIRK578Ck6j8Jde3aYJyJegIgQtu5sPaec9uLM2DEhYZNvgvl/kYwc09uMpB5GDCqGnNuHvpYtzWuOuSoXiHZhMxYprOSYm/K/HLGdApdMALiM6FrPd4bnA1l3E7BNYoYZdPFVcYlVG5+af9s7Gcn8bg9yPP5nJ/+6Z/m1Vdf5bd+67dOXYBylq034Skg5LtBVbl69Spvvvkm58+f5yd+4icea9u/k0m9qqp4/fXXOTw8vC8iHu7nfrToH78y5U/e22AyWNawZ2FTK7aoEH+dtoK9c89hxOA0TFdRMK5DylC1Vy4My1XLIsvoGmhXim8cxhm8d6h3WCNU9YZplkdHgpJZpatr8szSVDWHR0sslnPzWdCBnQPNKCdZKMe2E5zrUOdwbcty1YDZAJBnhlkhkFk6Y8lstqMBCxLIUIO+Ci34jqbaUEymsZkReIkVgGYbIYcxRPtCCyCQPEK3XpFPF7HuOGb5IISuvg26u2/QrqXzLhQ7uDaWRpvYAzmOHr2WbcFvsH4GalCCG6Sp1hTlFO06MMGv3NQNRZGDc6gRxHXgTNB2C6CY0omwt9hjsciDN0093nmcNHy82lBkBcZ4XCs4W9C6CZrlUTdWrAsrxSwMrDxkBXxxEa7Te3/mhPw4Wt3eDqr6wMQvIvzNv/k3ERH+4T/8h/yDf/APzrT1JjwFhHw7gvPe8/777/P2229z8eJFvva1r91xdY60j0fx40y2t5NE/Jf+0l96oOTjgyQHv3LB8P995MkMHNUNIkd06pjkz6LFVXRjcCW0ODIJ1WA2U4zz0d2glFPw6sgmQr5nWDw3xW0Ap7R2RZYJvvHgu5iYU6xCW1ccHrSoOi7szcjzjNptENeFhjbEiNooBodYQCx5LtjSUhiLV4drPeoaqnXD5maDnQKZYZqbsC6dMWgeEnHqW9QFHRm6kHSDEA1H8k2d1npCT243n5RljTZoH8RXCdo3sUACEfBpJXIXZwJrcDMkrhSqwewdvc8hWZh6aopmqHOIpI50EsqjvYskHmcBEiJwRDBqyASy5wrmlyehxDv2HlHrcerxEmyKPreoF7LpOToNNkOvLevjI2SywtcOL4rvJmAMtstZmjl2Ijw3kVApSXhOHnfF3EmcRZXe/TSjvx3+x//4Hzz//PN8+OGH/I2/8Tf4yle+8kDHeBS9Pj7xhDyE9553332Xd955hytXrvCX//Jfvq+m8Mn6dr/rbt0JXddx8+ZN/vRP//ShiDjhQQh5Nisx2RHtjddBSyR7noUWeAOtWjYWpp1iDVR4Jga6GsgcVkIXIYtSdx2FWIwGvdcU4bzPPb9PXmTMZYq2DumEdrPh4PqSqmvZnxgmk1nIy3mH1SywSErUpeiUlr7ajLCsfdOuyLMyVAlmOXmRMZnl5MaE9Q+dw7cVy6berjMXSW9SG1Q82rUpNA0d27xHbSTNPtEnUfaQPloWAXJCBOs1EK0S9uUcGBscJL5BfRcLox2aWr0aQ7NZkU/mpDajqNC2LVlZhGpEAcTSNTU2L0KULwZTCpor5xYLbJmzpmIx2wvXK4JmPqghXqldkFN8HFC8GLTzeAwOhxiLGEtVZ+TzGVYtaxUmtbJhibY1zq3xm7dp3Yb3JxMOozvBWvvIGgbdL86CkJOT40GvLbXOfOaZZ/i5n/s5/vAP//BMW2/CU0LI3nvefvtt3n33XZ577jn+yl/5Kw/U4Oe0hLzZbHjjjTc4ODjAWss3vvGNU/3Q75XUSzg+Pub73/8+3jnslZdw6wm+Dkv1yBo0h0I8jfOUuVKgtHhyGyxwG1pmgBcPVllWFWWeB21Tg84qeGrXkNs8WNisw88tl85djtWAXUjCuQ7tHL7pqNZrbG1wVY2qkokE8ipjva/fGoclLfucPHHeoV7DiibWIoUlm5ZYY1DvaKuKw01FXa1ZrjahH4W1zLKM3NqwvpTkgyo9ovc46rfRYYGEpCHSxUrn8Ebrw7WqaljeSDtEO9JifEJsROQJmTHfBSe1EsoWbfA722lOVubYMqPCMp8vgkaUhxpnH4zdeK+UTGh9EzqB+DBb86J0jUPy2OSIuI6fEag9tfXkuUFUcI2htIo6S6NKuRbUGjK3T+OAqVBc/iz/zxV2FgY9ODjg6OiIP/qjP+q9vslGdj9e34fBWbTeXC6XD9wLOVUR7u3tsVqt+M//+T/zT/7JP+FnfuZnzqz1JjwlhPxnf/Zn7O/vP3xT+IdcNWTYcOjFF1/ky1/+Mn/4h3946h/yvSLk5XLJ97//fdq25aWXXuoN8H/0/QbfeqqVUpRgVy1+Dpnx6AZMSYiIBfCeqSq1tExsaPaTWYndikJZiBdClV6WsamPmWhYOogip9XYBc0oDSvKyRwjGfiC6cVptL4FT/NmVbHIL4bGO43SuRZfO7StMW2Hq+PUXRX1IepT9b2/2IhSV0uKbAKilMYxn8/JpzmFCTKR6zp817DeHNL5EBpnNg/e3yxDixyfDLtKbDqvfaEIsXeEdhWKCfY474EOry5GxwY7yTBljtiMzGZ4I8zLPJRJZtFzaHIERYPkSwl0SSpRB11wr6hA65YYO4v9LFIrU/CdgvjoIoG682HAaTo0E6wK1hkUpXWOEht009rjRWhaCYnRQjC58GPPhN/kcGHQo6Mjrl69ype+9KXbNg3KsmzH67tYLE6t/55Vp7f9/f0H2ubatWv83M/9HBAGjb/zd/4OP/VTP8XXv/71M2u9CU8JIX/1q199aN0IHpyQTxLxsOHQac4j4U4ui9VqxWuvvcZms+Gll17i0qVLO+9//aWC7/zfBjVKu1KMLWk3Hi0FMR12FZrBb5yjtIpZe4qSOL12ZEDtGyZ++7Oomg7rPSazaGZoEHLncBKr9xxgLB1dTPhJ7zUWkwWb26LA0yHTSVwqaILxsI+EHhPAUXXMvp0DincNgomLA3rUeaqmxXYdVhVTz5mWU4zzoQw5NZBXT+GUnHAenXp8G2SGumlYGxALRWaxdkJRKJO8xOQZxljExqWNslCDftwKz8jzzMsMKXJi4XnvY1YR1nUdVm2OPjYVQXwb5RJh1W0o7QxE8bHAxaeFkrwHStquQ6zgfBwwnGLaWOHjPa3zWGOR2qM2VODlJkPVU688+SSj65ROPTiL64BccWohF378c7f/nSWXhTGmj46HaNu2j6avXbvGa6+9hnOOsix3SPpBelE4507dnvZeeJjGQi+++CLf/e53b3n90qVLZ9Z6E54SQr7fVWXvhPsl5LsR8aPEyQh5vV73Hee++MUvcunSpTse95UfLfjO/9vgjUeaBmcVNYq1gpMG24RS3da3mInBdEInNZkJnQxyIzT1GnTCKlba5ZlSikCzJMtn1OopxMaaN0+rIPUhWixCHOjBaxdadWpIxjlVcl/FpFjUfAmFHBhLYSe0NlnETIySLek5L31J23qmmTB1HrKMmfeIMX1CD4RJ7LmxXfYZ0oKC/S/EKevjFeV8SivBVmeNkInBInTWAAbVJcYWdBmhSAS3lTvUgzeYzFC7kNRTNDQRIljvvCiils634aYLOB+aIol30CyRYo5Xj/WC99GS2CqS2744JqzcovgWnDQYMjr1uLWHPKPtgi9ZGxuW0DKKXxmYw1e/eOff2b0S2Xmec/78+Z2KN1WlrmuWyyXL5XKnF8VsNutJerFY3Fb2OAsN+WFWC3lS8NQQ8mlwL0LebDa89tprHB8f88UvfvGxEXFC2ncaANJx76fjHMBXXxb+9LuCVg0+D44AnQROUOMQqxgDxncYQFqhsT6082yV623OlULZLwwHlQtWMlGQCdp6jAWV4BmW6OXdSEHpWlQNKiFasxqb0QNatbTTUNyRVicVHxcN9S0Yg9M2VM/1q7KGZFnq10MmtL4LGkPSob3r78nWIRH/EXVhTTaM6LVWa9BpjrMaCNDa2LQ9ROTeKZ0q6jo6Ad8aMLFzk4Yo2YvgNw12YvGxLY8juEnCiTjaRskKE6J878GAVyH3Hu08ZFNa15JJuC++C4RsBNSl1aAFMYZu06K5CR0/zf/P3psHWXZV556/tfc55w6ZWaNUUmkeqgQqCY1IqF4ThBDYbevZ7bbBIE8yAd1uZGMD7nhPirajG144mAJjcOD3uqNbAX7YBPBwv5aN8R8NGL8OwAJkCQwW1FylmqUaMvPmvWfYe6/+Y59z62ZVZVZOVZLqsYgUlZk3z52/s+63vu9bISopTFxOELxHc9BgoxJjIDAG118x/2tlKcoiEaHdbtNut8/Iomhoj8nJSQ4cOHBGVvL4+DhlWb5kt4W8FOqiAOTl1kX/jZgAACAASURBVFyA3HSmvV6PG264gVtuueWCTKXzPGcwGPDMM88sqRPPspTLLlWOTAe0UkgNflBgsiihkioQsmhUMCJIpeCgH5ROIqxtx+ByDVk0RqilCA5rDOILjLQpfKBlpLZKBxIF3AA1ragkUCi0ILM2SuBSoXI5xrTq0KMawmqnHaqxU6ylYsOg3xpEpQHUGjSx6Qgo6ymlRc0fQxP+3nTMxP+IgHqCiYO+YdtcKzjUKM0qLFopwXt80EifEJrMOTBQakUS2hgMTiHD1NcZTyoaHPiUoIJooApgxaBBoMpB2/XOu4BKnQlSVvh2h1Dv/1MlSg6tieo6K3gvaFmhNosKkIFBrY226kGMc5sYM5wLk1ayW52L9nDODSM4jxw5wgsvvMCJEyfO6KZXMoLzJ4D8Mq8kSRgMBsPvlwPEy9E0j4YNJUmyLLXGdddlHD1g0YGgAw9ZQpgpkLYgxiMzBm0LoYzh6FZKklaGN8TO1yaRx1SofKAxwYnNwDnECM43DuSAGMiDpYWLNmf1KNHp1+h7JQRyLWN2s4lA6lVQ9VgM5Dmukw0FFyphmEihGvtQV+UkxtZuvKFkogbuIfLGav5Zr4EaCpKJV+BHOO9QnxSaWDlxoAkE57DtLJ5AJIGguBAiLWMMvizjVYRAlViMmPhVBTRNaqdfowCMeR6hEkhaeI0uSYcQBEJR4LK4TTaEKHtT0ciAaJ2H7AWdcWjLolWIX6GNVh6cha5CS9i06dyvmwthDEmSZBbtUVUV119/PdbaIT99egTnqNpjKbv8Jicnz5ivvFzqogDklaIsVqIjbswhi3mhl2XJ7t27OXbsGNddF9dDfetb31r2/Rpfa+hpQGcMlCXaEnRQIamJmzgmA5JaJFN80orDJGWY2+CDhWqAS9Kai42uPXwJNo0ZFvU+OPGRpPW+gtplLQpeYlqbWCF4QawSUMQbggbECIWGyP2msZtWFIfGxaARyiO4o5TEE56EuHmjMdg1VDGAuCoOxBq8Dh6xdRaGxOAiVRAbZWNNjoXztdwOEPF4NXgNtFxzUjFQhz4nXuKajnqfkjM1PeIDlXp6gxlsK+b5jolFaqCuArWpJYucM3EYGQRCWRHSNriABkFF0DJH01bsqptuOTFoFekKnInuPxtXvohNuOPWhb2tL4TiYa7rbLVatNvtWcDZRHA2tMfBgwfJ8/yMZLdzrYianp7mhhtuuBB3Z8XrogDk5ZZzjiNHjnD8+HFuvPHGZVETi1l0WlUVe/bs4ejRo1x33XWzFqZC3VEtA5SNMdx4c2DX9xJCX+LOHudQG9CWjYMjIzGDt4zNoQuRLpWgSCr4QY5Lu4iJoT2qgEli4I7ErdjAMAujVFOH+0S5Vk6gLYZQhuhWy0u0lUZTR52VEWEuds1aFoQkoSJGfUZCNQJrGXz86K+KrcOG1DRqhVqqpzGljhEdtw+RH4+0R8yL8K0WSe0m1Pq2VkSmRAAtSnyWURHfJGZ4PCUISDFA2h0UpVBPx0QZmzEG9Q7bXYUFVOOwLviKgYArKkgyWlphbBofbAxBFa1PilCfmIxC0q5jQOtH1RtwEgG6DJFKSTOYBllluePuhWvpX2rW6dEIztFtH/OtiBoF6bGxuNHlJ5TFi1xLBa1+v8/OnTuZmpqi1Wpxzz33nHcNMUQg3rt3L0eOHOHaa69l69atZ7wxjDHLtrY2x7jngdV892+PEqaOotKGdgzD0QBSavz4SwyCp8wJrTZiQSpw0sI4h1hbz6p87KCDoCYgLioCmvB3QgBXUQJG4/CrsiZy1SEaSXrO0LXRNo3EQZTXEMEmTSNo+oCv6QStk9cqlLQ3TTU2RivErrWoHC1rQQNNxLyvh4JN6lsp0A6xC41PkqGsh4pQr0uSqH0OcfIGWUbQQBWUVoBQO/hyVbpG8FkWddjUIUzBo/VJoSg9aWpxJu7Lw1gUS4qQttLY+QbFB0WrCud8rT+22IrarJJGC7iFqPgQKEogif/O8+j8MSAnQFYZbr1v7niAs9WLAchLuc65VkSVZTlUezz33HP0ej3e/e53Y62lqioGgwG33XYb11133YKux3vPq1/9aq688kq+9KUvsXv3bh566CGOHz/OXXfdxWc+8xmyLKMoCh5++GGeeuop1q9fz+c///kFX8e56sI+Gy+R6vf7/PM//zPf//73ufzyy7nrrrtWzEY63xon5xw7d+7k29/+NlmWsXXrVq666qqzvkBXYoO1MYZer8dTTz2FmdiPyTZgxtpIO4bk4AStQKcHaGXQIqC2Q6gqQuXxXqMcqwp452tZsOArxQXB96uYKFbF37nKkxclRV6RABpiFnCvLDlWlJwYDJhSoawCuXM4H4HM+MDAxW7Z93oEFxW/HiWEOOwLXpFgcFlK6RXvwflApYLzAa9KVS+Va/7GKfh6w3Ol8W+8V7x1iFO8Kj6A9xJpJheiyaTyeK0bUA344FEfdceq4F0VTRxBo3Y4xL2ETj0Oj7EWHxRfxdvlXP3/3uMRnPP4YAkkqEmRINisgxBzjoOH0OsT+gVhqiD0C/TENOosWgAzOWiCoMjAYNqGjbe0F33yvhAStLPVSrzPRIRWq8X69eu59tpr2bJlC/feey//8A//wJVXXsmWLVv4zne+w8c//vEFH/MTn/gEN9988/D7Rx99lPe+971s376dtWvX8vjjjwPw+OOPs3btWnbs2MF73/teHn300WXfn6b+q+qQmw3S/X5/1uJS59yKLCeFs69x8t6zb9++YULUfffdd843wkLt03NVI+YHuOWWW1izZg0/+tEJZr7v0M6AYIGyh8oYSAaFjxkQdY6DahUlaU7RjkCvQLrtaORQwES+MlQxnhLvCAg2TWpTQuwMrRgUQzuGC+NUKfw0/bKNq1c9icT/VEZIrY0h8wimzofQWnnhUTAZLgS8VfCRV1ai5pd4cbTO+mmmeqEekg3d1FWGM7W6A1BCo7DDmkgVGO/pe1+7uZVg44LXRBWfO0wrQYFBCHSI1E98smsapTZ+aIgZGVpvVwlDrXJNlwQXd/KFuHUlqkcMdJJ4P9TGvV0mhdJBPyDeRCdjWWDG2tg1XdavX7zZ4sXokM93ZVlGv9/nV3/1V2fJ8s5V+/fv52//9m/5gz/4Az72sY+hqnzta1/js5/9LBCjN9/3vvfxyCOP8MQTT/C+970PgDe/+c28613vWja92NRFAcjnqlGH29mMFSvRjTY12iF773nuuec4cOAAV1xxBVu3bl1wR7KQTOSz1WAwYMeOHfT7fdauXcuqVauGfNorX7mW7z9X4I4WSCtHMxvT04iqBbUBTIhL2HyJtrO4064EMoO6CjU1mIS41kl7A0JmsFmKJCYKw0JcKoq1iCiGaAxBIj3Qdgl5apmwCYrg1VH4QBECfYUwyJEkGiNaqcUaIRWpKQHBeYevN06rKs7U7jklWraDi6BXpwspipO4sFUBHVSEboqvZWyiMbzH2thR0y/RTgsJEsHfRI5d4yI8bJrh6uD5KEoJ4OvhXnDYkNXXW/PbYtHSxSvQQLO2RBUogFZc+6FVFTllVSjq7bW+gkoQskjwpwaxFTaJFJNNDaw6wtNP7yKEMCuTYi5zRlMvRh7ySjhZz1XT09OLduq95z3v4SMf+QjT09MAHDt2jDVr1gz57iZeE2ZHbzZ0yrFjxxZ1ApirLmpAPhcQN7WS2mJrLWVZsnfvXvbv38/GjRt5zWtes+hp9lL28+3cuZPJyUk2bdrEJZdcwv79+8/osm/7qcv5/hcHhL4jSIlaj0ordmd1d4ypUJNBP8RMnbIG6eAg1Uh05RWOQNLKMLYO3HFx+iZW8d5iNI/dt0DhA21by93SDpSekOowmCeVJOoODIikePFMi6HykFcBrcN9EMHnYMaUxMRELx9xss4UjhRCDLqv5W4evKk5ZDXx/oUUb+LQDVUGITCmcUQpaVSbmBBpjiARRAuvtClw0qobcMWo1NE/gkqBuCx26w3/HaiT5kzTFNOcPbSIABu3pUrcXptX0MpOGWLyEqQTpYquQJIIyKYnmM44r3zwquFzO59KYRSkx8bGSJLkgsdvrlQXea4KISzq/falL32JDRs2cPfddw/D6OeL1zxf0ZtwkQDy6Q/GQoF4pSuEwNTUFMePH+eaa65ZEhA3tVBAHpXM3XDDDbMiP40xVFV1xt/c9ubr+cFf/gg/HdCuJ0hATQstFU0HUKV1SE5NWZQ1CBtgMsdZJckSbJrEj+eDAjpZVFpopAwEjXxnS8BFCVuMDdaYjxwUH2KSmUiUcA0U2lbwxUloraYrUVYXgkFICApF8OTWIZWPWuegEexEsMaSGCELUbdbN7QETi3+1Nocor4Gy5rWMBqBXX1ATIdQgQtC8Io3UtuzBT9QpBPvxsArHStD3Z0bKEmmRDG3Dk2Jmnto26iIaKiNAPGP9FTQUVUh6VhNXgviy8gVS0B8gSSChAIzU2HsBK/4uatmPa9zqRRGMykOHTrEzMwM3nvKsiRNU9auXcvY2BidTue8vk8uVBbyYrvwb3zjG/z1X/81X/7yl8nznKmpKd7znvdw8uTJoSpkNF6zid686qqrcM4xOTnJunXrVuT2XxSADBGUp6en2bVr1zB8Z926dYt6gS31DN4E4u/du5dOp8PVV1/NjTfOEyKwgDoXIDvn2LNnz1CpcbpkDk6pLM5Wr3zrJn78mR8S+lNIp41KTsgmUGfBRj5TjUBZ1l0zVFqRJEJia76yJG4hTTIoqshB28aAAcEkmDKAjbBXBcHagDohuIJc27STCKbBK149FQaS8WjAUMFK8+E/Ou8KF6de7ayLYuOgDaXygcpFDfDkTEnWDTE3w8QzSTuRuKcvAJohmFOpn0Qlh5PY5UsSqFy0fLvabyEajSSatRBvsAoJccBpDHXAfVqHHLmhcUURSIl0AxLXPqEwVUK7FU9itV4vBMEUDoJFKOpPGzUYG8G4gAxmMIxz+YMbFvxamiuT4umnn2Z8fJxer8fhw4cZDAazHHdNN71SYUAXYltIA8aLeR9/8IMf5IMf/CAAX//61/noRz/KX/7lX/LLv/zLfPGLX+Shhx46I3rzz//8z9m6dStf/OIXeeCBB37SIZ9eP/zhD+n1etx4442LBmJYmsxsdEXUJZdcwj333DPMmF1uzTXUawaEBw8e5KqrrjqrZO5cx4DIfY0/sIb+383gdYqQdZFkprbjKmpBS6VQCNM92p0WmYnpY1oMoNWunR8AGjdotOxQE4zUUrFejk7Ey5YaSFWjBtm2EefxYqJyoTZeBB+ZWVWHmgQvENQgUne0KlS5wWWR/w2qWIEEQ2JBNcGngVbapvS+VkFUzFRDkhnUYKyQ2LgQFom63iAB0wcdO+Xc0+Dx3lJ4aEtAJWZZlBClfzVNrL0SxixSxVwLpyGmzvUcdJL6QjKMJCWNsW1SD/2oHBoCRgOkIJWDLMG4IoatVxWmGmBcht06vuh4ydOreX9s2LBhFkiOan6PHDlCr9eblfDWfHU6nUXzzxeiQ+73+4yNja3IsT784Q/z0EMP8Yd/+IfceeedvOMd7wDgHe94B7/xG78xbPo+97nPrcj1wUUEyDfccMOyQrUbt95CXjCqyuHDh9m9ezfr1q3j7rvvptVqASs3IDz9OKPbUDZu3Lggpca5BoPXXnst226dQp4ZEHyfkGURiBNDKGbIc4uzMJ6l8aO8uHprc4oOihgGb6h5Xwv9nCptkUrcv+wN+FaKVBXBWATFS+1PE8H3gfHIz2odzVNB7IenA6yCvFKy+lWq9bJRQ4HTNs0sTbVO+6u3iXgxOA0IhkQMQcAksXPyrqz5bkdVKVWoozBNDBAyOsD4iZhjpwF1SpXEa6+mPWY8gpALQisy26goPoW2kzjga9QhKJoYpKiT7QKIBkJVYkzdHfuAUEJI0NIhLYu4PmIyjHMQSowXpJrBVIq9fh3Xbb5uSa+p0+tsKou5NL+jCW/PP/88g8EguhBPc9DNt+ThQiW9LXagN1r3338/999/PxAx5dvf/vYZl2m328Nc5JWuiwaQu93usmRiDSA3wHq2Gt1evWbNmllA3NTZZG9LqQZMVZWDBw+yZ88eNmzYsKhtKPNRFk3d9NpXsf1fvon0jyOhIlhHv/DYAN11BjkRMN0oWWtmfqhQhbijT72lxMd8CQD1OBG8KMFEk4bJFR2PFuESIZHYJUviGLgkfl9bOsp6w4hKAS4uO/VVLWsT0BBFdJU7lVxR1ZK3pjvXCqoMGn44ZhTFoKKgSeRi686cevGrqkIVcJrBTBFVJHVUaI6LtETLYiqtd/fVzj4CMhOgnVDhkRCHfCYo2vdI2+ICtDQar8uiILMtxFVoHb4vxJ14WjhsJ2ZdWHGIz5GQYKoZZFBi2pdz3evn3vO22FLVBXW5cyW8ee/p9/tMT09z7Ngx9u7dS1mWZ3TTTXDQhdgW8nJ26cFFBMjLrfkiOFWV559/np07d7J69WruvPPOOZemzmcMWUwZYzhx4sRwUes999yz6BVTCwFkgM2/9a/Y/qd/x6D3Aq69hlYmJHaM4DzBlBQldNoJgX6UX2Hq4UmJSoZBCaHCY0ArcjVYo4Q6NEdNIORR8hapidjNBkmgUpw9RXNI8zfSgTIO/PxwpXP83gRBqjDMl4h9ai09loCvlLRqJA2N9drVCo2KJEtjaE8dXBQD9eNJwdgUCKAZhAp1LsZx9isSbPwbG/cOVkFIjcVTkZS16y/iOi1R1NbLYVVr6iVeXwi+TpUDY1yddyRo6amc0g4W5x2toAQ3g8mnMMklXPu2Oxf1/J/vstYyMTExa13S6Q660eCgxnx17NixYTe90kPEpYTTv5TqogHk85GJrKq88MIL7Ny5k/Hxce644w46nc68x1luh9xc5+7du8my7Jwbs+erhQBynufs2LGDmbsmWPNkD1/mWCw+CfjQAZNHaVflETHkPidNEjDCwCuJLQhYykpJshB3xSk4F+qQNSH6NOK2C8HgRSIgSsAVnqSTDOVgxujQLOJCIEmklqrFOE7V+Kkh5M3H3yaus3n+BV84JIn/rh/V+v8Dri+kErvxeInoJhSBsgi0WlpfPFIZogYtBKkyTFbriF3s9lFlUOZ1znTAqY1Ku2AIJuCJ+cWZEbyACwWtJCFoiXeQJI6ghsIHuhi8n8FUHdRVpCFQuZKkzIE2a95y25JeAxe6Ggdd46Jrqtl7OTMzw4kTJ3juueeGKo/Tu+nldNE/AeSLpEYBWVU5fvw4O3bsoNvtctttt9Htdhd8nKV2yCdOnGD79u20222uv/56iqJYMhjD/IBcVRW7du3i2LFjw0ClPVfuofhP36BQQwgJiQEfPIntUYQ2iTEYo1Tq43DLKI6ASoKmppbTGlRKfElMQ0PiiqgkICEGD6kXMAExltQqWsTN0dGxV4cTiVD6gix0Ygdcb8iOscdK6R1pEs0YUcsQwVkRxJloZmlCjhj2ynhRTAmncpSbrOWAd7ZeKdVsyg5xx1+w0Y1YelATuV+J2R5iC4xv19rngIYSQShCqDljS5kIWMEaxWsVb5GJW7XLYEgCOC3wocIWKYXmpGXAhgq8xb7xupc1yEB8LTZqjyuvvHL486abnpmZYf/+/cNlo4sxuIzWTyiLl0itRIdcVdUQiFutFrfeeuuiJ7ZL6ZAnJyfZsWMHxhi2bNnC+Pj4rI96S62zqSy89+zdu5dDhw5x7bXXctNNNw0fu+uvv57tr96N+fYefDDkSYWKoSwz2jZnYAyJSXCmRKSFGnCiYEqQJFqbrak/1YeolhAbpXEOCtunRTvytwZEHYpS+kBm07hdOSjqFZMaWsbFxagx7gxszE4utaJAaVcJp9wWNe2BotYhVcNL15psiQtBrW+A3QwXiEYXhiGlD64NwYIJqHMoHjElhrSmVE5tBEEigEpaa6mNIpripSQxadQTh4C4QDEzwGiKq7t11wlkYjAq2BC5c5NW9N0kY16pXIFUgeymDVwzkq/wcq6zzWiyLGPdunWzdLynG1xO3z5yusFltH4CyBdJlWXJvn37WLVq1RAUl1KmSfhaQPV6PbZv3473ns2bN8/qgpZqnT79tjTHGFVpXHnllXOqNDY/8AD/8r2/QPIpWmGMGdtHdTVeW1gqQuJqXrcCm0WKQWLShDX11grvOTnZpystJDWY1IJYsk7AGB/pijpwPqiAieMxixAkLj4VINOMhvDAalQoBCJQtdoYcRCE4MEkkc6IHLOPjrYmByOuz0YQEjtAQhuoJWaGqBnWQJssSiFMBN7gPCEoZccyJj52yRWQxrS2HE830WHXHoP9lQQQV9KsDwzi6NoWDcesvohu6cKBKH2XY4wQXIWTlJ7PaVWOxK7mun/908t6DcxVF8LCfHotNH95sQaXJtT+X/7lXzhw4AD33nvvgm9Tnue87nWvoygKnHO8+c1v5v3vf/+LkvQGFxEgL7VDbrrTsixZv349t9xyywrfsjOr3++zY8cO8jwfahlPr5VKe/Pec+jQIXbv3s2ll166IJXGlvf+Ot/7wH+gX50keCVNJ6l0DDFK5RNMkqJSYYIiRlAMpXGkYiknHXYiYd2qDkrsGr1zMXx9EKjUkSSGYMC2LCaztI0QtELUYiTEhIm6iw3BYYKJWckQf156bDYFOlE79QJB45DP1NIyCQ0XHMFfTMwxTpwDG4auPfEgNZVg1EKltZIEkLiRo9319TAzRDobgEBbtd5/F3M9BCiqkjZJHf8J+IChPjZ1fjEuDiatElyBkYTEBUpf4EIB7iQ5HYrXXsuzzz47qytcKZPGixEstFzZ21wGl8FgwMzMDN/5znf4+7//e/7mb/6GT37yk7z61a/mE5/4xLzHbLVafO1rX2N8fJyqqnjta1/Lz/7sz/Kxj32M9773vTz00EO8853v5PHHH+eRRx6ZlfT2uc99jkcffZTPf/7zS75Pp9dFA8iLrampKXbs2IGqsmnTJpxzPP/88+f1OvM8n7Usdb6lpcsFZFXlxIkTTE1NceLEibNK9Oarq9/5Vnb/+8dBC3IqxnygSDKEAtUOxsBAe3STLBrNqgqfGdrjtWHEVcxQ0pJWzJxog8dSUGBNGxyEqsT3BaceLZSkmyKZwWYSaQMcJSVt6UR6gag3Ds7TkhSlQg0xB6IGZK3pC62phUAE0KYfNDYB8dFkIhBKxWTgKTFkqIZoSkHQ4HBa0HJdlGhBt/U8z4c+KbHTlhAHfCh0RKN2uO5Ac1/SRhB1EAIDLelgEe+jl1wVtKIKMwTvWKMJnoxLHvoFrrjiirMGs7fb7TNMGottSF6scPqVlr2JCN1ul263y/ve9z6OHTvGI488wi233MKuXbsW9PfNp+GqqqiqChF5UZLe4L9CQJ6enmbHjh1479m0adPwbDs5ObliEZynV1mW7Nq1i+PHjy94aely4jdPnjzJ9u3bybKMTqfDli1bFn2MdevWcfDnfxrzxBdwGApypCqjk88HJMnoSmBQDDBiadk0YmIoo9wLQ1vAaxEty7WFORPBu4rUStz6nAgpCf3uDJYM7xxlT3F9j2RCYR0mNZjMxDVIBMRr3HkXbRmNzoJ6ixKGKg4Oof499V5o6mGdr9nlEHlfD5WCxSMhoBojQKEOr/cVJkiM8ZQYo6nqauBuFqUGBt4xXgfdx5BkSMVHWZ0Ggne0hZiwF2JwKCHgfZ9ElRn3Arl2mLj3nmGa2KpVq2a58lSVPM+HsrIjR44wGAxmrTmamJg4K786Wi/HDnkhNTU1xerVqxkfH+e22xamTPHec/fdd7Njxw5+53d+hxtvvPFFSXqDiwiQzwVwvV6PHTt2UFUVmzZtYu3atbN+P58OeSm3JYRACIHdu3cPVzS94hWvWPCZdCkccsNJhxB45StfycTEBN/85jeXchcAuPX22/nmX3+Z0k+S6GpKA2iBSEJeRM4Ym9AyXdR7QnAUWpFpOszOqbQiNS3EmKjGUChxmJDWEjiHiKFDRqAiEYFUsassImCxsYOc9JGrVkVDBGyfBFLJ6pyLCJhGImWhpqrzjqMCI6gn4EFtnY8RKQvVSGWkWnfIhKhZRgmVR80MVKvwGrC1nqP0cSCHlpFXxlM6YUzqv1UlEChdSacOtQ/B49SRYBFVCt8jIQFfxi0j3mN8jzRZw82vf+Ocz4mI0Ol06HQ6XHrppcOfN5bn6enps/KrzVezNPTFCKe/EDv8Jicnz3hvn6ustTzzzDOcPHmSX/zFX+TZZ5894zIXIukNLiJAnqtGk982bdo05zbalQRkay27du3i8OHDXHPNNfPmTcx3jIUC8lBLPDPD5s2bVyx5CuCK3/gVdv/H/50p/zwZqylCjNQUUdqyGoIw46boJF2QgBVDVRb1Yj5DJhbn+tgkA6r6Z0pwcQMzxkT2VSAExZhkRFMMiQhlcKTtaL0Gocgj2PqqRIInlPWy1cxgxWDwqKQ0/XBjHAlaRRCUmNxWL2wiBLBGCFTNDlMUJQRHGhKQIorgNK6Fcr4gkTTyxhq1186XZJKi9bAw+IJUDB6wqpS+IpUEHwpCKLE4QhhQEf3fqjNAxp3/5veX9DzNZXlu1AoNUOd5Plwy2iSbjY2NXRBwvhAngeWoLNasWcP999/PP/7jP74oSW9wEQHy6WepZl9ev99fUATnSgByCIHnnntu+KJYTCD96bUQU8coFbJp0yYuvfTSFXc+GWO4/Jd/k91f+DOO+aN0pEtq2liB0k2T2JSMBFflYC2BQK4lnaQVqQQxuFBvFZE4AEQEHxRr07hRo862qHxFaltI7dirx2KkCmgjGBPEeEywZBqT1qQVoTp4j+JwriKatIkpaaYZwzmQbHhcIaAqVKGgZdJ4QpB62KeCCS52zGJjgH19ImlZYoB/PTAMoaIlBh9yossPfHAIgsUw8CUp4CkIwSNa4IFB0BgvrTM4LRi7fe7OeCk1yq9u2HAqHa6qKo4ePUqe5xw4cOAMtPioYQAAIABJREFU7e/ExMR5cdJdCEBulp8utJ5//vnhsHAwGPCVr3yFRx99lNe//vUXPOkNLiJAhvgC7Pf77Nq1a0GDs9FaqM34bDUav3nZZZdxySWXcMUVVyzrxTffbXbOsXfvXg4fPrxoKmQxpar0ej2OHj1K+86fJjz9N6AJeRiQqcVKivMDjBhyAi26BCwtSSjLArEGkQRLoCyjukJroFWEoLV+VyLDm2Hw1QBjkiFkItALA8Z0jEZZrCHUwzyP2FArkGNWhCAkKHZo+FCCq/AEyjAghAwxESiNiZuoTRCCKevjx/44BOiHGbpkOHHRdlIvMzUjsZ2oUvkcMRmhpiS8K4eB9EFLytAjEUtQRxECmShVkHjyCCUFPS6590E66zau+HN4tkrTlG63y6pVq9i8eTMQX8P9fp9erzenk25iYmKYS7HUOp95y0uR8h06dIjf/M3fxHtPCIG3vOUt/NzP/Rxbtmy54ElvcJEB8o9+9KNFDc5GaykvlCZsaNeuXaxfv36YN/HDH/5wxVZCjVajJd63b985ozeXWydOnGDbtm2ICFdddRWbNm3i/+2/QO/HX8doyUA7pMbhQ0LHeIxA7vokxhAkIWjA0AY8KoagjuCiAiNGNwg+eKw1eFEEE5XIwYMNMVQeMCK0ggUtT0VPhArUk2vOmHaxUTUcczAA1CEmhZojFgwJAatJrRkOqMYlroKn0AFp1EJgJA4ANSgtUbwWWBE8BtFAFSLPHT2CMejeikG9i0FIWhC0rF16nhAqMglUYUAIKQZHEYSSEtWSginWyZXc/do38KMf/ei8PJdnq9OHeqM5yKM1mkuxd+/eoVmpGSA2X4vNWTmftZj38m233cbTTz99xs9fjKQ3uMgA+YorrpjlPDtf1eRN7Nixg9WrV5+RN7FSiW+j19doiS+77DLuu+++8zYc6fV6bNu2DYjLUaenp8nzHICfeujt/Of3f4M+JyMEhgwrGXmwpBKXfhYhYEVRPM5VqEkQsYhYCjcVHWwkqAhOHS1asTMVg+DIg6NNQtzEF6M0DYKrNG4PUUW1inxugGBiYCcw7JSDFjUQQ1CPaZTDmmOlXffZYFQxItiQYaJjg0Cg0kAZKlIRjCpBkgj6QbHm1NJSVUcVprGmEzM2CLhQYMREblsDoaZFXABDScCRa4WQY8lJMbzxsfeT5/kF2WrT1EJVFnM56Ro53rFjx9izZw9VVZ0hx+t2u7Pu0/k2o+R5fs6smZd6XVSAvHr16mVFcALn1BQeP36c7du30+12uf3228+acbFSiW9NytyOHTtYs2bNkhLfGsXHud58o4PBm266aTip7vV6sx7TN7z3T3jiT96OZZqSLlZzUtoEtYgkFJrQkhC3P6tiQhimuHkFwaGYCIQklG6GxFiib8+QIXgXotxMoN51RB5yWtqOyRVaoZqRhDioq3d3RKs2Hq8VNkQCQ2vdBAilVrQkG9IhSoUPKamcMlkL8QRQaR+j6VA1Uaqn0h42pPUlbJ1pobjQq9dXRf1zUBvNMsGTCRRaUaonxZNT1SqOAkef+375j4ALL0NbDp9rjDlrytvpmcn9fn/ouhsfH8d7f163hpw8eXLZwf0vdl1UgLzcapQNZ3vBTE5Osn37dpIk4ZZbbpnXWr0SHfKJEyfo9/scOnRoTuBfSDXc+Fxvduccu3fv5vnnnx+GDI2ekE7n1letWsUtP/8/89TffIA2FSVtYiKFpasJIilFMHVIkCGoYMVjJcZalr6K9KoKgRyngtaxlg1tUWlOajo0njgVgTAzTKwIWsYtIkBwAlJGtQQRVB0FKWbYCTdgW1CRktf3JN4nH/okJhleUjSgCgk6NIMIBaKBFpEGCVQoOUWIcaRR6ezwGkgQLG08HksEcq8VUoNxgcdQ0GPAZZt/nk2bNsVrvkALQJta6RPAfJnJvV6PqakpvPd873vfw3s/q5uemJgYyvGWUy/3HAu4yAB5pSI4RwG5MZKEELjpppsWdAZejstulDIYGxtjy5Yty+oo5hpWNoqQ/fv3c/XVV3Pfffed9Q3adNijddddW/nB97dyYu9/YYxQA12LSaCjbUKzRE8slpRShUSjHtgRMEFqQiJgSCi8kkgM8FFx5BqQUNQsclQSexU8/Qi4Con0CBi8UnO8jVxNCJS19WN2JeriBulTKmQqjSl02uyOVig1kAnRQYhipRUBTE6ZUIIKRidQ8ZErJjoLKypy7VFQEqOPQr0ftmKAJ6GgT45ljF9882/Oej5eLh3yYspay+rVq2m32xw/fpzbb799lrllenqaw4cPn3U79vj4+KJu48s9ehMuMkBebqVpOuxsZ2Zm2LFjB0VRsHnz5kWJzZMkoSiKRV33YDBgx44dDAaD4fV997vfXTYFczogj66f2rBhwzk3Y88VlvTw2/4X/vTffYMp7dOmSw9fD8b6WFIKwKqNmmAgEHlksFQBEolvtCYakzo+UxQy4paNJidD6t86L9H2rAWVjCESKFVIqW3VdY/sNRpOqOkKg4lduEqMGNIw7J69WryEWl3RKCwkbj0hr80jllIh0fokK3EiL822ETylxvAhid+R1f8aUBCj/UsCJTkl4PjZB9/PCy+8wMTEBFmWvSgd8oUcxI2eAOYztzSUx8GDBxcdxXny5MmfdMgXUyVJQq/XY8+ePfR6vaGRZLFvlCRJFhydWZYlO3fu5OTJk2zatGmWTG8lAoZGLdjHjx9n27ZtrFq1asHZFvPJAd/6Pz3O4//Hr+I1kJIwINADEpIaIg02CswYYEjVYkhwGDoaE+BUY85bhFI77HJVFRtOfd+MxDIMleYYWtEBpwEnpzpLgQieI09ZINRZF+DV171wBORSYwcbgVWHhERQGV5OdYARagJD0VDVnwI8Bl93wxaPByockKIUDFAsOfHkbCgJUnLXHb/Hxo0bZ0VLisjwZDm69uh81YXuyBeSY5EkyVnDgxo53ujjlSTJUC/dPF4/oSxeYrWcDqMsSyYnJ3nhhRd4xStecQaXuphaCJA659izZw9Hjhzh+uuv55WvfOUZ17dSEZxTU1M8++yzGGN41atetaiM5/niRC+77HJue83bePLJ/4sOGblWtWqipEUbR/w+AFXMrYR6xHYCT6ZpPURLCOppkQ1BuY9nTOsOTiJYW/VUWLwKJYNIHig1WzsSQo+nUsvooxnwiDYrn2raQj0GS0l9IEKtyrC4ITSDw2Pr46l4lLLmveNzU1LgahImZ0ALSx9PiSNQopSIOE5QsJY7+Zmf+TmAWWaNo0ePcuTIEYqiGGZhN8E3C82nWExdaOv0Um3TzSLV06M4R+V4zz33HB/4wAf4wQ9+wPr160nTlNtvv50HHnhg3ut87rnnePjhhzl8+DDGGH7rt36Ld7/73Rw/fpy3vvWt7Nmzh+uuu44vfOELrF27FlXl3e9+N1/+8pfpdrt8+tOf5q677lrS4zFXXVSAvJSqqoo9e/Zw9OhRxsbGuPbaa2c98Uup+YZ6o9ztubTEy+2Q8zzn5MmT9Ho9tmzZsqTu4Wwc8mj97Bt/jW8++UWO8AKrpUOgpFCDJyclYZoZUjLAUtHH0KrphUhl+Jp7LfA4qnqwJ3VXHTvhCKQwwNPRBI8bniQG+DhMRNHaGuLwRCtHfR8IFDhaI8Adr9vFbl5PPcaOElOfFFzcnQ2cisBHA56KaNAO9eDPoFTEpU2BHEevdgomUqEEBlR4lN9/7KNnfRyTJKHT6XDttdcOf+a9H+ZTHD58mF6vh/d+1kf4hvJ4qae9rfQJ4HQ53l/8xV/wkY98hLGxMTZu3MhXv/pV3vCGN8x7jCRJ+OM//mPuuusupqenufvuu/mpn/opPv3pT/OGN7yBxx57jA996EN86EMf4sMf/jB/93d/x/bt29m+fTtPPvkkjzzyCE8++eSK3Se4yAB5MS9K5xz79u3j0KFDw7yJ/fv3r4hc7Wyyt1Et8eWXX35O7haWDsij65nGxsa4/vrrl/xRbq4OeXQb9kP//R/xqf/nnRQUKAYrKT0qUtpY1VqDYevsiEBct2TI6WNIEWxtLQ7Y+hIOyPF0RnffESgwdX8bM9w8JRXZrBGeI3bScCp2M8KhraM4IyQ7HKEG6QZy+1S0SRECLvbaZGQ0fsBQ38coXYvXnta3bYaSBIOT2F8HPL7ulKdw/MYb/3jOx/lsAGmtPWva22AwYHp6etZH+DRNhx/hJyYm6HQ68wLuS5GyWG71ej22bt3Kgw8+uKDLb9y4kY0boztyYmKCm2++mQMHDvDEE0/w9a9/HYjRm/fffz8f/vCHeeKJJ3j44YcREe677z5OnjzJoUOHhsdYibqoAHkh1XSoTUDI6OaMpQzjzlajHfLoxuq1a9cuSku8WEBuFkkeOHBguJ7pxz/+8bIE+WfrkI8dO8a2bduG98day4PH381/+i9/whgJGSUZCRUDSmkzQ06bLgmC05wuY4Sae22TQJOuRkVCCzD1IK4kCskiOMYuOccGS2UioxuBMtSXj510RVnL0U4BuaOEIXBrfbmCpB4JUkvXkrgLpU5Urqgo61FdBGxHjtBCCHhyDCm5eCoKAgll/fNo5K5wBI7j2LTq9bz61ffM+TgvdKg3mk9x+kf46elper0eL7zwwlADPBfl8XKhLBZTy+GQ9+zZw9NPP81rXvMajhw5MgTZjRs3cvToUWB29CaciuX8CSDPUfO9oEfzJi6//PKzut2SJGFmZmbZt6PpkBv7cbfbXdDG6tNroZnIp3ffoyeZ5eQqw+yhXq/X48c//jHWWm677Tba7fYwZvT1r30TX/nO1zg8eIZxiUGWVmPWsScwYBBtH1IBeT3uE5z2EWIQkaGkwiAkdR/sKOkhtGo6IpBSUZhQAzcoFXnN6TagVhJqoLY0PWCoB2tNsBBAST4E26hTjiYXJeYcOwpAKWultZJjyAjiatiNHXG8ZFxu6umTkeEZMBBloB7B8m9++9/N+zgvt2PNsoz169fPSjNsNMC9Xu8MymNmZobJyUmSJFnxEKGzlff+vKs6lgrIvV6PN73pTXz84x+fV9Z6vqM34SID5LPVqMzrkksumXeF0UpFcPb7fSYnJ9mzZ885TSTz1UKGei+88ALbt2+f08m33MFgk537wx/+kF6vN9Riq2ot/ZLhi/J//e2P8T9+9AF6BDooVjp4ZkDHUAZUJEDKgBlajGEx5DJgnKQWvWUESmw9IEOTurNNaCI0j4ecrokbPGL3m1DVx2s2hjgGNbVRoZVDrMWbkhQZ2k9ilZR11xx53pxOwz2LklNgaJHUQfjT9e8Vpaw77oKAY4CQYShBPD0dRKpCA1MB/uAX/uycj/P5kL01GuDTIzn7/f7w+Tx69ChlWZJl2RkhQi+3pLelZCFXVcWb3vQmfu3Xfo1f+qVfAuCyyy4bUhGHDh0aDl+b6M2mRmM5V6ouWkAepQrWrFmzIJnXcgF5dFdelmXceeedSz4WzE9ZTE1NsW3btuFEeS4n33JS7JoN1SdPnuTqq6/m5ptvHnbEInJGR9dut/n1NzzG//mVD1GK0mFA1CxUGGkDFYYU1NPHYUixGPoMMLSwCANmGMPGsZ4Iffp0SHDq8EHJbIXWBmyoUAyeihI/ZHkNJZ7o9DNZWqs8SpqIeXWKCwNs1qkFec3/ShwdtO6bB5S0SfEInhLB0h8ywzPAeLRsS7xfpfbx2qaiz0ChF+DetW9c0J7GC8XpNqqFJEm44YYbhp8SR23PC6E8FlsXgkOemppaVIesqrzjHe/g5ptv5vd//1QOdROx+dhjj50RvfnJT36Shx56iCeffJLVq1evKF0BFxkgN2f0Y8eOsWPHDsbGxhZFFSwVkIuiYNeuXbO0xN/61rcWfZzTy1pLVVWzfjYYDNi+fTtFUXDTTTed05m0FEBWVQ4cOMDevXvZuHEjExMTXHrppXjvhx3xXN3Tf7v1v+MLX/nPHAs/BqOUZGTSx+oElhkME4h0iSM7S0WC0T5CWlszEgbEfApTA+Fk2aedpRhrCCTAACWj2ZWXA916O3VUEnsaXjo69+LAMKk7ZE20ltcpRVBUHKUrMF6RbEBiDFJ3wP1ajezIUeoQfjzKeARuzfHawVPiaVNqSUlCHhxoxr/97f9twY/5i2mdbrVatFqtOSmPQ4cODXNNTs9NXoie/UJwyGVZzgr5Old94xvf4DOf+QyvetWruOOOOwD4wAc+wGOPPcZb3vIWHn/8ca655pphutuDDz7Il7/8ZTZt2kS32+VTn/rUit+HiwqQVZV/+qd/wlrLrbfeuii9LSwekEdzIObSEi+nrLXDIWMTRn/ixIkzDCTnOsZiALmhQNatW8c999yDiHDgwAGeeuqp4cS/meLPdf1//Lt/wq9+/F9zEqUtAzwTQCCTCSxh6OATKqwkqDCUkoVaqyw4KCpM0oFMKWIyBpDi66wKasiegRp2a6ddreY4pbEQCkLt24s/myHQhZirjCGkCSZNCCgFjmktaBcpqp6QBrwZgE1JFQJTKKuI2XCKJ+B1QEkXcPQD9J3wwV84u8TtbKWqF3TIpqrn7MjnozxOz01uKI8GpE+nPM43ZbGUwfVrX/vaOf/uq1/96hk/ExH+7M/OTT8tpy4qQBYRbr311iUPDxYKyI2aYf/+/VxzzTVz5kAst5oOeffu3Rw8eHBJYfTGmAXdp+npabZt20aSJLMGdgBbt26lLEumpqaGmth+vz+UWjUgPTY2hoiwZs0afvG2t/OXz3wKrFBJRdsUeJ3AUgBCJl1ggNUxbL292WKpCMyUJ2ibVaStpFYE+3pMF/9NrWLWWmEBjj7pEH8Dru5iTxmzPVVtkW5Eb1X8GyCCeBTZBQRVoS0FedbCGmpOexWlBnq+AO0gUmBNn8BErctYRR6mqTSj7xx3jv0r7rxj4ZRVCOG8d5ArUXMZNRrKY3p6elbSWwPSTYTrhbh9L+d66b8CFlmjQLLYms+VBrO1t3MpNZpaaOzlfNd1/Phx9u/fzw033DBLObGYOtdQrygKtm/fTr/fZ/PmzXMO7FqtFpdeeums7IFGajX6JrTWMjExwYOv+Rk++0//N9NM0bYl6scRcbQkxhFFE3SUhllJscxQ+g6uUCa6a4HqVIPLFIH1NAlt0fqR1gaTyCIjAR/T57FqcBJG4JhonSYmucV8ixLo1oGdURUNY/Xxc0pWMTNVMbYmxXMSWA8qJKYAxqg0J2iHQhXVnFw9QYXKe5y3PPq2319UV/hibIFeyToX5TEYDHj22WfPoDwaY8tyqyiKl1RI/lLrogPk81GjucSjm0Hmq0b6ttg32Wj4fbfb5dJLL+X6669f8m2fi0NurNtHjx7lxhtv5NJLL513YHe2OpvUyjk3BOl33f0/8IFvfoIyDbSSPi0xVGLJjFBpRSZdlByrDj/Txo5D1mlRalT5pki98LQLVHEDda1GNnSHNIXHQ70ZRBsPYL1xOorlCqCD16g3DvVAsSEwAgXCekAJGshnBoiM0V7dIdcCw3oCUGqBZTUepdICYRW5DjC6BqfTVN4wKA2/dvNDHD9+nH379g1lZg34zLVd40JzyBeiRimPgwcPcvfdd88ytpxOeZyeTbGYx+NiSHqDnwDyOasJpB8bGztjM8h81ZhD5pLYna0mJyfZtm0brVaLO+64Y8hRL6fOlvbWDOyuuuoqXvOa1wAMu+j5BnYLqSRJWLt2LWvXruWaa67haz/+R759/DvRpycpYvpUZRd0miqZgHwG05mg3U0pwzRIG2oFhaude9DC44gwpgjjOErSehDocdh6ESrG1B4+huEWHsVqGpPiMDX50R12z75WK/u+I+QO1gYMGaUKBY6UNl6VEo+hQxlKjExQhajs6PsAoUvuSy4x1/DOX3nb8HFsgtunp6eH2zWcc8M84AaEmhPhxVzNY9JQHk2p6jCb4vRPWwuN47wYgoXgIgTk5b6oG6qh1+uxfft2jDFL0hIvxmXX7/fZtm0bzjle8YpXDMXp/X5/2fGbo0O90wd2o79bLhDPVR999/vY+oe/QCBgjafFOIVAIi0q72l11lBoju8JQotc+2TtDGMnCMaTaoIhcsBB4snN0MKHAd7UygwdJ9eClDZ48MZjNcQuuQHkYFDbZFjUgB1AjVLmfXSmje0kuDWWRC+hQvBa1oSIUGkJdFC1FOqw0qbwM6AdSi2ofKCqUv7D770fa+2Q9oFTnyRGB7GjAHTw4EGmpqY4duwYJ06cGHbTK60Fbup8r1JabInIWSkP59wwy+N0lceoTTzLMqampl7220LgIgTk5ZaI8L3vfQ/n3IJkZXPVQtY4NdGbk5OTbN68edaLEVYmftMYQ57nfPe73x1qllut1ix64nx2Zp1Oh9+57238yf/3H+lk0PeKMSUtO4FKH6PtGP3TamMEnPTQSjCVUvWnSM3qSDtkfdKkhUkTECWoicI4rZUXoninYME7W3fWAYzgg8GOnNeqWnVM5ahmKrAldu1qAkIVAg5AJUryyFCEXB0JY7hQEBij9J4gGZX3BN8idxWvv+G/4brrrpt1/0MIQ3BuviC+PlavXs3atWsRkaFe3lp7hhZ4FHzGxsaWrVZ4MfjqpZwEmsdo9D0YQphFeezbt49Pf/rTPPPMM7RaLT7/+c9zxx13sHnz5nnv49vf/na+9KUvsWHDBn7wgx8AvKgpb8P7fF6O+iLWUsGlKAp27tzJzMwMV199NVdeeeWybsd8iW/ee/bs2cPhw4fnlcutRNpbk7V81113MTExcdaB3fmud7zpIT7+D59lJg+krUBbVlNVitguuXekZg0DApkIThIwhsQmhDUdKpJopC7WUQ5KbA8gEKoBadtiEoHMECQO80TBRSM1iGCCUKkhEUV9VDqXeOxUiVeFcSGxG3AhDnQL+iTEN2HONJmuxWnMhUNtBGbtMAg9TOhQUVA5j/qUj73zsTPuewMKoyA6CtKqOgSXDRs2MDY2xqpVqzDGzPq01uv1OHDgADMzM6gqY2Njs4B6MQqNCw3IK8mPNzv6RimP22+/nU996lM89dRT7Ny5k7/6q7/iT//0T7n88svnPM7b3vY23vWud/Hwww8Pf/ahD33oRUt5a+qiA+TFVhO/+fzzz3PDDTfgnJu1vHGpdbYOOYTAgQMH2LdvH1deeeW80ZuwdNvzqD76qquuGubqLmZgtxLVDEN37drFv33dr/NHX/ksloTCAklBhzFyZrDapmAKIxNYGWMAdESA1RQS4y0lsbhUSEhAlcrnSJVAEfC5I5QlSRaHfiHzpAKmVQfbq8St1qpUA0+Zz5B112G7llwLNAii1F3wGryamE2ha3AYcq3IGKPvS0TGGXgPMs7ADdCQUZWB33vgVxY85W8ef1Vl9+7dTE5OsmXLFiYmJoYgPUp5jI2N0e122bhx4xCkmy6xeXy993Q6nVkgPZdh40ID8vm+vubkde+99/K7v/u7C/qb173udezZs2fWz17MlLemLjpAXuiZ2HvPvn37OHjw4Cwt8Yn/v713j4+rrvP/n+cyl9wvtEmT3tNkkl4ovaRdltW1rlRQWZTH+kVAv7v8+nXp7kqLimCVB2x5qBQUVxTwBq6Ci4uCF0SwWlkqyNIL1CItuafpLWnSpEkmyWRmzvl8Pr8/pucwkyZtLpNJaOf5ePRRmKSZcybnvM/n836/3q93d3dS/CyGc3xrbGw8p59GPOeS4Q1luIKdZVkcOXKE1157zW3syM3NnbT8pIOja/b7/axcuZJLL72UJ3a+SHO0HdMryFQ5RDUFRgZhITH1fKIITF0jQg+mlo+OTkQTmKeLdxEtinFa7mZrXjSvwvR5MaQikqnhUT5EVBCJaNhKwuBpDbKMIgwdIRUYGjLfj1Imtg1RpTA0HRREAB0TlEZEgQ8DSxEbTKqM2Kw9/IRFH6bMQEgPtg15Koebr71h1J+NUor29nYOHTrE3LlzqaioSJgS4+AEZCfVER+knYGiRUVF7r91ioe9vb0cO3YsQb3gBOqMjIyUO71N5qRph97eXsrKyib0M6bS5c3hvAvI5yLe9a2kpOQMfW+yDIacdENPT4/r+DYWlcZYcQL+0IKdYRhceumlWJZFX18fwWAwoYrtNHXk5ua6jR0TIRqNJswGjC+0PPTpW7nyy18AZWAZNlHDIktlM0CIHD2DEANkGTl4uYgwFj7NJIqNF+10fhm3qdqjZRNRdswmSNOwZWwQquY10Xw56DLWeo2tMdg7iPLETD3Doh/PqWwGNYHhNYiYUbxmFlLF7Dg9KiNW9ddsPCoDW4GPbKJCgebDshUePYfBaBiEjrB07rjx/4368xkYGKCurg6/38/q1avPuqp2VpVDV5dDUx5OkPZ4PBQWFiaMHYuXIba3tzM4OOgaRrW1tZGdnU1WVtakrmBTZSw0WSqLVLi8OVwwAdlZlTQ3N591lZqsgCyE4Pjx42RmZrJ48eKkpEGGo6+vj7q6Orxe71kLdsNphuODdHNzc0JjR/xKejQ3q9O96OTF41duDoFAgOUzFvBG52EsjyKHbCzLwvDoWBZ4PNlEbYnHMLAQ6JqXTK0gNtVaM/BpeVjYqNNucELTsJUOMpYvFroONhi6n6DqI6MvIxa0svyYPj9KxdQVuuaFqGJQWGiRTAYsG0uzkYZJxCcRusJPLgKdPhUkh1zCYhA/WQRFP17hQ0kTW2iU6nlcs+7skykgdj0cOnSIU6dOEQgEJhQ8zpWXji8e6rpOXl4e+fn57vXQ09PD0aNHsSyLo0ePMjAw4MrR4lfTyQqiqQjIYzUWGo6pdHlzOO8C8nBPrq6uLhoaGsjJyTnnKnWiAdkpDnZ1dZGfn8/FF1887p91NsLhMA0NDQwODhIIBMZVsHNWVM4YHEgM0ocOHWJgYABd189YScfnQZ085qxZs9zV+Uh885bNvOe22/EIhbCihExFPpnYKoRJJrYKYyofEU3hUYChE5UWpu5FaQrbsc/UHNOg2HmGlcDwuh0DAAAgAElEQVQjY40hKiSJRsFn6OjZBigbYce+L+ZOrKPpoDSF1/SAX0OpCIbMQkhJyArhtTQEg+ial0HdxgaiQuA3MolaUQxhELU0tv7b2VfH8a6Ds2fPdv1Bks1oiodOkO7r68Pv91NSUuLmX4UQbl56qHfyuZpazkUqnN6S0RgylS5vDuddQI6nt7eXhoYGTNMc9XBP0zQZHBwc83vFd76VlZVRVFREV1fXeA77nO/jFOwck6GxdtidjeGCtLPtDQaDHD58mP7+fnRdx+fzMTAwQGZmJpdccsmoXPXmz5/PJUXzeKPjKLFeN5OILbFMnWypYekKXQhyjBwi0sInDQaVht/QQOlEGMDUPKctOC1MLfZwdcY+2UEbTQMtx0BhooSOrTQ8WkwbHDMYMhBKnbYFivkh21JiagaajOWRvZ6YpE0nA9sO45E++oWNITRsaaBsjRIjg7+9tHrEcw2FQtTV1eHxeFi1atWoXNGSydAgHQ6Hqa2txTAMysrK3BqFE6gzMjLw+/0UFxe7DUXxTS2HDx/Gsqwzmlr8fv9ZHzKpmhYyFi/k66+/np07d9LZ2cmcOXO4++67p9TlzUEboz5weinKR8DprrNtm4qKijE9OU+ePEl3dzeBQGBU3y+l5NixYxw9epS5c+cyZ84cdF2np6eH48ePj8oL92y8+uqrbjedo9CIl+VNdmPHcEQiEerr6xkYGKCwsNBtcnDMZJx0R3Z29rAPiIaGBtZ/5i58fjB1hWUoMj0+pIzg8XixhYXX4yGkQmQbWTE3NWnhNbz00E8+WWg69MkBcvQsFNA92E+2ZWLmetE1nX7VTxbZ6JrGgOojU8tGUzBIP36yUShCMkQGmWhodKsQeWRhiygezYtQigEVJkvLIGhFyMSDQGJbChXViFhw6z98kMsuXkI0GnUVDs4OorW1la6uLgKBwJhN05ONUoqjR4/S2to6rN59uOKh88e5puKvr/imlv7+fsLhMB6PJ8GfIr5o3N7eTjgcThjgmmzWr1/PCy+8MGaHxxQyqpvzvFshK6Wor69n3rx5Z1x4o2G0KYv4nPTMmTPPGFo6msaQ0aDrOh0dHQm57/h26FQGYkeZ0t7eTllZGTNnzjzDYtFZSR89epT+/n4A9yZ1gnRFRQWVhTOp6zqJ7dXIIJYHHtQ0POiEpTo9ZtTAtiWaHpN6SQW5ZBNRg3j1mAH9YDQMIYWeaaBneEHEJk+jDNBidkRSGsTeQiMqDbxaTI8cUTp+TSMiouTp2SBByJjqwrbDZOuZWLYgV/djWdGYG52QRGwo8XjZdOP/BWLXQjgcJhgM0tbWRmdnp5uL7+rqIhqNntOydLIIBoPU1tYmFHuHMtbioWma5Ofnu00tmqZh27YbpIc2tTjjmyYzlxwOh8c8Im06ct4FZE3TWLVq1bjbQ0cTkJ1ZednZ2SNOIjlbY8hoCQaD7jy0FStWpLTDLh6lFB0dHe7MPuehMBTDMMjPz08orjiOX8FgkGPHjrlB+iPrL+WrP/w1hopFzSg2uT4vdihKhtfECksyPX4sEcHv8WEJHY9S6JqOJnWELjEGDWwfZGV68aERscP4NP9pTzhn6GmsU0/qOlIJbBULzhERIVeLTVnRTvdSCymJSA2PrrCs2N+2LdF1jail4bElpoJoWHHdx94u5Dm/ixMnTqBpGpdddhl+v59IJOJalra1tTE4OIjH40nIx0+W/NC2bZqamujr62PJkiXjGiM2luKhpmnuOTmfh9PUcvToUXp7e/nzn//sNrXEpzzG4vcyHM69fj54gZx3AXmieDyeM6Z0OPT391NfX4+maef0t5jICtkp2IXDYXJycli0aBFerzflgRjeHhXlyPbGWtQZzuRcCEFVVRXf+eEz9A0qLFtDMzWwLYQOWWgoJWLtzXZsLogmT0+/1iAkdHzYeDwmuhCgTk+FVjqcLtYpqXN6BAlIHU0oItImX/ehBCC0WGFPgRA6HkMhLJscw4uwLDSpIZDoCuyIIAONAUthWQqPVNy84eNALEAdPnyY9vb2M9IB57IsbWpqSlC2DFc0HQ8dHR00NTUxb948AoFAUq+XsRQPIdbU4uilHUfBkZpa4lMe48m3pwPyNMVx2RoPw62Qw+EwjY2NDAwMjDonOJ4V8nAFu5qaGmpraykoKCAvL4+cnJwJryhGQyQScecDVlZWJlW25wTp//vh9/Pdp7eTYRjodqxAIc2YmqEfyLat2DQQZePTNKJCoWkCdA2vaYCtIaUCM5bv1JWO0mO29LrUQFeEpEWWbsYc3mwdDEAJNKmDLkFCWGj4pMKwNDShIWzw6wa2LfBqBoOWQCmFTypMS7Jq8VwMw+DUqVPU19dTXFw84q5hKGezLB1aNHXy8aOVoTlFO9M0z6lxTiYjBWkpJYcOHaKnp4fS0lJ3geL3+/H5fBQVFbmFxdE2tQwXdFPReJIqzo+zSCLx/hG2bdPc3ExnZyeLFi1i6dKlo34Kj6XLbmhhMN4Ss6KiImFF0dTU5MqR4jvvknVBnitPnEw2bfw43//JcwAYuk5Yh2zdJCIlhSZIAYUahAdjC2UBmDpYGkQsiccETYKSp+eAKBBazMdCKQ2lybf/RkOXoE7noqXj9GYrcnUNTUpCFmQbAmmBrissO+YN55GKqCVRQmFFbDb/v4/x5ptvIqUctbrkbMRbljrEp3qOHz9OX18fSqmEIO14WJyraDcV9PX1UVtbm/Cwii8eOitp514bbVOLaZoJ6Y6srCx6e3vPC6c3OE8D8kQCiLO6Pnz48KSPaIpvqZ45c+awBbv4yb+O9lEpxcDAAMFg0N2eCiFcYxrnhh1LkI5v5y0tLR31im8i+P1+qivmsrfuCLZHx+8xsCOxpbKOjhISS9dAgN+rEZbg94BfQUSAEBCSIHQZ6+RT4DNkLIcsAQP00/lhHYUtAV2iKbAkeDSFLkDTY1/zSpC2BKmwEfglKBHzPPYKxaAlyCa28ps1a1ZCKiLZDJfqcXKyToBqbGwkGo1iWRbZ2dksWrRoygOTEILGxkb6+/vPmGs51uKho3+Pb2pxHlR9fX0cPXqUX/3qV/ziF79AKcVDDz3EypUrWb169bg7Yrdv384tt9yCEIJPfvKTbNlypmHUZHJeBuTxopTixIkTDAwMYNv2GcqJZBIMBt0W2pUrV7o54tHkiR2zoOzsbLdjSErpese2t7fT0NCAlDJBhpaTkzPsttfRa2dlZaV0qwvwoQ++l9fefASv5kWLNdwh9dgopH4F+V4DKRS61FG2QqJh6Bq6rfB6NMJCkaFpiNMrZWHHDOujUkM3DGwFpq7F5uid9rIQQmEo0A0NaUkwNJSt8Boati3JMDSsiMQwNfqjgiwUli2RYYuVq8vP2fwyWTgBKjc31y3aBYNBKioqEEJw6tQpVyvsNHQ4v/dUaKCdBqw5c+aMKXc91ry0c+3rus6WLVtYt24dDz/8MF6vlyeeeIKCggKWLFky5uMXQvCpT32KHTt2MGfOHNasWcPVV189rp81Xs7LgDyeFbJzMTmV77KysknZqg8ODtLQ0EAkEiEQCJCdnZ0US0xHYpSTk3NGkHbkWPX19QlB2u/3097ejmVZVFVVjasSP1FuuO5q7r7n26gISNMgjIbX1FAaZOkGWAJNaYiwINPUsSIC06OjWQpN19AsAIWua2i2wufRkJhIqfAaIC2FrUlQgrCUoHuQUuHRdYRQhC1JtkdDWRKUjh4V4NEQlkATGtmaoidkoQmBJiRf+MK/TUkwjmekol38DmqoZ3AkEsHv9ycE6XM1dIwWy7Koq6vDtm1WrFiRFL+W0QRp57//53/+h3A4zE033TSh99yzZw/l5eWuSdF1113HM888kw7IqcRxJTMMw+3m27Vrl2vMMxHiB53G56OdPF8yO+yGIz5IxzeSBINBWlpa6OnpwePxYJomhw8fTmjoSFXQ0XWd8tkzaT56EikEGaaJaeooC8wMDVsoMoyY/lfTDXRLInWFtBXS0MnSYjI00xsztZeajq7hBmzDjn1N0w2kpeHRFBFLIvXYZx+VEBUQsiFXSsJRSYbS0G2JkIKIsMnUDKRS5OUoKisrU/K5DMdoi3aappGZmUlmZqY7GdopnDkyvOPHjxMOh/F6vQk56bHI8OLTXE536mQqHYYG6Y6ODm699VZ0Xeeb3/zmhH/+cK5uk+V7PBIXbEAeHBx0XckqKysTcnWO0mKiQck0TSzLor29naNHjzJv3rykz7AbC/F64tLSUpYvX+7mrIcWkIAz0h2T8dCwLIvZpfk0NR4h25+BrguUEERsMKzTOV2/QrdVrN/DkmAqIlGFz1QoBZpQYOtIS2Hose/TrFh6AkuCHpPASUuimRqmkHhMnaityDc1hC3xiJi6Q0mIRGO/m4gQZOmgkEjLYs6cidk7jhcpJUePHqWtrY1AIJDQ1j5aNE1LsOx0cNQNTqorFAphmuYZWumhv3vn4eDxeKiurk6J8sdBKcXPf/5zvva1r3H33XdzzTXXJOUeSqWr20iclwH5bB+iZVk0Nzdz6tQpV1o29PudgDyRvJtSCtu22bt377CV5lTriZ0Bqjk5OWesruJzkw4jNXTEO8GN1Bo9Ghzv5qNHj3L1NR/gj//zOugGShgISyPLZxK1ojEXOEMRiUj8ekztYHoMNCHRpIHP40X36Ph8fsiSmF4fuqljRyw8Pm9sFWiYRIWFLoJ4DS8D+iAIhS4FuogNAcj0ati2QBMqJnfzaGhKEQpbICXKijJvwSyamprc809FXra3t5e6ujp32nmydy7OLLsZM2a4r41kMOWsogcHB+ns7CQQCKRc0dHe3s5nP/tZsrKyePHFFxOOe6Kk0tVtJM5LLwsp5RnNHY6Av7W1lfnz5zN79uwRA+KBAweYO3fuuN2jnOAXCoVYunQpBQUFUxaIHQ11NBp1c9bjxWmNdm7W/v7+hA6t0TY1OB7RBQUFLFy4ENM0WbxwLZquo5smumFieIzTjR16zO/Yhpkz89EMg+Li4lhLrqaR4fUSjVh4/V6i0TBebywvGo6G8Xti3XIeX6xtV0gbn+kjEo2go9HVfYrIYJhgTw8DA/0E+6L4vTp21Mbr0dGQWFGBbdkIEeWFl3/pDtTs6+tz87Lxq0mfz5eU369t2672vaqqaso9Gmzbdhs5nBSbU1yOT3lMVqpLSsnTTz/N17/+db70pS/x4Q9/OOn3kTNH84UXXnCd+X7yk59M2I/mNBemlwUkrpCVUrS1tXHo0KFhDemHY7wWnE7Bzgl+R48eJRQKkZWVhcfjSWkgdub2nTx5kkWLFg27ExgrI7VGD9fUMFyQjkQiNDQ0YFkWS5cuTQgyhRflcqqrBxWruyEsgc9nMKNoJvn5M5gxo4CoZeHz+YnYFh7DQLNETKwsbbANsAWaKVEKsARKF6AkmlTISBiP14cSNjIawevP5KLcLFROLl7DYO7s2UgZ4VRXL+0nTqBJCyEUui4wdZsMv+HmF+PzsuFw2D3/Y8eOEYlE8Pl8CRrxsQTpeLvO+fPnU1lZOeUdaE7KpKOjg2XLlrkLlXgJWmtrqzsVOr7jLhmNTCdOnOAzn/kMubm57Ny5c9JW5aZp8tBDD3HFFVcghGDDhg3JCsaj5rxcISuliEaj7tj7goICysrKRi3namxsJCcnx73xzsVwaRAhBMFgkNbWVvr6+hLUDXl5eZNWOHOkey0tLcyePdt1n0sl8Z1nwWCQgYEBLMtCCEFJSQmlpaVkZ2cnBJqPfPAaGuoOoxs6Xp+fWSWzKS4uwp+ViYgKPF4TW+qYpkHUsvF5TaJRG6/PJGrZeEwvkYiFz2ee9p6I4jE9RC0br9eLZUXxeGLSQisSxuPz0nHiJB6Phs/rIzMzi8HB8OlUhUFr21FOtLUyEAqhC4vCmTPY+eofznnu8cUzZyUdDofdIO08qIZTOAwODlJXV4dpmgQCgZTKD0fCMSeaMWMGCxYsOOe1FC+/dM4/3lfZ+QxGc25SSn72s5/xjW98g6985Sv8/d///ZQ/nCbAhbtCFkIkjL3PzMwc0793inHnwlk5HDt2jPnz51NRUeHmjgE3+DrfO1zhzLlI8/LyJuxh0NPT4xrxp7rQEk9851lnZyeNjY2UlpaSn59Pf38/LS0tDAwMJIyQKiqeycG3aphVOJvyQDm6bmJ4dETEBgRSaEjbBs3EUCI2QVoKlIz9jbLRlI2mtNNeFQKlGbHuEWHHvteykMomHArR29tNhs9DdlYOlrCxIoP4PSaWsNE1SWFhITMKC2k51MLhY00EZo5uGsVIxbP4lXRra2uCwiE7O5v+/n46OzuprKwcV9Eu2QghaG5upqenZ0zmRMPJL5VShEIhgsEgXV1dtLS0nGFZ6milnYDb1tbGpz/9aQoLC/njH/84LT6TVHBeBmTTNFmyZMmYA3H8vz9bysJRKzQ1NVFUVOQW7M6mnBipcDZ0uz90hNJo5tw5ZkS2bbN48eIp0RMPxTFnN00zQZs60ggpw2vg8ZgUFObR1xtENw2ys3PxGDZRocjQNTQEUiikAkPaKBlF2RrSstEMIxZ0lYmmFFI4r0mksFBCYAmb7p5ufKaHgpwcpFRIO4qun+7I02K+GUIIvB6DcGSQuQtKECqEP2Ni2lonSMd390UiEU6cOEFDQwOGYaDrOocOHaKzs9P9/U+FZafj0VFaWkp1dfWE398ZD5WVlZWglXYsS3t7ezl69CiRSIRt27aRlZXF/v37ufPOO9mwYUPKd3hTyXkZkCHmMjVegyGPx0M4HB72a07VOzMzc8wddkMZLidr27a73XXm3DkypKE3qZMndrw2kllxHi+OQVJ3dzcVFRVnNWKKn05SvbaazvaumG1l2EZKm/7+bixhg1CEs3LQgayMLKSmMHQ/moo1fOiaRAobISJoUo9J4ZAoKdAQKCnpD/YgpCIn04/P6ydqW3g8BrYlMHUDgQANbDsSs+3UJDqSqGVTOruUReXJlbw5n9PAwACrV6928+nRaNT9/TsytFRZdlqW5TYtJcOj42xomkZGRgYZGRluavD48eNuKufjH/84zz33HC+99BKPP/74pB3HdOO8DcgTYbgV8uDgIPX19QldbZPhTWya5rBz7pyb9MSJE+6IqUgkQlFRERdffPGUm3PH566dttOxfCZLlixh+2+2I6XA49HJyMhGSoGGGVNNhCOEoxFsyyYaDePzZYACf5YfJBjZWbHBp8JC1w1saWEqnYFQH9FwrKBXmJeNLQUSGwMRq4gogVKghI3SFVKKWA7aFuiAVDa6ARWLRzdBZjSfkzNwYLiindfrZcaMGQkPV8ey0/EucYJ0/HZ/ohPDnR3fggULmDVrVkpX5VJKnnjiCR5++GHuvfdePvCBD7yTc8UT4rwNyMmy4Iwv2DkddkIIhBCT1mE3FI/H41o2OnnirKwsCgoKCIVC1NbWJkiw8vLyyM3NTVlRyJl8nZWVNe7c9apVq8griKUrDMNEKAukhiSKx+PB7/NgenW8phfLzsQwNMKRMLYVJRwK0z/Qj67p6IZGVoYfISRdwR6kUuTnFyCliDV4SAtd8yBjRshIZYGQCGJubkLaoGK/V4GN6YnJ7t797ndP+HMaHByktrYWr9c7Js+QkSaGO0WzkydPur7KQ4fRniuwRSIR6urq0DQt5T4mEFsVb968mdmzZ/PSSy9NeHL0O53zUmUBsQs23pBkLAwMDFBfX09hYaFbsCstLU0wOUm1ntjpLHS0kkN1qfE5OedPNBp1bTonw0s5Go3S1NTEwMBAUjyT//SnP/Hgtx7ENE10pWFgIjWJaXpiwVJIPD4T27LxeTOIWOGYrtiKPYykJQmFQ1i2RTgUxuP1oimFx+9H13X8Pn8sxWF6EJYVKxraNppuYFs2uqGBBsK2UcSCs9QUH/3oR/noRz867vOSUnLkyBFOnDgx7k670RCfkw8Ggwnm9/Eraccatq2tjcOHD1NeXj6pznXDIaXkxz/+Md/5znf46le/yhVXXHG+r4pHdXLpgDwEp4OspqaGhQsXMn/+/CntsHOmWXd1dVFeXj4mDWZ8ddv5E2/T6QTpscrvlFIcO3aMY8eOsXDhQoqLi5P2mbzxxht8/3vfp7u7G03FJnp4fR6UBbqhxxzbNA3D0IlEovgzfFhROyZxi1j0BE+Rm5OP4THwm17C0QgSSWQwgpSKaDSM4fVgagZenxdN1/B4PdgRC3TQDM0tzmZmZfLxT3ycdevWjft84jvtFi5cOCUSRGcl7UgQAfdhXV5eTm5ubkqP69ixY2zatIkFCxbw1a9+ddwNWO8wLuyAbNv2mEcoOR1kGRkZ9PX18Vd/9VdTFojjVzBz5sxh9uzZSblp4h3gnBtVSpmg7Dibb0V3dzcNDQ0UFhaycOHCSdFS27bNs88+y86dO+lo78DUTaSSmIaBkgr79NBMKSSmadLfN4AtLDR0/Jl+/D4ftrAxdRPbPj1YU1Mxe04p0YgpU2xpE4lE3Pf0ZfjweD3k5+Xz7r99N9dee+24c/OWZbm7h+nQaQexa+rIkSO0trYye/ZslFLu5Oh4udpE2+JHQkrJY489xve//33uv/9+Lr/88vN9VRxPOiCPNiCHQiHq6+vdCR1ZWVm8/PLLlJaWuibhqdT0OkEvLy+PsrKySX9vKWXCVne4lmjTNGlsbEQIQSAQGLekcCwopdi3bx+7du2itraW3u5eLNtC2AK/3080EnW36RcVFuLP8GPbAtMwsKSFoZkIYWOaHoRtoxtGrAirx1bBuhlz4dN1nazMLEpKS1i6dCllZWVYluXm5MfiXTG0aFdSUjItgk5/fz81NTVuu/rQB2m8BNO5BoaOkZqIwdSRI0fYtGkTixYt4mtf+1pSR4K9Q7iwA7IQ4pztz84qxpFoOQU7p9uqt7fX1Unatk12drZbMJuMvn2n9VpK6T4YpgrnBu3p6aGtrY1QKERGRgYXXXSRG6AmS341EqdOneKNN96goaGB5uZmmpua0Q0dj8eDsAWmYWLZFoZpIGyBx+PBFjaGbiBkbKVsmiZ5uXnkF+RTXFzMggULWLFihauPdRgpJ5+RkZEQpOOLYPFFu4qKimnRaefMtevq6mLx4sVjCoTDeZcAZ6ykz3YfSCn54Q9/yKOPPsrXv/513ve+902LB9QUkA7IIwVkp8hy/PjxURfs4rf6vb29Se20m0ieeLJQStHZ2UlTUxOzZs1i3rx5Cauo3t7ehLH2zp9kmZ6PhCM/1DSNQCCA3+/Hsiy6urro7e11p7049qmGYbjeCjNmzJiwg99IQVpKSSgUIhAIJHToTSU9PT3U1dVRXFzMvHnzkpKCiHcBjA/SQweyOh7bN998M1VVVdx3333TomFpCrmwA/Jwjm+OoXZzczPFxcXMnz/fNZGHseeJhwao+HZgZyV9tk4rpRStra0cOXKEuXPnUlpaOi26khyVicfjoaKi4qxBLL6Robe3N8G3wfkMkmFT6bj1tbe3T5tBnhALejU1NWRmZuL3++nr63NHKMU/qFKZ8op3ilu8ePGkp5eclJdzLzzwwAO8+uqrBINBrrvuOq677jrWrl07Za3804R0QI4PyM5qwRkG6fF4JqVgF9/E4awihwtQTp44Pz+fhQsXTouL1Zlq0tPTQyAQGLcmdOgqMhKJnHWrfy6cVl7nITodHlqWZdHY2EgoFDqjaDdU3dLX14dt2wlBOtkSRAfHUGvevHmUlpamPD1w6NAhNm3axOLFi7n++uupra3l9ddf55577jlr1+YFQDogW5aVULBz9LvOTK5UKSfie/Z7enrcgklJSQkzZsxwi2ZTRbyiYzJuZGfGW3yQHhqghvsMwuEw9fX1KKUIBAJT3o0I4y/anU2COLR4Oh6i0ah7nVdVVaXEPD8eIQSPPvoojz/+OA888AB/+7d/m9RraMOGDfzmN7+hqKiIAwcOALEH9cc+9jFaWlpYsGABP/vZzygoKEApxS233MLzzz9PZmYmP/rRj1i1alXSjmWcXNgB2bIs3nrrLbq7u10xvlOwS7WEDd72LnAsOv1+vxukg8Gga88ZXzRMxUrQmX6dk5Pj7hxSgVLqDPmdEMLN9w4ODrrF1ung0QHJL9qN9Bk4OnHnOjhbkI5vWS8rKxu1ZWwyaW5uZtOmTVxyySV85StfmZRi9EsvvUR2djb/+I//6Abk22+/ncLCQrZs2cK9995Ld3c39913H88//zwPPvggzz//PLt37+aWW25J+Wy8YbiwA7Jt2xw7dozi4uIp7bAbmiceaVKJY8/pBOi+vr4Eh7jRtsKOlmg0mjBTcDoUXKSUtLW10dzcnGDon6yxURM5rlR02jnvNXQlHe+lHa/wCYfD1NTU4PV6CQQCKU97CSH4/ve/zxNPPOGuiieTlpYWrrrqKjcgV1ZWsnPnTkpKSmhra2PdunXU1dWxceNG1q1bx/XXX3/G900hF64fMuC2jdq27QbhqbAxbGxspKCg4JweD8PZczpG7729vTQ3NzMwMIDH43FX0Xl5eWMeGSSl5NixYxw/fjwlk4JHi7PltiyL1atXu4Wo+Kr+kSNH3HTPZD2ohuLUHmbOnOnarE4mjvY3Ozvb9ROOV/i0tbVRX19PJBLBtm1mzZpFSUlJyh9SjY2NbNq0idWrV/OnP/0pJbr0obS3t7tBtqSkhI6ODmD46dHHjx+f6oA8Ks7bgFxbW8utt95Kb28vVVVVrF69mjVr1ky6rSDEHgYNDQ0ALFu2bEK+zI7Ru0M0GnVX0Y7Rud/vTwjSIwX+U6dO0dDQwIwZM1i7du2kzT8bC/Ft2IsWLWLmzJkJwdUwDLc5x7nJ4ieSOBaljrrF+Qwm6iMcX7RbtmzZlGrC47vo8vPzqampoaioiOLiYvr7+93xSUqphJX0ZEylEULwne98hyeffJJvfetbvOtd70rqz08G02F69Hg5bwPy2rVrefnll7Esi4MHD7Jr1y6eeOIJbrvtNshbe+wAABX3SURBVHRdZ+XKlaxatYo1a9YQCASScuHGewGXl5dPytbW6/Uyc+ZM1wwmXht76tQpWlpasG07wa/CNE2ampoAWL58+bQojsHbPg8FBQVjekAM96CKV7c4FpXORI6x7CYcaeShQ4dYsGABVVVV0+JmdmR/HR0dVFVVuf4P8UqYc02lmWi3XX19PZs3b2bt2rW88sorU34dFRcX09bW5qYsHP33dJgePV7O2xzySCil6O/v5/XXX2fXrl3s3buX+vp6ZsyYQXV1NatXr2bt2rVjMsyJH2k/VXKjocczMDBAd3c3x48fJxQK4fP5KCgoSNq4qIkQn7+eTJ+H+Nl2wWDQ3U3EB+np3mkHbz+4RjvXLp7hGjnip0WPJi9v2zbf/va3eeqpp3jwwQe57LLLknFaY2ZoDvm2227joosucot6p06d4qtf/SrPPfccDz30kFvU27x5M3v27JmSY47jwi7qjQVH9rVnzx43SHd0dFBeXs7q1auprq5m5cqVZwzmhLfTAI7ZzlTK1xzipVmlpaXMnTvXNZKJvzGTvc0fzXE5D65ku8SN9v1H6rQTQrgFzlRbUY6EEIKmpiaCwSCLFy9O2oNruJbood4lmZmZGIZBbW0tmzdv5m/+5m+4++673VFcqeb6669n586ddHZ2UlxczN13381HPvIRrr32Wo4cOcK8efN46qmnKCwsRCnFzTffzPbt28nMzOSHP/wh1dXVU3LccaQD8kQQQlBXV8fu3bvZvXs3f/7zn7Esi+XLl7N69WpmzpzJb3/7WzZu3EhlZeWUb98c+vv7qa+vx+fznXOVF7/Nd/xzJ6PLDt6W1zmGSdPhwQUxI6eamhqysrLw+Xzjkp5NBk4zjDM5fLIfXEPNhf793/+dpqYmenp62LhxI9deey1Lly6dFk0571DSATnZhEIhXn75Ze69915qampYtGiRO2mhurqaNWvWMGfOnCm5aJ3JJsFgkEAgMG6P2fgVZG9v7xkm92NtXnAMnPr7+93RV9OBc3XaDfUtGWpROhkFM+e46uvriUajVFVVTcmDvqamhk2bNnHZZZfxgQ98gDfffJN9+/bx6KOPTps0zjuQdECeDHbu3MmhQ4f4p3/6JzRNo6uriz179rB792727Nnj5pHXrFnD6tWrWb16Nfn5+ZO2wonXOU+G3eNIHWbnamKJ7/6bTjaUQ4t2o50fF18w6+3tTXA+S1Ze3vFZmYq5dhDLFX/zm9/k17/+Nd/+9rdZs2bNpL7fggULXE21aZq89tprI3bfnQekA/JUIKWkubnZTXW89tprDAwMsGTJEqqrq6murmb58uVJSQX09vZSX19PXl5eSv0whgtOTg7SUXUcPnw45d1/52JwcJCamhr8fj8VFRUTPq7hPITjRybl5eWNyqI0EolQW1uLrutUVlZOySr0rbfeYtOmTfzd3/0dd911V0parxcsWMBrr72W0Ik5UvfdeUA6IE8XotEof/nLX9wg/eabb+L1elm5cqUbpMvLy0e9uopEIjQ2NhKJRKisrJwW0yiEEHR3d9PS0kJ/fz8ejwefz+euolNhzTkS8U5xlZWVk7rickYmxeflTdNMKJ46n0P87maqWsQty+KBBx7gueee49vf/nZKi1/DBeSRuu/OA9IBebqilCIYDLJ371431dHU1ERJSYmbj66urj6jSSK+hbesrOyMr08V8WmA+PZwx5rTaWQZ2sSSisnY8Z12Y5WMJYt4i9JgMMjg4CCmaRIOh8nOzh52aG0qOHDgAJs3b+b9738/d9xxR8oNiRYuXEhBQQGaprFx40Zuuukm8vPz6enpcb+noKCA7u7ulB7XJJEOyO8knI61Xbt2sWfPHvbs2cOpU6cIBAJUV1cjpaSmpobPf/7zLFiwYFp02UHMO7murg6/3095eflZA2y87MwJ0pZlkZWVlRCkk3FulmXR0NBAOBymqqpqSlp7h8N5qLa2tlJSUoIQIikWpWPBsiz+4z/+g+3bt/Od73xnypzQWltbKS0tpaOjg/Xr1/Pggw9y9dVXpwPyGEgH5BRi2zY7duzgi1/8IoODg1x00UVEIhEuueQSdxVdWVk5JRIyIQTNzc10d3dTWVk5blXHcIoGpdS4i2XjLdqlgr6+PmpqaigsLKSsrCzhnEZ6WGVmZiYUTyea937zzTfZvHkzH/jAB/jiF784bVQTW7duJTs7m0ceeSSdshgD6YCcYn7729+SmZnJe97zHjd4vf766+4q2mk9jpfeTWanoFKKkydP0tTUxJw5cyZFI+tMoHAC09AmlpHm+YVCIWpra5NWtEsWQgi3pb6qqmrUc+3O5qE81tmO0WiU+++/nz/84Q9897vfZcWKFRM9rQkxMDDgSgkHBgZYv349d911Fy+88MKw3XfnAemAfCHgdOU5BcO9e/fS1tbGwoULXUOllStXkpubO+HAGQqFqKurw+PxEAgEUrq6cqZLO0E6voklJyfH9fIIBALTSibV3d1NXV0dJSUlzJs3b8K/g3jnN8emdaip0FAZ4htvvMEtt9zCVVddxZYtW6bFqri5uZlrrrkGiO0Eb7jhBu644w66urqG7b47D0gH5AsVKSUNDQ1uPnrfvn2Ew2GWLVvmBumlS5eO+sYUQtDS0kJnZ+e0CniRSMRVKTgDTadyll08tm3T0NBAKBSa9Ll2zo4iPkg3NDSwY8cOpJQ0NTXxox/9iJUrV07aMaQ5J+mAnOZtIpEI+/fvd706Dhw4QGZmJqtWrXLz0cOpEDo7O2lsbKSkpIS5c+dOm9bZ4Yp2zqgoZxUd38Ti5KMnq8MunpMnT9LY2DilRlO7du1i69at7jnX1dVx4403snnz5pQfSxogHZDTnA2lFN3d3ezdu9cN0i0tLcyZM4fq6mrmz5/Pr371K2677TaWL18+ZaYyQ4kfWTSaop2zxY+fxBJvpOMUDZMRNKPRKHV1dUgpp2SuHcQevPfddx8vv/wy3/3ud7n44ovdr0kpJ/WBun37dm655RaEEHzyk59ky5Ytk/Ze70DSATnN2HBSHVu3buXFF19kyZIldHV1JRj8T6WfcrKKdk6HnROkBwYG3OYNp1g2liaW+IfEokWLXF/eVLNv3z4+/elP8w//8A987nOfS2m6xhkivGPHDubMmcOaNWv47//+b5YsWZKyY5jmXNgjnNKMHV3XycvLY+XKlTz22GN4vV4sy+LAgQPs2rWLxx9/nL/85S8YhpFg8F9RUTGpaYB4c/bKysoEU/bxYBgG+fn5CT8nvnkjfhJLfJAeLufueCj7fL5zjumaLMLhMNu2bePVV1/lscceY+nSpSk/hj179lBeXk5ZWRkA1113Hc8880w6II+R9AoZeOqpp9i6dSs1NTXs2bMnoX1027Zt/OAHP8AwDL71rW9xxRVXABfu9szxVY43+G9oaGDmzJkJ0rtkeR13d3dTX19PUVER8+fPT1kOWylFJBJJyEdHo9EEW85gMJiSwadn47XXXuMzn/kMH/vYx/jsZz87ZbamTz/9NNu3b+fRRx8F4Mc//jG7d+/moYcempLjmYakV8ijZdmyZfziF79g48aNCa+/9dZbPPnkkxw8eJDW1lYuv/xy6uvrAfjUpz6VsD27+uqrL4jVgKZp5Obm8t73vpf3vve9wNuOc47B//e+9z1OnjxJRUWF63i3atWqMeVq44t2F198cco77TRNw+/34/f7KS4uBt5uYuno6ODNN99E0zS8Xi9tbW2EQqGUTsUOh8Pcc8897N69m//6r/9i8eLFk/6eZ+OdPMduOpEOyDDixfzMM89w3XXX4fP5WLhwIeXl5e4omPT27G00TWP27Nlcc801rrZUCEFtbS27d+/mV7/6FXfddRdCCNfgv7q6miVLlpyxoovPx07FVJGz4Wi+T5486Wq74yVnzlRsx/HNSXWMxvFtLOzZs4dbb72V66+/nhdffHFamP2/k+fYTSem/jc5jTl+/DiXXnqp+//OOHHgjDHju3fvTvnxTWcMw2Dp0qUsXbqUDRs2ALGi3L59+9izZw8PPPAANTU15ObmugG6oKCA3/72t9x4441Tlo8did7eXmpraykqKmLNmjXuKtjJuw+diu2kORwTfK/Xe4bz3VgZHBzky1/+Mvv27eOJJ56gqqoqqec4EdasWUNDQwOHDh1i9uzZPPnkk/zkJz+Z6sN6x3HBBOTLL7+cEydOnPH6V77yFT784Q8P+29G2oZJKYd9Pc3ZyczM5F3vepc7Ol4pRWdnJ6+88grf/OY3OXDgAOXl5Rw6dMjVRq9evZq8vLwp+3yFEDQ2NtLX18eyZctG5cpmmiaFhYUJeWVn4Gpvby/Hjh1zzYTig/TZHkC7du3ic5/7HJ/4xCe4//77p425lINpmjz00ENcccUVCCHYsGHDlBQX3+lcMAH5D3/4w5j/zdm2Yent2cTRNI2ZM2fi9/u58sor+f3vf49hGDQ1NbF792527NjBtm3bCIVCCQb/F198cUo0vl1dXTQ0NDB79mwCgcCEHgo+n4+ZM2e6A1SdJpZgMEhnZyfNzc0JTSw+n88dqvulL32J/fv38+STTxIIBJJ1eknngx/8IB/84Aen+jDe0aRVFnGsW7eO+++/31VZHDx4kBtuuIE9e/bQ2trK+973PhoaGlBKEQgEeOGFF5g9ezZr1qzhJz/5ybhWBFu3buWRRx5xb9R77rnHvahHUnhcaESjUd544w3Xr+PAgQP4fL4Eg/9FixYlrZgWP9du8eLFKWuKiW9ief3119m6dSvd3d2Ul5ezYcMG1q1bR3l5eUqOJU3SSassRssvf/lLNm3axMmTJ/nQhz7EihUr+N3vfsfSpUu59tpr3eLTww8/7G4Vk7k9+8xnPsPnPve5hNdGUnhMt61qKvB6vaxZs4Y1a9Zw8803o5Sit7fXNfi/8847aW5uprS01NVGV1dXM2PGjDGtap2iXXNz85QUFHVdd42B/vd//5fS0lKefvpp+vv7XXe/dEA+v0mvkKcYxwd2aEDetm0bAF/4whcAuOKKK9i6dSt//dd/nfJjfCeglOLIkSPuBJa9e/fS3d3tGvxXV1ezYsUKMjIyhg2y4XCYuro6DMNIuZNd/Dm88sorfP7zn2fDhg3827/9W0ofwOnd2qSSXiG/U3jooYd4/PHHqa6u5utf/zoFBQVnVXikORNN05g/fz7z58/n2muvBWJqh4MHD7J7925++tOfsmXLFjRNSzD4r6io4Kc//SllZWUEAoEpmWsHMX/grVu3Ultby9NPP82iRYum5DjSu7WpZXpYd53nXH755SxbtuyMP8888wz/+q//SlNTE/v376ekpIRbb70VSAvtk4FpmlxyySXcdNNNPPLII+zdu5cXX3yRT3ziEwSDQe68804WLlzID37wA55//nleeeUVWltbh/3sJwulFC+99BLr169nyZIl7NixY8qC8UicTY+fJrmkV8gpYLQKj3/+53/mqquuAtJC+8lA0zSys7NZt24dS5Ys4ec//zm/+c1vKCsrcwuG//mf/+kOkY03+M/JyUn6A7G/v5+77rqLxsZGfvnLX7Jw4cKk/vzxkN6tTS3pFfIU09bW5v73L3/5S5YtWwbA1VdfzZNPPkkkEuHQoUM0NDSwdu3apL3v9u3bqayspLy8nHvvvTdpP/edQlFREa+++iqXXXYZs2bN4sMf/jD33HMPO3bs4I033uC+++5j3rx5PPvss3zkIx/h3e9+N//yL//CI488wv79+7Esa9zvrZTij3/8I+vXr2fFihX8/ve/T1kwTu/WpjfpFfIUc/vtt7N//340TWPBggV873vfAzirwmOiCCEuWC+OeEaSyem6TlVVFVVVVdx4441ArOjnGPw//PDDHDx4kKysrASD/9GYH/X19XHnnXfS0tLCM888w4IFC5J8VmcnvVub3qRVFhcgr776Klu3buV3v/sdcKaiI825UUpx6tSpBIP/w4cPM3fu3IQuw4KCAjRNQynFzp07+eIXv8inPvUpPvnJT06b6SsObW1tlJSUAPCNb3yD3bt3u8W84fT46aLemEirLNIMz/Hjx9NeHBNE0zQuuugirrzySq688kog1tjR0tLCrl27ePHFF/na175GX18fgUCAjo4OMjIyePbZZ5k3b94UH/3wTMVuLU0i6YB8AZLOCU4Ouq5TVlZGWVkZN9xwAxDr+vvLX/7Cs88+y1133TXtVsXx/PjHPx7xa3fccQd33HFHCo/mwiQdkC9A0jnB1OHxeFxP6DRpzsX0fVynmTTirRKj0ShPPvkkV199ddLfZ8GCBVx88cWsWLHC9Qc5deoU69evp6KigvXr19Pd3Z30902T5p1KOiBfgMRbJS5evJhrr7120qwSX3zxRfbv389rr70GwL333usWhd73vvddkJK7ZPLUU0+xdOlSdF13P2OHbdu2UV5eTmVlpVvAhbTkcVqjlBrLnzRpRs38+fPVyZMnE14LBAKqtbVVKaVUa2urCgQCU3Fo5w1vvfWWqq2tVe95z3vU3r173dcPHjyoli9frsLhsGpublZlZWXKtm1l27YqKytTTU1NKhKJqOXLl6uDBw9O4RlcMIwqxqZzyGkmDU3TeP/734+maWzcuJGbbrqJ9vZ2V1pVUlJCR0fHFB/lO5v0+LHzi3RATjNpvPLKK5SWltLR0cH69eun1cih8530+LF3JumAnGbScJQbRUVFXHPNNezZs4fi4mK3AaGtrY2ioqIpPsrpT3r82IVDOiCnmRQGBgaQUpKTk8PAwAC///3vueuuu7j66qt57LHH2LJlC4899tiIASXN26THj104pFUWaSaF9vZ23vWud3HJJZewdu1aPvShD3HllVeyZcsWduzYQUVFBTt27GDLli0Tfq8NGzZQVFTkGjPByPI6pRSbN2+mvLyc5cuXs2/fvgm//3RkJHOqVEke04yT0Vb/VFplkWaa8sc//lG9/vrraunSpe5rt912m9q2bZtSSqlt27ap22+/XSml1HPPPaeuvPJKJaVUr776qlq7du2UHHOy+MUvfqFmz56tvF6vKioqUu9///vdr335y19WZWVlKhAIqOeff959/bnnnlMVFRWqrKxMffnLX56Kw74QGVWMTZsLpTkvaGlp4aqrruLAgQMAVFZWsnPnTjdXvW7dOurq6ti4cSPr1q3j+uuvP+P70qSZREaVqE+nLNKcl4wkrxvOWClttp5mujDWFXKaNNMSTdMWAL9RSi07/f89Sqn8uK93K6UKNE17DtimlPrT6ddfAG5XSr0+BYedJk0C6RVymvOVdk3TSgBO/+10oBwD5sZ93xygNcXHlibNsKQDcprzlV8D/3T6v/8JeCbu9X/UYlwK9Cql2ob7AWnSpJp0yiLNOx5N0/4bWAfMANqBfwd+BfwMmAccAf6PUuqUFuuCeAi4EggB/59S6rXhfm6aNKkmHZDTpEmTZpqQTlmkSZMmzTQhHZDTpEmTZpqQDshp0qRJM01IB+Q0adKkmSakA3KaNGnSTBPSATlNmjRppgn/P7Itued9pcXFAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "surface_obj = SchwarzschildEmbedding(5.927e23 * u.kg)\n", "surface_obj.plot_hypersurface(plot_type='surface')\n", "surface_obj.show()" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "LIlNZy3uyMpN" }, "source": [ "The plotted embedding has initial Schwarzschild radial coordinate to be greater than schwarzschild radius but the embedding can be defined for coordinates greater than 9m/4. The Schwarzschild spacetime is a static spacetime and thus the embeddings can be obtained by considering fermat's surfaces of stationary time coordinate and thus this surface also represent the spacial geometry on which light rays would trace their paths along geodesics of this surface (spacially)!" ] } ], "metadata": { "colab": { "collapsed_sections": [], "name": "Plotting spacial hypersurface embedding for schwarzschild spacetime.ipynb", "provenance": [], "version": "0.3.2" }, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.2" } }, "nbformat": 4, "nbformat_minor": 1 }