{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Einstein-Rosen bridge\n", "\n", "This Jupyter/SageMath notebook is relative to the lectures\n", "[Geometry and physics of black holes](https://luth.obspm.fr/~luthier/gourgoulhon/bh16/).\n", "\n", "The involved computations make use of tools developed through the [SageManifolds project](https://sagemanifolds.obspm.fr).\n", "\n", "*NB:* a version of SageMath at least equal to 7.5 is required to run this notebook: " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 9.3.beta9, Release Date: 2021-03-14'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we set up the notebook to display mathematical objects using LaTeX formatting:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The rescaled Lambert function:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "W0(x) = lambert_w(x/RDF(e)) + 1 " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The minimal value of the Kruskal-Szekeres coordinate $X$ on a hypersurface $T=\\mathrm{const}$:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def Xmin(T):\n", " return sqrt(max(0, RDF(T^2-1)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot of $r$ as a function of $X$ on a hypersurface $T=T_0$:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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BvPkmx+ocOUKRZZ22fc45TA9a5xQJghAcRFgJQujYtYsWCt9/r7e5XMwuNW4MXH45cN99wJIlvkepdu9mWY+1DKdrV56LrR3/3jh2jEEQlYVyuSjorF2FFVC3hBXAovPt2z3NPJOTKbCqUqK7d9P3yvrciv5IO3YwemU1LmvXDrj5ZnpdPf8811HWmiE2FnjxRX6BfJhJJAiCTYiwEoTg43YD//43C9BPnNDbGzbkebl1a+CJJ/j/hx/6FqUqKWETWnq63lZRMMTbenbv9uz6j43l+Tsmxqdfqe4JK0DnTK2jaHz94CoKK44YUb5OqriYXhq//KKjV1FRwJgxwJln0nph6lQKq507y3tuvP++346vgiBUExFWghBctmwBbr21vDdkWhqF1dVXM4q1dCnNPtU5UnX8jRlTPkrlrXwnLY2iqqrSH2+Bl5QUlv/4kAJU1E1hpfAW6mvd2rcZfxUVwvXtW75Oats2Km1rzrhDByrtY8eA557j65UVezEx/NmDD0r0ShACjQgrQQgOpaVs2nriCc9RMykpTP21bQs8+STPx5Mn8/yoqChK5a3hzB+zTxXg8LdUyAt1W1gB/KNu3+6Zg23cmH/cqhSqt9bNZs2opMvmYYuKgK++AmbN0tvq1QOuuop/+A8/BP7zH6rsnTupnBUDBwIffFAjJ1hBEKpAhJUgBJ6NG9nQtXSp3lavHi0UEhOB668H7ryTIumTTzyF18iR3qNUeXk8F+/dq7elpPBcXJWNgmkyqGE9j/va3FYBIqwAqttdu9jiqahfnx9sVe2VbjeNxn77Taf7YmLoi5GWVv7xmzdTgVvztz17AjfeSBuIZ55h5+LevZ5/6Hr1gKef1kMlBUGwFxFWghA4SkpoPfT0056BA2X02b49f9amDefy/vabfkyjRqxP7tKl/Ovu3k1RZRVgffqUN/X2RlERAyu5uXpbUhIjZX6k/soiwsrK0aMUWFYvqrZtqaKr4sAB5nWtxXc9egCnn14+jVdYyKHN8+frbXFxFFfdurG26v33GRHLyPD8Evbty+hV797V/jUFQfCCCCtBCAzp6YxSLV+ut0VHU0QlJFA03X67DjxkZ+vHnX46ByeXtTdyu9mtv2aN3la/PqNUzZtXvabsbDaZWct5WrWyxVNShFVZ8vOpYK3qt3lzpviqorCQXYPWwvaUFIYvvYmztWv5JbJ6Wp15JjB2LNOBTz/NL1rZsTiRkcDjjwN/+1v5kKggCNVDhJUg2EtJCfDyy8Czz3rOzU1N5Xm1c2ee59q2LR9saNAA+MMfOLKmLNnZLKux1iSnpTFT5Evn3oEDnmnD6GhmqMqKt2oiwsobpaUUR9augsRE/vF9KSJfv55eG6oILjISOOssemCUJSeHnYGrV+ttKSnslEhLY93V++/zcRkZnoKvVy/+7LTTqvFLCoIAAJg0aRImTZqE0tJSbN68WYSVINjAmjWMUllTemocTUICcNtt/Pnu3TyPWUVSjx7M4HgLSGzdCixYoDsEXS7WKffoUfWavJ3bGzbkmmxsEBNhVRneVG379r4VtB09SkVt/QN27EiBVbZGyjTZYfjZZzrtZxjA6NEci7NlC2uvtmxhHZZ1LmFEBP0/nnxSoleCUBMkYiUINae4mFNG/v53Twuhpk0ZpWrfnhGsjh3Lm2mrhq6zzy7fXV9cDCxaxCyOIjGRGaGUlKrXZXVRV/iajfITEVZVUTYP648lQ0kJvwibNultCQmcc+Tti3D4MOuntm3T21q3ZvQqOZm+Vx98wDquskOde/fmMOhevar1awpCnUeElSDUjPR0Rpq8Rani4ji27a67aG3w3nusaVa0a8cIlrcxM8eOcSCzNVDRqRNLZ3xp5jp+nOdMa/10u3Y8HwcAEVa+UFREsWM1DUtNZSeDL7P9vIUuBw/2bp/gdlPBf/ut/hJERQFXXkmDs40bGb3aupURNetcwqgo+l499FDVdv2CIHgiwkoQqofypXr8cc9mKxWlSktjlKpnT2ZnPv1U11y5XMDFFwPnn++9E2/jRgYoVGlNVBQzPx07Vr0u0+Q50joBJTaWUTMfBypXBxFWvuLNkiE+nqrXFxHjrdiufXtgyBDvinvnTtZXWYvWe/Rg90R0NGcKTp3KNtEdOzzDm4MGsSjeW02XIAjeEWElCP6zfTvPSwsW6G0xMaxJrl+fzVj33UeRM3WqZzQrNZW1Vt7GzJSU0JHdmvqrrBnM2/N37PDsMLTBSsEXRFj5y+HDLLaz5oQ7dPCt7srt5vyitWv1tsREDl/2llosKgK+/JJDJBUJCUwNdu1K/6ynn2YdmDdV/tJLwL33BvxLJAi1AhFWguA7pgm8+y4ng1h9oFTHX/PmwFNP0eB682YWqFvn4p59NuupvEWOMjM5Cs76+G7dOJfXlyLzggJmdaw1yy1bek8zBgARVtUhN5epQWtqr23bqh1eFRkZFEsqFBoRwdBmRXMB09NZW2W1ZTj3XE7zLioCXn2Vru6q9soaih0+nM+tavCkINR1RFgJgm/s20ffqR9/1NuUe3p8PHDJJRRcsbEsUP/xRx2MqF+fdVh9+3p/7a1babug6pqjopjZad/et7VlZTFSZe3Kb9+eNV5BQoRVdSku5hfAWnflT4dBdjaL8awO7J06UWB5Sy1mZ3PsjXVad+vW/HI3acIv4t//ztcr69oeHw+89hojXb7UhAlCXUSElSBUjmmyPmrcOM9okhpUnJLC+X9DhvBc9N57FDmKTp14HmrUqPxrl5ay/mrDBr0tKYnNXr4GLcp28sfGMqMU5I75sDjLOlJYAUzt7dzJjgVFo0ZU7b6k3/z9Ipkm67SmTdNqPDoauO461lUdP84219mzte+V1ZTtwgv5RW/atBq/rCDUckRYCULFHDkC3HMP8L//6W1RUbzAT0ykmHriCZ7Dli0DPv5Y1/66XIxinXee93Ojt0BD587s+vOlhrmm52KbEWFlBzVVyd5Cn0OHsjDeGzt3UiBZo1Knn06BFR0N/PAD3W6zs1kPZi24T0nhcy+91L/fURBqOyKsBME7333H7Ii1mapRI3b7xcUx7XfZZSxD+fhjCitF48Z8bps23l+7bGlMZCQFVUWlMWUpLmZpjrXOK0D+VL4iwsouaprX9Vas16sXC/+8Ke7CQoZkFy/W26xf4AMHaMuwYoWeOaiEG8DHvfZaUPPOguBoRFgJgicnTgB//jMvxhUREYxSNWoEdO8OPP88Bdbu3cA773he8J9xBuf8eRszY5o8P61apbc1bMiMjS8+kUDN650DhAgrO/HWidCmje9fkpIStqxu2aK3NW/OL1pF84+WLwf++1/PkOuYMSxuN01OCZ80iT/fudPTYK19ez530CA/f1FBqIWIsBIEza+/Atdfz3OaIiGB57ToaNok3HYbhda8eUwRqov3mBjO+RswwPtrFxSwZGXPHr2tXTtmanwx/ASY9svIqF6HfoARYWU33rwzmjXzbdq2Ij2dswaVQWhcHC0ZKpq6feQIPa+2b9fbuneni218PA3WHn+cwurIEV5ZWB1on3iC/8RUVKjLiLASBGZdxo9nxkNlYFwuXZzeogWjVL16sXmrrDdV69bAnXdWPGbmyBFmZ1SXu2Hw4r5nT9/XuH+/pzl2XBwDBQ45h4mwCgSmSfFiNQNNSqLS97Ur78ABFvOprsOqLBlKS+nWbp271LAhcMcdVPEFBUz9ffklI2o7dnjmpE8/nTuIL262glCbkCHMgkAyMhhpWrRIb2vQgOm16GjW5v7lL7RMyMhg6s9awztyJHD55RULnM2bmZVRgi02ls/xNfBgmgwQlK0bTktzVMe7c1ZSCWEnrBQHD3qGOv1V1Xl5VPbWgsGuXTkOpyKTtI0bmQ9XVwMuF3eG887jF2/ePI69ycwsPxKnQQOOJbjtNkd9SQUhKEjESqirqLKRcePKZ1uaNeNF+hNP0BfRW3d6/fp0X+/d2/vru93Mwljtgpo0YSamQQPf1lhSwqyM1c+xRQtHdrmHxdkzbIUVQAGzY4dOvUVHM4JUUc1UWarzhczKYmrQOvy5Rw+mBuPiGIp95hlg6VI9EsdqKnrJJRRnFaUeBaE2IsJKqItkZgJ3381mKEW9eoxSxcXxQv6ppxgZys2ln+KaNfqx7dqxGSo52fvrVydAUJbCQtYeq/OUy8UMkDc/LAcgwioY5OWxAFB1LkREMHIVH+/7a3gLoY4aVXFLqdsNfP89/6mPr1Ejpgbbt+fPP/0UeOMNfll37/b0EElN5QiCCy7w//cVhHBEhJVQ15g3jy7ou3bpbcnJrKeKjgb+9Cfg2muZwdi2jSNsrJ3r553HjEhFAsnfkhZvnDjB91aF8ZGRDE74GukKASKsgkVREcVVfj7vGwaL/CpS+d44cgSYMYNfNPUagwezUL0iNmxg9MqaGlRdg4ZBwfbEEwyxZmYyf221Zbj/fuAf/wjoJHBBcAQirIS6QlER58z+4x/6wttqo5CWBrz4ItClC38+YwbHplkbqm65hZmQiti4kUOUfW3C8kbZzr+YGNYBB9lJ3V9EWAWT0lIKGGsO218jM29tql270lCtIofZzEym9qw2Dj17csdo0IARq3/+E/j8c0bVMjI819inD6Nb/lxlCEK4IcJKqAts2kQbhZUr9ba4OKb+6tUDLr4YePhh1k3l5XHWrDX117EjU38VeUW53SwzWbdOb6vKNsgbZY23ExKYdvQ1fRhCRFgFG28dg/52NZgmPUZWr9bbmjXj1UBFX1y3m12D1mGYjRqxLVY5vM+fz9qr7GyavO3Z4zk48803WaAohe1CbUSElVCbMU1mL+6/X6fmDIOip2lTHuP/9jfg/PP5s927gf/7P10iYhjA6NEUXhVdxBcWMvVnFUQ9etBOwdfRMqbJc4/VaNSBnX+VERarrFXCSlG2YzAxkQLHn7lGW7ZQDKm6q/h45rwrMyRNT2ftlEonulzA2LHAsGH80h46RM+rVauYtty+XZuPAnTR/b//43oFoTYhwkqorWRlAX/8I/DZZ3pbdDTPOfXrA926MfXXsiV/tmgRR9OospAGDdgtXlnZyfHjwM8/62yHy8V6qi5dfF+n282MibWOK8TjaaqDCKtQUjZ/3KABi/L8MTk7dIj5b3UFEhkJjBhR8VwmwHtqcMAA4IYbuLOVlrJI8T//4e2yhe1t2gCffCKO7ULtQoSVUBtZtowF6Dt26G0pKSxQd7mAm24C7rqLjufFxTy2W32s2rShKKvsgn3XLlowqAat2FhmUPyxQigtZZG61TjU3zpkhxAWwir4s6mDRFIS89UqZ5yby/y3GkbpC02acPilKggsKaHQsjrhlqVhQw7NPPdcvW35cuCllxhJi4jgjvbWW3z91q09c9sZGbwSGT9eR8sEwUmMHz8ehmHggQceCPVSBCEkuN3Ayy/zWK1EVUQEj+WtW1NcTZoE3HcfRdWRIyxmt4qqYcNYb1WZqPr9dxpTK1GVnMxzkj+iqqiI5z5rk1X79mEpqsKGWhuxUuTnM3qkvphRUYxc1a/v+2uUlDAtaJ3r1K4dd4zKImC//QZMnqzTfTExrKPq25f3jx1j3dXixfzyb9/u6dg+YgQd2/0Z2SMIgWT58uUYO3YsEhISMHz4cLz++us+PU8iVkJt4eBB2ijMmKG3NWjAc0K9euwmf+YZLZjWrGGRusp81KtHB/bTT6/4Pap7zilLfj5fQwUUwsBOoSokYuUEYmOZh1aF58XFtEGwOsxWhUoBDhyot23fDnzzjacQKku/fixYVDnsggLWUE2bxiuepCS6sd9/P9fZubNnvnv2bM6M+u4739cqCIHixIkTuP766/Huu++ikUPdAwUhkMyYQQd0q6hq2pTH7thYHstff53HdrebNgqTJmlRlZoKPPZY5aIqL4/HfKuo6t+fnX/+iKoTJzyzNNHRPBeGsagKG2q9sAJ4hdC5s/5ClZYyipWZ6d/r9OnDrg41IfzIEWD6dM8aqbKoHck6ifznn2nBkJPDsOwNN7DmqkULRqc6ddLvcfQoO0Xuv9+z0F0Qgs24ceNw4YUXYtSoUVU+trCwENnZ2R7/BCFcKS4G/vpXNjApl/PISB6rW7TgBfF77/FY7nLxgvtf/2KnuEJdaFeWgTh2jGJMde1FRrKspF8//9ablcVznHUsTufO4pkYLOqEsAL0TqA67kyTUSfrwElfSEujCajKZuTlMXJlddctS3Q0uz6uvlp3Jm7cCPz971wDwLbZjz7iVUl8PDtJrN2B//oXcMYZnlcxghAsPv30U/z2228YP368T48fP348EhMTT/1r1apVgFcoCIFhxw7g7LNZU6VISGAXX3w8f/bxx/QvBNiR/sILNJAGeMy/6ira71TmNbVnD88lqqs8Lo7nmsqapbxx7BgL1ZV5aEICRZW6WBcCT62vsSqLtwnerVqxkNwfCgoYeVJXL4ZB4VOZWy5AYfTOO7yiACj4rruOJqRqfV98Abz6Kq+SynpexcczunXVVf6tVxCqy+7du9G/f3/MmDEDvU9Ogh02bBj69OlTYY1VYWEhCi1DMrOzs9GqVSupsRLCii+/BG69VdscGAYjVKmpFEz33st6KXXBvHw562pVTW9CAgVVx46Vv8+GDXRSV8f5xo0ZHfOnFhigh6P1Ij8picIsTDyqfCEsfpM6J6wUu3d7mqRVx8+jtBSYO5dXB4oePSiwKvsiZ2dTXFktGYYNo1hSOfT164FHHwX27fPueTVuHPDKKxLaFQLPV199hcsuuwwRFlvm0tJSGIYBl8uFwsJCj595Q4rXhXCisJAde2+8obdZvamaNGGnd69e/JnbzbIQa+1VmzbsAK+sHNE0adlgdV9v04Y1vf7UUwHl3dQbN2bQoBaJKkCElfPZtw/Yv1/fT03VJm6+YprAihU0/VSkpQEjR1Yeei0tZWRq9my9rWNHepqoAdLZ2ewumT+fO+7OnQzzKvr146ic9u39W7Mg+ENOTg527tzpse2WW25Bly5d8Ne//hU9qgrTQoSVED7s2MGyjeXL9bakJB7XIyKYXXj2WT12JjeX3oQq9QfwMddeW/k5oKSEx/+MDL2tVy8WtvsrhvbupbBSNG3KyFotRIRVOFDWpT05mT4k/n6xN20CFizQee3kZBa6V9WBsXgxa6uUC2+jRsDdd3MNAIXb1KkceeN2s1B+1y4dMk5IoNv7FVf4t15BqAlVpQLLIsJKCAe+/pqWOKqxyTAY9WncmOm+ceN0gTrAc8dbb+kGJpeLomzo0MrPIXl59KeyjrQ56yzOpvUH0+T5wNpA1aKFfz5XYUZYCKs6U7xeEampWsQArL3asUMLF1/p3Bm44AI9Gfzo0ao7BgF6njz8sL76OX4cmDCB4WGAO9yNNwJvv03TuZQU7nwqBZidDVx5JfCnPzF8LQiCIPhHcTHwl7+wWFyJKmVP0LgxU3/vvEMndSWqVqyg6ac6xsfH0xxajTCrCNX5p55Xrx7nBFZHVO3Y4XmOSUur1aIqbKjzESvF8eOegqo68wUB7pQ//qh9slS7bFUpxuxselxZ67VGjWIkSq3h2DHgiSc4JNrb3Kf+/TmvSg1+FgSnIBErwans3s0o05IlelujRrzgjohgau7vf9e1Usqf6uef9eNbt2amoSp7t337WIelvKXi4pjZqMx93Ruqq90aWWvTxv/XCUPCImIlwspCdnb5NtX27f0XV2U7Bl0uYMgQ2j1URkkJhdH8+Xpbly7sKlEpRbeb+fz33uPOdfgww9FqzYmJdPm97DL/1iwIgUSEleBEfviBqT1Vu2oYvAhWXeK33soCdHUOyMvjsTc9Xb/G4MHs7K7KzmDbNmDOHH2sbtyYoio21r81u90UVaqz3OXixbTVnqcWI8IqHDlxgt166ssfH88RAP6Kq5IS7kTW4ZwDB9JktCrmzwc+/VSbu6WksK3X2rW4dCmjV5mZ3Nl37PDsGrz/fvquqNSkIIQSEVaCkygpAZ58kp19iuhooG1bXsTGxQHPPccLYsXBg3RRt14wjx1bdeoPYNff0qX6flqa/07qAM9L27Zp+weXi+cn1fBUBxBhFa6cOEG/KSVs4uL45a2io7wcpsmhm+vX623du/MKp6odcetW1lWpHSgmBrjjDk+frEOHaMmwZg3XunOnZ2rw9NOB//2PxZeCEEpEWAlOYe9eduwtWKC3JSZSVEVEsDv75Zc9j5sbNrDGSo2miYtjB3dVWQjTZIpx3Tq9rUsXFqr7e7HudvO8YB2mXMdEFSDCKrzJzfUcCVBdcQVwQvmvv+r7bdvSp6Sq1zp+nFdIu3fzvmHQ62rECC3MiouB116j7QJQPjWYksLo18iR/q9bEOxChJXgBObMYT3V4cO8bzX8BIALL+QIMqtD+ty5LNFQx9QWLdgdmJxc+XuVlvL91HQNgHWw/o6nUa+1dat2ZY+I4PkoLs7/1wpzRFiFO3l5HNisxFWDBryaqY642rwZmDdPF8c3bUpn3aoMPgsLWTNl9ck6+2xecVnX8d13wIsvsiiybGrQ5QKef57RLX+vkgTBDkRYCaHENNlt/dhjWiBZU3+RkezOvvxyfdHqdlNQzZ2rX6dXL44nq2w0DcDj9owZ2ifRMHjc7tLF/7Wr2ba5ubyvomp1dJiyCKvaQF4ev9TKZ6p+fX6p/c2NA4w8/fKLp2fV6NFVX3WYJmdI/fCD3ta5M0PR1p1r0yYeHPbt43tkZOgCRwC45BKOW1DWDoIQLERYCaEiOxu45RZg2jS9LSGBoioykoXqL7/sWWaRl8fUn9X087zzaMdQ1cVpXh6P1aogPjKS9VRpaf6v3Zuo6tTJ/1E3tQgRVrWF/HxGnKziqlOn6kWuDh+mHYOKJjVowPCzL2Jn2TJgyhS9jiZNGJK2+pZkZQGPP64LJffvp9BStG/P+VcnR74JQkCZNGkSJk2ahNLSUmzevFmElRBU0tMZhdq8WW9r1owjzAA2FL3wgqdNQtki9YgIzgMcPLjq98vOpqiy1saOHs0OQH8pm/6LjORFfR0WVYAIq9pFQQF3TjVcsyZpwZrsfNu3A//+ty5gjI1l5MpqLud20xPr/ff1++3cqb1TYmP58xtv9H/tglAdJGIlBJvPPmPaTkV7oqLoN6VsCcpaKQDli9Tj4+lP5cvYsGPHeFy3FrhfeGH1bBDcbkaqrKKqUyf/rRlqISKsahsFBUy3qYhRXBzFVXXqlvLzGblSrrlRUQw1qyupyjh6lOJKjeJRYxSGDfN83Ny5wFNPcUcvKmLdldpRAR5UXn9dBjkLgUeElRAsiouBRx7hsU0RF0cDzehoRnyee6788XLePDb6+FukDnBO308/6YvXRo04iaM6dVBlu/8k/eeBCKvaSNm0YHV9rgDuhD/9pIdnRkQwF28dsVMRhYXAf/4DrF6ttw0bRoFlXcvOncBDD2lX+bJzpQYOpCVDdfL/guArIqyEYLB/P72lFi7U25KTeXxzuWih8MorntMpTBP44gtg5ky9zdcidaB87WyTJjT+9OW5ZSnrUyWiqhwirGorZbsFq+vQDnBnnDmTggdg98jw4RRrVWGanEdoHa3Qowed2q1RqLw8TmOfNYv3jxxhtEutPzkZ+OQT4Jxz/F+/IPiCCCsh0CxcSDsadaHqctFFXZVYDB7M0TTWr19REUsmrF3X557LyRW+HM/Luqm3bMnjaFUu7N4wTb6eajiq491/FSHCqjZT1ucqMZHiqirjT2+43dw5rXMCzzyTZqK+sGQJMHWqXkurVnRqtxbEmybw4YdMIZomxdauXbr+wOUCxo9nV2F1fgdBqAwRVkKgME3gX/9iZN7aYJSWpkXJTTcxrWcVS9nZLFLPyOB9l4ujac4+27f3Xb/eMzLWrh0viqtTd1t29p/LRVFVB32qqiIszk4irGpA2fE3DRty56qOMPHm0j5gANC3r2/P37wZeOstXTjZqBFw332sE7CyYAG7BvPyKMR272bNlmLsWF7ByVWSYCcirIRAkJsL3H47a6MUjRpRVEVGMnL/9NOMQlnZvx944w197IuJYaTf14vZsqbPXbvSTb26x/4dO/TUjDrqqO4rIqzqAmXFVXIyiySry6+/cqdV9OoFDBrk23O9HSzuusuzYxDgTvyXv+j0Y1lLhl69mGK01iEIQk0QYSXYTUYGfaWsdabNm9N+xjBoq/DKK+XHzni7CL33XqbxfGHlSv5T9OnDWtXqsnOnrnsVUVUlIqzqCtnZ7OJQH2WTJjWbz7d6NT2rFN26MTXoy9VQdjbw5pvcWQHuqDfcUN6DJSeHkavFi3k/M5PRK2tXy2efSd2VYA8irAQ7mT2b0XV1EVmvHo+5qvyhf38OWC7rD7h0Kb0AKyubqIxlyzyF3MCBFFbVZe9eXRNmGCwnqY49Qx1ChFVdIjPTs0aqeXNeMVWXjRuB+fP1/S5dmPv3RVx56xi88ELg4os9n+92U4RNmcL7BQUUV9bJ6S+9xNoFqbsSaoIIK8EOTBP45z95TLI2D7VqpbvwrrsOuP9+z1on0wS+/x749lu9rUcPDrb3pXvPNHkRmp6utw0e7OnW7i8HDlBYKdq2BZKSqv96dYSwOBOJsLKRI0d0pAhgnr86jruKLVvoRaX+RJ06AUOH+iZy3G4OZp4zR287/XSagpYdx/PTT/R1KSriwWrvXj2kFACuuQZ47z2puxKqjwgroabk57O0QV0IAswONG9OEVWvHqPwF17o+bzSUjb3LFmitw0dyuOaL51/psna1I0b9bazzy5fYuEPhw/rUgyg5ueKOoQIq7rIwYPauBOo+VXItm0Me6s/U4cO9Kvy1dph1iz6VFnF2T33lHfw3bCBdVeHDnn/PXr1Ar76ir+PIPiLCCuhJuzezdE0K1boba1aUVgBQEoK8OqrLJuwUlgIvP22jjQZBnDFFfQL9PUCdd48XuSq5w8dWr5uyx+OHWOdq6JFC8+xZEKliLCqq9idN9+xgwJJFci3bQuMHOm7uFq1iqlBNY6nZUt2DJatKzh2jHYLKoWYmUlxVVjI+0lJrLsaNar6v4tQNxFhJVSXhQsphtRFX9l6qm7dgIkTtchS5OSwmUdlESIjafrZr59v7+t287irRJDLBYwYUbOmnqwsXiyr025qqu9F8wKAMBFW1bC0FKqiRQsd1lX+JNZRMv7Sti3bhZWQ2rGDTr+qxqAq+vZlNEp5ouzZw2nuasioIimJ3TIXXcT7DRsyQqYibseOcezOxIn6wCAIlTFp0iR069YNAwYMCPVShDDDNDnTdPhwLarUMUmJqnPO4Wy/sqLq8GEe45Soql8feOAB/0TVL794iqpRo2omqnJzeS5Qx86UFBFVtRWJWAWIst4kEREsQK/OmAPFnj10Wbd2tJx7ru+GdAcPsvBTddI0aMDIVdn0nmmyjuHNN3m7tFS7tStuuIEHtJr8PkLdQSJWgj8UFvLY9O67elvz5rxgVTWid97J4vOyKb2dOxmpUrP2GjZkMbsvc1gBiqqZM7VxaEQEj7M16fQuLGSNljIwbdSIx11pCvKbsPjERFgFENOkDYPqsqtXj+KqOuMOFHv3UlypHbRlS0aRfBVXWVl0KVYiqV494I9/9N7dMncu8MQT7BYE+HuoWgOA/lrTptWs+1GoG4iwEnzlwAHWU1mLzdu1o0AyDB6znn3WuxXM+vWMcqnyhWbNKKoaNfLtvb2JqvPPL2+07A8lJRRVak01mS8riLASwB110yZtRhcbC3TuXL2xB4r9+4Eff9Tiyt/IVX4+U36bNvF+RV5XAB/z5z/rUHxeHsPZ6iDRogXw9dfAaadV//cRaj8irARfWLUKuPRSFqsDFFFt2+oyhsaNafpZtkgdoMfUhx/qWtQOHdio42s3c9maKjtEldtNQ1I1OsyO438dJyyElWjmAKOcdOvV4/38fM88e3Vo1owtxSrypaarqwNKVcTGAn/6E030AD5v8mTaLpRdV+fO/Jk6kNWvz2J8VXe1dy9bjz/7rPq/jyAIwrRpHAujRFWjRjx2KlHVrZvnsUhhmsCMGRzFpY6BffuypsofUTV7tqeoOu+8mokqVV+rRFVUFH8fEVW1HxFWQSAqigM11Q6Vne3pd1UdUlOB0aN1vcGuXQxh+yquIiM5Y2v4cL1t+nR6X5UVV40bs55Khd5jY5mCVDUH+fn0hHnySd/fXxAEAeDx5u9/Z+efiuy3asV/yhamoiJ106Qg+/JLvW3IENZf+VpyoUTV9u28r0RVTQvLd+1i6YV6zY4d9QW2ULuRVGAQOXGCYWH1kTdr5ntBZUXs28e0oCpob9eOLcG+5u9NkzVb06frbaefzmnwZa+s3G4Wk6qCUtPUv5PisstY+C5T2QUrkgoUvJGfD9x6q+cQ5U6dePxQhd0VFam73cB//8vh9YpLL+UFp69F4W43TZTV1AyXi6KqJoXqgOf8VcOgqJL5f7YQFqlAEVZB5vhxfWUEAK1bs+22JpTtFuzQgZEofzpOFi+mO7GKOPXqVfFVn9WpHWC9VXq6Foy9erHuqibDqIXahQgroSz79lEIWU0/e/bUUZ2oKOCZZyh0ylJSQm++337jfcPgKJshQ3x/f9OkqNq6lfddLtaqpqVV69c5RVkDUBlVYythIawkFRhkGjXyvBratUu3BVeXli09fa62bqVbsD91XIMHc1yESi2uWcPuQdURaOX889l5ow4W0dEUU6qeYc0aYMAAjoEQBEEoy4oVPEYoURUby2HGSlQlJrLBxpuoKiwEJk3SoioigmUN/oqq+fPtF1UnTuiOQoDHZhFVdQ8RViGgSRNdK2CaDEOrLrvq0qoV6xCUuNq8mcLGH3HVuzeL2qOj9Wu8+qp3c9NevVhI2r4970dGMtytUptHjtAd/r33qv87CYJQ+/jsMza8qFRZaqpnp1xaGvDBBxRaZcnLA15/nbYKAKNa48bpRhxfWbLEsyv6nHNqLqoKCz1d1VNS+LsJdQ8RViGiZUs95qa0lFdOvjqpV0Tr1hQzKgW4caOnF4wvdO4MPPigjj7t3Emn9czM8o9t1ozh+NNP5/2ICApG1bVTXMzaCOskekEQ6iZuN/DUU2x0UZHwTp14HFGiqm9fiipvIicri8ciVUoRG0srmO7d/VvHihXAunW8bRisSW3dunq/k0Idw5UFTnx8zYWaEL6IsAoRhsHcu+p6KSjwvNqpLmqOoBJX69YBK1f69xpt2lAMKeG3fz8wYQLHRJQlLo5u7pdcwvsREXRjP+MM/ZhXXmHHj2o7FgShbpGbC4wdCzz/vN522mk8fihRNXo0U3ze5qoeOcJj0N69vB8fz2OUipj7yurVOoUIMH1YkzE1gLZVUGIxJobrElf1uosIqxASEcEdUNU15eRoD5ea0K4dJ7ArVq4E1q717zWaNwceeUQX1h85wtlbKnxvJTKSVgv33MP7hsHC9mHDdGry668Z/lcHRkEQ6gZ79nDfV5YIhkG/KnUbYKPMc895tyPYt4/HHnVhl5zMY5O/dgjr19NEVDF4MCP0NWXPHj1dIzJSvKoEEVYhJzra8+rm8GHtcl4TOnXydFK31hT4SkoK8PDDum4qO5tXjdaOF4VhsG36+ed1J2FODgWesl5YtQoYONDzilGo3cgQ5rrNypXc51et4v0GDRglys/n/chIjqe5807vEZ5du5j+U35QTZvymFTWz6oqtmwBFi7U9wcM8D7Gy1+sx2vD4EWtqlEV6i5it+AQjh717Cbp2BGwoyt95UqdCjQMTmgvO3S5KnJz2SGo1hcdDdx7L8WbN377jWF6dRVXvz7FmJpPWL8+8PHHbLUW6gZit1D3+PprWiBYTT/btNH34+Mpmioah7V9O487SoS1bs3mGn898jIyOJlCner69KHYqyk5ORRs6nXbtGE0TQgoYZFglYiVQ0hO5tWYwjqPryacdpq+MjNNzsJSAsdXGjRgkWiXLrxfWMgD3oYN3h/frx/HS6hIV14ew/ZqHXl5NBJ95ZWa15QJguAsTBN47TXu40pE9epFYaXuN2/OIvWKRNWWLez+U6KqQwc21fgrqvbu5UQKdZzp1s0eUVVU5DmaLDVVRJWgEWHlIFq04AR3gF0m27bZMyLmjDN0dMnt5lytgwf9e42YGEapevbk/eJi4M03dXdNWdq04UBU1bFTXMxI19ln875pMqr1xz/yZ4IghD8lJbQ/ePBBLTqGDePxQ10oduvGY0NFBsIbNrAhRj2+SxdGqmJi/FvLkSM81qljaKdOwJln+vkLecHt5rFZdQAmJNRspqBQ+xBh5TDatNEHkPz8ms8UBJgCHDJEH8hKSjgG59gx/14nKoomon376tf597+B33/3/vikJODttz3nEeblARdfrO+/+y67gY4f928tgiA4i+xs7ttvvaW3jRnDlJmyWznzTB4TKjLNXLuWF2zqYqtHD17Q+Vu3lJ3NY5x6nTZteAy0o1Nv1y4deYuOZmmFdAAKVkRYOQzVKai6So4d8z+65A2XizYM6sqqqIgHHn8tECIj6U2lDPlKS3mgtI6lsBITA/zjH6y1UOzbx9ZrVeQ+axYL7dW8LkEQwotdu9jp99NPvB8ZSb8qa5fzmDE0HFYWM2VZtYqiTEWCevcG7r7b92HKivx84IcfdBqxaVP/5qdWxqFDrIcF+HrWrm5BUIiwciAxMZ5hcms7b02IiODYhsaNeT83l+JKzfzz53Vuuw0YNIj33W46rFtbma24XEwN/PnPetu2bcDll2s7h40baTRq7dwRBMH5rFjBfVdZujRsCFx1FeukFHfeCTz+eMU2BL/+Crzzjo5s9e/PMgF/RUtxMY9p6njZqBHH4tghfnJyPOtT27SpWCQKdRsRVg6lYUM6Eit27PBfAHkjKoqz/lRj1rFjngOcfcXlAm66SfvRmCaLUa2T5sty/fXACy/og9zWray/UPVfR48yqvbf//q3FkEQQsP06UyxHTjA++3acTzM5s2873LR464iOwWAA+Dff1/XQp1xBi/c/PWCUvWjR47wflwccMEF9tgflC1Wb9qUok0QvCHCysE0b65diEtK7Ctmj43lAUfVcu3fzynv/nbouVzAH/5AcQTw+VOmcLhpRZx3HjsK69fn/R07WJyqBqgWFQE33EBvG+kYFARnYpq0SrjiCp1yGziQzSpq5ExMDLsDK7NVWbyYxwy1rw8Zwgs2f9N2pgnMnasNiKOjeYxTo7lqgnJWtxarq45nQfCGCCuH07atvuLKy/PfKqEiEhJYNK6iR9u3+z9XEOBV6DXX0B9L8dFHlYurgQOZOlTtyXv38iB89dX6Mc88Q8NRO6J0giDYR3Exa58eflgLoosv5kWgmszQqBFTe5V14S1Z4imqRoxgLWZ1CsGXLmUEHOAx7fzzdYd1Tdm7V9ei1qsnxepC1YiwcjiqmF1dwR0+7H83X0U0bkxBZJ0ruGaN/69jGMCVV/JgpvjoI2DBgoqf06mT57DVo0cZObv/fv2YDz8ELrxQuy4LghBasrK4T779tt52xx0c0q6OS61acd9Ww9i9sWQJMHmyFlUjR7KhpTqCZd06Xd+lTJBTU/1/HW9kZurmIcOQYnXBN0RYhQGxsTxYKXbu1AM/a0pamk7DAZ5Xfv5gGOz6sYqr//638mL05s1ZW6GMQ3NzWQD/xBM6SjdzJr2v7IrUCYJQPfbu5b74yy+8X68e8NhjFDXKfqBHD+7Tlc3xW7rUU1SNGMFi9+qIqowMphMVQ4boi7WaUljoOQ2jVStdwiAIlSHCKkxISdGpM7ebqTs76q0ADiJV9gkAaxVUMao/KHF13nl629SplRe0N2zIFmtVBF9czJbtRx/Vv+/atew6Wr3a/zUJglBz0tNZVK4iQ8nJLEqfOVN7RZ11FvB//1d5UffSpYxEK1E1fHj1I1VHjgCzZ+v7/frZM1QZ0MdY1dTTqJHuphaEqhBhFUakpXmah1o9YmpKv35A1668rbprqmPxYBgcZXHuuXrb1KmeV5VliY3leJtLLuF90wS++45mpGqu4b59vFqeMcP/NQmhQ4Ywhz/z51M0qeNNmza0T/nqK31xd+GFLGavzB192bLyourqq6snqk6c4AWYKijv0MHz4rCm7NnjaQLaurV9ry3UfmQIc5hRUMCRD+qA1rZtxS7G/uJ282Cl0m6JiYxAVadd2TSBL77gFS3Ag+dNN/Gqt7LnvP02C9sVo0axY/HXX3k/IoJFsbfe6v+ahNAhQ5jDk//9j52/qomkXz8Wqn/3nX7MH/7AkTOVdfItW8a6K+uYm2uuqZ6oKioCvvlG13Q1bUph5689Q0UcP647G10udi2LX5VjCIu2AYlYhRkxMZ41BHbWW7lcFDIqlJ+VxXqK6qQcVUH7yJG8b5qsq1i6tPLn3HUX6zbUAXfmTIox1bJdWkqPm6eeEjsGQQgk//wnI0pKVJ17Lvdnq6j605+ABx6oXFT9+qt9osrt5jFBiaqEBK7LLlFVVOQ5RqxVKxFVgv+IsApDkpO1Y7nbTS8ou0RGvXosQFcHk337Ku/uqwzDYFGqmhVomkwFVOTQrrjiCuDFF3X3zcKFvCq95x79mOefZwRM7BgEwV7cblopPPCAPq784Q9Ax466psnl4sXNjTdW/lorV7KYXb3O0KHVF1UA6zVVRD06mpYx/g5nrgjT5LFU1VUlJenjrCD4gwirMKVVK31AycvT/jF2EB/PAnR1FbhpU8WDlqvCMHjVazUR/eADHnAr45xzgNdf17/jihUcKfHii/qgPHUqD6yZmdVbmyAInhQWckLCxIl62yOP8CJHRZvr1QMmTNA1kRWxZg3T+lbzz2uvrb6oWrOGZRAAhd1552kDZTvYv5+1WwBFm13dhULdQ4RVmOJyeRrVHThA4WEXTZpoMQQwnL9jR/VeS5mIWsXVe+/pDqOKGDSIHYOqJGf9egqs997Tgmv2bBbW7tpVvbUJgkCysnih8umnvO9yAS+/zP1e7asNGgBvvsnIU2Vs2MB6SVVGcOaZ1Tf/BFg4b410DxvGKLZdnDhBYQVwjW3b2pdeFOoeIqzCmPr1gRYt9P0dO3SXjB20bw9Ym7nmzKm+OakSV8qJ2e1ma/bGjZU/r2dPCinV6rxzJ4viP/5Yh+nT0ynCVq2q3toEoa6jPKrmzOH92FgKo3nzdCF3UhLw7rssYK+MrVuBf/9bH4sGDmQqsbqiKjMTmDVLR7769WMXoF2UlnpeNDZrZs8oHKHuIsIqzElNZeoOoJ+MtfDSDvr21QexkhIObK5usbxh8ACrxFpJCQ/A27ZV/rx27YD//EebpB46xKvmKVNY9wHwanPIELFjEAR/Wb++vEfVf/7DyJXys2vRgil8NTC9IjIygDfe0LWPffoAN9/s/+w/RVERjznq9dq0AU47rXqvVRE7d+rXj4uzNxIm1E1EWNUC2rbVhd6ZmXq6u10MGaKjQzk57MqprjmpywXccgvQuzfvFxbyQFxVKq95cx7s1YE9KwsYPx6YNAkYPJjbTpxg2/WUKdVbmyDUNRYsYBRZeVS1bctI8r//rWsXO3ViAbo1Ou6NPXvYSaguvLp357ib6qbUTJPHGjXSKimJjTB2zuk7doz2CgDXKXMABTsQYVULiIryNLDbvdvebrnISBaKWjsFK7NNqIqICB5wlSFpfj4L1asqwE9KooeVSkXk5bEz6YkngMsv57aSEnYLvvSS2DEIQmV88QWbRJSAOu004NVX+S8/n9v69eM+p6YgVMSBA9yHlalmp060TqnJXL1ly3QHYEwMj0FRUdV/vbIUF3te0LVuzcJ8QagpIqxqCQ0belowWGdc2UGDBjwIq5D+unVV10dVRlQUcPfdOs2Ym8sD86FDlT8vLo4RLjXfsLgYePppphjHjdOPe+wx4L77dOu0UH3eeust9OrVCwkJCUhISMAZZ5yBH3/8MdTLEmrAv/7FUTKFhbx/3nnA44+z61ZdlA0ZwpR7XFzlr3XkCPDaa7p5pl077os1ESmbN+uB8MpfT5U82EVGhqe1QmWjeATBH0RY1SJattQHs5ycqkWKvzRtqmf6AfSXUpPfq0N0NHDvvTralpXFA3RVBfLR0Wz3vvBC3ne7gRde4DzB8eP14yZN4slDXX0L1aNly5Z46aWXsGLFCqxYsQIjRozApZdeivT09FAvTfATt5v2CfffryO6N93ESQYvvqhT/Oefz47AqsRRZib3WRX1atWKFzQ18ZY6fNjTO2/wYJYC2Mnhw3pkV1SU55B7QagpMtKmlpGTw6s9gFd63bpVbyRNZSxezIgVwM7Eyy+v2dT33Fz65qhUYJMmPPhXdYXqdjPK9fHHetudd/L3vf123ZV01lnA11/bN/pHAJKSkjBhwgTcdtttXn9eWFiIQhUOAUfatGrVSkbahJDCQtY3fvKJ3vbEE2wA+de/9LbLL+cQ9KoKzvPyeIGj9ttmzYCHHqo6wlUZBQXAtGnaT6pbN8+LOTsoLGTBvhKRHTrY64clBJSwqICTiFUtIz5eWxOolKDdtUaDBukryLy8mhWzA0wz/vnPFFQAI21vvFF196HLxefdfbfe9s47jHh9+61umV64ULyu7KK0tBSffvopcnNzcUYlgx/Hjx+PxMTEU/9aSUggpGRlARdcoEWVy0WPuObNPUXVjTcyjV6VqCosZJpQiarkZDq110RUmSZ96ZSoatJEN6bYhWnymKiOVykpIqoE+xFhVQtp2VJHqU6csD8lqGoelHA5cEAPSa4uCQkUSQ0b8v7OnTzwV+XLZRicHfjgg3rbRx8Bv/1GTx4l1jZsYEu5qtsQ/GPt2rWIi4tDdHQ07rrrLkyfPh3dunWr8PGPPfYYsrKyTv3brdrOhKCzdy/rpdQ4mthY4MsveWz4z3/04+65h2m8qrriSkrocaVsUuLjKarUvltdVq70LFa31nTaxeHDnu7qLVva+/qCAIiwqpW4XPR7Uezda9+gZkXZA9+aNdV3ZlckJfEArdKKGzfywO9LNOy665jWUCeFadOAb75htEp5Xe3b52mCKPhO586d8fvvv2Pp0qW4++67cdNNN2H9+vUVPj46OvpUsbv6JwQf5VGlLiiSkzlYfc0a7bAOcDbgrbdWLarUvE9VXhcTw3otdQFTXXbt4sUQwDVYL9zsoqiIx0JF69biri4EBhFWtZS4OH2wM037jUMBvr41GzR3rvacqS7NmvGqWRXN/vYb0xe+pDPHjAH+/nct9n78kVfWc+bQ/Rlgwer55wOffVazddY16tWrhw4dOqB///4YP348evfujX/+85+hXpZQCd48qubN4wXHN99wm8vFrtqrr6769UyT+83y5bwfFcXmk5pmebOzdTQN4L5qd7E6wGOgukhr3Nj+LkNBUIiwqsW0aOGZEjx82P736N5dWyYUF/NquKZjddq1oweOEkjz57NmyhfOO4+F8MrvZu5cdgr+8ANw0UXcVlTE8TqvvVazddZlTNP0KE4XnEVZj6p+/She3n6b42EAeky99BJw8cW+veb33+tor8vFRhEVDa4uJSU8ZiiLh7ZttXmwnRw75tkFWJXZqSDUBBFWtRiXy9M4dO9eih+7Ofts7QFz7Jhnq3R16d6dHUyK77/3vKqtjCFD6ACtWr6XLgX++ldg6lR2CyoefJBdTDUpvK8L/O1vf8OCBQuQkZGBtWvX4vHHH8fcuXNx/fXXh3ppghe8eVR9/z0tSRYv5rboaBqBjhjh22vOmeN5cXPTTUCvXjVf68KFwNGjvJ2YWPVw5+pQUqKjdgCQliYpQCGwiLCq5cTHa9fk0lLPA4xdREXx6lhFibZsYW1HTRk40DNF8dlnvhfJDxxIHytVp/H770wxTpjA1IfilVdoLirBl4o5ePAgbrjhBnTu3BkjR47EsmXL8NNPP+Gcc84J9dIECxV5VE2dyu1qSHn9+uzo87XjbuVKz9T52LHsDK4pmzZpa5jISODccwPjfL57t46iN2pU8yJ7QagK8bGqA5SUsNhUHVzatw/MwWX7dlovAIyWjRmj3eBrwtdfM5WnXvfeexnR8oWNG+kCrWq/2rXjHLTp05luVNGqESNY8C6t14EhOzsbiYmJ4mMVICryqPrTn/j9376d2xITKarUOKmq2LKFXnHq2DF6NPfrmnL8OPdB9bojR/K4ZDdZWcDWrbwdEcHjhp1jcYSgIz5WgjOIjPQsMN29OzCjXtq1A3r25G23myLLjtTjJZfoETZuN+tEfPWk6tIFePddLfC2b+ecwosuAr76Ss8/nD2b71HVvEJBcBrePKr+7/94AXLnnVpUpaRwX/BVVO3fz4sQJX4GDwYuvbTm6y0p4bFBvW7XroERVW6353GiVSsRVUJwEGFVR0hKolcUwELRQAmI00/XBqXZ2fbUWxkGcO21evhyYSENRFVtRlW0awe89x47DgEKy9tvZ5Hs7Nk6VbpmDbscN2yo+ZoFIRh486iaPp0F6XfcoVP/zZvTuqRdO99eNzOTtVpqqHL37kyZV2XH4AuLFzNiBfC4VInPbI3Yt08XxSckVD1IWhDsQoRVHSItTXfaHTqkD5p24nIxrK+uDLdu1XUUNX3dW2/VV7bZ2RRXvv4OLVtSXKWl8f7BgxRXKSnAokXa92vXLraoL1pU8zULQiDx5lE1axbQpw+/2+riKS2NkSpfO+EKCrhvqZmdaWnAH/9oT8H3tm16eHtkJP2qIiNr/rplyc/XxsiGofd7QQgGIqzqENHRnv4wgRrxkpCgU3cAO39U23dNiIpivUhqKu/v3++bO7siNZXiSrWIHzvGVInbDSxZAvTty+3Hj/OAP316zdcsCIHAm0fV4sX8jt9xhxYVbdtyzJPaZ6qipIRpROWAnpzMpg875o1mZ9M6RXHmmYErJN+1SxfwN2tm/7xUQagMEVZ1jCZNtA1Bbi5w5Ehg3qd9e9Y3Abqmwo66rgYNWJCrzP02b6YTtK89GElJrNFSxe/Z2Zw1ePgwzRNVo1tBAXDFFawxEQQn4c2jStko3HmnTpF37Mjvuq8NJKbJDkKVCm/QgB2GdvQauN2Mpqmay44dgc6da/663jh61HNsja+iUhDsQoRVHaNsWHzv3sAUsgMsdlVXpMeOAcuW2fO6KSkszFXpxuXL/YsuJSQw0qUiVCdOMBK2dSvw3XesJQF4ohk3Dvjb3+wfZC0I1cGbR9Xcudy/7rpLi62uXSmqkpJ8f+1vvqHnG1A+OlxTVqzQBsWJiRyKHghKS3W0DfAsfxCEYCFfuTpIfLw29Cwp8ZyfZSeqhkLVZqxb53nQqwlt2vDqXBXT/vwzTzC+Ur8+T1IDBvB+Xh5THqtXA1OmAI8+qh87fjxw882BMVet7UyaNAndunXDAPVBC9WiIo+qb7/ljM6779bO4r168cLBn0jT/Pna0kQNNrerU2//fvrIAeVrMO1m3z5Pzypx9hBCgQirOkrLlvpK7vDhwBSyA7xiPv10fX/uXPsGQvfqxW5BxaefUhj5SmwsPXqUUWJBAU9cS5dSTL3xhhZuU6aw0yonx5611xXGjRuH9evXY7kaMCf4TVERcMMNNLdVPPEE8MEHwNq1jCzl5nJ7v370qYqL8/31164FPv5Y37/6ah3NtWPt1qHn/fvb423njYICHRVzuXiME4RQIMKqjlKvnrYfAALjyK7o3l0f5PLyWMxuF0OHMh0C8Er+3XeBjAzfnx8dzdmCqti+qIijbubPZ7rxiy904evPPwPDh7OjUBCCgfKoUsJHeVQ9/zynENx3HzvgAE4b+Ne/GI31lT17uM+oKNi55/I7bheLF+t6p2bNAjMHULFnj/49UlMD4+IuCL4gwqoOk5rqOaTZjs49bxgGMGyYfq/t2+nobBeXXaZTesXFHGWjWsV9oV494OWXmaJQr/Hww/QGuvxyFt6rWrGVK9niboeFhCBUxr59FPxqaLLyqPrjH3lx8uc/61qrM89k9FU1pvhCVhajW+o1+vXj990utm/X+0m9ehRsdvhgeSM7W09XiIoCmjYNzPsIgi+IsKrDGIZnuNx6xWc39etzWLNi0SJ9JVtTDIM1UMpGITub4sqf+X+RkcCLLwLnn8/7paWss/rpJxbaLlqk3et37OCJzK5ifEEoS0UeVZdcwtTaQw9p88vhwxl19SdCU1TEjldl1NmmDX3i7BI+ubme5sBnnulfetIfTNMz4m4tcxCEUCBfvzpOw4bauqCwUPvfBIJ27bT4UbUXdgm5yEgW8CrX9z176DStZgH6QkQE8NxzPHkBfO6TT7JAuFs3el2pkT1HjvCE9t139qxfEBTKo0r5zCmPqjPOAGbMAP76V12gfe65rAf0pxjcNFmfpVLmSUms07KroNw0aV2iLmys+30gOHxY1202aOBfJ6QgBAIRVoJH1Gr/ft8NN6uD9cp1/359RW4HDRqwLkrN/1u92n+TT5eLhcFXXMH7pgk8+ywHNLdowZPesGH8WX4+Z6e9955tv4JQx/nf/7x7VHXqRBH/xBP6YuHCC4G//91/5/KvvwZ++423o6MpquzsnktP192/ZSPVdlNSwuOIwjoTVRBChQgrAfXr6zlapaWeByq7UbUWihUr7K3tatqUNSgqFTBjhjZP9BWXi2lAa8fhiy+y6zAxkenBq6/mdrebTtfPPiteV0LNeO01fq/KelQ1bUph/+yzWlRddhnw9NP+p7wWLwZ+/JG3DYOWJXZ2z2Vns6heMXx4YF3PDxzQF4JJSby4EoRQI8JKAMBojNV+wS5LBG80a0arBIBCbt48e0VJ167ANdfo+//9r//F5obB7sAbb9TbJk6k7UJ0NLu0/vxn/bNnnuFJKpDRPqF2UloKPPAAv29qP7j5Zqag4+OBzz6jsFc/u/pqmtb6K6o2b+a+oBg7FujRw47fgKgUoNoHunf3fT5hdSgq0qULLldg30sQ/EGElQCA9RXKZdk0A2caqujfn9EfgPYF69bZ+/pDh+rIWGkpW9SVx42vGAbb2e+4Q2/7179Yu+VyAa++Crzyiv7Ze+8xkqA8hQShKvLzKXD++U+97emngfff5z45ZYqnf9UNN7Bw3d8i88OHuQ+oKQvDhtlrqwCw4F5Fu+Pjaf8QSPbt02KzSROxVxCcgwgr4RRNm+oC1szMwAqEyEiKH8Xy5do52i7GjtUzAXNz2VrurxGqYTC1eM89ettbb7GjyjQZZfjkE31Q/+47YMQI/0WcUPc4coSTCaZN4/2ICIrzZ57h9+699yjkFbffzjmZ/oqqggJ2yar9uXt3Rr3stD7IyfHskh06NHDu6gAFqZqJGBEh9gqCsxBhJZzC5fI0Dd23L7Dv17SpTkWUlNifEnS5GG1Sv9OBA8A77/jXKai49VamaxTvv8+Tnmky7fjTT7oA+NdfWaS/fXuNfwWhlrJ9Ox3/Vf1fXBxF+W238Tv1738zwqS45x7OAvRXDJkmI6wqktSsGfcJu+0IrCnAbt2A5s3tff2yWCPqzZrpsVmC4AREWAkepKTo6Et2duBHuAwYoO0e9u9nOsFOYmPZKag6ETdsYOdVdfjDHzivTTF1KuuuTJNplQUL9Allyxa2x69cWbP1C7WP5cv53VAmuU2bUpicfz6/S//8J4W74oEHKOyrwzff6M7b+vUp0FTXrF1s2KAvwuLiPEdYBYITJ7QZaL162mJFEJyCCCvBA8PwvNoMdNQqKsozJbhsmf1iLiWFV/vqqnb2bHpSVYexY4HHH9eRg88+o4+Q282C/CVLWDwPsLB2yBCe3OoqMoTZk+++Y32TKrru2pXfmX79+B2aMMGzwPyRRyjoq8OKFZ6Dle+4g7VIdpKby9maiiFDApsCBDwHuTdvLmaggvOQr6RQjqQkPRrDenUYKJo312KkpMTTsdkuOnb0tE/473/9mylo5bLLWAejDujTptFY1O0G0tI4buSss/izvDxgzBjPWpm6hAxh1rz9Nn3PVJ3fkCF09G/Tht+dF18EPv+cPzMMelaNHVu999q9G/jwQ33/yiuZorObRYs4AgoAunQJ/ODjrCxdKxYTI2aggjMRYSWUwzA8W5cD3SEIMH2g0nV79gBbt9r/HmefrYctl5SwCL26BfPKnFGJK2XeWFLCg/0vv2jLB9ME7r+fhceqK0uoO5gm7RHuukvX940dy6HejRrxO/HMM8BXX/FnLhc9q8aMqd775eSwWF0JnjPO0HMw7SQjQ1+cxMYGPgUIeHrsNW8euNmDglATRFgJXmnYkDUZADtw1EyxQFGvHgu+FUuW6FlodnL11UCHDrydmckC4ep6T517LvCPf2jn6xkzaCxaVMSr6Y8+4glV8cYbjHbZNSNRcD4FBcB11zFdrHjoIXaSxsTwu/f44zpl53IBL7wAXHBB9d6vpITfabW/tm0LXH+9/QKkuNjTeHfw4MAagQKe0arYWIpSQXAiIqyECrFGrQLpxq5o3ZppEYBizurgbBeRkbRPUAflbdvoqF5dhg+nl5Uq+J87lyfOwkJ9kvzPf7T4+vZb1pQFunZNCD2HDtF6Q32/DIMp4QkT+N0oKmIN1cyZ/HlkJPDyyxxpU10++0xHexs25PzMQNQ8rVypLxBatgTat7f/Pcpi3WcC3XUoCDVBhJVQIQkJekREfr69o2cqYvBgfSJYv57moXaTkMATjhI7CxYA8+dX//XOPBN4/XV9xb54MTu58vN5/9ZbOUZE2TH89hswaJC9cxIFZ5GeztSYapKoX59zK++7j/cLCynA1feuXj0azqo5lNVh8WL9emoouTLhtZMjR4C1a3k7IkLXEwaSrCxdmxYbS9EoCE5FhJVQKVZfq2BEreLi6MquWLCger5TVdG6NV2sFZ98UrO6roEDaUCq0qfLl9PmQaUuRo3iia91a97fvZsnpJ9/rv57Cs7k5595gaDqj1q0YEPDpZfyfn4+a+5UKi0mhsJ88ODqv+euXUw9K66/Xkd/7cQ0uU8qv7nTTrN3gHNFSLRKCCdEWAmVkpioxUJeXuA7BAE6Q6ek8PaxY/rq2G4GDdJFvW43u7Zq8vv17UtjR+XLtXo1owaqQL57d7amK+eBnBwWwb/9dvXfU3AW//43/6bqb96vHy1E+vbl/dxcCu4VK3i/fn3W3tVk/Eturmet4JAhNRNplZGerqcKNGqkZ34GkuxsHa2qX1+iVYLzEWElVEmwo1YuFzv4FCtXBm68zpVXsk0c4AH83Xdr1rnXowdPcioFs349u8FUMXHTpqzDuuwy3i8t5c//9CcZ4BzOlJYyCjVunP7+jBnD1JyqVczOpkHn6tW8HxdHIaZEV3Vwuzn6Ro13aduWDRqBIC9PC0KA+2gwPKQOHNC3ZXSNEA6IsBKqpGFD7dacm2v/TD9vNG6sfXdKSjznkNmJy8UZbOoqeMsW3fZeXTp3pkBTHjubNwN33snaFIBX3f/7H+cMKt54g51gge6+FOwnJwe45BJPr7JHHgG+/FLXKGZmUkCnp/N+YiIFuBrpVF2+/VZPK4iPZ2OGqh20m19/1Z26XboER+Tk5mrD4JgYiVYJ4YEIK8EnrFEr6xVkIBkwQBeEb90auPdVJyR19T1jBrBqVc1es107RhKU0/WOHXS+VsX4ERHsJnzvPV2s/8svLHjetKlm7y0Ej4wMNi8ou4TISP5N//EP/X06epTCevNm3k9K4sxKFSmtLqtXe9o03Hln4CwIDh3S669Xr2apS3+w7vOpqeJbJYQHIqwEn2jYULux5+TomodAEh2t65EAFvvaOaTZSrt2ni7XH35Y847EtDRGrlSx7e7dFFdWw9XbbgNmzdI1ZVu2UFzNmFGz9xYCz+zZbLRQNYANG/Lvdttt+jGHDvFvrgZyN25MUVVTe4JDhzznCV52GdCpU81esyJMkw7riv799bEgkBQU6E7kqCggOTnw7ykIdiDCSvAJw+AVoyIQNgje6NpVH1CPHAlsNGfYMC3kCgpYVF5Tk9IWLSiu0tJ4f98+nmh37tSPOftsdhH27Mn7WVnA6NEcxhsoISlUHzUo+dxzdW1Tx45sTBg+XD9u/37+rXft4v2mTfldqGm3XmEhpwYUFPD+aafVzPuqKjZv9ixYD8RoHG9ItEoIV0RYCT6TlKTrN44fD4wzelkMw7PD6ddfeWIJ1HvdcINOe+7dyxb2moqb1FRGKdq1430Vxdi2TT+mTRtGBVRLvttNL6ybb9Z+WOFIbRvCXFAA3HIL/zaqSH30aH4vO3fWj9u1yzM6qQR2TWfpmSa/k8p+oFkz4MYbAyc6ioo86xvPPDM4BetFRewIBpg2VxFdQQgHRFgJPuNy6Zoh06RACAbNmunUSUEBuwQDRXQ0661UbdfSpfYMhU5JYQRMpWuOHWNNzMaN+jHx8RzobB2DM2UKheWOHTVfQyioTUOY9+6la/7kyXrbo4+ygNxaVL1lCxsiVMSldWuKKmudYnVZtEgLnehoFsQHMi23cqWOjLVrFzwPqYMH9QVNkyYUV4IQLoiwEvyicWN9xXr4cPCGCp9+uo6WpacHtntORQEUn33mmbqrLo0asROse3fez8riidHq06XG4Hz6qe4o+/13pnt++qnmaxCqx4IFrC1SY5bq1+f3Yvx4z5P+2rUUzCra0r49RZW6IKkJe/Z4jl+68cbAduZlZ+suxogI+r4Fg9JS3UFrvZgThHBBhJXgF5GRuubJ7da1F4EmLk77/Zhm4OwXFP37c84bQLuHt9+2x0srIYHeRX368P6JE/Q2KjsX8eqr+Tt27Mj7x4/TjuH55wPjRC94x+3m/L7hwz0jUIsXezY7APwb3nOPtgfo0cPTdqMmFBQwnVxczPvDhnlOKAgEv/6qv2u9enEfDAZHj+r3tZYfCEK4IMJK8BvrFeShQ8ErsLYe3HftCvwg4yuu0HVRR4+yU9CO37VBA0+3bTXiZM4cz8d1786idlV3ZZrAU0/ReDIYcxvrOseO8bP/6191ZHbECJpk9u7t+dh58/g3VPVwAwZQQNsx7kXVVamGkVataGwbSA4d0p2MMTHlf99AUbbEQKJVQjgiwkrwG6tRX3Fx8E7yERGeV+mBjlpFRjKto8TcmjVssbeD2FjOhxs6lPeLi3kC/+47z8clJrLu6oUXdIHyt98yNVgLypYcy6+/chyN+nsYBvDkk7RTKFtI/cMPwMMP62jSkCHsGlSjoGrKwoU6ohkTwxpA5X0WKJYu1bf796d3VTDIytLNKQkJ2phYEMIJEVZCtSgbtQoWHTvq1Mrhw/qqOlA0agTcequ+/+WX9tRbATxZvfwyU3wA0x/PPONZRwOwzuRvfwN+/FH/7tu3s6h94kRJDdqJaTKaeNZZ+u+cksLP/rnnyhdR/+9/jCKqv8Ho0fyb2iVEytZV3XQT6xwDSUaGTnsmJtbcyNQfJFol1AZEWAnVIj5edyOdOBE8SwDDYCG7wloHEii6d6dnEcCU0Dvv2Pf7RkRQTFnrdSZO5HuUTTuedx67tNTvX1LCSMmFFwZX3NZWMjNZ2/anP+no0+DBdOE/7zzPx5om8MEHdFhXXHkl8Oyz9tUEKS81NUNy+HBG0QKJ2+0ZCT799ODYKwDcp1R9WnS0nrcpCOGGCCuh2livnINVxA6wxkS1fWdn61lpgWTMGA64Bdix9N//2ldb5nJRIN1+u972zjvAq6+WF41t2rBD7dFH9baffmINzMyZ9qynLrJgAT/D//1Pb/vLXzgwu6z3lIpqTZqkt918M1O5dokQ0+R3TAnm1q0DX1cFABs2MB0HsOOwpmam/mA9hki0SghnRFgJ1SY52XMeWrCsFwDP1u/ffgu8WWlEBA0fVc3HihWsfbELw6D1gnUw8yefAE8/raMniqgotvnPmKHd8A8cYFTtr38NnIFqbaS4GHjiCXbZKYf0hg05iHvixPK1TCUljEpNmaK33Xsv/9lp0rlkia6hi4lhrV+gu+OKiz094oJlrwDwAkJZVLhcMr5GCG9EWAnVJiLC03pBHRiDQUoK0KEDbxcUcCBtoElOZo2L4rPP7O9MvO461uwowfrjj+w28zab8Zxz+HurNKVpsr7ntNMCa6JaW1izhqmuF17QkcEhQ/iZqk5MK/n5jGJZC9ofe4zRKjs5eLB8XVUwnMfXrvU0Aw1m1OjYMX1hlpQkhqBCeCPCSqgRoUoHAmxpVwJk7drg1Hn17cvoBsAr/HfesT9CdMklwIQJugD6118ZsVBz6aykplJ8vfyyjq6kp1MwPP10cMYOhRtFRYw6nXYa66cARoPGj2fXp5rraCUzE7j7bj2MOCoKeOklWnLYSUkJ8J//6O/UWWcFvq4K4PutWcPbhuE5/DwYWI8dgS7OF4RAI8JKqBGxsdqOwFp8Ggzi4zmkGeAJKRhRK4C1LqruZv9+4Isv7H+PoUM5aFf5IG3cyBl1Kl1lRdVorVypTVRLS9nFdvrpdG4XyKpV9A975hldFN69O1Nvjz7qPVKybx9w223AunW836AB8OabwMiR9q/vm290N2JqankT0kCxZo0W4Z06BbdwPC9PR2Tr17fPpkIQQoUIK6HGWK8wvUVVAknfvvpkuH59cKJWUVGMIKmI0vz5gRF1vXszeqHGluzbR+sHNWakLD17sqPr6ad1Pc7vv9OH6MEHgyt6FU4ZwpyXx1qqgQP13yoigttWrqzYxXzLFn7mVuuF995jtMtuNmwAfv5Zr+2OO/TMykBSUKDHKrlcwYmQWZFolVDbEGEl1JiGDbW4OX48uEXs9et7Rq2CFZ0pG02YMoUdinbTti3w/vu6niwzkwaRixd7f3xUFKMxy5ZxpArAv8drr/Fz+vLL4DnlA6EfwmyaLETv1o21VCpK1asXU6zPP1+xePn1V3Zqqrl1rVvTYkGNGbKTnBy+tuLyy9n9Ggx+/11/Ll27MhIcLEpLdW1mRIQ9438EIdSIsBJqjMulD4hud2AHJHujTx8doVm/3nuhdyA46yw96uPECftG3pSlSRPOnFORhIIC4IEHgM8/r/g5/fqxc/Hvf9d+Y3v3Mo154YVMLdZ2tm4FLroIuOwyHXGKimJzwPLllUdmvvoKuO8+PR+yRw9GD5s1s3+dpklhrmwOuncPTJrRG3l5noOWVSo5WBw/7jkXMFieWYIQSORrLNiCtWtJXeEHi/r1GZEAeAUcrKiVYQA33qjroNLT6XsUCOLjWdczahTvq+HAL79ccYQwOhp4/HGua/Rovf3HHykU7r5bO2zXJg4fZidlt24cN6MYNYq1RM8+W7EzuttNj6q//11/rkOGsN5NjXGym3nzdOF4fDy7DO20bqiMNWv079m9e/Drm6ydxGKxINQWRFgJtlC/vvZ4ys3VbdvBondvHbXasEFHGgJNXByLyhVffBG44dD16gEvvuhp+fD554xenThR8fPatQO+/55ra9GC20pLgf/7P6YYn3228ueHCydOsGC/XTvgX//S/l8tWvBzmjGj8vEshYW0T5g8WW+77jr6WQVqZt3evZ6mpDffbM/gZl8oKNDmuhERTI8Gk8JCXfcXE8OmAEGoDYiwEmwjlFGr2FhecQMUDcHqEAQYGVGpG9Uur2pW7MblYorKWqC+ZAkLrCsTdIZBa4BNmxiNUXU0ubmsyWrblqJNpaPCiexsRu46dODnokRibCxnLG7YAFx1VeVRoMOH2ZAwaxbvu1w0W33wwcClp8p+V0aO1HVxwWDtWs/aKolWCYI9iLASbCMpSZ+8jh0LbpE04Bm12rgxuFGzyy7TY3b27AGmTw/s+118MfDvf+voxvbtTEtWJSgbNGB6cOtWuoWrz+vIEW5PS+P/4ZAiPHCAEaZWrSiCDh7k9ogIuthv28aC9aqKsdesAf7wB11rVL8+8PrrFGOB5OuvGbECGFW77LLAvp+VoiL9+7pcwY9WAZ4dxFK0LtQmRFgJthEZqf1viouD394fE6NTPSUl2ncoGERF0etICZWZMxkpCST9+jFt1bo172dmUlB8+23Vz23ShLVE69cz3aWiMtnZjFy1asWux9mzgy+QK8M02fF4yy2cY/fSS7ob0zAohtavZ02UL4Xm06d7mq82bUo7hcGDA/YrAKCNwy+/8HZkJCOOZcfnBJJ16zx9q5QXXbA4cUKboMbHV1zzJgjhiAgrwVasV57BHHGj6NVLi4R168rP2QskLVuyTV7xwQeBr/Vq1YrvM3Ag7xcXs2bqxRd9c13v2BH46COmCG+/XZ/cS0pY+zNyJMXqhAm6sy4U7N7NNfTtyxl2H36oT8xK1G7YwFqqTp2qfr3iYjqtWy0Y+vcHpk717fk1oaDAs4P0kkvKD3oOJMXF2rfKMNhVG2ys0SpJAwq1DRFWgq0kJmpPq8xM3UodLOLitOdTUVHgo0ZlGTFC+2plZXGQcqBJSGCxtjV1NW0ahZKvKb0OHWjpsG0b65Ksc+I2bwYeeYQRokGDKHBWrw5sJMs02d35j3+wKy8tjWuwpjoTE4GHHgJ27GCUqXNn31776FFG9r78Um+79lp2XTZqZOuv4ZXPP9c1iB07cuZjMNmwQYvSjh2DVyyvsFqyuFzB+cwFIZgYpu9HRwclBAQnk5Ghr0jbtQv+gTMzU3s81a/Pk2Ywh7pmZjJqpPy07rwzME7d3vj2W0ZiVLSqYUNGr1REy1eKiujl9NZbFVtINGnCiNaAAUxL9u1b8Uk6OzsbiYmJyMrKQoKXB+XnU0itWMFU38yZumaqLKefTpPUq6/2v+D6t99YQ6bcvuvVo5C86CL/Xqe6rF7N2jiAdhhPPRWcAcsKt5sDnlWB/9ixgbORqIjMTAp4gNGqNm2C+/5CWBMkI5KaIcJKsJ3sbNaQADxot28f/DXMmEGBBzDiUVmbfSD49Vd2fAEsGH/mmeBFBjZvZiRHdQm6XEyV3X579QTm2WffitTUcVi3rhs2barcd6BNG6a1WrTg/6mpTIdu356NqVMT8eijWWjYMAEHDwKHDlE8bdvGv1Vlh6KuXVkLds01OiLpD243HezfeUdHUZs0oZWC8kALNDk5FNyq9vDGG4EzzwzOeyu2bmXdHMAo4PnnB/f9AUYYVZlAKCJmQlgjwkqom5gmaziKi1nD0bt3cCNGAE/aX33F24mJvDIPlukiwM/gnXcYIQH4Gdx9d/DWkJ0NPPkksGiR3tarF0e4KC+r6rB5M/Dllzn429/mIDb2AuTnR/q6IgCJALIAVH0mbdAAGD6cJ/7zzquemFIcOcLI0K+/6m0DBrC+KljdaKYJvP02h0AD/Fvcc09wv5MAU8QqDXnxxYFxkq8Mt5tRO7ebRfu9egX/MxDCmrD4tkiNlWA7hqHTf6bJ0H+wadJE2x9kZbH4OZgYBiMsqtV/9WqmuIJFQgLnA95zjy7mX7OGaVGrG7m/dOoEXHXVQQCXYtGijVi5krVZd9/NFF11hEp8PAvHb74ZmDSJAujoUaY1x42rmaj65ReKaiWqXC7WV02aFNwW/xUrtKiKiwNuuCH4gmLfPi2qUlKCL6oA7osqYtiwoYgqoXYiESshIOTm6nl0iYk1OzlWl127gJ9+4u0WLTgjL9isWkWHc4CGlU8/Hfyas7VrgSee0J5JACNBjzzifxrGNE1ceumlOH78OBYsWOD1Mfn5wI4dhcjIKMHhwwZ27XJh5coT+PrrxnjyySz06pWA1FSmCZs04ffD7hNsdjatGGbM0NsaN2aUqrIZgYEgO5upYNUh+sc/Bn8NAPeFXbt4e+TI0KTot2/XheuSBhSqQVhIcV/j+ILgFw0asA2+uJgnltLS4KcDW7XigTs7m6Li2LHgGxH27ctIzrJlFBxTp9I5PZhX6j17Ah9/zG6+777jtp9+YhTnr39lJ6Ov67n33nuxZs0aLFy4sMLHxMYC3bpFo1u36FPbsrOLTnXxBfpkunAh3eWt7v8jR9JMNNiF2qbJz16Jqv79QyOqjh/Xoioujk77wcbt1s7+kZFVG7cKQrgiqUAhYKiTmGlqE8dgYhgUFYpgGoZaueYa/Vmkp/PEH2xUAf2LL2ozyGPHKKweeog1aVVx33334ZtvvsGcOXPQMpjGSz5y6BCjcA88oEVVQgKjVC+9FHxRBQArV3qmAK+5JvhrALRvFcB9IlBjeipD0oBCXUGElRAwrCkvFf4PNp06aVfnLVuCPxwaoCXADTfo+198EbrP49xzaUUxdKjeNm8ecOWVwJQp3k1FTdPEvffei2nTpmH27NloG4pwRyWUltLk9MordccbQPf0zz5j8XsoTuI5OZ4+Ztaau2BSVMRuQIBRZF/9vuzG+p0X7yqhNiPCSggYcXF6xIv1ajWYREVpq4XS0uAbhip69NCt9QUFFAKhGhWjbAZeekmnRvPyaDI6diyFlnVt48aNw3//+198/PHHiI+Px4EDB3DgwAHk5+eH5hc4iWkCCxawIP+117RvWKNGtDX45z9ZVxUqPvlE+0X16xc8L7OybN6s3eWtFxrBxBq1joiQNKBQuxFhJQQMw9CzA93u4M8OVHTvriMW6emhEXgAIyrq81i71rP9P9gYBjBqFKNnl1+uU0N79gB/+Qs9r5Yt4wnxrbfeQlZWFoYNG4ZmzZqd+vfZZ5+FbP1r17II/M9/ZkG0+p2uuIKO6hdeGNpU08qV/AcwDXvddaFZh2nqYctA8Dy7ypKTwwsbIDDNCoLgJERYCQHFCenA+Hg9qDgvTxfxBpv69YHrr9f3P/ssdGJTkZBA5/H//tczorJ6Na0ObrsNWLLEhNttwjQ9/918881BXatpAkuX0i7hllu0RxjAuqEPPmCBeqg7zZySAgTYtKEKxps3D10KTq0BCE2tmyAEExFWQkCJj9fRkKys0KW/1Pw+IHTpQIBGof3783ZuLseLOIFOnWgL8fLLnh1ja9YA997LGrFvvtEz5oJJYSG9t/7wB65lxQr9s7Q0rvn995ludQKffqoFc9++oUsBAsD69fp2qKJVgPayM4zQC19BCDRityAEFJeLB9LMTNZ55OUxNRJsWrakyMvJoVloTk7oogjXXENxl5tLkTBwIAVXqDEMWi8MG8ZZfe+9p9NsGzcCzz0HvP46U4ijR3PNgeouc7spCr77jtYQqlZJkZbGkTAXXaTr+JzAmjVa+KkUYKjSXidOADt38nb9+qGbyZeXp5si4uODb7siCMHGQYckobaSmKivWLOyQiOsDINF7MuX8/7GjRxrEgri4zlA+P33ef+jj2iW6O9A4UDhcrF7cNQodtlNnqyjfNnZHIsybRqL4M88EzjjDEbhahqJyMmhNcH8+SxKV4O8rXTtyjTgsGGhsQyojIICelYprr46tNGZDRt0hLhbt9B9XpIGFOoaIqyEgKMKtgGemNWomWDTuTMLit1uYNMmpmhCdbIZOJDF6+vW8cTz5ZeelgxOwOWiuBo5kgXQn38OzJql04GHDgHTp/Ofy8U6ts6dmVZs2ZJjU1JSeDItLuZzsrIYqcvK4oiVffvYtZaerqMrZYmJ4TouvRTo08e5hc9ffaXrCLt35984VKjvOMC/TbCHkFuxCivrsUAQaisirISAExVFN+78fJ5Ui4u5LdjUr8+T/44dTE/s3BkaB2qA4uAPf6BpZ0EBTUMHDAjtCbAiDIP1Sz16AI8+SjuGH39kykuleNxufq47dugxQorjx4H9+3l7yBAgObnq94yOpmP90KEUVaGIcvrDjh3A3Lm8HRUV2hQgwHS3sp9o3Tp00dCSEu06HxsbGqsHQQg2IqyEoJCYSGEFMGrly8k1EHTtypMgwFRJKL0uGzWiPcBHH/H+1KkUWqEQnb5Svz7rq0aPpiD87Td26v32G7Btm45MKQ4dOoQDB/JRXBwDoGKxERXFSFf37sCgQYz2xMQE+JexidJS/u1U2u2SSxipCyUqWgWEzhAU8Jy4IEXrQl1BhJUQFBITgQMHeDsrK3TCqkULXcS+Z09oi9gB4OyzmRLcsoVjWH74gSmvcCAmhu7mgwfzfnExRevWrUwTHj4MHDnSBFu2AL//no0dO2iL0K0bI1DNmjEt3Lo1h3SHazRjxgw94LpVK0bYQkl+vrYUqV+fadlQYRVWkgYU6goirISg0KABu4FKS3mwNc3QpErKFrFv2RKaobjW9Vx/PfD88/xsfv6Z0ZpmzUK3puqiok6dOpX/WXY2T6xTp9auyMWhQ3qwtWGwTi7URfVbtmgT3E6dQrseJaxcLj2jUhBqOw7rqxFqK1b/mtJSXf8RCjp21Lc3bw7dOhTNmnGeHaDn3oXK70vwHdOksaoaFzNqlDaiDSVOSQPm5+vUcHy8c5sOBMFuRFgJQcMaqQil43hcHFOCAK+oDx4M3VoUF1yg59pt2QIsXhza9QhVs2SJFjHJycDFF4d2PQAjaKozsWnT0KbfrN2AtSlKKQhVIcJKCBrWWiZr7UUocFrUKirKc9zNl1+GftyNUDG5ufwbKa6/np2MoWbLFn07lNEqwPP7K8JKqEuIsBKCRnS0LlA+cSJ0w5ABdgMqx+5t2/SA2FDStav2PsrN5YBkwZl89ZV2g+/fn92Mocbt5ncZYD1jKDteTVN/PlFR4dPhKQh2IMJKCCoqamWa2t8mFERF6RNPUVHF5pTB5qqrtOfQ0qWe9TKCM8jIoDM8wIuFq64K6XJOsW8fLTAAjvwJZZdlXp6+cApl160ghAIRVkJQcUqdFeDZvaZm4oWahATg8sv1/Y8+0sXRQuhxuzm2RjUXXHyxc8a0bN2qb3foELp1AJ77tggroa4hwkoIKtaDbKiFVbNmOkWxa1d5c8tQcdZZQPv2vH3wIMfICM5gwQId3WzenEOrnUBJiTa+rVePEatQIsJKqMuIsBKCirXeIjc3tHVWLhfQrh1vl5RoU8VQYxjAtdfq9vTvv9edXkLoyMlhbZXiuutYy+QEdu/WFwZt2oR2XWXrq5xQ1C8IwUSElRB0nFJnBWhhBejCXyfQqhXn5AEceiyF7KHnyy+1/9qgQZ6dpaHGSWlAqa8S6joirISgYx2oq65sQ0WzZhwOC3he9TuBSy/VbtUrVkgheyjZupW+VQC/L1dcEdr1WCkq0tHW2FimKEOJpAGFuo4IKyHoWEdbhFpYGYbuDiwtdU53IMDuQGsh+yefOMMWwh8mTZqEbt26YcCAAaFeSrVRBeuKMWOc5cu0e7f+XrRrF/qROiKshLqOCCsh6ERHs/YCYCow1ONbVKE44JzuQMXgwayZAYD9+4E5c0K6HL8ZN24c1q9fj+VqOGMYMnu2HrKclgYMGRLa9ZRFFa0DofWuUqj0vtRXCXUVEVZCSFBRq9JS7b0TKpo21d5Ru3YxteIUDINF0qqQ/dtvPUeFCIElJ4efOaAHZoc6ImSltJQRK4AipmnT0K6noEBHz6wpf0GoSzjoECHUJZxUZ2VNB7rd+kTlFFq3pgUDwBOXdZSKEFi+/loLf2v00Cns3avrAlu3Dr3os+7LIqyEuooIKyEkOKnOCvA8YTqpzkpx2WX6RLVsmedMOCEw7N4NLFzI2zExrK1yGhkZ+raT0oCA5z4uCHUJEVZCSKhfX19dO0FYNWumR4Ds3h1afy1vNGjgeWL/7DPnrbE2YZr8jFX930UXOatgHeDfXwmryEigRYuQLgeAFlaGodPrglDXEGElhATrgbeoKPRjW1wuekcB9I06eDC06/HGWWfpNe7ezVmCQmBYuVJHBZs0AYYPD+16vHHwoE5Ttmqlh4qHitJSID+ft2NjQ5+WFIRQYcuuWFRUhJJQnxkdTmRkJOqFciqqA2nQQEercnOBxMTQrqd1a20SunMno1hOwuXiwN9XX+X96dOB006Tziu7KSryrGMbOzb0osUb1kkBTqj9kjSgIJAaHy6KioqQnp4Ot+QlKsXlcqF79+4irixYUwV5eaEXVq1aMZJmmhRWgwaFdj3e6NwZ6NsXWLUKyM4GfvqJRqKCfcyYARw7xtvduwM9eoR2PRVhbbJQkcxQolzpAUkDCnWbGgurkpISuN1utGnTBrHKwlrwID8/HxkZGSgpKRFhZaGssAo1ql19/35aGmRmAg0bhnpV5bn8cmDNGqZeZsxgijA5OdSrqh0cP06xCugIobK6cBK5uVr8NWmi52+GEus+LB2BQl3GtgB3bGws6stlSqVkZWWhoKAA0dHRaCBHHsTEcFhsaakzhBXAdOD+/by9a5czhVWTJsDIkRRVJSVMCd5+e6hXVTv48kttXzB8uPPSwQqnRasAvQ+7XJKeFuo2Ul4YRL777jtMmTIFn332GXJDPX3YIVgL2J0wp896klJu207kggt0Hcvy5c4aIB2ubN/OzxLgZ3vRRaFdT2U4TViVlrLpA2DhuhOjfIIQLERYBZEGDRqgXr16yM7ORqE6CtVxnJYObNRIpzH273fubL7YWM/aqs8/D/1ooHDGNIEvvtD3L77YuXVCbrcW/TExQOPGoV0PIPVVgmBFhFUQiY6ORrTEyD1wmrACtB9QSYkzbRcUZ50FNG/O2xkZwK+/hnQ5XgmXIcy//66jfk2bAmefHdLlVMrBg3rsUsuWzogOKZsFQISVIIiwEkKKtdTMKcKqZUt9e8+e0K2jKlwuWgEopk1z1pxDIDyGMJeW8rNTXH45a/+citPSgIBErATBiggrIaRER2sjQetVbyixOlg7WVgBQNeuQM+evJ2ZCcyeHdLlhCXz5wOHDvF2x45Ar16hXU9V7NunbzvBbR3QwsowmKYWhLqMCCsh5KgDcWGhM8a0xMZq+4IjR7S7tVO5/HKdDvrpJ0+jRqFy8vOBb7/V96+80hmptYooLgYOH+btRo2cER1yu/U+IoXrgiDCSnAA1itcp0StrOlAJ3cHAqyzGjyYt/PzgR9+CO16wgmrEB0wwBkO5pWxf79uUnCKFURBgV6TRKsEQYSV4ACcKKysKRbla+VkLr4YiIri7blzgaNHQ7qcsODYMWDmTN6OjAQuuyy06/EF63dRNS6EGus+K8JKEGw0CLWDkSNHokWLFujcuTMOHDiAN998E3/5y1+QlJSEdevWYdOmTVi5cqWt77l8+XJ89NFH6Nu3LxYtWoTHHnsMbdu2rfFjBd9xorBKTdXjbcJBWDVqRNPQn35iN+M33wC33BLqVTmbr7/Ww79HjAgP93prfZVThJU1Ve4EB3hBCDWOEVY7duzANddcgzvuuAMAMHnyZLRv3x4TJ0489Zg///nPtr5nYWEhrrrqKixbtgypqano1KkTbrnlFsydO7dGjxX8w3owdko9U1QUkJLCepbjx7kup580zjsPWLCAqa1ly4BzzvFMaQqa3buBpUt5u0EDYPTo0K7HF4qKWPMHAElJzvk+SsRKEDxxTCpw5syZuOmmm07dnzVrFkaNGuXxmA4dOtj6nvPnz0dCQgJSU1MBAAMHDsTSpUtx0It5kT+PFfwjKoqpGMA5ESuAfkaKAwdCtw5fqV+fjuwAI21WCwHBk6++0rcvuMAZReBVceCArmVySrQK0BdDLhcgo1AFIUARq/79qz4RNW0KrFih799+++0wLO0ks2fPxmuvvebxnHvuuafC1zt27BgmTJgAsxL76djYWDz99NOn7mdkZCApKenU/YiICMTHxyM9Pf2UgKrOYwX/iY0FcnLY9VRSooVWKGnWDFi7lrcPHHB+YTMADBtGy4WjR4H0dGDjRqBLl1Cvylls3QqsW8fbjRoBQ4eGdj2+4sQ0oNutR9k4JYImCKEmIKevAwf876SyiqqNGzdi//79GDFiRIWPKUtSUhLGjx/v13seOXIEMWWOBjExMcjMzKzRYwX/UcIK4BWwmoMXSsItYgVQkF5yCfDBB7w/bRrw2GPSAq8wTc9olbXo3+lYg+PW72YosabuJQ0oCCQgqcCmTdlVVdm/yg4Ms2bNQp8+fZBsqSbNy8vDk08+iVmzZuG5556zZZ2JiYnlIlwnTpxASkpKjR4r+I910o9T6qxiYoCGDXn78GFnDIn2hdNP17VVO3d6RobrOunpwJYtvJ2aCpxxRmjX4ytut66vSkhwTnRICtcFoTwBiVjV9EDurb5qypQp6Nq1K0aOHIm5c+di/vz5GDJkyKmfHz16FBMnTvQrFdilSxe8++67p+4XFhYiJycHrVu3Lvdcfx4r+I/1oOyk+dTNmtHR3DTpzu0Up+vKMAyahv7rX7z/zTfAaadph/u6Stlo1aWXhs9ncuSIHgjupMoDKVwXhPI4oJLFE7fbjblz5+Kuu+7y2L5+/XqMPTkYLS0tDatXr/YQVsnJyX6nAocMGYJDhw5hz549aNmyJebNm4cBAwacEkszZ85E48aN0bt37yofK9QMJ3YGAoysbtjA2+EirACgWzegUydg82aue+lSbSJaV1m5Us/ZS0sD+vUL7Xr8QY3cAZwlrCRiJQjlcYywysjIwJQpU7BlyxYcP34c06dPR3p6+imLBbfbjciTFc2lpaWnbteEyMhITJ48GS+88AIGDRqEefPm4aOPPjr180mTJmHAgAHo3bt3lY8VakZUlPaNcpKwatxY31ajRMIBw2BEZsIE3v/uO2DgwOA3BUyaNAmTJk1CqQq3hAi3m5E7xZgx4VV3Zq2vatIkdOsoi4ouG4Z0BAqCwjHCqk2bNnjqqacAAFOnTi338549e2LfybaYbdu2YbRNxjOjRo06lXa02j0AwPTp031+rFAzDINXvPn5PFibpjNOfImJPGEUFXlGDcKBDh2A7t1ZV3T0KLBoUfA74MaNG4dx48YhOzsbiYmJwX1zC4sXa3HSqRMjeuGEWntkJD2snIISVvXqOWN/FQQnECYVBsD111+PVatWYc6cOTBNE8OGDQv1kgSbUQXspkkh4wQMg0ahAJCXx3/hxCWX6Ns//BA+Bfh2UlzMiJ0i3KJVeXnAiRO83bixc+rCiov10HRr84kg1HUcsotWTVxcHJ5//nkMHz4cEydOhMspRxfBNpxaZxWu6UCA3lu9e/N2ZiYwf34oVxMa5s+nez4A9OoFtG8f2vX4i1Prq6xNJlJfJQgaUSeCY7Be9TqpMzCchRXgGbX68UdnfbaBpriY8xMVl14aurVUF2WzAOjoqROwfo8kYiUIGhFWgmOwHpydkgoEPIuFw63OCqCnVf/+vJ2TA9Sl8Zbz5wPZ2bzdr194zk48elTfFmElCM5HhJXgGKxdRU6KqsTF6VRHOEasAOCii3Rd0U8/OWsmY6AoG6266KLQraUmqIhVvXo0B3UKIqwEwTsirPxg2bJl2LVrF0pLS7F3714sXbo01EuqVVg7i5wUsQJ01KqwUI/eCSeaNaMjO8Bi6FmzQrueYFA2WhUuHmRW8vOB3FzedlK0CvAUVmK1IAgax9gtAMDIkSPRokULdO7cGQcOHMCbb76Jv/zlL0hKSsK6deuwadMmrFy50tb3XL58OT766CP07dsXixYtwmOPPYa2bdt6fexbb72FyZMnAwD69+8vPlY2Yxj0syoqcp6wSk4Gdu3i7WPHgPj40K6nOlx0EfDrr+zkmjkTGDmy9rplFxcDP/+s7194YejWUhOcmgYEPK0WpJdIEDSOEVY7duzANddcgzvuuAMAMHnyZLRv3x4TJ0489RhlFmoXhYWFuOqqq7Bs2TKkpqaiU6dOuOWWWzC3giKUNm3aYM+ePTBNEy3DsVgjDIiOpqgqKeEIj4iIUK+IWMZW4uhRIBwN9xs35my8RYsYCZkzB7jgAt+eO3/+fEyYMAErV67E/v37MX36dIwZMyag660JCxYAWVm83bdveNZWAZ6F69bvYKhxu7mPAhKtEoSyOOY6Y+bMmR6mm97mBXbo0MHW95w/fz4SEhKQerKHeeDAgVi6dCkOWm2Oy9CiRQsRVQHEepB2UtTKasp47Fjo1lFTzj9fp1tnzvS9li03Nxe9e/fGm2++GbjF2URtqa0CPL9rThJW1n1ThJUgeBKQiNUNN3iGsL2RnAxYDdZvv/12GBbXvtmzZ+O1117zeM4999xT4esdO3YMEyZM8GsIc0ZGBpIsZ8yIiAjEx8cjPT39lNiykpubiw8++ADR0dGYOXMmHn74YXTt2rXS31Pwj7IF7E5JVSUkMHpWWhrewqpJE462WbaMtTvz5gHnnlv180aPHm3btINAs3Bh7YhWAfq75nIBDRuGdCkeiLAShIoJiLA6etT/tnSrqNq4cSP279+PESNGVPiYsiQlJfk9hPnIkSOIKeNsFxMTg8zMTK+Pv/LKK3H6yQrgJk2a4LLLLsP69evFrNRGnGq54HIBjRoxNZOVxTRIsOfu2cUFF7DWyjSBGTOAYcPsPzkWFhai0BIOy1ZV5AGmbLQqXGurAKbb1KEoIcFZdUxWB38RVoLgSUB21eRkXhlX9q+ysPasWbPQp08fJFselJeXhyeffBKzZs3Cc889Z8s6ExMTy0W4Tpw4gZQKqkRPO+20U7c7dOiATZs2Yc2aNbasRSBOTQUCOh1omvqEF440bQqor3JODuuR7Gb8+PFITEw89a9Vq1b2v4kXFi7Uf5s+fYAgvW1AyMnRI2OcNB8Q8Nw3o6JCtw5BcCIBueb2MkPZL7zVV02ZMgVdu3bFyJEjMXfuXMyfPx9Dhgw59fOjR49i4sSJfqUCu3TpgnfffffU/cLCQuTk5KC1l8rkpUuXYtSoUaeiXDkne+7ryeWarVg/TqfNtStbZ+W0Li1/GD0aWLGCt2fM4HBmOyNwjz32GB588MFT97OzswMurmpTbRWgx/AAzkoDApIKFITKcFwyw+12Y+7cubjrrrs8tq9fvx5jx44FAKSlpWH16tUewio5OdnvVOCQIUNw6NAh7NmzBy1btsS8efMwYMCAU8Jq5syZaNy4MXr37o2WLVvikUceOZU6XLRoEQYPHoxu3brV5NcVymC9+nVaxKpRI307nCNWAOuOevcGVq/m77J4MWDZnWpMdHQ0ooPsGrlokf679O4d3tEqwFNYOTliJcJKEDxxjLDKyMjAlClTsGXLFhw/fhzTp09Henr6KYsFt9uNyJOX1KWlpadu14TIyEhMnjwZL7zwAgYNGoR58+Z5eFNNmjQJAwYMOCWszj77bEycOBGlpaXYvHkzpk+fXuM1CJ64XLpI3GkRq8REfVsVR4czF15IYQUw0nPmmc6xt/CX0lJG3hThHq0CnB2xUvumyxW+tYaCECgcs0u0adMGTz31FABgqpdcYs+ePbFv3z4AwLZt22zrUBo1atSptKPV7gFAOeE0fPhwDB8+3Jb3FSomKsqZwio+nicSa1FxONO6NdCjB7BuHRtOli6luPLGiRMnsHXr1lP3d+zYgd9//x1JSUlIS0sL0oorZvly3YncowfggCXVGCWsnNYRCOiIldRXCUJ5HNRnUjnXX389Vq1ahTlz5sA0TQwbNizUSxIChDpYu90UWE7BMPSstuxsFrGHO9auuR9/1MXSZVmxYgX69u2Lvn37AgAefPBB9O3b99TFUCgxTc/aqjBxhagUa4OE0zoCS0v1filpQEEoj2MiVlURFxeH559/HgAkalTLsV4FFxc7Kz3VsCFPeKWlwIkT4Tnaxkq7dkCXLsDGjRwwvXy5niloZdiwYZU2hoSS1auB/ft5u0MH/gt3cnO1eHFatMoaSZaIlSCUx0HXQYJAnNwZaD3J1YZ0IOAZtfr55/CKxJkmI22K2hCtAvTwaEBHSZ2CGmUDiLASBG+IsBIch5M7A2tbATsAdOzIyBUA7N0LpKeHdj3+sGkTkJHB2y1bAt27h3Q5tmH9bjlNWFkvdqRwXRDKI8JKcBxlU4FOwiqsakvEyjCA887T93/+OXRr8Zey0apKhjOEFRKxEoTwRYSV4DjCRVgFaUpLUOjdG1DjMTdvBnbsCO16fCEjg7VhAKc59OsX0uXYipOFlUSsBKFyHCWsRo4ciRtvvBEvvPAC7rvvPhiGgYceeggvvvgirrvuOo+RMnZy4sQJXHHFFdi1a1elj1u+fDkeeOABTJ48GXfeeSd2hMPZJwyxHqytV8dOIDZWr+/EidCuxU7CMWr1yy/69rnnOqtzrqYoYeVyAXFxoV1LWSRiJQiV45jrjR07duCaa67BHXfcAQCYPHky2rdvj4kTJ556jDILtZP3338fO3fuxLRp0/DKK69U+LjCwkJcddVVWLZsGVJTU9GpUyfccsstmDt3ru1rqus4WVgBPNFlZtYuYQWwG/Cbb/i7/f47cPCgjmI5jSNHgJUreTshARg0KLTrsRslrOLinCcYJWIlCJXjmF125syZHgad3uYFdghAH/Wtt96KZ599tsrHzZ8/HwkJCUg9eaYZOHAgli5dioMHD9q+prqO04WVslgoKQHy80O7FjuJjARGjuRt0/R0Mq8ukyZNQrdu3TBgwICav5iFWbN09+Lw4bUrclJQoMWL09KAgNgtCEJVBOR648UXq+6YSkwE/vY3ff/222+HYak8nT17Nl577TWP59xzzz0Vvt6xY8cwYcIEv4Yw+0NGRgaSLAO7IiIiEB8fj/T09FNiS7CPyEgKFycKK2tq5sQJpgdrC2efDXz/PU/uS5cCl1ziWVfmL+PGjcO4ceOQnZ2NxJq8kIXcXM4FBGjNMXSoLS/rGKyRUCf6pKl9MiKi9jQLCIKdBERYZWX53zFlFVUbN27E/v37MWLEiAofU5akpCS/hzD7w5EjR04NYFbExMQgs7a0hjkMJwsr68kuJwdo3Dh0a7Gb2FgKlZ9/5mc/axZw+eWhXpUn8+cDhYW8feaZQIMGoV2P3ViFlRN/NxWxkmiVIHgnIKnAxEQaKVb2r7KL11mzZqFPnz5ITk4+tS0vLw9PPvkkZs2aheeeey4Qy66UxMTEctGwEydOICUlJehrqQuodKDbXfGYlVBRNmJV2xg5UrvdL1igRYwTKCkBZs/mbcPQqcvaRG6uvu20wnXT1Puj1FcJgncCsmtYU3zVwVt91ZQpU9C1a1eMHDkSc+fOxfz58zFkyJBTPz969CgmTpwYsFRgly5d8O677566X1hYiJycHLRu3bparydUjvVquKTEWTPJykasahuJicCAAUwF5uXxf6ek25Yt04XdffvWrmihwiqsnBaxskaQnTRqShCchOOuOdxuN+bOnYu77rrLY/v69esxduxYAEBaWhpWr17tIaySk5NtTwXOnDkTjRs3Ru/evTFkyBAcOnQIe/bsQcuWLTFv3jwMGDBAhFWAKFvALsIquIwaRUEFMB04ZEjo62lMs7zFQm3EyalA61B0iVgJgnccs2tkZGRgypQp2LJlC44fP47p06cjPT39lMWC2+1G5Mk9ubS09NTtmvLJJ59g/vz5AIBHH30UQ4YMOVUkP2nSJAwYMAC9e/dGZGQkJk+ejBdeeAGDBg3CvHnz8NFHH9myBqE8Tu4MjI2lyDBNRnRqI61aAZ060Sz04EFg3TqgZ8/Qrik93XPYctu2oV1PoJCIlSCEN44RVm3atMFTTz0FAJg6dWq5n/fs2RP79u0DAGzbtg2jbZq2eu211+Laa6/FW2+9Ve5n06dP97g/atSoUylKqzWEYD/Wg7b1KtkJGAbFVV5e7RVWAKNWmzfz9qxZoRdWdSFaBWhhVa+e8wrEJWIlCFXjGB+rqrj++uuxatUqzJkzB6ZpYtiwYaFekhBAnCysAKB+ff6fn6/9lGobPXvqGqYNGzigOVTs2+c5vqZXr9CtJZCYpk4FOq1wHZCIlSD4QtgIq7i4ODz//PMYPnw4Jk6cCJfT7IgFWwkXYWWa9Hyqjbhcnl13s2aFbi1z5ujbw4eHvt4rUBQU6K47p6UBAYlYCYIviDoRHIlVWDmtxgrQwgqo3enAwYO1AeqyZaEp1s/LA5Ys4e3oaK6ptmJ18rd+x5yCVVhJxEoQvCPCSnAk4RKxAmq3sIqOBs46i7dLSoB584K/hoULtSnl4MFAGZ/eWoVVWDnR0d96kSMRK0HwjggrwZGIsHIO1tTbvHnBjSC63Z5pwDLDGGodThdWErEShKoRYSU4EuvVsAir0JKcDPTrx9vZ2cDy5b4/t6ZDmFevBo4d4+0ePVi4Xpux1uuJsBKE8ESElR8sW7YMu3btQmlpKfbu3YulykFRsJ1wilhZowy1lbJF7L52Qo4bNw7r16/Hcn/UmAU1vgao/dEqwPO75MSUp3W8lPQPCYJ3HLVrjBw5EjfeeCNeeOEF3HfffTAMAw899BBefPFFXHfddTjttNMC8r4nTpzAFVdcgV27dlX6uLfeegutW7dGZGQkxowZg6SkpICsR2DqSaWfnCisrCe92toVaKVdO0ANGdi9G8jICPx77tmjfbRSU4Fu3QL/nqFGUoGCEP44pvxwx44duOaaa3DHHXcAACZPnoz27dtj4sSJpx6jXNjt5P3338fOnTsxbdo0vPLKK5U+tk2bNtizZw9M00TLli1tX4vgSUQE63mcKKyio/VtJw0pDhSGAQwbBkyezPtz5wbe+bxstKq2WixYcXoqUEWsJFolCBUTEGE1bVrV6ZHYWODyy/X9mTNneriZexvE3KFDBzuXCQC49dZbAQDPPfecT49v0aKF7WsQvONkYWWdXVgXhBXAwcz/+x9rylasAK66KnAmlidOAL/+ytsxMcAZZwTmfZyG01OBal+UaJUgVExAhFV+vue8K1+4/fbbYVguSWfPno3XXnvN4zFqhp83jh07hgkTJsCspPgjNjYWTz/9tH8Ls5Cbm4sPPvgA0dHRmDlzJh5++GF07dq12q8nVI46eFvrOpyCYTBqVVhYN1KBAMernHkmR8uUlACLFgHnnReY91q0SFssnHWWZ4SwNqOEVb16zowKScRKEKomIMLKlxB22cdYRdXGjRuxf/9+jChTrWpUkgtISkrC+PHj/Vqnv1x55ZU4/fTTAQBNmjTBZZddhvXr14sLfIBQH6tp8p/TUkFKWNWViBUADB2qZ/bNmwecc479J1nT1H5ZKgVZVygq4v9OFZIqYiWHPEGomIAIK2uKrzrMmjULffr0QXJy8qlteXl5GD9+PIYNG4ZFixadGtgcTKzF8x06dMCmTZuwZs0a9OnTJ+hrqQtYD95ut/PSDzExtB8oLHSm8AsEjRsD3bsD6enA0aP83+7hzOvX87UBFqyreYV1AScLK3WBAzhvXxQEJ+GY4nUr3uqrpkyZgq5du2LkyJGYO3cu5s+fjyFDhpz6+dGjRzFx4sSApQKXLl2KUaNG4ciRI4iJiUHOydke9azFNoKtOF1YWU9+RUXOPBkGgmHDKKgAFrHbLays7u6WXbzWU1KiU21OPKyI1YIg+IbjhJXb7cbcuXNx1113eWxfv349xo4dCwBIS0vD6tWrPYRVcnKy7anAmTNnonHjxujduzdatmyJRx55BDEnK0oXLVqEwYMHo1td6AEPEWWFldMo2xlYV4RVjx40DVURq8OH7YsqHT8OrF3L2w0bAr162fO64YCKVgHOFFZitSAIvuEYYZWRkYEpU6Zgy5YtOH78OKZPn4709PRTFgtutxuRJ+24S0tLT92uKZ988gnmz58PAHj00UcxZMiQU0XykyZNwoABA04Jq7PPPhsTJ05EaWkpNm/ejOnTp9uyBsE74SSsCgqAhITQrSWYuFyMJE2fztTQ/PnAFVfY89qLFum/9Vln1a3IiLVWz4nCSiJWguAbjhFWbdq0OVU3NXXq1HI/79mzJ/bt2wcA2LZtG0aPHm3L+1577bW49tpr8dZbb5X7WVnhNHz4cAwfPtyW9xWqJpyElTXaUBc480zg2291d+All7BrsCa43cCCBbxtGHr4c10hnCJWIqwEoWLCZve4/vrrsWrVKsyZMwemaWJYXWoVqqM4XVhZg6bKGqCuEB8PqF6O3Fz6WtWUtWuBzEze7tULaNSo5q8ZTliFlRPTytbyVRFWglAxjolYVUVcXByef/55AJCoUR3B6cLKGlWoa8IKYBH7smW8vWCBdxPPSZMmYdKkSSj1weW1rhatK8IpFVgXOmAFobrIdYfgWJwurKwRq5KS0K0jVLRtCzRvztvbtgH795d/jK9DmI8coc0CwML4utgT4vRUoESsBME3ZPcQHIvThZW1pqguRqzK1kEtXFj911q4UJ+4zz67bp64reK8pvVqgcAqrCRiJQgVUwcPX0K4IMLK+QwapCN3S5ZUL3JXUqJFmcvFwvi6iPWzs6np2VakK1AQfMNRu+/IkSPRokULdO7cGQcOHMCbb76Jv/zlL0hKSsK6deuwadMmrFy50tb3XLZsGRYuXIicnBwsWbIEf/vb3zB06FCvj12+fDk++ugj9O3bF4sWLcJjjz2Gtm3b2roeQWO9Kq7E9zVkiLACGjQA+vYFli9nEfvvvwP9+/v3Gr//Dpz020XfvnXHtqIsThdWErESBN9wzO67Y8cOXHPNNbjjjjsAAJMnT0b79u0xceLEU49RnlZ2kZeXh6+++uqUsegXX3yB0aNHY8uWLWjRooXHYwsLC3HVVVdh2bJlSE1NRadOnXDLLbdg7ty5tq5J0IiwCg/OPpvCCmARu7/CatEifbsuFq0rnC6sJGIlCL7hmN1j5syZuOmmm07d9zbWpkOHDra+59atW/HSSy9h69atAIDzzjsP+fn5WGQ90p9k/vz5SEhIQGpqKgBg4MCBWLp0KQ4ePGjrmgSNCKvwoFMnoEkT3t64kYXovnLsGLBhA2+npACdO9u/vnDB6cJKIlaC4BsB2X03bKj6RBMVBXTtqu/ffvvtMCx76+zZs/Haa695PEc5onvj2LFjmDBhgl+zAnv27IlFixahffv2AIBdu3YBADp27FjuuRkZGUhKSjp1PyIiAvHx8UhPTz8ltgR7cbqwqss+VlYMg3VRyk934UJgzBjfnrtkif7bDh5ct0/YThdWErESBN8IyO5bXOz/icYqqjZu3Ij9+/djxIgRFT6mLElJSX7PCjQMA4MHDz51/6WXXsIDDzyAvn37lnusGr5sJSYmBpnK0VCwHacLK+u8NCcW1weTwYOBr7/m57B4MZ3Yqzr5miYfC/Bv7c0Hqy7hdGElEStB8I2AXHdERfn2ryJmzZqFPn36IDk5+dS2vLw8PPnkk5g1axaee+4529f8/vvvo2nTpnj11Ve9/jwxMbFcNOzEiRNISUmxfS0CCSdh5YP/Za0mIQHo3Zu3s7L0IOXK2LxZpw27dgUsAeE6idOFlUSsBME3ArL7WlN81cFbfdWUKVPQtWtXjBw5EnPnzsX8+fMxxFLpevToUUycONGvVKDihx9+QGlpKSZMmICCggIcOHAAbdq08XhMly5d8O677566X1hYiJycHLRu3bqav6VQFU4XVtaTS10XVgA9rVat4u1Fi7TQqghrKWNdtViwYhVWVtHuFCRiJQi+4bjrIrfbjblz5+Kuu+7y2L5+/XqMHTsWAJCWlobVq1d7CKvk5GS/U4EAi9L37duHiy++GAcOHMDSpUuRmpqKNm3aYObMmWjcuDF69+6NIUOG4NChQ9izZw9atmyJefPmYcCAASKsAojThZVhUFy53ZIKBOiW3rAh5/2tXUsLhfh474/Nzwd++42369evWoTVBZQ4NwxnCisrIqwEoWIcI6wyMjIwZcoUbNmyBcePH8f06dORnp5+ymLB7XYj8mR8vLS09NTtmrB9+3ZcdNFFyFEmOifJysoCwDlnAwYMQO/evREZGYnJkyfjhRdewKBBgzBv3jx89NFHNV6DUDFOF1aAFlYSseJncfrpwM8/8zP59Vdg5Ejvj12+XNdhnn66M53Gg436DjlVVDl1HxQEXzEMYyyAvwNoB0DtadkA/m6a5oSTj7kSwGQA9U/+PBPAItM0L/L1fRwjrNq0aYOnnnoKADB16tRyP+/Zsyf27dsHANi2bRtGjx5d4/ds164dsrOzK/z5dNXmdJJRo0adSlFarSGEwGBNtTn1oB4RwRSORKzIGWdQWAHs+Nu40fsQZkkDlkd9h8KhfkkiVkI4Yprm5wA+NwzjHAAzABQCaGua5jHLY74wDCMFwOMA/gTgG9M0/bp0DoNdmFx//fVYtWoV5syZA9M0MWzYsFAvSQgw1oO3U4WLii5IxIo0awao8sTdu4FLLy0/hHnfPiAjg7dbteI/QV88OFW0OPXiRhD8xTTNXwCsBRAN4BzrzwzDaA3gcgADTdOc7q+oAsJIWMXFxeH555/H8OHDMXHiRLjC4bJOqBHhkgoEnCv8QoHVNmHJkvI/l2iVd5wurKyEwxoFoQomnfz/PrXBMIymAN4DcKtpmvur+8KiTgShBkjEqjwDBmi7gGXLPD8bVXsF8LMbODD463MqTk8FOvXiRhCqyX/B+qkzDcPoYxhGMoApAO4yTXNPTV7YobuwIIQH6iQowkrToAHQqxdv5+QA6en6Z5s2AaqssVcvPlYgErEShOBhmmYugA9P3n0MwEcA/mya5raavrYIK8GxhMPBW1KB3qkoHWgptcLppwdvPeGA04WVRKyEWsgkACaAsQAmmKaZXsXjfUKElRAWOPWg7tSTYKjp3l17WK1ZA+Tm6tsAvat69gzN2pyKEufynRKEoLEDgIpQ2eamJ8JKEGqAOgk6VfiFiogIHZEqKdFmoMq7qn9/Z45tCSXqOxQONVYi/oRwx+Dw4bcB/HBy0z2GYdiy9zl0FxaE8Dh4i7CqGGs6UBWsKwYNCu5awgGnpwIFoZbxTwCzATwARq3aA6i5QSZEWAlhggiX8KNlS/4DgC1b9PbGjYF27UKzJifj9FSgRKyE2oJhGC8C2GCa5scmBwyXs16oCSKsBKEGhIPXVihR6cAjRzy3yYm5PBKxEoTAYxjGowCyTdN8y7L5AwC5AM41DKNTTd9DhJXgWMLhBCPCqnIGDuRndPgw75umdANWhNRYCUJgMQzjTwAamqb5knW7aZqZoK+VAWBcTd/Hp/JRwzAMNZi4LAUFBQCA/Pz8mq6l1qI+m+LiYhQVFaGoqAg5OTm2DJKuzZSWAidO8LbLpf2PnEReHqC++tnZzj0pBpvCwkIUFhYCAGJj6yErix9S/frZiIlx5t8y1KjOyfx8Z34+OTl6f8zOlsHZQvBJTExMAJBzMn3nM4ZhNAPwDIBLADSv4GFfAPgjgJsNw3jONM2j1V2n4cv6DMNIAOBVWaWmpmLatGmIjo6u7hrqBMXFxXjwwQeRmZmJ6OhobNiw4dSJRxAEQRAEn0g0TdOnSw/DMM4D8AZYmK4ue38zTfO0Mo/7EsBFAOqd3JQPYCuAK03T3OzvAn0VVkZWVlaFFojFxcUoLS1FTk4OfvjhB8yYMQOXXHIJ6tWrV9FTyvHDDz/gggsu8PnxTn5OUVERpk2bhssvv/zUZ1BSUoKioiIUFhaiqKgIV199NRo1auTxvAEDBngMq/WF6jwnWO+VnZ2NVq1aYffu3UhISPD7fdxuYOdObouNBZo2tW9tdj1n1SogM5O3hw4tH7Gq7mdg1/pC9RxrxGr3bgNPPJGH2bM74ccfN2Dw4IouGIOzNrueU53nVfR9ME1g3jz+n5AAnHaa5/Oc8DkcPMgILQCkpelxTsE+LviLEz47bwTzc3Dyc/z5HBITExNRjYhVsPEpF+XrL9GgQQNERUVhz549OH78uF/C6uDBgzh+/LjPj3fyc4qKinDgwIEKP4OUlBSkpKSgQZl5HhEREX6ffKvznGC/V0JCgl/Ps75Pw4aBW5sdzxk61Lfn+fsZeHuvcH1Oy5bAhx/uQVoa0KNHXLW/C057Tk2e5+37cMkl9r6P3c+p6KVCcVzwByd8dpURjM/Byc9R+PI5+BqpCjW2Fvk0aNAAY8aMwQMPPICrr74a8cp62QfcbjduvPFGv97Pqc/JycnBU089VeFnEB0dXU5UAcC4cf7XzFXnOcF+r2C8j5OfU12c/Dv5+5zqFjs79fep6fOC8T5Ofk51cPqxzsmfg5OfUxvxKRV4Ep8emJ2djcTERGRlZVVbuYY78hkQ+RzkM1Ds2bPnVLi/pTK3qoPI90E+A4V8DsTPzyEs+lFt72GKjo7G008/XaeL2eUzIPI5yGegUL+/fA7yfZDPgMjnQGrj52B7xEoQBKEscnUuCIINhEXEyh9hJQiCUC0sli0+t0oLgiCEIyKsBEEIOCcnyccjDFqlBUEQaoIIK0EQBEEQBJuQARyCIAiCIAg2IcJKEARBEATBJoIirAzDiDYM43fDMEzDMPoE4z2dgmEY3xiGscswjALDMPYbhjHVMAzfZ3rUAgzDaGMYxn8Mw9hhGEa+YRjbDMN41jAM3635awmGYTxuGMZiwzDyDMPIDPV6hOBgGMYQwzC+NQxj38nj4JhQrynYGIbxmGEYyw3DyDEM45BhGF8ZhtE51OsKNoZh3G0YxhrDMLJP/ltiGMboUK8rlJz8bpiGYbwe6rXYQbAiVi8D2Bek93IacwCMBdAZwBXgMMgvQrqi4NMF/K79EUB3AH8GcBeAF0O5qBBRD8D/ALwV6oUIQaUBgNUA7g31QkLIUACTAAwCcA44+WOGYRjlx1DUbvYAeBRA/5P/ZgP42jCM7iFdVYgwDGMAgDsBrAn1Wuwi4MXrJ5X4q6CoSAfQ1zTN3wP6pg7GMIxLAHwFINo0zeIQLydkGIbxMIC7TdNsF+q1hALDMG4G8Lppmg1DvBQhyBiGYQK4zDTNr0K9llBiGEZjAIcADDVNc36o1xNKDMM4BuBh0zT/E+q1BBPDMOIA/AbgHgBPAPjdNM0HQrooGwhoxMowjFQA7wK4AUBeIN8rHDAMIwnA9QAW12VRdZJEAMdCvQhBEEJG4sn/6+xxwDCMCMMwrgEjmktCvZ4QMAnA96Zpzgz1QuwkYMLqpG/NhwD+zzTNFYF6n3DAMIx/GIaRC+AogDQAl4Z4SSHFMIz2AO4D8H+hXosgCMHn5PnhVQALTdNcF+r1BBvDMHoahnECQCF4HLzMNM31IV5WUDkpKPsBeCzUa7Ebv4WVYRjPnCwyq+xff/DEmQBgvO2rDjF+fAaKCQD6AjgXQCmAKScPLGFNNT4HnCzc/wnA/0zTfC80K7eX6nwOglDHeRNALwDXhnohIWITgD5gvdlbACYbhtEtpCsKIoZhtALwTwB/ME2zINTrsRu/a6wMw0gBkFLFwzIAfArgYnjOGIwAhcVHpmne5NcbOwhfPwNvXxjDMFoC2A1gsGmaYR369fdzOCmq5gBYBuBm0zTdAV5iUKjO90FqrOoudb3GyjCMNwCMATDENM0dIV6OIzAMYyaAbaZp/jHUawkGJ7tip4N6QBEB6gU3WINc6uWpYUGkv08wTfMIgCNVPc4wjD+BxWiK5gB+BnA1eGINW3z9DCpARarCfpS3P5+DYRgtQFG1EsAttUVUATX+PghCneBklP4NAJcBGCaiygMDteCc4AezAPQss+0DABsB/COcRRVQDWHlK6Zp7rLeP5lPBqjK9wTqfZ2EYRgDAQwEsBDAcQDtADwHYBvqUKHiyUjVXAC7ADwEoLHKhJqmeSB0Kws+hmGkAUgCa+0iDO3rttU0zRMVPlEIa052P3WwbGp78m9/rOyxshYzCcB1YI1pjmEYTU9uzzJNMz90ywouhmG8COBHMHMRD+AaAMMAnB/CZQUV0zRzAHjU1qk65NpQcxcwYSUAAPIBXA7gWbDrYz9YX3SNaZqFoVxYkDkXPKl0AD1crIR9rZmfPAfAmgZfdfL/4aD4FGon/cGIreLVk/9PBnBz0FcTGu4++f/cMttvARud6gqpAKYCaAYgC/RvOt80zV9CuirBNmQIsyAIgiAIgk3IrEBBEARBEASbEGElCIIgCIJgEyKsBEEQBEEQbEKElSAIgiAIgk2IsBIEQRAEQbAJEVaCIAiCIAg2IcJKEARBEATBJkRYCYIgCIIg2IQIK0EQBEEQBJsQYSUIgiAIgmATIqwEQRAEQRBs4v8Bby62xqrlILUAAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 10 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "T0_list = [0., 0.5, 1., 1.5, 2.0001]\n", "g = Graphics()\n", "for T0 in T0_list:\n", " alp = 0.2 + 0.4*(2. - T0)\n", " g += plot(2*W0(x^2-T0^2), (x,-4,-Xmin(T0)), thickness=2, color='blue', alpha=alp,\n", " legend_label=\"$T_0={:02.1f}$\".format(float(T0))) + \\\n", " plot(2*W0(x^2-T0^2), (x, Xmin(T0), 4), thickness=2, color='blue', alpha=alp)\n", "g.save(\"max_SigmaT0_r_X.pdf\", aspect_ratio=1, axes_labels=[r'$X$', r'$r/m$'])\n", "show(g, aspect_ratio=1, axes_labels=[r'$X$', r'$r/m$'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot of hypersurfaces $T=T_0$ in the Kruskal diagram" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We generate first plots for the curvature singularity and the bifurcate horizon:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "sing = plot(sqrt(1+x^2), (x,-3,3), color='brown', thickness=4, linestyle='--') \\\n", " + text(r\"$r=0$\", (2.5, 3), rotation=45, fontsize=16, color='brown') \\\n", " + plot(-sqrt(1+x^2), (x,-3,3), color='brown', thickness=4, linestyle='--') \\\n", " + text(r\"$r'=0$\", (2.5, -3), rotation=-45, fontsize=16, color='brown')\n", "bifhor = line([(-3,-3), (3,3)], color='black', thickness=3) + \\\n", " line([(-3,3), (3,-3)], color='black', thickness=3) + \\\n", " text(r'$\\mathscr{H}$', (3, 2.7), fontsize=20, color='black')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We add the inner limits of the isometring embeddings for $|T_0|>1$: " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 8 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph = sing\n", "var('T')\n", "Xemb(T) = abs(T)*sqrt(2*ln(abs(T)))\n", "graph += parametric_plot([Xemb(T), T], (T, 1.001, 2.5), color='grey', thickness=2, linestyle=':') \\\n", " + parametric_plot([-Xemb(T), T], (T, 1.001, 2.5), color='grey', thickness=2, linestyle=':') \\\n", " + parametric_plot([Xemb(T), T], (T, -2.5, - 1.001), color='grey', thickness=2, linestyle=':') \\\n", " + parametric_plot([-Xemb(T), T], (T, -2.5, - 1.001), color='grey', thickness=2, linestyle=':')\n", "show(graph, aspect_ratio=1, axes_labels=[r'$X$', r'$T$'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The minimal value of the Kruskal-Szekeres coordinate $X$ on an embedded surface of constant $T$:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def Xmin_emb(T):\n", " if abs(T) > 1:\n", " return Xemb(T)\n", " return 0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plot of the hypersurfaces $T=T_0$ for selected values of $T_0$:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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kuStEeIqc9HSOfPstaZcvk3T8OAO//BJjVlbeB72iKKVubrh+5gwrhg+3e61v9cgjtH/mmULHtxcqnnjiCQwGAwEBATz77LPUq1ePPXv2MH/+fA4dOkSlSpWYMGEC48ePp379+uzfv58vv/yS0NBQ3n///bzzzJ49m6effjobmKUoygyVSvU0EKgoytuleqA+zi3BAkoeLq7u3s3aRx8ly84sj6G1a5unXW/QwBnFE8KjSLAQnkAxmdj+xhvkpKVx/cwZkk6cQLt8ubnvRBkCRX4XN21i7WOPYSpQg93uqae4acKEQtsX1fyRlJTEzp072bBhA0FBQTceh6Lwyy+/8Prrr7Njxw6r/Z599lnee+89wDwT8eTJk3OH3X9fUZTnAFQq1UpgmqIo/5b5Afugcm0Kya+kzSLV2rXj1oULCale3ebx0uLiWDVqVKGJzYTwZnPmzKF169Z06dLF3UURAsVkolLjxnSfNYsWo0YBcGjhQoxZWU7rFFmre3d6vvvujWYTlYour7xS4lDx9ttvs3TpUmbOnGkVKsyHVHHnnXeyfft29uzZwxtvvIG/vz9arZZ33nkHMM90+vDDDzNv3jz+85//AEyz7DsFOCihwj63BQsoebiIbNaMQYsWEW5nCumMa9dY9fDDXC6QQIXwVpMnT+bAgQNs27bN3UURArW/P5kJCRxftox6gwZRo2NHTv3+OwmHDgE4bYyheoMG0fW111D7+9PjnXdodu+9hbZx5O6PrKwsoqOjC+27Z88e9u7dC0BISAifffYZ0dHRfPfdd6gtgebRRx9l8eLFNGnShCVLlgAoKpXqZaA58LRTHqiPcmuwgJKHi/B69Ri0aBGRzZvbPF52SgprJk7kfGysy8oshBAVTe4HePMHHsAvMBC1nx9dXnkFgIMLFgDmzpllueMivyZ33cXQFStoOGRIoXWO3lLatm1btm/fbrVNamoqL730Ek2aNOH8+fPceuutnD17ls8//zyvmVGv1/PFF1/g7+/Pd999x+XLlwE+B/YoijJFURQjwi63BwsoebgIqV6dW7/+mmrt29s8njEjg9gpUzgVE+OqIgshRIWS+2EdEB5OVKtWKIpCSI0atHjoIc6uWsUR87d6p44TEVanTqFlJRmnQq/XM3PmTFavXk1qaio7d+7krrvu4sUXXwRg6NChnD59mrFjx+bN27N06VJmzJgBwMSJE/njjz/4/fffASYrivKb0x6cD3Nb501bStqhMyctjdipU7m4caPtA6pUdJk+nWb33eeqIgtRLqTzpvBUyadPs+Gpp1AHBNDz3XeJKKYDfdKxY6TGxVGnd+8Sn6s0g1+tWbOGjz76iHPnztGqVStefPFFWrduzbhx41iwYAFhYWEcP36cmjVrcvDgQbp27UpKSgrNmzfnqaeeYvTo0YSFhYHMFeI4RVFK+s+l1q5dq4SGhiqYA0zev+HDhytZWVmFts/JzFTWP/208m3r1nb/7f3sM8VkMrm66EK4TFJSkgIoSUlJ7i6KEIWcNhiUb2+6STn2v/8Vud3VvXuV//XooXzfoYNycevWEp1j4cKFikqlKvTZ8Pzzz5f4+r58+fK8/adPn66YTCZlw4YNSqtWrRRA6devn2I0GgvuVprPywr5zyOaQvIrabOIX2AgPd59lyZ33233mHs+/liaRYQQwkXqDx5MuyefJNxGR8lcuQMaZiYmYszMZN3kycQfOODQ8Z05TPf169d54oknAFCr1cTFxdG6dWsGDx7MwYMHiYiI4Ouvv87rxClKziOfuZKGC7WfH11nzqT1uHE2j1enTx8aaDQuK68QQlR0rcePp+Ytt9jsvHluzRrWTJpETr5m7pzUVNZMnEjSiRNFHteZoSItLY2nnnqKc+fOAdCzZ0/69evHp59+SrplUK63336bBjIeUpl4VB+Lgkra5wLgwJdfsuuDD/J+r96xI/0//7zQmPJCeBPpYyG81cnffmPzyy+jGG3fSNFgyBB6vvuuzXXOChUJCQl88MEH/N///R/x8fEAtGjRgt27d+Pv70/Hjh3Zs2cPPXr0YMOGDfaOK30sHOSRNRa5SjNxWetx4+g6cyaoVES1bEnfOXMkVAghhBsc/vZbNr3wgt1QUadvX27R622uc0aoyMnJ4YMPPqBDhw4EBgZSu3btvHVz584lKCiIJUuWsGfPHvz8/Jg7d67MfuoEHh0soHThounIkfT55BP6zZtHoHy7E0KIcqUoCnv/7//Y8eabdrdpMGQIfT76CP/g4ELrnBEqTp06Rc+ePTly5Ag7d+4kOjqa/fv3AzBu3Dj69+8PwKxZswAYO3Ysbdu2dfgxCvs8uikkv9I0iwjhK6QpRHgLxWRix6xZHPnuO7vbNLv3XjpPn25ztlNnhIr9+/czfPhwZs+ezW233calS5do3bo18fHxdO3alXXr1hEcHMzOnTvp1KkTAQEBHDt2jPr16+cdIzk5mbCwMPz8/HIXSVWGgzy+xiJXaWouHJGTkUGKpSOPEEKI0jNmZbFx2rQiQ8VNEyfSWadzWajIyMjgvvvuY9GiRdx2220oisIjjzxCfHw8devWZfny5QRbaklWrVoFwJ133mkVKuLj4xk5ciRnzpxx6HELa14TLMD54cKUnc2GZ57hrwceyBvrXgghRMllp6aybvJkTq9YYXebDs8/T7upU20GBGd11Pz555/p2bMnXbt2BeDVV1/ljz/+IDo6mtWrV1v1s8i9O+SOO+7IW3b+/HlGjhzJu+++S6NGjRw6p7DmVcECnBcuFJOJzdOnc2HdOvPkZWPHcuVfmaxOCCFKKjMxkdXjx9sdBVmlVnPL66/T6uGHba535i2lx48fp1mzZiiKwqxZs3j11Vfp06cPW7dupXmBOaaaNm0KkDdmxS+//MLo0aOZN2+e9LcoA6/pY1FQWfpcKIrCjjffLFRd5xccTO/Zs0s11KwQrjBnzhzmzJmD0WjkyJEj0sdCeJzUuDjWTJxIsp3xKNSBgfR6/32iBwywud6ZoQJg165d3HHHHQQGBhIeHs5TTz3FmDFjbB4nMzOTcePG8ddff9G0aVNuu+02nnnmmdwhvAuSPhYO8tpgAaUPF8d++omtM2faXKfy96fb66/TaOhQZxdXiFKTzpvCEyWdOMGaCRNIu3jR5vqA8HD6fPopNbt0sbne2aEiV3Z2NpmZmYSHh5dqfzskWDjI65pC8itts0iDIUOo1aOHzXVKTg6bXniBg19/7eziCiGEz7i2dy+rRo2yGyqCq1Zl4Ndfl3uoAAgICHB2qBAl4NXBAkoXLgLCwug7Zw71LNPk2vLvu++y64MPbA5PK4QQFd3++fPJTEy0uS4sOppBixZRpVUrm+tdGSqE+3l9sIDShQu/wEB6vv9+kZOXHfjyS7a88gqmnBynl1kIIbxZ9zffpEqbNoWWRzZvzuDFi+1Ony6hwvf5RLCA0oWL3MnLbpo40e5xTyxdyvqnniInI8PpZRZCCG8VEBZGv88+o1LjxnnLqnfowK1ff01I9eo295FQUTH4TLCA0oULlUpFu6lT6fTii3aPe37NGtZMnEhWcrLTyyyEEN4qOCqK/vPmEVqrFnX69qX/F18QWLmyzW0lVFQcXn1XiD2lvVvk1O+/s+nll1HsNH1ENm9O/88/t5vGhXAVuStEeLLUCxcIqV4dtZ1rq4+ECq8opCfwqRqLXKW9W6Th7bfTd84c/OzMhpp45Ah/PfggyadPO73MQgjhrcLq1PH1UCFKwCeDBZQ+XNTp1YuBCxYQFBlpc33q+fOsfOgh4i2z5AkhhC/KSUtj/xdflKnzuoSKislngwWUPlxUa9uWWxcuJLRWLZvrM+PjWfXww1zcvNnpZRZCCHfLTEzk7/Hj2T17Nttee61Ut91LqKi4fDpYQOnDReUmTRi0eLFVj+f8ctLSiH3ySbv3cQshhDdKu3iRVaNHc233bgCO//wzu2fPLtExJFRUbD4fLKD04SKsdm0GLVpE1XbtCq9Uqeim19ttMhFCCG+TfPIkfz30EEnHj1stPzB/vsOjEUuoEBUiWEDpw0VQZCQD58+ndoGJybrodNTXaFxWXiGEKE9Xd+9m5UMPkRYXZ3P9wQULir3lXkKFgAoULKD04cI/NJS+n3xCQ8vEZDdPnkyze+91eXmFmDNnDq1bt6aLnfkWhHCG8+vW8fcjj9gfortuXW5dtIjAIm519uVQkZmZ6e4ieBWfHMeiOKUd50IxmTj3999E33qrV79JhPeRcSyEqxxfupStM2eiGI0211du1oz+n39OaI0ado/hy6EiH594EOWhTDUWhw4d4sSJE143UVdpay5UajX1Bg3ylTeJEKICUxSFffPmsUWnsxsqqrVvz6BvvqlQoSIxMZGNGze6uxherdTBwmg0smLFChYtWsSCBQvsfhh7qtKGC0dd3rGD9KtXy3QMIYRwBZPRyPY33mDPxx/b3aZu//4M+PJLu0N0g++FirVr1/LJJ5+wcuVKTstAiKVW6mBx4MABki0deUJDQ+02H3gyV4WL+AMHWPvoo6x86CEZpVMI4VGMmZn889xzHF2yxO42TUeOpPfs2fgHB9vdxtdCBUBUVBQmkwmATZs2ubk03qvUweKmm25ixIgR1KhRg94F7pgAOHHiBEY71WuexNnhIuXsWdY++ig5aWmknD3Lygcf5OqePc4sshBClEpWcjJrJk3i7F9/2d2mzeOP02XGDNT+/na38YVQce7cuUL97Nq0aUPt2rXp27cvw4YNc1PJvF+ZO28qilLoRXTx4kXmzZtHZGQkAwcOpE2bNmUspuuVtkNnfhnx8fz14IOknDljtdwvJIReH3xA3T59nFpmUXFI501RVmmXL7N20iQSjxyxuV6lVtNZp6PZPfcUeRxvDxVXrlxhxYoVnDx5kt69ezNgwACr9bY+0yw8+4F5kDLfbmrrD7BhwwbA3AkmNTW1rKcoF86oudjx1luFQgWAMT2d2Cee4PiyZU4rrxBCOCrpxAn+euABu6FCHRhIr9mzfT5UAAQGBub1n9i6dSsZGRlW673hMXg6l4xj0aVLF5o0aUJYWBgdO3a0Wpedne2x9wSXNVx0evFFqrZta3OdYjSyZfp09n32mdfdRSOE8F7FDXwVUKkSA+bPp97AgUUexxtDhaIopKSkWC2rXLky7dq1IyoqisGDB3tl/0BP59JxLNLS0gp9SG/cuJH169fTtWtXunXrRoidKcrdqSzNIjlpaWx47jkurFtnd5tm995Lp5dfRu3n57QyC98mTSGitE6vWME/zz1nc11orVr0mzePyKZNizyGt4UKRVHYv38/sbGxBAYGMm7cOKsyZmRkEBgYiFpdou/WnvUgPZhLR94sGCqys7PZtGkTGRkZxMbGFkqSnqIsNRf+oaH0+fhjmowYYXeboz/8wIannyanQBWcEEI4W4PbbqPjCy8UWp470aKvhYpcGzZs4MqVK5w/f54TJ05YrQsODi5pqBAlUK7PbHZ2Nk2bNkWtVtO6dWuqV69utd6TmgjKEi7U/v50ffVV2jz+uN1tzv39N6vHjZPZUYUQLtdy1ChajxuX93v1Dh24deFCwmrXLnI/bwkVBcunUqny7laMjo4mMDDQHcWqsNwypHdiYiKKohAVFWW1fMmSJVSqVImePXsS6SGzhpb1bpFjP/7INr0exXJvdEGVGjem/7x5hNWp47QyC98jTSGirBRFYfNLL5GdkkKPd98tcowK8I5QkZOTw7///svWrVsZM2YM4eHheesUReHMmTPUr1/fWWV1/wP2Eh4zV8i5c+f48ssvAahatSqTJ0/2iBculD1cnFu9mn+efx6jnaaPkBo16PfZZ0S1aOG0MgvfIsFCOIMpOxtUqiLHqADvCBUAa9asITY2FoDu3bszePBgV57OMx60F/CYRqZr167lVVd1797dY164UPa7RaIHDChyaNz0y5dZNXo0l7ZscVqZhW+Q2U2FI+zViBakDgjwmVAB5jsQ/S2PJykpyaOa0ysyj6mxAPNdJDt37qR79+745btjIiMjA4PBQI8ePQr1yyhPZa25SD55kjUTJ5J64YLN9eqAALrPmkWD225zWpmFb5AaC2HP9dOn2fDMM9yi11OldesyHctTQ0VmZiZbt26lRo0atChQs/vvv/9Ss2ZN6ri+OdlzEpWH86hgYU9sbCxr1qwBYMiQIW799lbWcJF+5QprJk0i8fBhu9t0/O9/aTl6tFPKK3yDBAthy9U9e1j3+ONkJiQQXK0ag7/7jvC6dUt1LE8NFYmJicybN4+MjAxq1qzJpEmT3FUWCRYO8pimEHsURWGPZa4NlUpFkyZN3FqesjaLhFSvzqCFC6nZrZvdbc6tXo0pJ8cp5RVC+KZzq1fz99ixZCYkAJBx9SprH320VHeaeWqoAPOAVlWrVgXg8uXLxNkZ6Et4Dq+oscjKymL79u2kpKQU6pxz4cIFTCYT0dHR5VqmstZcGLOy2Pzyy5z+4w+r5ZUaN2bw4sVFTlUsKh6psRD5HfnuO3bMmmWzb0X1Tp0Y8MUX+AUFOXQsTwoVKSkpnD59mptuuslq+dGjRzlw4AC9evXKCxluIDUWDvKKYGGPoih8/fXXnDlzhsaNGzN8+HDCwsLK7fxlDReKycS/77/Poa+/BiC4alUGL1lS6qpM4bskWAgwXzN2ffghBxcssLtNlTZt6D9vHkEO3LLvSaFi9erVbNq0CZPJxJNPPkllz/tyJcHCQR7fFFKUM2fOcMYy6VdycnK5Dw9e1mYRlVpNx+efp+O0afiHhtJv7lwJFUIIm4xZWWz873+LDBV1+vbl1q++8rpQkSsnJweTycQ///xT7ucWzuPVwSI6OpqhQ4cSFRVF7969Cw3RGh8f7/Lbj5wxK2rLMWO4488/qVKg+k8IIQCykpNZM3FioabT/Jreey99Pv4Y/wLXIlvcHSoSEhIwFWjG6datG2FhYXTr1i1v1Ezhnby6KSRX7gs0f7BIS0tj9uzZ1KhRg379+tG0mPHwy6qszSKOUhTFo+4jF+VDmkIqrtQLF1j76KMkHT9ud5t2Tz1F6/HjHbo2uDNUxMfHs27dOvbu3cuwYcNo166d1fqcnJy8cSk8jUYf8w7wOLAeiAfqAX2ATcAJIALoB/xt0GmHu7gsYcA0oArQHjgJTDPotBeL2EcFvAhUA64DjYApBp02ydnl8+oai1xqtbpQbcWmTZvIzs7m/PnzHDlyxOVlcEbNRXEUk4mNzz/Pwa+/loFghKgAEg4e5K8HHrAbKtT+/nR/+21umjDB40MFwPXr19mzZw+KorB+/fpCtRaeGiosOgBNDTrtEINO+xCwyLL8ToNO+5BBpx0G3IH5Q97VdMDnBp12CtAXqAms1uhjiuqx+zjQ16DTPmPQaWcAB4GFriicTwQLW6Kjo6lZsyZqtZqePXtarVMUpdAL2hlcHS52ffABp1es4N9332XHm29iMhrLdDwhhOeK++cfVo4eTfqVKzbXB4SH02/ePBrdfrtDx3NHqCh4nW3QoAENGjQgJCSEtm3buuQ67ApH45IAFhl02kv5FvcGDhl02sv5ll0E7A9S5AQafUww8AQwDsCg05qA/wNaYQ429kzDOkgsBO7Q6GOcfkulzwaLFi1aMGnSJCZMmFCod/GRI0eYO3cue/bscfoL21Xh4siSJRz86qsbv3/3HRueeoqc9PQylVeUj1mzZtGlSxciIiKoUaMGd955J4eLGCRNVGzHfvqJtY89Rk6BptVcobVqMWjRImoVMR5OfuUdKi5cuMCSJUv45ZdfCq0bNmwYU6dOpU+fPp5eQ5Fn96lrAD8XWNwbc7NIfjUx1wS4kh9wDQjPt+yo5afNgZ40+pjmQH1gf+4yg057HkgCBjq7gN7xVy0llUpFrVq1rJYpikJsbCxXr15l2bJlhIaG0rRpUxJTM622iwgJwE9tO3cV3DY8OAB/vxvb5oaLgn0uli5dyj333suPP/xgs89FcloWpnxv/NAgfwL9/Ti3Zg073nzTatvMwJC8AXL6zplDsPvu7RYOWLduHZMnT6ZLly7k5OTw8ssvM3jwYA4cOFCut0gLz6aYTOyePZsDX35JRlCY1RU6MCsdtWIisnlz+s2dS2i+a1tR1yR7oWLKU8/w4iuvkWNSCPCzHSzsXZNsbpueRaWQQHJycli8eDHp6emoVCr69OljNfZEwVmtvcGIbo24u3vjvIu5Rh9TF3MfhYLBYr1Bp3VpO7VBp00FGhRYXM/y014zTG7gSC6w/DrQ3ElFy+PTwcKWjIyMvJRcq1atvJE87/1gldV28yb1oWGNCJvHGP3JGjKzbzRDfDyuJy3qRFptkxsuBg7SYMy+8aZfvmwZ9913n80OnU/M38ClpBs1EK/d15lbmtUk7eLFQheFFQMf484VH3Bt714MDzxA/88+o1KjRg4+C6K8/fnnn1a/f/XVV9SoUYMdO3bQp08fN5VKeJKcjAw2vfgiZ//6C4Af7pphtf6OP96nZetG9J49m8AI62uTvWuSvVDRsOdwDkX1574P/+adUd1o19D2FxN71yRbnv16E1881hd/f3+6d+/O6tWrCQ8PJykpyZ2DWjmFjRqd3NtWrIKFq0NFEe4DjgDL7azPTXOpBZan5FvnNE4NFk/M30BCSmbxG7pdfXLC63AgBWI/Wm1zC6MT+i/07duX3uPfIHb+y5jyhYvcZhFH7xZpfv/9hFSvzsZp0zBmFn5+U8+d468HHqDPJ59Qo3PnMpdbuF5SkrkjdpUqVWyuz8zMJDPf3zo5ueAXDeFrds+enRcqbInu359+M/+Ln2UW6OLYCxUt+o2kfv/RTmn+OHfuHNu3b+f222/nYmIaD87+GzDXDGeHdCVAHcCOX09SPv0ZyyYqPIhPx/dydPNewDmDTnsq/0KNPmYs5oG0IoAjBp12RcEdNfoYP8zNKsEOnCfJoNPeW9QGGn1MW2A4MNig09r7ADYW+JkrABdUMDj1gAkpmVy9nuHMQ5YD23Ny/Pjjj/x3yvhCd5uUVPUmben40Ex2Lp5ZpnBR79ZbGfjVV6ybPDlvboD8spKTWT1uHF1fe43Gw4aVqczCtRRF4ZlnnqFXr160adPG5jazZs3i1VdfLeeSCXe6+fHHifvnH5JPnLC5vu1TUx0OFb/873teeOpxm30qTta4leT0st+ltnbtWtatWweYO8sbTUrh67+NL0I+olD/CkvzyCSDTtvNcmvnfo0+ZnXBD3uDTmsE7nRGITT6mHBgPjDCoNNuKWLT3B7ABT/QwjD3s3AqpwaLqHDHxqb3RAXfEA0bNihzqMhVpdHNTgkX1dq1Y/C337L2scdsrjfl5LD5pZe4fvo0bZ94ApWTyi+c64knnmDPnj1s2LDB7jYvvvgizzzzTN7vycnJ1KtXz+72wvsFVqpEv7lzMdx/P5nx8YXWqxwcUfrCrtW8sOxDux01Czb7llazZs3ygsW+ffvwU9ckKsx7PwMc/fzS6GMigTbAZwVW9QZ2grlJRKOPOQZ0B9Y6rZDW5VBZyjDNoNOutfzeyKDT2kqmuVVGNYHLlv3VQCTmMTicyqnBogTVSB4nt/NTXNxFtm7dgnbAbVbrFUVh9+7dtGnThoVT+lutCw+2Hwq+eKyv5Q1+K//c04l7RtxZqENnbrj4dHyvQh2lCopo0IBB336L6clnCjWW5do/bx7Xz5yh+xtvODwRkSgfU6ZM4ddffyU2NrbIifOCgoIIkr9dhRMeHU3fTz/l77FjeejvD+n+xptUa28eRCoixP51Jvea9P2Sb3l8hv1QoVKp8l2TzMKKuH7lXpPOnj1LWFgY0bWr5a2rW7cunTp1ok6dOrRr147hWUYqhThWo+LlemL+5l+w42ZdrDtHJgN1Cu7sxKaQl4GFBp12reX3+pgH6CoUFAw67UlL0GkB7LUsbmEpg+3+AGVQ4Tpv2hNpSdqRTRvQqmnBDrdw4MABfvnlF1avXs1tt91Gq1atHDpu5dAbbzTtfwbZvVvkRs1F8W/M4KgotF/MteroVdCZFStIi4ujz8cfyx0jHkBRFKZMmcKyZctYu3YtjaSjrbCjWrt29PrgAyIaNqRSw4YO7RMZFsSiRYt4fOL4Ym8pzX9NKo6Snc7yZcs4ffo0rVq1ovE991itvz3fGBqVQmzfLeKD+gIJ5Lt100KNddu6P4X7NDilKUSjj7kX6A/kaPQxHS2LbwLmWdZPAl4Cuhl02tx55r8BRgP/s/w+FvjVoNM6/b53CRYOyL1FFcwjxwU62M5pS1G3opakWcQ/OJhe77/P7o8+4sD8+Ta3ubprF4b776ff//0flV08pLko2uTJk/nuu+/45ZdfiIiI4OJF88i7lStXLvfJ84Tnq9uvX4m2d9U4FaGhoVy7dg2AgwcPcvnyZWrUqFGqY3mzy0npjPp49XeY+yQMAgKBpRp9zHXgEYNOmwOcB/JXQ0YBcYUOVkYafUxV4CsgBBhQYPWzlp9qzLUR+dvD3wbe0uhjPsHcr6I28LCzywc+MldIeYiLi2PdunWkpaUxduxYqzdqWloaAQEBJZoPxJlzixxftoytM2ei5NjuiBoQHk6vDz+kdo8eDh9TOJe9C/tXX33Fww8/XOz+MleI98u4do0jS5Zw8+OPO7X/k7NChaIoXL9+vdDra9OmTXm3Rbdp08Zpfc+8UJFPpEYfUxP4waDT9tPoY/yBU0BLg06bUh6F8yQSLErI1iQ5v/76K0ePHqVnz5506tTJ4VDgzHBxacsWYp96imw7tyWq/PzootPRdORIh48pPIcEC++WdOwYaydPJvXcOVqNHUuH555zynGdFSqOHTvGunXrSEhIYOrUqVbXHqPRiEqlqsiBIlexT6ZGH/M05rEiqgMHDTrtUpeXygNJsCijxMREPvnkE0wmE0FBQTz11FMEBzvSJ8fMmeEi+eRJ1j72GClnz9pcr/L35/bffiOifn2Hjyk8gwQL73Vh/Xr+ee45slNufHHtOmMGTQv0VygpZzZ//PTTTxw4cACAwYMH07179zKVzUfJtNIOqvARtKwURaFFixYAdOvWrVCoKC64OXNukUqNGjF4yRKqd+hgc33XmTMlVAhRThRF4dA337Du8cetQgXAttdfJ+6ff0p97LKEClvXpNzRX6tXr+71o2QK95MaCye5dOkSlStXtgoWJpOJr7/+mpYtW9K5c+ciO306s+bCmJXFFp2OU7//nres9fjxtH/66RI8IuFJpMbCuxizstj++usc/7ngvFU3RLVuzX9++KHE/S1KGyoUReHIkSPExsZy2223Fbrd+ezZs0RHR7t86nQvJk+Mg6TGwklq1qxZqLZiz549nD17lpUrV9qc5S8/Z9Zc+AUG0v2tt7h58mQA6g0eTLupUx3eXwhRehkJCayZMKHIUFG9Qwf6f/55uYUKMN8y//3333PhwoW8ga3yq1evnoQK4RQSLFzo8uXLef+/5ZZbit3emeFCpVJx8+OP03fOHLq/+aaMwilEOUg8doy/7r+fy9u3292m0bBhDFiwgOASzvJZ1j4VLVu2pHLlygCkpKSQlZVVovML4ShpCnGxy5cvc+jQoUIzWF69epVDhw7RtWvXQk0kzmwWKQlFUeQbi4eSphDPdz42ln+ee46cVDtj4qpUtH/mGVoVuF3dESUJFYqicPDgQTIzM+lQoL/VoUOHUKlUNG/eXN7rJSdPmIMkWLjJ0qVL2bt3LyEhITzwwAOF2jvLO1zEbdzIoW++oec77xBo+VYjPIcEC8+lKAqHFy7k3/feQzGZbG7jHxpKj7ffJnpAwfGMileSUGE0Gpk/fz4XL14kODiYp556SoaGdx4JFg6S+nE3SElJYf9+82iwKpXK5kh2zmwWKU7yqVNsePZZ4jZswHD//SSf9PwpjiuKOXPm0Lp1a7p06eLuoggbjFlZbJ0xg53vvGM3VITWrs2gxYtdHioA/Pz8qFmzJgAZGRns27evxOcUoqykxsJNrl69SmxsLLVq1aJHgRExL1y4QNWqVQkKCnJ5zUVWcjJ/PfCAVZgIiIig53vvUaeX904q52ukxsLzZCQksOGpp4rsT1G9Qwd6f/RRqebrKS5UKIrCiRMnaFpguP74+HiWL19Onz59aNKkiTR5OI88kQ6SYOFhcnJy+Pjjj8nOzqZ79+707t2b2NhYl4QLU04O6x5/3Ob99Cq1mg7TptHioYfkwuQBJFh4loSDB4l98klSL1ywu02jYcPoOnMmfqWYW6i4UHHs2DH++usvrl69ypgxY2jo4GRlokzkQuggaQrxMP/++y/Xr18nIyODCxcuoFKpXNYsknbpEonHjtlcp5hM7HzrLbbOmIFReo8LkedUTAx/PfSQ/VChUtH+2Wfp9sYbLgkVKpWK9PR0rl69CsDatWtLfA4hXEmChYdp0qQJ7dq1Q6VSWd1J4opwEV63Lv/54Qeq3nyz3W2O//wzq8ePJ8Myw6EQFVn6lStsmTEDY0aGzfX+oaH0+fhjWj/ySKlq+uyFimeeecaqT0WbNm2oWrUq9evXp2/fvsWO8CtEeZKmEA91/fp1IiIirJbFxcUxc+ZMFi5cSEaBC1tZmkWMmZlseeUVq5E6CwqtVYves2cXGUKE60hTiOc4vWIF/9iYRCy0dm36zplDlGWI/5KyFyoGDhzICy+8wK233mq1PC0tjZCQEGmqLD/yRDtIaiw8VMFQARAbG0udOnW47777Co3yWZaaC7+gILq/9RbtnnoK7Fyk0i5eZOXo0RxftqzExxfClzS47TZajxtntaxG587854cfnB4qevbsSa9evdi2bVuhPlahoaESKoRHkmDhJUwmU963k5tvvpmYmBinNouoVCpumjCBPh9/jH+B4+aVISuLLdOns02vl34XokJrO3UqtXv2BKD5Aw8wYP78Ut35AUX3qXjhhRdQqVTUrl2b9PT0MpdbiPIgTSFeJiEhgcTERBo1auSyW1ETjxxh3RNPkHr+vN1tqnfoQK8PPySkevVSnUOUjDSFeJ6spCQu/PMPDYcMKfUxiuuoef36deLj4+WuD88g1UMOkmDh5VwVLjITE/nnuee4uGmT3W1CatSg9+zZVGvXrlTnEI6TYFF+TNnZqF00bH5+ZZ37Q5Q7+YM4SJpCvFzfvn354osvCgWIst6KGhQZSb/PPqPV2LF2t0m/fJlVY8Zw7KefSnUOITxN4rFjxNx5J+dtzP7pTPZCxYgRIyRUCK8nNRY+IiYmhhEjRpCZmWm1fPjw4UybNo2bb765UJ8MR51esYLNOh3GItp4m44cSZdXXpFZVF1Eaixc71RMjPlW0vR0AiIi0Hz/PZWc2ARhMpnYu3cvW7Zs4dFHHy0UKiZOnMhnn30mocJzyR/GQRIsfIi9ZpFWrVpx//33M2jQILp161aqYyccPsz6qVNJOXvW5vrmDzxA55dfLtWxRfEkWLiOMSuLf999lyPffWe1vFLjxmiWLCEgPLzM5zh//jxLly5lzZo1LF++XJo/vJP8cRwkXy99iL1BtA4ePMiSJUtQl6E2IapFCzTff5/XEz6/qjffTIfnny/1sYVwl9S4OFaNGVMoVAAknzjBphdftDu5WElERkaybt06li1bJqFC+DwJFj6mqHDx1ltvWfW5yMzMJDU11eFjB0VG0nfuXFpPmJC3LLBSJXp98EGphi4WxZPZTV3n4qZN/DlyJNf27LG7Tfq1a2SnpJTouCaTicTERKtlS5cuZenSpYW2lVAhyotGHxNkY1mwrW3LSppCfJQjd4usXbuWjRs30rlzZ3r16lWiPhhnDAY263T0fO896uYbely4hjSFOI9iMrH/88/Z8+mnUMT1r+m999LphRccDs2KorB7925iY2Px9/fnscceQ6VSyd0fPkKjj3kHeBxYD8QD9YA+wCbgBBAB9AP+Nui0w8uhPCpgAPCKQaft68D2YwAdEAtcB5oDBww67bPOLpu/sw8oPENuzUXBcJF7t8jXX3/N5s2byc7OZsuWLXTp0qVEwaK+RkPNW24hKDLSBaUXwjUyExPZ9OKLXIiNtbuNX3AwXWfMoNEdd5T4+Dt27CAhIQGAAwcOsHPnTgkVvqMD0NSg014C0OhjxmMOFncadNrLlmV9gZK/cEpIo4+5BxgChAMNHNxNBQQB9wHngTnAx64onwQLH1ZUuDAajYwbN47du3dz8803ExUVZbWvoijFXvQcDRUp589zduVKWo4eLXeNCLe5smsX/zz3HGlxcXa3iWjQgN6zZxPZvHmxxyv4HlGpVPTr14/FixfTqFEjVq1axdNPPy2hwgccjUsCWJQbKix6A4dyQ4XFReCwq8tj0Gl/BH7U6GMeBjqXYNdRBp12rUsKlY8ECx9nL1z88ssv+Pn52RwDQ1EUFi9eTI0aNejZsyfh4eEkplrfxhoREoCfnZCQf1tTdjabnn6GpP37uLxtG93ffJPAypWd+AiFKJpiMnHwq6/YMnc+iskIQWEABGalo1ZudMysd+ut3PL66wRGRBR6vYcHB+DvZ369G41G9uzZw8aNG3nwwQeJzBewGzduzIQJE/j7778lVPiQ3aeuAfxcYHFvYFWBZTWBg+VRJk8mwaICKKrmAuD777+32v7kyZOcOHGCEydOcObMGSZMmMC9H1i/f+ZN6kPDGoUnSgMY/ckaMrONeb9r4xKpBpxfu5YVd99Nj3ffpXr79s55cEIUISM+nk0vvkjchg18f987Vuvu+ON9opIvofLzo/0zz9ByzJi8D/yCr+GPx/WkRZ1IALZs2cLKlSsBWL9+PUOHDs3bTqVS8ffff0vzh48Z0a0Rd3dvnHfx1Ohj6gKNMPe3yG+9Qaf15H6IgzT6mJ6YP/tbAE8adNqrzj6JU4PFE/M3kJCSWfyGwi26j9Wz9ouXMWbdmHJ96dKlNOk8gJ6jp6P2M78csrKyyFC3BQVCEkNYO/tvp5Uh9cIFVo0eTdspU2g9bpw0jQiXubRtGxunTSP98mW72wRXq0av99+nRufia5Nzr2+KopCiboeiKOzaC98fv/H+OLltJZuWvFOoU2ir/vdwrvZgHvpodekfkHCpqPAgPh3fy+Y6G2Gwt+WnVbDw8FBhBI4bdNoFABp9zAxgGTcei9M4NVgkpGRy9XpG8RsKt/Cr2YIOD85g5+KZmLJvBMCzezawesFrtB05LS9cQCCoICvDCBnGQsdKS0vF3Am65BSjkd2zZ3Npyxa6z5olE5kJpzIZjez//HP2/d//FTkGRbWbb+a2N6Y7/Pqzvr4FmN8fRkizLLuwazX7ln1YKFQ07Dmc6H6juCZfunxJL+CcQac9lX+hRh8zFnMnyQjgiEGnXVFwR40+xg9zs4ojt3omGXTae8teXDDotIsKLPofMFOjj+lt0GkL1ryUiVODRVR4odtkhYep1rYLlSe+Wajm4vKBjRxe9p5VzUV+BQPjokWLGTViCK1bty51WS5u2sSKESPoPmuWzYG3hCiNKzt2sPfTT4vdrutrrxJSPdL2ygLhwGQyFXl9O7ltpc1Q0ar/PbQfOkGaP7xACT+/elOgtsLSPDLJoNN2s9wKul+jj1lt0GmtEqVBpzUCd5axuM6QO4hRVwo36ZSJU4OFvWok4WkGsm5kp0J9Ls7u2UDWxs9tzoqamJqJ0Whk3rx5pKWlEaRWqFevns2jL5zSP+//6VevsvdEXa5uPWdz24xr11gzcSKtxo6l7ZNPykBbosxqdu1K8wceKDSa5r3LXiW4alW6zJhB9Q4diAixP4PpwicH8OOPP3LmzBkAVKnN7F7fFi1axBgbzR/Sp8I3afQxkUAb4LMCq3oDO8HcJKLRxxwDugNry7N8tmj0MSHAPuA9g04717I4d6z6HGefTzpvVlDFjXNRMFxEhpnT/NTHJ7Jx40ZUKhUREdZNIRcvXiQkJITIfHd9RIbVpeb8L4qtmj741Vdc3LSJHm+/TeWmTZ35UEUF1OG557jy778kHLzRQb9Rlw50nzWL4CpVrLbNzs7m1KlTNGvWLG9ZZFgQmgF9iI2NpW/fvtSvX9/meWTwqwqpJ+ZRqwt+y68LJOf7PRmoU3BnNzWFqDF/3l/Mt6yJ5edaJxzfigSLCqyk4QIgLCyMQYMGFTqWoij88ssvXL58mQ4dOqDRaPL2Vfv5cfNjj1Gza1c2TptG2sWLhfYHSDh0iD/vuYf2zz5L8wcekIuyKDW/oCB6vf8+K0aOxJiRQbupU2k1dmyhzsI7d+5k9erVpKamMnnyZKpVq5a3rkGDBowaNcruOSRUVFh9gQRgf4Hlaqy//ftj7jBpxclNIWpsTM2h0cdMAl4Cuhl02jiDTpuq0cfMxzzqZq77MY/NsdtJZckjwaKCK024sOXIkSNctASGuLg4/P0Lv7RqdOrEbT//zObp0zm/Zo3N4xgzM9nx5pvEbdjALXo9Ifku9EKURESDBvR46y2CoqKo3qGDzW3S09Pz5stZv349d911l0PHllBRsVxOSmfUx6u/A8KAQUAgsFSjj7kOPGLQaXMwj2YZnW+3KMD+aGxloNHH3AaMx9z8Ul2jj/kH82Bd4yybqDHXiOQPHbOB6Rp9TJjlcRwFXnVF+WSuEAE4NrdIUdLS0ti0aRNbt27lrrvuomXLllbrU1NTCQszD0ykKApHvv2Wf99/H1NWlt1jBlWpQtcZM6h3662lfFS+Q+YKuSHl3DkSjxwhesCAEu2XkZGBv7+/VejNysrio48+omHDhvTp04eaNWsWexwJFRVWkX9YjT6mJvCDQaftp9HH+AOngJYGnbZks9j5AAkWIk9ZwwWYvwEGBwdbXVyTkpL45JNPaN68OX369KFWrVoAJB45wj/TppF09GiRx2x4++10evHFCj0viQQL8wiax378kX/few9FUfjPTz9RuXHjYvdLT09n8+bNbNmyhQEDBtC1a1er9RkZGQQHOzbJo4SKCq3YP65GH/M05rstqgMHDTpt4SltKwAJFsKKM8JFQX/88Qfbtm0DoFevXgwcODBvnTEzk10ffsjhRQVvsbbW6aWXaPHggyU+t7ebM2cOc+bMwWg0cuTIkQobLFLOn2eLTselLVvylkW1bs3gb78t9k6iuLg4Pv/8cwAqVarElClTbDbVFUdCRYUnf2AHybCHwkpun4uCM53m9rnIzs4u8TGrVatGWFgYAQEBdOvWzWqdOjCQTi+8QP/PP7c7UFH1Dh1odt99JT6vL5g8eTIHDhzIC2YVjaIoHP3hB/64806rUAGQcOAAe+fMsblPfrVr16Z58+ao1WqaNGlSqtewhAohHCc1FsImZ9dcZGdnExcXV+i2vT179vDvv/+am0gqV2bbq69ybtWNeUn8goO5belSKjVwdGZg31QRm0JSL1xgs07Hpc2b7W+kUnHrN99Qo1MnkpKS2LhxI2lpaYwYMcJqs2vXruHn52c1YZijJFQIC/lDO0hqLIRNzq65CAgIKBQqFEVh/fr1nDp1ioULFxKfnk7v2bPpPmsWAZYPz/ZPP13hQ0VFo5hMHP3hB2KGDSs6VABNRowgqmVLFEXhm2++YevWrezbty/vDqVcVatWlVAhRDmRYCHsckWzSH7JycmYLANm1a9fnzp16qBSqWh0xx1oly/npokTaf7AAw4dqxQ1b8IDJR49yspRo9j22mvkFKgtyy+0Vi36f/45t7z6KgFhYahUKm655RbAHGIvXbpU5rJIqBCidKQpRBTLFR06c5lMJvbv30/lypUL1WisWrWKqKgo2rVrV2Rnuwvr13Pwq6/oMmOGz9Zu+HpTSE5GBvvnzePAggUoOUWPMBw1YgTJLVty54gRBAXdmN8hOzubjRs30qVLl0JhuKQkVAgb5I/uIAkWwiGuDBe2JCQk8Mknn6AoCjVr1mTSpEk2L+Y5aWnEDBtG6oULqAMDaTNpEq0eecTn5hzx5WARt3Ej2157jZSzZ4vcLrRWLQIefpjtJ04AMGjQIHr06OH08kioEHbIH95B0hQiHOLqZpGCDh8+nHdhb926td2L+d7/+z9SL1wAwJSVxZ5PPuHPu+/m8vbtTi2PcL70K1f4Z9o01kyYUGyoaDJiBEOWL6frf/6Tt+xgvnlAnEVChRBlJzUWokTKs+bi/PnzbN68mSFDhhASEpK3PCcnh3Xr1tG0cmU2PvIIirHQcPwANBgyhA7PPkuoZUAub+ZLNRbGrCwOL17Mvs8+Iyc11eY2Jj8/rjdoQOXAQPo9/TR1et2YWXTlypXUqFGDNm3a4Ofn57RySagQxZAXgIMkWIgSK+9mkYJ27tzJb7/9hkpRqLZzJ5HHj9vd1i8khDYTJ9JyzBj88rXHextfChbbXn+do0uW2F2fFRHBuf79MQYH06hhQ0aPGePyMkmoEA6QF4GDpClElFh5N4sUlDtYlKJS0fyWW6CIi74xPZ3dH31EzLBhnF21Su4e8QCtxoxBXUQfmFqNGxNumXzu5KlTXLlyxaXlkVAhhHNJjYUoNXfVXKSlpbFlyxYuX77Mvffey9U9e9g6cyaJhw+TERlJZlQUEadPo7bcyppf9Y4d6fDcc1Rr184lZXMVX6qxANj90Ufs//xz0qtWJTs8nEqnTxMQEUH7p5+m6ciR7Ni5k9OnT9O9e3fq1KnjsnJIqBAlIC8GB0mwEGXi7maRXKbsbA5/+y0rNm/meu3a+KWnUzc2lqCkJJvb1xs0iHZeNPiWrwWLrJQUPnn5ZVKqVEGVnU2frCxuef55u8O6u4KEClFC8oJwkDSFiDJxd7NILnVAAHWHDycl37fbgOvX7W5/duVKYu64g60zZ+bdVSLKzpiZydU9e4rdLjA8nDrNmgGgBAQQPHy4hAohfITUWAin8JSai3PnzrFp0yYqq1Qo//sf1/buzVuX3LAh6qwswuLiUOV73av9/Wly993cNGGCx91B4i2zmxqzsjixfDn7P/+crORk7vjzT4KrVAHgypUr7NmzhwEDBlh9YF+9coWf/vc/unfvTps2bUo142hpSKgQpSQvDAdJsBBO4ynhAixDfCsKJ3/5hd0ff0zq1aucHDoUU1AQAcnJNDAYrMIFQKcXX6TFQw+VWxlLwlObQnLS0zn+888cWLCA9HzDaLcYPZpO//0vq1at4p9//gHggQceoJmlliKXoijl+kEuoUKUgbw4HCRNIcJpPKVZBEClUqFSq2l8110M/eMPqk2YgMlyu2lwQkKhUBFSowZNR44st/J5u8zERPZ/8QW/ajTsmDXLKlQAHP3+e1IvXCA6Ojpv2Y4dOwodR0KFEL5HgoVwKk8KF7n8Q0LQTJnC3UOHUl2lIurkSav1CpB8xx3s2rePzMzMci+fN0k8epQtM2awfOBAds+eTca1aygqFam1anGhRw8yLbUppqws9s6dS/PmzWncuDEajYY777zTbeWWUCFE+ZGmEOESntQsUlDK2bPsmzePk7/+imI0ojRvzrH27QFo3Lgxo0aNsrlf4tGjhNaqRWBERDmW1sydTSEmo5EL69ZxePFiLm3ZUmh9UuPGXO7cGYDII0eovmsXAFXbtWPQN9+gduPfGiRUCKeRF4qDJFgIl/HkcAGQfPo0+z77jPPR0Ry4ehWAYcOG0d4SMnKlpqYSGhrKihEjuH7mDA2HDKHJiBFUbdu23D6U3BEsUuPiOPnrr5xYtixvLg+Tnx+oVKjzzUBqDAzk5O23o/j7E5iURLszZ7j50UeJHjjQ7R/aEiqEE8mLxUESLIRLeXq4AHMHwri4OHbv3s3AgQMJzDcqZO4sq7WrVEH59VfCz5/PWxdevz6Nhg6loVZLhIvHwyivYJGdmsr5NWs48csvXNy0CSzXh6zwcOJbtyalbl2qHjhA1OHDVvslNG9OlerV6fXAA0T37esRH9gSKoSTyQvGQRIshMt5Q7iwJzY2ljVr1gBQdc8eqhw6ZHO7qm3bEj1gAHX796dykyZO/9Aqj2Cx9dVXObF8OaasrELrssLDOT1kCACBiYk0+OuvvHW1evSg9bhx1LzlFo/5sJZQIZxNo495B3gcWA/EA/WAPsAm4AQQAfQD/jbotMPLoTwqYADwikGn7evg9i8C1YDrQCNgikGntT2KYBmUz43jokLL7dBZMFzkduj05HARHh5Olago4hMSiDhzxmqdMTCQi926EXb+PDlHjnBtzx52z55NWHQ0dfv1I7pfP6p36oRfEfNieBKTSkVytWqk1K1L6KVLVMr3eANTUgi+epWsiAiCr11DFRZGk9tvp8UDD1C5aVM3lrowCRXCRToATQ067SUAjT5mPOZgcadBp71sWdYXuMPVBdHoY+4BhgDhgKPVpY8DfQ06rcZyjBeBhcAwZ5dPgoUoF94aLjp27EjU+fOs++47AgrUuKTUqUNarVqk1apFTlgY1SwjTqaeO8eRxYs5sngxfkFBVL35Zqp37Ej1jh2p1r59uXf+NGZlkX7pEuH16hW5XVj37sRZPoyNwcFWwQKg1ubNVIqKouX999Pkk08IrFzZZWUuLQkVwhWOxiUBLMoNFRa9gUO5ocLiImDdTugCBp32R+BHjT7mYaCzg7tNA17K9/tC4E2NPibaoNOec2b5JFiIcuOt4aLR0KFEtWzJsR9/5OSvv5KdkgJAhmUGToCwc9bvS5O/P3HduhFy7Rqpx49zeft28wqVivB69Wg1ZgzN7rvPqeU0ZmWRGhdH6rlzJB49SsLhwyQeOkTyiRP4hYZy9z//kJqWxqFDhzh79iytWrWiZcuWefu37t+f31avJjs4mIwqVTCp1ahNJlRqNbV79aLJiBHU7dcPdTmNkFlSEiqEq+w+dQ3g5wKLewOrCiyrCRwsjzKVhEYf0xyoD+zPXWbQac9r9DFJwEDgG2eezzOvEMJneWu4iGzWjM4vv0z7Z5/lwrp1nPztN1i/nshjx0itVYvg+Hir7dOrVyetTh3S6tTBGBhIcEKCeYWikHLmDJt27yZ62DBCQkLsnnPra6+ByYRfSAgZlg/FXR99RKifH6asLHLS08lMSCAzMZH0y5dJzze9uEmtJrtSJfxTU/HLycGUnEzSiROkBAcTExMDmAenyh8s/Pz9uSkkhMvr1hFy+TKRDRvSeNgwGt5xB6E1ajjrqXQJCRXClUZ0a8Td3RvnXbA0+pi6mPsorC+w6XqDTuuJ/RCbWH4mF1h+HWju7JNJsBDlzlvDBYB/cDD1NRrqazRkJCRw5s8/ObtqFZf9/VHy3YKZnq82I9hyK2suk1rNyeBg3nnnHZo1a8YDDzxgtf7UqVNkZ2dzYN06Ai5dQqUopBmNABz59ltC/fzICg8nJzQUY1AQ4efPo8o3RXxSo0Zc7tQJ1GpqbdpEhOVW0as7d9Jw+HD8/PwwGo2cKdDUAdDzzju5EBVFfY2Gys2aecUHsoQK4Wo2XkO9LT+tgoWHhgqAKMvP1ALLU/KtcxqnBosn5m8gIUVGLhSO6T5Wz9ovXsaYlZG3bOnSpTTpPICeo6ej9vOG3FsDbn4Apc19GDOzMGZmYsrKRDGZUDLVKGo16s7NoNON642iVmNUBQOw+3QAMbP/tjpiamoqRqMR+j6Bf3o6oJCCGt56gB/umkE4JoyBQSh+fgD4ZaRbDVGu+Plh9DMPX67u2gp1B/Nop0sP+hP06TqygzqjVqtRm9RsKXBus9bwx1ngrPOeJhc5uW0lm5a8k3dbbK5W/e/hXO3BPPTRajeVTHibqPAgPh3fy9HNewHnDDrtqfwLNfqYsZhvS40Ajhh02hUFd9ToY/wwN6sEO3CeJINOe6+jhSqCscDPXAG4oILBqQdMSMnk6vWM4jcUAvCr2YIOD85g5+KZmLJvBNKzezawesFrtB05zUvCRT7qIAgOcnjzrBxILfSe8QOVOTRkhZrvKDFlmGt2TGp/0oKth0snpIi7TgICzZcOi+t55yp4ffE+F3atZt+yDwuFioY9hxPdbxTX5EuOcJ3eFKitsDSPTDLotN0st3bu1+hjVht0WqsXokGnNQJ3lltJzXLbSQtO4xEGePbtplHhjl9QhQCo1rYLlSe+Wajm4vKBjRxe9p4X1VzYp6Cg5ORgzMpGyckhJTWFkMgou/0rsrKzMBmN5KSlobbMrZJiuR6oTTmEpiWi+PmhqNWggMqYU2hSNTMVKn8/1P4BqP39UQf44xfoG+/Rk9tW2gwVrfrfQ/uhE6T5Q5SYo59fGn1MJNAG+KzAqt7ATjA3iWj0MceA7sBapxWy9HInSKoJ5N4aqwYiMY/B4VROvWKXoBpJiHwGsm5kp0J9Ls7u2UDWxs89us9FaahUKpYtW8addw60u03qhQv8OXIk2WlpmLKySDMaWQXcu+xVQv398QsMxC8oiMDISIIiIwmKiiKsTh3C69Y1/4yOplKTJvgHO1Lb6l0WLVrEGBvNH9KnQpSTnpi/+RfsuFkX686RyUCdgju7oynEoNOetASdFsBey+IWljI4vb3Qu78KCp/hzR06XSGsTh1G/PMPAKacHBKuXGFCnTrcvXEjkVWquLl07iMdNYUH6AskkO/WTQs1kJPvd39stDk6uSlEjY1ZyjX6mEmYx6zoZtBp4yyLvwFGA/+z/D4W+NWg0zp93A0JFsJjSLiwTe3vT0BYWN7/KyoJFcJdLielM+rj1d9h7pMwCAgElmr0MdeBRww6bQ5wHojOt1sUEFfoYE6g0cfcBozH3PxSXaOP+QfzYF3jLJuoMddG5A8dbwNvafQxn2DuV1EbeNgV5ZO5QoTH8ea5RexJSUnh2LFjAHTo0IEPPviA/v37U6VKFerXr1/s/u6cNt0TSKgQHqDIF5lGH1MT+MGg0/bT6GP8gVNAS4NOm1IehfMkEiyER/K1cLF27Vr69+9faPmYMWP4+uuvi92/IgcLCRXCQxT7QtPoY57GPFZEdeCgQadd6vJSeSAJFsJj+Vq4KIuKGiwkVAgPIi82BxXq9CGEp8jtcxEaaj1uQ26fi2zLrZjCN0moEMI7SbAQHk3CRcUkoUII7yXBQng8CRcVi4QKIbybBAvhFSRcVAwSKoTwfhIshNeQcOHbJFQI4RskWAivIuHCN0moEMJ3SLAQXkfChW+RUCGEb5FgIbxSRQkXc+bMoXXr1nTp0sXdRXEJCRVC+B4ZIEt4tYoyiJYvDpAloUJ4GXlBOkhqLIRXqyg1F75GQoUQvkuChfB6Ei68i4QKIXybBAvhEyRceAcJFUL4PgkWwmdIuPBsEiqEqBgkWAifIuHCM0moEKLikGAhfI6EC88ioUKIikWChfBJEi48g4QKISoeCRbCZ0m4cC8JFUJUTBIshE+TcOEeEiqEqLgkWAifJ+GifEmoEKJik2AhKgQJF+VDQoUQQoKFqDAkXLiWhAohBEiwEBWMt4ULb5ndVEKFEJ5No48JsrEs2BXnktlNRYXkbbOievLsphIqREWg0ce8AzwOrAfigXpAH2ATcAKIAPoBfxt02uEuLosKeBGoBlwHGgFTDDptUhH7jAF0QKxln+bAAYNO+6yzyyc1FqJC8raaC08loUJUIB2ApgaddohBp30IWGRZfqdBp33IoNMOA+4ATpZDWR4H+hp02mcMOu0M4CCwsJh9VEAQcB8wBDAAz7uicP6uOKgQ3iA3XBSsucgNF55Yc+FJJFSIiuJoXBLAIoNOeynf4t7AIYNOeznfsovA4XIo0jTgpXy/LwTe1Ohjog067bki9htl0GnXurRkSI2FqOCk5qJ0JFSIimT3qWsAPxdY3Btzs0h+NTHXHriMRh/THKgP7M9dZtBpzwNJwEBXnttRUmMhKjypuSgZCRWiohnRrRF3d2+cd3HQ6GPqYu7XUDBYrDfotK7uh9jE8jO5wPLcfhNFGaTRx/TE/NnfAnjSoNNedXL5nBssnpi/gYSUTGceUohy032snrVfvIwxKyNv2dKlS2nSeQA9R09H7ee+HH7lWgIAd7/7F9WrRrmtHCe3rWTTknegQKho1f8eztUezEMfrXZTyYQom6jwID4d38vmOhthubflp1WwKIdQAZB7AUgtsDwl3zpbjMBxg067AECjj5kBLOPGY3Eap14pE1IyuXo9o/gNhfBAfjVb0OHBGexcPBNT9o2AfHbPBlYveI22I6e5LVwYTUreT3e9xy7sWs2+ZR8WChUNew4nut8orsmXClFx9ALOGXTaU/kXavQxYzF3kowAjhh02hUFd9ToY/wwN6s4cqtnkkGnvbfAMmOBn7kCKOIz3aDTLiqw6H/ATI0+prdBpy1Y81ImTr1KRoUXuk1WCK9SrW0XKk98s1DNxeUDGzm87D231VxcyUoHwE+tolqES249L9LJbStthopW/e+h/dAJ0vwhvF4JP78K9a+wNI9MMui03Sy3g+7X6GNWG3Raq8Rt0GmNwJ1lKOoVy8+CfSTDMPezcFRujUdXCjfplIlTr5D2qpGE8C4DWTeyU6E+F2f3bCBr4+du6XORnJxM5dfhf88PLvdxLBYtWsQYG80f0qdCVEQafUwk0Ab4rMCq3sBOMDeJaPQxx4DuwFonFyH3dtaawGVLmdRAJObxNGyVOQTYB7xn0GnnWhaHW37mOLl80nlTCFukQ6eZdNQUopCemGsLCn7Lr4t1h8pkoE7BncvaFGLQaU9aQksLYK9lcQvL8ex1clJj/ry/mG9ZbifQtQ6Uo0QkWAhhR0UPFxIqhLCpL5BAvts9LdRYf/v3p3A/CGc0hQB8A4zG3E8CYCzwq0GnPQyg0cdMwjzORTeDThtn0GlTNfqY+ZhH3cx1P+axOXaXsSyFSLAQoggVNVxIqBDihstJ6Yz6ePV3mPsxDAICgaUafcx14BGDTpsDnAei8+0WBcS5qEhvA29p9DGfYO5XURt4ON96NeYajPz9MGYD0zX6mDDMj+Mo8KorCidzhQjhAHfPLVKec4VIqBDCpiJf+Bp9TE3gB4NO20+jj/EHTgEtDTptSnkUzpNIsBDCQe4IF3PmzGHOnDkYjUaOHDni8mAhoUIIu4p98Wv0MU9jvtuiOnDQoNMudXmpPJAECyFKwF01F+VRYyGhQogiyRvAQTJXiBAl4Ktzi0ioEEI4iwQLIUrI18KFhAohhDNJsBCiFHwlXEioEEI4mwQLIUrJ28OFhAohhCtIsBCiDLw1XEioEEK4igQLIcrI28KFhAohhCtJsBDCCbwlXEioEEK4mgQLIZzE08OFhAohRHmQYCGEE3lquJBQIYQoLxIshHAyTwsXEiqEEOVJgoUQLuAp4UJChRCivEmwEMJF3B0uJFQIIdxBgoUQLuSucCGhQgjhLhIshHCxsoSLOXPm0Lp1a7p06eLw+SRUCOF5VCrVPSqV6ohKpcpRqVSK5V+SSqV6Pt82d6tUqtR86xNUKtXv7ix3aci06UKUk7JMue7otOkSKoRwGae8eVQq1SDgLyATqKMoSnyB9Y8CLwNPAr8qimJ0xnnLk9RYCFFOXN0sIqFCCM+nKMpKYC8QBAzKv06lUjUAhgNdFUVZ5o2hAiRYCFGuXBUuJFQI4VXmWH5OyV2gUqlqAfOBRxRFiXNLqZxEgoUQ5czZ4UJChRBeZzGQCPRUqVTtVSpVVWAh8KiiKOfcWjInkGAhhBs4K1xIqBDC+yiKkgp8bfn1ReBb4GlFUY67rVBOJMFCCDcpa7iQUCGEV5uD+WaIe4B3FUXZ7+byOI3cFSKEmzlyt0jBu0IkVAhRvjT6mHeAx4H1QDxQD+gDbAJOABFAP+Bvg047vLjjqVQqP+AQ0BR4VlGUD0pQFhXmmo5qwHWgETDFoNMmOXOf0pIaCyHcrKQ1FxIqhHCLDkBTg047xKDTPgQssiy/06DTPmTQaYcBdwAnizuQyvwmnQf8YVn0uEqlKsnn8eNAX4NO+4xBp50BHMTcR8PZ+5SKBAshPICj4eL777+XUCFEOTsalwSwyKDTXsq3uDdwyKDTXs637CJw2IFDfgSsBp4CjgNNgNtKUKRpWIeChcAdGn1MtJP3KRUJFkJ4iKLCxdixYwGYNGmShAohytnuU9cAfi6wuDfmZpH8amKuCbBLpVK9CRxUFOU7xfxmLnTraVE0+pjmQH0gr0+GQac9DyQBA521T1lIsBDCg9gLF7/99pvN7SVUCOF6I7o1wqDT5nWC0uhj6mLuo1AwWKw36LQFl+VRqVQvAMmKoszNt/grIBUYrFKpmjtQnCaWn8kFll8H7O1fmn1KTYKFEB7GXrgoSEKFEOXDxnust+WnVYgw6LR2b25QqVRPApGKoryVf7miKImYx7VQAZMdKE6U5WdqgeUp+dY5Y59S8y/JxiqVSpWUZL8D6XPfbCIxNbPMhRKiolMUhc4PvMT6BTNRTDmF1jfrOYyTUT25923bNRlCiJKJDAvivTHd7a6vXLlyJeC6pfmiF3DOoNOeyr+NRh8zFnNAiACOGHTaFSqVqjYwE3PHzjoafYwf5maV4Nz9+j6/qOr1iydQqdWPD5qxrI3aPzC3x3aSQae9t0BRjAV+5grA/md6afYptZIeMKJy5crOLoMQooSO/vMLR//5xd3FEMKnfPFkkauTgMqYmxMK9a+wNI9MMui03TT6GFVOZtopv4DALKAxN1oHtht02k7Anbn7qVSqn4H+ll/9ge7AMeBuRVGO2CjHFcvPgi0OYZYy2lKafUqtpMHielE1Fk8v2MCh42eoXacW6hLdOWN26fIlatao6fH7lXZfk2Ii7sLFUj0/5V1Wd+znjufHU5/XkztXs/2nj4rcpu5N3eh2//Oo/Yp+G3vqY3TmfvLasa8sz01pz+mO/Uq7b+7z07JJfT58pJfd7Sqbv1Vf1+hjIoE2wGcFNukN7ARzk4hGH7P71leWfWDQadcWdX5FUUaUqMA3bmetCVwG0Ohj1EAk5vE0nLVPqZUoWCjFjKb14SO9HJra2Z7WrVuz7sABj9+vtPs6OvW1s85X1n3Lez93PD+e+LwuWrSIMS99XOxxzu/fjLLzW74tZsp1T3yMzt5PXjv2leW5Ke053bFfaffNfX5WFPP8KIqSDKDRx/TE/M2/YCfNulh3jkwG6hQ8jq2mkCIUagox6LQnNfqYY0ALzLOkYvl/MOZbWAspzT5l4fS2lbKYPNmRfivu36+s+5b3+bzpeS0tb3oNFLWfvcGvJk2axLx58wgJCSE9PT1vee44F98XES487TG6Yr+y8JXXjqt402ugnJ6fvkAC+W7dtFAD+TtE+VO4TwMGndZIvqaQUvoGGA38z/L7WOBXg057GECjj5kEvAR0M+i0cY7s40xOHdK7rMnY18nzU7SK/vwUNaLmlClTqF+/Pj/99BNjxowpcvjviqiiv3aKIs9N0Rx5fi4npTPq49VLMPdJGAQEAr9hvl3zEYNOm6PRxzwA3GLQaacCaPQxBuANg04b6+wya/QxAcBblnIkAQ2AJw06bYJl/WOYO4x2tIxXUew+TqUoSkn/2ZWRkaHMmDFDycjIKGqzCkuen6JV5Odn4cKFikqlUjAH97x/zz//vGIymZTLly8rgHL58mVl7dq1SmhoaKFthw8frmRlZbn7obhFRX7tFEeem6KV4Pkp8rNx8Gu/1xz82u9rLf/3H/za7+cGv/Z7eHH7+eI/mYRMCDdzZO6Pgt+qHJm4TAjhVMUOGKPRxzyNeayI6sBBg0671OWl8kASLIRwI0cnFLNVXSvhQohyJSPROUhG3hTCTco6S2lJZ0UVQojyIMFCCDdw1tTnEi6EEJ5GgoUQ5cxZoSKXhAshhCdxWbC44447qF+/PsHBwdSuXZtRo0Zx4cIFV53Oq5w6dYpx48bRqFEjQkJCaNKkCTNmzCArK8vdRfMYb7zxBj169CA0NJTIyEh3F8dpnB0qclXUcBEbG8vQoUOpU6cOKpWK5cuXu7tIHmPWrFl06dKFiIgIatSowZ133snhw04fssBrzZ07l7Zt21KpUiUqVapE9+7dWbFihbuL5RNcFiz69+/Pjz/+yOHDh/n55585fvw4d999t6tO51UOHTqEyWRi3rx57N+/nw8//JDPPvuMl156yd1F8xhZWVmMHDmSxx57zN1FcRpXhYpcFTFcpKam0q5dOz799FN3F8XjrFu3jsmTJ7N582ZWrlxJTk4OgwcPJjW14ASXFVN0dDRvvfUW27dvZ/v27QwYMIBhw4axf3/Bca9EiZXiHtVS+eWXXxSVSlVh77MvzjvvvKM0atTI3cXwOF999ZVSuXJldxejzIobp6I4SUlJCqAkJSUVu21FHecCUJYtW+buYnis3LFQ1q1b5+6ieKyoqChl/vz59la7fXwIb/lXLn0s4uPj+fbbb+nRo4fcAmdHUlISVapUcXcxhAuUpaZizpw5tG7dmi5dujh8vopYcyGKlzuBpFxnCjMajXz//fekpqbSvbv9qdOFg0qRRhw2bdq0vG9O3bp1U65evVqS3SuMY8eOKZUqVVK++OILdxfF43h7jUVZaypylaTGIldFq7lAaizsMplMytChQ5VevXq5uygeZc+ePUpYWJji5+enVK5cWYmJiSlqc7fXBHjLvxLVWKhUqpkqlYqi/m3fvj1v++eff55///2Xv/76Cz8/P0aPHl3oW5svmTlzZpHPTcHnB+DChQv85z//YeTIkYwfP95NJS8fpXl+vJmr+1QUR2ouRK4nnniCPXv2sGTJEncXxaO0aNGCXbt2sXnzZh577DHGjBnDgVLOrCpuKNHImyqVqtrBgwevFLVNw4YNCQ4uPBvsuXPnqFevHhs3bvTZqqarV69y9erVIrfJ//xcuHCB/v37c8stt/D111+jVvv23b8lfX4Avv76a5566ikSExNdXDrncnaoKMtEUhVlhE6VSsWyZcu488473V0UjzJlyhSWL19ObGwsjRo1cndxPNqtt95KkyZNmDdvnq3VMvKmg0o0bbqiKEV/KhS9LwCZmZmlPYTHq1atGtWqVXNo2/Pnz9O/f386derEV1995fOhAkr2/Hgzd9dUFJRbc1EwXDgy5brwXoqiMGXKFJYtW8batWslVDhAURSf/owqLyUKFo7aunUrW7dupVevXkRFRXHixAleeeUVmjRp4rO1FSVx4cIF+vXrR/369Xnvvfe4cuVGJVCtWrXcWDLPcebMGeLj4zlz5gxGo5Fdu3YB0LRpU8LDw91buCJ4WqjI5avhIiUlhWPHjuX9fvLkSXbt2kWVKlWoX7++G0vmfpMnT+a7777jl19+ISIigosXLwJQuXJlQkJC3Fw693vppZe47bbbqFevHtevX+f7779n7dq1/Pnnn+4umvcrRceMYu3Zs0fp37+/UqVKFSUoKEhp2LCh8uijjyrnzp1zZHef99VXXxXqUJf7T5iNGTPG5vOzZs0adxfNLmd11LSlNJ03bfG1Dp1r1qyx+ToZM2aMu4vmdvauMV999ZW7i+YRHnnkEaVBgwZKYGCgUr16dWXgwIHKX3/9VdQubu8U6S3/ZHZTIZzA1TUVZeljUVBF6XMhhJNJHwsH+X7DvhAu5qnNH/bI3SJCCFeSYCFEGXhbqMgl4UII4SoSLIQoJW8NFbkkXAghXEGChRCl4O2hIpeECyGEs0mwEKKEfCVU5JJwIYRwJgkWQpSAr4WKXBIuhBDOIsFCCAf5aqjIJeFCCKHRxwTZWFZ4no4iyDgWQjjAXaFizpw5zJkzB6PRyJEjR5wyjkVxZJwLUdHMX3WQ33ecpk39KkQEB3AlOYO9Z+JpFR1J7chQ0rKMbD5yKRn426DTDnd3eR2l0ceogBeBasB1oBEwxaDTJhWxzxhAB8Ra9mkOHDDotM86el6psRCiGO6sqZg8eTIHDhxg27ZtLjtHQVJzISqa45eS+Wpyf16/vyv/vasDA9vWBWDmPZ35710dePXezgB3ACfdWc5SeBzoa9BpnzHotDOAg8DCYvZRAUHAfcAQwAA8X5KTumSuECF8ha83f9jjq3OLCFHQ0bgkBt5cl6jwGy0A+87EU69qGJFhVq0CF4HD5V2+MpoGvJTv94XAmxp9TLRBpz1XxH6jDDrt2tKeVGoshLCjooaKXFJzISqC3aeu0atVbatl+87E06Z+lYKb1sT8jd8raPQxzYH6wP7cZQad9jyQBAx05bmlxkIIGyp6qMglNRfC143o1sjq/Xw1OYOLiem2gsV6g07rTX0Mm1h+JhdYnttvoiiDNPqYnpgzQgvgSYNOe9XRE0uNhRAFSKiwJjUXwpcVfD/vOxMPUChYeFmoAIiy/EwtsDwl3zpbjMBxg077hkGnfRVz88+ykpzYqTUWT8zfQEJKpjMPKUS5OrltJZuWvAMFQkWr/vdwrvZgHvpotVvKdeVaAgB3v/sX1asWdU1wne5j9az94mWMWRl5y5YuXUqTzgPoOXo6aj+pABXeKyo8iE/H92Lf2XiqVQqmVqR1kNboY8Zi7tgYARwx6LQrCh5Do4/xA34GHLk9M8mg097rhKLbYyzwM1cARXz2G3TaRQUW/Q+YqdHH9DbotOsdObFTrwQJKZlcvZ5R/IZCeKALu1azb9mHhUJFw57Die43imtuDM1Gk5L3013vMb+aLejw4Ax2Lp6JKfvGc3F2zwZWL3iNtiOnSbgQXm/fmXja1LOurbianAEwyaDTdrPcwrlfo49ZbdBprS4KBp3WCNzprLJo9DH3AyMc2HSxQaddXmDZFcvPgi0TYZj7WTgqt8ajK1D+wSJ/r1ohvMnJbStthopW/e+h/dAJbm/+uJKVDoCfWkW1iBKNVeNU1dp2ofLENwvVXFw+sJHDy96TmgvhtaLCg0jJyOb0letoOzWwWmdpHtkJ5iYRjT7mGNAdWOvKMhl02iXAklLunntrbE3gMoBGH6MGIoETtnbQ6GNCgH3Aewaddq5lcbjlZ46jJ3bqFeDT8b2ceTghysWiRYsYY6P5w5P6VCQnJ1P5dfjf84NdPkBW8QaybmSnQh06z+7ZQNbGz6VDp/BaW45ewqTAzQX6V1hqCfN3gkwG6hTc35OaQgw67UlLAGoB7LUsbmEpm702XTXmXHAx37LcTqBrHT23fLUQFZp01CwduVtE+KK9p+MJDw6gQfVwq+WW60P+b+z+FO674PSmECf4BhiNuZ8EwFjgV4NOexhAo4+ZhHmci24GnTbOoNOmavQx8zGPupnrfmCRQafd7ehJJViICktCRdlIuBC+4HJSOl/+fYiMbCP/nrhCtlHhtZ92EBLoz7N3tMVPraaqufkxIt9uUUCce0pcIm8Db2n0MZ9g7ldRG3g433o15hqM/P0wZgPTNfqYMMz9MY4Cr5bkpDJXiKiQvC1UJCcnU7ly5XKZK6SkZG4R4esSUjK578NV6ww6bT+NPsYfOAW0NOi0KW4umkeSYCEqHG8LFeDZwQIkXAjfp9HHPIP5DonqwEGDTrvUzUXyWBIsRIXibaHCHbOblpaEC+HjPOvi4MEkWIgKw9tCRX6eXmORS8KF8GGee4HwMDKkt6gQvDlUeBMZ/lsIIcFC+DwJFeVLwoUQFZsEC+HTJFS4h4QLISouCRbCZ0mocC8JF0JUTBIshE+SUOEZJFwIUfFIsBA+R0KFZ5FwIUTFIsFC+BQJFZ5JwoUQFYcEC+EzJFR4NgkXQlQMEiyET5BQ4R0kXAjh+yRYCK8nocK7SLgQwrdJsBBeTUKFd5JwIYTvkmAhvJaECu8m4UII3yTBQnilihIq5syZQ+vWrenSpYu7i+ISEi6E8D0yu6nwOhUlVOTnLbOblpbMiiq8gO9dWFxEaiyEV6mIoaIikJoLIXyHBAvhNSRU+DYJF0L4BgkWwitIqKgYJFwI4f0kWAiPJ6GiYpFwIYR3k2AhPJqEiopJwoUQ3kuChfBYEioqNgkXQngnud1UeCQJFdZ8/XbTositqMLV5q86yO87TtOmfhUiggO4kpzB3jPxtIqOpHZkKGlZRjYfuZQM/G3QaYe7u7wlodHHqIABwCsGnbavg9u/CFQDrgONgCkGnTbJ0XP6l7KsQriMhAqRX27NRcFwkVtzIeFClNXxS8l8Nbk/UeFBAKz49wx7z8Qz857ORIaZl2n0MXcAd7ixmCWm0cfcAwwBwoEGDu72ONDXoNNqLMd4EVgIDHP0vNIUIjyKhAphizSLCFc5GpfEwJvr5oUKgH1n4qlXNSwvVFhcBA6Xd/nKwqDT/mjQaR8Gfi/BbtMwB4lcC4E7NPqYaEcPIMFCeAxfDRVvvPEGPXr0IDQ0lMjISIf2MWZlkXrhAtfPnCHpxAkSjh4FIP7wYZJPnyb9yhVy0tIKPVe+TMKFcIXdp67Rq1Vtq2X7zsTTpn6VgpvWBA6WV7ncQaOPaQ7UB/bnLjPotOeBJGCgo8eRphDhEXw1VABkZWUxcuRIunfvzpdffunQPgmHDvHX/ffn/Z5mNAKwatQoQv388par1Gr8w8IIqV6d0Fq1CK1Vi7DatanUqBGVmzYlokED/AIDnfuA3EiaRYSzjejWyOr6cjU5g4uJ6baCxXqDTuvrSb6J5WdygeXXgeaOHkSChXA7Xw4VANMmTeLKzp2s37GDZ6tVY/3UqfT+6KO89SaTiePHj5OUZO4b1blzZ4Kjohw6tmIycblOHVAU/E+fJnzjRqsJDVT+/kTUr0+V1q2p3qkTze65x5kPzS0kXAhnKnh92XcmHqBQsKgAoQIg98KTWmB5Sr51xXJqsHhi/gYSUjKdeUjh405uW8mmJe9AgVDRqv89nKs9mIc+Wu2mkpWeYjJizMzCmJWJKTsbxWgEVCgNtCiNhrJTgc9m/221T/L1ZFBArVYTviEJk8lExh0v5a1PQQ1vPcAPd80gHJPVvjnBIaBSmcNFRrp1WdR+KGo1KpMJ9V4IuWB9Xm/WfayetV+8jDErI2/Z0qVLadJ5AD1HT0ftJ9+bhOOiwoP4dHwv9p2Np1qlYGpFWje5afQxYzFPRBYBHDHotCsKHkOjj/EDfgaCHThlkkGnvdcJRXcmY4GfuQIoQV5w6jsvISWTq9czit9QCODCrtXsW/ZhoVDRsOdwovuN4ppXh1QVqIMhyPb1Ja3Q+yTQfMlSICN3XWhk3lpThvmbuUntT1pwKDapICs0yPY6i1Qfen/61WxBhwdnsHPxTEzZN14rZ/dsYPWC12g7cpqEC1Fi+87E06aedW3F1eQMgEkGnbab5XbM/Rp9zGqDTmt1kTLotEbgTmeVRaOPuR8Y4cCmiw067XInnPKK5WfB/pdhmPtZOMSp77r8vWqFKMrJbStthopW/e+h/dAJHt/8kZycTOr16wSqVQSp1KhVoKjVKH5+KGo/1FlZqJQbNQuKSo0x2BwyVEYjoaGh+AXdeL9kZWcBoFap8ff3R1EUMq5eRTGZvzikWN7nalMOoWmJVmVR1H4oKnMqURutv2gYg4JQ1OY+GSEBAQSEhNxYZzSSnp6On78fgQGB+Pn5YczKIic9Df/gYNSBQR7/d6jWtguVJ75ZqObi8oGNHF72ntRcCIdFhQeRkpHN6SvX0XayvjPT0jyyE8xNIhp9zDGgO7DWlWUy6LRLgCWuPEcBJy0/awKXATT6GDUQCZxw9CBOfcd9Or6XMw8nfNSiRYsYY6P5wxv6VKScP8/pP/7g+KpfSDl50mpdfKtWXLv5ZgCq79tB5PHjeesU4HLnzgQmJxN87Rq3PPAAbR59tMhznfz1V7KuX0cdEEBqVhYdgPfamAgGctLSyE5NJSc1lcykJNIvXSL14kXSL17ElJOTd4zMyEgyoqLICQ3l4XffJaLBjQtmbGwsa9ZsAiNob9XSuXNnNk+fzollywAICA8neuBAmowYQfWOHT347zKQdSM7FepzcXbPBrI2fi59LoTDthy9hEmBmwv0r7DUxOfv0JgM1Cm4v7c3hRh02pOW0NQC2GtZ3ALz43G4XVqivChX3thR02Q0cmHdOo4sWcL57dtJqVOH1Dp1qHXmjFUNQejFi3nBIqvA6JgqoOb27SQajTQdONDqA96eRnfcGIsnOdl8TWs0dGiRI28qJhOpcXEkHTtG0tGjJB4/TsKBA2RevEh4/fpW26alpaFWqzGZTDRp0gRjVhZnV60CICc4mDPdunHx6FEOT55M9Ro1aHrvvTQaOpRADxz5Uzp0CmfYezqe8OAAGlQPt1puuV7l5FvkT+F+CE5vCnEiNTaGl9DoYyYBLwHdDDptnGXxN8Bo4H+W38cCvxp0WofH8JBgIcqNN4YKgFO//srm6dMBuNK1K9cbNgQg7fRpws+fz9suKDGRmlu2EHL5MgHp5k6UlZs0IaRlS/waNOCfM2eY9X//x/oJE0gAqqakEB4eXvB0ZaJSqwmvW5fwunWp2/fG6L05GRmFnt///Oc/DBgwgHPnzhEVFcW51avJvn4dgNQ6dcisUoXMKlVQ1GoC9+1jx5tvsuuDD2jwn//Q9J57qNq2rUf9zSRciNK4nJTOl38fIiPbyL8nrpBtVHjtpx2EBPrz7B1t8VOrqRoRDOZOm7migDjbR/QcGn3MbcB4oDdQXaOP+Qc4ZNBpx1k2UWOujcgfOt4G3tLoYz7B3K+iNvBwSc4rc4WIcuFtocJkMnH69GkaNmxITloaywcMIDslhdSaNblg+cCufOwYNXbutNrPLySEWrfcQp0+fajTuzdhderw8MMP88033xQ6x5o1a+jXr59D5SmPuUL+ee45Tq8wd3S/3KEDSc2aAVDvr78ITkzM205Rq0lu0ID6lSrR9pFHiB4wAJXac8bak7lFhLMlpGRy34er1hl02n4afYw/cApoadBpU9xcNI8kwUK4nLeFip07d7JmzRpSUlJ45JFHqFevHtvffJMj336LolIR37o1oXFxBMfHowL8goOp278/DYcMoXbPnladMp2lPILF3rlzObFsGamWWpjs0FDSatWi0okTVmNjpNSpQ1yvXqiMRqru3UuDnBxaPfIIDbVajxmMS8KFcDaNPuYZzOM7VAcOGnTapW4ukseSYCFcytNDhaIoKEYjav8brYI7d+7kt99+A6BLly4MGTKEpBMniBk6NG8blZ8ftXr0oKFWS/SAAQSEhbm0nOU1u6miKFzbs4dTf/zB6d9/JzNfTUWuuO7dSalXD4Da69cTHmeuEQ6pWZNWY8bQ5O67Xf58OELChXAyz/oG5MEkWAiX8eRQoSgKB1euZMNvv9GpbVs6TZiQty4rK4sPP/yQBg0a0KlTJ5pZmgT+HjeOlDNnaHrPPTQZPpzgqlXLrbzumDbdmJnJmZUrOfbjj1zZsSNveUZkJNcbNiS9enXqrVqFKt/fN7NSJRI7dKB9mzb0GjvW6vZWd5BwIZxIgoWDJFgIl/DkUHF5xw4MX33FierVAahx9CjjP/uMgHwdKbOysggsUK2ffvUqQVFRqPPN1VFe3BEs8ks8doxjP/3EyV9+yevgqVD4SmvVN+PkSR6eP9+qNsgdJFwIJ5Fg4SDP6XElfIanhor4/ftZM3Eiq0aPxrR1a944Ggk1a3KwQOfKgqECIKRaNbeECk8Q2bQpnV98kbvWrKHzyy8TVrduoausAqTXqAGAKieHNu3aWYUKd83EKrOiClG+pMZCOJWnhYqrV6+yce1alH//JXX5cqt1lzt0ICAtjYhTpwj292fYX38R5OC05uXN3TUWBZlycjjz558c+PJLEo8cyVuuqFSk1qmDEhnJ2C++ILBy5bx1W7du5ciRI3Tt2pVmzZqV+2tBai5EGUmNhYOkxkI4jaeFijPHjzNnzhz+3b+fwzY6Idb491+iDh/GPzOTnNRUjnz3XbmWz5up/f1pePvt3LZ0KX3nzqVG584AqBSF8PPn6TlggFWoUBSFrVu3cvz4cZYsWcKVK1fsHdplpOZCiPIhwUI4hSeFCsVk4sSyZWx75BECLCNWZlSpQk6w7VF2g6tWpdOLL9J63Dib64V9KpWKun36cOs33zDw66+p3qEDQVFRtBg1ymq75ORkTCbz3CkNGzakRo0aGLOyyE4xDwNQXs0kEi6EcD1pChFl5u5QkZ6ezvbt2zEajbSrVYttej1Xd+0C4Hq9euSEhFDp5En8CnxoBFaqRKtHHqHFgw/iH2pnxlA3mzNnDnPmzMFoNHLkyBGPaQqxR1EU0uLiCKtTaBoFTCYTR48eJTg4mAYNGnDgyy859M03tH3ySf5VFAICAujRowc1LP00XEmaRUQpSFOIgyRYiDJxd6gwGo3Mnj2blBTz/J+NfvsNtWU4bXv8QkJo9fDDtBwzhsCIiCK39RSe1seirNKvXuW3IUPISU0lKzyc07fdBioVERERPPXUU6jLYSRPCReihCRYOEiaQkSpuTtUAKjVaupZahtMJhOpRY0toVLRePhwhv7xB22feMJrQoUv2vPJJ+SkpgLmCdvUWeZp4+ump2MsJhg6izSLCOEaUmMhSqW8Q4WiKJw8eZK9e/cydOhQ1Go1SSdOsF2v59y+fSS0bEnk4cMEWj6sCqrZtSsdp00jqlUrp5arvPhSjUXCwYOsGDky73ZfAJO/P8kNGxJx+jQRVavS+eWXiR4wgOzsbL7++mvatm1Lx44dXVKLIDUXwkFSY+EgCRaixNxRU/H777+zwzL64z333EOrVq1Y8+ijxK1fX+R+YXXr0umFF6jbv7/bhw8vC18KFrtmz+bAF18Uu130gAGohw3j73/+AaB9+/YMGzbMJWWScCEc4L0XkHImTSGiRNzV/NGiRYu8/+/fvx+Azi+9hJ+dOz3UAQHcNGkS2l9+Mc++6cWhwte0mzqVvv/3f4TXr1/kdudWr2bHt9/m/X7LLbe4rEzSLCKE80iwEA4rj1CRk5PD9u3bSUhIsFretGlT2rZty913383w4cMBiKhfn7ZTphQ6Rq0ePRiyfDntnnwSfzfPVSEKU6lU1O3bF+3y5bR57DHURdQGVN+6lfoGAw2uXSPM0g8j17lz5/jzzz9JSkpySrkkXAjhHNIUIhxSHqHi3Llz/PDDD6SkpNCpUyduv/32Yvcx5eTw1wMPEL9/PyE1a9Lpv/+l3uDBPldD4UtNIQUlnTjBttde4/K2bUVu5xcSQvunn6b5/fejUqtZsmQJR44cQa1WM3r0aBo0aOCU8kiziLDDty4qLiQ1FqJY5dX8UbVqVbIs30p37dpV6MJui9rfn1v0elo+/DC3//Yb9TUanwsVvq5y48YM/Oorur35ZpFDqhvT09nx5pv8PXYslw4f5uTJkwCEh4cTHR3ttPJIzYUQZSM1FqJIrgoVqampJCYmUrduXavlq1at4tq1a7StW5f45cvp9uab+NmYEKyi8eUai/wyExP59/33ObF0aZHb+YWE0PLJJ7laty5RUVF07NjRav3+/fupVKkS9erVK3VZpOZCFCDfWBwkwULY5YpQYTKZMBgM7Ny5k0qVKjF58mSrwZCMWVkcmD+fffPmoeTk0HrCBNo/9VRZH4rXqyjBItfFzZvZotOReuFCkdvV6NKF7rNmEVa7dt6yrKwsZs+eTXp6Oo0bN+bBBx8s9YBbEi5EPhIsHCRNIcImV9VUqNVqrly5Qk5ODvHx8Rw4cCBvXdLx46x86CH2zpmDkpMDwMEvv+Tq7t2lfyDCK9Xq1o0hy5fT7N57i9zu2p49eQNt5dq1axfplkG2wsLCyjSKpzSLCFFyEixEIc4MFek2RlHs3bs3AQEBdOvWjfr166MoCocWLWLF3XcTb7mVNJdiMrHppZfIKafRGIXnCAgLo8srrzDgyy9tzj0C0P7ZZ6nctKnVsk6dOnHHHXdQtWpV+vTpU2ifuLi4EpVDwoUQJSNNIcKKs0JFQkIC69evZ+/evTz66KNUzTfUtqIoZGRkEBISQsa1a2x6+eViB7pq99RT3DRhQskfkI+oaE0hBWWnprLr/fc5+sMPectq9+5Nv7lz7b4mFUUptO706dN8/fXXNGjQgIEDB5aoD4Y0i1R40hTiIKmxEHmcWVOxb98+/v33X3JyclhfIDSoVCpCQkKI++cf/rjrriJDhcrPjzaPPkrLMWNK9mB8xJw5c2jdujVdunRxd1HcqmDtRVCVKnTT64t8Tdpat27dOsAcMK5du1aiMkjNhagINPqYIBvLbI9EaIfUWAjA+X0qMjMzmT17Noqi0L17d/r06ZN3DGNWFrs/+ohDX39d5DEqNW5M9zffpOrNN5fo3L6ootdY5Jd1/TrXT50q8etCURT27t1LbGwsJpOJJ554wrrjsNGIWq0u9rUuNRe+Z/6qg/y+4zRt6lchIjiAK8kZ7D0TT6voSGpHhpKWZWTzkUvJwN8GnXa4u8tbEhp9jAoYALxi0Gn7OrD9GEAHxALXgebAAYNO+6yj5/QvZVmFDylLqLh27Rrr16+nfv36Vrf8BQUFcd9991GzZk2C8w27nXzqFP88/zwJ+TptFqJS0WLUKNpNnYq/nSG7RcUVGBHhcKg4/O23BFaqRKOhQ1GpVLRt25Y2bdqQlJRUqFNnbGwsJ0+epG/fvjRu3Nju6z635qJguMituZBw4X2OX0rmq8n9iQo3f1lf8e8Z9p6JZ+Y9nYkMMy/T6GPuAO5wYzFLTKOPuQcYAoQDjo4gpwKCgPuA88Ac4OOSnFeCRQVXllCRmJjInDlzUBSFU6dO0a5dO/z8/PLW5x8JUVEUTi5fzvY33iiyI2ZI9ep0f+stanXrVoZHJQRc3b2bne+8g5KTw6WtW+n80kv4h4SgVquJioqy2jY9PZ0tW7aQmZnJd999x9SpU4usGZJw4TuOxiUx8Oa6eaECYN+ZeOpVDcsLFRYXgcPlXb6yMOi0PwI/avQxDwOdS7DrKINOu7a055U+FhVYSUJFYmqm1T+jyURkZCRNLT3yMzMzuXz5ss1t05Ovs3HaNDZPn15kqKjbrx+3LVsmoUKUWWZiIhuefTbvtuUTS5ey7KGHObvvkNVrOFdycnJekGjfvj0mvyCr13CO0VToHNLnwjfsPnWNXq1qWy3bdyaeNvWrFNy0JnCwvMrlzaTGooIqaU3FvR+ssvp93qQ+NKwRQb9+/YiOjuaWW24hKMic7kd/sobMbGPetiP3/o/Q/VvtlkUdGEiH556j+QMPyHDcoswURWHz9OmkFbitdH770cxfdhw4Dtx4DQPUrFmTxx57jAMHDlC3bt3Cr+HmJvp0aEGzZs2sXqNSc+H9RnRrZPU3vZqcwcXEdFvBYr1Bp60ofQwHafQxPTFnhBbAkwad9qqjOzs1WDwxfwMJKZnOPKRwgZPbVrJpyTtQIFS06n8P52oP5qGPVlstz8jIsHusOnXqUMfOGAO50uIuEGpnXeUmTejx7rtE5ZsWXYiyuLRlC+fXrCl2O2NGBhCR97tKpeKmm26yue2hQ4f443A6BBwhxMaMud3H6ln7xcsYs268V5YuXUqTzgPoOXo6aj/5DufposKD+HR8L/adiQcoFCwqUKgwAscNOu0CAI0+ZgawDOjt6AGc+mpPSMnk6nX7H0LC/S7sWs2+ZR8WChUNew4nut8orpVjMGx67710fP55mdpcOFWtbt3o+d57bJkxo9ConPlteO5Zqr75CpEFBtiyJ5sAsnJUpNq4xvnVbEGHB2ewc/FMTNk33kNn92xg9YLXaDtymoQLL7HvbDzVKgVTK9L665BGHzMWc8fGCOCIQaddUXBfjT7GD/gZcKTXeZJBpy16aFk3MOi0iwos+h8wU6OP6W3QaYsecMjCqa/0/J1fhOc5uW2lzVDRqv89tB86AZVKhdFkueUu31gwCgrXrjsvcARWqsQtej31br3VaccUIr8Gt91Gldat2fDssyQctN0snnL2HIZ776Xzyy/T+K67imyGG3TrrcRtPAcB1p8XJsWE0WgkwD+Aam27UHnim4VqLi4f2MjhZe9JzYWHy/382ncmnjb1rGsrriZnAEwy6LTdLLdv7tfoY1YbdFqrC6NBpzUCdzqrTBp9zP3ACAc2XWzQaZc767wF5KbzrkD5B4tPx/dy5uGEEy1atIgxNpo/cvtUJCQk8Pfff3PgwAEGDx5M9+7drbZLSMmwuvBGhNhvN144pX/e/w8vXszRhBsTSVVt25Ze779vd4hmIZwlokEDBn/7LTvffZejS5Zw77JXrdYHZqVjVExs0em4snMnnadPz7u9Of9rGCA8OABNzw6FzvHXX3+xadMWatWqxbBhw6hVayDrRnYq1Ofi7J4NZG38XPpceLiUjGxOX7mOtpP1nZmW5pGdYG4S0ehjjgHdgbWuLI9Bp10CLHHlOfLT6GNCgH3Aewaddq5lcbjlZ46jx5H4XAE40lEzOzs7b0KwjRs30rlzZ6sLYFS44+NJ5L9Fq+uEsaTv2s6F2FhaPPQQ7Z99VqZBF+XGLyiILtOnU7NLF7a88grZKSk2tzuxbBkJhw7Re/ZswqOjC95maFNqairbtm0D4OrVq4SFhQHSodOb7T8bj0mBmwv0r7A08SfnW5QMFPp25ANNIWrMueBivmVNLD/XOnoQCRY+zl6oePbZZ63u/qhZsyatW7fm9OnTdO/e3Wl3Z6jUarrPmsWVnTuJHjDAKccUoqTqazREtWrFP889V2iiu1wJBw/y58iR9HjnHer0Lr6fWmhoKCNHjmTdunXUq1ePiIgbHUH79u3L//73P+6++24JF15k7+l4woMDaFA93Gq55fqZ/xu7P+ZOjlac3RTiRGpsDC+h0cdMAl4Cuhl02jiDTpuq0cfMxzzqZq77gUUGndbhaaYlWPgwe6Fi6NChdOjQoVB4uO222wgKCnL4gpd86hSVGjYsdrugyEgJFcLtIurXZ9Dixfz7/vscWbzY5jZZycmsfewxbn78cdo8+iiqIqZcV6lUNG/enGbNmmE0Wn/GKIrC6dOnmThxIvPmzbOa5VfChWe5nJTOl38fIiPbyL8nrpBtVHjtpx2EBPrz7B1t8VOrqRoRDPlvIYIooGTT5LqBRh9zGzAe8x0d1TX6mH+AQwaddpxlEzXm2pX8L/TZwHSNPiYMCAOOAtbtiMWQuUJ8lL1QMWDAAHr37o1KpWL8+PHUrVu3xMdWFIWDX33F7g8/pNsbb9DoDq8a5dYryVwhznV21So2v/yy3aYRgDp9+tDjrbcIrFy5xMc/ePAgP/74IwDXr19n7ty5MreIF0tIyeS+D1etM+i0/TT6GH/gFNDSoNPafwFVYDLypg9ypE9FeHg4KUVcVO3JTk3ln+eeY9f776OYTGydOZN4O73uhfBU9W69Fc0PP1C5iFtNL8TG8ue99xYZPuwJCwsjOjoagIkTJ8oInV7OcsfILxp9zETgv5gHjJJQYYfUWPiY4kKFyWRi165dtGvXDn//krWEXT99mtipU0k6etRqeVjduvznxx8Jiowsa/FFAXPmzGHOnDkYjUaOHDkiNRZOlpOWxpYZMzj9xx8217caO5YOzz1XqmMrisKZM2eoX78+KpVKZkX1fjIssIMkWPgQZ099nt/5devY+N//kn39us31tXr0oN9nn6HONwmZcB5pCnEdRVE4YrktNXduEYAaXbowYP581CUM4EVZt24dGo2GzEzrcWEkXHgFCRYOkqYQH2EvVAwaNIi33nqr1KFCMZnY+3//x7rJk+2GCpVaTc2uXYvs6CaEp1KpVLR46CEGLlhAcLVqAITUrEnP995zaqgA6NOnD88880yhACHNIsKXSI2Flzt37hzLli1j6tSphULFqFGj+PLLL0v9LSjr+nU2vfAC59eutbtNYOXK9Hz3XWr37FmqcwjHSI1F+Ui/coWNL7xA2ylTqN6+vUvOoSgKP/zwA2PHji00D8+gQYN488036dixI2oJ6p5GaiwcJMHCS6WmprJs2TKWLl3K8uXLnd78kXzqFLFPPEHyyZN2t4lq2ZLeH31EuKWTmnAdCRblR1GUcpll116fi1atWjFhwgQmTZpUqMOncCsJFg6SSOylQkJC+Ouvv1i2bJnTQ8WFDRsw3HdfkaGi4dChDFq8WEKF8DmOvm9Szp9nzyefYMpxeKRjK7kjdBYMDwcPHuTbb7+V/hbCa0mw8BLJyclWv3/77bcstjHIT1lChaIoHPrmG9Y99pj9/hT+/nR66SW6z5ols5KKCisnPZ31Tz7Jvs8+Y+1jj5GZmFiq49gLFzt27CjU5+LUqVOFBuISwhNJU4iHO3PmDGvXruX8+fNMnTqV0NBQl9z9YczKYttrr3Fi2TK72wRXrUqvDz+kRqdOJT6+KBtpCvEciqKw8fnnOb3ixqzZ4fXq0ffTT4scF6Moxd2KmpyczJw5c6hcuTIDBgzg5ptvLtNjEKUiTSEOkhoLD7d3715OnjxJVlYWmzZtckmoSL96lb/Hji0yVFRp04b//PSThApR4R1csMAqVACknD3LXw8+yIX1Ds0qXYi9movcu0XWrFmDoigkJiaSkJBQ6rILUR4kWHgQRVEKBYZevXqhVqupUqUKW7dudXqoiD94EMO993J11y672zS8/XZu/eYbQmvWLPHxhfAl6VevsnfuXJvrslNSWPf44xxauLDQe9QRRYWLBQsW0KBBA4KDg7nlllus1huNRnJK2c9DCFeQphAPoCgKp06dYu3atfTs2ZPmzZtbrT937hx///03Y8eOdWqouH76NH8MH46xwC1veVQq2j/9NK0eeaRceskL+6QpxHNc3bOH9VOnkn75st1tmowYQefp0/ELDCzx8YtqFpk/fz5RUVFWy7dv38769evp1asXHTp0KPGIusJhchF0kNRYeIBTp06xcOFCzpw5w7p16wqFhzVr1jg9VACE169Pw9tvt7nOPyyMvp9+Sutx4yRUCJFPtbZt+c+PP1KtiHEujv/8M2smTiSjFM0WRdVcjB8/3qpDp9FoZMOGDSQnJ/PHH39w6dKlEp9PCGeTYOEBGjZsSE1LM0NmZiapqal561w5TLdKpaLzyy9TvUC/ifB69Rj83XfU7dev1McWwpeFVK/OwAULaFjEzL6Xt23jr/vvJ+nYsRIfv7g+F7nhIj09Pe/a0bRp01LNViyEs0lTSDlSFIXjx48THx9P165drdadOHGC1NRUbrrpprwR91wZKvLLiI/HcO+9pF64QM2uXen14YcyoZiHkaYQz6QoCge//JJds2eDnWtpQHg4Pd97jzq9e5f4+I5OXHbhwgX8/f2pUaOG1XZ//PEHVapUoVOnTjIuRtlJ1a2DJFiUE0VRWLRoESdPnsTf358nn3ySiIgIu9uXV6jIlXD4MCd/+YX2Tz+NWi5AHkNmN/UO51avZuO0aeSkp9tcr1Kr6fDcc7QYPbrE793Szop66dIlPvvsMwBq1arFxIkTpVmzbOTJc5A0hZQTlUpFrVq1AMjJyWFXEXdhlHeoAIhq0YKO06ZJqPAwkydP5sCBA2zbts3dRRFFiB4wgEHffkto7do21ysmEzvfeYetM2ZgzMoq0bEdbRYp6MSJE3n/b9u2rYQKUW4kWLhAbpNHwWDQo0cP6taty8iRI+nVq5fNfZ0ZKhRF4dCiRaRfvVryByGEKJGoFi3QfP998Z06J0wocafO0oSL7t278+ijj9K+fXs6d+5stS47O5vNmzeTVcKQI4QjpCnEyU6fPo3BYCAuLo67776bm266yeF9nRkqjFlZbJkxg1O//krVdu249auv8AsKcnh/4Vmkj4X3MGZlsXXGDE7++qvdbcKio+n3f/9H5SZNSnTs0jaLFLRp0yb++usvQkNDGTp0KC1btixROSooqfJxkNRYOFl2djZxcXEAxMbGOjxQjjNDRUZCAqvHjeOU5cJ2bfduNk+fXqpBe4QQJeMXGEi3N9+k/TPPgJ33beq5c2x49lkUk6lExy5ts0h+JpOJTZs2AZCWllZoXAwhykqCRRkoilKoKrFJkybUrVuXWrVq8f/t3Xd4VFX+x/H3pJAOKbQQQpcWkY5AaKEIbqzr2uhVOhZcimtEpKngT2kiRaqIWHAXQQ0gvYOhEwgSCCWU9N7n/v5IMZOZCZPkJplJvq/n4cHcc+fMYRfufOZUPz8/k+pRM1TEXb/OrtdfJyIoSOd62K+/cuHLL02uRwhRfBqNhpajRtFjyRJsDBx9buPoSNePP0ZjVfRHcEnDhZWVFUOGDKFVq1b4+PjkLVfNFRsbS6qxTfOEMIEMhRSDoigEBwdz8OBBvLy8ePbZZ3XKk5OTcXBwMCkQqBkq7h87xqG33y70ZNJnfvkFl3r1TK5TmAcZCrFcsSEhHJg4kaTwcCB7hUjPL78s1vLT/NQYFtFqtXnL23Nt3ryZO3fu8OSTT+Lr6yvLVP8mQyEmkmBRDKmpqXzxxRekpaVhZWXF5MmTcS3Gvg9qhopr33/P6blzUYwcq2zr7IzvZ59Rx8ikUWHeJFhYttSoKA5OmULk2bN0DAjgsddeU6VeteZc5Lp79y5r1qwBoFq1akyePBlra2tV2mrO1uwJZsefYTxezx0Xe1si4lO5cCuaFnVd8XR1JDk9i+MhD+KBPwID/P9Z3u01Vf85O52AaYA70Aa4AUwLDPC/X8hrNMBMoDqQADQEJgcG+MeZ+r4yFFIM+Q8C8vT0LFa3oVqhQtFqObNoEadmzzYaKpy8vOi3ebOECiHKib2HB33WrqXLJ5+oFipAnTkX+Tk5OdGmTRs0Gg3dunXTCxXaIs4JsRTXH8SzbqIfc1/vxPQX29LniewdTD98pQPTX2zL7Fc7ADxH9gezJQkAVgUG+E8GegK1gL395+wsbCb/BKBnYID/O4EB/rOAYGBjUd5UgkUhtFotFy9eZMuWLXr/oDp37sygQYMYNWpU3v4UplIrVGSmpnJ46lSC160zek/1Nm3ov2ULrk2aFKmNQgh1WdvZ0dDI2TwloWa4cHV15fnnn2fy5Mm0KbBsNi0tjaVLl/LHH3/o9ZBYsmv34ujTygs3578/ay/eisbbwwlXJ53P3/vA1bJuX3H1n7PTHpgEjAIIDPDXAl8CLcgOScZMQzdIbASe6z9nZ11T31uCRSF27NjBTz/9REhICOfPn9cpc3BwoEmTJkXedEatUJEaHc3eUaO4vWuX0Xvq/+Mf9Fm7FnsPjyK1Uajn5s2bjBo1ioYNG+Lg4EDjxo2ZNWuW7B8gChWyZQsPirApmto9F25ubnqnpJ48eZLY2FgOHz7Mnj17ilSfOTt3M4puLXQ3Nrt4K5rH67kXvLUW2d/eLYU1EAU457t2Led3g+uc+8/Z2RSoB1zKvRYY4H8XiAP6mPrGcr5ujtikNJ2fXRxsad26NWfOnAHgxo0beQm+4L3O9rbYWBvOaHHJ6Xkh4rstm5nwxmijoSIhJQNtvjJHOxuq2OiPb8aHhfH7pDfJDL2mV5ar1cSJPD5+vOy2V86uXLmCVqtl5cqVNGnShIsXLzJmzBiSkpJYtGhReTdPmKHbu3dzet480h2q0m7mDOr17w9kP5OsjawiiU1Ko3WHznz/03955aUXdHoUcsNF7pyL/M8kACd7W2yNPL/ik9PznkkxialgZY1G0eLr66t/b0o6VR2Kfkx8eXupc0Od52RkfCr3Y1MMBYtDgQH+FjPHMDDAPwmoX+Cyd87vxoZ0cgNHfIHrCUBTU99bggXZQx6v/p9uAl85tgcN6tenc+fOPPbYYzRs2DCvbOjSfaRl/D2fYckoX5rVcTVY95gVB4hLTif87F4u/vy53kFF+XsqJq05zIO4v88a+Oi1Djz5mO5SsIigIA5OnsyPXUbyQuj/6b2fla0tnefONXocuihbAwYMYMCAAXk/N2rUiKtXr7JixQoJFkJP5PnzHJ0xAxSFLc/9hy2XgEvZz6aVY3vQoKbh84XyP5NavhrApe/mkJJiOFzkPpNyfTqkM60bGO7VLPhMmvHsINyIw6NAL2hYWBgzf7jIqnE9cXZ2LliNWSv45evirWgAvWBhSaGiEK8BIcB/jZTnbmqSVOB6Yr6yR1I1WExac5iYxLRH32hGsrRZpCSnYOx/iv453xZKwpRQYYpbgYEcnTEDrZFu9CpVq9Jj6VJqFti+V5iXuLg43N31vg3pSEtLIy3t739L8fEFv0CIiibx7l0OTppElpHJ4FoThzPcG7Zi5abvGTf0FYM9F5onRxe7jY5OjrR5rKHe9X379hGd7MHrn+/GydHJIleSuDnbsWx0Ny7ejqZ6VXtqu+oOK/Wfs3ME2UtOXYCQwAD/3wrW0X/OTmvgJ8DehLeMCwzwf1WFppuk/5ydTwD/BJ4KDPA39kGdVeD3XLYUIS+oGixiEtOITLDEjVVKr+Mm7M89JQ4ViqIQvG4dZz/7zOg9TnXr0mvFCqo1alTiNovSc/36dZYuXcpnhfx/CbBgwQJmz55dRq0S5uCvrVtJjYoyWn5i1gd4LZqLnQlL2zt18eXXX3/VW4q6bds2vK49pMU/38XKWp3nXkxMDHfu3EGhOulUIT05AyjanA5zcvFWNI976wb/yPhUgLGBAf6dc5ZjXuo/Z+fegh/QgQH+WcALarWl/5ydrwMvmXDrN4EB/v8tpB5nYA3wUmCA/4lC6onI+b3g2JgT2fMsTKLqJ2r+WbXmSEFBq9VibaWbptPS0khIV7+Xa9OmTZz8bmGJeyrOL13KpZUrjZZ7tGpFj2XLcKhevUTtFab78MMPH/nBf+rUKZ3Dn8LDwxkwYAAvv/wyo0cX/q1x5syZvPPOO3k/x8fH4+3tXcgrhKVr/dZboNFwOWcfiYKiL11m95Ah9PrqK5y9vB5ZX+6EzoLh4u6Fw2RkaXni5WmqhAs3NzfefPNNji4+iLOdtd7eGRmZGVhbW2OlMe+1Am7OdiSmZhAWkYB/e92pCTnDI0GQPSTSf87Ov4AuwP7SbFNggP8WYEtJ6sgJQl+RvX/F/pyfGwYG+IcauD137kUt4GHO660AV8DQ/QapGiyWjTbPfRIUReHEiRMcOXIEjUbDlElTdGY8K4qiM+YI2ROljNk4WXerbmd7/XtzV38UDBXvTH3XaKhYNrqb3uRNAO8+fbiycSNZKX+PdT79xwoA6vbpQ9dPPsHGwcFoe4X6Jk2axGuP2I+gQYMGef8dHh6On58fXbp0YdWqVY+s387ODjs5NK5S0VhZ0ebtt3H29ubURx/x6s+6wbVKegrx8Q/Y9frr9FqxAvd8BxwaeyYZCxcPLx/F4cx6vt6wCVcX/S3Hcxl7JhXk4uLCd1P76U3eTE5OZvHixWSlZtGhQwed+Ubm6MS1B2gVaFVgfkVOT3z+8ch4oE7B15vpUMh/gI2BAf77c36uB/TCQFAIDPC/kROamgEXci43I/vPs9fUN6wUkzc1Gg03b94kMTERgLNnz+p8k9RoNAXXKxfqUfcWd0lpVUfDM6rdfXzotmgRBydPzju0yC49hWaDB9N22jSsLHA809JVr16d6ib2EN29exc/Pz/at2/PunXr9LZQFiK/Jv/6F0516nD47bfJyHlm5ZcaFcWeYcPo9vnneduCF/ZMMhYuftn+X8aNGsZ3330HRlaFGHsmGbzXwIqQkydP5i2tzjKygZ85uRAWjbO9LfVr6E5AzXmWZ+a7ZIP+PATVh0JKqv+cna8CfkBm/zk72+Vc9gFW5pSPBd4DOgcG+N/LKd8ADAV+zPl5BLA9MMDf5D08KuQTztCa7R49egDQokWLUu1SVnOb7vy8evWi/XvvZf+g0dBuxgzaz5wpocLMhYeH06tXL7y9vVm0aBERERHcv3+f+/eN7qgrBJ5du9Jv82YcPT0NlmempHBg4kSu//STSfWpvc+FqTp27Ei3bt1wcHDQW6KqKArR0dGl8r5F8TAuhQXbzjBr62m2n7pJclomH/3wJ5/+9yxZOV/kPFzsIXvSZi434J6B6sxG/zk7PYB1QG9gQb5fg8leGQLZGcAe3SzwCXCt/5ydS/vP2TkX8ASGF+W9K9RZISkpKZw4cYITJ04wdOhQPAv8o4yNjS3WmR6mKq1Qkd+5JUtwb9kS7759S1yXKH3r169nxIgRBsuK8m9PzgqpnFIiItg/fjwxwcb3ZXp8/HhaTZxo0vNF7bNFTJWZmam34VZISAhbtmzBx8eHnj17UqNGjVJ5bzXEJKbx2ud7DgQG+PfqP2enDXATaB4Y4K/fpSQqVrA4deoUv/76K5DdM/HKK6+U2XuXRagQlZcEi8orIymJw2+/zb0jR4ze0+iFF+j04YdYmRAMyitc5KcoCl9//TV3794F4NVXX6V58+al/r4l0X/OznfI3t+hBhAcGOC/rZybZLYqVLDIzMxk8eLFJCcn07p1a5555pkyGc8uaahQFIW4a9dwbWryxmaikpFgUblpMzI4+dFHhG4z/llWu2tXun/+ObYmbFBV3uFCq9Vy/Phxjh49ipOTE+PGjdN5Tho6zt0MyLdDE1lksEhISODIkSO4ubnlnTKaKzQ0FHd391Id8sivpKFCm5VF0Mcfc23rVnouX543GUuI/CRYCEVRuLhiBReWLzd6j2uzZvT66isca9Z8ZH3lHS4gez5cfHy83k6ev/32G5GRkfTo0YP69QvuSl1uJFiYyOwi4aMkJyezZMkSTpw4waFDh/QmHTVq1MhiQkVWWhpHpk4l5NtvUbKyOPz220RdvFiaTRZCWCiNRkOrCRN4cu5cNEYmbcdevcqu118n+eHDR9ZXXhM687O1tdULFYmJiQQFBREaGsrmzZtJybfMXlgGiwsWjo6ONGvWDMje2Cp3jK6slTRUpMfFsXfMGG7v3p13LTMlhQMTJpBw61aptFkIYfkav/giPb/8EhtHw/tP1GjXzuTN8swhXBQUGxuLi0v2Aoz27dvjIHv0WByzHgqJioriypUresuUHj58yLlz5+jatStOTk5l1Zw8JQ0VSeHh7B83jrjr1w2WuzRowD9+/hnrKpZ3UqAoHTIUIgqKDg5m/7hxpEZG5l2r2bEjfqtWFfnZYQ7DIvlptVouXLhAo0aN8kIGZA8H/fzzz/j4+NC0adOynhQvQyEmMttg8ccff3DkyBEURWHkyJFms51xSUNFbEgI+8aNI+XBA4Pl1nZ2dP30U1lOKnRIsBCGJIWHs2/sWOJDQ6nWpAn9Nm2iSjH/fphbuDDk8uXL/PDDDwC0bduW5557rizfXoKFicx2KMTd3T3vw/v48ePl3JpsJQ0VD06eZPfQoUZDRZWqVem9Zo2ECiGESZzq1OGpb76h3tNP02vFimKHCjDPYZGCrly5kvffLVu2LMeWiMKYRY/FvXv3cHV11RlLy8rKYu3atTRv3pxOnTqV+7kJJQ0VYb//zrEZM4wefexYuzZ+K1dSrUkT1dosKg7psRBlxZx7LhRFISQkhKtXr/Lss8/qPHdjYmIICwujVatWpXVsu/RYmKhcg0VUVBS7du0iJCSEnj170qtXL903UhSz2FiqpKHiyqZNBH3yid6BZLlcmzbNXiJWq5ZqbRYVw/Lly1m+fDlZWVmEhIRIsBAlkpGYCBoNto+Ym2bO4cKYX375haCgIFxdXXn55ZepU0fvjLCSKv8PIwtRrkMh1tbWXLt2DYATJ06QlqZztL3FhwpFq+XMokUEffyx0VBRq1Mn+m7cKKFCGDRx4kQuX77MqVOnyrspwsJlpadzcMoU9gwfTkq+CZ+GWMKwSH6JiYmcPXsWyD7awc3NrXwbVMmVWbBQFEUv/bq6utK6dWuqVq1K7969S6v7qthKEiqy0tM5OmMGwevWGb2n/tNP02vlSqq4uBi9RwghSkrRajk2cyYPTpwg5vJldg8eTEJYWKGvsaRw4ezszLBhw2jcuDGdOnXSW6L68OFDs2pvRVfqQyGKohAcHMyhQ4ewsbFh5MiROh/IKSkpVKlSpUKFiozERA6++SYPCpl02nzYMNq++y4a89u2VpghmWMhiktRFP5csICQzZt1rtt7eNBrxQrcfXwKfb2lDYsU3A5cq9WybNky0tLS6NKlC76+vsXtDS//LnQLUSafavv37+f+/fvcuXOHmzdv6pQ5ODhUqFCREhHB7qFDCw0Vbf/9b9pNmyahQghR6q5+841eqABIjYpiz/Dh3Dt6tNDXW1LPBaB3xsiFCxeIiYkhOTmZGzdumMUQe0Wn+idbwQ9jjUZD95zzLzw9Pc3xYBkdJQkVcaGh7Bo4kNirVw2WW9nY0HXhQloMH65mk4UQwqi6vXvj0qCBwbLM5GT2jx/PjR07Cq3D0sJFfnXq1OHxxx/X+SzKLzU1tRxaVbGpNhSSkZFBUFAQp06dYsSIETo7Ymq1Wm7evEnDhg3NOi2WdPXH8fffJ/Tnnw2W2To7033xYmp37qxae0XlIUMhoiRSo6M5MGECURcuGL2n7b///cgvPZY2LJJfbGws1apV03mOR0REsGrVKtq0aYOvr++jzpky3w8vM6Na98HBgwf5/fffiYqK4tixY7pvYmVFo0aNKnSoAOjw/vvUaNtW77pDjRr03bBBQoUQolzYu7vTZ+1aPAs5PfnMwoUELVyIotUavceSey5cXV31nuOHDx8mMzOT06dPc/ny5XJqWcWjWrDo2LFj3lyJ+Ph4taotE2qECgAbe3t6LFtG1UaN8q5VbdSIp779FrfmzVVtsxBCFIWNoyM9ly6l4fPPG73nyvr1HJs5k6z0dKP3WHK4yE9RFFxcXLC1tcXBwYEOHTrolYviKfJQSFJSknLs2DG8vb3zThnNFRQURJ06dahdu7aabSxVaoWK/JLCw9k1aBDOXl70WLYMuzI6xl1UXDIUItSiKArnvviCy2vWGL2ndteudP/ii0I30rLkYZH8kpOTefjwIQ0KzEM5efIkoaGhdO/eHS8vL5ChEJMVOVjMmzdPyczMpHbt2rzxxhtmPbzxKKURKnLFh4XhWKsWNvb2JW2mEBIshOqufvMNfxayeZ+7jw+9VqzA3sPDaB0VJVwUlJWVxZIlS/J63ydPnoy7u7vlftiVsSIPhdSoUQPInvQSERGheoPKSmmGCoCq9etLqBBCmK1mgwfju3AhVjY2BsujL11i16BBJNy6ZbSOijIsUlB0dHTeZ0PTpk1xd3cv5xZZliL3WFy9elW5ceMGXbt2tdhvTsUNFZmpqVzduJEWI0ZgZaFJXFgm6bEQpeX+8eMcnDKFzKQkg+X2Hh70+uor3As5TbQi9lxkZmZy7tw5PD09c88dkR4LE5nF6aZlqbihIj0ujgOTJhERFETD556j87x5ssGVKDMSLERpig4OZv/YsaRGRRkst3FyoufSpdR68kmjdVTEcFGABAsTVapPxuKGiuSHD9k9bBgRQUEA3Ni+nbP/93+l3l4hli9fTsuWLenYsWN5N0VUYO4tWvDU5s0416tnsDwzKYmDU6aQHhdntI6KOiwiiq7S9FgUN1TE37zJvjFjSAoP1ytrM3UqLUeOLJX2CpGf9FiIspAaFcX+8eOJvnRJ57rGygrfzz6j3lNPPbKOCtxzIT0WJqoUPRbFDRVRFy+ye/Bgg6ECIHjtWtJiY9VurhBClAt7Dw/6rFuHp6+vzvWOH3xgUqgA6bkQlSBYFDdU3D92jD9GjCAtJsZguaOnJ303bpQ9KoQQFYqtkxM9li2j/j/+AUDrN9+kycsvF6kOCReVW4UeCiluqAj7/XeOTZ+ONjPTYHm1xo3xW7UKRwvaCExYNhkKEWVN0Wq5s3cvdfv0Kfby+wo2LCJDISaqsD0WxQ0VId9+y5F33zUaKqq3aUPfjRslVAghKjSNlRXeffuWaE8f6bmonCpksChOqFAUhfPLlnF63jyjO9HV6dGD3mvWyPCHEELkE3n+POlGzoiScFH5VLhgUZxQoc3K4tRHH3FxxQqj9TZ87jl6LFmCjYOD6m0WQghLFX35MntHj2bPsGGkGNmNWcJF5VKhgkVxQkVWejpH3n2Xv77/3mi9zYcPp/O8ebLbphBC5BMfFsa+sWPJTEoiNiSEXYMHkxAWZvBeCReVR4UJFsUJFRlJSRyYMIHbu3YZrbfN1Km0+/e/ZZdNIYTIJ/nhQ/aNGUNadHTetaQ7d9g9ZAgxwcEGXyPhonKoEJ+WxQkVabGx7B09mvvHjhmsU2NtTee5c2UDLCGEMODkrFkk3b2rdz01Koo9w4fz4NQpg6+TcFHxWXywKE6oSH74kD3DhhF1/rzBOq3t7Oi+eDGNXnyxVNoshBCWruMHH1C1USODZRmJiex74w3u7N1rsFzCRcVm0cGiuEtKI4KCiPvrL4Nlti4u+K1eTV0/P9XbK4QQFYWTpyf9Nm3C44knDJZr09M59OabXN+2zWC5hIuKy2KDRXFDBUD9AQNoN2OG3nV7Dw/6rl9PzfbtVW+vEEJUNHaurvRes4baXbsaLFe0Wk4EBHB57VqD5RIuKiaLDBYlCRW5mg8ZwuPjxuX97OTlRb9Nm3Br3lz19gpRXHK6qTB3tk5O9Fy+nPpPP230nrOffcbZzz/Xe2aDhIuKyOK29FYjVORSFIXT8+bx8ORJ/FavxrFWLbWbK4QqZEtvYe4UrZbT8+dzbcsWo/c0efVVOvznP1hZW+uVWcD237Klt4ksKlioGSpyKVotGUlJVHFxUauZQqhOgoWwBIqicHHFCi4sX270nvpPP03n+fOxrlJFr8zMw4UECxNZzFBIaYQKyN4PX0KFEEKUnEajodWECXT4z3+M3hP2228cnDKFzJQUvTIZFqkYLCJYFDVUKIrClQ0biLt+vSybKYQQAmg6cCBdPvkEjYEhD4B7hw6x7403SE9I0CuTcGH5zD5YFCdUnFm0iKBPP2XvmDEkhYeXZXOFEEIADZ95hh5LlmBtZ2ewPCIoiD+GDyc1KkqvTMKFZTPrYFHUUKHNzOTEBx9wZf16AFIePGDv6NGkREaWVZOFEELk8OrVi14rV2Lj5GSwPObKFU7Pn2+wTMKF5TLbYFHUUJGVlsbhqVMJLbAZS0JYGPvHjjXY5SaEEKJ01erYkb7r1mHn5qZX5tKgAR3ee8/oayVcWCazDBZFDRUZSUnsnzCBO3v2GKwv5upVHhrZt14IIUTJFbbC0N3Hh74bN+JYu3beNcfatem9ejX2Hh6F1ivhwvKY3XLTooaKtNhY9o8bR9SFCwbrs7Kxocsnn1B/wIBSa7MQpU2WmwpzoWi1KIpC6LZt2Do7Y+fqSu0uXUx6bVJ4OHtHjyY9IYF+GzdStWFDk9/XDJaiynJTE5lVsChqqEh+8IB9Y8YYXf1h7eBA9y++oE63bqXVZCHKhAQLYQ60WVlEX7pE1IULaDMyqNOjB0enT6fzRx/h1qKFSXWkREaSGhWFW7NmRX7/cg4XEixMZDZDIUUNFfFhYewePNhoqLCtWpXea9ZIqBBCCJVYWVvj7OVF/QEDaD5sGGkxMdi5upIeH//I12qzsgBwqF69WKECZFjEUphFsChqqIgJDmbPkCFGl5LaV69Ovw0bqNGmTWk1WQghKiV7Dw+s7e05NWcOh956i/vHjvHXTz9xY8cOHhQyly13G+/wQ4eMni6dn6IoPDx9Wu+6hAvzV+7Boqih4uGff7JnxAiDa58BnOrW5alvvsG1adNSa7MQQlRGyffvc2P7dn795z8J++03anXqxFPffssTEyfi1qwZt377jYizZ/PuV7RaIHvVXsKtWxyeOpX948dzdMYMMpKSCp3weX7pUvYMG8alVav07pNwYd5syvPNixoqwg8d4tBbb5GVmmqwvmqPPYbfqlU41qxZam0WQojK6P6xYwSvW8e9o0ep1akTzaZPx9PXF2s7OzJTU4k8e5bIc+ewqlKF6q1bo9Fo0FhZEX/zJjf+9z9Cf/4ZRVGoP2AALUePxtbI3hYAwevXc2nlSgDOLV5Menw8baZO1flMyA0XBedc5IYLMzhbpNIqtx6LooaKW4GBHJw0yWio8Gjdmr7r10uoEBWKHJsuyps2I4Pzy5ezb+xYEm7dotWECfRZu5a6vXtjbWeHoihYWVsTvH49CWFhONaqhUajISEsjFu7dmXPhfvrLxo88wzP/PILnefNw61587zejIKub9vGmYULda4Fr1vHyVmz8uZp5JKeC/NULqtCihoqrm/bxslZs4z+RazdtSs9Fi/GpsBfLiEqClkVIsqLoigceustXLy98fLzo2b79nnX8z+rM5KSSI2MxKFGDWwcHbmycSPRwcF4dulCvf79jW7tnV98WBg7n30WpUCAyOXdrx9dP/1U72TUMlotIqtCTFTmwaKooeLKxo0EffKJ0frq9e9Pl48/NngErxAVhQQLUR4Khoe861otGisroz9DdtDISk3V2QDLWH35/fXDD5ycPRuMfDYZ+yJZBuFCgoWJynQopMg7aiYmcmXDBqP1NX7pJbouXCihQgghSoFGozE4wbJgiCj4M4Ctk5PerpqPChUATV5+Gd9Fi7CyMTwF8P7Ro+wdM4b0uDid6zIsYj7KLFgUNVQA2Do70/vrrw1u+dp8+HA6zZ6dt4RJCCGE+kwJA2qrP2AAPZYtw9re3mB55Nmz7Bk+nJSICJ3rEi7MQ5kEi+KEilxVGzTAb/VqbPN1/7aaNIm2775bLn/hhRBClL463bvTe/VqbF1cDJbHhoSwe8gQEu/e1bku4aL8lXqwKEmoyOXWrBl+X32FjaMj7WbMoNX48RIqhBCigqvRrh191683elBZ4u3b7Bk6lPgbN3SuS7goX6U6eVONUJFfSmQkDtWrF+k1QlQEMnlTVGbxYWHsGz3a6G7Ldu7u9F61Su+8EpUndMq3WROVWo+F2qECkFAhhBCVUNX69em3aRNVGzUyWJ4WHc2eESOIOHNG57r0XJSPUgkWRQkVabGx3NixozSaIYQQwsxoMzPz/tvY3kSGONauTd+NG3Fr2dJgeUZCAnvHjOH+sWM61yVclD3Vg0VRQkVKRAR7hg/n2PTp/PXjj2o3RQiz8Nxzz1GvXj3s7e3x9PRkyJAhhBvp0hWiorv1++9c//lnIHuZalGG4+3d3Oizdi012rUzWJ6VksL+8eO5s3evznUJF2VL1WBRlFCRePcuu4cMIe7aNQBOfvghYb/9pmZzhDALfn5+fP/991y9epWffvqJ69ev869//au8myVEmSj4eVCnZ09u79rF1W++AYzvlWFMFRcX/FatwtPX12C5NiODQ2+9RczVqzrXJVyUHdUmbxYlVMSFhrJvzBiS79/XbYyNDT2WLMGrZ8+itkkIi7F9+3ZeeOEF0tLSTJ48JpM3hSXLSk/X2cgwPS6O4wEB2YeZDR4MmLYrZ8E6j06bxu3du/XKmg0dSrtp0wzWV4IJnTJ500Sq9Fhs3brV5FARHRzMnmHD9EIFgJKZydnPPtMZgxOiIomOjmbz5s107dq10FCRlpZGfHy8zi8hLFVEUBCn58/Pm1NRpVo1Os+Zw4MTJ4rdc2FdpQq+ixbR8Pnnda43fuklo6ECCu+5GDhwYJHaIAxTJVi0bdsWT09PnWuGQkXEmTP8MWIEadHRBuup2qgRfqtXG93KVQhLNX36dJycnPDw8ODWrVv873//K/T+BQsWUK1atbxf3t7eZdRSIdRXu3NnbJ2cODZzpm64mDu3ROHCysaGznPn0nTgQADqPf00HWfNemTPh7FwMWDAANkjSQWqDYWEhITg5+dHeHi4wVBx7+hRDk6ZQlZKisFK3Vq2xG/VKuzd3IraHiHK3Icffsjs2bMLvefUqVN06NABgMjISKKjowkLC2P27NlUq1aNHTt2GH2IpaWlkZaWlvdzfHw83t7eMhQiLE7+A8rOL1tG4p07dJk/P+9aelwcx99/n1pPPlnsYRFFUbixfTv1n366SGdH5R8WWbNmDaNGjSrsdkkcJlJ1g6yQkBB+/PFHZs6cqfOX4vaePRx59120RibH1GjXjp5ffkkVI1u3CmFuIiMjiYyMLPSeBg0aYG/grIM7d+7g7e3N0aNH6dKli0nvJ3MshCXTCRdLl5J4967q4aK4Dhw4QGhoKCNGjHjUrRIsTFTqx6bf2L6d4++/j5KVZbDc09eX7osXY+PgUNR2CGGRbt++Tb169di3bx+9evUy6TUSLISlM5dwkRoTg62TU3FOxZZgYaJSPSskZMuW7DE1I6HCu18/eixbJqFCVFgnT55k2bJlnD17lrCwMPbt28fAgQNp3Lixyb0VQlQEGiurvPkVT0yejLOXF8fee8/wnIvNm7NfU8Q5F4+SFhvL3pEjOTh5MplGhuVFyZVasLi0ejWn5841Wt7ohRfwXbSoOKlRCIvh4ODAtm3b6NOnD82aNWPkyJE8/vjjHDhwADs7u/JunhBlqijh4sqGDdmvUanHIiMpif3jxhEbEsK9w4fZN3Ys6QkJqtQtdKk+FKIoCuc+/5zLX39t9J6mgwfTfvr0vC4wIUThZChEVCSmDIv8+fHHtH77bRxr1ixa3QaGTzJTUzkwfjwPTp7Uue7u40OvlStNXTQgQyEmUjVYKFotp+fO5drWrUZf7DN2LE9MnixLeoQoAgkWoqJ51GoRbVYWVtbWuq/JFxoyU1NJi4kh+uJFbF1cqFKtGu45p5sWDBdHp0/nppEzqao1bozfmjWmBBj50DKRasFCm5nJ8fff5+Yvvxh9YZupU2k5cmRR30+ISk+ChaiIdMLF8uXE37iB78KFj/ziGXnuHNe2buX27t1Y2driWKsWVra2PPb66zR+8cXsuvOFi+jgYPaNGUNaTIzB+py9vem9Zg3OdesW9rYSLEyk2ljE9R9/NB4qNBo6zpoloUIIIUQenTkXEyfi3rw58TduFPqa23v2sHf0aG5s34533770Xr2a/lu30n3xYsJ27vz7gLN84cS9RQv6btyIQ61aButMvH2b4++/r9KfSqjXY5GVxdFp07j1+++6b2BtTZcFC2jg71/MJgohpMdCVGT5ey70yvL1PPz1ww+czNmYrvWUKfi88YbOvTFXrnDhyy/pMn8+No6OenUm3r3L3lGjSLx9W+e6Y+3a9Nu0Cac6dQprpvRYmEi1HgurnABRp0ePv69VqUL3xYslVAghhDCqsIn8uaHixo4dnJw9Gytra9rPnJkXKhStNvuXohB77RrxoaGg0Ris09nLi74bN1KtceO8a/YeHvT++utHhQpRBKouy7CuUoVun39OzY4dsXFwoNeKFdT181PzLYQQQlQy4YcOcWzGDKxsbenw/vs0GzQIyA4VuSFCo9EQdf48WY84/tyxZk36bNiAu48PtlWr4rd6NVUbNCiDP0XlofppXzb29vRcvpyEsDDcW7ZUu3ohhBCVSFxoKH8uWICVjQ0dZs6kycsvA/lCRU6Pxu09ewjZsoXHXnsNWyenQodX7N3c6LN2LYm3b+PWrFmZ/Vkqi1LZSMLWyUlChRAqWL58OS1btqRjx47l3RQhylTupM57hw6RcOsWT0yaRJNXXvm7LF+ouH/sGH9+/DEAXj17AoUPrwDYOjvjlrM8Vair1M8KEUKUnEzeFJVRZkoKv774ItWaNKHnsmWAfqh4+OefnJ47l9hr1wxO6FSRTN40kWx9KYQQwiwl3rlDSmQk9QcMAPRDxYMTJwj69FNir12j2aBBf0/oVPF8EVF0qs+xEEIIIdRg5+qKa5Mm1GjXDsgODFY5Qxx3Dx7kz/nzSbxzh0YvvojPuHF5r5OdncuX9FgIIYQwS/bVq+NYqxZ//fADkL2tgTYjg79++IHD77xD4p07NBs0iDbvvGPqeR+iDMgcCyEsgMyxEJVN7qoObWYmh6dOxa5aNTRWVsReu0bkuXPYOjvTauJEmg8ZUlZNkm4QE0mwEMICSLAQlVHuQWTazEzOffEFSffukRYTg1fPnlRv25bqTzxRls2RYGGi4gQLIUQZ02g0VYE4oJqiKPHl3R4hysq3Pj7WAy9dyiqkXDPw0iX5IDMjEiyEsACa7NloLkCCIv9oRSX2rY+PFaBImDBfEiyEEEIIoRpZFSKEEEII1UiwEEIIIYRqJFgIIYQQQjUSLIQQQgihGgkWQgghhFCNBAshhBBCqEaChRBCCCFUI8FCCCGEEKqRYCGEEEII1UiwEEIIIYRqJFgIIYQQQjUSLIQQQgihGgkWQgghhFCNBAshhBBCqEaChRBCCCFUI8FCCCGEEKqRYCGEEEII1UiwEEIIIYRqJFgIIYQQQjUSLIQQQgihGgkWQgghhFCNBAshhBBCqEaChRBCCCFUI8FCCCGEEKqRYCGEEEII1UiwEEIIIYRq/h/BbLfqh1QNEgAAAABJRU5ErkJggg==\n", "text/plain": [ "Graphics object consisting of 56 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "colorS = 'steelblue'\n", "colorS3 = 'lightsteelblue'\n", "#colorS = 'lightseagreen'\n", "#colorS = 'wheat'\n", "T0_list = [-2., -1.5, -1., -0.5, 0., 0.5, 1., 1.5, 2.0001]\n", "for T0 in T0_list:\n", " graph += line([(-3, T0), (-Xmin_emb(T0), T0)], color=colorS, thickness=2) \\\n", " + line([(-Xmin_emb(T0), T0), (-Xmin(T0), T0)], color=colorS, \n", " thickness=3, linestyle=':') \\\n", " + line([(Xmin(T0), T0), (Xmin_emb(T0), T0)], color=colorS, \n", " thickness=3, linestyle=':') \\\n", " + line([(Xmin_emb(T0), T0), (3, T0)], color=colorS, thickness=2) \\\n", " + text(\"$T_0={:02.1f}$\".format(float(T0)), (3.5, T0), \n", " fontsize=12, color=colorS)\n", "graph += bifhor\n", "graph.save('max_constant_T_slices.pdf', aspect_ratio=1, \n", " xmin=-3, xmax=3, axes_labels=[r'$X$', r'$T$'], figsize=8)\n", "show(graph, aspect_ratio=1, xmin=-3, xmax=3, axes_labels=[r'$X$', r'$T$'], figsize=8)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Isometric embeddings" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The function $Z'(r)$: " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( r, T \\right) \\ {\\mapsto} \\ \\sqrt{2} \\sqrt{-\\frac{T^{2} e^{\\left(-\\frac{1}{2} \\, r\\right)} - 1}{2 \\, T^{2} e^{\\left(-\\frac{1}{2} \\, r\\right)} + r - 2}}\n", "\\end{math}" ], "text/plain": [ "(r, T) |--> sqrt(2)*sqrt(-(T^2*e^(-1/2*r) - 1)/(2*T^2*e^(-1/2*r) + r - 2))" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('r')\n", "zp(r,T) = sqrt((1-T^2*e^(-r/2))/(r/2-1+T^2*e^(-r/2)))\n", "zp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The exact integral is not known in the general case:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\sqrt{2} \\int \\sqrt{-\\frac{T^{2} e^{\\left(-\\frac{1}{2} \\, r\\right)} - 1}{2 \\, T^{2} e^{\\left(-\\frac{1}{2} \\, r\\right)} + r - 2}}\\,{d r}\n", "\\end{math}" ], "text/plain": [ "sqrt(2)*integrate(sqrt(-(T^2*e^(-1/2*r) - 1)/(2*T^2*e^(-1/2*r) + r - 2)), r)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "z = integrate(zp(r,T), r)\n", "z" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The minimal value of $r$ on an embedded surface of constant $T$:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "def rmin(T):\n", " if T > 1:\n", " return RDF(4*ln(T))\n", " return 2*W0(-T^2)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(rmin, (T,0,2), axes_labels=[r'$T_0$', r'$r_{\\rm min}(T_0)/m$'], thickness=2)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(1.796343137811716, 1.6218604324326575\\right)\n", "\\end{math}" ], "text/plain": [ "(1.796343137811716, 1.6218604324326575)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rmin(1/2), rmin(3/2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The integration of $Z'(r)$ to get $Z(r)$ is performed numerically, using an algorithm for an adaptive integration with (integrable) singularities (qags):" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "def zz(r1, T0):\n", " dzdr = zp(r, T0)\n", " numint = numerical_integral(dzdr, rmin(T0), r1, algorithm='qags')\n", " error = numint[1]\n", " if error > 1e-3: \n", " print(\"Warning: error = {}\".format(error))\n", " if T0 > 1:\n", " return numint[0] + 1\n", " return numint[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Test that it works:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(4.226847171416433, 2.4583755881988343\\right)\n", "\\end{math}" ], "text/plain": [ "(4.226847171416433, 2.4583755881988343)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zz(4, 1/2), zz(4, 3/2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Function $Z(r)$ for some selected values of $T_0$:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 6 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "T0_list = [0., 0.5, 0.9, 1., 1.5, 2.]\n", "g = Graphics()\n", "for T0 in T0_list:\n", " g += plot(lambda r: zz(r, T0), rmin(T0), 20)\n", "show(g, aspect_ratio=1, xmin=0, xmax=20, axes_labels=[r'$r/m$', r'$z/m$'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3D plots of the embeddings" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\phi}\n", "\\end{math}" ], "text/plain": [ "ph" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('ph', latex_name=r'\\phi', domain='real')" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "from sage.manifolds.utilities import set_axes_labels" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "T_0 = 0.0\n" ] }, { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "T_0 = 0.5\n" ] }, { "data": { "text/html": [ "\n", "