{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Gravitational radiation from circular equatorial orbits around a Kerr black hole\n", "\n", "This Jupyter notebook requires [SageMath](http://www.sagemath.org/) (version $\\geq$ 8.2), with the package [kerrgeodesic_gw](https://github.com/BlackHolePerturbationToolkit/kerrgeodesic_gw). To install it, simply run `sage -pip install kerrgeodesic_gw` " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 9.4, Release Date: 2021-08-22'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are interested in the gravitational wave emission from a particle of mass $\\mu$ on the prograde ISCO of a Kerr black hole of mass $M$ and angular momentum parameter $a = 0.90 M$. The radius $r_0$ (in terms of Boyer-Lindquist coordinates) of the prograde ISCO is obtained as follows:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.32088304176189" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from kerrgeodesic_gw import KerrBH\n", "a = 0.90\n", "r0 = KerrBH(a).isco_radius()\n", "r0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Waveforms" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The function `h_plus_particle` gives the rescaled gravitational wave in the $+$ mode, $(r/\\mu)\\, h_+$, at the retarded time $u = t - r_*$:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.5582496798737479" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from kerrgeodesic_gw import h_plus_particle\n", "theta = pi/4\n", "phi = 0\n", "u = 0\n", "h_plus_particle(a, r0, u, theta, phi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "while the function `h_cross_particle` gives $(r/\\mu)\\, h_\\times$:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-0.05710956283550757" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from kerrgeodesic_gw import h_cross_particle\n", "h_cross_particle(a, r0, u, theta, phi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot of the waveform on a time interval of twice the orbital period:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from kerrgeodesic_gw import plot_h_particle\n", "umin = 0\n", "umax = 2/KerrBH(a).orbital_frequency(r0)\n", "plot_h_particle(a, r0, theta, phi, umin, umax, plot_points=400)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The corresponding spectrum:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 20 graphics primitives" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from kerrgeodesic_gw import plot_spectrum_particle\n", "plot_spectrum_particle(a, r0, theta, legend_label=r'$h_+$') \\\n", "+ plot_spectrum_particle(a, r0, theta, mode='x', color='red', \n", " legend_label=r'$h_\\times$', offset=0.08)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Same thing for $\\theta=\\frac{\\pi}{2}$ (edge-on view):" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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GsXTpUqZPn86kSZNYsWIFffv2ZdeuXSFlc3Nz6dOnDytXrmTixInMmDGD9PR0Bg8ezJYtW0LK7t27lx49epCVlcXo0aNJS0tjwYIFpKamsn79erp06UJpaWnINRs3bmT48OEsWrSIOXPmMHbsWNasWUNKSgoFBQUhZbdv307//oMYNMjkFjn33K9Zvnw5/fr1Y+fOnSFl8/Ly6N27N5mZmUyYMIGZM2fy00/pnHnmjwA888yXv5YtKiqie/furF27lo8//pi0tDTmz5/PyJEjyc7OpmvXrpSUlITUX1xczLBhw1i8eDGzZ89m3LhxrF69mp49e7J79+6Qsjt27GDAgAFkZGQwdepUpkyZQkZGBv379ycnJyekbH5+Pr169SIzM5Px48cza9YslixZwtChQ9m8efN+NnTr1o1169YxatQo5s2bx7x58xg1ahTr1q2jW7duFBcX73evDR06lCVLljBr1izGjx9PZmYmvXr1Ij8/P6RsTk4O/fv3JyMjgylTpjB16lQyMjIYMGAAO3bsCCm7e/duevbsyerVqxk3bhyzZ89m8eLFDBs2jE2bNoWULSkpoWvXrmRnZzNy5Ejmz59PWloa6enprF27tsZnxMyZM+0zIsxnxMSJE8N6RhQWFnr2jHjttXf59FPzj+Hxx4siekZ88UUnTj65mIIC+M9/1oX1jBg4cCDLli1j2rRpTJ48OaJnRHp6OkOGDNnvXgt+RqSnp1f5jPjggw+IN1SVxYsXA9CrVy82b95MampqZBUk6gEcjllGeHGF9/8FrK7imllAIWYWvfPe7UAZ0LSKaxpj0gw4xxGEmXLggw8+qLGMJTISSdMZM8xS5DZtVAsLI79+0iRz/WGHqZaU1N6ORNI0VrCauk8saNq3r7nnzjuvdtf37Gmuv+wyV82qNdVp6qQcqGwZf6zh2PrJJ5/oBx98oD179tScnBxVjSzlQKJHmnYApewfVTqE/aNPDj8DP6lqcHB0FSDAkZVdoKpFqprnHEDY+ZhvuOGGcItawiSRNB092pzvvReaNIn8+htugLZt4eef4Ysvam9HImkaK1hN3ScWNB050pzvv792199+uzkvWADbtrljU12IBU1jiYR2mlR1H7AUuLbCR9cCVU3sXggcLiItgt47GRNp2uS2jUOHDnW7yqQnUTTdt8/kXAKT56U2NGpktlUBkyG8tiSKprGE1dR9/NY0OxsWL4Z69eCee2pXx9FHm1xsqjBliqvm1YpoaZqXl8ebb77J008/TWkM72Sc0E5TgHeBx0TkERFpLyI9gaOBAQAi0kVERgSV/wjIAYaJyGkicjnQAxiqqoVuG/f666+7XWXSkyiazplj9pNr1w4uvbT29fzud+Y8c2bt60gUTWMJq6n7+K2p8yXnsstqTjNQHbfdZs7O3Cg/iZamrVq14sorr2TevHnUry4Rnc8kvNOkqmMwk7nfADKAyzHpBNYHihyGcaKc8rsxkagDMKvoRgFTgOe8sM+ZfGdxj0TRdOJEc77jjuqTWdbEtdeaxHorV8JPP9WujkTRNJawmrqP35o6TpPj9NQWZ0Tsiy/MvnR+Ek1Nv/32Wzp27Bi19mqD3UbFAyLZRqWoqKhOOSMs+5MImqrCMcfAxo0mOeX119etvgsvhPR0k77g4Ycjvz4RNI01rKbu46emOTkmP1pZGfz4Ixx7bO3rKi2FAw80aQe+/toM1/lFdZq6vY3KH/7wB/785z9z55131rmuiji2Zmdns2vXLvLz83nggQdo27at3UYlnngvlrKYJQiJoOmqVcZhatIErrii7vU5SX3nz6/d9YmgaaxhNXUfPzX97DPjMJ11Vt0cJjCRZWdIvi4LONwgEk1VzVYw4RwV4zVlZWXMnz+fnJwcPvnkE/70pz8xb948l3+bumOdJp+54447/DYh4UgETZ35R5dfDk2rTKsaPhdfbM5LltTu+kTQNNawmrqPn5rOmGHOv/+9O/U5X5b8dpoi0bSgwGzfFM5RUBB67TfffEODBg24+eabufPOO7n00ksZO3asy79N3bFOk4uIyNMikgl8Fe41X30VdlFLmCSCps4DuK7Dcg4XXWTOmZlmcnmkJIKmsYbV1H380rSsrPyLjrPwoq44TtOCBe5sul1boqXp559/zv3338/hhx8OwNdff82pp55aadmfajs50wWs0+QiqtpPVU8DLgz3msMOO8xDi5KTeNe0oKD826VbTtMhh8Dxx5vX6emRXx/vmsYiVlP38UvTb76BHTugZcvyqG5dOeccaNgQdu6E9etrLO4ZkWjarBns3h3eUXEK1Ny5c7n66qsBKC4uZurUqdx5553squRb3uzZs+vyK9UJ6zT5TCwvrYxX4l3TefOgqAiOOgqq+KJVKzp0MOfADgIREe+axiJWU/fxS9NZgd1Nr7rK5EZzg0aN4IwzzOtly9ypszZEoqkING8e3iFSfl1JSQmLFy/m8ssvB0zU6ayzzqJly5aMHz/e7V+pTlinyWfW+/kVIkGJd02Dh+aCHyx1xXGaahNtj3dNYxGrqfv4pakTGQ4ESlzD2aD7m2/crTcSoqHp2rVr6dChAy1bmr3ujzzySA488ECGDRvGfffdB5i9XEeOHMnIkSP58ssvf3398ccfe25fMA2i2pplPy6tS9ZCS6XEu6Zuz2dyOPtsc16xIvJr413TWMRq6j5+aFpSAgsXmtdurHQN5txzYcgQfyNN0dD0lFNOYXrQlgWnnXYaY8aMCSlz/PHHc3xgjkFJSQn313afmjpiI00+M9rZXMziGvGs6c8/w5o1JsJ01VXu1u2E+tevh7xqM5HsTzxrGqtYTd3HD00zMswcnQMOKL/H3MKJNPnpNNl+Gop1mnzm5Zdf9tuEhCOeNXXC/OecYx7CbtK2LQQWpvDdd5FdG8+axipWU/fxQ1MnldCll5o959zkrLNMnVu2mMMPYrGfnnjiib61bZ0mn+natavfJiQc8ayp4zS5HeZ3OPNMc450iC6eNY1VrKbu44emjtMUmMPsKs2awQknmNerVrlffzjEYj/1c2jbOk0+4/cGk4lIPGvqtdPkDB+sXBnZdfGsaaxiNXWfaGtaVlaeZd8LpwnKV9CuXu1N/TVh+2ko1mlykdokt/R7g8lEJF413bat/NvkZZd500ZtI03xqmksYzV1n2hrmplp8ig1a1Y+/8ht/HaabD8NxTpNLlKb5JYPPfSQdwYlKfGqqfON9cwzzWadXnD66eacmRnZdfGqaSxjNXWfaGvq3LOXXGISUXqB306T7aehWKfJZ/zMbJqoxKumztCcV2F+gJNOMudt2yJbQRevmsYyVlP3ibamXs5ncvDbaYqWpnl5ebz55ps8/fTTlJaWRqXN2mCdJp9p37693yYkHPGqqdfzmQBat4aDDzav164N/7p41TSWsZq6TzQ1VS13mrwaTgc45RRz3rAB9uzxrp2qiJamrVq14sorr2TevHkxnS3fOk0+k5+f77cJCUc8arpzZ/k8Iy+/tQI4q3V/+CH8a+JR01jHauo+0dR03TrYvNkMyzkbYnvBgQeWf9H5/nvv2qmKaGr67bff0rFjx6i1Vxus0+QzlW1GaKkb8aips5P5qadCu3betuU4TVlZ4V8Tj5rGOlZT94mmpk6U6cILoWlTb9tyok1r1njbTmVEU9O5c+dyhZehdhewTpPPnOksZ7K4RjxqGo25EQ7OvKZIIk3xqGmsYzV1n2hqGs179rjjzPnHH71vqyIRaapqxhDDOVRDLi0rK2P+/Pnk5OTwySef8Kc//Yl5jsgxhHWafOazzz7z24SEIx41XbDAnL2cG+FQm+G5eNQ01rGauk80NU0WpykiTQsKoEWL8I6CgpBLv/nmGxo0aMDNN9/MnXfeyaWXXsrYsWNd/m3qjnWaXKQ2eZoef/xxDy1KTuJN0z17YOlS8zoaiW5r4zTFm6bxgNXUfaKl6U8/mTlN9eqZdANe46fTFC1NP//8c+6//34OD+z19PXXX3Oqs3QwhrBOk4vUJk9Tr169vDMoSYk3TZcsMTulH3kkHHOM9+05w3M//xz+apx40zQesJq6T7Q0dfIz/eY30KqV9+356TRFpGmzZmb34nCOZs1CLp07dy5XX301AMXFxUydOpU777wzZE7VrFmz+OorE5NQVbp3787evXvr+itGhHWafMamqHefeNPUeQBfdhmIeN/eAQeY1ANgljGHQ7xpGg9YTd0nWppGI9VAMI7TtGEDRDuFUUSaikDz5uEdQQ+7kpISFi9ezOWBsc7PP/+cs846i5YtWzJ+/Phfy1133XWsXr2alStX0rt3b+69916aNGni2u8aDtZp8hmbot594k3TYKcpWhx9tDmH6zTFm6bxgNXUfaKlaTTnMwEccYRJbVBcbIYGo0k0NF27di0dOnSgZcuWABx55JEceOCBDBs2jPvuuy+k7AMPPECXLl048cQTOeqoozy3rSKiFWawW+qOiLQCcnNzc2lVQ+x2x44dHHTQQdExLEmIJ02Li03kp6DA5GlyNtT1mptugmnTYNAgCGfKQjxpGi9YTd0nGpru2FGeN2nbtvLXXnPiiSYhbVqatwlwK1KdpgUFBaxatYr27dvTrMJwm1ekpqZyzjnnMHfuXG6//fawHSfH1uzsbHbt2kV+fj4PPPAAbdu2JS8vj9Ym/N5aVavdKyEpIk0i8pSI/Cgie0VkqYiE9Z1eRH4rIiUikuGVbZ988olXVSct8aTpN98Yh6lNGzjttOi1G2mkKZ40jRespu4TDU2dla6nnRY9hwn8m9cUS/109uzZnHzyyZx55pk899xzfPzxx1Gf09Qgqq35gIjcDfQCngIWAk8An4nIaapa5b8MEWkNjADmAJ6lG+zQoYNXVSct8aSpMzR36aVmJU60cCacr18fXvl40jResJq6TzQ0jfbQnIPjNGVnR7fdWOqn11577a+vRYRXXnkl6jYkQ6TpRWCIqn6gqqtU9XlgI/BkDdcNBD4CvvTSuE2bNnlZfVIST5r6MZ8JIo80xZOm8YLV1H2ioalzz0bbaXJGoaLdbWw/DSWhnSYRaQScB8yq8NEsoMrsGiLyMHAC8J8w22ksIq2cA2gZro12Tpn7xIumZWXlof5o5GcKJlKnKV40jSespu7jtab5+bBsmXkd7S86RxxhztGeCG77aSgJ7TQBBwH1ga0V3t8KHFrZBSJyEtAVuE9VS8Js5zUgN+jYBLBu3Tq6d+9OUVHRrysQOnXqxObNmxkyZAjp6els3LiRCRMmkJmZSe/evcnLywspu3PnTvr168fy5cuZPHky06ZNY9myZQwcOJDt27eHlC0oKCAlJYU1a9YwduxY5syZw6JFixg+fDgbN24MKVtaWkqXLl1Yv349qampLFiwgLS0NEaPHk1WVhY9evRg7969Idds2bKFwYMHk56ezowZM5g4cSIrV66kT58+5ObmhpTdtWsXffv2ZcWKFUyaNInp06ezdOlSBg0axNatW0PKFhYWkpKSQlZWFmPGjGHu3LksXLiQESNGsGHDBjp37kxZWRmdOnWirKyMzp07s2HDBkaMGMHChQuZO3cuY8aMISsri5SUFA4++OCQ+rdu3cqgQYNYunQp06dPZ9KkSaxYsYK+ffuya9eukLK5ubn06dOHlStXMnHiRGbMmEF6ejqDBw9my5YtIWX37t1Ljx49yMrKYvTo0aSlpbFgwQJSU1NZv349Xbp0obS0NOSajRs3Mnz48MDfZTE5OdCkSRnz5vWkoKAgpOz27dsZOHAgy5YtY9q0aUyePJnly5fTr18/du7cGVI2Ly+P3r17k5mZyYQJE5g5cybp6ekMGTKEzZs3h5QtKipi2rT+AGzYUMqcOWnMnz+fkSNHkp2dTdeuXSkpKQm5plGjRgwbNozFixcze/Zsxo0bx+rVq+nZsye7d+8OKbtjxw4GDBhARkYGU6dOZcqUKWRkZNC/f39ycnJCyubn59OrVy8yMzMZP348s2bNYsmSJQwdOnQ/u4uLi+nWrRvr1q1j1KhRzJs3j3nz5jFq1CjWrVtHt27dKC4u3u9eGzp0KEuWLGHWrFmMHz+ezMxMevXqRX5+fkjZnJwc+vfvT0ZGBlOmTGHq1KlkZGQwYMAAduzYEVJ29+7d9OzZk9WrVzNu3Dhmz57N4sWLGTZsGJs2bQopW1JSQteuXcnOzmbkyJHMnz+ftLQ0Vq5cydq1a2t8RsycOdM+I8J8RsyYMSOsZ0RhYWGtnhHPPPMRZWVw4IG57Nrl/TNizpw5jB07ljVr1rB4sZlbtGzZtqg8I7p3787atWtZuXIlaWmVPyM++OAD4g1VZfHixYDJQbV582ZSU1MjqyBRD+BwQIGLK7z/L2B1JeXrA+nAX4PeewvIqKGdxkCroOMIQHNzc7Um3n///RrLWCIjXjQdOFAVVDt2jH7bxcWq9eub9n/6qeby8aJpPGE1dR+vNf3nP8098+CDnjZTKd99Z9o+4IDotludpnv27NGvv/5a9+zZE0WLaodj6yeffKIffPCB9uzZU3NyclRVNTc3VwO+Qiutwa9I9EjTDqCU/aNKh7B/9AnMsNr5QN/AqrkS4A3g7MDPV1XWiKoWqWqecwD54Rp41113hVvUEibxoqlf85kAGjQoD/eHMxk8XjSNJ6ym7uO1pn5NAgezYwDArl3hZ/J3A9tPQ0lop0lV9wFLgWsrfHQtsKiSS/KAM4Fzgo4BwJrA6yVu29i/f3+3q0x64kVTP50mKH8Ib95cc9l40TSesJq6j5eaFhZCYAcPX5ymVq0gkPsxqvOabD8NJeFTDgDvAqki8jVmJdxfgKMxzhAi0gU4QlUfUNUyYGXwxSKyDdirqivxALuVgvvEg6YbN5oIT/36cPHF/thw2GHm/PPPNZeNB03jDaup+3ip6Vdfwb595r454QTPmqmWI46A1avNCrqTT45Om7afhpLQkSYAVR0DPI8ZZssALgduVFVnUOIwjBPlC3YrBfeJB02DN/xs0cIfGwKbiYcVaYoHTeMNq6n7eKlpcKqBaOwRWRlOdDiaWQBsPw0lGSJNqOr7wPtVfPZQDde+hZkM7gl/+9vfvKo6aYkHTf0emoPInKZ40DTesJq6j5eafvGFOft5zzpOUzSH52w/DSXhI02xzpAhQ/w2IeGIB01jwWmKZHguHjSNN6ym7uOVpkVFsHCheX3llZ40ERZ+RJrC0bSwsJCCgoKYPgoLC13RIykiTbHMdddd57cJCUesa5qTA999Z17/9rf+2RFJpCnWNY1HrKbu45Wm6elmIvjBB0P79p40ERbOitdoOk3VadqgQQPq1atHdrT3dqklqkppaWmd6rBOk4uIyNPA00QQwVu1ahWnRXOn1iQg1jV1wvynnQaHHOKfHZE4TbGuaTxiNXUfrzRNSzPnjh39m88E5dHhrZUlzPGI6jRt1KgRp59+OiUlJeTm5jJ16lSaN29O48aNo2dgBJSWllJSEm7O6sqxTpOLqGo/oF9gK5XccK5p2TLsHVcsYRLrms6da85+hvmh/AG8c6cZfqjuORfrmsYjVlP38UpTx2ny+55tF9g6fsuW6LVZk6aNGjWiUaNG7N27lz179lBcXByzTpNDUVFRra+1TpPPtG7d2m8TEo5Y1/Tzz835qkpTpUaPNm2Mo1RUZOY1HXts1WVjXdN4xGrqPl5oGjyfqWNH16uPiEMDaZq3bAHV6ES9wtW0cePGtGrViry8PPbt2+exVXWnVatWtXLurNPkM9999x0XXXSR32YkFLGs6datkJlpHnZXXOGvLSIm2pSdbYboqnOaYlnTeMVq6j5eaPrVV7B3r4nynHqqq1VHjBNpKiqC3Fw44ADv2wxX0+bNm3P33XfXKYoTTRo3bkzz5s0jvs46TT5z/fXX+21CwhHLmjpRprPPhgMP9NcWMPOasrNrXkEXy5rGK1ZT9/FC01iZzwTQtCm0bm0cpq1bo+M0RaJp8+bNa+WIxBM25YDPDB061G8TEo5Y1tRxmvyeG+EQ7mTwWNY0XrGauo8XmgY7TbFA8BBdNLD9NBRRVb9tSDicieC5ubm0atXKb3MsMcTJJ0NWFkyeDDff7Lc18Mwz0K8f/OtfYBP/Wiyh7N1r5v7t3QurVvk/PAdmWH/ePBg9Gu6+229rEoO8vDxn7lZrVc2rrqyNNPmMTVHvPrGq6aZNxmGqV8+fDT8rw0l5sG1b9eViVdN4xmrqPm5rOn++cZiOOAJOOcXVqmtNtCNNtp+GYp0mn/nHP/7htwkJR6xq6gzNnXeemZcQC4TrNMWqpvGM1dR93NZ05kxzvu46/+czOUTbabL9NBTrNLmIiDwtIpnAV+Fe8+6773poUXISq5rOmmXOV1/trx3BOKtxanKaYlXTeMZq6j5ua+rcs7/7navV1oloO022n4ZinSYXUdV+qnoacGG41/zxj3/00KLkJBY1LSuD2bPN61h6ADuRppoyDMeipvGO1dR93NR082ZYscJEmK65xrVq60y0E1zafhqKdZp85ssvv/TbhIQjFjVdvtw4Js2bwyWX+G1NOeEOz8WipvGO1dR93NTUiTKdf35spAdxiHakyfbTUKzT5DNHHXWU3yYkHLGoqTM34soroVEjf20JxnGadu+GgoKqy8WipvGO1dR93NTUuWdjKTIM5ZGmaO0/Z/tpKNZpsliiQKw+gFu1Kt9zbvt2f22xWGKFWB1OBzj4YHPescNspWKJLtZp8pmNGzf6bULCEWua7t4NCxaY17H2ABYJb15TrGmaCFhN3cctTZctg5wcaNkSYm2nG8dpKi42mcG9xvbTUKzT5BOqkJ4OJ5/8W/ttwWUuvvhiv00IIS3NPOCOOw5OPNFva/YnnHlNsaapH+TlmS1ncnLcqc9q6j5uaepEhq++Gho2dKVK12ja1MyNhOhEh+O1n6qaaNwPP4Cbfp91mnxi1y648EK48MJjadcOnnwSfvzRb6sSg3HjxvltQgixmOslmHCcpljTNBqUlZncWo89BsccY3JrHXccHHSQOf/zn3WbV5KMmnqNW5rGYqqBYJxoUzScpnjqpyUlMGMG/PnPZsL8wQfDSSfBq6+62Iiq2sPlA2gFaG5urlbFmjWqRxyhKlKmxidWbdhQtXNn1dLSKi+zhMG+ffv8NiGEk082f98JE/y2pHIefNDY16VL1WViTVMvWbVK9fXXVY85Rn+9N52jSZPQnw84QPXDD2vXTjJpGi3c0DQ3V7VBA/P3XbvWBaM84IILjH2TJnnfVqz307Iy1UWLVJ99VvWQQ/a/Z1u2VH3ggerryM3NVUCBVlrD/3cbaXKRSJJbnnyy2VbjjTe6MmsWXHutGcL517/gjjtM6n5L7ejWrZvfJvxKdjZ8/z3Urw9XXeW3NZUTzmqcWNLUbfbsgf/9D15/Hc44A9q3N/vwrV9vJso//riJFubmQmGhOY8bB+eeayLGDz4IL71kIlORkMia+oUbmn7+uYlYnHgiHH+8C0Z5QPBkcK+JxX66bRt88gk8+yyccIJJ49Knj3n/oIPg6afN/nwFBWZY/cMPXWy8Jq/KHt5EmipSVqY6ZIhq48bGO772WtWiorAvt8QoAwaYv+ell/ptSdX06GFs/NOf/LYkOpSVqS5erPqvf6lefHF5VCE44nvjjaoff6xaUFB1PcXFqm++WX7dE0/YKHEi8OST5u/51FN+W1I14USHE4mSEtW5c1Vffln19NP3jyY1b656332q06ap1iYwZiNNcYSzGaIIPPKIGY9t3twsd33sMbuktDbE0gaTsZpqIJiDDjLn6iY4x5KmdeF//zMRog4doHNn+PJLE1U45hi4/37zjXTbNpg2De65x0y6rYoGDeCtt8w1IjBwIPznP+HbkiiaxhJuaBrr85kgunOa/OynqjBypNks+aqr4L//he++M5+deSY88wyMH2/u2ZEj4cYbozBxvyavyh7eRpp++umn/d777DPV+vWNB/3vf9dYhaUClWnqB/v2qbZqZf6OX33ltzVVM2WKsfG886ouEyua1pZ9+1Sff778m2nTpqr33qs6dKjqjz/Wvf4PPiiv+6OPwrsm3jWNReqq6Q8/mL9hgwaqeXkuGeUB3boZO//8Z+/b8quf7t6t+oc/lN9XbdqYuUljxqhu3+5uWzbSVAEReUpEfhSRvSKyVEQuq6bs7SIyW0S2i0ieiHwpIp5955gxY8Z+711/vfnWCvD22zBqlFetJyaVaeoHS5aY8fS2bU10I1ZxIk3VzY+IFU1rQ2kpPPAA9Oplfn72WbME+aOP4OGH4dhj697Go4/C3/9uXj/8MCxeXPM18axprFJXTZ3I8CWXmBxNsUo0I01+9NP8fLPf36efmh0UOnc29+yHH8Jdd5U/s/wg4Z0mEbkb6AV0Bn4DzAc+E5Gjq7jkcmA2cCNwHvA5MEVEfuOFfaeffnql7z/6qFnSDGYi6jffeNF6YlKVptHGeQBfe62ZCB6rhDM8Fyua1oZXXoHRo03Y/pNPoHdvb/YS69IFbr4Ziorg9ttr3hssnjWNVeqqaTwMp0N0naZo99OyMpMyYPFiaNMGvvjC/C90clP5TcI7TcCLwBBV/UBVV6nq88BG4MnKCqvq86raXVXTVTVLVf8JZAE3e2FcbjUpXf/v/+CGG8yKndtvdy+pXqJTnabRJB7mRkC507R7d9WrNmNF00iZNg3efde8Tk01K1O9on59ExU+7TT4+Wf44x/NitiqiFdNY5m6aFpcDHPnmtexfs9G02mKdj/t2dNEmBo3hunTzfzDWCKhnSYRaYSJFs2q8NEsIKy95kWkHtAS2OmudYb8/PwqP3MewiecYJau33OPmbRqqZ7qNI0WOTkm4zuYpJaxTOvW5ZGwqhzzWNA0UvLzTZQW4G9/g7vv9r7Nli1hwgSTqmDBAnj55ersiz9NY526aPrll+aLw0EHwW88GVdwj2g6TdHspz/8AP/+t3ndu3fsOUyQ4E4TcBBQH6iYgWYrcGiYdbwENAfGVlVARBqLSCvnwDhZYdG+fftqP2/TBiZNgmbNzMqff/0r3JqTl5o0jQZz55rpi6efDkcc4bc11SNSPlxV1bymWNA0Ujp3NhGfE06Arl2j1+4pp8CIEeZ1795mVU9lxKOmsU5dNA0eTq8X4/8ZnehwYaHJM+Yl0eynL75ofqerry7/whNrxHjXcI2KC/elkvf2Q0TuBd4C7lbVajaZ4DUgN+jYBLBu3Tq6d+9OUVHRr8s2O3XqxObNmxkyZAjp6en07t2bCRMmkJmZSe/evcnLywspu3PnTr74oh9vvbUegO7doWvXdQwcOJDt27eHlC0oKCAlJYU1a9YwduxY5syZw6JFixg+fDgbN24MKVtaWkqXLl1Yv349qampLFiwgLS0NEaPHk1WVhY9evRg7969Idds2bKFwYMHk56ezowZM5g4cSIrV66kT58+5ObmhpTdtWsXffv2ZcWKFUyaNInp06ezdOlSBg0axNatW0PKFhYWkpKSQlZWFmPGjGHu3LksXLiQESNGsGHDBjp37kxZWRmdOnWirKyMzp07s2HDBkaMGMHChQuZO3cuY8aMISsri5SUFKZOnRpS/9atWxk0aBBLly5l+vTpTJo0iRUrVtC3b1927doVUjY3N5c+ffqwcuVKJk6cyIwZM0hPT2fw4MFs2bIlpOzevXvp0aMHWVlZjB49mrS0NBYsWEBqaioTJ5pvZ1dfXRZyzcaNGxk+fDiLFi1izpw5jB07ljVr1pCSkkJBQUFI2e3btzNw4ECWLVvGtGnTmDx5MsuXL6dfv37s3LkzpGxeXh69e/cmMzOTCRMmMHPmTNLT0xkyZAibN28OKVtUVET37t1Zu3YtH3/8MWlpaTRrZp683323ha5du1JSUhJyzdixYxk2bBiLFy9m9uzZjBs3jtWrV9OzZ092794dUnbHjh0MGDCAjIwMpk6dypQpU8jIyKB///7k5OSElM3Pz6dXr15kZmYyfvx4Zs2axZIlSxg6dOh+dhcXF9OtWzfWrVvHqFGjmDdvHvPmzWPUqFGsW7eObt26UVxcHNAZ/vtfE5a98cbZfPvtEmbNmsX48ePJzMykV69e5Ofnh9Sfk5ND//79ycjIYMqUKUydOpWMjAwGDBjAjh07Qsru3r2bnj17snr1asaNG8fs2bNZvHgxw4YNY9OmTaxY0YnXXzcPh7/8RXnuuaFkZ2czcuRI5s+fT1paGl27dmXt2rU1PiNmzpxZ4zOiX79+LF++nMmTJzNt2jSWLVuWlM+Il19+OaxnRGFh4X7PiFGjzCP+0EO/jcozYv369XTp0oXS0tKInxEtW0L9+qUA9O490tNnRNeuXUlLS2P+/PmMHDmS7OzsSp8RmzZtqtMzYtiwLKZMgfr1ldNPfx8Rb58RwfdaamoqYVPT8rp4PoBGQAlwW4X33wO+qOHau4EC4PdhtNMYk2bAOY4gzJQDeRGsa/373/XXRF4rVoR9WdIRiaZeccIJ5m81ZYrfloTH5Zcbe8eMqfzzWNA0Ep55xvw+l19ukln6QUmJ6vXXGzuOO041Jyf083jTNB6orabbt6uKmL9VvGSCaNfO2JuR4W070eqnHTua3+fxx6PSXAg25UAAVd0HLAWurfDRtcCiqq4LRJiGA39S1WlhtFOkqnnOAYQ9CPzee++FW5R33jHLMPfsgVtvjU4K/XgkEk294McfYe1aM0/oiit8NSVsako74LemkbBlCwwebF6/+aZ/myQ7cxKPO870iVtvDZ1oH0+axgu11XT2bDOcfuaZcPjhLhvlEW3bmvNOT2bblhONfpqeDmlpJmGsM6cpZqnJq4r3AxMx2gc8ArQHegK7gWMCn3cBRgSVvxcoBp7CzHtyjtYRtBnxNirhsmOH6rHHGo/8ggtiOwFbsjJ4sPn7/Pa3flsSPo8/bmz+z3/8tqTuvPWW+V06dPAvyhTM8uXlSU7/+Ee71Uos4mxL8vLLflsSPr/9rbH5k0/8tqTu3HWXRi1ZZ2XYSFMQqjoGeB54A8jA5GG6UVXXB4ocBgTnbHoCaAD0A34OOjxxtyNNUX/ggWYZ5oEHGu+84rdXi//bU/zvf+Z89dW+mhERNUWa/NY0XPbtgwEDzOu//c2/KFMwZ55pFnM0bGg2+n3hBRPViBdN44naaKpanh4k1le6BhOtSJPX/fSnn8xWKGA2vo55avKq7FGr6FbYkaYdO3bUWKYy0tNVW7Qw3vltt5nNQy2G2mrqBqWlqgcfbP4u8+b5ZkbEpKRotZv2+qlpJIwebX6Pww6r3cadXvLRR/rrlhBvvRU/msYTtdF0xQrzN2nSRLWw0AOjPMKJjnXt6m07XvfT//s/9X1TcxtpiiPGjq0yk0G1nH9+eYr5iRPhiSfs5r4OtdXUDVasMLlTmjeHiy7yzYyIqSnS5KemkfDhh+b86KNR2LgzQu69F5zpIW+9BU88sdpXexKR2vTTOXPM+bLLoEkTlw3ykGhFmry890tLy+cf/vWvnjXjKtZp8pmLL7641tdedZXZHqJePRg6FF591UXD4pi6aFpXnKG5K64wDm28UFOeJj81DZeffy7PtfPAA/7aUhXPPWf2kwQYP/63DBnirz2JRm36qeM0xdNwOkTPafLy3p871+wp17att9n63cQ6TS4iIk+LSCbwVbjXbNy4sU5t3nZbuafevbs5kp26aloX4nE+E9T8APZT03D56COzb9XFF8NJJ/ltTdX861/lmcIffxziJIgXF0TaT0tKzN5mkHj3rFt4ee87m9HffXf8RPms0+QiqtpPVU8DLgz3GnFhpuojj5Q7S//4B0n/7dUNTWvDvn0wb555fc01vphQa5wH8C+/VP65X5pGgpOF+8EH/bWjJkTM/fq7361HFe67rzxCZqkbkfbTr7+GvDw44IDY3zqlItFymry69wsLzZZDAH/6kydNeIJ1mnzmyCOPdKWev//d7OYO8Je/lK8GSUbc0jRSFi+GggI45BA44wxfTKg1bdqYc26umWdQEb80DZdvv4Xly82Q6F13+W1NzYhA586//Lqf5N13Q1aW31bFP5H2U2do7sory/dfjBei5TR5de9PnWr2hzzmGLgkrJ1gYwPPnCYRuUFE9gt4ikhDEeniVbvxxuLFi12rq2tXeOghM0Rx332waZNrVccVbmoaCcFDc7G+d1VFHKcJYNeu/T/3S9NwcaJMt9wS+rvEMunpixk+3Awn5uaa9CF2D9+6EWk/jdf5TBA9p8mre98ZmvvTn+LreemlqTOBu4MdJxFpBAwDPvGw3bjizjvvdK0uEejfH84910zovesuKC52rfq4wU1NIyFe5zOBWWnWooV5XdkQnV+ahkNZmVkQAXD//f7aEgl33nknjRubHDWHHQaZmfDww3YVbF2IpJ8WFsKiwL4Q8XjPOos3vHaavLj3d+40+QYhvobmwEOnSVXLMIki7xKRq0WkITAU6KWqS71qN94Y4GTic4kmTUwCvdat4csvzaTTZMNtTcMhLw++Ckz/j7f5TA5OhKYyp8kPTcNlyRLYvBlatoTrr/fbmvBxND3sMDO3o2FD40B9/LHPhsUxkfTThQuhqMhsm3LKKR4a5RFOpKmgwNsEx17c++PHmy/0Z50Vf1MZopHoUYABwBTgPK/bi4UDD7dRCZeJE03CsHr1VJct882MpGHyZKP3iSf6bUntOfts8zvMmOG3JZHx4ovG7vvu89uSuvH22+b3aNtWdcsWv61JfF59VX3duqOulJWp1q9vfofNm/22JjKuvdbY3aWL35YYYi25ZX2gBVAItI5Ce3GFVynqb73VTC4tKzMTwyub3Juo+LE9hTM0F69RJqg+0hSrW36owieBwf54yfPiUFHTf/wDzjnHDF0884w/NsU7kfTTeJ7PBGY6hnPPejlE5/a9v3MnfP65eR1v9yzgbaQJaAiMBC7ADAUOBq70ss1YOIgg0pSfn19jmdry88+qrVsbj753b8+aiTm81LQqTjvN6DxuXNSbdo3bbjO/w/vv7/+ZH5qGw1dfGZubN1ctKPDbmsioTNNly8qjB5Mn+2BUnBNuP/3lFxOFB9WNG721yUtOPlk937LJ7Xt/+HBj85lnulptnYiJSFPQHKbeqpqu5XOc7hORjl616ye1SW452MlM6QGHHgrdupnX//wnbN3qWVMxhZeaVsbPP5tJvCJm6XK8Ut1qnGhrGi7ORp+//z00beqvLZFSmaa/+U35pqWvvGLSEVjCJ9x+mpZmovAnnwwxnk2jWqKxgs7te9+5Z+MyyoS3q+euAvqo6q8ORMBx+gtwqYft+obWIrnlDTfc4KFFJuPwBRfA7t3QubOnTcUMXmtaESfMf+655Sta4pHqhueirWk4xPPQHFSt6T//afYCXL3aJqqNlHD7abwPzTlEw2ly897Pzy/PIRiP9yx4u3puZrDDFPR+marG5gQJH1ixYoWn9derZ/I3AQwYAD/+6GlzMYHXmlYkEeYzQfVOU7Q1DYdvv4W1a82K0Rtv9NuayKlK09at4Y03zOs337S5myIh3H5qnabwcfPenz7drFg86SQ4/XTXqo0qcZRSKjE54IADPG/jqqvg2mvNEs833/S8Od+JhqYOqvGdnymY6h7A0dQ0XJww/w03lOeYiieq0/SJJ+DEE82Q+n//Gz2b4p1w+unmzbBqVfwPp0N0nCY3731n25Q77jD6xyPWafKZli1bRqWdLoEc7CNHQgwGDVwlWpoCfP89/PQTNG4Ml8b5oHN1kaZoahoOqiYfGcRvmL86TRs1gnfeMa979ao8S7tlf8Lpp3PnmvNvflPudMQrjv05Od614da9X1gI06aZ17ff7kqVvmCdJp9ZtWpVVNo57zz44x/NP5sYXT3uGtHSFMqjTL/9bfxNRK5IdU5TNDUNh8xMWLPGOBc33eS3NbWjJk3vuMMMYeTlQd++UTIqzgmnnybK0BxEJ9Lk1r0/ezbs2QNHHQXnn+9Klb5gnSafufbaa6PW1r//bc7jxpl/OIlKNDVNlPlMUP0DOJqahoMT5r/2WjMHKB6pSdN69coz+vfsaRZzWKqnJk1VrdMUKW7d+85w+u23x+/QHFinyXeGDx8etbbOPNNsaKpanoogEYmWpiUl5UnaEuEBXF2kKZr9NBwmTTLn227z1Yw6EY6md91lJs3u3GkWcliqpyZNf/gBNm40W9bE+3A6RMdpcuPe37cPJk82r+N1ON1BVO3ukG4jIq2A3NzcXFq1auW3OSEsWQIdOkCDBmbl0dFH+21R/PLVV3DRRSbSkZMD9ev7bVHd2LmzPGVCUZEZ+opF1q+HY481kZgtW+Dgg/22yFuGDYNHHoF27czq13gfBvaTAQPgySfh8svhiy/8tqbuOM/zY46B7Gy/ramaWbPgd78zffinn2LvWZmXl0drE7Jurap51ZW1kSYXqU1yy2hvT3HRRSYqUlICPXpEtemoES1NnaG5q66KvYdAbWjdujxsXjHaFEvbqDhRpksvjW+HKVxN77/ffLnZutXmbaqJmjRNpKE5iE6kyY173xmau/XW+H9W+hJpEpFmQENVzY1641EgkkhTSUkJDRo0iI5hAebONQ+NJk3Mt5N27aLavOdES9OrrjLDc/36wVNPed5cVGjTxqzUWrUKTj21/H0/+mlVXHmlyej87rvwwgt+W1N7ItG0f3/Tx4480kSIYzUK6DfVaVpWBoccYqLCCxaYxRvxTk6OSYQKZgisYUP326jrvV9aCocfDtu2mYhTjE2PBGI80iQiXYG1wBUi8qKIJIjPXzv+60MSliuvNBGnvXvNcuZEIxqaFhTAwoXmdSJMAneoagNQP/ppZezYAfPmmdfxPJ8JItP04YfhsMNg0yb48EMPjYpzqtP022+Nk9GiBVwY9p4NsU1wCqXK5iK6QV3v/UWLjMPUpg107OiOTX7ix/BcOvCBqk5W1XeBMpF4nktfN+65556otylitmoAEyVJtBww0dB04ULzze7II81E3UTBCfdXfAD70U8rY8oUEzE45xwzrymeiUTTJk3g7383r7t2tXvSVUV1mjpDc5df7k1Exg/q1y93nLwaoqvrve8Mp990U2LoHnWnSVXHq+q/g37+XJN4NvqCBQt8afemm8xquvz8xMsBEw1Ng1MNJJLLX9UKOr/6aUUSYdWcQ6Sa/uUvZihm3ToYM8Yjo+Kc6jRNtPlMDl7Pa6rLva9afs/eeqsr5vhO1JwmEfFtK1MReUpEfhSRvSKyVEQuq6H8FYFye0VknYj81SvbjjnmGK+qrpZ69eC118zrXr1M0rFEIRqaJlJ+pmCqGp7zq58Gs2dP+WafifAAjlTT5s3L53C9846JuFlCqUrTffvKh3Wt0xQZdbn3v/vOOPmNG8N117lolI9EM9LUPYpt/YqI3A30AjoDvwHmA5+JSKWL7UXkOGB6oNxvgHeA3iLiSXaJ0tJSL6oNiz/+EU44wYzz9+/vmxmu47WmOTnwzTfmdaI+gCtGmvzspw4zZph5eMcfb6Kk8U5tNH36abPKMTOz/Bu8pZyqNF2yxMxDPOigxOg7wXjtNNXl3v/0U3O+5pr43B+yMqK5HMav9AYvAkNU9YPAz8+LyO+AJ4HXKin/V2CDqj4f+HmViJwPvAyMd80qVSgoYNuPP8IFF7hWbSQ0AN58Gf76JPTrDk8+YL7NxjteazrvM2iqcFp7OLQlkEBRukOaQzNgzzZCfi8/+6nDZ58Y2+6+CaTAV1NcoTaatm4ALz4B3brDf/8Dt12XWMPDdaUqTed9ZvrODZdDvcLo2+Ulh7Uyv1vez3jyLKrLvT9jvLHtzhvw/znZrJkrN0vUUg6IyFBVfSQqjZW32QgoAP6oqhOD3n8POEdVr6jkmnnAN6r6t6D3bgPGAs1UtbiSaxoDjYPeaglsqjblwJ49ieN6WywWi8USy+zeXWVUIKZTDkSZg4D6wNYK728FDq3imkOrKN8gUF9lvAbkBh2bANatW0f37t0pKir6NUFYp06d2Lx5Mx/adcMWi8VisUSFH3/8kW7dulFcXLzf/+PU1NSw6/Ek0iQiFwPBC7EFeBT4oELRzar6P9cNKLfjcOAn4BJV/TLo/X8Bf1bVUyu55ntgmKp2CXrvt8AC4DBV3VLJNZFHmgLDc0VFRTRu3LjyMlGiuNgs4c5eD+90hr/9rcZLYhovNV2/Hk47HerXM9sBtGzpSTO+MWkS3Hc/XNyhfLI7eKtpOLzwAgwaDA8/lDirPeui6datcPrpULgXxow2q2EtlWs6ezbcehscfZSZC5Zow5nvvgv/fgPuvw8GDnS//tr201tugTlzodPbMZKEtprhuUgiTV7NadoOVMxZuwfIxjhQDjkete+wAyhl/6jSIewfTXLYUkX5EqqwV1WLgCLn57DSTolA8+b06NmT119/vebyHtIQeOkNePRR+L8UePCp0KRp8YaXmv7vSzPee0kHaFlVrDKOaX24+f025wJBkWw/+2lZGYydZuz6/V2hdsUzddG03fHwlxegSxf4x//BDXfG//YUblCZpjMXBO7Za0EScEZE80PM77dtD57cG7Xpp7m5MGM+FAM3/tEbu3xDVaNyYKI3UWsvqN0lwPsV3ssEulRRvhuQWeG9/sCXEbTZCtDc3FyNF4qLVU87TRVUX3nFb2til3vuMRq98YbflnjDN9+Y3+/QQ/22pJylS41NLVqo7t3rtzWxwy+/qLZpY7QZNsxva2KXM880Go0e7bcl3jB6tPn9Onb025JyPv7Y2HTKKX5bEh65ubkKKNBKa/j/Hs05TX4lsHwXeExEHhGR9iLSEzgaGAAgIl1EZERQ+QHAMSLybqD8I5ihRU/2kYiVjVAbNIBu3czr996DDRv8tacueKVpWVniJshzCE5uGTxy72c/nTHDnK++2uR7SRTqqukBB5Rn9n/jDZOOIdmpqOnPP8OKFSawn6j3rBlV8m5nh9r0UyfVQCLkU6tIok8ER1XHAM8DbwAZwOXAjaq6PlDkMIwT5ZT/EbgR6Bgo/2/gOVV1L91AEI88EtUFhdXy+9+bvYGKisDnEcM64ZWm33wD27ebeUwXX+xJE77j5HwpKoLCoKXZfvZTx2m6/nrfTPAENzR9+mmzlc/GjRAj2wP6SkVNZ88253PPLd/YNtFwplJ45TRF2k9LS2HmTPP6lls8MMhnouk0+bZbkqq+r6rHqmpjVT1PVecFffaQqnasUP4LVT03UP44VR3glW2fffaZV1VHjAj06GFep6aajRbjEa80dR4EV12VGHsoVUaLFuVzY4ITXPrVT3Nzy/vh737niwme4YamTZtC90Da4HfeMQsVkpmKmjpOU6Jko64Mx2nKzfWm/kj76dKl5tnRunXibIwcjKdOk4i0DvrxGS/bilfOOussv00I4fzzwfli8eST8bkxqFeaOhGPRPvnHYxI5Vup+NVP58wx31xPOQWOO84XEzzDLU3vuQeuuMJEBl96yZUq45ZgTcvKks9p8mJrnUj7qaP5lVeaaR+JhteRpo4i8qGI3KWq+zxuKy7Z6VXu+zrQrZsZplm+PD6Xd3uhaV4efBlIWpHIThOUO03B31z96qeJOjQH7mkqAn36mAjh+PHl+/MlI8GarlhhUjM0a5a4w+lQ7jSVlZn8jW4TaT91UpVce637tsQCrjlNInK7iLwiIveIyKEAqvqpqj5oPpZX3GorVhGRp0UkE/gq3Gv2xOBOuQcdBF27mtf//rfJRxRPeKHp3Lkm6nbSSWbvs0SmsjkSfvRT1cR2mtzU9Mwz4ZlALP/pp0PnoyUTwZo6EY+OHRNrAUFFmjSBRoEEP17Ma4qkn+7ZAwsXmtfWaaoGEekFfAJ0BT4CNonIfBH5i4i0DEzGbu9GW7GMqvZT1dOAsEdyTz11v/yaMcGjj5pvZ7t3w3PP+W1NZHihaTIMzTlU5jT50U9XrzYTnBs3hssvj3rznuO2pv/3f3DEEfDDDxAji3KjTrCmzhzERB6ac/ByMngk/XTePJMs+Zhj4MQT3bclFnAr0nQacALQArgAs1KtGWb5/jYRWQIc61JbCcX//udZQvQ6Ua8eDBhgxqQnTIivHdXd1lS1/AGciBGPilT2APajnzqaX3GFGWJJNNzWtFUrM0wHZnL4ypWuVh8XOJrm5cEXX5j3kvWLjltE0k+d6N611yZe5nUHt5ymtar6o6oWqOpSVX1HVc8DTgc6A/OBP7vUVkLx0EMP+W1ClZx1Fvz97+b100+bB1E84LamWVmQnW1C4B07ulp1TFLZA9iPfur800vU/DpeaHrbbfCHP5ih5Cee8GZicCzjaDprlol4nHSSWUSQ6Hi5gi6Sfpro85kgAqdJDA+LyGmVfFwmIk0qvqmqq1S1k6q+rKqb6mRpgtK7d2+/TaiWf//bhFk3b4bXXvPbmvBwW1MnUdvll1e5SXZCUZnTFO1+WlZmQv1gIk2JiFea9uljUkcsWgSDBnnSRMziaDp5svn5llsSN+IRjJeRpnD76ZYtiZ9IFIhsGxVgH2Yvtx3Ap8DfgYuBs4A+BDYATvaDONxGpTrmzDEp8UVUFy7025roc8kl5vfv189vS6JD587m9330Uf9sWLHC2NCsmeq+ff7ZEa+8957Rr3Vr1c2b/bYmuhQXq7Zta37/L77w25rocNdd5vft3ds/G8aONTacc45/NtQWL7dR2RFwjj4HOmD2aVsAfAn8EfhCRC4REbt1ZJjEyjYq1XHVVfDQQ2Zuz1/+AvtiPHmEm5pu2VKeauAPf3Ct2pimsm+t0e6nTpTpkksSN5Gol5o+/TRccIEZrvnb3zxrJubo1KkTixaZHGNt25r+kwx4uZVKuP3UWTV36aXu2xBLROo0bQFeUtU/qmo7zJylp4EpmAjUpZj5S7tEZKaIvCYiF1snqmqeeuopv00Ii//+Fw4+GL77rjwDcazipqaffmqcxQsvNCuTkoHKnKZo99P58835ssui2mxU8VLT+vXN0Fz9+jBuHEyb5llTMcVTTz3169Dc73+fmMkVK8PL4blw+6mTuf+3v3XfhlgiUqfpUlUtdX5QM2dpgKreo6pHAKcAT2CG7k7FTAJfgHGiYnvyjk98/PHHfpsQFgceCL16mddvvw1r1vhqTrW4qenEieZ8222uVRnzVPYAjnY/XbzYnBM5UuC1puecAy+8YF4/9ZQ3iQ9jjY8++vjXOYiJuO9ZVXjpNIXTTwsKzN6ckNj3LEToNKlqQQ2fZ6nqB6p6v6oeg0lD8BgwHji49mbGB7VJbnlZHH2Vvvdes+R+377YXpnjlqa5uSapJVinKZr9dNs2s1pRxAwxJSrR0PStt0zOnA0b4M03PW/Od4444hp++MGsdE2GVAMOXq6eC6effvWVWbF5xBFw1FHu2xBLeLqNipo0BMPUbIp7r5dtxQJai+SW2dnZ3hnkMiLw/vsmZ84XX8BHH/ltUeW4pem0aWbZcvv2ybFs2aEypyma/fSrwFeOU08tn6uRiERD0+bNoX9/87pXL1i2zPMmfeXjj81Sueuug5YtfTYmingZaQqnny5ZYs6XXJL4qxW93nvOUgP168fXdK/jjoPXXzev//nP2NyuwS1Nx40z52SKMkHoA9gsBo1uP3UewBddFLUmfSFamt5wA9x9t4kMP/10+d800TBpKo4E4P77fTYmyng5ETycfrp0qTmff7777cca1mnymcMOO8xvEyLm+efh6KPNFhc9e/ptzf64oen27TB1qnn9pz/Vubq4wnGaSkvNXlIQ3X7qOE0Xhh2vjU+iqWnPniZCvHixyfCfiCxaBFu3NqNlS7j5Zr+tiS5eRprC6adff23O553nfvuxhnWafCY9Pd1vEyKmaVN45x3zuksXs5N4LOGGph99ZMboL7gATj/dBaPiiKZNy5f5Ow/haPVT1fIhpER3mqJ57x92GLz8snn96qtm2DnRGDnSnO+4IzG33akOL52mmvrpzp3w44/m9bnnut9+rGGdJp+5/fbb/TahVtx7rwnF7t5tJpvGEm5oOny4OcfwLjeeIbL/Qzha/fSnnyAnxywVT3RnNdr3/ssvwyGHmA19Ey1TeFERjB1rXifb0BxUPqTuFjX1U+dLzgknQJs27rYdi1inyWcGDhzotwm1ol49k7sJYMgQs9opVqirphkZ5mjUCO65xxWT4o6KTlO0+mlGhjmfeio02W9jpsQi2vd+y5blX3D+8x/Iz49q857y2Wfwyy/QsmV+UuwPWZHgIfWCate4R05N/dSZz5QMQ3PgktMkIgeLyDUi8piIvCQi/xSR50TkDhE5w402EpXXnVnVccgVV5g9hoqLIZYSm9dVUyfK9Ic/mKzCyUhFpyla/dRxms45JyrN+Yof9/5jj5lNbLdvN3vUJQpDh5rzX/7SkjhbW+MKzZrx6+/t9hBdTf3UuWeTYWgO6uA0icjxItI5kJdoCzAL6A+8hskS3g0YBywXkV9EZJSIJHTmjNrkaYqHbVSq4//+z5yHDzdh/1igLpru3QujRpnXDz/skkFxSEWnKVr9NJmcJj/u/YYNy6NNPXp4Mwcm2mRnly/aKC5+31db/KKyIXW3qKmfrlhhzmee6W67sUrETlMgqvQh8DUmA/gA4Dygrao2VNWDVPUIVW0KtMAkuHwayAfeF5FvRSQh9y2vTZ6mF1980UOLvOeSS0zCy9JSkyk8FqiLpiNGwI4dZnXgtde6aFScUfEBHK1+mkxOk1/3/t13m/liu3bBu+/6YoKrDBxo5vFcfTV06fKQ3+b4hldOU3X9dN++8t0hrNNUCYFI0efA98DxqnqnqvZW1QxV3VWxvKoWBBJcfqSqfwVOxGyt8q6IdBdJ9DRYNdPfyTwXxzjRppEjYfVqf22B2mtaVgYpKeb1Cy8kz75VlVHxARyNfrp7N6xda16ffbbnzfmOX/d+/frl92zPnuZLQrySnw8DBpjXTz+dGM/T2uKV01SdpmvWmFXGrVvDkUe6226sErbTJCK/B54FLlPVzpU5STWhhrGqeh6wExgSaR2Jxk033eS3CXXmggtMXpSyMjPB1G9qq+mUKfD99+bh8+ij7toUb1R8AEejnzoOd7t2cNBBnjfnO37e+7fdBr/5jXFUe/TwzYw607+/6aOnnGL2mkuE52lt8cppqk5TZ2jujDMSPxO4QySRpvbALar6ixsNq2pXYHSyTxT/9ttv/TbBFZxvrmPGwMqV/tpSW02dfx5//WtybcFQGRUfwNHop5mZ5nzaaZ43FRP4ee+LlA+n9+kDW7b4ZkqtKSwsH1589VUTQUuU52lt8Gr/ueo0Tbb5TBCB06Sq/1VVV7doVdVZqurZv1gRaSMiqSKSGzhSReSAaso3FJFuIrJCRPaIyGYRGSEih3tl44EHHuhV1VHlnHNMUjlV/zcGrY2mixbBwoUmzcBzz3lgVJxR0WmKRj91nKb27T1vKibw+96/8Ubo0ME4H126+GpKrRg2zCTWPfpouO8+857fmvqJV1upVKep8wXZOk2Jw0fAOcD1geMcILWa8s2Ac4G3A+fbgZOByV4Z2LRpU6+qjjr/+Y/5Bjthgr8bg0aqqSq89pp5/cADJntyslPRaYpGP121ypyTJdLk970vUp4qZMAAsy1SvFBcDN27m9evvFKewd5vTf3Eq+G56jRNtugwRMFpEpEPReRVETnK67YqtNse4yg9pqpfquqXwOPATSJS6Z71qpqrqtcG5l2tUdXFmHlc54nI0V7Y+f3333tRrS+cfnr5Pm1vvOGfHZFqOn06zJsHjRv7a3csUfEBHI1+mmwP4Fi496+6Cjp2NKugOnf225rw6d8f1q83898eeaT8/VjQ1C+8cpqq0rSoqDyp8SmV/kdNTNxKbnmuiPQVkXsrOkeq+iAmUvOCiNzrRnthcjGQq6pLgmxZDOQCl0RQT2tAgV1VFRCRxiLSyjmAsGfEXH311RGYEvu8+aaZWzBtGnz5pT82RKJpaamZDwFmWO6oqLr2sUvFB7DX/XTvXli3zrxOluG5WLj3g+c2DRlS/jeIZX75pXzByX/+Y/ZKdIgFTf3CK6epKk1/+MEs/mnZEg491N02Yxm3Ik0HAA8Bo4BsEckOzAV6XEROUdVMVX0RuNGl9sLhUGBbJe9vC3xWIyLSBOgKfKSqedUUfQ3jjDnHJoB169bRvXt3ioqKfk0Q1qlTJzZv3syQIUNIT0/n9ddfZ8KECWRmZtK7d2/y8vJCyu7cuZN+/fqxfPlyJk+ezLRp01i2bBkDBw5k+/btIWULCgpISUlhzZo1jB07ljlz5rBo0SKGDx/Oxo0bQ8qWlpbSpUsX1q9fT2pqKgsWLCAtLY3Ro0eTlZVFjx492Lt3b8g1W7ZsYfDgwaSnpzNjxgwmTpzIypUr6dOnD7m5uXTq1ImTToJzzvkGgIce2siKFSuYNGkS06dPZ+nSpQwaNIitW7eG1FtYWEhKSgpZWVmMGTOGuXPnsnDhQkaMGMGGDRvo3LkzZWVldOrUibKyMjp37syGDRsYMWIECxcuZO7cuYwZM4asrCxSUlL44IMPQurfunUrgwYNYunSpUyfPp1JkyaxYsUK+vbty6BBe1i50jxwGjT4L7m5ufTp04eVK1cyceJEZsyYQXp6OoMHD2bLli0h9e7du5cePXqQlZXF6NGjSUtLY8GCBaSmprJ+/Xq6dOlCaWlpyDUbN25k+PDhLFq0iDlz5jB27FjWrFlDSkoKBQUFIWW3b9/OwIEDWbZsGdOmTWPy5MksX76cfv36sXPnzpCyeXl59O7dm8zMTCZMmMDMmTNJT09nyJAhbN68OaRsUVER3bt3Z+3atXz88cekpaUxf/58Ro4cSXZ2Nl27dqVFixLAPIA7depE7969GTZsGIsXL2b27NmMGzeO1atX07NnT3bv3h1S/44dOxgwYAAZGRlMnTqVKVOmkJGRQf/+/cnJyQkpm5+fT69evfjss7WUlUGLFsVkZy9h6NCh+9ldXFxMt27dWLduHaNGjWLevHnMmzePUaNGsW7dOrp160ZxcfF+99rQoUNZsmQJs2bNYvz48WRmZtKrVy/y8/NDyubk5NC/f38yMjKYMmUKU6dOJSMjgwEDBrBjx46Qsrt376Znz56sXr2acePGMXv2bBYvXsywYcPYtGlTSNmSkhK6du1KdnY2I0eOZP78+aSlpfHSSy+xdu3aGp8RM2fO9PQZUa/eIs444ydKSuDOO7/1/BnhlN21axd9+/aN+Bnx5z+vZudOOPbYAho1Sg15Rjz88MNhPSMKCwvDfkbs2rUrpGysPiOyszMA2Lgx39VnxEsvvVTpMyIzsxQwUabOnTuxadMmT58RmZmZjB8/nlmzZrFkibvPiNTU6mbtVEBVXTmARsBvMQ7ENOAXoAwoBfYEfv4/F9p5CxP5qe44H/gnsKaS67OAV8NopyEwCVgGtKqhbGOgVdBxBKC5ubmajGRnqzZsqAqqn3/utzVVk5urethhxs5u3fy2Jrb46SejS/36qmVl3rc3bpxpr0MH79uy7M9XXxn969VTXbXKb2uqZu1a1UaNjK3Tp/ttTWzx6adGlwsvjE5777xj2rvvvui05yW5ubmO71Dt/3pVdW9Ok6ruU9WFqtpFVX8PtAV+AzwP/IiZlO3Guqq+mPQH1R0rMVu7tKvk+oOBrdU1ICINgbHAccC1Wn2UCVUtUtU858BkPw+LeN9GpTKOOQYef9y8fvVVE8KNJuFq+sYb8PPPcOKJdsVcRYI3AN2zx/t+6mzBc+KJnjYTU8TSvX/BBWavxbKy8m1WYpEXXjDzr6691uxEUJFY0jTaRHsbFScTeDLNZwLcizRVd2AiMf2Aw6PRXqDN9hjP8cKg9y4KvHdKNdc1BCZiHK+Da9l2K8KMNJWUlNRYJh7ZvFm1RQvzTWTYsOi2HY6my5aZb9WgOnNmFIyKM8rKyqOFGzd6308fecS09Z//eNpMTBFr9/6335q/Aaimp/ttzf5MnGhsa9hQ9bvvKi8Ta5pGE+fvd8gh7tZblaYdOpj2xoxxtz0/8CXSVINjVgT8C3g5Gu0F2lwFzAAGi0gHEekADAamquoap5yIrBaR2wKvGwCfYIb37gPqi8ihgaORF3Z2d9bNJhiHHVaer+mVV6K7MWhNmpaVwZNPmvNdd8F110XJsDii4gagXvfTrCxzTqZIU6zd+2edBfffb14/8YTZHiNW2L0bnn3WvP7736teYRlrmkaT4PvVfHd3h6o0dRbV2UhT7SIr52GW5p8DSDXlBrrRXgR2tQVGAnmBYyRwQIUyCjwUeH0sVc+T6hhBu2FHmrKzs2ssE6/s26favr35NvLcc9FrtyZNBw40NrVoobppU5SMikNOOsnoNH++9/3UmVv21VeeNhNTxOK9v2WL6gEHmL9Fr15+W1POSy8Zm447TnXPnqrLxaKm0SI3tzxSWFDgXr2VabpzZ3lbu3e715Zf+BFpOhroBSwFdorIVBH5h4hcEliG31hE/oQZ+ooaqrpTVe9X1VaB436tsGeeqoqqDg+8zg78XNmR5oWN8+bN86LamKBhQ+jd27zu2xe++io67Van6fbt5SkG3n4bjjgiOjbFI8HfXL3sp7t3m7llkFyRpli899u1g27dzOvXX4+NhJfffgu9epnXfftCs2ZVl41FTaNFixZQL/Af3c3IfmWaOqkp2rWD5s3daysecMVpUtWJmCjNo8CnwOlAF2A+ZtVcASYT96rAMn5LgOOOO85vEzzlmmtMwsuyMhP637PH+zar0/SVV0yel7PPhmee8d6WeCbYafKyn65da84HHght2njWTMwRq/f+Y4/BJZcYZ/aRR6K/kCOYsjKzF2RpKdx5p9n6pTpiVdNoUK8etGplXru5/1xlmjpO0wknuNdOvODm6rmNqjpcVR9S1eMod6JSgQ2AYHIe7RSR/4nIKyKShJKHUhJLEwc8ok8fOPxwM2/lr391d7y9MqrSdP58GD7cvO7fHxo08NaOeCfYafKynybjfCaI3Xu/Xj344AOTNPJ///N3X7oPPoDFi00UxYk2VUesahotvFhBV5mmzhed4493r514wbOJ4Kq6oRIn6hHMUv4TMA7UAq/a9wMReVpEMoGwB6K2xOP24hHSti189JHJFD5yZPnO5F5RmaZ795anQXj8cbj4Ym9tSAScB/Avv3jbT5P1W2ss3/vt25svOwD//jd8+mn0bdi6Ff7xD/O6U6fwhtJjWdNo4IXTVJmmzj1rnSYPCThRH1Zwou6IVvvRQFX7qeppwIXhXnPeeed5aFHscMUVkJJiXr/8cnnExwsq07RzZ5NX5NBDy+dsWKon+AHsZT/98UdzTraRlVi/9x95xKwyVYV774Uvvohu+88+a/reb34DTz8d3jWxrqnXeOE0VaapE2lKti86EEWnqSIBJ2qRX+3HCpMmTfLbhKjx3HPw/PPm9cMPlztRblNR0+XLoWtX87pv3+SaN1MXgh/AXvZTZ9PPZHOaYv3eF4H33oPf/x4KC8158uTotD1xIowbZ6LTQ4aEP5Qe65p6jRdOU2WaJnOkKZLl+3diNt69G2gS7nXJeBBByoHCwsIayyQSpaWqzz9fvlz1+edNagI3Cda0pET1ggtMW7fd5m47iU6/fka322/3tp+eeqpp53//86yJmCRe7v3CQtXf/c78jURU//tfb7fW2blT9dBDTXv//Gdk18aLpl7x4INGty5d3Kuzoqb79pUnBv7pJ/fa8RNPUg6o6ieYFXGXAZki8qGIXCcivkWrEoH//ve/fpsQVerVM3OanHxpvXrB5Ze7u7t6sKbvvQfp6dC6tYkyWcIn+FurV/1UtTzSdOyxnjQRs8TLvd+kCUyZYhJeqprh9bvuMuk7vODFF2HLFjj1VDOfKhLiRVOvcO5ZN1fPVdR0wwazqrFJE5PEOOmoyauq7ADqA7/H7Ce3FpOj6YLa1JWIBxFEmpKZceNUW7c231hatjTbrbj5DXbVKtWmTU39gwe7V2+yMG2a0e7cc71r4+ef9deNYouKvGvHUnfKykzCywYN9NftOiZNcreNGTPKI1qLFrlbdzLw5ptGv7/+1bs25swxbZx8sndtRBvPk1uqaqmqTlPVPwFnYZJavi0imSLypoicVFdnLllI5g0m77zTJK679FLIzzfznG65pTzRYW3p1KkTRUVm8mphockV9eij7ticTARHmrzqp06U6YgjoJEnGxXFLvF274vA3/5mUgCcfjps2wa33goPPuhOZGP7djP5HMz8x9qscI03Td3GizlNFTV1Ep4efbR7bcQTdR5aU9U9qpqqqtcDHTHJLEeKyBIReU5EDqlrG4nMY4895rcJvnLMMZCWZla0NWoEU6fCGWfA6NG1z+f02GOP8eqrkJEBBx0EI0aYB74lMoIfwF71U2flXLINzUH83vvnnQdff20SxYqY++vMM2HOnNrX6SS/3bzZDMt17ly7euJVU7fwwmmqqKnjNB11lHttxBOuzkdS1W2q2ltVLwLux+z99oWIzBCRP4tIkiVcr5kpU6b4bYLv1K9vHsBLl8K558LOnSZKdPfdsGNH5PW9/fbyXxPhDRuWpOPuLhD8AJ482Zt+mqwr5yC+7/0mTcwXnfnzzQqqjRtNRPf55010N1LeeQdmzTIJNceNq/3WHPGsqRt44TRV1NQ6TR6hqlmq+paqtgfeBC4AVorIxyJyk4jU96ptv6hNcstzzjnHO4PijDPOMKH/t94yS4zHjTPDAJEk1lu2DIYNuxowIf6bbvLG1mTAeQCXlcHJJ5/rSRuO03TMMZ5UH9Mkwr3/29+aIfa//tX8/N575otPJPtMTpwIb75pXr//vnkO1JZE0LQutG5tzm46TRU13bDBnO3wnIeo6hJVfQ44ERgB3AP8ICL9ROSiaNgQDbQWyS1zcnI8tCj+aNjQPECXLAmdN/HQQzU/CL75Bq69FgoL63PttZDkC2nqTNOm5u8BsHFjvidtbNpkzsn4AE6Ue79FC7Mt0fTpJqq7erWZj/SPf5hM/NUxZQrcc49xzJ94wtzndSFRNK0tXqyeq6ipjTRFkcAE8s9U9X7Mpr6LMFurJC2FtYllJwHnnmuG6/7xD5Om4MMPzVyHDz6A4uLQsmVlJsP4pZeaob2TTtrJuHHl//AttUOk/CGck1PqSRuO03TkkZ5UH9Mk2r1/ww2wcmX5Bt3du5uNsT/9dP9Nf4uLzbylW2+Fffvg9tvdSQmSaJpGihfDcxU1TXanybctS1W1ABgVOJKWk06yCw2ronFjk8n7llvMqpo1a8y+cW++CX/4A5x8snGSPv3UZP0GM6/i//5vC61bt/XX+AThgAPMqqY2bbyZdJTMTlMi3vtt28KoUWY+4l//Ct9/bxyjk04y9/FRR5m/+dix5cM8jz7q3gbaiahpJDhOU2EhFBWZZ2hdCdY0Nxfy8szrZHWaXIk0ichZIvKeiFztRn3JxOeff+63CTHPJZcYpyglBdq1Myts+veHF16At982n7VoYSaTzpgBX39dh2U8lhCch/DChd+5XndBgXF6ITmdpkS+92+5BVatgtdeg5YtISvL3L/PP2+GzTdsMCtbU1Nh8GD3osKJrGk4tGpV/tqtIbpgTZ0oU5s25pmbjIjWdl13cCUiEzDJLvNV9aA6VxjniEgrIDc3N5dWwb24EnJzc2ntzN6z1EhRkVllk5ZmbuCWLaFDB7jtNvMQBqupm1x3HcyeDQMGFPDEE81crTsry0QLmzc3ebqSLS1EsvTT/Hwzd2nhQsjJgQMPNHOe7rjDzJtzk2TRtDpatzbRoDVrzP1VV4I1/ewzuPFGOOssswAgUcjLy3N+x9aqmlddWbfmNG0Bfgc84VJ9SUOfPn38NiGuaNwYbr7ZfGsdO9Zs5vn44+UOE1hN3cSJNE2ZMs/1uoOH5pLNYYLk6actW5p5Tv36mfxr/fqZnExuO0yQPJpWh9vzmoI1TfbEluCe01QErFHV8S7VlzS8/vrrfpuQcFhN3cN5AF900fWu153M85nA9lMvsJqW37O//OJOfcGaOvPQknU+E7jnNP0HeE9EznapvqQh2dP+e4HV1D2cB/CMGYtdr9txmpL1AWz7qftYTd2PNAVrmuwr58A9p+m3wBVAuojMFZE3RORyEUmq3aRqk9zymWee8dCi5MRq6h7OA/j443/jet3JHmmy/dR9rKZmkja45zQFa2qH59xzml4FegMfAAdiMoB/DuwKOFH/FpFTXWorZqlNcsuRI0d6aFFyYjV1D8dpWrFik+t1J7vTZPup+1hN3Y80BWtqI03u5Wn6EeiiqmUAInIgcBVwJWYT3/8ATwKHu9RewnDFFVf4bULCYTV1D+cB3LhxO9frTnanyfZT97Gauu80OZqqWqcJ3Is0/RcYLCL/JyJnq2qOqo5T1acCkZfDAPdnkiYAa9eu9duEhMNq6h7OA3jHjhLX6052p8n2U/exmrrvNDmabt9uUr6IwBFHuFN3POKK06Sqy1X1UWA4sF8yF1XdqqrL3WgrEkSkjYikikhu4EgVkQMiuH6giKiIPO+VjY0aJdW0r6hgNXUP5wFcUODunjRFRWZfQUhep8n2U/exmrrvNDmaOlGmQw+FZJY5bKdJRNqJSPPqyqjqOlX9MhIDROSUSMpHyEfAOZgo1/WB16nhXCgitwIXAZu9Mc3Qrp37wx7JjtXUPcq3ZXBhP4YgNgfuqiZNzNYbyYjtp+5jNXXfaXI0tUNzhkgiTWXAUBE5zK3GReTPwHNu1Veh7vYYR+kxVf0y4Mw9DtxUk6MmIkcAfYH7gOLqytaVpUuXell9UmI1dQ/nAZyXVw8XNg/4lWRPbAm2n3qB1dR9p8nR1OZoMoTtNKnqduAfwFgReUREaj20JyLHiMgQzGRxT5wm4GIgV1WXOG+o6mIgF7ikGtvqYaJRPVQ1rA23RKSxiLRyDqBluEb+4Q9/CLeoJUyspu7hLF9Wrcfu3e7Vm+zzmcD2Uy+wmrqf3NLRNNnzqjlE5PioajZwA9ABWC0ir4nI2SI1f1cMOBQ3ikgqkA4sUdWHVbW0NoaHwaHAtkre3xb4rCr+AZRgUiiEy2sYZ8w5NgGsW7eO7t27U1RU9GuCsE6dOrF582aGDBlCeno6r7zyChMmTCAzM5PevXuTl5cXUnbnzp3069eP5cuXM3nyZKZNm8ayZcsYOHAg27dvDylbUFBASkoKa9asYezYscyZM4dFixYxfPhwNm7cGFK2tLSULl26sH79elJTU1mwYAFpaWmMHj2arKwsevTowd69e0Ou2bJlC4MHDyY9PZ0ZM2YwceJEVq5cSZ8+fcjNzQ0pu2vXLvr27cuKFSuYNGkS06dPZ+nSpQwaNIitW7eGlC0sLCQlJYWsrCzGjBnD3LlzWbhwISNGjGDDhg107tyZsrIyOnXqRFlZGZ07d2bDhg2MGDGChQsXMnfuXMaMGUNWVhYpKSm8//77IfVv3bqVQYMGsXTpUqZPn86kSZNYsWIFffv2ZdeuXSFlc3Nz6dOnDytXrmTixInMmDGD9PR0Bg8ezJYtW0LK7t27lx49epCVlcXo0aNJS0tjwYIFpKamsn79erp06UJpaWnINRs3bmT48OEsWrSIOXPmMHbsWNasWUNKSgoFBQUhZbdv387AgQNZtmwZ06ZNY/LkySxfvpx+/fqxc+fOkLJ5eXn07t2bzMxMJkyYwMyZM0lPT2fIkCFs3rw5pGxRURHdu3dn7dq1fPzxx6SlpTF//nxGjhxJdnY2Xbt2paSkhE6dOtGkCdSvbyaBDxo0lsWLFzN79mzGjRvH6tWr6dmzJ7t37w6pf8eOHQwYMICMjAymTp3KlClTyMjIoH///uTk5NCpU6dfH8Dt2hXTq1cvMjMzGT9+PLNmzWLJkiUMHTp0P7uLi4vp1q0b69atY9SoUcybN4958+YxatQo1q1bR7du3SguLt7vXhs6dChLlixh1qxZjB8/nszMTHr16kV+fn5I2ZycHPr3709GRgZTpkxh6tSpZGRkMGDAAHbs2BFSdvfu3fTs2ZPVq1czbtw4Zs+ezeLFixk2bBibNm0KKVtSUkLXrl3Jzs5m5MiRzJ8/n7S0NJ599lnWrl1b4zNi5syZ9hkR5jPivvvuC+sZUVhYmLDPiG3bvgfgl1/KXHlGPPvss6SlpZGRYf6dNmmyM+QZ4VyzadMmhg0b5tozwimbn5/v+TMiNTWsWTtAHTbsFZHfAH8HbsU4GenAT8AujOPQCGgbOI4DzgS2A0OA91R1Ry3bfQuTB6o6LgCuAx5U1ZChOBHJAoaoatdK6j4PmAacq6qbA+9lA71UtVc1NjUGgid9tAQ2hbNhr8US67RrZyZtL18OZ57pTp1/+xv07g2vvgpdurhTp8VigexsOO44s0/n3r3u1Xv11TB3LqSmmr0DE4mobNirqt+o6p+AdsBDwDKMg3QZcA/wB4yjVAx8gsnZdISq/ru2DlOAvkD7Go6VmE2EK5sVeDCwtYq6LwMOATaISImIlADHACkB56lSVLVIVfOcA8gP95exaf/dx2rqLm7PkQA7PAe2n3qB1bR8SL2oyB2nydH055/Nz4e5Nqs5Pql1pCnWCUwEzwQuUtWvAu9dBCwGTlXVNZVccyAmp1QwMzFznIZVdk0VbbcCcsOJNBUWFtLUi+2+kxirqbtcdBF89RVMngw33+xOnRdeCOnpMGkSJOs0FNtP3cdqCmVl0KCBSUb5888mRUBdcDRt08Z8cfruOzjtNFdMjRmiEmmKdVR1FTADk3Szg4h0AAYDU4OdHxFZLSK3Ba7JUdWVwQcmUrYlXIcpUt5//30vqk1qrKbuYiNN3mD7qftYTaFePTD//925Z99//30KC8vrOjzJ9/VIWKcpwH3ACmBW4FgO/LlCmVOA1lG261duueUWv5pOWKym7uK201RSAlsDA+TJnFnY9lP3sZoa3Lxnb7nlFrZsMa+bNCl3yJKVhHaaVHWnqt6vqq0Cx/2quqtCGVHV4dXUcWx1k8DryrJly7yqOmmxmrqL207Ttm1mCKFePTj4YHfqjEdsP3Ufq6nBzXt22bJlIfOZkjWvmkNCO03xwMHJ/F/DI6ym7uK20+R8a23XDurXd6fOeMT2U/exmhrcvGcPPvjgXzP4J/skcLBOk+80buzu9hQWq6nbuO002VU4BttP3cdqanDznm3cuLG9Z4OwTpOLiMjTIpIJfBXuNXZXbvexmrqLdZq8wfZT97GaGtzMCr527Vp7zwZhnSYXUdV+qnoacGG413Ts2NE7g5IUq6m7WKfJG2w/dR+rqcHNe7Zjx472ng3COk0+E0n6dkt4WE3dxTpN3mD7qftYTQ1Ogks37tnU1FR7zwZhnSafee211/w2IeGwmrqLV05TXZPuxTu2n7qP1dTg5j372muv/XrPJnuOJrBOk++88847fpuQcFhN3cVGmrzB9lP3sZoa3Lxn33nnHXvPBpGw26j4SSTbqJSVlVGvnvVd3cRq6i4//2y+YdarZxJT1jVPy7HHwvr18OWX0KGDKybGJbafuo/V1DB5stme6MILYcmSutW1d28ZTZsaTbdtS8zcanYblTiii93i3XWspu7ifGstK4Pdu+tWl7MfFthvrbafuo/V1OBmpOnf/+4LmP3sDjyw7vXFO9Zp8pk//7niri6WumI1dZcmTaBRIxORrutD+JdfYN8+8zrZ5zTZfuo+VlODm07TZZfdBZj71QbxrNPkO2lpaX6bkHBYTd1FBJo02QvU/SHsRJnatIFkz0No+6n7WE0NwU5TXWfgzJ27CrCRYQfrNLlIbZJbnnDCCR5alJxYTd3HrV3T7dBcObafuo/V1OA4Tfv2QWFh3epq2PBowN6zDtZpcpHaJLcsKiry0KLkxGrqPs2bmzE16zS5h+2n7mM1NbRoUT6UVtd7dutWU5G9Zw3WafKZ7du3+21CwmE1dZ9GjQqAuj+Anc167QPY9lMvsJoa6tVzLzr8009lgM3R5GCdJp8599xz/TYh4bCaus8RR7QAbKTJTWw/dR+raTluZQVXbQfYe9bBOk0+M3nyZL9NSDispu7zyy/rAOs0uYntp+5jNS3HrRV033+/B7D3rIN1mnzmqaee8tuEhMNq6j6XXHIa4J7TlOzpBsD2Uy+wmpbjOE2//FK3ekpLDwGs0+RgnSafSUlJ8duEhMNq6j7Ll88HbKTJTWw/dR+raTluDM+VlsLWrSZngb1nDdZp8pnXX3/dbxMSDqup+9x++1WAdZrcxPZT97GaltO2rTnv3Fn7OrZvB9V6iMAhh7hjV7xjnSaf6dSpk98mJBxWU/f5/POJQN2cpj17ID/fvLZOk+2nXmA1LceJNNXFaXK+5BxyiNlGxWKdJlepTXLLxx9/3EOLkhOrqfvcemtHoG5Ok5NuoFkzaNmyzibFPbafuo/VtBw3Ik02Mrw/1mlykdokt/z00089tCg5sZq6z7fffgHUzWkKfgCL1N2meMf2U/exmpbjOE11mQju3LM2R1M51mnymfPOO89vExIOq6n7XHDBSYA7TpNdOWew/dR9rKbluBFp2rzZnG2kqRzrNPnM1q1b/TYh4bCaus/evWZsrS4bgNpQfyi2n7qP1bQcN+c02Xu2nIR2mkSkjYikikhu4EgVkQPCuK69iEwOXJMvIotF5GgvbNy3b58X1SY1VlP3adjQJLgrK4Pdu2tXh30Ah2L7qftYTctxc3jO3rPlJLTTBHwEnANcHzjOAVKru0BETgAWAKuBjsDZwNvAXi8MtLtyu4/V1H3atz+ORo3M69o+hO0DOBTbT93HalpO8PCcjQ67R8I6TSLSHuMoPaaqX6rql8DjwE0icko1l3YGpqvqK6r6jaquU9VpqrrNCzu/+OILL6pNaqym7jNv3hd1niNhH8Ch2H7qPlbTcpz7dd8+KCioXR32nt2fhHWagIuBXFVd4ryhqouBXOCSyi4QkXrA74HvRWSmiGwTkSUicqtXRt5///1eVZ20WE3d5/777//1IZyTU7s6nJQD9gFssP3Ufaym5TRvXp5bqTZfdFTtPVsZiew0HQpUFh3aFvisMg4BWgCvAjOA64CJwAQRuaKqhkSksYi0cg4g7Cw0ffv2DbeoJUyspu7Tt29fDjzQvK6t02RXz4Vi+6n7WE3LEanbvKadO02UCuw9G0zcOU0i8paIaA3H+YHilY3kShXvQ7ken6pqT1XNUNWuwFTgr9WY9RomguUcmwDWrVtH9+7dKSoq+jVTbadOndi8eTNDhgwhPT2dCy64gAkTJpCZmUnv3r3Jy8sLKbtz50769evH8uXLmTx5MtOmTWPZsmUMHDiQ7du3h5QtKCggJSWFNWvWMHbsWObMmcOiRYsYPnw4GzduDClbWlpKly5dWL9+PampqSxYsIC0tDRGjx5NVlYWPXr0YO/evSHXbNmyhcGDB5Oens6MGTOYOHEiK1eupE+fPuTm5oaU3bVrF3379mXFihVMmjSJ6dOns3TpUgYNGsTWrVtDyhYWFpKSkkJWVhZjxoxh7ty5LFy4kBEjRrBhwwY6d+5MWVkZnTp1oqysjM6dO7NhwwZGjBjBwoULmTt3LmPGjCErK4uUlBReeumlkPq3bt3KoEGDWLp0KdOnT2fSpEmsWLGCvn37smvXrpCyubm59OnTh5UrVzJx4kRmzJhBeno6gwcPZsuWLSFl9+7dS48ePcjKymL06NGkpaWxYMECUlNTWb9+PV26dKG0tDTkmo0bNzJ8+HAWLVrEnDlzGDt2LGvWrCElJYWCgoKQstu3b2fgwIEsW7aMadOmMXnyZJYvX06/fv3YuXNnSNm8vDx69+5NZmYmEyZMYObMmaSnpzNkyBA2b94cUraoqIju3buzdu1aPv74Y9LS0pg/fz4jR44kOzubrl27UlJSEnLNQw89xO7d6wFYuHAV48aNY/Xq1fTs2ZPdu3eHlN2xYwcDBgwgIyODqVOnMmXKFNLTM9i+3dwsH3/87q9l8/Pz6dWrF5mZmYwfP55Zs2axZMkShg4dup/dxcXFdOvWjXXr1jFq1CjmzZvHvHnzGDVqFOvWraNbt24UFxfvd68NHTqUJUuWMGvWLMaPH09mZia9evUiPz8/pGxOTg79+/cnIyODKVOmMHXqVDIyMhgwYAA7duwIKbt792569uzJ6tWrGTduHLNnz2bx4sUMGzaMTZs2hZQtKSmha9euZGdnM3LkSObPn09aWhonnHACa9eurfEZMXPmTPuMCPMZAYT1jCgsLEyKZ0RZ2Q4A3nsvNeJnRKdOQwFo0aKIL7+s+RmxadMmhg0bxuLFi5k9e3bEz4iMjAz69+9PTk5OSNloPCNSU6ud6hyKqsbVARwEnFrD0QR4BNhVyfW7gIerqLsRUAy8XuH9bsDCamxqDLQKOo4ANDc3V2vi7bffrrGMJTKspu7z9ttv66OPqoJqp06RX79xo7m2QQPV0lL37YtHbD91H6tpKJdcYu678eMjv3bmTHPtIYdsdd+wGCM3N1cxwZRWWoMPEne7yajqDmBHTeVE5EugtYhcqKpfBd67CGgNLKqi7n0ikg5UnCh+MrC+GpuKgKKgtmsy71eeffbZsMtawsNq6j7PPvssnTub17UZnnOG5tq1g3pxF9/2BttP3cdqGkpdFm84iS3POKONewYlAAn7+FLVVZh5SYNFpIOIdAAGA1NVdY1TTkRWi8htQZf2AO4WkcdF5EQReQa4GXjfCztHjBjhRbVJjdXUfUaMGFGnOU12Fc7+2H7qPlbTUJwEl7WZ0+Tcs7t3/+CeQQlAwjpNAe4DVgCzAsdy4M8VypyCiT4BoKoTMfOXXglc+xhwh6ou8MLAK6+80otqkxqrqftceeWVvzpNtfnWap2m/bH91H2spqHUZcWrE2k666yD3DMoAUhop0lVd6rq/araKnDcr6q7KpQRVR1e4b2hqnqSqjZV1XNU1bNdILOysryqOmmxmrpPVlZWnR7AztJluwqnHNtP3cdqGoobX3RUN7tnUAIQd3OaEo2mTZv6bULCYTV1n6ZNm+LIWpdvrXa39HJsP3Ufq2koBwWCRDtqnAW8P849e+ihZe4ZlABYp8lnDnS+Clhcw2rqPgceeKArTtMRR7hnU7xj+6n7WE1DqYvT5ESajjuuiXsGJQAJPTwXD2RkZPhtQsJhNXWfjIyMX0P9v/xiNu6NhJ9+MmcbaSrH9lP3sZqGUlunSbX8i862bRmu2hTvWKfJRUTkaRHJBL4K95qbb77ZQ4uSE6up+9x8882/zmkqK4Pc3Miut8Nz+2P7qftYTUOprdP0yy/l2cDvvddOrg/GOk0uoqr9VPU04MJwr/nggw88tCg5sZq6zwcffEDjxmY/K4hsiK64GLYFNjSyw3Pl2H7qPlbTUBynKScnsuiw8yWnbVsYOdJqGoyoVrWjiKW2BPafy83NzaVVq1Z+m2OxuMYxx8CGDbB4MVx0UXjXbNwIRx9tNg8tKrLJLS2WaLFvHzRubF7n5JSnIKiJ2bPhuuvg9NNh5Urv7IsV8vLyaN26NUBrVc2rrqx9fPmMsweOxT2spu7jaFqbtAPOt9bDDrMOUzC2n7qP1TSURo3A+d4eyRBd8HC61TQU+wjzmZdfftlvExIOq6n7OJoefLD5uTYPYDs0F4rtp+5jNd2f2sxrCk5GazUNxTpNPtOnTx+/TUg4rKbu42h6yCHmZ2eOUjjYlXOVY/up+1hN96c2TlNwpMlqGorN0+Qzt956q98mJBxWU/dxNHUiTdu3h3+tXTlXObafuo/VdH/qGmm64YZbXbcpnrGRJp9ZunSp3yYkHFZT93E0rU2kyQ7PVY7tp+5jNd2fukaarKah2EiTi4jI08DTROCMHmo343Idq6n7OJrWJtJkh+cqx/ZT97Ga7k9dI03FxVbTYGykyUVqk6epQQPrt7qN1dR9HE3rEmmyTlMotp+6j9V0fyJ1moKzgR9+uNW0ItZp8pkff/zRbxMSDqup+zia1mVOkx2eC8X2U/exmu5PpE7Trl0mnxqYSJPVNBTrNPnM5Zdf7rcJCYfV1H0cTSONNBUUmIcw2EhTRWw/dR+r6f44X3TCvWedLzlt2kCTJlbTilinyWc++ugjv01IOKym7uNo6jhNBQWwZ0/N1zkP4GbNypPsWQy2n7qP1XR/2rUz561bwysfPJ8JrKYVsduoeEAk26iUlpZSv3796BiWJFhN3cfRVBWaNjXh+x9/hGOPrf66efPgiivgpJPg+++jYmrcYPup+1hN9+fHH+H44819u2cPiFRffsQIePBBuOYas51KMmhqt1GJI7p06eK3CQmH1dR9HE1FyqNN4cxrsivnqsb2U/exmu6PE2kqLIT8/JrLB297BFbTilinyWdef/11v01IOKym7hOsaSRzJOzKuaqx/dR9rKb706wZtGxpXoczRLdpkzkfeaQ5W01DsU6Tz9jNEN3Hauo+wZpGEmmyK+eqxvZT97GaVo4TbdqypeayGzea81FHmbPVNBTrNLmIiDwtIpnAV+Fe8+CDD3poUXJiNXWfYE2dSFM431rt8FzV2H7qPlbTynFyfoZzz1Z0mqymoVinyUVqk9xyzpw5HlqUnFhN3SdY00gewDbSVDW2n7qP1bRy6hJpspqGYp0mnzn55JP9NiHhsJq6T7CmTtTIcYiqw85pqhrbT93Halo54X7RKSwsT4LpOE1W01Cs0+QzhYWFfpuQcFhN3SdY03CdprKy8m+tzqRSSzm2n7qP1bRywo00OZPAmzUzyS3BaloR6zT5TE5Ojt8mJBxWU/cJ1tRxmpz5SlWxdSvs2wf16tnhucqw/dR9rKaVE26Cy+ChOSefk9U0lIR2mkSkjYikikhu4EgVkQNquKaFiPQVkU0iUigiq0TkSa9sPPvss72qOmmxmrpPsKbBkabqcuOuX2/ORxwBDRt6aFycYvup+1hNK8cZnqsp0lRxPhNYTSuS0E4T8BFwDnB94DgHSK3hmp6BsvcD7QM/9xGRP3hh4NSpU72oNqmxmrpPsKaO07R3b/m+cpXhOE3HHOOdXfGM7afuYzWtnNpEmhyspqEkrNMkIu0xzs9jqvqlqn4JPA7cJCKnVHPpxcCHqpqmqtmqOgj4FjjfCzuffNKzIFbSYjV1n2BNmzSBtm3N6+rmNVmnqXpsP3Ufq2nlOF90fv7ZzDWsCmdOU7DTZDUNJWGdJozzk6uqS5w3VHUxkAtcUs11C4BbROQIMVwJnAzMrOoCEWksIq2cA2gZrpHvvvtuuEUtYWI1dZ+KmoYzGdw6TdVj+6n7WE0r57DDzNzC4uLqo03Z2eZ89NHl71lNQ0lkp+lQoLKNHrYFPquK54BMYBOwD5gBPKWqC6q55jWMM+YcmwDWrVtH9+7dKSoq+jWraqdOndi8eTNDhgwhPT2dCy64gAkTJpCZmUnv3r3Jy8sLKbtz50769evH8uXLmTx5MtOmTWPZsmUMHDiQ7du3h5QtKCggJSWFNWvWMHbsWObMmcOiRYsYPnw4GzduDClbWlpKly5dWL9+PampqSxYsIC0tDRGjx5NVlYWPXr0YO/evSHXbNmyhcGDB5Oens6MGTOYOHEiK1eupE+fPuTm5oaU3bVrF3379mXFihVMmjSJ6dOns3TpUgYNGsTWrVtDyhYWFpKSkkJWVhZjxoxh7ty5LFy4kBEjRrBhwwY6d+5MWVkZnTp1oqysjM6dO7NhwwZGjBjBwoULmTt3LmPGjCErK4uUlBReeumlkPq3bt3KoEGDWLp0KdOnT2fSpEmsWLGCvn37smvXrpCyubm59OnTh5UrVzJx4kRmzJhBeno6gwcPZsuWLSFl9+7dS48ePcjKymL06NGkpaWxYMECUlNTWb9+PV26dKG0tDTkmo0bNzJ8+HAWLVrEnDlzGDt2LGvWrCElJYWCgoKQstu3b2fgwIEsW7aMadOmMXnyZJYvX06/fv3YuXNnSNm8vDx69+5NZmYmEyZMYObMmaSnpzNkyBA2b94cUraoqIju3buzdu1aPv74Y9LS0pg/fz4jR44kOzubrl27UlJSEnLNQw89xLBhw1i8eDGzZ8+mfn0zOWLYsJns3r07pOyOHTsYMGAAK1bkArBr17dkZGTQv39/cnJyQsrm5+fTq1cvMjMzGT9+PLNmzWLJkiUMHTp0P7uLi4vp1q0b69atY9SoUcybN4958+YxatQo1q1bR7du3SguLt7vXhs6dChLlixh1qxZjB8/nszMTHr16kV+fn5I2ZycHPr3709GRgZTpkxh6tSpZGRkMGDAAHbs2BFSdvfu3fTs2ZPVq1czbtw4Zs+ezeLFixk2bBibNm0KKVtSUkLXrl3Jzs5m5MiRzJ8/n7S0NE444QTWrl1b4zNi5syZ9hkR5jMCCOsZUVhYmFTPiK5dO3H44UafL774scpnxLp15h/aUUft+/UZccIJJ4T1jNi0aVPIM2LcuHGsXr2anj17VvmMyMjIYOrUqUyZMsXXZ0Rqak2zdoJQ1bg6gLcAreE4H/gnsKaS67OAV6up/2VgDXAzcBbwDJAPXFPNNY2BVkHHEYDm5uZqTbz99ts1lrFEhtXUfSpq+tBDqqD6zjtVX3PGGabMjBkeGxen2H7qPlbTqvntb839OG5c5Z+XlKg2bGjKrF9f/n4yaJqbm+v4Dq20Bh+kQfjuVczQFxhdQ5lsjMPTrpLPDgYqDVCKSFPgHeA2VZ0WeHu5iJyDcab+V9l1qloEFAXVU4N55TzxxBNhl7WEh9XUfSpqWtPwnKodnqsJ20/dx2paNc48pQ0bKv/8p5/M8F3DhqEpQqymocTd8Jyq7lDV1TUce4EvgdYi8uuWJiJyEdAaWFRF9Q0DR8WpcqV4pNWECRO8qDapsZq6T0VNHafJmThakV27ID/fvA6eH2Epx/ZT97GaVo1zH1blNDlDc8ceC/Xrl79vNQ0l7pymcFHVVZj5SINFpIOIdAAGA1NVdY1TTkRWi8htgWvygC+AHiLSUUSOE5GHgAeAiV7YecEFF3hRbVJjNXWfipoed5w5//hj5eWzssz5sMNMdmHL/th+6j5W06pxnCYnrUBFHKfp+OND37eahhKPw3ORcB/QG5gV+HkyZo5SMKdgok8O9wBdgFFAW2A98C9ggBcG/vzzz15Um9RYTd2noqbOg3XtWjMUV3FE+vvvzdluW1U1tp+6j9W0amoanqvKabKahpLQTpOq7sQkqayujFT4eQvwsJd2BVNaWhqtppIGq6n7VNT02GONo7R7t9ng8+CDQ8tbp6lmbD91H6tp1YQ7PFfRabKahpKww3PxwrHHHuu3CQmH1dR9KmrapEn5ZNG1a/cv7zhNp1SXRjbJsf3UfaymVeNEmrZtM9n8K1KV02Q1DcU6TT4zf/58v01IOKym7lOZpiecYM7OwzYYG2mqGdtP3cdqWjVt20KLFua1k8TSQRVWrzavTzwx9DOraSjWaXIREXlaRDKBr8K95t577/XQouTEauo+lWkaPK8pGFXrNIWD7afuYzWtGpHyyO+qVaGf/fQT5OZCgwZw6qmhn1lNQ7FOk4uoaj9VPQ24sMbCAd5//30PLUpOrKbuU5mmjtNUMdL088+wZ49ZtuyssrPsj+2n7mM1rZ7TTjPnik7TypXmfPLJ0KhR6GdW01Cs0+Qzr7/+ut8mJBxWU/epTNOqhuecMP+xx+7/ALaUY/up+1hNq6d9e3POzAx933Gazjhj/2uspqFYp8lnnD1wLO5hNXWfyjR15j6sWmWG5ByWLTPns8+OgmFxjO2n7mM1rZ6aIk2nn77/NVbTUESDn3YWVxCRVkBubm4urVq1qrZsXl5ejWUskWE1dZ/KNC0shFatoKTELGN2VufcfTeMHQtdusCrr/pgbJxg+6n7WE2r5/vvzbympk1NupB6gbDJ+efD0qUwfjzcfnvoNcmgaV5eHq1btwZoHUhyXSU20uQzw4cP99uEhMNq6j6Vadq0aXk4/+uvy99PTzdnm0i4emw/dR+rafUcf7wZMi8sLM/XVFpaPlxX2fCc1TQU6zT5zDXXXOO3CQmH1dR9qtL0/PPN2XGaduwo31rlvPOiYFgcY/up+1hNq6dBg/IVrcuXm/PSpcaJat26fJ5iMFbTUKzT5DOrnVmzFtewmrpPVZo6TpMTXXKcp5NOggMO8N6ueMb2U/exmtbMJZeY8//+F3q+8srQjXodrKahWKfJZ5o3b+63CQmH1dR9qtI0ONKkCp9/bn6+MOykG8mL7afuYzWtmd/9zpxnzjTnOXPMuaqAktU0FOs0uUhtklu2bdvWQ4uSE6up+1Sl6ZlnmizDv/xiHsIjR5r377gjisbFKbafuo/VtGauvtpElL7/3qyiW7jQvF+V02Q1DcU6TS5Sm+SWy52BZYtrWE3dpypNGzWChx4yr2+4ATZvhgMPhN//Pnq2xSu2n7qP1bRmWreGDh3M63vugaIis/K1quz9VtNQrNPkMzfccIPfJiQcVlP3qU7TZ58N/fm++2xSy3Cw/dR9rKbh8fDD5uz4Q2+/bbZZqQyraSjWafKZoUOH+m1CwmE1dZ/qND35ZHjySWjTxkSY/v73KBoWx9h+6j5W0/B45BH417/M6zvvhAceqLqs1TQUm9zSAyJJbmmxWCwWix9s3AhHHFGe5DJZsckt4wibot59rKbuYzV1H6up+1hNI+Ooo2p2mKymodhIkwdEEmkqKiqicePG0TEsSbCauo/V1H2spu5jNXWfZNDURpriiPfee89vExIOq6n7WE3dx2rqPlZT97GahmIjTS4iIk8DT2Oc0VM2btxYY6Rp3bp1HH/88dEwL2mwmrqP1dR9rKbuYzV1n2TQNC8vj6PMjuM1Rpqs0+QBInIEsMlvOywWi8VisYTNkar6U3UFrNPkASIiwOFAfg1FW2KcqyPDKFsdXxFBQs0Er8Nq6n4dVlP367Caul+H1dT9OpJJ05bAZq3BKWpQRwMslRAQvVpvFUDKs4nl1xQSrKGesrpcn0h1WE3dr8Nq6n4dVlP367Caul9HkmkaVt12Inhi0M/W4Tqx8rvESh1uECu/S6zU4Qax8rvESh1uECu/S6zU4Qax8rvUuQ47POcjTmoCwph8ZgkPq6n7WE3dx2rqPlZT97Ga7o+NNPlLEfCfwNniDlZT97Gauo/V1H2spu5jNa2AjTRZLBaLxWKxhIGNNFksFovFYrGEgXWaLBaLxWKxWMLAOk0Wi8VisVgsYWCdJovFYrFYLJYwsE6TT4jIUyLyo4jsFZGlInKZ3zbFEyJyuYhMEZHNIqIicmuFz0VE3gp8XigiaSJyuk/mxjwi8pqIpItIvohsE5FJInJKhTJW0wgQkSdFZLmI5AWOL0XkhqDPrZ51JNBvVUR6Bb1ndY2AgFZa4dgS9LnVMwjrNPmAiNwN9AI6A78B5gOficjRftoVZzQHvgWeqeLzV4AXA59fAGwBZotIy+iYF3dcgUn81gG4FrNbwCwRaR5UxmoaGZuAV4HzA8dc4NOgfzhWzzogIhcAfwGWV/jI6ho53wGHBR1nBn1m9QxGVe0R5QNYAvSv8N4qoIvftsXjAShwa9DPAvwM/CPovcbALuAJv+2NhwM4OKDr5VZTV3XdCTxq9ayzji2A74FrgDSgV+B9q2vkWr4FZFTxmdWzwmEjTVFGRBoB5wGzKnw0C7gk+hYlJMcBhxKksaoWAV9gNQ6X1oHzzsDZaloHRKS+iNyDiZB+idWzrvQDpqnq/yq8b3WtHScFht9+FJHRInJ84H2rZwXshr3R5yCgPrC1wvtbMZ3TUnccHSvT+Jgo2xJ3iNml811ggaquDLxtNa0FInImxklqAuwGblPVTBFx/uFYPSMk4Hyeixkqqojtp5GzBHgAE7lrB7wOLAoMI1s9K2CdJv+omIpdKnnPUjesxrWjL3AWcGkln1lNI2MNcA5wAHAH8KGIXBH0udUzAkTkKOA94DpV3VtNUatrmKjqZ0E/rhCRL4G1wIPAYqdYhcuSVk87PBd9dgCl7B9VOoT9vXlL7XBWfliNI0RE+gC3AFeq6qagj6ymtUBV96nqD6r6taq+hlm88DesnrXlPIxGS0WkRERKMIsYngu8drSzutYSVd0DrABOwvbT/bBOU5RR1X3AUswKpWCuBRZF36KE5EfMzf6rxoG5ZFdgNa6UwLLivsDtwFWq+mOFIlZTdxDMRFqrZ+2Yg1nZdU7Q8TUwKvB6HVbXOiEijYH2mAngtp9WwA7P+cO7QKqIfI2Z7/AX4GhggK9WxREi0gI4Meit40TkHGCnqm4I5G35p4hkAVnAP4EC4KNo2xon9AP+BPwByBcR55tlrqoWqqpaTSNDRN4BPgM2Ai2Be4COwPVWz9qhqvnAyuD3RGQPkOPMv7O6RoaI/BeYAmzARJBeB1oBH9p+uj/WafIBVR0jIgcCb2ByYqwEblTV9f5aFlecD3we9PO7gfOHwENAd6Ap8D7QBjPZ8brAQ9eyP08GzmkV3n8YGB54bTWNjHZAKuYez8XkE7peVWcHPrd6eoPVNTKOBD7GLFLajpnH1CHo/5HVMwgJ5F2wWCwWi8VisVSDndNksVgsFovFEgbWabJYLBaLxWIJA+s0WSwWi8VisYSBdZosFovFYrFYwsA6TRaLxWKxWCxhYJ0mi8VisVgsljCwTpPFYrFYLBZLGFinyWKxWCwWiyUMrNNksVgsFovFEgbWabJYLFFDRA4RkcP8tiOaiMjfReSmOtbxR7fssVgstcc6TRaLJSqIyLGYjYF3+2xKtHkXeFJErq/NxSJyCfCguyZZLJbaYJ0mi8XiOSLSEhgJvFDZRp8i0kFEroi+Zd6jqqXAn4EUEWlXiyruA0ZV9oGI3Cki34pIvoioiBSKSLOaKhSR20VkX+CajSKSISIn1sI2iyWpsE6TxWKJBu8CH6rqpio+nwQ8FT1zoouq7gRGAz0iuU5EGgA3Ap9WUe8nqno20AVIB5oAx9dQ54HAbUBDYKqqHqWq56jqD5HYZrEkI9ZpslgsniIivwGuBIZV8Xl7oB2wKJp2+UBf4OYIIzrXAwtUtaCGchcAHwZen1BD2ZeBZYHX0yOwxWJJeqzTZLFYvOYVYJiqllTx+aWB87wo2eMLqvoLMBd4NILLqhyacxCR+pgIU0bgrSqdMhH5HbAYODfw1ucR2GKxJD3WabJYLJ4hIq2AW6k+onEZkAt8Gw2bfGYeZmisRkSkBdAB+F8NRc/DRI7WBn6uNNIkIs2Ba1T1U6Aj8LOqrg7HFovFYrBOk8Vi8ZJrgFJgefCbInKPiHwtIl8D9wPFwFeB9y6KlnEicraIpIrIAhG5SUTaiEgvEekvIhNF5ByXm5wHnBLmhPDbgSnVROgcOgKfq+oWYA9VD8+9jJmMfiJwJDbKZLFEjHWaLBaLl1wCpAdWkP2Kqo5W1fMxURcB/quq5weOJVG072/Aw8AMYCgwGDNZeyzweyIbSguH7MD57DDK1jg0F+C3lM8HW0clw3MBRzQ74FhdGXjbOk0WS4RYp8lisXhJe+Cnaj53/oF/EQVbQhCRE4DNgUjO4UBb4B1V/Qk4EJNPaorLze7CRN6OrcG2dsAxNTmQgdV1DYImiq8Fjg6875RpBPxJVZ2J4o7mcyO23mJJcqzTZLFYvOQIjKNQFR0xQ0pfR8OYCrQDxgdeX4pZpbYMfl3K31ZVZ7nZoKoqZv5W6xqK3gOMCaPKCwjVbi3QADgm6L2/Ab2Dfu4IbFDVdWHUb7FYgmhQcxGLxWKpNS0wTkJVdAQWhjFvx0mQ+QnQOEIbXlXVxRXfVNVFgXoPAs4A/i/CemtLETX/DvdhEmLWREdCh9mcyeAnAmtF5DSgSFXXAojIKcBhlKcnsFgsEWCdJovF4iWlQKPKPhCRo4DjgA/CqSiQSfx37pn2K1di5lWlRXKRiFwGrAykEoiEtlSzlYyInAyIqq4Jo66LgZ5BP/+6gk5E6gFPAs8HfW6H5iyWOmCH5ywWi5fswjgJlbHffCYReUFExGujKrGjCJO/KBLupYa5SRUJLPtvTPXzvMKaAC4iDTHO1d6gt4PTDvwVGFJhEr6dBG6x1AHrNFksFi/Jpmqn6QJMJCodQESOB44NzPuJJlcCiys4H5Uiho8Dy/a3A9tF5CER+VuYbTmpBqqLIt2N2XKlJi4ioF0Q64ES4AqgjapmVPj8CmCtqm4Mo36LxVIB6zRZLBYvWY4ZgquMncAuVd0XSILZBXgrWoYBiMihwKmEOTQXcOi6Aa9inL5/YXIehTtH6GIgD1hZhT0dMJO0t9Rgd3PgNSCngn0lGMepFZBS4ZpzMU7b/DBttVgsFbBOk8Vi8ZJ5wJkickAln70HfCMio4F+wL9rMT+orrQDtmLyMoXLj0AWZpJ7A+AbVd0V5rWXA9NVtayKz6sdmhORJiKyDNiG2ci3t4isC8yDckgHHnciZyLSXUS+AxYEPr9LRFaIyEth2myxWAJI9CPhFoslWQhMRt4MPKaqU/22p64E5lt9CbyBiRp9iFnSv0tV/1PDtfWAH4BnVHW/bWUCuZV+AM4MTHq3WCwxhl09Z7FYPENVy0TkA0zeobh3mgLDcx0AROQW4ABVfSHMy+/E5KT6rIrPrwOWWIfJYold7PCcxWLxmveA60WkqrlN8co4YEME5V8F/lbNRPdwt02xWCw+YYfnLBaL54jIX4ELVfURv23xAxF5DThQVV+u4vPmQCZwoqoWR9U4i8USNjbSZLFYPEdVBwD1ReRBv22JNiLyO+AU4B/VFLsNM0HcOkwWSwxjnSaLxRItHgU6iEh7vw2JMj8DD1dIMlmRK4ARUbLHYrHUEjs8Z7FYLBaLxRIGNtJksVgsFovFEgbWabJYLBaLxWIJA+s0WSwWi8VisYSBdZosFovFYrFYwsA6TRaLxWKxWCxhYJ0mi8VisVgsljCwTpPFYrFYLBZLGFinyWKxWCwWiyUMrNNksVgsFovFEgbWabJYLBaLxWIJA+s0WSwWi8VisYTB/wP4ETvUW+E8AQAAAABJRU5ErkJggg==\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "theta = pi/2\n", "plot_h_particle(a, r0, theta, phi, umin, umax, plot_points=400)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 20 graphics primitives" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_spectrum_particle(a, r0, theta, legend_label=r'$h_+$') \\\n", "+ plot_spectrum_particle(a, r0, theta, mode='x', color='red', \n", " legend_label=r'$h_\\times$', offset=0.08)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Same thing for $\\theta=0$ (face-on view):" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "theta = 0\n", "plot_h_particle(a, r0, theta, phi, umin, umax, plot_points=400)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 20 graphics primitives" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_spectrum_particle(a, r0, theta, legend_label=r'$h_+$') \\\n", "+ plot_spectrum_particle(a, r0, theta, mode='x', color='red', \n", " legend_label=r'$h_\\times$', offset=0.08)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Signal-to-noise ratio in LISA detector for emission from Sgr A*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The factor $\\mu/r$, with $\\mu = 1 M_\\odot$ and $r$ equal to the distance to Sgr A*:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5.893577116499728e-18" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from kerrgeodesic_gw import astro_data\n", "mu_ov_r = astro_data.solar_mass_m / astro_data.SgrA_distance_m\n", "mu_ov_r" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The mass of Sgr A* in seconds:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "20.19522512635793" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "BH_time_scale = astro_data.SgrA_mass_s\n", "BH_time_scale" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The strain spectral sensitivity of LISA detector:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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euRr/93/7EBBA+P33mEaV23766SdVU+n2n1Gu3HbNNdfIltt69uwpOZXOGJMst918881O5bbWrVuLptIBGFpue/nllzWX24YPH849lS7oKpXbevfurVhu69Spk+RUuv14ClPpXl5eTlPpgwYNEtnv37+/4eW2Tz/9VFO5DYCqctugQYNcltuEsZEqt3Xq1Em23AbACSPuv/9+J4wQ7AsY8d577xlabmvVqpXmcluHDh24y22tW7fmKrcNGzZMttzWs2dPyXJb3759JTGiQ4cOIowA4IQRTzzxhKHlNvvvZWPKbR988IGqctsdd9zhstwGQLHc5ogRQrmtS5cuThgxYMAAJ4xo166dCCNef/11q3Hbky9ING57e3uTkeTt7U3nzxM9/DDR448T1dQ0zobe+ko6cjI1fEdeU8TdSBtaY64k54mvFM/omOvh0yy5LiczY9zNmOuu9LRiDO/YuJM8LdeV5Hrkup6N203+8vBPuaRekk6cOEFGkuBvyxYixogCAhpvQ099JR05mRq+I6+p4m6UDa0xV5LzxFeKZ3TM9fBpllyXk5kx7mbMdVd6WjGGd2zcSZ6W60pyPXLdWt3mQaRUbuvTpw8A48ptw4YNQ2JiIurqNuHVV3fj11/r8dNPgQ26POU2x1UGrqbS7T+jXLlt8ODBsuU2YWWD41R6nz59JMttP//8s1O5bcCAAaKp9D59+hhabvPz89NcbouKiuKeShd0lcptc+bMUSy3jR07VnIq3X48han0CRMmOE2lL1y4UGQ/PDzc8HJbSEiIpnJbnz59VJXbFi5c6LLcJoyNVLlt7NixsuW2Pn36OGHEiBEjnDBCsC9gRGBgoKHltv79+2sut33//ffc5bYBAwZwlduWLl0qW24LCgqSLLeFhYVJYsT3338vwog+ffo4YYS3t7eh5Tb772Vjym1Tp05VVW4bOnSoy3Jbnz59FMttjhghlNsmT57shBHh4eFOGPHtt9+KMMLf398qt3nyBYmZpPT0dDKS7P2VlRHdcANRly5E9fWNs6GXvpKOnEwN35HXlHE3wobWmCvJeeIrxTM65nr4NEuuy8nMGHcz5rorPa0Ywzs27iRPy3UluR65bs0kNRM6evRok/m77DJgyhRg5Upg2bLG2dBLX0lHTqaG78hryrgbYUNrzJXkPPGV4hkdcz18miXX5WRmjLsZc92VnlaM4R0bd5Kn5bqS3Gy5br0kNSHV1dU1qb/33we6dQMGDgRKSxtnQw99JR05mRq+I6+p4+5uG1pjriTnia8Uz+iY6+HTLLkuJzNj3M2Y6670tGIM79i4kzwt15XkZst16yXJzaTUk5SQkADAuJ6k3Nxcp36DO++cjLNngTfeSOfqSerYsaOqfgP7zyjXk/TXX3/J9iQxxiT7DdauXSvZk5SVleXUk7RhwwZRv0FCQoKhPUmnTp3S3JN06623cvcbCLpKPUlt2rRR7EkqLi6W7DewH0+h36C8vNyp3+Caa64R2b/88ssN70lq0aKFpp6khIQEVT1J11xzjcueJGFspHqSiouLZXuSEhISnDBi3759Thgh2Bcw4vz584b2JCUlJWnuSdq8eTN3T9KGDRu4epJuvvlm2Z4kxphkT1L79u0lMWLz5s0ijEhISHDCiCNHjhjak2T/vWxMT1JdXZ2qnqTdu3e77ElKSEhQ7ElyxAihJ6mqqsoJIzp06OCEESkpKSKMKC8vt3qSPPmCRE/S1KlTyUiS8zdlChFAlJLSeBta9JV05GRq+I48s8TdXTa0xlxJzhNfKZ7RMdfDp1lyXU5mxribMddd6WnFGN6xcSd5Wq4ryfXIdWsLAA+8pF6STp48SUaSnL/aWqKnnya6/36i6urG2dCir6QjJ1PDd+SZJe7usqE15kpynvhK8YyOuR4+zZLrcjIzxt2Mue5KTyvG8I6NO8nTcl1JrkeuW43bzYSmT59uCn8XXwzMmAHk5gLjxzfOhhZ9JR05mRq+I88scXeXDa0xV5LzxFeKZ3TM9fBpllyXk5kx7mbMdVd6WjGGd2zcSZ6W60pys+W6xx9w6ykkdcCt2WjIEGDSJCArC7jrrqZ+GossssgiiyxST9YBtx5ESo3bXl5eAIxr3O7Zs6diU+avv9ahTZvT+OKLKoSHSzdujxw5UlVTpv1nlGvc7tq1q2zj9uDBgyWbMr28vCQbt7t37+7UuN25c2dRU6aXl5ehjdt9+/bV3LgtXDxNmcKl1Lj9888/KzZuf/XVV5JNmfbjKTRl9uvXz6kpc8SIESL7Q4cONbxx+4cfftDUuO3l5aWqcXvEiBEuG7eFS6px+6uvvpJt3Pby8nLCiE8++cQJI4RLwIjvvvvO0Mbtt956S3PjdpcuXbgbtzt37szVuP3HH3/INm4PHjxYsnF7yJAhkhjRpUsXEUZ4eXk5YcQXX3xhaOO2/feyMY3bAwcOVNW43aNHD5eN215eXoqN244YITRuf/vtt04YMWzYMCeMePvtt0UY0a9fP6tx25MvSPQk2f/bCOLxFx9PBBCFhTXehlp9JR05mRq+I8+McdfThtaYK8l54ivFMzrmevg0S67LycwYdzPmuis9rRjDOzbuJE/LdSW5Hrlu9SQ1EwoLCzOdvzfeAD77DPjxR6C4uHE21Oor6cjJ1PAdeWaMu542tMZcSc4TXyme0THXw6dZcl1OZsa4mzHXXelpxRjesXEneVquK8lNl+ta37Ksq/EzSbt27SIjidff8eNEV15J1KtX422o0VfSkZOp4TvyzBp3vWxojbmSnCe+UjyjY66HT7PkupzMjHE3Y6670tOKMbxj407ytFxXkuuR69ZMUjOhPXv2mNLfNdcAEyYA8+YBf/7ZOBtq9JV05GRq+I48s8ZdLxtaY64k54mvFM/omOvh0yy5LiczY9zNmOuu9LRiDO/YuJM8LdeV5GbLdeslqQmpbdu2pvX35ZfAyy8D/fsDlZWNs8Grr6QjJ1PDd+SZOe562NAacyU5T3yleEbHXA+fZsl1OZkZ427GXHelpxVjeMfGneRpua4kN1uuWy9Jbial1W3R0dEAjFvdlp6ezr1yZf78eejbNx2HD9fjk09yGla3tW3bVtXKFfvPKLe6bcOGDbKr286ePSu5cmX58uWSq9s2b97stLptzZo1opUr0dHRhq5uO3z4sObVbVdeeSX3yhVBV2l1m+MzOK5uO3jwoOTKFfvxFFauHDlyxGnlyqWXXiqyf9FFFxm+uq2yslLT6rbo6GhVq9suvfRSl6vbhLGRWt128OBB2dVt0dHRThixc+dOJ4wQ7AsYcfLkSUNXt61atUrz6rY///yTe3XbmjVruFa3dejQQXZ129mzZyVXtxGRJEb8+eefIoyIjo52wojc3FxDV7fZfy8bs7qttLRU1eq2tLQ0l6vboqOjFVe3OWKEsLqtpKTECSMuuugiJ4yIj48XYYTwvbZWt3noBYmepFmzZpGR1Bh/f/xB1KIFUWZm42zw6CvpyMnU8B15nhB3LTa0xlxJzhNfKZ7RMdfDp1lyXU5mxribMddd6WnFGN6xcSd5Wq4ryfXIdetYEg+8pF6Sjhw5QkZSY/xVVxPddx/RM88Q1dWpt8Gjr6QjJ1PDd+R5Qty12NAacyU5T3yleEbHXA+fZsl1OZkZ427GXHelpxVjeMfGneRpua4k1yPXrcbtZkJz5swxvb9LLrEdWbJlCxAcrN4Gj76SjpxMDd+R5wlx12JDa8yV5DzxleIZHXM9fJol1+VkZoy7GXPdlZ5WjOEdG3eSp+W6ktxsuW4dS2IQecKxJErUrx+waBGQkwPccENTP41FFllkkUUWSZN1LEkzIaERzRP8+foCrVsDb7yxW3efSjpyMjV8R54nxb0xNrTGXEnOE18pntEx18On2vvdletyMjPG3Yy57kpPK8bwjo07ydNyXUlutly3ZpIMIqmZpOrqarRq1cqwZ9Dqb/FioGdPYMUK4L339POppCMnU8N35Hla3NXa0BpzJTlPfKV4RsdcD59q73dXrsvJzBh3M+a6Kz2tGMM7Nu4kT8t1JbkeuW7NJDUTmjx5skf5++gj4N579+Pbb4EzZ/TzqaQjJ1PDd+R5WtzV2tAacyU5T3yleEbHXA+fau93V67LycwYdzPmuis9rRjDOzbuJE/LdSW56XJda+e3dTV+ddu+ffvISNLDX1JSPrVpQzRwoH4+lXTkZGr4jjxPjLsaG1pjriTnia8Uz+iY6+FT7f3uynU5mRnjbsZcd6WnFWN4x8ad5Gm5riTXI9et1W0eREqbSQ4dOhSAcZtJBgYGatoobvz48cjPT8KLL67FlClA//5zXG4UZ/8Z5TaTHDt2rOxmkitWrJDcKG7YsGGSm0lOmDDBaTPJkSNHijaKGzp0qKGbSYaHh2veTHLbtm3cG8UJukqbScbHxytuJhkWFia5UZz9eAobxS1YsMBpo7jk5GSR/T///NPwzSRjY2M1bSY5dOhQVZtJJicnu9xMUhgbqc0kw8LCZDeTHDp0qBNGTJ061QkjBPsCRixdutTQzSRHjBiheTNJb29v7s0kR44cybWZ5JYtW2Q3k1yxYoXkZpJr166VxAhvb28RRgwdOtQJI4TPa9Rmkvbfy8ZsJhkVFaVqM8lJkya53Exy6NChiptJOmKEsJnk4sWLnTAiMTHRCSNGjRolwoiFCxdam0l68gWJmaT169eTkaSHv/Xr11NNDdG//030yCNE589r96mkIydTw3fkeWrc9dR1paMlvlI8o2Ouh0+197sr1+VkZoy7GXPdlZ5WjOEdG3eSp+W6klyPXLdmkpoJXXzxxR7n7+KLL0aLFra9k7KygEmTtPtU0pGTqeE78jw17nrqutLREl8pntEx18On2vvdletyMjPG3Yy57kpPK8bwjo07ydNyXUlutly3XpKakA4dOuRx/gQbjz8O/Pe/wMiRwMGD2nwq6cjJ1PAdeZ4cd710Xeloia8Uz+iY6+FT7f3uynU5mRnjbsZcd6WnFWN4x8ad5Gm5riQ3Xa5rnYqyrsaX2w4ePEhGkh7+7G2cOUN0881Eb75JVF/feJ9KOnIyNXxHnqfHXQ9dVzpa4ivFMzrmevhUe7+7cl1OZsa4mzHXXelpxRjesXEneVquK8n1yHWr3NZMaNGiRR7nz95Gu3bA9OlAfLxtN+7G+lTSkZOp4TvyPD3ueui60tESXyme0THXw6fa+92V63IyM8bdjLnuSk8rxvCOjTvJ03JdSW62XLc2kzSIpDaTrK2tRYsWLQx7Bj38Sdno0QPYsAHYvRu48kr1PpV05GRq+I685hJ3LbqudLTEV4pndMz18Kn2fnflupzMjHE3Y6670tOKMbxj407ytFxXkuuR69Zmks2EfH19Pc6flI3Jk4HqauDnnxvnU0lHTqaG78hrLnHXoutKR0t8pXhGx1wPn2rvd1euy8nMGHcz5rorPa0Ywzs27iRPy3Uludly3ZpJMog8/YBbVxQSAvTvDyQlAS+91NRPY5FFFllk0T+VrJkkNxNjLJoxdpoxttSBX8sYy7hwzdLqx9MOQVSy0bcv8PzzQL9+tlklNT6tA271tfFPOnxSiTzt0E/rgFv1NqwDbvXxZx1wq0BaO7+b4wXgFQDvAljqwC/RYNNpdVtBQQEZSXr4U7KRnU3UsiXRyJHqfCrpyMnU8B15zS3ujdF1paMlvlI8o2Ouh0+197sr1+VkZoy7GXPdlZ5WjOEdG3eSp+W6klyPXLdWt7mZiGg9AM4jXBtPa9eudbcL3f0p2XjgAeCXX4CxY21N3Lw+lXTkZGr4jrzmFvfG6LrS0RJfKZ7RMdfDp9r73ZXrcjIzxt2Mue5KTyvG8I6NO8nTcl1JbrZc9/iXJMbYi4yxWMZYEWOMGGPdJHS+YYwdZIxVMcbSGWMvNNLdZRfuT2GMae68ue+++7SaMNyfKxu//grccout7FZfz+dTSUdOpobvyGuOcVer60pHS3yleEbHXA+fau93V67LycwYdzPmuis9rRjDOzbuJE/LdSW52XLd41+SALQFsBPAd1JCxlhPAJMAjAbwGICNANYwxm5uhK9biehxAP0BhF9oxm40nTnj9skq3f25snHppbYm7o0bgTlz+Hwq6cjJ1PAdec0x7mp1Xeloia8Uz+iY6+FT7f3uynU5mRnjbsZcd6WnFWN4x8ad5Gm5riQ3W657/EsSEa0houFEFCWj8gOA2UQ0i4h2E9EgAAUABgAAY2ygXTP2JS58FV34bzaAHAB3y+kyxloxxi4TLgDtHXVKS0s5PqF+pIc/HhuvvAJ8+SXwv/8B+fmVmmzKydTwHXnNNe5qdF3paImvFM/omOvhU+39WuOuVmbGuJsx113pacUY3rFxJ3larivJzZbrHv+SpEQXXnoeB5DgIEoA8BwAEFEgET164TqvYOsKxlirC/++EcD9AA4ouB8KoMzuKgSAAwcOwM/PD9XV1UhJSQFg68ovKirC7NmzkZaWhvj4eERFRSEnJweBgYEoLy9v6Nz38fHBqVOnMG3aNGRmZiImJgarVq3C9u3bERISguLiYpFuRUUF/P39kZubi8LCQiQmJmLTpk0ICwtDQUGBSLeurg5jx47FoUOHMG/ePKSkpCApKQmLFi1CXl4exo8fj7vvvlt0z7FjxzBz5kykpaUhLi4O0dHRyM7Oxj33zMTFF9djwoQbGnRLS0sxdepUZGVlYfny5Vi9ejXS09Oxe/duHD9+XGS3srIS/v7+aN++PSIjI7Fu3TqkpqYiPDwchw8fRmpqKurr6+Hj44P6+nqMHj0ahw8fxv79+5Gamop169YhMjISeXl5+Ouvv1BZWdlgPyUlBcePH8eMGTOQnp6O1atXY/ny5cjKysLUqVNRWloqepaysjJMmTIF2dnZiI6ORlxcHNLS0jBz5kwcO3ZMpFtVVYXx48cjLy8PixYtQlJSEs6fP4958+bh0KFDGDt2LOrq6kT3FBQUICwsDJs2bUJiYiIWL16M3Nxc+Pv7o6KiAj4+PnjooYfg4+OD4uJihISEYPv27Vi1ahViYmKQmZmJadOm4dSpUyLd8vJyBAYGIicnB1FRUYiPj0daWhpmz56Na6+9VvQM1dXV8PPzw/79+xEREYHKykps3LgR8+fPR35+Pnx9fVFbWyvK2cLCQoSGhqKurg5r167FkiVLsGfPHgQEBOD2228X2b/xxhsRHByMjIwMrFy5ErGxscjIyEBQUBBOnjwp0j1z5gwmTZqEnJwcLFu2DAkJCdi6dSvmzJmDoqIikW5NTQ3GjRuHAwcOYMGCBUhOTkZycjIWLFiADh06YNy4caipqRHdU1RUhDlz5mDr1q1ISEjAsmXLkJOTg0mTJuHMmTOiPDl58iSCgoKQkZGB2NhYrFy5EhkZGQgODkZJSYnI7u23346AgADs2bMHS5Yswdq1a7FlyxaEhoaisLBQNDa1tbXw9fVFfn4+5s+fj40bN6KyshIRERHYv39/A0bYP4sjRhw9etQJIwT7AkZccsklqjBi8eLFmjBi27ZtqKqq4sKIKVOmoKysTKRbWlqKzMxMJ4yYMWOGJEb89ddfyMvLk8SI0aNHN2DEAw880IAR4eHhIoxo3749/P39RRjh4+ODjh07SmJEZmamCCNSUlKcMKK0tFQVRqSkpGjCCPvvJQ9GCLoCRrRu3doJIxy/a/YYcfjwYSQlJUlihH1cBIzYsmWLS4woKSlBcHAwWrRo4YQRN954oxNGbN++XYQR9fX1DRjh5+cn8b/kRpLWzm8zXbB1s3ez+/v6C7znHPSGAchVsBMPoBhABWwvN0/C9lKVBVtpL8Pej4yNVrCtaBOuG+Cwum3ixIlkJOnhT42NefOIAKI1axpvU06mhu/Ia+5x59F1paMlvlI8o2Ouh0+192uNu1qZGeNuxlx3pacVY3jHxp3kabmuJNcj163VberJccdMJsH7W5noTSK6mojaENGNRJRGRJuI6CEieoRss07LFR0SVZNtE6teALYASATEM0mnT58GYNxM0lVXXaV5JqlXr17cvxK7dCnD7bfvw4ABwG+/jZOdSbr44otlZ5JeeeUVyV+JpaWlkjNJbdu2dZpJqqysFP1KPH36tKEzSQ888IDmmaS+ffty/0oUdJVmkrp06aI4k3TvvfdK/kq0z1nhV+Ijjzzi9Cvxk08+Edl///33DZ9J8vLy0jSTdPr0aVUzSZ988onLmSRhbKRmku69917ZmaTTp087YcQ111zjhBGCfQEjnn32WUNnks6dO6d5Jqm+vp57JqmyspJrJumrr76SnUl65ZVXJGeSunbtKokR9fX1Iow4ffq0E0bceuuths4k2X8vGzOT9MILL6iaSerQoYPLmaTTp08rziQ5YoQwk/T00087YcQHH3zghBHnz58XYcSjjz5qzSS5uuA8k3QJgFoA7zvoTQawweBnc9onydvbm4wkPfyptTF48FS69FKin35qnE05mRq+I6+5x51H15WOlvhK8YyOuR4+1d6vNe5qZWaMuxlz3ZWeVozhHRt3kqflupJcj1zXcyapWR1Lwhgj2F6IltvxtgJIJ6Jv7Hg5AFYQ0VADn61ZH0uiRL6+wPDhQFoa8NhjTf00FllkkUUWNWeyjiWxI8ZYO8bYo4yxRy+wbrvwt7DEfyKAPoyx3oyx+xhjAQBuBhBs0PN9e+GlbBsgLrd5eXkBMK7c1rNnT83ltpEjR6qaSvfy8sKPPwL/+tdxfPVVLQIDpzlNpXft2lW23DZ48GDJqXQvLy/Jclv37t2dym2dO3cWTaV7eXkZWm7r27ev5nKbcPFMpQuXUrnt559/Viy3ffXVV5JT6fY5K0yl9+vXz2kqfcSIESL7Q4cONbzc9sMPP2gqt3l5eakqt40YMcJluU24pMptX331lWy5zcvLywkjPvnkEyeMEC4BI7777jtDy21vvfWW5nJbly5duMttnTt35iq3/fHHH7LltsGDB0uW24YMGSKJEV26dBFhhJeXlxNGfPHFF4aW2+y/l40ptw0cOFBVua1Hjx4uy21eXl6K5TZHjBDKbd9++60TRgwbNswJI95++20RRvTr188qt0ldAF6GbVrN8Qqz0/kGQD6AagDpAF5sgud0KrcVFxeTkaSHP7U2BP3Nm4kYI5o0SZ1NOZkaviOvucedR9eVjpb4SvGMjrkePhub643VUSszY9zNmOuu9LRiDO/YuJM8LdeV5HrkutW4bUdElERETOL60k5nOhHdSkStiOhxIkpuwkduoKVLl7pWMpk/tTYE/WeeAb75xrYj9+HD/DblZGr4jrzmHnceXVc6WuIrxTM65nr4bGyuN1ZHrcyMcTdjrrvS04oxvGPjTvK0XFeSmy3XPf4lyeykVG7LysoCYFy5rby8XHO57bHHHlM1lW7/GX/+uRQtWpzF55+XIzr676n0I0eOyJbbOnbsKDmVnp2dLVluKy4udiq37d27VzSVnpWVZWi5rVWrVprLbc888wz3VLqgq1Ruc9yjxLHc1qJFC8mpdPvxFKbS27Rp4zSV/vDDD4vs33PPPYaX22688UZN5basrCxV5baHH37YZblNGBupcluLFi1ky21ZWVlOGHHu3DknjBDsCxhx5ZVXGlpuy83N1Vxuy8/P5y637d27l6vc9tRTT8mW2zp27ChZbrvrrrskMSI/P1+EEVlZWU4YUVdXZ2i5zf572Zhy29VXX62q3Hb69GmX5basrCzFcpsjRgjltiuuuMIJI+69914njNi/f78II9q2bWuV2zz5gkS5LTY2lowkPfypteGoHxVFBBAtXcpnU06mhu/Ia+5x59F1paMlvlI8o2Ouh0+tua5WR63MjHE3Y6670tOKMbxj407ytFxXkuuR61a5rZkQkbErC/Xwp9aGo/777wNduwLffw+Ulbm2KSdTw3fkNfe48+i60tESXyme0THXw6fWXFero1ZmxribMddd6WnFGN6xcSd5Wq4ryc2W69ZLkptJqdwWFxcHwLhy2+7duzWX26655hpVU+n2n1HYTPLbb/fg9OkafPrpIaSnp2Pbtm2y5bb6+nrJqfT4+HjJcltGRoZTuW39+vWiqfS4uDhDy20lJSWay2033XQT91S6oKtUbmvVqpViue348eOSU+n24ylMpZ8+fdppKv2qq64S2W/Xrp3h5TbGmKZyW1xcnKpy21VXXeWy3CaMjVS57fjx47Lltri4OCeM2Lt3rxNGCPYFjKisrDS03LZu3TrN5bbU1FTuctv69eu5ym033HCDbLmtvr5estzWpk0bSYxITU0VYURcXJwTRhw+fNjQcpv997Ix5bbz58+rKrdlZ2e7LLfFxcUpltscMUIot1VUVDhhRPv27Z0wIjk5WYQRpaWlVrnNky9IlNumT59ORpIe/tTakNMPDLStdktNVbYpJ1PDd+Q197jz6LrS0RJfKZ7RMdfDp165zqujVmbGuJsx113pacUY3rFxJ3larivJ9ch1PcttTf7y8E+5pF6SSkpKyEjSw59aG3L6tbVETz1F9MADREVF8jbl7lfDd+Q197jz6LrS0RJfKZ7RMdfDp165zqujVmbGuJsx113pacUY3rFxJ3larivJ9ch1qyepmVBQUJDH+VNrQ07/4ouBGTOAPXuAzz/PVH2/Gr4jr7nHnUfXlY6W+ErxjI65Hj71ynVeHbUyM8bdjLnuSk8rxvCOjTvJ03JdSW62XLdektxMSj1JAhnVk3T33Xdr7kn66aefVPUb2H9GxwNujxxZjc8+O4akpBeweXOJU7+Bv78/evbsKdlvwBiT7Em6+eabnXqSWrduLeo3AGBoT9LLL7+suSdp+PDh3P0Ggq5ST1Lv3r0Ve5I6deok2W9gP55Cv4GXl5dTv8GgQYNE9vv37294T9Knn36qqScJgKqepEGDBrnsSRLGRqonqVOnTrI9SQCcMOL+++93wgjBvoAR7733nqE9Sa1atdLck9ShQwfunqTWrVtz9SQNGzZMtiepZ8+ekj1Jffv2lcSIDh06iDACgBNGPPHEE4b2JNl/LxvTk/TBBx+o6km64447XPYkAVDsSXLECKEnqUuXLk4YMWDAACeMaNeunQgjXn/9dasnyZMv/EMPuHWlf+4c0RVXnKJXXyWqr+e/3zrgVpuudcCt/vdbB9yaM9dd6VkH3FoH3CpdTf7y8E+5pF6SysvLyUjSw59aGzz6UVHnCCCaO5f/fjV8R15zjzuPrisdLfGV4hkdcz18uiPXlXTUyswYdzPmuis9rRjDOzbuJE/LdSW5Hrlu9SQ1E5o9e7bH+VNrg0f/0KEZ+PRT4IcfgJISvvvV8B15zT3uPLqudLTEV4pndMz18OmOXFfSUSszY9zNmOuu9LRiDO/YuJM8LdeV5KbLda1vWdbV+JmkXbt2kZGkhz+1Nnj0d+3aRcePE11xBdHnn/Pdr4bvyGvuceeNeWPkPPGV4hkdcz18uivX9ZKZMe5mzHVXeloxhnds3EmelutKcj1y3ZpJ8iBSatz29vYGYFzj9uzZszU3bu/cuVNVU6b9Z3Rs3BaaMgMDA0F0HC+9FIvwcOA//5nf0LgtNFc6NmUKDduOjdtBQUFOjdvjxo0TNWV6e3sb2rgdFRWluXF79+7d3E2Zgq5S43Zqaqpi4/aSJUskmzLtx1NoylyxYoVTU+b27dtF9rdu3Wp443ZSUpKmxm1vb29Vjdvbt2932bgtjI1U4/aSJUtkG7e9vb2dMCI0NNQJIwT7AkasWbPG0MZtX19fzY3bEydO5G7cHjduHFfj9q5du2Qbt9etWyfZuL1582ZJjJg4caIII7y9vZ0wYuHChYY2btt/LxvTuJ2QkKCqcXvmzJkuG7e9vb0VG7cdMUJo3F69erUTRmzbts0JI8aPHy/CiBUrVliN2558QWImKT4+nowkPfyptcGjL+jU1xO99BLRHXcQVVQo36+G78hr7nFXE3O1cp74SvGMjrkePt2Z63rIzBh3M+a6Kz2tGMM7Nu4kT8t1JbkeuW7NJDUTuvzyyz3On1obPPqCDmNASAhQUAAIq0jl7lfDd+Q197iriblaOU98pXhGx1wPn+7MdT1kZoy7GXPdlZ5WjOEdG3eSp+W6ktxsuW69JDUh7dq1y+P8qbXBo2+vc889wK+/An5+QHa2/P1q+I685h53tTFXI+eJrxTP6Jjr4dPdua5VZsa4mzHXXelpxRjesXEneVquK8lNl+tap6Ksq/HltiNHjpCRpIc/tTZ49B11qqqI7r2X6NlniQoKpO+XsyvFd+Q197g3Jua8cp74SvGMjrkePo3IdS0yM8bdjLnuSk9NrkvxecfGneRpua4k1yPXrXJbM6E5c+Z4nD+1Nnj0HXVatQJmzgQ2bwYGDNipyq4U35HX3OPemJjzynniK8UzOuZ6+DQi17XIzBh3M+a6Kz01uS7F5x0bd5Kn5bqS3Gy5br0kuZmsY0n+/oxyq9uuueYap5Urjz9eiWee2Yn169/A9Okx1rEk1rEk1rEk1rEkTqvbrGNJrGNJTHUsCYDrAdys03W91mkwT7pgHUuiWqe0lKh9+3J6913nI0usY0m06VrHkuh/v3UsiTlz3ZWedSyJdSyJ0sXI9j9wLmKM7QawGQDT+G4GAM8R0T062PEIYoxdBqCsrKwMl112GQCgpqYGLVu2NOwZ9PCn1gaPvpLOkiW16NGjBRYvBj76yPU9UnxHXnOPu9aYK8l54ivFMzrmevg0OtfVyswYdzPmuis9NbkuxecdG3eSp+W6klyPXC8vLxdWu11OROUuPo4iqS23lRJRbyL6j9YLgKYHbw40ceJEj/On1gaPvpLOgQP+eP994PvvgdOnXd8jxXfkNfe4a425kpwnvlI8o2Ouh0+jc12tzIxxN2Ouu9JTk+tSfN6xcSd5Wq4ryU2X62qmnQAM0Dp1ZWfrW71secIFiXLb/v37yUjSw59aGzz6Sjr79++nI0eILruMqE8f1/dI8R15zT3uWmOuJOeJrxTP6Jjr4bMpcl2NzIxxN2Ouu9JTk+tSfN6xcSd5Wq4ryfXI9SZb3UZEQTq+nE3Ty5an0ubNmz3On1obPPpKOps3b8b11wPjxgGzZgFJScr3SPEdec097lpjriTnia8Uz+iY6+GzKXJdjcyMcTdjrrvSU5PrUnzesXEneVquK8nNluvW6rYmpJtuusnj/Km1waOvpCPIvv4a6NTJ9t/KSvl7pPiOvOYed60xV5LzxFeKZ3TM9fDZVLnOKzNj3M2Y66701OS6FJ93bNxJnpbrSnKz5brqlyTG2M+MsUOMsXOMsTWMsXvsZH0YY9MYY2G6PqVF/3i66CJgxgzg0KG/jyyxyCKLLLLIIneSqpckxtiPAH4GkAQgGEBrANsZY+8AABHNArASQC99H7N5UkFBgcf5U2uDR19Jx152331/H1mSmnqG25Yjr7nHXWvMleQ88ZXiGR1zPXw2Za7zyMwYdzPmuis9NbkuxecdG3eSp+W6ktxsua52JqkzgIeI6Asi+pGIXgbwMoDfGWOvXdCp1/H5PJ6UNpNMT08HYNxmkqdOndK8meS///1vVRvF2X9Guc0k8/PzJTeK8/f3x3XXXSfaKO7GG+fjttvOIzDwQdTUOG8mefToUafNJHft2iXaKC49Pd3QzSRbtmypeTPJZ599lnujOEFXaTPJ22+/XXEzScaY5EZx9uMpbBR36aWXOm0U9/DDD4vs33PPPYZvJnnDDTdo2kwyPT1d1WaSDz/8sMvNJIWxkdpMkjEmu5lkenq6E0aUl5c7YYRgX8CIK664wtDNJLOysjRvJinY4dlMcteuXVybST799NOym0led911kptJ3nXXXZIYkZeXJ8KI9PR0J4w4f/68oZtJ2n8vG7OZ5L/+9S9Vm0kWFxe73EwyPT1dcTNJR4wQNpO8/PLLnTDi3nvvdcKIPXv2iDCidevWpthM0leG3wbAXACvAngTQJ3WjvLmdkFidZuvry8ZSXr4U2uDR19JR0qWmkrEWD1NmsSn78hr7nHXGnMlOU98pXhGx1wPn2bIdSWZGeNuxlx3pacm16X4vGPjTvK0XFeS65HrTbmZ5GgA3gBuBXA3EcU4yEcAuBLAQCK6WNvrW/MiazPJxunIyb75pg7h4Rdj1y7glluU9a0N9tTrWJtJmifX5WRmjLsZc92VnrWZpLWZpBKpLbdNATAVwBIAMxyFROQNIANAjZaH+qfQuHHjPM6fWhs8+ko6crIrr/RHhw7AN98A9u/5UvqOvOYed60xV5LzxFeKZ3TM9fBpllyXk5kx7mbMdVd6anJdis87Nu4kT8t1JbnZcl3VTFLDTYzdCeAcER2Vkd9FRHlaH645kdRMkkXaKCYG6NoViIgAPv64qZ/GIossssgiM1BTziQBAIhon9wL0gW59YLEQfanJXuKP7U2ePSVdORkPj4+eO894MMPgYEDgZMn5fUdec097lpjriTnia8Uz+iY6+HTLLkuJzNj3M2Y66701OS6FJ93bNxJnpbrSnLT5Tpv8xKAaQCGALhFayPUP/GCROP2kSNHyEjSw59aGzz6SjpyMoF/9ChRhw5EX34pr+/Ia+5x1xpzJTlPfKV4RsdcD59myXU5mRnjbsZcd6WnJtel+Lxj407ytFxXkuuR601yLAkRfQsgFkBfxti8C0vbr9b9re0fRHFxcR7nT60NHn0lHTmZwL/uOmD8eCAsDEhMlNZ35DX3uGuNuZKcJ75SPKNjrodPs+S6nMyMcTdjrrvSU5PrUnzesXEneVquK8nNlutqz27bRUTDiagXgHQAQxljYYyxzxlj7dzyhM2YHnjgAY/zp9YGj76SjpzMnv/VV8BLLwH9+gF33PGQSxvNPe5aY64kl+Lz8IyOuR4+zZLrcjIzxt2Mue5KT02uS/F5x8ad5Gm5riQ3W643+uw2ItpCRD8A6A3gKAA/xthMxtj7jLFLdHvCJiDGWDRj7DRjbKkD/zbG2HrGWA5jLIsx1laLn7KyMm0P2gT+1Nrg0VfSkZPZ8xmzHVlSWAhMm/Yvlzaae9y1xlxJLsXn4Rkdcz18miXX5WRmjLsZc92Vnppcl+Lzjo07ydNyXUlutlzXfMAtEdUT0Voi+gbAtwAYgOmMsamMsdcYY0zzUxpPgQA+l+CHAfiNiO4H8BKAai1OzpyRPlrDXaSHP7U2ePSVdORkjvy77wZ++w1YtuwW7NihrNvc46415kpyKT4Pz+iY6+HTLLkuJzNj3M2Y66701OS6FJ93bNxJnpbrSnKz5brmlyR7IqLzRBRFRH0ADAVwA4DQC5tQegwR0XoAoogzxh4AUENEGy/onCKiWi1+7rvvPi23N4k/tTZ49JV05GRS/P/9D7jzzvPo2xeorZXXbe5x1xpzJbkUn4dndMz18GmWXJeTmTHuZsx1V3pqcl2Kzzs27iRPy3UludlyXdeXJHsiojNEFE5EXwJw20sSY+xFxlgsY6yIMUaMsW4SOt8wxg4yxqoYY+mMsRca4eouAGcZYzGMse2MsWFanz0hIUGrCcP9qbXBo6+kIyeT4rdsCbz99nJs3w4EBsrrNve4a425klyKz8MzOuZ6+DRLrsvJzBh3M+a6Kz01uS7F5x0bd5Kn5bqS3HS5rnV5nNQF4D132JXx1RmAD4APYFvy181B3hPAeQB9ANwHYBKAswBudmH3ZQBL7f7+CMBJADcBaAVgPYDXVTyn0xYA5eXlZCTp4U+tDR59JR05mRJ/4ECiNm2IDhyQ1m3ucdcacyW5FJ+HZ3TM9fBpllyXk5kx7mbMdVd6jcEYV3qeFnejc11JrkeuN8kWACrpPTfZdSIiWkO2FXdRMio/AJhNRLOIaDcRDQJQAGAAADDGBjLGMi5cSg3nhQDSiKiAiKoBrAbwqJwyY6wVY+wy4QLQ3lFn8uTJXJ9RL9LDn1obPPpKOnIyJb6PD3DVVUD//rYjSxx1m3vctcZcSS7F5+EZHXM9fJol1+VkZoy7GXPdlV5jMMaVnqfF3ehcV5KbLddVvSQxxqYxxua4umCb1WlyuvDS8zgAx3m4BADPAQARBRLRoxeu8wrm0gBcyxi7gjF2EYAXAexW0B8KoMzuKgSAAwcOwM/PD9XVf/d8+/j4oKioCLNnz0ZaWhri4+MRFRWFnJwcBAYGory8vGE3UR8fH5w6dQrTpk1DZmYmYmJisGrVKmzfvh0hISEoLi4W6VZUVMDf3x+5ubm4++67kZiYiE2bNiEsLAwFBQUi3bq6OowdOxaHDh3CvHnzkJKSgqSkJCxatAh5eXkYP348fvrpJ9E9x44dw8yZM5GWloa4uDhER0cjOzsbU6ZMEa028PHxQWlpKaZOnYqsrCwsX74cq1evRnp6Oq655hocP35cZLeyshL+/v7o2bMnIiMjsW7dOqSmpiI8PByHDx8GYwz19fXw8fFBfX09Ro8ejcOHD+Pmm29GZmYq+vffiYQEwN//GFq3bo3KykrRjqzHjx/HjBkzkJ6ejtWrV2P58uXIysrC1KlTUVpaKnqWsrIyTJkyBdnZ2YiOjkZcXBzS0tIwc+ZMHDt2TKRbVVWF8ePHIy8vD4sWLUJSUhJefvllzJs3D4cOHcLYsWNRV1cnuqegoABhYWHYtGkTEhMTsXjxYuTm5sLf3x8VFRXw8fHB8OHD4ePjg+LiYoSEhGD79u1YtWoVYmJikJmZiWnTpuHUqVMi3fLycgQGBiInJwdRUVGIj49HWloaZs+ejd69e4ueobq6Gn5+fti/fz8iIiLQqVMnbNy4EfPnz0d+fj58fX1Ra9fo5ePjg8LCQoSGhsLLywtr167FkiVLsGfPHgQEBGDQoEEi+/3790dwcDAyMjKwcuVKxMbGIiMjA0FBQTh58qRI98yZM5g0aRJycnKwbNkyJCQkYOvWrZgzZw6KiopEujU1NRg3bhwOHDiABQsWIDk5GcnJyViwYAE+/fRTjBs3DjU1NaJ7ioqKMGfOHGzduhUJCQlYtmwZcnJyMGnSJJw5c0aUJydPnkRQUBAyMjIQGxuLlStXIiMjA8HBwSgpKRHZHTRoEAICArBnzx4sWbIEa9euxZYtWxAaGorCwkLR2NTW1sLX1xf5+fmYP38+Nm7ciE6dOiEiIgL79+9vwAj7Z3HEiPvvv98JIwT7Aka89957qjBi8eLFmjCiVatWqKqqUoUR9rqlpaXo0KGDE0bMmDFDEiNat26NvLw8SYwYPXp0A0YMGzasASPCw8ORmpqKdevWITIyEj179oS/v78II3x8fNC3b19JjOjQoYMIIwA4YcQTTzyhCiNSUlI0YYT995IHIwRdASM++OADJ4xw/K7ZY8Qdd9yBpKQkSYywj4uAEVu2bHGJESUlJQgODkaXLl2cMGLAgAFOGNGuXTsRRrz++usNGOHn5wfdSM20E4DPAGwDEOriOql1iqsxFxzKbQCuv8B7zkFvGIBcBTvxAIoBVMD2cvMk/V3aywKQDWCii2dpBVuJTbhugEO5zdvb22kK0Z2khz+1Nnj0lXTkZDz8jz8muuoqoiFD/FU/k55kdNy1xlxJLsXn4Rkdcz18miXX5WRmjLsZc92VnhaMkdPztLgbnetKcj1yvcnKbUS0AEAyEf1H6QKwXI1dA8jxFF8mwftbmehNIrqaiNoQ0Y1ElHaBv4aIHiKiB8m2R5S8Q6Jqsh2s1wvAFgCJgHgmSfgFYNRMUseOHTXPJP3nP/9R9SvR/jPKzSS1adNGdibpjTfekPyVWFlZKTmTdOWVVzb8Snz55eWora3D6tVeol+JFRUVhs4kPfbYY5pnkoRfUjy/EgVdpZmkbt26Kc4kPfTQQ5K/Eu3HU/iV+OSTTzr9SuzVq5fIfo8ePQyfSercubOmmaSKigpVM0m9evVyOZMkjI3UTNJDDz0kO5NUUVHhhBE33XSTE0YI9gWMePHFFw2dSaqtrdU8k9SyZUvumaT6+nqumaR+/frJziS98cYbkjNJ3bt3l8SIli1bijCioqLCCSPuvvtuQ2eS7L+XjZlJevXVV1XNJF1zzTUuZ5IqKioUZ5IcMUKYSerUqZMTRvTs2dMJIxhjIox46qmnmn4miWwzJB9z6HTV+vbWmAvOM0mXAKgF8L6D3mQAGwx+NqfG7enTp5ORpIc/tTZ49JV05GS8/DlziACiuDh1z6QnGR13rTFXkkvxeXhGx1wPn2bJdTmZGeNuxlx3pacVY3jHxp3kabmuJNcj15u0cZuIFnHorFBr1x1Eth6jdACvO4heB7DJiGe4cMZdDmxlStFMUnZ2NgDjZpLOnDmjeSbp3//+t6pfifafUW4mqaioSHYm6frrr5f8lbhr1y7JmaSSkhLRr8Tnn8/DTTftRb9+9fjtt3EAgOzsbENnki699FLNM0nPPvss969EQVdpJumOO+5QnElq2bKl5K9E+/EUfiW2bdvW6VfiI488IrJ/7733Gj6TdNNNN2maScrOzlY1k/TII4+4nEkSxkZqJqlly5ayM0nZ2dlOGFFRUeGEEYJ9ASOuuuoqQ2eS9u7dq3km6dChQ9wzSXl5eVwzSU8//bTsTNL1118vOZN09913S2LEoUOHRBiRnZ3thBH19fWGziTZfy8bM5N0zTXXqJpJKi0tdTmTlJ2drTiT5IgRwkzSlVde6YQR9913nxNGHDhwQIQR7dq1M8dMktkuAO1gW2X2KGxvjoMv/PvmC3JhC4DesG0BEADbFgC3GPycTjNJMTExZCTp4U+tDR59JR05mRp+cPCfdOmlRD/8wP9MepLRcdcacyW5FJ+HZ3TM9fBpllyXk5kx7mbMdVd6WjGGd2zcSZ6W60pyPXJdz5mkFvq9bjUZPQHbnkUCTbzw37kAviSiSMbYVQB+A9ARtqbrt4nokLGP6UxGn9iihz+1Nnj0lXTkZGr4N9xQid9/B4YNAz75pPnHXWvMleRSfB5eU5xOpNWnWXJdTmbGuJsx113pacUY3rFxJ3larivJzZbruu2TxBj7Xi9baoiIkoiISVxf2ulMJ6JbiagVET1ORMlGPZ9SuW3NmjUAjCu35eTkaC63XX311aqm0u0/o1y5bevWrbLltrq6Osmp9Li4OMly244dO0RT6Xl5eVi3bh0GDKjENdccQ9++wMqV8YaW24qLizWX22688UbuqXRBV6ncdskllyiW244dOyY5lW4/nsJU+qlTp5ym0q+88kqR/bZt2xpebgOgqdy2Zs0aVeW2K6+80mW5TRgbqXLbsWPHZMtta9asccII4TttjxGCfQEjKioqDC23JSYmai63paSkcJfb1q1bx1Vuu/7662XLbXV1dZLlttatW0tiREpKiggj1qxZ44QRhw4dMrTcZv+9bEy5rbq6WlW5LSsry2W5bc2aNYrlNkeMEMpt586dc8KIdu3aOWHEhg0bRBhx+vRpc5fbAMzRy1ZzvCBRbgsKCiIjSQ9/am3w6CvpyMnU8AVeWhrRRRcRdeu22eUz6UlGx11rzJXkSvFV4hmd63r4NEuuy8nMGHcz5rorPa0Ywzs27iRPy3UluR65rme5zXpJasKXpOLiYjKS9PCn1gaPvpKOnEwN3573449El15aT7m5Lh9LNzI67lpjriR3FV85ntG5rodPs+S6nMyMcTdjrrvS04oxvGPjTvK0XFeS65HrnnAsiUUcFBwc7HH+1Nrg0VfSkZOp4dvz/vgDaN26FH37AvX1Lh9NFzI67lpjriR3FV85ntG5rodPs+S6nMyMcTdjrrvS04oxvGPjTvK0XFeSmy3XrZckN5NST5JARvUk/VOOJXHsSbI/lqRNG6Bbt5VITgZ69dpoHUsC6Z4k61gSG1nHkljHkljHkjhjhHUsiVVuM6Tc5mlb1zfGRlMeSyLH8/b2pr59idq3Jzp82OXjaSYzHtVgHUui//3WsSTmzHVXetaxJNaxJEoXI5I9nUMVMcbmEFFvXYw1Q2KMXQagrKysDJdddhkA4OzZs2jXrp1hz6CHP7U2ePSVdORkaviOvLNnz6K2th0eeAB47DEgNhZw54pdo+OuNeZKcp74SvGMznU9fJol1+VkZoy7GXPdlZ5WjOEdG3eSp+W6klyPXC8vL8fll18OAJeT7XiwRpNVbnMzKZXbevToAcC4ctu3336rudw2ffp0VVPp9p9RrtzWu3dv2XLbmDFjJKfSe/ToIVlu+/rrr53KbZ999ploKr1Hjx6orj6Obt3isWoV8PPPGW4ttw0dOlRzuW3mzJncU+mCrlK5bcKECYrltl9++UVyKt1+PIWp9F9//dVpKn3q1Kki+wEBAYaX23x9fTWV23r06KGq3DZ16lSX5TZhbKTKbb/88otsua1Hjx5OGPH99987YYRgX8CIUaNGGVpu++STTzSX2z7//HPucttnn33GVW4LCQmRLbeNGTNGstw2ceJEyXLb559/LsKIHj16OGHEDz/8YGi5zf572Zhym7e3t6py24ABA1yW23r06KFYbnPECKHc9vvvvzthxKRJk5ww4v/+7/9EGDF8+HDTl9tC9bLVHC9IlNt2795NRpIe/tTa4NFX0pGTqeE78uz//vhjoquuIjp+3OVjNpqMjrvWmCvJeeIrxTM61/XwaZZcl5OZMe5mzHVXeloxhnds3EmelutKcj1y3ayr2wzboLG5UFZWlsf5U2uDR19JR06mhu/Is/978mTbf//7X1dP2XgyOu5aY64k54mvFM/oXNfDp1lyXU5mxribMddd6WnFGN6xcSd5Wq4ryc2W67q9JBFRqF62/inUoUMHj/On1gaPvpKOnEwN35Fn//c119helBYtAmJilJ+zsWR03LXGXEnOE18pntG5rodPs+S6nMyMcTdjrrvS04oxvGPjTvK0XFeSmy3XrZ6kJqT27dt7nD+1Nnj0lXTkZGr4jjzHvz/9FHj7bWDAAMBu1wLdyOi4a425kpwnvlI8o3NdD59myXU5mRnjbsZcd6WnFWN4x8ad5Gm5riQ3W6675SWJMZbJGHvFgfccY2whYyyOMRbLGJvlDt9mI6XGbaG5zKjG7blz52pu3M7MzFTVlGn/GeUat4OCgmQbt5OSkiSbMv38/CQbt2fNmuXUuB0QECBqyvTz8xOd3bZmzWq8/348Skvr8M472bo3bq9YsUJz4/bu3bu5mzIFXaXG7U2bNik2bkdHR0s2ZdqPp9CUuXLlSqemzB07dojsb9u2zfDG7Q0bNmhq3Pbz81PVuL1jxw6XjdvC2Eg1bkdHR8s2bvv5+TlhxPz5850wQrAvYERCQoKhjdsTJ07U3LgthRFyjdsBAQFcjdu7du2SbdxOSkqSbNzesmUL1/mOfn5+ThixePFiQxu37b+XjWnc/vPPP1U1boeGhrps3Pbz81Ns3HbECKFxOz4+3gkj0tLSnDBi8uTJIoxYuXKluRu37S8A9QBqAYwD0MJBdhGAHwDUucO3WS9ING4XFBSQkaSHP7U2ePSVdORkaviOPLl7p08nAojWrZN9nEaR0XHXGnMlOU98pXhG57oePs2S63IyM8bdjLnuSk8rxvCOjTvJ03JdSa5Hrpu1cduetgGYDeB/ALYwxu6yeymrJ6KJALLd5NtjKCwszOP8qbXBo6+kIydTw3fkyd3brx/w4otAnz6A3Sa2msnouGuNuZKcJ75SPKNzXQ+fZsl1OZkZ427GXHelpxVjeMfGneRpua4kN1uu67aZpMgoY+uI6FXG2PsAZgJoBeAHIpppp7OYiHro7tykJLWZpEXmo717gUceAb79FpgwoamfxiKLLLLIIrXkCZtJtgAAIooG8AiANADBjLEoxtgVF3Sq5W7+p5BQY/Ukf2pt8Ogr6cjJ1PAdeUr+7r4bGDUKCAgAtm2TVVNFRsdda8yV5DzxleIZnet6+DRLrsvJzBh3M+a6Kz2tGMM7Nu4kT8t1JbnZct1dM0kHieg2u78ZgF8AjAJwAsB/AHxORJ/r7tykJDWTVFtbixYtWhj2DHr4U2uDR19JR06mhu/Ic/VMtbXA008D588D6enAJZcoPr5LMjruWmOuJOeJrxTP6FzXw6dZcl1OZsa4mzHXXelpxRjesXEneVquK8n1yHVPmEm6hTH2sfDHhV4qXwDPA6gEEAfgLTf59hiaYHA9Rw9/am3w6CvpyMnU8B15rp6pRQtgzhxgzx7A11dRlYuMjrvWmCvJeeIrxTM61/XwaZZcl5OZMe5mzHVXeloxhnds3EmelutKcrPlurteknYA8GaMRTPGAgUmEf0F4DEA4QCucpNvU5HSFgDFxcUAjNsCoF27dpq3AHj//fdVLe+1/4xyy3vr6+tltwB4+umnJZf3lpSUSG4B0LJlS6ctAM6cOSNa3ltcXCzaAkBqeW9srA+GDAH++KMOW7ac0bQFwB133KF5C4CPP/6Ye3mvoKu0BcArr7yiuAXArbfeKrm81348heW999xzj9Py3nfffVdk/4033jB8C4DnnntO0xYAxcXFqrYAePfdd11uASCMjdQWALfeeqvsFgDFxcVOGNGhQwcnjBDsCxjxyCOPGLoFQFlZmeYtAKqrq7m3ADhz5gzXFgA9evSQ3QLg6aefltwC4LXXXpPEiOrqatEWAMXFxU5bAHTs2NHQLQDsv5eN2QLg8ccfV7UFQJs2bVxuAVBcXKy4BYAjRghbADz88MNOGPHmm286YURFRYUII+655x7P2QKA5wLwRFP5bqLP67QFwLx588hI0sOfWhs8+ko6cjI1fEce72eoqiK6916ip58mqq3luoX7mdxpQ2vMleQ88ZXiGZ3revg0S67LycwYdzPmuis9rRjDOzbuJE/LdSW5Hrluqi0AGGONLYRmaPXt6XTLLbd4nD+1Nnj0lXTkZGr4jjzez9CqFTB7tq2BOzDQtb4cGR13rTFXkvPEV4pndK7r4dMsuS4nM2PczZjrrvS0Ygzv2LiTPC3XleRmy3U9ym1JjbxvvQ6+PZrq6uo8zp9aGzz6SjpyMjV8R56az/Dcc8D33wO//gocOMB9W6P96WFDa8yV5DzxleIZnet6+DRLrsvJzBh3M+a6Kz2tGMM7Nu4kT8t1JbnZcl2Pl6TbXKvoel+zoaNHj3qcP7U2ePSVdORkaviOPLWfYfRo20G4ffsCjVkManTctcZcSc4TXyme0bmuh0+z5LqczIxxN2Ouu9LTijG8Y+NO8rRcV5KbLte11utgO4LkLwDrVFxpsI4loX379pGRpIc/tTZ49JV05GRq+I68xsQhIYEIIAoOVn2r4XHXGnMlOU98pXhG57oePs2S63IyM8bdjLnuSk8rxvCOjTvJ03JdSa5HrpuqJ+kC/RvAyyqux3Xy69G0bNkyj/On1gaPvpKOnEwN35HXmDi8/rptJumnn4BDh9Tda3TctcZcSc4TXyme0bmuh0+z5LqczIxxN2Ouu9LTijG8Y+NO8rRcV5KbLdc1bybJGKuD7Yy2k44i2DaQlNpp5nIAE4hI4zZ9nkNSm0lWV1ejVatWhj2DHv7U2uDRV9KRk6nhO/IaG4fycuDBB4F77gESEgDG+O4zOu5aY64k54mvFM/oXNfDp1lyXU5mxribMddd6WnFGN6xcSd5Wq4ryfXIdbNtJrmHiCYS0VyHKwzAMQn+XCIKBLBHB9+mJ6V9kt555x0Axu2T9Pnnn2veJ2nMmDGq9kCx/4xy+yT16NFDdp+kIUOGSO6B8s4770juk/Tpp5867ZPUrVs30R4o77zzjst9kuyfRdgD5fDhbPznP6n4809g+PCD3HugfPfdd5r3SRo/fjz3HiiCrtI+SSNGjFDcJ+mbb76R3APFfjyFPVAGDhzotAeKj4+PyP7vv/9u+D5JQ4cO1bRP0jvvvKNqnyQfHx+X+yQJYyO1T9I333wju0/SO++844QRX375pRNGCPYFjPjxxx8N3Sepa9eumvdJ6t69O/c+Sd26dePaJ2ncuHGy+yQNGTJEcp+kkSNHSmJE9+7dRRjxzjvvOO2T9PXXXxu6T5L997Ix+yT973//U7VPUq9evVzuk/TOO+8o7pPkiBHCPkk//PCDE0aMGjXKCSPef/99EUYMHDjQLfsk6TGTNJyIJA9NEQ66lZH9SkSjNTn3ILIOuG0+1LcvEBkJZGcDN9/c1E9jkUUWWWSRPZlqJknuBYnjvn/MC5IcCW/GnuRPrQ0efSUdOZkaviNPaxwmTAAuv5x/tZvRcdcacyU5T3yleEbnuh4+zZLrcjIzxt2Mue5KTyvG8I6NO8nTcl1Jbrpc19r5DaCzgmxdY+5rjhckVrcdOXKEjCQ9/Km1waOvpCMnU8N35OkRhzVrbKvdZs1yrWt03LXGXEnOE18pntG5rodPs+S6nMyMcTdjrrvS04oxvGPjTvK0XFeS65HrZlvd5t3I+37XwbdH05o1azzOn1obPPpKOnIyNXxHnh5xeOstoHdv4IcfgIICZV2j46415kpynvhK8YzOdT18miXX5WRmjLsZc92VnlaM4R0bd5Kn5bqS3Gy53tgjRezpfsbYIwBOS8guZYzdBNtKN3u6DMD9Ovj2aHr44Yc9zp9aGzz6SjpyMjV8R55ecff3B+LjbWW3NWvkV7sZHXetMVeS88RXimd0ruvh0yy5LiczY9zNmOuu9LRiDO/YuJM8LdeV5GbLdT1eki4FsF1Bnq+Dj2ZJp06d8jh/am3w6CvpyMnU8B15esW9QwdgxgzgnXeA0FDbzBLvM6klNTa0xlxJzhNfKZ7Rua6HT7PkupzMjHE3Y6670tOKMbxj407ytFxXkpst1/XaTJI14vrH07lz5zzOn1obPPpKOnIyNXxHnp5xf/tt4MsvgcGDgcJCaR2j46415kpynvhK8YzOdT18miXX5WRmjLsZc92VnlaM4R0bd5Kn5bqS3Gy5rsdL0hkAHYjoIt4LwJUANC3Law507733epw/tTZ49JV05GRq+I48veMeEAC0awd8/bX0ajej46415kpynvhK8YzOdT18miXX5WRmjLsZc92VnlaM4R0bd5Kn5bqS3Gy5rsdLUi6p3IeAiEoB5Org26Ppzz//9Dh/am3w6CvpyMnU8B15esddKLutWQPMncv3TGpJjQ2tMVeS88RXimd0ruvh0yy5LiczY9zNmOuu9LRiDO/YuJM8LdeV5KbLda3L4wA8aeR9RlwAomFrRF9qx7sHQIbdVQmgmwqbTlsA2P/bCNLDn1obPPpKOnIyNXxHnrvi/sUXRJdfTlRY6PqZ1JIaG1pjriTnia8Uz+hc18OnWXJdTmbGuJsx113pacUY3rFxJ3larivJ9cj1JtsCgDHm1OhNRGmNeDcDgB2NvM8ICgTwuT2DiHKJ6FEiehRAJwDnAKzV5CQwUMvtTeJPrQ0efSUdOZkaviPPXXEPCADatAH69ROX3YyOu9aYK8l54ivFMzrX9fBpllyXk5kx7mbMdVd6WjGGd2zcSZ6W60pys+W6qmNJGGObiOg5XRwzto2IntLDljuIMfYygO+I6EMJ2acAuhJRTxX2rGNJ/gEUGwu89x4QFgZ88UVTP41FFllk0T+PmvJYkhaMsZt1uG6BPtsPgDH2ImMsljFWxBgjxlg3CZ1vGGMHGWNVjLF0xtgLGt32ABCp0YbHbV3fGBvN8VgSJXr3XaBXL+C///17tZsZj2poNkcGKJCnHdVgHUui3oZ1LIk+/qxjSeRJ7UySP2wr0/SgU0T0o1YjjLHOAJ6Hba+mZQDeJ6LldvKeAOYB+AZAKoB+APoAuJ+IDivYfRkSM0kXZoT2A7iJiKoU7m8FoJUdqz2AQvuZpFOnTuHKK/UKp2vSw59aGzz6SjpyMjV8R5674376NPDQQ8ADDwBxccDp08bGXWvMleQ88ZXiGZ3revg0S67LycwYd6MxhlfXnRjDOzbuJE/LdSW5Hrmu50xSkzdJ63nB1qjVzYG3FUCQA283gLEX/j0QfzdjX2Kn8zLsGrft+L0AzOd4lt8vPI/o2rFjB40bN46qqqqoS5cuRETk7e1NR44coVmzZtG2bdsoLi6Oli1bRrt27aLJkydTWVkZeXt7N+iePHmSpk6dSjt37qQVK1bQypUrKT09nYKDg+nEiRMi3XPnztGECRNoz5491Lt3b/rzzz8pNTWVQkND6fDhwyLd2tpaGjNmDOXn51N4eDht3LiR1q9fTxEREbR3717y8/OjgIAA0T1Hjx6lGTNm0LZt22jNmjUUFRVFWVlZFBgYSKWlpaLPePr0aZoyZQplZmZSdHQ0rVq1iv766y/6+OOP6dixYyK7FRUVNGHCBPrtt99o0aJFlJiYSCkpKTR37lw6dOgQdenSherq6sjb25vq6urIx8eHDh06RL169aKUlBRKTEykRYsW0d69e+n999+nioqKBvtdunShY8eOUUhICP3111+0atUqio6OpszMTJoyZQqdPn1a9CylpaUUGBhIWVlZFBUVRWvWrKFt27bRjBkz6OjRoyLdyspK8vPzo9mzCwkgGjQolwYPHkzh4eGUn59PY8aModraWtE9hw8fptDQUEpNTaU///yTIiMjac+ePTRhwgQ6d+4ceXt709SpU8nb25tOnDhBwcHBlJ6eTitXrqQVK1bQzp07aerUqXTy5EmRbllZGU2ePJl27dpFy5Yto7i4ONq2bRvNmjWLfHx8RM9QVVVF48aNo3379tHChQtp4MCBlJycTPPmzaODBw/S2LFjqaamRjSeBQUFNGfOHPrxxx8pISGBFi9eTLt376aJEyeSv7+/yL6vry8FBQXRjh07KDY2lmJiYmjHjh00ffp0KikpEemWl5dTQEAA7dq1i5YuXUrx8fG0ZcsWmj17Nh05ckSke/78efL19aX9+/fT/PnzacOGDbRhwwaaP38+/f777+Tr60vnz58X3XPkyBGaPXs2bdmyheLj42np0qW0a9cuCggIoPLyclGelJSU0PTp02nHjh0UExNDsbGxtGPHDgoKCqLi4mKRXX9/f5o4cSLt3r2bFi9eTAkJCbR582aaM2cOFRQUiMampqaGxo4dSwcPHqR58+ZRcnIyDRw4kBYuXEj79u1rwAj7Z3HEiD59+jhhhGBfwIihQ4eqwojIyEhNGNGtWzeqrKxUhRH2uqdPn6aPPvrICSNCQkIkMeL999+nvXv3SmKEj49PA0YEBgY2YMTcuXNFGPHbb7/RhAkTRBjh7e1NY8aMkcSIjz76SIQRXbp0ccKIb775xiVG7N27lyIiImj9+vW0ceNGTRhh/73kwQhBV8CIX3/91QkjHL9r9hjx5Zdf0vr16yUxwj4uAkZs3rzZJUYUFxdTUFAQDRkyxAkjfH19nTCie/fuIoz46aefGjDi119/1a1xu8lfbPS8HF+SAFwCoBa22SV7vckANriwJfeSFAvgXY5naQXbijbhugEOq9t27txJRpIe/tTa4NFX0pGTqeE78oyKe//+RG3aEMXG7tZsS80za425kpwnvlI8o3NdD59myXU5mRnjbjTG8Oq6E2N4x8ad5Gm5riTXI9fNdsCtmelfAC4GcNyBfxzAdXI3McbiASwB8DZjrJAx9uQF/uUAngIQ78oxEVWTbZqvF4AtABIB4MCBA/Dz80N1dTX8/PwA2GqpRUVFmD17NtLS0hAfH4+oqCjk5OQgMDAQ5eXlDfVWHx8fnDp1CtOmTUNmZiZiYmKwatUqbN++HSEhISguLhbpVlRUwN/fH7m5uZg/fz4SExOxadMmhIWFoaCgQKRbV1eHsWPH4tChQ5g3bx5SUlKQlJSERYsWIS8vD+PHj8fevXtF9xw7dgwzZ85EWloa4uLiEB0djezsbEyZMgVlZWWiz1haWoqpU6ciKysLy5cvx+rVq5Geno6QkBAcP35cZLeyshL+/v7YtGkTIiMjsW7dOqSmpiI8PByHDx+Gn58f6uvr4ePjg/r6eowePRqHDx/GnDlzkJqainXr1iEyMhJ5eXmYNGkSKisrG+z7+fnh+PHjmDFjBtLT07F69WosX74cWVlZmDp1KkpLS0XPUlZWhilTpiA7OxvR0dGIi4tDWloaZs6ciWPHjol0q6qqMH78eOTl5eHpp5eiQ4dKfPddO8ydOx+HDh3C2LFjUVdXJ7qnoKAAYWFh2LRpExITE7F48WLk5ubC398fFRUV8PHxQX5+Pnx8fFBcXIyQkBBs374dq1atQkxMDDIzMzFt2jScOnVKpFteXo7AwEDk5OQgKioK8fHxSEtLw+zZs5Geni56BiEf9+/fj4iICMTGxmLjxo2YP38+8vPz4evri9raWtF4FhYWIjQ0FPHx8Vi7di2WLFmCPXv2ICAgALt37xbZz8zMRHBwMDIyMrBy5UrExsYiIyMDQUFBOHnypEj3zJkzmDRpEnJycrBs2TIkJCRg69atmDNnDoqKikS6NTU1GDduHA4cOIAFCxYgOTkZycnJWLBgAbZs2YJx48ahpqZGdE9RURHmzJmDrVu3IiEhAcuWLUNOTg4mTZqEM2fOiPLk5MmTCAoKQkZGBmJjY7Fy5UpkZGQgODgYJSUlIru7d+9GQEAA9uzZgyVLlmDt2rXYsmULQkNDUVhYKBqb2tpa+Pr6Ij8/H/Pnz8fGjRsRGxuLiIgI7N+/vwEj7J/FESMiIiKcMEKwL2BEUlKSKoxYvHixJoyYOHEiqqqqVGGEvW5paSmmTZvmhBEzZsyQxIhJkyYhLy9PEiNGjx7dgBEHDhxowIjw8HARRmzatAn+/v4ijPDx8UFGRoYkRkybNk2EEX5+fk4YERUVxYURixYtQlJSElJSUjBv3rxGY4T995IHIwRdASOSk5OdMMLxu2aPEeHh4UhKSpLECPu4CBixZcsWlxhRUlKC4OBgrFu3zgkjMjMznTBCwDYBI+Lj4xswQoiHLqT1LctMF5xnkq6/wHvWQe9XAHsMfjanfZJWrlxJRpIe/tTa4NFX0pGTqeE78oyM+8aNRIzVk6+vNjtqnllrzJXkPPGV4hmd63r4NEuuy8nMGHejMYZX150Ywzs27iRPy3UluR65bs0k8VMJgDo4zxpdA+fZJcOpY8eOHudPrQ0efSUdOZkaviPPyLh36gT06nUCv/0GZGU13o6aZ9YacyU5T3yleEbnuh4+zZLrcjIzxt1ojOHVdSfG8I6NO8nTcl1JbrZcb9YvSUR0HkA6gNcdRK8D2GTEMzDGvmWM5QDYBojLbaNGjQJgXLktKChIc7lt06ZNqqbS7T+jXLlt4sSJsuW2lStXSk6ljxo1SrLcNmXKFKdy25gxY0RT6aNGjTKk3CZMpV955SRcfXUpevY8D2/vcY0qt6WlpXFPpQu6SuW2tWvXKpbbhBKQ41S6/XgKU+mRkZFOU+kbN24U2V+/fr3h5bbVq1drKreNGjVKVblt48aNLsttwthIldvmz58vW24bNWqUE0bMmDHDCSME+wJGREdHG1puGz16tOZym5+fH3e5bcyYMVzltq1bt8qW21auXClZbktMTJTECD8/PxFGjBo1ygkjwsLCDC232X8vG1NuW7Fihapy2/Tp012W20aNGqVYbnPECKHcFhUV5YQR69evd8IIX19fEUYsXrzYKrdJXQDaAXj0wkUABl/4980X5D0BnAfQG8B9AAIAnAVwi8HP6VRuO3HiBBlJevhTa4NHX0lHTqaG78hrirhv307UogXRr7823oaeuq50tMRXimd0zPXwaZZcl5OZMe5GYwyvrjsxhnds3EmelutKcj1y3Sq3iekJ2I44EY45mXjh338AABFFAhgE4DfYlvm/COBtIjpk9IM6UkhIiMf5U2uDR19JR06mhu/Ia4q4P/YY8NtvwNixwNatjbOhp64rHS3xleIZHXM9fJol1+VkZoy70RjDq+tOjOEdG3eSp+W6ktxsue7xL0lElERETOL60k5nOhHdSkStiOhxIko26vmUym0CGVVuu/vuuzWX23766SdVU+n2n1Gu3HbNNdfIltt69uwpOZXOGJMst918881O5bbWrVuLptIBGFpue/nllzFv3jx8+ukhXH99ET7/nPDbb74N9/CU24YPH849lS7oKpXbevfurVhu69Spk+RUuv14ClPpXl5eTlPpgwYNEtnv37+/4eW2Tz/9VFO5DYCqctugQYNcltuEsZEqt3Xq1Em23AbACSPuv/9+J4wQ7AsY8d577xlabmvVqpXmcluHDh24y22tW7fmKrcNGzZMttzWs2dPyXJb3759JTGiQ4cOIowA4IQRTzzxhKHlNvvvZWPKbR988IGqctsdd9zhstwGQLHc5ogRQrmtS5cuThgxYMAAJ4xo166dCCNef/11q9zmyRckym3C5lhGkR7+1Nrg0VfSkZOp4TvymjLuu3cTXXop0cCBjbehh64rHS3xleIZHXM9fJol1+VkZoy70RjDq+tOjOEdG3eSp+W6klyPXNez3KbqWBIAYIz9DOBb2PYgSgYwiIhyL8j6AHgMQFuym8mxSPqA24qKCrRp08awZ9DDn1obPPpKOnIyNXxHXlPHfdIkYPBgIDERePXVxtnQqutKR0t8pXhGx1wPn2bJdTmZGeNuNMbw6roTY3jHxp3kabmuJNcj15vsgFvG2I8AfgaQBCAYQGsA2xlj7wAAEc0CsBK2DRQtgnK5rXv37gCMK7f169dPc7ktMDBQ1VS6/WeUK7d98cUXsuW2P/74Q3IqvXv37pLltq+++sqp3NazZ0/RVHr37t0NLbf9/PPPoqn0b7+tw2235eM//wGGDx/PVW4LCgrinkoXdJXKbb6+vorlth9//FFyKt1+PIWp9CFDhjhNpU+aNElkf8KECYaX23x8fDSV27p3766q3DZp0iSX5TZhbKTKbT/++KNsua179+5OGPHNN984YYRgX8CIESNGGFpu69Gjh+Zy22effcZdbuvZsydXuW3atGmy5bY//vhDstzm5+cniRGfffaZCCO6d+/uhBH//e9/DS232X8vG1NuGzlypKpy29dff+2y3Na9e3fFcpsjRgjltuHDhzthxIQJE5ww4pNPPhFhxJAhQ5q+3AbgTwAdHXhPAkgD8NqFv98EUKd1iqu5XZAot+3Zs4eMJD38qbXBo6+kIydTw3fkmSHuBw8StW9P1KtX421o0XWloyW+UjyjY66HT7PkupzMjHE3GmN4dd2JMbxj407ytFxXkuuR6025uu0vIjrq8JKVBuAlAJ8zxjiLBxYBwM6dOz3On1obPPpKOnIyNXxHnhnifuutwNSpwLx5QGRk42xo0XWloyW+UjyjY66HT7PkupzMjHE3GmN4dd2JMbxj407ytFxXkpst19W+JNUxxi5ljN3LGHtPYBJRBRF9AeB5AG/p+oTNmK666iqP86fWBo++ko6cTA3fkWeWuPfqBfToAfTvDxQUNM5GY3Vd6WiJrxTP6Jjr4dMsuS4nM2PcjcYYXl13Ygzv2LiTPC3XleRmy3W1L0lTAEyF7fDXGY5CIvKGbS+iGs1P1kxIqScp8sIUglE9SUI9W0tP0kUXXaSq38D+M8r1JCUkJMj2JJWUlEj2GyxevFiyJykpKcmpJ2n58uWifoPIyEhDe5L27t0r2W/AGHDnnRPQunUt3njjKFJS5HuSWrduzd1vIOgq9SSdPXtWsSdp9+7dkv0G9uMp9Bvs37/fqd+AiJzsG92TdOrUKU09SZGRkap6kojIZU+SMDZSPUm7d++W7UmKjIx0woitW7c6YYRgX8CII0eOGNqTFBUVpbknadWqVdw9ScuXL+fqSWrVqpVsT1JJSYlkT1JlZaUkRqxatUqEEZGRkU4YsXPnTkN7kuy/l43pSTp27JiqniRh3JV6kiIjIxV7khwxQuhJKigocMKI8+fPO2FETEyMCCMOHDjQ9D1J9Hd/zZ1w6E1ykN+ltQ7Y3C5I9CSFhoaSkaSHP7U2ePSVdORkaviOPLPFfd06IsaI/Pwab0OtrisdLfGV4hkdcz18miXX5WRmjLvRGMOr606M4R0bd5Kn5bqSXI9c17MnqclfHv4pl9RL0uHDh8lI0sOfWhs8+ko6cjI1fEeeGeP+009ELVsS7djReBtqdF3paImvFM/omOvh0yy5LiczY9yNxhheXXdiDO/YuJM8LdeV5HrkepM0bjPGpjHGhjDGbtFvHuufTXPnzvU4f2pt8Ogr6cjJ1PAdeWaMu48P8MADwKefApWVjbOhRteVjpb4SvGMjrkePs2S63IyM8bdaIzh1XUnxvCOjTvJ03JdSW62XFe1mSRj7AEAnwC4BcAWAIuJqNgtT9bMSGozSYsssqecHODxx4E+fYApU5r6aSyyyCKLPJOabDNJItpFRMOJqBeAdABDGWNhjLHPGWPttDxIcyWlxm0vLy8AxjVu9+zZU3Pj9siRI1U1Zdp/RrnG7a5du8o2bg8ePFiyKdPLy0uycbt79+5OjdudO3cWNWV6eXkZ2rjdt29frqbM0tJN6NMnF1OnAjNnFooat4WLpylTuJQat3/++WfFxu2vvvpKsinTfjyFpsx+/fo5NWWOGDFCZH/o0KGGN27/8MMPmhq3vby8VDVujxgxwmXjtnBJNW5/9dVXso3bXl5eThghbKZnjxHCJWDEd999Z2jj9ltvvaW5cbtLly7cjdudO3fmatz+448/ZBu3Bw8eLNm4PWTIEEmM6NKliwgjvLy8nDDiiy++MLRx2/572ZjG7YEDB6pq3O7Ro4fLxm0vLy/Fxm1HjBAat7/99lsnjBg2bJgTRrz99tsijOjXr59bGrdVH0viZICxiwC8BuB9AC0BrAawiojOa3+85kNSM0l1dXW4+OKLDXsGPfyptcGjr6QjJ1PDd+SZOe5EwNtvAzt2AFlZwNVXq7ehNeZKcp74SvGMjrkePs2S63IyM8bdaIzh1XUnxvCOjTvJ03JdSa5HrjfZTJIUEVE9Ea0lom9gO9ONAZjOGJvKGHuNMca0+miupOsyRYP8qbXBo6+kIydTw3fkmTnujAGhoUBdna3sJvyGUWNDa8yV5DzxleIZHXM9fJol1+VkZoy70RjDq+tOjOEdG3eSp+W6ktx0ua6181vuAtAewOcAwgCMdpcfT7kgsbotPz+fjCQ9/Km1waOvpCMnU8N35HlC3JcvJwKIgoLU29AacyU5T3yleEbHXA+fZsl1OZkZ4240xvDquhNjeMfGneRpua4k1yPXm/JYEjUvX2eIKJyIvgQw2l1+PJmSk5M9zp9aGzz6SjpyMjV8R54nxL1rV9tO3IMHA9nZ6mxojbmSnCe+UjyjY66HT7PkupzMjHE3GmN4dd2JMbxj407ytFxXkpst1932kmRPRFRhhB9Po9tuu83j/Km1waOvpCMnU8N35HlK3CdOBO68E/j4Y6Bjxzt09edKR0t8pXhGx1wPn2bJdTmZGeNuNMbw6roTY3jHxp3kabmuJDdbrrvlJcn+XLd/OimtbgsNDQVg3Oq2tWvXal7dJqy2Eu5xtXLF/jPKrW6Ljo6WXd2Wn58vuXIlLCxMcnXbqlWrnFa3LVy4ULRyJTQ01NDVbTt27GjUypXp0/0RGlqJvXtrEBh4K/fKFWGFidLqNsfndlzd9tdff0muXLEfT2HlSmZmptPKFftVYj4+Pjh58qThq9sOHz6saXVbaGioqtVtZ86ccbm6TRgbqdVtf/31l+zqttDQUCeMWLdunRNGCPYFjMjNzTV0ddv8+fM1r25bsmQJ9+q2hQsXcq1uO3/+vOzqtvz8fMnVbSdOnJDEiCVLlogwIjQ01AkjNm3aZOjqNvvvZWNWt+3bt0/V6rb4+HiXq9uEvJdb3eaIEcLqtj179nBhxKJFi0QYkZmZaZ5jSVxdAGa5w64nX5DoSYqIiCAjSQ9/am3w6CvpyMnU8B15nhb3kBBbf9LSpfr5c6WjJb5SPKNjrodPs+S6nMyMcTcaY3h13YkxvGPjTvK0XFeS65HrevYktVDzQsUYmwagNYdqNwB9VL2t/QPp8ccf9zh/am3w6CvpyMnU8B15nhb3vn2B5cvP4Kuv2uPxx4Fbb9Xuz5WOlvhK8YyOuR4+zZLrcjIzxt1ojOHVdSfG8I6NO8nTcl1JbrZcV1tu2wTgQdiW+Std2jZf+ofQ8uXLPc6fWhs8+ko6cjI1fEeep8WdMeCZZ0LRoYPt2JKaGu3+XOloia8Uz+iY6+HTLLkuJzNj3I3GGF5dd2IM79i4kzwt15XkZst11ZtJMsYmENFPLnRmE9FXmp6smZHUZpJVVVW49NJLDXsGPfyptcGjr6QjJ1PDd+R5atx37LgUL7wA/PILMFphvajWmCvJeeIrxTM65nr4NEuuy8nMGHejMYZX150Ywzs27iRPy3UluR653tSbSf7FoRPTCLv/OJowYYLH+VNrg0dfSUdOpobvyPPUuD/7LPDHH8DYscC6ddr8udLREl8pntEx18OnWXJdTmbGuBuNMby67sQY3rFxJ3larivJzZbrmo8lsYiPrANuLdKD6uqAN94Adu8Gdu78+9gSiyyyyCKLbNTUM0kW6UTCkkZP8qfWBo++ko6cTA3fkefJcb/4YmDePFtf0pdfAvX1jfPnSkdLfKV4RsdcD59myXU5mRnjbjTG8Oq6E2N4x8ad5Gm5riQ3Xa5rXR5nXY3fAuDo0aNkJOnhT60NHn0lHTmZGr4jrznEffVq27YAfn6N8+dKR0t8pXhGx1wPn2bJdTmZGeNuNMbw6roTY3jHxp3kabmuJNcj101/LAlj7GrGmBdjrA9j7EfG2DDG2EDGWHfG2IPu8GlWUtpMsn///gCM20xy5MiRmjeTjIqKUrVRnP1nlNtM8n//+5/sZpKzZs2S3Ciuf//+kptJDhs2zGkzye+//160UVz//v0N3Uxy4sSJmjaK8/HxQWxsrGijuGuv3Y7u3fdjyJB6zJ27T7RRnKCrtJnkvHnzFDeTnDBhguRGcfbjKWwUN3nyZKeN4pYsWSKyv3DhQsM3k5wzZ46mzST79++vajPJJUuWuNxMUhgbqc0kJ0yYILuZZP/+/Z0wYtSoUU4YIdgXMCIoKMjQzSS/++47zZtJDh48mHszye+//55rM8kVK1bIbiY5a9Ysyc0kFyxYIIkRgwcPFmFE//79nTBi7Nixhm4maf+9bMxmkiEhIao2kxwxYoTLzST79++vuJmkI0YIm0lOnz7dCSMiIiKcMOK///2vCCMmT55s7s0kAdwO2xltOQDqANQDqAFQAuAIgMoLvHoApwEsAPCmXv7NfkFiJmnbtm1kJOnhT60NHn0lHTmZGr4jr7nE/fx5ok6diG64gejECXX+XOloia8Uz+iY6+HTLLkuJzNj3I3GGF5dd2IM79i4kzwt15XkeuS6qWaSLswazYVt1ds9AIIBPA7gSiJqSUT/IqIbiKg1gHYA7gDwLYAzAKYzxnYyxl7S+hyeSCdPnvQ4f2pt8Ogr6cjJ1PAdec0l7i1bAosWAdXVwP/939/9SVpjriTnia8Uz+iY6+HTLLkuJzNj3I3GGF5dd2IM79i4kzwt15XkZst1TS9JjLE3AawHsBfA7UT0IREFElEGEZU66hNRBREdJKKFRNQfwJ2wzT5NZIz5McaYlufxNKqsrPQ4f2pt8Ogr6cjJ1PAdec0p7jfcACxYAKxdC4wZw+/PlY6W+ErxjI65Hj7NkutyMjPG3WiM4dV1J8bwjo07ydNyXUlutlxv9EsSY+wdAN8DeIGIRku9FLmiCzNji4nocQCnAMxu7PN4It11110e50+tDR59JR05mRq+I6+5xf2NN4ARI4CRI237J2mNuZKcJ75SPKNjrodPs+S6nMyMcTcaY3h13YkxvGPjTvK0XFeSmy3Xtcwk3QfgPQDnGGMPaH0QIvIFsOif1Ni9fv16j/On1gaPvpKOnEwN35HXHOP+22/Ayy/bji1ZvnyrZnta4ivFMzrmevg0S67LycwYd6MxhlfXnRjDOzbuJE/LdSW56XJda1MTgFDYGrU/1GqrOV+QaNwuLS0lI0kPf2pt8Ogr6cjJ1PAdec017seOEV13HdHzz9dQTY02e1riK8UzOuZ6+DRLrsvJzBh3ozGGV9edGMM7Nu4kT8t1JbkeuW6qxu0LFANbIzYAgDE2Uye7zZqmTJnicf7U2uDRV9KRk6nhO/Kaa9yvvdbWyL1p00X4/Xdt9rTEV4pndMz18GmWXJeTmTHuRmMMr647MYZ3bNxJnpbrSnKz5brmY0kYY+sB/I+I/rLjbSOip7Q+XHMi61gSi4yisWOBYcOA1auBzp2b+mksssgii4wlsx1LMgFAKmPsGGMskjH2XwCtGGPGHvmtIzHGohljpxljSx34gxljuxhjOYyxQK2r8Txt6/rG2LCOJTE+7jU1Pnj7beCzz4CDBxtnz2OODFAgTzuqwTqWRL0N61gSffxZx5IokNZ63YWZqOcBLANQCttmkXWwbSSZDSAcwCAAL0KH+qARF4BXALwLYKkd72oA+wFcCuBiAKkAnlVh06kn6fTp02Qk6eFPrQ0efSUdOZkaviOvucf99OnTdOoU0e23Ez36KNG5c+rtaYmvFM/omOvh0yy5LiczY9ybIte16mnFGN6xcSd5Wq4ryfXIddP1JBFRKhF1B3AlgMdg22E7CLadtbsBmAjbfkqnGWN5jLFFjLH/MMau08O/3kRE62HXY2VHLWB7SWp54Tqhxc/8+fO13N4k/tTa4NFX0pGTqeE78pp73OfPn48rrgCiooDcXGDAAMCxqu7Knpb4SvGMjrkePs2S63IyM8a9KXJdq55WjOEdG3eSp+W6ktx0ua71LUvqApDm8PddAHoA8AWwFsBJ/D3jFA/gCQ2+XgQQC6AItjfHbhI63wA4CKAKQDpsezu5svsy7GaSLvC+B1AO255OY1Q+p9NMUmZmptPbsTtJD39qbfDoK+nIydTwHXnNPe72uvPnEwFE06aps6clvlI8o2Ouh0+z5LqczIxxb8pcb6yeVozhHRt3kqflupJcj1w33UySBIk2hSSiPLJtGjmEiF4noqtg2237MwB7ACxjjPVspK+2AHYC+E5KeMHuJNh29n4MwEYAaxhjN6txwhi7AkAXALcCuAHAc4yxFxv5zACA/fv3a7m9SfyptcGjr6QjJ1PDd+Q197jb6372GfD998B//wts2sRvT0t8pXhGx1wPn2bJdTmZGePelLneWD2tGMM7Nu4kT8t1JbnZct0tL0lEFMyhc4CIFgHwA/AsgPcb6WsNEQ0noigZlR8AzCaiWUS0m4gGASgAMAAAGGMDGWMZF65LFFx5AdhHRKeIqBLAKgDPyCkzxloxxi4TLgDtHXUuuUTJnf6khz+1Nnj0lXTkZGr4jrzmHndH3QkTgGeeAT78EDh2jM+elvhK8YyOuR4+zZLrcjIzxr2pc70xeloxhnds3EmelutKcrPlurtmktRQOmyH457X2/CFl57HASQ4iBIAPAcAZDtr7tELl9IzFMA2e3QpY+xi2MpxuQr6QwGU2V2FAHDgwAH4+fmhuroasbGxAGxd+UVFRZg9ezbS0tIQHx+PqKgo5OTkIDAwEOXl5Q2d+z4+Pjh16hSmTZuGzMxMxMTEYNWqVdi+fTtCQkJQXFws0q2oqIC/vz9yc3ORmZmJxMREbNq0CWFhYSgoKBDp1tXVYezYsTh06BDmzZuHlJQUJCUlYdGiRcjLy8P48ePRoUMH0T3Hjh3DzJkzkZaWhri4OERHRyM7OxtTpkxBWVmZ6DOWlpZi6tSpyMrKwvLly7F69Wqkp6cjNTUVx48fF9mtrKyEv78/qqurERkZiXXr1iE1NRXh4eE4fPgwVq5cifr6evj4+KC+vh6jR4/G4cOHkZaWhtTUVKxbtw6RkZHIy8vD2rVrUVlZ2WA/NjYWx48fx4wZM5Ceno7Vq1dj+fLlyMrKwtSpU1FaWip6lrKyMkyZMgXZ2dmIjo5GXFwc0tLSMHPmTBw7dkykW1VVhfHjxyMvLw+LFi1CUlISjh49innz5uHQoUMYO3Ys6urqRPcUFBQgLCwMmzZtQmJiIhYvXozc3Fz4+/ujoqICPj4+uPbaa+Hj44Pi4mKEhIRg+/btWLVqFWJiYpCZmYlp06bh1KlTIt3y8nIEBgZi374cfPnlalRVVaNz5zMICZmDiy66SPQM1dXV8PPzw/79+xEREYGCggJs3LgR8+fPR35+Pnx9fVFbWysaz8LCQoSGhuLEiRNYu3YtlixZgj179iAgIADt27cX2W/VqhWCg4ORkZGBlStXIjY2FhkZGQgKCsLJkydFumfOnMGkSZOQk5ODZcuWISEhAVu3bsWcOXNQVFQk0q2pqcG4ceNw4MABLFiwAMnJyUhOTsaCBQsaZDU1NaJ7ioqKMGfOHGzduhUJCQlYtmwZcnJyMGnSJJw5c0aUJydPnkRQUBAyMjIQGxuLlStXIiMjA8HBwSgpKRHZbd++PQICArBnzx4sWbIEa9euxZYtWxAaGorCwkLR2NTW1sLX1xf5+fmYP38+Nm7ciIKCAkRERGD//v0NGGH/LI4YsWvXLieMEOwLGFFeXq4KIxYvXqwJI+Lj41FVVaUKI+x1S0tLkZSU5IQRM2bMkMSItWvXIi8vTxIjRo8e3YARV199dQNGhIeHizCiuroa/v7+Iozw8fFBixYtJDEiKSlJhBGxsbFOGLF//35VGJGSkqIJI+y/lzwYIegKGHHu3DlERUUhPj4eaWlpmD17ttN3zR4jduzYgaSkJEmMsI+LgBFbtmxxiRElJSUIDg5GaWmpE0a0atXKCSMSExNFGFFcXNyAEX5+fhL/S24kaa3Xab0ADIetXNZVB1uiniQA11/gPeegNwxAroKdeADFACpge7l58gJ/NIDdAHYBCMSFfaZkbLSCrQ9JuG6AQ09SSEgIGUl6+FNrg0dfSUdOpobvyGvucZfTTUkhatGC6L//dW1PS3yleEbHXA+fZsl1OZkZ426WXFejpxVjeMfGneRpua4k1yPXPaEniZuIyIeIHiGiFe504/A3k+DZP9ObRHQ1EbUhohuJKO0C/1ciuo+IHiCigUSkZKOabJtY9QKwBUAiIJ5JOnDgAADjZpIAaJ5JevPNN1X9SrT/jHIzSeXl5bIzSQ899JDkr8SDBw9KziRVV1c7zSQVFRWJfiUeOHDA0Jmk6667TvNMUteuXbl/JQq6wq/EnJwcREVF4ezZeAwadAiTJwOnTr0p+ysxIiIC//rXvyR/JdqPp/Ar8cYbb3T6lejl5SWy36lTJ8Nnkh599FFNM0kHDhxQNZPk5eXlciZJGBupmaR//etfsjNJBw4ccMKIFi1aOGGEYF/AiLvuusvQmaTCwkLNM0klJSXcM0lFRUVcM0nvvvuu7EzSQw89JDmT9Nxzz0liRElJiQgjDhw44IQR7du3N3Qmyf572ZiZpHvvvVfVTFJ9fb3LmaQDBw4oziQ5YoQwk3THHXc4YcQLL7zghBHHjx8XYcRNN93UPGeS9LzgPJN0CYBaAO876E0GsMHgZ3Na3ebt7U1Gkh7+1Nrg0VfSkZOp4TvymnvclXTr64n+7/+IWrY8Tzt2qLfBE18pntEx18OnWXJdTmbGuJsp13n1tGIM79i4kzwt15XkeuS6njNJjT6WhDF2LYCzRHRO43uao917iEip10fpXoLthWi5HW8rgHQi+saOlwNgBREN1fq8Kp7NOpbEIlNQRQXwwgvAyZNAWhpw9dVN/UQWWWSRRfqRWY4lqQcwhzHWUcsD2BNjrBeAgSrvaccYe5Qx9ugF1m0X/haW+E8E0Icx1psxdh9jLADAzQBcrsDTgxhj3154KdsGiMttXl5eAIwrt/Xs2VNzuW3kyJGqptLtP6Ncua1r166y5bbBgwdLTqV7eXlJltu6d+/uVG7r3LmzaCrdy8vL0HJb3759NZfbhItnKl24HMttwlR6RMRsPPnkaJSUnMWHHwK//z7Gqdz21VdfSU6l24+nMJXer18/p6n0ESNGiD7j0KFDDS+3/fDDD5rKbV5eXqrKbSNGjHBZbhMuqXLbV199JVtu8/LycsKITz75xAkjhEvAiO+++87Qcttbb72ludzWpUsX7nJb586ducptf/zxh2y5bfDgwZLltiFDhkhiRJcuXUQY4eXl5YQRX3zxhaHlNvvvZWPKbQMHDlRVbuvRo4fLcpuXl5diuc0RI4Ry27fffuuEEcOGDXPCiLfffluEEf369TNfuQ22PYM2AugN4CINdm6BbW+lUAAXq7z3Zdim1RyvMDudbwDkA6iGbTXdi1qn4BrxGZ3KbRUVFWQk6eFPrQ0efSUdOZkaviOvucedN+YpKUQtWxL1789vgye+UjyjY66HT7PkupzMjHE3Y6670tOKMbxj407ytFxXkqvN9RMnbG0E9jqmadwmonwAnWHbL2gPY2woY+wRnoNfL+wf9DZjbB6ANABbieg/RFSn8hmSiIhJXF/a6UwnoluJqBURPU5Eyao+qJto+vTpHudPrQ0efSUdOZkaviOvucedN+bPPw9Mnw4EB9suHhs88ZXiGR1zPXyaJdflZGaMuxlz3ZWeVozhHRt3kqflupJcTa4fPw5ccw0wbpz7Yq55dRsRnSWirwH0BPAQgM0AyhhjiYyxcMZYIGPMmzE2jjE2kzG2jDG2HbajSWbBNsNzPxHN0PosZiSlclthYSEA48ptLVq0MHx1m/1nlCu3VVRUyJbbHn74Ycmp9CNHjkiW2+rq6pzKbcXFxaKp9MLCQkPLbddff73mctt7773HPZUu6MqV22bPno2nn34aPj4+6NMHePrpNHz/PaF//4iGctu1114rOZVuP57CVPrNN9/sNJX+2muviT6jJ65uKywsVFVue+2111yW24SxkSq3XXvttbLltsLCQieMaNWqlRNGCPYFjLj77rsNLbedOHFCc7mtrKyMu9xWXFzMVW7r0qWLbLnt4YcfVrW6raysTIQRhYWFThjRoUMHQ8tt9t/LxpTb7r//flXltosuushlua2wsFCx3OaIEUK57c4773S5uu3EiTM4caIcy5YdBgBERp7ELbfcYr5ym9QF287SHwAYD2AlgB0A8mA7fmQLgEWw7VPUCQr7DDW3CxLltkWLFpGRpIc/tTZ49JV05GRq+I685h53tTE/f57olVeI/vUvooMHlW3wxFeKZ3TM9fBpllyXk5kx7mbMdVd6WjGGd2zcSZ6W60pyuXgWFRGtX2/7+667iG6++TQFBhIBRJ06ie/Ts9zWQutLFmPsLQApRHT2wkvXGQBRFy6LFOhqg5cV6eFPrQ0efSUdOZkaviOvucddbcxbtgQWLwaefBLo2tV2xpuW+ErxjI65Hj7NkutyMjPG3Yy57kpPK8bwjo07ydNyXUkuF8+BA4GlS4GjR4G8PADogPR0m/zgQffFXI/NJJ8AcJIxtpEx9htj7FkdbDYbUiq3RUREADCu3JaSkqK53CboCv91NZVu/xnlym1xcXGy5bYTJ05ITqUvWrRIstwm6NmX26KiokRT6REREYaW2/bs2aO53CZsy88zlS7oKpXb7MtKPj4+aN++Gt26zcG+ffV49dXDyM7eJTmVbj+ewlS6cPSL/VS642esrKw0vNxWUlKiqdwWERGhqtxWV1fnstwmjI1UuW3Xrl2y5baIiAgnjNiyZYsTRgj2BYwoKCgwtNy2bNkyzeW2lStXcpfboqKiuMptLVu2lC23nThxQrLcdu7cOUmMWLlypQgjIiIinDBix44dhpbb7L+XjSm3FRUVqSq3JScnuyy3RUREKJbbHD+jUG4Tjp2KjY1FWNhePPfcblRWVmHdulMAgG+/jWn4/+uqVTUAgCNHgJkzL0FIyFzzldsAtACQAtvM0RDYjhlpbye/CcB7sB1i2+gVcJ5+QaLcNnfuXDKS9PCn1gaPvpKOnEwN35HX3OOuJeZRUbbp6w8+2M59nxljrodPs+S6nMyMcTdjrrvS04oxvGPjTvK0XFeSz5w5n4SFaoDtCghYQjffbPv3hx/+zQeI7rjj73/X1Nju07Pcpsf//IcD+FJG9j/YDq6tu3AVAOiu1acnXlIvSYcOHXJKEHeSHv7U2uDRV9KRk6nhO/Kae9y1xnzUKBsyLFnCd58ZY66HT7PkupzMjHE3Y6670tOKMbxj407ytFxXkt9++3l65BHbv4WXn2nTiunii23/vvRS2xmUt956ngCib76x8W+++XyDDdNsAXCBXiWiMEcmY+wRAL4XZpoWwbZXUQyABYyx73Xw6/E0b948j/On1gaPvpKOnEwN35HX3OOuNeYjRgAPPbQLn39u25Hb1X1mjLkePs2S63IyM8bdjLnuSk8rxvCOjTvJ03JdTl5eDhw40BI7dwIlJX/zQ0KOoa4OaNsWqKoC7rgDqKqyld9efhkICAC6dg1V9Rl4SY+XpBoZfnfYDpJdSkSfEVEIEX0L4DkAw+x2yG7WpNSTVF9fD8C4nqQ77rhDc0/S4MGDVfUb2H9GuZ6kq666SrYn6cMPP5TsNyAiyZ6kG264waknqVWrVqJ+g/r6ekN7kl544QXNPUlDhw7l7jcQdJV6kr744gvZfoNFiyIwblwxbr+9HK+/XolNmwoa+g3sx1PoN3jllVec+g2+//57kf2+ffsa3pPUs2dPTT1J9fX1qnqSvv/+e5c9ScLYSPUkPfvss7I9SfX19U4Ycc899zhhhGBfwIh33nnH0J6kli1bau5Juuyyy7h7klq1asXVk/TLL7/I9iR9+OGHkj1JvXv3lsSIyy67TIQR9fX1Thjx2GOPGdqTZP+9bExPUteuXVX1JN16660ue5Lq6+sVe5IEjIiLA664ohSbN5/GmDHLGv7f6etr68pu0aIWe/c+AAB4912b7LbbavHww7ZDfaurV+D++xPwyScPmXMLAMgcFAtgHWwlth4Ssm4AFmn17UkXrANuG6VjHXCr3oZeh08eO0Z0881EjzxCdOaM/H1mjLkePs2S63IyM8bdjLnuSs864Nb4XD9//m/5e+/ZymUjRxKFh/9dYvvkE9t/P/rI9t/LLyeaPt32759+IvrjD2+qqpL2Z4oDbgVijE0GkERE0Xa8lgBKAVwKoCMRnZC4bzsR/VuTcw8iqQNu6+vrcdFFekzm8ZEe/tTa4NFX0pGTqeE78pp73LXG3F6elQU8/zzwyitAVBTAmOv4SvGMjrkePs2S63IyM8bdjLnuSk8rxvCOjTvJk3J9wwbAywuIjKzHBx9chHvuAfbuBd54A3j8cWDePMK5cwzV1cAllwCjRgH//a8Nh1auBPr0Afz8gFtvlR8HsxxwK5A/gADG2Ct2vO8BtAawS+oFySIbjR071uP8qbXBo6+kIydTw3fkNfe4a425vfyhh4BFi2zg9MsvfPGV4hkdcz18miXX5WRmjLsZc92VnlaM4R0bd5In5fry5UBtLfDbb7moqgL27QNuvBH46y8gKwu49NIDeOQRoKICuPNO4L33bPe9/TbQoYNtr6Tbbzcw17VORV2YiXoPQAWADNjOYRNWs/WT0WcAsvXw7SkXrNVtjdKxVrept+GOlSeTJ9umuX19S7hsNXXM9fBpllyXk5kx7mbMdVd61uo29+b61KlEjz5KVHIBOl5+2YYl111XQxkZtn8PH/53me3rr8voxx9t/x4wwHZPRkYB1dUpP4P932Zb3QYiigHwPIDDAO4AcAzAMCIKkbnlPQCpevg2Oyk1bg8ePBiAcY3b48aN09y4nZCQoKop0/4zyjVujxw5UrZxe9GiRZJNmT/88INk47aPj49T4/Yvv/wiasocPHiwoY3bM2bM0Ny4nZSUxN2UKegqNW5HR0fLNmVGREQgKChI1JR57pwv+vevx9ChlyMxUdy4PWvWLKemzLi4OJH92NhYwxu3Fy9erKlxe/Dgwaoat+Pi4lw2bgtjI9W4HRQUJNu4PXjwYCeMmDBhghNGCPYFjAgPDze0cfvnn3/W3Lj966+/cjdu//LLL1yN2+vWrZNt3F60aJFk4/aKFSskMeLXX38VYcTgwYOdMCIwMNDQxm17nG1M4/aCBQtUNW6PHTvWZeP24MGDL+R9KTIygLFjd2Hx4iXYvr0ON9xwHMeOtcDQoQkAgDNn/j6ctqRkPR544E8891wRvLx2IygoCKmpMRgzRowRQ4cOFWHE7Nmzzdm4zXsBaHfhv0/A9oJ0g1G+zXBBYiYpJSWFjCQ9/Km1waOvpCMnU8N35DX3uGuNuZy8poboqadOUYcORHv2KOs2dcz18GmWXJeTmTHuZsx1V3paMYZ3bNxJZsn1qiqihQttCz1SUlKouprokktss0K9ehEdPmz7tzAz/fjjRB072u5lzMabPz+dy5/SOJhuJskVMcauBBDCGDsI24zKNbD1LP2jqbq62uP8qbXBo6+kIydTw3fkNfe4a425nLxFC+DXXzNx/fXAO+8AJ0/K6zZ1zPXwaZZcl5OZMe5mzHVXeloxhnds3ElmyfWAAODTT4HJk2062dnA+fPAE08AW7cCmZk2vffeA9q3r0F6OnD//TbekiXA6NFAx46lXP6MynVDXpKI6BTZ9kq6DcDDAKYB+MUI32am4uJij/On1gaPvpKOnEwN35HX3OOuNeZK8srKY4iNtW361rWrbWM3M8ZcD59myXU5mRnjbsZcd6WnFWN4x8adZJZcT062/XfxYptOejpw0UVAv362FWxJScBllwG33AI88UQBANvKWQDo3h0YNsyEua51Ksq6Gl9u27t3LxlJevhTa4NHX0lHTqaG78hr7nHXGnMlucDfvNl2PMBHHxHt2WO+mOvh0yy5Liezcp1f150Ywzs27qSmyPXISCJf3795dXVEHToQ3XWXrWy2des+6teP6MEHifbvp4bG7E6dbPrr1h2g0aOJ7P6XKPssanPd48ptFklTTEyMayWT+VNrg0dfSUdOpobvyGvucdcacyW5wH/mGWDhQtty3P79S13eb3TM9fBpllyXk1m5zq/rTozhHRt3ktG5vnjxGvTsCQwZAuTk2Hi5uUBpKTB0qO3v6dOzkZ5u2/vo9tuBBx+08d9/3/bf7dujMGyYbWbJ1bM0Za5bL0luJqXVbeXltj2ujFrddu2112pe3da7d29VK1fsP6Pc6rZWrVrJrm574403JFeunDlzRnJ12+WXX+60uq2mpka0cqW8vNzQ1W2PPvqo5tVt33zzDffKFUFXaXVbt27dFFe3Pfjgg5IrV+zH88knC/Hxx1uQlPQkvv9+t2h12+effy6y36NHD8NXt3Xu3FnT6rby8nJVq9s+//xzl6vbhLGRWt324IMPyq5uKy8vd8KI66+/3gkjBPsCRrzwwguGrm6rrq7WvLqNMca9uq2mpoZrdVv//v1lV7e98cYbkqvbunfvLokRjDERRpSXlzthxJ133mno6jb772VjVre98sorqla3nTp1f8P/4375JRv5+fkYPnw1LrqIsH+/H267DcjIuBk7dhCINmHLli3o1SsdzzxTgE6d9kpiRElJCYKDg/H88887YUTPnj2dMKK+vl6EEU888YRnr277p1+wjiVplI51LIl6G3odS8LLf/bZLXTRRUQxMfJ61rEkrnWsY0nU27COJdHHn9L9yclE+/aJeS+8kELXXUfUuzfRvffaeF99RfTww7Z/Dxjwd3nN8V5XPvXIdVMdS2IRH0kdS2KRRc2B6uqAHj2AuDhbY+aTTzb1E1lkkUV60I4dwL//DVx1FXDkCNCqlY3/zDPAbbfZvvcffADs32/bEfuVV4CgIFvp7bHHgFdfte3WbzSZ7VgSixpJwvShJ/lTa4NHX0lHTqaG78hr7nHXGnMluRR/7FgfzJ8PPPww0KULcPBg08dcD59myXU5mZXr/LruxBjesXEnuSvXg4Js/z15Eli1yvbvs2eBtLR6vPSS7Qy2li2BadNsL0avvWbTueceYPDgCVi+XL1P0+W61qko62p8ue3YsWNkJOnhT60NHn0lHTmZGr4jr7nHXWvMleRK8T1xguiOO4juuYdo9+7jqp9Jb9Lq0yy5Liezcp1f150Ywzs27iR35Hp9PdEttxANHEj0xBNEXbva+AkJtjJaTo7t7/fes/3dvj1ReTn/M2nBcCme/d/W6rZmQitWrPA4f2pt8Ogr6cjJ1PAdec097lpjriRXiu/VVwNr1gAlJcC779ahqkrdM+lNWn2aJdflZFau8+u6E2N4x8adpMXfoUPAgAH5OHZMzM/Ls8neeAP45BPbd7usDNiwAWjfvhL33mvT8/UFnn0WmDIFaN+e/5m0YLgUz10xt16SmpAef/xxj/On1gaPvpKOnEwN35HX3OOuNeZKclfxvesuIDYWKCi4Fl9+CdTX8z+T3qTVp1lyXU5m5Tq/rjsxhnds3EmN9UcEfPEFEB39ND79VCxbu9ZWSnvpJeCjj2w7Zy9fDqxYATz3XCUYs+nddx+waZPNjppn0oLhUjx3xdx6SWpCOn78uMf5U2uDR19JR06mhu/Ia+5x1xpzJTlPfJ99FvjxxwwsXgz873/8z6Q3afVpllyXk1m5zq/rTozhHRt3UmP97dljmxl6+eUjWL8eSEv7W5aQADz3HNCuHXDTTcDrrwP/+Q+QnQ08//w+zc+kBWOkeO6KufWS1IR0/vx5j/On1gaPvpKOnEwN35HX3OOuNeZKcp74AsCTTx5GYCAwcSIwYYLxMZd7Lnfe765cl5NZuc6v606M4R0bd1Jj/S1fDrRtC/Trtx233w4EBtr4NTXAunW2UptA06fbZo2++gp48MEizc+kFWOMynXrJcnNpLSZZGJiIgDjNpPct2+f5s0kb7zxRlUbxdl/RrnNJHfs2CG7mWSLFi0kN4pLTEyU3Exy165dTptJpqSkiDaKS0xMNHQzybKyMs2bSd5xxx3cG8UJukqbSbZv315xM8lTp05JbiZpP56FhYUIDQ3F2bNnsXbtWtFmkh07dkRpqQ+GDbPNJqWl3Wv4ZpKtWrXStJlkYmKiqs0kO3bs6HIzSWFspDaTPHXqlOxmkomJiU4YcfDgQSeMEOwLGFFXV2foZpLJycmaN5Pctm0b92aSKSkpXJtJ3nbbbbKbSbZo0UJyM8kOHTpIYsS2bdtEGJGYmOiEEUePHjV0M0n776WazSSXLavDnXfuw6WX1uGFFzKxaFE94uJ24Jdf1uDsWaCgYFaD7k03VeOLL/wwdOh+7N2bi6SkJEmMsI+LgBFbtmyRxAipzSRramqcMOKqq65ywohNmzaJMOLcuXPWZpKefEFidduUKVPISNLDn1obPPpKOnIyNXxHXnOPu9aYK8l54mvPq6+3bTh30UW1FBfn8rF0Ja1xN0uuy8msXOfXdSfG8I6NO0nO36xZRHffTTRzprOssNC2Km3ePNv9p04RtW5NNGwYUefOtk0i6+vV+VOjoxfGSP2t5+q2Jn95+KdcUi9Jp0+fJiNJD39qbfDoK+nIydTwHXnNPe5aY64k54mvI6+mhujNN89T27ZE27a5fDTdSGvczZLrcjIr1/l13YkxvGPjTpLyt28f0SWXEF17LVHLlkS7donl06YRXXwx0alTf98/fDg17JS9ZIk6f2p19MQYx7+tLQCaCU2dOtXj/Km1waOvpCMnU8N35DX3uGuNuZKcJ76OvBYtgKee8sdDD9l25c3Lc/l4upDWuJsl1+VkVq7z67oTY3jHxp0k5S842NZvtHs3cPPNfy+iEGjhQttmkFdc8ff9I0falvJHRgIffqjOn1odPTGG95kaQ9axJAaRdSyJRf90OnkS6NQJqK62LRm+7rqmfiKLLGqeVF0N3Hgj0KuXbfHE4sVAz562lWwvvmg7RuTOO20vSp980tRPqz9Zx5I0E/K0resbY8M6lsScRzXoeSwJb8yvugqIj7cBeOfOQLkm6HJN1rEkVq7z6DXHY0lWr7Zt6vrVV7a/P/wQeOIJ4JdfbMW0KVOAyy8HunZt3POaFWPcQlrrddbV+J6k0tJSMpL08KfWBo++ko6cTA3fkdfc46415kpynvhK8ez/zswkuvxyoldfJaqqcvmojSatcTdLrsvJrFzn13UnxvCOjV50/rytz0/J3/vvE/3732KddetsvUavvkrEGJGvr/z9rsjsGGP1JDUTCg8P9zh/am3w6CvpyMnU8B15zT3uWmOuJOeJrxTP/u+HHgJiYoDUVODzz//elVtv0hp3s+S6nMzKdX5dd2IM79joQVFRth6i66+37WMk5e/UKWDlSuD//k987yuvAHPmAMXFwLffAj/91PjnNTvG6Epa37Ksq/EzSVlZWWQk6eFPrQ0efSUdOZkaviOvucdda8yV5DzxleJJ6SxbRnTRRUTffy+/1FgLaY27WXJdTmblOr+uOzGGd2y0Un4+UZs2RO++a5sN6tDBtoLN0d/Uqbbv1dGj/LaNznUluR65bs0kuZkYY9GMsdOMsaUO/J8YY7sYY9mMsf+Tu5+X8oxa5qOjP7U2ePSVdORkaviOvOYed60xV5LzxFeKJ6XzwQe2XXynTAH++EPxcRpFWuNullyXk1m5zq/rTozhHRutNH480KaNrdk6Kgq46irg009tu2ML/urqgIAAWw+SmoURRue6ktxsud7CLVY9nwIBzAHQcGQfY+whAJ8CEE7RS2SMrSSi0sY6ad26tZZnbBJ/am3w6CvpyMnU8B15zT3uWmOuJOeJrxRPzl6/frbywLBhQIcOwH//q/hYqkhr3M2S63IyK9f5dd2JMbxjo4WKi22lsiFDbGepAUBEhO1std9+A156yeZv3jzbyrWICHX2jc51JbnZct16SZIgIlrPGHvZgX0fgE1EVAUAjLEMAG8BWNRYP1dddVVjb20yf2pt8Ogr6cjJ1PAdec097lpjriTnia8UT8nfkCHA6dPAoEG2fovPP1d8NG7SGnez5LqczMp1fl13Ygzv2GihqVMBxmy9RAI9+STg4wMMHQrU1t6HSy4BBg8GPvvMJlNDRue6ktxsue7x5TbG2IuMsVjGWBFjjBhj3SR0vmGMHWSMVTHG0hljLzTCVTaAVxhjHRhjHQC8CuAGLc+ekZGh5fYm8afWBo++ko6cTA3fkdfc46415kpynvhK8ZT8MQaMGwf06QP07g2sWKH4aNykNe5myXU5mZXr/LruxBjesWksnTtne0nq08dWYrOn//0P+OYbYMKEW/Daa8A99wDTpqn3YXSuK8lNl+tam5qa+gLQGYAPgA9ga9Tq5iDvCeA8gD6wzQZNAnAWwM0u7L4MYKkDrx+A7QDWAwgH8F+F+1vB1qwtXDfAoXH7qJrOOh1ID39qbfDoK+nIydTwHXnNPe5aY64k54mvFI/nmWpriT76yHaUQmKiS3WXpDXuZsl1OZmV6/y67sQY3rFpLE2aZDs+5OBBeZ1164pp3Trbd6gxZHSuK8n1yHXr7Db5FxOpl6StAIIceLsBjL3w74EAMi5cl9jpOL0kOdiYBeAdBfnvF55HdO3YsYPGjRtHVVVV9NprrxERkbe3Nx05coRmzZpF27Zto7i4OFq2bBnt2rWLJk+eTGVlZeTt7d2ge/LkSZo6dSrt3LmTVqxYQStXrqT09HQKDg6mEydOiHTPnTtHEyZMoD179lCPHj3ozz//pNTUVAoNDaXDhw+LdGtra2nMmDGUn59P4eHhtHHjRlq/fj1FRETQ3r17yc/Pj3777TfRPUePHqUZM2bQtm3baM2aNRQVFUVZWVkUGBhIpaWlos94+vRpmjJlCmVmZlJ0dDStWrWK/vrrL3rvvffo2LFjIrsVFRU0YcIEGjRoEC1atIgSExMpJSWF5s6dS4cOHaLXXnuN6urqyNvbm+rq6sjHx4cOHTpEH3zwAaWkpFBiYiItWrSI9u7dS2+99RZVVFQ02H/ttdfo2LFjFBISQn/99RetWrWKoqOjKTMzk6ZMmUKnT58WPUtpaSkFBgZSVlYWRUVF0Zo1a2jbtm00Y8YMOnr0qEi3srKS/Pz8aO/evRQREUHr16+nPn36UHh4OOXn59OYMWOotrZWdM/hw4cpNDSUUlNT6c8//6TIyEjas2cPTZgwgc6dO0fe3t4N14kTJyg4OJjS09Np5cqVtGLFCtq5cydNnTqVTp48KdItKyujyZMn065du2jZsmUUFxdH27Zto1mzZtH//vc/0TNUVVXRuHHjaN++fbRw4ULq3bs3JScn07x58+jgwYM0duxYqqmpEY1nQUEBzZkzh77++mtKSEigxYsX0+7du2nixIk0fPhwkf0hQ4ZQUFAQ7dixg2JjYykmJoZ27NhB06dPp5KSkgbdkSPH0Kuv1lCrVtUUEbGfli5dSvHx8bRlyxaaPXs2HTlyRGT3/Pnz5OvrS/v376f58+fThg0baMOGDTR//nwaPHgw+fr60vnz50X3HDlyhGbPnk1btmyh+Ph4Wrp0Ke3atYsCAgKovLxclCclJSU0ffp02rFjB8XExFBsbCzt2LGDgoKCqLi4WGR3+PDhNHHiRNq9ezctXryYEhISaPPmzTRnzhwqKCgQjU1NTQ2NHTuWDh48SPPmzaPk5GTq3bs3LVy4kPbt29eAEfbP4ogRH3/8sRNGCJeAEd9++60qjIiMjNSEEW+++SZVVlaqwgh73dOnT9M777zjhBEhISGSGPHWW2/R3r17JTHCx8enASNGjRrVgBFz584VYcSgQYNowoQJIozw9vamX375RRIj3nnnHRFGvPbaa04Y8fnnn0tixM8/T6TZs6upf/+FlJv7N0Zs3LhREiOqqoguu6yMunc/q4gR9t9LHowQdAWM+P77750wwvG7Zo8RH330Ea1fv14SI+zjImDE5s2bXWJEcXExBQUF0TfffOOEEUOHDhXplpeXU+fOnWnXrl0NGPH11183YMSvv/6q20tSszqWhDFGAN4nouUX/r4EQAWAj4go2k5vMoBHieglBVsvA/iOiD60411DRCcYY/cAWALg30RUK3N/K9hmkwRqD6DQOpbEIouU6dw54PXXgdxcYONG4P77m/qJLLJIO8XGAh9/DFRU2P7u2hWYO9e287UchYQAAwYAOTnAvfca85zNgaxjSfjpXwAuBnDcgX8cgOwCScZYPGwvQW8zxgoZY0Ib3HLGWA6A+QD+I/eCBABEVE1E5cIF4IyjTlNvXW+EDetYEnMe1WDmIwPatgVWrbKdPfX668DBg9y3NtqnHvdbx5KYM9dd6RlxLMmOHUCPHsAbb9iOC1m61HaO2muv2c40lKKyMtvKtU8/df2C5Gm5riQ3W64395ckgRyny5gE729lojeJ6GoiakNENxJR2gX+c0R0PxE9SUTpPI4ZY99eeLHaBgAHDhyAn58fqqurUVtre8fy8fFBUVERZs+ejbS0NMTHxyMqKgo5OTkIDAxEeXl5QwL4+Pjg1KlTmDZtGjIzMxETE4NVq1Zh+/btCAkJQXFxsUi3oqIC/v7+yM3Nxa233orExERs2rQJYWFhKCgoEOnW1dVh7NixOHToEObNm4eUlBQkJSVh0aJFyMvLw/jx4/Hdd9+J7jl27BhmzpyJtLQ0xMXFITo6GtnZ2ZgyZQrKyspEn7G0tBRTp05FVlYWli9fjtWrVyM9PR1XXHEFjh8/LrJbWVkJf39/dOvWDZGRkVi3bh1SU1MRHh6Ow4cPo66uDvX19fDx8UF9fT1Gjx6Nw4cPo2PHjkhNTcW6desQGRmJvLw8tGjRApWVlQ32a2trcfz4ccyYMQPp6elYvXo1li9fjqysLEydOhWlpaWiZykrK8OUKVOQnZ2N6OhoxMXFIS0tDTNnzsSxY8dEulVVVRg/fjzy8vKwaNEiJCUl4dlnn8W8efNw6NAhjB07FnV1daJ7CgoKEBYWhk2bNiExMRGLFy9Gbm4u/P39UVFRAR8fH/z000/w8fFBcXExQkJCsH37dqxatQoxMTHIzMzEtGnTcOrUKZFueXk5AgMDkZOTg6ioKMTHxyMtLQ2zZ8/Gp59+KnqG6upq+Pn5Yf/+/YiIiMBTTz2FjRs3Yv78+cjPz4evry9qa2tF41lYWIjQ0FC88MILWLt2LZYsWYI9e/YgICAA/fv3F9n/8ssvERwcjIyMDKxcuRKxsbHIyMhAUFAQTp48KdI9c+YM5s6dhMDAXNTXn8Xzz1dg1artmDNnDoqKikS6NTU1GDduHA4cOIAFCxYgOTkZycnJWLBgAbp3745x48ahpqZGdE9RURHmzJmDrVu3IiEhAcuWLUNOTg4mTZqEM2fOiPLk5MmTCAoKQkZGBmJjY7Fy5UpkZGQgODgYJSUlIrv9+/dHQEAA9uzZgyVLlmDt2rXYsmULQkNDUVhYKBqb2tpa+Pr6Ij8/H/Pnz8fGjRvx1FNPISIiAvv372/ACPtnccSIO++80wkjBPsCRrz55puqMGLx4sWaMOKiiy5CVVWVKoyw1y0tLUXbtm2dMGLGjBmSGNGiRQvk5eVJYsTo0aMbMOKHH35owIjw8HARRnTr1g3+/v4ijPDx8UGvXr0kMaJt27YijKitrXXCiIcffrgBI44cOYZ33y3C3XcDDz88Fm3bVuHAgfGYO/cQ9u6twpNPnkV09DYRRtTW1uH553NQVQVcf/1klxhh/73kwQhBV8CId955xwkjHL9r9hhx0003ISkpSRIj7OMiYMSWLVtcYkRJSQmCg4Px+uuvO2HEf/7zHyeMaNWqFXJycrBs2TIkJCTgxRdfbMAIPz8/pf8tqyOt9TozXXDoSQJwCYBa2Epw9nqTAWww+Nmcdtz28/MjI0kPf2pt8Ogr6cjJ1PAdec097lpjriTnia8Ur7ExOHiQ6PrriR54gKi4WN29WuNullyXk1m5zq/rToxxNQ4hIUQAUWqqs63du4luusl2rV9v41VWEg0caLtn6VLZx+Z6Vl4yOteV5HrkurXjNicR0XkA6QBedxC9DmCTEc+gNJNUVFQEwLiZpEsuuUTzTFLnzp1V/Uq0/4xyM0lVVVWyM0mPPvqo5K/Eo0ePSs4kEZHTTNLJkydFvxKLiooMnUm68cYbNc8kdevWjftXoqCrNJP07LPPKs4kdezYUfJXov14Cr8Sb731Vqdfia+//rrI/osvvqhqJmnSpEnIyclBevoyjBqVgqKiGvz73yexa9dR7pmkf//735pmkoqKilTNJL3++usuZ5KEsZGaSerYsaPsTFJRUZETRrRu3doJIwT7Akbce++9hs4klZSUaJ5JOnPmDPdM0smTJ7lmkt577z3ZmaRHH31UciapU6dOkhhx5swZEUYUFRU5YcSVV16JtLQ0BASEY8iQejz22E4895wzRmRkLIK//2ZccUUZXnkFuO22Glx5ZSWmTSN06bIG3bvzYYT997IxM0kPPvigqpmkFi1auJxJKioqUpxJcsQIYSbp7rvvdsKIl156yQkjSktLRTNJt912mzWTJHUBaAfg0QsXARh84d83X5ALWwD0hm0LgADYtgC4xeDndJpJioiIICNJD39qbfDoK+nIydTwHXnNPe5aY64k54mvFE9rDLKyiK66iujJJ4l4DyzX6tMsuS4ns3KdX1fQ27mT6JdfiL7+migggKikRDvGKI1D//5El11GdOyY8vPV1RHFxNjOMRw5kig3V1mf91nddb/ZMUbPmaTmsOP2E7DtWyTQxAv/nQvgSyKKZIxdBeA3AB1h2xTybSI6ZOxjOtN1ag7XMYk/tTZ49JV05GRq+I685h53rTFXkvPEV4qnNQYPPgisXQu8+irw9ttAfPzfxzPIkVafZsl1OZmV6/y6V1/dEYMGAYGBwDXX2BYFhIXZzgwcMOARfPwxv22eGF933XVIT7etTgsIAK69Vvn5LroIePdd29UY8rRcV5KbLdc9vtxGRElExCSuL+10phPRrUTUiogeJ6Jko55Pqdy2YMECAMaV25KTkzWX2xxLRa6m0u0/o1y5bfXq1bLltqNHj0pOpS9cuFCy3Pbnn386lduWLl0qmkpfsGCBoeW2nJwczeW2Fi1acE+lC7pK5TbHz+hYbsvKypKcSrcfT2EqPTc312kq/fz58yL7Z8+ebVS5TZhK37p1K3bsmIP584uRnl6Nd98FfvvNV7HcduLECU3ltgULFqgqt50/f95luU0YG6lyW1ZWlmy5bcGCBU4YkZqa6oQRgn0BI/Lz8w0tty1evFhzuW3FihXc5balS5e6LLf98cdo/P77A5gypQ7Dh5/GmDHzMHlyKhYu3IgHHsjHmDH34aWX/sK5c+JyW3l5uSRGrFixQvT9WbBggRNGpKVtx+efn8X1159E9+6uMSIlJUUTRth/LxtTbisoKFBVbktKSnJZbluwYIFiuc0RI/6/vTMPj6LK+vB7RUHBuMDM4IbooKOOOq6oo8joGB0QRWUR9ENxIC4gguIGjDCfTgBFEEEUCCKRRUVlERAVhEF2RDDsILIjiyxGVlmS8/1RSb5Op7pSlequXjjv89SDnHPq3tu/On24Vt2uW/i4bd26dSVqxP79+0vUiMJ/IwtrxKpVq/RxWzIf2DxuGzp0qARJNPrz2oabeKeYSD4v9nBbquvuV3Mnvxt97WzR1HzmTJFKlURuv91a5BoJv30mSq5H8mmuu4v9179EjMmX8eNL+vLzRZo1myfGiGRkFH9jtdvvgF1c8+ZzBaxcDYJky3UnfzRyXd+4nYSH3SRp/fr1EiTR6M9rG27inWIi+bzYw22prrtfzZ38bvS1s0Vb86lTRU48UaRePZFDh+xj/PaZKLkeyae5XnrsqFHWv3IvvLDbsY2hQ0WOO06kWTORI0ec2y5N402bRNLS8qRlSxcfIEokW647+aOR6/rrtiTC6XFbRkYGENzjtg4dOvh+3Pb+++97upUe+hkjPW57+umnIz5u69u3r+2t9EcffdT2cdtzzz1X4nFbq1atij1uy8jICPRxW7du3Xw/bvvggw9c30ovjHV63DZgwADHx22ZmZm2t9JDr2fhrfRXX321xK30IUOGFGt/0KBBvh+3hb4n6dZboUmTD5g8Wbjqqh9YubLk47Z+/fr5etyWkZHh6XHbkCFDSn3cVnht7B63ZWZmRnzclpGRUaJGdOrUqUSNKGy/sEb06tUr0MdtTzzxhO/HbU899ZTrx22tWrWK+LitbduBPPywcOmly0lLeyfir9v69u3Lzz/34v33D/PBB/k0aQL/+7/dGThwoG2NeOqpp4rViIyMjKIasWjRUurU2UFeXi5Nmy50XSP8Pm4L/V6W5XFb7969PT1ue/HFF0t93JaRkeH4uC28RhQ+buvZs2eJGvHuu++WqBFPPvlksRrx2muvxeRxW0ptS5LIGGNOAX4N3ZYkLy+PcuXKBTaGaPTntQ038U4xkXxe7OG2VNfdr+ZOfjf62tlipfnnn0ODBtabjD/9FCqEbATkt89EyfVIPs31yLG5uXDddXDiiTB7Npx0kjttx4+Hxo2hdm349NM8Tjml9O9A6N87dIAePWDy5Dxuuy15dA8615380ch13ZYkRejevXvS9ee1DTfxTjGRfF7s4bZU192v5k5+N/ra2WKleb16MG4cfP013HsvHDwYvT4TJdcj+TTX7WPz8uB//sfa/mPMGOtXkG61vftu+PJLmDMH/vzn7Wyw+Q10JI379oXXXoPXX4c5c5JL96Bz3cmfaLmud5ICwu5OkqIo0WHKFOsfuJtugs8+g4oV4z0iJV689BJ06wZffAH/+EfZ2li40LpDuWcPZGVBw4ZgjH1sXh78+9/QtSs8+6w1SYoUqwSD3klKIpzWJKWnpwPBrUlq0qSJ7zVJ//73vz2tNwj9jJHWJN1zzz0R1yQ988wztusN0tPTbdckNWzYsMSapLp16xZbk5Senh7omqRHH33U95qkwsPNeoPCw2lN0gsvvOC4Jqlly5a26w1Cr2fheoPHH3+8xHqDzp07F2u/Y8eOUV2TVBhb+AqA889fS/v2k5k1K4+bbspl8OCRtG/f3teapPT0dE9rkjp37lzqmqTCw25NUsuWLSOuSUpPTy9RIx544IESNaLwKKwRbdq0CXRNUp06dXyvSbrrrrtcr0mqW7dusTVJ3bqtoGtXeOGFXL777v/fuP3KK69EXJP0zDPPlHjj9sSJmdxzz8tUr76Oxo3hqqt20qXLbL7/fgl33XUXubm5vPxyV776CipXXkG3bsLdd8+mefOljB07hubNm3uqEX7XJIV+L8uyJqlt27ae1iTdf//9pa5JSk9Pd1yTFF4jCtckPfnkkyVqRKdOnUrUiDvvvLNYjXj88cf1FQDJfGDz67aNGzdKkESjP69tuIl3ionk82IPt6W67n41d/K70dfOFpTmM2eKpKWJ1KolsmzZJl9tJUquR/Ilku7R7K+sub54scjJJ4s0bmz9tN9tm6Xl+oQJIldeaf1KLi1N5PLLD0nNmiKnn27ZrrjiN5kxo+yfIRr47S/oXHfyRyPX9ddtKcKUKVOSrj+vbbiJd4qJ5PNiD7eluu5+NXfyu9HXzhaU5jfdZL2Ze8kSqFfvRHbsKHtbiZLrkXyJpHs0+ytLru/YAfXrQ40aMGRIycddfmpMvXrW47f586FTJ6hceR1/+Qs88wzMmwft2n1IrVpl/wzRwG9/Qee6kz/Rcj0VtiVJWv70pz8lXX9e23AT7xQTyefFHm5Ldd39au7kd6OvnS1Iza+/HqZNg9tuO4VatWDSJKhe3Xs7iZLrkXyJpnu0+vOa64cPW2uGDhyAb76BSpW8tekm142Ba6+1jtq1d3Hjjf8fd/Sou2sTS/z2F3SuO/kTLdf1TlIcORj6U5wk6c9rG27inWIi+bzYw22prrtfzZ38bvS1swWt+ZVXwptvfsfRo3DjjbBsmfc2EiXXI/kSUfegc33//oO0bAlz58Lo0XDuud7b9Ftj3F6bWOK3v6Bz3cmfaLmuk6QY47RwOysrCwhu4faECRN8L9zeunWrp0WZoZ8x0sLtkSNHRly4vXTpUtuF24MGDbJduD169OgSC7ezs7OLLcosXAQa1MLtWbNm+V64Xbi42c2izMJYp4Xbq1evdly4PX36dNtFmaHXs3BR5pw5c0osyvzpp5+Ktb9u3bqYLty227stN3cBTZv243e/E2rWPMjs2d4WbmdlZXlauP3TTz+VunC78LPaLdyePn16xIXbWVlZJWrExIkTS9SIwvYLa8TChQsDXbg9ZMgQ3wu3R4wY4Wrh9oEDB3nqqTxGjBBatZrNoUP2e7cVfm8iLdxeunRpiYXbmZmZrFmzxrZGWLmVW+zahNeIKVOmBLpwO/R7WZaF24sWLfK0cHvcuHGlLtzOyspyXLgdXiMKF24vWLCgRI1Yv359iRoxdOjQYjVi7ty5unA7mQ9sFm6vXLlSgiQa/Xltw028U0wknxd7uC3VdferuZPfjb52tqA1D+3zl19Ebr5Z5KSTRMaM8X5+NOPLkuuRfImoe1C5np8v0qWLtXC6f39/bfqtMW6vTSzx21/Que7kj0au68LtFGHChAlJ15/XNtzEO8VE8nmxh9tSXXe/mjv53ehrZwta89A+TzsNvvrKWoDboIH1Hhtx8Xq4RMn1SL5E1D2IXBex3mz9yitw550zeOIJf236rTFur00s8dtf0Lnu5E+4XPc7y9Kj7HeS9u/fL0ESjf68tuEm3ikmks+LPdyW6rr71dzJ70ZfO1vQmtv1mZdn7QgPIi1aRN4YN9L5XvvzGuPVl4i6xzrXjx4VadXKuoa9e7vvL5Y1xu21iSV++ws615380ch1vZOUIrzxxhtJ15/XNtzEO8VE8nmxh9tSXXe/mjv53ehrZwtac7s+jzsOMjPh/fdh2DDrbcxOrwhIlFyP5EtE3WOZ63v3wn33wcCB8O678PTT7vuLZY1xe21iid/+gs51J3+i5bpuSxIQui2JoiQOM2daj94qVICPP4a//jXeI1Kc+PFHa4K0cSN89BHUrRvvESmJjG5LkkTotiS6LYluSxL7bUnsft3mtC3JDz+8x+DBCzn11F+4+eZ8OnbcRu/eui1Jom1L8vnnE3n55XVcdtlhDhw4SvPm/albN/K2JJF+3eZ1W5LMzEw6dOhgWyMKtyUJvTbhNUK3JdFtSfSIwpqkn3/+WYIkGv15bcNNvFNMJJ8Xe7gt1XX3q7mT342+dragNXfb5+HDIu3bW2tcGjYU2bnT2/le+ytLrkfyJaLu0cz1n38WadrUujaPPCKyZ0/Z+4tljXF7bWKJ3/6CznUnfzRyXdckpQijR49Ouv68tuEm3ikmks+LPdyW6rr71dzJ70ZfO1vQmrvt84QToFcvGDUKpk6Fyy6DiRPdn++1v7LkeiRfIuoejf4+/XQ0WVlw0UXWrxI/+MDaaiQtrez9xbLGuL02scRvf0HnupM/0XJdJ0lxpGbNmknXn9c23MQ7xUTyebGH21Jdd7+aO/nd6GtnC1pzr302aABLl1pv6q5XDx57DC6++Pqo91eWXI/kS0Td/fY3ZQq8/XYzHn8c7rkHVq2CBx7w318sa4zbaxNL/PYXdF138idaruskKY5s3bo16frz2oabeKeYSD4v9nBbquvuV3Mnvxt97WxBa16WPs86y7qLNHAgfPgh3HvvxQwb5u6dSm77K0uuR/Ilou5l6U/EWkj/979DejocOXKYb76x7h79/vfR6S+WNcbttYklfvsLuq47+RMt13WSFEfy8vKSrj+vbbiJd4qJ5PNiD7eluu5+NXfyu9HXzha05mXt0xjrLtKKFXDZZbt4+GGoXRsWLIhOf2XJ9Ui+RNTdS3+HD8OIEdaGxDffDLt3w7hx0KPHDGrXjm5/sawxbq9NLPHbX9B13cmfaLmuk6Q4ct555yVdf17bcBPvFBPJ58Uebkt13f1q7uR3o6+dLWjN/fZ5zjnw9tu7mDLF+sf72mutR3JLlvjrryy5HsmXiLqX1p8I5OTA889D9erQrJn1RvQJE2DhQrj7bjj/fOc2vPTnJs5vjXF7bWKJ3/6CrutO/kTLdZ0kxZEZM2YkXX9e23AT7xQTyefFHm5Ldd39au7kd6OvnS1ozaPR54wZM/j732HxYhg6FBYtgiuugIYNYcaMko/hYpXrkXyJqLtdfyLw/ffWizwvvxyuugqys6FRI1i2DCZNstaBHXec9zG7jY1ljXF7bWJJNHI92vEpU2P8/jxOj7K/AmDXrl0SJNHoz2sbbuKdYiL5vNjDbamuu1/Nnfxu9LWzBa15NPoMP//wYZFBg0Quvtj6WfpVV4kMHCiye7f7/sqS65F8iah7YX9btoh8/LFIRobIWWdZeqWliTzwgMiECZaWpbXhpT8/cX5rjNtrE0uinevRiI9njYnmKwD0jdsxxhjzJPAk1l27i77//nsmTZpEu3btqFevHl9//TWZmZm0aNGCL774gr/85S/s3r2b/fv3c/HFF/P111/zyCOP0LdvX1566SUyMzNp3bo1H374ITfffDPr16+nXLlynHnmmcyfP58GDRowcODAotj27dvTv39/7rrrLrp06cJjjz3GSSedxA8//MBtt93G+++/XxTbsWNHevTowYMPPsj06dM5//zzOXr0KNu2beOaa65h7Nix7Nu3jxNOOKHonIyMDMaPH8+VV17Jrl27OHjwIBdeeCH//e9/efjhh2nYsGHRZ2zTpg3Dhw/nb3/7G2vWrKF8+fJUrVqVV155haysLAYNGlTU7rPPPss777zD5s2bueGGG/j9739PhQoVWLNmDbfccgstWrRg0qRJdOvWjU6dOtG9e3ceeughnnnmGdq3b8+hQ4fYsWMHV199ddGL0nr16sVLL71Eeno6I0aM4LPPPuOaa65h+/btHD58mBo1avDNN9/QrFkz+vXrVzSWp556iqFDh3LrrbeyevVqTjrpJKpUqUJOTg5333037777blHsc889x1tvvcW9997LggULOOOMMxgxYgS1a9emdu3afPDBB7zwwgt079696JzmzZszZcoU/vSnP3Hw4EF27drFFVdcwYQJE2jVqlWx1+0//vjjjB49mpo1a7J161by8vI477zzmDFjBg888ADvvPNOUWzbtm3Jzs4mPT2dlStXUqlSJSpXrszixYtZtWoVp5xyStEYnn/+efr06UPDhg359ttvi/Juw4YN1KpVi48++ojnnnuOOnXqFF3PRx55pOiFiY0aNSI3N5fLL7+cL774gt27d1OhQoWi9vfv30/16tW54YYb2Lx5MyJCtWrVmDNnDvfffz/9+/cvim3Xrh2DBw/mjjvuYMWKFaSlpXHqqaeybNky6tSpw3vvvVcU++KLL/LGG2/QuHFj5syZQ7Vq1QDYtGkTCxYsoGrVqkUvlSw8p0WLFnz55Zdceuml/Prrr+zdu5dLLrmESZMm0bJlS/r06VOUJyNHjuTjjz/mr3/9K5s2bcIYw1lnnUN29maWL7+DqVOP54QTjuOCC1Zw0UVLuPrqnTRq9HeWLFnCaaedRlpaGitWrOD2228nOzu76Np06NCBnj170rRpU2bOnEn16tWLrtV1113HqFGjaNeuHa+//nrRWIYOHVqsRmRnZ9O5c+diNaKQwhqxYsUK7rjjDtc1YtGiRVSpUsVTjdi3L5/vvvsNkSsYMGAxJ554G2vXWreFqlTZRaNGJ1Kp0jQaNqzKnj07S9SIt956q6j9Nm3a0KxZM7p3716sRhS+dDa8RjRo0IC+ffuycOHCEjVi2LBhdOzYkW7dupGfn0+5cuV46KGHmDZtGjVq1CiqEXPnzuWcc86hdevWRTUiMzOTffv28cc//rFEjejYsSPDhw8vqhHp6emMGjWqWI0YO3Ysbdq0cV0jjj/+eNatW1fmGlG/fv2i76WbGlHYbmGN+PHHH7nllluK1Yi6desW+66F1oiOHTvSunVrypUrV6JGvPrqq0W6ZGdnM3nyZC655BL27t3rWCOeeOIJPv30U5YsWULdunWL1YhNmzZRsWLFYjWiSZMm9OzZs6hGjBo1iuuvv546derwzjvv0LVrV4jCG7d1khQQui2JoqQeW7fCyJEwfLi1uPu44+CGG+COO6ytTq6/HqzdEZKf3bthzRpri5Aff7RemZCTA6tXW4/UjjvOeoVCrVrWcdNN1i8GFSVodFuSFKHwNevJ1J/XNtzEO8VE8nmxh9tSXXe/mjv53ehrZwta82j06eb8M8+0Nlr97jt47rk+DBwIZ5wBffpYG+iefjpceik0bQovvwxNmoxm0SLIzS25psnr9yBauh85Ym30u2SJ9fLG7Gzo1g3atLEWq9esCZUrQ5UqcN118OCD0LcvbNtmfcZBg6zPv28f3HdfJn36QOPGZZ8gRTvXS4vzW2PcXptYEkSue41PlRqjd5ICwu5O0p49ewK9qxSN/ry24SbeKSaSz4s93JbquvvV3MnvRl87W9CaR6NPP7kuAj/8AHPnwrx51gLlFSusyUghFStav6I7+2xrElKx4mH+8IfynHaa9Yuvk06C8uWt4+jRA5x2WkXKl7fOzc+HffsOcOKJFcnPt/6elwe//HIAqMiBA3DgAOTmHiIvrwIHD8L+/dbk7JdfrLtCv/xiHfv2lfwsVapYE8CzzrLGWKMGXHCBddSoEfnuWCLmemlxfmuM2+9ELIlnrpc1JpY1Jpp3kuK+oPlYObBZuN2nTx8Jkmj057UNN/FOMZF8XuzhtlTX3a/mTn43+trZgtY8Gn3GIte7dRsos2aJjBwp0quXtW9c06Yi//iHSPXqW+Wii0SqVhWpUMFa7FzWo0IFkdNPFzn11L1ywQUil18ucv31Vj9Nm4q0bi3yr3+J9OwpMniwyOjRIrNmiaxbJ3LwYBkFc6lBNNtwGxvLGuP2OxFLEjHX41ljorlwO+6Th2PlsJskLVu2TIIkGv15bcNNvFNMJJ8Xe7gt1XX3q7mT342+dragNY9Gn/HO9fx8kd9+szZ2nTVrpWzZYk1i1q8X2bhRZOrUVbJli8i2bdZmsDt3isyfv1yOHi37Z/BLIuZ6aXF+a4zb70QsSbZcd/JHo8boBrcpwsqVK5OuP69tuIl3ionk82IPt6W67n41d/K70dfOFrTm0egz3rluDFSoYG3sum3bMs48E847z3oJY7Vq8MsvSznzTKha1dq+o0oV2LhxBeXKlf0z+CURc720OL81xu13IpYkW647+ROtxugkKY5UqlQp6frz2oabeKeYSD4v9nBbquvuV3Mnvxt97WxBax6NPhMl1yP5ElH3RMz10uL81hi31yaWJFuuO/kTLdd1khRHKleunHT9eW3DTbxTTCSfF3u4LdV196u5k9+Nvna2oDWPRp+JkuuRfImoeyLmemlxfmuM22sTS5It1538iZbrOkkKwxhTzRgzzRiz3Biz2BjTOMR3lzFmlTFmtTEmw29fixcv9ttE4P15bcNNvFNMJJ8Xe7gt1XX3q7mT342+dragNY9Gn4mS65F8iah7IuZ6aXF+a4zbaxNLki3XnfwJl+t+FzWl2gGcCVxZ8N9/ADYDlYDjgR+As4E0YDVQ2UO7JRZu//TTTxIk0ejPaxtu4p1iIvm82MNtqa67X82d/G70tbMFrXk0+kyUXI/kS0TdEzHXS4vzW2PcXptYkmy57uSPRq7rwu0YIiJbRSSn4L9/BnYDlYHrgGUi8pOI7AUmAv/w09d7773nc7TB9+e1DTfxTjGRfF7s4bZU192v5k5+N/ra2YLWPBp9JkquR/Ilou6JmOulxfmtMW6vTSxJtlx38idarif9yySNMbWB54FrsO4C3SciY8NiWhfEnAksA54WkVK3DDbGXAtki8hlxphGwC0i0qbA9zwgItLT5Th1WxJFURRFiTG6LUlxKgGLgDZ2TmNME+BNoCtwFTAD+MIYc65To8aYKsBQ4LFCk02Yrxlmsr26vixt6LYkui2J2zFFm2TbqiFe25JEk0TM9dLidFsS3ZbEiaS/kxSKMUYIu5NkjJkHLBSRViG2FcBYEelojGkLtChwXScih40xFYDJwCARGVZwzo3A8yJyX8Hf+wDzROSDCGOpAFQIMaUBm0PvJB06dIgKFSrYnR4TotGf1zbcxDvFRPJ5sYfbUl13v5o7+d3oa2cLWvNo9JkouR7Jl4i6J2Kulxbnt8a4vTaxJNly3ckfjVzXO0kuMcaUx3oMNynMNQm4EUBE+orIlQXHYWOMAbKBqYUTpAK+BS4zxpxtjEkD7gS+cui+I/BryLEZYO3atfTo0YNDhw5Rv359wJoBb9myhcGDBzN//ny++uorRo8ezfLly+nbty979uwpmiVnZmaye/du3n77bRYvXsy4ceP4/PPPWbhwIQMHDmTHjh3FYg8cOECvXr1YtWoVLVq0YMqUKcyePZvs7Gw2bdpULDYvL4/u3buzYcMGhg0bxsyZM5k2bRofffQRq1ev5vXXX6dnz57Fztm2bRuDBg1i/vz5fPnll4wZM4alS5fy1ltv8euvvxb7jLm5ufTr148lS5YwduxYJk6cyIIFC3jwwQfZvn17sXYPHjxIr1696Ny5MyNHjmTq1KnMmjWLoUOHsnHjRu655x7y8/PJzMwkPz+frl27snHjRh5++GFmzZrF1KlTGTlyJKtXr6Zhw4YcPHiwqP369euzfft2srKyWLBgARMnTmTs2LEsWbKEfv36kZubW2wsv/76K2+99RZLly5lzJgxfPnll8yfP59Bgwaxbdu2YrG//fYbr7/+OqtXr+ajjz5i2rRpPP300wwbNowNGzbQvXt38vLyip2zadMmsrOzmT17NlOmTOHjjz9m1apV9OrViwMHDpCZmUmfPn3IzMxkx44dDBw4kIULF/L5558zbtw4Fi9ezNtvv83u3buLxe7Zs4e+ffuyfPlyRo8ezVdffcX8+fMZPHgw//nPf4qN4dChQ/To0YM1a9bw4Ycf0rZtW2bMmMHw4cNZv349r776KkePHi12PTdv3syQIUNo3749kydP5pNPPmHlypX07t2bHj16FGu/W7duDBgwgJycHCZMmMD48ePJycmhf//+7Nq1q1js3r17efPNN1m+fDmjRo1i0qRJzJs3j/fee48tW7YUiz1y5AivvfYaa9euZcSIEUyfPp3p06czYsQIunTpwmuvvcaRI0eKnbNlyxbee+895s2bx6RJkxg1ahTLly/nzTffZO/evcXyZNeuXfTv35+cnBzGjx/PhAkTyMnJYcCAAezcubNYuz169KB3796sXLmSTz75hMmTJzN37lyGDBnC5s2bi12bo0eP8uqrr7J+/XqGDx/OjBkzaNu2LR9++CFr1qwpqhGhYwmvEY8++miJGlHYfmGN6NChg6ca8fHHH/uqEQ0aNOC3337zVCNCY3Nzc2nSpEmJGpGVlWVbIxo2bMjq1atta0TXrl2LakTv3r2LasTQoUOL1YjOnTvTq1evYjUiMzOTzMxM2xrRpEmTYjWifv36JWpE69atPdWImTNn+qoRod9LNzWiMLawRnTq1KlEjQj/roXWiH/+859MmzbNtkaE6lJYI+bOnVtqjdi5cycDBgzgxRdfLFEjunXrVqJGNGrUqFiNePbZZ4tqRI8ePWz+SS4bKX0nyRhzFvATcJOIzA6J6wQ0F5GLbNqoBUwHQn9P+JCILDHG1Ad6Yk0ue4hIlsNYbO8kbdq0qehO0tq1a/njH/9Yps9aFqLRn9c23MQ7xUTyebGH21Jdd7+aO/nd6GtnC1rzaPSZKLkeyZeIuidirpcW57fGuL02sSTZct3JH41c37NnD9WqVYMo3Ek63s/JSUT4TNDY2KxAkZlEuMMmIuOAca46FDkEHDLGPAk8SYHWBRdOURRFUZTYkgboJMmBnUAecEaY/Q/A9iAGICJvA28XPMY7C9hb4ErDegR3Togt1nyL9SqDINtwE+8UE8nnxR5qOxZ096u5k780fe1s8dA80rhieX6scj2SLxF1T8RcLy3Ob40J/3sy6h50rjv5o5XracCWUsZYKik9SSpYY7QAuB0YE+K6Hfgs4LEI1qM/AKw5EwB7/d4OdIsxJt9vX17bcBPvFBPJ58UeajsWdPeruZO/NH3tbPHQPNK4Ynl+rHI9ki8RdU/EXC8tzm+Nsfl74X8mje5B57qTP4q5HhXtk36SZIw5GbggxHS+MeZKYLeIbATeAIYZY74D5mD9pP9cYEDQY00A3o5DG27inWIi+bzYo/G5/RC07n41d/K71TfemoP/MSRKrkfyJaLuiZjrpcX5rTHx1hySL9ed/AmV60m/cNsYcwvwXxvX+yLySEFMa+AFrJdJLgWeEZHpAQ3RlsKXSxKFhWWKe1T34FHN44PqHh9U9+CJpeZJfydJRKZh/6LH0Jh3gHcCGZB7DgEvF/ypBIfqHjyqeXxQ3eOD6h48MdM86e8kKYqiKIqixIKUfpmkoiiKoihKWdFJkqIoiqIoig06SVIURVEURbFBJ0mKoiiKoig26CRJURRFURTFBp0kJTjGmKPGmJyC4914j+dYwRhT0RizwRjTM95jORYwxqQZY+YX5PkSY8yj8R7TsYAxppoxZpoxZrkxZrExpnG8x3QsYIwZY4z5xRjzabzHcixgjLnLGLPKGLPaGJPh6Vx9BUBiY4zZKSK/i/c4jjWMMV2BC4GNIvJcvMeT6hhjygEVROSAMaYi1ktfa4rIrjgPLaUxxpwJVBWRHGPMH4CFwEUisj/OQ0tpjDG3AicDzUWkUbzHk8oYY44HlgO3Ym1VshC4XkR2uzlf7yQpShjGmAuBi4GJ8R7LsYKI5InIgYK/ngiUo5SXxCr+EZGtIpJT8N8/A7uBynEd1DGAiPyXYDd7Ppa5DlgmIj+JyF6suv4PtyfrJCmKGGNqG2PGG2O2GGPEGHOvTUxrY8w6Y8xvxpgFxpibS2n2lIK4mcaYv8Vm5MlLjDTvCXSMyYBThFjobow5zRizCGs37x4isjNGw09aYpTvheddCxwnIpuiPe5kJpaaK6UTBf3PImRzeaz6crbb/nWSFF0qAYuANnZOY0wT4E2gK3AVMAP4whhzrkOb54nINcATwNCCPWqU/yeqmhtj7gF+EJEfYjLa1CHquS4iuSJyBXA+8KAxpmq0B50CxKLGYIypAgzF2gBcKU5MNFdc41d/uzvS7tcZiYgeMTgKLsK9YbZ5QP8w2wqge8F/twVyCo7yNm1+AVwb78+WqEc0NAe6A5uA9cBOrE0Tu8T7syXyEaNc7w80jvdnS+QjWroDFYDpwEPx/kyJfkQz14FbgE/j/ZmS6Sij/jcCY0J8fYAH3fapd5ICwhhTHrgGmBTmmoR1ERGRviJyZcFx2BhzujGmQsH55wB/BtYGOe5kpiyai0hHEakmIucBzwGDROSVQAee5JQx16sW3iUt+LM2sCrIcSc7ZdTdANnAVBEZFuiAU4CyaB70GFMZN/oD3wKXGWPONsakAXcCX7nt4/hoDFRxxe+wFqNuD7NvB86IcM4lwEBjTD7WDLqduFyRrwBl01zxT1l0PwcYXPCPtgH6icji2A0xJSmL7jcBTYDFIWs9HhKRJTEZYepRphpjjPkKuBqoZIzZDNwnIvNjNsrUpVT9ReSoMeZZ4L9YS4x6iIdfzeokKXjCn4UaG5sVKDIbuDzmI0p9XGte7CSR7JiM5tjBS64vAK6M9YCOEbzoPhNdmxoNPNUYEXH96yrFFY76i8g4YFxZGtYvR3DsBPIo+X8Xf6DkLFiJDqp5fFDd44PqHjyqeXyJuf46SQqIgmfRC4Dbw1y3A7ODH1Hqo5rHB9U9PqjuwaOax5cg9NfHbVHEGHMycEGI6XxjzJXAbhHZCLwBDDPGfAfMwfq57bnAgKDHmiqo5vFBdY8PqnvwqObxJe76x/snfal0YP2kU2yO7JCY1lg/Lz+ENQOuHe9xJ/Ohmqvux9Khuqvmx9oRb/117zZFURRFURQbdE2SoiiKoiiKDTpJUhRFURRFsUEnSYqiKIqiKDboJElRFEVRFMUGnSQpiqIoiqLYoJMkRVEURVEUG3SSpCiKoiiKYoNOkhRFURRFUWzQSZKiKIqiKIoNOklSFEVRFEWxQSdJiqIoiqIoNugkSVGUYxpjTCNjTI4xZpoxpkvAfT9W0O93xping+xbUZTS0Q1uFUU5pjHGPAKcJyL/eyyPQVGUkuidJEVRUg5jTL2COzTZBceJHs69zhgz3xizxxgjBcdBY8xCY0y9gpjOxpjlxpj8kJitxpjZxpjysftkiqIEiU6SFEVJKYwxNwFjgBeA04DmwIVuzxeRb0WkJnBuiPkmEblaRD4viPmPiPwZeL7A/z1wtojcKCKHo/AxFEVJAHSSpChKqtEeyAXmAwOBJiKyxGsjIpIb8tfdEcJ2Ffy5R0TyvfahKEpic3y8B6AoihItjDHlgHRgslgLLr+I85AURUli9E6SoiipxGXAKcCseA9EUZTkRydJiqIkPcaYVsaY74AJBaYWBT+rHxzHMS0oWNC9wRgzs2Ah+bwC29J4jUtRFPfoJElRlKRHRPqLyLXAWCAfuEFErhWRlnEc1qlAMxGpLiK1ROQWYBEgwNNxHJeiKC7RNUmKoqQSVwGrRGR/lNv9yBjzm439DIdzlonIiMK/GGPuAx4FeonI11Een6IoMUAnSYqipATGGANcAXwWg+abish6mz4fAYZEOGdTSNzZwLtADtAp+sNTFCUW6OM2RVFShQuBk4GF8R4IgIi0ATDGHAcMA04EHtD3KClK8qCTJEVRUoWrCv5MiElSCC8AtwLPishKKHrhpaIoCY5OkhRFSRWuLvgzJ56DCMUYcy3wCjBORAaEuNrEaUiKonhAJ0mKoqQK1wBrw96UHTeMMScDHwA7gZYh9nJAlXiNS1EU9+jCbUVRUoWrgaj9aswYc1rIX9MihJ1S6DfGmIK3fBfSF7gAqCMiO0Ps7YAj0RqnoiixQ+8kKYqS9BhjagCnA5Oi0NZ1xph5wIYQ81xjzHxjTL2CmJeMMUuANwr8VwM/GWNmGWPKG2NqAv/E2vPtYWPMcGPMJ8aYxUAv4Ge/41QUJfbonSRFUVKB6wr+nOi3IRH5Fri+lJhMINMhZD5g/I5FUZT4oneSFEVJSgru5mw3xlQD/gp8LSJb4j0uRVFSB72TpChKsnI/1hYf+cC9QOO4jkZRlJRD7yQpipKs/BtroXZvoIOIzIvzeBRFSTH0TpKiKEmJiIwBxsR7HIqipC56J0lRlGOdfcC9xphpxpguQXZsjHnMGDMN6+WSuUH2rShK6Zjir/VQFEVRFEVRQO8kKYqiKIqi2KKTJEVRFEVRFBt0kqQoiqIoimKDTpIURVEURVFs0EmSoiiKoiiKDTpJUhRFURRFsUEnSYqiKIqiKDboJElRFEVRFMUGnSQpiqIoiqLYoJMkRVEURVEUG/4PA5XU8+lFcxEAAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from kerrgeodesic_gw import lisa_detector\n", "hn = lisa_detector.strain_sensitivity\n", "plot(hn, (1e-5, 1), plot_points=2000, ymin=1e-20, ymax=1e-14,\n", " axes_labels=[r\"$f\\ [\\mathrm{Hz}]$\",\n", " r\"$S(f)^{1/2} \\ \\left[\\mathrm{Hz}^{-1/2}\\right]$\"],\n", " scale='loglog', gridlines='minor', frame=True, axes=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The effective power spectral density of LISA noise:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "psd = lisa_detector.power_spectral_density" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The signal-to-noise ratio for one day of observations is:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "103718.23722663395" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from kerrgeodesic_gw import signal_to_noise_particle\n", "theta = pi/4\n", "t_obs = 24*3600 # 1 day in seconds\n", "signal_to_noise_particle(a, r0, theta, psd, t_obs,\n", " BH_time_scale, scale=mu_ov_r)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot of the SNR as a function of the orbital radius $r_0$:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rmin = KerrBH(a).isco_radius()\n", "rmax = 50\n", "fsnr = lambda r0: signal_to_noise_particle(a, r0, theta, psd, t_obs, \n", " BH_time_scale, scale=mu_ov_r)\n", "graph = plot(fsnr, (rmin, rmax), plot_points=50, \n", " thickness=1.5, scale='semilogy', \n", " axes_labels=[r\"$r_0/M$\", \n", " r\"SNR$\\times \\left(\\frac{1\\, M_\\odot}{\\mu}\\right) \\left(\\frac{1\\, {\\rm d}}{T}\\right) ^{1/2}$\"],\n", " gridlines='minor', frame=True, axes=False)\n", "graph" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.4", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 2 }