{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# How to fit a rise time to an exponential instability with FITX\n", "\n", "FITX is a small library to help isolate and fit exponential rise times in unstable systems with saturation.\n", "\n", "In the following we show how to use the libary with the example of a dynamical instability in a particle accelerator which stops due to machine non-linearities.\n", "\n", "Copyright CERN, Adrian Oeftiger, 2019" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "import seaborn as sns\n", "\n", "sns.set_context('talk', font_scale=1.4, rc={'lines.linewidth': 3})\n", "sns.set_style('whitegrid', \n", " {'grid.linestyle': ':', 'grid.color': 'red', 'axes.edgecolor': '0.5', \n", " 'axes.linewidth': 1.2, 'legend.frameon': True})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Data\n", "\n", "We have stored the centroid motion of the unstable beam. Here we use both the $x$ and $x'$ data to obtain a purely positive signal to be fit exponentially. The quadrature signal $x'$ can also be obtained by using a `Hilbert` filter on $x$ (see e.g. `scipy.signal.Hilbert` with its imaginary part), e.g. for measurement data in a particle accelerator. In the present example, the data comes from a simulation with octupole amplitude detuning leading to a saturation effect." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "mean_x = np.loadtxt('./example_mean_x.dat')\n", "mean_xp = np.loadtxt('./example_mean_xp.dat')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(mean_x)\n", "plt.xlabel('Turns')\n", "plt.ylabel('Horizontal centroid position');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's construct the envelope or amplitude signal by using the quadrature signal $x'$:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "beta_x = 92.759\n", "signal_x = np.sqrt((mean_x)**2 + (beta_x * mean_xp)**2)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(signal_x)\n", "plt.xlabel('Turns')\n", "plt.ylabel(\"Horizontal amplitude\\n\" + \n", " r\"$\\sqrt{\\langle x \\rangle^2 + \\beta_x^2\\langle x'\\rangle^2}$\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Instability Fit\n", "\n", "Now let's use FITX in order to isolate the pure exponential instability from this positive signal and fit the rise time:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "from FITX import fit_risetime" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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KWV8isjfwyxDM6qiyoUhieYsNgS+BvTX7umhlrzfmrBbM+D0dkQ3EusHdQR3EnKGeXuyKlbHcfOiD+YVLRTRT9kcyeBtvILlcN4C3w3a/NMriUaTv+XqKhDJ3UZo4vyO9LdEzmLNXgD+JSEYbGhHJe4JJcBfyBNa7kexzbjANm0UZJ3qp7psugoj8BjNGXwIcoqovqOpjmJ8qgD/lUE7FvsSTiCvmm6WKICK7Yr78ALKZcDSUxrpe6ajY6+jKmFMwqrqAxAtvfxEZLbb8CiLSVkSOIqHIvAw8WIJqXIe5ApgF7BV8TGWkidT73bDdS0TSDZc+ifXE9AD+EZQgRKSVmLPV50n01BSTcpWbDz8DN4jIKcH3FiLSS0RuxpZWAhgRrnkxyOW6gdnmQPCRFIbsEJEuIvJb7GX4U6qEwcdSNMvsMBH5W9TrJCKdw2zhC0hjMB2cYJ6IvfTWxVaS2C+ST8hnVRE5QkSeJgc7nyzUWxtQzM/fruRvv/MI1sYGiUjH5IMicgRwTQger6pxpS+a2dlfRDIpB5thrh6mkXlWdCUQV8buEZGjxBbERkS6i8gZ2EdrC8w+7cV44tCuvheRd+NuL8Lz8HkRmRnklY6SX690VPp1dGXMKQrBOWjkZO8o4Csxh6mzMaPVTlgvwQHhJVFsomGYNsDTIjItw2/5y7MJ1PsurKt+LeALEflORKaE3zahjp+QsKXYN8Sbic0+Gof1jOS6LmfOlKvcPBmFORy9AZglIj9hKy2cEI7fjs3cKhZZrxuAqk4g4cfrOGB6aF8zsKWhbiFzr9F1mA8ksLVTvw/nNgNT1MaQoRcg+L7bH+vJWw8YC8wWkekiMg+biXk3tp5goTyGTcDZNabw7QR8oaqf55NhmLH5KmZzt2v8mIjsBdyBDRX/XpPW/lTViSTs1K6U9D7UIuXxEa27TFIlEiljtZgD7dHAvHDf/oS1p67YR8IJyYlVdTbwR2xJsUNg+VD6vdgIwb4a1pFNRSNdr3RU9HV0ZcwpGqr6O2ztsPuxqe4dsRf3i5iH763z9R/TANqR3XFtnZu8nPVWW/x6R8zL/zSsF2r18GsXi3ch5nT2ZcyJZ2vMs/+1mDPZhiwx05D6laXcPFiE2a/9DqtTG8yGaSJwqKoeV8wHdK7XLXAMtkLBZEyBa4G1rUNUNeMwr6ouU9UjMX95r2DXoBW2rNdJZHZEHOUxDrMlughbxmkmZle0BJPV7dhQYkFDzqr6E2an1oGEneXeFD6rLVWP23bAA5gs/qKq6Ya2/oApJusDx6aJU7FDWymIlrQ6FbuuX2LXuQ3m1uI+YJCqDlXVdGuojsLu8UuCQnQtsB+2WHc9x9YpKPX1SkdFX8ea2tqKUyAdx3EAEJFnMaVohKpeUt7aOGHo9WrgNlU9XkS+BA5SWxw63zzXBz7AbP56FbOHOvSSf4kp7itohSyVlQqp62ZmTVWdUkBew7B1HCdgvaanq2pOPculvF4Zyqz46+g9Y47jOE6xiHol9haRLbCe1NcKyTCsPvARtjpAITPtUhG54niiEl/gScQ9708pMK+7MWfXOwMjc1XEoOTXKx0Vfx1dGXMcx3GKgtpCy+9j5gB/BB4t0vBw1ll6eRLlV5FDW0lEythbRcjrBBLuWBrkkiRQquuVjoq/jq6MOY7jOMUkeiHuSv4uLZK5DjiI4r9s/xbyfajI+ZaDSBl7s5BMRGQ/bCLMzcCzwO9FJJsLl2RKdb3SUfHX0ZdDchzHcYrJw5jLjfmYr7SCUdWvgX8VI6+kfCtqyZwsRMb7eStjIjIAM/Ifh00C2BabBPN74Lxc8ynV9cpQXsVfRzfgdxzHcYpGcG77NbYmZr3lkZymidgqJBMx4/tBwc8dIvIEtszQ2o0wG77Z4sOUjuM4TtEINmI3Yr7YnAogzEYcD3yHrV4yP3b4Isyn4PBy1K254D1jjuM4juM4ZcR7xhzHcRzHccqIK2OO4ziO4zhlxJUxx3Ecx3GcMuLKmOM4juM4ThlxZcxxHMdxHKeMuDLmOI7jOI5TRlwZcxzHcRzHKSO+HJLjOGVFRJ4FdgRGqOolRcx3GHAn8IWqrpFnHoOB3wCbA92AGuAuVR0mIpdgjjCfU9WBRaiy4zjNFFfGHMcpCUEZWgN4VlWfLWtl8kBEDgQeCMFlwPSwnZlD2n2BfsBkVS3p4sUisj+wPbZQdB9gRaANVt+3gTHAPaq6NIe8BDgJW+S7D9ASmAa8AzylqjemSVcDHAwMC/XoBvwIvAbcrKr/yeO8bgeOCcGsCrWI7AacCGwD9MSu09vAnap6X0PLT5H/VsDJmKxXw96f04HJwD+Ae1V1WR75DgQGAlNUdXSh9XQqE1fGHMcpFcOwHi+AZzPE+xJQ7MXWlDg3bB8EjlLVuUnHp2P1/jJF2n2Bo7AlgUqqjAFXA6vHwrOAWmCV8NsDOE1E9lLV79NlIiLnAZcCrcOu+cASYK3w+xW2zFFyuvbYotB7hl2RwroSMBgYLCI3AaeEpZKyIiK7kFDEssVtAdwCHBt21QI/A92BQcAgERkCHKiqi3LJM0UZF2KyqQm7FgMLgJXDbw/g+CDj2Q3MfiChhxUYnU/9nMrHbcYcxykrqnqkqq6vqteXuy5JbBy2o1MoYqjq9aHeRzZyvZL5B3AcsCHQQVW7qmo7rPfmEkw52pIMa0WKyMXAldgH+l+B9VS1g6p2wZSaXYHb0iS/CVPElgEXAt1VtUdId3HYfxLwu1xORkQ6AbdiCs/rOSQZTkIR+yvQK5TfBevJWgjsDVyXS/kp6vMr4DJMEXsek2W7IJvewMgQdQDwx3zKcBzvGXMcx0lNh7CdU9ZaZEFVz0+z/2tghIi0A84DdheR1VT1q3g8EdmaxCLQp6rqqKR8fgaeCj+S0m4IHBGC16nqFbF0s4DLRGQl4DTgIhG5Q1V/yHJKf8J6+i7Hhkq3TBdRRHqS6MH8t6r+Jlb+fOAmEekIXAWcICI3qOp7WcpPJlK2Z2OLaM+KlfEdcL6IrA4cChwEnN7A/B3HlTGnshCRVYEzgd0we6TWwNfAf4GrVfXDpPjdMZuOvsBjqvrrFHnWAOOAvYCvgM1U9adwbBgxI/DwlXw2sBXQFRui+hcwMv6QTlHGSsBZoYw1MFucqdgL7ipVnZImXTSs8yvgDeD3wIHYy2oe8DJwmaq+mq7skM8uWO9Jf2z4aAHwQaj7qFQ9PyIymjDUFgzWD8ReqpsC7YCPgmz+FreVicksYriIDKcuv4rsyDIZ8IvIilivy57ARlhvT1vMjukF4K+qOinTuTcEEVkD+Dxp9zNmSmWoak2IewlJBvzB/ueZWNqjROSopPyObmTboJdj/1fF2nici7FRkonJilgO/JrE0N2f08QZibWbjsAhQNoe0CC/k7Dh38uBm7OUvzPQPkv5f8WGGDtgQ+fnZMkzmZXD9qMM9/gkTBnrkOZ4PVK0tR1j93vE8nsil4kumSaVxNNjsj0FOAxYD7Px209VH0rxzNsCe+4MAHpgz9uHsOfOjDT16IdNfNkBGyqvBb7HnnnPYTaMH6ZK21zxYUqnYhCRg4CPsYfpJphCsBRYGzgemCwih8XThIfFUMz2ZS8R+W2KrH+LKUlLgcMiRSxF+ScBT4e4bbH7Z13gfOBNEemTJt32mOLze2zoq2Uoaz3gVOCDYISdiZWBN4E/YIrYMuzBuBcwMRgvpyq7rYjcAzyJGVivhg3bdAS2xl5gk9LVPZbP9Zgx+wDs5dse2Ay4lrqKF5it0XfYMBPA3BCO/3K13fkzZkdzMKaMtcDktwZwOPCKiJySY165sDRWx4gZ1K17JhaFOAtCeAH1z31+PIGI1Ibf6EIrn4YBYVsLfJpU9krA7iF4Sx55rxG2M1X121QRQg9dNOkhZTsNdelAYij0OFVd2IDywe6xVOUvBj7JVn4GIpmtJyKd08SJeu9yGVaNiNpa9CG0mPptpRS9sm2BCdiw7RZYu0hpyyciQzFl/iDsnm8FrIk9MyeGIeXkNEMwOQzDbA1bYs+c1bHJD38AhhTzhKoBV8aciiB8Mf8DU8CuBwSz2+iE3eSjsIfMnSLyi3haVX0Rs50BGBm+9KJ8t8BsZcC+9J5PU4UVsS/sR4A1VbUb0AkbopmFKYT3B2PieL1XBR7GFKePgZ2AjqraGXsQTgrn9I/wNZmOG7AX/U6YItUJ+CXWg9AauDm57MCN2NfvN8AJQI9g69I+5PUWsAEwNvQQpmIwpuyehdkDdQdWIPHiPFJEdooiq+oYVe0NvBR2XaWqvZN+L5EbnwNXAL8AuoS6t8UU2VHYM+yvWWSXM6o6NapjbPf+8bpnSf9SiDMm7BqT4tzHZMqjGIhIZxHZRET+jPXkAvxdVZMnSfQn8R54TkR2EZHHReRHEZkvIp+KyK1hODITLXM8vkmGOH/E7qObVPWFLPk1tA7RKJCISJsG5nsTpjh1Bh4Wkc2je0VEVhSRy7EPvrnYB1dORG0NG0IFeClFW7kqUx55cir27DkOu6d6YM+n5HtyReAOzNawb3jmdcZ6ORdjH0d17ADDZI6bsGvxJLCJqrYJz4z22MfoxcCUEpxXRePDlE6TJzz4RmE3+PmqOjJ+XFW/BE4RkcXAGZgRcXJP05WY8rET8M+YwvZPzA3A81jXfTo6ABOxGVlLQ7mLgHtEZAbwKDalfj9s9l3EBdiDbhawU9xeR1XfDMOH72DDqH8kMSMtmSXY0F58NtykMKTwMqaQbgu8GB0UkW2xGWkzQ9kaK3sxNvy2I/A/7Mt+b0zZTKY7cIyq3hlL/6OInABshylzh2JDxUVFVUek2FeLKbanhLZxEvaCOb7Y5VcSIjKIFHZdWNu5E7s36iUL24XYy/niEJ5L3ZmUR4rI8ap6d1L6KWHbSURWV9UvUtRrTezjAWyYNFXd+2O2Vl9j9m25MiX2f2NsCCw57/bhHMA+XFYM5eSEqr4bhuhHY+YCbwKLRGQhppwswu754ar6fgPqXi46E4Ykox3BLjCZDsDdqnp8LN484AYR2QRzI3IoiTYDdg26hv/D4r2lqroAeD/8nCS8Z8ypBAYA62M2UplmREUvil1FpM5XcrBpOhz4AVgHU+5uCv9/xIYns/lhujxVHFV9DOvhAns4AcuVyENC8JZkw+mQdiZmsAxmYN0jTdm3agq3BKr6CtbrBWbLFSd6iI6NK2JJ6WeTcL2wR5qyvyLFTLygFP07TdmNRaQ8DsgYqwmjqjXhN6zArBaSGN6KhohrsbZ+WXgZJtM9bNtgL9XJwNaq2in03m6DfSy0AW4XkWRj+sdi/y9MU6+LYv9bBeVoOWGCwR3Y++iUTLaXKZhAYkj4D2ninIv1Pkd0aUD+AATFZRD2EQAmj2jIshWmbPZsaL5l4n+au++7dB+o0QfnOmF4OSLug69Xg2vWjPGeMacSiF60bYDP48bUSUQKWEfswVhHeVHVb4Mx9WPY0F3EMakUpSSWkOKrO8Z/MaP++MtqTRIP6KczpH0ybGuw4YNUvRuZDPS/woxkkxW5SG4Hiki6HjdI9Fqsnub4JE3vzDKSWzolsmBEZGPsK3wAJtNO1P+QXK1U5VcKqjoRc7VA+BhZC7PtORUYJiKHhg+HOJEca7CPnb1UNVLuUdVXReTX2HB4e0zh2jd2/H0RuQ8bpjtOROZiw/lTsZmQvwGOxpTDyH9Zclu6FOuhe0BVU/XMZjrnH0XkaqwHepdQl8sxpWklrGf44izlZyTI8v+w4d5PMfvFl7De7vUxZe8gYGcROUqL4GC2xOQ6BDxDVT9Ocyz+vOyOtR0w27wPsN7yJ0TkRuBxzPlxXj7emgveM+ZUAquEbSvsayvdb4VYmpSzmlT1cRI9aGDewXN5AUzPYlAcPZziX4MrpTieiqlp0sTJ1FsQGYS3Ttofya0zmeXWMcRLNxMsn7KLgoicjPXWnIZNGOiCuRj4HusBimZzdUyZQTNFVZeq6seqego24aUzcJ+IJPdWxK/tfXFFLJbXVCBSMAYl9zpjtojjw//fYArLorA9A+tZiyYHzI/fR2Je7c/CrmO+LiEuJuEs9VBsGGwRds9dig1J/ikWP+UMwAyciSli3wC/VNUHVPVrVZ2tqpNU9WBs1mcrbAivqfeQpXUPC0XtAAAgAElEQVT8m0Qu9z3E7v3w0XYIdu1Xwmx1XwVmi8gLIvK7CpBPWfCeMacSiB7+r6vqVoVkJCKrYNPxI7YRkbY5zNzKyXN4hniZ0tem+V8okdxOU9UbiphvoyAi62O9LC2x4dA/AW8lvcx3JnOvo2PDlFdiiuxQ4JrYsbjtVMrZiIH/hW29XmdVnRt6XvcL+W+M9aJ9iV23G7BhSLAetji3YNd3ODA3xey86B1VEzu2MNg8RuUvBY4Os4aHYZM9OgPfAv/BZvxGhuYzMFOFhhD5MbtT08y0Bv6C9d52w9xt3N/AMhqTrMtiFUKwsdsAs3/dFZsksilmX7od5pftIFX1+zaGK2NOJTAtbNcXkdbxB3FDCLMN78FeJp9jhrybYe4TUhk3x1kxi9IWGSbHvzrj//uQeKEl0zf2v6EvikxMw4YeM81ga8ochD2jPgQOSmPTt3KKfU4MVV0gIj9hslo36fC7sf+ZPgTiM23rxQv2g2PDrw7BdnKHEHwx6fCaYfvX8EtHX6xHFGzo9doUdZiA2ZDVI0xUAZuxmPMHT+jFiXoT601OiDEl9n/NdJEKZEnYtssQp2uGY41GeEY/HH6Rv8fB2BDyalgvbZ8cPoKbDT5M6VQCkY1DJ8yvVr5cgM2GWoS96CP/VKeLyN5Z0rYis5F45Noh7mfoc2xyAJjxbzqiY7WYY9diEcltXxFpW8R8cyWyzUnnMiMbke+ztzNMrtglz7xLTaHnXjSCb6wVQzB56OktEh8NmdxXRMdmk2jTubI7CZu+tEsylYrglqN/nuXH210mxT8+S7QhExAg97YSDa9m8gm4dQPLbhRUdYaq3kVivdEVgaK4o6kWXBlzKoFnSMxi+pOIdMsUOdWMxDB1PvICf56qvqGqfwf+HvbdGYYwM3FhKl9eIrI75vMLzFUGsLy3IAqfICL1jMzDizIaQhmfYRgkHyI7nV6Yr660iEjrVA4cCySaWdU9Y6z0RNPtN07lAy24J2mqziMLPfecEJFcbPXOJTEK8mz8QFByIxvKocEvXnIZfUjMEn4sw2SOVPXrSWIG9OOatFqCqnaLzSat9yOhPH0R21+vVyxD+e2xdS5rsF7Af2dOUZfg8iHykn9U0szBOHHHwy+niZOOXNvK22G7m9gST3UIvv62bWDZRSWHj755sf8lHS6tNFwZc5o84YVxItZNvy7wqojsF58iLyKrisgRIvI0NvOJ2LFumAFyKxI2JBGnYIpeT8xnWLp7Yh72dX2/2DImkQIzlITCNYn6D/srgZ8we50JIvKrmMPIftjMyTWw3roLchJIjqg5sL09BM8WkXtFZLkLChFpJSL9xBaJ/pTif6lGQ2B7SRYP/2mIjMI3wtYYXAHMFYLYSgtPkhi6ampE5z4gm8NUKcwD/8ki8m8R2V/Mm36UZwsR2UxEbiXhWmIi8ESKPP6ITYboAIwTkejDgvD/UcwGbD5mEJ9c/71E5DcisnZk3C8iHYJvrlewe/ZbSuQHTkS2FpELRGRDCQ5dw725G3bO/bF2coSqLkmRfmDsGgxLUUQ0fLoW5hh3+0gJFpE+YqtTREssTVDVyQ08haitbCgiO2SIdz/Wi9YTcxK9WqhD+zBL/N/Ys6acDBGRl0TkZBFZJ/asayG2Ekm0vNU3JJRLB7cZcyoEVX1GbMmgv2Pe18cCS0XkZ+wlEvdddFtS8lsx26lvMUeEy21GVHWO2PIdL2NDmBeQ2rfOD9gaezcCB8TKjbx5f04KuyZV/VpE9sH8Ya2HucCYJyKRR28wP0mH5fEQz4WTsWn9J2HG1UNFZD72Yu1KXa/lxZw8ANarcQ72EvtCRH4gMQtrSPCRlhZV/a+I3Iu5ITkB6138GRuuboVNo7+YxEy/psRYTBFfCXg/2GxFiuM5qvqvIpXTAnM1sS+AiMzDPhy6kGibYJMcDk5lL6WqM0RkD0xR2xz72JmN9SZFvaVzgENVNZWR/7rYpIBrsXtyFta2og+b94F91JZFKgUrYz2/VwC1Yk6Y4217KnCAqub78v8r9kFwHOa6ZiJ2nguoO4t3MnaPNZTnSLiDeE5EZpLoFb426glU1Y9E5ApMud4b2DvE7YjdDw8B75He31tjUIP1zkU9dItCW+pG4nrMxO7/vGx/qxXvGXMqBlUdhy2XchHm52cmdpMvwR74t2NGosunyIvIidjC2suwL+N6BvKq+iYJr9/Dw5BmqvJvwmZKPYYpOLWYQvB/wOapvI+HdC9g/oj+L9SzFpsO/jE202xDVa1n+FwMVHWxqp6M2ZLcji3uvQx7Wf+EGVRfAvRTWzaqmGV/ii1M/G9sMkEPTClencxGyHGOxK7nZExpjQz6L8NmzaVcD7HchOGtAdiEkS8xxTs692IOB4/BFO4x2ASR+dhw18IQvgvYXVV30TSLOof6RstiXYm10WgN0A+xYcaNVPXRNMmfwhSWN7A21Qn7eHkS6w3rF9pCqXgDm2n7MtbD1xmzr5qIuc1YP3l4tCGo6jI1L/Q7Y4r/Z1hPdhvM3u4p7GNha03hmDmH/JeGvG/CeqjbkWgr3ZLiXowtwfYKtkpCS+zeOAlbdaTcQ3+PYPfsHVi9IsV4HrZywZXY9ZhYtho2UWpqa4v9Mew41UMYtrgTs1lZo7y1cRzHcaqRkveMiUhvEdmo1OU4juM4juNUIiWxGQsO3/YJv60wh31fYD5HHgImNmRGjuM4juM4TrVSlGHKMGNiOxIK2NrYePYTmPL1Xdi/N+a8bwZmd/MQ8ISqzi24Ek5RGDFixBKsx7ShvnKqkk8++aTNa6+91r5Dhw61++67r8vEcRyn+ugCLBs+fHjZJjUWq+AHMOPBacA4bH2yCUkLgz6NOdf8BTbzZzBwOGZo2h6nqdACqGnbtm1xPDkvWGDbdrnaazct2rSxCWktWrQonkxSMXNm4n/XpGIqXIZNgmqRYaZ20hhUixzLicuwcIosw4ULF0KZJzQWSxm7H7gq21R1WD5z7U3gYhFZE1PKnKbDrLZt23Y977zzssd0ikdNzKepT6px0uHtxHGKzsiRI1m4cGFZRz6Kooypap1FUUVkE1V9N138WLrPSXhndhzHcRzHaXaUqlvu+SyehJ3mwtFH28/JH5dh4bgMi4PLsXBchoVThTIslbHau8B4ETk8lTNLEekFDFfVU+ondaqKPvmsguPUwWVYOC7D4uByLByXYeFUoQxLpYwNwjwVjxGRM1R1FICIdAV+D5yBGe27MlbtXFpvKTunobgMC8dlWBxcjoXjMiycKpRhSZQxVV0kIgdh9mDXi8iqmKuE32NLdTxJYvHaBiEiA7D17rbFpqN+hfkvu0JV81okNd88RaQVcBq2/MN6JJbluUVV78pS5urAH4DdgV7Aj8AzwJWq+l6GdN2B32JuQtYB2oa0rwE3qerjOZyy4ziO4zhNhJJN5QwL0p6JLYx8PrYm1WRggKruns9aYSJyMvAsNgNzMab4rIKtP/Z2UHAaJU8RaYutSXYNsBm2Xtk0oD8wWkTujlasT5F2K+AdbN22LtiwbmtskdnXRWTPNOnWCXEvCmX+gC0M2y7U/z8i8peGSaDEHH64/Zz8cRkWjsuwOLgcC8dlWDhVKMOSKWMicgim2OyM9TTVAIot8JxPfpsDf8PqfDqwmqpuAawGTAjbMY2Y55XAQGwR4M1UdVNVXR9bGHkmtpjrSSnKbA+MxZSwe4BVVHVLTAH8E9bT9c9gV5fMTcCq2GKym6nqWqr6C2AlTOEFOEtEBjZADKVFxH5O/rgMC8dlWBxcjoXjMiycKpRhSRYKF5G3gY0xReUS4G7gROB6bPhvqKoubGCeY4H9gPtU9bCkYytgPVOdgV+r6mOlzFNEVsQUzDbArqr6VFLaE4CbsZ6y1VR1aezYGdjw7efABnE5hJ60F7DetatU9dzYsU7YUG8NsK+qPpzifJ7FlMG/qOo5ucggmREjRvzsfsbKgPuPcnLB24njFJ3gZ2zm8OHDu5WrDqXqGeuNDfOJqt6lqrWqehNwELAH8JSI5HzSQRHZIwRHJR9X1enAv0LwkEbIcx9MEfs0WREL3A3Mw+SwY9Kxg8P2jmSFNAzt3pwUL6ItpoiB9YylItrfOs1xx3GcRmH7O7anZkQN73z3Trmr4jhNnlIpY2ur6nVJyyGhqv8GdgM2wnqAcmVzzC5qEfBqmjjPhe22jZBnFH4+VSJVXYAZ1NdJKyItgS0zpY2V2TdMfIjy/BGYGoIDkhOFyQRRWVlXQmg0hgyxn5M/LsPCcRkWhxzlWDOihhenvgjAZjdtVupaVRbeFgunCmVYEmVMVedkODYR2AGzmcqV9cL2C1VdnCZO1Cu0lojk0jNUSJ5R2k8y5B+ljQ9sr4H1cGVKOxVTEJPTAvwOqAX+T0ROFJGVRaS9iPTD1gfdAJsw0SDbuXrMmQOjR9v/xYth4EC45x4Lz5tn4TGhiJkzLTw2uJObPt3C48ZZeO214bXXYPz4cHZT7fjTT1v4s88s/FzQQVUt/FIwLXzvPQtPCvM9Jk+28OTJFp40ycLvhQmoL71kYVULP/echT/7zMJPP23hqUGvHT/ewtOmWXjcOAtPn27hsWMtHK0JOGaMhefNs/A991h4cWhCo0dbOOLWW2HQoET4xhthjz0S4euug8FJK4IdcEDi/8iR8MEH0K+fhS+7rK7h6sUX13V+eP75cMIJifA558CppybCZ55pv4hTT7U4ESecYHlEHH20lRFx+OFWh4ghQ6yO8bpfdVUiPHiwnWPEHnuYDCIGDTIZRQwcWLy2N22ahcePN/mtsUblt704xW57V11Vv+3FX3iXXWbnFrXFNG3vov/aRPk/PwHXB+OOf773z+bb9qDuc69fP+jbt/LaXimfe7m0vfhz74cf4JPYK7TQ5978+ZSbsiyMqarvY3ZRudIjbDO5roiOtSA3Ra+QPBuStnuKdGnTquoybAJAclpU9Z/AntgMypuAb7Dh0LewyQTnAruHPJoGp59uDx4nfzbYANyGrzDOO6/uw9nJj402ytoWL594eb19hz54aKlqVHmcdx6cVG9ul9MQttsONtmk3LUoKkUx4A9LH6mqftfAdO0wA/hHssS7CLgUmKiqKZdZEpG1SPRG9VHVr0qVp4h8CqwFHKuqd6RJeynmgmKCqg4K+waQGJ5smU5pEpEvgT7AEap6T9KxMzCnuWthvWgzgLWBTpiSdpKqvpjp3DPhBvxlwg2znVxo4u3k3x/8m/3v3z/lsdrhTa++jgNNw4C/WE5fzwX2EJHXgIeAh1Wj/tK6iEgPzGHpPsCumCf+llnyXxC2bTLEaRf7n0ufYyF5NiRtqnRR2ng4W1pE5HrgVKwnbJPQw0gYQj0bc7fxtIhsr6pvZKhb4xF1PT/4YHnrUcm4DAvHZVgcssgxnSIGUFtbS01NSteLzQtvi4VThTIsljJ2FKZgDcZ6g64UkY8JihnwfTi+LzY82QIzMh8RjmdjRtj2zBAnGgJchrmAKGWeDUk7I7Yv/r8n8HVyIhFpAXRNji8im2LLRy0BDlTVz6JjweZtpIisj12Ly7DhzPKzba7zKZy0uAwLx2VYHDLIcemypWmPASxcupB2rdpljNMs8LZYOFUow6IoY2HJoLuAu4Jn+l2wnq+jSBidLwCexhyhjlPVHxpSRNj2FZHWaQzu1w7bzzIY5BcrTwW2w5YjSsfasbgRn2PG+W1C2nrKGDY8GfW4xdNuj7m2+DiuiCXxH0zmv8xQr8blnLzcnTlxXIaF4zIsDhnkeOubt9YJf3bGZ2x040bMXzKfNi3b8OO8H1m1y6ppUjcjvC0WThXKsOgG/Kq6UFUfVdXjMa/y/bEesRVUdR9VvaOBihjYsNxCTEnZJk2cyJ/Xy42QZxSu52ICltvC/TIpLsH5a7QMVEo7tViZU1U1rqx1DttMhhfRGIB/fjqOU3Rue/M2ev6pJw99+FC9Yyc/dnKd8Jrd12S7vtsBsGjpIt77Pu2Su47T7CnpbMrg7PUVVR2nqnnPHQ2uMsIc4ZRLDK0AHBiC9zdCno9gPVxri8guKbI/EugAfEd9f2KRI9mjQy9ivMwabKWCVGV+FLbriciaKcoEW3Qc6vaolZfBg+u7bnAahsuwcFyGBbHvP/elZkQNKx16PHfe/hP7jdmPmhE1HP2wubb448Q/1ol/wfYXANCjfWIC+Y/zf2y8CjdlvC0WThXKsCyuLfLkUsx2a6iInBYtwh0mBPwT6zmaBNRZCklEXhCRKSJyZnKG+eapqt8DkcOa20Rk41h5O2BrTAJcpqpLksq8BXNJsWZI2yGkaw2MxHoS5wBXJaV7AlPuWgEPiMgGsTJbi8i5wLCw664U51oedt7Zfk7+uAwLx2WYNzUjang4rL42YS37RYyePJqaETX84b9/qJPmip2vAKBFTeIV89a3b5W+spWAt8XCqUIZ5uTaQkRuAt4Iv3dztMkqOiJyGvBXbDjuG2ztxw2wGZnfANur6udJaaYAqwMjVPWSYuQZ0rXDFKQdMIXufWzIM3LUeh9weFjiKDnt1sBTmLI3E3MAuzqwAtbjdqCqjkuRbidswkOnUOaXwM+YfVo0jDkWODi+HmZDcNcWZaKJuyxwmgiN3E72uHcPxn8yPnvEGGdtcxZ/2e0vABz57yP5+zt/X37M3Vs4TZGm4Noi156xEzAno5OA2SLyhojcErzAbyUimVw8FA1VvR5zbjoO82S/MfAtcC2waSqlqVR5hiWPdsZcSryDKUSrYDZix6jqYakUsZD2VWBT4HZgNrAJNkvyn8CWqRSxkO6/Ie51wIfASqG+87Eh10NV9YB8FTHHcZyIxUsXN1gRA5YrYgCtW/gyuY6TC7nOppyGLXoN1vuzOdAPODbsWyIi/wPeJNGD9nZQWIqKqj5P+nUdU8Vfo9h5xtItAa4Ov4amnQIcl2e6VEOuTZNoCYzHHy9vPSoZl2HhuAwbTJvL635jd27TmVnPm0E+jz/OJqM2qWeU//VZdSeIH7rJodwx2fxib7XKVqWrbCXhbbFwqlCGOSljqrqKiKwEbAH8IvZbPURpDWyG9fYMC/uWisiHJJSziar6dvGq7lQEe+9d7hpUPi7DwnEZNohvZ39bb9+s82dB18Taju+e/C4A0+dNp3WL1nRt17VemkFrDWLeBfP4Yd4P9O3qy6IB3haLQRXKsKDlkESkOwnFLFLU1ibhYgHqumKYBtwBXKWqM3GaHG4zVibcZszJhUZqJzUj6nrKn3DkBHZac6eSlec45aQp2IwV5PRVVWcAE8IPABHpjA1jxnvQBFvyaGXgAuBYEdlHVSfVy9RxHMcpG9/P/b7ePlfEHKe0FGs5pOWo6mzM/mq5DZaItAe2AvYCjsHszx4VkU0buri4U2EMGmTbp58ubz0qGZdh4bgMc6bXVb3qhD849YNEIA85vv/9+zz4wYP07dqXQzc+lLat2mZPVM14WyycKpRh0ZWxVASHr88Dz4vISMytw+aYIfr5jVEHp0wccki5a1D5uAwLx2WYEwuW1J9ztf4K6ycCechx41HL3TCyfd/tWadHplXkmgHeFgunCmXYKMpYHFWdISInYm4y9sSVserm+OPLXYPKx2VYOC7DnGh/Rfs64eeHJU0yL1COn/70qStj3hYLpwplWC4P/G9iC4evlS2i4ziOU3qW1S6rt2/A6imX320Qx//CXpz9evdjs96bFZyf41QjZVHGgjPUSZiTVaeaGTjQfk7+uAwLx2WYlQPuP6BO+JVjX6kfKQ853rL3LdQOr+WtE9+id6fe2RNUO94WC6cKZdjow5QRqrpjtC6jU8UMG1buGlQ+LsPCcRlm5aEPH6oT3nq1retHcjkWjsuwcKpQhmVTxgBUdV45y3cagSq8aRodl2HhuAwz8tGPH9UJj95ndOqILsfCcRkWThXKsFw2Y05zYfFi+zn54zIsHJdhRuR6qRM+qt9RqSPmIccXv3yRmhE11Iyo4e637863itWDt8XCqUIZujLmlJZddrGfkz8uw8JxGaYleRWWG/e8MU1M8pLjKf85Zfn/ox5Ko+Q1J7wtFk4VyrAow5QiUgP0BDqo6pfFyNOpEo5r8FroTjIuw8JxGaalxaV1v8mP2OyI9JHzkOMe6+zBO9+9A0Cvjr2yxG4GeFssnCqUYUHKmIj0Ay4EdgU6YutQtood7w6MDPvPUNVFhZTnVCCHH17uGlQ+LsPCcRnmTKc2ndIfzEOOZ25zJlutshUtW7Rk+77bF1CzKsHbYuFUoQzzVsZEZCi26HebdHGCg9e1gJ2AccBj+ZbnVCjzwhyNDj5xNm9choXjMkzJQQ8cVCc87tBxmRPkIcfenXpzwIYHZI/YXPC2WDhVKMO8bMZERIDbMUXsr8CWwPQ00e8GaoB98inLqXD23NN+Tv64DAvHZZiSf/3vX3XCv17v15kTuBwLx2VYOFUow3x7xs7CHLbeqKpnAojI0jRxJ4TtNnmW5VQyJ59c7hpUPi7DwnEZ1mPFP69YJ3zWNmdlT+RyLByXYeFUoQzzVcZ2wuzARmaLqKrfiMh8oG+eZTmVTBUu6NrouAwLx2VYh2W1y5g+r+5gxl92+0v2hHnIccGSBfT4vx7MXzIfgNrhtVlSVDneFgunCmWYr2uLVYG5qvpVjvHnAdUzuOvkzsyZ9nPyx2VYOC7DOmx3x3Z1wncMviO3hHnIsU3LNssVMYBFS5v5PC5vi4VThTLMt2dsMTmuKyki7YBuwM95luVUMvsEU8Fnny1rNSoal2HhuAyXs3TZUl75qu66k0dvfnRuifOQY4uaut/8cxfNpU37tPO+qh9vi4VThTLMVxmbAmwsIuuo6idZ4u4OtAQ+zLMsp5I544xy16DycRkWjstwOa0uq/vYP2XLU9LETEGecpx+7nRe/upldlx9Rzq37ZxXHlWDt8XCqUIZ5quMPQlsDJwGnJkukoh0IeFn7PE8y3Iqmf33L3cNKh+XYeG4DAHq9YgB3LDXDblnkKcce3bomX2mZnPB22LhVKEM81XGrgFOAU4Tka8x9xbLEZGWwF7An4D1sCHKUQXU06lUpgcj4RVWKG89KhmXYeG4DAHY9vZt64Q/Pv3jhmXgciwcl2HhVKEM81LGwgzJYcB9WM/XxQTnryLyKrA+0AnzL7YEOEJVZxSjwk6FceCBtq2isf1Gx2VYOC5Ddr9n93r71umxTsMyyVOOM+bP4Ownz2bR0kVcu/u1vPPdO3Rv153NV968YeVXA94WC6cKZZi3B35VfUBEfsB6vCR2aKvY/4+BE1X12XzLcSqcs88udw0qH5dh4TRzGS6rXcYTnz5Rd9/FyxqeUZ5yXPXqVZfPqLz33XuX7+/YuiNzLpiTV54VSzNvi0WhCmVY0NqUQcnaQEQGAAOAVTBj/WnAC8AzqprHHe9UDXvvXe4aVD4uw8Jp5jLc+e6d64TP2uYsampqGp5RnnJMV9bcxXN545s32GKVLfLKtyJp5m2xKFShDAtSxiJUdSIwsRh5OVXGtGm27d27vPWoZFyGhdOMZfj1rK95dsqzdfbl5OA1FXnKccTAEZz71Lkpj+mPulwZe3nqy/S/oz9jDx7Lfhvsl18dmzrNuC0WjSqUYVGUMcdJy5Ahtq2isf1Gx2VYOM1Yhqtds1qd8KdnfJp/ZnnK8extz6Zdq3Zc8uwl/Dj/xzrHdlpzp+X/+9/RH4D979+fOefPoWObjvnXtanSjNti0ahCGboy5pSW884rdw0qH5dh4TRTGb729Wv19q3Vfa38MyxAjle/fHU9RWzt7muzcMlCAH6Y+0OdY9/M/oZ1e66bd3lNlmbaFotKFcowqzImIjmuk5GVWlU9tkh5OZXC7vVncDkNxGVYOM1UhlvftnWd8Pw/zE8TM0fylOPUWVP5/OfP6+3/dManrHHdGtQOr+Xy5y+vc6zBMz0rhWbaFotKFcowl56xYZjT1lQWmLmu+FoT4roy1tyYOtW2ffqUtx6VjMuwcJqhDGcvnF1vX7tW7QrLNE85rtxp5axxpsycUic89oOxHLDhAQ0qpyJohm2x6FShDHNRxu4mvdK1D7bu5ALgDSBaOHxVYAugPTADeKSwajoVyxFH2LaKxvYbHZdh4TRDGXYZ2aVOeOGFCwvPNE85tm7ZOu2xwzY5DID91t+PRzTxqjjwgQOpHZ7r934F0QzbYtGpQhlmVcZUdViq/SJyH9AVuBL4P1WdlXS8M/B74HygjaoeVnBtncrjwgvLXYPKx2VYOM1Mhl/8/EWdcNuWbWnTsgiLcxdRjpFyGNVrWL9hXPPKNbzz3TtFK6NJ0szaYkmoQhnmZcAvIscDhwDDVfXyVHFUdTZwoYgsAEaIyDOqelv+VXUqkkGDyl2DysdlWDjNTIZrXLdGnfC8P8wrTsYFyPHtk95m69u2ZsGSBbx4zIsplcO3T3qba16+hsnfTeaSHS8poKJNmGbWFktCFcow39mUxwLLgGtziHstMBw4DnBlrLnx2We2XauAGVzNHZdh4TQjGc5bXF/xalHTojiZFyDHTXttytdnfQ1Aj/Y9UsZZsmwJv932t3lXryJoRm2xZFShDPNVxtYHZqpq1nUsVHWOiMwKaZzmxjHH2LaKxvYbHZdh4TQjGXb8Y13fXEsuWlK8zAuUY1wJ++SnT5i1cBazF86mf5/+bHDDBnw6w3ygvXTMS2y92tbFUyKbEs2oLZaMKpRhvspYC6CbiPRU1R8zRRSRnpiR/9w8y3IqmREjyl2DysdlWDjNRIa1tfUN3lu2aFm8Aooox/639+eHeeZb7Nuzv12uiIE5f91z3T15bOhjRSuvydBM2mJJqUIZ5quMvQNsC1wCnJ4l7nDMtcW7eZblVDI77ljuGlQ+LsPCaSYyPOnRk+qEf/rdT8UtoIhy7NSm03JlbM6i+oMs//n4P8xeOJvObTsXrcwmQTNpiyWlCmWYrzI2CugPnCIi3YDLVPWjeAQRWRe4CATtOr8AACAASURBVDgMc41xYyEVdSoUVduKlLcelYzLsHCaiQzf/u7tOuHu7bsXt4AiynGjlTaia7uudG7TmRY1LXj52JeZuWAmu9+bcOg5e1EVKmPNpC2WlCqUYV7KmKreKyI7Yw5hhwJDReRb4GtM8VoNiLz81QB3q+q9hVfXqThOPNG2VTS23+i4DAunGcjww+kf8urXry4PT/3t1OIXUkQ5jjt0XJ1wqmWa3vz2TVbpvErBZTUpmkFbLDlVKMO816ZU1WNEZDJwMdADWCX84swALgOuy7uGTmXzxz+WuwaVj8uwcJqBDLe/Y/s64dW6rJYmZgE0shw7tylPr9iCJQt48H8PsnaPtdlmtW2Km3kzaIslpwplWNBC4ar6VxG5GdgV2BJYKRz6HngdeEpVFxRWRaei6d+/3DWofFyGhdMMZJi8CHdJaGQ5vv7N6+y4Rmntg1a7ejW+nm0uNyKP/1c8fwWXT7ycFjUt0NO0uOtkNoO2WHKqUIYFKWMAqroQGBd+jlOX996z7cYbl7celYzLsHCqXIbLapfVCT8/7PnSFFQiOX7y0ydc98p1dGjdoc7+Azc8sKjlJDN30dzlihjA17O+pnen3lw+0XyZL6tdxsDRA/nqrK/SZdFwqrwtNgpVKMOClbHGRkQGAOdgszm7YOthPgxcoap5TR3KN08RaQWcBhwJrAcsAd4HblHVu7KUuTrwB2B3oBfwI/AMcKWqvpclbQvgCOBwYDNsWarpwIfA46p6VZZTbjxOO822VTS23+i4DAunymW49W1bL//fukVrBqw+oDQFFVGOU2dOZcrPU5izaA5fzPyC6yddD8BOa+7EY0Mfo23LttTU1BRcTia+nfNtnfAVE6/ggA3qLk5+ycBLiltolbfFRqEKZVhRypiInAxcj/k5+wZTfDYAzgIOFpHtVfWLDFkULU8RaQuMBwZiqxG8D7TBZpn2DxMcjlLVeo5/RGQr4GlM8ZuJuf1YHZsMcYCI7K+q/0lT3+5YL+R2YddnwBRModsRU86ajjL25z+XuwaVj8uwcKpchq9/8/ry/+v2XLd0BRVRjjdOupGRL44EqGOX1aF1B9q1ale0cjKRPGlg1OujWKnjSnX2RQuZF40qb4uNQhXKMN+1Ke/II1mtqh6bT3mhzM2Bv2FK0+nADapaKyI9gPuBnYExQM7WlgXmeSWmiH0J7BX1ZonIDsAjWM/Vy5gbkHiZ7YGxmCJ2D3Ciqs4TkdbA5cDvgH+KyLqq+l1S2pbAf0J9xgOnqeqnsePdgB1yPf9GYautyl2DysdlWDhVLMNkR69/3qWEL6oiyrFTm07L//ft2pchGw1h/pL5rNltzaKVkY0H//dgvX29OvaqE77yhSu59FeXFq/QKm6LjUYVyjDfnrFhmAuLdH3Iyb1BNWFf3soY5rOsJXCfql4f7VTVn0RkCNZDtLWI7KWqubptzitPEVkRODUEj4sPK6rq8yLyO+Bm4GIRuUVVl8bKPB5z/fF5SLswpFssIucB22O9a+cA5ybV9wxMEXsF2FtV66xzoqo/Y4pg02HyZNv261feelQyLsPCqWIZrnJ1YhJ7i5oW7LnunqUrrIhyXLP7mmzXZzs6tenErmvtyrG/KOT1kB8H/+vgOuFJx09i9OTRdfZd9vxlxVXGqrgtNhpVKMN8lbG7qa9wxemKza5cDbOFejTPcgAQkU7AHiE4Kvm4qk4XkX8BRwOHAFmVsQLz3AcbkvxUVZ9Kkf3dwDVAb2zo8L+xY9Hdf0ekiMXKrA2zU/uHeMuVsWAn9psQvChZEWuynHmmbatobL/RcRkWThXLcNqcacv/JxvyF50iynHoJkMZusnQevtHvjCS8yecD8AZvzyD6/ZoPM9IC5cs5MlPnyxtIVXcFhuNKpRhvk5fh2WLIyI1WA/aKGCWqv4mc4qMbA60AxYBr6aJ8xymOG3bCHlG4ZRTllR1gYi8hg1jbktQxsIw45aZ0oYyAfqKyKqqGk316YfZlc0GnhGR3YAhQF/gZ+AlTMGbkSbf8nDtteWuQeXjMiycZiLDe/cvsW/tRpDj/e/fv/z/9ZOuL6kytuUqW9axt9v+zu358Xc/sue9e9ZxoFtUmklbLClVKMMWpcpYVWtV9U7gfOA0ETkgW5oMrBe2X6jq4jRxItuptYL9VSnzjNJ+kiH/KG18vYY1gLZZ0k7FFMTktNEg+YfYEOh4TNndCdgfM9r/WES2o1DmzIHRo+3/4sUwcCDcc4+F582z8JgxFp4508Jjx1p4+nQLjwueTnr3tq+Y8ePD2U21408/beHPPrPwc0EHVbXwSy9Z+L33LDxpkoUnT7Zw1E09aZKFo6nOL71k4Wi5jOees/Bnn1n46actPDV4Jx8/3sLTQu/CuHEWnj7dwmPHWnjmTAuPGWPhefMsfM89Fl4cmtDo0RaOuPVWGDQoEb7xRthjj0T4uutg8GDqcEDsVhk50n5Rd/xll8HhhyeOX3wxHH10Inz++XDCCYnwOefAqacmwmeemfiqBDt2zjmJ8AknWB4RRx9tZUQcfrjVIWLIEKtfvO5XxeaPDB5s5xixxx4mg4hBg0xGEQMHFq/tTZtm4fHjTX49e1Z+24tzzz38b6OVaBWMII56C4aefkvieEPb3lVX1W97Q4YkwpddZnGitljEtqfTlW+H7s23px9Nv96W/x0PwR1vxBzXFrnt1Q4aRL9xCUXsmTtNhu1bteeFI57hmTvhsGh1qULaHtR97vXrB126VF7bK+VzL5e2F3/ujR1b99oW+tybP59yUzJlLMZt2JDmaQXk0SNsM7muiI61wIzjS5lnQ9LGF4frkeJ4HVR1GTbDMjlttLxUP8z2bgymFLbFevmeBXoCj4jIyjQV3noLZs8udy0qm59+SjyUnfyYNAnefjt7vArj+7k/NG6BP/5Ykrb4t9f+xjh9lNGTR7PJSpsw5/w5HLbJUI7a7KiilxWxaOnClPtnL5pNy5qWSXEXpYybF5MmwTvvFC+/5sg33yQUxyqhJnkmTikQkZ+AGlXNa9VaEbkIuBSYqKopZwuKyFokeqP6qGpGL32F5CkinwJrAceqasqZpSJyKTZBYIKqDgr7BpAYnmwZFK9Uab8E+gBHqOo9Yd9VwNkhyuvAL+NuM0SkQ6hrb+BPqvr7TOefjhEjRvzctm3bruedd14+yesTfS1V0dh+SYj7U0q+J12GhVMtMkxqJzUjEuEjNzuSu/bN6N6wcIooxzmL5vDily8yZ9EcDnwg4dz1yp2v5Lzti/T8ycAHP3zAhjduuDx8/C+O56AND6J/n/48+tGjvDT1JdZfYX06tenEkI2H0LplLgMuOVAtbbGcFFmGI0eOZOHChTOHDx/erSgZ5kHJ/YwFNxHdgHkFZBMtqdQmQ5y4Y5pc+hwLybMhaVOli9KmWyoqW9qrk/2XBfcYo4ARwJ5AXspY0bn++uxxnMy4DAunCmX41ay635slV8SgqHL8ZvY37H7v7vX2N0YHAcAGK27AI0Me4RF9hNO3Pp1Ne20KQN9r+jJ1lg3nTTt7Gr069cqUTcOpwrbY6FShDBvD6Ws0qK8F5BEZpffMECcaAlwGzCpxng1JGzeoj//vCXxNEmHWZNcsaT9IU2a0v/Ec9WSjiparKBsuw8KpQhn2uaZP4xdaRDkmLwJ+2CaHsWa3NRulVwzg4Q8fZt8x+wIwaK1By5WxSBED6P2X3qzRbQ0mHDmhnoPYvKnCttjoVKEM83X6emSWKO2wYbb9MG/2tcCd+ZQViBS5viLSOo3B/dph+1kGg/xi5amYB/xMq8euHYsb8TlmnN8mpK2njGFyi3rc4mk/jP1P16MW7W+Z5njjExmkVuHCro2Gy7BwqlCGfbr0qaM4NApFlGOXtl3YZa1d6NSmEyt2WJGb974ZgKXLlvLR9I94/ovn2XmtnYu7SHeMSBEDGPLgEA7Z+JCU8ab8PIVZC3P5vs+RKmyLjU4VyjDfnrHRZPYzFhEZNNwN3JBnWQBvAQsxY/VtgIkp4uwYti83Qp4vA8cAKReAE5F2wC+T06rqUhGZhClyO5BwY5GqzKkxtxZg7jeWYorW2tRVziIiBTCVklceLrjAtm4fkT8uw8KpQhn+P3vnHSZFsfXhdzYncs6ZIgpIzkgQAYUrqCBBARFEBDEnJKqgoFe8gAEJ8gECCgoIIiBJJEoGsciwRIEFlmXz7nx/9MTd2TS9O4l6n2ef6equqj7zo5g5U111jq0jdustF0W0yUUdw4PCWT9Ai+llNBo5+u9RRBHBwasHafJtE0s94zj9jy2NRiNf7/ual9e9zIFhB6hVrFa6OiWmleDfe/86bH/y5knLLk/d+OBYdDk+qKGzuykvZPF3BtgHzAE6SikHOsrRmF2klDFooRwAXkh7XQhRFDCvAF2W9noe9LkKbYarihCik4PunwHCgGukjyf2o+l1kCm/pe09DcAwR/eUUt4AfjcVBzuw1xzXDbS8l57B119rfwrnURrqx8c1LBjionXHeaTjS2tfou6XdWkzvw3GbP3OzxlzDsxh+JrhJKYkUntWbYd1bB2xhyo+ZHft4NWDuWeMj49Fl+CDGjob9LViLtuRHSYCjwF9hRA7sc8juQTIB+wlTfR9IcR2tEwAn0sp00aKc6pPKeW/QohZwGjgW1O6JNvclJ+Yqk5yECn/G7TI+pVMbdPmpmwBxOA42fdYoCPwuBBiJDDDZG8g8BFakvB44LNMdHQtQmRdR5E5SkP9KA1zhzzScdZfWvyvXRd3EeBn/VpqUqZJRk1yxPOrn7cr2+5CdcSmZzfZ1Tl1K7OQkjlEjUX9+KCGrogzlitIKfejpQMyoiX3viiE2AdcREvofRno7WAGrixa5Pp0Px119AlaMNttaBHwDwkhDgsh/kF79FgAWAzMSttIShmLFqT1LtAfuCyE+Mt0rzfRZtz6SimvOmi728beL0xtdwNX0XJZJgLPSilPOLDXPWzdag1sqHAOpaF+fFjDX57WlW0uZ7hAx2qFq2EcZ8Q4zsjuIXkUBT8NpSIyD81YILhAptdzhA+PRZfhgxo6u4C/DZAopdyVzfpNgBApZUYpgLKFlHKGEOIwmuPRAqiD5jitAj6QUt50VZ+mlEcd0JJ3D0ALwJqCtkZstin7QEb33C2EeAAYA3QG6qIFgV0CfCSlPJKFvftN9rZEC/h6HVgEfJxZW7cwbpz26kPP9l2O0lA/PqxhaGCo626WyzpuPruZ83fO250LCwxLV0/ekEzYOoHmZZszsunIHN0jO6Eypj8y3ZI0vHax2hz99yiLei4iOTWZiKAIGpVulEUPOcCHx6LL8EENnQr6KoRIBa5IKctks/5ZtKCprgilodBBrgd9NafjqJxL28J9lcyCvioN9eMrGtqME8N47TXp/SS7R3t5Si7r2Hpea7Zf2A5Al6pdmPjQRIeOj229Lc9uoW3FtunqZMSl6EuU/W/ZDK9vemYTLcu3xGg08vf1v3nwmwct13Jj80A6fGUsupNc1tDbg75m/tBdf32FL6A+cPSjNNSPj2o4vNFw1zlikOs6RgRFWI5HNB6R4QyU2RED+GLPFzlyxlKMKRlei3031m5mce9l+1RPladXJiYxhtHNRvNu63ezfc9M8dGx6FJ8UENX/S8OBdIuZFfcD5iTMtsmjVXkDKWhfnxUw+8OfcesbumWpuYduayjo0eSAFP/nMrt+NvEJcfRsFRDu2vvtsqZU1S+QHnW91/P8uPLGdZwGN8d+o4CwQWY8NCEdHWbl21uVz57+ywAUXGZpSHOIT46Fl2KD2roinRIZYFiwJW8vpfCA/ngA+3Vh/7TuByloX58VMO3Wro461ku6/ha89fYGbmTCgUr0KFyB8v5aTunWUJNdKnaxa5Nw9L2zll26FSlE52qaFGIGpRqkO767fjbFJtajORUbc7g39f/ZeqOqUzdMRWAlXIl0x6expz9c9h0bhOfPvwpJSNK5tgOwGfHokvxQQ2z5YyZFuy3S3M6QggxNpNmBqAQ0M1UztZif4WP8X//524LvB+loX58VMP3Wr/n2hvmso4tyrVgy8AtrD25lu+PfE+1ItVoVb4VoQHWR4czu86k8hfWx1L/d+j/GFBvQLbvcTv+Nsv/Xq45fJU6YDCkXzET4BdgccQACocW5sKdC5byqahTbDyzkSGrhwCw/vR6rr9xPUfv1foGfHMsuhQf1DC7M2MPAeOwj7ofbjqXFQa0hNeTc2aawico54b8eb6G0lA/Pqqhv5+LM5/lgY77r+znld9eAaBXzV60Kt+Kl5u+zL2ke4QEhFAwpCAr+6ykx5IeADzz8zMWZ8xoNHIz7iZFw4pm2H+hjwtZjjtW7siGARvS1bFduwZw7PoxgvyD7M49stCa1PxG7I0cvksbfHQsuhQf1DC7ztg57FP3tAWSyDz1UCpwBzgCfCelPOOMgQovZ50pycEjj2ReT5ExSkP9KA1zhzzQ0fwoEODnf34G4JXmr9jVqVKoCmkxGo34TdRCZVYrXI0TI7MOr7jxTPaSk3Rb3I3B9e0TnUxoN4Exm8dYykeuHaFuibrZ6s8ONRb144MaZssZk1J+B3xnLptCW0RJKR/KuJVCAUyZor360H8al6M01I8PanhmlBt+3+ayjoeuHmL/lf1Z1nO0I9I2XMXJqJNcir5Emfzpoy0t7rmYviv6AnDzzYxDUTYp04Q9l/YAcDH6Irsu7eLHJ38kIiiCkhElqVG0hp0zNufAHD5/JG1Sl2zgg2PR5fighs4u4B+E9uhRocicJUvcbYH3ozTUjw9oeP72eSrYlCsWrOh6I3JZx4vRF+3Kj1Z/NF2dV9a9wue70zs9l+9etis7WgsG8HTdp+lTp0+G183sem6XZaYNtNm4XrV6Ados3OTt9ittgv3tUgtnHx8Yi27HBzV0Njfld1nXUiiAkk7uOFJYURrqx9s1TE0m//yadqeyci7yhFzWsXyB8nZlRxsSHDlicUlxfNzxY97aqO0mHfrgUErnK63LlrR6+hv8KTGtBDGJMZTOV5pTUfb5Kd9u5WRgbG8fi56AD2qoIuIr8pbVq7XXxx5zrx3ejNJQP96uoTGVUw+8SGM+da8duaxj3RJ1ebXZq6w7vY5PH/6UxmUaA/D6+tdZfWI18cnx6do0L9uckIAQ3mjxBvVL1qdMvjJUKlQpw3tM2jqJqTumMqbNGN5s+Wam9tx66xZf7v2SakWq0bJcS2bsnQFAdEK0Xb0TL52gUGghR11kjbePRU/ABzXMMh2SEGKu6fCKlPK9NOdyglFK+ZwT7RQuJNfTIbVrp736UA6xPCGzdEhKQ/34gIYV317DuY9tHuM5kcpONy7Ssc6sOhy7fizd+R+e/IFu1bpZouanpKZQ6ONC3E28yxO1nuCHJ3+wq5+YkkjwB9bHiZmlNxq2ehjf7P8GgHYV27HiqRUU/qSww7opY1PwM/g5vJYlPjAW3U4ua+gt6ZAGooW0kMB7ac5lZ57cXM8IKGfsfuPHH91tgfejNNSPl2t4N95Dlui6SEdbR6xDpQ70f6A/DUo2oF7JegDcib/D+C3j+ePCH9xNvKuZ9nd6245cO5Lte5odMYAt57aQPzh/hnVbzW3F9EemW2bycoSXj0WPwAc1zI4ztgDNkbri4JxCkTlFM47/o8gmSkP9eLmGA+avA4KyrJfnuEjHPUP20GtZL8rkL8NPvX8iX3A+u+vHrh9zuJbMzNlbZ7kac9Xh7srskjaG27ut3uXLv77kVvwtdl7cSZNvmziXSNzLx6JH4IMaZumMSSkHZuecQuGQFSu015493WuHN6M01I+Xa3j4nIuDu2aEi3RsXKYx50efx2AwkJiSyB/n/+Dy3cvsvbwXf4M/q06syrDtlO1TeOf3dyzl1LGpXLt3Lcv0RXffuUu+yfkyvP7cg8/RoXIHOizokGGdbOHlY9Ej8EEN1QJ+Rd7yxRfaqw/9p3E5SkP9eLOG965ytOhTyOSK7rbEpTqadzfarvnKil9O/GLniAF0WdSF5NRkFjy+INMdlxFBESSOSSQqLooSESUA2PzsZvwN/oQHhVM2f1lik2IpFVGKuOQ4Olfp7MS7wrvHoqfggxoqZ0yRt6xc6W4LvB+loX68WcN/DxJmSKBBoHS3JS7XMTElMUf1f/j7h3Tnfjv9GwDvb3qfOT3mZNo+0D/Q4oiBtpDfaDQy58Acpu2YRp3idVjbby31S9bPkV12ePNY9BR8UEPljCnylgIF3G2B96M01I8XayiP/opwtxFmXKTjzdibnL19ljO30mcZKBBcgIMvHLQEvQ37MIy4ZG2Dw6LDizLsc+7BuVk6Y2l56LuH2HpuK0abJdJjN48leWxyJq2ywIvHosfggxpm6Yw5GcbCESq0xf3I0qXaa+/e7rXDm1Ea6seLNTx1ZB/CyWDvuY6LdFx2bBkvrn0x3XlHC+a/7PYlA1cOBBynTTLzScdPcmyHn8HPzhHL6h7ZwovHosfggxrmJLSFs+GeVWiL+5kvv9Refeg/jctRGurHizWsE3Da3SZYcZGO2yO325Xfbvk2zz3o+Ouj3wP92HxuM98dyjgxzCvNXuGNlm/k2I7NZzenO1c6X2nkDUnVwlXx9/NH3pC8tfEtJj40kQdKPJB1p148Fj0GH9QwJ6EtFIqcs3atuy3wfpSG+vFWDeNvU8H/KgBJRn8C0TkroxcX6fj8g8+z+MhiAAbVH8TkjvZ5IWfsmcHRf49SOLQw3ap1y9QRAwjydy4sSNpZMdByYtaYWQOAmHdiLMcr5UqS3k8iwC+Lr1VvHYuehA9q6FRoC4Ui24SFudsC70dpqB8v1fDWuT2Yk+6cSK5AbdKvoXIpLtKxXcV2JL2fxL3EexQISb8+aOSvIy3H1QpXy7K/j//8mCkdp+i264OHPmDM5jGW8p+Rf9pdX3R4Ec/WfzbzTrx0LHoUPqihk/kcFIpssnCh9qdwHqWhfrxUwxlLrbsDjyZXcaMlJlyoY4BfAAaDgXO3z3Ej9gYLDy8k4qMIDBPsV8wsP77cYftB9QfptqFSQWvOy6frPM17bewTmRcNsw8+Ou/gvKw79dKx6FH4oIZqN6Uib/n2W+21f3/32uHNKA3146Ua1rZZL3Y0uQq92eBGa3C5jiv/WckzPz+TaZ2POnzEmpNr0p3/tvu3Fufop94/OXX/zc9u5mbcTUIDQi0R+bc8u4Xk1GRCAkKoWbSmXf3i4cWz7tRLx6JH4YMa6nbGhBCBQCegEVACbX3Zv8BfwEYpZc4CxSh8iw1u/vLwBZSG+vFSDR8IOGk5PuYJM2Mu1jEmMSbLOkVCi6Q7d+zFY9pOSGfSFdlQvkB5ohOiqTWrluVc2j7Pjz5P63mt8Tf4Z+9RqJeORY/CBzXU5YwJIV4AJgAZJYq6KYQYL6Wcpec+Ci8mMNDdFng/SkP9eKGGxqQ4ivrdBiDZ6Eed+i3dbBEu0/FO/B0qfF6BOwl3ACgUUohhDYfh7+fP0X+PEpsUy4YzG2hVvhWl85UmZWwK/hO1mas1fddQq1itzLrPNjP3zrRbn5aWyDuRvLjmRZ6s9SSfdPoEP0M2Vv544Vj0OHxQQ6edMSHELGAY1pAXV4FLpuMyQEk0J+1/Qoh6UsphegxVeCnz52uvAwe60wrvRmmoHy/UcOLv65l/czHl/a5SOeAS3zze1N0muUzH6IRoiyMGEPVWlN11o9HI8RvHqV6kOgaDAQMG3bNgjggPDLcr+xvsc4R2WNCBk1EnWXNyDVvObWFej3nULVE38069cCx6HD6ooVPOmBDiSeAFU/EHYLyU8niaOjWAcUBvYIgQYqOUMn2uCoVv44P/aVyO0lA/XqjhvC3ax/P51NKcTyxNoL8H7LdykY5p114ZjUZLrkrQ8lbm1uxXZhz594hd+fiI40QnRHMr7hb3ku5xMsr6GHnflX088NUDWTuFXjgWPQ4f1NDZmbERaGvDvs1oxktK+Q/wtBAiGnje1EY5Y/cbW7a42wLvR2moH6Vh7uAiHYMDglnSawkvrn2RqLgo6nxZhykdpvCYeMwl9zdjTrlk5sM/PuRqzFVLvkunUGNRPz6oobM/teqjOWPvZ6Pu+6a6OjKrKhQKxf3Lw7VKZF3Jx+hdpzftK7UH4O/rfxOdEM3YzWPpsKADhgkGynxWhsErB+epDZ2rdLYrH79x3M4Rq1CgAoPr560NivsDZ50xP+COlPLfrCqa6tzWcS+FNzN7tvancB6loX68TMO/Th3iieCNVPW/gIFUJvfMYh2Sq3Cxjjsjd1qOE1ISmLRtEpvObgK0SPjZiuulA1FU0Lxsc0t587Ob6Ve3n6X8SrNXmNNjDqdGnuKrbl9x7fVrWXfqZWPRI/FBDZ19THkGqCWECJFSxmdWUQgRAuQDjjp5L4U3Y07o+vzz7rXDm1Ea6sfLNPzi/75nQf7PAdidWJsiEa59PJchLtQxJjGGS3cvWcqdKnciIigiW+EucpMdz+0gITmBIP8gDAYDC3suZEbXGQT6BRIepC3wr1K4ClUKZzP0iJeNRY/EBzV01hlbCHwCDAK+zKLuINN9Fjl5L4U3s3Gjuy3wfpSG+vEyDR/wtzohJ1Iq4AH7KDVcqGPHBR3tyldjrjK+7XgMBgNjNo2hYsGKzOw60yW2BAcE25ULhhQE4MTNE/xy4heerPUk5QqUy15nXjYWPRIf1NBZZ+y/QDfgMyFEopRyjqNKQojBwGfAFuBzJ++lUCgU9xX1Ak5Yjg8mCQa40RZ3sfvSbrtypUKVaFymMQCvNn/VHSbZkZiSiJghAHht/Wt5ElpDcf/grDP2HvAnUA/4RggxFtiMFmfMCJQF2gHl0NaL7QDeE0Kk60hKOdFJGxTewCxTvN8XX3SvHd6M0lA/XqThpVu3qB9odcZat37EjdakwY062uaBjEmMIcg/iCD/IJfbYeZ2/G27sv9Ef0QRwbr+6yhfoHzGDb1oLHosPqihs87YDxg70gAAIABJREFUeDSnC7Sgr+Ug3Y83c1CYgsA7mfSlnDFfZvVq7dWH/tO4HKWhfrxIw6em/syfRbQv+ujUMHq07+Bmi2xwoY7fPvYtQ1YPAWDFUyss55ceXUqf5X2oVLASB4YdoEBIgTy3xZbzt8+z7tQ6dlzcYXc+1ZjK8RvHOX79eObOmBeNRY/FBzV01hnbhtUZUygy5tdf3W2B96M01I8XaVg/UFqODydXo5Wffya1XYwLdRxQbwCJKYkEBwTznxr/AeDAlQP0Wd4HgLO3z/LZzs+Y8NAEl9kEcPjaYV5Y80KG1+8m3s28Ay8aix6LD2rolDMmpWyXy3YoFAqFAmgQ8I/l+FBydVq50RZ3EuQfxPDGw+3OtV/Q3q5sG5XfVYQFhtmV1/RdQ2JKIt/u/5Z2FdvxcJWHXW6TwvvRlShcociS6dO115dfdq8d3ozSUD9eoqHRaOTBQKszFlqlkhutcYCbdUy7Tmts27Eut6FwaGHLcecqnelarSuAZfYuS7xkLHo0PqihCsSqyFt+/137UziP0lA/XqLhpqOR1A44bSn3e3S0G61xgJt1nNppql3Zz+D6r7AGpRrwXuv3aFOhDe+2fjfnHXjJWPRofFBD3TNjQgh/oCpQGAjMrK6Ucpve+ym8jFWr3G2B96M01I+XaDhz6TI6FEoG4ExyaSrnL+Vmi9LgZh1HNxvNGxveAGBxz8Vus+OD9h9gNBrZdn4bv5/5nfaV2mf/kamXjEWPxgc1dNoZE0KUBT4EegGh2Whi1HM/hUKh8HWijPn5OrYnDwb+w4nk8lR2t0EeRoBfAMZxRhJTEt0a1gJgwE8DWHREi2XeQ/Tg5z4/k5KaQqoxlUD/TOclFIp0OOUcCSEqo8UZK441hEVWuH6lpcL9TJumvb7+unvt8GaUhvrxEg3PpZRh8j0t8bTBL45+WdR3OR6io7sdsasxVy2OGMBKuZKgSUEkpSbxwUMf8F6b9zJu7CEaejU+qKGzM1UfASWA68DbwG/ANSllSm4ZpvARdu7Muo4ic5SG+vECDY9fibYr/z0+mwvCXYkX6OgKSn1q//g4JCCE+GQtTXNcclzmjZWG+vFBDZ11xjqiPXbsI6XcnIv2KHyN5cvdbYH3ozTUjxdo2GX6H3bl0CAPXNXhBTq6mvOjz7Pg0ALe3/w+BgwkpyZn3kBpqB8f1NDZ/+0hQJw7HDEhRGvgdaA5kB+4CKwEPpRSRrmyTyFEAPAS8AxQHUgGjgHfSCm/y+KeFdDSSj2CNst4Ey2l1GQp5dEc2N4N+MVUPC+lrJjdtgqFQqHIOQF+ARanKz45njdbvskbLd4gyD/ILbHPFN6Ps/uCz+KGNWBCiOFoSce7A0lojk9p4FXgkMnBcUmfQohgYANa0vR6wBngKtACmC+EWCCEcKiREKIxcBh4Hs35O4K2E7Uv8JcQoms2bc8PfJWtN+oupkzR/hTOozTUjxdoOC78a5YXfJ23w+ciQo652xzHeIGOruDAsAP0qtkLgN4/9ibQL5DggODsOWJKQ/34oIbOOmNLgRAhhMuSpgkhGgD/Q7N5JFBWStkQLSn576bXpS7sczJaMvQLQD0p5QNSyhpAW+AOWq7OdDkzhBChwAo0J2whUFpK2QjNAfwECAaWCCFKZOMtTDXZ+FN23q9bOHhQ+1M4j9JQPx6u4aXbcbQIOkTDwH94IWwFn3Ut6W6THOPhOrqKOsXrsPy49qjs4NWD/HPjnyxa2KA01I8PauisM/YpcAj4RgjhqhDR7wP+wGIp5QwppRHA9BixD3AXaGp6bJenfQohigEjTMUhto8VTbHU3jQVx5risNnyPJoDddbUNtbULgltM8QOIB/aY9MMEUI8ZOprOeC5QVeWLNH+FM6jNNSPh2vY9eOViIALACQZ/andoJebLcoAD9fRVRiN9qmZw4PCOXf7HL+c+IWklKTMGysN9eODGjqbmzJOCNERmA0cFUL8COwForNot8CZ+wkhIoAupuKXDvq9YbJhENAbWJPHffYAgoDTUsoNDrpfgPb4siTaTNkmm2tPmV7nSikT0tzTKIT4Gu1R51PAGxnYHoamfTTajF7njN+pQqHwdBoF/m05PpZcmfqB4W60RpEVG89stCsH+gVScXpFElMSebHRi8zsNtNNlim8FT25JCqiLTwPBfoD04F5mfzN1XGvBmibBhKB3RnU2Wp6be6CPs1lhxkFpJTxwJ60bU2zZI0ya2tzz/JCiDIZ1PkAqAK8JaW8kkEdz2DSJO1P4TxKQ/14uIZNA617dvalVnejJVng4Tq6inkH59mVfz/7O4kpiQDM+mtW5o2VhplyO/42hgkGDBMMbDufwdekD2rolDMmhHgAbdG72dFIBC6jrZ/K6C9Sh53mT6fzpsd5jjAndKsshMhO+GM9fZrbnsqkf3NbYXOuItqasMzaRqLpmbatdkKIpsDLwHbgm0zu7zwxMTB/vnaclATt2sHChVo5NlYrLzUtpbtzRyuvWKGVb9zQyqtXa+WDB2HGDFi3TitHRmrXN5p+WZ45o5W3mnxQKbXyjh1a+ehRrbx3r7W/du2s6wX27tXKR01fZjt2aGUptfLWrVr5zBmtvHGjVo40Dcd167Ty1ataefVqrXzjhlZesUIr37mjlZcu1cqxsVp54UKtnGQaQvPna2Uzs2dDx47W8qxZ0KWLtTx9OnTvjh29bB5RTZkCc+ZY38+kSdC/v/X62LEwaJC1/M47MHSotfz66zBihLU8erT2Z2bECPvAiUOHan2YGTRIu4eZ/v3tPwT79LFfSNurlzUgI2jvzZzUF7T3Psvmy6pjR00jM+3a5d7Yu3pVK69bp+m3f79Hjr1Ied7OGWvduL124Gjs2ZLbY2/atPRjr08fa3nSJJg71/r+7uOxN6J6fzbPg8dNE5q1DSXYPA8elVA6X2l27F3Btkp+LP3UpI/t556U8NdfHjH2POZzz2bsDVk1hLf+gO9/gEnbTP/eaT/3li2z/luB/rEXl0VsOBfgbGiLCUAE2g7C54GtUsrUXLMqPYVNr5mFrjBf80NbHH8zD/vMSdtCDu6ZYVspZaoQ4g5QLE1bhBBBaDOMycBQ8xo3j2bmTPsPdEXOadbM+qWgcI6FC7UvogED3G1JOh6Zv4fDRbTfbqlGA9Vrdc+ihRtp2VKNRaBl+ZacLVie0vmSuPjKXuKuRJIcFEa1wqUpXLkFPZf2YokR5h2YT8voSZS1bbxwoeYkDR7sLvM9muXHl/OW6Tjt42ALjz9udSx9BEPahYjZQQhxDSgKNJZS7s91q9Lf731gIvCHlLJNBnUqY52NKielvJhXfQohTgOVgeeklA4fvwohJqJtEPhdStnRdK411seT/hk5sEKIC0A5YICUcqHN+UnAGGCClHK8zfmBaI+CdccZmzBhwu3g4OACb7/9tp5uFDnFdku8E/8nFd7Ls+9P5LuC4wD4O7kStd46k3FlNU48noTkBEI+DLGUqxSqwqlRmT1EUdjS6JtG7LuyD4CXm77M5498nuf3nDJlCgkJCXfGjRtXMM9vlgHOrhkLA+65whEzEW96zSwhWYjNcXbmHPX0mZO2jtrluK0Qoh7wFvAPWjoq72DsWPtHDYqcozTUjwdr2CTI+ohyd2IdN1qSDTxYR0/hbuJdu/LpW6ftKygNM6VnzZ6W4woFKnAv8R4A47eMp8LnFTgVdconNXT2MeUpoIYQwt9F+ShvmV6LZFLH/AgwlSx2deZCnzlpe8vmnO1xEeBS2kZCCD+ggIP6c9H+vYZKKRPTtvNYfGwq2S0oDfXjoRpeuR1H88DDlnKbTl0yqe0BeKiOnkTRsKJcevUSZT7LYP+V0jBTlh1bZjl+df2rPFzlYU5GnWTC1gkAVPtfNYyRA91jXB7irDO2AC3WWHdcE3DUtCqR8kKIwAwW3FcxvZ7JZEF+bvUpgZZA1Uz6r2JT18xZtMX5Qaa26ZwxtMeT5lkz27YPojmFPwiRbl1/qLmtEMK0IpOBUsp1mdjnGubNy7qOInOUhvrxUA3bfbKBLQW1RdOpRgNV6j2VRQs346E6egKLjyxm+u7pvNT4Jfo90M/umtFotEbnVxpmSnSC/VzKiZsn6LUsTdw9H9TQ2ceU04GNwNdCiOyGktDDASABzUlplkGdtqbX7KZz19OnudzaUSMhRAjQJG1b0yyiaXsMDtep2dwzUkqZ1lnzQwsnkvYvv4PrISgUCo8mIdWf5lHz6Rg1i1fuvgqhmU22KzyZfiv6sefSHp75+RkAUsemcuW1KxjHGVW+ygy4l3gPMUNgmGDgrQ3asn1/P/s46UXCirDkCfsAr1FxTqWh9micnRkbgxabqxGwXQixnewFfZ3ozM2klDFCiHVowVZfAP6wvS6EKAo8YSouIxvo7HMVMBOoIoTo5CDw6zNo6+qukT6e2I9os2qDhBCf2AZ+NeWyHObonlLKDP835+YC/lzHvFV98mT32uHNKA3149EaGjiVUp5TKeWZnnVl9+LROnoO8cnxhAWGUTLCQVorpaGFd35/hxM3TwDwyY5PmNxxMvuH7ufavWssPLyQ/9T4D/VL1sdoNNKb3pZ2N15+nsJFqvuUhs46Y+MB81YeA9oMUatstHPKGbNp+xjQVwixE5hpilhfGFiClkJoL2mi75scxbLA51LKtNsynOpTSvmvEGIWMBr4VgjRzZwSSQjRBi3HJMAkKWVymnt+gxZZv5Kp7TApZawpjtkHaNH3Y4Bp+AI3s4owosgSpaF+PFDDtUfP2ZX3vJedj1A344E6egqFQgpxK15b5tt2fluqFq7Ks/We5ZGqj9hXVBpa+Hb/t3blqLgoioYVJV9wPsa3G285n3Zm8e6V82S+ZNv7cNYZ24bVGXMJUsr9QoiXgS/Qknu/Y1ofVRNtzdRloLeD2FtlgQpAui2rOvoEeAdtHVcb4JAQ4hjaI0/zgq7FQLpQzCbHqyewAS1zwWNCiFMmG4uirSnrK6W8mratV/JN3sSlva9QGurHAzV8ceExu3LxfAUyqOlBeKCOnsLYtmNJTk3mjQ1v8Nflv/jr8l9ULliZcvnLUSpfKQqHmvZ0KQ0txCXbBz4oFFLIYb3YpFi7cvCc+VDcw3ce5xBnc1O2y2U7snvfGUKIw2hJtFsAdYCLaI8NP5BS5vgnh7N9SinjhRAdgFHAALSo/Cloa8RmSykzXGEopdxtymIwBi2vZF20ILBLgI+klEdy+j4UCoV38WDAcWoEnOOPxAZEpjp4nKXwKkY30yK8v7nhTYymuYqPtn/ER9s/olPlTqwfsN6d5nkkoQGhFoesh+iRbr2YmZLTrP8/9gzZQx0fc8TA+ZkxtyGl3EbGeR0d1a+Y233atEsGPjP95bTtOWBITttl0Nd8YH5u9JXrmFNOTPONp65uQWmoHw/TMDU1lSdCfqdvqLbheWuJ14Bu7jUqO3iYjp7IvB7zGLhyoN05u1hj97mGtjtLtw/ezumo09xJuEP7Su1JTk3m0NVD7Lq4i12XdlEsrBidq3S2i9129vZZGv/XlBrMhzT0OmdM4WV4QM4vr0dpqB8P07DrrB/4JuiApdyitRc4YuBxOnoiz9Z/lmZlm1FjZg3LuTO3bLIq3KcapqSmEDBJczn+2/m/jG42mgdLPciDpR601LkWc41GsxvZtYsIirArFw4t7JMaKmdMkbfMnOluC7wfpaF+PEzDe5djKF/kmnZsDCG8bEs3W5RNPExHT2T+wfl8tvMzgvyDSEzR4nO/2OhFa4X7VMM+y605il/57RXLY92/r//NwJ8HEuAXwHut30vXLiE5gZebvsz03dpe4wNXDtBq+qeEBPhW9KZcccZMIRkKAeFouysdIqW8kBv3UygUCm+mtc2s2O7EOrT3zyw7msIbmPzHZNafWc+Wc1vSXYtPjk/f4D4jOTVtYAGN2rNqW47HbRlnd21ap2k0KdOE1hVaUyikEOO3jufNjW8y9+Bcjo84nqf2uhpdzpgQoivwMtrC97Asqhv13k/hhYzWfv3wed4ne/VZlIb68SAN90eeo23QPku5auOemdT2MDxIR0/j+I3j6RyxLc9uoXS+0hQLL2Y9eZ9qOLf7XH7+52cA1vZdC2ibHWxpXb41O5/byamoU9QoWsMupMX12OuW42H/9w+cHO1TGjobgR8hxEfAaqAT1hmxzP6cvpdCoVD4Cr1nHqRF4CFLuXzDXpnUVngL4YHh6c61qdCGakWqUTAkXWSl+44UYwq9avaidfnWvLvpXa7GXGXqjqmW641KN6Jj5Y4E+gdSs1jNdLHFWpRrYTmuViSzTITeiVMzVaaQDm8DycB7wC/AMeA60BwoBTwMvIQW7uFZ4O9csFfhbfjQLxe3oTTUjwdp+GDgP+Tz0xYgR6aUoFyham62KAd4kI6exsimI3my9pP0X9GfKzFX6Fe3H6eiTnEn4Q4pqSk0LdtUq3ifathjSQ92RO6wlA9cOWB3fddzuzIMbQHQtkJb/hz8J6EBoRQdXRQKlMszW92Bs48Nh6M9dpwipZwKYEpenSKlPAOcAf4UQswBtgJzgHr6zVUoFArvxvYR5UH/ppRTeQt9glrFalGrWC0uvXqJM7fOcDLqJNVnVLdcN45zaZx0j8PWEQOoXKgyZfKV4dLdS4QHhmfoiN1LvEfEZOuOSl/V0VlnzOTi83Wa83afKlLKC0KIkWgBVN9CC6yquJ8YMUJ7vU93EOUKSkP9eIiGP+w7QzsbZ6xDl2fcaI0TeIiOnkxcclzGeSlBaQiMajIKUVRw8dWLRMVFWbITRN6JZNv5bZy9fZbVJ1ZTr0Q9x1H5fVBDZ52xYkC8lPKSzbkUtBRCafkVLcXPoyhn7P4j1NGQUOQIpaF+PETDz5ZvY2eRswAkGgMIq/qwmy3KIR6io6fy771/Kf/f8iSkJDCn+xy7a5Zgp/ephmNaj+GDPz4AYOGRhbzQ6AVqFqtpTRMF7Lm0h/4/9bcriyIiXV++qKGzzthdIDjNuWigoBAiVEppicgmpUwRQsSj5YhU3G/4UIRkt6E01I+HaHgjtSD9b0+ifdBewgzx9AnK526TcoaH6OipPPj1gySkJADw3Krn7K7FJ8cTGhh632o4qf0kizMWFRfFZzs/Y3b32Zy9dZat57cSnxzP//b8L127omFF+WvoX8Qnx5OUkgSAcerUdAv8vR1nnbGLwANCiAJSyjumc6eBhkATtHViAAghygH5gXt6DFUoFApvRl6NJolAtic1YHtSA4a084LE4Ipss/3Cdi7dvWR3rnh4cf699y8AdxLuaM6YArCmiNp7eS+DVg5yWOerbl9RJn8ZIoIiuBpzlYbfNCQ+OZ6KBSsiX5KuNDfPcdYZOwQ8ANQAdpvObQYaAeOEEN2klHFCiCBguk0bxf3G0KHa6zffuNcOb0ZpqB8P0LDz53/Yld/r7CVR923xAB09lbThK1qUa8G8HvMIDQilYEhBa1qf+1TDxJREHiz1IPuv7AegQckGGCbYz249Wv1RpnWaxuW7l2lbsS1+BmtErEC/QKITogF4bd4JODzUpzR01hlbCzwDPIXVGZsFjATaAheFEBKoBhRG23mZfv5R4fsUKeJuC7wfpaF+PFBDr3zM4oE6egpVC9vHvprZdSbVi1RPX/E+1DAqLooin2jvO8AvgGVPLCMmMcauztAHh1KvZD1EUYEomn6dmO1uy5th+JyOzjpj64AJwDXzCSnleSHE08B8tNRIzUyXUoHJUsqlOuxUeCuTJ7vbAu9HaagfN2uYnJJKnYBTnEspTYwxjAJhiW61x2nUWMyQkIAQfn/md979/V3eaPEG9UvW58ytM1yMvsiVu1doWrYpFQtWvC81/PPCn5bj5NRkHq/5OOtPr7er8/VjaYMzaMQnx3P57mWiE6LpXbs3K46vIOjjydDitTy12dU45YxJKaPRnLG051cKIaoAXYFywG1gvZTytC4rFQqFwovp/PmvfJ9/AgX97rIz6QFavrTG3SYp8oD2ldqza8guS7nKF1Usx0/WepJlTy6z7qq8jygQYl0fGRaoZU5sVb4VR4cf5fLdy5TLJIDrj3//yICfBljKCWMSCPLBXK65nitSShkFLMztfhVeyiDTwsx589xrhzejNNSPmzXMd0tSvNAtAGoHnCbANlehN6HGotOcvnUawwQDc3+GsvnL0mlrpLtNchnFw4szpMEQ4lPiqVZYyzgRFhhG7eK1qV3cmih8+d/LWXdqHSnGFNafXk+bCm34/uj3dn0F+Qf55DhUibsVeUs530pZ4RaUhvpxo4ZGo5FOwdbZkk0JjXkqk7QvHo0ai05jXrgemR8iuUgnN9vjSmoUrcHs7rP56/JfzNk/h0ErB9GwVENeavKSXb3dl3bz7YFvLeW0jlgP0UM78MFxqJwxRd4ycaK7LfB+lIb6caOGryzdx8ggayqYpg/3dZstulFjMUe83fJtpvw5xe7cuPba6/s+/LgyJTWFF9e8yMW7F5nRZQaVClUC4Nztc3y17ysAohOieanJS9yMvclHf3xEQkoCM/c6jqifOjYVg8HAdwe/o+LnFenVshefdPoEL/1J4xDljCkUCkUecuzIHqoU1uJP3TOGUKFBHzdbpHAVpfKVyvCarzpiACN/Hck3+7WwEx9FfMTs7rMBCA2wxlmLS9Jiw99Lusdnuz6znP/60a9JSknixM0TNCnThOCAYIwYMWBg4MqBAHy26zNea/EapfOVdtE7ynuUM6bIW/qbUlssVMsInUZpqB83atgl2DortjmhEY96c+BPNRZzxOAGg+lXtx/5g/Mz4KcBLD22lP9brl375elfeLT6o+41MI84e/us5fjbA99anLG6Jeoyq+ssQgJC2Hh2I2U/K8vt+NuWusXCijG04dAs+/+/5VDw75dg6YrcN95NKGdMkbcIB3nFFDlDaagfN2m4ZO95ugRbt/WXatrNLXbkGmos5oiIoAhLsNclTyxh6bGlyKLatd+2TvRZZ+ypWk+x7tQ6S3nNiTX8eupXQgJCaF+pPV2rdSUqLorFRxZb6nzxyBfkC848PVjr8q3558Y/3KnoT3K1KpnW9TaUM6bIW95/390WeD9KQ/24ScNvfl7HpsLnAEgwBtKwzQi32JFrqLHoNNfvXadx6cZ80HYvAL0LVXazRXnHoAaDGLxqsKW89uRaZv01C9CCvnat1tWSwxPgrZZvMbLpSId9nb99nkt3LxHkH8SyJ5dRMqIkvJG39rsD5YwpFApFHtEt2JoCaXNiIx7xtsTgilxh9r7ZDP3F+vgtX1A+3mz5phstyltWHLd/fHgh+oLlOCQgBIBRTUcx4IEBJKYkkj84f4Z9zTkwh0nbJgEwvu14xrUblwcWux/ljCnylj6mxcpLlrjXDm9GaagfN2i4ePcZHrVxxso2f8Jl984z1FjMESmpKeyI3GHniH3/A/Ss2ZGgdx50o2V5S69lvSzHQxoMYciDQ3i48sPEJcfRolwLwP4Rrpkp26dw6NohgvyDiLwTSURQBKtPrLZcDw4I1g58cBwqZ0yRt9Sv724LvB+loX7coOG7P/1Nl6C+dAveTougw9RpmfXCZI9HjcUcYcRIm/lt7M4dLAnJgSeoeXkfDUs3dJNleUdKaopd+atHv8Lfz5+mZZtyM/Ymw34ZxpTtU8gfnJ/FvRbb1d16fqvdWjMzgX6B1C1R17p70gfHoXLGFHnL22+72wLvR2moH7doaODXxFb8mtiKAJI5lWYWwCtRYzFHBPjZf8WWjCjJx62vAsdgdiOM44zuMSwPSUpNsivbJvhOTk1m+XFtO2mxMGsWikcXP8r12OvsubTHYZ9bBm6hRbkWnIo6xZ5Le0h4uiW1i9emcB7Y7y6ydMaEEHNz6V5GKeVzudSXQqFQeCzPL/oFsMaR2vzm/RRvXZERH7b/kOdW+fbXYEhACMZxRlJSU+wcMbB5zAjEJMaQakzFz+DH/iv7uRJzBYBpnaZRLLwYAX4BhAeGExIQQs2iNQF4ae1L/Hb6NwDW9l1Ll2pdXPSu8p7szIwNBIzYfrJYya5bbzDV9e1RqEhPL9PageXL3WuHN6M01I+LNdxwxP7jslzhMJfcN89RY1EXz616jh+XasdP9HavLXnN3cS7XIu5xr2ke5SKKEWpfKWICIpg2RPLCA4IZvia4fhP9Mff4E+K0fpos1etXlQsWNFhn+YE4T8uhXp/ToT195cztoCMna4eQEEgHtgHXDSdLwM0BEKBW8AqfWYqvJbmzd1tgfejNNSPCzWMT0qipv8ZTqeUI5FAl93XJaixmGPK5i/LxeiLlnLzJ1/l9K3TXH71Szdalfe8ueFNZu+fbSk/W+9ZQgNCGdFkBHWK1+H7o9+z5OgSUowpvNLsFXrX7k2QfxClIjLOWiCKCK6WvsrVOteJq+pb68aydMaklAMdnRdCLAYKAJOBj6WU0Wmu5wPeAt4BgqSU/XRbq/A+Xn/d3RZ4P0pD/bhQw4aTlvBHwTH4kcqqhLY8PmqBy+6d56ixmGNOvHSCsI+0mdEP239I6dbv4jtJfBxjNBrZdXGX3bnvDn0HwOM1H6dO8TqkGlMt11qWa0nTsk0d9vXX5b+IiosiyD+It1u9zdSHp8LzeWe7u3BqAb8Q4nmgNzBOSvmBozpSyrvAGCFEPDBBCLFZSvmto7oKhULhK7TiHwr7ab9N2wftIV++gm62SOFOQgNDfXKhfkZsOL2Bhxc+nOF1c37KpU8sZUmvJSSnJuNn8ANg98XdTN0xlcdrPE6/B7T5m/FbxrPm5BoAVj+92mezFji7m/I5IBX4PBt1PwfGAUMA5Yzdb3Tvrr2uUk+qnUZpqB8XaXgjJoFeIZss5ZUJ7Rhh+qLxCdRY1I+Pa7j02FK7snGckd9O/cblu5eJS46jauGqlmsGg4FAf+uj/GZzmgGw/PhyDlw9wP4r+9l8brPlunnNmC9q6KwzVgO4I6WMyaqilDJGCBFtaqOB+aYMAAAgAElEQVS43+jQwd0WeD9KQ/24SMPOH/7IriJ7LeWhwye65L4uQ41F3cS2aU5sUiyXrx2mYsGKmUaf90bqlahnOW5boS0Anat2tpxrMacFkdGRJCQncOiFQ5TK53iN2KmoU3aOWJsKbSgaZkrs6YPj0FlnzA8oKIQoIqW8mVlFIUQRtEX+95y8l8Kbeflld1vg/SgN9eMiDR8P2USgQdsZti+pBg2L+thvUDUWdfN4yS2sP70evvrAJ8IzxCfHE/qh9uhxbd+1/KfGf6hSuAoxiTEOd0VevnvZsqEhPjkegAE/DWDz2c129SyOF/BJx094o+UbnL11lt/P/E5i1+pULVyVann0ntyBs87YYaA5MB5wnN3Tyji00BZHnLyXQqFQeDwrD1ykd8gGS/lU6Xb4Xnx1hV7y2eQnvZt4142W5A5mRwyg6+KuGMcZKVegXIb1bWONnYo6RVhgGNdirnHp7iUAnq7zNIPqD6JM/jI8XedpggOCqWxKqj7nwBw+/ONDACY9NIkxbcbkxVtyC846Y18CLYAXhRAFgUlSyhO2FYQQ1YD3gX5ooTFm6TFU4aV0Mf3q+/VX99rhzSgN9eMCDb9bvoQVhSIBiEkNpXefqXl2L7ehxqJuJn6yl5fuhTByVFXLYnZf5GbsTRYfWUxsUiwFQgrwQqMXANgwQPvB0uibRpaF/mZnC+Cp2k/RqYoWJLlWsVp2fZrXjK1dCFXWzIc997kzJqVcJITogBYQti/QVwhxBbiE5niVBcwPgg3AAinlIv3mKryOxx5ztwXej9JQP3msYUJSEk+H/mYpr05ozdO+kP4oLWos6qbW4LeoBRwZ/qK7Tcl1Xmv+muX4eux1Rq0bZSmvPrGaYP9gFvZcSFhgGNdjr1uuzesxj8qFKhPkH0SB4AIZ9l+lUBUeqvgQp1teo6CP5fV0OjellHKwEOIgMBYoDJQ2/dlyC5gETHfaQoV386LvfeC4HKWhfvJYw8ZjV7CnyDZLuVvfsXl6P7ehxqJ+0mj454U/WX1iNYMbDKZ6kepuMip3eKvlW5bjtLN+a0+uBbCEsbClVEQpyuYv67DPVXIVyanJBPkH0bNmTy3kxbO5aLSHoCtRuJTyCyHE18DDQCOguOnSv8BfwAYpZbw+ExUKhcKz6RmyiRBDIgBHk6pQp1ILN1uk8AbikuJoNa8VAB//+bFXxiM7Peo0jWc3pmz+sryw5gVik2I5f/s8SalJVCpYiZ41e/Lpzk8t9c2PGtf1W8e4LePoVbMX1YpkvBR/2C/DuBpzFYBLr14iNNA3H+3qcsYApJQJwGrTn0JhT8eO2uvGje61w5tRGuonDzV8feWPrIl7mDhjMP1D1rLW8Bh1DI5S+foAaizqx0bDLee2uNWU3KByocrEJMZw+NphDl87bHdtSa8lPFX7KTpX6UxCSgKJKYkYMJCQnECLci3YNmibxTm7HX+bVnNbEegfSNGworza7FXGbx1vccQAgv1Ni/99cBzqdsYUikzp7ePZcF2B0lA/eajhjztNEcXjO7M0vjNnP3okz+7ldtRY1M2Nxzpw8uZJDuydRbGwYnbXklOTCfDzvq9lf4O/w/OhgaEYDAbLgnyAXst6seL4CgB+ePIHnqj1BKCFuTh2/RgAJcJLcDv+Nnsu7bG061qtKyEBIVrBB8eh9/2rK7yL530wiZirURrqJ480vHznTrpzBj/HX0w+gRqLutnUsQq9f3wX1s6zC3MB8MSyJ/i5z89ussw54pPjWdtvLa/+9irlC5Tnv53/S2xSLHHJcVQpVCVdfUsUfSAxRXu0P3bzWCZtm2Q5H+gfaHW8gB6iBz/3+ZmL0RdZJVeR0DiQMvnKYHXxvJ8snTEhxFzT4RUp5XtpzuUEo5TyOSfaKRQKhUfSYvJ2u/LRCZ0zqKlQaNjOfKWNM7ZSrnS1ObpYf3o9nRdax/z12OtciblCi3IZr5kM9g8m0C+QpNQkDl49SIOSDUhOTbZc71WzF++1fo8KBSuw67ldBAcEUzi0MAD7Lu+j74q+ADxW/TG7GTdvJzszYwPRwlVI4L0057KzMMJcz4iW01IXQojWwOtoQWfzAxeBlcCHUsooV/YphAgAXgKeAaoDycAx4Bsp5XdZ3LMCmp6PACWAm8BmYLKU8qiD+gagGfAY0BqoCRQAotEC6i4G5kopk9O2dSvt2mmvW7a40wrvRmmonzzQ0Gg00idkHRdSSrIjqR5gICLYxx82qLGom4cGTWDzVXhoUPpr83rMc71BOpiwdYJd+WL0RVrObWnZiPDBtg+Ye2Au9UvWZ26PuRQMKci8HvOY030OAZMCmLpjKtN2TGNc23GWPmoVq0WDUg0AaFq2qV3/5oCxm+dBodDt8HRevjvXkp1PjgVojtQVB+dcihBiODADLR3TZTTHpybwKvCUEKKVlPK8K/oUQgQD64B2aEnTjwFBaMFwW5jisD0rpUynkxCiMbARzfG7g+ZMVUCL2dZLCNFTSrk2TbP2pjZmzgFngXJAW9PfICFEFynl7ZxokKcMHOhuC7wfpaF+8kDDp2cuY07Et4Qb4vk7uRI/V/s41+/hcaixqJtCL7xC6tlNPFvPj7uJd0lJTSEyOpKNAzZSKLSQu83LEeZ0Rhnx/ub3ATh7+yzbL2zn8RqP8/VjX5OYnGipE+QfxOstXmdU01GEBITYRehPS5l8Zehduzcnu0dSLl856mVY0/vI0hmTUg7Mzrm8RgjRAPgfmtM0EpgppTQKIQoDy4AOwFK02SNX9DkZzRG7AHQzz2YJIdoAq4ABwE60bAW29wwFVqA5YguBYVLKWCFEIPAB8CawRAhRTUp5zaapATgPfAF8L6W8YtPnY8B3Jju/xJN+L6gPb/0oDfWTBxrWv7mO8Ajty8iPVN59/Ilcv4fHocaifgYOpD0Dae9uO3KBOd3n0Hpea2ISY+zOP/XDUzxdx/5r6HrsdUvi71RjKg1LNSQxJZFA/0DCg8IJJzxd/7FJsczeN5vggGAKhhSkT50+LHliCfjgf7X00dc8l/cBf2CxlHKGecbJ9BixD3AXaCqE6JbXfQohigEjTMUhto8VpZTb0BwqgLFCiLSreZ9Hy1Bw1tQ21tQuCXgb2AHkQ3tsasseoJqU8jNbR8zUdjXWHKFPmpKzewZJSdqfwnmUhvrJZQ1nbdrF4FDr+p6f/LuCr4azsEWNRf34kIb1S9bn7jt3SR2byuedP2dkE+1r6Ie/f6Dnsp6MaDzCrv7JqJMAhAeF89fQvzg8/DD7hu6zq5OSmmI5joqLYvRvoxm+Zjivr7f5SvQhDc14hTMmhIgAzKntv0x7XUp5A/jRVMzWnledffZAeyR5Wkq5gfQsAGKBkmiPD215yvQ61xSjzfaeRuDrNPXM16JNDltGmB9r+gNVM6nnWjp10v4UzqM01E8ua3hh2yKK+98C4GpKYd4Z/d9c69ujUWNRP2k0TE5NJvJOJPKG5J8b/wBaXsej/6ZbOuyxGAwGXm72Ml90+cLu/McdPybylUhL+eEqD5OUkkRUXBSXoi8RFWddkr3l3BYMEwwETAqg1KeliLwTSeXp1pyVtrsrfXEc6lptalpU3gttrVNjwBw05TqwF1gErHC0biqHNABCgERgdwZ1tgKD0Bbh53Wf5vI2HCCljBdC7EF7jNkc2ARgmiVrlFlb0z0BygshykgpL2X+NizYjFRis9km7xkyxN0WeD9KQ/3kooabT0iGhq6wlOfE/Yf3Mlnn4lOosaifIUNYc2INm9e/zqc7P6VJmSaWeFqVClZi53M7KflpSQD61e3Hwp4L3WmtHUajkc92fsa1e9d4uenLlMlfxu56qjGVYP9gElK0eYbQwFDCg8I59MIhDl87TM+aPZmxZwavrn8VgFFNRjG9i5Ytce+lvZZ+zIFek1Kt8w9P1nrSeiMfHIdOz4wJIUoAf6CtqeoBlEGbLQoyHfdAW3e1zVRXD+aEXeczmR06bXqtbFp/lZd9mtueyqR/c1thc64iYP7UzqhtJJqDmLZtVpgf0N8A/s5Bu/TExMD8+dpxUpK2g2qh6QMhNlYrL12qle/c0corTF9ON25o5dWmhAwdO8K338K6dVo5MlK7bo6cfOaMVt5q8kGl1Mo7dmjlo0e18l7Tf9SDB7XywYNaee9erXzU9Ctyxw6tLKVW3rpVK585o5U3btTKkaZfa+vWaeWrpijPq1dr5Rs3tPKKFVrZHE9q6VKtHGvydxcu1MrmKfP58607zgBmz7ZGiwaYNQu6dLGWp0+H7t2xo1cv6/GUKfDLL9C/v1aeNMl6DDB2LAyy2Zb1zjswdKi1/PrrMMLmUcHo0dqfmREjtDpmhg7V+jAzaJB2DzP9+2s2mOnTR7PR1vZp06zl7t2192imSxdNAzMdO2oamWnXLvfG3tWrWnndOs3utm1zZez9tGgOlQMuAxCdGs473U1fDK4Ye7bk9tibNi392OvTx1qeNMmqJaixl92xB/afe/37Mzp6GY8O/ZQ252DPpT1Uv6HtEKwub/D40sepfU0ry3WLtPYe8rkXPsaP1ze8zuUvp3LygbLIK0cZtnoYez58kRtN6vKfJf/h5z4/k1zyS5K2trXkoXxg+Xb6v7WIsMAwQgNDGbULVi6GuOQ4AI6+OYjKz5tX98Ck3REUe26kpfzRjjAmz48kJjGG/+3+H39unMfR723+bfWOvbg43I1TM2Mmx+RXQNvPreWhXI/mSIC2w68j0ARtd+FaIUSzLB6zZUZh02tmoSvM1/zQFsffzMM+c9LWdntMYQfX7ZBSpgoh7qDNMmZra40QoiJawnaAT6SUKZlUdy2xsZCa6m4rvJuUFE3HsDB3W+K9xMbmygfu32FFGRFmdYrmxXXn5cB8mbTwMZKT1VjUS2wsQYnpPxNDA0MpX6A854IiiHaDWc5Q58u6JPtDwgEY+C+sPnGU1SdWYyz9DWSQSSBfUD4MpmhXh68d5u/rf+Nvkzy8SZkmvNq8M0FHJUeGHyEkIIRiSV/BuavEJcUxat0oPjoFlWODqOOi9+kKDEZjzp8gCiFGoO1CjAEGSOk4Up1pl98iIBwYKaWc5aheNu73PjAR+ENK2SaDOpWxzkaVk1JezKs+hRCngcrAc1JKhwFwhRAT0TYI/C6l7Gg61xrr40l/KaVDL0UIcQHNoR0gpcx0jloIkQ/4E6gL7AJa64k1NmHChNvBwcEF3n77bWe7sEfFJcoetou/0/6fVBrqJ5c0HD72Hb4soM3GxKSGkvLcCQoULqvPtpyQ2ThxBWos6qddO7Zf2E7rZ62/mZ+o9QQ/PPkDqcZU/Cda93wdGHaA+iXru8NKklKSmL57OqnGVEY3G02QfxCGCdnbpJIwJoEg/yCWHVvGb6d+Y+7BuZQIL8GR4UcoFl6MXRd30XyOttqnSZkmfNj+Qzr9XycMGOhctTO/9vvVYb+xSbGEfxTO5nngZzDQ5mzu/NCfMmUKCQkJd8aNG1cwVzp0AmfXjPVGizM2MiNHDLRdfkKIkcA8tN2JTjljgDmYSVAmdWzXTGXnJ7CePnPS1lE7c9uMgrQ4apsOU5iM1WiO2EngcY8L+jp8uLst8H6UhvrJBQ23nzrNK+GLLeUF8d140ZWOmCegxqJ+hg+nReowZla9RaoxlZCAEBqWaghoybJtqVPcfXM//9vzP97Y8AagxQIb3Ww0/R/oz8LD2vzAj0/+yNBfhtotwjcTkxhD4dDCbD23lbkHtfmKa/eu0WFBBw4PP2xJgwQQ6BfIQxUfInFMIgF+ARgy2ZUcEhDCiMYjuJR4gSD/IIxGY6b1vQlnnbHaQBJa1Pes+B74xtTGWW6ZXjML2WB+BJgK2Zrl1dNnTtresjlne1wESLc4XwjhhxZZP239tPWCgZ/RdmueAzpIKa9mVN9t+GBCV5ejNNRPLmj4wpz9jIuoThX/i8Qag2nbb1LWjXwNNRb107s3fsCLDi4F+9tvBAmcFMieIXtoXKaxS0yz5bX1r1mOX/ntFUY3G82C/yxgfNvxVC5UGYPBQKvyrYhOiCY6IZp5B+cRkxjD1vNb+Xj7x4xqOoqwQPvH2cXDiwPao8qHKj5EfHI8dYrXwd/PH3/S53Q9fO0wP//zMxFBEdQtXpdOVToxo+sM6Jq3790dOLuAPxy4l501YFLKROCeqY2zmFYlUj6TxfnmjKRnsrk2TU+f5raZhZAwt5U2585iXZyfUdtyWGfcpKMKQoggtMCxD6M5dB2klJGO6rqdO3esi0AVzqE01I9ODX84uI8YYxhv3B1Nx1tf8sbd0dSuXCMXDfQS1FjUz507pNyKou/yvtSeVZudkTstl8KDwjGOM9K4tNX5mvLnFEe9ANBlURcMEwxM3zU9wzq5xSq5CoPBQOVCldlzaQ9Hrh2hREQJqhWpRsPSDZnRdQaPVX+Mc7fP8cmOTyj737L8p8Z/CA0ItfTRqbIWjqJBqQZsenYTO57bwVePfgVo8cXSLpvad3kf47aM47X1r7HoyCLrBR8ch87OjF0HSgshSqUNQJoWIURpoCAOZoFywAEgAW0nYjO0XZxpMcfz2ungWm73uRMYjJYjMh1CiBC0zQt2baWUKUKIvUBLoA3WMBaO7hnpKKyFyXH8Ae23wVWgvZTyjCM7PIIePbRXtcbEeZSG+tGp4RtLrJPOZ1PKsOLdgfpt8kbUWNRPjx6cv3WG73tqv59bzG3BPyP+4cKdC0QnRNOodCO7NEMZres+fO0w605puzVH/zaal5u9nKdmLzm6hCt3r7D8+HI2nNHCay7quYi+dfta6sQm2UdValm+Jf++8S83Y28SkxhD0bCiJKUkcTXmqmUnZfUiWnCCKdunMGbzGIL8g3in1TuMbzeewasGW/q6l3TPcpzS/VEM+OG31dFXqHfirDO2Ay0hwYdoTklmfGh63e7kvZBSxggh1qGFy3iBNI6TEKIo1gQJy1zQ5ypgJlBFCNHJQeDXZ4Aw4Brp44n9iOaMDRJCfGIb+NUUt21YRu/DlJh8KdAdzSHuIKU8kY236z5GjXK3Bd6P0lA/OjT8v13p090WCs9suagPo8aifkaNYu2eGViDD8DgVYPZEamFVHm8xuP0rt2bthXaUqFgBbpU7eKwm0bfNLIrxyXF/T975x0mVbH04Xc275KT5ChSooiAiBhBBUW5eD/BLIoYr5izmBAj1ywqKhivOQcQswQVQRRQAWmUKDkvLGze+f6oPhM278yyyw79Ps8+Z07u+W1PnzrV1dWkJqYWe2xl8Pnfn/PW/LfCtr3626thxlibem0Cn8/qomlRaifVpnZS7cD2Pzf+yQHjDgBAGgmLrlyE3+/njil3AOgUSXFFO6uObqO+j0s+vYTNzdScuHnVTHq3KvcMiHs0kXZTPoWmtBgmIu+KSOfCB4hIZxF5DxiGBvs/E3kxAR35WACcIyJXWsMFO4/k2+gUQrOBzwqV4wcRWS4i1xa+YKTXNMZsIDgY4QURCURZ2rkpH7Kr9xYTUD8enZC8vT03zZ6XCIxBU4FkAI+EnmRjyV4DTkXTYvQzxkSXT6wqGDxY/xyR4zSMnig0nDr5RRr7guGbf95zYmWVqubh6mL0DB7Mfx74KrDap22fgCEG8NGij7hjyh0M7jyYG4+4kQP3KT7cOjQhKhTKUB/Cnxv/5LAXDuOKz64o0ctWHD8MD/efFB5cADB37dyw9T7t+uAf5cc/ys9bQ94qcjwQZjCazYbM3ExW7wjvBKqXomHT+zXcL7BtQMcBALww9wU+OgA+OgBOfiN2gsciMsaMMT+gxoKXgX++iKwWkVkiMlNEVgPzAe9X+7A9J2KMMXOAa1DD7ilglYj8CqxCJ/ReA5xZTLb/VkBbtKu0sq4JMBL1erUBfhOR30VkEdr1WA8d3FBk9Kidi3IwOu/lUGCNiPxi73UzGlN2TjHB+GeiI1JBY/DGWUOzuL/iX6Wqg02bgokEHZHhNIyeCDW85LkJPF33IaY0vJTLU98jgTxSk6KauKRm4+pi9GzaRMKWbfhH+dl+63amXjCVRqlFx4LdPe3uUi/zxuBgDNW4k8fh8/nYnr0d32gfvtE+5qydA0DPCT35efXPjPtlHP/98b8AvDrvVeqNqRdmBBbmyDZH8nD/hwPr0qhoDvKNuzbS4tEWnPvhuXy95GtGTx3NdV9cx/QVwQ6hG768gSYPN2HyXzpjX63E8PDxh2c8TN3kumHbLup+EQBTL5jK2hvWsuXmLezbQMOwD291OI12QqOd8OXQL0vVqCYRcQZ+Y8zN6GTZW1CjrDk6JVIv+9mHJkkdYYyplKRVxpin0SmGJqKxXl2AtcATQFdjzLKquqYxJgs12G4AfkcD9ltg48mMMeeWNA2UMWYW0BV4ETXKDgLyUG9cTzvxd2FCh9m0Rrs6S/qLdsaDyuO00/TPETlOw+iJQMOCggIGbn6DVF82deIyGZj8A4vvH7ibClhDcHUxekI0rJOsCYNnXjyTZrWbhR12YJPSExCc3eVsvh/+PbMvmc3lh2rKkXpj6gX2HzJe02WExnGN/HYk27O3c8EnF7A9eztHvnQkoHFpp793Or7RPl777bXA8aHB9z2a9yDr9iyybs/ipVNe4rj2xwGwNmMt6VnpTP5rMndPu5snZj0RmNrot3W/8djMx9i0axMD39TfTpNaTTi7y9mB677626th94Ggl69FnRY0q92MBqkNiI/T0ZYzLprB39MPZtWMw6pllOnuIqpXPGPMsyLyEjqqryewj921Ae3e+7rwZNjRYoyZTsnzOhZ3fLvKvmbIeXnAY/avoucuB8o9wZYx5hXglYrep9q54Yayj3GUjtMweiLQ8Iy7HuH9BsEA4ft2XsTb8XuxVwxcXawMitGwY8OOrLpuFUM/Gsrb898G4F+d/sXK9JVhcViheKklSsPv99O7VW9mrpoJwHW9r2Pc7KLpPjfs3MD7C98H4PyPz2do16H4fD427toYOOat+W/x5hDNZjW8+3CS4pP4btl3ANRNrkv9lGDnk9el6aWy8Ni4cyNNajWhQ4PgBODDDh5GYnwil/S4hJfnvcxNR9xUZu6w+rfHXlqZqFsWa2xNtH8ORziDBlV3CWo+TsPoqaCGW3bs4p46zwXWJ2Udxdv3jizljL0EVxejpwQN4+PieWvIW7w15C0279pMp6c7BRKq+kcV7WR57bfXGPvzWH5Z8wt1kupwV5+7wvbff9z9TFo8KWCInSKn8NiJj7FkyxJGfhtelz0Pnccr817hui+vIz275PQRZx90NqfIKWzP3k58XDyLNi3imOXH4MNHvZR6bMvaRvM6zcPOaZSm3bEpCSl0bdqVOkl12L+xpogZP2g8Y08aW2LsWxgxWA8j6qYUkVPsX+PKLpAjxli3LjgZrSMynIbRU0ENn3nsGg5I0AiFTH8y37c5u4wz9hJcXYyeEjQs8BewZodOQB8fF18ks/38DfPp/UJvzv7gbHLycxgxeQS/rPkFgB05O9i4cyM3H3EzXZt2BWDkUSNZkR4cCfzH+j8A2Lfhvjxzso6n696sO+sz1hdJzpqenV7EEKuXXC9sPc4XR53kOrSs25JmtZvRt11f0hLTmLZiGjd9fRM/rvwRgK23bOWDMz5g002bAhOHz98wn9/X/86P//xIZm5woplyGWIQk/UwUs/Yx0A+pWegdzjgLDvmwOUlihynYfRUQMPBD73G/9KCwdFjd57Ff88rLl/6Xoiri9FTjIabdm2iycNNAJ16KOv28Jny8gvyOeWtU1i2bRmzVs9in7R92JmzM+yYzLxMRvcdzf6N92dAxwH4fD7Ss4IGVbv67QKfPeNr7rq5XP3F1ZzX9Tya1W7Guox1zLtsHvPWzQscmxiXyOfnfs7Ts5/mge8foEFKA+qn1Oe7Zd/RvE5zRvUZFYjn8vKeATRM1Ulo6qfUZ3Dn8BG47yx4J/A5Oz+CSKYYrIeRGmPbgAJjTE2ZXN5RXVTWhON7M07D6CmnhgX5+YzIe4rayfq2vjivDRdd+8TuLFnNwtXF6ClGw3UZQS9PTn4OPp+PuZfNpV5yPRqkNiDOF8eybcGxZGN/HsvF3S9mRfoK1mWs45vzv6Fecj2SE5K5oNsF/Lz6Z+Lj4rnu8Os4+6Cz2bxrc8A4mrt2bli+sHcXvMv8DfPx+/10bdqVJrWaMLTrUAbJILZlbWPgmwO58vMrWbRpER8v+rhI2a8+7Goap2knWUJcAnkFms0pNIasMFf1uoqnfn6KBikNOPPACKbYisF6GKkxthjoISIpdlShw1E8AwZUdwlqPk7D6CmnhtfcM5Kn6s4OrN+eMYL36pX8UNnrcHUxeorRMDSgHeCYl49h+vDgmLIV28ITD/vwMeGUCcVePiMng2+WfsMbf7zB98O/p229tsxePTuQsf/zvz/nqyVfhZ2zcKOmrFy/cz3nfngu53U9jwu7X0jD1IZsy9oWZizWSarDjpwdgfXhnwxn4tkaMj75nMnc/t3tnCKn0LlJkfSjAR7u/zDHtjuWbs26BXKKVYgYrIeRGmNvoikszqImjvBzVB3/2CzTrVtXbzlqMk7D6CmHhoeN/oDJtZ8PrL+WeTLv3XvL7i5ZzcLVxegpRsPCMVvfrwyfna/dk+3C1lddv6rEyzd6qFEgIeyva3/l+PbHc9YHZwX292rZq6RTAZi6fCppiWlc2F0n12mc1jhgjJ2474l0a9YtkK8MYNLiSXz050ec2vlU+u/bn/779i/1+gDJCcmc2vnUMo8rkRish5HmGXsGnT5orIjE3rAGR+Vx3nn654gcp2H0lKFhbl4+6zNTuGr7zazKb8Lq/Ca0/L/bq7CANQRXF6OnBA3vOuauItsWbFjApl3hSXYnDJpAizotihz77dJvueTTSwKGWGpCKtuztxfpWmxTrw1Httb8Ysnxycy8aCYXdw/PsuQlaAWNYfO4+cibGdNvDJ+e9WnY8cWVZ7cSg/UwUs/Y7ehckwByF7AAACAASURBVN2Aj0VkoV3fgAb2F4sx5p4I7+eoqdxxR3WXoObjNIyeMjTc7w4NPJ6R240BW5+hZdwGvuxyRFWUrGbh6mL0lKDhaQecxj3T9RH58r9f5uW5L3PhpxdSK7EWh7c6nJ9W/QTAwU0PZkvmFv7e8jepCak0TG1IizotmLV6Fi/MfSFwvVpJtbhi8hVFJu8ed/I4mtRqErbtsFaH0aN5D0ZMDg5UKfAXEOeLC2TyB3hpriZ7HWR9MGmJaezK3VWkm3W3E4P1MFJj7G50CiEvM9uBwAHlOM8ZY3sb/fpVdwlqPk7D6ClFw0MefBUIZunJ8Kfx5f1XVEGhaiCuLkZPCRoe1PQg5l02j027NnFc++OIu0c7rnbm7uTEfU9kxkUzKPAXAPDRnx9x2nvBmRB8+PATzEU28qiRPHD8A/hGhydPveawa4oYYh6dGnUKW4+/Jz5sgm+A39b/FvhccFcBS7YuoVntZkWmONrtxGA9jNQYmw6Uf8ZRx97L0qW67FDFb06xhNMwekrQcMu2dBJ2hB/6wrDuVVSoGoiri9FTioYHNzs48HlQp0FMXKyB8V7y1DhfHH6/v0gOMs8Qe+qkp8jJzwnEhTVOaxzo5lwwYgEHNAn6TLZkbmGimchx7Y+jdb3WHN/heK457Bq+WfoNizYtIt+fT0ZORiDlBcCQzkMC5/t8Pjo27BiVFBETg/UwImPMGNO3ksvhiFUu1CDQWMoHU+U4DaOnBA0/fXoonzeYzg07rmNKjs5z169zFce/1CRcXYyecmoYaujszNlJbn4uLR5rwbasbeQV5NGzRU/WZ6znn+0azN4wtSFX9roy7Bpt67UlKy+LnTk7A96rH1f+yKfmUx6a8VDguMnnTCY9O52H+j9EUnwSx716HFOWTwFgzPFjWLhxIb+u/ZWtmVuZvmI6x7Q9JloVoiMG62FExpiIHAPkGGNmlvP4XkCKnQPSsTcxenR1l6Dm4zSMnmI0vHrUzYytOwmAl+uN5rSt/+X9+26u6pLVLFxdjJ5yanh337u585g7qZNch0WbFvHW/LfCgvmnDJtCrcRa7MzdSWpCaiDxqkeBv4BfLtUM/X6/es52ZO/gqJeLzmd58psnA3BI80P45dJf+G7Yd+QXqGfs+5XfBwy3b5d9S9PaTavfGIvBehhpN+VUYC3QspzHvwO0juJ+jppKnz7VXYKaj9MwegppePnjL/NonbGB9cnZR/D23W4S7DJxdTF6yqlh3eS6AKzevpqDnj0obF+8L56MnAxqJ9UuEte1PXs73Z7rxrJty/jwjA85tfOpvL/wfWaumsnCTQtLveeva38NxJml35pOvZR6YaMpIZhZv1qJwXoYjXFU+rTq0R/viAWM0aVI9ZajJuM0jJ4QDd/+cTK35Y4kLV6nYVmS14oPml3JyQnxpVzAAbi6WBlUUEOz2YStZ92eRVJ8Ej5f8Y/U6764LpCtf/C7g/GP8vPF31/w0ryXKlTMNTvWUDe5biC7vkdZecqqhBish1XlqUoF8qroXo49icsu02UM9e1XOU7D6LEa5n75Oe2n30zrpPUA7ChI5bLtt/HNLW4i8HLh6mL0VFDD0NQUBzY5kOSE5GKP+8+k/zBv3TxmrZ5VZF9qYmrY+vBuw9mn1j6M6TeGlekrWbBhATtydnDm+8GpiVZsW8H+jfenQUqDwLYWdVrQo3mPcpV7txKD9XC3G2Mi0gpognZrOvY2HniguktQ83EaRs8DD4Dfz6ePDGRIygIACvw+rttxI9/cf3k1F64G4epi9FRAwwJ/AfWS63FWl7NIS0ija9OugE5ftC5jHakJqXRo0IE6yXWYtmIaizYtCju/ee3mrNmxhmPbHUu7+u1ITUjl6LZHB64DmgS2Tb02gCaOHT9nPJ0adaJ3q974/f6wOSbX7FiD3+8v0StXZcRgPSyXMWYD9vsW2lxbRIqmDA7iAxoAA+16uYL9HTHGES5xZtQ4DaPniCN4+p4zubLWlMCmMTsv4LlRo6qxUDUQVxejp5waTls+jWNfPRY/fvq07cPUC6YG9j0580nGzxlf4rm/XPIL+9TahzZPtKHlYy1pWadlqVMoeTw/6HlGHzua5o82p/5/69O8dnNWX7+axLhEcgty6dy4c/UbYhCT9bC8nrFjgVGE5xarZbeVhQ/IBB6sWNEcMcH8+brs0qV6y1GTcRpGzd2jL+Pu2u8G1t/MPJHzrnyKhHgXJ1YhXF2MnnJqWDupdiB/WHp2emB7bn4u63auK/acZ05+hv0b70+nRp1YmxHsjCrcTVka27O3Bz6nJabh8/mYP2I+Hyz8gNMPPL3c19mtxGA9LK8xthyYFrLeB8gFfirlnAIgHfgDeNUYszSSAjpqOFfavDcx1Ldf5TgNo6LdrZ9xYWrwPfKb7EP5seMwzmlUxVnDYwFXF6OnnBrWS6kHQK3EWqQkpAAw7ONh/O+3/wWOOazlYcxaPYvk+GRSE1Pp2aJnIMB+zY41tK/fnsy8TPaptU+R67/1x1t8seQLdubsZHi34QzspJ1Y2XnZNE5rTEZOBnWS6wCanX/k0SOj+tqVSgzWw3IZY8aYV4FXvXURKQC2GGOO3V0Fc8QIDz9c3SWo+TgNI6bdrZ8B8FLmv9nhT+W05O8YX/cB3j0r9qZTqRJcXYyecmrYoUEHcu/MJSc/h7GzxvLt0m9Jjg8G7z878Fn+0/M/JcZwSWNh6TXhPpCpy6dy7Kv62G5fv31g1OUHf37AYS0PY9zAcfRo3oMNN24ITL20RxKD9TDSAP7haNejw1E6hx5a3SWo+TgNI8IzxDzeyzqB97P6sWykM8QixtXF6CmnhnG+OOJ8cSTemxjY1qlRJ+J8cdRKrBVI5FrYEMsryMNsMmTmZZJfkM9hrQ7j59U/8+KcF8PizDxDzGPW6lk89fNTvDLvFQBuOPwGHjnhkUi+4e4nButhpNMhvVr2UQ4HMG+eLrt1q95y1GSchhXmilG3Us/XjXR/nbDty8YMqqYSxQiuLkZPFBpe3/t6Lj3k0lKD6NOz0unyrMZSNUhpwJZbtrB069JSA/491mesD3x+ctaTe64xFoP10GXEd+xerr1WlzHUt1/lOA3Lj9/PmHsu5Jm6rzAnVzh32/1kovE2y2c+THBwtyMiXF2Mngpo6E3Q7dG3Xd9iDbGc/Bw6P9OZ1IRUEuKCj/WsvCwAUhPCA/hH9BxBvw79GD1tNNn52bw95G0ycjL4xHzC539/DqiHbY8lButhVMaYiOwLnAF0BRoCiaUc7jfGHB/N/Rw1kCeeqO4S1HychuWjIJ+X7z+VW2tPBKBHouHGWq9x785LWH5WSzjL6Rg1ri5GTwU0fHLmk4HPNx5+Iy3r6gyEkxZPosBfQK3EWvRo3oNNuzaxdKvGh9VOqk3nxp3ZmbuTrZlbWbx5MW3qteHZgc+SmpBK2/pt6duuLwCndj417H7dmnVja+ZWNu7ayJh+Y8gryAsz7vYYYrAeRqyyiIwC7gDiKN9UR/6yD3HEHDHkRq42nIZlkpu5namP92d42s+BbTNzuvD4rnNZPsZ5wyoNVxejpwIajvlxTODzgfscGJiH8rJJl7FmxxoABncezId/fhg4rlZiLRZesZDxv47nskmXIU8LF3e/mAmnTCjzfrWSapGZl8kn5hM+MZ/wwqAXuKjHReUub5URg/UwImNMRM4lmGNsM/AlsAoX1O8ozOzZuozBgMsqw2lYKuavHyj48Dz6Jy8PbJuUdRR35dzE/AdP0Q1Ow8rB6Rg9FdCwaa2mrN+pcVyP/vQoQ7sOZUf2joAhBtA4NTh35NldzubmI28GIDM3+Dj2UmOUhzf+eCPweUvmlnKfV6XEYD2M1DN2hV1OBM42xuwq7WDHXsxNN+kyhvr2qxynYYlcP+Z+7oofQ/2EjMC253YN4Tn/+cwbfUrwQKdh5eB0jJ4KaHjOQefw+MzHAR3d+PGijzn9vWDi1ePaH0fLui1pnNaYlIQUerXsRbdm6jWqn1KfLvt0ISsvi2a1mxW59sKNCxn57Uh25uykU6NOjBs4rsgxx7bfQ7NXxWA9jNQY64J2O17uDDFHqTz9dHWXoObjNCxKQR7P3H8Oj6W9F9iU7U/gjh1XcNTgq5l3cIfw452GlYPTMXoqoOGjJzxK/w79qZtclyPbHMmkxZMC+07qeBKTz50MwF19is5MOKzbMIZ1Gxa2bcKvE1i8eTGpial0atSJT82nAHy77FuWb1vO5HMn8/3w7zn65aM5qeNJ9GzRM5JvuPuJwXoYqTHmB7YbY9aUeaRj7yaGpquoNpyGYbw4Yw5/ffUyY+oEDbG1+Y0YsX0kz99yKfvUqVP0JKdh5eB0jJ4KaOjz+Thpv5MC67WTalM/pT4pCSlhE3gX5vf1v7M1cyuZeZkc0foICvwFXDH5Ct78483AMY/0D09b8c/2fwA4qs1R+Eft4SHeMVgPIzXGFgHdRCTZGJNdmQVyxBgzZugyBid2rTKchgG8RK7x9Of0lG84JHER03O6c932G/j1wXNLPtFpWDk4HaMnCg37tuvL1lu2lnncsI+HMW+d5uL69dJfaVuvbZghBpqh/8bDb+SRn9Qo8wYH1AhisB5Gaoy9ADwPnA68XnnFccQct92myxjq269ynIZMWbSG4a/MDaznE891229gQPIMJmSeWnYyV6dh5eB0jJ7doOFEM5GLJ15MWmIa/9rvX2F5xbLysopMFD6qzyi6Nu3KgI4DuPGIG9mRs6PSylIlxGA9jDQD/wQRGQiMFZGVxpjplVwuR6zw/PPVXYKaz96sYV4Wjz1wMcckzSGeMeQTH9i1sqA5l9zwBLfVrlv2dfZmDSsTp2P0RKnhtqxtfPjnh6QkpNAkrQlHtz2a39b/xoadGwDYnLmZbs268feWv8nKy2Lx5sXs33h/Xjv1NVISUkhLTOPk/U4OXK9p7aY0pWlUZapyYrAeRpra4i7gN+BoYIqIzABmAdtLO88Yc08k93PUYESquwQ1n71RQ7+fOx+/nkvy3uL6Wjq0/7zUz3glMzhCskL5w/ZGDXcHTsfoiVLDlekruehTzf3VZZ8uPNTvIe6ccmdgf2pCKuMGjmNL5hbeWfAOwz8ZzpuD32Ro16FR3XePIgbrYaTdlHcTTOLqA44EytN564yxvY1p03TZp0/1lqMms5dp+NbEJ9l3wXjuTVxIiCOM/kkzeSVzEJ9dfRgHtmhSsYvuZRruNpyO0ROFhgX+Av7e8ndgPTUhNawLsnXd1tx33H1AcCokKD3P2MadG6mbXJfkhOQKl6faiMF6GKkxNh2XUd9RHkbZ3MAx1Ldf5ewlGk76dgK1Zj3P2cm/hk2strWgDo/uPI83s05k+Zh/RXbxvUTD3Y7TMXqi0DArL4sh7w4JrPfr0I+6yXVpW68tqYmp9GzRk+Z1mgPQqVEnerfqTVZeFo3SGhV7Pd/o4OQ5P174I0e0riEB8TFYDyONGetbyeVwxCovvVTdJaj5xLKGfj8/TJtA/k/P86+kORDycp7jT+C1zIGM3XUWM+8ZzH2JSZHfJ5Y1rEqcjtEThYaFPVz3HXcfcb44ll+7vMixD/V/qMi2Kz67Aj9+UhJSeOD4B8L23T31br4676uIy1alxGA93ANnAHXEFB06lH2Mo3RiVMNjHvmE9ZsKmNHoJholBcNNC/w+Psnuw2M7hzLqvBP5rXOr6G8WoxpWOU7H6IlCwzhfHB0adCDOF0daYho5+TnFdkEu2rSIJVuWkJWXxUFND6JTo05cOflKxv0SzLL/4PEPcsK+J/DVEjXALjvksojLVeXEYD10xphj9/LNN7rs1696y1GTiSEN//hnOYOeWWDXtPl5PfNkrqn1Nvn+OCZlH81Tu87k+KOO4fuTDqy8G8eQhtWK0zF6otRwydVLyjxm/K/jA9MoPdL/EW444ga+X/l92DFJ8Ul8ds5nTPh1Au0btGdAxwERladaiMF6WCnGmIj4gEZAmjFmZWVc0xEj3KfBpLH0o6lyariGO3dsYdQj9zIk5VvyiAfuC9v/euZAGsWl80Lm/3HRv/rzzeHtK78QNVzDPQanY/TsBg0vnXgpb/zxBmmJaYwdMDbMW+YF8oduG9J5CD6fjwRfApcfenmllaPKiMF6GJUxJiLdgDuAE4BaaFB/Qsj+BsAYu/1qY0xONPdz1EBee626S1DzqYka5mRwxf33cXLyDxyfNJtH6gZ/+q3i1rGqIDhx8UZ/A1qe/iJTpfnuK09N1HBPxOkYPVFqOHftXKavmE5qYioHNz2YXi178dOqn9iVu4tdubso8BfQuXFnkuKTSI5PZv3O9WTnZfPoCY+SkZNBakJqYDLxGksM1sOIjTEROQd4CSgxqtYYs1VEOgDHAROBzyK9n6OG0rp1dZeg5lNDNPRvX8Vtj/2XfkmzOCppHs/UzS1yTL4/jl6JC1iVrcbY0gdOIi4ubvcXroZouMfjdIyeKDV8fObjvPa7GiO3HHkLh7Y8lPkb5gf2pySkMOSAIdz49Y1s2LmBp35+ituOvo2j2hwV1X33KGKwHkaa9FWAF1FDbCzwP+ALtKuyMP8Djgf+jTPG9j6++EKXA2pQPMKexh6qYUFBAZPnr+HKN39jQt176Z88iweLmaMbYGFeez7J6sNH2cdy1aBjeOzwdlVa1j1VwxqH0zF6otQwPTs98Hn5tuXE+eKI98WT788H4Nj2xwKQmZsZOK60PGM1khish5F6xq5HB6GPM8ZcCyAi+SUc+61d9o7wXo6azJgxuoyhH02Vs4douGvLKl748Al+WVGX6bmHhO1bXVA0Ceufee34IvsIPss+ir/z27DswZMZ6fMVOa5K2EM0rPE4HaMnSg33bbBv4PPpB5wOQK+WvcjJzyE1MZXEOE3S169DP7Znb9e5KRNSi71WjSUG62GkxthxaBzYmLIONMasEZFMoE2E93LUZN5+u7pLUPOpBg1ztq/jhnHP0yp7GV0S/+bghMW0it/I1cCMtK5MTw83xqbn9ODslC/4ObcLU3IO5ZvsXqwsaM7yMQO5rspLXwyuHlYOTsfoiVLD24++nYS4BFrVbcXgzoMBmHHRjCLHfXjmh2HrS7cuZeS3I0mOT2a/hvtxZ587i5xTY4jBehipMdYS2GmMWVXO43cB9SK8VxgicjRwI3A4UBdYBXwC3G+M2VKV1xSRBOBK4HygE5AHLADGG2NeLeOebYHbgQFAU2AzMAV40Bgzv4xzTwGuAnoAqcAy4F3gIWNMZmnnVjnNmpV9jKN0dqOGefkFnPPC9/yzYhkXpX5Mp4SV7B+/nH3it/JUImGZ8D26JRoSyCMvpPn4Pqc73Ta9zR3/15O7erflrt1W4ghx9bBycDpGT5QaNkprVGxC11DW7ljLDyt/YGfuTprVbsaAjgO4a8pdvLvg3cAxNdoYi8F6GKkxlktYruySEZEUoD6wLcJ7hV7rcuBpIA5Ygxo+ndFu0zNE5ChjzIqquKaIJKNxcn2BAnteEjpH5xEicjwwzBhTZNooETkU+AY1/NKBP4C2wDnAEBEZbIyZXEJ5HwRutavLgZXAgeh8oUNE5BhjTNRaVxoTJ+py0KDqLUdNJgoNC3Kz+OrnX5jx21Qy12+iVfx62sav5ZYdV5Md8hNuG5fLxWmflHqtLH8Sv+d1ZE5uZ1J8OWT4tflYdM+JpCTt4SkLXT2sHJyO0VMFGs5ZO4cz3j8DgAEdBzCg4wAWb1682+5X5cRgPYy0BV0OdBGRjsaYv8s4dgA63e+iCO8FgIh0B55CjaargGeMMX4RaYh6hY4H3qECsWlRXvNB1BBbCQz0vFkicgzwKXAe8BPwbKF7pgIfoobY68BlxphdIpKIJmC6GXhbRPYzxqwvdO4pqCGWA5xjjPnAbm8NTAK6As8DZ5ZXg93Oo4/qMoZ+NFVOMRoW5BewNWsXL834k2e+3QDAJakf0ip+Pc3iNtM0bjPN4zbTJG4rA3x+BoDWOMszu87gr/y2gfV/CpqS7U8k2acjIDP9yZi8tizI68D8vI78ntcRk9eOR848hP90b8V/dvd3rmxcPawcnI7RUwUa1kqqFfi8M2cnAD2a92D2mtkAHNL8kGLPqzHEYD2M1Bj7CuiCdtFdW9JBIlKXYJ6xzyO8l8edqFH3pjHmaW+jMWaLiJwFLAUOE5GBxpjyjtqM6Joi0gS4wq5eHNqtaIyZLiI3o0bRXSIy3hgTOrjhEqAV2rV4sTEm256XKyK3Akeh3rUbgZsKlfduu3zEM8Tsuf+IyJmod+4MEbm3rK7OKuP996u7BHsUOXn55ObnsWLLTv5Y9xcrNsaRm5vK7SHH3HT3NdT17aSeL4N6cRnU7w/143ZQf0wnGsZtp4FvOzfsuI4vc8In9R2WOolW8RvKVY528WvDjLEC4rk34xI2FdTD5LdjRX4z/hh9Mt2S93CPV3lx9bBycDpGTxVo2KJOCwZ3HkztpNp0btwZ0DQYQ7sOJSUhhVZ1K2GKseokButhpC3t48AI4EoRWY2mtwggIvHAQOAhNJZqG4U8RBVBRGoDJ9nVItcxxmwSkfeB4ahXqExjLMpr/hvtklxijPm6mMv/D9WoGdAH+C5k3xl2+ZJniIXc0y8iz6PG2BmEGGMi0hHoblefK6a8i0RkGnCsPXfPMMYaNy51d0FBQbnyTBUU+ImLKzoSLze/gJ05mdRNTg1cJyM7j7FTf6SfdGTMF/OZszyPT6/szT5141iwOocV29Ywcd4m5q/K5oAWqazfnse69DwAEuJzqJOcxtZdeRF82cgJNcYerjO2xOM8GsZtL7JtQ0GDIsZYgd/HhoIGrC7Yh1X5TfknvykrC5qxIC84t9vRnbN49bzBxMUNjLj8ezxl1ENHOXE6Rk8VaNipUSc+OOODsG3tG7SnfYPdMLtFdRCD9TAiY8yOkLwAeBP1fN2FTf4qIrOA/YHagA8Naj/PGLM1inJ2B1LQ7rlZJRwzDTWcDq+Ca3rr04s7yRiTJSI/o92Yh2ONMWuk9iztXHtPgDYi0tIYs7rQPZcZY/4p5dxjiylvtZCZm0PnO4uzVauG8VPmBT6f8vTMYo7w8ds/WWFb8vKTqtwQi4SGcelFtr2eeTKTso9hfUFD1uU3Yl1BYzYUNCCtFrw+/Fj+3apSxtDUTD60I8sGD67ectR0nI7R4zSMnhjUMOLU18aY94D+wGJ0KqRE1Pg6FKhjP/8FnFCBbsOS6GSXK4wxRdN6K97sqR1s/NXuvKZ3bmnxct65ErKtHcGBDyWd+w9qIBY+N9J7VpyMDHjlFf2cmwt9+8Lrr+v6rl26/s47up6eruvej2PTJl2fOJGv/yzvYFtHKO9l9eOlXafw+M5zuDvjUq7dfgPD00dx6tZH6LN5PF03vc0zu87g0TOERfE/sXT9+ywfM5DHRj/GXVmNeGbtFj647yZ+fGA4f+X9wG/rvuYgzxC79lr987jiCrjxxuD6pZfCyJHB9eHD4a6QsZFDh8K99wbXzzormPMHYMgQeOSR4Popp8CTTwbXTzoJxo0LrvfrBxMmBNf79q2UugfAunW6/sUXMHYsPPSQrnuTDC9dquvT7PuPMbo+w6YJmD9f12drnA3z5un6PGvkz56t6/OtE3rGDF03RtenTdP1pUt1/ZtvdP0f+y71xRe6vm6drk+cqOubNun6hx/qero1vL3v7fH667o/1zZfr7yi6x4TJoTP3TdunOrv8eST+v/xeOQR/f95jBmj/1+Pe++Fyy9XLUHrxfDhwf0jR2r98bjxRq1fHntr3QP9n3t1b+xY+O9/a17d69tXdYDqqXtDhwbXr7sORowIrkdb9zKrPwlBVAEhxpipQGebGuJooAUag7UO+AGYYowpiLaQQEO7LC11hbcvDg1V3rwbr1mRcxsUc88SzzXGFIhIOtCkhHMres9qo1urJsCf1V2MPZbu7eLot3o+5/8R7rU7fU5d+MB2MYwZow3vSy9BvXraKJlpwYfEx1UwlVAs8MknsGpVeAPtqDh9+8L48dVdiprNJ5/A8uVwzTXVXZKay5lnwurVZR9Xg/D5/UUyL+xxiMidwD3A98aYY0o4pgNBz1DrsnKgRXNNEVkCdAAuMsa8VMK596ADBL41xvSz244m2D0ZX5KhKiIrgdZo9+7rdtuLwIXAa8aY80s47zh0xoN8Y0xEhvbo0aO3JScn17v11lvLPrgcPPD1Z4z/tuzjKoO+Up+pJWT1GNClPicclIyvoBlJSRlsytjFph25nNq9PbUS6pDrz8TvT6ZlvVTSM/PI9+fSuHatYq+1WwjNTF8DfpOOasLVE4ej0hkzZgzZ2dnpo0aNql9dZSj3A9ume2gF+I0xf5TjeB864tIH/BNlzJgX2FPipORo/JdHeXyO0VyzIucWd553bnjAUvnOreg9q5XbtmRwW3f0TWaPJjhdSINaSZQucxXjdY3s8RruwTgNKwenY/Q4DaMnBjWsSB/Hu8BcdBRlmdhkpyPsOa9XvGhheIZccRORe3jdeAVA0aFmlXvNipwbaoSGfi72XBGJIzhbQXHnVvSe1cuzz+qfI3KchtHjNKwcnI7R4zSMnhjUsFyeMZsx/jg0FqwiU81dB/wfMEBEuhlj5pV1QgnYqETaiEhiCQH33uypS0sJyK+saxrgSKBjKdffN+RYj2VocH6SPbe4Tu/WBN0yoed6nyt6z+plcrETCTgqgtMwepyGlYPTMXqchtETgxqW1zN2Fpq49UljTElda0Wwx45FuyrPqXjxAswFslEjpaQM+33s8qcquKa3fnRxJ9kpoHoVPtcmf7XDYyg2Ti3knv+EpLUIvU47m3G/IuWtPtLS9M8ROU7D6HEaVg5Ox+hxGkZPDGpYXmPMS/X9aQT38Ca8OyqCcwEwxmSg80ACRWdiEZHGwGl29d3C+3fDNT9FPVz7ikj/Yi5/PpAGrKdoPjEvdfBwO79l6D19wGXF3dNOO/VbKeXdn6AxE5e/6wAAIABJREFU9l4xZaoeXn89OPLPERlOw+hxGlYOTsfocRpGTwxqWF5jrCM6Qq/CeQqMMQuBfGC/ip5biHvQ2K1zRORKa7h4AwveRnObzaZQ9n0R+UFElotIcdM2RXRNY8wGwEtY84KIdAm53zHozAMA9xpjCmcQHY9OSN7enptmz0tEE+geAWQAj1CUUXZ5o4gEkrJYT9k76P/z/fIMsKgyXnhB/xyR4zSMHqdh5eB0jB6nYfTEoIblHU1ZDyia8rv8pBM2TXHFMcbMEZFr0G7Pp4CRIrIO6IwOhVsDnGkHDoTSCmgLFBmyGsU1AUYCPdDuxt9EZAHa5eklXH2ToMEWes9dIjIY+BoYCgwSkb9tGRsTnAR8XTHnfiIiD6PTJL0vIstQbQ9Ek+4uIOhZ2zP4uvoy8McMTsPocRpWDk7H6HEaRk8Malhez1gG0RlTdYCdUZwPgJ3Muy8wEc1k3wVYCzwBdDXGLKuqa9p4uOOBG4Df0eD5Fmi81oXGmHNLMOIwxswCugIvAjuAg9Bpo94GehpjJpZS3puBU9EplhqgU08tQb18vYwxpSWFrXoSE/XPETlOw+hxGlYOTsfocRpGTwxqWF7P2Hqgk4h0MsYsrsgNRGQ/1GuzvqKFKw5jzHRKntexuOPbVfY1Q87LAx6zfxU9dzlwcUXPs+d+DHwcyblVjje9yAUXVGcpajZOw+hxGlYOTsfocRpGTwxqWK4M/CLyEjAMuMMY82BFbiAiI4H7gVeNMcPLOt5RvYwePboA8CUnJ5d5bLnIyNBl7dqVc71YJT0kCqBeoQm9nYbREysallZPqoJY0bE6cRpGTyVrmJ2dDeAfNWpUtc0vV17P2ETgAuAGEflfoZQLJSIiLYHr0bQYkYzEdFQ9BUBcdnZ2eRLnlo3nStbK7iiJlJDJHgpr5TSMnljRsLR6UhXEio7VidMweipfw7ros6/aKK9nzAcsBDqhMz+faoz5q4xzOgIfocHli4wxB0RfXIfD4XA4HI7YotwThYtIL2AawTkV30CNrbnAFtT71QjojgaYn4uOSMwCjjHG/FLZhXc4HA6Hw+Go6ZTbGAMQkUHoPJN1UOOr1GujIwXPNcZMiriEDofD4XA4HDFMhYLVbMqFQ9AM737U4Cruz49mkD/EGWIOh8PhcDgcJVMhz1goIrIPcCwaE9YINcI2oYlHp9gs9Q6Hw+FwOByOUojYGHM4HA6Hw+FwRE+15dRwOBwOh8PhcDhjzOFwOBwOh6NaccaYw+FwOBwORzXijDGHw+FwOByOasQZYw6Hw+FwOBzViDPGHA6Hw+FwOKoRZ4w5HA6Hw+FwVCPOGHM4HA6Hw+GoRpwx5tjtiIivusvgcDhiD9e2RIfTr3KoDB0TKqMgDkdhRCQF6AHUA74Fcqq3RI7KQETijDEF1V2OmoqIpAINjDFrqrssNRmrYy1jzKbqLktNxOlXOdjnXLIxJj3aa7npkByViogcC1wF/As19ncCm4EngReMMTtExGeMcRWvhiAihwKDgAOAf4ApwLfGmJ3VWrA9HK+ei0gH4DT71wZYDfwMvGKMmVWdZawJhOi4H6rhqUAzYCkwGxhnjFlWnWXckylBv+bAEpx+FUZE9geGAKcAjYGFqI5PGGO2R3pdZ4w5oibkx34o8AJwEFpB5wG1gH/bQ98Ehhlj8qunpI6KICK1gHHAeSGb/YAP+BK42BizujrKVlMQkWbA/4B+QCbgeSJa2/Uzgc/db6J0rCHxKtAb1W07+rLXCNgADDLGzK6+Eu7ZlKHfeuAUp1/ZiEhP4CWgC6pjFpAMpAELgFONMX9Hcm0XM+aIGmuINQQeRA2x0caYLsaYocaYU9E3CIAzgOurq5yOcEqLc7D7nkMNsd+Ay4BuwIXAr8CJwFMi0qWsa8UyJX3vkO3vo4bYa8Bhxpi2wJHoS0sq8CzqdURE9tr2uIy6mAp8gBoSzwGHGmOaAycAHwL7AE+LSB97/F6nY5T6NSVcv/jdX+Kah4i0AN5BDbHHUR0bAYOBqcCBwCMi0tUeX6E20cWMOSqLfYHjgL9Rb4rXKMYZYyaJyL2oIXa1iHxujJlffUXduxGRJDReZGsph/VFjeeVwDnGmD/t9t9FZDHwDPB/wFrgCtRbtle42W2cSFe0bs8s7hj7gnIK0BNYBNxhjPnH7lslIncCecB/gCtF5NO9LRbP6nggkGOM+aOUQ89GH4A/ALd6XUHGmLkiMhL1TAxE6+E09q56WBH9vqd0/Uag+u2N9XB/YJsxZnkx+72wmvOA9sDHwE3e79UY85WIbAJeRB0P/6ChOhVqE/e6NwjHbuNku/wRSAewldXrfnkTbUxbonELjirAezsTkX1F5BYRmQbMB16z6+0LHe+1CYcDicB3xpg/RSQ55I35F+B++3moiLSOdUNCRJJE5BQR+Ryt3zOBj0XkexE5NeQ4X4iGHYEkYI4x5h8RSfSOM8asBx62q0djvWOxjoikisjpIvINsBWNtZkoIh95npmQYz3Pgtjlr8aY7aE6onFPD9nP/xaRg2I5HjVK/eaUod//xbp+HiJSR0TOFZEpwBY0hvNzEXleRA4OPda+WCWiMbMAPxtjCgrpOB94zH6+UETqVbRNdMaYo7KoY5ebjDE53oM75If9NzDRfh5c1YXbG7EjH71YvvfRbuRe6AjX4+36eBE5yh4fbxuZNLTh8aNB0hhjsr24JmNMrjHmA/R/WgdtxJOq+OtVCSEG6Elol+KJaMP7IfogOxJ4RkRus8f5rIZJQAe7bQ2obiHX9dmg6c9Ro/dE29Ufk4ToeBrwPOpFXwh8hsYv/Ruti+d7x9u6Wxv16uQBf1ndAjoaYwqMMd+j8amJwEDr6YgpqkC/ucSwfh4hOp4PjAf6AAbtZkwFLgFeEpG+hY5PAw5D48R+L0bHHOBTYLG9ToVfrpwx5qgs/rHLA+0y7O3KPsinoo1CFxHpXHVF2zuxRkFbNID8YHRE62FAW7Qx/wk1yl4UkdQQY2sX0Ap1s68rfF0R8cIbPrLLY4Amu/GrVBvGmHwR6YjG2jQHLgB6GmNOAwYAd6Ej+0aLSO+QroscgppkFGOsem2v94LSE+3qjznsgytfRLoDE9BuscFozM0g1NB9AdgPGCsibULqYgbQEDsyu7DXppi6eBT6/4gZQvTrgeqXQrh+Awjq91Qp+u3am/QrHLMVomNf4ClgF/pydYgx5gS0d+cLoDswQURqh+iYjraHqUCWNXR9ha6djr5cARwvOgCq3DhjzFFZeGkOWolIQgku2r9QtzrAoVVTrNhERBJF5CARaReyrbiA0X5oN8VPwA3GmN+NMVnGmJ/QkXx/oY34NfYt2sMzrpsXc23vf/uZXfZAUzbUGKx+fUXkStv92NBuL9KAoxo2Bb4B3rINcbwxZocx5j5gMhAPXC8irUNO90aaNqVoHI63/gM6mq0DNdAYszr2EZFLReQ40WDxsCD6kAfXGWi37QfGmI/ty0K8HZE7Au3+rovGlYZ6CRfZZYfC1yao45d2eRAaClEjqKB+p6P6vV9IvzUE9avDXqSfh9XxaBEZJiK9QnoFitPxMrvpRWPM11bHBGPMQrvPoL/F4Z6X0HrIFtjzuthl6EAHr9341C57oyNVy40zxhyVxVJ02H5zoDMUfbBZt64X8BwW3+AoGxFJEZGzROQLNG5pLhq39IGItCoh1uMsu3zWa7zttRKMMavQLg9Qw6xHyHnz7PIIuwxt1LwGfDaaQ649NaQBF5F6IjIG9fh9B4wF3ka7cC4I1VCCgbveaOB3jTG5IW/YnlfhOWA5+pZ9XMjtfrLLQyg0WCrkPgvRQRINgTZSQ0ayiUhzEXkCTSsxBdXgQ2ChiAwIfRkL0fF4u+kduz3O6phojMlDu4Ez0S633iG3m2uXRdqMkPv8CmxEU4bs8XUxRL+NhOv3ZyXpd1jI7bzf8jGFyxFynzkE9WtRSV9ztyMaC/ss+uyZBrwMTAJ+EZEexTgFfOiocFC9PR3zbJv4D5q6ArTt7Go/p6IvrqDeQwh5wQq5z89or5BQQQ+jM8YclcVfqDelEcGGIKx+WePM2NUDcFSUoWijfQIam/AD+oM/FfhJRAINsIjE2bfCPLupsNfMG1jxGWpUHYh6gLz/00K7/2gIdDMHsA1YZshxNeEBmATcDlyH1s0JwI3AV6jH4SURuVw0Zg6Cb75eIsdUu4wDsA9A0AZ4OuqV8AaygKYEAe2CDPWYeeXxZjNYbDc1ogaMcLfdL3cCVwO5qI63o7F0LYHJIjLEexmzHon62IE9aMxiKJ6OU1AtO2CNWnsNbyTvkdbwCHvAWu9QPvC73bRHd7MV0i+HoH4LUEOoJP28erhX6+dhvX+jUG/WDrSr9j7UMOsGfGm7JEPpiOYG87pvIRhS4+kyCXUuHIQOZMKe4+UP6ynFzERijead6P8AoJ23vTzfxxljjspiPcEfcz+7DKus9u0uF8gG/CJSuFFxlICIHIOmk8hBuysOMcb0Rd+WP0QfgneLSDcIvKm1QH/juQQHWHgxTaEDK2aghseRIpJi9y0DVgBpInK4LUNoo+J99jLIF9cFsqfRBzW+VgN9jDGXGWMeM8b8H9qIA9yKpuzAvi03RPUDzWcFRev1BlTDPODokHq9HPgD/R8cQVE8Db3fTUtjTHZ5G+9qZAiakuNXoJfV8UGgP/CEPeY2wr2EddEA8UxsXQyJr/Pb5XLUm+gHjhCROnbfUtRgjUdTrhSui15d/sUu97PH7Kl1sST9+lG6fgmoUVAe/Y4M0W8J5dPPCyHpZI/Z0720l6IvqF+h7eGlxpi7UB1fQl9uRorIQSHnJKBa7sK+bIXo5/2uF6EGVW3gMBFJsy9efwGrUCPrECi2OzkRfSmBoMPBGWOOqsMGLP+APpAGikiDwl0+9mN9NIB3OXtJPqCSsN6rw0XkfBHpLsWMYgrR7XT0YfY/Y8wHXjeZMWYB+pY9B/WYXRJy+ma08YlHGyAK/0/sG/FsdHj3/gQbkFWogQFB4yRwrr1/HGqEQ9Azttv/p54momkkjhKR0SLysohcbXVMKHS81879n12+a4z5XTRdhxdY/zKaH681cGXI6TtQ48sPNLZehOK+4x+oAdsMGw9pfxNf2P0niUjhQQ5e47/ZLlvY86rkdxGiY5yNtxklIs+JyFAR6VjYKAxZ97x/7xpjloum/UiyntJnUG9rd/Rh6bEefSilAPULG0oh156DejbaEayLq1HPI6gXuHBd9EavZtlN9bztFVOkYlSxfutQ/ZIpW7+NlKzfYChRv2y7ydOvSmeFsDoeIyJ3iMjjIjJQRJqXcKw3IhzgHWPMetG4sUQbQ/co6mnsAwwLOXUZ2iY2QY2twtf1uoRnofWpIxqGAcHpoyDYlhQmjaBH3fNslqseOmPMUZlMRhuDWsA5IY1VItoNBNYoQEf2bK8BXoBKR0Tai8iTqAH0I/CKXYblCvIaBhFpir6JZWA9UXaf1z1h0NgvPzDM88zYxn0D+jtvUYon8m80eWs97GhYOwrrE7t/oIhI4ZNsI+Pl5PnDuu53uyFhNekOfI0+ZO5EG9wn0BeCGyUkENo+bPZBH06Z2K5yo+k6cuznDej/IRPoLSKH2O25aGoKHzrCNGxAQ0j9XYdNA4J9a7a8b5d9gWMLfRXv3J52+WNVenOsjkehmk1Du3wuRUffTgMu8o6VYEB0W1vejahnB2NMToiOK1Ads4HTRaeDwhiTjcbG+dDRvCXVxWWolnWxsafGmCzgPbt/gIiExpN5v4UcguER06kCqli/HMqv33pK1u/EPUW/QmU4EdVjKnAPcA060vgrERkccpz3+2iBxsCttOd4KXdy7ec/UR3jgLNEpIHdnon+Tn1AewnPFQbB3+QC9EVsH4KDk9YQkp5JRFoUNrSMjqj0Ym8rNO+sM8YclYYxZi3wul0dgbrjvR9Jtn3LuRiNV3rX7turvGMiUgc1Hq5CG9z/ock/56EB4K+LyEn2cK9hyEDjF2qjHpgib7aoq34u+mbmnQ/Brpv9sakWJCQWxe5biT4cErHGhuVDu+8AQt7SJTgIIA3bJQTMtkbPbjeuRaQNOjT9OHSE40WooXMvGtd1L/CAPdz7jhttWUMDccMwxvyCPlhBH/reC8TvaPdwB4K5w7xzvOtvIZgGpFnI/tnoVDRNUCOxdsi+AhFpRDBYfcbu9uaEIjrh8Th7/8mojgPR/EvNgcdF5Bp7eKiOLdHvs6SES39PsN79K2S7N3jnAKxGJdTFLaj3or53ojHma/Rh3Q64KdT7aYKTYHujUUvLRl9pWP2eoWT9nnD6lY3ofI/j0DbuE/QZcRY6MvFA4DkJJlb2vmcG2l61IuhZLsx3aLxcC2z3rGWKXR5C0Dng4V1/EdqVWR8bK2o9he+gxq4ANxTzXXqj/9tdqGFcbpwx5qhs3kGz7XdGG6OrrOv5atRgaIZOJzGtGsu425FC8RYhRsppaK6q34DOxpgLjDG3oN0vH6BpEJ4T7eb1jJsCtJEFaGyvF/bbtW/U39nV0AZ8OtrAHIjNxF3YADbGrEM9QolAnojEh3jeHkMbn+tE00AkmeBIwpvQt+mfsSMHozWubZdNQnHfMYR/ozFYPxpjTjDGvGyMmWaM8YJ5c9FUHb3sg8brelhlz/eM0sD/KOReH9tlH6CB/fwL2q3eFuv1KkbDdILdjrkikhyy+1HUY9wTeFlEDhXtIu2Fjubshj7Mi51aKRJsl43nvSsp9mcYOkz/Y2PMv6yOn6MvUg+h3S3/FZG2Id83leCAg2LjBK2X8Ru7GjqgYTra9XMgQQ9sYR03ojomATmiXdHeb+ch1JA+Fc1Htp/9nr1RjfdD2545ZQpUBhXQ7yBK1i8OGFOKfu3t9YvT71u7Wpx+B1A+/bLLqd/h6O+80vTzCDX6ivs92/1XolpMMMacaox5yRjzLtpWvo8aRI+KSMOQ79sQNXYKsO1aMddfQvDl6t8h271cYL0olE4mJH5sFfqyXBdtG70R6Jmojl6bOFpE9gnR8QHUEH/Z6Mwl5X45dcaYo1KxjcEI1EPWAk00OhXtQjoQ9YhdbrstYgIR6S0it4rIw6KjoFpZgyXwQwxpRG6yy/uNMVtE4ySSjE6PcyvaELYGzrc/fj/a8Kyw53ldYMX9yL03vmNCvDpz7V9z4KhCRkJoY+nF2+TaN0Bv+7PoCE5Qw+FbEZmIBqmOQt3515jS57ksFRHpIiJ3ich0tLv2cRE5txQv0cV2eb/3HSQ448MEdDQUwKW2K8EvOoLNG/l5OEXx/j9f2WUPgrEzf6GGUirQTwp194Zo6MXYbLeeYK9MM4HRaPfoENRQWW+veTb64L0qGg1tObqKyN0i8p29x30iMrC42B9bNi+W5l7ve0gwR+D9qIcmCbgoxKNXm6BRW1pd9Lq6jvTqotH5E39GA6uPlUJJMUN09EYN5tv67+n4HjrQYisaAP8D2r0+A30B+Riti7lEwG7SL5mS9fO6p4vTz3tZLU6/xpRPv4Jy6vcj6tGLSr+QcnSzRsqXwCcicrOIHFHC7zkNzT+Xh50ezOropeu4C43TakcwTQ+o7bLNnldSAvEMgiMbA2k9rLd6JdrO9immTfSMby9PYB3CeQL4r/18py3fSlTHvmhvx032Xm5uSkf1YL0Q21GDrA/6Y/ofamgcbIw51xizqTrLWFmISH8RmYU+DB5A3dbvAT+IdjUWDrJtTTC40+sq8xudPirOGLMEeM1uP41gAG4WwYbBy5FTXMNm0Ia4FTaVgm3QPkW72QZ51wwxFPJE4yYKG8d5Epzy40E0D9lCdKTVQHuPd4FrjTEVio0IRUTOQh98d6NvqgehEz6/JiJPiUjdQsc3Iqhrhl0WWOPX0/Y1+32Pt9cENba8oelebExoniCv0VyKGkoNCU/XMRFN3XISNt2HNaQTAC8A2ns4eoZt6PUnoaMNx6APiPWoETYCGGaMWVaRt+jCiMgV6MP/LjQP0pHASOB9EblJbLqOkHt0seXcHlLOfFsf4o0xOwjWxX8RnFljB8GEwN7I3eICvZejgfhNCAZAg3p/09EAaG9EWrw1YvJEBzl4xu4Oe30vNhJjzGtou/Is+r/agep4GTDCGFNSl1WpOP2i089DRG5HXzLuROv7ALTOfyyaIzHRHufpeDT6O/4b+0JkjMkLif1ahM2rBpwmGnMH+vvZgL4s7G+PLRy/VYC+xKYDbUXDGzzetsshhLSJVkdv1o1m9tx1Xrns0g88jbYvr6F1IA/V8WLgZqNxehVij89p46hZhLh5M9DG7fvqLdHuQTTO4UHUg/IZ+rBeh7rc+6FG2VnAJAl2k7VD37IWo6PKQo0Ab/kZ6kU5GG1sf0djQJahnpeuotN0eIZIKBn2+KNsubyYlE/ttn7AcGBuoQfAAegoq3VYz5AJj0nLsd/nPRE5Ao2H+K08b30h3724fSegMTeJqJftI/QBcaX9uwJYJyKPhjRubdB2ax3B0VBenfO+0wz0bbU36gX72BizS0T+Qh+gPURkH2PMhsLls160WWii1/0Jehun2PJdA1wlIsZ6zArsd+mKernWWa2K60JaBdxmu1u2FNYj0i5e0fkIH0C7Z29FuzzXA7cAF6Jv8dvQbiDvHo1Qg3MlwbxphfMtfYO+BOyP1qdZ1pu7xN7r4JK+C9q1sxD1SHQnmF9wMtrFfCYwQkTmWsPFowca/7eYYHdSGMaY+cAVooMyNlZC17jTrwKISHJxPRsicgOakmML2pX3LdpW3AWcgxouuahBGYe2Z6mop28BwZcY73reb/ND1Bt1CGrUrjDGrBERLxD/INE0HqE6eKSj/6PO9s8L93gPbRuORuNhLy/UJh5uj/+ZYgLxrWE2BZgiIi2AtdHWQ2eMORyFsN2GOSXs85L9XY42fE8YY64P2f8j6qK+GQ2UXWG7F0CDd71cVWFdASFG7HIR+Qn1PvUUkQ+NMekisgDtUuiMNkrTpGjiQR/6tgghSUaNMfNE5FHUGLtIRLJRT1Se/Q4j0e6Ub40xhlIwxswobb/VIBltNJNsF13h/V4jew4al3WvMebekEMeEpF/gDfQVB3L0FgWUA3roN0bibZMhY2ezdagOhzoLiLNjMbFGfQB5z2w3iH4UPDKVhs7sTfq/fP+51tE5HHUaO0PvCsiN6PTgPVGB2TkAm8Yjd8rSRtfCQ/f4o5NQb0nzdGHwgZTaLJx1NN6mtXkWmPM2JBL3Cgiy9Hu5StE5G9jjGdcrkDjYZqGfn8Iq4vrbF08DTVgG9iu1D9Q705n1Mv4uQQTh3rEEfQaNQq59hIR+S/q2TkDTRdyC/os6kMwkeyLpXXbWh03lLQ/5Lh+aIzUYHRO0dVe/XP6la2fPTYF/b0Msn+viMj9od4f0a77wdjJto0xb4bsu8rqdQf6IvOHMcaLm/OmauqIGm4BQnRcJSKz0ZQx3UVkqtH5c39Bu1wPQjPl/yjB0dNeG5NpNdyOthkec1CP3dHAxaJJde9EDez+BHV8pjjDs1A515S2v7y4bkqHg0C6ietF5Gdgg9hs9lI0uLZARA5AYwM2YdM/iAaex1s3/1OoV6oX6i3xzl2ENg7NKGZoesi9PIOnI9rYg44Kmod61AbZbYW7tXLstXMpNMG3MeZL1Pu0C+1OXWT/fkS7Ud5FG6DQLoRyIyJtRGSENUbT0YbyXRGZLxr4X9ceF28fhB3RN/yN2IEHorEi3r0nowZYG+D8kO+xCvUA1gWaFP7/hKzPQw2llthM2OhbsReLc6a9XuEuolw0kDkP251kgsk1V6IPwJ9Qz+WXaNzNI2hw/9PoA6dEynp7tvXwchGZinYhzUCN0vnAm2JTbkgwjUgPtLtkMTanme1u8XR8A+026uJ9Z1uOJai3pwnFTPIuwS5fzyvQnuCLxJ+o5zEOO2K6GLajOuZTaNSgMWYeaogvQkfEzkY1HYN6Se5DNS2RcujoE03Y+xb64tSUYF6qUE+W068YRAeZ3G2NoF2ox/4/qLHiDfYJbSsOt3+zsb0BEhwItB31gK9Fjc/Q77zVfteWWH1C258QHb3f7f4EPeJzUI9aG4IDHQqPLt1AsEfCM/wwxviNDra4Fm2DzkTrwEyCo7Kvt926VYIzxhx7NSLSVkRuQrugHkGDamsTnMg8tGHwhWxrjzZK022Dk+M92I1OfPyqPXawiLQKuaXnKepKyXjD2tsQHNG3gmCOm7PsW3a+LVecNXK2oUZBIrbhkfBBBPeiMUovow1gCtrIjUC9AlsLd9uVBxE5HXX7P402tn+hgzY2oV2gT9h9EB7r1hH1TPxi75sX8jacbq+5GThBRA4MOe9XuzzQfodQvLL/iRozjbBpAKw+b9n9x4vIAFt+78HhNfxeV+iv3n67jDMaH3cO2gU9wZbxVqCLMeYGE2EGfRFpLDri+Av0wXUkaoB9Zrf50IfY8yLSPsQj6nX1pBljFlsd80N03Gq/cyaaLy509NiPdhmaF83D09HTug3BQOZVBPNWDRaR/Y1NAmx1jPv/9s48WqrqysMfCAhEoxCMKCrO2wEEW2yXqMuItm0HUaPptk207ahRux2WaVvjENF2SNBozIpRo4mtRg3GEcU5GgWJU7tAGg1sEAwRVBQaEBEVgf7jd8679xX1HtPj1YPa31pv1Xp1b1Wd2nXvOfvsMY1pU3QtNkrxT2N8GBUyPhVZKEcgOe7p7lesicunpKgORr9/VmYaNjGl3yjk1/i9B5jZBKREDkUxoq+gRKx/BPq6+4+zS7D0OVmX6OjuHydlpyzHWUiOHZAc85y4iCJ7c7k+uCVyQsiupeNOkf38L6bwjQY5pud7pvM/QZuzRiRL6LeQN+NxlPxzAbC3u9/YnKxamlDGgrrFFHR9JooJ6Y3ipZ5A90W1ZrB54umGbuwuQDnduqz8jEJKyc6l94JUoBD4RuWiXVpgxyHLzNYkF0gyld+FrDtbApeaapaZ5HcbAAAS/klEQVTh7jmA/ftoh/l6Oq+aC+9+dz8ZBdZu5e4HufuvkhtvleOWzOzbaDHYAdVXGogWhEFoMbwAyfOfzOzgisl7PpJl95LbqMw4CsW0XDvt6fS4D4W1IX+/cp2gxWgnv7h0/HX0G2+MyjbsVlo4lqCYsJ2QxWti+T1L7o/prtT70939WHe/xt3/XGUMq8LWyNXZHZVp2B+1yhni7kcj6+USpNyWLQtfRwvNUpM7ttq1+EqSRy8aN9t+IT0Osoril6VrcSy6B3qTYnqSrB5Cv8+mSI7b5eswvfZ8ZI16CDVhb5RZnOT4lrv/BviOux+d5DiRNST9Th2RDOeinoWQiu6WlX5k1Qr5FSxAFixQ4tWewEHu/gNX549pTbwuf78FySLZQMla/TxSRPtQZJJ+TlHVPivL5RjObLnOzc5z4gQuN+kdKM60F8p+7ZnlmM7/T3SvD3f3v1axpLdz91fd/TrgCHc/Ismx2XCNtUEoY0E98yWyOIxHcVN5l/klsJcVvd0q2RhNWgsoagVVKhKTKXbFh5Sez/WX9qMomNpAmhxmIxdZV9I9akr1/gwlDXyAXIrXmlm/9HcuMq8vAe7wZjJW02e869WzuFaVnEZ/jruf7u6veZFR9r67X4MUqk6o5EbOOOyGJv1cNwmWd7vOoqgTNLj0/B/SY3+K7NIGkmVkIVqIO1AE2ecF8xK0kPYF7jWzi8zsHDMbgVw9M4BhXiVJonw9rIn1pgpTkAVxkLuflxaIxWmX39Hdx6CFuTOKE8pNyzshN9JiUqXwfC2WxjeNQqktdwHIZTz2RYtcI9LCtRBZljqSYm5KcrwYJYwMAe40s9NNdQVHIlf4ZOAXaXGs3BSsLTlmOqEYprEokP0DoLuZ7Zq+Q4fSeSG/gunI9Qcw392neTMxU6V5bym615ZR1ELMx/L43kzv/VWKQseLKJK8Dk4W/2qZ4hugDWYnii4YHZPl8kqUKHE2qtF4nJmdYWZPoZqOY1GvymoZl2v7OlxpQhkL6pZ0Y/4MLYC/csUETUFp5duR2lrk3VRpcpmH4rO6UrTKyO+Zb+g5FA1j+5eOv4omjh7I/bZh5evNrBdFIH5lc+pb0W5vLgpufw3tsH+K4tAucfebVvC9W3LSGQPs4O53QyGrZKnLi04uRtsrKUkgGc5Fk+wuTYzzc4qFoX9+P1enh2eR/AebWaPJP1lGNknvD6mCNoWVcRzK1HwALaJXouvgiPR5F7r7E6sljdUkKX63uvuE5DbNclxKESCeM8EWuYpPgpINcnHK3lRnHkU2Xp+siLgSSyaizcXhVuoOUPrsndL7z6NwCWc5PoXiscYgK9RNyJ01GC2AF7l7q7fWSQxBLso7kTKUk2j+Pj1mN9b7hPzKY/4M3QOfoqSD7gBm1j1t+npXbDyzUjsV6RNbkGLoShblPN+8R1FextKGbSly985A89cQq+gtm+iN7uNJFHpLvi9+i+LZJqN7+B4Ut3sosmpe5O4tVsh2bRHKWFDXuPt7rlipfC/MREpUe4pCgZU75SkoHqobqYJzlZ1rDgCfC/Q0tRvJ5HiyY0mKmqVmwen5bdLz75JM+F7Eoy1zZSoNQnEOT6Od/6UoW2zYagtj9Vjk7g0xLRU7z1zfKFvPykkLM5CsO1FUE6+2I/4AKSGbIEtW5m6ksB6DJl2ADqWJfA+UKfVXChmWXc4TUdHO/qiEwdkoTqSvu9+zwm+9FvCittIyaKTYLjVV6/82ih8qL9CTkQWxG3KJV7sWlyBZz0nn7Vg6fHt6/GdkrcXUHSDLcSeksH5ACkavkOPLqLr5N9A1+B/IvTogueJaldJ9fCC67v6cNgA5KSZ3p8gLechveSaiuWdH4HRTJvYLKFnpKWC8qZDrZl5k945DJS22oUiYaUQ6dzpSTr9GquPnRVweFPckZta5tKHbFil5C9z9rWTdz4k1S939cZSI8S0UdnIeup8Hunu2YLZporRFENBogpyN3JZHkQJKK9157j7bzCYhy1lfq6gVZEUQ/Gy0IOQdYy70eh9SFA5Ak++x3riUxjGo1MQoV+BrtfGOR5Pi9U0oMa1Cc1Y2L+LAjkeuikdLxxaaynUcgeot9Xb36Vl2JRl+SrEIbkMR7PskUs7OBS40s3fSwkbazZ+E5ren3D0X2awc3yLkJvrfNRDBWiH/pqYs1CPRIrUEuU+fL503PwVcD0BybFQ/rSTHOWgRXEypVAKq+bQ3Cs4eairfMDV99mYUPUnvqeauSu8/FymItbKCNZAU1y2QZWyyu481BXPnkIED05hzUeOQ3/L8BVmgjkRNu3MA/ESkEBly53/TzI5x9zmucjLjkULU38xGurIogUYlgWai+3IDNMdl7kHz4UHAJWZ2kqcCtKZg/zPSeTfD8vNOev+Z6f0faTFJtCJhGQuCEmmBfhPFevRLE3ujjLp06oukAqIUFZwr76dcyR1SNezEBDTJLQGOMbPRZna0mZ1mZo8hBW0KcP1KjLdmithKMhglHMwnLTbWOO1/JrKMNZVJ9QlFEH5DdXBX261rkHK2G/BHM7vTzO5FytWJSGHLLZPWegPzlsTMtjeVFZiHLKmDUC/IoWZ2o5n1K50+Gl1ff0PhEq/8vu+jDUFnim4OJKvmJchysy+q1XSzmeVyGoNR5t+t1cZZ6zibJtgFXXN3Q8NmajJypW1AkVCTlYFRhPzKfIBclbNR0tAh7p7jvA5FG6DpyHNwrpnl8js5lnMgyXpY5b6bhn6DHsC7peMTkDVrMVKkR5nZdWZ2Vzq2N4r7erDagNeBeXCFhDIWBMszFcU29KRop1N5r7yEJlujiEOpdGd+hCbvXmi32YC7Pwd8F01O+6P4pZtRvZyxqCL0uJb6Qq1NSTH9HorHuSFZvtpTxL+NR0ptVxr3nauUYU9kGWtwhyaLwkdIXnejBfIEVAdsI+A24IJsFWuji15ztEMbgv9B18VZqFDvPBRndJupgwFIqX0dKWtHlV5f/t5fIOV/E+ROAhosCpORsvcE+m1OQ/XxOqXPvjjJuk1TuuZOTI+vpufboe+crWM5qzIXLR2TjtW1/DJJeX0duU3Pd/cc89ne3d929+sp6pgdTTFHPofmzX4oWxuKmm75nu9KEey/pCTfdu7+J2RZewnNmT9Ac+QSFEt3mVevsr9eEG7KIFie99BurB8ynT9C0XInTyqTUHbbAOA0M7s2uTzao4llCVLS2qMA1YZ7reT+uM/MXqSoCP8R8IKvQa/HtkAKzF1iZkeiGI53UKZgZbzM+2Z2JyrqOsTMBpUm/sx30KI2ilKF7iTD9q4q4ieaWU/0W8xcl5XYEtORgvphWWZm9lsUp3QgClp+Bi2Aw9E1dIqZ/dyLCueZE9A1OIIili+79dq7ChIfbmbbo+txmq8DQc9l0nfphZSDscCEkntstpk9h5T148xsNqq0Pjzdh79DcVt1K78KHqkWO2dFp4BH0b05AH3fkcginevu/buZ3ZpCOsq1C49Dc+J9NC4blMvGjDGzg1A9sT465FmJXq9pt2zZurZhDIK1SwoaPQvt/l529/2aOG9zFEC/B6pl9FNXv0JMGX4Po6De89392tLCsN6TkhFeQK6Nk9399mbOvQ8Fp08BfuTu96fX5wyznYGz3P3Giom9LqhQ8DE1V78NxSP2d/dZ6Zp9GikUo4HL3f2PSY6HALcga8N33X34+ipHMzsAKe4Xu/tP0nPbIeX1eIrSFNk9dg2yAH2BLDvfoI7lV0lz39PM7kYK2a3AuSkOdEukmO2JygQNc/fxSY5HIjl2Bo7ydSSwvrUIN2UQVODK+pmIYpR2M7OdoaFNSi5zsUEKrr8CxaOcAvzezK42s9tRkcL9ULzPLVbK/lmfKbmKzkSK2GukKtmWSjaU4u9y7NhFSE47AcPNbByKWXkWKWJXJkWsfT0sgJV4UdS3XFplPnLf9E7nLEZyfBLF8jxs6s85HlUV3wJtCoana3d9lWNuP9bFzH6RgvOnonijQUgJa4dij/YChrr750keIb8Kqn1PKzJFs6X6c+CzdH++h5TbsShb/EkzG5X+/z2qt3a2uz9TJca2rglhBEGJ0oL3DqottAlyVebK2Vmhyo8PIRfGy2hhPA/FrGyM2toMc/cFdTR5L02WiNxP8jpPpUNcZTkaClh6Ua7jbZS0cBGq0t0LBe0/l97n+vzerftt2g5p4cqlT3qgOLq5FPWvcDVlPxm1nnoTJTZsgQKrjycFkXvLFPttq8xIjz9CG4Ld03O3ofijXFZmRnJnL873fMhvxSRF9EtTfcScnJS7V2Q5PoZc7PehJKZ9USb0k6gI6+/SeXV7P1cj3JRBUMLMOqTJpgfa4Z0B3OjuZ6W4pH2ADu7+YMXr2qNYle1RUP5r9TrZmNnlaDEc4Wrlk5/fFMXhDQCmuvuIKq/dFJUOmFYvCmxTWOPCr/m53sj93R+4yt0vaeK1W6JEhin1JEdTPbbRKJZuJPC0q5hzPn4iirl7x913aMoNV6/yq0YT1+EpSDmdBRzeVFyXqZdnJ728PufDlSWUsSBoAjM7E1llZqFsvb2QNflN4OCcIVVPsWArwsz6IktCV5RRtQC5awciJWxnJMN7Ucbo/BoNtU1jZpsnNzjJCrE7kuepyHL4LHCKq7ZS5WvrIp6pGs0oV7lVzwDUEaILsL27/6XyNfUsv0rMrFe+xtJ12AfFd34fyfCX7v7DJl4bclwFQhkLghJmtjtqSn0gCvbtWjo8H6Vd3w486o0LtQaAmf0auXrmoIzAXSnaES1EQf3PAA+42hoFFZiKXN6Esva6o4bRW6Nr8TMU/3SFN1EQOGgUj7i0QtHqhVyWPVGx5VZvCL2uYGbbIlktQOEaPZG7sQvK/L7a3X9WswGuZ0RpiyBozC+RIpZ5GdUPetzd36jNkNYNTE3AB6R/v5b+XkMB0I+vJyUnWoOPUFD0YShIfyGq+/QkKjkwqYZjWydoKq4rWXkOq3YsWI73UbLIELQxWICuw5HoOsyZ42EBawHCMhYEJVJMyUBUt+lPXvReC1ZAskacg7Ii7wdGh/xWj2TB2QotgJNdvU6DoFUxsx1RYtIsYFJch2uPUMaCIAiCIAhqSJS2CIIgCIIgqCGhjAVBEARBENSQUMaCIAiCIAhqSChjQRAEQRAENSSUsSAIgiAIghoSylgQBEEQBEENCWUsCIIgCIKghoQyFgRBEARBUENCGQuCIAiCIKgh0ZsyCIK6xszWpA3Jf7n7ZS01liAI6pNQxoIgqHdmNfH8RsBXVnDOJy0/nCAI6o3oTRkEQVAFM7sMuBTA3dvVdjRBEKzPRMxYEARBEARBDQk3ZRAEwRpiZmcCNwBvuXufJs7pA0xI/27m7rOber2ZDQLOBv4W+Dpwr7sfb2YbAQvSy/YG3gYuBI4Gtk7HxgCXu/u4JsbRDTgHOBzYCegMzAE+BF4FHnX3x1ZLEEEQrBahjAVBELQhzOw84GqgHTAPWNLEqb2BB9LjImAp0AM4CjjMzA519xcr3nsbpKxtnZ5alj6jB9AT2AMYCIQyFgStSLgpgyAI2g7bAsOA3wBbuXs3oAspdq2CXwNzgQNQosFGwH7AO8jadUuV1/wEKWKzgCHAhu7eHdgQ2Ar4HvB8y32dIAhWhrCMBUEQtB2+Atzj7qfmJ9x9KTC1yrmfAge5+7z0/zLgJTM7FfgDsKuZ9XP38aXX7J8eryq7ItNnzATuSH9BELQiYRkLgiBoW1y1kufdWFLEGnD3Z4GP0797VByenx43X82xBUGwFgjLWBAEQdvh/9x94kqe+2ozx2YAuwHdK54fCfQFLjCzXijm7CV3n7vKIw2CoMUIZSwIgqDt8OEqnPtxM8cWpceOFc9fAeyCsi//Nf1hZg48A/y3u7+xCmMIgqAFCDdlEARB26GpzMkWwd0/c/djgD2By4HngIWAAWcB48xs2NocQxAEyxPKWBAEwZrzZXrs3Mw5m7TGQFYGd3/D3S9190OATYFByDIG8EMzO7R2owuC+iOUsSAIgjUnx1z1MrOmWift01qDWRXc/Ut3fx6VusiFaP+uhkMKgrojlLEgCII1J5eP6Ax8s/KgmW2M3IA1w8zamVllDFkD7v4FsDj9u1bdpUEQNCYC+IMgCNYQd59kZm8A/YGbzOwEVOl+GbKI3QB8tYZDBNUwczO7HWVVjnf3zwDMbFtgKLBFOveJmowwCOqUUMaCIAhahn9DAfHbAKNQRuMyoCsqNXESMKJmoxNbAhenv6VmNh9Z87qUzrnC3UfXYnBBUK+EmzIIgqAFcPdXgH2BB1Hs1Qao7dDPkcWsWhX91mQh8A+o7+UY4F2khLVDY7sL2M/dh9ZshEFQp7RbtmxZrccQBEEQBEFQt4RlLAiCIAiCoIaEMhYEQRAEQVBDQhkLgiAIgiCoIaGMBUEQBEEQ1JBQxoIgCIIgCGpIKGNBEARBEAQ1JJSxIAiCIAiCGhLKWBAEQRAEQQ0JZSwIgiAIgqCGhDIWBEEQBEFQQ/4fqXGBwJX2+MYAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# numerical parameters\n", "smoothing_window_size = 2000\n", "\n", "plt.figure(figsize=(8, 5))\n", "\n", "# set a minimum level below which the instability is not fit\n", "min_level = 5 * np.max(signal_x[:1000])\n", "\n", "# FITX me! --> returns the rise time in turns\n", "rx = fit_risetime(\n", " signal_x, min_level=min_level, \n", " smoothing_window_size=smoothing_window_size,\n", " matplotlib_axis=plt.gca()\n", ")\n", "\n", "# plotting\n", "plt.title(r\"Horizontal amplitude $\\sqrt{\\langle x \\rangle^2 + \\beta_x^2\\langle x'\\rangle^2}$\" + \n", " \"\\n\" + r\"exponential fit: {:.1f} turns\".format(rx));\n", "plt.ylabel(r'Centroid amplitude $J_{\\langle x \\rangle}$')\n", "plt.xlabel('Turns')\n", "for l in plt.gca().xaxis.get_ticklabels():\n", " l.set_rotation(15)\n", " l.set_horizontalalignment('center')\n", "\n", "plt.plot(signal_x[:500000], ls=':', color='green', zorder=-10)\n", "\n", "plt.savefig('fitting.png', bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note the isolated region between the red bars. The algorithm fits starting from a positive curvature point and stops when the curvature turns negative. Through this solid approach we avoid fitting the saturated part of the instability. The original signal is plotted in green. The fit itself is plotted with the orange broken line.\n", "\n", "We obtain an exponential rise time of..." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "... 36949.8 turns!\n" ] } ], "source": [ "print ('... {:.1f} turns!'.format(rx))" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.15" } }, "nbformat": 4, "nbformat_minor": 2 }