{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "In this post we'll look at eigenfunctions and eigenvalues of the Laplace operator $\\Delta$ on a domain $\\Omega$ in $\\mathbb{R}^d$. \n", "A function $\\phi$ on $\\Omega$ and a number $\\lambda$ are an eigenfunction/eigenvalue pair if\n", "\n", "\n", "$$-\\Delta\\phi = \\lambda^2\\phi$$\n", "\n", "along with the Dirichlet boundary condition $\\phi|_{\\partial\\Omega} = 0$.\n", "The operator $-\\Delta$ is symmetric and positive-definite, so the eigenvalues are real and positive.\n", "I've chosen a slightly different way of writing things in terms of $\\lambda^2$ because this makes the units of the eigenvalues an inverse length.\n", "\n", "The *Weyl asymptotic law* describes how the eigenvalues grow as a function of the domain size and shape.\n", "Weyl proved in 1911 that, if $N(\\lambda)$ is the number of eigenvalues of the Dirichlet Laplacian less than $\\lambda$, that\n", "\n", "$$N(\\lambda) = (2\\pi)^{-d}\\omega_d\\cdot\\text{vol}(\\Omega)\\cdot\\lambda^{d} + \\mathscr{O}(\\lambda^{d})$$\n", "\n", "as $\\lambda \\to \\infty$, where $\\omega_d$ is the volume of the unit ball in $\\mathbb{R}^d$.\n", "As a sanity check, note that $\\lambda$ has units of length${}^{-1}$, so the formula above is dimensionless.\n", "As another sanity check, you can look at the analytical expression for the eigenvalues on a box or a sphere.\n", "The proof given in volume 1 of Courant and Hilbert is pretty easy to follow.\n", "Weyl conjectured that the second term could be expressed in terms of the area of the boundary:\n", "\n", "$$N(\\lambda) = (2\\pi)^{-d}\\omega_d\\cdot\\text{vol}(\\Omega)\\cdot\\lambda^d - \\frac{1}{4}(2\\pi)^{1 - d}\\omega_{d - 1}\\cdot\\text{area}(\\partial\\Omega)\\cdot\\lambda^{d - 1} + \\mathscr{o}\\left(\\lambda^{d - 1}\\right)$$\n", "\n", "but this wasn't proved in his lifetime.\n", "Here we'll come up with a simple domain and show how you might verify this law numerically." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Making a mesh\n", "\n", "First, we'll use the package [pygmsh](https://github.com/nschloe/pygmsh) to create the spatial domain.\n", "Pygmsh is a Python wrapper around the mesh generator [gmsh](https://www.gmsh.info); pygmsh adds the nice feature of keeping track of all the entity ID numbers for you.\n", "The domain we'll use will be an ellipse with three circles removed from it.\n", "To keep the repetition down we'll first introduce a helper function that adds an ellipse to an existing geometry." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from numpy import pi as π\n", "def add_ellipse(geometry, x, y, a, b, N, lcar):\n", " θs = np.array([2 * π * n / N for n in range(N)])\n", " xs, ys = x + a * np.cos(θs), y + b * np.sin(θs)\n", " points = [geometry.add_point([x, y, 0], lcar=lcar) for x, y in zip(xs, ys)]\n", " lines = [geometry.add_line(points[n], points[(n + 1) % N])\n", " for n in range(N)]\n", "\n", " geometry.add_physical(lines)\n", " line_loop = geometry.add_line_loop(lines)\n", " return line_loop" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following code actually creates the domain.\n", "The calls to add a plane surface and a physical plane surface are easy to forget but essential." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import pygmsh\n", "geometry = pygmsh.built_in.Geometry()\n", "\n", "outer_line_loop = add_ellipse(geometry, x=0, y=0, a=2, b=1, N=256, lcar=1/4)\n", "inner_loops = [\n", " add_ellipse(geometry, x=0, y=1/2, a=1/8, b=1/8, N=128, lcar=1/4),\n", " add_ellipse(geometry, x=1/2, y=1/4, a=3/16, b=3/16, N=128, lcar=1/4),\n", " add_ellipse(geometry, x=1, y=-1/4, a=1/4, b=1/4, N=192, lcar=1/4)\n", "]\n", "\n", "plane_surface = geometry.add_plane_surface(outer_line_loop, inner_loops)\n", "geometry.add_physical(plane_surface)\n", "\n", "with open('ellipse.geo', 'w') as geo_file:\n", " geo_file.write(geometry.get_code())\n", " \n", "!gmsh -2 -format msh2 -v 0 -o ellipse.msh ellipse.geo" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To make sure everything worked right, we'll visualize the mesh after loading it in." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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YCgoKSKfT0ejRo0lRFM3kwiY6QRDI4/H0eL/qyUM9Ker1epIkiWRZJrPZTOXl5WS328lqtZLBYCBBEGjatGkkSRJNnTqVX5eXl6eZ0CoqKshsNtNJJ52kqRsAGQwGkvQK6auKafwPrqC8my6h/F9fneovf/8JVf58Ps1//M/05vZ1FI7Hjna3PijkCD9H+MccEskErWrYQd//z0NU9YtrqOjvP6GipYvI+5fvk/3KWZR39in063v+xI2SixYtIgD0n//8h5MAkx6tViuNGTOGTCYTybJMs2bN0hgrGXktXryYiouL6corr6Rzzz23B9lKkkQWi4WKi4v59Xa7nZONWno96aSTqKamhvbFbJAgCOR0OmnixImcyBkRn3rqqdy4a7fbqbKykkvko0aN4p8FQaDKykreZnX70yckURQ1hJiXl5dRgs9G1KIoaoicTQZ2u50cDofmOwDk8Xg48RqNRrJaraTT6cjhcJAsyzRx4kRen6IoXPLX6/V05513ks1m0/x2JSUlVFJSQmVlZSSKIsmyTKeffjp/14Ig0JgxY3h59QoLAJ144on8N7Ha7fTNX91MYxZeRo75Z9GQB1MrwqI/f58m3Pkj+v3bz9NuX9vR7vL9xmAg/EsvvZQKCwtJlmUqKiqihx56qEeZHOHn0CuCsSg9t2Elzf3H7ZT/o0u4VOb5yWVkPe8UmnLJeWTaR5aMzERR5OoSRgRFRUVcep4/fz4nptGjR/Myl112GQmCQD/84Q/5taNGjaLp06eTyWQiURTp29/+NgmCQGeeeSYZDAYuZaql6GHDhnGyZisL5tHDPF+YRM2uUa8AWF1qSVj9WU2qjNzVahBBEMjlcvHVBlsxOJ1O3hZWB/trtVpJkiQ+WbK6Ro8ezUn/nHPO0ZyTZZkqKipIkiQyGo0agrXZbJr29DWxqN8VU5Mx6Zyd//rXv04Wi4XuuOMOPsHo9XoaOXIkSZJEkiRRYWEhVVRU0LRp03r8LszTib1Pi8VCgiDQ5ZdfTjqLidynjCPr+VPJ+/vr+Wqx8tYFdP2/76eVe7dTIpk42sMhKwYD4fcHOcLPoQd8kRD9Y/UKmvHAYir8xVVUtHQRDbnnRrJfMZOMJ42ispHDNWRw/fXXkyzL9Itf/IIPaLfbrZFSa2pqNIRpNBpJlmUqKSnRkJssy1RYWMj18l/72tc44YmiSFVVVZx803XcRUVF5HQ6yWQykdVq5fp2SZL4BMDIlbVTlmW+Ykivb+TIkfzzqaeeyj+zens71Kol9WTA3hu7F5scMtXBJgj1u2ZSu3rlon6v7Hs14avvz1xRzWYzOZ1O/tzq30K9ChFFkQoLCzVtlCSJT5pM5+/xePgkkH6w98gmK+Y2m34IgkBz5swhu91OM+adT+aZtZT3k8uo6KEfp9xBb76ULnvsLlqxYwPFE4OL/HOEnyP8rxQC0Qj9c/XbdPJff0re/3cdFS1dRGX3/Iis50+lobOmkCBLZDAYaOHChRqpVBRFDVFeddVVZDAYaMmSJVy6+/nPf66Rpo1GI82cOZMT7ahRo8jpdNLw4cN5me9973sEgB544AFN/WeccYZGZbJw4ULKy8vjhKQmJlZ/QUEBDRs2jH+vJiaHw6GZnNTfM1JjPuyVlZWcyDMRLjvUk5j6KCwsJLfb3WNiYZNOtvrU5M3UJ+zdpj+v+jpFUTQSdqbDYDCQ2WzWTIhsQhZFUfO9ug12u53cbrdGJcTescFgoHPOOYd0Oh3JstxjQpNlWbNymD17NimKwlVt7GAqPGdRIRlPHk3O6+bQkAduSqkRf/INuuTRO+ntnRsHheSfI/wc4Q96RBNx+u+Xq+jUv/6Uhtz53ZQkf/f3yHruyeQ6oZqef+EFjcQ6ZMgQslgsZDKZyG63k8FgoPLycg0hFRYW0vDhw8lms5HJZCKn00myLJMsy5zopkyZoiFMRkpqwlKT4tVXX82DiJge22w206mnntqD0E444QT+2ePx0MSJE7kRc9KkSRpDrZp0GJH2dqg9Ytikx9qsbrtauk8/1CqZbEcm8k+fYFg97N33NmEoisKl/EyTW/q7sFqtmt9FkiTS6/VcomcTGpsQmH0DAA0fPpy35dvf/jYBKRuDLMs9Jg+Xy0UnnXQS/63VzyhJEm9Tfn4+DR06lAoLC8lot1LJ7Clkv3IWFe0j/6JFV9A1Ty2htc11R20s5Qg/R/iDFl8019H5D/yGSu7a51mz5Eaynj+VLGMqqbi0hGbNmkVjx47lgzhd3WG1WjVS9uWXX04zZ86kmpoajfFVfVx22WUEgKZOncpVCQDotttu60HasizTggUL+P+MKNQeLnq9nrxer4ao2cTCCInpkdMnEHaoyS8bEbJrXS4Xl/gBrU5fluUeK53+6s3T75PtXLpaqD9lWZnJkydr2sWIlZ3PNNlZrVaNSomVY7+BepJXH8yQnd5GZh/orb16vZ7OP/98vnJwu900bNgwPrmpVwDFxcU0+7xzyT19Ajm+eSYV/S2l9qn42Tfp1tefotbQkY36PVYJPxdp+xVFdzSMu958Do9v+AgBtwkUTyCw4jNUCmZMsg/BspdfQWVlJd5+++0eUZiKoqCqqgqbNm1CIpHApZdeimeffRaxWAxAKr9LWVkZurq6UFFRgTfffBNAKhpUFEXE43GsX78ewP6oVIfDgWQyiWg0CqfTCVEU0dDQAEEQeNRqfn4+HA4H2tvb0draClmWUVpainA4jL179wIAqqursWnTJkyYMAGffpraFK20tBS7d++GLMs8WMputyMSiSAcDsPj8fA8NJIkQafTIRQKad6X0+nkkaksgCkTFEXh7+FwgAVtJZNJHkyVnm8nHaycXq/nOXhGjBiBL7/8krdX3W6DwYBIJAKLxYLu7m7+XTgchiynYi3Ze2SwWCywWCxoamoCEUGv18NqtfL3WlJSAqfTibVr1wJIBZGxPEOsXbIsI5lMwmaz8d+xs7MTFouFB5upn0dRFCiKglAoxM8VFhYikUjg4vlX4p32XaiXozCdOApIJOHdE8Atl1yDs4ePP+yZQAdDLp3+4Kjk0jkcR07Cz4xP9myj2Ut+RcUPpNzenNefRxff9StyFhfSN7/5TdLr9WQymchsNvMApIqKCrr44os1y/0dO3aQIAg86Mfj8VBpaSnNnz+fJk2axMuKokhTpkzhemm73c4DlwDQxRdfTIqi8CAn7JOWM0nETJpmEqg64IgZfdn/alWNWpq85JJLyGg0cqnWbDb3qtdmLozq/3uTpg/X0d8VQno59TtRq2nSywmCQGVlZVRSUqJ5PofD0UN6nzlzJgEpjyRFUSgvL4+v+tTvXX2wOgsLCyk/P5+8Xi//DcaNG5fxGrVKh5URRZHOPvtsMhqN3JDP8iKx9o4aNYq8Xi8JgkA1NTVUNH40OS45ndw3p7zKht57M81/8A5q9HcdtnF2rEr4R53Ysx05wt+PSDxGSz9ZTuPv/WkqEdnNl5D72nPIXF1GVcOH88H4xz/+UUO8NpuN+1ELgkA33ngjybJMNTU1GhJUE0h6ABJztUsnn3/96180dOhQ0ul0lJeXxwN9DAYDnXLKKZo2DBs2TDOo1bpkdbI09d8xY8aQoih8cpAkKaPXSLo75EAT7pGaDERR1KjV1AczOGe7XhRFzbvJZIAuLCzUEHe2dyYIAlVVVfXLNjFx4kTKz8/XBLCp666trSWv10vnnXcer5u1gwWnsfI1NTUkSZKm/+r1ev4sOp2OIIlUdvap5L7pEsr71VVU9Lcf01lL/x99sHsTJZPJAR1zg4Hwd+/eTdOnT6eRI0fSqFGj6O677+5RJkf4xxDaQ3768UsPU/m9PyLPosuo4LfX0cxbvkeCUc8NcekSlToq9OKLL9Z4s7BDTdyLFi0ig8FAf/rTn/h3DzzwAAGgX//611zyUxs404kbSHmyXHjhhXywn3322eTxeHi4PpByhbRYLJoIT0YGkiRxSVStg06fgLIdmfTWzCCcPrl9lY7eiDebUTz9t2bn2PtlqzWLxaJxJwWyewllWrVl0/v31h519s8JEybsJ/Msz8RSXLAJhRmRDUV5NOqmK8m75AeU/+urqebeRfTP1SsomogPyNgbDIS/d+9eWr16NRER+Xw+qqqqovXr12vK5Aj/GMDOrla6/PG7qeAnqZTCxT+/inSjyslkNvUwaqolu5NPPpmuuuoq8ng8VFJSQnPmzCGn00lDhw7VkPy1117LB5ZOpyOn00l2u53y8/N5nhWDwaDxry4uLqZRo0ZxTw612gdIebyoJdR0rxcgNSmoSfjss8/WeMBkWkmw52WqBuYnztRKfaln0g2efR1HQ8Lv61CvdHojdFaGvft0Sb8319Penr8/0n56HaWlpdzwzQLImApPrVZTu/eKoqgJRmOpJlidTHiQZZkboA02C5mnn0BFv/9OymFh8dV021v/pkA0ckhjcDAQfjrOO+88ev311zXf5Yy2X2FsbN2L6+7/HXZ69QAB/nfWILj8U4it3bj44ovx6KOPYurUqXj33Xc12RPz8vLg9XrxxRdfAAAuuugiWCwW/POf/wSw3+gpiiKqq6uxc+dOxONxxONxTJ8+HStWrACQyrDIdnESBAGzZ8/GBx98gEAgAIfDga6uLjidTjQ3N8PhcEAQBPh8PphMJgSDQRiNRhiNRkSjUQiCgM7OTpx88sn48MMP8dBDD2HBggUAwNMRAymBg4GlL04mk3C5XCgpKcGaNWv4OXXKYiBlRN62bRuCwWDGlMZA7wbaryLUv3umd5IOtaFbDbWhmxn12V+v14uGhv2b0an7RSZIkgQAvC2sXQUFBak9f9vaNPdRPwPrO2qUlZVh165dsFqt3OgsyzIEQUAsFuPGYWb4jcVigADoxlTCdvZJ0FeXAJ0BzM4bhj/Ouw4OvanXd5QJ6cbQ+5d8cMB19IbrF55yQOV37tyJadOmYd26dXyHNeDAjba5TS8HAT7dsx3T7vkFZv73z9juEtH9ykc4YcUuBJ9cAWdMRCQSwRNPPAEiwrvvvovTTjuNDxiWP33t2rV8Fn/55Zfx6KOP8vrtdjtMJhOGDh2KL7/8EqFQiHtIsLS8AOD1erFs2TIAqQFWXFwMn8+H++67D62trYjFYpygOzs70dHRgZkzZ8JsNkOv18Pv9yMajaKrqwudnZ248MIL8eGHHwIArrvuOk7CJ5xwgnolx7165syZw5+rvb0da9asgcPh4Dnw1RBFEV988QUni/TzjBCONaifye12AwBPz5wO5lGVDkmSONkD+ydd9peloGbIRPaCaovEZDLJyd7r9fLPzc3NmDVrFm9LaWkpLBaLZsJikzWbNADw/QW6u7tRVlYGh8PBy5eVlSEej3NvIOahBAKiX2xHxx+fQutvH4N/1ZdYFmvAuH8txhV/+x06wtknrMEOv9+Piy66CHfffbeG7A8K2UT/o30cDyqdjS176Mylt3FDrGveDBLNBo3emyURU++cpE7SxSJLvV4vN4Jef/31JIoimc1m8nq9ml2W0nWkalWHJElUWlpKDoeDfve732mW0+qI0EzLfpYiQJ1zx2q19vCgYbYASZK4OkfthVNYWKhRU2W6lyRJGTNIsnMHqoIYLEc2dZL6HbIy7H0zW86BqKLSYwBYP9LpdJqMnun3Z4ZWdZ9Rew6xdrEcQmrbSbpRN9NhNBqptrZW87/6b/pzsufIFBin0+moeOJYcn1nLnl+djkV338T/eCFpdQZDvZrbA4WlU40GqVZs2bRnXfemfF8Tof/FUB9dztd+PDvKW/RZeS994c047c/JMVm4TpWddCQOnPhGWecwdMAC4LAvWNY2fHjx3OyPOGEE+iiiy6iIUOGcH2nIAj01ltvEQCe+RLYHwBzxx13ZBxYI0aMoIkTJ2qIuaCgQENEapJwuVzc5Y65RQ4ZMkQTJKS+JlPqApvN1iOBWfrgnzp16qDUuR+to6930R87xoG6rKYnf8v0GQCfoLMFxGWahJgBOS8vj0d5p9/T6/XSiBEjSBAEnh9J/R6qq6tJLvJQwY3zaMjffkxFt11Hi19/kkKxaK9jdDAQfjKZpCuvvJJ+8IMfZC2TI/xBDF8kRJfcdxsNuf8mKnrwZrJfPINcJfuNVsxTRVDlQL+VmDsAACAASURBVFfvXdqX5KqW/NVkbLfbyWg0UllZGfd6mTp1Kq8v02ArLy/nIfzpKw713qws+jU9ClZtZGTSaLorHrB/QisvL9cYINVEoJb40yXK3JG5b/R3IjSZTBlXEJnqVxvi1dG37DdTS+eZJg61gTb9YBN5SUkJCYLAs52mJ3lLf1a1t5r6e51OR5IkkaIoXFCRS/LJ/cN5VLR0EZXedh0tefflrHl7BgPhv/vuuwSk0lLX1NRQTU0Nvfzyy5oyOcIfhIgnEnTniuep7L5UrhD7JaeT5Lb1GBgGg6HHwFVnkmSfmbcD891mudzZAHC5XHTBBRf0qCOdEBjRs8yX7N6MoJlEpZbK2WYj7H9GFqIo0ujRozVuoGywqr13FixYoElb0F9iys/Pz5H9IDgY2af3U/U+AdnUN+p9Edh3LLEboCXvbP2CfW82m2ns2LGavsliTthYyJYDyTCqnJzXn0dFSxfRuHsX0Yota3uM2cFA+P1BjvAHGd7d+SWNvXcReX5xBRX8/Aoa+bWpNHbsWE3nHjZsGOXn53Npyev1Zg2kYe6Jat2ty+XKmO9E7f6m1+s1KhkmWbO/aj97NjDVA9dut2uSZbFMmJnSBpeXl2skdwA8olOdWEu99V9/yZxtL5hpVZI7Dv/R23tn5/qKe1BPFuoVrPq6dB9/vV7PVX/qyYD59atXoazvsTHEbFDqFbAkS2Q/bTzl/78F5P3L9+i8f91BDf5OPm5zhJ8j/ANCW7CbZv7lF+T9y/ep/J4fkXHSCKpQES4jbEaq6s7OJGzeOVUkyQYVS3qlHjCKomg2zWBEmq6PZ9eoSVYURRo6dKjGKJdJpVNYWKhR6RgMBiosLNSkW1DfL11SY374mfT2sixnjTYdLIfZ5CKPu4zcrhIy6Po2RA6G41DtHOmG/UzqGnX0NPu/N79/lgIk0/fqXbb6+2xsNcoEIrWwoh4jEydO1Oyf4C0tppJrzqUhD95MhT+/kn67/DmKJxLHLOHn/PAHGESEu177N/6y4yPEZRG+F95D/L31CHd1a5JkMf/ogoICNDU1afylR44ciY0bNwLY79M8e/ZsLFu2DIqiYNKkSfjgg5RfsCAIkGUZRqMRPp8PAPCd73wH999/P0+eZbFY4Pf7AUDzeerUqXjvvfcAaP2hWVvU7c3Ly0MkEuH3sNls8Pl8GDduHE+oVVhYiNbWVhgMBn4Ptc81+9/pdCIWi/GkWYlEAnq9vtcEYkajEYlEAtFo9JB+n4NBQX4Vhg2dDI+7DIqsB4FAlAQICIV9aGzais1bP0Ag0H7E23Y0kP6b9gbme99bzEC2c+q+qr5nbW0t1q9fj3A4DIPBAL1ezxPjsfspioJ4PA4iQmVlJbZv397jXiUlJairqwMA6ArdMM+dAtOJI+EIJPDoaVfihLHjDuCtHB0cqB9+jvAHEPXd7bj8qb9gS7gD0R2N6HpqOeJ79vs7jx8/Hhs2bIDRaERXVxdEUYRer4csy5xIGS688EK8+uqrEEURgUBAkw1RPRAYWEd3Op3cj5ldwyaEYDCImTNn4rXXXoPJZILBYIAoihBFERaLBdu2bdPUxf5myubIBo46wEkQBFitVvh8Pn4tmzwkSUIymcTpp5/OsyymD/SCggK0tbVl9B1ncLlcaG8/MsRqMjowqfZ85HkqkEjEoDfEMe20yRg7thqRSBTvvbcKKz9eB5PRhUQijh27VmPtuteQTPYeDHUsgmUBNZvNPFhKp9NBEAREIhHeh9ID4tSChtvtRltbm6ZvsXLs3NChQ3k/zYTy8nLs3buXx4wYjUaEQiFUV1ejrq4Obrebk7y6LzEBxjltPMSJVXjikh+gevhwFNvdEFUxB4MNuWyZRwHJZJLu/XAZFfzkG+S974dUefnZJGfI4MjUIJnUFmxHIva/WocpiqLGnY25IyqKotmqD9DmmGd509nyliWuMhgMvD71PY1GY8bluloloCiKxr5QVVVFxcXFGvuAOs88q1+t/1frgVnb1HVmyn7Jcvqkf3+4DrerlOac9WO6cO4tdOviBykczu7G19raTRdd8BP6+vn/RzOmXUuKfHwbl2VZzphnJ11Vyfqc2usnfVMVvV6v2eoxk5rI4XBw205fbWN9nGVcZWolNlacTieZ3A5668P36POWOlpbv4P8kfARZJMDQ06Hf4TRGuymk//0Eypauojybr6UzMU9t5DLZFA1GAxZdZjZUvi6XC7uBSPs20qQXcOJyu2mmpqaXl3g2J6lgNYzgtkRCgsLyW638/Yxrwz1BhrDhw/n7p7qtrMByTYRYQM/PSDKarX2yH6p9sA4moRlsXjo3LN/SnPP+Sl9ubH/uy7dd8+z9PXzb6UZp15LQC4+QP2bAlq3Ya/Xm9G4m07o/fXmUp83m8197nimHnusX06ePJl/XrZsGa1et5Y+b9xFnzfX0a7WpgHPyDkQOFDCz6VWOAS8vmUNJv5jMTbv3Y2up1eg5c6nEKhv4mHibLMJBkmSYDKZcNpppyEcDiMYDPKwcYZEIoFIJAKXy8XD1yVJgtlsRnt7O7Zu3QpBEGCxWLB161YAQDQaxS9/+UsAgM/nw9q1a3uoiIDUEpblq2ltbYXRaER3dzdvQzgcRm1tLRobG9HV1QWLxQJgv/6Ubb7h9XqxefNmdHV1aTYaiUQiXMdOlMqJw1RPTKXD0N3djc7OTk37aJ96MRAI8KW/LMswGAy8jsMPASdOvAiyrMNflvwI1SOK+33l9d+9EDPOGAuXuwxjR888jG386oD2qQZLSkrQ0tICIJUrp6GhQdN39Ho9DAYDotFoKlXCPqj17dmgKIom1UMgEMi6iQ0rFwwGuSqT9cuVK1fyz0QERGKI7WlFMhhCeyyEL1v3IprIrm4caITDYUyePBk1NTUYPXo0Fi9efMh15gj/IJBIJnH9E/fgmy88gIg/gO6n30bw9VV8Fx7WSZkuury8nCcVCwaDeOedd3jHY3lQ2P/xeBxOpxMtLS3Q6XQQRRGJREKTYMpsNiMajSKRSHD9/B//+EcAgMPh4IZQs9nMdat6vR6dnZ3Q6XS8fYyc2cAjIm6ABaDZRYrZAABtrpWamhpYLBZuC+DvaN892M5O6kHcH7CBF4/Huf2gr0RhA4GK8lo4nUWYfdZ4lJbnHfD13114IRLJbgytmAyj8RDznnwF0J9JmIi43hzYnytHDbZ7GaDdjYtN9urcP+mIxWJIJpOQJImPI71en7GsWohiAkleXh4URdH0X2BfAr5kEomWLlBXAFFKYkPDbnSGjkxeHr1ej+XLl2PNmjX4/PPPsWzZMk3uq4NBjvAPEK0BH6Y9dCteCtch9OlmNN6yFNFdjZoEUsB+Is/Ly8OOHTs00gxbXlmtVjQ3N/PvGDweD4DUIFAUhROuoii44IIL4Pf7EYlE4HQ6IQgC8vLy+GBxuVwAUmTOtpUjIkQiESSTSYRCIZx22mlwOp3Iz8/n92Gd/eKLL+b1JJNJyLKMaDSKUCjEJyDWVpfLhTVr1vDkWmoJ3mAwQBAEVFZWIplMcsPzYEdlxUSEwt1Y8K25B13HX//6U8iKHsMqTxzAlg1O9DUJO53OHt/5fL6shAzsHwuCIPB+nZ5RUxRFjVTPnASICDabrccWl6IoQqfT8T7K2m2329HS0sInDXV96okn0R1EvKENEATsCnSgrrNVM2YPB9hKHkhNarFYTPPMBwO57yL9athsAH8GIAF4iIjuSDs/H8AfAOzZ99USInpoIO59JPFZw05c8O8/w1/fBPOWJnT9Z3nWskx6ZqlhmVpEFEVOouofb8qUKVi/fj3PNmkymZBMJhEOhzVeOc8//zwqKyvR2tqK8vJyrFq1Crt27UJ+fj6am5uxadMmANkHIsuQmUgk0NXVBVmWodfrOWk/9thjAMC9F9SqlXSXSKayIiK4XC7+rDqdjg/Uzs5O7nVxOPeKHQgYjTbYrfmoqvZAFA9+YBWXuhAKtqMwvwpfrH9jAFs4+JHueZVJmgfA1YOZwMYKI/FMSHcLZWQP9JwcWPloNMr332X3YO6c7L7qeoD9E8lL9bekvtgBCIoMCKnyRll3UCR80xlP9atcIpFAbW0ttm7dihtuuAEnnnhoQsQhS/iCIEgA7gFwFoBRAC4TBGFUhqJPEdEJ+46vHNkvff91zHnqTsQScXQ/8zZ27yN79RKRQb00HDcu5cvLOijreIqiwOfzwW63w2634/3330coFEIymURzc7NGv19bW8vrIyKYTCaEQiF8+umnGD16NBRF4SsFhrKyMi79A6lNryVJwlVXXYVIJIJ4PM4JOxAI8M9sCc3yjzOSV0s7oijCZDKhubkZkiTBYDBwsgdSk53X64XRaER7e7uGAGRZ7lPSP+QUsAcJj7scoiDi6mvnHXJdxaVuWKxuCMLxtYg+EPJLVwMyJJNJjTTe1/1YmmgG1t/UbWF9jk00RqNRc43NZuNqIXaO2bvSQbE4KJFEkoBANIwkHb403JIk4fPPP0d9fT1WrlyJdevWHVJ9AyHhTwawlYi2A4AgCE8CmAtgwwDUfdRBRPj1m8/gb7tXI7SpDt1PLUe8o5tLCrIsIxaLwWazcWlmyJAhqK+vhyRJ2LJlCwBoNm3Q6XScSH0+H0pKStDV1YVoNAqbzYZwOAyXy8VJ/H//+x8URUEikUB+fj7/0UVRxObNmzNKzh0dHSAitLS0wG6348svvwQAPP744/xaIuJEnkgk+BJ61KhR2LBhA293PB7nKiq9Xo/u7m4+qBKJBIYMGYK6ujrY7XZ0dXXBarWiqakJVquVL61ZPfF4nG9wwfSo6kHFVirp6E3aGygYDVYIoog8j/WQ6xo7phorWtbDYLAgFOppQD9W0VsMRTp6I/S+6nG5XAgEAqisrORBigysn7jdbq77Z/cSBAFGozHrhi6yLGsCAhnmFP9fj7KCQQfZbYcgiaiwe2DVG3uUGSg4HA7MmDEDy5Ytw5gxYw66noEQP4oA1Kn+r9/3XTouEgRhrSAI/xYEIaPJXRCEbwmCsEoQhFXMon80kaQkrnryL7jn7Rdh3tkK3z+XQR9NEbaa7O12Oyf7yspK1NfX812dWMdiUX9ASgIeOnQoN7jW1dXBaDSCiNDV1QWj0diD4JiO0Ww2a9p40UUXAUgFsADghit1YFZFRYVm8xGdTgciQiwWg06ng16vR1FREb/fhg0bYLfbNWQviiKi0Si6u7thtVq5DcFoNKK+vh6lpaV8eez3+/lyuaamRhNFbDKZsGvXLgCpyYJ5cTBkInsAh53sAQCCsE8iH4B7CWKqriPQ7MEItlLMhHTvNaDnyiDThjdqtLe3IxKJ9CB7dV2tra1QFKXHDmuZVD7MrqAOMMzmbcdA4Sjize2gRALbWhrQHvRnLHewaGlp4Z5soVAIb7zxBkaMGHFIdR6p9eaLAMqJaByANwD8K1MhInqQiCYS0USmijhaiCbimLXkV1gRbkB0Sz3q73oCiXAEgUBA40ECQNNJ9uzZozmnBhHBYrGgqKgI27Zt4943RIRQKMSXuKFQCG1tbfjud78LQDt4tm3bhpKSEkiShIqKCjz55JO8DTqdDm63m+shBUHA6NGjsX37dhARqqqq8OGHHyIajfLz0WgUkUgERqORS/GKoqCrq4s/QzQaxfDhw3kb2KTT2dnJpaG9e/fy69ng9Hg8WLNmjeZdqAcbe15G5tkG1pFCJNQNoiQ6O0J9F+4DX6zbCKIkwpGBJYGvCnpLk5FtbGRDuktvtjIMzNAJpASl/q461JHs6kmit35JsQRiDe2AIKAu0Im9Hdm9iQ4UDQ0NmDFjBsaNG4dJkyZh5syZmDNnziHVORCEvweAWmIvxn7jLACAiNqIiFlpHgJQi0GMcDyGsx6+HV/4W9D19Ar4nnkbokoXyzqQWs3BEIlEMrqqMSnZ7/dz6ZuIOJFarVaNDnH48OG45557eJ1q1NXVIZFIaFzdFEXR7DfL6hdFET6fD0TUIySdDTKHw4EtW7YgGo1CFEWNishgMMBkMmHz5s2oqqqCTqdDY2MjnE6nZpCq89ww9VBvrnTA/m0IWT6gA1EHHA60tu8GEeHJJ18+5Lp2bm9EwN8GOoz63eMF/XHHVZdhqR0YMtkJMiGZTCIvLw9+v5+nA1F7CvVyIRJN7UgGQmiJhdDgy2yoPlCMGzcOn332GdauXYt169bhlltuOeQ6B4LwPwFQJQhChSAIOgCXAvivuoAgCF7Vv+cB6LkOGyQIx2M45TffwyYE4H/9E/iXrQSQWQKJRqOwWCwIBoMoKtqvxTIYDD2ChZhRCEh1zsrKSpSVlWHz5s0AtEvaUCjEdf/Z7i3LMjweDzdw3nzzzWhqagKQ6vDs/mqSnz59OgRB6DEA1AOETV7McBWPxxEMBhEOh7FlyxZOyul2g/Q2Zmpz+kQoiiI3jGUj+2z7tR4OBIId8Plb8eEH6w9JhdTa0g2rJQ+NzdsHsHXHJ/oi6/4YiTOtDtSrADXUnmhM5dife1GSQB1+CNE4msN+7G7LrJo82jjkNTQRxQVBWAjgNaTcMpcS0XpBEP4PqRDf/wL4viAI5wGIA2gHMP9Q73s4EEnEcdbDt6O53IH2B19E6KP9dudMej8A3NedqXIEQUAgEIAgCDAYDHA6nWhoaEBHRwd3BdPpdDx7n9vtRnt7O4+MZUTKOprZbMbQoUN5QJQsy5AkCZFIBHv37sXIkSPh9/txxx13aBKnRaNR6HQ6BINBLkEvX57yLFIPIiZZMxuA2WxGKBRCKBSCw+FAJBLR6NqJUpkI/X5/n1kTCwsLNUFaau8JFombDmYMZzjS2TF37vwU48aeiRdf+ADnnT/loOr43g2/RTKpYOv2QwuS6Q2CBBQO1yO/Sg9bvgS9RYTOKCKZICRiQKgzgY49MTRsCqN919FdOR0K+lLl2O32HhHbvWXmZFAbbVl/VGfdVKM/bqKCICCZSCDa2AbJZUOHTYDi64DX1jMO4WhiQJSmRPQKgFfSvrtF9flnAH42EPc6XEgkkzjrgV9jfXM9wu+u1ZA9kDI2RqNRxONxjb9uUVER6uvreTlmyAVSHa+hoYFnBBQEASeeeCLWr1/Py7Osmdk6aCAQwNq1a+H1ehEMBjW6dQBoamrig4IRfkFBAfbu3asxVKklcvX9WHoFNqGxlLNut5tPYsxDSJ2TA8g8GNWDQk327BxrT3pZht78s48Etm7/CBXltVj691cw9dTxcLlNB3T9s8++jXjcjJ27P4Hf39b3BQcInQmommZFaY0BeouIWIgQD4swwA63KR/JJCEQbofi6YSrXIdhU8zwt8axY3UIOz8O4lhL5NnV1QVBELgjBdA/FRDR/pTNrA9m63tql+re6mNItPsgyCKawikVaYHF3u/nOdw4ulayQQIiwpx7FmOzJYbgh+sQWP6p5rzBYOCEmC6B1tfXQ1EUrpZgZMwCrID9HYWI8PHHHwPYL4Ww8ix9bDbpxO/3w2q1cgmE+cm3t7fz9AkNDQ0AUp4u6pUAU+Ow79SrlXR9J3NH27t3L2w2G4LBIAoKCvikxiIQWTpZdSplAJg8eTJ/RvYeWMAZew9sVXFEPG8OEMlkAitXPYfTTp2Pq65YjH8+cgs8/XTTXPbqSjz+yNvo7m7F52tfHfC2lU8yYsQMC4w2EdF2I7595q9x+viLoZMze8T4Ix349/L78dw792P01yRU1Bqx9tVutGw98nsKHC6wlB99CQqZhIvDmaoj0dIFqcCJxlA3RALyrIOD9I+vqJAs+OVrT+CzcAt8z7+HwOs9c/CrjTZM78x03czIGY/HNeTHIllPO+00jSqjsLAQQE9pgdWnzjEPpHSNdrsdgUCA++wbjUbE43GN+oclN2M56ePxOB8EzOMgEon0UE2xgBRJkiDLMmw2G88l7vP5EI/HuZupyWTigyZd9cQk/48//hiFhYVcX8+e02q18uc62sbZvtDRWY+VnzwDRdZjwfzf4eknVyCRyC7dBYMRfO+GP+ChB5fB392G9z58FMnkwEUVixIw6RI7xp1thV4y4w8LXsVLd+7A7ElXZSV7ALDonZh/1s/wwm934obz7oKsEzH5YgeqZ5izXvNVQzAY7Jd3F+unhyO9RybdPhEh3tSBZDCEvaEu+KN9GH6PEI77DVDueeN5/Hb7ewh/tgXdS1/VqD7Y5gmZdNWCIKC4uBh1dXU9pP5sYBNCUVERV5eowdwd04NCrFYrl8Rra2uxevVqLrUzjxi1jh3YHyWYqd2sDIvYtdlsfOUwfPhw1NfXIx6PY8SIEZpkaux69SpEfb9sEhN7j+k4kJ2TjgYcDi8mTbgQdls+QuFuVFV78fULz0JJWQESScLnn23EY4+8gGTSBFGQsGfveqz+/L+IxQZucEsKcNLlTrjLFYwuOB23fetRiOLBZQ0NRrvxnd+dgfboLuz+PIS1L3X3fdEgxsEG4/Wn37366qvIy8s7oPrTVZb7bgZliBsCEUbkF0MnDaxS5UA3QDmuVTprm3bj9u3vIbxmK9r//jIQ37/LDtu6TxCEjJ3D5XJxt0i1YZFdbzabEQ6H4XQ6uXsiI2i154l6JytG9Iw8GVGq62d1seRr6vNq3Xg6+QqCgAkTJmDTpk3w+/0YNmwYT6/c1dUFl8uFrq4u7jXk9Xr58xsMBk1GTbWEzgYd26Yw08SXzdOCJWdj7pkM2SarI43Ozga8ueI+VJRNQHn5BNTtNOPuPz2zL5YqFSEcTyhobd2CzVs/QGvrrgFvQ+08O1ylCs6dcAMWnHtobnkmnRVLf/Ehbl4yFzjhE0T9SXz59pHJ/Hg4cLDCan/7Vab6e5tkMtrikknEmzogFzixpa0RI/OGaFy8+0IikcDEiRNRVFSEl156qd/XZcNxS/jd0TDOvesXiOdZ0Pn4m0B8fzpfADx9QbqBkZFxW1sbCgoK0NHRgWg0ClmWOfGZTCYEAgGYTCaNLzoj8V27dsFkMvEAp3SwezKSZVkzY7EYdu/eDUVRoChKD+8EANyzhl1bUVGBHTt2gIjw6aef8rq3bdvGt3jT6XQ8WVq6IYuIsi6ZdTqdJoNfJrJnXkvqVQpDNsk/20rhSKRXSAdREtt3rsL2naugKAY4HUUwGC2gRBL+YAc6O/ceNl/74dNMKKjS45Sqrx8y2TNIooQ/LnwBV992Eoaesgttu6No2T64k9oNFNL7z8H0p/SVtBrZ+i3F4ki0+wC3HVub9mJ4Yf/3WPjzn/+MkSNHZtzf4mBwXOrwiQiXPvEnxKu8aH/gRSS7eko5mbLxse+ZHr+pqYm7P8bjcU1+GaCnrzoAniCNedxkQjKZ5H70zF1SvVyMxWIaXXxlZSWAVII0Fv3KSHrHjh08VYOauEVRRCQSgd1u5ysE5o0zdOhQNDY2QpIkSJKEaDQKu72n0YlF7Ko9dwBoyjKdaSa31j4DWtJwtNWPsVgYzS3bsHv3GtTt+QIdHfWHjezNLgnDTjHDTPn4yWV/HdC6JVHCAz9djngUGHuODcKR2FfmKCNTIrSD7U8Hc10yGEGiO4iQDLT4M4/7dNTX1+Pll1/GggULDvh+2XBcSvj3ffgaVm78AuG12xHbmtKlZ5JAM8HhcKCjo0NjqGGbmwD71RdqV8z0DpKu785URr0zD0uBkCl9q8Vi4T79wWAQer2eB4Sp83AAKU8gNgmZzWb4fD6NEYvdkwVwqScwtVqpoKAAPp9PE7ZeXV2N7du3IxaLoaurC8OGDUMgEOArHIfDgba2NlitVvj9fk36h6NN5IMRI2aYIUjAXT98od+RogcCo86KGy/5I+598ceomGjC9o8zx5kcK1CrSA8G9W//akDaISgydgoCZn/3Wejl3g3IN954I37/+9/3i5f6i+NOwt/d2Yrfrk3lKGdRtEBP98RsYIFNaqu/WlJn3jJMomX5c9T5cNKXfsxdUg3WMdW5ZtIzSwIpd02DwQCHw4H6+npEIhFUVVVlVPeon9Hn88FsNiMWi3H1ElNNeTwenvaYga00HA4HmpqaEAqFNC6omzZtQiwW4+S0detWNDQ0cHsFa093d7fmGXJk3xN6i4iCKj0KTSPgdVQetvucWXslYkER5ZMOX5bHwYSDJfuBBMUTgCBga1tjr33/pZdeQn5+viY1+kDguJLwiQiXPnk3wjsa0Ln0FaCXF66WPNV5XtKlhL429cjLy0NvmT8nT56MlStTEw/TqTOoDbpAZu8CSZIQDoc16hEm8adDFEXo9XrumcP0gsFgkKc2jsfj2LlzJ/ckYomr2I5V6g1NGNQdN719bOLry+c5k6TfX++nYw3F4wxQjAJ+ed2Sw3ofQRDw9dO+gxc/uwfOEgUddceGLv9wrBqLp/9mwO4pWoyIJZNo8neh0OrIWOb999/Hf//7X7zyyisIh8Pw+Xy44oor8Oijjx5w2zX3PqSrv2L4yxv/wS4lishnW5Bo7alHU0vZ6tQGiUSi3/67LHEZ26awrzTPardHtQQuCAJisRj0ej3Xvafr4AH0UA2VlJT0IFcmrSeTSb4Fos/nw0knnQQAPIWs2nuITTwej0ezwmAeQJIk8TZky2wqimKPTdozlQG0kwb77ngkewDIq9QhFgLKPGMP+72+fsb1AAGF1UcuZ9HhxtFYNR7IPZP+EIREAk0BH2JZNkW//fbbUV9fj507d+LJJ5/E6aeffshkDxxHhB+MRXH3lvcRXrsN/jdXa84JgsANlmqIoshz5TBJm0n32ZJ6MdVFb2TFNhVnmfiY7px5vLAUx6yeeDyO4uJivsrweDwZXcskSUJ9fX2PzudyufgKoK2tDV6vFw6Hg2+IfOqpp6KtrU1jnA2FQhg7diyampogiiIsFovGe4fpREVRzJrDPplM9tjizmazaVRFmZ7jaLtjHm04ixSYhcJD3r+0P7Ab8xHpFuAsGvz7DX/Vof49Y61dgADsGsB0yv3BcUP4N/zjT4gk4/C//HEPVU56+/vepgAAIABJREFUrhmGZDLJs1Gqt0RjeXV6Q282AaLUpuJq10f1uba2Np46gaG+vp4TodrVk0nDiqL0SFfAVDgtLS0wmUx8a8KGhgbNhPTBBx/w1U1paSmAVOdkm0skk0mUlZVpnsHpdGr2BugPJEmCz+dDOBzO6PUDoNfNrY8HSAqgGERUlx1+6Z7BIFphsB0HrjqHGX1N0BpBLJ5A0h9EIBZGoI8o3OnTpw+IDz5wnBB+S7Abb6IVkfU7EN2mjXDN9iOx3DM+n08TeARopfcDkcIyrQrS99Zk6C3XzLBhwyAIAiZPnswJlxGyOu1rMpnkExnbuFnt43/GGWfwc4lEAg6HAxs3btSkeRAEAWazGevXr9eotfqzhE1XE6lXUNkmzONVjcOgM6d+o6HlmbaFPjwwKXYo+uOCCg4rDlSVlOgMAKKI3V0Dn2QvG46LX/m7/7gbkb2t8D3/Xo9z2X6kZDLJVSiRSAQ6nY7rqrMZLPtCNBrl6RMYqaZPGIIgoLy8nH9fUFDAz1VVVWHSpElcbbN27VpUV1fD6/XyqFn11obsOdxuN0/UFg6H4fF4UFxcjLfeekvzDCx3Dlt9sINFACeTSVRVVcHtdmf0AkoHEWUldnWsAHtu9v+RUGUMWgip3DmJI5hvSFJkiGLOW+qIgwiJLj8ikQh8kSPjQXTME35HOICPFB+oqQNo6z5gMtHpdNzPvrOzMyNBM7VKfzZrUEfP6vV6BINBOJ1OWK2pjIxEhLq6Ok7CagLfsmULPvnkEz7hRKNRbN68WWMYtlgsEAQBY8eO1Xyn3r6wtbUV9fX1fHXBzhERzGYzjEajZuVhNBrhdDohyzK2bt2qUeMYDIaMz81SUiiKws+nr2bUKRrUKRuOZ1fNWJCQiAIt7Y19Fx4g+INdiIaO33eeCUfKjpTsDkFQZOzpau+7cBoOKo/QAV/xFcNvXnkcoW170Pni+weVkjcajXLXQpZFUg11zpe+OgkRca8VRVG4+oK5OjKojZqhUAh6vV6jTmFbr+n1ek6UlZWVKCws5M+4fv16VFVVIS8vD7t27UI0GoUgCNwVk+X9KCzUGgdZWga1CisUCsHv93PJ3+fz4cwzz+T5gpLJJPfTB1ITDFsdMLUO21gF0EYPs3uz52f/H69SfjxCSCQIG7av7rvwACFCXQh1H2OJ8g8RW7duPTJZXZmUH4sgGOu/OpPZ+nrbLD4Tjmk//FgijucaNgLxBOJ7+mcNH8i9VTPl7mDujszlEkiRbGdnJ/R6PSRJ4jtmqdMeAykPl9LSUp7np6amBh999BHmzp2LF154AUAq6VlDQwMsFotmm0RAKxFUV1dj48aNaGxs5Pl38vPzs+5D6/V6Icsytm/fDp1Oh9deew1AaseutrY25OfnY+fOnfzZJEni0bwAUFRUxFVDLApZvVkMS+GcyZB9vMHfEkfSvvOI3CsY9UHUJ+BvyRG+GrfeeituvfVWDBs27LBEOmvQJkByWtG1pwn5WfzyM8FgMKC4uP95eQBAo6sdTEdtbS0dKp5d9zHl/+Ya0o+rJAA9DkEQMn7fn0NRFDIYDFnP5+Xl9fjO6XQSAJIkiWRZ5t+rP6vbVVhYyP/3er38vN1uJ4vFoikvCAKZTKaMz5bpOS0WC4miSKIokiAI5Ha7edskSeLljEYjjRkzhtehvgcAElPKX8090t8Lq0+n02nqZfWxa61W6yH/LsfCMWK6mS74fwXU2LXtkMdAX/jPe/fRBbcVUN4w3VF/7uP5sF40jYb8/jvkj4YP+TdFamvZjLx6TKt0fvfKkxCtJkTW78x4ntKkb4a+ZnS26Uk4HO5heGRQR8wCKem8o6MDOp0OiUSCp0m22Wx8RWE2m6HT6Xi72BaBRMR93UVRRFdXl0a3z1Qjag8XVke2CEDmUsk6AmsvaxtDKBTCtm3beB3qJGg6nU6zmxewP/JX/R7ZOfV7VW+gws6r00kcz9i9JoR4mPDbh35w2O/1jxd/j2BHAi3bjp1dsL6KiKzZBsFjw31vD4z7ZTYcsyMrEItgj0VAYMVnQC+7FQE9SbEvXTwzPppMph6Gx0yfgf1EqfZEUWe9ZKqcaDSKgoICCIIAr9erqaOioiJjquIxY8YgmUwikUjA6XT2yMvD7gfsz16pJuj09hoMBpSUlPBz2dIjszrVBJ2+tSMz3rLgL3YN2zhdbStg+wVnyuV/PCHYkUTLjii2tX0Mf6Sj7wsOEut2vwvRGsSuz0IpOTOHo4bo1j0If7kLT278uO/Ch4BjlvCf/HgFkgIQ2dD3phSZJGCg53ZoOp2O53d3Op09XAvVUE8abEIpKSnh2S/Zd/F4HEVFRZryzc3NICI0NjbyNiQSCezYsSOjm+PatWtRXFyMqqoqdHR08Jz87N7qZ1RvsM72p1WD7a1bV1fHjbHd3d09PGzYfrlWq5W3XZIknkHTZDJpVisM6veVKZlVpsk22+9zLGPjcj8AAT+8a+5hqT+RjGHRkksQ6kxgy3tf3U1QjiXEdjRibywAX/TwuWges4T/n02rQaEIolt7biXYHzDyUoPlfwdSWTMZYWeDmtjZxuBAisBYRKvJZMKePXsyrg7S28CiftMhiiLq6+uxZcsWOJ1OAOihVmHSOvurNpCqg6PUSdiIiLuLZss02N3dDUVRYDQauWSu0+kQDAYRjUb5Xrnt7e0wGo2a52H3z5Qr6HhH1944dn8eQmNwE/7x0h0DXv+ie+dBMiaw4Q0/EjltzqBAaM02iC4rXtu85rDd45gkfCLCmu2bEdm4C+lpFIDseXDUONQd7dW560VR5IFFzJ1yx44dAPbnuzcajZq0AmrpmxFhd7c2jsDpdMLpdKKkpIR/x1I1M2JPT7LG/mZS+wDACSecwHfUslqtPDe+w+GAyWTSuE/abDaUlJQgFoshFArB6XRCr9drXMUqKyt5m9nkkQ72nMd7WoV0rH+tG76mOJ798C4s//TfA1bv/2fvvcPcqq714XefpqM6kkYaaSRN81R3j3vBNsU2HQOm2IBNjSEQqsF2IIQLJCQkEG4IEJIQ35Cb8ktInuTmyy2QnnAvEEpCS2yMe7expzeNpPX9Ie/tfY6k8biMx2XW8+xnNKfu09699irveuony7D2k9ew9f1ubHn3+CiuPSRA77ptSO1qwgu//vmAneOkBPztHS2gmlIk123Pu75Q9mc+Rsy+7Mcyk6VdZNMEr5LF49g5wMkJT11dXcLpagdjvh0vo8ilra0NTU1N2LRpE2bPnm1JguLgya/VHt/OgV/XdUGfYJom/v73v6O3txe9vb0WPqDm5mZ0dnaK/VKpFFpbW0URd37snp4eSzm2tWvXore3F/F4HLt37xYJXPmko6PjkOOKT2bJpIE3ftSErpYMvvbzW/HDV752RMdLZVL4/HcX44///AF2r0vi7/9xdMrmDclRknQG6U9asNkzcCbMkxLw/7TmPfSs24aedYdmzumL276kpCRnGWeytIud+AzIdegOHz7cAsYyUHNzCwf6zs5ONDY25vRP5s3ZsGEDuru7kUqlwBhDe3u7mFnI55f74XA40Nvbi56eHsF3z/vOBwL7eYCs01qmROaDm50Zk4thGMKc1dHR0acmf7D6Aqea9HQQXv3ePrTuSeMnrz6Oqx+aiJbOvim388n6Xe/j0pXV+PvmV7Dtw2688eNmDFB1xiE5Aun+50bs277zkJKwDkVOSsB/ddNqGJWl/U626kuIsoXLd+/efVBud+AAa6UcuaJpWo7Gz4uUyAlWgJU8TD7fmjVrxG/uG2hubsaIESPEObnmLIM7Nylx4c5aADmDVVtbm8jU5VnFbrcb7e3tlgGsq6sLe/bsEZz4cohlPuGVtPg5C4F+PorqIQGSHYRXV+3Dhre70JLejGu+PAq3fuVsbG9e2+d+RITV21/Hkkcm4c5n5iCldOHDV9rw9s9aQUO3+biU1M590GsTWNO0a0COf1J6yd545y10N+8BUof3Vttrx3IQ4iGUfVW3sZtM5GWy9PT0iOPI6+WY9d27d4ttOjs7YRgGkskkEokEmpqa0N7ejnXr1qG3txfbt2+32NeLi4vR1NQETdMspqJ0Oi0qSaXTaUybNg2vv/56Tk6CoiiYMGGCKNBCRAgEAmhqahJ1c/lAxYvEJJPJgiGtfFCwD2y80pa9uteQWIXSwAf/1YbN73Si4QwPWM3f8ZnnZqJjL8FvRjG8qhEBXxiapmL91o+wcftq9Gh7oRkMyc4Mtv+zG2v+2IHu1iG1/niW3m2foGf1ZrxW/T4aS8qP+vFPSsDvivjAOg/O5lhI7KClKApUVRUmmEJgH4lEhJOTS1/F0TmY5zseN8fYKYV1XceWLVsAZGmSN27cCMYYVFXF5MmT8X//938gIkGRkE6nUVZWhl27dlns75FIBJ2dnXjttddyzk1E0HUdf/3rXxEIBODz+VBdXS22dbvdArA9Hk8OQyeXfIXcQ6GQhb6hpaVF5CQMycGldWcaf/1xC5xFDGVjnQhXO6CEtuOtjTuhGUAmBTAF6E5l0Ly5F7vX9mDbhz3oHSJHOyEkvbcVRl0ZPtyzdWBOUCgFd7DbkVArlNy3iLyXzjyiVGfGGOm6LqgD8jWXy0UOh8OyLBKJCLqC/p6nr//7ajIlg9vtJgAWWgQAlv6XlJSQqqoUiUQKHtMwDBoxYkTePg0fPpwA0MSJE3POy+8Dp4+w0z80NDRQRUWF+N9O39DXddqvaajlNkUDmR5GDg8jpgx+f4ba4bfiuy6j079492HjHwaaWoExdg5jbA1j7GPG2Mo86x2MsZ/sX/8GY6zyaJw3nxAR9PoEjjQ3k/bbsQuZKLxeLzo7O4VpBsja6nft2iUoCwqJruuWCB2+zO/3W8iQ7KGVdkmlUlBVFZdccomIn5fPq+u6pf+ffPIJ0ul0wZKEbrcbyWQS//jHP1BUVCSojfkxN23KJrG9/fbbcLlc0DRNEKJxjb+trQ0zZsxAa2urIFGrrq7G6tWrxf72fhaK8ecyZNc/uGRSQHc7oaedhpyxJ7ioQR96fAMTonzEgM8YUwE8C+BcACMALGKM2cv13AigiYhqADwF4PEjPW8h6Uz1gHY1I916wN5+OGKapqVQt13a2tpyuGL6y7LZ29uL4cOH5yxrbm4W5hHGmCgDWChvgJt8fvGLX6C6uhqANaSTm0n4PeBUDbTfb2APgZT7zwumZDIZhMNhhMNhkdRF+30KMgeQ3CduVuK8POvWrcvpNw9VlXMIhmRIhgTo3b4XzbsHptbt0bDhTwbwMRGtBwDG2P8DMB/AP6Rt5gP4l/2/fwbgGcYYo77U4MOUZCYDVhoU/x/uKTgxWl/aZV+cO3bHLg+35BE87757IJuOO1OBA4lTtJ/QzOFwWLJfZZGPv3Xr1oJ94tvt2LFD2P159Suv1wvGGNra2tDT0wNN0zBx4kRR4DwUCokCK5xegecD8Aidjo4O4ROQ/RXyvZNpp/m90TQNW7ZsEbb+ITk5pMSvoiykI+TT4DYZdJ2BEUN3bwYd3Rnsbklhy54U9g1x8OcVxWMCAc/BNzwMORqAHwewRfp/K4AphbYhohRjrAVAMQDLMMYYWwpgKXCgmPahChEh09oJyhz5WMI140AggNbWVhHx0leUjtwPp9NpqXAFZJ2cdnBLp9OIRCLC5CKLy+UqWOe1pKQEbW1t6OrqEsfMZDJwOBxIJBJYt26dyJrt7OyE1+vF+vXrLYMCz97lgJxKpfDXv/5VrJdZP/nAw4E7nU4jGAyiqakpx1nN74Gu6/D5fNi7N1u3k0cIVVZWChPPsQT7/jy7ITl0KQ9raKx2orrUgHt/fVwC0NNLSGcIRICuMZg6E+taOjL4eHsP3vm4CzubT23wl5U+6ulFpnNgMqCPqygdIvo2gG8DwH7H4CGLoWpgTgNMz08dcCjCbdA8oUg8EJvmbgfk2tpabN68GclkUpCRceEmG64l82O2tbXlgL2iKGhqaso5BpDVtmVbPH9hGhsb8c4772DdunWora0Vma7Tpk3Da6+9Jlg4FUXBtm3bxDXIxw8EAgKg5WuV/Q29vb3wer1iQOAho3x/HhLa29uLvXv3wu/3IxgMiggjXiwFyA/C+e6rXfLdl4PJENgfXamNGTh9tAvRoI5MBuhIuzF+ztWYdfZC+CI10HSr2TDZ3Y7W3R/jN//xb/jrn36BxhoFE2qd2LS7F79/twNbPzk1o7XkHBTm0KH2g/7lcORoAP42ALIhNrF/Wb5ttjLGNABFAAakVLtT1cE0FYp5dJweB/MB5AOltWvXwjTNHG55WbiWzMMvOzs7c2LRNU1DMpnM6xvw+XwWZyc/z9/+9jexjJuHAODvf/87gCzg7dixA8ABagge46/rOpLJJPbu3WuJtVcUxTIr6O3tRXV1taWWLu8rcMAJK5twmpub0dzcDK/XmxOC6ff7LVm6/QXyQwX7ITl64nMpuGCyF8OiBnqSGTRMXYgFNz0Ch6vv5ETD9CBUPg6Lbv86Ft3+dXS27MT3n74XvamXce1Zfny4uRsvv92OruSpNTDL77LidsKhHLnCmk+ORpTOmwBqGWNVjDEDwEIAv7Jt8ysA1+7/fRmA3w+E/R4AVEVBZmcTcBQ0fACCqiCfHIzdkZOiFVoHQPDY83PJkkwm4XA4cjJ3AVjAVpZYLAYAGD16NHbv3i326+rqQjweB2MMLpdL/O3o6BARSR0dHejt7RW2ef6IysvLhYO3trYWkUgE69evR2trKxRFgaIo6OzszMlXAHIjjPLx5XC7P3dOyy+/7BAudMxTjS9/sKU+YeDmc4OoLDFQUnsGvvjjLbjqjqcPCvb5xFUUxS0P/gD/8uLHcJWMwqgKEzefG0BZ6LgyPhxToZ4kHN0DU0/3iAGfiFIAPgPgZQD/BPBTIvqQMfYIY+yi/Zt9F0AxY+xjAPcAyAndPJpimib00uKjdrxCY1OhqBxe9UlV1ZyQQ4/HYwl15GBlmmaf5gY7oVohhzE30/C6t/J2e/fuFRE2xcXFaG5uFoRxM2bMEP3JZDLIZDICmDdu3IiKigoUFRVh7dq1loFE3i6TyUBV1RwaCSISxdIzmYwAdA7wfFBNJpMoKiqyXCsP+wSAkSNH5r32fPdtaBAYGJlS78SVM/1IZxTc+th/4/ZHfgLdyK/UHIo4nEW4/+nf46plL0JXFSw+w4+RFacgeypjMIbFMCw2MNFrRyUOn4j+i4jqiKiaiL64f9nniehX+393E9HlRFRDRJN5RM9ASVFbL+gwaRXyia7rAoRkhsyDgQofEFRVRXFxMaLRKNrb2wUwqqoqwCoej+c9Rk9PD1wuF3p7ey0zCm6C4aGSdiktLUUikRB95IMQpy9ubm62MHe++uqrmD9/PoLBICorKwFk/QQc2Nva2izO1SuvvBJFRUWorq4W2j0AwYFvH6B4/QC+ndfrtXDs8PuQz5fB5cMPPxT78ntQSIZs9UdfpjY4Ma/Rg/aUE1/60ceIV0846ucYPvFcfP6776ErreGiKT6MKD+1QF8JeJDctBONZdUDc4JCGVmD3Y4k0/bq7z9JsW8tIyhHXgybZ5L2t/WVmcvX6bpuWe50OkVB8Xz72bN58x1TztDlx2eMFcxSNU2TFEWhyspKsSwYDIr9zj//fLE8FouJY6mqatlHbpFIhEpKSvLeB94P/lfur1zcnLe+Mo7t92+oDXwbWW7Q/VeGaeU19dSb7Drsb7O/0tPRRHddEqGVV4SoouTUed6O0cMovmoF/WXLR4d973CqFTGfOWwEkuu3Q4vk134PRWSTQqECHrJwcwNng5Q1XZfLhWHDhuXs09XVJcwosvB9uckjnz/AXkScR8bwZXx5vv0ymQw2b96MmTNnoqKiAsFgUOwnc+xwswx3QssRNsOHD4fD4UBDQwN27dqF3bt3o66uTtSz5TTK6XRaJIq5XC4QZemfTdO00ER7PB74fD5Lv+WZVL5KZEMysBL0Krhgsg/dvQoe+c7bOZE3AyGGy48vfu89pFLApdN9cBqnholOCxch+dFWjAjFBuT4JyXgnzGiEY76chjDju5N485FTk/cl/DonXQ6LYC7vb0d69ev7zdgcXMH58fv6uqCYRgIhUKCo55vI9vDNU2Dpmk50TWyyCD7xhtvYMuWLSIjlsfkl5aWCnI0XiMXOBBZNH36dPzzn/9ET0+PqOAFQEQBEZFlPw7icp1e2cFLRGhvb7cUUOHnOxI50v1Pdbl4qg+qyvC5Z1+FbuY60QdKXL4S3PLQS/A4sxFBJ7MIk/HwCvjiEQQH6D6flF9CjT+MzOot0OLhvOsLlffrr/SlOQNZ8FVV1QJsdvF6vTnRKnabNB80ZMBKJpMWtklug+dMmoqiiASqfIVY5PMDwLx58wStMb8mXs1qx44daG9vR3t7u8V+z7d9//33xbKamhpBBZFMJqEoCvx+v4U/h0tLSwvC4TDS6bQYkBhjmDRpUk6pR8Ba+vBweHX6yogekr6lsdqBeEhH4xk3IBCtOebnrx5zOoorZ6A27kBlJLci3cki6XQaYABzmYjuHZjiJ8BJCvgKUzC8pg6uyQ0HlknVnw6XjCtfCcR865LJpDB/2MsgRqNRRKNRtLW1obu7GyUlJTkFSeTIHS5cU+ZOWvkaxo4dC5/PJ8je+H6yU5SLz+eDy+US0UN//vOfRSinLIZhWAYguUSi7MhVFAW6ruPDDz8Ucf/JZBI1NTU5wC0PPvbqWIwxvPnmm5ZSj1zyZeIOae0DLwzAaSPcaO9RcOmnvjho/bj1oR+gN0U4Y8yxm10cS+HfhZ4ogTm8AovPmT9g5zppv5q58XpkupPQ4iEAsGiwB5NC8fWyKcYOOBwcGWNoaGhAUVGRoGKQ4+h37tyJnTt3in12794NomxlKbs9nvP5ZDIZcfympibouo6uri643W44HA68++67lupYchw777NpmvB6vWhtbUVnZ6co2djV1SXKD8qSTCaRTCbh9/vBGBMDDWMMNTU1oj884kjTNDEoVVRU4KOPPsKuXbtw8cUXi/upKAo0TUMgEMgJaZWfzZw5c2AYhojxt4thGBat/UhnbEOSX0ZVOBDwqLhw8QNQBigRqD+iO9wYMeVilId1JE7C+Hz+7jvGDENqw05cPNrOTHP05KQF/BvPOB96aTGcE+oOeV+7pp1P7GaCjo4OMMYQiUSwevVqtLS0WAaIfGYFnlglx+vLtWQZY5bQznx94NqwbAvPt213d7elUInD4YCu68IRLO/D/QOqqorwTa69h8NhfPTRR8Jsw4+dSqWEJi6bcX75y18ilUrBMAxBHtfcnC1OI4M57Q/ZnDdvHn77298KM1O++2YfkIfokwdGxlY70ZUkzLrglsHuChbd+jh6U8D46pO3yL2zsRYlJSWIuHwDdo6TFvDDTi98G/bBOdXO1Nx/6e+MQN7eDmKapvVZtJuXGgyFsjMRmVeGiFBcXAyn02khMePZsHyQcLlc2LVrl9CwOUhyMOcDSHFxMRhj+Pd//3ds2LABvb29AqRlwOeDRyaTQVVVFZxOZ16en8bGRvG/bH5SFAVOpxPxeBxOp1PMCuwx9zySh/cxk8nglVdeEcfJR+EM5Jp4ZHPdkBwdcegMiZAGV6gBqjb4tnOHO4heLYDq2MkZl69Fg9BiIcwJVA7oeU5awAeA28+/HGqRB3p1/qSmwxUZXGRtkzGGHTt2CA0ZyGqfPT09BekAQqEQXC6XIEKTNXUgmx3b1dUlQJKbUvggwgux8Cge4IDmzP+n/fz3n3zyCYgIS5YsEQDPj8spDBRFEX1QVRUbNmxAV1cXiouzmcu7du1COBxGIpHA22+/LfrZ3d1t8ZF0dXVh27ZtcLvduPrqq7F27Vqk02kYhpE3vDTfrISI+sWXcyjmuiHpnwyL6tBVhsW3fG6wuyLk9POWwONQEA2cfGYdc2I9mKbis5cuHtDznNSAv3jCLCipDDxnjDsqx7MXPAGsGbI8ekemUyAi+Hw+4dS1a6KffPKJRWMtKioS4CpLSUkJXC6XKGLS1dUFv9+P7u5uMQhwbVjWxnnkjizxeFzw3nBpamrCiBEjLNoy9wsEg8GcwiociPk5PR5PXtBtamrCD37wA8HNk0wm0dXVhWg0ikQiIfp2sOIxfr8fPl/uVPdYaPan4uyhLKyDCChrmDHYXREyfc7lAAMqwicZ4GsqvHMnIr6vF2HnwIafntSA79FNzPSXQYsEoPgPz8Mvf+z5AG3Tpk3CeQogx/zBGENrayt6enoQCoXyHoMnJxUXF6OlpQV79+4VAMtJznbv3o3Ozk5s2bIFmqYhHA6jubkZvb294nxynD4nSOOROzLwb9++3ULVwK9x9erVSKVSAsQ/+eQT1NfXo7m5Gbt374bb7UY8Hhf/19XVCeDnSVs83JP3kUf1yLkLDocDO3fuxLZt2wra3+0af3Nzs4jP7+uZFALnIwHtU3H2EPJq6OrJwDAHphDH4YgvVA0CEPKfXIDvnjQc6a4kvrDghgE/10kN+ADwhQuXQK8qhWfupEPeV9Z2OX89YywHjDo6OoTzVA4p5LHoXOSEIg4iLpdLMF9yQFZVFQ6HA06nU5CdyVExqVQKe/bsQUVFBYADZh5OUczj9LlPgZtpuG2f/+V9lZk7gQMDEACsWbNG2No7OjosET2cMx+AiDxqa2uDz+dDKpXCvn37kEqlQEQwTVNE+sjRSCtWrICmaSJqqKioCIwxi+nKDtZ9AXChAeBUBO0jEbepIMOOnBTtaIqiqujsJnidJxFsMcB74TT4TSfmDBs14Kc7ie5cfqkOlKCmGdArIlC8h/YCy7ZhDoKcYgDImhlkc4k8GJSWliKTyaCpqUkwTXLbuMfjyYmOSSQS2LNnDxRFEeUCeeglkLXtyw5OVVVFNAwnWJOphGVwz2QyKC4uFn21A6i8nDGGrVu3wuFwoKysTGzLNXcZOPfu3QuPx4M5c+aIczscDjHHd6voAAAgAElEQVSw8epbvPLXvn37RL6Aw+HAlClT8PjjjyOdTotBj3Pwy5XC+sp/kCUQCFjukdxfOWw23z0YEqsYOgO0gSnCcSSSzjA4tBMbtmTMMCfUI9Xagftnzj8muSUn9p3rp3zrurthNpTDe960g3LY24UDxo4dO3IiRpqbmy1hg7SfVx7IavNerxfBYBCbNm2yFCNpb29HV1cXNE0TdA1yTVoZgPM5e4lIaN26rgvHLT+HoijC1CLvz/uqKAqKiooQCATg9XrFABYMBsWxU6kUtmzZIgYkmVNIllQqhT/+8Y/CD8FLQAJZX0FPTw86Ozvh8/ks19PT0yOcvkSEyspKeL1eSyIaF7sjO5+Ypimqg/FjcnoJ+Rh9afxDyVxWGczY+0JCOLFnaj6f7wBmKAy+S2cilIjhmnGzjsn5T4k3vKG4FFU7euAYXgEW6n+Mq8fjEZotpxe2SyFNsaurC21tbZZwSrvIoCNrsRz8iQhtbW0Ih8Pwer0WSgf+O5PJoKWlBZFIRICzfRACss5TGexaWlrQ1NSUdxbDGEMikQCQjSIqRNym67qIwc+XlLZt2zYoioLTTjsNbW1tICI0NzdjxowZIlSTUzA7HA60tbVh06ZNaGxshGEYFh6egwl/NnzAMQwDqVRK3It898YuQxQMBySdJvR0tR98w2MsKiOkjkK96sES2azrmjUWmdYuPDprAdRjpGycEoAPAC/d/QiMaBCeS2b2e5/29na0tbXB7/cXNCtwsJS1cofDIXhlZLEPDqKG5X7nqn1bfqw9e/agra1NmE1isRgYYxg9erQ4xq5du/I6QHlkC585OBwOkR0LWJPMMpkMEokEEokENm3ahLlz52Lnzp2C1MzhcKCm5gCfSjQaFb+501a+Lp4l/Oqrr4qZldfrxeuvvw4iwurVqxGLxZDJZLB69WpRkWvHjh1IJpOHVNzcnv+QTCbhcrmEM30oOevQpLOboOL4YiUlIpg6Q3vXiT8wM7cTvktmorqyEgtGDVxmrV1OGcCPuotwVWg4HMMrYI7LTwJVKEW/ubnZEmcui1z5iZtbenp60NTUZHHYAtkXtqqqKucYspmJDyxcg5edwBwAt2/fjmg0aiEvk8U0TdEvTlTGiyTLMfZyoXCPx4OPPvoIe/bsEYXGf//734tj8gHh448/FoPIli1bEAwGMWzYMAuhGxc+iPEIIZfLZSn6AsCixW/btg1E2Zq7PAOZO3oPpu3bHdKBQACdnZ0WE5Ndhkw4hWVvewoekyGdOrg57VhJZ/MOaCrD3tbjd/C2v2uFTMhFl89GpqUD37546TH1J51Sb/wXLrkOfsWA5/ypYM5ch1ShCkr5yMy4ZDIZYZaQI29cLpegEJBl8+bN4rdsb+bSF+f+1KlTxW95dgBAROOEQiF0d3cjk8nA7XbD7/djz549IjuXiES1Ke4Q5YXMgayte968eVBVVfgITNPE9OnTxf3xer2CiXPfvn1Yv95awIwDKdeue3t7hS2/ubkZc+fOhWEYqKiowPvvvy9mQ/KAm06nkUgkBMlaIXNLvth8wErOxu+v/cOSM32HxCo7m1JQGLB707uD3RUh/3jnFRCA7fuOr5mHLHbfUL78EqMuAeekBlwycjLGRMqPVdeyUqgyymC3I6l41Zf8ae0HFHv+HgotvShvxZl8VacMwyCv1ysqLfW34pJhGKRpGiUSCfL5fASAioqKSNM08nq9lm37e8yioiJSVZV0Xafi4uK829irXPn9fgJAmqYRAHK5XDn78EpVEyZMyDnGuHHjSNd1YozRokWLxD2yV+Li18CPz48hV7TifXY4HKKqFe+XvS+MMQqFQlRaWlrwOvuqMAaARo4cKZ6rvG2hSmBDLdu8ToUeXBim5x6+ekC+w8ORFUvG0orLQ6Qqg39/Drcx06DIV26hyi8spc7engG5TzjVKl71JbNqRuKy0pFg8WKYeYjVZGZKLslk0lJrtb/24GQyiVQqha1bt4ool5aWFqRSKYtNHkDeoiiyo9Tr9UJVVbS0tAibvxwHLwvvHydi4zONVCoFp9OJzs7OHCcsp3b429/+Jo7BZy4ffvihyJT95S9/KbTtiooK6Lou7Pdcm+GzBV53V57W8j739PSIAit2LUjOffjkk0/ymot4H6urqy372IXXwc1kMjmUF0NSWNq6MtjVnMKav718XOQwpFNJoHMbNu/uRfoENuF758+Aomv4/jV3wzkIYa+nHOADwFfPX4KIP4jA9edBDec6V+1hgNyBapomTNMUSUKFpLi4GLquo6qqSgBRaWmpOI6qqjBNs2CoI9+nt7cXjDEUFRWJAUcmFNN1HbquY+zYsQCyppSSkhIoiiLYKZ1OpwA60zRz2DV5gXY5s9fr9WLWrFnCNCRX7ZK583n1Lh55wIGdk7R1dXVZMoG5GIaBaDSK7du3Wxg8eRjrrl27hM+A3we7GIaByspKrF271nLufIlxXOyVtIakb/lwUzeKnAzr3vvdYHcFv/3512FoDO9tPDi30tGWo2X2c00fBe/Zk3FBSR1mVjQcfIeBkEKq/2C3gTLpcFnftJtK7l9MxcsXEjO0fk/J+lvUfPTo0QemcftNF7IphS/jfysqKsQ6bj7p6/j19fUWM5DL5aJwOCz2k00WwWCQlixZQj6fjxRFEX2TTSmhUIgURaFIJCKWcTOUqqpUXV1Nw4YNI+CAKaehocHSJ9M0ady4cWSaJjmdzoJmE25aMU2TysrKiDFmOS+/L7xPjY2NlnX5TFLhcNhyPfm2OdRmL65+MPPRydYMjdHyBSG6d2H1gH6LB5NMOk13Xhyi2y8MEjsO7svhNK0sTOEHl9DwR26hVDo9oPcLfZh0Bh3YC7WBBnwiop+99xrFX1hORdeeLR6MDLT8t6IoBYGeg4IdoFVVzQGMuro68dvj8RAAYcs3DIOmT59O1dXVYhvTNC3byM3r9Vr6V1xcTIZhEGOMHA4HzZ07V5yfAzdv8kAxbNgwYePn2+q6LkDdNE3LYGSapmV/+bfH47HchylTplBpaanl3sm/w+Fw3vsut2XLlhFjjBRFEYDudrsLbs8YO+hgye+Z/Vn0Z79C7WT1CZwx1kUPLgzT23/86YB/j4Xk199/hB5cGKYJNeag34/+NvldUrxOinxpKVU9u4x2trcM+P3CEOAXllte/DpFn7qNPBdMy3loHMz6AoK+gMfujARAkydPtgAWB1vTNMX2oVBIrLc7RoGsE1VVVWKMUSAQoHHjxol9PR4P1dfXk6Io5HA4aNy4cVRTU0NOp1Pszx2zuq6Tz+cT62QQlGcK8oBhGAYVFRXlveZFixblDC78mPwv7/O0adMsfbLvd6TtULTxQ9XcGWPi/h/O/idS01XQHRcG6d5LS6inq/WYfJOytO7bSssXhOhTZwcG/V4cVtNUKrn/Gir53BJ6dePqY3LPMAT4hSWTydD8f/8KlT5zF5mT6nMemMPhOCgYGYaRE0nCtcaDAQf/LYOovJybJuT18kDCzTiMMfL7/RQOh/Nqm9XV1eTz+ejssw/MZvgMAgDFYjECrODFBxvGGLndbioqKhJmn/LycrFenuVMnjzZch2jRo0i4MAsRb6XlZWVeX8DBwbCQtFLRUVFYsACDkT29Kfxa+yvee5QZwwnW6sp1emhRWF68IZGymQyx+S7JCJKp5J094Iy+uwVYYoEjp8ZVH9nkWAg3xVnUHzVClr15u+P2X3DUJROYWGM4SeL7ka4KYng0gvhGGVNjOrp6UFraysikYglsoUnAqmqimQyiR07dsDn84kYdO5YZYxh1KhR8Hg8wsnKJftssjJjRpZ33DAM1NXVWRy3AER0DnAgGqaxsREdHR3iYTY3N2PPnj0wDEPEwAcCARiGgfXr16O1tRUvv/wy3G63YP/kwp2eTqdT9HHcuGwdgaKiIpimiUmTJoExhl27dmHLli3CAcxj4XVdx1//+lfMmTMHALBgwQJ88MEHUFVVcAZxZ7GiKBgxYgQikQjGjx+PjRs3WqKjeGQRrzcgV9dqaGgQJSS50/dQsnL5dct1C/IJv9+8Gll/tj0Z5eMdvXj1H51Qurfh+UeuOibnpEwGj9x6GorMHvz2b23Y1XTsoqoMw+jzefLvDeg7ea9o4VnwnjMZF1AJrp94xlHv52FJoZFgsNux0vC5tPR0Uf3X76bie68koy7R5+iuKIplOq+qqsX0wrXO4uJioUUWiiWXHaVOpzNHo5XNSm63O8fswrV02YTEGKOioiKaOXOmZVv7ufl5vV4vFRUVWWzZ/HoikYjlnKFQiDRNI13Xye12i5lBvsZnGrJ5qKSkhPx+v3AAy8euqqqi2tpacf9kx7Z8f+UZzvXXX09AVsPvr+Zl963ke8YHO8ap2BZM99EDC8P07UevHlBNP9WbpC/cdho9uChM8xr7Nws73pp3/gwKfW4x3fiz547prIhoyKTTb9nd0UK131hGpc/dRUZNvM8HKgNtLBbLCzaapglw4cDPt5Pt1/bmcDgoHo+L7QHQmDFj8m6bD5xkc1IoFCIAFI1GhW2/rKzMAqAXXHCB+M3XcROJaZoW+zu/Lvka+e+GhgbSNM1yb/i+qqpanMPcxKMoClVVVVFlZaUYtEaMGJFzTWeddZalD4Zh0NSpUy3XfzAgl59bvma/Tvu9PBpN07QTdkBhDHTZDB89uChM9187lpLd7Uf9G+xs/YTuXTiMHrgyTOeMHzywz+d/482e8Chv63Q6yXPOZIqvWkGXfO9xSmcGNiInn2AI8PsvO9qbqeL+JVT69B3kHjUs52FzUHE4HGSaZl4gtkf1cPu7DDZ2Z6w8S8gHCOXl5WL5z372M2KMkWEYVFNTI86Z7+WUlxcCOzlahh/PMAwRncMYo7Fjx1pCJ03TJLfbLQBx7ty5Yp3P56OioiJKJKwzJa6Nc9u7w+EQMxg5EklVVaqoqBD+C/usR74m/lvTNHK5XAcFU3soaaHnIT/r/OCXe54TFcgPtc0d56bPX1VCyxaU0Lv/98uj8t1lMhn686+fp/sWhOiBK0M0raGwQjTYjStD+d6Z4bctpMhXP01zvn7/gIdfFhIMFOADCAL4DYC1+/8GCmyXBvD3/e1X/Tn2YAE+URb0G569jyJP3EqOUVWWBxqPx4kxZgH6cePGEZA1SfCPnmvoACgQCBBjTETHAIXD+OygYZom+Xw+YUY5/fTTyel0ktvtpquuuoqALDDlc0RGIhFqbGwU684//3wKBoOkKApVV1cLjbquro50XRcUEva+yBqMDILyLEUGZVlDv/nmm4kxRsOHDxf9kB20/Hg88giwgv/06dPJMAyxzuPxWDRxTdNo9uzZBT/OfCDMn5f8jMrLy3OutT8ALj9HOfpKUZScgepkGhDqEwbdNb+YPrcwTMuurKbtH795WN9aJpOhde/+hu69spIeXBimT58foLJQ//NiBqoVisDiM2b+vsjNe8E0iq9aQZf98MlBA3uigQX8rwBYuf/3SgCPF9iu/VCPPZiAT0S0p7OVav/lUxT7zr3knDoix2Qjg1C+D1lVVTr99NMtYAxkQZcxZrFTy0laMuDks/vLIMI1DFVVhaYtAzIHf1VVacqUKWI5BzxFUUQ/7BE3fD0P7+TLTNMUgJwvMobPfILBIMViMTJNk1wuF5122mliG7/fT6ZpivvHNXmPx0PBYFAMpnZNPl/YKL++g33A+XIZ7B+4PVKov8e2byPfQ13X+xXBcyIOBobGaG6jm5YvCNFDV4Xpzksi9OKTt9K+HWv6tFun0ynas/ld+vYXr6V7Lo3SQ1eFadmlxTRrpOu458nJ9z4YpkmBG8+j+KoVdOGT9w+KGUcW9AH4LLv+8IQxtgbA6US0gzFWCuCPRFSfZ7t2IjqkasgTJ06kt95667D7djSkLdmNOasexfqNG9D9wQa0/+frlvX19fVYs2YNqqqqsGHDBsuyQlJbWyvoAPx+P5qbm8EYQzQahc/ns/Du6LqOVColqALGjRtnYafkpQO5LFy4EC+99BIURUFvby8ikQh27dolionwyBdOi+zxeJBOp0Xxc84eWVtbizVr1qC+vh7/+Mc/AGS57zs7OwU9gWEYSCaTlmsgytbQzcdsWV1djZKSEqxZswbd3d2WqBqXy5UTZTNnzhz85S9/ESUPuaiqinQ6jVgshpaWFvj9fmzbtg1AlpqBF2TRNM1yD3j/DMOAaZro7u7OodDQNA2xWAybN28W23u9XrS1tUFRFDidTnR0dEBVVUQiETQ3N+eNDuLPhR+jLyl0v04kMQ2GqfUuDC8zEPJpYAzo6SX0ZHRoDi90ww0CIZ3sRKqnFaaWgqYyZDLA7uYUPtjUjTfXdiF1HNIbyc/QMAwRlcfpQswiL9zXzYMa8mNx4yx89bzFgx6xxRh7m4gm5l13hIDfTET+/b8ZgCb+v227FLLmnBSALxPRLwscbymApQBQXl4+gddsHUzpSfVi/otfxgdKB9p+8xZaf/oHcPamRCIhqlNxkV8QTdOQSqXgcDjQ29sLn8+Hrq4uEc7IwbLQR8/BTVEUjBkzBqtXr0YqlcKMGTOwdetWrF+/3gIo+c4di8WwZ88eaJoG0zTR3NwMIhLFSfjI39DQgNWrV1v6pWkaysvLkU6nRf1c3lc+sPF7wF9yomzB8rPPPhvbtm3DW2+9JTjwKyoq0NTUhNbWVkv9ACA7oHR0dAhw5feDDyyyXHTRRfjVr35V8Jnx+wZkB818XDyy8HvFr0/XdUsdAlny9afQuQ9H+jNIHM9S7FVQF3egNKAh6NPgNBh0lYEA9KYIHT0Z7GtNY3tTLz7amkRL5+ANdnI9iL6EP5OioiJLqVK12Ifg7ZfCiIdx97DpWHbmxQPZ3X5LX4DfH7PNbwF8kKfNB9Bs27apwDHi+/8OA7ARQPXBzjvYJh1ZMpkMLf3RMxR5/GYKffZqUnwHeFpkKgS5yXwx8nIexminELbvK3PRyM7P4cOH0+WXX05AbiSBbEoYNmwY6bpuiZiZM2dOTv90XRf2e75u1qxZom9Op5MURbGYRBYvXix+89DQaDQqlsnXtnTpUgqFQnTnnXeK9XI4qP3aY7EYud1ucW2cLkK+j7Kpq6amJieBSk7uspvdFEUhj8cjIi1ks5bcNE0TjnT5GRXKMuatr+irw0nOOlkpG47HViis154tDoCMujKKPX0HRZZfRf/5z7cHG6IsggG04a8BULr/dymANf3Y53sALjvYdscT4HNZ9ebvKf6tZRS841IyaxM5dmUgCzYyOMkvUDgcFjZ42f6e7+XjXPp8G36cSCSSN2RM7gcfIDhY6rpOw4cPt9jig8GgpX+appHT6aTzzjtPbCNH3hRqkUiESkpKBJBqmiYifQpdH3d8cQe4oig0YsQI0ScgyzvEGMshQVMURVyfnXBNbi6Xi8rKykQYZL6IimnTpolnwQc8VVUtUUv9bbquUyAQyOlrXwCSrw0B/LFrXJGQ8z0KPStZOXHPmUAlj9xA9c/dR6s/2T7YsJQjGEDA/yqsTtuv5NkmAMCx/3cI2YieEQc79vEI+EREb2xcQ1X/eifFvnMv+eZOtMSWyx8rB/ZCRUocDofQimUAl0EsEolYnLQ1NTXk9XpzIkD64nTx+/0iXFGObtF1XYCpDIY88oefj1/ffffdJ5afeeaZ4hgySMtRL+Fw2AKc/D5whyzXhIuLiy2hkvbBrK/CMGVlZX1+0PJ6OUEskUhQNBrtE1z74jLqq/GBI9+z4Mlq+fazF9c5EZ24J2oLBoPEGKMZM2aQ1+u15MzI24XipRS67RKKr1pBE754O7X0dA02HOUVDCDgFwP4HbIg/lsAwf3LJwJ4Yf/v6QDeB/Du/r839ufYxyvgExE1d3fSjGc/SyUPX09VD1xHwUSpJQqGNw5ymqaRoigiCkRRFKqoqLCAAk9+8ng8NHr0aMFBkw/wDMOg2bNn5xC0cRNELBYT57zxxhsLvuj8xZY1U4/HI0D+kksuIU3TaPz48QTAUvUrX/UseXbAW2Njo9D88/XBnqV86aWXWo47duzYnOgcRVEsA6394+S/eTYvY4ymTJlCgUAgb1IX/+j7Aw7y9eYbMPJFbhmG0aepp6+WD/j7GgT7WzntVG0Ws4wtIg3IZXzlbeS8WRT58s0UXr6IPvc/Pzrm2bOHIhhKvDr6kslk6JHfvkTx79xHxcuuIHPkgXh9u3ZYKB6bh1LeeOONBUMO7S+pqqo5CU08zFI2pdx6662kaRqVlJTkTeji5gxZ85e3Of3008UyPiDIpqphw4ZZsmjLy8st2pGqqgJwgQODi9/vFzkF8uwnEAjQyJEjxXZyxi1P0uLbaZpmyYDlg0m+mZKcnMb7BWRt8ePGjSOn00k+n08Afl8ZlvZmt+9z4jr5PnGgLzSbKOQT4Pbkg/kMhlruN3Kwxp+J/Tvkx0kkEgeeF2PkOWcKRZ/6DA17bhn9Yf2Hgw09BxUMAf7AyZtb11HVY7dQfNUKKl58NkG3AkZRUZF4saLRaN5sUDtAPProoxbbOi8Swl9Cu92RgwK32RuGcUiUAPfcc4/Yr7a2Ngeg3G43GYZBLpeLNE0Tg0E+bbKQCUS+5nwDoN/vF/1XVZWKi4st92XGjBkEHDDTqKpKU6dOpUmTJlnyAfh5ZMeuPLDIiVtAdhaTr19yf+1gIpuuDtYCgYDgWyq0zcGOZ79f/WX57A/VxMnU8hW96c8MSX7P5Nlu0bAEhe+/huKrVtD0L9xOTd0dgw03/RIMAf7ASmdvD137029QaMVVFPnSUgv5mswZY38J5UieSZMm0ahRoyzOWQCW6Be5ORwO0jTNEmHidrvpyiuvpGg0SsOHDxfn4s5DHp3CGKNp06YJigNFUai8vNxC9NbY2Gj5WPjx7O2MM84gp9MpPjY5iezBBx8UmqpMy8z5/ktLS0lVVYspyDAM4bvgFBUycPHjydft8XgsCU4OhyOHiK68vNziH+HHLORgtz8zABZ+IbkvdjDxer2WrGV5wDkUTVTmDbL3z+VyHfRYcqH4oXbgnqqq2uegqagqVV11LpV+4w4qffQm+tbrrxzXJhy7YAjwj428/NHfqea5eyn2rWUUWHgWqW6TysvLLVqew+EQUSoctPNN2znQ89BKxhiNHDlSvLRcEwey5hsANHHiRLFMVVWaOXNmDld/IRsv164B5C2IwvvMeegNw7Bo1qZpij7V1dWJ7UtLS8U5a2pqxDHnz59vOf+ZZ55JAOiBBx4Qy4LBIH3qU5+icDhckDwOyIK5x+PJmarz+yBv63a7BWDX1taKcpJOp5McDkdeGz0/ngzc3Ecib1sIXOVBu68QTzuA67pO4XC4YLRPofPafTunapNNn30537ny4HK5yFlZSv79WbOzv/MvtKVl72DDyiELhgD/2ElHsofmf+1zFH/hPop+7TZyjK+1AGNfBTt8Pp8gKmOMCd4bO2jwVlJSIoqSAAfMHvYXXB4c+AxAVVWKxWJUV1dHwWBQgPLSpUstg4LseC4EXMCBSAc7cIVCIXE8GeDsYMft/bqui/PItnfeB358bh7j5+bbxGIxofFzOmbZrFZcXHxQzZgPVrImz9fZfR66rluuhWvjfr+fPB5PzjXI+x0MsPriCLL3yx7lk2+bU7GNGjXKos2XlJRYiAF5U0yDPBefRrHv3EuJZ+6ir/z3T08orV4WDAH+sZc3tn5M1V/5DEUev5li9y8md1XckqQlmynmz58vCnbbX1g5Fj9fglA0GhX2epfLRRdeeKHlBed0x7qu08qVK8XyRYsWid9VVQcczm63m+rr68W5J02adOCj2B8OKvMAKYpCdXV1VFFRQaqqksvlonnz5pGmaaJeLg9548dwOp1iIPD5fLRw4ULLYMJBy85JYwcve+lF2W/BnbH8/3g8TpWVlaIWsM/nE1FTvK88l4APZnwgyRfBI1Nf2811hcJFvV6vmIXIpiR7xJF9n/6A9qEC+6k6EMjvxMiRI8kwDLpo5Wco+tVPU2j5Irr4xcfpk862wYaPIxIMAf7gSG8qRY//4RdU9vwyCj98PfkXnUXjpk22AJlsJuAv48KFCwXpmt/vpylTpuQtCsL3405UXjhdjrcv9GHLZp76+noB3g0NDVRVVUXz5s0jRVHI5XIJk5I8K+E2fbfbTeeeey4BWZCdPn26AMQLL7xQbM+T1OTr5ayf/NyXXXYZaZomtnG73TRy5EhRb8B+vxwOB4XDYQvQyzMbOdLIEnkh3T8ZzLk2zgcuAOLa5AGnEI01/5/7RRhjVFVVRYqi0NSpU3P66HK58g7idkrrwyVfk6mjT8RwzYMNSrLJpi+nuGyuBLJArygKlU0aQ4FbL6bYt5bRyOeW0+/WvT/YkHFUBEOAP7iyp7OVzv3aZyn+wnKKPXMneWaPI2iqABL+Io4dO1b8P27cOEvEgGyTdbvdlvBCTqNw9913i234vqqqCvDhgK0oCi1fvpwYY3TbbbeJfWSAlhs3t3DThcfjsYRqcuekbNc3DMPiwLU7jxljlvPZbc6yKUSefgcCAZo5cyY1NDRYwF++Tg66vH/xeJzq6upIVVUKhUIUjUZFn+XzcIDMF+0ht0Ix+4ZhWAbzfBS68nns//v9fovfQI7dLyoqItM088bzq6oqCsz0VduXbzdYAH64TX6uhaKn+GxN/p74LMo+2DkjxeS7/HSKf3c5lT13Dy3/f9+i3nRqsGHiqAmGAP/4kHd3bqaxX/oMxZ5fRmVP3U7OqSNIUbNa9OTJky02+KKiIiotLRUaO9cWGTtQGNxuPlAUhS666CJh4+bL7Zok/xAcDoclZVz+MBRFoeHDh1ucrj6fj+bOnUuJRIIYy9IJ19bWksPhoIsvvpiA7GBQVVVFuq7TY489JqgNrrvuurznGT9+PCmKQnfddZcFjHiyF+9nbW0t+f1+i7mKH4c7xOVr4VqtvIxTOPD/+Qwgn6bOBxAeisrNPfkANxAKeB8AACAASURBVBQK5S0uIzvZR40aRS6XS0QhcQAWINTPxCzTNHOis+SWL0SVNz4Yyb6QQlr08WLykQdQ/i3w5yI/63z7ygpTcXExBeNRGn77Ioo9fw9F/uV6Wvyjfz1hQi0PRYYA/ziSTCZDv179Do1+bkU2xvfLN9PEJZdQTW2tcHzyF5rbuu0foWEYYqpvdwrKGqLf77cUXSkvL6eysjIBmrqu02WXXZb3Q7/99ttzQETWbBsaGmjp0qUCOGTH8OTJk8WHOX36dMusxePxWMjX5MaTwThIR6NRUhRFUDTYNT3ujJU/7PHjx5Pb7Ra2b7s9XY5kypdpKTdOLAcgL8CWlpZa/B+RSIScTicxxsRzMU3T4sjlYG8/XiG+fvtAkm92YXeye73egpq8nQ7jWIK77NTv7wDHt8sXRqnrek601Ny5c8W7z++5vyREDUsXUOSJT1Pp03fQef/2GK1v2j3YUDBgMgT4x6GkM2l68c0/UP1z91F81QoKLL2Q6i+ZS2eceSZNnDhRaDBer5disVifU/Hi4mJyuVzkdrvp0UcfFR8Xj1YJBAJUV1cnPjZu8+a2ZLnwR18JUrJWJTs3AQgbtaIoOeGhXMuXAfbWW28lxphIfJI/Wnv8uPybA4AMkLzeLWf5zAeU8nE4GF9xxRXEGLPE8EciEcux+WxKrtXL/+e/+0qskpk/GxsbLX3h+/D1tbW1OeDbXxOMYRiWzOaDAXkoFLIwhnLnOo9ukmcB+fbPxyBZqPFj5Svek+86+PvCTYh8P7mimLw/zzTnCgO/b8w0yHPuFAqtWETxVSto1rcfone2bRjsT3/AZQjwj2PpTafoyd/9gqqe+AzFV62g6BduIuekBnJ7PQU/WlVVhWbJwebqq68WQC4DfL6P8n/+538IgNhGjl/n2rSu63TNNddQMBgU5qHx48eTpmlUUVEhNCuv1ysGAq5N//znP7eAjqIoObZlWcPjsxjuLA0EAlRcXCzOEYlEqKKigi699FJxLePGjcvJR5CbrHn3RUj2+c9/Pgc4ANDZZ58tQLSsrEwMAvbQU67Nl5aWWgaE6667Lu/5eEKYomQricnO83ymCX7f+gJvu32b/5UHi0QikXeWwiOygL5pHg4G6n01eX9e7cy+DV8mz8j6cjTzd13eXtRALvKQZ94kKv3GnRRftYLGPHQz/d+Wjwb7Uz9mMgT4J4D0plP03Td/R8M+fwPFV62g6meXkeuMRlLNXE2o0HSYf1gej0dophyoH3zwwRzw1zRNZL02NDQQY4zKy8vptNNOEyRmQFab+tSnPpXzcWqaRvF43BJpw4HmkksuIcYY3XPPPQRkTRixWIwcDgf5fD5atWqVxfFsBygg6yx++umnLdpcZWWluDZ7+cjLL7/cYvaZNWsW1dTUCBOG3++nYDBIV1xxRd77Z6e75r/D4XBejdThcFiib5YsWUJANtdB3q4v4PL5fMJcwVlDa2trSdM0cjgc5Pf7xSBcSNu3D+h8gHa73ZRIJCyhtaWlpZbrlAFTVVXxLPpKVOovtQN/J7jWnu8+eL1ei/O9kIIDHFBQCt0HTyJKRQvPpMS37qXo126jSU/dS69vXTvYn/YxlyHAP4EknUnTS++/Ro3f/CyF77+GYs/cSWU3XEjx4Qc02ZqaGmEiCQaD5PV6ye/3UzQapfLycpE6Hg6HLcRiF1xwgXC22j9qey1cu2knX61dmdZYTvVXVZUee+wxAUbz588XIaIvv/wyaZpGZ599NmmaRj/4wQ/EfjNnzrScNxgM5kTM2E0h9957LymKkjOdl/tiNwkpikLBYJBM0xQDEjdp8N/nnHOOAD9FUWjBggXi/HK4q3zsiooKYoxZTCt8cMxno49Go1RTU0O6rotnwjVuXdcLzl76AkfgADePPHOz12HgswxO2azrumWG01eTZwIej8eyn6IoFr9ToX7rum7hELJfi5zvIW/jdDot72I8HiezJk5jH/sMlT53N5U+9Rm68Htfovd2bR7sT3nQZAjwT0DJZDL0l42r6awXHqb4C/dR8X0LadjKa8msLydd1y1ZmPKH0xcRlwzwbrebamtrhUZ81113iXU+n4/+93//l5xOJ3k8HpoxYwb913/9V87gIH+Ql19+ucVPIM9C5I85HA4LDdHlclnAIxQK0YsvvkhAVvOsqqqiP/zhD8Kmyxij6upqWrlyJXk8HkskkmxiMU3T4sweN24caZpGN998s1gWiUTENrquW/jyeX+5PZvf074coTLXUCKRoNNPP50aGhpEvzjgysCfr4CLrAXLhWxqa2tzsq3tdnQ7GMpmNO7ElH0VfJ08MHD7PdfI7ZFbHo+HRowYQYwxiznK3kpLSy2Dotwv/h4qikKmaYpBUVEU0jTNMoNwOp3ifeODImOMiiMlNOmmKyj8ucUU+fLNVPb8vXTTS8/RltYTjwrhaMsQ4J/gsqF5Dy389peo/Pl7hYPXfWYjxYdVks/nsxQaqaqqEpwwdtMPj9OXAVjO/h0xYgR5vV7yer3k8/nIMAz685//LGz7p512moXwjZtnzj//fBEV8/Of/5wUJVs2UOYoAbIaO2fm5OecMWOGAExFyfL3u1wuWr9+vdhmwYIFVFVVRYsWLRIgZrd3X3nllaTruuDcYYzRhAkTKBwOWzJZ+folS5bk5EDwWROPn+f3QY50kp3GjDEB4HYSNn6NMj0DN6WEQiFyu92WEFG7Q5MzhgLWOgNykpnsOM9n/3c4HDRp0iRxH+zro9HoQbVxe+sv+ZscLVaI7kF+D+zavEw+x9/TQCBA7vIoRZecS6H7r6b4qhVU/+y9dP/Pvkvtye7B/kyPGxkC/JNEOnt76LGXf0qVD3+K4qtWUOz5e8h76SzyjqqmSZMnW2yhsjlg6tSp4gMqLi4WGpOu6xbnpqzZ5gMi/sEfTgJPIpEgh8NBgUBAgLbsMI3H45ZauHafgGmalhKRAOiWW24hxpiI0gEOZOLyfeQkNQAC+OQCNDKgc22+vLzcAoY1NTV5eZB0XaeysjKRI+ByuYSZSL6ncigk12C5hgscMI8xli3rOHv27LwgzgdyrjVbSu/tPy5/pvKMwO12W1hN5VZWVmaJVOKEfXLiWCKRII/HI7Rzp9NJiUSCpk+fbrm/p512mgBwPsDJ7xiQHQRnzpxpCSyw13iwDFweFzmnDKfATedTfNUKir9wH41/8BZ6ee27JyzfzUDKEOCfZJLJZOjN7etp3nMPUuzJ2yi+agUlvnoreeZMIDXoFSCfz8Yrh2Jy263D4RBslcCBWHXGmKAW4CA6evRocrvdpCgKVVdXk9frpbq6OmH3/+lPf0qMZYnfOPkbBwEOfO+++64AUb68oqLC8v+ECRNowYIFVF9fbwnzHD9+PAUCAYtJS9aouf2cVxADsjQQo0aNorPOOssCvLxmLx/EeEIZP6YMmKWlpWJfRVHowgsvzKbnS07PcePGiX24+YHvI4MbH6BUVSVd10U+A5CdacggzRijESNGiOcm5yTIAMqBXJ7N9FVlTB6w+G+uCNgZQ+X3SGZxlffJ18aNGydMRDynwn5euRCOx+Oh0tJSkbCmD4uRb8Esij93dzaC7d5FtOxX/0bb25sH+xM8rmUI8E9iaU920zdff5lGfi3rsIqvWkElK68m1/RRVF5fS1VVVQJgFEWhGTNmWGz5sVhM8N9Eo1EBOByMOAjpuk5PP/20+Ph5eCY/zhlnnCHARtM0C8DJyUey05Vr8XIN0Xg8TolEwmKCcLvdNHbsWAoEAnkzLE3TJI/HQ+eff75Y53Q6acSIERQKhSwg7/f7qaioyGJf55z73KTDBxDu17jssssEwyIfcPg+8j3goaR24ONmM4/HI5y/hmHkLWTv8/lozJgxwn/Alz/99NOWpCk+M7Cb7bgPgw+ifBkny5PX2xUBfj75/SguLu6zmI7D4SC32y0Svjiwl5WV5eQFTJkyhcLhMI0aNcoC/vI7Z8RC5DlnMpU+ni0qFFl5NZ236ov0m3XvUTqTHuzP7YSQIcA/RWRjyye07P/7HlV9/S6KPH4zxb9zH5Xffy2ZE+upbky2uEosFqOpU6fmLb1nj++fPHmyRbvjIZx8/eLFi8WgEIvFLCalc845RwCsDEDTp0/PMT3IGh8vkyhrzpqmUWVlJTkcDotGedZZZ5GmaZZooUQiITR2XddzCqFEo1EaPXq0MFcYhiG0VkVRaNKkSVReXm6JypFnHrITkYNYaWkplZSUiCQrOeqG8/fw7WWg4zMfuQYAY4wikQipqmqZ2ciNH4Oblvgz5M9U0zThRJaTwmRuI3lg4s57vh2PcuKZ3zyb2ev1ksPhEI5+ebCT3xO7/Z4P7LKTd+HCheIe6JEguedOoBHPZH1UoeWLaNJzn6XnXnuZWo/TQuHHswwB/ikm6XSa3tmxkW74yTNU+czdVPLQdRT/zn0Uve+qLH+P1yWyPhcuXGiJcBk1ahSpqkpOp5P8fj/V1dUJ6gK3203f/OY3yeFwUEVFhQj7nD59OhmGQRMnTqRhw4ZZbL+ydsi1c5fLRSUlJTR27FhBa6yqqiUT1ePx0BNPPEGGYdCXv/xliwbs9XpzQgF5/2v3U1TITJmlpaU0ZswYmjVrlqWQyvDhwwXoyhq3XXOWndVnnXUWrVq1ioCs7ZuDm+xY5dued955pKoqzZ49mwKBAKmqSp/+9KcJOEDNyzN4Z8+eTaZpWpLLHA4HvfLKKwSAfve73+UAKu9jocE7GAxaTDz2pCan05nXmWs/D++LfT0vewkcIIrjA4m8/cMPP0ymadKSJUsEl5CjrIQ850+lkc8up/iqFRReeRWNfW4FPfybn9LW1n2D/Qmd0DIE+KewpDNp+r+tH9H1P/kGDXvmHgqtvIpiLyynxudWkvus8WTEQyLzlodE2j9Yzo3DWS4dDgfdcsstYr2sYduduRUVFTkRKbxOL9cuZaAfM2aMyK6VZxN1dXUiLFMGLSBrMmGM0UMPPSTWRSIRamxspHg8nlPsgjfZXMEYE4OE1+sVy/kAoWkaPfroo6SqKs2ZM4eCwaCFh0ie3YRCoRzb9i233CKStAzDoIsuusgyGNrpHDRNEwyYTqeTvF4v1dfXC8cxnzXIg6t9BsYHAs45NH36dLGM91fup6zhAwd8HEB2NsFzHXi/TdMkXdfFDKivesaawyCjLkG+K8+g2mezmnzJg9dS43Mr6fMv/5g2tnwy2J/KSSNDgD8kRJR19r67azPd8YsXaOSzyym8MhvaVvPcveS/ei65GmspPixripCdh/log3nYJgcPbhbxer30xhtvEAB6/vnnLdrgihUrCAA9++yzlvh7HtcNZJ2buq7TsmXLLGaHxsZGKi4uJrfbLZyZPp8vx3nLtWZFUSgWi4mKYLyW7xtvvCFMFOeffz5dfvnlFAqFBO8/n73YBxX5PvDGI4+CwaA4J9f0DcOw7BsIBMRMSdM0amxstID8/Pnzafjw4eR0OgXFxNKlSy38QIW0bxnw//SnP5GiKPTee+9ZiufI/eC/eRIaNw1xumqejMXNWTzCRzZ/5esLHxyj0SiVlZVRYkQdeaaPovGP30mxZ+7KOl6/cgtNf/5z9MSf/mPI+TpAMgT4Q5JXtrTupSf+9B8061ufp9JHbsyGvH3nPgotX0TuORNo8cq7iKlZymWu0cnFWADQtddeKz76m266yWJCkOPUFUWhF154gQDQE088YbH5rly5kpxOJz388MMWR+r48eMFiMsDUCFN8txzz6WKigpaunSpJfLF5XLRxRdfTEVFRWQYBlVWVtKPfvQjYWO+8sorLeaOqVOnUiKRIJfLRR6Ph0zTpMceeywnhJX3Q04UkoujLFq0SNjGn3rqKYrFYoIg7YorrhBgW15eLmz38+fPz6Fm4AOrqqoib4GHb8qmK5fLZQlt5aG5MtU0L3Yjz5Rkvh5VVS1JWVdffTWZpmmpQRyNRi1x8hzoFaeDzr3zJvKcP5VKHslShJR+/XaqeOZuuuTFx+mn779GrT2dg/3an/QyBPhDclDp6k3Sb9a/Tzf85Bka9sTtFNsfClf67F1UdPUcGn/71eSuKyeH07QQbvVVQ7Wuro6ef/550nWd7r//fst2Tz31FBmGQXfccYcAeTmaxuFwUDQatWSwco01HA4Lk0Z9fT0pikJPPvmkWC/TTANZ27UcGcLZIWXNnYMiH9yArENWvr6Ghgb6wx/+QADo17/+tVjO9+XJXn6/nzRNEyUnr7/+erGtrLEHg0FSVZU8Ho9lEOWzFz6YzJ07l+LxuKVvgUBAzJI4V44cpcQHAH4vE4mE5bkBBzh7uHmHD9CGYYhcC/48fT6fmHmIzFing2771y+S79JZFLxjAcW+kzXVRB5YQhOeXk4P/PcP6YM9WymdHoquOZYyBPhDcsiyu7OVvv/On2j+qseo7LNLstr/qhVU8sWbqPieK2jifdeTa3Q1NU6dLBKI7rrrLqqqqiKfz0e6rlts+zJwqqoquHQWLlxoKQjy5JNPktPptCRDcdCKxWJ01VVXiWVy2J89Y5QXk7npppuIMUYzZ84U2vYdd9xhmQHw/tkpAHiuAQdDt9stTDaMMRozZozwTXi93oKhkvLx5PyIYcOGkdvtpng8bhmAysvL6fnnnydFUSxEb3IkjRw5xPvs9XpF0RyPxyNyKDgrp0yoJz8Tl8sliPP4uqeffloM2rwmshb00md/+DxVfHrBfoC/TyRCld+9kG5+6Zv02/UfUGdvcrBf31NahgB/SI5YdnS00Ivv/IlmfP5Wqnv6Hop/NxtdUfLIDVT15O3UsPI6cp82hlzVcVq7fh0xxuipp54S4Pboo4+Sz+cj0zQpkUgIcwOPYuEarxyvzwm06uvrhdlEtnvLg8JnP/tZUfu2tLQ0LxXwPffcQ+Xl5XTdddeR2+2mM844gxhj9MMf/lBsM2/ePMEYahgGzZs3jwBQR0dHjqlFTniSeWwWLFhAgUCAFEWheDxOU6dOpWg0SowxYc5atWqVMMsEAgHSNI2mTZtGNTU1FgZO2W/CBxR+bZFIRPgn5LyHb3zjG4J/aPbs2ZbM4Msuu4wcDgetXr0674DE7fSKy0FGfRl5zplMk792L5V+7TbBK5/49n1U//hn6PJvfoFeWffeEK3BcSZ9AT7Lrj/+ZOLEifTWW28NdjeGpIC0Jrvx6sbV+I+3/oIP2nZjK7rRtXE7jLoysHQGyS270f3PTWiIJNC1fjs2v/kuulvb8f3vfx+LFi3CpZdeil/+8pdQFAUPPPAAnnzySbz//vuorq5GKpWCqqpgjCGVSsHv96O5uRkAoCgKbrjhBrzwwgtwOp2YPHky/va3v2H06NF47bXX8Pjjj2PlypUgIlRWVqK5uRnFxcVIJpPYvHkzTNNEMplENBrF5s2bMWLECLS2tqKpqQlf+tKXcPfddwMAZsyYAYfDgd///vcAAL/fj9bWVjQ2NuLtt99GMBgEESEUCqGtrQ07d+4EYwxjx45Fa2srNmzYgN/97nc488wzAQCXXHIJ1q1bh/feew/hcBi33norfvSjH2Ht2rUAgMWLF8PpdOKll17CZZddhhdffBHJZBKqqmL06NFgjOGDDz5Ab28vNE1DKpUCYwz8+00kEti6dWvOc1JVFeFwWPTvvvvuw1e/+lXU1tais7MTu3btgi8eQW+xB5mSIig+F/xTRiHtdwEAMi0dcDtMVBtFmBiM49LpZ2J0OAFdUQf2BRuSwxbG2NtENDHvuiHAH5KjIUSEja178er6f+CPa9/D65vXotVkILcJAOj5aAvMkiCq3UG8+5s/o3vjDnzh7uX40rL70dnSCq/Xi3379sHn86GrqwsXX3wxfvzjHwMArrnmGvzwhz8EAIwbNw6bN2/G3r17AQCBQADJZBIdHR1wOp0IBALYvn07FEXBeeedh//8z/8EEeHCCy/EBx98gA0bNgAAfD4fYrEYurq6sGnTJgGiiqIgk8kgFArB7/fj448/BpAdaJYvXw6Px4PHH38czz//PJYsWYJ0Om25DxyEVVVFJpMRgBwOh7Fv3z6xfVFRERwOB3bv3g3GGAKBAPbt2yeOUV9fjy1btiDw/7d37sFxVfcd//z2qfdqV9bL8i6yCBUmITaCYoOdDAGCGRNQoHHiMOPak7gGAp32j06HkhmPmg41KTOdaYd0UmE6AU8mCXFxTRIbYhqomxJsBw+2bMuSjdDDth7W0/KuVivt/vrHXmtkIclSpN1VtOczs7Pn3nt0z/f87tX3nnvu2Xu83jEj93g8jI6OEgwGKS4upqura6yszZs38/rrryMiFBQU4Pf7qa+vp6+vj+3bt1NbW8tzz/89L/6oFnuBB9fyUpavuY1ODYPNhs06Tpy9yI2Bcv60rIL7VtzGnWWfoSAzOyHnjCExGMM3pARV5WJwgKPnz/Gr9/+HlliQtsggg24hFhrGlpMJQPjUJ6BQ6srhM94i3tr9U6K9gzz75F/yDztq8Hq9BAIB7HY7+fn5hMNhDh8+DEBNTQ07d+4kFApRWVmJx+PhyJEjOBwOKisrOX36NKqKz+dj1apVYy327du3c/nyZd56662xu4fq6mrq6upwuVw0NjayevVqPvzwQyKRCJs3b2bPnj0MDQ0B8QuA3W7H5XIRCoVwuVz4/X6ampqIxWIAbNy4kT179lBaWorb7aa5uRkRITs7m2AwiIhQVVXF0aNH8Xq9DAwMAODz+eju7ga4phXv8/nGLgrl5eU4nU56e3vp7+/n4YcfZt++fRxvPMOaDfcTy81g3aMP0TESoiN8GWdZIbbceKt9uLGNjOVLKRi143fncXNOAY/cfQ+3FvnJd2cl/LwwJJaEGb6IbARqgBXAnao6qUOLyIPAvwB2YJeqvnC9fRvDX7yER0doGezlWNs5jnzSwLvv/5aRZT6uuIWo006ktRNXoBiAkfZuNDjMrYEKhtq7Of7O/yLhCLt/UMs3H6rmhsISWpubqa6u5uDBg4RCIbZu3UptbS0vv/wyTzzxBNnZ2ZSXl7N+/XpeeuklAoEApaWlPP/886xdu5b8/HyKioro7Oykv79/rLUP8MYbb/D444+za9cuWltbee65566pS1ZWFkNDQ6gqNpuNHTt2UFNTw5YtW3j11Vevybtp0yYOHjzI008/zQsvvEAkEiEjI4NwOAzAU089xWuvvUZWVhZ9fX0UFBTgcDgoKiqioaGBz61aybGz9XzxofX87vQJ7J5sVt37BXqiYTq7OnH/SQBblhuA4YY23JV+XOFRssMxSnCz9rOrWHPjCj5X7Gdptgeb2BJ9qA0pIJGGvwKIAf8O/M1khi8idqAR+DJwHjgKfFNVT0+3b2P46Yeq0jsc5JP+bk6cb+LkxRaO1Z9iIEMIOmHIJQyfu4Cr0j/2NyPtPbg9OWTH7HSePotEY3zlS/dz+N1DtJ1sID87hxe/949s+cYm7JEo3/nWX3BX1R184+tfJy8vjzVr1rBy5Upqa2txuVz09/cTi8XweDyEw2FGRkbIyspi5cqVHDp0iG3btvHKK6/g9Xrp6ekhLy+Pxx57jN27dwPwwAMPcODAAYqKiggGgwwNDZGbm4vX66WlpQWn04nD4SArNwdHdiYjdmHYptxy+yrqzjUiGS4yCr2s/fK9HPq/3+Is8eENLCVkU8ItHWTcHBire7S9F+cSDzmjgqs/RHlhKSsDN/J5fwW3lPi5IbeALKcr6cfRkFoS3qUjIu8xteHfBdSo6npr+e8AVHXndPs0hm+YSExjXBq6QkfoMk3dHZxqa6KxrYVBe4zucJCOixcZLcwj6rYTc9jHWrlXGTl/CeeyQgCiA1cAyHFlYIsql042YvfkcGP5cj4+00ikq49bV99Oa3MLg/0DxMIRSpeVUVV1G7/cuw+b28m6dV/g/d+9z+hgiMLlfkrKllLf0EAsGMa5xENF5U00tbaC3YavtJgrkTCRrl5cFUsRpwOA8JnWa0x8tKMXR4kPeySK9F0hy5VBaW4+hZk55I0In69cQWVpAH9+ASWZeeRnmC4Yw7Wk2vC/Bjyoqtus5c3AalV9ZpK824HtAIFA4PaWlpY5azOkJ0OjEXrCQQaGh+gNB2nv6+HCpU4uj4TpCQ3SdvECw3ZQh52h6AhdzW24lxYStUEkFiV0vhN3oISYKJHoaNzE83NRINo7iHizsYkNUSXySQfu8hJsgEZjhJvb8Vb4cWJjNDyMfSTKEl8BmQ4nVy52sSwQoCTfhy8rF68rk7KiYoo9PrwZWXicmfgys80oGMMfzHSG75jBH78DlEyy6buqum+u4sajqrVALcRb+PO5b0N6kelwsSzHxbIcb3xF2U2pFWQwLACua/iqev8cy7gA+MctL7PWGQwGgyGJJOMx/VHgJhFZLiIuYBPwZhLKNRgMBsM45mT4IvKoiJwH7gJ+JSJvW+uXish+AFUdBZ4B3gbqgddV9dTcZBsMBoNhtly3S2c6VHUvsHeS9ReBDeOW9wP751KWwWAwGOaG+eWFwWAwpAnG8A0GgyFNWLDv0hGRS8BcBuIvAbrnSc58YnTNDqNrdhhds2Mx6rpBVQsn27BgDX+uiMjvp/rxQSoxumaH0TU7jK7ZkW66TJeOwWAwpAnG8A0GgyFNWMyGX5tqAVNgdM0Oo2t2GF2zI610Ldo+fIPBYDBcy2Ju4RsMBoNhHMbwDQaDIU1YNIYvIi+KyBkROSEie0Ukf4p8D4pIg4icE5Fnk6Bro4icEpGYiEw5zEpEmkWkTkQ+EpGEz/wyC13JjpdPRA6KyFnr2ztFvqgVq49EJGEv47te/UXELSI/s7YfFpHyRGmZpa6tInJpXIy2JUHTf4hIl4icnGK7iMi/WppPiEhVojXNUNc9IjIwLlY7kqTLLyLvishp63/xrybJM78xU9VF8QEeABxW+vvA9yfJYwc+BioAF3AcuCXBulYAlcB7wB3T5GsGliQxXtfVlaJ4/RPwrJV+y1u9fAAAA4BJREFUdrLjaG27koQYXbf+wHeAH1rpTcDPFoiurcBLyTqfrDK/CFQBJ6fYvgE4AAiwBji8QHTdA/wymbGyyi0Fqqx0LvGpYCcex3mN2aJp4avqrzX+Zk6AD4i/d38idwLnVLVJVSPAT4HqBOuqV9WGRJbxhzBDXUmPl7X/q7N/vwp8NcHlTcdM6j9e7x7gPhGRBaAr6ajqIaB3mizVwGsa5wMgX0RKF4CulKCq7ap6zEoPEn+bcNmEbPMas0Vj+BP4FvGr4kTKgLZxy+f5dIBThQK/FpEPrakeFwKpiFexqrZb6Q6geIp8GSLyexH5QEQSdVGYSf3H8lgNjgGgIEF6ZqML4M+sboA9IuKfZHuyWcj/f3eJyHEROSAin0124VZX4G3A4Qmb5jVmc3o9crKZyXSLIvJdYBT48ULSNQPWqeoFESkCDorIGatlkmpd8850usYvqKqKyFTjhm+w4lUB/EZE6lT14/nW+kfML4CfqOqwiDxB/C7k3hRrWqgcI34+XRGRDcB/AUmbE1NEcoD/BP5aVS8nsqw/KsPX60y3KCJbga8A96nVATaBhEy3eD1dM9zHBeu7S0T2Er9tn5Phz4OupMdLRDpFpFRV261b164p9nE1Xk0i8h7x1tF8G/5M6n81z3kRcQAeoGeedcxal6qO17CL+LORVLMgpzsdb7Kqul9E/k1Elqhqwl+qJiJO4mb/Y1V9Y5Is8xqzRdOlIyIPAn8LPKKqoSmyLcjpFkUkW0Ryr6aJP4CedERBkklFvN4EtljpLcCn7kRExCsibiu9BFgLnE6AlpnUf7zerwG/maKxkVRdE/p5HyHeP5xq3gT+3Bp5sgYYGNd9lzJEpOTqcxcRuZO4Lyb6oo1V5itAvar+8xTZ5jdmyX4ynagPcI54X9dH1ufqyImlwP5x+TYQfxr+MfGujUTrepR4v9sw0Am8PVEX8dEWx63PqYWiK0XxKgD+GzgLvAP4rPV3ALus9N1AnRWvOuDbCdTzqfoD3yPesADIAH5unX9HgIpEx2iGunZa59Jx4F3g5iRo+gnQDoxY59a3gSeBJ63tAvzA0lzHNKPWkqzrmXGx+gC4O0m61hF/dndinG9tSGTMzKsVDAaDIU1YNF06BoPBYJgeY/gGg8GQJhjDNxgMhjTBGL7BYDCkCcbwDQaDIU0whm8wGAxpgjF8g8FgSBP+HztJsOTdG2FUAAAAAElFTkSuQmCC\n", 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