{ "cells": [ { "cell_type": "markdown", "id": "8cad06d6-2274-4e76-ba6a-aede1ef91f85", "metadata": {}, "source": [ "**SOLAR WIND HANDS-ON NOTEBOOK**\n", "\n", "Our goal is to numerically integrate Parker (1958) type critical-point equations (with a number of physics bells and whistles added) to solve for the radial dependence of the solar wind speed." ] }, { "cell_type": "code", "execution_count": 149, "id": "9913e4d6-488c-45b9-b218-b81efe2c5f36", "metadata": { "tags": [] }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy import interpolate" ] }, { "cell_type": "markdown", "id": "5160d461-ad8b-482e-ab8c-e4d5c2c8f40f", "metadata": {}, "source": [ "Define a function to integrate the critical-point equations for one choice of temperature parameters:" ] }, { "cell_type": "code", "execution_count": 150, "id": "97345fc4-9940-4e60-a89a-27e73d55993c", "metadata": { "tags": [] }, "outputs": [], "source": [ "def wind_radial_onefluid(nr,rxmax,mu,Tmax,psi,delta):\n", " xRsun = 6.96e10\n", " boltzk = 1.380622e-16\n", " xmHyd = 1.677333e-24\n", " Gconst = 6.6732e-8\n", " xMsun = 1.989e33\n", " \n", " # set up radial arrays (\"rx\" is in units of solar radii)\n", " \n", " rx = 10.**(np.linspace(np.log10(1.000001),np.log10(rxmax),num=nr))\n", " rcm = rx * xRsun\n", " drcm_mid = np.gradient(rcm)\n", " \n", " # use the Cranmer & Schiff (2016) parameters to set up a T(r) function\n", " \n", " xstar = (psi-2.)**(1./(psi-3.))\n", " zeta0 = (xstar**(psi-2.))/(psi-3.)\n", " T = Tmax * (zeta0*(1./rx - rx**(2.-psi)))**delta\n", " \n", " # now that we know T(r), set up the sound speed and right-hand side of the Parker equation of motion\n", "\n", " a2 = boltzk*T/mu/xmHyd\n", " da2dr = np.gradient(a2)/drcm_mid\n", " RHS = -da2dr + 2.*a2/rcm - Gconst*xMsun/rcm/rcm\n", " dRHSdr = np.gradient(RHS)/drcm_mid\n", " \n", " # integrate the RHS to obtain the Kopp & Holzer (1976) quantity that is minimized at the critical point\n", " \n", " RHSINT = np.cumsum(RHS*drcm_mid)\n", " ircrit = np.argmin(RHSINT)\n", " interp = interpolate.interp1d(RHS[ircrit-5:ircrit+5],rx[ircrit-5:ircrit+5],kind=\"linear\")\n", " rxcrit = interp(0.)\n", " \n", " # at the critical point, interpolate to find quantities needed for L'Hopital's rule\n", " \n", " interp = interpolate.interp1d(rx,a2,kind=\"linear\")\n", " a2crit = interp(rxcrit)\n", " interp = interpolate.interp1d(rx,da2dr,kind=\"linear\")\n", " da2dr_crit = interp(rxcrit)\n", " interp = interpolate.interp1d(rx,dRHSdr,kind=\"linear\")\n", " dRHSdr_crit = interp(rxcrit)\n", " \n", " # apply L'Hopital's rule to find the slope du/dr at the critical point\n", " \n", " ucrit = np.sqrt(a2crit)\n", " ducdr = da2dr_crit/2./ucrit\n", " dudr_crit = 0.5*(ducdr + np.sqrt(ducdr**2 + 2.*dRHSdr_crit))\n", " \n", " # find the array indices that surround the critical point\n", " \n", " indr = np.linspace(0,nr-1,num=nr,dtype=int)\n", " indcritLO = np.max(indr.compress((rx < rxcrit).flat))\n", " indcritHI = indcritLO + 1\n", " drLO = xRsun * (rxcrit - rx[indcritLO])\n", " drHI = xRsun * (rx[indcritHI] - rxcrit)\n", " \n", " # set up the wind speed array u(r), and get ready to integrate up and down from critical point\n", " \n", " u = np.zeros(nr)\n", " u[indcritLO] = ucrit - drLO*dudr_crit\n", " u[indcritHI] = ucrit + drHI*dudr_crit\n", " \n", " # integrate up!\n", " \n", " for i in range(indcritHI,nr,1):\n", " drcm = rcm[i]-rcm[i-1]\n", " DDD = u[i-1] - a2[i-1]/u[i-1]\n", " u[i] = u[i-1] + drcm*RHS[i-1]/DDD\n", " \n", " # integrate down!\n", " \n", " for i in range(indcritLO,-1,-1):\n", " drcm = rcm[i+1]-rcm[i]\n", " DDD = u[i+1] - a2[i+1]/u[i+1]\n", " u[i] = u[i+1] - drcm*RHS[i+1]/DDD\n", "\n", " return rxcrit,rx,T,u,ucrit" ] }, { "cell_type": "markdown", "id": "4ed37bc2-6f66-49b6-8fb7-836f38a0e5a4", "metadata": {}, "source": [ "Our FIRST TEST will just run the function once, for representative values, and see what we get..." ] }, { "cell_type": "code", "execution_count": 168, "id": "e8181ca5-0042-482f-9803-2a45ffc8c99c", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Wind speed at 1 AU: 459.8572233748986 km/s\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "nr = 90000\n", "rxmax = 2150. # that's 10 AU\n", "mu = 0.5\n", "Tmax = 2.0e6\n", "psi = 4.2\n", "delta = 0.6\n", "\n", "rxcrit,rx,T,u,ucrit = wind_radial_onefluid(nr,rxmax,mu,Tmax,psi,delta)\n", "\n", "interp = interpolate.interp1d(rx,u,kind=\"linear\")\n", "u1au = interp(215.)/1.e5\n", "print(\" Wind speed at 1 AU: \",u1au,\" km/s\")\n", "\n", "plt.figure(figsize=[13,5])\n", "plt.subplot(121)\n", "plt.xscale(\"log\")\n", "plt.yscale(\"log\")\n", "plt.plot(rx,T)\n", "plt.xlabel('r / Rsun')\n", "plt.ylabel('Temperature (K)')\n", "plt.subplot(122)\n", "plt.xscale(\"log\")\n", "#plt.yscale(\"log\")\n", "plt.plot(rx,u/1.e5)\n", "plt.scatter(rxcrit,ucrit/1.e5,s=40)\n", "plt.xlabel('r / Rsun')\n", "plt.ylabel('wind speed (km/s)');" ] }, { "cell_type": "markdown", "id": "1ee0c01f-5817-49ba-b972-085fdfc55d3b", "metadata": {}, "source": [ "Nice! Now, how about reproducing Figure 1 of Parker (1958)? Isothermal temperatures have delta=0" ] }, { "cell_type": "code", "execution_count": 169, "id": "b0d0b017-35b5-4187-9d82-02c0c2f511aa", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Tmax = np.array([0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 4.0]) * 1.e6\n", "nTmax = Tmax.size\n", "\n", "nr = 90000\n", "rxmax = (95.*1.e11)/6.96e10\n", "mu = 0.5\n", "psi = 4.2\n", "delta = 0.0\n", "\n", "rx_grid = np.zeros((nTmax,nr))\n", "u_grid = np.zeros((nTmax,nr))\n", "T_grid = np.zeros((nTmax,nr))\n", "for i in range(0,nTmax,1):\n", " rxcrit,rx,T,u,ucrit = wind_radial_onefluid(nr,rxmax,mu,Tmax[i],psi,delta)\n", " rx_grid[i,:] = rx\n", " u_grid[i,:] = u\n", " T_grid[i,:] = T\n", "# print(rxcrit,ucrit/1.e5)\n", "\n", "for i in range(0,nTmax,1):\n", " plt.plot(rx_grid[i,:]*6.96e10/1e11,u_grid[i,:]/1.e5)\n", "plt.xlabel('r / a')\n", "plt.ylabel('wind speed (km/s)')\n", "plt.ylim(0,950)\n", "plt.show();" ] }, { "attachments": { "1d165079-b44e-470b-a3c3-3739274c0cc6.gif": { "image/gif": 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7AABlMFzwIAQUkwXg8CQPMwyh1iWlIhFGAGaFUA0tIAQn1Qcn83UIEGEXuBnsIArKlmxK8GwOEG0IUACpMgA/sHaT4AzskAv+wg7wAG6+J5jMWRcy4oWCwXMCYAbOOBCaIg+xECvn/vMASrAIApEPl+ABt1AQ7KAkTCIPXHkux0CWB1AI7MCQECEefkAP68AFBCAIaPmaBXEMGyCfgCkYzsAIypabSeIACjBt0mY6brIDHiB/x/kvyQlu9cA9R9ScFsoXLCgY3JAqjbCc+1BVN6B1XdJmCLFwBOAERAgxCkR0F+GaQ7BW0LFqrskALecGbVJ0j3EPrTBETOd0T4cLqHahQjoZeOKhfaGA0EEAAZAFNgWVPQAAc8AOw5CbTsAIQDkQ8VALHwYBVPkwoAYAdsAOa1cI1JCeDCEjaXcwSHBShQBmibAP+RANWaAkDzCSdHEPjEcP3RYLotAHmAZVZel9D2AE/rfJCIs5pIjaGr0CHYU5GJcIHUNwAgGABpVoENngAgAgCoCJD/EgBQNAAAvgdT7zpV0ieQDQBdogEcPnAAiwA9U5EBM4BfRADTswAA0gBJXaFvQAD6siD92WC36Kac9Uec92AYeXqMjKHA3yf476BjHqLACwCfApEGECAHwwm/vwDrVQBAfwAFHQcjxDqgCwAV3AB31yZxHRDhSCEM+BPwlZBPRnFvdAfexQDn30BjewA28wBV1iAAHifRHwMUhgCBZmpMl6sLChRo/xqMsDBYuzCU26D9UadAMBD43gAAdgAYZgsOcirsAgD8hwrh8hBNCSqmOhSOxQSH0UDNj3/gY+kKbOFgEV4HlIYAUmQLDlh7A6qx4KSxgM2zjXkAHQkVAEMbEGgQ/UIFsYQAZN4zaoEAJd0giCoAIEMIQfATojWgq5WhWg1EfakAyZQQ3O8AuQ8DItoC8M4AEf4wPdhQrAwAk8uLNyS0UlFaR/8aggMDbjsAFdUhBGW4zQYAcw8AFewAr/GTGoIAYregBC4AYpyhFYewArhQFnUAvaYKZKwQmd9QVOtQMrBQAwQAK0AR3iZQRQRwm4EDVzu7oL0rODMQ6A8gO9sAx1cG8OQmtGAALEqESYMAUEAANS1zOx2Ae4wAl2ug/doLl+UAiiCBKggwBWUAlfgCo30AXO/mUUjRU1FdcHK5oqBPBUT6BtmdAJSBU14Mq66KsgDRJzj7GhePMFMoAAfKALOACmBXENywCay/AC2TEE03C442IHMgAcHvB6x3sSohAoqbEOxDBELcAJh9oTnJAHRCBeLwkCn3sE16QImeELOSlf6RvCNtIgAKwX7ksACCAAU4AYUgkBVWYQYCBlCtAKH9IzazA0YBYGBzMBFqgS5BAcdDAQulAEaQcBqWcTqGCCEWJjCpAvv+kDQsYN6JBkfCfCVjwlDXKlgkEP5tolfIBc+zAPpaCWBqEJXTA0N9ANHGsnmmACVnC++xANCoQGpcAN6hAMYdBOmbDGHMEOo0IE/gNRD+VQB8+RACOgDC9BD4wgBy1gBS0wATnWJgegAlPwY56ADf9EDpJ2xZxcJYSZo6EAHUxSD6nERhvlDGgAAQWAA7GwtbviHPdpEM6AAwFgCu8wQPkgD5XgATXwlCjhxw9gCQUxD7XQJSOgEpOQbM6GAAYQAEoKHThgbXYgdu8pD+AGmp2czXPiuhqqwA3hBtTryuPiHqu2D8J4A+K8DQxFsSPhx5l4ELxwmQAAXB5xD7WAVCYXVQjgBBanzf78ynX7GpbWAgJgA6HAx5VyTllDENfgAgbwqgMRJm9gjSHBDmnnA8E2EPiQnR65EPiwq7WwdqLiAXMKZpW3ABdw/puFEAsI/c8uHSkNcgiuAQ+MFAApIAoUzSL5QA/xgJwY0QTvQRCa8ABfQNESndMfAQ9GMAAv8LgRQQ+++ngQl6YmnQDOZgfKBokvvdXkksWt0Q1oEAALQANwrCDsECTsoA4rywc+cAA08BBnfRBtersC4ZpFiRBhEgYSeRLx8ARIEK8J0Q71+k/OsK+p8oEX8AEmcIJc3dg/M3e02QstEAAb0Esuwg7d1Ai38AX8qi8HsQ7oQErGMAYVORBznZ+lkNECQQscwAG7GxN5KFRrAL+/+TGDKF5rkAlO7di8DTGQXRnsIAkHIwNh+SLv0yUD8DEv8DWifBCsIAhlKhDr/tACBSAHcg0d1emaRf3ZhcAA1+oSRsYNzeALvbDZX5AqHFBjy+0DSsBdtDCtvR3f4VpSqvENZmAAnATRKyIKFQxRhRA1hFNVIDZhRxAL4uIHArACqzjXmOIc220QO4oBxVChJ0EOjfAETSUCiUYAPuAFEEULjTV18j3ibmML8AMAERwZtMADi9MISG3WzGgQ4yADAKAC8L0P45AHOyACPeADEFAkCNENN2MF+bQMSnAE4fJgCGAH4hwS3BUHliBeM9Am7xiPmfEL2xA7JL7ll9MODgAdLywZkCAD4lEIWj4nrCBlDkAJCDEOzyAEaXoAx3oQVYUB6xrGsCADLDAM/jr0DqgAHLGAuRkxDpzwHeNFGxGgnRjgXvOok1z+6JmToYPxDXLQAIvjDFU8J/adXg/wAWVtDl/OLVKQEPnlcQRRD2ZwAIltYYZgBOc0BTV8ERo2aFLwMRwAAZa1aHKQCn30DSUM6cDuM5IeGM6wAr4ZrRReJfmgazTwBhjFAKJqELRnAlo8ELgAHSZQEPJQCM8hbZPnAbGAnhTBDrGABh7wALyZoG6SBZjWDdwGbske7PION8PuF/SQCpaOTsCAzXWiSMn5DpfJpQaxe/MyAil+D9CBbvVXC3pwmXYwCe0Q7wtBD33wALvZzMmyA3qQC+zQDvEAboI+7yIfN/XO/hf3UApd8gVnjivcoigDsQxSFnNS6c0GkfAdQQyFgFSAmvJ9sPIj//PeU/J7gbXvPC68EG8ctr8gZi3DcwG7bfMWwQ5JtfOy0gf9CPRY7z9Cfxf3AA+XGQAa0NG6cu0DMAUDsQb28+IDoQQLAAYPgaeCLaZ2UL+jsmcNwHmBoNVZv/e9gyfeCRj0oAqAkgAtgMjl4pqdNhBQEAF9gNBhfhAdX2ncUArDAh0feD0foAMWtop83/nd84iB4QrwgwBdYPjl4qwBkGYCEQ2agK0Qoaf26nTUYK4f+ACnV4KQYPqev/taDx3s2xeLRSKCciv6oA7eAN/MAB0JUNoVQQ/c/mBMkyAGNA4AF6AEhshdN8772v89Wy8XKXUzWUDPk1IPkTAEdiAzAyEKwFEAaHAR2pALmbBWP2CLOyBefQAKu739+t8/3Q8X88AJAPECwBVq+wweRJhQ4UKGDR0+hBhR4kSKFS1eZFgvEQAIP770AVkCAIBB3SqOAwbqD8guOziMBIDhxpZbvHhhxJlT506ePX3+BBpU6FCiRY0eRZpU6VKmTZ0+hRpV6lSGD0bGopqV5ztSGACQQKdP61iyTfWBE0QCJswvvSTWM8apkBUZISQEgMngy5pMvZJhSye27GDChQ0fRpxY8WLGjR0/hhzZoSYEI+dJJtsOjgQAHHJh/gZtWF88aonenHbGbR1ERomkeLgAgQGBkTHWvOHGrdu6dvVC/wYeXPhw4sWNH0ee3DCjAyOVJ43nhEHnRvaeXw+a79067vkaomLU4sMHCA8qj7zx5lK1cdyxv4cfX/58+vXt3zfO3Dl+nfCM0G4BGuv4I5CibtB4IAEE8BrJDjsKYYedd+YZsEALL8QwQw035LDDxfQDwMOHgHkAQGG8E9HCQvp4oAEDYELDjlbYmWceelLEMUcdd+SxRx/jA/FHYGC6YJkfgfTDj7U4cgKkbY6EMkopp6SySit7CpLHe2pZAAAEpDjmSuDooQceckSxYweYCDjggAcuKGQSZ8Sk/vMgdlqxI4sH7LCGonvYqaUdfBSK0KF7yqwzUUUXZbSpR87jER9duiSgikYbKzNCO+agYc0DFHjAiEIKuVRMeHAYic0CApkInlhQtWCYQRGy6saF6KlFjx1sLbVXX38FFqFeugxRx3pwqcBLK4ItCx92yMmNjx0GgCkACDL4wApGeuGVWSjLuQGAADAg4w85iJloiJGsYgEYhNpxAAA/FKqnnD6ae2ASb/flt98j/2iuWBznIUWtB9LwN6p1lumllC9gWOuBD3zwQQlRrklYSjUBMGCNYKi5bCKraqCEAwbEQAiVBORFiB1qOtmBAhd64CRjm2/GGT8rqBVYxHt4/lHLgTTkyTkpdrjppIW1MPhABx/WqLloKK3K64hWyBEZgE9umQIAHxKy6g2D8KGmkSMYcGAMY2aVum233w5NjgL2S5EaiGGAxDe4f1qHmF4MCSMIEAA4wIcmWeEl5L15BIZYwiGG4A12JFLag5EQWBYhJQAAIR9o7ID8CUreWbx0008nK0sP66Gl6zWSuQd1nN6BxAobRgCBNgBg6AWYbcaRXT5RktGpmwYAGAAHYJJZg6NiJHIGYo6vwBihQkbqQYWRYKiEHBTdXkaU4McnXynVOTwWBQaOoCb28iFahpM1fHDpPACm+OILZt6HD5UTXjASROrxiWgsRE0B8MA+/qZxhJG4RSLL+EIZflE96y2JBLRYDc7GwQkOclAJPnjBCVDBPxLiDB+2eMJ4dNCCPzCiW0I5n4bw4YpkqYAZ3yshQpRBhhHExn7pCQY31OGeHD5HP4Z4CCPGAwEM6GCECCFHuALwAQ28iAPKoMg6JreQ68GkArhwX7C+AR5GlLGMUhiBFYoAATayUQCXY0QR5eiteEjBAgEjgAAcAIEPoAshY9SBHNqxkHbIYTxPMMQLExLDDOUiWQ4wQxhz2A5UyKEFGFgZTA5QhFm0R5JzTI5+5sUQTZgAAmshQAieeBBWLIkD1elJF0eSgDwkqh3RGKMZzTie8WxgAm1sY2UQ/vCiJQHgBnNwICiVean/HGAIWQDADpzBjlwsgAEIccYKEiAAAzyAFmzbhzN0QEw2GcFdDDEBTDrUOMINrYj0KIQddKAAAzAIAA6qBTviAc5lhrI5o1TIJC5QTHGhYE4HuQc4UAUAD8yiQjvp4kIrID4qLeIBF32AAxjQAAUhwKMeJWhIWwCMCJWUHfCYxyf7udIr7YAAmUvI5twyj1IQFCsGGQfEfNAHVqxICABIZkJ2NpJzaggmH8ghMPywsbXAwA4ZZGlh+gAAAjwhgD0hRpd+sBBOWGUHNzHIPDhxt/0hZUgA4AUrwgUCP2zRQ4VIUlz98IWQ1nUkfcjDDR4A/hJOLKwQiotqYH1lh5j48SCMqMxNoug1TvCib10yyD1q+oInIcQHPUNIVkeiBHr4IWoW+sFILmBY8i2jEPaDCQS80FfBZmUdnUjS4GCipiIBhWoK2YZAAODWg/RiJI1QpFDOSqp10BUAwOUPXIdAWLs2FwAggS4HWQHY1laXX+wI2AOyYAclNAcB7rpHKHZnkoMcAgF22Mc7aBACiiJkqoKoypIeoIYC0YOBALhAmMZHD3mwYxKWo+oBFnABRhzUulTxLcfatNd90AMR+v2JBUbyGYTgwgMKSAU/98ENIADgC7wlShdJtQ92oGEBAaBBNYILGTK1mEzxMGksHDRj/u5SbUlsalOOF4BRjCphVD8+cJBzNg84hBQNN5pHGASghIQcYzokDgARFjLVIdzKxjCJAYE625z8ym4e6+CGM97QNY49wANSYASEhZwTffSXHOgABzfIQV2I+JYBcCjjih1iD3AIZh/z0A1DCvFPhNwjDwBgRXDboYYBfBgpIs4sDVaGhmqQQ89k0Qc71BHn3HT6NJ8+TRECFlIDUMADvByPCcigyzKSds2vlho4aBCABGAL1QgoBT3YscfPHsQqJD4AGqYMgAcsZFiXu2gEoMCfetAQv66GWzuOVgo0wGQAE+gAEhIJ653ogxuXeMMNpvASGnji0grx7RgGiZFl/oAAHGFVBX4FTeiDXEMLAOBGQ3jxgSxAtSiQRkg0yOAVY6oCxFKZh0kjBC0xh+Elzh2JAx5gAYxeazxIQMW5ub3xtmUhABvIAwUNQthWzOMNEOg1ieNF4miSrmV0bcFCVDaSOHAQFSKnD8E484Crwm0d0PjFGowLAAFE4ARWoIXLOY6TfAxDewRg2njw0gjyRsS3dtDwRK7xtD6LQgEQQC8X6W0QXlw23wzZNwnE8eiRjDghqKjBGw2AhnUTBR+dxvsverF3vveiEfkD/BeUtqSoj8cHIIgBxRTvA0hwIhkdvNjSJS87ACRglQjphrxMzgC3G+S0IGA5Buzwu8sQ/qMMRF2IZjF7n3VwwiscqMTe6NGKuaJAdyDwgRACAYqeT/4is7DcBdyAOJsEojnClohvn4A1nCzjAFPQgwkE0IeGDJplByk7vvX9Ae0fBeAK6YYZRrIAaO/EF4KIqx1+sH72/0B3zh2AD4wAXZ7axCb78MU3fL//EgKgAfpPiG8QPz8wuZc6iHEghRMAgU7YB3gIF9Uygzrog//wMIZgpPoQK4F4pYfKGV3QhD4AHZiYCT7oBF4oKv7DiB0QABagBODRHACIueTjnDeALk0wwYoYqJHwgMoSuwrEvssqBTozCFa4AAx4t6MYroboBj8IAjMAQIr4Bl+wvynkBJAA/oL3ay4RaL8fuIIj2AI+SJJA4IXyQ8EyJKEsGAAe4CAjoQU6sIE3aoV8OAYV2IBC4IQ88IEJcIFhMAg5VIslyYJe8DeEuED6mAaIIYFc4ECbEQVO8IEPsDGnigXA8DMzxAgYyIECUghoKraIeAfmIoHpIDYQCAEiiLyI0AJi4rnqaw4IQIhpsAIAKAJzWIh3cAMCsAN4SIpGAICbaghuOLiD4CBneAe5WLwYAIFkVMZkPKViMoAdyB87iIVJuAW+Y4ZtwEZsPIdvCAxL9EZQooYsIIBkfAEfOAEJEIAWaITVqIdcQAEMAAEKQIEsMIbvqYdeEATAi4Ve0AaHKET5/kiHK0AADCiFRfQXWsgDIggB2RqAGliDXliGcVCpb6wIZjAwhLCDZOlEiCguADiC3umFMqCrLBAAFOg8h3CDUYOBi0QIcaSbP6sDAHAAb1iIaXgBEugFHCqKdeiFYGwIR1y8ZISBHQABgoM4GKQFvvuFZ8BGiWwHnaTIqFwmfVgHMRuzKSgCNHCGOTsIsjGNS6CGdajEfciHeOCOdYBKhfhH+DCHJjCADbQZerAFQ5oABWCQN6gDOas7qfyJaJiBTFIFicgHZkiEGzIIdgAzWQsAG9DEh0iBALCN5sgChlAC3UmIZ9AeVuCnaBgCAhAEdJAKMjIjKUC1ZoQ42ziN/rzEu9wgh7Hky9dsLX2oEXmQB5RyTX2oBwpxzYtYS+yAhyCgjS3AhrjsgxsgJgCIkTkTQtjUCVFQAbzAgViYSIbIh3pIy3GggQE4AojoBrzwhHdgIAZYhIUwvpckSzUQMFroyljIgQHwgGTYzZ7ohkn4sR8zAh5LkI/yKCxcCzigsQdROJSqkeVkzgI1UNYIGPzoAwCZhrQMlkK4zwOglh0QhW6okQP1iRLbJhpIBXaYTou4B08Yr4cYBADYBHdIr1hAgJP0vARNCHmwHM4rhEAwAgWgli1QB6DAB15YqhbRz4/iz2JKnj2RxpIa0AHVOAxV0iVVSxetD14Qrd7z/hZGUJfL8QIpZVKMmIdOkJ5GIFCc4AbOASuGKC4YYL4RIZbUy8G1gAA36AlOSJIqPUoA+AD6o4UPzdI81dOJMAQnlY97iIWRaAAw2Bd9cJXuGgk3cQJ92dOcmIdNEBcFQIOq4xsuAIExbQifVIhFIJbxFLQ3ebCEuIdBaTGFY4d4chCmIig22TEzQ4P6ZNFGldVZtQjuM0/4yIXLIVRmSThn2Bg2eYBC4ENavYh7MAVxwYD2ugh9+NBsaAEQ8IWfqII2kYh7OJQW04VYQAcHKbK6wjEEYAD8fAAlQIRhJdZzRdeLSCcvoY9y+CkA2NVfmQdyqIYwSBUG2ABEStJ0/k0IdiC6F7g8ixjMUiAHftKHbIgBAbCBJ8SSOCo0aSspaMGGUgC3T4uXtQgA/OwAXtIWRpiExuTXkBXZiSAD2oCB+WgHHaCWF/iVduiGX2gE6RmAoysEFxzZiXAGAJgA9ZSIP/gDhehIGCiFPjsIWmgBApABSACKo+GGbVAGvisFoQM86SkmFeiBxVOCDuIgpbvZrvXaJPJT7HgHTFgZACqVefiGYpiEMngRCEA8JeDZr5UIwkKqnh2Jn0WId+iDZlyDatw7a3mBuMWIhOq7XoCE/OEC7SkmiUG1DzgBxdOFrJPbyaXcJr1V5RiHPpiOLODBRZkHZvCDI2hGD1it/vyr3Lml04n4g7sFWk7wghMIGA/wgT/wBDJkCL/hu01IEju4r9k6PMVrEjeQwD6wwSnkBSw93eRN3t4sjkIYqB2QBkbJh2yghTp4gma8ATvYhM5VXodQk70qBOKbQl+g1H3w2YbYBlKAKz/YBExdCJvQBVBIK5AwgvYDMARAgfW7Aj3wg1zghRK0CSNZhy/t3gJWXuYdDlrYAABQgWiIzyrhhB54gYeDgS8oBWzAUwM+CFSCx2UkxR3YCXyIC639oMMDgQ+QgKJckhYAvDLoBKbchnNwUA2m4RreBwQOjm9Ygje6hAyOkmOAhGbcpETwJBt+iIhLBG4ohU8LmAMI/ruKUAZIKKPxiA1geqO1KJzTCCLWPEt20BsjBuMw7gLLvI52sITK4IMcrRNU6IINOKX4a4Vy4NowXggaUIBWIJ0v4w6801SDoIcy+gMd4CUMaKO14IBP84Q6qIZO6wZy4A4fpuNINuARUKfnoAdJWJlCoEUx6QZRaIEEmJt7OilIDuN38NCIYAdRGBUPwE+POoArXpJ8ipB2GFB72FdJxuUattXVM44wBYAfODsr2VLZGokd0INcxon1tQMEeIOj3CnoImBkluZcHipeJg4H5IiUkxLJWpIvGMRpdojW8wNirisaBAn3Bed0VmeEmAKeUY51QBUB2M4puQd4YAfm/vKSBlCC8s3lQ5mHdnCHCEFVO+jWtTAAiROV+lTWdWbohkaIar5lyJiHWTMBkPUReACHRPAB7/oASMAiSb47JWZiggrXieMlMwpYh1bplV6Ikr0K5OgEL9EEKKEHarADguMAHnBTMP6GToPakOKlEaAYO+SEtWHpo0bqhgARRi2O6BGABvYRqpzY+2qivNHg3MCGvpPaoROACXBcp1G8DkrppCbrsr7hgOFn4OiGFQAABjhBHdkGTOiCcOGcLyi5090Gm1gR6Fo/ui4mEFi/I2CE441mszZspMbhx4gGHHgjptYRZ6CDF7AKAziCTFiGbxZZDrIExYOBZAzSmNBH/mvExm6Y48M27cNObMdAgjdyNB25hjyQgQjgGDGohGko7XSlBQ4iAhMGsCXBn15oi70jhmwk5dM27qRObcbQBNmmgT7WkD84gUzCDXaIaCU1I0P6gF+CALy4ATQ4gDdIYrwbon3A7OM27/NObsVwBlsNBx051QrACzi4a1rt5B9zgov6qOOECRxAKRr54vMG8ABfiPRGjG7AAbwwheLGj3vWgQNwgUlNqUYFhlHxgxbpKATAQiKdhFiIBXI4KQEH8RC3XGuWjKkCgFJQcPugh2YeiQUsbwOFUz9ArWIy5z54axHH8Rw3CAIvDH3IBA8YgCAoBxFxlYVKgB1I66i8/lZ7fhZgcAY9SdQcM7NCqFAdt/IrX6SwxYx0gKYaONMNuYd42BgE8ICFpshDkQdpywU9SBOMNYAGuKg+GBVPxfI6r3MeH4x8WAUvuYTqjo95AAdWKAJiM4GZ/saIzY1qALcpuNh1uahraQE5YFg7p/Q7b8XfyAdnUAECWIJJt5B8YIdUeLgPcNgyxAdoyY06OA2/pqqStoDxMKOPrfRZr3T9+ILQ0Adq0J4XYIUNsQfg9goHyIEy1Adt2LtSoNqR4KMPEGofsAKiNmpal/ZZl4MXAT3QkIeuuQDWwhB7yIQ58AoIOANMuO01Q4m9Qz9dSa0boJg86IPGGsNpl/d5/rcC2rh2zAhUAnCCF7cPXMCDl0CAH/CDLxeybLAJVgAJMxCC9dMdBIirRqgFm0jxead4Ef+DFzlZzFgGDzCAIcA5/hAFH4hRj9mGwlamaGhENwChZDTKkciC/Omdipf5md+HMb4n0HACALAAW7gQZVCBN/aBVthLwfoGM9IBQoYA1DrkUui0s6T5p6f4dXVFybACBFAAV/Bz5IgGQ+LuVCiHrCefSWAE0uSANnq/9EiF3PiGAYb6tpf5XZaMYaCNI5h45AAGFQhlU4CHug976cBwmPCA7VIFD0cpvnf7wxdxW90qyFC9G6ePdeDFkXgDk38fdvCDNyDnRC11xOf8/rZX/Mio9+u7j3toBemBgU6gfNlRKiUJqR2ohc6H/cO31Sp7jCloDiPAjz9JhVkrACRIctm5h3mwZ2eYBERNlTZBAFcthN+P/eafd1sFqMYYKAJwfPgocgAogA2Y1PIhE3tGh1Z4g04ZiQFokx3zsThx/vSX/ZGI/sV4hzaJAvtw2XdlgC6waNPRDnPwBj54A1WltQkAiA1IDDECtu8gwoQKFzJs6PAhxIgSJ1KsaPEixowaF+Jjxw7fxpAiR5IsafIkypQqV7Js6fIlzJgyZ9KsaZPhBwAA/NzcWAjAlHg9h+4bF2yNAQAQZNCJRvQp1I36uGHrZWcHA50PPsDw/uGDSB5a46KSLWv2pD5spb58SXbvLNy4cufSrWv3Lt68emPm3KmX3AwVuEDuFTlvm56sAFq4cVb48cl23Lj16nXryxQUGD580OFjDSfHkEeTRqnO2BQCE16geocR32RyhBPS67WsNO7cunfz7u37N1+dPPHO84Og2FvgDtk1+oEAwI081ZT7Zle5kZ8xQX7o1OqEEy9e86iT740HxIpCpLZhzAfNzo8fTxopvFcKgI/y+vfz7+//P4AV9TXcXdPAAIA9/tUDzBYQAHBELNjkE+BenFiCxg0ggPCcTjB8IQYkvRDzzXgUmijXMg8ogEpRnIxlUTxTdAcAA/UkNM8b/vhBdI0Vbrx4IpBBCjkkkUVShMQAADyB1zudIHCEgo6wkNUX1CRnZFmicOIVCB44MOMUX9zCzDbcsIMlmjXxAgACiIiR4Q2FuEYRPDfMCAA6CdlzCQAb0OJQOlcgAEExaRp6KKKJKkqXIQewidczOwBwSH/ERPGlA4mcuShN7aBCRgsfQOBgdw68Ucpk6qyjD6etnjQPGgE8QIEKOjHgBz0U7XlnNwpVoxQnDOFjSxNJTWGOq8kquyyzzS7EiKMA3MWOGQPscA1/hSxAwAFKBGOjsykVYscDDihQQADd2WGHHx7Nc2W48U5kh048vBOLBwDsAE9F2NyJymz7cANA/gB/LASMEQoQ4EEs8rAqL8QRSzzxb9DqZBc+qCSlx8PlVfHcAYXEEzDFGC1SCALR6pSFHa2gMw/MJcusEDk6hVAIGQ7ewC9F8mwy4zcKjdOCB7gkNIwSC3SbSzvwzvw01FFLLZPF0tZVJwAvsFeeFRz+MDVFnPhBqlZ9MLI12FC/I+mMMJBz0TyNdLjQOl+AwAtCVhCgkxJp+/034IFLVHVd98SilBvlLfNCd30IfmMtb4Bw58WPh8vOGxD4wQ1DOHYHAzMZrcNJH2gjVPfd+yxzQeOWu/467OXpkw3RLKvSx7p2bIoQPvHAkytH8cxDDz0kK0Q4XeEQDKVy+YBD/u4ACgjBs9/10NMOO+vC0Z0ACDjwgBCBAB+7kfOwMz5t2d/pwSTodAwTO2Xoq8QDAChgBPkS5eOOR7mQUwu70Je/ARJwJuOwE+W0gpB7nGMWU7jBGqoxvv2VoghheMMbRPG2hiBPLvOgAQAw4BTgyCMXtWIAEWwhQKjlAx7g4EYi3vCl7kBgMzpgRDsKiCU7HMBgCmFHHdgEAc50YAKOigHnZtKLGTnAFcabmgD14RGPmEMd7OjGZLLIjVlwgHIIYIQOwyjGlZjDCRfYAGc+gIF0AaAEB7FHMWRkgA44qBUH0Qc4+ECjB/AROrs7XrTo0gqCzUA557hErRYAh6BN/o0d6+CGMxLRxe7w8QMmmIQyxggX802xRDOh1wcWwkMAWGESB/GUFBYAAEgkSCZL7A4a1iE1861DHOAgx2RYUQ0tOgODGLTgG1TGvQU8oAIXgMBWTKAJTTKzmRupxzJ+RAxVvsAx9igFBjCgAzGkQxQYgMFB4GEHApygEJw4JxEe8IU/IgR5+phTWdgBgwBsYIS+MUYWAECAC/QBnjNrRzN80Ysv5FMnCMDACnjgA0sEy5nxZIYi2MKWRhSDHO9ziR0EoAOFRKMBAADBQsZRCI+KJiZLRMDeVLAKbbCTWbDRIjd+UZmIZoEE30ygTgQwgTTy1Cs+VYI5gbEMLTm0/qhGxQgqEgAC9swjFSDwASc8iQYAAOMeTvXBbRLiBQCIgiFV84Mf9PCGP5XlJwnoqm+60Yl8LcANrJDl05bRC0OYQAA6GYAPnGA2VkzDaUcdCjDKMLk7QeAJsVjhSuzwRYXowK54Y4gcFpAFJQIABnYwgyp38IUkomkbwMgHNmphiFa0whBgPS1Y4ROf1e4NACHwKWy9koc+0LYPgSBFeHIbnr/ytrcYkUMBOnGQcezgB7yA60F+IqcMNTQhfQBAIbwqTDY5oSzASAEA+vabQoBAACTw0czmwQtW9MEJPyABCHrwgzAEghdZ9S1UUEEEAoAgDKeFj86SMaGRbMMX/oxkiGLBmJCc7MAh35CCCB4LkyX+gBvjQAQL7PoFtAJpHtMIDykC0QcvCGEPW7gBAmAAAw5xjwSrPfFqPaHbFfsVvi5+sUSicQIXHEQeYXAAJBbyk1VMwgBe8OdBnhvdheiAjTMqMFlakK5e9SYadKgAAMzQjBxSjBOZQMMOQICB7vAhGdvYRkthbJNrnCAAhWDG7u6xjT5khQ/gCsniVEAMh2R0owMGQEmlS6CXMDiJ0YDEgSqQB3vyZhnnPDSi6RCE2OqABRqigF27Y4AaSLTSjeiFL5rx5U1z2nRi/jSoJ0KGBMDhIOw4AASai5B8rYNclmCIEaCLk+7sAA0H/piCLspSvzf45g8fSAAAShFmZyljEiYQ1QNUdoNLOEMooX5KHhIQS4a8AwcAcACVKfINOXxAE9lm3RAQexBQKiQnwz4ItCDgSgA0GCHzOKD9TMCiwgCDEYzgNk85c8xR8ZvfwMYpUJyhxW6QYx0GP/g6PPnshTO8IiYIgCpMDSyFTAIBN5iHHS5gjIWA4Tm5mLVOCt6Nc7z5KWsoAA3O/ZhtbyBdm1B4uIhhBTVCgI14fUMiuEGOeOy34TZBRQog3uJ9+AAAYYB5RNJRCQ5IIBO5AoNOyvEQct9Z5dDitUnZzdnhglCnVpizWept77GT4dj6HpViAJ5ANPgSg3yY/sVk3OfzudM9I87Ycp72wY6JH8QZWVBlLTCeADoopOMAiEWL+4Jksziji4TfTTfMgC4agGPorqKHH4TwAAa0Vic70B085lHyutMkGS7AU0O6caA3iNsh+qgHNFqQADtE4Tl2gAjVEfIBHABZIVkgwJ5d0me6/UyfR2AyTIBRiOVPwhndEEUWLsBHPi4AAda/fgHUrhMavCF3dijEFMMPs/EP74mkPz/6FUIHBKChRLAKQDmXbwUG4KDy9xikATyAhkJEvwA4YMfQ9YUewMX64UDe5Qa1ZF8WhEO8FAIfHUDntcAbqAI6hF769QQ+CMMGLYQorIAA0MDWVUQ+CEML/hxA9u1A6x3EIIVSQkzBAajcCPhF1olAMzCEOxRfFyBXSyxf9VlfAqgAEiRA9mlfd+CAHeDAAAzBJIRf6JFfCl4gFEahQhQd651OjsxIKVyJfVDOzjzEgJwFJ+SEHTxhXrDDF+hEI+hgsogNiXXHB3CCp0lhVMxDKxxIZW1gRqyOcETE3rFgOx1ALDgEI9SPgvGZ1jnEmhUiRlTGPjACatkBBFyh2kGAD/QFANgBbcmhJm7iSQDDCRwAwNCGKLTAA6DBYS0EO8TC8p0iRHxhWeRDD+iTyuXFPPxMAEjbLKYJOZQC2+jTASzABRSCKXEiWdADOcwBCCFAAygB8mUE/j6oQbSgIETs3QUkQ0IcwwPgwArdgzBYAAAIwUwAQynmousRjzCMCzn4wbogIxFyzwG84wMsXyEwQp4Roz3eY0iIAvi1xD24Illcw+kFAfWMBjyYAsFsAIUtyj3QAzx0Axq0AAAYwAHcTyAYBD5ChTgZFPs0Y0aMIEQSQJKM4UOcWqopRBQQgEjeET3MQr4QAFmRhT7YA/HEQ/hNkTOsS77MSJIkCbdMZMr84vRNXwt8XyGQ4UUeJVL2hDJsmQzOISQ4AAN4Q2nMAznYiQC0AKElCvaUwhp0XQN8gBwwQi+YX1LKBDsIAQAkgDKVBDWwAAAcQBNYQf3UwX8tBMaV/uQ1bgAAvAE3dMM49BIHGIAFOIGzyUQLTZE3kAM78FIMvYEPTNeMMAAfecAQWcEIPIEJkIG92cIk2BvYlSVohiZc+CNU1OEl9p5etIMkHIgEQEFWGso8fMNRnGEAQMBr5ZhoEgUaGAAE3F5JwIMfMAADjEE67AMn1A8H1OWN2EEEzFtCiMILfEAAlIARZAUEaAEwjN5KPNI2KEMvxIIdSBQDtMAZzggfMQAypREIdIVPmRMn1ENC5qZ8zudZkCZReA4GFAppXAKwfYBvIko+kEMxcKVifAAJxIEoYAt92sQ3NMADJE5JzEMsbNkRnANCuMEL8IBzKgQ9GAINKKhC/hgaEViIGPgAeJlEX74UN1BDMFRGLzTCF3BBrXQHA3hAvo2AV7iBG4iBjmbCOX1CPS6okA5pVNjnUDDD5KQhadDCc3iBImLJNuRCWD0BqdyAD+QBL1gkkdIEtEyWSTDDgWBAK8DLNihnQuRDNnymSuBDZbSCH3QCdpzWDwyBav3AiN1JAYhBbfUBJeDCiqnplgaqoJKFHCRF8A3FEmGANY4GLZyAChyCGhqJKPjAC+RkCB1BKWDDNvTcoMYEtPwnSSSDTZXCQN4EKsTBovlAD2jIlkFAG+rEpFXaIeiCi/5CtnUqruZqWRRZUxJFOsjIE+ChXrzDlhDAL6hDmtCC/hL4QAjcFaXZQTFQA9LpaktAi3aVxL1UQqmuBCogGonC1ghEgJGFUKV9wazWqqZtWjpcFLW2q7vahJHeRDcYwA3EAqfmxTfAAQQQAB/ca5B4ig58wAREGnSkQsGh5ruuBLQgwAeMQBYsU0J4G0bcw7SGBDGMHb5xRgT0GzIlxYxsAjZo0Tcg3DrIQ8KeLMo+RV/UAlS0gx6l5F6YQxEwAAe8ATgQCT4Awx90AAV0XhiIgs5VbMqmRNWkZQRk5r21QAR4wK3CRDtkbBrtGwSkXXe8wQ20Xc5lkckOLdd2LVH0xZPWRMYcQNE8BjwEwQA8QCXQA7uayAMoTXdkgQa9/ovXwoTF7AA5bA8AFAACGAAbkeNGDAMiFMIw0MO46IDH6oQRet+6xIL4NSHMaGfdTi7lukS80oTn5EdhHA7iFMlPuOHZVK6nHsDizQMt7Gkf0ILlUQQwgJUeHIEd2CGIdUchzEMhkBdtxaHo7i7v3gQxsA67PcU7gBiE7oVBFS+QuAGJEYAQCFjvvkTtlgTm+YHktONe1paWPq/2bq9NmEB3PAU6KMUn6MU91IKkIAAYVJg7xAL9vOUBPMAwcC9ZLCTxzAP/TFEt6IEdzIG19aQCfE9QyuMkcKT8FrABv0SjVM5Q/IwI5QU9qIICAEADpC+FrMNfhkEXGYAGfABB/hzwTEgRO6CDN2hRKfgSBs8IAvDRBViSZjKCLTStB8ewDLfEEySJ1fTEOgDAVeZFPbhCBF8ABf+HR5DDGsQAAKTtBSDBa86w9JYDTPXSG0zBDBkUH0FABuSbFCQCIxwDE3exF7eEFdjwUGyDPlkBXqyDE9ie0fTHOixDKSwBh4BA+JDCj3yxRNwDNVSGaZ1WF8THDTAlAHBAD/iAF9TWbeXWNayuHS8yI58EcAVvT3CC/WzoXMwDJ7DOFGztfqwDK7iBE6DA3uzAm2ZvIw8XMegW6fRBHlxBfLyqTkBAfFyBHWTCLvCC7pYyLucySihZr9ZETpwBDMPFO5AC66wB/ji0rW/ggzFgCFNCSC9ogy7vQz3QQonKwAhoiIaQDQNgwBGwhSK4aGUQw5edgyJHszmf80VcLkyIgk4EYl3UAymQAAA0Ajj4q284Ayf0gAvMEKZaCSNfg5ZwQhz4FA+gANV2yBeESC8EAzFQw5chKzpHtESfRF+o201EgU4IbTG6ggQABbKQhyaYwDHphAO8HTkz8cUygiE8QRplgL8xURFgUDCwQsgWnEZPNE7nNEb0BajOxDE4SE/DBTwIQQS3ADUg826IAvC+ZbsUzwF3gzx6APVZHwRSDhysS7uwQzs0YT6Us05/NVhLhDq7RBfsjVEClhFwCxq4gz3vBjDI/p7iOu5NV24fTJ8DXN+4JmHuDLC7jF9Y/zVgi8RYt0ROHKpZ8AJ3AMAFvJdvzEMn2OFe4oJXc+02OKIfDEHntc0b7Glgd7Znn8QUJIlhI3D9kHJZlG93mAAX+8Y9sIMogFAAeM8knHWn0u/1TNG6vAEI3dU7vuMCLF9BBOlnD7cM24NUksVgq0Q95AsCyMU96IIqAYAG/EZrx4K1paUH7GPC2jY9eIQo5E79tFZPHkACPMDnyaNpE7d6ay8DbaMnOEBZJHdKHKeswUUPQxkCXMBq70Y9lMMg6UQEtAAlt+s7gAMryAEGTVV3EMD3dIAUcEYWjN2ArzeFy28xPEEw/thljsT3HtJEIdCsO2wSKXT0gzI2bhxGJ+wAb34AEUy4oD7SZOSxVQDyEH3Aa/mAFUACJyBshfd4AeMICkCDhhMAh/fyS4zDDAAAH9C2TIiXPDtAGvBGgLbCF2SFA7iBqgUqjAfDMjADjLLFEdjKDPgUlnNCfPo4mstw3bSbQuAIBhT5aLMEIzxHMLR1Tzj2gXDAHMw1XuBD/lJpCF0BJQRqZdTCaX1BK3vA5PgAEGiBEZgBn9Zxmk/6FzfCE4TgPuAISCF3h8fEOrgBdAjrU9wDL4RpI1CDnefFNmiCHiAQCHxBJfizfK7DKYPCH9CWH7fND7ALWPGCL1wDMUg6/qUPexfTQh1gOjwUAQvA+UwQQ6wFA1naRD3ggjzDQCy0Emk4Ax28QP1Mmh0sQ6QmJT7oglfYwDVLABt5CFvYQWU49GQTO7x7MC8YQYbTRiEcAA8wu0zcuwoI+1DggytAGQdEQrTjxRpsALDhVSuQA4/bozJAQhZ8wINDmU5MwSVUQyrU9ME1fLx3fBfPQx0EwUeHkxBUQK5xupGzxDeEeRaEe0/kApQ5QCNsq15sWwtEcMGWA5OjHz3Ygr0FLAZAALClDB9kETrEgz7wuccvvRdrggSgwvgYwa0VPE3Id0kwgwgAwC1YlyodQBpILl649gqgCwDAQSvAw7vX3TEM/q4DTjUCRNpV6875MD3d47QbHMAN6IEfcMcCAKrKdrohsjlUJPYF+L1e1E13fIHLXyA3gNUXkA1heQEnLH7dVz46/253GEF6f61OhK1KbMMZxnlNKIFOEIAZE6SrdwLl113r0ksC7UAmWr7sd/YwFMLm//0Nv4QuAIAIjO+oH0GSLED8PkZ3b08AYAAaEHDd6QM8eEQh/EBv81ELLJ/yz771X/9I9EVMyIMgAIARGD5N9HAEQwD410U7dEMQpaWA1113e4QWBYOdGMADWIAU2Bv23z/+U7RO7LxGjIMKEABAFNo3kGBBgwcRJlRYsB6uCgAQMFo4kWJFiwnfeeNz/gDiBjAXQYYUOZJkSZMnK+qTxw6dN26s5Lx5AyDAgwgZPnxAYggYPpQ/gQYVOpRoUaNHkSZVupRpU6dPoUaVOpVqVatXpbbrAABAp6X6nAHgQOsqKhIAHqTBGnLeNDsMuLZw42xtXbtA13HTVkzQlyNwuUJ44UMJJ1TX7iZWvJhxY8ePIUeWPJlyZcsl1xXr1cvn4mgZuD5Zeq8UAAqkrJKbwTVLPMr0ah3h6oDHsMu3nY7j1sxXL0VfsqgInFOHDzfLcCdXvpx5c+fPoUeXPt3kOkYQuLJr/IGrn6X1EgGAsa3quC8IAEyhlk/yPFpvQADAcKWSPer3F85bxsjJ/g8RAgAQQIQfhjjDj0544WUe/Bhs0MEHIYxQwgkptIqVF7gCQLuB5EFDDLu4A8A7peApgoEPqRpHD/TWAEcfyYwpgwOujugFHfYqfC4ZTiDxQYcTECABBi5u6cUXZrbp5p0cmWzSySehjFLKKat6B75MgjBgEoLacYAEu5AYQESl8AnGAQ4goaoeUDAAYI31JHPDBQfka4Sae6ikLBpROOHEhxdAmJGrRpJZZhsc80xU0UUZbdTRR5nrZogr0DHEAVUIYgcAF+yyQswRkaKnDwB2WFIqfFyRID1wEHUMjA/QO4CJbxaE9K52UGFEBwwg6JWrA2RKhBt6bC3W2GOR/k1W2WUV2uYHPvQB5gI9MgWgB7tG6E4pdjjygSp4fEALkxcfm8QDAmhkxzVmoyqkED+EcEABBACkYQ477GCHnXnmqYfdfwEOWOCBCb7NWe8egcCOgUQFwNu6QgT1KFrQsmQqUQlIy1/HnNkBgQC4igWego8SJYoJHngAAQQOQNeDLJxhBx5+ayXZ5ptxzlnnnUM6eB9GHtgQHo/dAFHbpHYA4AOqYoGoaMfW8QM7rhbm2aR5WvHjhwy57kMiq8EOW+yxyT6WmyDwyMcQCzZEBwAIRDF6TKTm4coEqe5pGoC7G7MnmiwAGECBfMueCB964GEnFjgAIOCABBzYwY9C/ngpnOR7EO/M8s0577xCdsLwYBgP3iB2n1YAGOGuiJPSA6Ito8qFKwZgV+wedkRpAYACdBDFdM8xTxyYPn4QE4AJsihElA09DxifeHLR44dcmq/e+uufK+QAFQ6ow3Q4CCBj9aOPuiEAD6QqR4jdP1psHk9oCLABOdrxnJ11xqnmkjduyBCBlFWgDOwF7B64mAJHIjJABS6QgYwhhhG4UgqfkIMGFBCgUfRVv5Cw7iiaQsAiotIOIYipBIxhR2kAkIAT/GFz72BHObjBjTesIQYZIoADNvABKSTiaw1UVj6WoQIDPMADUvDhEZGYRKdQYgEA4IMuegGDAqDBJNro/sUvmDGOgrCjGb34whfaQA1TZYoZm/kFNMa4Dw4apRAAYABdntIOOBgAAC+AY2KcYQaakCAPiCHbPcihGTt8oQbGC8AHRuADH1gBElpUYrLuQY2/XMESG3vkJTGZyZGsow9CGAHIQGCGbpCkF35IGgFA0ENikOEsXCEADN6AnIGgYgzxaRwK/LAOgqyxKEoAgBKgMg43wCUL5EnMMgxhAgGAIBDAINsuNuEHOzxhamLpgQ/6EAheEEOTyhqHHQBwhFKEAhCb6OY50ZnOfYwDGKD4w4FGORJRbI0AR/CDHyq3TjcUYAdf+EEQtgADBLhBl6h4wTK/IM0bYIATulQj/vmIAowmCuQpnHgAADwAjcSsgxVWQM/cwgaMQPShBx7IEARgcAU9ZGIX+VTnsbbxBfH8gAQC8AAnLnKP/fSBEngyyDhIYcyXDpWo1vvDQ2Dgi28YpBAZcEE01rENbqQjGWv4ATeucQIBZIEZurwHM45whGIMRA50lNhQWgCyeDaFFlpVwTBahZVlmOEC6CqELhy6s2VwIg9ECAHIDPCFMmSiF8WgxjniWlRIEaNNXFEBFwwAt4qkwwwoQA8DcqG5gQSDAj1MyDiWkUbFjpa0AFMGd0pBDoQQIQDWINdA8nELEjhDFNhZ6z7WcR5DDIQRHPEOPRihiWgI5aI3eAox/pQAIGS8Fiv0QMUM0KOCS7hjZ/ToxR+QcAEIKCAANFhDDNfBDkuW1ljYmAJXplCNddCJogvBRysO4IApTMEBRVgXQXoBACMsNSHfkMIF4qBB8g6YwBQiBiMgcYyQTAICNFgQMBgR3KWiYgRhqBl+CfALOiDAwgXJ7dx6+zZDfAACEoBCUJQBl6oxpR1q4Agk7ouVdviBAuiawjHkkbMDS8EDF3AAHQGgAjSkAh0FVlY6DjE7P2ShAACg3kToUQcA5OAc51DEAZg3EGWo4KoIoYctioCeL2TZyGU2M3QWsYCVYUDBFnEGd3ZQiAeoGQEJQAIwOPGB0hmkG2XYgTaC/gAAUfh0IB8eURbQBZEMhSAoXUDX75byCzoWgrp1wYUQOOIBO4wjsQFzBiM8MGcEoOsASrDDJJQ0D0Kf2Vb6qMckLtoyHMRi1QqpBgAkgIZCnIAGotUGF7psEHgIQQED0LQjWZ1sZUtmHb3gxkCI0cQf7IAAVrjIMi7ANSMQw9B51tAWZeqFdYTr2QUhBwxA4JWfcYRrdQwKd1a8lHMDAATMqAsvtsaVD7h0YOzwwxdsmaEfBIKby2aXGy4KgFhcZB4o5Eq5CxLTYBMk3xeQpcExnvHEbMMPvRiIFQjwg31oamkXCREA+oBfAHyhFxjawcjuUYv+gaBy4brByAbC/g2ueMGYIQbAAeyAAC9c/CTYBkC8k7KOmYD0Km3MkMUJRg899K/db0i5xsk2D1ZsDQYXHojEIe70A3gW62U3e1R6IQRn9uICIt/HPOxwgWRcBGhcgQc91pE7ARShG3aoZoYSAMx9OEMEAcABvnCwux2sNcRDKEomLkpmpGSDBgEQw23VZIEMLSALbV4W5twRvXxzBQEMUMLyzs6ow9GDHu2ANFPyGwt25MICBFCCM1Ofe90nRR+30AM+8HHAq8MdAji1yCQmwJUd2AENNElB3PaB/AEQYAFEhP5AjhEix02gfQQxhG+Jgg8XI0DyRllH/Cpw/arUgxK/egAImaUP/nvMwg4mbdwBqu8BRtxx9xSyxzyYiyFiAV/s4AHggB00Synyy5UUwAj67wEhEC/8qReAwQIcQIPmAQ6KDyTWYANSJmUiQAcKDvu6wAo8zyA0wQQ+gJEuqCB4CSiMQXfs4PWMYh42IYXyACvgoREc4AD0j1nmAX+cIRE4wAAcwAJ0iBFOMAIl5B4i4Qy04SDygRv4ACI+kCNKoRxo0CgW0GFqIQGZMAzFUCHaYQ1goBGmwAASYWPeoQU2ECScoU/6BBWI4gV/ohDapBC2kCg6oXFowI+o4h7AwQ7axAxyTFm6wTe4QDgWwAbEABKMAQwXYrzGcDmcBQbsrSDy4RhU/qAR3UAO48AHHsAG1A8punAKovCSviGGMrESXXH9MiFDOAAcCCIsJoAsIAaigCJcAKAnlGIdYCAAQoAOqyIfqGENIAIFKBFS5uEbnOEXyoArhFEGxADZXhEyuoEbyugX+OsknGUHNKog5GEKCsAKrHEg3GAAdkDATNGN0IUPAHGA9CGGYogagqEX1uCLYADzrrEfmWIaYEA8WKFmskAAdGB8mO4n1sEGAODmlkKmEoAYqQIfYkE2XqAPiM5R7gEbeqET3uAISABdfAAMmukc/ZEpprAbE+KrGqERDOGehuAH4mMBRtAkLrEVByIWCMAGTHIgsiCBkq4RwskOxGAB/iQH4sAmETdjKXuhFV7ynu5Jen5gKgWq3UrxJLHSKCKpF+6kIB5AASRyLezwJFgh2/YsKcAJAGpnKuRBDWaEBBTEVpbBEnjABUBgalRAEHRhG8ovK5XCHWAACSYiHCxr1P4CALLgC8RgLW1yazyOIJbBAyggLA0CHFzgBOKxKBpu5bihHTChBsQD6QJmGT4hGXpEkVDTB9ANBFizNTEg0dotQzBgCr4oFnqhEfrSL3XTKBThDNgRK8bSJAoBXYIhAIkiGjZAPHKTKZaBBx7AAI6AFLxOUaLhE/7E/sTjC0pBGdDBOHdzW5RmInQOA+yAK4GhF7RBqpYTJJwFAB6T/rcGwAh+UxzRAAMysijy6wuerR2aISBNbLhshU/ksE8KgZH6SpEA5QUEJTZjEwa+6AsOQQwedDE3oxiwYRu2AU/y6js51ChWIjGeQEyOYChGRQV6cigmAT1EEyqyzQG64RyWkUpQgQxMgFcyxAHqYBbGYR1qrUOX4h1iAAMA9LNUYAeeTCvB6T33oQ8OYLcU4h5SAeqSQhk4oAbuaBzeAA0G4APIABVUkkkmIcIizBCQICfMtFfQtFcY4Ia4i2uARSZk4hKqgR7plBt2dB3WYSXwNLz20Ef9tEEQgSMIgETFQ7WQIvtIpU+XYhik4OfOKk/6rgUSoMkA4PBkjx3o/kES/zQp5mENAmBEFWIdgE1JKWIYcI8gRGEHykEh/MA9C6IPgFIh0OFTlUIbemAAfKEg5uEdbrAAFCAJ+JFB6MFdiLUQooABVmZlDsB4GDRDNI0A8UVf9oVm5sE+NvVaFcXnCJULNrQougA9qGUqwOAB0KUWpjNK8IEWHqAHAaQF3kAV9qVHsXUp5mEmHiYhcusHSHUiNIABTpUdxgAGDBUhWhUSfkcIYtXLRuVej6I9DdYg3CF3GkcHJkdRI2MRirUAWwANWuADPTZZk5VSBwAHDmAIoBVfyEFapbUdqJVf5vVlmYIYAsFiHUNbg2IbwqURzpW4uIIq3AA9doDf/qjElLjGB1ihW2HWKerVYRZC58ZkGXbWIICBKygqv3DyIFpVZwkCVslO2JKGYY2iPccMIbbBC07u5SKDHu4JPpq1bWPzAUAAlvogapO2bq0iRPZVMmwWKHAWE5NiGUJmKpbB5XCOShjho36uD4zPbqViacHWIJy23RZuInjBjbgpv5C2IFpVSbl2ITRFSpGiPbU2IbYBQ6gGK3IBKlX379y2Wb+gD2CXbhl3dusC1rLjMvYWJWKLM5HiHtKAAFBBU5MiHyrhARIgFYR3Qu5hHtwhFpQg4Q7gAaTANmi3ce11IbpBARKgAZbvZJbVD5YTGIxAAhLBGIBgIjbXIBRg/go0FR5wAAKW0Cj0oQrztiCcwQRSBheHIh9Yr38HEFqzYAfAQaKa1QAO4IAROHqJSNeIlR5OtXohmDLMhSu6YT4fI3e9UabKIFiBIh9igQOYwBygQh/cYRY4gAEsgWYfJC88IQwEhQE64AOcNIKjgh6q8HEL4su8tCAmwQri60uFrQh8YApQhFVdtSAKgQNegRLngRxugACygCk+rH5/oh7oQVphSF/ygh6DgQ/g9A3ix4YY4AFaAdQugIggAAPMVA7EVEwZk4bh+DKOIdsO4A9U2C4wuIoAZxIsGCjM4bw4GCmmsAoZAA6AeELYgRy4gYZ+ZQI6gH7ieCp0Docr/sKXOiAdFGIemu/o0PeICaJEKuAWZEYfrlgVbgABRCB+jaId3CACHpgk6kFfspEeq2EWSgFOfWAAZGKTucaA/+cCzPQDdICN20EZiOHA6GESWjCSmdk5lkEUJeASTnQxQgwCgiIZSAACxsoo4CEWGQCTnSIfcoER+0C0JGQcnrEMAjJwEskNaMGcm5kpJpkkhKEFDKCID2IYWCACMAAGkjd9CwIfcEEFMOAL7CAWJqEMSOAF5iI3UGGaD2KW6bSMMqEMvgDI2tYDcgIEYiA1fUAM4uAT+S+eSbpBKIEDEOAK7pMxQuwLgGIehHLihuIeWqFNXPopKmFGLqAPMtdB/uaBGTrhCUKSK0ayEGqypJ2CNJh2JPIBGjgABlZ6H7bgBUCBFGCAGhYia1/vHp7BDVKzDnBBqKpiKbNGdf0gJqcyrW3pBjzaCGD3rWEXFxJEqZC6rnOkHophDRAABEohRu9CB0DmUUniGzCAASrBKPDBFtrkLJfCGTBkAIbgGeCZQTJBDVzghLMzFpRBHeyaKhyXJOAhuQTPIDgBBEZ7HqhBeItB9qKiHoxhQOUQNXsABQBDLAigBR60DCahFL6gEZhyM5AEQ4UbsTq7uBdFH6ShfyTgkO8iRBOyJHTOA450KNrhIVTgGZpCGUSAK4RAhCNkErLgA1QGAOQrGMhh/h06zbiZ4rPJkDIJAhcQwAHS5CAoZkVXMr1/oh1sQUxbIJg/oMfSFE25hgPi1Bli6LzxFFPvYR1kV70dXFFoun9C2DE85blHwoY3BRuKYljJ2wzktSiUIa0aclUjRBMuIAECZwf4wBvO4cMfnF6vlyD+gIUGwhycYALk4EuJwQIGwAngeR64YT2PIkwZwUw7wALQFECa9Qa++A3o8RvwNB7w+8WpvFju4R3QYAGCABcaI1ssXCSWtgemvCS4ZVOMgSnsYAJARmQgpBvQwAM+yg5q4e6qfCrYex/+gCtovOHsmQXsoFghaAGoWCkydgc+dmW44gFOlgBVVlpnhlrr/jzSB0YezsVfGSM4Q4JbHmANjGJUHqASkjcoROEhAMAUXBw66CEW0KABCqC7iEzVJN16D4DTByLPAYDG98EewGEStsACQFYPwPfUTQIYiNWUUmYHlOCMVSZZlzU2VbZlaSbWpX1nKtztEgPTc6ppQGBxhaJyw3MpOsGWSkHYm4Me7IDquOILenraYfwNax3XEYIRGnwkSrd12w2uYZfb2X3fC6cKRLRwc/HLQWIe6AAAQuAqUeIekgZ+lSJaPEAAGiAV7jg5BtCVEsAD0CCQ+T0pBHr/iAJzWC8e6IF5XYgdakEP8AUOSg1wDEABPPYBnKBYX3njad5zlGAABuAI/mIMOHVxJN4h8Sj5JCqXAKJAKewhLAYgBUY6OlZCU37uAqIA4Ws+Mpa35GXG5PFlDkz2zVuA3Ryn+jwWDWJh4qe+7AvHCni8CYos4AU7JMghQEY7KODONFRZKNwBEnZHCo76OfABHcAhDDgCmN/Y7BnjikeOHc6hhYWDK2KA3dAiAvw7J6RACQm/8pFoGHaAAo6AG0LdKbDdIkThbfT9J0RBAQCAipBiHdqoHCEaN/RBHbChFI6gsD1AB6La8quiG/LBHIKBGsqoFyZBDG7hi7QA8s3UBjzaMHB/+TFJHsJg5ZKB7JHi8yui+W6RKHZATJZeKNZBKAtACDKzOdQh/hkO4bwe4AS8wBImm/nld4uxQTN+uxfQwB34gAGOYJ05ICdeoAdkgA4GtPUBYp/AgQQLGjyIMKHChQwbOnwIMaLEiRQrWryIMaPGjRw7evwIMqTIkSRLmjy4zgwAGJ3onVT4AQAAPxg9APjgEZUCAF5EivoCoICbby9fAuu0xeYBJ5yWzSsKNarUqVSrWvwGCpAfPl1+/LgBQaZYED6UnPNipo/aPrR48dqWr5vVuXTr2r2LN6/evXz7+v078N0RABhu4bMac+bFZQAGIPHYIkCLdSHtVFj5qx3giKiIhAibYBKwcZtLmz59mpNqToV8uPYRI0IAmQamMPiCW9Ct/l69mG3rlm/dO9TEixs/jjy58uXMAfM6wsCZ1WgZZNK0yAjAgT8dITUAMCkkKgyzOzXft8yKjxECVkLKfD6+/PnvVOch8hqEfhAYxMpswUUjvfiCDTDbHHhOPvMtyGCDDj4IYYQSUnTPOd0cVhUxF1h3kREAPKDZRtHYEAAN54AUjQkylfLUcu1ocgEBMqEhCjktTohjjiShwkiPPX4ApAcQQKDAbP4N4MMbfATDTZPkrHOjjlJOSWWVVl6J5XH02KSYRQh82FEeEwAgyj0fRSNEe5tEiVw7cEggEx/VrCNPlnbeSdA3f+gwwZB++gfAFG8MWk2TTq7Tjpl4Lspo/qOOPgrpnYldV5F2lGbUjQwlUuZRNzgIQEMqbBrHSx8PGADADs7UE2mr8nUzSSGyXvBArQ84cEB7ANAwhx2+sgMsO/LMQ6yrxh6LbLLKLkvXpBbxAgAChXDESVilKMoRNz/IxA1zfogFgRvMjssXL36c68cbIADKLgSckAtvvPLOS2+9AjlbUR8ALAAMR/rCQI5H6zQiUyOjElfIlzI98K69Dn80TyvnrstuxTfooda0D2/McccefyxfFjLu8CwAEAyzETZbACAGOx3pQ0tQZ8hlXD7u5GKBTAdcsAjIPiOkTz300BNPsKngINYAByztgK0PeBDez1JPTXXVVkPF/sgBMlkUsxQb5VMJBwZU4tJG+jijglAhEocPOsWooJ0FHzBy9cb0BEuOoc4kMqgPA4iVAAZAWuHj2nUfjnjiikvZDrBNdlO2XVlvXZEdXWaEzhUA1CCd2dnEUIAQRBGnjzrBTCG2BU70guHiy+ojDzrgNMmKHIPSACgDtcr9wQhdKON68MIPT3xy0bSBm0wJaILX5ABYBAMAWWiUTy/92UHaRsO0QIAS1xSnTSxTRAuCF8CwWjyk7RjKWyyCHNEfuECG8IIMrhWiWjKtp89///7/HxVOsIAAO3ANCEYgh+Zp7XkU6YZMRKGRd1gOBMzgSCc8IAAZLIM4vfDDDgBA/oAX9IEXBwOglcZBDEMMwStieYBr3LAWTrjFQNkzoQ1viMMcUmQbL+DAHHLhlk6AYnSSW2BFRCETmmFkHNH7gss0IgoQCAAFqEDNNwaxrWgtgRWc0qGOeIGLjDHCDEYgQQ+8EoQw+IERbumiF98IxzjCkRcfSAQ8/EIGGTFwIi2gHEbekYiVtGIjztgAABrQudJcIw820FUZgEFEOcanHsBQjXpe4wMQcIkAN8DNIa5xIG48UZKkLKUp00dHZyioL1bQY0Ue4MeLlKMIALgCNTQSjU+B5zS0UMIE2vOFXijxlMYRxWos4QMesEA/CmsBbsSgiDJkojcHSoc+iInN/mxq02p0ZEXk9qKiWEJEGQwAwBsygo9WHMABlMCWRZQRGQCwaDPtQAWfZAQJbLhxm3+pJyN08AE/QQCWMuGAoN7gjCetQ1jsQB8/HwrRiNbrHmmQQCr2lxdDaI1kE3nEl3KREXbshAcOtYgzRDCbbriTL/iIhQ4U0J4sdMMeEi2XrOzwUgToCgC+8kOw3DGseVyzpkQtqlGTJQ8PLKAPfREZAPRAEaeulCL6OsAaMIWD2ZhiqnqBhxEU8DcPAEMeQz3qVIAhq0LQ6gELQAACLNAEX9UIWMQqoVnvite8Wqla/tEYXvAlkZj8QCMfxAlGtuGFFXFVLx+8CSO2odeX/uTCDjeomEwIIIQ+MGKDke2sZz+bo3xg4gEKqNUCBtC9vCQGqhOJyaUqUotodQEj5sgCABKQim/uhR612AEBHgAG0GqEHvN4B7CcUQg7EJQASzsAAhrwgB34QVa8EK51r4vd+GSDCwbI7T6A4csqqFYmQ6CIazPyQQ4c4yLzOAQABBAJ3eYFH+3wg9acgLLsTuQe9LDDG/ooluY+QAlpncQw9YvgBCv4L7zwQRb2qRfAQqQdHbhcRdYBQjJcJB9oIwAMouGXd9ziMgj4wHoXjJB8yIMd5vBGk1LxBgAEoFYT2MAH/tAjFOt4xzy2CzHKKI6/6GA2r3UII2DZMIsA/mUDIK6IPqgBtxewoi/sYIYdMMABHly1x/tYBze0oQz3fWEH5ZTJB8qiGlrUkMtsbrObQzIOlQQDo3mZ3DklcuQ9VsSB0ruIOfiwrz6sGS/wqAQMGIACR5RUweNo0i960YgvZAFuMhGcDlyT5DdretOcxkjWbhAJmvJFDqgarETkUE6MoEEm/bKI5ZYKYbrkgxqZOAMEQFCIZSz2uuzohB+e4BU9IkkIaekDK0jY6WQre9kOYcWGOIAHyO6F1AAwdUR0QMCLfGMF1b4IJzyAACkM2i62uAIHEPCETsQatN3gxFoCYYh1YWAHXjlXIHgxGmbre9/8FsgyvLDAlfjg/hOJLKI5W8vTi8ihAADoVkWWAYEBFCGSdlmGD2zCAD2M27PjQIV6LFGDsACAAW3ohR0akQxtHKjfLG/5sq+hhXaNAHh3AXCRGxITO7wzJjewyDE25ABz6GUSGwJABVoxHNDioxdy+MAGIiCjB6ThDangRjfakY932NXlXO/6jis0izoMaux2kO9EvoEKWxgOH8BghCaa7JA/aO3mC0FFBABw4IiQIQEAGCRFlCECmahCLzMQeR28YXazHoMRQPrABcocKGdwYx1Q8rrlL69pfBC3rsWaCDCc9oAGJGABkygbMIzQ1gRsAIIEQaupHtCCVu/DqXRXSD1sMkqJOIMD/gCAw64Z0oWR/X4qzpjNDtix9YiyQxSFaIFpFbYwJRiYrJivvvWvry9wUcyJ32XXDxy+j0JUjPuTq31COAHL3EcE/QmnSJ6tfRe+xgKvvNBDZS3bh0DI/vr877/loUUAVkAQnCBtSnBZTrAMywACjeAyxLAA1fYDTkAMCggAvbAP5ScR7Kd+EOEDMrGBD1F01XUX2iIT6/ZQjDAEegQoIPAGfWCC/geDMbhv2lEI8NAO9FBWvLAAC5BfAvEHWaANW4IA+7cPnhACTjQ5tSAQiXcQHfgGTLgQuGATcgCFtncACkALd+EOk9ACA5ACrPdQ9LAOomAHWbBcS7MAExAF/oxQcDLohm+YYPLADd+waA6hMzHgAG9QDPBwTXZwAMRQEJ0AAb1wZH41EA3mRHIHADfADdXAB+JQh01oTlWYEFXVCnTWEPfgCAdwiXZxDpAQFFIAiPwELOTwBmFwWRTQAR8gBYnACKMIh7Eoi501NAaxCQBwAcYwEUUnFhyQCODQDg6gZwKRCRTwC4bwABuIiOwQTv6hArrAEPfAA5M4EfNQBwDgA+UwEfnADCpQBNpIF/NQDWgQAA2ABBRXSnczO9wgdpUVABPwATqACoYzi/Voj2bVCpVwRwOBYQEQAlkoERaHSS9gVXNwAB5QEPPwBjsADUhgABvYCjBgB++Q/kfs4gMMMQ3cxgeUeBARyQCLkHQRQQ5PAAC4EIlR0Q0EEwApAAnE1CTYAGlfED9iAQNKAJD3iJM5WVSF8AG9UFasAAAGwB0ZsQwyMAAqMABoUBDXcANTgA2RcWAKWYH7oAkKAwEfEAEnIC4LQQwjIE+YuBD3YDkAQxHJ0B8nCRXOoBICcAJVRErfwA3M0Au4MT4ywQAc0AI94BptqJN96ZfZtIwD4QWpJRHAoBb7Z3EHMAUkAALStg/zwAog4AfkgAoTkAWOeQ+0AAIwcEsOKBOBsAugwFkLsQ42AACJIGoQsQ5AcQToMBHjMJZ0gQon0B6PJEfb4BaFYAQ/QDEg/gQDb+AHlVAL17BKf2mcx3lK1sgA3uBvEKADedcQ4gcAIUAEbiAGPnACBEAC1BAKCQADccAJluAFMOAH+6gJ3qkakMADJIABjWAmweiBELEMJ0CNEYEM/VEKYGl7ncAAGDB/VnENJzAbDPhG9WAJ1wkD+qFHMPAFkNALvzANyYecE0qhOEQJDDALrPIC7ScRKRk9AgABZXYEsWAP7CAJABABmoQBV1BD7aADAKAfYrMDlRAwAkFQEUFH9fkQ75AJK3FLEhEOJAAAT1CjVAEJPlAALUALL9g/buADPeABZYYBUxALvOEbH1ihWaqlN4QLHVAH7QAGi4ilDTEPjWYo/k2CDooyD6UwdouQDgVBDqVQWUdXDlFyoxCRo3zJEN1QBgCwBeogEfHABADAAbBQnFKBChsgAJAADmVlQ5rACCYAfb7IDeCgDoe6pZmqqTYkjQfwADKihCJxD3UVifdgXIlSEJOgMDgaE+D3EMwgAx6QCY7aEPTQB7+lBsM3EssnoC2AjvzDDrGgBLXiVqliBz7VDmi5qcvKrMSzBgtkB7o6Fc7Dqg0XEexgBgOwBdggEbSwNGlQJ1NRDi8lAFkQDbRaPOYiBA6wACrYe/DQec0qr/OaOP4BAejSm+ZnFdSKp60aEdwgE0wlETJxAaMZFeRwf1/ApIpTCFnkHyzo/oL0KrETezhsVSu4sjRGEmB2YAjKGhX8+hD68gZjihDSAKMiCBGxhQDBJRX3kAq4YwA7AJ2HQ1zv4AyTsEloeAFRMAl6SrE/C7Qf02rskFbOx1YH8Dcm8wl3AbINkQ97YE4kaxDvQAMBQAJEyBDw4FtRMBX3EAsyNgE6tzhDww7k4F99JABMYwSy0oNBOxL3sGLC4rZzuyiLZwVAMgNwRxdNyxAwBwB8QI8KoQ8OJAF0EBHzMAQAQAEnBhXsUAoy1gI0dzjvYA7dwI4xJhMBkAAXoAM4Frh0+xH6AA6eUJdTIHSgi7rFw7cL0WDW+hDzAAfTCYYOEQsPyLJQYQ7X/ogAIiC5V4MP7NAIRRBwtRIBJkAGsJi6I5ENVWtaA2CByQu9i7O6ChGRrusQ4NACAuAD3/MQLjoAICAV0TAEAxAuPgsy+rAOMFkKMskALKCXPqAabhm9JBEZIaAahWAFBju/+0s105sQ32K9DTEJH5JpDDEObmAAHoCyJ7EOrAADBOABBTw1vcAV9wcAX0AJ04Cp/CsSfsCW8osRy0AN+snBJcwokwO+D/EtZPkQH7QBG3d+sCS2L7EOnPACBMABlVA14wAMoPAHWYQAP/AEfuCqJiwSDkQARoALpEAMC6sQkOkEVxALEmrEVUwlkwMBEPEt3OcQjOEYEHENPiAA/i0ADkXxDn2wISqQCxvcMe9AC24gAyEgAbMhA4+0DTBsxR0xwAEQAR5AASRgBvq7o6RwaIRaBuG6D/WgC2KAxwYRDSScx5GMGv6LEFsstQTxAAMwBBwpEN8QAwAQBlS8EfTgCnAyBdTAxg7DCHd7GQUVBpLnxJK8EQT1APRQD6sAAEPAnNfap0xVD37QNPyoLgt8ECOyAO1RdrKszMYxORzVEN2QuFzMEIugHYIAEYMwxkU8EviQCjuRBdSArvaCsw+AACroAbHgDkK1zCfxLQNwBPQQC336fRKxmgAgBLEADIkxEPpQDRHgCQlBD6KQA7qCBpe8zgfNtHP3ENuw/i3P2xCw9AAQ0QnrYjAv8bUA8AKO6TDr4GtPAH0/EAjIi9AnwS4gYB4T0Qvs8p8CAbACaxDwYMGNEMsjTdNVQckGwdBT2RDA8IBKsNBZ5NAlAS24KMjycg+1ABT+8Qa4UNMdwQgAPASCINKHaDk30QcESBE1vC5fwBbu1NIGwQtVjdEa3dRlndDR8hApLQLN4BBH8Dc94xC68F6RYNAZ4bUyIQKMKy/0AA/s0AqxGwAHsABoMLNumw/zAA+p6RF+8AXaLBD6QA/QUAjLtYPfishR8dVLyA7f8gBOEDVmDdoKZGELkdLzHI2wRACv614kwNYlcdQEq9fkUg9F4wcO/rsALVAIWIu62IAHO5AJohwR+sAHXEDWA5EOdqAUTaMEwFAqDiABagDJIsENAcAd9FUIB/BbbRva2723Cu20X2vapP2AR+AQ+VANKkAAZ/C5HkEPqrATFxDby9I24JAIwisTCHABKtC785sJvCfNHJEOW6DfB5EPuEwAFOAH9GgOQiACsRDOJcENDtAI6DBiAGABXsPdGV4XGNgQ9fwEjTwQiijBCIEO42MDNykS74AJfPcCRX0s+oAOylAK8CMTDuACPeAG5pu8ADyRH8HQGFAMBmEPuUACF+AEtBCJ1zAFR1DGmE0YRwADBTQM0a3hVU4Siqiv/AgU0coQ72AE/gPQAuUdDNFCNyVBCxQAAB7g4q7iZbogCJSGACigA2hgDFSOutcNAA7u4z/glAXxZCqwVI1MDA8QC3beEQArE1MAqFbO6FSxcKOdEPX8BhJKC2Oi4wQhDZWV0Wb+AwQUqsnyDcAgCF+QRSHkBpsF3KnLChtqB/uoEN/gC646DxWUEOPwBEBeEPIwBQTgBEy6DT5gB0X6EohOGHMADQ/e6MkeEhWZ5QJRz81uBQOQBZetEOLHAIYYErSQnaeM7I6SHjEQArpSA5MAoakOvXn23wihCSYAAwSBDCigEPUc1PvADoqL4ghxDlbAkE5+BKWQCRKgApaQDMpO8PRLZA7x/ux9KwM8xckGyAEg/ke00OlHwAzdvijjAAlW8ALNJCDNsN55XL3pfhCTs5USRN6R/gVH8KMDAQwGYAQhmRD3UAcMEAxObgTEoOI7QD9bWfA93xESphDdcJeZwBCiEAJ45xDEgAAOMJQiIQwUQAAq8AsWbydL9wQc4AAyogJokFDmzsF+K/IG0Q5CEC1gQA+tgAKwEPRD0NgFEQsPYAgN8Q1G0OdQAbA/YIH0UA5CMAAI0AXx7fOBPxFT8Dfl1RDj0AImzRBxEBZ1DS0IoAW72qcAcAiLHimn164ysQOxoHVUH8mi9QAyIOwJIUEgRFogQMwFoQ5dIAOtzY88EPkM/vHrrR8ViC8CSysQ79BbBAABUTC7gg/8D4EIWpPaHc4FAgAIDOEG6ecQgfAhiSAS+IAKqJIFpxspShV1uf0O0qrM19CFdcCR83DRGJ0NgssHA+ALCbkGFPD7B8EMIUDcUbEOx5/8A2GqsVsACSCzwc//DXHTBAEQ5GD86LXP4EGEBn0AuAEv4UODvAAQsALR4kWM92IBgOBlG0aQIUWOJFnS5EFOfhAAACCk0EmYMWXOpFnT5k2cOXXupLnwDT2SdljC+IjRD4CCCbkBIIpx2xekPEWug+oH4rsbLEEwk9rV61ewYcWOJVvW7Fm0adWuZWuT0QGWI5cSBMnrA4BS/vdE/gCAgJHXjQBAcGpbuC4IlgDs8DLc2PFjyJFLLgTALihLCISNAmgEFOFSAF+4WZzXKPQ6tFQBWIW4zg0Mll8sS6atc5mTlaxr7+bd2/dv4MEN33sQV+TcpBdxeTDQTeQ8lhe6amTZwI5wsvPCoWkh4EADIYE8Yydf3jxtyrND1mJJwACIdJtlJ2RXZwCALOMQ0oOXioYAHJxLrSqM2CmkApZweOe8k/Sxhx4II4TwHgkr5A8eckSZxJlJ7OiGHRDtEHHELHZAY8TEHsgiMRYBYPBFGGOUcUYaZeplAeNAyscZAOi6KJ88AFijHZGEAmASqeZRpbo1arRpHnKq/kEjBgAGkOGPb5zUcksuQVLiPvUwWueGADDoYg8SVsnnokACmC8hc4QgAIApnOHmzjfQ4EiIaNRSTbeL/jhBgAfChGy8feYBcVFGG3X0TkidSeQNSit9Qw5PLNX0jRtoaPFTUENlaYAAJIDggQc+6HJVVlt19dWc3spRzDcAMIIYjNLRIqqQ2nGAo65iwbEBMGAdqZ1SsgoAggx0wNVYaKP1jZO7DIVonloR0GSfb5RQQT+LQIlgCnUgisaGCR5YKbEETJikT7XaYQMBQUSKZgZDEB1rHnnoAVFRR8G5kxVs7sQm000T3lRUhkUNIIEINvhgYoonxqBijDPWoQVN/iZh5C9pQxZ5ZJKx02TdqWrtAyRsbmAgGJFkBXmnaHIYAILrSjZoHWh+WYMjGJQQ5RqdizZ6LGorC0kUljw4iJYVwrnILgBGg2gcWjihgwgfus65rWvcoOUsfbDppZhIf+llbbbXbkSQRsr4QpEv6rb7Cwwa1jsxBwLwwQUQYvBBhxds8CEGHrp+oWvGC2f8cSLyQAXchPCB92jMM9d887O+aWDWi9ZRGaRiIDiCGpGsIACEonRCBQYBPNCsZHZaeQOFOb3gREDOe/e9pKStfUhPEERBaBq9LLILBnKk3abtXjr5BPpG/LDeej2yguAH7kmYc29QYXh8fPLzAMOL/j7SVz99TP7YJxtfspxnG9S+Sb51g+j/fX/++/f/puK4KCSiA8DKQmcaOzQPJMS4wGp4sgwZEMADlShZPqaBiTfAAAIMsQP+/vdB3wUvJMDwQydKso06lEJf58kGL1zIi2XMYxm8CMT6+hAITjDCC9zjIQhEwEPubVBvHOgBD3dAAiAmkXtDOIP1WvFCKEbxhffohgdBeEUsZlGLJUFFAkBnkW9wgAGUcApUYpG8i1yDBvdBjW18cJ9J2INkxlADC36FgS/EAhto3GIfSSZCnryDj455R9Y4cchD+oAIlkAD+RoHAkiCAAU7OAEIBNAiAUBgXSxpQYsYQAIMTOFu/l8oA/TWpoxtpHIb2WiGKl3pym4syI+zpGUtbfkQWQkQJEvJTBk5oIylbRANO/mGGuYECXeMbBIfsMBKHJAIcLBjTbekpquM0Unh8eYbqPhYNw3Sjm4yggwfywLGOkABCKRTnQAIwAPgAj4V/AoNlIJUPSE1Dnt6QxzgUMc6/OnPbFZToAMlKC1zeRwAeAAXGGlGDXagjZAoIQAA4N1N2uEGHEGiXNHiJiNMsMEDyIEVsSxoSZ1UD1xUQx+RIUY36XEMRkihYhuYgDrT+QEpeMCmCkinF1nkAA4kJgyVEmk1LlGKO/HBE9hIBVIjFQxxeIMb/zRpVa161ZIeFCT4/kAFAF6QDYz4YgB6WClGugEbGsjyJvSQhAEAUIhkRqsQCUDAunbAjnkMEqt7FQ4+vuIMRhRCsIMVrBJaoIQLoApVgTCCYhdQVwQ84LHfY5gQ3kADD4xIRK3QbCGC4Y5FzUO0otWLPZJHDzneg4/6mCZfXfta2H5QqxkpBQB60NqHsKMMDgSJuADgCb3OpBtezII5ouWMHbwTAHAgh0Ni+9xVTYKw00WDBxgAWezWlQACoCxLENDdTx3BUY6Cxzze0Y7Rkja99PArdN37XvhikRg40uVFsAUAH2BkKSBIzkX6AIA3BBQm5MgKCEwIK3pkLzEweEMb4/vg3XDDD7xI/sn1rlerHj1hk+AjgBFsSAsaMgbCIyZxiU0624vAQwcIiIN+BeMLkORiBwBAxQplQg5PVcB4ruJPLHDAkgIwQAkVNXGRYWKhCsGjUe2YhWad/IZOVukAU6bylCOrWCw/4ALTjYWNjfxlMId5iygmDRp6eZFqMIXICdEHHwDQHJzc48cJ+Nqq7tEOP/BlIhNAgzPE/OeEIJkeTia0nlPkgRYRoMoJQNUO7DBdwSIJ0JOmdKW1SGaIsIMjs3vIPNAgACKAxBxTEBKRblLbBMygVfc4RysQ1JcNdAGYlobvaBclVXKQI1IKS0wADmAAAjAgyw+AwMUyhtNwooLWy2Z2/rP9h+ncbvoi71ABBfKQkY1AoBg4YQYACsCGy23pHtxoxRHc+gAXuMHPzt7rOIpBvUYcwm4MAEALYCMqDwTgA+IjghvEYIVCIBKRnwg3uw1+cIRnDtoJ6Ya0LaLpwWDkHILokdVq4gzY4KDgNcoHOnqBNwBwQAdrMEbCa7kOe95JG22zQ94axoFjj8BwXbMEETixbpPnXOc7L9rCETIJAFxgGRbZkVeHfhFmwOYLDp7JN1YgmDXTKBd6uELeYFAHWsyD5/wbBz2I0TYL++ELSvzBjFt0A/IJwQzqA7EUicH0rcdd7nNnlc8PIhRVWYQehcAvRt4hFBi0wibREMIl/rmyJU74ANEAwEAjqBFcuo8MH8ZoZNdksIMRRBIxDbNSiepWil5g45XbIGnkTX961G9JVl8ICd7tK5T8hg4qAbaJHHDUiC2hggibZ8Aa3p76VyVD4IVQwvh64IJficoAdVtDKRoB+rb5ghnaeEYqtQ587Gdf+wySFaAsYgcHuO/hD3AAJMzKAAdg4iYRCAANrk8jVLSA/SypQzdMvf0YtaOjjOjCCCZ2AZtigEtqkQHwgU1ZKkjxp3a4h7zCPwd8QAgMju4LCWKbmWi7gJLTOzfLAbWaiT8IgBgAKxohBh2YgAG8AW4QsAisjWOAhIoxAnTqKYZRgXl6A6cih3/6/id5WEEe7EEfjIwJBAmOsMCE+K8PaK9MO4AHaJKa6AYZ+C3IK49uQAMBZAk0aK4fjAxgmC4lcKwNu496ewMnK4RGeYfRisIsTEM1XMOwCEKMGMKLcL2LgDhOk4mjKIX3e5F7qK3EWDo2PIt7IAZ2CDs/GIKG2YFa6ANceIk/bERHfESR8L6cUB3emho4tIi+IEKEmAfYswlmQAwFghFOTAwDgztItIl16AQLM0TwSQwI+AL1ycNTnEVa/EPoAIB6qRwIwYcV4sUIQcKHEAGW0AOQCAQAOMKLGAC/mLYdYLGaSAe+k4EY0YgfK4ANQIOoq8UfqQcJWRRyEJHqahG4/rAyxdoBPxAsYNBGdVzHRzSSIdhEc6iFOngDUXiDckCIe8AFPqiUUgjFhOiCObmBBQq6/koIGlhGi3gHGjgzmdCHW5iINniRduiGVAAyMtg4dvSXRVkHfAqGSakU5UoMJZSYiWGED/iYbWFHlVzJPzQHC7iLBziI/iiC5GMJIbjHfcgHZlABAFBCd7oBG7M7g7hEiOgLSYMIcuCIHZMJdXCzE3iG83gHc+iDd4KAFlBJb4QUVpCDSpmS9hhAAFAsCKAYK2CELGFJtExLNXyHZxiCJglLg5gHQ8AABkCBxOkaCdgBIgGHIwAAEjADS+AEN/CBSNg4odwGokwIxGQA/ow0CKDLAKKRCXtIhIlwgw4MjvnRgx1wqxbwgaWkRXYwGLu5txahmBPwASsoPpo7pM9US9d8zRVchz4Ygi2IB4lQAoOgBhgAAUNYBjSaBAOQg3UwjSPgBT7qgRs4y4MQyv+6gGd5iP+KyYvwAIqYiXyAhqA6gaPDDnZohB9YCQ7Ag2o4RXpYG1W0njAIgh/oARYBAR+og/V5oe2ETfqsTx5cB064gESghnz4r5e4h1Z4RUOBhx34gGk4AhCoBVm0AwpQNoTooi8qwmO8CC8gANxUHgBggOeEiVHEAEYUjnmghTdADAx4gkqQIzUcB2DgBU9IH03oAzvgns1jEQE4/oLr6QRekEX73FEefcBxMIMLWIO48s99aIc1CLxOs4MGuAIG+ImHEAUIIEJfYYlDsoQ8GBsJzTuI0KQPhc4B2AGaoIQHMAAvuEzfkIcyCCqmiAVywC0IrIcqFQPLCwEQiACWCKDEOAK7UYReiJ8e/VNAhcB38IMNioVp+q+rLIcduALUSQh4UAIHIDUDSohCsABbSIhooDfBAAEPoICKSIi70NKH6IsuBVUFaM2TUAIAoAAsDQ5O4IE7agRm0NHtiwY6CAIf6AFIsq5PgYEvEINJuIVMWBtqUKWNClRkTdbUwzNNXYNuKg5t6QYytSJ2QIAO2AgxuL+DkAAn0JdJ/tgwlog9hLiBAxA/XArLbAK6B6BVkiAGBFAAV6iH4FimDXIAPvgGdk29b/gYHfgADPCps6sUO8FBdqAHfZBXZU1YhV22KWwBxTKCdHyOUHiAHWAOHhgCTfWLdciCIPgFL52CXvBLnDMIJViAgtyHXGKJA8iCYXgIAkBI6IRLi7AAADgCmliAATgCNIwME1iXIcgFL4u8RRCsPkAVB6grsIQDEfGDRTFD0SqrhY1aqQU0fMAF8DMAsAy2B5CClgUJe2iH82IHeHgHTatZepgHRSCAMggTYFDCeNCGLBCABkADMlyEByAAP9CrXFqUeADGoYTZhBCCSnyI4siFmagC/gBYAMMFDjuYKMWAh53VOXbohi30AHWBLFC5wvSaWs7tXEDjBbPTijdIH8FtjyeYT5EAhhwJWV7ZB75bgIhdhhlNDBHDJbj4ASEEXIRgiVI9iEKAi5kABhzp3droBT2rM7krBOsxEobpsD6oQ8+NXuk1MomQoKNECGBQAuWyIow4BAB4R4PoBiIIgBY4kSmL2IMABod9gEdD34d4hJVAgIzoi0e4FpZYBIsoDvA9suIggK7ljXGYBERLAJzcuXmIBhHRXhZRtClLgAYwx8GaXgmeYDADhgeoApAo2gMggGy0iGF4gC4VhRVAgANQgAeYVJgQXsXACFzI0GOACL6r/q/9KA7iFQl8MIQNvtDduIdwWBEBUIDrPbgImVzuYJEDWABUcYLBEoUOpmAnfmIxowdD+FSa+AZNYIRe8NuTsLvo/L4I3Qcclt+YAAaajYLeOAdPiAEBWAAbcFBnywclExhumEcMEwBGI0lDcF8o3mM+rkUullnCFQyLQIIB0GGTeAcvMAAPiKvaYAYfPoFCoBxLQ7llWJtYsAOQY5EPGAElyANOkOQ+DmVRji98AOXdsLtacRqIKA5N3Id36IAjiQlaQAEHoASElYxu4AYYCIAIsAHzo7R5wCdnUJtG+IIo8y6YmxgX8AFOcONRfmZojq3rxGTulQy7QwxDPgjP/gEA7qWFCdgB5zKJbTACBHiDfC0MYjgCviACUFBOMMOHXLiwJ/gB70kMARgBtesDRmg7XhDBaP5ngN6reCA1EKhd3pCDAvjioQSAYbJdGfbdBbCDoA0dRngADCgGN3UMWlACCfIDPS6yFeUFzfwUDtgB7vEDQAAFYDDlgG5ply6psr0BU6SNP3Crh97dt4KIFggAGLAIJRAAiT4JSmigTEBRyFgGK9gAAWiB/yWxegAGRLICH6DTGWWAHfiCRugFZdCGVHppr/7qqtK08gMOWXmDN8zph7gL5DUIVBgBijqJb+jLKcAGyYiGCAKAEIRa+IIpYkiEJ/AAC1Cn7qqD/jvxhnJYh3MGa8VebD/SNIbsDVmBgIsAOrQG1cE9CDqIgDBI7IegB0tAAA74BS1uC3rQBA2YEz7gBr1+rpbqAhMAwMQKSZaIgTUQhRRkbNzO7WrCisfmDUq8aYOIYYioaOBeiLwoiXmoLQODjFrIimM0aKxaBuW1noZBYd2+buwWqD3su9+4C4UW7oewAuB9CKqxuJEgsAKCjKNgiRdA3avihNllkY6A7uyub/u2JXLwgQfIhNWGBz042bbw7v19CIq7abWGCE14gDcZCU/zy49Wi3uoBbODgGKpKv5AB84q4jc7YlQpBER44fsOcRGvJXpgBTpJBiScB3KVxABn/gkWNwhDlOyEqAdEs+59uIc6AIC1LYmGS4BrMwxzaAUF6AsTSMmB8hdzyOU6cO5RQRU3YARgGO0Rn3Iq/yB94BGGCAZuGId1aIWJkALIMAEXv4jikERjoNmFUsyFmISJTghP07fGNAseZgK4eAAqriZ2UAduKIU3KALlIraJ0YGPcecqL3RD5598+AVSYxEV4ALYSABUbQtCDg0yv+x94ITisBbdfJmS6ITElYPCYIdaIAFOgt5Z6gZm6IVb+IJFZwkH8IBl5oRIP3Rar/XNobaenBjZls7H2GmFLvOHwHSlSYiQ3QFoKIldPoE4Jwt4qATYcIAcaGo/6sheKAPS/sz1E9ABNLCEZLB1b/92znEHDugwF2IE6xkCxIBdyPjtbAR2SsURQ0nu0DDvungzUGeLeagEIUqEcO4jGWIEJ/jOBR6CMWAEGOJscE94hYcVeL6BXz6IblgGGECAGl6LmmaJB9+H4gCBh4CEzzGU4Zx3knACAHAAQj+LdCCDvMGATGjz/6kHUkCBTWr0rPYF+1t4nM95aXGGo6uHZmBpTriBWICMvc1fSk8ITFeBy/yGn1GhkXCGDQLTtRiGHPiVI2iFfs+iZbAEH+ABUq/ZPEKlmdZ5si/7LSmBJwiJeSgHhDcLn3N3hJAoNJBFYGCAXyKJEmCJAkYLRqDZAwiD/nOI3N+54tcOIA5IBG5Ah3XIaLNvfMefkSMggIo/5XeS9oMojhXyCX0J2R6o5oc4Bnpb67JQgpU4ACnYQSzqBlHIAg+oK5EshHa45ceffdqPkRZGAMuHCHoQhcl3+3d68EVYiYc4KwBDFHqAhIobCYAEAJf3iiqYE8WNBywyECRIgAJwXBywAxBp/trvfu/fjYXQUJDYbj8sjIX73Ycu74RQjfIHCeKm77GYr8TI+N/xA+ZdMDto++/ff/6PjJI1fYBwd28fwYL30MEBEABYwYYOH0KMKHEiowMAAEQsZPEhrw8HujnkBkCAoIkF63kAIMQky5YR5VF6AOCAEoYu/m/izKlz58179NoVsnMRAIELhQqJYsdzKdOmTp9CjSp1KtWqVq9izap1K9euXr+CDSt2LNmyZs9+paUAgIdY7OTRowePXSwcCjegLVjxYsaNDnV9eKO0YTUAIHq1tPSAAC2w+uilkbmgT97KJvXNcxfLjkyiCyZEmWR5NOnSpk+jTq16NevWrl/Dji07LL5XHRoQADDlzZsdFxFAmBHN8l6MEO0cgPAQkwPBDee9ARDC5sR5OgAUgQcW3RwHACrkwjcb7LpxwcJwAGDgwQMPVoiNjy9/Pv369u/jz69/P//+7f7YMAF7A36QhWijFReRTIU4dE8eADhX0DxhABDD/jcs0cLBAa2I55U9uXBggAavdNjfU+xUs0YMFx0wgRGGMEKPiTPSWKONN+KYo4478thjQePQwomQQp6WIEQyteLQNFYAkMg7DbFzkQ8sreOGbud8ZU8pJCBwxTU+utRNM19cNMAIMrhBy5Ngstmmm2/CGaecc9JZZ1NGPiSTHw7x4gMG4DR0TywAQOAGS52AAEMyA3VlTyMYIODFOHWuQ0wjfgwhgnRCFELMpHaCGqqoo5JaqqmnouoUng7J1IlDnHxwBDrPCYVCYxOtQ2YjMnZVDR4cIPDDMnPeMw0rbhgBwUUe+OEJdalCG62001JbrbWhfjLca3t9AVE0DACw/o5DfgDwxWAEtZOSDmtKRAwEMFDj1TItqOelnPVAwgMLGAw1xS3DXhuwwAMTXLDBB1cGQQvKbGuRcg9NgoBxDZFrLpQzoWHSN2sAsIU6XR1zAQADNJFOnIxY8YF3F3GQiDPq6IOwzDPTXLPNNxc8cgvasraqXn5RXO65+xQCwAOWmAQMuHrkw9Uxmh5QhzlwatIFBBLPNMUs4MDTNM5fgx222GOT3R85aASwgSit+UzQXg51MwQAtzjkA6GcTMROGQDskIvTIgNQyzxudiNKCwgUcNEPhbATT4llQx655JNTXvlW85RykcWq7fUDRG83tM0PACDW0EUfmCQSAJRt/kWMyDvw4iY7ZA61uuW345677rvrPk8jF+3KuUWeP2QFAXY4xAwIIDDTEC+np373Vm5IvIN2YNKjxw21f9HHrbyDH77445NPLTtoJAAADdk8TtpeBED0AQDIN9QLAD9w01AfACDACK40BEAGIMGKPSqxmCBcT0f4oAc7auGbixRgA4UYYPkqaMELYjCDOhIFv2iQCni0rzJ7GUL85tcQfdwCAEHIX0H2h4ADQeQerQBABOiQlQJ6YABBKAeP5BGMPliERRfIgjM0aMQjIjGJSlwNKj4QAADcoBRDE6FF9vQQ+TGoILkCwBja0RChPKA6aKgQz6iiD3UkggMEGMLU/nKUD3mQIwzeQcADLmACGC4xj3rcIx/7GBVNRGAoeKQiAKzoEPkNbYuGJAgMBNCCiTiDKFbACjwSAYALOOFLObJHLwQBAwZwoAVqyATA/GjKU6IylXucxzQqIYGLvKCI7qtiCRP5BQQYInT8y2JEsgCACXyPKvnIhQqi9qkbqWMZqyDBRaYACWOEUJXSnCY1q0m5eTCjETDIjQf6sA3T7GWRBFmGyIZGDhjAIEktBMACnvUQSV5lG7+K1Ddt1A1f+GELKUHAC9xQT2sCNKACHejB6qELHaBAWSoQRDJQE86HcEImQxPJD0pHECcYbSKc4J//qrKMFwCAAW84Zn/G/oEKTigBBiC4iAHWEIxpDI6gMp0pTWsKqkyYQQUXwUAmlIGOmBWJlq+SaENEcoV4FURZO5gIRh1woaqAdABFeKqJxtGHEYAgNwCAQRl8QVWbgjWsYh1rf4hhhQccoDmJKIY9VvPQoQLgXO3gAwDywCiCXEScDTkGAg5Av6koowsXEUIb+0MPVNhgAUNBgyjIMUWyQjaykp0sagJBgAFIgR3zqIfXVJOF3Og1DgjAAbvWER3WEWQYF+HlQw5hNF5NpQsSs0MC+VMOIShAABdBQzfmcVfKAje4wh0uV3BhBz/EAzaJsAgJHUI960koFAAAAwWBsVqJNAEAR6jKJCgw/r+Y9ocWDtCqHTQLVOKiN73qXW+NOgNRohLEtPezqHUBwFpW2bcqnYldf3gxuotAAG/sHTCBC2xg2BBDsRMryHMTKF/U7qO+EtEIANz5lGVcJBZlNcJQHlCIUh44xCIeMYnB4t66AYAO4F0HG2xXkFoQJSL3OMIAjEAVbLjAAamI5nzq4Q4pWIQAB5DCMUps5CMjOclMOXFD7AZdgowjBgIIRENksl2I9EKx8IlKPtyRCAcU1j75gAc40jgTC1iho0peM5vbrOR2rOwhdhtCAkUiAVAUhB56isgfDhDGqOgDHHSVQH4CbWYDWMAJFnUzoxvtaD/O4xvc+Ng+uGFp/m6QFCfr4IY3vNgQVKRvwft4x3XswCt9RBIE/N2HLdYiYIe8owP5jQo8hAKBUOAn0BxDAAq8AIx6PDrYwh62BrfhhR9sgQ9++AGzf/CFf1LMD35oBIgJ0okv/GAIZ2iFuArCZILQ4gTz41U9LPmCf8rBAKIuCCcg4AFoRMVRkHJDt+uTCz5MgZ99WAZ4ie3vfwP8duvowxCa/V8AoADEwPDE/gDsBFaAVxQrJcAPdgADTnQ7wfdzyEcBEIsOQQcAUyqIDgRAPIeMwwnHg21T7jELYAnLPt3ghG9Eyop6BzznOt852N7RjW0AnRUtMEAQkAHeP5AgkGXoxS0EcQQM/pTiSajgVyN8sQ1sZAIGZ5jUXp7gkHDHtSDwKILIGyI/ve4DFSMAQDfO25RgeMAA9qJPNOggA2UlABPs4jnf++53hF0AARawxaf5hQbn6CMe2pjCDqChDBPQgBvgrUcjflDEvSDgVYgsCDvSComCADJwEFHCAMLQb6YQwwIkM9l8oiGHD4S6Dt1g+d9rb/vbpypzAzABKgqihABs4hw4z4ceDPALMiQADg/BhQ8qQQ+fwSrsBIlSgPUik9Pvgxhr98RvmXKBARCWPqg4wQKeiAZuPBb36l8/++F0D3K8oQYYWJsoQgCAWT2EXDhoAA3w35BscIEYsENxFMIisNvm/k2f9BCECfDFQwTCE2EDVFTBTJSEfLBDIZzAE3nQ3rVfB3rgB+rIPJyDIZyAKCSDC6AB9u0DucAAArAB9vkCEJhLcSAAHbWAKETfuexP9RGE/ODAQ7ADGFwECzVFFUjMEdAebNBDLOgAAjjSJKBD94GgZAFDC+wAD01hFtrMMoCAufjADdRWfH3BF3DDB4AhR/jADAbRUIAAJ7iBspyLUKDOOInMXxXENtjN5qCeYp3cbMDD9hiGH+CcFkLWPHQCDAxFhBDiIlJLEu7DMngA83wCBJjCb83DMABBM+yDpphCXPzIFpiAJhaHnz3ADdrNG8CWHLKbTEDYPuiDLlyE/gAyBT4IgwUQgI3Nxj3QhV0UAA5QECOSFTnQgEIUQAOgQfoBYzKOSj0UQjg8zjwMCgk0gzNsANsxEDt0Axq8gBkoBRiAix2UFzZqwQkwzj4UhwEWhN28YEHAQQCYQEEohvQVhDoognpIgiPehDG4gEqEoWu0A4zNxBDJkjKK1TvYhQBsAG8R5EKaSkTFgCdcmjNQyAK4gRetAbhEB6FkABJQ1RpsQGcEQAKcQO+5jUVkXpOJXAIRiprZzQFMETZMAQCUwS/qxDuMgQOAB4+pxjtUwEU8wCAxpE11w0jwQDTQAzi4Q1AqpZ3QwgTUTpmMQB8ckx3IwAf4ABGIgiY1/oQzcIIPXGUeaKU5WoTXNcR1oGJ8rSRBWAd2JFf9XEQmcKCmFQIDMEAt6CRqsJJQeIAPvNpS2lTRSEAoUMOjrAE4uJ1fIiaYWIFXeiUIxIASoEKmceVS9FkhOcQKNAmw7QMr0JAmEMQ0YOZZGkTmQEAxLMU9lMInXQHrvQY8tMIRAAALVEJihtWgSIAgLMEFrMAC8IE0HCZtAiePeFVVWMEAWKbZAQAR7s8GPFVHAEAp/BY6wOYTZBpOUAMi2kF1qgY9tMIZKAsMTENnBadMDcpFnAArMMJKTYE8jGd7XktxHmdByI9yAsAcimVyOoQ3fKMUukQ6xOQRAIpr4IMx/pQBv2CAHSCVe8oUONALAJwAJ8gAAahALoinSdSDJYiBEhSCdipoh+qI8cRnD+InQfTBACDBOqmAOIRESM3mTrzDIjAADEDna1RCjgEACbQCOXioTOHDMOgUAoAAApBALrSVSwxDD3gAAxAABoTC3i1DtuxolM6IIQhVQRgnERrBAeTSPnyDGAAAGuAcPdCVB/iNTuBDKziAA0QCPprGMXyATBxAGIQDf0qpHj0fI5DkQ+hDNfDGGwSDOFSoSVjATIRBMNyABAxDQ1xAcLDEYSGBHHhanUqq8IToPgxhQdRgRwGDEEDI0LCDd+wAm07E2AFADsQlajzNTMgea07q/h6hzAdAAARMgBx8VUHkwzrgKp1KBCPMRB+kwz0IxaJFh31GhDk4AQUYwBB4Q6syKzhVKV61wDFxFEH0CQCIQr9FyQOsAU/0AQFYQKK2BhjIxA4ITrMKTDdM0DHECNEUIFU4gwn0AZsegwk8AAJoFUudATLyBC4QxRQAgygw4KLtD7E+BDwEgVZ1wSCa68KShfxUqtCQaEYRBAvqqIQIxQtUm0v8QP+0RrtdxJMxbLWozlPWDsE6hd2YGkR4rMehIQxQxTtsDwT0wSA+j8nugxJcBAE4wZaFbM+WxRQY50kShD5A7D7sz5/pA13p4T7MQ0KMXE7YWpGlhj2AQ9Ek/oAOfJzPxkmXTQJy5FU/PoSdrY1DFAIiSG1L3EM8/CaKpewJ3YJvHMCOQcT+fEUg1GdDGJQSHICfVYHW+u1YMKAJaZFMelodXJIYEi6UHEAAEIFORMl0qUY8XIJOMQAmROrfssk9LINODQUCSMAQXC5EVAPj7oRjNQQtFAERRgQRAAAcnN4WAUAdhG5BIEIBKCxWEMMBfACvrMOXOYAUqBnmCi9XkEFu3EBDtAMAHEJMcVhzbdHyNsQ70MABZExOkIvQnoY8IMNIUOTsDq+O5AMzxORMPACaFYIF+KpEoOYBnIGuSsQNSA1BOIgBtIKo/oEC0AAHpsMWqEf9RsQ3/sQAh16FEFhALagDOERHBfiBqH5vA0NFqzVgQQDAGnja0RLEOVxB0RLEUBLAJOFEO1yHF6QGMxyCChSAD2yoA/sIOTzBjeoAGmRCQ9UDJYjA3D0Eat6o/+LEAwzAEbTDPfTCE6ymSYxDNb7k9uxAmMmZ6m6FHRhADUwBpMyALmimClvxVPjMczIKmTzSPogOADRCv03CLwUTS3yDGxgACEDbaHSDH6wURQrwFc/IPFTCu/DC6ZUbAnjwQ+QDMviADYDAG/hBJmDD2kJUkq5BKzDbGkMEOXlAUjZEMShLGE+EDzCxVggFgH1BHMtxJ+dEcfwi6RTE6FTvFy/aPgjF/gZwskMwwp6ZBip4KQCYACLUqifXSK5AgB9gXz4UAwY87UPMAy/QgjYRAAdsQSa4RCUAyw1AwBuo4BVlAXu6ZWniig0EaFc8kGG4ii1z81IUx9CIMkEoSxa5SzgXhCrexDWcgABkwe2exTXkwQY8USMMZDfbyDdgwBM0D0T45y9LxDT4whrIgAQYCkvgwyxcRDq1RFO2bUEkAwbcQARKBCtcAKV1Re0ES1ja80abxKqMQzhHEsvWQyZsVYISRA6d6E0UgmLVc2XQgg9MgCM1gjtz9H6IRB08c67IwCoTxDcwQxlAAB20NESoDgqUQktEVEMTxDXcAP5IxDIYjzRf/jRGzwAknGpNY/WqbEM4L8JFDI7e3I/q8uoCEJ5LEEMKBAAkFGlltAMjvIBuQQI4PDNW64dItGJD5IoIWFjevEEDZIFJ4ANnEgUMlFFERBRNejGzXXJPO8EBqIAhXwUAOAAfOMMbpIcDKBpda3ZJRrAXh3PRGAc3qJtTr9MDuG9DdAMZBAAN1LJZsMMZOOENQvJmz8g4tAB1RUSuqFpOzENIAWVDwIMP0MQOCAA3mkREPZY6dAEB3OND0EMk5EYZb8VKYsYzZMEBEAADeBht1/SqMMNnN6Dq6IHbWcSftQQobN9ci8VtGYAHZEE0rDV398c6cEEQ/EJEiPZu5wRR/mjBRBjBAkgBPMDDJFRAKohqRNFC+6DQDtQAFhbEbaVPFrAqV6TlPuRDPBRCZyDABfy2fFuxd5MhQeBsaOeVQ+ySS2wRDFRsXtRCzPalh8/3F4DANjdI5ug3TkxrRDzPBWzZNoBUKehkRIFs6IDUDeiBtA2FzDKyVjwPBAQvQQBDwykgjF/xqjAdULmySAgAIDQEvyLAfUVEPhiDBwjAmuYFPDwQBNghlfMHPUCCAHjMQ7wDGwhA40IEO7QDPQAbozCQb1yARABkCjSEKHiAUg8VASCjM4jAvQJAAUzAmnfF/mDA2ToEMBiBAhjnA9iBErM55lo5F9RTlgOACHyC/v7wDzqahDb4kjSihS4+kAZ0eKfjRzOQgAcMg3jOQyrQAAmM7UMMgKZPAl04lh9YBAOg+kP4BgVQekuIwgUYAdgSxDFkgYA8wARkwbJ7xcCyKT7EQhAYJwAoAk3LOsPiCbdPaNPIREdRlLCyRUugEFGcgfeCRTuowlo8gAowzLibSDuogWPPgjp0g6VtAg39QUH8QcEXRBQ4wBr6ZB2BwUR8wAfE+kRoAgNTkZObhDkIgbrNpL57ehDJby/AJglQQzc0gHHcQzDMV0EM5ayZRK0BgA1Id1hcQxuo2wu8uMfvxzK4wQlMABWom0KQAMLvwx9cBNFfKBp4pQ54pSVw/kLG6kgavECeSsQ1iIEPoMJV63yzGol0DsUlBIJfyJcR8CxoTzxB5MMxcMmTi8U1XIG6tQDUb71+0EIe2EAgfUAN9HrRH31EaD2P1APVz30nG8nIQgixg0B8RUeIEwRoI/ZDyMMUPIAXLPlXMMPGAkAWTMPg3zMo/AEvIPbBc/7o10jXw+ZFJAIgHEC37MM4bI8+F8QY9WGYQwMHnMDMf8U43BIGzIE1BCrpA3/wG5EOPJFx5AM4bIkdgAMLBIAVqc5RFURKoJ1DxIMvwYDcc0Xgz4CQlkJ8C//3g78FPcG3B4o4wIM+yEQtEIRIcAAsMIomSMz0Q0lfmUEVgwU+/rjCK93AMXh/+POcJgAEI4H79tHrJZAYwX3HIDEqKFCgLWLE8DGSMqILRI0bGaH6xnHjHx0fSJJk9CHLnw86QLYU2GWEQpkzada0eRNnTp07efb0+RNoUKFDiRY1ehRpUqVLmTZ1utTQAQAAaipjAGAeQW4AXFxTyEgqO51RAFgA9lQnvlwVAHBohQ9tXLlz6da1exdvXr17+fbVCTKhpoHEXG6UUxJxYsUkrUhZHAFCZJIeLkTGULIyBJKRI1vAcOEDBAQAEnA2fRrCBA6oTzsgMBU2BNIOABBgfTtyAqp+eff2/Rt4cOHDiSsFO7Xmo9EE6dUB8GKbQhPIcwIj/nDAEFy9fRYAaBHsXnHx48mXN38efdNuhdjHojeJfXz58+ln8fAAf379+/n3R/AfQARU8ADABxYIEEEEDYCNwQYdnIqA1x6ckMIKLWzQgywuBGAHDzb8cLf0RByRxBJNPJHE40KU6TiC5nkDAB9k+gCAH3TqA4AH+PphqguWQRHIIIUckkikWqFHJj+U5EShZQoZ4gde/EBgyV6UlA02BPS4wUE7oPTDDhDFHJPMMgH4oI801VyTzTQf2EGPPuwgwIg1P3gjTV4IWqcPTnjpg5WsCmmTzQN8MOIsonBRk5HodFqGkT5wuaePQHihhdA+ityU0049/RQ9KySsqcV9/l6M8asHAPCjOgAQKGQvJWpTAtRabb0VV4Xo8YOReVpRElgl9wGWk204CRZZJXk0k9kP6XzDCS8+gMGONH1wEIRlJ/xCTal+YNMLH6pVcwc6+/gCABjwTJOne2hxSKZANIU113rtvRfffPUtKotRaQILAYLYAQACJgkyRFVWcToCAAqGweuedo4Y4IAq9r0Y44xlCq8mfej5uB126IGHnZJLtsMOVcgxGeWWXW4Zh2YfDAAAig+4GeebE0jAgQcOWGCBnx1IQL8FjAiEPvlwQSTpQmIBhhH2CkLkmJ+Q1BjrrLXemuuuc1Kxpj8OsENggg2ux0ME4LWJHdrotase/lfYsmBtr+2++7d85IGHnpDZ6YYccrgZnHBuWKmmcMKDeYNx2tDgsllV+9OvMsoy+OAC/CzAXDEdWkDCkJZQQaWdfSYBhhhIjmkHFZmU0Q7v2GWfnfbatwabJhrJ3occgkUhyBgLABgiJzsOQGCSu+axZe5cbH8e+p2yMrlkefxmR3BuuqHmkkRK4YPxA26AfEwDLIBAcv4QOAC/D/qroHJGTCiMEWImoYeYaPYhjJFe8Kk6egEU4AAJWEBbiY06MnlHBwCwO1EAIANe2QcnVLU7m7SDNk+4CzkqgQEAqEAYsDPgCDG2Dm304hfU6MUKWdiLRtziCzGMoSDWIEMY/kzFACQAEQM88IEAPGBaPuDBCkhiAzEA4xOc8AEnmNhETtDBDZlgkhObCIxlfKIeJNTiFrnYRS+iBwkDSKBCgMGW5O1DQx9QCAUBcEab2EIBAKibXODhBw+qABci/OIe0TOPbyQuccxIRjBY2AgNGYBhzSLABD5gAx88EpKRfKQYLMEJIqyBE87YRz2AwcRx8BGUoRTlKEm5Fx0IYIwEYaNY9uEBAuhAIYXoDittYoUBeMBRc3mHH2RzBGZwrJTBtMs4iMELXniCUG4wwg+Y2UxnggADo5kQBG5Agh04s5lHeEOygGUIUvBiHcIU5zjJWU5zEgUVugGAJmVSRgAk/moHCLCCQpQgABW84ybXyAAA0FCXdyziKjBIRj7OWVCeLAMYoqAiEwvxSBmMAAQgiACZGHAEDBxBho1oYS+KgY1mZGMbIRXpNr6RFYOeFKUpVWkwNSFNNxJkgQCgFxoE0AKFiMEADiidTVAx0d/NBR+24AAAjlCLq600mO9YBi0Wmgk0QPIFLBBBRKkaUQ9aCAMyjKEiNtqLYFCDGNQQaTiRWlaznhWtXFTR2wjSUwCogiCqUiNB3HCAGODTJhSkwTnoYgi2qGAZwEzrFxlhCCR04AITQI3PPuSAKRQhEdVIhRwS9411XPay8hjsZjnbWc/WDhjdkelM2IgOgkxl/q7A0CEbTEoTZ9QAAHRoLVqUMBoLCIOgn7UdMJLWAvz0oRAPWJ8YN+QBNLxMD7UoWTviAY8s3mO2upXudKlbXXwpZypsnaCqxAIM1BKEFzR6w1FncgRUukKwTlHCayygCz1ad1/44MV8fIufAyUIla6S5gGU8LKWUa9k7pjHgAk8j/TCF8EJVvCCT6SiRK2Ru/vAEQTgxQnZjNcm1wIALZ8iq9rMk8H2OpYfhmAmdbFpjiFW8YpZ3OL04E4mazieWHA013zsYSrcsIkuaCQH8jIlHlIQ4wIe5mIRjYwe83gHgNmBMjhQ6Do3Q8AC8NMCO7DnAkqQz0+N3GUvfxnM/ryBsUKuZQck6eFMBMkGFwBwgG50DBMPGAAq3qsUKUjlAA8OM3DyATKW/cAOb2iBhQKQs54ZIT6MAOCeGd1oRz/aKWMmSJmRxCUTgPdafNjpTNKhBQDUoBxoqQdtHpBiSN9lHeMYXDH88AbaUIgBHVgMSyCy6VPfGte51rVNJL2Pa/UBSbXpAkFqwSUd12Qb1yoDh5dyD1wAoAKG2HVT5kE9cCRuDTGYCgdow778XMADlyGJHGw9bXOfG92nlvQ7dPBOuLgKXn4AAAbAYRNq3DATWXRKMUiAxzqneyft6AY3mMENXRxCq1dt0CJPoAMfoEGKTHRGPfQHcItfHONG/j4OCGZCixNseB/bgDdB5P0FZruoFOlixlPI8QQABDbjN1FLJfzQiVYYYgxQylaDQCBJNRWCFMuIbsyJXnSjU3fjpKWRWDgx8nWgy+Q1GUeY7EAOp4yDlzA48MXHAYxj/kkPO/AgCGAgzRoxcwhjUFInjNn2o78d7nH/rKQ58YF7ShgAC7BFyHlUijo/YwcAiMXWjZKOKzAABr24eDKa2FAfyCAEEgUBbLIqw0Pcohci7Ua55d55z39epZKmQwTQkBXJIakZJOCAMmzyCwOsvin06ENOI/HvR/OvC1awAuY4cxUHDUAI3LAsZuWhD9AfH/nJL6ikiSAADE9FR/v4/gUBdqCNmrwHAHOwB1PwgQsHOGAMeL09RFTCewgk4D8Ncizj3lCNOgwu1MqX//zp3zXesuelSDnODmZyrecTtSAgoUaObSbYQQweYBOagha6wwWM4dEmIXPua30ahAYCD2UKYbnkgcBMpf460AM/EF88LDYMRv+kYkV8DQD8zrtG6+kA4AvIaiaeDgQUbyl4AfpIsMt2xQ++4Acmb0LQJE1oYehAkAiL0AhBhUaiBBfqgEt+gAYVghfCJF1+pJ20BQOokCAkzf/ooRCyax9aUGFoYitmcClWUG28rBC0xUHgJE206wjfEA7jkEhMwAhkYh4awQMSkCDqaCpu5gHU/oBjgqxn8kMBPAAXvkIqCGAmaKQO6EEQqGMrVsUmqiFd3iwpaqE7COACFs26PuZj/qZlPKRBpKwB0IA9fkwOU1EVVzE97kcm3KEQBiAQmOMIbuYCCsEOHOAEbmEf5EEKIoAWdAUVDEAPtGP/RIhGdCyRCAIbakMQamIe2CAAgkAp4kFVCEAKiky69MEe6MEdSgZM7ODJGMRmbmYBbrEQJsESWZEd29EdyWMdqgESCkAKEmIf/uABomBt2mEStoAczKACXEGE2KEMdsB59kFFUmFwvAEdPsAA3kxVqEIePKFGnlCBYkAC6CAp0qEJBgABnIC69IEduKER3mCoHOSH/iZgA0AHIjjxHV8SJmOSL5ihF7JgAEZADD5pHxZICeJhJnrhBjphBd6A2eJBEFCgFLLQBGGjoj5gB8yhbQCA49YBRpwACxVCH7oBAE4gGI/iGq5gQbLgKgdr4LhhhWLhC6ZA4XLkA17gkZSAE2hBJ2WSLuvSLufCGWAAAnxACVqnSS7AzOywFFDAD0aAKGXCHn7hCKxSKR0EATjA5GIhjliFKgnADffBHiYBVY5iHrzgKlpAGDZrHbihGHqhDGKIQTRxBRzOBzBpLO8SNmNTNoviG1YAAHBQIWhhAgKTIO6h2NxgGpxAB1qBhXahETjgAlgBEaciBIQgTRgBAUyu/hCkglXI4QYwQDlpwh08REaMYh04wYOmYBpyC6lOKBdojgexpEEQwAY4YRqGcDbjUz7nEyfkoAC+wCbGYQN6cpMywQxIYAY+STc5gKo+gAJ2gBRaS0WYYR1dkB2mEwB0bAz1hCa8iwEu8yfeoQ8ugKi0wfhWShQe6QVAwAN8j0GyQKNWKBjekz5b1EVflCCi4QQC4AlwUyGQQAJ4gBMq4QM0YA388h2EoYZiqAx+4RnEDyFNcCYcdDphQCukkkJnogsLpijqgRQ8iARiwfbGaRnygAh8IAQc5KJiKBZ6QRtgEEbTVE1ncxJkAwE0oySswB7NoQ4OAAIsoA42T98I/qIdMOvkkhQAbmBJY0EfpnN3tqIraiJMPABJgYIeXEEC2iIXtu+c6MGwSOICFIBmYGMAfIAPuAEc0OGyyHNNS9VU65IRHgAHTgYNpsIJFaLaYoEd4PNrpEIPZGJgFK8JCEBhtqIHSFUhbkbaiIIcrsUDKgFYxQkYjMBniAs2jssOZJVvTpVaq7UugcEPTMtUqq0bpEGPCG8njiNgFGIrFG8CJBEfUGEzaWLkhgIeguA18IBSxUkUCiECJSRHssAORIEcCAxcrRVgA9ZaiUG0ZGIdAKAR6EEJBsBGTgUGcgkKP4woYmEqQCBKSYkb0MVBDqAPTE1gPxZkBdbBFOJg/k1uvajiVKCjJtpVKALvOSCWj3hhSyoEQ0PWZm+2VMdM5BRPVRziHWKASmniDQJgA1gvKFoBAALABIx2i+ZBHbjBGRJhCl5tKhDgASKAJewRZ7eWa6tVRY5qZ+lBVcomaJf0VYSCHbgEebaoZLBBFMJgY0EjCxhBE7rWbu82Z03wwXYWFeKIILSybBVC5M4WKNrhDKYCByrOgL6hGcxAY2HjARru4V4TbyvXcuNTRdZxGjCgGE5pNzRzArpSJnBkAfSMJ77BDRYEBNZRgNihF0rBEI5ABPJLAEZACMyAE4TucneXdzFXSZvkCKiBRvhvH8JkA+ZSIXAk+n4iVaWy/hME6B4upQ/e4AdQQJo84AeCYAxAARiQt3e/F3xjcsyC4Qu4QXcIwkPmaiacgJ+A4hpOAJWeN3qcwQ16AAROEjamQBGSYRu44U/DF4ADWBXHrBfK93z3gQYc4A9q4loO0iegAJVogFbvRhm6YAPMLn+DQR00S4A72INXcdDGqIDNt4EI4k1T7BgQ4AYmuCZQgS0AgMtm5xs0oQUwQJ2mwgHeIBG4AR3+9YN/GIjpj0YSqBvK4BZCQTZ2h2BSjCxu1SeAgQhohgbQFG+6AQ1WAAE2lUP8oGTmYU+DGIzDuP6GOES24Qt6gY1c4bQ+ABXPNQx5whPClAayQXbwIRaE/sABDCC/aGAOyAEeWFiMA1mQ446MBfeMVwnv1FcmEsYnmMEHSwGQM0beGgQGWiGSBxmTMznmRAA2DPkXLOEBCEAs9IAAQEwmeqE7TBcn1OEQAEAAzOB/M6Ye2iENYaMAJiALRIF1NZmXe9nopoC4FEIbuIAbruUH4GEfykULaAKYFZEn9MEYBo0EmoFrPIYfI/I6FiALXNKXu9mbLa6QCaIZaqCYGyjYzlAm6MFDjqAn1kFDEGANOA9j7kEbXK0PLcAKGCH/vpmf+3nXwnkfqOEIoKHdCoEeDjYB/FIhmEcSd0IfqEGHGDNr9AEdYiGRMEAH0MAB/ZmjOzrXwjkf/ihWEHQIGPCBFXKEJv6gAW6TJ+qBD/KOErLGhHRhpDXRBgqhUT1ap3cazIaY4/KBGRJpKmgMpWdCB16DJzLTVZyAivcFGL7AZRHAB1ihqXnaqq96xYbYRuJhChpELNiXeGfEO3giGFSFAyAhY65BFIggTGumBvRAgrBarueawYYYAkwFbhlELJJ4JvSpfXfikLbAe/EFEsA0v2ogEpphsOmasRv7swr5HigSAGgjDLLCC2VCFGRjl2tpNDogHS4GFXSgAfILDbihHC7ZsVNbtVFqiN+AIOIhGPggZv5PuyjornZiNAZAg/LFIOSAAiQkDKqhqlebuIs7pYY4DPss/kzHaxGmwiL3IQ4QgLV0ornbLBHyBReEYAEWxAPUEbWNG7zDe5SQexEBYLy68ARREMNywsOW1160BQL6AGbFm77rO5iIgUMbWiGScR/Qeya24QXMGxVpIiLd+1aIwQiyRKLtm8EbXJSO4areeB/4uwuJRybCiwAI8CYEQSoQYBFy5R7cISIPYAO42cFPHMVJSJ2nQsLz+M3CRMJpgQN8IP5ugh6GQIw8AFfygR1SYaiAyGNTXMiHHHrweyosiCACAAasTngkHEfQYLgVApUvu1bowRlMsiyGlci3nMufJxr2KV1mYgJIQBzQSL8JAkdUoMxxAoFGC1T0ARsaoWpR/qCku9zO7zx2bCmV+FtWnLwt6u0mxsEG8kuViwQbLkFtnYARKBfPG93RL0bS+JuRSdYNAGAKtDWvItJGPmUbtsBDIOAKGP3RR53Uc4UM/EUhzlXHJp0gEBwAgmFL68k7NLxInIEOAtwA1oAYFrvUe93XPaUFNnUmXmPVI1QmSOHjaJ0mNKyfOuUPZGCicMAXvuHXq93aPQWgT2sK1GESlkMmBIHY2fyFNztIQjuOArXGr13d1x1Fsn0fmFQqZKIbSiwLorwbZIBm4OC7zeNBMSC/4ACZ2V3gB15E3N1BhQfJt4FHFIFWfcEH0z1IuuEMDoBm0KBfCR7jM348sv1g/nn2zB0ZAJ7bYL1gKtY7SOYh5aTyDeZb41ve5f0i23f2ON64F1zZF25CGwIvAcidROAhFWgAAAygBQr95Yve6O0i5kP+ON5GH24BAKbZJvKBFqYCEgb8yNgh8AJgN4+e67se6TtZIZrxIOKdZNFlDOR5H5RBBQCAAYIBReihHJyDNFqAab3e7u9+KXz6lDlXDhbEYNFFwhXiHlJ+DajdRK6hEnZAjD6ADhQX7x8f8oeitU/ZgMcIHY4AAbR8Ji7fVTohp89jHqZhCrh7iSLf9E//J/Reyis/rPdhKyq5JvIhGKYCBqihRNihEW7oBurgEFHf93//JlSfIEb4gE0l/uVelSbqIRGmIupEZB5o4Q1AAALOoBb2Hfivv+snnyCmrhRa4VwtqByKoCJroh2GigEqYUTkoQyGCgP8IOCxH/6Bn7wJwozRWFXWsRukgjfTGb1ZwPZfDCA8HACgohi8fQgTKlzIsKHDhxAjSpxIsaLFixgzatzIsaPHjyBDihxJsqTJkyhTqlzJsqXLlzBjypxJs6bNmzE/AADgJ+G2L704PQDADiE+VgA40GoITwgAB2bu4ax47AOEp3zCSZ3KtavXr2DDih1LtqzZs2jTql3Ltq1bsTp5+vyyTChRhPTkAADBqyE7AgA+ZEq7aMLOBbnovV3MuLHjx5AjS55M/rmy5cuYM1eMq5AZDG5uENzdN+/N3r4M7ex8sezssgs7f/TRTLu27du4c+vezbu3799p4/ZCOK8RgEYwANhRvA/eDQAvtjXcCYETWh87dwDfzr279+/gw4sfT94yvUKtMOqzR6+9xLiFEHLbSX85Qng6AhBpOG8nBmdl5QNNCwMoQAs+5SWo4IIMNujggxBGaBkjQy2EDzvsgIOOPgvpAw81ibwhojPrQMSZfAYAYEAAyjE3TxgRoNKQaQCYQJY+6MzCAQBB2IKghEAGKeSQRBZp5JEKahIBAAnpE08wInIwRTUcJqROIirQdwACaJDzUFxF7WOOEAbksGQfzHUj/kALDu1EABlj6VPNFAAcsAExSOap55589unnn4Cm9M0GTN6XCH07qTBMPgjVw0edJ4zwARlukAADMw7F1RNC14hRiE7A/GgHBIw0tA0AAWwQjVja0JLlAmaME+istNZq66245sodhYXmk4sKB5xggw8+VNACOPvk44wAG1hBCyqcvLOPKB/AEOZCmi7EiU7XokFqQ18AUEAWYjGTBQDMiiGrruy26+678MYrL0u8IqQjA3UsU+I+chQwyT7v7FBdQ5wAEN9Cg+60aULbjraPB98uBMxOCBzsVTeggIAuDEvN6/HHIIcs8siA1ruPHQYYIW1CjBygxD6TDKByQ+sA/uABQ+10sNMT9YiSkBUDXQtAxAqdC4AO3XwVDQ5L4uDLqiRHLfXUVFdttW22VABAa6IgYMVCtijwwLQEfN2mdgwhMcDQPYTggxWoiMGACisvM3SpCymx08teocKDAAB8AeDVhBdu+OGIJx4TPR4AYMg+5ATwAdQIkQEY5ABgICNDxMjFkCEDIUqABJZ0cECYhdzNkAUKe/UHBixucq3itNdu++24Jz7JVYq9Q0MAOCQtShYNAADHPuygWsPgCQ2zAADDMdQyoju1EMdVYfahukLHMLBT9Dh1g0aKAJgyT+7op6/++uzbavI9ngAwQAMPJFAAADigQxoc8jOgRCEA/ozCUGKxlYVMDwC1wBA73BEEFmUPABcIxkIeIRoAFNAm3UDC/WhQjQu274MgDKEIR+idE5GGFcnZCQxaUcB51CGFiLIDahpihbUtDCHYGc1OPsAQKwDmB1MhRwq/sC8SGvGISEyiEhczCQ8Y4SLsiAUAATi7hkzvhvvAzukQshMbKQQYsDHYTdixCVSlwGdLTKMa18jGNkIGdJ5LCHbeoJj+IABvCUnEUBBgk3uwAweoUgEw3EjIQhrykIjMSesUwgMA0HEf2kOAJhbyhIFYTCbsKMVOFDADyiXyk6AMpShHia1FJmQFAOCDYnYyNoVAwgE2o8kzhrC2F9iBlLjM/qUud5nEbClEJ4mwx8QAwLefAeaWMlkGCgDjBenw8pnQjKY0D+fLhMCmFPhInRh98oKd/Csmy7BCUvDgzGma85zoTCe7qokQwHBjH9q8JC90MoV1veQaPyCACnLBKHX6858ADeiQ2LmPnbyzcQ6D59oe+RJiaMCd/RSoRCdK0YoCh6AG3cdQbqCQb4hhJ57woErMEYSkzKJKFk2pSlfK0sdgNAslGooeFOILIOwEGy7BBy0cMIAHVCKiLQ2qUIdK1Kmw81RfYEchBnJDP+zkDVVMSSxW05qiWvWqWM0qSY4aOHYMpVAJcaojo3qSH7DSOlpNq1rXylaGcHU4QyGA/kK2YdYBvHMl8DjCTi5wjLb69a+AFepbNQqAIShEGzsAgAy8lBJ8tOMIa7vAMAJL2cpa9p+DHcoNe7GTpKbkHbfQGgI+0NfLmva0qCVlwuK4j1P1oh2wxOM9NKmclZlkHHrAAAAekIbU+va3wG0jr1iLDQwUAxUK2JqV6IQACZrkHtzwg/dUoAZ5BPe62M3uB4d7w2J8gRs6EMDNEgIO3cKAGs/txQ+ucoRlAFW78I2vfAnHXYX04rs6QRvADgWAK+iPJPXABQkyZwdqvHe+CE6wguVV34T0ohTQyAAA0JCQddDIDiL1CD5wkSUM+IEcGV6wiEdM4j81eB/tmMQk/ihxFWRCDjscGAxJcqE1DqTiICXOsY53fKQTc0MMutjEUMqREG4Apge7IIkSnmeBYISYx1COspTDM9xcWEkRvSDCTq41HwDo4UcgGcYDAGMBXYB5ymhOs5p7M9y5fgEGVxlNaXYym5AQ43nEXLOe98xnzRAjjAvjLH12gOPZDg2tIIkLWPvM6EY72i2KdjCifoDjebABVX/4SD7cIYUDEOABg3y0qEdNarDEhY8IAYb3dmIfgMUAABIAhUfusYwsHSAKpc61rnetSABwFCHfkEMDWNTq5AFgBHjiSD6YQacKOCEevI62tKcdkrhAYCFuuMok6oEQZ+zEBx2hRzL0/ooBW3Cb2uhOt7ojEpcvLMQKornWucrGEXgYAs4/IMX51s3vfquboDm8VuMYcMmLzGMOuv1BK/bt74Y7PNfRkDBr93ECAEzBulwEgAVCjRFjoAEADJjCNBj+8JKbvM+7MyVCdBJShDBiJx4490WIoQTRsIDjJ8+5ztF84pUDoBoJ0d4BnqARJyBgAEXAhcx3zvSml7jn+2DRXfcxkAckIiNVIMAAjhCPMzv962CXL9QzmvEPMMciVRDNEXAc9ra7Hbtj9+w+eLFDjPgQAEB8u973ntqeq6OrCFENAr5JEWNowdNP5LviFx/Ynp+qDEW5BystUo80POAARmA74zfP/nmsDveSyoAeQnABc4psOhEOkIAfzt751ru+pcOt6j7uMdXofRwAhIdIPqixBgCQgBRLf73why/R4V6LHKoZTjeKBwHmQcQdvUdAJ2xL/OpbP53D7QRC7tEK3WJzqYGbiD0OhYAv2PP66E//MxscjgEDYA3uaAGLsNgQeaTBAQy4AmPVz//+j7LB4uB+pVAKCQAAnyERlmcAV3AN/teADohIDYYPq5BK5tACO5EeEUEMR9cE6fCAHviBa3Ri9OAM7vAMugUAJNcQfzYAQmAOIPiCMGhEw8V6HPIJV3E8EOE8AIAYMdiDPsg+UJdFOxELEfFVOPeDSJiEiTNcM4QQ/g2TUAtBDE4AGE2ohFZ4hVXTZgthCY2DJg2RD8LAOgRQcFhYhmYIMjO4EI20RQ3xDFniALh2hnI4hwz2VbWwECwAAEwAbQwBD3NQJ15Ih4I4iLiiJE+1EEPhfAkxD4agW1PwX4QYiZLoJ6sFAgshGsFwYNSQHDCADE82iaAYihGyWotWMzCwfwnxDn4AASDQCSk4FttwhKI4i7SIE4a4EwrROdi0EOkwBgxwBLXwimLhDC9wAmiEGePQMbWoRqKAaMs4MsMFVuNgBySQDFuYA/jHCMIoFpMgLuSCGemwBT4ge8+IRKhwAiDgBuUIjV8FVqomCPpzDJBgBR8wFA6w/gjUZxbadAGZ0Q0GIAGhcBmM8AFy0A6ZMQmsZxnAkHv09QGakJCSoQzE4HWSMT2oto4gwzj0gRDsUAYAcA11cAELgACAMQBSwA7BZxMtoIwPoU0MUFqVgQ+ogCqAYBnd4BQGkDSXAQYMkHiXUQgLAAEMCRkbBgaa0Q1DAABiQFaQkQI9KZChM1kY+TEpx0oP4AAp0gHkgygUUAh2oARoUAhRcAEPMEVmeZYA9ABquZZsaQRKwJYPAJYeEJZoWQho8AA74AEBMARnOQk6mRBNQDGQsBDHgAhoeYxsgQ0qJxnbkENTRxmiQAEAMIaYoT01UhnssAAFcAEuVhl0BXiW/qETcmUeX4UIU/kx0Ug9qrmarNmarvmasBmbsjmbrmkHfqAHidWaBHAEfuAHX/ADb9CbwjmcvhlnyrGaPzCcVrYP9EAjcgdPfiAIuSCcnMAJwokR0QU+DLEOnaCdD2GdvRk99JBsENGYZHcSy8ALEOkSdjFxk2GZPEQZxgYA4HYZn/mck/EauHgZRniaHjMJhkGbAjqgBFqgBnqgCJqgCrqgCUoDfzgAP3CXFrgTDmoHudmaO7ADA7ADNGAzWfAALfAG5OAHdoADAzAEaDChr+kBX2Wi8jMEdhCjMdqOqrkDShA6uXmiMvqVoaMH4PADO7qjrRALsRCkkyBFQRqj/kf6oWiQpDGaoU7qB92QpD+wNjswBzTwADKqBG/gpEGqCuggVnViB1mAUPVhBx+Hl1nwlk26o2+gBDH6lq8ZorSkJTL6oTuBA3+oHG/QoYgCSGNqB4UADArEDiRqB/wzaDyaHVeapVvapj+wA176VZIao2/QAjZ6ABW6ox+aBXYgCuTADrXgpTGqCnoQowmEId0wCaWKDuxADxgyD1FUPdVQqLZqq3ZwqwqUC6eaq/CgQEVqB92gq8TKDsgnqM5QqM1hq+0AD+1QqO0Rre1RCV8VC7fqDs/KDvAAq7a6rdIao3qQC8WKIdJartE6D796q9H6q/Fgrmd3D+1hD+yB/g+9gGc4pg/0gCD1gCDwSpHMuZ7+aSRgMAFquQAHcLAHSz9wubAPYLAFe7AJ4AAJgLAIy7ALO5IPoAAUu7EImwBriQBrybEcy5oEILIBcAAFcLIDULJrA5slq3WAw6AyO7M0W7M2e7OyeaE4u7M827M++7M4qxoHcHs2OwB+SrPdoLO7tQM06qRmuposmqd7iiiVKqOyeQCkKqN9upoxiqUu46QYgg6qoKSsqgpK0LJHgCHOYAfWOglgOqqpaqteCYkByyfAwAh4i7ffMBHKMJj7cLeMgArtgAp5m7cTAQwPaQuFu7h5uzn78JAux7iL+wGUW7mU+wSJsLh/oAOM/iAHLfAHXWAFjECPllu6lDsCWWAIVmAFOmC6rku5FwABltsBFTABHeC6HnABGUC5GXABHvABZPkAEGABE0C5BKuWv2u6G+C7GMCwC+AAD8AiIDsQEUC7D2C7GAABawkBF2ABankBH5AB2muxD7ABpuu9DNu9V4kAE2sADjC94Eu5HUC+wwuXBQiyQ3GVAuCxDMuiD9AAC/AAa3MAasma0Eu+cBk6AfAAq1YnobNb9nvAAzoALauaByAAAayWFfSaX5XArbm/A8EAD4C/A4G/ahkAB7ywB+C+a2mVq8bCC/u+GayWBLyWsEQfBlBB3zu/almANZy/17sBH0sfNLzA/uQbACZcwYhyslt5wKFzlSkCvRsMmyCLKOxroAIAGCJMo/RBAAjAIrM5xQkaAIABtGZ8xrNJA3UbXM7wCQrxDsBAC/nYKMvAgPtwDcvAbc5QnZ9gDB1DC9XJCSm5D+OQx9EQyIhcCJDACUrgA2vACWtABKgAx5wgx9HQjHy8DMZQna1xDZiMyIh8fvuAD5sMypycDJxgCW6QB24gBpBAB5kQB7L3DqYcyH0MynlABGuQCZxABJwACUqQB7UsyNUJCYXACVbgA2jAy8TSzM28yMNsym5ALErACYXQzGjgBkHgA76My5ZQnc4czuLczKs7zkSABv8TyHSwzeNMLDHw/gKVQCygPM3tHMzTfMxxwMtrEAR0gMhKAM3S7MqBzM3Vec0+INCmrMrHHMj5HMiQ4MxioM0+UJ3OQMvVmcvLXJ3dTAvjoM7szAmZgM7RbAlE0M/VmcziTASt/MzVOc2+bAli4AOLvM7OzAMvIAPEcgI60MxuYAnOvMpE0M7EIgM7Lc42IAPJvNBBHc5W4AaN3MyuuwI8wNM+wAMtICwn8AEtEAKV28w6sAKUOywwAAI64TY+oAQoDdXV4gOtW7qSU7oYgAI+ICmU+wIu8LquuwEIwAAc0LJ4Xb2UK7uVq9erKQA3vBMOoJcMysUCusaODSTRsAz+Oi/1UMcIIccc/nENc0zILFkRtQwMwVcPfpyMnGAMn5yKwFCdstLGnOADiKktnAAgFo3I3ZzISwEtpxzNpjyPrvzU0UwH38wJboDI82jOaODMaEDSQt3OX025Uu3Ma0AsNlC6PMDVr7s24/XY2r3d3N3d3v3d4B3e4j3e5F3e5s0+VTABSiCVDbEI5/3eV8gJP7B/vGAHu+mMjPFnduAUBFBM+7AMXrDBbAGevWkb3NAJTDlUwBAI3gnfZsgL2FEKijFM1KGOjgFvRYEdd4QQ29BNiHIEsjgW8yQ6/u1yvVmFi8FZP/CYvKAHR0Cei7EOvBAmwFCFvYDgInN3bnIE+H1nP9Dg8EIP/n5gCOSoELzQm3jk4IcE4WOVC89TsgpgAA9wCSj1FiJAAGFiBIFRD/qwBwCQAIIKlFvHh2chClGgBIGwExOQEPlQCU+7dQCLFveQDS0QAW58H3q1EwewBMawGOlwCCveEPpgNABAA9mwFvpQD85wCH1gB/m4DqJgB5MgymzhDCbAls8DAm5cD8HAOgcLAFznFveAfOfiAXbgggrBrQtkD3KuV2UMAC1ADShFe4jiAbPA6kpeSEz+BuVASwiQBZDQC27AADeAU4yxBlYAbfNgDUMjCuhwBQZQCcxBDAcwAETHFpMpBQkxDXlYAcB7AQf7OG4BDp9wAwYAAuDj67LL/gEHUAbbeBaecQPMQJE1QwAiHAAxcOhokQ/awAc9+QctkAs/Ig/OEAb0MQXcUOWLcQ+pAAAxEA3z8EoH0AGGwAgXYO1xThaisBMC4GmpRObkQLQcUAkKLxa4MJJS4AFYaXHMUCWqQB0WAEsjX/K5nka77grPcwQJ8Q29dws0zxbsUA6l8Dsm8AzFwAHLoxBOEZ9qkTwHsCn5QAmp5wr4cAzEEAXW7hbkQAMFYAVBgO4IAVte8y/eUAFK8RbKkCVTEAzjQHLqIAAvIAeMYAICoMZoMQ5TUABuYJAKYQ9lFAAeuwABEAbq8BjzgAYC8DK1YO5NgOrEYAEXAORm0aED/tACViADA/FO7MANz6GW3uNfZ7FUHEUPhlBS/aU/5gBLFxDsfiABALAFhV/zbbTrfsBU9gUA8MgY7fAMZiADqHICqHAOgvB+e5sQqsH0abHxG2qQ5yBOmSBzyYP8aeEZArAD+RALYL8PfzC0CVEPswAAddYWqkYfKnAIqJ4PwbABHRMNFXcW+mAOfLAAVkDpE8MswlwIJxAAj7kY3jYBtFAaAIHgSrp9BfcBc/DH4EKGDR0+hBhRYkMAADhw49YJBgBu7c4AgECEE6c+EDAkm5hS5UqIhQ4A6FYwGAMAJ9sZGQBiWcF6oCD84MZS6FCiRY0eRZpU6VKmTZ0+hRpV/upUqlWtXn1a6waAN5kSAPBjcF4pAFOwYZ2KqseABy+IiNq37QuATO8WZgHwAa1THy0SaNqH7QaGYgu75d3L1NlGBs7g2QHRqyCSAewWcgPQJ7HTa2J8+JAxAUAhy/PCWFlIhsC6zUTtTRLg41rDdS0ALJBjME+CYPpaQ80iQEfcHzCmMWRnAMlvpMwqMvjyZSMAZ6cUQHBj8NsRAJKZsxSFAUAZX8oykajYy1YFAJwWbvsB9Pt8+vXt38efX/9+/v2NNoKAK3aUIOALg5bZ6Iug/JtoHBsI8KCSbQySq7uFeAGAANQYhEiaHS5YphgIFFxoEsQ4ZOibFSo64I9G/jCAoJOCPgDAsoLuCSYzFFMah5QTBAjLHQ7cM4iRAybk0B0PCHBiGUYooWWegjgBwAA3vjGIkwdugGdHiTBUAJV9lgHhDSkXcuZEL/fpBoSK3nxzChSAXGidubxDUZQfABCAAwAQCLCRQh4AYKF7aAFBvjUXZbRRRx+FNFJJnfKjojfYieU6UfABZoqaerknUlQiAACYfBYaiy679nGGxgVseTQfZyDgpBcASDRIiQGWW1QTBN4MwIGKdLomgxZW3acdPnSctCA7DIBgH3YAGMegaGgIYMdpASChk2IEmWGHYfDpAwAH2lnIigGmkGdSJww4A11bw2LINr3WdAaH/irFmKSXXkr5gqaKWDNomo3wRHEbXRQpIxNUtvrCD0J32qceXNB7g55mN+a4Y48/BjlkpCoVkB1hQ+iBBZqeIEdSdQFAIxOGqIHhiFjqybfKeB+VBw1abcV1zAfCZPQbM6KDE4AjwBn1AXT3wccWDkgg5tF6ZlvIpUKnxXofORYoFMVtWQBmn3G0MCALecp9YCFaNgDgklAjnXWBWAqy9YlqswRAAsDWnORXXzoqaB5W4K6IyIo7QQAGahbVR51u3nkGBQAEsQZuGEZyRAWlCxM5dNFHJ7100+nLxE9PpFRlqzc5gOXUSNF4CYEHPhghi0miuYcVESj44IIAALDD/sYdiSHDFo33KQSBC4wRjIE3nnZCAVWWX5SdddbhJpoYAFCBmXyMsWA0qHOp4AAz5mYUn1dOkAPLgjwA4IZ93omBDSyj+WD4He3ZBABgQLF0MGEBuFgHDRAAmHYw4gUCCMPeIgWM25RtH+aYAgLewAh0EYNQHsDejnABtmMwBBSkqggErMAIQzhBAgDYgjoe9QsCAKAR8/jDSyAAAWHBjn2nA2IQhThEIg7xGloAwBwsc4936OsAWRDGDx+VCULBiQAQoMM+cDQoAOAgFiFEES9EsAAhBEIJL/kAPvJhiQcYoIwXIMAR8DGpaAgwKPiYwgBsFwghAOABMnsUNgJg/gAW2KEQ9ANALQoCDgM04AEMGJ4pvIQOAAzgCAVxxhMGcDdwgEQJOkCAAFqwIEkdQmlz3Ic+brEDA9juAWBbgC4YdQ/uPGEYBgGGGAhFuwwh4AA1vJXxdmSECxTCDvryAEroUQs7vOkAapBiEaU5TWpW05r8yQcmHiCKM92PHeyIByolpSU0kANTtSBHIdoFNXp8Ex7R5BCOLEAABNQwljxBwwPoWZEuTUoesRCG7OBxhAH8iQAW0EU9ICUPUQTnAAgIABxaMTd94OVNm+gmh+aBhkoqoRAqKAAOWNPEDBV0B9HwzaQKAYBcGCoatqnIDuxQC3hyCBcZYsADWoAG/gYYIACbWAc7mgmAAwzBDrGQR0q9tIM/HaCgMbzRPL75zXVe06pXxWpWtbpVITJCCH2w4EJI0gfNhG6lBFACx7bBiD4QjCGc+MAX3Lqje5AFTlwyyKHs4ARelI4YvKjpopiatBtyjBaDBYAXkMRVxjbWsY+FbGQlO9nQdcMOO/0iZfeDD1wIwQNZKIQohKlZ0pbWtKdFbWpVu1rWtta1r4VtbGU7W9rW1ra3xW1udbtb3vbWt78FbnCFO1ziFte4x0VucpW7XOY217nPhW50pTtd6lbXutfFbna1u13udte73wVveMU7XvKW17znRW961bte9rbXve+Fb3zlO1/6/tbXvvfFb371u1/+9te//wVwgAU8YAIX2MAHRnCCFbxgBjfYwQ+GcIQlPGEKV9jCF8ZwhjW8YQ532MMfBnGIIYIRbnhDxCdGcYpV3FpifAIQ8fmBE1Y8YxrX2MZWhUQKIjA8A5RBGDcGcpCFPGTDykAAAMhCL3wREyI32clPhvJ94BqDaMy1dKhowSvAGGUud9nL9IUrGzJaOlGcIADZ+HKa1bxm9cJ1B/0sxCJI140iCECdbMZznvW8XR8AYAd6eFO0QmenW1l5z4dGdKKNu4wXJA0koiMHDBSraEpX2tK8zYSrFnCABTzABEOhR6hFPep4zCPU39zyROThTnEW/gQeU231RNbBBgEE4tK3xnWuW4sGBzggF8RgRAmH8o06vMHYxz52EdBg7IrQayXvIMNLaNAKg+gDHa4DAFxUog9nxGAEVSsIPcpB4hIjS9fnRne6qdnnOqR6JSb40wPk7QADCKDTCbCABz6wbzAIBRUpeJP99qEOZ3jqTTRYyTliIAAoGIQerujzmxyQCHTEWt0Xx3jGPaarRGCDG8xQcjSE8ocgrGEknLCEGDzKiTwAQ6FGgQQRYHBkZhjDUwSwwWdG4AKVmKMQAjhB19aTlxf0oAV+OkIr+qlxpjfd6WsqxAU40IMfuEkAM9BPNxoAABDQjwA+IBgx0JySZk5A/kwGIUYh+sCLbeTjGrDgDgRa4e6n193ud09M1JN29f1UMY6CoMVQ+uABBDBiIveohZvs0DK8N97xj5cKgZAcnQHkQOT6qaIZ5CeUZiZgEiqZxxtqAjrIl970p2dJn2MAju1xoxxDUUYXRrBvEzDC9rYngwn2ve8RrKEohLrBaFUyiQCpYsz7UMYksrBCSCijICRDGOqlP33pQ4IDB4hCIsA9FDIIDAAB2GH4FTC8N2no9wCg9lDWQIEAlOL4f/gABBIAKJN8QAfcUYHzqb9//j++HpQYgofKqQlQAmdgiV7QAztQQDt4gxZ4gCywA1Ewp6kCp/MLLIiwg60zBSnq/gY0MAAAoIE5UEB94ZMa4oLF6r8UVEGmq4d3YAc/OKYMwQEmS4l7mIcbxMF3aIdSswemIJShEAX0MIXjA4URAIBNQIccZIdusKigWcEnhMKLO5QbAIG+wg9C+QGW2IZGy5iGgI9gcogvdMIoJMMyvDVyCACFoI96SIOXeJMJSIl8GAYPGAAzEL594IYgAABZcgh9WJYxNMNAFEQu04dRW55QqwYKAIX6CMIDcKoDeIAqmAh9GIYWEIAcMECHYAcxCIBCMLfCAQe8yAJtGMRSNEUnwwZke4Nq4IY3QIMAiB/7+ANDYIQsMLxJdAbPYYHLewgfAQBIYEUScwY08JyK/ogFpTrFZFRGFUOGC3C070uBWBkGFSCADVCchxiHPhAeRxuAfSMUmyGIZRTHcfSwdyiEz0DHzyCCs2uUd7CNDYAEHikEIpg9GomAGFCCkXCDDSioSehBcgTIgDy9d/ABISgEofgrXugDUNi8faAFNxCCPDg+gaTIimS6fNiGyWmKd+gGdUBGiwTJkBTJkSTJkjTJk0TJlFTJlWTJlnTJl4TJmJTJmaTJmrTJm8TJnNTJneTJnvTJnwTKoBTKoSTKojTKo0TKpFTKpWTKpnTKp4TKqJTKqaTKqrTKq8TKrNTKreTKrvTKrwTLsBTLsSTLsjTLs0TLtFTLtWTLtnTL/reEy7iUy7mky7q0y7vEy7zUy73ky770y78EzMAUzMEkzMI0zMNETKfUh3qQnYjIB7pLzA57Od9iB264w6LQh1VjB3AYh8asCnaATKfAh28yh26Ih47JB3Egh9DMKnkYB24QB4tzlHaqTG7oBtY0Cqm6TPzIh2Pgg2eYiGv4g2qoqqvAzd9AtcSoh3HDiNtsFnpAB2/ghnH4yKrQTXIAh39sOnaYwOOEiMxEB4zwzqRITqkAzYWwB3Dghlmgzt4yhzrgitdLisi5BGPjgBggpagwBxKTA1W4inxgBmMrggPwhAtcFFlRgRs4xsiyh0v4Hhc4i0npBQasiAWIPqYo/odSeAM7eBr+4DaQQoSJAIYQiIFL0M6pIAduwIZWQIfJvI9WlINXSAxdKIKCuo2WkpR7aIUpEJYY+ESqsAdPMLYb4AD9Q69v8A3L1I9r+IXxhIp2aAYzgIEvEINKcIaPYwYnzYdv4Q4LsQpiKIMvaAQaZAom7YUyGNN9yAdwyATxEJDeooyYUop6oAXvixsDRYo4/T4PuIp2kIMLcMNEcFFI0QdqKMYrQIfI2paaSD9J0YQWCJA/ucWnGKwW6Q99AAcVWAArkCCIGAcrKIBS8Uyo6IbpMIAlCLz8eBMP6NCrsIL+qYgE0LZIGQcvqKIaQQt3OLo3udDregdh8Jde/mgGEqOGYF2DW+iFL/g8/BiHKzAAZ6hOrHgHTKiBEPiMHoiBIZAORXm2HHik9LCKb0Ac83GKPHDGijjIntiAX3lT1FqHhlQJGqmItlGKdBCDF6iiLpQKK/CBFyqALLiKegCGQrCBisjPSMGHWXgTbnWsRSUAQ2iWaBAFMYhVdnSKKtoVhyBT5vC5ArCCrpGIaxCCAmgBcKAKjqoiBhAD/XgTC4AVqdhYh+QEM/OjjVkGMwAbXMUKfDAGRnDTXrUuBzkyABABGHsCP0DaMQiCGmoAeGUOw3GCXwmGUcWKbFyAHVAkNZ2GFxGgx2GJeugERuhSoHUKYjjXbHuKZQCF/h8h13WghSewlN2ULD1wgu1TCTn4QJhpim3wAktxUqJYKQNAg73ghAApBTz1EnDwEwi4lMiSB4OLDI45jJqNCpgyP4YQBSJAwd94Fjfo1In4BikgAICVCmBYABDIBLzADpatCAywW6fgBCRwWuZ5CXptlnUoWJ1FC0LzUu6KBn+ZDm5hx3bgBl+AgQWqj3EIBDfliN8QgwWYAmrwzHdoJgQIBqI4B0EAV6vQhK+AAbk9imch1+eriGCQzclahgeAgElViXaQBDEFX6EYBzPw28/c073gBRrR10mph2+pBMaDLH0wh1iwA2SYSEh5Dl50Cmf4AnhxWg8IgPitivQ9/pdh27prdAqXeAN9SIdbCIXPrY9GgIEa+JuogACn0dits91miTgJdoq62t7vohIAYIBA+NFlKDz6eAc/YN7mbY0+29+CyAdq4A6yjYh7iIUYpop2+IVGYAap0JqDNAiSOVjSYgSLmF2JYIdtMDSk4Nv6rYp5xV/9/Vv/yIdz6GLHugcQnpRYLeGn2IYlawhU+Ar6eAHBLQoPBIFMfIosIAAQEOIfrY91YIZmaFXYpVyHIJQVlpRxkIGKcOGNHCojvq55SCEMNogcng95GAU+KAWDq+KrIAYjDGIhrgQOoGSIsJXetYoDXoooXggqRi0PUpP5uIc8AGOqEGO0yF+u/ijjJpvXQ7aKLqih+TiGGy2KEUKyqDhXaTKCRG6IReaYe+ABSE4M3k1lR7W9102Kb+Bm/aCgP4mDh+ABLSCKYUCEsFIKe6CHe9AmAECF86WKbHABP8MFi6uHdpBniVgG+oGEX84PWDaITSAUVADoIOKFYHOInMUAYaOPcvHlgkCEW4qKXYYIRHDooqCHQmAEA+zlUqYKeuDjqKCHWFDnptjoQpiEkV6JQnDpQigbZ2AEl7bCiBhYip4IdgCGmDWIWAgtdjgGYNjnhmAHlz5piDgGRuCFoV4IesCFlyYNg+AFOZOWmKUHjH6I58johRiGOJuIlJ7ViBjGrQubqVgE/pemap2mQVM6AsR1iHuoFAjAaaHo6kKYa4MgKAC4a/NUaZ4uiqAuCHzYaoaYaIc4BtGFZoaQZmnxab9mB1FwaVxgzUWo6adwBrpbA0KhBaZeCHaYhG7ohkkQvqJ+aZ6eB0VQ4n2gB3l7ACXw64aYhMrO6ULIpwdAg3tuiG5QAta2A9kuhN3egderggfYgLsWhQtAAARgACWg6oII7UKIggkIPHrogwf4rKPeB3gQggdwgAVogeLpj3uAg4oIgoU4BkTQmHeIB3ZAAyVAA0OK7tZuCFFwwAVQbnnzgGVVCl2gnzk4aKPIh0pYkiFYuqXQhh4AADGwjLrea6NYwqVI/mqYjgiBLgj+TiIbKQREeGoJX4izzvDBJmrILgTJXgQLAuvQJlPqvgA04ONJeOmycWqj5mq0ZohJ8ADWlhY7kDfXNohhkLcJ6DeHGBT7ZgAPKAQaRCQASAAncGnRKoizfoAJkERn2AHbZoeZlre9lmknmIAHcILmTgmIzpjhVm4PmFU7uAAj2O0JkAJh60B5M0iG6MAbtwONsWhg2G15swwlQAAKCPKCEIX4jnIn0G+GwPMHSO4NEIWPpgdgICbatvKCQOdCCARiAoPHLgQHTAVOGZQLyAKWNojqfqTWZnGG6KwdB4ZhvIAHMAILemwHRANhMgJ5W4AUCOtwM6Yd/o+FSN6H3U7uBFhuGhxuqBYF+mZtj0ru5DYCNFjX5F5uLc+CLrdvCMgCh3YGE2DtttFuB2AAB0CDmGUH+1YANNAABrCRbDfzhhD15L7akXZ0/BaFbtgBIm91legG+052IegS03WlB0gCGhwGXy/yz2YIpkKAeKzxC8D3Cfh0hzj0X28BG5l04nZzHAhVdB0UEzgG9n6AHVCCVU8rqIkFJQCtQsisiDiGLGCAZG+BffgFBiAEg2iCy7FpGE8FIydTS0aAEGUJZ8gChXd2jWeIQHgJnl+JOT/2u3YGFy8EJndIRE+ABoj1lnbpQkfzBcipQdmAQt+HSeByRKf2kT4G/hEAJgTI9W9fiEXGh1TobgRwgOBmiHLQAQVwdiHABYfTcXkrGzBggOUW+e1u7W5I+S5XApx2Bgd8gE3P7d3OqQfog5BfiEygHz04TlGP+gZAAPAO7M5KdrfXd+SgWFYGhlslAAeYBOzBB1o49lQ3AeXG7obgLCFAgAqgHwNgACMocHYwAxGAwCHgdshnh3qqJG6oAnbdAIPohkLAgBrYUJz680FI7lAdgkH5lQAogHpniD4ggAewgywAAUhU/P14Ex9YCCMxnnlohGcsFbEKkBugKYiuZaRg9NaAq5j6ASl2CCUINI14E5AWQ3YACCsEAAAg8ITYvoQK9xUiSOAI/qeFxAL5IbiP3A0AIDotKwSB4I+FCZc5GUiQAUKFnD4SBHAkpchCBwAUEukDwBt2CVu29JOQ0cyWGJaJFDmvEc+W++bZSQqAW8I+PEHw2sfpQU94GQlu1FkIgVCiCT/w1LO1ZSl6SkwShCFWoRKChda9IfhF5764TgH02ge05QNyMFr24llzIScQBHeELep4n1QAN9gShOBm5IWWBIyk5EQWpMKjSXfoIfhAYcWWsX60hBBx24vFtfowRnBZJDCHRvp84fmGXuSWIJglxMrzwzLFBG+U5um2KOvNbgYDuLswlvAvypUKTop3H/aeInnVpg4ABrnH0AEsQLhsMAzi/jL3JiU/9c06hjMZAFu4LDZIBCFghUIkBQXAD4w5l55CWn3Qx00E4ZWUTwoBw9oBjOyzDWsApJWQfSB1yJN6RpXS0g2t3JOQgnbltw8wCwAgRB91VQeVQgJqWGBsdvTRRx6MPbdQQwAcUCNBjdCzj3EAILCjVZ8B8OMOFxCzTm88hbSUjS3hqJ6UBH2AJYI4YtWfY8TICMA9J2rUiUimlVgUL4rdUMs+9tmmUIQFMebDnAlt4wVBbwgxQEFKLORGkwDs45SSgebV0gcK8ULWDSNCAOU+y2RmBy+0MGbZQn8Z2UcdMHixzUJYIdBUUjkphBEAq+5jxUx97cMOT418/gGWXPN0CcIbLDlkhWg87QDPQswMRqwRQVWoEll2LBkoL046wUqHsiYU3gtE/QfAsguRyZelBF3pGUFf3kPLViBoR2KgvAIQ7j6MEmTHrDe4ptBfW0a515P7nPvlTQMW6MWBSryb5bRRAbCpxDhdKynGGUvaEqAJyeMBAN9ZSla5C+VjjAc4OLMQLTNVqnGJl1oMM80l2pEATwMokYs7KypUxQOIAtDCJN04g0MAODCoEIcOKWCEEmt+UM9C7RwxwAJO9OEAADxQvc8xGwgNDg0tffGLCWwtNE0WEijwwANrPmDIPvdY8gABdfBSiBAAWKBLUfMdxidOeAFjBKIR/niy0CIyEvBAFis/Nk8oAYhhdBYTELQkPXYwQJAYsVwcLQAV8KtQFiYR4EEhdqSAaCFKOGBEIUbI6IIxCoHBFut2rFAAADTs4EAf+wRiBEE+5JPQPX4cQACa9ESyeu4KzURxN2juM4wTPB1ggAACmDHJmoPnY4sHAwTBLDBB9fD1nME9QMs+8CCvka77VDHQaQt1M5gDFCKPTQBAAEjoBtikEJT+JQQYIWjJAoICAVHYDSvrS4j9BvCANSwvIb2QEQKGoRBRnKBQS7IfQV6gjYVUoTKMOMY+ukGGAAhICYXYGqJ6gI+FVIQATkgIM0TQLpGQQwcOyYEdCuGEmdAB/gctKAQaMEBDOMxjVkYEQMTgQZALwNAZJSAIGqo4p1oQJAoKYcYDD1HFYRRCRhGIQ54+QIAgBCIh+EAFQUogCsYNYABHuFY2XEAQWuywSP9aiAUcsoFjsEMUXwQABZnXCgBI7mYAKIcdUTGTAAAiNEcAAANEmJBuyIAg1VAIPergkDLo5BhSGMgRMtYMgohCjHXDjgF2gMB9fBAARkgIPVBhAA9cQh8KkUrBEnINQdbhYvC4iQuuoRBDzOSXCfmFAQaAo0UgKpkK+Yxj/revhbCjDAMQQAMmcTHHXIVcwAgEAh7BDjEQpC/zcQw+dKGBlqyjbAURhEikwsBAWSML/uRa2jMB4AFLJEQUxmGAER6gqDmpowt20ckwCLIAwI1QAzQsyCL2Ib2BtGAckhpGUF6WDS4YYJd5GQDF9pEPYbSAAITM5DBvYcwcAWCgIjEOAiK3D1FIwJQJmQcazuNSE2wuIeVsSQKABYCQBtMABDGAEPxQiKD1FA0VQAMwJlFCANBBIeswqAg+kZDUWWQhQdjXOh9zD1DCMIb09NY8xCS5fTgDAwDAwQ6dSk90JQRWo+zbzBTyVAAYwAFxO8BESzQPHADgA3s9Ag0RkJB+AkAGLt1HIgGAp12BgSBHit0EqrAPfdyiIJJY50wsIEqrYIUAkWUHJMoUmso8AkSf/hFZzYKLMY7Zwx3sQMNMgBvHxCrkGlkQgC9EApwBvEy4C5HZb6yr3X20QGg88cAs7CGSvmlWIc4gCw7W2TQABCEWO2zfxCICTJAhAE3dSMADiqmQJgDmAQpIgBl0wlZHKWQLAKgBLN67phHsIxeM2QGDilRdhQjOZD0oXINu8gGOwgUATpjtY+hySLBpro4J8YVVFfGio97sdACbCQFU20DEKuCm+KBFT9fQKoJoQCHdKK2RbrqrmbyAVTCS0RAWso0LW6ewE+OUQjK6xda1oAUr4y9NFFLQv2IyKogKwR4DFZkDfIcdMwFB/kDbU2YpJB89OIBLqwGAAHiWhXJa/kiE6rvVB7RgH7u4cEsXAg8jtuCUdZsC7ETiiY9kd1eI+sAu4sSAkI7sVFasbKSZ56rDrPdLm62LAIrg0igUBAwjfCAA0mFWG01rHoyhwGwHIQAjKVe6xpntkof2JRwv9HwhCEKXE8INghRPJMg7QCJ8W5DvVEa+FC7jQgJBw0bPAw7lTUgKEFBsg9XlAZtAzUwmIJI4fAQNbN7HsGekPSb1NGP2QsOK79EKBMDRjogGgPbItIMVSuwAdKvb3Z6ykDv2NBPzJYj22GGGHASbvFAGp2MwS1aRLKMFJGhGoETxERzsoxYMOAY9cgtd/RB44MLogBBMYgqCGHDdkOlp/mDnlI/myOE7BO+aeEk+uECtl5UJEdqEweZXAES2G0MYoqQkDCIfcGHF+xACBHq7j2Wy99wG680WsLGQOzumtjJOSISyS47kLSQRM3FxYRgrCUZcAG5m7Y34voPYBLhY4+RSCDZAoitTjfsjeYirY3DR7hFioOZORsAkRMJUAMQClbkl7D6CckwTiiTtYWglIiTVFG/yVQRHSsgk6S2SRXA9MnKI61l1uxBYdYy2CKo8ufjNkEfXVRe/3S7uH9MSFSziBFwNGZ3I0miPCQIAJNhrg4oQdOtiF/C5zxgYKHCBAwGAA43IucQuIBJNgOUNSmYNA7yx+vgq5A9cG5xo/m6g9YQUyQMitQUqvpEQ7jupzRwAgDoVkosPfEDHgUCUtzxKZQXOTOwcbGCYHbECADgAJojEECBAXZUIXThAJcTcJHwATHRDGQDAFKzfUaVBn4nEX8TSQkQGK8ScmQFA67EbAETgyzFXKgFANCUENRUON9zgLNzfFKgDT0WAJuiekyReTMgF88BKmsVDFEAAFGBMZAyfsOAP4wDAACSZQkwDC/BBOxxVGACABJRVnAwe4WSZSGTC/flcaNhIsfVCaAVfYsFDESygwSkWAGTBeAjfxdAFF4aCQhyDEEGAEHaaSOAhCejhHoJhQigBDanCqhHEtMDKzn2DEERAHzhf/qkExQ3i4P21IUHkQDJcQRCYg0ik27YpBDFI4RM00AkEQBGwWV6RH5Eg3HXZoVM9wAGAAzvAgz4oQ/59WgEBlEgZhxSIBLsAgCIKG7H9lCEGypoY2lKgQQSggkIYQ2ixwzp0wzpUwxQQRCzslFQEQAjWQkYE2kKk2xbwoPm1lUJ8g/xNHuftA8QVRTT4FQ1cTD7EAgGsQRYGSgs8gAXMww1oH4wgwPFBxkwUhS6oAB+YQ5MkAAYgwTqWIHukmXpog4KwwjqlmwPEYYVhTDcgjgH8gkJkhDcWBVlcW0KkhqfNiZjMmAogAw8mRC7MgDIkBCZwTUqSCQfE4U4k4449/oDIhN2SwMFyXCI3MIHQKETarcFDmktvDOTkDeBCMBUN2JErSIAAKEFK8N1CWALIqILPlEhDOMA3zAM7VBEq9MKSrAPXvRg68lI9AcwFMNg+4AOsDJ8HMSLM6IhIKAMkXEtTPGNRmAZemGDMrZacAcAQfNY+sJ5KYIWL3SXk3coF/GA+wEMkcA3wPZ9mCmAANEALyAEj0MCsKVfzLcQ4qIDqDdwr6MDzlWa9sANswiY4EOUleoM6eAM6xKZu6qY7FOYkEIMUeABmVt8v7NTLRUBRTCPTsEaTOdmIfUY3xCY5FB/jBVaRUJqtuYRCmANjgeTAzeQ+kMIKHEk+tuLy/m2koMRGAKLb2V0MOzjADwUKHk5BMaiDcVYNJSDKNvoYAvygCM5ExLygp71DDKjgjpVcxfDBxdyDJ2hEVezDEwiNKs1ZAizAAjyASxGEB+RjYIISeL6iGK6XRNLDJEQDE1LeUdUFmi3EMWDFA3AoJmiA+DkVQYBZh/pUhADXPcBKpJzhvuyQIWAFBLBho+FDK3yOHcRcU7jgcg0fHq7oHn6AqekDOzDDVtxkXfyARCZjwG0bHmKRQhjHzu1DNGgCh6qHqSAA3KxpBXTAH1wLPnCNA9wACHjnOB5jh3rAO+zDN8hBC7zCDq2Dm4wY+8FipTUacFTfGySCM9inudSF/gQQYi9NlTB+houJIjL6ZMaYAQ1dgs90w0gqRMDhBHKhQYE6iRvkIzLtSGrUQLCN0ufsmztWRvw4ycO1peIRxGjtgzpMwQjAxJxoAiMAA47R4Yb8wBHI3xAgikjcAw+0lC2sSQOQwYcGlK1KijLcnzgqRLqBqc5lTDswgg4ggYmSpV6KBFmQIGog3cZA5TcMVhhUAzfAZpvlAbtuFsRsHU+GqZNg5z4A5T74kwatKdxcQHWlnUS+XWq+nACEoEJEaMnRgya0ADS+Azs4D66iAddYS6CUYul4whuUAjicW5H4lF8ExXcgrEQYjDgEw1bYpVsSgC9iTCv2Z4kk1dR0/igCHEZkpKQ8NCgAjMGZMgTZNdRHPKZbRuY+TMI8qIMzQIIQfFStbaZwEYQC5EFzZUBmxiJz5UMwEESyUi2RUqKSfYHZnu3QJQUDTAEDHMHZvu3brkExOEY9QAIPkADYosPkdUBRsNXgNE1zLqYrzuocnm0W4C0AKGWhUpJj2IICeKtb7gA0qMc4cIIbqBo7cANSQCWRFKCSqafInEM2wkArKAQaGMBblMg7JAJBYMAUxEIvLANwPUMJHYHeJsQWOGwlQq7EhB85FW1x4GpkBINxPiFV7MM4bABXuIEP+AAR5EEhFAIn7OlOTgA0OsZaPpsYYkNGYMDcClcTXozx/kqkVBiAHGyWG9gB9fIVQciANH0hjhKEYq6XIMjDQtADH4AEVCCBVQVok15MO6zBeVDDKDUACIztImJA6YqEPmhDLHzBJ90rtyHIlvqUGFhVvrFaQrQDZoYZzciBVQFAHHACCZMwMKxvQrBuWxBwKOLpFxJqOzSDL7zBZxAq0eIb1xYpMAwnB8aCqiWEOmyhAv9EULgcLYzVpbpw8CaABwcKKWiOClBvFiTA9SbEBSdP82axD7iBSSVEXRzAH/wEVgTu1QEABiQD4fqvtbbjOxaFHMiIdeiDMyiMxrBDb0gONcBAhYAMgiKvEmhBOiCB0CCtSPRGOz5G2qGHSHxD/iZWCHpqzDg4QyQMlvmSJO/uA0pmzEomBCWsiV2UwTBk4TlYgQS/A6xETPbuGAMgnxIA4JI4hA+UcAmnbtrFwlcy5cJKBQOc70K0sVMxgx18wefgaoRwbKAAiFDYATgYkwLypKkMjsouhDZkAQpMgHHAbGGgQCloTHi8aIkQRAa8r77ubMVg6Y+KRDcALzBUAAAgbTRv5yFYwQm4QR1oztaKrXbVxm0khBUMAGnKYooWii0VBT04nXC5ZsxocfO6wY80tEM7tBHUQUNzARB4gRUYASuoxz3wAnUEQ2BJxQYQoBgea3WITFMckqcoFB489I8QgxgVicslhJpUB1Le/kjHGkIYfMFncEAXU5jnFkgJrec9EINfWYeaGKuknEMEt4QHfIGnrQOheMgO8QITO8ZfRMw6uIFL3C6NGii/9nFkJAL8GG9VpPQlYy/n3qhjFMlhFMNHHAELB1f4+iiUWgrIYABCtMIPfK+TeTX82gRBIB9JtzMK14MK/wBUfMYXIDDzuEkj6MRaPGgOX8zq4uVC9IIe7MABaE2HmLOWxkn8bu2XVggq4AwAKGbG9DOuPgY4DN1eFya6KTFPHdI4sMIZkAAI9EG2DO7iNjFC123ajlNCgMP9IUAjELGh8ohwx/aUiEQL7Kt6HCDj5YltAfZqF8VNCABr5slNkPG5/vTFZ6gxRLLxdSfENygvAMCJPEwBvmhMkTQ2BBz3PqAB8BTFMqwDMWTG65UIWbSHpCTy0iQErXjr6Y40xiyDITwBCWzBHkTI8pGFwJykBH8z565DH5yAd4HSG4zDNkRISiYtKkM3u/EHkWRGdjXbnKRdKQy0wiI2RBLAdn9TW7JDK2gHDEi05C2KY5KtkhnUAKTtFDCDPkSGyT5zY7+loPjBDqxAIZBCVGMzBWuMKBBEAyxlh/J0h1a1gIpEZVeHQU8C8LaTOyO5oGQBAjgBUUj31OIzzCjICqICEVidsjmhBvvYQ9tBRm8XQscML/R5nxv0Y7i0QmSDL2zDNFyJ/mQ1gmIkAptJxXn+NEkH7knLVzuVjHqw9WNgxQHfpVNLICUYwYJ3AicQBAXQT+caOHYBl1IP8D7IwQhMLsbcQy88wXbYhQiCxRTYrw+sAGqfLO9mdUn/Lh0HL1gThFjT9YOGd6BsMlqb7A239VvHdc3MdUDXtUI0xS7TxRN4Gqy0t76GNnCtVync8hMGuw4MxKZPdrMMBlx/QwPsgGMg9Dy4ScSIwg8IgAkUAlFk8qNG+daB+yJ6a2nLb3CZSkwXRTEMHQScAXBhaof+i4W/AAFkQSawCoovhF7s3J7PQyX4wRegwEB4wIMSt5PI90xDUqUShBAy9yhyF3scvHoI/sTd+QCJ45lSzElUvwwvdLeqf9JwEG6EO8aqoqtClYjMf8E9xMKeaMw3rMB+Ywnpsl9BOgauQCF/i7hIMINiYAA4tHDJH+JAjKlk8YIXIAAGzIE15ENkPLhGiAS/YwuzIy8pBMIQbEepQ7UEt4ll76TuIiM5U8vM0Nc+IzKZB2JvuPjkwTjRl9w7GAIMQMATtEIVGUfKTwL2zYk1+EEgVMIb/ED30cNuF3kRJ4Qpk7lUCMD1UntNf3bGpDMAVDmFlzpuUPku9Wyzfi1OsPjm7TMtaM6YQ96gmHFKrIMNVJ87sPl2cUzVcEMHLcQTM1e5P0FP27FBtW6ea9eeI39R/rhBIaDwdd2Etzi6SP8tc5q0K7aTN4MlERbFwJdcYXT6Y4xDHyyACuTCSxIElp+6xgsfcMVD8SEAQHRadiLNvH0HESZUuO/euGW9JpUxAACAqITjZABw0E5UxYUHGR0A4OeiGQBf2CWUN4WAkoQPKCrsQ/ENPYTz3gAAwesgkgE6Pyqk+CHoPooPPhaiWOjgtRsAdkArOhXhTAA1b+ZE0GhhNwACWjz70eheQmcUQXBaeFShD4opE+KkmKle3JwA+hxENSGmQl4frtq8WQoAg2ByCjj7+DcwwnZ8KJI86GwDgAaKD/qhyG0f5n3rcv7oJXRH27cIQUc+2M4BRc9U/hfaUrB0IS1j+A7iU4HhCEUGtermnkUx71oAHMbto7QAAB9z+g5ShKB2WfJ9MAEwRcgY68J1z4RMlJwuTOFKCLFrR8gJMIBuCLkRV4hG43vYCGnxBeC2tMJCDChahiqriNpnGisAwAAchbwBECskJgJgQAAQYEQhwNCY6psGAICAGCWQuy8hTRAY6SBvMDAErkJECqq9N2ADYID+YNvmh80Uiu+4Wg6yYyL1YJvmBgRIKMWegwhcCDAIFNIMAM7uS3KfcWixrpuHlCLAin2smgU3x9ZI8DyEKLKjKJgWiCUh9hqjbz+qeqFotI/W+QKAH6BEcqgL+8KnFgDPIAc9/orqiQYhK0SK5UsRD5qHmBM0ascoAJBSiAwCTkLNTgDmFAUCAA6oiiZ6nFHroDhFY/QgGAAwQI6psujQVIRiBSBDPZ9cSBwSAHjCOoSUAMACYBBa5gIAzEwoTk4R8kJGJBAiZoRI93HDIlWxzfYgN324LxABGjvoHk8owjOhdcihzwFGDNLWL8C6c1fefXxgwJugeHHLGeiuA6DAhFjMDiEbT4Krx69c2ocT7AwOSimBF2Ktr32UAaCG1xJqxw3mkMmHTH8XChhI7hreRx9pntrhiRwWZLQdVBCih51UaEsIjdYKUeKGdhcKyUSE7smj4ITYaa3bQSVMyKrX5Nrp/iBDRALAwoRQaeEVwfYMiq2Qa05ni1YrEUxbWjgIdx+5HMhkoXdokFGDLahRaJ7y0jKuUoTcAqDkfWpJ2Ry7jqPlIHo8oIiYd80+SJmyMVBgkyMX4k5secjlgMeDFinx7n2c5KyEqVNLNaGf8aYIF9TukmyfISjKwl16sPNAIVReuEOwXCqwRZspKKrgm4SqkU8hRmR8Yp92xqComtFlRUWGNyRlHeKDJB/ckBkSMqdsychxy4NcELJDJNkToiMCACCBfB8di0NIqc3vq6dwigBQU6GFKTI+oW/k0ESwmQ7wB3FRojWsWBQ+WKERTBzEFhWgyNQQEg2xzaRCfBoC/lWkdwEJvCJbLVDNY1gwDYTggjmTWAgqzgeAyxXlGKBSHVXuYQeK8EFSuUmgA8ogGJEx6heYyoI2ROWvlzGihu1pEo6ilDVgKAF6CTlHDN5ENgDUQWyfsdMV4vYxKZwJAAsg1nrgZROvAKACMEsIIz5wjFPJKSh1ulOeuKQRASbEiPugRx2EdxDseMMEZsxbLMpCFTSqEWiOaE1KCIMATSQkGu0xWD5iwcZ9PAwBQazJIpi0RtExCo/+MlRCwLClfdBMAAlTHAVOgys4HiQeggAACV5DDAQcwAnB2YexkKWQZc1pHyUCgAkQAooUsmMSCADSvJCpEOwcjSqYaE28/tangldibB4ynE4yqQeYjWBTW27hQxWDOa08ZS0h8wPfQQhWg3IkhGZv2sc7OlCz/dVwkvJU5sSy0apfKAQfvdBEN6QHR4pgIBrEkMMnd7gdeO0thq1CACYCeZ92+IEHv8vK9A4CjBVQKgGtKIrPXvgNMQwNIeygCDP7lbQgwrFpPDmeEH4CAULug3YsGGeClHGQbxCDnlvzT83yoQeK7OBvCMHHK5DwSaoU4ifxkosABLEQe3REI5SIqLjI1RK7mUZvC5kHHg1gn4MUDSo8+4NI9KfQxO0jGzqgn6AWE8aS4lECoXCfSO4WDRZQhBXFlEzoeLmPSQBgiwnJm+pS/kM6q1Bgpgf5gxXiARtVUKQAa0DIN3gwAE+U5UO1hORTAMCEyO4DgRQRg0UHtQBb7AOgfP0SMSiSADOcgQCxgI4F7Fm9s9lBAXySjDroU9eSCoFS+7MBuJYHnzweRCkMaOx9/tCaq/AMIe9owk8QYMLVbOwWoiJAFxAyjY0WYbT7gEcRABDCwTkhpgo5AWopCMGDAKaSBzEHGZR6EHJQZABDAOd9nvCTI+CjFRUwQ0TnAZNj7kMJAQAADaj7kUV08Zz3gQbv3mCw8wLAA5a4K0bhRJGLIcQIQ+nGGY5wr33UESFOYsV/PyKlfDHAFWKbBxoOkKF5kMEB28xNKxjg/gCrMu8CCEEFEQdVQTDuBx5nK08pD3eQYzxgZ2tkFp3sZC5RQUC+K+6LXPCCkDUUYIbXpFdkYCyTX97vATF4x9nQEAATKDUPCQDAJnQpSVxQJADHQ8VG94OIYyEkTiSwq6rW0bYBCOGT0SBDA+rrDkiASg6/04QJHFwKx4y0OeDURzE4QICwHYQYx+pAUQ+CywsqiyKTEAxoB9ACRsjhBeDKzrH2xs150Q+lRfnDqFRyiK9EomHVlFVCJuGEL2KLMWiIsK5h45YD0GJRYx2DAAohj49hQCHFhEpECQYDuB4EHSdFiCFgUl+EOGMF+2SuPV8ysXxQBAfrzA0tFmAC/oIBABWCAYZ0PhGIETCDuSIZGWB2MO6EbGJ+2ED0GwZgBrHug7jHxEcP6H3V4Ylk1QfxBRBaNXGTAgAG75lEFDAFgEWMVRTEBUAQmjxWkUTAE9XFDgUKUQg0KEAAtODXpAIwAmd0AwlksM8wKJLdhTSBIk5AiDViNQCYD64PCgjBJ2DTDTBQZNq4oUcg3AqAIRRi4p9pmwuu8ZFvtC0Ey94H0gszU2CEgCKCW0g1PDh185a4BcNICD16Q4CVZ9QIDj5AyfIhNFs9+yCe+FS8UhOAMaxIJAhYBD1EkQNbL6BENsEHLNwqAqy7r0MzdQar7gSfqJlAFDaZxw4GSshu/qChAgTItULuAXsAFMADhbDDCrDtjn0sYgFaol7eCPAAptBDDhQxQBLEWoUu1qIsQT1pkwvBHMoawAMC8jYAluB31pLhUwfoA0+M3YIvgsHONilEHUQieYPhYgcEkAIhBwGufcWsk2AQ6zD4wv6whXAoosJ0SfsYQAqAIRZ0wACyIB0EK2AsIwosIh8qwQMIoA9sAh6MgABaQBg85lS0bwPUqBuUwAV+hbgIQAv4BABcAh6CgAJGLyFk6ACiKlsQQSSSLwKkQNsSQjOKzCxQLxxgA7f8QOOmIh9swQMOwA7+J/kqwZaaAFMWrCiWoXAGIBLoYRikIOUgwAwMQA+g/mMSPkWl2MEOTIAiFsAOeKHaPsLlCiRfuigVvqQPDuAB1GYfjMGDjOB06KHqHiANbCk6AIAAwKAzUGAIukEUCsEJvJARhq4QTsDBMvAguKFtCEAF7KAQouABdiDm2KEMKAISSgYfcKEOJkIEQkGHiCsAPsAzPIUiiAXMhAAYnCELOITrPqAegKEQ6O5OAsHtYqwQswAXJqEXMQAANusgzgEHAkAFcq4FJsIUeIYeYgEHKKIMUiL3KEIJdIDnKIIASkRN6MEPsFEAiqAQcCHNPmIcsHEAoDELNoDMTAEh3GETWsUBHgABAgAH2CGQ6MEByAxUHsAI+GkWdiABHmAh/pnjCOipG3aAASjxAaqAtR4AQABAIZ2QFugnAIgED7Kg8nIJ2riJ15IIAG4g5lCjESTpICLp2A7CCnwJ0QSEE8rQfkjyPvKmfnhpHjoBBECA4D4GAAQk1Y6FRtZnU66iFr5E90DAD+bECn5CYHwSBrQMGLRvCPygy4hB+9TDWcIlkriMcyjiBuzAD26EfsoFSpQAU0xpHfygDG9ghbbDLUqB8YoisVDi3VRqTWACJxXCDXwp6djlJ+nnBvTAJmRIOr6AG7CDfiCgEFhSLXNJ9+inEQxmJ9GiE/yCMoNyH7qSMiHADRCiDKVjarbhBYZKD5wEAUhzKtyIMiVENkmq/lFyotcuglU+kxg6MByPgBNikzIXYhlUcwdYsxCdoChNgwCOwA+Ukn4WAn9W6SCYAQQoczRekn4a8yCCRS1foA/ao34ORi0b02foBwZ44TljgjYz7CDyBgL84A2sEwBKAQmDwirUshHWYZKixjX3TS39AMx8IG/ewJfcjjHo5wd4ITtBgDPDkzCXhTIDdDEpU03wMz/FxjIpAgY6gbpkczQe1NwYRSr7ciGwUja9YBv2gREe0yRTjb3ohwCS00RpUygLYTB1YlbMM+lESc3gR1W60/g+gkKAhE2gKSlEQhjvA5fU8gEgaBkYwZcQYCvv4z/p50JfYBuWwQtw9AHm/oEwKPMTp6I7pYMT5FA2EaBHbwlG6cc1h1EtG/TMKNM1IxQ6D2IcUI9+doAn7iE71dJgRo4yuYFMeS01KdMl8JQyS6HEAOACiCE4E3RCZBMGWoG67oEV8vQL9rOk2JMeeAEyU9QNsKM0+lQ271JVwOwwVbJReIEXOKEP+oAWrmoe3MALYPVWPyI138AIfOD8FGIbGOFWYZUp1kFYYXVTP5VSGEFFV9QT6TIn5cVJSI4XOqEV9kZH1BL2fiAhtsEtKLUXAuFGDqDLwtOlYGMeJpM2oZUq3OIGUk4r7eApfMBcCREmnvIJPkVMGQJMKZMdLpQiNBU0jWAqIdNUSFQt/i+gKJm0TS3EUIeK66bmTK+UQTuBTdSyQtYhXYdqGKeTKhJLNum1WHAtKJahEIyVXVjBWPvAIIRgMT+gD4CVFgIhL+ahYVXWIHDBWJl1O2TISXc2IWgBtD7ApYghEITAWGdFNhM21bwgatQwyqYCXUHgC5ygDnA1Z3VWbt7AzIJiG9TTDnbyBRTWZHM2ZBGCEWAKAISgCrdD9yAAZt1AJJIlIf5iL73jVYWVJ7D2CyCAaoXyzAjACGblVTd1KoBhZvugEASEF4S1XWD1DV4WVmmBZyh0Q/9WRHChQJ3AVzMKcfsAOMHzC4T1bO4iL/AWVj+COIeKT2lha2dlH4Ch/n0+I2WNlRf6FAFY4UZgwA5kFUlU9mfvAWth9WcPQng/dz+LFmmxpRDMdiH6IA92AAEENyiqaUb9I3EltUPap0UpIksRAhgY1QigVs3YVkRgVUmrQqtKJ1eooi231V2CFVYDYXy39AcIlmunQmJ3gEde8gNM5XRRdyGIQR3t0300M0s5wUwlcH4/4nDld3z9AvYQIEXPtg9Oh1HWgRO8wAd4V+PWIWVZgRF6V1xooRBYgRO0lBfmIXaFlRFq0li/aBl08w0KV3YT4nBh41ORtnAZ5R5oQWULFxfkq2TxEpm2oQ9YgYfXdYmZmJse4QEO4AAW4AEU4AAQoAF2AGP2/qEcduABWsADFnIhTekgZs8DEGCKH2DwFAIMIIAAFkBVuqEQRAEYJiHncg59m9gZgMEmhsFkF/IC0KDsjEJL4hgNPGAHFMWocOFanGFv6OG5MCeMAVmLi6KO7bgQ1NgZ0OACongBKjIhZu8CCpJY8CEWhED9DoIRLxkR1IgdBFkhsGELtHEAYyGQe9GOiyITHkADm7iXfXkYEKF8SXIdagCYYOOWC0GHWNmX7yPxEsDdmDma94EdCmESXrmXwcyGp8LVoI0etEuawTmcoe313riJpVgXvsQZJmEdp+IeoKacxZkqGLFkSCWe7fme8Tmf9Xmf+XkqjiGYC2EYTLGa/q85WyahDbdZ2fqZiWVkChZaRBahEPB4ifUhE0gAmqHtHoKjHtLAAW7voUG6m+nB9UwBAr45pIviHkZ6pKmhB4gNpWH6XEs3pmm6phkFH+CBHeahHBFgonWtDwbAAsRPRHrhAhDA7mw6qZV6qZm6qZ36qZ2anKCaicmBG7yBHbThCs6AnnTNHTwhEbwBHRpBBHh5qs06HfrgDd6AGzYhALDHqUtBrdV6Clggv8y6n29sue56r8X5HlrhKcLgDZzUl+MhCg5gB97sPtKhCRwgmfn6sSE7siV7sikbn9dBqivbXdaBVRjgC5bAB5Ba16bKN46ABK4AAjO7psUgQr4C/gfsWqkpcwEoIbXteRikCVnYkbZ1u0rTUiPSIJrlwQyMwIw8VgsoYAx8cLeVe7mZu7mdG6QTiMOe+z4+NQAi4ANkILR1TR7chEKuIO2mm5/FYCAhAAcoOamxQwA2QAx+Jbyh1YMo4ghK4aPde7fHwQsuYAA4gAyS25frYRnAmyqWwQes4Bzq+8ARPMEVPMGTlQGKob0T/IjFABR4QTlJsh4sYUB9wA0gfMGleRzcAAh8gBMK2qZfdQ/MQLs9HJm4YECdYIMtfMVpextYoRAmF6YBvIBlfMd5vMd9fKEbwQC+oBFiXMHpm5vyYRuUXIl/nInbgRuIF6r1gav1+RrE/gAN+nuq1UHJx2EdtqGImzzMxXzMybzMzTyf18EXtuEbEvvM3VxeosEN31ycxWABUhKkxyGB84AIBHrOFUbDiQASnroeOEHFlRofjIG43eUdErgQrAAVBtHP8XkZOOG8jSoZOAESxMAHCqHNJR1bqIQTPP3TSf25v0ETqDymGYEREuEJ1BSqvwEJPgADPsAQbNoQPsAE5qimiUEHPuADCgta3cLZHjoaigACIEABAkAJykuyL+0DXj0nybAjiaCpreDXIeAFFB0MRuADugykiUEKLiACkAC1sCUenADZGYAAiKrU41kZZuADLgACjLkoyhECHGAihkDF4vnUGaEF/qSg2Wn7Gz5gAyYAAvj9qeFBCBYgAQL5PpRgHxGAADbA3Zn6RhEg44064zl+4iliBLC5FHSvPWu6mrDRnaYaGE75MW8Qph8GAF4gGWi6G4oABNAAO15I17oBBrLAwB9aH+qBHSzzyKE6FlsSWu9hHt6hTJt6HsABG+vmIL4PABABpgOBMrWZUeyBHbKzYy2+ie8BHmrBp1J6Hjjyjew5H97h5inCFZpaFFBZW8yhVrxeqQN1k6ZiGdj0R78eprlOO/KmPsfzX5pYDkk+W4CV6Ely5HCzqTVDP0mUn7806oVCRGPaRvCk1JAS2myyEcA8ny1W8Z86PHWNHGCg8ScF/n+V2tgoP6UAwKfzmSIu9Qa8FzagNNf2re77nqGLq0qzTPeZOW9Ef6E1I7CwpXPM+h1Ai4IVIhe+HXaZg+9V5R56AYITHBhy/qEfZtk2dNyMjfCZ2PCH/13q3iaNP5lGrvWduvgzSsfDGTTU3yUPQHFrGlWA34i9AAYuF6TdoAzHn6kBgtgCO7z2GTyIMKFChdwA+Fi4zw4ACJwgWryIMaPGhPMkgqiIsFCfghtLmsxYCACAk/t8AOC2kBkIlTBZ2ryJM6fOnTxVPti4DAaAHzV54nQJgJ3RpRq3/QDQC6cfmkyrlsSX6oEHUQrvAfgA8QGAnzlbEdBiNa1ajPce/hBYy/PeEQLADupT+UXpQXYHPuCDe9AXEABs1tnMtwdANojquECtCs9lj3qAK6vrAuBL0colqwH4yBlwLwE9tsHVxaOR3tA240BQuZq1bKvz0DiEKJHi7KX08nzNtHvnIZV/S1pr0WJcTBFUgzt/LnvA2OIYt30BIKIZdIOcxMbevtFeLJVRb/4JoBg84FZfw47ViQYBI/X0E75ScKP+QmUbnCBch1ds9PRRwjKcfSMGADEoxxI1VwDgyTwLabPDY0x1BEAIXOnHUjdDAJCFNhx2E8ZnINk0TzvqLQMCB8rAlQkHk6jIYUKcfACbQTRaNA877Eh4kz7zuHNPjd9B/iSPMyo9tFBuFb3zY40X4YMLAA6gISVGx6iUS0n2zNFcQk4116N689Czkz70FJklXEYAsEB51V1H1D7t+HjkXnhulA891F3UHQDllKQOOOzAow9LPbJD5D7vmNMNOUBqpA4kKgEQy54IocNNp+pABMoIEE6K0TzkdApOowbR4yM53aCJz6nirJNocOzc0N5CYj2Q50bzACBfm9CZ04FKwu4zCTEIpaNSGd+1M0k0RkFJakJ9hJlQO38iZE8jHABQx44G6QNPLt/K2RWUPmYEJIYuGLPRnZou1CM35LCjjjfvbFSPvL1C1M4YAKjwYkL6+EgqnrEtqtc863Cj70Xq/nTaqTjyGEQODSp5MImPF+vZDmUcscMNNp7wAU61CquYDzzmqMNOrRutIw7FsxrMTjAz3XLSai0jCtE9diAQjEWsFlcOmjapiyc9QioM5Moi3wjbPNjw4Q06bCJktSdvvFEKOPAghGfI+9ADjjj5/FfNycGIjSJl95yztkX9slMON0ofRI853qhTDjlv/GvQPJtcugOeMkc0ESfgJPKGJ9jsjdCj3XTKDuU80swNOvrU4429COUjj+IYtXO5UuwsedCdeZNzED4+gqOOzD5OLM62+/iIZp+6Q4Q3N91kvtDqAPgRnrlUfTfmS/R0U8ob3JijuUHskFMOO/ua1E7e/sKzIy7X7JTCSsQj876PPeCgs+0845QSDDm647lvv6EbZvTl94avketKac6q1xkkHqgCWtDW4Y1xXOxawcqIdYZijXL04WtvMIdCUFeHr9XBfCOzVzm0UQpoaCRQqigc/xACjjBw4A2JoIY9FMI5e33MIOsQxdf48Ix3LKIIB6CBJ2CXkXuU4gCXmsLX7ICQeEzhUmGoRrX2wQuXDG4fFOtU1v40j1JozAEi4EMylPYKObzhBguohTqCgSsVoGEzackHOlKGEGdcJ1cKEUsCROFGilUPItxoBLDmAxF9UAyOTCFZp1TkPk9ZZBzF6EUvlsHGhayjGwl5xzcoBpFr/gzBAMbSxzcOMg6KLe4e4CjG2KzHDWb0YhjtuAc1epGMFx5EHctwZDHkhxNsqCQTItsJOxzZi19cw5V2+MIhbmEghVzrJQnJBzmSsYZS9EIb+DOIPUqBAZXw4RaOrIk77ECCXf7CkbGBRyvsYAcxfOEWeWJkLyChC3tJ5AS0YBcy1vCFfH7hF5TMliQSBIMvTEE3bNlGJ/CZz144g3D7uAc2ejHHTIxTRNroRSzyyQqDfAMYZcjnGT5JxUbokxrraEQWAMAAO3xRIfkwxhQEMIELHIAEggDHPpxwKQbsIJ+lkFA3IPqFMqBCIaL4AgRCoAMOYKAR1ChON8ygzzd8/oMadtjBFPZZN4yk4xZZQMEFTjCBE2TBGHXLBzMEms01cDOZF/llGepCTDvYdCHYuMETGJQQeCRDpLHQxi9w0AqbjKMP+vwCGWLhjkMUthJjK2wa6rIPqgEAGH5E6RF6QbmSBqACPtABBjAg10R1Q5+PhUclMECCXNSNGVkYwAhsAAHQgmNxWtXFIUJBjVYcQRwXoYUbviCDATTiIKRsxA4YMIUaCAV5F+GFWFSCgXyu4VMHkYgDDJHNSw03IePQww5E8AEIfCESzsBIPQ6RhXBegRukkAAAWgATfaCjF4LQZyyUQV3uBmMNJPiAGyzKun2M47cyAAAMDJKPZOQT/gNTQAcN87lEFlCDbBAVwyQs2ohiaCQYZSiwAcRQiWsgBIMqwYEjk/FE4sYinCqRZhnQ1bxZVCIBKhnADjKxPev94gswkMEXVJrihVyjDcEFgAG+sIZk5NhOvxApCFagATtQY2/diEQ+yWALeGDzCLGQZTpse4URfMAGpTCHzG6hTz+QgxRrYACIenGkcQRjEif4QEDbIK2NvOOewP2CLjIhLlSYocAw2EYy+ABdKdN2H85sxRlQgIRC6OI6DZyTgQWxA06q5AjiGrIBHvABsTBADyKOo0gHAIMaHOF4IxTLGnWhiDX8ghpPZEYLYtDZC5CgFLJktDGysIIPXMAG/oIohiw50QIH4MUPKPhABFQCA4buAx/AMEM4IXADH/hgDeMyBx8WYAMZXAA9hVBIFAEwxVBfCgJeMI1BqgwACRDBElrAAAxK8RcrwEAsA6hBFTZggxMQcQozXAg9gOlIbOhjGwgvhnJqCUxuWMMPerjCETJqEGKkYN1+6Di6dmXWK/xg5G+AxqITIoqnGHkNtahEI4BokG1c4gdD2MIR/IDZg3Si436YDzt27odMyDIfE/eDIeB8kJSP3A3M8MMTRr6FW+iOGVeAAAd6EIIfMHcf5GgEz5XSiS8UYUPz4MUbjjByrYeinzE3AgEuRfEj7GMerHj6yE9JDz/Y4QgQ/tCwQdDwg5lQgBS9EAoGUqG0bWzBAwewAQqeUAppQ6QYAMCA33kCjEsR4AeNcEMf+iCGBXigEwlZhxsAwIG5WrMSTzhBH5xwgB10oSimf4FYODAHMPgAJOPwgVAM/IMQBIAkXPcDCJ7AikKsIABfQNc+llH1bPvAC12o0A3wCpF1cCKbU9iDEABAgCMoC5RuMMAOPl8hBLihVL34AQK+8PkSAMAE5b7IOyABW+iCIABIpIQHLtUHGScD6PFHBsELXvBcsqdtFfIZzrcPleABC2AGpMAKXkBEbwBFd/AtH/B5fUAMRQIMSHEbCIEKKPARwDAPtGAGEAADE7YPokAE/jgCLEdwBB/gA7dXCRohEQTgA6ywDKTgAwPgATnYULCgTtB1BUKQBxjxVCrBAMDQC6tmIQlxD60AAtuVV37wAm5gAx+wA293IiaxDHVwAgQYCMCwDnkghUdACfvSBziyAGqQTJLlASDQB0tkYIF1EFNxAPMxD5zwAuimFMDgBf+HAE9wBq+Beu4ARSBQAGpADOvACIE4RU2xBSWQBywYW6q3ELRgBURkLAbBDUZ1BqDnBQXAahexDZhwUhDgBJ/XhgixgyDgBaC3AOTxH26AADDQCrzgCR8gACowfhAxD3WAK59xBdk1FPngIBjAgX1gAwPAAXiwEFeAADdAC7zA/gknFWDLoAYjQIAGcQ+88HvMtA/boAX/BwAnwFZNGAI+cIyp2FskgAeftwdZsHn1ZBCMYATMAQADoG1mUE0KQXduMBMwYAd9IARegBDNwwEgUI9e4IT1ZxBmYAB22Ady8FmdIG2ccAMEsAN50AfcCBoaVX526AvTwAj21glKIwonoBIEsAR+kF0YYFPbkAUCsAKFQAwHeABTwAy1kgfHCAFPcATaJh0AQJE0ZAYIwAGzwAvXQgAzwFYXsQ59wH2JMRGAZBCChooA0AMjIAZcKBZH4GAIcQ/M8ATHxwq8UAjyV4AONEcAcAN10AcSCQFcuQxuBwCTwAuWkH5PUE3f/rACAFCLeWAF2bR1F6GLAOABPyAEfZAHVwADfsAMDQkCBPBJf3gBh1ccs+ABCOAFvFCBB8ABqVAc1fAGKiFe2QgKYoCKWKIRQvQZl4kQ9TAJAGAD6zBYtziFBihFShGV4HcCbsAK1aQEb7ch60AJLOiC3SCR4PcCtLAOY3iLsfA7c9cKaTdykWAPXsCdT1ARbsCdnQCaAHgQxEAGMyEAJDByT6CHBiEWB7AHV4ACPwADCIBuexQSMwF+R7B3IGCbBuEFIGACgpAJZwACP9ALbPIF/nkBtGAI/jmN1bAPrKgSCPADnQAkwKByC/AFb9BxY6BTlyAmT4AAR1AJuxAI/iqxIdRQjqXgCeyZAsRQdj7wfh1nAvO3lNvACEegn1qnB0Mwd4ygiElhEPAQj3JSCCqHAEIghXQJO4QoAPQnoSAAA7WwNSbRC5kRSTjRDX7AgEVJEt9wkmFoeqinevcwC0pVB8+nBpz0BcSlkoGYCPDQDbzgbmVXWXaQC57wB3t6Wk9gm6hAYz+AEMvgBe9XC7ygjdyIAvpoEawQiAAQDPngoeAnBXjVHTtQCwZxC0vEJBbxQBaSEgLQAmxxDbTwBHiRCX/QJddwCccYgF1JBBnKldvAlyDiqLkwBxiAAG8wkLzgAQQgBSC1DDDJAQO0RC9QlQbIgKO6D6jwAgKw/pjj0Kp2oBzd4AuccCnXyAm8UAdu5gHuZhHECgAUIKm0UK3lKo7fUAyvIWXAsBgX8ZYzoQCcIBG1KUlfwKAKUQ+NAAN9sA60AJOOaa4nMQ6kQGMrIY6tIK855gXGClKRJYM7QHrJ8HtbBwwzsQIglaYcUAxrsw37igD3iQIIQHDd4BIfS0NGeppbChHQiQKicA+/lxcYsQxO8HYOuw/FgAFPADvfsA1IMBQZkQ9KAgHr1yTQZRrfIAVvh6iFQws40ghK460EYAWlkgo1eQM/8HZfgCEjGCgeoBDLcI2twCbUwI2j+g2DAIoHMQ+d8HtFcQ25qZvVJAoJ8AOewAu1/nAGilkdRvAGSpMP0nADCGAE7oYKgfAhAGAEjvqs/ZoZg5iwzXMD3nmO0YoQRER6jkKTvKizyjoLRSIN6be4AuYGove5jiIRLfhuoKByBAACNWlTXiAAKDBUBpGsAEBw4pgK32JgpeCogbCjKQBZBsEKF+C7H5N+TIsRvIAjN5AM+fAUBKADCUGYKmEAZvANBYtT5ohgy7BET9ALQCIKM1FpqjhHXCYh25CZ2WsQhcC8SIqbKoECbGWoP2Aa9zANEvEFAwkRVtCzXwBXzMB3X4BX18IAB7EONkCXY7MNFYIBydS7N3BK+RAMKvGv79YA7zGbpcCvlVMhTLIM9buY/lAUnAbRBzJJCtgnEEd7ECwCAI0AJNciADCwuwK2AQBgB/x5D9JgB9lVCgrXC5UlAZ0gYuTLSYXADengUipRq9azDJq6DdswDqTyXAlQCc+wDbwAkw5ACb1UPMtwHfS5DdRgStUFAA1QXqCLWrx1jlUMfigwBdJkB26WBT5QAS9WCquGAclwENvgRxIACvjTDpiQAA8AveMgEUdQvQbhRxgwVPNwVirBAc+mEgtgC9MgheUhCgAQAGarvT2MPPnQT+sACiymF4e7Brg4yL9nfjwGAHzAiC3Qxm88D4bAACQgxybxDhIRCzK7E0oCADNQajqiAxPxxiwcJu3gAQbg/gXb0w46IB1heG5fug9d+pvTZgsYwACUgBC2AQAbMg7WeAQuaBDggMslaRFTMTByvEwSsMNKIAA/PC7UoALSGhO/Vx7GQxYZAc/Op8FSjBDdgKsIAQkf3AKqlw5LVCcG4QxwaAskWAaHkKRFQJfYl3QBtg/XcAICkAUCPBUM0Am9dFIGcAWl9g5GwElYCBE4ZQBykBB/wEkHdhDBoJ92sGQQgQoYEAynhwB/kF2FuxDegAGM8ETBQAHTPL9uJps4gQac1Mw0vAMWxMIOULEWqxJvTJvyiMs+DEpmoBIqsD0Ifcxe/AzAYGZ4i0QHQQoTsJ8ZYRsbIsKYklUWwQhx/rsP9ZAJADDF+zBaMA0R1FZ5SymLKBUIB7HXobgPngwA6YwQKtEAf6BVeJgJ2LANvtAL6wAPnOsoxeKzBvEOb0ACx0Ad+oDW0soOyjbaxei7Z2k9Hr0PLRAAW/cO2JTC3FUHB+AMMlPQ65sSSmkSU5GzCtE8wUAdxjyq1xAAWYAQ11C+HI0QA/Z2s1BW0aACDLAFhlEItzgJCcHNPH0Q88wJvVBMjTA2AKAAG3IQSBHeBpEOJcIAjbA1EoEAFDkOZD3XjDOC9vcGbzdFywQWCbGvZ7AarJBNs0AdSgQAJDCMBiHUXMm+KhELWXV6Bb4PbqCISqHaKgECxEcGBLCY/uBgBy2ZEQsNItWUYPl50gbxGg1sELTQw5OFDxI50wiBFFHdEOCixSCcEe3wyn2XEPJwUmJwEDKYwuc2RZwAAZGw1ftIROLJCVWuB/ppk858AJaNEDjiAYwYSO8AJuI7DxoDAe5tCVeCP/pgzIFtEOC3tboCAAeAzw3lCN9S5xfBQBRuEJMgrwiBC8vMBzuiEgcwBudQJO/QBAOgn6mgFGmJK2uwI7/iB2RMD0PA6PENDG6GnQfBC6KcqjP+LTEQDZ0iB6pAD8zgz4XjEwuBI7tdDzyQI+NSDCrQzXWgEh1QDrzJDfGgD5Ow0wgRKHzAnxbRDQzgIlZhPPy8D+Mx/n8IsUxFkRIPYAkIEQsKMBEIkc0Qwc3ORw+4rhuowAiMoAQqIQUGAQz62elyu5ruDBHwjAb4QwsqcQHwYhAuMQSnNG3jQN0JkQ0nxQdYvQ9OWDAYMdAJgQ+sYNCTHZfcIRZwMCnrQCdFsQg+QTn1wA4fwxcAMAI7jBDkYCWQkHR/nhDwXAY78n3UjhCGoGy7nRD6GScJ0dijzc2xcHLibQr2IBYB4AArlAgidEF8wALTsBAWYAHJSwfBnhO4cItc+QtvZwBsZwRvfRCStRrcvHXPBQEfwPUb4JtIuju0bRBRQO9/wPUfMAECYCUnhBBg0AA3ACR464ALMfPjcguQ/rvV6xBkCDEg4KcEuAEAAvD3Uu7Yv8BJNcAH484IVqASAWACGCHxqFfwhbOaKqALSa4SEf4MKDDSCbHsCfFc1iKIZEPbYgEBt2koF0EKMMlGPW4EFTvciH0R37Bqxy0mKrcZn28QoUykq2IJbkYCzawQwPB9KoB9+jAO3pAO05oCARAD5yDeTugN5f2PTlAP+fAO6+DruTkE1YIUAb0Oq+kBXXIQKZHfxOUbMWChBrGvzM5SlaBsEbIPBK4Qw03+BogjdaA0VEJEPCCzew4Q+wQOJDhw2xcAHJQR7AMgAiqBwKigEWVPIDsAAEDwGmjowBFiA/O9m1fQpEBODwDY/imYbgsACd/2TcoY4MPNCQIy+qGHAACBJ4yEyqmQEcFAbhn7FFTJ4NhJk/liAbiBraC+c6zSCUQVYWdBXj4AvGF37EGpkiYZHQCAAMJbCAwyqhgnsCECRgU/ZGQHdWCtGwBY0Ru4A0ACOgNTdiOYFMBSgox+WoE6pG0hgpz22iHs127bvAULsZWyj14vTYVGAPBRbmDGDls7sn2Tdt+2HwC+9H3dwmQf0gJ7ZVwjVKiTjBE0CeS1F01adiWzZQHAx9xrAAwWEtTk1c9JsQB4C/RlAECvgg0PPDE5GsAS44yW6HTQzrNJfKwA7NB2f1+0GW4KyT+MWDNpnoweYCgj/m4GUsmDdwiaRyUAnmJOrAZPGu68guZ5AwABJvhggrcSyEiJfdpZIyP0JLRDI07uY6eUN7jRR6BCMvKgnoHQOAABD27qYrv77tGmFHDyEegYoybxbx8/WCzonlKUKsio0FBSibOB1kGIBGcGynGAITybJ4z9ImwPAAhiFIgOn1gqKErdxvOpzchU+s6zjBYYcKC1MnJSOCn9o6ekjACowJZ13rnnpG4c4OFRkwDYcSAiAgCAsSf9mtBSgVTkgAPBCCMGgVwK0oyvgTbccx8KD3hjVlqdsfGijHww6YKMCAiPgymKQKM2z5ShYKWByqDKKv8CBWAgZVRAgIMP/mjB/pBO9ekmIUigevEANABl61lCATDAAbh8kvWP+7zcrz+CsCoFFx7/wyAjbAf6hYDdCipQV4IoTG+s8fb5l6AhBgDABEaWe1IQAgBQp6BxVADghwz3yREAzDrFrc6TPgYgY4NzHUiJtm76wAMJev3FL/eyWMevVZ8rCJvARh5IvXwJyvHVgSBxIKMuPwShRRx/Kq3LREqRRyBGKAT4vncUuUSdG43I6IM1AbBtn+bG6oyehgwcGK8nD9KIGYJosVTNes5R52liDPEgo41aXQABDEawwgo5ZHoyJWQJykePjAbbWFZaZ3Vm5kQTgIsBncJ4AykrA84OmCfpoQmBYE6i/ucbOVrI6SuCwhqLFxFu+JqgFjIqhRvaa+dGHCX3cRttgvYS775suABgjvEiBiCIgeKA42vHIBsIl8mgCuSyzDbrzLO7shzIgl4feGBvBHS6gRzsuI6MLaDV6QLk18yXUKUJyjUAAfoRMP6C0MHe643rBcpnnFiY40b7GIZRupUnAABtIOEp2IaQ9pkHJKI9bCFA/eyXERqoqVP0kAMAujAzz3QDBzWoxhEYwDkZmaxSAFCQQLoBBgCgAYT72JpJKISIgaiOZARxoL/Y8oAs2MEZhVAFOtjBDnjsgxwyeFeHXvSCZPjnHvO40SIuMC4MhEkgmaBQrxhgAi16Rh/3/tCHMxhxgQX0KX/3odMDBYKNzGGHd1payfXcBQK2CaQJADiAIDwDDx0AIASiOEkr2OSmfQQhI3IiSC4M0y+BwOGQCFTgChFwwIEAI40ca1WhnrSIjBzAEPjwCz3q8ABLnAQYA5jCQJwBAwDgQIOdOkmUGDAMJUJBFndgjWsCsQNKKcZ343GVQCbhkwTOQ5nLHCCuUFmQRSDTD+84ojvkAQ9l3qcLEUuVQJj4wSc5ayDpOESiDhAABDwAhZ7Bh9sEQARvsTATmdykQOgBiYy0ABhH5Gd0+ncSd2HsJPfABztE0QIGaAoA3TQNPiE5kINpjlw7IxhBIioQXGySfg/Q/ud9NnG3gu1jHcIjwMuSxkmP5eahBBEZyS4qFhzYQaYznYQzSAkVOq1UVfv7Z0spSgAtrKljmRGYQNZhtAfmiAAoIkg9LFKFByDTbP5x6kwuYDz3iYloqeOpQOARnqlRdI6eUZsAfEGQewAgqwKx4t4SlTeB3OMIiSIAAQywAkL6h3CuMAmdiLexByyTmQTMyACk0M8jZlMgzSvIXB8QTM+wQwxNNAk7HGAAF6CBQgpU3QHSSIB16iUjHPHM9Ma6j2HeJx974COnCjEAGgAABmFyhgxEAVnGojV6J8kRAoa6j1Vx6T7Zs2FGjsCObhSin/BoZg3Pl8DGKHKlaj1J/lOGwQ5leWCfiGVHOygVttuaZIxlPOMmF7BGqOkJPKwayDJi58aGQEB7AuEeAGrBXSTS0quBzEQzoTIIAUhDH+8AwBEIpMIrtWVQq62oQJwrUaTpECo9tOjWbDGPfNDDIgQhBywF6iKNfOJJoojCBRAAhxexScQCqYcUFJYoAAQAB5wK4Q4YcOIU+4lAaOJQQXIrR+0RTrj7mIciANCDbQxkAj9xQmQj1oN6FQQdMYanQMLDyByK5aEvwhOg1MsnAJy3II9A5lAp/KT6PuCfHXrDB6JMkAUsAGmfAAEA6PA6/eawLYigByqAcI+GEKBBB9CDSVb1u3LtiR4U+u1J/jDS5YF8CqX6FcWxcBBMhfHBv34Rp0D0YQ7qwDg7hsqDpVJ5khcFoMr7uEdR59GIjHAhyXkWKUI+XBDPOUABW7ADhUhrsMneorIIFkhRKUqWCk+V1bUQtQAWgIaQEkQXPEB0lxDSY41lpNFkVWm0b5MbnUEUwWK5s2DnUY/c4TQjOq2e2Ari088cQIKimbRijH1UjTyQF3z0Y0GOYYIdxIIdklT2fUThgTg9WKsTZU5XDRaxZ55tvlBRG7b3AQzqDuTgcarFtjTy6328wzAwFkARaEwzleShrxkhC2ChgnE+ztsvPxZIy275pIDusJ3emwRJ7gbd1IWHBgq7uUl8/tdvvxC3d+z1TNhKQcofFCIpEHADcJ1AvsbE8TMEoAxvqSfMOvpH6RLd9grXGqh3d5sgGWfKZe6YR7+EbYcGecEiy8aAP6UX6AVhIEsRAl82TZxCoaW1uC1+krBAMiOEH3bBHRzmPzVkfOUrLsMlrCFPCuQdgYErQBGCRyfCSK8QoEotHpURSEfECH0IzyQ9w4w6fwGEWPKPuw5PpXUXjPb2DrtRPw93lLEwssQmyFSmKmSTdCL240E9IvcRtb1DJUFqGRcPM+8Z9/hWRvKVfgsF4gbSswPjlczzT5RwVF2F7Q25AADIUZLaRDto+sNPfbG1TWvkCwRBP+iFGxAw/veC6LTMcIIDuIEXKzsQAwHnI4gUCytj2xAYgDv9yjmTgIfA+ADS8p1XeTUAaIR/uij7szyxQDbDC6uByIORwxsJBAuxCKm3WzgEDBm1Mwl4w5WpEgss65Sc8rb3czeCgD3Zwrp9GDut2jb/24+iyTefMT+W8gKf4I0GTJu6GwtEYbuFAwuHE7m2qDqJS5tre6CGcJ9DiwUb7LwcsgMEyJnDW6/CIQg6abn5O4le6bqZ07p9QJkFYDzPu5gdggfD4ELUQp2BoJPx2Ri8MzpBhIp9Oy34CyFYYoN5gJ594Aa26AF76AExCCmaG0LQgIre+q3gWrPfaItH8DcKMbD7/lC4fciCiPExRcrEtZs4WBE+23Mjk5C7qBgGDzCAM+CN3fOy6FsgptuHM/sM7mu7eis8IqODjDi5k/goxQMApIOKR1vAx/M+Tgy3fVCYteKFNCqTgVA+bSyI4ZCBZsC1DqqOTTMNYMsIXQg9BfSMw8mIIHCNx2sTfVASfLgpe/IDRXKek3AvACgDGsMSfcCHdKul68MHVLDDXwSuLbmeewIAEThHtkoQfmw8ExwIt5kqUSA9HFi5AYiE62k+SroPtpCzAGSLo+ikNYSKI1CYJrsPOOAACwELALiAgbgHatsBeBCEMFPGgdCaBRAFIhCxbqiBGPoBcCwIUQgBptuQ/iDglD1ioX/ShT6ADtcjiKpUs4KIB3bIyIJYA7ZwnnUAADDYhh4ggDoQRXHZqn3QB3QriB+6j3l4kXhEtS2UqIEoD3esQPvwDAokiHfAAUHKq0CELoLaB1/gl5ACwVlkOGAQggYTiClTtnuQyFg4A/Ngt4igzLrIOrQcj42JQRqcwYLoBssYxwIJgRUjAgCAg5NISJMIBIXhghkyCTqLodfRhYyAhOshQoEoJwXKhx7ICFpIwqMhiAIigJncB2x4iQNIhZuKwnuArIKYRwBAhc6oIXu4HjrBQh8kG+LjxNOiuC+8EvPJBhdYpM4okI2oh3YYo39STfbxiyPMQe3M/hCFOYCCwAddSKJx+QCxBEvMeQx6w0bBRAgkK4gUQyQNvAdayBfbBIA66AslUBgPiIeCOKaM6J98iAdjSItFnK9G9AxFogF20IOjYIcOAoFMiAGS9DE7FE6t0j6wG7Kky46bHIgmgDixxIf+UUVEYIuCcBdFsI20mrhP0UnsyohbWMdgwsWCEEiCBLJ9QEi9I7++c0nAO0aCqC/yE0uqMUwB8I8oiUZU9ItqPJCM0MmfyhjKdDOfYYvf+qhxtD5Z+09UUJgtYJaBgIfvuCedUITcvEtT4zYGWbtDSgebGgZawM6kAEiTKEajeAR1oIVq8Iw2MgnH0INmQpBO5D0d/h2OW9uHlHxHgqAH3vgXMi0ZZUsBTQFRPACAGrDIe3Q+6CO/JWSlgvCIeivGUqKQRSgSAugCqAClodqFvagDeDiCPPS0d3AHt/SLVcoIDtAiwklGFqO2atsQcNqHRejPURoIefAAAmjVrRyIceWjchUIeZCCBUhOqIDNasMGAQiEa4iBeryPTtMHajCEaxiY+DGTF/mAedLLA1gDibopbpgsADiEr1kHGlgrkxjMElw6AAiEfaiFd1RN3PQX4jO2z0ADdNhJVSC2WtCD/pGsAPBMgQiEANhUgqgGEOFYGKSlj/HM/Uw2KBKIT/jQgrAHaJCNk/AFIACAFgAHk6iH/nfIh9rKCKMlsnIyAJP6jPMsoAfIyGtoTwUYD3xbzrXD0X3AUxLchwbMB1tAhdxkKXDLkLRSK33IBD0AIZLVHx80GLbwAdq00ZARHotLKwLFWztLi8vciEz4AG7QBT0QyyiBRc8gyzYUCLUEgAHIEK0BAA5lMWHQgD6gh+nJSWNAqykYgAOlVKD0SgKZLA+Ion2Ah74oNQBIJXyIh5/Tg4Ezn104zoxBmQOQgqchCA3YCXggJX2QhiwoA97YN3kTLQCYWr/IAxPZhBvADHpoBQYAliEIo9PtQq8jW+CyHrGzSpOIpjBjKFbDhTqYmMdbq21iuH1wift0m54ZRDuN/gi5mAJAFQhweIUc2ou5s1QFk4dVeIYtZUN7jMtbuL74mjgPfYCCqYdw0AXsDCG8QVP2iUNqZKFTY0AFW5DWeJ4HcABMogc7OAA4HYgKdYYBIocEHg4VIJKBKAfD4IBIuKl5IIcbKAGBeAYUAIAsgBf9I7iNdNuMYGGBIAfU04RbKCkfiIFsaCZ9qIZ89YwNiYWbKhA5ixZKNRzEWUNuMA/+CJUUGyshux59WOCqeK4OuA7N8wMHuAi2YAHOkWD2hdWwUob96Qt9kIdc4AAGwITAzFUEysGT4J7YGKcOAAALIMfrgwpgTWG/KAXt8Augs4dGGBpniAUNGBB94AYV/uCAN3BjWqLMBEBWrvCKljQJS/g5a9A/49sBZ0gL5FCUVjAHdiCHMHCAJthcJSbhk7CCjKgAVzgiXT4AJtjckyAce3QHSPCAWIiEJyBlvwBWACAM7HKARtgwInuRpSmlhnCAM3iUdOgGfZiHI0KDjMgBeqgHdiiHoQEAgaOHdrAEtlCBWRaIc9gEAZiBdqGONU62HVCTd/i5WtiHio1ZFSAZfbAGYpO0/ikbSIgQdoiG2DoyfuSeHMwEDlBevyCGFAgD21iHMBCAFMi70tTZ3JiC0CSHjNGGkUOG3JkHj/OASWCuaGC5zsgHeGgEFBAGv/gGNygAAJhoghgHPniB/iT7A69ATKhVgQVwg0FG21GlywUgQ6/KZGLmx7B9IAQ5AEaq0DCYmHTOiB1ghitYA8E5zYyg2SoBgA6whisYAk6hkP4JG5uxpzoAABaYBgn5kPOsrF+wGAAoBaxB5yqpgFuAh2BYDQCgAXSYB3DYBGwthTCggG4wgcK+Hnx4kUmoVivLCNkcCH0oBg4ggCFwY2LgFSbwBnMgh0QQASNIImJQiQMYA3R4lHdwhQpoZJEKhoyYA3QgpXYoB8oEa3aYJdGhhIjhg2rgBiHQSVxgixwgh1qYgnG5ATQIAH/Oh0oglXwmslAKA3BgriXZAMv1AVbghmC4AQYAanrohioZ/gAm6IatWAduIBUA2ARu4MGBuIYT0BQIWAbfW6TQFE1KbQgDkAP9G4fr+USCgARSyYLgxZ4wswX9m4YkcgaL4UXBYYdaIAEVCAfKIwg5MI+C2dnxaIgjmKVvyIEBgIC8Goc88IlGwIYbWQdmeAEd+F8A4N5yKYXO8LgFsAVxIAHIgL5+sQcCFwgl0JRBOd4VAYBMSKKB+BAGYHCTMAwDMANooOhQIIFEeDNq5AZmCDUOwOBo9I3hM4AtOPB2eIYGoDoJ2espEOJ6mAQHmIGBfQdMSIAWaPKBIIUTAIApYAYzh4EsyCS2yISTbSpSIAHZKgVscIZIgIEX0KJ36IML/iCBUnj0dRiG2KGKtj3qJ8iIQ+eGX4Cl7FiDNXiBaRCLFhgG2tmGYuCDC2AFzwAGuTiCXlB1ZTGXNWiEBaCEk8AHMz91KteG3DyHucKATKCGYFgD8zCXN5CJedgGPZCLLKAGdtCHdZCGKc8EbLhjdTaAICgGM7cDBlABgYiHKciOKeiFTICBReARboA5GCgGcuiMP5D0L+iFWxAEEriAPtCgbmCGjGAAPwCHeRiHYlgDuYCBXnDGghCGFjCAK4AGbiiGKaAAFwDquEQHZYC1Zb9jqECCAXgAQac4pfUMHv8GeoiFezH0ILiEgYiHS0gUW7yPF1GOpWMqi+qFKZAL/qXthW04hLkCAAyYgkNwh31YhhdQCQPYgS+AAQYYg61gh17YGIpnhn/ygab4gqtngBw48JOgBaicBHY4B5pggCM4AmS4j3HghiJ4sUhwhnPIBKandHyIhkuX8fvAB2AYGk8nehhwh1gg+0RhgFLgBTSogReTATIIiXGwAoVRgUPQhV7IAgEQgmjwi3xQhlWQ9A7sBVJmB5XAAD/oeHZft14QACQQCFoYAD6QBtphBloY9Qikh3d4hkgwEQCIBGgITErYpELohS/wnowggVroDFacLd6AhzNAgE4gc9EIgFjQBm64hkIQgBPAJIFIsTPQhtD3j3FQdj64hlV/AdOg/veaV4FV0IZtaIRQY4AdsAOmLYqi/gVt6AWAsHOizrt9Bg8iHKfkAIBCybhpuzVlgZVxBv9saMGMW7pVKhb0sWiQHTcYAAy84QZuHkI3EnI46wbODgYSuOodVPdrCgAMndDha8dNEgAADZyBe0fqRNFSvb588VAUwxEQwRBi/XakaCJqzSAUNQADxJt30X4xKBrJWbt51BphAKBiWD6D+HCpYOCHGjduwSCFbQOtIFaD+ah92VoUwBRmsL4sxmCImhWGDRu5gMBhMeN0ZAgAaNRtnblSMDAgK1zYR1GN7Pbhk7YGAIxpCJe1AMBgBwwGV4DhMzjpge4jTu0wUCHM/iCayE+w7fsjY0DYL4VUY71mhHjrZfviZdF9GgUPCUUDbIhGL5biKYdwNuKMwQ64g6JecAdw4EWhgsRSfBDgByXksQ8jAgooCnYIkZEAAE8c9I4dACBwFUL6qDNLUWdwE5xBnBSlgTPc1OIHdEKdcVIZv1wDTzFTpAVALL0saFAfJ8Xxzj28HJGMQaIQZ8AavfTSyGm24NRXiNQQNs5mAHRy0D3M3ADAEegcdKMEoXDzWjt9MOQFQtPYQN0UtxR5Gir73ENOJ3Elgg03CAGT1hG9cPNLGWGtUcoClBiEygRFNaLNKmIcVMgCALRA5C1YkFAUCZmYo48zvZjUUy/U/tCDkDMfADDADpkUWVM4NRr0TSRfZKpbL8nAs2AhB3zx2j5FXVcjOwAIcIIgr2JzyQ4SuCElNaUoxkcyde0jjxkwTNFLJhK0sBxWy3jB0BSsvqCgQWQOQIIgunho0DuonKBtDRK84N1B4/SxgLi6FMmDVD2Rco+slm1rwAu5FYUAQawxChUXLExQUY3TLGTlFwa04AN3BPggElbr6KEFCpJmoQhOBtVDSqRWMuAAD9wx0MY129QRIwBZ8HKPRIuRMMUo+u7zzg4O9MQqBjroYhcuK8ToWzr7sPMFwD0xso19PiB4QiEW72NHqxwEsg0kG3DwAVgA2FEjPsPocMIR/l+QwAEZxnh4jytICGiDFpXYs+A4G7yM6j43eovdMkKm4sULizqQhjwRKhIjjXojNEkAJ0SDkA4D5ErnARh8EIGAjSAYYAun7rNMGh04cMAHJ3hx9D6fdu4F1Qap0cJmD6Cueo1/VNBCI4g0gQMAF/RBmKxfuDzADbb0QsAFK0wRSxDsFqu3PGTEJSku+Nz3QQg+cF8IKkpwH/4Rke9Diw+LLhYBDuRjBw8SHkyAICo4g8czBl/UxEMFi6V30AkBbOsLP/DBzvTjhG0AwwfUKcoAerCmfYzDChMIQFE+4IbmFAUGydDXrABQA0gQKRMnMMI1UHUNG4BAC1/QAghs/gAJhBCjF747SRaMILwacWID1MmCv7zTjdJ94AJd+4AhONG506XGDiMzQBZIsAAzuKtGtFBCAQqWhQAkrIQH+QMJYPAFSnxgBGKgWiwAAaoAaOALdXAaQtIQghqcoQ8feAEqPmYQWqhgMTAoxTqIQQYDMLAGcwDGMqywQABAwAeWwAHPEPADLarmHfGSSxZk4AYXbOYARqDFPuRwAgGJwArR+IYcELSEWIEMFySgClRq0IMXACAAF+BCFLFSDzAekRGceEH4fOCGZZgvAhWUQRwccQIGPGAFqWGE6R4ghkbwYT/90ZsSAuCBD/gAhLGYAgGkdsN9GEMHAXqBGCDZ/iw15HExDGDB9Qyyhl5aoYR/CEIvfcm4ZbghfMOwyzB4MEcx0KIedpDBB4IQtnCsAEEtcMc+6sm9Wi7jndyzQhSj8QlOYBSjnFxGRjPKOEYQhxMI6QVtqIGVW2zhSRD4QSNQuQ8vAIAAJPiBF8exDDUEATQCCIERODGNH9ygnqjiRVEYcAarHcE2HwrPYlZKCpZ04wc/KAoBYGAHbnDiCQgoCggEAYx5lOIJX3tDLYJzIyPU4Qlf8MMYUAACPLDRIPPghRXyAwIveGsbXwBBUTjQgy8gZBtmIA4MfkCALPThXgRwwjoOwogSFGUHC7DYONxQxaIUwA2l0CMr5oEG/h+AoJd9iKtBeKGFewHAgsTAWY2IYYR6GsEJbiAtVnjhg1oZpCh9w86uGOAGRrihD30QQx40gZB5sKIPbnitFjBhx3sQow4+sEIeqsEsrLBMCNwb7XHpeoIBeICh12KEcPugCdruYx2UcMIIrOkFT9hCCz7oKUv81ocXDMCvedjGNLiggxescR+FEEIewFDeQJDidYWZBz65p4U9VGMflvCBENzASdXMgxa6LK9w6ytXXjjBwZSoRx98sD0l0GIdyeXwNvJRDQ4LlxasrQcm8mAFH3ihswi5xzQoIVxKiKQbMO4DKxqLEF4gmRe1/BGHC1FkWhSCFrzwhHB3i50M/vuYErTw8D7ycY0k84IUgXDugpbhBC4otUZS1VseKsyKbfTBCyO+mBnAsjjGyfUPDzwIMQoRYayMgxGs4AUodIHkboAZyddg7T1wgQlGKJnLieYFert8DVr0gRPL4HKNRCEGHwQCGO9wQpH1xgnhEli4gSDGNpzMCDMIoQ7nxfM+kFve1RpkG7wABq0hSAkxACEPfQBFN1C1I1yQAszXYJaXIcE9J9RhtaggAo53S4tAGEHYIqVxHyC9jmUUAsaB2PM4xCxcXtS6D3XwghuIwRJREKEPeQifEzhR6cJ8wxeB6EMgfPENrMhBCFzwQXkRoWDs0MINqWbjOx7NC1ZI/pkX2djHpDdtEGD0YeBCMAMljKy3cSCiD2Cg8B8SXBiM98ETvCDGyZHchz9gog8dx0qj+Z1s9L6Yw+7+xiBgzAjv4POTeBBpzijhhT4suTDr6ANz97CPbGC6aakCBph5PY9pJJq1bCKGG7xQhz48Ix9w/gMogHFwg+xo0iyp9DJA8Yc+8KLY91gGJXzKEmIEghecaLMYpM44TojBFnof+HwLkfQPU1o1+XhGHaxwdEpMQ+u9njzNE38QREsJ60leNuU7T+tvZMTj+6DGEa6AJYSgAiqq/0JLD7KOW6i+EuSAoBtUbwZmdOMdbsHGNnrfe73dgqkYaAQ4tJ6OXtzi/hBraAU3cMYOIkG/F8VgxzKi34tfdOMeyWiEHb4giFtgQx97AwAj3lGMRnxhRsu4bkJiSCRmeNz81mfGjsdBCagcQhdHM8YXylAJc64O+vWCtRxEO/wCJPTfL7TD8xEJNaRDPnTDNjCD723DOHDaPqRD9RGJxeFZBFLgN4zDOUjecdUBBtTHrcCArSzIrkAAJ9zDPLzDNzzglX3DNqSD+NHcNpwD+xXGO3ggdozDM/jC+nkeBDVDLyxDY+lDOmzDN1wgVlydLyhDi+0DhmTDNBCGD+aDCvbaOvTeDRrGNuReEUrJOHxhXXjhBP4bGXbZOWyD6LFhHMohG36DOuDg/oKIAgC0gt5AYBauAw922TJUyZ3NYSEa4uSxQ1yd3YJ0AyCaS/YdIuUJhSMW4T303jiwVgTCYapQIhnewzp4GEl0me8toiR2gzrcm95o4Ryi4hhSXiIWWyTKIla8wzMQ4UHkAygyTgza4B0W4jyswwjOYq9BYDv02jusAw6iYhOy4T2cwyYOYzRKI6oQw5K5BTVI3jJS4A4ihNj1nsfVYO/FYhHmgzYQCTFAY5elgxN64jqYITfaCPkZhBcKYyF6YS+GYTcYo9KlIixOYySyAgbMQj04A5ToDQsS3T8q5EIyZEM65EM6ZAvAQDp23jb8wBGcIERq5EZyZEd65EeC/mRIiuRIkmRJmuRJouQh3kgXpGRL9to82IIKBFEpPCFWFAIiJaRL6uRO8mRPagIC7OEc0oMlkEAldGJPImVSKuVSMmVTOuVTQmVU8uSNGIJUtmQ9eENf1CRWTEgLWuVXgmVYYkVubOXk0YMrSMAVmJRYsmVbuuVbwmVcyuVchuWNMAJd6uQwFAJrIEAc4OVfAiZEGkJQymE3KMADYMJRBuZiMmZjOuZjQmZkliQwTFVPHJ5kPuRNNtUT+MGcYOZnguYwjoMTXGZomuZpomZqquZqWqVmLkYfsOZC3sgBlBe6xeZt4mZu6uZu8mZv+uZv0howDAMuWBlwGudxImdy/irncjJnczqnNOrDOnxDpyzIPLADO7hDuaiGPtTjc3rnd4JneIrneJJneTokPaCDOmjnNK4DGlwAIWLFOXjCG7wBHxRD3RSGPqCDMzDDeqbXPppngArogBJogRrogYZmPphDkRzBFCSDL0YjM9wkBNylajBDFgiA5mAABmQCONxhPiwDewCAF8QVA2aBHCBoiqroirJoi7roi2rkPSBDq9iBSw0jMHwCXyFShWJFJ4AAASgBKIQZLOGWQUADarmBxwEDqKQWjDrpk0JplErplMamem1ZJILVD4DFlUija4lAU/HoQQADXzEAy9UaI0DA8HGeNfiBHmxFkl4eJ0DG/gaUIpXa6Z3iaZ7q6Z6SJDGMwBtwYSFaohkwhjpIoy0oQAtAxo4WhmbuAEKsgxaUjBYcjkG0w2wcQTFcDAB4wDfx6aeCaqiK6qiSKqowE6AO440U6TAa4DJsQ1FQaGEATNggxNYAwAMA6DpAxg/A5618QKkCa7AK67ASq4q6FgCgqix+gxgAwKpOI6yG6T4oQ4xUjrnoAK643q72KhpgAPsU67eCa7iK67iupjOkAHUkq2o4wyQUAi/4Jx/uQbMGao0UAiMcQxFCK1Y8wlYBAHUiBMH8QLYCAK8WxuWUpmqwayEo7D6Ra8M67MNCbMSWZDnkgABEVh8oLK8dBDsU/sIGIAACIFO14pmqzqtqDMMDfCwDtIDGTl6+IoQJLIZqEAwBHMQ8KMLA9ioOfMC7YocdQMDHfiwEZMG97oMoeMADPIARGMR2PEAL9M0xSMEEPMAGMKzEWu3VYm3WRqyucsZi2GZ6xQcMdMI8AMOiHAHLMs6NwAA5FAK/lmmjbhUwrMMbNKtn9prLHgSTAoDMRpbAEixX/iqecQII3ECs2FYFlZbe8kJlwmqUuAG/Bky0au3kUm7lWm6eekIIAMCfIYQ83KQJOANCGMEAHEE84Fk+xCsAKIARBEIhYNsBGM5B9MKiKO0+lIPvbIGh3i2jIoTe8i0A4IDf9mqT8uEl/jxADczexTEEBXiLM1QPkMJGKqSFB/gAEsRCcDRM4F7u9nJv93pvge5CDwBAHXChPlQDrwgCVgBDqExBB4LBSaRCubDDYaoBzkwBdWisPtwCp/rI7sZq78bsagRwenEBAOxALpQLPdADp8ZDdxqENuwAAECCv+7NBYABAAOAEoxUUchAMyDEhOzs94rwCJNwCQNnJmyGM/hiewIACPQqQ3TqyMorQuADKwAAB1wYk/YFNzgDTwDAIZRlYeCtQfiuABdFFa4DMqTTHBxDfdGnfhRBK1AwzcVCUfRqYTApVpAUAKzBGhrEhLynCYvxGJNxGT8mSAFAItyQOOTRCSRd/gR7ZdrOMEJ0Q1rYAT68QwdU0BEFD62twxDvgw5Q0N4a8QPswy2FgAxMVEAZRPgEiBeUpl5Zsd6Aigdo8SR/MABIgHGZcSd78ieD8lPWQpUEg3ZyQ1HcwLwqAU7KsLPabgSbHjDsjwd0VEbVaW0BMjMdsRFr8CGLAgBiBUYdrCQDwBVjBaigwSUXM1cCQAZ4ayhDczRL8zRvZCOABU0ixCm3cK/CcU4uyDbAlCtz7Q9gFXE8Khu+Ku8eBCo4CACM40EQzCQYIjEbMwBb8gYvcyZrLzXzcz/78z+zoR8Uhd0aBDhshgsLMSvrzeGK866W8y6zISB/QwPo1rXAEgCE/m4h0jMlQ7RBbDF8gjBAi/RIk3RJ74NAAwBBY2AYbPO19NUtUxxrNPTAcoMsF8XB4hkg7wMGiWweDEoWVOocnoMgFEUm2BF2ZDE+gzTxmnRTO/VTkzFKq3Q+FCQBVCVC3OQAQAjjMHSgkkMNAEDu1oMTUMdWpwojPLPe6DQuFIUUYAURWOw7y2E+7K8BmwNWtMMksE9Syy4mH0RIQ3VgC/ZgVy5Ks8IUj0MejQGA7sMDDIAQ3DVXyzQX4kMrAFIe1AWiUkgBusEK0B/jTAI9EENRJEAXtAMxeDFYIRIn74OfSjB+GiI2VIkBNIHpGkQuXFPf8LVH+/UXMzVhA3dw/gs3uG6CVPhAOewDMDzAIlThMLSAAUyCrVQBACxALtDa4cpA8hoEPLBGC/zZPfgBQ1xAIfiBDhhA7oI2BDwA+gBAATgAAxDCjlXxB9xrNxhBABSCeB1iPhhvTD0AxirBAliALuAEMGRBO+fKXewJAJTBOzNEAkRBcQ73hFN4hdspOHdtwB7ENsj0EYDGD6DtQhPMDZTVPtBDV0aPmHIGBHAX4+DdkJ1bYdBClXBVJ1CkHOaTZRTFAVQohnNGwO5K15bCPRAHh3mzhSN5kiu5ioKzZWh4MJdXEKuGbTXCOhgSZ1zAZQqX4UVjhnVbKkYiMOTdkpN5mZv59naDCi6CTcIy95m7+ZvDeZzL+ZzTeZ3b+Z3jeZ7r+Z7zeZ/7+Z8DeqAL+qATeqEb+qEjeqIr+qIzeqM7+qNDeqRL+qRTeqVb+qVjeqZr+qYfYkAAADs=" } }, "cell_type": "markdown", "id": "5b78aada-e97f-47b1-bc3d-ae41ba50b879", "metadata": {}, "source": [ "![parker1958_accel.gif](attachment:1d165079-b44e-470b-a3c3-3739274c0cc6.gif)" ] }, { "cell_type": "markdown", "id": "63819de2-668a-4c39-a8ff-acbd77c2b34f", "metadata": {}, "source": [ "For you to try:\n", "\n", "First, note that my integration method was the simplest of the simplest methods... 1st order Euler steps. If you know of something more sophisticated that's already coded up nicely in python, maybe one could get away with fewer than 90,000 radial grid points!\n", "\n", "(Of course, one must be careful with L'Hopital's rule around the critical point. One other thing you can do is verify that my expression is correct.)\n", "\n", "Second, there are all the other physical processes (bells and whistles) discussed in the lecture notes.\n", "\n", "Third, if you choose the negative root of the L'Hopital slope at the critical point, you can integrate the spherical accretion solution worked out by Bondi (1952) (earlier than Parker!)\n" ] }, { "cell_type": "code", "execution_count": null, "id": "db9566c2-2626-45ec-bf33-f9cf2a7527d8", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.2" } }, "nbformat": 4, "nbformat_minor": 5 }