{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Convergence rates for different NLP methods\n", "\n", "**Randall Romero Aguilar, PhD**\n", "\n", "This demo is based on the original Matlab demo accompanying the Computational Economics and Finance 2001 textbook by Mario Miranda and Paul Fackler.\n", "\n", "Original (Matlab) CompEcon file: **demslv12.m**\n", "\n", "Running this file requires the Python version of CompEcon. This can be installed with pip by running\n", "\n", " !pip install compecon --upgrade\n", "\n", "Last updated: 2022-Sept-05\n", "
\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## About\n", "\n", "This demo shows how quickly different NLP methods converge to a solution. In particular, we look for the root of \n", "$$f(x) = \\exp(x) - 1$$\n", "\n", "starting with a guess $x_0 = 2$. The true solution is $x = 0$." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from compecon import NLP" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Define a NLP problem\n", "\n", "Here, we set convergence tolerance `tol=1e-20` and the option `all_x=True` to record all values taken by $x$ from the initial guess `x0=2.0` to the final solution. These values will be stored in the `.x_sequence` attribute.\n", "\n", "We also define `err` to compute the base-10 logarithm of the error (the gap between the current iteration and the solution)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "A = NLP(lambda x: (np.exp(x)-1, np.exp(x)), all_x=True, tol=1e-20)\n", "err = lambda z: np.log10(np.abs(z)).flatten()\n", "x0 = 2.0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solve the problem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### * Using Newton's method" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "A.newton(x0)\n", "err_newton = err(A.x_sequence.values)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### * Using Broyden's method" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "A.broyden(x0)\n", "err_broyden = err(A.x_sequence.values)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### * Using function iteration\n", "\n", "This method finds a zero of $f(x)$ by looking for a fixpoint of $g(x) = x-f(x)$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "A.funcit(x0)\n", "err_funcit = err(A.x_sequence.values)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot results" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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CKAsJ6vpvlpKSIj0OCAjApEmTsHTpUmRnZ+PRRx+FTqfDwIEDcdlll2HYsGFVPs9ERNTyMVAgIqJWIzo6WnqcmZnZKPesHExUfge3JpX7FBQUVBso6PX6Gq+v/K79+SMcQkNDcemll2Lbtm349ddf8fTTT0svEs9Nd9Dr9bjqqqtq/Bjqw2QyVdvu7e1d4zU5OTkA6jblJDAwsEqgYDKZ6vVitrLCwsJqA4WGfL5zc3Olx/WdPtPYn++6qO3fBCibDvTNN99g7dq1SEhIqPZzfG4qQn019ON1OBwoLi6WRjQ899xzUCqVWLp0KZxOJywWC7Zu3YqtW7fi7bffRmRkJK699lrcd999CAgIaNBzEhFR82KgQERErUbv3r2hVCrhdDprHK5fm19//RWJiYkYMmQI+vTpA7VaXeO0hZpU3i6v8hSMxjJhwgRs27YNmZmZ2L17NwYPHgy73S7N9x89enSVIeeVa1qxYkWtuytUVtML6ZqmKgAVU03q8sK0us9t5VECV1xxBZ566qkL3uec9u3b17nvhdQ0faIuKn++P/vss1pHSFRW21SBi5GUlIT77rvPLbxRq9Xo0KEDOnbsiJ49e2LIkCFYtWoVvv/++3rfv/LHO2nSpFq3mTxf5REiGo0GL7zwAh544AH89ttv2LJlC/bt2ydNv0hNTcWXX36JZcuWYcGCBejVq1e9ayUioubFQIGIiFoNLy8vxMXFYdeuXTh79iySk5NrnYN/vm+//RZ79uwBACxZsgRDhgxxm0ZR+V3rmlTu4+vrW/fi62jMmDEwGo0oKSnB2rVrMXjwYGzdulVaRK+6+f6V6zAajYiJiWn0us7x9/dHZmamtNVibap7Z7vy57uoqEi2Ye6V66hppElNKn++NRqN7EP1H3/8cSlMuOOOOzBx4kR07dpVWrPgnKVLlzbo/pU/XrPZfNEfb3h4OO677z7cd999sFqt2LNnD/766y+sXbsWWVlZKCwsxLPPPovVq1fXGm4REZH8uCgjERG1KjfddJP0uPIq8hdy7NgxKUwICQnBoEGDAMBtPviBAwcueJ/9+/cDKBuCHhwcXOfnryu9Xo+rr74aALBx40aIoohffvkFQFndQ4cOrXJN5R0l/v3331rvf/jwYXzxxRf45ZdfkJaWVu/6unfvDgA4deoULBZLjf1MJpPbHPpzNBqNNNLg8OHDKC4urvX5fvzxR3zzzTfYuHHjRY0qOF/l3Skqr0FRnXvvvRfXX389XnzxRQD1+3wnJyfjk08+wapVq3D69OmLqLh6hw4dkhbwvPHGG/HSSy+hZ8+eVcIEANIaHPUVFRUlTSvZtWvXBUenfP311/j++++lhRyBshEtycnJVRam1Gq1GDp0KGbNmoXff/9d+nqMj49HRkZGg+olIqLmw0CBiIhalXHjxqFdu3YAgO+++w67d+++4DU2m016MQgAU6dOlaYrBAUFSS9iNm3aVOvaDDt27JAW8xs6dGiTvXt6bhRCdnY2du/eLW0JOW7cuGqnWZzbGhEo+5zU9sJ77ty5eP/99/HEE080KFC48sorAZRNffjtt99q7Ld69eoaX3ieq9dut9f6rnl6ejpefvllvP7665gzZ061L5Ib6pJLLoFSqQQAKbCpTnZ2Nnbu3ImTJ0+67exwrpYVK1bUGop8+eWX+Oijj/DMM89c1LaRNam80GPlRTzPl5ycjL1790rHlacxALVP31Gr1RgyZAiAsrVLzk2/qc6+ffvwzjvv4JVXXpG2YwWAF154AaNHj8aUKVOqrKtxjsFgkJ4HQJVdIIiIqOVhoEBERK2KWq3G66+/DoVCAYfDgYceeqjWFzj5+fl4+OGHpRdzffr0we233+7W59577wVQ9gLmiSeeQElJSZX7ZGRk4PnnnwdQ9uJrypQpjfQRVTVo0CApNJkzZ4603WFN2xv27t1bGnERHx+PN998s9r1C5YuXYqtW7cCKNvZYMCAAfWubdy4cdKCee+++261OxckJCTgo48+qvEed999t/Rift68edi1a1eVPjabDU899ZQUjtRn3n5dhIaGYvTo0QDKtpCsbstFURTx5ptvSjVMnDgRABAcHIzrr78eQNkilc8880y12zBu2bJFum9ISAiuueaaRv0YAPd1MP78889q+2RlZeHRRx91C5rOr1ej0UiPK2+vec65rxEAeO2115CQkFClT2FhofQ1Arj/m40YMUJ6/O6771ZbZ3FxMf766y8AZVNSzn0NEBFRy8U1FIiIqNW59NJL8fLLL+Oll15CcXExHn30UfTv3x/XX389unfvDr1ej+zsbPz7779YsWKFtP5ATEwM5s2bV2XRwgkTJuCPP/7Apk2bsGvXLowfPx733nsvevfuDYfDgV27dmHhwoXSmgAPPvgg4uLimuzjEwQB48ePx8cff4wjR44AAHr06FHr3PXXX38dN998M4qLi/Hdd9/h+PHjuPPOO9G+fXvk5OTg119/xerVqwGUvXh89dVXGzTCwmg0Yvbs2Xj88ceRm5uLSZMm4f7778eQIUPgcrmwbds2LFy4sNZ37Tt06IDHHnsM7733HqxWK+69917ceuutGD16NIxGIxISErBw4UJpe8n+/fvjjjvuqHetF/L8889j586dyM/Px+zZs7Fr1y5cd9118PPzw9mzZ7FkyRIpiLr++uvd3j2fNWsWdu7cibS0NGzYsAE333wzpkyZgtjYWBQWFmLLli343//+B6fTCUEQ8Morr0Cr1Tb6xzBw4EAEBwcjOzsbf/75J6ZNm4ZJkyYhNDQU+fn52LFjB3788Ufpa+CcoqIit+PK03cWLVqEwMBAOJ1O9O/fH0DZiI7bb78dS5cuRV5enrQ447Bhw6BSqXD06FF8/fXX0rSKsWPHYtSoUdI9R44ciZ49e+LIkSP4/fffceutt+L2229H+/bt4XQ6cfr0aSxatAiJiYkAyr7GGnNEChERNQ1+pyYiolbp1ltvRXh4OF5++WWkpqZi37592LdvX439x44di5dffrna7egEQcCHH36I559/HmvWrEFycjJeffXVKv1UKhUee+wx3H///Y36sVRnwoQJ+Pjjj6Xj8ePH19o/JiYG3377LWbMmIHU1FTs2bNHWjOiMj8/P8ydO/eiVtC/7rrrkJ2djXfeeQcFBQV4//333c4LgoDHHnsM8+fPh91ud3v3+5ypU6dCEATMnTsXdrsd3377Lb799tsq/QYPHoz58+c3yYvL0NBQLFmyBNOnT0dKSgpWrVqFVatWVek3ZswYzJkzx63N398f33zzDWbMmIHjx48jPj4ezz33XJVr9Xo9XnnlFYwcObLR6wfKwqF3330X06ZNg8ViwebNm7F58+Yq/WJiYnDTTTfhgw8+AFA2iqRyKNa7d2+EhYUhIyMD//77LyZNmgQA2LBhg7Tw6QsvvACtVovFixejtLQUn332GT777LMqz3XNNdfg7bffdmtTKpWYP38+7r//fpw+fRr79++X1iOpTBAETJ48uVm+xoiI6OIxUKhFRkYGFixYgL///luaZ9quXTuMGDEC9913X532KycioqZzxRVXYN26dfjjjz+wefNmHD16FJmZmbBYLDAYDIiMjMTAgQNx0003oWfPnrXeS6vV4r333sNtt92GZcuWYc+ePcjOzoZWq0VkZCQuv/xyTJo0CdHR0c3ysUVHR2PAgAHYs2cPVCoVxo0bd8Frunfvjt9++w3Lly/Hxo0bceLECRQWFkKr1SImJgZXXnkl7rjjjmpDlfqaMmUKBg8ejCVLlmDHjh3IycmB0WhE//79cf/992PAgAH48MMPAZSNaqjOAw88gLFjx+K7777D9u3bkZaWBovFAj8/P/Ts2RPjx4/HNddc06Qr/cfGxuLXX3/FDz/8gPXr1yM+Ph7FxcXw8fFB3759MXHiRGlqxPnatWuHFStW4JdffsG6detw+PBh5OfnQ61WIyoqCpdddhnuuuuuOm8r2VCXXnopVq5ciQULFuCff/6R1gHx9/dHly5dcPXVV+OGG26Aw+HAp59+CrPZjN9++w233HKLdA+dToeFCxfi3Xffxd69e1FSUoLAwEBkZGRIgYJSqcSzzz6LG2+8EUuXLsXOnTuRkZEBu92OwMBA6fN1xRVXVFtnREQEVq1aheXLl0ufa5PJBLVajZCQEAwZMgQTJ05Enz59mvTzRUREjUcQ67sBdxuxe/duTJ8+HSaTCUqlEtHR0XC5XEhJSYHT6URwcDC++uordOvWTe5SiYiIWpyCggJpisDdd9+N2bNny1wRERERNTYuylgNk8mERx55BCaTCZdffjm2bNkivQP2+++/Iy4uDtnZ2ZgxYwZXICYiojZl9erVeOSRR/D222/DZDLV2G/Hjh3S48pbcxIREZHnYKBQjRUrViAvLw8hISH48MMPERISIp2LiorCxx9/DF9fX6SkpNS6sjgREZGn0el0+OOPP7BgwQKsWLGi2j75+fnSLg8ajcZthX8iIiLyHFxDoRrn3lW58sor4eXlVeV8QEAA+vfvjy1btuDQoUMXXCiLiIjIU1x++eXS4n3vvvsuTp06hZEjRyI4OBhFRUU4evQovvvuO2m1/8cee8xtBwEiIiLyHAwUqjF9+nSMHTsWHTp0qLHPuaUnXC5Xc5VFREQkO71ej/nz52P69OnIzs7GsmXLsGzZsir9lEolHn74Ydx7770yVElERETNgYFCNfr06VPrCsN5eXnYuXMnAKBz587NVRYREVGL0Lt3b6xbtw4//PADNm/ejJMnT6K4uBheXl4IDQ3F0KFDcfPNN6NLly5yl0pERERNiLs8NMATTzyBX375BXq9Hhs3buT2kURERERERNTmcFHGevrkk0/wyy+/AAAefvhhhglERERERETUJnHKQz3Mnz8f8+bNAwCMHDkSU6dOlbkiIiIiIiIiInkwUKgDh8OBV199FT/88AMAYNiwYfjwww8hCEK975WbWwROMiEiIiIiIqKmJghAYKB3k92fgcIFFBcX4//+7/+wbds2AMC1116Lt99+GxqNpkH3E0UwUCAiIiIiIqJWj4FCLTIyMjB16lTEx8cDAO6//3489dRTDRqZQERERERERORJGCjUICsrC3fffTeSkpKgVCrxwgsv4Pbbb5e7LCIiIiIiIqIWgYFCNWw2G6ZNm4akpCSo1WrMnTsXY8aMkbssIiIiIiIiohaD20ZW48svv8SRI0cAAC+99BLDBCIiIiIiIqLzCKLIJQIrs9lsGDZsGAoLC6FSqdCnT59a+w8fPhzTpk2r8/1zcrjLAxERERERETU9QQCCgrjLQ7OJj49HYWEhgLLtIvfu3Vtr//bt2zdHWUREREREREQtCkcoNDOOUCAiIiIiIqLm0NQjFLiGAhERERERERHVGwMFIiIiIiIiIqo3BgpEREREREREVG8MFIiIiIiIiIio3hgoEBEREREREVG9MVAgIiIiIiIionpjoEBERERERERE9cZAgYiIiIiIiIjqjYECEREREREREdUbAwUiIiIiIiIiqjcGCkRERERERERUbwwUiIiIiIiIiKjeGCgQERERERERUb0xUCAiIiIiIiKiemOgQERERERERET1xkCBiIiIiIiIiOqNgQIRERERERER1RsDBSIiIiIiIiKqNwYKRERERERERFRvDBSIiIiIiIiIqN4YKBARERERERFRvTFQICIiIiIiIqJ6Y6BARERERERERPXGQIGIiIiIiIiI6k0ldwFENSmxl6DUUQKtUgedUgu1QgNBEOQui4iIiIiIiMBAgWTiEl3It+Yh05yBLEsmMswZZY/Nmcgsf1ziKHa7RoAghQtlf+ugVeigVWrLHivLHkvHivI+lfvXen1Zu0pQMbggIiIiIiK6AAYK1CRsThuyLVlSOHDuT5alLDDItmTB7rLX654iRFicZlic5iaquoxCUJaFDhcKJBTu5zSVgomyc7Vcr9BCqeCXHxERERERtV58RUMNUmwvKg8JMquEBZnmDORZc+UuscFcohOljlKUorRJn0etUEsjJM4fZVFzIFHRT1fp2sqBhVaphV5pgEFlgFqhbtKPgYiIiIiI2i4GClSFS3Qh15pbPgWh0uiC8vAgy5KJEkdJoz+vj9oXIfpQhOrDEKoPRaguDN4aH9icNlidFlhcFlidVlicFljL/1ic1vK/y85ZXVa3cxanGSLERq+1MdhddthddhQ7iprsOdQKtRQuGFQG6FUGGJTlf0t/jFXa3K85d14PhcB1XImIiIiIqAwDhTbI5rQi05zpNqKg8toF2ZYsOERHoz6nAgoE6YKlsCBEH1b+OAwhulCE6kOhVxka9TkBQBRF2F12WF0V4UPlAEIKJ1zWagKKSn1c1VxTKcCwOC2NXntjKAstCmGyFzbK/XRKfVnQUCmAOBdSSI+rhBbGaoIKIzRcZJOIiIiIqFUTRFFsmW/feqicnCI05WdcFEUU2YuQaU53CwzOTU3IMmcg35bf6M+rVWilgCBUH1ZppEHZ42BtsEevGSCKImwumxQ2XCiQsEntFxhxIY3MKDtnd9nk/lAbjUJQ1hpEXDioONenLLBQefD/LyIiIiKihhAEICjIu+nuz0CheV1soOAUnci15LiNKMg8b6SB2dn4c//9NH4I0YVVM8KgLDjwUfvy3eZm4BSdVaaAVA4wzk3zMDvMKHWWwuwoRamj/G9npceOUpQ6S6THNg8IKjQKTZWQoT5BhVHtBW+1D7zUXlAKSrk/HCIiIiKii8ZAwcNcKFCwOC3l6xZUv9hhtiUbLtHZqDUpBCWCpekI56YguIcHOqWuUZ+TWhaHy1ElZKg5iLhQUFHa6P9Hm5MAAV7l4YK32ge+Gl/psY/aBz6ac499pccMIoiIiIioJWKg4GFOpaUgo7TyQoeVpiNYMlBgK2j059Qp9W7TEUJ17tMRAnVBfCFEjebc9I9SR0lZ0OB0DyhKHCX1CiqaepvQxlI5iKgcNvicCyM0Ze3nPzaqjfz6IyIiIqImwUDBw1zy/SUosTfuDgn+mgC3NQvOTUMoG2kQDm+1N6cjUKvlFJ2wOCzlgUNJRTjhrH0khdlZKbyo1GZ32eX+kNycCyLcw4aKkQ8+Gt9KoUTFYy+1F3fdICIiIqJaNXWgwFXMWjilCPi7tPAXDAhQ+iNQE4wQQyQifTsgKrArogM6QafWy10mUZNRCkoY1UYY1UYAwRd9P7vLXs3IiBIU24tRZC+CyV6IIrsJJpsJJrsJReV/yo4L4Wzk6RwiyhZSLbLXb/tQAQK81d7nBQ/e0uOKKRq+btM1jCoGEURERETUOBgo1MBsNuOrr77C2rVrkZKSAqPRiF69emHy5MkYPnx4oz2P0eVCuMOBCIcT4Q7HeY+dCHI6UdtgaKuoRr7gC5PSDyUqf1g1AbBrA+AyBEFhDIbKOxg671AY/EPh7R8KtYZrIVDbplao4avxha/Gt97XiqIIs7MUpvKA4VzYUGgrPC94qBxEFMJkNzVJEGGylz1XfVQOIirCBm/psbfaB75qX3hrfBhEEBEREVGtOOWhGqWlpZgyZQoOHDgAtVqNLl26oKCgAGlpaQCARx55BDNnzmzQvT/5+DKEF2ejs8OE9k4LfFzN++k3iUYUKHxRpPRHqdofNm0AnLpAiIZgKL2CoPEOgd43FEb/MBh9AqFQ8AUE0cWSgohKYcO5oOHc47LREWWjIIrKw4qmCCIaSgEFvNTeZVMuKoUNgbogBOuCEaQLQbAuBMG6YPhrA7guBBEREVELwDUUZDBr1iysXLkS3bt3x6efforw8HAAwKpVq/D888/D4XBg4cKFGDp0aL3vfW6XB9HlQmlJIUryM1FakAFbURacxdlAaQ6U5lyorXkw2HPh5SiAj1gAP7EYCqF5/6nsohIFgg9MCj8Uq/xhVgfArguAqA8CjEFQeQVD6xMKg18ovP3DoNUbm7U+Ik8niiJKHaVSuGAqHwnhHjy0vCBCKSgRqA1CsL4iZKgcOATrQhCoDYRSwUFyRERERE2JgUIzS0pKwtVXXw1RFLFmzRp07tzZ7fzcuXPx2WefIS4uDkuXLq33/S+0bWRNHA47iguyUJqfCbMpEw5TNpyl2VCU5kBpyYXOlgeDPR/ezgL4iQUwCtb6P8lFKhF1KBB8YSof/WDVlI1+cBmCoDQGQ+1TFkB4+YfCyzcEShVfTBA1BfcgolCanmGyl4+KsJmk6RJF0nEhTPaiZtvyUwEF/LUBCNaFIEQfUiVwCNaFIFAXBLVC3Sz1EBEREXkiBgrNbN68eZg/f36NgUFmZiauuOIKAMDmzZsRERFRr/s3NFCoL0tpEYryM2EuyIDVlAVHcTbEkmwoLblQW/Kgs+eVjX5wFcBfLIRKcDV9UZW4RAEFgjcKhXOjH/xh0wbCpQ8EDEFQegdD4x0KL/8Q+AeGQqnzBTh/m6hJnQsi3BemrDQqotIIiCK7CYXWAuRYs2FxWpqsJn9NWegQrC8b5RAiBQ8hCNIFI1gXDI1S22TPT0RERNSacZeHZrZ//34AwIABA6o9HxoaisjISKSmpmLnzp2YMGFC8xVXDzqDN3QGbyCy8wX75rqcKC7MRUl+BsyFmbAXZcNZnA2hNAcqSy40tjwY7HnwchbAz1UIH+Hit71UCCICYEKAaALsSYAdQCmA/Or7uyCgRPCCReULh9YXgj4AKoM/tN6BUBgC4NL6QdT5w6Xzg6j1g0vnD1HnB1HjzSCCqI4EQZB21AhH3cJSURRR4ihGtiUL2Zbssr/NWcixZCPLkolsSzZyLFkocTTs+0a+LQ/5tjzEm47X2MdX41dlWkWILrQ8cCgLHvQq7oZDRERE1NgYKJzn7NmzAIDo6Oga+5wLFBITE5upqqalUCjh4x8CH/+QC/a1Aki1mlFUkIXS/AxYTZlwFGXDVZINhTkXamv59AtHAXycBQgQC6ARHBdfI0R4i0XwthcB9hSguG7XiYISota3LGjQ+ZcHD+WBQ6XgwS2Q0PlDVHuVxXlEVCtBEOCl9oaX2hsdvDvV2K/EXoIcazayzVnItpQFDmUhRMWf+m6deU6hrQCFtgIkmE7W2Mdb7V0eLrhPqwjSBSNEH4pgXTAMKq4DQ0RERFQfDBTOk5ubCwAICAiosY+fnx8AID+/hrfTPZxGq0dgaHsEhra/YN+C8xaftBZlwVWcDZRkQ2kuG/2gPzf9ogkWnxREJwRLHhSWvHpdJwrKCwcPbu3lIyLURgYRRNU4N/KhvVdMjX3MDrMUNLgHDufaslBgK2jQ8xfZi1BkL8LpolM116gyVhs4nHscrA+Gl8obAr/GiYiIiAAwUKjCYimbC6zRaGrso9Vq3fpSzQSFAkZvfxi9/YHobrX2dQLIrLT4ZKkpE5bCLJSacmEvzoNozoPCWgAvVxH8hGL4oVj6W9nIO2AIohOCORcKc269rhMV6vKgoeYREVXDCD9AbWAQQW2eXqVHlFc0orxqHiFmc1rLp1FUHzhkW7KRZ63f1+05JY4SlBSfwdniMzX20Sn1tQYOwboQ+Kh9GToQERFRm8BA4TxKpRIul6vWXwbPrWOpUHBufmNTqdTwC4qEX1BktedFUUShxYHUAjOOFliQUmBGan4J8vLzUFSYA1gK4C8UwQ8l8JP+rgge/IVi+JYHEb4oafwgwmWHYM6Gwpxdr+tEhaaaEKJq8FA2OqJiVARUOgYR1KZolFpEGtsh0tiuxj52lx25lpwaA4dsSxbyLLlwof6L0VqcZiSXJCG5JKnGPmqFpso6DpUDh1B9GHw1fvV+biIiIqKWhoHCeQwGAwoLC2G11rztos1mA1AxUoGajyAI8NOr4adXo2e4T5XzpTYnUgrMSCm0ICXfjORCM7YXWJBaYEaGyYrK8YEAF7xRCn9ptEMJ/FAEP6EE/kIRfMvDCP9KIyH8hGL4oLRRp2UAgOCyQVmaBZRm1es6UamtNnhweUXA6RMNl08UnD5RcBnDuDgltRlqhRphhnCEGcJr7ON0OZBrza0xcMg2ZyHHmtOgbTTtLhvSSlORVppaY59AbRA6+3RBJ58uZX97d0GksR0U/DolIiKiVoSBwnn8/f1RWFiIgoKCGvucWzshMDCwmaqiujJolIgN8UJsiFeVczaHC2mmslENKQUVfycXmHGk0AKHq24hgQIu+FQKG3yFYvihLITwE0oQrjYjTFOKYGUp/FAEL7EYOocJarupsT9cCE4rlCWZQElmrf1EpRZO78jygKE9nN7lQYNv2WNR59fotRG1ZEqFCiH6UIToQ2vs4xSdKLDmI8uS5R44nLewpEOs/8KzudYc5GbnYEf2P1KbTqlHR++O6OQTi87lQUMH707QKXUN+hiJiIiImhoDhfN07NgRiYmJSElJqbFPamrZu04xMTHNVBU1Bo1KgZgAA2ICDFXOOV0iMous5SFDRdCQWmhBcr4ZFkfF0GgXFCiANwpEbyQCwPk5hAOAuerzK+FElM6Grj42dDTa0V5nQaTOjBBlKQKVJTA4TVBYC6Gw5EOwFJT9bS2Awtawle8rE5xWqApOAwWnqz3v0viUBQw+0XD6RLs/9m5XNrWCqI1RCkoE6oIQqAtCd/Soto9LdKHQVuA2siHbUnUnC5vLdsHnszjNOFpwBEcLjkhtAgS0M0ZVGs1QFjYEaBloExERkfwYKJynb9++2LRpE/bv31/t+czMTKSlpQEA+vfv34yVUVNSKgRE+OoQ4avD4Pb+budEUURuqR0p+WakFJqRXD6F4tzfhZa6vTvphBKJFj0SLfpqzxvUSrTz06Gdnx7twvRo56dDlJ8e7XyUCFVboLIVQrDkQ2EpKAsazg8eLAXl53OhKMmEINZ9frjCZoIi5wiQc6Ta805jaFnA4B1VHjicm04RXTadQqGs83MReRKFoIC/NgD+2gDE+natto8oijDZTcixZCHLnIXkkrNIMJ3EKdNJnC05W+u0ChGitGbD5vSNUru/xr9iukT5lIkoYxSUCv5YJyIiouYjiOdWGCQAQGJiIsaOHQulUolffvkFHTt2dDs/d+5cfPbZZxg8eDC++eabet8/J6cI/Ix7FpPFXmUKxbnAIafkwu9K1oVGWRZ4tPPTo52fHlF+OkT66RHlp0eEjxYq5Xnzrp02KIrToDQllf9JhqLy43puo1kbUaEun05RaXSDdzScvmXHotaPC0cS1cDmtCKx+AxOmRKQYIpHgukkThcloMRRUu97aRQadPDuJK3J0NmnCzr6dIJBZWyCyomIiKg1EAQgKMi76e7PQKGqJ554Ar/88gs6d+6MTz75BO3btwcA/Pzzz3juuefgcDiwcOFCDB06tN73ZqDQtpjtTqSWhw2Vp1CkFFqQYbKgjss21EohAGE+OrTz1SHKvyxw6BpiRO9wH+jU1Y8cEGzF5QFDMpRFyVAUnoWyKLns2HQWgqPxtkR1qb2k0QwV0ynaw+kTBad3FKCufsQGUVsliiIyzOnSKIYEUzxOFSUg05zRoPtFGtqVjWLw6YzO3mVTJoJ0wdzakoiIqA1goCCD/Px8TJ48GfHx8VAqlYiNjYXJZJLWTnjssccwbdq0Bt2bgQKdY3e6kG6yuo1oOLeGQ2qhBXbnxf1HUSsF9AzzRlw7X8RF+aFPhA/0NQQMbkQRgjlHGs2gNCVVhA+mJCiK0yA0YOX7mjgNIWWBQ/l0Cld56OD0iYbLKxzgEG4iAECR3VQ+kqEsaDhVdBKJRWcatCikj9q3LGA4tzaDdyyivdpDxa83IiIij8JAQSalpaX4+uuv8dtvvyE5ORkqlQq9evXCXXfdhbFjxzb4vgwUqC6cLhHZxVZpCkVKpbAhpcCCUnv9X9ArFQJ6hHpjQJQv4qJ80TfCFwZNA9Y+cNqhKEmHsjAJyqIkKMqDBmk6hTmn/vesgahQweUVKQUM0toN3lFw+raHqAvgdApq0+wuO5KKEytGMxSV/V1kr/9irmqFGu29Okg7TJStzdAZXuqm+yWEiIiImhYDBQ/DQIEuliiKyDfbkZzvPoUipcCM5Py6LxKpFIDu50YwtPND30gfeGkb4d1JW0ml6ROVRjcUJUFZmATBUXrxz1FOVBnKw4b25VMpKh47faIBddUdPYg8nSiKyLJk4pQpoXzKxEkkFMUjvTStQfcL04dLC0CeW58hVB/GKRNEREStAAMFD8NAgZpaXqkN+1MKsSe5EHtTCpGQU7fF3RQC0DXEC3Ht/BAX5Yv+kb7w1jXy8GdRhGDJk0Y0VIxuODedIhWCq/7Dt2vi0gdWjGzwjipbKNK7fB0HrwhAqW605yJq6UrsJThdlFBpbYaTOFN8GvY6bGl5Pi+VNzr5dJZGMXT26YL2Xh2gUWqaoHIiIiJqKAYKHoaBAjW3ArO9LGBIKcTe5AKczC5BXf4LCgBiQ7wQ184XA6J80S/SF776Jn4B7nJAUZwBpels2fSJomQoyxeMVJiSoSzNarSnEgUlXF4R5aMZouD07QBnYHc4grrDZQznVApqE5wuB5JKkqSA4VRR2d+FtoJ630spKKUpE528y8MGny7w1fg2fuFERERUJwwUPAwDBZKbyWLHvhQT9qYUYF9KIU5kFddptwkBQOdgo7TIY1ykL/wMzfwOv90sTaeo2AazYltMhb24UZ7GpfWDI6g7HIE94AjqAWdQDzj8uwAqXaPcn6glE0URudacsi0sTQlIKA8ZUkuSIdYpjnQXogtFx/IFIDt7l4UM4YYIKATFhS8mIiKii8JAwcMwUKCWptjqwP7UQuxNLhvFcCKzCHXdYKJjoAEDovzKQwZfBBhkHO4sihCsBZWmUpwtn0qRDIXpLJRFqRBc9obfXlDC6d8ZjsDucAT1gCOwO5xBPeAyhHA0A7UJZkcpThedqliboagscLC6rPW+l0FlQMfyUQzngoYY747QKrVNUDkREVHbxUDBwzBQoJauxObAgVQT9pZPkTiaWQxnXYYwAOgQYEBclG/5Qo++CPJqQS8OXE4oSjKhNJ1135miKBmKwiQoSzMbdlt9oDSS4dyoBqd/Z4BzyakNcIpOpJYkV2xnWT6aIc+aW+97KaBAlFf7SltZdkEnn87w1wY0QeVERERtAwMFD8NAgVqbUpsTh9JM2JNSgL3JhTiSUQRHHQOGaH+9NHohrp0fQr1bUMBwHsFaCFXuMShzjkKVcxSq3GNQ5R6H4Kz/u6+iQg2nfxe3aROOoB4Q9YFNUDlRy5NnzcOpSos/nipKQHLxWbjgqve9ArVB6OTTBf0C43Bl+CiE6sOaoGIiIiLPxEDBwzBQoNbOYnfiULpJ2kXicLoJ9jrOkWjnpytf5LFsmkSYTwtfk8DlhLLwTFnAkHMUytzyv0syGnQ7pyEUzqBzUybK12fw6wgoGnk3DaIWyOq04kzRKWmXiVNFCThlSoDZWb+tZHv798XIiNEYHjYSflr/JqqWiIjIMzBQ8DAMFMjTWOxOHMkowt7kQuxNKcCh9CJYHXV7FzLCR4v+UX4YUD6KIcJH1yr2thcs+RWjGHKOlo1qyIuH0IDt90SlFo6A2LKpEpXCBlHn1/iFE7UwLtGF9NI0JJjicarSlpbZlgvv6KIQlBgQOBCjIq7CZaFXwKg2NkPFRERErQsDBQ/DQIE8nc3hKgsYyqdIHEgz1TlgCPXWYoC0BoMf2vm1joABAOC0Q1lwqjxoOApVTlnYoDBnN+x2XhHuIxkCu8PpGwMolI1bN1ELVGgrrJgyUXQSh/IOIMOcXmN/jUKDS0KGYmTEVbgk+FJouLgjERERAAYKHoeBArU1dqcLRzOKyhd5LMSBtEKY7XULGEK8NOhfvk3lgHa+iPbXt56AoZxQmi2NZDgXNijzEyC4HPW+l6jSwxHQVVqT4dyoBlHTdD8kiFoCURRxrOAINqWvx+a0jci35dXY16gyYljocIyMGIO4wAFQckoRERG1YQwUPAwDBWrrHE4XjmcVl29TWYADqSaU2Jx1ujbQqClfg6FsBENMQOsLGAAATiuUeQkVIxnK12ZQWGp+kVTr7Xyiy7azPLelZVAPuHyiAUHRyIUTyc8pOrE/dy82pa3HXxlbUOIorrGvv8YfV4SPxKiIq9DTr1fr/H5BRER0ERgoeBgGCkTuHC4R8VnF2JNcgL0phdifWohia90ChgCDumwEQzs/xEX5omOgAYrW+oJBFKEozaxYk+Hc+gwFpyCI9V8Z36U2whlYeQHIssABakMTFE8kD5vThl05/2Jj2nr8k7kVVlfNu7KE6sNwZfhojIoYg47enRkuEBFRm8BAwcMwUCCqndMl4mR2sTRFYl9qIUyWuk0P8NWpEFe+g0RcO190Dja23oDhHIcZqryTbrtMqHKPQWEtrPetRAhw+saULf4YWDFtwuUdWfbThqgVK3WUYHvmVmxM+wO7c3bCKdYcTLb36oCREaMxMnwMIo3tmrFKIiKi5sVAwcMwUCCqH5coIiG7pCxgSCnE3uQCFNYxYPDRqdA/smwHibh2vugS7AWlwgNeOIsiFMVpFWsylE+bUBacgYD6f4NxaX3hCOxWviZDj/LpE10Blb4JiidqeoW2AvyVsQWb0tbjYN5+iLV8XXTz7YGREWNwZfgoBOqCmrFKIiKipsdAwcMwUCC6OC5RxOncUmmbyr3Jhcg32+t0rZdWiX6RvuXrMPghNsQLKk8IGM6xl0KVe9xtbQZlzjEo7DXPMa+JKCjg9OvotsuEI6gHXMYwjmagViXbnIXN6RuwKW0D4k3Ha+wnQEDfwP4YFXEVrggbAW+1TzNWSURE1DQYKHgYBgpEjUsURSTmmbE3pQB7kstGMeSW2Op0rVGjRN9IH8S188OgaD90D/XyvHnVoguKohS3XSZUOcegNJ1t0O1cOv9KazL0gD1iMFy+MY1bM1ETSS5Owqb09diUth7JJUk19lMJKgwKvgSjIsbg0pBh0HO0DhERtVIMFDwMAwWipiWKIpLyzdibUog9yQXYl1KIrOK6BQzdQ71w75BoDO8c2PrXXrgAwVYEZe5x96Ah9zgEh7ne93L4d4at/SjYYkbDHj4I4DZ91MKJooiTpnhsSluPzekbkG3JqrGvTqnD0JDLMTJiDAYFD4FaoW7GSomIiC4OAwUPw0CBqHmJoojUQou0i8Te5EJkFNW8EjwAdAg0YMrgKFzVLcSzpkRciOiCsjDRbZcJVc5RKItT63wLl9YXtugRsMWMhi16BESdfxMWTHTxXKILh/IPYFPaBvyZvgkme80LnnqrvXFF2JUYGTEGfQL6QSkom7FSIiKi+mOg4GEYKBDJL61ywJBSiLRCS7X9Iny0mDw4Ctf3DINWpWjmKlsOwVIAVe4xKM+FDLnHykYzOGsPZkRBCXv4QNjaj4atwxg4/Tpx/QVq0RwuB/bk7MLGtD+wLfNvmJ2lNfYN1AbhyvBRGBkxBl19u3vedCkiIvIIDBQ8DAMFopYnOd+MpXtT8fOhdNicVb9AA40a3DkgEjf1DYdRw+H8AACXA6rcY9Cc3QTNmfVQZ+2/4CVOn/awxoyGLWYM7BGDAaWm6eskaiCL04J/s7ZjY9of2Jn9D+yumhd/jTS0w8iIMRgZMQbtvWKar0giIqILYKDgYRgoELVcOSU2LN2Tip8OpKHEVnUPex+dCrf0i8CtcZHw03MedWVCSRY0SZuhTVwPTdJfEBw1v7MLAC61F+zRw8sChvYjIeoDm6lSovorthfh74w/sSl9Pfbl7IELrhr7dvLuglERY3BlxGiE6sOasUoiIqKqGCh4GAYKRC2fyWLHj/vTsHRPKgotjirn9WoFbuwTjrsGtkOwl1aGCls4pxXq1H/LwoXEDVAWpdTaXYQAR1gcbO1Hw9phNJwB3Tg1glqsPGsutqRvwqa09ThacLjWvr38+2Bk+BgMD78S/tqAZqqQiIioAgMFD8NAgaj1MNudWHkwHd/tTql2pwi1UsD1PUMxeVAU2vlxW7lqiSKUefHQJK6H9uxGqDL2QBBrfncXAJze7WCLGQVr+9GwR14KqHTNVCxR/aSXpmFz2gZsSl+P00WnauynEJQYEDgQIyPGYFjocBjVxmaskoiI2jIGCh6GgQJR62NzuPDr0Uws3pWMlIKqCzgqBGBM12BMGRKNzkF8oVAbwZwHTdImaBI3QpO0BQpbUa39RZUetqgrynaNaD8SLmNoM1VKVD9nik5hU9p6bErbgHRzWo391AoNLg0ZipHhY3BJyFBolBzlRERETYeBgodhoEDUejlcIjbFZ2PhjmQk5JRU22d4p0BMGRKFXuE+zVxdK+S0Q52+E5rEDdAkroeqMPGCl9hD+paFCzGj4QjqxakR1OKIoohjBUewKX09NqdtRL4tr8a+BpUBl4eOwMiI0YgLHAilgou+EhFR42Kg4GEYKBC1fqIoYuvpPCzckYRD6dW/wz4o2g/3DonCwCg/bidXR8qC09CcWQ/N2Q1Qp+2EIFZdGLMypzG0bEvKmNGwtRsGqDnthFoWp+jE/ty92JS2Hn9lbEGJo7jGvn4aPwwPH4VR4WPQw78XFELb3aqWiIgaDwMFD8NAgchziKKIvSmFWLgjCTvOFlTbp1e4N6YMjsblnQKgYLBQZ4K1EJqkLWWjF85ugsJaWGt/UamFrd2w8qkRo+DyjmimSonqxua0YVfOv9iYth7/ZG6F1WWtsW+ILhQjI0ZjVMRV6OjdmaEkERE1GAMFD8NAgcgzHckowqIdSdiSkFvt+U5BBkwZHI3RXYOhUvDFQb24HFBn7CmfGrERqvz4C15iD+ophQuO0H4A3+2lFqTUUYLtmVuxMe0P7M7ZCWcto3Hae8VgZPgYjIwYg0hju2askoiIPAEDBQ/DQIHIs53KKcHincn443gWnNV8rUf66jB5cBSu7xEKjYovchtCUZgIbeJGaM5uhDr1Hwgue639XfogWNuPgi1mFOxRV0DUeDVTpUQXVmgrwF8ZW7ApbT0O5u2HiJp/Sejq2x0jI8bgyvBRCNIFN2OVRETUWjFQ8DAMFIjahpQCM77dnYLVhzNgryZZCPbS4M4B7XBjn3AYNEoZKvQMgq0I6uS/pIBBYa5+hMg5okIDe+SlsMaMgi1mNFw+0c1UKdGFZZuzsDl9AzalbUC86XiN/QQI6BvYHyPDx+CKsCvho+EisEREVD0GCh6GgQJR25JTbMV3e1Lx04E0mO2uKud9dSrcGheJW/pFwFevlqFCDyK6oMrcB03iRmgT10OVe+yClzgCusIWMwrW9qPhCBsAKBjuUMuQXJyETenrsSltPZJLkmrspxJUGBR8CUZGjMbQkMuhV3FxUiIiqsBAwcMwUCBqmwrNdizbl4b/7UuFyeKoct6gVuLmvuG4Y0Akgry4L31jUBSlQnN2Y9naCynbIDhrXgQPAFxaP9jajyxbeyF6BEQt3/Ul+YmiiJOmeGxKW4/N6RuQbcmqsa9OqcOlIcMwKuIqDAoeArWCISURUVvHQMHDMFAgattKbA6sPJiB73anIKfEVuW8RilgXK8w3D2oHSJ9+U5jo7GXQpOyVVrYUVmaWWt3UaGCPXxwWbgQMxpOv47NVChRzVyiC4fyD2BT2gb8mb4JJnvNu594q70xPGwk7ug8GWH68GaskoiIWhIGCh6GgQIRAYDV4cLaIxlYvCsFaYWWKueVAjC2ewjuGRyFjoFGGSr0YKILquzD5VtSboQ668AFL3H4dYSt/WjYOoyGPWwQoOQ7vyQvh8uBPTm7sDHtD2zL/BtmZ2m1/QwqA2Z0/w+ubncdt58kImqDGCh4GAYKRFSZwyVi/YksLNqRjNO51b8gGNE5EPcOiUaPsKb7YdCWKUoyoDm7CZozG6BJ+QuCo2rAU5lL4wNb9IjybSmvhKjzb6ZKiapncVrwb9Z2bEz7Azuz/4G9mp1PhoYMw+O9ZyFAGyBDhUREJBcGCjLZunUrvv/+exw8eBAFBQUwGAzo2rUrbr75ZowfP77BKT8DBSKqjksU8fepXCzYkYyjGUXV9rmkvT+mDIlCXDtfvtPYVBxmaFL/KZ8asQHK4rRau4uCAo6wgbCemxrh36XsJzeRTIrtRfg740+sTlqJE4XuC5P6avzweK9ncHnYcJmqIyKi5sZAQQZvv/02FixYAAAwGAxo3749MjMzkZeXBwAYOXIk/vvf/0Ktrv+QVwYKRFQbURSxK6kAC3cmY3dSQbV9+kT44N4hUbisQwCDhaYkilDmHivbkjJxPVSZ+yCg9m/gTp9oKVywRwwBlFxgk+ThFJ1Ydvp7LIz/Eg7RfSHYqyKvwcwej8FL7SVTdURE1FwYKDSz1atX46mnnoJSqcTTTz+NyZMnQ6FQAADWrVuH5557DiUlJXjwwQfxxBNP1Pv+DBSIqK4OpZmwaGcy/jqVW+35LsFGTBkchVGxwVAqGCw0NaE0B5qkzdAmroc66U8o7CW19nepjbBHXQFrzBjY2o+EaAhqpkqJKpwyJWDOgVdxuijBrT1EF4qn+zyPuKCBMlVGRETNgYFCMxs/fjyOHz+Ou+++G7Nnz65y/scff8Ts2bNhMBiwY8cOaDSaet2fgQIR1VdCdgkW7UzC+hPZcFXz/SPKT4d7Bkfh2h6hUCsVzV9gW+S0QZ22A5rE9dAmboDSlFRrdxECHKH9YYsZDWvMaDiDejRToUSAzWnD4pNf44fT38EFl9u5m2JuwdSu06HlaBoiIo/EQKEZFRQUYMiQIQCA//3vf+jfv3+VPnl5ebj00ksBACtXrkSPHvX7pZCBAhE1VHK+GUt2JeOXI5lwVJMshHhpcNegKEzoHQa9WilDhW2UKEKZnwBN4npoEjdCnbELguiq9RJb+BCYB8yALfpKrrlAzeZw3kG8dfA1pJWmurVHG9tjVt8X0M2PQRcRkadhoNCMzGYz/v33X2RkZGDcuHHw8qo6t7ByoLB8+XL07t27Xs/BQIGILlZWkRXf7UnBigPpsDiqvnD106txe1wkJvWLgLdOJUOFbZtgyYfm7GZozm6E5uxmKGymGvvag3rCHDcT1k7XAgqGQNT0zI5SfHb8Y6xJWunWrhCUuKvTPbir8xSoFPy+QUTkKRgotDDfffcdXn31VajVavzzzz/w9q7fPw4DBSJqLAWldvxvXyqW7UtDkdVR5bxRo8TEfhG4PS4Sgcb6Tc+iRuK0Q52xW9o1QlVwqtpuDt8OMMc9DEvXmwEl/62o6e3I+gfvHZqDXGuOW3usTzc82+9FtPeKkacwIiJqVAwUWpCsrCzccMMNyM/Px9ixY/Hf//633vdgoEBEja3Y6sCKA+n4bk8K8kqr7j+vVSkwvlcY7hrUDuE+OhkqpHOUefHQ7/8CuhM/QXBV/bdyGsNg7vcQzD3vBNQGGSqktsRkM+GjI+9ic/pGt3a1QoOpXafjpphJUAhcl4WIqDVjoNBAs2bNwsqVKy/csdyqVavQvXv3Gs8XFRXhnnvuwZEjR2AwGLBq1Sq0b9++3nUxUCCipmKxO7HmSCa+2ZWMdJO1ynmlQsA13UNwz6AoxATyxaqcFEVp0B/4Avoj30FwmKucd+n8Ye5zH8y9p0DU+ctQIbUlm9LW46Mj76HIXuTW3i8gDk/3fR5h+nCZKiMioovFQKGBGjNQyMvLw9SpU3H48GEIgoAPP/wQV199dYPqYqBARE3N4XTh9+PZWLQzCYl5VV+sCgBGxgZhyuAodAttuh8wdGGCOQ/6g19Df2gRFNbCKuddaiMsPe+Cud9UuIxhMlRIbUW2JRvvHXwTu3J2uLUbVAbM7PEYxkZeC4ELiBIRtToMFBrIZrPBbq86nLQmer0eCkXVYX1nz57Fgw8+iMTERCgUCrz66quYNGlSg+tioEBEzcUlitiSkItFO5JwLLO42j6Xxvjj3iHR6N/Ot5mro8oEWzF0R76Ffv8XUJZmVTkvKjSwdJuE0rjpcPnGNH+B1CaIoog1Savw2fF5sDgtbucuC70cj/d6Bv7aAJmqIyKihmCgIKPdu3djxowZKCgogFqtxjvvvINrr732ou7JQIGImpsoithxNh8LdyRjb0rVd8EBoF+kD6YMicbQGH++CyknhwW648th2PcJlKakKqdFQQFr53EojZsBZxC3+KOmkVqSgjkHXsXRgsNu7X4aPzze6xkMCxsuU2VERFRfDBRk8uuvv+KZZ56BzWaDn58f5s+fj0GDBl30fRkoEJGcDqQWYtHOZGw9nVft+a4hXrh3SBRGdA6CUsFgQTYuB7QJa2DYMx+qvBPVdrG2H4XSAY/AET6wmYujtsApOvHD6e+wKP4rOET3XWTGRl6LGT3+Ay911e21iYioZWGgIIO1a9fiySefhMvlQrt27fDll1+iY8eOjXJvBgpE1BKcyCrG4p3J2HAiG9V9S2rvr8c9g6NwTfcQqJRc5V02oguaxI0w7J0PdcaearvYIoagdMAjsEcNL/utgagRnTKdxJwDr+J0kfuWpyG6UDzTdzb6Bw6QqTIiIqoLBgrN7MCBA7jzzjtht9sRGxuLBQsWIDg4uNHuz0CBiFqSs3ml+GZXCtYezYTDVfWbU5i3FncPaocbeoVBp1bKUCEBAEQR6rR/YdgzH5rkP6vtYg/qhdIBM2HreA2g4L8VNR6b04ZFJ7/CD6e/g3heBHlzzK14oOs0aJVamaojIqLaMFBoRk6nE9deey0SExMRGBiIlStXIjQ0tFGfg4ECEbVEGSYLvtuTipUH02F1uKqcDzCocXtcJCb2i4CXViVDhXSOKusgDHs/hubUrxCqGV/i8OsIc/+HYel6E6DUyFAheapDeQfw1sHXkF6a5tYebWyPZ/u+iK5+NW+/TURE8mCg0IzWrVuHRx99FAAQGhqKyMjIWvu/8MIL6NGjfotiMVAgopYsv9SGpXtTsWxfGkpszirnvbRK3NIvArfFRcLfwBerclLmn4J+7yfQxf8EweWoct7pFQ5zv4dg7nEHoDbIUCF5IrOjFJ8dm481yavc2hWCEnd3noI7O90DlYKhIxFRS8FAoRm99tpr+Pbbb+vcf8mSJRgyZEi9noOBAhG1BsVWB37cn4ale1KRb666Ba9WpcCNfcJx98B2CPHmUGc5KYrSoN//OfRHv4PgsFQ579L5w9znfph7T4Go82v+Askj/Zu1He8dmoM8a65be1ffbni274uI9oqRpzAiInLDQMHDMFAgotbEYnfi50MZ+GZ3CjKLrFXOGzVKvD+hJwZE+TV/ceRGMOdCf3AB9AcXQmEzVTnvUhth6XU3zH2nwmVs3Ol81DYV2grx0ZH3sCV9o1u7RqHB1K7TcWPMJCgELupKRCQnBgoehoECEbVGdqcLvx3LwuKdyUjKN7ud06oUeOeGHhjaIUCm6qgywVYE3eFvYNj/JRTm7CrnRaUWlm6TUNp/Oly+7WWokDzNprT1+PDweyh2FLm19w8cgKf7PI9QfZhMlREREQMFD8NAgYhaM6dLxOaTOViwIwkns0ukdpVCwBvXdcPI2MbbFYcuksMC3fFlMOz9FMqi5CqnRUEBa+cbUDpgBpyBXEyPLk62JRvvHnwDu3N2urUbVUY80uNxjIm8GgK3NSUianYMFDwMAwUi8gQ2hwsv/Hocm07mSG0KAXhxbFdc15PD6VsUlwPak6th2PsxVHknqu1ijRmD0gEz4Qgb0MzFkScRRRGrk1bi8+PzYXG6r+cxLHQ4Hu/1NPy0/jJVR0TUNjFQ8DAMFIjIUzhcIl7//QTWHs1ya396VGdM6hchU1VUI9EFTeIGGPbMhzpzb7VdbBGXoHTAI7BHXVH2GwhRA6SUJOOtA6/haMFht3Z/jT8e7/0MLgu9QqbKiIjaHgYKHoaBAhF5Epco4t2NCVh+IN2t/ZHLO2Dy4CiZqqJaiSLUaf/AsGc+NMl/VdvFHtwbpXEzYOt4DaBQNnOB5AmcLgd+OP09Fp38Cg7RfVvTq9tdhxnd/wOj2ihTdUREbQcDBQ/DQIGIPI0oipj/9xks2ZXi1n7fJdGYNrQ95023YKqsAzDs/RiaU79BQNUfTg6/TiiNexjW2BsBpUaGCqm1SzDFY87+V3Gm+LRbe6g+DM/0mY1+gXEyVUZE1DYwUPAwDBSIyBOJooiFO5Lx6bZEt/bb4iLx+IiODBVaOGV+Agx7P4E2fgUEl6PKeadXBMz9HoK5xx2AWi9DhdSa2Zw2LDr5JX44/T3E84KriTG34oGu06BRamWqjojIszFQ8DAMFIjIky3dm4oPNp9yaxvfKwzPjukCpYKhQkunKEqFft9n0B9bCsFhqXLepQuAue/9MPe6B6LOr/kLpFbtYN5+vH3gdaSb09za23t1wLN9X0CsbzeZKiMi8lwMFDwMAwUi8nSrD2Xg9T/i3d6HHNM1GK9e0xUqpUK2uqjuhNIc6A9+Df2hxVDYTFXOu9ResPS6G6V9p0I0hshQIbVWpY4SfHZsPn5J/tmtXSkoMbnzfbij091QKlQyVUdE5HkYKHgYBgpE1Bb8cTwLL/52Ak5XxTe8yzsGYM64HtCqGCq0FoLVBN2Rb2DY/yUU5pwq50WlFpbut6K0/zS4fKJlqJBaq3+ztuO9Q3OQZ811a+/m2wOz+r6AaK/2MlVGRORZGCh4GAYKRNRW/HUqF8+uOQqbs+Kb3qBoP7w3vicMGu4c0Ko4zNAdWwbDvs+gLEqucloUlLB2uQGlcTPgDOSwdaqbQlshPjz8Lv7M2OTWrlFo8GC3GZjQ/mYoBAaQREQXg4GCh2GgQERtyc6z+Xjy5yMw211SW+9wH3x0Uy946zisudVx2qFNWA3Dno+hyo+vtos15iqUDpgBR9iAZi6OWiNRFLEpbT0+OvI+ih1FbufiAgfi6T7PI0QfKlN1REStHwMFD8NAgYjamgOphfjPysMotjqltthgI+ZP7A1/A7cibJVEFzRn1sOwZx7UWfur7WKLHIrSATNhb3d52W8zRLXINmfhnUNvYE/OLrd2o8oLj/R8DGMiruZuMUREDcBAwcMwUCCituhEZjFm/nQIBWa71NYhwID5E3sjxJvbxbVaogh16nYY9syHJuXvarvYg/ugdMBM2DpeDXD4OtVCFEWsTlqBz47Nh9VldTt3eegIPNbrKfhp/WWqjoiodWKg4GEYKBBRW3UmtxQzlh9EdrFNaovw1eGTSb0R6auXsTJqDKrM/TDsnQ/t6XXVnnf4d0Zp/4dhjb0RUKqbuTpqTVJKkvHWgVdxtOCIW7u/JgBP9J6FoaHDZKqMiKj1YaDgYRgoEFFbllJgxozlh5BWaJHagr00+HhiH3QINMhYGTUWZV48DHs/gTZ+JQTRWeW80ysSpf0fgqX77YCaQRJVz+ly4H+nv8Oik1/Bed7/o2vbjcP07v8Ho9ooU3VERK0HAwUPw0CBiNq6rCIrZiw/iMQ8s9Tmp1dj/sTe6BriJWNl1JgUphQY9n8G3dGlEJzWKudd+kCY+9wPc+97IGp9ZaiQWoOThScw58CrSCw+49Yepg/HM31mo29gf5kqIyJqHRgoeBgGCkREQF6pDY8sP4T47BKpzVurwoc39UKfCB8ZK6PGJpRmw3Dga+gOL4bCVlTlvEvtBUvvySjtOxWiIViGCqmlszmtWHjyKyw7/T1EVPwSJUDAxA634f7YB6FRci0WIqLqMFDwMAwUiIjKFFkceHTFYRxKN0lterUC70/oiUHRXHjN0whWE3SHl8Bw4CsozDlVzotKLSzdb0Np/2lw+UTJUCG1dAfz9uPtA68j3Zzm1t7eqwOe7fsiYn27ylQZEVHLxUDBwzBQICKqUGpz4omfj2B3UoHUplEKeGtcD1zeKVC+wqjpOMzQHfsBhn2fQVmUUuW0KChhjZ2A0v4PwxnIF4jkrtRRgk+PzcPa5NVu7UpBicld7sMdHe+GUqGSqToiopaHgYKHYaBAROTO6nBh1pqj2Ho6T2pTKgS8dm03jOnKIfAey2mH9uTPMOz9GKr8k9V2sXYYi9K4GXCExTVzcdTS/ZO5De8dmoN8W55be3e/nnimz2xEe7WXqTIiopaFgYKHYaBARFSVw+nCi7+dwPoT2VKbQgCeHxOLG3qHyVgZNTnRBc2ZP2DYMw/qrAPVdrFFXobSwY/DHjGkmYujlqzQVoC5h9/BXxlb3Nq1Ci0e7DYD49vfBIWgkKc4IqIWgoGCh2GgQERUPadLxJvr47H6cKZb+xNXdsJtcZEyVUXNRhShTtkGw5550KRuq7ZLycBHUTrocUChbObiqKUSRREb0/7AR0feR4mj2O3cgMBBeKrPcwjRh8pUHRGR/BgoeBgGCkRENXOJIj7YfAo/7HNfdO3hYTG4d0i0TFVRc1Nl7oNhz3xoz/xe5Zyt3eUwXTUfop5rbFCFbHMW3jn4Bvbk7nJrN6q88GjPJzAq4ioIgiBTdURE8mGg4GEYKBAR1U4URXy2LRELdiS7td8zOAozhsXwRUEbosw9AcOeedCdXOXW7jSGwXT153CEDZCnMGqRXKILq8+uxOfH58PqsrqduyLsSjzW6yn4avzkKY6ISCYMFDwMAwUiorpZvDMZ8/8+49Y2qV8EnhzZCQqGCm2K9uQaeG1+Egp7idQmKlQoGTob5j73l/22RFQuuTgJbx18DccKjri1+2sC8GTvZ3Fp6GUyVUZE1PwYKHgYBgpERHX34/40vLMxwa3tup6hmH1VLFQKvohsS5T5CfBZ9xBUeSfc2i2dx6H4yncharxkqoxaIqfLgaWnv8Xik1/DKTrdzl0bNQ4Pd/8/GFRGmaojImo+DBQ8DAMFIqL6+eVIBl77PR6uSt87R3YJwuvXdYNayRXc2xR7Kby3PANd/Eq3ZodfJ5iu/gLOwK4yFUYt1cnCE5hz4FUkFruPdgrTh+OZvrPRN6C/TJURETUPBgoehoECEVH9bYzPxuy1x+GolCoM7eCPt8f1gE7NFf/bFFGE7sg38Pr7ZQguW0WzSo+iEW/D2vUmGYujlsjmtGJB/Jf48cxSiKj4HiJAwKQOt+O+2KnQKLUyVkhE1HQYKHgYBgpERA2z7Uwenll9FFaHS2qLa+eLD27sCaNGJWNlJAdV5n74rHsIyuJUt3Zzr3tQPOxFgC8Q6TwH8vbh7QOvI8Oc7tYe49UBz/Z9EV18OcKFiDwPAwUPw0CBiKjh9iQX4PGVR1Bqr5gT3TPMGx/d1Au+erWMlZEcBEs+fNY/Ak3SFrd2e0hfmMZ+DpdPO3kKoxarxF6CT4/9F7+mrHFrVwkq3NPlftzW8U4oFQwoichzMFDwMAwUiIguzuF0Ex5dcRgmi0Nq6xJsxLybeyPQqJGxMpKF6IJh939h2Pk+hErD2V1aP5jGzIO9/ZUyFkct1fbMrXj/0FvIt+W5tffw64lZfV9EO2OUTJURETUuBgoehoECEdHFO5ldjJnLDyGv1C61Rfvr8fHE3gjz0clYGclFnfwXfP6YAYUlX2oTIaB04KMoHfQYoOBaG+Su0FaAuYffwV8ZW9zajSoj/nvp5+jg3VGewoiIGhEDBQ/DQIGIqHGczSvFjOWHkFlkldrCfbT4eGIfRPnrZayM5KIoSoPP79Ogztzr1m6LugKmMfMh6gNkqoxaKlEUsSHtd/z3yAcocRRL7R28OuKTy76GlmtxEFEr19SBAvfbIiKiVql9gAFf3tYX7fwqRiSkm6yY+sMBnMopkbEykovLOwIFNy5HaZ/73No1yX/Bf9lYqDL2yFQZtVSCIGBM5NX4+vJv0NO/t9R+pvg0Pjs2T8bKiIhaBwYKdXT48GH07NkTXbtyBWAiopYi3EeHL2/ti46BBqktt8SGh344gGOZRTJWRrJRalBy+aswXfUJRFXF/wtlcTr8Vk6E7uACcKggnS9EH4pX4+YgQBsotf2ctAJ/Z/wpY1VERC0fA4U6sNlseOaZZ+BwOC7cmYiImlWQlxaf39IX3UO9pLZCiwPTlx3E/pRCGSsjOVm73ID8SWvh8O8itQkuO7z/fhHe62cCNo5iIXf+2gA81/clCBCktvcOvYksc6aMVRERtWwMFOpg7ty5SEhIkLsMIiKqgZ9BjU8m9UG/SB+prcTmxMyfDmFHYn4tV5IncwZ0Qf7EX2DpMt6tXXfyZ/gvvw7KvHiZKqOWKi5oIG7reJd0XGQvwhv7X4ZTdNZyFRFR28VA4QL27NmDRYsWQa/nAl9ERC2Zl1aF/97cG0Pa+0ltVocLj606jC0nc+QrjOSlMaJozHwUXfE6RIVaalblJ8D/x+uhjV8lX23UIt0bOxXdfHtIx4fyD+C7hMUyVkRE1HIxUKhFaWkpZs2aBYVCgf/7v/+TuxwiIroAvVqJDyb0wojOFfOg7U4Rs9YcxbpjWTJWRrISBFh6T0HBjT/B6RVR0ewohc/6mfD663nAaa3lBtSWqBQqzO7/Cowqo9S25OQCHMzbL19RREQtFAOFWrzzzjtISkrC1KlT0bNnT7nLISKiOtCoFJhzfXdc3T1EanOKwIu/HseKg+kyVkZyc4TFIf+WdbBFD3dr1x9aDL8VN0NRlCpTZdTSRBgi8Z9eT0nHLrjw5v5XYLKZZKyKiKjlYaBQg+3bt+N///sfunbtiocffljucoiIqB5USgVeuaYrbuoTLrWJAOasP4lvd6fIVxjJTtQHoPC6JSgZ9DjESovvqbP2w3/Z1VAnbZGvOGpRRkVchavbXScdZ1ky8f6htyBylxAiIgkDhWoUFxfjueeeg0qlwltvvQWNRiN3SUREVE8KQcCs0Z1x54B2bu0f/XkaX24/yxcFbZlCidLBj6Nw3Ddw6fwrmi358F1zNww7PwBEl4wFUkvxSI/H0M4YLR3/nbkFvyT/LGNFREQti0ruAprKrFmzsHLlyjr3X7VqFbp37w4AeP3115Geno6ZM2eiR48eF7iSiIhaKkEQ8OjwDjBqlPjin7NS+xf/nEWJzYlHh3eAIAi13IE8mT16BPJvWQef36dBnbkPACBAhHHXB1Bn7oFp9DyI+gCZqyQ56VUGvNDvFcz850HYXXYAwMdHP0Qv/z7o4N1R5uqIiOTHEQrn2bRpE1auXInu3btj2rRpcpdDREQXSRAETB3aHv8Z7v7L/3d7UjBnw0k4XRyp0Ja5vCNRcONPMPee4tauSfoT/suuhipjrzyFUYvRxbcrHuxaMf3V5rLhtX0vwMqFPImIIIgeOubTZrPBbrfXub9er0dhYSHGjRuHgoICLF++HN26dZPO79ixA5MnTwYAnDhxosF15eQUwTM/40RELd+Kg+l4a/1JVP42fHX3ELx0dVeoFByp0NZp41fBe/PTEBylUpuoUKN42Euw9LoH4GiWNksURTy/+yn8m71darsh+ka3hRuJiFoiQQCCgryb7P4NHqGwa9cuFBcXN2YtjUqj0cBoNNb5j0KhwCuvvILs7GxMnz7dLUwgIiLPcFOfcLxybVcoK70uXHcsC8+uOQqbg3Pm2zpr7ATkT/oFDv/OUpvgssP7r9nwXj8TsJXIWB3JSRAEPN3neQRoK7akXZ20En9n/CljVURE8mvwCIWxY8ciJycHGzZsgL+//4UvaAW6du1ar/5z5szBTTfdVK9rOEKBiEh+W07m4Lm1x2B3VnxDHtLeD++O7wm9WiljZdQSCLZieG1+GrqE1W7tDv8uMF39BZwBXWSqjOS2N2c3ntr5KMTycU7eam98OWwJQvShMldGRFS9ph6h0OBAoU+fPoiJicHq1asv3LmVuP3222s8V1xcjPj4eABAXFwcAGDatGkYPnx4jddUh4ECEVHLsCMxH0/+fASWSiMT+kX6YO6NveCl9dg1i6muRBG6Qwvhte01CK6KKZSiyoCike/B2uUGGYsjOX15/FMsPf2NdNzbvy8+GDIPSgW/bxBRy9NiA4URI0ZAEARs2rSpTayQzTUUiIg8z/6UQvxn5WGU2JxSW/dQL/z3pt7wM6hlrIxaClXGHvj8Pg3K4nS39tLe96LkshcAJbeWbmscLgce/Xc6jhUckdru6XI/7ulyv4xVERFVr8WuoTB9+nSkp6fjzTffhMViacyaiIiImkW/dr749JY+8NVVvLN4LLMYDy07gJxiruBOgCNsAPJvWQdb1BVu7YZDC+G3ciIURWkyVUZyUSlUmN3vFRhVRqntm5MLcTBvv3xFERHJpMEjFH744Qf8/PPP2LdvH7RaLbp3747g4GDodLrqn0gQ8Pbbb19UsXLiCAUiIs91KqcEM5YfQm6JTWpr56fDJ5P6INyn+p9r1Ma4nDDsmgvD7o8gVNonxKULgOmq+bCfFziQ59uY9gfe2P+ydByiC8UXwxbDR+MjX1FEROdpsVMeunXrBkEQcKHLz/URBAHHjh1rUJEtAQMFIiLPlpxvxozlB5FuqhiZEOKlwSeT+qB9gEHGyqglUZ/dDJ/1j0BhLZDaRAgoHfw4Sgc+CggNHvxJrdA7B9/AupS10vGw0OF4Je7NNjEdmIhahxYbKMyaNave3yznzJnTkKfyKAwUiIhargyTBTOWH0JSvllqCzCoMX9ib3QJ9pKxMmpJFKYU+Pz+ENRZB9zabdEjYBozD6LOM3a/ogszO8yYtu1eJJckSW3/6fkUbmh/o4xVERFVaLGBAjUMAwUiopYtt8SGmcsPISGnRGrz0anw35t6oWc4hzJTOacVXltfhf7wYvdmr0iYrv4cjtB+8tRFze5k4QnM/OdB2Mt3A9EoNPj0sq/RwbuTzJUREbXgRRmJiIg8UaBRg89u6YOeYRU/fE0WBx7+8RD2JBfIVxi1LEotioe/UTYiQaWvaC5Ohd+Km6A7vAR8B6Ft6OLbFQ92fVg6trlseG3fi7A6ubArEXm+ix6h4HK5sHbtWmzYsAFnzpxBSUkJjEYjYmJicPnll2PChAlQq7n11jkcoUBE1DqU2Bx4YtUR7EkulNq0KgXevqEHLusQIGNl1NIoc0/AZ92DUBWccmu3xN6IohFvA2quweHpRFHE87ufwr/Z26W2cdE34rFeT8lYFRFRC5/ykJmZiYcffhhHjx6tdnFGQRDQvXt3zJs3D5GRkRdVqKdgoEBE1HpY7E48s+Yotp/Jl9pUCgFvXNcNI2ODZayMWhrBVgyvzU9Bl7DGrd0R0BWmq7+A05/D3z1dgTUfU7feg1xrjtT2ctybuCJshHxFEVGb12IDBavVikmTJiE+Ph46nQ6jR49Gr169YDQaYTKZcPjwYWzatAlWqxXdunXDsmXLoNFoGrv+VoeBAhFR62J3ujB77XFsOlnxIkEhAC+MjcX1PcNkrIxaHFGE/uDXMG5/HYLLITW71EYUX/kerF3GyVgcNYe9Obvx1M5HIZZvLeql8saXly9GqJ7fK4hIHi02UFi0aBHeeustdOjQAV9++SXatWtXpU9ycjKmTp2Ks2fP4sUXX8Ttt99+0QW3dgwUiIhaH4dLxOt/xGPtkUy39qdHdcakfhEyVUUtlSpjD3zWPQRlSYZbe2mf+1Ey9HlAyTdYPNlXJz7D96eWSMe9/fvigyHzoFSoZKyKiNqqFrso42+//QZBEDB37txqwwQAiIqKwocffghRFPHLL780uEgiIiI5qRQCXhwbWyU8eGdjAhbvTJapKmqpHGEDkH/r77C1u9yt3XDwa/itmgRFcZpMlVFzmNLlAXT36ykdH8o/gG8SFslXEBFRE2pwoHDq1CnExMSgW7dutfbr1q0bOnTogNOnTzf0qYiIiGSnEAQ8NbIT7hkc5dY+/+8z+HTrmWrXEqK2S9QHonDctygZ+KhbuzpjD/x/uBrq5L9lqoyamkqhwux+r8CoMkpt3yYswoG8fTJWRUTUNBocKFitVhiNxgt3BGAwGFBaWtrQpyIiImoRBEHAzMs74OFhMW7tC3Yk4/3Np+BiqECVKZQoHfIUCq9bDJfWt6LZkgff1XfAsPsjQHTJWCA1lXBDBB7v9Yx07IILb+5/BSabScaqiIgaX4MDhfDwcJw6dQolJSW19ispKcGpU6cQEhLS0KciIiJqUe4dEo0nrnRftf+HfWl44494OF0MFcidLWYU8m9ZB3tIX6lNgAjjjnfhs3YKBEt+LVdTa3VlxGhc0+566TjbkoX3Ds3haCYi8igNDhQuvfRSWCwWvPPOO7X2e/vtt2G1WnHppZc29KmIiIhanNviIvHCVbFQCBVtqw9n4oVfj8Ph5LvO5M7lE4WCm1bA3PNut3bt2U3wX3YNVFkHZKqMmtLMHo8hyhgtHW/N/BOrk1bKWBERUeNq8C4PiYmJuOGGG2C32zFs2DBMnjwZPXv2hLe3N4qKinDkyBEsXrwY27Ztg1qtxs8//4wOHTo0dv2tDnd5ICLyLH8cz8KLv51wG5kwrGMA3hrXA1pVg3N78mDaE8vhvWUWBIdFahMVGhRf/gosPe8qW5KbPEaCKR4ztk+F3WUHAKgVGnw69Gt09Ol0gSuJiC5ei902EgBWr16N5557Dk6ns9rzoihCpVLhjTfewPjx4xtcpCdhoEBE5Hn+PpWLWWuOwuas+AY/MNoP74/vCYNGKWNl1FIpc4/DZ92DUBW4L1ptib0JRSPeAtQGmSqjprAicRnmH/1QOo7x6oBPLvsaOqVOvqKIqE1osdtGAsANN9yA7777DkOHDoVKpYIoitIfpVKJyy67DN9++y3DBCIi8miXdwrEhzf1gl5d8WN1d1IBZi4/CJPFLmNl1FI5A7uhYNJaWDtd59aui18B/+XjoMw/JVNl1BRubD8JlwQPlY4Ti8/g02PzZKyIiKhxNHiEgslkgo+Pj3RsNpuRnJyM4uJiGI1GREdHQ6/XN1qhnoIjFIiIPNfBNBMeXXEIxdaKkXuxwUbMn9gb/gaNjJVRiyWK0B/8Gsbtr0NwOaRml9oLRSPfg63z9bVcTK1JgTUfU7feg1xrjtT2cv83cEX4lTJWRUSersVOebjpppug0+nwySefwM/Pr5HL8lwMFIiIPNuJrGI8svwQ8s0VIxNiAvT4eGIfhHhrZayMWjJV+i74/D4NypJMt/bSvlNRculzgFItU2XUmPbm7MZTOx+FiLJfBr1U3vjy8sUI1YfJXBkReaoWO+XhzJkzyMzMZJhARERUSdcQL3xxa1+EeFWMSEjMM2PqDweQUmCWsTJqyRzhg5B/y++wRV7m1m448CX8Vk2CojhdpsqoMcUFDcQdnSp2+ih2FOHN/a/AWWl0ChFRa9LgQEGtVsNg4IJBRERE54sJNOCL2/oiwrdiwbW0Qgse/OEAzuSWylgZtWSiIQiFN3yPkgH/59auztgN/2VXQ528VabKqDHd0+UB9PDrKR0fyj+AbxIWyVcQEdFFaHCgcMMNNyAhIQHr1q1rzHqIiIg8QqSvHl/e2hcxARXrCWUX2/DgDwdwMrtYxsqoRVMoUXrJ0yi8bhFcWt+KZnMufNfcAcPueYDokrFAulgqhQrP93sFRpVRavs2YREO5O6TsSoiooZp8BoKJ06cwCuvvIJ9+/Zh4MCBiIuLQ0hICLTamueHTpw4scGFegquoUBE1Lbkl9owc/khxGeXSG0xAXosvWcgVApBxsqopVOYkuCz7iGosw+5tVvbj0LR6I8g6vzkKYwaxea0DXht/4vScbAuBF8MWwxfjW8tVxER1U+LXZSxe/fuAABRFCEIdfuF6NixYw15Ko/CQIGIqO0psjjw6IrDOJRuktpeuCoWN/TmQmx0AQ4LvP5+Cfqj37k1O72jYLr6czhC+shUGDWGdw++id9SfpGOLwu9Aq/Gzanz79ZERBfSYgOFkSNH1vuaTZs2NeSpPAoDBSKitqnAbMeEr3aixFa2pWSotxY/3TcIWlWDZx9SG6I9vhzef86C4LBIbaJCg+IrXoWlx51lvzFSq2N2mDFt271ILkmS2h7t+STGt79JxqqIyJO02ECBGoaBAhFR2/XVP2fx+faz0vFjIzrijgHtZKyIWhNlzlH4rHsIqsIzbu2WrhNRNHwOoNbXcCW1ZAmmeMzYPhV2V9lWs2qFBp8O/RodfTrJXBkReYIWu23kO++8gx9//BE2m60x6yEiIvJYtw+IhL9eLR0v3JGMEhu3i6O6cQb1QMGktbB2vMatXXdiOfx/GgdlwWmZKqOL0dknFg91myEd2102vLb/RVicllquIiJqGRocKKxatQpvv/02nE5nY9ZDRETksYwaFaYMiZKOC8x2fL8nVcaKqLURtT4wXf0Fii97EaKglNpVucfht+xaaE79KmN11FA3tp+ES0Iuk47PFp/Bp0f/K2NFRER10+BAobi4GNHR0dDrObyOiIiorm7uG4FQ74odkb7bnYICs13GiqjVEQSY+z2Iggk/wmkIlZoV9mL4rnsQxq2vAk7+n2pNBEHAM32eR6A2SGpbk7wKf6VvlrEqIqILa3Cg0LNnT5w5cwY5OTmNWQ8REZFH06oUePDS9tJxic2JxTuTZayIWitHxGDk37oOtsihbu2GA1/A7+dboSjJkKkyaghfjR+e7fsiBFQssPneobeQaea/IxG1XA0OFF5//XV4eXnhzjvvxMqVK3H27FmUlpbC5XLV+IeIiIiAa3uGIiagYoTfj/vTkFVklbEiaq1EQzAKb/gepXEz3drV6Tvh/8PVUGXskakyaoi4oIG4o9Pd0nGxowhv7H8ZThfXWiGilqnBuzzcdtttyMvLQ1JSUp32yhUEAUePHm3IU3kU7vJAREQAsDE+G7PWHJOOb+wThufGxMpYEbV2mjPr4b3hUShsJqnNpfNH/qS1cPlEy1gZ1YfD5cB//p2OowVHpLbJne/DlNgHZKyKiFqrFrvLw/79+5GUVLZnriiKdfpDREREZUZ2CUL3UC/pePWhDCTlm2WsiFo7W4cxyL/lN9iDekltCks+fH99ALDz/1ZroVKoMLvfqzCqjFLbtwmLcCB3n4xVERFVr8EjFHbu3FnvawYPHtyQp/IoHKFARETn/JuYh0d+OiwdX9U1GG9c313GisgjOMzwW3Ur1Jl7pSZLl/EoGjO/7K0qahU2p23Aa/tflI6DdSH4Ythi+Gp8ZayKiFqbph6h0OBAgRqGgQIREZ0jiiKmLTuIvSmFUtu3d8eha4hXLVcRXZiiJAN+y66DsjRTaiu+9HmY46bLWBXV13sH5+DXlDXS8WWhl+PVuLfqNN2YiAhowVMeiIiI6OIIgoAZl3dwa/t0a6I8xZBHcRnDYLrmC4gKtdRm/HcO1Elb5CuK6m1Gj/8gylix/sW2zL+xOmmFjBUREbmrU6CwceNG7NnT8FWCX3/9ddxzzz0Nvp6IiMhT9YnwweUdA6TjbWfysL/SiAWihnKEDUDx8DekY0F0weePGVAUnJGxKqoPvUqPF/q/CnWlYOiTY/Nw2nRKxqqIiCrUKVCYMWMG5s6dW+P5Z599Fl988UWN548ePdqgNReIiIjagoeHdUDlAcyfbD3DxYypUVh63AFzr8nSscJaCN/fHgBsJTJWRfXR2ScWD3Wr2BbU7rLhtf0vwuK0yFgVEVGZOk95qO0Xm5UrV+LPP/9slIKIiIjams7BRoztHiId70s1YXtivowVkScpHvYy7OEVC2Or8k7AZ+N/wEWdWo8b20/EJSGXScdni8/gk6MfyVgREVEZrqFQA5vNhgULFmDixIkYMGAA+vTpg+uvvx6ffPIJLBYmwkRE1LgeGtoeSkXFOIVP/j4DF1/wUWNQalB49edwGsOkJu3p32DYM0/Goqg+BEHAM32eR6A2SGr7Jfln/Jm+ScaqiIgYKFQrJycHEydOxNtvv42jR48iPDwcQUFBOHnyJD766CPccccdKCoqkrtMIiLyIO389JjQu+IFX3x2CTacyJaxIvIkoiEYpmu+gqjUSm2GHe9Ck7hRxqqoPnw1fniu30sQKk2Qev/Q28gwp8tYFRG1dQwUziOKIv7zn//gxIkT6Ny5M9auXYtffvkFmzZtwrfffovAwEAcOXIEH3zwgdylEhGRh3ngkmhoVRU/mj/ffhYOp0vGisiTOEL7oWjE29KxABHe62dCmc8F/lqL/oEDcEenijUxih1FeHP/K3C6HDJWRURtGQOF86xbtw67du2Cl5cXFi1ahA4dKrbzGjRoEJ544gkAwKpVq2C32+Uqk4iIPFCQlxa39o+QjpPyzVhzJFPGisjTWLtNRGmf+6Vjha0IPr/dD8HGkZetxT1d7kcPv17S8eH8g1iSsFDGioioLWOgcJ6VK1cCAO677z4EBwdXOT927Fg88sgjePLJJ2Gz2Zq7PCIi8nCTB0XBS6uUjr/65ywsdqeMFZGnKRk6G7bIodKxKj8B3usfBUSOhmkNVAoVZvd7BUaVUWr7NmER9ufulbEqImqrGChU4nQ68e+//wIArrrqqmr7eHl5YebMmbjzzjthNBqr7UNERNRQvno17h4YJR1nFdvw0wHOkaZGpFTDNPZTOL0ipSZt4h8w7Kp5i3BqWcIM4Xii9yzpWISINw+8gkJboYxVEVFbxEChksTERFitViiVSnTs2BF5eXn4+uuvMWPGDNx77714+eWXsX//frnLJCIiD3dbXCQCDGrpeOGOJBRbOUeaGo+oD4Tp2q8hqnRSm3HXXGhOr5OxKqqPEeGjcG3UOOk4x5KN9w69WetW70REjY2BQiVpaWkAAB8fH/z777+45ppr8M4772DDhg3Yvn07li5diltvvRVz5szhN2siImoyBo0S9w2Jlo4LLQ58vydFxorIEzmCe6Hoynfd2rw3PAplXrxMFVF9zej+H0Qb20vH2zL/xs9nV8hYERG1NYJYh1fG3bp1g7e3N7p3717t+Z07d9Z6/ujRoygpKcGxY8curtp6mDVrlrQeQl2sWrUKZ8+exaOPPgqdTgeFQoGoqCg8++yziIuLQ2FhIZYtW4aPP/4YLpcLTzzxBB588MF615WTUwRmEUREdCE2hwsTF+5CuskKADColVj1wCD4GzQyV0aexrjtNRj2fy4dO3xjUDBpLUStr4xVUV2dMp3Ew9sfgN1Vtli4WqHBJ0O/QiefzjJXRkQtgSAAQUHeTXZ/VV07FhUVYefOnQ0+LwhCjedaCovFIv0dGRmJb7/9Fj4+PgCAkJAQzJw5Ey6XCx9//DE+/fRT3HrrrfD15Q9bIiJqfBqVAg8ObY9X1pW9W1xqd2LRzmQ8NqKTzJWRpym59Fmoco9Bk/wXAEBVmAjvP2bCdN0iQKGs/WKSXSefLnio20zMP1q2BobdZcPr+1/Ep5ctgE6pu8DVREQXp04jFJ599tlGebI5c+Y0yn3qwmaz1WtbR71ej/Xr1+P//u//AJR9zFOmTKnSz2KxYNCgQbDZbPjoo49w9dVX16sujlAgIqK6crpE3L54D87klQIANEoBP903CGE+fJFAjUuw5MP/x+uhNJ2V2krjZqLk0lm1XEUthSiKmL3nGfyTtVVquz5qPB7v/YyMVRFRS9AiRig0ZxDQWDQaDTSa+g0LPTcaAUCN0zd0Oh2io6ORkJCA5OTki6qRiIioNkqFgGnDYvDM6qMAAJtTxFf/JGH22FiZKyNPI+r8UXjtV/BffgMEhxkAYNg7H/bgXrB1vl7m6uhCBEHA032ewwN/T0auNQcA8Evyz4gLGoQR4SNlro6IPBkXZaykY8eO0mObzVZjP6WybPhffQMLIiKi+rqycyB6hFW8s7DmSAYSy0csEDUmZ2B3mEa5bx3ps/ExKHOOylQR1Yevxg/P9XsJAiqmGb9/6C1kmLntLBE1HQYKlYSGhiI8PBwAcODAgWr7OJ1OJCUlAQCio6Or7UNERNRYBEHAw8NipGOXCHy+LVG2esiz2Tpfj5IBj0jHgsMM398egGDJl7Eqqqv+gQNwR6fJ0nGJoxhv7H8ZThe3nSWipsFA4TzjxpXt57ts2TIUFxdXOf/DDz/AbDbD29sbQ4cObe7yiIioDRrS3h8Do/2k4w3xOTieWSRfQeTRSgc/CWv0ldKx0pQEnz9mAHxR2irc0+V+9PDrJR0fyT+EJQkLZayIiDwZA4Xz3H///QgKCkJmZiamTZuG9PSKYWJbt27FBx98AAB48MEHodVq5SqTiIjamBmVRikAwCdbE2Wpg9oAhRJFV82Hw7eD1KRJ/gvGf1rfmlptkUqhwux+r8Co8pLavk1YhP25e2Wsiog8VZ12eWhrDh8+jKlTpyIvLw8qlQqdOnWCxWLB2bNlKx9ff/31ePfdd6FQ1D+P4S4PRETUUE/9fARbEnKl489v7YO4dn7yFUQeTZkXD7/l46Cwl0htpjHzYI29UcaqqK62pG/Cq/tmS8eB2iB8dfkS+Gr85CuKiJpdU+/ywBEK1ejVqxd+/fVXPPjgg4iOjkZiYiIKCwsxePBgvP/++3j//fcbFCYQERFdjGmXxVRabg34+O9E8H0BairOgFgUjf7Irc1705NQZR+SqSKqjxHhI3Ft1DjpONeag3cPvsnvGUTUqDhCoZlxhAIREV2Ml387jrVHs6TjDyb0xOWdAmWsiDydYef7MO6q2P3B6RWJ/Ft+hajn/7uWzuwwY/q2+5BUclZq+78eT2BCzM0yVkVEzYkjFIiIiEgydWh7qBQV4xQ+3ZYIF5NqakKlgx6DNeYq6VhZnAqf36cDTruMVVFd6FV6vND/VagVFVudf3p8Hk6ZTspYFRF5kosKFJxOJ/Ly8pCamor09HTk5eVxGBUREVETivTV48Y+4dLxyewS/HE8W8aKyOMJChSN+QgO/85SkyZ1O4zbX5exKKqrTj5dMK3bTOnY7rLhtX0vwuwwy1gVEXmKek95+Oeff7B27Vrs3LkTqampcLlcbucVCgWioqLQv39/3HTTTRg0aFCjFtzaccoDERFdrJwSG278aicsjrKfwe38dPhxykColBx4SE1HWXAafj9eB4WtYstS06i5sHabJGNVVBeiKGL2nmfwT9ZWqe26qBvwRO9ZMlZFRM2hqac81DlQyMzMxBNPPIE9e/YAQJ1GIgiCgIEDB2Lu3LkICgq6uEo9BAMFIiJqDB//fQaLdiZLx8+O7oyb+kbIWBG1BZrEjfBZOwUCyn6ZEZVaFNz4Exyh/eQtjC6o0FaAB/6ejFxrjtT2Yv/XMSJ8pIxVEVFTaxGBQlFREcaPH4+0tDR4eXnhmmuuQVxcHCIjI+Hn5wedTgdRFGG1WpGfn4/U1FTs27cPv/32G4qLi9GuXTssW7YMAQEBTfaBtBYMFIiIqDGYLHZM+GoXiqwOAECwlwYr7hsEnVopc2Xk6Qy758G4423p2GkMQ/4tv0E0BMtYFdXFvtw9eHLH/0EsD4SMKi98OWwxwgzhF7iSiFqrFhEovPfee/jqq68waNAgzJs3D35+fnW6eWFhIR5++GHs3bsXd911F55//vmLrbfVY6BARESNZdGOJHy8NVE6/r8rOuDuQVHyFURtgyjC5/eHoD31q9RkDx+MgvH/A5SaWi6klmBB/Bf4NmGRdNzDrxc+uuQTKBUq+YoioibTInZ5WL9+PbRaLT766KM6hwkA4Ovri//+97/QaDTYtGlTQ2skIiKiatwWF4lAY8ULuMU7k1FcPmKBqMkIAkwj58IR0FVqUqfvhNfWl+Wriersns73oYdfL+n4aMFhLE5YIGNFRNSa1SlQSE9PR+fOnRs0ZSEwMBCdO3dGZmZmva8lIiKimunUStx/SbR0XGhx4JvdKTJWRG2GxojCa7+GS+srNekPL4Hu6PcyFkV1oVSoMLvfKzCqvKS27xIWY3/uXhmrIqLWqk6Bgl6vR25uboOeQBRFZGZmwtu76YZZEBERtVUTeochwlcnHS/dk4LcEpuMFVFb4fKNgemqjyEKFb9Oev05G6qMPTJWRXURZgh32+FBhIg39r+MQluBfEURUatUp0Chf//+yMzMxPff1z91/uqrr5CTk4N+/frV+1oiIiKqnVqpwEND20vHZrsLC3ckyVgRtSX26BEoueRZ6Vhw2eDz24NQlGTIWBXVxYjwkbgu6gbpONeag3cOvlmnndyIiM6pU6AwdepUCIKA1157DU8++ST++ecf2Gw1v/vhcDiwd+9ePPPMM/jggw+gUCjwwAMPNFrRREREVGFstxB0DDRIxysOpiPdZJGxImpLzP2nwdJlvHSsLM2Ez28PAk6rjFVRXczo8R+094qRjv/J2opVZ3+SryAianXqtMsDAPz666945pln4HCULfYkCAKCg4MREBAArVYLALDZbCgoKEBWVhacTidEUYRKpcLs2bNx2223Nd1H0YpwlwciImoKfybk4Mmfj0rH43qG4sWru9ZyBVEjspvht2IC1DlHpCZz99tQfOW7ZUuMU4t1ynQSD2+fCrur7M1CtUKDT4Z+iU4+XWSujIgaQ4vYNvKcM2fO4PPPP8dvv/0Gq7X21NlgMGDUqFGYNm0aOnXqdNGFegoGCkRE1BREUcT9S/fjUHoRAEAhAP+7ZyA6VBq5QNSUFKZk+P94LRSWfKmtaPibsPSaLGNVVBcrE5dj3tEPpONoY3t8etkC6FV6GasiosbQogKFc2w2G44ePYqzZ88iLy8PZrMZSqUSBoMB/v7+6NSpEzp16gSNhnsRn4+BAhERNZXdSQWY/uNB6XhklyC8fUMPGSuitkadsg2+q++AIDoBAKJChcLxP8AeMUTmyqg2oijihT3PYHvWVqnt2qhxeLL3s7VcRUStQYsMFKjhGCgQEVFTmrn8IHacLZCOF9/ZHz3CuNMSNR/9ga/gtfVl6dilD0L+pF/h8o6Qryi6oEJbIaZunYwcS7bU9mL/1zAifJSMVRHRxWrqQKFOizISERFR6/DwsA5ux59sPSNTJdRWmfvcD0vXm6VjhTkHPuumAg6zjFXRhfhqfPFc35cgoGLNi/cPvY2M0nQZqyKilo6BAhERkQfpEeaNkV2CpOMdZwuwO6lAvoKo7REEFI14C/bgPlKTOusAvP98Dhym2bL1C4zDnZ3vkY5LHMV4ff9LcLocMlZFRC0ZAwUiIiIPM+2yGCgqLaz/8dYz3FuempdKD9M1X8GlD5SadMd/hP7gAhmLorq4p/N96OnfWzo+WnAYi05+LWNFRNSS1SlQcLlcjfKHiIiIml6HQAOu7REqHR9OL8Jfp3JlrIjaIpd3BExXfw5RoZLajNtehTplm4xV0YUoFSo83+9lGFVeUtv3p5ZgX+4eGasiopaqTosyduvWDcJF7iEsCAKOHj164Y4ejosyEhFRc0g3WXDzgl2wO8t+6HQMNOD7yQOgVFzcz3Oi+tIdWgzvv56Xjl06/7JFGn2iZKyKLmRL+ia8um+2dByoDcJXly+Br8ZPvqKIqN5axKKM/fr1gyiKF/2HiIiImke4jw439QmXjk/nluL341kyVkRtlaXXZJi73yYdKyz58PntAcDORRpbshHhI3Fd1A3Sca41B+8cfJO/0xORmzpvG/nee+/hq6++giAIePLJJ9G7d+8LX3SewYMH1/saT8MRCkRE1FzySm2Y8NVOmO1l0w4jfHVYfu9AqJVcQomamdMKv5WToM7cKzVZuoxH0Zj5ZW+fUYtkcVowfdt9OFucKLXN7PEYboqZJF9RRFQvTT1Coc6BAgC8/fbbWLhwISIiIrBmzRoYjcYmK8xTMVAgIqLm9Om2RCz4N0k6fnpUZ0zqFyFjRdRWKUoy4LfsWihLK0bKFA+dDXP/aTJWRRdyypSAh7c/ALvLBgBQK9T4ZOhX6OTTRebKiKguWsSUh3OeeuopDBo0COnp6fjoo4+aqiYiIiJqJHcPbAdfXcWieF//mwSz3SljRdRWuYxhMF39BUSFWmoz/vMm1El/ylgVXUgnn86Y3u0R6djusuO1fS/C7OCUFSKqZ6CgUCjw2muvQalUYunSpUhNTW2quoiIiKgReGlVuGdwxeJ3uSU2/LCXP79JHo7wgSi+4nXpWBBd8PnjYSgKE+Urii5ofPubMDRkmHScVHIWHx/7UL6CiKjFqPckypiYGDz77LO4/vrrcfLkyaaoiYiIiBrRpH4RCDJqpOMlu1JgsthlrIjaMkvPO2Huebd0rLAWwve3BwBbiYxVUW0EQcBTfZ5HkC5Yavs1eQ02p22QsSoiagnqtYYCXTyuoUBERHL46UAa3tqQIB1PGRyFGZd3kLEiatOcNvj9fCvU6bukJmun62Aa+xkXaWzBDuTuw+M7ZkJE2S+zRpURXwxbjHAD12Uhaqla1BoKRERE1DqN7xWGdn466fh/e1ORU2KTsSJq05QaFI79HE5jmNSkPbUW+r0fy1gUXUjfwP64q/MU6bjEUYI39r8Eh8shX1FEJCsGCkRERG2ASqnAQ0NjpGOLw4WFlXZ/IGpuojEEpmu+gqjUSm3Gf9+GJnGjjFXRhUzufC96+ldsH3+04AgWn/xaxoqISE4MFIiIiNqIq7oFo0twxZbPKw6mI7WQK7WTfByh/VA0fI50LECE9/pHoCw4LWNVVBulQoXn+70ML1XFEOrvTy3B3pzdMlZFRHJp8BoK3bt3r3NfpVIJnU6HoKAg9OzZE7fffjsGDhzYkKdt9biGAhERyenvU7l4fNUR6fi6HiF4+ZpuMlZEBBj/fhGGgwukY4d/FxRMXA1R03Tzfuni/Jm+Ca/smy0dx3h1wNeXfwuBa2AQtSgtdg0FURTr/MfhcKC4uBiJiYlYu3YtJk+ejEWLFjXih0FERER1MaxjAPpE+EjHvx7Nwqkcrq5P8ioZ+gJskZdKx6r8k/De8B9AdMlXFNVqePhIXNtunHScWHwG8YXHZayIiOTQ4EDh2LFjuOqqqwAAw4cPx9dff40dO3bgyJEj2LlzJ5YsWYJrr70WANCvXz98//33+Pzzz3H77bdDEAS8++67OHjwYON8FERERFQngiBgxuUx0rEI4LNtiXKVQ1RGqYZp7GdwekVKTdozv8Ow60P5aqILur3T3W7H69PWyVQJEcmlwYHC999/j/Xr1+Ouu+7C559/jssuuwy+vr5QKpXw8fHB4MGD8cEHH2DGjBk4cOAATp8+jeHDh+Oll17Ciy++CKfTiaVLlzbmx0JERER1ENfOD5fG+EvH/8/efUdHVX1tHP9OJr0TUgghBQKE3nvvRVFpFlSKioIdFZEitldBpFhQUZqCIiBdkN47oXcILT1Aeq8z8/6RX24S00PCTcL+rJW1cubeO/NkEkJmzz7n7L8ZyaWwOBUTCQEGi+rEPfafRRpPzsP0zk4VU4nCuFnVyrVA497QXbLjgxCPmFIXFNasWYO1tTWTJk0q9LzXX38dW1vbXMWD4cOHY2dnx6lTsniLEEIIoYY3unjlGv902F+VHELklOHUlPies3PdZrPrHbRRN1RKJIrSz22g8nlMWgwnw0+omEYI8bCVuqDg7++Pl5cXpqamhZ5nbGyMp6cnN2/eVG7TarW4ubkRHh5e2ocvd2fOnOGtt96iY8eONGnShC5dujBhwgQuXbqkdjQhhBDigTVwsaFPfUdlfCowhhMB0SomEiJTqs9QklqMU8ZG6QnYbn0ZTWqsiqlEQXq49sLEyEQZy7QHIR4tpS4oWFtbExYWVqxzQ0NDMTc3z3VbamoqFhYWpX34crVmzRpefPFFdu3aRXp6OnXr1iU5OZlt27bx7LPPsnHjRrUjCiGEEA9sXGcvtDkWZP/5sD+l3PxJiDKV2HEKabW6KmPj2DvY7Hob9DoVU4n82JjY0sGpszI+cu8QCenxKiYSQjxMpS4oNGrUiMjISFasWFHoeWvWrCEiIoLGjRsrt4WHhxMQEEDNmjVL+/DlJjAwkM8//xydTsfIkSM5evQoGzdu5MiRIzz99NNkZGTw8ccfExQUpHZUIYQQ4oF4OVgyqHENZXzlbjz7b0aqmEiI/zEyJq7/z+hsPZSbzAL2Yuk7V8VQoiD9ag1QPk/Xp3Hg7j4V0wghHqZSFxTGjBmDwWBgxowZzJkzh+Dg4FzHg4KC+Pbbb/n888/RaDS8+OKLQObuEB988AE6nY6+ffs+WPpysGXLFtLT06lTpw5Tp05VpnSYm5vz2Wef4e7uTnp6Ops2bVI5qRBCCPHgxnb0wDRHm8KCI/7o9NKlINRnMK9G7MDFGIyzO1qtTv+A6c0tKqYS+Wnn1BFbEztlvDN4m4pphBAPU6kLCp06deKdd95Bp9OxZMkS+vbtS+vWrenatSstW7akX79+LFy4kIyMDF555RV69eoFwOeff46vry8ODg6MGDGizL6QsnL37l0A6tWrh5FR7qfH2NiYRo0aARR7uocQQghRkdWwNWd4i+yOwTuRSWy7ek/FREJk0zk2Iq73t7lus93zPtrIqyolEvkxMTKhZ80+yvhi9HnCkkJVTCSEeFhKXVAAeOONN1iyZAlNmjQBIDExkfDwcJKTkzEYDPj4+PDTTz8xceJE5ZqEhAT69u3LihUrsLOzK+iuVePq6grA9evX0ev1uY7p9Xpu3MhcZdjNzS3PtUIIIURlNKadO5YmWmW88GgAaRn6Qq4Q4uFJqzuIpFZvKWNNRhJ2W8eiSZFFRCuSfm4Dco13h+xQKYkQ4mHSGMpo9aV79+5x8+ZNoqOjsbCwoH79+ri7u5fFXT9Ud+/eZeDAgSQlJTFq1Cg+/PBDTE1NSUtLY86cOSxbtgwbGxv+/fdfXFxcSnz/ERHxyHpXQgghKpqFR/1ZdCxQGU/s6c2zraR4LioIvQ7bf8dgFpg9Nz/NvTuxg5aDkbaQC8XDYjAYGH1wBMGJmb9Halm6s6z7KjQaTRFXCiHKk0YDjo425Xf/ZVVQqErOnDnDlClT8Pf3x8bGBnd3d4KDg4mLi6Nx48Z8+eWXytSHkpKCghBCiIooITWDwYt9iU3JAMDB0oQNr7TD0lRerImKQZMai/2axzGO9VduS2r5OomdpqkXSuTyx83f+M1vkTL+qdMiGto3LuQKIUR5K++CgvGD3kFCQgJ//vknu3fv5s6dOyQlJWFpaYmnpyfdu3dn9OjR2Nvbl0HUkpk8eTIbNmwo9vkbN26kYcOGQOaWmE2aNMHf35/4+HiuXLminOfk5FTmWYUQQgi1WZsZM6a9B98fuA1AVFI6q86E8HIHjyKuFOLhMJjZETdwCfbrnsQoPREAy7MLyHBqQmq9p1ROJwD61hyQq6CwM3ibFBSEqOIeaA0FPz8/nnzySb7//nsuXbpEYmIiBoOBxMRErly5wi+//MKQIUO4du1aWeUtd8eOHePZZ59ly5YtjBw5kt27d3Px4kW2bdvGsGHD2L9/P88//zwnTpxQO6oQQghRpoY3d8XZ2lQZ/3EqiNjkdBUTCZGbrroP8X2+y3Wbzd4P0IZfVieQyKWGpSvNHFoo431hu0nXy+8QIaqyUk95iI+P58knnyQsLAxHR0eGDRtGkyZNsLa2JjY2lkuXLrFx40YiIiJwc3Nj06ZNWFtbl3X+AqWlpZGeXvxfYBYWFuh0OgYMGEBwcDDPP/88n376aZ7zvvzyS/744w88PDzYtm0bxsYla/KQKQ9CCCEqsg0Xwpix64YyHtXWnbe71VYxkRB5WZ6Yg9Wp75SxzqYW0U9vxWDhoF4oAcC/Qf8w9+LXyviLVjPpUqO7iomEeLSV95SHUncoLFu2jLCwMFq2bMnWrVt577336Nu3Lx07dmTAgAFMnDiRrVu30qJFC0JDQ1m1alVZ5i6SqakpVlZWxf4wMjLi8uXLBAcHA/Dmm2/me79vvvkmWq2WwMBALly48DC/JCGEEKLcPdGkBh7VLJTx6rMhRCSkqphIiLyS2r1PqldfZayND8Z2x3jQZ6iYSgB0r9ELE6PsTqddstuDEFVaqQsKu3fvRqvVMnv2bGxtbfM9x9bWltmzZ6PRaNi+fXupQz4soaGZ++Xa2dnh6OiY7znVqlXDwSGz+p1VfBBCCCGqCmMjDeM6eSrj1Aw9i48HFnKFECrQGBHf9wcyqtVVbjINOYrV0S9VDCUArE2s6ezSVRkfu3+YuLQ4FRMJIcpTqQsKAQEB1KlTh1q1ahV6nru7O97e3gQGVvw/RqysrABITEwkKSkp33PS09OJj48HeKhTOIQQQoiHpY+PE/WdrJTxxot3CY5JVjGREHkZTG2IG7gEvWl2K6/l+cWYXVurYioB0M9tgPJ5hiGD/WF7VEwjhChPpS4oGAwGTExMinWusbFxidYzUEurVq0wNTUlIyODdevW5XvOv//+S0pKCiYmJrRu3fohJxRCCCHKn5FGwxtds9dN0OkN/Ho0QMVEQuRPV82b+L4/YkCj3Gaz/yOM759XMZVo49gee1N7ZbwrtOJ3KgshSqfUBQU3Nzdu3LhBVFRUoedFRUVx48YNXF1dS/tQD42NjQ0vvfQSAHPmzGHdunXodDrl+Pbt2/n8888BeOmll7Czs1MlpxBCCFHeOnlVo4Vb9pTGHVfvczM8UcVEQuQvzas3Se0/VMYaXSq228aiSQpXMdWjzdjImF41+ynjy9EXCUmUqcJCVEWlLih069aN9PR0PvnkEzIy8l8AJyMjg48//hidTkf37pVjddd3332XQYMGkZKSwtSpU+ncuTPDhw+na9euvPvuuyQlJTFo0CAmTJigdlQhhBCi3Gg0Gt7skt2lYAB+PnxHvUBCFCKp9duk1hmojLUJYdhuHw+6it8hW1XlnPYAsCtEuhSEqIpKvW3kvXv3GDRoEAkJCdSvX58RI0bQuHFjbGxsiI+P5/Lly/z111/cuHEDa2trtmzZgouLS1nnLze7du3i77//5uLFi8THx2NjY0PTpk155pln6Nu3b9F3UADZNlIIIURlMmH9JY7cye5GXPxcc5q7SYeeqHg0aQnYr3sK46jrym3JTUeT0O0rFVM9ugwGAy8feoGABH8AXC1r8mf3NWg0msIvFEKUqfLeNrLUBQWAY8eO8eabb5KUlJTvLweDwYCVlRU//PADnTt3fqCgVYUUFIQQQlQm1+8n8OIfZ5Rxq1p2/PJMM3lRICoko5g7VFs7CKPUWOW2+J6zSWk0QsVUj66/bi1n8fVflPEPHX6hiUMzFRMJ8egp74JCqac8AHTs2JEtW7bwzDPP4OzsjMFgUD6cnJx45pln2LhxoxQThBBCiErKx9mafj5OyvhMcCwnAqJVTCREwfT2tYnr9xMGTfafuNYHpmF897SKqR5dfWr2R5NjwcydIdtUTCOEKA8P1KHwX4mJiSQkJGBlZSVbKhZAOhSEEEJUNoHRyTzz20l0//v/q6GLNcteaCldCqLCsjjzM9bHZihjnaULMc9sRW9VeabfVhUfnHibs5GZBR1rYxvW9v4HU62ZyqmEeHRU6A6F/7KyssLFxSVPMSEhIYGEhISyfCghhBBCPCQe1Sx4smkNZXz1XgJ7b0SomEiIwiW3fJ2Uuk8qY23SPWy3vwa6VBVTPZr65licMSEjnuP3j6qYRghR1sq0oJCf6Oho2rRpQ7t27cr7oYQQQghRTsZ28MRUm92RsOCwPxl6abkTFZRGQ3yvOWRUb6TcZHL3NNYHp6sY6tHUrUYPzIyyOxJk2oMQVUu5FxSylOHMCiGEEEI8ZM42Zjzdwk0ZB0Qns/XyPRUTCVEEE0tiH1uC3ryacpPFlb8wv/SniqEePZbGVnSpkb19/InwY8SmxagXSAhRph5aQUEIIYQQlduYdu5YmWqV8cJjAaRm6FVMJETh9LbuxPVbgEGT/XNrfWg6xqG+KqZ69OSc9qAz6NgbulvFNEKIsiQFBSGEEEIUi72lCS+0qaWM78Wnsu58qIqJhChaunsXEjtnT3XQ6NOx2z4OowT52X1YWldvg4NZdWW8K2S7immEEGVJCgpCCCGEKLbnW7tRzcJEGf9+IojEtAwVEwlRtORmr5BSf6gyNkoOx3bbq5CRomKqR4fWyJjeNfsq42uxVwhMCFAxkRCirEhBQQghhBDFZmVqzJj27so4OjmdladDVEwkRDFoNMT3nEW6U1PlJpP757E5MAXZz/vh6Oc2MNdYuhSEqBqkoCCEEEKIEhnWvCYuNtmrtv95KpiY5HQVEwlRDMYWxA1cjN4iu/Xe/NoazC/+pmKoR4e3bT3q2Hgr492hO9AbZA0WISo7KSgIIYQQokTMjI14raOnMk5M07HMN0jFREIUj97GjbgBv2IwMlZusz78OSYhR1VM9ejom6NL4V7yXS5GnVcxjRCiLBgXfQqcPHmy1A8QHx9f6muFEEIIUTE91tiFP04F4R+VDMCac6GMaOWGc47OBSEqovSaHUjo8hk2Bz8GQGPQYbt9PNFPb0VvW6uIq8WD6F2zL4uu/YyezM6EXSHbaV69pcqphBAPQmMwFD1xrEGDBmg0mlI/iMFgQKPRcPXq1VLfR1UREREvU/WEEEJUCXv8wpm8Ofv/9iHNajC1b30VEwlRTAYD1vsmYnF1tXJTumMTYoZuABMLFYNVfR/6vsvpiMw3K62MrVjbewtmWilEClFeNBpwdLQpt/sv9pQHg8FQ6g8hhBBCVD096znSwNlaGf9z8S6B0ckqJhKimDQaErp9RbpL9rvjJhGXsNk/SRZpLGc5F2dMzEjk6L1DKqYRQjyoYnUohISUzerNbm5uZXI/lZl0KAghhKhKjvlH8c66S8q4n48TXw1qqGIiIYrPKCEM+zWPo026r9yW0PkTklu8pmKqqi05I5lhewaRosssPrZ36sjMtnNVTiVE1VXeHQrFKiiIsiMFBSGEEFWJwWBg/N8XOBMcq9y2YmQr6ufoXBCiIjMOO4X9xqfR6DN3KjFojIgZvoUM52YqJ6u6vj7/f+wM2QaAkUbL37024WDmoHIqIaqmCjPlQQghhBDivzQaDW92rZ3rtgVH/NUJI0QpZLi2IaHb/yljjUGPpa+8Y16e+roNUD7XG3TsC92lYhohxIOQgoIQQgghHkizmrZ0rZP97uLh21GcD4kt5AohKpaUxi+SWru/MjYL2IPxfdnSsLy0qN4KR3MnZbwzZLuKaYQQD0IKCkIIIYR4YG90qU3O/aB+OnRHFmYWlUpi2/dzjS1PfqtSkqpPq9HSp2Y/ZXwj7jp34m+rmEgIUVpSUBBCCCHEA6vrZEX/hs7K+GxIHEf9o1VMJETJ6Jwa5+5S8N+N8f0LKiaq2nJOewDYJV0KQlRKUlAQQgghRJkY18kTrVF2n8LPh+6gly4FUYkktX0v19jy5HfqBHkE1Lbxpq5tfWW8J3QnOoNOxURCiNKQgoIQQgghykQtewsGN62hjP3CE9l9PVzFREKUTIZTk/90KezEOPyiiomqtpxdCuEp9zkfeVbFNEKI0pCCghBCCCHKzCsdPDAzzv7z4tejAWTo9ComEqJkktpOyDWWLoXy07tmX4w0WmUs0x6EqHykoCCEEEKIMuNkbcazLWsq48DoZLZcvqdiIiFKJsOpKalefZWx2Z0dGIdfUjFR1eVgVp02ju2U8cG7+0nOSFYxkRCipKSgIIQQQogyNaqtO9Zm2e86LjoWQGqGdCmIyiPvWgqy40N56Zdj2kOyLokj9w6qmEYIUVJSUBBCCCFEmbKzMGFkG3dlfD8hjbXnQlVMJETJZDg3I9WrjzI2u7MDbfhlFRNVXZ1dumFpbKmMZdqDEJWLFBSEEEIIUeaea+WGg6WJMv7tRCAJqRkqJhKiZP7bpWB1SroUyoOZ1oxuNXoq49MRJ4lMiVAxkRCiJKSgIIQQQogyZ2mq5eX2Hso4NiWDv04Hq5hIiJLJcG5OqmdvZWx2ezvaiCsqJqq6+rkNVD7Xo2dP6E4V0wghSkIKCkIIIYQoF0OaueJqa6aMV5wKITopTcVEQpRMni4FWUuhXDRzaIGzuYsy3inTHoSoNKSgIIQQQohyYWpsxKsdPZVxUrqO332DVEwkRMlkuLQg1bOXMja7vU26FMqBkcaIvm79lfHt+JvcirupYiIhRHFJQUEIIYQQ5eaxRi7UdshecG3tuVDuxqWomEiIksm7lsL3KiWp2vrm2O0BZHFGISoLKSgIIYQQotxojTSM7+KljNN0BhYfC1QvkBAllOHSklSP7EUDzW79izbyqoqJqiYPay987Boq4z2hO9EZdComEkIUhxQUhBBCCFGuetatTqMaNsp4y+W7+EclqZhIiJL5b5eC5UnpUigPObsUIlMjOBNxSsU0QojikIKCEEIIIcqVRqPhjRxdCjoD/HokQL1AQpRQRo1WpHl0V8bmt7agjbymYqKqqZdrH7QarTLeFbJNxTRCiOKQgoIQQgghyl17z2q08bBXxrv9wrl2L169QEKUUGLb93ONLWUthTJnb1aNdk4dlfHhewdJykhUMZEQoiiPVEHBYDDw3HPP4ePjQ0ZGRqHnnj59mvHjx9O+fXuaNm1Kv379mD17NnFxcQ8prRBCCFG1vJmjSwHg58P+quQQojQyarQmzT27S8Hs5ha0kddVTFQ15Zz2kKJL4dDdAyqmEUIU5ZEqKMydO5ezZ88Wed7WrVt58cUX2bdvH2ZmZtSrV4+wsDAWL17MU089RVhY2ENIK4QQQlQtTVxt6VG3ujI+5h/NmeAY9QIJUUKJOdZS0GCQLoVy0Mm5M1bG1spYdnsQomJ7JAoKOp2OWbNmsWjRoiLPvX37NpMmTUKv1zN9+nQOHDjA+vXr2bdvH23atCE0NJQPPvjgIaQWQgghqp5xnb3Q5Bj/dMgfg8GgWh4hSiLDtQ1p7t2UsdnNzWij/FRMVPWYas3o4dpLGZ+NPE148n0VEwkhClPlCwr+/v6MGTOGpUuXFuv8hQsXkp6ezuOPP86LL76IRpP5Z4+joyM//vgj1tbWnD59mqNHj5ZnbCGEEKJKqutoxcBGzsr4Qmgch29HqZhIiJKRLoXy189toPK5AQO7Q3eomEYIUZgqXVBYsWIFgwYNwtfXF1dXVyZOnFjo+ampqWzduhWA4cOH5zlerVo1Bg7M/AW3ZcuWsg8shBBCPAJe6+SJsVF2n8KCI/7opUtBVBIZrm1Jq9VVGZvd+Adt1A0VE1U9Tao1w9WipjLeGbJdOpmEqKCqdEHh4sWLAIwcOZItW7bQrFmzQs+/cuUKqampaDQaWrVqle85Wbf7+vqWbVghhBDiEeFmZ8GQZq7K+EZ4IruuhauYSIiSkS6F8qXRaOjj1l8ZByTc4UacTC0RoiKq0gWFfv36sW3bNj7++GOsra2LPD8gIHNPbCcnJ8zNzfM9x83NDYCQkBDS09PLLqwQQgjxCHm5gwfmxtl/hvxy1J8MnV7FREIUX0bNdqTV6qKMzW5sQht9U8VEVU/O3R5AFmcUoqKq0gWFXr164e7uXuzzo6Iy53A6ODgUeI69vT0Aer2e2NjYB8onhBBCPKocrUx5rpWbMg6OSeGfS3dVTCREySRJl0K5qmXlTiP7xsp4b+hOdPrCt30XQjx8xmoHKMrkyZPZsGFDsc/fuHEjDRs2LNVjJScnA2BmZlbgOTk7F7LOF0IIIUTJjWxbi3Xnw4hPzXyRsPh4II81csHcRKtyMiGKll6zPWlunTANyVyo2+zGJpLaTEBXzVvlZFVHX7eBXIm5DEB0WjQnI3zp4NxJ5VRCiJyqdIdCSWm1mX/AZO3skJ+cC8IYGcnTJ4QQQpSWrbkJo9rWUsbhCWmsOReqYiIhSiZXl4JBL10KZayHa2+MNdnvf8q0ByEqngrfofDFF18wffr0Yp9vYWFR6seytLQEMnd7KEjOYwWtsyCEEEKI4nm2lRurzoYSmZgGwDLfIIY0c8XarML/iSIE6W4dSXPriGnIMQDMbmwkqe0EdPZ1VE5WNdiZ2tHBuTOH7x0A4Mi9gySkJ2BtUvTaaEKIh6PCv8VuamqKlZVVsT8epGugWrVqAMTExBR4TnR0NJDZnZC1noIQQgghSsfCRMvL7T2UcWxKBn+cClYxkRAlI10K5Svn4oxp+jQO3d2vXhghRB4VvqDwMHl7Z855u3//PmlpafmeExISAoCHh4cyRUIIIYQQpTekWQ1q2mV3/a08Hax0LAhR0aW7dSKtZgdlbOa3AW3MbRUTVS3tnTpia2KrjHeGbFMxjRDiv6SgkEPdunWxtLREp9Nx4cKFfM85e/YsAC1btnyY0YQQQogqy0RrxLhOnso4OV3P775BKiYSomTydin8oGKaqsVUa0oP197K+HzUWe4mh6mYSAiRkxQUcjA1NaV378xfWKtXr85zPCYmhm3bMquiQ4YMeajZhBBCiKqsfwNn6lS3VMbrzocSFpeiYiIhii+zS6G9Mjbz24BRzB0VE1UtOac9AOwJ2alSEiHEf0lB4T/Gjx+PiYkJ//zzDwsXLkSv1wMQGRnJm2++SUJCAq1bt6Z9+/ZF3JMQQgghiktrpOGNLl7KOF1nYNHRAPUCCVESGg1Jbd/PHhp0WJ2er2KgqqWRfRPcLLN3hNkZsi3XzmtCCPVIQeE/6taty7Rp09BoNMydO5du3boxdOhQevbsyalTp3Bzc+O7775TO6YQQghR5XTzrk5TVxtl/O+Ve9yJTFIxkRDFl+7WiXTXdsrY7Po6jGL91QtUhWg0mlxdCkGJgVyPvapiIiFEFiko5GPEiBH8+eef9OzZk/T0dK5fv46joyMvvvgia9aswdnZWe2IQgghRJWj0Wh4o0ttZaw3wC9H/NULJERJaDQk/qdLwfKUdCmUlT5u/XONd4ZsVymJECInjUH6hR6qiIh45BkXQgghCvbW2gucCIhRxsteaEmjGjYFXyBERWEwYL9hKCZhJzOHGi1RLxxAb+elbq4q4t1jr3Mx+jwAdqb2/N1rEyZGJiqnEqJi02jA0bH8/g+VDgUhhBBCVCiv5+hSAPj5sCxuJyqJ/LoUZC2FMpNz2kNsWgy+4cdVTCOEACkoCCGEEKKCaVzDhp71HJXxiYAYTgXGqBdIiBJIr9WF9BptlLH59XUYxcoCo2Whh2svTIxMlfEumfYghOqkoCCEEEKICuf1zl4YabLHPx2+I6u6i8pBoyGx7XvZQ32GdCmUEWsTGzo6d1bGx+4fIT49TsVEQggpKAghhBCiwqld3ZLHGrko40th8Ry6HaViIiGKL929G+k1Witj8+trMYoLVDFR1dHPbaDyebo+jQNhe1VMI4SQgoIQQgghKqTXOnlios1uU1h4NEC6FETlIF0K5aadUwfsTO2V8a6QHeqFEUJIQUEIIYQQFZOrrTlPNamhjK/fT+DAzUgVEwlRfOnu3Ul3aaWMza+twSguSMVEVYOxkTG9XPso44vR5wlNClExkRCPNikoCCGEEKLCGtPeI3eXwrEA9NKlICqDfLsUflQxUNWRc7cHgN3SpSCEaqSgIIQQQogKy8XGjKHNXJXxjfBE9kuXgqgk0j16kO7cQhmbX1uNUVyweoGqCB+7hnhYeSrjnSHbZDqUECqRgoIQQgghKrTR7dwxM87+k2XRUelSEJWERkNSu/ezh/oMLM9Il8KD0mg0uboUQpNCuBJzScVEQjy6pKAghBBCiArNydqMITm6FG5GJLLvRoSKiYQovjSPnqQ7N1fG5ldXYxQvc/4fVG+3frnGu0K2q5REiEebFBRElRYWFkqXLm3o0qUNX375aZHnnzlzSjm/IoqLiyUyUr0/onM+P2fOnCr3x+jSpQ2rVv1ZrOvmzZulXPP666+Uaabbt2/luW348Cfo0qUNmzdvLNPHKq233nqNLl3asHDhz2pHEaJcjG5bK1eXwkLpUhCVhUZDUtucXQrpspZCGahh4UoLh+xFL/eF7SZNl6ZiIiEeTVJQEI+M7dv/5ciRQ2rHKLW///6LZ58dku+L26ps3749RZ6j1+vZv7/s96GOiIjgs8+mMXHiO2V+30KIknG0NmNY8+wuhduRSey+Hq5iIiGKL82z13+6FFZhFB+qYqKqIee0h/j0eE6EH1MxjRCPJikoiEfKN998RVxcnNoxSuWHH+YRH69udo1Gk+/n5UWr1XLlyiXu3btb6Hlnz54mKqrsF2nz9T3G7t07ZKEnISqIUW1zr6Ww+FggOr38+xSVgEZDUq4dH9JlLYUy0K1GT0yNTJXxzpBtKqYR4tEkBQXxyNBoNERGRvD997PVjlJpOTu7KJ/XqOFayJllo3XrthgMBvbvL7xLYc+enQDUr+9T7pmEEOqpbmXK0y1qKuM7UdKlICqPNM/epDs1U8bmV6RL4UFZmVjR2aWbMj5x/yixabEqJhLi0SMFBfHIGDr0aQB27NjG4cMHVE5TOdWs6YaFhSXW1ta4utYs+oIH1KtXH6DwaQ8ZGRkcPLgPa2sb2rfvVO6ZhBDqGtm2FuY5uxSOB0iXgqgc8nQppGF55icVA1UN/dwGKp9nGDLYH7ZbxTRCPHqM1Q4gxMMyfPhz3Lx5g/PnzzJ79gyaNWuBra1die4jKiqSVav+5OjRw4SFhWJkpMXT04vevfsxdOjTmJmZAWAwGBg69HHCw+/zySdf0q/fgFz3s3PnNr74YjoAy5evok6durmOz58/j9Wr/2LYsGdISkpi27YtyrH33nsTgKlTP+Wxx55Qbg8MDODvv//i5MkT3L9/D1NTUzw9a9O7d18GDx6GmZl5rsf46qvP2LZtCxMnTqZ9+0789tsiTp48QUxMNPb21WjfviOjR7+Sq3Cg0WioU8cbrVab6750Oh3//LOBPXt2EhQUSFxcLLa2djRq1IRBg56ic+euJXqes3Tt2oO5c2dx+fJF7t+/l6tDIsvp0yeJiYnh8cefxNi48F9p586dYe3aVVy8eJ7Y2FhsbGxp0qQpw4c/R+vWbXOdm3NhzvDw+8r48OG8i1FeuHCOFSuWcenSBZKTU3B2dqFHj16MGvUSlpZW+WbZv38Pmzdv4vr1KyQkJGBnZ0eTJs0YOvSZPFmyxMfHs3btKvbs2cXdu6FYWVnRqVNXxo4dX+jXLURV4mBpyjMta7L8ZDAA/lHJ7Lx+n4EN8/5+EKKiSfPqQ7pTU0zCLwJgfmUlSa3fRG9d/kX6qqqNY1uqmToQnRYFZO728JTnMJVTCfHokIJCJafTG7gRnkBKul7tKA/M3MSIek7WaI3KZ26+RqNh6tRPGT36OSIjI/n229l8+umXxb7+woVzTJnyAbGxsRgbG+Pu7oHBANevX+XatSvs2LGVuXN/oHp1RzQaDZ07d2XjxnX4+h7LU1A4efKE8vnp06fyFBSOHDkMQJcu3bl69TJNmzbn4sXzANSp442VlTXVqjko5+/cuY2vv/4/0tLSMDMzo06duiQlJXLlyiWuXLnE1q2bmT37+3xfkF+/fp0FC+aTnJxMzZq1cHNzx9//Nlu2bOLw4YMsWfIHLi41lPN//fW3XNcbDAY+/XSKsihirVruODk5c/duGIcO7efQof2MGTO2VC96raysadu2A0ePHmL//j0888zzec7Jmu7Qp08/Llw4X+B9LVgwnxUrlgFgY2OLt3c9IiLuc+jQAQ4dOsDzz4/ijTeyF19s2rQ50dHRBAcHYmJiQoMGjfK9323btnDx4nlMTEzx9PQkNjaW4OBA/vzzd44cOcjixctzFXMyMjL45JMpHDy4D4Dq1R2pV68+YWGhHDiwjwMH9vHMMyN4550Pcj3O3bt3+eCDtwgI8Eer1VK7tjdpaals3ryRY8eOYGFhUcxnVYjKb2Qbd9acCyX5f//3LT4WSF8fZ4zL6f8PIcrM/7oU7La+nDnUp2F55mcSuhX/7xGRm9bImF41+7LOfzUAV2IuE5wYRC0rd5WTCfFokIJCJZau0/PqqvNcvhuvdpQy07iGDYuea46Jtnxm47i51WLcuLf4/vs57Nq1nZ49+9CtW48irwsPv68UE554YghvvPEONjY2AISEBPP55x9z5colPvlkCj/9tAiAzp27sXHjulzFgyw5bztz5iRPP/2cMg4KCiQ4OBBraxtatmxN27btGTXqZeUd8rfffp+2bdsr51++fImvvvoMnU7HE08M4a233sXKyhqAGzeu88knU7h16yaTJ3/AwoW/53kXf/PmDTRu3JRp0z7Dw8MTgEuXLvD++28TExPNqlUrePfd3C9uczpx4hj79+/F3r4a33+/AG/vzOKITqfjr7+W8+uvP/HHH7/x5JND8i1oFKVXrz4cPXqIfft25ykopKenc/DgfqpVc6BVq7YFFhQ2blzHihXLsLa24f33J9GvX2Z7pMFgYO/eXXz99f/x11/L8fDwYNCgwQAsWLCErVs3M2PG59jbV2PBgiX53veFC+fo128gEyZMVDpesjpQ7ty5zdatWxgyZLhy/vz58zh4cB8WFpZMnfoJPXv2UZ6vjRvX8cMPc/n775W4uNTg2WdfUK6bNev/CAjwx9u7HjNmzMbNrRYAV65cYtq0SQQFBZb4uRWisrK3NOGZlm4s8w0CIDA6mR1X7/N4Y+lSEBVfmldf0h2bYBJxCQDzy3+R1OpN9NblvzZRVdXPbYBSUIDMLoWX6r+qYiIhHh2yhkIlFhKbUqWKCQCX78YTEptSro8xfPiztGiRuW/xnDkziY2NKfKalSv/IDY2li5duvHRR9OUYgJkFim+/nouVlZWnD9/lmPHjgCZCwpaWFgSGRnBzZs3lPNv375FREQ4zZq1wMjIiLNnz6DXZ3eYHD2aubVlp05dimzhB1iy5Fd0Oh3t2nXgo4+mKcUEgHr1fJg7dz5mZmb4+V1T3s3PycTEhBkzZivFBIAmTZrx2GODAJTOiILcvOkHQNOmzZRiAmTu0DBy5Ev07NmHPn36Ex9fup/Vrl27Y2pqyqVLmdMecjpx4hgJCfH06NE7zzSMLOnp6SxduhCAKVM+UYoJkNm10rt3P954410AlixZSEZGRonyeXnVZtq0z3JNn+nXb6BS9Dl//qxy+/3799i4cR0AkyZNVYoJkPl8DRv2DGPHvg7Ab78tIikpCcgsGp08eQKtVpurmADQqFGTEnXaCFFVvNimFpYm2f/ulxwPIEPWUhCVQT5rKVic+VnFQJVfXdv6eFnXVsa7QrajN1T+7l0hKgMpKFRibnbmNK5hU/SJlUjjGja42ZkXfeID0Gg0TJnyCebm5kRFRTJv3jdFXnPw4H4A+vV7LN/jDg7VlReQR45kFgRMTU1p1y7zNl/f48q5p05ldid069aD2rW9SUiIx8/vunL86NHMgkSXLt2LzJWcnMzZs5lz+p9+ekS+59Ss6Ua3bj0BOHRof57jDRo0pHp1xzy3e3pm/seckFB4IcDd3eN/uQ/zxx+/5dni8f/+72umT/8iV7GhJKysrGnfvuP/dnvYm+vY3r27gMzpDgW5ePE8UVGRWFpa0bVr/s9pv34DMDIyIjz8Pn5+10qUr0uX7vkWM7y96wEQExOt3Hb8+FF0Oh3Vq1end+/8Mw8f/iwmJiYkJCRw9uxpAI4dy5wC06xZi1zFhCwtWrTCy6tOiXILUdnZW5jwXKvseedBMSlsu3KvkCuEqDjSavcj3bGxMra48hdGiYVvkSwKptFoci3OeDc5jEvRF1RMJMSjQ6Y8VGImWiOWjGghayiUgptbLcaPf4vvvpvDnj076dWrD92798r33KSkJO7eDQPg998XsWbNynzPyzonMNBfua1Ll+4cOLCPkyeP8/zzI4Hs4kLr1u0IDQ3h1q0bnDlzkgYNGpKUlMiFC2cxNTWlQ4eidywIDQ0hPT0dyCwMFMTHpwG7dm0nMDAgzzFHR+d8r8laYFKn0xWaoXPnbrRo0Ypz587w668/8euvP+Hp6UWbNu1o374TrVu3Ve6rtHr27MuhQwf+N+0hs3CSmprK4cMHcXZ2oVmzFgVee+fOLQAyMtJ5882C2x+NjIzQ6/UEBPjTqFGTYmdzcnLK9/asNQ1SU1OV2wIC/IHMzhEjo/zruRYWFnh4eHLr1k0CAwPo3Lmr8n2rU8e7wBz16tXH3/92sXMLURU837oWq8+GkpiW+XtqyfFABjZ0xricps0JUWay1lLYNjZzqEvF4szPJHb9QuVglVfvmv1YdH0BBjI7lXaFbKeZQwt1QwnxCJCCQiWnNdLQwKVqdSk8LMOGPcv+/Xs5d+4Mc+Z8TfPmrfI9LzExQfn89u1bRd5vznf0O3Xqglar5fz5c6SmpmBkpOX8+bPY29tTt249Wrdux/r1azh9+hTPPz+KEyeOkZ6eTseOnbG0tCzysXJmyznV4b+yjmW10OdkYmJS6GMYDIW3EBsbG/Pttz+xbt1qtm3bwq1bNwkI8CcgwJ916/7GysqK558fxahRL6PRlK5Y1KVLN0xNzbh06QLh4fdxcnLm+PEjJCUl8uSTQwq934SEzOcoLS2tyOkbOc8vLlPT4hdLkpISgcK/V4CyM0TW+fHxcQBYWBT8M5FzGo4Qjwo7CxOea+XGkuOZa4iExKaw9cp9nmxao4grhVBfWu3+ZFRvhHHkFQAsLq8gudWb6K1kLZDScLJwplX1NpyOPAnA/rC9vN3oPUy1D/amhhCicFJQEI+srKkPo0c/R3R0FPPmzWLw4LzbDJmbZ6+en98Wj4Wxs7OnSZNmnD9/lnPnzmJiYkJycjIdO3ZBo9HQqlUbtFotFy6cIyMjQ1l/oTjTHYBcWxImJiZgauqQ73lZL0iLU6QoDRMTE5577kWee+5F7t+/x5kzpzhz5hTHjx8lKiqSRYsWYGZmxnPPvViq+7e0tKRDh04cPLiP/fv38vTTz7FnT9HTHSC7U8DHpyFLlvxRqscvK1nPf85CUH6y1pvI+v5mrc+QmJhY4DU5OyGEeJQ839qN1WdDSEjN6lII4LFG0qUgKgGNhsS2E7Db/lrmUOlS+FzlYJVXX7cBSkEhMSOBo/eP0MM1/w5UIUTZkP9txSMta+oDZM7H379/T55zbGxscHCoDsCdOwW3lN+6dZMbN64TFxeX6/bOnbsB4Ot7TJkT36ZNO+W+69dvQHJyEpcvX+LYsSNoNBq6dOlW7PxZCzdeu3a1wPOyjtWq5VGs+y2JuLg4Ll26qKyd4OzswoABjzN16qesX/8vnTt3BWDHjq0P9Di9emUuYLhv326Sk5M5evQQbm61CtzOMYu7e+Zik0FBgQUuuGgwGDhz5hRBQYHKFJLy4OHhBWTuvpFzIc6cEhMTCArKnOLg7u7+v+s8lesKUtjPphBVma25CSNauSnj0LhUNl+WtRRE5ZBWZwAZ1bOnLFpc/hOjRPn5La2uNbpjrs1ei2tXyHYV0wjxaJCCgnjkDRuWvevDhg1r8z2nU6cuAKxb93e+LwQTEhJ4993xvPTSC3nWWMhaCNDX97hSUGjduq1yPKu4sGLF70RHR9G4cdN8F0nMbuvPnoJgYWFBq1aZ20kWtLZDSEgwhw8fBCjWugwlNXPmF4wf/xIrVizLc8zY2JgWLVoDFPgCurg6d+6GmVnmtIctWzaRkpJS4MKGObVo0Qpra2uSkhLZunVzvufs2rWdd94ZzwsvDM+1k0TWc17UtI/i6tChE1qtlsjIyHx33IDMnzGdToe5ubny3PXo0RuAy5cv5rto5M2bN7h69XKZZBSiMhrRqhY2ZtlNl0uPB5Kuq/xrC4lHgMaIxLYTsoe6VCzOLlAvTyVnYWxJF5fsLk/f8GPEpEYXcoUQ4kFJQUE88rKmPlhYWBT4wvHFF8dgYWHJhQvn+OKL6cTExCjH7t4N48MP3yUmJgZra2uGDn0617Xu7h54eHhy585tLl26gKtrzVwr9WcVFI4ezVzJv6DuhKz583fv5l4F+uWXX0Or1eLre5xZs75S5t0D3Ljhx4cfvktaWip169ZnwIDHi/msFN+AAZk7X2zatJ7t2//N9Rzevn2LtWtXAdChQ+cHehwLCws6duyMXq9n0aLMP7aKmu6Qdd2LL44B4Pvv5/Dvv//kKm4cOrSf2bNnAtCzZ59c35usKQrx8XG5ntfScnGpwZNPDgXgm29msG/fbuWYXq9nw4a1LFnyKwCjR4/F2jpzrQVv77r06dMfg8HAtGmTcnUq3L59i48/nlRmRQ8hKiMbc2Oeb53dpXA3PpXNl2TFfFE5pNUZSEb1BsrY4tIfaBLvq5iocuvrNkD5XGfQsTdsdyFnCyEelKyhIATZUx++/XZ2vsdr1XLniy9m8umnU9m9ewf79++hdu06pKdnEBQUgE6nw8LCgtmzv6datbzrGHTp0o2//vqDjIyMXN0JAE2bNsfMzEyZA9+tW498M9Sv78O5c2f49ttv2LhxHUOGDGfQoKdo0qQZkydP55tvvmLz5g3s3LkVL686JCcnKbsDeHvXZcaM2Ziamj7As5S/7t178cQTQ9i8eQNffvkpP/74HS4uNUhMTCAkJBiDwUDDho0ZPfrlB36snj37sn//XpKSEqldu06x17N44YXRhISEsHnzBmbO/IIFC37A1bUm4eHhRESEA5nfh8mTp+e6ztu7HkZGRqSmpjJixDAcHZ2YN28+dnb2pf4a3n77PSIi7nPo0AGmT5+Mo6MTTk7OhIWFKIWqYcOe4cUXR+e67oMPJnPv3l0uXjzPSy+9QO3addBoNNy5cxtraxtlpw0hHlXPtXJj5ZkQ4lIypzYtPRHEoMY1MDWW905EBacxIrHNBOx2jM8c6lKxPPsLiV0+UTlY5dTKsQ3VzRyJTI0AYFfINoZ6PV3EVUKI0pL/ZYX4n6FDn1GmPuSnY8fO/PHHap599nlq1XInMDCAkJAgXF1rMmTI0yxbtoqmTZvne23ORRb/W1AwNTVVtj309PRS5tn/15Qpn9C2bXu0Wi2Bgf4EBQUqxwYOHMTvv6/kiSeG4ODgyJ07t4iNjaFp0+a8994kFi5cRs2abvneb1n48MMpTJ36Ka1atcFg0HPzph+xsbE0a9aC996bxIIFS3ItIFlanTt3VRZZLM50hywajYaPPprGvHk/0q1bT7RaLX5+10lKSqJx46ZMmDCRH374RbnvLLVquTN16qe4u3sQFxfLvXt3CQsLe6CvwdTUlBkz5vD55zNp164D6elp3Lzph5mZOb179+OHH37hvfcm5dm5wsbGhu+/X8A773xAvXr1uXs3jIiICHr06M2iRcuoVcv9gXIJUdlZmxnzQuvsDqN78an8I10KopJI836MDAcfZWxxeTmapHAVE1VeWo2W3jWz/0a4HnuNgAR/9QIJUcVpDNIn+1BFRMQjz7gQQghR9hJSMxi82JfY/3UpOFubsv6VdphJl4KoBExvblG6FACSWowjsfP0Qq4QBbkdd4uxh0cq4+e9RzHWZ3whVwhRdWk04OhYftuLy/+wQgghhKgSrM2MeaFNdpfC/YQ0Nl18sK4iIR6WPF0Kl5ZJl0Ip1bH1xtumnjLeHbIDvUEWahWiPEhBQQghhBBVxjMta2JvYaKMf/cNIjVDXkiISkBjRFKbCdnDjBQsz/6iXp5Krq9bf+Xz+yn3uBB1Tr0wQlRhUlAQQgghRJVhZWrMyBxdCuEJaWy4IF0KonJIrfs4GdXqK2OLS8vRJEWomKjy6l2zH0Y5XursDNmmYhohqi4pKAghhBCiSnm6ZU2q/adLISVdp2IiIYpJY0RS23ezhxnJWJ6TLoXSqG7uSGvH7IWwD97dR4ouRcVEQlRNUlAQQgghRJViYaJlZNvsLoXIxDTWS5eCqCRSvQeRUS17/r/FxWVokiNVTFR59XMbqHyelJHEkXsHVUwjRNUkBQUhhBBCVDnDW9TEwTK7S2GZdCmIysJIS1Kb/3QpyFoKpdK5RjcstJbKeFfIDhXTCFE1SUFBCCGEEFWOhYmWUW3dlXFUUjprz0uXgqgcUus+QUa1uso4s0shSsVElZO51pxuNXoo41PhJ4hKlW4PIcrSI1VQMBgMPPfcc/j4+JCRkVHouVu3buWVV16hQ4cONG7cmA4dOvDqq6+yd+/eh5RWCCGEEA9iWHNXqluZKuPlvkEkS5eCqAzydCkkYXnuVxUDVV593QYon+vRsyd0l4pphKh6HqmCwty5czl79myh5+h0OiZMmMB7773H4cOH0ev11KtXD51Ox8GDB3n99df5/PPPH1JiIYQQQpSWuYmW0e2yuxSik9NZey5UxURCFF9q3SfJsPdWxhYXfpMuhVJoUb0VzuYuynhXyHYV0whR9TwSBQWdTsesWbNYtGhRkecuXLiQbdu2YWlpyaxZs/D19WXjxo34+vry2WefYWxszF9//cWqVaseQnIhhBBCPIghTWvgmLNL4WQwSWnSpSAqgXy7FBaqGKhyMtIY0btmP2V8M86PO/G3VEwkRNVS5QsK/v7+jBkzhqVLlxZ5bkZGBsuWLQPgnXfeYfDgwcoxjUbDiBEjGDt2LABLliwpl7xCCCGEKDvmJlrG5OhSiElOZ410KYhKIrXeU2TY11HG5hd/Q5MSrWKiyinntAeQLgUhylKVLiisWLGCQYMG4evri6urKxMnTiz0fD8/P6KjM39JP/744/me06dPHwACAwOJjY0t28BCCCGEKHODm7nibJ3dpfDHySAS0wpfS0mICuE/XQpG6YlYSJdCiXnZ1Ka+bQNlvCtkBzqDdCoJURaqdEHh4sWLAIwcOZItW7bQrFmzQs93c3Pjp59+4tNPP8XZ2TnfcwwGg/K5Tie/iIQQQoiKzszYiNHtPJRxbEoGf5+VLgVROaTWe4oMu9rK2OKCdCmURl+3/srnkakRnIs8o2IaIaqOKl1Q6NevH9u2bePjjz/G2tq6yPPt7Ozo06cPzz//fIHnbN+e2SLl6OhItWrVyiyrEEIIIcrP4KY1cnUp/HkqmIRU6VIQlYCR8X+6FBKwOFf0umAit141+2Kk0SrjnSHbVEwjRNVRpQsKvXr1wt3dvegTi8nPz48//vgDgCeffBKNRlNm9y2EEEKI8mNqbMTLHbK7FOJSMlh9NkTFREIUX2r9wWTYeSljiwtLpUuhhKqZOdDOsb0yPnT3AMkZySomEqJqqPAFhcmTJ+Pj41Psj6tXr5ZLjrCwMMaPH09aWhrOzs6MGzeuXB5HCCGEEOXjySY1qGFjpoxXnAqRLgVROeTXpXB+sYqBKqd+tQYqn6fokjl874CKaYSoGip8QaEiCAoKYuTIkYSEhGBmZsb333+Pvb292rFEMYSFhdKlS5t8P7p2bctjj/XmpZee59dff1IW5KzMvvrqM7p0acMXX0xXPcPw4U+U+2N06dKG7t3bF+t7l5GRwcCBvZTrNm/eWGZ5MjIyCAwMyHXbmTOnlMfKyFD/BUvOfwvBwUFqxxFCFSZaI17K0aUQn5rByjPSpSAqh9T6Q9DZeirjzC6FGPUCVUIdnbtgZWyljGXagxAPzljtAEX54osvmD69+C+OLCwsyvTxL1y4wBtvvEF4eDhmZmbMnz+fVq1aleljiIejTh1vrKyy19LQ6XTEx8dx+/YtbtzwY/PmDXz//S94e9dVMaUoKZ1Ox4EDexk8eFih5/n6Hic+Pq7MH9/X9zjffTebHj1689prb5T5/QshytYTjV34/UQgYXGpAPx1OpjnWrphY17h/yQSjzojYxLbvIvt3vczh2nxWJxfTFL7wncxE9nMtGZ0r9GLrcGbATgbcZrwlHCczJ1UTiZE5VXhOxRMTU2xsrIq9oeRUdl9STt27GDkyJGEh4djY2PD4sWL6d69e5ndv3i4Jkz4kAULligfCxf+zsqV6/nnnx106tSFmJgYPv54Enq9Xu2olVrW2iIPY40RrTZzcaV9+/YUee6ePTvLJcPy5UvzdCcIISouE60RL7fP7lJISNXx1+lgFRMJUXypPkP/06WwRLoUSqhvrQHK53r07Aktn78PhHhUVPiCglp+//13JkyYQEpKCm5ubqxcuZJ27dqpHUuUAzs7e6ZN+wxTU1OCggLx9T2udqRKzdnZBQAXlxrl/lgtW7bGyMiIc+dOFzrtIS0tjcOHD2BvX03JJ4R4dA1q7EJNO3NlvPJMCHEp6SomEqKYjIxJbPNO9jAtHosLS1QMVPk0rdYcF4vsv1F2BW/LtS28EKJkpKCQj8WLFzNz5kz0ej2NGzdm9erV1KtXT+1YohzZ2dlTu7Y3ALdv31I5TeWWNWWkbt365f5YDg7Vad68JTqdjoMH9xV43vHjR0lMTKRHj95l2sUkhKicjLVGvJJjLYXENB0rTstaCqJySK0/FJ1t9s+vxfklaFJjVUxUuRhpjOjrlt2lcCfhNrfib6iYSIjKTSYM/seOHTuYPXs2AO3bt2fBggVYWVkVcZWoCrIWzrO0tMx1+1dffca2bVuYOHEyGo0Ry5YtISYmGmdnFyZNmkarVm0AiIuLY+3aVRw6tJ/g4CD0ej01arjSsWMXnnvuRRwdHZX73LhxHXPmzMTOzo5Nm3ZgbJz3n+K9e3d5+unM7UnXrduCo2Pm/L7U1FQ2bVrP9u1bCAoKwtTUhDZt2jF27OtFfo2HDu3nn382cPXqFRIS4rG3r0aLFq0YMWIkPj4N8pzfpUvm17ZnzxGOHz/K2rWruHHjOunp6Xh4eDJgwOMMG/ZsrvzZBYXca1GEh99nxYplnD17hrCwUAwGAy4uLrRp055nn30eV9eaRebPT69efTl79jT79u3mqaeG5ntO1nSHvn37c/z4kQLvKy0tjY0b17Fnz078/W+Tnp6Bi4sLnTp1YcSIUbm+h1u3bmbGjM+V8fLlS1m+fCkDBw5i2rTPct2vTpfB+vVr2L59CwEB/piYmFK3bj2GDHma3r375pulJD9POfn5XeOvv/7gwoVzxMTEUKtWLZ56ahgdOnQq8OsW4lH0WCMXfjsRSHBMCgCrz4TwfCs37CxMVE4mRBG0JiS1fhubfR8CYJQWh8X5JSS1e1/lYJVH35oD+PPm78p4V8h26tqW/xshQlRF8lZdDvHx8XzyyScA1KlTR4oJj5CQkGDu3LmFkZFRgS+8duzYxuzZMwCoVcudyMgI6tXzAeDWrZuMGvUsS5cu5Natm9So4YqHhyfBwUGsWvUnI0c+w5kzp5T76tu3P2ZmZsTGxnLs2OECHm8rer2etm3bK8WE+Ph4Jkx4nR9+mIuf33VcXGrg6OjEvn17eOWVkQV2V2RkZPDFF9OZMmUix44dQaPRULdufdLS0ti9ewevvTaadetWF/j8LF78C9Omfci1a1dwda2JpaUVN274MX/+t/zf/+VeNNXDw4vDh08xaNDgXM/vyy+/yNq1qwkNDcbV1ZWaNWsSGhrC2rWrGDNmBH5+1wp8/ML06NELrVbL2bOniYmJyXM8JSWFo0cP4ezsQrNmLQq8n4iICMaNG8MPP8zlypVL2Nra4eVVm3v37rF69V+MGvUsFy6cU86vVs2Bpk2bK78jnJ1daNq0Oe7uHnnu+4MP3uGHH+YSERGBp6cXer2ec+fO8OmnU/jtt0V5zi/pz1OWnTu38dprY9i9ewfJycnUqeNNVFQk3377DV9//X9FP5lCPEKMjTT5dCnIWgqickjxGY7Oxl0ZW1yQLoWScLf2oKF9Y2W8J3QXOr36OzIJURlJh0IOf//9t/KCJD09nbFjxxZ6/g8//ICTk8qrwup1GEdegfRkdXOUBRMLMqo3AiPtQ3k4nU5HQkI8Fy9e4KefvkOv1zNq1MvUqOGa7/kXL55n2LBneOedD9BqtURHR2NjY0NSUiIffPA2ERHhNGnSjOnTv8DNrRYAUVGRzJr1JUeOHGLq1IksXbqCmjXdsLKypkePXuzYsY0dO7bStWuPPI+3ffu/ADz22JPKbT///D0XL17A2dmFr7+eS/36mV0FgYEBTJv2IdevX803++LFv7Bz5zacnV346KOPad++o/IcbNiwhvnzv+W77+bg4eFJ27Yd8ly/cuUfjBz5EmPGjMXMzAydTseiRQv488/f2bNnFy++OEYpruRn4cKfiI6OokeP3kyd+qnSBRIVFcm0aR9y8eIFfvnlJ+bNm1/gfRSkWjUHWrRoxenTJzl4cB9PPjkk1/EjRw6RnJzMk08OLXChSIPBwPTpk7hxw49mzVowefLHeHh4AZCQkMD8+fP4999/mDp1IsuWraJ6dUc6duxMx46deeut1zh37gwDBjxe4C4PV69e5uOPP6dfv4EYGRmRlJTE//3fJxw6tJ9ly5bwzDMjlB1ISvPzBJlFm6+//pKMjAyeffYFxo9/CxMTE3Q6HX/99Qe//vpjiZ9bIaq6AQ1d+O1EEIHRmf+Hrj4TyvOtamFvKV0KooLTmpDU5m1s9k0CwCg1FosLS0lq+57KwSqPvjUHcDXmMgBRqZGcjjxFO6e8fwMJIQonBYUcTp48qXweFBREUFDhe7WnpqaWd6TC6dKwXz8Uk/vn1M1RhtKdWxAzdD1oTcv8vt95Z3yhx194YTSvvlrwtAFTUzPGj39b2VmgWrVqAKxbt4aIiHAcHKrzzTffYWtrq1zj4FCdL7/8hrFjR3Lr1k2WL1/K5MmZ7+g//vhT7NixjaNHDxMXF5frukuXLhIYGICtrR1dunQDMt9B//fffwCYPv0LpZgA4OHhyddfz+OFF4YrUzeyREdH8ffffwEwc+bcXFMbtFotw4c/x/379/nrr+UsXLgg34JC585dGTfuzVzXvfrq62zatJ74+DguXDhfaEHh5s3MuYn9+g3MNaXEwaE67747kUWLfsHLy6vA64vSs2cfTp8+yb59u/MUFPbuzZzu0KdPvwKvP3z4ABcvXsDR0Ym5c+fn2n7W2tqayZOnc+fOba5cucTq1X/xxhvvFHhf+Rk9+hUGDHhcGVtaWvLBBx9x6NB+MjIyuHz5Eu3aZT7vpf15WrnyD9LSUmnZsjVvv539B6VWq2XkyDEEBQWwdevmEuUWoqrL6lL4dNt1AJLSdfxxKpi3u9VWOZkQRUvxGY7lqflo4zP/XrU4v5jkZq9gMLMt4koB0LNmb366+h06gw7InPYgBQUhSu6RmvLQvn17rl+/zvXr1/Ods/7LL78ox4vzUatWLRW+imzauKAqVUwAMLl/Dm1c4YWc0qpTx5umTZsrH40bN6V27TqYmmYWL1avXsF3381Gp9Ple339+j65XmhmOXr0IAADBjye68VfFhMTE4YNexaAw4cPKisJt2zZmpo13UhLS2Pv3l25rtm+fQuQOTUiK9/x40fQ6/W4utakZcvWeR7Hza0Wbdu2z3P7sWNHSEtLw8urTr7rJGRmfwzIfCc9Ojoqz/HOnbvluU2r1VKrVma7ZUJCfL73myXrvF9+mc+hQ/tJTU1RjjVo0Ii5c3/g7bdLP/ezR4/eaLVazpw5RWxsjHJ7UlIix44dxc2tFg0bNi7w+oMH9wPQtWuPfL/HGo2G/v0HAnD06KFS5OuV5zZHRyfs7OwAiInJ3qGitD9PR49mTp157LEn8s0wZMjwEucW4lHQr4EzntWy/92vORdCdFKaiomEKCatKUmt31KGWV0KonjsTO3p4Jw9zfXw3QMkZSSqmEiIykk6FCoxna076c4tqlRRId25BTpb96JPLIUJEz5UFlDM9Zjp6Wzduplvv/2Gdev+RqfTM3Hi5DznVa9ePd/7DQgIAMDHp2GBj511LCYmmri4WOzs7NFoNDz22BMsXvwLO3ZsZfDgYUDmwoB79mQWGHJOdwgMzHycrN0o8lO3bn2OHcu96GDWugrh4fd4/fVX8r0u53ZJAQH+VKvmkOt4QVN7zMzMAAoswmQZO3Y8Z86cJjAwgClTJmJqakqTJs1o27Y9HTp0pl69B1sIyd7enlat2nDy5AkOHtzPE08MBjJfcKelpdKrV/4LH2bJeo6OHDnIzZt++Z4TH59ZNAkKCsRgMBQ4fSI/jo7O+d5uYWFJbGxsrm6n0vw8mZubc//+PaDgn4+6deuj0Whkaywh/sPYSMPYjp5M35q5jktyup4/TgbzTvc6KicTomgpDZ7G8tQPaBMydymxOL+I5OavYDC1UTlZ5dC35gCO3Mt8oyBVn8rBu/sZUOvxIq4SQuQkBYXKTGtKzLBNsobCgz6siQlPPTWUyMgIli5dyObNGxg5cgwuLjVynWdmZp7v9YmJCUBma3xBci7umZSUhJ2dPQADBw5i6dKFXLx4npCQYNzcanHkyEHi4+Pw9q6Xq6Mg6wVtfu+gZ7GxyfuOdla+xMRELl48X+C1WfLrNjA2Lnw+cVEvUuvV8+H33//izz9/5+DBfcTGxnLmzCnOnDnFr7/+hLd3Xd5/fzLNm7coMl9BevXqy8mTJ9i3b7dSUMi5u0Nhsp6j+/fvKS/MC6LT6UhKSlTWPCiOrC6T4ijNz1N6eroytrTM/+fDxMQEc3NzkpOrwO8KIcpYXx8nlh4P5E5UEgBrzoXyQptaVLcq++l3QpQprWnmWgr7M98IyexS+I2kNiWbmveo6uDcGWtjGxIyMv/22RmyTQoKQpSQFBQqOyMtGU5N1U5RJXTt2p2lSxei0+m4ceN6noJCQSwtrYiPjyMhIaHAc+Lj43Kcn72GgItLDdq0aYev73F27drOmDFj2bFjKwCPP567dT2rPT4pqeB2vLS0vOt6mJtnvsDs0aMXX375TTG+ovLh5laLjz76mA8/nMr161c5e/Y0p06d5MyZk9y6dZMPPniLFSvWFvt5/6/u3XsyZ85MTp8+SWxsDEZGWnx9j1O7dh3q1Klb6LVZz9F7732oTCdQS2l+niwssn+mEhPz//kwGAykpUkbtxD50RppGNvRg2n/ZnYppGToWX4yiPd6FNwRJkRFkdLgmcy1FLK6FM79SnKzl6RLoRhMtab0dO3N5qCNAJyPPMv95Hs4W7ioG0yISuSRWkNBiMJoNNn/HErSFu7p6QVQ4A4LANeuZR6zsbFVuhOyPP545rSGgwf3kZKSgq/vCYyNjenbd2Cu8zw8PIHMBQ4LynfnTt5tI7Ouu3PndoH5UlJSOHv2NCEhwUVOXygpg8FAWFgoJ08eB8DIyIiGDRvz/POjmDdvPsuXr8bKyoqUlBQOHNhX6sextbWjdet26HQ6Dh3az6FD+0lPT6d374IXY8xSnOfo3r27XLp0kYiIiFJnLI7S/DyZmpoqu5P4+V3P95rAwIAy/94KUZX0ru9E7erZxbl158OISJQinKgEtKYktX5bGWZ2KfyuXp5Kpm+t7L+3DBjYHbpDxTRCVD5SUBDif44dy1zUTqPR5NpBoSidO3cFMrd5jIuLy3M8PT2dDRvWANChQ6c8x7t27YGtrR1+ftfZtGkdaWmpdOrUVdlFIkuXLt0wNjYmPPw+hw8fyHM/kZERysJ8OXXs2BmtVktAgL/yov6/Vq9ewdtvj+Oll14gJaVsW+Lj4mJ57rkhvPfeW1y7diXPcQ8PT6UrQa9/sBe8vXr1AWD//r3s27cbgD59Cp/uANnfw927d+a7KCXAzJlfMH78S3z22dRctxsZZf4aLau1CUr789S9e+bCj//8syHfwsE//2wok3xCVFVaIw2vdvRUxqkZepb7ls8iwUKUtZSGz6CzrqmMLc79iiat4E43ka2xfRNqWrop410h22W9ISFKQAoK4pFnMBg4cGAvy5dnrozco0fvErXdDx48HCcnZ6KiIpk0aQKhoSHKsejoKKZP/4jbt29haWnFyy+/lud6U1NT+vUbAMDixb8C+a/Ub2trx4gRIwGYOfP/OHXKVzl29+5dJk/+IN/58TVquCprCnz22TQOHz6oHNPr9WzevJGlSxcCMHTo0yVaG6A47OzslRe+M2Z8TkCAf67HX79+Dbdv30Kj0dC+fd6CS0l069YTY2NjTp8+yalTvvj4NFR2mChM79798PauS0JCPO+//5aySCNkTjGZM+drTp3yRaPR8OKLY3Jdm7Wmxb17dx8oe5bS/jw9//xIbG3tuH79KjNmfK5MjTEYDGzYsJa1a1eVST4hqrLe9R3xdszuUlh/IYyIBJW3iBaiOPLs+BCD+cXf1ctTiWg0GvrUzH7zISDBnxtx+Xf7CSHykjUUxCPju+9m53mxnJGRwd27Ycq70j4+DfPd4aEwNjY2zJo1jw8/nMClSxd47rkheHnVxtjYmNu3b5GRkYGtrR2ffvol7u4e+d7H448/xdq1q0lOTsLBoXq+nQwAL730KoGB/hw4sI8JE96gVi0PLC0tuHXrJlqtlo4dO+fZ5QHg7bff5/79+xw9eojJk9/H0dEJJycnwsLClC0Le/Tozauvvl6ir724PvxwGjdvjuH27VuMHPkMrq41sba24d69MGJiYgAYN+5Natd+sFXVbW1tadOmHcePHwUo1nQHAGNjY2bMmMPEie9w44Yfo0Y9i4eHJ+bm5gQFBSqFmrfffj/P96Z+/QYcOXKInTu3cevWDZo1a8kHH3xU6q+htD9P1as78sUXM5k27UN27NjKwYP78PKqzf3794mMjKBLl24cO3ZEpj0IUQgjjYbXOnry0ebMaUWpGXp+9w1iYq/C12ERoiJIafgslqfno00IA8Dy3K+kNB2DwbRs3yioivq6DWD5zewtN3eGbKO+XfG7VYV4lElBQTwycr7rnMXU1Ax7e3s6depKjx696NdvIMbGJf9nUb9+A/74YzV//72SQ4cOEBIShEZjhIeHJ126dGfo0KdxdMx/60WAevXqU7dufW7e9KN//8cKzGBqasr//d8stm//l3/+2cCdO7eIidHQpk17Xn31dY4fP5JvQcHMzIxZs+axd+9utm7dzPXrV/Dzu46lpRWtWrVh4MBB9O//mNK+X9YcHR1ZvHg5K1f+wfHjRwkNDeHevbs4OFSnd+9+DB/+LE2bNi+Tx+rdux/Hjx9Fo9HQu3fh20Xm5OZWi6VLV7Bhw1r2799DQMAdUlJSsLevRvv2nRg+/FlatGiV57oXXhhNREQ4Bw/uIygosEw6PEr789SmTTuWLl3BihXL8PU9zq1bN3FycuaVV8YxcuRL9O7d+YGzCVHV9ajnSD0nK26EZ3b5bLgQxqi27jjbmKmcTIgiaM1IavUWNgenAWCUEo35xd9JztG5IPLnZlWLxtWacjn6IgB7Q3cxvsHbGBvJSyUhiqIxyCShhyoiIh55xsV/ZWRkMHTo40RFRfLHH38/8Dv1QgghSm/fjQgm/ZO95svTLWoyqbd0KYhKQJeKwx+d0SZmTsPTm1cjcuRxMLUq4kKxOXAj317K3g3rq9az6egihXhR+Wk04OhYfru+yBoKQlQAR44cJCoqkqZNm0kxQQghVNajbnXqO2W/ANt4MYy7cSkqJhKimLRmuddSSInG4tLv6uWpRHq49sLEyEQZ7wrdrmIaISoPKSgIoZLAQH/u3g3D1/c4c+fOAuDZZ19QOZUQQgiNRsNrnbJ3fEjXGfhddnwQlURKw+fQWbkoY8uzv0JaooqJKgcbE1s6Omd3JBy5d4iE9HgVEwlROUhBQQiVrFq1guHDn+D9998iKiqSdu060KNHb7VjCSGEALp5V6eBc/aaKJsu3pUuBVE5GJuT1Cpnl0IUFpeWqxio8ujrNkD5PF2fxoG7+1RMI0TlIAUFIVTSsGFj7O3tsba24bHHnuDLL2epHUkIIcT//LdLIUNv4LcT0qUgKoeURiNydymc+wXSk1RMVDm0c+qIrYmdMt4VItMehCiKFBSEUMkTTwxmy5bdbN++j6lTP8XSUhZMEkKIiqRLHQca1cheyOqfS3cJjZUuBVEJGJuT1OpNZWiUHCldCsVgYmRCz5p9lPGFqHPcTQpTMZEQFZ8UFIQQQggh8qHRaHitY+4uhaUnAlVMJETxpTR6Hp1lzrUUFkiXQjH0yzHtAWRxRiGKIgUFIYQQQogCdKpdjSau2V0KWy7fIyQ2WcVEQhSTsTnJrV5XhpldCn+oGKhyaGDXiFpWHsp4V/B2DLLnuxAFkoKCEEIIIUQBNBoNr+boUtDpDSw9Ll0KonJIbvwCOktnZZzZpSAFscJoNBr6uvVXxsFJQVyLvaJiIiEqNikoCCGEEEIUoqNXNZq62irjfy/fIzhGXpSJSsDYguRWbyhDo+QILC5Ll0JR+tbMPe1hpyzOKESBpKAghBBCCFEIjUbDuBw7PugMsES6FEQlkadL4Yx0KRSlhqUrzRxaKON9obtI16erF0iICkwKCkIIIYQQRWjnaU/zmtldCtuu3CMwWl6UiUrA2ILkljnXUgjH4vKfKgaqHPrmWJwxLj0O3/BjKqYRouKSgoIQQgghRBE0Gg2v5elSCFAxkRDFl9z4RfQWTsrY4uwCyJCCWGG61+iFiZGpMt4ZLNMehMiPFBSEEEIIIYqhrYc9Ld2yuxS2X72Pf5RswycqARMLknLs+KBNuo/F5RUqBqr4rE2s6ezSVRkfDz9CXFqciomEqJikoCCEEEIIUQyZXQpeylgvaymISiS58Uj0Fo7K2OLMz9KlUIR+OaY9pOvT2R+2R8U0QlRMUlAQQgghhCimNh72tHa3U8Y7r93HP1K6FEQlYGJBUsv/din8pWKgiq+NY3vsTe2V8a5QmfYgxH9JQUEIIYQQogRyrqWgN8BiWUtBVBLJTUait6iujDO7FFJUTFSxGRsZ06tmP2V8OfoiIYnBKiYSouKRgoIQQgghRAm0qmVPGw97ZbzzWji3IhLVCyREcZlYktRivDLUJt3D/Ip0KRQm57QHgF0h0qUgRE5SUBBVXpcubUr0ER8fr3bkErt9+1ae24YPf4IuXdqwefPGhx+omN566zW6dGnDV199lu/xuLhYIiMjHm6oUkpJSSEsLDTXbVu3bqZLlzYMGfKYSqmEEOVlXMfsLgUDsPiYrKUgKofkpqPRmzsoY8szP0mXQiHq2frgaV1bGe8K3Y7BYFAxkRAVixQUxCOjVi0PmjZtXuSHVqtVO2qxRURE8Nln05g48R21o5S5v//+i2efHZJvsaSi2blzOyNGDOXUKV+1owghHpIWtexol6NLYY9fODelS0FUBiaWJLXM0aWQeA/zKytVDFSxaTQa+rr1V8ZhSaFcjr6oYiIhKhZjtQMI8bCMGvUSjz32hNoxypSv7zF2796Bk5NznmPff7+AjIwMqld3zOfKiu+HH+apHaHYFi78ifDw+3lu79atJ40bN8XYWH7VClEVvdbJE9/AGCCrSyGAr59opGomIYojucloLM/+glFKFJDZpZDSaAQYm6ucrGLqU7M/S67/ioHMzoRdIdtp4tBM5VRCVAzSoSBEFeXmVgtPTy+sra3VjvLIsra2xtPTCze3WmpHEUKUg+ZudnTwqqaM9/hFcCM8QcVEQhSTqRVJLccpQ23iXcyvrlIxUMXmbOFCi+qtlPG+sD2k6VJVTCRExSEFBSGEEEKIUhqXY8cHgEWyloKoJJKbjEFvnl0QszzzE8iL5AL1zbE4Y0JGPMfvH1UxjRAVh/ThClGAsLBQnn76SQBWrdpArVruec4ZPvwJ7t4NY+rUT5XpFGfOnOKdd8bTqFETfv55MWvWrGL79n8JDg7ExMQEH5+GDB/+LF279sj3cSMjI9iwYS2HDu0nNDQUg0GPh4cnffr0Z/jw5zA1NQUyF5vMEh5+XxkfPnwqV7aPPvqYJ54YnOsx4uLiWLt2FYcO7Sc4OAi9Xk+NGq507NiF5557EUfH3NMktm7dzIwZn9O7d18mT/6EP//8nb17d3Hv3l3MzS1o0qQZL7wwiubNW5bsSc7HV199xrZtW5Txe++9CZDrOQYICQlm5co/OXnyOOHh9zE1NaVOnboMHDiIxx57Is9aGFn3O3HiZDQaI5YtW0JMTDTOzi5MmjSNVq0yn78bN66zfv1aLlw4S3h4OGlpqdjY2OLj04DHH3+Snj37KPe5ZMmv/PbbImU8a9aXzJr1JS+99CqvvDJOed6cnJzZsGFrnq/11ClfNmxYw6VLF4iNjcXa2hofn0Y8+eRgunfvlef8rO/pihVriYqK5K+/lnP58iVSUpJxda1Jr159GTFiJJaWlqV89oUQJdXE1ZZOtatx9E40APtuRHD9fgI+ztIdJio4UyuSWozD+vjXAGgTwjC/upqUJqNUDlYxdavRg+8vzSFVn1l02RW6nW6uPVVOJYT6pKBQyekMOm7F3SRVV/lX5zXTmuNtWxetpvIsiliYjIx0PvjgHU6f9sXe3h5Pz9oEBQVw+vRJTp8+ycSJkxk8eHiuay5cOMe0aZOIjo5Cq9Xi5VWH9PQ0btzww8/vOseOHWHevB8xMTGhadPmREdHK4WKBg2KN2/31q2bfPDB20REhGNkZISnpxfGxsbcvn2LVav+5N9//+Grr75RXmDnFB+fwLhxY7h9+xaOjk54edXG3/8OR48e4sSJo8ycOZdOnbo80PPm7p65eObFi+cBqFPHGysra6pVy16R+sCBfXzxxcekpqZiZmaGh4cXKSnJXLhwjgsXzrF7905mzpyT7wvrHTu2cfHieZydXahVy52wsFDq1fMBYMOGtXz77Tfo9XpsbGypVasWqamphIWFcvz4UY4fP8rIkS8xblxmkcPFpQZNmzbn+vWrpKWlUauWO9WqOeDiUqPIr/Pbb79h3bq/AbCzs6NevfqEh4dz4sRRTpw4Sq9effnkk//Ld/2Ff/7ZwN9//4WJiSnu7h7Ex8cREODPb78t4tSpE/z446JKtbioEJXdax09lYICwKKjAcwZ3FjFREIUT0rTMZlrKaTGAGB5ej4pDZ8FrZm6wSogS2MrutTozp7QnQAcv3+U2LQY7Ezt1Q0mhMqkoFCJpevTeffY61yLvaJ2lDLTwK4R33dcgImRidpRHpif33UsLCz55JMv6dcvs00uISGBadMmcfq0L4sWLWDQoMHKC8a4uDimT59MdHQUHTp0YsqUT5QFFa9du8LEie9y9uxpli5dyLhxb7JgwRLlHXB7+2osWLCkyExJSYlKMaFJk2ZMn/6FMr8/KiqSWbO+5MiRQ0ydOpGlS1dQs6Zbrut9fY9RvXp15s37kXbtOgCZO0188MHb3Lp1g4ULf37ggsKoUS8zatTLSsfF22+/T9u27ZXjN2748fnn00hPT2f06FcYNeplzMwy//Dx87vGJ59M5fRpX+bOncn06f+X5/4vXjzPsGHP8M47H6DVaomOjsbGxoagoEC+/34Oer2eV199nRdeGJ3jexPLnDlfs3fvLlau/IMRI0Zia2vLoEFPMWjQU0rnwAsvjM7TDZKflSv/ZN26v9Fqtbz77kQGDx6GkVHmDLS9e3czc+YX7N27CweH6kyYMDHP9atXr+Cxx57gnXc+wNraGoPBwIYNa5k3bxYXL17gyJFDdOvWo6RPvRCilBq72tKljgOHb2cucHfgViTX7sXTwMVG5WRCFM5gak1yi3FYnZgFZHUp/E1Kk5EqJ6uY+rkNUAoKOoOOfaF7GOw1TOVUQqhL1lCoxMKSQqtUMQHgWuwVwpJCy+W+Z8z4nC5d2hT48dZbr5X5Y77yymtKMQEyF+l7443MLR5jY2MJDAxQjv3zz3oiIyNwda3JV199k2t3hgYNGvHOOx8AsH37v+j1+lLlWbduDRER4Tg4VOebb77LtVigg0N1vvzyG7y965KQkMDy5UvzvY/33/9IKSYAODo68vLLrwJw86YfSUlJpcpWXEuXLiQtLY1hw57l1VdfV4oJAPXrN+Crr75Bq9Wyc+d27ty5ned6U1Mzxo9/W3kHv1q1zPmjvr7H0Wq1+Pg0ZPToV3J1Btja2vHmm+8CkJGRkev7VlKpqaksW5ZZ/Bk7djxDhz6tFBMAevXqw0cfTQNgw4Y1hIXl/fdQt259pkz5RFlwU6PRMHTo03h71wNQujuEEA/Pqx1zr6Ww8Gjpf08I8TAlNxuD3sxeGVueni9rKRSgVfU2OJhVV8Y7Q7apmEaIiuGRKigYDAaee+45fHx8yMjIKNG1u3fvxsfHh1698s5rVourZU0a2FWt7aka2DXC1bJmudx3rVqZrfQFfXh71y3zx+zcuVue27y8vJTPExLilc+PHDkEQP/+j2Fmlnfbpp49e/PbbytYuXJ9rhegJXH06EEABgx4HFtb2zzHTUxMGDbsWQAOHz6IwWDIdVyr1dKhQ6c813l61lY+T0wsvxXO09LSOHEicxGk/v0H5nuOt3dd6tatj8Fg4OjRQ3mO16/vg4WFRZ7bhw17hj17jvDzz4vyHAMwN8/+nqSmln6K0YULZ0lIiEer1TJ06NP5ntO7dz+cnJzR6XT5fg0dO3ZGo9Hkud3T0wvI/XMlhHg4GtWwoZt39guNQ7ejuHJX/i2Kis9gakNyi+w3VbQJoZhfXaNioopLa2RM75p9lfG12CsEJkjxUDzaHqkpD3PnzuXs2bMlvi4qKopPP/20HBI9GBMjE+Z3+lXWUCimUaNeyrWo38Pg5OSc57acxQKdTqd8HhISDEDduvXyvS8TExNlrn9pBQRk/qfn49OwwHOyjsXERBMXF4udnb1yzMbGNt9iR84ugZxfU1kLDg4kLS0NgLlzZ2Fikv/UmHv3wgAICPDPc6x69ep5bsvJ1NSMK1cucfv2LUJCggkNDebWrVsEBmbfV2k7RHJmcnf3wMoq/0XbNBoN9ev7EB5+P99uiPx+riD7+1Ce3wMhRMFe6+jJwVuRynjRsQC+HdJExURCFE9ys5ewOPcrRqmxQNZaCs+A1lTlZBVPP7eBrLmTvcXmrpDtvOIzrpArhKjaHomCgk6nY86cOSxdmn8Ld1E+++wzIiIiyjhV2dBqtNS3e7AXmaL85LegXk45OwBiY2MAsLAovxX6s7oHslrl82NlZaV8npSUlKugUNAL+Jz+29VQlhISsrsfrl0rerpPzvOz5FcQybJjx1Z++20xwcG5t31zdXXj8cefYvPmDSVIm7/ExESAAosJWbKO5zeFpKjvQ3l+D4QQBfNxsaZH3ersv5lZVDh8O4pLYXE0cc3bESZERZLVpWB1YjYA2oQQzK/9TUrjF1VOVvF429ajjo03t+NvAbA7dAcv1X8VI80j1fgthKLKFxT8/f2ZPn06vr6+pbp+8+bN7NixAwsLC5KTk8s4nagsCnqBlpJSdj8TFhYWJCQkkJSUWGb3+V+WllbEx8fl+0I7S3x8XI7zK9b2gzmnKuzcebBM823btoWvvvoMgPbtO9GtWw/q1PHG07M2tra2ZGRklElBwdIys2BT1NSQrO9DRfseCCEK92pHT6WgAJlrKfwwrKmKiYQonuSmL2FxbmGOLoUfSWkgXQr56es2kF+v/QjAveS7XIw+T3OHB986W4jKqEqX0lasWMGgQYPw9fXF1dWViRPzrpZemPv37/Pll19ibW3Nq6++Wk4pRUWVc9u99PS0PMdTU1OIjy+7+bHu7h4A3L59K9/jGRkZvP76K3z88SRlekRJZc2xv379aoHnXLuWeczGxjZXd0JF4OZWS/m+5LfgYparVy9z69bNEi0Q+ccfvwGZ60vMnfsDTz01lKZNmytrTdy/f+8BkmfL+h4EBQUWWFTQ6/X4+V0HMtf+EEJUHvWdrelZL3tR3WP+0VwIjSvkCiEqBoOZLcnNs//e1cYHY35N1lLIT++afTHK8TJqV/B2FdMIoa4qXVC4ePEiACNHjmTLli00a9asRNdPnz6dmJgYJk+ejKura3lEFBWYnZ2dsvBdfnPxDx8+VKZz1Tt06AzArl3bSU9Pz3P8+PEjXLx4nhMnjuHgkLkOQFa+4ra4d+7cFcjcKSIuLu8fuOnp6WzYsOZ/efIuvvgwZS86mP21WVpa0aJFawDWrl2Vz1UQGhrCG2+MZfTo59i3b3exHy9rN4WC1pfYvHmj8vl/v++a/7U5Fuf70KxZC2xsbNHpdKxfn/8fart37yQyMgKNRkP79h2LE18IUYG82jF3IXCR7PggKonkZi+jN7NTxpanfwRd3r9JHnWO5k60cmyjjA/c3Uuq7IwhHlFVuqDQr18/tm3bxscff1zonPH8rFmzhv3799O1a1eefjr/ldhF1WZmZk79+g0AWLJkIRER4coxX9/jfPvtrDJ9vKFDn8bOzo7g4CA+/3wacXGxyrErVy4xe/ZMAIYMGa60/me1w8fHxxVrqsTgwcNxcnImKiqSSZMmEBoaohyLjo5i+vSPuH37FpaWVrz8ctlvo1kSWWtJ3L17N9ftr7zyGlqtll27tjN//rxcXQi3b9/kww/fJT09nRo1XOnbdwDF5eHhBcCmTesJD7+v3J6YmMCSJb+yYsUy5bb/7vJgaWnxv6xhRT6Oubk5I0eOAWDx4l9Yv35NrkUe9+/fw+zZMwB48skheHh45nc3QogKrJ6TNX3qZ3cpHA+I5nxIbCFXCFExZHYpjFXG2vggzK+vVTFRxdXXLftvjMSMRI7ey7srkxCPgiq9hkJpt3gMCQlh5syZ2NjY8OWXX5ZxKlGZvPrq63z00Xv4+9/mmWeewsurNnFxcdy9G0bDho1o2rQ5hw4dKJPHqlbNga++ms3kyR+wf/9ejh49jJdXHRIS4gkLC8VgMNCuXUdeeWW8co23dz2MjIxITU1lxIhhODo6MW/e/AKnKtjY2DBr1jw+/HACly5d4LnnhuDlVRtjY2Nu375FRkYGtrZ2fPrpl8oUDLXUr+/DuXNn+Pbbb9i4cR1Dhgxn0KCnaNasBZMmTWP27BmsXv0XGzeuw8urDklJiQQHB2EwGHBwqM68eT9ialr8eZ+vvfYGU6Z8oHyvs17IBwUFkZaWSs2abmg0GkJCgrl//36ua+vV8+HWrZusWLGM48eP0K1bT8aMGZvfwwAwYsRIQkND2bhxLfPmzWLp0l9xdXUjPPy+Urjq0aM377zzQSmeOSFERTC2oyd7/CKUHquFRwP46emSdUoKoYbkZi9jcW4RRmn/W8vn1A+k+AwHbdELMz9Kurh0x1xrQYoucz2tXSHb6Vmzj8qphHj4KnyHwuTJk/Hx8Sn2x9WrBc8NLw6DwcDUqVNJTExk6tSp1KhRo4y+ElEZdejQiZ9/XkLXrj2wsLDA3/8OZmZmjB07np9+WlzmOzK0aNGKP/5YzTPPjMDFpQb+/neIjo6iYcPGfPjhVObM+T7XFo21arkzdeqnuLt7EBcXy717dwkLK/xd8vr1G/DHH6sZM2YstWt7ExoaQlBQEB4enowa9TLLl6+qEG32U6Z8Qtu27dFqtQQG+hMUlL3zwuOPP8nvv6/kySeHUL26I3fu3OLevXt4etbm+edHsWzZyhK/s9+5c1cWLVpO1649cHCojr//He7du4u3tzfjxr3F77+vpF+/gQAcOXIw17VvvjmBHj16YWFhQUCAf75TZHLSaDRMnDiZefN+pGvXHhgZablx47qSY+bMOXz55axc32shROXi7WhFHx8nZewbGMPZYOlSEBWfwcyO5OavKOPMLoV1KiaqmCyMLehWo4cy9o04QVRqlHqBhFCJxlDB9xebPHkyGzYUf2X1jRs30rBh/nOgT5w4wahRowC4fPlyvlv6LV++nK+++ooePXrw66+/KrevX7+eKVOm4Obmxt69e0v4VWSLiIinYj/jQgghhCgLtyMTee7300qXQht3OxY801zVTEIUhyY1FoflHZUuBZ2tB1HPH5Auhf84HXGSD33fVcZvNnyXYbWfVTGREHlpNODoaFNu91/hpzx88cUXTJ8+vdjn59xWrqT8/f2ZN28etra2fPHFF6W+HyGEEEKIOtWt6NfAiR3XMqcynQqK5XRQDK3d7dUNJkQRDGZ2JDd7GatT3wGgjQvEzG89qQ3lxXJOLaq3wtHciYiUzH/ju0J2SEFBPHIq/JQHU1NTrKysiv1hZFS6L0mv1zN58mSSk5OZNm0aLi4uZfyVCCGEEOJRM7aDJ0aa7PFC2fFBVBLJzceiN81+V9Pq1A+gz1AxUcWj1WjpU7OfMvaLu4Z//B0VEwnx8FX4gsLDEhoaytmzZwH46KOP8qzNMGXKFCBzwcas206cOKFmZCGEEEJUcF7VLenfwFkZnwmO5VRgjHqBhCgmg7k9yc1eVsbauADMrq9XMVHFlHO3B8hcnFGIR0mFn/LwsJiZmdGqVasCj0dFReHv74+pqSlNmjQBMlfMF0IIIYQozCsdPNhx7T76/y2m8OtRf1q7N0ej0RR+oRAqS24+FovzSzBKTwDA6tT3pPoMBSN5CZGlto03dW3rczPOD4DdoTt4xWccRhp531Y8GuS3wf84OTmxcuXKAo9nLcpY1HlCCCGEEDl5OlgysKEz/17J3HL2XEgcvoExtPespnIyIQpnMK9GcvNXsDr1PfC/LgW/DaQ2eFrlZBVLX7cBSkEhPOU+5yLP0MqxjcqphHg4pHQmhBBCCFHOXungifY/aylU8I22hAD+t5aCibUytjz1vayl8B+9a/bFSKNVxjLtQTxKpKAghBBCCFHO3KtZMLBR9oLPF0LjOBEQrWIiIYrHYF4t11oKxrH+mN3YqF6gCsjBrDptHNsp44N395OiS1ExkRAPjxQUhBBCCCEeglc6eEiXgqiUklu8it7EShlbnpQuhf/ql2NxxmRdEkfuHlQxjRAPzyNVUGjfvj3Xr1/n+vXrGBuXbPmIoUOHcv36dfbu3VtO6YQQQghRldWyt2BQ4xrK+GJYPMf8pUtBVHwG82qkNH1JGRvH3sHsxiYVE1U8nV26YWlsqYx3hmxTMY0QD88jVVAQQgghhFDTyx080Bpltyn8Kl0KopJIavFa7i6FU9+DXqdioorFTGtG9xq9lPHpiJNEpkSomEiIh0MKCkIIIYQQD0lNO3OeaJy9lsKVu/EcuROlYiIhisdg4UBK0zHK2DjmtnQp/EffHNMe9OjZE7pTxTRCPBxSUBBCCCGEeIhe7uCBcY4uBVlLQVQWSS3GYcjR1i9dCrk1c2iBs3l2wXBXyA4V0wjxcEhBQQghhBDiIXK1NefJJtlrKVy9l8Ch29KlICo+g4UDyc3GKGPjmFuY3fxHvUAVjJHGiL5u/ZXxrfgb3Iq7qWIiIcqfFBSEEEIIIR6yl9q75+pSWCRdCqKSyOxSsFDG0qWQW85pDwC7QrarlESIh0MKCkIIIYQQD1kNW3MGN83uUrh2P4GDtyJVTCRE8RgsqpOccy2F6JuY3dysXqAKxsPaCx+7hsp4T+hOdAYpuIiqSwoKQgghhBAqGNPeAxNt7h0f9NKlICqBpJbjpUuhEDm7FCJTIzgTcUrFNEKULykoCCGEEEKowMXGjCFNXZXxjfBE9t+ULgVR8WV2KYxWxsbRNzC/sgKkIAZAL9c+aDVaZSzTHkRVJgUFIYQQQgiVjGnvjqk291oK0qUgKoOkFrm7FGwOTMV+/WBMAvY98oUFe7NqtHPqqIwP3ztAckaSiomEKD9SUBBCCCGEUImTtRlDmmV3KdyMSGTfjQgVEwlRPAZLR5KbvZTrNpO7p7HfMhL7tYMw9d/9SBcWck57SNGlcOjuARXTCFF+pKAghBBCCKGiMe3cMTPO/pNs0THpUhCVQ2K7D0luMhpDjvZ+AJP757H7dwz2fw/E9PZ2MOhVSqieTs6dsTK2VsY7Q7apmEaI8iMFBSGEEEIIFTlamzGseXaXwq2IJPb4SZeCqAS0JiR0/4qoFw6S3GgEBiPjXIdNIi5ht20s1Vb3x/TmlkeqsGCqNaOHay9lfDbyNOHJ91VMJET5kIKCEEIIIYTKRrX9T5fC0QB0eulSEJWD3s6ThJ6ziXrhMMmNR2IwMsl13DjyKnY7xlNtVV/MbvzzyOwI0c9toPK5AQN7QneqmEaI8iEFBSGEEEIIlVW3MmV485rK+E5UEruvh6uYSIiS09vWIqHHTKJePEJy0zEYtGa5jhtHXcd25xtUW9Ubs+vrQZ+hUtKHo0m1ZrhaZP+73hmyDYNMZxJVjBQUhBBCCCEqgFHtamGeo0th8XHpUhCVk96mJgndviRq5BGSmo/NW1iIvont7neo9ldPzK6tqbKFBY1Gk2txRv+EO9yM81MxkRBlTwoKQgghhBAVgIOlKU+3yH430z8qmZ3XZc61qLz0VjVI7PIZkSOPkdRiXK5tJgGMY+9gu+c9HFZ0x/zKKtClq5S0/PRx659rvDNku0pJhCgfGoP03TxUkZHxj/IOOkIIIYQoRExSOs8tP01KeubidbXszfn9hZYYG2lUTibEg9MkRWJx6XcsLq1Ao0vOc1xnXZOkFq+RWn8IaE1VSFg+Jp54l2uxVwCwN7FnWfeVaP+zgKUQ5UWjgerVbcrv/qWgIIQQQgghhBBCiJKSKQ9CCCGEEEIIIYQoMSkoCCGEEEIIIYQQosSkoCCEEEIIIYQQQogSk4KCEEIIIYQQQgghSkwKCkIIIYQQQgghhCgxKSgIIYQQQgghhBCixKSgIIQQQgghhBBCiBKTgoIQQgghhBBCCCFKTAoKQgghhBBCCCGEKDEpKJSj5ORk5s+fz4ABA2jSpAnt27fnlVde4cCBA2pHE1XM3bt3mTFjBgMHDqR58+Y0b96cxx9/nNmzZxMZGal2PFGFZWRkMGzYMHx8fFi/fr3acUQVc+zYMd566y26dOlCkyZN6NKlCxMnTuTWrVtqRxNVSHR0NN988w39+/enadOmtGrViueee47Vq1ej1+vVjieqgFWrVuHj48OaNWsKPCc6OpoZM2bQu3dvmjRpQqdOnXjrrbc4d+7cwwsqKr3i/KzdunWLjz/+mD59+tC0aVNatmzJkCFD+Pnnn0lISCjxYxo/SGBRsKSkJMaMGcP58+cxMTGhXr16xMTEcPjwYQ4fPszbb7/NW2+9pXZMUQWcOnWK119/nbi4OLRaLR4eHuj1eu7cucPNmzfZtGkTixcvpkGDBmpHFVXQL7/8wqVLl9SOIaqgOXPmsGjRIgCcnJyoU6cOd+7cYfPmzezcuZMFCxbQuXNnlVOKyi4kJIQXX3yR0NBQjI2N8fLyIikpibNnz3L27Fn27dvH/PnzMTExUTuqqKQuXLjAN998U+g5ERERjBgxgsDAQCwsLKhfvz737t1j165d7N27ly+++ILhw4c/pMSisirOz9q2bduYNGkSaWlpmJiYKL/zrl69ypUrV9i0aRPLli2jRo0axX5c6VAoJ1988QXnz5+nYcOG7Nq1iw0bNrBv3z5mzZqFsbEx8+fP5+jRo2rHFJVcXFwcb7/9NnFxcXTt2pX9+/ezfft2du7cyY4dO2jVqhXh4eG8+eabpKamqh1XVDFXr17ll19+UTuGqILWrl3LokWLMDExYebMmRw6dIh//vmHQ4cO0aNHD1JTU/nwww9JSkpSO6qo5KZOnUpoaCj16tXj33//5d9//2Xfvn0sWLAAMzMz9u3bx+LFi9WOKSqpEydOMHbsWBITEws977333iMwMJDOnTtz4MAB1q9fz6FDh/jggw/Q6XR89tln0pklClWcn7WgoCClmDB48GCOHTvGli1b2Lt3Lxs2bMDb2xt/f38mTJhQoseWgkI5CAwM5J9//sHIyIg5c+bg6uqqHBs8eDBjx44FYP78+WpFFFXE+vXriYqKwtnZme+++w5nZ2flmLu7Oz/99BN2dnYEBwezfft2FZOKqiYtLY1Jkyah0+kwNTVVO46oQlJTU5k9ezaQ+WJv6NChaDQaAOzt7ZkzZw5WVlZERkayd+9eNaOKSi4sLIzjx48DmW8EeXl5Kcd69eql/L22du1aNeKJSiw1NZX58+fz0ksvERsbW+i5J06cwNfXF0tLS+bMmYOdnR0ARkZGvPbaazzxxBOkp6ezYMGChxFdVDIl+Vlbvnw5aWlpNGzYkBkzZmBjY6Mca9iwIfPnz0er1XL27FlOnTpV7AxSUCgHmzZtQqfT0aJFC+rWrZvn+PPPPw/AmTNnCA0NfdjxRBVy4sQJAHr27Im1tXWe4w4ODrRs2RKAixcvPtRsomr74Ycf8PPzY+TIkTg5OakdR1Qhe/fuJSYmBi8vL5599tk8x21sbJg+fTqTJ0+mdu3aKiQUVcXdu3eVz/ObFti0adM85wlRlICAAPr378+PP/4IwIQJE3Bzcyvw/A0bNgDQu3dvHBwc8hwfMWIEAHv27CElJaUcEovKqqQ/a1mvGwYOHIhWq81z3Nvbmzp16gCUaDqrFBTKQdbiKa1bt873uIuLi/LN9vX1fVixRBX0+uuvM2vWLIYNG1bgOQaDAUAWlhJl5ty5cyxduhQvLy/ef/99teOIKiZrOmCvXr3y/YMHYMiQIbz00ks0btz4YUYTVUzNmjWVz69cuZLn+PXr1/OcJ0RR7t69S1hYGC1atODvv//m9ddfL/T8s2fPAgW/bmjWrBnGxsYkJSXJmkUil5L+rE2bNk1Z+LMgWa8bdDpdsXPIoozlICAgAAAPD48Cz3FzcyMkJAR/f/+HlEpURc2aNaNZs2YFHo+KilKKVvl1ywhRUikpKXz00UcYDAZmzpyJubm52pFEFZP1Iq5evXoYDAZlUbK7d+9iZ2dHly5dGDx4sCySJx6Yi4sLvXv3Zs+ePXz++ef89NNPyt9ux44d49dffwVgzJgxKqYUlU2NGjVYuHAh3bt3L/JcvV5PcHAwUPDrBhMTE1xcXAgJCeHOnTu0adOmTPOKyqskP2sA7du3p3379gUev3HjBjdv3gRK9rpBCgrlIGubvvzalrLY29sDmVvECFFevvrqK5KTk7GwsKB///5qxxFVwJw5c/D39+fll1+mVatWascRVVDWVEBjY2NefPHFPPM4t2/fzvLly1m4cGGuNYqEKI3Zs2czbdo0tm/fzsCBA/Hy8iIlJYXg4GBsbW2ZOnUqL7zwgtoxRSXi6emJp6dnsc6NjY0lIyMDKPp1Q0hIiLxuELmU5GetKDqdjs8//xzILLZ27Nix2NfKlIdykDW/qbCFyszMzHKdK0RZ+/nnn9myZQsAb7zxBtWrV1c5kajsTpw4wZ9//kmdOnVKvAKwEMWVtUL1zJkzuXjxIlOnTuXYsWOcO3eOX375BTc3N/z8/Bg3bhxpaWkqpxWVnUajoUGDBtjZ2ZGRkcHNmzeVd4xtbGykC0uUq5yvA+R1g1CLwWDg008/5eTJkwB89NFHJVpwWwoK5SBrzmfWqtT5yZqfYmQk3wJR9n788Ue+//57IHMe8quvvqpyIlHZJSQkMGXKFIyMjJg5c6byx40QZS3rD+aoqCjmzZvH6NGjcXBwwMLCgp49e7J48WJMTEy4fv06GzduVDesqNQSEhIYPXo03377LW5ubixbtowLFy5wFMXNDwAADzpJREFU/PhxvvzyS+Lj4/nkk0/47LPP1I4qqqicrwPkdYNQg06n4+OPP2bNmjUAjBw5kscff7xE9yE/leXA0tISyNzGoyBZ76rIH+WiLGVkZPDJJ58oW5J26dKF7777rtD/pIQojpkzZxISEsJLL71EixYt1I4jqrCsd4QbNGhAnz598hyvU6eO8sfOnj17Hmo2UbUsXryYCxcu4OzszO+//06HDh0wMzOjWrVqPP300yxZsgStVsvKlSuV1dGFKEtWVlbK54V1XMnrBlEekpKSeOutt5StcYcOHcrUqVNLfD9SUCgH1apVAyAmJqbAc7LmQEkbuigrCQkJvPbaa6xevRqAxx57jAULFsh/PuKBHThwgLVr1+Lt7c27776rdhxRxdna2gKZe2IXpF69egAEBQU9lEyiatq+fTsAo0aNUn7ucmrWrBk9evQAUKYQClGWLC0tldbywtZHkNcNoqzdu3ePF154gb179wKZi8/OmDGjVF0wUlAoB1n7d2bNwctPSEgIAF5eXg8jkqji7t69y4gRIzhy5AgAr7zyCvPmzSvR/CchCrJt2zYAbt26RdOmTfHx8cn1kfX7bMqUKfj4+DBy5Eg144pKztvbGyj83Tpj48w1peV3nHgQWQuAZv3dlp+slc4L+5tOiNIyMjKidu3aQME/Y+np6dy/fx+Q1w2ibPj5+fHMM89w5coVjIyMmDZtGlOmTCl1R7Ps8lAOmjdvzt69ezl37ly+x+/du6f8J9ayZcuHmExURffv32fkyJEEBgai1WqZPn06I0aMUDuWqEK8vLwK3dHh0qVLpKWl4eXlhYODA/Xr13+I6URV07x5c44cOcKFCxcKPOf27dtA4dszC1EUa2trUlNTCQ8PL/CcrJ27rK2tH1Ys8Yhp3rw5169f59y5czz99NN5jl+4cIGMjAzMzMxo1KiRCglFVXLz5k1GjRpFdHQ05ubmzJ07N9/phSUhHQrlYMCAAQD4+voqf/Tk9NdffwHQrl07atWq9VCziaolLS2N8ePHExgYiImJCd9//70UE0SZGz9+PCtXrizww8nJCYBx48axcuVKpk+frnJiUZkNGjQIyJzOsGvXrjzHIyMjlfZz2Q5XPIgOHToAsHbtWnQ6XZ7jMTEx7N69O9e5QpS1gQMHArBjx458p0uvXLkSyJzKKruOiAcRGxvLq6++SnR0NDY2Nvz2228PXEwAKSiUCy8vLwYNGoROp+Ptt98mICBAObZp0yYWL14MwOuvv65WRFFFLFq0iMuXLwPw6aef0rdvX5UTCSHEg/H29lbepZsyZYoyvxMgPDycCRMmkJiYiI+Pj/zOEw9k3LhxmJiYcPHiRSZNmkRUVJRyLCgoiHHjxhETE0OtWrUYNmyYiklFVdaxY0dat25NfHw8b775JhEREQDo9XoWLVrE5s2bMTExkR27xAObNWsWoaGhGBkZ8e233xbafVoSMuWhnHz88cf4+fnh5+fHwIEDqV+/PnFxccpc4/fee49OnTqpnFJUZmlpaSxbtgzInE+8fv161q9fX+D53bt3Z/z48Q8rnhBClNrHH39MeHg4+/fv5/XXX8fV1RUHBwf8/PxIT0/Hzc2Nb7/9VtZQEA/Ex8eHuXPnMmnSJLZs2cKOHTvw9vZGr9dz8+ZN9Ho9bm5uLFy4UN4ZFuVGo9Ewa9YsXnjhBU6dOkXPnj2pV68e9+/fJzw8HI1Gw4wZM5T1ZYQojfv377Np0yYgczeln3/+mZ9//rnA84cNG8bw4cOLdd9SUCgn1apVY/Xq1SxZsoRt27Zx69YtjI2NadeuHS+++KK0aYoH5ufnR2xsLJC5XeSZM2cKPd/T0/NhxBJCiAdmbm7OL7/8wubNm1m7di1Xr14lOjoad3d3+vXrx5gxY5QdlYR4EP3796dBgwYsXbqUo0ePcvv2bYyNjfHx8aFPnz4F7gAhRFlyd3dn48aN/PLLL+zduxc/Pz8sLCzo2rUrY8eOlSk34oGdPXuWjIwMIHO7yKJeN5TkjW+NwWAwPFA6IYQQQgghhBBCPHJkDQUhhBBCCCGEEEKUmBQUhBBCCCGEEEIIUWJSUBBCCCGEEEIIIUSJSUFBCCGEEEIIIYQQJSYFBSGEEEIIIYQQQpSYFBSEEEIIIYQQQghRYlJQEEIIIYQQQgghRIlJQUEIIYQQQgghhBAlJgUFIYQQQgghhBBClJgUFIQQQgghhBBCCFFiUlAQQgghHlGTJ0/Gx8eHkSNH5jmWnJxMcHCwCqlKLiMjgzt37uS67cSJE/j4+ODj40NGRoZKyYQQQoiqTQoKQgghhMhl8+bN9O/fn2PHjqkdpUiHDx9m0KBBbNy4Ue0oQgghxCPHWO0AQgghhKhYvv32W+7du6d2jGL59ddf83QnADRr1oytW7cCYGwsf+4IIYQQ5UH+hxVCCCFElWNhYYG3t7faMYQQQogqTaY8CCGEEEIIIYQQosSkoCCEEEIIAObPn4+Pjw8hISEAfPzxx/j4+DB//vxc50VERPDNN9/w2GOP0bx5c1q2bMmwYcNYunQpqampBd7vnDlz2L17N/3796dJkyb06tWLf//9VzkvICCAr776iieffJI2bdrQuHFj2rdvz6hRo/j777/R6XTKuevXr8fHxwdfX18AfvnlF3x8fJg8eTJQ9KKMFy9e5MMPP6RHjx40adKEdu3aMXLkSNauXZvrcbKMHDkSHx8fDh48yLVr13j33Xfp1KkTTZo0oXfv3syYMYOoqKhSPOtCCCFE5SVTHoQQQggBgKurK61ateLSpUukpaXh6elJ9erVcXV1Vc45ffo0b7zxBjExMZiYmODl5YXBYODy5ctcunSJTZs2sXjxYpycnPLc/8mTJ1m6dCl2dnZ4e3tz69YtGjZsCMDu3bt57733SEtLw9LSEnd3dwwGA8HBwZw4cUL5mDt3LgDVq1enVatW+Pn5kZCQgKurK66urnh5eRX5dS5atIh58+ah1+uxtrbGx8eH6OhofH198fX1ZdOmTfz888/Y2NjkufbgwYOsWrUKg8GAl5cXVlZWBAYGsmzZMvbv38/69euxtrYu5XdACCGEqFykQ0EIIYQQAAwfPpyVK1cqxYBXX32VlStXMnz4cADu3bunFBOeeeYZjh49ypYtW/j333/ZuXMnzZs359q1a0yYMCHf+z937hy9evXiwIEDbNq0iYMHD1KnTh1iY2OZOnUqaWlpjBgxgqNHj/LPP/+wefNmjhw5omxruWXLFm7cuAFA9+7dWblyJY0aNQLgqaeeYuXKlYwfP77Qr3HHjh3MmTMHvV7PG2+8wbFjx1i3bh179+5l2bJlODo64uvry6RJk/K9/o8//qBz587s27ePf//9l127dvHzzz+j1WoJCAhg7dq1JX7ehRBCiMpKCgpCCCGEKJYlS5YQExNDr169+L//+z9sbW2VYx4eHvz8889YW1tz6tQpDhw4kO99fPTRR5iamgLg4OAAwKlTp0hPT8fJyYmPP/4YCwsL5XxLS0smT56MiYkJAH5+fg/0NXz77bcAPPvss7z77rtKFoAOHTrw448/ArB3715OnTqV5/rq1avzww8/4OzsrNzWu3dvunXrBsCZM2ceKJ8QQghRmUhBQQghhBDFsnv3bgCefPLJfI87OjrSuXNnAPbt25fnuJOTE+7u7nlu7927N2fPnmX37t35bvGYmpqKvb09AMnJyaWNj7+/v7LF5OjRo/M9p2XLlrRs2RKAPXv25DnesWNHzMzM8tyetaNEfHx8qfMJIYQQlY2soSCEEEKIIiUmJiqLNf78888sX7483/Oyzrl9+3aeYznf1c+Pubk5165d49q1awQFBREYGMjNmze5ceMG6enpABgMhlJ/DVmZitpSskmTJpw9e1YpPuTk4uJSYHYg3wUghRBCiKpKCgpCCCGEKFJCQoLyeXGmHeT3Tn1+7+xnOXDgAN999x1XrlzJdbuzszMDBgzg4MGDxMbGliBxXllfQ1GLJlpZWQGZRZT/ypp6IYQQQggpKAghhBCiGHKua7B582bq169fZvd9/Phxxo8fj16vp0WLFjzxxBPUr18fb29vqlevDkDXrl0f+HGyCgU5iyP5iYuLy3W+EEIIIfInBQUhhBBCFMnW1hZHR0ciIiK4efNmgQWF69evo9frqVmzJnZ2dsW670WLFqHX6+nQoQNLly5Fq9XmOp6WlkZ0dPQDfw116tQBMtdhuHXrVoHTHi5dugSAp6fnAz+mEEIIUZXJooxCCCGEyEWj0QB51yvo0aMHAH/++Sd6vT7PdfHx8YwePZrBgwezbNmyYj9ecHAwAA0aNMhTTADYuHGjsobCf9coyMpaHLVr16Z27doABeY7c+YMFy5cAFB2bhBCCCFE/qSgIIQQQohcLC0tgewFFrO89tprWFpacvr0aT788EOioqKUYyEhIbz22mtER0djY2PDCy+8UOzHy+oc+Pfff7l165Zye2pqKn/++SdffvmlcltKSkqxshbk3XffBWD16tX88MMPpKWlKcdOnDjBO+/8f3t37Er7H8dx/HUXRQaM1OGUSSZJsZgkhc1ikEVE3TIZzTKwWGQ5qw3HYCKDv+EcA+d8J6WMUtT9Db+6pdvt3m939Hj8A+/vZ332/ny+35P8f8Viamrqr88AAF+RKw8AwCcjIyO5v7/PyclJbm9vMzMzk83NzQwODubw8DDb29up1+u5urrK8PBw3t/f02q18vHxka6urhwfH/98++BvbG1t5e7uLs/Pz1lYWMjQ0FA6OjrSbrfz+vqavr6+VKvVNBqNPD09/fKt19fXubi4SLPZzPj4eHZ3d387a25uLkVR5ODgIEdHR6nVaqlWq3l5efkZJSYmJrK/v19q+wEAviIbCgDAJzs7O5mdnU1nZ2ceHh4+bQ1MT0/n8vIyq6urqVQqeXx8TLvdzsDAQJaXl3N+fp6xsbFS80ZHR3N2dpbFxcX09/enKIoURZFKpZKNjY3U6/WsrKwkSW5ubj5dxVhbW8vS0lJ6enrSarXSbDb/OG99fT2np6eZn59Pd3d3Go1G3t7eMjk5mb29vdRqtfT29pY6AwB8Rd9+/MsPnQEAAIAvyYYCAAAAUJqgAAAAAJQmKAAAAAClCQoAAABAaYICAAAAUJqgAAAAAJQmKAAAAAClCQoAAABAaYICAAAAUJqgAAAAAJQmKAAAAAClCQoAAABAaYICAAAAUNp/SvKU544tMxwAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.set(title='Convergence rates',\n", " xlabel='Iteration',\n", " ylabel='Log10 Error',\n", " xlim=[0, 12],\n", " ylim=[-15, 2])\n", "ax.plot(err_newton, label=\"Newton's Method\")\n", "ax.plot(err_broyden, label=\"Broyden's Method\")\n", "ax.plot(err_funcit, label=\"Function Iteration\")\n", "ax.legend(loc='lower left');" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.9.7 ('base')", "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": "3.9.7" }, "vscode": { "interpreter": { "hash": "ad2bdc8ecc057115af97d19610ffacc2b4e99fae6737bb82f5d7fb13d2f2c186" } } }, "nbformat": 4, "nbformat_minor": 0 }