{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

Jupyter Notebook Introduction

\n", "

MCHE 485: Mechanical Vibrations

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Dr. Joshua Vaughan
\n", "joshua.vaughan@louisiana.edu
\n", "http://www.ucs.louisiana.edu/~jev9637/

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For most of our work, we will leverage the great set of tools available for scientific Python. The main of these tools is [NumPy](http://www.numpy.org). We'll also use parts of the [SciPy](http://www.scipy.org). Of course, we'll spend most of our time working in [IPython Notebooks](http://ipython.org) like this one.\n", "\n", "A great tutorial on using these tools is availabe at http://scipy-lectures.github.io" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x = 4, y = 50, z = 9\n" ] } ], "source": [ "# The \"#' is a comment in Python - USE COMMENTS!\n", "\n", "# more comments\n", "\n", "# We have to import the modules we want to use\n", "import numpy as np # numpy is the heart of what we'll use, we import it with the \"nickname\" np\n", "\n", "# Simple math works as you'd expect\n", "x = 2 + 2\n", "y = 10 * 5\n", "z = 3**2 # Exponentials are with ** not ^\n", "\n", "# Let's format x and y for pretty printing\n", "# You can just add strings together to create longer ones\n", "string = 'x = ' + str(x) + ', y = ' + str(y) + ', z = ' + str(z)\n", "print(string)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## This is Markdown. \n", "You can change the \"cell\" type to be [Markdown](http://daringfireball.net/projects/markdown/), a shorthand way of formatting plain text, often with the intentions of later converting to HTML. Many text editors and blogging engines will take it as input as well. \n", "\n", "We can make simple, unordered lists: \n", "\n", "* Item \n", " - Subitem\n", " - Subitem\n", "* Item \n", "\n", "* Item \n", "\n", "We can also do numbered lists: \n", "\n", "1. Item 1 \n", " a. Subpoint a \n", " b. Subpoint b\n", "\n", "2. Item 2 \n", " a. Subpoint a \n", " b. Subpoint b \n", " c. Subpoint c \n", "\n", "3. Item 3\n", "\n", "To italicize an item *wrap it with astericks* and to bold, **wrap it with double-astericks**.\n", "\n", "We can also dislay figures or pictures inline. It can be helpful to include images of the models you are simulating. \n", "\n", "\n", "

\n", " \"Tiny\"\n", " Figure 1: A Tiny Motor\n", " \n", "We can also generate plots inline. To do this we issue the command:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting\n", "We will use the [matplotlib](http://matplotlib.org) library for all our plotting. It's a powerful package and with a few tweaks to the defaults, we can generate nice-looking, easily-readable figures. \n", "\n", "Some great tutorials on the features of matplotlib can be found at:\n", "* http://www.labri.fr/perso/nrougier/teaching/matplotlib/\n", "* http://matplotlib.org/users/pyplot_tutorial.html" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# We want to show the figures inline\n", "%matplotlib inline\n", "\n", "# Import the plotting functions \n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let's try a simple plot." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "t = np.linspace(0, 5, 1000) # Define the time vector (start,end,number of points)\n", "y = np.sin(2 * np.pi * t) \n", "y2 = np.sin(4 * np.pi * t)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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RC4RSWre8AjVS9Ukb3n4/9SxLh27OxPdMut9FGAEScxpWigjtdm5DHu9T2aDQ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\nFzJ8xB4AN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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# To plot, we need to preface our plotting commands with plt (the namespace we imported matplotlib under)\n", "# This effectively says \"use the matplotlib version of this command\"\n", "plt.plot(t, y)\n", "plt.plot(t, y2)\n", "plt.xlabel(r'Time (s)', fontsize=22, labelpad=5)\n", "plt.ylabel(r'$\\sin(2\\pi t)$',fontsize=22, labelpad=8)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That plot isn't very easy to read at all. In fact, it's terrible. We can also issue commands to better format the plot and make the plot a little bit easier to read." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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vTtsPMJC5pT5ctWa2pXaPmeRzMr7ALyiffNzC+GenOs4g+OpuwGZTvHkBAO+V\n8XdnZ+42L1ONzPLhF8WFKfIRFviWvjGMv8C7ET2XXwaSJvg+FVtxMdznnwdQitArr6od9llBJtm0\n9fOykQp7EeRzrGtE3IB4r71G8b2911wNAAj87eWcbS7H4wkqSyQUsN+83oLLH/w7TvTkNmbQCJgC\nppNMMWBKCL70NwCA+5JLFE9SAPhsOwCh114HFwjoHkcmKKVoj7fomFc2UWGx2Yj4svePWSOdPmOc\nBAVcDhtWzi2apFDOKeHlcHrAj/FdrwAAX/5DBZ74Ih/4299UnacVSqnlShnIkUk+wgK/YMZkl7yg\nMJ86eAKIROA695yM8UXJuC84H8TnQ+TQIURPW6/SuRWQk8/geBiD42H43HZUFE6MiSzwOlGS50Io\nwqFz52sAAO81yhd4APBs4ee2AFOQJcn07gitlKQyu6vjFsuTxzvAdffw7se1axXf27l0KRyLF4MO\nDeVsc3nzpvl44MY1uGb9nEnf9Q4HEeOoJWvpZYIpYDoJ6whEHPaH8bWn38fbbxwAAHivulLV+fZZ\ns+Bcvx40GETotdc0j0MpfSMhBMIxlOS5UOSbrHj++1XLcNsliyZZk8xCaJKaDo/Ljh1f+AD++5OT\n+2r63A6UF7gRiVH0DIzDVlYG5zrlkxSQUMCCL+/MSX20J946iQ9971U0nJwaE1Em+Zw8k94CVlXG\nf9bWwRf/9Vx6qap7E48H7ot5lxizgkkjJ5+TSfFfUlZhYQ5oP9UDuN1wX6ZOPkIXg9Brr+U02Huq\nkOndETfKEhYwIVxkvJd373quuEK129UTl2cwB+sOAOR5HNiyqhIux2SVRfiNgtVvKsEUMJ0oaUWU\njubOEew82I0djirAbofn8stUX0N0pcTdZNkkXUyOwIaFZbjt0sWWcXONj2d+IcsLJwZ4JzM3buXr\nKqqA57JLVTfYdtXWwlZWhlhbG6JHj6o6Vwv1rf2glM8SnArIyYdSKj5vC8onW8Cq4rLp8POKrfuS\nS1TfX7CyBHeaX8rFisjJR6j3N69Mei4QFLCuwgq4zz1XdYNtR1UVHDXLQMfGEHrnXVXnZoP/fbMV\n//jTtzASsEZ4Raa5rT2ujFSVTf67L5pZgIf/YT1uf59PcvBccrHq+7vj54R250YBk0NYj06dsU4N\nSqUwBUwnSirhp6OymHdzdRbOhHPt2kmtbZQgvgg5KHcgNNtOdT9alZqaGl3nC4tLZ9FM1e5HACB2\nu6gY5CIlSWBuAAAgAElEQVRjSFgUpSZdKyInnxhHEeMoygvcKPZN7s8pLPA9vhKgYiacK9VXBhc2\nPKG33wFV0FJML1bqEqEEOfl0DvIhD7OLpUMmBBd+T2E53B/8gKb7C+9c8O/Z31xmor51AC29Y5Zp\nmi4nG0qprAsSAC6a6cSMvW8ALhdf9kMl7nPPBTxuRA4eNL3jh7AeMQvYWUg0qt3aMLvECxsozuSX\nwnbhRZqu4VyxAqS4iLeytLVpHosSOof4SdcqLsZM9OvMoJpbyC/8XUWz+IxTDbgvvAAAEHoru/3T\nOI6ie5hXIiqLlMcRmomcfBx2G37+mXPx409tlHSP5LkdKLFFEXa4MHapehcKwDeBdixfDoRCCDe8\nl/kEHdS3DuDq7+3GnmPWaE+lBDn5CHNBZYn0syYsikPeQu0KWDxrMvz2O5rON5LkmFArICebvtEQ\ngpEYin1OyVARIL5hpxSujRtVWycBgHi9cJ93Hn+t199Qfb6RVBZ7YbcR9I4EJ9U9szpMAdOJnhgw\nh92GGcERUGLDcO15mq5B7Ha4zz8fQPatYN3xSXdWml2v1cgUJ5GJWf2dAIDe2dWarJNAkgL2zrtZ\nrYp/ZiyEaIyiJM8l9hu0Opnks2JO0aQSB8lUjvOLUN/68zWPwX1B/N3Zk913562jfRgcD+N4d/pM\nrafePoUH/3QIHGcNS5mcfAQLWGWaueBCtx83vPdnfLijDk4NfQsBwFW7HnC5EGlqAjdoruVpTnzT\neXrQGgqYEtnIdVYIvv46AMCjUTkGAM/FvPclaLIb0mG3obzADUqBnpHsW7KNhClgOvFp2D0IxAYG\nUDbIV/MemLdY83XcF/LWmWxbWboEBWyKdKJfs2aNrvNLjx0EAPSXzNR8DcfcubDPmwc6MoLIoUO6\nxiOHIJt0C6IV0SMfGo2iouskAKC/apHm64gK2Ntva76GEjrjC7ecfJ6rb8fz9R2WqaUnJ5/ReKmZ\ndC4uuudN/EP981i2ZlHavqmZIF4vXBtq+XIUe/dquoZRCFb/joHsZ5srQU42PcPCXJB+nhZCIrRa\nJwHA/QHeaxN+x3wLpWAUEIwEUwWmgOkkUxC+XNxH+K09KB/jd/E9Ae2m04Sba09W40wEF9dUsYCF\ndDYqL6rnrSK9dn0u12T5ZIuEAjY1lGNAn3wiBw9ixnAvAGCAaGtMDIB3oxCCcMN7oFks5dI1FHcP\np3HZAUBZAf87uoetsYjIyeeLH6rB165bhYo0m7FwPHBe2BxqRbTu78megjzsD+Pzj+/D6829aY8R\nXJBdFlng5WTTE5+nZ6YJRYh1dSHW1gZSUKC4sLQUjmXLQIqKEOvsNL2Ui2AUENaoqQJTwHQiVwn/\nwT8dwo0/fjOtXzr0zjuYMc6XDNCjuTuWLIGtogJcby+ix49rvo4cwXAMg+NhOOwEM/K1L3i5pKlJ\ne5sZLhCAp+5duKIhjMegq7is+4K4ApZFN1f3kDLl+Jm9bXi1qSdr41CDHvmE3t2Li4+9g/MjPfhA\nTYXm69iKi+FcuRIIhxGqq9d8nUwosVDOjNfT6rHIIiInn02LZuCadZNrMgH8pjNUtw8A4Dr3HF1j\nEBSwbMaB7Tl2BnUtA3jlUHfaY2YWJWRjhWQKOdkIyv7MNMpxKF67y7WhVnVmdzLEZoNr40YAQPhd\ncy2UgrJpFQVZKUwB04lcFuSrTd3oGPCL5vpUwvUNKB/lLWB6NHdCSOJFqM/OIiLsymcWemCzSJmJ\nTKzQGHsCAJH6BpBwGOUR3h2kZ1EUglXDdfWgOsqWyKFkgQ9HOTzy4mF8+/mDllhE9MgnvHcvZo/0\n4Ftr3brbKwluyPC72Sl3MB6MYiQQgdtpQ2le+sLNwoLZa5E4Fq3yiXXwBT5JcTEci7S7h4F4HJjb\nndU4MGHzW16Yfi7P9zjhc9sRjMQsUYpCTjYD47x1LN1cEK6LK2DxNUMP7k3n8tc02UUsWP6ZC/Is\nI10rovFQFCOBKNxOvhl3Kpzfj0hTE8r9/KSi98FxbagFwCt12WA8xGd7TpUSBwDgdmu31IX28Tv4\nmR5evnoUMPvsStgrK0FHRrJmoVSigDntBF6nHWPBKEYtUCtMq3wopQjv5eXj3qQ+hT4VcfPSkJ13\np2tYiJ30ymZrVljMAqZVPkJ1dPfGjZrjvwSIxwPX2jUApQg3Nuq6VjoSLjt5970gn94R8xvay8nm\nuo1VuHrdbJy7SLpht/junHuu7nEIFs5sxehRSvGb105g92F5q70YA2aRd0cpTAHTid8vnRUjZgym\nmXQjje8DsRgqZ5Xwx+t8cFwb+Gru2bKALassxJeursEXrpSvrUUpxe7DPWImjpns378/7XevHOrG\n53+7D4NpWveE3+Mn+8vn+zB/Rp5kMVA1OGvjCnKWFvluBQkShJAJrhSzkZOPHNHjx8ENDMA2swL2\n+fN1j8NVux4AL/NsWCgFi1amBV6UjUUsYFrlE45vXlzn6LewAIBrfVw+WSoVIsa2ZpJPoXUslHKy\nOW/xDNx33Wp4nJPdi9zYGJ8MZLfDuX6d7nG41qwB3G5EjxzNioXy1JlxbHvlOH69+4TsccLG84xE\n83ErwxQwnaTrBdmdYVclKEpzVvIm+p7hgK70c9fqVYDTiejRY+BGRjRfJx0Ouw03bpov9hFLx4ne\nMXz1D4343gva43uMQq5f2rN17ahrHcDRrsl/K0opIu/xk/1Ht6zFU3dehNkywdNKyKaFklKKvvjE\nk9qXLxUhVqLHAoHeGXt1pkFYiF0bpGuEqcVemWShPCE/0WuhL24xmVEgb1GaJcrG/AUe0C4fMcbI\nKAUsy5sX4V1IF7QuUGGhzYuud4fj4Fy9Ck39Yfx81zFEY9o3HcTthiveoi0bMZRCvbl09cwE5pX5\ncNOmebhp0zzDx5BNmAKmE4dDuo1Nn7DrTbMghuMPa+HG9Sj0OhGJUQz5tdcUIx4PnKtX86b697Jb\nVFIOoVeXFVLpy8qkTfBAYqdUKpFQEDt1irewlJXBrnGiSyWbFspwlEMgHIPHaUd+mrZKAjMtlC0k\nJx85InFXlMuAHbxANi2UwlxQXpDBxSXEgFkk0FuLfLjRUUSbmwGnk7eOGIBTsIA1Gm+hpJRqcEFO\n3XdHeL5dGzbiibda8fgbLdjXoq9gtWChjLz/vq7rSNGrUDaEENx19XJ8/FymgJ1VpMuCFCwSUrte\nSmnSi7AB6+aXoMjnhM8lv3hmIttxYEooj//eM6Mh0xeR5ubmtN+dES1Gk+UjKLCu9esNsbAAgGvV\nyqxZKN1OOz7zwWr825XLMo7XSpl26eRzZjSER15oSttaJByf6F3rjFPARDdkvfGbF2EuKJd41pLJ\nczuQ73EgFOUw7Dc/0Fvu/UlH5MBBgFI4VywH8RpTrsY+uxK2WTNBh4YRbWk15JoC46Eo/OEYvC47\nCjJtXiykgGmRDQBEDhwAALjWrUWBl+/0IWRQa8W5lreAhbOggAnzdNkUybxXC1PAdJIuCP+MjAIW\na2vjLSwzZsBeVYXv3rwOz3/xYt0VzN2ClSVLpnoleF0O5LkdCEc507OF8vKkGwUHwlGMBaNw2gkK\nvZP7DArxX0bESAgQj4evuZOlYOKtly/BdedkttYJSkC/BWIl0snnxcbT2LG3HS/v75r0HQ2FEGk6\nDBAC55rVho1F3Lw0GG+hFCxgmdzDQJKCbIFFPp185AjvjyvH8UX58Olh1Om0sBBCkuLAjJ3bkhf4\nTJuXTYvLMH9GHjYuLDV0DFrQIhsAiLzPx44516xOJH3ofNYEF2Sk8X3DN939Y7xXaEaBvAtyqsIU\nMJ2kiwGTU8AiB/gK6841q0EIgc1GDGkf41zLm/wj+w+Yan0SfrPw8phFujiJhGw8kpOuGGMUd0sZ\nhWBlESZBMxCKfZ4ZM18BSycfwT0qpRxHmpqASISvfZevLzEiGdeqVYDDgWjzEXDjxrrPhb91phiw\n5GOsoCBriTNKLPD8XPRfT7+PLz5Rj3GdWbfCuxgxWAET5qiy/MwL/MwiL5668yJcnab+WS7RIpvY\nmTOIdXWB5OXBUV2dcKnqtIbbq6pgKykBNzCAWEeHrmul0h9/d8oUvDtTEaaA6SRdL0g5BSwsmIF1\nVCGWwl5VBVJcBK6/H1xX+qKC2Ub4zX2j5u7i0/VLk3MJ0UiEX+QBPv3dQISq0+G4Am4GQhFdKyzw\naeUjxExJWIzCjYL7ca2hYyFeL5xLlwKU8hY2A7lk+UxsXFiqqF5ZWZIL32zSyedv+ztxoke6p2U4\nnp0nxH/ZbQSRGEWvzrlAsKgJc6dR9KtQjq2Elj63kf383865ehWIzSbOf3o3Y4QQOJOsYEYirqPM\nBcmQIl0rojOj6QNvhZ6AztXGuVCAuKl+FX/N8EFjJyo1lFlkkR9PY8kQXupyiUk3evw4EArBvmA+\nbEVFho7HtZpXwCImyiahHJu/wKeTT5+MfAQFTIg7AYD2/nGMGuDudoryMVZB/n8XL8JPbj1HTFCR\nY/38EthtxBLtvqTkc6JnFPc/cwA/fOnIpO+4oSHETp4CPG44li4BkJgLBnQu8s6VfOHRSHMzaNS4\nGnb9Msk4VibduyOHEKMlrDviPG2ANdyVpTgw0QI2xeSjFKaA6USqEn40xmFgPAxCgNIU0zaldMJO\nxGiEuBjhHmYwwyK7+Joa6ZplcmUBIgfjyvGKlYaPx7FkCeBxI3aqDdzQkOHXV0KxzwW7jWAkEEE4\nTYusXJFePoIFTEI+goUlvuMeGAvh5kffxNd26J/4hYUpYrCVRQ0frp2Lv997edoimrlESj6n4/X9\npJRJwbLrXLESxMm7j0tFBUxfOIKtuJjPSA6GDC0VIrqHp9gCn+7dkUMMwI9b9oWuDHplAyQF4hto\nAaOUMhckQ56oxG5syB8Bpfxi57BP/BNz3d3g+vtBiotgnzvX8PGIbi6mgKG/Xzr4V846GY5bJ12r\njFfAiMMB5/LlABKKXq6x2Yi4KTBi56sHKfkkb15Sd700GOQXX5sNzmXLAACRGAeOAsd7xnSPR3h3\nIia6iAEYEg9qBFLySZTUkFGOk1z3ZQY+a6IV7JBxNQYXlufD5bBh7fwSw66ZC9LNbT3DAXQMSBcH\nT2z8efmU5LlACDDkD+uqBQYkZB45dMiw+OORQATRGEW+xyFZVHY6wBQwnUjFgJXkuXDe4jJ8XCIr\nTdglulauMqzEQTIuwQJmoJtr2B/GM3vbFDektooCli5OQowrkLKwCBawlRMVMKOsRULcn5ku4kUV\nfCyS027u6y8lH7nNS+ToUSAWg2PRIrHEQWlewsUV01HIGACcK5YDhCBy9ChoyHwXrdlIyUc2uUhc\n4BOhFQk3lwFWllXGu4ivXT8Hr/zH5Vg3xRSwdHPb1l/txWe2vT2pqHesr48PwM/Ph6N6IQC+uHaR\n1wlKobvsia2iArayMtCREcROn9Z1LYHpXoICYAqYbny+yb0R7TaCH/7TRtx26eJJ3wmTRzbcjwBg\nX7AApLAQXE8vYj3y/bOU8vS7bfjeC4fxkkRZAClmWCTTbk2aQpDp4goopWIAvjPJAtZ4ahCXfWcX\nnqtTH/iaipAdZqaV5Zs3rMHvP3+h6YHHUvIRYoWkmlYLlg/BEgIATocNxT4nOAoMpWkrpRRbXh7f\nPDoaReTI5Binsw0p+cgqYIf55IXkzYuR1lbhukZbj1MV/amAlGz8oSi6h4MIRzmk7u1F5XjVygn9\nOY2KAyOEJKz7TcZYKNVkDwsMjYdxOo0F0IpMvSfPYqQLwk+H4IfPlgJGCDF8ohLKAii1mAjxFGZb\nwEJprBgD8YU6dZGPdXSADg/DVlYG28yZ4uenB/2IxigaTurvdSYGepvoIi70OrFQZ29LI5CSj9Cb\ns0SiLICoHK9YMeFzI0triPIx2Q1pBaTkI2Q2p2aocoEAoq2tfI/BJYmNp1FB+EBCAQsb6OaaqkjJ\n5kxSvFSqd0XITk1N/BJj9HRuXoC4BRkwLItYKEy+eKbyueqLT9Tjlp/v0V32JFcwBUwn6Srhp0Os\nAWZwCYpknMv5AM2IxmrJqYiLooRVQoryQjecdoJozNxJsinNTmzxzALMKvZgTulE66WYnbpq5YQJ\nbIaB2ULOpUsBux3R1lZwAWP6MTZ3jih2D1sJKfmkU46BZAVs+YTPjVT4Bcun0ZmQUxEp+aTLUI0e\nPQpwHByLF4G4E9+VGuiCtM+uhK2kBHRoCLHOTt3Xm8pIvjtiTTOJ7O5m3qLrSgmtMNRCGd8YGaWA\nra4qxh8+fyE+t2WZ4nMCkRgC4Ri6LdDrVglMAdOJVBZkOmL9/bwf3ueDY+HCCd+92Hgan/r5HkNK\nN4imYMMUsPRuISm8Lge+/8kNeOBGY+toqWVFiqVE4IEb1mDHFz4wKbAzXfyXMEnpdXEBfPNaR3U1\nQCmix47pvl5r3xhu3fY2HvyTOUH9epCSj7CICLFdAjSpPldaC5gF352pjJR8+tPE5Yjux+UTlWMj\ng/AJIVmJA1NLOMqZboGTkk0iZkpi8xJ/nh3LJ2ZPLqrgrUtKSqRkIqGAGZcksSCeJKEUwUgwaMBc\nnQuYAqaTdK2IpIgejr8ENTUg9omL/55jZ3C0exT1Jwd0j8kZT1GOHDZmEREWRaUWMAA4d1EZ1s4z\nN7DV7ZaOHSCESMZ9JFvAkin2xdO1DXqpnTXxDD4D5CM0PTe7pIQWpOQjKPupz1qsowN0ZAS2GTNg\nq6iY8J2wMTBCQRbfnSNHTV9kzSZVPjGOYjgQASFAkW9il4JIE/8spypgYqbdeFh3kgSQnUxINYwF\nI7j2kd349vPmbnik3p20sa3BYMI9vHhiXPI/nL8Av916PjavnKV7TI4liwGHA7GTJ8H5zYnDKmUK\n2NmFX8WDJgT2OpdPruEiLPKDBpjqHcuWAuCLitKIPtcUpVS1C9Iq7N+vruVPOguYIJthf3hSdpEW\nHPFFPmqAlWVQg3JsFaTkk+fm4z4WpcR9JLsfU+NbxF2vX/+7Y6uoACkuBh0eNqSbRDTGIRiJ6b6O\nGaTKZ9gfBqV8DOGkDNU0FjCH3YZin4tPkjBAPma7iIf8EYwEImgwYKOsB6l3R7ROpriHI8eP89nD\nCxeCpHhsnA4bamYXGpKRT1wuXgmjVHR55hphLjBqs5xtmAKmk3S9IKUQFbBlk33apUYuInl5sM+f\nB0QiiLa06LqWPxxDKMrB7bTBa5H6REpR0y+NGx5GrLMTxOOZ5B52Omwo9DrAURjSYNzIGL0B0WI0\n9VK1peTzqQ9U4/efuxAXLi2f8Hk69yNgrNuBz+YSrGD65XP7L9/FLT97yxDFPdekyifdRoxSimga\nBQwAKuNV/fXWmgKS3FwmuYiFebp/LGSqhVTq3UlnARM8L04NxVvV4lxuvBtSDcwFeZbhcDgUHyvs\nCqQUMKMfHNGVonOiSp50s1G3LJuUlSmvJh45ehQAX60+1T0MJBQcI+QjFhE1oNSBMJ7UjgtTASn5\n2G0ECyvyJz1r6TIgAaDYQBckkCQfnbv4SJTD4c4RdA2pS9Q52jWCT/70Lew9IV1sM1ekykewYJX4\nJj5rXE8PuMFBkOIi2Conu7L+62Or8J2b1mJmkf72So6FC3k3V1u7YUksavC5HfC67AhFOPhD5lk2\npd6ddH0txfivGuXB7FpxrjS2FIVajJyncwFTwHSiNAuSUiouuFIvQnG2FDCdGSmDMllpVqdZhfIZ\nPRJXwJYulfy+OB7zYoSF0j5vHojPx9dqG9BX2uJskU+6DEggoRAYv3nRp4AJ4yn2OWGzKd+87G8f\nwoneMbzaZEwdP62kykcw+FSWTFSkROvk8snuYQCorsjHZQbEGAFxN5eBSSxaMDKxQCtS785AGgul\noIBJhb4YjWihPGxsQ3ulCBtRpoCdJUgF4ftD0cmViDs7QcfGYCsrg33GjEnnGG0BS8QZGbOITEUX\nV15enuJjBQuYc5m0Amaom8tmS8Tp6bRQilmDU9ACplQ+NBBA7FQbYLfzhVJTEGJe/GFjav8YFaMn\nuIfVNnoWYg6NiJnSQ6p81s0vwbdvWot/3TzxHUkX/5UtnPFNkrBp0soze9tw86Nvqs6eFeZCM+OM\npN6doXE+PKLYl0YBy4kLMm4BO9xsiouWuSDPMlJjwAbGQrj2kd341vMTg0QFRcgh4X4EkrM3jNlV\nGRVnJFeZ3OqoiQHLZAETTdsGJEkAxrmIBzQqyHuO9uHbzx00NXtSqXwiJ1oASvkgYomYy4pCDz6/\nZSm2Xr7EkHEJSnjk2DHQmHY3k1xNMzlK8nhrq1EuVa2kysdht+HylbMmu7hyrIAJmxdh06SVXYe6\ncerMOFr71PURtYIFLFU2lFIMCy7ivESGKjc4CK67B8TrhX3evKyPy15eztdqGx0F160/iUUtYhC+\nyV1YlMIUMJ2k9oJs6R2DPxxD19DE+IREAL68hcWoXZVj4ULA7UasowPc6Kjm66Qza08F0vVLkyKz\nBcw4FyRgvJtLrXye2deOP793Gu+ZmM2lVD7RY/LKMQDcctFCbFlVaci4bIWFsM+ZA4RCiLae1Hwd\nLeVbAOPLnmhFsXyOCO9O9mOMgIQFLKLTAjYkuojVyUcsLmtip49U2cQ4ikiMg89th9eViEsW47+W\nLZ3QgiibOJbyG6GICS5iVobiLCO1FVG6mJyITAA+AOR7HHDYCfyhmCFp68ThEGu+6Frk41bk2SX6\nA2hzzfj4uKLjuMFBcL29/C5x7lzJY4RFdNhgBUyPmysa4zASiMBGgCKvM/MJSQjlHsxc5JXKJ3qU\nn8idS42xcClBsFTrkU8iQUKddVJ41sx2QSqRD43FEGk5ASBeByoHiO57nRawIb/gslP37ggxh8MG\nZERrJVU2DrsNX7lmBf7zoxM7rIjrTg7cj+JYlsTlc+y45mv0jQTx1T+8h4MdQ6rOy3M74LQT+MMx\nBMPWL//CFDCdpFbCT2cxEiaLdJkohJDExGuUFUxYRHRMVDedNw8P3LAGH1o7W/W5rxzqxp6jfZrv\nrZcaiUnnu386hH/9zd4J8QliBuTSJWl3iRctq0DtghJ8sGam5PdqEZ6DyJEjmmMlxCDvPJeqIG8g\nsUEYMMilqgUp+Ugh7KQdOVTAEqUotG9etLrvi3x88dKRQMSQ0g1aUSKfWEcHEAzBNmsmbIWFORgV\n4FiwAHA6EWtvB6dQiU+F46hYUkatBUwoQmvUZkwLUrK57pwqXJ6S7GCGAiZslCJHtVvAXm3qwe7D\nvdh5oEvVeYQQw2NCswlTwHQSjU4UspRLiMZiiMTdKE4ZN4rhpSjiO9Loce07kXyPE1tWV8LtVFcD\njOMovv7sAfzX0++bVi+nv39iGj+lFH99vxMNJwcnWBlFF4qMbCqLvfjZZ87FuYuUl7aQwz5jBmyl\npaBjY5oLfuopkFtscMyhFlLlkw7RArYkvXyMxohSFOJmTGWChN1GUOh1glJzrSxK5CMsss7FuVOO\nidMJx6JqANCcCTkajCDGUd5iorINj1j2xG9t2QBA9AQ/98ttXtrOjOO+HfvR3q9NmU3FsYS/lxA6\noAVhbsv3qLNOAsAXr6rB1ssWq7Y8mwFTwHSSGgMmlTUYO9UGBEOwV1bCVlSU9lpG+68Fl0BEhwKm\nFZuN8C7VcAxjJnWmT42TEIrKepwpcRKCBSxHMSwCeuXjj5vYywuU9yMVKLHAIqIkxoiGQoiePAnY\nbHBUL8x4vFEIshEWMC3oKRFitDVcC0rkI2zucmmdBJJr6Wlb5IXnPjlgXSmCBcxMF7Hi+Lzjcffw\n4vTu4d2He/DygS682GhMg3Nh46+nnVe6mnNKuHj5THzm4snZ0laEKWA68fl8E/4tZZWIHEu4uOQ4\nf0k5SvJcqCrzyR6nlMROJPcKGGB+QOSaNRObgQsuoUl1chRYwLKBMClqtVCumFOEf75kEbZepj72\nxgrp2qnyaTg5gP94qnFCBlO0tRWIxWCfP39SG5VsIpS7iLaeBI1q20AM6bBQlligFEWqfKQQLFBy\nC3w2EBIytIZXCH/XIg0LvOCyNKIrhlaUyIYbGgLX18fHtlamT1AR4kGNetZss2aBFBSADg2BU2ip\nS0WMz5uCyV9qYAqYTtIF4SdPutETfDugTJPUzefNx4tfuQRVZcrrV8nhmD+frxrd0WFK1Wiz6+WE\nQhPda+lcdmJ8XpoMyGzh1KmAuRw23H7pYiyfk96qmg4rKGCp8nlmbzteaepB46lEcdqICQH4QLyd\n1+zZQDiMmIps2mQE92GhV7uL2MwkiVT5SCHKZ4m8fA51DOGP+7T9HaVw6ixFoTUDEgAWVeTj4uUV\nuGbtHE33NgIlshHXnUWLZDMgjXapEkISm3+NcWAJ+ai3UE4lmAKmk9RK+EJMTbLbQTTTV1dnvJ6R\n7X6I08kHrFIqvoy5xOxFvimlHYZU1lNsYADcmTMgeXl86YEcIijkERMslGJlfxMX+Mny4ceS50m4\nh6NJLaJyjWMxbwXTKp/RIP+8FWlYRKzggkyVTyqU0sTcliED8tGXj+KhvzShpVddza10iJl2Whd4\n0QWpXgFz2G146BPrcfP58zXd2wgyyQZIhDYIz3E6irPgUk0E4mtTkIVyP8wCxpAlNQtycHzypCso\nP84cm+kBY2JZtGL2Ir8ipW+g4DJIdjtET8RjJBZV57zXpZmyKbVAz7RU+QhZZUVJFqOEBSy31kkg\nyUUcf0bUctOm+fjkBQtEF48aRBfkuHlurmT5hKMcfr37BFqTFCiupwd0dBSkuBg2ie4eyTjs/LvV\nN6KuL2ba682fx1v3T58G1WDdFxRbLcqxFUh9d6QQ57YM644wHw4bGA8qWsA0WvdF970GC+VUgilg\nOkluRRSNcRgPRWEjQIEnWQFLLPK5RoxlMcHKYvYu3u2emAWTWOClZJP7oE37nDkgHg+4nl5wIyM5\nvbfPbYfTThCMxBAwKV17knwCEpsXIcZIgXu4uXMEpwf8ho1PfHc0LiKfvXwJ7rxSW2LHxupSFHod\nWMG2o9QAACAASURBVDY7N6UdpEiWz5tHe7H91eN4cs9J8TPBMuhcsiTj5sXo9krE6YRj3jzeun/y\nZMbjUxnUEeRtBVLfHSnEdyfD3JaN1ldOHS7IWFKJkKmqICuFKWA68fsTE34i5iPRfDc2MABucBAk\nLw+2WcY0pFWD08RAfCH2ZThgjgK2f//+Cf8WdniFyQt8SysAZe5hoyE2W9Iir83KovnehCTaK5lk\nZUmVz0iKi5hGo3wQPjIvIsFwDLf/8h186XcNho3PzHdn/YJS/O2ey/DBmoqc31sgWT59I3xohTup\nZIO4wCsowJpY5A20sgilKDSEVwxP8SDv1HdHCmFOyeR5ETakw/6IYSWD9FTDHw1EwFGg0OuAwz69\nVZTp/etyQHIvyPF4uQWruLiApDgWE9xciYKF5izwqf3SRAuLpAUs9woYkBxnlPu2HYJ8RkxSkJPl\nE4yXCHE5bPDEa87FOjqASAT22bNh88p3YiAEiMQoOgb8xi0iSe+OGbXszJgvkkmWT0I5TprbjikL\nwOfPM76/pbh50eAiXjuvGOWFbqybX2LYeHJJ6tzW3DmCY90JKzoNhxE9dQogJGP5FqfDhjy3AzGO\nGlYySLTu9/aCGx5Wda4Y/zVFrZNqYAqYThyORHzH7BIvNq+ahX+8YIH4mZI6LNlEjGNpaVXdWLhv\nJIhf7T6uOU5IVMBMStcuK5tYNHVYIvU8OVNICf1jIUMXYzFWQmOckR6WzCwQi36aQbJ8BCtpkdcp\nKh6ibBRYJ91OOzxOO6IxKtZH04utoiKeTj+sOZ1+KpMsn5F4QkGBN6l+3jFlAfhAtixggoKs3gL2\nsY1V+POXLsHcUmNK/uSaZNlEYxw+99t9+Pf/rU98duoUX75lXpWi8i1ivK5RLmKbDfaFvOInWLGV\nkojPYwoYIwPJWZAOuw3funEtProh0U9QtLCY4OICAFt+Pl8DJhRCrK1N1bnP7mvHY6+eUN0OQiDZ\ntG0GzSl9/FJjjGg0KsaPKJHPuyfO4Jrv7cbv3z5l2BgTMXq5t4D9x0dX4vm7LsbsEnMWoWT5DEm6\nhwXlWNm7k7DoGZhOL2xgTJCP2STLR/ibFiRbj1uVb16K8oxv3yO6IFtyv3kxm9R3ZzwUBZe0LxSz\nUxcp2/hnJRC/WpCPSgVMR4aqwOkBP5o7cxtXqwVNChghZB0h5HpCyJfj/11PCFln9OByCSGkmhCy\nWe15tgwd5hMvgnmVecVyByrjjM7EC2K6VLbqECgSCxaa4+LKy5tYT20kxQUZa2/nXVyVlbD5Mish\nZ0b5v8fRLuNe7ES7qNwvIg67DTMKzGvXkSwfYeKf4B5uUW4BAyBa8oxcRJyLzYnRswLJ8hlNim8F\nAG58HFx3D+ByKSrfko1Ab3GBP9FiWrszs0iWzaBEzaxE/JeydScbpSgE16fwHiulLJ/vhVpTqT0B\n5Su/fw9bf/WuGBZkVRTnR8cVrK0A7pA5BgC2AXiYUnpS7+D0QAi5A8BA/J/VlNKHM5xSC+AxQkgx\ngCEAdQDuoZTKRvUmx4BJYWYJCgHH4kUIvfEGX+5gi3IdU1wUNZqCZxS44XbYYM+gpGaL1DiJDQtK\nAQrMn8FPXmIAvkLlWLToGehSdSxcCNhsiJ46BRoKgSjIbhKoa+nH3FIfZhXLx0dZlWT5iC5IKfew\nQgVMkI+RFcoTmxdzukmYSbJ8RuMLmZDdLSZHLFgAYs/cJzYbLkjbjBkghYWgIyPgzpyBvbzcsGtb\nnWTZDEnUzIqoDH0pzqoFTJ0CtmZeCV748iW6LGDhKIdQlEPfaBB5nnzN18k2ilZGQsjPAdSDV8AI\ngGEArQDei//XGv+MAPgsgBOEkJ9lY8BKiCtfoJTuoJTuALCLELIt03mU0hIAJZTSEkrplkzKFzC5\nF+SE60UiiLa18YGQCxcoGvsTb7biYz94Df1jxjVJTrwIJ1Wdl4iZ0hYjlOd24KefOQcPfcIc42hq\nv7S7rl6OJz93odhYPOEeVtZjMBtmeuLxwD53LhCLIaqi4np7/zg+/3gdvvOnQ4aNJdcky0feAqZM\nPqIFzECLq2OxvlIUU5lk+YykWMAS2cPKZJMNCwshJCkTMvcWymF/GNEYl/nALCD17kxIkDihrAir\nwJJZBfFrGBcPqtUFCQCl+W5dSSjFJscfK0VWASOEFBJCjoNXvL4HYAt4BaWUUrqYUrox/t9iSmkp\ngJL4MY8A+Cwh5CghpCDbP0KCrZTS7cI/4oqUItMPpXRIzY1SWxElEz11CohGYZ87FyRDFpfAe6cG\n0T0cxKEOdZkjcgjKn9pgSKmsQbWsmluMBeXm7EDGx8dlv4+oDMBPWFiMdamK8lExUXUO8cUnY9zU\ndb0ky2fEPzE+j/P7EevqApxOXkFVgBgDlo1dvMp3ZzqQLB+hqn9BvEuBqBwvVL95MTSJpVrIhMxt\np4/+0RCufWQ3vvnHgzm9r8AE2QQmyobvUKDOAvaJ8+fj+bs+iIuWGVf2xLkoYQHLtYs4G5vlbJDJ\nAtYAYBd4peurlNK/U0rTagaU0uH4MfeAV8ZejV8jZ8RdiLUSXw1pifHKRGol/GS0lDgozIYbJT5J\nxtQqYBI7q6lETU2N7Pdq5ZOtshoODdlCIxIWo6lGsnwqivj3aFk87iPWehIA38+UOJRFShRmw0U8\nbx5ACGLtHaAy1u5UgpHYhKbiUxFBPpTSSUH4auvnuRw2+Nx2Q0sdABMX+VwyHIggEqM4YmA8qBqS\n351U2XC9vYkOBaWliq5HCMHMImNDGWwlJbCVlICOj4Pr7TX02plIJICZ1+lDCWkVMELIVwA8RCn9\nrJzSlY64MrYVwMOEkNv0DFIl1eBjuFIZgLRiJkII2Zz0391xZU6WaDT9ZCLuQhRmogDZeXDsc+fy\nbTu6uhQ35U6edM0qU6CX/gylA4TsKaUWsHyPE4Tw8TBGuh5EBUyFBWw4xWI0FUmWz7Xr5+DFr1yC\ny1byxYojmjYv8aQPo13Ec+YAHIdom3IX8RefqMcNP3rDtC4DRiDIJxiJIRqjcCfVaBNjwBS6IAFg\nbokPNgIYaQtJBOLn1gVZlAWXqhqS3x2hREihEJ8XV0adixaZXktOaxyYXgpNrkGplLQKGKX0e5TS\nx/TegFL6GKX0l3qvo4JSJILvkxkCUCbxuUADgBZK6S5K6S4AOwA8LXUgIeQOQkgdIaSuu7tb9Me3\nt7eL6cH9/f3o2bcPAEDnVaG+vh6BQAAcx6GxsVF8gZqbmyecH/bzum53/wgaGxvBcRwCgYDi85Pv\nL5wfjEQQnTkTABBpaVF0fltXL2Ichc9lRzQS0nV/vePXev7hw4fTnn+mrQ1cTy+o04muuBs50/3D\noaAYhNzW2WvY+AcLeC/9ePNhxed39fPPScQ/Ytm/f6bzheOF88cHe8XzRw/xsW32hQsV3z8WHAXA\nWwSMHD+ZPw8A4D9yRPH5R7tG4A/HEAxHNd//8b++g2u/9yrqjveY+v70DfL9H/M9DvF8QUE+GYsp\nvv99H63BT2/diJYjhwwbf3s8wSd6oiWnz28skHjWTsXL++Ty/i1xhaa5uRndZ3h7QzQ4iubmZkTj\n1uOR4iLT33+hFtiJV3fn9P4u8BufIX/YlN+vGEqpYf8BWGDk9TSOYTOAExKfPw3eoqfmWicA1Mod\ns2HDBpqO3g9/lHbMnkuDb7yZ9phUntnbRjfd9xL9zvMHFZ+jhDOfupV2zJ5L/X95QdHx7f3jdNN9\nL9GP/eA1Q8eRS2KxWNrvQu+/Tztmz6Xdl16m6po3/Oh1uum+l2hr76je4YlEWlpox+y5tGvjuYrP\n+f4LTXTTfS/RJ99qNWwcuUZOPv13/hvtmD2Xjj35O8XXe+1wD91030v0rifqjRieyOBX76Uds+fS\n0W3bFR0ficbopvteoufd/xKNxjjN9/3ZziN0030v0V/vPq75GnoQ5NM/GqSb7nuJ3v7LdyillEb7\nB2jH7Ln09JJllOO0/z4j4Px+2jGninbMW0C5cFj5eQaM+7Jv76Kb7nuJjgaU39cokt+dr/7hPbrp\nvpfozgNdlFJKh779Hdoxey4d/sF/53xcqYz86Me0Y/ZcOvTNB3J632fj6+i3nzuQ0/smoUjHUF0f\ngBDyYNJ/X45/djshJAY++zFmZgZkHCnHdzEAteWshwBslDsgOQh/2B/GeCjhclBT5FMgW6Zt+8IF\n/JgUxhnpzYC0AqFQ+hgcrU24s1GKwl5VxbuIOztBFbqIpRpXTzVk5dOiLkMV4OsHAXwKupGojdFL\nLtlgt2l3AWUjpk0NgnxK89345W2b8MANawAkYkkd1ea0V0uGeL28izgaRfSUskLTrzb14MqHXkHj\nqUFd9xa6AhgZr6uU5HdHDMKPj0ewgCnNvM8mZrkgze7CohQtBZoWAbgHwI0AWgghC8HX/gKArwI4\nB8C5hJDvGDNE1dSBV7ZSKUWahIB4EVap0IQBSLszRYRK+OEoh0/85C38y2/2AgC4kRG+fYnHDdus\nmYoHL2bamRzoLTy4RqYl55qmpqa036mtMSWQlVIUDgevhCGeOasAqbINWnjqnVP45rMHwJmQTZlO\nPpRSTU3SV8wpwp1XLMXWy42tuZdoqXJS0fFDBm1espGQo4Zk+ayqKhaDtBMZkAtMGNVk1FbE39fS\nj5FAdELvRC2YKZ9k2UyKAUuq0WY2ekpR6CEbGdHZQIsCtg/ALsqXnngWwA3xz4coHzfWAOAm8Apa\nzqF8GYkWiQD6YsrHdkkxAL7URiobkSGLU8iC7B8LYXA8LFYlFhZSx/z5ICoKkWZLc1e7ExEWeCGw\neSqyYsWKtN8l2txos4AZPemqVZBHJAqXauGPde148f1OtPXLl+zIBunkww0MgA4Pg+Tnw6aiuCYh\nBJ+8cCFWzc2YO6MK1ZsXg5Rjs1Pp08lHbYeCbKN2bhuVaKukBTMtlMmyEUrRlOa7QClFTPC8WEAB\nEz0vp06ByiSsGY2wbk1HC9gdmFgNfwv4xJbkulst4LMRzeIhAPcK/yCE1IIvpyH8u5oQ8rSgpFGJ\n2l/xYq7/F/8taRFaEaVOuqIZWOVLUCQ8OAa7IMW2EAp38U47/7uqpmizWgBwp1SVp0m1aKLxwFm1\nu3ih2vRYMFsK2ElFxxu1yOe7ebeFGRNVqnwEkntAmu3iAgDHvCrAZkPs9GnQpN6v6RBbXulUjs22\ngKWVT6t662Q2EebY2Ell1uPRFIuRVrK1GVNCsmy+fPVy/NfHVmFmkZcvQREI8CUgio3diGjB5vXC\nPns2EIkg1tGR8fhIlMNXfteAP+5TnnEshViIdaqWoZChmk5sMyTU1topfEAIWQ++Qr4pUL4I64l4\nOYkbAGymfEkMgWrw4y5NPideeuIOQsjd4C1mUlaxCfj9fgCTJ92YYAFTqYAVJlnAkhUGvdgrKwGP\nG1xfH7jR0YzHX7K8Aj/+1EbcctECXfellOK3r7egrkVt+J1+9u/fL/7/r3Yfx4e/n+gwEIvHizjm\nzVN1zavXzcYlyytwwVJj2544qhcAUO8i1uvmMtPKkiyfZMxuYJ8Kcblgr5oLUCoq7nIYFT9p5gIP\nyMhHcA8rLMKabYQ5NqpQAZNqLK6FwiyFiyghWTbrF5Ti2vV8P05h/rBbwPoloMYNeaR7BG8c6cML\njad13bPI54LDTgyPBzUaxb0gk2glhKyllL5PCPm48CGl9JWkY74L4Be6R6cDmlQJX+K7XeALxaZ+\nnqlf5CSEXpBiLzvBAqbRDOxx2uFx2hGMxOAPx5Dn1iKiyRCbDY758xE9chTRkyfhWr1a9niH3YZz\nF8lV7VBGx4Afv/j7MSydVYD/+ZcLdF9PDcn90t462oczoyF0DgZQQsPgBgb4+LwKdZWfF88swHc/\nsd7ooapyc0VjHMaCURDC1ybTg5lWltRenQKJIGJrLPAAP5bYqTZEW1vhXLpU9lijrJNmW8Ck5EMp\nTVjAFi7I7YDSICgbSuMnRwK8K0xvfUNLvjvCuqPh3XnjSC+eq+vA169frVs5TcZRvRChN9/kLduX\nXSp7rPC3zPfoW/dcDhvuv3417BawoMuhxQL2VQCvxPtDCnXCHgYAQshlhJB94K1L+4wZorVxxKt0\npxbGFF4ELTuRrFdcz2FGitvBF240srelUsrKEgpk8qIYixfUdFTNs4SLC1Anm0iMAyFAWb5bV5Yd\nYG7F6GT5JKPVepxN1CjIw1lwQRppDVeKlHy4nh5Qvx+20lLYSibtYU3BUTWX71bQoaxbQWpbJa0I\nNQHNUMDSvTt6MiBfer8Tbx3twz6DvRXiu6OgWG6irZJ+BXDLqkqxsLNVUa2AUb659c3gG2/vAt93\n8V5CyOXgi5cuAt+Y+5X0V5k+CFmQIylB64mdyALV17xidSVqZheivEA6BkMrZmSkZMulqoTkonjJ\nLrtoG7/A21W6H7OJfc4cwOUC19MLLkMPS6/LgfuvX437r5e3YirBzIrRgnza+8fxr7/ZK5YFENx8\n9nnSu3wzSCjIJzMeKyizejOInQ4bfC6+fU9yeZtcIVVUUkt2arYhbrfYrSDWIe+6ojTRCkmvBUzY\nKFtFNoD22GMAorfFaIVSjYVyNG6dNNICZ2U0bQHiLrxdKZ/9HdL1t6Y1YhB+IBH3wfn94Lp7+EbC\ns2ervubntsi7OLSiNtDbCDxOO9xOG0IRDoFwDD6DXKpKyMvLAzDZZecX4r/mW0cBI3Y77yI+dgzR\n1pNwrVope/xVa9Q/V1Jko66ZUgT5vN7ci4aTg3jjSC/WzS8R6zmpjc/LJqosYMJmzIASLoVeJ/zh\nGIb9Ed3uZrUI8klGr/vxzw0d8Ljs2LKqUsfIJuOYPx+xjg5ET56UrR3nD8UQ4yi8Ljscdi0OoAQX\nLi3HpStm4kNrjXkX1SAlGwCJDMiFC1RfsyBbGd4L5gNQpoCNBI2zgE0F9D2BSRBCCgkhhUZdb6og\nxIAlxxWILpR580DsdtPGlorwUqpp+mwEQrbRqMGZg5kQ4iRGkszadhtBrM16CzyQkI/apul6SATh\n594FKchnyJ+QDzcyAjo0pCk+L5uokc14vP9jiQFN7AUlzipxRqJ1cv581dfjOIrv/rkJ33ruoOHW\ncNHKEldA0mHkAl+a78aDN6/D+gW5tztkjM/TEvqSpc2YIz7WWMfpjKUoEv2Hc7dRNxMtlfC/nOar\nmwGcJIT0E0K+pG9YU4dwPOYgOfNJT/xXNjEjBgxI3lnl1lQv9OhKzRiMxj+3W8gC9v/Ze/PwSK7q\nfPi9VdWL1IvW0Wi0z2aPx/Z4vDHeANvYQNghYIctIRAwhB9ht8OSCSEhbIEvEDAYE9aw2gRDWAbw\nivE+Mx6PbY3sWaXWPtql3qvqfn9UV3VJ05J6ued2t5j3efTYI3XVLenUvffcc97zHqBwvSkRsNMw\ntnq7TDj2iWULWOyG11pXd8Xw8wBXt4I8Gtpft6sbL7+gHed2li4DUE6it22f3z4xjJ89ajle7sNl\noVAUBo9qRcNjKUPcg8J1uFylEnKpany1wraNG+bJk+CxGFh9XVH8PKp3jdXUQGltBXQdxtDKKeJ5\nxwE7HQFbDp/N9U1uNd1uhKWE/64yKuFLhd2KyNnkazzOIlBJJGIAUNavB6utBZ+ZgTk7K21cm+wq\nOwIWzXCpllalFStBQY3yOGAZ25Rhg3fs43KQ7eikukyV12rQDRN3Pz2KKcFFH+5uBcYqUZbnbWvB\nx155TskpLgB4wfZWdDcHsLElWPK9CkU0GgXnHJ/55dP44m/7YJo8e3gpcu5QbfJaJiK3WgRMlAZY\nuRHNwRMtpQIScB3GCNaCfNOQThuv0w7YsljxWJoRLr0FuZXl1xxsJfxsFaS3onpxucEYc6I++ZZs\niwDlxF4J27ZtA7BYo42bZsmbCBUKLacXAaeSS7JzDGTt41YmtwskiuXnPXZsEh/96RO49Z4jYh7S\nBcdBXmWTF4lXX9yJn7znCrSE/dLGtLFt2zbEUgaSugmvpkBRmOvwUpyDHCbqn5gVYz2x4ufm1gjJ\n2547bpTagoiKAwbkL5YrsgqyGrBiHDbD6XKXuzAAnDF2HnI7Yo2Zz78jx8/WJPRMTjuW4X3U13qQ\ndjTACudJUEPr6oJ+qM9aSHfskDJmqExprsnJSTQ1Nbl4BR6rOCKVgtLcDKW2slT+Ncc5zq+psAg4\ntpGcHgay9nE3ry41Omm3tByZWV2xvlBoPd1IQq59yonJyUmkVWuOhPwemPPzMKenS+LnUUXAnINl\nJAJuGMtyb8/cEMbmliBecHb+/XkrEfbcGZ9L4PETU3jB2a0lVUACtOluJ0K5yuHS6WtZ5SnifLHa\nb3ktrJTjJljthgDL8VqxP2LmM7es8pk1AZsD9jdXbMJsPIW6Wi9GnT6QPWV8stzIZyIYJsc37j6M\nXVuacYEAgmm4THo5kUgETU1NTtugkF8TIkGhGyZGZuLobMpdiVQs1LY2QNNgjo6Cx+NgNTVC758L\nQZ+GzqZa+D3yi0Vs+8y7iLel8vOy6vHiiwpsp9CQGKEsJyKRCGrXW+fvUI2W1c8rgZ9HFQ1XAgEo\nLS0wx8dhjIxA6+jI+bm2hhr84N2XCx27HLDnztfvOozfHBhGY9CHzSX2gAwTcnXVPB0wR4bidAQM\n4Jz/DMDPAKc34tdhOWLLkVRmABwD8Bjn/PMCn7NiUZuJolx/qfWC8WTSIhqqKtSO9nI+Wk7kk4J8\nMjKD795/HM+MzAlxwEJEaYfVsCMT4XNry+gCJCi+9LtncNsjA/jODZdgW1td6Q+aAdM0qB3tME70\nQ49EVlVcFwFFYfjB319eFqFP2z7uyrRYiREwylO8M3fyaEe0FrBjxw48ntFmC/td+nlF8vMA4ihL\nTzdS4+MwTvQv64CtFdhzZ2zWivSanJfcQYLaNkAeRRKJLB1BBB48fBJdTQF0VGhP47w5YJnWPi/M\n/P+WZb4u4pxf9+fifAFZEr4NPRIBOIfa0Q7mLb0MXTTsCJixQhplKmoRmL2amKiIfZqRzQFLJq3f\nw028FSFBYfP9jp9cWTC1GGQjlPI2ea+mwFeGCFgymYRumIglDTAG1HoY9EzD3mI3eaouEkB5bFNO\nJJPJRfI6Ig4vUtJcEjl65YKzttmcKZ+Wrb7f2FPUPWu9KlSFIZE2hPdQzO47/Sse9jqbarGpJYha\nb+nr0fB0HB/4n/341B1PlXwvKhREws8IsN666gf/jGAr4dsoNQ9vwzA5SVTCTouuFAFbcMLAYvLw\nnU3W6UN2mqu3txcA8JzNTehZF8BzNje5dIxK2UToInr5pLn6hmfxyJEJ4WPLRm9vr6NKHvJr4GPj\nWX7eMkKTqyHo94Axi2+oG2I3ETttbQwOghtiZRQqEb29vYsKJIyInYIs3QGjEP7NVwtsLcBe2+zo\ncSAZBV9YAAuHi24RxRijSxHX14PV14HHYjAnll+7vvl3l+B777xUiASNmdk/R2fF80FFoZhWRO/M\n53OMsasLf5zqg10FacMoMQ8PWIJ6b7v1Ybzne3tLeLLcUDvaAUWBMTy8bN800WHgXZub8fW3Pgdv\nv2qLkPvli+3btwMArjizBT/+f1dgY0vQxWMpfhOhjOipdqh+hTTXR37yBD7wg/1ICNZSko3t27c7\nG0jQ74ERsVsQFW8bVWEIZrotiG4Ro9TUWOTzdBrGyIjQe1citm/f7hIx1gQdXiSkuSRy9DjnGJiI\nSk/h22ubTa+oHbUix9rGnpKcl+3tdQjXaKj1iT8sZyOUy9vHqylC5FuA8skfFQJhSvg5cBvhvSsG\ndisiG7oAB8zkQN/wHPYem4Jhip3YzOu1yN4r9E1z0g6CiJCKwrCzuwF+AWHlQuDzndpLM9tnsPgK\n1WxVJ0UEbOVFinOO8bkEDJOX3Ii73PD5fIvKzkWkuADicvo8UvhrBT6fb9FhzKlQrVgOWA8Aua3W\n7tg7iOv+60/Yc1CuQ+7z+Rb1CPUPZxywEqV1Pvf68/Hz9z8fNV7xVYjO3JEUobSj4QsJXfg+KgrL\n/pUZY6+BpW5/E+f8hOv7n87jvpsAlC4DXQWIxWKL/i1CBV9VGIJ+DQsJHQuJtNMuRhScvmn9ufum\nZRfd6i4FPnjwIHbu3On824zHYY6PA14v1Nbiy9DDhNINziK1TAQslrJ62fk9Kjwa5fmJHgcPHkT7\npm2o8ao4t7MORu8DAErfRIKZk+8CgeyJ2tUFPPYY9P5++C6/7JSf64aJExNRbG4JVpSSfzE4ePAg\n5uLW2hPyaUL082Q4YDbPSMbf306lnji5QD6WGwcPHsTGM6woWMivgdvR4yJaRLmhKsxpyi0a+VZC\nChsvEw2fJ9pHRWClv/Q3AdTBqmr8iOv7N8GqhFzu7bZ/Vpkup2B4lxDt9RKaoboR8nuwkNAxn9CF\nvzhqdxfwwAPLkondvI9qxtJ+aY7Kent7ST067dA2CY/FVWnHTRNsSYR1rbRSASz7NIX9+O2Hr4LP\no2B6z9cBAGqRIp82woTisquluX744AncfOdhfOavduLKs8RoTXHOYXJIj3h2dnZi7lkrshJKRUvm\n5wFAW0MtGAN8ggp83HB4RjOzME+ehCqhl6i9Fsiu8O7s7Mymh2s80I9XZncPN8qRIg7VeDCf0DEX\nrz4H7B2Zr1x6Xo8DuHOFazcDeE0Jz1U10LTsn5DrupPWKyVMD1gb7MgMUVsIV0VKLqyVdh1NTU2L\n/i0qxRUmTEEqwSCUpiaYk5Mwx8agbtiw6OdrxTZA1j52atqtM1UKKMVlVyuSOJGpjBUZffu3O57C\n/hPT+NG7L5eaxrdEci3Fodq5KQClSVAAlg7Xt95+CVrraTTutJ4epA88Af3ECSkOWLmapTc1NWFs\nyGonFxLEn6RGPhww0bD4uvGy9LrNB8s6YJzz2wHcvsyPX+tOS+YCY2yqhOeqGrirII2REUDXobSu\nB/OX1jqEUrzUnqTLEb3XSruOvr6+RS07REhQAO4NnmbRVbu6YE5OQu/vP8UBWyu2AU61jwiSmRZU\n9QAAIABJREFUN+Ai35ZBC2zOJforCoeG5zAyE0dkKoatrSFh910NfX19qMk4fOunxwCUfngBgLPa\nxWnnLYXW3Z1xwPrhe85zTvm5bphQFSYsPUlZ1bkS+vr6MK81A7AO66IOl5SwK/BlChmHytjrNh8U\nQyL5BoB8nKvXFXHvqoOiKIindPRPRIVU2NlwuBJlSKMsOJVp1Z3mCixJlYja4G3nmOpUlbXPqZv8\nPMEGXy647ePw8zweqK2tJd23OWQVX5gkMi4ra4FRpO/LVc0VCATw8Veeg+++81JsGM9096jgCAuw\nck/IeErHq//zj/jE/z4pbLw6Qk7bSggEAlln36vAHB21xL/b2qQ+RyFQWtcDfp8V3V+Qw5krl33y\nRVEyFJzzuTw+d1dxj1Rd8Hq9+NyvDuH6//oTjh62RSRLX6RI0yiuSq5c5dO2Y1Htaa5TOGCOynqp\nKS7aU9VKKWKKDT6RNvCe7+7F/z4WEXbPfOC2jyh+HgC8blc33v8X2/DCczes/uECoaxbB+b3g8/M\nwJydPeXn7r6WokAdcV0OnZ2dCNV4cOaGsONwVnKKC1g5QhmZjOHkXBJHxuaFjUdZVLASOjs7nb0h\nqFtyQmp7O5hWuQczpiirVnmLRqhMbfDyBVkZFWPsMNW9KwmpVAr9E5Y3Pz88DkBMGJgyjaLU1S0r\nisc5X0TurGZEIosdCl0QT8LvUaGpDEndRDItXovLSRHncsASYkVyAaB/IorHjk3i53vlOmBu+4hM\noTQEvLj+km6S95cxtuIm7+5rKQrUEdfl4LaPqPQ9NRyO3sCp7zIFf7JcG3wkEnEOz41pa/+pdNsA\n2fktKw2ZlQyqMg5YPmCM9SC33MRmWFIUax6maTq8nJrRTJl2iURVgDYFCWS4EjMHoZ/oh7punfN9\nzoGAT0OtV4W3ymUOolGLEG3zPrIRsNLswxhDfa0XE/NJJNKG8DY+K6YgXbpZomALl8qOsNj2ASBE\nZV0WtO5u6M88a71P55676GfuvpaiUC4ei9s+zuGlgjlGgOvwEjnVAaPgTwZ8GhQGxJIGdMMUJiK6\nGqLRKF68YwsUxvCcg3cDKL16WAZWkqL4yUP9uLdvDP/fmy4U1jWFMpAhAkU5YIyxr8GqkPyzh9/v\nd05W/kiGJyEkAkZ7stK6u5F+4qB1sr34Iuf7isLw7XdcAk0VW/LePxHFTx/ux1ufvxlNoVMFUimw\nbds2HBqaxTu/9Sjec3kbLk0koDQ0QAmHS77331+zFf0TUZLS5pUq7UR3KQDonf3lsIiAb6e4StQx\nkoHlIpQp3UQybTn7NQKrFYNOBKw89uHxOMzRMUDTTikKqTSora2AxwNzfBxmPA6lJlttmT28iItO\nKgpD0O/BXDyN+YSOhoAcqQPbNq++uBOzvx3AAqrk8OK0izp1bfvl/kEcHV/A4FQMW9aLKTZZF7aK\n4QzJnQryRcFvImPsMwBuyPxzBrkJ+Y2wNMTWPHRdd0rOa45bWVdNAAfMLm+mrLQDcp9E2gk6x//m\nwBB+9lgEHY21eP1lPcLvnwuTk5N4anABSd3EkRMncSnEnRJfsrNdyH1yQVmfIatOTcGcn4cSyi5G\n7ubIohDwaWBlOMVPTk46UhTGQHWQvIHlifjZ9KNHqAhotiJabhrFto/TIL2jdH4eNZiqQm1vh3Hi\nBIxIBMoZZzg/o6JWhGs0ywGLp6U5YO65k+3uIWbufOqOpxDwa3jfi7et/uECsRK/laKC+Krt6zEX\nS+PK7fSSJMWgmJX2tQCmAVzIOW/knG/J8dWI5YVa1xSSyRQMk6PGo0A5aamsKyWorNuwI2AUat7A\nyicRCtjCizMxeaf4SCTiEFUDcYt4Ww0bPFMUx4k/NQ1pneTWCYwiKgpzFj2q9y0XFnHAnE2k8tMo\ny3UroNhAgGwKckFyBMy2TzZ1X/lzB8hmIE5xkBNZB1kkQoTCv8thET9PELUCAAyT4/8eH8JPH+6H\nSdC+x57fdkrbDXutFpm+93tUXH9pN9bX0ejOlYpiHLBGAJ/mnD++yuduKuLeVQevzwpxBjXL39Q6\nOk5RLy8GZ3fU4ZyOOmFq2kuxWssb0aAUL10OO3bscBbF2rlpANWR4gKWt88NV2/FR15xNi7oaRQ6\nXjk2kXPPPRe7bz+Iz/+qV6iECzUcEv6SUzxVB4lyEYl37NgBAK4WRNUxd+wqdGMJD0x0j1sbNg0h\nkRJfkLMcbNtwzrP2EbC2qQpDrVeFycU3swes/REAjKFhcCP790rrJhJpQ3j6vtJRzFFtLyyS/WrI\npaC/5qCbJgAgyKyXSdQJPuDT8M23XyLkXrmw3CZCBfsUL7NaKJlMOptiYCpToVoFGzywvH3aG2tJ\nUsShGg8wHZdKVp2YjeL3T44g5FPxhngcrL4OSl3lMxe0jg6AMRhDQ+DpNJhnsYMk8gTvvp/sSrtk\nMomamhrnHRQRYQGA2VgKt95zFK+8sB1bW0vnYy6FtpyDTNTj9s1X9GB9nR/bCQVml8K2jTk9Az4/\nDxYMQmloEHLvcI0HsZSB+URa+GGC+f1QWtfDHB2DMTLiOGRzCZr0faWjmFDNTQCuZ4xdtcrnjhdx\n76pDPJEEAAQN679Vs8G3tgJer0VWXdJQnALl0DLq7e3N8vMmRgFUvo6RjdXaRYlGqAxSB48/1QcA\nCChWqqNa5g7z+635Yxgwhoed79uSJPW1oh2w8qQge3t7AYiXoHjs2BRuf3QAP3qI5t2228AtjYBR\nRSgv3NiEj7zibNQSNbHOhaxtrL+h2tkpzHEJ1dByDm16hVsqhKJAohpQjAN2Iawo2J2Msd8xxr7G\nGPu7JV+fRm55ijUHTbNe1kDCKtmulg2eqWo2HJyjZFs0wmWo5Nq+fXs2BTmcSXFVeBm9jZWKJCgQ\nLoPUQWtHDwAgCGuhL1UgVyZyRSgv2tSEv7y4E391aY/QsewNUSY/DwBq1nXj0798GidHJgGIk6Dw\neaxtZ5aID+rwjAaW4YBVucA0YK1tAKAPiF/XqDsv2DJN+kB27qwV7clCUYy7+Q1YTGAG4FrYrOA/\nU5iZ/wailip2tZziAWtB1Y8dg94/AM+ZZ5KORX2qygWfz+c4FDUjgxXfqsMNbZWeg6JhR8Bk9rRL\nGNaJPZiOAxBLwB+YjOKpyAz+4rw2kpSG1t2N1MOPOARowEqffPhl24WPtS7kw/O2taCNqIH1cvi/\nA2P4xb5BdPA6XI1sZKlUkEvsuMRYOeeO/ddSH1WfzyrCoRDIpc5W2KnsRREwovR9paPYeN9xAMdW\n+PlmAD1F3ruqkEhabSBqZzOnxCqo4rKhdXUhCTlE/HKQ8A8ePOhM7EAyapXRV3CrDjfsU6IxOARu\nGOTl/+EypIifeuYoACAQF6/k/ZXfP4s/9o2jqzmAczrEB+NXa2gvEowxfO7155OPsxT9IycBAL7o\nPFg4DFYv5u9I3b6H1deDhULg8/Mwp6ehNloFKzapfC2kuQ4ePIidO3cKl6AA3LInxBFKV+ZljqCD\nRDWg2N/2Gs75iZU+wBgzV/r5WoGiWBtjKMMxqqoImMRNxC1z4D6VUsLql2a1WgokY9C6xEcnqKDU\n1EBZ3wJzbHwRWZUK5ai08wfrAcyidmEGAI3K+sm5pPB7Aq4IpSQZl3LAUL0Akggko9C6usRxjIhT\nXIwxaF1dSD/9NIz+fscBe/GODZhcSEnT6qJER0cH7tgbQc/ILNaBKAJGJYG0IgfszysCVgwH7IbV\nnK8MXlfEvasO9QEfXnlOM57X+0ewuuqo4rKR7cuVdcDuPTSGL+3pE64Bo6kKar0qDJMjlpRTrl1X\n34BYyoACjpp0Qnh0cnAqhsl5mg0eyHKijBwtiUTjnI46eFSGjesC5GPZMFVrIwxMW5EWkZtIkJi4\nrnX3AJAn41IOJPRMijgZEzp33CkuTqRQnuWBZTf59754Gz752h1rospuMKriM//Xi+8ELLFUkYcX\n6vY9Dn/SpQVG0eGjGlCwA8Y5v3W1zzDG6gD8tKgnqjKYegof3KxgXXSqqqJfQHaDd0fAbrnrMH70\nUD+GpsVXRoYkt7zZ/+QhAEAAOhRwofZJpg286eYH8d7v7xV2z6WQGaE8v6cRd330Grz8AtpImxsn\nhsYAALVTJwFFgdourrsAtXq8m4RP5USUG1Nz1hoQSMWEzh2/x+ozmzY4kmmaREmWB7Y2HeQDfRYD\niGUq2EVGyEPEKWKnXdTYOHjc4n9SiLDamI6m8It9g0ik5em05QvhPUcYY2EA14m+b6VCURSnmkNE\nE26ZUB0y5ICzidgkbFHNUN2wT1bS9Iw0SyQ3oFtRKpE8Cc6BRNrAwCSdhIfmso8MyG6+njSt8QLJ\nKNS2NkdPSwScBtZEzr7S2AgWCIDPz4PPzJCMUW5EM85RMBkVXt3trAVUlXY5eEZrCXqGPRRMLEBp\nXQ/m9wu7dx0xX9dqF2UVQ9ltrra0huDzKNjRJZ6v+eOHTuDTv3wadz41KvzepaLgFZcxZqz0BatN\n0dfFP2plwuv1ZlW8CTgslF67EgpBaWgATyRgnjwJzjmZVg4AdDcHAVgiszJwwVkbsWtzE148uB+A\nWPv4PAo8KkMqo+BMgaURsPl4Grc/MoDZWIpkPOnQrEoumg2etqiAMbas3MFagGFyxFKWA1abigkT\nYbVBX2knL31fDmg1Vn9Y0dFJQE7F+lIe2MvOb8ddH3kBzu2kU68an0uQ3btYFHPkZQV8rXmkUqls\nJYrgCNi+41N4wb/fhV/sGxR6XzdUV9+0ZNpE2uDwagpJBOxjrzwbP/5/l6ODQMk9F0aGh/Cfb74Q\nr3j4fwGI5Rgxxug3kSU97e7YN4j/+M0h/OrxIZLxZGN82qp+DCRjwg8vIQlVt265g7UGmztXm05A\n5Vx4GyJq4d+Veg5SYGohichkVMpYADA0PgUgc3jpFDt3tq4PIeDTsKmFjg+ayz6aShOBpz6MlYJi\nf+NrOOeK+wtAAyxdsNsB3JL53pqHaZpkEbDBqRgMk+PJCF2Kw82VoGombKPWp6FnXZDk3rkQjUZh\nTk+DLywILaO3Qb2JLOWxTMxbJ7i1QCIGss5RkOIU71Ta0Z3iZXL0ZMP+uwUTCwBj0DrE8fMAeikK\nR2R6cAhcp6/sff//7Mdff/0hkv6JuTAbtWgVFIeXppAPv73xKrzvxduE3tcNmYeXcvVSzQfFOkmn\nMI8557Oc87s459cBYIyxD5b2aNUBv9/vioCJPsXTq5O7NxHK9GM5sG3bNqeVj8gyehvUm4iyfj3g\n88GcnIQZjTpE1fAasc95G1vQaMTRPjMivEJVRusrexOxI5SHR+cwHV0b6WGnh2oyCrW1FSwj/CkK\n5FIUmZ6DMAwYIyMkY7gRTeqIpwxMEFZFu6H4rCxCMBUlKf7yagrpQS+rhi9Pg1J2L9V8UEwVpMI5\nn1vlY7cA+KviHqm6oKfTVj84ilOin75q0N1zcK2pEU9OTpIIFdogF5RUlOxJXkKEUjbeftl6/Pdj\n30BtOiG8DVFYQm9L5xQfGcDkfBJvueVhfOynB8jGS0qs4rLf6WAySqLP1t1spbco+aAyoyyyW3lN\nzVvVg4FkjMQ+1Milhk+FcrRZyxeUacILCO9dMUjH44Bh0JwSZZ7iBwZcasRrwwGLRCIOCVc0iRig\nP8UDLo7ewIDTCzC4RhzkwUgEvP8EAPEirNSl9MBi24zMxGGYnKwgY3Aqhhd99h587c7DJPdfCtvZ\nDybFp4cB4E2Xb8T333Upnr+tRfi9bdgZCTlC03IldqYzDlgwGRPWIkomnMyLhCpV2bYpBAUfPxhj\nV6/ykU0AbgKwv6gnqjL4FMuHpWhBRM0xAhaT8B1OzhqJsOzYsQOz//MDADQRMFkOchJWNdd82uLP\nrZV2Hed0dWNsfh4sEICSUSsXhZBLiJWq84KbZzSX4eRQRY9HZ+JIpA0cjEyT3H8p7Ahi+8wI1Au2\nCL+/R1OwtTUs/L5uOELTGZmdeMpALVHETcZa4EbKlnBB2qIqVBmUxkaw2lrwuTmYMzNQBPNz3cja\npvI4YMW8jXdi9QbcDMA1Rdy76hCLp5DQvKglSXFJ4IBt2ACoKsyxMcxnTlVrJQWZTCYdfg6FRIiT\n5iKc2A5XIhLBXP1WAGvHPvFjVi9ItatTuIPk86gI13iQ1A2YHFAJ6CzM1S5qZtRS86fiT8re4Hdt\nacbN479H0+O/gvaWL0oZUzTcPKMv/KYP/7d/ED95zxVoJWhqHpKwFrhhvwf16xrAlOqrd2OMQe3u\ngn6oD3okAi+lAyYhU1EsirXcLIDHl/n6GYBrOed3C3nCCsdgWsN3d11HEmGp9WpQGBBLGdANGsVo\npmlQO9oBzjGbKW1eKxGW3t5eGJkQt2iOEZAtkqDl6LkilLZaNNEmf9+hMbzx5gekldP3P/gQALr+\nqf/xhvPx+ddfAFWhIxPb79XciNVzlMo5lhENX4rG3v3QuEGytsmAM3cGIugdmkFSNzGxQEOSD0tY\nC2zohomYzsG4iVAbXQqXGnbqlFqrzd5H44T7aLEodqe9IM9+kH8WSGg+kk1EURiCfg1zcR3zCZ2s\niazW1Q2jfwBzk7MA1k6E5aytWzE9NAQwZjmZgmFzsRZIid7WBp+IDCKx0YCqMNR6xWu0AcDDRyZw\ndGwBjx6dRGcTfU/INs4RB016GAB2dDWQ3NcNtbMTeOwxzE7MAKghO7yUg0jsnZgAB030WAayYp8D\njqhomNhBllFpZ5gcGjjqo9PwVqlzDLg4esQ8MGsf9WAunibdR4tBMRGwzwGYEv0g1YxgSmyzWjey\nJ196KYpA1HLAeiQ2ZCbF+ASSTLXa3HjFTzp7IlNWp9nv1dyYFWEJ+jWy8vCg5CgLGx4GkK3ErUbY\nzsnczDwAusNLrVcDI46Gu2HOzYHPzFhyDuvWkY9HAaV1PeD1wpyYwHzckgdZCylin0fFvxpP4qY/\nfKVqo5NAtjDq+MAErvvy/bj30BjZWJVaCbmsA5bp6XgKOOf/mIcMRV73WisIJGm0WABJRO/MJvJX\ns7340bsvxyVbmsnG+vFDJ/Ct+46S3d+Nv/vJ03j/X/4LGJFtLt7UhL+6tBuvv6yH5P5Atl3UQiZY\nTRmddLgSkhapmd5eAHQpSBmwN8C5BUskl2qDVxTmKiygd5D1jDyASqCfJwu2jIsJ5pLYoYpQyj28\ndD/1IDZNRkiqu2XBPlzunQMGJmPYe2ySbKyWsLhemSKxUgTsesbYT0odIHOPNd2cO2ikoLTQ5OJl\ncD/sDZBHBrCxJUi64H7rvqP4xt1HyBWjTZPjeMqDsXALmU6OV1PwvhdvI+1fBliVqlGvFZWk5Oc5\numaSyKq+CWvBpYoey4C9AWb5eXT2kVlOb3dfqGbnGLDmTtzjh8mBWq9K1u5GdoTFP2kloSi4rQBw\nZGweb7z5ATx8ZILk/kCWAzY/R1/8ddPLz8a/vm4HOpvktMHLF8u+jZzzWwEojLHHGGNXFXpjxtjV\njLHDAKY4598s5SErHaFQDVklij2xKU+9Tl8uCY1r/Z4MWZV4oYomdXAw1KZi8FahTo4bWlcXFG6l\nnShPcjI4bTa4roNnFMptOYdqhL0Bzmey0FQcI0BumisrYFzlc6ezE9GMajxlhw+ZzjHnHHzY6gdL\nZZ+DAzM4OraAe3vp0oJO9DhBW1wEWMK/156zoeKiuSt6DZzz18HS87qLMfYoY+zTjLHXMMZ63GlF\nxlg4873XZD5zGMAfANzFOX8X7a9QfoTr6fobvnRnOy7oacAOwiiLu+cg56spjJQGGe2VgCxnrjYZ\nr1oSsQ21qwubJvrx8doIaX82WbYBgN8/0If3vOqfMbJ5O1iNeFkAWbB5RgvM2jxkbPIy0lxrKQK2\nYDtghPqG9Q4fVAI/b3wcSCShNDRACYVIxpAh3aAEAlCamhDVrEPlWhEALwSrvpGc8xsYY38A8A0A\nF8GlAbaMN8kAzAC4jnP+M0HPWdGoa6Zzji47Yx0uO4OWBMvq68HCYUsUb3oaqmBRTDfCEooKADhV\nT1avNDqnRQa07m4o4Lhs+Gk0EmgY2ZDR+srGvU+PYbh+A05s3oGLyEejA1OUxVEWGRw9GVIHdgSM\n8PDyx75xPPjsSXzopWeRpQa1zmz6ntI5bgn78ffXbEVbA32KK8vPo4tO2n+rWeLDmNrVKcVBrlTk\n9Rtzzm8HcDtj7LUAbgDwghwfm4HVpPuWSnC8GGPvQLZacxPn/HMU1wBAXSsdaV0GGGPQurqQfuop\nGP39pA5YtkUM7Sne3qSqtVeaG7agpBGhTRHLVIyem48D8CDUSMufkwG1qxNp1QMGoK5WRgpSRgQs\no59HmL7/ycP92Hd8Cn+xsw3nEUmGuCNglOlhAPjr524ivb8NR9uwk25dC0t617TOTkRN+hRxpaKg\nYwfn/HbO+bWccwVAA4DNma8Gznkj5/yFFeR82c97O4A7GWO3iL7GRn3HhlIfuexQXT0hKSGr0s7S\nZQKCRhJKUxPpWNRwi7FSwt2+hxq2LEB9C52zLwtaVxf+9uEf4731U6TNpWXZJ63r+HLH8/CnTReT\nyhz4PZae3WyMsMK7sxNRnxUBWyst1vT+fgDEETBJ0Va1qwvzGfusFf3JQlD0G8k5n4WliF+JuIFz\nfqH9D875fsbYaq2RirkGAFC3sXpJxDacvmnUm3yNpBRkpjVM0KtUHPGyUKhtbVa7qNFR8EQCzE9D\nxHdI+EkdpsmhECrIL6Q5oAF17XRK3pxz/HL/ELa2hrC9vY5sHLWrC889+j0Eps4mGwMAXnB2K54a\nnMUuQpkYAOh7qh93bb0ckcZ2XB+g0wQMS1gLlLo6RMOWkx9C5fUCLAbZ7h4yImC067TW1YXopJoZ\nc204yIWg+ppIrQLGWD2AC3L8aGY5h6qYaxxwjuDG6k5xAdnJTB0Bc3hGxKHt2bFMW6XaylE9LhZO\nuygA+uAg2TiqwhDwaeDccsIoMQ9r0a3vFt+hwMbITByf/uXT+PyvesnGANxFLLSK3me11+Hrb30O\nztxAK6s4FbEEcgMa7fYgKxqeaLac/EBCTostasjggC09jFFBdfEn1wIJ3xgdRfSHP8r782vOAQOw\nCRYfbSmmkNvJKvYaAIDKTah1dKdrWZAlReFU2hFHwGanLK3gUKiydF+KRbatCu0mL6MSknOOqGI5\nxvWb6A4vSibySdX/z4as9L0szGb6WgY8tJHjLB+Udi241BvDuUO9eC6jE/qUiScWFPzhzOeScsBk\nHcaMtnakNC80U3dS0tWM1IEDmPnwjXl/fi06YI3I3SppBsByZKCCrmGMvYMxtpcxtjecnEMkExKO\nRCLo6+sDAExOTuLAgQMwTRPxeBz79u1DPB6HaZo4cOAAJietxaCvr68irp9pbscXrr4BT04mSccP\nZjgyE7NR0t9/ZtpqDRNuCJL+/Z56+hB+80gfUrpJar/pWqv6MX3iBOn7s61ZQ2udH0gtkL1/j97/\nIExFhS+dxInZGbL3//jhQwAsZ5Jy/oxlKvjS/f3oO3SIdP7IuH4uw5/UFIN0fDsaPnxymvT3P6Ol\nBp/47RfRMnS0Kv7+K11vJJP46raX4OvP/RvM1TeTju9TLUmNkzPzZL//k5l1OpCMYfD48Yr/+692\n/fDefSgInPM19QXgGgBHc3z/NgCfFXWN/XXhhRfytYDbHjjGd+3ew//lLz/MzVSKbJw/PTPOd+3e\nw9/7vcfIxuCc8w+972t81+49/P9+8HvScW57uJ/v2r2H3/ZwP+k4c//1FT7Y1sFnPvEvpONwzrlh\nmKT3jzx6kO/avYe/5Kafko5jmia/7BO/47t27+Fp3SAda2j7OXywrYPrY2Ok48jAVz70Jb5r9x7+\nn//5c9Jxfv34IN+1ew/fffsTpOPMf+e7fLCtg0998EOk48hA+vhxfuU//pzv2r2Hz8Xo1mnOOX/z\nzQ/wXbv38ENDM2RjHBub57t27+Gv/odv8/TRY2TjcM75/X1j/E/PjJOOMf2xj/PBtg7O8/RXVuoF\n+bXCXLmKQq7SqnoAK8Wgi7kGpkkvvCcDcynr9/CnEzCGhsjGsXkf1BywaMqSJg+30ZG8ASCRacQ9\nNB0jHUdmmouSfA8A0wPW+xUEXRNzwJJXCfrldF6QVakqA3NRKwoeIBSYBuQp+zsFRsTpexlInBhA\n3FsDxjlpxS0gRwuspc6PltQ8Lho4CJ1YZmf3zw7ioz85QNrMfj4ygsc78i/GWSkFeUMxLYgqAHth\nOU5L0QhL1V/UNQCARCJR0MMVA90wESVWv7bFN4PJKOkm39FYC6+moCFAR47nhoHnP30vzo88iQvP\n30w2DuCu6qS1zz2sGfs6zl0Tm8js8DgAwE/sgAHy1OPd3SSqHbZDlACtYyTLNmrn2uHozWUOL7Vm\nivyglC2SoLNPwKfhO8mH8DeP3ka+tqmMIambpH2Ib2Pt+LcXvz/vz6/GAbuFMUbT7ZMInPMZAMcy\nlY1u1HPO7xR1jQ0/kSSAGx+77Qm8/Iv3kp7i7UU3kIyRSlE0Bn24/b3PxaeuO49sDGNkBFccfhj/\ndOBHCNRRn+LpSevRhI5P7ZvDLVe8GbqEdlHUmBuzgsoNIfoWRLKaJK8VIj6PxzFvWtvClnO3k44V\nlkTC1zraAcZgDA+Dp2mLSw70T5P+PtORUQBAWIJiw67NzQj5NfSso5MiAbJiv3qE1gEL+mnfN845\nxszCDLOaA7YZlmPywaKfqjz4LICP2P9gjF0A4E7Xvzcxxm5b4nCteM1yUIiacLsxMhNHLGlgaIou\nzWWfQoOpGPkm0hL2k1a82A6k3SiZEjLa90zHUjA5oIKDLyzAnJ4mG0sGZietCtVwmL5CVVaT5LUS\nAdMHBx1ZgKY62o1Xltgn8/mgtrYChgFjeJhsnKcHZ/HObz2KL//uGbIxZketCtUQcfoRAF59cSd+\nd9PV2LKept+kDWfuSKrAXyCKuJoTE1hQfQVds5r38DiAzwP4GGNskjH2tnxvzBj7SUFEumkUAAAg\nAElEQVRPIhCc828AOMoYuybTPukazvkNro9sgkW8byzgmpyIxWi5P4CcTT4bAYtWPY/FdiDnw7QL\nByCHx2LfO5gRkjQyStjViu6BQwjH59AVSJGPJcM+UwtJHAy2g6P6I2BG/wAWMsrko5HjpGO5bUMd\n1bXbkemEaa6knuGDEh6UZyezFaoyQJ3mBFwSSMQcMOp91BiIIOot7FC5mhv9Ws75CQD/yBi7EcDn\nGWOfA3Aj5/y/l7uIMbYRwGsLehLByDhUy/3sTlitlPK+Zjl4vfRCnzJ6wGU5YLHqP8VnHJTgGWeQ\nj5VtD0Nvm5BmLYb6QATe888nG48S3DTR3bcX3zrwAPwPPUA+nsMzIpw7//HrQ7i7N4kvNHZgMzGP\nhXOOhYRO1jdPHxhweiduIRTJBaxWRO0NNUgRkqJtaJ2dSD38iKMiTwEnpUp5UJ5ZAAA0NVW/9qQN\nRwRcVhcWorVAH+h35k6+WCkCdnvG+QIAcM4/xzlvBPBNALcyxp5ljL2aMdaz9AtWdOnPAppGHwqW\noRhtv5SBVJT8JEIN24EMnXkm+VgyUly2bez3oJodZHN8HEgkoTY1oZmwlYqNsATh36HpOABA1zww\nRkbAk3TCr1/63TN48efuwcAkjaq7PjCAqNeKgHURVxADwLdvuBTff+dl5O3C1G6LjqATRo+pnX0z\nGsV8plq9aQ30ULWhtLQAfh/4zAzM+Xmycaj3UWMggliBEbBlHTDO+XXLfP8mWNywZgC3Azia4+vr\nBT1FFUNGFaSM/on2vUMKwGdmYc7kagxQHbDTQHRiGlkEfBoYA2JJg6y82V4wQkGr4KOa01z2s6td\nnY7oISVkVNrZzbHDDSGAc+iDdG/eyHQchslxZIxmozIGBtAQm0Wrl2Pg2GGSMdwI13hQT1gRDQCT\nC0moHVaaizICRr1OGwPZ9HA6RueoyAZjTEqnD2r76JGI0AhYTjDG/g6WbEMdALbC158FZJDww8TV\nG7phIp4yoCoMwUxzZOqKFErYk9i/eRP5WIrCyNOQ884Gb1V0UpNVKZEtkOhCgLDRs43WeqvSkpLK\n4hxeWqymGQZhBJk+jTKAz93xr/j2i1sRDNJWEMvA04MzeOnn78V3k1YDc8rDS61XhaowxFM0hzE9\nkuUYNQTpq+9lIltFTBehpN5HE5EhpDRfQU7VSkKsv1vy752MsccA3AKLP8VgaWS9LsfXrQU+e9VC\nBgcs6FQL0Sy69gsZ9GvwSKpIoYK5sABzchLw+9Cxc6eUMYN+2pOVbfdwk1W0S+kcc87xnu/uxe7b\nD5Lc3352tasLnZ10zYRtXHlWC/79uvPw18+lccZNkzv2qe9oBUDLZQkRCstyzmH0DyCQjqNuU7cU\n+1Dj8KgVKZpSLceFMsLCGCO1jzGQjbB0tDYLv385IUPImFqzMVuhmr8LttInr2GMhRhj4UxF4z5Y\njakZrB6Jr+OcX8Q5/9nSL1iSDn8WSKXoK7lscucC8QYf8nuqXs/IXmC1zi4MEir6u0Gd5rJTkPXr\nmyw9o6EhMj0jw+R47Ngk7np6lKQyzV5gte5up4caJTRVwdVntzpzSDSiSR2cA7U+Fb5MNRclR4+y\nqtOcmgKPxcDCYbD6ein2oYaztjWEAJ8P5uQkzCgNfw6g3eT1gQg006p+1NILwu9fTthaYKQpYidT\nQXB40XXMTc5a49TmL0WxkgPGYHG8pmFVNNqpxc9yzhszjtZymARAW8NcIZDRiijkCBbSbPDhGg80\nlWHz+qC0ihQq6AP94ADmes5AlHChdaMxaEVBUzoRB8xOQYZqyPWMNFVBjVeFYXLEkuJL3Y1MikHr\n6pJmH0o40Um/J1tOTxhlCRNGW93pYcbY2rBPxlEN13iymzylg0yY5jIG+vGGvT/Hv281sClX35Yq\nxAf+Zx/e9/19LpkQ+sMLxT5qDA8jqlmOV7g2/8PearGya5B1vG4H0MA5/8jKlwCc81nO+Za8n6KK\nIUMJn1qwsCHgxS8+8Hz822vPcwlK0uXiT84lcNOPHseBfvGConr/AO4+43K8ufvVGDbkrFI3XL0F\n77hqC85upykNtxeMUI0nu1CRprnoKjvdJPxt27YJv79sOPyvGo8j/EsbAaPrpWrzb2xHcq3ZJ+sg\n09mHsvOCHokglIziih0d2H7WWcLvLxuJtIEHD09g3/FJqLZzTLiutdZZe7VKQAg1BiKOgLFNSckH\nqzlgDMAxANdyzq/jnM8W/YRrFLpO28cMkCMm2RT0waMpUgQL95+Ywn1947hjr/gxjIEBHG+yfocT\no1PC758L29rq8NYrN8Oj0RRkOJuIX8s6yFUYqueJBMzRMUDToG7YgMnJFfvcVwXmXfxJmad4kgiY\nnb7PvGNrwT62oxqu8bgOl5Rzh+bwwjl30Ss6pdnm5j88izfd/AASKfHRcKe6u8YDzZYJGRwEJ8oq\n9awL4otvvAA3vkx8iy09EoGuWOtmYwFVvav2guScb+Gc31XCs61pyOCA1WUWXcomoja0jg4AgDE4\nCG7QqC3X+uiIqvrAAKKZUu1UdG2cFzSFQWHA+roaKRw9qlC9PjgIAFA72sE0bU1xjMJ+D5TGRrDa\nWvC5OTIZFycFSTR3gGxF2tqwT/bwYkdZpDjIgu1TLn7eI0cncWRsAcdPiuecubnHSiAApakJSCZh\njo0JH8vGZWesQ1uD+B60xsAAdgwdwt96R/G3z9+c93WrOWB/NmT6YlFbS9/Prq7Wi+sv6cJ1l9D3\nNmQ1NVBa1wO6DmNkhGQMStK6MRDBQqZUe/tWehkKGfjka3fgq2+5GM0hn6tvGqWgJE3K2+gfQNzj\nw98/7x/wtTufxY4dO4Tevxxwn+IZY+RRsDBhBCxbIGH9DmvNPvbvRRkBs6MfKV1sAYud1tY6O8EY\nk2Ybp6qT4H2bc/HzgOpuaK9HIvAZKbxpSw26m/OX11nJAbvWrYR/Grkhg4QPAO//i7Pw1gI861JA\n3RzVadkh+JTITdPSysnk4v0qbX85WWhrqMX5PZbytcwImOhTvD4wgP7GTgx767Dv+BSShIrxsuCO\nsAD0c4eUSGxLhGREMWXYxzA5/uV/n8SvD9BULDsFLH6P83tRzp1XXtiBtzxvE160Y4PQ+7q5k4Ac\n2wC0unOnzB0J/FYqZNP3hUm3rKSEfzrtmAdkKOHLhpohE1MtVFQRFnNsDEgmsVAbBgCMDVV30+pc\nkHGKzwoWCk5B9vc70clQjQe9vb1C718O6Ibl5DdkIh9OmosoReTm55mmuAMGT6dhDA0BjEHrsHpA\nyrDP0FQMv31iGN//E03RvLuARXPJhFA1/14X9uOdL9iK5lD+UgT5wM3/AuTYBqDVnXNHJ4Hs3KHk\nt1Ih6yAXlqWil3Ff45BRBSkb9kJF1TfNHWERuRDak2DBbyl47zybvhekbCjr1oH5/TCnp2HOzZGM\nESQi4RuuVh0hvwfbt4snw8rGS89vx9uv2oyXX2BxJx0yMdEpXlMV1PpUmNyqIhMFY2gIME3ce/FL\n8PFfHIJumFLsQ8kHNU3uvMMhvwYlw5/iiQTMkyeFj0cJR8A4cwCTNXfChAVg2R631hjUc4cKZjxu\nvU8eD9TW9QVde9oBKxEyWhHJRrZaiGYi+D0qvJqCtMGRTItL4er9A+AAoprlFDfX0be6kQ3GmCsN\nSRRlIeIZ6f3ZAolwjQafT2yUYDkMTcXwzXuOIErAOWwO+fC2K7c4ETAZMi5vee4mvObiTsd5EQH7\n8PKLM56Pu54ew8BkTIp93A2SRUelYikdJrdaBGmqtU5rEqq8KeAWmAYgbe44dBFSDtiS9H2VccCc\n1H17O5iqFnTt2vMeJCMWi5X7EYRDRjl9kIDcaQwMIKl5oTMFPk3BM4eeFnbvSgL1QhUm4BlZZfQD\nTi+7kN+Dgwdp2h0txe2PDuCb9x7FXU+Pko8lQ4z1r5+7SXgpvc1Zs1PEQZ8mxT4+jwofwWEMgCMk\n7O6CkG36XF2b/FKNNllzJ0RYdWuv/Q4J3953CHupUqBY/hdw2gErGTJ6QcqGTL0ckRNb7x9A1GtF\nWEI1njXRyy4XqB1kCo6eOTUFHo0iGrLEcYN+efbxZKIfU1F6yRiHx0Io40IBJ32vWOtZqEaTZp8Q\nUZRlXdjnkOJtyDhcigY3DBhDw5j1h/CNI2mMzsSl24aiYv0UDtiGDYCmwRwdA4/HhY9HBX1J8Uoh\nOO2AlQhNE5cGKBe+duez+Mrvn3H+rbS0AP5M37QFmp5jYYKJbQwMuDhGGpqamoTdezUcH1/AU4M0\n2k9LQd1SZXt7HTbU1+DCTOWlCNjPGmtYB8BKO8iyT9BPp06+FEpNDZT1LaQyLhTQT/QjqXqQggJN\nZfB7VGn2oSJ6M8bwkVecjVddlHVWZLQjEg1jZATQddx7wQvx/Ycj+M2BYXm2IVT2d+uAAQBTVaiZ\nAhBbM7Aa4EiEdJ92wKSj2qsg07qJ795/HD9+uN/hYDBFcYXqaau5RC66esTlgNV40NfXJ+zeq+HD\nP9qPd3/7McRT9GK51Kf4xqAPP3//8/CmKzYKu6f9rNGgFQGTaR9KHksuUM8dChgDA458SzijaSbL\nPjI6fdiQ0elDNOz3aK7ZkrbwaIq8uUPYlmx+SQoSoJdxmY+n8d/3HsHwtLgIWzYCdjoFKR3VTsK3\nJ1bQp4GxbI+sLNGbuBJS0MQ243GYY+NIZCogwzUeBALySPhpgyOpm5iO0m8i1IsUBexnjdaEAFin\nXln2kbnBA/RzRzQ45xmJkEz6PrPpSrMPoTDzUmhVKHVgc6KidVbUK+TXyjB3xNvmks3N2NwSxNbW\nkPM9R6uNyD739Y3j1nuO4scPnRB2T3tt2+9rwcBEYQ3sq9t7qADI5ICNzyWgG2KJqkvz8DayUhQ0\nm/yZGyytrnUhMTIedhj4LE8CLzh7PV63q0sqB4xK2+zo2DxuueswYq42VM4GT9g3TTRsSZOo12oD\nEpbJMZK4wQMurbYqcZDN6Rnw+XnEMhu8HZGQZR8qYeZcUNvbAcZgDA+Dp+U45KXCObxk9A3DtfL4\nk5Q6YG+9cjN+8O7LEXBV82bFWGkOL5pqBRlE8UE559AjEUzWNuDDD87gkz9/sqDrTztgJUJGL0gA\niExG8aov3ofP/kqsAN/SPLwN6kq711/ajd98+Eo8Z7MYLoM9YRs61uNT1+3Ers3NUnvZUUVZvnv/\ncXz7j8ew70S2sbhSWwuluRlIpazm1lUA2z4LzPo7Bf0eafaxy9wp2vfkArUYq2jYkhnxDkuHyd50\nZdknJJGjx7xeqG1tgGla2mcEmFpI4oFnTwqT1bDfIydFLHXueHDxpiZh6/RqIK/wzuxzojQO7cPL\n5Lo2cABmgTY/7YCVCFmtiGZiaZgcODomlhQ/v0SLxQY1z4gxhsagOC0b+5RoT2AAiEYLCweXAiqu\nxHTmpOZVF0/VaktzOTIHmcLAsN8jzT7Zilu5EbBqEZS0nzPaahGg7YiUNPsQ9rfMhaxUCI19vvL7\nZ/HBH+zHEwNiinJsDtiCYq2XoRp5c4cxhv/6m4vw6et3ShmPmqMnupWX0X8CAJDo6LHuvySQsRpO\nO2AlQpYSPlWKa85Ril4uAlYdp3g7wqJ2Z1tBbNu2Tdr49sReELzJO/3SlqaIq2iT58mkVcmlqrjs\njHW4/Ix1qPWp0uxDtcFzznF37ygm5xf35dMy7UiqpdLOqVBtbAGQ/XvJsg9V66vlQL226ZlD+ciM\nGKK3zQGb55bIZ8jvkbq2yYS7SpWiXZTofdShVrRanTDCNacdMKnQdTmLBlWKay52aiUK4IqwRCJV\nwTOyHRF3KfDk5KS08ckcZJuj518coawm1Wg9MghwDrW9HZ+6/nx84Y0XgDEmzT5WgQmwkNBhCOyf\nuP/END76kyfw1TufXfR9pXU94PXCnJiASSTUPLWQFNaKyN5EHA5YxiGSZZ8zNlgk7JawHHV3J0VM\npqMnbq3mmeIiaBoWMkK14RpN6tomE6y+HiwcBo9GYU5NrX5BgRC9j9qR/VjT4sNLvjjtgJUIWRyw\nsItILPJksFyERQkELJ5RMmk1ua5wGJlNRHNFwKRywIhO8dkU8RIHuYrK6XPZBpBnH0VhCPrE97cc\nnbUiHEubYjNFgdZhnYgpHORYUsdfful+fPAH+4Xczz68LAQyJO/MuybLPuf3NOI3H74SbxYoe7IS\n7PeQ6vAiMuJq62Hxjg7EUgYUBtR6Nalrm0wwxkgPl6L3UefwUt8M4HQKUjpqa2uljOPRFPg9KgyT\nI5YSp7C9tCGqG1meUWVHWbhhuJrVZjf5HTt2SHuGEAHR2zQ5FjLVj8GlKeIqaqlivz+qi58HyLaP\n+ErI5SqIAVoOZTxtIJ4ycHRsXsj97HeoY4MVAbMjUjLt0xj0LZLBEYH5eBqTC8lTvi8vAlb6u6af\nsDb4xMatAKx1QFGYVNvIBiVHT/Q+6qQgA3UATuVSr4bTDliJkEXCB2hUibP9uE59cailKETBGB0D\nUiko69ZBcTnEyeSpiy8VKFLEC0kdnFtK7qqyeHOS0VJFWBXXiRMAAK1ncQRMpn3aGiz5C48qbpPP\nVhDnmDsOl0V8pELkKZ6nUjCGhwFFwRtedA7+8I9X4/xMBwSZ9qHADd96FG/46gOnSPc4MiFE0WN7\nLRVRkGNk5k68swcAUFdr2b7abbMSqHUORe6jjkSIf7GGXr447YCVCJlK+GECPaOVTvHVwjNaLsXV\n2ytWsmMlkNomV3SytRXweGCOj8Mk6Ju27/gUXvTZe3D/M+Ml38tp1bEkAibTPv/86nNxy9ueg/V1\nNcLuuaJ9CB1kkad4Y3AIME2obW1gXu+idUCmfUTDNDmOn1zAbCx9SmRNWbcOzO+HOT0Nc15MFNEN\nkYcxJ8W1wXqf7Hetmm2zGqgzL6J0AXkiAWN0FNA0zGfkdcK1px0wqZBVBQnQVHPNLcMxAlybSIVH\nwGwphqUpru3bt0t7BgrbZPl5p0ZYrL5pGZ4RAR/kmZE5zMXT2HusdLKvU6G6JAIm0z7rwn6c19Ug\n9J5OBCzn4SXDM6rwU/xycweQax/RWCl6zBhzfl+KKJhI4V977tS2twIAOhqtCH8128bGUu6kDeoI\npaiCKT0SsYqLOtoxnzQy9z7tgEmFzFZEFIKFbQ218HtUdDef2trC2UQqnPBp8yS0nm6cnEs4qvE+\nn5yqKgBoClodEURW2dmE/vAyk5oyRew0Sy+Rx8I5z6nRBsi1DwVWPLzYtonQCkqWvInkqB62Uc32\nWck2gJsHJl5HLywyxZVZ2848qwvf/Ltd+NBLzwJQ3bYBgDv2RnDtZ+5G3/DcKT9z2hFRF0mUaB/3\nuracnuZqOO2AlYgYUZl5LlAQiT/+qnPw6w9diaYcoqjZNAqN2OcdeyP40A/3I6WXxqOzU1yJ9i5c\n919/wgd/aFWHHTx4sORnzBdtDbX4yCvOxvteLE6fZ7kKVRuUKWKnBUmJG7w5Pg6eSEBpaIASDi/6\nmUz7UMCxTy4OmCvCQqJnJEhQcrn0PVDd9lnNAdMIq4hDgkSZ3cVFWk8Pzumsd34f2bYR/Q7vPT6F\naFLHiYlThcW1jky7qKEhknZR7TYfVCvN/dFdc2c5Pc3VcNoBKxEye0FmBQvFvZSqwhDIsYEALp7R\nGA3P6NcHhvGnZ06ib3i2pPvYE+HkunbEU4ajbSazFyQAvPLCDuzsFpfmsn+PXBs8kK34pIiAiTol\nOhWQPadu8LLtIxoLidwVqgCghMNg9fWWjtPEhPCxhaVRlqlQBarbPqs6YC7BT9EQFT02RkaAdBpK\nS8ui4iJArm1mYym84ov34Wt3HhZ2T9s+dTnsw3w+qBs2WO2ihoeFjWnj7VdtwZf/+iLs2txc0n3c\n1ArOrT6Tdac5YHKhaYWFHEuBTfCLp+SIvzJVtZrXgiYNaTdhLTWiZ6cglyp5NzXJ6V9GBb/XUr62\neR9L4URZCNJc9ga/UKJt7BSK/axu3ke122e1tANlilh4GiVHCrKa7bNqCpIwAlbjVaEqDIm0gXQJ\n0X1n7uSITsq0zchMHCfnknjoyElh91xO39AGJf846PfgOZubTuEGFopsCrIb//Tqc/Dv1+1Ejfd0\nClIqZFZBvujcDbj2nFZcvb1V2piULW+ccu0SNhFzdhZ8ZgaspgYLPrsU2LpvX19f6Q9ZRlx7Titu\n/tuLcf0lpy7AAK1ejqg0iv1sWnc3vvqHZ/HS/7gXM5n+ltVun9XSDpQtiUS07+GcL0qjLEU122e5\nDh82KHX0GGNoDvnAGJAyinfAcrVXsyHTNhS9VOdWqL4HaCOUouCeO7s2N+N521oKvoe88M0ahUwS\nfntjLf71dedJGw+wIhdJUPGMSj/FOymU7i4nWmNP6kDg1MKCaoKmKrggo8mU8+cuvRzOuVAhy5Cg\nNIodnVS7u/DI0QlMR1MYmYmjPuCtavukdBPJtAlVYajJRCqXglKKQoTwrzk1BR6NgmXSpUsh0z4H\n+qdx6z1H8JFXnL1sxLcQ5B0By7RaY4LX8Y+/6hycnEs4Uf5i4GzwOdL3Mm1DWX2fKwUJVL4IODfN\nRXtPsTgdASsRMjlg5YAUnlEJE9tdibK0arCaOSz5QKmrA6uvI+EZ1YpKo7giYE7XhZrqt49umGAM\nmUhHbseX8hQv4vDinju5fgeZ9rnv0Bj2HZ/C/X2l684BqztgSiAApaUFsBvFC8bFm5rwkp3tJd3D\nXd29FDJtI7qXqmFyh3aSiz8JZH9n/fiJksejgDk2BiSTUJqaoASDRd/ntANWImT1giwXZPCMSomy\nuMP0S3Wz1mq/NDc0Ij0jxpiQSkjHPl3dp2yK1WyfWp+GT752Bz7xmnOX/QxlBKzO4YMWL8TqaIB1\nd+P4+ALe/s1HcKB/2vm5TPtk+aBioiyrOWBAdpM3KnSTz1ao9pzyM5m2Ed1LdcFVPbwcD0vbaPUF\ntTsBVBpWSg8XgtMOWImQ2YqoHCBNowjgGS0qBV6iTB6NRkt8wspHVjNHvFRIqURvMxaDefIk4PWC\nt7QgmtShMDiLuWz73LE3gl89PiTsftees8Fp25MLVM4xAFy2dR1eeG4rXnZB8VEWJ8LS3YU/9o3j\nycgMHnw2S7SWaR9Rsho2ZvNxwDKbvH78uJAxRcLNz8tVQSx77mTtU7oDlp9z3APAamNGIeNSKlZK\nDxeC0xywEiFTCb8ckMMzEpBG6e7G/ORiYue2beI0uSoVlEUSpSp6Oyf4zs6sUnSN1UwYkGsfzjm+\n8JtD4ABecl6b8wyUUNvbAUWBMTwMnkqBCaQrhGo8+ORrS+ODultE5SJFy7RPWDDPyK4UX0kWwL3J\nVxrMqSnw+XmwUAhKw6nSNrLXNmstiAvRoFyNgA8ASn29JeMyMwNzfBzq+vUljysSy4lLF4rTEbAS\noetyJCHKBUvPiIZn5ChGlzCpc6UgbWLn5GTpbXQqHTLEWIvdFN22yRWRkGkfxhg8mgLd4FhISpJx\n8XigtrUBnFs9FysMbhJxrqiETPuI7vLxhst68JqLO3F2e92yn1Er2AFzS1AwxvDt+47iD09muWqy\n1zaRDazziYABrghlBdrndAqyQlDNHLBHjk7gnd96FENTK6v525u86ChLqMR2KjydhjE0BDAGraPd\nSV+EysQx0g0Tv39yBJPzSWljUuoZXXvuBmxuCWLL+lBR17vb3OSqepJtn7AA4nqhcKq5iFoSlQKb\n4OyOgIXLZB+RKS4AuOLMFtz4su3Q1OW3OG1jD4DK3+BHZ+K45e4j+MY9R5yfl2vulCpLAxTigPUA\nqMwUcZb6cjoCVlbU1pZeMl0u/O6JERzon8aBgekVP0elZ1Sq1IExOAiYJtS2NjCf75TWMDt27BDz\noHni0aOT2H37QdzqWiipQRkBe9n57fjBuy9HS7i4NLtNoNW6uzGb0WWqq82m4WTbh6KcfjXYYqxU\nTbmLhRmPwxwdBTQNakdHzk1Rpn3CAhtY54tFPKMK4/I6G/zGHszErEN+jScrd1K2uSOAo+c0sV+l\nbY9jH4IiiQcPn8R3/nisaH6Zm/pSCk47YCWimkn4dloouIpWTVaVWCzRu9SGwvbEtMPAiUxFmL3J\nJ5PyIlFujM6Kb9u0HJbyjCoJToRl48acG7xs+9hjz0qMgGkVqmfkOMddXWCaVnb7iI6A5QMlFILS\n3AwkkjBHx6SNmw90VwoyV/pe9twRmSI+r6sBZ7SGcPXZK/O6spWQ4guMbrnrCL5+12H0TxRezGDO\nz8OcmgL8Pijr12NgIoo9B4eLcuZOO2AlQqYSPgCkdRPHT57awLQY2I7PqqFgR4pCbNi71qdiU0sQ\nnUUKL9qhaW3TJgDA3z5/M9525WY0BCwHrLe3V8yD5gm7VZQd7SkFumHiS3v6sO/41Iqfq2SekW0f\ndePGbATM9a7Jto899pwA++QLyhRxKXAOL5lNLleKWKZ93HxDmVVvlUrEdzdJt6NO4TLOHXtsESnI\nra0hfO9dl+HiTSu3U8pGwMSnIL2ZRtwzRawFzr7T0wPGGL7wm0P4xM+exNHxwvfl0w5YiZBdBfnl\n3z+D13/lATw1OFPyvebzqEYB6FSJGWP43jsvxTfffklR1zsTYWMPAOA1F3fi7VdtcX6+ffv2Uh+x\nINQJjLA83j+NHz3Ujx8+eGLVz1Yiz4gnEhY/T1WhdXViLm5F58KuqjTp9hHoIOcLJ31fYRv80rmT\nKwIm0z4+jwpfpkgikS5e26xQUPKMHj4ygcOjc0Vd65agKLdtAODSrc3obg7goo3Ly66IhpujJ9op\nL6XqVj92DED24D8+V3wQ5rQDViJktiICsk5TMaHTU+6VWKwcvxxsoiEFj0VTFec0UiiyEbCNOX/u\n8/mKfq5iYKc+RWzwUwtWisHvyd3mxg1K+xQLfWAA4BxqZweYx5PtUuDaRGTbJ1yTsU9cXqrWvcFX\nkp5R1gHbiETaQFI34dUU+DzZuSjbPiJ5RvmCqhIymtDxgf/Zh4/99ImCrzVjMWx4SOcAACAASURB\nVJjj44DXC7W1NacDJts2W1vD+Ml7rsClW9dJG1NpaLAq8KNRS09QIEpJqbqpFYDr8LLKPpoLpx2w\nEhGLrVxBKBoitLMASxdpNnZqVCIX1LY2i2c0MgJeJl5VLrg3kVw4ePCgzMdB0KdBYUA0qUMvoQkv\n4EoJrWIbINvyppJ4Rkttc+nWZpzRGsIlW5qdz8i2j8gI2BMD03j4yOqyLNYmUg9ub6oVAvfhJStg\nrC3S+ZNtHxGdFwoFWSUkA0wOjBURHXHr5zFVzemAybZNuUCVIg6XwDnUj2XXNs6zbZVWo/LkwmkH\nrETI7gXpEIlL3ERiKQNpg8PnUVaNsjCPxyJ7cw69QnhGPJWCERkEFGVZMTzZvQYVhQkjeufiTC0H\nh2dUQWmupQ7Y87a14HvvumxRo2XZ9qmvFZcivvFHj+PGHz2el6Ntpyrs1IUocM5xdGy+qP58bvss\nJwsg2z7ndNaj1quiKSgvukOlhm/3Uk2mTaQK7KXq8PMyzkcu+1RzH9VCkLXPCaH3tQ9jxXHA7BTk\nRsRTBlK6CZ+mwO9dPVuxFKcdsBKhaXKbCYjiGWU3+PwcyKzcgfiKlGKgDwxYEhQdHWDLhOObmlYm\neVLATkOWSvSeLSQCZm/wFaSXox87AWD56CQg3z6iUsSJtIHZmEUWX66XnRtZ+5woadyl+NXjQ3jj\nzQ/il/sGC7rOjEZhjmVSXG1tyzpgsu3z0VecjV9/+EqniEYGbBkB47hYnhFj2cNYodkK21H3bN60\n6Ho3V7cca1s5QEXEt/e9YtYC9+HFqVDNY53OhdMOWImQXQVZHxCzidik6Po8XxyVsOVNMciGgXuW\n/UxfX5+ch3FBeASsdvXNyH1KrBQ9o6Uk71yQbR/n8BIrjQOWTQ9782rN5aS5BEfAFjKpj0Kroh0O\nS3c3mKqitc6PWq+Knd2LW97Itg9jDDXe0g+0ybSBvuHZvBwqpa4OSmMjeCIBc0ysFEWxKdWlJO9c\nDnI51rZywHbARBex2AfbuQL5oMbUNPjMLFggAGXduoIyFblw2gErEbJJ+NkIWGmbiP3i5Ou52yfF\nSklzrcb/AoBAICDrcRxkeUalbvLW9flMbCUUgrK+BUgmYQwPlzTuUnDOi+KzOZtIBdlnQ0MNNJXl\nVdiwEpy5k+eiS5WCrCsypWoscY7bGmqx56ar8a5rzlj0uXLMHxH41n1H8ZZbHsZDeXD0ADoifrF8\nXedwuYIDVq22KRRUKchiJYMM177DGHP24XwOyrlw2gEDwBjbxBi7pphrZXPARBGJnRRXvilIZxOp\njDSXkYcDVg6eRJ0gjl7BDjLRJv+5Xx3Cy/7j3oLIqktV1peDbPs0BX343jsvw6ev31nSfXJpZq0E\nu0pXPI/FjoYX5uznOrzkqkSuVp6RXSFuCzOvBqpNvthm9tkI2PIabdVqm0KhbuwBIF6KwklBFpke\ndmyTWafzzSQtxZp0wBhj72CMvTbzdWMel1wA4DbGGGeMTTPG/sAYuyCfsWT3ggyXkLt2w1608+EY\nAYCW4SPoR4+WNK4oLC0FzgXZ/dIAgSnIgjd52z5iHbAjY/OYiaVxrACRQcOd4lqBI1kO+2xqCTpp\n/GJhn3rzjoC5mgpzQ5zGVbHOfj7RY6A89hGBuRycqZVAVQkZzjSwLujwMjMDc3ISrKYGSmsrACDg\n1xCu0Ra9t9VqG8DiUObrTCkNDWDhMPjCAkyBDciLDWQsnTvZaPjpCBgAy/kCAM757Zzz2wHcyRi7\nZbXrOOcNABo45w2c82s55/vzGU92K6Js2qE0x6+rKQBNZTivqz6vz2vd3QBjMCKRimh5k+uUeHyJ\nkxCNlq6VVijW11nCvGYRlWluFMIBA1xRFqo0VwFRlnw3+HLYRwTmCoxOKoEAlNb1QColNEUcLjIF\nmc/hBahi++TZ7NmG1pOhV1BFwAqwj7u7h80v/OpbLsb33nnZoihltdpmeDqGF33mbtx85+G8Ps8Y\nIxHLLZYPunRtmykwkLEUa84BA3AD5/wb9j8yjlRe6UXOecHy8rKV8Gu9KjyqVd5cimL0ri3NuPuj\n1+BFO9ry+jzz+6F2dgKGIbQnpGFyvPd7e/Gt+/KPrPF43NrINM16JgCf+NlBvP6rD+CkS3dn27Zt\nwp4zX7z8/A7c+LLteNVFy6feVoNumIgmdShs9T6dNsh4RkVEWbItiHpW/Fw57CMChW7wgCsKJtA+\n9UVWdbpbRK2E6rVPYbpMTs9BwZV2xfS3zPK/srZpCvrQWl+z6HPlsk2p+oZ9w3NI6iYGChASp2jK\nXeNVsS7sg9+rFpTaXMrPKzRTsRRrygFjjNXDSicuxUyxHK/VoOvyVJsB60QgSuqgUAV6Jw0pcBOZ\nmE/gkaOTuGNv/qX0TpuOzk4nxXXC5n24nNJJgSHrfBHwa3jNxZ1FkzKBxRu8kofMAUDH0XN4RsWc\n4lfZ4MthHxEoZtGlsE8xwr/m/DzMiQnA74O6oXXFz1arfQpVJneLfYrkGWU5YIU4YJnI/ubNK36u\nHLa5/ZEBvODTd6FvuLj2SkBWd6sQGoBTCSnQQWaM4da37cK33n5JXpXMQKYgaZnDy/r64gIxa8oB\nA7AJQK4o1hRyO2YOGGPXuL5uzDhzy332HYyxvYyxvaOjo04+PhKJOOXBk5OTOHDgAEzTRDwex759\n+xCPx2GaJg4cOOBMoL6+voKv9yuWkxFN6UVdX+z4yGiBDdz/p5Ke3z3+aMR6oWfjqbyvP3z3PQCs\nDd4e344CjA+dcK4/dOgQyd+f+nqvpkBTGJprkPf1WlcXuKpCj0TAk0lhzx/OlNI/ezyS9/X2ItVv\nms74Dz2695Tr7c9X2t9/teuPD44CsBzkfK8f9VibcfrYMWHPrygMAa+1hM/G0nldn85s8Ky9A0xR\nVhy/GufPE0/1IpE2oCkMzx56Mq/rh+bnLSmKWAzP/ukBYc8/OzECAJheSOR9/dSBAwCAREvLiuMf\ny9hR5t+/b3gaybSJ3z38VNH2m45anVR8TM/7erOjHQCQPHJE6PvTWl+D+fGBvK+PRSJWW6RgEDPc\nOvBcvsHEu5/Xhued2bLo+rzBOV8zX7BSjUdzfP82AJ9d4bpNADYt+fcf8hnzwgsv5LLxp2fG+Zf2\n9HHDMKWOO//t7/DBtg4+9YEPCrunaZr8uZ/8Pd+1ew+PJ/W8rpn76s18sK2DT//TP3POOU/rBt+1\new+/9J/3LPqbGIYh7DllIzIZ5TPRZEHXjFx2BR9s6+CpZ54R9hw/f2yA79q9h//bHU/mfc3wzgv4\nYFsHT0cinHPO7+0d5Zd94nf8rqdHFn2uWu1z4w/3812795zy+6yE2J49fLCtg59845uEPst1X76f\n79q9hx8dm8/r89E7fsEH2zr4xFvftupnq9E+ozMxvmv3Hv6yz99T0HXjr3o1H2zr4PE/3i/sWR4+\nfJLv2r2Hf+JnB/O+ZuzaF/HBtg6e3L9/xc+VwzZf+f0zfNfuPfzb9x0t+h5f/E0v37V7D//BA8fz\nvia5bz8fbOvgY9e8sOhxRSDx8MPWc7z05fl8PC+fZa1FwIoC5/wY5/yY+98ANuVTCSmbhA8Al5+x\nDv/wojPzTk+Jgh0WF1lpxxgrWNssS1TtyVyXO2WXrKC+lYWio7G24DRmthJSXKWqTfTON91tRqNW\nz0Ofz+ohCuBgZAaGyRGZWNw3tVrtU6iEC0DXrSBcIJk4H302G+Wwz+d/1Yt/+d8ni04FzjjFK4Vx\ncrQtWwAA+tEjRY2bCxdtasI/vnw73n7VyulEG5zzvO1TDtsUq+zvxkwRsg029SV97GhZhabdPSBF\noWIdsEya7w95frnThY05blcPoNCk+QyAi1b7kGwl/HLCYztggonehYriLV2k5papGOzt7RX1iFWB\nbCWkyGoh6286k+8Gn3H+tJ5usIxI8XKNxavdPi3h/HsWal1dVkP7AbFVxIX2t3Tss3XLqp8th31+\n9+QIfvvEcMHaWTbs97S+0MOLvbYdEXd4URWGV13UibaG2tU/DMAcHQWPx6E0NUGpX7k6vRy2ESGx\nM1uEfZS6OigtLUAiCWOwsLZbIuFuYC8KchsZFgBuVTJ+Y9UPLsZeWM7WUjQCyCkrwRjbBCttuTSc\nNJX5WhGyqyDLCaV1Pf7/9t48TI7qvPf/nt67Z181M9pGo320oZGEWASWQSBsgxciltg4ToyRwo0X\nnGvDD9txch3HuXBtx1sSI7i+No5NjBSCbTA2ktgkQIA2JLRLI2m0zL5vvdb5/VFL93RXdVd3VXfV\niPfzPHpgpqtOn56365z3vCvz+yH09kIYGMi4SOhFtoDpbYwqL5LyqXVQIyutubnZlPlNFvKRCZlt\ntfW4bOYqv9Mq2zBZ5fPQrc042zOK6VX6q5EzrxfOadMQa2tDtK0N7jmZFSA9yH0Tx0L6FBZFPrPF\n9w9HBXz+F+9g9ewq3Lt24pyskE+Z342RYBQDY+GsskxlBkZzq0wuy8NMBSxbkjPs0mGFbMqVBta5\nHyCMWCjDXV2Injqt9CUuNPGDf6NpY9rWApYLXCwj0aoSQF/OOd+ucVsfgE0qv18JDaUtkUK3IrIS\n5nDkpeCnkk6vwwUp9PdD6OkBCwTgrK8X79OoxeLVaNJ9uZIXBSzLMhTRU6ILxz0n7nbRyhq0Qj7h\nqID/89wRvKWzTY0as2qL8cHmKVnfl4+ekHdeNRO3r5qOq+ZUZ7yWC0JcPpJb53TnMA62DeC1Y90p\n11shH6O9bnNxcQGAa45sATPPBZktybUN0zEZZQPkbqF020E+J8X3TjxcGuVy1B4eAfCw/IMUx7U9\n4ecmxtgWWUnjKrW/pGKuTyfGhWkxNjaW6ZLLCsUfb2KcUTZViSPKCX624uLSaoh68OBB0+Y4GchH\nqQOl5Ml4RFdcTkRZpOLWlHhZjYmLrhXyOdE+hP965zx+/pq5bnQ95COGcs6UEjx4azMqizNvyLH2\ndtHFVV0NR4XYeDu+IaYqLFbIR96Y+0dzs7LI7YeqdPw9EnFOnw54PIi1t0MYya65uVkkN+FOx2SU\nDRBfq7N2EUvrScQiCyWPRMROCYwpe6AZ2NYFmSuc881S/Ng6iO7IJs55ooWrCWK2ZCWkkhXSPQ9K\nP8uKmZpVLIVC94K0Glce4sDkjVlPoLccJJsYw6JYWJIe6vdLvzQZZ30dmM8HoacHwuAgHGVlhsf0\nuBwIeJwYC8cwFo6hKENhWFX5jKk3FrdCPn6P2Ii7z8AmkitKoPdJfVXAzUa2HiTKZiBNxwUr5FNu\nsJn9zUvr0T8axq0tU7O6jzmdcDXNQvTYcURbW+FZujSn9zeCmgvy+QMXcfzSEL78oQUT6lVZKZtc\nXZDBSAzj4RhcToaA15nVvYqF0sQkiWyInjsHRKNwTp8Oh9+f+QadXHYKGKDEj2m9th1AhcrvH83l\nvVxpet3ZlUv94/jqr/fhrz4wG+sWpy/GmEw+XJBlWTzYihk4oVDhgMYGX1VVZdYUs6JnOISXDnfg\ntpap8HsK9/2QXcSRI0fETWT5clPGvWP1TFzoG0XAk37R5NFovM2N9D3hnMdj9ALWyyfRoldo3HNF\n14VsJSw0yfFfQDxmSs0CZoV8jFpZ6sv9eOBDuVWJd82eIypgp05booDJXoVEF+Tml06hczCIT6+Z\nhZrSeLyxFbIp8bnhdDCMBKOIRAW4syzkPZRg/dJb/FQmfnix6NmRDk16kley4XJ0QRaUyZgF+U5r\nL053jeQUBxOvhm+eKTibTC55E5E3MyAxC3LiJpJ1UTyT2PLWOXz/hWN48VBHwd9bPimaucnfv24u\n/unOKzIumrG280A4DGdDAxxFYoC6WKWdI+BxwueeqMBZIZ+yhPYwuZY6yBXXPPE7Gz15suDvDajH\n56WrTG6FfMyIM8oVK+OMeDCI2LlzgNOpZHdzzhUFudg38SBnhWwcDmYoE3JQIxtaD876erBAAEJv\nL2J9/Vnfr8UTL5/Cc/svZrxOVvzMSp6RIQXMIJMxCF827+eSZRSvZ3QWPJZ7L8pElHY3OixgkVPS\nSSRhExmX2g8lx8EUFenPUjMTh6SodA0VXjl3zZsHwBo3V0TFxSW7+tQ2eCvk45ZcqjGBYyTHUge5\n4qiqAisvBx8ehtDZWdD3BhLiJ+ekWo/VYnKskI98GOs3kGmXK1bGGUVbzwCCAFdjI5gUYB+MxBCK\nCvC6HCmHF6vWNjnrNhcL5czqIlw7rwZ3XJl9FiNzOBJiKM2Rz1goiideOY0f/el4xmvVYlt7h0P4\nj11ncnaXA6SAGcaqGLCuoSBOdw7ndK/88FQWZz93R0kJHFNqgZB5NVkW1Jei1O/G/PrStNfxYFC0\nsjidSn8wALj76pn45DWNKZlgVsWAZZNUoMbml07iN7tza3guWwajJwqvgCk1puakurgqVBQwq+RT\nmmVpDbNgjFnqhlTi8xLlkyYI35I4IwstYFbGGUVOnhDnMC9u2U+Mz0u2Plv17MjfkyGdRbMT8bgc\n+N6nWvDxlbnN3Wz5+NxOOB0MQ+MRRKLpC7yqxbY+/VYbfrLtBLa/l7ungxQwg4RNLKqYDQ8+tR+f\n3bw7p1iW/jRWCT2454pWlohJm3xViRcvPPhB3L9uXtrromfEU6JzxgzllAgAi6eV44vr56c0F5d7\nfBWaeJxR9t+NgdEwfvZqK57cmVuMnbyAywt6IVHiJBLi85TvmoqFxTL5+PVbXM1GXsAL7eYShoYg\ndHaJTbinxgPUB9O4IK2QjxmZdrkSTzA6Y5p1PxSJYevbbWgfGE97nXxgSlSOB9Mox1Y9O7e1TMPy\nmRWYM6Wk4O+tyMekw4vDwXTFH3POVesbyh4Orzu7hIIJc8j5TgKANa2IACASFRCKCugcTP9gq9Gf\nxiqhB9d8yc11wrxN3qmjrVI8/kufH350dNTQnHJF/rvmkmnXp8R8ZO8eBiBaBl0uxNrOQxjP/rth\nBNX4POmAUKnyXbNKPuUGLZRGUCyUBXYRK7JpipdvAdIryFbIx2gWpBEcRUVibcFwGDGTFJy3W3vx\n3eeP4mevpHebyYdZ97z4ITTdQdmqZ+dDyxrw75+9MutCt2aQj2K5elyqsUvt4KOjcFRVwVkZz9+T\nG4urrW16IQXMIFZVwjeyySsuyFwtYNIiETleWCuLEmOkMxBywYLcsqGMYiROwuhDzTweMYiXc1N7\nQmaCc54gn7gF7IqZFVg5qxIfvqIh5R6r5CNvHrnEGR27NIQtb52DIOQWRC9bwMyyHutFLT4P0C5i\nDFgjn3IDsjEDl8mbvEs6WHZmiAdVSoSouCDVLGBWPTtWojw7JlqP9azVcdf9xJ6efQYNGQApYIaJ\nRgsbyCtjbJO3nwVMD4qLS6cC1tubbftPc6g0IBszHmqXBXFgQk8P+OAgWGkpHDU1yu+nVxXhJ3+5\nCssbU1u0WiYfKfaxfyR7+fzgj8fwvT8cw5nu3Ip1KrIxcRMZC0Vx4Fx/2sxKZYNPcA/HBB7v06mS\nkGOFfIp9LjRPLcP8uvTxoPlCySI2ST6yQpnWxRWJiHUVGZsgn7hynLoWWPXsWImrsVHqp9oGblIz\n8kodhgytCvhG91GAFDDDWBUDpihgWW4inHPldJltNWKZRDdKIbvTZ5sKbFWchLLojoYRy9JSMmAw\nPg8A3HIcWAEV5MQYFr01fqySjxEFWY77SI431IuzoUHsp9rdDWEgpQlHTvzb9hP465+9jX1ntdPz\nI8fETC/3/PnK70aCEQgcKPW74HKmfh4r5MMYw/+9bzX+9S9XFfy9gYRAb5NcxPJzPDCq7e6Onj0r\nFvmcMbHIZzoLmFXPjpUwnw/OGdMBQVAaYxtFlwVM+i4khr5wzg3HUgOkgBkmENDX6d5scrWAjQTF\nukxFXlfOwYOO8nI4ptRKWYltOY2RLTwajRcqnDc3w9UiSy0opgiIpQ5K/S4IPPuCn2acqhLrTRWK\niFSXyL1Qv2vEKvnI5UqMue9z68XHHI64K8WkYOJITFTyz6axykUl+bgSXFdFXhcaa4qwZl6t6j1W\nyYcxBoeOmNBkIlEBu0/1IBjJPYBeVlAjxzOXJtBDYvV4LQulfHiRk5tk0lnArJKN1bglK5RZ4S8V\n0nM8kGYtiJxMLX0k76MBb2p9w2wgBcwgVgXh56qAxTf43IK8ZdzzpIWqQFaW6JkzQCgE57RpcJTo\ny8AJmWSmzgX5wc5dPgYsYHNlF7F5ClgoEku7sSkKWBaxKVbJR87gSi5umYlgWGyl4s6hlUoisivD\nLAU5kxtFGB5G7OJFwOuFq3FmfB5OB576m2vxzduXqN5n5fOTC3949xIe+OVebH0r90Oha774/Y0e\nP2GKdd/vccHrdiAcFTAeVn9+5DU0+WCZLkFissnGLFwLxH0nalIh2kz7KOdcdW0zGkctQwqYQayq\nhJ/rKT4eY5TbCV5GKfhZoED8yNHsN/gjR47kazoZUTbFkewWSlMsYE2zAIcD0bNnTYuV+Pwv9uDO\nH+1CNKa+KSnySXBxZcIq+SxoKMXWL12HL63XP1cgHhheXpR9K5VE3FIMpewWNIoS06axFsjWAvfc\nuWBJrdPSfQ4rn59caOsVMwOjOSZIAICzskK07o+NmWbdzxQHFm9zM1EBk9dqtXqNk002ZiFb2CMm\nK2Cah5eODvCBQbDyMjjq4m37zNpHSQEziNVZkFZYWICETaRAgd5RySUgn4D00NzcnK/pZMRK+TCf\nD86ZM8VYCZOapncMjqNrKIie4VSFjguCkpDhysIFaaV8plUGVOOe0pGuqGw2uBcuBABEjh41NI6M\nvAloKfuK+zEL5RiwVj650CfFw1aXGNsU5UOeWZt8ptpmSgmKpAzV8oAHXpcDjdWpVe8nm2wA0aWq\ndYDTS1w25hxeMq3T8dCKhRMOK2bto6SAGcSqVkS5bvCNNUWoKPLg6qSq8dmiWMAK5ILUijHqHw1j\n75le1fgKr9fYQmyEaZW5xQaapiDLgfgmxbLIMU9qJ8XYhQtinZzaWjgrU7MdtbBSPrkgW8AqDNZA\nkhWw6NGjpvSElC0kWqd4+TuQTXweMPnkIyugRt1CyiZ/1CwFTI4DS40H5ZFIvINEkgXs23cswzNf\nvj6lxRow+WTTOxzCbd97Ff/wzCFD47hmzwbcbsTa2iCM5JaJnEhGBUzD80IKmE0YGxuz5H1zVcBm\n1RTjD19di0+sMtbKQtngT500pWr0aDCKu3+yS7NgoVaM0b+8cBR/8/M9ON4+lHLPwYMHDc8rVz69\nZha+c9cyrF04Jav7Bkze5CNHzLKyaH/fFNlkaWGxUj65YNqiW18HVl4Gob8fQleX4XllyurMxT0M\nTD759MoKmIrCkg1yokLUNBexdjxo9NQpsYF940w4iosnvOZxOVCl8VmslA3nHMNZJhed7hpBOCpk\nHZKRDHO745mqJoS/1JR4Uep3o0QjHlRbARM/BylgFmNVL8iAxwmvy4FgJIbxcHa1yIzEr8g4ysrg\nqJsCBEOInTMeK3FpYAxnu0ex43BqXy1hbEx8D7d7Qp0cAGjrFRVgtXIPVvVLA4ASvxs3NNfBnUW5\ngkhUwNB4FA6WW6P0RNySiyJiUqxIupg2eaPKxj0MWCufXDCjRAgg9YRUrCzGFWQljkWlJA3nXHFB\nZhM/CUw++fRKn78qhx63ibgXmJsJKVso1dz38gHJnaVL0UrZ/PBPx3HLoy8rMXd6kJVjLYUyG5TD\npQkuYq/biac+f61m2RO17GEgvofm6umQIQXMIC5XdplUZsEYQ02p+GXWyq7JN2Zu8hVpXFzR48cB\nzuGaMxvMPVExSReXU1VVZXhehYQx0V0xt640pzT8RNzNsgXMHAWsIk2gd7oSFL3DIU0322STjxJ4\na0IblngcmPFNpNTvhsvJMBqKIpSUqSp0d0Po7xcL5NbXaYygzmSSTzQmYGAsDMZMcN/PnSsmsbS2\nmpLEUi0pHb0qhxf5+cxWAbNSNl2DQcQEjmOXUr0OWsiHA7WEgmwxO0avqtiLEpUDL49ElIK87qTD\n5Z9fPRPf/eRyrF9Sb+i9SQEziFVZkADw1Y8044Fb5hs2ueeKooAdPmx4rMQecMnWLKWIZNIpJLEY\nntqie8ykB7RQuJwO/OYLa/DYZ680PJZz5kywoiIInV2ImVA1uzKNlUXLPfzGiW585Luv4GmNsgCT\nTT5mBeED5rqIGWOaLuLEAqzZWr4nk3wGxyLgXAxczza5Ihnm94tV12MxU2q1Ta8SrSRqB5G4ArYw\nqzGtlE2VlOTQq2LR06Jv1EQLmMkxelpEz5wR3cMzZqS4h/0eF9bMr83Kw6EGKWAGsSoIHwBWz6nG\n3Vc3Wvb+7kWLAADhw8atLC6nA6V+t2rxUi0//Fg4hlBUgM/thN+TaoksKkrNHrI7ZQEPfJ7ca0zJ\nMIcjvlCZIB+tsic8HEb0tNRGJaGRMAAck+Ly1JQ2YPLJp88kFySQj0xI9UB8OXs4+QSvByvl8/Wn\n38UDv9yjO0mh16QAfJl4HJjxTf6auTX4zl3L8Lm1qR08cnVBWikb2aLXk0U8V9wCZlwBS5SNGUks\nWsjPZi7Pjl5IATOIVTFgdsCzeDEAcyxgQGIsy8QHWyuGJd4KQj1earLFsJiNmW7I+AafJJvTp8U2\nKjNnTmijAsRPyFpuh8kmH9l+NKPKePcL1/x5AGOInjoFbkI7s0qNUhTyJqIWn5dp87JSPu+09mD3\nqV7VzEE1zArAl1HiwExQwBwOhhua61IU91hXF4SeHrDSUjinTctqTCtlk5MFzEQF2dlQD1ZaaloS\nixa51J7MFlLADGJVL0g74GycCRYIQOjoMMfNpRJnxDmPbyJJMUbxh1p90X0/9ktLRLZQmmEB03Rx\nHdZ2ocgnZK26TJNNPg9/dBH+9S9XorGmOPPFGXAUFYm12hLKEBihVo4HTYoBi7wnHo7cixZP+P1o\nMIoNP9yJn7yoHWhupXwq08RNqWFWAL5M3EWcv4Knivtx4YKs3cNWykb+L4gpQwAAIABJREFUG/dm\n0YfYTAVZTGIxT0HWQgnAX5idezgbSAEziFWtiOwAczhMjQNTa6kSu9QOoa8PrLwczoaGCdfLWUU1\nGhv86Kj+LJ3LEUU2R01wQWooYOFDYl0fz5LUdjbyCVkr7sNK+QTDMXz96QN4SSXrVouaUh9WzDIv\n+Fmp6m1CLMs9a2bh3rWzJ9T346GQmMnHGNyLJrq4jncM4WL/OA6e124IbqV8qrJUwPpMzLIDAPcS\nybp/8FDe3FyK+zGHDd5K2cgHKr2yAdJX9c8F5XB56D1TxlMj3eHSLEgBM4hVlfDtgrywm2NlSXWj\nRN6Lb/DJp0RZAdOysCzIo+l4MuBauEB0c508ZTibS7aADYxOTJKIvCcugPKGlUgmC5iV8jndNYwd\nhzvx6zfOWjYHM60sM6qKcN8H56DYF3fHR44fB6JRuGbPhiMw0W2qpyyAlfJRFDCdbq5QRDwI15aZ\nsx47p00DKy+H0N8v9tHMA0qMUQ5V7a2UjWzFUiuroUZM4EoCi1kxem6pGXn4oLHCrlrEensRu3QJ\nLBCAa9asvLwHQAqYYaLR7GpwWY3Zpzm3iXFgshuleyhBATuUZoOXLSwaG3yvCW7RyYwjEICzsRGI\nRg1nc7mcDpQHxCSJkaAYl8MFIe7iWjxRPpxzZfOs1tjkrZSPXGct216qZuKWrIaRPG0iimxUnp2+\n4cwuOyvlk62b62Mrp+H+G+fiw8saMl+sA8YYPEvzLJ80GZD/95VT+Kdnta07VsqmIuCB08EwNB5B\nOJrZAzQwFobAgbKA23CGqkxcNvkpSCuP6168CMxpPClKC1LADDKZYsAOnOvHLY++jNeOmRe4qFjA\n3jOugMmWku6Ek5V8wnGruLhkC4uWC9LqGKOe4RD+fftJdA9ZV6rETBfxvWtn42MrpinKS+zsOfCR\nETjq6uCsqZlw7dB4BJEYR5HXpZnVaaV85O9aT5o6ZflG3kTChw6B5yGUISK5h5OVY0BfTI4d5KPX\nzVVb6sNnrm9SreeUK3Eri/mbPB8fR/TkKcDhSCnyyTnHk7vO4Pf7LyIYUa/xaKVsHA6WtjBzMma7\nhwHANWcOmN+P2PnziPX1mzauTPzgv9T0sRMhBcwggYDxjKhC8fbpHgyORXDs0qBpY7rnzwecTkRP\nn4YwPm5orOoS0X3QMxxXWOIuyOwtYEuX5vfhycS2Q+34xc5WPLvngmVzMPOkeMfqmXj4o4sUV3A8\n/kttg8/cGNlK+fg9LhT7XAhHhZSyJ4XCWVcHx5Ra8KEhxM6eM338sLSJeNIoYOk2RSvlU5mlCzIf\neKTPLyuyZhI+fASIxeCaPy8le3gsFEMoIsDvccLnVj+8WL22VWZRimJoPCrdY17FAOZyJcSBGV/b\nHn/5FH74x3gsprK2LU09+JsJKWAGmUxB+PGYKfPi1pjPB9fcOYAgIGowmLimZGJsQayzE0Jnl5im\n3diYcr3cAaC+zJ/yGgCETKhibYQir1ibrH3QmGJqBM8VVwAAwu++a/rY8fgvFeukEoCvvehaLR/5\n+9Y1ZP0mHzZhE0mER6OIyjFGixelvK4na9BK+WQbhJ8P3AkuSLOtpBHpefQsW5bymp6aZlY/O9VZ\nlKJY0FCKDy9rwD3XmhtL5V4mKcjvGn92tr7dhqfePIdBqRdvRPG8pB5ejl4cxE9ePJ51C0A1SAEz\niJWV8AGgayiIl4906logMgWt54qyiRw4YGic6VUBLJ1Rjitni5lmihl40SLVNO0vrp+PB29txqxa\n9bIAR/KYQq4HuVWUnmDVcFTAV3+9D8/uMde1oGwih4+YUm8qkXTxeb0ZAvABO8hHPIh0D1voIl5q\n3iaSSPTkSfBgEM7p0+EoL095XY9byEr5xF2Q1oV4KIH4fX2IXbpk6tjyWqmmgPXocA9b/ezI8tFT\np63I68I3b1+CqxIydM1AzrwOm2ChLA/E+3XG+voRu3BB7IgwJ7V47s9ePY3/eP1s2gxivZACZhCr\nsyB//KfjePg3B3R9GfKmgC1fDgAI79tnaByX04HN967GVz4ixi3JsRdqLi4AWDK9HLev0i5I2JxD\ndpGZyJZGPTFg710YwM7j3fjjwXZT5+AoLRUbmIfDplVdB8QAfNmqplaCoidDCQrAevnIFrBuO1jA\nTI4zCu+XNvjlV6i+Ht/kta0sVsonHoRvnWwmBOIbVJAFgePnr7Vi39k+cbwD4rPjviJVAeuS1ova\nUu29xepn52MrpmHtwlrlsGwFZlrAEr0vskvTvUg9AL9Tkk+Jz3i8ISlgBrGyFREAOKWmzed7xzJe\nm6ksQK64WyQFbP9+U8cN790rji8peNni9VrTI1Mm2aWaDqVqvElp2om4ZTfkAfPckNFTp8CHhuCs\nr4ezPrUhrWzKT+futlo+ajGHhUaxUB56z9RAfPkw5GlpSXktEhXQNxKGg6VXkK2UT6nfDbeTYSQY\n1QxELwRmBeKf7xvDT3ecxI/+dBzC4CCira2Ax6NaZb1rUFbA7CkbAGieWob/ffdy1Jerh38UAtfs\n2WCBAGIXLxouBJ6YABbeJ+5jsoKXjJmGDFLADDI2llnxySfVOjf5aExA/2gYjJm/ybsXLADz+RA7\new6xvj5TxuSCED/Fr1iR0xgH85SirJeygLiJDAejCIbTbyLyqbcmzaKbKx7plB0x6CJORNngNWSz\nbnE9bl5Sh5uX1GmOYbV8alTKnmjxu70X8F9vqzcVN4KzthbO+nrwkRFET540bdx0Cpjscq0u8aUt\nC2ClfBhjioLcZWEWsWeJOUksSjzowHg8s3tRM5hKKzv5805JU9PM6mfHDjCnU4lvNGoFS9xH061t\nZu+jpIAZxOpekDU63VzdwyFwLp54zarFIsNcrvhJfr85m3z09GnwwUE46urgmppbbR+rew0mbiKZ\n4ow6BuVF1/wTZT4C8cN7xUVKtn4ms6ChFN/asEyJs1LDavnUKjFg6RWwcFTAI88dwY9fPJGXkhWe\nleJCH35nj6FxwlEB2w61o7+zF9ETJ0ULi0oAfudg5g0esF4+H17WgLl1JWldcflGVmDD+/aDx3K3\nxFUWeeByMgyORTB8QAqtUIn/AuLySfe5rZaNXXBLf0Oj3hd5neoaHI8rYCtTFbDeEXEfrSjymLKP\nkgJmEJfLZen7TykXvzjyBq6F/FDXmVQpOhlloTLJDSm7H3O1fgFAVZV18QkyipUlwyafT/m4mxcC\nHg+iJ05CGDSnBEk6C4terJZPPAYsw+FlKIiYwFEWcGfds08PnlWrAADhPcYUsFePdeLvth7E/3vu\nAMC5aGFRcVXJ38VMio3V8rnvhjn45f3XaJZiKATOhno4p04FHx5G9PiJnMdxOBimSH/vSwfEbHGt\nZ0fOyk1X1d9q2dgFr/zsvP2OoXHkdbe9vQ98QDz4J7e+A+L7bJ1JB2VSwAxidRak/MXpyFDqoH1A\nfD0fFhbAvEB8GdnC4tGwsOjhWB4btepFkc9AevnI8stklcgF5vOJp23ODVtZAECQNyO3WzNBQg9W\ny0c59WZQwDp0WCSM4Fm1EgAQMigblxSPeq5dTMjR2uAX1Jdibl0J1i9Njd1LxGr56OVM1wi2HWrP\nW0Fdz5XiJh96x9gmLz/bF1vFuoCe1VeqXqe4INN83yaLbPKN/OyE9+0DN9CVRt4XO3qGxXFXrFA9\nbMnreH25OWsBKWAGsToIX9bEOwZ0WsBM+uIko7hR9uw19CDIZIox0kNRUZHheRhFDlJtz6CAdZp8\nskpGXuxDb79taJyYwHH0tX3gnIttOgxkAVstn8oiD2ZWF2U8lMgbYr6sx+6FC8Wq3mfPItbTk/M4\n8vw6R8TSAFoZkDOqi/DL+6/B9Qtq045ntXz08p3fHcbfbT2Ii/35qbfnWSlt8gYVsDppLeiGF86G\nBrimTUu5JhSJoX80DKeDpS1DMVlkk2+ctbVwNs4EHxsz1FNVVqg6ghwcgGeF+uFF3mfNMmSQAmYQ\nq2PAygJu+NxOjIaiGE5T0btTsrDkaxNx1tXB2dgIPjqqFOjMFWFgwBQLix3iJPQoyOPhKAbHInA7\nmdL02my8V4oKmFFT/S93ncG9bwfx9swr4GnJXTkGrJePw8Hwq/9xDR7/3Oq01ykxOXl6dpjbrWT6\nGnFDysp+F/OBA/CuvsrQvKyWj17O944CALyu/GxnipvLoIVSXnt7iisVq1oysnu4psSrZLirMVlk\nUwjMcEOW+t3we5wYZy6MefzwSkp3Mh0m76OkgBnE6l6QjDHFqpXODSnHFeTLBQkA3qvFBT+0e7eh\ncUK7dwOcw7OixZCFxepekABQX5HZApYYFO1Is+gawbNyBcAYwu++C27AbR6Rmu+2Vs+Ed801huZk\nB/m4nA54Mmzc+T68AIBXdqUY2OTLAm74XQxjHj/G5yyAsyG9izETdpBPJoKRGAbGIhktRkZwLZgP\nVlKC2IULiLXnXqdPXnt7iqvguVLd/VgecKMs4MaqDPW1JoNsACAYjuHIxcG89luV/5YhAwoYYwxT\nisS6Xt2VDarJK0BCDJhJ5TdIATOIHVoRKVaWNIH4a+bVYPG0MrQ0VuRtHt6rrwYAhN4wpoAFX38D\nEYcL3muv1bxm23vtON4+lHac0dFRQ/Mwg6baYjgdLK1i1ZnHDEgZR1kZ3AsXAuGwoY4FU4rEgOiu\nkhp4V6e3HGXCDvLRQyHko7iI33gj5zEYY5gC8aA1sPp6w3OaDPJJzBhMZzEyAnM6FZeUkcOlYgEr\nqoRXI/6r2OfGc/9zLb7+sfSW/8kgGwB4/JVT+Ozm3dh9KnfXeiZka2L4nXcMKXq1MfFvOrB8tWry\nCkAxYLbD6kr4QIL/Oo2V5ROrpuOJ+65CsQnVe7XwXCVawMJvv20oZfuxSx785T0/wGCLugvlfO8o\n/m7LQXz3+fSV3ReoFDksNLWlPvzH/dfg23eop5wDCSUo8pxur2zyb+a+idS0nwUA9EyZDkdZmaH5\n2EE+erg0kH8LmOfKKwGPB5FD7yHW15/zOLWDXQCA3oXa3ze9TAb5XOwT6zBOqwzk9X28a9YAAEKv\n7cx5jOpRsUZid1kNXPPmaV7n1uFKtYtszvWMYiSoHfpy7FL6Q7IZuGbPhqO2FkJXF6Incs9UXdJ7\nBq5YBHWL56q+zjmnLEi7ETUh4NwoegPx841ragOcM2eADw8jcvhwTmPEurtxMeZC0OPDifLUIFUA\nONsjnlT8nvTp6b0GqyObxazaYpT6tRXfS/3iJtJQkd+q0t41okUx9OprOY9ReVgsM9JVUmN4PnaR\nTzpiAi/IJu/w+8VYFs4Rfv31nMbg0SiqL5wGAPTUNxqe02SQz3lFNnl+dq67DgAQfG1nzlaWsr1v\nAgC6iyoRM+iRs4NsOgbGcfdPduEfntHuxXhRWtum5vHZYYwp8jGytt32yq/x5JNfxJK16vFfnAM+\ntxPTKv0oSbOeZwMpYAaxOgYMAGbWiBkxYxmqrRcC7zViXFCuJ8XQG2+iZkQ8KbaPqCu3ctulGVXp\nH+rJEicxvaoIXpcDq01uVpuM99prAZcL4X37cq4HVvLma3AIAnrhUeLBkjnbPYJLOjLSJoN8uoaC\niMQ4qku8CHjzW/PPe51oZQnuzO3Zibx7ELX9HQCAjpjxuU4G+RTKAuZuXghHVRWEjg5ET53KaQy2\n81VUjfQhxhwZs6IzYQfZMCYqJYcvqK8lkaiArsEgHAyoz6P7HgB8HxBd7sFXX83p/uj584ida4Ov\nyA+3Sm9bQEzaefKvr8bjnzOW3DJhTNNGep8SCOT3wdfDdfNr8Y2PL8ZnP9Bk9VTgu+EGAEBw+46c\n7g+99hrqBzsBAG296nEOctbT9Kr0qdhLl6r38rIbty6fih1fuxFLppfn9X0cJSVi3ZxYDKFd2VtZ\nYn194O/uR9VYPzjUEwuC4RjuffwtfPHJzMHkk0E+srKf7w0eALzXS6f4nbtyuj+4Ywdqh7sBQJcC\nnAm7yGc8HNW0Ol3oy7+FBQCYwxGXTw6HSx4OI/T6G5jX1SqOZ7Cgrx1kU1Pig9ftQP9oWDUDv31w\nHAIXs4f1uFWNoMhm9+6ckozk9dB79VWqDbhlakp9pmaqkwJmEDsE4TsdDLcun5q27Uuh8F5/HeB2\nI7x3b9axLDwWQ3D7DkwdFE/xbRoNxtt0WsBCocw9/uyC2e2htPB94AMAgOArr2R9b2jHS4AgYBoT\n/66yKziR832jGA1FdQVETwb5XCiQhQUA3IsXg5WXIdbWhuiZM1nfH9y2HXVDogImu+aMYAf5nOsZ\nxS2PvIx/267eJ1Ou/TW1ogAKsuyGzMHNFd6zF3x0FF9s34XffGGN4e+THWTjcDBMlz6H2vdNtk4W\nQjbOmhq4Fy0CgqGcsiGD27YBALzS+lgoSAEziNWV8O2Go7gY3quuAgQBoSw3+fC+fRB6ejA9IFX0\nVtnggbhlLJMF7IiBwnyXK94PrgUAhF5+JetYlvEXxUVqVr0YfH+2eyTlGtliND2DcgxMDvn43OJ3\nMd/WSUDMtvOtXQsAGP/jn7K6N3rxIiJHjmBqdBgOJm5+oUhqSEI4KmA0qC9u1Q7yGRwLIxQV8E5r\nasxTTOBKjFG+Y8CAuJsr9PouCFlmIcquscrrrsbMauNFVO0gGwDKZ1HzVlzsk5Xj/MsGALyyG3JH\ndt4XYWxMkY//5ptMn1c6SAEziB2yIO2G70bJDZnlgxD804sAgKkfWA2f24n+0TAGxybG2I2Ho+ge\nCsHlZBmz0pqbm7N6//cD7uZmOKbUItbejkgWzbl5MKgo1E1LxSwhVQuYrIDpOOFPBvl8aFkDtnxx\nDW5bPrUg7+f/8IcBAOPPP5/VffIJvvi6azF7SgkEDoyrxITe98RbuPtfd0EQMivfdpCPfMg63zuW\ncmDoHAwiGuOoKvbA78l/T15nXZ3YmSMYQnDHS7rv45wj+IcXAABeKUTDKHaQDZAgn55UC9jZHvGA\nNiPDQdks/LfcAgAIPv8H8Cw8U6FXXwWCIbiXL4ez3ljtvGwhBcwgVrcisiO+dTcCAIIvvQyehalc\nVsCK1q/HjGpxA092Q15IMGtnctt5NWq5vJ9hDgf8t94KABj/7e903xd6803wsTG4Fy1C01xRGTnb\nnaqA6bVOAvaRT1vPKG7/wWt4/sDFlNcYY5heVZS3ArnJeG/4IJjfj8j+A4hevKT7vuC27QAA37p1\n+PYdy/CDT69AeVKsysBoGMfbhzA8rs8CZgf5lAfcKPa5MBqKom904mHsVKfYt29WbXHB5uO/9SMA\nxE1eL9FjxxBtbYWjokIpVm0UO8gGiIeBqFnATneKCticupKCzMXdshzOhgbE2tsR3rdf933jfxT3\nHf8t6/M1NU1IezDI2JjxWIvLDdesWXAvWgQ+NITgS/pOihFpkWLlZfBcuQozpQ082Q3Z2iU+1HrM\n+AcPHsxy5u8P/B/9KABg7He/131SHP/9cwAA3803obE6Lptkq8TJDnFTnD0l86ZoF/m09Y7iUv84\nXjyYe5Vzs3D4/fB+8IMAgOALL+i6J9bTIwbuu1zw3bQOM6uLcJVKRu1JSWGZW1eiS6G0g3wYY2iS\nFKxT0ndLZjQkKpJLC+AelvF9RLRQBnfsgDCuL9FhXFLWfB+6BcyV3lKnNyzADrIBxL6iAHAmKRyB\nc64oyHOmFEYBY4wpCvL473+v6x4eDiO4XbQe+0gBm3xY3QsyEzGBK1ajQuK//eMAgLH//q2u68e2\nbBXvu/U2MJcLjVJpjdOdExfdo1Jhv/n1mR9q6pemjmdFC5zTpkHo6EBYR3NuYXwc48+JLjH/Jz6B\niiIPKoo8GA1FJ7i5wlEBp7tGwBgwV8eiaxf5xDcRe1QX93/kQwCAsWf1PTvjv/0dEIvBt3YtnJWV\nmtedaI8rYHqwi3zm15cCQErni5sW1+H7n2rBp9fMKthcXFOnwr38CvDxccXqmA4uCBj7r2cAxK1n\nWnz5P/bic0+8pWsedpHNnNoSOJj47AQTYg67hoIYDkZRFnCjqrhwe6Ri3X/ueV2Hy+D2HeADg3At\nmA/3nDn5nl4KpIAZxJXhRGM1T71xFht+uBM7j3cV9H0DH/0YwBiC27YhlqFoII9GlUWq6M47AADN\nU8VA78MXJ9aYOS4pYAsbMldhr6pK30+tkPQOh/DAL/fgtWOFlYMajDH4PyZZwaS/ezqCL/wRfHQU\n7pYWuGc3gTGGv799CR68tXlCbazWrmHEBI4ZVUW6ambZRT5TKwLwuZ3oGgqib8T67DLfzTeDlZQg\nsn8/IkfTd3vgnMcPL392e9prT3aIz848nQqYXeSjpYC5nA5cM6+mIPFfiQQ+Lh0un3oq47XhN95E\nrK0NzoYGpZq+GoNjYbx5sgetXSO6rGB2kY3P48Ss2mLEBD7BQqm4H6eUGC65kQ3uluVwTp8OoaND\njO3KwNhvngYAFN1114Tf57N3ZSKkgBnE7lmQu0+LPbgK9H1ScDbUw3fjjUA4jLFfp1+ogi/8EUJ3\nN1yzZ8PdshxAXAE7fmkI0Zh4khEErizC8xtKM87h2LFjRj6CqbR2j2D3qV786vXsywvkg8CddwIA\nxp/5bwj96cuFjPzs/wEAiu66U/ndVXOqcfuqiafw45KFRY91ErCPfJwOhuap4vfp0PkBi2cDOAIB\nBG7/BABg9Fe/TntteM9eRA4dgqOiAv6b1qW9NtEFqQe7yEdLAbOKwIY/A3xehF7bmbFcyOivfiXe\nc/ddaetLKa772mJdCotdZAPED8NHL8UPyz3D4kFGll2hYIyh6FOfBACM/uLJtNdGL1xA8OWXAZdr\nwuHlyZ2t+NCjLxsulqsHUsAMYucgfEHgSi+uhToUFrMp+qvPABAfBK1gfM45hn/6U/H6ez+rLD5l\nAQ9mVAUQigpKUcmowBGJCWisKUJVceYg1KKiwmTf6EG2OhxLUCg55whrVJPPN+45s+Fd+wHwYBCj\naRTk0J69iOzfD1ZentHCIn/X5tXp+67ZST5LZ4hN6g+2Wa+AAUDRPfcAEE/osb4+zetGHn8CABC4\n51Ngfu10//FwFGe7R+FgwOxafQqYXeQzq0bsFHGhb1y14GehcZSXIyDFUY5sflzzuujZs6Lr3uVC\n4O67044pV5Ofp1NhsYtsAGCBtLccTej7eMOiKXjglvm459rGgs8n8Od3A243gtt3IHK6VfO6kc2P\nA7EY/B+9Dc4Ei+LZnlEMjEXwxgmxpp4gcHxjy7v4P8+ZX/rDvtrDJMFOMWCRqIAfvHAMrxwVK8mf\n6x3FSDCKmhKvJUVavddfD9f8eYi1t2tu8qFXX0XkwLtwVFQgILkfZb6wfj42XDkDdeXixuJxOfDk\n/dfgR3+h3qsrGbvESQATFUo5OPWJl0/jpn/eoVpPqxAUf+5eAMDIv/8UwlCqdYFzjuHvfg8AUHTP\np+BIs8EDwIFzoqKwaJq+Jt12ks/SGWIg90EbWMAAsfWN94YbwMfGMPLYZtVrwu8dRvAPfwDcbhR/\n5i/Sjvdu2wBiAsf8+lL4MvRQlbGLfFxOh6KYvNuWe6NyMym+/68BxjD6n7/RzFYd/sm/AoKAwO2f\ngGtqQ9rx9p8TP9fymRW63t8usgGAxdPEZ6dzMO4NKva5cffVjajUcVA2G2d1tWil5BzD//IvqtfE\nOjsVz0zJ/fdPeG2B9F2TleJzvaPY/l4HXj/ZbfpcL1sFjDHWwhjbksX1GxljG6R/D+q9zw69IGV6\nR0L4z93n8OhzRyAIHLtPiu7Hllnagbn5hDkcKH3wqwCA4R/8MOUkzyMRDP7DtwAAxf/j/pQN/rr5\ntfjKRxbCk9DGYlZNMWp1KpN26JeWiFzM8+3TveCc4/kDFxGKCghGrLGCedeuhWf1lRD6+zH8wx+l\nvB7cvgOhnTvByspQvGlT2rG6hoI40z0Kv8epLMiZsJN8Fk8rB2PAsUuDGAvpK9OQb0of+BIAYOSJ\nJxBtnejq4pxj6B+/DXCOos/8Rcb6RW+fFuMws1kL7CSfVU3ivN86bX0TagBwz5sH/0dvA8JhDH3r\nH1NeDx84gLH//A3gcqH4b/4m5fV9Z/tw14934b0LAwiGY9gvHV6u0KmA2Uk2CxpK8fe3L8EXbp5v\n9VQUSh74EuB2Y/zZ3yK0Z2/K64Pf/g74+Dh862+Gu3nhhNfkZ2T36R4IAsdbp8R9NB/ZtpedAiYp\nXo8AuAuAruaIjLGNAMA538o53wpgO2PsMT332qEVkcyUMh+mlPnQNxLGwfMDeOmIaAm7Zm5+mzyn\nw7d+PTxXrYbQ04OBr3wVPBbPlBn8x28jevIknI2NKL73s6a/92iW1arzzZr5tQCAl4904vCFQXQM\nBlFV7NEdFG02jDGUfeMbAGMYeWwzggk97mIdHRj4iqg8l3zpi3BWpt8Y2qRyIVfNqdbd981O8in1\nu7F4WjkiMY5dJ7oRiQoFC8TVwrOiBf4NG4BgCH1fegA8oezByGObEdq1C6y8DCVf+lLacQSB46Uj\nYnuv66TvoB7sJJ9r5tUAAF450omYjiKyhaD04f8PLBDA+HPPKYkQACAMDqL/gb8FOEfxfZ+De87s\nlHtbO0dwrmcUT+48gzdOdSMUEdA8tVS3p8JOsgHEgsULLAhz0cI1bRqKN20EOEf/A1+GMBC3bI89\n+yzGn3kG8HpR9vffTLl3dm0x6lT20Wul76CZMKsXmXzBGGsB8DjnfIWOa/cmX8cYO805T31ykli5\nciXfsydz4+FC8e/bT+IXO1vhczsRjMQQ8Drx/FfWFjxTKJHo+fPoumk9+PAwfLesR/Ffb8L4fz8r\nBkm63aje8jS8q/S5FSczwXAMH/3+Kxgajyry+eQ1jfjiemtPjkPf/R6G/+UHYH4/yv7pH+Gsq8PA\nw19D7FwbvNdei6qnfpU2gBgQLTI7j3dj6fTylAKgk4Wtb7Xhu384Cp/bCYcDuKG5Dt/4+GJL5xTr\n60fXTTdD6OiA56rVKH3wqwjteh3D3xddK5U/ewL+9dr1izjn+PUK+rrYAAAN3UlEQVQb5/DjF4+j\nrsyHZx64vmBFZc2Ec447frQLF/rG8NTnr8WsmsIVX03HyC+exODXvg44nSh96EF4rrgCg9/+NiIH\nD8E1bx5qnvsdHCrxWj3DIXzs+68iJnB43Q6EIgIeuGU+7r66sfAf4jKFh0Lo+sitiB49BndzM0q/\n8TVEj5/A4P9+BAiFUPat/6V58P/pjpP4+WsT99Hn/udaXdndEroessvOApYtjLFyAC0qLw0wxtKn\nFQGIRu3hrpD5syuno8jrUmqy3LV6pqXKFwC4pk9H1c9/BlZcjOAf/4Sej98uKl8eDyq+/728KV+9\nGcpfFBqfx4m7rpoJAAhGYvC5nbhb+tlKSr78AAJ33Qk+Po6Bv/0Kej95D2Ln2uBesgQV//aTjMoX\nIFrTrl9Qm5XyZTf53Lp8KqpLvAhGYhgLxXQ1FM83zsoKVD/1KzgqKxHe/RZ6bt+gKF9lf//NtMoX\nAGx9uw0/fvE4AOAz1zVlpXzZST6MMXznzmX42w8tUIo024Giv/g0ir/weSAWw9B3/hk9d96FyMFD\ncE6diqonf66qfAFAdYlXaW8VigioKPLgtuXTdL+vnWRjV5jXi+onn4Rz1ixEjhxB7yfvweD/+hYQ\nCqHovs+h6LN/pXnvn62auI/euXpmNsqXbt73ChhEN6Va5G0f1BUzOV5sD2NsT0dHh+KPP3/+vJIe\n3NvbiwMHDkAQBIyPj2Pv3r0YHx+HIAg4cOCA8gAdO3bM1Pv7Lp3Fd+5chjm1AXygyY/PXDeroO+v\ndf97bjdKn30G/k/+OaKzGuG48UbU/Pa/0da8MG/vf/To0YL//TPd/+k1jVjb5EdTtR+P3H0F+trP\nWv79uXDpEsq/910IX3sY0aVL4F62FM6N9+HSP3wTrLIyb+8vX2/155fv7+68hC9cU4llM8qxZk4F\nPtgQssX3Jzp9Ojp+8H147/kUXM3NCK1cAffmn6J4430Z71/YUIrlM8tx0xw/1i+qmtTPz/RyNzZc\nOR0HD75r2fObfP/x48cx9KlPouqXT4KvWoXYnNko3rQRrqf/E+/19qa9/ws3z8dVMwNYVB/Ao3++\nHH3d7brfv7W11Raf3+73s7opKNn6NEbuvAPO5mZ41lyLwa9/DbEvfB6MMc37HZFRfG5lMebVleDj\nLQ1YXjqY1fvr5X3vgpSsXI8luxulAP5WzvlD6e63mwuSiCMIgq3LhLzfIfnYG5KPfSHZ2B5yQRYC\nOwXhExMJZdEInCg8JB97Q/KxLySbywPbKmCSm2+bzn9G80PVc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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Set the plot size - 3x2 aspect ratio is best\n", "fig = plt.figure(figsize=(6,4))\n", "ax = plt.gca()\n", "plt.subplots_adjust(bottom=0.17,left=0.17,top=0.96,right=0.96)\n", "\n", "# Change the axis units to serif\n", "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n", "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n", "\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.yaxis.set_ticks_position('left')\n", "\n", "# Turn on the plot grid and set appropriate linestyle and color\n", "ax.grid(True,linestyle=':',color='0.75')\n", "ax.set_axisbelow(True)\n", "\n", "# Define the X and Y axis labels\n", "plt.xlabel('Time (s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel('Y (units)',family='serif',fontsize=22,weight='bold',labelpad=10)\n", "\n", "plt.plot(t, y,linewidth=2,linestyle='-', label=r'$y_1$')\n", "plt.plot(t,y2,linewidth=2,linestyle='--', label=r'$y_2$')\n", "\n", "# uncomment below and set limits if needed\n", "plt.xlim(0,5)\n", "plt.ylim(-1.1,1.5)\n", "\n", "# Create the legend, then fix the fontsize\n", "leg = plt.legend(loc='upper right', ncol = 2, fancybox=True)\n", "ltext = leg.get_texts()\n", "plt.setp(ltext,family='serif',fontsize=20)\n", "\n", "# Adjust the page layout filling the page using the new tight_layout command\n", "plt.tight_layout(pad=0.5)\n", "\n", "# Save the figure as a high-res pdf in the current folder\n", "# It's saved at the original 6x4 size\n", "# plt.savefig('plot_filename.pdf')\n", "\n", "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also write equations in [LaTeX](http://www.latex-project.org) and have the output beautifullly formatted using [MathJax](http://www.mathjax.org).\n", "\n", "\\begin{equation}\n", "m\\ddot{x} + c\\dot{x} + kx = F_{ext}\n", "\\end{equation}\n", "\n", "\\begin{equation}\n", "\\delta_{oc} \\bigvee = \\forall \\sum\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "


" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Licenses\n", "Code is licensed under a 3-clause BSD style license. See the licenses/LICENSE.md file.\n", "\n", "Other content is provided under a [Creative Commons Attribution-NonCommercial 4.0 International License](http://creativecommons.org/licenses/by-nc/4.0/), CC-BY-NC 4.0." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# This cell will just improve the styling of the notebook\n", "# You can ignore it, if you are okay with the default sytling\n", "from IPython.core.display import HTML\n", "import urllib.request\n", "response = urllib.request.urlopen(\"https://cl.ly/1B1y452Z1d35\")\n", "HTML(response.read().decode(\"utf-8\"))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "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": "3.6.2" } }, "nbformat": 4, "nbformat_minor": 1 }