{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Goal of this notebook: understand aliasing." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll follow the example given here: .\n", "\n", "The gist of it is: when going from a time continuous function to a sampled function, we lose some of it uniqueness, depending on how we sample it.\n", "\n", "Let's suppose we have to time signals:\n", "\n", "$$\n", "\\begin{align}\n", "x_1 (t) = \\cos(\\frac{\\pi}{2}t) \\\\\n", "x_2 (t) = \\cos(\\frac{9\\pi}{2}t)\n", "\\end{align}\n", "$$\n", "\n", "These are time continuous. Let's now sample them at a sample time of $T_s = 0.5 s$. The continuous time variable gets replaced by a discrete time $t = n T_s$.\n", "\n", "Our signals become:\n", "$$\n", "\\begin{align}\n", "x_1 [n] = \\cos(\\frac{\\pi}{2} n T_s) = \\cos(\\frac{\\pi}{4} n)\\\\\n", "x_2 [n] = \\cos(\\frac{9\\pi}{2} n T_s) = \\cos(\\frac{9\\pi}{4} n )\n", "\\end{align}\n", "$$\n", "Note that we are using brackets $[]$, as in the original article, for the discrete waveform.\n", "\n", "\n", "Now $n$ is an integer. What does it change for our signals? Let's try to plot this." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "t_continuous = np.arange(0, 10, 0.01)\n", "t_discrete = np.arange(0, 10, 0.5)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def sample(func, t):\n", " \"Samples a function with a given time vector.\"\n", " return func(t)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "x1 = lambda t: np.cos(np.pi / 2 * t)\n", "x2 = lambda t: np.cos(9 * np.pi / 2 * t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we plot the continuous versions of our functions:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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xT7JjJcvxSXBWaQbo6brSXXhm9R4oFDhpTDWOGlju065i36Dq0ukqE/fiR/vQ\n3sGMb7RYnRMA3zy1DD9xztF0grFJlNGTGfZjgZAAO0gpw3iVMuPOYZdSaMChoDOZQXc6gxAhqCqJ\n2l/vQZcXqSqJIUwIutNqCa5RlwArIWiXpR4QQz+QAHAEwieRIvilOi85aSQIAd777CAam7VmTBxO\nIU9SFs5KhuPTgVCaEwjJYjj0ewlF1AQsESDEMkvZcecFekzMXtSJ6roiRVkHoyQ78czqPQCAS6eP\ntLvSQhfLnvmbDycfUY0jakrRmczgrfU7c7+IFOWAHtd3KDHPyAD0BMG6JcMh8znkZfQy+brSAiEV\nQozOijcREshzfIc0dqOqOIqw1yZnAk40HMoBm6bOlESQYGZLJDEcFk3K+HUFgOPwFEJ8LyrDqopx\n8hi12+i6HdpRxSzgkOLYC5GXIOgYhBkOZiEHco6PZwE2hFSY749nATbE7EXZoPxx33+oGXUtCVSV\nRLOhDv+6/M1RQggunKq2RH/zYy15NFKkxsajAgDUkFei2eQxHJkn7P2JzAXAJoejl58dlp0UfXay\nzips2mnLcXyU5pJFq8vy24HbihXz4nQEvUmqStS/1dKVArViE0QAldkul7EaPXo05s+fb62L1QMg\n26nVj8hkqXpQAsAhWziYiW8cry7mG3fW5XREGMDBk8lsCF1ITBoVYTgoZZw7m5cgsDvWx1tkV8uG\nVHSbaIaz8sLKsfMyS0yYQJsPtQ3qAV5fnTQkr0W0o3Amjery9SnaHN2t5o5kx0nkHq1CFwAfUMgm\noBaJzQXAVKUi6dmJFIs9O7pN4ZjK6IkmXANGhgOQtmunigKFUsQjYcsj6r3pMiZ6Pv/88zj77LNR\nU1ODiooKfOELX8Drr79uuLwkFkYsEoJCKagsh8xeY6Fr0aJFqKrKP+Jh9erVuPLKK+3vj/03YDgC\n4RYOavgrEwcjHgmhvV2Lj0eY2DggYfcoaZcWKRJzMCwtLJqQxzp2QGxXa5V3wb7PpYsFHDJCKur9\nNTWrlSI6APAkbEWPmcXxKCOqS3DS6GrEqZYwmmWWBHIJ8pJiBSovdHARLfnPZDhYmwCxUJahRwWB\nlMoLQqC7E51dqCqJeksWzdOV70T/9a9/4eyzz8bSpUvx4Ycf4owzzsD555+Pjz7KnRZLCEE/jeWg\nVuELrvtjGmwR4llXTU0NSkpKjG/aAg7RHA7BHJUelABwyBaOBM3yoijOPmYQiqDtqFmGA+ADHFbl\neNyOj1kyZ5unAAAgAElEQVTMhSh05u+LJuSZF2ApDEeZunvUs9qFgF5pQUIqEaUbw6qKccKofg4X\nmiSdQLbZk0BS5TeOH4ZiaM2V9PGOigA9JizGhiN5kpsNYyUzh0NgjrKdVA3sIEcrf3aOAmK5RlJ3\n2vlhAqIDjmJvyaINDQ0YPHgw7v2/v8vqWrFyNWKjT8Kb7ywHAMyfPx8333wzTjzxRIwdOxb33nsv\nxo4di7/97W8GXfrfJJpdGzd9gq9dNAsV405F+fDxOPXUU7F9+3YAgKIouOeeezB8+HDE43FMmTIF\nr732WlbXzp07QaJFeH7pmzjj27NRUlKC406/AO99sA6gCpYtW4YrrrgCLS0tIISAEJI94dUcUiGE\n4PGFf8I3fjgXJaOOw9ixY/HyP97RxlCxZEpefPHFPMC2YMECHHnkkYgNGIVxp34DTz77fHbcd+7Z\nB0II1q5dm/18c3MzCCFYtmwZAKCpqQmXXnopampqUFxcjLFjx2LhwoWevicZEgAO2cK5a7/w+GEo\nJupCpESK1DMOPLSgthVZuRKsLhYIidgUjqn3JyNpNMtwSABCMZPjE7VLZkhFu89i0o3zjxvqfG6K\nnU2AMbfEp13nTRqCsrCaX5FAPGcbwFmlwoTXDLoksVTpLs48HJucHr/CzkUWCInkGenfnVe79DAm\n++ruUMc43a3+nEmqP3e353/W9dWuXptKaP92IZTuQim6EXc6N4WRmpoaPPHEE/j5r3+LD9ZtQlt7\nB773w6vwk1kX48xTT7a8RlEUtLW1obq62vB+PBpGaSyMEKHYV3cAp/3XmYjH43jr2T9gzduvYPbs\n2Uin1Tn88MMP48EHH8S8efOwfv16nHPOObjggguwdetWg87b7n8EN865AmvXrsXRR47Bd665FelU\nEqeccgrmz5+PiooK1NXVoa6uDjfeeKPtfd597wO46Pyzsf6dv+O8887DpVf/FIeaWjwDvRdeeAHX\nXXcd5s6diw0r/oEfX/ZNXHH1XLy97B1P1wPAHXfcgU2bNuHVV1/F5s2bsWDBAgwYMMD9QkkSHE8v\nWzhp9FPH1qA+oj4ItR3AcEBdpLpTYnS1dFpYAoUu28FI11WklteK6mKZJUqNmemedOkhlWJ0ZKIo\nBRBHEjOnDnW8LE8M8X8G6PlkEiqLozhpeBFQDxxKhjEUEMvDYZkEQAygZcEZU1JOFTUPJ+IjcdFs\nV6ab3yYD0GPBuiBjqevzYleqE7jX53yRIEcCwK21uWfARc477zzMvvSbuPQnt+GEE6ejtLQU993y\nf2ybdc2bNw/t7e246KKL8n5XVRwB2oBHFj2DyspKLFn0KKJd+4GiKow94XSDjp/+9Ke45JJLAAD3\n338/3n77bcyfPx+PPPJI9nM3XvV9fPXLpwMDj8bdP7sBx55yNrZt347x04aisrIShBAMHuyewD3r\n0ovxnZnnAkX9cO+99+I3v/kNVq3dgHOPPN7TGM2bNw+zZs3C1VdfDTTtxA0/vgzvf7wV8x76vzjj\nsV960rF7925MnToVJ5xwAgCVielJCRgO2cK5e4yGQziySqXytxzUsvSF6GqbszP87vgM8X/BCgA2\nkVW3TbfLt65CMBxmulowt0TXQxU+Gp3pf/JhnXpfVZE0xg+u4NQj7thPHKZeu79LA08i1VS2TlQk\nd4YB2IBgTo8gw5Fl9OJqoycpDIc+RwWAXh+VeXfORTqTwXPPv4C//OkJxOMxy/Xq6aefxt13341n\nn30WAwcOzPt9RVxdR9du+hQzZnwR0ZjGxjFMQmtrK2prazFjxgzDtTNmzMDmzZsN702eMDYbthgy\nVO2ue+BAo+/7m3zsBPU/hKC0tBQV5WU40NjkmeHYvHlzzl7tmhknT9fs9baZmTNnDpYsWYIpU6bg\n5ptvxooVK/zehpAEDIds4agA0GVUZQhoBj7en8QZCkVIpPmXoR8E4/gySSDi4VwDXTJJGOP/IrkS\nMlkJE+CQwXDI2GkbHF+p8X02EdhNKDXE/5fv6sBpAKpiHO2ZbUMX/ufoxIFar4NkGNsOtOEoKeOu\nA1BJ8yEcg7oAU/V9/SBEL8JWUsVKct+BzMRmEYbDPEfdgF60RGUaWGmtBToa1CMBKoYCB7eroZGq\nUUBxfsWFo+jXVo5Eo1KC6tYtCBEK1Iw3JmB7kO07d6F2fwMURcHO3XswafARec54yZIl+NGPfoTn\nnnsOZ511lqWeaEhdr4ricSQzinBSZTQSyeWnaPldCkfpdjSi5YZldREoigJQBaFQSO2Qykgq5VAl\nZ5GHo4dZWT1mHV/5ylewa9cuLF26FG+88QbOPPNMXHPNNZg3b57v++GRgOGQLT7aRpulpkidRA3d\nYXy0p1lsx2fVYAvwn5DH/m3RCoC8RVPSjhaQk5Ano/KCvcdwRHN+8H+PzH100gje263aUkp4zoph\nwCcgdG5JMVEXsC7E8OrH9WI5PWwllcEugaTRSLGWh8Npl12DLSmVJRrQF2Hh/IJ1QnIn1eovveop\nVpZ7T99MmD/r9tJ1xcvQmolB0RmmaLGvEGIymcRlP7kVF5//Zfzi7p/jRz++GgcaDxlAwuLFi3HF\nFVdg8eLF+OpXv2qvTHO4kyYcjfeWL0cqrX2fjK6KigoMHToUy5cvN1y6fPlyHHPMMRbjaEqw1TZh\nsVgMmYzHTQCbYGt4X0FNTQ3a2trQ0ZGb+2zyJwBMmDAhZ69W9rv8/VWqvSSEmmo1kbyurs5WB6Dm\nzFx++eV46qmnMH/+fDz66KPe7JcgAeCQLQJONJxRF6IEjeG1DXWCdDWzQIWj/Amo5o6eIkmCbIMt\n3TYem9hrzAwHDxBikzMNdkkI9fAyXszffndHO1ozKhkZUXgAlblnCT8Lp9uVQByvbqiHUNWS1KRR\nSSE22wZbEueCUI6KhDmatzsWL4vNgKCjOwMlW2LrL3R72623oqWtHb/5xU346U9vxtFHj8UPbvg5\nALXT59NPP43vf//7ePDBBzF9+nTU19ejvr4eLS0ttjZddcV30NbWiou//0N8sG4Ttm7fgSeffBJb\ntmwBANx00024//778cwzz2DLli342c9+hrVr1+K6667L12lT0TN69Gi0t7fjzTffRGNjIzo7nb4P\nO8BBMX36dJSUlODWW2/F9u3b8fTTT2PRokWGj910001YtGgRFixYgK3bP8NDf3gKz7/0NzVRlYRQ\nXFyEk6efiF/96lfYvHkz3nnnHdx+++0GHXfeeSdeeuklbNu2DRs3bsQrr7yCCRMmONgsV3oEcBBC\nriGE7CSEJAghKwkhJzl8dhEhhFq8NjKfmWXxe84aOMni8ehvS9EWoi7E8OqGelChnbZpV8vr3PPi\n/yIgKJeTYNAlZfcoEOrR2YSIufJCRgIqJ5ugjy8J47XNh5CgKlNChGwqNf7LNUdVu7oRw6a6VrSk\ntKis0Bw1h1R60bnbAWwl7b8RnC0L18tzNA9wCBxupl3TkVRAQblKbJctW4b5Dz+MJ3/zC1SUlyEU\njuDJP/8Z765aiwV/eg6gCh599FGk02lcc801GDJkSPZlCQ60v92/uhqPPfMSWtra8aVv/gjTzv4W\nHnvsMUSj6ubr2muvxQ033IC5c+di0qRJeO211/Dyyy9j7Nix+TqJMRyiA6pTTjkFV111FS6++GLU\n1NTggQcecB0rK4ajuroaTz31FJYuXYpJkyZh8eLF2RJbXWbOnImHH34Y8+bNw7GnnY8/PPVXLHx0\nAU4//fSszid+/wjS6TSmTZuG66+/Hr/8pTGZNBaL4ZZbbsHkyZNx2mmnIRwOY8mSJfY2S5aC53AQ\nQi4G8BCAqwCsBHA9gNcJIeMopQcsLrkOwM9MNq4D8Jzpc60AxjE/c9S/FUCyFQD8i6YSjmNvUxc6\n+kdRxrzvWTLMMe0sUOhu8b+Ys82n2H+5Gn/pi6a5S6VEByPCcERMQEiot4QeJuC8R00PjZbgzc37\nQfQyVCWlfr9hH49uXldW8VBWVUUlcBDYciiNkxh7fUke8yIzfMHp3O3mqP43wj7yQQrBcGSfQ5mA\nQ28jzg842pMKgDBIKKR26vYBOE4//XSkEh3Afn1PSTB69Bi0fPKv7N/Q+0j4sYmEQjh6wkQ8ueQ5\nDE3tVlnewROzHwuFQrjrrrtw1113WaoZPXo0aGst0FafZYGq+vUD3bcGiOcStxcsWIAFCxYYrt25\nc6fRJEqBQzuARHN2vJt3bQQ6G6G3Np85cyZmzpxpuG727NmGn+fMmYM5c+aoY5VJAgOOhnazAIAJ\n48bmJYKyOR233357HuvRk9ITDMcNAB6jlC6klG6CCjw6AfzA6sOU0hZKab3+AnACgH4AzN1JKPs5\nSun+Qt6EZ5HgRI8cqmZeH+jSvh6/jo9dZPUFStDx5S2auuPzZZfNLk2ILTFR6FwMh76YC+4elQxD\nfZca7fJ7j9rnU6EYWhNplJUyCah+54PZGYs0JNPsGlqjxos3NaT4bGJ0ZZ2nCFhny2IB/u/QPEfD\nsZxD9ju3zGGQvsZwhEwhFZ4zPbR9XkdS0VRysiXmzpmE5FgFv0CIGm3RbRNubMb+K9yVlflXtLW5\nqF09KAUFHISQGIBpAP6pv0fVnrP/BPAFj2p+COCflNJdpvfLCCG7CCF7CCEvEUKOdbAjTgip0F8A\nPJ7pzSEiTlRbtCeNVmu69+nhZL8LXYZJLMwuULyAw2bnCPADIakMhznUw+P4zLtaTgbA3HcByCWN\npn0me2q6OhWV/p0xfjjzO5/zIWVyxiKOTxuTkYPVZkGfHkzx2QTk5qneJ4N3PhhKtwVDf+Y5KtII\nTmavGFlzFChIi+0MJYiFQwiFOB2fVUJlFgj5LeXXAUcI0XAIGcqph9GVAwmSzj8x6BI5VE6CXT0o\nhWY4BgAIAzCzD/sBuHZKIYQMBfAVAI+bfrUFKkPydQCXQb2PFYSQ4bCWWwC0MK+9Hu33L7wOBsgu\nRFOPUhv11GUBB2f8PxRR6/8B/lCIHZMAcOz4dAcjI1dCJsNhF+qRwCzxOnftbzdrORJnjB/Ef36G\nOUygj3+GZ46q91FdUYExA0rRrnBW4QAWAJRzjpo7erI6fevSxiTMNAsTzQeRwnAkjHaJhJ/Yk1QB\nZqfN0aNH06WAoLwoAsLr+Mw2AfxOVLsPQkIoL4owiawK3z0CyLrKggCOgOHoK3I5gGYAL7JvUkrf\no5T+mVK6llL6DoALATQA+LGNnvsAVDIvO2AiLiKlb9riMahfFcYNKkcn1cGLX8euOZgw02+Dt2w0\nbVo0QyFGF6dj0O3SHYxAtUSOjpfAcOiLOS94YZ2CvtPTd+9+nbumqy0TQSREMGPsAIEwgcmJ6uPP\n1Ywsl3dx+rgadINzjhrs0uzRxz3j0y52PPLmgyDDwerkZjgscjj8Or48UCx4ajPAsAm81D5l/kdQ\nXhTl37VblozyAqGcM64oioKyIMY3m2BiOHhtYq8RBQmUIlfxIiE804NSaMDRCCADYJDp/UEA6p0u\nJOqpNT8A8CSl1HG1ppSmAHwE4Cib33dTSlv1F4A2j/b7F6HdY865nzF+IBL6Yi4ahwb4HZ95lwaI\nO+SIycGI7PjMuoRyOARDPY5Azy/DoZefxjBtVD9UFEX5QVVewqH2r5LyHx9n8hL+i5mjVCgRksmX\nALjDTwhFc8m03AyH1bPDuYlI2cxRUP8VL3l5RgLhyDxnxQsScnOHkhBK4xGBnbbJJvb/vnXlAEdp\nPAJqADGCoR6peRfiQE/4O+xhKSjg0IDChwDO1N8jKud2JoD3XC7/ElQA8Ue3v0PU9m+TANS5fbbg\nwrt7zKRVBwDkLeaK7yoVi0UzzLtomqpUNPtUXbyLucnx0YyacCmiS0oOh4l54WWW2LM7sk7U765d\n/dtdNI7Tx2ntm0WaWbF2sfbxsgnRYpw0plo9aBBAsoujWZd5nvI6dnNyJvt/Gc8OLzuYV/Ei0HI9\n+x2aq8Wsx0pxApJ2js+3M1Y/TylQEosgHCICu3Yzk8DYx5nDARJCOERQGo9Coabf8drFa5PJLsO/\nAkBP+Dt0+jMFAC890dr8IQB/IoR8AGAV1LLYUmhVJ4SQ+wAMo5R+33TdDwGspJRuMCskhNwJ4H0A\n2wBUAbgJwCjk53r0vHBXJRgTDo8fGcdyTdeh5hb4Os/PcZfmc/eYMeVdAPy7x4zJIbNx8nR3rnrC\nl12CYRBK8xkAbtBocjDs/33qSnV3IAq138UZ42s0XZzUvh3Dof+OdYSuhuU6esYjYYwfPhCoBboT\nHYg7X2lhlw3g8B1+MoXEAIHnUCI7mBfKYluuJ/y1XM9j9PSxMs6rWCyGUCiE2tpa1NTUIBaL5R1x\njqSi2pBIAhkCJNNAmgLdaSDhY7zSSSBNkaEERUUKEokEkFI0XUl/uhLd6nWguevSmq5ENwAfurpV\nu5DKAIkEikgGXWmCMFGAri4g4sMpdzNjE05k7xlQ/N0foI4N1cZGCeXGnaT86cqkNBugjg0hzLj7\n1GUjlFI0NDSAEJLtWyJDCg44KKXPEEJqANwDNVF0LYBzmTLWIQBGstcQQioBfBNqTw4r6QfgMU1f\nE1QW5RSt7LZ3hXtxYhaOcByRUAjDa6qBBqChqdkn4LCKQ1svUJ51sWEC4ZJDU/Ji1i4fgMMcvuBl\nOJQ0sruV7GLOyUpYJRxy7tp31R9U44PRIowbVG7SJeiQQxFkHR+vLs2WqUcOAWoBJelz3CnN/w55\ngZ7ZGQMCc9Ti2REGoNr1esv1VKcAO2gOPxltCoVCGDNmDOrq6lBbazpDRZeW/er4t0XVuZDsVPtB\nRNqAZu9Mo5JOItTegAxCUMpjaAmH1D4TiVYgngCKfQDjrA1Falo/ALQfUL+PJsXzqbMAgK4moLsN\nKOoGirqQzig42NaAMBQoLWGE/JwerNtQogCxZnW9aG0AQIAOn6cQt+xX2YlWralcqks90yYcB5p9\nsAkGG3aq7yVa1Fe8CyjmYHkthBCC4cOHIxwOS9EH9AzDAUrpbwH81uZ3syzea4GD96GU/jeA/5Zl\nn1QR3VmFotmEwyOGDAAagNY2nyknEh1frrJExu7RtJiHtJgvz2mqebtjwbwSVldYEJxZMUs+AegO\nDXD0q6zI7VC5QaMJ6BGi/j/d5f87NDnRE48aBrwLRJRutHSmUFnicTeUSSEf6HHO0YzVfBd8Dg26\neAGo1XwoUgEHd/6TCaxb2BSLxTBy5Eik0+n8cz4oBR75tvr/K14HSvsD294Clt8MDJ4CfMs7Sbzu\nw+U47r25aEA1BlzzujpPVz0GrPoDcOyFwBm3er+/TS8Dy+8BRs0Azn9Yfe9vDwO7/g2ccQcw7uve\ndb29BNj4V+CkK4EJVwIAGn57NWpwEGtPno8pJ3zRu66//g9QtxY4935gzJlAxyHg1e+ov7tmta/z\nYvC776ph8+//DagYAux+H/jHXKB6LPDdxd71NO0CXp0LRMuBH7+tvvfBQuD9R4DxFwBn3eldl4NE\no1GpYAPoIcBxWAlv4ptF7Pioof2B9UAi0YXmziSqSjwiasddGq9dFjkcotUShKh2pbvEd4+iDgZg\nqiV4d7QO4Sefdu1tbAYADOzHHEUvcW4hElPHnTtMoOqqqVLZlxhSeOuzRpw7cYg/m1i7REMqUuao\nQ1jMN9AzVeHodnVBnOEwJ/6GjOl4OhWeR4enk0D7HvX/JaVAUREQi6jvdfRXf/Yo6z6rw/T2PSiO\nA8XFehVbWtXV3ehLFzJt6nWZ9tx1Srv6ntLmT1d3o3odSWevK04dRFH3HmzcVY+Tv+hDV8deVVcs\noukqzY1fNGR8ppyEUqD1M/X/JWWqrnhc0x31d3/6GJfW5K4LK9q4H/Cnq4elr5fFfv6E2/Hl79Iq\ny1QaMUbTeG/7Qe+6LB2M4O7Yii3hLPU0LuaCIShziS0vhW4oZRXNJWCTdf2DhNrmLnRoh0AN6sfE\n+WV+h7xJxOY8HM2mGMlg+VarkwpcbGJt4Q5dWLFwEucob+KvUwKqb4bDBITY79LPPVoCPb5n8JN9\njQCAeBGTA8QdFpOX/2Q17rqNm/c2+rTLpqTcr12GZozGZ8d/WFPiHO1hCQCHbOF1oA6VJTGSwr+3\n+XhQHJNGJezahRcVCdUz5ooQPaFSSfmreLFa6GTmEnAA0OXbGhGD2jY+HpewqDgu5oKginF8K7f5\nOF3AqWcJ7/2FJcxRqeDFKZmVk+EIm5wV4A+AWjJ6/ufovuYuHGptBwCUFLMl8/r6JwGcia4zzLgX\nF6sR+oMt7aht9jH2dqEsv3Y5MancIVIJ63sPSwA4ZItEhiO7e0QKy30BDomJb1ZJo8KgSoLjy5ic\nTIRzx+dUlSAlpOJ/3FdsP4gYUva6fI+7lRPldQzm6qCcfXUHW7C3yWOioFPPEim5M5z35/jsCLIS\nBrt4+3BYMBx+nh2LXDGeObp8WyPiGigOR63GSiwZmdcuAJbPYUSz0f9aapH4G+aYW+wzm9eAT0II\nkffZ6WEJAIds0SeRkva307ZE+OrEjCONnQc7seeQ18XcKWmUMw5t6C0hynAIOr5MOleLbk709GuX\nk4ORUdHjcxdDKdUYjlS+LmHmxQroCXaxZeZYDCms2OYx9GfJdvHmqFjM94I4PglATxY7yOv4JG1G\nVhjmqBUbJIGlkqort5b6Ahyy+rJYAj1eUGwVIhU4UqMHJQAcsoWbcrN3VuVR1bmu2O7xQZFZFmtm\nEoAC7R79AA6LOHSYSY7jYTgswRlnQqUVHe/x/rY3tONAWzeKQxkLXRLLdXkWqExabdIGWDq+GNJY\n7nWOOuUZSWES+rbjk8IOcj074nOUUorl2w9mw37WoLEXwwQOQE8NTx/03tTKMuTKcY9WLBz7/flp\nsiVzfe9hCQCHbOGOrVo9JOr/S8PqIv9vr7tHywdO0FlZ7tJ4HbJg+MIqHsru+EQZDlFwJuAUlmvf\n8eBSYrye/b8MoMfDcLB/14JNiBGVrva0mFs6GJ0WlsEkcO74ZDIvlp1nOZyootiE6wSeHQFAte1A\nOxraulESTtvrkpFgK5zDkW9XaTiDxvZufLq/3acuQRbHsnRb/z/V+gH51CUD6PWwBIBDtoSY8wR4\ndu0WD0lxSJ2MK7Y1QlG8LOZODkaGExVkOETj9vo9kBCyZ2ewekVzOETpeIH+JzrdO6hE771hxXBI\nKosF+MbKRldFREFjexJb9nvoG+NY0dObrIQDAOWu6BF8dqwYPVYvz7NjB/Q8nK2jz9Gj+lu0yg9z\nMjhOPWy416x8u3SbPSXhU2qTd8ZhlxNT4luXU3J6ADgOL9F7SwA+J5F9NUiEplASC+NgRxKf1PtY\nzAtWFiu647OiJzlK+1g9rF08ZYKWiX28tLBVMpe7TRmF4v3PVIZjgJ74LyWp0ikO7Yfh0O6BhLRu\npUYbpw5TKwH+vdXDYu7o+HxSzA4Ohh+cFSovgcMuQ3M6Wc+OxdoAeJqnK7QS/aOqtTCmDIbDqmdJ\nAcJiYzWbPeVxGEpZBZkXp3we899yE5nrew9LADgKITwPncMulGSSOGF0NQBg5Q4PYRVJ/SAMuqwe\nOKmdODnAGQuCWLu4dh5WC0pC3PH52B1v2NeC1kQa5UURlEdMSbGAXAaAK/zE6GE7LGr3O3WoipJW\n7jjkrsuJdQE483As7k8GaORumufgZHzdnw3Qk/XsGBKunecpC4qP6KcBDsv7k7g2yDgPR7vf0VWq\nzat3HELGjS226kIMiLGDhjnKyYY79uEIkkYPP+FaCKwyj3MOdProfgCAVV4Wc0n9IAC4JI36mNwG\nelJwUbG6P167nBY6wF/5ohO172FBeU9byE8+oj+IZcyXw1mxnxelYK0cKJC934mDVJ2rdx5yD/05\nAT2/dslMOJSagOrU6I7TwbBAj8fJWDqrKNSzdeA6XptqW7OgOBv2E2VwAJd+PxKqljS9A0uAsngE\nbd1pbK5rddZjyBWz6qXCkf9k8+wI+wre9b2HJQAchRAuhsMhKQwUJ49WW1yv2nHIPSnPSRdvK2vR\npFFXepJDV9gEOGQxHKJNlTiTRnUwefIR/SUn0UnqU2EFqBhdY/pFURILo7kzhU8PuIT+nBw7+3sv\n4pREJ6NZl2jCtWi5rpVNAB9Yt5pXhHgGVTrDetLoaoQUB5DQW4nNgCPDEcokcYK2eXNl4uwYPVF2\nkBWuEJtTGDhgOA4/EXF8VlUJACYNLkY8EsLBjiS2N7hkWMt8eB2SWbl2aXl2CSB8M8Mhuy8BwLkQ\n+C85zCgUq3eqC+BJo6utnRVXjgrTs0TU8Vk5K0ZXRElh2ihtMf/MbTFnOo3qwt1bQoxZsrSrQC22\nhZ4dc86SyO44jx30Nl46KD5xjMsc5a1gE53v7Odt2MHpY/oDAFa5haetHDv7s+jGBuD8Dl1KbPuw\nBICjECKSkGflrKD2ODh+pLqYv++6mEvqu8B+XrRMkP2s6O7RNaTCEQZhdYWYWDlPNQEHOPukvhVt\niTTK4hFMGFIuj+GwBXocc9Qud4a5x5O0XCPX0J/dYi4tIU/QWYmyg0omV+oomkvlChIEcwnYnx3G\nXWFB8Zhq5zna5xiO3P2dNCY3Rx1Df3ZhEJGyWBnfYVaXxcaNZtRNRh+VAHAUQmQlFYXCAAlnfz/9\nCK+LucTeEtISPZmSWEPCoUAugdSkUTvHx+GQOXIJVmvf6bRR/RAJh2Cdtc/DcNiEsoQqemyYpXQS\n049Qd48rd7g0V7LTxVVy6NDhVUb4SWRe5ekSKIvN22mLOD6zE3V/Drc1tKOpM4XiaBgTh1basBL6\nSa9+Oy1L6qWiKOp5SqwtrN5MEpOGVaI4GkZTZwrbnNhiW2ZJADTmAT0RVlZCGLiHJQAchRCu3aM7\nmtaRuftiLilJkNUlq8JBRimr7Y5PIGnUNj4umoDqbdxXsTtHwKbUUyDBNhRRAWyeXRxz1IHhmDy8\nErFICI3tSXzW2OGuyw5wiIYJskcMpHx2cXSonpHSO0Mk0dMMsCUljbI2OtyjnvNw/KgqxCIh90oj\n0fqt4nIAACAASURBVPVBhCkGbBPwY5EQjh9VBQBY+ZlDWMVqAyFql+36Lql3EPv7PigB4CiEiNTH\n2yHgdBLHj+yHaJhgf2s3djudq2K5SxMsqRQ9PdMl/i+cJMity+KQNPZn0W6CrOOz2fFRSrOsVRZw\nyMpLcNtZyaD2mblVFA1j6gh9MXdg4mTa5ZhwDc7FXDCHI2s/sexZ4u/ZsThXB+AEZy5hMQcnqrNw\nJ442z1G73hKieTgCLBzgCBr1PA7HxFEr5ozXroI8h2zeGVNi24cTRwPAUQgR6gBov3ssioZx3HAf\ni7ldGMTrjo8tZRVmONyYBI5du+1CICM8Iyt73H3n8VljBxrbk4hFQpg8vNJol2hegi2TILBLs2U4\n1N9Pz8bInXaPEu1ySbjmA2jWu2PvemxKWWUBWfZn0X4/7M82uixBsWV1EHOmkXBDMhGgB8ck6Rxb\n7FD155boyTXuNt8hFziLGt//HJTGBoCjEMJzxoFVIhCQ5/j0PA5nZO6wO2b/lqtNTPKlqOPLMgky\nKUUJICG7mJsfXknZ4x5iq/rOceqIKsQjuZwd1S7BBdjWwQgsdC6Jnrk8DofF3NUuHobDYo7y6hKu\nDrLrWcIzR3WGw2aOyki4dnGiew51ob41gWiYYOqIfsbP5lUaSXp2RBx7OGZdyqr9fsqIKsTCITS0\ndWPnQRu22BWcCYJigy4eACqBLelhCQBHIURWWSyQ96CcNCaXlGcrTtnjfuxyK2XtrURPtz4cXHS1\nnV2CDICHs3X0neP07M7R4lRWgJPKdYtDSwiLmQD21JFViIQI6loS2NvUZWOXTT6ICJtgSLgOqUeB\n+9FFqXNYTErfBYkMBxeTavPsuGyS9PVm8vAqFMfMoFhG/pMT0JMx7sb7K4qGMWWESx6Ha1WWIPvJ\n6hYFxQa7ghyOw0u4GvK4JBVpE3baqH4Ihwj2NnWhttlmMbfaEfE0VTIkYFmAFz/lp7ZMgkhZrIyz\nVOweXkkJeYbeEtbjtZLtbQAYFwxZ1L5tGaSEsljTjrYkFsmGht63W8ztgB7X7tEtIc/jeCkZABoj\nY/XsSOm7IMLCFTBplM01spBV5vwNwL1qyeu4U2rDDjIhAq9hYJduuOx36Fr15+bYC7C+e9Nlw3h9\nDnpxBICjEBLhcMiuDIc6YcviERw7VO06+uGuJmtdVg8KT1Ml3aZQRN0x6sKVK2HnYAR2aR4WFXe7\n7ICQTLvsgdC+5i7sa+5COESyfVZsSyq5knXtFjqOniWuDEfOLh08rdntY46yukUP4GN1e3XIdhUO\nXKyEJGcMuIdUZJTF6rptxl3vv5Fl4QAHtsTnc8gCPatEd8D78e1uDAdzfzp4+tDvHBXqFuu8vnsS\nVyAUAI7DS0QmkQcErDsme8DhFibwynDYPSQiqFxGTNttUeljdmUX83znrudvTBxagdK43mzMrsKB\nJzfI5f54wjMuDAcATHOdozZAT4h5EQxfuJVUKmlPx7erNhUiZi8xsdnW8eXP0QOtCew82AlCgOO1\nTrLqZ90SIQWBHk8ejg+GY8rIKhAC7DrYiYY2i+/DNXdGwlkqPPNBcWEHD/eQCiHkGkLITkJIghCy\nkhByksNnTyeEUIvXYNPnvk0I+UTT+TEh5LzC34lHcdktWIoPBKw/9Pa7R7sHxeeu1paqFkHlMpIz\n3RaVXoqH2pXYOizAukM+gaWqWTrersLBL8UcMjt2jjnqMYcDyM3RT/e3o6XLYr5lu3DazS0f3RLd\nHJ9nhoOx0xBSYR2fT/Bi64x5wpEy5qh/Fk6fo+MGlaOymK1CkQSq2L/JzlMewOEjd6aiKIpxg8oB\n2Kyldo5d/9kr6wLYg2KZjFeQNAoQQi4G8BCAuwEcD2AdgNcJIQNdLh0HYAjzOsDoPAXAYgB/BDAV\nwIsAXiSETJR+AzzCtah4L1fTz6vYWNuKzqTFpHfbEXneLfQEwyGwW+iRh1dCeMaB4dAXummGnaPL\n4mSjy59NHHPULdGTmVcDyuIY1b8EAPCR1WIua44a7JLEcISipgoHNv/J4zyVmjTqNkf9PDt2z6E9\nALWco+xnhRkOG6AXCiN7iq3nTZI/8DlVY+LWWDFxUueo3XEMBdgkHeZlsTcAeIxSupBSugnAVQA6\nAfzA5boDlNJ65sVymdcBeI1S+mtK6WZK6R0A1gD4SUHuwK8ILZrudPXQyiIMrihCRqFYv7fF+Hkl\nk6twsF1UBB9etm+/1/bFbsmZvna0MvMSJMZDbdkE6/nQwRyRnc3fYP+m3bgD3hcVqSEV76AYyIVV\nrBdzOycqwA7aOhmfgMPuuQG8z1OpZbFuc5RDl+0czX92dIbDMEcBDwyH1zlqA/QMeWeCmyQboKeD\nKMvQnxvQk5F3wVNC7AaE/DAvPSwFBRyEkBiAaQD+qb+nAYd/AviCy+VrCSF1hJA3CCEzTL/7AqtT\nk9c96OwZ8evYAYfFPH+BIoTYPyh2uwWAP7bqtNP2vZjLeHgl5agY7JJQ4WB1Kiv7s+ke1+1thkI1\nAFnJJDy6MUsWuuztctvRcrBwHhPf9LCKZVKe6+6RBzQKJuTZORguxycxzi4zsdmnE+1OZ7BhnwaK\nbRkOQQbUbo462GUrPquD9HV0/b4WdKdNmyc3AMozRz2s7+66JAKhHpZCMxwDAIQB7De9vx/A4PyP\nAwDqoLIg39ReewAsI4Qcz3xmsB+dhJA4IaRCfwEo93UXfqUHELD+8OfR1XbxUB67bBcUnpi2TMdn\ns0sTShq1GyufO1pLXda79o92NwOwWMjtclTYU2x7A+i5lZ+aGQ7tvtbubkbGfCqnLLqaZfR8ds/M\n1yXR8dkyCTyshNuzw8EO2ukyjdXG2lYkMwqqS2MYrYXIsmLbh0MS0GPf8x1C9Ab0RvcvQXVpDMm0\ngo21rTa6CrlJ4lmzJIZ6elj6XJUKpXQLpfQPlNIPKaUrKKU/ALACwH8LqL0FQAvz2ivBVHsRqlLx\nhoCPH6k2rflwV5Oxm6Mjw+H34dU+x1ZKmPX6LTmU8ZC4VjjIAHoicWhvumypajsmgX1PGOiJjLs3\nJuHoQeUoi0fQkcxgS32bjV02c4tn3PPmKS+jZwU4eB2f3TPYSw7GLRHSdH9rsnO0CoQNdxhOZRVk\nOBzHXdYmybrSiJBcOXpe6K8gIRUJiZ6u4Ugfm7celkIDjkYAGQCDTO8PAlDvQ88qAEcxP9f71Hkf\ngErmNdzH3/YvIrt22+6Zxof32KHqqZxNnSnsYE/l1PWQsPF0UEDeAszTvljqw2tT4SB1tyDg+Dzc\nI6U0m4znmeEw2OWTeZFKC3tjOMIhgqk6MLZj4kRDKnYllQ522ety2mlLDqmkOSqNpO60venS5+jU\nPFDsMO66bq+5BHb352CXuy4b1gXIWx/sw9MFeHakhtgChsMglNIkgA8BnKm/RwgJaT+/50PVFKih\nFl3eY3VqcradTkppN6W0VX8BaLP6nDQRqpYw7dJsFs1YJITjtG6OhgdF6m7BgWL229ysRx7eQsRD\nfd6fJdDLv8fPGjvQ3JlCPBLCMUMqrHXJ3PHlMQkCc9QuTGChy373WAhmSVbOkoRxd2MSQH0kXBcg\nHOlBF6U0u7bYVqhY6ipASMVvabMd+wnYhv5s2eKCAj2BZn4B4LCUhwDMJoRcTgiZAGABgFIACwGA\nEHIfIeTP+ocJIdcTQr5OCDmKEDKREDIfwH8BeITR+TCAcwkhcwkh4wkhPwdwAoDf9sD9uIvUHA77\n3YJlPw67/gasLr8hFaedh3AFQAFCKr3x8PrcpekOePJwlamy1mUVUpEEGlk9vnfa3nMJ7HeP+jwV\nrFLRHbsV0PPbtbQnQioeDvPzbFchqH1GV21LAvtbuxEOkdwpxlk97MGOosm6hQDYNnMUyFtLJw+v\nRCREcKCtG/vY4yKkhiPtGC+fmyRDcnoQUskTSukzAG4EcA+AtVDZinMppXrS5xAAI5lLYgAeBPAx\ngHcAHAfgLErpm4zOFQC+C+BKqH09vgVgJqV0Q2HvxqP4/eIVxR4oOOy0Lbs59gQ9CXD0OPCwW/Ds\n+Nwam0noDxIyd/3k1MO+xwIOu3CKQZfDjs83Xe19AXbXZfMdWpzDoXdz3H3I1M1RdkjFctz7QkjF\n+07bVuyOIw/5BGeOdtmD4mOGVKAkZmLIsoxeyIHRE5yjBl2CQC8UVkGpha6iaBjHDvPBFktlliR1\nw2V/PswZDlBKf0spHUUpjVNKp1NKVzK/m0UpPZ35+QFK6VGU0mJKaX9K6RmU0rctdD5HKR2n6ZxI\nKV3aE/fiSXjpV8DXjk93VlsPMN0cC7JbcMoel+X4/FDMLg+vjOPpuR2fk7PK6VqzS6tQMcfGAcnV\nEi4OhkuX94WuoiiKowdadHOUHVJxBGcywIvfnB67+2NODxYe9wKEI9k5ujuXMJonUueoDdvFpYvP\nLv0e13jZvIkwHHYJ+DJylnh62PSw9Lkqlf8IEUo4NO+07Sek3s2RUmDtnmbj56SUmDno8ru7cnt4\n/ehSvO/SvNsl6Ph8LMCtiRQ+PaCmEVkCDk9ATxJI8KPLNi9BZ4Os51U29GdYzCU1/vI0VoUBjc66\nZLIlMkMq3kFjtkLFkYUrYBiES5cXuyzYYqueMb2UO+Osx0vO0mEcUjkshXd3zF6bp8v6gcuGVbTT\nHKWGVAqy05bg+GQtBJ66skrcaWu61u5uBqXAyOoS1JRb5Gk4LpqS+hKwOy1pbdJt5qi2mH/gia6W\nGVLpmd0xvy5B8MLjYDyGVBKpTLYvhX9Q7AxA7XUVMKRisCv/O9Tn6Oa6NnR0p42fE+1nZLBLUq6Y\nuSsrr109LAHgKITwLk6O8VBrXXrZ4Vq9xXlBaOECNuQRcnw2D69nCl3ibsGT41N1OVLVnnUJAiGZ\n3TNd9OhzdMO+FqQyipqro39Hws3pnOh4SXPUoKs3E1AlUOi2TtRo08f7WpBWKGrK4xjer9i7Tex7\nfueVOdwgosunXUMqi7PHRWzYZ15LJQAOxSVJujfCfr0gAeAohEhd6HQnap0rMWWEiszX7WlWS7o8\nUbl+d1ZOdgnuPIQcn6QySPZa889+78+8kFvYtUbrMJpXamjWZS5lNeiSb5dnXbaOz3qOjulfioqi\nCLrTitoATGpzOi/314shFSlOVBLAZoGeC2jUwynTRvYzNvzK2mQDGHnsKkjemYNDtl1LVWC8bq85\nPG0z36kiIe+sEKG6IKRyeEkPxjDHDS5HLBJCS1cKOw92FubhleKsHMALbz5I3i7NL5XLfM5lx+dZ\nl0tIhVKKdVq+jQ4W7XUVcHfMpYsP6IVCBMdpi/naPc3egF5fi/9z5yw56ZI07qbuma56LHWZwn76\nHHVl4QqdOyPzOXSeD/ocXbdHYzhce6nY6zIIpfLYkoDhCCRPZO3Y2fdsdMUiIRw7VG0ctY5dzAse\nUukLcVpZ8dCIek6JkC5vMftdBzvR0pVCLBLC+CE2R/r0REiFS5ddWIyhhW1Km48bri/msgGHU2Jz\nIeZoLzgGN2YJ8MYmeBp3VY9+CrX+vXm2yaCrN3Jn+O06boRaGptLwHcBCV7tYhkV29LmIKQSCK9I\npYXddU0x7B69lJh5tcupiRjvQiDD8dnFQxk9Xnp69BiVm9Ol07XHDq1ANGzz+Hlyoh7tKsSBZHa7\nY8B2bh3H0tXZBZh46srqKD1xfwZdXu3y8ByKhhx8Oz6HajhmrA60JbCvuQuEAJPMDb+yf09iKWtP\nHJoHuALQScMqQQiwr7kLB9oS7iEVB11Gm5zGXWZyehBSOTylhxG+IfbY405UYj6I1B2fh9hqT5UQ\n6++lk9ndk+3O0aBLxrj3YEiF/Xsm0XePWw+0o6OrK3edaKa9p/ynPjRHAXlOhtvxOQG9JNZrIYWx\nA8tQFrfIQdE+p15nFTLiZZZ6N6RSXhTF2IFlAKCOgd09EuIvxOaDWfKsS8Yc7QUJAEchhHunzffA\n6c5rY20r0imtY50jWyJjx9dLuQSGeKjgjq83GA4dcIyw2TlKt8tpAZbU+pv92ca5DywvwrCqYlAK\nfLKv0VoP+57v+7NKzuzNfJceeHYM3TP9zHfnkkqdhZvsCIp7aI5KbU/v7tyzob+9zS5zy8c9GnLF\nJDX+kjFHe0ECwFEIMey0PXTiFHxIRvUvQVVJFMm0gv1Nrfk2+NBltEtm/F+SLiUDgFrrYkFWrwEO\n+/tT0slsbwNnhsODs+rpMjonoBcKA9AcmNNiroGsT/cdMv59S5t6I++iD853gy7Beeo57Kflb4zw\nwsLJrA7qqdwZpzlqkdws6tzZMI8woydxXvWCBICjEMIbW7WM2bs/cISQrAOrO6QDjgLv2mVm7fMs\nmoA8irmHQirtnZ3oTiuoKIpgdP9SD7pkhlQEHQMborIsbXafD/oc3VbX5MGmHp5XPapLJlvi4zv0\nMEdpJpWrouJmOHrp/gBvuTNewtN7mkFlr1kFB1QB4Dg8xTe1L+5gdGS+v6nNQZfPye0EhHqLCnRK\nfGNjq36y9mU8vB4S39o6OwGo31UoZNHbwGyXlLCYpB2RUxzaoy59Md+xX2c4ZOYGOY1Vbx4i1lN5\nOJIYjnQyW0U1brBNFZVBVx9icAx28Y3VuMHliEdCaE2kQdOyWFkPIMjrWVIyQ3W9IAHgKIT47Z4p\nYUGZotHVDc064JAZUpGZkCeYte/UO4PV1Qd3Hp2darJk3lHftrpk5uFIooVdddk794nDKhEiQEt7\np/EaSz294awkzVEAjlUcfthBp/b7rH5JGxuiJAFQHDOkArGIg3voiXJrVr9MXQ5h7mg4hInaybHO\nDAfHs+Okh/2coy6J7GcvSAA4CiF+u2dKWOh0urqtk6kAsNPVVxcCPyDBqncGAF/9QXoqpKKdxJlI\nJAC45G8YdMlkAERpYYfEN4+6SuMRHD2oHDFSgHJryzLIXqSrZbFUTs26DLpE53vuniPIZNkoe11O\nY8XZgK+P5J2pzydFSFa5rpd5JVNXEFI5DEX6Ttv5getfFseI6mJEoe+GJDpRSwfDSTGLtqB2GiuD\nrt5KGrXXpVcQuS7mnha6Hk78Ze/PqtW1j8U84jhHNT000wulzRLpai9zy09CuZsuX2DdGXBEkXau\nogK8zdE+V47scY6OqEQYCohdcrpfu5yqXQyJ7n7WPwlrci9IADgKJbIpNw8T+7jhVYhC5u6xh+lq\nPw+v1aJp0CUph8Nz22j3HW0UaQypLMLAiiIXXV6caC+FVOyAnsfeC1NGus1R3gW4D81RmbpcGQ75\nO+0o0j5YOIkhFaml/PzzfeqIfrk5KqjL1aZQyGdps8Q1uRckAByFElkI2IeeKSPYxfxzGFsVDT8Z\ndEkKqQD+ckscxj2KtHv+BuDRifZSSMWK7fKhiwXFNCSBYpa60+6p+e6jW6z+GRLOb9ZlsEtwjobC\noFppc3URnKuoWLtEnbFBl8yQigOb4DLuI6qLUVPMsHjCuWIOc9Sgq4cBdi9IADgKJbJ3Hh5OJmQB\nB+Vsk260y8suxgMt7HRKpUGXjJ225Kx9z3a5359KVbvsHN3s4j7oTrR5kcdQlotzP3pQGUojKmPU\npVgsP74p5p6qpPLp+HpqvsvSRQgUbewnDy5xrqJy09WrTKr4d0gIwZRhJcx1kvJwbDdJPN9hUKUS\nCCu9kMV87NBKxLWEvLY0f5zdm129RQt7fXj9OFHnmLasPJwYSTv3Nsjq+hyGVDzqioRDGNNP/Wyr\n1S2EQv7Oi/G0APdmSMUJ6AkCWb92OZW5A0hBtXXSkGIfdjkl68pklmQwet51TR6sAo40Ii45SzKf\nnSCkEgivyHKiPnbaxbEwqovUh2NviwUbwg04rBYVDqfA2mCwSxIrwerylJDn8PCGwgAJGT/nSVf+\nWDVp3eajSGOir5CKU9WSh/tTFJeSyt4BemOq1M/q4yJmV08l/vZyVVahQ4gAuqkaspkw0Avg8JJ3\n0cOJzeznBHVN1ACHDsKE7HIaK0De+seyjF6O1OgFCQBHoUQWavVJMQ/QYo97Wi0ckt+FwFPXPh8I\nn71OVJdUhkPC7tFB15YGtRy2KJRBRZGN3V7t4tnRAuIMgFOIwKeukVXqIt6UsPmA7Dwc342/BOe7\nojDPjlNYrO9UZXV0p5FQdMDhktTsZpdfkCD1tFg5usZrY9BNw2hLWHxPhcg787VJcsk766NhlQBw\nFEpkUW4+s5j7aWcd7WmxekgKEFLx1azL4pRKv3Y5gSC/ugoCXvJ1bdyvbuXjxEOZJ+DRifYW0BML\nqQDA8HIVcBxMUCTTFhVAshLyeiuXwBXo9b0Q4oZ9LdndfH8PeMMTK+G5tFlSXoJrkzTv/UH0dTSF\nSPb8I6MuPwBUYljMc95Z3wyrBICjUNJLi0qF9qDsaEqBmmk13xnfsmnhmE08VOaOj6fxl7gTdQJC\nG/ernTWjVGYcuq/mznhYzLWwXzeN4NP9bYJ2OdDVbJt7X6c2S5rvrrp6Fug5zav1e1uQpNqzkxYF\nejITfwuQK+bj2IMkIvhYO8yO364eYmUDwHEYi9RFxftiXhpWd4ytSWBvU5eNTTKT6PoOLdwXdVFK\nsa5WBRxhKsPxcdjkWlIpMXfGgy61fTaQpGFs2Ge1mBegtFma4/PD6MH5OxQ978dgl9h3uHZvcy5f\noU8lXHPcnxRd6neTpmF87DhHBcGZQZd4abOvvLNekB4BHISQawghOwkhCULISkLISQ6fvZAQ8gYh\npIEQ0koIeY8Qco7pM7MIIdT0sosI945IRcDaQuBhgdLb8SYRwXozMucNqchqzywF4fdQiRn7vgCo\n2tvUhYYuBmTIitNKzXeRoMtXXoL6mRQiWG+5mBdgx9eTh/m5hhALEP8X1PXx3hYGcAiyg76Bnhdm\nySfQE01m1WxKIWIDOHrr2ZEIQHtBCg44CCEXA3gIwN0AjgewDsDrhJCBNpecBuANAOcBmAbgbQB/\nI4RMNX2uFcAQ5jVKvvUCIisO7VuXw4PiJ7ZKqURqXyYt7DXju4dLDm0WczY27l2XF8fXW/cnd45a\nMxy9RDFLc3wFmO8S2M/sZ0zPTktnCrsPdXIyHFZ5Z8xOW1LTPH/hNbtzlvjm6I7GDrSaE0f7YkjF\nr65ekJ5gOG4A8BildCGldBOAqwB0AviB1YcppddTSh+glK6mlG6llN4KYCuA8/M/SuuZ1/6C3oVf\n6WUnqgKOZms9XnQpGcDTWQKC5acGXRIcn6zGX77tstb1sV/AwTZJk3YarsxyPHk77TQi+KSuLT9x\nVFLujMouEO+6ZDu+z0nYb0OtCvpIpA86UR4mwW4d9bU2GKuM8oCxrzXZoWLJty6vjNdhGFIhhMSg\nshT/1N+jlCraz1/wqCMEoBzAIdOvygghuwghewghLxFCjnXQESeEVOgvTV9hpZcRcEpLdjIkjvrZ\n8cmMh7o0HOqz4RmP54MY/p5J18f7WpAGQ6u76XJLfPNlk1egJzE84+NAstD/Z++9oyw5r/vA3/dy\n556e0DPTPQkYYDDADIhEgEGCGE1agSYlUZZIaxVNW2uFVbD28OjICj5nIa+X0tqmVjQpHnppQaQY\ntFyK5JIyKJEURRAg8gwwgzixJ/b0dO6Xv/2j6nvvq3oVvnCr6pH97jl9gOlXfevW9+53v3t/N1Sh\nhHqr3Vs4SrV3GKND4jJL+6nqqPlaCSS0Uq7QyUWAvHj4k9ZKqOtoqexU4fcUjmbmNBIGbxlQ0gjH\nNgB5AH704TKAnYo8fgvAKIBPSb97Hg5C8s8A/As4z/EtxthsCI/3A1iSfs4r3tucMoarea6I5WoT\nZxfWu5/pzPSIczgSyTsSwtVKB19NUS6NiEhaY86521LH0M6X1XglUPhG65zR6ejUuPO+DqtaIypj\nzjldSiWuDdLIkSVMqfgRDuFwDA1572klF1EQkXHgVqk4TlhoejozpJEALcmA+rpLhTH2HgC/B+An\nOOdXxO855w9zzj/OOX+Kc/51AD8K4CqAfxXC6gEAE9JPmGNCR5R52o6BUk9fzG51Jlp6jLnO2Gj5\nwLYdGtWvOcyEeV1YqmJhrY5CjoGprhepw5FmLYFOpO3cb9uEAzSGpv5IIeaYvROr71mnG5LbO8Lh\nGB0e1uBF6cwqIEsqdWcJIAnDQ86a9DocBjoalzK3LSgHNj3CMQ+gBWDa9/tpAJei/pAx9pMA/hyO\ns/FQ1LWc8waAJwEcDPm8xjlfFj8AApr/iUl88c2w+c0SxaYc9NMXB3Y6Dkdv7lGRl1yAFfkuAUqo\nk8LQJcHLLHoUMOxN02NgqpFox+jEdDhopC7CDZ2GjiYAoe/YIhyOPkA4Yh09Sa/iWptTRZY09D3A\nzixXGzh9zUFBx0eEw0GB4ig6erEvdpRRWcUgibDrbHTIQTjOXFvH0npAu3MfBDYe0n25Y8qUqMPB\nOa8DeBzAm8Xv3JqMNwN4OOzvGGM/BeBjAH6Kc/7FuPswxvIAjgK4aCszGWUMV98wPQUgCK5W3HSk\nqQvCSFu5HiTlFrOASFQ4e0dnxvUPvnyJ0NHrz5TKri3jAIDnL62g1pSiV8q8vaoBVnU4gHidT3Xv\n2NWDCB2dmRxCqVPDkWJKRXVYlxIv+v1cLJWxd8pxxERxrUdWkhq2JNIzmzel8scA/iVj7GcYY4cB\n/BmAETgOBRhjDzDGPi4udtMoHwfwmwAeYYztdH8mpGv+HWPsnzDGbmCM3QXgL+C0xf55Cs+jRpm1\n0TnX3LTbcTiOX1hCux1QOKpqCFKdnUEZLRA6HIYzHI51HI4JM4cjSialSDvNlIq+jk6OjWByuIhG\ni+P5SxLoaFRwGPaSLVUHW57hEPGGV0DjO0wxpWKoo8c9OppB8bZqrZh8zzhesY6eHmJ5dCYgPU1Q\nO9MjV9qt7hlQ4g4H5/yv4BR+/iGApwDcAeDtUhvrLgB7pT95H4ACgD+Fg1iIn/8kXbMFwEcAnADw\nJQDjAF7ntt32B2Wcp92/YxKlQg4r1SbOyIWjZAdfEoVO3wspFedvOOcdY37EY8wVD75QmaTDFPpV\ndAAAIABJREFUMC5CTuQdDhQpFYcXK8QZc0IHNO6QUUWWVORSboPMPh15bM55T8jR2Qmj79D6EPW8\ndybI4dCoOyPdz93nOzobkJ5OJA2SMiqbAaVSNMo5/yDnfB/nvMw5v49z/oj02c9yzt8g/fsNnHMW\n8POz0jW/LvHbyTn/Ic75k2k8izIlYVTijKZUaV8sVXDrLgey9uTIdQ++uPw/bxMWc1EU2Ga0eX2w\n6aXlKq6t1ZHPMRzeZZJSiVl3JV4pplQM558Ih+N4oI6mmOqJ1St5loqi80IyVyfZveN1ig0O0Tj7\noJNSCapZ0uKVzH7uOMVycbNRwEXxqntCpyoD6usule9qyiRa8Fbai41y7Ly8UahSKjpQZ5o5zKx5\nOX/TKRjdMYpKMa9uoFSNJkAHMZPqqIbRzBVw+6wtXB33HSq2oMbpKGP0TiPl/BMDHV2pNnBqfg0A\ncGT3eDIpFVtkSb6Htb6bpUGO7HZ09NzCBhbXffdIPaUyQDgGFERGXqulB+zLhwoo8JgJFKh18FGl\nZ1Q2XO+8i2BelHB1nKPXcpAeiZcncpTvYXvwmUTaJCmVuFoJccDoFUIenZ0EALxweQXVhu/V4mkW\n5MWtlRYvylQW5WEl9o7zHYrXru+eqGDraJk4SFJ19JJYd8t6Hp9cE8NF7N/qa48l/Q6TqGEbOByb\ni0hrHAwdjg5cvdwtHKWKFkiLuZLI2VN2AOisu7MunoJRmVdcC2qccdKKtFUd2aw6ekrYPVHB1EgJ\nzTbHSVE4qrp32m2pFTLhlIpHLtu9k8TgL/29E+4Ux+ho3HuWdOSKc7C1eKmmW/XRzyP+WqPM5hAN\nUioDCqIsUipyz3uugJt2jKJcyGG11sSpa2s+uSwNQS7nvPacgldmEDNRAarP0eOcd4rxusZcN6US\nYYB1Wz1J0iCEKJU0L4Ex1pv6U9UHT8Fh3HcY18qqc/CpOhz93eHV6xS792jGOXox71nSkStNR69T\nd6YyRMy77rf7C0dJUyribeCEQZJKJ04GNHA4kiLVUdaAwuGuueFyRYAxFPI53LbbKRzt3ShxRiXF\nyIO0LSwJZEnH0SviykoN86s15Bg6hbv6KZUUDXCazlmAXB2HQ1dHfY5esFwZpFRiB1BJh0Kqrc3e\n71Cs95FZH8KhWndBIVciKRWKujOvXL0Ih4GjZ1tgGzd+X1euDGjgcCRFBqOekzCaPW2HSRgC5UFI\naczhyKAAS3zO8kAu1ykYPbhjFEOlvJeXThFdGCnLpXjwqUR8ibTYug6Hv3DUZHZGbPqCAFkic/Sk\ne1gPETNb99Vas1Mw2pP2U30+Crl8dSWRvGzTkfLvNfVBOBxzixtYWKtbOXqhcsU6sirI0iClsjlJ\ndfMqea3mMxxEUZ5+9KiCcKhC+xqHVVzEp1wkSGEIdA8rL1TdSafI97CF46X7WDsvFhFfKC+N9/2I\nvxEH3otXVp3CUV0dDRsDL8tLgizpOv4qkTZR1K7pcDx3YRmcA7smKtg2Wtbj5XH0LPehTkrFOrDR\ncfS8tUHjlSIObHNeNnhsbknP0Yt11jVtQySvAcKxOYnUa7VHOJ6dcyeOdpQ7LlrQya0SpVTAtXOr\nxjIpyWV2WB3358Z15Iqbf+LhRZRS0ZErAZTKOfRKaLU5nru4LPGi0FFKZInYwVbilUTtTKHjFN+2\nW9JR7dRtyHuWxGc6vEhTKmFoVx5gOUVe4bb02PlFddQlhJdXLkqHQ8P+ZUADhyMp0vXKgURSKjdu\nH8FQMY+1eguvzK9JvFSL6ChrCWIOK/naWF6Wm5cyH+p7vp5iPCNelAcfRcSXXD2IXDh6fG5JHS1J\nc63k+1B1qQD2z2jo6AU7xRnUu6S57lpy9dqs2+UxA6r2HaBz1j1D0gg6zzKggcORFJEWvilWMQco\ndiGfw627xcTRRY0Oh5i5C7K8mUR8tvnQmNeRy7/XMMBXlqu4suIWjLrr7uVFmFJRlSsMLcnlNTqN\nFA9Rw04jT62Rro6mUXchf2a7dxIZIqbncHSc4tkAHTWwM8ZyaTmNlHtHP8V2pINwLKnbBhW5THQ0\ndEjaIKWyOSkRr9XMOHWhwGW6NIhHLsqIj8h5Iam0V3w+qStBvFHyxu2jGC5Jz6XNi9IApxCJWqRU\ngK4xP66TH08kok0hpQIk0NqsXrO03srh5aurAPx1RqrOeorop45cWqisvrMuOv4uLFWxUOXd66w7\njRLQUZVUTwY0cDiSIt0cptvKGkiWhiDQmNtC6ACdUfFEfFTFiyk6HNLzHTvvm7/RwytNRy8JBECh\n1TOKAqayAt1OlRevrKIOgboozuEgeb60oX3q1mZ1ZOmF+Ro4B6bHy9gxVgngRaijsY6/inOmWbwd\nWf9kvnfGKkXc4BaOPnel2r1WuQDVcu/o6KhKqicDGjgcSVEmkGKwQnYKRy8sgVPmtLWhb4qIj2i0\nuRKypB+FBnaoyPdIM+LTikRTirRDOhx2jncLR88tu98xpQGmcBJIUz1Eh4zMJyrSlqayPnd5A4Cv\nfgMA2Xtn5M+UdZTyO1SxWWb60AneLm1I19o6jZQFtoOi0c1JpFGonfNy4/YRVIo5rNVbWKwxNV5K\nh1Uf5mlNDphYZEn9OwwsxvPwooSFs8hpE3VSyX8Dp3BUGPNTCw09Xn2XUklRLtXWZsmxOX55HUDS\nKFwWbeDJO9hiXz99cb332iBKpDh94HAMyE+UG87SKy/kc52Jl1fWWnRy9WORWYaHQgMFXFqugrFu\nvreHF0V7JiWypKunKshSVKTtQZaCkbiXrtX0ZIrcO6pwfMqRtjaaYFlwLd3n2MUwhCOLbpAknAQK\ndDA4DdKZODq3Jt03ytGTxh5Y1+gR6mhGNHA4kiJt2Lscwcs+Dy2My6W1tppcqVeiE0PMGdQ3rDWd\n7XTDthGMlH3GRfs7jOoOysKpcg1wIURPVVtsO45LwXkfj0TCmL/YcTgoDqsEDtHYOpWYnL1HLstD\nVNnh6H528qpTf9CLcGjqKEkHG2HNUiLFrF5et804gcTcUhVcxfFXqhVLogh84HBsLupE/zG51ZQO\n9s5o3pWmNS9Kubq8iIvo4sZ1kyIJzpouN5zUTE/kKN+HsvDNdvKifB/Sgy/iO4x4PrFup66rplTE\nwUcBx2eVUrHt8MoDEGnSqHV3PuNgaPActo+VMT1e8V5DpQvyZ8pzRgjqQXQcUEN9kCeOtlXWy/OC\nQbri9FAapFQ2KanmVilhwAheogtgblmkVCgMAWWRGVEhpKfFVmXd6RyqJTcw74kcAX2jGYYkaMmV\nQJdK3Auo4uSKOBR2TVSwdaSEWluxSyWRw6rfulSI9o77mXNIMkunWAWV7deUir0+iP3dgIL9CymS\n9pByypwQ0cuIBg5HUiQrRZQ3rWScNA/2gEPh4PZRVIo5rDZVR/uqzINIAjaNihbklkqigy8SFtY7\njK8rORwpdgCQrXvbQYyieGk7er3PJwpH6yqGXP48DeRM/ozCeSFFE9QdDnFIJq6jus+n1MpKUStm\nX1t31E2r1LjrGKvY98ixBxmkSDOigcORFCkffJT53nADXMjncHjXuOSVUxoCCmOuEi3I+dCY4kVA\nrZZABUlQrCsRKZWeglGZV79Gx1HP2FaI0hhTO2RiEKqjMxNoqM7hSCTtR4Ho6eydCLk8HQ6WNV7u\nZ3X3kIxEOEjTT2l26aXTWSectY2WwpTelBDsDulM/M2ABg5HUpQEtK9sCIIV0syYU0QLKoWQ6lGa\n53o/qY7rTqB2poECbtg2grFKAM8kajhI4WpVR8/SmMes+5GZCTS47lt6KVAqjXoQynWPcorlGiQi\np7HaVnA4WvWYujPKQzT5VlY7ucJTKrV2znutJp8emXjLQRPjeFHoaEY0cDiSItX3JSgdMDQ5Pj1j\nnk600MtLMR+qtF5mtQS9fNSq4xu8EAxV6/Dqx5SKSh5a/kwFWQpDOGYnOigcj63n0Un79VlKhcrB\n1uRVRwHbRsuYHg9ATGTHLfI7TLmDTbfGgSRNGm4fxitF7N86rIYW69gZgCD9PnA4Ni8ptU2lt3lv\n1zHmWoaA4uBTh4WDWiq9vFScF/oDpoFCcOQIqK+V1sA1ypy2wsHHcm5XRJxcKhBz8PPtnqhgbHjI\nuV2qnUY6iF5Kb7FVdjjU906D53FkZhwsqJ5ANQ2s037aTzN6ADXnhfP41N/spKLDoaELyrwsnf4M\nKRWHgzH2bxhjpxljVcbYI4yxe2OufwNj7AnGWI0x9hJj7GcDrnk3Y+yky/MYY+wHE3sAU1IxUCqb\nV3vwV7BCHtw+2vmsWot5uQ/peyqI6lRU0CBVuTq8FOddKEDMDeQ7ffq9vFIusJU/t0XPVKI0Dy9z\nB5sxhoO7p3qvD+RFmfZLu0haY93l603lktJ+oU6xx+FIu7NOxXlRQxrTQPSOzoyrFTfrOFRxvLQQ\nvU2KcDDG/jmAPwbwBwDuAvA0gK8wxnaEXH8AwBcB/D2AOwD8nwD+nDH2Numa1wH4BICPArgTwOcA\nfI4xdiTBR9EnrYiPspUrWCEL+Rx2TjkHYrVaDbyml5dl7hggjPhUDz6dWgJVqDPcaRRr2YBCSkU5\n4kt78JclGuSRy+6wumVma/cfkRBzVmk/1X2oUrOk6BSHdTjI91GwM80oHVWuO0u7lVU1LUYUJCkg\nS0dmJhTbYhWc/lzeQQ/99w7jNXA4Iuk3AHyEc/4xzvlzAP41gHUAPx9y/b8GcIpz/puc8xOc8w8C\n+AyAX5eu+TUAX+ac/0f3mt8F8ASAX07uMQyIoIjOy8e+0HPPNsfY1GtxDgeRcivAkwDUUBwV46TK\nSycaku8dQPNLKwCA4aEhjAcVjMq8sshpW0fHCrlxZV7xz3d4VnI4bI05UcG15zPSTiPL1IX8eYRc\ndRfRrCMfjnBkWneWFlqiWTsT8oxyPdzq+nrgNcoyeeSyRZY2cZcKY6wE4G4AD4nfcc7b7r9fG/Jn\nr5Wvd+krvutVrpHlKDPGxsUPgDHlh7AhrYhPYZPE5rTjN+++HY6xadZjUipUyu0p9CTqUiGB9jUi\nqxhe11ec9ypsGRuJ55VmsS7VqGdSoxmvo0f3TKHJHdNUrW6EXkc7d0GBF2UdjpKDrSCTfJ8IueYW\nlt37lrBrohJ6Xep1Z0o6msCbllWQM7DQmqXxShGFonOf89eWwnmpjLkH0l/3jChphGMbgDyAy77f\nXwawM+RvdoZcP84YG4q5Jozn+wEsST/nYyWnIIKcds9nllH7gR1bnEubdbTbUXUJRPlC7cK3qIhP\ncfNSIUseiDk8FbK06kQ42yZGI2RK4NXfab0ITjnSpqkH2T1RQZM56/XKpetWvPqtpVKLF2Eq6/y8\ncyiWypXgglENXnpOMUWBLeW6azrYEWs1NOQcRxeuLavxiiLq4DSu7iwj2ixdKg8AmJB+ZlO5q443\nTVrFHM5rdruDcOTQxOlra6HXJQJPqvBSaqlULBq1bTFThJhX1hyHY8dkBHBGWuipgCSoTGVVlUs1\n0tZ5mVXEujPG0HYdjhcvLljx0o+0U06pqE6pjCIFfbgw7xyKQ5UIdEPmZd2eqVt3RlnDQdQdFOMk\njLgOx+UFCoeDKv2uVneWFSXtcMwDaAGY9v1+GsClkL+5FHL9Mud8I+aaQJ6c8xrnfFn8AFhRlN+O\ntLolCKqYFRSyUHT670to4thcBBSoNGRGpQtHfBYOTzq8KCM+onyoglyL63XU3fTU9BYVhyOliE8b\nWUp+rTz3UeT1shLCQdHKqhG1Rw7YatPNByFMqVy67hyKI8NDodeo8urqQ1pvi1VsZaXaO4pI6tjI\nMADg8mLEcaJSQCzLRVUkLV/fR5Sow8E5rwN4HMCbxe8YYzn33w+H/NnD8vUuvdV3vco12RNVl4pc\nxUw0GKaIJo5HOhw61eOKToISlEtxWKnwUjgUPLyC1/343DKKcHhFRo+kER/RGHhAM6JVRZbMB38J\nyhWcz09dXrSTK+2CQ3kdVVuuQ2WiaUeuNlpYWF4FAIzGOhw6rZ4KqTqKWSpK694C4KYQlNbdXkfH\nR52ardX1KhbXQ2TLKqUiX99HlEZK5Y8B/EvG2M8wxg4D+DMAIwA+BgCMsQcYYx+Xrv8QgBsYY/87\nY+wWxtj/DOAnAPyJdM1/AvB2xthvutf8PoB7AHwwhedRJy1vmgJyU8nZO5uxGItwEOX/dQ+r1Nsz\nY3jFPOOxuaWOw5FeoacGkgDYj0JWds6IHGwAhZKDxF1YWEKtGXJgaRVnxuS0yfL/8gyHdKD9OLTk\n+UsryHPXKR4iQDh0ipEj5PJ8FuUk6NiZWLnokNRSyfm8hCaOz4WkVZKYYRO5VoqtzRlR4g4H5/yv\nAPwWgD8E8BSc2Rpv55yLos9dAPZK158C8ENwEIunAfwmgF/knH9FuuZbAN4D4H3uNT8O4J2c8+NJ\nP48W9WEHgIxwPDu3HF44qgIrahWYUcLxhCkVy1bP43NLKKk4HGlHfPLzRU5lTcLRUzGa0fqQd1N/\nrNXA85dCIGutnDZXW3dr50z34LMcIa4g17G5JRRcHWVpOY2qkTZVSqWt6ujRp/0igzdSVFax7ky1\nmyoDirG2NOTO0ghEHzjnPxvwu6/BGegVxfPTAD5NIF5ypIUAxHwVOfXhPipGs8RaWKk2cGZhHQe2\nBbRz6hgV2zSPfB9CQ0ALV4ekVC4s4T1oea+N4iN4hdWzaA3+soS9PbwUnRclXvb6wFwdLrIWjs0t\n4fbZSTNe8mftRvi6khUcxrdUeu5DgQ7GvCH02QtLmFLRUflzJUeIoJaAqg3cgywpdJ4R1iwVWUR6\nWrvw13Iqtfi83ehLh2OzdKlkQ6QHAxEUKG2iAloRnjlVpK37fAq51bjNq+OcqcoV4FQtbTRw5to6\nikwjpRLCS0uulAsOk9FRtYOvFFVrpF1wTdQBQNBSmYiORiAcJRUdVeDl+Sxyemau+9ZmpUJIosAm\ndiorvY5GIxw036HzmS5asglTKpuatA6GdFMqQEThqKel0hLqJD34Uk4/xcj1rLt2owWV9lOFnDbn\ndO9L0EaWKCIrykJIIrhauZaAOJWlrFdRaQL7uTO1ZgvPX1pRqzMC6AZQxcjV5UWUUknkYFfjVUIT\nZxfWsbQeIF/aKRX58wHCsckoAW+aDJ6Ea8zPBxhz5Q4HHTieYsNpGrrI9kX7lIo4CMcKPF6uXL4b\n8YU9oyosnLoB1j1EiWBhOCjc85dWggtHVfSdsXg0QbulUqENnEJHdZ3GgO6gFy6totHiXaeYJC2W\nRJBkm8pSXXeVTiq955usOIjK8QtBwZsiL8pXO6joVkY0cDiSJMIiOrJoQcorl9DC8QtL4P7qfeVK\n+5RRCdJIW/cQ7eUlHI6RggIapCKX/Hvr4kWFinZdXqQRrdrBMFnmaLQ4Xri0GsHL0qmSWyqpHGxS\nHTV/PqGjO0fy1rz05SKqYZNlCus0ysLBdvfWjmHnGA1E4gjsTJfXIKUyoChKvdVTQSGl6ZnDhRZW\nqk2cueZ7+ZBySyVhSoVoSiW5XBFGU6SjKnlVhyPGqdLucCBYK60iuvRTKge2ODyDjTmRAVZG9JI4\njC1bRmPkEuu2fSSnJ5dt3UWMXF1eenVnociEdnEmnY5uG3IQDhodTcnRy4gGDkeSpAXtp1/jcHi7\nM6iqZ6MIPiwf01KpApkm4SSk89bSKLmWqw2cdh21MtPtAAh5RuWprFnltAnqEjTXfd9ElMNBVC+h\n21IZ1drcZ51Uz7owvzgUaWpLiBy9dttZS/m+UTJF8aKM/jX3zpQ77y+wHk67OJ0u1TNwODYbJRDx\nUUJut+xwhgD1bJRE0iBpOlTJH8hizWYmh5DXfo14TEolX7KvtE/kRXeUcLVaLcGeCec6EmOuUjsT\n2XmhMFSJtGbJ7vnqzTZOXnRmmIhDsV9SPQB8jp5lp1ESKRXFepcJl+WZa+tY2vDpxSCl4qGBw5Ek\naUV8lJ65mnLfst0ZrtQTPSpPP03AoSIpolNZd80iM98zPutOFjw6M2FwyMQcVjprZZ3TVimiS6Lw\nV+0Zd485SM/zl1ZQb7a91yg7VYrrHjskLYmDj2LwV/C6v3B5BfVWGxNDRQznFTqpIniZyaXoYMvX\nBpGKo0fl9Mv3UORVQhN7ppzg7dme4I3SlhI6VRnRwOFIkkiL6HQ8czVeN21zHI7jc77CUeWiKcri\nTBWHijJq1835eg8G4aQdnZ1QN8Bx66WcMpLuQ+W8kOqoyrwENV6TZYaJoSLqrTZeuOybOKpcp6JY\nrKt6KAAR656AjhoiegIVOjIzDqbtJNi/ayTe0VNMZalMz0wkpaLeDXJ0xnkLd2h6mhKVpahTyYgG\nDkeSpDTch2ggj5wPLZSV5No3UUQpn8Ny1ekj78qkueEic9oJOFR9lFK5bfc4IbSvySeSF2GxGun7\nfly5CmrfIWtRGHPFlErsQLl8/DCrRHTUbO+I9Tqye4JureTPbA++Tq1YLrpmSYdXqinEbsH1kTgd\nTbVbTOjW5ns9/eamNKMF1XyodK8imrhll/NKdc9G0VXsKLm0C9/SQoPMD+SVagOvzK8BcFMquu26\noYeVJizsk8vLK4lUXQYptlY9wpirdnEoRtpxa+WTK5gXoY5q1+GEIRwGOqoUJBE5HHGOi3yvuC4V\nCkfPID0jnOLeejj7wl9tufr4XSoDhyNJ0jn4qKIF+VoFXoHG3CTSTiXiS3lmiYdXV65nLzj1G7sn\nKtg6XJCmslqmHJRTM3knKozklURKRTVKI3BeJKMZbswNal5sZJKvse6WSBbRa7TaOOG+9M6pM9JN\n+6XQeaZ6GMvXhNq/LFJZkh3d7ejo6WvrWK5Kz0tad0bo+GdEA4cjSUozalfNh8r3ajeDjbmuV+6/\nf5Bc/ZZSsYgWPJGjx9FLM+JT1AeSnL1uxFdT4KWOvAgdPXlRKhxVHQPvkctyrTxyEdWDJJRSefHy\nKurNNsYqBezbOkyXBlGdyqrCS/X55GvIinUp0c8GtoyUMLsloOuPtEuPsD09Ixo4HEmSyhdPMGLb\n+b1ZPrTrcCx3C0e1Im3Fcd3Kho6gxVbrfRCqcHyXV6dgtMfhiKmdyccM2TKKtKkOPoo0SDK1M3um\nhnoLRz0OdkrdQR5eYbVUSeio/nd4XKrfYIx1P4ur74pL+6lOZQ2Ry0NG607UjszbCnVnes4LSfCW\nYE1PP9DA4UiSEvFaKTdvHTdPj6GUz2Fpo4FzCxteXiSRdgIplUxg065cnWI8uUOFQi7VnL18Tewh\nSrlWGax7uwHGGI7MjAOQjHkSyBLJwWeQ9iMb192ro0dnJ7yf2UbHBrVi6aRUNJ8vkpdu2s+5dzc9\nvRzAy9Y2tGnHFWREA4cjSRIRrcqMA+toQWfzdjdKqZDDoZ2+wlHSnHYSh5VilEYZabuGdrXWxCm3\nYNRT/Z8rRg/rknlRRNrKbYKKRlNleibp2Gg9VKKn1kirZkl1rWLQLvlecYeVKpIArrDuMXIF6MIx\nOe0nf2a9Vkmsu05gQzSHg0Iun44GIxxUDgeho5chDRyOJCnhSDuYjz4q0WvMdQxwTOuvyeCv2IhP\nccORvA/CazSfu7AMzoGd4xVsHyvTwvFG3yFRsS4lrwTakXuMuXwP2y4V1cPKIxeRgy3fv4eXbu2M\nc32z1caJi06UfWT3uE8uIicBsB8El0RKJVV9D9bRU/Nr3cJR5ZbruHSrTo2egv3LiAYOR5IU67W2\npA4HqgIs/c3bY8w7BjgmSqOUS2lstH67WigZ1pb0Ro6EUVoixYuUB18Whb9eY37i0goarbbXSVBG\nllJMqZBE2mZr9dLVVdSabYyWC9i/dcQnl20aRCB6MVNZlXiZ7B1LlEppiJgZKrFlpISZSTFxdNkr\nVyzipaij8rWhvBTmP2VEA4cjSVI1TvK1sbzo4Ul5sBLnHGjWvNcpyRUXPSq2VAKEBjhEJs6NRyEf\nlwtGdWQC6CZeBsjVy0sz3wvQwdUJpFT2Tg1jvFJAvekWjhrpKOXeIdJR+f6hvPQQvWPnu0Ppcjmm\nKRdh2o/S0Ut175gXevYicUQplc49Yl7s6OE1QDg2F+l4rbZdHBaFnjfvHEUxz7C00cD56xsJRe2U\nER/V5lXh5YU6u8V4mlC1fC9ShMPyYFDqNNKtM1JIqWjWgziFo65jfH7JUEcth0YFyNXLS1EurXHd\negdfj1NsxCvGkdUZ1tVPKRUtXvp2RhTpPqNbDyeNKoiWiUBHM6SBw5EkxQ3Roexw0IoWvJBbuZD3\nFo5mEcXk8gDcaCx00xFF2lrwZJfXWq2Jl6+uArBMqdjm7H1yBfPSqQchQgDiZDJClnqjx8x0FFDI\ntRPKZTjDoadDxSOXarsuZa0YYUoldO/odHgRo1RS3dmRUIQji5T5wOHYXKQ8OyOvAJMlW/FtbsyJ\nonbG6A1B3Lor8erK9NxFp2B0eryMHWMVPZl8vCLlIh38RVkIaQvHm6QQu3/jMeZGXVlxUTthl0pG\nkXaz1cZzomB0JsjhSPPgS/EQzQKlkj93g6SewlEqZ12rZX6QUtmcpBzBpHgohMgVbMxTjBaUeJl1\nlvSQjKAoO3oNzzClrkwZHDBavChrHGzheDNHT5BcONpsVL33VOKVRl0CZeGv5rrzNl6+vIxqo42R\nUh4HRMGoVnG6FLVHypR2SoUypUzV8dKbBp7yF45SB0mDlEowMcamGGMPMsaWGWOLjLGPMsZGI64v\nMsb+A2PsGGNsjTF2gTH2ccbYbt91X2OMcd/Ph5J6DitKJAoljBbawQgHz6yYiwiu1jlgNGZn9HSo\nyPegMMCqg308clGkVIigb8pUVoBe7ds6jDG3cPT8/JIanxBegXJp7Z006kE0DysAz52fBwDctnui\nt2DUd220THEFxP3WlZVEkKTR4eUJ3twhdecXDRyOFNJ+GVKSCMeDAG4D8FYAPwzgfgAfjrh+GMBd\nAP69+98fBXAIwOcDrv0IgF3Sz2+TSU1Jyl6rCpQbx8sOcju0cwzFPMPiegMra+6r6uMNwbP1AAAg\nAElEQVReIa4jV5pwdULwa3AxXlYQM6Uzq6inqoWeYWOjO4e0SqV9r0yMsQ66dObKoveeSrzSPKxS\nTEdK9zo5dw1ASDpFRa7v1pSKEVock2KLdYqDW/mFfXh2bqH3nsYyKXb7eXj1n8OhIL0+McYOA3g7\ngFdzzh9zf/crAL7EGPstzvkF/99wzpfgOCcyn18G8ChjbC/n/Kz00Trn/FISspNSbKFT/xxW5UIe\nN0+P4dkLy1hYXsV4n8jl5UUVaetHVu1mHS9dcQpGjYrx5GtiuyUoHNBsI2206kBuKJyP4eyMo7MT\nePiVazing3D0bUpFkVfs0Kju5y9ecByOTheVzEeFVyzKmEEnlXxN7N5JUS5Rd9aq+xAOxz684Dp/\nSrwGKRUrei2AReFsuPQQgDaA+zT4TMB5U9Ci7/fvZYzNM8aOM8YeYIwN24mbEMleedD0zCwqqwGE\nDYYRnvn1lTUNXklEMSFGRXX2QlykbbB56/Uq2hzYPlbG9HhF4kUZWSXBS0G34lIOqgVrIRBzz+90\nns/nrAtjPndtWZ9XbHRMcFhpzQchcoRyuU60/dIlx1QGonBaw7r6KIDoZ14BXT1i7c9fk0ackyEc\nBDqaISWCcADYCeCK/AvOeZMxtuB+FkuMsQqA/wDgE5xz6W04+EsAZwBcAHC7e80hOCmYMF5lAPKo\ntzEVGazJX8XsVxadzVuIM072udUjMxPAd85haVU4HBrKHdvKamkItFoq5Ui70Qvfq0aO0jWNunOQ\neAy5LGvfoUFJFLMq1l2E8SIwmmL9L19fBvKavPquEJIopSLu126i3axjuJTHgW1SuVwSxZn9llLJ\nklcDnvXaOlrG7okK6kvC4dAZ1mU5EsDD67sc4WCM/VFAwab/5xZboRhjRQCfgjOY4ZfkzzjnH+ac\nf4Vzfoxz/iCAnwbwLsbYjREs3w9gSfo5byujEqlGfGm+lTWClzDmq6KGo5+MisnMkjheGgdMq+Hw\nuX02zOFQcV76HK4OOpA5V39GKdImQzh8fPZNDWOsXECujzq8vLyyrQcpookjMxPI56SUFale6dRk\nqaYQzZAEL6/+0ocjMxMoQqoFiU0hptj2myHpplQ+AOBwzM8rAC4B2CH/IWOsAGDK/SyUJGdjH4C3\n+tCNIHrU/e/BiGsegJOeET+zMTxpiPTgSz6iPbRzDIUc0+tSIYWrIwyBTuFbbKSt/3xiTV41O+nj\n9T2QUoniJSNXtrwIdDSXY7htZtxrzG1k8siVVV0C3SFTRBOvCnWKFfj04whxLV79kZ45OjOBIktA\nR7Ucve/ylArn/CqAq3HXMcYeBjDJGLubc/64++s3wXFwHon4O+Fs3ATgjZzza2HXSnSH+9+LEXLX\nANSk+yiwJSBPFXOAl68VpSVRae9VyErRKRwtzrc0eBHCwlHGTsvhcCPtdpMs0hYRdTjCYYkkyLz6\naWy0B1kyg5h7eFmmLo7OTKB2Rqf+Kc3omAhNaLfglK+p8uo6HLf3OMWGTgLnvZF51ikVyr3TrAV/\nTrB3jsxO4HMwqNHjLee7D0sDU6xVhpRI0Sjn/ASALwP4CGPsXsbY6wF8EMAn5Q4VxthJxti73P8v\nAvgMgHsAvBdAnjG20/0pudfcyBj7XcbY3Yyx/YyxdwD4OIBvcM6fSeJZrCjufQlZbd4ImY76ocBY\nuVLKrXY2tEI+VL4fUUqliBZmJoewddT31sdEomNLNMjDy3bdNRw9j1zJ6XsPXB3Lq1/z/wprJd8z\ngrgb3JTQjEDhNHQUPKTgOom0X9r6HsHLk0I014ejMxMouTra1km3hsm1SVMqOvReACcBfBXAlwB8\nE8D7fNccgpPiAIAZAO+Ak+54Cg5iIX5e515TB/AWAH/r8v4AgM8C+JGkHsKalA4+gt5qooPvyKyu\nMU+gtiSoAFXmo4JQReV8DQxdEU28as9E7+eUsDDp4C8iiNnTUmk5S8XkgAnoNHKMufO7NuUYeK3n\nIzj4VOpdFHnVuMNrqgLsmYpoR44j+ZqgCJl03kUfplQMkSX/Wm0bLWPXqHO8NriGXoXKNehSiSTO\n+QKA98Rcw6T/P43O27tCrz8H4Aco5EuNIiFmysiKZsMdnZlAjTm8eK4Y/YV45KLsnrGMjj1yRW1e\njdw4a+H2mfHez7OsjifnFaGjuaKao6eSntGKtN2/k1Ct/VtHMFpwHI6lOsMWG5k8cmV18MWkshSc\nqo1WDhUAN2+v9KaMTR2OVh0ohjkvBI6e1j6McM60eSnoO2A9Jv3Q9jJwAai28yj3fBrCJ1SuTdil\nMiADUkI4skISehX7lp1jnehxISTFGSxX0tC+hiH3yGWbUun65HfsHrHkpXrwUUTaGq2/Ubx0DLmH\nF1FKJYBXLsewa9RxQOY32hoyJYxK6PJS0VGV2RkAVpvONTdtDbivjaNHwSt23VNGlpRTWXa8btrq\nuBnrLYVjNpd3XuIJBCNLg5TKgJQoqlCQCGLW5xVuCCrFPEaLjhE/taCgsFFOAufdNIHtwWeMcNjx\nurreHdh2ZOdQ7wVUuWNjXnEHH1FKJW1HL6bTSMDVV9YDBurpyCT/vh9rZ1T2DYDlhoNq3DAVEEvr\nyMRY4q3NXV5JFOvapv3kImm7vXPjlPOZcAbt5NJxzvo3pTJwOJImFYhZB7oDEkdLRguOw/HydRWH\nQxEWth2qpPN88nWWjt4zF9c7/z9aCJoWm5UBTjmlouxw0Dh6yOW6EV/AM+4YcUzXxdUA51tHJvn3\nWaVUAmuW1GVaqzWx4jocB7YE3FfbWVfY06k72N99KcT9k85nq80cVmshs0g8vIjWPa61OUMaOBxJ\nk0oUYwkx6/OKVsjhvONwvDiv43BQwJMKa6XyQrlYudQdvacvrKIlSo0iDYFC5EE6+CsqDdJy2uvk\n6yLlItJRj1zJ8to25Hwnl1ZbaLZi0iqktQSK7Zn52Ky94lrF68LxuSXU3cLEiaBH0CmKle8ZGSTp\nRNoJ17sAUH7hmocXgY5G7J2JkhOg1FHAcxfixkmBLuCSHdmgV2pkSAOHI2mKrIimg5ipUioAUMk5\nh9Xz8zXwOIVNpKUy6ZSK+uZ95vwiGkgLYtaA0VOChbXe96Mqly6vAARgvOjo5XqrgJeurprLJP/e\ntpZAZ/w+QBaMPHN+iU5H5evS0neKqD2zFGK8nanzAo7NLfV+riWXgX0PkytDGjgcSRPRwRc7Npqw\npVIUjV7b4LiwVI2RS+H5tGdnWBareXiZb17OOZ45v4Q6ucNBCTHHVNprRe0x7cgqRKXvHl69687c\ng72OAo6djzHmysgSUaEnQIBSqTt6T59fRBPh6SfttBj17CAxzMqKl2IBqmVniXmRdPg+bKCA40oO\nR4SemuioJEO/0MDhSJqovFZlXvYHH2s7vOoo4Olz/hf1msikmw9NOkpT27znr29gYa2OJlQMgYah\nI3mJWFoIh17xYlopFdmYP33eQkd15YpqzzRG9Oxsw9MeFI7S0SNubbbiFYUUt/VSiFnoaJwdVZVL\nB/0M45UhDRyOpIk0aic2BDERXwMFPBXrcBDNu5Cv65MuFXGQ8VxKEDPVUCXxO5ZPdyqrfB0Jr/hD\nVE1HpQLioBQh2eyMBGqWYvgsrNVxbmGDDoWTr6Ma/EUhl4pMgKb9S0ffGyjglfk1LK3HpDeo9mEu\nj85Iq0FKZZNRFJxr2nmRUm61wQt46qyqMY+qtKeAcikNgVrO/hkXqs8ViDov5NRFO6DQkTqloqxX\nETqaqdOoEj3mcfLiCqqNiG4VWWcsO0LUkCXVFKJ9APGM6xRXypUIuZJAUinrztJOISaho+G8SiWn\ngPipWCROPKPle7cYi7Z/GdLA4UiaUobvtAqwQiO+LhR4bG4puguA9PkoD9EoCFat3kXAoAXXYFg7\nQp6Dz7LjheD5lHhlpaOKvCqVITTbPDpHThppK+qoUgrRfq2EUzw+Ouz+naVDBSghS2oOR0zdmREq\nm1IKkaDOSPxufNQZGKgcvCW9dzKkgcORNKlsFMp2NdvcarvlDBcDUCpXsNFo4fnLKwoy9dthZee8\ntKRDrBTpcBggS5S8Eo9oNZwg+Z6kKFX4ITqz1Xm/TWRaJXbddVo900r7qTkJAuHYMjbilcFKrj50\nQJVSiDlNZIlQRyMCiEn3u3nq3PUYXgmkNoMQvQxp4HAkTSlDzNYHn/TvQzNTABSNuW3PvswrMvpP\nBxZ+5eoq1uotDJfyKAm4mmpaLNC7XpxrQvuUaFDUwU4PMVPq+97tjsPxZJSOxuW0yQ4+Sh2N58U5\nx1PnHKd468RoynKljFomgn6mw2vruPPdPHVuMXrMAOkAvgHCsTmJqgBLvo7S4fDLJfG+bc82ADFQ\nICnCkcQhGuUIhW9e4WQd2T0BplT4q5LKyjtRWBAv07dU9t0Bkxby4vxu/w7nVeyROhqV0zZ+HXlK\nB1+Ejl5cqmJ+tYZ8jmHr+BihXPHIUupzWaj2YKxM9Dq6ZXwEpXwO19cbOLuw3nudoLQG8GVIA4cj\naYpso0ugS0UFTYiK+JpdOW/fux1AHMJBOXchCUNgZoBFbvz22QlaiDnMqMj/Tvu9M4kU65o5el65\nImoJXD3dP70FjAFzixu4uhLxtsGw71DX0VNaq3QcbJFOuXl6DMViymmQtNukZT5+lCCrbj8Pr/Dn\nKxTLuHW386ZpNbQ44X2YIQ0cjqRJ6WBIefNGRXySQbljr/Pi75eurmKlGqK435WRdrxcT7r51lft\nmSQ2UCFyyf/WirRTQpb6dA7H8NAQbtrRhazDeYU8o6el0vbgS6J2JkJHXVTnjj0TMfpA2S1GpFvt\ntl5xcyeQ4r1DxLLU0cjBh11ed+xxkLgnldDihIO3DGngcCRN/ViAFcVL4rN9rIyZySFw3o34k5Up\nqjre1NDpOy8b9RZOXHQKZe/atyWdw5200j6Jepd+g6u736Ew5pFFedSOXtTBR7FWCulWcXjduXcL\nLeKVhoOtPTsjqu6sH5DUaF537hU6aopwEKKWGdLA4UiaIg8r3fdUJAEFhhx87ud3xG0UpYLDlPv/\nPbz0DfCxuSW02hzT42XsnqgkcyD7a2fEv5XfUunyCRobTSUToDVi23MdSZQWUWkv6cMdexwkzqi4\n2dTRAwLqnyih/ejvsNFq45k553nv8jgcCTuNVHVnnnXXrDsLc16y1NEYXq+adezocxeWUWuGzIyJ\n2oeUHV4Z0sDhSJo6G46yA4DSqIQUjbqf3xkHBX5Xp1SC612eOOtEynfu2QLmST+lkFLRNXRBcmVa\nrJs+oicQjmfOLaHdDukCCHWwBRxf0HP0guQifb5oHXWGnbUxXinghm0jknNGqKO2XVnydWHrLt9P\nhQ/Q64D2hY5G7519W4exZbiIeqvdQU97eaWU2syQBg5H0kRagBVRaU817Mm34bpwdUhLl1JOW/fg\nI3DOIgcORfN6UjgcLrpDC1eHpI20512oQMxZIkvppVRunh7FUDGPlVoTL4e9ObYfHT2LWomOU7x3\nC3I59t2XUhF8VGdnMBZfcK27d1LT0SIYY049GICnzoak/kgdoUFKZXMS1aQ9gA4Wlq8L41Vw7nVk\nZgKFHMP8ag1zixvhfIJy2tpQZ0oplQhYmHOOJ1w05659W6Ll0m2pjOLVFwgHhY5GHFbaTrFaTU8h\nn8PR2Zh5HKFF0popo8iDL72USrhTnPBhlZW+R8lFmgbR1VGV79AZHCgHb9G8glJZuqnNCPuXIQ0c\njqTJ8OCL5mVZ+AYoRAsOn0oxj1t2OT3+gRvF876EJIu50ulSEe2VhRzD0ZkJ73U9lfYSEmPbRqf7\nfLm883K2QF5EsLeJXGmkVAIcvTvjjHlYNwHpwUcJ7UcfMMKxumvvFu91SaISHrksD2SrdQ9DB7PQ\nUXXnTN3hSDi1mSENHI6kiTRqjzF08v1M5QqQqbNRguo4KHPakS+6SydKE7Uqt+4eR6WY915Huu7+\nPLTmoSBfS+bopdUWa9vh0Ds7I1JHo3iRHnzJ5P/9NL9aw5lrzgApAdMn00lFUAhOhQYB8d+hyUTj\nFFubhY6evraO62sB15M6QhHIeoY0cDiSpqhiriaRger8W/EtlbJcCtFCZBeACrSvawgoD6uoDoeA\nQ7RbMDoZL1cSjp7qwe7hlcLBV6DM/1sefAHrLrqpnr+8go16QBdAnHOmqqPSPclSKlHFmQH6IJyq\ngztGMTFUjJZJ/h0lAmBbd2bk6MXoe6GsJ1MgryQ6qRxek8MlHNjmvlcl6M2xSqlNXVs6SKlsLoo0\n5u5kROWNohClqVTay7zCRpt7HA7HmB+bW0K96XtzrFJOm+LgSyel4pltICgMeZH/rXpghdX0JALt\nWx4KANB0dTSvqaPNgKmf1Pl/6ZpdE0OYHi+j1eadCZzBvCigfWpHT09HhVN8117ZKU6iZd6PLLWd\nNmyALkgyQvR8vEx1FLDfh5qOXuQAMNLC3xD7njEl5nAwxqYYYw8yxpYZY4uMsY8yxkZj/ua/Mca4\n7+fLvmsqjLE/ZYxdY4ytMsY+yxibTuo5rCnSmJtCnWnkobuG4IZtI5gcLqLWbOPZCwEDwEKdF9No\nIcI5IynmCpar1mzhuQvLAKTcuHwdpaMXGqWZHHy29SAKcDwpwkFU7+Ljdbdb5PvYmYAuAA0HW10u\nPy9dHZVQuLbPkY+o7wp0iikRjtB6F8mJVNYHylRWDC9dmQJ5JdHK3+UlCtEfP7MQwcu37kZdiJuv\nS+VBALcBeCuAHwZwP4APK/zdlwHskn5+yvf5nwD4EQDvBvADAHYD+GsakROgSANMhXDY5EPjnYRc\njuHuvWKjBBlz977NeOdFTSa9iE+flzgYvLyOzy2j3mpj60gJe6aG4nlRGk3dKA2gc0DFdUFDxEyj\nx0QPPgnWlxy9u/c5bzeO1lEf8qJb/Q/Qp1SAXkeoGayjzVYbT5/3FYx6ZEoQHZTXTlkfCFMqYY6x\nro5GvUvKuN5FDZW4x3U4njy7iGbL52R2ePl01KgLcROlVBhjhwG8HcAvcs4f4Zx/E8CvAPhJxtju\nmD+vcc4vST8d68EYmwDwCwB+g3P+d5zzxwH8HIDXMcZek8SzWFPY5s2ypRLQNgR3749yOIRcIRuF\nIuKjhDpDkKUnpdkGTEYswvK0NrBwWKRNgnCI51PN90bltA2j9iRrCUL43LOvq6M9A8DSjLR1n0+D\n1wuXV7Feb2G0XMDBHRJgrHTwWdaWeFJZlgefUe1MHLKk0dpM9R1qzlK5eXoMY+UC1ustnLzkGwDW\nSUcmWCuWMSWFcLwWwCLn/DHpdw8BaAO4L+Zv38AYu8IYe54x9meMsa3SZ3cDKLq8AACc85MAzrr3\nDCTGWJkxNi5+AIxpPo85xUHo8jWxvOIKPSk6HIKN0z1u9PjYmeu9A8AEQtOzUTQNQVTEZxp5+GWS\n5fIhS12oetJ7fSKHVVhEm0FKRb6uJ9JOIqWi6QgpIgm37h7HUDGPpY1G7wCwjo76nOIQJCGSQmt6\nDA92oFdPmyE66r4v5o49k8jnZKc4CUcvQke1U4iEeycsdauKFEfKpekIaaKy+RzDnSL1d9qXVhEI\nTU/gJvHWLtbdBAgHgJ0Arsi/4Jw3ASy4n4XRlwH8TwDeDOB/hZMy+f8YEwMHsBNAnXPur7i5HMP3\n/QCWpJ/zao9BQHGwN0BYNJpch8PtsxMo5hmurtRwbsE3ACwM4TCtUZHl6PzbNKXi37xNgLvoSaHi\n+ahnmJJfrkSRpSxTKgqdRlmkVGTEy8Mn2Dkr5nN41R5ndkpPHUcqCIfNLJWQQ8bH64kzmk6xRy6q\nzhITHf1eTUdGtBCHBBH3hNUaCac+zPlkOXVn/Xvh5W2MsT8KKOr0/9xiKgzn/JOc889zzo9xzj8H\np/bj1QDeYMrTpQcATEg/s5b81Cl0k8gIh63DYRMdq224SjGPIzPCmPs887DosYMkeA/2WJk05Aql\nONTFx+vC4gYuLFWRz7HOi5Z6rqNElnqMikVKJRQNUp2VoDBEzLZIMKUUYgeJO+035jEIh6qOGsoV\nSuK+oXJ5bYMoNvTUbwCKKRXNde/ZzzZpvwS7VEjTkZQpxOBnlFN/Xl5hCAehjmZMugjHBwAcjvl5\nBcAlADvkP2SMFQBMuZ8pEef8FQDzAA66v7oEoMQY850ImI7iyzmvcc6XxQ+AkLfnJEAdTzNEiXIF\nIKf4NYS2hYkNRxF5hBuCUM88LvJQNQS5vOPFB8pl6HD0oC613msAfMeFN2/bPY6Rsi+KII3SYoyK\nVpRGFGkDkiMUlnLQLRKkQPT0dfTusC6Ajj5YOlTyfUNfIqZxiBbiDr7uWl1ZqeL0tXUwJo3dFxQW\n0Zo4emFrZYQkJFB3ZqujHrksbans9Cu+S+qOvU467OJS1fu6iFCEwwZJ/S5+Wyzn/Crn/GTMTx3A\nwwAmGWN3S3/+Jvd+j6jejzE2C2ArgIvurx4H0ICTchHXHAKw171n/1EhTLEpN68BL4NRz50uANXo\n0QiCJYqI8jEygXnytMLhEBFysEwEqazQSNvi4COpBxGHTEhBnm3az6rDQV1HReR/+to65lcD7kl6\nWFE4eur6IFCbQ9Nj3YFffpn8B5/R+P2YvUOho1aorGWtmEeuEF7K+i4FJ/IzRjh6w6UCbt01DsCH\ncsQiHAQ6mjElUsPBOT8Bpx7jI4yxexljrwfwQQCf5JxfENcxxk4yxt7l/v8oY+w/MsZewxjbzxh7\nM4D/F8BLAL7i8l0C8FEAf8wYe6Pr0HwMwMOc828n8SzWRLp545AEE4VUyx0D3ejxhSsrWNqQW7WS\nkMsW4VCQSSp8E8b83gO+yBGIMJqiwMzA4SDJj8eslc66F0L0wXQarv/gs6m0D3Vke/lMDBdx87TT\nveEx5mHP1zHmFHU4JikV9SBCOMWv3h/kFIfU4Zh0lsTtHQodNUFlQ/cOYdGoqb4DXt0KGL8vUweJ\nkwtH44IRinXPmJKcw/FeACcBfBXAlwB8E8D7fNccglNTAQAtALcD+DyAF+A4Fo8D+H7OufwN/DqA\nLwD4LIBvwEml/Ggyj0BAsfAkRbRgY+jUkYTtY2Xs3zoMzrvTDh1ecQgHxTPqdl6ooy5L6w08f9nJ\nst0diXCEIAlaudW4ehcKo2lyMMTIZVuAKvjmihopRDO0K3AeR+f5wg6YDFA4j1zqCMerD0ToKOCt\n6fGkEFVrqeJ0lBCV0NJ3SpQqBnlRRjik60IdvYBao/0B6enYtSKwoxmTRhO0HnHOFwC8J+YaJv3/\nBoC3KfCtAvg37k//UydKq3p/TxnRGiEJZmmQu/dN4fS1dTx++jreeGiH99qwegkduUJrXjTTF+Ke\nYpiVeMdMQF3J42cXwLkzUXX7WICscRGtjiEIjR4JnTPd2hkVuUynOBZ8+m8U0Yahg8G87tm3BZ94\n9Ky37TCUl8neCaklMHL81Wp6VmvNzpTfV+8PQuF8644Rr0y+FGK0TCHIkpFzRpj2C5MrCbRYOe1X\ncOrOeNsrV0zNkkjdnri4jNVaE6PlgkLrtsm616KvS5kG71JJmkRU0aoHQ8wUUK7R5hXKHeYIBR/s\nXc9cNuYhxU5UyAvndu9L8BiCXj6PnnKijHuCDLnMq8doikPUBOHwrztl+skAeel0S1g6xp6Ir977\n/0YdHH6ZopEE8T0en1tGteF79wdJQV4CKcTQriWH15Nnr6PNgdktQ9g1MYQeCpueKeuo8uyMBGoJ\nwiapmuhoWGCjcyDHIc9aznqAnsa8Z2nnRAUzk0Noc+kNx7EpUpOarM2TUhkQ4FUS+cunrKw2OmDC\nNlyMw+HmHp8+t4SGGM1LiXCEbl6ux0u+TpYrEKqOyI0D4fUulFGaFcJBmGuXD752u3tQqK576MFn\n0doXNpcgpHZm79Qwto2WUW+1cWzOffdPaNeSCfKi18oazSvGAXXX4DunYnRUnp7ZjNb3eJnE8+nZ\nhkAiTRNQIhxxKRXLFtSWpKMhjl5P8BaKcLi6YeJQBb1EMUMaOBxJk6wkQZAbCQxo4QFrzs64cbvz\nSuyNRgsnLi577xs6adQy1eN5aZTqwVdA5+BrBhgC9z7VRgvPnBdQdYzDEYbgmBxWJDntMAfU5JAJ\nOJBNCj3DxkZTyST/O0RHGWPdFm7RURV6WFmgg0m1NssdDu69vnM6BoXzyBWu70oUV2BLklIxSM+Q\n1sMRpjaDDncFB7tnHodYi3bD+2oHI6dx4HBsTiqEOBxJIBwUHnBMlJbLdY35o27UFY5wEG0Uk5ZK\nxoIPBp9Mz5xfQr3VxvaxMvZtHQ6RKQTaN4mOYwvfTCK+MLlM0ARLR0/mZYvoGeoo0D2YHz11zXst\nZbcEKcIR7ug1Wu3OSPN7w5xiDy9JH2wLm+U0sEm6gVJHY9PAlOlIy+9QSUe7xc2NVjscDae07xnT\nwOFImjwRHxHCQWnoDPKh993gbJRvv+Iz5raTRsPkMulwAII7E3ybt9tq6HthW6BMBB0OoW2QNgcf\nRZQWkCZoGiAcQHCqxwhCNz/YX3OD8wqm75y+7ryV0xDRo5arh6L03f38+NwSqo02JoeLuHH7KEIp\nSC6bAmJw7xwPk4M9dOKvDSpLwStIR6XXHtgO81NwXA5Nj2FyuIj1estJ/Xnqn/ScFyWZ+oAGDkca\nFGUISAbfEMGA8r8VjPkjpxbQanOFim9bhMMgGgKkVE9QxOd3ODQjR1O5KFv7worobKK0IKMZkYcO\nJGqEg7fgmZiooKOHd41jvFJwuzuWwx09KghdUa4eCnSK657PRVronn1TyOUivodAtMTCoQJ8tVQ2\nKUTKQk8CXoE6Kj2rbU2Pgi7kcgz3HZCCN0+he1A6coBwDEiFgoxdImmQdOZB3LprHGPlAlaqTaeO\nIxEDbIkGybyCkKV8Ca0270xNjXQ45Ipv206jWISDAq626LxoBjgJOt+ffL1mTjuUDxDsCEXsnXyO\n4d4DjmPsGHNzfQ+Vi6LGIRLRc1578KiEwhnzMnGoAJ8+2DhnIWkQI32naE8PkJEKsSMAACAASURB\nVMvn6KnzCirWVdMFEbx9+5UFB70NGgtAmY7MmAYORxoU1TZl2n5lm1sNnSwZX5dQyOc6w4c8nrm8\nYdstJzIF7DeKNcIRfIg+e2EJK7UmxioFHHZHDUfK1COXSWQVhpaYHAxh3RIW+XHPwW4wqtsjV1B0\nbABVA9rRIwC8Rk79pYJwiGe07MSRHJdWm+MRN3V5n3s4acllNAsn323l1EwTKMkEGOpoWC2VBToY\ntFYsD+W3ssr3NUiDCIfjsdMLbh0HUcAVVpyeMQ0cjjQoKno0OYx7cqtEG06WMcYQeI15TKGnbWeC\nyaEAxCIc33rZNeQHppCPhKqltbDNrYbmtImiGJNWViC6aNQY4bBtAy90X+ZngJZ46jhY2LAuIhQO\nkA5RIn0vlPDchWUsV53BUEd2RzjFQPCeNoHjAbo0cKyTQIEOEqVuKfVdMZXVW8dBlI4MQz8zpoHD\nkQZF5cdNvFYgpC6BoiBPredbruNo5yJSRgq8PBRYaU+IcEgG+GHX4XhNXOQozx2wNVCheWibeQkB\nBwxAVzSaFcIh8/IcyGoHu1zH8dK1Ri8fwBKulp6Pc8N6iQhHL1/Gw6/MAwDuPTCFQj7GXAfO4TCY\n4QCEpIEJC5tNeIWmxWzQYgp9D7JZaja5p44j0hEyRDj8b7HNkAYORxoUNZDHxGv18zKqHo8p9Iwx\nBHIdx8XVdi8vT4eDybslLGc4yLwCUIl2rtQpGH3djdui+TAWfIgaFf7G1BJQOWfy50q8gjqpbCO+\nALl0D77AlIMaCifXcTw+t97Lx8PLBJUIK/S05CU5n8Ipft2NMU4xEK2jpnsnUN8NU4ieNLDNMCuC\nlErg8xm0uQPRBagKzqenjiOQl4V9B/qqjmPgcKRBgZGoSW41FwyVGRXkhY2NVpNLruN48VrdK4fM\nJ1/W63AgRTjC86HzVWC93sKW4SJu2TkWzyvIETJad8LhbZQHX9TzaUfHRLUEHl5mzotI/X3n3Krz\ni7CaJaN0ZMAelD9XoaCDz5WR58udWTexKBwQ4jQa1JUAIWkCcfAZvB0ZHN7JsxZoSVitGNX8E20d\njagHUdiDch0HD0xlWUzDBfqqNXbgcKRBkXUJGpsXiMnTElR8axwMwpifmK955ZD5mh4wgTlMQ6gz\ngNeFFQeVue/A1uhWQz+vgIOBBha2qcMJiUJtHT2TA0aWK/Dgo9AHdV7CmD963kU4eNvXYku0d+Tv\n02jUfS+vjXYea/UWJoaKuDWqqLnDK+jgM02pmBdCBsrk50W1d4zXPWbv6FBk+328oyfXcWxw9yWT\nIXVnyhSGhmdMA4cjDYqpRNciKrg6rphLAwp87krN+7eAWSFXmFwmSAIQ2WJ7dtk5dF6rAlXL96Yq\nGvXPlmhRFXom4OhRtsVqp1TsEC9Rx3FdtrmaLbY9FFijIum7yXC6gANmpekcPvcdiJm/0ZEraN0J\ni0YpDz6j7qC4WrGsikYDOkI06nnkOo6VhiiSttyHjIUHNxnSwOFIg5Ioogs0KgYbTry+HXAOQO57\nu2YEiTqOpbp4WRcBhB7lnGkbgvCK77NLug6Hea+9hzyvEafqALCEX4GQAybjtlggJj0Tz0vUcdQR\nUvhrBO0TdRLIvAIOmMWas6+UdTTqPUSEe4cmDUzUFmtaKxYYQFh2wxnqKNAN3q4H2VITRw8I3jsZ\n08DhSIMCN69BIRAQW9WuzUfm5Sk4jDcEhXwO9x6Y6hpz2+l48n0jpoMqU4QBXm8VsG20hJt2RIyK\njpPLpj9elsvT4WCZh7Y9+AKjNAIdtYb2zaJHwDmwW8ijLcyd7TNS6mhE+uma+6vYomYVuYwP0aAU\nG0GNg1GXSkQBsXYKMUJHTZ2zQF7qOgoA16oBL5w0RXjDOuIypIHDkQaRRh4RXr5pblXwkg2xIq/v\nv2kb6jxgSBDlwWfNqzeKqaGA19ywNfz9KX4KzNubjDaXZkuIZ5SL6WynONp29FAcVpE6mr5c99/k\nHNg1oaceR8+iW4wChQt0zpz/r7YL2DpSws3Tqk5xFCpB2VKu+x1GoYOWM0soAxtjJMEeLTk0PYbt\nY2VU20QD14BBSmXTUqAHTAiTGRVgBRx8YvPlCs60QQX6/pu3o+YiHNy2kBVICOHoPRjqKOL7DipG\njqFymaJUvu/Q9K2sQbljWySBsh7EYBBSL6+oabFqvA7uGMXO8QrqEMa87v2vfB8lmSgRjnAEp44i\nXndwm7pTHFVbQjL/xNTx98lliujJrxgQr2+3LSgPTIPo1orZByOMMSd4g88plvkOUioDUqLI4UWE\nKQfbgjwDPjdsG8GWMScCa9QpZEpg4qW07o2aI2MdRdx/83YNXlG99rqGwMfLk4c2SalYol3y9STO\nCyG0T3C4d425b9qop8PBYN3bjYCDjyAKdb/DOgoddEaNF9FEYw8viiDC72DrI6k91/qDJBKEw9Q5\ni+pgU+d1/03buzpKkdocpFQ2KUVBisZ5OQKo0x+JGkRpjDG8av8OAABvUDoJBG2xAQZ4ccWZxzA1\nNordk0MackUZKMvumc5bWQuGHQ5SxEcJvzbcZy3SzT8hGapk8IwyEtf5e+OZJXLhr3/vWDqfANbW\n1wA4TvEPaDnFCSMvtnNZWkSOnoeX7Ywegrq6yBZidblef7Cbnl5bXw+QiyCVlTENHI40KHDzbjj/\nLWocejIviimOPYbAbPPedcNOAABrU8zOIGyLDVir5VXHmB/cHfF22EheCUCdDVcXTJ8P6D34tGWK\nKnyj0FHLw8qiIA8Avu/gNjRcY359edXLM1fUc/QC65+InE8AZ68uAgCGh4awY9zgBXxJFVxTDeCj\ncPSaPoRD145GDFyjXSt1XtvHyhgZHgYAnLt63V6usPdlZUgDhyMNCjpEG1Sbt+kMM5I/M+ZlhpTc\nc+M0AKCEJi4tihHStkV0QRGtoYfvPhfnHBsbjsNxaFYDqgZ6jQrn5ga4I5dtlBZw8Bk7ZxFpP1OE\nIzDio3hPhb6jNzVSAis6vI6fveLlqa2jUvtlAo7enHvY7NiiMOzLw8u+oydKro5jrK0PPvvXCZA0\nZ5Z4Zku4PIztqN100HheZmjJdvc7n3OdTq9cBN0zGdPA4UiDAnOrpgiHb/OaFhwCvYeo4cE3MT7R\n+f9vPX/elcuy4psU4XD+/qUrq8i763XzzA5DXq5c7SYA990QtrNUGqZRWhGAaKPzpWcoHL0O8mKq\no0EpNkMEQOiThaNXqji1Rs+fu+LlqaujQe/WMS449DpnnHNcub4EANi5TReFiypspigaJUpfmB6g\nMq+Oo0eJFFs6Z4bvUpFp51bnO79yfRFcvHvG2FkP+A4zpsQcDsbYFGPsQcbYMmNskTH2UcZYZH8X\nY4yH/Pxb6ZqvBXz+oaSeg4SCIj5rhMNn6ACClIqhcZI2+6MvXvDKp20IKNtivQb46y9cRRkO31Jl\nRJOX39DZrLu/aNTQaDJG9x0GohKmCAflwedH4RowdfRGRh3z89KFeceYm+oo0NsBZYqWiHu7z3fi\n4gp43dGHnVsnNWWK6pYgdECLw5q8fDbLtObMI5fPWbdB9MTBTtlSbshr5zbnO+f1Dbx4xZf603X8\n+/AV9UkiHA8CuA3AWwH8MID7AXw45m92+X5+Ho51+azvuo/4rvttMqmToMCiUVuEw3fwsZzT6qrF\niwbhQC6Pds6BmZ98+QKarbZknCwRHFk+bWPuGkZXlm+8OI8h5q6bNSxsgSz5eZkaTfnePd8hRdGo\nZW0JyVClqBZiPbnGXIejWVvDsxeWzXXUI5f/EDV0OBpOKvIbL15FhTnPWChpHuyRw+ksdbTV6E4h\nNi4i9qdULBCODi/TNE9Ex4txnZE9wlEsO995hdXx9yddJM7VDeuzog8oEYeDMXYYwNsB/CLn/BHO\n+TcB/AqAn2SM7Q77O875JfkHwD8D8Pec81d8l677rl1O4jnIKAhibtgaYP+G0zROQHi3hK5MAJi7\nGerVdTxxdtEcjqccqlTsGs2NeguPvHINFQiHQ9eY+4yKp7NEbWZJl5crV8P/HZocfP6DgbBn3xil\nCnIaLYv7bDscAOTcA7yCOh46cdlcR4EAZMmyhbjdBFoNfOOFq/Y6SoEOFv1O8YZ0H0N98LeBmyAc\n/mfs2FFDmYBex980PRM0+MswSKqgjq+euOLU6LUbdnJtAoTjtQAWOeePSb97CEAbwH0qDBhj0wB+\nCMBHAz5+L2NsnjF2nDH2AGMscmcyxsqMsXHxA0DhfeSE5N+87bZ0iJpWV/s6HIwOKx/yYookoOtw\n9BjzvkA41vGPL82j1mx3EQ7jbgKCKE2Sy/mvIZLgkUsYYEMHVHxPrVq3xdZUrkA4XkRpuodoiI7q\ndpYAnb1WttVRIABZsjtgAGBpZQWPnlpABeKAse/Kotg7zn+Fw8H0efnfpmoTJAl7KeQxRTjyAe/W\nMdXRqC4VQwe0gjoeO7OA68tSLG3sCH2PIxwAdgK4Iv+Cc94EsOB+pkI/A2AFwF/7fv+XAP4FgDcC\neADATwP4ixhe7wewJP2cV5SBhvybVzYIttC+ldEU+WPfIWoE7Tt/M4SaY8xtoU6KoUoSkvDQicsA\nuBQ9mkYL9s5ZF0bf8P6XAto35SVfL747SoTD2AEl1FFXF4dYA8fnlrvGXFdHATp0sFCGKPz99vPn\n0WxzTJXc1IVxOzJBKsuvo03J+dR5Z4n4G1kuG33v2TuGCEdQ4a/x3qEMkpx7T5XbaHPgWyfPdT+j\neFt2xqTlcDDG/iiisFP83EIk288DeJBz7sGDOOcf5px/hXN+jHP+IByH412MsRsjeD0AYEL6mSWS\nUY16Nq/0SLZGxdQrD5TLEI6X7j+ca+CVq2tYWVkxkytwuI9hlbZ7b95Yx0MnrqAM6Z0ltrCpWPeS\nZvGpfG+/A2rh6HWNpimSIK1HjzG3rOHg3Dx94ddRm4JDd032jzsH5slzlz2/16IwB9Sk48V9xodP\nOnHQjiHX0TaeLRHUyqqLePkRDsMCYoBOR4HwvWMkF5Et9esoYJEGdnjtqDg68LDo+isMGTh63+UO\nB4APADgc8/MKgEsAPH2HjLECgCn3s0hijH0/gEMA/lxBpkfd/x4Mu4BzXuOcL4sfOMhJehQGT+YK\nBoWehAWHYciLRfR4x07nv/OLS2a8Ag8+YQg0D3dXpmZtHfOrNWwrt4PvoyQXYSqr05lAgVL5Ol5M\neeVyEiIk9IEoLdasodNZoh09Euqo+zcHp5w99/LcVXNePXvawgF17//kqYsAgC0l2+JM2dEzdUBD\n6oxM6l38KTarveMtBLerwwmZD6K77rIu9LSymiHYQgeeOXXJTCa/XH1CWqcd5/wqgKtx1zHGHgYw\nyRi7m3P+uPvrN8FxcB5RuNUvAHicc/60wrV3uP+9qHBtNhSGcFgVq4nNS4lwGMKvQOdZ7p4pA3PA\n0vKSmVz5gmOgWnX32aYsoE7n3u26s0ZvvGEUOAVDR48wDRK27hRFo6YV7eJvmlU6hMOvoyZyhULo\n5qms/eNOnHVh/jqQN5ApUC7LQ3RjAe3aOraNljDEXCTOFA0SzoGns4Ro3Ul0NIm9Y4Nw+G2p4Vrx\ntqPzhbLkCJkhHBXUsX2sjPbqOlAGjX3vA0qkhoNzfgLAlwF8hDF2L2Ps9QA+COCTnPML4jrG2EnG\n2Lvkv3WLOt+NAHSDMXYjY+x3GWN3M8b2M8beAeDjAL7BOX8miWchoY6n6d9wNpuEcvO6G63uTOG0\nSRPcPu3IV3cnelp55nURPRrK5Rq6fMtZqzfcOOrlryWTb62sHL2wolELB7Thj9II5KIaqiT+myt4\ni/VMZBK6oIt2AZ3nmCg2sGdqCMV2zfN7E149e8do3buFgm+6ZQeYbR1Ou+kcoh5HzzKlYtVJ5bdZ\nfbJ3eqaWWqafhFythtRZYpaeYY0NvPmWHd2aMxMUTrRViz3TB5TkHI73AjgJ4KsAvgTgmwDe57vm\nEJyaCpl+Ek4V1ScCeNYBvAXA37q8PwBnRsePkEmdBIXm7AkOGJuIVhzgPVGa+YG8tdzGoemxzoAt\nUqNiaIALaKGca+G+Wfd5jTavWCu/TITIEgVsmkhBnmFhc7vptPXZrFXJB6ELJ1R3RgXQ2W+sUcVb\nDk9LHUs2e8deH7i77kOshrccnrbQd8kJa6x3ZcsVDOqfiHQBiFirrBEOgbxYolT5otM1BTj6KTt6\n2kFSF6WSdZQbrZVv7/QBaeLK6sQ5XwDwnphreqpgOOcfRsiAMM75OQA/QCJgmtSJPBqO92uDcITl\ntCmitIaNMRc53w287bZpDH3TMIcp37+x7hxYLUPnRVqT+/ePYixv2G4o37vuj2gtuoP8NSokB59l\nSkXw4Nw8qpWvlw8+G5nqFI5eF9p/2207ceIRR69a+Qo0J6kEyGW+d9bbRYwAmCi08P03bTevUymU\nHOei3XTXncApbvp01Obg868VCdJogXCEpcWMeA0DtSWHB3PjeJY3mNrcrZ35vpu24XOFJoCujmjL\nBHTXvQ9o8C6VNMgDuW2YFxTJvEgOGB8vK1i4u3l/+FW7O1Dgatukm0AyKjawsLS+P3h40q7/P8zQ\nUSAcNh0APcacqCCv1bB4KWCla3Q9Bx+BjjZsdLTL69X7pzBVdIz56eV2xB+pymV+iF6pOmt190wF\nQ8UcTcqhTuTo9dR3WQYQMk+KqN2m7kw46yR7J8BmFYf1O0vE8zU3UCnkcM+Mw1foiBGvPioaHTgc\naVC+JBngDbt8aOgmoTj4CCKPZhU3T49h1EUTHj5noOyyUbEYOPTK/BrWufM3b7phjAYWFk4ZZe2M\nPOPAWK5VL09bfWhKMKzJjIOitF6UUahVSqUbPeZzDAcmHVzj2GWDwUj+g69udri32xzn3a/unpmK\nt4XRCgFdoznYm1VnHo4VKuvfO4SOkM0zdtDBNecZSQKSDakWzkJHAaBZdXQCwNwaQ7vNDWUaOByb\nixjzepskB584YChz9u5/LVMqADCScxyOr764ZCCXHKVJBaOa0cIXn7mIKpzc6kSxRYQGUThnfl42\nabEkokdJR00mSwJdHaoTHXytGtBuWa67N2e/x503/MzlGqqNlh6v0KhdD/h+8twilhpOZvvQVMHO\n0fPItUGDWAKOTDZ1Z6FrRVHYTDAWoL7mG8Zos3fWLJ9PTkduODoBYLGRx5Pnruvx8tc/9QENHI60\nKCh6pDxgjKJHX/6/btMB4FXuEncitX84vY6l9UbYX8XwsoPjv3jsIjYgimzX7epdhKPXOfgsnDP/\nZEIruShTKgE6ajJZEvB9hwTOmZDLauCat1tssug4GYuNAv7hxXlDXv5Uj966f/GZi9jgTtqx2K51\nHT2W1+/okeWqWx58nnk4VRqnmFpHbXnJe8fW4ZAPd5u0X77o1OEAQLOKomtHqyjjb57WnPwg60Kf\n0MDhSIvkjUKBcLTqvgJUis1rgwBICEerAdZ28uOr7SK+/KzmRpEjorrZYfXi5RWcvLSCGqT3ONgU\nZ8prUl+jrZ0hcRrX7AY9Ab48tEVdCQCU3BZkz8Fn0UkAuFG7xbr7UDjRflpFCX/z9IWwvwqmsGJW\nDQe01eb40rGLqAodlR2q4hCho2ewVrlct220sU6TBm74UyoZIxxCRxvSfs6X9F/GCPhSKhZpP8Bb\nVC50lBfxpWMX0dJJq/Rhl8rA4UiL5I1CkbMH6A4+f27VaFqiVNUuKXgVJXz28TlNuUIKsDToM084\nI4EL5YA0gfHB5x4AnoOBonbG4kCWo7RWvVvoaZs2spks6ZFrze6wyuUkA7xmFz36Oy/c/26gjK88\newnLVQ0kTt7P7baRPvzjS/O4tFxFW947Ngco4Iu0LRAOwBckWdisRBEOCuTFMu0n87LtDgK8wZvL\nq10YwpWVGr75kgYSJxWgdt5LlTENHI60KAjhMHppVMmBWwF75Q4ryLPi1Z1UycHQYEU8enoBp+Y1\nYL2iVBhr0G7YbLXx1084Ts7Y6Lgrl2UqizFvpEbZeWFzuAdFtPLvtXgR6WiPXIQHX93CKZZ1VPAD\nsG1yHLVmG1/Qgaw9AUS19/cK9OnHHad43/RUV57OupuuVdKHKEU6krJ7xiZ4C+rooXDOLJximZc0\n9Xff9FYAwKcfOxf2V70k20y5NihDGjgcaVEgwmF58Mm5R5vo2J9SMapLkFAJ9/lYcQj337wDAPCZ\nxzU2imfz6huCr79wFVdXapgaKWFiXDgc0shu06g9sOXQ/N0Z3YPP5jsM6AYxmegJ0OlomFymB588\na4SiLkHMGXF5vf7wHgDAp3V01IMkyI6e2jMurTfwlWed92Tcsne6lxeJo2cxOViWoVmlKc4E7GtL\nPMhSS5rRY+IIySkVS2RJ7sQhS6l09+Etexwd+dtnL2NxXbGrSt67fTKLY+BwpEWJRI9rRgdyL591\n+/y//L4ECX59992OMf/s43Pq+ceSXXT86cecyPGdd8wgV5LTMxapCyAYYqbovCBDOCghdNsaDqK2\n2B657EeIA9x9V48j1/237kU+x/Dk2UW8dEXxvY5ByFKhopz///zTc6g327hl5ximpyZdXpQpFUtU\nAqBDOAplwrkscmGz/NZty1QPK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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(t_continuous, sample(x1, t_continuous), label='x1 continuous')\n", "plt.plot(t_continuous, sample(x2, t_continuous), label='x2 continuous')\n", "plt.legend(loc='upper right')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And now the discrete versions:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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L6V5qrinJp95qp1ofycA+lhNeKnE6JXuP1mBzOIkLC1DN7Lpwop99dXV1y622Yc29rbpF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\nlzMVQvwGWAb8Rkr5SVfvI4TQAyOAwtP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6/ijSk+OYmt0Tp6N7ns4LFY/XsCbvMD/6x3sM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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(t_discrete, sample(x1, t_discrete), '-o', label='x1 discrete')\n", "plt.plot(t_discrete, sample(x2, t_discrete), '--x', label='x2 discrete')\n", "plt.legend(loc='upper right')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can overlay the continuous versions for a better view of why this is so:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Y9dkfANh0xA8pKjHZqj3P8MuICSfzTslknteP4cGVxr4TyTHaFGsirsfzIiZ5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\nKN5+/XWuufpquxr+fwsvzGERqY1pyD9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ulQ9yVIakql/yl2Q+HhwmLzvZdyTjurmMxReU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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(t_discrete, sample(x1, t_discrete), '-o', label='x1 discrete')\n", "plt.plot(t_discrete, sample(x2, t_discrete), '--x', label='x2 discrete')\n", "plt.plot(t_continuous, sample(x1, t_continuous), label='x1 continuous', alpha=0.2)\n", "plt.plot(t_continuous, sample(x2, t_continuous), label='x2 continuous', alpha=0.2)\n", "plt.vlines(t_discrete, -1.1, -1, label='sampling times')\n", "plt.legend(loc='upper right')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The sampled signals are the same! One can say, they are \"aliases\" of each other (see here for more explanations )." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Where did that come from? Well, doing the math for the second discrete signal yields:\n", "\n", "$$\n", "x_2 [n] = \\cos(\\frac{9\\pi}{4} n ) = \\cos((\\frac{8\\pi}{4} + \\frac{\\pi}{4}) n ) = \\cos((2\\pi + \\frac{\\pi}{4}) n ) = \\cos(\\frac{\\pi}{4} n) = x_1[n]\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How do we solve this? One way of doing this is to only keep sinusoids that have a unique representation after the sampling operation. \n", "\n", "If we have a continuous time pulsation $\\omega_c$, it will get mapped, through sampling, to $\\omega_d = \\omega_c T_s$. But the discrete pulsation has to be below $2 \\pi$, unless you want to have aliases possible. Therefore:\n", "\n", "$$\n", "-\\pi \\leq \\omega_c T_s < \\pi\n", "$$\n", "\n", "$$\n", "-\\frac{\\pi}{T_s} \\leq \\omega_c < \\frac{\\pi}{T_s }\n", "$$\n", "\n", "This is strongly related to the Shannon-Nyquist sampling theorem." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In our example, that means that we cannot use pulsations greater than $4 \\pi$. That's why $x_2$ is not \"allowed\" with our sampling frequency. \n", "\n", "If we increase the sampling frequency by a factor of two, the limit goes up and the two sinusoids are not alises of each other anymore." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": true }, "outputs": [], "source": [ "t_discrete2 = np.arange(0, 10, 0.25)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Se71LUgKHquSYNSJqDTEmGRsRA8y0LXL3gy5JCW1XLq0rguIt0O04\niI6Gx13KCnfvhZhuzR/bwrneZ36fGNsB/c41HHBUQPUB6NoXwuT8DYNDbxKDs4THZ3YhIzmGWdXv\ncJd1MbnO7mSaDrPMPo551sUIYFHCFYzPDLCGRkcTmwJjfiv//3mZXL/u6je5qG2oRktUfKcohOXb\nD1RWOYbr0w+0OhwVhyB/kwzAyzw16PMdZs4DYKszky8dYzpHv1X7UlSCR+dFD969Qkp0//5LzXtV\n6/se7Yi2H3Q3eQIxn7JdEnw/cAfYxkuPhiVGpsMH6E3WnuuN1s/c29+1T+5kfTb4ekl6YRgcYYbZ\nJGQK4Y7FPGe7iNusUoJkm5LJTltf7rIu5vwBPTGbprTQUgQw6Bz50IMGP8qZEaw0qu0HT9kuYaDp\nEBeY1/KtcwSbnFnB9wN1MLLGyeWoD+dA5mkBGxza833HPpkrLCtJpZrnHTMREPn99qoP5FJpos6Z\nT+pNNDZVpnsqDvnbRKjBoe0HZc54Uk2yn+nSD3y9ctY4aXAEGC/nPdbO4DbrRwB86RxDga1r5PdZ\n9RpvYw2VUBLuwl+Rx4b/wqe3w/71ATcxMC2OPUNuY3n8Be5tcaKet2IuY8+Q26SeQaRScQj2fhNw\nqlaTaGMSoiLfwwGyH+wechv/dM7kqCJdonHUsyjhiuD7gXu2GKcRrAsulkbtt+tjpdGSIUoA9Dnf\njiaxO3RzFcD6+mFZvqB4d/Dt2jSGXyfwzIHsB0u7XcepDc9yYf3DnFL/DKBDP/CtcGwNXmhR7bPv\nJlzNSscISpRErDh4L+7yyO+zlhhI6SsL3YUJhodDb/Z8BbuXQc/RgcsUT76fgcCnR/a6Q21TqGb2\nuN4MPPuvup1qh7D3a/jkVhg4Da78n37tdkKDg8n3E1NSQ+qmJYwxyZvbxb8Zwl1nnxHcrMvpdKUn\n46m1AMFrS7j67TP/mQz5Mt4k0erk27snE2WJ0FmiP35eDkU/wairIC0r8HYcNk8cU1Qc9J8sZ+ym\nCB+WJ9/P4n0bqKaIYRPOYFy/LqQnxjA+s0tw/VarWQL6KDu7+uwPToXsX0dw8UfbyCup4fGzshg4\nbmrg7YYDY38nH2FEhPfsMEQneXMAsyaYMkUcZUluWdBtdjjadcXC7fD2LOlOvnlNcO1qYxI6QdCo\nyvrcEgab9pNlOgTpJ9J/ug7JWULAHdukgRHXRZeZolfzrhvmUSUGu62B3YerGNorMpcIABnEueLP\nsl+depdGCj7I7CqtQWyNg0tfD669MMHhVNjgKuA3e2wfhvXW6bdv0EwqQL/fATCX7GZiySpu7m3l\nnpLubMwrY/a4Pi0faNAmjCUVvXFfBDoM3poBKYUqcg6WU2drPi0t7FGNgOgEGYlflQ9VOgjExqTI\n9K+k3tL1PXW+TIuNcLJzS0nFFYsSp1PwmhCQ0gfST5C/gU5LKm5c3pOF3f9CLTFkR3r12IajMs36\nuwXyuV6TCvX7FmYwh0dxLT3YWVBJVb2dJ6JfZth/+8gK2noos8YkQ/JxnutAB8E6NweyYdk9nFH1\nMQDZeRHeZ8MUw+DQG/Ui0OMC08zQ34++GJtDYfP+8mYOiADqNTocOlQpdTPhBrhlHZx+NyT3hlPu\nhBGzg2+3g8nOKyVFqLVndNJ88EVnD4f6G/fvJdeOO4XBAdIwsMTo931pYxK0SpYRXjgsO7cUgZOL\nxUq5YddnsspusJz9KNy5HcZcK5/3HgvHn+kREAwG12/cLX8V91veZV9JDYUVEaoZo7LsXvjPJNj1\neUefiRvD4NAbHd18boOj729gwBmAdLFHNNr0QnXgttfKuAIDLwor6thXUkOqanDs/BQ+uD74hisL\n4IsH4AcZzKe7weH6jQf3SiGaBrLzSiO7+qZWrE4I3WrPEJUAE+d61tk/vAH+1h02RfbSyvrcEhKp\nxYTmmg5FPNVZf4WrFkO/U4Jvq8GT0TY+VupxRPxYe2Q35G8Oq2w9w+DQG7d6pg4XmDDLJYLEHkxw\n5YJ3mtliVLzHNQ2eIEY9cDrg0CbI/V7+H6GoA96ABI+QFmV5wTdclQ9rX5AZVSA9J1P+Amc9oo/h\n57pBD/5sJhdHraP0aAO/FEVwPI12GRD0c+Undodpj8CZD8vnitOV5hm5wc6KopCdq/HKqTSEz03P\nL5rvvIdV/q4RP9a6vcnho8NhGBx6o+cywZAL4I6tMPq3THGuwYKdTfvLaIjkCobqwBMVDxaNymWw\n39cnt8IL46UXwOmAlybD6+eFlXXfVtQBLzPeUzZbl5tRg6+eQSycOg9OujEgiWgvnA6vG/GQFGnw\nrY/kwdtXQEnPOC0tYSxv3lp+KaqmrMZGusXnu9Gj375/Fbx0hpy1643mO09BnmvEGxxab3KYYBgc\nejNsFvzhexm0qAsC3ryIjBU30j+unjqbk22HdFgP7ShOnAmn/p+s3WEyeYyOYAeksn1w5Gew1Ulp\neTUIL4IzVdSbdIZVY4zpMVPUanDojdPuWWMHspKkdyaiDQ5t3BHAaXfDbZvh5FuDbLcKyvdDbZl3\n+52gz45N91lC08OIKtwmpeDtDfL5N4/AIz3hq4eCb1sz/sTYZJzcnqJqSqrrmzoi/Gnw6bdhgGFw\n6E1id8gYDkk99WnPZJIZGMBvesmfK6LXFofOhCl/hl5j5PPUfrKqqxLk0oevCqE7NTYy3dNHquvd\nyxCxJ98AI66QL+jxebRiUyqF26TiaLDtW6Lh/Gdh0v0A9ImVA3Z2bknkxnE0+LimE7vLPhusGujP\ny+GZYfC/a1ztR75+jGpwjPSN49TDiNKmvgOgyL6sR9saQ17YjnJiuhTa2xDJ2Sq+S4FhgGFwhDPf\nPQkvTYFaddYgN0e8q0/LLevkbLFL/+Da8R2MohLl3wh1T290DXSDuieSMPw8mCxv4PoYHL4DN/DW\nJfDqOVCyN/j2AWJlzFGa+ShWs+BwZT37S3VegmgvBpwB130BZ/1N33bdRrLLkImObA+HjN+Qk6FB\nyTbvF3UxCprS4dChX028FS560f30tOOklkxEe+aMWirHAGX7YNsiOfsZH2RGQcleOLTR/XRoFxm7\nsTGvDIdTwWwSTR0ZvhzeIZc7UvrIpQ+9cNcGcV1cES7+te5XOdC5C0eps197HTjsYA7i0nV/V5oY\nGr20OOwNctYZLQ0+c10ZI3qnsHFfGet/LaVv1/AZ/FpNXBfoc5Ln+aFNsPMTaSSPvibwdjuZV25/\naQ2HK+uxmgUZp18H48+VQc6JPaR+RjAoSmPPnJ4SBH0myMcX90NdJeMzzCwE1v8aoQaH0wEmK1Bv\nLKl0aioOwjd/hfX/Dr4tn5vlcTG1JMZYqK63syO/Mvj2O4LXz4MXxkCpTjNplSYH78g0OFQv1vh+\nKfDLVzLFzRwN8en6CU5ZNTd/d7BzkDe7g9nweD9YcqN8XlvuNpoieraopXgX/PAP2PFxcO24dThc\n331CD0gfAkm9gmu3g1BvziN6pxCTkAJpgyBrGmSMCF60ztEgs3jA833pKUGgcsd2+EsJJw4fC8DO\nwkoqam0tHBSGmMzwx4PwYJlUcg4TDA+H3uip2uhzszTVljGu3xC+2VXE+twS/SSD2xNfN99nd0mV\nv6nzYWAQtQvcywS+7unImy1W1NrYWSgNypMyzLDwYvnCn4r18QoNmyVjaLQ3Ab2yq9Tv2xIDGSOh\n20Am9O/Kv1btJTsvQmOPfl0liw32Hg+9x+inw+G7RHDCdPmIUFSDckL/EJRz95WBB30lCHZ9Dgjo\n9xsQgvSkGDK7xZN75Cg/7ivljBO6B/8eHYEILy+4YXDojV4zRfBcZMl9oEJGs4/P7MI3u4rIzi1l\nzqlBxj20Nw67XBIAj5uvLA8Ob4OjRcG1HRUvZ0DqzWDIhdBjuJQ5jzA25pWiKJDZLZ40Nb0wKkG/\nJaikDPnQotdNVE1D7j0Orv0MgDH1dkwCDpTWkl9eS8+U2GYaCEN2fAwbX4HT73MZHDrpcIQyW6gD\nUA3K8ZldYcPLUF0kl06rCyHtBDjh3MAbt9fL78lpB7NVbtPTw/HJbVBzBG5a6w4GHt+vC7lHjrL+\n1wg2OMIMw+DQGz0vAjXgcegMeREcdxLjTXL2sCGvFKdTwRRJcRxaj41qcOhVl2LeLu/nY68Lrr0O\nxLOc0sWTMhkbglmjFr0MZT+5/wnRFob2SmbrwQqyc0u5aFSELRmon8kt/KVTsKK/bKEIJb+8lgOl\ntZhNgjF9U+GNt2UKa5+TYf8aGH5ZcAZHUgY8UOAtTBfXVRoyKX2D/wDq2LRjCax6DE68iPGZE3h/\n44HIXAos2gVf/FFmAZ73dEefjRsjhkNv1NmPvS54lUv1IjjhPCnM1O83DOuVTKzVTFmNjT2Rpt6o\nfh6T1TNb1zPwq5Pg5ZqucQ12sSnw2Z3wyjlyIA+GPV/C+v/Iar0qei0F+i6ZKQooilspNyIHb1/F\nRr2+q4yR0hOXPlg+L8uDF8bBP09q9rBwRDWSh/ZMIiHa4jGUU1zBonrFUmmF6fqcBLesh0teDq5N\nree1LE8GBBdsdS8NbT9UwdF6e3Dv0d5UH4a9X8tU9zDCMDj0xqqjeqY7SMozW7SaTXIGAe4UtIjB\nd6YIoVNtrK+WGUNVh/VtN8Qcrbe7hd3GZ2o8HHFdoCBHzhaD/Uxb3oZld8O+1Z5tA8+SdT16DAuu\nba1mxb9OlrVBinZKNzsRqiHjK6CkeiSCjQ8a+zu49A2pKAxgssjg4JJfgmu3A1ANSXdWlWooJ+ts\ncIQCrVdPPd/aMnqnxtErJRa7U2HT/rKOObdACcOUWDAMDv3xMjiCvIneuR3+UgqpfaFgKxyUKbIR\nG/Xvq9gImsCvIL6r8v1y5v/+1Z5ta/8Jzw6HVY8G3m4HsGm/THnulRJL79Q4twYLsan6CUP5SpsD\njLhM1vUIthCWW2woERz18lFbyrh+qQgBvxYfpbgqwtQbfZeJ9CxfoEVt32nzqGlGCOrkZ3xmV+nZ\nVavDuj0cQfbZQ5vg7Vmw4s/BteOPeo3nNVFWOFYN/fGRWsPKV6wuTDBiOPRGCLj8PRmlH50UfHsm\ns5z1/GcSJPaEeTu93NOKoiDCLBK5SWJTZGyFS6MB0CdYsbZczvwTeni2RWiWijqwqb+xVwyHehMK\ndrZo88mO0JMu/aVQVtogmX0EUFtGSlwUg7onsquwig15pUwfltF8O+FEI6XRHnDNJ8F/f/Z6eZNT\nlwm0hnhDNVhCHLejE8VV9ewtPooQrrijugrApSqb1Fv+DVaAr/IQ7Fkhr3WVo0fgtXPl93jb5sAz\nMrTeADWF1HXdTcjswkebD0Xe5E5r+IcR7eLhEELcIoTIE0LUCSHWCyHGN7PvJCGE4ufRw2e/WUKI\nXa42twkhwiefbNA5MGAyWGP0aU8NGHTNdkccl0KU2URxVT15JREU+9B1AJz3D091TJCDtsmKe4AK\nBHe0v1bIKjILYTVyTfc9GU65C46fop8SpT+Do+EolB8IfrlmzLVw9UdSECvO270esRWPfT0clmjo\nfzocNy64dl8+Ex5OlTorIMXcLK4xI5yXIHzYoFHFTY6zepZTopPkJAOCN/z9qeOaLFITpSwXHEFo\nZaiy5tGJjQwO9TrccqCcOlsEVZ4Ow0qx0A4GhxBiNvA08BAwGsgBvhBCpLdw6CAgQ/Nw500KIU4G\n3gVeBkYBS4AlQoihun+AjqK6GN6+FD643nMR2OvAVkuM1czI4+SFHHFxHL6ccif85Qic+1Tgbdj8\nrFdGYCGsOpuDLQfkDM5tcPSfBFMflBH+eilR+hu8N74CzwyFFX8Krm0t7sFbNaJkHMe6XyOsz573\nDMz8L3TJ1Ldd1atn8WMoR5BnrmmvXIp+16E/I1l7vQeTXZXUC6Y9Bqfc0chIzuwWT7eEaBrsTnIO\nlDfTSJhxDMdw3AW8pCjKq4qi7ABuBGqAlvIWixRFKdQ8tDXZbweWK4ryhKIoOxVF+TOwCZgbkk/Q\nVnZ/ARtflaqjgVJbBnu+kI/oRGnNg/tCiMg4jvpqef7a2Ygey0F+PRyRt6SSc6CcBruTbgnRZHbz\nM1DoNXg3+EnHtOqUnqwl1vsGNC5TGiA/H66ivCaCYhQGToXhs7yF0ja9AWue99xcA6GTeOY8XjlX\nxbb0E2TtmYsWQnJvmP0WzHotuDfxFUkDqcehjovBLMkm9oCJN8O4OY08HEKIyPTMhWGlWAixwSGE\niALGAF+p21yGw1fAxBYO3yKEKBBCfCmE+I3PaxO1bbr4ohVttg+rHoPP7vBOO2wr7g6TKG/KPrNF\nNWUrorT+f3wVFmTCx7fo266/IMgIlDbP1qTDuuNyinZC6a9ynVovI8qf4JReBsfL0+Cx4+Qygdpn\nXUZyemIM/dPiURRZDyii+Wq+9AZVFQbehj8djoTu8hFs9eR2oqLGxi6XKq7bKxedKFNW+50ilwEH\nny+XoILBVwZexS3CplMAb1JvuH0r/N9u9yZ1rM2OpMqxU+fDvXlw2t0dfCLehDpotBtgBnwXhg8D\nJzRxTAHSC7IRiAbmAKuEEBMURdnk2qdHE232wA9CiGhXWyqhjaTRQ4nQN1AttgscLXZb3qP7pGI2\nCQ6V13KwrEZmNIQ7/tYV8zfDtwvkTGj6E4G161t1EyIyaHS9r2sa4N3LpDbAdSvgN7fLhyXafwOt\n5YLnZGBfcm/PNr20Jeor5cNkle2nnQAJntXTCZld+LX4KOtzS5g6JALUG221sOMT2Z8GTfd45Kxx\nQElw17i/pa05vvOo8GaDSxW3f1o8aYlB9svmaCrQ2RoL9RXBLalUHJLe6MQeMiMw1VtITDWkftxX\nhs3hxGqOgOROszWsaqiohF2WiqIoPwM/azatEUIMAO4ErvZ/VIvcDzwY7Lm1Gj20JXw1K3xmi/Eu\n9cacA+VsyCuNDIPDX6pWbTn8vFQWrQoUf67p+DQYcpGcLUYANoeTH/d5B6oBUKPR4dArCHnQOY23\n6aUtoU19Hnm5fGgYn9mFd7MPRI57+mgxfHSDLJz3Z438vvv7CvAadzo8YlMRrDSqzvq9jORfv3XV\nnhknpeB/+khe50NnumXD20xTMvB6GMo/fSi9VcNnw8z/NHo5Kz2RlDgr5TU2th+qYFSf8LuRRwqh\nNtWOAA7Ad9TvDrTFF5kNHK95XtjGNh8DkjWP3k3spw96XAS+QT9DZ8LJt8m0QxcnZUbYsor7M2kc\nTHrocEz4AzxwGC58wbMtuTdc+jpMXxB4u+3I9kMV1NocpMRZyUp3fT8Ou5y9QehnK7oVb2s+On6C\na51/e34l1ZGg3uhPrA6CL2GgPS6CDY71rgBg9XcFpFLn8nth93L5/PN5com5siDwN5o6H+7+VQZ2\nat/GolUAACAASURBVInrJh/BqDr7el7XvACf3AqHfwLAZBKM6xdhcRzfPQmf3iH1m8KIkBociqI0\nAD8CU9RtQgiT6/naNjQ1ErnUorJW26aLM5tqU1GUekVRKtUHUNWG9247eswW1SJY6s15wh/grL9C\nxnD3LhEnSuPvZqTHjU4IOfsPs4jstqAup4zr18VTH6dOExUfkyIHwA9vCC6TxFYH2xbDrqVSdlxF\nr5o27vx//8FqPVNi6Z0ai8OpuD06YU1T0f7BVipVHNDvVOg52pMKCzIQ9eVpsOWdwNptR6rr7WzP\n94nfAE9arBpkq0c8lSUa4rs29pDM+RLu2SurvAaK77i081MZFKxRfI04af5dn8uYucr8jj4TL9pj\nMepp4HohxG+FEIOBhUA88CqAEOIxIcQb6s5CiDuEEBcKIY4XQgwVQjwDnAH8U9Pms8DZQoh5QogT\nhBDzgbGAZorbgehxE21FWtPYfl2keuORoxRV1QX+Xu2Fv8+kV5VSfzid0nDTFnwKUxqlFoJGzyBZ\najTUlMLW92H3isDfqKYEPvg9/O8a7wyhuG4w+AL/yy2txd4ADlf2SVS8TO3+50nwj2Fexo3HUI6A\n9Fi34a+zhyMmWVbTvWGld32Qsjw4sA5KcwNrtx3ZtE+q4vZOjfWuAOxOi3V55cI9Rd3X8+qzfA2e\nPrshrxSHMwjNoPaiBcO/owh5DIeiKO8LIdKAh5FBnVuAsxVFUYM+M4A+mkOigKeAXsj02a3AVEVR\nVmraXCOEuAL4G/AosAe4SFGUINJCdMQ9GAXh4Rh/g5SbFq7ByFbnKuEu3HLBybFWBvdIYkdBJRty\nyzh3eJirN/pTv9MuqShKYGmyG1+B/etg6MWQNc2z/e/Hyfe8PUdWTQxTHE7FLZ7k5Zp211FRB24d\nZor+AhVB9qnZbwbeLjSuBmyvh+KdrvetcZ//SZld+XDTocjwzPmpfguEJo1Y+z4REOzsMZK7er/g\nluNXPRyuzxRMqu/q56QxNvoa6Dky8Hb84evhUD0zmpTnIRmyKF1VnZ1dhZWc2DPAWJT24hjW4UBR\nlBcURemrKEq0oigTFEVZr3ntWkVRJmmeL1AU5XhFUWIVRemqKMpkrbGh2W+RoiiDXG0OVRRlaXt8\nllZx4gy44Hk4cWbgbViiIL6bp/PnvAPPDINl93jt5tHjiIDZYq8xcPxU7+wI1ThTHJ7ZcVvZv07O\n/I/s9t6uVyBkiNlZUElVnZ2EaAuDMzTGmLaOCngMtaAMjhCWRHc6IGMEpA2WUfJR8S4VWfzOFnMO\nVIS/emNTA/dJN8Elr0oZdz1xGxyhXfXVA3XM8fLKgSfQOdbXUA7iOtz1OWx8WdZN0vLDM/DqdLlM\nGCi+v7GPBAGARVM0MyJi5vzVrQoDIiC/JwLpPVZa4r1G69dmbGOrGyJMLnrqfLjqA5mjr6K98QU6\nW3QLWcV6b48QESX1txvTNxWLNuUuqaesPXPCufK59vMoAbp1/QkoqSiKfD3QJaiENPjDd3DLOvlc\nCL+zxb5d40hPjKbB4WTz/jBXb3TLXvsM3H1PloHcmiDuNrFvDSzoD69f4L09QtK562wOcg5oqhpr\n0VY4Bo3BEYQR1ZQOR8kvsupxWV7gbft6Xn3Ev1QiJmZOUcJW+Cvs0mINXGx8RQYJDr1YDm4+krsq\n41wXwa5Cqd6YEhfV3mcaHGYrzPtZ3gADLTTkTpnzDewL87VjF9m+9VNUMkbI2jMq6sCtOORyRSBp\nsk3pGSgKPNxVtj1vNyTqlE4c2wWqD3vNFoUQjM/swmdbC8jOLWXigK7NNNDB9JkIZz/eSJshaOqr\nZDxNfaX39giRNt9yoJwGh5P0xGj6dtX0JXuDx7Bo5JkL4jM1qcOhw9LWiTMg/UToliWfu8faJiZ3\neWFeNNNe5xGOC7MlFcPgCAXVRVC4VQYh9ZkQWBt7vpT6FN2HSoOjCau7W0I0x6cn8EtRNdm5pZx1\nol/ts/CgqRiNxCDP2eZHaRT0K3YWQhRFcWsZnNS/heqgXtVEjwZncPjOFIWQ2RK2ozrLmzcOwAOY\n0L8rn20tcLnlB+r3fnrT/UT58OXIL3B4u1we7D227e36k5cHfeId2gF1WWFC/67eN14h4PL35Til\nZpSMuFwaboF8Tyr+tHZAHwmCsT5VNvwsqQAM751CtMVE6dEGfimqZmD38KrE6kZr2IWZwWEsqYSC\nvO/hrYvhm78G3oavS0xbMdbHnR4Rrj5Fgb+lw6O9gq9I6ov7JtpE6mIYzxZ/Kaqm9GgD0RYTw3ql\neL949Ii8UatLHCazp9BXoO7ppgZu7bZAB+89X8Ezw2XqroqfJRXwzBY37S+jwR7+WUSN2PkJLPqt\nrJkUCE0KWbmud7tOUt0hIjtPxm808sqZrTDobCn4ZjLLbf1PhzG/9W+4tRa3geZzjeuh6uxL5ulw\nw7dwyStem6MsJka7RL/COj02JgVu3SSXN9XfIEwwDI5QYNXhRteU0qjT7knVc6F19YUt9noZFNpQ\n3fhm9+0Tsr7KkT2Btd1UXEIExHCoA9foPqlEWXwux8/nydoz2Rr1w5tWw107Zc2HQMgYAdMehdG/\nbfxasFocNSVQvk8uoagkpEu1Vx/P1vFpCaTGWamzOdl2qCKw92sPDu+AfWsbG8nB6nA05ZUbcAb8\nqRiu/yawdtuBBrtHFbdRwGioaOr70iOtvmSv1KtQxcPiushMmKSejXaNiMmd2QJdB8hrPcwwDI5Q\nEOxMERqr30XFeQSCmghm2nawgvc37Gft3pLwyxVvzs2342PY/FbjCPTW0tRg1H0YZJ7mVcsjXHA4\nFdbuLeHDTbKisFpJ1Qvf4DuQA0lSTzmoBELaIJh4iwx49CXY9XB/gWrn/UMWwvJxW0v1RvmZX1ud\nF559FuD7J+HVs6X8tZaglUab8MqZLTJDLUxxOBXezd5Pnc1JYoyF/r5VjUt/hZz3YP96z7bKAvjl\nazj4Y4BvavfWd9ESrJGsKPDP8fD04FYV4lMLuX2/p5iPNx8K334bphgxHKEg2NkP+E/HG3YJIKTb\nUkPOgXLMQuBQFO79YBsAGckxPHj+EM4eGqA2x8rHpDvu9Hsav/btAjkbmHx/69tTlwCscY3dfMGu\nw875Wt7sko/z3n763fIRKHp/By6Wby/goU93UFDhEWt7a91+hmQkef9evnoGoSbY+iBtiIxfvr2A\nta44gE+35vPp1vzw67Pgv+AgBJ9y7a/CsR6EqM9C435bVWfn1AUrvX+zvNXwyVwYeBZcuUhu27MC\nPr0Nss6GK95v+xsLE9yyQY6nvkqjwYosOhqk1xg83mSnE9Y8K5czJ93vFe9UXFUPQFmNjdvf3wKE\n4VhbvBu2vgepmTA60PJjocHwcIQCPTwc2vL0Khf+U9YL0bj6lm8v4Ka3NuHwiesorKjjprc2sXx7\ngPULTGZY+Yjs8Fq+XSC3t3VtsDkhmmCL3SVlQLeB+hU3U9H7O8Dze2mNDYCyow2Nfy9fPQOAH1+H\n5fdD/pY2vzcgZ6AHsv1LHgdb16aVYkPqd1BV511LJez6LDT9mYK90UUnQErfxsUF6yrhg+vh3SsC\nS30OxXdA0/220W/mqzIKwaf6mkyQlgU9RzU+/xNnyjpKV30QWNva5VZ1KVwIaQSseU4W73OxfHsB\nd7zX+LoLu35bvBO+f0p6jcMMw8MRCoIdjLzyqJsevB1OhYc+3YG/YUkBBPDQpzs4c0gPzKY2pnCp\n1vbKR6CqAM56BNa+IJ9PfsC/Nd4cTc0UITSBX3qg/Q6qD0sdkXULA/4O2vx7+SqNggxW/OUr6DE8\nMMXF9f+B9QvhlDvl59HSwyVBHpvi78iW8Vfo7EA2fPmgzOa4+KX267MN1TJOZfsHgfdZ8G/4Q/Cu\n/JNvlQ9fhAm2/c/TdluzDLy+gxoYeQXsWBLUd9Cm38yfV86deRMCMbNgl5/U39cS61mmVPVjqgrk\nNZjat/36bWU+TH8Sfng68N8sTFVGwTA4QoPW3RqoXPdNa+RNWht/4DZEBEQnkJ1b2mjGoUUBCirq\nAtc6OP0eGTS38RX48TVQnPoP3BBc4JetFr5+WH7nk+73jm3Y/JYsdHb8mXDxS21vG+RnLd8HG/4L\nG14GlIC/gzb9Xn0TPEty2tlisPLm7ngXP4PR2Y8F1qaKv7oj9nrYvwa6ytTXdumzigKrHv1/9s47\nPI7qbPu/2VXvki1Zzb03yTa9mziU0EKvSSgJJYXQyUvqmwYJSUjyQkgllIROCL2DqaYb5G5s46Jm\ny029a+f749nZHa12Zs6Z1Rrni+7r2gujPTu7e/bMOU+5n/uBt34vf/O7ZsHZ8E+WtLmd+Nzb4e/Q\nsB9gb4V1XBKYA63fLF6EI1G59ratcu9lF8MBl3iP14HT4ZxpGRxiQO2RdbvxNWm4tvQe0dHwvdc6\ndDjeCzCSUkkGMvLh8Ovh8z+SQ1oXhiHkvsp9BvM1nrwCbqoULxuUG7Yl1NitLRwmNEMQTPO/cadk\nSGfMkhlDn0uk90xPG7xzu5D74oUeu3YPIdlqY9554X+YCc2B1u9lfWYjIM3bLCQqZuZEsB0OpGTI\nRp1hi5DElMXukTU779zovwMp/tcsOG/eBePhqJ/IfT6cCASGR7DO/p0NB36AInytWzvROdHy9OZa\neP1mePvW+M89eik88W1/13Zqchaje7RH1u2mN+W/5kBie61Tw8G9ACMGRzKQmgGf+56ErYezDtoK\ndYet7pJcNc6C6ri4GD0l+u+B3qF5RlVMOEQ6Y572t6HPRbgDPlJQdgXC2EjScDXC+vS16L8TmAPt\n32v2KTD9uMHdRBMVhnJq3jYcOO5m+M7GwV6ofeM2zT2zZl/8YfTfoX7/axace1LkjoFDroD55w19\njQqeugr+fDh88vzQ54ajnHuxLVplDiQ0B1q/mSXwNojDkWAPILeoXF+XECRXP+Hv2k5E56zBgnV7\nZN3akche69RwcC/ASEplb0TbVkljZBfD/hdH/x7TT2X/iUWU5WewtaU7bm7RAErzM4aK86jitZuj\nxKPMImlYtfjn8v+JeI2xOPhy6T2T40Nx1K03yHA0wnrtZnjtF5BbDm0NMOtk33Og9XsFDDjjrqGD\nEvUWnQSUAF7/tUSL9rkQFv3A3/VjYR085gD0tO6ZNWsvYU3g9wKkhLinbbDHPhzYsQ4aa+Ifwon+\nxtaanXmSHMR5lQnNgdZv9kK4N45TGtBPitktKpeoDkfWaKg6a6jmRkyEI+nr9gXb/bbf14RM7Pc3\n24s5HCMRjmRh5wZo+MjfjdBcC6/9EpbEhBBj+qkEAwY/OnEWIAveDuv/f3TiLH0SE0QZ0geHQ5Xd\nzXDYtZJXjMeoTgT5laJCmO0j9+mk2AiJs+OtOZh1shgbAHkVvufA/nvFQvn3SrQRltvmPdAn4l3d\nw9hQLTUzqo7atdt1zVpIeM0e+T2Y9UX52/hDEluzR94Ax944+AAFKZ2s+xA2vhEVjNKBU28QSCwy\nZ5+DReFIT+dOOOIG33OgtW6PuB6OuQmKbanTjALZOxb90F+K2UmzxP63gR5/v0NZFZz6l6EE6hjn\nLul77ZL/k3+XzIbjfyPz6HfdWnvDXmhwjEQ4koW7T4TWepHI1a0m6HXIwcXpp3LsnDL++KUFQ3Qd\nxuRl8L8nJVAbHhqQg3ZjOJ1ghqCnJWpt697cb9wihKgF58Ph1/r7TPFg8T7ipQgS9RRDYeJWY030\nbw0fwUXPRp/XhPV7Xfngx3T3RTff0tha/v5eScfFpuQSbYTl1EsFEvcWH/qKGMNfuBnG2A6ozEJo\n65LnCic4rtncjBR+dXpVYmvWItqt/LdU3VTuG+3a7OdAcoI5AH8Lt6a/fqN+BCRZkTn7HIRCkJ4n\nDeJmHi+pOZ9zcOycMq49Zhq/ev6TQX8fsm5nnTT0xakZiUXM3DRL7H/r6/TfADIW878Ek48ULYsw\nnNbtkDnQRWhAoryjpgp3w4LfvfaQq6TpZ+EEf58niRgxOJKFRLQlnIhq9n4qNhw7p4yjZpXy3sZd\nfOPeD9nd2cdvzqjmkKmj9d/bwpE3wNPXSkmdhc5dcnj4CU23N4mSaLyDcutyWPOMdOSsPlvvum69\nQRLlO1hiO3ceH/1bY41sAAmklI6dU0bx06up3d3FNxZO5rCpxew/sWiwd/TuH6WcdJ8L4MTfRf8+\n80SRLI7Vb1BF9Tkw/lAomDD0uUQrL2rfl0iQpQppIatIvGxb+sC+Zh94fwuPf9zAQZOK/G/aIL9X\nT5vIkM8+ZfBzfn6vvm6pUErPHRpyD6ZCIBVCfYlzj2Jx+h1CFo6NqqjAWrPrXxbvOLcULnhaIg6l\nc/WvZ0NmqhwXC8YVcP7BEyjJzRi6bpMBtyhmSgYSYzBlnK7B0dctKZ5g2uBUz+ip8oiBtW7fWLed\nC+98HxN45LKDqShMgITtJurlZ92OnjKYe7cXYSSlkiwkotropFnh0HkTJOR30ORRHDhJ0hIrGoah\nP0XDR/Lf/b4Gl74hqQ+/cAvzbVspZYw1D+hf141Qlp4nVv6oSf5ElCzYDbzsUUoSyG7Y3dFL7W7Z\nRC89fDIHTR41dNPu3AWYUTl7C3nlMO5AKJqILxz0TfjCL+JvSIlqS0QY/zGb/sWvwPe3icy8Ddaa\nPWf/cQAsr49p1e4Ha5+F30yD+89J/Fo714ns9V8Wxn8+kflyI+/mlYuhkJKuf10LzVug/kMomixp\ngxh1Yj9YVieptoXTS/jivIqh67a3Q0iwdR8MffGujSJW58f473PhJBhGYqqvr/9Kmko+9z/KLwkG\nDBZOL2F6qazzYdlrQVKat8yCn5UmXlm3l2IkwpEsJOItOjGnc0pgwmGQNcqRfFVVWcCzK7ayrC7B\nm6C/VyIPAAd+Q3p4JAI35nQiQmkTj4CLnh96MIMYB1fUDP27Lqyb//ynYOJhCV9uWbhZ2YRRWeRn\nORwE8coLk41EFHLdxOo8Ds45FfkYhugYNLV1J8b0t4zkrCLYukL+XTrH37XcxOpA1m13i7+DLpnl\nyZCU9WPtKVWV+fEH7N4E950pRMzrNwx+7p+nisrthc/B+IP03nj2qRKdyXboiZSaKUZJItHk2OhJ\nx85w5Ys5tH19GFWV+azZ2sayumaOme2D8G6hbSusfhIq94OuZukUbEWT/aDmQbnGtGPFcN2LMGJw\nJAuJeD9Oh3P2aLjgKdeXVoc3g5q6BIl/TauEiJWRD0WTErsWuIvRRAwOHxt3VpF4/MmCaUYjSoXj\nh+WSy8O/TVWli6JnV5zyQpDU1Ip/ib6EvYJJFTs3yHznjBlcbguJdTnu744SAjXJajnpKUwpzmFd\nUzvL61pYNDMBg6N+qfy3pw3+dAhU7OO/86pXeaFfQ9k0hZtjBOJH5j55ATa8AuMPjs+JUIG1ftLz\nRLSu4SNRsPRp4LR09fHpDpkPx3Vr3SfxjJxE+FSF493vva+9KCkRP2lGJyO5fRs8daU4d44GRwEP\nfVCXuHO36U145lrRKcoqgpYOMTz84rVfiHF30fN7ncExklJJFoYjwuFDKW52hRgcdbu72NXR6zHa\nBQ3hjbt8Pnz6qmjzb17i/3pu3mKizduSib4uMbzAVuKZWHfIGi9PEeL3UQHxhp77HwkF62KgH25d\nALfMiF+JkpEPBeP8bVLxelJYWPW4pDje+ZPjy+dGDOUENu+B/ijBd8rn5b9x0o/K8GpG59dQNgz4\nny3ww13xOxnXvSccnk1v6F3XDivCkT1aNDk++mc04uMDK8NRucrCTIqyHeTE46mMWkhLUIvDDUWT\nJN3rJ23k9BvbCfqh+JU11v27rK4FM5E9wYrKVSwYorXkCyNlsf+FSITxP+88OO8RIQzGg2k63gT5\nmamRltHLEolyWDdB+QIJ9738EzE8/MJt805krjYvgbdvh81vx3/+n6fDrfsIT8QPrBs/kCoe/D0n\nw2+mS8rJJ5YpRTgcQuKJlPrajd94BLzxB8GVy+Gc+/Wvbf2+qdlDIye7N8PaZ6JGbBxUh+cioTW7\nfY2EktPzJDwNieXCvQz/RA1lw4ivSZFodRVEDdasomiVjsv8e8EyBKuVonJuEQ4fBseGV0Tue/ta\n/dd6wSnyat13ZkiqfOJgRmkeacEALV19bNmVgMS9fa+NKcf1BSexur0AIwZHsjBpIez7VdGX0EXR\nRJh6VPzX3n0i/GQUbHjZ8eV2yzshpGaHre6h5bjayMiX8GR6Xvz3AX/RoLXPwvM3wNqn4z+/exPs\nXO//s2eNhgufhbPvk8/e+LGEW7f58xa3tXazrbWHgAFzKuLMhQWnlIpd9trB6HRE5GA0EiMkxr22\ni1aCC9nZwrB4i9aBWlYtaw2EY+G3HNbLU5xzmujUFPok8DphOJqd2aMN5ZbB8ZHvy0WNZLeonMOa\nhcQM5Q/vgicuh42vx39+6T/gue9G02k6cIq8pqRH9yWHaENaSoCZZRK58R2ZCw1EOz+Xz1e6V9yv\nF7KRbPc+g2OEw5EszP+SPIYdhmgAuBygVZUFPPZxQ2Le4km3wgm/Ewt/92b5WyLhaTfuSUJsf5fy\nQkhc/Cs1Q3LpFsrni8fV8FHUc9RATa38JlNLcslKc7n9yuZJuD27ePDf7RtjX6de2s3O9vfTUNAN\nY2bDD3dLhCEWWd5e28yyPFICBrs6eqnb3cXYIh/S6xFP0bZxY4rR4Yc86dWx+YBL9a8JIuz35BXC\nOTjlj0OfHw5J/v6wTkSmLcLh50AOI0oY9RGVg8QiHG6aJSDkznUviPaL7j3pFnnNLJR7xmOvralr\nYVltMydVlzuOc8SOT+Q9UrOlf5bCveIKe3pvL0ypjBgceyPWPCO6BRMPGyreEqM2Gg/VY6P5cNM0\nMfweLoEgEEz8JvBC1mg450ExPHSlj910OGB4GmHZUb4gbHAsBb6q/fLl9Qr8DYBzHUqEU7OI6A70\ndmgaHB5z1bkL/nGKHFbfeEffKAkEHCIc8fVj7MhIDTKjLJcV9a0sr2/xZ3BMOFSiApOOkHx+Wq6U\nY3fu8mdwFM+EqrNh7DCTkjt3SoQy1+GASrQjMEjfooE+wIjO+45PZH40tSp2tPdQ39yFoRyVi2OU\nJKKJ47VuE0nJls+T+Y7HpckqhNa6aHoqDhKOJtfbonKBoHCoRk/zL2BmGalGIHkVUAlgjxgchmF8\nE7gOKAVqgMtN03zPYeypwNeBeUA6sBL4X9M0n7eNuQC4M+alPaZpDlPnnGFAf6/c3Iahv9m9fRts\nfkt6acQaHArpjVll+QQDBtvbetjW2kNpvua0hEKD8/CR90wgwuGG1AyYfqy/17r1BoHEG2E1fCSC\nVmNmSwO6iLfoLzytRBh1g2HI5t3bFj6QNJj5Xp5iMFVSRiBGx3BtWIph4rkVBayob6Wmrpnj5voQ\nAJtzmjwsZBXKPPk1lGccJw8ndLfItdNyhJypCq8GeolG5SxYJMqcEumn0lon4XvN0u7l4TU7aXQ2\nuRkuxMwZJ4r0//hDhz437kARhKvYR+u9AXcdDkgsJXtSnA60FhT2PSvis6KhhYGQqS+CZieMgjT8\nPPQqvWvYYedvDHcUcxiQdA6HYRhnAbcAPwYWIAbH84ZhOBRVczjwInAcsA+wGHjSMIz5MeNagTLb\nY3hqFocL7/8NfjUJnrlO/7Vu7YUVvMXMtCBTS+S1vspjH/8G3LqvkEUHvafPjbu3A/58hCh29vf4\nu4YTlCMcPjfvDa/As9fBx/fJ/1v58O2rta9pmqYaYdQL6T6jNm48CxhsiOh6ixteEWnzt/8w9DnL\n4PbgU1gl3ctqh0lIad55cNC3kqdlsvhG+H11/O/sBusA9VqziXA4YlER3j59cI+sPcSVMAriNBz5\n3fg6G7NPgRN+CzNP0H5/5QiHX8E6Jxx6FZxx9+CUagymlOSQlRaks3eADdt9ODWHXQ1n3iMN5IYD\nOcVw2h3Sj2UvxJ6IcFwN/NU0zTsBDMO4DDgeuAj4Rexg0zSvjPnTdw3D+CJwIvDR4KFmYpKPycRw\nSJv7JOCBbA6+RWnqPhCVRUtMK1HSaE+7eM5GYHCvADuWPyKlmnNO0xO8cesNAomHpztjwsR5ZZBb\nBm2N0LhMS8SodlcXzZ19pAYNZpS5hEw3vg4Pfgkq9oUvPzr0+eNvkf8WaNrYWaNg7pnOZa+BIATT\npQy4rxPQaKa3Y52Uv2KImqkdGdZB5c6niHiL9S2EQiYBHW9xxzoxZkZPjfafWaiuHhkX3a0SJUjJ\niO8t+tXhiESaHAy/kpnw1ReFaO0HbVvhsW/IOj05bAwt+hEccyPkj9W+nKfgV7LhNV+JKuQ6YfLn\nPIcEAwZzyvN5b9MuamqbmTZGMxWSVx5tNDgcyMiHuacP3/WGGUmNcBiGkYZEKV6y/maaZij8/0o7\ntWEYASAXiD1hcwzD2GwYRq1hGI8bhuFYDmIYRrphGHnWI3y95CItgTCfm+CQIp+iaqzP3GJ3ixgb\nIOQ7kBr3M+6Gs+7Vu5aFXoUw33P/A09fA60Netf2Io1m5EN6vv/woiXAYz8kK/eD0qooMU8Rlqc4\nsyyP9JSg88DOXfI7OK0dK9QfL1fuhtI5cNpf4eifOo/xayi7lZCmpMHVq+F7W12jDdPG5JCRGqCt\npz8iMqWMN26B2w+A13+t9zo3PHwB/LwUahzKhP3qcHh57Om5MHZ/IRH6Qfs24Yisfyn6t9FThR+g\neR8MisqN9Vhv9R/C9k/C3JEYDPTLum7frvX+gLcqa0SwTnPN9rTDz8vhV1MT0gAatqpAgG2r4PaD\n4Y5jEr/WXohkRzhGA0FgW8zftwEzhg6Pi2uBHOAh29/WIhGSZUB+eMwSwzBmm6ZZF+caNwA/0vjc\niSORXipu7Pi8chgzx1P1MqproEkctUq08sdF89JpWTD7ZLXXx4MX2x/8z9fn/1eadZVVx3/+6J+6\nH7BeiFeeeuY9vgwYZcKom55BspGWLZEmbYPDoxQvtvlZHKQEA8wuz+fDzbtZXt/MlBINQqy9SBxr\nFgAAIABJREFUJNZCXzd07girUDplcF3g9Z386nBEUio+iLEqcCtP1URDSzc72ntJCRjMKnMhjJqm\nHJKhPrhyBRTERFLWPi0pt3EHwUXP6X2I426WaJPTGvJtJHfIb9HfFb81QnMt1H8g8zhpoeNlLENM\nuypw/cuybqd8PurcBVKgaaX/6NbuzSJ+l1/pq4ou2dirq1QMwzgXMRS+aJpmk/V30zTfBt62jVsC\nrAYuBeL1Qb4J4ZFYyAXiGSbDB783QSjkvtFNWghff8vzMtPG5JKWIqI0m3d2MmG0YomUtXFXxFJm\nEoBXTwrwr8wa0xBs2BHRM7Ad/j6jJVZJrCd/w02xEcIprw2ySRVPU/8AllhZikNaC/wz/odJbKiq\nUgyOmtoWTpmv2Cywpz0qClVuW7dv/FoUWfe7GI73EfnwMpT9plS8SKOhkCiN9nYIB8VpnBOcylM/\nvAvWvSi9kSYconSpZeE1O700l4xUl6hcb4cYG/HeFxIjb9uJwE7Pjz1AXyHXK/K68XXhs01e5Gpw\nWNyj1Y1t9PaHSEtRTBys/Dd89A9ZD9a6te757haJCgU1j+iNr4lmybRj4dwH9V67B5Bs0ugOYICh\nVPoxgCv/wjCMs4G/AWeapvmS21jTNPsQfkfcnrymafaYptlqPYBhZGM5wG9Kpb8LCAsf+ZA2j7x9\nSoCZYY/EahamBKtMqzzGOl73Irx/B7T4sNO8PEVIXh42Ubj1h+jviR8+joOBkMkK1QhH5D0dDI53\nbod/X+Iq/hb/dX+AnxXD4990HpOWI4+Q2veKwEsk64M74d9fdxZvCiMantbwFhtrAFMqJHJtW40C\nwdoVqtLmuoTk/S+B72yS3ibxYBjw4g+lvXw8CXovOInGbXoT1jyl1aJgmW5ULpgeP3KTTGnzgrHC\npdLtoOxlUCqmr8cVZZGfmUrvQIi1WzWOFrvCqAX7b9btI0Wj4tx9hkiqwWGaZi/wIbDI+luYk7EI\nW4QiFoZhnIOUvZ5jmqaDhOSg8UFgLtCY6GceNvj1FAMpcMpfhGWcklhZYpT1r7FpxZZpWVj8c3j6\n6mgHWR30ulTdWPAb4Vj+iFTTOM3zpjdFjvxZnwRCp2jDg1+CGyvk+gr4dHs7Hb0DZKYGmVLsYUh6\nRTj8aotYnrXburrkVfhuvatHFxdeh/PG16HmPs9+Hlb0Z2VDK30Dikqq9r4/diSq2ujWcBD8p1SC\nqfLZnDg4hpFYRMBp/UQUR9UFwJSrquzv6SrXrrtmu2HN04m1VXCC1+GsKAdgGEbEIFOuCuzthKbV\n8m/7ug2mRNWY/RjKKs7dZ4g9kVK5BbjbMIwPgPeAK4FswjoahmHcBFSYpvmV8P+fC9wNXAG8axiG\nFSfrMk2zJTzmh8A7wHqgANH4GI9ERPYOZI2CqUcPVYr0Qko6VLuUSIVCQo7r3AnffF9asDtANonN\n6mSm/l4hQ4YGhnIiEimN7e8BDPeIjR8Oh2nCv74GmHDNJ/FDz13N8Oli/57VF2+Djh1DK0ICqRIF\naFgKk4/0vIylvzGnIo+UoIedHy+NY4dfEaVej3JM8E+u9eo7ougtThyVTW56Cm09/XyyrY3Z5Qq5\nbCsqF2skJypY53Ug5Y+Vcs/RPsmdbkjLEQ/Xz7rtdEipaCqOhkKmeoWKWyQQ/GuLdDTBA+cKx+L7\nsVTAMJprJXKTnqun7ux1OGvseVWV+byxbkfYQFOoHtu6TBSjc8YM5aZkFkr/Fj/r1svw/4yRdIPD\nNM0HDcMoBn6CCH99DBxrmqa1esqAcbaXXBL+XH8IPyzcDVwQ/nch8Nfw9XYjUZSDTdNclaSvoY/8\nSjjv4eG/biAgJMmeFrGAXQwOK8KhLEqTkgbn3Bf/uUS8xXnnQvU57ukHP95ifzeR9JOjpkGCjbCm\nObDFKxbAykeVN2+llvQWskeLgePUbtvvd4pURySBrHjaHbJJZjh8P0VvMRAwmFuZz5INO1le16Jm\ncMQLTWu8Z1yEBqIy7U6bd/k8EefTxdJ7pKJj1hedSy8T0Y9xinCUVoERhPatUg3mQeTdtLODtu5+\n0lMC3uWeTmkcC9b36euUuQ248EHs8KroAdi9UarcimdoGhwekVe7fowHn6LKRtJXgj11HWvkZxZC\n82Z/e20Cncb3BPYIadQ0zduA2xyeuyDm/xcqXO8qIAE5tr0Y7duh7n2JjIzdL/6YrMKwweFuAU8q\nziE7LUhH7wDrm9qZXppANXCi3qJhuJMV97kQphwV7fKpArtx4thLJUm540h4+mOl4VoKo27qhzAM\nwl8uBsc7f5RyynnnwZxT1a+dWeBepqvlLRawZMNOaupaOHt/j8GmCUd8RyJN5fMc3tMHD2KgVyKU\nvR3D7y1++hqseEQkrB0NjgT0Y066FY76ydD7LS1LND62rZADz8PgsA7P2eV5pCpH5TwMDpA5zXCp\neLHDS0kY/KdjUzIkOuVU8Wc3nrtbPJw7GfvJtjY6e/vd+ySBjZwfp5IkZ4zs/6F+92vEw17cmh72\n8iqV/y9gdb5UDVU3fgwPnCMpjUsdCHaZhdIF1cMCDgYM5lTk8+7GXdTUNXsbHJ27nHOwyZY3n3SE\n/musmyuY5ux9JJILb2+S3HFu2VA56LIqwBC56PYm17LL3v4QqxqlxbWnWqMKfOfDPTRLQPLK618S\n1v9wQqEHkIVqHeKoYcC8c+Th9J49rRJdC7rIcsciNVMtQhkaEMPXV08bl98hkchcMEUUJ+OhfL4Y\nHA1LPVU/a3SicsUzhQzr1B07JV0MuNQsaQipCpUIh1++3Izj5eGEYIpo+ChEk0vzMyjJTaeprYeV\nDa3sN8GjpN0pKgdw3kND/6aK//aUyn81bhorm93Va0ShUgURWXMX40Azt/juxl0sr2vhzH1dVAZN\nE/5wAGDCBc8MLbdMhMPx3l+FNDj3DJh1kv7rnaC0cScQmt66HB69GEpmwzdimP3puSLMtH2NeIsu\nvWA+2SblcnkZKYwfNQzpDN8cDgWDw2911Qvfl/8efEX8w07DYJ0bNjjWbm2ju2/AvRzTDRn5MP14\nee+BXj2DQwUt9fDbWWLw/kBD0EpFhyNpkbn5UorZ5i3SvFwnKjfhEPdSW8Pwl2JWicr5LU9WwaIf\nCJE/y1t1t6oyn5dWN7GsrsXb4Lj4FYmOxhKdE0X1uWLE6ESK9yBGDI5kwopu6GzeKiExjc07mlv0\n8BZb64WgFUgZKtoDWh7qENR/KC2k3Ro37d4sWgo5JUND405Q2biteRzo0fdy3dptg9zY29eIt+hi\ncNg9RU8Btp42+OMh8p4XPS+eYSwq9oFjfzm0sZ8XSmbIAeZm/Pr1Ft+/Q9b5fl8D4hkc6gZrRUEm\no7LT2NnRy6rGVhaMcxGwWvOMzFXZPGkCaEcg6MxJGg5YczXQq6eZ4KXDAdLHY8H5og6riye+LUbQ\nEd8ZavzNPSPcPsA9atE/EGJFg0JL+mRDJSpnT6nodpv2wv4XKw+tqiwIGxwKkbmMfH9RXS94NRz8\njDFicCQTaVlCTNIyOBRIPxoETiuE7ylKY5GYSmbGD19W7gsn/h4KNWvdQe07rXpMtAeqz4FT/qR2\nXZWNe1DuuF1PfTGSl3bYcCccKoaaR08TLU+xc5cQxtq2OvedGT1VHro4+mfeY/zkw0MDNk/U4Tce\nMxu+vkRJPdUqM1y8djvL61rcDY6nr5a+Nhc+69pkSxub3oR/ni7Gr5Mypv0Q7OuEoCovQeEQHetF\nXnFAKCQRDDMEh10z9HlF7sS6pna6+0LkpqcwSUU0sKVe1mtmobvhZZryCCgqMihF5aznTL0ux4tv\nhFVPwAGXwL4Xqb3GBcMmcf7J8/DW74XfoXLP/gdhxOBIJiJqoxqhPhUZ8LwyaTcd69HFwdiiTAqz\nUtnd2ceara3O3oqTloGFokny8AOV2nA/B13BePH03eYqJQ2+s1nG6IbUvcpT558nDw9ECaMKnqI9\nqvJZtJf2E562p6ucfou0LOf8fhxUVRaweO12d12D1kYxNoyAs7S9acqaMoJK90sEPe1SpTLQ6zwm\nJV3e2wzJfKkSIZMpbd7TGuVIJCBtbnnpcyry1ZroPXIh1L4LZ/7DOW165/Gw+S045wHXiOAglM6F\nz/1A+sA4YZDh16VucDRvka7P3a3OY3ZvkkdeJYyOqysZgXV/b9zRQUtXH/mZDvvN4ptkn19wfnyl\n4K5mmaeAj+O59n0x+IpnqM/DHkTS29P/VyPVB/FLRSL6sGvg6pVw+HWelzMMg7nhG6HGzfJ2Uhgd\nDqh8Jz86HPkVcOBlsODL7uMyC/zl74ehJ0VX7wCfbBNeTvVYhQiHSh+Vvm7Y/HZyxJD8KL5a69sI\nxu9J4QPVKs0HLSO5eIazoXP/OXBjuVSF6EDF8DcMfw3cVCJz2z+Bmgdgk3cbg0Gw1k9qlrOBtfop\nOfwX3+h4mYiRrLJmQe1eMQzA1OOllM6Bw6+FqjOdxwSCUpZ91r16RpzKb7zkNrjni7DsAc/LFWWn\nMbZIDvnlbuv243vh7dukyV48JFIReP9Z8JeFYiTthRgxOJIJXxGO4VeKq6qQTWO5k7cYCkXLO50a\n/oQGYMNiWPEvZTnvCFR4KX7mKtnw4nBY6NwllSpxsKpRNFBG56RTmqdwGHuVF4Jwbe48Fu512YTj\n4ffV8OtpsGO98xg/kSaVbsAAb/8BnrtBqSPw3Aoxkjdsb6e9x6E8UMVItsiXutwjVba/n3V74TNw\n6RswyiUttu55+PelsPRu9euCd1QOpMRz85uuKrmRNGCFIn9D5V7xq5CrgrmnS9WNThQroiTrRtDX\n0x+y5mtZvcNe274dWmoBw5mrFuHo+TA4hqmnUbIwYnAkE34auE3/Ahz5/WElFHnmFnd9KqVfKRlQ\nMsvhKgb881R45CJROdWBJbDjdmNHqiM0PMWWOukLsetT93Gv/hIe+aq+LLtKtOGlH8PNE8VjiYOa\nWpnz6sp8tY69Xn1UILqZDKj3cgHEKGrf5p5jn3kiXL8RztUozVMVG3rvr9IHpnmL5yWLc9Mpz8/A\nNF28xYgMvwvT36+3qLpx+4nMFU2SsmoV7pFuJVKngsFqORUNH4sjEYOe/gHWbJU0gxLvyDTVDB0/\naqPNW6Bxmb+29l5Q6TuiuX4ie22t05oNG8mjpznvh34NjoE+2RNgr9XhGDE4koniGVJR4HbQxmLK\nIjjiOiEkOmHHevjb5+Eu9zp6C9VjB4vSDIFhiNDTzJOcUw+BQFQIR9tbTFKEY+VjcOcXXEPDAKx/\nUULqCgfdIOx3MRz9c/cSM6tSxEFxNNqSXtNTdDswYkWUVBAKKTL+M2WTjVcd4wTVhlG63mJ4zpbH\n8xZN08Y7colw+NWPURVQGru/dCzW8axV4DcaEIk0uKyf0dMk3dvXATs+GfL06sY2+gZMirLTqCxU\n4AH0tIpMN3isWx+aOEtugz8fBu96EMk/fRWWPaRU7huBSjRZswGgZ1VgRH/DxUi25rC3PdrhWQX2\ntbKXRjhGSKPJhJ+W2CowDFEjVVxUY/IyGJOXzrZWB1GaUZPh5Nu9L5RVJDeeruV9+YeyyThJdYON\n76LhKapKdfsV/5p2tDzcYHmLjTVyqMew7yMlsaq5cAwpmXOr+09Ji/Zy6W33LHEEwjLwYQw3WbF8\nPlzymvc4XW9xbD7Prdwan3u0e5NcJ5gGY1xKR/3qx0Rkrz0MjtM02zf1dsIbv5bf4NCrnCW+/Yq7\nqUTlAkEh2W5ZIoZyycxBT0cbtmlG5dx4I+DPiLIinm7RIIAXfiD9Sc77l3qbepW0mWa0YW5lPoYB\nDS3dbG/roTg3xnB36vtjR0YBEOa7dO0e3AHZDXYhRDdV588QIwbH3oatKwBTyk+dQtSxFrDC4qqq\nLODFVduoqW32FqVxgl9vMbPQm3iZXwkLb1AS2ImgT9ELTWbuuHimdF/taYWd6wexzlu7+/h0u3xG\nZYXRI66Th6Xh4oS0bGldrhrhsKf13NjrrQ3w2s2yaR13s9q103PUtFM0vcVqN28xp0SqHVrr3de/\n3x5AWaMkQplXofc6L3S3wBu/keqWeGWrFvw2O5t3nsile1U4VCwQg6Nh6ZBKKysNqB6VUyRX+xHh\nUymLtT+vk5JNyZB7VyWl0qlmcOSkpzC5OIf1Te0sq2tm0UybsaAalQsExInoaZf1ompw7OWt6WHE\n4Nj78Ogl0LQSvvxv5z4LGQXRcjxFC7i6Mp8XV20byuMY6IemVeLleFVyJKI26oXcMbBQs4W8iuwx\n+NvoQiHY8LJsouXznT3RYIrk42vflc3EZnCsCM91ZWEmRdmaHoeXZ5meGzY4FI0oy+BIyXBvnNXb\nAR/eKZLOqgaHKjS9xTlhsnPtri52dfQOnsO0bOE7ecFKLej2Uzn0KnkMNyJprWz339hvVC49B9IV\nNFqskH6cVKBl4FWr8DdAVJHnnuldFlwwVg5ajx4ug6AcxfRRzv2t97zH+HCyqirzWd/UTk1dy2CD\no2OHlOAGUrwF3a5aKd9ZpzQ+kiJKoGdWkjHC4UgmltwKv53jzTGwIxLmc1k0dj6F4o0wN5IPjzE4\ndqyVHOkts7y9aj/eYsdOePIKePFH6q9RhQonAfyFp7ub4d7T4W+L4hLrBiHSyO2jQX/WatimC90D\nKeIpehhnfqpUtrwLb/4W1r/sPk5TrTY/M5WJYdEpJfXGeMirgPGHuIewE8FTV8EvxsP7iqkVZSM5\nSdLmFioWQDBdPoftvu/o6Wf9dnnPuarrtnganPZXOP437uPmfwkuWSxlrqpQ1SyJkHd9doV2Qk4J\nHHKFfGav/TEMx6rAnGL4br0I4Hn+/h4GaTxkj4KDL1fSBvqsMBLhSCZ6O6QEyqFkMv5rNAh4GnwK\n6yYYIkpjeTjF070XuB/Gf8d2+PAu+bxH/dh5XCgkxk9vp+SXVWSiVcOtfsLT1ndMy/FOWVmHWYy3\nuEyn+ZWFB86Tz/mFm+OLAllYcL58xvxK9WuPngbpHl6o5SmG+tSl4De+Bot/DvtcIKRnJ/j0Fjfu\n6GBZXQsLp4cb5IUG4PVfyzqZssj9M5bMlDLUZKG/R4xTqweSF1R6g4DwEL7wK3UxMQvv/VX2mzmn\niZS9Ewonwg11Q9b2ivoWTBPK8jMoyR1mIqwfqGiWQPL6qaTnSuddDVSNjbaqN01zMA8mmCp7bTJQ\nOGGvVyYdMTiSiURUG70Mjqwi2LVB2VsszE5jXFEWW3Z1sryuhUOnjpYnvBRG7Zh2jBA/dWSXlXVF\nTLj9QPnndZ+6dmaMQHUz8sPhUCnzs1C5H8z6IowbLK29zE+EY/MSOZBNj6jKQd9QvybI4fOt973H\n2Y233g41Qmqk4aDHbzzjeFEb1eBFVFUW8PjHDYNTgTvWwas3ymf9n1rla2nh/nNg5wY44bfuTcl0\ne8+oRuUy8kRyWxc190vvovL57gaHYcQ1pH2t2d5OSRMkg6ioHJnTlCBob4KHL5T1ffa9/j9fHMwq\nyyMlYLCzo5f65i4qC32QtJf+Az55DmafIhoj/59gxOBIJiI3gaJnPdAfrSbwKqXNLJQN3l594IGq\nyny27Oqkpq45anCosKYtTFooDx2oCigFwiqV/d3h+VIwOGaeAEUTYcxc93H7XiQ3rYrxYMGrj4od\nRRPhzHsG/Wlnew/1zV0YBsytUNy8QyHxliEhddOEEEwTxVAz3HZd5furGpX5lXoRGRxa1VtGsmok\nDKLhcNUw9a5PJeIWchAds6CbglKNyvmFH3Xc0ECE16PVkt7CS/8L7/1ZmsUd+V3ncXUfiAR6XoVz\nf5pYzDkVWvaDfBdpc9Dvcty1W8TPVOaptUEMlMLxSuMzUoNML81lZUMry+paxOAIheDvx0iU8Zif\neV+naRWseUp6JqkaHF27JcWaka8fGdtDGDE4konITaAY4RhUR+0R4TjnAXfyXxxUVxbw1LLG6Obd\n3wPbVsq/kyFpDuopIhADrb9b3Vucd67auOzR8tBBgrLmlqc4aXQ2uRmKsuo9LbY+GArqph3bhcuj\nymJXgSXXrdN0UDUq5wOzy/MJGNDU1sPWlm5K8zNsWgaKa/YPB0oF0aWvwxgnYbsYRFQoFYW/VOdK\nNaUCwo3pbpGmdF6fw4KqOi6IoNa/L5N95LI3gOi6Va6qsr+np96QIVo4alQIgSrfY8bx0m9FdU2o\nOkIAD34Z6j8Q6fSZatpHVZUFrGxopaaumePmlokBW/eelO6e+DvvC/jhyy39B7z4A6g6C079i/rr\n9iBGSKPJhG641drkAinOnUItaBobECWBRcLT21ZIrj6zyL05UuTzdcpmv+Vd9TfVOYxSNb2UZEJn\n4wbxoHd9KuFsfHqK1uaiwht55Wfwh/3hg7+rXXv1k3D7QfCsQiWQbj8VVaXR3g7hGLyurk+TmRZk\n2hg5yCKN3HSiciBRilCfXjm3appItzpi4uHw5cdgkQKJ+oFz4L4z1AXrQgNioICaoZxdLBVx21ZA\nbye7O3rZskt+c+WoHKhpf4CNvK3Id9HBhEPhwK/DuAPUxutIgPvgrg1RHLWicqVVarwoP2qjSWiL\nMdwYiXAkE5EDVDGlkpIBB35DNo4kdAqdUyGiNI0t3TS1dVNi37hV3m/HWmkMlFsG16xRe9PIYaRQ\nqqWbh921UYyznDHuB/TODdKyO7NQGOcqUFH8tGPNU/Dgl6S75WVv+suF67ynbuVN+zYJ046a7D32\nK4+LsFjBWLVrq3qLA33wTNhjPehbyuqcVZX5rNnaxrK6Zo6ZXhSVqFfhHYE/b1HVUNatjsgpkYcK\n0nKkjYDqtbtbiIQPVNZQXhnklEL7Vti6jOXdsjYmjMoiP0uj2aHqutUlb5umdANOzQxLAQzjnqjj\nCPkkO4OQcEMhk4CukezL4Nj7dThGIhzJREYeZJeoH1rZo+DYm9T0DzYshnvPkPypInLSU5hSLDf9\n8roWKJsHB35TiEkq8KPDoSNGo+st3vkF+N0caTHthrZGKdv86J9q1wUhCh5+HUw5Sm18WVj4qmk1\nZm+nzeDwEZpWMjg0N29VPQOQyo7RU9TlzVU9q4x84YeAprcYZf3TtEr6RWTkS08SFeh6qP29EhEB\n7++UNUoqPrKL1a6tA12ys2VQpeepd0e2VVj5qqqyv69XNNDaAwZ61SS7B/rglpnwywnRyI0TOnZK\nB+XGGu/rgt7h7GPfmzYml/SUAG09/Wzc2aEm+DXoPRMwOHRaaexhjEQ4kolxB8J165Jz7c6dsO4F\n7TKwqsoC1lmiNEftB2Nd+oTEwroJLJ6FSh563nnSiE4lzKfrLdpFlNwQiQZolMVOPFweqsivhKzR\n0LmDHRuWsqO9h5SAwexyDfJWTytgqBkc6ZqHkSrb3w+O/rlEULy8N8MQEmrnTvEW88qULl9t05Ax\n6+swQKIbqh6vroeqw6Wac6o8VFH7nvCmyqqkz5IbdKNYOkRnC+ULYO0z0LCUmg6pPtPWjdFVGgX5\nTikeBoo9MuxlKG94BR79Gkw8As5/wn2s9f6gdjhr6scApAYDzC7PY+mWZpZv2cHkxmXyhGqEw8d7\nJpNLNVwYMTj2JvS0y6GTnut9I/hZkED12Hz+tbTOn5BSeq6kMEL9srmpGBzZo9RKXAFmnCApicLx\nauNVD1FLRElXtVEHhiGbyboX2L52CTCbaWNyyUjV4NrMOQ1mnaxmROoaUarGGcDyR6BptXSOVZEs\nV82bg3iLnTu1PLfppbmkBQM0d/ZRO/ZExl04Uy+8ruuh9ndLZDKkqEOig1WPS2fhQ67wNjh0UxAl\nM+GrL0WjMyqwOu02fMSytrDC6FgNg2UQb8TDgAimitjYQI98J6+IiHUfqJTc6qZjfaVU9BSWqyoL\nWLqlmcZ1NdDfJZGnIoWUpt/33Mtb08OIwbF3Ye2z6la6T5lxK1xav3kdb71QR+rYBewzfTzBgMIG\nboS9747t4tXkD3OfiYO/pT52oM8W9tZQGjVNtcNq20rZHAvGqqcWysXgaP/0fWA2pfnpDIRMtbm1\nEAiqVSRE2pdrCk6pRDiWPywaAAXj1AwOHWQVwU60DOW0lAAzynJZVtfCHe9u49g509h/YhHKppwu\nhyOvPHmRSR3DL6Imq/gbp+foRSwBysIGx871dHXvwiCbGaUaIfn+bph6tMytSmSlcLxUx6kYRTpp\nQN107EHfgv2+5q0iDL4Njupww8YtWzbQk1ZId8EMcjDU1m1eJVy5Qp20Dv8RHI49YnAYhvFN4Dqg\nFKgBLjdN01HI3jCMhcAtwGygFviZaZp3xYw5A/gpMAFYB3zHNM0kSgr6QHcL3He2bDIXLx7SSXQI\ndEq1/DRSW3wTGds6gIM4ou8tDllyL88P7MuhWd/lnsmvMrU4C468weN9i8IGh+LNt+JR2L0Rpnxe\ndBOGC4OakSkaHOaAbJAqh+4D50pH0oteUPPgF99E/caVVABFzSsAeGXNdg795Svqc6sDbQ6HRjmm\nrmDd0nvkNTNO8CaC6q7bxTexbnsn65tEfOvutzdz99ubKcvPUJ/XgrFQMsu9W7FfbF8L//qqkBov\neMp7vE5qy08PIB2E57bXmEpTfxZ5RgetZjZH//Z19blNy4bzHlZ/TxXxOQvW91YxOHTTsYahnl4c\nPQ0WfEUaNapi8U2Mr2sFDuX+XdO5n9vIae0iV3U/CKaok7YtTDxcDJTCiXqv24NIusFhGMZZiPFw\nGfAucCXwvGEY003THKL5bRjGROBp4E/AecAi4G+GYTSapvl8eMzBwP3ADcBTwLnAY4ZhLDBNc0Wy\nv5MyAinSkRFkw/csG1QsL4So5dvfLQeDws2zbnsnM9bcyuXBRqYG6gGoCU3ijPb7mLrqEdbN+jae\nbZ90vcXlD0uOOGuUt8HR1yXeXDDN21uyNm4j4F1CbLf4ezvUNhqrO6Sih7FueydTtzwJwCSjkRw6\naSdLb27f+I1UYOxzgbfAWsE4qDpbreoEZJ5SMtU8a53Om/298MTl8u/vbFIwOPQic+tzEUF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atm7Z4aLjk2QupaRr66CUJpKQyaodIABwQnGEVBeDN12hrDD0Z7V6gS1xMv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\n/hlKn1KeuR6gNhqKi6Yol/QHG/ZT09QWZe9O0HQI3v4pvPEjU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886mutmDoPmWrh/oPrg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\niIiIaN3flyydXfXkve0AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(t_discrete2, sample(x1, t_discrete2), '-o', label='x1 discrete')\n", "plt.plot(t_discrete2, sample(x2, t_discrete2), '--x', label='x2 discrete')\n", "plt.legend(loc='upper right')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now the highest allowable pulsation is $8 \\pi$, so even if the sampled waveforms are not nice looking, at least they are not confusable anymore." ] } ], "metadata": { "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }