From 2775e76cbf2efbfeff77ab8729ae7883129956ad Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Sun, 28 Jan 2018 11:42:35 -0800 Subject: [PATCH] Added gaussian named tuple. Use a named tuple instead of a tuple for gaussian so the code is more readable. --- 04-One-Dimensional-Kalman-Filters.ipynb | 924 ++++++++++++++---------- 1 file changed, 539 insertions(+), 385 deletions(-) diff --git a/04-One-Dimensional-Kalman-Filters.ipynb b/04-One-Dimensional-Kalman-Filters.ipynb index d73d17d..384787b 100644 --- a/04-One-Dimensional-Kalman-Filters.ipynb +++ b/04-One-Dimensional-Kalman-Filters.ipynb @@ -239,11 +239,14 @@ " },\n", " displayAlign: 'center', // Change this to 'center' to center equations.\n", " \"HTML-CSS\": {\n", - " scale:95,\n", + " scale: 95,\n", " availableFonts: [],\n", " preferredFont:null,\n", " webFont: \"TeX\",\n", " styles: {'.MathJax_Display': {\"margin\": 4}}\n", + " },\n", + " \"fast-preview\": {\n", + " \"disabled\": false\n", " }\n", " });\n", "\n" @@ -271,7 +274,11 @@ "source": [ "Now that we understand the discrete Bayes filter and Gaussians we are prepared to implement a Kalman filter. We will do this exactly as we did the discrete Bayes filter - rather than starting with equations we will develop the code step by step based on reasoning about the problem. \n", "\n", - "\"One dimensional\" means that the filter only tracks one variable, such as position on the x-axis. In subsequent chapters we will learn a more general form of the filter that can track many variables simultaneously, such as position, velocity, and accelerations in x, y, and z. " + "\"One dimensional\" means that the filter only tracks one state variable, such as position on the x-axis. In subsequent chapters we will learn a more general multidimensional form of the filter that can track many state variables simultaneously, such as position, velocity, and acceleration. Recall that we used velocity in the g-h filter to get better estimates than by tracking position alone. The same is true for the Kalman filter.\n", + "\n", + "So why not just jump into the multidimensional form of the filter? To be honest, the math is difficult, and my intuitive approach to developing the filter starts to break down. This math obscures the rather simple principles that allow the Kalman filter to work.\n", + "\n", + "So, in this chapter we learn how to use Gaussians to implement a Bayesian filter. That's all the Kalman filter is - a Bayesian filter that uses Gaussians. In the next chapter we will switch to a multidimensional form and the full power of the Kalman filter will be unleashed!" ] }, { @@ -307,7 +314,7 @@ "data": { "image/png": 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VdC8Yx/U0L1xP6brVYeotwahSDwAymaxJj91IEATMmTMHe/fuxebNm9G1a9dG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\nREREREQS9/+MJ8pC4RMwSAAAAABJRU5ErkJggg==\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -316,7 +323,7 @@ ], "source": [ "import filterpy.stats as stats\n", - "stats.plot_gaussian_pdf(mean=10, variance=1, \n", + "stats.plot_gaussian_pdf(mean=10., variance=1., \n", " xlim=(4, 16), ylim=(0, .5));" ] }, @@ -338,14 +345,14 @@ "name": "stdout", "output_type": "stream", "text": [ - "Mean of readings is 9.865\n" + "Mean of readings is 9.949\n" ] }, { "data": { - "image/png": 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BNNGMXQERThXHnDqXzZaycIuClNdmBbrsBBpzzjGvYfxRGzoqSZfo7wALDh6V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\n247lNjXSz/pXXtKqUce8whBzu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+dO/MZv/MaluuzzsiLEfPfabtz/4VvwX752FH/09Wey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\n2WdfXx9WrlyJtrY2xGIxjB8/Hg888EBQl5SGEWzevHmsvr6e/fa3v2Xr1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oLLIFXRJE6VYzzfJWDakmIipliZabM0o1NeaNSN4TMuYk82idRtZEObyW5/EM\nehzoexLbJfuTla1vZBob9w7EXm9s2sKJsWJgWAX6ZWYcaEweL54cx9u+sgmvvmWD1jPMFgYmypHv\nmmWY/+/vbsFvfnoDHt83GHzXCFkQ7QON3s04NlrE7Y/sx6fvfzE1WTIbshpx3lC9D5l0ZbriYHAy\n2h5k0H02+soc18Pzh4bx8n9/CJ9bv0frfIZQyhLDmDvypGqtCGOYC2B2UC2OCDohexhUnbigYMyp\nsSBKWXQGr+mKjXu3H+MYNBXcGphP9plGN+AY8xRSFmrc942kDwu4s28MJ8b0z5sJZxAu6yJLqlRD\nuERm/Na6S8IYzLMWtlevoy9lkelxS5aD/gmf9bM1nT9rkbLwvgteU43nEWKYnrGgkPp823HxrnXP\n4OZ7X2hksSLQiWMuk6/Q72XSuVodi7myVSd2Ggq2XlnChOAfobuAqHBSFrlhztr0az77KN7zrefw\nxD61cd71ifX4rVseCXaOysK4r8OYb9Ygbyju33kCH/qh3m5sIyGrs0oN4fN08PBuP5oNdTRvxG4w\n7SeN1v9bdbDxlmROaDZ0GfOKU18d6+4aiVFZ9pyagOcBL55IF3I0YMxjfZv8/43z5xwEM4RqmfjT\nyAzSMuZ0cCnkshyjr9MJfvjcUXzoh9txxxMHE4/VzcYlM8xTa8wD9hjSY/uG0zHmvYNT+L++/CR+\n65ZHtM+Zia0tGWOupTEX/k6TNVQGZpifyaQsic6f0XdDJ5HrbtuIaz61ASfGitykFzf/1ZL5kzoT\n2a7b1HCJVF5QS+KPI8PTePrgEO7Z2txwnzpRWWQ7UTRykpwxr1/KUpQYkPUmERMdl3UXEPEa8yqh\nIBgoOoYzMyAZIx8mOZE3/ud6hwM2Pk3/dVwPH/z+Vty7/Th+ueOE9nmNgKzOmsWYS+/fAIO1whnP\njR046I5i2vcSJ/VsFsQ5RyXhUiUV0nUC1U4wJMwFrF+kXZBVgr6nPo/NT4Yxn4NgeuNadpmcFI1K\nNUmpTqVMSSGX5YwgHSnL0JS/BTU4mTzp0mePm0z5sHf+/6qoLBHG3GJSFnaeXAealjF/4dhYquOB\nmXH+lCXNoN+NTlfwnacORaKBiPr3YPFX40DOWMflTMqSwvmTgZ5zdNivn6cPDPFSlpjy1RJRyOHa\nVXMnMaqhr0UmFu5qNNeAKQvGr6wu+dBz0QWhjDHX2VVLgozZrZf9FKUrI5oLCGpMRDTm1T8rQpvS\nkRSyxQe7fjmGtXNcD3/y9afxnm89h+GpSqrdg+d6h4PPzQpvqYJsAZE2Qkc9qCW+vAgqZWp0n6TE\nRdqxgo5jM6VqEdudUsqieBbhSLKlAAAgAElEQVTdxYfuexalLLVKNYPdqpj7BuES54DVOweKOLNg\n3awWwydkf5PPVXUIFZNCV7CZDH8PnS200OEw+dh6GHPKAtgxGnOmUw4zf4a/0c6VVmOuEwdexExs\nbcn013SQ/LsfbMPNP+/BB763hTtPpTGvdeuTaX7PZFKWhOvIFi3sWWgc42ULCtoMEO+Jn1xmsZzN\ncOCiOEkN8xruxcra7O3piJRFxphLE38Rw7xJGvOSRO5QL/vJFpVMXjSmK2Uh2/IRKUv1FYq+FjqL\ndTGJUpzOlfplTJXtVIb5Ay+ELPlM+z/IFhm1ZIKsFQ2JytJExtx1ax+XODJqphhz4T66UVkYdBcf\nuotw0d/IrnF+Y+XyPHWbCcMltj5lbgxzAXVJWRx9iULgIZyRfy+Cbg27rsetsHUGBDdFg9dNXiTT\nCnOMuYIFB8LU32yg4AyIOjTmNMqEbh3OhJTF4dgR1k7C35+oOjxRdgyIxreVse268DwvkAMwKUuS\n4SmLFsDaG3UEas/neLmOUN+e5wWMZy1SlnITHbhEUClLxa49653tNlcLH8hRqm1exhZxCTwkbUcW\nlUWXiY5DsRItS6MY84uWLwQA3LfzhJaTWTxjLt/d0DPMGVPOpCzqMZay/ZlMOsPlVy+cDP7W1u66\nHt73nc3415/t1DpeeR1J+61lsVorGq4xJ+9vx6kyvr9jrC7jn76ftIw555PTTG0egXgfVXtSM+Z6\nizLdMVpkzF2JPaADK4G4oQkOT8twiRMTE7jppptw/fXXY8WKFchkMli7dm3kuCeffBLve9/78MpX\nvhLt7e3IZDI4dOhQA4rcXLDxuJbOGhiZGueyAWdxB+9cpjqXspO263ETiU4nSOM0qGs4JWrMJcYo\nw2TZ5rSuKm36UMpELzRBk+4EMluMuY7RFtWY806zaTBdcYLzmJQljfMnA6vXfhKxwXLc2Pr+8N07\n8LK167H96KiwoNN7DiqNaDZjzpxZGdIaB5zWvonzLStXe5X1TmLMZUnAZIx5IzI6ijIbQN5mPc/D\nk/sGMZQQ7cFy3MAQ/uC1l6Itl8VDu07hq48lh6mrxEjqVFIW1ZhAz0/DmFPHVcvxtNv9eMmO9DMd\nHB8r4uHd/fifZ4/UtTiUtamZlLI0InJJReH8+YknRvHjngncveVozdemzSntgoUe3+y8KQziWKZ0\n/pwxKQtva7DipH0ffB1LxkHy3WnJmA8NDWHdunUol8t4+9vfrjxuw4YNePjhh7F69Wr89m//dl2F\nnEmEGvMaDPMUjcoJDPM8973reXj6wBA2H+KZU7o17DtJhL/pDAihU0VKKUucJIFcKohjrli5MgOB\nLXwsx0PZdnl2XlLGtExCgTBdKgcWETPCmEskBTqsQFRjzl8jDZjjZyGXCRaESanIZe9Gxphbjscz\n5sJl797SBwD42mP7uTalazOUbH5h2kyIfhjpt6jpIrN5RgzrG+2FHACFxlzW7kgfbZPQR41w7pM5\nf8rexc+7j+Pd33wW1932eOz1qGH7ul9bgX+6/nIAwNYjyU6aHGMekbL4f4tSFtWYQM8PEwu5XHZJ\nWW4AWn5bWMTGQTSqdVlZtmhwvfoYbmlUlgYujE+OlWIXDo0wWCnLK2OIXzyZLgIIRT1hi3WjWDUS\ntcYxZ9CWstSUYChdYITwGh6fREryTHRMPi015hdeeCFGRkawceNG3HLLLcrjPvaxj+HQoUP46U9/\nire85S11FXImEUpZ0p8bsJkaJ7OGt0RgzKcrDv7y28/hvd/ezDWwEg075njcPdJozFNLWbQ15uw+\ncj1f8Lyd4fOKWkvZjkNaOUCW85LXY/5moqPKEwzJn4u+c1FKkqaNiWDGwaL2fKDFT3KukrELrF6p\nYe4bG8ka80Iuy3viaw7AdJHV7Pi/I8IuTT0TbjOYsL6RaX+Holp3HYUqYy6RD9FqkGnM85LGX6+G\n2C9bPGvF8PDufgCIOD2LYFKQBW055HNZrFzSrrymiHIMM8n+tByX63cq50/V/cq2SyJDyBjzUMpi\nOZ6Wrw8tX3iurmEeHlfPQksalaVBjPk3Hj+IV9+yAV96ZL/ymEZowvk45tGyT9WR6ZaTsqRdwM8C\nYy6Oy0opiyIsp7aURfN5oox5esM8ugsQPZfe57SUsmQyGa0QYtmZSmXVYARSlhkKlygy5lMVB2Xb\nxWTZ5hqYyJg7CgM46X5aEWNc+WcRMjZOlfmT/V7IZbGgzWf4Jsu2/BqOfPLUAZ1cdSeQmZCy8NlU\n/XKpjFe+jjLS32ohYtkE1ZbPBgZZ0kJNZqAwg5AmH6k4rvCM8uu25bINkLI0dxIbFjTWaSdclSyr\nEXjm4BBe89lH8e47ng3eYyhl4cup0lOzd57PZqRa6noTlqlibcvehU70EyB0nlzY7o+Xuaxe+wV4\nI0Nsb+x0y3G5elYy5jGGeRguMZ4xtxxXe34Ry6vbFumORT2xz6VRWRrk/Pmp+3cDAG59aK/ymMYw\n5vEyh6lyHe+nDo251cRxQoV6GfNGh8rk5gK3NsNcfO+ynTn6fueClCWffMjsoKenB26Tw42JsCwr\ncLY7duw4ursnU53PEi8cPnIU3e3xW6wWG9wqfNSR8Ymp4PP2HTuwoMqGvXgkPK6/fwB79obHDY+O\nobu7O/Z+A4O+NGZE49ixsTDkYP/AgPL40WI4oB052ofuzlHsGQiNtYGh4eDcA8O+sePaNtpzHqYB\nbN2xC6VKaAR179iBjnwWA0O8jGfb9m7taCv7ToT64B09uzC8JDlBTKkYOphalpX4fmoFu27F8ifp\nsfFJ6b22k+9Ghoe4Y/oH/XZVLJdTl3PPoF83nmPj0EGfpZoqxV+nXIqmDD/Qexjd3gD2kFjPB3sP\nY2AoPPbQocPoRjRJy/jYCI4cDdvuyMio1nNMFcN2tetFPitcPfVlWVbwP7vOgJCcqntnD1Yu1B8q\n9x0P30P3jp1Y0p6ruXwivrxpCADwbO8wzl7oX9ez/T7Ud/wEurvDcUJcwExNFdHd3Y2BKb/9ZTMe\nBgeidTQ4kjxGxIGOCxSHDx9Bd4Hv2+OjYRuKuydruxnXRnd3N/qq4+HYxERiWQ8fHQ8+HzjYi7PK\nvjOlZVmBgTxdKmNb947guJPH+tDdPQoRUxKnVgDY1r0zMBDGJqL9eveBcC7ZvWcvTpwM28i27duV\nxsKw8C6PHjuB7u4p6bEUu8g4uH1HD85eVNtUP036P3umYsWOfFcvlHPMeHL9JmF/b/i++qrvj/V7\nADgxOFzzPQ6OhPPXnr370TnRp33uvmPhOHP8uF691gs6PwPA3v0HsLR4HIC/w3ZwxML5S/LoPSwv\ny/7ew+jODEp/UyHu3R4/HvbN/QcP4viQ/z6npqe162SizPfJnS/sQr/Q3sfLVHFgIZfJNHWup8hm\ns1i9enWqc1rWMLdtG06d2adqARsgbcfhOq8OguyXdvK5bEIQCHM+q2LZQqG6qTFd5hkXZtyxv5Pu\nR7PSJR3LO5aqn6VCWczqM5fJoF0h74GVN5vx0J7LYAT+9i5dGZcqFnJeFpZQ7+WKBeT1DPOKTcKS\nlSxYncnnZEiCd89Lfj8UYyUXH310GL93YQf+5KpFscey6zJ7yXXl9VaqkNTjwjF29d24LlK3z3K1\nDnIZ3zgHfFlU3HXou2GoWDYsy8JwMXzXZdvm2q5l29Lr5uDBFuIK6zxHmRiZZeH4tO9BBcvy2+Ok\nYHyVyhasNn0Gp0z6ZqlioTPbOIKBskPBLlQ2/I2+i7LgP+C4HtdHs8jwjiLBeXp1ooKKgaxIx0Ui\nyYu5Z6la5ny2epzr38PWGM+43RaLb5dBuETHw3SZfi9/B6pduMlSJZTFSM6ljHmpYofEDPzxTbVz\nUBHY7ooVP7e4noeBKQfTFRqe0YLVXhsjy+UPYItYR6/O0kB1HVtjbktCSTEnMUxXar8HnYeLFfmY\np0KZm8PT2xsifvDCJDYfL+PfX3cGFhbkigVaXlYGdt8nj5bwhWfHcMkZebz6vA7p+aWUzwjEtxHb\noTaEHcwNtqs/DxeF8aZUsWBZwk4TGdPpm2lU+41DLpeemGlZwzyfz8+4HMayrDB8YTaHQiFdOm42\nhmWy2cRz2bGL2/kqoHNpNpdHoerYZYOsdDNZZEhlO14muazVBYcHJB7rEflEJqN+lpxF6qd6XCYb\ndhIP4bmZnN8xctlMdRfAQcXLwvMyYJNzLldAoZCFJyissvk8CoqBRkQ2Fw48nmYd5gkbb3vAgrbk\nc/YOVbB7oIxzFudxcsrBs8cq+POu+PNYWVjde5DXWy4ffpfL8e+fvRsXyfUYQbVu8tkMOtv9c23P\ni72OTOrgVet6rEwWNJkcPML6ZRTvvi2fQyZLBqqMRtsFHzUjk+X7TOr3QEAH5kKhgOmSE5iKi9oy\nmKx4QC6f7h7ZsA36fbhxw6xL+iabapiU5cSki2NTwEXLqo69cIVz/WfMVF9/LivXmNtufe/UUayh\nZW2ChmuMu6dXbbuF6tjaVvDfsc545pDxJJMLy+Az5v73tsu3q6xiDM8pyCLLC9u0KxmPS+S0TDYH\nZMIy5fIF5Y5grsJ/7yrGDIbv7xjDj3sm8LurQ0bCzUTf+7Tl4qmjRVxzXkfsjg5tb+wadCOmnnaS\nz/rvHfDne9X967mHf40s+exfj/b7ol37c+RyZAzUmPcpvAwxCmPmWV1s6ivh5KSDw+MeulbJr5XJ\n8e3XI23j0UP+DtGBERvXnCefbx2kL2fc8XQuyGbzQMYvn2pulELoIxnJeJ2pLnCzGT43SL3vXAe1\n2LEta5ivWbNmxg3z7u7uoAuvWHk2urouT3W++0N/G2vVOeeiq+ti5XGe58H9gX/sxeevAvaGzi+5\nfBsAf4vr8iuvxDlL/QF28/hBAH7HWXbGGbjoJecCj/pbSm0dnejq6oot2+KerQCKaO9ckHjsws3P\nANWFwLIzz0JX18ukxx0fLQL3+skvVq46B11dl2C4ox94zC/XwsWLg3tVDg0DDw1gQUcHVi7twP7h\nIaw49wIgOwZmYlx51VU4a1E7FnU/H7wD//s1WLagLbbMDAOFUwD87f4LLroYXZcsTzxn8bPPAP3+\nOdlcPvH9AMDbPnIfAOCGl60CAOQKbfLzfhBubbLfvR/7qdo7FpC6IMddceVVAPztxRXLl6Or66XB\nb0t2bQMwDWSyWuWkGNs7AGAQixYuwEuvuhK47xQ8xF9n0aZNwDC/pb/q3PPQ1XURiusfBeBvPZ69\n6lwsnBwE4G99n3fBBejquiA8qfp8565aiVVLO4At/jUXL16a+ByO68Em7+fCl1wMEJlM2vdA0d3d\nDcuyUCgU0NXVhf39EwBOYGlnAZ2FHCYrJbzkksvw0vOWal+zL3MCrA1e/mtX4oIzF9RcPhEdm58F\ne8fZXB5ABcvPWAqc6sfTfUVsPVnG5n99I5Z0FPwMnncfD84ttLWjq6sLC/sngPtOoa2Qx7nnrAJ6\n+KgUubaOut5ptm8MwKnI92efcy66ul7Cf3foBWC/v21O7zk4WcbSzkJguA+39wMYxJJFfp8Z6egH\nHh/SGvuWHdkFwH/GC1ZfiK6rzwXg1z3bufQyWVx6+RUA/PHsnPPOR1fXhZFr9U+UgJ+eiHx/zoUX\nA/AdWfPV90zRcXAnAF/Osvqil+BguT/4e81LX4oFbfKp+OjwNPDzMI75srOWo6trjfJZ/2vnFgAT\n6JsO587VL7kEXRedyR33zSd78aVnj+OD116Cm37/CuX1sr8cAOAbNbKxqp520nbPCdjVoAZXvfRq\nAMcix7Rr1G8SNo3sB+DLM884awW6uq7iJAxOVm/Ml8E5MgKs9+v93PNXo6vrPO1zD7p9AHxp14qV\nK9HVpa4HHXj3+XV13uqL0HXl2dJjxvf5cwDDuedfgK6u8wEAC597BjhVnfeXrwAwHjl/+dmr0NV1\naXJhNNvIowN7gZ3+fS5YfSEGMQJgErnqeKyD3sEpAGEfufjSy7DmXH68ZrZKvrp4omN+s+G6LiYm\n0kX+mZsemk1E2gRDY0ULH/rhNjy2pz9gQpMcF+jvYhxzPuxPeJwYx5zPOKbh0Jkm+ZFLP6uP5x03\nXe4+AM9ysmfJZjNYVN0lmCzbfMpwSZxl2d9xkIUzSwLHmKdUHeyphtpK4xQTOnDKnysuwVOYJCZN\nKX0wqUkhlwmY0qS2ExuVRYxjrojmQ5+nUIPzp+hs1sw45kPVUIlnLmwLYnzrONxtOTyMB3b6BhuX\n0a/BTl2y2McdZDepbLs4Meob7pGY3YKDdi6blTo+y5zYTo2XuOyVcZCFSvTvH72uzMlyf/8kXvXJ\nh/HHX3sq+K5MHJcBIF8lbbSislDHeTEqS7VIFceNzRAqHi9CDIcY93tF6CtxzyAWI6nts3dP48LL\nnD+Hp8rV/+Oj4YhlE+fFehLjUPmO6rka0ddVccwZ6orKUke4RD5qWc1FCMD6SFyYYLE+VSEbmWRL\n3MnRCaiQJooaFzXKC6PNpXEvjDh/yvI5BGNe6zt+AsYwjyBtHPP/fPBF3Lv9OP7y25uD75IMSWo8\nilFZ6EBEr0OjsrguHzNaZ/Bi99Qy4nXjmJOfwgRG8tBUNBJEYJiXbMGY468VlCfF4M9HZdHzUaBb\nW1oJmMgxbXl/K043UoHrhiHsVJEZ+Hjg8ndRi8HH6r6Qy2qHS5TVv+24mK7YmBKTXkni1gP8uxHD\nJeoY5uJE08zMnyzr5ZkL28J3lDDhuq6Hd3ztadz4/a04OjzNla/R0RZk40NHnpcisGcQ25cY9SiX\nlRvG4iKzf6KE3/z0Brzi3x/SKmO9UVl+3u2z/N19oRM6XVT6Zc8orymCTtyxUVmIjlCZ1lvRXieJ\nPl02xtJwibbj8YtvzchXQHLeAUbgjFNNu8SYYm0gaT4Q34N4rXpSydPkVqo5rNFRWWTPW19UlvCz\nagHvuh6++PA+PLSL30VqdBxzZjTHReGJi/JDn4WN2aIhq0NApRnzuLmARGVJk/9BbDu266JvZBp3\nPHEw6HdzzTCvScrywAMPYGpqKqDnd+3ahbvvvhsAcMMNN2DBggUYGBjAxo0bAQA7d+4MzluxYgVW\nrFiB1772tY0of8PBbDTdAefIcDRlfBKLQAcbGtcb4I0AyjDRFNeOJzjl6BjmKQw6GYstPS4xXGLU\nQMlmMlhUXYxMieESgzjmYkdrLmPOx9VOPn60SHTJVUNBdi+ROaAphwH1hOzEGOZJMdDjwAa7fDaD\nQpVx9KptSTVgydqy7XoBs8xQsQXGnJxGJ/N8LiONfx8HcaJpZtKe4Sm/bs9Y0BYwaUmM+bHRcAyY\nqgix+ZtomIcJhnh+ZXTafwax7YjJO/LZLFfvnYUcipYTWWRuPexHTkmb3EaE43iwHBfv+87zeMny\nhVj71jVB2EOKQkwIR7YQZrtceow5HVPD713PC/wJPI9n+tl1b7q7G2XbxRf+168jk8kox/ZJyphL\n2ueE8Lssf4MM0bjT8XVQktSRrD5kRIr0/sLzUqdSwH9PhRqDDrVpZGlWZYvVCdkcXDshjrns3o7r\n4VP37carLjoDN7zsHOW1dRIM3bO1D7c97IeEPPSZMKdLI3fWPM8LyDvVjpV/H/5v2p48ydwpNk2d\nMSDNzgF9bIcLl6h9icjcazke3vblTRiaqqBvpIi1b11DdglPY8P8xhtvxOHDh4O/77rrLtx1110A\ngN7eXlx00UXo6enBO9/5Tu68D37wgwCA1772tXjsscdqLHJzkTbBkGx7NpExp4a5IGXhPN6plIWb\nNFxuwE5i9Og9kxhSgJ8o4t4DfUyZwUjvxQb4fC5kzCeEBENBFj6B1XBSMKT0erpxzGXMPy2TyCqy\nbWAgZKhkhrnYDCq2Czqf6MQxF6urngRDNmXMBbYql5XPrrK2bDluRNZgiQmG6G6PMFFwUpaUhpV/\nr5lgzAsYmGByn/h2tK8/1A96XnMzf1LGlN2nXWDMR6vPIN466KNeOEnRpr2wPe8b5kK/SWszqAwD\n2/Wwcc8ANu71//mGefQ42jYZWB20RRjzdIYCbW/ic1Gj03E9lG0HP37e18r+/RsuwyUrFikNqAku\nalY8Y14hMc/ZvVRIG8ecJqILvpMZ5jEx17njhLKJdVsP08uPQfLriPPVx3/Rg4d2ncJ9f/e7WLpA\nz3GvXEPW4J9tO4ZvberFtzb1csa0CGrMqsaJB3ui/hb+8Y1bwFtOuBMbx5hHSC9H3h9UxrXOzrB4\nbtxCSiTmQvKgDsbc8TBUlWg9f3i4ej1GRpzGhvmhQ4cSj7n22mtTaY1aBUGCIc2OIhvYkgYrXmPO\nV4FMQwrwsgxHkLJUdOQpaRhzYRWrPk7CmEt05QDPmC8kUpYk497/3pUayEll0pWXqBLClCwHb/rC\n41hz7hJ89c9fGXxPU7azNPcsLTcvi+EHjLLtcFEoZO82k9FnzFMzR9W2lc9lIvrODgXtJSuj5bgS\nFpvfnneE98jgup7W4oRiJhlzthNwxsK2oK6SGKA9J8MY1baQ1bFRjPnXNx7Axr0DQXuj1xYZ85Fp\nFpYzusik5+WzGc6HYGF7DoOTfKbMWp5BtSB2XA+HhsL4yJ7ncYw527lpk1jrgWEeaMyrjLlOgiEq\nA4zZHaNaY8fzOMOpf7zsG+aK9iomEIr73XY95TgvQvxJdm3H9fD//mg7rj5vqXRRJCMNWHKbpEUn\nJ2t0Pc7XKansSaBjoYpcEuv325sOAQC++8wh/O3rL9O6T4WTssjvU7FdTlpzYEAvhwl9P6pxYtsR\neU6TRmb+pG1cZpgXKw7e99+bMS3UHy9lic6d4vRC29LN976AAwNT+M5fXcMx0eLi0fOi1wnvSY+j\nUhb99yHWKV3MLV/EZwjWsSFaAUZjLoBVm25HkR2XzvlTvTaiDU7cZqXMj46hosqqKYOulIUuvNh1\naVlkrFA+mwmemRoZXBmF9/ezbcdw9cfX4/G90WQoImgfjXOCoeBX7eH3Tx8cwuGhady/8yR3PHWY\nohOuOAGK7aAsyD1k7zabycQ6f6aVgVBwjHkuma0C5G3ZdrzIu/VZQPmCgh7rCGniazHMZ4QxX0Cd\nP+Pvt+9UyJhbrqvc9aoH//30YTx1YAgnxsKEL2EuBBVjzt87cK4mjth0Ql1YjQzCFpnBeSkbWhxj\nTstvOZ7UAZAyqczYYX2Ltds0GnNOyiKRzjFQrbHr8j4Tg1VnSi0pi0bmT07PnkrKEj12z8kJ/KL7\nOL628YD03ccy5gnvj59nvIhhV88amR+D5BdSlY++zyRwmT8V/VGci8S/VUiSsliOG7C3st+C6wj1\n/PyhYVx/20Z88eF9WgQTfUbZvLf96Cg27R/CtiN8hC0VY86ud+NrL+VCOrNntBwX33n6MJ7cP4ie\n46EvCD1G9WwUooyUvZI0TsXi/SgxIBrmc4UxN4a5AMYg6bL9soFD1zDPZsIU03HHAfzgSrVYQDop\nSxojHoh/D3QsZSyhLQzk4jVpVBamhWVwA8OBL+Ptj+zHZNnGX3zrucSyc86fmoy5SsqygLDI9P3T\niAd0ohKZAnESLVsuv5UuaSfZDF9HEcY8Yfvz0T39+Oef7IgwW0B43UIuw8kYZLrLuHtYjidlsVVM\nv+i4zL8D5a3D82fQ+ZMtus4kjHlS/9pDDHPRsa9RjLnMUGCvOMqYV6T3DiP6hJMUZ5iTeNa8Ljvd\nMyg15q7rhy1jx9mOlGlrJwYbMzSp47JfdnlUFs/z8IHvbsFff/f5YOyqTcrC99+BagQitfOnWmPu\nuB73u+XwjHmcEaKTQn2qWu7Jsi2VssgY89D5M75ti2O4aJjX5fxJIn6o/IGUhnmKSCqyqCzivDZe\n5PuXruFPLyNbwO8+EYYcXBIJ9KCeC9bvOoW9pyZx28N78Q8/2p5YDtrnZP1P1SeVGvPqmPuSFQux\n9d+uwyff7ofsZXMqi/wEILLbKtZlHPmikrLUw5hTn5+lnSz2PrO55oZh3rJxzGcLgZRFc8CphTFn\njS6fzWJBm9pzRqkx9/jy6bBybEDSYswFtszzPPxixwlcfd5SXLR8ofQ4qcZcwgjks6GUZbwUdSQS\nr5EWtTh/OtxzhN+3kwFnZLoSxJRXMSBlywVIwrQoY+6g06WJSKLXiDLmcuNK9hsAvLcaHWjF4g78\n43V8HH7WTphRU8hlUbbdWN2qbIC03aiUxbI9bguR37mgbddDNm1UFju6CGgW+KgsyeESHdfD/n4q\nZXHRaI25Kxh2IqJRWeKlLNQRipeyhNNB2Q7lTWmNL3W4RKBvJJw0y5bL3V+2ACpWHCztLBDnz3jG\nfKri4Fc9/g7XZNnG4o6CcpEh9s/JMt9Oad2dGi9Jz2HgGXFeZibWne24qMSEcKQQX71sTGOL8Irt\nShfZMqOMSVnSLHIdz0NRyBxZT/suSBZgIlSkQZoQh7KoLOIrF+ciXcM8iTFnjtMAIjmU45w/aZvZ\neYxnpGWgzyh7l6r3++VH96NsO/joW66SSlna8/7uKktixu5zdGQ6fA6hDUU15upy08em0ebS+C6I\nfeIIkcux9sOIw7wikVerwTDmAkKNufx3caUtZcw1NebZLJSJJehxAFCkcgCBnaw4biLDH2a4S2uY\nA/fvPIm//8E2XPu5x2KOYwwMMUo4dtcvfy6bCbbGRJaiFn2ZCE6Xr2mYy54D4CcFyu6LEUnC+8Ub\nkGXbVd6LIZvJKKOb+NeU70iIODQ4FfmOLZTY4MQmxrjJWcmYi7HFYxjzssUb7NxgrDEAi2Ev08YL\nTgPGmC9b0BZMRnGs4tHhaa6dVRy34RrzqYodO7mJjJVKymK7Hu544iB+/PxRAFHGfEFbLtCC0ndM\nxxadnUSVhMx2Xa5div2lUvVdoO2asdih86egMRcZZYkRRp+FNnWx2VPG3JeyhAcwCY46jrl8LJP9\nZjm83KneqCzU6JI1t3gpi7ptR6RQTvOkLOI7YlCNcbohDkuWI2XMI4Z5hDHXlLJQjbkkK+wwmTci\n/TGmDdAdz7Hp5LLQMYDdm4UAACAASURBVFbW/2Q7qAzfeKK3Wr7wu2D3qjoGMpKKvcs+YpiLfVAk\nMtL4qYnkgQ5EYvLIcFg2tovBiiTL29CKMIa5gLgEQy8cG8M1n96AHz53JPhO5j2sK2Vh4co6FOnm\n6aApOn+qtqnV93S1jhOP8TwPWw7LnVdkEhD6PniNuf9/LhuGSxwr6klZ0oDWW5x3On/f8LNF/qAd\nnhrmqqQcaTXmMqM0m0Gs3CXJsGeQGa+2aNywON0ppSy243LhO/1r8IaMKiqL63m8rlBj/BUnmmZq\nzJnhsbgjH4TCjFsIiLsntsM7DTYijnkSeyeOHyrGvGy7+OR9u3HfDj8RUjab4SaqfJYyY3S8Afms\nY5jL+92p8RInQShZ/EL1H3/Ujav+7Vc4SBzvWH2wyT7KmIttgyySAn06L6VSPQsvR/G4a52sGuY6\nUhZ2PoNYf5bjKeU1InSkLHFGFyA31FgbjetLooFlu25DpSx0Uahq42rDPJnR3rR/EGtufhBP7g8z\nXYaMOX9dcS4aL+pKWeIZ8yJd7AmPEidloc83ISTik6GU5PypMRe6kmdhcwX7P2DMSZhoMXKO+B50\nc6G4xPnT8/R15mKfOEwNc5tfgM6VcInGMBcQl2Doud5hDEyU8WBP6AxYk8Y80Dv5fy9UsOZc5k8u\nsoWeUxBfJnZcstFLi+94XiT7V3hcdJJTa8yrHYNGZSnLpSwNY8x1nT+5cobf03c1VgwNsEGiMaeo\n2C72nJzAH3/tKTy1fzDCRJdtJ9YwAGSMuZpliRu4ZPUcSFkExjyu7ajCJUalLC6/NavQmDsuH8td\nh4EVmVXdBVctYAvg9nxWK/OnLIIQJ5dowCIiyTCPhkvkk2qokM9muCgF+VwmMgEDfF3qdE1V/ezr\n5yNdiP3h6YNDcD3gjid7g+/YuMcmWDYWqeKYVySGeUXyLKPTFZSFupku8wtI2vZPjBel92MQDUXa\n/8T6s11XWiYZIsacJMFQktElj2OeTNTIiIZI6NMGjdWilER2DMVUJdlw/sB3t0T7J5M2iIx5qUbG\nnJsvomWlCxmxnvnxUn2e5wGTCc/LM+b6GvPwHp6UaGMZopkfCxuL00hZdBNoOa7HvSPdRZ94vyND\nYdlYP2TtwBjmcxSMQJKNB2zQpyyZbODQDZfIGr0qHiudGIpclkU32hmSwl7VyJi7nlqX5Uo6MjVE\nZFkKqZQlej3Guqcf7B958RTe953n0U/SxGtn41RJWciIosuYP9hzEs8fHsFPtx2riTFPCpeoCu0o\nQtYewgRDVY25RixoWRktNyplEdskLRoXlcX1UktZRMZPNBgaGZaVJWhpz+eI82fcwkWyc6BZR7pI\nMhLEdj46XeEmWln4QcDvi/SnQjYbbFlz8iNFSDUVmBHQKUhsDg7w8ipf2hV/LTbuhZk/4zXm1Dhi\nfUDUmA9MlPHrn3gIf3MfH196SohjTif8U2Nl33FZlzEn5Xjx5Dj3m+j8Ga8xT2bMRRZbhCzpUCg9\nVPd9WXSNCGNOyr750DDneJcEzjAvyts483ESj9dhzGUOoqGGmf9eZMhVC4VI+ZIYc0u+WwPIk4Ux\niAsP1fth4MIlSua9pF2ViiOXWbJ+xnbSQilLWM/iDrco6dFnzNU7Wv0TJWU/iWb+jNaJMcznOLKB\nYR5tBKySqcZYps9NcqgRG8nH3nIV3njl2dHrkEm/JDh/ps0IF2Z68xINGT47pRcYcrTs4nHM8KdS\nEBm7myPOn5EyOmEZ0+Kv7nweD+8+ha8+diD4Tl9jHn6mNiAnZSEDo9r50wnqadpyohpzi9cfyx4z\nl43XmPPspT7bBdDIFlXGXENDLZMV2Y4bRH9gEXYqgkEaJ2XRyX5KIbI9cQmL6oHthGx3RyFLnD/j\nEnbIGPOoprUeJDHm4ja87frOoqxsqh0v0fkzl8uEEzDnuB2eo7NoZsbI0s74BDBly01kxaYrPGPO\ndjFo5lra1uRSFl4v/+R+edhVjt10xVwRLoanK8rnFw05ur3PwryyV+2HS6RGmfSS/m/C7WQL7iQ2\ntGQ58DwPzx8aDkgF9p7SLO5tica8f6KMR/f044VjY3jnfz2N3/nMI7FloaB1H9fGWRlp3SZpzFVM\nvq6UhS604nYFZNkyKYoxjDkveePPnRaej5WvbDtY+/Me3FX1E5HdW2aEy4x18XwumEMQKIA3zEMp\nC2GlRQJKIFJ0fSjEXSrW17YcHsE1n9qAG7+3RVl2FUTG3IRLnKOISzDEKnlwsixdxTPoOn8yfefr\nrliJf7r+cuVxgMg6upH7JhnmSRKKuGPpxE5X8rI45iqjhDLmqkg0YZxlxlrW1zy1DXP6vJJnAvgQ\ndOyz7H7snqWKE5n0yrYj1evS9+hHZVEzKbqh+FQxdQEaco5pzNXXkWvMvYCFYzHpbYePCMFJWQTG\nXNQVJiHKmDcu+yB3H/LO2vM54vwZw5g7Yj/kNeaNcP6Mi6mcz2a4SElMbz46bQV10KboR7lsljPM\nC9nQMKc+LbxPgH59JRnmJdtJJAlYFBDR+TNHxiTaz+g4yD5zshFXLXHjjDHPiyxKT46VlEaa2N9Y\nuyjbDp46MAQAeMMVZwe/UaM3bvGmM85PJ8gcSpaDpw8M4Y//62m85fYnuPLF+fNEGHPX4zTTAPDR\nn+7Ee7+9GV9//GBsGWSIc5CVHUfrOYkxp4msKNjzitXIJZcSx9yYNqqKQsYgSlL4OZNvl1x5Ioy5\n//dXHtmPO586hA/fvYP7nQ+XKFsg8N+95tLleNc1q4O/y5YrSFmq0tPAMA930kqWw+1MRxlzQcqi\nKdUSZY6svr++0Sfb1u8Kd7h0Mq7SsoQBN4xhPieRqaYYimPMy7aLqWqHkzEOSbo7aqQyyOJr0qgC\nFaETi/dNk1o5iZEWWVn6KmgiDbFTiddmYcPo77lsBpmMPLsfm5/CVOP1NU9950/6bkA+h38wz/ix\noqWMkFGx3cBoLFqORGPO67DFTIwAkMlkuEE6mvlTbwtc7vxZZQ1yYbhEIMH5UyVlsXjG3HLUMp0I\nY54g5xEhGuIRRqZBlDk1RlmYMCDe+VPWD/nIPvWXLY5NzGUzuPbyFfiPd1yN+/7+NVjW2QbAX0iy\n91xQSFnEqCz5XBZtbAJWhBjU0RSz+l7SGR+Ntyw4f8qgcv6kzJcjjDkMFcfPG1ARFoyqBftUxPmT\nL9uJsZK27pX1qS2HRjBdcbBicTu6zl8a/MYx5rFb/f5vIdsePVY0ukSULReP7xsMnsHzPJL5U31v\nsd85nhdpi8wpNklqIYOOxtwvY5XdJ/U4WbFjF3UvHB+Xfh8GKeC/p4sykT2PG1+SwiWK7DW/O6se\nB1lbDCKYlSyULAfrnggXQHRc5RIMyaQswly4ckk7bvmjl3HO3jIpC5Ox0p00Ua4UJaAEwzymeYqJ\nzGRjjbhI2bh3AC//94fwqxd8Xz8dOZZhzOc44qQstMENTzIGVWIAJRm+EsNcNneya4tsgpikBUjW\nmIsZ3J4+MIR//NF2qV5aNAzpc08ptvgCqYww0Ivxzdkzy1g8RzDi2yVp4tMYYbWES5Tp04BQYx5n\n7JdtN2AripYj1ZjT5sKel06O2QzfpiJSFk02Nk5jzrTltYZL9KOyhNFL2DOoDLio82d4LZ3qFAde\nceJplMSctZe2XBbZbEbT+VPUN7rS7di0eGjXKfzRVzehd3Aq0TDPZDL4k9+4AGvOXYplVX+VkWmL\nSFnUGnNKCOSJlKUe5092bqKURdhBkiGM0c0/Cx07VdmGRUID8NulyveEspt+TGX+XFmfVoH16Xu2\nHgMA/O5ly4l0jI/4EvcO2O1YrHpprHcrwTHQdrBycXvw96nxsla4RBljLu7esLpWLZTikJYxp3Xp\neVFdP4WYjZKBvXdxfqf3F+fEOMOPXkY2TogGsSocr/jOGPG3aqmfGGOsaOGXO05wbHj/OPWnCr8/\nNVbCX3zrOU7uIs5bbLee9ndahDDXCj9fly0n8n4SnT9TSFlkPlSTgqznPd96DqPTFj5QlbbEEScB\nYx4E3DCG+ZxEnJSFdrzBKb9TSBlzXedPTcZcZBNsN6rNTJPBzXZcfPPJg/jJtmPYsPtU5FhPmIhp\np54oxzPmUS/46vfVa7IBQaZ7DWKYVs+RhZHU8cZn0Hf+DD+rnCtHq1FZ4oz9su0EvxclUpaKGLmE\nsVbku6SoLLpe67LBihk3IWNeDQcYpzFXSLpCKUshuJ9KGx+NY56OgRVZPXGrtmFSFhKRBYBW5k+x\nbP4CJSrhSov3//fz2HpkFJ/85a5Yo0V0Zjpjgc+Yj05XkqUsGZ4xLyjCJSZlmxXB+sCSjiTDPDn/\ngsr5U+X3Quuq4riR/up4npaUxXG9iMEhkxCqYLsudvaN4Sfb+gAA7371hUQ6JkRliWNkPUZSqBeJ\nOuES6Xl7T00QKYv+GGI7UcacXZe2I53QfICe8yegJn1etnY9/vPBF6Xn7D05If2eXUN85fS5RKmi\nTv0A8jFXlBnJdNzi97R9nLPMT2o3XrRwYICPanRqIsy+SXf7pioOHt87wMldxDYSMOHE2ZtjzIVk\ndO1kJ03sP+LiTragUyFOysI+q2RL2ZhdJIaIxtwkGJqbCBnz6G900B+alKe9Vn0n+z2bYJiz4yKM\nuSfRHsZEjhDLZLuhE49sEOWMP5dnzKmUhdPLscyiYpQKFg1GCNUnZcwDOUzIXIqYlLCHqvetHS5R\nkLJ4nof+iZI0wVCcse8PWlTK4gq/84wbu60dYcxjDHNNNla2UAsY8yDknP9+nz4whBck2eVc15Oy\n0ZYTSlkYYy6y2Lx/RIzzp4ZRzZ6FGY0i+yNboOw9NYF7tx9LFbGFtXM2WeksXGTh2GSJteJQsV0u\ndjf3m+MmMuYUC9v9sk9XnGB3RhmVJcdHZcnnMpFEIoAQPSKF9GhxR5KUxUm83rTlcIYKGzfoY4tO\nmsFn242yd65ayjJNDXPPi/QhUaYUB9vxcOtDe+B5wNt+/Vy8YvUZ4Q6MRnQm8be4ZFfJUVkcbtzc\ne2oiGJdTRWVxPS3JyrRmVk5t58+YRcRXHj0Q+Q7wdwWk11IkGKKLshGREdaUsujEmOcMcMVYTuvz\nnCU+Yz5esoPsswxMRgSoCSMmOxHneWZvdJAwiDL2X4zK4tsO0bj8FOJ4GdfFucWAijFXtA2WiTuO\nLBOlLIYxn6NgFSdj8miDG5pUM+a6hnmek7JEG8zxsSJuXb8He4TVv6jFAqJB/iP3FFbqrDHLVvmi\nYUiN0ak6GfNswJjLpSwukTqI8ZkB+falikVP8kRnEKUsn/nVi7jmUxsCpy2AeMXHGPsVO2SSixWJ\nlMUSYlwLzq6An7aZj2bD30NXJhGnMS8IjPmdTx3C//3NZyNGrIqRt12XGOY+K1qKmYC4iEIRVkT5\nCJFyM6fhSLhESZV8+O4d+NAPt2PXCbnWVIbAMGfZ7nSi1oj9UNDa6zDmf/eDrXj95zfi4apzE62H\nFYvaYxlzUTPZRsoc7FIpdJV5QcoiS70NCBFadBjzah9ZkihlcROlLF977ACuXrs+SEveVm2zmUxG\nmv2TGgmW40YW0o4bjcXNMBWRskQXxbq7MxXHxfOH/MRs7//diwGE7KM4XumES2TZXWWkjE4cczpu\n7jlJGPOYe5eFynE8T6kFp30kaaHAQOfYOAdnZkwnzXEUzDnxorMWCOVkjDn/3JxhnoIxT0owNB0j\nZbEUuybM8C3kMjhrkb8DNl60OOkKAM5QF7MjM2zuHQYQbSMRp04hKgvr8zIiLRIFSnT+rDXBkKvQ\nmCscc89e4suzWNuT2dyW0M6NxnyOglWuzCihDY6FzKuJMZfonWTewl/feBC3P7I/2JJizJfjelEp\nS4KemmqTbTecsGSrTdE5j0oHJoTIBeE1/c/i6tkWt5JiNObiZCiTssgMc9WKWj/BUPjZccNt0B7i\nQMQG60QpC2PMpVFZBMM8kLLw7zEuJGKcxjxpkrCEwZYujkamrcTMpUEZCWO+pMqKigM/b5jzemWV\ndEgFNiGzuNg6jDljvVQx52UIpCwFXspSidmNEhlxUWuv4/z5YI9vkH/p0f0AwsydAHDWorZYLa3I\nALURh1UaolRmnIvf54iunk70aaUsbFLXkbLoGLpFYljScUMWyzyiMZdIWeLeZ3icPD5y0kKC4fDQ\nFCbKNgq5DC4/ezGAsN+lyZ7Jmhd1hBfLpSNlmRAY80BjnkLK4riucpFIF2+6csO47KjccUGWUr2X\nbzsuhqpS00tXLor8BkgYc07KEg0/qgLtD0nhEgF+ruECAZA2wEJBLmzPB34a40UrMMSvWOW3Jz5n\nh/zdPHfIN8zFMTMr1ZiHZWAfRcYckIUGFRhzSZ9TQSRpHIlNQZMrHSeOp0y2x9rFAolPmoljfpog\nVspCNeZVxlweLjH+Hmwyp3onnfbCHLsc14tkFEzM/Cky5paaMecNJ8Qw5tEJO8rk89+zBYhse90W\nVsxSxlwygKsm2lqdP9mAQLfsStUwUbFSFivUtMqdP53IIOW6HreoirAGcRpzcXeCThKSSSzQ6Waj\nOl1AnYlVdh1mbC9WGOb09nTnwpfH0AlAwzBnPgdtcsNcmgSpWgDdxRkQthfmaCc6fw5MlPGazz6C\nWx/aGykbg+/86ZK/9RhWABisTrTHSPKOTCYTG7FCxZjTiTabCX07KHKZDPd9Pit3/qTjng5hzIz6\n5KgsyeESRdDFZMCYK5KaVeyoxtzz5IlnRDiSJG4yQkSFHX0+w3/ZysVBnbAxTzTMQ98aF+/42lP4\npx93h/cMpCzhWChKBfQY89DY3HtqMrhGHAst05izsH2LhFwUtJ/pMuYq+YaIQCYpmePOWtgW+W5o\nqgLP89v9RWct5H4LGXP+HNomRClOXPZe+pO4cBBloP7x8t0dGWO+sC0f7DqNl6zAEL+6Gt2HSllU\nu0DPMcZc1JiL8cktR2rzsDkin8sGRq0oZ3JExjwiZeEvvGn/INZXs6eLJI08nHD4nSx+OmunnSSD\nupiPwRjmcxyBYS5ppbST0SRDIpJ0pWyA4dgqDe1TYJh7EsY8jfMnGTBk+llHMJwo48lrzMn1FVuj\nlrBijWXMPT4SQrsmY65iW2rJ/GkTnZs4WYwVrXCbXqKfpXHMbcmWuZj5E/DftZjKPi7BECdlEdqA\nrTBQxHMLeVYHfJsTnWxURqXleIExEEhZRIdMcm5EykIO1ZOyVBmRwDBP3ioNDHPNxRkQGpQiY87a\n8HefOYy+kSJu37AvOEcm3UqrMWcYYIb5aDj5VOwEjbngzERDPNLFsGxCyuf8iC70XGYAqjTmOoYp\ne+crSCQQrszVspTs5ARDIuiCPmTMeWOcwZI5f7pRB0YZHDcalcV2o9GwVMM2M8yvPGdJ8B0jYlT9\nrG+kiC2HR/CL7uPBb8yooeOlaDCrDHP2fspCGypaTuAz43kxPjrCfaYrTjBfLBOyVasid8VBP3qL\n/79Uwy15dtaPli9qxxmC4W4FGvPqe2V+JCTUrUhqxEWu4XYpNRZMPAkkl7IwxnxBWy7YdeqfKAcS\nkqvPXwZAkLIoxrn9/ZMoWU5E1imTssgWyXTcYH1PltCMIrrTEn62HBd/fsez+N/f3YIhkg8GiIbS\nlbWPI8N0bOSTjzH/GgA4s1rv0XCJc8PknRulnEGwFyKNysJJWcoRbRVD0oDDOmcuQcoiYll168aR\nTBBJhjnvVBEOQlLGXOgc1MCl20pyxlw+qOkw5mIkhA5NjbmKMS9ZyVEf/Pvyn1kZRMN8ZLoSRpyQ\n6GcrjstJAEQDoGy5EfbF9aIJaeJSoKtCEgI8++V56nTe+ToZc9txI86fIlRSFtH5U8cwY+VmUhad\nOLlhzgG9xRkQJhhi7S7M/MkvDChkKeHTasyDMlfvQ9Nd+86fMVFZRCkLYYroOKMjZVGFS6RSnk37\nB/Gudc9gf7/cWdXzwkX/y85bho/ecCX+n9e8hDuGsa0qli4OBWKg5om0j4H2pbJKyhLzPoPj3Ohu\niCwqi8gcM+wMDPPFYXmzjDEXInUEMsCQLGHfsdvlspnAJ0RXykLDVYpEkkr+QyG+Oybny2bCBTkD\n7WfajLnmoiyQ/MliuEt2Xfqr0UpWLmmPjNNsIcIef2Fb2P4Z6SQGUoiNykJ+iyyYyHvISAg/bgFP\nnoG1jwVEysL6W3s+G8hzdKQsrBxirHs2D7cX6A5b9FwaPY0dK/oDiPUSGZ/Js9HFxHjJ5sg9cUfK\ndqP9lxrmZdvF1iMjeKIao/+8agQbICpzkQXcaGUYw1xA4Pwp05hzzp8VZbSGJJJMlmBIizHvDKUs\nMoNABU/0dk5y/hQMJxVjTosQOOgI5XjjrY/jzk29EecLqfOn8FwFCasulbLEMGBxETXKtoNihR/Y\nbQlTxnBqvBxMQDL9bNlyuEFJHMBKUimL6OypTm0fqUcJW8vdTwxrFTh/yutAfI9KKYsbtgmVYcJn\n/lTHMU8jZWFblaKjk5wx97+rhzEXnT/PJOwbeybZQlQ3co4MnufxhjlhO1XGNQWN/MGafjabkUrl\n8tksF5WlkM2SiTp8x9Rw+9efvYCnDw7hr7/7vLT8tL+1F7J4/+9djN+7fAV3DFvMlYkOXhdyxlzO\nQlYceVQWHcbclUVlkUhZVDp69h6uOjdkzNkOlZhOnl1T5nAbRpOgOzh8GVSM+TJilDLppQyqxWNF\nWNQyf41F7fmIhKoWxly37oNoXdV3ctnKRdi59noAvqEt9nHmJLlycQeuIjsWDL5jtP+5kM1gYXXB\nzYiJisM/d9zimv6kWjB1FnKh7IqTslDGPDyPlWNhWy6Qg7HFztlLOrCqGqnlZDVZFKCTXyM+jnlJ\nEkUM4McXdiyTMzGI58kkPQzHR0PDfLJkx8Yxd90wTDHg94HDw/xu4v/3425UHBfXX3U2Xn/FyuA3\nNWNuDPM5ibgEQ7zGvKLUr8ZtfQFyvZNOGB+qMRfLF8eYy+QQKo255/Eh8sSBL63GHADW/mJXyN5V\nWSOVlIV2oIKkE0mjssRMBCrDzHJc/O5nH8WbvvA49+5sVz0QHx8tEsZcJWUhuwtCuR7adQrPHhzm\nvnM8j2O6HU8dtUQsljixie0uGtbK/12MysKgGy2CZ8zlhgktG5+sJhonPwnsuTqrRqO4LRuvMQ+P\nfXRPP/7P3TuUKcwZYy7GMWd9hDLmbLtcFsdcpTF/9uAQth0ZidyXyqLGihZnmJdtN2hHZ0ukIaJh\n3k6lLAmMeTYjSTCUizLmsvHs6HAx8p14HnuPIunA2oyu8ycFHTdkUVk4KYvtRYwsx9V0/nQlccyd\n6E7leWd0Ig5XriJSlurYp0o6Q8chNj6HfgKZyA4Og8hQM5Z1UUc+qPehGCdo1c6veB8mf1nSWYgw\nj/S9yxjzYsXBk/sGhbFW0zCvvgOmKc7nssHuGbs2BWOSVyxqxysvPAOfe2cXvvNX13D3pf4Xi6r9\njy3Y0sXh5ndraPuYriZ+WtCWCyRjqt0d7rwKk7LkIwu/s5e04+yqYV60nEAbH0dAlCxHKyqLrD7o\nrmpbYJgLjHn1vDs39WJ9z0lJUILwM3XenChbERtC3NkfJY64rsefX7ZdHBycAgB84m0v5cYGZpgz\n+dlcSzAU750zDxFEZUmQsgxPlZVMRbLzp8Qw11ginUGkLGL50sZaDqQswnniY0ekLGRSE5lm+r+I\nYJcgLlyiGxoBuWxGuu0kM8LjnLnKlgt0RL/f0TcWDOC0r8omZIbjo8XA2UiW1ZBm/gRCBvp3L1uO\n9nwOD+8+hW9t6uXOcVzR+ZN/hypNIhCvMQf8Af4s8jebCMIEQ6KURWSKFAtPSRxzEbQZcHHMhUWl\nVlSWKkPIJmPRGBaL6RGdPp2w3vvtzQCA1WctwN+87tLIfZgRz0LTic6ftKw9x8exv39SEutajGPu\nfx4vWfhf654BAOz71Ju5d0913n0jRS7l9VgxzOB57rJOHB/jYxnnhIGDMuZJUVnyOVHKkpXGMZdF\npVGNN5SsYOy2eG+WZrxkOchl001BBQljTuuAto2K40TKLksrL4PjehHHSBljvqyzgOWL2jAo8Tnq\nKGQ5jbMquQnrD/Sd+2NugYuOETDmQvhK0ZA8a1EbxooWOvI5dOSzXBhIGVS7rSopy5KOAsRH4cgb\nycL3H360Hb/qOYm//r2L8c83XAkgDWPuX5stINpyGeRzWbTlsqg4LoqWgzPI8WzRvLIaTu+PX3k+\nvyBwQtlGNpNBZ3sep1AO5rboYlt/bq04LjqyYS4BAOhsywWfeb8snpBhYHPcwvZcRIqzckkHOtty\nWNyRx0TJxrMHh/HJ+3bh8NA0RLTls6hUF/ZiOcVoK2Xbkc57tOsyI17cCbYdFy8cG8PaX+wCAPzB\n1edwv9Nno2PbRMmOBJoQAx+IMeXpri6V+C3qyHOLCLq7WXFcjvDzgxK3NgxjLiAuKgsdqFwPkYD/\nwW8JA47MMNfxFg405p5MyqI/eFA9WRI74Lh8prwJhZRF3G4Uwd5JkHFMlmDI80Bjbcu2nWRGeJyU\nRbXFR5lLOlhakkUPC9t4bCRkzBdKJBwVBWPens9i7VuvkpZDlK44Hh9xR/aOGZKkLCJzFSQYqr5X\n0VAQFz2qjZ+iFYaCVG3lx0lZaDG1EgwxxrwtWc8ORHXGIlSO22Icc1HTS9//B763Be+9czPu33mC\nu4Yt1Cc7l7ZRsV5oH+wbKeLkWDh5sXwJuWxG6kwprm+5OOZEV6mSwXBxzDWisiSBtf/2fDZYcIjt\nrC4pSwJjLhrp4gLCdupgzN0oY17IZ7H6TD5WNoPYN1SJnkLnxmi7Zc+WyWQi0ipALmNZvshvJ51t\nuWCRySAbd9m4cGy0iL+6czOe2u9rdlWG+WLBCAL4nSmZ5v1X1SgcX3/8ILmvrmHu/x+Ge/XvzcZl\nsT8FGnPSX+hcYjkeMcyBRdV6qpcxB/gFaylgvnNB/+PaqkKyyDPm/Jh39mKfZWJt6+Z7X5Aa5UAY\nsWZ0OupTERjm+M/6VAAAIABJREFUbBdSyA4L+O+MkgbtCsbccT2cIISB2G/oOzouGOZihC4xM+qo\ncC9a11RS05HPcuOMaJizMhmN+RxFrMZc6LBUL0WRNODI9E46WyxnUClLglHG3U94FmqAxTlqAMyZ\ni6b7tbGjbxTX3boRG3b3h/fXZMzDBEPR56VGqorlk4dLVDtzqbb4th0dlX7vuNEQYizk1jEiZeko\n5CKT3HTF5iZXqg1eoDAqxQyDos6ecxYS3m2SlEVkruwExjwaLUIl1Qrvq2TMyTHROOZ0MJaezkF0\n/ozcK0bWJWoMAX+3Y2CiHOnPgcZcdP6UXINh7ynfKYt1X2oQ03No/xalNLR/9Y1Mc4tfFgFhQSEn\nfdcRxpxJURwqZZH7sOQlccwpg8aQzjDnFzfsuhShYZ6c+VMEHTdqiWMe50hL4ZMEEsZcaANtuSwu\nFELyMYhsZ15hmLO+QmU37P1TyYXM+VNmBL/5pavw+itW4i9+68KIYS4LL8jGhQd2nsAjL/bj+88d\n8csgPP/IFJWy8Nfg4piX4xl6Bl3nT9F/ic2bbEwVyZdAykIM80wmdJ613XBBmM2EOzhsHhHnjFiN\nuUiQSSQ9nYVcQPhVHBcHBib9XT0VYx6ES8whn8ty2mmWcIj59sSFUmV1T3XaDGEcc/+YomSXQ+W/\nwsaktmAHx+N8bcT3RY1vasBPlCyeeBI05o7nYVRI9kTHTrYozWf9HRQ6NpxBogZZRNZnNOZzFKza\npFIWwfilqz+KOBaob2QaO6pZ7LgEQyk15qIdHpfUQYwEQo+NSlmiW7+iPOMvv70Z+/oncc/WvvC4\n6jOr2IWAMY8Jl0gnvnw2I+1EMilLHAMmY8w9z8OWQ1Gtr1gGBsaIHR8rcoygaJiLgyTb8stno8cy\nuF6UmVOlQBfbVRKDLk7arK5D50/+/epGZWHIZOQ7B7TcnufFxjHXkbKw99PZpn6HFJxWt3pvlnAE\n8GVov/Gph/G2r2zizgsXXaLzpye9Dz2WRXKxFVFZ6CKHGi50Wx0ADg5OSROvtBdyeP0VKwM2lCEa\nxzyUolApi4wpygracxouke6SpTLMq+e1E4NQLCPT9JYseSSIOFDWmbG2nMacq3s3UnYx1JsKrutF\nEqc4rhsZd/PZDMeY00cV2U6VUcCMBiq7YWNuIGWhGnNynMwwX33mAnzrL38Db7jybHQSv4i2fFba\nX9k7Ym2NxfEWfag4KYvwLJSQUPlwiNDdLWFdh/UhNnewZxN3DZjz54rFvIaRtRebY8wzwUIxiMoS\n47woQlxc0PbHsn52tuWC/vc339+KN3x+I+7a0qdM3DXNwiVW6+rz7+wKfrusGpGFhQaMszPZ+CVj\nzMU45rI5VGyvbIxj0ihWBtt1ufqPSC7Jn9RmEp0/RYmu43qRssv8F9gChO7iLOksBPObL2UJJbJz\nAcYwFxAvZfEbxfLqqvWYwjCPc/58zWcfxf886zMSeQn7E4elnSHbYQtGVtyEE2FSiWEget6Lg5Dr\nQZBnONJsikEmuSTGPCYqi+t6ZLsyE2EDAbmUJU4zKjPMj4+VcFIhQ7K96O7DRct9RuzkWCkYGNrz\nOc74AKJbfGywy+cyEeaKwXWj9aMyzGUpwlXnARIGnMiEgGi4RPF4cdIRM7G257PSnQ+/bP7/fshK\n/pp8HHMNKUsQrjBZzw5EjTMAXDrrX+zw5Se7T4xz54VsL8+YMxZM1rbZgpq9G8txeSaMxfcnbSpu\nx+qIsC3NGN6OQha//9JzsPmjbwgy/wFRJrxA4jKz4mYUzp/5bNT5U9TV+8+kbz2z8+IY80XtzPkz\nGqUoCYmZP4nRakmisuga5irGXCZluZCkfV9I2qjImMvICCDsxxXJgpL1j0xGrjEvSnw96M7S+cQ5\ndXF7Xpobgr0/1i7ZGCeSNlTKEkckJWnaxfsmHydnzNmYSo01z/MwMMmisgiLWLLjwElZqgYwm1si\niZVipSz83/RcxkIvaMsH/XRfNezh1zce4J3+yYUoYw4AZyxsw3P/8gZ86V0vxxuuPNv/TUGIULD5\nSdbmg3CJ1bFONoeKOzziPdnfYrbjuARwnMa8zGvMXY/34XBcL5KFVbYD3hHknQjb5KL2PBfFiDXl\n09Ywn5iYwE033YTrr78eK1asQCaTwdq1a6XHbt26FW984xuxaNEiLFu2DH/0R3+EgwcPSo9tFcQl\nGGID1aql/kpcyZhrzjXU8NRpL2csDAd6NgAwLZVoFFLESVmi4cT4c22HXw2rZCNJGnNxK0k2SdGt\nrHw2K3WWkoV3jGfMo8dv7h2WHFktgxsNl3jesk7kshlYjhdkZZQx5uLgRqUsNA4xdz/Pi+zEiL4M\ntGziuRTigkJkkthz5ZWMuXC8cL2FgmHcUchxW8QUbDCeENqL6PypJ2XxgvvJEKsxr9Y/053Kjmco\nBc6ffOQgtqUvGxPYOYFjqisPaUkn9+d6h/HndzyDHX2jkfYs+q2w01hbE43s2HCJCVFZcjk+jCLd\n2amdMQ93lOh1KQIpi2aeAQou82eO6XblZa3UwZg7rhdZkIhxlgGfwaeMOWWoRY25kjGvVjKVQbD3\nH0aTCMPH0mdi7PSSjv+fvTePk+SqzkS/2DKzspauqq7q7up937tTUiMJBGgBgSRAXtjGfoxnZLAN\nwsbGZjODDWjGfjZj/3jzPO83Hvv5B56HbcYswjbCYjOSZYSEwEil1tKL1Oq1eql9r8rMiHh/RJx7\nz71xb2RmdzVCss4/3ZUZGXHjrud+9zvfCcRpQomVYUu/TEnfUfKNPHcRB5HOo9SnsxxzSWXJc3D0\nzJlANhFTK7EFNF51jjmpJPFTA65drydBor5jU2UhxFzfkOQlCbPlE3n05DgeOJJw9TliLt8JDRFz\n7giv6Crh9spqUe80F+dRWYoa9YQbTdm0UTOdROv9VafS0YamHqqKLvOWZHNTCzVljZxeqGVOT3XE\nvBnqGW0u+DzTUfQZyBCKNnzRUllGR0fx53/+51hcXMTP/MzPWK87dOgQbrzxRlSrVXzhC1/AZz7z\nGRw5cgSvfvWrMTw8fEmFvpxGSIAJyaGJemBZgkIMTZod82a1i7k/4ziONYscWXebGtAAAL3tCSqQ\nt+Do5eGIRmYS0t5bPzoyObqAdDxM7+44EjlsmGCoAcfc5CTkBX+agqO+9+yI9XoTlaXou0I79rlU\nnqkYuJnNhR6tTuXyNXSCWxRlkTneJq0g5vr3OtdTIk7ZAL/kejOVpa+jiFdv68M7tUQxbYYjRL3c\nGW30WNUxbwYx1TN/6pY5OcioW6iIOV9MTQF31E5F5uTWQrOcGH1EmwZ9kRKKEmxx//1/fBoPPjOK\nd/y/38+0ge0kp2ShhmTkEnmCIT6WmuCYB57TUMe8kel1aCpjlxL8ab9XV8kX4w5I5hHTu9sy3ibB\n2BfvmFObUdWZ5obAc7CeIeZ846BLqppOCelZgPmkh1MuCiaOOaNLkOPEN9Cb+yX/nTsr3Kj+ZjTE\nXEc+yeHtKvm5eTdMtEp9U98MWu5r7Uv/0tpB8898TT6PACrXyT6T7sd1zF3HYRxzM5UlN35Le4/F\neoTZxTre8Rffx9fSwPC2wMvUVyaWyMQxL5rnu+S7JhDztK11ZRMA8DyVrmcCt/Rxq5eH+ltdW8MW\nqjpinvx7VovJm84kGMrGVDWTh4LmLA7kdZR8hfpFxXuhBH+2LJe4YcMGjI+Pw3EcjIyM4C/+4i+M\n13384x9HsVjEPffcg66uRMv1wIED2LZtG/74j/8Yn/rUpy6t5JfJbDrmfDe3WiDm5kW0acdcc2g8\nx0Hd4qg4jjrR0ySZF3ltK08uYh5nJ5pmTCDmhnfvKPpNIebcSbVxzI2OeQ5ibnbMR63X16Ps0X3g\nuVjdXcKZiXnpmPtextHWNzG026d2LgUu9DwfJvWHxbrZMW/IMc/oG5t1zGlh0xF+G5WlXPDwuXdd\niziO8UffOCy+J2cx8Bzo/g6VTX9GGOk65o3HCp0o2II/9VvUDA7OeeaY8z46U43gRBG6A+mI0ETf\n215AOZU6Ozk2lzuui8IxtyDmhsV9erFuCE4092XumDeNmDP6WHM65oxjrqiyNI9uCsecUSbsHPN8\nKsv//IUD2LaiE1f//rcBJAmQuEqEUcdcoeBI9LTouynnvLl34eOy5HuYr4VGHfPAc9HPeP98LtIR\nc5tjriPCgNwY0Vjhcon8hG2eKX/84iu348mhKcFDBoDNfQwxL/oiBoEbbUCyjrl57u8qZXXMuZl4\nwOWCp9QNH/cke6hb4LmoR2FG550cMBoTPKslgSOdhjIKxDyjynIpOubq39V6hEeOjyl1UC54mRPx\nvGdwVRabdVicdpJRfMXm5WIs68omAE8wlENlsVDQyGhzoCtR6XkmaIzzU0t6ZibBkLbemU7IddMz\nNQNAZ1GeIHGO+YsWMU+Q3fyXq9fruOeee/CWt7xFOOVA4tTfdNNN+MpXvtJ6SX9MZqOy8A6yKkXM\nTVxroBXHXH+2vV6TbGvyBxIxTxzzVhBz7rCZMuOZLOGjWh+BehRnIs35PYVEpJODmHMqi+cY68O0\nsOZyzLVF4tTYHE6Pz8N3nQxnGsgep1FZ6JSEJiBOZbEFdtLJRC5iHmf1khUqC/uqVcQ8I5cYyroF\nso64LfiTyq/TKPREPNwEYp6RYMxSWRrRGUSCIQtinidZJjjmbFHg9fLfHh7Df/yHYTw1vCiDP9N2\nchwHm9L4gmPDs7mbCMExj1T6hED7LONqsZ51Ykxmo4Zkgj890nqXyXs8xzy36Ii5z1RZ+Ia2mcWR\njN7HlKGTTHLM86ksvusqKJ3uxBszfyo65rItbDSo5DnZz5LMn6ljHkgKhF6GwEs2C289sBYDy0p4\n7S6poJFVZcmnsqg65pHyneNkYx4A2U6lwMM7rt2A//Nn9ykO6ZYVEjEv+K6FypI8Y1ajstj6Zldb\nNvMnNxMtQkd4eZvZkjQRRU4kGNJO/MqG4M/JVELPlACO6r8eqWOD+qPumJv6l24mGt1DGvBjorJk\n6TIMMReZP+2OuQ0x/6t3XYvfeO02/Pf/40qxOZ40yiUm/9J4N51yeJ4+bj3tb0ll4X3XxjHXA5UT\nVRbVMdfXu6Yc84BofqxsJV+RjtVV4X7S7bIkGHr22WcxPz+P/fv3Z77bv38/vvWtb2FhYQGlkiHz\nS2pPPvkkoka57ZfYarWaaNyFxUUMDg6K72bYrrw2eUH/qWKL1aryW5tNjo9r1+Us/G6MJw4+Ln87\nnSC34XwSwDY8OWt95ukpdWCeOS+pHDPz6nuOzJmd3MAFYjhYMCQbIXv0sUHMLWRTP1frISYmEyWa\nM2dOYbAwhpEL05nrhs6ew5F6opZSW1zEyIXzmWtm5xcy7zk5Zz65AIBnjp/EYEFyyr/1bFJv23oD\nnJupQ6ew1cI4ExB75tRJhHPqe104ewb1xSRQr80H8qSRJ8ZGkzKH2QnyqacP4cR59d4jY1IxZoH1\npVOT6u9PnDyFwUC+25EhtR6OnRrC4KAMJiQn5cihpzHc5uH0BXUBGZmYVur28PnkftWq7COeE4Nq\nJ66ln0fZBXxqagaDg4M4eEqle83Oz2PSVTe0jz42mMtZXUwXjXOnThi/P3T4CJ54Gvj7Q9P4pQPd\nmFiQY3VkfBKDg4M4etpMX3rsXFL3fz04ATdd8M8NncbgYFKvvX5S5999/GiuYx4uJu85NTOLRbYA\njU1MYHBwEIeGs+PCc4CDTx0y3q89cDBbY07mvBzfc3Oz4vOZ6SmlzU5eSJ4zNTuPU2eGAACTExNY\nNMSGnDs7hEOu7GvHnjkq6BJnJ+bx2GOPwXEczC+a07k/+thjmYXu6HOzmfIOz6qD48KZpB3nq3VM\nTKoBuNyOH3sGwaSk74VRrLzr/GzyrGPHT2AQCT1ymI2d8ckpnHGTPuzDvpbsXF7AE8OaLNv8AoZH\nk/Hhpr8dGR2Dt6g6J6PD5zE4OI9f2A68Y9tyfPbRSfHd1Mg5DA7OiL/5GsLt9NAQBgdncOK0rIuj\nx05g0BnB6dPJPDk1OSHm3mMnTmLQT8p25Fi6DizMGed/vvE5PTyJ1V3ZJf/w0WfQNn0awxNJWWcW\nahgcHMToRFKewAU4eH7+zElMTc1m7kM2OZudo51Q1u87/+w+5btOzzx5OnHy0GPPncBgPIzTZ5Ly\nTE0m6+bcdCJ5e+zkaQwOJt8NDiXjMIjrmTKEtaQMh448I+Z4BzHGzp8BAJwbTcbqzHzSZ4oeMBep\n/Uu388OqutfTh4/i2wcnlc+mxkZQr2n9SxuPtXooyjs+nczZQyePYXDujPG502PmcTN77jm8ZoWL\nM88ewtxUUo5z49lrz5w+jcHCOM4NJc+a0I9yAYS1mlKHEyPqmr04m9x3dHwCz7lynZnR5BmfffYY\nehfO4vAJNbB9ZHIGnUxpa2JySqH8PXf8BEbGzRrt3OqL88kcOyTXmmOHn0JUS97p6cNHMTySfDdy\n4Txq6Uawpr3f5TLXdbF+/fqWfnNZHPPRdELr7e3NfNfb24s4jjE+Po6BgYHM92T1eh1h2ByatJQm\nOOZRjFpNDp55xtddVshH+PTfkmXQoThSrstDpFe2ewjr8lracXf4hExGxmcCQLWmURaY41AL1bJW\nLRH1BDjlJc1brNaMpwX1SCJZcRSiVquJxY5brR6KsjpODMSGa7TyxnGMuZq9PeaqdeX6Z0eTSXd7\nr48Ls9mXqcdZxBxxiJIGuLmI4KftVfYdmFXR6fdJ25hAu2qtjkWtfThKELO+pLdjta6+m36frx6e\nwfKSg9u2lhHGsdj2xWEdtVqEbi1fzVxN7UP0PNeB+Nx3HFTTOwVuUjbPydZ/GCX3mkl3PkUPWAyJ\nrqQh3LVaLgIn4g5g7pu1eh1fPTKH759ZxObuGezpV4Oka7UaxiwbTrK2wMXUYlLvLkLxvqvak4Xj\n9MQiVrQnDbii3UPgAmemZXkCV1JWFCpLmDxfbxsgyWA4X62lv1edn86ii1mGPPmO7Acu28A7UMeD\nEye/qYUR6mKDGRmPRuMoRMQ2i3FYx7I2Dy4SusTIzCK6S56VYzu7UEPJV9ttoUpxFbLPxNo8XnCo\njOYTNl6+sK7Rsfi7pvVQq8lxUKtzpF/mYMgBzLGmy8NU1cfJSfksnlGTfIdaGKIequ/raHO4w+as\nkqvNVZZ6rNfDtI/wJD3JO9Wp7uJYtPsCm9MIXQ1c85rDbXw+xLqubEUspvebSzvgYhijWq1iIX3/\ntsBBbVGW3YtDODmb1IVadi3iSqffeU51tpa3mcc+obq1dJ4jZ9pFcv+CK5FYeh5xzMs+MmWgKWax\nWmPBnw4CJ3nPuVpyH0Lmi56DuVqMaq1urdtQ67/npqt4bly91jeMP1MSHnrGfFrvPuxrOs03ujlR\nHbVa8qJ+es30omGM0Tqczhd6wCaQzDP8+UXtmfR3LYzUEzZd/jdtP1KpWVZ0MbkYYbYaoczmjzBS\n44+q9SzVj8x3E78CkHOjQt2M6iKGb6FaRy0kaph6v0ZjZinM83ImH4tdFsecLI/y0ogO4/u+QLB+\nXFar1SSVBQ6CgB1FVqmzS7lEm0UAgiDAQ6fmMV+P8JpNyXFihiLhe8ozLCed+MirerGnv4hCylWL\nYiCMkotJSH+uHsP1fDOXVBtQi2xxqUexUgbXNxeiKI5A7Zsl1/eNijQxIIJtCr6PIAgyUoMA4Lgu\nkKYzDlwXgZEPCaW8cxYt5JKfoPth7CrXz4ey3jw3ixLUI1lWca/AR4d2uNNWkEdl7QUXefUSpO1s\nory4nofYUT+vx7INYgDTdRftgQPHUwvmuGr/gZtMTGs6fazq9PGvQwv4xrF5/NSuZYjYSUepGCAI\nXLxjfw/m6w42dQf47GOTWKirfcHxJBWHPk/6V7pwBcnzE5UEdcKL0/GzECUboY6Ch8X5MLlKG/u+\nH1hlFwHZHu2WLKOe52Oqmlw0shAjdmW/qcdJfxlfyN9Mt/kOxlLApVzwxfuu6y4CmMXZ2Qgr0nF/\n5UAJ7YGDu5+WaCjRX8JY7T9iHnGz/aPgOYic5HfLSh5G5uQ1XUUP52bk36VAtrUis+qp/butQNQZ\ngLLA+J4Hz80ucAXfR7Egf1ssBCgXffSWk7KMLTro7wxgOyQL4SHQxnEISe+ichVDtX93pUHsMWC9\nNwAUA1/t31DHvqBQuR5838fIXIiQjZ16LLckyfxlHqOeA9ywsYzPDUpkMYqTPkzvAoTJONXGajFQ\nx2CB1UdnW6CNT8vLpuOYu28Rkvpz0r7suS4K6QY4dmTdVtN1oFzwMnWlW2fRNc679Hx+Ghq7PsjX\nKgcuphgwVS4G8D3zKQoALIRxpix5nPQVHQGA7KknZSim8tE8WfCSv9uCVK4vlvPTQrSYvquh77D7\nRamD5joyo3CYri3k8JX8dF7T51luWn94cqSGGEBPm4vx+Uhco7+/3u+jWPZtAr86SgGCwOyidVio\nLG3FQPhWNCeZTmqCdB1uK4TG8gBJzAl/746S6sQStSWKHWXN0n18x02eFSJpm542D5OLUQKosbVA\nX8cd17POD22+i+kqxbMk7dNTlg8OgkCoGCXrQUq71HyKRmNmKexi/NjL4pgvX74cgETOuY2NjcFx\nHHR3d+feY8+ePT92x3xwcBAOUmTQ91GpSGH/JOjvHEqBj1ce2A987VvW+ziOhx279+KnP/91AMB/\nfN3L0NteSKgEfyuPplb296NSkana/b87Dxh2cG+/8SosTwOM/C8OoVqP4Hg+gDr2bd8M/PBHAICN\n23crqWjJvDOTwNcl/cYJSkA6SOqxo7znspFZ4KvnMvfoLJcABxiesx9h7tqzF/jaMHQnDQD8YhuA\nKjZv2ojKvgEcrp4CfqjizMv7+rFufQ+AUXR1tmPd2gHgMfVYMHZcpbyJZOVQtrxtBSxML6JreR8q\nlV3i88LgDwHMYdumdWg7dQyYVdEb0wZ9+9atKI3NAY8dFJ/t2LoZj0+eBs6cxarly3B0zK70snrV\nSlQqO9D7/YeBEXVMnIl78MyM+ttiWxnUPuMLEX7x786ir6OAz9xxNQDZjgMDq1GpSKWUU84QgFGs\n7evCh2/dibf86ffg+gVUKpUkEPWLSd+7srJfcG5fdQ1wYnQWn33sfixGDnbs3ou7vvokbt61Ehs2\nAsAIOtrLos5L9wxjupqUbeXyblQqFXR8ZwKYTpzU7nKAibka2srJbx4YOQpgEv3Lyhidn4YfFNDe\nLt8PAPbu26ekcOcWRjGizyeJrCp7din9mGzT5i2Yf+wggCrmnBLWb9wMIKlTLyhh3779mGTjzmTt\nRQ/ugg+ghp3bt6KypQ8A4C6fxKcf+i7OzwH9K1YAmMLK/r4ksO/pZ8TvV/b3AqfOwA8KiLAA2ryU\n2ztQqVQwXrogykTWWS5i3YZNAEawYlk7RuenRCDr2v5uHBllbb1iOSqVhBrY8+gPgLPJd329Pcp4\naL8wDXz9AiLHw4oVqwBMob9vOSbDGWBElQnduGE99u9aCdydqEfs3rUL65eXsfmhOYwcH0Nb31pU\nKqsRfnEIJprdxm07MlkvH5p4FsAkVvYtF+WanKsBXzkrrrn6in1ijvEKybxgsj27dmLbyk7g8zKR\nGX/XnsEfAkMLGFizBt+5sIA/+c4zyu/9QhEdy5YBmEVPVztOTJrPtQLPw4d/9uX4l9PfxdDEAqph\nBD8ooNzRAWAB3Z3twMQEOjq7sHx5GYA80t+wfh0qlQ3i7/uGjwBPJt9fsXs7Kut7xHdxHANfyPbD\n/hUrUalsxz2nnxL3Xr5iJSqVbfjeeFKfy5enp88nTqN/5QAqlS0AgH849RSAKWxbt0qZ57h9cdk6\n/NevH8Inbt+DL/zwFPCsOoevW78BlX0DWPiCnEe37twD/NM4gDp6OttxbkZuWvbt3okHh48Bx800\ng3oE7NqzTwnwLz74IEzt7LkOKts24m+fOJj5rr1cAmZnsWbNWlQq60X9DKxagUplFzaMHAWenkbH\nsh4xNr479gyACaxbtVzpKwDQ+d0HgfEJrNuwCeOHn02e77nYvWMbcN8InHSujL6c9NXuzjLOzkxh\nYPUapY25dR8dBMCoZXERwDx2DHTj4WPJeHPae1Bui4CpGeM9gGQTWKlUkpOatL+/7Ip9xvUcAIbc\ns8D3VRpNf2cRV1xxhfh7zdAh4MhMxlEGgE2bNqCyfzUWOkeB+81rV0d7m1KHU+Vh4LuPiL+3blgL\nPPE0SuV2dPV0AlDfr+C7qNYjbNiQ9K9HJo8BmMC6/mU4PjGC+XqcrnVJvyiw/wPA6jVrEQydgt5v\nCp6LcikQ69Cqvl5UKhXsj2OMOM9gx6oOVPYOoPvhh4CRMaxZtx5d0+cBzGHdmtUIgunkBDsIMn3k\nclgURZiezlJ38+yyeL5btmxBW1sbDh7MDraDBw9i69atufzy59NoY6ufsIpjTd81Zj7jVo9iRUif\njhtNQYXcbPdUkmqkzgtRWQq+K+Se9PS1ZFm5RDXzp6IlajmiLPiuVRVD/JZlPdy3ZpnyHUX40zsG\nBmQ+jBhtwaLKogfN2IJeCVHQgz8pGLGjaJb8WjRs0X3PyWi4JqosSbvY0tKT0Tubgk3/6BuHMyox\nJiWckZlqJggp8zdLIKQrVvCjUz1YkwKJ5qohHnxmBJ9/5BT+r28fMSZlCNj/V6ZSdvx+lNCEHkf1\nTYFwevAnkGg23/Z//wve87l/zbw3D6S0B38CIylH8tTYfEYucaZabyjP5ruOUBPggYKbUrm50dkq\nRtNgb5clexFlIx3zFlRZ2gJPyTbKUbCesrog2+QH9T5MwZ9cx9x1kEmhTvfhn9Ot1vYmbXgq5Xfa\n6s6Uel1m/mRzljbPtRc98SyTggcvX55JHfM445QDSR1UBR3DPnd5bqLi8a3fugFfvvM6cU96b/pt\nEhie/GZzXzsObOjBjdv7lXupcokqGuc46pxGKeNDLYEOwOUSZRuaEgyNpv1+ec4p7tUbe/HF91yH\nvWuWmYOWIExYAAAgAElEQVQ/o4Tyo2StrNbFnN2ujbtS4GWEC3TTFaFsggie42BlV9H4XUCZOoUq\nC81v8pQAUIMKSZVFV8Thv+PZdl2H5StI65zqge7fiioLrftdpQDvvn4zSoGLd1y7oWHQIb0jrzeb\nPCyQDf78zgduwP0fvFH5TD+hXcb6o1BlyR0X5nVC/zuMYmMiPzplpzqia7iKEdcpNyV2MlFZApYI\nDeDBnw5+4+ZtuHVvQpE2KVS9aBMMNWO+7+P222/H3XffrewUTp48ifvuuw9vfvObL8djl8Sow9rS\nfBe85Fgqj84SxjFOj0vHnPhX+j31wWobvKZsd9RhfdcRC4DNSc2odbAFNY7V722qLKXAy1U2oOfQ\nAPj02yv4m1+6VnxHTo9UZTErlIgkOK6b0VgGknbgGwlbYiVSc9DlEme5Y24YpIsGzmtgcswDKS3X\nWcw/Dgs0ea9GZuPVmXiJyvd8U6NpHteYJnNWJUO+2/B0stCPTFeNElM8G9ya7sSB484IJVuRSSVS\nXmHaR8M4zsgbHjo3hUPnpvH1J89l+jDvm2XLse5CLRSKCkMT84pc12I9Mi4autXCWDqVbLx1FH3h\nODyTZu3zWf2SlYRjruuYE7UkO65Kgads+DtZO/S2B5lryZqSS2TjxHMco9a8Xia619qepA1Pj88b\nVYrITKnXidOtqsjomwfXqP6im01eUJZXyt+ZrBbGTJXFfi+adwNPzjlhnP0tT0xz275V+PKd12Ed\nSy6UlEm+q8k55P1mhXDMk78XlQ1l8n8ul0iBuT86OS7GKW0Wl7ebnVvdzDrmUWaTtVALBaihO2RF\n323o4NgUnnTzXEds8HUj8IbqnK8NgDnz59S8CgRwo9/VIjXBEM3j1XqUZp9WN2S5qizadxfSdulq\nC/DRN+zC4Cdejx2rOq31xT+Ooli8i8cUkkymt8nannK2nbQ+z9F3Kk/eMzIJhmyZP6PYKK1JfY0A\nApqXu9qklCFfv3Up5EQu0UAB1NSFTGpngFSGqoXSMX/RyiUCwL333osvfelL+OpXvwoAeOqpp/Cl\nL30JX/rSlzA3l6Asd911F+bm5vCmN70J9957L77yla/gjW98I/r6+vCBD3xg6d5giY18Y5ueN00W\nb9q/2nqPKIpxmkUT02DTx7feSWx9JnANjnnaiV3XERnOJuZr+NrjZ/GxrxxUgqr0d9GlkbgjqOuN\nkxV9N3dxA1SUqb3o47qtfeKdyDkSiLkpCyYLDPQ9FV2iSTKO1UnelvmMpKb0oBZKu9xuccxNqjO+\n66JTW2S5XGJHyVdQJb2eyIHImwS5mTR9gezGS7+M2jzwpCMmNYAlmq4bX2hpoR+bkwg93zDydiN0\nnH+2LnXqdLnEbnLMI0OOAPb302dVBQGOfpcK5vrjUoj1KMbJMTn2FuuRksXSZot1ifroE72exCtx\nktSylERinizqk/xrCK5yHSUhTwfb/HVnEHOz/KC+QRCLYRQrc4SJ41sLI23zm/yW2vX0+HxuciFT\n6vUqex9TeYEE2aLvdQk1bjZ5QVFeg445N54FUj9t4eOVNyWVlQcplwRizpA3C4jC+5rpJI2PP0LM\nTTrm1Bfpo0SqNPnt/YeHceMf3Ycv/PAURmZSx7xB3BOZyYmph3FG4nCuGgpHSuczFwOvoWOezV9g\nd8wpk7ZuvrbxqtVVxFwmGOKOOSHmOXKJCmIuHeDFeqRI11Kf+cYT5/Bzf/6Qcgou3ittO1qDaSqj\nTRnVt62++ElOGMt2KBe83Dg8LiNa8LLJ7gDJMSfrYZlQm3HMswmG9MyfMqmaaYNNZaLN5QI7TaOx\nQRspICuFXGdzmK/NU1yP3wZ4ccRcrGUvZsf8zjvvxNve9ja8853vBAB88YtfxNve9ja87W1vw4UL\nCfdx586duP/++xEEAd761rfijjvuwNatW/HAAw+gv78/7/bPq0kqi9pJBLKVTqy//ppt1nvUIxUx\nJ2RJv6feSUyDN/DURVVHzD3HEWjk1HwNn/7WYfz190/i0VOST6kjSvokbNLNNiGCjags9ShSEgQl\n5U/qi1B6GiymieTYyAweeW5M/J6/N19Y+QBuRGXRF/5GiLkJrA48NzPRF30PV67vhu86uHJ9t0AZ\nATVDK70LcOmIuZ7BTU8VXROogHS0JZUiddoN7+w4jnBURtOFvlqPxKTJ+0KgIOZl8TwyQWVJn0uq\nLNRHozhLZeFo3VNDmmPOkH7TMTwgUX6yY8OS87lYC3NRWbJqGCu0Em7UfvQ9P5Ego7Gho/NU7yZU\nt8Ycx4Kvbv662gIlRtaW+VM/ZePjipxEz3GMgeX1MEK54ONXb9qCX7l+s3AUhWM+NpfrmJtSr8uN\nRpZ+x42+vxQqSyOd6SqjZ+hjr8ycDF4+6mL1KBbjSWZ1lTrmtgV+jqnvmMY7/5VEzOO0vAwxr2Wp\nLLxfzlZD/Ke7D+J4mvCsr+PiEfNaFGUc6ZnFuphndUpF0XdzM38CwLhGq7S1kec66C2bNxUFQYWI\nRTkBeWpH5eJjTlBZDIi5LcGQpLKEShvQ/R85PoaHj43hvkPZ+Ba6T7f2PF1H3eZk83UtZIi5LbiT\njGuc2zKEZhFz2Ueo/+ZRWXRwjjvmBc8Vp9710Exl4SABINupxEAIPSEYN55giPfBgq9uRGybC3l6\nKBODvVAQ84sK/jx+/HhT1x04cADf/va3L+YRz5sJVRZtIhFUlnSntqwc4H+84yr8t28fwdR8PZNK\nm6N25JTq99Q7s4nKojsjrqDaJH97rnTMJ+drAkHm3C3dEdLnSFMK+MB1scCCOIu+K6KcbVZjEx4t\nmgUvybg3k25OijmO+YPPSK61zjFPsqAtivK2IWkHQkgo6FBcX6S037pjLie+ZvlmCZUli5j/9BVr\ncMueVSgFHu7+0RkcPj8tysL7g7dEjvnEvO6Yq9+TdJfnOQqfEmDJOSzObUfRx9RCHaOz0sklh5dz\nDXlfosQgnNKw1oKYCyqLJoml//4pHTEPZX900vTZ05pDeCHjmMsgpGapLIvMMddRxcxm2M1yzKlt\ndcQ8j8pSCyOF+sEX446iJ8ZOcn+OmOfTRMj4KZWpr1PdfuiWncrndOpxemI+N8GHCTEX78PKa3Ji\n6ftcKotL3NFsdldAbhht7VsLY4Gy6mOvveAJZWq+aRHzaySlHKnuw0gu8DbHNO8EAIDSdymgX89s\nCRgyfzoO3rR/NQZPT+Dnr1mPP7z3EE6Pz6Oe5hBoFjE3U1nizCkqn0tNVJZGyKOeiToPMXddB//y\n4Zvw7PAM7vjsD8R3MiGQGqdBY69UMFFZ7BxzGis15eRDrkm1UKVk6ECUKfaH+sMy3THXnm87/OGO\neRTHYr7M45cDquNuSzaUPfkzcMxbQMz5M4uBK+mSkflUku4tOeZyk2w6TdIdc84xb0/XJyClwrF5\nzrauiky59RdegqEfr+zJC8AczfElk4i5bNg37BvAN3/zBuzVAh2BROmCbI6OJbXVZVrLbmMK0NIn\nUn0h9jiVZa4mEGGOQjYKfFOoLOm1uhNeDLzM0VjefcgBpMFLry4Q8wb8Ud9TeYx8AuEDmBBzPViu\n3RAYFEVy4rNRWWxlMXHMATkpEN8akEfU8veNJ0FuNirLuL7YWTjmAXPEdCqFTZaQJneezXZ4Jtlc\n8J9wdJqORrljTAsNdTlC4paVZfCnrufP+ag6lYXTcwCguz274J7XNsXHRuTYq7M2z5NknGWSYjrS\nRL8jZylxzDWql2Vx0E8suPGU8QXfVags7UyOE1AXWQUx1/owLxc5va5rzqJrotcAwMCyEjzXQbUe\nYWjCnrzLzDFXTxZtZuK8Z67x1FM33aiP6xszsmoYiZgRfe7i6c5dBTGXHHNyBKnueQyNFTFv4Jjz\nrk+nV7SJNWb+TL9zHAe7V3fhr3/p5XjT/tXYqKnh2NQ7dDMi5mGEGQ0x5/OA4pCl6kmtIuY2x5zq\nfl1vGTtWdSrfUbuHljnMSGVZsHPMeeZUhcrCxi6tn75h823KhEpl05+n/90UlSWKxZiyOdtk7com\n3uaY2xFzmY3aPg719/dcR5S36HsM/ImVuB4y6mu0eVmwgBBkOpUlilXHnJfLFPxpez7PgtyIHveT\nYi855poJKoslzbdpYjMdj5wY4Yh5Mth05FrnR5smO9PgUP+Wk8D4XFUsDHzR1CkPunEkwMYxLzXB\nMefIlU5lIaNFzlSP3HxXDVgLPFcJ5iCjo0vOnwPkQOaT9hz7f2fJrMpiK0v2OFf9ey1LK71KC2ai\n98g7NuRWu1gqC0PFMxxzwc801zu9H0e6LkxlEXO+OaBNLHeMOOIIMMecBX/qY4tTq46en1EcFB3p\nNx1761QWHa0jSo7O2+Y2zRxz3YmjMcepITZVFt3yEPNqPVJQek6X6ij6yqJZsiDQ+jh1HKlYQJtS\nz8lSb4DsQiju6blio3nUkKGXLF+VJb+vN7Mppj5sol/x7/WNGVkYxSKAsU2LT+DH/yaOeRjFgjrR\nxtQ5qO/ayt8IMefmsmcB6oZcqrKk12pzFQ867Sz51gA43YqG8c83r2Sk8FXwXaXvEBDRqP2aRczz\naFnk+Emqj6TqAYzKYkLM23I45lrwJ99EUj0UDAGuJlSY7qPPLTqCbkNq29gGMYrkmGqEmBd8V9SP\nHTFX23o527wJKktOvzG1MYEHpUBdY4xUFo2KRAm0SoGncMTJMqosoeSYt2tUFnVuzA/+rNYjscl+\nCTF/gZqNysKRLd10OTBAPbIUwZ/auNZRChMKoz9PB5o81xWc5rMM3aIBfnxkFs9esGuPA1qmydjs\nwBWDxnKJ3MH3rI65a/xcN/343Wf0jBoL0CSnq1dTJTA55lTfFPHeLGJeSFEijkbqk94a5pjrKgOS\nY36piHk+lUUJ/mSLUBzHjJ9pfmdypDhdZjiVYmvEy+OLLjVrmEdl0crNHbxqGOFZRkWp6Yi5wbmm\njcGKTjPPVtCdDCiaKENVctl1NJwWIMEx95wMJcg2NgjlMyHmCa/djCK1F33FYbByzE1zhqfSRGyI\n+YAl6A4ANvYliOyR83bt5XufOIsHjqipyk2qLNyoGM1sigVibrkXjd9zk3ZUnyga+Yh59p4RQ8xL\nDDFvRGX59ddug+sAd1y30Vom8SxNAUxFzFUlL326XM8c82b55YBdlUV3zMdmkzFT8l2lv1G72k4M\n6PT27OQ8/uJfjuHkKElumuc0L9cxTznhDRBzAlziOM6VS+RBnpxjHniO6Jf0ey45S2akssREZVGd\nYz0myeqYszUhjBliXmjMMqY1zuqYa3NSj0GVhb+7bqZ5n+aoUuApyl9NqbIIKotrpPbo6149ilic\nA0fMzXKJtudXw4gBji8Ml/eFUcofo1GF6Oi2QMwNDmUjx2W+WSqLiWOeobJoCDoL/hyaVCUaF2oh\nbvzj+/H7//h0bvn4gKD/6s5JyW8sl8iP+mhSzR75ZznmxqBXV50Yk0ygcqCREZVFl5ejiHGOpnAN\nc8eCIpqMyqFKNGmOOaOydJR8xcnymkAnuNmQTJ3KkiuXyOqOq90ElomJFrmJWfkMyTHP1pPNEXWZ\nsxEzzmRe8KdOiTjOqSgar1Q/GQEksr9heTnzHSA3GzrdiRsh5iU/q4ZA/YT6nec4CqUNsC8OYZiH\nmMtgs8Qxl+/WXvQVh9SqypKzmRccc0fd5H70tp14741b8NNXrDGWGQA2pXV55LwdMX/89CT+w2ce\nwSf/4UmxoTcFf3IjZ7Q5xDy55k9+7koAwCdv32383oaYA/I0JqPKoiDmjMriSJQ2yzGPhD6/rfw7\nVnXiqf98Kz75U3ty3ixx3DwNEVY45qkTEwsHUn0e7+vLm6SxAOZ2qRlUWQgESDTLsxtE28aENgl/\n9fBJ/N7Xnsbb/ux7API55qb/A3LM02YowzEnKks6xy/UpCNnorKIOJBaKGOhHCdVCUruSeBNwXcz\ngJuJyiKDP9U2aJbKwteEeiRlK8sNqCyAdN47LMGfpTzEPG0//u66GRHztFxFXyLm9Sg2xorQu1Ed\nLbI8EbpGOpDlmPPTJ0WFRgv+tFFsyfd4Scf8RWA8uJJzYWkBNSG9jRr7yPlp/Mb/fhSPn1Izz+0a\n6FLv01Twp1ZeVzo9QwpiXs9FkriZOOYZRLDgNUR8+VEflVO/j6CysM9N3F/Pc5SJkQfcGaks2uJk\nQsy5IktSRnn/vJNDegc+GejOG1dlcR31KJMcu2YRc5vpCaR0pQ+bBnydORm2zQg52vykJ88xX8GS\ngrz/5kSh6A/fvI9RWZK6p/7EEXM9kG9Go0ScYIHTVa3cejvza3RNaTLavHWUfKskKQ0BnV8OmOM6\n9A2ybdMq0T5T8GesOLIKxzwN/jTd31ecmWx5M4i5o84tr921Ah++dWfuvLVJIOaNM9b95feO47F0\nbrMF0JK5OY65vpmlMXb99n4c+i+34o5XblKu1yU+TUaOTkaVhSFwSvCnK+d/XdFFQcxz6q6ZIO+u\ntkC0CfUNDjgQH5fGjz7fcMS82cBPwIKYG1RZiGOuJxMiJ872/vom4Xy6aab3uHGHqsiWlyxLD/6s\naXMB0T0WU8eL1gLPdTJJkXjZF+qRQmUB5JgRVBbPzYAYpkBofX4j0x1z2wkDp8x8/O+exHdS5RdT\n+XWj8WJD1/MQcz6H2PqradNPDnIWMW+CY84Qc9O99XWBr90qYq7pmNsQc0q2xnJLvOSYv0CNtxut\npd9+6jz+1/eOA2ieY87t7x8bwt8/NoQ7//pH4rNfvWkLPnyrqoZgVC9ogJj7riv4dJT9EEjoM1xh\nI88UuUSmAsDnye5yoeGCQ4uJzxZVfSNjkks0bXZ8Vw0w8j3HzDEnxFxDQ0XmT7ZZkIGfnngGmec4\nsLUibRzyePE84dT4XA09PAKeqCxNIuY2a4iYs8x4vE65HqyNQmTKqklOFq+nD92yA57r4I/eKlMZ\n/8Zrt+Hhj74WP3fNeoWjS+iT60huYhRnT450tO7EqHTM61q581Dv9RbHnPiubZrkp74xBsyBVNm4\nDidDr7BtuloJ/uwsaVQWy3GtsmHNOWWjvq/rmDdznEtUFi77mmekp21SZeEmqCxanf7OG3eJrJtJ\nGfUTiWz/bEb6zCaXqOiYO+b61BVx6mHj4M9mbVmbzB5Njgun6JnkErmtUxzzS6WyZBHzCYGYu2bE\n3PL+fRY6GY2DT9y+B1dv7BGf89vo3TIjl6jNBXwjOz5XVTTMTfKEJsScnk9O7PRCDsc8l8qiq7Ko\n84jtcJZLT379yXP47jMjAFRH1Ga0jjXLMTfpmANA2bKumzb9dKpXCuTGpc6Ss3HT24/LJZrov7pZ\nEXM9+NOGmKc5Z2pp4ijghSOX+JJjrhkfz9Shfun/+yGOpln/jBzzFnlLnSUfH7plpyFAJHut7khl\ntc+RkfIDEmeHjvgbWTVkyiVCBUBdpHrKQWMqCwXHcQqKTmUxcMxNg0WnYwSeDHYxOeY6klouSMQ8\n1vjO5Hyp/EbA5neTI5PnmPOFYGR6UXEgZfDnpQ23bPCn6uDyQEn+bmHIEzeZy5DXtrzP/epNW/Hk\nXbfgmk294jPHkUlCOJVlmtU3dwb1chOVhTY3pxhiLpVmUsc859ien1pwI8S8GLjKe375zlfgT9+0\nUrnWNJYy9DHXyQQkFjzPyNUUOuYGxJwfARd9T8msl6fKom9YdctQWfSx1IQ6ECHmjWzHyk7lWabs\nqdyoX+pOz941y7BjVadYzJtZQFuZd3XqFacK8Ntwh0E65obgz0sMIusqBWKs0MGXKfiT9rB6fS1r\nC8T60dcClcVExeTBn/SYMUZlMXHMbY55v2WTwBMzqXO//L9O15EJgdRTJ1oHir6H1em8c2J0ViDm\npjFM7wIkG1Y9qFZQWRhi3grHPMkEnfLvnSyKbasv0wYAsGuTq9cQlaWxY14uqFRUXtdbV6pqOGRm\njrlUZeEUP50f7jo8XiP5TKiyBF5T44fmRh1oyuiYNwr+DP+NJBh6MRtvtzCKM7yni+GY62YbpKbP\ndWdQf7zrOMYsZ3O10CojppuJykL6smTdTTjmHDEn4wMqcX6z6LMJ3Qg055JTWao8+DNFOHTEnE9s\nNKESgttudMwdazsKxLxBwOqe1QkC+8b9AyqVZYkQc9250/8OI4lw83epR5EMnLK8Y15gbzPoJRmt\ns1EcC/SpsxQoE7E+pmgxJLm0E2OSY56hshg45mQ2ri055m2BujiVfC/Dw8zLGEhmQsx9zzHy94Uq\niyVuYJapQBAC2JZmVuRjhyPmeUoWgOynnGPOx7KtD3Bb093WcF7bvrIDq7sTx4gW0YulstDfVNe2\nDSS3vBgRfWOQUWVpAjGvao55PYoYlaVh8Yz2i6/cCAD48K07Moi5KfjTRmUB5AnRpSPmMviT7jUh\ngj89pe9QXdiCGXWpWCDVhKd605wsU/I8siCDmGcD+Ohk57mROSGyYFM0kVSWMEtlSb+bzuOYG+ga\n4gTFkbkuOktBxgG0JRiyiRA0hZgXmg/+7NCCyXlxdhtODgHz+GoXwZ9SrccUP8DBoWapLLpRexaY\nyhhwcXKJeuLDn3R7yTHXjE84UZw94jMj5q01tm1Sayb4U0eJEipL1lmZW6wrqcrzbNFEZXEdZZOS\nUFnyuwtNahyNUpVMZGBdIydXz67Id83k2PEFRUdSOYpAR2Kk0ECUAd5ujgUx57Qck8QTty+8+xW4\n532vwg3b+xXEnCb4ZhMMNWuZJFiRXLgcR9Uyl2i6xTG3pLsHWuvfPHhOboQ8BZXUnVSagHesTBaI\noYkF1sZqwJctSyBglkgDpGNeCjymP58kSdGDOE1oW8aJNGzifNccTJzHMQfkmCn6MvMnOehFG2Ke\nk2AIkHMG9XvXVWlajRSRgGRhXW8JpgWAz9zxMtz93lcq9AAASjCryWiK08vtap/nac6T5fVLHUVs\nVZVF+a0BMb9Y2bWPv2k3nrjrFly5vicjl1gzIOY2KguQ8LULvour1vdkv7SYacNUi+QmmhBvOu0q\nFWyIufn+fQa++/RCXaES2E5LM1lshSpLUhc6xxyQjvnxkdmGUp0SMTdQWXyispAqS3aMmxMMybLT\npt40D9kQ4oLnGtu2GcT8xh396C4HuHZzr/F7PgY7tGBy7kzvGmgBMSe5RN/LpcQl62by/wyVJQUe\nGhlt9gu+K2gp9HczCYao//zjwXOC8dBIhvInxV5yzDXj4+fbT18QwStkrSDmNufTNqkbEXNdx1y7\nxHVhzKI1Ww0bUll41DKQUAj++BtHRBlVKkuhoVwiUS046sgnYU7laLTwJkdh6pFn4KuOOQ9Y0pFU\nHiBCA1xwzAvkmJvRfG58EWikvd5e9LF3zTI4jqOURyRzuEQqi26ZBEPawqU65g045jlt24pjzhN0\nEerXpk3EunQabX43LC+jFLgIoxhnUm5zM3KJZDo1jExBzNMFWCTK0PqhETE3ccwN+QX4ddT3JGJO\nAaptuL2yWlzHdZP3ru7CG/atwntu2KLcA9CCP1mZ8yRW5wVirsYjNKtGtLmvw/rdVet70FH0FXoA\nwJUX8uc+vU/JzW8+VYJbHvqlx0zozpoaaJotHzc6VeEJhi42iMxxHEmlE1SWbPCn5JhDuZbbB16/\nA49/4vXYtzab4M5mNsR8Ih0jdAJCVtIQ3UaIuS5bCyS0GJ55seCb+68NMadqoTHEx8WmNNHSc6Oz\nDRWBBGJei8Q9pWKWRmXx3QwIZlZlkScotA6bpBqtqiwWJ7UZucSfu2Y9Hv3d11k3ZnzOKPhqwCSf\nD+ikN1vmbD1Sjo7lHYXceYTHiFH/XmSZP5uZgwhYKPhqIG7gucp4trX3lhUdwp9zHeDXbtqKK9Z1\nN3zuT4I1bv1/Y8bHyK9//lHcvGuF8r2Jn2kLZOhtLyip2cX1Fv/MyDHPIOZZJ6Hoeyj6rrKjn6vW\ncb4BlaWzFGBstioWhD+492mREt11VMevGY45RfJzBF/hhilHafI99EyQQKKmwBden6Gb5KwRp7C9\nkJVy9FwHxcBFlUWME4JLu37ebI4D+Kb6ZxOCKTmHzbgD2WzwZ2fJz6gj5Jl+hFhnqBT9W4XKMbc5\n5nlt2xJizo4vOa2BL+S6HCQpZ7QVPKzvLePI+RmcGJvDxr52iZKl7ZCX4dC0IAIy+LMUyCRZ5Jj7\nboJO0MgxbXJ1WoXJMfddjffou4LbGMfyKP+nK2vwwVt24N6DZxVub8LZdPE/3nFA3EPlUcr/N5RL\nFBQAeT3fCzWDmAPAleu78e2nzxu/I4eK6nOhSSqLjWNOizi1czMBqnn9UndAsxxzC5UlDzEPY+VE\n8VKNmiFKVZN4YrGFehIbQ0izjRvb6imcyYmphzEmU075wLI25bsMxzzI3ziZNvijTJQgHzFXfyep\nEoSYZ+NkFMS8gYa+ON2ph4g8M5VFyiV6TSHm/ASlI8cxt6qyeBfPMQfsFBlArQceowWoJ3ibLBtw\nk/P89petQ3vRx827Vlqld+l5NOfHcbJWiUBs323qxIkj5gpAxoQgAPsYuHpjL+77wI04dG4Km/s7\nsN3Cpf9JtJcQc830MfLkkJoivBXE3Bao1gqVRXcGbQuaTmeZWwxxIUffF5BOSDWNWn7o2VHlOVzR\npLMUNKSykPYtn5hMk3ozNjFXVR0QRmWpphP0pMjyFmTqxXWcTMpmXS5RQcxh5pjzjVEjxJxbt4KY\nS/qEyd56YC0e/d3XtTxxZBxzbeGi96lFkUwwdBELfCu8PI6ScIUO3j46x1xoTQce1vcmC+3JNABU\nbCjSuu/O4ZgXfbOkJ6ey0HuWUkTV0TTJTbQwM2KufuZ7qoQi7+tRLE8JqB6yjkC23DblgUaOZDYp\nmaMgZM065i/bYKdIyKRZ6hhbZCozJqPi6ggwzX0iqVATiJreLrxv6PO03i84IsmLYurqXC6Rc4ov\n1ege/3ToAvZ98puYZSoUcZw4ojwYfylMVcOi+SEWiPmAjphrY5c2XLY5wdQfuVqYzjHn/cDRlMAy\niJXLqBYAACAASURBVLlhDtvUl9CtTozOifXKtik0B3/Se2kcc8/JvItJLjFi/aEzVSwxUVlsU2jB\n4qQ2wzFvZL62fnIn3pRnQzfzhsHH21+2Dr3tDRBzz1GoWvy0Qd/s2Wyecczzgj/z1q6Nfe24de/A\nC8opB15yzDOmV4ievMLUWW3qAHrSG/GMVqgsTSDmQPYIfq4aZlKV6/eiwVmtRzh8flqR49ORW0Lm\n88yImFt4stxM7NvJ+VpGr1lwzCmYc1EGc5rqhY6zF2oh7nl8CF87eE5cn1wjr0+oLNly8DK869Wb\nAGS1eE2mqLIwFQGTlQIXPe2FlpUeMlQWLTOeLxa2xoh5HpWllUh2zivkCh383XSOOXH/ywVP6KOP\npH1XUFk0R9BkvufkLmjcMW9TjnnlNSbE3CiXmEHMVY45b+sk+EhVlKDfTy9KjrludI3rqI5qXlIW\nwER/c8D3cM2ivZWcY1+aw7izUwtlIg8bammnsiT/0js3U0Z93uWnKWpweXbu41xTPox4bAaZTDAk\ns9YuBWLO+4spQctiPcylslyMmZDGaj0Um1c9G6zOB6a6sM0JJmdteEaqSemIeSaTNXvPwIKY87Zc\n11uG6yRrwdBEQn+zAUD8dCeryqLmcSj4zaqypOV2nXwqi41jfgmqLI3MUeoyefdPvWUffut12zOO\n6hv3DwDQAaX8Ppf3ve9K7nwUxwrIZ0swpBupdemnF5ngzxYAsxeKvURl0cxJ9axprtZjtkwBlbYO\nqvPtiG5im9SbCf7UrxGOuYb0Tc7XMpN90XeVXT9HzB8+Nqpce+hcNrGISeuaGzn2CsdcQVtaQMzn\na6qShCH4U0zUBmkrjyHmZyYW8Ouff1R8Z0LMk+BPA2LOFpGbdqzAP3/oRqzubstcp5tpguOoneNI\nh0A4YC3OL6Hm4OqqBYJjHsbGwClueW3bEmIuqCwsW67vKm1Z0zjmNMbaAk/0F6HEEOVvKLgFnpu7\nwUgc8+Q+3DFLEPPkOabgzwyf3DFzzG3xFCFXpUjbRioM2RFm+owHTQNqG14MYt6sNXOKQkj+Qj1U\nAuVtShE6Mk5G76FvXPJMD0rkcpNq+2adH14+fY73HAchgwu4KsulBn9ya3SPxXokaH5L8TxA7Rtt\ngYfphTrGZ2tiLlrZlXXM1XpOdcxbOPXlAJGrnVDplCXXdUSD8MySAAv+1MqzursNp8fncehccrpt\nowxS2RfrvB3pO+KYJ2uYqc+YOOZc155iXEyxLq1SWZYCMdefAwD/7ur1xu8//fYK7rxhC776+BD+\n7J+PAWi8+XTSIHhTYLvPThyiKBZUtyD9vCmOOQ/+1BFzdircjILTC81efG+0BJbXH3l2TbJms6Dl\nZb0DzIPXhMyZfqPv0vNS5AKJY0iTcDXMOubq74iKcWkc81Yc8y39HRrH3BVBQ8Ixp2ysBtTBcWR5\nz2sZUDusiHm2/vUJZMPy9qacBhPHnAes8LvSYtkMr5bKCmQRc5G1lZwccsyjiPHPm0PMubpCK3rR\nIsGQgpirSUlsPmKpIJEUoVRRz99QcAs8R0Ga9ObkwZ9KYBSnsjSjymJYWHzXNTowgJp5VWowq3Vq\nGhu0+Og0DAUxb3IzfzGOOZDIJppMxE0wFJIHztnGCP1Od+CEw65tKvOMX9NZCpT3Xs5AkYJ2YgOo\nG1G9bhRdc1dS3BJK0lJyzM33oKJyB3KpqCy8n1EdENWkXPAyTqXOB26ImLsOPnrbThR9F5U0KJU7\n5lnEPAuoAMn70lih9rGd+hHKT8mwGiHmxgRDGpUl8LJ92JREh6vmvPVla/H63Svxtpety1xn28jo\nND+yZoI/W7FG82fR97B3zTKr1LHNbH3Ydx0lizpPLpT3O26CmqTx4zlivtRKZz8p9pJjbrC8SfDm\nXSszn1k55pqCBCGItvubxk4jKgs923QErxuflK/Z2Cuksar1CI+fngSQZODzXQfvvXGLuJYc7UZH\nRoLzzTnm2k63kf32bTtxx3Ub8Z/esKshx7wmovSzx8+eKxHzcS2VPQ1mPbmFqXjN8nF146ostO7z\n+ucgQ8HLX+x001Mdk+moOAUlc26sjburT3A8CKyVY3SFyqIFYzW6TxtL/y3UTAQ9J78dSNayjS1o\nGcm8QEbzt1kcc2PwZzNUFk9Fbnhbc8TcJgdoGhu2DbHOHdXNlPvAotbY0P7XO6/BroEubGTSiY4j\nj8k5XYyCeG0JT+i3+jsA0kHSaVh55isbKjUhE09TX/DczNhSFSrU+yoJnFw1doBOOJYCpLONB3LK\nFg2Ui0s1n8nz0RgYTh3z7rYgE1xd1BQ0GiHmnuvg3TdswRN33YLXpmulwjF31RwAprEFJO9LbVYP\nY0wt1KynfjQ+KNlco+DPhXo2wZAp5iOLmNsdc89xsHNVF/78P7xM5GPgZsM2Cl520wiowclLYc2u\nYxyEacZ5tt03obLIjdWCJmXZypqSBH8yP4I55q2AfS8ke3G+1SWaaRJ80/4BfPaOq/Hvrjbshm1U\nFk3TlWc/a/a5Gb5oZkFLEXOLVBw3jiT81BWrRederEcYTXmAt+0bwMFP3oIP3bJDXEvUlEZUFnE9\nC34pGCb1PLt2Uy8++VN7kuASTa9Zp7LwNPMmx5wQEj2VPaHBvL4dWBDzi0TG+OaEa1WbjNq4SRU7\npu/bKPhTos9UZ1Y1hYLumMsj7Wbl9QDZt+M4GwjYCHhvCwyIeZjdUHzzN6/HR27diVv3rMqUkaeX\n1mkpbYzKwt+32NAxN9FWTM66/IzrE9cjyTH30rbRnWfT2KD+rvcbT9tQ6qbPGZeCmG9d0YF7f+PV\neMO+AfEZHxOCylKLWMxHTrxCWl7dUXbFhiWl+rSMmKsJVHS+eUYj27JJ1ssWeK6WDTRU3uNSzLQR\nV2NjoiVVgSHT0Uaan5aVC1jZWVJoQDofuNRAlUUG77pC/IAccy/dPKtJ59T7cHk76mc/PDGOK+76\nJsv8qfZv2mBMCMfcEsvjy02krg9PY4yeYeaY51NZ8szWX3SaH9lS6203E0wNaJv+JvqcbW3wPUc5\n2V3QZFRb6c96W/Dgz5cQ839DZuoz63rLuGnnCmOHsnVgkyYy0BqVpfngz8aOOVfxuG3vgLj35HxN\nOLk95QBtBZXTKhHzJh3z0sVTWbhjpCLm2eDPGjvazHAVHbnA8VT2v/cze3EgVZvgk0rCMc+W52IR\nc5ch9pTAwSZt1Yp2M79ed7b07J5ClYUF5TUb/Ml59BcjlwjIxEE2xFy/bbkgEfMMr5SVe/vKTtx5\n4xZl8SLpLu4UruzSYjxswZ+KY25QZTE64VmKmRqsLJHWp4amMm2j/95IZbEsPvynprkn68g7mdOV\nVo23K3cyiozKMqvlCTAZ3SaLmBNS7mSeZzN+j85SoDhkyzXHXO97vP71caSf1PHnSMT80h1lIw3J\nk5Ke87WQqX5c8uOUZwDZMd/dlmSs3JRKENI1Ro55DoWBjE4NicpC7xso40T9Pd3XcSQVYmy2qmye\ndJk+muf1+UY3c/Bn+l5aXZg55lFG2rfZEw2rjrnWNzf1teOO6zYuOce8ecTcMf7fZjZqJM/8GTMq\nC7VNK4CXrsoSeK4AYF4oCYNatZeCPw1m6jN5x7OepdPbdnM2B802Uatl05wEgZjbNwHklL1yax96\nylN41dY+9LYXxMJPyjMF3xw8R452kinRVRJhAEndzLDAL47eK8f7lvrgc11H0RwVbtIx50lz9DZL\nEPPkeWMplWX/2mX49y/fIK7hdek55smiFbRYtx/+zs2Yq4a5SXEArr7R3LNocbTpmOta0SHL/Nms\n/jBHzFujsshr58VknCYlydCw1L5k4pjXWYCvbgqy6RMSLsfB6u42/OjkhLx/4GLfmoT3uneNTMrC\nKanGrH2GzbDpCJ73dRH8FAJ3fPYHmXu14pjr46bRcbMpWPViEXMy3jcVxJxlU9TlSI330fqmvH/y\nr0DMm+K3yms6NSoLD7wPPDdzWsPHdV85hyrkqg6acMyXADE3t52Dvo4iTo3N48LUApNLXErE3ANQ\nz8QuUMD65v4OIRNcCswcc7vEHmuDchYxB6BRWbJ9FUgR8xw0lps+d9k45jQPRTEy86E+v+ja2YCU\nsOQJkniCoTxrFjH/9NsruLKFTK6NbOeqThw6N423XLW2qes91zzObWZD4nnG7JDltKD5wpb7xWSm\n4M+rNvTg569Zj1dt7Wv6Pi8ke8kxN5ipP+ZxuFvVhrYNYtPmU0fM+bMcRy50JqQPAHas7BRJgzqL\nPv7uV18pvqOJ6lwaHNlTDowLAHe0KWkPt9XdJRw5PyOvL9moLDY+Gke+GGLOo/fzOOa+I2TOOF2I\ndtMUlJrH1XVsHPNWpVKYtRd9qzoFNxtiziPe2wue0Dmm621UFqonWlgSjnl+EGWpoDp7KxjafLGI\n+YKOmJtOe9jpMEfnKOjNpMRAxj+i7zmVZU2PGrjYFnh4w74BDH789VjGYgB4NZpOnkyKP8mRvINa\nGItFiC/uOoJORm2jj2tTP6H76eNGR+YzvzOqsmQua8kUxJz9X+YKiBT5UpvZAuDpc73v5pk+b7zl\nqrX4+8eGcGBDT4Zjrj+v4Ln4xI19OD62gL0r1JMV7kQVPDUDMs19rUiI2sx0D9d1sK6njEdPTuDU\n+Jwix7dUVhSbWA0xT8fEln6JmOtZGsUmuwlwiagsxC+W8RWMyqL3A5ccc8f6DH3Tps/rNioLd9jn\n62YqC1nSZ7JzfzWMlPHVrK69HTH3FH9gqZHyu997HU6MzmHXgDm7p266RHEjU+hkRV/ITSbBn8nn\niXQuUVkulmPOQJjUF/iDN+9r+h4vNHuJymIwB9lOk4uY2xxziyPaEsfcsMia7sOdYT64drJAFH0S\npKNGSuaiB6uSLWMooglR1+UDbYi5/i7/9S37sXdNF973mq3iM340pUSIu65AWgTHvK4GBqrOg5zk\niMqil51f78Ds/AWmdKCXYBvSIDq+0zcFf3JVGQDYxBZLoVbQIPhTyI2FMZNSbLyJLPquUYe9GeN9\nck7bSOj9nt+XYggEyi82XypvnhsfL9QHeNDU2u5sFkMAilMOAFx10rR51OtMr18qsypj6IpFyvRb\n7sR7rmM8kqX+bspqa/o/WYb+5jjG7LqtmGkTxMu22AAxJ7WPV2/rS+9hntd87d8801VZrt28HA98\n6Cb8zS9fm6Gy6HOr7zq4aqCE27e3Z8AInULnMidjKakspnecXaxjXW/Sb0+NzTO5xEt+nDBbUPGy\ntqTONvfLTJB6gqGGiDkbA3o/8ETft6OyEjF3Mn2ETEdp9Q2GLZFb0XcFh32hrjrUOsoeGDjmAISD\nSRY16Zjb2k+nWeXJvV6MlQt+0045YD8ZsxnfJK3tLSufq3KJhJhfHMdcj995sduL/w0vwmoGeCnP\nMbd1YFuwpA1t4Z01MCzggOrc8Ou5M8wzjvIIcb2cJJdIyKstq2JlrUw0YjoFyDjmTXLM3371Otzz\nvlcrjhJfJF3tXW065gJl0xwWXZUlT3bOdc0c82YlDJu1b/7m9fjBx27GeqZyYXJci75Kz+FpkwWV\nJcMxV49nBfocSY65DQXhC0Ip8BS5uVYC3fil8xqvMEtlyS5IXG4xeSepvKObrnMPqBs7E2Jushrz\nzE0nRjpVTaK7dmeywxIAaVJl6Sr5xufuSJOA7NRUHhoh5iaOuU57atVcyzM5b5dOdEzBn/e871X4\n5O278eFbdib3s8QbyLHceNyZTtrWLy+j6HtK8Kfr2GNzTKY4J9omjBzzy6VjXgtjrOtJ5oaTY3Oi\n3ZaWymLhmJsQc9/T5iUap+Z760F63ATHPCf4k36etJn5GXpdZKgsFsTccRwxNhZEO6Zl1aksFn1x\nXZml2RONPB1z5QTqeeZM+1627+dez8q+vlfOtzzTqEkusVWOOZ8PWsnA/UK1F/8bXoRVQ4NjnkNl\nsSLmFkfANqm7hgkw0I+xLclFuDNcZ1STjSyQRy/nik71CFdHzL985yvw0dt2Kvw0ExqxWssWx+ko\ngeEYVLcdK807el9zvHSOeT3UEHPNqScHgSew4aY45jBPFs1GszdrRd9Df2dRcbpNiL+ecW8Tc+Tp\n/XXEXA/wpN/XozgTfKhbEkCbfFfyXfS0m7n+jYyXWTjmluNLRe2hoF4jVVmywZ9kpjrkR8Fc8hGw\nj0dTggxuep3pPHEqGyFTr97Wh/ffvN14L1pg+OJiU1S6ZlMvHvnYa/HR23Yqn9ucZDK9ny8JlcUC\nCHAJujwqy7reMu545SbheGQCavXNThPjTkfMufG4jtnFMNP38hxdBSDRk3X9GHTM16fIo0JluQyO\nuS7r1532Qx78OV8LjRuxZrJXm5Jw6Z/b8nK4rtMUlQIwOeb239EatKBTWfTgTxtirjnmzerM52X+\n5JmQn2/HXAfDGhmfl2lDCSTtKubyWCYYkhzz5l3Pop8N/nyx24v/DS/CTItYZ9GuesJ3c9yRK/ke\nPnzrjsz1zVBZaHLJC/7k9+F0E6IQACrSrz93RafqUOtBigc29OLdN2xRHAGTc6Pz4vg1zaiy7F7d\nhb/5pWtx/wdvVD63qbJU61kdc0A9Rk1kx+zl0u9v45gvNWIuns15rH52sSv5nvL3MtY259JgXd2h\n1PnYVF/1MGZyffbJlha4ooaYt8Qx58GfRGUxbDx4OQGJdOsOkKSyGBBzR+0f/D70PrzL2/qfYR+u\nmA1t1U9qfut12/Gvv3MzPveua5UNsfJbQ2bLPEWlFZ2ljBOpIOaGuUTv566TVR5p1TzLMwkBm682\nF/wpy2R2lH2tTvOM9wk9BoiXd3qh1hIn3KQTb6NcXIrZ/It1qWN+enyeyfFd8uOEUWD3ntVd2LtG\ngiKEmPP5fHN/h1nH3FKfeYi5mJfY55kEQ+SYO06mfiprl+Ge970q88xSoXnHXJzw6FQWI8c8+46/\n/vlH8Wf//Kz4O25SzjJPlYXLMC41laVV0wOfGxkHAdf1csdcnvjGcSxOKIgylDe+9aGVobK8hJhf\nmj3yyCO45ZZb0NnZiY6ODtx000148MEHL+cjL5s1i5jzBbcUuHjvjVvxpfe8Qrne1t/5RDTQnUye\nAxoarSyQrLOuWtaGcsHD+t6ysqvnO3DdKetqU5UMeixUFm56Agogn/+oTOoW7h8AXLe1L+PMUEAn\nYKayVPOoLI6jBAIC+cGfrgP4mmwVAKuDdalmomHw9i8FrpqGnV0/keqyZ1RZwjzEPP0uZ7KlBa7o\nu2greBfFBzRSWUS2QPVa3jdoQaLPokjffDXimCf/VyQUfTVNu805a4SY29LH69J+juNgeYfc0PzP\nf39VZkwFRsS8tYAvXc5Pt8wGdIlVWZSNeoEcnbCp4E+yJUkw5PLNjf2ZJq5/nvH3E/JuWj0vhaNs\nQ50HlpXguQ6q9UhswpcqwRAA/MGb9+N//8rLcdX6Hty4fYX4nDjmAPDgb78Gd7/3Omzqa1c3Yg3m\nBNO8RmbimGfkEpkqi46YX7+9X1FTIsuqstidW37CQ88Bss6eLXvtwTOT+IN7D4m/G+UmIcuTyq2y\n9Xopg3wvxlqVSxxmyaM4hdb3ZIKoMDIg5jn1Zdok+S8h5ktjP/jBD3D99ddjfn4en/vc5/C5z30O\nCwsLeO1rX4uHHnrocj32slmzHHPe3WiCyESeN3EM+Om3X4G/+eVrsX/tMus1vHN3FH184/3X48t3\nXqdIQPFJy3Scy7WebcGf3D72hl342Bt2qe/jOtadviJzdBEDSqKTTib4U8glGhBn180G1OnHhMr1\njsoxf/3ulbjvgzcqiZaW0kyIeZbKwq53HZEe/ZpNvQASFPTwuWl84AuDODU2l8sxb+YIniPmgExr\n3ppjLgPl5quqXGKeljRN2NQmRL2p5wStmoI/+SlJ4DlNJd5qz9kwAlkHwWfjy1Y2ALh17wB+5427\ntXupvwWay0GgPl/+1nTcr9PNXNfBz129HgCEhn+rxl/RFPwZx3LD2Ixj3uwpRLP3sKlSAVCkXJsx\n3k/pvno9X04qi++5ApA5MToLYGk55r3tBbx883I4joMbdvSLz/mpw5ruNlyVyvbxcjbK/Kkg5pb4\nKJXKku2rQArK5MwX3FqhstAJDx0q0x5Bp1maMn+arNkYgDwqiymj6PNlrcolTrDkfYH2W5n5Uyrz\nlBqcuAAW6cqcfvVitMsml/i7v/u76O7uxte//nWUy8kRx80334zNmzfjgx/84AsOOc+TS+RINA/I\nE+hCTtQ/Nz64V3QWsX1lNrWvyaEjo6Okv/zFq/Gfv/oU/vAt+1TH3PDcFZ0lnBqbB2AP/uS2bWUn\nNvd34Pf/8Wml3OWCJxBSbnwQ5SEZNvNdB1UkE3jBUx3ymsYxp8FL75mJ1tcmXyXBEJA5wt50mdBy\nXkaAqbJwKlOgUll818FXfvU6PHBkBP2dRTzy3COoRzF+6v/5LhbrEc5MzLH09SqiWwtjxsdv7JiT\nmlBPe4AzE/MtOyGe6yAKY9EfZOZP+zgQiLnYTCAtu7r54mZyFvmiHLhu6vTO55b3zgNd+JMfTOFD\nb9xv/F7nmOvJcPLQXb0PBi1SWUxm25yLZxooW2/aP4CtKzouuk/b5BL5mBpN0TNb4KvtfgCjsrhm\nhNpkeVQWbq0eFvD3o5PSy0FlyUPB1/eWcXp8XuptL6Fjzu3KdTKwn3OEubWkyqLRA3neCxPHPD/4\ns0nHvKB+nssx1zetFirLyq5SrmNaCyMEniv6VmMqi6U8nvcT65i3ojWu/zZJMJT8P4pjTKZZWel0\nMG98Nzq9+LdAZblsjvmDDz6IN77xjcIpB4DOzk5cf/31uPvuu3H27FkMDAzk3OEnx3zXyR3sfADz\nU3Ebt7YZDVircgvr0BuXmxfZV2/rx7d+6wYAMnmQqRyAGgDaDGIOZKkrrpPI1KXgjmIqP/HiEXOS\n0wMMOuYax5zqUee+6xO4ipjrmRsv7+B3DBssZQHUJN4818GKzhLeemAtfnh8DEBC96BJ/bmRWYYu\nu8q/IaOy5L2XoLKkjt2b9q/G+GwNV7DFu/l3ixlibt6gKqosBfV0iXTXhWNuKLeyuUmfwTcege82\nRRNZ0+Xj07euRGXvKuP3WW48Pasxuquj1+TE88VFl29sZI2Om00nQ47jtCSbphufj/SgbNdJ5r2R\nmUT9KC/zJ1l2TpT3S57RDJWlOcS8VeNOFFFkMuW9jIg5AHE6Jp53efxy+J6Lhz76GsxXw6b6oS1Z\nmLif1m6B5wh0Wh83yfPNa6PrOJnvbA6ZTt3KS9OugzM2KsvG5WXhTJpsvhYi8FwBxDXaOFlVWTQq\ny/NtpsDnZn+nBmgyxDyKMZEqo5GP0SpirszrSyzI8JNol837qFarKBaLmc/ps4MHD16uRy+5dVjk\nzMh4J+N6wfSbZqW6GiFh+ud6VL3J+CRlotIqjnl7c4sbpysAyST6kVsT5Yifv2adcm0zwZ95JqTo\nWPDnA0eG8a6//AFGU0dABoy5afmS3+pUlvwEQyqVxaZeslTG5x5T5s+SFrjIFynhvLK+trKrlNEx\nVzjm2ncma0udSELM33PDFjz426/BWguSZn23tOC6XGLGwWVloX7oszLzf03lNnHw9cWhVTTaZDZ+\nsW/ZeHPLnNIYypnHjzaWp4FjnhfkfLGmKx6ROY6ksY3OEmJ+8VSWqzf2olzwBF0r3/IR83dcm9B3\nbq+szn12pmwaRRDI9oFWlIqszzHc452v3AQgO3ctJZVFt4FlbYp2uW5cTrRoOQUm01+JO7w0b/HM\nmZlM1q50zPXvTJKpQIuqLLpkrpP9TWfRR297IXdzSMnTJJXFeikAOxhX0II/n29rNLfYrK+joOWl\nkMBSFEvJYjqVz9vI6KejBe8lxHzJbPfu3Xj44YcRRRFcSnRSr+P73/8+AGB0dDT3908++SSi6Me7\nk6zVzDvkNjfG4OCg9XfHL8gACB6QR785Oaned3p6yni/0RGZPvzJJ55A0ZDcZmR4Uvy/XJvILReg\nTqonT53B4OCU8n04K/8+d/IYBidO5d6PjFAyADhz+jRet6Udf3b7KvSXI6VMp89IGsHZ06cw6Iw0\ndX+yKEwmrVMnngMTm8E/Hbog/j987iwGB2dQqybt4CBprzNTar0PnxvC4KCsvzNnGMQfx8qkdOHC\nOQwOzrVU1lZs+IIsx7FnjqB6IcDYqGz/xblp1Fl/PH3qFAbdZMwcG00mufEZeRpSjBeF833k0CGM\nlj1MTyb3O3n6DMbT7K5Dp09hMBgzlqk2n7zv/Iy5fzZtsTpuTxx7Bu54AYsLC8rniwuyb5RqyTPP\nnErKMDk1jcHBQYxPTslye+qcwcfC3Gxy/Uk2Fp964iBWF+QzTe9EY75Wq1nf+eRZtdxUv7WFpKy1\n6qL1t6dHFpW/n33mKMKRAGMjsuxToxda6mvHx6vi/88cPYyF8+rm4/yMyql+9pmjcMaaOw2zGR8r\ntcUF5X19J5kIiEc6dPI5DM6eyb3fhXPTyt9PHEzmu34Af/Wzq+BFFzA4eMH849SOjcl6OH7kaZzR\nHLef2RBjU3E59q1U257mB1vbL7B+OTsxisHBQdSr8lkAcPjQIUx0XNryeZrNT1t6A9x1Yz86CtWk\n349NKNeePHEcg+H5S3rexdronJx4Dz15EI7j4NmxauY61wEef/xx9cNY/ra6OI/BwUE8Nyp/OzJ8\nAYODcozQnFCrVfHcs88otzp3Vp2/yU5OqPP8saOHMT1kbpvq3IzydxSFGBwcxAk2pla0O3j88ccx\nPGuPTfjR409ioNMXJ3uHDz2NsXZ7fzh/djrzmecATxx8XFmjL2neXQI7eVr2/ePPPYvyzOnc63f0\nFXB4pIrXbyzixHPHxOfjY6Mo1ZK2Gh0fx9nJpC4nzp3G4OAITp1W6YXcn4hqat86d+Y0jtTkXHD0\n8CGMtl28ek0zc/5Smuu6WL9+fUu/uWyO+fve9z68613vwq/92q/hYx/7GKIowl133YUTJ04AHOXW\nUQAAIABJREFUgHDWbVav1xGGz+9OckXZxdWrS9jVF1iddgCIIzmAOSpNv4nq6gB34th8P+bQRGEN\ntdiwq2TXrG53cssFqAj+Qq2euX4ZW6/b3Kjh/ch460VRiFqthuVFIArriHizsYnZjcOm709Ga20c\nhXAsXFEHSbmpTC6Suveg9h8f2vuxgroaYo6o+bq4KGPt6EQhajX1M99RA4kRybqLwqQ/zVRlhbiI\nhexfHNZRq0VwkNJB6qGUtYrt7xW4RIWx9M8mTQdDnLTsjtaAfGpdWU7aLE7bpB4m5azJl8qUKWYb\ndxdJmYuObNOwXsetm4uYq7bjipWFhu9k+z6O1H4UhjXUapHsb469vtxY/W3SNoAHWfaS11pfi1h5\nonpyP26O9sworKNWuzTENWZzsQP1fXXmQIDG4zzWQJewrs53URNTf9ln94jqqGk4jgPgihV+2nfY\nWEe2rfnfDpszi+lYcLW+m9TppSnd0DgGgMABSm4IWiocbXMbha3PnUtlXQHwngOdKPsu6mkBednJ\nPCdbrwE/WUX6PVsvHW0+cti/+jMcy/rhxdp1UWhtG99VP3fTMjusw60su6jVagIUMtnsYhW1Uiyd\nyQb9IY6z9wrc7Pr9fLUxGZ/rkrkq30/77euW4fBIDVeuKuDoGB9Dkai/MIwwtZj8vy2d6/Q5teA5\nQsJSB8QdhIh5X0jXt6WwH0d9e95FxNZdhnIAAN75zndieHgYv/d7v4c//dM/BQC84hWvwAc/+EF8\n6lOfwpo1a/IL5vsNnfelNr2R2gIPv3J14yPVYmAekEGQIFkFDazyPFd8x40HkRULgfH4qxrJzzYt\nb0PQQFGCW+xkn9vXkQwQB4mOebPHVy7b4gaeZ3wfACgGTKO14FuvsxmVpxj48C1jsRgk9xXHoG5S\n9x2xrsqiPj/wZXsnjrl892Jgf6elsIAN1lIhQBB48Plngcoxp3dM/p/tbwts3ioVAwSBK5/huIhA\nx8j29yqJ4M9Le3cv5ZiTtRUDBIGfS+la31NCEAQoBOSZOAiCQGw2+PuT+WwGL6R9cGufj9u3d6C3\nLfk7APCOih0tVhxMax9WOx61F+dD235b1th8yW99FAI59S4rBS3VN0+pUEzvx60Dar8vBK3d32SB\nL1EsT3vfoucCbKPR2VZA0CDQO9AoPsVC0DLlZlUQ4K4b+9BesNe/yVw36Vu2tudH8h2lpN8ltAY5\nlyV1emma00XmtZYC9R0K2r2DyzwfNbLbtqvqYEXDkPLSeuXms77hp9+X2G99ba5xGZWlqPVr0xwA\nAOWiugaWS4F1XdTVV9x0nmkryrZYs6yAIAhQDO1ra4ik3OSYN+oPgZ91tQIvW1/PZxsDQCHQ+3h+\neXoD4BWpehfvEwXfk2PccTBdTfpAT3shnf9Ux7y75OLcjJr3gqwt8FFiTlRb0d6+zVgzc/5S2sX4\nsZfNMQeAj3zkI3j/+9+Po0ePorOzExs2bMC73/1utLe348CBA7m/3bNnz4/dMefHmwDQ09WOSqXS\n8HfemUngm9ljV/pt79gccI88huzt7jbed+XQIeBQctR25RVXGJ81/egPACTXvPLqKxuWDQDw+eQ4\nqmd5PyoVVeqwfWAauP8BLO8o4Korzc80WXD3OSyk6MmGDetRqaw1Xlc/MQZ8J6Gv7N65DZUNzXBH\npZW/OQbMzWHn9m0J3/j+LBVmc/r8jge+C0xMohAEqFQqCef6y0Piut3bt6KyrU/8fcoZAh5KaB2e\n64KP9fXr1qJS2dhSWVuxB0aOAgcTmsaV+/eip72A1ecOA08nR55rVvbjxMwoMJ209dYtm1DZuRIA\n0HZ+Gvi62t/ioAQgORKu7N+HjqKPlcefAJ6dRV//ChQnRwBUsXXzJlT2mIMcVx87CBw/iTWrVqBS\n2W28phkr/MMFgB39X7F/D1Z0ltD54IMAo+vU3AKA5LrXveIqFHwX5/1zwHdHUWwro1KpwPvOAwBq\n2LVNbTsAuH/4KPBEUl/9fb1iTP335ruxGPNB2mdMVj8xDvzTsPh7/959WFYOsPyxHwDnLqCrwz5P\nrJicB74mx/6e3buwrreMH808BzyWHPVWdm9HZWPz46J7dFbcc++e3VitBQrWwgj4kuz3u3buMCo8\ntWLH4zPAw+MAgK5O9X27/3kKZ6YlJe5lV+5ryO1/YuEE8K+yL1xRqVxUQGUT07O0dB4MPA+VSsXa\n9l2PPAxcSGhTe7ZtQmXvgJhbyPbt3YP+zmwMVSt2ZmIe+Oo5AEBfj7om3Dd8BHhS0h+2btmCyvb+\nzD2eL2u/MAP8o0qtCXwvMw667pvE0HTyHp2dHahUKkn/TX+7dvUAKpWt8vqHvgeMVNFWKmLXrp3K\nPLdt80ZU9mYFIybna8DfnxV/H7iiYuUhr37uIPDcSfF3IfBRqVRwYXpBtMU1uzahUlmXBCx+Jbmv\n46jqPms3bsb+zctFn9q3d4+Sw0C3x+eOK/0dSBzMSqUi7gGgKX/jctpM+4hYY3ft3I49q7O68Tbj\nftDqgZVJ5uUfTsArtaMeJXTA6w5U0F70MV0eUdby1b2dODeT1E93VwcwKumWO7Ztxcs392LFt0bh\nuw6uvuqKS4qbaWbOX0qLogjT01kqU55dVsccSII99+7dCwA4efIk/vZv/xa//Mu/jLa2tga/fP5N\nD8CxWSNpr4yOuTX4k/6132+22pomLzeTLNOW/g789m07W5ZR4++QJ/vFA2h0tKIZ+4WXb8A/HxnG\n3jXL8OTQlPGaQAsupPIEXhLNTXQIXZVFDWi7+MCXizEeuCl02BVZMlUukaupmOqbgmuAbLBlPYpF\n7ENeX13bk4zJNT2XNjb1QLWiZ9auJZlOQAb0UPmovPMiMUW+XOLljNTPpg2nz1sP/qQgJiX4swmt\ndW6NVFkCL9H9pcDZpUhO4+WMdz3YtClVlkxOhUsoXIvWaAPA37WjGGQ+M/19MWZK3EOmSwNe5uno\n/2/vzKOkKM/9/62q3maB2VkGGPZFmGFQgeDCpiJGRSGKmmNcUBAU4/JLorhdBTei8RyXczH6C957\nfuKSi0S9KD+XyEBuctHEBRQ1Nz/jToLsODPMMNPT7++Pnqp+q7qqurq7tq5+Pudw6Kmurnr393mf\n93mfJ2v08q93IFbtszz94HO6u8Tk34KQ/g4jYZs//CkI5mOBkVeWKLdbKY9//PtLwxLauUNOnd09\nqvNkmdqD3uFds4B7XqF20Ztd+rSHP+Vqlp00RCQxLcKzTC23qNFzlxiSRLx540wIovNzsx9wTDDf\nuXMnNmzYgMmTJyMajWLHjh1YvXo1Ro8ejbvvvtup19qK1fC4mU7op/kxN7hdvs+s4d125ngsf/Z9\n/DyHwDfdPemCuSAIWDZzZNbPUvurNb4vX68si6ePwOLpIwAYBxaIKCYFcvmlvisJS+jutU/TLgy0\neVB7ZXF20OQHdcWtJm+6EhLVXlkM3NXJ7GvtUn6ndePXk2BprhT1uPLk4TiuoSrnIDQy2mpSIn9q\nGoqe33uJc/EIIC1iHI86yqBz9WXoLjGULmRrSfMEpEQ/5L2y5BNgSL/zxcKSEljHbiFSu7jjhcqS\nsGTpfWpB31mvI1oyJY9vp32c9GPONRttO9EKl3ZG/rQDvfzruWLlhSw9P+ZpkT+VMdx6gKGwlIwQ\n3ZNgiIUk07akLWdFMOfacENvPBCtJxBeMO/oSqiUKxkDDOk0Oj8GylEJ11kqO/hxKSQJSpnsb+91\nlVgWTsUr0Dyb323gy6W2PILx9Uk3r9m6lS1kHBPMI5EINm/ejEcffRRtbW1oaGjAsmXLsGLFCpSV\nORe4xU4GW9QcZvJ5rf3aSGOjuFc06eRNgyvwh5tmW0qXFisR+ayi9QFuBO8aK183R2EdLzVAegh6\nvvxKIyF832uArfXvrA2G4abGnA8DL0/C/DitDTCUSUsqC7m8qzr5zEJ3D1OCD5ktIqMhCdNG1GST\nDV207dfIn7/yPT95C2qNualgnod2JxvStJe9f4Y5IcII7WJULv9u7vCjFV/rPFbcqqoEc1uESBON\nObfgtTrGmGngnSZT3+b7SLmhH3Mb0qFZiKvToP7bZ3K5Kv/ycSM9OTOiozE3E0j5XU+rAYZkl51t\nR+MZtdDacpbbXiws4bYzj0EPY4p7WP792t3mju4elWlLNi44ZSIG2nsv0Qa1y4awpP6tnGc58Bgf\nJ0VbXnXlqe/69Y2hT+848uySaZbcrwYNx3I8ZswYbN261anHO8pNJ1Xj/QMh/K/TrWmls9WYGwYY\nsjDR58JDC5vx4ge7cM2s7DXjRkiqgdk4vfmasvAYa0w0piz8FiQXhdDMv7PWK0u22oJs4TXm8oJM\na8piFB65rk8UNWURJBjD1bNG4r5Nf1W+4wWjlMY8wfkDd15LowqeJIlKvrTtesqwKvzly4O48uTh\nyjVJSXOvYN47IWY0ZTFYtNlBPgGGtItwufw7OO2b1Z251Ps5wdygnfLlZYcQaTZhx7gFr5Won4C3\ngnkm7Sb/fR8DP+a27EJwz9AqLbQac6cif+YKn/ZoKBn1WW9xHNbTmHN9VbuJK5e9kIVgDqQWopl2\nZY005gCwZMYI1Xd8mWt39zo0piwZd2H0NOa9aX3w/IlY8buP8OQl5ufu3CAf5RQ/t4QkURl35GLi\nI4trY4hUl6UE8z6xELb8YhZiYclWZWIhUZy5zsBJDaW4Zp71QwGZNTDGts16z7F75Xze8YNx3vH6\nhzNzRWufbQQ/MOdiysJjpGlJ05jzgjknNGgFIL5eRGjNRZwVYOM96Z5VtDanfLmqw2JL2PKLWcnD\nkoePGgrm6gBDLO05TmEkcIiaNvPEJZPx33/fh7ncYVReME8kmBIVL5PG3EnTozQb894/tYGcjODP\nOcjP6uQm+mzNOPhJ3mgs4du6PUIk/9lYY85PsGao+p7LO/qZhFw+4IscUVS7K2q33b52bNMuoO2I\nNGon2rGqo7sno7mGnilLgqnHQXk9klSU6O+86SGfH8qk/NEu8M2KlS9zTTJxtLtHZcqSqT3ovSfa\nm5+Fk4dg/rGDHDXHs4qUxxzIB+XjI3/K8BpzVZAyJL218GkwO0hbDJBgbgOZNOZWTVnkxuqGVjNf\n+DyYCRZ8Z833sIvRwCWbyyg25rwpC+dySyuY8/WitTF3WoDVTkjad2ptJbWDpCwwxDQHWvtwgrlc\nXvGe1OFPN8IZq7Vp+vbQoiCguiyCsyfqR2WMJxg6OQHJSxtzXlsqiSnbSb2DnHpIYrpgnk8Y7tKI\nhIqSMETBeLHLl5ctpiwGZlUA0NqZ8mR16QnDLD3P6o6bE2Tq2vxuhizIpdmY26wx17Yho8WgX9Bq\nzIFu3XmQN2WUxzD+voQmHLUq8qdWY26yKyaP7ZmUP1HtrmmOba+jq0cVRy2jKYvO9/x86AehHMhs\nMmmGSmMuiumCOSd8qyJZCwJqylKCuN92h7zAH62hwCmJJM0OjLak0+wTDdqdfN1vB3300JqBGFES\nkSAKSc1pvoddjIRKM1MW3q7czI5T1NiYOy3AxnWi2ooqLZRkqDHnKdV4wCiLpmtK4wmmHPx1Q2PO\nN9+oocZcPx38gdVOLohETGfC5bPipOmR6rClkN5GMmrMdQ5r/mTaUFSWhnHJtKFZpycsifjPa0/C\ny8tPNlzEq01Z7BUitfnlteTnNKsXWsbP028XbpCpPI50pe9mpHllsXmxoxXMtKYtfpsTVIJ52PgM\niZ7GnFc4aORyJZ9Za8xlwTyD8kd70Npq15inadcdWWvMzcvGL2RyMmD6W62Nueb3VQamLLKSRvnb\nb6tQDyCNuQ30iYXxyEWTUBqRsOtgB+54+WOsPGeC8r22UxpN5ClTDOfSaheSBSELSJbN6vMmoiQs\n5b0TYPR788OfKU2KtsOrtXYuu0vUUZiqzVVE9baikS2xZgI3sjFPacydb1x8+au9MqTuMWoykkow\nTwpIYUnQrXu+3Tk5yRkJpVZszAF13clCSb++Mbx722k594mhNeYH6PktfTuESLP+fs2sUZBEAVfN\nGGF5UrXSFpwiU98+ouOSNt1lps0ac402WLtD5jfBnM+/1j0rT1hHMOfp0ZqycMJ7tjbmybSYm7LU\nlKtNrTJV469/cjz2tHbioikNmDuhP/7rb/vw23e/ydrGnM9LQ3Upvvu+E5OziF3gFiozuSyVHWGN\nVxZtmagPf6bu1dqYk1xOgrlt8Fvy5zQPUrn2SdeY67c8+XohbOWovDRkkC0umDzElndWlCQ1jC9v\n36V4WgF4AUlMS5usMdczhVANDtAc/nTcXaKOxlxjR85rloyEiZCU3Ino6pX0y3UE826XNebp29zp\n1zMtTntYSjDX+h6W4cvLWY25frpDkrFAovq9gUDhpMmakW1/rqjNqtTPa6gpxb0LmrJ6nqSzi+AW\nmcZXfTee9i/aJZOFpbY9+00wV3uU0fdNDei7S+TRmrLwGnPt/WZevVLjvHmfqinTCubm5XpGY+r8\ny9kT6/HF3nYAyTMijMlxAjKfE+GzclxDJX55/sS8nSE4gWrXOMs5UDs2asu2khfMNQv9qrKUvNR+\nNPdYLUGhAHSzhYfW32aaH3NDG/Pe/wtgycgn0U0fxHfPb0wTArTu+Pi0yRpzPTMj1eCg2Xpz2itL\nXLuHq0mP9vCnmVaWN9dRHf7sLZce3sbchZN2Kt/1YX0BMZNnIt6URWsXmnpG6rOTQq7aHjJ1XXbx\nlemgUtiD/swLera49hPVfSVftFvZbpLpdbwpi4xqcWZTes3OSGhN6Xwml6ft7gHWAwzxaM/aiMoY\nnp3GvMSqxrxM3VezbcryWNvRlTJlsdJ+tcHi/CiUA/ktQLXuEtMPf3LKSs2YypfHoSPdKHZIY+4C\noiioQvoatXe5I2Rr2+UFVv2YO0GarbjG1pcfUOQohFof5tr7kl5ZuGc6bsqid/gz9TkakiwPkiVh\nKRmWGvqmLPEEQ3fv+7LdnsyFhupSfLQrGb7c6PBnJlOWeE/CNOonoDVlcVJjrnYDJnP+8UNQURrB\nzNHmodLdKHMtem7q8kGyuW9oPfS4SWZTFuPAV4AzXmTSD39qPHn5bE4QLWrMVWdMrJiyyMopQS/A\nkPkYqH2fHn1LQpqouKa3pyHvvHZ09yj28VYWquqxPLt3uomRi14ryOZHPQmWFMw1+eQjHJstzA91\nkGBOgrlLSIKAuLzCNtKYy9oCnw3Celg9/OkE6VHytBrzVIJKIsYDtlZQVB18cXj01BPM0w9/8oNk\n5m1cQO1HWtfG3IXKGlGXsn/WCx4EZD78mWBJl2SAsZ9vyWL55IuRz+2SiGTpsKMbuxRaVBpzh72y\n5ILWK4ObZHqfXt90QmPOoxU604Ja+UxlHpYEHNdQiSNdPYp9sF4f5Pu/nqCndU4lz32CjimLqY25\nyTjPIwgCqsoi2NuaDHqTbbmWKIJ5QjHDsdIeVLbbHowHVpHzFwunn8myQqhXMA9LYprypVzHlS+A\npB0px2ESzEkwdwtRFJQj6EYduZBszL0MEKIdfCOaQ3h6fswzaswFdzXm504ahFc+/CdG9yvXTY9W\nS5xJYy5THuW0Er2TfTdnyuKG5m14bUow57coRQuLObktxRMJxV2i3vkAQK11D+fpI9+MfDwVAM6b\nRenBu6mz27WfHc/zcsctl/eptt4d6EOZAgz5TVcjCAJeWHYiGICbN3wIQH8nIePhT627RMXGXEgz\nkbTklcWCiUgNJ5hn2zXleaSzK3X400rd5BNR000qSyO4Z36jSrudDWFJxNF4AiFJSFt06Z1/0iV9\nXVx0kGDuEiFRQFfvZ0P7WgPXXH5EFSDAa415SL3TIKm0mr2mLLqHP/k8qN0lOl0Hpx3TD6/89GSV\nEKvVmPOYbuOqbMz5w5bJiYwPmOKGj/wRdanFRjRbjXlvPhMJKDbmRqYsKq8WDtaXKCY9DCTDjucg\n1HmsMbfdj7kNzwtZWKQ5RaY6HFxVgm8PdmBYTalyLezw2JBmyuLzAENAKk0h5f/sNeZpz5QFc50u\nY1YGshvE8lhmkUYV6CbLrlmiMmUx3wHn4fuM3+f3n+TgwlWGNys1E8z1gjc9fOEkPPz7v2HV/Ako\ndkgwdwntQUM9jEKX+xFPNeZhrXZJrTHnB1t5cm2oLoUWrXDAK62c9mMuCAIaB1WornVzPhS1grl1\njTkXYKj3N7w/cDe0Nfxig8+TlaBUEq8x7zbXmJv5gbabkJj0fJNL33QjqFP6O+31Yy5aGL+ywe7D\npNmQ6X3/54qp+N//9TmunjlKuabyIuPAeDegIqb6Oz3AkH/nBL2zPTJG7fDa2aOw/r1vsHTmCNX9\n/OHPbLhgymB839mNS0/ILFTyoeGzfU9MRzC3Mibwc1IhzO+5Ii/OwpKoGvsB/fNPQOoA8PxjB2H+\nsYNcSKX/IcHcJayE0ZZvKYSO66UGQOs+T2vCwqfn5FG1eOWnJ2Mkp8WVUZlWIJmnlGbUfS2nHB0S\nSPon57d5rdqYl+nY8fHh390wq6jgtkF3Herk0pO6x6jJyGlOsNQhPCumLE7nKyQJ6OrJra17sXVt\n5louF/I5FJbpeW4LnZmayoi6ctz/o4mqayGHTFkev/g4fHXgCI5rqFJdT7cxt+2VtpPSmKcn0khj\n/vO5Y/Gz08ekLdDlbGfbJgZWlOCOs8dbulctmGf1GrVXloT8jGBpzPOBbwuJRCqf0ZBo6DpTLwp2\nsUOCuUtYOZWtd3jRr4gWhCyn4AW1iCQqg3tIp/z0NNMy/EQh/yQqCeiIs4z+cJ2A1zCEJFE1YOWi\nMZeFCT60vdP+2bXsOnhE+WxlcuLTJwd6MRLM+Wc4HUXPTCuYCTfMh7TYvYOgWlTZcfjTQ1OWgZUl\nWf9GNX7bOD7/sGmg7nW/+zHnMdvp5b0laZUdertmKRtzO1OopqKE96ed3W/lsfZonDNlsSKYu2gm\n6SUnj67FH/62FyP7leN/drcq1/toTIz4cV7nrHXRQ4K5S2iFRbN7CqHjau2z3YS3Ww7raLKslp/e\nAbRFx1ZA6lOLgRXZT975ot364xUJpn7Mw/oac3nwO9pryqLn6cBpSiP6doVGgiM/d7cflQMMZXaX\n6LTwq+zK5NDWg6Axt/vwmjpAmTvl8++LpuDZd77GXfOyt2F18/wJkL7Q9KONuYyiJdWRcrO1MRcU\nwdy5/FblYcqi2JhnefhTFSzOx4usfPnVwmb0JBgkUe3HnJ+XAHWZMdKYp0GCuUtYGdhrewOV1GUI\nWOIHvPSqwGtQwzoDv9WBT09rN3dUOZqbx9qQyuzhTVkAtWBuNjEbHf6U8yebsrgpIG64+gSs2vgJ\n/mVeanuZr5dhtfoh5XlNihwBztjGnPud46Ys6VFls/2tm2RyG5ctzh7+dKddzhrbD7PG9svpt3wa\nK3L0WJEN6Rpzx1+ZM7ImXK8eM3llSX9W8h4nlT35mLLIO6ntXT04+7E/AsguX1bvL2T0Av2VawRz\nvn5JY54OCeYuYWUr9AfDq/Fvl0/BhEF93UpWznjpx1ytMecH/uyEJ94Fmh+UGHGNxtyq7Z3aj7mO\njXk8+Vw3zViOH1qNl689WXWNbzO8m0gelcZcMWWxEmDIHY15LosbTyJ/Omhjbsf5Cy8DDOXCqN72\nOn5gXzxy0STH36ftq342ZTG1Mc9RMHfLlCVrwVzH7W62NuZ+dpdoJ3x9awVzHtKYp0OCuUvw46xR\nPxZFAbPH5abRcRsrru+cQhQFRKSklww9t3BWNXqSz4QDbbItC+a9GmVRUJu1yJraLkUw9zaT/IJp\nlIFgzgskbUfNAwypTVmczZsiMORQhqP6l+Otv+6xO0mm2G1jrg6Qkv/zvAwwlAvzmutx/NAq9O8b\nc0Xjme7H3L9llDp/YaO7RJc05tlq5vXGIivrVNWZLD9MNi7A16HWxpyHNObpkGDuEkE7la12fef+\n+6OhpGDOT2C8D1UrqLT+2vBjHvCTaUPx4ge7cNbEZDRJq+OVPFmURUOqiUY7EXoR6IaH7wNGgjmf\nZNmUJWokmKvcWzqrMde65MyG604ZjY6uHpxpcNDPCezeQbDi7jWr53nolSVX6nM4NJoraX7MfVxE\nKa9Y6d9lrzFP/u/k5l7z4ErEQgL6lWUORqRFb5yxFPmzCDXmZjbmhDlUWi6h1jgVfsf0UmMOJIW1\n1qNxXRtGy6YsHi8utFSWRvDWz2Ypf1vVJMimLNrtQm078zoUNB/oaJSO+0ogqcGSxGRY58w25qn8\nOR32XtEK5tBQyqIhrDq30e4kmTJ9dC0AoF7jHztX+OK1xV2iStDP+3GBo5A05jPG1OHF7btw+vgB\nad8ZucgzQs6nkzbmJREJT/+oHj1xe0K/WwowFLD53wp8vzYzZSHSodJyCS8OOzmJ1xov2c6cF8zl\na1a1hX4zZdFi1faO15jzaLU7XgS64fliX8p1YlVZxPA+RTDPwsY8HHI2b1pf+X6nX98Y3rv9NNs0\nVXYvxEMOB+wpdLQLTT+bPzQPqcRmTqHAk+3hTyNTFrubSEQS0J2w56FW+oMYsB1zK/B5thKRlUhB\nugqX8NKLiROo3J15kB1ZWOO9spzZNBDnHTcYl51oLaSwKArKgO/HKrF6JkYWvrR2fOkac68F8zZL\n98mC2hHFXaIFG3O3NOYFNKnWlEcNdxuyxX53ianPbrtbLQS0gngBNTsV2dqYGx3+9NPibcn04agp\ny+4AaVFqzHkbc9KYZwUJ5i5hJcBQIcErX72YWGWBg/d40b9vDA9d0IyJgystP0cJSuQDG3MtVg9/\nnjSqBmc1DcTSGerw1tqJ0Gk77EwsOmk4AOCc5nrT++R0t/WaspToeEIAAMZZ4Tu9GyDb/BbLpKrF\nblM8fiFVpEWaFYWqzOHHnGwC8Wjv9dOOwW1njcefVpyi/C3HWzCDT36xjCFm7hIJc6i0XMJr0w+7\n8VpjrmfKkgvJumC+FA6s2pj3iYXxrxcfl3Zde9jT6wnh4h80YNKQSozp38f0PtmNZduTGKOBAAAa\nMUlEQVRRc1OWngQvmLsUYMiPDcUF7HaXWIwaxHwo1DLiXdtaOXyesjFXX/eTxhxQn3s50N6V8f5i\nPPzJt1k6/JkdAdDdFgZBE8y9PvypaMzz9NcsD5J+rJJ8/btqzTu8nhAEQUDjoIqMPrYVU5Yuc1MW\nfkfBLXeJhSog5Yvaq5QNz1MdvC7OMs2E3w6n54JenAkzJg+rQt9YCCeOrFVd93O36+jOrDEP2vxv\nBavuEol0qLRcImjuEr0eaFIHPfN7t6hsneadJNuxaspihLadee0u0SradBu5S4xzkVKd9soim8r4\nTXPnFnzx2hNgSP8zkUISBPRADvtemIXEL8Kt5GDKsGps/5fT023sC7yR8GNaoYzD+cLXWXnU+Wi5\nQcLR2eyDDz7A/PnzUV9fj9LSUowbNw6rVq3CkSNHMv84YKhMPwp8kAG892OuaMzzVN8pNuY+nPjy\nDbygtbv22l2iVbSCuZEpC18+TvcpueyCsKjOBdFmjbnsFjP5vOIs00yogtL4cHyyAi+YW1U06PVl\nP+Y/m3MtQXP+YAWVjTlpzLPCsdL65JNPcOKJJ2Ls2LF4+OGHUVtbiz/84Q9YtWoV3nvvPbz88stO\nvdqXqDTmAeiYKo2XBxOrXTbmslDgxyqxW2PuRWj4XNCm2yjyZ77lkw1Fb2PugGAhu8UsFkElW/zu\nztUKvPDak4emwY/5ryqNYE/rUUv38ul32oOUX+DbLx3+zA7HSuvZZ59FZ2cnNmzYgJEjRwIATjnl\nFPzzn//Ek08+iYMHD6Kqqsqp1/sOtemHhwmxCa8nDbs05opgnneKHCBPuVM7ARSKUKm1hTdy+Rd3\nMZZzsQvm/OLbLsFCHkPIxlwf9a5kYZYRH1MiH8Hcj/2uusy6YB40r2xWEEgwzxnHmkg4nLQpqqio\nUF2vrKyEKIqIRIwDjAQRlWDuw0EmW9ReWTy0Mc8zsIwsHPjR7C9fjbDWltFrd4lW0fYPI8E84aZg\nLhW3YA7wB2DteZ6y2CneIjUlCG2NF87yGc78uKsypLrU8r1qd6OFMQ7nS1dPQvlcFrUnnkKx4Ngy\n5rLLLsPDDz+Mq6++Gr/85S9RV1eHrVu34oknnsDy5ctRVlZm+vuPP/4YiUTC9B676e7uVv7fsWOH\nrc9ub2tVPn/91ZfYEf/O1ue7zYF9h5TPn37yCXaXuNvxvj+YfP/hgwfyqis5LLPc1pyo+1zpPJrS\nxuSSJq1gf6S91Td5MyPepdZC/b+/foyYjieXUGsqpHau+bLa51sPHwYAHMqzvRUyQu8WztdffYUd\nPXvyfyBL9rm2Vm/apZPjvR2wnpS3Dz+mL1u++vpr7IgcyOm3PT1xW8vAjrq/cJSAv+0K4+wxZRmf\n0dGdkmW+/uoL7OjendM7C4ku7nD+Z3/92HRx5Wb7drvfi6KIhoaGrH7jmGA+bNgwbNu2DQsWLFBM\nWQDguuuuw8MPP5zx9/F4HD09md0QOYVcebbBCUmJnh77n+82LDXQ9MTj6O52dxE1skqCJAAjKqW8\nylIv8qdf6obXCOeaJhFAQvnMfJM3M7TDt5CIo7s7fVAfUArcN7saVTHRlnyZPUMWSoUCKUMnkJdG\nLGHP+CUIyTJlzPsy9fr9evhxTMqHrnju7cbJfpfrcysjwENzqi09oyeeGstZEOZ/CwgA/m1eHUQx\nKSOYSXNelYcb75Wk7JWWjgnmX375JebNm4f+/fvjhRdeQF1dHd555x3cc889aGtrw9q1a80TFgpB\ndHnLh68k2RTHLnizgkgoZPvz3SbENbZIJISwTaG/rTJ9WBhTB5cjmqcpS8orS+qab+qGm5lzTVMk\nJKCzd1IISaJ/8mYCb2MeFoGoidnbhAH55cdqn5fNgAqlDJ1AFAUgwRAJ2zN+JU01GEKS4EmZOjne\n24FkQ//3E4Io5ZwPSbC3jbhe92JKMLer/xQC1Raz6WZ5uF33ucixjgnmK1aswPfff4/t27crZisz\nZsxAbW0trrjiClx66aWYOXOm4e8nTJjgumC+Y8cOdHd3IxwOo7m52dZnV+98D/g2uX01atQINI+u\ns/X5bjNw9/8AnybNc5oaG1FZWphnBso2Hwa+b0W4d6HhRN3nSmjTPqBXz5Brmmr+737sOtSR/Fxd\n5Zu8mVH+xz8BvaZKJZGQo2m22uf7/f1D4Isj6F9Xh+bmCY6lx8+Ef7cbnfE4Ro8ciebRtZl/kIHY\npn1ARyeqKis9aZdOjvd2EN20D+jIr//7gue+BQCcNvkYNA+vzuqntRv3YF9bF+Y0DUJzc5NtSXK7\n7uM9CeA/dgEARo8aheaRNY6/0/f0tgvA3fbtdt0nEgm0trZmvpHDMcF8+/btGD9+fJot+ZQpUwAA\nO3fuNBXMgwZ/4CMQ7hID4DEASOXDj3mw42xjRUlYEcy9jvxpFf4woNHBT7cJFbkfc4ALxmWTvkRS\ndquKt0zNCIKTAAB4/YYZ+GJfG6ZmKZQDwMvXnow3Pt6NC6cMcSBl7lGMAYaI3HFMMK+vr8fOnTvR\n1taG8vJy5fq2bdsAAIMHD3bq1b6E74t+FAKzxWt3iXahZ8riF+zw011VltqqKxT/uXw6/SKYUzCc\nVN7takdK3yviMjUjKG1t7IA+GDugT06/HVRZgkUnDbc5Re4jOBAHgAgujgnmN9xwA+bPn485c+bg\nxhtvRG1tLd5++23cf//9GD9+PH74wx869WpfonaXVPgdUwpAVDqA0wL6MAt2OAOsLEmZGBWKxpyX\n+4yCC7nNoMoSAMDAipjHKfEOufnY5S7Rz33PDwRhZ5VIIQfUKpRxmPAOxwTzc845B2+99RZWr16N\n66+/HocPH8aQIUOwdOlS3HLLLcXnx9zmkNZe47Ufc7sIKaYsHidEB2aDxryylNOYF8gWqlpj7o/O\ncvlJw3Dc0EpMHFzpdVI8Q+7ndvlhDpEpiym0kxAsJEFAD1ggFHOEszgajmn27NmYPXu2k68oGHih\nKGimLIWcnTMmDMC+tqMYWxNFyrGgP5g+ug4vfrAL/ftGc35GVWnhacz5iSvqE415WBJx/NDsbWSD\nREVJGHtaj6JvzJ5pQxbISTDXhzTmwUIUAfQEY8eccBaKk+oS/OQThAFXCojGfMmMEVgyY0TvSW1/\nCeYrz52ACfV98cOmgTk/Q60x94f2ORN82/KLjTkBPLiwGZ/tacOIuvLMN1tAVlaQnKIPacyDhTzv\nF4qChPAOEsxdQgqYjbkYkMOffqZvLIzF00fk9YzKAteY60X8JLxh0pBKTBpinymPRBpzUwqkuxIW\nSSpGegpGQUJ4BwnmLiEG7FR20BYaQaWqAG3M+R2lkghpzIOK4i6Rxg9dCmUhTVjj6lkj8bfvWjG0\nutTrpBA+hwRzl1CZfgRgwRwUP+ZBhzdlsevQntNIEq8xJ8E8qMiHfEn+1IcWLMFi2cyRXifBV/QG\nEiZ0KIyZOgDw2o9A2JgLZB9aCPCmLOECqayQysachqigIq8Tg7CD6ARULkSQofZtDM16LqFyL1gg\nApIZEk2qBQHvlaVQ4BeudPgzuFA0VXOCoMAhCCNIdjCGBHOXkAJmY06uzgoD3rVdW1fcw5RYx4/u\nEgn7kRUUNIToUyCWZwSRE9TvjaGu7xJi0ExZaFItCHgPAG2dhSeY+yXyJ2E/FGDIHNpJIIIM9Xtj\nSDB3CZXGPAClLtGkWnC0HS08wZxszIOLXM8kgOpDYysRZKjbG0OznkvwruqCMBEJdPiz4CgUjbn6\n8CdpzIOKrKwg+VOfIMwTBGEELTyNIcHcJQLnx5xszAuOEXVlXifBEiJpzIsCSaIxxIwgmDwShCHU\nvA2hWc8l+GBfQZiI5PwEICuBZ+O1J2PpjBG47tTRXifFEiqNOfkxDyyy4EkCqD4UH4IIMoMqS7xO\ngm+hAEMuwQvjQdiiVLyyBCAvQadpcAWaBld4nQzLqDTmFPkzsKQOf3qcEJ9CkduJILPm4uNw539+\njOWzR3mdFN9BgrlL8FrAIExEdPiTcArSmBcHKc9ONIboEQQFDkEYMaKuHE9f+QOvk+FLaE3uElLA\nAgyJpO0iHELi3BaRjXlwkV15hmgQ0YWUHgRRnNCs5xKB82MukLaLcAaK/FkcnDupHlOHVWPOhP5e\nJ8WXnNU0EAAwoG/M45QQBOEmZMriElLAbMwl0pgTDsG7FqUAQ8Fl2oga/MeyE7xOhm85o3EA1i87\nAaP7lXudFIIgXIQEc5fgNeZBUDKL5C6RcAiRNOYEAUEQMGVYtdfJIAjCZciUxSVCQTNlocOfhEOE\nyI85QRAEUaTQrOcSvPlKMExZkv+TXE7YjUSRPwmCIIgihQRzl+A1y0E4MDmkuhQRScSIOrJ/JOyF\nF8yjIRqiCIIgiOKBbMxdQhY2gqAtB4B+fWL471tOQd9Y2OukEAFD7iOxsBiIRSxBEARBWIUEc5cQ\nAxh+urY86nUSiACSEszJjIUgCIIoLmif2CWU8NNU4gRhiiKYU9RPgiAIosggMdElyIsJQVgjxJmy\nEARBEEQx4djMd/nll0MQBMN/b7/9tlOv9iWyH/MgmbIQhBOQKQtBEARRrDhmY37HHXdg2bJladfn\nzZuHaDSKKVOmOPVqXyIL5GJADn8ShFOQYE4QBEEUK44J5iNHjsTIkSNV17Zu3Yp9+/bh9ttvhyQV\n16RLIewJwhrDa8sgCMCY/uSKkyAIgiguXPXKsnbtWgiCgCuuuMLN1/qCoLlLJAinmFBfgbdvOZW8\n/hAEQRBFh8AYY2686PDhwxg4cCBOOukkvPnmm6rvEokEWltbVde+/vprJBIJN5Km0N3drXwOh+31\nz/3p3qNY8fu9qCoR8e/z6219NpE/TtY94V+o3osXqvviheq+eHG77kVRRENDg+panz59IJq46HNN\nY/7cc8+ho6MDV155paX74/E4enp6HE6VMXzl2UGiNy+iA88m7IXqpzihei9eqO6LF6r74sWNus/F\nbNs1wXzt2rWoqanBggULLN0fCoVMVxRO4ORKqqFKQllYwKjqCK3QfQhpUIoTqvfiheq+eKG6L168\n0JhniyuC+Ycffoh3330X119/PaJRa3ajEyZMcF0w37FjB7q7uxEOh9Hc3Gz789+dNBHRkEieWXyI\n03VP+BOq9+KF6r54obovXtyuez1T7Uy4IpivXbsWALB48WI3XudbSiLF5YmGIAiCIAiCsI7jKumj\nR49i3bp1mDp1KhobG51+HUEQBEEQBEEUJI4L5i+99BIOHDhQ9NpygiAIgiAIgjDDccF87dq1KCsr\nw0UXXeT0qwiCIAiCIAiiYHHcxvyNN95w+hUEQRAEQRAEUfC46/aEIAiCIAiCIAhdXPNjboZe8FG3\no34CSX+TkiRBFEVP3k94B9V9cUL1XrxQ3RcvVPfFi9t1r/cOPZmXR2CZ7nCBeDyO9vZ2r5NBEARB\nEARBEI5RVlaGUMhYL06mLARBEARBEAThA0gwJwiCIAiCIAgfQII5QRAEQRAEQfgAX9iYJxKJNAN5\nQRAgCIJHKSIIgiAIgiCI3GGMpR32FEURomisF/eFYE4QBEEQBEEQxQ6ZshAEQRAEQRCEDyDBnCAI\ngiAIgiB8AAnmANra2nDDDTegvr4esVgMkyZNwvPPP+91sogcaG1txU033YTTTz8ddXV1EAQBd911\nl+6977//Pk477TSUl5ejsrISP/rRj/D555/r3vvYY49h3LhxiEajGD58OFauXInu7m4Hc0Jky+bN\nm3HFFVdg3LhxKCsrw6BBg3DuuefivffeS7uX6j5YbN++HWeddRYaGhpQUlKC6upqnHDCCVi3bl3a\nvVT3weY3v/kNBEFAeXl52ndU98Fhy5YtyllE7b+3335bde/vf/97nHDCCSgtLUVtbS0uv/xy7Nmz\nJ+2Z3d3dWLlyJYYNG4ZoNIpx48bhsccecytLKRjB5syZwyorK9mvf/1rtnnzZrZ48WIGgD3zzDNe\nJ43Iki+++IJVVFSwGTNmKPV45513pt336aefsj59+rDp06ezV199lW3YsIFNmDCB1dfXsz179qju\nveeee5ggCOyWW25hLS0t7IEHHmCRSIQtWbLEpVwRVjj//PPZ7Nmz2Zo1a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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -358,7 +365,7 @@ "import matplotlib.pyplot as plt\n", "\n", "xs = range(500)\n", - "ys = randn(500)*1 + 10.\n", + "ys = randn(500)*1. + 10.\n", "plt.plot(xs, ys)\n", "print('Mean of readings is {:.3f}'.format(np.mean(ys)))" ] @@ -403,7 +410,7 @@ "data": { "image/png": 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Fi3j00Udd9j333HM888wzCuwiYlkK6yIizk4B84CDTnV/YBia8aUE8vHxYfr06bz00ksu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\nadasGdOmTSMrK8uEDkWKjp/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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -497,7 +504,9 @@ "\n", "It makes sense that the predicted position is the previous position plus the movement. What about the variance? It is harder to form an intuition about this. However, recall that with the `predict()` function for the discrete Bayes filter we always lost information. We don't really know where the dog is moving, so the confidence should get smaller (variance gets larger). $\\mu_{f_x}^2$ is the amount of uncertainty added to the system due to the imperfect prediction about the movement, and so we would add that to the existing uncertainty. \n", "\n", - "Here is our implementation of the predict function, where `pos` and `movement` are Gaussian tuples in the form ($\\mu$, $\\sigma^2$):" + "Let's take advantage of the `namedtuple` class in Python's `collection` module to implement a Gaussian object. We could implement a Gaussian using a tuple, where $\\mathcal N(10, 0.04)$ is implemented in Python as `g = (10., 0.04)`. We would acces the mean with `g[0]` and the variance with `g[1]`.\n", + "\n", + "`namedtuple` works the same as a tuple, except you provide it with a type name and field names. " ] }, { @@ -508,8 +517,107 @@ }, "outputs": [], "source": [ + "from collections import namedtuple\n", + "gaussian = namedtuple('Gaussian', ['mean', 'var'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can create a print a Gaussian with:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Gaussian(mean=3.4, var=10.1)\n", + "Gaussian(mean=4.5, var=0.04000000000000001)\n" + ] + } + ], + "source": [ + "g1 = gaussian(3.4, 10.1)\n", + "g2 = gaussian(mean=4.5, var=0.2**2)\n", + "print(g1)\n", + "print(g2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I find that the printed value is a bit verbose, so I replace the `__repr__` method:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def gaussian_repr(self):\n", + " return '𝒩(μ={:.3f}, 𝜎²={:.3f})'.format(self[0], self[1])\n", + "gaussian.__repr__ = gaussian_repr" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This gives us the more readable:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "𝒩(μ=4.500, 𝜎²=0.040)\n" + ] + } + ], + "source": [ + "print(g2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here is our implementation of the predict function, where `pos` and `movement` are Gaussian tuples in the form ($\\mu$, $\\sigma^2$):" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from collections import namedtuple\n", + "gaussian = namedtuple('Gaussian', ['mean', 'var'])\n", + "def gaussian_repr(self):\n", + " return '𝒩(μ={:.3f}, 𝜎²={:.3f})'.format(self[0], self[1])\n", + "gaussian.__repr__ = gaussian_repr\n", + "\n", "def predict(pos, movement):\n", - " return (pos[0] + movement[0], pos[1] + movement[1])" + " return gaussian(pos.mean + movement.mean, pos.var + movement.var)" ] }, { @@ -521,23 +629,24 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "(25, 0.530)" + "𝒩(μ=25.000, 𝜎²=0.530)" ] }, - "execution_count": 6, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "%precision 3\n", - "predict((10, .2**2), (15, .7**2))" + "pos = gaussian(10., .2**2)\n", + "move = gaussian(15., .7**2)\n", + "predict(pos, move)" ] }, { @@ -594,23 +703,31 @@ }, { "cell_type": "code", - "execution_count": 7, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "𝒩(μ=10.377, 𝜎²=0.037)" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "def gaussian_multiply(g1, g2):\n", - " mu1, var1 = g1\n", - " mu2, var2 = g2\n", - " mean = (var1*mu2 + var2*mu1) / (var1 + var2)\n", - " variance = (var1 * var2) / (var1 + var2)\n", - " return (mean, variance)\n", - "\n", + " mean = (g1.var * g2.mean + g2.var * g1.mean) / (g1.var + g2.var)\n", + " variance = (g1.var * g2.var) / (g1.var + g2.var)\n", + " return gaussian(mean, variance)\n", "\n", "def update(prior, likelihood):\n", " posterior = gaussian_multiply(likelihood, prior)\n", - " return posterior" + " return posterior\n", + "\n", + "update(pos, move)" ] }, { @@ -620,14 +737,12 @@ "Perhaps this would be clearer if we used more specific names:\n", "\n", "```python\n", - "def update_dog(dog_pos, dog_var, measurement, measurement_var):\n", - " estimated_pos = gaussian_multiply(\n", - " (dog_pos, dog_var), \n", - " (measurement, measurement_var))\n", + "def update_dog(dog_pos, measurement):\n", + " estimated_pos = gaussian_multiply(measurement, dog_pos)\n", " return estimated_pos \n", "```\n", "\n", - "That is less abstract, which perhaps helps with comprehension, but it is poor coding practice. We are writing a Kalman filter that works for any problem, not just tracking dogs in a hallway, so we won't use variable names with 'dog' in them. Still, the `update_dog()` function should make what we are doing very clear. \n", + "That is less abstract, which perhaps helps with comprehension, but it is poor coding practice. We are writing a Kalman filter that works for any problem, not just tracking dogs in a hallway, so we won't use variable names with 'dog' in them. Also, this form obscures the fact that we are multiplying the likelihood by the prior.\n", "\n", "We have the majority of our filter implemented, but I fear this step is still a bit confusing. I've asserted that we can multiply Gaussians and that it correctly performs the update step, but why is this true? Let's take a detour and spend some time multiplying Gaussians." ] @@ -643,23 +758,23 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 12, "metadata": { - "scrolled": true + "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "(10.0, 0.5)\n" + "𝒩(μ=10.000, 𝜎²=0.500)\n" ] }, { "data": { "image/png": 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zoP6vb/SzX7+p/6uO2WymTRvHNrxzKFlPSkqiQ4cORY4HBAQUnC+JzWbj9ttv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\nmKyv4btC+MVKfUFINHQcA85i6PaQfuGoHDSFqN/MNmjRo/J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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -667,15 +782,15 @@ } ], "source": [ - "z = (10., 1.) # Gaussian N(10, 1)\n", + "z = gaussian(10., 1.) # Gaussian N(10, 1)\n", "\n", "product = gaussian_multiply(z, z)\n", "\n", "xs = np.arange(5, 15, 0.1)\n", - "ys = [stats.gaussian(x, z[0], z[1]) for x in xs]\n", + "ys = [stats.gaussian(x, z.mean, z.var) for x in xs]\n", "plt.plot(xs, ys, label='$\\mathcal{N}(10,1)$')\n", "\n", - "ys = [stats.gaussian(x, product[0], product[1]) for x in xs]\n", + "ys = [stats.gaussian(x, product.mean, product.var) for x in xs]\n", "plt.plot(xs, ys, label='$\\mathcal{N}(10,1) \\\\times \\mathcal{N}(10,1)$', ls='--')\n", "plt.legend()\n", "print(product)" @@ -696,14 +811,14 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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IYSEBAQG88MILJdb/8uXL+fLLL0us/9Jm1gqmkZGRNGzYELU6+2HNmjXL2t+h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NOu32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\n/BSHdSIiIiIiP/UPGKpfVEWEna0AAAAASUVORK5CYII=\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -711,25 +826,25 @@ } ], "source": [ - "def plot_products(m1, v1, m2, v2): \n", + "def plot_products(g1, g2): \n", " plt.figure()\n", - " product = gaussian_multiply((m1, v1), (m2, v2))\n", + " product = gaussian_multiply(g1, g2)\n", "\n", " xs = np.arange(5, 15, 0.1)\n", - " ys = [stats.gaussian(x, m1, v1) for x in xs]\n", - " plt.plot(xs, ys, label='$\\mathcal{N}$'+'$({},{})$'.format(m1, v1))\n", + " ys = [stats.gaussian(x, g1.mean, g1.var) for x in xs]\n", + " plt.plot(xs, ys, label='$\\mathcal{N}$'+'$({},{})$'.format(g1.mean, g1.var))\n", "\n", - " ys = [stats.gaussian(x, m2, v2) for x in xs]\n", - " plt.plot(xs, ys, label='$\\mathcal{N}$'+'$({},{})$'.format(m2, v2))\n", + " ys = [stats.gaussian(x, g2.mean, g2.var) for x in xs]\n", + " plt.plot(xs, ys, label='$\\mathcal{N}$'+'$({},{})$'.format(g2.mean, g2.var))\n", "\n", - " ys = [stats.gaussian(x, *product) for x in xs]\n", + " ys = [stats.gaussian(x, product.mean, product.var) for x in xs]\n", " plt.plot(xs, ys, label='product', ls='--')\n", " plt.legend();\n", " \n", - "z1 = (10.2, 1)\n", - "z2 = (9.7, 1)\n", + "z1 = gaussian(10.2, 1)\n", + "z2 = gaussian(9.7, 1)\n", " \n", - "plot_products(z1[0], z1[1], z2[0], z2[1])" + "plot_products(z1, z2)" ] }, { @@ -749,14 +864,14 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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F0fHRaA1aGnk1Itgz2HaJnP0Jrh0CjQt0f80sTfau25uTySdRKszQD6RxNi6W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sFscnk5p9DV9XBybXcJnGPysvZqP9o/FpUruxla39XYnt1hyAWRtP2nSzpEHN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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -774,10 +889,11 @@ } ], "source": [ - "prior, z = (8.5, 1.5), (10.2, 0.5)\n", - "plot_products(prior[0], prior[1], z[0], z[1])\n", - "prior, z = (8.5, 0.5), (10.2, 1.5)\n", - "plot_products(prior[0], prior[1], z[0], z[1])" + "prior, z = gaussian(8.5, 1.5), gaussian(10.2, 0.5)\n", + "plot_products(prior, z)\n", + "\n", + "prior, z = gaussian(8.5, 0.5), gaussian(10.2, 1.5)\n", + "plot_products(prior, z)" ] }, { @@ -800,7 +916,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 15, "metadata": { "scrolled": false }, @@ -808,7 +924,7 @@ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "9059fd1da4fb4d0fa87bd0db474ac9bc", + "model_id": "575bf26bb2794e9094e1ccf47eb34876", "version_major": 2, "version_minor": 0 }, @@ -823,7 +939,12 @@ "source": [ "from ipywidgets import interact\n", "\n", - "interact(plot_products,\n", + "def interactive_gaussian(m1, m2, v1, v2):\n", + " g1 = gaussian(m1, v1)\n", + " g2 = gaussian(m2, v2)\n", + " plot_products(g1, g2)\n", + " \n", + "interact(interactive_gaussian,\n", " m1=(5, 10., .5), m2=(10, 15, .5), \n", " v1=(.1, 2, .1), v2=(.1, 2, .1));" ] @@ -834,12 +955,53 @@ "source": [ "## First Kalman Filter\n", "\n", - "Let's get back to concrete terms and implement a Kalman filter. We've implemented the `update()` and `predict()` functions. We just need to write some boilerplate code to simulate a dog and create the measurements. I've put a `DogSimulation` class in `kf_internal` to avoid getting distracted with that task. The filtering is performed by 3 lines of code inside the `for` loop." + "Let's get back to concrete terms and implement a Kalman filter. We've implemented the `update()` and `predict()` functions. We just need to write some boilerplate code to simulate a dog and create the measurements. I've put a `DogSimulation` class in `kf_internal` to avoid getting distracted with that task. \n", + "\n", + "This boilerplate code sets up the problem by definine the means, variances, and generating the simulated dog movement." ] }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 16, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import kf_book.kf_internal as kf_internal\n", + "from kf_book.kf_internal import DogSimulation\n", + "\n", + "np.random.seed(13)\n", + "\n", + "process_var = 1. # variance in the dog's movement\n", + "sensor_var = 2. # variance in the sensor\n", + "\n", + "x = gaussian(0., 20.**2) # dog's position, N(0, 20**2)\n", + "velocity = 1\n", + "dt = 1. # time step in seconds\n", + "process_model = gaussian(velocity*dt, process_var) \n", + " \n", + "# simulate dog and get measurements\n", + "dog = DogSimulation(\n", + " x0=x.mean, \n", + " velocity=process_model.mean, \n", + " measurement_var=sensor_var, \n", + " process_var=process_model.var)\n", + "\n", + "# create list of measurements\n", + "zs = [dog.move_and_sense() for _ in range(10)]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here is the Kalman filter." + ] + }, + { + "cell_type": "code", + "execution_count": 17, "metadata": { "scrolled": false }, @@ -867,47 +1029,19 @@ } ], "source": [ - "import kf_book.kf_internal as kf_internal\n", - "from kf_book.kf_internal import DogSimulation\n", - "\n", - "np.random.seed(13)\n", - "\n", - "process_var = 1. # variance in the dog's movement\n", - "sensor_var = 2. # variance in the sensor\n", - "\n", - "x = (0., 400.) # dog's position, N(0, 20**2)\n", - "velocity = 1\n", - "dt = 1. # time step in seconds\n", - "process_model = (velocity*dt, process_var) \n", - " \n", - "# simulate dog and get measurements\n", - "dog = DogSimulation(\n", - " x0=x[0], \n", - " velocity=process_model[0], \n", - " measurement_var=sensor_var, \n", - " process_var=process_model[1])\n", - "\n", - "# create list of measurements\n", - "zs = [dog.move_and_sense() for _ in range(10)]\n", - "\n", "print('PREDICT\\t\\t\\tUPDATE')\n", "print(' x var\\t\\t z\\t x var')\n", "\n", - "# run the filter\n", - "xs, predictions = [], []\n", - "for z in zs:\n", - " # perform Kalman filter on measurement z\n", + "# perform Kalman filter on measurement z\n", + "for z in zs: \n", " prior = predict(x, process_model)\n", - " likelihood = (z, sensor_var)\n", + " likelihood = gaussian(z, sensor_var)\n", " x = update(prior, likelihood)\n", "\n", - " # save results\n", - " predictions.append(prior[0])\n", - " xs.append(x[0])\n", " kf_internal.print_gh(prior, x, z)\n", "\n", "print()\n", - "print('final estimate: {:10.3f}'.format(x[0]))\n", + "print('final estimate: {:10.3f}'.format(x.mean))\n", "print('actual final position: {:10.3f}'.format(dog.x))" ] }, @@ -920,9 +1054,25 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 18, "metadata": {}, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 1.000 401.000\t1.354\t 1.352 1.990\n", + " 2.352 2.990\t1.882\t 2.070 1.198\n", + " 3.070 2.198\t4.341\t 3.736 1.047\n", + " 4.736 2.047\t7.156\t 5.960 1.012\n", + " 6.960 2.012\t6.939\t 6.949 1.003\n", + " 7.949 2.003\t6.844\t 7.396 1.001\n", + " 8.396 2.001\t9.847\t 9.122 1.000\n", + " 10.122 2.000\t12.553\t 11.338 1.000\n", + " 12.338 2.000\t16.273\t 14.305 1.000\n", + " 15.305 2.000\t14.800\t 15.053 1.000\n" + ] + }, { "data": { "application/javascript": [ @@ -1721,6 +1871,22 @@ "from kf_book import book_plots as book_plots\n", "from kf_book.book_plots import reset_figsize\n", "\n", + "\n", + "# save output in these lists for plotting\n", + "xs, predictions = [], []\n", + "\n", + "# perform Kalman filter\n", + "x = gaussian(0., 20.**2)\n", + "for z in zs: \n", + " prior = predict(x, process_model)\n", + " likelihood = gaussian(z, sensor_var)\n", + " x = update(prior, likelihood)\n", + "\n", + " # save results\n", + " predictions.append(prior.mean)\n", + " xs.append(x.mean)\n", + " kf_internal.print_gh(prior, x, z)\n", + " \n", "%matplotlib notebook\n", "fig = plt.figure(figsize=(9,4))\n", "canvas = fig.canvas\n", @@ -1741,7 +1907,7 @@ "\n", " book_plots.plot_filter(xs[:i])\n", " plt.xlim(-1, 10)\n", - " plt.ylim(0,20)\n", + " plt.ylim(0, 20)\n", " fig.canvas.draw()\n", " time.sleep(time_step)\n", " \n", @@ -1756,18 +1922,194 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Ignoring the boilerplate, the filter is:\n", + "I've plotted the prior (labeled *prediction*), the measurements, and the filter output. For each iteration of the loop we form a prior, take a measurement, form a likelihood from the measurement, and then incorporate the likelihood into the prior. \n", + "\n", + "If you look at the plot you can see that the filter estimate is always between the measurement and prediction. Recall that for the g-h filter we argued that the estimate must always be between the measurement and prior. It makes no sense to choose a value outside of the two values. If I predict I am at 10, but measure that I am at 9, it would be foolish to decide that I must be at 8, or 11." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Code Walkthrough\n", + "\n", + "Now let's walk through the code.\n", + "\n", + "```python\n", + "process_var = 1.\n", + "sensor_var = 2.\n", + "```\n", + " \n", + "These are the variances for the process model and sensor. The meaning of sensor variance should be clear - it is how much variance there is in each measurement. The process variance is how much error there is in the process model. We are predicting that at each time step the dog moves forward one meter. Dogs rarely do what we expect, and things like hills or the whiff of a squirrel will change his progress. If this was a robot responding to digital commands the performance would be much better, and perhaps the variance would be $\\sigma^2=.05$. These are not 'magic' numbers; the square root of the variance is the distance error in meters. It is easy to get a Kalman filter working by just plugging in numbers, but if the numbers do not reflect reality the performance of the filter will be poor.\n", + "\n", + "```python\n", + "x = gaussian(0., 20.**2)\n", + "```\n", + "\n", + "This is the dog's initial position expressed as a Gaussian. The position is 0 meters, and the variance to 400 m$^2$, which is a standard deviation of 20 meters. You can think of this as saying \"I believe with 99.7% accuracy the position is 0 plus or minus 60 meters\". This is because with Gaussians ~99.7% of values fall within $\\pm3\\sigma$ of the mean.\n", + "\n", + "```python\n", + "process_model = gaussian(velocity*dt, process_var)\n", + "```\n", + "\n", + "This is the process model - the description of how we think the dog moves. How do I know the velocity? Magic? Consider it a prediction, or perhaps we have a secondary velocity sensor. If this is a robot then this would be a control input to the robot. In subsequent chapters we will learn how to handle situations where you don't have a velocity sensor or input, so please accept this simplification for now.\n", + "\n", + "Next we initialize the simulation and create 10 measurements:\n", + "\n", + "```python\n", + "dog = DogSimulation(\n", + " x0=x.mean, \n", + " velocity=process_model.mean, \n", + " measurement_var=sensor_var, \n", + " process_var=process_model.var)\n", + "\n", + "zs = [dog.move_and_sense() for _ in range(10)]\n", + "```\n", + "\n", + "Now we enter our `predict() ... update()` loop.\n", "\n", "```python\n", "for z in zs:\n", " prior = predict(x, process_model)\n", - " likelihood = (z, sensor_var)\n", + " likelihood = gaussian(z, sensor_var)\n", " x = update(prior, likelihood)\n", "```\n", "\n", - "I've plotted the prior (labeled *prediction*), the measurements, and the filter output. For each iteration of the loop we form a prior, take a measurement, form a likelihood from the measurement, and then incorporate the likelihood into the prior. \n", + "The first time through the loop `prior` is `(1.0, 401.0)`, as can be seen in the printed table. After the prediction, we believe that we are at 1.0, and the variance is now 401, up from 400. The variance got worse, which is what always happens during the prediction step because it involves a loss of information.\n", "\n", - "If you look at the plot you can see that the filter estimate is always between the measurement and prediction. Recall that for the g-h filter we argued that the estimate must always be between the measurement and prior. It makes no sense to choose a value outside of the two values. If I predict I am at 10, but measure that I am at 9, it would be foolish to decide that I must be at 8, or 11." + "Then we call the update function using `prior` as the current position.\n", + "\n", + "For this I get this as the result: `pos = (1.352, 1.990), z = 1.354`.\n", + "\n", + "What is happening? The dog is actually at 1.0 but the measured position is 1.354 due to sensor noise. That is pretty far from the predicted value of 1. The variance of the prior is 401 m$^2$. A large variance implies that confidence is very low, so the filter estimates the position to be very close to the measurement: 1.352.\n", + "\n", + "Now look at the variance: 1.99 m$^2$. It has dropped tremendously from 401 m$^2$. Why? Well, the RFID has a reasonably small variance of 2.0 m$^2$, so we trust it far more than the prior. However, the previous belief does contain a bit of useful information, so our variance is now slightly smaller than 2.0.\n", + "\n", + "Now the software loops, calling `predict()` and `update()` in turn. By the end the final estimated position is 15.053 vs the actual position of 14.838. The variance has converged to 1.0 m$^2$. \n", + "\n", + "Now look at the plot. The noisy measurements are plotted with black circles, and the filter results are drawn with a solid blue line. Both are quite noisy, but notice how much noisier the measurements are. I plotted the prediction (prior) with red triangles. The estimate always lies between the prior and the measurement. This is your first Kalman filter and it seems to work!\n", + "\n", + "The filtering is implemented in only a few lines of code. Most of the code is either initialization, storing of data, simulating the dog movement, and printing results. The code that performs the filtering is very succinct:\n", + "\n", + "```python\n", + "prior = predict(x, process_model)\n", + "likelihood = likelihood(z, sensor_var)\n", + "x = update(prior, likelihood)\n", + "```\n", + "\n", + "If we didn't use the `predict` and `update` functions the code might be:\n", + "\n", + "```python\n", + "for z in zs:\n", + " # predict\n", + " dx = velocity*dt\n", + " pos = pos + dx\n", + " var = var + process_var\n", + "\n", + " # update\n", + " pos = (var*z + sensor_var*pos) / (var + sensor_var)\n", + " var = (var * sensor_var) / (var + sensor_var)\n", + "``` \n", + "\n", + "Just 5 lines of very simple math implements the entire filter!\n", + "\n", + "In this example I only plotted 10 data points so the output from the print statements would not overwhelm us. Now let's look at the filter's performance with more data. The variance is plotted as a lightly shaded yellow area between dotted lines. I've increased the size of the process and sensor variance so they are easier to see on the chart - for a real Kalman filter of course you will not be randomly changing these values." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\t4.4502 2.6507 2.2871 2.1955 2.1712\n", + "\t2.1647 2.1629 2.1625 2.1623 2.1623\n", + "\t2.1623 2.1623 2.1623 2.1623 2.1623\n", + "\t2.1623 2.1623 2.1623 2.1623 2.1623\n", + "\t2.1623 2.1623 2.1623 2.1623 2.1623\n" + ] + }, + { + "data": { + "image/png": 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TISFVc0szWSwWKlZ8jQsXYti1azvNmrXK86kQyWPhUWBuW7du3QKLxYDJZMrvUARBEP6z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\nusQRYMGChZw/f4HatcNYunQJK1f+yCOPNCcjI5PZs2cXLc7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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "process_var = 2.\n", + "sensor_var = 4.5\n", + "x = gaussian(0., 400.)\n", + "process_model = gaussian(1., process_var)\n", + "N = 25\n", + "\n", + "dog = DogSimulation(x.mean, process_model.mean, sensor_var, process_var)\n", + "zs = [dog.move_and_sense() for _ in range(N)]\n", + "\n", + "xs, priors = np.zeros((N, 2)), np.zeros((N, 2))\n", + "for i, z in enumerate(zs):\n", + " prior = predict(x, process_model) \n", + " x = update(prior, gaussian(z, sensor_var))\n", + " priors[i] = prior\n", + " \n", + " xs[i] = x\n", + "\n", + "book_plots.plot_measurements(zs)\n", + "book_plots.plot_filter(xs[:, 0], var=priors[:, 1])\n", + "book_plots.plot_predictions(priors[:, 0])\n", + "book_plots.show_legend()\n", + "kf_internal.print_variance(xs)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we can see that the variance converges to 2.1623 in 9 steps. This means that we have become very confident in our position estimate. It is equal to $\\sigma=1.47$ meters. Contrast this to the sensor's $\\sigma=2.12$ meters. The first few measurements are unsure due to our uncertainty of the initial position, but the filter quickly converges to an estimate with lower variance than the sensor!\n", + "\n", + "This code fully implements a Kalman filter. If you have tried to read the literature you are perhaps surprised, because this looks nothing like the endless pages of math in those books. So long as we worry about *using* the equations rather than *deriving* them the topic is approachable. Moreover, I hope you'll agree that you have a decent intuitive grasp of what is happening. We represent beliefs with Gaussians, and they get better over time because more measurements means we have more data to work with." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exercise: Modify Variance Values\n", + "\n", + "Modify the values of `process_var` and `sensor_var` and note the effect on the filter and on the variance. Which has a larger effect on the variance convergence? For example, which results in a smaller variance:\n", + "\n", + "```python\n", + "process_var = 40\n", + "sensor_var = 2\n", + "```\n", + " \n", + "or:\n", + "\n", + "```python\n", + "process_var = 2\n", + "sensor_var = 40\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### KF Animation\n", + "\n", + "If you are reading this in a browser you will be able to see an animation of the filter tracking the dog directly below this sentence.\n", + "\n", + "\n", + "The top plot shows the output of the filter in green, and the measurements with a dashed red line. The bottom plot shows the Gaussian at each step. \n", + "\n", + "When the track first starts you can see that the measurements varies quite a bit from the initial prediction. At this point the Gaussian probability is small (the curve is low and wide) so the filter does not trust its prediction. As a result, the filter adjusts its estimate a large amount. As the filter innovates you can see that as the Gaussian becomes taller, indicating greater certainty in the estimate, the filter's output becomes very close to a straight line. At `x = 15` and greater you can see that there is a large amount of noise in the measurement, but the filter does not react much to it compared to how much it changed for the first noisy measurement." ] }, { @@ -1838,14 +2180,14 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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2WYP7E0Jg9+7d6N+/P9fmJiIqrqaWjyEiehI8vnW8EEXLE8bFxYnFixeLli1b\nCnNzc+Hs7Cy2bt2qs58dO3YIb29v9fb13t7eYufOnRp1EhMTxfDhw0Xr1q2FpaWlsLe3F56enmLT\npk2isLBQo+7KlStF27ZtRZ06dQQAsWTJEvWx7Oxs8cEHH4jOnTsLS0tLYW1tLTp27CgmTpwokpKS\ntK4jMTFR55gfX2ZR5cCBA6Jfv37CxsZGWFhYCFdXV7Fp0yaD2xfvB4D48ccf9dahiuMyi0RPHoUQ\n5Xjqh4joKfL41vFRUVEYN24cEhMT0atXr5od3BNs8ODBuHbtGn777Teu4lKFIiIiMGHCBADAuHHj\nEBERUcMjIqLSMMWFiKgUn376KV544QXs27cPfn5+JdYtKChQr59enIODA0xNTatqiE+c5ORkxMbG\nIjExkcE5EdFj+JAoEVEpVFvHlxacA3LVlaZNm2p9Xb9+vRpGqtuDBw9gYmKic/wXLlxAp06dYGFh\ngU2bNlXbmFxdXVFYWKh+mJaIiIpwBp2IqBI1adIEcXFxOstrysmTJyGEgLu7u0b5Dz/8gMDAQNSr\nVw8HDx5UP3xKREQ1iwE6EVEZjR07Vr0ay+MsLS2rZA1yADhw4AB69+5d5tz3kydPAoA6QBdC4IMP\nPkBISAh8fHzw7bff1ugbCCIi0sQUFyKiSpCTk4MWLVqgVatWUCqVGscmTpwIU1NTbNu2rUbGduLE\nCQCAh4cHMjIyMGjQIAQHB2Pq1KlISEjQCM6nTJkChUKBmzdvavXz559/wtzcHEFBQdU2diKipxED\ndCKiSlC3bl2EhITg+vXrCAsLU5cvWLAA4eHhWLduHUaMGFEjYzt58iTs7OygVCrh6emJuLg4REZG\nYv369TAzM9Oo6+3tDQA4fvy4Vj8zZ86Era0tgoODq2PYRERPLQboRESVZOzYsXB2dsZHH32ErKws\nrFmzBitWrEBISAjeeeedGhlTVlYWLly4AFNTU3h5eSEnJweHDh3Sm6KjykN/PED/6aefsHv3bnzw\nwQewt7ev6mETET3VmINORFRJTE1NsWLFCvj7+yMgIAAJCQmYPn06Fi9eXOa+CgsLce/ePY2yjIwM\n9WtaWprGsQYNGsDERHvOJTk5GYWFhcjPz0dmZibmzJmDLl266D1vhw4d0KBBA40APS8vD7NmzULn\nzp0xefLkMl8LERGVDWfQiYgq0cCBA+Hu7o79+/fjjTfewNq1a3XW8/T0xDfffKO3n2vXrsHBwUHj\nKyAgAAAQEBCgdezatWs6+1Hln69duxbdu3dHSEgIfvzxxxKvwcvLC7/99htU+9itXbsWFy5cwJo1\na7iWO1W6AwcOQKFQICoqyqAFdtmNAAAgAElEQVT6bdq0qbYNwkoaW0pKCurUqaNz1SZDxMTEwNzc\nHBcvXqzgKKk24gw6EVEl2r59O5KTkwEANjY2OjfhKSgowOnTp+Hq6qq3H13LNf7++++YM2cOVq1a\nhRdeeEGrvi6qFVy8vb0xYMAAdO3aFW+++SaOHDkCFxcXnW28vLywa9cu/Pnnn2jQoAGWLl2KgIAA\n9O3bV/+FEz1lZs2aBR8fH/j6+parfUBAAFxcXDBv3jzs2LGjkkdHTzoG6ERElWTfvn0IDAzE4MGD\nYWZmhoiICMycORPPPfecus6tW7fg5OQEpVIJDw8Pdbvu3btr9KVrucY6deSfbA8PD4NnEE+cOAEb\nGxu0b98eCoUC33//PV588UX4+/vj+PHjaNy4sVab4g+K/vzzz1Aqlfj0008Nvg9EZfHSSy8hJydH\n64FlY3b06FHExcUhJiamQv0EBQVhzJgxOHPmDJydnStpdFQbMMWFiKgSHDt2DEOGDIGPjw+2bt2K\nZcuWwcTEBAsWLNCo17RpU0RERMDT0xNZWVnIysrSCs4rS05ODs6fPw9XV1f1TL6rqyu+/PJLXLt2\nDQEBAVpLQgJAt27dYGJigvDwcERGRuK9996Do6NjlYyRnhwFBQV4+PBhpfdrYmICS0vLJyp9Kiws\nDA0bNsQrr7xSoX6GDBkCKysrbNy4sZJGRrUFA3Qiogo6d+4cXn31VbRv3x4xMTGwsLCAk5MTJkyY\ngNjYWBw5ckSj/smTJ+Hm5lbl40pOTkZBQYF6pl7l9ddfR3BwMI4ePYoJEyZotbOxsUGnTp3w888/\no3HjxvjPf/5T5WMl4xIVFQWFQoH4+HgsXboUTk5OsLS0xPbt2wEASqUSy5cvh7OzMywtLVG/fn34\n+/vj1KlTGv08evQIwcHB6NChA6ysrFC/fn24uLhg7ty56jr68ryvX7+O4cOHw87ODra2tvD398fl\ny5d1jjc4OBgKhQJXr17VOvZ4znpmZiYWLVqEbt26oVGjRrCwsEC7du0wf/58g96A5OfnIyYmBr6+\nvlqz/mXdR8Da2ho9evTAt99+W+p56enCAJ2IqAKuXbsGPz8/2NnZYffu3bC1tVUfW7x4MerWrYv3\n339fo83JkydLzD+vLI/vIFrc4sWLMXz4cPVs/+M8PT0BAB999BFsbGyqdqBktObMmYNt27Zh0qRJ\nWLt2LTp06IC8vDz0798fISEh8Pb2xurVqzF//nycPXsWPj4++O2339Ttp02bhpCQEHh5eSE0NBQf\nfvgh+vbti4SEhBLPe//+fbz00kvYsWMHAgMDsWLFClhZWaF3797Izs6u0DXduHEDX3zxBbp06YL/\n/ve/CA0Nhbu7Oz7++GMMHjy41PYnTpxAVlaW+t9IceXZR8Db2xt37tzB+fPny3dBZLQePnyIpUuX\nYtKkSQCAixcvlvqQvpogIqJq1bBhQ3Hs2LGaHoZeubm5wtHRUXTp0kUUFhbW9HCogsLDwwUAAUCM\nGzfOoDaRkZECgGjfvr3Izs7WOBYaGioAiD179miUZ2RkiJYtW4qePXuqy+zt7cWAAQNKPFdiYqIA\nICIjI9VlCxYsEABERESERt2goCABQOMcQgixZMkSAUCkpqZq9d+6dWuN+kqlUuTm5mrVW7RokQCg\n8W9T19giIiIEABEbG6vVx/nz5wUAsWDBAo3yH3/8UQAQ69ev12qzefNmAUBER0drHaMn2/Dhw8XK\nlSuFs7OzEEKIhw8fihdeeMGgtpxBJyKqRnl5eUhPT6/pYZRo1apVSE1Nxbp163SuQkNPj6lTp8LK\nykqjbMuWLejYsSM8PDyQlpam/srNzYWvry8OHz6MnJwcAICdnR3OnDmDlJSUMp03JiYGzzzzDEaP\nHq1RPm/evIpdEABzc3N1akp+fj7S09ORlpamfij72LFjJba/e/cuALn3wOPKs49Aw4YNAQD//PNP\n+S6IjNbly5fx/vvvq/97q1u3rnr52tJwFRciompkZmaGOXPmwM/PD/n5+fjjjz+M4gHMe/fuYe/e\nvfjjjz/wySefYNasWepdRenp1b59e62yc+fOIScnBw4ODnrbpaWloWXLllizZg0CAwPh4uICR0dH\n9O7dG/7+/vD399e5sZbKlStX0LVrV60HR5s2bYr69euX/4L+T1hYGDZu3IgzZ86gsLBQ41hpb6BV\nb1r1BVpeXl44cuQIhBBQKBTqfQTi4+N1Pgir6odvhmsfc3Nz5OTkqH+3ly9fhoWFhUFtGaATEVWz\nlStXYuXKlTU9DA179+7Fm2++icaNG2PmzJlYsWJFTQ+JjMDjs+eADChdXFwQGhqqt50qeB80aBCu\nXr2KXbt24eDBg4iPj0d4eDh69OiB+Ph4mJub6+1DX8CqKzAuKbjNz8/X+Dk0NBSzZ8+Gn58fZsyY\ngWbNmsHc3Bw3btzA2LFjtQJ2fdf2+E6/KmXdR0DVT0lveOjJFBwcjP79++P69et46623cOTIEURG\nRhrUlgE6ERFh5MiRGDlyZE0Pg54Azz77LO7evYs+ffqUOAuu0qBBA4waNQqjRo2CEALz58/Hxx9/\njNjYWAwbNkxnG0dHR1y4cAEFBQUas863bt1CRkaGznMAMtht06aNuvzRo0e4desW2rVrpy7bvHkz\n2rRpg927d2uMf8+ePaVeCwB07twZAPTuAFrWfQQuXbqk0S/VHn5+fvDw8EBSUhKEEFi7di0aNWpk\nUFvmoBMREZHBRo8ejdu3b+udQb9z5w4AuW76/fv3NY4pFAr1EqP6ZqABOfN+584dfPXVVxrl+j55\nUqXixMfHa5SvXr1aa0bc1NQUCoVCYyY+Pz/f4E+N3NzcYGtri6SkJJ3Hy7qPQFJSEp555hl06NDB\noPPTk6Nv375o2LAhXn31VQwcOBCNGjUyeEdmzqATERGRwYKCghAXF4e5c+ciISEBffr0ga2tLa5d\nu4b9+/fD0tISiYmJyMzMRNOmTfHaa6/Bzc0NjRs3RmpqKjZs2AB7e3v4+/vrPcf777+Pr7/+GpMm\nTcKJEyfg7OyMAwcO4OjRozpnIPv164eOHTti8eLF+Pfff9G2bVscPnwYSUlJWvWHDh2KBQsWYMCA\nARgyZAgePHiAr7/+2uCdTE1NTTFkyBDExsZCqVRq5RQX30egSZMmJe4jkJWVhUOHDmH8+PEGnZue\nDI8ePcLDhw+RlpaG9PR09ZvBBw8e6FwjXxcG6ERERGQwMzMz/PTTTwgLC8PmzZuxZMkSAECzZs3g\n6emJMWPGAJD56++99x7279+P+Ph4ZGVlqQP2BQsWoFmzZnrPYW9vj0OHDmHWrFn46quvIIRAr169\nkJiYqHMG0tTUFLGxsZgxYwbWrVsHc3Nz+Pn54eDBg/Dx8dGoO3fuXAghEB4ejqCgIDRp0gRvvPEG\nxo0bh06dOhl0D6ZOnYqoqCj8+OOPeP3117WOe3p6IiUlpdR9BL777js8fPhQ5+ou9OT6/PPPsWbN\nGty8eRMeHh7qAN3W1hbTpk0zqA+FMHS9FyIiInriREREqHeMHTduHCIiImp4RLVD//79kZ2djUOH\nDmmU5+XloWPHjurlFkt6gNXDwwOtW7fGjh07qnq4VAPWrVuH6dOnl6stZ9CJiIiI9CgoKFCvfV7c\nxx9/DHd3d+zbtw9+fn7qctU+Alu3bi0xOI+JicHp06exbdu2Khk31bzp06cjJSUFZ8+exaNHj9Tl\nj6/vrwsDdCIiIiI9rl+/jrZt22qVp6amqpdwLM8+AgEBAcjNza2SMZNxCAkJwYEDB3D27Fm88sor\n2L17N1588UUG6EREREQV0aRJE8TFxeksV+E+AqRLdHQ0fv/9d7i5uSEyMhJ37tzBxIkTDWrLAJ2I\niIhID0tLS/Tr16/EOtxHgHSpW7cuTExMUKdOHTx48ACNGzfGlStXDGrLddCJiIhIw5QpU6BQKHQu\nCffnn3/C3NwcQUFBVTqGvLw8mJubQ6FQ6PwaMmRIlZ07JycHLVq0QKtWraBUKjWOTZw4Eaampswd\np1J16dIF9+/fx6RJk+Dh4QF3d3d4enoa1JYz6ERERKTB29sbn3/+OY4fP46AgACNYzNnzoStrS2C\ng4O12hUWFpa4AdHjGjRooHc30tzcXJ0rzqxevRonT54scR31iqpbty5CQkIwceJEhIWFYebMmQCA\nBQsWIDw8HOvXr8eIESOq7PxUO4SFhQGQb3j79++PBw8e4PnnnzessSAiIqJaKzw8XAAQAMS4ceMM\nanP+/HkBQCxYsECj/McffxQAxPr163W2S01NVZ/LkK/U1NQyXcvcuXMFALFq1aoytSuP/Px84ezs\nLBwcHERmZqZYvXq1ACBCQkKq/NxUO/Tp08egMl04g05EREQaOnTooF7HWyUvLw+zZs1C586d9W6s\no++BSn2KP2hZEiEEZsyYgfXr12P9+vV45513dNa7f/8+1qxZY/D5Z8yYgQYNGug8ZmpqihUrVsDf\n3x8BAQFISEjA9OnTsXjxYoP7p6cTdxIlIiKiKuHl5YUjR45ACAGFQoG1a9fiwoULiI+Ph6mpqc42\nhjxQWVaFhYWYPHkyIiIi8MUXX2D8+PF6696/fx8hISEG9z1q1Ci9AToADBw4EO7u7ti/fz9GjBiB\ntWvX6q3r6emJ2bNn44033jD4/FQ76dpJVKFQwMbGBu+++65BfTBAJyIiIi1eXl7YtWsX/vzzTzRo\n0ABLly5FQEAA+vbtq7eNvk199HFwcNAb7Kv6Gzt2LLZt24YtW7aUulJKmzZt1LOVlWH79u1ITk4G\nANjY2OjdeKigoACnT5+Gq6trpZ2bnlxBQUEICgrCBx98gPfeew+2trZYunQpTp48CW9vb4P64Cou\nREREpEUVSBw/fhwLFy6EUqnEp59+WmKb69evo2nTpgZ/Xb9+XW9feXl5GDFiBLZv345vvvmm2pcx\n3LdvHwIDAzF48GCMGDECEREROHfunFa9W7duwcbGBkqlEh4eHrC2tsYvv/xSrWMl4xQdHQ1bW1sc\nPnwYcXFxGDt2LKZOnWpQW86gExERkZZu3brBxMQE4eHhOHz4MObOnQtHR8cS21RWDrpSqcSwYcMQ\nFxeHHTt24NVXXy3T2Cvq2LFjGDJkCHx8fLB161b8/fff+O6777BgwQLExMRo1G3atCkiIiKwZs0a\nJCUlVes4ybipPh366aefMGXKFAwaNEjn6ke6MEAnIiIiLTY2NujUqRN+/vlnNGnSBP/5z39KbVNZ\nOeijR4/GDz/8gLFjxyI9PR1btmzROP7aa6/B1ta2wufR5dy5c3j11VfRvn17xMTEwMLCAk5OTpgw\nYQI2btyII0eOwMfHR6PNyZMn4ebmViXjoSdX8+bNMXnyZMTHx2PevHlQKpUoLCw0qC0DdCIiItLJ\n09MTKSkp+Oijj2BjY1Mt5xRCYPfu3QCAqKgoREVFaRw3MTFBZmZmlZz72rVr8PPzg52dHXbv3q3x\nJmDx4sX48ssv8f777+PIkSMa7U6ePIlhw4ZVyZjoybV9+3bs2bMHc+bMQf369XHr1i188sknBrVl\ngE5ERERa8vLycODAAXTp0gVjxoyptvMqFAo8ePCg2s5XXKtWrfTmxTdt2hQPHz7UeSw5ORnLly+v\nyqHRE8jKykpjx1vVsxeGYIBOREREWlatWoXU1FRs3bpV7+olJN/IpKen1/QwqJZhgE5EREQAgHv3\n7mHv3r34448/8Mknn2DWrFnw8vKq6WEZNTMzM8yZMwd+fn7Iz8/HH3/8UerDtESlYYBOREREAIC9\ne/fizTffROPGjTFz5kysWLGipof0RFi5ciVWrlxZ08OgWoQBOhEREQEARo4cWe3rjRORNm5URERE\nRERkRBigExEREREZEQboRERERERGhAE6EREREZERYYBORERERGREGKATERERERkRBuhEREREREaE\nAToRERERkRFhgE5EREREZEQYoBMRERERGREG6ERERERERoQBOhERERGREWGATkRERERkRBigExER\nEREZEQboRERERERGhAE6EREREZERYYBORERERGREGKATERERERkRBuhEVL169QLatCm9rKrORURE\nZOQYoBPRk23NGiAqqqZHQUREVGnq1PQAiIiwbx8gRPnarlkjZ8nHjq3cfomIiGoIA3QiKllmJmBj\nU7XnMDd/svolIiKqQkxxIartoqIAhQKIjweCg4HWrQELC+D554Ft2zTrtmkj87ZPnQJefhmws5P1\nVJRKYPlywNkZsLQE6tcH/P1l/celpwOTJgGNGgH16sl+T5zQPUZ9ueKXLgHjxgEtWshgu1kzYNCg\non4UCuCvv4CDB+X3qq+rV0vu9+efAV9feX116wLu7kB4uP5x3bwJjBwJ2NvLa3n5ZeDCBd3XQkRE\nVEGcQSd6WsybB2RnA1OnyiA2MlIGnY8eaaaHXLsG9OkDDBsGvP46kJUly/PygP79gV9+AQIDgXff\nBTIygE2bAB8fGfR26VJU9+WXgV9/lXW9vIDkZKBfP6BhQ8PG+9tvQN++sq8JE4DOnYF792Qw/ssv\ngIcHsHkzMHOmfBPwn/8UtXVw0N/vDz8AgwcDTZoAs2fLTwe2bQMmTgSuXAE+/FCzfnY28NJL8hqW\nLwdSU4G1a+UbhZQUwNTUsOshqiHPPfeczu+JyIgJIqrdIiOFAIRo1UqI+/eLyu/fl2X29kI8fCjL\nWreWdTdt0u4nNFQe27NHszwjQ4iWLYXo2bOo7PPPZd3FizXrrl4ty1u31izv2VOzrLBQCGdnISws\nhPj9d+2xFBQUfd+6tea5S+o3P19es52dEDduFJUrlUJ07y6EiYkQFy5otgeEWLlSs9+PP9Z9L4iM\nUGFhodi8ebP45JNPRGZmZk0Ph4gMwBQXoqfF1KkypUPFzg6YMkWmohw4UFTeoIFMK3ncli1Ax45y\n5jotregrN1emixw+DOTkyLoxMXJmefZs7THY2pY+1uRk4MwZOY7iKTYqJuX803XihPyEYPx4mS6j\nYm4OzJ0LFBYCsbHa55oxQ7OsTx/5evFi+cZBVI0U2dkYlZ+POUolrKOjiz4VIyKjxRQXoqeFro+2\nO3WSr1euFJU5OelO2zh3TgbgJaWPpKUBLVvK/po21Q7GLSwAR0f5pqAkqsDXza3kemWVmipfnZ21\nj3XuLF+L3wtABvKWlpplqjSdf/+t3PERVabsbPkm/OhR4PLlovJlywBvb2DjRvlMBREZHQboRE8L\nhUK7TNcShFZWutsLAbi4AKGh+s+hCt6F0H0+fefUV0dfH+VVniUXS8ox5xKOZKyys+UzH0lJ2scu\nX5Zfly7Jh8cZpBMZHQboRE+Ls2eB117TLDt3Tr46Opbe/tlngbt3ZXpHaSkmTk5yDfIHDzRn0ZVK\nOYttb19y+w4d5Kuu1WEeV5Yg3slJvp45o33s7Fn5asi9IKpJqanARx8BrVrJh5ubNNGuM2WK7uC8\nuKQkWW/z5qoZJxGVG3PQiZ4WGzbIVVdUMjLkR9z16wM9e5befvRo4PZt/TPod+4UfT9oEFBQAHz6\nqfYYHjwo/VwvvCDTUCIidAfTxWeura3l6i6GcHeXQU1kpLwWlbw84JNPZLA/aJBhfRHVlPfek6sn\n/fe/ctnUMWOAkyeLjmdlybQWQyQlMSedyAhxBp3oadGoEdCtm3xAUggZpF67Bnzxhf60luKCgoC4\nOPkwZUKCnEm3tZV97N8v87QTE2XdceOA//0P+OADOdvn7S1nw7/9Vs5i5+eXfC7VMpB9+wKenkXL\nLN6/L5dZ7N8fmD5d1vXykmuY//e/Ms/exESuza7rY3tTU+Czz+Qyi127Am+/LZdZ/OYbGagsXCg/\nKSCqTnl5ckOwzEz5BvbBA83vH//50qWitrm5wFdfyS9HR/mpWHS0Zs55SS5dkvV17cRLRDWGATrR\n02LlSuDQIRmg3rkjA9GtW4E33zSsvZkZ8NNPQFiY/Eh8yRJZ3qyZDKLHjCmqa25eFMzHxADffScD\n4rg4YM6coo2EStK1q1xHfelSYPt2OdvfqJE8l49PUb0PP5Qz6OvXywBeCPmmQF9erb+/fEOxbJmc\nNc/NlYH9pk0yXYDIEIWFMs9bVwBdUnCt65hq9aOKunJF/hu9caNs7W7erJzzE1GlUQjBp5yIarWo\nKDmjnZgod8YkeloJITfmKmsArev7rCzje0jY1lYG59HRupdK1ScykjPoREaGM+hERGTcVCkg5Zmd\nfvz70tKraoJCIYNr1ZeNje7vVT8nJMhPlVRsbOSnVfPmyU+vhg6VnxAZkubSrp2sT0RGhQE6ERFV\nvsJCOctckdQP1fePHtX01ehWr17pwbQhx6ysyrYaUbNmMm0MACZPBkJCZPqXirW1fO7DkADd21vW\nJyKjwgCdiIgkVQpIZcxUZ2bW9NXoZmY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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1866,7 +2208,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 21, "metadata": { "collapsed": true }, @@ -1880,15 +2222,15 @@ " K = P / (P + R) # Kalman gain\n", "\n", " x = x + K*y # posterior\n", - " P = (1 - K) * P # posterior variance\n", - " return x, P\n", + " P = (1 - K) * P # posterior variance\n", + " return gaussian(x, P)\n", "\n", "def predict(posterior, movement):\n", " x, P = posterior # mean and variance of posterior\n", " dx, Q = movement # mean and variance of movement\n", " x = x + dx\n", " P = P + Q\n", - " return x, P" + " return gaussian(x, P)" ] }, { @@ -1897,194 +2239,13 @@ "source": [ "Why have I written it in this form, and why have I chosen these terrible variable names? A few related reasons. A majority of books and papers present the Kalman filter in this form. My derivation of the filter from Bayesian principles is not unknown, but it is not used nearly as often. Alternative derivations naturally lead to this form of the equations. Also, the equations for the multivariate Kalman filter look almost exactly like these equations. So, you need to learn and understand them. \n", "\n", - "Where do the names `P`, `Q`, and `R` come from? You will see them used in the rest of this book. In the literature $R$ is nearly universally used for the measurement noise, $Q$ for the process noise and $P$ for the variance of the state. Almost every book and paper you read will use these variable names. Get used to them.\n", + "Where do the names `z`, `P`, `Q`, and `R` come from? You will see them used in the rest of this book. In the literature $R$ is nearly universally used for the measurement noise, $Q$ for the process noise and $P$ for the variance of the state. Using $z$ for the measurement is common, albeit not universal. Almost every book and paper you read will use these variable names. Get used to them.\n", "\n", "This is also a powerful way to think about filtering. This is the way we reasoned about the g-h filter. It emphasizes taking the residual $y = \\mu_z - \\bar\\mu$, finding the Kalman gain as a ratio of our uncertainty in the prior and measurement $K = P/(P+R)$, and computing the posterior by adding $Ky$ to the prior. \n", "\n", "The Bayesian aspect is obscured in this form, as is the fact that we are multiplying the likelihood by the prior. Both viewpoints are equivalent because the math is identical. I chose the Bayesian approach because I think it give a much more intuitive yet deep understanding of the probabilistic reasoning. This alternative form using $K$ gives a deep understanding of what is known as the *orthogonal projection* approach. Dr. Kalman used that derivation, not Bayesian reasoning, when he invented this filter. You will understand more about this in the next few chapters." ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Code Walkthrough\n", - "\n", - "Now let's walk through the code.\n", - "\n", - "```python\n", - "process_var = 1.\n", - "sensor_var = 2.\n", - "```\n", - " \n", - "These are the variances for the process model and sensor. The meaning of sensor variance should be clear - it is how much variance there is in each measurement. The process variance is how much error there is in the process model. We are predicting that at each time step the dog moves forward one meter. Dogs rarely do what we expect, and things like hills or the whiff of a squirrel will change his progress. If this was a robot responding to digital commands the performance would be much better, and perhaps the variance would be $\\sigma^2=.05$. These are not 'magic' numbers; the square root of the variance is the distance error in meters. It is easy to get a Kalman filter working by just plugging in numbers, but if the numbers do not reflect reality the performance of the filter will be poor.\n", - "\n", - "```python\n", - "x = (0., 400.) # Gaussian N(0, 20**2)\n", - "```\n", - "\n", - "This is the dog's initial position expressed as a Gaussian. The position is 0 meters, and the variance to 400 m$^2$, which is a standard deviation of 20 meters. You can think of this as saying \"I believe with 99.7% accuracy the position is 0 plus or minus 60 meters\". This is because with Gaussians ~99.7% of values fall within $\\pm3\\sigma$ of the mean.\n", - "\n", - "```python\n", - "process_model = (velocity*dt, process_var)\n", - "```\n", - "\n", - "This is the process model - the description of how we think the dog moves. How do I know the velocity? Magic? Consider it a prediction, or perhaps we have a secondary velocity sensor. If this is a robot then this would be a control input to the robot. In subsequent chapters we will learn how to handle situations where you don't have a velocity sensor or input, so please accept this simplification for now.\n", - "\n", - "Next we initialize the simulation and create 10 measurements:\n", - "\n", - "```python\n", - "dog = DogSimulation(x[0], process_model[0], \n", - " sensor_var, process_model[1])\n", - "zs = [dog.move_and_sense() for _ in range(10)]\n", - "```\n", - "\n", - "Now we enter our `predict() ... update()` loop.\n", - "\n", - "```python\n", - "for z in zs:\n", - " prior = predict(x, process_model)\n", - " likelihood = (z, sensor_var)\n", - " x = update(prior, likelihood)\n", - "```\n", - "\n", - "The first time through the loop `prior` is `(1.0, 401.0)`, as can be seen in the printed table. After the prediction, we believe that we are at 1.0, and the variance is now 401, up from 400. The variance got worse, which is what always happens during the prediction step because it involves a loss of information.\n", - "\n", - "Then we call the update function using `prior` as the current position.\n", - "\n", - "For this I get this as the result: `pos = (1.352, 1.990), z = 1.354`.\n", - "\n", - "What is happening? The dog is actually at 1.0 but the measured position is 1.354 due to sensor noise. That is pretty far from the predicted value of 1. The variance of the prior is 401 m$^2$. A large variance implies that confidence is very low, so the filter estimates the position to be very close to the measurement: 1.352.\n", - "\n", - "Now look at the variance: 1.99 m$^2$. It has dropped tremendously from 401 m$^2$. Why? Well, the RFID has a reasonably small variance of 2.0 m$^2$, so we trust it far more than the prior. However, the previous belief does contain a bit of useful information, so our variance is now slightly smaller than 2.0.\n", - "\n", - "Now the software loops, calling `predict()` and `update()` in turn. By the end the final estimated position is 15.053 vs the actual position of 14.838. The variance has converged to 1.0 m$^2$. \n", - "\n", - "Now look at the plot. The noisy measurements are plotted with black circles, and the filter results are drawn with a solid blue line. Both are quite noisy, but notice how much noisier the measurements are. I plotted the prediction (prior) with red triangles. The estimate always lies between the prior and the measurement. This is your first Kalman filter and it seems to work!\n", - "\n", - "The filtering is implemented in only a few lines of code. Most of the code is either initialization, storing of data, simulating the dog movement, and printing results. The code that performs the filtering is very succinct:\n", - "\n", - "```python\n", - "prior = predict(x, process_model)\n", - "likelihood = (z, sensor_var)\n", - "x = update(prior, likelihood)\n", - "```\n", - "\n", - "If we didn't use the `predict` and `update` functions the code might be:\n", - "\n", - "```python\n", - "for z in zs:\n", - " # predict\n", - " dx = velocity*dt\n", - " pos = pos + dx\n", - " var = var + process_var\n", - "\n", - " # update\n", - " pos = (var*z + sensor_var*pos) / (var + sensor_var)\n", - " var = (var * sensor_var) / (var + sensor_var)\n", - "``` \n", - "\n", - "Just 5 lines of very simple math implements the entire filter!\n", - "\n", - "In this example I only plotted 10 data points so the output from the print statements would not overwhelm us. Now let's look at the filter's performance with more data. The variance is plotted as a lightly shaded yellow area between dotted lines. I've increased the size of the process and sensor variance so they are easier to see on the chart - for a real Kalman filter of course you will not be randomly changing these values." - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\t4.4502 2.6507 2.2871 2.1955 2.1712\n", - "\t2.1647 2.1629 2.1625 2.1623 2.1623\n", - "\t2.1623 2.1623 2.1623 2.1623 2.1623\n", - "\t2.1623 2.1623 2.1623 2.1623 2.1623\n", - "\t2.1623 2.1623 2.1623 2.1623 2.1623\n" - ] - }, - { - "data": { - "image/png": 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NzZo18zsUQRCEf+zChQukpqby0ksvodUqrYV79uzhyJEjNG/ePLfw9eHDh5k8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\nusQRYMGChZw/f4HatcNYunQJK1f+yCOPNCcjI5PZs2cXLc7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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "process_var = 2\n", - "sensor_var = 4.5\n", - "x = (0, 400) # gaussian N(0, 400)\n", - "process_model = (1., process_var)\n", - "N = 25\n", - "\n", - "dog = DogSimulation(x[0], process_model[0], sensor_var, process_var)\n", - "zs = [dog.move_and_sense() for _ in range(N)]\n", - "\n", - "xs, priors = np.zeros((N, 2)), np.zeros((N, 2))\n", - "for i, z in enumerate(zs):\n", - " prior = predict(x, process_model) \n", - " x = update(prior, (z, sensor_var))\n", - " priors[i] = prior\n", - " \n", - " xs[i] = x\n", - "plt.figure()\n", - "book_plots.plot_measurements(zs)\n", - "book_plots.plot_filter(xs[:, 0], var=priors[:, 1])\n", - "book_plots.plot_predictions(priors[:, 0])\n", - "book_plots.show_legend()\n", - "kf_internal.print_variance(xs)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here we can see that the variance converges to 2.1623 in 9 steps. This means that we have become very confident in our position estimate. It is equal to $\\sigma=1.47$ meters. Contrast this to the sensor's $\\sigma=2.12$ meters. The first few measurements are unsure due to our uncertainty of the initial position, but the filter quickly converges to an estimate with lower variance than the sensor!\n", - "\n", - "This code fully implements a Kalman filter. If you have tried to read the literature you are perhaps surprised, because this looks nothing like the endless pages of math in those books. So long as we worry about *using* the equations rather than *deriving* them the topic is approachable. Moreover, I hope you'll agree that you have a decent intuitive grasp of what is happening. We represent beliefs with Gaussians, and they get better over time because more measurements means we have more data to work with." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Exercise: Modify Variance Values\n", - "\n", - "Modify the values of `process_var` and `sensor_var` and note the effect on the filter and on the variance. Which has a larger effect on the variance convergence? For example, which results in a smaller variance:\n", - "\n", - "```python\n", - "process_var = 40\n", - "sensor_var = 2\n", - "```\n", - " \n", - "or:\n", - "\n", - "```python\n", - "process_var = 2\n", - "sensor_var = 40\n", - "```" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### KF Animation\n", - "\n", - "If you are reading this in a browser you will be able to see an animation of the filter tracking the dog directly below this sentence.\n", - "\n", - "\n", - "The top plot shows the output of the filter in green, and the measurements with a dashed red line. The bottom plot shows the Gaussian at each step. \n", - "\n", - "When the track first starts you can see that the measurements varies quite a bit from the initial prediction. At this point the Gaussian probability is small (the curve is low and wide) so the filter does not trust its prediction. As a result, the filter adjusts its estimate a large amount. As the filter innovates you can see that as the Gaussian becomes taller, indicating greater certainty in the estimate, the filter's output becomes very close to a straight line. At `x = 15` and greater you can see that there is a large amount of noise in the measurement, but the filter does not react much to it compared to how much it changed for the first noisy measurement." - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -2169,14 +2330,14 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2200,7 +2361,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 23, "metadata": { "scrolled": true }, @@ -2209,7 +2370,7 @@ "data": { "image/png": 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K9pjbA4Cu4V09HVqhNp/cTEb2xZ0L/H386VS9U6k//7qkdQCsGbHmso4/mX6S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\nBcaOdToq5QkBAXb+l0GD7OS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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2241,24 +2402,14 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 24, "metadata": {}, "outputs": [ { "data": { + "image/png": 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qz1b+nPlZ3HExdb+uS9MpTVnVdRX3F70/WzMolRYtVpTb2XtmL49NeowA3wCW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\nUkoppVza/wMzmLJ74Q2kbgAAAABJRU5ErkJggg==\n", - "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2276,7 +2427,7 @@ "plt.gca().bar(x, belief, width=0.2)\n", "plt.plot(xs, ys, label='A', color='g')\n", "plt.errorbar(160, [0.04], xerr=[3], fmt='o', color='k', capthick=2, capsize=10) \n", - "plt.xlim(150, 170)" + "plt.xlim(150, 170);" ] }, { @@ -2303,7 +2454,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 25, "metadata": { "collapsed": true }, @@ -2326,7 +2477,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 26, "metadata": { "scrolled": false }, @@ -2335,7 +2486,7 @@ "data": { "image/png": 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Qpk2bom+88UbBatWqlezTp0/Bex1v6tSpPg0bNizxwgsvPFegQIGgTz75JNfo0aPzBAYG\nlipXrlzAlStX7AFCQ0Nz1K5d26906dKBlSpV8j9w4IBT6nG6detWqEKFCgEFCxYMmjt3rhfAsGHD\nCoSEhLgFBASU+uijj3KHhIQ4BQUFBQYEBJQqWbJkqSNHjuTIynuZmZmL7LTWV+94HUXmElYhhLiv\n7du3A2CxxNC1ay3c3XOzbZv146ZSpUrUr1//SYYnhM2cOXOGevXqcenSpbRly5Yto3Xr1ixZsgSD\nITNf18+uL7/8MrfZbFbt27e/vnjx4jA7Ozs2bdrk2rhx44Affvgh16RJky57eXk9dBb/+uuv3xg1\nalS+V1999dbx48ddevbsGbVr1y43gA8//DBf/fr1by9btuzC9evX7StXrhzYvHnz2/nz5zft2LHj\nlIuLiz5y5EiOjh07Fj969OjxOXPmeDdo0MA4YcKEv0wmE9HR0Q/Mqc6ePeu0c+fOUwaDgb59+xbI\n6HgAp06dcj506NCx+Ph4O39//zIjRoy4dPz48WM9e/YsNGPGDJ+RI0defeONN4rMnDkzLCgoKHHL\nli2uvXv3Lrxnz55TAFeuXHEICQk5cfDgQadWrVo9171795vjxo279Nlnn+XZunXrGYCuXbsW6tOn\nz5XevXvfSEhIUCZT1gY+ysxf8gal1EZgccrrV4H1WTqKEEL8g4lu3RoyY0Z+goJyc+XKUW7fvoqf\nnx2BgWVZsGCNzIQknhnvvPMOly5dokqVKgwaNIjLly8zZswYVq5cyYIFC2SChgc4duyYC0CPHj2i\n7OyseVyjRo1iixQpkhgWFpbj1KlTOapVqxb/sOVXq1YtPiIiIsesWbO8GzZsaLxz3bZt23Ju3LjR\nc+rUqXkBEhMT1ZkzZxyLFCmS3LNnzyLHjh1ztrOzIywsLAfA888/H/v2228XTU5Otmvbtu3NGjVq\nPDCu1q1b30y9+LjX8QBq1KgR7eXlZfHy8rK4ubmZ27VrdwsgKCgo7vDhwy5Go9HuwIEDbu3atSuR\nWnZSUlLaB23z5s1v2dvbU6lSpYSoqCiHjGKpXr167OTJk/NFREQ4dujQ4WZQUFBiVt7LzCSefwFH\ngPKAAmZqrVdl5SBCCGE2m5k5cya///47ixdPRalI8uSB06dXYW9vT0xMDNeuXcPX1xd3d3fgCuDC\nmTNR5MmTJ2WZEP89V65c4ddff8XJyYkNGzbg4+MDgIeHBz179pTEMxNy586dHBoayq5du1ybNGkS\nA3Dx4kXD5cuXHZVS5MuX75EbRzZt2vTWqFGjCv36668nr169mpY/pXSEPFOuXLl0CdjAgQPz586d\nO3nFihXnLRYLzs7OlQBefPHFmO3bt59csWKFR7du3Yr179//St++faPuvNCOj49Pd9Xt5uaWVlt7\nr+P98ccfro6Ojjr1tZ2dHU5OTjr1uclkUmazGXd3d9OJEyeOZfQ7pm6fepyM9OrV60bt2rVjV61a\n5fHiiy+W/Oabby40b948+n7v3Z0yc8vcHRiCtW3nWWBXZgsXQohURqORYcM+ZMmSJWzbtorUmXft\n7e0BcHNzo1ixYnckmJrw8F3Ur1+X+vXrc/369ScTuBDZ7NatWwDkypULb++/+3AEBgYCcOPGjQz3\nE3/r3r37dYBPP/20wFtvvVVw7NixuevVq+efnJys6tatayxcuPAjT4TTu3fv64MGDbpctWrVdDWU\n9evXv/3ZZ5/lSW2Pu3PnTmcAo9Fony9fvmR7e3u++eYbH7PZDMCpU6ccCxQokDxo0KDrnTt3vr5/\n/34XAB8fn+T9+/c7mc1m1qxZ43WvOO51vMzw9va2FCxYMGnOnDleABaLhd27d993fw8PD3NMTIx9\n6utjx445BgYGJg4fPvxq48aNbx08eDDTx4dMJJ5a64+01qWBd4D8wO9Kqd+ychAhxL9DXFwce/bs\n4fDhw/e82r1bbGwsw4YN+8dg7126dOG5555j//79QBLe3rf46qtBLF8+gXr1KmWq7ORkEzly2OHk\nZIeLi0tWfx0h/hWKFi2Kj48P4eHhrFplvaFoMpmYOnUqAFWqVHmS4f0rdOrU6Vb37t2vJicnq1mz\nZuUZMWJEofPnzzsVKVIkcfbs2Y9lCMgSJUokjxgx4urdy8ePH3/ZZDKp1M5Cw4cPLwAwYMCAq4sX\nL/YpV65cwKlTp5ycnZ0tABs3bnQvVapU6cDAwFJr1qzxGjx48BWAjz766FKLFi2eq169uv/9es3f\n63iZtXjx4nNz58719ff3L+Xn51d6xYoVnvfbvmrVqvEGg0H7+/uX+uijj3IvWLDAu2TJkqUDAgJK\nnT592untt9+OysrxVWa/XJRSebEOqdQBcH/SMxcZjca0wD08PJ5kKALrh+SMGTP4+uuviYqKonLl\nygwaNIgXXnjhSYcmUoSEhABQuXLlf6zTWjNx4kQ+/fRTjEZr86WAgABmzJhxn57lFuAGsbG3cXMr\ngbOzE3FxxwEzYKZhw65s3ryHX3/9lkaNqpIyEVqW/fXXdXLkcMTLqwRQ+KHKeJrd77yIJ8fW5+XT\nTz/lww8/BKwd665cuUJERAROTk7s27ePUqVK2SQOW7t58yaffvopw4YNS1vm4eGRdpv5woULC4oW\nLRqY2fI2b97s+sMPP3jHxMTY1ahRI+aNN9644ebm9nAfPuKhXbhw4XjRokVfz2jdA9t4KqV6Y+1Q\nlAtYDryptc6wbYB4Nmmt6dixY7rBvtevX8/69euZO3cu3bp1s0kcsbGxWCyWe7YFTEpKYubMmSxc\nuJBbt25RtWpVBg0aRLly5WwS39NsypQpDBkyBIBSpUoRFRXFiRMnaNq0Kfv27Uu75QcQExND7969\nGTeuF4ULO+HiohkzphceHm5ofT2tQ9CMGUOwWCwULJibh006AfLm9U15dg2tkxk5ci6NGjWWoZbE\nf8oHH3xAQkICn332Gfv27QOgRIkSzJw58z+bdEZHR1O3bl2OHDmSLvF8FA0aNIht0KCBDAD8FMtM\nG88iwACtdWmt9ajMJp1KqTlKqatKqaN3Le+nlDqplApVSk28z/72SqkDSql1mTmeeHI2btzI8uXL\nyZkzJ+PGjWPlypVpScyAAQOyfRDwvXv38sILL+Dm5kbOnDmpVasWf/zxR7ptTCYTLVu2pF+/fvz5\n55+cPHmSBQsWUK1aNX77Lftbjpw6dYpu3bqRP39+ihQpQr9+/YiMjMz242ZGcnIy48ePB2D+/PmE\nhoYSHh5O+/btiY+P5/PPP0+3/fDhw1m4cCGvv94fAKUUI0a8Qf/+HdL1Qi9RoiB+foVxdnZ6bLGu\nWrWSsWPH8corr3Dz5k3A2nZ0zpw5bNy4Md22cXFxmW4uIMSTZmdnx0cffcSlS5fYunUrwcHBnDp1\n6j991+jbb7/lyJEjlCxZ8kmHImwoM208h2itDz5E2fOApncuUErVB1oAZVPajU6+z/7vAscf4rjC\nxlLbJL3//vs0btyYQoUK8emnn1KpUiWMRiPbtm3LtmMfOnSIevXqsXXrVhwcHHBwcGDnzp00aNCA\n3bt3p223ZMkSNmzYgK+vLz/++CP79+/n9ddfJzExkV69emXrIM1Hjx6latWqfP/990RGRnLx4kWm\nTZtGtWrVnorkMywsjCtXrpAvXz46d+4MgIODAwMHDgRgz5496bYfOfJ92rdvxIwZH9o81hYt6tKn\nTztmzRqFl1cMcJkLF/bRs2dPBg0aAEQD8UASpUuXxtHRkUWLFtk8TiEeloeHB/Xq1aNKlSqkDgv0\nX/XTTz8BpF34ZkRrLSPo/wvd77xl24i0WuvtSqmidy3uDYzXWiembPOPRroASqmCwMvAOGDgg46V\n2hZHPBmXL18G/u6ZCdZzklr7FRoaSp48ebLl2IMHDyYuLo6GDRsybNgw7OzsmDx5MmvXrmXAgAF8\n/fXXAMyePRuAHj16UKJECcxmM2+++SZLly7l7NmzLFq0iICAAMB6FX78+HH69OmTtuxRDBgwAKPR\nSM2aNenfvz8JCQlMmDCBY8eOMWDAAP73v/898jGy4u7/l9Qes1FRUWzevBlPT2s789QaRIPBcMc+\nJpydLzBq1OtYLHEcO2b7VjfvvPMKAMeObQMgMvIKLVrUIlcuT44dW522XVyckUKFcuHvn4N9+/ag\ntQGt9VM7Nqh8jj2d5Lxkn9T25OHhF+65TVJS0vG4uLggFxcXSUD/JeLi4uySkpLuWXFo66kQSgK1\nlVLjgATgfa313gy2+xIYjHUop6dKTEwM586dSxv65Wn7EktKSmLbtm2cPHkSb29vmjRpgq+v74N3\nfARVqlRh3bp1/Pjjj1SvXp0iRYqwefNm9u3bh4ODAxUqVHhwIQ8pODgYgHfffRc3NzfAmuitXbuW\nkJAQzGYz9vb2JCQkANbZQezsEjAYbgJJJCZah0FzdIzA0dENpeD48X3s3n2ILl0a4ODgTXJy7oeO\nLykpid27d2NnZ8eoUaPw8rKOkDFkyBC6dOnCtm3bbJ543s3b25vnn3+ePXv2MHDgQLp06UJUVBTT\np08HoGnTply/fp1t27bx2mtVUCp75go+GGngl9M5eDUogWJe5kzvV7hwHj755K1/LN+6dQomkxmD\nIQ6tzxId7U737h/wyiuv0KZNm7RhnIQQtqW1Zv78+Zw7dw5vb9i69Su6du2R4bYxMTETw8PDcXR0\nDFRK/bergP8DtNaWpKSk4zExMfdsSonWOtseQFHg6B2vjwJTsQ5EXxU4T0rP+ju2aQZ8k/K8HrAu\no7Jv3bqlUx+2YDKZ9IcffqhdXV011p4SukKFCnrfvn02OX5mnDlzRpcoUSItPkA7OjrqBQsWZOtx\nExISdPny5dOOeed7NGTIkGw9to+PjwZ0aGho2rLw8PC0391sNmuttX7vvfc0oO3tlT58eKG2WPbq\n1atH6iJF0AEBOXRc3A6tdYjWOkTv2TNP//zzl/rq1U1a6xAdGxupt23b9lDxxcbGakAbDAYdHR2d\ntvzYsWMa0Hny5HmE3z5r9u7dq/fu3ZvhulOnTum8efOm+9sB9EsvvaQTEhJ03bp1NaDHju2tU9+n\nzD7OnVuu9++frY3GLRmuvxi1R789f5Mu8sE6XeSDdTpo1M86+PyuLB/nQY9580ZrQJctW0YnJyc/\nvjf2Ed3vvIgnR85L9mrVqpkGdKlS7rpiRfRd3+nZmpvI48k+bF3jGQGs1FprIFgpZQF8gWt3bFMT\naK6UeglwAnIqpRZqrTvbONZ0Ro4cySeffAJA2bJluXTpEgcOHKBBgwYcOXKEggULPlS5kZGRrFix\ngtu3b1OjRg3q1q37ULWoWmteffVVzp49i7+/Px06dODAgQP89NNPdOvWjapVq2ZbA+4cOXKwbNky\n6taty19/XcbDIxYPj3wMGvQ+7733XrYcM1XLli357rvv6NmzJ1999RUGg4FBgwYB0KxZs5Q2UmZG\njOjBkiXfYrEk0L17Fzw9c3Lz5i18fKBfvzdxdv57/Ntq1cqkPb958zaVK7ckMjKKo0ePUrx48SzF\n5+LiktbZadCgQXz22WckJCQwePBgABo3bvzob8Jj4Ofnx6FDh5g+fTq///47rq6utG/fng4dOmCd\nG7gHkZHn6dmzRabLPHPmDGPGjCE01Ho73tHRgTZt2vDuuwNwcDAQn6T5dlsMM7bHYqcU7zd248Ug\nJ96cf5POs28w7TVPGpV6fB2TunR5GQ8PN/Lk8cZguAgUIjY2iejoaPLmzfvYjiOELWituXDhAmaz\nmeLFiz/17UF//fVX/Pz8KFYsFxDBhAk96NWrKeXKFWPatGlPOjxhS9mZ1fLPGs9ewJiU5yWBcO6q\n8bxr/3o8BTWeRqMxrRZv/fr1Wmut4+LidKNGjTSghw4d+lDlfv3119pgMKSrYapdu7a+efNmlssK\nCQnRgPb19dVGozFt+euvv64B/cEHHzxUjJmVmJigK1YM0p6ebvq77/6nzeZj+sSJo3r69OnZetyL\nFy/q/Pnz/6OmztXVVXt7e+vTp/dorQ9qrUN0RMQaPWBAbV2pErpiRXSTJr568eL3tcWyV9+vpqxD\nh8a6bNlAffjw4YeKcdu2bWnn2WAwaDs7Ow3onDlz6hMnTqTb1mKxpHt9+vRpHRISopOSkh7q2Hd6\n+BqcRK31QZ2cvEdntnbxxo1NukEDT12xIrpePXf92msBumJF6/v+6aft9NpDO3T1T9brIh+s0/0W\n/aYv3/ozbd+omGDd/KuNuviZAOlVAAAgAElEQVTQdXpJ8PZMHzPrj/36ww/7a3d3d7148eKHeF8e\nD6lZezo9zedlzZo1OigoKO3zLnfu3Hrw4ME6ISHhSYeWoYkTJ2pAd+jQTN/r/1FqPJ+dR7ZdIiml\nFgO7AX+lVIRSqicwByieMsTSj0BXrbVWSuVXSq3PrlgeVWhoKLGxsZQtW5YXX3wRAGdnZ/r3tw4n\nc3ev38zYtWsX77zzDiaTiRYtWtC/f39y5crFjh076N27d5bLu3jxIgDVqlXj1q1bDB8+nMWLF9Og\nQQPA2nP5cbt+/Trx8fFAPI6O51iyZAyrV3/C888HkZR0k2bNXqJXr17MnTv3sR87VaFChQgODqZf\nv34UKVKEwoUL89Zbb/HSSw25ceMGS5Z8T+rUjAUKFOCLL75gy5YtrFu3lnXr1tGhQ4cH1jBPn/4h\nISFzCQoq8VAx1q1bl02bNlGzZk1MJhNaa1588UV27NiBv79/2najR4+mePHiXLhwEq0vY7Gc45tv\nJlO5cuW02nawjldqiyn0Tp8+zfnz57DOlGvCYMj8DZLVq1dz8+Ytypcvx/r16/nhh4XMnj0bS85i\nfHe+En0XGfF0sWPp295M7ehJPo+/21t6u9qx6E0vapRwZPCK23yzLSb1QvSx0trMqVOhREdHU6RI\n9raDFuJxSEpKok6dOrRo0YLLl49QvXpO6tTxJCrqKhMnTuTLL7+0eUxaa1KnggTrGM7169dP+cwy\nA7G8+mot8ub1oWLF4tnyvyz+XbIt8dRad9Ra59NaO2itC2qtv9NaJ2mtO2uty2itK2qtt6Rse1lr\n/VIGZWzTWjfLrhgzK7WXb0REREqiZXXmzJl067Pi22+/BaxDEK1evZopU6awZ88eDAYDy5Yt49q1\naw8oIT0/Pz8AduzYwcSJExg3bhy7d2/ml1+WYjBAwYIFqVOnDh988EGWY83I5s2bKVOmDMOGDcA6\n6lUczz1XiFy5rO+Fk1MORo7sSY0a5Wjfvul9y3pUBQoUYPDgwfz555+EhR1jxoyBfPHF2/zyy1cM\nG9bzH9vnzJmTfPnyZTqR8vBww8HBAIQB+qE+OOvVq8cff/xBbGwscXFxrFu3jvj4+DvKSuDEiQNc\nuHCB3r3bULt2CapVe47t23+iUKHcVK+eGzgNRPLTT0vw8fHh7bffznIcmRUTE0PLli2pVKkie/dm\n1P/v/o4etQ7f27ZtO5ydnbkZa2FlWHFuVp2CybUQPctdZ20/H6oWc8xwf9ccdnzX1Yvm5ZyY+EsM\nH6+LxmJ5vF9YSimWLZvAwYOLqF7dC2uTczP79+/P1uG1ROZorQkODmbp0qUcOHDgmU1YYmJi0p47\nOpo4ezYUpaBp02r8/vtGNmxYy0svVSJnTti/fx7WG4mxDBo0iF69enHu3Llsi+3999/Hy8uLlSuX\nYR3K7BqxsWFs27aN3bs3AgeBExQu7EhY2Dr+978uT12HXGF7tm7j+a8UEBBAhQoVOHDgAM2bN+fd\nd9/lzJkzjBw5EoDXXnsty2WePXsWgJdffhmwfsgaDAYCAgI4evQoFy9eJFeuXJkqS2tNwYIFqVev\nHgcPbuPQocWUK1eI06e3cvXqOapUcaRqVR8mT96ByRQHXAecAWfq1KmHr68vs2bNwsfHJ9Px58zp\nxPXr1zl4cD/JyckpiVl6r7/+Mp06vYidXSRgwGLx4erVq4+9PV1wcDCvvPIKpUqVYNOmLzAYDBQo\nkJsCBR6+N3pG4uNvMGbMu1y5EsOcOXMeqozU+carVatGcHAwe/eup3LlwkACffq8yMWLf3DlivWL\nxSqSPHkUTk6JwG3gNpGRR8iRw5HChZ2Ai4AP4Pqov1461nZjBbFY4ggIKJrhNokmzYlIEzGJFqIT\nNNEJ1p8xiZrjTo2ICQxiakgufoy8wcHwZGISNV7XN8PR2bTq8TX2dvf/AnI0KL581QMfNzvm7Izj\nRqyFiW09cDQ83i+ucuVS2z7f4ODBfVSv3on69euzdu1aHBwcHuuxROacPXuWdu3aceDAgbRlNWrU\nYMmSJQ/dnv7fRmvNm2++yeLFizl2bCdFijgBsRQqlISPD0ycOCxt7OKlS6dQt25dzpw5QULCRZSK\n4LvvZmE0RvPee73Syjx//jy+vr73nN3tfk6fPs3ChQtp3rw5338/nTNn/iQ8PAqj0cipU9sBa+VH\nvXp+bNgwlTJl0t8hcnSU/yVhJYlnJiilmD17Ng0bNuS3335LN9NNp06daN26dZbLLF68OLt372b9\n+vXUq1edP//cQvXqL6GUwt7enkKFCmWqnMjISLp3787169dYt+4L/ve/Xhw7dhx7+5tcvQru7m6M\nHTuWoKDybNyY2oDbetvdaIxhx44dODnlwMMjHmti40K/fu8RFhbGmDFjKF++fNqxwsPDU+K6RpUq\nLuzYMYtq1crct1G7dZ0GLvLhh6OZN28Fa9eupUqVKll+z+6lUKF8KGXBYDATG5uAh4fbYyvbZPr7\nFvPly9f58suZJCYm8cEHH6S7TZ6FEoGrVKlSgsjIMP766yRgTZCPHt1LYuINSpUK4JNPPsHb25tv\nv53Ojz/+yNSpU6hduxZKKQYO7Ezfvq+SmJiEdRrJKCZMWIenZy569ep1v4NnmoeHA2vWfML16zdw\nd/9nUpuQrHl1xg0ORWQ8tFIO+7Ik5SrM6WtxGM1X8feyx/X8Eg4fXE3hwoUyPQWgnZ1iZDN3fN3s\nmLQxhhtxFqZ39sTFMXtu1ly/fhV3d2eKF8+b4cWUyH5JSUk0adKEs2fPkjt3bqpXr86OHTvYtWsX\nzZo1Y//+/U99R5rHQakk4uOjiI+PZ+vW1XTrZh2/1sfHjeTkGK5du0b+/PkB63znJpMZBwcD9vYG\nDAZ7tm+fyZYte/H3N2MdUMaL3r3fZPPm31m7di1Nm2btTtSbb77B779vZ968T/D1NaXECEFBYDSe\nxGKxYGdnR65cXjRtWuNxvhXiP0Y+WTOpYsWKHD58mFGjRnH+/Dk8Pb3o1KkTrVq1yvKHYEJCQlov\n6oULJ2E27yU8PA47O3B317Rq1YLcuXOTnJzMiRMnCAoKumdZOXO6Ehp6mJiYGKKi/mL+/PmEhOzj\n1CnrOJ5169ZNq2Vr3Pj5dPu6uTlz9OgSwsIiMRiuAFcA2LBhDWfPhjN27LukJqOffTaF999/n717\nV6bU0EH16mUz/TsnJ5sICQnh+vXrGI03M/9m3UN8fHzKexhLvny32LlzNkWL5nssYzOaTCbmz5/P\nsmXLuHr1Gnnz5uXVV9vTqVMnpk8fir9/qSwlnSaTiffff5/mzZvwwgsFgSTGj+/NV18NTHfbaefO\nXQD07duXwoWt7/GAAQNYv/5nzp+/QGRkZNoXjaOjQ1oNwh9/7GPo0JE4ODjw8ssvZ/qiJSPBwcFU\nrFgWg+EcdnaQO7d3htuN/uk2hyKSGf2KO4H5HHB3UikPO1xzKAx2MGHCfJYtW04i1laiAK6uLowe\nPTpL/zNKKd6p74aPqx0frrpNx1k3mdvNC2/Xe5ehtebIkSPs3LkLpaBOnTqZSnYbNqzG4cM/4unp\nDpwCihEZGYWnp2e6kQ9E9lm9ejVnz56lZMmShISE4O7uzo0bNyhbtiyHDh1i8+bNNGrU6EmHmS2S\nk5MxmUw4O98GIhgzphtjx3anWLECads0atSQBQsWMmbMGPr374+jYw6mT7c23WrQoEHaBVPZsn6U\nLeuXslciWkdiMkUDUKGCB/AXkJPJk79h+/btDBo0iLp16wLWHujfffcdkydPolAhdyCKN99szLlz\nIbi4xNGwYQM6dOjAhQthfPnll2zevIWtW7em9SkQ4n4k8cwkrTWTJk1i7ty5rFr1JS1aNALy0rZt\newIDAxk0aFCm23pevnyZBQsWAODra5c2pWSZMlC6dGmmTOkLHGX9+r20bNmDTp06sXDhwrQ4Vq1a\nRfPmzTEYjLi6XmL58k8pXrwAuXJZByevUqUyVapUfmAc9vb2lC5dgtKl098S2bBhCvv2HScw0A1r\nu0LYu3cT9vb2hIQEpyWeWeHgYGDDhqns2nWIunULAUlobU2cstrm5+jRo7Ru3ZqhQ/vSvXstQFOi\nxOO7/TZq1Gh++eWXtNd//fUXU6ZMJSzsIiNGDE9ZegPIOCm727x585gyZQpLlvzAuXOrcXZ2ws3N\n5R/bpb4N6duy/d2m9F7vU+3aFRg16k3Kly9PoUIP/z789NNPtG3blnbtGjN//sh7JvFL98bx4954\n3qnvSrea977F/8EHH1CrVi3WrVvHrVu3KFWqFO3atSNfvnwPFV+Hqi54udrRb/Et2k6PolcdV3I6\n2+HhrPBwtsPDxfrcUZkZMWI4v/22OW3fWbNm06xZM0aOHPHAi5P8+VObuMRgMh2mdeveREfHs2rV\nqrS21OKf4uLi2LlzJ1pratSokTahQ1YdPnwYgPbt2+Pu7k5ycjLe3t60atWKadOmcejQof9s4jlg\nwACCg3ezevU4ChTIneHnWvfu3dm1axdnz55j4MBBacvz5MlN37797lm2UorffvuGmJg43NwcgUvA\nJVav/oGdOw/yxhvtgSTAke++m8HSpSupUCEPQ4Z0BaBixaLkyhVHrly+jB07DgcHAxUqVCAuLpbP\nP/+CX3/9NV3iGRn5F/Pnf8+uXbuxt7ejdu06dOnyepaadIn/Jkk8M0kpRd68njg4GIiONgJxhIZu\nYsWKFbi7uzFo0P3Hq7x+/XrKDEKJFC9uZsqUgfj7F6F0aessPzExMZQrV47KlSunJBiJXLlyBg8P\nNypUKATcBDzp3LkzixYt4quvhtO3b0sg/biTj4OfX2H8/NInlxMn9uPLL98jb96H7/3r4GCgbt1K\nQBxwgiNH4nnttZ688847WerJv3fvn5w+fZoZM2bRtWv1x3rb7fjx4/zyyy84Ozsxfvx4atSowfbt\n2xk6dCirV6/mtdc6UqJECSCcI0fCAMN9a6QBund/mT17WtC9+ys4O997XMratWtz/PgJpkyZgo+P\nDz4+PkyfPp3o6Biee+65+7aNHT06taNROJD1CwMAX18vcuRwIF8+r3u+p0cvJTN8zW1qPufIwEb3\nTyyUUtSqVYtatWo9VDwZaVLaiQU9vHlrwU0Gr7id4TZ2WNDJPbCv9So+7o7kM1zhypYJrFu3joAA\nfzp27Jjp40VGXuHmzWvExibh45P1ToTPAqPRyFdffcXkyZNJSDBiMoG9vSNjxox5qM6MqdPr7tix\ng3bt2nHy5En27NmTNnVldk2/e6fLly8zYcIETCYT06dPt8kxb9y4wfr1P3P58mXCw6/cs426h4cH\nc+bMYdmy5fz++zbMZjPVq1enQ4cOeHs/+GL47ovexYvHsnnzXurVKwQcAex5552mlC+fj06dmqRt\nFx8fB4CPj0+6Zii5c1vfm7i4uLRl4eHh9OjRgxs3/r67FRa2kM2bf2Pu3HnkypX+eyTZ/Gx2HHtW\nqX9rT0Gj0ZgWuIeHR7YdR+vUuZ2voHU4J0+GpetssXPnQc6ejaBLl5ZAbrTOxfvvf0DHjh2pXNla\n6zh58mRGjhzJ+vXfU69eCaxtHjMnPj4Bs9mS8mFhYPXqXbz99nCmTBlEhw5NHri/raXO3f2g25rW\nD8vu7N17jEmTRvD++0MAF65cucL27dtp0qQJOXPmzGBP643befOW0r59I1xcsj7A+MUoE7+fSiLZ\nrLFoMFvAoq3Pg/fuI3jvPgJLleb56jXwcLajaw0Xxo/7iLVr1/HeewPo3LkzGzbspHnzQQQFBREc\nHPyPHvIhISGUKhWIi8sN4Gqm4jIajXTt2pXw8Ih0yw0Ge6ZMmcLzzz9/jz3TO33axLRpi/j888/T\n1e6lfnGn/l2mZwZOcf78aYoWzZ9h7aoxzkKzaVGYzJp1/XzxcXty7ewSkjXXos0Y4zW34y0Y4zXG\nlJ8z5y0iJsmeis/XQTl5s/tcEm4OJiz7p+Kf4zwrVyzL0rFiY+O5cOEypUuXAoqxffs+Vq5cSe3a\ntWnTpg1grRXv168fvr6+aSNWgHW++0KF7t+m9f7n5en266+/0qJFC0ymBIoVgypV/Dl48DrHjkUB\nsHjxYjp06JClMq9evUqRIkVISEjAzk4xYEBbwsLiWLHiZzw8PIiIiHio2tSrV68ybdo0fvvtNxwc\nHGjZsiVvvfUWrq7pa+2XLl2acnFiwdERzGYH+vbty6RJk7J5mlUz16/vYu/eA7z4Ys1sPM7DiYmJ\noWnTpsTHJzB58iTq16/P7du36d+/P0eOHOWdd/rQo4d12sshQ4awadNvVKpUkf79+2MymZg8eTLH\nj5+gbdu2DB06BLB+v/5yNJGJG6NZ/Wb1tGN5eHhI1/f/MEk872P9+vV89NFHbNw4C0/PzM1PvX79\nLl5+uT/58+cnLCwMg8HAxx8PY+TITxg2rAdjx/Z5pJi01sTGxmd4q/ZpkNnEE6zJ5+7dRyhevEDK\n7U0HZsz4mV69PqRVq1asXLkSgEuXLtG/f3+mTRtHvnwJWJOkrLsVZ2Halhi+3x1H8gOL0BjsFCYL\nvFnbhfjdE9mw4RcGDnyPTp06ERsbT9myHWja9EUmTZqS1o4WYNWqVXTo0IFXXqnP0qUfZ6lGNioq\nilmzZrFp028kJMRTsWJFevbsma6T1/2YTCYCAtpy9mwEn332GQMHDkxbl1GCs3btWnLl8ub5572x\n1kRnzGLR9Pz+Fn+cSWTp295UKJzxMEgP69q1m8TExKVry/YwTCYT1apZE/Tg4D+xt7fnSEQyw1be\n5PBlC47GE6wcXpMyBR62h63iq6/W0r//aN55pwvTpo0BNBcuhFOsWB2KFCnAhQvbAI3FYqFo0QaE\nh19i796990ws/02JZ2xsLBERESltnJOIijpFnjxlcXHRfPZZL9588w2OHz9P69YDiIu7RP785di9\n+2CmyzcajXh4eLBq1TxGj36DyEgzefJYm6GEhzvx8ceT6Nu3b5bjvnDhArVr1yYiIv1FXcWKFVm6\ndCk///wz77zzDvv376Rdu/rExlpwdHSmatVCrF9/mqQkzUcffZQ2ksnjZO3AaA+cwdqm/un17bfT\nmT17NgAFCuQnKiqKhIREfH19+PHHJXh5eWI2m6lRwzpm8fr1P6fVFp86dYqOHV/Dx8ebX3/9lb0X\nkvh0fTT7Lybjl9vA8p5/X1hL4vnfJrfa78FsNjNs2IccPHiImTNnM3hw10ztV768H//73+sULZof\ngyECSOZ//3uZevWKUbt2hUeOSyn11CadAOdu2BMc4cCQ5ywP7Hlsb29PrVp3JlTJ5M7tQO3aFWje\nvBzWLimenDhxlJUrV+LgEM2PP36a5ZgSTZoFu+P4aksMtxM07Ss506e+Kx7OdtjZgb0CezuFnYJz\nZ8/y2msdyOHowKhRo9hsrMzsHbF4hZxHYb0dDuDq6syhQ4txc/PCOrPr3/z9i+Pk5EiePDnTenpm\nlo+PD0OGDGHIkCFZ/j0BDAYDM2cO4+uvl/Pmm13uu21wcDBt2rTBycmRQ4cW3Tfpm7Y1lq0nE/m4\nRc7HnnT+/vs+WrQYRIUKQWzZshmlLpCYeAuDwT7LNUzWobTyc+nSZbZu3UrDhg0JKuhA98K7Gb5p\nN4kBPWk+LYpO1VwY1NgNT5es1tpqatf24/PP36N8eX+sQ5NB7tx2LF06Hnd3F8AIWGuImjSpQkiI\nKxUruqVs68UXX0zFy8uLtm3bPnQ7yCchJCSEBg0aUKJEUfbtW4ZS0fj4QLly9oAprWYzMLAYBw4s\noWbNWiQmHkLrCMaNm4uDgyMDBw7McIiqmzdv0qtXLw4c2M+RI6tp1SqIKlVW8NNPPxEZGUmhQoW4\neTMH/fr1w2g0MmzYsCzFPnjwYCIiIqhatSqjR48mJiaGIUOGsH//fqpXf55r165TooQjO3euwsfH\nwttvt6F58+YopRgwIIF69d7iiy++YMiQITg6Pr6//5iYGOrVq0eXLq/Qr9/LT/0Yl2+//RaOjg4s\nXLiQS5cuA9Y+BUOHDsXLy9oURWuNyWTt9X5nbXLqEE4xdr68Nf8mvx5LJLe7HRPa5KRNRWdiYxDP\niP9EjWd0dHQ2jO0Wx4UL21my5GcGD+761H8gPGkms2bG9li+2BSNyaIIKmBgdlcv8uR89FtTEybM\nY+vWfSxYMCatA1VmaK3ZcDSR8RuiuXjDTJ2Sjgx90doL+37GjRvHypWrALAYXLhV41vsEm/xdvE/\nGfz+wAz2yIPZnA87OzuUigPOcPFiBIULP+n5v50Bf8B6Du6uWTOZEuncuRUFCngzefKAe/6N/34q\nkW5zb9KyvBOft/d47P8LN29q/PyaUrlyZZYuXYqrqxPt27+CnZ2ZhQs/JkeOrH3RL1q0iM8++xyD\nwUCDBi9gNpvZunUrZrOFQUNHccqxLvN3x+HpohjcxJ32lZ2xe8CYoo/i7+Y6EB+fRJ48jYmOjuHk\nyROULOlPSEgIJpMp000pbOH06dNMmjQJb29vxo8fDySQkBBJwYIVKVmyMOvXT0np+Q8vvfQSV65c\nZdasmVSsWBGAI0eO0q1bNzw9Pfn++x8oVqwFZrOZ4ODgDGt2k5ISKFcuiIsXI9i06Wtq1Cj3j23m\nz19H9+5j+OKLifTvP+gf6+8lMTERNzc3zGYzJ0+eZM2aNfTq1YuQkO106fIy7u6elCgRxLBhPZk0\naTTnz1/ghx8Wpk0icOhQOK+9Zk10T5w48ZDDqGXsxx9/pGPHjpQsWZj9+3/A1fXfMXJCYmIiERER\n5MyZM8Pxpt966y327dtP27ZteO+99zCbzQwf+wXrL+YnqWBTXJ3s6VXXlR61XNIqKIzG59L2lxrP\n/7b/ROLp6JiEs7P1jz86OvqhBscFazutn3/+mZ49WwMXAJm9JDPOXzcxcKmRAxeTqVUkkeqFkvk6\n2B0PZ8Xsrl6Uzv9oAwff+cWdWfvCkhj3s/U2TkBeA0NfcqduyRyZ2tdisbB8+XKWL1/OpUuXcSn5\nEqfz9OCDpm70rvfPGqqjR88SFPQqo0d/wKhR7clKG96MxCdptp1MJNJopnxhB0rndyDHQw6abrG4\nM3nyajp16kRkZCSQmnha23SazdEpCXPG5UfcNNPsq+vkzWnPqj4+ODs++vfBhQuXmTVrFR9/PAA7\nu8KAJxERERQoUAClFCdOnKBatWoopfnzz7n4+xfNUvkWi4VJkyaxdOnfbTmVgi5dutCvXz+UUhy7\nnMyon26z90Iy5Qo6MKZFTsoVyv4BruPjE1i4cAP795/g229HAJ7s3x/Ga6+9RXR0NJs2bUprpnL8\n+HGMRiOBgYHZ2o59y5YtzJ49mxdeeIE33ugJxBMaup8yZWpTrFhBzp37idTPwmvXbv7j4u/rr79m\nzpy55MrlS9eu3bC3t+P777/nr7+u0LlzZ957bwAbN+5m795Qhg8fDBQEHNiyZQs1atRImRwhnAMH\nDuHj43nfC7YTJy4QEOAHlOTuOw33cvv2bTw8PMiRIwfVq1dn27ZtfPfdxzRsWJpWrVrj6+vLxo3W\nUSxSE6bhw4fj72+dWMBisaNixc7Y20NExPXH3Cs7hiVLplG+vF+W/s7NFs3WE4ksCo4nJtHCi2Wc\neDnIidyP4UL/cdi3bx99+vTBZDLj6OpJdP6XiSnYEuwcaF7azMg2BfF1Sx+rJJ7Pjv9E4unhcQZw\nwmz24rnnalKkSBGWLl1K7tz3nrnGbDYTHh5O4cKFsbOzQ2tNy5Yt+emnn1i5chKtWtW3xa+RLcwW\nzY7TSbg4KvzzGvBwzp5OIFprFu6J55P10TjYw8ctc/Kcw3nrsECefvT8/ibGeM3UDh40LJX1TkAP\nIyzKxMRfYvj5SAK53e14v7EbbSo5P3CWnAd5a/5Nfj+VyK/v+VLEJ30LlYUL1/P66yMJCnqOgwcX\nPVQv+7gkC1tOJLL+SAJbTyQRn/z3/6WjAcoWcKBSEUcqFnGgYmEHcrln7gtm7NjZjBgxnWrVqjF1\n6lT++OMPDh06yHff/Q+DIem++yYka9rPiOL8NTM/9fOhmO+jt8wxm80891wrLly4zPz583j99Yyb\nsBw6dIjo6Ghq1SoMZG362FTh4eHs3r0bpRQ1a9ZMGwM1ldaa1QcT+GR9NNdjLHSo4szwl91xzWHb\nTlPHjh2jZs0+3LoVw7Vru/H1zQfkoFevocyYMY+pU7+gX78BABw8eJDZs2dTs2bNdL3z/x7XNj2z\n2ZyuucLkyZNZvnw548aNo0GDukA88+bNpXv3d2nXrglLl34CWG+VTpu2lIoVA6hTp+J944+Pj6df\nv34cOJC+LWeZMmX45puv/9F5B+zZvz+KSpUa8tFH7zJy5OtZebtSOHD1qicrVvz8wBExzGYz5cuX\n5/z5o3Tu3Iy9e8/w+ecD2Lp1HWvXrqNhwwZMmDABsLZ5Hj36I1xcnNM6OP7++++cPRtGw4YNmTz5\nZ+DRb7VbL6aTgRNA5voPAFyLNrM0JJ5Ff8Zx6ZaF3O52eLnYcfKKCaWgWjFHmpV14sUyTjbv/GeM\nt3DmqomzV02cvmoi5FQUxy7Fk2jvCcqO3IlH+bhtfprUzLj9vySez47/UBvPBE6c+IOrV/9CKTO+\nvn/XXgQHB3P16lWaNft72vcSJUoQFhZGWFgohQvnQqkE/Px8qFmzHDVr/vM2z7/F/otJjFpzmyOX\nTGnL8nv8n72zDoj6/v/44/roEkFMBBQUUbFnd+dmzZyxGTPmXDg7f+o2a9Z0dkwFFVtBN2crBgah\nKIiChHQex919fn+cnqKggLjtO3n8Be/71MXn8369X/F8ialqL6OqvRRXeylV7aU42UrfqfVgdIqW\nb71TOBuqplkVOYs/tsDeQsKz2iKqOcg4MNaG4VuSGLktmWmdzRjW2Pi9pSxotALLT6Wz9q8MpGIR\nE9uYMrKpcbEZEXO6m9N2STw/7E9l+3CrXO9j4MBO1KjhjKOjQ6GMzoxsHadCsjl2W8Wfd7NR5UAp\nUzEf11HSqYaSyqWkBOtoFzIAACAASURBVDzO4fojNdcicth0PoNfz+j3rWgjoU4FGZ4V5TRykuNk\nm/etPGrUJ+zb9yezZn1NVlYWc+fOJTk5mXbtqjBgQMc3Xt/sQ6ncitTw6yDLdzI6c3I0iMX6jlwS\niS2zZ8/F1/cPWrVqk+8+NWu+fA/K+PPPg1SsaE/lygVPqSlfvvwbxfRFIhE9axvRxk3BspPpbDyf\nycUHapb3s/xbvJ8v89dfv2BmZo2NjZTneaPlyinx9HTFzU2Ovue1ghs3TrBq1SpSUmLo3789ICct\nTYW5uS0ODg5ERkYafptNmzbl6tWrPHp0H1tbMyCL8PBbXL58mYCAo7Rurc/Ja9XKifXrp9GwoTvP\nvfVSqZSJEwvWCtjIyIg1a9Zy6tRJzp49iyAING7cmHbt2uXTclTLpk3rMDZWYlzEdHWNJot27Xpz\n8+Y9BEFgzJjXizZDQkKYNGkSTZs2YtGiz5k+fTxXrhymdOlSzJnzHcnJKchkUoYOHWrYp3Pnzvj7\n+3PkyFH27/cxjDs5VeK77yYDYWRklCM5OYWyZYtWCHfr1i1Gjx7Njh2zqVTp7alDgiDg/zCHbZcy\nOX5HRY4WPnKSM62zMW2qKZBJRNyP03DoZhaHbqmY5pPKzIOpfOQkp6uHkvbVlVgUOpf5zaRk6jgR\npCIwSm9k3o/TEJf2IkIol0LlUma0q2NFOTMNTZwlNHbN/34v4cPiP+Tx1JOams79+5F4eroCcjIz\njSlTxhOlUkFs7A30cjwqmjUbyP37jzl4cAl16+pXYFFRcZQubf23t8pTa/RSMAX1YuVFfLqWRcfS\n8bqWRWkzMd91MMPaRExITA53YzSExGh48FRjqOaWisHJVm+EVnOQ4u6gD+lavaEbDOgfggcCVEw/\nkIpGC1M7mzGggZFhsnu1qj1TrWPS7hSOB2YzoIERs7qZI5MUr/EZn65l3M4ULoap6eWp5PsOZu8l\n5LTtUibTfVL5qbcFn9QpWi5WRraOk8F6z+bpu9lka8DWTExHd72xWa+SLF/vrCpHIPBJDtcicrgW\noTdG49N1iESwZoAlHdzz9irrC5ykXL+eQlDQeUJCwpg7d/QbFwFeVzP5xjuVUc1N+L5j3qkrr6ZA\nzJ69jrNnA5g/f4xBW3b1ai/Gjl3EunWzGTlyElD4YpqAgACaNGmMqakR/v5bKF/+/eTOXgpT89Xu\nZJ6m6ZjUzpQvmpm8s6e8IBRGCSI4OBxf30u4uJSnUye9PuqDB5FUq9ab8uXtuX//BCADJNSv3x1/\n/9ucP7/BkDN55859EhJS8PBwwcoqL7my1wkJCeHWrVuYmJjQrFmzIqcyvUpOjuadnrU7dx5n4cIt\n+Pn5YmdX6bXXT53ypU2b9pQtW5qwsAP4+fmyevVqYmL0HdoqV3bkm2++oX79+rn2EwSBy5cv4+Xl\nTU6OmpYtW9GhQweMjJSEh0fRtes3KBSmnD9/HqWy8JGc9u3b4+vry5df9uGXX77Nd7s0lQ6fGyq2\nXcrkXqwGM6WIT+oYMaCBMc6l8/7cBEEgOFrD4VsqDt1S8ThRi0wCzVwUdKqhpGkVOaWLOM9otAJn\nQrPZe02FX7AKtQZMFSKcSktxKS3FubQEZ1spLnZSyllJCn3vlHg8Pxz+c4bnq1y9GsRXXy2hUqUy\nbNo006C3+K4PveLizL1sph9IJSJBS/1KMj6pa0TnGsoCe+o0WoFtlzJZ4pdOllpgeFMTxrUywTSP\n/dUagfB4vRF6MSiOv25G8VRtjkbxQsy3nJUEdwcp7mVlVC8rw91BajCIEzN0TPNJ4ejtbOpUlPFz\nbwsqveIJy2sS1ekEFp/QeyObushZNcASc2XxrMCvP1IzZnsySZk65vUwp3fd91fxr9MJ9Pk1kftP\nNZycVOq1HKW3cScqhxFbkohJ1WFn/sLYrFMxf2PzTahUKvb5XmF1gD1Ps03ZN6YU1cvmHwYsqIET\n+CSHXqsT8KwgZ9twK6R5LBSuXLnDmDGL+P33dbi4VAHE9Or1Gfv3H8bbe/szfUsJW7ZsZ9iwEXh6\nenL58uUipSGkpaXRs2dPHBxKsXnz5PdaCJSSqeOH/akcua2iYWU5S/taUMai8BP106fxhIeHYW1t\njZOT0xuN/MIYnvmh0+lITc0wFPwAhIVFYmNjiYVF0SrnMzMz+eGHHzh79pxhTKlUMmXK97miR/8k\n+ue4EqhCRoaOy5cv06pVS/TaudGsXr2LTz5pbWj9qtFoePToEVKplPLlyxf6e0lOTsPTcyAKhTEn\nTpw0tLZ9G4IgcOXKFYKCgrCx0XD69GkWLBiLUvl63rkg6J+XWy9kkqEWcC8rZVBDY7rWVL5VKeTV\n49yK1HD4VhaHb6mITtF7JKvaSWniIqeJs4L6jrK3zjVBT3LYez2LAwEq4tN1WJuI6FbTiI89jXAv\nKy22KFaJ4fnh8J83PN8HjxM1WJuI3ymMG5eqZc7hNA7fUuFYSkIXDyVHbqkIi9diLBfRuYaS3nWN\nqFdJlu+NfSlMzayDqYTEaGjqImdmV/N8V8Ivc+fOHb74YhQqlQoAncwMjVllTMrWpkbzPoTGi3iY\n8ELo0s5cjLuDjJuROaRk6ZjU1pTP8/EGvWkS3eOfyQ/7U3EsJWXjUEvKWxfd8BcEvcE993Aa9hYS\n1g60fOcipoIQGquh04p4OtVQsrxfwTvZnAhUMXFXClbGIn7qbUHDyvJ3MqCuX7/Od999R2JiEjqF\nNcn1lyKTivAZbU01p7w9ggUxcKKStfRZm4BWB4fH2+RrXLdrNxY/v8tMnjyZH3/8EdBXzSclJVGz\nZk1DfrVWq31j8VJByc7ORiwWI5OpgAcIgua9pW0IgoDXtSxmHdTnLi/sZUHHGgXzbGVlqVi0aCFH\njx5Fq9VP9NWquTFnzhwcHR3z3Kc4DM/3wezZszl48BAmJsa0bNmKmJhorl69hlgsYsuWLf+y65Uy\nevRK1q79jUePfClfvmDtbN9Eft/LvXsRODjYY2paB3h7waKfnx+DBg0iNjYWGxuoWBEcHMqwaNGi\nPD/DlX+k85NvOl08lIxoakzNcvnPAQVFpxMIfKLh3P1szt1X4/9QjVoDMgnUriCjibOCJi5yPMrK\nkEpEPE3TciBAhfe1LEJiNMgk0NpVwcd1jGheRfFOaVr5UWJ4fjiUGJ48C08EB/Po0SMcHByoUaNG\nvjf6vutZfOudgpFcRO86RgxqZFyo/DetTmD7pUx+OpFOtlZgbAtTvmhuglImQhAErkXk4HVVv0LN\nUAtUspHQu64RvTyNDJ6XmBQtC46mcfCmirKWYqZ3Mad9dUWBH04jR47k+vUbtGnThi+//JL09HTm\nzZtHSEgIgwcPYsKECaSqdAQ90XAnKocroSnciMhEIVLzTQuBbs2r5Xuut02iFx5kM3p7MlKxiHWD\nLalTsfCJ+plqHVP3p7L/hopWrgqW9rEo9hymN7HsZDrLTqaz6TMrWlZ988QjCALrzmSy8HgaHmVl\nrB9s+c5pAElJSfTo0YP09AyqVHGhRo0a+F6N5KHTd5hrovBf3BCF7PXP423fTVSyln7rEknO1LFz\nhDU1yuVvyKemmvDjjzuYPn16seoaFoScnBR69eqGXC5h794fDeP79v2BSqWmQ4dGWFvrq8CzslQo\nFPIieVrD4zVM2JXMrUgN/eoZMaOr2Vs9TlOnTuX48RNIpRLc3d0JDw8nJSWVUqVK4e3tlWeY+p8w\nPP39/dm1azcREQ+xt7enV69etGzZ0nBfJycn0759B3Q6Lbt27XrWJhYWLVrEnj1edO3ahVmzZr12\n3Cy1gFhMkVUYikpYWCTVq/fF3d2JTZtm4O7u/Pad3sLbvxcjwJXs7BwUiryfA4IgYG1tRXJyCpUr\nK+nXrwV37twhMjISS0tLfHz25/pN+Aaq+HxbMj1qKVnat/ily56jyhG4+lDN2ftqzt/PJvCJBkEA\nM4UIZzsptyJz0OqgZjkZH9dR0tXD6K1pWO9KieH54fDBG56xsbF899133L59xzBWpYoLixYtei2M\nsv5MBvOPptGwshw7czFHb+sTvVtUlTPkIxOau7zZi3U7Mocf9qdwO0rvoZzT3TxfozVTrePo7Wy8\nrmZyOTwHsQiauMipVkbG1ouZaHQCo5qbMLq5aaEkbtLS0mjRoiVyuYyTJ08aKk5v3AhgxIgRVKxY\nwdAxSBAE1q79lQ0bfuPln0mTJo1ZtGhRnvlNBZlEHzzVMGxzEtEpWjpUV9KmmoLmVRQFqr5/GK9h\n1PZk7sZqmNTGlLEtTd5r6DUvsjUCnVfEk6UW8P2qVL6eb7VGYLpPKruvZtG5hpKf+1iglL37tW7b\ntp1ly5ZRt25dVq9ehUQiIS0tjTbDfyS28hjaOWXy6wjH1yatN303Lxud24dbv6W4xgxwAf6ZueHA\ngQP06NEDR8eKhIVdRS8NpcXdvSWBgfe4efMgHh4ugJZp05bx++/HWLXqOzp0+KjQ58rRCiz1S2fN\nXxk42khY3s8yX4M8MjKS7t17IJfL2Lp1Gy4uzmRmZvLFF18QFBTM5MmT6d//9faRf7fh6eXlxcKF\ni14bHzp0COPGjQP0Uk4DBw7C2dmJ3bt3G7a5evUqX3wxCg+PGmzatMkwficqhx2XMzkQoMJIJmJa\nFzN61FK+k+Gk0eoX6XuvZzG7uzmeb2lckJWlQqks+AL8TQiCgM/Ze+RoRfRpWSXPbXQ6HfPm/Y6X\nlx8XL17E1NSUu3fv8uuvvzJ27FicnEpx44YvvXv3ITtbzt69a6lf34OcHA0jR47g9u07fPvtN/Tt\n2xeAuzE59FqdiFNpCXu+sCmWZ8VzUlNTSUtLo3RpuzxTzBIzdFx4kM35+2qCnmho5CTnkzpGBYqg\nFRclhueHwz+f5PgPotPpmDhxIvfuhWJpaYGnpyc3b97k3r1Qxo0bh5eXF3K5HJ1OYOHxNNadyaRz\nDSVL+lqgkIqY2knLzitZ7LicyWebkqhkI2FQI2N61zXKlcOYqtKxxDedrRczsTEVs6K/BV093vxQ\nNpaL+aSOEZ/UMSIiQYP3tSz2XsvizD01bdwUzOhiRgWbwn99z0WRxWJxLpmV5yLdz8OD8ELfTywW\n0aFDeywsLDhy5Ajnzp1n5cqVTJ48udDnB31Rk88YGxafSMM3MJuDN1VIxdCgspy2bgpauynyDMP7\nBamYtCcFiRg2f2ZVYF3Ol8nOVnPx4i1atHghYj19+hr++MOfefPG0LKlfvzAgdNMm7YGhULOzp3z\nqFKlomF7hVTEwl4WfLI2kZ9905nR9fUijeRMHaO2J3MpTM24ViZ81ca02AzkR48iAGjZsoXhOzQz\nM6ONi5Z99/fgSx+2XMhkaONXZWzypqBG5+HDZ7l58wFTpvz8txv7L9O9e3du3bpFXFwcUOql8U9w\nd3+AvX0DQB/qT001IiwsipiYorUilElEfNvBjKYucr7anUKvNQmMbmFCJRspOVqBHK3eONVoIfhe\nPJmV+2FTwRHv+3YIoanUrySna/deBAXNJygosBje/buRlJTMkiVLABg27DPatGnD1atXWbFiBZs3\nb6Fjx444Oztja2uLSAQRERHExsYa2h4+b0JgZ2dHplrHoZsqdl7O4mZkDkoZdKtpRGichq92p7Dv\nehbzepi/Jj9WEK4+VDP9QCrB0RqM5SIGb0hiyzCrN0ZIjIzeXbItJVPH/htZ7PLPIiTGArFIwNFR\nTb1Kr583KyubXbt8CAl5iJ+fHz179mTBgnls3bodmSyZRYvG8ujRbSwsoGPHVtSv7wGATCalXbt2\n3L59h7CwcACSMnSM2JqMsULEukFWxWZ0RkdH8+OPP3LmzBkEAaytrRg8eDADBw7MNf9Ym4jp4qGv\nL9C38Cy+3M038eBBJDNmrGXu3HHY2Ly7l7qE/w0+aMPz8uUr3LsXip1daX7//XcsLCzIzMxk0KBB\nPHwYwenTp2nZui3feaew74aKwY2MmdnVzJDbWNpcwsQ2poxpYcKxOyq2XNDnHP7sm07P2kqGfGTM\nvVgNcw6l8TRdx+CGxnzd3rTQhTUVbaR83c6MiW1MiUvTFanY4TkWFha4ubkSHBzC8uXLGTduHBkZ\nGaxYsQKARo1edE/x9vYGYOLEiQwYMADQy40MGjSYAwcOMH78+CKHWa1MxPxfLwvm9RAIeJyDX1A2\nJ4NVzDqUxqxDabjaS2lbTUEbNyXVHKQs9Utn9ekMPMpJWT3AinJWhf8MMjNV1Kr1KeHhTwgKuoyL\nizMgIiQkgQsXbvH0qT50BiJSUq4TEhLBtm2rcXF5vYCgbiU5AxsasflCJt1rGeUy1sKeahi+JYmo\nJC1L+1rQs3bxdiN5bgT4+1+lb9++iEQisrOzCQi4iVFMLNU/6srcI+BcWkoTlzcb5wU1OlNS0hk8\neCZJSam4uDSlT58+xfqeCkuNGjVeG5s/f/5rY0uWLKFhw4b069cXvUxRNFev3sbNzbFQXWIaOSk4\nPrEUU/alsOJURj5b2YPTQO4JOiLOZyAIsO5MJgqRJ7iOJsNIWqRmCMXJuXNnUatzaNiwIWPHjgWg\natWqhIeHs3+/D6dOncLZ2ZlSpUrRvHkLTp8+zbBhw+nWrStPnkRz9OgRNCYVSa48nAbzn5KWLVDF\nTsrsbmb0qG2EhZEYrU5g5+UsFh9Po93SeMa3NmVkU5MC5QXGp2tZeCwd72tZlLEQs2aAJbUryOi/\nPpEhG99ufBaF53JFv1/J5OhtFdkaqFFWypj6GfgEK/lyZzJH8sh3NjExwtt7EY8fx9G+fTMgjLFj\n2yKXp9O/v1466HlXn8DAwFwFrTdv3nz2eilytAJjdiQTm6pl9+fW2L/D8/1l0tLS+Pzzz3nyJBqp\nVIKFhQUJCYksW7acrKwsPv/8c8O2Go2Gbdu24+W1h9jYOGxtS9G7d2+GDBliKMh9H8ybt5GdO48j\nElmzalXj93aeEv5dfNCh9m3btrFs2XL69u3Dt9++kLVYs2Ytv/32GwOHjuCmaR9O31XzdVtTvmxl\n8tZJ43ZkDlsuZnLwZhbqZ1Ka7mWlLOhpgccbcub+Ti5dusT48ePRanWIxSJ0Ov1HaWlpyfbt2yhT\npgyg9yxFRkbh7e2No2Mlw/6tW7chOTmZY8eO5hLpz8nRMGHCQs6du8Xq1T+80oe9YITHazgVnI1f\nkAr/hznoBDCWi8hUC/Svb8TMrubv4A0wZvjw/+PSpWts2rTJIKMSFBREQkICbm5ulCql96AlJSXx\n+PFjKlasiIVFApD02tFSVTraLonHyljMoXE2yCQiQw6rRAzrBllRNw9PybsSExNDz549UatzaNz4\nI2rU8ODUqZOEht6nYsUKbN6xh95rk4lO0XLgyxfC76+GdAsXXoejR+/i7X2SDRs2/M+2kE1KiqNq\n1WoolVIuXNhIuXJ2hdpfEAQik7RodSCTipCJ9V5RqQTEgpben/QkNiaGpk2b0KlLN47fSORIoJZs\n2wYgUVLeWkL3mkp61H4Rxvw7Q+3Pw+ydO3dizpw5hvHVq1ezYcNGhgwZzPjx4wFITEzkyy+/5O7d\newhiGerSjVGV64jGqjpyCXT2UPJpA2PqVsy7+CU2Vcusg6kcu5NNVTspC3qZ52s0anUCOy5n8uOJ\ndFQ5AiOeqXM8z6mNSdHSf30icak6tg4vHuMzIV3HvutZ7PLP5MFTLWYKEd1rK+lXzxj3sjKCgoJ4\nkCjh6+MW1KskZ+swq0KrT2g0Grp370FMTAw1a3rQtm07AgICOHnyJFKpFB+f/ay9YsKWi5n83NuC\nj4so05YX27dvZ+nSZVStWoUVK1ZgY2PDyZMn+f77KRgZKTl27DhmZnrFg1mzZnHo0GFA3+XruVnQ\nsWMH5s2bV2zXlJWlIjk5nTJlbAFbHj3KYfbs+cyaNQtz8xeRo5JQ+3+bD9rwPHr0KNOnz8Dd3Z3N\nmzchEukLfMaNG8f5q4GYdvqVqCxz5vc0p3/9wsn0PH+omSlF9K777p1ziht//6usXbuWgIAApFIJ\nzZo148svv6RixRch5TFjxnD58hUmTpzAoEH67iLPezCbmBhz8uTJXB5PjUZDjRr9CQkJJyBgFzVr\nvlvoJClDx+l72ZwLzaaxs4JenoV7KD94EMmUKSuZNm0UHh4tABtSU1MxNjYu5Co+h+jo02RkZODs\nnFuQ/ESgii+2JfNtB1NsTMRMfVa1v2GIZZFSIQrKH3/8wbRp08jOftF9qHRpW3755RecnZ15nKih\n28oErE3E7B9rg7lSnMvAiUrW0n9dIkkFNDrBGsi7KvvvJDExkY0bN3L58mUsLS0ZOHAgzZs3L/D+\noaGh9OvXDzMzY/78cy0aTRoHDhzA19eXjIxMatb04NNPP6VcuYIL1b/MtWvXmDBhAllZqlzjg4aN\nokKjAey/kcX5+2p0gn5B2qOWEa5Gj7A2Fv4Ww/P+/fv07dsPpVLJ2rVrqVHDnYcPH/LFF18QH5/A\n8uXLqNugMXdjNAQ+yeFOlJrLdxOJSJWjEaSUtdAxtLHeQLIuYLHJySAVMw6kEp2q49P6RnzbwSxX\nPve1CDUzDqQS+ERDE2c5s7rlrc4Rm6r/zcam6tgyrOiLOv+HajZfyMQ3UJ+jX6eijH71jOjskVuu\n6Pn9ciu9Et/vS2V8axMmtS28hmlgYCDjx48nOTnFMCaVSpk1ayZJ1s35YX8qI5saM7VzwXRVC8qk\nSZP4668zzJ07h06dOhnGBw0aRFBQMGvXrqFevXqEht6nX79+KBRyFi1aROPGjbl48SLffvsdKpWK\nHTu24+rq+s7Xc/HiLfr0mYKHhxtHjhznVUWAlJQXn0+J4fnf5oM2PDMzM+nUqRNpaek0adKEFi2a\nc+nSJU6cu0V6nbmIzcrxy6eWtK/+97R7fBOCIBAYGEhsbCwVKlR8FiZ+d9RqNWKxOE9D7M8/TzN5\n8mREIr2X09LSgmPHjpGRkcmAAZ8yadIktFotGo0WhcIIKIeX15/4+/uzePEc4D56wf5/hokTl7B8\n+U66du3CwYOHinycc+fO0aVLZ6pWLc+FCxtz5cYCjNqWhF9wNlod76xTqlJlc+LERZycyhkqc7Va\nLUlJaZQqlVu+KSEhgRMnTvD06VMqV3aiTZs2ufLcLoWpGfhbIo2d5WwcasXdkGAALByqGozObcOt\nqFU+/wncy+skHh7uVK3aEfh7W/C9SnBwMC1btiQ2NjbX+MSJE1myZEmBvbBarZbExEQsLS0YMKAd\nQUF/kZAAdnYgkYCpqQlr1qwpsiEYHR2Nt/deQkPvYW1tTbdu3fD0fNF2Mi5Ny6GbKg4EZHErUoNY\nJFDeQotLGRMq2kioYC2hgo2UCtYSyllJir1CfMqUKfj6+gFQyqES0SozNKZOmFWog3nFuoTF6z26\nAGZKEdXKSKnmIKO1q4KPnIomA5aRrWOJXzqbzuvz3Gd1NadhZTmLjqex52oW9uZ6dY5ONd5cHPSy\n8bl5mFWeuZf5cT9Ow8JjaZwMzsbSWN+1qn99I6rY5b3oem54urm58bVXCvtvqNjymRXNipBbnpqa\nypEjRwkPD8PW1pYuXbrwWGXDp+tf3J+FcU5cvRrEqlVezJz5OZUqlQO0JCamoNMJhufE8+950qSv\nDKlSOp2O7t278+RJNJs2bcTDw4OtW7eyfPkKunfvxowZMwznWLBgAXv37mPs2DEMGzas0O85O1tN\nVFScodtYXFw2zs4dcHZ25vTp07k8nFBieH5I/OcNz9jYWJKTk6lQoUKevYwvXrzI5MnfGDQtNSYV\nSfOcjcLUis3DbGlQ+e+VismLR48e8f3333P37j3DWN26dZg/f74hNPwqgiAwf/4GqlSpyMcft3rN\nWCoo69f/xrp1vxrC8QAtWjRnwYIFREcnMGTILDw83Pjll42A3FB8ULduXUDDqVPb2bhxN7/9Nq1I\nyf9Pn8YTGHgHExMTatWq/UbR/+xsNU+fJlGunD1Qivh4OdOmzWLatGlF9mCB/oFYrVo1atVyYceO\nWblEukE/GX68JpHWrgqmdzHLU3C9oEybtob58zcwZsxnrFq1DMggIOAKtWv3oG3bBvj6rjJsW5B8\nwR2XM5n6zKPS0zGSuHQxM07bFMjovH49hEaNPkOhUBIYGPjG9pN/Bw0aNODKlSs0bNiQUaNGERoa\nyo8//ohareb48eO0b9++UMdbv349n3/+OcbGSjIzVTRvXpNatcw4e/Yc1aq5sW3btvf0Tl7w4KmG\nDX6PCUuSkJxjTESClqycF/eaSAT2ZiKMtImoEsKQ5yTgVtGazq3q41rBGnsLca5mEYIgcP/+fRIT\nE6lc2Qlb21IIgsDTdB33YzXcf6rhbrSav25E8CRDjk7+Qu+ytKkI93JyqjtIqVZGRnUHKeWtJcWa\nVnE7Mocp+1O4E6VBLgWdDoY3NWF8K5MC6yLHpWrptz6RmBS95/Ntxmd8upblJzPYeSUTI5mIMS1N\nGNbY5K0pOy9HCDLVOnqsSiQ+XcuR8aXeKc8eIDJJS/eVCVgYidg/1qZAih4vM3DgTHbsOMKUKd+x\nYMECIJX58+cyc+Zy/u//xvLNN4M5efIk3333PebmZkyePJnKlZ3YvXsXhw4dxt7enoMHDyCRSAwh\n+VfTL57ruI4b92WutqKvkpWlIjAwDMDQBTAuLhEHh46Ym5uQkHANkagUYElgYCBubm55ypuVGJ4f\nDv/Z4qLHjyNZsGA+V674A2BsbETfvn0ZNWpULu9eo0aN2L9/HwcPHuRqRA5/ajtjbSRj24hSuJX5\n53Mys7OzGTt2LE+eRGNtbUX16tW5cSOAq1ev8fXXkw0pArkREx0tMH36WiwtzenduzOgD8n++ONW\nBEFgyJAu2NnZvPX8I0eOoEuXzpw+fZrs7Gzq1atH9erVAUhOTufixduEhkYzd24mlpa5JwC1Wsfw\n4bOIiIigYUN3xo17XUomP3JyNPz880/s27fPUGlfqlQpZsyYTuPGryehh4Y+olu3SVhbW3Pu3DlE\nIiNKlYK1a9cWgYhvpwAAIABJREFU+Jz5YWFhgb+/P2XKWCESBfO8n/Vz7MwlnP22VKEn6NOnr7J2\n7V4+/bQj3bp1Bqzo1etzjh27QY0a9QFzwJzwcB1GRkaULu0IVAAyyMlJwtGxAx4ezvj4/Ixcnvdv\ndUADY+7GaFh/NpOcdCXHQxVkaN5udAK4uJSne/fO2No6/ONGZ0hICFeuXMHS0hI/Pz9MTfW5aUql\nkunTp7N58+ZCG57PZYK++eY7zp49y9q1P1GunJoOHdoQFBRMZGTkOy1YCoKTrZSBtbIAqFatAoIg\nEJ+u41GilogELWGxKryOXeRRtgKtsSOCWR0eJsIxbx3Pe7qbKUTYWYixkKl5fPcaaXEPEGlV6Ezu\nYVa2BtmKMqSqXvxmzRQinOzLU89GhJ1RFp6OpnhWNi10J66iUKOcDJ8xNmy5mMn1Rzl81ca00JI9\npc0l7BppbSg42vyZFfUdX/8tq3IENpzLYM3pDLJyBAY0MGZCa1NsTAvvuTeWi1kz0JJuvyQwdkcy\nu7+wLnLr30y1jpFbk1BrBdYPsX6r0XnvXgRr1ngzaFBnPD0bALaMGzcde3tXhg0bgT4SYUlsbA4A\n1ap9BFjSsmVr3N3rcubMVaZOnclz34NMJuWHH6YYnBFNmjRh6dJlnDjhS7169WnatAkXLlzg2LFj\nADRr1iz39WeqyMnRGDpi+fpeoUePSbRr15QTJ3YDSmxtq2FhYYG1tTVpaaUN3s3nc0cJHzbvzfAU\niUQbgS5AnCAI7i+NjwO+BDTAEUEQvn1lv/LAVsAe0AHrBEFYXphzp6Wl8cUXnxMbG4dSqcTe3o6H\nDyPYtGkzKpUqlwxQtkbgZrw5t0w+4Q9BRTlrCVuGWb1TVx3QT5QXLlxAJBLRpEkTXFxcinScU6dO\n8eRJNJUrO7JlyxaMjY1JSEigX79+3Llzh4CAAGrVqoWPz2l27DjG7t2/IpFURCxOYMqUKeh0OkSi\nGug/yiyWLdvDkycxfPxxd+zsZEAOW7ceJiDgHgMGdKROHbfXrqFMmTL0798f4KXcNWNq1erBnj17\naNKkCZaWr3fxkcvlHD58mLVr1zJ27EQgpsDve/XqVXh5eSORiKlfvx6xsbFERDzi66+/ZseOHQZB\n6+eYm5uRmqpCEDKIi0vFzq54K8kdHBye/VUGePLa64X3Com4di2c3bv90Oks6NbtKwA8PW25du1a\nri179uxJSkrKM49AKcCW27cTiYqKw8TEHLm8FJDy2hmeM72LGffjNGy+ASYyHTs+f7vRCWBmVpnd\nu/eh1Wrfuu375unTpwA4OzsbjE6AmjVr5nq9MGRk6KvTGzdubBBDF4QcRCJL4uLSuXPn/ns3PF9F\nJBJhaybB1kxCnYqwYcNONOfXUNXengkTxqMwTmXtZi8Cw+OpWrsJbbp+SnSKlscJ2Zy//pBsqROC\nY10QiRGpk9EkPKKyzVMmdf0I59JSnEtLsTN/905S74JUImJ4ExOGv8MxSptL+P1za/qvS2TopiQ2\nDbUyRKd0OgGfABU/nUjjSYqOttUUfN/RDCfbd3umO9lKWfixOeN+T2HhsTSmdyl8TqZOJ/D1nhTu\nxmjYMNSqQNe0bt0Bli37ndRUBRs26EPmDRo0oEGDBrm2W7FiBTNmzMDCwgKQIZFoMTevxcOHV6le\n3RZnZxOqVatGv379cqWRVKpUif79+/H777teawrQp09vKleubPh/wwYfvvpqKZMmfcasWbMBE6pX\nt6B69Q24uHigfz7qPfUxMTHIZP+886aEfx/v0+O5GViJ3ogEQCQStQS6Ax6CIGSLRKLSeeynAb4W\nBOG6SCQyA66JRCI/QRCCCnriAwcOEBsbh5ubK6tWrcLCwoIrV64wZswYvL29GTx0GMGJJhy+qeJ4\noIo0lYCVsb4T0aS2ZkVaERsuXqNh7ty5HD58xDC2cuUqevTozg8//JAr5K3RaLh9+z61a1dD3wUj\ng9WrvfjoIw9q1aoKwL17+vB6+/btMTbWFzjZ2NjQrFlzfHx8uHv3Lq6ubowb9xNRUbF4eV2lXz9n\n7O3tn4VgniNGEIyZOXM2QUFBODq2RL9S1rB37wwOHjxK/fr1qVNHAWRz/nwAv/9+gs6dm9Cxo97D\n6O19krFjF+Pjs4lGjboCInr06PHGz8Pd3Z2VK1c++8+IzMxg/P0Dad68Tr77ZGZm4uXlBcCaNWuo\nU6cOOp2OmTNncvToMXbt2sXUqVNfaseoxM6uMX5+p6hYsaJBFP99EBsrYsKE6fTs2ZS+fdsVeD+d\nTseMGWtp3rwBbdv2Aizp08cWQSjFJ5988tb9ZTJZrrQKT09PHj16RHR0NOAE3AXylvmRSUSsHmDJ\ndzsf0bFKNrXKO+S53XNOn75Ks2bNEYvLIhKJ3qucSkGpVq0acrmca9eucfnyZRo0aIBGo2H9+vUA\nuXIoC0rTpk25dOkSixYtokGDBpiZmbFp0zb++isSgH79ZvHw4aHXUiuKk7S0NG7duoVMJsPFxeW1\nidrX1xeAH36YYvD0u7u50LFjRx7+FcSgOQMwNjZn+/btBFxYRgN3d1auXg0SJTGP0xg0aAaJGg3t\nxx8yqFX8Vyhtpjc+P12fyGeb9canVhCYfySNwCcaPMpJWdrXsljTpbrWNML/YQ4bzmVSr5KcDu6F\nSx/65Y8Mjt3J5odOZvl2PYuOjsfMzBhT09KALaNGTSM5WcaYMWPeevzcqVcSGjRoTkBACEuW/Ei9\nei5AKrt27aFr1ylMmNCf8eP1Uaivv/4aJycn9uzZQ2RkJA4OZend+xNq1qxPREQ0FSuWAYyoUKEG\naWkZBAfHoS841C8G79y58+qllBidJeTLe5tRBEE4IxKJKr0yPBpYKAhC9rNt4vLYLxqIfvZ3mkgf\n2ywL5Gt4+vn5UbZsWcP/586dA/QTS1RUFFFRURibmGLv0ZHQbEdaLk0nQ6vGWKbjowo5NKukplaZ\nHKRiiH0EsfmdqAAcOXKEw4ePoFDIady4MTqdwIUL5/HxOYCpqakhHJiRkcVnn/0fYWExeHntwM6u\nAnFxkXz55WKkUglnz67EzMyYnBy9JpO/vz8ffaTvvKLT6bh27TqCABkZKu7eTWfixK+Ji3uKo6Oj\nIc8yLzw9PfH09OT69euGsU6dulG2bEVMTZ24elUFaNm27Ty//upFamo25cvbIRbncOzYBeLiEvnp\npy1MmfJm4yWva9DpdEyZ8gOnT59l/vzP6dYtb922iIhHZGWpsLe3x8jIyJBrVbt2bY4ePcbNmzc5\nffo8kyatpGvXNnTtOgTQi3MHBwe/8breFR8fH3bvPsaFC9eoVs0BiaRgi5TDhy8wf/5GVq7cy4ED\nVQ3GcYsWLYiPjyc+Pr5I1yMWi7l69RpqdQaLFk2nZctatGtXL89tJzxr3PP888yL/fvPMG3abzRt\n2pifflpSpFaT74tu3brh7e1N48aNqV27NlFRUURHR2NkZESTJk3e+LvPi2bNmrFu3TpOnTqFvb09\nZmZmz0TpwdXVlTZtWhAZ+ZQnTx4X+3sRBAEfHx8OHz6MWq0Pka5evZrBgwdTr96L7+953lt6errh\ne9NqtcjlcrKyVNy8eQsLC3MuXboEQMOGDXkc8dCwv6urK7dv38HPz+9Z3vV/j9nNRXzva86n6xPQ\nCiJsTbR80ySL5o5qxKo43vBzLxCv3i8fV4ZL98yZtDsRaXoqDua6fPbUo9LAmXA5R+8puZcgpVXl\nbBrbJOZ5XZmZ2QwaNBetVsKSJSuwt08DYNSoUeh0ukL/xl1dXVm6dCkAV6/qxeq9vf0JC4siLCyJ\n27cfIRZnEhPzlKNHb9KpUx/q1NE7PXbs8KV374X07t2R77//AZ1OwNy8Il5eXlSqVKnQ1/I2ihoV\nLOF/j7/blVEFaCoSieYDKmCyIAj++W38zHCtDVx+00Fnz57N1KlTDVJASqUSQSTmQZwGUYSMoDgZ\nZx7KSCw9FrQqqlmk0tlDQd2yOcgLmdb05Ek8s2Ztom/fVrRu/brX7tSpUwCMHj2GOnX0XpgaNdz5\n5ZeVnDp1ymB4GhubYm9fnoQEFXFxKdjZgSDI6N27Nzk5Ochkrmg0KTRq9BE//7ybpKRryGRrcHev\nzr59f3D69CNsbRW4un6MRmNKixYtC/dGXqJOnTrUqfPye5HQtGlrFAozatSogUrlBOgYPvwbKlas\nQ8eOHYt8LkdHF/z9b1CtWt5t6ACDtlxiYgJpaWmGXsYPHz589ro5/v4h3LgRSlxcJu3bD0Re2C+y\niHTr1o3Hjx/Tt2/TAhudAO3atefcuSjatWv3Xjyyfn6nOXjwLOfO3aRpUw+MjApfeQvg6FgBExMT\n6tat/68yOgG++uorcnJyOHz4sGHSc3BwYObMmS+lQhQce3t71qxZw+LFiwkICCArKwtra2uGDh1K\nv356T5BKBTJZHCEhV8nIUNGwYfFIHp04cYJ9+/YDeo9Reno6MTExrFq1imnTpuHsrFc0cHFx4enT\neA4dOsTIkSORSqUcP37CsDAzN9ffGyYm+nsmKirScA6tVktMTMyz199fFOB9IggCT58mU7q0Vb7b\nWBkJLGyXyi+XTHCz1dDdTVXo53phkElgSvN0xh02Z8FfpvzcMRVFHjPpo2Qxx0KVnHogJ10tpryF\nllH1MuhYJZv8Mh2Sk9PIytKg0wl5FsMWB9988w1du3bF1taW7OzSgMDp0zf57bfDhIfH4enphk5n\ngodHc5RKb8Ric3Q6vWdXIpFQqVKl93JdJXw4vNeq9meG4+HnOZ4ikegO8AcwAagH7AYqC3lchEgk\nMgX+AuYLgrDv1ddfrmpv3tkNpzptadl9GPdiNQSEp/AoWQxivatfKhaw04WRcmsv5SQRHPHZU6Qq\nb0EQaNBgCP7+QYSEnKNqVUtARXBwODY2FtjaWlG3rt5bcenSJUMFdkZGBs2aNScjQ4yf30HKl68G\nlCc+PhmlUpkrZ+1VAgKuU7t2HcRi8PAAsRhiYyEqSu8BvHbt2r9KzDt3VXve6FvwlQLCyclJ4PPP\n59OuXQP69m1nMHbGjh3LpUv67kJ9+/YlJiaG7du3o1Jls2jRT7RpM5KVK7fSu3dvQyefvxcteie8\nOt8tbt++j6OjA6amLuhTlt8fgiAwZcoU+vfvTM2aeWvOvl2oXA5UISYmCXv793u978KTJ0+4fv06\nVlZWNGzYsMiKDS8TFRVFWloaTk5Or4UI09LSqFXLg/DwCA4eXEKXLk3f6VxarZZOnToTHx/P/Pnz\nqFBBX1R06NAhvLy8adOmNYsW6Xuph4aGMmTIELKz1Zibm2FkZERsrN4rO2/eXMMi8Lm+rlQqYfDg\nwbi6unLw4EHOnTuPg0MZfHx8iuVzyovU1HQWL97K1avBHDu2EZFIn0/+cqeeorJz53EGDJjGxIn9\nWbJk0t/6rJs6dTmPH8fx22+z8izeOxWsYviWZPrXN+L/elkAoNYInAhUseNyFpfC1Mgk0MFdycAG\nxtR3zFtoPzcmJCfbER+fYFh8/B0EBASwY8cOGjRokCv1JyMj429btJRUtX84/N2G53H0ofbTz/5/\nADQUBOHpK/vJgMPACUEQluR17JcNz5r/d84wXtZSTBU7KfEP/AkLOIU0PQJJRiQiXTYKhdzQQq+o\n3LqVxujRUzl69OizJO502rbtwOnTlzlw4Cd+/fVHIiOjWLx4Ea1btwbg2LHjfP75NCIjoVu3Tvj4\nHC7wAzQxMZGtW7cSExODRKIlLi6csmWrU6FCRYYMGfLeJpOiUhDD82X+/NOPVq3a4epameBgb/RF\nUHDrVhA//PAt0dF6j41Wqze2Bw7swpIl3ohERfPoFS8pnDy5g8aNa74mFXXixEU+/vhb2rRpyb59\nh/5m7+ETnmWr5CI/w3PjxgNUqeJEkyb9eFXUuQR9Lvb8+fM5dOgg589vRaFQkZKSztChszA2VrJj\nx4vOLkOHziIg4B5bt87Gw0MfOszMVKFQyAz3alxcHB07dsLCwpxTp04Z0kMUCgV9+vSlbFkHDh48\naDjm9evXWbx4MaGhetm40qVtGTVqFN27d891nWvWrOG33zbkGjM2NmLFihXUrl27+D+YZ2RnaylX\nriPx8Yn4+/tTt24dEhNDqFu3LWPH9mbixP6Fek69kAmTkpFhialpJdq1a8yhQz/lq95QHKhUes1h\npVIBSJkwYSkrVmxh2rThzJ07Os99Fh1PY83pDKZ2MiM5S8du/yzi03WUs5LwaQMj+tQ1KpBaQHx8\nMqVK2QJuwIeZG1lieH44/N2hdh+gFXBaJBJVQe9iyZXcJtI/cTYAwfkZna9iHrISUsI4uXcdpa31\n3kOdri2nTkk4fPgwyclKXF3d6NevX67WjwXlxcq9Ah4etpw/f/6l1xSYmJRCqVTSqFFn4uKi+eWX\nRUyY8AOtWjXD0tKI48d90WjA3Nycxo2bF6pfs7W1NRMnTiz0Nf+v4OrqztKlS595fWsCqaSnP6F+\n/RG4uJTn++8nERQUiK/vXeLjHxISkvMvMTph+vSfmDdvHlOmfMaCBWNzvVapUgVkMgXm5jZoNJoi\n97QvGg788ccfHD58jJ9//uqNv7U//vBn+PC5mJqacu9eu/9cAUpxIJVKmTFjBk5OTnTsOI6kpIc4\nOlbCx+c0lpYWgAsgAkSEhsZz8+Y9UlNtgWpAKkuWLGDNmt/56acJ9O/fAVNTU6RSCWlpacTEvMgo\nDw0NBcDKKndY2dPTk99//53IyEhycnKoUKFCngVfo0ePpkGDBhw6dIjExESqVKnCxx9/XKze6+xs\nNYsXb+XYsQucObMDqbQMCoUVv/yyirJlyz5L2RHh5XWG8PAoDh++wKRJAwp0bEEQ2L79KCtX7uHP\nP70xNnbGxETK+fPnqV3bA7k8kvwK6N6VNWu8mTZtDQsXTmbkyLGAJc7OdXBzu8K4cYPy3e/rtqZc\nj1Az/2gaYhG0clUwoKExzV0KLrR/+/Z9mjQZwZQp3/DddzXyDcOXUMJ/hfcpp/Q70AIoJRKJIoGZ\nwEZg47OQuxoYIgiCIBKJHIDfBEHoBDQGBgG3RSJRwLPD/SAIwtH8ziV7fBwPjxoGoxP0RRdt27ah\nbds27/Q+7t9/TMeO41m9eglt276e0ymTyfDx8THkIg4aNB9//zjWrdvEgwd/UqECPH4Mw4aNZdGi\nRf+zuVbFiVqt5tChQ4SEhFCuXDlGjBjxUrqBJYGBd1EolJib2zJgwCQglQkTRAwZ8hXLlxdKWeu9\n0qlTJ5YuXUrp0no91BcLCmOqVu3A9evXqVSp0t+eCpGUlETPnmNJTU2lSZNa9OrVKt9tmzdvwMCB\n/alVq06J0fkGJk2axLJlywz/BwToCzX69/8Uvd6qng0bNqFSqZ6FSY0AI86fv8eTJ0+xtKwIKDA2\nhrp1P+Kvv84ybtyXtG7dmvT0DI4e1SthdO7c+bXzi0SiAmmpPi8eLE4SEpKxsdHLpcnlSrZv9+Xe\nvTB8fR/RqZNeKe95TuxzvvjiC8qXL4+Tk9Mz8fBIUlKSEYtFmJnl/QzU6XQsXbqLGzeC2bLlT0aP\n1rdpfF5UCS4Iwj28vQ/yySet3+m+ysxUodFoMDc3BWSYmpYhMTGF8+fvM3Kk3vBv1KgRjRo1onTp\nakAIr+r3gl4aavUAKw7dzKJtdSVlLQsfgTp3LoDU1HRu3Qop8vspoYT/Jf4TnYvatbNh1apV76Vq\nc9q01cyfv5F27dpx/PjxAj3sMjMz6d+/P0ePHmXQoIF89933VK1atdiv7d/I20LtwcHBdO7cmfDw\ncMOYtbU1e/fupUWLFoYxtVpNdHR0rt7x/0aSkpKwstKSmHiLvn2nMH78cLp2fS7q/M/h5eXFtWtX\nmD+/PxKJ/lZ5OdSuN5LlQFUEQf6vyhP+txEQEEDt2rWRy/WpOi1atGDPnj3MmTMHhUJBVFQUNjb5\nN2MQBIFLly5Rt27dZ/mj6YwYMZwNG/ZQrhyUfklUrkWL5ixcuOidcyOLgiAIxMcnY2trZfjfze0T\n7t6NIC7uIra2ToANhw8fRalU0qpVq0KkkGgYMWIAJ078xc6d83B1LfdssW6JsbERJiZmgAOXL4cR\nEhLCoEGD8jz2pEkTWbp0OV999SlLlkwq0vtcsWIX06evYfLkEUyfPguwICtLRVBQUK4iy5efZYIQ\nx65d6+nevQXGxsXdQtkeP78gmjRp8t4Kiv4XKAm1fzj88wJ9xcCaNWuKfZX/nDlz/g8bG3dGjhxZ\n4MnZ2NiYAwcOkJ2djUwm+9dVB/9TaLVaunfvTnh4OFWrVqVr166cOXOGK1euGMatrfXacHK5/F9v\ndMKLsOjOnac5efIKERFJdOw4DKn0n/3Oe/fuTe/evYF04B4ve2s2bPDB1/cK27fvRSZTlIT23oK3\ntzcAI0aMYOxYfUrF7NmzuXjxIn5+fhw5coTBgwfnu79IJKJRo0YvjZhiZFQaIyMjhg79gvDwy5iZ\niZFIbDhw4DqVK+9j7Ng+gF52LTT0EU5O5fL1FBaF9PRM0tIyKVNGr/sYERFNzZr9sbQ05+HDvwBj\nRCJjbGwcMDVNIDxcjK2tLQBdunQp9PlUKg23boUTG5vIkiXLefToDikp8PixiGbN6uHrew6RSEaD\nBravCaO/TLt2Hdi4cTPt2xdVxUOEu3sdUlMzuH37CaD35BoZGb2i7JGbadOWs2DBAj77rCsbN84s\n4rlzo1Jlo1SWBsrStm3Zt25fQgn/Ff4TFlFxG51hYZHPEs0rIRaX5quvvnpj5Xl+KBSKEqPzJU6e\nPEloaCiVKlXixo0b/Pjjj1y8eJHmzZuTmprKjh07/ulLLDJjx85k5syZnDp16l8huP4CUzIybJg0\naQkpKRkkJ6fzzTcr2LPHl2PH/vinL+5/ApVK363rVa/m8/+zsrIKfcxffvmFuLg45sxZwsSJKxg+\nfBk6nQMPHkSi0Vijb41qx/XrkdSuPYC2bXPnEE+ZspLFi7eQnf1CVUGne11PMjExhbNnb/Dw4Ytu\nW/v2/YGZWTO+/PJn9CLg5ShXrjFqtRaVSktGRhnAAbDk4MFDpKSkUL9+/UK/x5dRKpX4+PhgamqK\nj88dkpOVWFmVQq0WOHnyCvPmLSzQcTp06MDDhw9p3/4z4O3PZJ1Ox7ZtR1iyZDtgBVSnVat+hIaG\nsmfPngJff9++fbG1taVNmyYF3udNrFu3D0/PQYSGaorleCWU8L9EiVX0CkFBYXz00XB69pyBSlWS\nj1mchIWFAdC6dWtDSEksFtOpUycAHjx48I9d27siEkmYNWvWP97TPC9Gj57O0qU7mTlzIxYWlpw4\ncZTly5fTrVu3f/rS/ido2VLvXVu/fr0hXeHMmTPs36/X4Xw5RaQwmJqa5oqiLFmylKCgIPr1GwrY\nAuVQq21xc3OjevX6gAfgikrlwMKFm5k6dQ1SqS16A0xOz57fYGvbhpMnX8gez527kWbNRvL772eB\ncoAzjo7NkMvlaLXGgCNgh0RixePHj4mJicmVh25jY1Nsi+d169aRlJREkyZNuHYtmitX4pgzZw4A\nP/30k6GF6dvQt+eVAM7cufOE77//JU+jG+DmzXsMHjyTqVPXEhkp57lqQ2Glijw8PAgPD+fTT8fz\nrtOmRqNh7dp9BAeHcelSvjLWJZTwn+Xf5Jr5V6DTCWi1oNGI8n2YlVA0HB0dAfjzzz9RqVQolUp0\nOh3Hjh0DyNUTuITiY+7cuTx48IAxYz5FpapIvXofUa9e3l2jSnidDh060LhxY86fP0/16tWxs7Mj\nNlZfjT5o0KBiy99WKpW4ubnlGmvduvUrnXNk6HQifv75Z9LS0pBIXhhQ0dGZxMcnY27ujr5XhxJP\nz/bUq3cPGxtnQK93W7NmPTIyMl7zzL8pT7U4OHv2LKBvz6g3HmH69Ons3r2bwMBAbt++XSipu+xs\nDZ06jeXx48eUL29nSE/QSxNZAgpq1+7ExIkTqV27dpGaDLzMC4O8IlFRlzEzM35WnFQ4pFIZf/11\nkr17/Rg0KP+K+RJK+K/ynygusrC4/07HEgQBnU6HRCIFKnHvXjzly5f/oBO9i8qbiou0Wi2urq7c\nv38fNzc3unXrxpkzZ7h48SJmZmaEh4e/98nvQ0UQBK5duwYUXGO1hBekpKQwefLkZ00MVFhYWDB6\n9GjmzJnzzj2pC6t9mx86nY64uDisra3/ZvmugtG9e3cOHjzIqlWrDH3H1Wo15cuXJy4ujtu3b+Pu\n7l6oY/r5+bFmzWp27pyNQqFm3LjFbNhwkJs3/6BKlUboZa6KRn7fy9mzZ+nVqwctWtRmz56FBc79\nj4iIRqGQYW9fi+eLgBJeUFJc9OHwwYfab9wIoWXLL1ixYi/gDFhTpUqVEqPzPSCRSPDx8aFChQoE\nBwf/f3v3Hlx1nd5x/P3knBWEuiFboOFqzBjEoLsol4Ego4lII2VAp4Kw7CodWCpTK1jrDttxd2mZ\nToTdWhDLjgQQtOJyiZZQ25V1XS4ykZUgI7cxclmQkkkCcieECE//OIcQssFBkpzfOSef1wyTc37n\n9zt5mO+ck+f3vTxfZs+eTUlJCR06dOCdd95R0tmCtGq9aVJTUyksLOTYsWMcPHiQiooKCgoKmpx0\nNqeUlBTS09PjMumEyDxJiPRyLlmyhE2bNjF+/HgqKyvJzs6mT58+3/g9H3roId5++x3atr0Ls29T\nUxOmtvYrNmzYRVOSzq+Tnp5OTU0tp06d59y589d1zdy5y8nMHM1LL61BSae0dq1+qP3IkeNs2LCN\nI0dOM21aAVoL1LL69OlDWVkZa9asqavjOWbMmLr92EXiWbt27ejZs2fQYSSkxx9/nBUrVlBcXMyk\nSZPqjrdr145XX321iTdHKUAvZs16iWeffeFrtoVtuqysLEpKSujd+zZCoTIi2+deraLiGOf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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2365,8 +2516,8 @@ "process_var = .05**2\n", "actual_voltage = 16.3\n", "\n", - "x = (25, 1000) # initial state\n", - "process_model = (0., process_var)\n", + "x = gaussian(25., 1000.) # initial state\n", + "process_model = gaussian(0., process_var)\n", "\n", "N = 50\n", "zs = [volt(actual_voltage, voltage_std) for i in range(N)]\n", @@ -2375,11 +2526,11 @@ "\n", "for z in zs:\n", " prior = predict(x, process_model)\n", - " x = update(prior, (z, voltage_std**2))\n", + " x = update(prior, gaussian(z, voltage_std**2))\n", "\n", " # save for latter plotting\n", - " estimates.append(x[0])\n", - " ps.append(x[1])\n", + " estimates.append(x.mean)\n", + " ps.append(x.var)\n", "\n", "# plot the filter output and the variance\n", "book_plots.plot_measurements(zs)\n", @@ -2445,14 +2596,14 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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Q5/Xq1euLj/tLIDg4mAEBARw1ahTd3d1ZoEAB8UHXJ2tarVZ8sP+XjXczGxn1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\nn5+fXLlyJd/PpKamynvvvSePPfaYdO/eXSIiIu54yai0Jr6UlJR87ZPc3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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2460,19 +2611,19 @@ } ], "source": [ - "sensor_var = 300**2\n", - "process_var = 2\n", - "process_model = (1, process_var)\n", - "pos = (0,500)\n", + "sensor_var = 300.**2\n", + "process_var = 2.\n", + "process_model = gaussian(1., process_var)\n", + "pos = gaussian(0., 500.)\n", "N = 1000\n", - "dog = DogSimulation(pos[0], 1, sensor_var, process_var)\n", + "dog = DogSimulation(pos.mean, 1., sensor_var, process_var)\n", "zs = [dog.move_and_sense() for _ in range(N)]\n", "ps = []\n", "\n", "for i in range(N):\n", " prior = predict(pos, process_model) \n", - " pos = update(prior, (zs[i], sensor_var))\n", - " ps.append(pos[0])\n", + " pos = update(prior, gaussian(zs[i], sensor_var))\n", + " ps.append(pos.mean)\n", "\n", "book_plots.plot_measurements(zs, lw=1)\n", "book_plots.plot_filter(ps)\n", @@ -2501,14 +2652,14 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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FihU5fPgwc+fOZfPmzeTm5tKhQwfeeecdGjVqdN/urTySQEMIIcQjIyIigmXLlnHy5Emc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\nLAwhBJs3b+ann37C1taWzz//nG7duhEcHExgYOBtx41CQ0NZtWoVbm5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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2516,12 +2667,12 @@ } ], "source": [ - "sensor_var = 20\n", + "sensor_var = 20.\n", "process_var = .001\n", - "process_model = (1, process_var)\n", - "pos = (0,500)\n", + "process_model = gaussian(1., process_var)\n", + "pos = gaussian(0., 500.)\n", "N = 100\n", - "dog = DogSimulation(pos[0], 1, sensor_var, process_var*10000)\n", + "dog = DogSimulation(pos.mean, 1, sensor_var, process_var*10000)\n", "zs, ps = [], []\n", "for _ in range(N):\n", " dog.velocity += 0.04\n", @@ -2529,8 +2680,8 @@ "\n", "for z in zs:\n", " prior = predict(pos, process_model) \n", - " pos = update(prior, (z, sensor_var))\n", - " ps.append(pos[0])\n", + " pos = update(prior, gaussian(z, sensor_var))\n", + " ps.append(pos.mean)\n", "\n", "book_plots.plot_measurements(zs, lw=1)\n", "book_plots.plot_filter(ps)\n", @@ -2556,14 +2707,14 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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wYAGHDh0CYMmSJSQnJ+faPiMjg+PHj7Njxw4uXbr0r5f3URqNBkdHR4NqYADq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\n7CUuXEtm8+bN9OnTh+TkZObOnQtA8+bN8x33Wg1bfhrdlOFrTtBn2Z9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SmD59uj5nhYOD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\ngJydGcuCcgAAAABJRU5ErkJggg==\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2571,10 +2722,10 @@ } ], "source": [ - "sensor_var = 5**2\n", - "process_var = 2\n", - "pos = (1000, 500)\n", - "process_model = (1, process_var)\n", + "sensor_var = 5.**2\n", + "process_var = 2.\n", + "pos = gaussian(1000., 500.)\n", + "process_model = gaussian(1., process_var)\n", "N = 100\n", "dog = DogSimulation(0, 1, sensor_var, process_var)\n", "zs = [dog.move_and_sense() for _ in range(N)]\n", @@ -2582,8 +2733,8 @@ "\n", "for z in zs:\n", " prior = predict(pos, process_model) \n", - " pos = update(prior, (z, sensor_var))\n", - " ps.append(pos[0])\n", + " pos = update(prior, gaussian(z, sensor_var))\n", + " ps.append(pos.mean)\n", "\n", "book_plots.plot_measurements(zs, lw=1)\n", "book_plots.plot_filter(ps)\n", @@ -2608,14 +2759,14 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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XLlzgkydPWKBAAQsyYmotUZ7/kSNHSGpERMN7gKb00h+0OUlfsDYfCQkJrF27tsULu2jR\nooyKikq1v4iICHp7e1uca2Njwz179qR5XBs2bCAAVq9eXdW+ePFiAuDnn3+e5r7eFqdOneKsWbO4\ndOnSv/VdLssya9SoYdVlMGvWrBTPS0xMFFYIxb3j5OQklLU1cXR0VLlDFPcHSUZHR4tjrEFR5itW\nrBBtU6dOFX0p+86YS65cuejn5yf+VuJDFCvGJ598woCAAAJgq1at2KNHDwLgsGHDLMagpBtLksTP\nP/+cXbp0EW6p/v37kyRXrlxJAKxXr57q3kwtRwqBcnR0VI3b1dWVERERGhHR8O7QlF76gzYn6QvW\n5mPy5MkEQA8PD06ePJmzZs0SdSU6d+6can8DBgwgYIxHuHTpEiMjIxkUFEQALFWqVJrHpaxus2XL\nxvj4eNHet29fAmCPHj3e7kbTgJiYGNatW1elPDNkyPDG2Iz3iSNHjvDrr79m8eLFmSVLFlarVo2b\nN29O9ZwnT54IpRofH8+WLVtakIB8+fJZ3TBOkiQC6voZCgnMnTs3Dx8+zMmTJ3PKlCm8cOECSdLW\n1pYAGBMTQ9LoqhkzZkyKpMdUevfuTQAiSFRxsZhK1qxZOWrUKGFFOX36tNX7HjNmjIU1o3HjxsJy\nt3PnTgLGuCKFaCUlJYmgVVNxd3cXVpwiRYoQAMeMGaMREQ3vDk3ppT9oc5K+YG0+ChcuTADcsGGD\naLt48aJYOaaW1qmslg8cOCDa4uLiRFplWjMykpOTRV8VK1bk/Pnz2bt3b6F4/vzzz7e80zejXbt2\nwrTfvn17VqxYUbgWUlKG7xt79+7lwIED2bhxY7Zq1YqrV69WWSusQZZlEf+wZMkSkkarjmJ98PDw\nEBauJk2asHjx4gTAQoUKCUXs4eHBESNGcOjQoaq0YXPp3r27mJdly5Zx9OjR9PLysjhOSUM2d8lk\ny5aNANiwYUMCRrfLzJkzmT9/fqvXs+aWMcWtW7f4/fffc9KkSRbf45cvXwqiExgYyB9//FEE/qYk\n9erV44IFCwiAzZo104iIhneHpvTSH7Q5SV+wNh9K0N6tW7dEW1JSkjBjp/Z+e19EhDQqU/PqncCH\niQ95+PAhDQYD9Xo9L168KNq7dOlCAOzUqdN7v6Y57ty5IwJyTaV+/fpvrOmhxHUA4GeffcaSJUuK\nv9u0aUOdTkdJkhgVFSVqcgwZMoQAhIUjNTGN8/j8888JWMZWmErDhg2Fy8Wa9SFfvnwE1CnFu3fv\nZqNGjVigQAFWq1aNK1euTFPtE2u4fv06p06dykaNGlkdZ9GiRTllyhSL+xgwYIDI5vnqq680IqLh\n3aEpvfQHbU7SF6zNh5I5MXToUNGmrBJz586dqnJQXDNlypThpUuX+PDhQ3755ZcE3s41o+Dhw4ec\nPHkyW7Zsyd69e/PEiRNv3UdacOzYMQJgsWLFVO1KRkfFihU/yHVNoSh4Pz8/LliwgNOmTaO7uzsB\n8Mcff0z1XFmW+b///U/lflHqaeTJk4eSJFGSJIaEhAhyp5REz5QpE7du3co+ffoIC4ISb7F06VIR\nS6KUQc+fP79FWjUAq5YRc1FcQYAxRsQ0zuR9YfTo0arrpCQFChQQhMia7Nu3TyMiGt4dmtJLf9Dm\nJH3B2nwoyldZOZYvX178/dNPP6Xa3/sKVv27cefOHQLGTJB79+6J9m+++YYA2Lp16w96/WfPnlGv\n11On0zE4OFi0//bbbwSs1wCxhqioKK5bt47BwcF89OiRULRKYKhSL6R06dIiMLZ9+/Ykje4w03oi\nAJiQkMC7d+8SeF211MbGRgSnFihQgFWqVGGzZs3YpEkTi3k3Ly6miGKFkCTpjTEwbwMlvkWSJGbI\nkMHCqqNk6ihExVrKsyIdOnTQiIiGd4em9NIftDlJX0hpPhYtWiRW44oSGjt2bJpM5e8jffdjQAlU\n9fHx4ahRo9i+fXuhsD40ibp9+zYBY7aGafzLuXPnhCXqryAsLEzUIUnJTXL16lWSRquKQhyUKqNr\n164V8UEKmTEYDCxTpswbLQ6mogSClitXjsHBwYyPjxfl1c0tZXFxcdy+fbsgU2nBgwcPeODAARHX\nY1ql1VS++OKLFMfo6upqYbHRiIiGd4am9NIftDlJX0htPuLi4rht2zYGBwfz8ePHf9uYZFnmwYMH\n+eOPP3LVqlV8/vz533LdiIgI1V4vysp5woQJH/zaSUlJYrWuxMDIsizqgzRv3vyd+r948SJnzpzJ\nKlWq0MbGhnZ2dmzevLkoCPbo0SO2bNnSwqVha2urIqTWxNyKYipZsmThli1bhDvoxo0bvHr1Kjdv\n3szjx48LchMXF0eSXLJkiep6Dg4OHD16dIoE+Pnz5+zYsaPox1QUi4gSIJuaKARMkiRVTRSNiGh4\nZ2hKL/1Bm5P0hfQ2H5GRkaLapSIeHh5Wt6JPCUlJSTx06BC3bNmSanDsjRs3eOrUKRXRSUxM5O+/\n/87+/ftz1KhRvHz5MpOSkhgbG/uXAyfTiunTp4t7LlWqlEgzNRgM77WsvSzL4l4ePnzIU6dOsVSp\nUoJUpEYsmjZtytOnT6foclHEdCO7kydPiiBcaxvVGQwGvnz5krt27RJEqEiRIiqXYEp1VJRYFb1e\nz5IlS6rGrgTlphZUa3p8uXLlePfuXS5cuFAjIhreH9LbS1aDNifpDeltPqpXr07AGEAZFBQkClw5\nOjoyPDz8jefv3r1btZGZjY0Ne/Xqpco6OXfunErJubi48Ntvv7XYUO/hw4fs1KmTiI0oUKAAFy1a\n9MYxJCYm/qXN+WRZZpcuXVQr8mzZslmUOI+Pj+fatWs5YcIE9u7dm0OGDOGSJUuEVSE1hIeHc8yY\nMfziiy9YtGhRlSJ2cHBgSEgIw8PDRaaNqSLfsmWL6Mdapo0pOTENmh09ejT79eun+iwgIEBcO0OG\nDIyPjxcpxoMHDxbXWbRoEQFjMTRzInj58mUCxvopyl43K1asENfx8/OzmnVlSkyU6rMKETHf80Yj\nIhreGentJatBm5P0hvQ0H0osgpOTk9grRJZl1q9fnwA4YsSIVM+/cuWKUIa5cuVipUqVhNIZMGAA\nSaP7RUkrdXZ2VmVNDB8+XPQVGxsr6qmYr5wrVqzIy5cvW1x/y5YtInbC3t6eX3zxBW/fvv1Wz+D4\n8ePcs2cPd+zYwQMHDlik7R46dEi4cMzF29ub586dS7HvNWvWWCUQpvEUtWvXFscrVVoVt0dERIT4\nzFr1VMWqYl44bfTo0dy8eXOqFonffvuNWbJkIWB03yhITk4WRFDZMC8+Pp47d+7kwIEDCYD+/v7s\n2LEjhw0bxsuXL6usMX9VMmXKRDc3N42IaHh3pKeXrAYjtDlJX/iQ8/HkyROuWLGCCxcu5M2bN1M9\n9ty5c6r4DF9fX2F9UMq6vylOQqna2bRpU1EEbO/evcKi8vTpU3777bcEwEqVKvHZs2ckyY0bNwoC\n9PTpU5KvN4PLmzevqCthvvo3DWBds2aNcCuYxlnkzJmTkZGRaX5mpvPx8uVLfvfddyxUqBDd3NxY\nunRpEfegXEMhFooVxbSKqCkePHggjlHcI8q5ptkwAIQbqE6dOgReFydr2bIlHz9+zMePHwvSYXqe\nNdIGgKdOnRJuJ3d3d7q7uzNnzpwcMGCAIBMDBw4U11m7dq0Y96VLl8T9JSQkcOXKlaLOjTXR6XQp\nBucaDAa6uroSgMpVpJBVNzc30bdSHl8jIhreGZrSS3/Q5iR94UPNx9y5c8X+J4ri7Nq1K1++fGlx\nbFhYmCpA0VSRL1iwQJSIV6waKUFRQNu3b1e1+/v7EzBWY1UUzLp161THFC1alAB48OBBkq+3qO/T\np48gKT/88IModQ8YM1mSk5OZnJwsqpgOHjyYz58/5/Xr10Xdjf/9739pfm7KfMiybLVWBwChTGvW\nrMlHjx4JS4JiKdm2bRtlWebRo0f5+++/MyQkhDNmzCAA1qpVi8OGDRNjVaqsmj7zXr16CYJga2vL\nHTt2CEuTaQxJarEXirRv354vXrywCAJWnp/iiuvSpQuHDh0qyMqkSZM4a9Ys8Vy//PJLHjx4UFyz\nYMGCKuuOt7c3q1atquq/VatWzJIlizhHqT5ragEKCQkRBNZc7Ozs3i8RATAfQCSA8yZt7gB2ALj6\n6mfGV+0SgB8AXAMQAiDA5Jz2r46/CqC9+XU0IpK+oCm99AdtTtIX/up8REdHc/r06ezUqRNHjhyp\nMqcre3zgleWhUaNGYtVszb2iKPvAwEBBCJTiWIoC1Ol0qoqn1tCgQQMC4MiRI0XbkydPhBXhxo0b\notbF9OnTxTHx8fFiS/qzZ89y27Ztwn2jKN3hw4dTlmVh9lfuJzAwkL///jsBMHPmzCprxNatWwm8\nXSE3ZT6UnXhdXFy4Zs0anj9/3iLeoXLlykxISBApqYqlY9SoUWK/FEUUC8CoUaM4YcIEAsaKq4r7\nRXl25qLUjTl27BgDAwNFe2BgIA8dOiRIkLno9XpOnDiRSUlJHDdunIrspEZgrMV0FClShFFRUWzc\nuDEB434127ZtE1YMa/0oBehkWeY333xj9ZpTp05lYmKiqErr7+8vvne2trYcPHjweycilQAEmBGR\nyQCGvPp9CIBJr36vA2DrK0JSFsAxviYuN179zPjq94zUiEi6hab00h+0Oflr+PPPPzlq1CiOHj2a\np06dem/9/pX5OHr0qEVKp8FgEPucKDEdprumbt++Xax2ExISVP0pRaX27dvHK1euiJWrad+//vpr\niuNRNl0ztcD4+flxypQpLF26tEoxKaTBxcWFs2bN4o4dO8R4CxcuzJUrV1qtypkhQwZWqVLFqtJT\nlJz5vSnFtcqWLZvmZ6vMh7JK/+abb5iQkJBi4a1WrVoJK41CnhRS5eXlxQYNGggLCmB0s1y4cEFU\nWlUqqJqWbQ8ICGDr1q2FdcgUL168EJvKnTx5MsXy8IsXLxbnKOStdevWKRIQmJDObNmysW3btmzV\nqhV//fVXEYSrfC9CQ0OFu65Zs2biHipUqCBcRp06dWJkZKTKhWQuWbJkUc11p86deSc6hlVa9aBL\nmc/p9tmbC5pJNJKDNEOSJB8AwST9X/19GUBlkhGSJGUFsJdkfkmSfn71+2+mxylCsuurdtVxAPD0\n6VMxqKtXr77V+DRo0JD+8ezZM5w/fx62trYoWrQobGxsPuj1kpKSMHLkSGzbtk3V3qBBAwwbNgx6\nvf6DXt/aeBo2bIjIyEgUK1YM1atXx5kzZ7Bjxw7o9XqsW7cOPXr0wJ07d7By5Urkzp1bnFujRg08\nfvwYmzZtQpYsWUR7UFAQzp07h0mTJqFq1aqIj4/HH3/8gYkTJyI5ORlZsmSBLMsoVqwY2rVrh/z5\n86vGNHv2bCxYsAAA4ODggBcvXqg+9/T0xOzZs+Hj4wNZljF8+HDs2LFDdYyTkxMmTZqEb7/9FtHR\n0Wjbti3OnDmD8+fPWzwDvV6P5ORkGAwG1KpVC8HBwaKtUaNG6NSpEx4+fIhRo0YhLCwMhQoVwvPn\nz+Hg4IDAwEC0aNECDg4OqT7nyZMn4/fff0e3bt2QM2dODBs2DF5eXoiMjDQqQEmCNR2YIUMGxMbG\nws/PDwsWLICDgwMePXqEli1b4vHjxwCAzJkzw9XV1aqOGjp0KJo0aZLq2BQMHDgQ+/btQ40aNfDJ\nJ5/g6NGjuHz5MqKiopA5c2YMHDgQlSpVQvXq1RETE4NixYrhzJkzAABXV1c8ffpU1V/hwoXx7Nkz\n3L59G+PGjUONGjVUn7dr1w6hoaEYN24ccuXKhbZt28LR0RFxcXEwGAzYvn07+vbti5CQEPTv3x8H\nDhzA8ePHxT3b29sjPDzc4j70LpnhkLsEXMo0hY3b6+8l5GSc/eYz8aerq6tkfq4hTU8qdXiRjACA\nV2Qk86v27ABumxx351VbSu0aNGj4l4Mk5s6diyVLliAhIQEA4O7ujkGDBiEwMPCDXXfJkiXYtm0b\nHBwcUK9ePciyjODgYGzcuBF58uRBq1atPti1reHYsWOIjIxEzpw58dNPP8FgMKB58+aQZRm7du3C\nli1b4OnpiTt37uDs2bOCiISFheHx48ewtbWFq6urqs/AwECcO3cO06dPh16vR6ZMmbBnzx4kJycD\nAO7fvw8A2L59O/bt24cffvgBAQEBAICYmBgsX74cADB16lRUqlQJu3fvxoQJE/D06VNUqFABI0eO\nFNfU6XQYM2YMKlWqhD/++AP0RSliAAAgAElEQVTPnj1D4cKFodPpMGjQIMTFxQEAzpw5AxcXF6vP\nQBlXixYt0KdPH4SEhCA8PBw6nQ7r16/H+vXrxbGSJOHixYvi70uXLmHv3r2YM2cO7O3tU3zOZcqU\nwe+//45Vq1ahePHiAIAiRYpg586dAGCVhABAbGwsAKBq1aqC7Oj1ejg6OgoiEhkZicjISACAs7Mz\n3N3dodfr4enpiYcPH+L+/fsqopgSFCVvY2ODadOmqT6LjIzEoEGDEBAQgDx58uD06dMIDQ0Vn/v7\n++PQoUNwdHREQkICkpOTceHCBXTq1Anz5s3DhQsXLIhIvXr1EBoaiokTJ6J9+/bIlSsXbt26BQDw\n8PBA27Ztce/ePbi5uaFgwYL47rvvBGGbNGkSChYsiO7du+PMhctwzFMaDnlKw867MAzOHgCAhHtX\n8PLyHnzTpysKeNrB2daCd1jCmpkkNQHgA7Vr5onZ549f/dwMoIJJ+y4AJQB8DWC4Sfv/AAww7UNz\nzaQvaG6A9Id/6px89913woRbrlw5scusTqfj4cOHP9h1Fd++6X4cq1atImCsa/GueNv5mDdvHgGw\nbdu2qnbl+XTv3l3UfrC1tWX79u05btw4sf9Mx44dLfp8/vx5iiXDs2fPzh07dvDixYvCtF+0aFFR\nU2Lp0qUELOMwlPYGDRq88Z5Gjx6tuqapuV6v14sgSlPx9/cX8SDK2KdPn8569erR1dWV2bNnF8Gj\nDRs25J9//smNGzcK98LUqVOtjkWZj6SkJFauXNnqM+nVqxenTZsmsmAyZszIYcOGccGCBcINU6hQ\nIZLG4m6mz9Z0Y7pKlSrxt99+s8h6sbe3T9P+L6buOSWWxtRVo/Rr6jIzF9N9iXQ6HVu1akXAuPPt\nmjVreOzYMTHXiYmJVjOYTMXPz48nT54U9USUMc5ftpJLj4axxKClzPn1BuYaHMzsPRax1Q/buejw\nTXbsN1z0cfXqVYaEhPDw4cPvP2vGChG5DCDrq9+zArj86vefAbQyPw5AKwA/m7SrjqNGRNId/qlK\n79+Mf+KcJCYmCr+7sluoLMvs1asXAWO66IdAUlKSeDmaBkE+efJEKIx3xdvOx5EjR0Q8gpKWmpCQ\nIJTdhAkT2LRpU6tKImvWrMydOzcdHBzo4ODAOnXq8MiRIySNZGTSpEksUaIECxQoIBTmmjVrxLXj\n4+NFcGJwcLBKwep0Ok6aNEkorTFjxhAA69evn+r9xMbGiiyKlStXCuKnXD9jxoyCdNaqVUtcLyAg\ngLIsC4Xn4OCgKoMfHh5OwJh50b17d/bs2ZO//PILly1bRiDluBHT+YiJiRF7pyji4ODAcePGsV27\ndqLtwoUL4nwldgIw7qtimhGSMWNGxsXF8fTp0yKAV6n50bJlS86fP58NGzYkYMzMUdKbU4KSzaT0\nrRC01IiCqZin+fr6+lo9rmjRogwNDSVpjAdat24d27Vrx0aNGrFly5Zs1Lgx67bswO9+/Y3Hb0Tx\n6PUoLt+8h86lGjNzs5H07rWEuQYHM9fgYPr2nE/36t1p7xvAwp8U4eDBg+nr66vaIM+0DsnfQUSm\nQB2sOvnV73WhDlb9k6+DVW/CGKia8dXv7tSISLrFP1Hp/dvxT5uTZcuWCeUEgOXLlxdb0Z8/f168\nQD8UlJfz6tWrRZticfD393/n/t92PmRZFtkZ7u7ubNmypRij6WpYkiT6+vpaFLcyFxsbG+7evdvi\nOkqQoWkqbnJyssjSUMiDs7Ozap+R7t27i/oXiuTOnZu9e/fmzp07LapzHjt2jDCxIKQUrFqoUCHe\nvXtXKFxJkkRwKKDOBvrzzz8tAm4VUc4pWrToG+dj1qxZFueZi06nU1VUvXLlSorPeceOHeK4Dh06\niM9Mi5g9e/ZMBPiaBpxag0K2zMXanFeqVEkQnLSQlAwZMrBOnTqCEHp7e3P27NksVKwU7X2KMWu1\nIHp3m0fvr5apiIa5ZP1yNj3q9KVL6aa0yawmOtb2p1Ekc+bM9Pf3f+9ZM78BiADwEsbYji8BeMDo\ndrn66qf7q2MlALMAXAdwDkBJk36CYEzrvQago/l1TAf9ItGyqIyGvxf/NKX3X8A/aU6WL19u9SXl\n7OzMy5cvi8/TukX7X4Hi8rC1tRWZBMoLdM6cOe/c/1+Zj4iICIv9YKylR0qSZGH6z5Ejh4XFJCAg\ngHfu3OGsWbM4ZcoUHjt2jEOGDBHE7969e0xMTBRWDoWE1KhRg7Gxsdy2bZuFewGAqlS6IuXLlxcV\nOsnX1Vw9PDxENsjWrVtF/QrAWPCrQ4cOwjKi3BtgzLyYNm2aIDgPHjxQlQ03Pda0fkXv3r0tnmtc\nXBzHjx/P/v37c/v27YIAz58/n4mJiaoxmZKlMmXKUJZlJiUlsXPnzgTA6tWrc8iQISKN17wYnFK/\nAzCmJpvuXJvaGM2hVKZVvpPWNphzc3PjzZs3BSGaO3cu8+fPTycnJ7q4uLBAgQKsWLGiSCHOlNuf\ne05f5arj4Ry06hR9e/zK7N0XMFvXeWqS0XEms9Try8ARv7Fip5HMUKQ6nfKU4lfjf6KLfxXaevlZ\ndQuZz09q8o8vaLby+Jv3RdDwYfFPUnr/FfxT5kSWZbHp2Lhx49iiRQuxUlPIh/JC+/HHHz/YOJKT\nk0WtB1Ml1K9fv/eyCdvbzkdSUhLHjx8vVqp2dnZi9a+Y5Rs1aiQKYpkWAAPAnTt3kiS//PJLQbCs\nrU4DAwOF9UOn04nqn8Br07mptSQkJERlXjdNFVXmSVFKn3/+uThPlmVRu6Ru3brcuXMnf/75Z+EC\nUr4D1sTFxYU5c+Zk48aNuW/fPsbExHD8+PGCcKWm4NavX8/IyEiOGjWKVapUYZkyZVTjV8TV1ZXJ\nyclcvXo1gdepuZ6eniLtGDAW61JIgOkmecp+LDqdjmPHjuWRI0fE3CjkzdvbW8yDKaGzs7PjmTNn\nUv0+/Pjjj1bnz1wUEgmAiYmJPBP+mCuPh3Px4Zv8Zf919v7tFEsMX8fsPReryIbP4GAW7fMLPer0\noWfTEWwwbhVHLwymzslNkLEpU6ZQlmWxV42pODg4sFu3buzevbuIucmRI4eF1cvJyckqmf3HE5Ea\n3+374Ls1akgd/xSl91/CP2VOlJWym5sbX758yYiICObPn9/iRdWwYUOL/UA+BC5dusQZM2bw+++/\n57Vr195bv287H0pcjCkpU2TatGkEjPU44uLirK5GlbLoP/30EwF1nEDDhg3ZtWtXYTlo3bo1Gzdu\nLKwthQoV4qpVq1i2bFkCxpiTSpUqcd68eTx//rxQJL6+vmzfvj0BY2VUJY6jcuXKtLGxoU6n4717\n90gay6gPGzbM6o6zTZo0YWJiorCE5MmTh/PmzbNaJdT8mSjujc6dO6vImFLz4scff7RqPXB0dGTD\nhg1VhcJu3brFnj17CkKRmsLPmDEja9WqxWnTpvHhw4ckyZEjR1o9dvbs2SqilSNHDkHAlLlzdXVl\n48aNBYE0R3JyMrt3727Zv05Px9wlWLbzWGas1o1Zmg6n66et6d9hLCtN3m3hQvEZuJY+HabQo3Zv\nepRvxr7fLWHdVl9SZ/vaqmVvb8/r169buN4AY9Ez82ejuIjs7OwYHh7Oli1bWn0OxYoVs0pC/hVE\nJNfgYG49dy/N/+Aa3j/+KUrvv4T0Pif3799n8+bNVS+1gQMH8uXLl4yNjRUKIWPGjFy3bt1f2mU1\nrZBlmffu3eP9+/c/2DXeZj7CwsIoSRINBgM3btxIWZZ5+vRpocRHjRolLCX169e3ukouXbo0L1y4\nIBS1IqZl0E+fPi1WszExMXz+/Dmjo6MpyzI3bdqU6jb15gp/x44dnDhxIgFj8S+lpPmRI0eYlJRk\nNQtDp9NxyJAhTEpK4o0bNwgYrR8xMTFcs2aNSlGnlBGiKPRatWoxNjZWEAulaJcSM2FNAXbv3p3R\n0dHCSpEnTx7VBnxpFTc3N65bt47Dhw9nuXLlmCdPHubPn58tWrTgqlWrOGLECFGt1FRSim/55ptv\nGBQURC8vL3p5eTEoKEhU1L1w4QJtbO1on6soK/SbRe+vljHX4GDm/HoDc/RfzRz9fjeSjoHrmLXF\naLoG1KHBLQt1Tm7U2TkROutzak4uFIsQ8JrEmj9D02OUzKUmTZoIK0i9evVUgcepyT+eiNSasZ9l\nx+9kUrJmFflYSO9K77+I9DwnL168EO4FSZJUCq9JkybcsGGDCMwcN27cBx3LH3/8oSrTXapUKe7b\nt++9X+dt5mPBggUEjK4XUyixBR4eHpw6dWqKAarWgkAVUQKAFSjK0HSX28TERGbPnl0QA2tKy7z9\ns88+E1aKefPmqSwiK1euFKRywYIFPHz4sHDB5cmTh8nJyYIU5c2blyTFNvFdunQR18iWLZvVe1Pa\nFLeSolTN42vMN7BzcnIiSdarVy/F51WyZMkUPytQoAADAgJS/DwwMNAqAerduzc3b96sUv46nS5V\n4pcpUybuP3WBQ9aEMFe/lcw1OJh5h25iyx+2M6BhJ+ozeIh+dPbOlOzUxM1092NlLqxdx3wMpjsQ\nW/u+mZIRU7G1tWViYiKvXbuW6vfxX0NENofcY67Bwdx7Oe07L2p4v0jPSu+/ivQ8J4q74E1SokQJ\nxsTEfLBx7N69W7x4nZ2dxarb1taWf/7553u91tvMh1KbIzAwUNWuWImsEYMsWbIwW7ZsFiXhFWWq\nZOAoxC4pKYlTp04VCnr48OEiTXj//v1CUVu7nr29Pbdt26aKJ1GkYMGCwlqjpFsrQbPff/+9uJeX\nL18Kl8nJkycZFxcnrBu1a9cWbhpT94yPj4/qnqxdX5FSpUqp3C6mViOFZAFGi43yt2mabErKNbXP\n9Xq91ZiVZs2ace7cuWI8BoNBuN5MlbvOwYV23oVpmzUfMxUN5KQ1hzlm1SEWbz2YGat2os+gDcw/\nfAtrjlxBh7zlaO/kwq5du7JXr15iriRJok6n46xZs8R9WbOY6XQ6QfYUyZ8/f5o22Eur/PzzzyTJ\nUaNGvfGZ/uOJSPzLJBYdtY09lp5M0z+5hveP9Kz00jtCQ0O5cuVK7t271+q24n8V6XlOlNWZk5MT\nv/76a3bo0EH1AvTz8+PEiRM/KAkhKcz2PXv2ZHx8POPi4kTMw5vqYrwt3mY+oqKiRCbKuHHjePPm\nTS5evFgo3jZt2jBPnjz09va2WPUrUqlSJe7du1fswrt582ahgFq2bKnKDFEka9asvHz5Mv/44w8L\npWV+bOXKlXn16lWxeZr5qtc0a0Yxz69atUp1n8q+Lvv37+e9e/dSXF2nxUWUKVMmtm/fnlOmTLHq\nBipfvjznzp1r0a6QH71ez88++0wobVNLhnL/itI0t6woEhQURFmWOWnSJBUBcnBwoL29PYsUKfJ6\nR10HF7pWbEvPJv+jZ9MRLDR0A/MM25xiemyuwcH0ajiIYQ8e8+eff2bOnDkt7kXZhbhx48aMj49P\nlailVZycnDhq1Cirlh9rlo6hQ4eKZ+ju7s6XL1/y6tWrqrRoa8HC/3giQpJjgy8w99DNDIuKTdM/\nuob3i/Ss9NIrnjx5oorGVxTw+1qJp9c5iY2NFS/jzp07i3YlABMAN27c+MHHkZSUJF6kpgWlbt++\nTcBoIXmfMJ0PWZZ54MAB/vrrr9y+fbtVAqpsJ28uHTp0EMH5MTExIkbDmmzYsEHV55gxYyyUR548\nebh48WIRmFqtWjUeOHDAoi9ru78uWLCAOp2OBoOB58+f58yZMzlmzBiLOiLKrrBlypQRMSjKpngZ\nMmTgs2fPxP9CxowZ31gTBYBFQLO7uztz5coliIVyn6apxTlz5nxj1okiSh0Oa8rWWrqyIv7+/iJo\nVzLY0jFfebqUbkr3mj2ZrfNcerUcx2xdfhHkInvXefTrv4LNvwum/xff0j53CTr4laJdjk84ZPQk\nrtm4mfMXL6Vk60BbW1uLmB/AWBRu+/btIrOmVatWwvWlkKy3uQdzady4sco6ZjAY6OnpmeLxBQsW\nFL+buvBMd/w1/z79K4jIg2cvmO+bLRy4KvUUKA0fBulV6aVnKC9eR0dHNmjQQPjqM2bMKEzk74KP\nPSfHjh1jjx49+Pnnn3PMmDGMiIggSRGUqNz7nDlzeOrUKZEGqtPp+Pz5c5JkZGQkR44cyUqVKrF6\n9er86aefGB8f/17Gl5ycLBTezZs3RbsSq5A5c+b3ch1Zlnn8+HGOHTuW8+bNY1hYmMXq0s/Pz2r6\n5saNGxkYGEgvLy8WKVKEP/30kypod+3ataIPJycnDh8+nNOnTxfKOH/+/BZ9Xr9+XWSXDB48WBCG\n6OhooZze5IJQRDnuiy++sHrfW7ZsYevWrVmtWjVBmOzt7VXui5EjR/LevXuUJIl2dna8d+8enzx5\nwsmTJ6eaNaPIm+IPUtsVVhnP4sWLeevWLY4dOzZNfVpT8JLBljaevnQsWImejYcxW5dfRCBprsHB\nzNF7+SsSMpdebaewfJdx9A2olOb+gdfF1nLmzMl58+Zx4cKFIhunZ8+eosiaQrbs7e1TnMu03qO5\npETkihQpwiVLloh5NrWiKVsQREREcMiQIVbJ87+CiJDkyI3nmXvoZt58qFlF/m58bKX3T8OlS5eE\nIlai4RMSEoSrYPLkye98jY85J6a1DBRxc3PjsWPHUkw3VaRYsWIkjYTF1JevSIUKFVQVLt8FCvkp\nV64c9+/fz127dolsjx49erxz/7dv3xaxGaaKDzCuYtu0aSOCcrNkycLYWPW768SJE6riVwULFuS6\ndevE56aF4ObPny/alSJlOp3OqntLqedhunePLMuq523N9G+6olWkWrVqfPr0qap/WZZFwS9TMXV3\nZMqUiRMmTOD69esZGBgo2k6ePClcDKZiGh/ytqLMqTUxrXVCvg4I7tSpExs3bsxy5crR19fXqlXB\nJlNOZihWm5kaDWXOAWsF6fDutYSejYbRo94A2ucqSsnWwUL5S5LEOXPmqPqzFgRsTQ4cOCDGe+bM\nGQJGC44syxa1cN5GUrKuTZ06VVWYrWzZsqogVoWgTJw4URV3EhgYyIiICIv/1wsXLrBDhw7CRVOv\nXr1/DxF58PQF/Uf8wcazDjIx6cOl+mmwxH+ViNy+fZuzZs3i9OnTefbs2TSfp2ymZh6HoGx01qZN\nm3ce28eak+PHj4uXar9+/bh48WJWrVqVwOsMib59+xIwBuplzZpV5TP+448/SFLsxVG6dGlu2LCB\nixYtEopy0qRJ72WsYWFhVmtM+Pr6CgvOX0VycrKIgfDw8GDVqlWFktHr9aL/+Ph4oSh//fVXcf7F\nixfFc7G3txfnSpIkXC6KGwkAf/rpJ8qyzKtXr6rSQsPDLQs+KiShefPmojaL4k4AjMXRdu3alaLC\nUla7JUuW5MyZM/ngwQNV/xs2bCDwer+WVatW8bPPPiNgXDmHhoYyPj6enTp1suhbUfje3t4qE78i\nBQsWTNUtkBapXr266MPW1pbnz5/nd999x65du7JQoUIEwGXLlon7iYqJ5+Hjp5ghez46FqxEr5bj\nmbXjTOYctNGYOjtgLTNW60rHAhVo6+VH6K3XyjCXevXqpZqVo8inn37Kfv36ib+VuiWkMQNNaU9K\nSmJSUhKbNWumOt/W1lbclzIvSnqzqZh+bxTSlDVrVvE9TW0BYS52dnbcvHkzo6KiVN+N/fv3W+3n\nX0NESHLjmbvMNTiYS4+GWfzzafhw+C8SkbFjx1qsklq1asWEhIQ3nrtv3z4CxlWn6fFdu3YlAPbv\n3/+dx/ex5uSrr74iYCxwpSAxMVGY4w8cOMAXL15YlB83GAycNm0aSeM+HEo6oykh2LhxI4GU9w/5\nK7h79y4HDBjAwoUL09/fn8OGDXsvrrGdO3cSMKacRkdH8/jx4+zTp4+436VLl4pjlRiKAQMGUJZl\nHjlyRNSzKFu2LB8/fszExESxO22hQoX4zTffsGDBgipTeebMmVWr7kyZMlktAnfx4kWhiLJmzapK\nXwaMVqfo6GgOHz7cQmGkpHQWLVok+lcUoSlhjI2NFSmjFy9eFMGzjo6OnDJlCmvWrKnq09R9pdyT\ncq/mVoOU6lyYx5q4ubmlXMFV0tHgnp0u5ZrTpVxzdp+ymF//foaVJu+m75Bg5hq06XVcR4+FzNxs\nFF0/bU29S2Y6ODlbtd6ZStWqVS1cci4uLiKjRLk3BwcHi+DgFi1a8Pnz5+LvoUOHUpZlyrIsKswG\nBASIZ/3w4UPxLBwcHLhmzRphdXpbadGiheh38+bNVl09Tk5OFjE7yvdLp9OxUaNGvHPnDpOSkoQF\nsH79+hw2bNi/k4jIsszaM/az5nSt2urfif8aEVGKLUmSxCZNmrBjx44iQn3o0KFvPD85OVm8ECtU\nqMC5c+eq6iWEhIS88xjTMifPnz/nvHnz2KlTJw4cOJCnTp166+tcvHiRQUFBzJcvHwMCAoTZ39RV\nQL7OnFi7dq1oO3XqFKdPn845c+aoCEdERAQBo7nZNJDz3LlzBIxm+vSMiIgIsRtr9+7dSRrnwzSb\n4uuvvyZJVcnsKVOmsGPHjhYv+oCAAD579ozx8fEpVqY0VdqK4h4zZkyKY9y7d6+qtoSzszMHDx5s\n0b+Xl5fVuAAHBwf269dPjF2n04nvraL0Nm3apLqmYvlZuHChcLVky5aN06ZNY3R0NKtUqWKhqBVL\nCmC0DKUUo/Cm52IuOntn2ucuQY+6/Zmj/xrm6L/aIkulwDebGbTgT45cH0L3KkF0KdmAP64/QFtH\n5xSvmdZgWMBIApVFiSLh4eEWFh9HR0cePHhQ1ZY3b17VnjymmzWStLCK/FXZu3evql9TQmNK9KzF\nnOTKlUs8o3z58gly7uPjw5cvX1KWZVEG/19FREhy+bFbzDU4mEevR1l8puHD4L9GRJQX5tSpU0Xb\n3r17CRiDTZWUydRw4sQJqz736dOnv5cxvmlObt68abE/CaCuvPkmHDlyJEVz7aeffioCS0NDQ8VL\nS4mJSQ2yLIuxff/995RlmYmJiWzbti0BY0lyU1y4cIGtW7emp6cns2XLxh49eojS4n8VCQkJXL9+\nPadPn84NGzakqbz8kydP2LJlS9WK1s3Njffv3+fx48d56NAh8Rz8/Pw4ffp0sQGZvb09p0yZIl7w\n5tY2T09PYRF5k/IzGAzs27fvG9PBlYqtBw8eZExMDO/cuaMy2ZuvzM1X/V999RXHjx8vSLiTkxMH\nDx4s6nHUqlVLfAf27NkjlLe1rJgSJUqoLEb+/v48deoUnz17lmLxLavZNZKOOkc32mTKRQe/0nQO\nqEfPKu2ZMbALMzcbxew9FjFHnxWCbOT8egMztxjDjIGd6Vy0Jp28clGydaDB1Yu16jYQ86rMUUJC\nApcvX55qSrHy3FJyISnBxL1796Ysy6xWrZr4zNRVaLovjdJer149UacFMFq9fvnlF4u5VVxtyjNS\ngplNLRpKvFJqgavly5cXwePKdgzK8QcPHuSYMWMsvn86nU7sT3T37l1BmJTaKVWrVlWN9dtvv/33\nEZHnCS9ZcuwONp51ULOK/E34rxERb29vAuDVq1dV7coLJq2lwqOiojhlyhS2bduWAwYM4Llz597b\nGN80JwqZKly4MGfMmMFevXqJl2tK+12YQpZlYWpu2rQpT5w4wQ0bNqhepNmyZWP16tXFy898Z1IF\n9+/f59q1a7l161axM6tSXRQwxiwoNSbs7Ox4+vRpce7p06etBtnlyJHjL5ORM2fOWARr+vj4pDo/\nsiyLWBi9Xq/yybu4uHDIkCEqhWOuUNesWSNiSkwlJSUhSZLVgNIFCxZYve/79+/z559/5vTp01O0\nfA0aNIiAcSVr7v6wt7cX7pTUgj/Nx50lSxaWKVNG/K2QCsUd5OPjk2IRLb1er7La5MmTh3Xq1BF9\nGDy86ZyvDO1yfkLnkg3oXusrevdebrUGR45+vzPrl7OZqeEQetTsSeeSDWmfqyh1jq6q75kSvwW8\nzpySZVm4ysaOHcslS5akeN+maanbt29P8bh8+fIJF2BMTEyagnE//fRTxsTEMCEhgYcOHeLBgwfF\n/4s5nj9/riJwI0aMsCjYptPpVEGoKYmfnx9fvHghCu0pi4Rq1arx4cOHYudqRapVq6Yay6xZswgY\nqybr9XoaDAZRpiAmJoZly5b99xERklzxp9EqsvHMXaufa3i/+K8RkQoVKhAwbmal4M8//yRgNHGn\nJU7kQyO1Obl+/ToBYw0H063aR4wYQcAY62KKxMREXrp0iXfvvv5/UtJwXV1dVVHxykrMtJiSJEls\n0aKFRQZHcnIyBwwYoDJxe3h4cMWKFSTJ2bNnq4pcFShQgLt27VL1obxIGzZsyMuXL/PUqVMiZTMt\n26ub48WLF4JM5c+fnz169BBBfI6Ojhw0aBCvX79ucZ5iOnd2dlaREGvKde7cuZwxYwa7d+/O8ePH\n886dO5RlWbVa1ev1qVa5XL58OUlaBHyePGlZ2PH777+3cCM0btzYIptBqVGxfft23rt3j2fOnFFl\nsGzdulUQpzcpL3Oxs7MTFi0vLy/evn07bdvE6wy0y/EJi3/ek1tD7rJ422H0bPwNs3efb0k2+q5i\npgaDmKF4XWPgaNZ8RqKhtyEk9bO05lapWLEiDx8+rCImCkwJiqkFQFGs5n1JkmS1VodOp+Po0aP5\n6NEj1bM/e/ZsilYWT09PLl++/K03fVTmy5ooxDA8PNyiAJxer2fr1q1VcVz9+/cXhe5y584trLkG\ng8Hi/v39/VVGACXWqGvXrmI3aEmSWKpUKfEd+FcSkaRkY6xI+Qm7+CLx/VWr1GAd/zUioqwMDAYD\ng4KC2K9fP/EP1bdv3489PJKpz8mhQ4cIGM3hplBeXJUrVyZpXAnOmDFDRQYqVarE8+fPCzNt9uzZ\nVS+dHTt2EDBmVBw9epQbN25kWFiY1XEodRt0Oh0DAwPFKlmn04nU0vj4eJ48eZIXLlywsHDev39f\nHL9w4ULxoj527BgB41WjVNUAACAASURBVMr+bbFs2TICxtLi8fHxXL16tYXSsrGx4Zo1a1TnKeXS\nFfLg4uIiLGTmUqhQIV68eFF1vkJkFWnbti3Dw8NTTKmsXbs2Dxw4YFGl0sbGRhUIq/jllTkxXbGX\nL19eRZqVeAzFpeDg4KCq+XHjxo00raBNxcnJSWRPKBlV+fLlSzHV1NHNk44FP6NXm0kqF4qKcHT/\nlXk6TGKGojWZ69OGtM9dkjYZs7Jg4U+EIn3TuKxV9yxevLiKZH377beqOVqyZInKPVWoUCHu3r2b\n4eHhqudi7q5s2rSp+C44ODgwISGB58+fZ+/evRkYGMimTZtaBOuafpcAsF27dn9pgVO3bl0CRgth\nr169uHnzZqsZM6ZiWopfIVM6nY61a9cWBKRSpUoWFrypU6eK707nzp157Ngxzpo1SyxKdu/ezfj4\neHbv3l1FukuVKvXhiQiA/ADOmMgzAH0BjARw16S9jsk5QwFcA3AZQE3zPt9EREjy0LWHzDU4mDN3\nXXnrydPwdvivERFZljlgwACLf+BatWoJf+rHRkpzIssyIyIixKZkStqxLMts1aoVAaMvl1RXO/X2\n9hYvFA8PD1Xq63fffcekpCRGRUUJZTZo0KBUx5eYmCgKNCmVVGVZFlk35vUdzLFr1y4LRZ87d25e\nunSJISEhYszm2LFjB5s2bcpSpUqxdevWqloapNFfDRiDjqOjo8U9K1kBSpEtJycn1ar2l19+EePo\n2LEjX7x4wbt376qUYs6cOQURyJEjh8oiYV5TwsHBQRULYNpPSpYSpbaDwWAQsThKGrSikMylZs2a\nIpbEtNKveXaEJEns37+/1fog5seZtx06dIik0dqkKLI5c+awTp06NLh60b1sU7rX+oq5vxgngkaz\ndZ5Lv2ZD6FbxCzrm/5Q2mXIxi/+nlGzs6eDgIFbhO3fuFO4bvV5PvV7PwYMHvxVZsia+vr4W9VFI\no8tDIaamlrFt27al+DwUcqM8m969e6focsuePbtq3k2Pq1ChwluHG5w5c0aQCUdHR4sKqTqdjtWq\nVVNl9Fy7dk31v2Au1qxJEyZMIGkM5LdmIVLK3yt4+PAh9+3bJwj532oRAaAHcB9ALhiJyEArxxQC\ncBaAHQBfANcB6E2PSQsRIcmui0+wwPCtvPfk/RRA0mAd/zUiouDixYscO3YsR4wYwX370lem1t69\ne7l161YxpsjISHbt2lWsBBWFYG9vz8aNGwsFa2try9DQUL548UJsoLZgwQLKsswnT56I2JIhQ4ao\nlK+zs7NQXp6enrxz5w5JI7nYsGEDGzVqxHLlyrFbt268cOECw8LCCBjN9KbP7ezZswRe78JqDQ8f\nPhSWAuV+lJgGPz8/1qhRQ7z8TKGkOpqLabDf/PnzCRjLkc+ePZuAMbhOiYtYsmSJiAVRNvUijfE+\nSn/t2rXjypUrrQbyenl5CcW5ZMkScb6SiWWtlHpa5fTp02zevDmB16t5xU2kPKdRo0bx3r17qr0/\nNmzYwCdPnrxxpZxm0RlocM9Oe98AOub/lNV7jOWg389yzKYLbD5mMTM1GMSsHX6gd49Fr4uA9VnB\nHL2WMFO9gcyYt4RwpaSWhWKNkGXPnl3EcFkTUwuTjY0Nvb29LVxirVu3tkpCFChFu3LkyMECBQrQ\nw8NDKPuU6oLkzJmTjRs3thi3eWCyMr6UsoB8fHx469atNLwBXuPgwYNWq9S6u7tz9+7dJMnVq1eL\n9iJFivCLL75QHevk5MSJEyeKcQUFBbFhw4bs1q0bjx07prreiRMn2LZtW37yySesVq0aly1bpqoI\nbA1vIiIGvF8EArhO8pYkSSkd0xDACpIJAG5KknQNQGkAR6wdfOLEiRQv1iBnMnaHJuPrpYfRt4zr\nu41cwxuR2lz8W1GzZk3x+8mTJwEAz549w9KlS7F7924kJiaiRIkSaN++PXx8fD74eO7evYsZM2Zg\n//79kGUZ2bJlQ5s2bbB69WrcvHlTHBcdHQ0AiI+Px7p16wAAbm5u+PbbbxEbG4s1a9bg0aNHyJEj\nBwoXLizurVGjRtizZw+2bt2KIUOGIGvWrIiIiEBMTAwAIHPmzJgxYwYiIiIQERGBqVOnYuXKleK6\nR44cwfz58zF69Gjo9Xo8fPgQwcHBsLGxwfbt23H06FEAgIODg+r7lJSUhD179uDEiRO4ceMGYmJi\nULJkSQQFBeGrr77Cs2fPAADXr1/H9evX4eLignr16ok+bt++jW+++QaSJKFTp04oXbo09uzZg+XL\nl6NXr17w8fGBm5sbcufODRcXFxw7dgy3bt0CAISEhCAqKgoZM2aEj48PsmbNCgA4ffq0aowZMmRA\nbGwsFi9ejMWLF6vmRafTwdPTEw8ePICTkxMAYMeOHShQoAAA43fGYDDg/v37f2neg4KCkJSUJL5j\nZ86cwYkTJ+Dm5gYAiI2NRaFChVCnTh0cPHgQ0dHR0Ov1SE5Oxq+//oqwsDC8ePEixf7t7Ozg7++P\nxMREhIaGIikpSZyvz+ABuxyFYZetAOyy5YetV25Iehtx7hUAYaduQwaQJLvDs2BpxEbeRVzYKSTH\nPUNc6H7ont5FfHy8xXWTkpJSHJMsy2IMCu7evQvA+F1+8uSJ+Dx//vy4fPmyOE6n0+GTTz5B69at\nUbJkSYSGhsLW1haFChWCwWDAlStXUrxumzZtsH79ety+fdvisxMnTkCn00GWZeTLlw/lypXDokWL\ncOfOHTFOWZYBGP9XFi5ciLp164rzlf+jlO47LCwMlSpVwooVK2AwGCDLMm7duoWYmBg8fPgQkiQh\nICBAzDsAGAwGPH36FACQLVs2fPbZZzhz5gxCQ0NRp04dzJo1C0WKFEG1atWwc+dOhISEICQkRHXd\nGjVqIDAwEKdPn8bKlSuRkJCA4cOHq+7bFH369FH9ferUqRSfJwDkzZs31c/fNxFpCeA3k797SZLU\nDsAJAANIPgaQHcBRk2PuvGp7a2R20qNhfif8HvocNXI7oJCn7V8dt4b/IK5du4bVq1cjLCwMXl5e\naNSoEYoXL57qOTExMejUqZNK6QcHB2PPnj2YM2eOUDwfAk+ePEGXLl0QGRkJnU4HGxsb3Lt3D1Om\nTAFgfPH98MMPyJ49O5YuXYqff/4Zrq6u6NOnD9zc3FCmTBnY2hr/R+zt7QEYFWRiYiLs7OwAAFFR\nUQCML7eePXvi0aNHcHFxQdasWXHlyhVERkZi5cqVGD58uHhp2draolu3bihYsCDWr1+Pbdu2YerU\nqahSpQp27tyJoKAgPH78WKVQwsLCcPPmTfj6+iImJga9evXCxYsXVfcbGxuLgIAAzJo1CzNmzMCl\nS5cAAJIkQa/XY+7cuWjXrh3y5s2LnTt3giRq166NLl26AACKFSuG69ev49ixY9i/fz8aNGiA6Oho\ndOjQAb/++qsgBVFRUXB2dsaUKVOQkJCAXbt2AQDy5cunGk+dOnWwatUquLi44Pnz56r7kWUZDx48\nAADcuHEDAODh4QEAuHXrFnr16pWq0tXr9dDpdHj58iVGjhyJMWPGqPrfv38/ChQoIMamEJImTZr8\nn73rDovi6t5nd+kL0nsVEI2K2AWxEI0i9m7sHRV7iQ3UqLF3RTEYG8EuUQm22EswYjcaPw12UYMN\nEJS2+/7+WO91ZneWYjT5fvlynuc+4uzuzJ07d+557ynvoeTkZCIievr0Ka1YsYJ2795NALiSvnfv\nHt24cYOfq2nTpnT69Gl68+YNP5aXl8fBKBGR3MScjD0DyKRsdTL3/4JkcgWpC3Ip/8nvlHVuDxU8\nf0CFGU9JnZdDUBdSvYDy5OjoQEoLKwpr2pg8PAIpPd2bNmzYQAl/3Na5X5lMJuqjPmGfdezYkRIS\nEphVnTIzM8nY2Jjy8vKIiCgoKIhu3rzJFb1araaLFy/SxYsXKTAwkCIjI8nJyUnvdYTy8uVLysnJ\nIYVCQW5ubmRtbU1lypShkydPEhFRw4YN6eLFi3Tr1i2SyWTk6upKaWlplJaWJupTs2bNyN7enuzt\n7Sk9PV10DXYfREQeHh6Ul5fH58/9+/fp559/JoVCQYsXL9YBREZGRtSnTx8aMGAAyWQySklJoQcP\nHpCLiwtt27aNCgoKaMaMGXTjxg3Kzc2l/v37k7+/P02fPp1sbW1FGwcmiYmJVLVqVXJ0dCQizUZm\n69atfKNVqVKlEo3dB4uUmeRDGhEZEdFzInJ8939H0rhq5EQ0i4jWvTu+koh6CH63log6CM9VUtcM\nALzJK0TQ7MNotvQkClX/Pabzf5L8E10zO3fulDQLF0cvzjJPKlSogGPHjuHKlSvcT9+wYcNP2ucZ\nM2aASEOAJZXaSfSeulqtVvNS8FIVf9VqNQ9Ga9OmDU6dOoXvv/+em/SZCdnKyooTV6WkpHA/fVpa\nGoYMGQIijRuHiUql4vEW27dvl2S6ZJVPK1asCJVKxTND3NzcMG/ePFEaLCuaJxV8SO9M7Vu3buUc\nHJMnTxbdJ4vinz59One5sFaxYkXunrKyskLz5s15XErlypV1eDr++OMPvcydtra2ouA+xrXw+PFj\nnk3SsmVLXL58WRT7wtwMzZs35/Px6tWrRWauWFpaimjAGWlUUU0YhMkq8fJ+KAygrNwITr0Ww330\nDvh8lQCPcbs0gaNjEmDTZAgMHbx1MlP0NZlMhrlz5/J5dvjwYfTu3RstW7bUm3FkbW3N70MqG6U0\n1O/CjC7WlEold1O8efOmyMDQyMhIEGkKzbHnztwu7P5atGghcn9JNV9fX6jVaowZM0bvdxwcHBAT\nE6OzFvXt27fYoFzmOmTpswMGDADwPtOMnZO5pry9vfH69WvRXFAoFPx9UygUPM1YO8aldevWf6oG\n1F8WI0Ial8tPej7zIqJreB+oOknw2UEiChJ+vzRABACSrjyG54QkxJ7QTbv7V/68/NOAyOvXr3nM\nQZ8+fbB//35MnDiRs1bevHlT72+ZL5YR+gBAZmYmVxzCdFmh5Obm4tatW3o/L4mwQFHGF+Dl5YXL\nly+LfP+urq4oKCiASqXiaan6nt0vv/yiV8FrK5a4uDj8+OOPHADFxMRwX/rq1atF52UZAjt37uSL\nuoeHB8LDw3Hw4EFkZ2fzxfDw4cO8/yywLT09nSsjc3NzHQ6Gvn37iiinLSwsePqls7Mzvv76a1Su\nXBlKpZL76xmAYGXt2W+dnJx0wEVwcLBkDRdAEysydepUDqaISp7uOnfuXFEgtHCxZzE9X3zxBS8F\nQESiwEamXE6fPq3TL8b0qt28vLxEz9isXCCUlRuhTGAnOHSZCbs2E+D6LpbDpf8q2DSNQIt5SajU\nYyqMnP1AcgM4OTlJUnxr1/EZMmQI+vTpw//PFL9QVCoVz0AyNTXFsGHD+Jz68ssvdfofHBwsyuwh\nPUCDNWHNnq5du4r6bWtry0GYQqFA27Zt8Z///EenjwwQRUZGoqCggMcPaSvnsLAwREZG8jlmYGCA\ntm3bimKHrKysSlztWDinGGATvtva84zFWTH+F29vb54xZ2lpye91zpw5vK4PuzdfX18OkNl7pv3O\nd+zYEYMHD+ZjKizrUFr5K4HIViLqK/i/s+Dv0aSJCyEiqkTiYNU79IHBqkzUajUGbDyHcpP34Vpa\nyX7zr5Rc/mlAhHFhBAYGigIpe/fuDSJN6XJ9whY2YQBXfn4+tyBoF1MrLCzEtGnT+O5TLpejXbt2\nIs4OKSksLMSZM2fw008/8cJSLEiTkS/NmjVLdG22gzp06BBfcNzd3Ytkgv39998RERGBqlWrcoZE\nBwcHDiaYVUUqC6B58+Yg0mSazJs3DzVq1OD1UGQyGR4+fMhBU0xMjOi6HTt2BBHx3RyrLspkw4YN\nkot127ZtAbwvvscW+fj4eM6T8aFNLpdj4MCBJQpKvnDhAv+d1A5eXxs3bhzS09MlCa6MjIywe/du\nEfg4efIkTp8+jejoaK6UpAj11Gq1iLnU3NIaX46YimPXHqDh5DjYt4+CY9c5ojRZtyHr4To0Dvbt\np8DE6z2JGbM8lLaUfGhoKFq2bMn/b2pqiiVLluiM57Nnz7hlLTU1Fbt27ZK8lkwmQ1RUlCgN2N7e\nHvn5+YiNjS2yL4GBgTh37hy3DjDLl3YzNzfH3bt3Rf1jae4ODg6czMvBwaFYmnnGj/Po0SMdAMnu\nx83NTYfB1sjISIeXRzute/78+ToWPSJCbm4uCgoKOAkZy6xiz9DCwgLPnz/H3LlzQUTc+tGtWzfk\n5uZi5MiRomuzOcayZID3qefm5uZ6CdaKk78EiBCRGRG9ICJLwbHviehXIrpKRIkkBiaRpMmWuUlE\nYdrnKy0QAYAX2Xmo+c0hfL7wGDJySkcM898oWVlZiI6ORrdu3TBo0CAcP378b8va+KcBkZiYGBAR\nevbsKTrOeC+K4gph7oimTZvi+fPnuHnzJq8jU7FiRZ1nxCrREmlAAduNly9fXm8q8NGjR3nxKCLN\nTmjcuHGIjo4G0XvA0a9fPx79LrUrl8lk2L59e4nHhaX3Ll26lGd5SDULCwu+CxRykGi3jRs38gWw\nadOmPLL+xYsX3AJw5swZvmizqrMAMGXKFBAR38kxRTVjxgwA4Cm8bOFctWqVTkVZQ0NDBAcHS/ZN\nOyMjJCSEX0O7jo6UXLp0SXJnrr37lVJewiJlpqamop2wsLGdtaOjI8aMGQNTa0cYWLvg5cuXOHLm\nEiJjtuOrtQex8ugtLDt8C+ErEmHbfBTKD1qBcpH7OODwnZgIl4GxcBkQgzKBnWBg5QS5mRW/X2EW\nCgNVAQEBRRKuFTWm2qBi1qxZOuPXrVs3Pn/Gjh2LBg0aiH6jLzOGPX/gfW0bAwMD/h6wd8PU1BRT\np06FTCaDgYGBDpOssAUFBYn6plKpRDVwhK1Hjx4YPny4qIgd+0yYOfLixQs+FuXKlSvWjSNsXbp0\n0QEr+jKeDh48CEBTp0nbclSmTBnOosysHyw929bWlldVfvHiBef4YQDm2rVrojFh2V76OIOKk38k\noZk++eX2c/hO3ovua375fx0vcufOHVHJZtYiIiL+FjDyTwMily5d4gqVmWbT09P57p/tbKTkzp07\nehkjmU+ZyZMnT3gu//79+wFodkvM8hAbG6tz/v/85z980fHw8EBQUBBf2PX5yI2MjLgPW6FQQKlU\nonHjxiWichcKs1LExsbyGilSbfbs2byirHYpd0NDQ74rs7CwwO3bt7nZt1q1ahg0aBD/vE6dOlCr\n1ZgzZw7ve/PmzVG3bl1+vp9++kkEJry8vHD16lVuHWKK/uLFi/j6669BpHHdXL58GS9fvoRKpRL1\nz9raWtL3vnjxYp6uXKVKlSLH6dq1a3pdWtpKmP1fCihaWlpyWvkdO3bA29tbMm5JYWEL68/787gN\n7zHSRGCeE5LgFrEBLv1XocPCH7Hr4kOsP3IVfv4aDok+ffoU60aSun7NmjVLDUqEzcTERId199Wr\nVzogUS6XIyQkBEQaN01SUhI6deokArtXrlzBy5cvkZqaysFsx44dUVBQoBd0Ct1FSqUSCQkJePr0\nKd8kyGQynXL2WVlZiIiI4PPLyMgIU6ZM4aR6DDh99913vH/Hjh1DZmYm1qxZw1lLS8tS26RJE+Tl\n5UnyGElZjczMzDiV/Nu3b7Fhwwa+frRp0wY7d+7k3D1yuRy3bt3i42RjY4Mvv/ySW1NsbW15+v6C\nBQv4WFy8eJFf60PjRP6ngAjwnv594UFd39//F2Hms4CAAMTGxmLy5Ml8p7Jr166/vD//NCACgLsV\nDAwMULNmTb67rVChQrEMh3v27BEpM+HiLSyX/sMPP4CI0LhxY9HvGX9F9+7ddc4dEREBIkKnTp24\nS0VIpuTq6or69etLKobSWkCEkpubyxdPoc9bSAPNFt+WLVvil19+KdHCam5uLmkVqFq1Kh4+fAhA\nswMdOXKkaEyVSiUPxjtx4kSRfBPNmzcH8N6KIrRoJSUlib5bvnx5LFu2TOccixYtQnZ2Nr9vJk+e\nPMHGjRuxYcMGzp3SpUsXvtDri83QbkIqdQsLC/Tt2xe3bmnIGJ8/f45y5crp/MbQ1h1laneA27B4\neIxPhF3r8fDuPBm2YSNg/3lvNO4+FJ7lKkJmaKwJJJWLx8jJyYmPqZubG6ZMmYJp06ZBLpdDJpOh\nc+fOqFKlCry8vPQWN9RuwmckpRj1PafRo0frzDmVSoVDhw7h66+/xqJFi7Bv3z7+XhJpSMdGjBjB\nAbhcLketWrV0gCQrTpmVlSVy4zBrhHD+jRkzhl9fWBmXUeprC6sILZfLMXXqVBw/fpy/oyYmJnj5\n8iWnODc3N5d00zGLl7CuTmhoqI7VJT4+nm80X758Kaq+W1TT5tPZu3evJABavnw5CgsLce3aNR3Q\n5uXlhXPnzmHXrl38frt3744RI0bwjZf2Rqs08j8HRNRqNcZuvwzPCUlYf7r4SqD/bfLgwQMQadCn\nEKWzAK82bdr85X36JwKRrKws9OjRQ7SoNW3alCubooSVcm/Tpg0ePnwoCsDz9vbmJlpWu0G7NgPL\nvAkPD9c5d506dUCk2V0xuXXrFu/jpk2bMHbsWFSpUoUrD4VCgZCQEG6mLU6ePXuGOXPmoFWrVujR\nowcSExO5haGoxgrV1ahRQ7TLZMq1qN8KF8bOnTtLEiA9evQImzdvxnfffYdZs2Zh9OjRWLNmDV6/\nfo1Tp04hKChIR+n17NkTWVlZAN5T21tYWODQoUNQqVQlLpd+/fp17Nu3jy/KarUa06dP16k7MmnS\nJL4wHzp0CGPGjCkRSZlQaYeGhnJ2SwCYMGEiDB3KomLdL9B3ylJYBneFa8/57y0dA1bAv957inAL\nCws8ePAAarWaW7GINBYz5hpiYFIul+u4Jdicl8lkqF27No+fECpRYbAja0ZGRpKF+7SbXC7XoTSX\nyWSYNm2aXuKr48ePF2k9KGp+2djYcKtAcnKyDlCRyWTcSlCxYkXcunULKSkponsZPHgwtm3bhlev\nXun0jVn/pFrVqlVx8OBBSQp39szZJkcIPJydnXlMD+uH0AoBaILqmzVrJnldYYE7pVKpM66pqan4\n6quv0LJlS05KNnv2bO4GNTMzQ4cOHRATE4ODBw+K4simTZumAzJDQ0ORnZ1dovVFSv7ngAgAFBSq\n0G99CspF7sO95x8+eH+HsCC4zz77THT86NGjINIEYf3V8k8EIkyePn2K06dP6wSsFSVs9yosQFZY\nWMgDUhmYyc3N5bu58PBwnDt3DqtXr+YAQsp1wnaEK1as4MeYZYUtOtqLkpubW4lddr/99ptkIB1T\nZN9//70oVVEul3NLCNtZamdLlKRZWVlh8+bNkMlkMDQ0FAX1FhQUYNGiRfjss89gamqqswg6OTnx\nirx5eXm4ffs2kpOT8fDhQ6SnpyM1NRURERHw9vYWuUxK6k7w9/dHWFgYBx1t27bFd999x5VJWFiY\nKIaEKcWirDTFNWsnNxxMvoRj//kDZfsuFrlXPMYnwnf4BljX7QKFuS0yMjI4eCXSFLQ7efKkjhWl\nVq1aePr0KQ9mDgsL47EJZcqUQb169TgzqFwuF1kKqlevzmnAWbyAVGNAx9bWVm9sS7du3fTGZERG\nRurMSbVaza/Zo0cP3LhxAwkJCdz10r9/fx7XZWJiAjc3N7Rp04bHdLHjQjdhy5YtER8fj3379uHe\nvXs6FWT1NWNjY/j7+6NatWro1q0bzpw5A0BT06d+/fr8e5aWlvz+jYyMeHaYs7MzJkyYwIskCpsQ\nTBkZGXEAy+j5hQGiQhHWualQoQJmzpzJj7E5WVwQ6bBhwyT7Ua9ePZ00dUADZBYsWIAZM2bg5MmT\nfzok4H8SiADAk4y3qDztAOrNO4LU9NfF/+C/RDIzMzmCPnXqFACNCZMFdw0ePPgv79P/dyCSlpaG\nYcOGwd3dHS4uLujdu3eRKbrFCdvBMH4NQGNeZwu7sEZJQkKCZExC7969JV/uLVu2gEgDOGbNmoX4\n+HgEBASIftuyZUssW7ZMtPAmJSWVqO/MJBsUFITNmzdj1qxZvH99+/bl3xNmYNSpU0ev0mnbtq1e\nThPh4s76yCobu7i4oGrVqpgxY4ZOdVBhY2NatmxZvmvLzs7G8OHDi3QnMBBS0tRJ7cZ20EOHDhWZ\n1LXPGRYWhsWLF+vNyuC/cfKFVcM+CJmyBX4j1sNj7K734GPEJljW/RKLd57AvO+2wdBEKbr3rVu3\niuKSnJ2dRcGLwvm1cuVKTJw4sci+MCA6fPhwHDt2DNeuXYNareZWsdjYWCxZskRkLdHX3Nzc+FhL\nzXOZTCYCrmZmZjpWh9TUVBBp4ndyc3P58R07dnBlyYIto6OjoVarsW/fPnTq1EkH8JiammLUqFFI\nTk4WrVmFhYW8arNUMzAwkLxXmUyGDRs2AAD//YQJE1BQUIDc3Fyeacey6aKiovg1he447eBbBiAq\nVKjA57FUZWVAYymUshaxOVC5cmWoVCpkZmZKgop79+7xtPXExESo1WpcvnyZA6ERI0agRYsWqFq1\nKqpXr4527dph9erVf8oCoi3/s0AE0ASvVpyyH51WJ/+/qtLLCHAY2QxbCI2NjXH9+vW/vD9/JxDJ\nzc3FqVOncOrUKdEiVVJJS0vTiSYn0uxotCPDSyosuNLDwwPbtm3D4cOHudnVw8MDAwcORHx8PO/v\nuXPn0L17d1SqVAmNGjVCXFycXhO1SqVCr1699CpkuVyOwYMH850tW9C6du2qt783btxAeHg4XyxN\nTExEfCZsN1q1alV+LC8vj+9IWStTpgz69evHA9qINMF1d+7c0bEOsIwGovdBtgsXLtRL0qRUKvln\nDIize2P3/uOPPyIxMbHEvvPSNLlcjg4dOiA2NlYUKF6aFFZR3JCNGyq2jYBTW03dFWbpKDtsPXp8\nexo2jQfCvEoT7Ey5iwHhg/gYFHX+Fi1a8IBqImnLlLOzs6SrhTWhQuvUqZNonrBgXUdHR2zbtg1n\nz57lrh87OzuEPW52UQAAIABJREFUhobC19e3xJYmAwMDnonl5OTEFfPRo0d5YGV4eDh38zk7O4ve\nCxYbVbt2bZ6ZNnXqVEkCNwMDA0RHR/MaMlJrFntvi2rsedeqVYuDcaVSyStBKxQKUcDm3bt3Rc+u\nevXqPKB18+bN/Lyurq46Ac7CcezSpUuRa862bdtE80xIivfll1/yAHArKyuMGzdO1EeWCq/t1mcx\nVfpahQoVdOgIPlT+p4EIAGw79wCeE5IwMeHqnz7XXyX5+fkIDw8XLWzOzs7Yt2/f39KfvwuIrF+/\nXpQpYm9vL0qtVKlU+PXXX3H16lXJnQDwPvizdu3aOH/+PK5du4awsDAQaSwLHyI5OTk6/nOpVqVK\nFe67Lo2o1Wrs3bsXPXr0QJs2bTB//nxJXg0TExMeLMkCNrXl5MmTkmmmYWFh3MLAzmFqaopbt26h\nsLCQuybMzMzw3XffYc+ePXxxY9Y5pugqVKggchPI5XJRtU+ZTAaFQsEBoUKhwJEjR7Bv3z5uaRGm\nKy9cuJAHbAvBUHE8DkU1Q0NDhISEICgoSMfCJFzgT506hZMnT5bsvAoDGBoawqVibVTrPwsew76H\na8QGnt3iOSEJrhEb4dDpa1jV7wm5qWb33rNnT66EMjIykJqaWqRy9/DwwDfffIO8vDycO3euWMZN\nbaXKFJT259pp6nl5eTytWNjMzMy4dZZJcnIyhg4dim7duqFXr14oX758ka6quLg4bhVISkrSCyZn\nzpyJ/Px8PH78mMcETZ48GYcOHRLNOQMDA84bwyxUzs7OHARor1mFhYUcuAmtS+y37BhT6C4uLgDA\n3TFxcXF8/gmL0iUnJ4NIAzRY9oy/vz++/PJLyffOysoKdevW5S4ze3t7TJ06lfe7KNm6dSvvH5Em\nNoZZGIVjQ6SJd2MWVwaIGjVqJDofy1Bi92VmZsbHiIGmL7/8sth+lUT+54EIAMzdfwOeE5KQdOXx\nRznfXyWPHj3Crl27cPjw4RJN1E8lfwcQSUxM5C9VhQoVRObxkSNHYuvWrSLl5eHhIZl2y/LxhWbP\njRs38t/Vrl0ba9euLbJ6ZEZGBr7++mv4+/vDz88PQ4YMwfXr17F06VLUr1+f98PExAQTJ07EwoUL\n+bFu3bp9lPF48eIF380OHDgQUVFRIlfHwIED8dtvv4ncPWq1mjM0duzYEYcOHRLtiOPi4pCfn69T\nQl6o6Hr06MFLzufl5aGwsBDLly8HkSYLQLgwlrQtW7aM95GlCQsX0eDgYO7+Kin4EM4FYROe18LC\nglff1deMjY1RJUArIFMmh6GtO8w+a4AydTrCunE4XAZ9B4/xiXAbsQWeE5LgNT4R9m0nw671eFg1\n7APzKk1gaOdZbL8bN27MgbG+1qNHDwDA/fv3MXny5CI5MVjT3n1rW7eISHJjk5ubi2XLliEwMBCf\nffYZ+vfvzxlvtUWlUnGLh7754+fnh0WLFvGqwT4+Pny+KZVKuLu7w9/fXwTEhHFCzs7OePLkCdRq\ntaSlkFH8M2DDGI+11yxm0WDxERYWFiKgwCwawiq7wHtunW+//ZZnSwUGBuLw4cPYu3cvd4+OHTsW\nKSkpRb4PpqamfB1SqVTIysoqtmqttuTn5yM5ORmnTp3iGT2Ghobc5ZKcnMyfNYtBe/HiBb+vmTNn\n4vbt29i4cSMfY7ZBiI+PR1paGs+qYu4c7dTrD5F/gQiA/EIV2q48jUpTD/xPMq9mZWVh48aNmD9/\nPg4cOFDqyf9XAJG3b99i27ZtmDt3Lnbs2MEtDtOnT8eJEyckd3RsoRL6X7VjJdguhfGFLFiwQPI8\ngwYNkuxXRkYGKleurPN9a2trzgHB3DLCsvF37tzhL3JRJcdLI8KaFb6+vpKmfG9vb5w/fx6Ahu+C\nSEMaxVKSJ0yYIFK6TNEbGBgU6RoQmvs7d+7MF1ylUikCAaGhoahatSpXLEqlEi4uLqJofSGoXrp0\nabFKlTV7e3u9O2l9u3EpPh4igszIDM4urjByqQDzqmGwaRoBx+7z4D5qG3ejuA39Hu6jtsPjqz2i\nYFL3Udvh2HUOrBr0hk2z4fAM6QKFUjM/nZycis0gklLYrJUvX55bAVnsjZWVFY4ePSq5w1YoFAgN\nDS0y40SKf0ahUEhmiJRGGOmdhYUFoqOj8dNPP3FLllRfTUxMOBW/vucnZAlu164dbt9+X7ZDpVJx\njhknJyd8+eWXnOGYgTmWvq69Zr1584ZbP9hYCUGU9tyPiYnB+fPneRzG9evXce/ePR2iMSJNYgHL\ncHz79i13SwYHB+PJkydIT0/ncVAdO3b8U2MulNWrV4NIk4UmFBYjNH78eH6MbR6kGls/r127BpVK\nxddaZiViafZ/Rv4FIu/kScZbBM0+jFrfHELaK42JOTMzE0+fPv3bGEv/ChGav1kLCAgo1eT61EDk\n3LlzencS8+fP1+unNzU1RWZmJlQqFY9a184qYkFun3/+OaKjo0UKq2bNmli7di3fLZw5cwaPHj0S\n+VdZtoKfnx8OHjyIs2fP8lS9Jk2aAHhP+3758mXRtdk9lSYjRyiFhYU4deoU9u3bhz/++AMFBQUY\nP358kbU22CL+448/cneOMAOroKBAh8VS2Hx8fPRSlmvXRhGCQ4VCgf79+/O4mMzMTFy/fh23b99G\nQUEB1Go1H6evv/4aBQUFyMzM5LV7/pImk8PY3R8OnaZrwMa43e/BxcitcOw2F9ZfDIZl3S9hVb8H\nbJuPgnXjcFg16AVlpUYwdvSGlZ10xhFr58+fx9WrV0tNj87aL7/8gitXruiMd0nBTXHzgv1dXExC\ncZKRkcFdXMHBwTh58qSOO9nKygo1atRA9erVMWjQIPz2229cIcpkMkRHR+P48eOiGjM1a9bEy5cv\n9RJnsZIAAQEBPCj87NmzMDAwgEwm48yfUmsWCyxlY2lpaamXWl7oahQq+qdPn2LixImoVq0aatas\niW+++UYE6NRqNV9jhG7Ze/fu8Wt/LFm7di2IdF3MjMBMO0MpKSkJX3zxBVxcXFCrVi0efMvA+tCh\nQzm4Ya4jJyenIktElFT+BSIC+c+TLFSaegAtFh1GaLP35tDy5csXyab5/1UePHjAEX1QUBCGDx/O\n0W9QUFCJAdinBCI5OTl8t1y5cmWMHj1ah62TSLObkqp8ygjEcnJy+DFhvMjp06cld8uGhoY4ceIE\nAGDo0KEgeh+FbmpqioEDByIjI4O7Ng4dOsTP+eLFC25JyMjI4KRfQrIkFminnQkAaMyrCQkJiIqK\nwvLlyznVMpOsrCxs375dlI0ik8ng6OiIkSNH4urVqyJQJZPJ0L17d0yaNEmvK2PdunVQq9V48eIF\n3/25uLggOjoa8+fP1/m+i4sLr2hL9D6w7tSpU5LkW2xM2d+mpqZcKdnZ2aFdu3Yif7aVlZVoFx8U\nFPRxlK25DRQW9jDxqgbLet3g2mwQbJuPhGOnr+E+UsNI6j56B6wa9IJ143AoK32Oxq066p6nhHEY\nCoUC8fHxfM6y6s2sIrPw+QnHVt/YeXp6YsqUKXotPEXVtRECw6LiNaysrDj3yofIzZs3JS0DbDxE\nRfbMzJCamorCwkLcvXtXlCF19uxZqNVqJCYm8v56e3tLAvf8/HzuzmCK09TUVHQtX19fvsGSWrOe\nPXtWJPAtW7YsGjZsKKKJHzp0aKnqq6jVam55EXISMS4gKyurDxt0wfnz8vKgVqvx+PFjPm5LlizB\no0eP8P333/N1TKrqtlAuXLhQrOuTkcX9WfkXiGhJ7KEr8JyQhDJBnWFoaCha/FgJ9U8tubm5iI+P\nx7BhwxAZGfnJMmEY5XWrVq046Hjx4gU3uelLF9OWTwlE4uLiQKTJsmAm+9zcXJ1UutDQUMlCYaxA\n3W+//QYijW+c3atareYBb9qKxdnZmS8wQmIjoS+9bt26nP744sWLvM95eXl8Afzjjz9w6tQprmhq\n166NFi1a8OuNHz8ey5cvR//+/TF58mQcOXJEp5KpsbExNm/ejN9//x2tWrUSKS2p9FOlUilyUTRq\n1Ah5eXl4/PixaGFmfRcqOyF4YQv+vHnzJBchBhQMDQ15psyPP/7In4O9vT3S0tKKNPsWZ71h9/Po\n0SM8e/ZMhyhNuxlYOkLp/wWsvxgMmyaDYd9hKlwHfQeXAavhNixeh/Lc46s9cBsWD7fhm2DfcgzM\nygdDZmgsuQAbGxuXqoAd0fvKw0KXX4MGDXTI17QVnvaxolJLSwvQrK2tMXv2bL2f6Yv5KKkI3SNE\nYmDFsltMTU15AbxGjRpJAhcjIyOdOcre4ZMnTwLQFKBjbloTExP06NEDp06d0st14uHhgadPn+pd\ns96+fYv169eja9euaNCgARo3boyBAwdi//79fN149uwZfv311w92qbKNSbNmzfCf//wH169f5+9P\nr169PuicjDSRbU4cHR0xbdo0zJgxQ3Ic+vfvX6LzHjhwQPIZmJiYIDIy8qN5C/4FIloyctQo2LUa\nB8/xiYjaeQHbU+5h5sxv+AJR2viJ0sqDBw90eAmINEFEH1uYW+K7774THWe7tW3btpXoPJ8SiDDX\nx+TJk0XHWbaLdtNmdhw2bBgSEhJ4HEe/fv3w3XffoU2bNnzBVCqVmDZtGicGY4o+Pj4eu3fv5uea\nNWsW1Go1rl27xt0qzOfdqlUrZGZmIj8/n1M6V6pUCWq1GtnZ2ejSpYsI7MjlcnTu3FlvUTgfHx9M\nnjyZ+7YVCsUHVz1lix5zTxWl8Fjz8vICoHH/6CswxpqhoSG/jz179vDjrFaMMA6DmXSF7J3CMRky\nZAgHOCNGjCj2Xi3dykHp3wS2zUfCJXzNe1fK6J1wH7MTzv1Wwq7NBNi3nwK7sJHoO2cjLGu0gKlv\nHciMlZAZ6MZOSMVTyOVynhLNmpubmyRLJ1OiwkySlJQUhIWF/amaLFL1a+zt7XXclv3798fhw4f1\nnqd8+fKcDTQkJAStW7dGo0aN8PXXX0tW7i2N3Lx5U/NcLC1x69YtvfWPJk+ezJlqWWPuE31zXMjI\n6uPjg4SEBMnvu7m5cQtU+/btcefOHdy6dYuDuUmTJv2tlAM3btyQrEdlb28vinkpjbBim9pj0a5d\nO2zbtg3BwcGws7NDtWrVsHr16lLpMZVKhYsXL+L48ePYu3cvkpKSdGrv/Fn5F4hoSUBAAGTGSjSf\nv58vam1XnoaDj0aRfehEKYncu3ePL9pKpRJdu3bFgAED+OIlpPX+GMIUZufOnTmyzcrK4ouHsJR9\nUfIpX2qWxVCrVi3uUsnPzxfteJhVwMXFhUffSzVfX18dZaLdhG4FobXB3t5e9PIya1KvXr14loKJ\niYkoY+GHH35Adna2ZPl5CwsLvlOsWbMmoqOj0apVK/55cnIyv1b37t358bp16/LUV+3aK9rXYCZY\nNn+EfWOLlZ+fH7fAMF88+2zr1q2iWhrFKUo/Pz9OMkWkAW73798XfYdZlIQ1P7SVjfYxmaExFGUc\nYOpbBzZNI+DUeylch8aJYjjchm+CfbtIWNRso8lGUUi7HkJDQ/n9mZiYYMmSJbhw4QL3mxMRtmzZ\nUmScTEnb559/jt9//x0AMGDAAL33W5SVZcCAAVi6dKnOd2xtbTFq1Cg8fPhQJ6W2Ro0akgRzMpmM\nz2k2F1hF49evX2PmzJmoXLkyypYti549e+Lq1dJTGrDU5lq1amHHjh061j1Wk0WlUoloyLX7KfyX\ntbFjx6KgoIBncbB/v/rqK2RnZ+POnTsiy5GlpaWoLtT+/fv5PE1JSZFcs7KysnD37t0P4iQqjdy8\neRM9e/aEnZ0d7O3t0bdvX559Vlphbh0jIyMkJCRApVLh8OHD/BmfPn36I/f+48u/QERLmNLYs2cP\n3uYXYvu5B/CfdgDuwzfByKUC0tLSPvo1Ac2OSWrH07VrV0yePBlE0kXQ/ozcuXOHm6BDQ0MRFRXF\nFXG1atU+eYyIWq3GhQsXsGvXLr3up9evX3PlVbt2bURGRnJFzJSvg4ODzsJrZmaG0aNHIyQkBA0b\nNsTcuXM50ZG7uzuvB8NauXLl+GIv3MWx3XFISIioX4zMaMKECbh48aKoTsRnn32GhIQEAOBl7r28\nvLBr1y6cPn1axKHB7mPGjBkiqvaxY8fyazH3FBFh//793KQtbMePH9fZnetT9kTvI97Xrl3L7/fK\nlSs6ikOK7K2kbciQIdwlxhq7d6FrQqhwDGxc4VI7DGafNYRty7Fw7rMc7mN2vrd0jEmAQ6evNYGi\njQbAPKAZDG3d9VpOpNJStRWj0PSsUCiQmZnJ4ync3NyKtMqYmZnp3fUzhX/s2DFRXIH2dwwMDNC6\ndWs4Ozvz75UrVw43btxAfn6+KCWXZYsICeeE4K80rX79+igsLEROTo6k68fU1FSHH6Q4efbsGQwN\nDUVjJvxboVAgJiaGr2lEGkB48eJF/PDDD5JB6SYmJoiKiuIbEeG7ZmdnJwqWFBaALFOmDHJzc6FW\nq7F8+XLRGlG2bFlRFtuLFy/Qs2dPvh5aWVkhMjLyowRifmqJjo4GkS5p4ejRo0EkZnP9b5V/gYiW\nMMXh7e2NAwcO4PLlywj7sj9cB6+F5/hELDt8C9m5H3dyCmspEGl27suXL+e+X2ZS11aGH0O2b9+u\ns9vy8fERFd0qTj4EiKSmpupYJxo3bixpGj59+rSOQnFwcMDRo0clfe2+vr6SRGEsduHYsWP82uze\nFQqFKP1VoVDg8uXLePr0Kf/OtGnTcOPGDcTGxnKAIgz4ev78OdLS0kQAjinexMREAMCVK1dElhah\nf19Y2rt9+/YAoFO4bMuWLZKKRzuAV6lU4tSpUzqgR7ux4DxGA82UckREhCSltXZMijDo0dDQUFLR\nChWSlM/awMYNlvV7wK7lOBHZl8dXe+DQeQYcWo2FRY1WMHb9DJY2dpLXlmrF0bfXq1dPVMadKSiW\nbRAYGAiVSsUzBUrSPvvsM+zatUtkoWLuQjaPqlatKmLCJNIUPMvLy+OAgCnJ/v378+84OTlxpV6z\nZk0eM6VWq0VstlLNyckJjo6OOhanwMBAns7p5eWFffv24erVq5wTo2rVqlCr1bh58yaGDh2KOnXq\noHnz5ti6date876wzyWJAbKzs+MWCFY4kT0LIo2Lj3FVJCcnQy6Xc8BmZWUlsnqwasrsugMGDNAJ\ntmafGRsb49q1a8jPz+fviUwmE4GhgQMHAtBUu129ejWioqKwadOmUgWofmphdXY6dOggOs6C7KdO\nnfo39azk8pcBESK6R0S/EtFlIjr/7pgNER0iot/f/Wv97riMiJYTUSoRXSWi6viLgMjr168lF28L\nFx+0X/ITPCckoc6swx+1Pg3jc7CxsYGBgQEUCgWuX7+OJUuWgOg9X0BERMRHu6ZQ0tPTsXz5ckRG\nRmLbtm3Flrln8vr1axw7dgzz5s1DVFQUNm/eLKqjok9yc3O5wrOzs0NYWBhXyCyuQFuysrKwbt06\nTJkyBRs2bOB1DvLy8hAXF4cuXbqgc+fO2Lhxo16zKtsRPX78mP8ttDYIW0xMDP8d23Fot379+uHX\nX39Feno6MjMz8ezZM52+s6BR5uZiKYJCtsIVK1aASAOu2E68TJkyGD58OM8kYQuvh4cHfvzxR8ld\nuHDnGRgYiKSkJE4+RKShcJaqomtmZoa9e/dyBeLo6Ij8/Hy8evUK33zzjU45cn2NKVq5XC7K0JC0\nKMjkMLT3gm2LMe/dKyM2w7b5KBg5+8HAxo0zjQpjNvQV5NPXiuLPkMlkGD58OEaNGsXnQ1RUFHe7\nTZw4EQB01oOiAE5KSgoKCgqKDC5l85zFy7DGsr4cHByQlZWF27dvc3fK0aNHAWjM8MxKtXPnTj7P\n3r59K6pdUlzz9PTkz4jdz44dO0TnY59v2rRJEmDqq4d04sQJyTkmDEht1KiR6NqdOnVCSkoKxo8f\nz7+zZMkS/rxNTEzg6urK51J4eDiP++rfvz8ePnyIlJQUnsXWp08fyYBjLy8vpKWl8aJwffr04dwl\nHh4e3JV25MgRbtnZsGGDTkCwu7v7B5eA+Nhy7949TjAWGxuL58+fY+vWrfyZMd6g/2b5q4GIndax\n+UQ08d3fE4lo3ru/mxPRftIAkkAiOiv83acEIoBG6c2YMQOVK1eGt7c3+vTpwyPJU+6+QPUZGkAy\ne99veJVTMqVdlLDy5AEBAVxRKZVKkZ/a0NDwb5n4BQUF2L9/P9atW4eUlBSo1Wqo1WrMmzdP0pVk\namqK6OjoIs/JKIXLly/PI8+fPHnCAx5Z2mxx8uLFC+zcuRM7d+4Umar1CQssdXFx4YqdKQx7e3s+\n3jY2Nvw+T548iTFjxqB169aoUaMGvLy8ULduXTRp0kRyca5SpYqo2N2gQZo6IS1btkRWVhZfKNlY\nEWmsIkKFqb1rtbCwwLZt2/TSxuuLMRAe9/b2RkZGBlQqFV/s9aWgGhsbY8iQITpumpJcs0KFCrh/\n/z7UajV27dqlmbtGxli5YQvcglrCtvlIjXVRUEnWqn4PKCx0gRWzyIhqtOixgri7uxebPcKU2Jo1\na/QWazM2NuZKslKlSnj79m2pgoM7duxYbCE4BiKlAI2npyfPVmM8L+3atRPNYxZoOmzYMNHx3Nxc\nrFy5ElWqVIG9vX2RlYY7deqErKwskVVSmIKuUql4DBMLVu7YsSOOHj2K5cuXc4vP3r17dd6zc+fO\n8XMqFArExcXh0aNHolingQMHciAmBRjKli2Lp0+f6gSfE2l4SfLy8nDo0CHJ31aoUAGvXr3Czz//\nzEG0TCZDeHg4r43y/fffg0gTL8IC37Wr27KgffZuNmzYEFFRURwA+fr66i0d8VeLMJVe2ISFKv+b\npTggYkCfVtoQUci7vzcS0XEimvDueBwAENEvMpnMSiaTOQN4on2C8+fPf5KOhYWFUVhYGP9/Tk4O\nnT9/nmRENCnInDZdy6ZvT9yhH87do55VLMjfwYgsjOQfdK38/HwyNTWlK1euUNeuXalhw4Z04sQJ\nOnnyJBERGRkZ0cyZM+nt27ef7H6Fkp2dTYmJiXT8+HG6ceMG5ebm8s+qVatGwcHBFB0dLfnbt2/f\n0rBhw6iwsJCCg4Mlv7N//34iImrYsCHdunWLHw8ODqZdu3bRnj17yMzMrMg+bty4kdasWUN5eXlE\nRGRsbEzh4eHUq1cvvb8xMjIiIqLHjx/zY+fOnSMiIm9vbz627du3p5SUFJo+fTrvK5OqVavSmzdv\nKDk5mYiIZDIZA9Ukk8no6tWr1Lp1a1qwYAE1bNiQQkNDKT4+npKSksjBwYEKCgr4ucLDw2nv3r2U\nmprKj5mZmVHZsmVJqVSSq6sr+fv70+eff07m5uY0f/582rp1Kx06dIiys7Pp7du3lJGRIXo+RERy\nuZzUajU/LpPJyMvLixYtWkRNmzbl9//FF19Qbm4unTx5kgCQXC4nCwsLyszMpJiYGCIi8vDwoJYt\nW9KZM2fo0qVL/Bq5ubm8j8Jn2KxtZ7r/+CndvP+EnhvYk2/vuZRr6UHzb1iQosFgUubl0Jt7l8nw\n8VV6dvc3qmAtI3d1Dv38+hk/h4ODA6Wnp9PLly+JiEilUvHPCgsLRffq5OREO3bsIBMTE8rIyKD2\n7dvT69evJZ8/e07bt2+nmJgY6tKlC39+MpmMXF1dKS0tjY4ePUpGRkZ0/fp18vHx4b8jIjI0NCSZ\nTEb5+fmS19i5c6fkcaE8e6a51/z8fLK2tqZXr16Rj48P9erVix4/fkxRUVHk4OBANjY2RER07949\n0Xt/7do1IiLKzMzUWQ9q165NtWvXJiKiIUOG0Pnz58nS0pIyMzOJiMjOzo5evnxJP/zwA0VERFDT\npk35OcaPH09z586lMmXK0ObNm+nx48dkbW1Njx49IicnJxo7diwZGBhQUFAQ9e7dm1atWkXR0dHk\n4OAg6kNhYSFZWVlRRkYGWVpa0sWLF6lfv36iZ7dp0ybq06cPrVq1igoKCsjQ0JC/G0qlkpYvX069\ne/emy5cvk42NDdWrV4+ePHlC586do59//pnWrl1LtWrVom+//ZbWrVtHly5dIlNTU2rSpAn169eP\nUlNTycjIiKZMmUInTpwgAwMD6tSpEz169IgePXrE3wEDAwM+Nr/++qtoPO/du0dERHl5eRQYGEgL\nFiwgmUxGzZo1o86dO1NqairFxMRQYGBgsc/8U0u7du3I0NCQtm/fTg8ePCBHR0fq0KEDdezY8S/R\nGX9WypUrV+TnHxOIgIh+ere7+BZALBE5MnAB4IlMJmMz2pWIHgp+++jdMR0g8neIl5UhRdazplsv\nCmhZSiYt/iWTzAxk1K+aBdX3MCGFTFaq85mbm1PXrl1p3bp1NHHiRPL29iYzMzN68+YNmZmZUXx8\nPLm7u3+iuxHL06dPadCgQSJlTURkb29Pubm5dOnSJbp+/ToRaRaMnJwcWrRoESUnJ1NCQgKVLVuW\n7t69S1u3btULRKytrYmIRAoMAN28eZOIiC/A+mTfvn0cCFWvXp2IiC5evEgrVqwge3t7EYAU3teB\nAwdIJpORmZkZ5eTkiD4/e/YsEWmUc79+/WjLli20f/9+kslkZGlpSe7u7vTw4UO6fPmy6HcAyNTU\nlCwsLCg9PZ3q169Pp06dom+//ZYaNGhA7u7utHr1alq0aJHot4aGhrRy5UodxfrmzRs+vkRElpaW\nZG5uTkREpqam1LdvX+rbty8RaUDf+vXracOGDQSAbG1tKS8vj96+fUsmJiYciACgo0eP0tGjR2nW\nrFmkVquJiOjIkSOi6xsaGvJFmYmjoyNt3ryZMjIy+DGmvHNycuhW6h0yKVudrIO7ksLKiXbBmnbt\nfg8qyMqT3t76hWr5uVLBs3t0ZNsasjQ3ozmrV9PgwRvowq/i6xERpaen6xwTilwuJzs7O0pPT+cL\nbUpKChkYGJC/vz8HiS4uLqJ5bGBgQIWFhXTo0CEKCAjgY6NQKMjU1JSsrKyodevWFBcXR9nZ2WRv\nb6/zHgiylG7YAAAgAElEQVSBJJOQkBA6fvx4kX3WHjsmr169IqVSSV27dqV58+bRmzdvRPdpaGhI\nly5dohUrVlBYWBhduXKFEhISiIioUaNGRV7rxYsXREQUHR1Nz58/p9GjR1NBQQGZmJjQmzdv6NWr\nV3T//n0i0gD5S5cuUfPmzcnExIS/H82bN6dNmzaRvb09GRi8VwdOTk5ERKL+MjEwMKBBgwbRvHnz\n6OXLl7R06VL+GZuXb968oStXrtCkSZNo/fr19PTpU5LJZBQcHExjxowhExMTOnz4MCkUClq7di25\nubkREdHq1atp7dq1lJCQQLVq1SJ/f39asmSJ3jGwtLSkoKAgOnPmDI0ZM4b69OlDGRkZtGrVKiIi\nCg0NJX9/f9q0aRMlJCSQu7s7BQQE0P79++nKlSt8ztSpU4dk79Z1Y2Njql69Oj1+/FhnfvxdIpPJ\nqFWrVtSqVau/uyufRqTMJB/SiMjl3b8ORHSFiBoQUYbWd169+3cvEdUTHD9CRDXY/z+1a6Y0kl+o\nwpnbz9Fs6Ul4TkhCxKYLeJNXenOdSqXClClTRObUmjVr4tKlS5+g1/qlXbt2IHpfZdLb25v7iufO\nncuj91nAl6WlJVJSUrifVWjO1SePHj3iJtXevXsjLi6Om0Gtra15/Ic+YdTRQhcQi7OoVq2a5G9W\nrVoFIk0QaFZWlqQP387ODtevX8fLly8lXQ/CwLtKlSqJAmiZf/6LL77gZnBPT0/06NED3bp1Q4cO\nHTB79mxcunQJwcHBes323t7e+OGHH0TsmcJUXm1hfBElZdQsrtnZ2UmW/65Spcp795HCAH6NO6NC\n+DJ4vMto8R27HXatxsGqYW9Y1usO86phUJYLhMzITNKdMnz4cNy9excjR47kMVAeHh4YPXo06tev\nj44dO2LmzJkYMWIEhg0bhpEjR2Ls2LFYt24dsrOzOSGXdpwFa8JgUWE8DZu/RRWGY+6AefPmca6d\notqiRYtEAcXC95fVFRHeN6vYqlAo0K1bN1y+fJnHQjRt2hSrV6/mwaf63EJDhgwp5k0GT2UfOXIk\npk+frnMOT09P/h5u375dVNzQ2dkZ69evx/Pnz2FsbAyZTIaDBw8CAF69esWzC+fPn6/3+sJ3zMjI\nCJUqVRL9n4hw7949qFQqPHz4UESFfvnyZRBp3LdCOX36NB/bksqtW7c4uZr282FBp1IZZjKZjNeb\nadiwIQ/Off36NY/TOXLkSIn78a/ol78la4aIviaicUR0k4ic3x1zJqKb7/7+loi6Cr7Pv4f/MiDC\nJLegEDN/vA7PCUmoO+cI9l19/EGsc69fv8bZs2dx69atT9DLoiUjI4MXYmOcEqtWrcKmTZtApEm5\nFFIwsxiHLVu2cPZNplTq1KlT5LU2btyoE6NgYmIiWfFTW5iiF9abyM7OBpHGF37u3Dnk5+dDrVYj\nJiYGlSpV4teqWbMmz9ywsrLSUZIsPZL9f8OGDThx4gRXHqzVqlVLxF5aUspvX19fTlLm5+eHFi1a\n8DgSIg1pFbsvlm4cERGB/Px8HD16FImJiaLMojNnzvDfVqhQAZcuXcKrV694ei6rjilFoKSz8BoY\nw9TtM3z/UwoM7Txh5OQLZaVGcK3THLEnUlGp1wzYthzLC7+5Dl4HmyaDYVouCGZligY7lpaWmDx5\nsoiWfsSIEViwYAEHStqZUV5eXujXrx9WrVqlw2L58OFDPg+MjY3RrFkzEfGasD5JcS0wMBBpaWmI\niYkRKf7atWvzTCY7O7tSxYqYmpri8OHDPE6GNQaiid5nxrDv+Pv74+bNmzqEhsbGxqhXrx78/PwQ\nEhKC+Pj4YteWH374ocR1eiZMmIDnz5/rBCXb2triwIEDomyu8uXLi0oAFBWblZaWpsNvI5fLsWjR\nIg5koqKicPPmTZ3fvnz5EoaGhpDL5SKm16+++oo/39LI06dPMXXqVDRo0AChoaGYPHmyCOCr1WrE\nx8cjJCQEfn5+aNeuHX766SeMGjWKP3djY2OEhITwQPuKFSt+coLL/xX5S4AIESmJyELwdzIRNSOi\nBSQOVp3/7u8WJA5WTRGe778RiDA5e+cFQpecgOeEJJQPXwaltT3c3d0RGRlZ7E7/7xZWeMne3p6n\nDHfv3p3vTnx9fUUsmSwoT6lU8h0522GtWbOm2OvduHED48aNQ+fOnREVFYX79++XqJ/M6iIkeGPk\nbKw5OzujWbNmkgsv66MwuFFYaVOocGbPng0AePz4sc7nzAoipaBYBgT7bMyYMXxHyK7LaOGZImIW\nBxa5z9JIGzRoIKLJNjAwwIgRI1BQUIDCwkI+9vXq1UNycjLWrFkj6pPQWsKZTc1t4FO/DcyrNIF9\n+yi4DlkP9zEJOhTooqqyI7fCbfgm2LUYBRPvGiC5LviSqgPEWnJyMh48eFBkWrCvry/q1Kmj87mD\ng4PIOlhQUFBkqrBw7EeMGIGVK1eiXbt2fCyEAFQmk2H69Ok4fPhwsZYwBtT1XUsbkEoBVBMTE8yY\nMYODCZYe3KtXLz5HypYtK7KcWVpalpjNsihKfZlMhoCAAD7GhoaGyMzM5ODYxsYGvXv35pYcU1NT\n3L59G5GRkaL3JSQkRBJAaMvAgQNBpAFgs2bNwu3bt3mwurB17NhRZ31kXD9WVlYYPHgwmjdvzr9f\nWn4TbWGUA7m5uTh//jyuXbsmAncqlUrv+kGk4Xn5OzaL/1T5q4CIN2ncMVeI6DoRRb47bksat8vv\n7/61eXdcRkQrieg2aVJ+a0IPEGnfvj1atWqFZcuW/alCTR9T1m3YCIsareAxVsOJYN8uEgY2bjza\nuyhJTU3FN998g7Fjx5YqlfZjSEFBATdhLl26lC+ibAfAdqxeXl6SBeZY69ev30fZKWRnZyMuLg7T\np0/H5s2buRmVgQ57e3vMnj1bVH/EyspKRF2uUCgwadKkIk3xLVq0QH5+vl720M8//1xktvbz8yuS\nadTMzIyngzJ+mKFDh+Lhw4cixbR06VIAwP3797kiMzAwQEZGBrKzs7myEJJchYSE8Gsz2nupzALt\nJjcxh9K/CWyaRsBt2Pc6ZevtWo2DdaMBMC0XCGP3yrCp2gTW1cNg5FIBJmWrw8jJF9bW1lizZo3o\nvIGBgbx2RnGN7WJZeqeFhQW6du3KFU79+vVx69YtrugZYGTK2dvbG/v378eECRO4tcjU1BTTp0/n\nmS78fgXPx9HRET179pR8ZsIsJmELCAjA0qVLuYtSKiOnTJkyPNNq/Pjx3JIhlU3GSPV27dqlY0VI\nTk7m5yPSuDXT09O59YSdl82XoiQjI4NbIebOnYv09HQRKd369ev5d5l1ipGAmZmZ8aJwarWau0tZ\nldbs7GxcunSpxBsGALh06RIf92bNmoneVXNzc7Rt25YDyp49e4p+m5WVpZNubmRkhFWrVpX4+vrk\n3Llz+Oqrr0SuvfLly3NXCxsTGxsbnDhxApmZmYiIiOBpsqyK77/yceT/PaGZcJL6+fnx9KxPJXl5\nedi+fTsmTZqExYsX4/Hjx6LP3759yyf34Mi5GLXpLMpPToLH2AQoK4Zgw4aNes+9ZMkSncWyYsWK\nePToEdLS0rB06VJMnToViYmJnyxtbNGiRfzaUkXk7O3tcfHiRWRmZmLJkiVo2bIl/P39ERgYiNGj\nR+Pnn3/+KIWQfv75Zx3/v7OzMy5evIg3b97o0Fqz/ubk5ECtVvOaFLa2tvw8DRs21GEKlcvliIiI\n4LtI4TWrVaumN/bCz89PVCeGLab6OCZ69eoFtVotOr+hoSG6du2Kzz//XFRsLigoiFsN2Hnr1q2L\nFStW4MqVKzwuRKlU4vHjx5x8StxkMPGqijK128FrYDQnCvMYtxv2bSfDonpLGLtVgoGNK2RGpqJ5\n5+HhIbJ8EWnA2KxZs+Dj48OPdezYEWq1Gs+fPxf9XiaTYcuWLZzZkTV/f3+kp6dzDodatWohLy+P\nU32vXLmSc3h07tyZx12sW7dO5NLRbsHBwbxfbGcfEhKiw54r7AdzDchkMsyaNQvt2rUT3QNj+j12\n7BiIiANLfbWBFi5cyFMoJ0yYgDVr1mDcuHGYN28e0tPTiyT9U6vVvO4RkSYVmVnAXF1deTyMdrqu\nlDDrWnBwMD/WunVrfu7w8HAAGoDA5tfWrVtBpIlPEQpzyWoTZZVW1q9fr8PnYm1tzatKX79+nfMn\naa+narUaZ86cwYIFC7B69WqdStQfKsK6S76+vjxGx9jYGJcvX8aoUaNApMtKysowCAHdv/Ln5f89\nEFm5ciXi4uL4zkYbVX9MuXv3rk6JcyMjI8TFxfHvHD9+nAMIppCfZr5FrSiN2dtj6EZU6TcHAyMX\niF46tisiIvTo0QMzZszgi2vFihV18uWrVKmi89J+DFGr1Zg+fbrIt1umTBk0a9YM0dHRku6wj11r\n5vXr11xh16hRA+PHj+f+bldXV+Tm5qKwsBB79uzBwIEDuQJ59uwZP4d2xdjq1atDpVJJFhQUNgZU\nGKAwMzMTgYvw8HBRvIWxsTEiIyMRGxsrOo92vYzg4GDOpung4IARI0ZIXl/oUqlRo4ZkSXhhzIs2\ncFWUcUCZwE5w7hfNLR5OvZfCKqQvjBx9QFTyOAd3d3cMGTJEb2yEsFiiNumXlEvC3Nxcp78+Pj6c\nAbJHjx68JsuSJUs4ED5y5Ah/70xNTfVao4T93L17N27fvs2fEbufxMREqFQqFBYWioJ4he+XcA15\n9eoVnw/az1TospkyZQpCQkJA9L7ibmnekadPn+pUjK1YsSKuXbvGrS5t2rTBr7/+WuS7s3PnThBp\ngCMTIe25p6cnBg8ezIHVkCFDcPHiRRBpQLjQqswq5Y4cObLoF7YEkp6ejlWrVvHnyEogMGFA7K8I\n/lSpVNzStXLlSqjVauTn5/PA5O7du3OWZUZqx4S5a4Rr/r/y5+X/PRBhkpqayheMT1GwSK1Wc0Kp\ncuXKYcqUKXynoVAocOPGDQDA0aNHOVBgolKpULtOHSgrfQ6nnovhPnqHJtiv01Qc+0UTJ8B2b8Ia\nI+np6aIded26ddGnTx++O2zSpMlHv08mGRkZOHz4MH7++edi6y18LCBy+/ZtREVF8XEOCAjglp8/\n/viD70Y/++wzzJ8/nwcwsuNCunXtIMGIiAgRQyojJRI2Br6cnZ1x+PBhUZQ/a6ampti2bRv27duH\n3bt349mzZ/j5559LVVV14cKFvH9yuRyVKlVCx44d4eTsCpmRGRq2/hI7j53HnC1HUSawE0zKVke5\n8p+hZ8+eMDKzgMxYCUNbdxg6eKNMnY6wbT4aLr2XwGf8e3p05z7LoazUCAaWRTOR6uu3oaEhNm7U\nWO9u3ryJqVOnYujQoVi/fj0HR46Ojti5c6cooK8kTSaToVmzZhwUVqxYkQMXBmiYK8Tb21tUOI8p\nsn79+mHx4sU65zYyMsKiRYsAAD/99BOI3tfVmT59umi+MdDDnjuzSi1cuJB/h1kjgoKC9FpDhKDE\n3Nxckl24JO9IYWEhf7fLli2LyMhISatkt27dOL27tjx79owDr7Vr16KgoAApKSmSrqXmzZtzCyIj\nNqtUqRJmz57NrWwymeyDit/pE+aaESp4YW0fYWDqp5K0tDQ+x4Qu5CtXrvA5xzaUFhYW3J3GMvMM\nDQ0/yDLz7NkzXL58uUTs0/9r8o8BIoWFhXwx+BQPmgVs2tjYiNLMGBMqAxA5OTn8pVq4cCFyc3NF\ntQ46deqEbQm7UKXnVI3S+GoPwuPOIbDDIJBMjqSkJH7unLwCODg66SgMS0tLvmiywMYPlYyMDKxd\nuxazZ8/Gli1bsHLlSkybNg0JCQnIz8/H/fv3cfbs2SLH9GMAka1bt+pYfQwMDHDgwAH88ccfkgty\nxYoV8fz5c+4C8PHxwffff49NmzYVafnw9PTkrKHaAY8GBgaYP38+8vPzuVIICAjAnDlzuNnfxMSE\nuwALCgpE2TNFNRMTE0yKmob0rLd8ZzV3/kKsOXkbwzdfRIXIvXoDRT3G/gCf8Xukg0hHbYNTj4Vo\nNX0z1p5MhVO59zvroijOpUCJMM1RLpfzgFqhJCYmlvic2q1WrVq8DlBWVhZX7pGRkZKBns2bN+du\nKmGWTHZ2Nt98CLNtKlWqhB07dmDjxo3cutW+fXs+X1hA5PPnz/mu+NChQ3j9+jV3RRDppt7u2rWL\nz89WrVqhbNmykllfQlbdD3lHfv31V1H2D2t169ZF7969+XxlcRtSIkzVFa4btWrVwrJlyzBv3jwk\nJyfjwoULiI2NRadOneDt7a0zVxQKhaR158/IqVOneL8iIiKwYsUKHgsTGBhY6vPl5OToBWX6JDMz\nk9erEWagsc0BK/jZqVMnyTn8zTfflOp6L1++RNeuXfl8MTIyQr9+/Xj9nH/lHwBEmPuDFf7x8fH5\nUzEKarUa+/fvR9++fdGlSxesWrUKr1+/xu7du0GkCbgSSnx8PIg0/nImK1eulJzArq6uPDUzOzsb\ntn41YNM0ApWn7tNYSCI2ouKYeNSZdRjlJu9D2YlJcB+9A/YdpsI8IBRmNk6Qm4nTJBmF7w8//ICA\ngADY2dmhfPnyWLlyZbFxJHv27JEMrGNNqKSNjY0xePBgyWJPfxaIPH36lC+CXbp0EQW0WVhY6HAA\neHh4cJ9u+fLlERsbq2PWZkpp+vTpXIEIA0L1AQX2N+PS8PPzExUXY5H7CxYsAPDefK3dFAoF5GZW\nMA8IhU3oUDi1nYAqw2PhOfadi27MTriN2MzBRN05RxARfwFOId2hrPQ5TLxrwsjJFzIjU5j61IJ1\n43BYNxqAMnU6wDKoC5T+TTB57T607f6+wBgrlCdVWE67SVkwGjRogJycHJFit7W1xaBBg3R2qosX\nL5a0puizsLC5pJ1NxQIit23bhtTUVEydOhWtW7fW4T7RLq6XmZnJC1Sy3bzUcw0MDMSzZ894zIuT\nkxPatWvHwQ1z2TFZunSpyHpgaWnJ6w4xcMtqsjx58oSb862trfHo0SO9c7w078jbt28xf/58PgYD\nBgzgaxqzuNrY2Oi1VKrVasTGxvL+WltbY8yYMVzxHTt2TMfFLGx+fn6YOXMm7t69W6L+llak5qe7\nu3upslASExO59czQ0BBdunQpVQApc3fVrl0bu3fvxrp16zgwZe92fn4+FixYAD8/PyiVStSqVQub\nNm0q1b2qVCpemFOhUKBChQr83QsLC/so8XT/BPl/D0R8fHxEuflCv3VRsn37dgQGBkKpVMLHxwez\nZs1CTk6OqB4Ca76+vjhy5AhXjAxFCyujTpo0SXT+rVu38mwGhoS3b98u+g4z/f985hfEJP0C+7aT\nYN8+Cl5dpiBw8Hw4hg6B9ReD4T5yq3gXPDwe9u0iUaZOR1gGdUFAvS+KXFD279/PQcmFCxewZMkS\nzJkzhyv/2rVri3Z3jo6OfFGXy+WoUqUKf3m6d++uM5Z/FogsXboURBpTMSCOESlpCwoKwsKFCxEa\nGoqmTZti2bJlfOG9c+eOaI6wps2tMWbMGJ6Rw6whzC8/cuRIeHp68syGHj164O7du+8VutwAZcoH\nwSqoE2ybj4Zz/5XwGJ/I015dB62Fc79o2IQOhWVwV1g3GgDbsBEInRiLIzc080kfgBUqRSGQeP78\nOQ+mZH0ODAwUgYHSuIxWr14NlUolmV5rYmKi479/+PAhj91h742NjQ26d++uk87K+hEaGsoX3xcv\nXvBrsfoqTPLz85GUlITY2FgkJydzYMjOK4ydYdatQYMGYe7cuWjUqBFCQ0MRExPDgfPNmzd1wGpw\ncLAkeHj9+jUOHDiAgwcPilJKWRFKExMTDBgwAOHh4RxgMeWlT0r6jqjVahFvB2utWrXi98LmQUnc\nA7m5uSJld/36dVFxQuE1OnXqxEHY/v37iz33n5HLly9j3Lhx6NevH2JiYkqV8cjIE7XBp6urq2T1\nbinZvXu3pKutYcOGH7Wy7v79+0GkAcC3b98GoClyyp4hK4b5vy7/74GIcJGeOnUqUlNTi00dlfIt\nE71PtTQ3N8fMmTMRGxvLwULbtm15iqCTkxOGDBnCka6xsTGuXLmCs2fP8snGpKCggC8sYWFhPH6F\nTVBzc3Pcu3ePV1mVbHIDGLlUgFVwVwT2mwb7dpFwHbzuvdl+3G7Yt4uEY90O6D3sKzi7uuuco2LF\niqICV8J7njp1Kog0hdmESogpkV9++QUXLlzgwCU1NVV0j38WiLBsA2G56jNnzuhkoNjb20tmsbAF\nVRsMCkWtVuPEiRNFEnt5enrizZs3OiZ3mbESJmWrw9S7Jqwa9EaZwE6wqtEcvaathG3zUfAYsZnH\n/XhOSILbsO9h32EqrBr2gYlHFSgMNBaZ8PBwnDlzBsuWLRO5ob744gvJNFIpUMwUsbe3Ny5duoS4\nuLgiWVVL01JTUzFnzhzRsaZNm3KGTm9vb513ixUMGzVqFN+Bjxw5sshxrlWrFoYPH85dEEFBQZI7\nwz/++ANLly7FhAkTsG7dOvTs2VPvOV1dXZGWllbkPFOr1UhOTsaWLVt0gE9JpLCwkMeVCFufPn2K\ntT6uXr0ajRo1gr+/P1q0aIHExETJ77FibAYGBlxRsuf71VdfISUlBUSaDdGHpPYzXg8WWFuxYkVs\n2bKFv1/Tpk0DkSYG579RVCoVpxOIjIzE27dv8eDBA57qzlLai5Nz587hp/9j77rDorje7tldehNE\nRUUpRhRFhdh7LLF3MSr2gj3G2Hvv0diN+sMWu8bYsSvGFhU1lthbNLEjigJK2/P9sbnXmS2ASUzQ\nj/d57gM7Oztz596Zec99y3n37uW4ceNYpUoV1q5dm2FhYf94fKFY2AwePFi1XcyDiGf6/y4fPBA5\nfvw458+fr4raz5cvH9euXWv2gqOjo+Uq5ttvv2VUVBR37typUsBK8/H9+/dpZWVFjUbDbdu2mXA2\nODs7q3LhAQOx1NWrV+UxfvvtN7mSzp49u+oYw4cPlzwM2bNnZ2hoqAkjoiU/v3dACToVq8GstXsz\nT6+VakXYZDizVGzF3NXbM2tgdWps1VkwSvO7yNUPCwtTpfoJYCbGUnxnbJ5MC4j88ssv7NWrFxs1\nasRBgwbxxo0bPHLkCEeNGsWxY8dK5efv7y+tGFFRUSbxG5a4HMT/uXLlUp33woUL7NmzJ2vWrMmu\nXbvyzJkzciVSqVIlCTiGDx9OjUZD6xy+9K7Rns4lGtAxoCqzlGvBrDW606v/pregb6A6TsNr4Fbm\nazeFbtW70v6TUqpxVgKaoKAglbJNqwKuAFiW3EjGTVgFXF1dOXXqVLOuqrSaudTjw4cPMyEhQT4f\n/v7+7Nq169tq1H8qRq1Wy/r165t1+eTJk4f79u0zm4IbGBgouSuUsmnTJpP5z5MnD7dt28aQkBB6\neHjQxsaGrq6uDA0NNXuM9yXnz5/npEmTOHHixHSVYBDlBYzbyJEjTfYV2SMLFixQgRLxHhAA7+uv\nv/5LfReWwWnTphEwWAD0er0EhSK+JCQk5C8d/33LjRs3CBgyz5TgTwQmp5f6/Z/O9LMkwn3YqlUr\n1XYRb/a///3vvffhQ5APHohcuHBBVU5dWVdi48aNJhcs0tsqV66s2q70W4obNDk5mQkJCSZxFKVL\nl+aIESO4cuVKFT13kSJFpLLMlSuXirjo5MmTqkwNBwcHDh06VJJZ2djYqHycovaBWBWZe8Ebp3bm\nLFWHzqUaM1vDQczTdZF0DQj3gEerKczTYSazB49irnYzmLPtDLrX60e/qs1ok7sgy7bqxxyffk6b\n3P6Ezor2zq7U2jpy16Gf+fOtKAYEGSwqzZs357hx4/jrr7+SNDzUp06d4i+//MJt27Zz48aN3Lhx\nIy9fvizN2cYK1nibsBC4ubmxcePGqRKQiabRaGSpdPHCFrJ69WpTy4ZGI8ds9dr1bDNoCrOUb8mc\ndXoxR4uJFoNEszUcRDufT2nrWYhaW0dq7V1okzM/rbLmobWzuwokWcoeEW4nIbNnzyZgcP1otVpq\ntdp0UXJrNBrVOdzd3aU7AngLGnfs2GHCBaJsSiVvbj40Gg2nT59OvV5v1jJjZ2cny8ZPmDDB4nna\ntWsnLRXh4eEEDHwv33zzDXfv3m3Wevn7779L8F2rVi2OHTtWjo0yZVa0Pn36pMvX/vvvv7NPnz70\n9/dnQEAAhw4dqkr5fhfR6/Uy4yQ1UWaxtG/fnpGRkZwyZYq8N0W2nRARp3Dnzh3q9XoTLhYxJnFx\ncX+p38ISMmfOHJmSvGrVKglChVXrnw5S/afk9u3bBAyAW2m92Lp1K4G0S0sI+beAyO3bt+UzO2rU\nKB49elSS8dnY2MjA7f/v8sEDEfGSbN68OePj45mcnCxJkQICAkxeFMK/WK1aNdV2pUn6s88+k6BB\nuUr09fWVLxVfX1/evn1b1kM4dOiQHFBBlmTsN9br9bxw4QKPHDki2TNF7YScOXPy3Llzct+dO3dK\n0GPOl6kEXKL5+fmpGE81Vra0c3ajbd6idK/Thx6tpvLzidtYqO8K5mg+jjmaj2Oe3qstZ2oogIyS\nhTN31zB69vyeOZqPY5mB37PyuG306f3WIpO722LmbDeT2ZuOoGPRGoTGvKLr0qWLfPFaakJJKgmf\nRFu5ciUfPnxI6KxplcWDQZ83YdjhW5y/91c65SlIK/c8DO4+mH0WbGOlft8xe9ORzN1pPj1aTjSJ\nu8ndZRGzVGhFnaMbtfYutM7mRZ2jG3Pm9iTw1uKg1WotsnSmBh6srKz4008/kTRY2cQLX3Bo1KhR\nQ4JkS4DBUsufP78MvhPgOzIykseOHVNZ+sqUKcPmzZurOGICAwN55coVnjhxgmPGjJHuxsDAQD57\n9ozbt2+X+1pbWzM8PFzWcfH29par0tOnT7N3795s2bIlBw8eTMA0oHLfvn0ELBcmTElJ4YoVKyQz\nbq5cueSYxcfHS7Dn7OzMAQMGsGvXrvL5TIvX4datWzLA2fg5atiwIVu0aMHVq1enmYGRlJTE8ePH\ny/EYfgUAACAASURBVABqDw8PjhkzxuLvBE1/2bJlVYpPpOuPGzdOtb+oaTR79my5benSpfJeOHDg\nwN8KcBTMuG5ubiakgALgFihQIMOWo9Dr9dLa1759e96+fZtHjhyRz9PkyZPTdZx/C4iQb60ixi2j\ngr3/Qj54ICJS9MTqnDSwn4qVk3F9BuUKZfHixUxKSuLx48flS8rSijZHjhxMTEzk48ePJUgRSqRS\npUqqc6xYsYIA2KRJE4sDf+vWLbMpqblz52bPnj3Zrl07AgZypbCwMNatW9dsFVUPDw+VUlRaAcT/\nSsvJ9u3beezYMQJ/VmXVaGmfryTtPylNK9dctM0TYHBLlG9J10pt6VL2CzqXbEj7fCXpUrops9Xs\nwVzBw5m98RDmbPstPbsvoWfrKczeeBhdK7VhloqtmL3JcOZoMYGePb83cFp0nMs2U9ex4dhVdKve\nhVkqtqJTUB1WC25HjY09s7jnkGMslKSYh3nz5imuT0M770A6Fv2cTp/Wo39wP3q2nqxynVhqQWP3\n0LvbQuZoPo45235L97p9aZevpIFV1N6FVlZWLFWqlCzqJwCScKMJhVerVi0575Z4Jdzc3Ni3b1+Z\nEaJsPj4+0vpTsGBBaSXw8/Pj1q1b3zneQ9y3ItU0ICCAV69e5ZEjR6QfOnv27GZjNkJCQkyU2rNn\nz+T9Ym9vrwItIgYnOTlZWlvMVQbW6/USuPXv35+xsbG8ffu2rMZqLpZHr9fL/hq31q1bc8CAAfJ+\nVro0Fi1aRMAAVFMTkYpZqVIlHjt2jNu3bzcL8kTmkCVRxqko3WYtWrSQ+yQlJXHt2rVs1aqVnJc6\ndeqoFN+wYcMImMYOCNI7rVbLL774gp07d5bvstRSdtMrSUlJZu9L8b4IDg5OM9bmv5aDBw+adSMW\nKVLEpDiiJfk3gQhpqJLdrFkzlixZkiEhITx69Oi/du4PQT54ICI4HPbv3y8v6tGjR4b0Sa3WLLI3\nVxIbMETRm7vBhSIUWS/i5ff5559Lhb5o0SLJtSEsMh06dLA48GLlExAQYDb2QTTj7zw9PdOtpIQS\nVYIrR0fHNLklcufOzQ0bNjA8PJzNmzdn+fLl06wuK7739vZmaGioHDMH/0rM1XGuoVT84K3M+/UG\ns5aW3KELmafzPNaYtI0erab+WVK+A2ftPM9u3+3mJ6GzTWqkeA/ewVydv6Nb9a5sMHA2d//6kGNn\nL6ZjHn86FKxAh0KV6V6yLid+O1flpw8KCmJwcLAqYLRNmzbygVAq33r16pnwm4h7Qrld+NjFb1ML\nrNRqtWzUqBHv37/PxMREsyXKjcfVeG5EvIUl4KzcvnLlSv7xxx8cOXIka9asyRYtWnDbtm1mV9aJ\niYlcunSpiZuoadOmKjeKsJyI0vDGsnXrVhMmUsCQpmku20PwS9jb28tYJHNuGEBt/RDsqZ6enhaf\nteTkZDlXIpakd+/e8nhZsmTh3LlzJfhUBk0rRXAJ2dvbc9euXdTr9dy7d6+c89OnTzM+Pp5Vq1Y1\nOx9iBawsSx8eHq46h16v56hRo0wsbi1btvzH6k4lJydz3bp1bNKkCWvWrMkxY8YwMjJSxY+U0SUy\nMpJNmzZltmzZ6OPjw8GDB78Tf9S/DUQyJXX54IGISOvLnz8/t27dyoiICGmmbtCggdmL1uv1DAsL\nkyAmW7ZsHDhwoFyNVKhQgQcOHOD48eMJvF35CmAhzmm8yrSysmLLli3lSmvv3r1mz3/9+nUChkBL\nYbpNTdGXKFGCbdu2lYGWBQoUUIEJnU7HVq1aqUytxoDK1tbW4mq7SJEijIyMZHh4uDSLT5kyhUeO\nHGH16tVVL0UXFxeGh4czOjo6Tbp01djYKZSKVkcrt9yGImxVO7Lu2HXM3mQ4/UJnsc6Mg8zZZjo9\nuy2WRQO9Bmw2WDHq9aNjQFXqXHJQ55SVGht7FipUiJs3b2ZKSgo3bdpkMh9KBS7+FxkLSupre3t7\nuUqxZEpVNmWV2axZs8pKvJZWm0FBQVIhu7i4qMj4zKVrKude+blAgQK8evWqWeuYsbuuUKFC3LJl\nS5ovASEHDhwwAbpijkuWLCljnoTb0NbWNtWKsLt371ZllrVu3dpiwbQ+ffoQUKeQGt+/4v88efJI\nUCSCLpWU5saSkJBAwAAAX716Rb1er0qFdnNzI0lZw8fHx8fscQQxYWhoqGq7iOeaOHGiXIR4eHhw\n1qxZnD9/vgpQ+fj4yOepXLlyFjP87ty5wzlz5nD69Okql22m/DOSCUQylnzwQOTFixdmq4/myJEj\nXQQ5SUlJcmUoGCMFw19CQoJqtVq3bl3OnTs3Xebzrl27WvTliuqj/v7+Mp5EFLQD1HwRovn7+3Pa\ntGm0traWtMs//vijCQ25RqPh1KlT+fTpU86fP5+9e/c2ywuhbPb29jKPXwR9FShQwGzGhr29PR88\neGA2jVE0rVZrNkNCmakj+qr8u3LlShNrldbehRorW5M+iHESCjlbtmxSiU6cOFHGlBhfg7u7O3ft\n2sWUlBSmpKSYWBSUMSvu7u7ye5FZJOI9lL+pVKmStI5ZynKpWLGiVLYAOHfuXHk/iEDTEiVK0M/P\nz2LhPKGMU0uNFeC6dOnSDAoKYtGiRdm1a1eToEhjuXXrljy+g4MD/fz8VJ/FuCuL3g0cODDN54s0\nWFlSS6m/c+eOBFwCkKcVF1WjRg0V6Nu0aZPqmHq9nvHx8fIZFPdD7969+erVK9VxBRHckydPCBis\nWuZEFIQU1jMhgoBvypQpEsiLQF5SXUcKMMTatGvX7oOyQJCGMT127Bhnz57NVatWZZhq539FMoFI\nxpIPHoiQBqroKVOmyJdv//7936lUtZCYmBiZIfPNN98wOjo6XSyVgME0LF6iHh4eqQaUCcuLslWt\nWlXGJ6TWxItOkEslJyczPDycw4cP55QpU0x4TEhDKqxxUTJjMLV8+XKS5NGjR1Xfd+vWjdHR0SrA\nI/L402ppuXOULV++fNKSBRjAjDlAZq4Zu06eP3/OqKgosxV6RatTp44MDvX09OSAAQNULhnlWNet\nW5d6vZ6jR49+pyBVwGCZMgdO2rdvzz/++IOxsbFpjqdxv4xbWkATMIAJS35pvV5vlvDNyclJujiV\nPDeCs+evVoCOjY3l0aNHeebMGS5ZssRkfKytrWVKu7IdPHjQJK5Kp9Nx4sSJ8tivX7/m0KFDJSGe\nl5cXp0+fzj179si5c3Z2VrHsnj17Vs4vYGBn9vf3p52dHQMCArhgwQLq9XppybSysuLixYv56NEj\nLlu2TN5/V65cke8PZTZEQkKCPN+FCxfMFo7MSKLX63ngwAF27dqVISEhnDdvHu/cuaN6PgGDZe9d\nLG4ZSTKBSMaSjwKICNHr9Vy4cKEMlPPw8JCkN+kVUQ7euHl4eDB37twmyrVevXpy5ahMtRO1SIzl\n+vXrKhBgzsdvnNUglIJyn3ehQ46Pj1fxSuTNm5cbNmxQpXc2atSI0dHRskS76IcYO2O3R3qb8fW5\nu7tz3bp1kpG2UKFCJkDC2dmZly9fNhubYa5ZWVlx48aN8lwLFy7krVu3zGYWif2FEgMMK9krV67I\nlGGdTqc6d8WKFeVY/vbbb2nWltFoNFLpWYrhEH0QHDWpHS+1zCKlu0d5XAD86quv+PPPP0ulbi6L\njHybVgsYVvtbtmyRFiBxrypdQeXLl0+zCqxSEhMT+euvv/L27ducPHmy2dTsZs2aqVwYyjERQG3B\nggUyOPfrr7/mwoULVcyoSgp+5fyK469Zs8Ysv4qwHKU2B7179yZp2Y321VdfkXxLHT5mzBjZL/FO\nyZcvX7rH7L8SvV5vtmyBmBt3d3eGhoZKl5uNjc07vYsyimQCkYwl7x2IAMgLIALAFQCXAPT5c/sY\nAPcBnPuz1VX8ZiiAmwCuAahlfExLQGTIkCFmXxK1a9dOk21VKRs3bmSZMmVobW1NOzs72tvbW1zd\n79ixg8OHDycAVf0GSxUrRfn3Jk2ayGJcaSk14TMXyjEoKCjd15KUlCRN/8ZN6YvXarXSJSCUjqOj\no6yNk5ycbBKvoPxtp06dVGOk0Wg4cOBAmTXg7OzM/fv3MyEhgS9evJAxGwcOHOCjR4+4du1aNmnS\nhAA4aNAgrlu3zuy5lCDOxcVFBomOHz9eVblVZGik1Tp27Mjk5GQZXFq5cmXu2bOHz549U/FnrF27\nlsnJyTImQTQlSFDS4qcnzsRcU16Tsjk6OprEToh50mg0EnwrmyBRevPmjQRlly5dMrlHWrVqJX8z\ndOhQPn/+nPv27TNxAeXNm1elkAQIiImJ4ffff8/p06er0kv1ej3nz59vNm22aNGi8nq0Wi0vXLgg\nM0mMmxhXcQ3Fixc3C6hEGQY3NzcePnyY9+/fV92zIpaqf//+ZjNmBECys7PjunXrGBMTw5UrV8rn\n7tq1a9Tr9Vy6dClLlChBV1dXfvrppwwLC5P92bFjhzxeYGCgis3YuPpvRhRBb2Bvb8+RI0fyf//7\nnwTeWq2W9+7dI2mYW5HGrawY/qFIJhDJWPJvAJFcAIr/+b8zgOsACsMARAaY2b8wgPMAbAH4ArgF\nQEcLQOTx48dMSkri119/LR94a2trduzYkTt27JBxCbt375YX/eDBAx48eDBVv7mSKMu4KQP67O3t\nJUueaA4ODhYrK3722Weq/ly5coWTJ09WKVih0IODg82ulo394anJ//73P/lyTo8irFKlCkeMGCHN\n/Z9//jnv37/PX3/91cS9o2zmAgyNsx7y58/PDh06SOVdrFgxpqSk8PXr1xw8eLBUDnZ2dnKchKJN\nq986nU4VQGrcsmfPbpZGvXHjxvz6669NVuk6nc6kMJiyH0I5Xr9+XRZEVF5vamRif6UdOHCAKSkp\njIyMlHOTlutLackRQOXUqVMm94gSqJqLgQEMqcb9+vXj+fPnZVbI4MGDuXXrVpOxK1WqFB89eiQL\nUQKGAFMxfnZ2drxx44asXA0YAsHv37+vAghlypQxucYiRYpYLG4m2GqHDBnCpKQkaf0Q1iljt1rF\nihVVQCUkJIQA2KVLF9VxRWG7GTNmpOuZW7Jkiep5c3Z2Zt++fT8IxScsSkoeE6Ur+cGDB3K7cG3W\nr1//v+jq35JMIJKxJC0gYoW/KSQfAnj45/+vNBrNFQCeqfykEYB1JBMA3NFoNDcBlAbws7mdc+XK\nBQ8PDzx8+BAAYGVlhaSkJCxbtgyRkZFo1KgRli5dimXLlsHBwQGTJ0/G3r17kZKSAgAoWrQoxowZ\nAy8vL3nMN2/eoHfv3gCAunXrYufOnXBxcUFycjLi4+Px8OFDBAUF4dy5c3j9+jV27dql6lPTpk1x\n9epVsxdnbW0NANi2bRvc3d0BAGXKlIFWq5X7ODk5ISYmBocOHUL58uVx7Ngx6HQ6pKSkIFu2bMiV\nKxdOnz6dyhAC9+/fx5QpU3DixAkAQFxcHJydnfHq1SvVflZWVkhOToaDgwPCwsIwdOhQHDp0SH6/\nf/9+eHqaTpe9vT1ev34tP4vjuru7IzY2FgkJCYiPj4efnx+aN2+OpUuX4ubNm7h58yYAwM/PDxMm\nTMCZM2fQr18/HD16VB7rzZs3+Omnn+RnGgCqiWg0Guh0OiQnJyMlJQVXrlyxOB5Pnz7F06dPTbZv\n2bLF7P4pKSm4ceOG/Ozh4YHHjx/Lzw4ODnj58iXmzJmD4sWLAwDi4+Pl93fv3rXYl7TE0dER8fHx\nqus+efIknJ2dodFo0KNHD0ycOFHewwBgY2ODKlWqwNnZGT/++CMAw1xERkYiPDwc165dg4uLCxIS\nEuS9k5SUhOnTpyMiIkIehySSk5NN+nTt2jVcu3YNCxcuRNeuXREREYEtW7ZgxowZSEpKQmBgIPz8\n/BAREYHIyEjUr18f9+7dAwAMHjwYZcuWRZMmTWBtbY03b95gyJAhqvvq0KFDePDgAYYMGYLRo0fL\nawaArFmzolGjRihevDhKly5tcS6fPHkCwDD2M2bMwIULF5ArVy54eXnh5MmT6NatGxYuXAiS6NCh\nA3r16gUAWLp0KRYsWCDv++joaNXz9eLFC3nctJ47AChWrBi2bduG8+fPQ6/Xo1ixYnB0dASAdP3+\nv5Q7d+4AMDzfoq8ajUZ+v2PHDnz66acAgHXr1gEA7OzsMvx1WZIPtd8fm/j5+aX6vTbVb99RNBqN\nD4BPAZz8c9OXGo3mgkajWarRaNz+3OYJ4HfFz/5AKsBFo9FIEAIAJUuWxIYNG5A9e3b8+uuvUiFo\nNBqMGTNGgoaiRYvC2dkZFy9eRM+ePREXFyePcebMGbx69QoFCxZElSpVABhehuXLlwcA6PV6nDt3\nzqQvWq0WTZs2lS84c9KgQQMAQFhYGObMmYNNmzahe/fuiI+PR2BgIAoVKoSYmBgAwLNnz3Ds2DEA\nBsWo1WoxcOBAWFmljg9jY2PRo0cPnDhxQgKcxMREExACAMnJybC2tkZ8fDymT5+Oe/fuwdfXF8OG\nDUPVqlXl73U6HWxsbAAAvr6+WL58ucnNY2NjA41Gg4SEBAAG0PXgwQOcO3cO8+fPx6xZszB06FDM\nnDkTkydPhqurK86dO4ejR4/C2dkZixcvTnXslKLT6SwqTfG9sTg5Oak+Z82aFRMmTICHh4dqe6NG\njVCvXj3VtqSkJNXnly9fAgDmzZuH0NDQVPvq7OxsMmcBAQHYt2+f2bm0sbExAV/Dhg1DmzZtcPPm\nTQlya9WqBW9vbwBAtmzZkDdvXjx69Ej+ZufOnahXrx7Gjh0LAOjQoQPs7OwAGJR2586dsWnTJpBU\nKRtzUqlSJVSqVAnx8fFYsWIFAAP4TEpKwueff46wsDAMHjwYq1evhqOjI06fPo0nT57A3d0dwcHB\ncHJygkajgV6vBwCcP38eDRo0kP15+PAhRo4ciRkzZgAAvLy80LVrV0ydOhXh4eHo2bMnypYtqwLs\nxlK5cmUAwObNm7Fjxw4Ahnv11KlT0Ol0qF27thzXrFmzyt81btwYAPD8+XMAQHh4OI4cOYLk5GRE\nRERg7969ACCf//SInZ0dypQpg3LlykkQ8iFIgQIFABgAupirZ8+eye/Hjh0rFywbN26ERqOR45cp\nmfLexJyZ5K80AE4AzgBo+udnDwA6GMDORABL/9w+H0Abxe+WAAhWHktpxpk+fbqJuXzevHkybkPE\nPSxbtoyAwZUiCnbFxMTIYFAl3a5IYS1btqzZIDZPT0+Vmbdw4cKcPXt2qoW3fvvtN06bNo3Dhw+X\nsRDKljdvXt64cYMvXrzggAEDmDNnTup0Otrb2zNLliysW7eupJFPS4SvvWjRotI8rgzcFGy0Io5D\nZJdotVrqdDru3bvXJC3YuDk4OHD58uVmYxPMtZw5c/LChQts27at9Lk7OjrKWI5+/frJ/lsqkGbc\nhKlfq9XKeAlnZ2d5fWm19evXk6TMsEirlSlTRqZYW8qeEeMh+mBcD0i0mjVrSuru9DSlW0NsW7Zs\nGWvUqGHiStHpdKrskpw5c3LWrFkyjkFZ/C+9zc3NjQcOHFC5HIRbw7gIogh0Fc+biOVSBpIWKFCA\n8+bNMxu4WrFixXSVuDcWvV4vGYmN29ixY6nX66WrRxmvISphf/LJJ9INY9yMuUPeVT4UV8DFixfl\nO7NgwYKsVq2avNeNs7N0Ot0HS1P+oczH/xf5V7JmAFgD2AOgn4XvfQD8yreBqkMV3+0BUE65v7LT\na9askQ+GuXokgCEOYNKkSfJhatq0KcPDw6nX62VEe+fOneWgREVFqQiULDGROjs788SJE2kO8syZ\nM00Ul7+/Pzt16sTWrVtz7ty5vHfvHn///Xc+evSIkydPZuPGjdmhQwfu27cv3bUlLl26JMthC+WV\nJUsWiwyV06ZN46lTp1SZG+7u7jJDJ0uWLGkWnzOXTin+79mzJ2/cuCFTP1NLM+3WrZvqWkQg7/jx\n4zly5Ei2bduWo0aNkuRRLi4ukmq9V69eEog0aNBA1u8xji8Q6ajiswjEVdbncXNzo7e3twywVM7b\nqVOnmJycbLYInDiu+CvATceOHU1igFJrGo2GAQEB1Gg01Ol0qlgZ5T6dO3c2C4YKFizIu3fvMjIy\nkrt37+b169dVdVD0er0MIAYMKcrffvutyT0iwI2lzKUSJUrILDElg/Dz588lWBGBmtWrV+f+/fs5\nY8YMs32uU6cOt27dysWLF/PkyZN/q5ZKcnIy586dq4rvadiwIffs2aMqUJk7d27OmDGDU6dOlXM1\nfvx4JiUlcfLkyRII+/j4cPr06X85VVnIh6T4duzYYRKE3bNnT8bFxXH9+vUcOHAgp0yZ8pcoEjKK\nfEjz8f9B/o1gVQ2AFQBmGW3Ppfi/LwxxIQAQAHWw6m2kEqwaHR0tX/4VKlTglClTVKvpHj16cMOG\nDWZfgIMGDWKPHj0IgAMGDFANjPKlZS7C3s3NjSdPnkxzgAV1NWAozDdkyBCp5Bo2bMg7d+6wYcOG\nFgPqxDWk9XKOioqSx01P6XidTqcizmrVqlWqVPOiWQI1/v7+vHr1qur8fn5+JA0F0dI6ro2NDZct\nW8bff/+dc+bMkRUrFyxYwB9//JHHjh0zIUQTTaksK1euLIMvU7PW6HQ6GXgnghzF9tGjR8t6QkoA\ncfbsWZJvV9DG94NY8SutDY0aNbKYRmypiXtA/E6r1XL8+PHyumrVqiWJ9r766itev36dmzdvlgp1\n/fr1Fl+0ly5dIvA248bFxYUxMTEqyyLwlrJeeT8KXhWdTsf79+/z8uXL8tlr0KABR4wYIQnPypUr\nx4sXL5oFn76+vqxRowYbN27M1atXqwrj/ZMimFCVTaPRqICnaDVr1jRJ8/+74EMpH5riS0xM5IED\nB7hlyxZVgOrHIh/afHzs8m8AkYp/PuwXoEjVBbASwMU/t2+DGpgMhyFb5hqAOsbHVHZ6woQJFrMq\nunXrxvj4eKnABKAICAiQL1Dxol2/fr1K2YuIcKHkbG1t2aRJE6kMjMu6WxKxeh48eDAvXLjAChUq\nqPqo5H9QrtZbtWrFMWPGSEU4btw4fvbZZ7S2tmaWLFno7+/PmjVrctSoUbx//z6nTp1KwOA+EMpA\nq9VKha7MSDEHdgICAlTbs2bNapbhc8yYMSaslxqNhlu2bJGMlQKIeHt7kzS4AsS+RYoUYVRUFH//\n/XfJRpoaWDC3PWvWrCZzniVLFlV/dTqdClh5eHiY8HE4OjqyRo0aZunSlU0o/WrVqkmgJL4rV66c\n5I4QY2wJrKXWqlWrxrCwMBPLiZWVlSSbE4BJ1GIpUKCA6p6dOXMmAUMBNksvWlHwMDAwUFoQS5Uq\npWJ9Nae8lZ/79Okjj7dixQqT+6RAgQK8c+cOSfLevXscMGAAS5UqxSpVqvC7775TlW9/33L48GG2\nadOGlStXZpcuXXj27FkmJCRwzZo1bNeuHTt27MjNmzf/o6DDnGQqvowlmfORseSDJzQz9+LMnj07\nlyxZQr1eL+M9goKCuGfPnlTLqpcoUULGj4h6MspmbKZu165dmoWoBPBYt26dBEROTk6ql7enp6dU\nEEKJubq6Mi4uLl18FK6urhIgiZVtWmRgefPm5Zw5c/jDDz+omD0tWR1E27Jli0xXVsYLtGrViq9f\nv1a5x0JCQnjr1i0V+AoMDOSECRN48eJFXrx4UW7v0KEDS5YsSVdXV5UrLGvWrCr3j6DXjo2NTdNt\nZK7lyJGDs2bNYq1atVTby5Qpw7FjxzJfvnwSSNnZ2TE0NJQXLlywGEeydetWPn782MSF4uPjI9NB\n7ezsJHV99erVzcaNtGvXjqQhtVxp0frss8/4ww8/cMSIEXJOZ8+eLe9XpYiYkyZNmlh80b548ULe\nY4sXLzZLlpYjRw7WqlWLtWrVUlG629nZsX///iYWjAcPHnDGjBkcOnQof/jhB5UrKFMMkqn4MpZk\nzkfGko8CiGg0GgYHB7NDhw4SaIwYMYLk25dz2bJlGRUVxVu3bnHAgAFytazRaFi5cmWpgHPnzs3d\nu3erXszmVrgCSFSoUIFDhgzh9u3b5arq9evXvHz5Mh89eiTrUAh/eZUqVXj27FnVat/BwUEW3AoK\nCpJ8Fxs3bpSrXACylLmNjY3sr/CFi1W9cCnpdDq6urqmSkmePXt2Pnv2jJs3b5bbBM21RqNho0aN\npDneGIzZ29tLBlElXfa7gAIl70dUVBS3bNli1rqlPG6pUqXkzStiRLRaLYcNG8YWLVpYDA4FDHwH\nytX41atXuX37dp4/f171ULx584Z3795VlYO/fv06v/jiC3n9AgRlz56dbdu2lcXhHB0duWXLFiYn\nJ3P16tUEDHwwe/fuJWCwFohKwEogJ6wMer1eggNz1O6DBw9WlSJYunQpU1JSeOvWLUk8NW/evFRf\ntIMHD5bHK1KkiLy/lbFCwcHBHDlypJz/EiVKZHhq8owsmYovY0nmfGQs+SiAiJJoSLAruru7c/Xq\n1aqXvbW1NYcPHy6tDwA4adIkkoYVtsgCEMF8oaGhZuuALF68mF26dDHZXqpUKQ4dOlR1znLlyqmU\na/Xq1aX5Xbl99+7dUsmZAw82NjaS/XP06NGSebRKlSqplpFPq1WtWpWHDh2Sn2vUqCGLe6WnpeaG\n0Gg0dHBwSLN/+fLl45UrV0wUrznrla2tLUkyJSVFxoCI6qmPHz+W+7Vs2ZL79+/ngAEDVH1NK9ZG\nr9czISHB4n4pKSlMSkri/fv3ZcFC0fLmzauKGxLFDfPkycOXL19KIjwRf6FkHD127Bj1er2sxpwr\nVy7evn2bI0aMYN26ddmhQwdGRETIY4vga0BNJufv789Xr16l+qJNTk7mkCFDVHMXFBTE06dPc+HC\nhSaAsnDhwqlmhGVK2pKp+DKWZM5HxpKPAogIfzRpUCRK6mgAJjEAYruSwpykXKmK/U+fPs03b95I\nlkxx3MWLF6uO161bN5OVuLe3twQWdnZ2abKDpiddVSjqtWvXSirmatWqyayU1GqSGAMHpbukVqRP\nsgAAIABJREFUUqVKEuwAhrTfhg0bSiDg4eFhthqq8XgCBkvMsGHDJPgQNWXepQkgt23bNrMukQYN\nGqgAoqgCu3DhQrnt22+/ZWBgIB0cHFSK+sKFC9y0aZMsdCYkJSWFM2bMkGm3wqLUpUsX7t+/n1On\nTuWECRN44sQJnj17lp07d2aZMmVYpUoV9unThzt27DBxSaSkpEgrRVBQELt06WIx7sXd3V0VRDln\nzhyzD+wff/zB8PBwnjx5kvPnz5f3po2NDdu0acNHjx6RTN+L9sWLFzx69Ch//fVX1Vjcu3eP33zz\nDYcMGcKNGzdmulr+AclUfBlLMucjY8lHAUQWLVpE0lDcTVl4DjDQNcfHx7Nnz54mcRP58uVTBan1\n7NmTwNuU1BkzZvDNmzcyG0LQX9evX18qYJ1Ox6ioKJ49e1Yed9WqVZw0aZJF8OHg4MAvv/wy1eqw\nqTV3d3fpCujduze1Wi2trKzkSjZfvnz09fVNd9E4AZZ8fX1NVsPFixeXWSD+/v4msRBKECKCT0NC\nQrht2zYCb105VlZWPHfuHIODg9OkJhdgKWfOnGaLlCmbt7c3o6OjSVIG7FpqxuctXbo0b9++TfJt\nDaD0NHPzKlyBxnLx4kUTkKrRaOjp6akqsqec2xkzZkhg8PLlSz558oRxcXFs3769arzFvo8ePTLJ\n+Mh80WYsyZyPjCWZ85Gx5KMAIkLhmVO82bJl44ABA0wKb4nP9evX54YNGzhgwAD5kjdOZVQq5wIF\nCqhqzTRr1owkuWfPHrlNkCopy6dbitWws7OTx3dzc5NWjSFDhkgFZalMvL29vTyuiB8x7q+y+fr6\nmtRPsdRsbGzYoEEDadFwdXWlv7+/SYDojz/+KP8XRG3e3t6yZLqy7dy5k4cOHTI5hjnFbm5b1apV\nWadOHZPr8/Ly4qlTp0wqJzs6OppYw5ycnFi3bl1VjM3Vq1dldhFgCKidOXOmKmg2T548KndcYGAg\nIyIiOH78eDlPlgodvnr1imFhYfzqq684adIkyXNifJ3FihXjy5cvSRpiUurXr29SXdfcfRQUFMSo\nqCjVOTNftBlLMucjY0nmfGQs+WiAiLK5u7ubVbhKE33BggXNBgNOnDiREydOTJeyzpYtm2SA/P77\n783uY45HQaPRSDeIjY2NVGSFChVi2bJlCUAVULhz506LReusra3ZvXt3GRj5rk2pCLVarQpkpafN\nmjVLum3E+AYEBEh+FqXiNAcu0kv0NX/+fMbFxUnrgr+/P3v37i3jRFILylW2jh07MjIykk+fPpX3\niAAYwhIjSOqUlgytVqsiz3N1dZXWNEGyNmzYsDQfuGfPnslrDgsLY1JSEk+dOiXPtX79et6/f18C\nZZ1OZxKHo9FoGBISonLnNW/eXHWezBdtxpLM+chYkjkfGUs+CiCirH4rlLpy1QkYmFOFD1682L/7\n7jsOGzaMDRo0YJcuXXj8+HFGR0fL2IiRI0dyyJAhDAkJkSvo+vXrs3HjxvK4NWrUYIcOHcxaY1JT\nwpUqVWK5cuUsKkyxGtdoNPL6ChUqJMuMFy9enPv37+fjx4+p1+vTpGRPq4n+W3KbWFtbmz1HoUKF\nTNw1AjTpdDqVWyu181sKaNVqtdL1JoBA0aJFZdq04HsBDGnQ5sjDBDmZ8fkEH4cYXzHmV69eJUl5\nn4i+ixgiMUbPnj0jSZli3atXrzQfOJGhVLlyZdX2adOmSaAkQGjZsmXZq1cvk2saOXIkSXLVqlWy\nfzqdjk+ePJHHy3zRZizJnI+MJZnzkbHkgwci1atXJ0m5Ghepr4JEyVgBubu7S26E4OBgkwERvCPK\nEuokOWPGDAJv+R4WLlxolvDrrzZz1hllc3Jy4vbt22U6pUajYZkyZbhlyxbpBkkPM6pyHJRWHGVN\nHWOOjb/S8ubNyy1btvDx48fpCqK11EqWLMnJkyfz4cOHHDNmDAGD20qIkrdk/Pjx/PXXX1V9+OOP\nP9iiRQu5zcPDw8TVNXr0aBUAq1evnirbBjDEk1y+fFl+zpIlC5OTk/nw4UMJcI1rrpgTETtTtmxZ\n1XaRBRMaGirvW2P6fNGGDh1K8m0arnA/nTt3Th4v80WbsSRzPjKWZM5HxpIPHog0bdqUJOVqXWRZ\n9OnTR7KaajQaizTbjRo1UnFLCItD6dKlVQMlVr0dO3bkgwcPVPU6lK1IkSJmV+CiBQcHm3WzVKtW\nTWUh0Wq1KrdF7ty5LcZ+jBs3jgBkoTytVsvatWubpbIWzdnZmbVr1zb7nUhjfpdmZ2fHiRMnct26\ndVy+fDmfPHnC169fc+nSpdIF4unpySZNmnDp0qWyloy5Zu46HR0dJTgoVaqUdIsowWCbNm0YFRUl\nuVvMtSZNmvD777+XxQ41Gg0fPnwoi9lZai4uLmzfvr0KsBQpUkRaUQoXLpwuxtCYmBgJOqdMmcKn\nT59y586d0uK2detWVUZTgQIFePjwYRV4cnBw4KBBg+Q4CVefCNolM1+0GU3e93xcu3aNX3/9NatX\nr87WrVvzwIED7+1cH4NkPh8ZSz54ICIUgrFFIb0VVQGwf//+ckBevXolLQsTJkzg48ePuXPnTnm8\nLVu2SBbT3Llzq9w0ANi9e3eSZMeOHc2eS0niJZpQbl5eXpI1MzUXyeLFi/ny5UuOHz+egCEORXBT\nCBDk4eFhwsOh1Wpl39PTjH9vrmKrVqtllSpVuHr1atarV0+13Rx1ep06dXjx4kUOGDDAYjFBZbOx\nsZGAydXVVcbclC1b1mylVRcXF86dO1f2QShqwHLxwsTEROr1eq5YscIkTVkQhynbJ598IgGQRqNh\n/fr1ef/+/XQ9cL/88ovFCq+1a9dmcnKyisdl9OjRvHjxImvUqGH2N+KaOnXqpDrPf/WivX//Ps+d\nO8fY2Nh//dwZWd7nfOzatcvsvS1ceJliKplAJGPJRwFELDVLAZ4AVArHycmJe/fuZa9evdipUyeL\npcQLFSok04OdnZ35+PFjRkREmOwXEhJikpqbK1cui4pw1apVLF68OAGomEzr1KnDPXv28Ntvv5XA\npFOnTty0aRMHDBjAsWPHSjfTsGHD5O9Si8fw8fFJleZe2YwtE8rgTeNzpAacJk6cqPo+rXgR4+Pe\nvHlTkoeNGDHCbACws7OzTGkWAKRv375MTEyUIO2HH37g8OHD2bx5c3bq1ImAwdKSkpIiHwjholq+\nfDmfPn1Kkty+fTsBAygShGXR0dE8ffp0ugFIVFSUyT1ha2tLBwcHfvLJJ5wwYYK0qMTGxpp11dna\n2pqNRapbty5fvXqlOt+//aK9ffu2Ciw5OTlx8ODB762g3Ycm72s+3rx5IwObmzdvzh07dnDUqFHy\neROFGjNFLZlAJGPJRwVEtFotu3fvznXr1rFZs2Yy5VGZdWCcxmupeXl5sWzZsnR2dma2bNlMsjLc\n3d356tUrvnnzJs36LOZa1qxZ2b59e/lZKEvR3NzcVNwQgk/DUpbJoUOHuGHDBrNuoeDgYF67ds2i\nO+ld+m8MYipUqKACdXZ2dmzdurVqvGbOnMm1a9eagBU7OzuLbiDl7zt27MjevXsTAL/55hu+fPlS\nul98fHwkiFM2T09PPn/+nOTbWApfX1+uWLGC69atk7FEoaGhqgdCuPDu3bsnt6WkpMhx/6s050JJ\nZ8mShc2bN5duM1dXV1WQqRBR4M7e3p6enp5s2bIlu3btKu/NsLAwzpo1y+LL9N980cbExEhiNTs7\nOwkIAQPPTaa8v/kIDw8nYMhUU5LSffnllwTU1t5MeSuZQCRjyQcPRETwn2hLly5NteaJpdW4Tqdj\n+fLl2bhxYxkkKGjCxT6NGzdm8+bN5ee2bduSfJu9YKl5enpKhk3R8ubNy4SEBI4YMUJl/hduoSJF\niqgmSihiwBALMnToUFWZ+7x583Ls2LF8+fKlJFdzc3OT19u2bVuGhoaa9C0sLMyE1VUZuAq8DQA2\nbvny5ePTp08lfwgATps2jc+fP1eNdYECBUhSldI7depUmfETFBRk9vjC7eXm5iYZT3fu3EmS0i01\ncOBAvn79mkuWLGH58uVVMSOFCxdmeHg4Y2JizAIef39/mX4tpGrVqgQMga9CBJ1+1qxZGRAQQI1G\nw7x583LcuHFpFj0kyQsXLsi5/eOPP0iSSUlJMtvom2++MfnNkydP5DWL+1P8v379+jTP+W++aAV/\nS2BgoLQiHTx4UBLtPXz48F/pR0aW9zUfIm2/UaNGqu1iToxddplikEwgkrHkgwciiYmJZoHH38lo\nsbW1lSyqDRo0IKBmzlRaFnr16iVTVM21atWq8fLly3z69KmsgyMUdPv27Xnu3DkuX75cxl8sWbJE\nApMtW7aQNJjqBb9IWq106dIyc8Td3Z1z5syxyLHh4OAg91WOobHlonDhwpKYTQl8fvrpJ+r1elll\nVvRfr9erMj7c3Nyo1+uleyV//vyqm1C4SQCwX79+MrZEWK/EeAUEBMgg1R9++IGAgQ8mPj6eR44c\nUV2DcG3odDoePHiQcXFxnD9/PmvVqsXPP/+c3377LWNiYkweCBGsDBisPTVr1kzVldSwYcM069es\nXbtWAiulLFq0iMDbTCxjuXv3Llu1aiXv5RIlSnDbtm2pnkvIv/miFVlJixcvVm0XoC69ff6Y5X3N\nh8iYs7Ozk8Ubnz9/LhcTIvX9YxW9Xs+oqCg+efLkndqVK1d45cqVd/5dZvv7LSoqyuSdmWGBCIDa\nAK4BuAlgiPI7ZaeVloZ3iT0w14KCglScJMDb4NJTp06RJCMiIqQZWtm0Wi2bNm3KU6dO8dChQ3KV\nL9xDGo2GdevWlRkk5nz9tWvXZlJSkqyACxhW7cog0axZs6oCccV5ChcuLPs1e/ZsOS49evTgzz//\nzC5dusiYmUaNGpm9fmVwqfg/rYBSf39/Fa1+/fr1efDgQVXmh6Ojo4qq3dvbW8Y0PHr0SOXaadmy\nJTds2GDCvlq0aFH+9ttv8sZNSEiQYMfHx0dFxObl5cXY2FhpRapSpco7vdzmz5+vitGwsrKSVYaX\nLFnCly9fctWqVXJe0spQEEUFvby8VJk1wr2kTEc2J0lJSSYU7mnJvwlEOnfuTMAQWCskJSVF3uvK\nYn3/X+V9zocAglqtlqVKlZJWVR8fH5PYoY9NoqKi3vnZIA2Lu8yA6v9GXr9+bcIEnSGBCAAdgFsA\n8gGwAXAeQGHxfXqDVcXDmV4g4uTkxPj4eFkEzs7OTlpExo4dyytXrqQZ6KnVajlv3jyVn9zT01OV\nZQGAO3bsYOvWrenn58fSpUtzzpw50syfkpLCsWPHqpTxp59+Ksu0CxdH9uzZZdxAx44dJeFX1apV\nuXPnTrMBpAULFuTz589VVh3RJ3OkZhMnTuS8efPMxpek5gIz19zc3CSIypEjB+vXry+vMSAgINWx\n9fDwUAERkrx8+bIJg66vry8vXbokb24xJ2lZLYzlxYsX/PHHH7lu3TqZyVSnTh2OHDlSBsuK6+/R\no0eqx1Iq5TJlynDOnDmykrJWq5UEav+k/JtAZN++fQQMFrbZs2fzp59+kqnznp6emQGrfL/zERcX\nx06dOqmex8qVK/PWrVvv5XwZSczFV6VHMoHIfyvG85ZRgUg5AHsUn4cCGCo+GwMRnU7HadOmmcQa\n2NraqvzsymYpy6N8+fISvBQrVoy7d++WylpkqAhQoQzytLe3Z8uWLeVnodRtbW05duxYzp8/XwbN\n5suXj6Qh4j08PJxLly7l+PHj2alTJ/br149nzpwhaXjBnD59mjdu3OC2bdtM3E0CQGi1WkZGRkq3\nQoUKFUiSR44cYa1atejg4MAcOXKwd+/e0od/9erVNAN3bWxsOGrUKH799deqc3/55ZcmAa4ODg4m\nsSWAgdF22LBh7NGjB7dt28YrV66YzFPVqlX58OFDRkZGqtwx1atX56ZNm6RbyJy/Ozk5mbt375YW\njF9++UV+d+3aNQkw3xWIKGX58uUEoLqXlFapXLlypalsf/nlFxMuGyVr7D8t/yYQ0ev1ZuOPbGxs\nuGvXrn+lDxld/o35ePz4MY8cOcIbN2681/NkJMkEIh+mvCsQ0dAABP5V0Wg0zQDUJhn65+e2AMqQ\n/BIAYmJiZKdcXV1RokQJLFy4EE+fPkXdunXlcaysrJCSkoK/eg1dunRB165dsXz5cixYsAB6vV5+\nlytXLjx8+BBZsmSBvb09Hj16BG9vb9y9e1fuY2dnhzdv3pgct0SJEmjbti3GjRuH6Ohos+fu3Lkz\nunfvDgC4d+8eWrZsiaSkJDg5OSE2NlY5Vhg8eDBI4vvvv8ejR48QGhqKbt26pXl9UVFR2LhxI375\n5RdoNBpYWVnh8ePHSEhIQFxcHF6+fGnyGycnJ+zfvx9JSUk4dOgQrl69itWrVyNXrlzYunUrzp49\ni1OnTsHKygqenp6YO3cuoqKi5O99fX3x7bff4uXLl3j8+DG8vLyQP39+AIBer0eFChWQnJyM8PBw\n5MiRAwBw+/ZttGjRAlmyZMH+/fvNXsuUKVPw448/ws/PD71794ZWq8X8+fNx5coVNGzYECNHjkxz\nPFIbp3r16kGv10On02H69OnQarUYOnQo4uPjAQDTp0/HZ599lupxXr16hZ07d+LGjRtwd3dHvXr1\n4OXl9Zf79b7l5s2b2LVrF2JiYlCoUCHUrl0bjo6OZvcliQMHDiA8PBzR0dEoWLAgWrRogU8++eRf\n7nWm/H8SJycn5M2b97/uRqa8o/z+++8qPebn5yf/z5Ili8Z4//8KiHwBoJYREClNsjegBiI5cuRA\nYmIiQkNDUa1aNbRu3fovAw8bGxskJiYCAGxtbbFp0yapDC9duoQuXbogKSlJ9RsfHx/cv39fbndw\ncJDKCQDq1asHAIiLi0NycjKOHj2KChUqIDIyEomJiRKsaDQakES+fPlw9+5dpKSkYMGCBShZsiRm\nzpyJNWvWoEaNGpg4cSKuXbuGsLAwHD582Ox1FCtWDDNmzECWLFnSfe2JiYkYM2YM9u3bJ7fpdDoU\nK1YMRYsWRbly5dCrVy9oNBrs2LED2bJlAwD89NNPGDBgAPz8/LBmzRr529jYWDRu3BgxMTHIly8f\ngoKCcOzYMTx+/BiffPIJ1qxZA61Wq+pDSkoKypcvD71ejwMHDsDFxQUAcP/+fTRu3BhOTk6IiIgw\n2/9nz54hNDQUf/zxh2p7rly5sHjxYjmPf1X69euHI0eOmGz38fHBb7/9hhYtWmDAgAF/6xzmJC4u\nDrt378bVq1fh5uaGunXrwsfH5x8/j7EsX74c8+fPV23z8PDA/Pnz4e3t/d7PnymZkh7JCEDExcUF\nAQEB8vO6devw7NkzrFmzBtOnT8eqVatw9uxZzJgxA9u3b0f+/PlRqFCh/7DH/728KxDJ8K4Zc/Vk\n/onWqlUrlelIyUhqbW1tls+jbt26rF+/vnRV4E/z9N69e9mhQwfpwxXpsIKJ1MXFhYcPH6ZWq6W1\ntTX79+9PwEBZTlJm5WzatEnVJ2PuEY1GI/vVoEGDd7GUsV+/frLf7dq1UwXt7t27lyRlkGvp0qW5\ndetWLl++XJKcKfkibty4IevVeHl5yZTVly9fyj5bCvAUfBtt27blixcvGBUVJdODv/jii1SvISoq\niqNHj2aJEiVYvHhxjhgx4i+bbo1FpEk6OjpSp9PRy8uLEyZMkAGxgwYN+kfOo5RLly6pSOTEHM+a\nNSvN3/4dV8Dx48el66hbt26cM2eOdKcZlz7IlPRJZrro+5GM4JpxdHRM9ftly5bJgpjt27fnDz/8\n8E7H/xhjrD6UGBErALcB+OJtsGqA+N44RsTR0VGV3dGzZ09VSqhx8/Pzk0DBysqKO3fu5O7du/nl\nl1/KbI/WrVvLQRIprs7OzqxZs6bF44rsDxsbG1XWiKUmsg3y58/PZcuWyQwdUYlVFPQTAal9+vSR\nfbpz545KOSnjFwTguXnzZrpuitevX8tI+59//lluF/VXBKi5ffu2KjtFtE8//ZRHjhwhSX7//fcm\n8Te2trZcu3YtybepupMnT+bx48e5b98+3rlzR57zxIkTci51Op2Mg3FycuLFixfTdT3vQ4yrMl++\nfJmLFi2SwE8wrv5TotfrZT2c4sWLc/bs2aqyAcpYGHPydxSfiPcYMGCA3Pby5UuZdfVfzsOHKplA\n5P1IRgUiERERrFevHsm3QOTYsWN0c3Ojj48PAwMDefPmTd68eZO1atVi8eLFWbFiRV65coWkAbD0\n7duXVapUYb9+/f6RfmYk+SCACA1gpC6A6zBkzwxXfqfstDIN1tvbm6tWrSJpeJGLQnjOzs6sXLmy\nWQZRV1dXXr16VVXFVSi+Q4cOkXxbur1OnTocOnQoAUMarTIzRql0LQEPKysrVfEyS+nGAux8/fXX\nJA0vMfFd69atOXHiRFXgY1hYGMm3lV1FsK0g/0pLbt++TcBA4a6U8+fPEzBk2ihvoLFjx7Jy5cqs\nWbMmFy5cyGPHjjEyMpJ3796VIMgcvX7fvn1NVviiNWrUiM+ePSNJ/vzzz5KDQqPRsHbt2mkq3n9D\nvvvuO7N979at2z9+LjHnOXLkYFxcnNzes2dPEwuUpd//VcUnLHUbN25UbRfZZMJClinpl0wg8n7E\nWKE1X3g8Xa3Zd0fY7Lsjae6XHtFqtQwMDGRgYKDkCjIHREhTi0i1atV4/fp1koZFWNWqVeV+9erV\nk7xJH5u8KxCxwn8kJHcC2JnWfklJSXBzc8O+ffsQFBQEnU4HADhy5AguXbqE3Llz49q1a3BycgJJ\nVKtWDYcOHULv3r0RGRmJEydOoFixYkhMTISVlRWSk5Oh0WgQGxuLBg0a4Pr169Inf/LkSTx58gQA\nsGbNGqxZswbXr19HtmzZZEBmQkICrK2tkSdPHty5c0f2U6PR4NKlSyhQoAC++OILbNy40WIsy969\ne2FnZ4eePXsCAEqWLInZs2ejb9++WL16tcn+Z8+eBQA0aNAApUqVQmRkJACk23eaI0cO2Nra4sGD\nB7h8+TIKFy4MADhw4AAAqAIqs2fPjlGjRmHUqFFy2+nTpwEAq1atQnJyMvz9/XH16lX5vRjXmTNn\nWuzD1q1b0bRpU0RERKBs2bI4ePCgjJ2xtbVN13W8b+nRowfy58+POXPm4PLly/D09ERoaCjatm37\nj5/r4cOHAIDAwEA4ODjI7eXLl8d3332HBw8e/OPnFFKkSBGEh4dj5cqVaNKkCbRaLa5du4YTJ05A\nq9X+v/dvZ0qmKMXe3h7nzp1759/Fxsbi+PHj+OKLL+S2hIQE+f8XX3wh9dn/d/nPgEh6pXTp0jh1\n6hROnz6NEiVKyO0CBHz22WdwcnICYAADwcHBOHToEN68eYNFixahSpUqeP78OQAgOTkZLi4uWLdu\nHWbOnIl9+/Zh2bJlGDJkCMqUKYOTJ0/KQNThw4fjzJkzAKDKCgEM4OjOnTuwtbWVNxZJ2NnZAQBC\nQkKwcePGVK9r+fLlqgCer776CvXq1cOaNWsQHR2NU6dO4fjx49BoNFiwYAGio6MREBCAX375BYBB\nmRQpUiTVc/z666/4/vvv8fjxYwQGBuLUqVOoWrUqOnfujKdPn2L58uUAkK4MHAB49OgRAEOWDwBM\nmjQJEyZMUAXvCsmXLx8iIiIwaNAgrF+/HjY2Nvjpp59w4sQJlCtXDgDkeGUkqVGjBmrUqPHezyPA\n4JEjR3Dnzh34+voiJSVFAtG05vbvSPfu3TFnzhxs3boVRYsWhb+/P3bv3o2kpCSEhIQgT5487+3c\nmZIpf0fWdyuXrv3i4uIAwGIW2L8her0erq6uFkHMf9m3jCbatHf5byU4OBgAcOXKFdX2fPnyAQAO\nHTqEV69eATCAgfDwcABAzpw50bx5cwlChCQkJMDFxQXNmzeXx9VoNFi7di38/PxkOu6ZM2eg0RiC\ne7NmzQrAkHVjfCylnDt3Dnq9XmXV8Pb2RqdOnTBhwgQsXbpUgo88efLg8ePHGD9+POrVq4dWrVrh\nypUrGDFiBGbOnIkhQ4bIc2q1Wqxfvx6jRo1CcnIyrKyssHnz5lTHbdasWShatCimT5+OlStXypTb\nJ0+eYPLkyVi8eDGSk5MxePBgNG3aNNVjCSlatCgAID4+Ho6OjhgyZAhOnTpl9oFq3749vLy8MGHC\nBACQGTTCuvL/XT755BM0atQIb968QWBgIJo3b44iRYpg165dcHJyQpcuXd7buX18fLBt2zbkzJkT\nly9fxqZNmxAfH49GjRph0aJF7+28mZIpH7s4OztLfeTi4gJfX1/88MMPAAz66fz58/9l9zKsZHiL\nyE8//QTAACwWL16MzZs3IzExEb6+vnB2dsbDhw/h4eGBqlWrIiYmBseOHYODgwPi4uJw7do1+Pr6\n4s6dO8iePTtKly6N8PBw9O/fHwUKFAAA6ZqJi4tDxYoV0aZNGyxYsACPHj2SrpXo6GjY2tqidu3a\n2Lp1q+ybo6MjkpKSZEpwcHAwsmXLJi0HAFC1alUsWbIEgCEFtXfv3gAMnBNFihRRWVvWrl2Ljh07\nYsmSJahfvz5CQkKwdu1a1XhYWVlh06ZNkpvDnFy4cAF9+/YFAHTt2hUlS5bEihUrcPToUeTOnRtt\n27aFg4MDmjVrJlfm6ZGQkBCMHj0aDx8+RFxcHD777DNcuHABcXFxcpyFXL58WV4zAMnRIkBdphis\nYiEhIdi9e7d8WeXKlQtr1qyBp6fnez33559/jrt372L//v2Ijo5GiRIlMl0ymZIpf1NatmyJLl26\nYM6cOdi4cSNWr16NHj16YMKECUhKSkLLli0RGBj4X3cz44m5wJH/uhlnzdja2qa7KJyLiwt37dol\nMxKUjKfpaTY2NtyxYwdHjRolsyjKly/Ps2fP8urVq+9c70akSE6fPl3Wh6lWrZosEFepUiVu2LCB\nkydPlv0UabzJyclcsWIFq1evzmLFirFSpUosVaoUixQpwnbt2lkM8BSpusogy4SEBJntWEdmAAAb\nN0lEQVR5c/jw4fTGHJFUB+JdvHjRJCjYw8PDLB18o0aNVJV/XVxc+PLly3c699+RqKgozpgxg927\nd+ekSZNkmnFGkwsXLnD58uUMDw9nYmJiun6TGRyZsSRzPt6PZISsmUx5d/lgsmZSa8pOW1lZybTX\nnDlzct68eSqOj+rVq7Nr165SEe7fv58kZUaNoAY3BhDis7+/P48dO8bbt2+zffv2BAyF5vR6PadP\nn07AkH57+PBh3rhxw+Q4Op1OlUlTvnx5Dho0iJcuXeK4ceNMlHP+/PkZEREhM3qUxeEGDRpEAGzS\npIlqElNSUlT08qJZW1tzx44d1Ov1quhrUQfEuFqq4EB51zx345dsfHy8LHGvbKGhoaoCd8Z9/fHH\nH9/pvMai1+v5008/cenSpYyIiGBKSorFfQ8fPqwqJggYagtt3rz5b/Uho0im4stYkjkf70cygciH\nKR8dEDG2VghlXaJECWo0GlpZWTE+Pl5aAfr370+Sqoqx1apV461btySZlgAQgLqE+evXr6Xy+u23\n3/jq1StpWTFulSpV4q5du/jkyRMOHDhQgpunT59Sr9fzyZMnjIuL44ULFzh06FB2796dy5cvZ3x8\nPE+cOEHAUOvm5s2bqn4BhqqaSiW7fft2AoY05cWLF/PUqVOSc8LR0VGm0hYtWpQrVqzg1KlTCYCf\nffaZXGHfvn1bWlzetQibpZfsqVOnOHHiRE6bNk2mqN27d499+vShj48Ps2bNyvz587Nbt25/u/Db\nzZs3TWrdFC5c2OxxX79+LQFRlSpVOGvWLFnc0N7eno8fP/5bfckIkqn4MpZkzsf7kUwg8mHKRwdE\nPv30U9XKVlg+qlSpQicnJwLg06dPOXnyZAIGsjOS3LNnj6oyr6VKsr6+vjx//jxJA8OdKHYmKls+\nf/6cQ4YMoa+vr0np+lq1arFr165SwefJk4cLFy6U5eutrKzYokULE5dATEyM/I04n62trcrSM3Lk\nSMbGxvLhw4ds06YNAQNJmJDXr19b5DQZO3asBCfe3t5s2LChtAy9KyMrmfpL9vnz57x27ZqKC0Mp\ner2ejx49ksX4/ookJSVJTpfcuXOzdevWksHV19dXVjUWsmHDBgJgYGCgtBTp9XrJBjtz5sy/3JeM\nIpmKL2NJ5ny8H8kEIh+mfHRA5M2bN2zWrJlczRor3bx58/LGjRsyFmHx4sWsXr26WQVtDCREc3d3\n5/379yWZWf78+c2a/Z8/fy77oCRaE01QtQvrhXDjfPLJJ4yJiVEdS1h2hFVDVKUVYESn00nwJM65\nZMkS+fuVK1fK38+aNYsJCQmcO3cuAQNZ28GDB1XkagBYv359Pn/+/B1uJ4OYe8k+e/aMrVu3ln10\ndHRk3759+ebNG7mPMlYHMLitjh9PH4mQUrZu3UrAUNVYxJjExsayYMGCBMANGzao9p81axYBsHv3\n7qrt48ePJwAOHDjwnfuQ0SRT8WUsyZyP9yOZQOTDlI8OiJAGF4AyNsP4f/H5008/lTVjsmTJwiJF\nipi4Yiw1pfUktVgGQYsuwIb4nZeXl7Tc/O9//2NKSgrv3r0r3QkzZsxQHScpKckEKPj7+3Pfvn0q\nS4eyX1mzZuXDhw+p1+tZuXJlaXWJioqSxy1TpgwBA+tqcnIyIyIiuG7dOl6+fDmte8eiGL9kk5KS\nWLJkSdk/b29v2ceQkBCS5L59+2TfnZycJJiyt7d/ZxbVSZMmEYAJFfKQIUMIgKNHj1Zt37t3r7RQ\nCeD1+vVrCYqWL1/+F0YhY0mm4stYkjkf70cygciHKR8dEHnx4gV/+eWXNEFEmzZteOjQIWn5+OOP\nPxgbG/tORfNKlizJ7du3pzrAer2e06ZNkxYMrVbLxo0b84cffiBgiPtQyqpVqwhA0gErpXnz5gTA\nHj168MyZM9Tr9Zw5c2aqfdTpdKpieNWqVVMds3jx4gTAXbt2pXod7yLGL1lBiZ8nTx5Z7+bnn3+W\nYOPy5cuSUv+rr77imzdv+OrVK4aEhBAAmzVr9k7nX758OQGwbNmy0lKlBGOLFi1S7Z+SkiIBoIeH\nB1u3bi3BUu7cuS26kT4kyVR8GUsy5+P9SCYQ+TDlowMiefLkUWVomEuf1Wg0PHTokFT6wcHBcgBi\nY2NVmRw2Nja8evUqN27cqDpGx44d32mgExMTeefOHUZHR5OkDEA1DjSdP38+AdNMGJKyD66urlyy\nZAmPHz+uAhnZs2fnli1beOPGDZOUWREf4+Hhwf379zMqKooTJ06U1qB/8iE0fsmKQOD69etz+PDh\nXLVqFV+/fi0ze+bNmydBmrIfouaNu7v7O53/5cuXdHV1JQDWqFGDs2fPltWDnZ2dzbqbfvvtNwnK\nRPPz8/toCrplKr6MJZnz8X7kXYFIYmIiDxw4wPXr18s4v78rwNtK6eTbWEJzi8uPUe7cucPVq1e/\n028+OiBiDDgAsGLFirx9+7ZcYQNguXLleODAAQkGlAGMxjwiNWrU4OrVq2ljYyO3pWUJSUuSkpIk\nT0f37t159epVbt68WYKglStXmvwmJSWFwcHBFq0fs2fPJmlY/SsBSlhYGOPi4mThOOO28P/aO/Ow\nqq5rgf82F4KKCmIdcARRY6wK4qxo1NKq0YifQ15ftagxDi8SFU1N9KVYU2ycgjGSmsY4oHEgwSZB\n0ySSvDhVUmNNnLBxHnFEirlXQYb1/rjnnl4EFEXhivv3fee7dw/n7HXu/va566y99l7vvluqe7md\n2x+yRS0lbtCggWl9io+PN31onB11HYHe6tevf88yJCcnm8qX46hSpcodA//l5+fLjh07ZPny5ZKc\nnFyhAkzpPz7XQvfHw+FeFJG//e1vBYJuuru7S2RkpOTk5JRKBi8vLwkODpYbN26Y7QQFBZWLIlLa\ne7kfnAP8lZQKp4hs2bJFFi5cWMDR9E9/+pNMmjTJVEwcPhVXrlwx/S66du0q77zzjkRERBT48ypq\n9cwTTzxhWjH2798vr732mkRFRcnGjRvvqeOTkpKKvH5YWFixG1Xl5ubKihUrpFevXhIUFGT6uIB9\nBdDevXsL+ZJUqlRJVq9eLTabTWbNmiX+/v5SpUoV6datm3zyyScllrekOD9kL1++bDrUKqUkLCxM\nAgMDTdkqV64sGRkZpoNxjx49ZNeuXfLNN9+YPhqTJk26LzkuXbok8+fPl/Hjx8vcuXPlwoULD/I2\nHyn0H59rofvj4VBSReTAgQPmi2Xz5s3l6aefNn3UXnnllVLJ4OXlJTNmzDD3X/rtb38rc+fONf+c\nrVarjB49Wtq3by/BwcHmM/jkyZMSGhoqbdu2lbZt28rf//53ERFJS0uT7t27S1BQkPz85z83N5j0\n8vIy2/zoo49k5MiRImKP1BsVFSU9e/aUqVOnFtveypUrJTw8XAYMGCD+/v6yZMkSefPNNyU4OFg6\ndepkRj8/duyY9OnTR0JCQiQ0NFQOHz5stvPSSy9Jly5dJCAgwLzfTp06SfXq1SUoKEhiY2Pl4MGD\n0qFDBwkKCpLWrVubWzc4U+EUkfz8fBGxL8ctalpm7ty5piKSkZEhe/bsKTSNUdRUjnP65Zdflvz8\nfHPVjPMREhJyT0tPU1JSZMiQIdKwYUMJCgqSBQsWFFhJcjdyc3OlZcuWxcruGFxubm6ye/fuEl+3\nNDg/ZGNjYwUo4KDqfEyePFlERI4ePVrk5maBgYEVYh+P8kb/8bkWuj8eDiVVRMaOHWtOoeTl5YnV\napXPPvvMnMYuzVS1l5eX7Nu3T4YMGWI6vTtbCWbMmGFavDMyMqRZs2ZitVrFZrPJzZs3RUTkyJEj\n0q5dOxERWbhwocTExIiI/XnvWAl4J0Wkf//+pkW3uPZWrlwpgYGBcv36dbl8+bJUr15dli5dKiIi\nU6ZMMbct6N27t6k8fPvtt9KrVy+znaFDh0peXp4cOnRIAgMDRaSwRSQyMlI++OADEbHv2O2wFDlz\nr4qIy8eaCQ8P58MPP+RXv/oVo0aNYuXKlfj4+NC3b18iIiJYt24d2dnZhIaG4uPjQ7t27Thy5Air\nV6/mwIED+Pn5MXLkSKZPn84nn3wC2JUvByEhIcyfP5/Nmzfzxhtv4O7uzpgxY6hXrx7vv/8+e/fu\nZeLEiSQkJJRI3s6dO9818u6dsFgs7Ny5kxYtWnD58uVC5XPmzOH8+fPExcURFxdHfHz8fbd1Pzji\nybz44os0bdqUZcuWce7cOaxWK6dOnaJFixYANG3alD179rBw4UK+/PJLLBYL4eHhTJ06lZ/97Gdl\nKrNGo6nYOKKSjxs3zgyw+fTTT9OsWTOOHj3K8ePHadOmzX1fv02bNpw6dYr169fzzDPPFCjbsmUL\nSUlJLFy4EICsrCzOnDlDvXr1iIyM5IcffsBisXDkyBEAOnTowPPPP09OTg6DBg0iODj4ru0PGzYM\ni8Vyx/bAHtusWrVqVKtWDW9vb5599lnAHrB0//79WK1Wdu3axbBhw8xrOwdvHTRoEG5ubrRs2ZJL\nly4VKUuXLl2YM2cO586dY/DgwQWiyN83RWknJT2ABcC/gP3Ax4CPke8P3AR+MI53nc5pBxwAjgFv\nA+r2697uI+IwraWlpRXwlXAcnp6esnPnzkJa2e3Ex8dL8+bNxcvLSxo3biyxsbHm1Itj+/N58+aZ\n9U+ePCkWi0UsFkuBJbJlwcWLF6V///7mPQYEBMi7774r+fn5sn37dgGkY8eOZSKL89ve22+/bU65\nODR0q9Vq+sckJyeXiUyPO/oN3LXQ/fFwKKlFxLGHk8Ovzmq1yqlTp8xp5LS0tPuWwWGpmD17tvj6\n+sr+/fsLWAlCQkKK3OF51qxZMm3aNMnLy5OcnByxWCxm2fnz5+W9996TVq1aSXx8vIiIVK1a1Sxf\ns2ZNAYuIc1iO4tpbuXKlTJw40Uw3btzYtOY7yjIzM6Vu3bpF3uft7TjuuygfkWPHjsnixYslICBA\nvv7660LXuleLiFsp9ZhkoJWItAGOADOcyo6LSLBxTHDKXwqMA5oZR9+7NfLee++Rl5eHn58fKSkp\njBkzBh8fH6pUqcKzzz7Lzp076dat212FjYiI4McffzTf3qOiorBYLHz11VekpKQA9mixNpsNsIdL\n9/f3Jy8vr1jtEOyRdHfv3s3x48fvKkNJqVOnDitWrMDNzQ0PDw+2bdvG+PHjUUqZEYkbNGjwwNor\nKcOHD8fb25vt27fTsWNHpkyZQps2bTh79ixPPfUUvXv3LnOZNBrN482oUaMAePXVV4mOjmbVqlUM\nGDCArKws+vTpg5+fX6nbeP7554mOjqZ169YF8vv06cOSJUtMS7vDOpOZmYmfnx9ubm6sWbOGvLw8\nAE6fPk3t2rUZO3YsY8aMYe/evYD9mX/48GHy8/P5+OOPi5WjuPZKQvXq1QkICDCjfYsI+/btu+M5\n1apV46effjLTJ06coEmTJkyaNImBAweyf//+ErdfHKWamhGRLU7Jb4Ghd6qvlPIDqotIipFeDQwC\nPi/uHE9PTzIyMti+fTvVqlUDYMKECUyYMKFAvT179hR5fnZ2Nrm5uXh5eRUqy8/PJyYmhk2bNpl5\n8+fPZ/369SxdupT09HSOHz+Op6cnV65cKdRGbm4uS5cu5aOPPuLmzZuA3QT22muv0aRJkzv9FCWm\nR48ebN26lU6dOjFw4EAuXrzI5s2bAejZs2ex9/0wcLS1YMECpk+fzt69e81B1KhRI2JiYsy0pmwo\ny/7X3B3dHw+WqlWrUqVKlbvW69evH6NGjWLVqlX88Y9/NPMbNWpEbGys+XJ5v9hsNmrUqMELL7yA\nzWbj5s2b5OXlYbPZmDp1KtOnT6dVq1aICI0bNyYxMZFRo0YxfPhwEhIS6NGjB15eXthsNr788kve\neustPDw88PLyYtmyZdhsNv7whz/Qv39/6tevT8uWLbHZbNhsNnJzc8nKyjLvobj2srOzycnJMeuJ\nCDabjcqVKxcoW7ZsGVOmTOH1118nJyeHoUOH0rRp00LtOO47MDAQpRStW7dmxIgRZGVlsWHDBjw8\nPKhTpw7Tpk0r9Pump6dz+vRpM3236Rvl0KpKi1JqE5AgIh8opfyBQ9itJ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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2623,10 +2774,10 @@ } ], "source": [ - "sensor_var = 30000\n", - "process_var = 2\n", - "pos = (1000, 500)\n", - "process_model = (1, process_var)\n", + "sensor_var = 30000.\n", + "process_var = 2.\n", + "pos = gaussian(1000., 500.)\n", + "process_model = gaussian(1., process_var)\n", "\n", "N = 1000\n", "dog = DogSimulation(0, 1, sensor_var, process_var)\n", @@ -2635,8 +2786,8 @@ "\n", "for z in zs:\n", " prior = predict(pos, process_model) \n", - " pos = update(prior, (z, sensor_var))\n", - " ps.append(pos[0])\n", + " pos = update(prior, gaussian(z, sensor_var))\n", + " ps.append(pos.mean)\n", "\n", "book_plots.plot_measurements(zs, lw=1)\n", "book_plots.plot_filter(ps)\n", @@ -2654,14 +2805,14 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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bt2+vqJwrmxuWLFki2ozrtOTPn18wc61WS1tbW7q6urJ3794iB0flypXZo0cP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\n1E6upGnakeoF/53c3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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2669,19 +2820,19 @@ } ], "source": [ - "sensor_var = 30000\n", - "process_var = 2\n", - "process_model = (1, process_var)\n", + "sensor_var = 30000.\n", + "process_var = 2.\n", + "process_model = gaussian(1., process_var)\n", "N = 1000\n", "dog = DogSimulation(0, 1, sensor_var, process_var)\n", "zs = [dog.move_and_sense() for _ in range(N)]\n", "\n", - "pos = (zs[0], 500)\n", + "pos = gaussian(zs[0], 500.)\n", "ps = []\n", "for z in zs:\n", " prior = predict(pos, process_model) \n", - " pos = update(prior, (z, sensor_var))\n", - " ps.append(pos[0])\n", + " pos = update(prior, gaussian(z, sensor_var))\n", + " ps.append(pos.mean)\n", "\n", "book_plots.plot_measurements(zs, lw=1)\n", "book_plots.plot_filter(ps)\n", @@ -2708,13 +2859,13 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "7cdc56e40a90494cbaca4f5fb4d145e7", + "model_id": "41913d828ed64349bcefc35aa3bad9ad", "version_major": 2, "version_minor": 0 }, @@ -2735,7 +2886,7 @@ " process_noise):\n", " plt.figure()\n", " # your code goes here\n", - " pass;\n", + "\n", "\n", "interact(plot_kalman_filter,\n", " start_pos=(-10, 10), \n", @@ -2755,13 +2906,13 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "c60f71af532746729d0fc85ce753d6c3", + "model_id": "8375a30f5dcd44699c7380d0ad65af2b", "version_major": 2, "version_minor": 0 }, @@ -2786,13 +2937,13 @@ " seed(303)\n", " dog = DogSimulation(start_pos, velocity, sensor_noise, process_noise)\n", " zs = [dog.move_and_sense() for _ in range(N)]\n", - " pos = (0., 1000.) # mean and variance\n", - " process_model = (velocity, process_noise)\n", + " pos = gaussian(0., 1000.) # mean and variance\n", + " process_model = gaussian(velocity, process_noise)\n", " \n", " for z in zs: \n", " pos = predict(pos, process_model)\n", - " pos = update(pos, (z, sensor_noise))\n", - " ps.append(pos[0])\n", + " pos = update(pos, gaussian(z, sensor_noise))\n", + " ps.append(pos.mean)\n", "\n", " plt.figure()\n", " plt.plot(zs, c='k', marker='o', linestyle='', label='measurement')\n", @@ -2833,7 +2984,7 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 34, "metadata": { "collapsed": true }, @@ -2851,7 +3002,7 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 35, "metadata": { "scrolled": true }, @@ -2860,7 +3011,7 @@ "data": { "image/png": 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A+6pVKWBX0hwd3apgx/nHCpHzFvRSeKmA8qCs+LtPI1iYGqLRhN0YvfYcnr2P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\nt3Il7X8vXkxGRW2sgJSkUycyvqQ6ILYambfcQsG+8+ZRfIUtpaWXLKE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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2870,10 +3021,10 @@ "source": [ "import math\n", "\n", - "sensor_var = 30\n", - "process_var = 2\n", - "pos = (100,500)\n", - "process_model = (1, process_var)\n", + "sensor_var = 30.\n", + "process_var = 2.\n", + "pos = gaussian(100., 500.)\n", + "process_model = gaussian(1., process_var)\n", "\n", "zs, ps = [], []\n", "\n", @@ -2883,8 +3034,8 @@ " z = math.sin(i/3.)*2 + randn()*1.2\n", " zs.append(z)\n", " \n", - " pos = update(pos, (z, sensor_var))\n", - " ps.append(pos[0])\n", + " pos = update(pos, gaussian(z, sensor_var))\n", + " ps.append(pos.mean)\n", "\n", "plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n", "plt.plot(ps, c='#004080', label='filter')\n", @@ -2951,23 +3102,25 @@ }, { "cell_type": "code", - "execution_count": 31, - "metadata": {}, + "execution_count": 36, + "metadata": { + "scrolled": true + }, "outputs": [ { "data": { "text/plain": [ - "(11, 7.000)" + "(11.0, 7.0)" ] }, - "execution_count": 31, + "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import filterpy.kalman as kf\n", - "kf.predict(x=10, P=3., u=1, Q=4)" + "kf.predict(x=10., P=3., u=1., Q=4.)" ] }, { @@ -2985,7 +3138,7 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 37, "metadata": {}, "outputs": [ { @@ -2994,14 +3147,15 @@ "(11.364, 4.455)" ] }, - "execution_count": 32, + "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "x, P = kf.predict(x=10, P=3., u=1, Q=2**2)\n", - "x, P = kf.update(x=x, P=P, z=12, R=3.5**2)\n", + "%precision 3\n", + "x, P = kf.predict(x=10., P=3., u=1., Q=2.**2)\n", + "x, P = kf.update(x=x, P=P, z=12., R=3.5**2)\n", "x, P" ] },