From a4bcbd0f14bd7b6fc7a90a6716866c00df420c0d Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Sun, 18 Jan 2015 10:04:31 -0800 Subject: [PATCH] Added section on fat tails. --- 04_Gaussians/Gaussians.ipynb | 199 ++++++++++++++++++++++++++++++++--- exp/distributions.py | 42 ++++++++ exp/doppler.py | 140 ++++++++++++++++++++++++ 3 files changed, 365 insertions(+), 16 deletions(-) create mode 100644 exp/distributions.py create mode 100644 exp/doppler.py diff --git a/04_Gaussians/Gaussians.ipynb b/04_Gaussians/Gaussians.ipynb index 4fa0046..781038c 100644 --- a/04_Gaussians/Gaussians.ipynb +++ b/04_Gaussians/Gaussians.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:f08e94cbb6c00464eb37c3fd1d0eafa5e7453f677f35d30f69a0eafd0f7f71c4" + "signature": "sha256:0e132ac8cc355b74191dd1be26d43c2cb06906e475027ce68a2bc08a6fab0984" }, "nbformat": 3, "nbformat_minor": 0, @@ -261,7 +261,7 @@ "output_type": "pyout", "prompt_number": 1, "text": [ - "" + "" ] } ], @@ -302,7 +302,7 @@ 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B8OI8/KfcSofeKoiUy2bqpmiP9uzmlyVdhfOw811iSgMjo/RRnXTv6x9rZq86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\nBQUsXLiQAQMGUF5ezpQpU4iJiWHevHm6FEzOSXN9GBERwY9//GM2b97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e+rJauw+51SM2Qj8Zkmx2OUBAGZIWpcv6J8prSI9vLpXfYG8UAF2HgAIg7JU3\nerV0a4Uk6e5R6YpmzxPgCHecnaqUKJs+K23Su9/UmF0OgBDGpzCAsLd4S7nqPH6N7xmjidmxZpcD\nBKSESJtmjmxZdnvxlpbFJACgKxBQAIS1LSWNem9PrRxWi+4ZlU5jPHAcF/eN16iMaFU1+/XMlnKz\nywEQoggoAMKW12/oycON8dcNSVZOPI3xwPFYLBbNGe1UhFX6v69rVFDaaHZJAEIQAQVA2Hrryyrt\nrmppjL9+MI3xwInom+jQtYNa/n95fHOpvH4a5gF0LgIKgLBU1uDV0q0tezrcMypdUTTGAyfshqEp\n6hEbod2H3PrDriqzywEQYvhEBhCWlhxujD+3Z6wm5sSZXQ4QVKIjrPrFOU5J0tKtFXLVe0yuCEAo\nIaAACDufljTqvb0tjfF3j0o3uxwgKE3IjtUFObFq9BpakF9mdjkAQggBBUBY8XynMf4nQ5KVHW83\nuSIgeLXsG2TR6v31+vhgvdnlAAgRBBQAYeXNXVX6usqt7Di7rqUxHjglmbF23XxWqiRp/idlcvv8\nJlcEIBQQUACEjbIGr174vKUx/u5RaTTGA51g6sAk9U10qLDWo1d30DAP4NTx6QwgbCzeUq56j1/n\nZsfq3Gwa44HOYLdZ9IvDvVwvbatUUR0N8wBODQEFQFjIL2nQir21irRZdE8ujfFAZzonK0ZTesep\nyWfoaRrmAZwiAgqAkOfxG3pyU8sPTdcPSVZPGuOBTndX7uGG+UIa5gGcGgIKgJD3xq4qfVPd0hh/\nHY3xQJdwxkTQMA+gUxBQAIS00gavXthaIallx/hIG297QFehYR5AZ+CTGkBI++WnZWrwGjovO1YT\nsmPNLgcIaTTMA+gMBBQAIesTV4P+3z/rFGljx3igu9AwD+BUEVAAhCSP39ATm1t+OLphSIp6xNEY\nD3QXGuYBnIoTCijPP/+8+vbtq+joaOXm5mrdunXHHb9t2zZNnDhRMTExys7O1rx589o87nK5NHXq\nVJ155pmKiIjQ9ddff8Q1li1bJqvV2uaPzWaT2+0+iZcHIFz9YWeV9la7lRNv17TBSWaXA4QVGuYB\nnIp2A8qbb76pGTNmaO7cuSooKFBeXp4uuugiFRYWHnV8TU2NJk+erKysLOXn52vJkiVasGCBFi1a\n1DqmublZ6enpmjNnjkaPHi2LxXLUa8XExKikpEQul0sul0vFxcVyOBwdfKkAwkVpg1cvfk5jPGAm\nGuYBdFTa5N1SAAAgAElEQVS7n9qLFi3S9ddfrxtuuEEDBgzQM888o6ysLC1duvSo419//XU1NTXp\nlVde0aBBg3TZZZdp9uzZbQJK7969tWTJEk2bNk0pKSnHfG6LxaL09HQ5nc7WPwDQnkWHG+PPz4nV\n+J40xgNmoGEeQEcdN6C43W5t2bJFU6ZMaXN8ypQpWr9+/VHP2bBhgyZMmKDIyMg244uKirRv376T\nKq6xsVF9+vRRTk6OLr30UhUUFJzU+QDCz+biBr3/zzpF2SyaxY7xgKlomAfQEccNKOXl5fL5fMrI\nyGhz3Ol0yuVyHfUcl8t1xPhv/36sc45m4MCBevnll/WXv/xFf/jDHxQVFaVx48bp66+/PuFrAAgv\nHp+hJz853Bg/lMZ4IBDQMA/gZEV09gWP1U9yssaMGaMxY8a0/j0vL0/Dhw/Xs88+qyVLlhz1nPz8\n/E55bhwb/8boqO64d96vcGhvdbScdp8GN+5Rfv6eLn9OdD3ed4LfJSkOvV0arUfWFuqh0+pk76a2\nMO4ddBT3Ttfq16/fcR8/bkBJS0uTzWZTSUlJm+MlJSXKyso66jmZmZlHfFPy7fmZmZntFnwsVqtV\nI0aM0O7du485Jjc3t8PXR/vy8/P5N0aHdMe9U1Lv0Xt/2SfJ0AMTcjSW3pOQwPtOaBjmM/Tpe/u1\nt9qt7dGn6cahx+4/7SzcO+go7p2uV11dfdzHj/s7DIfDoZEjR2rlypVtjq9atUp5eXlHPWfs2LFa\nu3atmpub24zv2bOnevfufaJ1H8EwDG3dulU9evTo8DUAhK5Fn5ar0Wvogl6xGkc4AQIKDfMATka7\nX7LOnDlTy5Yt00svvaSdO3dq+vTpcrlcuuWWWyRJc+bM0aRJk1rHT506VTExMbruuuu0fft2LV++\nXPPnz9fMmTPbXLegoEAFBQWqrq5WRUWFCgoKtGPHjtbHH374Ya1cuVJ79uxRQUGBbrjhBm3fvr31\neQHgWxuLG7RyH43xQCCjYR7AiWq3B+XKK69URUWFHn30URUXF2vo0KFasWKFcnJyJLU0vu/Z8695\n3gkJCVq1apVuv/125ebmKiUlRbNmzdKdd97Z5rojRoyQ1NKzYhiG3n33XfXp06f1WtXV1brpppvk\ncrmUmJioESNGaM2aNXzlBqANj8/QU5tLJUk3Dk1RViyN8UCguis3XWsP1rc2zPNtJ4CjsRiGYZhd\nxKn47hy2xMREEysJfczJREd15b2zbHullmypUK94u/54aS852JQxpPC+E3pe2X5Ii7eUKyferre7\n8P9Z7h10FPdO12vv53c+yQEELVe9R7/+vFKSNPucdMIJEATYYR5Ae/g0BxC0vm2Mv7BXnPJ6MFUE\nCAY0zANoDwEFQFDaWFSvVYcb4+/KTTO7HAAngYZ5AMdDQAEQdNw+f+uO8T89i8Z4IBjNHJnWusP8\n+iJ2mAfwLwQUAEHntZ1V2lfjUZ8Eu645M9nscgB0QEasXTeflSpJmr+5TG6f3+SKAAQKAgqAoFJc\n79H/ftsYPypddpvF5IoAdNTUgUnqm2DX/lqPfkfDPIDDCCgAgsqi/HI1+QxN7h2nMTTGA0HNbrNo\n9jlOSdJvtlWquJ6GeQAEFABBZENRvf6+v6UxfuZIGuOBUDD6Ow3zC2mYByACCoAg4fb5Nf9wY/xN\nZ6Uok8Z4IGS0Nszvp2EeAAEFQJD43Y5/Ncb/mMZ4IKRkxNp101kpkmiYB0BAARAEius9+s22b3eM\nd9IYD4Sgqwcm0zAPQBIBBUAQWJhfpiafoSm94zQmK8bscgB0AbvNontomAcgAgqAAPfxwXqt3l+v\n6Aga44FQNyYrRpNbd5gvN7scACYhoAAIWN9tjL/5rFRl0BgPhLy7DjfM/2N/nTbQMA+EJQIKgID1\n6o4qFdZ61DfRoakDk8wuB0A3yIi166dDDzfMf0LDPBCOCCgAAlJRnUcvHW6M/wU7xgNh5cdnJqtP\ngl37ajx6bScN80C4IaAACEhPf6cx/hwa44GwYrdZNHtUuiTpfz+nYR4INwQUAAFn3cF6rS5saYy/\nKzfd7HIAmGBMj1hN6tXSML+IhnkgrBBQAASUZp9fTx1ujL/lrFQ5YyJMrgiAWe7KTVOUzaK/76/T\nRhrmgbBBQAEQUF7d3tIYf1qiQz86k8Z4IJxlxtr108M7zD9JwzwQNggoAALGwVqPXvricGP8Oemy\nW2mMB8LdNTTMA2GHgAIgYDyVX6Zmn6Hv9YnTqEwa4wEc2TDvomEeCHkEFAAB4aPCOq05UK9Yu1Uz\nR9IYD+Bfvtswzw7zQOgjoAAwXZP3X43xtw5LUTqN8QD+TZuG+eIGs8sB0IUIKABM99svDqmo3qt+\nyQ79zwAa4wEc6bsN8/M3l8rjM0yuCEBXIaAAMNW+GreWbT8kSbr3HKciaIwHcAzXnJms3gl2/bPG\no9d2HjK7HABdhIACwDSGYeipT8rk8Rv6/unxOtsZbXZJAAJYm4b5bTTMA6GKgALANKsL67W+qEHx\nDqumD08zuxwAQWBsj1hd2CtOjV5Diz6lYR4IRQQUAKZo9Pi18HBj/M/OTlVKNI3xAE7Mtw3zq/bR\nMA+EIgIKAFP8elulXA1enZkSqcv6JZpdDoAgkhVr141DaZgHQhUBBUC321Pt1ms7Dski6d7RTtlo\njAdwkq4ZlKRe8S0N86/vomEeCCUEFADdyjAMPbmpVF5D+mG/BA1JizK7JABByGGzavY5LQ3zv/68\nUiU0zAMhg4ACoFu9/886fVLSqKRIq35GYzyAU5DXI1YX9IqlYR4IMQQUAN2mzu3T05+2NMbfMTxN\nSZE2kysCEOxm5aYrymbRShrmgZBBQAHQbV74vFLljT4NTYvSf5+RYHY5AELAdxvmn6JhHggJBBQA\n3WL3oWa9satKVot07+h0WS00xgPoHNcMSlLvBLv21nj06g4a5oFgR0AB0OUMQ3pic6l8hnRF/0QN\nTKExHkDncdismnOOU1LLDvMHammYB4IZAQVAl9tQbddnpU1KjbLp9rNTzS4HQAganRWji/vGq9ln\n6MnNpTKY6QUELQIKgC5V0+zT26Ut35jMGJmmeAeN8QC6xsyRaYqzW/VxUYO21EaYXQ6ADiKgAOhS\nz3xWrlqfVSOc0bqkb7zZ5QAIYanREbpjeMu3tG+URKve4ze5IgAdQUAB0GUKShv1zu4a2WTovjFO\nWWiMB9DFLuuXqCGpkaryWrW0oMLscgB0AAEFQJfw+A09tqlUkvQfqc06LdFhckUAwoHNamn5hYgM\n/eHLKu2qbDK7JAAniYACoEv8fmeVvq5yKyferkvSms0uB0AYGZgSpQtT3PIb0qMbS+Xz0zEPBBMC\nCoBOV1Tn0QtbW6ZW/OKcdDl4pwHQzf4rrUnOmAhtr2jWO7urzS4HwEngxwYAncowDM3fXKYmn6Ep\nveOU1yPW7JIAhKEom3R3bpok6dnPKlTe6DW5IgAnioACoFOtLqzXmoP1irNbNSs33exyAISxC3vF\naXzPGNV5/FqUX252OQBOEAEFQKep9/j11CdlkqQ7hqcqPYZ9CACYx2Kx6BejnIq0WfS3f9ZqU3GD\n2SUBOAEEFACdZmlBhUobvBqSGqnL+iWaXQ4AqGe8XT8dmiJJenxTqZp97I0CBDoCCoBOsbOiSX/4\nskpWi3TfGKdsVvY8ARAYpg1KVt9Eh/bXerRs+yGzywHQDgIKgFPm8xt6dFOp/Ib0o4FJGpgSZXZJ\nANDKbrPovtFOSdJvtx3Svhq3yRUBOB4CCoBT9sevqrWjolkZMRG6bViq2eUAwBFGZkTr+6fHy+03\n9MSmUhkGe6MAgYqAAuCUlDZ49auClj1PZo9KV4ydtxUAgWn6iDQlRVq1ydWov+6pNbscAMfATxIA\nTsnC/DLVe/w6NztW5+Ww5wmAwJUSFaGZI1uWP1/0aZkqm9gbBQhEBBQAHfZRYZ1W7atTlM2i2aPS\nZbHQGA8gsP3nafEanRmtqma/nmZvFCAgEVAAdEid26cnNrfsefKz4anqEWc3uSIAaJ/FYtF9Y5yK\nslm0Ym+t1hfVm10SgH9DQAHQIb8qqFBJg1eDUyN11YAks8sBgBOWE+/QzcNa9kZ5bGOpGj3sjQIE\nEgIKgJNWUNqot76sVoRFun9MBnueAAg6Pz4zWQOSI1VU79XSzyvMLgfAdxBQAJwUt8+vRzaWypA0\nbXCyBqREml0SAJy0CKtF9491ymqRXt9ZpR0VTWaXBOAwAgqAk/LyF4e0t9qtXvF2/XRoitnlAECH\nDU6N0o8GJslvSPM2lsrrZ28UIBAQUACcsG+qmvWbLyolSfePdSoqgrcQAMHttmGpyoqN0K7KZv1+\nZ5XZ5QDQCQaU559/Xn379lV0dLRyc3O1bt26447ftm2bJk6cqJiYGGVnZ2vevHltHne5XJo6darO\nPPNMRURE6Prrrz/qdd555x0NGjRIUVFRGjx4sP70pz+d4MsC0Nn8hnH4N4zSD85IUG5GjNklAcAp\ni7Fbde9opyRp6dYKHaj1mFwRgHYDyptvvqkZM2Zo7ty5KigoUF5eni666CIVFhYedXxNTY0mT56s\nrKws5efna8mSJVqwYIEWLVrUOqa5uVnp6emaM2eORo8efdS9EzZs2KCrrrpK11xzjbZu3aqrr75a\nV1xxhTZv3nwKLxdAR739VbW2ljUpLdqmGSPSzC4HADrN+J6x+l6fODX5DD22qVSGwVQvwEztBpRF\nixbp+uuv1w033KABAwbomWeeUVZWlpYuXXrU8a+//rqampr0yiuvaNCgQbrssss0e/bsNgGld+/e\nWrJkiaZNm6aUlKPPYV+8eLEuuOACzZkzRwMGDNC9996r8847T4sXL+7gSwXQUSX1Hj3zWcsqN7NH\npSsh0mZyRQDQue7OTVeiw6qNxQ16b2+t2eUAYe24AcXtdmvLli2aMmVKm+NTpkzR+vXrj3rOhg0b\nNGHCBEVGRrYZX1RUpH379p1wYRs3bjyp5wXQNQzD0OOby1Tv8eu87Fhd2CvO7JIAoNOlREdoZm66\nJOnp/DJVNnpNrggIX8cNKOXl5fL5fMrIyGhz3Ol0yuVyHfUcl8t1xPhv/36sc07mOidzDQCn7u/7\n67TmQL3i7FbNGe086pRMAAgFl54Wr9GZ0apq9mv+J2VmlwOErYjOvqCZP7zk5+eb9tzhgn/j8FLv\ns+jRb+IkWfVfqfXav6NA+zt4Le4ddBT3DjqqI/fOf8VaVGCJ18p9dTp9dYFGJPBNSjjifadr9evX\n77iPHzegpKWlyWazqaSkpM3xkpISZWVlHfWczMzMI77l+Pb8zMzMdgtu7zrHu0Zubu4JXx8nLz8/\nn3/jMDP3Y5dqfLU6Oz1KMyedIWsHfwHBvYOO4t5BR53KvVOdUqX5n5TprYoE/c+43kqk7y6s8L7T\n9aqrq4/7+HGneDkcDo0cOVIrV65sc3zVqlXKy8s76jljx47V2rVr1dzc3GZ8z5491bt37xOtW2PH\njtWqVauOeN5x48ad8DUAdNyaA3V6b0+tIm0WPZSX0eFwAgDB5soBiRrujFJFk08L8pnqBXS3dlfx\nmjlzppYtW6aXXnpJO3fu1PTp0+VyuXTLLbdIkubMmaNJkya1jp86dapiYmJ03XXXafv27Vq+fLnm\nz5+vmTNntrluQUGBCgoKVF1drYqKChUUFGjHjh2tj0+fPl2rV6/W/PnztWvXLj3xxBP68MMPNWPG\njM567QCOodbt06MbSyVJt52dqt4JDpMrAoDuY7VY9ODYDEXaLHpvT63WHqg3uyQgrLTbg3LllVeq\noqJCjz76qIqLizV06FCtWLFCOTk5klqa2ffs2dM6PiEhQatWrdLtt9+u3NxcpaSkaNasWbrzzjvb\nXHfEiBGSWnpWDMPQu+++qz59+rRea+zYsXrjjTc0d+5cPfDAAzrjjDP01ltvadSoUZ324gEc3dP5\n5Spr9GloWpSuHphkdjkA0O16Jzh029mp+uWn5Xp0U6nedvZSvIOpXkB3sBhBvhvRd+ewJSYmmlhJ\n6GNOZnhYd7Bed6wuksNq0Rv/2Ut9E0/92xPuHXQU9w46qjPuHZ/f0PXvH9C28ib94IwEPTA2o/2T\nEPR43+l67f383u4ULwDh47tTu249O6VTwgkABCub1aIHxzplt1r0f1/XaGMRU72A7kBAAdBq8afl\nKmnwakhqpH58ZrLZ5QCA6U5PitTNZ6VIkh7ZWKoGj9/kioDQR0ABIEnaWFSv5V/XyG5tWbUrwsqq\nXQAgSdMGJ2tgSqSK67165rNys8sBQh4BBYDqPX49fHhq181npej0pEiTKwKAwGG3WvTQ2AxFWKQ3\nv6xWfkmD2SUBIY2AAkCLt5TLVe/VmSmRunYwU7sA4N8NSInUT4a2TPV6aH2J6pnqBXQZAgoQ5jYX\nN+jtr6oVYZUeYWoXABzTjUNSNCA5UgfrvPrlp2zgCHQVAgoQxurcPj20oUSSdNPQVJ2RzNQuADgW\nu82ieeMyZLda9M7uGn18kFW9gK5AQAHC2ML8chXXezUoNVLXDWFqFwC0p19ypG4d1jLV6+ENJapp\n9plcERB6CChAmPqgsE5//qZGkTaL5o3LlJ2pXQBwQqYNStZZ6VEqa/Rp/idM9QI6GwEFCEOVjV7N\n29CyatfPh6fqNDZkBIATZrNa9EhehqJsFq3YW6u/76s1uyQgpBBQgDBjGIYe21SqQ80+jcqI1lUD\nk8wuCQCCTu8Eh2aMTJMkPbapTBWNXpMrAkIHAQUIM3/dU6vVhfWKs1v18LgMWS1M7QKAjriif6LO\nyYxWVbNPj20qlWEYZpcEhAQCChBGius9eurwfOm7R6UrK9ZuckUAELysFosezstQnN2qDwrr9dc9\nTPUCOgMBBQgTfsPQgx+XqM7j1/k5sbr0tHizSwKAoJcZa9fdo9IlSU99Uqbieo/JFQHBj4AChIk3\ndlXpk5JGJUfaNHe0UxamdgFAp7j0tHidlx2rOo9f939cIp+fqV7AqSCgAGFgT7Vbz3xWIUm6f6xT\nKdERJlcEAKHDYrHo/rFOpUbZ9GlJo17dccjskoCgRkABQpzb59e9a11q9hn6/unxOj8nzuySACDk\npERF6OG8DEnS81srtKOiyeSKgOBFQAFC3K8KKvTloWZlx9l1d2662eUAQMga1zNWVw1IlNcv3bfO\npUaP3+ySgKBEQAFC2Maiev1uR5VsFunx8ZmKc9jMLgkAQtr0EWk6PdGhf9Z49PSn7DIPdAQBBQhR\nlU1e3b++RJJ081mpGpoeZXJFABD6oiKsenxCpuxWi97ZXaMPC+vMLgkIOgQUIAQZhqGHN5SqvNGn\n4c4o/WRIstklAUDY6J8cqZ8PT5UkPbyhVGUN7DIPnAwCChCC/vhVtdYcaNkt/rHxmbJZWVIYALrT\n1DOTNPrwLvMPbSiRn13mgRNGQAFCzDdVzVr0abkk6f4xTnaLBwATWC0WPTIuU4kOq9YXNeiNXdVm\nlwQEDQIKEEKafX7NWfevJYWn9GG3eAAwizMmQg+MbVl6eMmWcn1Z2WxyRUBwIKAAIeTZLRXafcit\nnHi77hnlNLscAAh7F/SK02X9EuT2G5q9tlgNLD0MtIuAAoSItQfq9fquKkUcXlI41s7/3gAQCGbl\npuuMJIf21Xj0+KZSGfSjAMfFTzBACHDVe3T/xy5J0q1np2pIGksKA0CgiIqwav65WYqyWfTe3lq9\nu6fW7JKAgEZAAYKcx29ozlqXqt1+5fWI0XWDWVIYAALNaYkOzRndMvX2iU2l2lPtNrkiIHARUIAg\nt7SgQgVlTUqPtmneuAxZLSwpDACB6NLT4nXJafFq8hmavaZYTV76UYCjIaAAQezjg/V6efshWS3S\nExOylBIVYXZJAIBjsFgsuvccp3on2PV1lVsL88vMLgkISAQUIEiVNng19+MSSdKtw1I1MiPa5IoA\nAO2JsVs1f0KWHFaL3tldo/f/ST8K8O8IKEAQ8h7uO6lq9mlMVox+MoS+EwAIFgNSInVXbpokad7G\nUhXW0o8CfBcBBQhCL26t0JbSRqVF2/QYfScAEHSu6J+oSb3iVO/x6541LjX76EcBvkVAAYLMxwfr\n9dIXh/tOxmcqJZq+EwAINhaLRQ+MdSo7zq5dlc2av5l+FOBbBBQgiBTVeXTvOpcMSTeflaLczBiz\nSwIAdFC8w6aFE7MUabPo/76u0Z++rja7JCAgEFCAINHs82vWR8Wqcfs1oWeMbhyaYnZJAIBTNCAl\nUve27o9Spp0VTSZXBJiPgAIEiSc3l2lnZbOy4+x6dFwmfScAECK+f3qCLuuXILff0KyPilXd7DO7\nJMBUBBQgCCzfXa0/fV2jSJtFCydmKSHSZnZJAIBOdPeodA1KjVRRvVdzP3bJbxhmlwSYhoACBLjt\n5U168nDz5H2jnRqQEmlyRQCAzhZps2rBuVlKdFi17mCDfrOt0uySANMQUIAAdqjJp1lriuXxG7qi\nf6IuPT3B7JIAAF2kR5xdj0/IlEXSC1srtb6o3uySAFMQUIAA5fMbum+dS656r4amRWnW4U29AACh\nK69HrG4eliJD0py1LjZxRFgioAAB6lcFFdpQ3KCkSJueOjdTDhv/uwJAOPjp0BSd2zNWNW6/7vyg\nWPUeNnFEeOEnHiAArdhTo2XbD8lmkZ46N1OZsXazSwIAdBOrxaLHxmeob6JD31S79QBN8wgzBBQg\nwGwvb9LDG0oltazqMorNGAEg7MQ5bPrleVmKd1i1urBe//s5TfMIHwQUIICUNXh154dFcvsNXdYv\nQVf2TzS7JACASXonOPTkhExZLdILn1fqH/vrzC4J6BYEFCBANPv8uuujYpU1+jTcGaXZo5yysBkj\nAIS1vB6xmj68ZZGU+z92afehZpMrAroeAQUIAIZh6PFNpdpW3qTM2AgtPDdLdhvhBAAgXTMoSRf3\njVej19CdHxapip3mEeIIKEAAeH1nlf7yTa2ibBYtPq+HUqIjzC4JABAgLBaL7h/j1JkpkTpY59U9\nHxXL46NpHqGLgAKY7OOD9frllnJJ0iPjMtgpHgBwhKgIq355XpbSom36pKRRj20qlcHKXghRBBTA\nRF9WNuueNcXyGy3r3k/uHW92SQCAAJURa9fi83ooymbRn79pWY4eCEUEFMAkpQ1e/fyDIjV4DV3U\nJ163DksxuyQAQIAbnBalR8dnyiLpmc8qtGpfrdklAZ2OgAKYoMHj1/QPilTa4NVwZ5QezGPFLgDA\nibmwV5ymj/h2Za8SbStrMrkioHMRUIBu5vMbmrPWpV2VzcqJt+vpiT0UaeN/RQDAiZs2KEk/PCNB\nzT5DMz4sUlGdx+ySgE7DT0VAN1uYX6Y1B+uV6LDq2Qt6KDnKZnZJAIAgY7FY9IvRTo3OjFZlk08/\nX12kWjfLDyM0EFCAbvT7nVV648tq2a0WLTqvh3onOMwuCQAQpOxWixZMzNJpiQ59U+3WPWtcLD+M\nkEBAAbrJ6v11WphfJkl6OM+pERnRJlcEAAh28Q6bnjm/h1KibNpY3KCHNpTIz/LDCHIEFKAb5Jc0\naM5alwxJtw1L1UV9E8wuCQAQInrG2/XsBT0UE2HRir21Wnx4by0gWBFQgC72ZWWz7vygWG6/oSv7\nJ+rGoclmlwQACDGDUqP09MQsRVil3+2o0qs72CMFwYuAAnShg7Ue/Wz1QdV5/JrUK073jEpnOWEA\nQJcY0yNWj+RlSJJ++Wm53ttTY3JFQMcQUIAuUtno1a3/OKjyRp9GZUTrsfEZslkJJwCArnNR3wTN\nHNmyR8pD60u0vqje5IqAk0dAAbpAvcevOz4oUmGtRwOSI7XovCw52OsEANANrhmUrGmDkuQ1pFkf\nFWt7ORs5Iric0E9Mzz//vPr27avo6Gjl5uZq3bp1xx2/bds2TZw4UTExMcrOzta8efOOGPPRRx9p\n5MiRio6O1umnn64XX3yxzePLli2T1Wpt88dms8ntdp/EywO6n8dnaNZHxdpR0azsOLt+dWEPxTnY\n6wQA0H2mj0jTxX3j1eg19LPVB/VNVbPZJQEnrN2A8uabb2rGjBmaO3euCgoKlJeXp4suukiFhYVH\nHV9TU6PJkycrKytL+fn5WrJkiRYsWKBFixa1jtm7d68uvvhijR8/XgUFBZozZ47uuOMOLV++vM21\nYmJiVFJSIpfLJZfLpeLiYjkc7BuBwOX1G/rFumJtLG5QSpRNz0/qobToCLPLAgCEGavFoofGZmhc\njxhVNft1y98Pan8Nv+RFcGg3oCxatEjXX3+9brjhBg0YMEDPPPOMsrKytHTp0qOOf/3119XU1KRX\nXnlFgwYN0mWXXabZs2e3CSgvvPCCsrOztWTJEg0YMEA33nijrr32Wi1cuLDNtSwWi9LT0+V0Olv/\nAIHK5zf04PoSrd5fr3iHVc9f2FM58QRqAIA57DaLFk7MUm5GtMobfbr57wdVXO8xuyygXccNKG63\nW1u2bNGUKVPaHJ8yZYrWr19/1HM2bNigCRMmKDIyss34oqIi7du3r3XM0a6Zn58vn8/XeqyxsVF9\n+vRRTk6OLr30UhUUFJzcqwO6iWEYenxTqVbsrVVMhEXPXdBTA1Ii2z8RAIAuFBVh1eLze2hoWpRc\n9V7dsuqgyhu9ZpcFHNdxA0p5ebl8Pp8yMjLaHHc6nXK5XEc9x+VyHTH+279/e05JSclRx3i9XpWX\nt2wuNHDgQL388sv6/+3deVxU5R4/8M+ZhVnZYRiG1V1EXHLJPa0kLa+VluVWlLmUmamlr+7NX94W\nzbwtlma7WvfnzRazMm9KimZlv8QFFVwDlB3ZGZaBmXl+fyBznUAwUwaYz/v14gVz5jlnnoNfec1n\nzvM855tvvsF//vMfqNVqDB06FGfPnv0Tp0d0/Qkh8K/EAmw5Wwa1XMLqm02ICVS7ultEREQAAJ1S\nhjU3m9DNV4Xz5bV49IcslFhsze9I5CLXfHD8tbrHw6BBgzBo0CDH4yFDhqBv37546623sHr16kb3\nSZ5LEQIAACAASURBVExMvCavTZfH33FDX+WrsL1QDYUkMNtUAWSkILHxKVpujbVDV4u1Q1eLteNs\ndoCEVRU6nC2pQdw3p7EwvAJaruHSKNbO9dWlS5cmn28yoAQEBEAulyMvL89pe15eHoKDgxvdx2g0\nNri6Ur+/0Whsso1CoUBAQECjx5XJZLjhhhtw5syZy/a3f//+TZ0O/UWJiYn8Hf/Bu0cLsb2wCHIJ\neOUmE0aF6V3dpVaJtUNXi7VDV4u107joXlbM2JGJc2bgo+IgrL0lBDoll8G/FGvn+istLW3y+SYr\n0sPDA/369cPOnTudtsfHx2PIkCGN7jN48GDs27cPFovFqX1ISAgiIiIcbeLj4xscc8CAAZDLG4/y\nQggkJSXBZDI1eUJELeWdpEK8k1QEmQS8MNTIcEJERK2eQavAu6NDYNQqkHShGnN3ZcFcw+Fe1Lo0\nG5kXLlyIDRs24MMPP8SJEycwf/585ObmYs6cOQCAZ555Brfeequj/ZQpU6DVahEXF4fk5GRs2bIF\nK1euxMKFCx1t5syZg6ysLCxYsAAnTpzABx98gI0bN+Kpp55ytPnnP/+JnTt3IjU1FUeOHMGMGTOQ\nnJzseF0iVxFCYF1SId49WhdOXhwahLEdPF3dLSIioiti0ivxfmwojLq6kPLYrmyUM6RQK9LsHJRJ\nkyahsLAQL774InJychATE4Pt27cjLCwMQN3E99TUVEd7Ly8vxMfHY+7cuejfvz/8/Pzw1FNPYcGC\nBY42kZGR2L59OxYsWIB169YhJCQEb731Fu6++25Hm9LSUsyaNQu5ubnw9vbGDTfcgB9//JGX3Mil\nhBB4O6kIHxyrCycvDTViDMMJERG1MaGeSnwwOhQz4zNxrKAac3dlY+0tJnjyxsLUCkhCCOHqTvwV\nl45h8/b2dmFP2j93H5MphMDaI4X48Hgx5BLw0jAjbotkOLkS7l47dPVYO3S1WDtXJttci5k7M5Fd\nYUVPfxXevjXE7UMKa+f6a+79O2dFEV0BIQTePPy/cLJiOMMJERG1ffXDvUL0ChwvtGAOlyCmVoAB\nhagZdiGw/LcL2JBcDIUEvDzciNERDCdERNQ+1IeUUL0SKYUWzNyZiQuVvJkjuQ4DClETau0Cz/6U\nhy9Ol8JDJuHVkcG4leGEiIjamWCdEh/eFoqO3h44W1KDh3dkIqu81tXdIjfFgEJ0GdVWO57ak4P/\nppdDq5Cw9hYTRoRyKWEiImqfDFoFPogNRQ9/FTLNtXhoRwZ+L7E0vyPRNcaAQtSIilo75u3Oxo9Z\nFfD2kOG90aHob9S6ultERETXla9ajndvDcENBg0uVNnwyM5MJBdWu7pb5GYYUIj+oKjKitnxmUjM\nq0KARo4PbwtFdIDa1d0iIiJqEXoPOdbeYsKwEC1KLHbMjs/CgdxKV3eL3AgDCtElzpfVIG5HJpIL\nLQjRK7D+tjB08lG5ultEREQtSq2Q4bWbTIiN0KOi1o7HdmXhv2nlru4WuQkGFKKLjhdUI+77TGSU\n16K7nwobxoQh1FPp6m4RERG5hFIuYfkwIyZ394HVDvz9p1xsTC5GG7+FHrUBDChEAH7MNGPmzkwU\nW2wYYtLig9hQBGgUru4WERGRS8llEp7uH4AF/QIAAG8cKsArBy7AZmdIoeuHAYXc3pYzpViwJwfV\nNoHxnTzxxigTdEr+1yAiIgIASZLwQA9frBhmhFIm4dNTpVi8LwfVVruru0btFN+FkduyC4HVhwrw\nwq/5sAtgZowflg0OglImubprRERErc6YDp54+xYT9EoZdp+vwKz4LBRW8YaOdO0xoJBbqqy1Y9Ge\nHGxILoZcAp690YDH+vhDkhhOiIiILqe/UYv1t4XCqFPgWEE1pm3PwKki3iuFri0GFHI7ORW1iNuR\ngT2ZFfDykGHtLSGY2NXb1d0iIiJqEzr7qvDvsWHoFahGbqUVD+3IQEKG2dXdonaEAYXcStKFKkzb\nnoEzxTWI8FLi47FhuDGYN2AkIiL6M/w1Crw3OgR3dPBElVVg0Z4crD9exBW+6JpgQCG38e3vZZi5\nMwtF1TbcaNTg4zFhiPDycHW3iIiI2iSVXIYXhgbh8T7+EADePFyIpb/kcfI8/WVcR5XavVqbwL8S\nL+Cz06UAgEldvfHUgEBOhiciIvqLJEnCjBg/dPD2wD9+ysV3qeX4vaQG/xoRjBDeS4yuEq+gULuW\nX2nFI/GZ+Ox0KZQyCUsHGfDMjQaGEyIiomvo5nA9No4NQ5inEieLLJiy/Tx+ya5wdbeojWJAoXYr\nMa8Sk787j6MXqmHUKrD+tlBM6MLJ8ERERNdDV18V/u/tYRgRokNZjR2P78rG+0eLYOe8FPqTGFCo\n3RFC4OOUYsyJr5tvMtCowf+9IwzRAWpXd42IiKhd8/SQ4/VRwXi0tx8A4O2kQizYk4NSi83FPaO2\nhAGF2pXiahvmJ2Tj9YMFsAkgLtoXa28JgZ+a062IiIhagkySMKuXP9682QQvDxl+zKzA/d+dx5H8\nKld3jdoIBhRqNxJzK3HftnPYl1UJLw8ZXhsZjPk3BEDB+SZEREQtbliIDv+5IxwxAWrkVljxyM5M\nfHisCDY7h3xR0xhQqM2z2gXWJRViVnwWLlTZ0NegxuZx4RgVpnd114iIiNyaSa/Eh7eFIi7aFzYB\nrDlSiMd2ZaGgyurqrlErxoBCbVq2uRaz47Pw3tEiAMAjMX54b3QojDoubUhERNQaKGUS5t8QgDU3\nm+CrkuO33Crct+089mVylS9qHAMKtUlCCHx9thSTtp3HofwqBGjkeOfWEMzt488hXURERK3Q0BAd\nNo8Lx0CjBkXVNjyRkI0X9uehopY3diRnDCjU5hRVWbFwTw6W7c9HRa0dN4df/IMXrHV114iIiKgJ\ngVoF3r4lBAv6BUApk7DlbBnu23YOh/I4gZ7+hwGF2pSE82bc8+157MmsgF4pw4tDg/CvEcFcpYuI\niKiNkMskPNDDF5tuD0M3XxWyzHUT6N84WIAaG6+mEAMKtRFF1VY8sy8HC/fmoNhSd2+Tz/8Wjjs6\nekGSOKSLiIiorensq8InY8PwSE9fSBKwMaUY93+XweWICfzYmVo1IQS+SyvHq4kXUGKxQy2XMK+v\nP+7v7gMZgwkREVGbppRLmNs3AMNDdfg/v+QhrbQGD+/IxKRu3pjXNwA6JT9Ld0f8V6dWK9tci8d3\nZ2Ppz3kosdhxo1GDz/8WgSlRvgwnRERE7UivQA02jwvHjJ6+kEvA5lOluOebc9iXxZW+3BGvoFCr\nU2sX+M/JEryTVIgqq4CXhwyL+gfibx09OZyLiIionVLJZXi8bwBGR3ji+V/zkFJowRO7s3FbpB4L\n+wXCoOXbVnfBf2lqVQ7kVuLl3y4gtbQGABAbocfiAYHw17BUiYiI3EE3PxU2jgnDf06W4O0jhdiR\nbsa+zArM7u2Pyd19oOTtBNo9vuujViG/0opXEy9g5zkzACDMU4nFAwIxLETn4p4RERFRS1PIJEzv\n4YtbwvVYdeAC9mRW4PWDBfj6bBmeGRiI/kbeWqA9Y0Ahl7LY7Nh0ogTvHytClVVALZcwI8YP03v4\nQCXnFCkiIiJ3ZtIr8fooE37KqsArB+pGWMyMz8JtkXo80TcAJr3S1V2k64ABhVzCLgS+TyvHW0cK\nkVthBQDcHKbDov6B/GNDREREToaF6DDAqMHHySX46HgRdqSbkXC+AlOifPBwT194eshd3UW6hhhQ\nqMUl5lbitYMFOFFkAQB08fHAgn4BGGzicC4iIiJqnEouw8xefrijoyfWHC7Ef9PLsSG5GFvPlmJm\njD/u7eoNpZzzU9oDBhRqMamlNVh9qAA/ZtYtGRiokWNuH3+M6+gFOSe8ERER0RUw6ZVYPtyIqVE+\neO1gAQ7lV2FV4gV8eqoET/T1xy3heq762cYxoNB1d66sBu8dLcJ/08ohAGgVEuKi/TAtygca3oCJ\niIiIrkJ0gBofxIZgb2YFVh8qQHpZLZ7+MRdRfirM6e2H4SE6BpU2igGFrpuM8hq8f7QI36WVwy4A\nhQy4u7M3Zvfy47LBRERE9JdJkoSRYXoMDdHhqzOleP9YEU4UWTA/IQfR/irM6e2PoSYtg0obw3eJ\ndM1lldfi/WNF2JZaBpsAFBJwV2cvzIjx4wR4IiIiuuaUMgmTuvlgfCcvfHmmFB8dL0ZyoQXzdmcj\nJkCNR3v7YVAwg0pbwYBC18ypIgs2JBch/pwZNgHIJeDOTl54JMYPoZ4MJkRERHR9qRUyTI3yxYTO\n3vj8dCnWJxfjWEE1HtuVjSg/FeKi6+6twrmvrRsDCv0lQggcyK3ChuRi7M+pBFB3xWRcR088EuOH\nCC8PF/eQiIiI3I1GKcMD0b64p6s3Np8qwScpJThRZMGSfbkI81Rieg8f/K2jF9QKzoVtjRhQ6KrU\n2gUSzpuxMaUYKYV1ywVrFBImdPbG1B4+CNbxigkRERG5llYpw0M9/TC5uw+++b0Mn6SUIKO8Fsv/\n3wW8k1SE+7v5YGJXL/ip+Za4NeG/Bv0pBVVWbDlTii9Ol+JClQ0A4KuSY3J3H0zq5g1vFW+URERE\nRK2LWiHDpG4+mNjFG7vOm7EhuRgniix4O6kQ7x8rwm2RetzfzQfRAWpXd5XAgEJXQAiBowXVeD9L\ng0On0mC1123v4O2B+7t5Y3wnXiIlIiKi1k8ukxAb6YnREXr8lluFTSdKsC+rAttSy7EttRw9/VUY\nqFKil80ODznf27gKAwpdVonFhv+mlWPr2VKcLq4B4AGZBNwcpsN93XwwwKjhahhERETU5kiShBuD\ntbgxWIvM8lp8froEW8+W4XihBcehxZYv0zGuoyfu6uyFTj4qV3fX7TCgkBObXeC33EpsPVuGhIwK\n1NoFAMBHJcdgfQXm3dSd80uIiIio3Qj1VGJBv0DM6e2P79PKsf5wDjIswL9PlODfJ0oQE6DGnZ28\nEBuph6cHh7K3BAYUAgD8XmLB92nl2JZWjtwKKwBAAjDEpMWdnbwwMkyHo4cPMZwQERFRu6RRyHB3\nF2+ElpyBpkNPbD1bih3pZhwrqMaxgmr8K/ECbgnXY2wHT9wYrIWCSxVfNwwobiyzvBY70suxI70c\nZ0pqHNtD9Arc2ckbf+vkCSMDCREREbkRSQJ6BqjRM0CNRf0Dseu8GV+fLUNiXhW+SyvHd2nl8FHJ\nMTpCjzGRnuhjUEPGIe/XFAOKm8mtqMUP58zYkV6O4xeXBwYALw+Z41OBfkEa/kcjIiIit6dRyDCu\noxfGdfRCRnkNtqeW4/v0cqSX1eLz06X4/HQpjFoFYiP1uDlcj5gAhpVrgQGlnRNC4HRxDfZkmLEn\nswIni/4XSjQKCaPC9LgtUo/BwToo5fwPRURERNSYME8PzO7tj1m9/HCq2ILv0+o+8M2ttOLjlBJ8\nnFICf7UcN4XqMDJcj4FGDVRcCeyqMKC0QzU2Ow7lV2NPhhl7Myscc0qAulAy2KTFmEhPDAvRQcPl\ngYmIiIiumCRJ6O6nRnc/NZ64wR9JF6oRf86MPRlm5FRYseVsGbacLYNWIWFoiA43heowOFgLPw3f\ndl8p/qbaASEE0spq8Wt2BfbnVCIxtwrVNuF4PkAjx4gQHUaG6TEwmGmeiIiI6FqQSRL6GjToa9Dg\n6f4BjlErCRkVOFVsQfw5M+LPmQEAUX4qDDZpMdikRe8ADUeuNIEBpY26UGnFofwq/JpTiV+zK5Fb\naXV6vrOPB0aE6jAyVI/oABXHQxIRERFdR5IkoZufCt38VJjd2x/Z5lrsyTDjp6xKHMqvwokiC04U\nWfDR8WJoFRIGGOvuw9IvSIPOPh58r3YJBpQ2QAiBbLMVB/OrcCivCofyq5BRXuvUxlclx6BgLQaZ\ntBgUrIVBy39aIiIiIlcx6ZWYEuWLKVG+qLbacSi/Cr9kV2J/diVSS2uwN7MCezMrANQtVtTXoMEN\nQRr0M2jQzU/l1ssY811sK2Sx2XG6qAbJhdVIulCFQ/nVyP/DFRKNQkLvQA0GGjUYbNKiqy+vkhAR\nERG1RmqFDENMOgwx6QDUraq6P7sSB/OrcDCvCrkVVqfAor34Pi8msG6542h/FfzU7vO23X3OtJWy\n2QXSy2pwvKAayYUWHC+oxpkSC6x253belyTrG4I06Obr3smaiIiIqK0y6pS4u4s37u7iDQDINtfi\nYF5dWKkfKbM/pxL7cyod+4ToFXX3Z/GvCy3d/FTtdrEjBpQWVF5jw5niGpwpseBMsQWni2twtsSC\nKqtwaicB6OjtgZ4BKkT7q9EvSIMO3hybSERERNQemfRKmPRK/K2TFwAgv9KKI/lVOF5YjeMF1ThR\naEGW2Yossxk70usm3UsAwr2U6Oqruvjlga6+KgRpFZDa+HtGBpTrwFxjw7myWqSX1SC9tAanS2pw\nptiCnApro+2NOoUjDUf7qxDlr4ZO2T4TMRERERE1zaBVIDbSE7GRngAAq13g95K64f/HC+q+Uktr\ncK6sFufKah0rhQF181m6+KrQxccDHbw9EOFV9z1QI28zwYUB5SrV2gSyK2pxrqwG6WW1OFda9/18\neQ0KqmyN7qOSS+joXZduu/h6oIuPCp19PdxqTCERERER/TkK2f9WCJtwcVhYjc2O1NIanC6uweni\n+tE5FpRY7I7hYpfSKiRHWIn08kCktxIheiVC9Up4qeSuOK3L4jvjy6i1C+RVWJFtrkV2RS2yzc4/\n51daIS6zr0ouIdxLiQhPD0R6KetSrK8KYZ5KzhshIiIior/MQy5z3DCynhACF6psOFVsQWpJjWM0\nT3pZDUosdsdSx3+kV8oQolciRK9AiGddcDHp674HaRUtPrLH7QKKEALlNXbkV1pxocp68bsN+ZVW\np21F1TbYL5dAAMgkIEirQKSXByK8lIjwqgsjEV4eMOoUnC9CRERERC1KkiQYtAoYtAoMD9E5PVdc\nbcO5shqkXRwall5Wg2xzLbLMtTDX2nGq2IJTxQ3DC1AXYAK1Chg0cgTpFDBoFHWPtQoEaet+9lHJ\nr9kH8VcUUN5++22sWrUKubm5iI6OxhtvvIFhw4Zdtv2xY8fw+OOP48CBA/Dz88Ps2bOxdOlSpzZ7\n9+7FwoULkZKSApPJhMWLF2P27NlObb788kssXboUqamp6NSpE1566SXcddddl33dI/lVKLbYUFx9\n8ctiQ8nF75dus9iaSB4XSagLICa9om7ikk4Jk15Rlyh1Shh0Cih5NYSIiIiI2gBftRy+ag36GDRO\n24UQKLbYkG22IutiYMkqr/ueXVH3wb251g5zaQ3SSi9/fAmAt0oGX7UCfmq548vX8XPddh+VHH7N\n9LXZgLJ582Y8+eSTWLduHYYNG4a1a9di7NixSElJQVhYWIP2ZWVlGD16NEaOHInExEScOHECDz30\nEHQ6HRYuXAgASEtLw+23345HHnkEmzZtwr59+/DYY48hMDAQEyZMAADs378f999/P55//nlMmDAB\nX375Je699178/PPPGDhwYKN9fWhHZnOnA+BiCtTIEXgx8QVq6hJgoEZe912rQIBaAaWcAYSIiIiI\n2i9Jki6Gh7pljP9ICIGyi6OP8i6OOPrj14UqK0otdpRY7CixNB1kAGDPeEPTfRJCNHk54cYbb0Sf\nPn3w7rvvOrZ17doV99xzD5YvX96g/bp16/DMM88gLy8PKpUKAPDSSy9h3bp1yMysCxBLlizB1q1b\ncerUKcd+M2fORHJyMn755RcAwH333YeSkhLs2LHD0Wb06NEIDAzEpk2bHNtKS//3G3j859KL6VAO\nX9XFlFaf3FT12+XQcIWsq5KYmIj+/fu7uhvUBrF26GqxduhqsXboarF2ro7VLlB6cdRS0SVfxdXW\n/z2+OLrp41G+jv28vb0bHKvJKyg1NTU4dOgQFi9e7LQ9NjbWEST+aP/+/Rg+fLgjnNS3X7p0Kc6d\nO4eIiAjs378fsbGxDY65ceNG2Gw2yOVy/Prrr3jiiScatFm7du1l+/vJ7eFNnQ4REREREV0HCpkE\nf40C/prmZ5BceoGh0WM19WRBQQFsNhuCgoKcthsMBuTm5ja6T25uLsLDnYNC/f65ubmIiIhAXl5e\ng2MGBQXBarWioKAAQUFByM3NbbTN5V4XaP5k6a/p0qULf8d0VVg7dLVYO3S1WDt0tVg7rnfNxzq1\nlRvAEBERERFR69NkQAkICIBcLkdeXp7T9ry8PAQHBze6j9FobHCVo35/o9HYZBuFQoGAgIAm29Qf\ng4iIiIiI2p8mh3h5eHigX79+2LlzJyZOnOjYHh8fj3vvvbfRfQYPHowlS5bAYrE45qHEx8cjJCQE\nERERjjZfffWV037x8fEYMGAA5HK5o018fDyeeuoppzZDhw512q+xiTVERERERNQ2NTvEa+HChdiw\nYQM+/PBDnDhxAvPnz0dubi7mzJkDAHjmmWdw6623OtpPmTIFWq0WcXFxSE5OxpYtW7By5UrHEsMA\nMGfOHGRlZWHBggU4ceIEPvjgA2zcuNEpjMyfPx+7d+/GypUrcfLkSaxYsQJ79uzBk08+eS3Pn4iI\niIiIWpFmlxkG6pYOfuWVV5CTk4OYmBi8/vrrjhs1PvTQQ9i7dy9SU1Md7Y8fP465c+fit99+g5+f\nH+bMmdPgRo0//vgjFixYgOTkZISEhGDJkiWYNWuWU5svv/wSzz77LFJTU9G5c+dmb9RIRERERERt\n2xUFFCIiIiIiopbAOxaSg9Vqxd///nd07NgRGo0GHTt2xNKlS2Gz2ZzaLVu2DCEhIdBqtRg1ahRS\nUlJc1GNylR9//BHjx49HaGgoZDIZNm7c2KBNc3VisVgwb948BAYGQq/X484770RWVlZLnQK5SFO1\nY7VasWTJEvTu3Rt6vR4mkwlTp05FRkaG0zFYO+7pSv7u1Js9ezZkMhleffVVp+2sHfd0JbVz+vRp\nTJgwAb6+vtDpdOjXrx9OnjzpeJ6107IYUMhh+fLlePfdd/HWW2/h1KlTWL16Nd5++22sWLHC0Wbl\nypV47bXXsGbNGhw4cAAGgwGjR4+G2Wx2Yc+ppVVUVKBXr15YvXo1NBpNg+XFr6ROnnzySWzZsgWf\nfvop9u3bh7KyMowbNw52u72lT4daUFO1U1FRgcOHD+PZZ5/F4cOH8fXXXyMjIwNjxoxx+qCEteOe\nmvu7U++LL77AgQMHYDKZGrRh7bin5monLS0NQ4cORadOnZCQkIDk5GS89NJL0Ov1jjasnRYmiC4a\nN26ciIuLc9r2wAMPiHHjxgkhhLDb7cJoNIrly5c7nq+qqhKenp7i3XffbdG+Uuuh1+vFxo0bHY+v\npE5KSkqEh4eH2LRpk6NNRkaGkMlkYseOHS3XeXKpP9ZOY1JSUoQkSeL48eNCCNYO1blc7aSnp4uQ\nkBBx8uRJERkZKV599VXHc6wdEqLx2pk8ebKYNm3aZfdh7bQ8XkEhh7Fjx2L37t04deoUACAlJQUJ\nCQm44447ANR9wpCXl4fY2FjHPmq1GiNGjMAvv/zikj5T63MldXLw4EHU1tY6tQkNDUVUVBRriZzU\n383Z19cXAGuHLs9qtWLy5MlYunQpunXr1uB51g41xm63Y9u2bYiKisKYMWNgMBgwcOBAfPbZZ442\nrJ2Wx4BCDo899himTp2KqKgoeHh4oGfPnoiLi3MsKV1/48ygoCCn/QwGQ4ObapL7upI6yc3NhVwu\nh7+/v1OboKCgBjeGJfdVU1ODRYsWYfz48TCZTABYO3R5zz33HAwGA2bPnt3o86wdakx+fj7MZjOW\nL1+OMWPG4IcffsDkyZMxdepUbN++HQBrxxWavFEjuZc333wT69evx6efforo6GgcPnwY8+fPR2Rk\nJB5++OEm973cWGCiS7FO6EpZrVZMmzYNZWVl2LZtm6u7Q63cnj17sHHjRhw5csRpu+BCpdSM+jkk\nd911l+Nee7169UJiYiLWrFmD22+/3ZXdc1u8gkIOL730Ev7+979j0qRJiI6OxrRp07Bw4ULHJHmj\n0QgADT4tyMvLczxHdCV1YjQaYbPZUFhY6NQmNzeXtUSOoTrHjx/Hrl27HMO7ANYONW7v3r3IyclB\ncHAwlEollEolzp07hyVLliA8PBwAa4caFxAQAIVCgR49ejht7969O86fPw+AteMKDCjkIISATOZc\nEjKZzPEJVIcOHWA0GrFz507H89XV1fjpp58wZMiQFu0rtV5XUif9+vWDUql0apOZmYmTJ0+yltxc\nbW0t7rvvPhw/fhwJCQkwGAxOz7N2qDGPPfYYjh07hqSkJCQlJeHIkSMwmUxYuHAhdu3aBYC1Q43z\n8PDAgAEDnJYUBuqWHY6MjATA2nEFDvEih7vuugsvv/wyOnTogB49euDw4cN4/fXX8eCDDwKoG57z\n5JNPYvny5ejevTu6dOmCF198EZ6enpgyZYqLe08tqaKiAmfOnAFQd3n83LlzOHLkCPz9/REWFtZs\nnXh7e2PGjBlYvHgxDAYD/Pz8sHDhQvTu3Ru33nqrK0+NrrOmasdkMuHee+9FYmIivv32WwghHPOW\nfHx8oFarWTturLm/O4GBgU7tlUoljEYjunTpAoB/d9xZc7WzePFiTJo0CcOHD8eoUaOQkJCAzZs3\n4+uvvwbA2nEJ1y4iRq2J2WwWixYtEpGRkUKj0YiOHTuKf/zjH8JisTi1W7ZsmQgODhZqtVqMHDlS\nJCcnu6jH5CoJCQlCkiQhSZKQyWSOnx966CFHm+bqxGKxiHnz5gl/f3+h1WrF+PHjRWZmZkufCrWw\npmonPT29wfb6r0uXBWXtuKcr+btzqT8uMywEa8ddXUntbNiwQXTt2lVoNBrRu3dv8emnnzodg7XT\nsiQhOIOMiIiIiIhaB85BISIiIiKiVoMBhYiIiIiIWg0GFCIiIiIiajUYUIiIiIiIqNVgQCEiIiIi\nolaDAYWIiIiIiFoNBhQiIiIiImo1GFCIiKjViouLQ4cOHRpsr6iogNFoxPr16x3bli1bBplMoEbA\nyQAACJJJREFUhvz8/Gvy2unp6ZDJZFi5cmWzbZ9++mkMGjTomrwuEZG7Y0AhIqJWTZKkBttWr14N\nlUqF6dOnu+T1/2jRokVISkrCt99+e937Q0TU3jGgEBFRqyaEcHpcW1uLN954Aw8//DAUCoWLeuXM\naDRi/PjxWLVqlau7QkTU5jGgEBFRm7Jt2zYUFBRg0qRJru6Kk/vuuw8//fQTzp496+quEBG1aQwo\nRERuwmw246mnnkKHDh2gVqthMBgwatQo7Nu3DwAwcuRIREVFISkpCcOHD4dOp0NERAReffXVBscS\nQuCtt95CTEwMNBoNgoKC8Mgjj6CwsLBB2507d+Kmm26Cp6cnPD09MXbsWCQlJTVot3XrVvTs2RMa\njQYxMTH46quvGj2PrVu3wmQyISoqqtlzzs7ORo8ePdC1a1dkZmb+6fOsP9f3338fnTp1glqtxsCB\nA5GYmNig3S233AJJkrB169Zm+0VERJfHgEJE5CYeffRRrFmzBhMnTsS6deuwZMkSGAwGHD161NGm\ntLQUY8aMQa9evbBq1Sp069YNTz/9NF555ZUGx1q0aBEGDx6MN998E7NmzcIXX3yBUaNGwWKxONpt\n2rQJY8eOhVarxcsvv4xly5YhNTUVw4cPx6lTpxztdu7ciYkTJ0Imk2HFihW4++67MWPGDBw8eLDB\nHJBffvkF/fv3b/Z8z507hxEjRkAmk2Hfvn0IDQ0FUDen5ErPEwA2b96MVatW4dFHH8WLL76I9PR0\nTJgwAVar1amdt7c3OnXqhJ9//rnZvhERURMEERG5BR8fHzFv3rzLPn/TTTcJSZLEyy+/7Nhms9nE\nqFGjhE6nE6WlpUIIIX7++WchSZL497//7bT/Tz/9JCRJEu+9954QQgiz2Sx8fX3FjBkznNoVFxcL\ng8EgpkyZ4tjWp08fYTKZRFlZmWPb7t27hSRJokOHDo5ttbW1QiaTiQULFjTo/3PPPSckSRJ5eXni\nzJkzIjw8XPTt21cUFBRc1XmmpaUJSZJEYGCgKCkpcbT95ptvhCRJYtu2bQ36EBsbK7p27dpgOxER\nXTleQSEichM+Pj749ddfkZ2dfdk2crkcc+fOdTyWyWSYO3cuKisrsWfPHgDAZ599Br1ej9jYWBQU\nFDi+unXrBoPBgISEBABAfHw8SkpKMHnyZKd2VqsVw4YNc7TLyclBUlI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deEqKxuS7rY4DxIwpI7OV7rJpradNy/YwehfAyaF8AIh6m2va9dcdTXLaDN0x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\nYII=\n", "text": [ - "" + "" ] } ], @@ -540,11 +540,11 @@ "input": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", - "\n", + " \n", "xs = np.arange(15, 30, 0.05)\n", - "p1, = plt.plot(xs, [gaussian(x, 23, .2) for x in xs], label='var=0.2')\n", - "p2, = plt.plot(xs, [gaussian(x, 23, 1) for x in xs], label='var=1')\n", - "p3, = plt.plot(xs, [gaussian(x, 23, 5) for x in xs], label='var=5')\n", + "plt.plot(xs, [gaussian(x, 23, .2) for x in xs], label='var=0.2')\n", + "plt.plot(xs, [gaussian(x, 23, 1) for x in xs], label='var=1')\n", + "plt.plot(xs, [gaussian(x, 23, 5) for x in xs], label='var=5')\n", "plt.legend()\n", "plt.show()" ], @@ -554,9 +554,9 @@ { "metadata": {}, "output_type": "display_data", - "png": 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w3IOD5x4cwXruOwsrpC+/0VldOygjY1C7vW96Wb6+OlCmbn3PUcbZ/lnDvzX4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nHhw89+AI1nPfUVghffWNzuraQRkZg9rtfdPL8rXvQJm69T1HGWf7Zw3/1uDf\ne/uL1GdeWVkZ7BICym63a9y4cVqyZImqqqr0xBNPeF7r1KmTRo4cqTlz5qi6ulp9+/bV1q1btWXL\nFnXv3t3n8NHaHo+HH35Ye/fu1TXXXKO0tDR9/fXXeuGFF1ReXq558+a1+H4tkZSUdMZ/z431trRE\nk2PBcXFxGjp0qNavX+91fMOGDcrMzGzyxvn5+Vq7dq1Pox0AAPiLtaSt1fDdXqz3Y0ldIHxkZ2er\noqLCswrr6V555RXdcMMNeuGFF/TII4+otLRUmzZtUseOHWUYhte53/66rUaNGiXDMDR//nzde++9\n+uMf/6grr7xS27Zt01VXXeXX92pPzX4qz5gxQxMnTtSwYcOUmZmpRYsWyel0atq0aZKkmTNnavv2\n7Q2GkZYsWaKOHTtq/PjxgakcAIBGWL/4t9dSupbURIIHEG6GDx/eaKO4JPXs2VO5ubkNju/bt8/r\n68mTJ2vy5Ml+rSs7O7tBEIoEzX4qjx8/XiUlJZo9e7YKCgo0ZMgQrV271rOHh9Pp9DS6WEzT1JIl\nS3THHXdE9NxAAEDoOdzOK1pZGPEAgKb59Kmck5OjnJycRl9bunRpg2OGYTQIIwAAtAdr88Ae7R08\n2L0cAJrEen8AgIgSrBGPHgQPAGgSwQMAEFFOBY/22cPDYgWdogpXi5bbBIBoQfAAAEQMt2mqyJpq\n1c6rWjlibEqKs6nGbepoVXD38QCAUETwAABEjKOVLtW6pc5xNiXEtP+POKvBvKic4AEA30bwAABE\nDM80q8T2He2wsKQuAJwZwQMAEDGCtXmgpQdL6iLC0K8UXQL9vzfBAwAQMayldNt7RSuLZ0ndCoIH\nwl9cXJwqKysJH1HCNE1VVlYqLi4uYO8RnE9mAAAC4HB9b0Wwg0dhGcED4c9msyk+Pl5VVVXBLqVR\nJ06cUFJSUrDLiCjx8fGy2QI3LkHwAABEjMPlNZKCGTzqlvAtYsQDEcJmsykhISHYZTRq165dysjI\nCHYZaAGmWgEAIoY14tHeu5Zb2L0cAM6M4AEAiBjWL/ypBA8ACDkEDwBAxAjW5oGWrvF2xdik49Vu\nVda6g1IDAIQqggcAICJU1rp1otqtGJvUJT44P94Mw1ByfegpqWATQQA4HcEDABARiut/0U92xMgw\njKDVYY220GAOAN4IHgCAiFAc5GlWlmQHK1sBQGMIHgCAiGD9om/94h8snhGPcqZaAcDpCB4AgIhg\nTbUK/oigDdnrAAAgAElEQVRH3fsXM+IBAF4IHgCAiFBUbo14BDt41I24EDwAwBvBAwAQEYpDZapV\nB6u5nKlWAHA6ggcAICJ4VrUK0uaBlh5MtQKARhE8AAARwfpFP4WpVgAQkggeAICIECqrWnVNsMtu\nSMeq3Kp2sXs5AFgIHgCAsFfjMnWsyi27UfeLfzDZDEPdPdOt6PMAAAvBAwAQ9oor60Y7uiXYZQvi\nruUWplsBQEMEDwBA2LOW0u0R5MZyi2cTQUY8AMCD4AEACHueFa2C3FhuYcQDABoieAAAwp71C36P\nIDeWWzwjHuUEDwCwEDwAAGGvKMRGPKwpXzSXA8ApBA8AQNjz9HiESPCwploVMdUKADx8Ch4LFixQ\nenq6HA6HMjIytHXr1mavee6553TuuecqISFBvXr10syZM9tcLAAAjSkOkT08LKeaywkeAGBp9k9D\nubm5mj59uhYuXKgRI0Zo/vz5Gj16tD799FP16dOn0WtmzJiht99+W7/97W81ZMgQlZaWqqCgwO/F\nAwAgndZcHiKrWllTvorLmWoFAJZmP6Hnzp2rKVOmaOrUqZKkefPm6Z133tHChQv11FNPNTj/iy++\n0PPPP6+PP/5YgwYN8hy/8MIL/Vg2AACnnGouD43gUbefiHS0yqUat6lYW/D3FgGAYGtyqlV1dbV2\n7NihrKwsr+NZWVnatm1bo9e8+eab6t+/v9auXav+/fsrPT1dkydPVlFRkf+qBgCgXq3b1JFKlwzV\n/cIfCuw2w1NLCdOtAEBSM8GjuLhYLpdLqampXsdTUlLkdDobvWbv3r3av3+/Vq5cqZdeeknLly/X\n559/rhtvvFGmafqvcgAAJB2pdMlUXeiICaGRBWv0hZWtAKCO38ek3W63qqqqtHz5cp1zzjmSpOXL\nl2vQoEHKy8vTpZde2uh1eXl5/i4FzeCZBwfPPTh47sHRHs/96wq7pI7qYFaH1P/OMdUdJMXq/z7+\nXJVJ7TvqEUrPIVrwzIOD596+Bg4c2KbrmwweycnJstvtKiws9DpeWFiotLS0Rq9JS0tTTEyMJ3RI\n0jnnnCO73a4DBw6cMXhkZGS0tHa0QV5eHs88CHjuwcFzD472eu5lB09KXxeoX3KSMjLODfj7+Wpg\nTaE+3nNcnXqdrYxBXdrtffn33v545sHBc29/paWlbbq+yalWcXFxGjp0qNavX+91fMOGDcrMzGz0\nmhEjRqi2tlZ79+71HNu7d69cLpf69evXpmIBAPi2UNs80JLMJoIA4KXZfTxmzJihZcuWafHixfrs\ns8/0wAMPyOl0atq0aZKkmTNn6tprr/Wcf+211+qSSy7RnXfeqZ07d+rDDz/UnXfeqcsvv5xUCgDw\nu1N7eIRY8GATQQDw0uyn9Pjx41VSUqLZs2eroKBAQ4YM0dq1az17eDidTq/RDcMw9Je//EX333+/\nrrjiCjkcDmVlZWnu3LmB+y4AAFHr1FK6obGileVUcznBAwAkH5vLc3JylJOT0+hrS5cubXCsZ8+e\nWrlyZdsqAwDAB9ZUq1DZw8PCqlYA4K3ZqVYAAISyovIQn2pVzogHAEgEDwBAmPP0eHQIralW3Rwx\nMlS3z0itm32sAIDgAQAIW676XcslKTkhtEY8Ym2GuibYZUqeGgEgmhE8AABh61iVSy5T6hJvV6w9\ndHYtt7CyFQCcQvAAAIStohBd0criaTCnzwMACB4AgPAVqpsHWpJZ2QoAPAgeAICwVexZ0SpURzyY\nagUAFoIHACBseaZadQjNEQ+rLjYRBACCBwAgjBWHyVSronKmWgEAwQMAELY8e3iE6FQrVrUCgFMI\nHgCAsGWNePQI0REPploBwCkEDwBA2Coqt5bTDc3gYW1qWFLpkovdywFEOYIHACAsmaap4sr6qVYd\nQnOqVazdUJd4m9ymdLSKPg8A0Y3gAQAIS8eq3Kp1S0lxNsXbQ/fHmWcTQaZbAYhyoftJDQBAE4or\nQnualYWVrQCgDsEDABCWikJ8RSsLK1sBQB2CBwAgLIX6ilYWVrYCgDoEDwBAWLJWtArVzQMtnqlW\nFUy1AhDdCB4AgLDk6fEI0RWtLD2sqVbljHgAiG4EDwBAWLJGEMJlxIOpVgCiHcEDABCWiivCY6rV\nqeV0mWoFILoRPAAAYak4XFa1qp8KVlJRK7fJ7uUAohfBAwAQdkzTDJtVreLtNnWKs6nWlI5VMuoB\nIHoRPAAAYedEtVtVLlOJsTZ1iA39H2WsbAUABA8AQBgKl80DLT3YRBAACB4AgPBTHCYrWlmS2UQQ\nAAgeAIDw49nDI2xGPFjZCgAIHgCAsFMUJkvpWthEEAAIHgCAMFRcHh4rWlnYRBAAWhA8FixYoPT0\ndDkcDmVkZGjr1q1nPPfrr7+WzWZr8N/69ev9UjQAILqFXXN5B1a1AgCfgkdubq6mT5+uWbNmaefO\nncrMzNTo0aN18ODBJq/761//KqfT6fnvqquu8kvRAIDoZgUP6xf6UJfMqlYA4FvwmDt3rqZMmaKp\nU6dq0KBBmjdvntLS0rRw4cImr+vWrZtSUlI8/8XGxvqlaABAdAu7Va1Om2plsns5gCjVbPCorq7W\njh07lJWV5XU8KytL27Zta/LasWPHKjU1VSNGjNDq1avbVikAAPWKw2yqlSPGpo6xNtW6pWNV7mCX\nAwBB0WzwKC4ulsvlUmpqqtfxlJQUOZ3ORq9JSkrSM888o9dff13r1q3TNddcowkTJmjFihX+qRoA\nELXKatyqqDWVYDfUMQx2LbdYK1vRYA4gWgVkjLp79+768Y9/7Pn6kksuUUlJiebMmaM77rij0Wvy\n8vICUQqawDMPDp57cPDcgyMQz91ZZZOUpCRbrT744AO/3z9Q4msTJcVo278/U2nHwIYP/r23P555\ncPDc29fAgQPbdH2zwSM5OVl2u12FhYVexwsLC5WWlubzG1166aVasmTJGV/PyMjw+V5ou7y8PJ55\nEPDcg4PnHhyBeu55znJp7yGd1TVRGRnn+v3+gdK/0qnP951Q1z79lTGgU8Deh3/v7Y9nHhw89/ZX\nWlrapuubHaOOi4vT0KFDGyyFu2HDBmVmZvr8Rjt37lSvXr1aXiEAAKcpCrPGcksymwgCiHI+fWrP\nmDFDEydO1LBhw5SZmalFixbJ6XRq2rRpkqSZM2dq+/bt2rhxoyTpT3/6k+Li4nTRRRfJZrPprbfe\n0oIFCzRnzpzAfScAgKhg9UiEy+aBFqteltQFEK18+tQeP368SkpKNHv2bBUUFGjIkCFau3at+vTp\nI0lyOp3au3ev53zDMDR79mzt379fdrtdgwYN0tKlS3X77bcH5rsAAESNcNs80HJqSV02EQQQnXz+\nc1FOTo5ycnIafW3p0qVeX0+aNEmTJk1qW2UAADSiuDw8p1pZmx2yqhWAaBU+6xACAKDTp1qF24gH\nPR4AohvBAwAQVjzBo0OYjXicNtWK3csBRCOCBwAgrITrqlYdYm1KjLWp2m3qeDW7lwOIPgQPAEDY\nqKhx62SNW3E2Q53iwu9HWDK7lwOIYuH3qQ0AiFqHPdOs7DIMI8jVtNypJXVZ2QpA9CF4AADChrWU\nbkqY9XdYaDAHEM0IHgCAsGH9wh5umwdaTu3lQfAAEH0IHgCAsFFUv4dHuAaPU3t5MNUKQPQheAAA\nwsbhMJ9qZe09UsSIB4AoRPAAAIQNz1SrDuG1eaClB1OtAEQxggcAIGwUVURGj4c1ZQwAognBAwAQ\nNjw9HmE61er0fTzYvRxAtCF4AADCgmmaOhzmq1olxtrkiDFU6TJ1sobdywFEF4IHACAsHK92q9pt\nqmOsTR1iw/PHl2EYp6ZbsbIVgCgTnp/cAICoc2oPj/BsLLd4pluxiSCAKEPwAACEBU9jeZj2d1h6\neEY8CB4AogvBAwAQFjz9HRESPNhEEEC0IXgAAMKC1RMRro3lFis4MeIBINoQPAAAYaEozFe0slg9\nHkX0eACIMgQPAEBYsKZapYTpruWWZKZaAYhSBA8AQFiImOZyploBiFIEDwBAWIiYHo/Tdi8HgGhC\n8AAAhDyX21RJRWT0eHSMtSnBbqii1lQZu5cDiCIEDwBAyDtS6ZLLlLrG2xVrN4JdTpt47V5OgzmA\nKELwAACEvFP9HeHdWG5JZroVgChE8AAAhLzDEbKUroUGcwDRiOABAAh51i/oKWG+opWlh2eqFUvq\nAogeBA8AQMizfkEP96V0LVaAOkyPB4Ao4lPwWLBggdLT0+VwOJSRkaGtW7f6dPPdu3crKSlJSUlJ\nbSoSABDdiiJkRSuLtaTuYaZaAYgizQaP3NxcTZ8+XbNmzdLOnTuVmZmp0aNH6+DBg01eV11drezs\nbF155ZUyjPBegQQAEFynejwio7mcEQ8A0ajZ4DF37lxNmTJFU6dO1aBBgzRv3jylpaVp4cKFTV73\n6KOP6qKLLtKtt94q0zT9VjAAIPpEXI8HwQNAFGoyeFRXV2vHjh3KysryOp6VlaVt27ad8bq3335b\nb7/9tn7/+98TOgAAbRapPR5FFbVy83MSQJRoMngUFxfL5XIpNTXV63hKSoqcTmej1+Tn5+vuu+/W\nihUr1KFDB/9VCgCIStUut45VuWQ36jYQDBTTNGWWnZBZmC/z5PGA/uHMEWNTUpxNtW7pWBUrWwGI\nDn7/09HEiROVk5OjSy+9tEXX5eXl+bsUNINnHhw89+DguQeHP557cbUhqZOS7G59uOODthdlMd1K\n2ve5kvZ+oqT9Xyjh8CHZXKemPrltdlUl99SJfoN0In2wjg84X7L778dmktFRJ2TXe3kfqW+C22/3\nlfj3Hgw88+DgubevgQMHtun6Jj9Bk5OTZbfbVVhY6HW8sLBQaWlpjV6zefNmbdmyRU8++aSkur8g\nud1uxcbGauHChfrv//7vRq/LyMhoTf1opby8PJ55EPDcg4PnHhz+eu47D1dIX32jszo7lJExqM33\nMysrZP51lcx1r0vOby2UkuCQEjtJFWWylZ+U4/AhOQ4fUsr2TVL3FBlZt8j4wQQZSZ3bXEe/Y4eU\nX1CuHmcPUsZZiW2+n4V/7+2PZx4cPPf2V1pa2qbrmwwecXFxGjp0qNavX69bbrnFc3zDhg269dZb\nG71m165dXl//+c9/1i9/+Utt375dvXr1alOxAIDo41lKt439HaZpytyyTuZLv5NKDtcd7JEm44rv\nyxgyTBo0RIbjVAAwqyqkPZ/K/DhP5t/fkQ59LfPVhTL/8qqM23PqQoi99VO/WNkKQLRp9lN8xowZ\nmjhxooYNG6bMzEwtWrRITqdT06ZNkyTNnDlT27dv18aNGyVJgwcP9rr+/fffl81ma3AcAABfFJW3\nfQ8P88hhuZ99XPr4/boD5wyWbfxd0tD/OGN4MOId0vlDZZw/VOaEu6WP3pd71WLp4+0yX/iVzI1/\nlu2hp2Wk9W1VTZ6VrdjLA0CUaPZTfPz48SopKdHs2bNVUFCgIUOGaO3aterTp48kyel0au/evU3e\ng308AACtVVRR13zd2qV0zQ+3yf3cLKn0qNS5q4xJD8i46kYZNp/20JVU/3Pswstku2CY9M935V76\njPTVZ3LPuF3GPbNk+4/vt7iulA71mwgy4gEgSvj0qZuTk6N9+/apsrJS27dv14gRIzyvLV26tMng\nMXnyZB0/frztlQIAopJn88BWBA/326/J/fMf1YWOCy+T7bmVsl1zU4tCx+kMw5CRea1sz62UkXmd\nVFEm85mZcq+Y3+JVsFIcTLUCEF1a98kLAEA7KWrFruWmacq9fJ7MF38tmaaM7Gmy/XSBjK7JfqnJ\nSEyS8fCvZdw9U7LZZb7+R5nPPynT5XuI8OzlQfAAECUiYycmAEDE8jSX+9jjYZpmXQ/GO69LNruM\nHz0h29Vj/F6XYRgyfjBeZkqa3HMekfnumzLLTsj28K9l+LDsLs3lAKINIx4AgJDWkh4P0zRlLn2m\nLnTExsn2P88FJHSczsj4D9l+8YKUmCT93yaZv3tCpqv5TQG7JtgVY5NKq92qrPXvPh4AEIoIHgCA\nkFVW41ZZjVvxdkNJcc3/yDJfWyTzf1dIMTGyPfpbGUNHNHuNPxiDLpDtieelhA51S/YueqrZng+b\nYSi5fhSniJWtAEQBggcAIGSdvpRucyskut/9X5m5f5BsdtkefFpGxn+0R4kexqALZJv1OykuQeaG\nNTJXL2n2mlN9Hs2PkABAuCN4AABC1qnNA5tuLDc/+UDmwl9Ikoy7H5XxvWsCXltjjO9myDbjl5Jh\nyHz5eZnbNjZ5PitbAYgmBA8AQMg67MPmgWbhIbmfflCqrZVx4x2yff/W9iqvUcblV8uYeL8kyf3c\n4zL3fn7Gc1PYRBBAFCF4AABC1qkRj8aDh1lTLfdvHpFOlEpDR8iY/OP2LO+MjP/8LxnX3CRVV8r9\n64dllp1o9LwebCIIIIoQPAAAIcvqfUg5w4iHueQZac+nUkov2X78Sxl23/f6CCTDMGT8v5lS/3Ol\nwm/k/v3PGm02t74v9vIAEA0IHgCAkFVYfuYeD/fW9TLXrZRiYmV75DcyOnZq7/KaZMTFy/bwHKlD\nx7pldt96pcE5KYl1waOQ4AEgChA8AAAhy5qClNoh1uu4WeSUuXC2JMm48yEZ5wxu99p8YaT1ke3+\nJyVJ5ku/k7l/j9frqR0IHgCiB8EDABCynGU1kqSeiaemWplut9zzfiqVnZAyrpAxOrjN5M0xLr9a\nxnVjpdoauZ/9icyaas9rqR1OTbVyuZve9wMAwh3BAwAQkmrcpoorXDLk3Vxu/uVV6eP3pc5dZfvR\nE83u7xEKjDsflHr2kb7eLXPFAs/xOLtN3RLscplSSSV7eQCIbAQPAEBIKiqvlSmpu8OuWFtduDDz\n98t8+feSJNu9T8jo0j2IFfrOcHSQbfovJJtN5psvyfziI89r1qiHNboDAJGK4AEACElWf0fP+l/M\nTbdb7vm/kKqrZFx1g4xhI4NYXcsZ514o4+ZJkmnK/fyTnilX9HkAiBYEDwBASHKW1f0ibq38ZG5Y\nI33ygdS5m4wpDwaztFYzJvw/qVdf6eBemauWSJJSrZWtyggeACIbwQMAEJIKPSMesTJLDsv80+8k\nScZdj8ro1CWYpbWaEZ8g271PSJLM1Ytl7t/jaZx3MuIBIMIRPAAAIcnqeUhNjKnbKLD8pDTsShnD\nrwtyZW1jnD9UxqhbpNpauV/8tVIdjHgAiA4EDwBASLJ6PAYf/FDmP9ZL8Qmy3fVoWKxi1Rzjh/dJ\nSV2kXXn6zmdbJNHjASDyETwAACHJWV6rWFeNBq9+TpJkjL9LRo+0IFflH0ZSZxk//JEkqc/q3yuh\ntpLgASDiETwAACGpsKxWP9z9luIPH5TOSpcxZmKwS/Ir49qbpf7nyX7ksO78/A0VV9Sqlk0EAUQw\nggcAIORUu9zSsRJN+fwNSaqbYhUbG+Sq/Muw22W7+1FJ0g93v6VeJ5wqqmDUA0DkIngAAELO4XKX\npn3ymjq4qqRhI2VceFmwSwoI49wLZVx1g+LctZrx72U0mAOIaAQPAEDIKf3iM9309WbV2uyy/df0\nYJcTUMakB1QZ59AVzh2qzft7sMsBgIAheAAAQoppmuqRO082mfrXhTfI6N0v2CUFlNE1Wf93RV3/\nyoDV82TW1AS5IgAIDIIHACC0fLBV3Xd/oNLYRH10dWQ1lJ9J/hXjtC+ptzqVHJL511XBLgcAAoLg\nAQAIGWZtjdzLnpUk/fG8ceqa3C3IFbWPlE4Jev67t0uSzJV/kFl+MsgVAYD/ETwAACHDXL9G+maf\nijr30usDRim1Q0ywS2oXqR1i9Le0DO1OPVc6fkzmm8uDXRIA+B3BAwAQEsyTJ2S+ukiS9PKw/1Kt\nLUY9EyNrCd0z6ZkYIxmGFl5YN7XMfHO5zKPFQa4KAPzL5+CxYMECpaeny+FwKCMjQ1u3bj3juZ9+\n+qmuuuoq9ezZUw6HQwMGDND//M//qIaGOQDAGZh//pN04ph0/iV6O3moJCklSkY8kh0xshnS35MG\nyrx0pFRZITP3D8EuCwD8yqfgkZubq+nTp2vWrFnauXOnMjMzNXr0aB08eLDR8+Pj4zVlyhRt2LBB\nX375pZ577jktXrxYP/nJT/xaPAAgMpjHSmS+tUKSVHPH/TpW7VaMTeqeYA9yZe0jxmaohyNGpqTi\nW6ZJNpvM9WtkHtof7NIAwG98Ch5z587VlClTNHXqVA0aNEjz5s1TWlqaFi5c2Oj5AwYM0KRJkzRk\nyBD16dNHN954o26//Xb94x//8GvxAIDIYK5aLFVVSsOuVEHv8yRJPTvEym4zglxZ+0lLrBvdOdil\nj4yrx0hul8wV84NcFQD4T7PBo7q6Wjt27FBWVpbX8aysLG3bts2nN9mzZ4/++te/NrgHAABmUYHM\nd1ZJhiHb7feooKxuWq71i3i0SKvvZykoq5WRPU2Ki5e5bYPML3cFuTIA8I9mg0dxcbFcLpdSU1O9\njqekpMjpdDZ5bWZmphwOh77zne/osssu089+9rM2FQsAiDxm7h+k2hoZI0bJOPs7yj9ZK0nq1TE6\nGsstvTrWBa38kzUyklNl3Fi3vK57+bxglgUAfhPQPyetXLlSJ0+e1M6dO/Xwww/rkUce0Zw5cxo9\nNy8vL5CloBE88+DguQcHzz04mnvu8SVOnffu/0qGTZ8OGaGqvDztOBwvKUHu0sPKy2u8lzASVR+N\nldRBH+93Kq9mn+zpF2lwQgfFfLxdn696WSfPPtfne/Hvvf3xzIOD596+Bg4c2Kbrmw0eycnJstvt\nKiws9DpeWFiotLS0Jq8966yzJEnnnnuuXC6X7rzzTv3qV7+S3d6wWTAjI6MldaON8vLyeOZBwHMP\nDp57cPjy3N2/fVSm6ZZx3VgNybpekrTm706p5IQyvtNPGQM6tUepIaE6v0zLnfmqSeisjIzzJUnu\n/MkyX1mggTs2yXbLHTKM5nte+Pfe/njmwcFzb3+lpaVtur7ZqVZxcXEaOnSo1q9f73V8w4YNyszM\n9PmNXC6X3G633G53y6sEAEQcc+8XMreul2JiZYy/y3M8v77Ho1eU9Xj0qu/xsL5/STJuuE1K6ix9\n+qH0738FqzQA8AufPtVnzJihiRMnatiwYcrMzNSiRYvkdDo1bdo0SdLMmTO1fft2bdy4UZK0fPly\nORwOffe731VcXJzy8vL0k5/8RBMmTFBsbHTN2QUANM79St2KTcbo8TJ69PQcLyir6/FIi5LNAy09\n64NWYVmtXG5Tdpsho0NHGTdPkrn893K/ukC2Cy/zadQDAEKRT8Fj/PjxKikp0ezZs1VQUKAhQ4Zo\n7dq16tOnjyTJ6XRq7969nvNjY2P1q1/9Srt375ZpmurXr59+9KMf6cc//nFgvgsAQFgxv9wl5f1d\nSnDIuOVOz/Eal6mi8lrZDCklykY8EmJs6pZg15FKl4orapVaH7yMH2TL/N+XpS8+lnb8Qxo6IsiV\nAkDr+PypnpOTo5ycnEZfW7p0qdfX2dnZys7ObltlAICI5V75oiTJ+MEEGV26eY47y2tkSkp1xCg2\nivbwsPRKjNGRSpfyy04LHo4OMv5zssxlz8r96kLZLhnOqAeAsOTTBoIAAPiL+dVnUt4WKT5BxpiJ\nXq8V1C+lm9YxukY7LGn1SwgXnKzxOm6MvlXqmizt+VTa/rdglAYAbUbwAAC0K3fuHyRJxvdv9Rrt\nkOTZPLBXlPV3WHqdtong6Yx4h4xbpkiS3K8slMlCLQDCEMEDANBuzL1fSO+/J8XFy7h5UoPX8z2N\n5dE64nFqE8FvM7JukbqnSF9/Kf3fpvYuDQDajOABAGg37tfreztGjZPRNbnB69YUo7Qo27XcYgWu\nb494SJIRFy/jlqmSJPfKPzDqASDsEDwAAO3C3L9H+ue7UmycjP9sONohnfqFO9r28LCcmmrVcMRD\nkoxrb5K69ZC+3k2vB4CwQ/AAALQL0xrtuO4/ZXRLafSc/Ggf8eh4qsfDNM0Grxtx8TLGTpZUtzJY\nY+cAQKgieAAAAs48uFfmPzbU7VI+dkqj57jcpg6X14149IzSEY/EWJs6xdlU5TJ1pNLV6DnGdWOl\nLt2lrz6TPtjazhUCQOsRPAAAAWe+/kfJNGVce5OM5NRGzymqqFWtKSU77Iq3R++Pp14dG1/ZymLE\nJ3ga8xn1ABBOoveTHQDQLsxDX8vc+lcpJsZrl/Jvy7f28IjSpXQtVoN5YytbWYzv3yp16iJ9+bH0\n73+1V2kA0CYEDwBAQJmrFktut4yrxsjokXbG8/LrG6qjdSldi9Vgnn+GBnNJMhIcMm6q23zRnfsH\nRj0AhAWCBwAgYMyCAzL/tk6y2WWMO/NohyR9c6LuF+2zkqJ7xKN3/fdvPY8zMX4wQerYSfrsQ2nX\nB+1RGgC0CcEDABAw5qolktsl46obZKT2bvLcb+qnFp0VpStaWc7yNXg4EmXceIekul4PAAh1BA8A\nQEDEHS2S+d7b9aMdU5s9nxGPOlbw+qaJHg+Lcf1tUoeO0sfvy/xsZ6BLA4A2IXgAAAIidds6yVUr\n48rRMtL6NHs+waNO744xMiQ5y2pV4266d8PomCTjhtskMeoBIPQRPAAAfmcezle3f2+TbDafRjsq\natwqqXQp1mYoxRHdzeVxdptSO8TIZUoFvox63HiHlNBB+nCbzC93tUOFANA6BA8AgN+Za5bJ5nbJ\nGDFKRu+zmz3fmlbUu2OM7DYjwNWFPmvU55AvwSOps4zrJ0hi1ANAaCN4AAD8yiwulLnxzzJlyLj1\nv326xppm1TvKG8st1nM42EyDucUY80MpPkHK2yJHwf5AlgYArUbwAAD4lfnGMqm2RscGZ8jo09+n\nazwrWkV5f4elT5LvDeaSZHTuVrepoKSeW98OWF0A0BYEDwCA35hHDstcv0aS5Bxxvc/XWSMefQge\nknxfUvd0xs2TpLh4dfniQ5lffxmo0gCg1QgeAAC/Md94Saqplr53jSpTmt6343Ts4eHtrBaOeEiS\n0dV/+sEAACAASURBVDVZRtZYSZL5+uKA1AUAbUHwAAD4hXm0WOZfV0mSbLfe1aJrD7KUrhfPXh4n\namSaTS+pezrjPyfLbY+RuW2DzIN7A1UeALQKwQMA4Bfmm8ul6ipp2EgZ/Qf5fJ3LbXqWjaW5vE7n\neLuS4myqqDV1pNLl83VG9xSVXDRCMk2Zr/8xgBUCQMsRPAAAbWYeOyJz3UpJkm18y0Y7CstrVWtK\nPRx2JcTwY8lyVgtXtrIUZn5fiomRufWvMg+xwhWA0MEnPACgzcw3l0tVlVLGFTLOGdyia5lm1bg+\nLdjL43Q1nbvLuGqM5HbLfJ19PQCEDoIHAKBNzONHZa7LlSTZsu9u8fXWL9asaOWtNStbWYxxUyV7\njMwt62TmM+oBIDQQPAAAbWK+uVyqrJCGjpBxzvktvv4gmwc2yrOJYAtHPCTJSO0l46ob6kc9WOEK\nQGggeAAAWs08fkzm2/WjHRNaPtohsYfHmVjPo6U9HhZj3FTJZpf5t7UyCw76szQAaBWCBwCg1cy3\nVkiV5dLFmTK+M6RV99h/vFqS1LdTnD9LC3v96p/Hgfrn01JGz7NkjLxecrtkrmLUA0DwETwAAK1i\nniiV+ZdXJbV+tMNtmjpQ/xf9fox4eOnhsKtDjKFjVW4dq/J9Sd3TGbfWj3q897bMwkN+rhAAWsbn\n4LFgwQKlp6fL4XAoIyNDW7duPeO57733nm666Sb16tVLiYmJuvDCC7V06VK/FAwACA3mWyukijLp\nwstlnHthq+7hLKtVlctUssOujnF2P1cY3gzD8Ix6fF3aylGPtL4yrhwtuWoZ9QAQdD4Fj9zcXE2f\nPl2zZs3Szp07lZmZqdGjR+vgwcbnjP7zn//UhRdeqNWrV+uTTz5RTk6O7r77br366qt+LR4AEBzm\nyeOnRjuy/1+r7/N1/TSis5lm1ah+nepGgfa3crqVJBm3/rdks8nc9JbMwnx/lQYALeZT8Jg7d66m\nTJmiqVOnatCgQZo3b57S0tK0cOHCRs+fOXOmfv7zn+t73/uezj77bE2bNk1jx47V6tWr/Vo8ACA4\nzLdekcpPShcMk3HeRa2+j/WXfOsXbHizAtnXx1vXYC5JRq9+Mv6jftRj9RJ/lQYALdZs8KiurtaO\nHTuUlZXldTwrK0vbtm3z+Y1KS0vVrVu3llcIAAgp5skTddOsJNkmtH60Qzr1C3V6Z0Y8GnN2/XNp\ny4iHJBnjrVGPN2UWFfijNABosWaDR3FxsVwul1JTU72Op6SkyOl0+vQmf/nLX7Rp0ybdfXfrmg8B\nAKHDfLt+tGPIpTLOv6RN97J+oe7HVKv/z959x0lR3g8c/8xsud57b1zhjqN3EBUBQWOJLRpN8Zf8\n7IlGjcao0SRKYstPE0tMNGpiNJYkFiyASD+BO+DgKhxcL7vXe92d5/fH3h0cHHBwe7dXnvfrta/Z\nm52Z/e4DuzPfedqgoofZx6OPEhaNsvRisMhaD0mSHEc/0m+wc+dObrzxRv70pz8xd+7cU26XkZEx\n0qFIJ5Bl7hiy3B1Dlrt9qJ3tpPz37+iBghnn03qGcj1TuR+u9QBUWkryyagS9gt0gujSALwobe5m\nd3oGOmVo+w1W7k7Ji5i67Uu0Df8lK34ePV6yFYI9yd8Yx5DlPrri4+OHtf8ZEw9/f390Oh1ms3nA\nerPZTEhIyGn33bFjB5deeim//e1vufXW01fHny4pkewvIyNDlrkDyHJ3DFnu9qN98Bqisx1SZpN0\nzY2n3fZM5d7Wo9GYdxSjqrBq4Wx06hCvqieZ4LIiTO0WghOnD6lm6HTlrmXvQOzYQOqRvai3PmTv\nUCct+RvjGLLcR19TU9Ow9j9jUyuj0cicOXPYsGHDgPUbN25k8eLFp9xv27ZtXHLJJfz617/mpz/9\n6bCClCRJkhxPtLYgPvo7MPy+HXCsmVWEh0EmHadhj5Gt+ijX3QKKgtj4X9nXQ5KkUTekUa3uvfde\n3nzzTV5//XXy8vK4++67MZlM3HbbbYBtFKsVK1b0b79lyxbWrFnD7bffzg033IDJZMJkMlFTUzMy\nn0KSJEkaceLTt6GtBVLmQOq8YR+v70I6WnYsP62+8hnOyFZ9lMg4lKWrwNKDeP+1YR9PkiTpbAwp\n8bjuuut4/vnneeKJJ5g1axZpaWl8/vnnREREAGAymSgsLOzf/q233qKzs5NnnnmGkJAQQkNDCQ0N\nZcGCBSPzKSRJkqQRJZobEJ/0jmR1450oyvBrKPoupKPlULqn1dfBvGSYHcz7KNffbhvhatPHiKpS\nuxxTkiRpKIY8c/ntt99OUVERnZ2dpKens3Tp0v7X3njjjQGJxxtvvIHVakXTtAGP47eRJEmSxg/x\nn7dss5TPXoySPMsuxzw2h4es8TidvsSsyA5NrQCUsCiUCy8DzYr411/sckxJkqShGHLiIUmSJE1O\nor4G8fl7AKjfvcNux5Wzlg9NVP9cHsNvatVHue4W0OsR2z5HlB2123ElSZJOZ8SH05UkSZLGN/Hv\nv0F3JyxcjjIlxS7H1ISgtK+pldfoNbUSQtDZ3UFHVxsWaw9WzYLFakHrXVo1C1bNiqqo6HV6dDoD\nOlVve967dHZyxdnoiqqMzr27IFc9zjqF+k4rzV1WPJ10wz6mEhSKsvIqxBfvo737Z3QPPGOHSCVJ\nkk5PJh6SJEnSKYmaKsT6f4OioF5/m92OW9lqodMq8HfR4WEc3oW0JjRa2hppbK2loaWWxtY6Gltr\naWqtp62rlfbOVjo6W2nvaqWjqw1NaMOOX1FUXIyuuDi74ebkYVs6e+Dp6oO3hz/e7n74ePjj7e6P\np5sPOvXcP6OqKER7Gcmv76KwqZuZgS7Djh9AufZHiE0fQ9pXiMJ8lNgkuxxXkiTpVGTiIUmSJJ2S\neP+vYOlBOW81SvTwJo46XkFjFwBTvJ2GFocQNLbWUd1Qgbmh3Lasr6CmsZLGtno0zTrk93YyOOPi\n5IZBZ0TV6dCrtpoNvapH1enQKTo0oWHtrQGxaBbbc6sFi7WHju52Orvbae+yJTN1mE/7fqqi4unm\ng793CEE+4QT5hBHoE0aQbxg+HgFDqjmZ4m1LPAoau+yXePgGoqy+FvHJ22jvvIzukT/a5biSJEmn\nIhMPSZIkaVCiqhSx6RNQdSh2rO0AONJg698xxfvk/h1d3R1U1BZTXlNIWXUhFbVFVDdU0t3Tecrj\nubl44uNuq2noq3HwdvfDzdkDV2d3XJ09cHVyw8XJDb1u+E27rJqVjq422jtbaO9qo72zlbbOFppa\n6/prXBpb6mhoraWlvbF3XR1HyrMHHMegMxLgE0qofxQRAXGEB8YSHhCDi5PbgO3ivZ2Alv5ysxfl\nqpsRG/4NGdsR+QdQkmbY9fiSJEnHk4mHJEmSNCjxziugWVEuugIlLMquxz7SW+MR66lQWJlHsekQ\nZdWFlFcXUt1QgUCctI+7i9eA2oJA7zACfULx9vDHqB9azYm96FQd7i6euLt4nnHbHksPja211DRW\n9dbYHKu1aW5roLK2mMraYjLyt/bv4+8VTHhgLBEBcUQFxxPtEQYcqymyF8XbF+WyGxEfvIb2jz+h\nPvFXuwyVLEmSNBiZeEiSJEknEUdyENu/BIMR5frhz1Lep62zhaLKfMyFu5jedpSt68vZrFkGbKOq\nOkL9IokIiCU8MI7wgBiCfMNxc/awWxyjyaA3EOAdQoB3CMnRswe81tHVhrmhgoqaIsqrCymrKaSy\ntpjaJhO1TSYyC9IAW5+SmWoY7Z0x7C9YSFzoVDzdfOwSn3LF9xFffgA5e2HvDph7nl2OK0mSdCKZ\neEiSJEkDCCHQ3noBAOXSG1ACQs75WB1dbRSUZ5FfeoAj5dmY6ssA6Ksn0IAQv0hiQpKIDJpCeEAs\nIX5RGPSTY1JBFyc3ooMTiA5O6F9ntVow1ZdTXnOUsuqjFFblU1FTjIe1DI/2Mt74fBsAAV4hxIWn\nkBQ5k4SI6UOqfRmM4u6Bcu2PEX97Du3vL6DOWoyiG/7IWZIkSSeSiYckSZI00L6dkJUO7p4o1/zP\nWe1qsfZQYjpMfukB9ubt5B9pVYjjRpHS6wwE+MWxuzkUZ88p/O3by3B1drf3JxjXdDo9YQHRhAVE\nsyD5IgA6uzv46Wc7MVcfYr5nJQ0NR6lpqqKmqYpdOV8BEB4QS2LkDJROF7otqWfV/ExZcx1i3btQ\nehSx+VOUFVeOyGeTJGlyk4mHJEmS1E9YrcdqO675EYr7me+iN7XVk1O0l5yidA6VHRzQCVxVdcSG\nJJMQOYPEiOlEBE5hQ2kH7+80c1Gou0w6hsjZ6EJs2HTSW6O4aro/v5jqSXl1IYfLszhUmklhZR7l\nNYWU1xQCsDX/Q+LCU5gWM49pMXPx9Qw87fEVgxHlxrsQ//dLxDsvI867GMXJPqNnSZIk9ZGJhyRJ\nktRPbPkMSo9AQAjKJd8ZfBshKK8pIrsonZyiDErNBQNeD/aNIDFyBrouN1ZfcCXOxoEXsEcamwCI\nH2REK+nU4nuHHi5o7EKn6ogKjicqOJ6Vc6+i29JFYUUeh8oy2Z+/i/o2E/kl+8kv2c+HW/5CqF8U\n02LnkRIzj6igKaiDzCuinHcx4uN/QGEe4tN3UK750Wh/REmSJjiZeEiSJEkAiK5OxDsvA6DceCeK\n8VhTHU2zcrQyl8yCb8gq3E1ja13/awadkYTI6UyLmUdy9Bx8PPwByMjIOCnpACho6J3Dw2d0R6Ia\n76b42BK1wYbUNeqdSIqaSVLUTMKcp5GYPIXc4n3kFGWQV7qfyroSKutK2JD+Ie4uXkyLmcvM+MUk\nREzvH15YUVXUH9yN9thtiP+8iVh1FYqnfTqwS5IkgUw8JEmSpF7is3ehzgwxiSjL1mC1Wigozybz\nSBoHj+6mtaOpf1svN19SYuaSEjOXxIgZGA1DTyKONJ56Dg/p1OK8bOVV1NSNRRPo1VMPe+vh6s2C\n5OUsSF6OxdrDkfIcsovSyS5Kp765ml25m9iVuwkXoyupcQuYMWURSZEzMcxYALMXw740xPuvofz4\n56P18SRJmgRk4iFJkiQhmhsQH/4NqwJHLruczE0vcbBwD+2dLf3bBHiFMDN+MTOmLCIiMO6c5nto\n7rJibrfgrFMId58cI1fZi7tRR4ibnqo2C6UtPcR6DS1x0+sM/bUhV5//Y6rqSjlwdBcHCtKorCth\nT95m9uRtxsnowrSYecxceRFJmd+g//J9xKXXo4REjPAnkyRpspCJhyRJ0iQnhKDo7afZG2Zgf2gM\nrVnv978W5BvOzCmLmTllMaH+UcOeXK6vtiPGy4juNHfspcHFeztR1WbhSEPXkBOP4ymKQqh/FKH+\nUaxZ8B2qGyrIPPINmUfSKK8uZO+hbexlGy7nxzCjspE5bz1J/IMvoyrqCHwaSZImG5l4SJIkTVLV\nDRVk5G8jI+cranvqINwT0Aj0DmVO4jJmxi8hxM++d7sP9/bviPeRzazORbyPkW0VbRxq6GJV9PAn\nVAz0CWPVvGtYNe+a/gkL9x7eTkVNEbtCPdiFCe9Xf8CcaRcxN/F8Qv2j5czmkiSdM5l4SJIkTSLN\nbQ3sPbydvfnbKK0+0r/eo8vCbLcI5l1z3zk3oxqK3DrbULvJfs4jcvyJbmpvueXVddn92P5ewayY\nexUr5l5FVV0ZGR//kb3VedTTwqa9H7Fp70eE+EUyJ3EZcxOXnXGIXkmSpBPJxEOSJGmCs1h7yC5M\nZ1fuJvJK9vdP6OdkdGGGRySzN20j3uqM/uWnUdyHfxf9dHJ6L5hTZOJxTlL8bJ34c+s6EUKMWIIY\n4hfBt773JGt+eg1F7Sb2nb+EzJ5qqupKWZf2NuvS3iY+PJUFycuZOWXxWQ0uIEnS5CUTD0mSpAmq\nvKaQ3blfk5G/lbbeTuKqqiMlZj7zks4nOXQa+ruvh4ZOlNvvH/Gko71Ho6ipG70im1qdqyBXPb7O\nOuo7rVS0Wgj3GLkO+orBiO5/7if2ybuJ/WoPV734bw41lpBxaBtZR3dTUJ5FQXkWH2z5C3MSlrIg\n+SKigxNlUyxJkk5JJh6SJEkTSFtHMxmHtrE79+v+WawBQv2iWJBia6fv4eoFgPbuK4haE8Qmoay4\ncsRjy6vvQmCbv8NJJzsrnwtFUUj2c2JHRTs5dZ0jmngAMPe8/uF1de++yrQ7H2Va7Dzau1rZf3gn\nu3I3UWI6TFr2RtKyNxLkE86C5OXMm3oBXm6+IxubJEnjjkw8JEmSxjlNaBwqPcA3ORvJKtyD1WoB\nwNXJnTmJy1iQvPykfhvCXIn471sAqD9+AEV38kzW9tbXv6OvuZB0blL8nNlR0U5uXScX26GD+eko\nioL6o5+jHbgW8dV/ERdfjTIlGVcnd5akXsyS1Iupqitjd+4m0vO3YG4o55Odf2dd2ttMjZrNwpQV\nTIuZi04nLzckSZKJhyRJ0rjV0t7IrtyvScteT12TGQAFhaSoWSxMvojU2PkY9IM3adLeeA66u1DO\nW42SPGtU4s2RHcvtIrk3ccsZgQ7mg1HColG+dQPi43+gvfY06tq/oajHaqxC/CK48rwfctnim8gt\n2cfu3K/JLkonpziDnOIMPN18WJi8gkXTVuDnGTQqMUuSNDbJxEOSJGkcEUJwpCKHnVnrOXDkG6ya\nrXbDxyOARSkrWJC8HB+PgNMfI30b7PoanJxRfnDPaIQNQK7sWG4Xyf0jW3WiCYE6Cn0qlO/cgtj6\nOeQfQHz1Ecqqq07aRqfTkxo7n9TY+bS0N5Gev4VvsjdibihnQ/oHbEz/kKSoWSyetkrWgkjSJCW/\n9ZIkSeNAW2cLe/I2k5a1AXNDOQCKopISM5elqauZGjULVT1zcynR0Yb26u9s+994J4r/6NyBbu6y\nUtbSg5NOIdZbdiwfDn8XPUGuesztFkqae4g5h4kEz5bi6o7y458jnv0F4s3/Q8w9D8X31Amuh6sX\ny2dfwYWzLudoZS5pWRvIPJJGXsk+8kr2yVoQSZqkZOIhSZI0RgkhKDYdYmfWevYf3kmP1Tbrt6eb\nD4tSVrIoZSW+nqev3TjpmP98GWpNMCUZ5dIbRiLsQeXW22o7EnycMMgZy4ctxc8Jc7uFnLrOUUk8\nAJQlqxCb18HeHYjXn0X5+VNn3kdRmBKWwpSwFK7u+BF78raQlr1B1oJI0iQlv+GSJEljTEdXOxmH\ntrIzaz2VtcX965MiZ7IkdfU5X6CJw9mIz94FVYd6x6Oj0qG8z7GJA2XHcntI9nPm67I2cuu6+Fbs\n6Lynoiiotz6E9tNrEDs3IC64FGXesiHv7+biyYWzL+eCWZfJWhBJmqRk4iFJkjRGlFUfZWfWl2Qc\n2k53j+1C3d3FiwXJy1k8bRUB3iHnfGxh6UF7+TcgBMoVN6HEJtkr7CGRHcvtqy+By67tHNX3VQJD\nUb57J+Jvz6K9+jvUaXNQXNzO7hhDrAVZknoxKTFz0Q2hCaEkSeODTDwkSZIcqKunk32HtrMzewOl\n5oL+9VPCUliSuprpcQsx6Ic/V4P45G0oLoCgMJQbbh328c7qvYUgs9p2gTzdXyYe9jDN3xkFyKvv\npNOi4awfvXlRlEuvR2z7HI7kIv75MsqPf37Oxzq+FqSwMpedJ9SCeLn7sShlBYtSVuLj4W/HTyFJ\nkiPIxEOSJMkBKmtLSMtez568LXR2twPg4uTGgqnLWZy6imDfCLu9l6gqRfzrVQDU2x5GcXKx27GH\noqS5h/pOK37OOqI8R3jCu0nCw6gjwceJQw1dZNd2MjfYddTeW9HpUO/4Fdr9NyI+exexbA1KwrTh\nHVNRiAtLIa63FmR33mbSstZT3VjJl7vfY/2eD5gWM5clqatJipqJqsgJKCVpPBpy4vHyyy/zzDPP\nYDKZSElJ4fnnn2fp0qWDbtvV1cWtt97K/v37ycvLY8mSJWzevNluQUuSJI1HPZZuMo+ksfPgegqr\n8vrXR4cksjR1NTPjF2PU27cPhLBa0V78tW3OjvMvRZm1yK7HH4p91R0AzA5yGTCJoTQ8s4NcONTQ\nxd7qjlFNPACU2ESUK76H+O+baH96DPXZf6I42ac2y83Fs39ErILybHZmfcmBo7vIKtxDVuEefD0D\nWTxtFQuTV+Dp5m2X95QkaXQMKfF47733uOeee3jllVdYunQpL730EmvWrCE3N5eIiJPvylmtVlxc\nXPjJT37CZ599RlNTk90DlyRJGi+qGyrYmbWe3Xmbae9sAcDJ6MK8xPNZknoxYQExI/be4uO/Q84+\n8PFH+dF9I/Y+p7PP3Jt4BI5uTctENzvQmXfzj5XvaFOuvwWxZwuUFSL+8adhNbka9PiKQkJEKgkR\nqTS3NbI7dxM7s9dT31zNurS3+XzXu0yPW8DS1NXEh6fKpFaSxoEhJR5/+MMfuPnmm/nRj34EwB//\n+Ee+/PJLXnnlFdauXXvS9q6urrzyyisAZGZm0tjYaMeQJUmSxj6LtYeDR3eTlrWew+VZ/evDA2NZ\nmrqaOQnn4WQc2QtxUZiPeOdlANS7HkPx9BnR9zuVvcfVeEj205fIHazppMcqMOhG98JbcXJB/dkT\naA/+ELHuHdvcHjMXjsh7ebp5s3Le1Vw099vkl2SyM+tLsosyyCxII7MgjUDvUBanXsyCqRfi5uI5\nIjFIkjR8Z0w8uru72bdvHw888MCA9atWrSItLW3EApMkSRqP6prMpGVvYFfOV7R02Gp7jXonZiee\nx9LU1UQGTRmVOERXJ9r/PQwWC8qa61DmDN40dqRVtvZgarPgYVSZIicOtCtfFz0xngaKmnvIre9k\nRsDoJ3bKlBTbrObvvIz2x1+hvvABiofXiL2fqqgkR88mOXo2DS217Mr5irScjVQ3VvLR9jdYl/Y2\nM+MXszR1NTEhSbIWRJLGmDMmHrW1tVitVoKCBo6pHRgYiMlkGrHAJEmSxgurZiW7MJ2d2es5VJKJ\nQAAQ4hfJktTVzEs6HxensxtydLjEP/4EZYUQFo3yw3tG9b2Pt7e3GdCsQBdUeRFod7ODXChq7mGf\nucMhiQeAcvXNiL074NBBxJ/Xwv2/H5ULfh8Pf9YsvJ5V868lpyiDtKz15JXsJyN/Kxn5W3u/fxcz\nL+mCUf/+SZI0uDEzqlVGRoajQ5h0ZJk7hix3xxiJcm/tbKTAnMkRcyYdPa0AqIqOGP+pJATPIcAj\nHKVHIScr7wxHsi+PwlymrHsHoeo4dPGNdGTljOr7H29DThlgJKi7loyMSofFMVH5tBkAVzYfNpHa\nWdi/frR/Z4wXfYekokPodm6gyD+ChtSRaXJ1ajrmhl9Cov8iCsz7OWI+QFVdKR9u+SsfbXuTaP8U\nEoJn4+8ROmIRyN92x5DlPrri4+OHtf8ZEw9/f390Oh1ms3nAerPZTEjIuU9mdaK5c+fa7VjSmWVk\nZMgydwBZ7o5hz3K3alZyi/eyM2s9ecX7+ms3An3CWDLtYuZPvcChbcxFcyPay78EQL3+VlIuv8Zh\nsWRkZFCquQE9XDEngRQ5h4fdhbf18Np/iinqdmLW7KnoVMVhvzOa0oV46TdEb3yP2EuuQgkauYv8\n07mQlVisPWQV7mHnwS85XJ7FkepMjlRnEhEYx5LUi+3ex0r+tjuGLPfRN9wBo86YeBiNRubMmcOG\nDRu4+uqr+9dv3LiRa6+9dlhvLkmSNF40tNTyTc5GduV8RWNrHQA6nZ6ZcYtYnHoxU8JSHN6eXFit\naM8/DPU1kDgd5eqbHRpPQ49CaUsPLnqFRF/7DhMs2QS7GQhz11PRaiG/vsuhyZ2y4kpExnbYvRnt\nmZ+jrv0bitEx/+56nYFZ8UuYFb8Ec0MFab2jypVVH+Vfm17mv9vfYF7SBSyZdjFhAdEOiVGSJqMh\nNbW69957+d73vsf8+fNZvHgxf/7znzGZTNx2220APPTQQ6Snp/PVV1/175Obm0t3dze1tbW0trZy\n4MABhBDMnDlzZD6JJEmSnWmalbyS/ezMWk9O8V6E0AAI8A5l8bRVLEhejvsYGkFHvP9X2JcGHt6o\n9/0ORefY1rRZrbb3nx/sil6V/TtGysIQV/5d0MyOyjbHJh6KgnrXY2hFh2yzmr/2DModjzgsnj5B\nPmF8e9n/8K3FNw2YR2fHwS/YcfCLEZ1HR5KkgYZ0Vrruuuuoq6vjiSeeoKqqitTUVD7//PP+OTxM\nJhOFhYUD9rn00kspKSkBbD9Gs2bNQlEUrFarnT+CJEmSfTW01LI7dxPf5HxFQ0sNADpVz/Qpi1iS\nevGYnDNAZGxHvPcqKIot6Qh0TDOX42W12mYpPy9MduwdSeeFudkSj/I2bp3u59BYFA8v1AefRfvF\nDxEb/o2WMA11xZUOjamPQW9kXtIFzEu6gMraEtKy17MnbwvFVYcorjrEf7a+zvzk5SyZtoog33BH\nhytJE9KQb4fdfvvt3H777YO+9sYbb5y0rqio6NyjkiRJGmU9lh6yi9LZlfMV+aWZ/bUb/l7B/bUb\nHq5jc5ZkYSq3DZ0LKN+9c8TmUjgb3VaNvDbbKWZJ2OjOqj3ZzA92xagq5NR1Ud9hcXQ4KHFTUW77\nJeJPjyNe/R0iJhElbqqjwxog1D+Kay64hcuWfJ99h7azM3sDpeYCtuz/hC37P2FK+DQWp6xk+pSF\nshZEkuxozIxqJUmS5AiVtcXsytlEev4W2npnFdfp9EyPXcSilJUkRE5HVVQHR3lqoqsT7an7oa0F\n5p/v8H4dffaZO+gSCvE+RoLdDI4OZ0JzMajMDXYhrbKdnZXt2G/Yl3OnXnQF2qEsW63HU/ejPvtP\nFM+xl7g7GZxZNG0li6atpNR8hLTs9WQc2s6R8myOlGfjstmV2YnLWJi8nMig+DFX0ylJ441MPCRJ\nmnQ6utrYe2g7u3I3UWou6F8f6h/NopQVzE1cNi5mPxZC2OZNKDoEIRGoP/0tijo2kqQdFe2AbGY1\nWpaGuZFW2c6OijauHSMVTMr/PoAoyoeCHLT/exj1kT+i6HSODuuUIoOmEBk0hSuW3kzGoa3sQR/X\nBAAAIABJREFUzv2aUnMBO7O+ZGfWl4T4RbIgeTlzEy/A023sJVGSNB7IxEOSpElBExpHynPYlfsV\nBwq+ocfaDYCL0ZU5SeezMPkiIgLjxtUdTfHftxCbPwWjM+qDz6K4ezg6pH7bK9oA2wWxNPKWhrny\ndDqkVbbz7ThHR2OjGIyoDzyDdu93YX8a4o0/oPz4544O64xcnFw5b/oazpu+hsraEnbnbiI9fytV\ndaV8tP1NPtn5D1Ki57AwZQXJUbPROXgQB0kaT+S3RZKkCa26oZLMki18lvVX6pqPzUeUEJ7KwpQV\n47YNt0jbiPj7CwCo9/wWJTrBsQEdp6S5m9KWHlxVjVQ5d8eoiPAwEu1poLi5h6PtOhzfy8dGCQhB\n/cWzaI/dhlj3DlpIBOql1zs6rCEL9Y/i28v+h8uXfJ+c4gx25X5NblEGWYV7yCrcg4eLF/OmXoC7\nCHZ0qJI0LsjEQ5KkCae1o5l9h3eQnr+FEtPh/vU+7v7MT17OwuSL8PMKcmCEwyPyD6A9/ygAyvfv\nRlm8wsERDbS13FbbMc3dIofRHUVLw9wobm7kQKuBGx0dzHGUlDkod/4K8cKvEK8/gwgIQZl/vqPD\nOis6nZ7pcQuZHreQ5rYG0vO3siv3K8z15Xy972MA9ld8xdzE85mduBQvN18HRyxJY5NMPCRJmhB6\nLD3kFKWzJ38LucV70TTb0N1OBmfCfRJYveRq4sOnoapjt435UIjSo2hP/BS6u1BWXoXy7R84OqST\nfFFk66Q/x6PHwZFMLiui3Hk7r5H0ZgNWTaAbQ0mfeuFlaKZyxHt/QXv2QdTHX0FJnuXosM6Jp5sP\nF825kuWzr6DEXMDunE3sydtCWfVRyqqP8tGON0mMmM7cpPOZEbfQrjOkS9J4JxMPSZLGLU2zcrQy\nl72HtrO/YCcdXbY77YqiMjVqNvOSzmd63EIOHsgiMXKGg6MdPlFdifbrO6C12TaC1W0Pjbk+KYVN\n3eTXd+FuUEl1d/zQrpPJdH9nwt0NlLf2kGHuYEHIGOll3ku5/jaor0Fs/C/ak3ejPvk6SnS8o8M6\nZ4qiEB2cYHt4zMLJRyPj0FZyivaSX5pJfmkm7+v/TGrsfOYmnU9S5EzZH0Sa9OQ3QJKkcUUIQbHp\nEPsO72B/wU6a2xr6XwsLiGF+0oXMSTwPTzcfB0Zpf6KuGu2x26CuGpJnod73e4fPTD6YLwqbAdvd\nd4PacIatJXtSFIXVMR68llXPF0UtYy/xUBS47ZeIlibY9TXa47ejPvkaSli0o0MbNp2qZ2b8XGbG\nL6ats4XMgjQy8rfabowc3s7ew9txd/FiVvwSZiUsITYkadzXvkrSuRh7Zy1JkqQTCCEorylk3+Ht\n7Du8s382cQA/zyBmJSxlbuIyQv2jHBjlyBENtWiP3gJVZRCbhPrLF1Ccxl6nbSEEn/c2s7okxgPK\nHRzQJHRJb+KxqbSVhxYE4KQbG8Mr91F0etR719qaCx7cg/boLbbkIyTS0aHZjZuzB0tSL2ZJ6sXU\nNZvZm7+N9ENbMdeXs/3g52w/+Dmebj7MnLKYWfFLiAlNGtNzBUmSPcnEQ5KkMUkIQWVtCZlHdrLv\n0A5qmqr6X/N292NW/BJmJ5xHZNCUMdfcyJ5EfTXar26DyhKITrC1jR9Dw+Ye70BNJ5VtFgJd9cwJ\ncmGfTDxGXYyXkUhnK6WdsK28jZVRY+//imJ0Qn34ebTf/ARy9qI9cgvqb15FCZt4Nw78PINYNf9a\nVs67hvKaIvb31tTWNZvZduAzth34DC83X2bGL2ZW/FKiQxJkEiJNaDLxkCRpzNCERnHVYQ4e/YYD\nR3dR13Rs+FsPFy9mJSxhVvzSSXOHUJgrbc2rTGUQOQX116+Mydmf+/TVdqyOdkedwMngWLfAs5vS\nThe+KGoZk4kHgOLkgvrIH9F+cxfk7Ud7+Ee2pHoc9/k4HUVRiAiMJSIwlsuWfI+y6qPsL9jB/sM7\nqW+pYWvmOrZmrsPb3Y+ZUxYzfcpCYkKS0MnmWNIEIxMPSZIcymLtoaA8m4NHdpFVuIfm9mP9Atxd\nvJgeN5/ZCecxJSxlUrWJFmWFaI/fAXVmiJuK+tjLYzrpaO229icel8aO/VnfJ7L5nj38p8aFbeVt\nmNp6CHYzODqkQSkurqiPvYT2u5/Bgd1oj/wY9dE/oSROd3RoI0pRlP5Z0i9f8gNKzQXsL9jJ/sM7\naWitZUvmp2zJ/BQ3Zw+mxcwjNW4BSZEzMRrG33xDknQimXhIkjTqOrraOVSaycGju8kpSqeju73/\nNV/PQKbHLWRG3AJiJmkHTJGzz3Yx1toMU2ehPvICitvYvHPd5+OjzbT1aMwOdCHBR14gOZK3QXBR\npDsbSlp571ATd8/2d3RIp6Q4u6A+/ALasw/Cnq1oj96Kev/vUOZf4OjQRoWiKEQFJxAVnMAVS39I\nsclW43vwyG5qmqrYnfc1u/O+xqA3khQ5k9TYBaTEzMXD1cvRoUvSOZGJhyRJI04IQXVDBTnFGeQW\n7eVoZR5W7dhQqyF+kf2Tc4UHxEzoPhtnou1Yj3jhV9DTDfOWod7/exSnsT0PgFUTvJvfCMBNyWO3\nVmYy+V6yDxtKWvl3QRP/m+qLq2HsNk1UjE6oDzyDeOVJxKaP0X5/H8qPH0C95DuODm1UKYpCTEgi\nMSGJXL7kB5jqy8kq3E3W0d2UmAv6Z0tXFJXYkCRSYuaSHD2bEL+oSf2bKY0vMvGQJGlE9Fi6KSjP\nJrc4g5zivQP6a9hOnFNJiZ3HjLiFBPqEOjDSsUFoGuLdVxAfvAaAsvpalP99YEwOmXuiLeVtVLRa\niPAwsCzMzdHhSMA0f2dmBDhzoKaTTwub+U7i2E4IFb0B7noMAkIQ//oz4i+/RyspQPnxgyiGsdlU\nbCQpikKIXwQhfhGsmncNTa31ZBXu4WDhbgrKsjhamcvRylw+2fl3vN39mBo1m+To2SREzMDFaWwN\noyxJxxv7ZzRJksYFIQTmhnIOlx0kr2Q/h8sO0mPp7n/dzdmDqdGzSYmeQ1LULNycx3bTodEkWlvQ\n/vgo7NkKqoryg3tQLr9p3NzF/GeerV/ODUneY2q27MnuxqneHKgx8U5eI9cmeI35Dv+KoqBcfyta\ncDjipd8g1v8bUVaIev9TKL4Bjg7PobzcfVk6fTVLp6+mo6uNvJL95BbvJa9kP42tdXyTs5Fvcjai\nqjpiQ5KYGj2H5KjZhPrL2hBpbJGJhyRJ56yptZ5DZQc4XHaQQ6UHaGqrH/B6eGAsKdFzSI6eS1TQ\nlEnZX+NMREEO2jMPQHUluHvaLrJmLnR0WEOWYWpnf3Un7gaVK+Jkp/Kx5MIId0Lc9JS29LC+uIU1\nMePj30e94FJEWLStn1PufrSfXY9675MoM8bP92IkuTi5MTthKbMTlqIJjYqaInKL95FXvI8i0yGO\nVORwpCKHT3f+HU83HxLCpxMfkUpCRCp+nkGODl+a5GTiIUnSkHV0tXGkIodDpQc4VHYAc/3AiRo8\nXLxIiJxBQsR0kqNm4+Xu66BIxz5htSI+/Sfi7T+BxWIbuernT6MEhzs6tCHThOAPe2sB+H6yz5ju\nRzAZ6VWFW6b78utvqvnT/jqWR7qPuQkFT0WJT0H9w7toz/0SsvagPX4HylU/RLn+9knZ9OpUVEUl\nIjCOiMA4Lp5/Le2drRwqO2BLREr20dzWQMahrWQc2grY5hWJj0glITyV+IhUvNzkb7Q0umTiIUnS\nKTW11XO0IpfCylyOVuRSWVuCQPS/bjQ4Ex82jYTI6SRGzCDEL1JW6w+BMFeg/fFXkLMPAOWS76Dc\nfC+KwejgyM7OF0Ut5NV3Eeiql53Kx6jLYj15J6+RgsZu/pXfxA9SfBwd0pAp3n6oj7+MeP+viPf/\ngvj3G4i9O1HveYKJOt/HcLk6uzMrfgmz4pcghMBUX8bhsoMUlGdRUJ5NXbOZuhwzu3K+AiDIN5z4\n8FTiQpOJDU3Cx2NyN2mTRp5MPCRJAmx9NGoaKzlakdvfcfH4DuEAOlVPVHA8iREzSIycQVRQPLpx\n0Pl5rBBWC2Ldu4h3XoauTvD2Q73rMZS55zk6tLPWadF4cX8dAHfO9MNFPz7upE82OlXhZ3P8uWNT\nJa9l1XN5nCc+zuOnyaOi06HccBtixgK0Fx6F4sNo930X5bIbUb5zC4qL7Eh9KrYO6pGE+EVy/sxv\noWlWymuKKCjP4nBZFkcrcjDXl2OuL2fHwS8A8PEIIDYkiZjQqcSGJhHqFyWbyEp2Ja8YJGmSau9s\npcRcQKm5gBJTASWmw7R0NA3YxsngTExIEnFhycSGJhMVHI9RL+doOBciPxPtL09DYR4AytJVKLf8\nAsVz/NyBPt5rWfWY2i0k+jhxaYwcKGAsWxTqxuJQV9Iq23lhXy2PLx5/7fyV5Fmoz7+HeOsFxPoP\nER+9hdj+JeqP7odFF8ma1iFQVV3/xIUXzfk2FmsPpeYjFJRnUViZT3FVPg0tNextqWHv4e0AOBld\niA5OIDY0mejgBCKDpsiBQaRhkYmHJE0CPZZuKmqLKTEdtiUbpgKqGytP2s7dxYu40KnEhiUTF5pM\nWEAMOnm3a1iEuQLxz5cQ22x3FAkIRr31l+OylqPP/uoO3shpQAEemBcgR7IaB+6d40+GqYyPjzZz\nXrgbF0W6Ozqks6a4uKHc9kvERVeg/flJOJqH9vTPYdZi1P+5FyUiztEhjit6nYHY0KnEhk4FQBMa\nprpSCivzKazKo6gyn7pms61PX+mB/v38vIKICoonInAKkUFxhAfEySF8pSGTiYckTTDtna1U1BZR\nUVNMRU0RFbXFVNWVDpiwD2wnnfDAWKKC4okKiicyKJ4A7xB559BOhLkS8eFriK8/BasFjE4oV34f\n5aqbUZzH9oSAp9PSbeXhHSY0ATen+DA7aPx+lskkztuJu2f780xGDb/9xkyqvzOBruPzEkCJT0F9\n+h+IDf9GvP0i7E9D++k3tlrE625BiYh1dIjjkqqohPpHE+ofzdLpqwHbyIWFVXkUVuZRaj5CeU0h\ndU1m6prM7Du8AwAFhUCfMCKC4ogMnEJYQDShflG4uYyPUdSk0TU+f3UkSULTrNQ1V1NZW0xFTTHl\ntUVU1hRR31Jz0rYKtra+kb1JRlRwPKF+UbJ/xggQNVWID15HbPrYlnCoKsoFl6LccAdK0PieKFET\ngid2VVPVZmGqrxO3z/BzdEjSWbghyYudlW2kVbbz8A4TL18UhkE3Pm80KDodyprrEItWIN57FbHx\nv4jt6xE7NqCctxrluv9FCY9xdJjjnpe7b39ndQCrZsVUV0Zp9RFKzUcoMx+horYYc0M55oZyMvK3\nHrevH2F+Ub3JjG0Z5BMmzzuTnPzXl6QxzmLtoabRhLm+DFN9Geb6ckz1ZVQ3VNJj7T5pe4POSKh/\nFGEB0YT5xxAWEEOofzTORnlneqQIISArHe2L92H3FtCstoTj/EtRrvsxSli0o0McNiEEz2XUsqGk\nFRe9wpNLg8ftRetkpSgKjy8K4vrPSskwd/Bomom1S4PH/MSCp6N4+6Lc+hDiqpsR/34d8dVHiG1f\nILZ/aWuCtfpamLMURSebjNqDTtXZzi0B0SxKWQFAj6WHqroSSswFlFcXUllXQlVtCU2tdTS11pFb\nsu+4/fUE+YYT4htBoG84QT5hBPmEE+ATIvsPThIy8ZCkMUATGk2tddQ0mqhtMlHbWEV1YyXm+nJq\nmqrQNOug+3m5+RLqH02YfzRhATGEB8QQ4B0iRyEZJaK1GbF5HeLLD6Ci2LZS1aEsWzPh7rj+LbuB\nd/Ib0avwhwtCifEaX0P/SjYBrnpeXB7K/26sYH1xK95ONTw4L2DcN7FUAoJRbnsYcfX/ID583dbE\ncd9OtH07ISAEZdXVKCuuQPHxd3SoE45Bb+jvtN5HExp1TWZbjXxtMZW1JVTWFlPbZKKytpjK2uIB\nx1BQ8PUMJMgnrD8hCfQJxc8zGG93X3lOm0Bk4iFJo6Szu4PG9hpyi/dR12SipjfBqG2yJRsWa8+g\n+yko+HkFEewTQbBfOEE+EQT7RRDkE4aLk9sofwpJtLYg9mxG7NwIB3bZJv8D8A2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pc4Znm44D4Euc3D9dQ3OSVN0e1HPrGk3HARClKP4APscXDOvBFZHZ4JeMyVOK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\nCESzK664QgsXLtScOXP00Uc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52KxHt1RJku6bkM7Ub4SUIUmRWjzFKatZ+ssX9XppFwP9APQcFA0AYWtrRZt+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\nXaWjvFWb3a2qbvPpzQNNevNAkyTJYTX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"text": [ - "" + "" ] }, { @@ -788,9 +788,9 @@ "output_type": "stream", "stream": "stdout", "text": [ - "[ 3.39543572 3.92455822 -1.47839831 -1.33968944 4.64280739 3.57337785\n", - " 2.4334426 -2.65214049 0.09098526 0.59452311 3.72292568 4.64627724\n", - " 2.35639579 2.19228319 1.02386714]\n" + "[-0.91921644 4.58775212 1.05856827 3.83479323 6.01848015 -1.41305258\n", + " -1.97691685 -3.00926484 6.59031405 -1.99993401 5.14010913 4.05641238\n", + " -1.57482631 2.70415239 0.49846418]\n" ] } ], @@ -860,6 +860,173 @@ "There are many other functions available, and if you are interested I urge you to peruse the documentation. I find the documentation to be excessively terse, but with a bit of googling you can find out what a function does and some examples of how to use it. Most of this functionality is not of immediate interest to the book, so I will leave the topic in your hands to explore. The SciPy tutorial [2] is quite approachable, and I suggest starting there. " ] }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Fat Tails" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Earlier I spoke very briefly about the *central limit theorem*, which states that under certain conditions the arithmetic sum of **any** independent random variables will be normally distributed, regardless of how the random variables are distributed. This is extremely important for (at least) two reasons. First, nature is full of distributions which are not normal, but when we apply the central limit theorem over large populations we end up with normal distributions. Second, Gaussians are mathematically *tractable*. We will see this more as we develop the Kalman filter theory, but there are very nice closed form solutions for operations on Gaussians that allow us to use them analytically.\n", + "\n", + "However, a key part of the proof is \"under certain conditions\". These conditions often do not hold for the physical world. The resulting distributions are called *fat tailed*. Let's consider a trivial example. We think of things like test scores as being normally distributed. If you have ever had a professor 'grade on a curve' you have been subject to this assumption. But of course test scores cannot follow a normal distribution. This is because the distribution assigns a nonzero probability distribution for *any* value, no matter how far from the mean. So, for example, say your mean is 90 and the standard deviation is 13. The normal distribution assumes that there is a large chance of somebody getting a 90, and a small chance of somebody getting a 40. However, it also assumes that there is a tiny chance of somebody getting a -10, or of 150. It assumes that there is a infitesimal chance of getting a score of -1e300, or 4e50. In other words, the *tails* of the distribution are infinite. \n", + "\n", + "But for a test we know this is not true. You cannot get less than 0, or more than 100. Let's plot this using a normal distribution." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "xs = np.arange(10,100, 0.05)\n", + "plt.plot(xs, [gaussian(x, 90, 13) for x in xs], label='var=0.2')\n", + "plt.xlim((60,120))\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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CAo/V5ZyWud19K294O9QRDFtcDQDgdBFWAAA9vNo9BeziwnS57In5MZGX7tCUkW75Q6be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\n3lr1zjvvoKioCGvWrIFer8fDDz+MkpISdRl05q5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+ "text": [ + "" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So the problem with this chart is that the area under the drawn curve cannot equal 1, so it is not a probability distribution. What actually happens is that a few more students get scores nearer the upper end of the range (for example), and that tail becomes 'fat'. Also, the test is probably not able to perfectly distinguish incredibly minute differences in skill in the students, so the distribution to the left of the mean is also probably a bit bunched up in places. The resulting distribution is called a *fat tail distribution*.\n", + "\n", + "We are not going to be applying Kalman filters to grades of student papers, but we are using physical sensors to measure the world. The errors in sensor's measurements are rarely truly Gaussian. And, of course, the signal itself will have time dependent correlations. For example, consider a sensor mounted on a helicopter. The rotating blades cause vibrations in the air frame, which will cause small deviations in the flight path. This deviation will be related to the frequency of the vibration, hence the values at t and t+1 are not *independent*. The vibration will also effect sensors such as the INS. No physical object can react instantly to changes, so the INS will somewhat lag the vibrations in a perhaps quite complex way, and so the noise introduced by the vibration will be anything but independent. \n", + "\n", + "It is far too early to be talking about the difficulties that this presents to the Kalman filter designer. It is worth keeping in the back of your mind the fact that the Kalman filter math is based on a somewhat idealized model of the world. For now I will present a bit of code that I will be using later in the book to form fat tail distributions to simulate various processes and sensors. This distribution is called the student's t distribution. \n", + "\n", + "Let's say I want to model a sensor that has some noise in the output. For simplicity, let's say the signal is a constant 10, and the standard deviation of the noise is 2. We can use the function `numpy.random.randn()` to get a random number with a mean of 0 and a standard deviation of 1. So I could simulate this sensor with" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from numpy.random import randn\n", + "\n", + "def sense():\n", + " return 10 + randn()*2" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 16 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's plot that signal and see what it looks like." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "zs = [sense() for i in range(5000)]\n", + "plt.plot(zs)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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GDDFXE2lu1muYFMN2ReTmm2/Gt771rb7/VhQF559/Pq666irccMMNhr9XANy0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+ "text": [ + "" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That looks like I would expect. The signal is centered around 10. A standard deviation of 2 means that 68% of the measurements will be within $\\pm$ 2 of 10, and 99% will be within $\\pm$ 6 of 10, and that looks like what is happenning. \n", + "\n", + "Now let's look at a fat tailed distribution. There are many choices, I will use the Student's T distribution. I will not go into the math, but just give you the source code for it and then plot a distribution using it." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import random\n", + "import math\n", + "\n", + "def rand_student_t(df, mu=0, std=1):\n", + " \"\"\"return random number distributed by student's t distribution with\n", + " `df` degrees of freedom with the specified mean and standard deviation.\n", + " \"\"\"\n", + " x = random.gauss(0, std)\n", + " y = 2.0*random.gammavariate(0.5*df, 2.0)\n", + " return x / (math.sqrt(y/df)) + mu " + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 18 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def sense_t():\n", + " return 10 + rand_student_t(7)*2\n", + "\n", + "zs = [sense_t() for i in range(5000)]\n", + "plt.plot(zs)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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lFPNWsBV0LFRQrshhLQ6pdnj894EqfHykZ1Vst1sRY6a+080r8kIOkkb3YCsf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+ "text": [ + "" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see from the plot that while the output is similar to the normal distribution there are outliers that go far more than 3 standard deviations from the mean. This is what causes the 'fat tail'.\n", + "\n", + "It is unlikely that the Student's T distribution is an accurate model of how your sensor (say, a GPS or doppler) performs, and this is not a book on how to model physical systems. However, it does produce reasonable data to test your filter's performance when presented with real world noise. We will be using distributions like these throughout the rest of the book in our simulations and tests. \n", + "\n", + "This is not an idle concern. The Kalman filter equations assume the noise is normally distributed, and perform sub-optimally if this is not true. Designers for mission critical filters, such as the filters on spacecraft, need to master a lot of theory and emperical knowledge about the performance of the sensors on their spacecraft. \n", + "\n", + "The code for rand_student_t is included in `filterpy.common`. You may use it with\n", + "\n", + " from filterpy.common import rand_student_t" + ] + }, { "cell_type": "heading", "level": 2, diff --git a/exp/distributions.py b/exp/distributions.py new file mode 100644 index 0000000..39654a7 --- /dev/null +++ b/exp/distributions.py @@ -0,0 +1,42 @@ +# -*- coding: utf-8 -*- +""" +Created on Sat Jan 17 20:17:14 2015 + +@author: rlabbe +""" + +from scipy.stats import t, norm +import matplotlib.pyplot as plt +import numpy as np +import math +import random + + +df =4 +mu = 10 +std = 2 + +x = np.linspace(-5, 20, 100) + +plt.plot(x, t.pdf(x, df=df, loc=mu, scale=std), 'r-', lw=5, label='t pdf') + + +x2 = np.linspace(mu-10, mu+10, 100) +plt.plot(x, norm.pdf(x, mu, std), 'b-', lw=5, label='gaussian pdf') +plt.legend() +plt.figure() + +def student_t(df, mu, std): # nu equals number of degrees of freedom + x = random.gauss(0, std) + y = 2.0*random.gammavariate(0.5*df, 2.0) + return x / (math.sqrt(y/df)) + mu + + +N = 100000 +ys = [student_t(2.7, 100, 2) for i in range(N)] +plt.hist(ys, 10000, histtype='step') + +ys = [random.gauss(100,2) for i in range(N)] +plt.hist(ys, 10000, histtype='step',color='r') + +plt.show() \ No newline at end of file diff --git a/exp/doppler.py b/exp/doppler.py new file mode 100644 index 0000000..67c4d51 --- /dev/null +++ b/exp/doppler.py @@ -0,0 +1,140 @@ +# -*- coding: utf-8 -*- +""" +Created on Sat Jan 17 15:04:08 2015 + +@author: rlabbe +""" + + + +from numpy.random import randn +import numpy as np +from numpy import array +import matplotlib.pyplot as plt +from filterpy.common import Q_discrete_white_noise +from filterpy.kalman import KalmanFilter +from math import sqrt +import math +import random + +pos_var = 1. +dop_var = 2. +dt = 1/20 + + +def rand_student_t(df, mu=0, std=1): + """return random number distributed by student's t distribution with + `df` degrees of freedom with the specified mean and standard deviation. + """ + x = random.gauss(0, std) + y = 2.0*random.gammavariate(0.5*df, 2.0) + return x / (math.sqrt(y/df)) + mu + + + +np.random.seed(124) +class ConstantVelocityObject(object): + def __init__(self, x0, vel, noise_scale): + self.x = np.array([x0, vel]) + self.noise_scale = noise_scale + self.vel = vel + + + def update(self, dt): + pnoise = abs(randn()*self.noise_scale) + if self.x[1] > self.vel: + pnoise = -pnoise + + self.x[1] += pnoise + self.x[0] += self.x[1]*dt + + return self.x.copy() + + + def sense_pos(self): + return self.x[0] + [randn()*self.noise_scale[0]] + + + def vel(self): + return self.x[1] + [randn()*self.noise_scale[1]] + + +def sense(x, noise_scale=(1., 0.01)): + return x + [randn()*noise_scale[0], randn()*noise_scale[1]] + +def sense_t(x, noise_scale=(1., 0.01)): + return x + [rand_student_t(2)*noise_scale[0], + rand_student_t(2)*noise_scale[1]] + + + + + +R2 = np.zeros((2, 2)) +R1 = np.zeros((1, 1)) + +R2[0, 0] = pos_var +R2[1, 1] = dop_var + +R1[0,0] = dop_var + +H2 = np.array([[1., 0.], [0., 1.]]) +H1 = np.array([[0., 1.]]) + + + +kf = KalmanFilter(2, 1) +kf.F = array([[1, dt], + [0, 1]]) +kf.H = array([[1, 0], + [0, 1]]) +kf.Q = Q_discrete_white_noise(2, dt, .02) +kf.x = array([0., 0.]) +kf.R = R1 +kf.H = H1 +kf.P *= 10 + + +random.seed(1234) +track = [] +zs = [] +ests = [] +sensor_noise = (sqrt(pos_var), sqrt(dop_var)) +obj = ConstantVelocityObject(0., 1., noise_scale=.18) + +for i in range(30000): + x = obj.update(dt/10) + z = sense_t(x, sensor_noise) + if i % 10 != 0: + continue + + if i % 60 == 87687658760: + kf.predict() + kf.update(z, H=H2, R=R2) + else: + kf.predict() + kf.update(z[1], H=H1, R=R1) + + ests.append(kf.x) + + track.append(x) + zs.append(z) + + +track = np.asarray(track) +zs = np.asarray(zs) +ests = np.asarray(ests) + +plt.figure() +plt.subplot(211) +plt.plot(track[:,0], label='track') +plt.plot(zs[:,0], label='measurements') +plt.plot(ests[:,0], label='filter') +plt.legend(loc='best') + +plt.subplot(212) +plt.plot(track[:,1], label='track') +plt.plot(zs[:,1], label='measurements') +plt.plot(ests[:,1], label='filter') +plt.show() +