From 6fc51e2e19132b0d0259c45d38e98db0b7d7e24e Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Mon, 1 Sep 2014 18:47:34 -0700 Subject: [PATCH] created chapter 5 --- Chapter05_Kalman_Filters/Kalman_Filters.ipynb | 2166 +++++++++++++++++ Kalman_Filters.ipynb | 2164 ---------------- 2 files changed, 2166 insertions(+), 2164 deletions(-) create mode 100644 Chapter05_Kalman_Filters/Kalman_Filters.ipynb delete mode 100644 Kalman_Filters.ipynb diff --git a/Chapter05_Kalman_Filters/Kalman_Filters.ipynb b/Chapter05_Kalman_Filters/Kalman_Filters.ipynb new file mode 100644 index 0000000..83d76b9 --- /dev/null +++ b/Chapter05_Kalman_Filters/Kalman_Filters.ipynb @@ -0,0 +1,2166 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:293a09cc844ccb8d9ee5a2a79a6375ecb56770e0e5e90dd5d3698900e6006206" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Kalman Filters" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#format the book\n", + "%matplotlib inline\n", + "import sys\n", + "sys.path.insert(0,'../') # allow us to import book_format\n", + "import book_format\n", + "book_format.load_style()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n" + ], + "metadata": {}, + "output_type": "pyout", + "prompt_number": 1, + "text": [ + "" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "One Dimensional Kalman Filters" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now that we understand the histogram filter and Gaussians we are prepared to implement a 1D Kalman filter. We will do this exactly as we did the histogram filter - rather than going into the theory we will just develop the code step by step. But first, let's set the book style." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Tracking A Dog" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As in the histogram chapter we will be tracking a dog in a long hallway at work. However, in our latest hackathon someone created an RFID tracker that provides a reasonable accurate position for our dog. Suppose the hallway is 100m long. The sensor returns the distance of the dog from the left end of the hallway. So, 23.4 would mean the dog is 23.4 meters from the left end of the hallway.\n", + "\n", + "Naturally, the sensor is not perfect. A reading of 23.4 could correspond to a real position of 23.7, or 23.0. However, it is very unlikely to correspond to a real position of say 47.6. Testing during the hackathon confirmed this result - the sensor is reasonably accurate, and while it had errors, the errors are small. Furthermore, the errors seemed to be evenly distributed on both sides of the measurement; a true position of 23m would be equally likely to be measured as 22.9 as 23.1.\n", + "\n", + "Implementing and/or robustly modeling an RFID system is beyond the scope of this book, so we will write a very simple model. We will start with a simulation of the dog moving from left to right at a constant speed with some random noise added. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import print_function, division\n", + "import matplotlib.pyplot as plt\n", + "import numpy.random as random\n", + "import math\n", + "\n", + "class DogSensor(object):\n", + " \n", + " def __init__(self, x0=0, velocity=1, noise=0.0):\n", + " \"\"\" x0 - initial position\n", + " velocity - (+=right, -=left)\n", + " noise - scaling factor for noise, 0== no noise\n", + " \"\"\"\n", + " self.x = x0\n", + " self.velocity = velocity\n", + " self.noise = math.sqrt(noise)\n", + "\n", + " def sense(self):\n", + " self.x = self.x + self.velocity\n", + " return self.x + random.randn() * self.noise" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 2 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The constructor `_init()__` initializes the DogSensor class with an initial position `x0`, velocity `vel`, and an noise scaling factor. The `sense()` function has the dog move by the set velocity and returns its new position, with noise added. If you look at the code for `sense()` you will see a call to `numpy.random.randn()`. This returns a number sampled from a normal distribution with a mean of 0.0. Let's look at some example output for that." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "for i in range(20):\n", + " print('{: 5.4f}'.format(random.randn()),end='\\t')\n", + " if (i+1) % 5 == 0:\n", + " print ('')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " 0.4900\t-1.5190\t 0.0639\t 0.5312\t-0.4402\t\n", + "-0.8721\t 0.4444\t 0.0782\t 1.0500\t-1.4336\t\n", + " 0.3928\t 1.6109\t 0.3260\t 0.4645\t 0.2985\t\n", + " 1.2323\t 0.6590\t 0.9813\t-0.7694\t 0.2915\t\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You should see a sequence of numbers near 0, some negative and some positive. Most are probably between -1 and 1, but a few might lie somewhat outside that range. This is what we expect from a normal distribution - values are clustered around the mean, and there are fewer values the further you get from the mean.\n", + "\n", + "Okay, so lets look at the output of the `DogSensor` class. We will start by setting the noise to 0 to check that the class does what we think it does" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import matplotlib.pyplot as plt\n", + "import matplotlib.pylab as pylab\n", + "\n", + "dog = DogSensor (noise=0.0)\n", + "xs = []\n", + "for i in range(10):\n", + " x = dog.sense()\n", + " xs.append(x)\n", + " print(\"%.4f\" % x, end=' '),\n", + "plt.plot(xs, label='dog position')\n", + "plt.legend(loc='best')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000 10.0000 " + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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mTJni+76oqEiZmZn1ffqo4/0prri42OSVWBtzulpN5/BOe9Cp0VkZKi0tMXmF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\nQFT4/6CvGxlaM3r6AAAAAElFTkSuQmCC\n", + "text": [ + "" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The constructor initialized the dog at position 0 with a velocity of 1 (move 1.0 to the right). So we would expect to see an output of 1..10, and indeed that is what we see. If you thought the correct answer should have been 0..9 recall that `sense()` returns the dog's position *after* updating his position, so the first position is 0.0 + 1, or 1.0.\n", + "\n", + "Now let's inject some noise in the signal." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def test_sensor(noise_scale):\n", + " dog = DogSensor(noise=noise_scale)\n", + "\n", + " xs = []\n", + " for i in range(100):\n", + " x = dog.sense()\n", + " xs.append(x)\n", + " plt.plot(xs, label='sensor')\n", + " plt.plot([0,99],[1,100], 'r--', label='actual')\n", + " plt.xlabel('time')\n", + " plt.ylabel('pos')\n", + " plt.ylim([0,100])\n", + " plt.title('noise = ' + str(noise_scale))\n", + " plt.legend(loc='best')\n", + " plt.show()\n", + " \n", + "test_sensor(4.0)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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ozFXTmlQrxcDOtejx/mJ2HT1PxxELmT64DSX9vQDYc+w8T360lOQ0M483KM8H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+ "text": [ + "" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "> **Note**: numpy uses a random number generator to generate the normal distribution samples. The numbers I see as I write this are unlikely to be the ones that you see. If you run the cell above multiple times, you should get a slightly different result each time. I could use `numpy.random.seed(some_value)` to force the results to be the same each time. This would simplify my explanations in some cases, but would ruin the interactive nature of this chapter. To get a real feel for how normal distributions and Kalman filters work you will probably want to run cells several times, observing what changes, and what stays roughly the same.\n", + "\n", + "So the output of the sensor should be a wavering blue line drawn over a dotted red line. The dotted red line shows the actual position of the dog, and the blue line is the noise signal produced by the simulated RFID sensor. Please note that the red dotted line was manually plotted - we do not yet have a filter that recovers that information! \n", + "\n", + "If you are running this in an interactive IPython Notebook, I strongly urge you to run the script several times in a row. You can do this by putting the cursor in the cell containing the Python code and pressing Ctrl+Enter. Each time it runs you should see a different jagged blue line wavering over the top of the dotted red line.\n", + "\n", + "I also urge you to adjust the noise setting to see the result of various values. However, since you may be reading this in a read only notebook, I will show two extreme examples. The first plot shows the noise set to 100.0, and the second shows noise set to 0.5." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "test_sensor(100.0)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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i+ujS0gidN4/YESPw3bNHfbz2FExFXAOtCCurzZzJKUGj8T6I7h4TwvSRSUy+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\n+BaEgebnpyNVr8aV9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8tbtLS9FVLAK4k5MTfn5+nD9/Pt827mIbTk5OuLu727oMERGRAmOMj8dz6lTS\nBg/GXPrKDZW7Y84x6NN1xJxJxejmw+DH6jCwYx2cHDU4WNwUiwAOV0JfQECArcsQERGRIuzvN1fG\nXczm0xY92HM8iS0Hz2C2WLivjC9TXnqI2pW0S3dxVWwCuIiIiEhBcTh9Gvd338PjhwUYzWbyDA7M\nCQrn7fNliPl575VrDAZeeOR+hnWph6uzIlhxpu++iIiIyB06EXeWiAXzsVhgxp+rmiT7l6F2pVK0\nDw0gPNSfOqH++PtoCqYogIuIiIjckR82HuXNr/by1H3tOV7lfh7v1ZpZof4EB3rr3jO5LgVwERER\nkZtkjI8HgwFThQpXVjSZvYWv1x4GIPmJrkzr1wQPVycbVyn2TgFcRERE5C/MZgufLNrJ8p3HKefn\nTq3gUjRwyaTmdzPxWLCArEceYeeYd3jxw9UcPJGCi5ORcb0a8nRUNY14y01RABcRERH5U0paFq9O\nW8fqPQkAhGSm0DB+AxFn9+CIhTyDA9tPptFh5ELSsk0EB3rz2cCWhAX72bhyuZfYzcKTR44coXv3\n7kRERNCmTRtWrVoFQG5uLiNGjKBu3bpERUWxdOlSG1cqIiIiRdH2I2d5eMRCVu9JwNfThY/7NeHg\n3i/od3Y3GAzMDKxNtciXecjnIdKyTbRvEMKyCZ0UvuWW2c0I+LBhw2jbti3fffcdmzdvpn///qxd\nu5YFCxZw7NgxoqOjOXjwIC+88AJ16tQhKCjI1iWLiIhIEWA2W/j45728t2AnJrOFupUD+PatzlQM\n9CFnSx/MSUmkDRpEhF8QY2PPsz8umeAgb9rXD9GUE7ktdhPAjx8/TuvWrQF48MEHcXFx4eTJkyxf\nvpzevXvj6elJ/fr1qVOnDitXrqRnz542rlhERETudedTMxn46Vo2/J6A2eDAS+1q8UbXSIICfQBI\nGzEC/gzZfkBU7fJE1S5vw4qlKLCbAN6kSROWLVvG888/z+bNm/H09KRKlSrExsYSEhLC0KFDad68\nOaGhocTGxtq6XBEREbkHmcxmjp2+yJ6YJHbHJHFo/W+8uH8lY/LSSJg5h5Z1KuR/gka4pQDYTQB/\n8803eeaZZ5g6dSrOzs58/PHHuLi4kJmZibu7O0ePHiUsLAwPDw/Onj173Tb8/DQHS/6fk9OVZaDU\nL+Qq9Qm5HvWLoi/69xOs2HmcHUdOs+voWdIycgjJTGFk/Aa++vPmSovRSG5FTyx/9gP1C7meq/3i\nTtlFAM+fmKVBAAAgAElEQVTKyqJPnz4MHz6cli1bsmvXLvr378+PP/6Im5sbmZmZLFq0CIAJEybg\n4eFx3XbGjx9v/bpp06Y0a9asUOoXERER+5NnMjPyy7VMWbgj3/FPz6zjuT+iMVrMmI1G8ro/iWnE\ncAgNtVGlYs/Wr19PdHQ0AEajkaZNm95xm3YRwP/44w/S09Np1aoVABEREZQvX57du3cTHBxMTEwM\nNWvWBCAmJoYWLVpct53+/fvne5ycnFywhYtduzpqoX4gV6lPyPWoXxRNKWlZvPTRajYeOI2j0UC/\n1mE8UL004ZX8qTQ3G4d3N5DxeBfSBg3CFBJy5Ul/6QPqF3JVWFgYYWFhwJV+sXHjxjtu0y4CeLly\n5cjKymLVqlW0aNGCffv2ERMTQ2hoKG3btmXOnDlERUVx8OBB9uzZwzvvvGPrkkVERMRO7Y9Lpt/k\nFZw8f5lS3m58PqgFDaqVtp5Pf+YZMtu1+//gLVLI7CKAlyxZksmTJzN58mSGDRuGn58fI0aMoFq1\nalSuXJnjx4/TrFkzfHx8mDhxIoGBgbYuWUREROzQj5uOMfSLaMqkJjE96w/C/zuZMv7e+a6xeHgo\nfItN2UUAB2jevDnNmze/5rijoyMTJ05k4sSJNqhKRERE7gV5JjNvf7udVQvX83F8NL0Tf8doMZOy\n/XGy2rWzdXki+dhNABcRERG5Wbl5Zg7EJ7PzaCI7/jhL4q6DvLhvOR8n/o6jxYzFaCSjc1dy/5y7\nK2JPFMBFRETknpCSlsVXyw+w9fAZ9hxPIjM7z3rumTOH6Ht2D2YHIxldupI2cKCmmYjdUgAXERER\nu5eUmkG3iUs4cvKC9Vil0j5EVgkkskog9Ss9RtqMIDJ69VLwFrunAC4iIiJ2LfFCBl0n/sqx0xdp\n7p1Hr14tqFuzPH7ebvmuSxszxkYVitwaBXARERGxW2dS0uk68Vcsx2NZcH47j8ftIPUBdzIaVrF1\naSK3TQFcRERE7NKp5MsMGT6bEb8toXfiXuvNlcbTp21dmsgdUQAXERERu3MyKY3Rr09nzcpJOGKx\nrmqimyulKFAAFxEREbty4twlurz9KydzPDnoX5EKTSLIHvyagrcUGQrgIiIiYhdOnb/M9xv+YPaq\ng5y7mEnd+wJx/nQFGT4eti5N5K5SABcRERGbyT16nPSx/2ZjhjMvuodjsVw5/kC1IGYOaY2Xu7Nt\nCxQpAArgIiIiUujitu4lZ8K7NN4TjaPFjL+TO0Ob1qZ5/cp0a1qFxmFlMDo42LpMkQKhAC4iIiKF\nJzeXlD4vUX/9chwtZvIwsPi+Bzj93Itse6wpPh4utq5QpMApgIuIiEihyMkz8a+52+n2+1GqWSys\nC2+K26g3qdewtq1LEylUCuAiIiJS4M5dzOD5KavY8Uciu6q25cwT9WnTvbmtyxKxCQVwERERuSNx\niZdwdTYS6OuOwWAAwBgfj/OuXWR26sRvRxN5fsoqzl7IIKiEB/9+rSN1QgNsXLWI7SiAi4iIyG37\ndt1hhk7fAEAJTxea+5gYdHg1jXavx2I08k1eKQb/8gc5eWYaVA3is0Et8Pdxt3HVIralAC4iIiK3\nZcVv8Qz7YiMAtbjMwJ2L6H12D45YyMPAnICaTJy3nRwXb/o+XJPRTz+Ak6NWNhFRABcREZFbtu3w\nGV76aDVmi4XXOtVlwobZuJ/djdnByK4GUXwZ3oZ16c44ZuYyqVNdujWrYuuSReyGAriIiIgAsGRH\nLHNWHaJfmzBa1qnwj9cdOpFCnw9WkJVrokfzagzpXJe0Or7g4EDawIEEhYQwEhhZeKWL3FMUwEVE\nRIQzKem8Nm09l7Nyid5/ipZ1KjC2Z0OCA73zX3cknqc/3MiljBweiQxm4jONMBgMmEJDuTh5so2q\nF7m3aCKWiIiIMGbOFi5n5VKjQkk8XZ1YtfsEUcPm8+78nWRm52GMj8f1lUGEtWyC36k4GlYvzUf9\no7Rbpcht0Ai4iIhIMbd6zwl+3R6Lu4sjM4e0xsnRgbe/286CDUdZ/O1qHvjv23Q98RsOZhN5GOjq\ncJ5ugx/G1VkxQuR26CdHRESkGMvMzmPUzM0ADOkcQdlSngBMefEhhhkSqDN+qnXL+FlB4cys05Yp\n7/fF293ZlmWL3NMUwEVERIqxKYt2cyIpjeoVStKvdVi+c+Ufb4PDpAn8Hv4gfZzu54xvIAtGtSfA\nV+t4i9wJBXAREZFi6o+TF5j2y+8AvNO38TVrdJv9/Uncvp1SPj78kGvCbLbg5qLoIHKndOeEiIhI\nMWSxWBg+YyPlLp9n7aV1PJgce/3rfHwAcHEyKnyL3CX6SRIRESmGli9Yz7M/fUbvxL04WsxkT84j\ned48W5clUiwogIuIiBQjDsnJuIwdT6+FP+BoMWN2cCDjiS6kDRpk69JEig0FcBERkSLIYrFgtlhw\nMBgwGAz/f9zVFcclS8Fi4deqDYn44l3MlSrZsFKR4kcBXEREpIjZeOAUb3y5kbjES/mOXwnj8HDl\nR4n19OezD5/HXMbXRlWKFF8K4CIiIkVEZnYeE7/bzlcrDhCSmUK93Ex2epe1njdbLGCBZaWqMLxb\nJJUVvkVsQgFcRESkCNh5NJFXp63DEBvHjBMb6Jm4F1OVKpxftBIcHKxTUiyWK9c7GrUQmoitKICL\niIjcw7JzTXzww28sn7+OUXHr6ZX4O44WMxajkexatTBkZGDx9MRgMGD8y1xwEbEdBXAREZF71P64\n8wz6dB2HE1I4vHcuVTOTsRiNZHTuStrAgZhCQmxdoohchwK4iIjIPSYnz8SUn3bz0aI9mMwWQkr7\nkDFoIBnHDyh4i9wDFMBFRETuIQcOn2LQzK0cSkgBoO/DNRneLRJ3Vycu2rg2Ebk5CuAiIiL3ANOx\nGE6/PpbQ33cRU/9lgkuX5IPnmvJA9dK2Lk1EbpECuIiIiB0zxsWR+/a7lF76M+UtZvIMBiZWceCx\nEZ1xc9GvcZF7kX5yRURE7JTjpP/iN/kDjGYzeRiYHxyJ7/iRPNk80talicgdUAAXERGxMyazmW/X\nHWH3hnPMMVuYERTO0R796Nf/UY16ixQB+ikWEREpBBaLhX/N3cqWQ2doUDWIJmFleaB6abzdnfNd\nt/XQGUbP2cKB+GRwCybrqfG89PKjtA72s1HlInK3KYCLiIgUgs+X7uOLZfsBOBCfzFcrDmB0MPBI\nKQPDTm3h1MDBfL3rDD9vOw5AGT8P3nqqAR0aVMKgDXREihQFcBERkQIWvf8UE77ZDsDopxuQlpHL\n8S17eHT9j/Q6swdHLIw5lcnPwQ/h6mzk5fa1eal9bU03ESmi9JMtIiJSgE6cu8RLH63GbLEwsGM4\n/WuVxHPyZNznz8dgMmF2MLKpTlN2hTSlc7XKvNElkrKlPG1dtogUIAVwERGRApKRlUvfySu5eDmb\nFuHlGfpEBA67d+Px3XdXtozvemXL+JCQED6zdbEiUmgUwEVERAqAxWJhyPRoDp1IoVJpHz7qH4XR\nwYHciAhSR48m6+GHtWW8SDGlAC4iIlIAvpuxnG3rD+LpU5KvXmuFj4eL9Vz6Cy/YsDIRsTUFcBER\nkbvIGB/P5X/9m0Erf8GldD08Pv0v95UtYeuyRMSOKICLiIjchtPJl4lLvMTlrFwuZ+ZijI+n/k9z\nCd+yisA/d66MCPGjYkRFW5cqInZGAVxEROQWLdoSwyufrMVktgDgl5POyS2TcLWYyMPAjKBwoh/p\nzvixPUBreIvI3yiAi4iI3ILofScZ9Ok6TGYLdUIDKOnlgqebM9sym+DkYGDdI91wqnIfoxpXxsFB\n4VtErqUALiIicpP2Hk+i36QV5JrMPNsmjH/1eOD/d6l8OQoMBvrYtEIRuRc42LoAERGRe8GpHftI\nfupZPt/zPY83qsyYpx/Iv0W8ppqIyE3SCLiIiBRr783bwr+/2UzHhpV4uUNtQoJ88p03xsdjfG8S\ndX5aSKTFTK6DkaYdq2p6iYjcNo2Ai4hIsbX3eBL/mhVNRnYu3647QtOh8+k/dQ0HTyQD4D1qFAFN\nmlDqxwVgsbD4vgc4tXI1xrJlbFy5iNzLNAIuIiLFUk6eiSGfR2MyW+jZ6n7ycnNYsOEoi7bEsGhL\nDC3rVODjtBwqmS3MCQpnbr1HmPJ+P5y9XG1duojc4xTARUSkWPp48V4OJaRQqbQvU15+mMz0S7z2\neF0+W7KPr9ccYtXuEzyYUwbfyJdJL1uBxf96lJIK3yJyF9jNFJSsrCxGjx5NgwYNiIyMZOzYsQDk\n5uYyYsQI6tatS1RUFEuXLrVxpSIicq87dCKFKT/tBmBmlzC8Pv4QgLJ+nozr2ZDtU57klY7h5Pj4\nciGwLN+82YaypTxtWbKIFCF2MwI+ceJEEhIS+PXXX/Hz8yMmJgaAmTNncuzYMaKjozl48CAvvPAC\nderUISgoyMYVi4jIvSjPZGbI9PWUu3yeGbn7aNxlPAaTCecqVch58EEA/LzdeLNrJIMeq4PZbMHD\n1cnGVYtIUWIXATwrK4tFixaxcOFCSpUqBUDlypUBWLZsGX369MHT05P69etTp04dVq5cSc+ePW1Z\nsoiI3KPmz1rBK0u+pHfiXhwtZixGI6YePTCVK3fNtW7OdvFrUkSKGLuYghIXF4fBYGDVqlU0atSI\ndu3asWrVKuu5kJAQhg4dypIlSwgNDSU2NtbGFYuIyL3o2OmLpMz6jn5nd+NgMJDRpQs5v/9O3hdf\nYKpQwdbliUgxYRf/a3/58mVyc3M5efIka9euZffu3bz44ousWLGCzMxM3N3dOXr0KGFhYXh4eHD2\n7NnrtuPn51fIlYs9c3K68idj9Qu5Sn2ieDObLbz59lJ+D6pH85IONJ4xCWNoqPqFXJf6hVzP1X5x\np+wigLu6umIymXjmmWdwdnamQYMGhISEsHfvXtzc3MjMzGTRokUATJgwAQ8Pj+u2M378eOvXTZs2\npVmzZoVSv4iI2AeTyUxmTh5uzo4YE05AhQrgcOWPvdN+/o0tB08S5F+Smp/PA61oIiI3Yf369URH\nRwNgNBpp2rTpHbdpFwG8fPny+bfz/ZPFYiE4OJiYmBhq1qwJQExMDC1atLhuO/3798/3ODk5+e4X\nK/eMq6MW6gdylfpE0ZWSlsWsVQeZueIgXomnGBm/gd6Je3mmdjeWVwzH1dlI4oUMACb2eRBzTjrJ\nyemA+oVcn/qFXBUWFkZYWBhwpV9s3Ljxjtu0izngPj4+REZGMnPmTPLy8tixYwexsbGEh4fTtm1b\n5syZQ1paGtu2bWPPnj20atXK1iWLiIgdOHHuEqNmbaL+oG9ZOGcl/9n+LX9sn0q/s7vBYiHk4hmS\nUjNJSLpMTp6ZxxtVpnW9YFuXLSLFnF2MgMOVZQiHDx9OZGQkgYGBvPfee/j7+9OnTx+OHz9Os2bN\n8PHxYeLEiQQGBtq6XBERsaHfY5P49Jff+WVbLGaLhcYX41m3dxbGP1c1Se/cleSXXqZ72fI8lpNH\nVo6JPJOZ4EBvW5cuImI/AbxcuXLMmTPnmuOOjo5MnDiRiRMn2qAqERGxF0mpGSzecpwfNx9jd0wS\nAI5GA50aVual1h2w9F5PRr16pA0ciCkkBEfAF8DDxZZli4hcw24CuIiIyN9dzsxh2c54ftx8jA37\nT2EyWwDwdHXi6ebV6NcmjLJ+V3aoPLdyJbjqxkoRsX8K4CIiYnfOXcxg/DfbWLIjlqwcEwBVsi8w\n5dJvuDZ+gPJvvIKby99+hSl8i8g9QgFcRETsSmp6Nk+9s5RDCSkAdApy4F+nNnH/9lUYTCbyLsVz\nbtQgG1cpInL7FMBFRMRuZObk0eeD5RxKSOH+ADdWZW/Df/4iDCYTFqORjK5dSRs40Lq2t4jIvUgB\nXERE7EKeycxLH61m+5FESpf04MsRHfDt9TWANXibQkJsXKWIyJ1TABcREZuzWCy8/sUGVu46ga+n\nC9+80Zay/l6kvvsuZk9PBW8RKVIUwEVExKaM8fH8OH0x38e64ubiyOyhralSrgQAufffb+PqRETu\nPk2iExERmzDGx+MzZAilGjem++zJ+Jmz+HxgSyLu02ZrIlK0aQRcREQKlTE+Hs8PP8R9/vwrq5pg\n4Meg6vynRwOah5e3dXkiIgVOAVxERAqVz1tv4bp6NSaDA7ODwnm7QhN6vdCeZ9uE2bo0EZFCoQAu\nIiKFZscfiSwrWZ/6Qcm8XaEJZ0sGMaRzXYVvESlWFMBFRKRAGFJTsfj4ALDjyFkmLdxF9P5TgAtz\nwrvQt3VNnm97PyW9tIOliBQvCuAiInJXXZ3j7bZ4MStn/sDE6JN/Bm/wdHWib+uaPKfgLSLFmAK4\niIjcFX+/udJkcGDu6M+JDqqNp6sT/dqE8VzbMEp4KniLSPGmAC4iInfM7bvv8B02zBq8r95cmVgy\niEEK3iIi+SiAi4jIHYsLrUFNDHz9Z/A+WzJIc7xFRP6BAriIiNyRzQdP89wXezA2eI1MLx/6PlyT\nF9rVUvAWEfkHCuAiInJTrs7xTn/uOfKqVQNg7ppDjJy5iTyThRb1qzH5hWb4ebvZuFIREft2UwE8\nNzcXs9mMi4sLAOfOnePo0aMEBQURGhpaoAWKiIht/f3mSoeMDJKmfszYuVv5asUBAF5qV4vh3SMx\nOjjYuFoREft3UwF83rx5VKxYkSZNmnDhwgWmTZuGg4MD2dnZPProo0RGRhZ0nSIiUsgcEhPxevdd\na/C2GI1kdO3Kqede5Nl3lxG9/xTOjg6807cJ3ZpVsXW5IiL3jJsK4AkJCbRs2RKA/fv34+fnx4sv\nvsiuXbvYvHmzAriIyD3m4IlkZq48SHglf6Jql6d0SY9rL3JwwO2nnwDI6NqVtIED+cO1BH0+WMHx\nM6n4ebvy5autiKwaVMjVi4jc224qgOfk5FinnyQkJFCrVi2MRiOVK1fm119/LdACRUTk7krPyuXZ\nySuJP5fG12sOA1C9Qkma1y5PVO3y1LsvECdHBy57+ZLw+hh2epZmY6YL+7/cw+GEFHLyzFSvUJKZ\ngx+mnL+Xjd+NiMi956YCeMmSJdm5cyfVqlUjJiaGJk2aAJCRkWEN5iIicm+Y+N124s+lUbmMLyFB\n3pzcsR/DoXN8fCKFj3/ei5ebE/6+7sSeTcViAYjL9/wODSrxwfNN8XB1skX5IiL3vJsK4C1atGDe\nvHlER0dTsWJFypUrB8CRI0coW7ZsgRYoIiJ3z8YDp5i58iCORgMzOlWhzg+zcd88n3M1wxn9xAjW\n7k3g6OmLpGWm4mg0cF/ZEoRV9CMsuBRhFf2oUdEPb3dnW78NEZF72k0F8Bo1avD666+TmppK6dKl\nMRgMAFStWpVatWoVaIEiInJ3XM7MYcjn0YRkpvCdwyEiu4+z3lzpVbUSY54IZ0yPBziZlMbF9Bzu\nK+uLi5PR1mWLiBQ5N70OuKenJ56envmOafRbROTeMf6bbZw9l8qp32cSkHnpyqomXbqQNmgQppAQ\n63Xl/L0o52/DQkVEirhb2ognKSmJ5ORk4Mq88ICAgAIpSkRE7q71v59k7prDODk5kfrs83iejb8m\neIuISOG4qQCelpbG/PnziY2NzXc8ODiYrl274uWlu+BFROxObi44OXEpI4ehX0QDMKRzBB4dw7lo\n49JERIqzmwrgP//8M1lZWfTr14/SpUsDcPr0aZYsWcLPP//MU089VaBFiojIzbu6c6XT/v2cX7qU\ncV9v5XRyOuGV/Hmpve7bERGxtZvaMzgmJoaOHTsSHByMi4sLLi4uhISE8Nhjj3Hs2LGCrlFEpFjL\nyslj2BcbqPPyXH7c9M//zTXGx+MzZAgBTZrg8d13OB06xN4FK/l23RFcnIxMfqEZjkZtFS8iYms3\nPQf86sonIiJSeM5dzKDf5JXsOnYOgAGfrGXP8SRGPdkAJ8f/D9Ne77+P54cf5tsyfl+3PvSdewCA\n15+IoEq5EjZ5DyIikt9NDYVUqlSJRYsWceLECXJycsjJyeHEiRMsXryY0NDQgq5RRKRY2hd7nkfe\n+oldx85R1s+T1zrVxdFo4Itl++n+7185dzHDem1e+fLAlS3jY5evYnC9bjT+ZAdnL6QTcV8Azz9y\nv63ehoiI/M1NjYB36NCB77//nunTp+c7XqFCBdq3b18ghYmIFGeLtsQw+PP1ZOWYiKwSyBevtqKU\njxvNapXjhSmr2Hr4LG1H/chng1pS775AMh9/nKzI+nx/KpeJU7dz7mImBgM83bwaw7tFYnTQ1BMR\nEXtxUwHc29ubZ599lsTERFJSUoAryxAGBgYWaHEiIsWN2Wzh/R9+Y8pPuwHo3qwKE59pjIuTEWNc\nHC2+nsHyMa/y/LQNbD+SyBPjf2Fcr4bUrRzAyNn72Hk0EYCI+wKY0PtBaoVoQW8REXtz03PAY2Ji\n2LFjh3UdcD8/PyIjIzUFRUTkLsnMzuOVT9aydGccDgYDY3o8QL/WNXGMj8frww9xW7AAg8lExZAQ\nvh/Ri/HfbOXL5QcYPmOTtQ1/HzdGPlmfzo3uw8FB9+6IiNijmwrgW7ZsYenSpYSGhlKpUiUAzp07\nx6xZs2jTpg0PPvhggRYpIlLU5eaZeX7KKtbsTcDb3Zlpr7Sgua8ZryFDrMH76s2V2Q89hJOjA+N6\nPUjtSv4M+3IDuXlm+rauyeDHI/B2d7b12xERkRu4qQAeHR1Nhw4diIyMzHd8x44drFmzRgFcROQO\nmM0WBn++njV7Eyjh6cLCtzpQpVwJHFeuxH3ePGvwThs48JqdKzs3vo+G1UtjsUDZUp42egciInIr\nbiqA5+TkEHKd7YqDg4PJzs6+60WJiBQXFouFcd9sZeGmY7i7ODJ3WFvrcoHZLVuSNngwGY8/fsMt\n48v4KXiLiNxLbuq2+PDwcDZv3kxeXp71WF5eHlu2bKF27doFVpyISFH3yS97WbUwmlLmbL58rRXh\noX+5adJgIG3IkBuGbxERuffc1Ah4YmIiJ06cYN++fZQsWRKA5ORkcnJyqFChAl9++aX12n79+hVM\npSIiRczS79dS6T8f8EfiHnY/0Zuy95ezdUkiIlIIbiqAlyhRghIl8u+gFhAQUCAFiYjc63LzzIya\ntYm1e0/SoFoQjWuWpUlYGetUEWN8PKmjJ9J79RIcLWbMDg5U9zZyycZ1i4hI4bipAN65c+eCrkNE\npEjIzM7jxY9Ws2r3CQAWbjrGwk3HAKhcxpfHyjryzqRBBJpM5GFgW/3mBE8ap2kmIiLFyE2vAy4i\nIjeWmp5Nnw+Ws/1IIr6eLnzwXFNOnb/MhgOn2HzwDMdOX+T909DEN5RkJ3f2d+vD4NefwGTQet0i\nIsWJAriIyF2QeCGDp/+zlEMJKZQu6cG3b7blvjK+YDDQr00YuXlm9sScI3r/Kf5TJYD7KpRifO+G\nGBS+RUSKHQVwEZE7FHs2lafeWcqJpDRCS/uwsMf9hE6agMXDg0vjxgHg5OhAZNUgIqsGQecIG1cs\nIiK2pAAuInIH9scl0+PdpSSlZtKulIE5OZvxfXQoBpMJs5sbaUOHYvH2tnWZIiJiRxTARURuQ2p6\nNvOi/2DSD7+RlpHDoqQ1dNiwOd+W8WkDByp8i4jINRTARURuwdFTF/hqxQEWbDhKRvaVzcnaP1CJ\nqKP74Qj/uGW8iIjIVQrgIiL/g9lsYfWeE3y1/ADR+09ZjzeuWYZ+rcNoWacCGWeqkzH4NQVvERH5\nnxTARURu4HTyZXq8u4wjJy8QkpnCK5diufDk0/RtXZOq5UparzOVLWvDKkVE5F6iAC4i8g8upmfT\n491l5ByN4dvErXQ5sROj2cy5Rq+S95fwLSIicisUwEVEriMzJ4+RY+by+tof6Z24F0eL2XpzpcXL\ny9bliYjIPUwBXETkb/JMZgZ8vIYWG5bS7+zuK8G7s26uFBGRu0MBXETkLywWCyNmbmLZzniOVX2I\np+qWxjhssIK3iIjcNQrgIlLsOZw5g7l0aQAmL9zF12sO4+pk5L3hT0DVIEw2rk9ERIoWB1sXICJS\nmC5n5pBnMgNgjI/HZ8gQAhs0wHnzZuasPsQHC3fhYDDw8YDm1K8aZONqRUSkKNIIuIgUC2azhdc/\nW8XHi34jOCOZsac20/3kLhwtZkwGB1ZM/4kRuVUA+L/27jyuqjr/4/jrrlzgAqJsrizuiJO4lZk6\narlmZZblWGl7o2VZWWnTMpOZtmjjTDP9ciodtTI0h0pzaSrJKE3TTHFFQTQFFZBFtrv8/nC8k4nW\nlHKA+34+HjzCcw/X982P9O5w7vf73G09GdQ1ztjAIiJSb9W6K+AbNmygXbt2pKSkAFBVVcWUKVPo\n3Lkzffv25aOPPjI4oYjUNS63h4fmpPGXpRsYeHQXO9f9hZtyNoDXy9zoi2jbbTyjK1vj8Xp56NrO\n3NSvvdGRRUSkHqtVV8BdLhcvvvgiLVu2xGQyATB37lz27NlDWloaGRkZ3H333SQnJxMTox8Ni8hP\nq3S5ufeVT1m2fh9BATbun/kgplGryb+0JxmjbycgJJIJx8s4WlRG88gQhnSLMzqyiIjUc7WqgC9Y\nsIC+ffuydu1a37EVK1YwduxYnE4n3bt3Jzk5mdWrV3PzzTcbmFRE6oKyChd3/fljPvk2h9AgO6lT\nR9IjsRl56V/gDQoiAUgwOqSIiPidWlPAjxw5wnvvvcfixYtPK+BZWVnEx8fz8MMP069fP1q2bMm+\nffsMTCoitZ0lO5uAmS/zl6IGfFLZhIYhDt56dDA9EpsB4A0KMjihiIj4s1pTwGfMmME999yD3W4/\n7XhZWRlBQUHs3r2bpKQkgoODOXz4cLXP0ahRo5qIKnWEzWYDNBd+Ze9erDNmYF6wAJPbzQ3B0fxz\n4MMse24U7WMjNBNSLc2FVEdzIdU5NRe/Vq0o4Bs3buTAgQMMGTLEd8zr9QIQGBhIWVkZqampAEyd\nOpXg4OBqn+eZZ57xfd67d2/69OlzAVOLSK1RWIj10Ud9xdtlMrMg+iLmdh3Kxy/dTELjBkYnFBGR\nOnwdg5oAACAASURBVGrNmjWkpaUBYLFY6N27969+zlpRwLdu3crmzZtp166d79jXX3/N7t27iYuL\nIzMzkw4dOgCQmZlJ//79q32ecePGnfbrY8eOXbjQUuudumqhOai7Fn++m/9bvoUnRl9C76SmZz+x\nqoqozz4DYGnL7kxqdDGmVi15Z/IQwuxu3wxoJqQ6mgupjuZCTklKSiIpKQk4ORc/vFX6l6oVyxCO\nGTOGHTt2+D66devG1KlTmTJlCoMHD2b+/PkUFxezbt06Nm/ezBVXXGF0ZBG5wHILTjBl7hdk7M/n\nludXkPpl5tlPttk4OG0GVw3/A9c2HwItE1j8h6E0blj9T8tERESMVCuugJ/L2LFj2bt3L3369CEs\nLIxp06YRHR1tdCwRucCeT/ma0vIqohoEkldYxvhXPsGTuZcb4gKpvOyy084tLa/id58VsOGoidio\nEBZNGUpkmN5oKSIitVOtLODz58/3fW61Wpk2bRrTpk0zMJGI1KStWUdZlLYLq8XE4j9cyfqPviT8\nlb9yy6ffUhLWkIpv1mNyOICTSw2OeXElG3bn0rSRk3en6Mq3iIjUbrWygIuI//J6vTy94Cu8Xnik\nSyO6vPAnLlu82PfmyqWBzVk/5xOmjB9ElcvD7bNW8eX2Q8SEB7FoyhCaRYYY/RJERETOSQVcRGqV\njzZk8eX2Q4Q7A3h89RsEbfoGr8XCiZEjWd5vBOOW7KL8q4Psd39CldvNmu8OEhEayKIpQ4mPCTM6\nvoiIyE9SAReRWqOiys0zC9cB8PB1XSkzN4UPP6R4wgTc8fFcCixs1ZJbZ65i+dcnN+Rq4AzgnclD\naNVESw2KiEjdoAIuIoYzlZbiDQ7m9RVb2X+kmDZNG3BTv3ZUWBKp+NGyo5e0b8ySJ67k5udXUF7l\n5p3HhtC+RUODkouIiPzvVMBFxDCW7Gycs2fjWLmSjI8+5s//2gTA0zf1wGo5+yqpiS0a8cXMG3C5\nPTgD7Wc9T0REpDZSAReRGneqeAelpGByu/FaLHz88luUlIfQv1Nz+vym2U8+h8Oub18iIlI31YqN\neETEfwS/8QZRvXoR/M47AJwYOZK1b6XyUG4IVouJJ0dfYnBCERGRC0uXkESkRlUmJwNQfP31HLrj\nHvKjmvDoa2l4vTDmig56M6WIiNR7KuAicl54PF6eW7Setz/bCYDVYsZiNmExm7FaTFgsZqpcbkrK\nqgi9dCLZR5zw3Oe+r2/gDGDi8GSj4ouIiNQYFXAR+dVcbg8PzUlj8ee7AYgvy2dK9uf8Me63HHCc\nuTZ3gcWJ1WLC6bAT7LARGmzngWuSCXc6ajq6iIhIjVMBF5FfpdLl5t5XPmXZ+n0kuotIDdxNy8+X\nY3K7uapPe/ZNvhu3x4vL7cFmNeN02Ah22AiwWTCZTEbHFxERqXEq4CLyi5VVurjrzx+z86ut/PNA\nGqO/34zZ4/btXOm9bxzNtTW8iIjIaVTAReQXKS2vYuxLK0nPOETnQDOjD23GZDq5qsmpnStFRETk\nTCrgIvI/O15awc0vrGDj7jyiGgTy4uQRFH3emIpLLlHxFhER+Qkq4CLys1mys8nOK+b2f+1ia9Yx\nmjZysmjKEOJjwjgxapTR8UREROoEbcQjIj/Jkp2N6Z57ieh5GVl3TmRr1jHiokNZ+uQw4mPOXOVE\nREREzk5XwEXkrCzZ2binvUDEslQsXg8uTJywBnDTb9swaWR3IsICjY4oIiJS56iAi8gZCksr2L3z\nIJePGEBwZRkuTMxrnMy2G2/l+rEDGRDhNDqiiIhInaUCLuLHCkrK+fTbA+w7fJys3CL2HT7Ovtwi\nCksqAJgW04WmrlJ2jLqVEWMHcUXDYIMTi4iI1H0q4CJ+6nBBKVc99T4Hj5Vg9nrwmP77lpCgACtx\n0aFkD36AQUMv4vLwIAOTioiI1C8q4CJ+qPhEJTc/vwL7gf0sPrqODpZylj81i/iYUOKiw4hqEKhd\nKkVERC4QFXARP1PpcvPkn97mwdUpjMn9FqvXg9diIbyZBXerxkbHExERqfdUwEX8iNfr5dsbf8/C\nL5djxXtyy/gR2rlSRESkJqmAi/iR51M2YM+tZKjJxIFBw7A9/oiKt4iISA1TARfxE/P/vZ3ZqZsJ\nad6dnpPvpPuQnriNDiUiIuKHtBOmSD1kyc4mZPp08HgAWPVNNlPe/AKAp+7qR/chPY2MJyIi4td0\nBVykHrFkZ+OcPZuglBRMbjdZMbEsaNCO2amb8Hi9PHhtZ0b9tp3RMUVERPyaCrhIPfDj4u02m3kv\ntiuPvb+fvYElANzYpw0PXtvZ4KQiIiKiAi5SB5WWV3HgaDE5R0o4cLSEZstTueXdd3CZzCyIvoip\nsb3JDGpEo1AHNya3YGCXOC5PbqG1vUVERGoBFXCROuL7YyU8+/Z61nx3gIL/bBV/isUTTl6zHrza\npCvmVi0Z1CWWKzrH0rlVJBaz3uohIiJSm6iAi9Rybo+HuasymJGygaiCXEoDQgkICKBphJPmEU6a\nRYTQLNKJI+Jy5raMJCEmzOjIIiIicg4q4CK12Hf7jvLoG59TvG0Xs7PTGJO7hX2PPI7j3lsxm3U7\niYiISF2kAi5SC5WUVfLC4o189q/PmZy1hltyt/i2jI8uLaBY5VtERKTOUgEXqWXWbDnAQ3PSiNif\nyfaNr/mKt7aMFxERqR9UwEVqCY/Hy8tLv2Hm0m/weiGqYwdKypKwd2in4i0iIlKPqICL1AL5xeXc\n97dP+WzLAUwmeHhEFyZc04kT7mGcsNmMjiciIiLnkQq4iIEsWVlUTH2e5dnlfBbVg3BnAK+M70ef\n3zQ7eYKWEBQREal3VMBFDGDJysI5ezaBKSmYPR5uswaytPsQZj84iKaNnEbHExERkQtIBVykBlWV\nV2K7fyKRyz/A7HHjwsS8mE7sGn0bb0+4BrvVYnREERERucBUwEUuAK/XS15hGduyj7E95xg7cgrY\nnpPPnoOFLN20jYEeD/NiOjGzVV/GPTCc+3q0NDqyiIiI1BAVcJFfyePxknmokG3Zx37wkc/RorJq\nz3+p+7UsbhJO2G/a8/derbVzpYiIiJ9RARf5BbxeL5syj/D+V5l8uG4fh/JLT3s8viyf4eWH2Hrp\n5SS2aEi75ic/2jYLJ9ihVU1ERET8mQq4yM/k9Xr5Luso73+5lw/W7eXA0RLfYzHhQXRqGUmvoCqu\nS3+f1hs+ArOZ3DmT8DRtamBqERERqW1UwEV+hi37jnDvK5+Seei471hMeBBDL07gqksS6GYtI/Sv\nfyEoJQWT243XYqFs+HAtIygiIiJnUAEX+Qlbs44x6rmPKCytIDIskKHd40+W7jYxmM0mAMImTiTo\n3XdPbhk/UlvGi4iIyNmpgIucw46cfG58bhmFpRUM7BLLqxP6V7tUYPGECb5/qniLiIjIuaiAi5zF\nnu8LuWHacgpKKujXqTl/v68/jsICPBERZ5zrjo+ncNYsA1KKiIhIXaMbVEWqsffwcUY+u4yjRWX0\nTmrKm8PbEPXYI0R37Yp1+3aj44mIiEgdpivgIj+yP6+Ikc8uI7fwBCOaWnkjdzUh/e7xvbnSvn49\nrvbtjY4pIiIidZQKuMgPHDxawvXPLuNQfimTLQd49p03fcVbb64UERGR80EFXOQ/tmYd486XV3Pg\naAnJLaO47c6heK9YRNngwSreIiIict6ogIvf83q9LPhkB0/N/5KKKjcXJUSw8NFBBAUHkLt+Pd7Q\nUKMjioiISD2iAi5+rWLnHjIfeIKPTPFUhMczul87/nhzDwLtJ/9qqHyLiIjI+aYCLn7Jkp2Ne9oL\nNF+WSrzXg7XhAbY+fhvX9mxldDQRERGp51TAxa+Y8/MJmTqVwJQUzB4PLky8l9CdZi8+zbUXq3yL\niIjIhacCLn5ly6ESur+/jACPl3kxnfj2+lu4b+IIAgP0V0FERERqhlqH+IWvth9iduom1nx3kEGt\nriYnLIo7xl/FI73bGB1NRERE/EytKOAul4spU6aQnp5OeXk5iYmJPPnkk7Rq1YqqqiqeeuopVqxY\nQVhYGI888giDBw82OrLUEuWVLkrKqggNtmO3WnzHLdnZsGcPK80RPLsgjfU7cwEIdthIGDOC6UM6\nEhkWZFRsERER8WO1ooB7PB5iY2N56KGHiI6OZu7cuYwfP56VK1cyd+5c9uzZQ1paGhkZGdx9990k\nJycTExNjdGwx2ObMI9z0/EcUlFQAEBhgpaO3mEmZn3HN3q/JCo3imk534TWZaRAcwO0DO3DrwA6E\nOx0GJxcRERF/VisKuN1uZ/z48b5fX3vttUyfPp38/HxWrFjB2LFjcTqddO/eneTkZFavXs3NN99s\nYGIx2sGjJdw6cyUFJRU4HTZijufx2I40xhzejBUvLkysdUQT77QyalhXbrm8Pc5Au9GxRURERGpH\nAf+xTZs2ER0dTXh4OFlZWcTHx/Pwww/Tr18/WrZsyb59+4yOKAYqKatkzIsrySss49LExix8ZBBN\nL++P7fAevBYL3w8cytYbbyWqVXs2dmjKiZIioyOLiIiI+NS6Al5cXMy0adN47LHHMJlMlJWVERQU\nxO7du0lKSiI4OJjDhw9X+7WNGjWq4bRS01xuD7e/vITtOfm0adaQJX+8gfAQB0yejPvTT3FNnkyj\nli3pA9hsNgACA2zGhpZa49RM6HuF/JDmQqqjuZDqnJqLX6tWFfDKykrGjx/P0KFDfW+0DAwMpKys\njNTUVACmTp1KcHBwtV//zDPP+D7v3bs3ffr0ufChpUY9/spHrPg6k4YhDpb+6fqT5RvwjB6NZ/Ro\ng9OJiIhIfbNmzRrS0tIAsFgs9O7d+1c/Z60p4G63mwcffJC4uDgmTJjgOx4XF0dmZiYdOnQAIDMz\nk/79+1f7HOPGjTvt18eOHbtwgeW8KimrZNU3++nSOorYqDO3f7dkZ3Po0T9y/9freP2S+/jHA5fT\nIMBzzj/jU1ctNAdyimZCqqO5kOpoLuSUpKQkkpKSgJNzsXbt2l/9nLWmgD/55JOYzWaefvrp044P\nHjyY+fPn07dvXzIyMti8eTPTp083JqRcMI+8vpbULzMBSIprxJBu8QztHk/bykJCZs/GkbKYaI8b\nFybm9Qzj4naNDU4sIiIi8svUigJ+8OBBlixZQmBgIF26dPEd/8c//sHYsWPZu3cvffr0ISwsjGnT\nphEdHW1gWjnftmUfI/XLTGwWMwE2C1uzjrE16ximF2dxadanWL0eXCYz82I6cfD2e7ht3DCjI4uI\niIj8YrWigDdt2pQdO3ac9fFp06Yxbdq0GkwkNen5lA0A3HJFIlNu6Eba1oMsX7+PzJJ9sM/LmzGd\neLZFLxL7duNv9/QzOK2IiIjIr1MrCrj4rw27c/l4036CAqzcd9VFOOxWBnSOZUDnWKpu78Wyz4bz\n7/3lXOKFP97SA7PZZHRkERERkV9FBVwMtWDOcv6+8wOy7p14xtbwNpuFbld0o5tB2UREREQuBBVw\nMYQlK4vSP07nrVUfYsXLke/XUUVfo2OJiIiIXHAq4FKjLAcOEDJzJoGLF2Nyn1zVZMMll9N81A1G\nRxMRERGpESrgct6cKK/i3c9388bKrZhNJl6d0J92zRuedo75yBGCFi3CY7YwN6YTf0+8grfmjMft\n0G6VIiIi4h9UwOVXO5RfytxV21jwyQ4KSyt8x4c9lcrs3/+Wwd3ifceqkpMpfPIpbvjWzarjVv40\nugdBKt8iIiLiR1TA5RfbmnWU/1v+He9/lYnL7QWgS+so7hiUxJZ/b2DppoPc8fLHTBzemQev7exb\nwWRhUj9WpX1Kk0bB3NS/vZEvQURERKTGqYDLL/LSko3MfO8bAMwmE1deHM+dgztysb0c5+zZBKWk\nMPayQfQwdWfW0m/Yln2M2b//LQ67lReXbATgoWu7EGCzGPkyRERERGqcCrj8z9ZuO8ispd9gMZu4\ndUAH7hiURNyJfJyznycoJQWT243XYqFDswYsGD2Qca98yqpvshn2VCoDu8aRlVtEQuMwruvV2uiX\nIiIiIlLjVMDlf1JYWsH9f1+D1wsPDE/mwRFdMOXnE9WvH6bycrwWCydGjqR4wgTc8fH0AZY9cw23\nzVzFzgMF7H5/MwAPj+iC1WI29sWIiIiIGEAFXH42r9fLY6+v5XBBKZ1bRTHhmuSTxxs25MS112Jy\nuXzF+4fiokN5/+mreODVNXy0IYukuEYMuzjBiJcgIiIiYjgVcPnZlqzdw4df7SHIYecv4/qedgX7\n+PPPg+ns28Q7A+28dv/lrM34nqTYRtpSXkRERPyWCrj8LHmbMmjw0GMsrKrg0KzZxEWHnn7COcr3\nKWazid5JTS9QQhEREZG6QQVczsmSnU3wn/9M1LspdPJ6cJktHGkbitfoYCIiIiJ1lAq4nFXoE08Q\nPG+eb8v4d1p0pfOcGTgbNzY6moiIiEidpWUo5OwCAvAC8xp3ol33e+G1V3AmtTM6lYiIiEidpivg\nUi23x8PnA6/jhZxwPi2xc8egJHp3bGZ0LBEREZE6TwXcz1myswn84ANK7r2XskoXn289yKqN2az+\nZj9Hi8oAO+2ahTP5hm5GRxURERGpF1TA/ZQlO9u3ZbzJ7WZqpoe/Hg+hrMLlO6dFZAgDusTy+yt/\ng8OuURERERE5H9Sq/MyPi7fLZGZ+TCdSssspCwzkN/ERDOgSy6AucbRrHo7pZywvKCIiIiI/nwq4\nnzGnfkDwO+/4ivezLXrhSYjn9gEdGNQ1jiaNnEZHFBEREanXVMD9xPHSCt5YuY23vnUwpUk3ZjW7\nBHu71jx0VSeuvDgei1kL4oiIiIjUBBXwesqSk4O7aVO8JhPL1u/jD/PSOXK8DIA3h97Kk1cn079T\nc91iIiIiIlLDVMDroA/X7QXg8uQWZ7w58of3eO+b/hLjDoexcmM2AF1bR/PoyK70aN9YxVtERETE\nICrgdcyaLQe4e/a/AQgLsnP1pS25oXdbOltKCfnLX3xvrvSYzbzzf++zsllvnA4bj4/qzk392mM2\nq3iLiIiIGEkFvA7xeLxMfXsdADHhwRwuKOWfH29nz5KVrNk8F6vXg8dsYVmbS3igQTcygxoxsEss\nz47tSeOGwQanFxERERFQAa9T3vtiDxn782ncMJjPXxrJvsPHeTdtF6mf29izI5yvQpsxNbY3mUGN\niGoQyGtjejKkW5xuNxERERGpRVTA64jyShfPp2wAYNJ1XQm0W0ls0Yinb+rB4zdezJr1PVi0LpvC\nXbn8rnMsj//uYhoEBxicWkRERER+TAW8jkh969/88YuF5MS24bpet5/2mM1q5vJL23L5pW0NSici\nIiIiP5cKeC1nyc7GPnMW9y1ZgtXrocRziCKv1+hYIiIiIvILqYDXUqayMkL/8If/bhmPiWXtetBl\nzvNgsRgdT0RERER+IW1/WEt5HQ5sO3YA8M8mybTrfi/mOX/Hk5BgcDIRERER+TV0Bby2MpkonDGD\nZ97fyl+3FXPVJQlclBBpdCoRERER+ZV0BdxglqwsHCtXVvvYltDGvJJRjM1i5tGR3Wo4mYiIiIhc\nCLoCbhBLVhb2l2YR9q+luB0O8tasJbRJ1GnnPPfO13i9cHP/9sRFhxqUVERERETOJxXwGmbJysI5\nezaBKSmYPR5cmFgQ2prJExZgaRJDYotGJLZoSEignU++zcHpsPHA8GSjY4uIiIjIeaICXsNsjz1O\n8Oef4cLEvJhO/KvX1eSERnE8J5/yY6V8f6yUjzft953/+yt/Q6PQQAMTi4iIiMj5pAJeQypdbv7+\n4Ra+qGjL7TGF/LV9f26+60r+1qs1JpMJt8fDvsNFZOw/xrbsfDL2HyPQbuWuwR2Nji4iIiIi55EK\n+AViKizE26ABAOt3HuaxN9ay80ABBDWmyZ2TmDf6EhqGOHznW8xmWjVpQKsmDbjqkpZGxRYRERGR\nC0wF/DyzZGefvMc7NZUlf13IyxuPkJ5xCID4mFCm33YZl3VoanBKERERETGKCvh5cqp4+3auNJn5\n4IV/kh7TCafDxh2Dk7jvqk447PpXLiIiIuLP1Ab/R8dLKyivdFPpclNR5abK5SEydQlJzz+D2XOy\neM+P6cSzLXpR0SKWpwYlMapPW0KC7EZHFxEREZFaQAX8J3g8XjbuyWPVxixWbswm89DxM85peeIY\nW73w9n+Kd2jH9kwa2pHBXeOwWrTXkYiIiIj8lwp4NcoqXazdepCVG7NZ/c1+jhaV+R5z2C2EBNqx\nWy3YbeaT/7RGMLTNc4S1aMxLV3SgW5toA9OLiIiISG2mAv4juw4UcN2zH3KsqNx3rHmkk9/FBXL3\nlpUETLwXOnYwMKGIiIiI1GUq4D8y9e11HCsqp3WTBlx9aUuuibHQKWUeQTMXY3K7KbO6KXjtNaNj\nioiIiEgdpQL+A+t3Hubfm3MIdthIvediWvztz75VTbwWCydGjqR4wgSjY4qIiIhIHaYC/h9er5dp\n76wH4O4hHQkPCyIwNRXAV7zd8fFGRhQRERGRekAF/D/+vTmHr3flEu4M4K7BHfEE2SmcNYuqpCQV\nbxERERE5b/y+gFuys/GWnmD6uxkA3Hd1J9+a3eXDhhkZTURERETqIb8t4D/cufL7Nklsj7qGxo2c\njLk80ehoIiIiIlKP+V0B//GW8V6LhfQyOwEeFw+N6Kyt4kVERETkgvKvtulyETF8OJbcXN+qJv/s\nOoTfL8+iZeMwru/VxuiEIiIiIlLP1et90nceyOfVZVs4XFB68oDVSsk993Bi5Ejy1qzh0PQXeCo9\nF4BHru+qbeNFRERE5IKrt1fAt2ce5roZqygsrWDGu18zsncbxg27iNi77vKd8/r7m8krLOM38REM\n7a6VTkRERETkwqt3l3wt2dmYf38f0VdeSVFJGXHRoVS5PSz4ZAeXPfgu977yCdv351NYWsHfPvgW\ngMk3dMNkMhmcXERERET8QZ24An748GEmTZrEd999R0JCAjNmzKB169ZnnBf20EO+N1dGYOKOyCoe\nnT6CnCPFvPLBtyxN38PS9EyWpmcSFx3K8ROVXJrYmF5JTQ14VSIiIiLij+rEFfAnnniCtm3bsn79\negYPHszEiROrPS/4nXdwe7zMjb6I60c+zaQZd+OwW2ndNJyX7/ktX7x0A7cOSMRhs5CVWwTA5Bu6\n6+q3iIiIiNSYWl/AS0pKSE9P584778RutzNmzBgOHjzIrl27zjh3aUJ32nUbz0uD72Da1JsJcthO\ne7xZZAhTx/Tkqz/fyMPXdWHG7ZfRuVVUTb0UMcD27duNjiC1jGZCqqO5kOpoLuRCqfUFPDs7G7vd\nTlBQEL/73e84cOAALVq0YO/evWece22LIZhbteStRwcTFhxw1ueMDAti4vDO3NSv/YWMLrWAvnnK\nj2kmpDqaC6mO5kIulFpfwMvKyggODqa0tJTMzEyKiooIDg6mrKzsjHNbRIbw9uQhNAoNNCCpiIiI\niMhPq/VvwgwMDKS0tJSYmBjWrVsHQGlpKUFBQWecu+L50SQ0blDTEaWWstls9OvXjwYNNBNykmZC\nqqO5kOpoLqQ6Npvtp0/6GWp9AY+NjaWiooLc3Fyio6OprKxk//79xMefvm53cXEx32du5ftMg4KK\niIiISL1XXFz8q5+j1hdwp9PJZZddxmuvvcYjjzzCvHnzaNq0KW3anL5tfGJiokEJRURERER+vlp/\nDzjAn/70J3bt2kX37t1ZsWIFs2bNMjqSiIiIiMgvYtq5c6fX6BAiIiIiIv6iTlwBFxERERGpL1TA\nRURERERqkAq4iIiIiEgNqvWroPyU48ePk5KSwsGDB4mMjGTEiBFER0cbHUtqkNvtZunSpWRmZlJV\nVUXjxo0ZNmwYUVFRuN1uUlNT2bZtGw6Hg8GDB5OUlGR0ZKlhWVlZvP7661x99dV07dpVc+Hnqqqq\nWLZsGdu2bcPr9XLRRRcxbNgwzYWfO3z4MO+//z65ubmEhIQwYMAAEhMTNRd+Zvv27aSlpXHo0CE6\nduzIiBEjAH5yDr788kvWrFmD2+2mW7duDBgw4Jy/T50v4KmpqcTExDB27Fi+/PJLFi1axIQJE4yO\nJTXI6/XSqFEjBgwYQGhoKOnp6SxcuJCJEyeSnp5OXl4ekyZN4tChQ8yfP5/mzZsTFhZmdGypIW63\nm1WrVhEZGYnJZALQXPi55cuXU1BQwP33309wcDBHjhwBNBf+bvHixSQlJXHXXXexZ88eFi5cyKRJ\nk9i4caPmwo84HA569epFZmYmlZWVvuPn+v6Qk5PDJ598wp133onD4WDOnDk0adLknP+jVqdvQSkv\nL2fPnj307t0bq9VKjx49KCwsJDc31+hoUoOsVit9+/YlNDQUgOTkZPLz8yktLWXr1q306NEDh8NB\nfHw8zZs3JyMjw+DEUpO++uor2rZtS3BwsO+Y5sJ/VVVVsXnzZq688kqcTicmk4moqChAc+Hvjh49\n6itMrVq1wmazUVBQoLnwM/Hx8SQmJhIYGHja8XPNwbZt2+jQoQNRUVGEhobSpUsXtmzZcs7fp04X\n8Pz8fKxWK3a7nTlz5lBQUEDDhg19VzPEP+Xk5BASEkJQUBBHjx4lIiKClJQUvvvuO6Kiojh69KjR\nEaWGFBcXs2nTJnr27Hnacc2F/zr155yRkcH06dOZPXu27z+imgv/1rp1a7Zu3YrH42H37t0EBAT4\nZkBz4X+83tNX6T7XHJx6LD09nY8++uhnzUidLuCVlZXY7XYqKio4cuQI5eXlBAQEnPYjA/Ev5eXl\nLF++nCFDhmAymaiqqsJut5Obm0tRUZHmw8+sWLGCPn36YLWefred5sJ/VVRU4Ha7KSgo4OGHH+bK\nK69k8eLFFBcXay783KBBg9i4cSNPP/00b7/9NldffTU2m01z4adO3bJ4yrnm4FQfLSgoID8//2fN\nSJ2+B9xut1NZWUlYWBhTpkwBTn5zDQgIMDiZGMHlcrFw4UI6duzo+zHiqW+e9957LwDLli3T5K8s\nSgAABUBJREFUfPiJ7OxsCgoK6NixI3DyasapKxqaC/9ls9nwer307NkTq9VKQkICERER5OTkaC78\nWFVVFW+++SZDhgyhffv27N+/n4ULFzJu3DjNhZ/68RXwc83BqT46dOhQ4ORP2Ox2+zmfv04X8IYN\nG+JyuSgqKiI0NBSXy0V+fj4RERFGR5Ma5vF4ePfdd4mIiKB///6+4xEREeTl5dGkSRMA8vLyaN++\nvVExpQYdPHiQnJwcnnjiCd+x7Oxs8vLyNBd+rGHDhmd9THPhv3Jzc6moqCAxMRGA2NhYwsPD2b9/\nv+bCT/34Cvi55iAiIuK025/z8vKIjIw85/PX6VtQHA4HrVq1Ii0tjaqqKtLT02nQoIGWIfRDqamp\nmEwmhg0bdtrxpKQkvvrqK8rLy9m7dy85OTm+b7BSv1166aU888wzvo+4uDiuueYahgwZornwY4GB\ngcTFxfHFF1/gdrvZt28fR48epXnz5poLPxYeHo7L5WL79u14vV4OHDjAkSNHiIqK0lz4GY/HQ1VV\nFR6PB6/Xi8vlwu12n3MOkpKSyMjIIC8vj6KiIjZu3Oj76evZmHbu3Ok95xm1nNYBl4KCAmbOnInN\nZjvt+JgxY2jWrJnWbxUAXn/9dTp16kSXLl20rq+fKygoYMmSJXz//feEhoYycOBA2rdvr7nwczt2\n7GD16tUUFhYSHBxM7969tW+AH/rmm29YunTpacf69u1Lnz59fnId8M8++wyPx/Oz1gGv8wVcRERE\nRKQuqdO3oIiIiIiI1DUq4CIiIiIiNUgFXERERESkBqmAi4iIiIjUIBVwEREREZEapAIuIiIiIlKD\nVMBFRERERGqQCriIiB9YsmQJr7/+utExREQEbcQjIlLnndoN9rbbbiM+Pr7acyoqKvB4PAQGBtZw\nOhER+TGr0QFEROTCCwgIMDqCiIj8h66Ai4jUUaeufFfn1NXw1NRUNmzYAEBcXBy33377aec98cQT\nJCcns23bNrp06UJxcTG7du2id+/e9OnTx3deWloaX3/9NSUlJURERNC/f3/atWt34V6ciEg9pivg\nIiJ1VFhYGI8++ijHjx/n1VdfZdSoUbRo0QLAd6vJoEGD6N+/P8uWLaOkpKTa54mKiqJNmzYsWrSI\nAQMG0LFjRxYvXuwr4KtWreLbb7/lqquuIioqiszMTN5++23uvvtumjR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+ "text": [ + "" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You may not have a full understanding of the exact *meaning* of a noise value of 100.0, but as it turns out if you multiply `randn()` with a number $n$, the result is just a normal distribution with $\\sigma = \\sqrt{n}$. So the example with noise = 100 is using the normal distribution $\\mathcal{N}(0,100)$. Recall the notation for a normal distribution is $\\mathcal{N}(\\mu,\\sigma^2)$. If the square root is confusing, recall that normal distributions use $\\sigma^2$ for the variance, and $\\sigma$ is the standard deviation, which we do not use in this book. `DogSensor.__init__()` takes the square root of the noise setting so that the `noise * randn()` call properly computes the normal distribution." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Math with Gaussians" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's say we believe that our dog is at 23m, and the variance is 5, or $pos_{dog}=\\mathcal{N}(23,5)$). We can represent that in a plot:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import stats\n", + "stats.plot_gaussian(23, 5)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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aqESkslNZFpEyc+RkJrOW7wTghcGdsFgshhOJlI7n7uiAq7MTC3/dy64DWqhE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\nDPPh0Zv6M7iXp0KyiIhIK9a/exdWPT6eIydzePPzA3y5/xQ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+ "text": [ + "" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This corresponds to a fairly inexact belief. While we believe that the dog is at 23, note that roughly 21 to 25 are quite likely as well. Let's assume for the moment our dog is standing still, and we query the sensor again. This time it returns 23.2 as the position. Can we use this additional information to improve our estimate of the dog's position?\n", + "\n", + "Intuition suggests 'yes'. Consider: if we read the sensor 100 times and each time it returned a value between 21 and 25, all centered around 23, we should be very confident that the dog is somewhere very near 23. Of course, a different physical interpretation is possible. Perhaps our dog was randomly wandering back and forth in a way that exactly emulated a normal distribution. But that seems extremely unlikely - I certainly have never seen a dog do that. So the only reasonable assumption is that the dog was mostly standing still at 23.0.\n", + "\n", + "Let's look at 100 sensor readings in a plot:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "dog = DogSensor(23, 0, 5)\n", + "xs = range(100)\n", + "ys = []\n", + "for i in xs:\n", + " ys.append(dog.sense())\n", + " \n", + "plt.plot(xs,ys, label='dog position')\n", + "plt.legend(loc='best')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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NPhRdXjk8VZL60y7k8kJvgdvFlSxEGUETIWhW8XzkOA4rh4TpsEZWCqYWrxnu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\nt3d3MU1ffxzH3yRtKYKdQOmmk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+ "text": [ + "" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Eyeballing this confirms our intuition - no dog moves like this. However, noisy sensor data certainly looks like this. So let's proceed and try to solve this mathematically. But how?\n", + "\n", + "\n", + "Recall the histogram code for adding a measurement to a preexisting belief:\n", + "\n", + " def update(pos, measure, p_hit, p_miss):\n", + " q = array(pos, dtype=float)\n", + " for i in range(len(hallway)):\n", + " if hallway[i] == measure:\n", + " q[i] = pos[i] * p_hit\n", + " else:\n", + " q[i] = pos[i] * p_miss\n", + " normalize(q)\n", + " return q\n", + " \n", + "Note that the algorithm is essentially computing:\n", + "\n", + " new_belief = old_belief * measurement * sensor_error\n", + " \n", + "The measurement term might not be obvious, but recall that measurement in this case was always 1 or 0, and so it was left out for convenience. \n", + " \n", + "If we are implementing this with gaussians, we might expect it to be implemented as:\n", + "\n", + " new_gaussian = measurement * old_gaussian\n", + " \n", + "where measurement is a Gaussian returned from the sensor. But does that make sense? Can we multiply gaussians? If we multiply a Gaussian with a Gaussian is the result another Gaussian, or something else?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is not particularly difficult to perform the algebra to derive the equation for multiplying two gaussians, but I will just present the result:\n", + "$$\n", + "N(\\mu_1, \\sigma_1^2)*N(\\mu_2, \\sigma_2^2) = N(\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1}{\\sigma_1^2 + \\sigma_2^2},\\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}) $$ \n", + "\n", + "In other words the result is a Gaussian with \n", + "\n", + "$$\\begin{aligned}\n", + "\\mu &=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}, \\\\\n", + "\\sigma &= \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\n", + "\\end{aligned}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Without doing a deep analysis we can immediately infer some things. First and most importantly the result of multiplying two Gaussians is another Gaussian. The expression for the mean is not particularly illuminating, except that it is a combination of the means and variances of the input. But the variance of the result is merely some combination of the variances of the variances of the input. We conclude from this that the variances are completely unaffected by the values of the mean!\n", + "\n", + "Let's immediately look at some plots of this. First, let's look at the result of multiplying $N(23,5)$ to itself. This corresponds to getting 23.0 as the sensor value twice in a row. But before you look at the result, what do you think the result will look like? What should the new mean be? Will the variance by wider, narrower, or the same?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "import numpy as np\n", + "\n", + "def multiply(mu1, var1, mu2, var2):\n", + " mean = (var1*mu2 + var2*mu1) / (var1+var2)\n", + " variance = 1 / (1/var1 + 1/var2)\n", + " return (mean, variance)\n", + "\n", + "xs = np.arange(16, 30, 0.1)\n", + "\n", + "m1,v1 = 23, 5\n", + "m, v = multiply(m1,v1,m1,v1)\n", + "\n", + "ys = [stats.gaussian(x,m1,v1) for x in xs]\n", + "plt.plot (xs, ys, label='original')\n", + "\n", + "ys = [stats.gaussian(x,m,v) for x in xs]\n", + "plt.plot (xs, ys, label='multiply')\n", + "\n", + "plt.legend(loc='best')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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CIKbrpXh7BJqcpnOKCBhCqF9/Sivz2Zv9udlxRERqVWcRffz4caZPn05sbCyT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+ "text": [ + "" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is either amazing or what you would expect, depending on your state of mind. I must admit I vacillate freely between the two! Note that the result of the multiplication is taller and narrow than the original Gaussian but the mean is the same. Does this match your intuition of what the result should have been?\n", + "\n", + "If we think of the Gaussians as two measurements, this makes sense. If I measure twice and get the same value, I should be more confident in my answer than if I just measured once. If I measure twice and get 23 meters each time, I should conclude that the length is close to 23 meters. So the mean should be 23. I am more confident with two measurements than with one, so the variance of the result should be smaller. \n", + "\n", + "\"Measure twice, cut once\" is a useful saying and practice due to this fact! The Gaussian is just a mathematical model of this physical fact, so we should expect the math to follow our physical process. \n", + "\n", + "Now let's multiply two gaussians (or equivalently, two measurements) that are partially separated. In other words, their means will be different, but their variances will be the same. What do you think the result will be? Think about it, and then look at the graph." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "xs = np.arange(16, 30, 0.1)\n", + "\n", + "m1, v1 = 23, 5\n", + "m2, v2 = 25, 5\n", + "m, s = multiply(m1,v1,m2,v2)\n", + "\n", + "ys = [stats.gaussian(x,m1,v1) for x in xs]\n", + "plt.plot (xs, ys, label='measure 1')\n", + "\n", + "ys = [stats.gaussian(x,m2,v2) for x in xs]\n", + "plt.plot (xs, ys, label='measure 2')\n", + "\n", + "ys = [stats.gaussian(x,m,v) for x in xs]\n", + "plt.plot(xs, ys,label='multiply')\n", + "plt.legend()\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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ahyVqiV6vp6ioiPT0dK1D+R1z87KUrDrbbYs7U1UVFxeX8i3Na4ok0UIIIQAw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\nqlu6+yTWJ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+ "text": [ + "" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Another beautiful result! If I handed you a measuring tape and asked you to measure the distance from table to a wall, and you got 23m, and then a friend make the same measurement and got 25m, your best guess must be 24m. \n", + "\n", + "That is fairly counter-intuitive, so let's consider it further. Perhaps a more reasonable assumption would be that either you or your coworker just made a mistake, and the true distance is either 23 or 25, but certainly not 24. Surely that is possible. However, suppose the two measurements you reported as 24.01 and 23.99. In that case you would agree that in this case the best guess for the correct value is 24? Which interpretation we choose depends on the properties of the sensors we are using. Humans make galling mistakes, physical sensors do not. \n", + "\n", + "This topic is fairly deep, and I will explore it once we have completed our Kalman filter. For now I will merely say that the Kalman filter requires the interpretation that measurements are accurate, with Gaussian noise, and that a large error caused by misreading a measuring tape is not Gaussian noise.\n", + "\n", + "For now I ask that you trust me. The math is correct, so we have no choice but to accept it and use it. We will see how the Kalman filter deals with movements vs error very soon. In the meantime, accept that 24 is the correct answer to this problem.\n", + "\n", + "One final test of your intuition. What if the two measurements are widely separated? " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "xs = np.arange(0, 60, 0.1)\n", + "\n", + "m1, v1 = 10, 5\n", + "m2, v2 = 50, 5\n", + "m, v = multiply(m1,v1,m2,v2)\n", + "\n", + "ys = [stats.gaussian(x,m1,v1) for x in xs]\n", + "plt.plot (xs, ys, label='measure 1')\n", + "\n", + "ys = [stats.gaussian(x,m2,v2) for x in xs]\n", + "plt.plot (xs, ys, label='measure 2')\n", + "\n", + "ys = [stats.gaussian(x,m,v) for x in xs]\n", + "plt.plot(xs, ys, label='multiply')\n", + "plt.legend()\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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/KYkWEQl1gVpU6KXFhSIiA6YkWkQkxJkVnTPG3hnkATI6xzFVFy0i0m9KokVE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+ "text": [ + "" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This result bothered me quite a bit when I first learned it. If my first measurement was 10, and the next one was 50, why would I choose 30 as a result? And why would I be *more* confident? Doesn't it make sense that either one of the measurements is wrong, or that I am measuring a moving object? Shouldn't the result be nearer 50? And, shouldn't the variance be larger, not smaller?\n", + "\n", + "Well, no. Recall the g-h filter chapter. In that chapter we agreed that if I weighed myself on two scales, and the first read 160lbs while the second read 170lbs, and both were equally accurate, the best estimate was 165lbs. Furthermore I should be a bit more confident about 165lbs vs 160lbs or 170lbs because I know have two readings, both near this estimate, increasing my confidence that neither is wildly wrong. \n", + "\n", + "Let's look at the math again to convince ourselves that the physical interpretation of the Gaussian equations makes sense.\n", + "\n", + "$$\n", + "\\mu=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\n", + "$$\n", + "\n", + "If both scales have the same accuracy, then $\\sigma_1^2 = \\sigma_2^2$, and the resulting equation is\n", + "\n", + "$$\\mu=\\frac{\\mu_1 + \\mu_2}{2}$$\n", + "\n", + "which is just the average of the two weighings. If we look at the extreme cases, assume the first scale is very much more accurate than than the second one. At the limit, we can set \n", + "$\\sigma_1^2=0$, yielding\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mu&=\\frac{0*\\mu_2 + \\sigma_2^2 \\mu_1} { \\sigma_2^2}, \\\\\n", + "\\text{or just}\\\\\n", + "\\mu&=\\mu_1\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "Finally, if we set $\\sigma_1^2 = 9\\sigma_2^2$, then the resulting equation is\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mu&=\\frac{9 \\sigma_2^2 \\mu_2 + \\sigma_2^2 \\mu_1} {9 \\sigma_2^2 + \\sigma_2^2} \\\\\n", + "\\text{or just}\\\\\n", + "\\mu&= \\frac{1}{10} \\mu_1 + \\frac{9}{10} \\mu_2\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "This again fits our physical intuition of favoring the second, accurate scale over the first, inaccurate scale." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Implementing the Update Step" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Recall the histogram filter uses a numpy array to encode our belief about the position of our dog at any time. That array stored our belief of our dog's position in the hallway using 10 discrete positions. This was very crude, because with a 100m hallway that corresponded to positions 10m apart. It would have been trivial to expand the number of positions to say 1,000, and that is what we would do if using it for a real problem. But the problem remains that the distribution is discrete and multimodal - it can express strong belief that the dog is in two positions at the same time.\n", + "\n", + "Therefore, we will use a single Gaussian to reflect our current belief of the dog's position. In other words, we will use $dog_{pos} = \\mathcal{N}(\\mu,\\sigma^2)$. Gaussians extend to infinity on both sides of the mean, so the single Gaussian will cover the entire hallway. They are unimodal, and seem to reflect the behavior of real-world sensors - most errors are small and clustered around the mean. Here is the entire implementation of the update function for a Kalman filter:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def update(mean, variance, measurement, measurement_variance):\n", + " return multiply(mean, variance, measurement, measurement_variance)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 13 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Kalman filters are supposed to be hard! But this is very short and straightforward. All we are doing is multiplying the Gaussian that reflects our belief of where the dog was with the new measurement. Perhaps this would be clearer if we used more specific names:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def update_dog(dog_pos, dog_variance, measurement, measurement_variance):\n", + " return multiply(dog_pos, dog_sigma, measurement, measurement_variance)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 14 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "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 don't use variable names with 'dog' in them. Still, the `update_dog()` function should make what we are doing very clear. \n", + "\n", + "Let's look at an example. We will suppose that our current belief for the dog's position is $N(2,5)$. Don't worry about where that number came from. It may appear that we have a chicken and egg problem, in that how do we know the position before we sense it, but we will resolve that shortly. We will create a `DogSensor` object initialized to be at position 0.0, and with no velocity, and modest noise. This corresponds to the dog standing still at the far left side of the hallway. Note that we mistakenly believe the dog is at position 2.0, not 0.0." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "dog = DogSensor(velocity=0, noise=1)\n", + "\n", + "pos,s = 2, 5\n", + "for i in range(20):\n", + " pos,s = update(pos, s, dog.sense(), 5)\n", + " print('time:', i, '\\tposition =', \"%.3f\" % pos, '\\tvariance =', \"%.3f\" % s)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "time: 0 \tposition = 0.655 \tvariance = 2.500\n", + "time: 1 \tposition = 0.170 \tvariance = 1.667\n", + "time: 2 \tposition = 0.110 \tvariance = 1.250\n", + "time: 3 \tposition = 0.047 \tvariance = 1.000\n", + "time: 4 \tposition = 0.053 \tvariance = 0.833\n", + "time: 5 \tposition = 0.174 \tvariance = 0.714\n", + "time: 6 \tposition = 0.159 \tvariance = 0.625\n", + "time: 7 \tposition = 0.167 \tvariance = 0.556\n", + "time: 8 \tposition = 0.039 \tvariance = 0.500\n", + "time: 9 \tposition = 0.070 \tvariance = 0.455\n", + "time: 10 \tposition = 0.074 \tvariance = 0.417\n", + "time: 11 \tposition = 0.036 \tvariance = 0.385\n", + "time: 12 \tposition = 0.133 \tvariance = 0.357\n", + "time: 13 \tposition = 0.344 \tvariance = 0.333\n", + "time: 14 \tposition = 0.252 \tvariance = 0.312\n", + "time: 15 \tposition = 0.273 \tvariance = 0.294\n", + "time: 16 \tposition = 0.210 \tvariance = 0.278\n", + "time: 17 \tposition = 0.210 \tvariance = 0.263\n", + "time: 18 \tposition = 0.168 \tvariance = 0.250\n", + "time: 19 \tposition = 0.206 \tvariance = 0.238\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because of the random numbers I do not know the exact values that you see, but the position should have converged very quickly to almost 0 despite the initial error of believing that the position was 2.0. Furthermore, the variance should have quickly converged from the initial value of 5.0 to 0.238.\n", + "\n", + "By now the fact that we converged to a position of 0.0 should not be terribly surprising. All we are doing is computing `new_pos = old_pos * measurement` and the measurement is a normal distribution around 0, so we should get very close to 0 after 20 iterations. But the truly amazing part of this code is how the variance became 0.238 despite every measurement having a variance of 5.0. \n", + "\n", + "If we think about the physical interpretation of this is should be clear that this is what should happen. If you sent 20 people into the hall with a tape measure to physically measure the position of the dog you would be very confident in the result after 20 measurements - more confident than after 1 or 2 measurements. So it makes sense that as we make more measurements the variance gets smaller.\n", + "\n", + "Mathematically it makes sense as well. Recall the computation for the variance after the multiplication: $\\sigma^2 = 1/(\\frac{1}{{\\sigma}_1^2} + \\frac{1}{{\\sigma}_2^2})$. We take the reciprocals of the sigma from the measurement and prior belief, add them, and take the reciprocal of the result. Think about that for a moment, and you will see that this will always result in smaller numbers as we proceed." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Implementing Predictions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That is a beautiful result, but it is not yet a filter. We assumed that the dog was sitting still, an extremely dubious assumption. Certainly it is a useless one - who would need to write a filter to track non-moving objects? The histogram used a loop of sense and update functions, and we must do the same to accommodate movement.\n", + "\n", + "How how do we perform the predict function with gaussians? Recall the histogram method:\n", + "\n", + " def predict(pos, move, p_correct, p_under, p_over):\n", + " n = len(pos)\n", + " result = array(pos, dtype=float)\n", + " for i in range(n):\n", + " result[i] = \\\n", + " pos[(i-move) % n] * p_correct + \\\n", + " pos[(i-move-1) % n] * p_over + \\\n", + " pos[(i-move+1) % n] * p_under \n", + " return result\n", + " \n", + " \n", + "In a nutshell, we shift the probability vector by the amount we believe the animal moved, and adjust the probability. How do we do that with gaussians?\n", + "\n", + "It turns out that we just add gaussians. Think of the case without gaussians. I think my dog is at 7.3m, and he moves 2.6m to right, where is he now? Obviously, $7.3+2.6=9.9$. He is at 9.9m. Abstractly, the algorithm is `new_pos = old_pos + dist_moved`. It does not matter if we use floating point numbers or gaussians for these values, the algorithm must be the same. \n", + "\n", + "How is addition for gaussians performed? It turns out to be very simple:\n", + "$$ N({\\mu}_1, {{\\sigma}_1}^2)+N({\\mu}_2, {{\\sigma}_2}^2) = N({\\mu}_1 + {\\mu}_2, {{\\sigma}_1}^2 + {{\\sigma}_2}^2)$$\n", + "\n", + "All we do is add the means and the variance separately! Does that make sense? Think of the physical representation of this abstract equation.\n", + "${\\mu}_1$ is the old position, and ${\\mu}_2$ is the distance moved. Surely it makes sense that our new position is ${\\mu}_1 + {\\mu}_2$. What about the variance? It is perhaps harder to form an intuition about this. However, recall that with the `update()` function for the histogram filter we always lost information - our confidence after the update was lower than our confidence before the update. Perhaps this makes sense - we don't really know where the dog is moving, so perhaps the confidence should get smaller (variance gets larger). I assure you that the equation for gaussian addition is correct, and derived by basic algebra. Therefore it is reasonable to expect that if we are using gaussians to model physical events, the results must correctly describe those events.\n", + "\n", + "I recognize the amount of hand waving in that argument. Now is a good time to either work through the algebra to convince yourself of the mathematical correctness of the algorithm, or to work through some examples and see that it behaves reasonably. This book will do the latter.\n", + "\n", + "So, here is our implementation of the predict function:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def predict(pos, variance, movement, movement_variance):\n", + " return (pos + movement, variance + movement_variance)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 16 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What is left? Just calling these functions. The histogram did nothing more than loop over the `sense()` and `update()` functions, so let's do the same. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# assume dog is always moving 1m to the right\n", + "movement = 1\n", + "movement_error = 2\n", + "sensor_error = 10\n", + "pos = (0, 500) # gaussian N(0,50)\n", + "\n", + "dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n", + "\n", + "zs = []\n", + "ps = []\n", + "\n", + "for i in range(10):\n", + " pos = predict(pos[0], pos[1], movement, movement_error)\n", + " print('PREDICT: {: 10.4f} {: 10.4f}'.format(pos[0], pos[1]),end='\\t')\n", + " \n", + " Z = dog.sense()\n", + " zs.append(Z)\n", + " \n", + " pos = update(pos[0], pos[1], Z, sensor_error)\n", + " ps.append(pos[0])\n", + " \n", + " print('UPDATE: {: 10.4f} {: 10.4f}'.format(pos[0], pos[1]))\n", + "\n", + " \n", + "plt.plot(ps, label='filter')\n", + "plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n", + "plt.legend(loc='best')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "PREDICT: 1.0000 502.0000\tUPDATE: -5.0106 9.8047\n", + "PREDICT: -4.0106 11.8047\tUPDATE: -1.9323 5.4138\n", + "PREDICT: -0.9323 7.4138\tUPDATE: 2.3085 4.2574\n", + "PREDICT: 3.3085 6.2574\tUPDATE: 4.5496 3.8490\n", + "PREDICT: 5.5496 5.8490\tUPDATE: 4.5375 3.6904\n", + "PREDICT: 5.5375 5.6904\tUPDATE: 6.3341 3.6267\n", + "PREDICT: 7.3341 5.6267\tUPDATE: 6.4186 3.6007\n", + "PREDICT: 7.4186 5.6007\tUPDATE: 8.5696 3.5900\n", + "PREDICT: 9.5696 5.5900\tUPDATE: 10.7097 3.5856\n", + "PREDICT: 11.7097 5.5856\tUPDATE: 9.8509 3.5838\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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PFX2dZzRq1IigoCCOHj3KyJEjq3WOc+l0Okw1ne5GCCGEqCqzGdcNG/CIjydv1qwLhyao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\ndSUYC3EeqxXd6NFQyTvDlVE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5x1Ax61ca9C9VD5TdwHHaUIjJbLV9PV3bNC4bMtEtlBaN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\nAAAA/0U5rs78oBgfyS/SiElrtGnXEQUGWPTYnzr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+ "text": [ + "" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There is a fair bit of arbitrary constants code above, but don't worry about it. What does require explanation are the first few lines:\n", + "\n", + " movement = 1 \n", + " movement_error = 2\n", + " \n", + "For the moment we are assuming that we have some other sensor that detects how the dog is moving. For example, there could be an inertial sensor clipped onto the dog's collar, and it reports how far the dog moved each time it is triggered. The details don't matter. The upshot is that we have a sensor, it has noise, and so we represent it with a Gaussian. Later we will learn what to do if we do not have a sensor for the `predict()` step.\n", + "\n", + "For now let's walk through the code and output bit by bit.\n", + "\n", + " movement = 1\n", + " movement_error = 2\n", + " sensor_error = 10\n", + " pos = (0, 500) # gaussian N(0,500)\n", + " \n", + " \n", + "The first lines just set up the initial conditions for our filter. We are assuming that the dog moves steadily to the right 1m at a time. We have a relatively low error of 2 for the movement sensor, and a higher error of 10 for the RFID position sensor. Finally, we set our belief of the dog's initial position as $N(0,500)$. Why those numbers. Well, 0 is as good as any number if we don't know where the dog is. But we set the variance to 500 to denote that we have no confidence in this value at all. 100m is almost as likely as 0 with this value for the variance. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we initialize the RFID simulator with\n", + "\n", + " dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n", + "\n", + "It may seem very 'convenient' to set the simulator to the same position as our guess, and it is. Do not fret. In the next example we will see the effect of a wildly inaccurate guess for the dog's initial position.\n", + "\n", + "The next code allocates an array to store the output of the measurements and filtered positions. \n", + "\n", + " zs = []\n", + " ps = []\n", + " \n", + "This is the first time that I am introducing standard nomenclature used by the Kalman filtering literature. It is traditional to call our measurement $Z$, and so I follow that convention here. As an aside, I find the nomenclature used by the literature very obscure. However, if you wish to read the literature you will have to become used to it, so I will not use a much more readable variable name such as $m$ or $measure$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we just enter our `update() ... predict()` loop.\n", + "\n", + " for i in range(10):\n", + " pos = predict(pos[0], pos[1], movement, sensor_error)\n", + " print 'PREDICT:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n", + "\n", + "Wait, why `predict()` before `update()`? It turns out the order does not matter once, but the first call to `,DogSensor.sense()` assumes that the dog has already moved, so we start with the update step. In practice you will order these calls based on the details of your sensor, and you will very typically do the `sense()` first.\n", + "\n", + "So we call the update function with the gaussian representing our current belief about our position, the another gaussian representing our belief as to where the dog is moving, and then print the output. Your output will differ, but when writing this I get this as output:\n", + "\n", + " PREDICT: 1.000 502.000\n", + "\n", + "What is this saying? After the prediction, we believe that we are at 1.0, and the variance is now 502.0. Recall we started at 500.0. The variance got worse, which is always what happens during the prediction step.\n", + "\n", + " Z = dog.sense()\n", + " zs.append(Z)\n", + " \n", + "Here we sense the dog's position, and store it in our array so we can plot the results later.\n", + "\n", + "Finally we call the update function of our filter, save the result in our *ps* array, and print the updated position belief:\n", + "\n", + " pos = update(pos[0], pos[1], Z, movement_error)\n", + " ps.append(pos[0])\n", + " print 'UPDATE:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n", + " \n", + "Your result will be different, but I get\n", + "\n", + " UPDATE: 1.6279 , 9.8047\n", + " \n", + "as the result. What is happening? Well, at this point the dog is really at 1.0, however the predicted position is 1.6279. What is happening is the RFID sensor has a fair amount of noise, and so we compute the position as 1.6279. That is pretty far off from 1, but this is just are first time through the loop. Intuition tells us that the results will get better as we make more measurements, so let's hope that this is true for our filter as well. Now look at the variance: 9.8047. It has dropped tremendously from 502.0. Why? Well, the RFID has a reasonably small variance of 2.0, so we trust it far more than our previous belief. At this point there is no way to know for sure that the RFID is outputting reliable data, so the variance is not 2.0, but is has gotten much better.\n", + "\n", + "Now the software just loops, calling `predict()` and `update()` in turn. Because of the random sampling I do not know exactly what numbers you are seeing, but the final position is probably between 9 and 11, and the final variance is probably around 3.5. After several runs I did see the final position nearer 7, which would have been the result of several measurements with relatively large errors.\n", + "\n", + "Now look at the plot. The noisy measurements are plotted in with a dotted red line, and the filter results are in the solid blue line. Both are quite noisy, but notice how much noisier the measurements (red line) are. This is your first Kalman filter shown to work!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "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. This time we will plot both the output of the filter and the variance." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "%precision 2\n", + "# assume dog is always moving 1m to the right\n", + "movement = 1\n", + "movement_error = 2\n", + "sensor_error = 4.5\n", + "pos = (0, 100) # gaussian N(0,50)\n", + "\n", + "dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n", + "\n", + "zs = []\n", + "ps = []\n", + "vs = []\n", + "\n", + "for i in range(50):\n", + " pos = predict(pos[0], pos[1], movement, movement_error) \n", + " Z = dog.sense()\n", + " zs.append(Z)\n", + " vs.append(pos[1])\n", + " \n", + " pos = update(pos[0], pos[1], Z, sensor_error)\n", + " ps.append(pos[0])\n", + " \n", + "#plt.subplot(121) \n", + "p1, = plt.plot(zs,c='r', linestyle='dashed')\n", + "p2, = plt.plot(ps,)\n", + "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n", + "plt.show()\n", + "\n", + "plt.plot(vs)\n", + "plt.title('Variance')\n", + "plt.show()\n", + "print ([float(\"%0.4f\" % v) for v in vs])" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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HtFoty5cvp6Kiolaovvrqq2nTpg2TJk1iy5YtZGZmsmrVKqZMmYLL5Wq8CxZC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\nKScdlHNzc5k5cyY5OTlHLHvvvfeYOnUqvXv3JjMzk8suu4x33323VYV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CcklJyelB7XYVFxeruLi4y+O5E9ofBiQkAwAAINqMPJZaOn00dX0TIRkAAADR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\n8fHRngoMEL6SHBcXp9bWVj3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+ "text": [ + "" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[102.0, 6.3099, 4.6267, 4.2812, 4.1939, 4.1708, 4.1646, 4.1629, 4.1624, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623]\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we can see that the variance converges very quickly to roughly 4.1623 in 10 steps. We interpret this as meaning that we become very confident in our position estimate very quickly. The first few measurements are unsure due to our uncertainty in our guess at the initial position, but the filter is able to quickly determine an accurate estimate." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "> Before I go on, I want to emphasize that this code fully implements a 1D Kalman filter. If you have tried to read the literature, you are perhaps surprised, because this looks nothing like the complex, endless pages of math in those books. To be fair, the math gets a bit more complicated in multiple dimensions, but not by much. So long as we worry about *using* the equations rather than *deriving* them we can create Kalman filters without a lot of effort. Moreover, I hope you'll agree that you have a decent intuitive grasp of what is happening. We represent our beliefs with Gaussians, and our beliefs get better over time because more measurement means more data to work with. \"Measure twice, cut once!\"" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Relationship to the g-h Filter" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the first chapter I stated that the Kalman filter is a form of g-h filter. However, we have been reasoning about the probability of Gaussians, and not used any of the reasoning or equations of the first chapter. A trivial amount of algebra will reveal the relationship, so let's do that now. It's not particularly illuminating algebra, so feel free to skip to the bottom to see the final equation that relates *g* to the variances.\n", + "\n", + "The equation for our estimate is:\n", + "\n", + "$$\n", + "\\mu_{x'}=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\n", + "$$\n", + "\n", + "which I will make more friendly for our eyes as:\n", + "\n", + "$$\n", + "\\mu_{x'}=\\frac{ya + xb} {a+b}\n", + "$$\n", + "\n", + "We can easily put this into the g-h form with the following algebra\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mu_{x'}&=(x-x) + \\frac{ya + xb} {a+b} \\\\\n", + "\\mu_{x'}&=x-\\frac{a+b}{a+b}x + \\frac{ya + xb} {a+b} \\\\ \n", + "\\mu_{x'}&=x +\\frac{-x(a+b) + xb+ya}{a+b} \\\\\n", + "\\mu_{x'}&=x+ \\frac{-xa+ya}{a+b} \\\\\n", + "\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x)\\\\\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "We are almost done, but recall that the variance of estimate is given by \n", + "\n", + "$${\\sigma_{x'}^2} = \\frac{1}{ \\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\\\\\n", + "= \\frac{1}{ \\frac{1}{a} + \\frac{1}{b}}\n", + "$$\n", + "\n", + "We can incorporate that term into our equation above by observing that\n", + "$$ \n", + "\\begin{aligned}\n", + "\\frac{a}{a+b} &= \\frac{a/a}{(a+b)/a} = \\frac{1}{(a+b)/a}\\\\\n", + " &= \\frac{1}{1 + \\frac{b}{a}} = \\frac{1}{\\frac{b}{b} + \\frac{b}{a}}\\\\\n", + " &= \\frac{1}{b}\\frac{1}{\\frac{1}{b} + \\frac{1}{a}} \\\\\n", + " &= \\frac{\\sigma^2_{x'}}{b}\n", + " \\end{aligned}\n", + "$$\n", + "\n", + "We can tie all of this together with\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x)\\\\\n", + "&= x + \\frac{\\sigma^2_{x'}}{b}(y-x) \\\\\n", + "&= x + g_n(y-x)\\\\\n", + "\\blacksquare\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "where\n", + "\n", + "$$g_n = \\frac{\\sigma^2_{x'}}{\\sigma^2_{y}}$$\n", + "\n", + "The end result is multipying the residual of the two measurements by a constant and adding to our previous value, which is the *g* equation for the g-h filter. *g* is the variance of the new estimate divided by the variance of the measurement. Of course in this case g is not truly a constant, as it varies with each time step as the variance changes, but it is truly the same formula. We can also derive the formula for *h* in the same way but I don't find this a particularly interesting derivation. The end result is\n", + "\n", + "$$h_n = \\frac{COV (x,\\dot{x})}{\\sigma^2_{y}}$$\n", + "\n", + "The takeaway point is that *g* and *h* are specified fully by the variance and covariances of the measurement and preditions at time *n*. In other words, we are just picking a point between the measurement and prediction by a scale factor determined by the quality of each of those two inputs. That is all the Kalman filter is. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#####Exercise:\n", + "Modify the values of `movement_error` and `sensor_error` and note the effect on the filter and on the variance. Which has a larger effect on the value that variance converges to. For example, which results in a smaller variance:\n", + "\n", + " movement_error = 40\n", + " sensor_error = 2\n", + " \n", + "or:\n", + "\n", + " movement_error = 2\n", + " sensor_error = 40 " + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Introduction to Designing a Filter" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So far we have developed our filter based on the dog sensors introduced in the Discrete Bayesian filter chapter. We are used to this problem by now, and may feel ill-equipped to implement a Kalman filter for a different problem. To be honest, there is still quite a bit of information missing from this presentation. The next chapter will fill in the gaps. Still, lets get a feel for it by designing and implementing a Kalman filter for a thermometer. The sensor for the thermometer outputs a voltage that corresponds to the temperature that is being measured. We have read the manufacturer's specifications for the sensor, and it tells us that the sensor exhibits white noise with a standard deviation of 2.13.\n", + "\n", + "We do not have a real sensor to read, so we will simulate the sensor with the following function. We have hard-coded the voltage to 16.3 - obviously the voltage will differ based on the temperature, but that is not important to our filter design." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "temp_variance = 2.13**2\n", + "def volt():\n", + " return random.randn()*temp_variance + 16.3" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 19 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We generate white noise with a given variance using the equation `random.randn() * variance`. The specification gives us the standard deviation of the noise, not the variance, but recall that variance is just the square of the standard deviation. Hence we raise 2.13 to the second power.\n", + "\n", + "> **Sidebar**: spec sheets are just what they sound like - specifications. Any individual sensor will exhibit different performance based on normal manufacturing variations. Numbers given are often maximums - the spec is a guarantee that the performance will be at least that good. So, our sensor might have standard deviation of 1.8. If you buy an expensive piece of equipment it often comes with a sheet of paper displaying the test results of your specific item; this is usually very trustworthy. On the other hand, if this is a cheap sensor it is likely it received little to no testing prior to being sold. Manufacturers typically test a small subset of their output to verify that everything falls within the desired performance range. If you have a critical application you will need to read the specification sheet carefully to figure out exactly what they mean by their ranges. Do they guarantee their number is a maximum, or is it, say, the $3\\sigma$ error rate? Is every item tested? Is the variance normal, or some other distribution. Finally, manufacturing is not perfect. Your part might be defective and not match the performance on the sheet.\n", + "\n", + "> For example, I just randomly looked up a data sheet for an airflow sensor. There is a field *Repeatability*, with the value $\\pm 0.50\\%$. Is this a Gaussian? Is there a bias? For example, perhaps the repeatability is nearly 0.0% at low temperatures, and always nearly +0.50 at high temperatures. Data sheets for electrical components often contain a section of \"Typical Performance Characteristics\". These are used to capture information that cannot be easily conveyed in a table. For example, I am looking at a chart showing output voltage vs current for a LM555 timer. There are three curves showing the performance at different temperatures. The response is ideally linear, but all three lines are curved. This clarifies that errors in voltage outputs are probably not Gaussian - in this chip's case higher temperatures leads to lower voltage output, and the voltage output is quite nonlinear if the input current is very high. \n", + "\n", + "> As you might guess, modeling the performance of your sensors is one of the harder parts of creating good Kalman filter. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we need to write the Kalman filter processing loop. As with our previous problem, we need to perform a cycle of sensing and updating. The sensing step probably seems clear - call `volt()` to get the measurement, pass the result into `update()` function, but what about the update step? We do not have a sensor to detect 'movement' in the voltage, and for any small duration we expect the voltage to remain constant. How shall we handle this?\n", + "\n", + "As always, we will trust in the math. We have no movement, and no error associated with them, so we will just set both to zero. Let's see what happens. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_error = temp_variance\n", + "movement_error = 0\n", + "movement = 0\n", + "voltage = (25,1000) #who knows what the first value is?\n", + "\n", + "zs = []\n", + "ps = []\n", + "vs = []\n", + "N=50\n", + "\n", + "for i in range(N):\n", + " Z = volt()\n", + " zs.append(Z)\n", + " \n", + " voltage = update(voltage[0], voltage[1], Z, sensor_error)\n", + " ps.append(voltage[0])\n", + " vs.append(voltage[1])\n", + "\n", + " voltage = predict(voltage[0], voltage[1], movement, movement_error)\n", + "\n", + "plt.scatter(range(N), zs, marker='+', s=64, color='r', label='measurements')\n", + "p1, = plt.plot(ps, label='filter')\n", + "plt.legend(loc='best')\n", + "plt.xlim((0,N));plt.ylim((0,30))\n", + "plt.show()\n", + "plt.plot(vs)\n", + "plt.title('Variance')\n", + "plt.show()\n", + "print('Variance converges to',vs[-1])\n", + "print('Last voltage is',voltage[0])" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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63esGg0Evvvii8vLydOutt2rSpEm66667JElJSUmSpDlz5ig6OloXXXSRrrnmGo0ZM0a5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\nBQgnhGEAQFAJh9VnCJpA8GDMMICwxBn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LkwEAAMBMcQy8GZJYqQEAAADmilvgLWBKAwAAAJJA3ANvNVMaAAAAYKK4BV53xxzeWkZ4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\nnfY7OvalHbbfabfJYbcozW6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+ "text": [ + "" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Variance converges to 0.09072976736236911\n", + "Last voltage is 15.592455113316198\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The first plot shows the individual sensor measurements marked with '+'s vs the filter output. Despite a lot of noise in the sensor we quickly discover the approximate voltage of the sensor. In the run I just completed at the time of authorship, the last voltage output from the filter is $16.213$, which is quite close to the $16.4$ used by the `volt()` function. On other runs I have gotten up to around $16.9$ as an output and also as low as 15.5 or so.\n", + "\n", + "The second plot shows how the variance converges over time. Compare this plot to the variance plot for the dog sensor. While this does converge to a very small value, it is much slower than the dog problem. The next section **Explaining the Results - Multi-Sensor Fusion** explains why this happens.\n", + "\n", + "##### Exercise(optional):\n", + "Write a function that runs the Kalman filter many times and record what value the voltage converges to each time. Plot this as a histogram. After 10,000 runs do the results look normally distributed? Does this match your intuition of what should happen?\n", + "\n", + "> use plt.hist(data,bins=100) to plot the histogram. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Your code here" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 21 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "######Solution\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_error = temp_variance\n", + "\n", + "def VKF():\n", + " voltage=(14,1000)\n", + " for i in range(N):\n", + " Z = volt()\n", + " voltage = update(voltage[0], voltage[1], Z, sensor_error)\n", + " return voltage[0]\n", + "\n", + "vs = []\n", + "for i in range (10000):\n", + " vs.append (VKF())\n", + "plt.hist(vs, bins=100, color='#e24a33') \n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "######Discussion\n", + "The results do in fact look like a normal distribution. Each voltage is Gaussian, and the **Central Limit Theorem** guarantees that a large number of Gaussians is normally distributed. We will discuss this more in a subsequent math chapter." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Explaining the Results - Multi-Sensor Fusion" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So how does the Kalman filter do so well? I have glossed over one aspect of the filter as it becomes confusing to address too many points at the same time. We will return to the dog tracking problem. We used two sensors to track the dog - the RFID sensor that detects position, and the inertial tracker that tracked movement. However, we have focused all of our attention on the position sensor. Let's change focus and see how the filter performs if the inertial tracker is also noisy. This will provide us with an vital insight into the performance of Kalman filters." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_error = 30\n", + "movement_sensor = 30\n", + "pos = (0,500)\n", + "\n", + "dog = DogSensor(0, velocity=movement, noise=sensor_error)\n", + "\n", + "zs = []\n", + "ps = []\n", + "vs = []\n", + "\n", + "for i in range(100):\n", + " Z = dog.sense()\n", + " zs.append(Z)\n", + " \n", + " pos = update(pos[0], pos[1], Z, sensor_error)\n", + " ps.append(pos[0])\n", + " vs.append(pos[1])\n", + "\n", + " pos = predict(pos[0], pos[1], movement+ random.randn(), movement_error)\n", + "\n", + "plt.plot(ps, label='filter')\n", + "plt.plot(zs, linestyle='dashed', c='r', label='measurement')\n", + "plt.legend()\n", + "plt.show()\n", + "plt.plot(vs)\n", + "plt.title('Variance')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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WmZEBuNenC99IxVmEjKN3bw7u2KF1GG2eKyUFOFKxESJcbGedRcGXXzZ6lcll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\nvQtiFStl9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IiYiROhOX0aWb//7pcVVl9RVOAMQKyh7GDZTQp0AeDr30/god7N0aJ+jLjD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\n8nxCArK2b4du82ZEfPCBfamOKJOldWvo7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JkQl4BGMAAAB0JcsH40sYZwwAAIAosHwwHtYvRelJbh07Uad9R06YXQ4AAADO\nUZYPxqH1jENPwWM4BQAAALqK5YOxJE0a1U8S6xkDAACg63STYNzUY8w4YwAAAHSFbhGMR/TvpdTE\nWBVX1Gr/UcYZAwAAoPN1i2DcfD3j9TuOmlwNAAAAzkXdIhhLzR8PfdjkSgAAAHAu6obB+CjjjAEA\nANDpuk0wHtG/l9KT3DpaXqNNe0vMLgcAAADnmG4TjG02Q9+ZMlyS9OcPdphcDQAAAM413SYYS9L3\nZ4ySJP1t/X6VVdWbXA0AAADOJd0qGGdlJmnauAFq8Pr1+urdZpcDAACAc0i3CsaSdMtloyVJiz7Y\noUCASXgAAADoHN0uGM/IHah+afE6WFypf35ZZHY5AAAAOEd0u2Bst9l087SRkqQ/f7Dd5GoAAABw\nruh2wViSvjdtpBx2Q+99VqDDpdVmlwMAAIBzQLcMxhkpcbpyQpYCwaBeWbnL7HIAAABwDuiWwViS\nbm2chPfKyp3y+gImVwMAAIDurtsG40mj+mp4vxQVV9TqH58dNLscAAAAdHPdNhgbhqE5jQ/84El4\nAAAA6KhuG4wl6dtThssd49DH2w5r7+EKs8sBAABAN9atg3FyfIyunzRUUuiBHwAAAEB7detgLDVN\nwlu8erfqGnwmVwMAAIDuqtsH47HZ6cod2lsnaj16e/0+s8sBAABAN9Xtg7EkzZkR6jV+7p2t8vj8\nJlcDAACA7uicCMbXXzJU2X2StPdwhZ7/+xdmlwMAAIBu6JwIxjFOuxbePlmS9NTSTSo8VmVyRQAA\nAOhuzolgLEl5Of113aShqvf49fM/rzW7HAAAAHQz50wwlqRf3HyxEt1O5W8q0D8+PWh2OQAAAOhG\nzqlgnNkrTvd/Z4Ik6ed/Xqfaeq/JFQEAAKC76HAwnjNnjsaNG6fc3Fzl5ubq3//93zujrna7deZo\njc1KV1FptZ5ausnUWgAAANB9dEqP8YMPPqjNmzdr8+bNevzxxzvjku1mt9n02A8myzCk55d/oZ2F\nZabWAwAAgO6hU4JxMBjsjMt0mvOH9tacGaPk8wc1/09rFAhYqz4AAABYT6cE4yeffFIXX3yxfvCD\nH2jfPms8fe6BGy9UepJbG3cVa/E/d5tdDgAAACzO2LVrV4e6U7/88kuNGDFCfr9fzz33nN577z29\n++67cjgckqTCwkJNnjy5U4r9ul754Ev94L/eUVqSW1v/8G9KS3KbUgdacjqdkiSvl8mRaEK7QGto\nF2gN7QKfGZT9AAAYDklEQVStcTqdWrlypQYOHNjua3Q4GDcXDAY1fvx4vfbaaxoxYoSkUDBeuXJl\n5Ji8vDxNnTq1s255xnqufOBVrfq8QDPHZ2vpr74jh/2cWoijW+IfNLSGdoHW0C7QGtoFwlatWqXV\nq1dLkux2u/Ly8qwVjCdMmKBXXnlF5513nqRQMB41alRn3eJrKyip1DW/WKbSynrNmTFKj95+qQzD\nMK0eSGlpaZKk0tJSkyuBldAu0BraBVpDu0Br0tLStGbNmg4F4w51n1ZVVWnVqlXyeDzyeDz6zW9+\no/T0dA0bNqwjl+1UgzKS9Md7LleM065FH+zQ88u/MLskAAAAWFCHgrHX69XTTz+tiy66SJMnT9aW\nLVv029/+Vna7vbPq6xQThmfqqbmh4RsPv7JBK3gqHgAAAE7i6MjJqampWrp0aWfV0qWumzRUB4sr\n9evFn+qu51bqzZ9fo3HZvc0uCwAAABbRo2ai3X3d+frOlOGqa/DptifeU1FptdklAQAAwCJ6VDA2\nDEO//uEUTRrVV8UVtbr1iX+ous5jdlkAAACwgB4VjCXJ5bDr9z+9TEP6JmtHQZl+/MwHavD6zS4L\nAAAAJutxwViSeiXEatF9Vyo1MVYrt36lmx9froqaBrPLAgAAgIl6ZDCWpKzMJL36wFXKTInTuh1H\n9C+/fFtfHasyuywAAACYpMcGY0nKyUrT3355nc4b0Eu7iyp07UPL9OXB42aXBQAAABP06GAsSf3T\nE7T0wWs1aVRflVTUafbD72jl54VmlwUAAIAo6/HBWJKS42P08r/P0r9cMlQ19V7d+sQ/9OpHO80u\nCwAAAFFEMG4U47Trmf8zTXdd+w35A0Hd+/t/6j9f3SCPjxUrAAAAegKCcTM2m6H5352oR2+/VDbD\n0HPvbNW1v1imnYVlZpcGAACALkYwbsUtl43WG/9xtQb1TtSXB0s16z+W6rfvfC5/IGB2aQAAAOgi\nBOPTuGhkX+U/Ols3Txspjy+gR17dqG8/8o4OFleaXRoAAAC6AMG4DQlul379wyn6831XKDMlTht3\nFWvm/CX68/vbFQwGzS4PAAAAnYhgfBZmnD9I7z92g7518RDVNvg0/08f67pfvq1PdhebXRoAAAA6\nCcH4LKUmxuq3/3eGnrtrutKSYvXZnhJd/8u39aOn87XvSIXZ5QEAAKCDCMZf03WThmrtkzfpp/+S\nK3eMQ3//5KCm3f+GFvzpYx0/UWd2eQAAAGgngnE7JLhduu/bE7Tmv2/U9755noJB6aX3t+vSe/6q\np5Zu0omaBrNLBAAAwNdEMO6APr3i9V8/ytP7j83WZbmDVF3v1RNvfKYJ//cVPbhonQpKWMECAACg\nuyAYd4LzBqTqpXuv0OL/d7XycvqrtsGnF1Z8qUvveV1zn3lfm/aWmF0iAAAAzsBhdgHnkktG99Ml\no/tp26FSPb/8Cy1bu0/vbDigdzYc0IUjMnXHlTm6/ILBinHazS4VAAAAJyEYd4Exg9P0Pz/+ph64\n8UK9+N42Lfpghz7ZXaxPdhcrJT5G118yVN+ZMkLfGJIuwzDMLhcAAAAiGHepvqnxmv/dibr7+ly9\nvnq3Xlu1S18eLNWL+dv1Yv52jeifohvzRmj2pcOV2SvO7HIBAAB6NIJxFMTHOnX75WN0++VjtO1Q\nqRb/c7fe/HivdhdV6JFXN2rha59o0ui+mjUhS1eMH6x+aQlmlwwAANDjEIyjbMzgNI0ZPEn/77sX\naeXnhXp99W7lbz6kj7cd1sfbDus/Xlqr84f01pUTsjTrwiwN65didskAAAA9AsHYJE6HTZePH6zL\nxw9WRU2D3t9UoBWfHtTKrYXasv+Ytuw/psde/0TD+qXom+MGaOrYAbp4ZB/FxTrNLh0AAOCcRDC2\ngJT4GH17ynB9e8pw1TX49NHWQi3/9KDe31SgvYcrtPdwhf6w4ku5HDZdeF4f5eX019SxAzRmcJps\nNibvAQAAdAaCscW4YxyadWG2Zl2YLa8voE92H9XqL4v0zy+K9PmBY5EhF4/+9ROlJMTowhGZuui8\nPrrwvD4al50ul4Ol4AAAANqDYGxhToctsjbyAzdeqLKqeq3ZVqTVX4R+ikqrlb+pQPmbCiRJsU67\ncodlaOJ5fXTBsAydP6S30pPdJv8WAAAA3QPBuBtJTYzVty4eqm9dPFTBYFBfHa/Whp1HtXH3UW3c\neVR7Dldo3Y4jWrfjSOScfmnxOn9Ib32j2U9SnMvE3wIAAMCaCMbdlGEYGtg7UQN7J+rbU4ZLksqq\n6vXJrqPauLtYn+8/pq0HjutwaY0Ol9bo758cjJw7qHeiRg1K1ehBaRo9OPQ6qHci45UBAECPRjA+\nh6QmxuqKCVm6YkKWJMkfCGjf4RPasv+YPt9/TJ/vP67tBaUqOFalgmNV+sdnhyLnxsc6dd6AXhre\nP0Uj+vfSsH4pGtE/RQPSCcwAAKBnIBifw+w2m0YM6KURA3rpxrwRkiSfP6D9R05oe0GptheUaUdB\nmbYXlOpoea027S3Rpr0lLa4R67JrWL8UDe2bouw+ScrOTFZ2nyQN6ZusXgmxZvxaAAAAXYJg3MM4\n7E1h+fpLmraXVtZp11fl2nO4QnuKyrWnqEJ7iipUXFGrLw+W6suDpadcKyUhRtmZyRqckaiBGYka\nnJGoQb2TNCgjUX1T4+Ww26L4mwEAAHQMwRiSpLQkty4Z7dYlo/u12H6ipkF7Dldo/5ETOnD0hPYf\nPaEDRyt14OgJVVQ3aHN1iTbvKznleg67oX6pCeqfHvoZkJ6g/mmhn5xh0oDeSdH61QAAAM4KwRht\nSo6P0YThmZowPLPF9mAwqJKKOu0/ekIFJVUqPFalgmOVkfdHy2sjY5lPe+04l/qmxqtPanzotVfo\nNSPFrcxeccpIiVN6kpueZwAAEBUEY7SLYRjK7BWnzF5xmjSq7yn76zw+FR2v1uHSahWVVqvoeI2K\nSqv11fEqHSmv0+HjVTpR69GJWo92flV+2vvYDEPpybHKSAkF5d7JbvVOcis92a3eyc1ek9xKSYiR\n3UaIBgAA7UMwRpdwuxwa1i9Fw/qlnLIvLS1NwWBQew8d1uHSGh0tr9GRsqbXkvJaFVeEfkor61VS\nUaeSijpJp45zbs5mGOqVGKO0xFilJbmVmhirtKRYpSW6lZoYo14JsUpNbPrplRAjd4xDhsGqGwAA\ngGAMkxiGEQmoOVlppz3O6wvo2InaxnBcq2Mn6nTsRK2OV9aF3lfU6VhlnUpP1OlErUellfUqrayX\niirOqo4Yp10p8TFKSYhpek2IUXJcjJLjXUqJj1Fy409S5LNLiW6XYl38zwcAgHMJ/88OS3M6bOqX\nlqB+aQlnPNbrC6isql6lVXWNATn0Wl7doLKqepVX1ze+Nn6uqle91x/pnf66Ypx2JcW5WvwkuEOv\niW6XEt1OJTbbnuh2KsHtUkKsUwlupxLdLsXHOlknGgAAiyAY45zhdNgi457PVp3Hp4rqhtBPTYMq\nqusbXxtUUePRiZqGZj8eVdQ0qKrOo8oajxq8/sYe7LoO1R0f61R8rEPxsU4lxLqU4HY2vg+9xkX2\nORUX61R8TOO2GKfiYhyKi21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+ "text": [ + "" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This result is worse than the example where only the measurement sensor was noisy. Instead of being mostly straight, this time the filter's output is distinctly jagged. But, it still mostly tracks the dog. What is happening here?\n", + "\n", + "This illustrates the effects of *multi-sensor fusion*. Suppose we get a position reading of -28.78 followed by 31.43. From that information alone it is impossible to tell if the dog is standing still during very noisy measurements, or perhaps sprinting from -29 to 31 and being accurately measured. But we have a second source of information, his velocity. Even when the velocity is also noisy, it constrains what our beliefs might be. For example, suppose that with the 31.43 position reading we get a velocity reading of 59. That matches the difference between the two positions quite well, so this will lead us to believe the RFID sensor and the velocity sensor. Now suppose we got a velocity reading of 1.7. This doesn't match our RFID reading very well - it suggests that the dog is standing still or moving slowly.\n", + "\n", + "When sensors measure different aspects of the system and they all agree we have strong evidence that the sensors are accurate. And when they do not agree it is a strong indication that one or more of them are inaccurate. \n", + "\n", + "We will formalize this mathematically in the next chapter; for now trust this intuitive explanation. We use this sort of reasoning every day in our lives. If one person tells us something that seems far fetched we are inclined to doubt them. But if several people independently relay the same information we attach higher credence to the data. If one person disagrees with several other people, we tend to distrust the outlier. If we know the people that might alter our belief. If a friend is inclined to practical jokes and tall tales we may put very little trust in what they say. If one lawyer and three lay people opine on some fact of law, and the lawyer disagrees with the three you'll probably lend more credence to what the lawyer says because of her expertise. In the next chapter we will learn how to mathematical model this sort of reasoning." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "More examples" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example: Extreme Amounts of Noise" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So I didn't put a lot of noise in the signal, and I also 'correctly guessed' that the dog was at position 0. How does the filter perform in real world conditions? Let's explore and find out. I will start by injecting a lot of noise in the RFID sensor. I will inject an extreme amount of noise - noise that apparently swamps the actual measurement. What does your intuition tell about how the filter will perform if the noise is allowed to be anywhere from -300 or 300. In other words, an actual position of 1.0 might be reported as 287.9, or -189.6, or any other number in that range. Think about it before you scroll down." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_error = 30000\n", + "movement_error = 2\n", + "pos = (0,500)\n", + "\n", + "dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n", + "\n", + "zs = []\n", + "ps = []\n", + "\n", + "for i in range(1000):\n", + " pos = predict(pos[0], pos[1], movement, movement_error)\n", + " \n", + " Z = dog.sense()\n", + " zs.append(Z)\n", + " \n", + " pos = update(pos[0], pos[1], Z, sensor_error)\n", + " ps.append(pos[0])\n", + "\n", + "\n", + "p1, = plt.plot(zs,c='r', linestyle='dashed', label='measurement')\n", + "p2, = plt.plot(ps, c='#004080', label='filter')\n", + "plt.legend(loc='best')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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92/Z39+7d0aNHj4BiZTMyYBo8GGxmZkCvFwrbpo3QIdTGjbo3GoWNgyeSl1+G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\nb0Kxfj1YpRKav/wlHCGGXl2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kBdJdyrYf2CVy/lTT4I5Z8hDOFCwqLYW4qAhxU6ci+r33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Co6oqiAgGgUGckiBhoOtlpemYlEEG7cWIR+NG8O54IF8NDCPQBSJk9GZo8eCoEp1uVC2oQJSKIp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\n5eWwnDnDGlVULuhhQRN1SLXrU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lwffSTQJTL6PUVBYOxY4d8AqcYExo5lC1reXXfBRen8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50HFSlyxJC6/faoNcP+0UdIevVVGKS5jSDYoQMCHTpozhmJwE+YsyCySpAUBjo2yTtJkL2C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+ "text": [ + "" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this example the noise is extreme yet the filter still outputs a nearly straight line! This is an astonishing result! What do you think might be the cause of this performance? If you are not sure, don't worry, we will discuss it latter." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example: Bad Initial Estimate" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "Now let's lets look at the results when we make a bad initial estimate of position. To avoid obscuring the results I'll reduce the sensor variance to 30, but set the initial position to 1000m. Can the filter recover from a 1000m initial error?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_error = 30\n", + "movement_error = 2\n", + "pos = (1000,500)\n", + "\n", + "dog = DogSensor(0, velocity=movement, noise=sensor_error)\n", + "\n", + "zs = []\n", + "ps = []\n", + "\n", + "for i in range(100):\n", + " pos = predict(pos[0], pos[1], movement, movement_error)\n", + " \n", + " Z = dog.sense()\n", + " zs.append(Z)\n", + " \n", + " pos = update(pos[0], pos[1], Z, sensor_error)\n", + " ps.append(pos[0])\n", + "\n", + "plt.plot(ps, label='filter')\n", + "plt.plot(zs,c='r', linestyle='dashed', label='measurement')\n", + "plt.legend(loc='best')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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jRjVofLWkExERERGjCGrG2Ww28/777/PUU0/hcrno1asXc+bMIT4+ngkTJpCf\nn096ejpxcXFkZGTQqVOnBo3/Y3BWSzoRERERCa2ggnO7du14/fXX6x7YaiUjI4OMjIxGj5/UtbqX\nc/6ew/h8PkwmU6PHEhEREREJhmG33AaIjwrDERtOeaWbPQfLQl2OiIiIiJzGDB2cQeucRURERMQY\nDB+cz+qs4CwiIiIioWf44JzUxb/OWRcIioiIiEjotILgrBlnEREREQk94wfnms4aakknIiIiIqFk\n+OB8RscYLGYTOw+U4qxyh7ocERERETlNGT44260WzugYg88HBXuPhLocERERETlNGT44w48XCGq5\nhoiIiIiESisJzrpAUERERERCq5UEZ804i4iIiEhotZLgXD3jnK8ZZxEREREJkdYRnLv+uFTD5/OF\nuBoREREROR21iuDcPjaC2Eg7R8qrOHDEGepyREREROQ01CqCs8lk+vECwd1ariEiIiIiLa9VBGeA\ns9RZQ0RERERCqNUEZ3XWEBEREZFQakXBWTPOIiIiIhI6rSg4a8ZZREREREKn1QTnnp1jMZngh8IS\nqtyeUJcjIiIiIqeZVhOcI+xWurePxuP18UNhSajLEREREZHTTKsJznDUco3dWq4hIiIiIi2rlQVn\nXSAoIiIiIqHRqoLzWbpAUERERERCpFUFZ804i4iIiEiotNrg7PP5QlyNiIiIiJxOWlVw7tIuivio\nMA6WVLDrQGmoyxERERGR00hQwdntdvO73/2OoUOHcv7553PzzTeTm5sLgMvlYsaMGaSmpjJ8+HCW\nLFkSdLEmk4nz+3QC4Kvv9wU9noiIiIhIfQUVnL1eL2eeeSYLFixgzZo1jBgxgjvuuAOAuXPnkpub\nS1ZWFo8//jgzZsxg7969QRecdnZNcN4S/FgiIiIiIvUVVHC22+3ccccddOpUHWavvfZatm/fzsGD\nB1m6dCnjx48nOjqatLQ0UlJSWLZsWdAFp/XpDMBqBWcRERERaUFNusZ53bp1dOrUiYSEBAoKCkhM\nTGTatGksXryYpKQktm3bFvQxBia2x241s2XXIYrLKpugahERERGRU7M21UAlJSVkZGRw//33YzKZ\ncDqdREZGsnXrVpKTk4mKijrhUg2Hw9GgYw3q05WVm3ayda+TK9K6NkX5YiA2mw1o+HkhbZfOCamL\nzgupi84LqYv/vAhWkwTnqqoq7rjjDq666ipGjx4NQEREBE6nk8zMTABmz55NVFRUnc+fNWtW4Oth\nw4aRnp60epcvAAAgAElEQVR+0uNdnNydlZt28vnGnVyRltQUP4KIiIiItCErVqwgKysLAIvFwrBh\nw4IeM+jg7PF4uOeee+jZsyd33XVX4PaePXuSl5fHgAEDAMjLy2PkyJF1jjFlypRa3xcVFZ30mAN6\nxAKQlbONoqLkYMoXA/LPEpzqPJDTh84JqYvOC6mLzgvxS05OJjm5Oic6HA6ys7ODHjPoNc4zZ87E\nbDbz8MMP17p99OjRzJs3j5KSElatWkVOTg6jRo0K9nAAnN+7+mLEb/L3U+nyNMmYIiIiIiInE9SM\n865du1iwYAEREREMGjQocPsrr7zChAkTyM/PJz09nbi4ODIyMgLdN4LVLiacPt3i+X5XMesLDgSC\ntIiIiIhIcwkqOHfr1o3vvvvuhPdnZGSQkZERzCFOaPDZnfl+VzGrt+xVcBYRERGRZteqttw+2mD/\nDoJbtIOgiIiIiDS/Vhuc086u2Qjl+734fL4QVyMiIiIibV2rDc5ndIihU3wkh0orydtzONTliIiI\niEgb12qDs8lkYvDZ/uUa2n5bRERERJpXqw3OAIP7VC/XUHAWERERkebWqoNzWs2M8+rvdYGgiIiI\niDSvVh2c+5/hIDLMSsG+IxQWl4e6HBERERFpw1p1cLZazKT26gho1llEREREmlerDs7wY1s6rXMW\nERERkebU6oPz4JrgvEYzziIiIiLSjFp9cE5N6oDFbGJ9wQHKK1yhLkdERERE2qhWH5yjI+z0P8OB\nx+tjbV5hqMsRERERkTaq1QdnOKot3RYt1xARERGR5tEmgvNgXSAoIiIiIs2sbQTnPtUzzl/nFuL2\neENcjYiIiIi0RW0iOHdOiOKMDjGUVbj4bsfBUJcjIiIiIm1QmwjOAINr1jlruYaIiIiINIc2E5z9\nG6F88s3OEFciIiIiIm1RmwnOVwzqSbjNwvJvdrD5By3XEBEREZGm1WaCc/u4CG4c3heA597LCXE1\nIiIiItLWtJngDDD5qnOwWky892U+2/YeDnU5IiIiItKGtKng3K19NOOG9sbr8zHnv9+EuhwRERER\naUPaVHAGmHL1uZhNJt7+bCu7ikpDXY6IiIiItBFtLjgndYnnp0MScXm8vLh4/amf4HZj2b4dKiub\nvzgRERERabXaXHAG+O3Y8wCYv3wzBw47T/rY9mPG0Omii7Bt3NgSpYmIiIhIK9Umg3P/MxxclnIG\nFVUeXvnfhpM+1tOjBwDWbdtaojQREWluTiemI0dCXYWItEFtMjgD3FUz6zz3w40cLjvxMgx3YiKg\n4Cwi0laEffYZXfr1I37KlFCXIiJtTFDB+aOPPuL6669n4MCBPPDAA4HbXS4XM2bMIDU1leHDh7Nk\nyZKgC22oQb07cVH/LpQ4XcxdtumEj/MHZ4uCs4hIm2D77jsAvB06hLgSEWlrggrOsbGx3H777Ywb\nN67W7XPnziU3N5esrCwef/xxZsyYwd69e4MqtDHuGpsCwCtLN1Be4Trufo/XyyZrHKAZZxGRtsK6\nZQsArn79wOcLcTUi0pYEFZzT0tIYNWoUcXFxtW5funQp48ePJzo6mrS0NFJSUli2bFlQhTbG0AFd\nSUnqwMGSCuZ/Uj0DUV7hYumaAu55aQU/nDeMxGn/D4AjtvAWr09ERJqerSY4J9x7L47rrgtxNSLS\nllibYhDfMe/oCwoKSExMZNq0aYwYMYKkpCS2hWBG12QycdfYFG55+kPmvP8Nn23YRfbG3VS6PODz\n8VLxLmI9VbS/6D4SenZjaZWbCHuT/JGIiEgouFxYc3MD31q//z6ExYhIW9MkKdFkMtX63ul0EhkZ\nydatW0lOTiYqKuqkSzUcDkdTlFGn6y9rx1ML17GhYD8f5+wAIK1vV67r147YFVV44xNof1YPtuw8\nyF/eW8+Tky5rtlqkfmw2G9C854W0LjonpC51nhc7dkD37vgA9uzBcuAADpsNYmNDUqO0PL1eSF38\n50WwmmXGOSIiAqfTSWZmJgCzZ88mKirqhM+fNWtW4Othw4aRnp7eFGUBYDabePGeK3np/XVc0L8b\no9OS6NwuGlN2dvUDevfiH7+7mmFT/8nfFq3hqgt6c+m5ZzbZ8UVEpAX16EHV5s1QVYXtggswbdqE\nKTcXX2pqqCsTkRa2YsUKsrKyALBYLAwbNizoMZtlxrlnz57k5eUxYMAAAPLy8hg5cuQJnz/lmJZB\nRUVFTVHWj/U47GT8ekj1N75KiooqifjmG+xARY8e9HTYmfqzFJ5auJZbn3iPj/80jthIe5PWIPXn\nnyVo6vNAWi+dE1KXU50XCWecQcSmTZTm5FBxpiZEThd6vRC/5ORkkpOTgerzIts/aRqEoC4O9Hq9\nVFZW4vF48Hg8VFVV4Xa7GT16NPPmzaOkpIRVq1aRk5PDqFGjgi62KVkLCoAf29H9dmwK557Vnt1F\nZcz85xchrExERJqCx9+nf+fOEFciIm1FUDPO7777LjNmzAh8/95773HnnXcyefJk8vPzSU9PJy4u\njoyMDDp16nTCcUxOJ76IiGBKabCS3/2OsptvBrsdPB7CC7bx+pAYLthxiLc/28pPBp3J6MGJLVqT\niIg0ndL/+z9KpkzB165dqEs57Vl++IGYJ5+k5P778XTrFupyRBrNtGXLlpA2udyxYwfnFhdTdeGF\nIavBdPAgXQYOxBsdzaPPvsPMN76kXUw4yx//OR3iIkNW1+lKH7PJsXROSF10XrQeHUaMwLZlC2U3\n3MDhp55q1mPpvJC6+Jdq9OjRI6hxDLHltn316pAe35eQgDcuDnNpKbeldmLogK4cLKngvlc+O+7C\nRxERMSbz/v3Y1qzBVFIS6lLkGN6EBAAqrr46xJWIBEfBGcBkCqx1tm8v4OlJ6cRG2lm29gfeWP5d\naGsTaaCwTz9V71oJGUt+PtbNm8HpbPFjhy1fToexY4m7//4WP7achM+HbfNmAFx9+4a4GJHgGCI4\nVzZBe5Bg+YOzZds2ujmimXXzRQA88Fo2Ly9ZH8rSROrNkpeH46ab6Dh8eKhLkdNU9Asv0PGyy4j6\n979b/Nj+cOY+++wWP7acmHn3bsyHD+NJSMB7kuudRFoDQwTnsokTW/R4JqcTvN5atwWuvs7PB+Dn\nQ3sx44bB+Hzw8Btf8od5K/F6tWxDjM2al/fjN21lmZHPh23ECKwTJ1b/2xVD87+Gus86q+WPXbPV\n9nGzmpWVmEpLW7weqWb7rvqTW3e/fnBM+1qR1sYQwbmlxfz5z3Tp3ZvI118P3Obq35+q88/H06UL\nUN2b+o6rz+NvU4Zjs5h5ZekGJv/tYyqq3KEqW+SUzMXFP3596FAIKzmxhNtvx3HtteDx1Ovxlp07\nMX/xBebFi/GFhzdzdRIs67ZtQGiCs60mOLuPCs7Rf/87XXr1IvrFF1u8Hqnm7diRsvHjqbjiilCX\nIhK0JtkApbWxbNuGqaICb3x84LaK0aOpGD36uMdee3EvOsZHcPszy/jgq23sP1zOP+65nIRo/QIX\n4zEfPgxA6a234jViCy6nk4glSwCw7N1br7ZUtpwcALznn6/ZKoMzlZVh2bsXn93e4i3HTAcPYtm3\nD29kJJ7u3QO3exwOTF4vlpr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rnjlv5tBZ/qtfEfPXv1bvpvzii5RNmtQk41ry8oh/4AGc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+ "text": [ + "" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again the answer is yes! Because we are relatively sure about our belief in the sensor ($\\sigma=30$) even after the first step we have changed our belief in the first position from 1000 to somewhere around 60.0 or so. After another 5-10 measurements we have converged to the correct value! So this is how we get around the chicken and egg problem of initial guesses. In practice we would probably just assign the first measurement from the sensor as the initial value, but you can see it doesn't matter much if we wildly guess at the initial conditions - the Kalman filter still converges very quickly." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example: Large Noise and Bad Initial Estimate" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What about the worst of both worlds, large noise and a bad initial estimate?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_error = 30000\n", + "movement_error = 2\n", + "pos = (1000,500)\n", + "\n", + "\n", + "dog = DogSensor(0, velocity=movement, noise=sensor_error) \n", + "zs = []\n", + "ps = []\n", + "\n", + "for i in range(1000):\n", + " pos = predict(pos[0], pos[1], movement, movement_error)\n", + " \n", + " Z = dog.sense()\n", + " zs.append(Z)\n", + " \n", + " pos = update(pos[0], pos[1], Z, sensor_error)\n", + " ps.append(pos[0])\n", + "\n", + "plt.plot(zs,c='r', linestyle='dashed', label='measurement')\n", + "plt.plot(ps, c='#004080', label='filter')\n", + "plt.legend(loc='best')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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DN8WGcyEnnw27T3g6HCFEbWVNsKVqkXCRSafzdAhCiHLIp7sdlUrFgM7NAHj/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CkyUTySwYux4E2mYBvF5x8u93Jcn6b444Nn8cfRJVhx/ju8fPM4DiZdwvJR7VAp1YKz1/IwfPHP\naDH2Gzz66hq8s+4wPL4AoNGA1+tDFnZ327YCFZhiYjZt2IDkQYNCUhdCwo0qhgLPsiGUXMroCme3\nI1CtmuSJdowZg2LCeBPFwLbOnCnw/54+DXf79tAdPw7LwoUwff215JWOBEa52VDSKS5ahIRNm+TG\nHbUR4ZOSJC5g2XcquL1rF3x16sA6fz6Shw8PqWWQcpI5LqLnnlFhaiFt12zaBH2XLkhv105SYfPV\nro28VauCBibE6Asp4onGkUxo9Xw+genC4RAKiigPECmWIZzC4DjZ9ejiLU+TJshbsSJYBClO7pqr\nV5HWogVSFKk+mn/+QepzzwkbCtmDYIT0KzF1ImnyZOgPHIDlgw9QoWJFpHbuLFOFo4tZi4cORcHs\n2XBRkuK8wQDDoUMSNaNZZDUCqOgO6SfUvSv7dx6lhCqNXb8/pOBVcgZEWCANR48G6RLVDAJqM0Cz\naUjzTxRqs0hIe+oppLVuHXEMkjqbkEgNBN5ui8gmwYhpEmSdIPOqc8AA5C1ZItH9yRBmntXcvg3L\np58KwlIhXwrPkrdY4O7aVZbvbdyxA7YxY6Lmu5KNpSySplBzJH2Wfub+atVgHzgQZlGISlKvZVnZ\nvCDziIpjxFu/vuRdNBw4AOv8+dATA1uxlslYU0wm8CkpQt8imwCSplYKA5vIifNqqVJh5jZf3boo\nGjcOpp07kf7EEyFOCuk04lzFWa2wDxiAVGpz7BwyBEXTpqkWf3PJyXAOGCAJd+l//VXaiJF+JYE8\nA9GwJ9HlwrffDnJME/pMlX7AWywomjQJrg4d4GrfHgWzZsEVQYpcCZKuqVTbLJw2DQXz5iF37drI\nx1PphIC6iJbu2DGkt2oF8+rVyF+0SBK+Y3NzkTJwIGxiISZA3aPPB/uAAUimU4Op9ZqM43uFf72B\nrblxA7bx42H56CO4undHyfPPg83Phy4zM0QNCoCUx8Qp1dGoydzdrp1gUIkdVH/gAMo99pjkbYxW\ncUsS/enra69ehYUqKiA7f61aVTsgm0T1R48CgYA0QFmHA+ZPP41ZdAMAdBcuwP7CC0hXyb0Kh0DV\nqigeMQKeNm2guXxZJgJAKt69derASRb+WHa01OQWyUMVCZInIkLupB4cHnVmY9CtP/DZha2oq/ei\n/WNVsXdeb0zo3RCtzV6kGTXILXJjyfY/MfTDH3FnwUJkDhmBgpXrggpSAAoWLoRj7FhoKPo9y+LF\nSB49GqZdu0Ly2z2tWiFAhTGt8+aFyg2reb0U9H7EYGTy8qDftw+6U6dQNH48si5ciJq7blm6FAkb\nN0q5p4b9+2GdN09gghDV9NSgO34cOopCi6c8ImpQFWBiGPjq1kUuxSxDy3bTXoFbx4/D//DDcjYe\npREttiXlpZdUDRYC4g1RnoOhebkRzB/31qsHf40aIdc2iDm/mnChXxFEIIg854x69VDukUegP3JE\nJmglnExgjKlw332yTSnZvDJOJ9Jbt4Zt0iT4HnlEbKjQZs3Nm9BlZsKoKIim56HUTp1g+fhjmaec\nHl/azExpo6I/cUKmagYqXcHbogVKBgxAwQcfBK/j8cA2bhzyxZQxmq6SM5vBWSyScRSyOFPOCGKg\nBVJS4HzpJfhq1ECgcuWQcSxtMBQb8MIpUySRGiAYXlYNadOGv9hH/VWqBBmCYkxPo8EUFsKwZw90\nZ85Ad+GCQF3Zp0/Ixodum57KuSWQ0X0GArI1gNSx+OrVg7tr19B1CuHTHCWHEMchtUsXWN95B5rM\nTNh79AgaxSrHprz8Mszr18MkRqvCQoUHXfJgK9MbAgGp7ZJolfhOuPLlUTx4sGAY0k4SjgP8fuiO\nHoWnaVPcvHEDOdu2IX/xYtzZujUoyEX6msLRpcb0kPjee9DcuIHCmTOltCrL0qXQRSAxUIUipce4\nc2fEAm39vn3Q/fEH3OJGhnG5wipLE1aRmJRS6ePS01E4ezaKR44EQPHzi+1UKwb1tG4N53PPSRob\nrj59gpuHCB5sACgePhyFs2bBvH49Ehctkr072+TJSG/USDVdC0CoCJYI/8MPo+T55yWmtHCIpc6B\nzEH+ypXheuYZqfiYcTph3L1bLkhFaECpjT5BNGO/LPGvZxFh8vNhFh9I8Usvwd2uHbREOpT2JL3/\nPsxLl8IxZgxu3rgB8DwMe/bATuS9qReYr1BQUxrUUSltVDwvmsuXkSguWpzNhvwPP4R9wIDwNDSK\n1AVlvpNtxgy4unUTduh+P9j8fPBaLXiRiSDk+rTXkudjDn1oMjOR3ro1mEAA/qpVcZsU2JBF0WAI\nGja08E0Y7xMdnjNt2wZ/jRpxV+Ez4TzYPA9240Zw9euH3B8xNkx6LcaZc2HfPhs8gO/2HMOLC3Zj\n9+/XUHXAcgBWMKa2eGXVr6h3oQDl6tXEo1XtqPDkk+ASE3FLzH+kJ3fV/qCYpHTHj8slwjUa8AwD\nhufhrVdPEiICAF/16kJoeMsW8AYDfLVrwzZ9OtytWiFv7VqwV69Cc+sW/FWqgKMVF1UfVqiXJVJ6\nib1/f7AFBSgR01JsM2fCRqcxKEDn0hIvRdK4cRKjBrlHmcIfhcR581A4f7584Ve0z921a1BsIYIH\n2926NRinE97GjSP2d1+NGigeOTKYF6qkv6JZC3w+QKeDcfNmsA4HXJ07S9LlXEYGuKQkIQ3k5k2J\nXSj12WfBWSzIFj1tgNj/1CI21Jhhi4vBUe3kkpMRUKYY+HxgPJ6QdBn9H39A/8cfcLdvDz8Jt1LX\nS1JSM1L9oeS//xWMb2rTx9tsMpYXhn6GtIFlMIAtLg4ajYp3pz96VKJWJGNQk5cH7dmzyFu+HIEa\nNUIXZRWOYWffvnB36gTnsGFI6d8fxj17JKNRlbVIPIfh6NGgxLRGA2f//nA/+SQ0t28LG6nu3WP2\naGozMyUueABAIADDgQOq+bH0b0JAzfnexo3lXj2F4qpqvnUYRwYZ1zpR2lz/+++SkiF9TkDw/iYP\nGSLL5VcaQWxWFmxTp4Kz21H47rvyOZX0B6UHm1Y3JZ+J/YoY4YFKlVAkMno5X3wRnNUKNjcXvNEI\npqQEad27g7NYcEuMDAbuuw/648eldDXJwFbMu/QcSqC9eBGanBwEMjLg6twZps2bob1+HZp//oH/\noYeQ0q8fNP/8g7xVqyKL+LAsbv/4o1DDcfSovChP5X1Y586F/sQJ5InPX3PrFgqnT5eYzAgcI0eG\nRKyU5zPu3AnNlStwP/10RBVPqRj02WdR0q+fbFyRsVLSp4/gmKP6bPGQISjp1QuM2w394cOqio8S\nwnBq644dg/bmTSR+9JGsWJmAV6QpajIzob1yBf7q1aV0sYiIQypdtlHhOGm8aa9fF5w1BkOQ8YbY\nENQ49ceqlFoG+Nd7sGUiCcuXw3DokFARD7lnI2HdOrAuF2xiARqRYwYEgwaBAOD3I/H995HerJls\nNx+zgS1OKK6ePWXV3wVz5sj4UHmWDU464QxsZW5aBG5qzfXrKFevHtJUpJ5JAUSAUrOLhVReIxaY\nmVetkjwmtIeVVnIsHjoUWefOSYqJ9j59UL5KFaGSWQE6RSTpzTdhWbwY+qNHkd6oEZKHDo3aLgAS\nx7KyYMLwyy/Q9esHQ+3a4C0W3P75Z0lsyLx+PRLnzAGbmystJAyAx2uWx5oJ7WG3Bo11nmGwxGXH\n0J9uoduCvXhw9P/weIOX8WLlp3D1dqjwjrI/sLm50Cg8mKrvOUyYmp7oE775JpgLLF4z4z//QWrP\nnrCo5FoSkJy29CZNYP7ss4h8qjIoFfQUcHXoAGe/fkLBarlysnQYUvxHjD/Djz+ipE8fQVyBNpZo\n1gcVDzmXlIRbVO1BSffuwTSlCAZ2oHp1FL/xBrxNm0qUd8IJOWipnNNA5cpw9egRpIhUnJM22Eia\nSOL8+UiaMAEaRd2AlF6hqI5ni4tlHivG7VYtNJbei8rClbNtG7L//FO24Jm+/RblH3oo1GAm53O5\nhLoNj0cuUhEBRTNmCJLPyohQuBQN2ghUpBAp+zn9LHmTCUVjxoA3GmEfNEiiSjSvWxdsy+TJ8DZo\ngNRu3WCbOhWOESNQMG8eSvr1Q9KYMUicNUvapBODy6DGqkG10fjjjwhkZCBgt8NfuzY87drBOns2\n7P37Q//wwwBZeD2e4H3k58P6zjswL18ePKey75FrRPA4/j/q3jtKimrtHt7VOU1PHoYhMwKSUQEF\nBAERBMEhgwQFRS4oBhADiugVrwRFRXwVFBABRRBRFBREEEQl5ySgiODA5OnpmelcVd8fp86pU9XV\ng/e997c+32etu670dKg6dcIT9rO35c8/NXAcfoyqR46EbLNpqzLRKExXr8K2bx9yGjSIw3AH+/XT\nsAtp7C9QmrH5FonAevassSgWAEgSrKdPkyZ5rnmQzffKSnjeegtSSgp8r74K2WJB2qhRMNMqpyjG\nKw1GIuR/uv2nYt48lC9dCikrC1ndupHv1zWVWblglQby+gx2RGF80BiH/ZWyshBt25bdn6msDPZ9\n+2DJz1eTcolMEBBr3hyS241MLlFSPXassVqnASOIEeSMD5RpllafTHOuXYvk2bPjONzNly7BduAA\nm190DxLr1IHsdMYJDflefhnW48eR1auX2vsRCrFKe/SGG1A9aRJCNUA/4iBh9FqUa9CoVHOmlzp3\nbtyI9HvvNeyfAIgSZ3aLFki6lgy85kfI/Tp27kTt3Fzk1K2L5Gef1Zx9tIGRrhXqD2q4xBPseyIv\nsPVfsr+9g+1NhGFGDc6rYjTzYP3tN+TUr4+0e++FqaQElosXNdQ7egfKO3cucurUQdL8+fC8+SZy\n6tRBTp06yFQit8gttyAwejRERVwm1KcPRKVJQXI4EGvSBKkKlV1Ch4FviAgGjbtm9c0GBlGe7/XX\nUbZ4MSqffJKpQOqhM+bLl2HfuZNhLE1Xr6JW585IHz8erk8+0bzX+emnsB48qJWudjjIJkOd7kCA\nbK66iWo5c0YjQEKv3XroECxXrmgUxqjZt21DRv/+sP30E5LmzIFr1SqWMecPB1N+fpyaXqxpU438\nddLbb8NUXh7HJ3pDbhYOvDUKu14dhjPJZ7DizOfoWX4BeSW/ICdSiUhMwn5vXXyY2Rp3zNiAeesO\n4Gc/x++rmx9ZRhs99zzNf/wB+7ZtbEPky97RFi0QvOsuFacIlZM9TpktEd84wOaCKRgkG7te5jmR\nKWvGKIovWbsW5YsWoWLePBTt3o3CQ4cgcxunrMNfpj3wANyffEJKu9zc5MUI3B9/jOTnnou7Nykj\nA8G77yYlVrNZxRAq2ELrsWMa+IHewj17wv/006gePTpOuVKoroZt/37WQFw9YQLK3nsvTkBBFgR1\nTivXl5GXh4x+/dTnSee40bMQRabkFxg7Fm7dWgr27cv+zh9c5j/+gOeNN1RYEc9NrTgXemVYau6l\nS5HZrx9qde4cL0DBj4Esw3LyJGrXrYsMA6lxIHFTqeZZ6cravrlzNfAoTeDhdKJq2jRUKcqS3tde\ng/OzzzTZraqHHkK0TRvCHlFWRpqdRo2CqbQU9p9/JtlZXWAauekmQLcGJS6hINavj8LDh1HKw7So\nI/3nnxBCIaTfcw9yGjdmDXzm4mJ43n1XE6TooRkpTz5p+DoADQtMNlUepEbPJYslztm0792L7Pbt\nkUYrq5xVzJwJ/6xZiPFwK84SNlQavlltsvTNnYvKadM0jbFCKMSy9ZZLl5DRvz8sp06xZ2/y++Gd\nNw+WixcJxMBqhUNxxCWvF5BlRK+7DtHcXOZ8ObdsQU6jRnB8803Cy2L8+fqzjG+mV5xvvYMd0mVO\nzb//DqeSxWUOoYG0O7lo3d4ajcJ6++1xPVL6gKRizpw4ETkAhpR7en+k6h//0ApnJcJ0J+iDcX/4\nITIGDoTr88/JC7QZnBPaC99yC3u/WL8+62OiY2e+ehWZffsiTa9kmMj+TcpaU2kprIcPo1pJdEm8\n3wDjPirLL78g6c03YaqoQNJbbxHstK7KpM+Ia64N3NyIxbSBJ6U9fP55FOub2J9MWAsAACAASURB\nVOl3u92aPQwAAnl5kLix/G/Z397BjuNI5Ram9fBhgrUKBg2zDLLHg1C3bgwjJvCZYlrO/PNPlhGv\nGj8eVzjqIdfatRo8nVmPAeO+i3ZCm0IhQgVGI/REzo4gIMqJ2GToGiQB9VDWR5WOrVvh+PprQJIQ\nbdMGoQEDIDZsiPLFi1G4Z49KBh+LIfWBB1DrlluQPno0XArUJs6R4yz18cfhWrdOXRgGhzhlEUid\nNAm2ffvYhpg0fz7Sx4xB2bJlKFEoigRJimtgAMAclvRx42A7cgQZw4cj6e234fzsM/iVg42qHlpP\nnEB2x47wKiwtMgebiLZpg8pp09TvVcZEttkQ4zC7dqsZ1+WkoL5VxH2Fx7D92Ep8cfITnDm8GG9O\n7Iqtx1ZhWNEpVIeieGvjUdx5IRnZnafjupsfxaMH/MgvVbMThuNHs8+tWpHgZdw4BAYPxtWTJ+Gf\nPRt+RSgk1LMnQnffjRJeCIVe448/anF2NZS2y99+m6mh8ap3AGrMAlOnLNKxI8p0GXIhGkVW797I\nbt4cTiVbbWh6tgndeIjXXQffv/7F/u1esUIb9CjvL3/3XdKEmJyswXa61qwhzb/XwKFXPfooKubP\nj2s6tVy8iIxBg5A+dCiymzRBymOPIXTXXayiRR3sYF6e6jhTcRmfj8xvXcbZMJg3mSAlJUG22+NY\nKySPB+VLl6psP9z3WS5cIM4nlUzm9i4a8CZqvqEZIaP+E+0FENhZHFUaAITDEKqrUTF7Nkq5hkb+\ns/w98q/FWrbUcOwawTf47Jdj0yb2bMspMwB1ynnoBeeU6iEZtkOHCLMSZ7EmTdSGYPrZcBhp992H\nlIceioNiUKw0hRbRBAvPm1tTpUNvUb2CowFES7Za49YGpZCkzjIdK8nrRfXkyTXyVvNMExUvvRT3\n96IdO2DOz0fqpEkqK4kkITB2LFEc5uFmunu1HTmCLMWBrR4zJm6N0/kfzc1FwZkzkOrUQcnWrSjZ\nvBneV1/VfFfaxImodeONSBs71phzGYiHU/FS6QoPdrhbN1TMmsUy5Py88ixahFp8kzVt8uRVm42Y\nMei/d++G6aefkKQwYXkWLkTSnDkaTLwsCImhCxSCwAepurO++r77GDOUqaCAXa9Ypw6hoFy8GO4l\nS9SeDf25QueRjj+fOtjhbt1Q+tlnCClVAZjNmsoz+eG/KEwXjULw++M/Ry3BODi2bEHmgAGEkhQk\n4QOOKMJUVgbHV1+Rvh/FrCdOaCqFji1b4H/ySZR8+imKN29GYNgwVBlUu43UgYVIxLB6Kycnx68l\nLmnC+17RZs3ge+cdSH+xwv7v2N/ewY4zbiMzVVcjs39/UoIzcLClzEyUrVmDcoqB4ztvKYE915go\nZWZqnRrdwzP5fIAsI+Ouu5CRl4fqCRNISdTtjuPeBYCSzz5DBedoaMzhQPG2bRphitI1azR8pHEZ\nbOWaUydORNqDD8ZtkrHmzUm5mZMQNmQBSUQnRE0UYSovh//pp1FBxTcMzFxYiIzBgwkLCtRMj6yT\ndNcfmJazZ5HTuDG8s2YholOQFCQpLtK3Kw2JDK9YVsb+Fm3XDpVPPKFK40oS5KQkXP39dxTpG5DC\n4bhN0Buqxtiq39C7/DesPf0pVj/ZB+PuaAErZBTaPPjNmYbV+RJ6P7sB2w4TBSgjlUVBFOHYuFHT\nOCdlZhLMPE9rd43MgJvDVNZENxXu2ZNlW6ikNxUZEK+F2wahzdNvmmnjx8Ny4QJMfr9xgy33flNJ\niep0GnHS6h2L48dRcPAgCg4e1GTFmVHHKhqNzx5fy7h1ELr9dsZXbwoEYAoEIASDyOrUiWFXqYPn\n+uILZN9wg2FZm23UFgtkq1XjYJds2EDEKxo3RvkHH+DqhQtaRhUQCIn14EHV+aNwr9JSlXNccRyi\nvEIddy9iTg7KuP0J0FZDqPm4NVo9ciRCPXpA8npVeXNuziUtWICcxo1Ru2lTRFu3hlVhagj27o1Y\ngwbw/etfquMKGAZRvjffRIAmBLi1kD58ODL69GFMGeSGzepckGWyp+ocBciymvGyWuGfMQOFu3Zp\n+H/10B3+80I0CiEYhLmoCI7vviPN6rqAkyYpaPMbU6gMBFTMrzL2YlYWirZvV5vT6LVzFtVlmTMG\nDGC/GRw0CEVbt6J68uQakxmAuk5qcuap0YBazMpC9QMPIKRraJeSkmD+4w84v/qKVW8SNkzWUOUK\n9eunzhn6/HUy6QARYslUmvykpCS1SRHkbHDs2EG4hqnxQUgkAtvevUh+5hl4//lPjaMa7twZQlUV\nxAYNUP3ggyrsg88W6/cnesbwDmUi1iH+fYq5ly8nCtD8nlvD/kOd9ySOqlZs2JDA5Qzu11ReDpPP\nh2izZijetg21unUj/S9coGTfsUMDN6L3SIPu0F13oeKll+L2Gv7c1TjYsowUqgB7jXloO3QItZs3\nR5YiJGO5dEmbZEngYFOqQPvevShfuBBlCpMMbdj2LFmCtEmTtBl0/bVYrRBzcxHp3BnRdu0I6QCn\nXEst0qULCvfu1d57NIqYkjgBdPAb7vmVfvCBtkrC7edGFYr/lv2fcbApxsepSEnzToRL1x3tWrEC\n7vfeUzmm+UVHcTxbtkDw+1ljWuSGG1DFiz9AcaT0kyEUgu3oUVgPHULVI4+gato0yC5XQmcops90\n8GYyaZSRwt26IaJkaqK5uaoqoR6/+W9EpZr70RHeJ7ysqipk3nknPIsWwbF1K2q1bw/H1q0J38/K\nObxjxJeW9ZuZgnv0LFsWd1DBwMGmG2XV5MkEexaJkK7tK1dgOXMGAscDWhNeMu2BB+D64gvNQQCQ\njAtAApQeLWvjX+O64ODrw7Djud7YOqsferatB19VGOMWfIuhL2/CeWca/rR7sTG9GWY0uh0jR7yI\nr27pB8tpbZAlm81wL14M7wsvQHY4iFy0AuNJZC6+rPVXaQ4BhHv1Quknn+BKfj7KE2G3+RJbOBzP\n8sJvQEYHMIWlFBTAzR0kzq++0rJWAFrnBABkGVLt2oSOyuDgqpgzByVffIHkWbMYTZxst8P10Ufx\ntIOSpD1geUaeQ4fieyhkmQVFwf79UT1+PEqU7LEQiRDMvj7DJUlwfPklxDp1SNm+QQNEW7RAIC9P\nqzRH388xWVClscy8PFbdkTIz2W9SqV6WmUtJwZX8fNKczV92cjJCeXnwP/kkJIcDgbw8BA36MAL3\n3MMOmapHHkHZ6tWw//CDmgXnM8ocHrh2q1bw/utfkK1WlC9fjrQHHkDKc89pMOEUZ67Hb0spKaTv\ng3uW1uPHYTt5UiPjbvn1Vza23pdfRk6jRvAohzC9f9vevUhTYCXOLVvg/ugjImTDlYmjRg1qdH1E\no0iaM0fNcuszx3rGGagZbOvZs6xKJ6WmItSzJwLDhyN2/fVsvgcMqotiw4aMQQIgGWBa7ZTS0hBr\n1YpA3fjAJAHcMXzzzQRKdC12CR23Nu8MVt9zD6SMjPjmrgTfWZPjz4sOyboKDt9jYyorg4U2mAqC\nYeUsMHgwGetYLO7vGUOGwL1qFTzvvYckPpC0WJA+ciSy27RBRl4ec+I0XNG6+0qZOhW2PXsQGDMG\n5W++SYLsmiAiOugCqzpw1Sg9JIW3UI8ekFwuRikIkKpVqF8/tbJYVQXz5cswlZSwviD63UYUeO5P\nPoGd6+OgeweFXUY6dkT1Aw+oEKJYDKbiYpXlymxmzjh1sGly6lpzyzBpxO2j5QodKb03alR11HLx\nIoJDhyLUvz9gNsdB3Mx8v4ruWRg1Edt/+EErQkbfq+8jCYchJyerdJfc+zXnG/cb6UOHaiqE9h9/\n1DCI/Tftb88iAgDRJk1QMXs2MkaOZAtazMhgZVLB54P/xReR+vDDAMAgHwAp5bFyGi2ZAnDs2AHz\n5csQFTobIwEbvVQ6oFKAyU6nJqqjG5p/+nR4lYxS0uuvo5SWgRMYZWkIKFKeNBr1z56tYktNJogZ\nGWr56i862HFl7RocbMnrRahPHyKiw5VwTWVlZGxqwHvS0jvfQEcxttEmTYi0Nm/8gtI7W7xDzjV5\nAkQBShowgLwnGkXySy/B+dVXJMuXAK6gvUnyt1D37hACAdh/+omxRABA8bZt7HsyaqUioxZppPtw\neg4Wbz6O1z47hD1nrqLpzY9qv7cQWPvlRbS0uDGg0e1IiYVQbbbh699TYTrmwxXJC0uJC1263I/M\n/b9gxJIhON07D7fmjUCzjYTqLiqYYJUlXLEl4Q9HMkTBhOtqEViF8/PPCUsJbdyT5WtzOBuZyYTq\n0aOJAxMKIdK+PcrfegvO9esR7tGDqUwCRO5c8PsRGD4ckgK1EevXR8lnn8G9YgXJ9iiW+vjjCPbu\njQgHNwgOG4akBQuYWmVNG7xLEV+w79wJQZJYpcL59ddwfv01xFq1UHj4MBybN8P7z3/Ckp+PcNeu\nKKWHCV+R8fmYAAY1QZLYZuufNYsoyfHQM0lCcOBAmDjGIkgSzFevwr5/P6Jt2iB2//1kfiQyynWb\nloaKV1+Fa+1aCLKsQhBMJm1jJsgBaiouJuuaOi4GFY6qxx9Xqbq4A52a53/+B74FCyCEw5CU/YR3\nkm1Hj8K1YgWCgwYZQl2kpCQy7w2EZuja0Jdb/S++yJgi9GPAm/X8eQSHDSOBTEEBgdnRfUhxEN0K\nJSi1pDffhPXoUU1JmHe23UuXwr1sGeSkJIQ7dYJYp46GIUPD4wxoHS3qYFdpIV8ygGjr1ijjBV+U\n94a7djXO4OkPf25fs+3eDefmzZC8XkRat0a0dWsExo5F8owZcU1upZ9++teqNTyDB7S848xoj0XD\nhqh4+eXEVbCalGLN5viKGz0TeHw8f806zmtqrg0b4NqwAVXjx6PqUbJvynY7gSQk2qutVtaXQu+n\nbOlSxJo1U9+j+y1zQQG8L78MiCIRpmvQgJzvWVkQKitVakz68WbNEF25En76PVwPRuGePYxJKJH5\nX34Z4TvuYNoVsfr1kfTmm3B/8AGrLDo3bULSokUIDBnCAmNWvUv0vK9xpruXLYPnrbdIMu7GG5Ey\ncybEWrVQcOgQZLcbGYoCdKxhQ813WfLz4VqxApY//oCUno4qnhcaMO4x4T4fa9WKcGrrBXESZLaj\nrVqpz1Bv+rknSYz9g1rqAw/AFAjg6i+/aGBcekw3S2w0a0a0NBJUIPjAkPa58Ja0cCHMrVsDSs/M\nf8v+b2SwTSZEunZl4ghly5ejhMuomnw+BAcOJOqLFI9E/1ZcTIQxTCZAEOCfMUNtdorFINaqBVkQ\nCMemPuMbicQtZOpgmwIBOL75BpaTJ5E6fjySFH5TGHBT1mShfv1QuG8f/M8/T17gYRaKxZo1Q+Gx\nYyhVMvX0igRZRto99yB96FCYSksJNy8fieqjUgOICECyHwVnzrDXaaewzG20aQ89xDqTS3SdwaxU\nS8vqJhNiTZui/N13UTVtGmIKRpZK0Ee5jTIu0ylJpDS+eDE7wCmGW6xXD7GVKxFbtQrmoiLGUiCI\nIqrHj4f/qacSlnu8M2eyJh2xcWOUrluHK/n5KFAwzzXh7UwmAQ8NaIuDi0Yh7xZCe5UUC6Nd5VUM\nzE3Cg31aIDPZiVMxB+Y26Ipncu/A7Ia34VDQigPWdOTbvfjDF8bHO89i4Z8COmfeiQlHwri+ojnq\n3TIV7q7PwtltJhre8jjqdpqGzjdOQNcb7kfLH0W8/PE++Hf9DM8HH7Auc8HnQ20OQ1alBJZ/xfjm\nVTktDcEhQ1C2Zg2qJ07UcJFaz5yB97XXYOGyxxn9+yNjyBDDxhW+FO155x2kTp6sOteAZh2ZL19G\nrTZtkHHXXQBIedY7fz47BPUd6bT3wXr8OCxKltdy8iSshw7BnJ8P2eFA+NIlxOgairtpmd1HilKl\n4jHMsiILXTF/PtsbNKqHf2Edyx4PQrfdhsgNN5AmYFmGxIlgkBvQNu85fvgB2e3aaajaaId/nCqs\nYtEbb0SF7j6FYBCRTp0Q7t6dPV89TCjluedgKi42zFQxloS/IJVeo3H7SkA56AEyP3ln0Hr2LEo+\n/xz+Z58lzZ4G/QgQBJR++ilKlIolf3CaCgthuXQJwf79Ubp+PYJ5eXEcxFWTJ6No505E9u6FzGe/\nKbSMd7gSOZtG48GZfox5h9F65gzcq1ZBCIVQtno1pPR0uFasiKtKlS1ZwuaIbfduJD/1FByJmrMM\nRF70xlRR3W7Err+e6ULEv1FArFEjYwdc6S2onDIFQjSK5OnTIUgSSlevVs8pGDTJ1rBOPB98AHNh\nIQoOHkTR7t1qhpxzqipeeAGlH33E1qBss7HAzr1kCcuWJjLLxYuwnTihCQoLjxxBwa+/kooEb6mp\nkIYPVwV5lDlgLipiTptj40a4PvhAy2vOm/I8wrfeiqI9exBr0AB2DpZI9zEKD+Ff088pltHmnq3R\nsxOCQZhLSuDasAEpM2eSj3i9SJ0yBbUU1iQpKQnly5bFnfOWS5eIUBFN+kkSvLNmwfHNN9ckjJAU\nbnsNFa3uPoSqKiAWg+XUqbg9XGPKWFM/wHLlihaFEIuxpJx+v5KdTgapq3zkERYQly9ZgpJvvtHQ\nHMpuN/xPPIGqCRO0SAJl7hUcPszG3fnFF7AkOj/+A/vbZ7D9zzyjZn7ogtZNBhNHSxeHOTObEbn5\nZlzlDvtYkyYkulI4cKWsLJgLC2EuKoJYpw6qx4yBe/Vq+ObPR6hvX1Q9/DBkhwNSWpom0209ehSS\n18s6mQEt68m1pJ8BMmE0VGgrV0KIRAwB/eoNq3AIh0KuntW1K0wVFfDPmIGqiRMJhILL6oS6dWPw\nBLFRI1w9exau1asJBzIng0zeoIyh1arFzdEstg6XSjfJaPPmRLlNF/1HOneG75VX2O8HBw5ELDcX\nUmoqYi1bItq6NdKUBoPqceNgO3QIUkoKIko0SXluzfn5sIwfD6lbNwg8l2cshgAnBmG6cgW2o0ch\n1q6NqIJZdXKd7bKRA/EXnKi0JAfeeeR2LLyzIep37wYBQPnYNxHpWBdPDu+Ibfc9ibLLhSiyulGa\nkoE+PdvA+81mZFy6gJ/zxuBohYgvyiwwQUYzSwSHZQ/+dKgb0R+OFFgkEa2qihBIScO5SuDdzcfx\niZCLfs0HI+9KCJ1lGSZ9ic2IRkqW4Vy3DtGbbtLAUqhzbD15Erb9+xFr3BhSRgbS7rmHNKjojf8t\neigazWvuffYdO+Ka9DROQSwGc2kpzKWlsH/7LUwUt06/PwG9IQ9bMZeXI/PuuyE5neTAbtUKcoLg\ninemaRNpYPRoBIYNI4EGdxiUrlsHyLJ2/dXgXDo2bkTyCy8gOGAAyhQ6OspUYQoEYN+2jTU68vdV\n+eijTAWSX2OxJk0Quu02VlmLHwRBw6ABwDjrpTyj0B13wHL+PGFOkiRDqjcW5P4FBztt7FgIwSDK\nli+Pm3d8ZjbSpg1c3EFuPXkSNmXsbUeOINKxIyznzyM9AX86BIFQxdHEBe9gK/u947vvELnpJgii\nqIVWAUAshliTJpCVjFv1vffCvXIlO9RjLVtCSk4me2QCB9v3xhsE324wH1MeeQTWs2dR9t57DGKm\nZzmi924qKkLSokWIXn89os2awfLnn4jVrw/b8eNInjkTzq++QqxBA3iWLCHQGIcDoby8+AtyOBAY\nNAiyywXHli1AOMxK8kJZGYRQSKW/4645R6lAlb/9NoJKpVTKzETRjz9CqKqC9eRJpDz6KAteZZMJ\ncmoqKmfMgPX0abjXrEHozjsR7tULQnU1hIoKyHa7hlZOrFMHZStXIqtzZwaBijMFJsZXkmWnk+HP\nw507I9aqFROUkbxeti/bDxxA7OuvEaE9S/TzDod6LtHg4n8hcKbxG5T/Tlq0CNYzZ1DUoUMcUxHA\nnSM6DD81Sr9qKipSISLK2agXVtEnqQDCoZ30xhua+zHaey0XLiAmSayfiiVA9OcEpQ5WrtN67Bg8\ny5ZB3LABfkpvzNm1+gcA7dlTu1kzlL3zDoN7JbJoq1aofPhhxHJzSZUzP580Q27eDPfy5Rru9rjM\nutmMUK9esJ46Zcw0oljqhAmwHT2Ksvfeixe5Ue4r8847WU+LUeLhv2F/ewe76pFH1H/Q6J9GQE2a\nwKpQzzHTTwqDw5FNNOXA9iudyuYLF5DVpQuirVtr8ZDc4uJxSYIosoUhm82oHjcOHp5XtaaFHo3C\nevIkZKtVQ8tUu3lzCNEorhiUMaiF7riDTAhevU5ZwN45c+B55x2YKipQPXYsypYuhWy1ItKhAxxb\ntsCxdStCffpA9njUhags2kjbtrCeOoXAffcRcQS+VAiw/4506ICrFy/C8/rr8C5YwA6/uJKxYrGm\nTZkcLkDKZBGuUSPUty+unj8PCAJkpxO1GzWCEIngym+/ARYLirduBUQRzi+/hHnNGlJK4lgpvPPn\nQ8zORkSpXtgOHkTa5MkId+mC0tWrAZtNm3Xln8u/SUsEAA6HDXRWpT7+OMrffBPuYcPwQOwy7H/s\nRemqVQh37470kSNhP0GyLreufIU0AlWHIECGU4rhtyat8eeceThQFEbbUCkyvt+GBqVXkHZoN6oH\nD8G3D8/Aq+sJLOWjWm3w0eEYGk1fh8Wj2oHPnRk5pM5165A6bRrEjAwUcpzTwSFDEGnfHklvv42M\nQYNQ/uabCA4bBruueSRufAB2kOjp6ABonAsjhgvL2bPwvP46ou3ba9hd0sePj3tvpFMnBEaMgP37\n7+FZtgzVlJ/UABduCgYJx21aGkwGfQKh226DEA6r98c/Z5stLoPHGqrAHTA8hvnrr2Hfvh3h225D\n6I47iAhNcbEGlsDjBJ2bNqlMIspziuXkoPLpp2HftYswlnBjXP3AAxoVT9vPP0OIRkkztLL/BYcO\nheXcObVqZnAQsoNYltWDiOMu5o1WGoSaMrbKGNgOHUrslPIl5euvh2yxkN8TRaQaHLo1OkKCAJPf\nz+A+Po6pguKnbYcOwbN4MaoN5pD++iJt20IYOBBSaipzOKmzQyEicVZDk7H1zBlYz5xBrGFDiFlZ\nMBcVIbN3b/hefx3hHj1UBURRVJvQLBZWeU29/37g+HGYi4vh3LQJUkqKquyawOG3Hj8OKSuLSGYr\nUKarvXtDdjqRPn48bAcPwjd/PsreeUdlkuLMZKBcKns8iNxyC4r274d78WIkz54Nz/Ll8LVqRUru\ntGFeuaaMgQNhPX0apR9+yKA9oV69UD1mDKyHD6Noxw7Yf/qJUQCKqalq4zff7AriZPL7su3gQbi+\n+AIuJSspJScb79UAqqZORdWkSYDTiZTHH4dz0ybVSfo3eleo+adPZ5zJ6ffcQ2jnrlW10cMSdeuQ\nBpTmoiIERo1CqGdPklj44w9ImZmINWgA2W5HuHt3FbbAO5Q66lIIguE5JYii5nXW6KiH7NBzQtdE\nLtata6yk+Bcc7MhNN6nN40DCsddQ1d50E9MoMBcVwTt3LmMIA6A5i2i/leX8ecQaNIC5qEgVCqvh\nOZuLikgyVBRh++EHmIJBgm5wOtn8MxcV/aUg4j+xv72DzRtd7OaSEmTedhsEUURg8GCt3KzuADHM\ntnGZcPPvvyPcsSOkWrVIw5zSkZ7IYg0aIDBoEFyffw7Pu+/CojQgRFu0QHDoUI2D7dixA6kTJhg2\nnZn8fiYcE775ZpS/8w5SH3tMLdXU8OB9OmaBuO9WnG3ZZkOob18ApKSeqtDZ0eAhetNN8M+YwRoN\nWXnRbkf0uutg/fVXOHlsuh5aMnEigsOHQ1K4N/83ljRnDqxnzsD/1FMk0BBFksEXBIbJks1meBcs\nYDSDsFq15PJXr8L+44/MwaZ/s//0E2z79yNy661aR0q3SQX79jXExFlOniSNmM2aqWpcQBwlG/2s\nf9YsmHw+RNq0AUymeJy0LMMlqRnE+pYYnJ3agjF5j+gL4fPPgZ93Q5BE3Hx9bax79i4cenoOTv54\nHHOb9MTvBX7cs2QvJjXqie6+i2izZQ3EunVh37kT1tOnEcvNRfT66xl3qp59gQY7zi+/JM1D+sYp\nvfGNkTWVpmvAdFZNmKARzalJqlY2m+HYvBm2vXtRPXGiJtBNyO8tSTB99x3MmzdrXq6cMgWBUaOQ\nzInQXKvJVHsxygGlMJsIgQCc69fDuXUr3J98gpL165kgjJnDmsdycxHq1o1Ul/iSb1oaypYvJ9AR\nQM3Off89UqZORaRzZ9Ivoswny7lzjL7z6pkzkL1euFauhPX0aQRGj4aclATv3LlIWrQIoX794Fy/\nHp5lyxDq2RNVDz0E38svQ6xXj1XVhEAA/iefhCBJsO3bp/LSRyJwfP01q855Fi5EhSKkxcO+yE3E\nCxUJwSAQjaL000+RQUvIVAUwFiP/0x3gtj174vjqeXNs344YN2c8CxeiYt480hfCC2kJgmbPjzVu\nDMuFC3FzJThyJIIjR8LM0bBKqamGVHpp994L8+XLKFu5MiFtHh2rpLfeQslXXxHK0iNHIPj98Lz1\nltrPIIqsamC+cgWm0lJI6emonjwZwbw8lu3TBBuJHOxjx1iDKLNIBOAc4VijRgmVc68lR109aRI8\nb78N55dfouJf/yKBok7J0Uh4KdSrF9LHjUOoZ0+UrVqFsPL7ss1GsNAGDna0aVNAEFD1yCNIVfDA\ntv37NZUIKSND2wDHPSfZ6WRqwyyYMeCm/qtWPXky3MuXw3LlChHo+f13NmfjHFXFYk2aoOof/4Bn\nyRJk9OsXj/1XzFRSAtnhgFivHmp16wbZYsHVP/6An7L8QK0yWC5eJPtOOAwhEkH1ffeRMZdluN97\nT8M6ov0RzsGm42KxwDdvHmMSYYkYA/GrUF4eymWZMIfIMoJ5eTCXlMA7ezaqHngAUoKKWrh7d0he\nL1yffAJzSQlSJ09mfxOzs1F9332QMjIYw5Xe9H0pehMiEaSPGAHboUMI9ukD59atiDZrhvKFCxlU\nxHbgANzvvEOaQOnvUz/KZkPqpEkwFxSgYP9+0k/EzSNHTX01/wX722Owkj9aJAAAIABJREFUhYoK\nJD/1FLyzZyPSvj0CgwcjVr8+rL/+ClNJCXyLFiHSuTPcy5bBdOUKoq1aQbZaVSylwWKLtG+PYN++\nkNLSkD5qFLI7dID50iUVn1pDQx+cTkQ5ajmaYREiESZbKwsCEUcAEgP9+ZL6vn1wfvkl7D/+yF7z\nLFkCkwE11V8xtuFw5WAjkYJo69aomjIF4ZtvhvnCBbKpgDRIFe/axSLhKiqao28suXgRaePGIXnW\nrP/VdQIE762RRaYy6Xa7usFJEjzvvaeWwKzW+FI3f3jwrAEKlosvJyXNm6eyKdhsKF+6FP6nnoLl\n5EmWQfDOmoWsPn3gWrcOdgWGQ01OTkbh/v0M7588YwbcS5ci2rYtwrfdpsrZ6yJsk97hVq5TqKyE\n7YcfSCPjXXfh6tmz8L3+OvmMScDtyRKeu7Qbv7aPomurOiirjuCVBt3Qu+29uGnO9zhwtgDOL7+E\n91//Qtr99yNj4EAIyqFWwmebFalc64kT8TzPf8HBjqMq46oSGmYN7lkUKFAdjSUox3mWL0fltGmo\neuwxmIuL4wPdBA62YMBUAxAKR7FBA8292Q4fhnfmTGR27w6XrrlOb7Tx2LN0KWz79yOzRw84+Sy5\nHhIgisipWxe1mzYlpXDuPZbz55Hdrh08ixap0uLKfmO5cAHWc+fgXrFCZQQANLji1ClT4FqxAknz\n58O9ahWBTXH3bP7zT+b0OHbsIAIh48cj3KsX2w9SJ00iLCG1a8M3Zw6DS5gCAaQ9+CCj2LJwpf9Y\n3bqQPB6Y6XXR+aAwGAg+H7wvvYTazZsT7KUSfEavv54IkTRrRpo99ZSQY8Zo1kesYUMUKYcnu38O\n4ub+5BO2n2kcbJOJBQHBPn1U/twE85nfE4u2bUPh0aOsb8OUnw/79u1wbN8O67lzEEIhpI0bh/Th\nw+PVXJX9yrlpE1m/yj5v37dPzbAp40WdcXNZGZKUTF2kQweE8vKYWJlGGTZBIGsUYLpXrEBOnTpq\n1q+m5sW/YvoGenp+6pxXOtdiDRowYTC2P1itiLRpQ6j4eHlzhZPdevgwfPPno3jHDkJpuH07ir/6\nSv0excpWrIBv0SIElV4NweAMS3nkEdgOHEDZ0qXMiUt54gnYdHu2kQm//ALb3r2EhYq/VxBqPJaZ\nNXCwHUqCIjBkCPmucDihgx1r1oxcOwftTB80iKghK+xLVJAq1KsXrCdOICc3FxlDh6LilVcIfMNk\nglOXQNCY8t3hjh0RHDCAvGa1IjBmDAIUbsRBROy7dsFM9SmUzwYHDkTlU0/BsWsX3CtWwLF5MzyL\nF8NcVIS0sWOR1bEjLKdPq2OwcSMcmzahcvp0VvljVJfZ2Sh/6y1UPfooAqNGJQxUE8EB2d8dDsbU\nQjVRoq1bIzh0KFNENl25Aue33zJ9DkBd5zLHq0+vrSRBj8P/C/v7O9ihENwffQTP4sWw/PYbqidM\nYHADusjdy5cjedYsZHfogGj79rh68SIKTp1CwcGDKNFR+AFA5TPPoHzpUsRatlSxUcnJmgYw64ED\nSP3HP+B+7724zxvRygjhMJPEjbZrhzKayU7UPKBbtMlcNAsA3ldfVfHekQg5zLgDp0ZLgFU3fGt+\nPmp16oRaXbuyiczDXgCumYeWqijmLByG9cwZ5pjzJvh8cGzcCLuO0SHOdBkxFtxwpUN9Gd/85Zdx\nsrJIkAFiDCacg20/cACu9ethPXKE8DkHAki/915k9enD8N48DZxRRUOsU4fRKJqqqjRyw+y6OUgA\nbzTDYz13DimPPw7b/v3IuOcewo9ss0EIh2E7dowpbzqVOeyEiDXP9MXyMe3QporAMPJ9IQx5eROe\n8Wfi3Zz2GNV8CKZk3Yo50Tp4vW4n7LJmIhghhyPlLU998EHmlKROmcKyJ0bG9weYdEJLtBNd8nhQ\n+cQThp93f/hh3FzXO/O88qPl99+ZKIh+nQWGDUP5ggUo3rIFfv73aPmUs/JFi0glAYhzWBy7dsF6\n/rzmQHSuXQvX6tUaxUApJ4cJith37tQ0fAK6jL7JpD2g167VvicWg6mqSjOXpPR0wnLABRxCJAKB\nvo/PtGzfjpTnnmPZQFNZGRNNAYDk559XxUVARJ/SRo+G9eBBhPr3J5kwjoVITkvTMI3wZj9wgASb\nIPPcVFXF5iK9H9cXXyC7XTvS+MxDSzgxrIrXXkPxjh2wnjoFq06q2qTQiFELDhqEWKtWKN6xgzVx\nCnpIA6Va5BQJbfv2wUI1CMxmhLt3R+kHH0CsV8947+HHWjcPHbt2MWgDQKjfHNu2Ean2GiqjWRxd\nn33bNvbeSOvWCPfqxWjmAF02VBQNncaE1UuD/dyrVBr09yT4/cjs2ZPwc9dgyU8/jbRx49Rkjs7B\n1jsn7O+Uy9xiiYdKWCwMLhju0AGVDz+MYN++rNchc+BAjRx57PrrIVRVaan6ANZcSB1Ls56uE6SX\nxHLlCmKNGsE3bx5pMg6FYPntN5gvXULq+PHIuPNO2PT8yYcOwdauHTKGDEHtFi0g+P0oXb2aUbhq\nnGX985BlpE2eTLD3FG5w+bJG3ZNa+cKFKP7uO7L2uLEVolGCtxcE2HfuVHtWLBZW4dLLydO5W2rA\nHkN1OCpmz0bw7rsJRbEyX/zPPYei775DYOBAVDz/PEK33470UaNUrLTR2cnvZ9EoLL//Dkt+vsZP\nSXvoIbg2bIDz8881Z26scWP4Xn2V7GvX4ne3WhM62WJ2NsT69RkdJqNN5Cl5w2EWeFpPnVKrxnSt\nWK1x0GLRAD71/8r+9g42//A9y5bB8c03qKU4KEI4TAaZ2+woVR8sFsK7m51N3iOKQCyG5GefRVaX\nLkRhSpIgUNo93sEOhWC+ehXOTZs0myO1SKdO8HGUZmXvvw+fbqPjMXiG9lewPxyrR3a7dkgzwBrS\nCFrz2wZlPL2Zrl6F/dtv4fr4Yw1HZdXEiWqTgTLxg4MG4eqZM6iYPRvmP/5ATt26yOrSRcV0GWz8\n5vx8wjzyyiuALCOrQwfUuvFGQJFwdr/7Luw//BAni8sUoHw+tbSvc7SEP/+EUFGBou+/Zxy1rjVr\nkDRnDsnk8QpeiqPsf/ppjaysY/t2ZPbvj+y2beH45pu4BhDeedJzLptKSyGUl8P59dfq60bPmR5O\numfNc/q6Pv0UDqVJlr7Pvns3MgYNQpKSxabvj7ZqBUEQ0KdvBxws/gZbj63C0KJTkCUJi4IZeKhp\nf6yp1RqLM9rgxdqd8MR1fTB00W50fHQN3tp4BN+eLMBpVyaOOLNQKQK7k+vjkev6Ynn2DTjhzsLi\nnPb4athEnGndEVcbNkVZ/7s1XdnF332nuQ/rsWOoHjkSvgULNK/zypoyl2GkFmvcGAXHjjHnterB\nB5nD7Fq/njg03PixcWvfHsGRIxFt3ZrR0QEke2vlcMuRVq0QHDyY0QvGrTVl03du3gz3kiUwFRYi\n+aWXkPL003HBlFE1iBkfyJWVwa6IKxi+h/4/FwiUL16MwiNHWMAFAI5vv0XtZs2Qeg2RkpSnnoKb\nO2j1uHdzUREcO3fCVFmJqkceQcUrr7DGSZpNNkoUUMtSGJvi+OUpnpjuleEwHIoD5PzyS1ROmYJY\n48ZInTaNJSeSOPw0z6PrefNNVE6ZAv+zzyJWrx7Shw+Hc/169tz55nFAzeDKHCTN5PfDs3QpxKws\nSKmpEOvWRbhXL3jnzkX62LGwduwIYfduQjMaDmueo/ell2Dme110+6Wm+phI3lpnQjTKfoPKR3v4\nJI0kwXT1Kkz5+cjIy4uTu6+6/34EDfZ0/v5rNPoeWSZQB0VIKM5CIZh//RWutWvh2LZNdUyU+zIV\nFcGjNOH6Xn0Vgt+PtNGj2Zho8M600hiJkDGUZfUMEkVUPvssypVeIMp0Qa+RGs+kQ02PGQ/rhHUA\naBI0YoMGTLhMkCRYjx4lmc0TJ5D02mtImjNHTQ7peJod27dDvO46xHSZVgpx0JgRJ3h1dRw9KL0u\nZjzkhAtGHDyLjtnMWLwsFy/CduAA81HomIt16qBSoe3krXTNGsSaNkXGsGHI7NePBE2iCHNpKYRY\nDFJODqonTUKkY0fN5zTwJK7vhA+u6LnMV9nZvfv9mgqxUFmJ1ClTkD5mTHyQoJjl9Glkt2gB94cf\n4urFi5okCzWG29adra5165A2ejRy6tZFTuPGbJ5YLlyAVUkM0DWY1aMHo02sCcYIIDEL1X9gf3sM\ndpKenF+/0UWjKpl6ArOcOoWsPn0QbdECsQYNSEd9MBhHp0UhESafj1FHOTdvhlXpjJatVpSsX08a\ntZo2ZdimUN++pEHPbicCHg6HmgmpATd6TdM3Txhs6pXTpyN0xx0Q69eH9fhxpDzzDNu0bUpUrD/8\nLSdPsgNU0rGVRFu0ICp/11+vZmnMZtYtzDZ5UWTXxSLII0cgBIOkXMQdzPbdu9XsnyjC/tNPrKGE\nmveVVxDauxdCKIRo06awnjunZqD4sU1KglBZCdnpRKxpU5ZhNRcXI+nttxG+/XZNqZEu8Ejnzijt\n3Bne2bM1Qhh0fHjRCnZ/9Ds4p8vk8yG7TRuIek5j7v2WX34hAgNKxjfatClzgEK33YZgXh5shw+z\nw8q9ejX5oC5rFMdbzuNeBQG9y4kC5ZY2k/BKsQdCaQmGF52C6HDgtwkPocwfxM5fy/BnSRXmrVMC\nxY4kALUEZMRu4A47asUA0nOAdMARMWPmt6cwrGsTeJy2uCwx7TfQq27xm6VX53yTQTRByshAqFcv\niDk5BFJjMLdrYuEJjB5NMlVnz0LMytL8TZAkUnqNRhHp1AmVTz2F6tJSuD76CI5du9hBZT11Csmn\nTiGiBH4AkDZhAqFWW76cBOd6HmDeuGceGD0a6RyTDQBUTZrEgiPGmmA2w7Z7N2yHDiHcpQuiHTpo\n5o71+HEyRMXFf22PuIaljxmDUK9eKPvww/h95K809uoymqXr1hGlVyUoF8JhBm+w/vILSj/7DFJ2\nNoG0bNhAaL14ZoRHHkGqEkxZfv8dpcr8SJo7F/affkK4c+fEFF8JWCJCPXvCxynqaZRqjx+HUFGB\nWp07w1xYiDJOKdX90UcI3n03o0OrkapM9yzKli3TZLupCdGoum4N8N2moiJkt29PYIQ6+ffg3Xej\ncupUyAaMFQCuWZEUs7PVxkwOM1/xwgswVVYiOHQoe6/13DlkKv05AJA+ejTK3nuPOVLmwkJ4581D\ntHlz+N5+G66PP2bqfFJSEmSbDdHrr4dYty7rP7Dv2YOcRo1Q/PXX8YEZlLnCV8H4ypPBXKcZ7Fj9\n+oSWUYFs8UYrI2yP5n6XX1f2PXtg37MH4S5dSK+ObiwptElTYXI6UWFAl8kCPbNZW5HQS6WPHq1V\naeUp7ejv86JsIHObz9RnDByIknXrEOnSRaOAarQ3xurWJY3bHImDEAwis29fSG43CpSqL8+QFBg8\nWNOUze7HZFLZYBIk6iSvl8C1BAGV06ah4tVXkd2mDRCLqVBPvTAMFKz9ypUwVVTAdvAg3EuWxDOe\nmM2sd435HNz4OTh/hoeSmS9fBm65BSVffgkhHEYtPpjgnk/JZ58hQwlkYw0bEoIH/ln9l+xv72Ab\nMhZwRqO9Go1f7NwhwyYsjb4cDlz54w9kde2qyU7SicZnJ5gzpPAnu1avZt9n279fzYQmcrCtVkTa\nttXghuJMkiBUVhJKJoBNMPv330MIBhHq0QNi/fqs1Btr2BDhzp2RMn067Pv3Izh4MFInTICpvFzb\nmVvDRp36+OOkWaVbt7gGFwBsY7JcvowMqiqnvJYyfTqsv/yCom3bNDRVFr7LOMFvW0+fJk169euj\ndP16sjCUxZ7dsiUbW2n4cJiXLWPZPYpdS3rjDfZ74e7d4X/ySXiWLInLPhhtTKayMk20nvz003Bx\nXN+arCZXQos2b85Kc/T1lMceY5+tnDoVJRMmkGa0f/4TnmXLEO7ZE9GbbkLJpk2oXa9eHHeu+ddf\nVaycMlaMhYDbYHxz58I7bx5sR46gq7kSW135cG4nQaHkcKDgPoIPFyUJ63efx7ELJfjtfD4unLuM\nlFgIZ92ZsJkFNKoshluM4DdnGiosJMCsE6lEvi0JoYiImR/+jJkf/oy8TrlY2LcRyi0OpMZCKF25\nkjijBmqncnIyKqdM0YjRaEx5P++YG2V/k2fPRvLs2URo5tChOAefsm2Y9Yw7soz0oUNJCdZqhZSS\ngsKjR1lDi16WWuCCRevZszD5fOp7aqgGyTYbpKQkIvCicwpjjRppOIP5eWP/4QckvfMO/FYroh06\naNaXS5Enth09+p/jadmFypr/F0QRQiCAqokTERg6FGkTJybeE3QONs1+2WnVhR9LfUMkSDWGvl6y\nfr3mXvleF4F3ShMEVkJ1New7dqiy6hxLCUAqKklvvKF1agBCC6k4dqbKSoQ7dlT5irks/rUcbCEQ\nACQJssej6cPhLdqqlQb/aQRPAogjo4e+VT34YGLnGkC4Rw8mzV3x4otwrV0L65kzCAwbhooXXoCc\nmgrn2rVInTRJVfyUJFRTGkHedHPLcvEispQSfNU//qGpEtDvAYjTSBtggyNGEE57XaCQyasU8r+j\nPwuvoS7IhGUMGmuT5sxRExOACkXgHXaD58mcMd21eGfPRvD4cVRPnAj3mjXkqxJdHw8/4Cudut8L\njBzJ4KzpQ4cyyGesfn2WfEl67TU4uMqgbLfH00LSf9M9yG5n67LykUcIh/Ply+r48O83EKWjjYWS\nxwPXhg2QXC74Z84k7+V0OOiaEUIhwwZZMScHJr8fybNmIdaoEYqVpmkhFmP7gqm6GrbvvoOUlsYo\nFm0//sia8AHCHuOfORNVDz8MsV49JC1YoCESCAwbhvDNNwNWKyxnz8Kqq8rw0NnUxx+H7HYzPQFq\n0ebNNYFF5JZbcPXMGdh//pkkhGw2pKenAwYZ+v/E/vYO9rUsI0E5TWM89ok/BCQJsYYNteTv16D4\nca5fD+8//4lgXh7806ezTUKD8VJeK1u6lMgJG5iUmYmSr79G7fr1mQPFd/zS6zX/+afKTKLcR8r0\n6aQr9sABSFyEKCcnQ0xOVrHBZWVwfvMNJA7PHO7YUbO5xKksAhCqqmA5dw6Vjz8OKStL6zwYyA4z\nfCW/ERqMOaBsQtxGSTuD+XvWCypQPFzFSy/BXVTE3gcAkS5dEOnSBbY9e0gQQQ+C++4j4il8hl5X\nIqbm+ugjtYkrGtU0eYVvvRXV992nuT56jxpnXZKQ8vjjGsdczMhQca9GVQij5pnvv1chOjVksCNd\nu8KmSHLbDh1C1eTJkNLT4V6xggRc0SjhPzaZMLJNLfzjs/8hKod7SKNI8Q0dUD3jGTQcrq4fKSUF\ngs8HAQR69NGYqVi8+TgO/1qEjXt+w8Y9vwG3PoMegXw0PCuhbeYNuLXiEq78XorGnhSkejgqxATZ\n14KDB+NLrqgZrmAuLCSHRQLeU7am7XaEb70VYr16LPARolGCsefkceOc5VgsvnrA/VumbBiKlS1b\nhtCdd5L7oaqTiiAKM/39U7jX8eOwKVlq+luhu+6K68EAiLOm55WVPJ64ZtnyBQtIz0ZBAYL9+kEI\nhbTlamXOyTYbJKcTqRMnQojFUPrhhwj37o3A8OEwlZVBrF0bgbw8uDZuJBRoAKBbi8yUZ8GPpcnv\nR/qQIVraPJ7qU5Y1DjnLbskyU4qVLRYE774bkVtuQVaPHuy9Yu3a8CxbBvfKlXH3JYgiEAzC8ssv\nJIjS4z75JtcDB1D6+efIGDAAtsOHSZZU0UNgGO8BA+LEbwQA2Yoc85VLlxIyJ8lWK/wvvIDKxx4j\n7D6KQy2bzRBzcjTiSw5938Y1AqrIzTcz/YHqe+9lPMvVY8eyxmrb8eNwfvUVIrTpTE8dt28fYXqo\nAW4SGDVKVe7Vs8dwjpZtzx4GW4zVqwfZ41ETDmxAuAy23qk/fx62vXthO3o0jlgg1KsXqU5Kkspu\nxe2dQiAAk88HsVYtRDjaN825YzSeCfqTrOfPw/z++6iaOtXw2nmj32uqrIR7+XKI6ekwl5ZCrFUL\nZe+/jzRKCsCNvfnSJVjy81G4dy/EevVY3wvvXAd79yZntx4S8eGHiLZsicqnnoKpogKS0j8R7tyZ\n7PW6AIQGbqbyckK3C22wEOnUibAzhULIyc2FEIshWQnYqLI0L5gTUxhf9FYxZw6pPO3bB8vvv0N2\nu1H6wQcQJAlpSvIjW5mHsfr1UUT3X70CqtXKGhYBwKdcMxsXzserMugZinTsCHDsbe7ly+Mc7JKv\nvorLpsteL9vH/1/Z/zkHmzowsXr1tEpxnDm2boWpqAhSWhpCd92ljeKUSe/YuhVS7dooMlKHqqE0\na7l0CbYTJxDp1An+F15gr7Pu2dq1WaQq0wxVDRZt0wa2I0cgpaQg1LMnYg0bwqJgkqSsLM1GQDcY\nhm9LtAHQQ49iLZ1OIBRCuFMnlK5fD6sBrpw329GjyOrRA+Gbb4aUng7v88+jfPFiRG+6ydBBrVDG\nQeAWOlOb5MYcgCbjBBBlOr2DzRYz11AJkIyle+FC9j5TaSl7zprPACqTB2eZ/fvDevo0gnfeCSet\nCgDMuY62bAnYbGxzKXv/fYRuv13r2PFNIIqDVH3PPQj16YNkPQ+4yYSkOXMghEKsWUOD8TOb45un\nrNa4DLaRg6234NChCA4diqrJk+FesQLel18m2NRatVD68cdwUUU85YBOCVUBdoNmXfofsRju6tgI\nd3VshGMXivHYuztx/goJdL531QF+ugg0UUrMb/8Mm+lntM7NQucWORh7e3M0TUtDtcmKM+5MXLEl\noX/pOVS2ao1IVi1YzPHQhOrJk2EuKtLiVfnrCgbVSpMsE3hXOEyePYUqhcOwHj7MqhrqoMpsTUTa\ntUOVghNOeewx2E6c0GSw+YYY15o1gCDAN38+ZLcbtmPHELzrLuNNWXmOYnY2wt26xV1DtG1bXD1z\nBrW5g4QehGKdOoyOkA+4pexshO6+G5WnT8O2bx9iTZsSdiKzGalcQ1Vw5Ei416yBuaAA1RMnItKh\ng+YQovtF+fLlAIC0cePg2LYN6ffdh9I1a1hGMrtlS5h8Plw9cYJlUmmwqWd4kFwuiOnpkDweVMye\njWQlW289dkwzTy3nz7OMc/Izz2iaHWmmWQgG4fngAwBE9t1UWoqgTmiletw4DeacfFDNVnrefVeF\nI+mDNQOpdPpa2oMPoujbbxFr2RJigwYI9eyJUK9eGge76oEHVFYqgOzJDgfE7GwN9j3coQNCd95J\nHEMFukb36GD//vC98w6yc3PjcNdiRgZizZuzxEiNZjYz2kjZbifJE35f4EXClLHRj4VZ16ysN9lk\nYmJWejEVDUytulplpxKEuN+6kp9PGnYrK0miQ3d2ZAwYgHD37tpeFpCsLOXx9r74IusR0jhIyvVU\nPfwwhHAYmXfcgSqF+jDaogU5VxXBJ2qBwYPVdWkQYNB1QnnNKSuJ6+OP4X35ZQRGjiSaGWYzggMG\nwHL2rCahIns8CPXrh8hNNxHCAFkmIjM+H4N90MpA9T33sEw5Nee33yJ6441xZ6zriy/gf/ZZBJV+\nIwAIDh5MFEzLypDMUYXav/uOEQCYKipUhUQjX4HroaI4b/3ckC0WiA0bouSLL5Ct82UiHTtqGX2s\nVoR790ayQcN7jU2jBskVy+nTMP/5JxGEUhI/sstleK5LaWkI3XYbC1hZ9QZAwbFjJAPPzZ3MO+4A\nIhEUb9lCyAR++YWwYHHaHP8t+z/hYId69kRg1CikPPoo29Bq2ozSlOYSgETCtFRrPX+eCdO4P/kE\nsNlQMWdO/BcoE6Bi5kwkLVgAUzDIHBOK6Y1TEVI2topZs5CmcDF6li5VpVgTGD18Sj79lHBN0t+e\nPZtwiHKqWEw1yaDsozGdg80YOShsxWCxyYKAitmzkTJzpuqgm80wFxbCcuWKhg1Bb1EqQ8tVB2S3\nm+Abs7K016mHFOiiWUGStJAenXS83LIlxMGDEcvNheujj+CdNw+VU6Zce0zo94F0I5sqKyH4/UwM\nQMzIQPG332qaMiSPJy5ryrC0JhP7zcCIESSQ0tMVms1wf/ghTJWVuHr6NKonTiTiPK+8gsqpU1Ex\ndy5Spk+P+4yUmopI+/aMBq9y6lSI69cTWqVbbiEYtwRc7d5//lN7YEWjGqlf34IFSH30UQjBIGLN\nmqH89dfhWr8eob594eFwrK6NG4mqYP/+aNukCbbPG4JNu8/Ck38ZJXsOYfNvfmxPJZn2OmE/rtiS\ncOh8EQ6dL8LiTcfhdXtQ2u25uOtLn/IRZozogF431MeXey4gEI4hY89ubPFbcDmQiZy29yFiMiMr\nUo0hxafRyf8nksQwhGAQrjVrYD13DqHevZE2YQIi9euj6KeftSI35eVx+H5IEqs2+GfNYpSClJ4N\nsRgCI0dCiERYP4cgSeTA2r8f4W7dUDV1KlHNS2B0fYS6d0eFEe5c6WOQkpKYUyLIMsEym82qUpxS\npmUNVIKAyhkz4r7OtXYt7D//DIA4IRWzZsFUWYmokmX1vfwyk1J27NwJ1wcfIHzHHURUgi9B89le\nA6EZ2iQX4QR4ACDaoQMKlUy8S5dVFrkGVMf27Qj16oVQ7doaCkIApOR77hzsCv0WQILdpP/5H1jP\nnoWYlsbw3bLNhsopU5DyHJlTkRtuQOUTT8Dz9tuINWmixWfqm834PYbCZHioCqX5GzSI4Xy9c+ey\nREm4Wze1CmA2x+2n1PyzZjHVOMupU4ROsaAAkdatGU2Z0d7rf+EFBAcPjntdqKyETFU26eULAgTl\nmkv1VRPummS7HUXbt8fh7I0a5eNM4V1m/w0OpsZ/H+/YKxVhvWX07w/r+fPwT5/O4BLR3FwSaNls\nhs5VJcdbT59rxaxZGvgML4pkKiyE9ZdfkPrYY4i0aQPfq68i1qwZTCUliDVuDNlmg2/uXE2yS7rt\nNkRXroRPaYzNvuEGog57220oXb0aMR5mFInAVFGhUr4mJ6N88WIMVmrCAAAgAElEQVRYjxxhWhax\nevXgWrcO5osXGSZdkGV458xRFU0BteKcKFkiSYaYZ6bt8O23SHnySYi1a6Nq8mSkPfQQZEFAwaFD\nsO3bx9ZHtGVLbTAUDsO2Zw8cW7cCgkCSg2YzmU+ybChCBKiNnFLt2qh46SUy/3nsvEFm22Eg+JVI\nMIhZJKIRdvIsWQLX+vUof/11mAsK4J0/H5VTpqByxgyUrloF9/LlMJWWwnr6NIRQiFR9KfyKW5dG\n1VLLb7+RSpogwLlxI9wrVyJ4550w79kD6JMz/6H9n3CwYTIRyfLJk+FdsACV06YhOGCApoQIEDGG\nzNtv19BpmUpLiWKUMpEAIFanDiz5+Vp2CM5Y1uHuu2H/4Qc4fviBNNlFo6zbOmnRIkhZWai+/36k\nTp6sclT+myT3pWvXQqiuVqnw9OUeZQMSs7NRTkUGaNk2FEL6kCGQ7Xb43nqLOLYpKaqDTA8F2vGv\nhxwoVjF7NrkPTkyF/jZ1ODMGDkRg8GD4Fi1C4U8/oRaVrAVUJ5TLtEq1aqFcaSjyKPjo6pEjIWVm\natTy4sZLliElJ6Ns8WLSdKobD2nECEjDhsHTsSNstGNYFBEYORLhLl0gNmgQP8gA3IsXs/Kl2KgR\nadYCoZ7LvvFG9SDhyu+JWBzEtDTIKSmoePFFCNXVqkqlvvSlcCPz128uKID13DmYKioQGD48zsGW\nrVZEW7fWcHWa8/NJpsRkQnD4cNgOHUIGdyD7FUcKQJzjLYiixsHm6RDlpCQER4xAcMQIAITVgTfv\na68h1qQJYk2awGwyYeLU0TAXFsI/YwambiD46kKrG1nRapQ2bopP5y/Fu5uO48TFEpT6jbnkS/0h\nTH9f35SsQkvOpqqsJZ9nqtneW9/5CRPPn0Ho19/xs6sdylqNxD5vXdge+xhTB92I8b9eQOGLc9B0\n9fssCy9BwB5vXbQQ/bAeOorLzjRUvbUMmas7QhAEhPr0QSw3F2LdukwqOJPuKZSSEjA8RPQmZmUh\n1K2bRrHUyHgojOObb5D8/PNsXQGEwtGxaxfKlIxuwt/jnFihulotkSvG85IL4TBSZs5Eab16JLvK\nOzVGkCUjqfQaGiLDXbuq8DazGdEbb4T/iSdYRtn/9NOItWiBDIXPWEpJQfnChYg1boz0MWMMpbUl\ntxuFJ04g+Zln4F61imRrFdlz9rs9eiDcoweEykp4dYmS8K23wvfqq0gVBMg8HSHNfE6YwIS3jJIG\nod69mVIhBIFlXwVRRNq4cYg1aIBoixYwczAPjfhVfj7cq1Yh1KsXSrhqmX7vLfnkE8aLbjl1Cu4P\nP2TsOinPPYfyRYu0zjfdLxPxfFNH2GpFjCY++L/zojyNGpEqIJ+FBEiQlJmJyilTYDt8GMnTpyPa\nujVKV63SVDLi+lmMzj5lvL2vvYbSDz5AwcGDMFVUIOv228m5zM2rkk8+if8O5d+e995DrHFjVRWV\nU4PkP2M7fpztgZEuXVCUiAAhNxdSbi6ipaUwcf6C9ddfmV/g+PprmAoL4zngqSnrJNKmDUq++QaZ\nPXrAvn+/KnwnSZr1LptManDGrTGxdm0Ehg9H0sKFgCQhOGAAYrm58CxdqnJx0+RYNApzSQnMJSUM\nOialpcE7ezZcX3wBAAjk5cH3zjsw8XzsILAaz/vvQzaZ1Oq7Ao2KC36p0bNdEDQKs/oxAMg+JDud\n12xYZxU6Be7m+uwzmIuKUKr02wnV1bAq/OlCOKzKyCtrMNyzJ8I9e5J1q4xvuGdPwGolFdBr0RPT\n58jRijq3bAG2bAF0TFn/qf3/5mAXFBTgySefxIkTJ9C4cWPMmzcPTZo0iXuf/5lnEKNOE4+f0g2i\n75VXILtc8U6R2QwxNxfFW7Yw5oxIly6wrFuX0MEO9ekDobwcsssF38KFEAIBwpPtcsE7dy4rc9p3\n7kT1/fdrGrTSuIYSUXcgWA8fRtIbb6D6vvsg1q+PWNOmJMLioqziXbtIBkvBDtOMu4aGi07gaJQ1\nL1Ks09VTp1D+9tswFxSwDJeYmYlYvXpMxS7Svj2unjuH5GeegWvDBrYJ0LIoK31aLFqOXuq8WSws\now+ope7IDTcQVghelhxk8vvS0hBt0wYwmxHp3BklSpNDpF07IBKBd8ECUnobNAj2n35C7PrrSWaK\n/qbZDNdHH8Fy7BjkzEzG0wsAiMU0h5Dl7FlYLlxAtEkTiMo9W5VMNaBtitAsNkBLK2RwiIl16qCQ\n+y7e9NgyKSeHzUfHd9/B8ssvTOLYduSI5gAMDBxINkgjLLK+2VT/O5ySadycjkY1myc90MwFBbDt\n30+EQGIxpE6cqB4kmi/n1hPHhEGtVpSMV0oshLxOueh/cyP82m8UTJcuoWHIhwbhCkQFE0rrN0b1\niy/g26QGeHnFblypiqJD1RV0bN8E/p0/o0WwBE3bN4dt506EO3fGwZOX8Xlmc1SabfBZHPjxQjl+\nNLcGmrUGLkaADGXsygKYtuxHTFv2I4A6QPcXcUfZb0iOhXDMk43zrnTYpRiiggmSQO59yOKdmDGi\nIw5c1wnmpl1we6N6cAAIhKJY/I8XkGIButSuA6dubhiZ7cABpD74ICI33YQyruRrzs+H84svIObk\naNkPlIxQYMQIiNnZsP/8s2bORVu3JkGmbu+IswQKd+oFkGcUzc2F2KAByerqcebAtR1sPpMZDCJ9\n1CjITifKPv6YvUVs1AjBlBTiYCvfF+nSBVAcbEEUYTl5komOmHw+UtkTRUPnmr8Gyu0tiKKWnq+s\nDM4NGxCrVw/2AwdUZ5hdlAixfn3Iyjj65s9HylNPsb0pOGIE3KtWESYfg3XOKh4zZgCShBxOAZQ2\ny0batkXJ+vVImzCBlMD570lQUZNSUiBEo4g2bQr7/v1ImzSJ4I3r1yfNahcuINSrF8PmJj/3nGZv\nC+blQQiFiGqkz4fIzTdDys6G4PcTOAZ1lrnfz1Gy577XXtOcm0U//gihrAzWc+fg/f/Ie+9oKcqs\n7ftXVZ375OYkcs4giiCgICooGEBFnQGGYEYFBAODihEDOgZUZFRMYCIpiIoKA4qiBMkgOR3iyaFz\nrPr+qNDVfQ7O877v86x5v+/ba7mk+3RXV9111773vfe+ruvppw1sAJKE3LgxvkceIfOFF8icMwdv\n8+YEx41T2bfq6hASiRQtgkRxMVVLl9Lo6qtTBT/M1y9JqgCTXkExVQEBY6PR0H2QSktxLVlSL8BG\nEOrjN/4Xk1zpMYP+2j1vHvbNmwnq438uqsY0Cks5Lw+xtlZVNzSt24rb3WDmV7FYjGNlvP02jh9+\nIHD33VSsWkVB//6qMqk+txpYH6SqqlTfrSdRziGVrkuv2375xVjfGxKig1RazXTLnDUrRSa9uH17\nyn/66c9731GTCIooEm/dGtu2beqamEhg//FHsp5+GjknxwAyCubMdnrgnDYWkb59VfKB7t1VOkhB\noGzz5voBv8mnpTMS/XfbfyzAfvzxx+nQoQPvv/8+8+fPZ+rUqXyjS/eazD9pUvKFqT9SsduTvU6o\nQTEWS/0sojaA8Q4dkN1uxEDAaO9oqMxepJHelx48qPb8pH/AfJP1bIE2AWIdO6bweaY31Te66SaV\nN1YrYVZ8841KN2cKtNK/ows8mC0yYACxysr6bSpAweWXk2jaFNvWrWomeN48Ek2bImdnq4CSTZtU\nsIzbnUSxaw9eIj8fqaIC35Qp5Eyfrj745uvVHE+iaVPOHj9O/qBBWPftM46TLuEu1NSQM20awTFj\nCJqBgpDCxemfPJnAhAkokoRr8WI8Y8cm0eoOB2f37wdZJvvJJ5GWLEE2Z8+BjHnzCI0YoQYngHP5\ncjLfeAPfxIlqH53dnuJEUxgA0oIK0RTsRHs2QGP3Z6bNh7L160k0a4bju+8M8E7uffelsAa4Fi3C\nuWwZ5evWodjtaplcURoU/1DSe7Ib6tvWrF4GOx5PyWArDgfVH3ygKj7ecAOVn39OonXrFJaZ1IMr\n9f5drwXDdG6SKHJJuBRrXTJwsioyeY2yce3ZwYgrC7jhts6Uj5lA52AFli2ycV5BezPcVQepO+8W\nBv5lEE98+in2n37i5O0TmNPmQvZ+sRpXdSXnjRhEx7dfx5mIUWrL4PHzb+BsKHl/V+elCglERNVv\nZMQj+C12vlh/mC/WJ5HobRvn0K9zMWu2n+R0lVrBKPrpNHOyrFxmceKVRfQ751y0CNvWrYSHDCF6\n4YUItbVIFRX1VNykkhKynn+eSN++KQG2Hgz4HngAy9Gj8PrrKXMuvR3EumULYiBA9MILUwLMaM+e\nBuPIny1ogqLU43g3pJSBI744Hy/cTG6mg2mCRAakZqXMrEvxuJqhawDgJ5gziqgZ9GiPHmpQHY8b\npesU+7PFTcePaDzqkYsvJtGsGXWPP072zJlYSkrInTRJVfbVQcFmS3tG4i1bErz+eoR4nMZNmqAI\ngsGl3lClSsnKIlFYqDIunAOAa9u5k3iHDsQ6dcK+YQONRoygfN06NZFxjkxzmbbJ8GjALbG2Fsfq\n1ShWK5Iu9mI+H9MYORctQsnIwHLoEJ5RowBVdCRSVETWs8/i/vRTgrfcQvXcucR0DmEzoL26OvVa\nw2GUvDyiffpQ+d13ZM6aReabb5Lx5pv4HnxQbaFKu46ce+/FuWoVwZtvNuZfrEMH/HffrQJIFy/G\numdPMsli/j393+aqiGmuiZt/J/DjenL6XGBwXscEkTrJTpktg6Zy0hd5H38c78MPozid9QRq/h1R\nQbrJmZl4H3nEqIJ4Ro2i7Jdfkudmyh6nWBoAWH++LBqrkWvJEkOZ1HfvvQRHjVLbRxIJ5Lw85Kws\n1e+NGmX0aIt+P7bduwnprbBp43+ugLDB1p10didRNCr5WU88QYaGyQhfcQVSSQnp2xLflCn4Hn64\n4UGDBrPeihnUbLLIwIHJf+sZaFTVaPenn2L/7TcjIWg2IRrFqYl2Wf/4A8uhQ8i5uQ22fkSuvJLI\nlVeq5BClpaovEkVVUK6igtj556tz+hzz73/C/iMBtt/v57fffuPZZ5/FZrMxbtw45s6dy8GDB2n/\nJyVWQ/QhHifz9dcRKyuJ9uxJvE2bZPCSXu4zUdcER4/GtnmzUV4VKyqQjhxReyP1fkxZTiWCTz/3\ne+9FLiwka9YsHD/9RMacOcZvh4YPTwmw3VrPaNWCBeQ8/HA9erD8a68l1qYNFT//jHT4MDmPPUa8\nTZsU7k19cQyYOFfrNG7whlTApLIyI/udKCoy0LTOL78k94EHiDduTPn69WC3E77mGhItWxqKd/pu\nVs7KIta2bX2hh7QxqVq4ECEUqsdDrFvWiy/iXLkS58qVBogr3XImTkT0eqmZPRvy8pIUXA4Hgt9P\n7p13EhoxAsHvNxx6YsQIxDRwqnXPHiPA1p2RVF5Oo7/8hXjLlgagqva555L3GsDhIDR0qEFdpGcT\nI717o+TkkPXEE4hVVdTNmlWvHzLdat55RwU0Nm6cIsBgWHpGIR43qgrB8eMJjh/f8IHTMtjmgKr8\nhx+Id+2K46uvkM6eTWahNIt16ED4qqvIevll473wVVcR6ddPdWhmaiaHox6aX2hogWzIGgKSaab/\nlm3rVrJeeYW6J5+keyANTCMIapZSEMh+9lkS+fnUvvoqNe+9hxWYCjRaMBPb3u1UzBpD/sykZO81\nV99BbVY+zW8dzVFnLt/ntSUjEcU+5T769+vEyTum0KTkEO1DVXz6l/uYHGxGNJagZ7sCjpbWcfhM\nLYc1AGez/AwkUeR4mZebarLhkr/DFmj94CJaNHLj21FC+6oQti1Luf2SLVzyvga6TQukogqU2LNp\nfOIE4pkzKr4C1P7saBTZ40HWFlH7+vVkD76K8E03ERk3xigj2zZuNFiSyteuJd6iBTmPPqoGBE8/\njeJwkDtlCq4lS6i+byJZb7zBql/2Udu7DxeOHcbuh2fidbh5+7cTRHoU0+HXcrpY97Cq8WBKLy3g\ncMJO3aLjxjnPvGAKmfEIrce8jiceInPoIPKPigzK70JfRcJ6DrCtXjWpXL48lXrOLLPd0EKmvRcT\nRLZlFLM9s5il+Z1pH6wif3sNLSc+w8Eu11EeVeCpz7np1iH00RbWBAISai+oOfAJX3YZjh9/VCka\nFYVEQkaSRINtyPXRR7gWLzY2BIn8/HoUZNnTp2PbtImauXOJ9umDTaPuivTrh//OO/GY+pgVQaDm\nrbcouPRSNQsYiZB7xx04v/tOvUQ9OAsGESsrUZxO5Px8tc3x4EFyZsyoH5QkEvjvvpuMd94hYgJe\nOVavNo5rDKF+7ZqPiHbvTtgMEE0TQ9Lt7IED9fAlvunTcfzwA+6PPyZw663I+flJ+lL9+U7jhY+3\nbIn/nnvwjB9PtGdPKlesSPJ7mzA0xmugKhgjt3174nke1l14BTW/HGRB0Xmsf3M7QTmDG4/upFVl\nBntPVLNxfx41/dVNZ+dwkAve/4X7rjuP5gVZ4HIRT8h8XOekusUAzvOXsiOjiH3fHeV6yUOLgiwS\nskJpdYAebfKxWyUEQVAVNLdtQ9HWPSU7G//EidjXrVMrSuGwOq7avHBp7XquJUtSGC7iTZoQ+Otf\ncS9cSN7Ikap+RJrpz4PcqBGJVq0oat8eMRDg7P79KcFrOjOG6PMh1NYSHjqUSP/+KBYL2dOmpYof\npXzBxKVtsSBWV+P4/nvqnnwyyVCkqzPG40ZwDWpcVbFuHdbffyfrhRcQa2rwTZmCEIup9IVDhxK7\n8MJ6P+k2VbF0y733XqPlqGbOHGy//krs/POTVYB0+3fVhkjEyGbbN22iYOBAfPfei8+0YXcuXIjj\nhx8I/eUvKgBdn6va3M189VUca9eqrEmDBiXXNI1i+X/S/iMBdklJCTabDZfLxahRo3j22Wdp3rw5\nR48erR9gy7Kh6BceMoTgjTcS69YN18KFWEpKqJw1C2w2XMuWEenTh2ivXoh1dVh37lTR2qYB1PuO\npMOHse7aheXUKQoHDFB5n3WZ4XRaojSTGzdWhSk0y/jnP40SvY5yV+x2FYn+7bfYtm5FiERU5ciG\nTBSx7NuHc+VK7OvXI/j9OH74AamkhPCQISnk8vVPpuGAp0H1OW3SWc6cQaqsJNGkSXInmUggHT1q\ncIRGBg0iPHw4jYYNw7Z1a7J9QZYRq6vVYFQQkD0e8q+8EhIJKtasqTdZG8qwp5v9l1+QKivV4ApS\nCOqdX3+NQ+uBNy80mANkfShMWTXBFDAa1645d/v69Ti/+orQ8OEEx49Hzsuj5r33kE6fVttOJInA\n6NG4P/2Uos6djTHxzpjRYIAtlpWR+fLLyI0a1RNcSQfipmdADIaVaFSVB7fZ6olPQAMZ7AaoEt0f\nf5yU29Us0qePAYQKjByJa9kybFu3qhk/8y5eHy+gnrtpoEVEt+ANNxh8puErrkCsrkY8ezZFKKF0\nxw4y3nwzJTuRHsQDiKEQrkWLVMq4qioca9bU3yynOU7d7CK0znNik2N0DZTTNaAudGdGDACHg/7h\nUiwhNdsyaunb3NSlC0IohG/cM1T1GsSXvx5mxcajXNSxiPuvP59gJM7Tn2xkxW+HCcdlJEXmaKmX\no6VesOSypVDdjH1yROGvHW8gIloYIkbJ/OMMa3eeZOuhMnYfKSfcdyr50QDXTXiVGZOuocXECUQG\nDKBm3jy2Hipj6vz9nBjwOHY5Tli04FgboXDXIiS3i79c2oHba46j52myZszAO2AgrkWLkLOy8D79\nNAFZoNzp4VtPe56d9TM14W7QpRsEgH/u0L7pBXIgJ4d1x6JwTJsjQjZYINNp5fy605TINkocOfgs\ndnZmaHiQDUcAife63Ezx/ghPbD7OWNHKj9mt+ebTjew+dJamOU7G/bGGoSs/o+att6i79jqW/rif\nbYfLETwX4+7VEc/WSmyODuQ2dXD/qY1qBS4uM2vx7yzv+yAByYbPkvQVOniWGsBTbLz/wfzdeKwg\n9XuIcpv6bLmqZC4Jx5C7j2FvUWsuau2hsqYlVpeDPRM/pcYf4bzWhbxy5yU0aZSB2/QMVs+bZ4AS\nQWVAESsrse7YgfXgQQSfj5xJk4zWOeuOHfUD3FBIBcBpx814773UqqMOTlu7lry77yZ09dXUzJtH\n9OKL1c31jBkGkNM4ZiJB6NprUdzupJodDWRQSVas/KKVqMWBmEgQT8h8sf4Qy347QptGLp61ZeKJ\nh9QeWauVRJMmKb7JF4zy/KLN+IJR3Ll9KW7dgksWfE3sWpnZB11U97qXO8otDIvG+VYuQCo6n2GR\nOC7UNpnaJs3Zld2C3oqCoijU+COsXr2d0tfepmWikF869SYiSuRvqiJ8+lc+XrMXsekoXA4b3h/K\nobNGw6a5mi/9TvhS17dIBo57FRd71+7n858OcFXPloDCT7tOEYxYoZVJCXBXBZ/vSmUmASiK+Jgw\noBV3Bw9je3M28XvvRRo/Htvvv6sYKFOwl1jwGZOq8yluOZBpOXW4d2zHp/U8C9XV2H/5BdnjIXTT\nTbgXLkSIRBqkvE0UFxMLh5NUt1p8UdS1K6D6RyU312Au0S3z9dfJfP11amfNIjhmDGJZmdFe2KDp\nlfrGjYn27UveuHHYtm0jMG5ckvddkhpkrtK/G+vVC/+ECXhuvRXXsmUkiopwf/wx8ebNyXnoIYRA\ngIo1a5JkC5r57rsP15dfqgkerX3SN3EioWuuqScOJFRXk/nqqwT/9jfiHTv+2xaNREMtKmnfse7f\nj3PVKpyrVqFIUhK/YhLKg2RcUP7TTwZQM9q7N2iCNv8T9h8JsEOhEG63m0AgwJEjR/B6vbjdbkIN\ntGx4PB7s2sSy5+YiP/00ktuNVXsv2+FAWL0ai1Ymiq5ejdK/P7FIBCoqwGpVCcRTDworVsDy5fDX\nv2LNyDA+I2iLt6eyEunxx1FatSKRVhIXzGhmSULUSq46xY1y/vmIX3yB0qYNwunT5GZkIJ6D9UGy\nWPC88w6Slp212GxkL16M9P33uHr0MM7HGY1itVrBPLnPMTklLRiXEgnjukRTX3RORoY6BgBlZViH\nDkXcm8wI5ml9chY9k6ZRJjnWrKGoWzfiTz1FQtv0WPbvR5BlPDk5qYFPOIxFAwwmhgxJ3oNQSP3P\n5QKHw6CDym3UCDweJC1Id+bmImt95fLFF2MxLQgWHVBqsszGjXFrvyFpAaldy0pLsmyMo72mBnHz\nZqyRCK5Bg1A0cKnllVeQFi0i9uGHyO+/j1xRgWjK4Oe6XMkxM5lQWYnts8+Q27XDptGdGX8rLq73\neYDETTchafROhQ89RPzJJ7GPHInSpAnRI0dUvu6tW9UesT59sE2bpp7jFVfg8XgQTbzk2ZmZKB4P\nVt1JvvkmwsmTWF56CUteHh6dxu7DD4lfcw2Zf/sbrrNnEbTPNzJRP9WjDxs+HPdFF+HS55CpYqLY\nbEjPPw/LlqE0b47lo4/wzJ2L1SSTDuD56SeEtI2WK22zmLj7bhSXC8trr+GoqVGvHcjKy0vpRRae\nfppYeTlZ3buTGDUKScugZLhcSOmy6h99hKe4GEQRKY2L165l+bMkiYymxUy9pYgHvftBPIVcqOI0\nFjx6IxW1QQLjb6f1D1+xvMcgSir9nNaClRJ7Nu817sknReocXQLwfOq8lBSZCpubD2wdWPvlCa4t\n6s/WUCecL6/m9wNn8AWjIErERHUB8IsS/too1EaZ+dkmZlsEep03FqccZ7dcwKkNFq7qNppGYpzf\npnzOkQo/XKS10IVTEwLFER9ihpuoK4NRTa1cWF3Cp3sqsCgyfUZeTUG3DmQ4bdxwSQds/frh27WX\n1+9/ifafzKNVqIYaq5OyRsV87OnCGnsRZ7Fzz0ebuUdnhlmZxCEsoj3dL5xA4W9+fl4+n0hMP5c8\ncOfBL6fA0QnadmJ660FcL1az5ZEvOXKmBuzqprVlppXWbZuwr6SSYqtMr+0/cyy/GR185bSrOkmJ\nI4c5TS+iKiaBLekLgoisCtghrw1EYdn+asjRMDu1qs/dcvAslz6s+tcLMgVadrkFUVE4s/gQ7p+q\nmXDdBQy6oBXud99FWr6co45cYk4PnukzWCPm0l100YI6xGAwhRECwHP4MNaRI43XrsWLUVqpQN34\n5MmInTrRqKSEY2drWVrck1ssdmKCnZwMBw6/HxmBnRmFnLBns6igK5uymtC1tpxGH2/GdtFAzsss\nZHRWDjarhDU9gQGsfHYey467+fZ4E8KXTOe8LRA4+CWHT6usEL8AH/V7EKuc4JqIhdavrcAfDJO5\nfBftm3lYvXA1q8+EqNNDAWcraN6KfxwH5qwHJHAX8MAZeODWD4HW0LE1zcNh2p3nYYevBVVv7YLz\nb6W1HKD2nk+o9ml+pHka7dl+P+xX1xlZAW8wSvumebRvmkd3N9z6/GQ+LuzO5swmdGmaQ9dJt9Gj\nTSHdOjSjzuJga2Yxbw+/h+Ungqz8/Zhx2GYFWQzt3YYdu4+Tfeo4uWdPcrRVZ47JNkLhKPlyhBLB\nSak9k6c2VbJEtDO9sDvOxT9yuiSOd89+op27srbDXxF8bamwuTm6N5dYY3V7uzpRwxN5Pi715OPx\neBAOHsR2773IF11E/JlnALCdPk1s9mysaRLm0qOPIvfpgwtwgeF39YpAXn4+wq5dKcG12TJOnsTp\n8YDme5XCQqKbNmFPCzwdGhOP8sYbuM47D9vkyertXL+e2NdfEw0GKREzeWrkEzTatZUBR7ejAAPq\nSrA5HHg8HmLxBD7BxhFHLkcs+VzuzkBGIMNuRzp7FsHvp+CZZ4jPng2mNchpsyGmJV9sjz2GpwFK\nPXHFCizz5+Nwu0m8/DKCx5OC5zKb3KcPrjvuQPnHPxBKSkiMG4c0fz5Olwubvi7E41jMNMCJBFl6\nrGCx4PF4KHNkI9izKHK51BjBvI6PHUti9WqCX35FoHnqmP532H8kwHY6nQQCAYqKitikcVUGAgFc\nabLdADOffRY9vLXMmUPc4cBiKncTiaSiiAcPJhIOq+UvjYmuPNcAACAASURBVIvUUHCUZSy33Yaw\nbRvxBQuSFFXmAEB/AKqrkb74ArlnT9Jz2UrbtsSfeALLM8+AKBJ/7TWEcBjr9denflDvjf0TUn9E\nMfX3TchWZNkg/JcWLIBQiLieaQfIyCD+yitY0nknGyLTN2c9EwmUigrEzZsRDh5MCa7jkycnA2Wd\noufSS4lMm4atY0eEmhosTz2FcOAA8Q8/VD8TiSDNnYs0dy7RH36AFi3A60XSUcHxOJbRo9W2DpcL\n4ehR5M6dib/7bhLE6PerYE/ttWXmTBTdiSQSKWMkLFxIYswYElOnYr3pJoSjRxG//hph/XrkUaOS\n5Ux9UxGLkZg2DXnsWIT16xE3bkTcuRPLlCmIGzageDzIumzwOZhWhEhE7cePxaC2VgVeZGfX2x2n\n2DmoJJWOHQ3pd2nRImQ9O687qcpKbJdfjlJcTPTYMZUZpqICWWv3kYcMQe7ZE3HrVmwXX0zirruS\nWejOnUHfADocWK++GmH/fqIHDiTnQwMKc7olbr0V6cMPUYqLiX/yCQQCiO+9B1lZRI8exa7zeNvt\niAcOkBg7FlnjhbY0IJYC9VuL5IsuInLiBJbHH0eaPx+lRQtjoyNqADKgHnhJNokH6EEMgPjrr+o5\n6n8rLkbWRHjUi9LAR126IJpAOcL69UjHjiEPGIB10iRVvtqElM/PdlJsiSEpMiN8RxFPpiqIjepR\nzM+bDhAVJb4t6ERlfmNG9G7JFZf1oFewjEZDBrExqylTOg1jG42Y0/QiNSrafhyAizo25psnr4eH\n/67OaUFk511TWLZqB+uLO7I7nslaPZur2XceDQhekWS76eov4/mq38mtLieBwIC6EgQ0KrKvk5RZ\no/r1Q9y2jejAiSg9uycPKklkJyI80iMX66sm8HD1YcbxC3FB5MW2lzG/5zUcKvVSEA8yfkQ/+j37\nd1YWd+HdRt3ZlVEEp9Vnt3OBmxGbV+JoXIh98n2smb2AXUImp+1ZREQLiyiAMzV4spwsaOqjhyNG\nge8M4vbVxGfNgupqbIumQRJDB8CM2p14/WGU/pdQtXEbWzOLuaz2OOuyWxDKySU69Br8551PS4fA\nz0++xtVVh7i4WSa3dr6R706rfnSbT2FbvsrSwUkvnPSyeusxMl02bosWcbrzzSwtSFWClBSZzoEK\nWoVryI2HscnqfIqIEtuXHCPR617scgKrkqBluJYr4hXsbNeJzXVtaflzFX988Cn73PnQ4Tru9gKj\nVAaeYotM6OJp1FpTcTdHnXlQDnytZnGnvbuGqy5sze2xDHz5nZEUhZP2LPa583mn8YWw7SQgYJUT\n7PRJ4KuhZVE29/3+FT87i/m6UQdiosTycgWWpnJDq2bBIcLlvdrQYd33nPZGOOj0sCOzmHGeKL1b\n5DFtu5eAItIlUE5EkDjs8nAit7WRdQY4KrpBC677tMnnvF++Y72nNbkXnsfoK7pSs2krZ1euoe/Z\nAygIXLDmS1q1U/2J9PLLWELVPH38JwASHW8mfrl6HyQU8uIhBtccZfBHD7Pn8Bnuef07yqoDfPzI\nMM5rU6i2fgDSrFlYnnoNkkuaeq8EiVV5bXiw/3j+qIUxnbSWhQDQqjGEgMMVyc2ZyTZIuQzt/jd6\n7oC/rdjKjdYgzQEsFqoDUQoB4dQppHSgLaTEJiVldfyj+SB6VpUwpnQnNiUBFgvx735AESRsSqJe\nBbFm/mfEZzxFnharlGbns/VUkN5z51Fw750pn43u2YPSpAnKvfepFTE5TnzgZazdepR3Npzgq71a\nEJ/VHXokn/+23giNpn7MwVNV6uaoz/0QAusBBUv/R7lzd5CXZIXjTg+5S1eoGJx08TmnE8XtTgK2\nzyWaFIkgaOJB1i5dEMrKiB4/jnXIEMQ08gBFy/LXEzkSRX7ZfYJv315K3fpNFMQCeNtdQ0IQaBWu\nZUBpkL7AMk8HZt0/n999XaFvV/p+eZxXupRyQbsiYvEES9bt480lv1B3tik1fabitdppgGDw/8j+\nIwF2ixYtiEQilJWVUVhYSDQa5cSJE7QyLZq6/d3M+ACEgkHMhfpASQk5Jv5egKq05nudii2Rn0+i\nRQtsR47grahAqqoiF4goCrXadwoFAQmILViAFRC3bkVq355Yt244Vq/Gd//9+KdMQbz+eoqeeQYZ\nqNR6f/Pbt8d68CDxQAAGDwat77i2spJCGjaltJSwoqA3OETtdpR4HCfgq6tD7tGDHE18JhKPG+ep\nmzB0KHanEzkvDyEWwzNmjDFREzabOhahELkrVqBD4UJLlxp9WemMH742bZAXLiRy5ZXkKQoOwOfz\nEYnH8bRrZ4iwRIJBak+fpshiQYhEsGhZVmnQIMrXr0f0etEKzcgHDhiiQIniYiRA3LsXm7ntY/x4\nohdeiGvhQqIXXohtyxaE48cBiEcixFEzALqFnE68hYXk2+1YAeX777GcOkV1x46IrVphHzKEcJMm\n5AJKNEplq1bQqhXu3bvRXUMMsANKPE44kcANBGprCVZV4QmHMedda8vLiRcUYN29m/whQ4h27Url\nDz8geb0UAolYzJh31u3bsRw/TrxZM9KbWYIjRuAbMoScNWuMlg6rBuSVEwmqqqoQ/X6KADkSoaqq\nioJYDBGo8XpJaL/RKJEwgHfR0lKkaBQbUOf3E+vXD3HXLhRBoFibm3WbN2OtrVXneyKB0q4dzv37\nU8B5NXPmqCU9vWLj9SIdOULhxInEW7Wi5vzzk/fUaoVp05AOHqRq/HjiVVUUN1ClSc/oAHiDQaKS\nhPO883AOGkTQ40EIhUjPd3iDQaLnoo+6915cublYt28nkZuLuWgpx+PUrVuH6PUS69YN24svIgQC\nWA4cIMsUYPPVV1hKSqh7+ml1LEWR+O23Y929GyUzE7upz18OhUivF10Ur+SyknUkiop4pEtLMj54\nDF+7qfhaD0Q4EyQ2fBj9ly9n/fEveWnUwxxe+TODmzqx9eiGy1fL+bf2ICrHyAn7cMXVsRuw/UcG\nH/qNmHiYNcPHsvPzlQQkG329JymMBliS35nGNpk2d46iz/TJ5MZDCKi0fVJdal+7uG4dNqeT4KhR\n1L30Eo30OeLzETONqz6XfH4/6ULduoDDI6c3MO77eZT/spmiTDtCt84UTz3AtaGTDKs5hDemcNSR\nS9ePZtMvXEb+4ofhOFRMH8X9Zf/CcuwY37fowe4LL0XctJkuvTrS9uUncTk0gPWNN2LZtAnvqVPq\nOTVwy7MDdeREwoSFKC38Z7nAr/JUN2/fjMqVycSDWFbG2AMr1BeVsGLoIAILX8Fqs/LNyHsIrlxN\nSLTQNOJlwxMvsnjjcY6creN1iqCgCEmRcSeieC2qb0wIIrszCtmd0YAXr46CO4lB2ZzVFCPHXVLN\nFgB3/ZY2gLNxEaxOCqN+cuJhegh+/vLMBHxj7yYiSpT+ZTSfVVrYf6qGpT/vZynnQZfz6h1n0vAe\njDu+iQ6LF7DilruJDx7MgG5NaN7tSR7yeqmZOIkSSwbrzh/I2UAMt93KnnXbOL37EMMqD9DDX8ol\ndSfwT/+WvEW/YtH8bkC0YrnoQqreWMrwF14i8t4CWoVriGZms6rPEGoramjXpxv785ow5OUn2O0u\noFnEi+PnVThEKHr/PhL5+ZQtVVvnnCUbyd2Z5O4+KyV9ZmZpacq6HonF1LVOUWicdr15ToVF04eg\nKAqCIFBtarHJCIfJor7ZlQTXVR2k21X5vLL2CEf2nyQiSrTNsZN78hhlTVvRfcJI2j8wEU/QS3Y8\nTLtQNXv/OMis6fNYWmtjq09i69zVPGUTmda8P79I3fn+ja0w8Cl6e08x2OJFbJmDiEL7YBXre/Tn\n29c2UB38mWb5mRw4VYPs6cZ7nm7c0/5aHIkYd7y/luW7nZy69HFciSh9ver890k2/JKNfa58lJFv\nYVcSFPWZwml7FvEZ6gxr11tdN7oGyjlpzyL44ho82S42nm1HvP9jZCYiWErsVL+vCss5rBJ/HdiB\n8K69nDh4gt3uQnwWO4dlO4f3qbGKKKjVBYCYIhCTrLxxPMEbvdV+cUFR6D3zG24f3pOxgoRdSeDt\n1o3E5ZdT1qYjh4ePIaOmiv3fbeOP2jhOm4Uaf5jurfK5pEtj2tfVkQ3E3vuAne5Cyu2N2fj0fDpK\nxdQ0cVFrcfBjTkty42GEwoG4XlpOh6xu5DRpTI7XzrY2V7F4q43TG7X+7+JkC5Vhiw+TM/Q5akMx\nOHAWKzL2eIwN5XDJ5PkU5bmo8UcIRfSWw+z6x/hvsv9IgJ2RkcEll1zCu+++y7Rp05g/fz5NmjRp\nEOCY+dZbf3osaxqoq0HTqckqKoxeKEUQkhKspuxo2ZYtFHXqlFRAQlVvjHXsiBCN1lfX0+l1Zs82\naItsaTsxM/do5ZdfIuflUaChahNNmqQwhyQaN04GPbKsgnPOPx/L8ePGcWy//opYV6fS3eTkGKAW\nIRCg/McfKbjsMhRJIt6iBbkTJuB78MEUwGJDPbC65d5/P7GOHam48spUkBIqwFMPsF1ffaWyoWhZ\nbh3tbzl5Us32artNOSeH8JAhZMybd87fBLBv3Ih940YUh4Pyzz6j2DQXbNu3G+AOuWtXxD17jPEP\njBuHdOYMto0bsZw6BbJMcPRogqNHI4RCRD7/HNncO23KKCjmCoPpWjNmz8auAZuMMdOrHWYlR/Px\ndPncsjJDfKD6/fcp3b1blad+4AGcK1YQufxylYd76VKKmzZNoVKSysoQq6vrA4sa4CL2Pv44GW+9\npd4DTdnNOB+brT7Nm9VqHM+1dCnhAQOoee21FMCWEA5j/9e/iPbpk+zRNFFRmcFgNXPnkq1zqTYg\nQhQcMcJQj6xnurCHiYPbsWJFvY81uvlmQkOHYt2/H+/DD6eCt4DgyJEwcmQKTaZ+/Jzp05NzxuGg\n9MAB3GlAWyWd/kkUsRw+jG3XLpU+0mQNlTAVlwvZ6STesqXRn6/jH+TGjQkNH45r+XKcpWeY1NFN\n3qvLCLUairR6IbadO6m4rj+xpk1Ssj16r7rl2DH6ZMOQk6lg3gv8Z0kUFhKoOkpWPLmhqcdJrJ+3\nuT3GxOIgBINJXt4/6YMMDRumKqTJMqLDTtFglUpN0em9YjGGBk4aPutMhyKUPZXG9627dxuVmfM/\nnUOfX38l54sNBAa0os5hYr/RfbHFkpLFi/bsSaxDB9yffWb4LZ0mL5Gbi1RTY4yfY8UKnMuW1Qdk\nRaNkJyIQijAkT8HWxWOU1Hte252JN/Vm66EyVj4+B8eZ09wRPEyXs0cos7rVzYsgcMjp4aQ9C79k\no3bsOPZlFtEsP4MB0ydikxPUurPIDPrZkNWUI8488uIhuoy9HnHuO/glGzdJVeScKmFbZjGtQzUs\nze9Mo6svp+/Hb9M46sOiyNS+/DLBrs1oXKbS3NW0u53bH76eknIvb63YyZHdR4gfPU5cEOmcLdH6\n6D6aZFi47uY7EIReeKdN5NrXXsP67gv4Jk827mv47rsoyMvjZtOQOP37yV3wQcowua68MuW1W44R\n0Y6RJchkhmvwTpuG//770fmVLHv20Eejvy2KalWVC5N97X8mKmbGdNQTjktj8NAt0q+fej4zZuBa\ntoy6mTNTecL/TU9vlqTwfFGAzCVqi2nommtwHv0XHIXaIa2Iz36CRqbqV6NsJ+808/Pmvz5m3sip\nfGUtZuP+Uh5rfUXKcTdnNWUzQEvTm1GgWu3L3neyGhGF1okAWfEwO+yNCEtW5qz8AzT+jqBkS+IP\n9GFQFDLjEXwWOyWOHCRFpkVBJiXlPg65VB+v/5+TNXCyRhUiQlE3iJpLHlm2mwc/eoLipo1wf3CA\n7EUf4Lt0IOUHSgh5A5Q8/RxZ/XrRefuvuCbdjzUrA78/zE53IXf1HcfBsEhmPEJYtLDpeA2bXv8X\n918yndbhGqo+PIArsZsS904Sza+B5sCn22jI8iwKF3cdyW/Zzaiyaimzg1HI6Qc5aR/+VasYFlwE\nBUA10KwYYuB2WLm9uYWuXy+i3OrGa7GjIFBrcfBNYSfOhlxkOKxMGt6Du0o24t6ynSe7XM27u2s4\nU6Vm2ds2zuHGi9vSLD8TT6aDnJxsCJxq8Lz/d+0/RtP3zDPP8PDDD9O7d2/atGnDa5oYyf+q/Wnj\nv26mwEBHpCKKKC4X8RYtUilfzCpnZtOC8MzZs7H/+CN1M2fifeghIzh2NEBQXvuPfxBv1y6Fek3O\nyyPerh2KzYYQjVK5bJlxDfHWrQncdhuZOlJZc046kEwvv2TNnIlt924qvvuOmIkDWXG7DSEAIZHA\noVHA1ZkUBiO9e6cAJhsKtqXSUiwHDxIYO5bgqFEqfzXUAzek9OS63QariSKKRq+ZWZ5e/WPD8u7J\nAZJTnGSkf39DXa/umWfIKCmBPXvIeO89xJoaat94A4DcO+9Mfl//KaeTKpOUrX5uhmmBrBgIYNNo\n6oR4PIWb13/PPcQ6d06CLdKYFAzZelnGc8stKb8lBINJhb40GjMUpUFVN+nYsSRtYzqo0RRERfv0\nwaExTFgOHSI4ZgzRXr1SGF10FT5QmRHMIhGOn38mlNbSlD1tGoIsU75mjXEOOmDLcvy48RzJWVkk\nWrXCeuBAyrX9VxhHKpYvN+ZTip2DWksHlemqeg2a3gLSty9Rlws5K8t4ZkDtLc+ZPNlgA9DNoOs0\nCzPp8yOdp9YUYNe+/LIa3AN1L74IQKbO/GO6jhTKRG08zCA5ne3HP2kS9o0bU69REIgMGJDKAqCZ\n99FHcZtaYmpeeQXX4sVYzpwhcskl9TaHhuCU3Y7sdJIxdy7Ob77BN3kyvr//nUjfviQKClTJYRMH\nM2BIVp+TUzcWI5GRYQTYuXfeiW/q1OTnzAwZspzcqKYFQsb7Fguxjh2pfeEFch55BMVqVSk4zz8f\n18KFBi2r+RhCIgGRCLatW1WgU3ZaRsp07+ybNlG1cCHFzZohmEDbPdsVclVoF7YjW6iZMwcmTjQ4\n3gGKo8mWnOo2dxO+RqUKbXy3SsmGVmi9vPYYlYsXo2RloQgCBU+qwXKsQwekrAz61qkL+H1nfof3\nfk89T20e6xR4GXPmEB48mBYFWbx0R3+gPwUXX4zl+HFq//EPch6eS6RXL6pMc1WnOwuMHp3im8x3\nL+fee+s9C+c0kxw9kHLfpJMnk9oSXbtiOXGivmiN+VBprZKWY8dAlnF/8gmx9u0JX6EGrQ4zYP4c\nrGCi36/OubSN77/lNU4kUtYg2bSmub74gsoVK+r1BPsefRQefZSxwKiEzNxXv2DvvzbRzxmhU1Em\n+0qqEGpq+K5VT3Y7G6H4A9jlOO1a5DP1zkG0Wb+G8Mtv0Oyay1BeeREUBVfLtrzStC9rclszuOYI\n95zZQpnVzSGXh6x4hMxEhNiDU2lRfpIWb80mKFo58OhTuPOycd9yPYe/+YnqjxezrUUXTm3dS9tQ\nNS3/+RK1gShXffsJLRa8z65xE9hTl2DIN59QGAtwNud5FCBw220ENLXrZldfje3sMbo+dCfhyy4j\n3qoVTjkOtbXkAJfWlfDLhAtQbh5NbjxMQLLy2jPzWLCjnJJyH3+YqjcWoHehA28kQbMWBfTd9Svh\nklOcsmdxKruALdlNqY7E+bqRSl3YJlRNk4iXji3z+S2nORkOKx2a5pGQZZrlZ5Kf7SIQjrL7eBUW\nUaC0JkhClrnvuh706VSEe9Uq8t7dRrxJE8Q6v0FIEJT38/tny2jsycDtsAI9iDGBGcBNJ6v5ZO0+\nLunShCEXtkyZGh6Ph/Xr/z8SYBcVFfGxuZ/4T0zPjoKafQPO2RgPYNuwASEaRTp9mvDll6dIcOrm\nWLWKWKdOqtJTOu1UQ1LiplYK286dKHY7fvNCojnHSN++RulfsViIavKsMa19RH/AjUXdZiPWtSuR\n/v0JDx5MvEsXwoMGQTxO1gsvYNu2rd5v/KkseBoVYKKwMMlz7fFQtWwZDrOyWAMm1tZScNll+CZP\nxrVwoZpV3rCB6EUXUffMM2SnSYKXr1mToiyIJBnnKHq9qQCO/0KAbf5EeOBA7L/8QrxpUwK3345r\n0SKDr1MqK8Oyb58aqPxXpNKB8NChBA4fxv3RRyn80dbDh1VltqNHDSCT97HH8N95Z+qmK60fTMnJ\nofbFF1FcLnLNnO2QImgT69YNIRRC1hU7z3WeVmu9DLY+9/9s8QjccYfxb+fSpVgOHjSqP5GLLsK+\nYQPRHj2IdehgBMZCmiSvESCb7lEK7Z/OFe71kjVzpvG244cfiB86ZPSVx5s2TaVCNJmcl5fspzdx\nkIevvtpoR2jI0ikuU0yvHmzYgDU3l7rnnksJsCGZgU7k5eGfOJHIwIG458/HtmdP0o+Y8Q8mq5k7\nF8uhQ0ZQGh42rP75afcqRblNC/TCl15KeMgQzu7bR97Ysdh/VwMrPcCOd+hA2ZYt5I0dmwQrCQKJ\n1q0JjhyJWFWF5cQJ5MxM4h06qMwFpgA79Ne/Gt8LjBlD+PLLydbAV+rAqNdUqekMZLz5Js5vviHz\njTcIXXONwb2tB51nSkqQSkqwHj5sCFjE9H5I44IF1bcIArVvvkkjjS3Aundvij+1HDpkyDDnTpqU\nFCFJ87lWDQeSc//9RC6/PClwYbUS7dNHpcvbuDE1wDZlOV2ffUaGPiZpYMCUuROPq4G+NteLevWi\n+p//JDxsGNELLkDOzEzSfWomu1wpDBFmYSezxVu2JDxkCLFu3VCyspA0PmSAyKWX4ps8meL0cdT/\n3r+/sTmufe01XEuWYN23D/dHH+G/7z7jcwZDVCBAIjcXOZ0i1SxIks6HrM3zhtguzmXmIB1IvW/m\n9VcQ6vm0M6dPqwI4Pp/K4Z62XueNH0/wr381/O0Zjckp1rmzoWbpNimaBkaPVsXHIMVHWXfvJmfq\nVGIdO+KfOJHanJx6CrkA/gkTCF93HeHrrsMVDCJ98AFyQYHB4KGPbbxtW6z79hkMLvZ//YvcyZMJ\nX345tXPm8OCV7ck4sgbF4cC1ZD56Xe3+1haqP/iM3FtvxblqFdV3fkCkyEnm8f1k+E4TsEv6PgzL\nHeOZ+fbbzDyeZBcrivppf/F5WA8cwFJyiorz25E7WW1/dckxCu8Zb3y23XWXwbUD6VteTtEFF6AI\nApVyJdZDu3Ae+gOrItOp9gw9NXVHoOE1x+SvxMpKMtLYzkJDhhDv1Qvx1x+xDhhAbjjMxH7NuHPM\nQPYcr8I17lYKSk8iKgrCN1+S0bo5WS+9hCJWkvnjRynHivTvz8bu/Shb/A058TCDao4iouDvfRfe\nJ+vT+Fn278e57Gt1M5BIqMxlJuIAPbkZb9OGROPGuHXMV/t2tGtSH2AJ0DHfxTvvPwIOBxWrVqmM\nQTt2qOrSgwY1+J3/E/t/hVR6cMwYoj164Pr8c6NFQXE6zxlge0aONP4Wb9mS8l9/pfaFF8h84w0j\nS5Sp9W2fvfLKeuIu+kSsmT2bXK2HtB7lXFrvsg5y8z75JPka6Mu1ZAkhLauZKC5WM1qSZATBitUK\nokj0oosMmVBQS+exLl0ouOoq7D//bLxvBPl/EkymB01yXl59IN65sotff03+ddclf89uRyovRzZf\na7qKoMtFvGNHtbVFDyglKTV4Naku6kwr57S0DHa2Hsjp77VJiojYtmyhYNAgwpdfniwx/psAXi4q\nIjR0KJZDh4h36QI/qLCGWKdOVKxeTdZTTyU/m5FRr6JhCGroGWyXi+Df/gaxGLmTJqFIErWzZ+Nc\nsiSldOm/7z647z6ynnqK7OnT8c6YkTK/dFMkSQ0qevZUKw2KQuWSJWTOnk2RJs5TN2OG+pvnMOeK\nFUbABckAw7ZjB74HHiDRpAmOtWuRc3Koff55nN99R2j4cDLmzFEz1bKM/ccfse7YgW1TEhSlOJ1U\nfvEF9vXryTRVnHSObT176nvkEULXX4/ju++M3nvjXEzz03LoEPlXXkmse3cqV6xoGChquobsRx5B\niESomzkzRXTFnDmXamoMCeHUA6hBl/fJJwnddBNgyl4pCoHRo8FiQTqmshOY+WbF8nL8U6bgb6Cf\n3LCGKAT197R7qlitKVUgPeiwHDumKuSZAh/9+pTMzHriMwDxzp2NVrSce+/Fd//9BEePVgOTRIJ4\nq1bJ9p94HNeCBQjhMIG77koVJmqIv1wQSLRpQ6JNGzI1zn09u2i2Mm3zn9KmJ4rqc6NZxvvvozgc\nhAcPTqoMknx+HF9/jVhZaWz8rEeOYD1yhHjLlmoAaRqvupkzjbYj7yOPEB40iOzHHiPRrFlKUJ3O\n9IHZJyYS9bKi+vwx5KNR/YF13z4AIldcYVD1Rfr2VVUqNYu3bm0Ii/imTCGksfKIpaUplYdEcXGD\niRuA8ODBVGsUr+qPJDcErgULUgJs3Q9GBgwgcOed9fydYKp2VS1ZAopicPy7PvmEnBkzGjwHswXG\njzcoZ9NpaxsUNNE/18DzW3DxxUjV1dS+8IJRvdGrknJ2dj1hrHjXrvjMmxBt3Q2MH0/dc88l3zcL\nhMViWPftw7pvH5bDh1PHEpVONDRiBJHLLlNP+/hxhK1bkTt0IHjTTUQuvphGt9yCffNm8gcOxPvo\no6pgiW6yrFIxahXk2HnnUfP220iHDxvaDPHmzXGsW4fnhhuSvkmWcX3xBRnaJsF47hpQn5QdDsRw\nGLmwEFmnObXZ6mldWPbvx/OXvyD4/VR/+CGNtEpa2ZYtuBcsIPP110nk5RHr0gUlbSNoOXIE+7p1\niNXV+KZORcnNTfEFcl46AoMk0UGTJtS+9BKCz0fC40ESRc5rnU9h4AxSUG0JK7OouKGMf/4zxQcY\nv3/4MJ1mzODSt15M/UMsppI5pMVUWTNn4vjpJ4R4nIy331Z/Y8MGoyNAcTiM5GtCB9/Dn5JKCLKM\n9cgRI6axr11L1iuvELn4YqTt26Fv33N+93/H/md1Iv+bTJEkQrfcgv+eewAIXXmlKmGbZmf1krjp\nwRe1gC44diyha64B1CyPETCnBaRAskf0+usNlbD0iSEIrwAAIABJREFUADvr8cfJ0sBg7nnzDMnQ\nc2UZqz/7jPKNG9UduCRR+/LL1DWgiGeYqbdXl4r3Pv64+p6OmK6owDNiBLm3345YXq5K2KYH2Dk5\n9dSg0gPsipUrKd2+HVdau41+zWI4TFGHDnhuvpnAXXdxxpSZ0R/AChP7A1pvp84Xrm8MfFOmENWc\nZ6RPH2pnzaL2H/9I+U1Bc2bVb7+NbN74aOMqX3UVMe08zT3UoWHD8E6blqKKabbMF14gb/x4LHv3\nEr3kEqoWL8b34IOUawG2ocplHr+0ccp+8EE8Ws9wPU5s08IWuvFGqj//vH6pGpDOnFE5dgMBQjff\nXF+KVtt0Va5Yoba3aJkhl6nVJfvZZyk2XWetJkmtWzpwNSWDF40mN5SKQnDcOKoWLlRbHrRNqXPF\nCuxr1pD18stYd+wwvlrUqRONRowwRHvSLdqrF2UbNmBfs4bce+5pUH5XiEax//QThd27kzd+vLoR\nTpMarnn11frfi0RwLluGa9Gieg40fNllRE6cIKGVqxsyp0btaK7eRHv1wn/HHUR796bupZdUgaeG\nnt//ghhBvHVrwgMGkNCZizhHVtu8oLlcSGVlFFx2GXm33ZbCY16ZloFPt5gJoyD6fMS7diUycCBy\nQQFycbGqYGo6/5xHHiFLD1DOIZUumIMW44SVep9Lt3jz5kZbiCJJyE2apAhL1D37LNUffmg8W7H2\n7fFpNJ95EyaQM2MGvmnTqDTN8cgll1C2Zw81776bPBXT8xRv25Z4x45UffEF3sceS6ogaibn5FC6\nbRuxZcuSbERo90QQqDMHmg0syEFtEwbgv+MOqjRKSPuGDeTecQfSiRPqOZnH0izqUleX0moTuOuu\nBhMbFd9/bwSEYlUV2X//O9mmc6vXwpfuy9Pnph4ISxLxdu2It29v+OiGqGIbEgkzr3WJJk3Ifugh\nEASqPv6YsM62ZD4X/TwaavPS5k/OI48gVlRQumULPp3KUxQbDurMX9fmnfujj1JxGmapdNP52nbv\nTvF3Z/fupXbOHCO4BvXeiDt3gstFonXrlPtmPXTISBTZV6/G9eGHSBp2o57ipzb28ZYtKd+wAcVm\nUxOAprYaMzaiQS0L1A2HV0/syDK+adOoee014k2b1vehioJUWYkYDhvBtSIIZLzzDpmvq6JXgbvu\nIta1K450Ott4HNfnn5Px/vvJ45rumdwArZ75nEMjRhAcPx7FfM/MSqF1dalJhTSTzp7FM3p0vfcz\nPvyQggEDjNdCdTW2TZuMKqjVhGlrZGprjPbuzdkTJ6hatAj/lClULVigfv8ciVf1gtL8mXav7L/+\nikWPr/4b7f/6DLZ3+vRkz6ZJyTG9n8t/xx0pu2zd7aQETNpkirdogZyRgRSJIESj9eTQQ8OGGZnU\nyoULEWIx5MJCvI8+SmGvXkjV1Th+/pn44cN4Z8xIERYoMO1842mgzZxJk7D9/jv+CROInX/+OQMV\n87kafa6YJo5etguFDIlr5/ffq6qQ//oX5WvX4vrkEzI++EDNmNlshAcMMHbW4SFDOHvwIPlXXonl\n+HEUiwXp1CmjxGKYyXGJfr+qxvfbbyky54YDURQVgKIRuINacgI1GxT429/UvmEtoK17+mniWrBt\nX7cOp1a+BhXEFBw9msjy5Ti1gEiRJLJmzsTi86Fo/NiGAEs8rjr+oUMhGsX99tskmjQh2ru3IYds\n27oV+4YN+O+6K+US6wUVpoczPaOqj0/Nm2+mAmtQVSuh4Q2WdPy4mp3bs8cI9Kx79yIXFRHr1s1A\n7UN9ajr1w+fABWiW7hidaY7VvOAIsZgRgNt//pnIoEFIR4+S/eSTWLSFJHPOHPw6XZ3NBsEgvqlT\nyfjnP9VzPAegLvO119TM9dq19aTD402b4n36aeItWmAvLVVbD7T2A0OYRh/vhq43Gq2XJbZt2oTl\n4EF1Pvbrl8oRfw4zL+iRK64gkpaZrXv6aXx+PxlvvYVzpSZW8ScBtnTqFI2uu45EcTGVK5PiFkJd\nHRk6u5H5nuo+qHlzsNsNMKqYJjYinT4NktSw0AKkjlFDFSkTRqDu+edxf/KJ6jNlOTXg/5MNhXve\nPDLnzDHekw4fJufhh0k0b06ttpiD2iYVuvZataqhHS903XUGUDznoYeQ8/KMqoD14MGUCgSoeAWl\n0MTScY6AvmL5cuybNhFv0wbnl18Sb9uW7Mcfx7ZlS+oHEwnkwkIsffsiRCJ4p08na9YsdY5ZrQTu\nuQfr/v3qxvVPpOYDo0cT79AhZUPr/O47nN99R6xLF6rfe4/cqVNVQTHzcUzPiF/rdwW1RUnOzQW7\nHevevSomQ5bJmjkTqbQUZxrYNz3DGx40SM1Ops/1UAixttZIKBm9yhUVFGmA3XTFypq33iLSty+W\nY8eSgGnUdrbQsGGEhg1T2X0mTSJ4ww2qKFk4jKC1/embDFBbESu//Za80aNxmEDH5qy9paRE3QDq\nlU5RJHDXXVj37iWk4UnqmWkcs594gkSLFsQ6dTINkFC/uqz5iURBQYNJDiMBoVWM6lXOtOfJvWAB\njrVrkyrK6c9Z+hzVW/m083F+801qu5H5mU3HeGjHspw4QeYrryDn5xO65RYiffrg+PlnvDoVbwO+\nV1AUow1LP57t11+RKipSrzs3N+mLEgmcX36ZgtdoaLOT0FsaGzDHypVGCxlA/rBhlGrVrHOtEeaN\ncO1zzyGEw2TPnImQSJD58su4Pv2U6AUX4Pz+e6N6ZQ6wUyrgafM53qKFur4LAoUXXEC8XTuqNJn1\n5EXKqd/9dz37/4f2f30G2z9pEpFLL1VfmCSjEx4P0Z49jc9FLr44pf/M6B0zPTwpva36ziwt45t/\nxRU4ly3Df//9oGVjEi1bqlk/hyMlsDcUA9PKIfpvp/fqSeXlWE6eJOexx8i/+mqyH30Up1ZiSrf0\nCSq73UbPZqRPH1XeO83JWo8coeCyy8j8xz8MKdTAyJEoTie+6dMJDx6MZf9+dXzc7mQ2zWo1MiWR\nPn0Ia7v9hpQYcydNAouFUn1B048hilQtWZICKrRoDtj5zTcEx49Xs8v6+Jl2xjVvvsnZQ4cIaZsT\n/br0knn1u+9S+e23OL7/HunTTw3SfV0BzawSmDFvHtkzZ5I3YQK2HTuwbd6Mfd26ZCYo/YHSWz70\n+aIFo4ExYwiZ2mXMZlYqBBBPnyZDz7Q1ECA7vv+evNtuI9OUmc3U+lYD48dTtmEDgdGjCQ4fnpIZ\nz3r2WfLGjMFy8GC9Y6bYOQCChpkz2LGYsclwf/450smTiNXVxkYNtKyFntHXyqKK02mMlZl5JN0U\nh6PBgCV0/fWEhwxRy5ZpC5WkSYYLpoWx6pNPiLdsSbxFC2reeAP/hAnJ500XX1q2TGUL2bgRvN4U\nYSDdzABf/+234/03JfJE27bEevRIeaYdP/yA67PPEHw+3B98QPYjj2DbtAmxshLB70cqL0dMpwb1\nerFp2X/zb+rPnE/LCipOJ7LLlZII8N13H41GjsRzyy1Y9uwxyrpmi7dtS0JfEP8kwEZR1JYtU6k/\npcJhAt2mvyeaFmjp5EkKL70U++bNKQueYWkguMiVVxIwtTFlP/po/e+YTLFYUhfMc2xqYr16qbLW\nP/1E7qRJOJcuTfHhsq6loOMXtLkv1tURHD4cqbSU4tatKejfX1VPpYHMJCBnZpIoKkL2eM6ZebT+\n8QeJNm2IacF3zrRpyfY/s58xyWWX7d5Nxc8/p7Y4JBJkvPtuveAatABbUdQ+4wceUM/H5cKZ1gbj\n/PZbii68ECEapXruXHUDp123caz0FpV4HLmwkGifPlR//DGBceNQrFYs+/fj/fvf1aRFWjti1nPP\nUdypEwWXXopnzBj1T04nwZEjsf32GzVz5lC5dCnl+rOofU92OBDCYbVF0zRXFJeLmnffJXzVVVh3\n7SLj1Vexm59j0zooVVSQf/XViBUV1M2axdnduwlde+052zXPdd/0+a9vXuKtWuHVKioAuaYMuz5O\nAI61a/HccAOuzz/XfigNAKr9rt4K41yxwpgPkX798N95J9Lp00jHjxsbJNnhIDx0aFJmPR7HtnMn\nFq09SV8P4m3bgqKcG4djfl5EUWXUSr9uE4jbPX9+CmYokZubSvYABMaOVQGe5zAhrZdfdjj+NIOd\nbqFhwwygvVRaSuZrryGVlxtJNR33YQbOyk4ngmkzYbZE27Z4n3yS4I03GoxcANLRo9hXrVLX0fQM\n9v/fA2yzKaYMdnj4cCpXrKDuqacI3nILcnFxMpgWxQaBjYniYqI9evw/7H1nmBRVGu5b1Xmme2Z6\nckAkq4CsBEkiCoIoKiIKKKCAgSSIsiAosioriqiIigEREQwImMAM6AqKSnINJCWI6DB5pme6p3NV\n3R9V59SpU9UzuLv3PrvPc78/uw7dXXWqTvjC+70vpLw8uvgcR45ACOkd4pTdIQVOufrdd1GjlfRs\nFRVIW73aSAMH0MnuW7YMuVdfDdeOHci+8UZTd3/666+bMLjEnBz9YO3atbT8HLznHoRmzjQcgMTs\nJ07AduoUJG2xJLVo3/P++/DPmoWMRx6BoE28xsmT0TBvHqTcXF2S3e2GVFiIZJs28LANEprZysth\nO34ccn4+yvfuRRWTeU5l7IFOsvCKwwEhFEL22LHwz5wJhWkkIpsPiXZdO3dCsdtpplceORLlP/xg\ngpcAKvaRXtdmg//WW5EzZoyeUeUWlOzzITJ0KOIa/RNxdGJ9+kDOz4fn7beRNX16aql7GMu4tatW\nmT/QxGYjZ2dDatkS9UuWIPDcc4bmQMfevXB//nmTDX7Vb74J6cwzkfb660hfsQJCQwOq3n8fkcsv\nR7xLF8geD6JXXkmrJUI8jmTnzki0a0efB3EwJO3aybZt6XOKa/K58a5dm29QhRaU8cIyWVkQwmHk\nXn45Crp3h4vBhwMqHID97dzRo5E1axaqN25E5ddfI3LttZBLSoxCOYDBORSOHjU0lQJA5aefIjJy\nJHVqG+bPN2f+UhkzBvf27ciaMwe2kyeRvmIF0teuRe6IEcgZPRr5WgbclAVj5xnz/xsnT0bNmjWU\nbgwwN50ltIyjvbQU+UOGIGfMGFXGu6ICmXPmwPf444hddBHqNPVa944dEDW4WHFJCXyPPALbr7+i\n/u9/V2FoikKfmRAMIjJqFHUKIYpw7NljKCcXl5SgoFs3Q4M1dSr4sUENwuTsbFS/9x7qNFYfdQDW\n8AnWGm+4AVJ+vpodZX43fc0a5GgwDdeOHcicPRtulvmCyUSxJWFSWRIkyYBfjVx+OQLPPYd4164q\nb//x4xADAcNZQMz71FPwrliBhvvuQ3DuXEPm0QpbGmScM9eXXyKvf38djgMtqIpEYDt5kmaYG+67\nD7XPPafu6U00ZguyrGKMf/gBaevXw/PBB0h/9VUDjSygO5PxXr0QvfpqNVsJWD73hnvuQdn+/Wql\nlrH6hx9GvGdP+JYvh03rnTAlqrjAJzhzJgLLliFnwgRk3nsvFL8f8T591P4WRaFrVtI0LmwnTqiN\n/R06UOgjMcePPyLjiScoDSNgnQkVIxE1QZSdDbjdJkiclJuLumXL0DB/vum7AHMeafu21KqVmsjr\n1cv4QVLJ0eBBAODavRui1scl5+YiMnQo7CdPwj9pkjXGXnsvUmEhFL8fOddcg4ILLkDkqqtwqrQU\n5ceOIXLNNbSPhax9cqZEB6oS8NlTpyK/Xz9DpdfqXgGkTriIIn2eLG1u47hxqNi/H+EbbkCiUyfI\nGRmoWb0akaFDkfHQQ3Br/QcGkyT4Z840/s1uR6YGdbFVVam6CsOGqZSRVrfT2Njk2ahYVDLFSMQA\nlxTCYeSMGoWsGTPoGWJKxGzejJyJE+F5993/n8G2soyFC5F5991Q0tMRHjHCgC9svO02hCZPhnPP\nHji/+Qaxvn0R69mTdgAnGWqy8IQJqP7wQ0Suv55O3JyxY42ZA66pg7fk2WcbMufpa9eayp1KWhoi\nmuqcc+9eiBUVtPx2OubasQNZ06cbf5M7BLLuvFOPtHmTJH2RkewOicK3baOd+OEbbkBoxgwo2dl6\nltRuR/3jj6Pyyy+R1DbFqMbZTSz/kkvU7H5RETIefRR5AwfCzjQyEotpDQOGDZDcj8MBIRaD+4sv\n4NRo+MiBSDLYJIJNX7PGEDApTifk3FyER49GcMYMVDPZHENUbbfrh6PmpLq+/BI5w4fDq2WTpdat\nUbdyJULTp8O+fz+SrVuj8YYb4L/zThR27Ii0jRuR9u67xiwyu5Emk8iaO1cfHiueQ6ypRZxMApIE\n544dcDINrQAo24RVoMPfi/epp5C5cCHE+nokunVD3UsvoX7RIoiRCLwrVtB34Th0CGJZmb4JaRk0\nAPqmw7BpRAcORMOCBWoAwh0gZI2xZj92TN04Nav65BPE+vaF9+WX4fzxR9jKy+k7igwZgup161D7\n8ssqQ8R33yHWu7cqmlJZaTw0ZBkSOZDJpswyHHDPWCosRLJzZ7XsqY3P9scfSF+5EsUlJcgbMMBQ\n4jaZhdOTM368MTPEYv24Z8NmmvIvuACeN99E4VlnwbNxI2KDBhm64XnjoWUA4Fu6FN5nn0X6G2/o\nzjCLnw6H6aHsW74cns2b0XjzzQhPmKBmyrXPFp17LmxlZahZtw4Vu3cj2bYtfE8/jezJk1V6Os1s\nFRUGTDifIQMAoa4OYlkZssePR2H37hAaG5HU2B8AjcGIDkqv/CWYRuX6xx9Hxb59ULxeyDk5kBi4\nEwmo7T//jPR164wMIkwmigSgldu3qzh67XqEplLu3BkJbc9mKwUN8+ej4vvvKTzBtW0bXJ9/DltZ\nGRy//AKxthaZ8+bRvgtAhcqxJlZX67AMABkPPwzHsWOGioPicsG5dy8K+vSBX9vXYxdfrDrCmZkG\niBh9dnl5aJgzR82sKgptziclex5KRrOyfDDOnWOKKKpBhd9vmYQi7zbt3XfVDC/fUM85RPFu3ZA8\n6yztx5k1oCgobtECYiQC2eulZ4n9t98ghMMILFlCA0RqjEPr0s7LyLBhtPeKfoyDzchZWXrGHFD5\n+SWJsv3Yfv8dRW3borikBGmvvEKdQEHLGru2bIFn/XpDpjTtlVdog7ep/+qJJ+DetAn2X3+lcyeV\ntoScnY1Eu3Y624v2PAt690YB4Wtn3lGaxqxGfi9y/fW0wdh+4oRxDTDGwn9YCE3kqquQJH0hNpu1\nQ0sq7vn5aBw3DmJDA9yffQb7H3/A+/zz8Lz7Lgq6d0ce2/jJrGdytsBuh12DtIaHD0fkmmtQ9/zz\nCDKOeOVnn9H1L4RCTWe6BQFBq4Z1dt8LBODauROunTtRcN55KDrjDFoRpb+tzXMhkYDi86Fy+3ZU\na0EDzxj0n7b/CQfb89ZbSH/9daS/9BKCs2YhPHq04QB07t2LzAULkD1pEgKPP4661atR++qrKN+z\nB1UpKOkaHnoIYY1ayuC8Enq5QAD+yZORycuQA6YmIb7hLdGpE+pWrkREawhJlaVOZe7Nm03RsBgM\n6jKkQJMTU5BlOiYKaeGk0un/b2hA3sUXU1ovdqMgmzZPBSXE47rTcvIkxRfzZew6gtNk7jUyahTC\nI0eqkTSHqSXlTFIRaNDKU1JurrFxdds2OL77DrDZEJw3z9DVz26+is2mVz20g1UIBODaswfpa9fC\nfvQoxJoaiOXl8LzzDvKHDIEQDKL+8ceRbNMGYn29jvO2aoYFAEWhjgjrOBg+wjl/sQsuoBWGrHnz\ngERChQRMmEA/Y2fk6wkWWLHZEO/aVS2LkvFyHNTstdjDNnLVVQhNmaJyBb/3Hj0MCy66CDkaxpDQ\nKSqiiFi/fgjOnIlEN0Y0gpk3sT59UP/II+q4mV6CXA5L6fz2Wx2GQ2AnzHuPk94A4rSFQjrOjl1n\ngoDINddQ+i7DWBncPzHaQKwo9Nk4jh6lhyulzASASARpr76qwg3I8xoxAvUPPGDINPNc3IZmGj4g\nZ9enxv8shkKW86iSbRCGufQKAM7vvoOXVEeY6gKBRKSvWkUhKYDqBDgIJR7U5AIxRRBUerKSEvXw\nsYKJcMZC48iayr32WhT26AH7sWOG+0I8DteWLUh06kQFe2xMWdcEydC+J5WUoGL/fpRrToRYVQUh\nEqHOpHfVKhR07470l16i7ELOXbsoi4fidAKiiLpnnkH4xhthKytD4qWXIDGUbYbnz/XxZE+ejJwb\nb6TPP/Nvf4Pj++8NEDTe0t58E/kMvRfpmZFatqTZbsfhwzr21OIZeziufkB16kJ33onQjBlqLwzf\nMMvv/xaQR//EicgfPJj+d2jiRJSdPEmZTqyMrKm09eshBAJmqj9uLzPAydj3yqzH8kOHVHrUG29E\nsm1bZE+ciLzhw02wKvY7pBnZVltLez/ox/j1Ybcj2akTKj/9FI1jxyLtnXfg/O47eDZsQMbChcgd\nNoyea4IsGxI+9v37kfnAA/DPmmVobM2aP79JTu/sadPgWb+evk9baallRTU6ZAiqtm83ERQAoN9l\nK0UkgDOcw4yDn2zdGuX//KepkkL6gwKLFhka/RVRRM0bb6By2zZIBQUITZliHgz7Tln4Djk7o1HY\nysvhOHAAmffcA/v+/YZ3Tc5cxWajQn5hDT4EAHC7qZOftmED7L/9hsabblJF9mw2Q7AY5BKLIS2J\nqLjdaNT2MPaMI9hzIRyGrbpafb/kGZM+FHZt2Gxqg7RWwY31708bxiWN/e0/af8TDjaNqt97DxkP\nP4zCbt2MjBfMZlOgHYiKxwO5uNjY8QqoZd0LLoDt5EkdFsFmRxksrueDD+C2wHUqHo/e+KAJQtSs\nWWO+79PAIVl+zyLjmTNmDHxaGQnQN1rLMpgs6yVhzQkwlLCTSQjBoBq5b9oEB9OkGWW6rWlDVrt2\nJihIOoc59v/1r8hguXeZfyPOR/4FF8C3bBnSNm5EYY8eyNEUs2xVVRBraxHv2hXxHj2g+P3wT5kC\nv5a5IId7xVdfITltGhzTpxv4UQHA/fHH8C1ebMASsxnshnvvRc3q1VQ4w1ZVhfQXX0R+//40+8Y+\nL9qwwmSGWMYPCiti3jHb+GUw7n0mOnSgv+vct48K6bBBY5YVS86RI6j+4APUrViBqNaXkDNmDPxT\nplgegIbmRlmm96y43SnL0o033ojo0KGIDRiA4N13I961K9Jeew2eN99EGXGktOuIlZW0itCkkWtp\n8yE6aJAJ4kPWnZ25hsI52ME77kAVW67UNtK0devgZMq7iiDobAfkPVpQY9mPHEH6iy/C8+GHyJo3\nz8DtHRswAI233tpkkw/rrNmqqlSsNHGkOHYOA3yNs2THjghpuPbGG29EHsvUYHlh7QBxOmmfB9to\nTT/GOAgNCxboGWXeSTqNfcpgRLiGsFNogXWWxiQihMPImTiR9mvwZv/1V6RrtFuWxvTK+BYtMvyG\nrbzc8NwJr7aUm6s6IoKARMeOSF+zBr7HH4c8bhzkUaOASEStODBrwstnUK2C6OZKyCkYC6SiItRr\n+6Hngw8M55VYXQ2xtFS/F+YatLmYpwclwUCK0jYVTWLGxwpmAZoDrFWnxOpq2I4dU51o1pjf9T7/\nPGy//67Ss8ViyB47Fk5exMjt1kkCYjHD86COkCwjMmIEpIIC+G+/Xc8w8sGGFQbfopLMZ7CJJTt3\nphALz7vvwn/XXfCuWGHUYdD4lInZamooq5KJrheqUrBUzIu1ayaKdAyOw4eRbgEPNGGmmf8m6865\n06jWCoCKJwFGB1vxeCDn56OGhWxpVrF7NyKjRhkgeIIkQWrbVoWKOp2IjBxpCCT4e6SJGptNX4fM\nukhfu1adV6yDHYtBzshQE408y41mybZtVerLgwchJJOUK17JzETZb7/Rfaxx8mT9O61bG1hxrJhz\nCKkEy7ZCqXS1+6dJshRrlfb+LFli+e//jv3XO9i+Rx4xdMOSxUkmveOnnyxJ5VOZ7Y8/1JKcJOkP\nnC0BaS+H8J7aamuR37cvxS2rF3UgPGaM+v9FEVJJCWKDBtEmPVt5OXKuv97A/0wssHgxda6SxcWI\nWZGbMxM+3rWrmf8aoBM5dv75qFm3DrWrVlFqL8fhw7AfP65OWm0hsHLS6S+/jKKzz0bOxIm63LVm\nQjxOIQnUIVEUSPn5BudbDIeBaNSAkzKVLV0uxHr3hq2yEpnz5plKoQ4GdpF79dUILF+O6k2bIOfk\nwP3xx3qJmmCEW7eGogn38A6i6/PP4XvmGZr9lN1utSFIu6dE166IXXqpkXGDidJpBpVTT6SbbjyO\n+ocfRqxfP2QsXowsgitj3klCYzfhjeXoDE2ZgvBNNxmyDDRzzapQcrhCAGZaLDKMmhpLtUdDuViS\naKZPOvNMJLp0MWXc6xcsQP3ixWqDL/mNeBxZc+eq4kJc57t3+XKkrV8POS/PwM6SZMYr+3z6pk3m\nhwbxMXT4c+8BgNk5czoNDU3x7t1VlgcOyykoiqGJrPall1C3YoXp95w//ojMBx+Eh2B7BQG+JUuQ\ne/nl8E+ciOIWLUxYV4NpcyXWqxfiXbuqWGktG6WkpRlL29pn7ceOwbdkiRnXqI3bxcGELM3iQLRy\nZH3Ll6OoRQv4CI1jiiykpdNfUoLKbdsMpfdk69aI9eyJeo0bGwyLDwBTaVasr0fd0qWUbjPRsSMt\nJ6esCIFzSux209h4bKbs9aLihx8oYxA/TuHAARS3a4e8yy4zOqAaa45j3z44vv9ez34xa8jJVAF4\nSs2GefModtY0howMRBhoCcE0E6x8Yc+etFmUOngOB1UINTWYa+ubBON8tVBJT1ebMrn9DQDCo0Yh\nsGgRrQgCaoKkoH9/pGuQBLG0FPaDBw1ZW++qVXDu2YPw2LHqnvzFFxDr62mFMXHWWWpTpAabspeW\nGthWeGdLrKvT5wgAY83JCHNoCqpp1XxP/41UoFOJ6UiScZ+12+nzt8pY1z/8sJG1hDVRbFKlODpw\noKXTTo1tROYsOH069UsM4yXJQC4olnJy1Izx6+PEAAAgAElEQVRwWprx81ac0NwzFSIR2vBLxmOr\nqYFNC9B42JGQSBh+o+a111B+6BAqd+7UnXLuGrVvvIEqLYsOWAT1DNkAcbZDs2YZq9wW+1fIouHe\nfvAgyvfuRR0J4skzS+FgRwcNUgkGTrc/50/Yf7+DzeACAdBuW0nDMIrNCZfwxr4kiwixRmP1YMUK\n+EwA+ztkQWfOnw+PdhjZT5yA68svTU1XgFoGrdUaDKywlvTeNAvdfjvFi5OxO/bsoWUlMRxGrH9/\nRC+7DPG//AUBDYMY69cP5QcO0GuwY3Ax4iH8Yst49FFkkuwpWQTJJOSSEtS+9hr9nG/pUhS3bWtc\nfPxBmJWFmrffRmTYMLqRpzL78eNw7mGkg1kHsqGBZrspVWMKTlIpNxdSdjaC996LZIcOiPfooVIU\nEseMd1J5xy6RgGf9eji0TCrZIIVYDLGLLtIrFxaZiFS4/djAgdSxiA4YgGSHDgg8+qjpcwKz+Vs6\n2Mw1g2xJU5IsHWywuEDGwU62bYu6FStQzWG7xWAQrm3bjMEki8Fkrz93rv7fimK8X5uNQivk7Gxd\n0Y7Mj6ZYL5hrFJx3HtJeew25l12mNrFwFr36atQvWYK4lTiAtmHn9+2LrOnTEe/VywQjURhsHrm2\n7eRJOH/80UQzyJuclgbZ74fs8UA64wzdsWEEiBIEmwrdCbUfOQLfU0/RAJ6a9mws9xp+aKwDSg5n\niyy0YrNBUBTdceHKujQTaOFg1z37LJLnnINkp07UQa7asgU1775LcYtWTUj8vdj/+INmlKo3b6YZ\nxiarexxvOH8Yk+vSwEqb++kvv4zsCRN0mjguC+o4fBhScTFt8CSMN7nXXYc8TSOhKUpMAmlovOEG\nnCotVeEbmsnp6QbWKL6ET96/4+hRODRsOM20aTCfxvHjDU3grEWuvBKBxYspLRov/JPo0gUV+/ZB\nzsmBf8oUlWlBG3/olltU/mLmnniO9syFC5E/eLAZ48thsIOzZ6P88GGcKi1F1eefQwiFDNzGQjSK\n4pISFJeUmL5ragTmHMtkp076M0yRwW4cNw7xPn2QdeedKOzUycg4wn4vhQmybPxNu53219gPHUK1\nRWaYCKfF+H2GyWBbWeSKKwCXC5nz5iH//PPh2rLFkA23nzwJ36JFcHMN9ME77zSKS7EZbG3PImuC\nNKYb1jAzd5JWwYH2G8Hp0xHr3VvtbyBnr/auPJs368EjHwwzEFE5M1NXJ2buizrGiQTc778PN6Ew\nTUHFWrNmDarfekvts7vmGoRHj1bH6nKhYc4chKZPh5yXh0TbthSGAqjiUIFFiwywyfRVqyAXFVHC\ngGSLFqpKdopAqeH++xF47jmgiWrlv2r/9Q42byRDSSaqif+0CROrqyl1HEQRcm4ukmecYXhhKUuC\nfBNVQQEaZs+minpWjWih6dNRf//9esc+oGbOtQmbkkaIuVayVSuKwSVOtY/p1DcwmLhcusoRrxTF\nM51oxvOJA6pDazt6FJHhw1H70kuGycubgd4tVfdyCjiCzEX3hq1KewZJsiFxNHuezZvV8jEdiLqx\nRkaMgK22lpbr6p94ArXr1tHnwrM7EEeKbDBCImHg2oxecgnqnnpK52m1ygISTOp11yGrObw93zTE\nG5Fgt8p8sNny7t1pN7WtogLhCRMQuu02w/dYzLB/2jTYysuhuFy6GAo3p33LliFn/HhDZYGUtsVI\nxHB4yRkZ+ruXZWMZ02aj43N/9hkNVmo2bED53r1GsQr2O8z4AUCMRpE1dy6cP/0Ex+HD5udBTJvD\nyTvuQHTQIEQHDaIHnxCNQoxG1XvkHWxyz2z5nXsmkaFDUff004YsVsP8+Sg/cgRV27ej/OhRFRpk\noeQosuInJMurzS3CB09MtuDrDSxahNBtt5n+zjp29fffj7onnqCOSZypohDZecrO43ZD9njg/OYb\nFLVrh2ytcpLo2hWRyy5TZcI7dVJVFNmyuIWDzo6Vfa7eJ5807F8Km+WTZT2p0RR7gHbIkmvEe/RA\ngC3fMop4gOY0xeNwfvUV3Fu3UmEQCAKEAwcgMhh3565dCGgqpMmSEpVqkXEgFLsdjSloKEkZ2orV\nR2xspHtJ/YIFZopPC8fPP2mSmiBioHSyz4fIVVcZhYIAJHr0QPjGG1XGHQDRFHuy+9NP4Xn/fbWh\nK0Uywrt0KbwrVqj/QTKOKZr0TO+efW+Kglwt8RG3aBZTRJEq7QEwZVNtXDCZOPdcBEnPkxWum73f\nUAhiIGAu+zcH6ZEkg1Os2Gy0Kdu1cyfi/ftD0rjpidW98ALKTpxAiGu4E0IhuLdu1decKKJ25Ura\nqEvuXaypgf3UKQiJBGo2bkQl41D7nnuOKoay98Ra/YMPouq99xBYtIhSFiteL2J9++pNeqygDVFf\nzMyEWFGhYsUZCyxdilOlpQjecw9NumRoiTmeglYqKECErEUy7kQCSno6alavRuKcc5BO5hKA4F//\nipo1a5Do0kVtLG3VShWTuusuIBajlRd+jInzz1cTJQ4HGh56CIGlS6F4vVA8HrUXYdo0BOfMQdWO\nHYhefbX+RYdDpQAmrFgwz5n4hRei9pVX0EjgV/8P7X/CwWYPNxrhawdSmgWPtCVPKwA3gyN2fP89\nooMHo+btt5Fg2RBYDBJrPC91YSFCd92lS1Zr32vUSnzEGidNQtVnnyGqNZsIzCFj2cUNIN6nDxon\nTICUl2dwpq2csgTP5JCKh1L77/IUzwYwksrnjhwJsbISmfPnU1l5AAizkxtq5iZMSqGpDs1UDjbH\nu2kFgYgRhScL3kpDGZDgQrUsjZCiQSXeuzdV9FREkR6u7q1bkejYEc69e1W1QACNY8YgdskliFx3\nnS52ZOFgE+YC5969JseJXrd7d0QHDaKZTivu3cCiRbqDTdQvNZnk5nCywdmz0fDAAzQbBsCQjbLV\n1EAqLFRhPlZwDNaYAyidUdJjnYQshprM+d13BmotqU0bSMXFSLZpQxl2IlddhUSXLpCLiiyDh2Tn\nzpAKC1M2FjkOHkTulVdacoKTZ2l/+mk49u1DaPp0fYyMgyCVlCB0yy0I3XorKj//nM4/6mCxDrb2\nPc9HH6mZk3POQeKcc1C5bZvpoAWYjCAL0dH+Fpw+HaEpU1B26BBtSjQJZc2cqb5/8gzz89WgafJk\n9fuTJ6Nx7Fg03H03oiTbCjWLH7n+evqcwyNHGgN6gO43lbt3o/zoUZrZcX31FcRTpxCaNg2BZ55B\nzoQJsB07hsqdO1VaRKgMC2I4DKmoCEVnnYU8RnFNzsmBVFiIGkagylZWZlzHTLCVPX485ee3mntC\nIADf4sUGOJLidEJq0wbhsWOpE6dwDjaSSXg+/BAebe0Rh18RRdgeecSg0CZIEi0VO44dQyHTxBvr\n1UtVw2xGXZA9zFmT8vMRmjwZsYEDdZo8zRKdOpmaWW2VlRAiERVi2K+fum5at0bdCy8gOH8+0l5/\nHXmDBiFr+nSaAKDzK1WAzmhBsBVIIRBQAw9FMQQIVkkRlsmFp+kzVE/YYJhtwNes/MgRKjxiuDfN\nsubMMX0n3qULgjNm0B4TJ9Ng2jh2LOIEIsgJhGVPmIC8/v0hFRQgysxR1uqefBKh6dMReOYZyMQp\ndjgoVI5UxQkTDoEEOX78EYUdO8L35JMo37MHdUuXquwcbdog7e23DTCi6NChegJBUSBEInBoDeu0\n8tK+PRruvtvyHuPnnmt2BB0OJM4/H+EJE+g5JLVqhZqNGxFkfsf12WdIe+UVCsMR6+tVRha2Ys2Z\nyCmgEjEoYsE77kDjrbeifPduRIhSbiIBOJ2I9+oF17ffwrdsGf28VFAA565dcH/wgSFoE0MhFLdp\nQ4P+ZrUbNPOsXw/v0qUQT52C0NioVvGtYC9WVT2r8VZVIa9/f0oBaj98WGWMaaKR+d+x/3olR0CT\nrXU6IVZVwff002r5rYlSUOY996Daii+SeanelSvh3LdP5SJlqPyog+3xoG7JEmSTw/R0ImOo5YZ0\nrczk3roVjVrXrpSfj+QZZ0BxuShbRqoMdvSKKxAdMkSVh2X4aennLUQh6H9yHJD0u83AGAC1ibBY\nOzwUux1iOKwStrNiBdz3pTPPRLx7dzi//Zaq0pksxYRnnUEAxtKwIECA3h1NHWjmXSlcNhpQHX5A\nyzZZsEvI2dmIDB8OMRBAsk0b+vdkq1ao2roV+X37Uqy44vWaggbBIgAL33AD7QOwYoAAQEt+mXPm\nwLl3Lxruvx91y5ap79ThQLxXL8PzS3bogFifPoiffz7KDh1SITna2AOPPkoJ+ps0bg7UvvSSISBT\n0tJQv2ABXDt2IDJqFLzLl6vZFFmGc/duOL/+GnY2oyHLqH7rLTgOHlSdIM28L7xggFQEnniCjoXK\nGzfB9cv+PqCq3dk4jCmgbv6WnODMhmurq4N/8mSER45UnzkDY5HatEED04hLGgMVpxONY8eqGR8i\nXsQcSmJNDQJMkGlpFhlsQ7DrckFxuRAeMwbel16iQR61WMzIgKPNY7moyFguZsx+8CByRo1C8qyz\nUP/II2oZtH17JLp3h9DQgFwS+CqKSkMWCKgYX7Y8S9amlUw6QOW+wyNGwPfss4bnX2fRqChnZZkc\n7Ojgwar6rkVAzJqtstIQzEt+v2GPqH3jDSAWg5KVhbJBgwCbDdkTJxqFdKBKLwOqI2zj98d43AxV\nIONZvhxycTGEUAjRgQMptWqsTx/aDxK84w5Dj0Jk6FBaYQyPHq1zYsfjhjUi+3zWa0AQEB0yBFHi\nvDCWtmEDHIcOwXHoEBJ/+YvqXDZDI8s6wnXLl0NIJJA84wykvfcesmbPRuMNNxhZoSxwwIGnnqLM\nQqbrpTgHBc7BDt1yC4RIBEWdO0N2u1F+7BjFapNna9VAnOjRAwlCXwfQalt04EDUs1UMbr7af/kF\n9t9+Q/att6LhgQfgZnoZGubPV2ECDO93ctEiCNXVSLZsicZbbkHWvffC+dNPyLv4YjSOH28IGqEo\nVAZcLi5GZPRoREaPhlhVRdlsZJ8PjkOH4L/lFn0fl2U4fvxR7z0i5zcnK08pDH/9FXJBgaX6JH3O\nkQjye/eGrboa1Rs20PdUs349fIsWwbNlC4J33IFEx44mxx4A0jT2rMabboLUrh3qFy9G1t1304Zz\nE8+71gMhl5Sg8dZbEevfH/FevdR9UnOg2bPQVlEBn8Y3n8ri3boZqI4p5MTtNu0/6a+/Due+fYhf\neCGyRo6E/cQJVHz5pSpxz5hUWIhEu3Yq/KopqfR4HI5jxyBpe5Fz925kzZ+PeJcuEH/+GejdO/V3\n/wX7n8hgQxTRePPNCM6di/I9e1CRAhZCmvxSZlJJY2DPnpQ2xtRswzQNRa++mmYS+W5g3xNPIGvm\nTDWikmU9gk+xAdUvWYLKb79F7OKL1ZLnY4/pmd8m7lWQJDRqZTjSYctmv3KuvRb+qVNVSqtwOHUG\nm1HB5O1UaSlq1qyBlz0wHQ46UcXqahSefTbyLroIdStW4JTWsAOoiys8diwqv/4aoRSE8uSZGlT1\nJk1C/UMPoZqhqGIXqsmhIQ52r15Iko2WWYzRQYPQcPfdiPfuDcXlUg90JoLOnDsX2RMmQDx1CtGh\nQ1GzYQPCEyeiRhMRIMpnfGMgazmjR8M/fbqqqslwnxMeb6vv8Gb//XcVgiEIiIwciejVVyM6dKgp\nOAlNm4aat95CbPBgKBkZcDOd4Vlz56KIwffWkqwgZ6bslMWcaJwyBbVvvIHI8OF07O5PP4Xz22+R\nwbB8RC6/HMUtWyJn9GjEuE2IONfRwYNR/s9/InPePHMTKHOAe959FwVduiCDmQ8A6Nys4jJ9TY4J\nKhd+7ORJyBpvuq2iQm/qTQVvAJBs0wahW29F+Lrr0PDgg0aHnL1mc8E11AbXaP/+Bhwuj3MFNDab\nV15BgMn6AIBr+3ZkEmpBwFBGTmmyDFtdHcT6ejUgu/hiSCUlSHTpYuBjFxQFviefVHnS6+qMz5B/\nP/xYyd952k/OSPOSnJ0NiCLiWmZYEUXUrViB2pdfpgFEol07NDK4XdO9QK3cVOzfb2AVkLOzaQVE\nyc6GkpmJmo0bEVi2zCDZTH9j3jzTeIRoFFJxMervu88QYAMMlMbr1ZvYAdQ/8giCGvTLhDtn1xS7\n9mXZ0HcSufpqayES7v68Tz2FzL/+FbY//jBK2jOKuaZrscZksKXWrdUeHI+HsoUomZmGe6bQJBY2\nwWJ427ZF5uzZgN2OmrVrEe/Z0/KyQjisVhvy81F29KgayBJHR/u90LRpiA4YoEMOTmNdkXt1f/65\nEerAOdgkEBMbGylmOHb++ajYvVu9LieqowwaBPn666H4/YaAy3HkiC5wtn070lavVsVxAPMeQvp+\nsrNRqQVjzu+/N8AA2TPNQAjAjD3WqxfqNfrQ5hIRiiDQ+8sdNYqecY59+2gPWLx7d1Rt3UpZbNjr\nej76CN5Vq2iDb3jsWJQdOEDnu0nTg5mD8b59EZ4wAVJBAQrPPReFpJrAVu2YQIzyb3MWHTjQgNsu\n6tBBTexp700sL4dz927YfvtNTyrGYno/lEUSKzx2LD03UrGFAEzfA8fG4/zxR9ibUfn9V+y/3sFu\nmDdPLwsBKvUegycmmLTIpZfSBZ2q+YY2BrRsSRek6WU4HAhfcw3NMFV+8QUqdu40Mo1ApYVLe+st\nVU2RxRw6HIhrEXicc0RyRoxQo8+KCiQ6d6ZCKpbGiEPQLC4JBpgNwfXtt/Bs3ozC885D3qBBiF10\nESo//xwNHDtIrG9fFR7gdCJ0yy36AagFEJ6PPjJ0xCsOhw7HcTohBoNqg85331nij1OZ85tvILVu\njcCiRfQ9StnZaLj/fsT79kW8Tx/KQ8n+Fo/TNUAkLPCAsQEDEJo5E4nzztPlkZmOddfOnXBv3Wqm\neOIhH+x84JlKNIqquuXLDdkUluXG6hAVy8rg/vRTeJ96irIA2H79Fc49e0xsAKmsqc55E9SGGF/F\nSHGgubZsQc6111I8nnfVKtPhR3CrVjhlYu6tW6Gkp8Pz0Ud6U4sFx7IQicBWU2PaKOnmnKKyw4/J\n8f33SHv1VTUTnZ8PsBUREqBq1Re/BZ99smNHNDz4IDIeewxF7dpBrKhAaMYMVH34YZMZGOOPJFHQ\ntSs8mzejdt06nR1GluElQSI7d10uNWjiqjd8Zt5+/LiOJU5lTbAQALrIVui224yMDlYONq9wBsC9\naRNVsSMNfrbycgOdITHa1KrBTxpvvBENc+YgY8kSFLdsCd+jj9IeEsfRo4AFTMgwimaa1ewHDsDz\nzjtwfvMNCnr2RCYDA9EfQJKOu27ZMgrPkbOy0Dh1qomujJ2PZL+J9eunivFoAZFj/344fvwRRa1b\nI+eaa9CwYAHCo0ap32edXuadV69bp75zQYDk9yPWt6/eWyIIEOrqkPHgg/A+/TTcn3yC9DffVM8V\n9j1p/z/Wty/CI0aYhYoUBWJ5uZ7o0a5v//l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/URQhFxWp+FQmy2Yo3bK4UN4IF/0776Cw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\nRP0xi8y0xUKU2rZF6K67mrxv6YwzEJw9G8HZs5Fx//0qY8mfKIF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q7d1bimYoPY7mb78N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qWsgZQ33wRXUoKUpUtx6sQJ8CYTKl57DVlizY2S3lENjocfRs3Uqap6AtGQzPeQzNc1U6ei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\nLxSOsbxVNTWQDrVtcDAsH38Me2gov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+ "text": [ + "" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This time the filter does struggle. Notice that the previous example only computed 100 updates, whereas this example uses 1000. By my eye it takes the filter 400 or so iterations to become reasonable accurate, but maybe over 600 before the results are good. Kalman filters are good, but we cannot expect miracles. If we have extremely noisy data and extremely bad initial conditions, this is as good as it gets.\n", + "\n", + "Finally, let's make the suggest change of making our initial position guess just be the first sensor measurement." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_error = 30000\n", + "movement_error = 2\n", + "pos = None\n", + "\n", + "dog = DogSensor(0, velocity=movement, noise=sensor_error)\n", + "\n", + "zs = []\n", + "ps = []\n", + "\n", + "for i in range(1000):\n", + " Z = dog.sense()\n", + " zs.append(Z)\n", + " if pos == None:\n", + " pos = (Z, 500)\n", + " \n", + " pos = update(pos[0], pos[1], Z, sensor_error)\n", + " ps.append(pos[0])\n", + "\n", + " pos = predict(pos[0], pos[1], movement, movement_error)\n", + "\n", + "plt.plot(zs,c='r', linestyle='dashed', label='measurement')\n", + "plt.plot(ps, c='#004080', label='filter')\n", + "plt.legend(loc='best')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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g97tdIuMoW0LmgHiaLwg+PPMMAEBqrYqrz0hFRAr2oUOHcObMGYwcOdLzGs1YDLRaLcxm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\nZAMubcwYZBYWQhYsRR8P7ImAgTnm5k6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7/5m1zKXV+m9MRGBlakD4pmUFAM3mzci47TYk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Zypz8FO1jrpfoLLBa51a1UqV86998I/cqRqXcx66CHk9emDSL9+8kacFKM6tm2Dbe9ehPv2Raxn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\nItbVsc+gvVeRHj2UN2rulZ+jXrUUFcE7axZcy5fD9+yzKs0EWnGl5n32W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l/L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\ntH/jJfL27eTVbqM5a/M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NGyZCp0wLUmD0aKY26Ny50/BdNc1SUcGn06cNNR+x1q0RvPXW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dOJusWLUf3ppwieey6jwNj37IH14EHWFCQG+LyBECwWFhS7OV3xaMeOTNNZCoWQPm8eHBwP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\nihUkoOShXrtIl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bWykklGacAbzxg5IwrwfPABsmbORPO4cWhQnT4dW7fC9fXX8F9xhfkX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kZGQAoNfreeWVV4iJiaFbt26MGzeOb7/91nb/vn37kpiYSHh4OM888wzLly+ne/fuvPTS\nS3WeZ+DAgYSEhPDoo4/W2OkXICgoiI0bNzJhwgRCQ0MZM2YMWVlZNZ4nKCiICxcusGLFCoKCgggK\nCuKtVnCZ2RgYCIBu8GCFI6nFMiRBo9MpHEjbZoiMpGTlSkyWPFG71tJzbaWq2WHWjWU00KgNSUQr\nZenBtrvLp0qyfOBprl1TOBBRn8LCQmbPns39999PUlISW7duZf/+/axevZr+/fvzu9/9DmdnZzZs\n2EC7du1Ys2YNU6dO5cCBA3h4eHDlyhWioqJYsGABWq2WtLQ0Fi5cSKdOnRg4cCAA69atY9u2baxe\nvZquXbty7tw58vLybhlbQz3AixYtIjExkbCwME6dOmXboOW5554jMzOTVatW0bFjR7Zv384TTzzB\ngQMHuOeee9BoNPj6+rJhwwYmTpzI9OnT2bx5MxMmTOBPf/oTWq2WTz75hL///e+8+uqrxMTE8MMP\nP/Dcc8/h6+vLiBEjbDF88MEHvPbaa/j4+DBnzhyWLVvGxx9/DEBqaipGo5FRo0Yxfvx4Zs+eDYBH\na1hJx047lVwtfxB67NxJyapVCkcjWo1WdhVKVQW2o2U8mvO331I1bJjC0Qil2VYPkQLbxv2LLwBw\nzM9XOBLldezUqd7jv9zQc9uc2zeFVqslNjaW8vJyduzYQVxcHJWVlXz11VccOHCAEydOcOLECTpY\nVhlavnw527ZtY//+/YwbN47Y2Fhib9hw5Mknn+Tjjz/mq6++shXYeXl5BAYG8sgjjwDQqYHzqs3c\nQBE3b948hg4dCkDnzp0ByM7OJiUlhd27d9PLsuvaggUL2LFjB9u3b2fOnDkADBo0iD59+qDVahk0\naBDR0dFotVouXLiAVqvlrbfeYv78+YwfPx643ludlpbGxo0baxTY06dPp2/fvgBMnTqVlStX2tr8\n/PwAcHR0xNPTE39//9s6X1Ww04Kjcvx43HfvpkommAvRIFUV2LohQ3Dbv1/pMISdMFt7sGUmu1AJ\nNzc321fr966uruh0Ok6fPo3ZbCY+Pr7GfXQ6HectW2FXVlby9ttvs2/fPvLz8zEYDOh0OsLDw223\nnzx5MsnJyfTv35+HH36Yvn37MmbMGFyscxYayVrY3ui05VLuY489VifW3Nzc2zrfoqIi8vPzeeON\nN2pMTjQYDNx33301Hjc4ONj2ffv27SkpKWnSuaiO9aqtnfVgW/ceMHt5KRyIaE2q4uJwTU9Hb29z\nDppIVQW2vS5ZJJRhiI6m9H//l6paY0eFgMb3PLdkT3VjWXuPfXx8SE1NrdPevn174HqPdnp6OklJ\nSQQHB+Po6MgzzzyD6YaJ37179+bo0aOkp6dz6NAhFi9ezKZNm9i2bRtQ/1AQ000mjvv4+DTYtnPn\nTjw9PWsc8/b2vsmZXndjb/lf//pXW2+7lVOtte1r/9xWmHx9MQYG2joT7IZlDLZslS5akvHeewGo\nvqHDQM3U+a4lBbYAcHCgfN48paOwK0ZLz5/JUpAJ9QgPD6e0tBSDwUBoA1tfHz16lBkzZtiGbFRW\nVnLhwgUiavX4eHl5MWLECEaMGEFMTAxz5syhpKSE9u3b2wrm8vJy2+0vXLjQqFU4rD3m+fn5JCQk\nNOo8rfz9/bnnnnvIzc3lqaeeatJj3MjZ2RlDKxsuVj5rFmYHB5yys6lq4u/5jrCuu2xnG+AIdTNE\nRlK6aBGGBx9UOpQWoa5Xh7XXQwpsIeplsvQeVtXqERT2r3///kRHR/Pss8+SlpZGbm4uaWlpvPji\ni+Tk5ADXh0p8/vnnZGZmcubMGebPn4+x1iYTa9asYfv27WRlZXH27FlSUlLo1KmTrRfcx8eHrl27\nkmxZQzcjI4Mvv/yyUbGGhIQwduxYFi5cSGpqKrm5uRw5coSXX36ZI0eO3PbjzJ8/n7Vr17J27Vp+\n/vlnTp48yT//+U/Wr1/fqHjg+u8mLS2NS5cuodPp6vxe1MjxwgU8N2/G9euvlQ6lJgcHTB4emC3D\nfoRoCdU9elA+Zw5VgwYpHUqLkAJbiNbEzQ2jn5+t0Bb25cZe4trfazQaPvnkE2JjY1mwcV1rzgAA\nEYZJREFUYAEJCQm8+OKLAPj6+gKwdOlSPDw8GDt2LNOmTaNPnz5ERUXVeA5vb29Wr17N6NGjGT9+\nPJWVlWzYsKHGbf7xj3+QmppKZGQkb7zxBpMmTbplvLW98847TJw4kaVLl/Loo48yZ84cioqKbntS\nJcC0adN49dVX+fTTTxk6dChPPvkkaWlpdOvW7ab3qy+uv/zlLzg4ODBgwABCQ0N59913bzsOu2dn\nPcW60aP59exZSm6YbCqEqEmTmZlpZ7MnfpOXl0dYWJjtZ48NG3AsKODatGmtZt1H0TharRaAy5cv\nKxyJUEphYaFtlQ0hmkItOeS2dy9+M2dSOXw4xR9+qHQ4rYZ8jojatFot6enpdSZYN4eqxmB7r1yJ\n46VLVDz5pNKhCCGEEHeWTOwXQrXs67rTLZjtdNF9IYQQoqU5WJYj1FRVKRyJEKKxVFVg2+uuVkLY\nC8ecHHxnzsTnlVeUDkUI0UwemzYBv22ZLoRQDymwhWhFHEpKcN+7F5dDh5QORQjRTNWWnTP1siqQ\nEKqjrgLbOpP6JpsiCNGWWS8lO5SWKhyJEKLZpFNJCNVSVYHtZNku2OnsWYUjEcI+uaalAeCUna1w\nJEKIZpMCWwjVUlWBbd0S2+zlpXAkQtgp+SAWovWQAlsI1VJVgS1LFgkhhGgrTO3aYQwMxOzqqnQo\nQohGUtU62LKToxA3V929OwBmFxeFIxFCNJdu/Hg0lZVorl1TOhQhRCOpqgdbIwW2EDdl8vMDQN+3\nr8KRCCGayzE7G8/Nm3E9fFjpUIQQjaSqAlt6sIW4ObOLC0Y/P0ze3kqHIhpQVlbGzJkzCQsLIygo\niLfeeqtG+4IFC5gyZUqd+y1ZsoSgoCCCgoLqbRetkHzmCaFaqhoiUvHYY1T17091C+4VL0Rrou/X\nj/xTp5QOQ9zExx9/zLFjx9i+fTsdOnTA09OzRvsrr7yC0Wisc7+FCxeSmJjI+++/z8mTJxt8/IMH\nD/L4449z5MgROnXq1OLxi7vHetXW7KCuvjAhhMoKbM9163DOzKRyzBhM99yjdDhCCNFo2dnZdO/e\nnbCwsHrbvRpYJcnT0xNPT088PDww38aqErdzG2HnZGK/EKqlrj+LZckiIYRKLViwgKCgIDZv3szh\nw4dtwz2sQ0QWLlzYrCEgBw8eJCgoiMcffxyAuLg42+NdvHjRdrtLly4xe/ZswsPDiYiIYNasWVy6\ndKnGY23ZsoWgoCBOnz7NmDFjCAkJITY2loyMjGb8BkRjaSwbRml0OoUjEUI0lqp6sKXAFkLcjk5P\nrbljj31x46wm3W/58uUsWrSIJUuWcOnSJT744AMAPDw8AEhKSuKFF15gyZIlFBUVNfrxH3roIb7/\n/nuOHTvGrFmz2LNnDx07dgTAzzL5taKigilTphAREUFycjJOTk68/vrrTJ8+ndTUVDS1ekoXLVpE\nYmIiYWFhnDp1Cmdn5yadu2gat/37r38jPdhCqI4U2EIIcRd4e3vj7e2Nq6srTk5O+Pv712j38vLC\ny8sLV1fXJg3vcHZ2xt/fn3bt2gGg1WrrPMfOnTspKSnhvffesxXLf/vb34iOjub7778nKiqqxu3n\nzZvH0KFDAejcuXOjYxLNUx0Sguvhw+gfekjpUIQQjaTKAlsjBbYQ4iaa2svc2p06dYqysjLCw8Nr\nHNdoNJw/f75Ogd1XlntUlnQqCaFaqiqwHc+fB8Asl8uEEKJJQkNDWbduXZ3jtXu7AXx8fO5GSKIh\nUmALoVqqKrAL9+zB+T//oToiQulQhBCiyWqPdW5Mu6enJ7qbTHqzDv2orq6u09azZ0+2bduGt7e3\nbVy2sGPSmSSEaqlqFRFjcDC6ESOUDkMIIZql9hhrk8lEQUEBBQUF6HQ69Ho9hYWFFBQUYDAYaty2\nd+/eZGRkkJaWRkFBAddqbaPdpUsXHB0dSUlJoaysrEYxPnHiRAICApg1axbHjh3j3Llz7Nu3j9mz\nZ1NZWXnnTlg0icnHB2NgIGZ3d6VDEUI0kqoKbCGEUDuNRlOnh/rixYtER0cTHR3Nrl27OHHiBFFR\nUcTExHD8+PEat42Li2P27NnMnTuX6Oho3njjjRrtHTp0YOnSpWzcuJGIiAi6detmW6bP3d2d5ORk\nOnbsyIwZMxg8eDDLli0jICAAFxeXOnEKZen79UOXkCAFthAqpMnMzLTbwV15eXkNbsYg2iatVgvA\n5cuXFY5EKKWwsJAOHTooHYZQMbXkkOf779Nu+XLKn3mG0pdfVjqcVkM+R0RtWq2W9PR07mvBncKl\nB1sIIYSwR9ahRLJVuhCqI69aIYQQwg5pLFulm6XAFkJ15FUrhBBC2CNLgS2riQihPlJgCyGEEHZI\nU1Z2/WtFhcKRCCEaSwpsIYQQwg65nDwJgGNRkcKRCCEaSwpsIYSqmM1mTNZL50I0kslkqrMOub0y\nWLa0N0RGKhyJEKKxpMAWQqiKr68vBQUFUmSLRrNu6OPr66t0KLdHtkoXQrVUtVW6EEI4Ozuj1Wop\nKiqybYbi5HT9ray+7cFF21U7L8xmM1qt1radvL0zS4EthGpJgS2EUB1nZ2cCAgJsP8vGEaI+qs8L\nKbCFUK1mDRFZv349CQkJREVFMWnSpBrj2j766CPi4+OJjY1lxYoVNe535MgRhg8fTlRUFHPnzqW8\nvLw5YQghhBCtjtnLC2NgIGYPD6VDEUI0UpML7N27d7N+/XpWrVrFd999x2uvvWa7XPvDDz+watUq\nPvroI7744gt2795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+ "text": [ + "" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This simple change significantly improves the results. On some runs it takes 200 iterations or so to settle to a good solution, but other runs it converges very rapidly. This all depends on whether the initial measurement $Z$ had a small amount or large amount of noise. \n", + "\n", + "200 iterations may seem like a lot, but the amount of noise we are injecting is truly huge. In the real world we use sensors like thermometers, laser rangefinders, GPS satellites, computer vision, and so on. None have the enormous error as shown here. A reasonable value for the variance for a cheap thermometer might be 10, for example, and our code is using 30,000 for the variance. " + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Exercise: Interactive Plots" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Implement the Kalman filter using IPython Notebook's animation features to allow you to modify the various constants in real time using sliders. Refer to the section **Interactive Gaussians** in the Gaussian chapter to see how to do this. You will use the `interact()` function to call a calculation and plotting function. Each parameter passed into `interact()` automatically gets a slider created for it. I have built the boilerplate for this; just fill in the required code." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from IPython.html.widgets import interact, interactive, fixed\n", + "import IPython.html.widgets as widgets\n", + "def plot_kalman_filter(start_pos, sensor_noise, movement, movement_noise, noise_scale):\n", + " # your code goes here\n", + " pass\n", + "\n", + "interact(plot_kalman_filter,\n", + " start_pos=(-10,10), \n", + " sensor_noise=widgets.IntSliderWidget(value=5,min=0,max=100), \n", + " movement=widgets.FloatSliderWidget(value=1,min=-2.,max=2.), \n", + " movement_noise=widgets.FloatSliderWidget(value=5,min=0,max=100.),\n", + " noise_scale=widgets.FloatSliderWidget(value=1,min=0,max=2.))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 28, + "text": [ + "" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "######Solution\n", + "One possible solution follows." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "zs = np.zeros(100)\n", + "ps = np.zeros(100)\n", + "def plot_kalman_filter(start_pos, sensor_noise, movement, movement_noise,noise_scale):\n", + " dog = DogSensor(start_pos, velocity=movement, noise=sensor_noise)\n", + " random.seed(303)\n", + " pos = (0,100)\n", + "\n", + " for i in range(100):\n", + " Z = dog.sense() + random.randn()*noise_scale\n", + " zs[i] = Z\n", + "\n", + " pos = update(pos[0], pos[1], Z, sensor_error)\n", + " ps[i] = pos[0]\n", + "\n", + " pos = predict(pos[0], pos[1], movement + random.randn()*movement_noise, movement_noise)\n", + "\n", + " plt.plot(zs,c='r', linestyle='dashed', label='measurement')\n", + " plt.plot(ps, c='#004080', label='filter')\n", + " plt.legend(loc='best')\n", + " plt.show()\n", + "\n", + "interact(plot_kalman_filter,\n", + " start_pos=(-10,10), \n", + " sensor_noise=widgets.IntSliderWidget(value=5,min=0,max=100), \n", + " movement=widgets.FloatSliderWidget(value=1,min=-2.,max=2.), \n", + " movement_noise=widgets.FloatSliderWidget(value=2,min=0,max=100.),\n", + " noise_scale=widgets.FloatSliderWidget(value=1,min=0,max=20.))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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sevbsCUCrVq2oXbs2Bw8epF69esTExNC0aVMAYmJi6N69u812IiIiCnydamte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\n7rtLh2ezmdR58zi4dSspc+eS+dxzpH71FYc2bcLdoEGFaxERERGp7c7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+ "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 29, + "text": [ + "" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Exercise - Nonlinear Systems" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our equations are linear: \n", + "$$\\begin{aligned}new\\_pos &= old\\_pos+dist\\_moved\\\\\n", + "new\\_position &= old\\_position*measurement\\end{aligned}$$\n", + "\n", + "Do you suppose that this filter works well or poorly with nonlinear systems?\n", + "\n", + "Implement a Kalman filter that uses the following equation to generate the measurement value for i in range(100):\n", + "\n", + " Z = math.sin(i/3.) * 2\n", + " \n", + "Adjust the variance and initial positions to see the effect. What is, for example, the result of a very bad initial guess?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#enter your code here." + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 30 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "###### Solution:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_error = 30\n", + "movement_error = 2\n", + "pos = (100,500)\n", + "\n", + "zs = []\n", + "ps = []\n", + "\n", + "\n", + "for i in range(100):\n", + " pos = predict(pos[0], pos[1], movement, movement_error)\n", + "\n", + " Z = math.sin(i/3.)*2\n", + " zs.append(Z)\n", + " \n", + " pos = update(pos[0], pos[1], Z, sensor_error)\n", + " ps.append(pos[0])\n", + "\n", + "plt.plot(zs,c='r', linestyle='dashed', label='input')\n", + "plt.plot(ps, c='#004080', label='filter')\n", + "plt.legend(loc='best')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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IiNyUypEnf/rppxg3bhw0Gs0Dr9Pr9QCAGlUtAIDsXGvB16jiUavVAMB7gO7B+4IKw/uC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\n1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+ "text": [ + "" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "######Discussion\n", + "\n", + "Here we set a bad initial guess of 100. We can see that the filter never 'acquires' the signal. Note now the peak of the filter output always lags the peak of the signal by a small amount, and how the filtered signal does not come very close to capturing the high and low peaks of the input signal.\n", + "\n", + "If we recall the g-h filter chapter we can understand what is happening here. The structure of the g-h filter requires that the filter output chooses a value part way between the prediction and measurement. A varying signal like this one is always accelerating, whereas our process model assumes constant velocity, so the filter is mathematically guaranteed to always lag the input signal. \n", + "\n", + "Maybe we just didn't adjust things 'quite right'. After all, the output looks like a sin wave, it is just offset some. Let's test this assumption." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Exercise - Noisy Nonlinear Systems" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Implement the same system, but add noise to the measurement." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#enter your code here" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 32 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "######Solution" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_error = 30\n", + "movement_error = 2\n", + "pos = (100,500)\n", + "\n", + "zs = []\n", + "ps = []\n", + "\n", + "for i in range(100):\n", + " pos = predict(pos[0], pos[1], movement, movement_error)\n", + "\n", + " Z = math.sin(i/3.)*2 + random.randn()*1.2\n", + " zs.append(Z)\n", + " \n", + " pos = update(pos[0], pos[1], Z, sensor_error)\n", + " ps.append(pos[0])\n", + "\n", + "p1, = plt.plot(zs,c='r', linestyle='dashed', label='measurement')\n", + "p2, = plt.plot(ps, c='#004080', label='filter')\n", + "plt.legend(loc='best')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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XrSLsxRfJve8+Mt991+3X98hfBUudOmRMnUr2+PFQWIhu375y9+/VpgE6rcLO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\nF34sIiLC4XOcF/4rJycHOp0OnTp1AgC0b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+ "text": [ + "" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "###### Discussion\n", + "This is terrible! The output is not at all like a sin wave, except in the grossest way. With linear systems we could add extreme amounts of noise to our signal and still extract a very accurate result, but here even modest noise creates a very bad result.\n", + "\n", + "Very shortly after practitioners began implementing Kalman filters they recognized the poor performance of them for nonlinear systems and began devising ways of dealing with it. Much of this book is devoted to this problem and its various solutions." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Summary" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This information in this chapter takes some time to assimilate. To truly understand this you will probably have to work through this chapter several times. I encourage you to change the various constants and observe the results. Convince yourself that Gaussians are a good representation of a unimodal belief of something like the position of a dog in a hallway. Then convince yourself that multiplying Gaussians truly does compute a new belief from your prior belief and the new measurement. Finally, convince yourself that if you are measuring movement, that adding the Gaussians correctly updates your belief. That is all the Kalman filter does. Even now I alternate between complacency and amazement at the results. \n", + "\n", + "If you understand this, you will be able to understand multidimensional Kalman filters and the various extensions that have been make on them. If you do not fully understand this, I strongly suggest rereading this chapter. Try implementing the filter from scratch, just by looking at the equations and reading the text. Change the constants. Maybe try to implement a different tracking problem, like tracking stock prices. Experimentation will build your intuition and understanding of how these marvelous filters work." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 33 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**author notes**:\n", + " clean up the code - same stuff duplicated over and over - write a 'clean implementation' at the end.\n", + " \n", + " " + ] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/Kalman_Filters.ipynb b/Kalman_Filters.ipynb deleted file mode 100644 index fc7189c..0000000 --- a/Kalman_Filters.ipynb +++ /dev/null @@ -1,2164 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:a0b2a1f17afd632455ef42c5fbf5e58dcb19dae1c24d5fc069bfb071867ceb33" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "Kalman Filters" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "#format the book\n", - "%matplotlib inline\n", - "import book_format\n", - "book_format.load_style()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "html": [ - "\n", - "\n" - ], - "metadata": {}, - "output_type": "pyout", - "prompt_number": 1, - "text": [ - "" - ] - } - ], - "prompt_number": 1 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "One Dimensional Kalman Filters" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now that we understand the histogram filter and Gaussians we are prepared to implement a 1D Kalman filter. We will do this exactly as we did the histogram filter - rather than going into the theory we will just develop the code step by step. But first, let's set the book style." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Tracking A Dog" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As in the histogram chapter we will be tracking a dog in a long hallway at work. However, in our latest hackathon someone created an RFID tracker that provides a reasonable accurate position for our dog. Suppose the hallway is 100m long. The sensor returns the distance of the dog from the left end of the hallway. So, 23.4 would mean the dog is 23.4 meters from the left end of the hallway.\n", - "\n", - "Naturally, the sensor is not perfect. A reading of 23.4 could correspond to a real position of 23.7, or 23.0. However, it is very unlikely to correspond to a real position of say 47.6. Testing during the hackathon confirmed this result - the sensor is reasonably accurate, and while it had errors, the errors are small. Furthermore, the errors seemed to be evenly distributed on both sides of the measurement; a true position of 23m would be equally likely to be measured as 22.9 as 23.1.\n", - "\n", - "Implementing and/or robustly modeling an RFID system is beyond the scope of this book, so we will write a very simple model. We will start with a simulation of the dog moving from left to right at a constant speed with some random noise added. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from __future__ import print_function, division\n", - "import matplotlib.pyplot as plt\n", - "import numpy.random as random\n", - "import math\n", - "\n", - "class DogSensor(object):\n", - " \n", - " def __init__(self, x0=0, velocity=1, noise=0.0):\n", - " \"\"\" x0 - initial position\n", - " velocity - (+=right, -=left)\n", - " noise - scaling factor for noise, 0== no noise\n", - " \"\"\"\n", - " self.x = x0\n", - " self.velocity = velocity\n", - " self.noise = math.sqrt(noise)\n", - "\n", - " def sense(self):\n", - " self.x = self.x + self.velocity\n", - " return self.x + random.randn() * self.noise" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 2 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The constructor `_init()__` initializes the DogSensor class with an initial position `x0`, velocity `vel`, and an noise scaling factor. The `sense()` function has the dog move by the set velocity and returns its new position, with noise added. If you look at the code for `sense()` you will see a call to `numpy.random.randn()`. This returns a number sampled from a normal distribution with a mean of 0.0. Let's look at some example output for that." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "for i in range(20):\n", - " print('{: 5.4f}'.format(random.randn()),end='\\t')\n", - " if (i+1) % 5 == 0:\n", - " print ('')" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "-0.7733\t-0.9997\t 0.0225\t 0.2023\t 0.0525\t\n", - " 0.4358\t 2.5341\t 1.9472\t 0.4157\t-0.6211\t\n", - " 1.3083\t-0.8065\t-0.1134\t-0.3974\t-0.6619\t\n", - "-0.9567\t-0.9989\t 0.5416\t 0.7023\t-0.9270\t\n" - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "You should see a sequence of numbers near 0, some negative and some positive. Most are probably between -1 and 1, but a few might lie somewhat outside that range. This is what we expect from a normal distribution - values are clustered around the mean, and there are fewer values the further you get from the mean.\n", - "\n", - "Okay, so lets look at the output of the `DogSensor` class. We will start by setting the noise to 0 to check that the class does what we think it does" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import matplotlib.pyplot as plt\n", - "import matplotlib.pylab as pylab\n", - "\n", - "dog = DogSensor (noise=0.0)\n", - "xs = []\n", - "for i in range(10):\n", - " x = dog.sense()\n", - " xs.append(x)\n", - " print(\"%.4f\" % x, end=' '),\n", - "plt.plot(xs, label='dog position')\n", - "plt.legend(loc='best')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000 10.0000 " - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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- "text": [ - "" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The constructor initialized the dog at position 0 with a velocity of 1 (move 1.0 to the right). So we would expect to see an output of 1..10, and indeed that is what we see. If you thought the correct answer should have been 0..9 recall that `sense()` returns the dog's position *after* updating his position, so the first position is 0.0 + 1, or 1.0.\n", - "\n", - "Now let's inject some noise in the signal." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def test_sensor(noise_scale):\n", - " dog = DogSensor(noise=noise_scale)\n", - "\n", - " xs = []\n", - " for i in range(100):\n", - " x = dog.sense()\n", - " xs.append(x)\n", - " plt.plot(xs, label='sensor')\n", - " plt.plot([0,99],[1,100], 'r--', label='actual')\n", - " plt.xlabel('time')\n", - " plt.ylabel('pos')\n", - " plt.ylim([0,100])\n", - " plt.title('noise = ' + str(noise_scale))\n", - " plt.legend(loc='best')\n", - " plt.show()\n", - " \n", - "test_sensor(4.0)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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9Z3BzsuPF+5ri6mTHaw+3pH+7mrw+axOf5WSRFZTFtPJN8Qssx5q2dYp8b4Xs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\nGRkEBwezaNEi/Pz8CA4O5vTp0wraTYjdbjD7nXX8dDKbTi3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- "text": [ - "" - ] - } - ], - "prompt_number": 5 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "> **Note**: numpy uses a random number generator to generate the normal distribution samples. The numbers I see as I write this are unlikely to be the ones that you see. If you run the cell above multiple times, you should get a slightly different result each time. I could use `numpy.random.seed(some_value)` to force the results to be the same each time. This would simplify my explanations in some cases, but would ruin the interactive nature of this chapter. To get a real feel for how normal distributions and Kalman filters work you will probably want to run cells several times, observing what changes, and what stays roughly the same.\n", - "\n", - "So the output of the sensor should be a wavering blue line drawn over a dotted red line. The dotted red line shows the actual position of the dog, and the blue line is the noise signal produced by the simulated RFID sensor. Please note that the red dotted line was manually plotted - we do not yet have a filter that recovers that information! \n", - "\n", - "If you are running this in an interactive IPython Notebook, I strongly urge you to run the script several times in a row. You can do this by putting the cursor in the cell containing the Python code and pressing Ctrl+Enter. Each time it runs you should see a different jagged blue line wavering over the top of the dotted red line.\n", - "\n", - "I also urge you to adjust the noise setting to see the result of various values. However, since you may be reading this in a read only notebook, I will show two extreme examples. The first plot shows the noise set to 100.0, and the second shows noise set to 0.5." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "test_sensor(100.0)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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aiYsyMt712wGDXs+EbFdDZLfyEXX9ejDKRkAC7aAymUy8+OKLFBYW8tBDD3HX\nXXdRW1tLcXExN9xwA3fddRdfffUVzz33HAaD89dLL774IkePHgWc5R5Hjx7VAu2Bnk8IIYTojUdG\nu59bCwOpypXJTTU5A8zEuGEQaJf2ntGGrjptfzZE1jd34FAUTLERPkf29eClyVFntRJ2+DDQ9UPA\nsW6Btq9lNYPBvXxEDbR7a4aErhF/7uUj6tr1mePS0Ou7MtRq+Uj3QLsiiI2Q8DVshswcMcLr7afL\nyvw+3texfbnmmmu0rxcuXEh8fDzHjh1jx44dzJ8/n0WLFgGQm5tLbm7ugM7R1/kKCwuZM2fOGT+3\nEEKIs5d7oD2kMtr1XRltQMto1w3hGu1jWkbbd6A9vh8NkVojZD/qs+PXryf2uecAnE2OP/gBLTfc\noM3AHttHRrvHsppBoE4eOVJaR0VdK2EGHRlJvQe/3hoiv+jWCKnyFWh3NUKeeX27P752gXYo/fOf\n/+SZZ57h9OnTKIpCU1MTVquV8vJysrKygnY+IYQQojfda7SHyuQRNaOd4spoazXaTUMz0O602TlR\n2YBOB7mZPSeOqPoTaPs7Q9td+6JFRL/+eo8AW6VmtAu7/VClLofxtqzmTKmTRz796jTgzFa7r6f3\nJstLRrugWyOkavIo7yP+tEBbMtqB0d9s9ECz192VlpayZs0aXn31VWbOnAnApEmTUBSFzMxM9u/f\n3+vjvf0FFxHh/AvGZrMRHh5Oc3PXB6+386mMRiMAdrtdxvsJIYTQqFNHwFmvXVXfFrSa1t5Udxtr\nZ9KmjgzNZsiTFY3Y7M6JI1HhvkOufgXarvegr/Xr7jrnzaOyoAAl2vufoceIPzcl1WpGO3ClIwVH\nnBsde6vPVmkZbVeg3dpu5eCpGgx6HTPGpnocm5+diEGvo/B0A20dNm0RTqXUaJ+dWltb0el0mM1m\nbDYbf/zjH2lsbESn07F8+XK2bNnC+++/j91u58SJExQUFHg8PjU1lcOuWiqV2WwmPj6e3bt3A/DO\nO+/0eT53KSkpxMfH89lnnwXoVQshhBiO1Iy2WhPrT5NeMFR1Kx1JGuJztPtqhFSNTI0j0migvLbF\n47cJ3lS7Rvt5zNBWFMK3biXpmmvQe+vF0ul8BtkAGUkxxEQaqW1q95jSodVoByCjrZaOtFvtQO8T\nR1TdA+3dRRbsDoWJI83ERBo9jo0MD2NcpgmHonCopOs9UQPtYKxfBwm0gyYvL49bbrmFZcuWMWPG\nDFpaWrSWqO0xAAAgAElEQVRykezsbJ577jl++9vfMmnSJK6//nptkohq7dq1PPDAA8ycOZNHH30U\nAIPBwE9/+lPuuOMOrrzySpKTk7XMd2/nUxkMBn7+85/zox/9iLy8PN5///0gvBNCCCGGOnUu9WxX\n3etQGfFn6dYMqdVoD9FAu6/RfiqDXq/VcPdVE6+Wjpjjo7QA27xiBcmrVhG5ZQsxf/5zv69Tp9Mx\n1lXa4l6nXWoJXEZ7VLfGR78y2mbPGu2Co85s+Ky8VK/HT9LmaXeVjwRzWQ18DUtHQmnt2rWsXbtW\n+/7ee+/Vvr7gggv417/+5fOxV199NVdffXWP21etWsWqVau079evX+/X+VQrVqxgxYoV/r8IIYQQ\nZ7UOq532TjsGvY5puSm8+VnRkGmIrNKW1biaIdWM9hBthvQ3ow2Ql2Vi/8lqjpTWaj/geKOWjkyu\nK8W84r+JcP0G3L3JcSByM0zsPV5N4el65oxPp6Glg6Y2K9ERYQFZ7BIdaSTVFKX9mfY1cQQg0xVo\nl9e2YHc4+PJYFdA1P7u7yTnJvLat0GNDpLp+PdUkgbYQQgghgqyx1Rm0JsREaLXD/oydCwaLtn7d\nmdGOiTRiNOhp67DR3mkjspc66FDwN6MNkJ+VBPT9XqsZ7YTYSCIKCrxOERkIbcSf65pLLK5GyOTY\ngDXCjkyJ71egHWE0aMF5eU0LXx7zPnFEpa5iP+jaENnabqWpzUqE0aD9NiTQhtYnUgghhBAhpTZC\nJsSEa+UMR4bA5BFFUbqaIV2j7XQ6HabYCCwNbTS0dA6pQNtmd1BU7gxa1WbD3qiztA/3FWg3OGuo\nddPOofaPf6TjkkvOKMBWqddY6LrmMrUR0o+SjoEalRanzcEe6ed5RphjqapvY/O+UhpaO8lIitFK\nSrqb5Aq0D5fUYrM7uhohg7QVEqRGWwghhBBu1DIMU0wE6YnRxEUZqW/uoKYxtJM9mtqstFvtxEQa\niXZrfOuq0x5ak0dOVTXSaXMwwhzbo1HPm3xvvz1wLZoxlJRoN1U3qg2hUbRffvmgBNkA4zI9R/yV\nVHdltANFnTwSHRFGUpx/U1TUhsiNnxUB9FpmkxATQXZKLO1WO4Wn64Nenw0SaAshhBDCjTr1Ij46\nHJ1O59akF9ryka6JI57zo01DdPJIV9lI39lscAaQMZFGLA1t1Da2eWxyjH3iCe04depIcj/G+/lj\nVFo8Br2Okuom2jptXWvRA9AIqVInj4xKjfc7w6xmrz8/XA70HmiD+zztGi2jHaz6bJBAWwghhBBu\nukpHnAGsGiiGuiGy+8QRVaI2S3toBtq9bYR0p9PpyMs0cWndcdK//S1tVbrDZMI2diwALe1W2jps\nRIYb/MqS90d4mIGctHgUBY6XNwR0WY1qzvg0oiLCuHBypt+PUTPs6loQX/XZqkluGyLV9evBGu0H\nZ1mNtqIoOBwOWb4ySBRF8VhwI4QQ4uynZrTVQFsNFEM94k/NaCfHewZJQzWjrf4GIC/Lv4w2wLkm\neGLfi4QrDq9NjtpWyPiogNQYj800UVTeQOHp+oAuq1GNTI3nwB+vJcJo8Psx7vXYURFhTBxp7vV4\ntSHywKlqdDpndjuYpSNnVaCdmJhIVVUVqampEmwPgoaGBmIHqfZLCCHE8FDfLdDOGyKlI9U+MtpD\ntUa7a7SffxltgHGzJrIh6zxMmSl886+P9ai/Vt+D5Hj/16/3x7hME//+8hSFp+sDuqzGXX8bWEe4\nBf7Tc1P6XNs+OccZXB88WUOqayxksNavw1kWaBuNRsxmM9XV1SHtjD5bGI1GonvZJCWEEOLs0+gq\nHTHFhANdpSPHQlw6UtVt/boqMW7oZbTf2XGcAydrCA/TM95boK0o6FpbUWI8A74ls3OYlv8fdNrs\nzO7UkdHtYVqgnRCYQHus6896z3EL9c0dRBoNAQvqB2pEctd75mt+trv0xGjM8ZHUNLbzZaFzwolk\ntM+A0WgkNdX7hiAhhBBC9K6h1TOj7dGk19Tu93SIwdY1Q7tb6Yia0R4iNdpF5fXc++xWAB5YNZe4\n6PCuOxWF8G3biNuwASUhgdrnn/d4bHx0OAumZfNuwUne3nGcW5ZM8bg/UI2QKnXE3/avTgPOP/uh\nlrg0xUQQHRFGa4etz0ZIcNa+Tx5lZsv+Mm02eJo0QwohhBAiFLrXaOt0uq7Rb6dDl9W21HvPaKs1\n2nVNoQ+0W9ut3PLEBzS3W7l87hi+v3iS8w7XmD51ikjEzp0Yv/gCfW1tj+f45nm5ALy5vbDHfeoP\nG8kJgQkUx2Y4/5zbO+1AYEf7DZROp2PJ7BzGZCQwZ3zfGW3oKh9RSUZbCCGEECGhTh2Jd8vEjhth\nYs9xC0fL6vwObgZbVYM63q97M6Q6dSS0NdqKorDuL9s4XFpHbkYCv755njMbrCgkXXcdkR99BNDn\nJscF00cSG2lk7/Fqjlc0MCY9QbuvJsAZ7bjocNITo6lwzZsO5LKaM/G72y7p1/Hq4hqAyHCDx2c7\n0CSjLYQQQgiN+8IaVVdDZOgy2tpWyG7NkElDZOrIS5sP89q2QqIiwvjf1QuJjXIFczod1smTcZhM\nNK5bR+WOHTTfeafPRTNR4WEsmZ0DwMbtRR73uU8dCRT3LZZDMaM9EO6BdnpiTFDLYSTQFkIIIYSm\nq3TEM6MNcKyP9eCB4nAo2hzt7kGm+gNBKOdo7zth4acvbAfgV9+fx/isJI/7m3/4wz4DbHfLz3eW\nj7yxvdBjzK4lwM2Q4BloB3JZTTCNSU8gOsJZxNF9ak2gSaAthBBCCE33hTUAeVmhzWjXNbdjdyiY\nYiN6zFzWarRDlNGua27nlic2caGlkE1t27nSFSS7U+Li+rUq/cJJIzDHR1JU3sDBUzXa7TVByGiP\nOwsz2nq9Tpu3HczRfiCBthBCCCFcrDYHLe1WdDqIi+rKaGclxxIZbqCiroXG1s6gX1eVqxEy1Usm\nNybSiNGgp63DRnunLajX5bA7eOH+P/DSpif5cO9fWbjjfSK2bDnj5w0z6Ll87hgA3nArH7H4GHE4\nmHLdA+0hWqM9EJNdGyJTg9gICRJoCyGEEMKlqc2VzY6OQK/vqmM16PVaSUEoFtd0TdvoGWDqdDot\nq61m44Mh/PPPURYs4Vev/Zp5DcVYExJoXLeOzlmzBuX5l5/vXLu+8bMiHA4Fm91BXXMHOl3X7PBA\nUOvxw8P0QR2DF2jXLpjA7Lw0vn3huKCeV6aOCCGEEAJw3wrZcypD3ohEDpys4VhZHbPG9T2/eDCp\nmdxUH2PtTDERWBraqG9pD9roNuOBAyQfO0BNWBRHvvU9Rj/0X/0qD+nLrHGpZCXHUlrdzM4jFYzJ\ncE4fSYqLxBDA7ddpidHce+UMkuIiPX7YGu7ys5N488Ergn5eyWgLIYQQAug5Q9ud2hB5tDT4ddoW\nHxNHVKGYpd24ahXrxv8HOeeuJu7BtYMaZIMzU79cnan9WVHXexCETY33XDWT678xKeDn+TqQQFsI\nIYQQQFeg7W3OsFpScCwEpSNV9a6tkD4y2onaLO1BDrQVhfDPPgNbz9rvQ5Z2Hss4l+QRKZgDFPx+\n09VY+c6O41TUtQBgDmB9thh8EmgLIYQQAvA+cUSlZbRDMHnE34z2oM3Sdt/k+K1vEfXmmz0O+bKw\nEoAZY1MH55xeTMhOYnxWInXNHby+zbkpMhgZbTF4JNAWQgghBOB9WY1qVGo84WF6ymqaaW4L7uQR\nNaPta9rGoM3S9rIq3WEyoevs+Xp3FVYBMDOAgbZOp9NWsr+z8zggGe3hJuSB9lNPPcWyZctYtmwZ\nTz31FADvvvsuixcvZvHixWzevDnEVyiEEEJ8PXhbVqMKM+jJzXBmtQtPNwT1urStkL5KR+LUGu0z\nW8Ou27TJI8BuXLuWys8/p/Waa3oc++UxZ0Z7ZoAbQ9XlNTa7c3FNoNavi8AI6dSRkpISNm7cyL//\n/W/sdjtLlixh2bJl/OY3v+HVV1+lo6OD6667jksu6d9OeyGEEEL0X2MvpSPgLB85VFLL0bI6puWm\nBO26qtSpI75KR1zXW3eGGW1lwQI6Zs+m49JLabnhBpQ473Oka5vaOVHRSGS4gfzsJK/HDJZRqfHM\nGJuqZdADOUNbDL6QBtqxsbGEhYXR3t6Ow+HAaDRSXV3NuHHjSEpyfnDT09M5fPgw+fn5obxUIYQQ\n4qzX29QRCE1DpNXmoLapHb1OR1Kc92xuv2u0FQUcDjB4bpnEYKDmjTdA1/tYOzXonTYmBWNY4IsD\nlp+Xq50zUI2XIjBCWjqSmJjIddddx8UXX8zFF1/MjTfeSE1NDSkpKbzyyiu89957pKSkUFVVFcrL\nFEIIIb4W6rWMds/SETizhshjZXXUDqC0o1pdO57ge360yTV1pK65j+d3q8GO+dOfvB/TR5ANXWUj\ngWyEdHf5uWPQu65LMtrDS0gz2qWlpbzyyit89NFHWK1WVq1axW233QbAypUrAdi0aRM6Lx96s9kc\n1GsVQ5vRaATkcyE8yedCeCOfC99arQ4AsjNSvL4/cyY564SLKhr79f4Vna5j0f2vM3fCCD54/Lv9\nuqZTtVYA0pPifJ5z9AjnMc3tdu/HKAq6zZsJe+QR9Nu3A2BsbCTyvvu0wLo/n4v9p5wZ/YtnjA3K\n58hsNnPTsml8eqCU86bmEhPp/QchMfjUz8VAhTTQ3rdvH1OmTCHWNeR94sSJlJaWYrFYtGMsFgsp\nKT3rwB5++GHt64suuoj58+cH/oKFEEKIs1i9K+NsivFeopGbmUiYQc/Jinpa261ER/oXhHx6oASr\nzcG2/SWU1zSTYfZ/uUuVa350WmKMz2MS45xZXq8Z84YGjCtWaAG2kpSE/a67sN92m1/Z6+7sdgcF\nR8oBmJOf2e/HD9Tv7lgctHN93W3ZsoWtW7cCYDAYuOiiiwb8XCENtLOzs9m/fz+dnZ04HA4OHjzI\nLbfcwuuvv05tbS0dHR1UVlZ6rc/+4Q9/6PF9TU1NsC5bDEFqRkE+B8KdfC6EN/K58K2m0RnUYmvz\n+f6MTovn2Ol6Cg4eZ3JOsl/Pu33/Se3r1z7ey6qL/e+7KipxlmmYosN8/5lZnSUvtY2tPY9RFMxW\nK0aTieZbb+1qcrRawe1Yfz8Xh4praW7rJDslFqPSQU1N8LZRiuCYPHkykydPBpyfi23btg34uUIa\naE+ZMoVFixaxYsUKAK6++mry8/O59957WbVqFQD3339/KC9RCCGE+NrobWGNatyIRI6drudIaZ3f\ngfbe49Xa1x/uLulXoF3V4NoKafI+2g8gJtJImEFHa4eNDqudCKNbk6NOR/0TT+Awm31OEemPrkU1\ngR3rJ84OIQ20Ae644w7uuOMOj9uWLl3K0qVLQ3RFQgghxNeP3eGgsbX3ZkiASaOSeLfgBHuPW7jq\nwnF9Pq/V5uCr4q4s8dYDZXTa7ISHGXp5VBdLvTpD23cToA74ZmsJpppK6pu/S1qiZ1Buz8nx61z+\nCMaiGnH2CPnCGiGEEEKEXlObs6EwLsroc7oHdC1o+cI1eaMvR0rr6LDayUmLJz8rkZZ2KzsOV/h9\nXWpG22ugrSiEb92KecUK/vnZn3ii8P/RUlbu93MPxJfHXIF2gBfViLODBNpCCCGE6HOGtmp6bgp6\nnY6Dp2po67D1+bz7TjgHHJwzJoUF00cC8OGeYr+vy9dWSDXATl61ioiCAhoiYvj5qItwDSkJiPqW\nDgpP1xNpNDBxVGAX1YizgwTaQgghhPA70I6NCic/OxGbXWHvcUuvxwLaMVNHJ7NgWjYAH+4p8fu6\nfG2FjPnrX4koKHCuSl+3jv+8+XEeHTWParvvkpQXPzrExT9+lV/+vYCy6ma/r0G121U2MmV0st+l\nL+LrTQJtIYQQQmjLauKj+57RPCvP//KRfSecjZDnjElh5rg0EqLDOV7ewImKBr+uy1LvKh3p1gzZ\ndPfdNK5bR+WOHTTfeScRSc5lOr1th/zLvw9y7HQ9T721h3NXv8KNG95n6/5SHA7Fr2tR67ODtahG\nDH8SaAshhBBCy2ib+shoA8xy1Ser9cq+dFjtHCquRaeDyaPMhBn0zJ+aBfiX1W7rsDKi+jThYXoS\nuv0AYJs0ieY770Rx7eJQr7u+xXug3dzWyZGyOowGPcvPy8Wg1/HvL0+x6tH3mL/mVZ56s4CGlt43\nS6obIaU+W/hLAm0hhBBCuJWO9J3Rdm+IVBTf2eAjpbVY7Q5yM0zEuQLlBdOcddof9Van7VqVnnLV\nVewveJoZhlavW6LdmWKdgXadjzXv+05UoygwcVQSv7/jUgqeXMWab88iIymG4+UN/NcfP+TcO56n\nyTV5pTuHQ2F3kbMMRjLawl8SaAshhBDC7xptgFGpcSTHR1Hb1M7Jykafx6nzs6eO7pq3fck5Weh0\n8Nmhclrau3UuugJs85VXkrxyJfG7v6QhLJJZjr7LTBLVQNtHRnt3kTP7Pm2MM0hOSYjmruXT+fyJ\nlfxp9ULyR5o5UV7PL/9e4PXxhafraWztJNMcQ0aS7y2VQriTQFsIIYQQNPqxrEal0+mYlecMWHur\n0953vGviiMocH8X03FQ6bQ62HSjzOD72D38geeVKInbuxGEy8cW1t5Jz7mqOTJnd5zWpGW1fNdp7\nXNno6WNTPG4PM+hZMns0L92/HGOYnhc++IqCIz3HD0p9thgICbSFEEIIodU2+xNoA8x0bUb84qjv\nQHuv2gg52nOD5KU+po+0XXEF9tRUrcnxg4XfojksgtQE31shVabYSI/X0d2uQlegnes9UJ6Uk8K9\n3z4XgB//6RM6rHaP+6U+WwyEBNpCCCGE0Navm/yo0YauySNfFnpviGzrtHGktBa9TsekUWaP+xZO\nU+dpl3jUeNuzsqjcuVNrcrSoM7RNvrdCqpJ6qdEur22hoq6F+OhwxqQn+HyOdavOJzcjgWOn6/n9\nW3s87pOMthgICbSFEEII0a8abXDOkjYa9BwuqfXaQHiouBabXWHcCBPRkUbnja4a7IvvuZlF1FJR\n18JXxbWeDzQatS+1QDu+70C7t6kje1z12eeMSUGv991UGRkexq++Pw+AJ9/aw7GyOgAaW50TS8LD\n9EzJSfb5eCG6k0BbCCGEEDS0OgNUf+ZoA0SFhzE5x4yidDUautvntqime5NjxM6dPFj9BdD7lkhL\ng/cZ2t70VqOt1WfnpvS4r7tzJ2Tw3Uvy6bQ5+PGfPsHhUNhz3IKiwKRRyUQYZVGN8J8E2kIIIYTQ\nSkf8zWhDV72yt3naan32JdEdHgG2usmx6IGfAfDhbu/ztAtP12vPm5rQd0Y7JtJImEFHa4etR331\nLtcPAr7qs7t7YNUcUk1RFByt5G8fHXKrz5ayEdE/EmgLIYQQQiu58GdhjUoNPL1NHlEz2qMnjcb4\n1VdagK1ucjx39jiMBj27Cquo7VZX/fmhcr75s7ewNLQxPTeV6X7URet0OhLVhki3rLbd4WCfa8zg\nND8y2uD8YePh684H4Bcv72TTrlOA1GeL/pNAWwghhPiacziUfo33U6kbIncVVnmsMW9tt3K0rB6D\nXse4KWOoff55LcBWNznGRoUzNz8dh6Lw8b5S7bFvbi9k1aPvUt/SwaIZI/nH/UsJM/gXrnTVaXcF\n7oWn62lutzLCHEuqHyUoqmVzRvONGaNobrdq88BnycQR0U8SaAshhBBfcy3tVhyKQnREGMYw/0OD\nTHMsmeYYGls6qN74HsYvnHXXB4trcSgK47MSiQoPo/O887QA292C6V1bIhVF4am39nD77zfTaXNw\nwzcm8ue7F3U1UvrBW522r/nZfdHpdPz8+vOJdZ0/zRRNplkW1Yj+kUBbCCFEyDW3dWoTHkTw9Xfi\niEZRuCGsmq17/sK0O24m4aGHQFG8LqrxZoFrnvbmfaWsfW4bv/x7ATodrP/uXB6+7nwM+v6FKWrp\nSJ1boK2O5fO3PttdpjmW+1bOAeCCSZl9roEXoruwUF+AEEII8dO/fsarnxzlvYdXMGW0jE8Ltnpt\nhrafgbaiEL5tG3EbNvDIzp0ANEXFonzjG2C3s/eE28SRXuRmmMhJi+dkZSMvfXSYSKOB3/3wEpbN\nGT2g1+E1o33c/4kj3vznwglMyE5kfHbSgB4vvt4koy2EECLkdhwuR1F6X+ctAkfNaPs72o+ODhLv\nuouInTvpjE/gvtELuHDZAzTfeSeEhWnNh31ltAEWuspHEmMj+PsDywYcZEPPWdptHTYOFTuX5gx0\n/rVOp2Nufka/mkSFUElGWwghREi1ddootjQBUFReH+KrOfscKa3lXztO8MPLzyEy3Pv/9tUZ2n6X\njkRG0rhmDQaLhbprr+OJ1a/RXt1BbVM74WF6CsvrMRr05PuRBb798nOIjgjjO/PHk5MW7/fr8kbN\naKulIwdOVmN3KEwYmdSvWm8hBosE2kIIIULqeHkD6hbuwtMNob2Ys9CG13fxzo4T5KQncOUFY70e\n01Wj3S2jrSjoa2txmM09HtO2ciUARpyZ6x1HKthVWEVspBFFgfzsJL+Wu6Saoll79ez+vSgfErVA\n2zl1RJ2fPWMA9dlCDAYpHRFCCBFShae7stiS0R58ZdUtABwqrvF5TI9lNe6bHJcvB5ut13PMynOO\nvfviWGVXffaY4Nfad6/RVieO+Ds/W4jBJhltIYQQIXWsrCu4Pl3TQmu7VX7NP4iq6p1rzI+U+p7q\noma0TdHhhH/yCXEbNhDhanJ0mEyEFRVhGz/e5+Nnuha5fHG0kjTXrOpzRgc/uDWpC2tcr2d3PzdC\nCjHYJNAWQggRUsdOewaAxysamDzAxjXhSVEUPwNtZ0b7u/94iuRt7wPOALv5Bz+g5YYbvM7Adqeu\nYt9z3EJKvHNd+jkhyGgnuWW0qxvaKLE0Ex0RRl6WKejXIgRI6YgQQogQK3RltNVlIO6lJOLM1DV3\nYLU7ACitbqa5rdPrcWpGu2LG3B6r0vsKsgGSE6LISYunrcPZ2BphNJCXlTh4L8RP6mSQuuZ2LZt9\nzpiUfs/jFmKwyCdPCCFEyNjsDo5XOBsgF88cBUhD5GCqqGvx+P5omfcfYtRA27Jgcb8CbHczx3WV\nZ0wcmUR4WN+NkIPNvUZbnZ89zY8Rg0IEigTaQgghQqbY0kSnzUFGUgxTXTW90hA5eNSyEdXRklrC\nP/mExBtvRNfWpt2uLqyJj4vqd4CtmuUqHwG0P8tgi4k0EmbQ0dphY8fhCgCmj5X6bBE6UqMthBAi\nZNSykbwRJsZmOutopXRk8FTWuYJpReHS+hNc/pO/k3zyEACdL75Iy803AwOYo+3FTLdAOxT12eBc\nLpMYG4mloY2Co85AWyaOiFCSQFsIIUTIqI2QY0ckkpuRADibIR0OBb1eF8pLOytU1rcwu7GU35d8\nyGzLCcDV5HjrrbS65mCD+xztgQfa+dmJxEYaaW63hiyjDc46bUtDGza7QpopmsykmJBdixASaAsh\nhAgZdbTfuEwTCTERpCREYWlo43RNM1kpcSG+uuGvqr6VOHsnsy0nqAmL4tm8+Vz/+hMocV3vraIo\nNGpztP1cwe6FQa/n8Zvncaqyifzs4DdCqtQ6bXBms3U6+YFNhI4E2kIIIUJGLRMZ5yobyc1IwNLQ\nRlF5gwTag6Cyro2PTKP56IdrWXk4DIvDyHJ9OAlux7R12LDaHUQaDT5XtPvrinNzz+yCB0Gia5Y2\nyPxsEXrSDCmEECIkFEXpymiPcAXaUqc9MK5NjvraWo+bK+tbQKej4apvkz4yA4Cj3eZp1w9C2chQ\n0j2jLUQoSaAthBAiJCrqWmlut5IYG4HZteREbYgsKpcRf35RFMK3bsW8YgXJK1cS88wzHnerU0dS\nTdGMd5VzHO4WaDcMQtnIUKLO0tbpnDO0hQglKR0RQggREsdOe2azAa0hslBG/PXOlcGO27CBiIIC\nwNnk6EhJcTtEoareOXUkzRTN+BHOQLt7RnswGiGHEjWjPTbDRHz02fHDgxi+JNAWQggREoVlzoBv\nXGZX45yW0ZalNb0yFBWRvGoV4HtVen1LBx1WO3FRRqIjjdqmxsOlnuUlaqB9tgSl6YnOKSOz8tL6\nOFKIwJNAWwghREioGe2xbhntrORYIowGKupaaG7rJDZqeAd/r35ylJy0BGYPctBnHzuWlmuuwT5y\nZI8AW+VeNgKQn6VmtD1/W1CvlY6cHRnty+eOpqW9kyWzR4f6UoSQQFsIIURouI/2Uxn0ekanxXO4\ntI7jFQ0hncd8po5XNLD6j1tISYhi11PfHdhccEWBjg6IjOxxV8Pjj/f60Eq1bCTRGWiPSI4lJtJI\ndWMbNY1tWl28uqzGdJYE2tGRRm5cPDnUlyEEIM2QQgghQqT7aD/VmAx18sjwLh8pcr0+S0Mb+05U\n9+/Bbk2OCQ88MKDzV9a1AM76bHBuTcxz1WkfcavTbjzLMtpCDCUSaAshhAi6uuZ2LA1tREWEkWn2\nLHsYm+lqiBzmI/5KLE3a1x/uKfbvQe5TRFatIqKggMgPP0TX2trv83cvHQEYn+X8Ica9IbKrGXJ4\nl+kIMRRJoC2EECLoCl1lI2MzTD1KKnIz1BF/wzvQLu5voO1wYL76ai3AdphMNK5bR9W2bSjR0X0/\nvpvupSMA47OTAM8Rf2fbHG0hhhKp0RZCCBF03kb7qc6WySPuGe29x6upqm/1yC73oNdjGzMG41df\neZ0i0l/dS0cAryP+1Iz22VKjLcRQIhltIYQQQac2Qo7N7Bloq7O0T1Q0YHc4gnpdg6m4yhloq4Hu\n5r0lfT6mae1aKnfsoPnOO88oyAYfpSPZXTXaiqIAXQtrzpbxfkIMJRJoCyGECLrCXjLacdHhpJmi\nabfaKatuDvalDQpFUbSM9rULJgDwwe6SrkUzjz7q9XGOpKQzDrBVlXXOQNu9dCTNFE1CdDj1LR3a\nMpuzbWGNEEOJBNpCCCGC7thpdVlNz0AbINfVEDlcV7HXt3TQ1GYlJtLIt+aNA0VB9/EWklyr0uOe\nfBfNBv0AACAASURBVBLj3r0BO7+iKFS6MtrupSM6nc4tq+1cXKOO95NmSCEGnwTaQgghgqqtw0Zp\ndTNhBh05aQlej8nVRvwNz4ZINZs9MiWO3GP7Kfjqb7xT8ByRbk2OttzcgJ2/qc1Ke6edmEhjj6U/\n3Uf8qeP9pEZbiMEnzZBCCCGCqqi8HkWBnLQEjGHe8z1aQ+QwzWir9dnZKXFEbNvGLMtxasKi2Lrw\nSs797fpBKw/xRW2ETDVF9bgv3zV55GhpHe2dNtqtdowGPVEREhIIMdjkvyohhBBB5W0jZHdqQ+Rw\nz2hnp8bRfNnNnGy2c/6RONKT0tgS4CAb8Fo2olIz2odL67RGyISYCHS6AWyuFEL0SkpHhBBCBJU6\n2m+sl0ZIlZrRPj5cMtqKgvGLL5wr0+maoT0yJQ4lMZH49WvRx8dReLqeU1WNAb+cKm2GdkyP+8Zn\ndY34q29pB6Q+W4hAkUBbCCFEUPmT0R5hjiXSaKCyvpWm1s5gXVr/uaaImK+8kpRvfpOIjz8GoKSq\nK9AGMIbpuWjKCAA+3O3nlsgz0FvpSHJCFOb4SJrbrRwucdZpy8QRIQJDAm0hhBBBVahOHOklo63X\n6xidMYQnj7gF2MkrVxKxcycOkwl9rXOSh5rRznYF2gALpo0E4MM9fc/TPlO9lY5AV/nIjsMVACTI\nDG0hAkICbSGEEEFjszs4UeEsnRib4TvQdr9/KNZpR771lkeA3bhuHZU7dtB21VU4HAqlrvnfI1O7\nAu1Lz8lGp4PPDpXT2m4N6PX1VjoCkO8a8bfzqCvQloy2EAEhzZBCCCGC5mRlI1a7gxHmWKIjjb0e\nq87SLiwfeoF2+ze+gTU/n7bly3usSq9qaKXDaicpLpIYt9eYnBDFtDEp7C6ysO3gab4xc1TArq+3\n0hFwa4gscWbgJdAWIjAkoy2EECJoetsI2Z2a0S46HcLSEUUBRWHjZ0XMvOMlCo44M8BERWH54AOv\nq9K712e76yofCWyddl+lI+qIP1fvpjRDChEgEmgLIYQIGrURcmwvjZCqru2QIchou9Vgt7/wEmv+\n9AkVda289fnxrmN8jMPzVp+tWjA9G3DWaStqlBsAfZWO5Lkmj6gkoy1EYEigLYQQImjU1etq6UJv\n1O2QJyoasDsc/TqP1ebgwMma/gezXpoc2598hmZXTfWBU9V9PoU22i+1Z6A9eVQyKQlRlNe2cMhV\ntjHYmts6aWm3EhluIC7Ke3mOKSaC9MRoj++FEINPAm0hhBBB05/SkZhII+mJMXTaHJRYmv0+R4fV\nzqpH32XxA6/3a8KH3mLpMUXk05U3MXfsd4h11Vp/daoWh6P34L2kl4y2Xq/j0mmurPbuwEwfcS8b\n6W0JjfsPO1I6IkRgSKAthBAiKBRFodBVb+1P6YjzuP6VjzgcCqv/+DGfHSoH4ON9/gezjqQk9HV1\n2hSRA+9v5rKmXJrDInj4P88nzRRNc7u1z4Uzxb3UaEPg67Qr61yBdqL3+mzV+Gz3QFsy2kIEggTa\nQgghguJ0bQst7VbM8ZEkxUX69Zjcfo74e+TlHbz1+XH0rkxuwdFK/y/QYKDumWeo3LGDpjvuYN0/\n9lLf0sElU7P49rxxTMoxA3DwVE2vT+O+ft2biyaPwGjQ8+WxKmqb2v2/Pj9VuTLaqT4aIVXj3eq0\n46Ml0BYiEEIeaO/du5fLL7+cpUuXcvfddwPw7rvvsnjxYhYvXszmzZtDfIVCCCEGw7Ey16IaP7PZ\n4J7R7nvyyP++t59n3t1PmEHHn+9eRJhBx1enamlxn1mtKOg++gj9a695fQ7b+PEosbG8s/ME731x\nkthII499fx46nY5Jo5yB9oFeAm2rzcHpmhZ0Oud2S2/iosOZk5+OQ1H4IABbIvuaOKIan5WkfW2S\n0hEhAiKkc7QdDgdr1qzhl7/8JTNmzKCuro7Ozk5+85vf8Oqrr9LR0cF1113HJZdcEsrLFEIIMQjU\nTPA4PxohVWqJSVEfGe23dxznoZc+B2DDLfP5xsxRTB6VzJ7jFnYVVjFvUibh27YRt2ED4Tt3oqSm\novv0U5TonsFobVM7Dzz/KQA/uWYuI5KdAfPkUX1ntMtqmnEoChlJMUQYDT6PWzIrh08PnuYnL2wn\n0xzDhZNG9Pr6+sPf0pE8tzp5KR0RIjBCmtE+cOAASUlJzJgxA4DExET27dvHuHHjSEpKIiMjg/T0\ndA4fPhzKyxRCCDEIPj14GoDzJmT4/Ri1dGTviWoe+0cBXxX3nCTy+aFyfvT0ZhQF7l85m6suHAfA\nzLw0UBTq33nfo8lRSUrCfvvtPsfzrf/rdmoa2zl/YgbfvSRfu13NaB886TvQ1iaO+KjPVn3v0gms\nOD+XlnYr1/7q//H/vjjZ+xvRD/6WjsRGhXPr0il879J84mQFuxABEdKMdnl5OXFxcdx0003U1NTw\n7W9/m6SkJFJSUnjllVdISEggJSWFqqoq8vPz+35CIYQQQ1KH1c4O17KXCyZm+v24jKQYJueYOXCy\nht9t3MPvNu5hTEYCl80ZzWVzxxBm0HHjhvfptDm4ftFEfnjZOdpjZ41L5c/vwXmvvUDE6WM4TCaa\nb72ViHvvhfh4lJqeAfP7u07xxvYiIsMNPH7TRej1XcH4qNR4YiONVNa3YmloJSWhZyCrLqvxVZ+t\nMobp+d1tl2CKjeAv73/FzU98wK9vnsd35o/3+73xxd/SEYD13z33jM8nhPAtpIF2R0cHu3bt4p13\n3iE2NparrrqKb33rWwCsXLkSgE2bNnkdT2Q2m4N6rWJoMxqdo7fkcyHcyedi6Niy9xTtnXYm56Qw\nfkxWvx77+e+/z9Z9xbz+yWE2fnqU4+UNWtAdZtBjszv45vl5/H71ZRgMXb+oXTTHCLqPWJd9MRtv\n+R6OH95GRHy8z89FU2sHDzy/HYCHb7iYmRNH97iWc8am8emBUkpqreSP6fm5sjTbAMgflebX5+7p\nuy8nIyWRX7z0Kfc8u5VOxcDqq+b6/+Z4Ud3YAcD4nEz57PeD/H0hvFE/FwMV0kA7JSWFsWPHkp6e\nDsDkyZPp7OzEYrFox1gsFlJSUno89uGHH9a+vuiii5g/f37gL1gIIcSAbN5zCoBLp+f0+7FhBj2X\nTs/h0uk5PHH7N/hkfzGvbXUG3ZaGVs6dOILn11yGofgUjO4KjrNS4slOjee9Ktj3nRuYHB/f63k2\nbj/K6ZpmZo5L54dXzPR6zDljnIH2nqJKFs0a0+P+kxXOWvKc9AS/XptOp2P9tf+fvTOPb6s+s/65\n2m15keV9i53dSZyFEBqgIYQ1NKRs7UyTbhSYGVLepqWllEDbaWeYKX1pSzu8dKELBUoLdCi0QGlJ\nCiEL2QPZndWO90WWJcvat/v+cfW7kqztStZi2c/38+GDI11dXduKc/T4POdchfLiAjzwi39gy6+2\nY2TMif+4c3XcDOx4DIzYAAA1MZYxCYKIz44dO7Bz504AgFwux+rVq1M+V06FdmtrK/r6+jA6OoqC\nggKcPXsW//Zv/4ZXX30VIyMjcLlcGBwcjGobue+++8L+bIzyK0Bi+sAmEPQ6IEKh18XkYevB8wCA\nS2frJ/z9WNJYjCWfuQzf3nAp2jqNWNx5EgU3Xg/liRMY2rcP/pCJ5KWzK9E9ZME/Dp5FbYmwnBjr\ndfHqjpMAgDuunAWz2RT1uefUCJXmB9u6YTTOi7j/fI9wTn0Bl9TnueGqmVBgDb72yx14/KW96DeY\n8dhdH01abNudHljsLqiVcvhdNhjd9qQeP52hnxcEo7W1Fa2trQCE18Xu3btTPldOhXZxcTEeeeQR\n3HnnnfB6vfj4xz+O+fPn44EHHsDGjRsBAI888kguL5EgCIKYIGN2N462G6CQc7i8pSY9J+V5FL6/\nG2ueeALqgwcBAH6dDorTp+H+6EfFw1bMq8af917AwbMD+Nx1C2Kezun24r1jPQCAG5Y3xTwuUcRf\nvFbIRHzyqrko0arwxSffwe/eacMNy2eI5TZSGRQXIQtSnogTBJE+ciq0AeCmm27CTTfdFHbbunXr\nsG7duhxdEUEQBJFO9p7uh8/PY8XcahQVpCfdovjxx1H85JMABIFt3bQJtrvuAl8Ubpe4bF41AODw\nuaG453v/VB/sLi9am8vFOL9ozGsog1IuQ8fAKGxOD7SaoH/T7vRg2OKASiFDTZk2pc/rxuVN2Hzr\nMvzglcN47f3zSQttqYkjBEFkh5wX1hAEQRBTm92BWL+rWtOXFe1Yvx4+vR6WLVswuH8/rJs3R4hs\nAGhp1KNQrcDFQQsMo7FtFG8fFjzkN8aZZgOASiHH3HodeB441TUSdl/3sDDNrq8oCksrSZbbrpwj\nXpPD5U3qsckkjhAEkXlIaBMEQRAZZfeJXgDAqkXSY/0S4V20CIMHD8YU2AyFXIblc6oAAIdi1LH7\n/Tz+8YHQ0Lj20vhCGwBamysARBbXdA1Jy9BORHN1CS6ZXQW7y4utH3Qm9VipZTUEQWQHEtoEQRBE\nxhgy23Gmx4QCtQLL51ZJfyDPQ7VzJ8o/+UnIO2OITY1G0qlWBOwjB2MI7aMdBgya7agr14oe7HgE\ni2uGw26fiD97PLddORsA8Oc9F5J6HFlHCGJyQUKbIAiCyBisDXLl/BqoFLEryUWYwL79dlRs3Aj1\n3r0oevrpCV0D82kfOhddaIfaRqQsEIpV7F3jJtqsFTJBWY0UPr5yFmQch+1Hu2G2uSQ/jqwjBDG5\nIKFNEAQxTRhfXZ4Ndp0UbCNS/NmK06eDAvvgQfh1Oli2bIFlgulTy+dUg+OA4x3DcLojPc/bAkJb\nim0EABYGhPbpbhM8Xr94ezon2tVlhbhyYS08Pj/+drBD8uPIOkIQkwsS2gRBEFOcMbsbGx97C9dt\n+RNcHl9azrn1cCcee/kg3N7Y5+N5HrtPCBNtKf5svqgIqiNHRIEdb8kxGUoKVWhp0MPt9eN4R7jd\no3PIgtM9JhQXKHH5glrJ52uqKobL48OFfrN4e9CjHb8YRyrMPvJaEvYRso4QxOSChDZBEMQUZszu\nxmce/xt2nujFmR4TOgZGJ3zOXqMV9/30XTz1+hE88/bJmMddHLSg12hFWZEaC2ck9j77Ghow8swz\naRPYoVwa8IeP92lvDUyzr1naKM3aEkDM074o2Ed4nhcn2umwjgDAxy6bCZVChj2n+sRJdSLYcanG\nCxIEkV5IaBMEQUxRmMgOzZAeMNkmfN5Hf79fjJ37yWsfYHjUEfU4Fut35cK6YNwdz0O1axcUbW1R\nH+O69tq0CmzGZfOEopzxPu23k7SNMMSFyEDyiNnmwphDyNUuK1JP9HIBADqtGtcsbQTPA2/sb094\nvMPtxajdDaVclrZrIAhiYpDQJgiCmIKEiuz68iJcuVCwRfSPTExov3+yD2/sb4dGJcdl86ox5vDg\n8f89FPXYXSdC/NkBgV1+xx2o2LABJd///oSuI1lWhCxEMq+6yerEgTMDUMg5XLO0ManzBRsiBSuK\nOM2uLE5rI+OtV7D0kfMJjzUEbCOV1ApJEJMGEtoEQRBTjDG7G599/O+iyH7lWzdj+RxBaA6MSLMg\nRMPj9ePbz+8BAGy+ZRl++K+roZBz+MN7p3FiXNSd389jz6k+gOdxs61TFNjqAwfg1+ngXrECyOJy\nZlNVMSpKCmC0OHGhzwQAePdIN3x+Hpe31KJUm9wEmGVpn+ocAc/zoj87HYuQody4vAmFagU+vGDA\nxUFL3GPFRUgd2UYIYrJAQpsgCGIKwUT2oXODosieUVWC2kAKRf8ErCPP/eMUzvSY0FRVjE03L8Gc\nOh3uvrEVPA/8+/N7w1JNTnUZYbK60FKqwMJv3C8K7NAlR2Rx6spxnBjzt/eUMGlP1TYCADVlhdAX\na2C2udA7bA0mjqTJn80oUCtw04pmAMBf9sZfihSj/coK0noNBEGkDgltgiBS5pVd5/CLvx7DmN2d\n60shAFgd4SL7fwMiGwBq9MKUM1XriGHUjh++IlhEvvu5K6BRKQAA999+CcpLNNh/ZiDMR8xsI8su\nmY2x++9Pa4pIqqwQhXYPXG4v3jvWAyBx7Xo0OI4L5ml3GoMZ2mmeaAPh9pF4EY2UOEIQkw8S2gRB\npMTImBP3P/0eHv3Dflz+1Zfw1OtHYHN6cn1Z05r/fulAmMhuqgrGzNUGhPZAikL7sZcPYszhwbVL\nG3HDJTPE20u1anzjnwQbyJPP7oAjkFPNFiFXLaqHbdOmnApsBhPa+071YsexLticHiycoUdDiuK4\ntZn5tI3oTlP9ejSuXtyAsiI1zvaa0dY9EvO4oHWEhDZBTBZIaBMEkRLHO4bB84BCzsFsdeGxlw/i\niq++hF/89ZgotojsYbI68cedZwEAzz+4NkxkA8G4twGJMXGhfHB+CC/vOAuVQob/+PwV4Yt2PI8v\nKAw41PY7PPPeL/CLN4/C7fVh/5kBAMBHJeRnZ4vFzRVQK+U41TmM3207DgBYe2lzyudbFGWinW6P\nNgAoFTLc/JGZAIC/xMnUDlpHSGgTxGSBhDZBEClxPLD89rnrFuDFh9dh+ZwqGC1OPPqH/bjyqy/h\nmbdPxC0zIdLLi9vPwOn24ZolDWhp1EfcX1GqgVzGYWTMGbUdMRZ+P49vPfc+AODfPrYYs2pKhTtC\nUkSqNm7EpUPtmOsYwet/fA9v7u+Aw+XF/IaySWVjUCvlWDJTWGL83x1CvOCNl86I95C4sIXI4xeH\n0TNsBZC+DO3x3HblHADAn/deiGkfIesIQUw+SGgTBJESxwINe4ubK7G6tR6vf/cWPP/gWixursCQ\n2YFvP78X//XigRxf5fTA6/Pjt9uE4pi717ZGPUYuk4mTTjb5lMJLO87gaPswasq0+PJtl4i3l23a\nFJYiYtmyBV/80o9xVl6Cb/xmFwBglYTa9WyzYm61+HGtXovFAbGcCjNrSlCgVqDPaIPL44O+WAOt\nRpmOy4xg5fwa1JRp0TNsxaGQXPRQKHWEICYfJLQJgkgJFufGJoQcx+G6ZTPwt/+6Dd/97OUAgDNx\n/KRE+nj7cCf6jDbMqi3FmiUNMY8T7SMSfdpmm2AJAoB//8zKMBHpXrkyIkXkgS+sgUYpF8tspNSu\nZxuWPAIIS5ATyZuWy2RYEPLbg0z4sxkyGYdbr5gFAPjL3uiZ2pQ6QhCTDxLaBEEkjdnmQufQGDRK\nOebW68Lu4zgOVy4UBJYhRmMgkV5+8/cTAIC7b1wUbGCMQrI+7Re3n8bImBOXt9Tglstnhd1n+/Sn\nI1JEGiuLsWn9EgCAXMbhipbapD+XTHNpyER7IrYRBvNpA5nxZ4dy25VC+shz29rw5Z9vx4V+s3if\ny+ODyeqCXMahvJiENkFMFkhoE0Qe8sH5Iaz/9z/jyAVDTp6fTbMXzCiHQh75Y6SyVPiHnoR25jlx\ncRj7zwyguECJf7pqbtxja8uTiPjjeah27cbvTv0Jd1w+M3Lyq9FETRH5P+uX4qrWety9dhGKC1WS\nP49sUVFagNtXzcdl82txxYKJT9xZ8giQOX82Y3FzBe5bvwQyGfCn3eex5sFX8KWfvotzvaZgK2Rp\nYdw3WwRBZBdFri+AIIjk+dvBDnx4wYDX913AstmVWX/+ExeNAIDFM8uj3q8v1oDjhCQMr88fVYwT\n6eE3bwve7E9dPR9FBfGFrVhaE09o8zxUu3ej+Ikn8O0Dgsd+76l9wA3Rvd/jKdQo8dLD6yQdmyte\n/NbtAACj0Tjhc2Vzos1xHL65cSU+d90CPPX6Uby88wxe23MBf957QbTEkG2EICYX9K8fQeQhZqsL\nANBtsObk+YOLkNEXyRRyGfTFGvA8YLQ4s3lp04rhUQf+vOc8OA6468ZFCY8PWkeiC23lwYNhVekm\nVSEennkdZLfcnNbrnkq0NOohC0z7M+nRDmVGVQke/5er8P6PPoXPXbcACpkMB84MAqDEEYKYbEgS\n2haLBXa78Gspl8uFPXv24IMPPoDf78/oxREEER2zTWhiZLXP2eb4uEXIaFSWkH0k07zwbhvcXj+u\nv2QGmqtLEh5fm6AdUt7XJ6aImL7xDTSt/Aoeb16NmsbqqMcTQIFKgUvnVkGjlGN+Y1lWn7uhshjf\nv3sV3v/xp/CFGxaiSKPENUsbs3oNBEHER5J15Pe//z1uueUWFBYW4rXXXsPw8DB4nkd3dzduvfXW\nTF8jQRDjMNuEKXH3cPaF9pjdjfb+UagUMsxriC0sKkoLgB4Thi12ANEtJkTqeLx+PP8PIQv6nhiR\nfuOpEdshoy9DOtevh9lkguOTn8QFqw9jB/6IxgotlAr65Wc8fn3/DTDbXOJvDLJNfXkR/vsLH8V/\n3XnlhFJUCIJIP5J+eg4PD6O+vh4+nw/nzp3DXXfdhXvuuQcnT57M9PURBBGF0cBE22x1Yczuzupz\nn+wUfK0tjXqoFPKYx7FfYdNEOzP89UA7Bs12zG8okxyjV11WCPA8FrYfB2+NMtWWy2H/whfAFxWJ\nleKZ9h1PBSpKCzCnTpf4wAxDIpsgJh+ShLZKpYLJZMKFCxdQXV0NrVYLlUoFn49a3wgiF4zaXOLH\n2Z5qM9tIoqKPioB1ZJiEdkZgS5B3r10kTWDxPEr378We489h64fPAb9+Ju7hnUMWAIiocicIgiCk\nI8k6snLlSjz55JPgeR633HILAKCzsxOVldlPOyAIIrgMCQA9BisWzsieNYMtQobGmkWDIv4yx4cX\nhvDB+SHotGp84qPxI/1CU0TUBw6gAoBRUYBRLxBvBttFE22CIIgJI0lor1mzBosWCVOTigphilVW\nVoZPfOITGb04giAi8Xj9sDo94p+zvRAZbISM/0a7YhII7e8+txP723rxqy9fiwL11EkzfSYwzf70\nNfMTfl7KI0dQsWEDAMCv0+G3C67FV+Xz8OQ1t+DGOI/rCryumjKcDU0QBDGVkfwvz/jptV6vj3Ek\nQRCZxGJ3hf25K4tC2+704HzfKBRyDi0JEhZyPdHmeR4//cshjNndePdoN27+yMycXEe6GTLb8ca+\ndsg4DndevzDh8Z5ly+C46SZ4li6F7a67sP3lIxjbfhp9CUpr2ER7BllHCIIgUkay0O7v70dbWxus\nViuKiorQ0tKCurqJt2oRBJEcZlu40O7Jokf7ZNcI/DyPlno9NKr4Pz6Y0M6VR7tn2Couim77oHPK\nCO3D5wbh8fmxurUeDaG2Dp4HvF5AqQx/AMfB9JvfiH+sCZTWxMrSZrDflGQrG5ogCGIqImkZ8tCh\nQ3jmmWcwMjICtVqNkZERPPPMMzgQaA0jCCJ7sMQRZaBtMZulNcc7hMr3xXHysxm5to60dY2IH79z\npBu+KZL7PxwoAGqoCNSf8zxUu3ah/I47UPyDHyR8fDDiL7bQNttcMNtcKFQrUF6imfhFEwRBTFMk\nTbR37tyJf/mXf0F1dbC0YGBgAC+88AI+8pGPZOziCIKIhC1CtjTqcfzicFY92scD1etLEiSOAEB5\nsSC0R8ac8Pn9kMuym8V8qitYrz0y5sQH54Zw2fyarF5DJmC/Iago0UC1a5e45AgA8t5ejD34YORU\nOwRWWjNgip6lDUCM9ptRWUyRcQRBEBNA0r98TqczwpNdXl4Otzu7+b0EQQSj/WbWlKBQrYDF7g6L\n+4uHw+WF15f6ZJdF+7VKmGgrFTKUFanh53mMjGW/hv10twkAUKsXJr9bP+jM+jVkgmGLAyq/F1/7\n+bfFqnS/TgfLli0wvPtuXJENBGvYY7VDAkHfP/mzCYIgJoYkoT1nzhy8/PLLaG9vh8FgQHt7O15+\n+WXMmTMn09dHEMQ4mKjWFanF6DUp9hGrw42V97+Iz//g7yk9r8PtxdkeE2Qch0US4wRzWVrT1i1Y\nR77yicsAANs+6Mr6NWQCw6gDbpkCPr1eFNiD+/fDunkz+KKihI+v0Qc82vGEdiBDu5ESRwiCICaE\nJKF9yy23QKfT4dVXX8VPf/pT/OlPf4JOpxMztQmCyB6mgNAu1apFn263wZLwcScuGmG0OHG0fTil\n5z3dPQKfn8fcep3kqLyKHC1EOtxetPePQibjcM/HlqG0UIVzfWZ0DIxm9ToygdEifC1PfuWhpAQ2\nQ6dVQ6OSw+r0xGwVFaP9aBGSIAhiQkgS2hqNBldddRXWrFkj/rdq1SpoNLQkQxDZRpxoa9WYEZg4\ndg8nnmif7hGsFKN2F/x+PunnlVpUE0ploB1yyJxdoX2+1ww/z2NuvR7FhWpcs7QRALDtwzyaavM8\nVDt3Qvvzn4fdzH47UDy7KSmBzeA4TrSPxEoeEctqaKJNEAQxISQJ7SNHjuB//ud/cPz4cQwNDeHE\niRN48skn8eGHH2b6+giCGAdbhtRp1WioEIRQj4SFyLMBoc3zwJgj+f2KEx3SimpCESfaluwK7VOB\nxJHFgWu98dImAMDWw3ng0w4I7PLbb0fFxo0oeewxyC9eFO82BlJH2Nc2FdhCZH+Mhchg/ToJbYIg\niIkg6fe/27Ztwz333IP6+nrxtp6eHrz44ou45JJLMnZxBEFEwuL9SrUqFBeqAEgrrTnTE4y7G7W5\nUKpVJ/W8LHFkcTIT7RxF/J0O+LNbZ1YBANYsaYBCzuHAmQGYbS7okvzcs4Vq1y4U/+hHUB88CEBo\ncrRu2gR/oJHX7fXBbHNBLuMm9DnUxon48/n96A38hmRGJS1DEgRBTARJE22/3y9WrzMqKyvhnyK5\ntASRTwSXITVimUhPgmVInudxJjDRFs6R3ETb5fHhdPcIOA5Y1JSK0I4dJZcJ2CJka7Mw0S7VqvGR\n+TXw+XlsP9Kd1WtJhoI334T64MGYS45sml1eooFMlnrsHiutiZY8MmCyw+31o7K0YErV1hMEQeQC\nST9Fly1bhueffx4rVqxAUVERxsbGcPjwYSxbtgwXLlwQj5s9e3bGLpQgCAGzuAypEieT3YYx8Dwf\nM/PYMOqAyeqKOIdUzvaY4PH5Mbu2FEUFKsmPy9UyJCuraQ2xudy4vAl7TvVj24dduP2jkzMxDmte\n3QAAIABJREFUybp5M3wNDbDddVdU/3UwQzt12wiAuB5tMUObbCMEQRATRpLQPn78OADgnXfeibid\n3QcAX//619N4aQRBRGM0JHVEp1WjSKOE1emB2eZCWVH0BeXTIdNsALDESJuIBVuEXCyhqCaUXFhH\nDKN2DFscKNIo0VRdKt5+w/ImfPeFfdh+tBserx9KRXYLdER4HoqTJ+FtbY24y9fQAOvmzTEfyrzu\nExXateXMOhL5m4bOIapeJwiCSBeShDYJaIKYPLBpdJlWDY7j0FhVjLauEXQbxmIK7bPjhLbUghsG\nK6qRUr0eChOE2VyGbAsU1bQ06sMm/M3VJZhXr8PZXjP2n+nHqkX1sU6RGXgeqt27xSZHw1//Cs+y\nZUmdgr1hmcgiJBC/tKabymoIgiDSRo5GOgRBpILT7YXT7YNSLhP9s40ViUtrzgQ8y+wxSQvtFCfa\nTBAaLc6UIgVToS1Qvb5ghj7ivhuWC+kjWS2v4Xmodu1C+R13hDU5ynt6kj6VMU0TbebRjmYdYYkj\nNNEmCIKYOCS0CSKPCCaOqMVpbWMlK62JnTzCrCPL5wgpHOYkliE9Xn/IcqH0RUgAUCnk0BWp4fPz\nMFmzU8POqtejCu1LZgAAtn3QCZ7PjvAvfOGFiKr0wf374Vy/Hm/ub8cnHn1D8rIom2hXTnCiXaUr\nhIzjMGxxwO31hd3XRR5tgiCItEFCmyDyCLNNEKu6omC0W4NYwx5daPM8L1pHVs6vAZDcRPtcnwku\njw/N1SVJRwIC2S+tYYuQCxojhfbyuVXQF2vQOTSGc73mrFyPY/16eGfMiJoi8uy2U9h3egDbj0qb\nbqfLOqKQy1ClKwDPA0PjsrTZ66iJrCMEQRAThoQ2QeQRoRnajBkJhHaf0Qar04PyEg1m1ZQGziNd\naKdqG2EwUWjIgk/b6/PjbG/Qoz0euUyG65YJLZFbP0hzeQ3PC/+Nv7msDEO7d0etSj/fJ4j9aF7p\naKTLOgKE+LRDhLbD7cWg2Q6lXIYafeGEn4MgCGK6Q0KbIPIIc0jiCENsh4xRw87ys+c3lImPS0po\ni4uQydlGGJVZjPi7OGiBy+NDQ0URSgqjxxCylsi0+bRDPNjq7dujHyOXR9xktrnECbVUoZ0u6wgQ\nUloT4tNmDaP1FUWQy+ifB4IgiIlCP0kJIo8IrV9nMI92VyBLezysEVIQ2oL4TKawhlksFjROTGhn\no7TmVGARMto0m3H14gaoFDIcPj84MfEfZclR+5vfSH44m2YDyUy0g4U1E4VNrEPbISnajyAIIr2Q\n0CaIPEJshQwR2qVaNUoLVXC4vBgZi1w4PC1OtPXiRDuZwhpj4JxVutSmqNksrRH92VEWIRlajRIf\nXVgHngfeSbElUt7TE5EiYtmyBaann5Z8jgtJCm2/nw/maKdhoh0t4q+LJY7QIiRBEERaIKFNEHkE\nm0SHLkMCoQuRkfYRtgjZEjbRli60TWOB3O4YGd2JyGZpjZg4EmeiDQDXizF/qfm0fRUVUHR2xqxK\nl0LoMqYUoW22ueDz8ygtVEGliLSiJEvQOhL8TUOXgRJHCIIg0gkJbYLII1jqyPj0j6B9xBJ2u88f\nXA6cF+LRttjdkuLteD4Yy6cvTk1oi6U12ZhodwcytBMIbRbzt/tkL7w+f/JPpNFg5Le/TUlgM873\nB4X2yJgTTrc37vHDaUocYYg17GETbSqrIQiCSCcktAkij4iWOgIAjYGJds+4iXbX0Bicbh9qyrQo\n1aqhUshRoFbA5+dhdXgSPp/D5YXL44NGKRfLbpKlSid4gTOdOjJmd6PbYIVKIcOs2tK4x9ZXFGFm\nTQnGHB4cbTdEPyjgwVa/917Uuz1Ll6YksBlsoi0L5KEPmOJ72NNVv85gHu0w64iBPNoEQRDphIQ2\nQeQR0ZYhgZB2yOHwiL+zoj9bJ95WWig9eYR5vstSnGYD2fNoMy/6vIYyKOSJf7SxCvbdJ/vC7xi3\n5Fj6zW8C3vjT5mRxeXzoGhqDjOPEEqBE9pF0ZWgzagMT7UGzHTzPg+d5KqshCIJIMyS0CSKPMEdZ\nhgSCE+3uoXChHboIydAFpuFS2iFNAWGfqm0ECE5gDaOOjNawt0lIHAll1aI6AIJ9BEDMqnT7hg1p\nF9odA6Pw8zxmVBWLxTCJhHY6M7QBoFCjRGmhCi6PDyarCyNjTticHpQUqiJeXwRBEERqpPa7YIIg\ncsJolBxtIERoj8vSFhchG8vE24I+7SQm2kWpCy+1Uo7SQhVG7W6Yba4JifZ4SF2EZFy5UBDah88N\nweH2okAhQ+m3vw3luXPw63SwbtoE2113TcgeEgsW7TenTicuJfaPRM9BZ6QzQ5tRo9di1O5Gn9EG\nj0+oYm+sLAYXsLMQBEEQE4OENkHkEeJEe3zqSIUgBnsCWdpMKJ0JsVMwkimtmegiJKOitACjdjcM\no/aMCW22CLkwTrRfKPpiDRY1leNkpxEHzw5idWs9xrZsgeLcuYwJbMa5gNCeW6dDVVmkVzoa6czQ\nZtTqtTjTY8KAyQabU/DsN5FthCAIIm2QdYQg8gSe52NOtIsLVdAVqeH0+MTJp8frFyen8+pDhbb0\n0prgRHti4i7TEX88z4sT7YTWEZ6HrL8fQNA+8n7Ap+286aaUU0SS4ULIRLtOH5lnHY2MTLQDIn/A\nZBP92Y20CEkQBJE2SGgTRJ5gd3nh9fEoUCugVkbmKM8Qs7QFwXRxcBQenx+NlUXQapTiccmU1qTD\now1kfiGyz2iDxe5GeYkmthAN8WBXrl0Lzm4XFyLfZz7tLMEm2nPqQ60j8YV2ulNHAME6wp47WFZD\n0X4EQRDpgoQ2QeQJLHGEpYaMpyGQPNIT8GlHW4QEgouUSaWOTMCjDWR+oh1avR7hL46y5Mj5fFC0\ntWFlSw0Ucg5H24eTKvGZCH4/jwv9owDGe7QTCO00p44AIaU1IzaK9iMIgsgAORfaVqsVq1atwjPP\nPAMAeOutt7B27VqsXbsW27dvz/HVEcTkIZg4oop6v1haE7AAhDZChpKMdSRtE+0Ml9a0dQeq16PY\nRuQPPhhelf7QQxjctw+eSy+FVqPE8jlV8PM89rX1Z+TaxtNntMLh8qKytAA6rRpVukLIOA6GUQfc\nXl/Mx7GJdnqtI8F2SIr2IwiCSD85F9q/+MUv0NraCo7j4Ha78aMf/Qgvvvginn32WXzve9/L9eUR\nxKRBzNCOMV0OJo8Igol5ludFCO1UcrQnNtHOdGkN+1yjLUL6b745TGBbv/xl8MVBMRkzTztDsEbI\nOXVCtrlCLkOVrhA8DwzFKK2xOz2wu7zQKOVhNqCJwoR2z7AVvUYrOC64WEsQBEFMnJwK7fb2doyM\njKC1tRU8z+PYsWOYO3cu9Ho9amtrUVNTg9OnT+fyEgli0jBqj74IyQi2QwpC+0yPMOUdbx3JVeoI\nkDnrSLwMbX7NGgwePBghsBkRedoZ5nxf0DbCSGQfEf3ZpQVpjd6rK9cGrskMn59HtU4LjYrCqAiC\nINJFToX2E088gc2bN4t/Hh4eRmVlJV566SX87W9/Q2VlJYaGhnJ4hQQxeYiVOMIQrSOGMTjdXlwc\ntEDGcZhTF15HHlyGzEHqiDn9Qtvl9qLp5Id4++jv0KLxRx7AceALC2M+/pI5VShQK3C214zBBDXo\n6eBcrzB9jya0+2IIbbEVMo2LkIDgvQ9drKVoP4IgiPSSs9HFu+++i+bmZtTW1oLnw9viNmzYAADY\ntm1bzOlNeXl5xq+RyB+USuHX6VP5deH2C39daytKo36eSwoFkdRrtMFg4+Hz85hbr0d9bXXYcU11\nwt83q9Ob8OvFPNpzmupQVBDdGy6FuV7h2kesrvR9j3ge3PbtcH3rO9h65CAAwPvKy/D9x3+Ih0h9\nXaxqbcS2wx042mXBxjmN6bm+GHQaBDG9vGWGeF2z6suBgx2wuPio1+o6K0zs6ypL0v4ary0vwsWB\nwJS9sWJK/x1iTIefF0Ty0OuCiAZ7XaRKzoT2sWPHsHXrVrzzzjswmUyQyWT49Kc/DYPBIB5jMBhQ\nWVkZ9fGPPvqo+PHq1atx9dVXZ/yaCSKXMBuHLsZ0uahAhcrSQhhG7Xj3w04AwKLmiojj2OPNgfPF\nwu70wOHyQpUGX3B1wAs8ZLaFFeqkCnfkCBRf+xpke/ZABcCoKMDfV92CTz7wQErnu2ZZM7Yd7sD2\nIxex8dpFE7q2RJwJFOvMD7G51AcSY3oD/vrxDJmFSXtlqTbt11NfUSwK7Zk1ugRHEwRBTH127NiB\nnTt3AgDkcjlWr16d8rlyJrTvv/9+3H///QCAp556ClqtFp/97Gdx0003YWRkBC6XC4ODg2hpaYn6\n+Pvuuy/sz0ajMePXTExe2ARiKr8OBoaFJTqVzB/z86wv18Iwasfr77cBAJqrtBHH+t1eAIDJ6sDw\n8HBM0dtrFGIC9UVqjIyMTPj6iwuUGHN4cKGrb8JWFIXFgqo9e+DT6fCLOavxsGYhNn3yo7jG4wFC\nPl+pr4vlMwWB+c7hjrhfk4lisjoxZLajUK1AAecRr6tUIzxfe68x6rVe7BUGEMUaWdpf4xUhi64V\nRfIp/XeIMR1+XhDJQ68LgtHa2orW1lYAwuti9+7dKZ9rUm29KJVKPPDAA9i4cSMA4JFHHsnxFRHE\n5EFMHYkR7wcADZVFONJuwMGzgwCA+eMSRwBAo1JAo5TD6fHB7vLGnFabxoTnm6goZlSUFmDM4cHw\nqGPC5/QuWgTDz36Ofz3px19OGlCr12LjmuhvyqWwqKkcuiI1eo1WdA6Nobk6M6UtbBFydq0OMllQ\nzCdahmT16xVprF9nsHZIAGiishqCIIi0MimE9pe+9CXx43Xr1mHdunU5vBqCmJwkWoYEgmUjPr/g\nw25piF5HXqpVw2m2Y9Tmiim0R6zpifZjVJYWoGPAAsOoA3PrI98ARBAomvE1N8M3Y8a4u3h8ebAU\nfzl5FjqtGn946GOoLou98JgImYzDlQvq8NbBDuw+2ZsxoR2sXg9fUE0ktDNRvz7+uQGqXycIgkg3\nOc/RJghCGmJhTZyWxoYQoaSUyzCzpjTqcVJKa0xpShxhVJQEsrQTRfzxPFQ7d6L89ttRsXEjin/y\nk4hDvv/HQ3hpx1loVHI89+DaiKzwVFjVGoj5O5G5PG2xer0u3AvN3iQMme3w+iKTU1i8X3maU0eA\nYA27WilHtS71NysEQRBEJJNiok0QRGKkTLQbK4JCe3ZtKZSK6O+lpWRpM6E90QxtRpUuQTtkYIJd\n/MQTUB8UUkT8Oh08c+eGHfbrv5/AU68fgVzG4ekvX48Vc6ujnS1pWJ72+6f64PfzYdaOdHE+htBW\nKeSoLC2AYdQBw6gjbMoMBL9mmZho1wWeq7GyOCOfM0EQxHSGhDYxJeB5Hh5vlAzlKQSbPuviWUdC\ncpDjTXklCW0r82inxzrCSmuGYght2dAQyj//eXAeD/w6HaybNsF2113gi4JNhX/ecx7f+d1eAMAP\n/3U1rr9kRtRzpcKsmlLUlGkxYLKhrXsEi5rSH/HFhPbc+sh0j1q9FoZRB/pHbJFC25KZHG0AWDa7\nEnffuAhXLqxN+7kJgiCmO2QdIaYEX/3ZNjR86smsFI7kAr+fF5shSwpjL0PWh9RnR1uEZDDrSLzS\nmpE0T7TZNHZ4NPr3yF9dDeu998KyZQsG9++HdfPmMJG941gP7v/FDgDAtzZ+BP+8el5arovBcVzQ\nPpKBlkin24uuoTHIOA7N1ZGWnlg+bY/XD5PVBRnHpc0vH4pcJsOjd16Jj102M+3nJgiCmO6Q0Cam\nBFsPtcNid+FYhyHxwXmIxeEGzwsReQp57L+2BSqFKGij1ZEz2FScifdopKt+nVFZwtoh7eBs0Zf+\nxh5+OEJgA8CAyYZ/+ck2eHx+/NvHFmPTzUvSck3jCdaxp9+n3TFggZ/n0VRdHNbGyBDbIQOxiozQ\nNzxyGf3IJgiCyCfopzaR93h9fnQNWQDETm3Id6T4sxmrF9dDp1XH9S5LsY6kq36dUVGiwbWmdjz+\n0mMo++IXk3rsnlP9sLu8uGJBLb796ZUZy7letageALD/9EDarUjn+6P7sxmxJtqZTBwhCIIgMgt5\ntIm8p3/EJiY1TFWhLWZoS/BL//jeq+Hx+qFRxf7rnYxHe8ITbZ6HavduXP1/f4CPHz0MAPC5RyAb\nGYFfH3vqHkpbl1AgccWC2owu7NXqtZhdW4oL/aM40m7AZfPSs2gJhPizkxTaRjFxJP0Z2gRBEERm\noYk2kfd0BqbZADAwRT3ayUy05TJZXJEtnCdxvJ840Z6IL5jnob/zTlRs2ICSDw/DqCjAt2Zfj8G9\neyWLbABo6xKaKRfMkP6YVGFT7ffT7NM+30sTbYIgiOkGCW0i7+kcHBM/nqoTbZPYCpmeZbjSQuE8\nZikT7YlYRzgOniVL4NfpYNmyBYvWPIj/blyFUVnshc5otHULQnvhjPQngYzn0rlVAIATF9Nbw5yq\ndURMHCGhTRAEkXeQ0Cbynq6QifZUFdpsop02oS1OtKMLbZfHB5vTA4WcQ1FB9OZIqVg3bRJTRArK\nBZGZsLQmhJExJwZMdhSqFWLzZSZhYp6J+3Tg9/MxM7QZrDhmwGSDP9DsCQQztDMR7UcQBEFkFhLa\nRN7TOTT1J9rM4sEE8kQJerSjW0dCE0cSLh4GimZKH34Y4PnIu4uKxBSRYMSfdKF9KuDPbmnUZ6VQ\nZXZdKZRyGS4OWmBzetJyzj6jFU63D1W6gpj2nwKVAmVFanh9vDjFBoITbbKOEARB5B8ktIm8p8sQ\nnGjbnB6M2WP7jvMVKfXryZBoGVJS4khAYJffcQcqNmyA9vnnod6+Pe7zVoqlNdK99Nn0ZwNCS+Oc\nQKHM6SSm2sOjDlhivPZY9frs2ujTbEY0+wh7U5KJ+nWCIAgis5DQJvIeNtFmInQqTrWTWYaUArOg\nxBKGicpqVPv3iwJbfeCA6MF2f+QjcZ+3IoWJdjb92YwFgQxyqfYRu9ODq7/xv7jyqy/hwJmBiPvj\nNUKGElVoW4TvBU20CYIg8g8S2kReM2pzwWx1oUCtwNLZQhQbCe3EaFRyqBQyuDw+ONzeiPsT1a8r\nTp0KE9jRmhyjIZbWJGMd6WRCOzsT7dDnYtP0RBzrGIbZ6oLJ6sKnvvdXvPr++bD72UR7TgoTbQN5\ntAmCIPIWytEm8ppugzDNnlmjQ0NlCYCpKbTTnTrCcRxKtWoYRh0YtblQMC4OMBjtF32ibd+4EZzb\nDftnPpNQXIeS7ETb6/PjbK8JQPymy3TDpufMH56II+1CI2lFSQGGLQ5s/tl2dAyM4mt3LAfHcbiQ\n4kSb53nK0SYIgshjaKJN5DXMNjKzRof6CiGRYioK7XSnjgDxfdqmMSfA87hs4BzgjZx4Q6OB7d57\nkxLZQND+YLBIE9odA6NweXxoqChCSWF6FkGlsCBkos1HWfAcz5ELgtB+6J9X4NHPXwEZx+GJVz/A\n5p9th9PtDXq0YySOMGr1wteTvYZH7W54fH4UFygTZqMTBEEQkw/6yU3kNSzab1adDvXlAaFtmnpC\nO93LkECc0hqeR9WRg9h55FlctaMLpnnFcPzTP6XlOStKCwFIn2if6sq+PxsQ3hCUl2hgtDjRO2xF\nQ4JYwaOBifay2ZVYOKMcM6pKcN9T7+K1PRfQMWCB0eJEoVqBusDEOha15eETbTHaj/zZBEEQeQlN\ntIm8ZvpMtFm8X/on2mJpTUiKyNd//Z+4arQLjqIScNEm2ikiTrSTFNrZShxhcBwnLkSeSrAQOTLm\nRJdhDBqVHPPqywAA118yA6/9+8dRq9eKtpI5dbqEUYl1+hhCm/zZBEEQeQkJbSKvYRPtqSy0PV4/\nbE4PZByHIs3EymNC0Y2zjqh37BBTREY1Wjw88zq89syrsG/cmLbnDM3RlmLJaAt4pLMttEOfM9FC\nJJtmL26ugEIe/JG6qKkcf/3P27BkZgUAacucoR5tnudFiw0ljhAEQeQnZB0h8hpxol2rgz4w9Ztq\nQjuYOKJKa2HLeOuI66qr4Fq5Eq5rrsG63krs6R7D61XpFbhajRKFagXsLi+sDg+KE/iuWbzegiwu\nQjLEhsgEQpv5s5fNroy4r7qsEH/61nr8Zd8FXLO0MeFzajVKlBaqMGp3w2R1wUgZ2gRBEHkNTbSJ\nvMXr86NnWBDaTdWlqCgphFIug9nqihpZlw36jFa4vb60ntOc5mg/8Dzg80UuQ8rlMP7pT7Bu3owe\nIXQkZo72RJBaWmOyOtFntEGjkmNmTUnaryMRbAKdKHmEWUOWzYoU2gBQqFFi45oW1JTF92cz2FS7\nz2ijiTZBEESeQ0KbyFv6R2zw+njUlBWiQK2ETMahRi8s2w3kYKq9t60fl9//Er77u31pPW/aEkdC\nPNjaX/0qeupIwEMcWsGebqRG/J3uDsT6Neghl2X/R9WcOh3kMg4dAxY4XNHfuPE8L1pHlsYQ2skS\ntI9YqRWSIAgizyGhTeQtnQF/9oyqYCJEtMKPbPE/f/4QPj+PYx3DaT3vhBNHxlWlqw8cQOFLL6G0\nQBl2fobb68OYwwO5jMtIpB6bzg6a40+0c+nPBgCNSoHZtaXw87yY5T2evhEbDKMO6LRqNFenZ+oe\n+hoepok2QRBEXkNCm8hbugL+7BlVQYEzPoc4WxzvGMauE70AgGFLfAGZLBNJHOHGxqJWpQ+/+SZK\nizRh52eYxVZITcKUjFRgxTM7j/fGPY55o3Phz2YsSODTZv7spbMq0va1ChPao1S/ThAEkc+Q0Cby\nFrYI2RSScVxTFrCOZDlL++d/PSZ+bDBLS9SQijlg42DLi8nAFxUBMlnUqvRYhTViK2QaM7tDue2K\n2QCAtw50wOWJ7WcXM7SbspuhHUqiiL9020aA8CztYWqFJAiCyGsodYTIW7pE60joRDv71pGuIQve\n2NcOhZwDBw5Oj09SooZU2MQ5JY82x8H8xBPwl5dHtDgGU0fChTare8+EPxsA5taXYeEMPU51jeC9\no91Yu6I54hif34/TPYK4bWksy8h1SGFhE4v4i74QmWgRMhXCJ9rMOlKYtvMTBEEQ2YMm2kTewqwj\nTdW5Fdq//Ntx+Hket185R1zGlFoxDgCP/PZ9fOLRN+CMkZSSMHUk4MEu/P3vo97ta2qKWpXOzmex\nh1tHxIl2cWYm2gBw+5VzAACv7bkQ9f6LgxY43T7U6rUoK8rdNFecaEepYvf7eRwTGyGr0vac7DXc\nMWCB1emBSiFDcUH68tMJgiCI7EFCm8hb2DJkUw6XIUfGnHjxvTMAgE03LxEnj1Irxnmexx93ncW+\n0wPYf3og6jFMaEdYOcYtOZZ85zuQGeNH0YWiG98MGfI5AYA+gwL31oB9ZNsHnbA63BH3t+WoEXI8\ntXotdFo1zFYXBkzh3vv2gVGMOTyoKdOiuix9E2e2Z9BrtAIQUloy4ZUnCIIgMg8JbSIvsQQKPTQq\nediiWLaF9rNbT8Lp9uG6ZY1oadQnXTFudXjE6Ljtx7qjHjMaZaI9PkXEr9PB+uUvg9dIF8eFagUU\ncg5Oty/MK82i/coyZB0BgPqKIqycXwOnx4e/H+qMuF/0Z8/InT8bCFSxx2iIDBbVVKT1OYsLlNCG\nNIBS/TpBEET+QkKbyEu6xGl2Sdi0r0pXCBnHwTDqgMfrz+g1OFxePLP1JADgvvVLAQQzog0JousY\noRF37x3tiXpMNKGtff75YIrIQw9hcN8+QWhrpZWiAIKIjLYQKU60Myi0AeC2K4Wp9p/3nI+4r00U\n2rmdaANB+0hbd/hvC46K/uz02UYA4fvC3jACwdcUQRAEkX+Q0Cbykk4x2q847HaFXIYqXQF4HhiS\nKHZT5eUdZ2CyunDJ7CqsbKkBEIxhk+rRDr3Gc31m9BjGIo5hcXuhy5BjX/tauMAuLo54nBSiCW2T\nNYZVJc2sXzkLCjmHnSd6I6w2TNTmMtqPEVyIHDfRZokjUarXJ0qY0KaJNkEQRN5CQpvIS6IljjDE\nCusM2ke8Pj+efus4AOC+jy8Rp+rMoy3VOjL+zcD2YyFTbZ6H4ty5kBztYIqJd8GCCQlsRmkh82kH\nfdLBZcjMTrT1xRpcvbgBPj+PN/e3i7db7G50G6xQK+WYVVua0WuQwoLGyCxtt9eHk53Cm4GlM9Nr\nHQHChTZlaBMEQeQvJLSJvCRahjYjtMI6U/z1QAe6DGNori7B2kubxNsrJdaLM5h1pDQQBfjesW5h\nyXHnTpTffjsqr7sOekM/gDRUsEdBFyXizzQWLKzJNNHSR04HMqvn1ZdBIc/9j6j5DWXgOOB8v1n0\nsp/pNsHl8WFmTUlKRUKJCBXalKFNEASRv+T+XzGCSIGuKPXrjJoyQaSMT4lIFzzP4+dvCgU1m25e\nArks+NeICe0hs9SJtnDcbVfOESbY7+2E/rbbULFxI9QHD8JfXIyZlkGoFDIUqNMfex/dOsI82pm1\njgDAjZc2oUCtwKFzg+gO2GZOTZLEEUaBWoGZNaXw+nic6zUDCNpGLkljrF8o4RNtytAmCILIV0ho\nE3mJONGOYx3pN2bGOvL+qT4cvziMipICfPKquWH3scU1qTXszDqybHYlHh/9AG8c+i00hw6JTY7H\n334Xb5XPQ6lWnZGIt6hCW2yGzPwkVatRYu1y4TcCf9krTLVZOcxkEdpA5EJkJhohQwn3aNNEmyAI\nIl8hoU3kHT6/Hz3DgtBujDLRznTEH5tm3712EQpU4VPmqpB4Pyk17Mw6Uq0rhPGmm9GnKsLr6z4r\nVqWP8ELMWyZsIwBQIlpHBI+21+fHqN0NGcelVPmeCreK6SMBoR2wjkyGRUjGwnERfyzaLytCmzza\nBEEQeQtVsBN5R7/RBq+PR01ZYYTQBTIrtEfGnHjvWA/USjk+f/2CiPu1GiU0Kjmcbh9sTg+KCuKL\n1aGAvaVKV4hlay5B056vYn5lFbYGmhyjRfulk/GlNSzhpFSrCrPEZJI1Sxqg06rR1j3vg4IwAAAg\nAElEQVSCU13GSRXtx2B53m1dI7A7PTjTY4JcxqG1OTM535Q6QhAEMTWgiTaRd8SK9mPU6JlHO/1C\n+8AZob1x+ZyqqNYKjuOCPu3xC5FsyfG226A8ckQ4hk20ywrxkfk1UBaocbLTiMGAAI+WOJJOSsct\nQ2YrQzsUlUKOm1fOBAA8+ecjsLu8qNYVonwSCUxmYznVNYITnUb4eR4tjfqob/TSQVmRGjVlWuiL\nNVn9XhAEQRDphYQ2kXd0GWJH+wFATaAOe8Bkg9+f2L6RDPtOCwkgl7fUxjymomRcDXtIighbctT+\n8pdwuL0YtbuhlMtQVqSGRqXAlQuE874XiPljmda6DGVaBz3a7sDzZV9oA8H0kTcCMX+TyZ8NAA0V\nRSjSKDFsceAfH3YBAJZlyDYCCG/Y3vzPW/H3/7p9UiSvEARBEKlBP8GJvCNetB8AaFQK6Is18Pp4\nDEssjpHKvjZhon35gpqYx1Tpgj5teXt7mMBmS46jjz8utkdW6grERcdrljYCCMT8ARi1R5bVpBOW\no22xh0+0s7EIGcrK+TViWgwwufzZQHgV+x93ngWQOX82o1avRX1FUUafgyAIgsgsJLSJvKNzMP5E\nG8iMT9tid+NkpxFKuQyXzqmOeVxFyEKkX6+H8vRpUWCzJUe+qAiDgWi/al0wvm3NkgYAwM7jvfD5\n/SGe6WxNtIXny0a0XygyGSdWsgPAwqbMeJ8nAhParIxoWQYaIQmCIIipBQltIu/oEqP9YrciMvtI\nOoX2wbMD8PM8ls6qjJtpLdawj9rB63QYee65MIHNYP7sqhChPbOmFM3VJTDbXDhywSB6pzM10WaF\nNWZbbifaAHB7iNCebBNtILgQCQAalRzzG8pyeDUEQRBEPkBCm8gJfz3QgR++clhSBN54OuPUrzPY\nRHsgjUJ7/+mAbaRlnG2E56HatQvKgwcBAJUlwYk2ALhXrgwT2IxoQhsITrXfO9aT8dSR8TnauViG\nZCxqKse1yxqxbFYl5tTpsv78iQj1jbc2VZB3miAIgkgIxfsROeFbz72PIbMDt14xC3PrpU8GLXY3\nTFYXNCq56IWORiasI3vbAouQgYVF8DxUu3ej+IknoD5wAO5lyzD85puo1I1bhoxBaIZ2KGuWNODZ\nbaew/WiPOHHOVOpIUYESchkHu8sLj9cvWkfKsmwdAQQf9O8evCnrzyuVlpAJNtlGCIIgCCnQSIbI\nOkaLQ6we7xm2JvXYrpBGyHhNibV6YYLclyahbXd6cKzDABnHYcWcKqh27UL5HXegYsMGqA8cgF+n\ng/OmmwCvN8Q6El9ox5pof3RhHVQKGY60D6Ej4EfXZcjKwXEcSgqDEX/iRDsH1pHJTlGBSrQrZTJx\nhCAIgpg60ESbyDpnekzix31J1qQHo/1i+7MBoFafXo/2ofND8Pp4LJ1VgWIFUHb//ZAPDMCv08G6\naRNsd90l2kPEGvZEQlssqwmfzBdqlFjZUotdJ3pxkQntDLY0lmrVMFldMNtcYrxfGWU3R+XOGxbi\njX0duGZZY64vhSAIgsgDSGgTWSdMaI+kNtGO588GQjzaaSqt2R/Iz145vxZQq2H5xjcgHxoKE9gM\n5tEeGrWD5/mYk/fBkLKa8axZ0oBdJ3rFP2cqRxsILlqGTbRJaEfl3nVLcO+6Jbm+DIIgCCJPIOsI\nkXVOd4+IHyc70WaLkLEytBmhHu1UFi4BADwP2fAwAGBfwJ99RcCf7fjUpyJSRBhFBeE17LFg9pnx\n1hEAuGZpQ9ifM7UMKZybWUfcQY92BoU9QRAEQUwXSGgTWSfcOpLqRDu+0C4qUKG4QAmn2ydG10km\nkCJSfscdqLj1VjjtTnx4wQCOAy6bHzs/mxFawx7Lp+31+WEcc4DjgIooVePz6svENwsFagVUCnly\nn0MSlARKa0bGnBi1ucBxmRX2BEEQBDFdIKFNZBWe58dZR1KcaCewjgAQmwYl+7RDBXZgyVFmNqN9\n+0G4PD60NOol50tH1LCPwzDqAM8LIjtaTBzHcbgmEPOXqQxtBptodw1ZwPNCWyRF1xEEQRDExKF/\nTYms0j9ig8XuRmGg8KXPaJVs7fD5/egxCBPwxgTWESA0S9su6fylX/96WIoIa3Lc6hbOE5GfHQc2\n0R6KIbRjJY6EsiZQx55JfzYQFPIs4SQX0X4EQRAEMRWhZUgiq5zuFqbZS2dV4njHMKxOD8w2l6RJ\ncb/RBo/Pj2pdYdxmRkZteXITbdfq1Sj4+98jUkT2iUU1tZLOAwCVuvjWkVgZ2qFcf8kMfObaFlzV\nWi/5eVOB2UQ6BgJCm6L9CIIgCCItkNAmRHqHrfjHkS5suHo+1MrMeILP9AiLkPMbymC0OHC214w+\no02SuOuU6M9mJFta41y/HoPXXRe24Ojx+nHo3CAAYGUKE+1Y1pHgRDt26Y5aKcfj91wl+TlThQnt\ni4OjAChxhCAIgiDSBVlHCJEfvHIIj/z2fWz9oDNjz3E64M9uadSjrjxQKiNxIVJqhjYj6NEOnD/g\nwS676y5w9ih2Erk8IkXkWIcBDpcXc+p0qCyNPX0eT7CGPbptJZihLf2cmYJ5tClxhCAIgiDSCwlt\nQoQtGvYYxjL2HGcC1pGWhjLUBSbOUhciLw4GWyGlIE60jdawJceCrVtR+MILks6xP2AbSWaaDQRL\nayZiHckW4xNGaKJNEARBEOmBrCOECLNYMBGYbnx+P871CkJ7XkNZyERbmtDuDCzrNVdLF9qXWXrw\nw5efR8VT7QAgNjnaP/1pSefYGyiquSIJfzYQnFTHEtpihnaUsppsMz7VhDzaBEEQBJEeSGgTAAC/\nn8dgwM5gMMevDk+VzqExOD0+1Oq1KNWqURdYVpRqHWF15E1JCG2tz4MVhvaoVemJ8Pn9OHhmYhPt\nxB7t3Avt0nH17jTRJgiCIIj0QEKbACCUlbi9fgCZm2ifCTRCtjSUAQBqAxNtKcuKPM+L1paZEoV2\nWZEaeytn486W2/Ctlx6FtlKf1PWe6hzBmMODpqpicfouFdGjbXFErWGf3NYR8mgTBEEQRDrIqUd7\ncHAQGzduxPr163HHHXdgz549AIC33noLa9euxdq1a7F9+/ZcXuK0IVTsxrI7TBS2CDm/URC8okdb\nwkTbZHXBYnejSKOMnLjyPLh33wWGhsJu5jgOteVFeL5mGfo9yb/U9wVsIyuTtI0AgRp2pRwOlzei\nht3v58UlSZZOkkuKC1QIfR9A1hGCIAiCSA85FdoKhQLf/e538eabb+Kpp57Cli1b4PF48KMf/Qgv\nvvginn32WXzve9/L5SVOG0KF9lDGJtoBoR2YaNeHTLT9/vilNcw20lxTEpwOhzQ5qtatg/wnP4l4\nXLIRf6EwoZ1MfjaD47iYWdomqxNeHw+dVg2NKve/VJLJOJQWBqfYZB0hCIIgiPSQU6FdXl6O+fPn\nAwDq6urg8Xhw5MgRzJ07F3q9HrW1taipqcHp06dzeZnTgn5TUIha7G443N60PwfL0G5pFIR2gVoB\nXZEabq8fxrH4U3S2CNlUVRK1Kp3X64GaSB91qkLb7+fFxJHLFyTnz2bEqmEflJChnW1CfdrUDEkQ\nBEEQ6SH347QAu3btwqJFi2A0GlFZWYmXXnoJpaWlqKysxNDQEFpaWnJ9iVOa8ULUYLZjhsQYPSm4\nPD5c6B8FxwFz68rE22v1WpitLvQZbXFzqi+GJI7IOzpQsWEDgECKyL33Qv3AA0BJCWA0hj2uJpDq\nkazQPttrgsnqQq1eixkS6t6jwWwhBss4oT2JMrQZgk9biE/UaWmiTRAEQRDpYFIIbYPBgMcffxw/\n+9nPcPLkSQDAhoCQ2rZtW8QiGSBMw4n0MWILn2A7eWVav8bH24fg8/OYU1+Ghrpq8fbmmjK0dY3A\n6pHFfb7+UaFMZdGsOuguWwrf3XeDb2qC74tfhLqkBEqlEkDk62JOYxUAwGT3JfX5nNgjlPasXtqE\niooKyY8LpaFaB6ATDm/452bz9gIAGqvLJs3ruLxUC2AYpVo1aqorc305aSPW64KY3tDrgogGvS6I\naLDXRarkXGi7XC585StfwUMPPYTGxkYMDQ3BYDCI9xsMBlRWRv7D/+ijj4ofr169GldffXVWrneq\n0jssTDML1UrYXR4MpuBpjsfJTuF7uqgp/HvZUClMzXsCrY9h8DzgcgEaDdr7zACAWXU6AID3Zz+T\n9Lz1FcI0um9YWgnPmW4jfvqXQ3hh2wkAwKrWRkmPi0Z1oJlywBT+tRwINFXW6pNLMskkbAGyvGTy\n2FkIgiAIIhfs2LEDO3fuBADI5XKsXr065XPlVGjzPI+HH34Y69evx6pVqwAAixcvxrlz5zAyMgKX\ny4XBwcGotpH77rsv7M/GcZYBIjm6BwUh29qsx4Ezg7jQPQijMbVJbjQOtXUDAGZWa8O+V3qtHABw\nrmsoeDvPQ7V7N4qfeAK+5maYf/xjnO8V7tMXRP9eswnE+PuKlMKS5ZnuYRw62Y7GymIo5OGrCX4/\nj+3HuvGbv5/AjuO94u3XLWvExy6pS/m1VRR4E9zVbww7x8W+YQBAsYabNK/bAqXwW6PSQuWkuaZ0\nEOt1QUxv6HVBRINeFwSjtbUVra2tAITXxe7du1M+V06F9uHDh7F161a0t7fjj3/8IziOw9NPP40H\nHngAGzduBAA88sgjubzEaQHP86KHeemsShw4M4ghiRF/PM/juW2ncPmCWrQ0xs6pZouQLHGEUReY\n6vaN2MQlx+InnoD64EEAgK+9HXajGYZRB9RKOWoDU2Kp1FcIx5/vM2PVA3+EQs5hRlUJZlaXYGZN\nKXRFarz6/nm0948CADQqOT6xai7uWbsI8xuSy90ej1haE+HRFv48GTK0GWwZsowSRwiCIAgibeRU\naK9YsQInTpyIuH3dunVYt25dDq5oemKxu2F3eaHVKDG7VrBmSI342396AN98bg+aq0uw64f/DJks\n0k8PBKP9WsaJV9YO2T9sQfmnPgX1++8DQFiTY4dR8Gc3VhbHPH8sKksL8e+fWYl3j3SjY8CCXqMV\n7f2jAWHdHXYdX7hhITauaUlbvJ24DDnuTctkaoVksNKasiJKHCEIgiCIdJFzj3Y24HkeR9uHMbu2\nFMWFqsQPmGawaXZNWaE4ZZUqtFkayMVBC9471oNrl0V6mm1OD7oMY1DKZZhZUxp2H2tc7B1xwDt7\nNpQnT0ZUpXe2Cf7uZomNkOO5d90S3LtuCQDA4fLi4qAFHYOC2O4fseHyBbX42IrmCEvJRKkMfC3H\nV9oPTcJ4vyWzKiHjOCyfXZXrSyEIgiCIKcO0ENofXjDg49/5C/559Tz8+F5amhwPW9ar1WvFkpUh\nszTrSG9Iq+Nvt56MKrTP9grT7Dl1OigV4WKW5VwPmGwwf+frsHzzm6LAZogZ2ikK7VAK1AosmKHH\nghkTs4VIIbSGncHzvCi0J5N1ZHVrPdp+9XkUFdAbUYIgCIJIFzktrMkW3QYhceJsoAKcCIdNtGv1\nWtHOIHWi3TMcFNrvHu1Gx8BoxDFiI2S9DqqdO1H82GPifWqlHBUlBfD5eQxwmgiRDQAdLEO7KrU8\n61wRrYbdYnfD6fGhUK2YdKJ2sl0PQRAEQeQ700JoM5EzPmaNEOg3hky0Qxb4fH5/wseyiTYrdXl2\n26mIY053G3HdyAX8+H+/j4qNG1H81FNQfviheD/zafeFTMdD6RTLakqj3j9Z4ThOXIhkPu3J6M8m\nCIIgCCIzTCuhPWR2wOtLLB6nG6JHW6+FSiFHWZEaPj+PkTFnwsf2BibaD/3zCgDAyzvOiF9vAFDt\n2YMv/c/D+Mex36H5win4dTpYtmyBd+5c8RhRaMfI7r4oWkfya6INQGy7NAQE9uAktI0QBEEQBJEZ\npoXQtgaEn5/nI6LWCGAgUAnO/NLBhcj4Xyu/PxgLeOPyJlw2rxpjDg/+tPuceIx6zx4s6T8Po6IA\nXV/6Kgb374d18+Ywiwh73mgTbbfXhz6jDTKOQ2OKVei5ZHwNO/ua0kSbIAiCIKY+00Jo20MmrAMj\n0rzH0wkmlusCgrdSok/bOOaAy+NDWZEahRol7rpxEQDBPsLzQlFM94bP4aFZ12Ph1V+H7KEHonqw\nWZZ2f5SJdrdhDH6eR32FMG3PN8ZH/InWkTIS2gRBEAQx1ZkWQtvm9Iofk087ktBlSCAYO5doot07\nLDyuvlwL5cGDWLeiGdW6QpzpMeH9U30AgLYxPx6fsQr1zTUxM7CDHu3I741oG6maeOJILmApLsMB\noT1oYtaRyRPtRxAEQRBEZpgWQtvqdIsfM5vEVOfBX+3Ef7ywL+FxDpcXZpsLKoVMLGqpKpU20e4x\nWHCtqR0v/uP/ofK221C08z187roFAIBntwpLkWe6ozdChsKytKMJ7eAiZJ4K7RL2psUe9n+yjhAE\nQRDE1GdaCG37NJtom20u/OG9M/jl346H2Wai0W9iZTVacJwwcWa2hphCO1CVvvahL+Kdo8+jtfcc\n/DodZGYzPnNtC5RyGd4+3IkewxhOByIV58epZ2eWlf6RSI/2xTwX2uNr2GkZkiAIgiCmD9NCaNvC\nPNqTT2jzPI8fvnIYL+84m5bzmULSQs72muMeGxrtx6gKiMOh0ehCW/PGG6jYsAFN50/CqCjAttu/\ngMH9++H4xCdQpSvE+pUz4ed5PP9OG870CBPtljgT7eoyLThOEKEeb3gqTL4L7ZgebRLaBEEQBDHl\nmRZC2xoitAfTZB2xOT0RojBVzveZ8ePXPsDXfrkDb+5vn/D5TFaX+DETurEY788GkLC0xnnjjfAs\nWIBnr/okmi+/H+2fuydsyZEtRf5++2mcZmU1DbEn2kqFDNW6QvA8MDjuNw6dQ0LZUDpaIXMBWywd\nJqFNEARBENOOaSG0w1JH0mAdGTDZsOy+F/Cln7074XMBwIX+YJvi/U/vwKku44TOZ7IGJ9pM6MYi\nNEObIQptkx2IVlqj0cCwbRt+PGcNrAo16svDk0SWz6nCkpkVMFtdsNjd0BWpxQXLWNQGkkdCs7R9\nfj+6hvJ8GbIkONF2uLwYc3igUshQVqTO8ZURBEEQBJFppoXQtrlChfbEJ9pHLhhgd3nx5v6OqJXj\nydIeENoalVDXffcTWyWVxcTCNCZ9os3eeIy3jlxrascLW59EwSuvRH8gx4mtkOOFNsdx4lQbABY0\n6kX/dyyitUMOjNjh9vpRpSuAVqOM+/jJCqtht7u86BgUvs+VpYUJvx4EQRAEQeQ/00JoWx1BoW2x\nuxMuCCaiMzBlBYAX3zszoXMBQHtArD/4yRVYNqsS3QYr7n3yHylbU0In2md6pE20a/Vacclx5mc3\n4J2jz+Oj5k4UPPts1Mc53F4YLU4o5TLRhxzKLZfPElNM4iWOMKJF/DFhmq/TbCC8hv1kp/CbCrKN\nEARBEMT0YFoIbbtLSB1h9oWBBLF1ieg2jIkfv7zjLNxe34TOxybaC2fo8euv3oAqXQH2nOrHo39I\nHM8XjVCP9oDJDrPNFfNYJrSb4ET5HXegYsMGqA8cgElViIdnXocP/9+voz6OVa/XlWuj5mNrVArc\nu24xAOCq1vqE1yxG/IUkj3QOCl/nfF2EZLAadia0q8soQ5sgCIIgpgNTXmh7vH64PD7IZZw4GZ1o\n8ghb0JPLOAxbHHj7cOeEzscm2rNqSlGr1+JX998AlUKG37x9Ei+lMDEPnWgDwNk4U20mtPUz6yEz\nm+HX6WDZsgW3bfxvfL/pKvS7o1scmMWjrjyy6ZHxfz6+FAef3Ii1lzYlvOZaMeIv+L1hvznI10VI\nBpv4n7hIE22CIAiCmE5MeaHN/NlajRI1ZYKYm2jySFdAaG+4ej4A4IV32lI+15jdDcOoA2qlXBSt\nK+ZW47G7VgEAHv7tbhw6N5jUOZlHu1CtAACc7o7u03Z7fTCMOiDjOFTpi2B6+mkM7t8P6+bNKKoS\n7B6xIv6YP7uhIrbQ5jgOdeVFkvzILEs7zDoyEIj2y2PrCBAU2qfIOkIQBEEQ04qpL7SdIUJbLwic\niSSP+P28aB25//ZLoFHKsftkX8pLkcyHPLO6JMyCsWHNfNx94yK4vX7860+2hU16E8Em2pfNqwYQ\n4tMOeLA1r78OIJAqAkH4KeQyeOfNE2P6ghF/0WvYxfr1OEI7GaK1Q7KJdnNNfgtt5tEetQsNpVRW\nQxAEQRDTg6kvtP9/e/ceHGV97gH8++492Wx2s5uETQLhokhAwDPq4SLa1BTRscqxVEdpp1hn2ini\nwXHUOdrbOZ0zndPL0Q4z5x/bTuvRzplhcMqB1lGnF++CB2pFQAilQiCBXNnNbW/Zy3v+ePf37n2z\nu8mS7Lvfzz8V2Gxe8Gf65OH7e55AZke7fwYd7cFRP0LhKBrra9DqqsO9G5YBKP1SpMhnL2uxZ/za\nv351A25Z1YKh0QB+9cbJgt9TZLQ3rGwBoKxBN733nprBtn/ve5D8/qwztAV10UqOPHuuiSOlanbU\nwKBXojihcBSyLKvLair5MiSQWACk/piFNhERUVXQfqGtRkcMcMdXi6cvRSmGmOvc3mwDAHy1ayWA\n0i9FqoW2O7PQNhp02P75DgCJwrYQoqO9cYUbXd5zeH7fj9VLjjGHA75vfhOQJHVmdYszs/BbIP6s\nrlKhrdfpsMCRyGlfGQ/CFwzDXmuq+JnTjWmFNjvaRERE1UH7hXYws6M94Cm9o61uKowX2jcvb0bH\nwoaSL0WKi5BLsxTaANBYr4zIu1LEXG3R0V7Z7sS/976LjZ4eROzKJUeRwZZravJ2tEXXVawOTyem\njsxWdARInaXdk3QRstJnTqePP2RHm4iIqDpov9BOio4kurQz6WgrhXZ7PM4gSRK+2qV0nf/nze6i\n309c+MsWHQEAp00p0q7kKHjTBaciCIQiMOp1sNaY8NKmbfj20i/g4H//r1JgJ61Kz7asRmi25+5o\nx2JyYupIlo8tVXJOu2dAG7ERILWjrZMkNNotc/g0REREdLVov9COz9C2mo3qmvFBrx+yLJf0furI\nuXhHGwC+fOtyWIx6vHfyUlGXImVZThntl40oyvJ2tGUZ+gtKN110sxtsZkiShMA/rsOPF9+GTz1T\nGR9WSEd7KEuhPTIewFQkBqfNgtpZ3NioTh7xTGrmIiSQ+KYFUP596nWa/8+OiIiIUAWF9mRAKTCt\nNUbUmAxwWM2YisRKXnGe3tEGALvVXNKlyCvjQYz7p1Bfa4KrPnuXU2xX9EwEEYulfXMQnyLi2rYN\nTV/4AnQjI2o+u6FO+biORU4AyoXIdKLQFpGaZK56CyRJ+bzpGypnO58tJG+HFBchK320H5BYww4w\nNkJERFRNNF9o+5M62kDikt9AiZNHLg6nXoYUSrkUmdzNzpVDNhn0sNeaEI3JiQ2PSQW2uOQIsxmG\n7m51hra4QCjWn3dnWVqjdrRdmYW2Qa9DY30NZFnpYCdL5LNnLzYCJEdHJhOFdoUvqwFS17Cz0CYi\nIqoemi+0xWXIuhql0HY3lD5LOxCKYGg0AJNBp76PUMqlyHyj/ZI5xYXIeMFre+65lCki4888g8EP\nP8TUrbdmdLRFoX2mz5sSl4nGYmosJNcUDHXEX9rSmnJ1tFvU6IhPM1shBfFnyYkjRERE1UPzhfZk\n0mVIAFgwg8kjopu9sMmWkbMt5VKkOnFkmmKysT5+IXJcKaID99yDaEODWmBPPv44ZJvSYVcz2vGO\ntqu+Bo31NfAFw2onGgBGxoKIRGW46i2wmAxZP68oCtM3aV6KL5XJt369FCI6cn5gDFfGg7AY9Zop\nTJviOW12t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Z87UlgkUsTUFbRERESoT45HTe+nobAJ/UsaF6n8ex37EDALOHB8lDh2LY21uy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\nOJ1OHA4Hvr6+lJSUaC68UPPmzQkMDKz5+nqfDzfzueEzffr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- "text": [ - "" - ] - } - ], - "prompt_number": 7 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "You may not have a full understanding of the exact *meaning* of a noise value of 100.0, but as it turns out if you multiply `randn()` with a number $n$, the result is just a normal distribution with $\\sigma = \\sqrt{n}$. So the example with noise = 100 is using the normal distribution $\\mathcal{N}(0,100)$. Recall the notation for a normal distribution is $\\mathcal{N}(\\mu,\\sigma^2)$. If the square root is confusing, recall that normal distributions use $\\sigma^2$ for the variance, and $\\sigma$ is the standard deviation, which we do not use in this book. `DogSensor.__init__()` takes the square root of the noise setting so that the `noise * randn()` call properly computes the normal distribution." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Math with Gaussians" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's say we believe that our dog is at 23m, and the variance is 5, or $pos_{dog}=\\mathcal{N}(23,5)$). We can represent that in a plot:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import stats\n", - "stats.plot_gaussian(23, 5)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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ND2Y/cSOe7q58GpvI52uTTUcSESdlSUpKqhbr5KSkpBAcHGw6htPQK1SzdPyr1vSYjcz6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\nZOZVk+D69et5/fXXAXjqqacYPXr0Tx7b1H2cu5hPdn4pmZd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- "text": [ - "" - ] - } - ], - "prompt_number": 8 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This corresponds to a fairly inexact belief. While we believe that the dog is at 23, note that roughly 21 to 25 are quite likely as well. Let's assume for the moment our dog is standing still, and we query the sensor again. This time it returns 23.2 as the position. Can we use this additional information to improve our estimate of the dog's position?\n", - "\n", - "Intuition suggests 'yes'. Consider: if we read the sensor 100 times and each time it returned a value between 21 and 25, all centered around 23, we should be very confident that the dog is somewhere very near 23. Of course, a different physical interpretation is possible. Perhaps our dog was randomly wandering back and forth in a way that exactly emulated a normal distribution. But that seems extremely unlikely - I certainly have never seen a dog do that. So the only reasonable assumption is that the dog was mostly standing still at 23.0.\n", - "\n", - "Let's look at 100 sensor readings in a plot:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "dog = DogSensor(23, 0, 5)\n", - "xs = range(100)\n", - "ys = []\n", - "for i in xs:\n", - " ys.append(dog.sense())\n", - " \n", - "plt.plot(xs,ys, label='dog position')\n", - "plt.legend(loc='best')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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hizdRIUQTTBG2I5BqkBujoRoEQRAEURayVlLLly/Hzp07M/79hhtuoOzgMjA6IS+hj4fj\nVAhXISw6zeWww+9NFcJkjSAIgiCIskCT5aqIkKIQJhWxOolpKMI0ZpkgCIIgygMVwlXEyHhU+m8a\nzVudxFLjlV1OOxqkZjn6LAmCIAiiHFAhXEUoFeHxCC2nVyPMI5xmjSBFmCAIgiDKAhXCVcQoWSOq\nnpgUn2aTrRHkESYIgiCIskCFcBUxoiyEaTm9KokpFWFKjSAIgiCIskKFcBWRbo2g4qkaUXqEA16m\nCNNnSRAEQRDlgArhKiKkbJajQrgqUXqEKUeYIAiCIMoLFcJVRCicniNMVB9Kj7DfI6ZGUCFMEARB\nEOWBCuEqIjROzXLVjuQRJmsEQRAEQZQdKoSriLSBGpQ0UJVEmUfYYUdDqhAepc+SIAiCIMoCFcJV\nRJo1ghThqkSpCPtpshxBEARBlBUqhKuEWCKJcDQh/UzWiOpE8gg7bHA77XDYOcQSvFQgEwRBEARh\nHVQIVwnKYRoA5QhXK6wQdjnt4DgOAdYwR58nQRAEQVgOFcJVwoiqEKbl9OokmpA9wgDIHkEQBEEQ\nZYQK4SqBKcJetwMAWSOqFTk+TSyEWXJEvSrCgiBg+84jGBqNlHtXCIIgiDqECuEqgSnCU1v9AChy\nq1qRRyyLX716H7P8zr5enPft3+Of//P5cu8KQRAEUYdQIVwlsKly01KFcL0WTtWO0iMMQJouNx6p\nzwi1/d0jAIBPu4bKvCcEQRBEPUKFcJUQUivCkTh4XijnLhEFoByxDAABr9gsN1qnCv9AKJL6/3CZ\n94QgCIKoR6gQrhJYIdwccEs+4YmoucXTx4cH0yLbjLDr8AC27jxm0h5VP1Edj3C9Wl1YATxIhTBB\nEARRBqgQrhJYIdzkc0vL6WbaIz440Ifzb9uAH/z21by2+8YvXsCX7noWIykrB5FOTJosJ371rPgs\nK5mBVJPc8HgESZ4v894QBEEQ9QYVwlVCaEIsLBt9LrnBykQV8XDvqPj/faN5bdc/EkYiKWBojAph\nLZST5QDAL6VG1KdHuH9EVIIFARgZr8/3gCAIgigfVAhXCUwRbvC55OV0E1XESCyZ9v9GCcdEKwXl\n4mqTYY2o8xzhQUVs2iBFqBEEQRAWQ4VwlSBbI1zycrqJinAknkj7fyMkkjwSSbGBb6JOC7tcMEXY\n7UgvhOvVGtGv8AbTKgJBEARhNVQIVwmh1LJxo99tyTQypgTn0ywXicmPrdfCLheSRzjDGlGf7xdL\njQCA4TFShAmCIAhroUK4SmCKcKPPJUVumVlssqI2H2tEWFEI1+tSfy5i6vg0C9T9SiUcTWBCcaNF\nijBBEARhNVQIVwlphbDH/AYrSRGO5aMIy0XzeCS/2LV6ISoN1EilRkg3NfXXKKbODh4iRZggCIKw\nGCqEqwSt1AhzrRGJtP83gtJGYXbGcbWS4RG2oPGxUukPpRe+pAgTBEEQVkOFcBWQ5HmMhuPgOKDB\nK6dGmGqNSDXJhWMJCIKxCXbKxrp6LOyMoPYI17M1YmBUpQhTagRBEARhMVQIVwGsSAp4nLDZOEty\nhJnNQRCAWMLYoAOlIkyFsDYZOcJ1HJ/WPyIWvixKjhRhgiAIwmqoEK4CZH+wG4A1y+lKS4RRn3Ca\nRzjP0cz1QiyutkakPMJ1qAgPphTheTNaAeTnER4Lx9A7PGHKfhEEQRD1AxXCVcCIFJ0mFk2W5Agr\nilqjPmHl4yhHOBNBEBBNpDfL+T0OAMB4NG7YglIrMI/w/JlBAPkpwtf+5Bmc861H61JJJwiCIEoH\nFcJVAGuUa/KJhbCVzXLifxuLUKP4tOwkkgIEAbDbONht4lfPbrPB63ZAEJAWJVYPsNQIqRAeNVYI\nC4KAXYcHMRaJo2tgzLT9IwiCIGofKoSrgFHFeGXAmsitSFwufo0O1UiPT6NCWI3aH8xoSFldRk2M\nw6tEBlSKsNGBGqPhuBRDR2OZCYIgiGKgQrgKGFFkCANWWSMUirDBMctKRbje1E0jRFX+YIYVzY+V\nCEuNmD25CW6nHZF40tBNF41lJgiCIEoFFcJVAGuWa0o1y/mtaJYrSBEma0Q2Yip/MCPgEW9w6u09\nY6kRbc1+BBu9AIBBA6pw/4iyECZFmCAIgigcKoSrgNC4qHo1qBXhSvMIU3xaVlhihEulCEu50HWk\nCAuCICnCbU1etDaIhbARn3CfshA26CsmCIIgCC2oEK4CQmFta8S4RakRhuPT4jRiORssj1ntEa7H\nLOGJaAKRWBIepx0BrwutKUXYiMKrLITJI0wQBEEUAxXCVYBkjUjFp3ndDtg4DpF4EomksWEX+ZKu\nCBv0CNOI5azoeYStUPgrDZYY0droAcdxkjXCSCFM1giCIAiiVFAhXAWExtMHanAcJ+XPmlU8pXmE\nC8gRHo/UXy5uLlghrPYI+yVrRGWkRgiCgLs37MB/v/ixaa/BMoQnpQpgyRphoPmtb0QepEHNcgRB\nEEQxUCFcBTBrBPMIA4CfNViZYI8QBKEgj7CyeE7yglT4ESK6HuEKs0Z8cmQI92x8B9/7v9tNG4zC\nFOFggwcAZGuEAasDi10DqlMRFgQh75vERJLHp8eHTdojgiCI+oUK4SqAKcJNikJYarAyIUs4luCh\nvE4XYo0AKEJNjX6OsPi5jlZIs9zWj44BEAeAvLWnx5TXYMVssEksgIONYkFsTBGu3mY5QRBw9Y+e\nwnU/fS6v7f7Pn3Zg1bcfw7bUZ0MQBEGUBiqEqwA2Wa5RWQibmD2rLnwLsUYAlaNwVgqSR1jdLOet\nLI/w1g/lYuvVXV2mvAZLjJAU4YY8PMKKHGEjcWuVRH8ojNc/6cZL7x3Jy9+/99gQAOBAd8isXas4\nkib1PxAEQSihQrgKGJGa5dzSv5mZJay2QhQyYhmgQlgNS43Qa5YbrwCPcCyRxGufHJd+fvXj41ke\nXTgsQ5h5hOVmufwU4eGxaFV50bsHZX8za4I1AntsvTShfnRoAFP+5uf49ZPvlHtXCIKocUwthJM8\n3dEXiyAI8ohlr4YibEYhrJokl++IZRvHAaBCWI3kEdaJT6sERXjH3l6EownMbm+A3cbh/f19pjTx\nSYpwo9ojnL0QDkcTGI/E4XLYEPA4keSFvArKcnN8aFz675Fx47aO4dRj68Vu9P7+PoxOxPDK+4fK\nvSsEQdQ4phbCRgsoQp+JaAJJXoDX7YDTIX9cZo7lVVsc8h2x3NIgKtfj9PmnIXmEHarJcl7zc6GN\nsnWnaIu4YOlsnDxnEpK8gDd3l94nLHmEmSJs0BrBbBGTmrzScVZNyRHHB5WFsPECnhXNZjUvVhrs\n2jE4Gs7xSIIgiOIwtRCuF/XCTNgFUNkoByiKJwusEfmOWGbL3fVy0TZKVEcRrqQc4S0pf/CqJdNx\n1qJpAIDXPi69T1guhNMV4eEcRS2zRYjT6MRtq2moRvdgYYowa5itl3Mqu6kerjIPOEEQ1QcVwhVO\nSMMWAVjbLGc4Pi31OFagkDUiHT2PMIvCK3chPDIexfv7++C02/CZBVNx1qKpAIBXd5XeJywpu6kC\nuCXgAccBIxPRrJYqNkwj2OhFS4AlTVRPsdQ9JHuERyaMFcKJJC8dG/VyTmWFcDXd5BAEUZ1kLYR7\nenqwfv16rFu3DldeeSVeffVVAMD777+PSy+9FGvXrsXNN9+suz0VQsXD/MGN/vRC2ExfaYYibDQ+\nTaUI0+efjp5HOFAhAzVe3dUFXhCw7KR2+D1OrJg3BQ47hw8O9JfUhysIglTgsNQIu92GJp8bgpDd\nMqBUhFsCKWtEFUWoFWKNUL739fKdYqtQRnKlCYIgisGR9ZcOB+644w7Mnz8fXV1duPbaa7F582Z8\n5zvfwU9+8hMsXboUQ0NDutvXi3phJlJihM+d9u+BlEI8bkKOMFOEm3wujEzEDOcIs8ex5W76/NOJ\n6niEG7zmqfv5sHWnaIFY2TkdgHizdcoJbdixtxdv7u7G+afNKsnrjIXjiMaT8Lod8KVu6ACgOeDG\n8HgUg6MRaVVBDZsq19bolY6vqlKEC7BGDCseVy99F+xmfCwcQzzBp/VHEARBlJKsZ5dgMIj58+cD\nAKZNm4Z4PI4PP/wQra2tWLp0KQCgpaVFd/twnUT9mAlTgxrVHmEzrREp5bI5pbgZsUYkeR6xBA+O\nk7erF/XKKLlSI8r9fm3ZeRQAcE6qEAYg+YRLmSc8oFKDGbLVQb9ATGuWSx1n1bR83l1AakRIoRzX\nS3yachUqHy81QRBEvhi+zd66dSsWL16M7u5uNDQ04Gtf+xquuOIK/OEPf9DdhhTB4pE8wqpC2Nwc\nYfFzYwWtEWsEK5a9LkfFjQyuFPQ8wm6nHQ47h1iCl5IlrOZo3ygOdIfQ4HXi1BPapH8/a6HoE36t\nhHnCan8wQ06B0C9sWf6wslmuWlIjxsKxtOmBIwbtJspCsF7OqUrle5gKYYIgTCSrNYLR19eHu+66\nC/fddx/effddvPPOO3jqqacQCARw1VVX4ZxzzsHMmTMztrM5PQgGgyXf6XoiAbFomhxsSnsvp7WP\nAACiSZT8PXa4xAKjvaUBQD9iCT7naySHRaXL53GiPdgs/hvsads5nWKBXK/HhM0u/v0tzQ0Z70GD\n142hsQhc3gYpUsxK/vKWqAafe2oHJrfLhfBFn2mE0/Ecdh4agN3tR3NA27KQD/E9gwCAKcFGBINB\n6biYEmwUfy84dI+R4QmxkDxh5mT0DYs2iYmYUBXHVP+RgbSfI3Fj34WkrVexTe7vYi2QBCf9N293\n18XfTBij3q8jRCbsmCiUnIVwNBrFTTfdhFtuuQUzZ87E0aNHceKJJ2LKlCkAgM7OTuzfv1+zEH50\nw5+xb/tGAMCqVauwevXqona2HhlJqV3qAoR5hMdMGCbA1JiWVLarEV8ie4zX7ZRTECogF7eSkEcs\nZ37tAj4XhsYiGJ2IlqUQfundgwCA807rSPt3n8eJFfOn4dWPjmLbh0ew7syTin6t3lQB29bsS/t3\n9ndny45l27Y3+5HkxYlyA1WSNXu0bxQAwHGAIBj3NisjxOpllUV5zqGGucL4yv9+Em6nHb/+57Ul\neb7n396P0EQMV61aUJLnI4hi2Lx5M7Zs2QIAsNvtWLVqVcHPlbUQFgQBt912G9atW4eVK1cCEAvf\nrq4ujIyMwOv1Ys+ePZg1S7uJ5vQzV+Iba5ZIPw8MDGg+jtCnZ0BUfu1CPO39S8bEgmB4LFzy93Vg\nOAQAYEEVE9F4ztc43iM2TbrsHISEeOEaCo2lbcfu4Ov1OAiNiap5PJr5mflcovJ/9HgfGpzW2iN4\nXsCL7xwAAJw2pzlj306f14ZXPzqK597cjTPntRb9eoeP9wMAAi4OAwMD0nHhsYuF7dGeId1jpGdw\nDADgFKJw8OJNYO/gaFUcU3sOifaSjsmNONAdQv/wmKH97uodlP57PByrir+1WELj8s3N4eN9GBjQ\n70UhMglHE3jk5Y8AAP/2pRVw2ItrNnx/fx8u/5cnIAjAqR2NaPa7c29kEvV+HSFEOjs70dnZCUA8\nJrZt21bwc2X9duzYsQObNm3Co48+issvvxxXXHEFwuEwbr/9dlx//fW48sorsW7dOsyZM0dzexqo\nUDzMI9ykOvFYkSPc7BdV6HA0AUEQcmyT8gi7HRXT/FVpMI+wS+URBso7ZnnX4UEMjkYwLejH3KlN\nGb8/c2Fp84SVDW9KWhqy5wLHEkkMj0dht3FoCXgUAzWqw0PKGuUWzBBvJow2gSkfVy/fKaUinM8E\nPkJE2VRZ7DETjiXwj//5CpK8AF4QpCxvgqgVsirCy5cvx86dOzP+/eKLL8bFF1+c88nrpbHDTEKp\n0P2M1AgpPs28HOGA1wmHnUMiKSCe5DULOHkb8bP2OOVIrPEIff5K9FIjAOWNjfUX/a2KtAiO4zJ+\nv+ykyXA5bNh1eABDYxEp3aFQWMqDOiItVy6wPEzDA5uNkx5fLdPHWIbw/JktePbtg3k0y8mPiyf5\nuogTUzbo5po2SGSivPaOheMZQko+3PnHt7Cva1j6mawqRK1h8mS5+lAvzEQvPk1WEGM51dp8icRZ\nUWuH1yXeK+XyCbMLl8dlh98t7ht9/uno5QgDCs93GRS/rTtTY5UVsWlKvC4Hlp00GYIAvPFJd9Gv\nxwrajNTqKPETAAAgAElEQVSIHJPi2Fhmtp3X7YDbaUcknqyKfN3uQdHONG+6uMwfGo+B53N/d9UT\n6OrhexWOyvag4XEqvPJFKZCMFZE1v/2jLjzw152w2zh0TBabWUuV0rL5g6O478n3S379Ioh8oRHL\nFc6ITiHsdtrhtNuQSApSE1apYIqwx+WAJ1UI58oSTrdGiNvUyzKuUWJSs5yGIszi8CxuMIzEElJx\nu3KxdiEMKO0RxecJSznCjdo5wnoKoHKqHABwnKwKD1aBKsysETMmBRDwOMELgqEbH7U1oB7Oq+xm\nHCBFuBCUx8hogeeU0YkY/vm/NgMA/vHzp2H5vMkASjfA5o7fvYZ/f+RNHOgJleT5CKJQzC2EaWm8\naKQRy77MpS2zsoQjCnXXk2riUl6YtAgrrBHkEdaG3bBoWUwCZfIIv723B5F4EotmtWZ4dpXIgzWK\n9wkPFJgj3CdZI7yKbVIqchUs1zJrxNRWvzQy3YhPWP2YevheRcgjXBTKVYNC7VZ3/O41HO0fw5KO\nSbjp8tNk61KJbkzY89DAFKLckDWiwpGsEX5Xxu/MKp6UirBRawQrnpVjc+tBucoHNixDyyPs95bH\nI8zGKp+jY4tgnDa3DR6nHR8fGSxqkpsgCJLFoVWlCLcqJstpLZf2h1Kxa4qCXVaEK/tiGk/w6A+F\nYeM4tDf7JM+mkSKPFQo+t7HvYrXD84I03RKonoEplUSxivCmHYfwyOY9cDvt+OX/PBdOh022LpXo\npnM0da6rhxs7orIha0QFE4klEI0n4bTb4MnaYGWmImzMGsEuzh6XHR6nHXYbh2g8iXgqKYEAYnH9\n1IhyTeNjjXKrlmQvhD0uB5ae1A6guClzoYkY4kkefo9TuslieN0OeJx2RHU8v2prBICSX5zNond4\nAoIg7rvDbpPipwwpwqmb4amtfgC1LzBEVJMsySOcP+G0Zrn8bq4HQmH8rwe2AgBuuWY55s0QPe2l\nHGkeT/DSNYXqBKLcmFoI17pyYTbsjrnR79Ls5jfNGhGXbQ6SIpxjzDJTcLwuBziOk+wRtX7RzgfW\nLMfsJkrKYY0YGovggwP9cDlsOH3elJyPZ/aI1z4u3Ccs+YMbtJMnmgP6Y5OlJjsNRbjSVcMuhS0C\nAJqYNWIi+37zvIDQeHohXOtpLOxcwk555BHOn3RrhPFziiAIuPU329AfCuPMhVPx9YvlOQClHGmu\nbOCjmFWi3JhaCNOSR3GwZVN1oxzDPEU41dSl9AjnKIRlRVgsnH1u8gmrkeLTNFIjZGuEde/X9o+6\nIAhiPBqzs2Tj7BL4hAc0fL5KsvmE+1OWijRFuEo8wqxRbkqrOE2Pef5zKcJjkTh4QYDf45TOA7V+\nc8nOJZObxcJ/xGC6BiGjvFnK55zy5Bv78cxbB+H3OPGzv18Nm00WYHKluuSDcp9IESbKDVkjKhhp\nmIZGoxwAeZRxEfE4Wigzgb1ug4qwwk4h7pu4HR0DMtk8wmYOSNFDik3LYYtgnHJCGzwuO3YfHSo4\nVF8vMYKRzfMrx67Jo5lbcwzhqBS6U4rwlBaVIpzDI8wK5Sa/S/ou1vp3ip1rGnxuNPhchtM1CBnl\nzdJoHtaI5985DAD45yuXYmZbQ9rv5JvU4hVh5T7V+vFMVD7ULFfBsGEaDXqKsGmpEfISvsdp0COs\nsEYAoOQIDbJ6hL3m3NRk4739fQCAMxdMNfR4t9OOFSkLxWufFKYKS1PldAthfYW3T7JGeBSPrw5r\nxPEMa4QxRZgVyk0+t8JuVNuFA1OEfR6HIlKvsm90Kg31QA2jsOPxhCmZEybNUoTpGkGUm5r1CD/y\nym6s+Mc/pE3EqTb0hmkwTLNGxGWbA1OhclkjIiprBBXCmTCPcNYcYQvfr8O9owCAudOaDW9z1iKx\naL77Tzuw82B/3q/JEiN0rRE6hW2S56UmnWBD9TXLdQ+JiRdMEW42mBqhVISZ3ajWPZVhKYHGidbU\nZz1MEVt5kZ4aYfzmmj1WS3xRTn4sdggGKcJEJWFqIRyJJ5Hky5Ma8OzbB9E1MF6SAQDlQrZGaBfC\nkq/UTEU4ZXUwOlnOK3mEaaiGmpiRHGGLrBHD41GEJmLwe5zSBc4I68+djzlTGrG3axiX/OBx3LNh\nR17JICxDWNcaoWN1GByNgBcEtATcaeOFq0URlqwRkkfYWI4wa6Zr8rul71StFw7sptvndqK5IfuQ\nFUKbcNpkOePnlNEJ8bFa4gsTRuJJvujzVJpHmK4RRJkxfWB9uVRh5idkSkw1wrrFda0RHnOmkbHB\nDx6XQ7ZG5BiokekRro9lXKMkeR5JXgDHAQ67RgKIxQr64V5xmtOs9gbNRBI92pp8eP7HV+F/XLQY\niaSAuze+g3X/8jg+PjxoaHtJEW7ITxHuH8lslANkj3ApIp3MpFBrBDsHNPnddZPEIlkj3A4pW5oU\n4fwYLzA+LdcqZGuJ7BHpinBtH89E5WN6IVyuQoj5CXtS3drVSChs0BpRwuKJ5+WRzR6nXW6Wixof\nsQyQNUIN8we7HXbNwlPyCFukCB9K2SJmqRpijOB1O/Bv152FP31vHWa1NWDnwQGs+d6f8csn3kUi\nmV0dljzCTfl5hPtCmdFpgL6CXEkIgoCeYfGGfGqLqhCeyF6ksAKw0Sc3y9X6d0ppjWhh1ghShPMi\nvVkuD0U4izUCKF3DXLpHmMQSorzUZCEsCIJ0wa0FRZhdNNWYkSOsLII5jjMen6ZImgAgxXFRt7dI\nNEtiBCCnbIxH45ZERR1hhXB7/oUw48yFU/HCnVfhy+ctRDzJ438/+jYu/9e/ZFWgBjR8vkqYIqwu\nfPqlYRq+tH9v9Lpg4ziMhuMVO7xlaCyKaDyJJp9L+l40GxyxzH7fXEfWiLBiSiW70SFFOD8mClCE\neV6QC2GvdpxiqRrmSBEmKgnTC+FyqBej4bhU0PVUcyE8IatBWpjhK5UK2pTX1/BADcXFCwD8daJe\nGSWbPxgA7DYbvG4HBMGaC8OhlDVidntjUc/j9zhx59+txMO3rsHUVj/e/bQPf9q2T/fxhXqE+0bE\n77E6bcJm49DMiucKnUDWNcD8wX7p34yOWJZSIxTNcrU+qEi2RjjlQpgU4byYiCib5YydT8YicQiC\n+J2227RLA2XDXDGMUo4wUUHUpCLMLpoAcLyKrRFs2VRvmcpvQuSW2usrj1jOVQinT02T/IxUCANQ\nFMJO/a9cg0nNj1qwxAh1VmihrFoyA/90xVIAwPaPjmk+hucFOfkhz9QIraly6m0q1ScsDdNokdVs\nZbNctg58+WbYLa8a1Ph3ip1LfG4nWgKUGlEIYcXN9Hg4bijlYZRdb7za1xugdIrwGCnCRAVhQbOc\n9Qe5Mux/eCyas4irVEZzpEYETPDhRhSNcoBSEc6RI6xSkmWPcHW+96VGskboKMKA/J5Z4RM+3CcW\nwrOLsEaoOadTnDy3/aMuzbSYkYkoEkkBDV6nZoQckMUjLFkjMgthaahGkSqVWbBCeKpCERYbUe2I\nJ/msGd1ainCtK2jSucTtkD7bXBYSIh3lMRJP8tIKaTbkRjn9KZPMIzxYrCI8QR5honKoUUU4feoV\na1SpNuQTk7ZH2AxrhDxVjinCxjzCkYz4tFQhTHf7ABTNcjoFIAAEUpMCzVb8kjyPo/1iITyjRIow\nAMxqb0TH5EaMTMTwwYHMjOFcGcKAWPBxnLgaomy8Y9tO0ti2lEH/ZnB8MNMaAcj2iGxq57CmR7i2\nv1NkjSge9XnXyDUiV6McULrUCFKEiUqiJgth9fjXavUJMzWo0Z89R7ikinBMpQgbHKgRjqZbKqQR\nyzW+jGuUmAFFmA3VMFsRPj4wjkRSwORmn3TjUipWLhZVYTa+WclgjvHKgOiV1ooW69NplgNKO/rV\nDNTjlRlNBhrm5IEabqnRrl4UYZ+yWa5CP9tKhR0j7LtmZKiGJLxks0ZIHn7yCBO1gwWFsPWFEIta\nYnRXqU9Y8gfqnJhMVYSZR9hpsFmORixnxYhH2Kr3jNkiikmM0OOczukAtAthluSilxjB0PIJZ7NG\nVIsiPFWlCLOVnmyFsFSc+F11owhHtOLTyBphGJ4XJGGiPXXjaEgRztGTAiib5UqoCNM1gigzNakI\ns4smW4auxgi1RJLHRDQBG8dJBZIaqXCKGmuGMIK+IqzvMUvyogeN4+T3nDzC6RjxCJuRC63F4RJE\np+lx1qJp4Djg7T09GekGsr1BXxEGMn3CgiBkTZtoLZFv0SzU45UZsiKsrdYJgpCuCEsjlmv7OxVW\nNMu1Unxa3ijtbawp08g5JWTAGiHfdJZOEY4leMPRh4IgYNfBPiRz5JXXO796+gNcdscTJEQZxPxC\nuAwfBLNGLJzZCqA6rRHKCT82m/bkL4fdBo/LnorcKs3FkU2Qk1Mjco9YjiqKZzYsgjzC6RjxCEsj\ns/OYBFUILDptVltx0WlatDZ4cPKcSYgleLyx+3ja7yRFWEPVVaJWhIfHo4gneTR4ndINWvrjK1sR\n7pYU4XRbhzxUQ7uoiMSSiCV4uJ12eF2OtBzhUt34ViLsXON1O+BzO+Fy2BCJJXOuShEi7Frg8zgl\nu5URa8SoIWsE+26WRhG2pa4XRlc5/vL6fiz9fx7Efzz+VlGvX+s8/Mpu7Njbi7f39JR7V6qCmlaE\nF3cEAcgXomoiJC1T6XfwAnKDVansEUz5dacsEVJ8WpYRy2FVgx1AHmE1hjzCFqVGHDHRGgEA5yxm\n9oiutH8flMYr51CEVVnC2aLTgNJlm5rBRCSOkYkYXA6bpG4ymnNkCbMCmSnHDrsNbqcdvCBIVqRa\nRDlZjuPknGhKjjAGEx98bocUhVY6a0TxI815XpAUarbCY7RO2H98BADw8aGBgl+/HuhNBQQc6B4p\n855UBzXpEWYXziUdkwBUZ2rEaI7ECIbUYFWiLGG1R1iKT8syYlltpwDIGqEmaihH2PgyZjGw8cql\njE5TslLHJyyNV86SGgFkKsL9qQJayx8sPr5yFeHjQ3KjnHq0dmOOZrmRcTlDmCGPPK/d75WcGiH+\nrU0+7WmDhDbMOuNzO/JShJk1Qm+AEyBmnTvsHCaiCUORbFqw5fqAx5l3XwQ7Nw6OhnM8sn4JxxKS\nkHagJ1TmvakOalMRTl1wO1OK8PEqVIRHckyVY5S6wSqiGpVsZKBGWDVVLm2/yBoBQFEIZ8sRtmig\nRqmHaahZMW8yPE47Pjo0kJbgMmAgNQLI9AjLU+UyEyMAOUe4EgdqdA+K+65ulAOgmY6hRJkhzJDs\nETW80sJWn5i9qlln7DahzYSkCDsVirBxa0S2gRocxxV948mK8oDXJV0njN7Ysb9DnQxFyPQqhL+D\nVAgbwgKPsLWF8HgkjnA0AY/TjhOnNgMQFeFq89SxO7omneg0RqmX09UT4oyMWFZnD6dtF01oDleo\nN5g1wpM1Rzh182CiR3giEkd/KAyXw5bRvFUqPC4HTp8/BQCwfZdsjxgYYQ1veSrCWRIjAPPj097e\n21PwEqNehjAgK51sgqSaYUWjHMNfB0M1wgqPKwCyRuTJhMJj7c8jklHZl5KNYq1IbF8avE7pxs6o\nkDNOinBOeoeoEM6XmrNG9Cn8hA0+8Y4zHJWXCqqF0Hjuu3Og9CpiRDUhzumwwW7jkOQF3c5e1uWt\nVIRtNk46ydXyMq5R5Pg0A5PlTFT7WHTazLYG3SbMUqAVo2ZYEVZ5hKXvtM52zX45a5bnS3vDOzga\nwVU/fBJrvvdn7Osaznt7rfHKjOYc1gh2DmhWFMI+Nma5hlda1FMqmw0MHiFk2PnW73Hm5xE2kBoB\nFG9FUirCygZQY9umCuEQFcJ6KK2gh3tDJEQZoOasEeq80cmpC1ClJUckeR4He0K6SrXk1/Ln8AhL\nKmJpLozReLoiDMjqrp49Qn3hYpBPWCaWuokwMlCjVJ+lFlJ0mkm2CAYrhLd8eAyCIIDnBcm6oG4a\nU6OnCOs1yzkdNjR4neAFQfrelIojfaNIJAWMhuP46j2b8lYltcYrM3JbIzLtUfUQoaacLAfI71Ol\nDkypNCbSmuXySY1gSm2OQliKKyysEFYqwvla6JgiPDAaLvlNb62gtEbEEjyOD1SfNdRqTC+ErVYD\n+5mfkBXCzWIhXClDNXYdHsC//f51rLjxYZz9z3/E/7fpI83HMTWoKcfdeamzZ8PxzMY3Tw57hHq8\nMoN8wjJRA4qwFTnCUnRae+mj05Qsnh1ES8CNYwNjONATwvB4FEleQJPPlfVmANDwCIeyWyOU25Ta\nJ6wc177/+Ai+ee9LeSks2awRjTlyhEc0rBHeOhiqwRIxmPoteYQrTBGOJZIVabkbT2uWM64Iy9aI\n7ElFxWYJKxVh6Xg2eGPH/g6eL/1Nb63QM5yulu+vIHsEzwt4/p1D+Ns7n8GyG36PPUeHyr1LACwo\nhK0OdJYU4ZQPkSkx5Ryq0T00jl89/QHOv20DLrhtI379zIfS8sXDr+zW3IZNlcu1TFXqMcuafl+3\nPe13atTjlRn10NhjFOYRdjuyTZYzPzXC7Og0hs3GYeVi2R4xYDBDGNBShFODODTGKzOYylzsxCs1\nrFHvrEVT0RJw4+UPjuLOPxrPMGXNclp+7JyKsEafQK17hAVBnormdYl/a0uO96kcDI1FsPSbv8ct\nD24r965koGyWYzfXhhRhg9aI1obirBGSIuxzKprljJ3zlH9Hqb/rtQJThJ128VpzsAIi1EITMdz/\n7Ic459uP4it3b8LmD4+he2gCz+04VO5dA1CD1gj1Mmo5FeF4gsfXf/48Vtz4MH74hzfw8eFBNAfc\nuP78Rdj4/XVo8Dqx6/CgZiOOdBHMqQiXOkc40+aQa8yyVnwaQGOWlRjxCAcsGKhxyMSpcmqYPWLb\nzmPSVLlcGcJAukdYEAT0h8QTe3ZF2Jzlc3ZjfeoJbfivm86Hw87hvqc+wMbt+wxtz8470zQUYSlH\nWKd/gRV+Wh7hWlWEmRrsdtolD3slpkbsOTqEobEoXv/keO4HW8xEVKkIGzsH87wgF8K5rBFFNsul\ne4QLs0YAlZkSUwn0pQrhk08Q42PL2TC3r2sY331oO5bd8Hvc8bvXcbAnhBmTAvjcqTMBAJ8ez7/v\nwgxqr1lOtYzKliTL4RHefXQQz7x1EDYbsGZ5Bx78pwvw7v/7Rfz4q2fjjAVTccHS2QCAZ946kLHt\nqMEO3tLnCGd6hOUINe3cSBZ3pGuNqGE/o1GizCOcpRBuyKPDu1AOmzhVTs05ndMAANs/6pJWQHJl\nCAPiceRx2RFLiGPG1b5/LdQNdqWiL7XM2Nbsw1mLpuFfv3wWAOB/3b8F7+/vy7ptIsmjdzgMjgPa\nmzPVbJ/bAYedQziakFYMlDDLRLpHOL+l5GpDVoPlc0klFsJsX4worVajnCzHitrRHOeU8UgcgsCO\nyexlQbHNcmke4Tyb5ZSrZeQZ14adaz+zYCqA8hXCOw8O4HO3/AkPPb8LE9EEzlo0FQ/+0wV49Wdf\nwP+85GQAwKfHy69WAzXpEVYpwi3lU4TZAIEzF07DA/90AS5e3pHmj7zk9DkAgKffzCyEQwYHavhL\n3CynpQgza4TeZ6lvjSCPMCNmJEfYZAVdEAQpNcIKRXhWeyM6JjdiZCKGVz44CgBozZEYwWAX26P9\no4jEkvC47FIRqP14cxVhZrW6/vyF+OJnFyAST+J//Oz5tMYUNb3DE+AFAZMavXBqWGI4jpO+31rL\n/loe4Vq3Rmg13jZVYGoE25dKTCMKK5rljK4yGRmmwSj2u6ZUnn15nPOSPJ92DarEATqFIAgCbrzv\nZaz9/p9LYiPsTd28swjLchXCuw4PIMkLOHnOJLzwk6vw2HfX4eLlHbDbbJibirbdf3ykInz2phbC\nHCcudVkZ3yGrR2IBzLx55VCE2XKwXpf86pNnwOd24P39/TiaKlAYWh3jWpS6wSqi1SznzD5mWb9Z\njjzCDMkjnGWynNtph8POIZbgNRXCYukbCSMSS6I54DZ0wSsFKxeLqvCzqVUPI4owIF9s9xwTl87a\nmrwZk9nSHm/SUA1pGl7qxprjOPzoK2dhxbzJOD44jq///AXdCVusL0ErMYLRlKVhTs4Sz2yWq9Wb\nS+lc4pZvGKX4tApSAFkhHIklTfmuFgMrKpUDNXIpwkaGaTCK/a4xRTigyBE2cmOnXimrFWvEi+8d\nwcbt+/D+/n48rbE6nA+JJI+BUXEVavm8yQCAQz2hsiRssL6QzyyYioWzWtN+197sRcDjxPB4tCI+\nR1MLYeVQBatQL6Oy/M7jg2UohEez+yK9LgfOO3UWAGR8AUal+LTy5Ah705rlsn+OYfII58SIIsxx\nXMk930rMHq2sBfMJswuxEY8wIF9s96a6ivWmykmPD5jTLMcU3/ZmuYB3Oey4/+bzMS3ox9t7e3D3\nhh2a20qJEVkGlzRnaQSTBmoorRGeGleEU6PctawRldQspyzKRytMFVZ6hJXn4GzFkFQI56UIF5cj\n3KDwCBsRS9TXuFqwRiSSPH70hzekn/+0dW9Rz9c3EoYgiIJDs9+NSY1eROLJMq2IsybnzHM+x3GY\nO60JQGXYI0wthH1lWMZTWyOYN69vZMLyYGlJEc6yHHzJGdr2iJCGP1CLUucIazW+5fQIa4xYBsgj\nrCQaz+0RBsy9eZASIyzwBzPOWjQNSiFXLwtYDbvY7u2SFWEjjy/1xbFftcLEaGvy4Vc3ngcAePCv\nOzUvNN2D+hnCDDk5IrOYymaNCNfozaWWNaLR5wLHiU2FlTIcQPl5VZo9QlkI22ycoXNKftaI4uLT\nlIqwtGpooEZQX+NqITXi4Vd2Y2/XMGa2BeB22rF9VxeODYwV/Hzsxp2dLzsmi+f6A93W2yOk1TSd\nVUBmj6iEhjmTC+H8jPDFEo4lMBaJw+WwSSqK22lHa4MHSV6QClOrYNNvsqlgnztlJjwuO3bs7ZUU\nJGVGYq6lqoBpk+WUAzVS8Wk61oiwRuQaIH/+tbqMmw9yfFr2QjhgYsOcnCFsnSLc2uDByXMmpf1s\nBHax3XvMYCFsQrNcJJbAyEQMDjuXltzAWHbSZKxdMQeReBK/fPy9jN9LU+Va9dVsVnio1c54qlHQ\nbuOkYwJQfqdq8+YyrHFTbbfZ0OjNnrlsNUq/cqU1zEnxaakC2MhQjXysEUqFvpAbEy1F2MiNv/oa\nN1hgakWlMBaOSatJ31t/Bi5cOhuCAGzYVrgqzBrlWFpWxxSxEC6HT3ggJSIEdQrhE6amFOGumleE\n85sjXiz9ijde6SecUqaGucExNlJW/yLu9zjx2ZPFKBHmoxxLdfD6Pc6cHbylVhCzKcJ61gitBjvl\nvpFHWBmfZuzzNCNC7bCF0WlKzknlCQP5e4SZWpBLSW4tMtJJC3bjPKnRqzuO+n9dvQwcB/z+5Y+l\nRA6GEWuEXpYwyxEX1VD5tX01PlBDr9+g0oZqDCtuuCqlOGeEFYowAENDNUIGU4oAwGEXhSZBKOxv\nL9wjLL6WPfVdrPZmuf98+gP0jYSx7KR2XHL6HPzNqpMAiPaIQhvIJCtXquZhivDBHuuLzX7F+VOL\nuVPrxBrhtdgaoRezxC5EVg/VMJqdqk6PMBqdBpiQIxzXUoSzWyMkX5+uNaI2L9r5wBThXFPVzJwu\nJw/TsM4aAQArO+VCOGg0NSL1nWGjqSfl2M4MRbhXNaVSi3kzWnDVypOQSAq4Z+M7ab8z1iynnSU8\nrGGLAABvzXuEsxfCleITVhaAlacIp4+oNqQIGxymwSjm+6aVGpGPR3hGytpVSc2T+XJ8UByyBQDf\n/9vPgOM4rF4yA21NXnx6fATvfpo9mlGP3iHW0yAWwnMml08Rlq0R2ufuurFGMP+P0akxxaL2BzMk\nRXjQWkVYapbLcRE//7RZcDlseGN3N/pGJjAykdkko4dZOcJuZx4jluPa1gjyCMsY9QhL6o0JhbBk\njWizVhFeMW8ymv1uNAfceVgj0gvA3Iqw7FssVRwPu7FuzzLRDgC+deVSOO02bNi2L21k6HEDHuFm\nv7Y1ghVaTapmWX+N5whrWbOAykuOSLNGVJhHWEqNSF1/DXmEJ+RsXyOw72ch9gT2fhWaGtExpSn1\n2tWrCP/0T28jEkti7Yo5WJFKd3DYbbjirBMBFN4015s6ZzFrxJzUe3XA4kJYEATp89G1RqT27VBv\nCPFEeb3/NdUsp6cIT2YRalkyP81gMJTbGgGId+GrlsyAIADPvnVQapQzcnfuczvEmLpYEolk8QeT\n1oWI/bfeiGW9ZjnyCMvk6xHOt/nxUG8o67JxNJ7E8cFx2DgO04OBvJ67WDwuB/78g0ux4Xvrclp9\nGMwjzFA3q6nxuh3wOO2IxpMlS6nRu7FWM6u9Ees/Ox+8IOD//En0/AmCIN14sxtxLfRyhEPSzXD6\nDYF8Tq3N75SkCLvVirB4PFRMIazYj0pulgNgKEItn1VIoPChGoIgSPsR8Lhk+5yRZrlUIT97cpP0\n2pWQQZsvuw4P4I9b9sBh53DbtSvSfnf1OaI94onXPtWNZcyGnHIjnnNmKxRhK9+rsXAc0XgSPrcj\n47vM8LodmB4MIJEUcLivfNPvgBprlutLLWW2qQpP1qxipSIcT/AYHo+C4zJVHS2U9oh8/Focx0md\n5MVaEOIJHklegI3jpDnlgCIGT6cQZtYI8gjrY9QjzBSZgdGw4ec+0D2Cz37nT/jinc/qnuyODYxB\nEIDpk/yawx3MZt6MFiyY2Zr7gSnUinCuZjlALpZKlRwhXVQMvPZNl58Gj9OOZ946gA8O9GF4PIpI\nPIkGr1NS+bXQyxGWFWFVIVzjI5bDOh5h9j5VgkeY5wVp1Q6oxEJYzhEGjI1uz9ca0VygJz8cTYAX\nBHhcdjgdtrzEEraP7c1+eN0OafJktfHvD78JQQCuP3+RpIoyFs8OYtGsVgyPR/HCu4fzfm51Idzs\nd6Ml4EY4mpAGbVhBrsQIRqX4hC0qhC2yRoS0FRy2TGDlUA12p9wS8MBuy/02X7hsNhx2Dq99fBwH\nU9skBmoAACAASURBVEvY6ougHqVKjlCqwcoGHRqxXDxGPcKnzW0HAPz17UOGn/uxrXsRjSfx3v4+\nvL+/X/MxrJFrpsW2iEJpUVkojMSutTaw5drSLJnqnU+0mNLix1cuXAwAuOvRtw01ygH6U9PYz+oc\n8VqfLMfOMRmKcAVZI0LhGJT3m5VUCPO8IL+HLuOKsCS+GEiNAOT0l3wV4VFpvLL4OsqM+lxDH9gq\nWYPPhdYG8TtZbfaIzR8cxSsfHEWD14mbr1iq+Zi/WTUPQGH2CDk1Qj5ndaQU9APd1hWb/QZXw1mW\n8P5aLoStbuxgdzxq9Yh59KxsljPaKMdo9ruxcvF0JHkBj23ZA8D4MlWpxizLjXLpF6GcAzV0RixL\n+1Wj6lU+RCVFOHshfNGy2fC5HXhnXy/2GzhxCYKAjdvlE+Yjm3drPk4epmFto1yhKBVhp91myC9f\n6oY5vfOJHt+89BQEPE68/MFR/OX1/QCAKVn8wYBc4KmLKWaVUMe2WZ3EYzV6inAlpUaobSyV1Cyn\njJ9jSSeBfOLTDFsjCsvtZvvA9slus0nXDb0VRwYTehq8LunmtJqSI5I8jx8+LA7P+MfPn6bbL3HF\nWXNht3F46f3D0nQ2IwiCgD52zmqW7VhzyhChNiCJCNnrH6lhrqu8DXPWKMIWx6dlKMJliE9jS9tG\nu+QBYO0K0R6x6/AgAOMnpVIpwlEpOi29WPPkyBFWKxAMqz//SoYVwrk8wj6PE2tTNpmN2/blfN63\n9vTgSN+YdNP0+Kv7NG9YjpQpOq1Qmnxu2FKrEuo4RD1KPVRDb5iGHq0NHnxj7RIAwH8+9T6A7I1y\ngNIaofII6zTLKVdnyjE21Wzkm2q1IpzyCFdAIaxWpSupWU4eryy/f0b6DvIZqAEUftM5plKEAYWF\nLodgwq5vAa+sCJcyLtFs/rz9U3x8eBDTgwH83UWLdR/X1uTDuSfPQCIp4PFXPzX8/ENjUcSTPBp9\nrrRrsTRUw8JCmKwRCiz3CIe0FZxggxcOO4ehsahuw1epYUs27AtrhIuXz5Yu/oCx1AhAkT1brDUi\nru31zRWflitHuFbVq3xgMWC5FGEAuGql2DCxcXvuPMk/pcLXv/S5BThtbhtGw3E8+/bBjMcxRdjq\nxIhCsdk4qQg0qsiWesyy3vkkG99YswTNATcSSfFzy9YoBwCNOjnCWlPlAPF9kVZoLDqXWYmuIsw8\nwhVgjWD7wM7V6ui7cqJulAPkJBpTFOE8v2tqRVi5r7ksdGMKHzNbcq8ma8T2XV0AgG+sXZJxrVTD\n7BGP5WGP6FFFpzFYcoSVWcL9OYZpMOQItRouhP0WdzjrKTg2GycdHL0WJUfIiRHGFeFgoxdnLpoq\n/dzoM+gRTmUJjxe5RBfRmRBndKBGpiIse4Srsbu3lLBmObeBQvjsRVMxpcWHQ72jeHtPj+7jIrEE\nnkotwV+18iR8YfV8ANr2CNaVa3WGcDEw1cloIcqWGkt1cexj40qbjRfCDT4Xbrj0FOnnXIpwo1cc\nHzwajqdN6RrOMmLd6vOqlegl0EjWiEoohFM3KdOC4mdbSYqwulEOkNXXbFnz+UyWAwofszymMTHV\n6PEsqck+N4KNvtTrV08hzGoPptBm44LTZqHJ58KHB/vxyZHBvJ6/XXW+6ihDlvCgwejYqa1+eFx2\n9IfCZc0Iz1oI9/T0YP369Vi3bh2uvPJKvPrqq9LvxsbGsHLlSvzmN7/R3d6XxxzxYonEEghNxGC3\naY9DtXqohtEMYTXMHgEADT5jmY6lskaENabKAQpFWMMawfOCpCSrizynwwa30w5ekB+jxdG+UXzr\nvzajq4gZ65UMzwuIp6LtXAYSG+w2RZ5klnGbL71/BCMTMSyeHcSCma34/Jlz4XHasf2jrowpZ0ck\nj3B1KMKArDoZaVZTPr4U1ohwLIHRcBxOu03zfJKNr1ywWGrQnT4pe1SdzcZJDUpKnzBLJdB6baMK\nWjUiK8KqHOEKGqjBCmHWeFpJzXLqYRpAbo+wMtIs70I4b0VYnirH8LqNNVWPKzzCrY3sprf8x4NR\n1OOPs+FxOXDpZ04AYLxpTu/5pUK427oItVxT5Rg2GyclZ5RTFc56VXY4HLjjjjvw1FNP4d5778Wt\nt94q/e5Xv/oVOjs7s3r3pMxLC07YucahWj1mme1PayC/QnjN8g6wt1SdIapHyZrldMLspWYGjRsa\n5n31OO2a77sRn/BDz+/CI5v3SJN2ag05McJmyOsKyPaIp944oJsnyWbSX3m2WDQ3+lySv/jRLfLJ\nc3g8ipGJGHxuh+GBFpUAu9jmbY0ogUqk7Dcw+pkxvG4Hfn3T+fjmpadg9ZIZOR8vj1mWC5WQTnwa\nUNtjlnVzhCvQI8z89hVZCHvk9y+XIjweiYMXBHjdDsPRiiyhpRSKsM/g4C2lv5gtuVejIqy2Luhx\n9TmiPWLj9n2GZgSw+Fj187cE3GjyuTAWiUveXbPJNVVOSSVMmMt61AeDQcyfLy63Tps2DfF4HPF4\nHPv378fg4CA6Ozuz3mF4LTxh9+UIv5cb5qxShPNvlgPE/fzsKTPhsHM4YWpT7g1QurG8el7fbPFp\nTMHx6IRmG/EJH+0XleC3stgAqhnJH5yjUU7JwlmtUp7ki+9l5kkOjkbw4rtHYOM4ST0GgGtT9og/\nbtktLbUzdXh2e2PeRV05yVsRLvDirIXecB6jrJg3Gbdfe7qhASKNGg1zeh5hAPJY2hqMUJPOJ870\n80mTwiNcbpvViEoRHp2ImbpPQ2MR/OvvXsc+A531E1rNcjmuD/lGpwHpzXL5/O2yIpxpjcjVSyKp\n1n6lNaL8N0ZGiCd4DIQisHFcziQFxvKT2jFnSiN6hiew7aNjOR/fk0qMUBfCHMehY4qsClvBgEGP\nMCBHqJVTEc7u2FawdetWLF68GE6nE/fccw+++93vYsOGDVm3mdImBujHeQ7BYLC4Pc1BdJ842nTa\npEbN1zphehsAIBTmTd8X8XXEorFj+uS8X++PP7gafSNhnJC6U8pFW6t4ICU5R1F/m9MtzjdvCvjS\nnicG8WIcTWS+dxO8+MXye1yar93o9wD9Y3B6/HA6xROe+nG9I+Jd/c5DA3B5A2gwqIRXC0m7uArh\ncef3+Vx30Sm49f6X8eSbh/Dli5en/W7j6+8inuRx/tI5WHTiTOnf161sRceUbTjYPYIPjozh/KVz\nMLRL/FxPnBG05NjPF73j4itrluHoQBh/89mTEQzmHsbRMV28KIbCiaL/zuge0Zc3bVKT6e/ZpOYA\ngAHwdrf0WqyLv2PGlIyLSVNA/Nnu8lbk51kMbPFjSnsw47jwuh0IRxPw+BuzDikxm3Dq/uOE6e1w\nOe2IxZPwNzRJS/yl5tHtO/Bfz34IwebAf9x4UdbH2pzdAIDmBr/0vs2MijdjE7Gk5vHSPSreMLc0\n5nc8FfJ5JCGKAZOD8vequdGf2ndP1tdnN36tjX60t4iWo9GI9t9UCroGRvHKe4fwhXMXwW5wIqYe\nR1M9Gu3NPrS3tRne7roLT8G//nYrnnjjMK767KlZHzsyIb4/c2e2Z7wn82a24f39/egbt6b+GUzd\noJw0exqCOSaZnnLSDADv4uhAuOB9Y+eKQjFUCPf19eGuu+7Cfffdh5deegkdHR2YOnVqzjvBP/7h\ndwAc2Lv/IDZv3ozVq1cXtbPZ6ElZHtp1Auynpj6MYxb5UPtH8m+0YTT43HkVg6zTd6zIJbpwTLzj\nzidHOKKzlMkIGGjUONov+ld5XsCbnxzHeUs78tvxPHjp3YN44Ol30dbsx6zJjZjV3oRZ7Y2Y2d6I\nKS0BTXtHsUjRaU7D950AgC+cuxi3P/gKnn3zUwyEwmkF0e9f3AkA+Nvz0mN4bDYO111wMv7tv7fi\nt5s+xPlL5+BAt6gkdUwxtsJQKZy3tCOvY4G9P/lkb+rBLFSTcwzEKAXM0jGSunjwvKCbIwzU9sRG\npgj7NIrK1gYvjkVHMTQWKWshPCQlAnnQ7Hejd3gCI+NR0wrhw6luf3ZNyQZTVdkxAsjXh9EJbfVU\nWn3IU4Bgn0f/yIThz0Oemiq/lhTvluV4FgQBYxGWOOGSFOFBE5f6/+WhLfjv5z9Ec8CDtWecmHuD\nLEjj1lvzG29/1TkL8K+/3YrtO4/kfOzxwTHd1zhxegsA4NOuobxevxB4XshrGNG8GaLIseeosaZA\nxubNm7FlyxYAgN1ux6pVq/LcU5mcV+ZoNIqbbroJt9xyC2bOnIkNGzZg06ZNePHFFzE0NASbzYb2\n9nasW7cuY9sv/+0X8NAHGxBobEVnZycGBgYK3tFcHOxKqZkem+brBJxi0X6kZ8jU/WD0DYsHvp2P\nmv56HC+eIPqHR4t6rf5B8YRrE5Jpz8M8ruFoPOP5u3rEn512TvO1md34eG8/4vHpAJD2uHiCR9fA\nqPTzS2/vwamzzWvo+uFvN+O1j49r/s7lsOHCZbPxqxvPK6mFoKdXfF8dNuT1+bgAnLN4GjZ/eAz/\n99m3cf35iwCI3b+v7zoGr9uBlQsmZTznuuUz8MPfAU9s341PD3fh4wOiStTe4LTk2M8XpgIUu29c\nQrygD4xMFP1c7HzSoHM+KSXe1Fn4aE8/BgYGMDIehSCI47aHhzMvXA5OPJf19FtzLrOSsVSxFg2P\nIR4XCyP2NzZ6nTgG4MCRbvhs5bsJ6BsSz1d2IQZ/yt966FgPnII5y/T7u8S/v3co9/m9b1C86bVz\nvPTYeOrmIjSufS062i0e615Xfsd6ky/1eRztRoNTvxlaSf+QqIxyfEx6LZsgbts7MKz7+hOROHhe\nHM0s8Ek0+cXiuW943LTvwNEe8bu3c98xnHFiS1HPtfeQeM1pbXDltb8tHvFvPtY/ik8Pd2Vt3D2W\nUp09XOZ1enKj+H59fLDH9HPG4GgEPC+gOeBGaCS3nSeYqpX3HRtEb1+foUm8ANDZ2YnOzk7xOYJB\nbNu2reB9zvqKgiDgtttuw7p167By5UoAwM0334xNmzbh2WefxZe+9CV8/etf1yyCAWVQtvleNr1h\nGgzWLMdGn5oJzwuKHGHzm5OkHGGTmuWcdhtsHId4ks8w7UvT6HTUzlwe4e6h8bRxpW+a7BNmDQs3\nXHoKvr6mE2tXdODkOZPQ2uBBLMHjqTcO4K8aObzFYHS8shasaW6DIj3iz9vFQRtrlnekKT+M6ZMC\nOGfxdETjSTz+6qc40seGaVRPdFohNPpcsNs4jEXi0nteKGxCU3uBHuF8UGcJs//Xi080OoCgGgnr\nnIOAyolQY6/f5HdL8XZmNswxpc9IYoaWR9jttMNptyGW4DUbb/ONTmNIPuE8khu00inY8awXz6m1\nXZCNWDaxWY5NRO0dKV51zicxQonNxmH+DLEI350jRi1bMx4bs2xFlrCUIWyw9mnwuTClxYdoPIlj\n/eVJjspaCO/YsQObNm3Co48+issvvxyXX345ent7DT+5ld3NfTmmQLH4tJ7hCdObLUYmokjyAhp9\nroKKn3yRcoQjxeYIa8encZwc4q8eSCJ3eWv/nXIhrH2SY5FpLNZrx94eQx2yhcKOk7+/5GTc8aUz\ncf/NF+DZH12BD3/1Zfzo+rMAAHc99nZapmuxxOLGh2moWbO8Az63Azv29uJA9wgEQZAi1a5OFcla\nXHtuqmlu8+6qG6ZRKBzHlaxYytV8W0rk6XKxtP9XT5VjePMYs/zW7u6SWEWsQjqfaAwckBrmypwc\nwTKemwNuqTAzM0uYiTdGCuGwxkANjuPgz2I/kO0K+RXCrQWktIxlHaihfzwzWwS7njT4XHDYOYSj\nCdOGZDFhyYglJRf5JkYoWTBTtA58clTf1jAWjmEimoDHadf8HOew6XIWRKgZnSqn5IQyT5jLWggv\nX74cO3fuxOOPPy79r729Xfr9DTfcgK9+9au62zOfV7Y7vVKR68IV8DrhS5n7R4tUTnMhRadZFFVV\nqhxhWd3NLNj05sHrJU0wpJOczs3QsQHxJH/KCW3omNyIiWgCuw6bs3TDsqb1smG/+LkFmNkWwJ5j\nw9hgYLyxUaJFKMI+jxNrVnQAEGN03tnXi4M9IbQ3e7Gyc5rudhctm40mnwsfHOiXgtRn1nghDMgX\n52KHavSHUh5/SwrhVPHOFOEJ/cQIwPjEzk+ODOLyf3sS33lwa6l21VQEQdC9GQdkv3TZFeFx8dhq\n9rsl1T5U5DAjPXheQPegeCwq4/X0GNcYqAGINhtAO0t4VDGxLR8KSWnJpghnO57HpfHK4mM5jpOu\nr2YlR7D9KaUiXEghLCvC+oWw8vm1bH3BRg8CHidCEzHTkzZYIWwkMYJR7glzpk6W87js4DhxdG8p\nFTYtpKlyOm8+x3GYkpry1G2yPcJKWwRQyhzhVFOXxrKk3phlNihDS8EB5GY5vcYepghPCwawYt5k\nAMBbu82xRyjHPmo1xbkcdnz7KjGd4e4NO3Tze/NFnipX2Nftamnk8j5JDb78zBOzeqk8LgeuOFtu\n8Ghv9uo2NNYSpYpQ69WJIjIDVuCFVIqwnh/QyFIyAOzvFi8qx/qtyU4vlliCBy8IcDlsmrFzzayp\nsIyKcCSWQCSWhNNug8/tQGNq6FHIQJFaCAOjYWkYT2gilvM6qjViGVCMWZ7QUoRZcZpfs18hQzWy\nKsJZVo7ZfgcUVrCWEt306sGKb2aTKoZeyRqR/431glQz2e4szWS5zlfKCLUD3eYWm9JMB4MxcQAw\nV1KEy5MlbGohzHGcVCCZrQr3hXLnfjJ/TrfJY5YHQoVlCBdKyRRhnQxPQH/MMvtZy9MHAP4cU7BY\nisf0oB+nz58CAHhzT3e+u24II8fIFWfPxfwZLTjaP4bfv/RxSV63GI8wAJy9eBqmtPhwsCeEh18W\nxydflcUWwWCZwgAwq622/cGMUg3VyNVzUErYUmaGR1jHGmFkKRmQL0jZCoxKIqwzqp3RrFLOy8GI\nwhbBcZycyGCSItw1kH4Tk0sVZsOr1L0DrMgd01KEC7RGsJzvfHy6WoqwlIudZfCWrAjL28mTJM0p\nhNn1tK/M1oj5M0VF+JOjQ7q2BiPPP0fyCZubJVyINaKmFWFAMV3OxEI4nuAxPBaFjeMkRUiLqRYp\nwtJ4ZausESYP1AD0xyxHcly8fDma5Zg5flowIBXCb+3uMcXHxO7ss0Xa2W023PI3oir8i8ffM+TD\nzEUxHmG2T5enhmbEkzwWzGjB4tm5c3U7O4JYNEt83KwqGq1cDNLFsYjRq+FoAmOROFwOG5ryLA4K\nQZosN5FeCOvFWRk9p7Ib8mqJWZNvqrXPJcqhGuWC2SLYZ6Y1HruUqJu7c6nhrB9HvfojKcKltEYE\n8m+Wy6YIZ+slYtc2pSJspjUiyfPS8dg3EgbPF3c96hkSv4v5NsuxbZr9bgyPRSXlV42kOLfoX9uk\noRpmF8J5DNNgSEM1umq2EDbmZyuGfoUCm225mB2EPSZPl2NLNfkcCMVQamuElrqrN2Y5nMMjLO2b\nzkmuK3Winx4MYO7UJrQE3OgZnpCSDkqJ0WlhFy6bjaUntqM/FMYDf91Z9OsW4xFmXLVStjlcufJE\nQ/FuHMfh62uWAADOWDCl4NeuJtjFsZjlUqYAFTJeuRAymuUmjDXL5WpCZu9BsWkyViEpwjoWnuZA\naWwvxcCKcKZOs8QPs5rlMgvhHIqwnjUiiyBRyGQ5QGlDMvZdi8aTiCV4OO02uBWigHxjl6UQThXQ\nfq811gjldS7JC0WpzmKuLpsrkH8hzHFycsQnOskRxhRhawph9nkYGa/MmDEpALfTju6hcc1VC7Ox\nrBAuhbKmh9FlTMkjPGSyImxxs5zbaYfDLsabFeNrZdtqFbV6Y5azNbcAuYv0LkkR9oPjOKyYl7JH\nmOAT7mVDTnSSRRgcx+HWa1YAAH719AdFL70V6xEGgEWzgvjMgilo9Llw5dm5bRGMa1bNw1u/XI+/\nPXdBwa9dTZTCGlHseOV8adaJT8vlEc62lAwA/QprRLnHEhsh1+qS5BHWGQxhBUprBCAv8Zu1T4Uq\nwpnNckwRzjwPS/Fp+aZG5KnIKtVg5Q0my2LWs8+J22p5hNnqT+kLYfXqal8RDXODoxEkkmKurrvA\nVUHZHqFdCBuJZ+tQJEeYSSHNcnabTdq//SZ7mLUwvxC2IEu4L0ejHGNyi9WKsDWFMMdxigi1wm84\n9HKEAWWznLYi7M3lEda42x8LxzAyEYPHaZdOqqfPFxvmzPAJ9+dR4Jy9eBpWdU5HaCKG+558v6jX\nlTzCBZ4EGb/7zhpsv+cLksXHKNOC5kzMq0RK0SyXK4qx1EjJAxMxCIIgFVuNOVMjcnmExb9DEDJv\nYCuRXNaIlgpIjRiSMoTF8y1rltNqQisF6kI4lz+a3RxlNsvpe4RZ4kX+HuH8bjq1/MHivhpQhCOZ\n27aYaI1QX0eLSY4oNENYCYtQ260TocYsE9nOWVZlCbMb8HwUYUDRMFcGe4RlinDYxIYNo5mfLEvY\nfEVY3B+rFGFAOVSj8GUFlgCh3SxXYHxaliU51ggybVJAUghWSD7h0hfC+Sp9t35BVIV/89xHRR0z\nUeYRLjJT2ut2WHpMVSPVqAg7HWICQZIXMBaOIzSeXmypMewRVihlZq7IlQrZGqH9PamEgRpM+WXq\ntNnNcqwQZmpZbkVYuxA2QxHO14+v5Q9W7mu2hnpWCFtljVCvtvQV0WBfTKMcY0GOCDUjr9He7IXP\n7cDQWNTUhtOBAjzCAHBCGRvmaqJZzmjmJ5su122yIiw3y1lzIQVKkxyRVRF2a1sj5IEa2a0RWsu4\nXamJSdMUCueSjknwOO3Yc2y45N3AfSP5ZcOeckIb1q6Yg0g8iZ//+d2CXzeaajAsVhEmciN1shfj\nER62LkOY0aSwRwxLAzX0rBHG+i4GQ/J7UGwjrRXkbpYrf2oEK8KZOt2kUPPNgBXCC1JL47k9wqmC\nUZUakU0RLnSyXL6THHUV4RwN1QAwzopopTWi4f9n783DJLnKM983Ivel9r1631tSa0Ni0y5hBEYS\nIwljkGcGz4w9vpgxxgabxePHBuPHY7CNGY8exvjxcm3fewdj44HBgBFYaENgoKWW1EJLL1Jv1V37\nklW5Z8b9I/KciMyMPU7k+v3+UqeyKiOzIk988Z73e7/gboxEWiPYDjTbkfbCQVYIX1g1bNybd9As\nJ0kSv6F6NSB7RLFcwXq2iJAsWY6DNqKdEWo90SznVMFhd0sLa9lAc42ZR7hV1ghATMOcld+XqcRN\nirCFiqwel7lHnOWbbhtP88dikRCu3jsBAPiR4HHL7Dxxc2f+4XdeB1mS8L8eedFzkwFLjYiFA/+6\n9T1MhVjyceFyErMnGi0arKipjqbWCPvCQVGUupuBrlKETQrhgUQEIVnCVr6EUjnYXHoz1hqsEQN8\nxLL4YkxRFF0hrG6N290EaJPlTArhhvNAURTTAtUO/SRHJ6pwxkYRzhbKpl52dowpw9QI8YpwkzXC\nhyIswhoxko5jeiSJXKGMc0v1jeSFUgVrmwWEZMlWfAvaHqGvfdza8fa1cbpcCwvh9jfLxWpe1EpV\n4X8w0egvQK2KTwPERKjlHCnCJvFpZiOWY+apESxDeHY0Xfc4t0eILoTX3GfDHtg2gnfecgDlioI/\n/dqznl5XlEeYsIft+vgZpe7lPPELK6w2sgUtR9hkqzrhYCt5I1vkgxiA7ohQYzfiZrtLkiTVKeft\ngDcy1rbl2d8oCI/w6mYBhVIFQ8ko7wuwet+VahX5UgWS1LyGmw3U2MqXUFUUJGJhRDzcqLuxIm2a\nFNzRcAiRkIxKVTFt9t4y8ggL2P0xo7EQ9qMIi7BGAOYT5vQ7WHbF5x42VCOg5IhlD41yjH2zqjXi\n9KV133F1bgm8EE60slnOwYVLs0cE4xPOFsoolCqIR0N8y6cViLFGWKVGmMSn2WxnWoWls6ly28br\nm794w5xAn7CfbNgHaokLT59a8PTaWmoEFcJBk05EkYyFkS9WPI9S5zsHLWqWA7SGufWtAp9SZm6N\nsG8uYp3bjG4YqmGnCAM6n3CbCuG1Bv/2gC5HWHQyB+uhmBlNOboBYGtsIhpuiv0zG6jhNTqNMeIi\n0s5MEQbsxyzz1AgDj3CQzXKsr0hMIezvxvpQbcLcCw0Ragsudjp3BxyhxhVhDyLgcCqGscE4coUy\nLgbcx9VI6xThVsSnDdqfCFrDXDA+YX5H1EJ/MCDIGlEyvxBpAzXcjVhOWfi/tKly9YrwdQemIEnA\nM6cXmxRor/jJhmWNCicurKFccb8lKyJHmHCO3gLlBT4ZqQ2K8KXVLEqVKuLRkOmNUzQsIyRLKJar\nphaBlYYdr27IErabUglontx2ZQk35ghHwjISsTCqiiLcfsJ6KPSFsNUNQNbEFgHoB2rUH6PXYRoM\nN/YEVoQbWTASNnUC+2z11oihVBSyJKm7H4KtMuz1dk+pg4j8NMuJsEYA5skRbhTnoD3CXqbK6WmX\nPSLwQjjVgmY5N54+rggHNF1uucXRaQyhzXIGF2D7EcvGhXA0LPOM42JDEc1TIxoK4eFUDIe2jaBY\nruK5V5Y8vJNm/CQBDCSj2DGRRqFU8TSnnXuESRFuCX4H54jaynQDK3TOLKgXKLOpcoBqEbCznC03\nbBdbZbR2Ck4U4RGeHBGMtc2ONW6N0P4+QU2XY/7gmdEUhhuGrhihNco1f35pk1Shjaw3fzDDTXJE\nxkDVZdgpwkZqckiWtWmDW2LPB60QVgtHP/FpotYT1jD5UoMi7KbQ3jOtFppBZfXyDGGPIgIbtXx6\nrrUNc13vES5XqljJ5CFJzorPqZoiPO/jDs+KVg/TYKRqOcJe49MURXFkjTD1CJuoOJIk8Zuhzbx2\nbNWq1ggya5CLy3zCovKE/WbDsrvxxm0pJxRJEW4pfhThrXwJ2UIZsUiIbye3AqYwsomKZtFpDLs0\nnsYeiCB7NERh5xEGtALULj0hKNYMhp0EFaGmL4QdWSMsFGFW6DYKJSwxguUhu8VNhJmVIpy0pYG4\nkwAAIABJREFUyJsHjHOEAV2WsI+R6kawQnjn5CBkScJKJu9JdVYUhWf8+lWED8wOQ5KAkxfX6lI6\n3BTa0yNJpOMRrGTyfPdaJMseM4QZPasIJx1G/XhlJZOHoqhfyHDI/u1MjwasCLepELYaoekE1qQQ\nDcuGhnsza4TdiGVA8wnri/TlTA6FUgXD6Zihl/p1ghvm/GbDskL4RZMcRyv4Z+tjshzhnEldw5xb\neCb5YGvGKzNY09XZBVYIW0cPaeuqmSLc4BHugmY5Rx7hNkaoVauKoX97kCdHiP2MeSE8lmqaPmhE\n1iLK0iw+za81ws2YZU0RNi+EzaYlbhmkRgDAqIDccMPXqx3HYDLKBbZG370T1rNFFEoVpOMR3z1D\nyXgEuyYHUa4odTuTC6tsfLP9tU2SJBzYpqquJy6IV139WyNYlnDPKcLOxoF6xW2B43fb1I6VDOua\n7C5rRN5ivLL+8UZrBFdxLC5eRv5lZoto9AczXntQbZj74cvzQjpI3UyVM+IypgifJUW405mqXRC8\nKMJaxF5rPf6ssHJcCNusq2y6E2sM7YYc4bxNJjnQ3qEamVwRVUXBQCJSJ7oMBhShpleEBxJRSJJa\nTJr1KTB/beMwDaD++qBfT/03yzlvWOOKsIH6zLOEDW7sCqUKSpUqIiG5yV7GCnHRyRFbulHV7Jrh\nJZKRFamTPjKE9bDkCL0g49aDfGCb+jtevuBe1LFjad1fIby3VxXhRMDWCKfRaQzeLBewNaLVzXJM\ngb604u19MYuDmY/VbMSyFp9mVQir/09vjTBrlGNsH09jeiSFtc0CTgrwCy24HKbRyGVcEfZQCJNH\nuKX4sUYs6ZoqWwmzQrCC1W7crZ3lbKWmzOyYVJt9uiE+je8umWSSA/qhGq33CGuJEfU3KXxqW0Ae\n4dlRdUS63fCOrK54ayQkq9MLFaX+nPE6VY6hpUaIUYSNIgFZAZ0ysCoFlRyxpfMzs2sGu4a4QVSj\nHINHqOka5pj1wqkH+WBNERZxXW3E7wyFXZODCIckXFjebJpZECRdP1CDK8IO70CCtkasbLanWY5v\nd8x5u8vT/MHGxZrZiOWcRYMdgy3M+m05rVGu2R8MqFs4PEZNgE+YK8IeF6Q900OIhmWcXcy49mGT\nItxa+K6Ph0J4oQ3RaUDz8Ay7qUx2zUXsgrRzQi2Eu8Ia4UQRTrVPEV43aJQD9IqwuEJYP0yDZQhr\njWHG752dC0bNcoCmCuuTIzZEpUY48OhqHmGrZrnm81TzBzf/XFBDNbSUijC/ZrB8cTeIbrw9bCDI\nLLgstvfX8npfDsAascx3xL0JCZGwjO3jA1AU4NxCxv4HBNEya4RV+Lsf3EYdjQ0kEA5JWN0sCIvm\n0uMnR88P+2aGIUsSzsxnPL2vvI0aYzRi2a7BjmFkjbiwZK0IA2J9wuyu2ekNUyORsMwXkMb4GjvI\nI9xaNEXY/YXL7Q6TKBpVRntrhPnERkBLjdg5OVh7XuenRuRd5Ai3o1lOmypnXAiLbJZbzxaRK5SR\njkd4kWrXMGfVLAdoSqz+nMkIs0Y4V4Qtm+UMzlOeIRxv/jltqIZgRZglcMQimPShCIvKEGbw5Ija\nNahSrWpioMPXOMjjQAOwRvhslgN0EW8LwUS8GRF8fJpNU4df3HqEZVnynTNqBW+W81hweSUWCWH3\n9CCqiuLJX2NX0BqNWM7rBkVYTbRJxZtTI/hUORNFGND5hAUM1hCRDes1OYIpwjFShFvCJO8DcL/r\ns7Dmz0LjlcGGlAi71IiEzU4bV4Qnu0gRdmCzGnYxwEE0q5vNiRGAbsyywOL84nK9Ggw4KYTVv7HZ\n5zfAFWHtODf8WiNceHQ3rQZqxMwVYaMMYf76QTXLsea8RMSXIizaGrFnegiRkIwzCxvI5ktYyeRR\nVRSMpGOOdxy3j6cRj4ZwaTUrdBcjmy8hVygjHgkZ/q2cwtass72oCAelSCx68H5ODdci1AJomGPN\ncqMD1opOEBzk3aDu7/TyFuOVAeMRy1a5w3pStZ/ddNEsB6iFZzoewZmFDH7n//0+j5bygogtqst3\nevMJM48wjVhuDepFQUYmV3K9E7XkIpNcJM0qo8NmOYP3p455V99HV1kjbNYgQJ8a0XqPsK01QqAi\n3GiLALSbIzM1XFOEzawRzUM1WFFs50k3YzgV58dk19RspQgnLBRhq4l07DorPD6toBXfTBH2Ml3O\nrX/Xjmg4hH0zQ1AU4MTcGuZX3UezhWRtd1OkKrykG6/sJ3FnV20X60xA0++M6PocYS9bmTM1n3AQ\nY/w0s3hrL6QAcHBbs5HeKQXb1Ihmj7ATTx+g6wiu8wgzRdi8EA6HZPyHN18OAPj815/DDb/6d/hP\nn3kITzx/wdU4U1HZsF4j1Mgj3FokSeJ50W59wn5j9rySiIbrmimHbRRhprjkDNbVTK6EYrmKZCzM\nexW6YsRywYE1oo0eYaMMYSCYZjk+VU63Y2YXHaelRhivcUZjlnmznEdrRCQsYyARQVVRsG6RmlGu\nVJErlCHrhsHosTqfjcYrM9zkGLuBFeSpWITXFou+rBHieg4O6a5DXn//gVnxEWrcFjHkzxa6q6YI\n95Q1ImiPsJcL19RIMBFqhVIFm/kSwiGJxxa1ElYIezm57RTheLTZI2wXucZotEYUyxUsrGchSxL/\nW5jxsXe/Dl/7nXvxjpv2IyRL+ObRM3jX730db/rol/D/PPyCo/NKf474uVM9rItQc1OIk0e49bDz\nyq39iW1/em2q9IPeDuHcI9x8/vMx74Nx7bvXBSOWnQzU0OwB9gqkaBrHKzOYrUXkNrORImx3E2DX\nLMfOhYwu75jHp/m4XjlJbtA3vBmtwdrOsbk1Im1kjXCRY+wGbsdIRHjjrJfpcqKtEYA+OWJFK4Rd\nxrMFEaGmV4T9sKvmEe4pa0Q8GoIkqUVTpSp2HjjgLcCZR6gJLoTZBWh0IN7SMH6Gn5ObF7VmzXIG\n8WlOFBxAW5iZ7+rSyhYURU3wcDIE5Zp9E/iTX7wdP/iTB/Br77gOk8MJvHR+FR/5iyfw7//gn21/\nXpTKNz2SxHAqhrWtgqtzhzzCrcdLcoSiKNq49jbs6OjtEE4LYaOdNj7mfSBh2Y3faTgZqBEJy0jH\nVQWy1dnIptaIAEYsG1sj/DXLDfBmOZ0i7DM1AtAnR5gXo5tZZm8wfp2UxeCtDI9Pa/5ZLTVC3A5B\nqVxFoVSBLEmIR0K8CW3RSwqN4BxhADjMs4RX+Po26fLadjCAoRorvFHO39rJ7FznFjMtu9kNvBCW\nJIkvbKJV4WpV0Ub6eVKExVojWOdqqzOEGftmhyBLEl6d3+AqpFPsFOFoWIYkAcVyld/Q2P0Mo3HE\n8oVlLR/TDZPDSfzq/a/Bv/73B/Dg+24HAPzo5XnTgHmG5iP3txhJkoTLPPiEySPcenhDrIsbli3W\n7BENGW7DBo1eEW5snmskaRGftqLL8kwF3KMhEqc31tpQjdb6hE1zhJPirRFBNMsZeoSzznKrrRhx\n0MCo+YONv1eWirDFzzKP8tpmQVjRlOX+4DAkScJwKoZIqNZz4CKRKZsvYTNfQiwSErpDzKwRL533\nYY1gu8ce41aN4Iqwz8SsdCKK8cEECqUKLgVgXzWiJXu1Vo0djMeOX8DH/uoJVwXc6mYelaqC4ZTz\njkkgOEWYN8q1OEOYkYiGsXNyAJWqgtMukyNyNqkR+hsatoXpJDoNaB6xzPzB28bdFcKMaDiE+27c\nj+mRFEqVKk+gMEOk75PF17gqhJlHmArhljHpYbqcKAuNV/QFll2OsFV8mj7LUz+KudVWAjcoiuJo\nXDugH6rRWp8wa1Jr/NsMBdgspxcL/DbLNXqEFUXRFGGPHmEAGBmw9+lqiRHGr2OVgrJpYY1w6lF2\nwyZPqVCPVZIkrgq7mS43r4tOE7me7JwYQCIWxqXVLN/9dVsI754aRCQk49ziprBhOyKSmRgsOeJM\ni+wRLSqE7YdqfOZLR/E3334B33/houPfu+gx83O6pgiLvttoV4awnoMe7RFO1N3GMctOtjKB5hxh\nHp02ah6d5oS9M6qXyK7oX3KZs2gF8wn/2MWo5WKJrBGthu/6uCiEtfGgrfcHA1qBFQ4ZNxTpseq9\n0K9DIVlGojZRzO+kJkVR8N+//DQeOnrG1+8xolSpolJVEA5JiIStL0tMEfbSxe8H7hFOt0ARZtaI\nsWZF2GuzXKMinC2UUakqiEdDtp+5FU6my9kpwlqznHkhbBbJJdoekdUN02Bwn7CL9SSIRjlAjYA9\nVLvO/6iWse/WgxwOyXyc8cmLYuwRfqfK6dnNfcKtaZhrSSHMCyGLO49zi2pxxO4qnOBV6dMrwm6a\nnuxg3rzRdhbC2/0WwuYX4EafsGNrRMOIZR6d5lERZuyZVr/Ir1yyLoR5NqwA36fRZB8rFEVBoUzN\ncq3GS1Y4nyonKPzeLYO6wQl2CpKVR3hJ1ywHQGeP8Kf8PH1qEZ/++x/h1//8caHrJqBrlLO5qQa0\ni+Qvf+4RfOmJE8KPxQyzHGH9xDYRfTCZbBGb+RISsXDdlvqwU4+w2WS5hp05EY1ygLNmuYyNImy1\nw7FpMZpZ//qikiN4YoSu8B73EKEWRKMc41BtZ7JYVs83Lx5kNo325fNiCmFNSBCnCL/aogi1llyZ\n7cLfi+UK5tfU4sjNybzsoVEOUBeuZCyMXKEstMFhWZBHxg8HPZ7cWrOclSJcH6HmdCuTX4gbFGGr\nDGEn7K0VwqdtCmGRWzasUeHk3BpKZfuLXqlShaIAIVlCSKZCuFVMeZgu53WHSRRM8XNSmFiNWOZD\nfWq9CrxZ1Wch/NTJBQDq90n0lqXTKEYA+PBPXY/br9qOta0Cfvl/PoL/+JmHWuIlZFvvjYpwSJZ1\nRab/bWZ9o5z+hshuqh5PjbCLT6udB36j0xhcEba0RjhThA2tERY5wk5f3w1MsNEXwny6nCtFWGyG\nsB6WHMHwUmwfmGU+YftaYX2rwL//ZngJLjCDZQm3KjmipdYIo4xAQEsRANwWwt6keEmSMD0qfqgG\nV4Tb0HHO0CLUAlCEY8YeYTsVp9EjzBpBrKbKOWEvV4St7xpFLkjpRBQ7JwZQLFdtlWhAs0WQP7i1\nTHpIjWBNlZM+myq9wjygdv5gwFpBY2soy/PkOd4+G+b0F8IfCRh7rsepzQpQb1T+9sNvxWd+4VYM\nJqP41lNncceH/wFffOzlwNThfLGMXKFsalthzY0i7BFGiRGAA2tEgVkjrJvlWFG64XOYBmPEgTXB\nsSJsMVnOyCPs9PXdkDVQhPl0OReKcFDWCAA4vH2U/3cqHvE0ye2AiwFcH/6Lx3HPb38F331+zvQ5\nIq0Ru7hHuIcUYbtmufNLWrOTq0LYhxWB3UGJVBJWBJ4IXtk/OwxJAl6ZX+dNWk5w0vjWOGaZK8I2\nKk5jjvAFB8M0nMA8Tk49wqKUPjejltnWVYwK4ZYyNhiHLElYyeQdfw/arQizAtguOg2w3mXTPMLq\n+0jzQthfkfbUSa34PXpScCFccLa7xJAkCe+69SAe/tRP4U3X7MB6tohf/fyjeM8ffpMXkiLRGuWM\nozFZhNq6gEKYD9NoKITT8QhkScJWvmS4G6VZI0wU4WT9iGU2Etq3IuyoWc4mNcKBR9hUEXbw+m4w\nGunsRRFuhTUC8G7lctpPlC+W8S/HzgEAvvmUcX+Aoih1Tbp+YVnCfdUsV18IO7+rW8l4b05ji4zI\n5Ag/xyOKRCyMnRMDKFcUR4olI88VGXtrRKNHOGE3YlmXI7yxVcBGtoh4NMS3tLyyc3IAsiTh/NKm\nadqIoihYWPeWtWgGS45wUggXqFGuLYRkmfcOOFVx+DCNNhXCLNKIKTVWWDUXaRekeN1z/SjCi+tZ\n3scBAEdPWG+TuiVfcq4I65kZTeGvf+0t+Ox7b8VQMoqHj53Du37va8ITMswyhBkiG+aMotMAtUlK\nG97RfJ20s5c0KsIiMoQBTb2zEiS4ImzyWvGIOm+gUKo0xWGy4zVTPZ3Et7nBKKWCKcJueph4hnAA\nhfDUcJKfi153sPbOqHGrZ+YzdfMBGvnBy/P83Hrs2fOGz1nPFlGuKBhIRISIPpNDScQjIaxk8kKb\nUM1ocSFsbI3Qx1+5mRDDvXAeFNggFGEeZN9GRRjQN8w59wk7UYTNrBG2irAuR/j8orrVsW0s7TtS\nJhoOYcdEGlVFMe0u3cqXkC9WEI+GPG0fGeEmS7hIjXJtw23DHCuYRd0wueU1+yfxvT9+F37zgdfb\nPtcsd1VRlKb0Gv5cH0M1nj65CAC4dt8EwiEJL5xdqRvV6xc3HuFGJEnCO28+iIc//VNIxMI4dXFd\naJQZoM8QNi7kBgRGqJlZIwDzMcvlijoEQpLM+zxYYZcR3Cy3Y3wAqXgE82tZ3ifTyCaPaTNegyVJ\n4teJRsFMU5ONj1NLjRCrCOubDie4ItwZ1ghJkni/itffH4uEsGtqAFVFseyzeVRX/J6YW+Pxp3rY\nrqsINRhQb/paGaHWmmY5CyM8AFzwaI1gJ74Xa0QgHmHeLNc+jzCg2/I479wnzBQZq7u5JmuEwwD8\neDQMSVKf/+q8+oXz2yjH4A1zJmoETwIYSgrLcrzMRXIE9wiTItxy2Jah0+/40ob6vHZZIwBg5+Sg\no2mL+l02vS92K19CoaTe+LHtZj61y0ez3FOnVAX4xstnccWuMVQVBcdOL3r+fY248QibMT2S4uqg\naBWJFZ5m/u0hkYqwRSFsliWsb5QzW+f4ZLmc2GY5WZb4mvi8Saxkxib5AdAKz8abO2apM/UIC26W\nyxpYI7TdJef1wiVmjRgJZj05VPMJ+5lap/UUmYtmjzyj2iLYZ/D48QtNz/EaXGDFzklmjwjeJ9ya\n+LSY9ULstRD2U3iKzhKuVKvaYulzy98vPBbFRcOcpgibF2yaIlyzRpSc+fpkWeKq1EvnlgH4b5Rj\n8Ag1k5gV0f5g9pqxSAjnFjdtL3wFmirXNtyMWVYUhVsjglBwRBMOyYiGZVQVpc4WpB+vzEjzQQo+\nCuFao9xr9k/iuv1TAMTaIzSPsL/vSRDjjgHzDGEGV4QFFsJGOetDSeMINd4oZxKdBqifbUiWkC9V\nUCxXtGY5mymGTmC7ZC+cXTb8/3aKMKDvJdLO03KlinxRHXdstlvgJL7NDUbWCLYmLK7lHDVkFkoV\nrG0WEJKlwISxe96wFzsnBvDma3d6/h0HbArhueVNvHh+FclYGO+96yoAwGPPNRfCSxv1Dboi2NXC\nLOHOaJZbri+EnXb+Mj+xp2a5EbGK8GqmAEVRF0onik6QsGgVN3PEeWpExHohBXQDNQr2vmIGU6Ve\nOLsEQKAibNMwtxhANmw4JPObjRdtVHdmjSCPcOthSokTa8RmroR8qYJELCzMQhM0RmOWlw0uSCmf\n1ohKtYpjp2rWiP2TuO7AJADgRyfENcw5jWK0I4jhFoC9IiyyAOeFsMEaaTZmWZsqZ37uSpLE1d/N\nXIl/RoM+FWEAuHyn9aAhR4owF8y083lTN9zCTOnm1gjBzXL6psNUXI1czZcqdSOqzVhk2fVDSchy\nMFMq33jZDL732Xfj5iPbPP+OgzaiGSt6b7xiFj9RK7gfO36hyYOvZZeLu87ummhdlnDbPcKKomCu\npghHwzIqVcXRYlKtKr6sETO1i+TFFTGFMG9QaWOjHGP/jHpyn7647ijrFnDoEWYDNUruRiwD2gL9\n4lmmCAu2Rph4nNiCJHLLBnA+WEOLTyOPcKvhWcIObnZZQ6WIoSutImmw02a0S+Y3Pu3EhTVs5UvY\nPp7G5HAS1x9QFeGnTi4IiyvjUYwePMJ6RHp19azbFMKiCvCtfAnr2SJiEeNmYqZIrzWon6x4tPv8\n0roxy+w667dZDgAu2zkGAHjBpBD2qghvOSig2ee0IsgjbJbHzFVhB/aI+YBtEaKwi1D7zrOqLeK2\nq3Zg38wQZsdSWMnk8eMG5X9Z4DANhqYI94hHWJt3bxz1ky9VMJyK8YlvTuwRa1sFVKoKBpNRT+Mh\nmVq0uJ4VMg1IZIaeX5LxCHZMpFGqVLkn145CyX5r0uuIZUDzW/FC2OdUOcaeafXLYpaQsbgRzHY3\n88SZLfwM3ixHinDLcWONEDmGu1UY7bStZJobiNkWr1ePMLNFXLtPVYK3jacxNZzE2mYBp2yiC50i\nwiMMaOqmcEV4kzXLmSjCggpws2EaDLMsYbsMYYbWMFfiTXN+m+UA4LIdWn69kfjiRBFOGdQJdv5g\nQJcjnCkIuTHTJtnVvyYr8hYdNMwF2SgnEiaavXJpo+nvVq5U8XhNEb7tqu2QJAm3XrkdAPDoc/Xp\nEcsBJGa1Mku4tdYIA0WCRafNjqW4suukEF7xOc44Gg5hbDCOSlXB0rr/O8kVA29eO9EyAp3ZI1wp\nwi5HLAPaIsdif4z8b17YNp5GNCzj0mrWcLgAW7REN0CxCDU7RbhAAzXahmaNsL9weR3X3k6MCocl\ng+mWWo63t0L4aeYPrlkiJEni9oijguwRflIj9ARmjbDxCPNC2GTqm1OsGuUAYNi0Wa5mIbCwRgBa\nIbqVLwlrlmO/d9ekOmjo1MXma46mCFtZI5qTUMyKUj2JaBiJWBilStX39ERAsxA15jEze92CI0W4\nO/oN9KJZY8F57PQi1rNF7J4a5GPNmQ3j0QafsMjprYwdNWvE+aXNpkg90bR4xHLzScqi07aPD/Ci\ndtlFIexHgdUUI/8Nc8sGSkw7cZsckXekCNc8wrXizpUi3LBAi/IIh2SZj2M0mjAXVIFz2Q51K/DF\ncyuWKgQfqEGKcMtxE5+mnSedfeHSY1Q4GO1MmXXjO0XfKMe47oDYhjnuEfZ5wyhKmW3EcY6wQEXY\nCO4Rzpp4hC2a5QDNmpDRWSNEKMIAcHnNHtHoE65WlTqvrxlGO8d2GcIMbo8Q4BPmqRENN2VsbXCj\nCAcxTEM0B0wGazzyjKr63n71dv7YzUe2QZKAH750qS7DPIgd8Xg0jOmRFCpVpS5iNwjaPlDj/JLq\n/9g+nsbIgPMYFL+KMKBFqF0S4BNe2Wj/MA09Zie3Ga5yhAtlxz/D0N9djw7EfSs/enjD3KVmJYL5\nuUQXOJPDCYykY1jPFi0nWdGI5fahH6hhZ3/qRkXYSGBgN+R6r17KhzUiky3ipQuriIRkHNk1xh/X\nCmExijAfzuNXEQ7KGrFlY40Q1CzHMlptC+FGa0TevlkOqB+qIWqgBoM3zJ2p949mCyUoinoehmTz\nkkPbOdYpwnnrDGGGyOQIMxV6givCvWONAIADs7WGuQbR7JFafjCzQwDqtfvK3eMolqv4/osX+eNL\nAXiEAWD3VGuyhFsTn2YxBelCbYrOtvG0K2tEY2i8F6YFDtVgzXJ+CnORuE2OyDtQZBpzhN1cvPR3\n9KKi0xhWWcJBFTiSJDkatax5hKlZrtVEwyGMDsRR1Q2ZMIM3VXZRIWw0gIDdkOvXobQPa8QzryxC\nUYArdo3V3fBeuXsMkZCMly6sCklKcJpJbofIGDM9rMAyTY1IiSnA7RVha2uE3VqsV4QzWfVnRCnC\nPEKtYT3M2IxXZqQMUlC4ImzzsyKHamyZ2EzYBDdXzXJdUAiz3eOTc1qtsJLJ49jpBUTDMm64fLbu\n+bfUCmN9jNpSADnCgC5LOODkiLanRlyoKcJuC2GhirCACDVta6AzLqT7Z9Xi8NTFNVt/TaVaRbFc\nhSTZDNRoGLHsZjtTvyUmyhbBMMsSVhQlUKXPyWAN8gi3lymH9gjeVNlFhbC2laxXhJtjjLQRy+4L\nYd4ot3+i7vF4NIwr94xDUTQPsR9yghThQW5R8O8V1cMUWLOx8AOCFGF7j7BZsxxThG2mfLJCOFvU\nFGEBHmEAuHwXs0bUK8LMH2zVKAdox66P+dty0CwH6K0R/hVhrq7HjRVhJyPbu0oR5hFqWiH8+PEL\nUBTgdYemm2wpt16p+oQfqzXMlStVrG4WIEngu/qiYA1zQWcJt7RZzii+58JSTREec6kIGyz4bpmq\nNdPMC1GEO8sakU5EsW0sjWK5apvDV6hZHGKRkOX0NdMRyy49wsIVYZMs4UxOnbKVDCgbVhu1bG4/\nIY9we+HT5WwK4QWuCHf+hYthlLvKGn/rPcLWOe5WsNHKr6kN0dAjsmEuV6jFp/lVhHWFniiqVYUr\nsIPJ1qVGGMEL4ab4NGdeWlb0LqzlUKkqiEdDnlKXjGCjlhfWcnyrHPCgCOvOZ542YVsIi8sS3jL5\nLLnVylVqROffWDMb5am5NW4hY7aI26/e0fT86w5MIREL48Xzq5hfzdaJklbWFy+w/p9X53vAGmGl\nCOs9wmO8ELa/q2MKLPsCeIHFtYlQhFc6KD6NwewRdj5hlgtsV9A2jVh2oeLo765FK8LMGtEYoca2\nsIK6K3dkjSBFuK04aZgrV6p4qeaP21e7qeoGjOLTjPLMUwZNdU5QFEUXnTbR9P9ZnrCIwRp5QQM1\nBgOwRmzmS6gqCtLxiGnRmIpHIEsScoWy4+x2I7RhGi49wg4VYeZ7nVtRvciibBFA/ajlH+vWRKeK\ncMJQEbaPXQP01gh/inChVEGpUkUkJDftjjq1RlSqVSyt5yFJ3dF8O5iMYnokiXypgnOLm1AUBY/U\n8oP1/mBGLBLCGy+bAQA8dvy8EJuqGTxLeLGHFOFGj3A2X8LqZgHRsIzxwYQrRXhVQGrENFeEBRTC\nAqwaouFbHjbJETkHU+WA+hHLiqK4jE/TK8JiC+HJ4QRS8QhWNwt15w6PTgvIrsJuNE5eWDO9+BXI\nI9xWeDKMxXf85QuryBcr2DGR7qjvrx2NAkM2X0K+WEEsEqr7vvEhCi4L4XOLGSxt5DCSjvH4JD2s\nYe7pU4tNk6bcIipHWFR6g561mu/UrFEOUHsGBn2+dq5YxupmAZGQbBrDmU5EEJIlZBsKbieT5QBN\nEZ6r9eaIskUwjEYtO1WE2fmcM/AIW8WnAeJSI8zUYEDrH1hcz1me70vreVQVBaMDcWGfT5QIAAAg\nAElEQVRqe9Boo5ZX8eOzK1hYy2F6JMljQhu55QizR1wIZKocg2cJz28IG95jhOVfaX5+Hg888ADu\nvvtu3H///XjyyScNH7MjHg1BklTlUd+9zSIxZsfSkGVJK4QdGN6XRXiEa4rwRZ/WCEVRdHFunbMV\nctBmjjjDaUGrH7FcKFWgKGqB52Q7RO8RFl0IS5JkOFhDG6YRzN8kFY9g1+QAShXj7EyAFOF2M+lg\nqMYzp9Xt/6v3NquenQyfGFcrHJZ14oDe4pTQDcJxMzzo6VPMFjFpaJmaGU1hdiyFjWwRJ+acpdOY\nISo1QuSoY8aaTXQaYyAZ8fXal2pq8PSo+VhefcGtV4UdD9RginCtEBapCAPGo5adKsJGXnY2UMM2\nPk1Qs1yWj1du/hxjkRCGUzFUdFNtjegmfzDjIJ8wt4ZHa7YINkTDCKYUP378QmCJEYBa36XjEWRy\nJSGJIGZYVjDhcBgf//jH8U//9E948MEH8dGPfhSRSKTpMTskSapbjBlsmMa22pQxL81yfhTh0YE4\nIiEZa5sFvhB7YSNbRKlSRToesWw2azUHa4rlS3bWiKIzf55+xLJTOwVDr1RsE+wRBoA9U8weoW2h\ntCIJgNkjXjJR3ckj3F60oRpWhfASAOCabiuEmYJWu3hrW5T157ssS4Zqmx1HeaPcpOlzuD3iZX8N\nc6JTI0R6hNdq/mDbQthndJudP5hhNF0u63AgSTrOPMLq90G0Iswb5s54V4SNUiPsFOFRFr3qs1hi\nuyZmnmR9JKMZ3ZQYwdjPItQurPKxyrde1WyLYBzYNozpkSQW13N44nk1PWJ8SPxumiRJ2NmCCXOW\nhfDY2BgOHToEAJidnUWpVMLAwEDTY6WS/ZabUTSKNkxDLYSHUjFIknqna5d0IKI5TZYlR4qRHSLU\n6SBg+YCnL65bfp7OFWHNGuH2wsX+/iFZ4k2KItGyhHWKMEuMCFClZ/5ks4ZENrqaFOH2oFkjzC9c\n3aoIN8anaQ3EzesQKySMGpbNYGkQ11kUwjxP+KQ/n3DOhc3KCr0NxI36bQW3Rpg0yjFYgepVEdYK\nYesds2EDn7DzZjn1/1dr28yiMoQZh3Wxncy6kXGqCPPzuTlH2O5nWa9QkNYIQBNVrLKEu1MRVv9u\nx04t4ocvzUOWJD5FzghJkniM2td+8AqA4HbDmS0ryAg1xwaWxx9/HFdccQUikYjlY2YY3e0xRXh7\nbas8HJIxlIpBUZqbAfTkCmohFg3LvtMApgT4hIOYqiKCgWQUM6MpFEoVnF0077rM61IjrEjoVCU3\n/mBAW1hmxweEd5YCxg1zvBAOcEFid6vnTD7fYkm9GJBHuD3YNcsVShW8cHYFkgRctWe8lYfmm8a4\nKZYYYXRDznZk2FazHYVSBcdfVZVyqxsELTnCnyLMd6V8WiNCsqzlJguKUGMJDWbRaQwtQs2bKsns\nCvaKcHOWsFOPcGNBKdoakU5EsXtqEKVKlefSbjpUhBN8oIZWI2w5To1girDPQphP6DN+PbaeLFoI\nZ/PdWAizG5i5NZQqVVy7f8I2iID5hJniH1QvDs8SDnCohqNVZ3FxEZ/+9Kfxuc99zvKxRsbGtElE\nA8k4gAwi8SR/fHFD/QAP7p7mj00MpbC2WUA1FK/7eT1nF9RiZ2I4hfFxfxevXdMjeOrkAjZLsunr\n2VGCug00PTbo+XcExZE9k7i48gourpfx2iuMjy0aVxesgVTC8vhTA7VBGqUK4kn15iWViDl6z9ce\njiIckvHaQ7OBfEbXHFIXwLOLW/z3r+fU4927fTKwv8uRfepiMLeaM36NkPoVGx0Z6rhzo1NgN9JB\nfD6JlLqILm7kMDo62uR5++FLcyhVqji8cwy7ts8If/0gmZpQLwylqoSxsTHkK+rN1vbJkabPcigd\nB+Y3EImlHH3OP3xpDsWy+rns3Tlr+rxbBocRj4Zxcm4NUjSJUZMmLzuY1Wrb9CSGaxdgr+fFUDqO\nzXwJoVgKY2P+U0BKivodnpkYtjyW8RF1TazKUU/n8mpW/Qz275iw/PnJ0UEAF1CWIvx5xYqq8M5M\njln+7I5y/SV/clT8NevqfdN4dX4D51aLuOnaMZSq6nk5Nd58XurZXlCfly9X+fOytRuk7dPaZ2J0\nXkQT6me/tln09X7ksHrzNzpo/D3ZOa0WjFslyfR1NvKq+LF323jXrPljY2rCBUvE+MnXH7Q99rff\nEscvfe47/N97tlmft165Yu8MgGdxab1g+vudiLFW2BbChUIBH/jAB/CRj3wEO3bsMH3MiE9+8pP8\nvyvF2gmkM8KfW1QLWlbxA8DYUAInLmiTSoxYXhfXpci2oS4ue7/b4OkEHRiVctnOcXzr6Ct44ewS\n3n7DQcPn5IrOphKpOcOqWsTu8u0UCMa28QGc+cIHahdKMVuWeg5sV726J+dWoSgKJEnCfG2rcWpE\nvCeZsWdGtZ+8YtMsZ5fIQQRDMh7BUCqG9S01UaRxzTj6kjom9LqD3VUEA82jk5fYOHEDJSpV84Y6\nVYR/8MIcAOB1h82LYEC1/LzmwDSefP48fvDCHN76un3ODr4BrdnLf973UCqGC0sZrG/lAfgvhFdr\nlpNhG4VMs0Z4U4QvLKlbv9vGByyfxxrD1nTqp92WPqPRCjFokYThlSv3TuIrT76M504v4IE7ruCf\nh1kGM4PPG9ClbvBGOxvlOp2IIhKWkS2UkCuUuLrsFj7JLm78elO1mx2r2QOXatF00zYWl07j0M4x\nLD6nriF3Xr/X9vmTwylcs28Kx06ptqig6p/d08bX2EcffRSPPfYYACAUCuGWW27x/BqWV2dFUfCx\nj30Md999N2666SbTx8x43/vepx30730NmNvEpYVlLE+pF6NXa29sIFLF8rKqqg7WujVfPT+Py2aM\nP9jT5y8BAIaSEf5zXhlOqnehp84vev5d5y6pd5HpqOT7eESzc1xdNJ85MWd6bIvL6t9BVqq2xx+P\nhpErlHFmTt0KDcuK4/es3s3Zv4ZXhtMxrG0W8MKp85gaSeLiinpzE0UxsNdMhSuQJOD8YgaX5heb\n4nIyW+rCUixkO+7c6BTYXX5Qn8/EUALrWwW8ePo8b25kfPe5VwEAh2cHuu7vUy6o59bGZg7Ly8s4\nv6A2bCbCzd+xeFhVwi8uLGN52f7G8PFnVN/f5duHbD+Xq3eP4snnz+M7T53Ea/cNu34fpXIVpXIV\nIVnCxvoqV+29nhfJml3r3Nwitg35vwG9tKwKNlGpYnksUVlVZS8trnk6l85cUtfhdMR6TY2F1Ne5\nsLDCn5epFZvF3BaWl82HIjXGPIZh/Z68sLt2zXnq5QtYXl7G8rpaGKJSsHytYq3o3cxp6/VGzSJZ\nzm9heVktUs3Oi5F0DAtrOZw8M+c5mWh+Wf0OhU3+1qmI+tmfvbRi+l7OzavnSzIk/rMNkj2TaTwB\n9Tq6e8xZbXXDZVohHAnoOjta0y5OXqj/zI8cOYIjR44AUM+JJ554wvNrWBoXjx49ioceeghf/OIX\nce+99+K+++5reuzee+/F4uKi7Qs1hr+XK1VcWmXh4dpJy7o/rYZqME+uiOa0qWH1otCLHmFAywc0\nSzUA9BPi7P2+bJwy82L57fIWCfMJn760DkVReKxLkKHm0XAIs6NpVBWFN3/q0TzC1CzXLlh8npFP\nuFsb5QAt4ol5hJdZnqeBPYE916lv9ulT6o3uaywa5RjXH/Q3WEM/TMNqsqVTBlNiprwxmEfYLjWC\nx5p5VISdpkYYNcvlHKZGRMJy3TovOjUCaB61vMlHOdt5hLU+ompVQbWq8HM7ZRBn1sho2v9QDe5J\nNvlcnKRG8Ga5AJrCg4RF39125XbHfTy36AZuBOUR3jaWRkiWcGl1y1e6lxWWZ9f111+P48ePNz1u\n9Jgdjc1y86tZVKoKJocTdU1aTiLUVgSOM54eVU/WSz6yhFm3tld/XJCw5Ag2PtHoBGfJBk6i0BKx\nMFY3C3yx8TsJSiR7Z4bw1MkFvHJpHZftHEWxrEba+W3AsWPn5AAuLG/i7MJG0+ABPlCDUiPaxpRJ\nMsxWvoQTc2sIhyRcsas7vHx6GtdUPtTH4IZcS+2xL4SXN3I4s5BBIhbmQ2OsYA1zx04tmq4xVuRL\nYqLTGIM+Y8waYTFlrEnNDD/xaYVSBUsbOYRkyTb33KhZzqk1gh1nvqheswaT4kfPN45aztgUl4yQ\nrBbp+WIF+WIZVUWBoqjXHCfn1IiL+FUzeOFtcs1goopZs5yiKIFPNA2Kd916CNlCGffdsN/xz7z2\n4BQmhxOIhkPCGy8ZkbCMbWNpnF3M4PzSJo96E0nLWtkbpyAx9WzbWL0fykkhvGyx4LtFxJjlFa5Q\ni/db+WUoFcP0SIqPTzRCU4TtL0TsOWyyX9BFphv21IrQ0xfXNTW4BbPetZzDZp858wjHKDWibZgl\nRzz3yhIURc2C7qQbOqc0xqfxCU8GAoE2ZtleUWFjla/ZO4FwyP68nRhKYufEALbyJbx4zv1gDU3N\nFHOzKDpLmA/USFlfb7SBGu7TKtj1cGokaVv0NY5ZLpWrKFVUa4mTdBp9Jq/o+DSgedSyU0UY0PmE\nCyXbTN9GRtL+h2ps8YEaZqkR1vFpq5sFFMtVDCajHbVb6oRYJIT33nWVq3jTeDSMb/zuffjqJ/6N\nkN0cM4LOEm5dIdyQI6wN06jfBnIyXU7kOGM2ZvnS6pbnEX7LHThVTs9Bm1HLbqLQ2JebXRziHaR0\nsizhV+bXedEzEeAwDcbOCfMItSIpwm1Hywqvv3gd62JbBKDdlOZqW8maRav5nE/xHGH7Io0Vwtfu\nc/65+LFHiBqvzGDKlHBrhI0izHKGvYxYPlWLGmP2Lievwwph/VQ5J8VIWtcIFpSKd/muWiF8Ztmx\nIgzU73I4HabBcGKrtGPL5jXHBuOQJQkrmXyT3xrozgxhv0yPpAJ/v7sCzhJuvSJcW4jPL6lFw/aG\nDlkn2xsrG+KsEelEFKl4BPlixXMQeid7hAF1CgwAnuvYSN5FsgErlldri00nKcLcI3xxnXu4xgeD\nX5C0nMPmLyl5hNsPs0YsNOz6MH9wt02UY8iyxL9/q5t5ZGvZ6kbKm6YIOy+EnfiDGawQ/tcXLzn+\nGUau4G5KpR1+J7w14nzEsvcc4VMX1QarfTP22758stwmK4SdZQgz6hThADzCADRF+OyybsSy/fHp\nxyxvcUXY2THyMcu+rBHqZ5ky+SxDssyv80bJVk88r6at2Pm8CXfssth1FUELC+F6RfjCUv1UOcao\ng5NZpCIM1KvCbukGT9C+mqfmpEnElxdFmG0/ddKW8h7dlDct1Lx11oizBl9S5hHupNHb/YaZNYIV\nwlft6c5CGNAEBrbDNjqQMFQFWbORk0KYTWe8bKdz3/RNV6gxa48fv4Bq1d3OmmhFWCtI/RfChVIF\nuUIZ4ZBk678d9PG6p3khbK8Is+ERbPQzU4SdihL64jc4RVg9d54+tYhyRUE8EnIkBugV4YyLAhrQ\n1Q4CrBFWf2s2XW6pwR7xyqV1/P4XfwgAeM9PXOb5GIhmdlmITSJon0eYWSPGjAthJx5hUQqsn+ly\n3eAJ2j9jowh78Qhvdp41IhWPYHokiWK5imdOqUXOeAusEexu1Wh6H/MI02S59sG/37pCeCWTx5mF\nDOKRkKOGsE6FKVfs3DNbE/VKmxWKovAdNze2or3TQ5gdS2Elk8ePz644/jlAuxEXtbvEiruMgMly\n67xRLmZrO9CUaPeve6omUjhpBOLNcjXlmU1iczplNWiPMKCNWmYFvhNbBFBvobSzKTQyKmDMspNC\neJKPWdbWk0q1ig/+2aPIFcq494378LbX7vF8DEQzrBA2EptE0EKPcH2HM2+WM1GELQvhjVzdc/3C\nGuYurrgvhJka3Aovqlf28+SIdUMfdM6FIsytEZud1ywHaKrw92tbtJMtGHIyPphAIhbG2mahaTQ4\neYTbz6QuNYKd/8+9omZ/X7F7rCn7uZtgAsO52gXCzC7mtBDOFsrq5MhoiP9uJ0iShJtrI1efeP6C\n458DAlCEa4WTCGuE5g+2b4RmsW2ePMIuFOFUPIKQLCFXKKNYrtR5hJ3ACnanKq0X2Khl7d/Oilm9\nhdJ1sxz3CAdbCE/wMcuaIvwX33weP3hpHpPDCfzuf7jB8+sTxnCP8MKG514uK1pvjciXoSiKrlmu\nvhAeTEQRkiVkciVeROipVKvcs2U3C9sp01wxcm+NYA04nWqLAFR7wEAigrWtAvcz63GjCCcaFeEO\nU8GZT5jZXFpxgyJJkmnDHHmE289AIoJ4NIScrgHnWJf7gxlsgta5JTGKsD6L2G0X+M1XqIXw48dd\nFsIOM3Cd4sei0Mi6Q38woBaWkZCMQqniKu90I1vE4noO8WjI0SAISZLqkiM0j7Czz48VpUGpwYzL\ndMNrnHqR9Ukomy4i4QC9NcJHsxx/TfPPslERPjm3hk/9nWqJ+NTP3SysLiE0BpNRjKRjyBcrWFgz\nz3D2SssK4YTOGrFW+/Km4xEMNXwZZVnSYlAMuj/XNgtQFPUO3Um0jxN4hJoXRbgLukQlSeKqsJE9\nguV4OrE56DvVgc4aqAEAe6brc3xbEZ8GmEeokUe4/UiS1JQl3M2DNPSwCzZXhE2Sa7RC2LpAW/LR\n+HvTEdUn/P0XL6JQahYxzOA7UoK+Izw+TUBqxKrOGmGHJEmeXpvZIvZMD0GWnd186LOEvTbLBV0I\nswEN+te0gxXzW/mSrsnOYbNci6wRekW4XKniV/70UeRLFbzz5gO48zW7PL82YU2QPuGWFcL6O70L\nOjXYSHUYtdjisAqN98qUD0V4oYVNWX6wapjTT3ayo7HwdWKnaCWN8UMTLYq0Y8kRzYow8wh31ufU\nb7Dv+EKPFcJJrgira6qtImwzUGPZIovYjomhJC7bMYp8sYKjLmLU2I6UMEU4EYAi7KAQBryp0afm\nnNsiGOx4VFHJW7PcYECJEYzLdUNqnCrCSd3gF/fxaSIVYWce4T/92rN4+tQCpkdS+MS/f6Pn1yXs\n0dsjRNNyj3CuUDa1RTCsfMLLAqPTGNOj3hVhpjBNdbAiDFg3zLlrlqsv6DpNEd7bcDFpRbMcoGUJ\n67+klWoVlaoCSQLCoeDCxgl79MkRl1a3cGk1i4FExFFuayfDUyNYs5zJdEteCNs0kPkVGpgq7MYe\nIXp3SeRADTceYcBjIVwTJ5xEpzH0EWpbHpvlArdG+FCEs/myLj7N2c8OJCIIhyRs5UueRvEqiuLo\ns2TXlGOnFvFHXzoKAPijX7jZ0a4B4R2+6zovvmGuLakRZokRDKuhGuwxUY1yADA9zOLTvFgjahPM\nWtCU5Yf9s+oFn6kPenjXtpP4tFijItxZhfDOyUHItV2GwWS0ZcdnFKHG/MGxcCjQqTuEPXprBEsU\nuXLPuOOt6E6FXbBZFri5IlzbcrZVhJnQ4O0GkjXMPX58zvHPcGuEIEWYFV2b+RIq1eahB40sb+Tw\n/33nxaZGV8B5hjDDSxHuplGOMazzCOdcNsvtnlJfJ+ibwB3jA7yIdewR1ivCeXeKsCTpbJUeVOF8\nsYKqoka9WdkuWQP2+aVNFMtV/Ns7DuO2q3a4fj3CHbt7wRqR1I34PG+SIcywGqoRhCI8Wds2XVzP\nOlo49fC8WhdjCduBtUfYuY+1sbDsNGtELBLi51UrkzyMItQKlBjRMWiKcK5nGuWA5htT09QIhwM1\n/EZTvuHwDCIhGc+cXjQsLI0QrQiHZJkXYJsOItT+x/85hl//88fxpo9+CY81KNmurREebBmnXQzT\nYBg3yzkrGK8/MIlv/7d34Lf+7esdv54XZFnC4VrDnJPxyoDeI1zmMXROlW7AX5aw3Xhlhr7vZPt4\nGr/1M8F+joRKkGOW26MIL1sXwmMWhbDoYRqA6t8cG4yjUlWwtO7uC8QmmE12cHwaoKoA4ZCEc0sZ\nrsAw/HiEOy0+DdAa5lpZCO+oTUg8v5jhN1PkD+4c9NaIZ2vRad3uDwaaVUAzS0MiFoYkqaqX1c0+\n9wh7LIRT8QiuOzCJqqLgey9cdPQzORfrj1PcKLNsh/LiyhYe+G9fx2/+9Xd5cc6sEU63vd1GqFWr\nCl655F4RNm6Wc/b5SZKEy3aOtmS37IqaT9jp56cN3iphK69+hm6m3zmJXzWD7ZZYJUYA6k0RK+w/\n8wu3Om7mI/yxb2YY990QTEZzyxXhnL5ZzsYaYTRdbjmAZjlAlxzhcrpct8wWj4Rl7JochKKAL7wM\nzSPsPEeY/9vBWOZWw3zCrfIHA6qKMDGUQLFc5RYbXghHujentlfQWyN6SRFuVAHHTZpDJUnSqcLm\n/kmuCHu0RgDATUfcxajlBecIAzqvroOClO0y3vW6PQiHJPzVQz/Gm3/jSzh6Yl7zCDu1RiS0AtUJ\nF5Y3kS9V1IhLF57dIYNmOTe5z63iF952Jf7jnZfjvhv3O3p+Mq4pwm5zhAFt6p6XQpg359mMdJYk\nCX/5wTvxN7/+FtxYm6hIBM/USBIP/pc78N67rhL+u1t2hY5HQ6oiUarw7WMvzXIrgodpMLxMl8sV\ny9jIFhEJyfwL2MmY2SO4IuygqG1UETpREb68NhqWeYpaRaNPOE+KcMfAblSfObWItc0CxgbjputP\nN6FXryIh2XJkrpMsYTZVzo/QcLPLQpgP1IiJ+55oU97sC9Kl2jXlQ+94Db72O/fi8PYRvHJpA/d+\n4qv4wctq+oXTQnjQZXyal0Y5oN4jzBVhFwVjq9g9NYjf/dkbMVNrSLdDE8xKvLEz5dBWAWi2Si8e\n4Sy3Rthf0264fBZvuman69cgOpOWFcKSJPGTfCWTRzgk8eKzEctCWIBiYcQMmy7nQhFmGcITw+7D\n59uBfsKcHpb52QvxaQDwjpsO4PO//Ca8756rW/q6LDmCFcJFyhDuGNhaw1Smq/dOdMV31g69Ijw6\nELd8T5raZl4IL2e8x6cxrtk7gXQ8glMX17kNzoogMsndpDfoGwSP7B7H1z55L37xrqugQOGflVOP\nsNtmObYWN6bd2FFnjch3riLslpRuxHIm514RFmKNcOi1JnqHlu7Z6r+oM6MphGTjl9dO5ua7uuUA\nPMKAN0WYTZXr9Og0xj6DCLVSWY34CsmSo1GznR6fBqiF592v39vyOBuWJXx2UTXz89QIKoTbzkg6\nhoiuE/zqPd1viwDqd2TsVFy25Zu1SI5gRaGZxcIJ4ZCMGy5Xt4yfcJAeEahH2KZZrlRWJ5VKkjai\nNx4N4zd/5vX40m/ejd1Tg5gaTjrePRhyGZ/mJTEC0Fsj8q6b5ToZ3ixXKGnxaS48uGxn1shWaYfb\n3GKid2hbIWzmDwYcKsId4BHuFn8wg0Wo6YdquGmUA4wU4c4rhNvFrkljRZisEe1HkqS6bu+r9463\n8WjEoe+ot1NxmY3CLEkhVygjWygjGpZ9FwM38zzh87bPFT1QA9BSCuwKUn3zdaMw8/rDM3j8D38a\nT/7xuxzf8A+4LoS9WSO01IhiR3uE3aK372zm2WQ5L6kR7q0RzDvfiRYTIlhaXAhrJ5jVHbZZjrCi\nKNzDJjI+DfCmCHNrRIcnRjD26TzC1aoCQDde2aHFQV/4hkOSsDHXvQBXhGuFcIGa5ToK/c7NNft6\nQxHWFz92Km7SxiO8zPsv/Fu99HnCiqJYPjcXYLOcnUXBzgoiy5Krm/0Bl/FpXhVh5lmu9wh3fyHM\nboZWNwsoVxREw7IrIcGPNSJL1oi+paVX6IRDRTgZCyMWCSFXKHP/GKAqFvlSBfFISHiTFleEV5wr\nwt0yVY4xnIphYiiBfLGCuZp3jydGOEx/0H/unWiLaCfcI8ysEcwjTIpwR8B2bmbHUh0/AMcpenHB\nbpdMP+beCL8Zwnr2zw5jeiSJpY0cXjy3avlc7hEWqQg7bFpbYsKKoFHsbprlsvkSLq5sIRKSsaO2\ndjilfsRy71gjmCLM0jrcZAgD4AM1fKVGkDWi72ibNWL7uPkXXz8hRq8K66PTRDe6TNcU4UtrLhTh\nWobwRJcUwoAuOaK2JadZIxwqwjq/K9ki6pkeTSISkrGwlkOuUNbFp1Eh3AmwQrgXYtMY+jXVrm+C\nXeDNFWFxu22SJGkxas9bp0cEE5+mFop2yuxybQ3344muf13nzXKnazGWu6cGXe+sJWNhhEMS8sUK\n98P2gjWi8T24yRAGfA7U6CGLCeGOtlkjzIZpMEZrjQvMCgFoC7XoRjn2OyMhGWubhaaBE2Z0myIM\naFtwJ2vdylqGMCnCfgnJMrZPqOf12cUNFMtqsxx5hDuDa2t2iDuu6Z1xqHUeYYfWiE2zQjjjb5hG\nIzdf4SxGjSnCIhNonFsjxPacsNddd1AIc1vErPtRx5IkcZ8w88P2grc1Gg7VNbW6iU4D9DnC3uPT\n3KrQRPfTvmY520K4eYtDi04TXwjLslQ3fcoJ3dYsBzRnCbtWhHXFbydGp7UbfYQaeYQ7i3fefBCP\n/sE78e5bD7X7UIShvzG1t0ZYx6dxoUGQOnpTrWHu+y9c5DYhI1jetsgba94sZ2uNEKsI6+PT7LzR\nbA122yjHaEzF6RUlU/8+3ESnAeqNSEiWsJUv8fXXKXyAB1kj+o6WXqH1d1pWHmHAuBBmikUQijCg\nbm0Dzn3Ci2vMGtEdzXJAcyGcc5EhDNRbIzpxmEa70TfMkUe4s5BlCftnh3siP5ihLxrsBAJ2gc+a\nFMKihYbpkRQObhtGtlDG0ycXDJ9TqVZRKFUgSWJjBnmOsM2EN958LUgRjoZDiEdCqFSVuv4WI7w2\nyjGGklohHA5JPbPzlNDtHLsthCVJ8myP2OJ5zFQI9xttaZYbHYjbFlFWirAoxaKRqWEWoWavCFeq\nVc0j3CWpEYBuqEajR9jhRUiSJK4Ed+J45XbDItTOLGbII0wETiwSQkhWC3s7awRrljO1RmyItUYA\n9ekRRvDotGhY6A2K82Y59p7FreGDKWfjndkavNejIjyc0vyzvVS86acluskQZvv+jFIAAB2WSURB\nVHgds5ytxaeRNaL/aIs1ws4fDBhHqAUVncaYYYqwgyzhlUweVUXB6EC8q+7Et42lEY+GsLCWw/pW\nwXWOsP65pAg3wxThcwsZ8ggTgcMai2VJsrVo2canBWA9u8lm3HIQiREAMOgwxkyzRoh7zzxCzUKN\nVhQFp30qwvqxz71UCOvfixebAleEXfqEeW4xFcJ9R0srGXaC29kiABtFOKBCmGUJX1qxV4TnV9UF\ndLKL1GBA3R7eNzOM588s49TFdV2znPNiLRENYw0F8ggboHmEN3hWLSnCRJD88f91K9a3CtwOYAYf\nX5s3iU8TMFWukTcenkFIlvD0qQVkskWu1DK0HSmxlyKno46XBcenATpbhoUifHFlC9lCGaMDcc/X\nM71HuBcyhBl6RdiLOms2h8COLVKE+5aWKsKsQe7wjlHb5xp7hIOZKsdgWcLzDprlurFRjqH3CXtT\nhMkaYcZOnTWCNWvEHIyuJgiv3HHNDtx3437b56WdDtQQqY4mo7h23yQqVQXf/XGzPYIP0xCsCDMl\ncTNfQqVaNX1eEHYQJ4kVfv3BQEMh3EO7c34VYa9Zwtwj3EM3FYQzWnqFfvsb9uLvfuNt+C/3XG37\n3BGjQph1NaeDskaohfCFpU3b5y6u16bKdVGjHGN/bfE9NbfGO7adeoQBrbubrBHNDKViGE7FkCuU\ncbHWdEmKMNEJ2ManBaCOAsBtV28HADzybPO45SCmygFqlCEr/M1GShdKFWRyJYRDUl3jmV+cjFkW\nUwjrPcK9sxbrC1G3OcKAVjuseiyE03H3r0l0Ny0thMMhGTddsc1RAcWKXb3Ph211BKUI75muFYi1\nJgYrujFDmLFPN1TDj0eYrBHGsClRJy6o5xEVwkQnwLacjVIjCqUKNvOsKBRbCNx+lZrb/Miz55oi\nxTSPsPjviJ09QhspHYcsi2vUc+JPPn3RX3QaoE2XA3rXI+zNGlFrltt05xHe4jnCvXNTQTijY/ds\n+cmcaW6WCyw+bSSJVDyC1c2C7bZKb1gjdB5hN4pw7UaGBmoYw+wRJ+fU0bLULEd0AqyoYBO09OiL\nQtHxclftGcfoQBznFje5EsrIBeQRBuy9ukEp4JoibF6IibdG9E4hXJca4aEQHkm7V4SrVaWnRlUT\n7ujYQlhvjVAUBeVKFWtbBUhSfbesSCRJ4gtT44LdyEItQ7gbC+G900OQJODV+XW+TepKEa4VzTRi\n2RgWoZapbcnGaKAG0QFoHuHmZjktQ1i81UuWJdx6pZoe0WiP4PFpAWzts211U0U4I3aYBoMlx3zz\n6BnToRps15HtznmhV5vl6hRhX6kRzgvhrG68ssjdAaI76NgrdCIaRjIWRqlSxWauxMOxh1MxhOTg\nDnufzj9rRTcrwolYGNvH0yhXFLx8XlUtXaVGkCJsCbNGMEgRJjoBq/g0bapcMLtttzF7xDPn6h7n\n1ogA1pJBG6/u0nowcZzvvPkARgfiOHpiAd95xtgXfX5pEyFZ4rtHXhju2WY5fx5hL6kRlBjR33Rs\nIQzUn9BcsQhomAaDebbsfMLdOExDz/7a+zz+6hIA8giLZFdNEWKQR5joBOKREGRJQqFUQalcn6QQ\nRIawnluvUhXh771wkdshgOBSIwD9UA3jZjk+TEPwGp6KR3hD+B/8w4+aVOFXL21AUVQLlZ+b5KEe\nHaiR1BWj3qwR7gdqMLsQFcL9SUcXwqwpbiWT1/xcAS3UjL0OrBGKonR1sxygbcmt1hoK3BTCTDXf\n68Pf1ss0qjw0YpnoBCRJ0hrmGnzCQcSI6ZkYSuLK3ePIlyr41xcv8seDVIQHatvqZoowK5REDtNg\n/OxPXI7J4QSefWUJ3zx6pu7/nRLQKAf0hyLszxrhvFluK6dZI4j+o6ML4VFdHmDQwzQY2ghi80J4\nM1dCrlBGIhb2lHPYCexv8Ka5UXd/6Z5r8P3PvptvdxL1bBtPQ9Y1HEXJI0x0CKlaNFSjPWI5QI8w\n49ar1Bg1vV0gX2KpNeJvFu3yfLkiHMB7TsTCeP/brwEA/OE/HEW1qqnCIhrl2GtEQura0ktKZirm\nTxEeTEYRkiVs5ks8y90OHp3Wpddzwh8dfYXWN8yxhTooDxtjby1C7dX59abtQ8ZCLUN4cighvMO6\nVTQVwi66tmVZavLBEhrRcIhnUgNAjAaPEB0CU4QbC2E+vj7A9fX2q5rzhHOFWrNcEIowt0aYeYTF\nj1fW8zO3H8bMaAovnFvBV//1NH9clCIsSRJvmOulTHe/HmE2dhwA7y2yg1sjeshiQjinowth/XS5\noKPTGIlYGNvG1Eays4sbhs/p5sQIxv7ZejWC/L5i0dsjojRZjugQUibJEVwdDbAH47oDU0jHIzg5\nt4ZzixkAwXqE7fJ8+S5jQO85Hg3jV+67FgDwmX98ik+4Oy1IEQY0n3Avbekzj7AsSZ6vSyx+1ak9\ngg1dSfaQsk44p6Ov0FohXNDF+wRbCANakWhmj+jmxAjG+GCiLjifotDEsktXCMeoWY7oEFImyRGt\n6MGIhGXcfKQ+Ri1Qj7BDa0RQijAAvOuWQ9g5MYCTc2v43989BUVRNGvErIhCWC34eqpZrlbUpxMR\nzzuubscsM888WSP6k64ohFf11ogWFMJsy+q0bSHcnYkRQC0zWWePIEVYLHrrCMWnEZ2C2VANlqkb\npDUC0I9bVmPUch4mWzplwOFADdE5wnoiYRm/ev9rAACf+cejuLSaxUa2iMFkVMjr7p5SE2q2jaV9\n/65OgZ2jfopStxFqPD6th24oCOd0RSGsb5YLeqEGtC2rkyZZwr2gCAPAgW36QpgUYZHoI9QoPo3o\nFHghnDPzCAd7c3/blWoh/MTxORTLFT7iPUhrhJEinM2XkC2UEQ3LgauA99+4H3tnhnBmIYPf/+IP\nAajXGBH9JZ/82Rvwv3/rHly9d9z37+oUdk0NYu/MEO642nszttuhGmyHhKwR/UnXFML6EaBBs3fW\nOkt4odZkMTnU3YXwfl2zhpsRy4Q95BEmOpFUreDUK8KlchXr2SJkSaqL5AqC7RMDODA7jM18CUdP\nLGge4RZbI5Z1ufRBNzyHQzI+VFOF/+HxEwDERU8Op2J43aHprm3aNiIRDeOxP3gnPvVzN3v+HW6z\nhHlqBBXCfUlHX6GZ4V1VhFXTe5DxPoz9NlnCC6u9oQjvnyVFOCh2kkeY6EBYLqveI8yKhZGBWEvG\ny2r2iPPcIxwPQhG2sEa0whah5+1v2IfD20f4v/0mRvQ6fgt7ljjFcvLtYN+HVA+Nqiac0+GFsHoy\nL2fyWMm0ThGeGU0hGQtjeSNvGL/SK9YIfbMGjUsWy/hgAsPpGCIhmbbbiI7ByBrB/cEtWFsB4HY2\nbvnZc4EqwlY5wksBDxBpRJYlfOinruP/FpEYQZij3012glYI01rdj3R09TOcqj+ZE7FwS/ISJUnC\n3pkhHH91GacuruP6A/WLJbdGdHGzHKD6WAeTUSiKQqqlYCRJwv/9wTuxkSvSTQbRMbBmoK2CFp+2\n3CJ/MOP1h6cRj4Zw/NVlPpkzEUCzLvP+buZLqFaVOrV7uQW5yY385PW7cd2BSTz3yhKu2TvRstft\nR5g1wq1HmArh/qSjr9CRsIyhZBTrtTv6VikWgOqfPf7qMk7NreP6A1P88WK5gpVMHrIktXQRDYJw\nSMbf/9e7UGm4SBBie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- "text": [ - "" - ] - } - ], - "prompt_number": 9 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Eyeballing this confirms our intuition - no dog moves like this. However, noisy sensor data certainly looks like this. So let's proceed and try to solve this mathematically. But how?\n", - "\n", - "\n", - "Recall the histogram code for adding a measurement to a preexisting belief:\n", - "\n", - " def update(pos, measure, p_hit, p_miss):\n", - " q = array(pos, dtype=float)\n", - " for i in range(len(hallway)):\n", - " if hallway[i] == measure:\n", - " q[i] = pos[i] * p_hit\n", - " else:\n", - " q[i] = pos[i] * p_miss\n", - " normalize(q)\n", - " return q\n", - " \n", - "Note that the algorithm is essentially computing:\n", - "\n", - " new_belief = old_belief * measurement * sensor_error\n", - " \n", - "The measurement term might not be obvious, but recall that measurement in this case was always 1 or 0, and so it was left out for convenience. \n", - " \n", - "If we are implementing this with gaussians, we might expect it to be implemented as:\n", - "\n", - " new_gaussian = measurement * old_gaussian\n", - " \n", - "where measurement is a Gaussian returned from the sensor. But does that make sense? Can we multiply gaussians? If we multiply a Gaussian with a Gaussian is the result another Gaussian, or something else?" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "It is not particularly difficult to perform the algebra to derive the equation for multiplying two gaussians, but I will just present the result:\n", - "$$\n", - "N(\\mu_1, \\sigma_1^2)*N(\\mu_2, \\sigma_2^2) = N(\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1}{\\sigma_1^2 + \\sigma_2^2},\\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}) $$ \n", - "\n", - "In other words the result is a Gaussian with \n", - "\n", - "$$\\begin{aligned}\n", - "\\mu &=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}, \\\\\n", - "\\sigma &= \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\n", - "\\end{aligned}$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Without doing a deep analysis we can immediately infer some things. First and most importantly the result of multiplying two Gaussians is another Gaussian. The expression for the mean is not particularly illuminating, except that it is a combination of the means and variances of the input. But the variance of the result is merely some combination of the variances of the variances of the input. We conclude from this that the variances are completely unaffected by the values of the mean!\n", - "\n", - "Let's immediately look at some plots of this. First, let's look at the result of multiplying $N(23,5)$ to itself. This corresponds to getting 23.0 as the sensor value twice in a row. But before you look at the result, what do you think the result will look like? What should the new mean be? Will the variance by wider, narrower, or the same?" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from __future__ import division\n", - "import numpy as np\n", - "\n", - "def multiply(mu1, var1, mu2, var2):\n", - " mean = (var1*mu2 + var2*mu1) / (var1+var2)\n", - " variance = 1 / (1/var1 + 1/var2)\n", - " return (mean, variance)\n", - "\n", - "xs = np.arange(16, 30, 0.1)\n", - "\n", - "m1,v1 = 23, 5\n", - "m, v = multiply(m1,v1,m1,v1)\n", - "\n", - "ys = [stats.gaussian(x,m1,v1) for x in xs]\n", - "plt.plot (xs, ys, label='original')\n", - "\n", - "ys = [stats.gaussian(x,m,v) for x in xs]\n", - "plt.plot (xs, ys, label='multiply')\n", - "\n", - "plt.legend(loc='best')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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5WHyJdYwFYLvrE5PTiIj8lwpmEWmxvF4PO34qvOLDJ2rf5WYgJuwSbJYAXCXJ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\npRW7OVFUwyNvfMniDzK5bUo6t04Z2CH2CRD+IwmzOG82h4t3vzjMv9b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- "text": [ - "" - ] - } - ], - "prompt_number": 10 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The result is either amazing or what you would expect, depending on your state of mind. I must admit I vacillate freely between the two! Note that the result of the multiplication is taller and narrow than the original Gaussian but the mean is the same. Does this match your intuition of what the result should have been?\n", - "\n", - "If we think of the Gaussians as two measurements, this makes sense. If I measure twice and get the same value, I should be more confident in my answer than if I just measured once. If I measure twice and get 23 meters each time, I should conclude that the length is close to 23 meters. So the mean should be 23. I am more confident with two measurements than with one, so the variance of the result should be smaller. \n", - "\n", - "\"Measure twice, cut once\" is a useful saying and practice due to this fact! The Gaussian is just a mathematical model of this physical fact, so we should expect the math to follow our physical process. \n", - "\n", - "Now let's multiply two gaussians (or equivalently, two measurements) that are partially separated. In other words, their means will be different, but their variances will be the same. What do you think the result will be? Think about it, and then look at the graph." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "xs = np.arange(16, 30, 0.1)\n", - "\n", - "m1, v1 = 23, 5\n", - "m2, v2 = 25, 5\n", - "m, s = multiply(m1,v1,m2,v2)\n", - "\n", - "ys = [stats.gaussian(x,m1,v1) for x in xs]\n", - "plt.plot (xs, ys, label='measure 1')\n", - "\n", - "ys = [stats.gaussian(x,m2,v2) for x in xs]\n", - "plt.plot (xs, ys, label='measure 2')\n", - "\n", - "ys = [stats.gaussian(x,m,v) for x in xs]\n", - "plt.plot(xs, ys,label='multiply')\n", - "plt.legend()\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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xOI2IlAYVzCIi5ZD94rPcLbDbdMC0bON0nErFNGiK6dQDsrOxMbOdjiMipUAF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\n9uxZAoEAy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- "text": [ - "" - ] - } - ], - "prompt_number": 11 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Another beautiful result! If I handed you a measuring tape and asked you to measure the distance from table to a wall, and you got 23m, and then a friend make the same measurement and got 25m, your best guess must be 24m. \n", - "\n", - "That is fairly counter-intuitive, so let's consider it further. Perhaps a more reasonable assumption would be that either you or your coworker just made a mistake, and the true distance is either 23 or 25, but certainly not 24. Surely that is possible. However, suppose the two measurements you reported as 24.01 and 23.99. In that case you would agree that in this case the best guess for the correct value is 24? Which interpretation we choose depends on the properties of the sensors we are using. Humans make galling mistakes, physical sensors do not. \n", - "\n", - "This topic is fairly deep, and I will explore it once we have completed our Kalman filter. For now I will merely say that the Kalman filter requires the interpretation that measurements are accurate, with Gaussian noise, and that a large error caused by misreading a measuring tape is not Gaussian noise.\n", - "\n", - "For now I ask that you trust me. The math is correct, so we have no choice but to accept it and use it. We will see how the Kalman filter deals with movements vs error very soon. In the meantime, accept that 24 is the correct answer to this problem.\n", - "\n", - "One final test of your intuition. What if the two measurements are widely separated? " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "xs = np.arange(0, 60, 0.1)\n", - "\n", - "m1, v1 = 10, 5\n", - "m2, v2 = 50, 5\n", - "m, v = multiply(m1,v1,m2,v2)\n", - "\n", - "ys = [stats.gaussian(x,m1,v1) for x in xs]\n", - "plt.plot (xs, ys, label='measure 1')\n", - "\n", - "ys = [stats.gaussian(x,m2,v2) for x in xs]\n", - "plt.plot (xs, ys, label='measure 2')\n", - "\n", - "ys = [stats.gaussian(x,m,v) for x in xs]\n", - "plt.plot(xs, ys, label='multiply')\n", - "plt.legend()\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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ziIjd2q1yjCTWLzO0oNDUDLOISFyUMIuI2CwlHTLglJIMzTCLiMRDCbOIiN1S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\nIg5rAsXpkVHm8sb/lrnMQ5CGeRwFgmGe2BoZXf7uZxfhsMn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- "text": [ - "" - ] - } - ], - "prompt_number": 12 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This result bothered me quite a bit when I first learned it. If my first measurement was 10, and the next one was 50, why would I choose 30 as a result? And why would I be *more* confident? Doesn't it make sense that either one of the measurements is wrong, or that I am measuring a moving object? Shouldn't the result be nearer 50? And, shouldn't the variance be larger, not smaller?\n", - "\n", - "Well, no. Recall the g-h filter chapter. In that chapter we agreed that if I weighed myself on two scales, and the first read 160lbs while the second read 170lbs, and both were equally accurate, the best estimate was 165lbs. Furthermore I should be a bit more confident about 165lbs vs 160lbs or 170lbs because I know have two readings, both near this estimate, increasing my confidence that neither is wildly wrong. \n", - "\n", - "Let's look at the math again to convince ourselves that the physical interpretation of the Gaussian equations makes sense.\n", - "\n", - "$$\n", - "\\mu=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\n", - "$$\n", - "\n", - "If both scales have the same accuracy, then $\\sigma_1^2 = \\sigma_2^2$, and the resulting equation is\n", - "\n", - "$$\\mu=\\frac{\\mu_1 + \\mu_2}{2}$$\n", - "\n", - "which is just the average of the two weighings. If we look at the extreme cases, assume the first scale is very much more accurate than than the second one. At the limit, we can set \n", - "$\\sigma_1^2=0$, yielding\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - "\\mu&=\\frac{0*\\mu_2 + \\sigma_2^2 \\mu_1} { \\sigma_2^2}, \\\\\n", - "\\text{or just}\\\\\n", - "\\mu&=\\mu_1\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "Finally, if we set $\\sigma_1^2 = 9\\sigma_2^2$, then the resulting equation is\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - "\\mu&=\\frac{9 \\sigma_2^2 \\mu_2 + \\sigma_2^2 \\mu_1} {9 \\sigma_2^2 + \\sigma_2^2} \\\\\n", - "\\text{or just}\\\\\n", - "\\mu&= \\frac{1}{10} \\mu_1 + \\frac{9}{10} \\mu_2\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "This again fits our physical intuition of favoring the second, accurate scale over the first, inaccurate scale." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Implementing the Update Step" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Recall the histogram filter uses a numpy array to encode our belief about the position of our dog at any time. That array stored our belief of our dog's position in the hallway using 10 discrete positions. This was very crude, because with a 100m hallway that corresponded to positions 10m apart. It would have been trivial to expand the number of positions to say 1,000, and that is what we would do if using it for a real problem. But the problem remains that the distribution is discrete and multimodal - it can express strong belief that the dog is in two positions at the same time.\n", - "\n", - "Therefore, we will use a single Gaussian to reflect our current belief of the dog's position. In other words, we will use $dog_{pos} = \\mathcal{N}(\\mu,\\sigma^2)$. Gaussians extend to infinity on both sides of the mean, so the single Gaussian will cover the entire hallway. They are unimodal, and seem to reflect the behavior of real-world sensors - most errors are small and clustered around the mean. Here is the entire implementation of the update function for a Kalman filter:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def update(mean, variance, measurement, measurement_variance):\n", - " return multiply(mean, variance, measurement, measurement_variance)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 13 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Kalman filters are supposed to be hard! But this is very short and straightforward. All we are doing is multiplying the Gaussian that reflects our belief of where the dog was with the new measurement. Perhaps this would be clearer if we used more specific names:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def update_dog(dog_pos, dog_variance, measurement, measurement_variance):\n", - " return multiply(dog_pos, dog_sigma, measurement, measurement_variance)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 14 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "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 don't use variable names with 'dog' in them. Still, the `update_dog()` function should make what we are doing very clear. \n", - "\n", - "Let's look at an example. We will suppose that our current belief for the dog's position is $N(2,5)$. Don't worry about where that number came from. It may appear that we have a chicken and egg problem, in that how do we know the position before we sense it, but we will resolve that shortly. We will create a `DogSensor` object initialized to be at position 0.0, and with no velocity, and modest noise. This corresponds to the dog standing still at the far left side of the hallway. Note that we mistakenly believe the dog is at position 2.0, not 0.0." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "dog = DogSensor(velocity=0, noise=1)\n", - "\n", - "pos,s = 2, 5\n", - "for i in range(20):\n", - " pos,s = update(pos, s, dog.sense(), 5)\n", - " print('time:', i, '\\tposition =', \"%.3f\" % pos, '\\tvariance =', \"%.3f\" % s)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "time: 0 \tposition = 1.635 \tvariance = 2.500\n", - "time: 1 \tposition = 1.179 \tvariance = 1.667\n", - "time: 2 \tposition = 0.914 \tvariance = 1.250\n", - "time: 3 \tposition = 0.575 \tvariance = 1.000\n", - "time: 4 \tposition = 0.675 \tvariance = 0.833\n", - "time: 5 \tposition = 0.386 \tvariance = 0.714\n", - "time: 6 \tposition = 0.014 \tvariance = 0.625\n", - "time: 7 \tposition = -0.306 \tvariance = 0.556\n", - "time: 8 \tposition = -0.229 \tvariance = 0.500\n", - "time: 9 \tposition = -0.277 \tvariance = 0.455\n", - "time: 10 \tposition = -0.323 \tvariance = 0.417\n", - "time: 11 \tposition = -0.248 \tvariance = 0.385\n", - "time: 12 \tposition = -0.262 \tvariance = 0.357\n", - "time: 13 \tposition = -0.159 \tvariance = 0.333\n", - "time: 14 \tposition = -0.082 \tvariance = 0.312\n", - "time: 15 \tposition = -0.098 \tvariance = 0.294\n", - "time: 16 \tposition = 0.002 \tvariance = 0.278\n", - "time: 17 \tposition = 0.063 \tvariance = 0.263\n", - "time: 18 \tposition = 0.062 \tvariance = 0.250\n", - "time: 19 \tposition = -0.011 \tvariance = 0.238\n" - ] - } - ], - "prompt_number": 15 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Because of the random numbers I do not know the exact values that you see, but the position should have converged very quickly to almost 0 despite the initial error of believing that the position was 2.0. Furthermore, the variance should have quickly converged from the initial value of 5.0 to 0.238.\n", - "\n", - "By now the fact that we converged to a position of 0.0 should not be terribly surprising. All we are doing is computing `new_pos = old_pos * measurement` and the measurement is a normal distribution around 0, so we should get very close to 0 after 20 iterations. But the truly amazing part of this code is how the variance became 0.238 despite every measurement having a variance of 5.0. \n", - "\n", - "If we think about the physical interpretation of this is should be clear that this is what should happen. If you sent 20 people into the hall with a tape measure to physically measure the position of the dog you would be very confident in the result after 20 measurements - more confident than after 1 or 2 measurements. So it makes sense that as we make more measurements the variance gets smaller.\n", - "\n", - "Mathematically it makes sense as well. Recall the computation for the variance after the multiplication: $\\sigma^2 = 1/(\\frac{1}{{\\sigma}_1^2} + \\frac{1}{{\\sigma}_2^2})$. We take the reciprocals of the sigma from the measurement and prior belief, add them, and take the reciprocal of the result. Think about that for a moment, and you will see that this will always result in smaller numbers as we proceed." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Implementing Predictions" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "That is a beautiful result, but it is not yet a filter. We assumed that the dog was sitting still, an extremely dubious assumption. Certainly it is a useless one - who would need to write a filter to track non-moving objects? The histogram used a loop of sense and update functions, and we must do the same to accommodate movement.\n", - "\n", - "How how do we perform the predict function with gaussians? Recall the histogram method:\n", - "\n", - " def predict(pos, move, p_correct, p_under, p_over):\n", - " n = len(pos)\n", - " result = array(pos, dtype=float)\n", - " for i in range(n):\n", - " result[i] = \\\n", - " pos[(i-move) % n] * p_correct + \\\n", - " pos[(i-move-1) % n] * p_over + \\\n", - " pos[(i-move+1) % n] * p_under \n", - " return result\n", - " \n", - " \n", - "In a nutshell, we shift the probability vector by the amount we believe the animal moved, and adjust the probability. How do we do that with gaussians?\n", - "\n", - "It turns out that we just add gaussians. Think of the case without gaussians. I think my dog is at 7.3m, and he moves 2.6m to right, where is he now? Obviously, $7.3+2.6=9.9$. He is at 9.9m. Abstractly, the algorithm is `new_pos = old_pos + dist_moved`. It does not matter if we use floating point numbers or gaussians for these values, the algorithm must be the same. \n", - "\n", - "How is addition for gaussians performed? It turns out to be very simple:\n", - "$$ N({\\mu}_1, {{\\sigma}_1}^2)+N({\\mu}_2, {{\\sigma}_2}^2) = N({\\mu}_1 + {\\mu}_2, {{\\sigma}_1}^2 + {{\\sigma}_2}^2)$$\n", - "\n", - "All we do is add the means and the variance separately! Does that make sense? Think of the physical representation of this abstract equation.\n", - "${\\mu}_1$ is the old position, and ${\\mu}_2$ is the distance moved. Surely it makes sense that our new position is ${\\mu}_1 + {\\mu}_2$. What about the variance? It is perhaps harder to form an intuition about this. However, recall that with the `update()` function for the histogram filter we always lost information - our confidence after the update was lower than our confidence before the update. Perhaps this makes sense - we don't really know where the dog is moving, so perhaps the confidence should get smaller (variance gets larger). I assure you that the equation for gaussian addition is correct, and derived by basic algebra. Therefore it is reasonable to expect that if we are using gaussians to model physical events, the results must correctly describe those events.\n", - "\n", - "I recognize the amount of hand waving in that argument. Now is a good time to either work through the algebra to convince yourself of the mathematical correctness of the algorithm, or to work through some examples and see that it behaves reasonably. This book will do the latter.\n", - "\n", - "So, here is our implementation of the predict function:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def predict(pos, variance, movement, movement_variance):\n", - " return (pos + movement, variance + movement_variance)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 16 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "What is left? Just calling these functions. The histogram did nothing more than loop over the `sense()` and `update()` functions, so let's do the same. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# assume dog is always moving 1m to the right\n", - "movement = 1\n", - "movement_error = 2\n", - "sensor_error = 10\n", - "pos = (0, 500) # gaussian N(0,50)\n", - "\n", - "dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n", - "\n", - "zs = []\n", - "ps = []\n", - "\n", - "for i in range(10):\n", - " pos = predict(pos[0], pos[1], movement, movement_error)\n", - " print('PREDICT: {: 10.4f} {: 10.4f}'.format(pos[0], pos[1]),end='\\t')\n", - " \n", - " Z = dog.sense()\n", - " zs.append(Z)\n", - " \n", - " pos = update(pos[0], pos[1], Z, sensor_error)\n", - " ps.append(pos[0])\n", - " \n", - " print('UPDATE: {: 10.4f} {: 10.4f}'.format(pos[0], pos[1]))\n", - "\n", - " \n", - "plt.plot(ps, label='filter')\n", - "plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n", - "plt.legend(loc='best')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "PREDICT: 1.0000 502.0000\tUPDATE: 1.2790 9.8047\n", - "PREDICT: 2.2790 11.8047\tUPDATE: -2.8806 5.4138\n", - "PREDICT: -1.8806 7.4138\tUPDATE: 1.1053 4.2574\n", - "PREDICT: 2.1053 6.2574\tUPDATE: 3.3238 3.8490\n", - "PREDICT: 4.3238 5.8490\tUPDATE: 3.4857 3.6904\n", - "PREDICT: 4.4857 5.6904\tUPDATE: 4.0837 3.6267\n", - "PREDICT: 5.0837 5.6267\tUPDATE: 4.1329 3.6007\n", - "PREDICT: 5.1329 5.6007\tUPDATE: 7.5553 3.5900\n", - "PREDICT: 8.5553 5.5900\tUPDATE: 7.5774 3.5856\n", - "PREDICT: 8.5774 5.5856\tUPDATE: 8.1573 3.5838\n" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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MExERURFp2flYsOYAvt1zGgBQLzwAix7vjC5NuWawR0kS/Jcuhfrvv2EYNQqp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\n3TBtweCYqnDjyG71ID10Gv6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QBygSExE6YABCe/YETCa3tXs1PQ+PLN6CheviYLNLeO7B\n1jjx+Xi88FBrBmEiIiK6Y7KE4exXX4W9WjXUvbclPn32Pvj7qLHl4Dn0nbkBf55JkaMkcjPfFSsg\nWK2wNWgA6HRuafPnQ+fQc8Z6/HbiCqoF+ODLl/rg7Wd7QafhoihERERUOrKkCNFgQPLOnZCCg9EP\nQHRkBJ55/384di4Vg+ZvxOyR7TGuD6dNVFSC0QjfVasAALnjx5e5vXyzDfNW7ceqHfEAgG7Na+Gd\nZ2IQGqgvc9tERERUtcn2DiMpONj5+V3VA/DjvAcwrncTWO0i5ny1H0+9y2kTFZXP119DkZkJyz33\nwNqmTZnaOn4uDX1nbcCqHfHQqBSYP6YjvnypL4MwERERuYXX/H5Zq1Ziwdh70SG6BqZ+sgtbD53D\n8fOp+GhSD7RqECZ3eeQqux1+y5cDKNuosChK+PSX43h9XRwsNhGNagbhw4nd0aSuwV2VEhEREck3\nMlySAe3q4ZdFQ9C8XjVcTMnF4Pmb8OnPxyFJktylkStEEbmTJsHUvTtM/fqVqonkTCPGLPkZ81f9\nDotNxKM9o7H1tcEMwkREROR2XhOG1UeOwH/JEgBA3bAA/DD3+rSJuV/tx5Pvbkcmp014P7UaxhEj\nkP7VV4BSece3/3rkAnrOWI+dRy8h2E+Lz5/vhdcf7wwfrdf8EoOIiIgqEa9IGEJWFgzDh0ORlwdL\nq1Yw9+zpnDbR8e4amPrJbvx86DyOn/seH0/mtInKyGSxYeHaOHy+7QQAoHOTmnjv2a4ID/aVuTIi\nIiKqzLxiZFgKDETO1KkAgKDp0yFkZzvP9W9bDz8vHIwW9avhUmouBs3fiE+2HuO0iUok/mI6Bsz+\nAZ9vOwG1UoFZI9ph7cv9GYSJiIjI49wehrds2YI+ffqgT58+iI2Ndfm+vCefhKVVKygTExGwcGGh\nc3XDArBhzgN4om9T2OwS5q/6HeOWbkdGrvs2c6DyJ0kSVm47gf6zf0D8pQzUrxGIjfMfwLMDW0Ch\n4LJ6RERE5HluDcMWiwVvv/021q5di5UrV2LRokWu36xUIvPttyGp1fBdtQqaffsKndaqlXh1TEd8\nOqUnAvQabDt8Hn1e2YA/Tie580ugUlIfPnxHO82lZefjsbe3YeYX+2C22jGia2P8/NpgNK8X6sEq\niYiIiApzaxg+evQoGjVqhJCQENSoUQPh4eGIj493+X5b48bI+b//gz04GIqcnGKv6de2Hn5ZOBgt\n64ficlouhizYhGVbjnLahIyErCwYHnkE1Tt0gJCeftvrdx29hJ4z1uPXIxcQqNdg2eQeeOupLvDV\nqcuhWiIiIqLr3BqGU1NTERoainXr1mHr1q0IDQ1FcnLyHbWR+9xzSNm5E6Y+fUq8pk5YADbMvR9P\nFkybeHX1ATy+dBunTchEv2YNFHl5sEVGQgoJKfE6s9WO+at+x8g3tiI5Mx8dosKxffFDGNi+fjlW\nS0RERHSdR1aTeOSRRwAA27dvL3ZLZYPhNuvF1qjh0nM+mDIQvdtF4umlP2H74QvoN/tHrJrxINpH\nR9xxzd5ErXaMkN62n7yB1QrNihUAAMVLL5VYc8LFNDy6eDP+OpMMpULAnEfvw4vDOkCpLNvPYxWq\nr2TEfnId+8o17CfXsJ9cx75yDfvJddf66nbcGoZDQ0ORkpLifJ2SkoLQ0KJzQBcsWOD8vEuXLoiJ\niSn1Mx+4NxLN64dhzOs/4mDCVfR4cTVeGxeD/xvSrtggTu6l+O47CJcvQ4yKgti7d5HzkiTh85//\nwosf/4p8sw31agThi+kPoF1UTRmqJSIiosps165d2L17NwBAqVSiS5cut71HSEhIcNtkW4vFgn79\n+uHbb7+F2WzG2LFjsW3btkLXXLx4EdHR0e565PVn2+x4fd1BfLL1GACgZ6s6eGd8DEL8dW5/lqdd\n+2kvLS1N5kpuQ5JQrW9faI4fR+aSJTCOHFnodHqOCdM+3YOth84BAIbe1wivPXov/PUat5VQYfpK\nZuwn17GvXMN+cg37yXXsK9ewn1xnMBiwd+9e1K5d+5bXuXVkWKPRYOrUqRgxYgQA4JVXXil7o3Y7\nfD//HOZOnWC7++6Sn61SYu7oDugYXQPPL9uFX49cQJ+Z3+OjST3QplH1stdBxcp58UXov/4axiFD\nCh3/7cQVTP5oJxIz8uDvo8brj3fG4E4NZaqSiIiIqHhunzPcv39/9O/f323t+S1bhoCFC2Fp0QKp\nGzcCqluX3Lt1XfyycDCe+c8OHDmTjIcWbMLLD7fF+P7NuXatuwkCzL16wdyrl/OQ1Sbire8O4cPN\nf0GSgDaNquM/E7qiTliAjIUSERERFc8rdqC7lbwxY2CrWROav/6C76efunRPrVB/fD9nIMb3bwab\nXcJra+Pw2Nu/ID2Hq0140r+JWRg0fyM+2PQXBAh4Ycg9WD97IIMwEREReS2vD8OSvz+y3ngDABCw\nZOW7Z60AABt2SURBVAmUZ8+6dJ9GpcScUR2w4oXeCPLV4n9/XkTvV77HwVPcpMPdJEnCN7tPofcr\n3+PPsymoVc0P62cPxNSHWkNVxtUiiIiIiDypQiQVc/fuMD70EASTCUHTpgGi6PK916ZN3NMwDFfT\n8/DQgk3476a/IIrcpMMdsvLMmPDBDjy/bBeMZhse6FAf2xYNQbvG4XKXRkRERHRbFSIMA0DWvHmw\nV6sG2GwQsrLu6N5aof74fvb9eGZAc9hFCQvXxWHsW5w2UVqauDgIGRmIS0hErxnfY+PvZ6HXqvDO\n+Bj8d2J3BPpq5S6RiIiIyCUe2XTDE6SQEKT+8APsdesCijvP8GqVArNHtkeHqHBMWbYLO/66iF4z\nvsfHk7qjLUcxXWcyIfjJJ2HLycW0VuNx2ScELeuH4oPnuqFeeKDc1RERERHdkQozMgwA9nr1ShWE\nb9TrnrrYtnAIWjcKQ2JGHh56bTM+3PQnp024KH/laijT0nBCE4x/fIIx8YGW+GHuAwzCREREVCFV\nqDDsLhHV/LB+1v2YMNAxbWLRuoOcNuGCDXtOwbr0PwCAz6K64ZuZAzFjeFuoVVXy24iIiIgqgSqb\nYtQqBWaOaI8vXuyDID+tc9pEXEKi3KV5nRyjBZM/isVPC5cjKi8FqX7BmLByLu69m1sqExERUcVW\nocOwIjkZvsuXl6mNnq3qYNuiIWjTqDoSM/Iw9LXN+GAjp01cc/ifZPSZ+T3W7/0HL17+HQCgnvws\ngoP9Za6MiIiIqOwqbhi2WFBtwAAEzpsH3c8/l6mpCIMfvps1EM/d3wJ2Ufr/9u48Pqr63v/4e7Zk\nMlkhJARSUkW4bAIii3rDIotsKhUQBRGKtm4XqRVkBys/K4i4ewVJlR/gLWJbYtQKmKgUSl0RJUgE\n0SqSCCQh+z6ZmfsHSi8VcCAzOZOc1/O/mceZ73k/vuQxeTP5zDla9vJHmrpiq46XVQcobNPj8Xr1\nVMYnum7JazqUX66LL4hX3ONLVTV+vKpuvtnoeAAAAAHRdMtwWJgq77pLkhQ7f74sJSUNWs5ht2rB\nxH5aP3uEWkSFa1t2roYvSNcH+48EIm2TkldYoRseekOP/HmXPF6f7hjdXa898AslXTVAJU8/LV8s\nX5YDAADNQ9Mtw5Iqp01Tbd++suXnK+bBBwOy5tBLUvTm0nHq+x+tdbS4Stf//g09/eonphmbeP2D\nf+qq+Zv0/v6jSoyL0EvzRun+yZcr3GEzOhoAAEDANekyLKtVpY8+Kl94uCI3blT4jh0BWTY5Pkp/\nXniN7r62p7w+n5b/aZdufmSLCkub79hEZY1bs9K2686n31ZpVZ2uujRFby0br4Hdf2Z0NAAAgKBp\n2mVYUn2HDiq/9175rFbZc3ICtq7DbtX8if304uyRahEVru178zR8Qbre+7z5jU1kf12gEQvTtXH7\nF3I6bHpoWqr+/8zhio+JMDoaAABAUDX5MixJFXfeqYKtW1V5550BX3vIJe2UuXSc+nVqrWMlVbrh\noTf0VEbzGJvwen1a+foejfnda/r6aJk6/6yF3njwOk27qqssFoskKey992Q7dMjgpAAAAMHRLMqw\nHA7Vd+sWtOXb/jA2MeYSeX0+PfLnpj82caSoUpMe3qyHNn4ot8erX43opjcevE6d27X810Eej+Jm\nzlRi//5yfPyxcWEBAACCpHmU4UZgt1k1/8a++p85I9Uy2tmkxybe3PWNrpq/STv3faf4GKfWzx6h\n/zf1P+UMs59ynHPLFtm//VaelBS5L7nEoLQAAADBQxk+R4N7nhibuKxT0smxiSdf2S2P12t0tJ9U\nXVuveWt26tYnslRcUavBPX6mt5aN19BLUk57fNTq1ZKkittuk2xcTQIAADQ/zbYMh+3YIfu+fUFZ\nu03LSP1p4dX6zS8ukU8+rfjLx5q8fKsKSquCcr5A2HfouEYtekUvvv25wuxWPXDz5Vo/e6QS41yn\nPd6xa5fCdu+WNy5O1Tfc0MhpAQAAGkezLMPOV19Vq0mT1OLeeyW3OyjnsNusmntDX/1xzijFxzj1\n989OjE38Y993QTnf+fJ6ffrDlr265v4MHfyuRB3bxun1JdfptlHdZbVazvi6qLQ0SVLllCnyuU5f\nmAEAAJq6ZlmGa4cNU327dnLs26eo554L6rkG9fiZMpeO0xVd2ii/pFoTl23WE+mhMTZRUFqlqSu2\n6oH/eV919V5NGdpFW34/VhdfEP+Try1btEgVv/61Km+5pRGSAgAAGKNZlmFfZKRKH3lEkhT9xBOy\nf/llUM+X1CJSG+eP1j3X9ZJPPj266WPd9PAWQ8cm3v70Ww2dt0nbsnMVFxWuF+69Sg/f2l8R4faf\nfrEkT0qKypYskbd16yAnBQAAME6zLMOSVDtwoCo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- "text": [ - "" - ] - } - ], - "prompt_number": 17 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "There is a fair bit of arbitrary constants code above, but don't worry about it. What does require explanation are the first few lines:\n", - "\n", - " movement = 1 \n", - " movement_error = 2\n", - " \n", - "For the moment we are assuming that we have some other sensor that detects how the dog is moving. For example, there could be an inertial sensor clipped onto the dog's collar, and it reports how far the dog moved each time it is triggered. The details don't matter. The upshot is that we have a sensor, it has noise, and so we represent it with a Gaussian. Later we will learn what to do if we do not have a sensor for the `predict()` step.\n", - "\n", - "For now let's walk through the code and output bit by bit.\n", - "\n", - " movement = 1\n", - " movement_error = 2\n", - " sensor_error = 10\n", - " pos = (0, 500) # gaussian N(0,500)\n", - " \n", - " \n", - "The first lines just set up the initial conditions for our filter. We are assuming that the dog moves steadily to the right 1m at a time. We have a relatively low error of 2 for the movement sensor, and a higher error of 10 for the RFID position sensor. Finally, we set our belief of the dog's initial position as $N(0,500)$. Why those numbers. Well, 0 is as good as any number if we don't know where the dog is. But we set the variance to 500 to denote that we have no confidence in this value at all. 100m is almost as likely as 0 with this value for the variance. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next we initialize the RFID simulator with\n", - "\n", - " dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n", - "\n", - "It may seem very 'convenient' to set the simulator to the same position as our guess, and it is. Do not fret. In the next example we will see the effect of a wildly inaccurate guess for the dog's initial position.\n", - "\n", - "The next code allocates an array to store the output of the measurements and filtered positions. \n", - "\n", - " zs = []\n", - " ps = []\n", - " \n", - "This is the first time that I am introducing standard nomenclature used by the Kalman filtering literature. It is traditional to call our measurement $Z$, and so I follow that convention here. As an aside, I find the nomenclature used by the literature very obscure. However, if you wish to read the literature you will have to become used to it, so I will not use a much more readable variable name such as $m$ or $measure$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we just enter our `update() ... predict()` loop.\n", - "\n", - " for i in range(10):\n", - " pos = predict(pos[0], pos[1], movement, sensor_error)\n", - " print 'PREDICT:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n", - "\n", - "Wait, why `predict()` before `update()`? It turns out the order does not matter once, but the first call to `,DogSensor.sense()` assumes that the dog has already moved, so we start with the update step. In practice you will order these calls based on the details of your sensor, and you will very typically do the `sense()` first.\n", - "\n", - "So we call the update function with the gaussian representing our current belief about our position, the another gaussian representing our belief as to where the dog is moving, and then print the output. Your output will differ, but when writing this I get this as output:\n", - "\n", - " PREDICT: 1.000 502.000\n", - "\n", - "What is this saying? After the prediction, we believe that we are at 1.0, and the variance is now 502.0. Recall we started at 500.0. The variance got worse, which is always what happens during the prediction step.\n", - "\n", - " Z = dog.sense()\n", - " zs.append(Z)\n", - " \n", - "Here we sense the dog's position, and store it in our array so we can plot the results later.\n", - "\n", - "Finally we call the update function of our filter, save the result in our *ps* array, and print the updated position belief:\n", - "\n", - " pos = update(pos[0], pos[1], Z, movement_error)\n", - " ps.append(pos[0])\n", - " print 'UPDATE:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n", - " \n", - "Your result will be different, but I get\n", - "\n", - " UPDATE: 1.6279 , 9.8047\n", - " \n", - "as the result. What is happening? Well, at this point the dog is really at 1.0, however the predicted position is 1.6279. What is happening is the RFID sensor has a fair amount of noise, and so we compute the position as 1.6279. That is pretty far off from 1, but this is just are first time through the loop. Intuition tells us that the results will get better as we make more measurements, so let's hope that this is true for our filter as well. Now look at the variance: 9.8047. It has dropped tremendously from 502.0. Why? Well, the RFID has a reasonably small variance of 2.0, so we trust it far more than our previous belief. At this point there is no way to know for sure that the RFID is outputting reliable data, so the variance is not 2.0, but is has gotten much better.\n", - "\n", - "Now the software just loops, calling `predict()` and `update()` in turn. Because of the random sampling I do not know exactly what numbers you are seeing, but the final position is probably between 9 and 11, and the final variance is probably around 3.5. After several runs I did see the final position nearer 7, which would have been the result of several measurements with relatively large errors.\n", - "\n", - "Now look at the plot. The noisy measurements are plotted in with a dotted red line, and the filter results are in the solid blue line. Both are quite noisy, but notice how much noisier the measurements (red line) are. This is your first Kalman filter shown to work!" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "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. This time we will plot both the output of the filter and the variance." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%precision 2\n", - "# assume dog is always moving 1m to the right\n", - "movement = 1\n", - "movement_error = 2\n", - "sensor_error = 4.5\n", - "pos = (0, 100) # gaussian N(0,50)\n", - "\n", - "dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n", - "\n", - "zs = []\n", - "ps = []\n", - "vs = []\n", - "\n", - "for i in range(50):\n", - " pos = predict(pos[0], pos[1], movement, movement_error) \n", - " Z = dog.sense()\n", - " zs.append(Z)\n", - " vs.append(pos[1])\n", - " \n", - " pos = update(pos[0], pos[1], Z, sensor_error)\n", - " ps.append(pos[0])\n", - " \n", - "#plt.subplot(121) \n", - "p1, = plt.plot(zs,c='r', linestyle='dashed')\n", - "p2, = plt.plot(ps,)\n", - "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n", - "plt.show()\n", - "\n", - "plt.plot(vs)\n", - "plt.title('Variance')\n", - "plt.show()\n", - "print ([float(\"%0.4f\" % v) for v in vs])" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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/wdriNzAJk+jIYFTWFLrGtezKb+1RJC0t1iV0eArGIiIi0mHYv/qKLn/+MwAV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\nA/v27bSOGMbKk/fT2LKXZEcOpw/9z288jVraFVeQ+OKL2O6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P+e5I+wS72gEAAMAG4grF+/btU0VFhd58802FQiGVlJTopz/9qSSpuLhYklRZWSnDMPqc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\nE3WBWKgLxEJdICI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- "text": [ - "" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[102.0, 6.3099, 4.6267, 4.2812, 4.1939, 4.1708, 4.1646, 4.1629, 4.1624, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623]\n" - ] - } - ], - "prompt_number": 18 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here we can see that the variance converges very quickly to roughly 4.1623 in 10 steps. We interpret this as meaning that we become very confident in our position estimate very quickly. The first few measurements are unsure due to our uncertainty in our guess at the initial position, but the filter is able to quickly determine an accurate estimate." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "> Before I go on, I want to emphasize that this code fully implements a 1D Kalman filter. If you have tried to read the literature, you are perhaps surprised, because this looks nothing like the complex, endless pages of math in those books. To be fair, the math gets a bit more complicated in multiple dimensions, but not by much. So long as we worry about *using* the equations rather than *deriving* them we can create Kalman filters without a lot of effort. Moreover, I hope you'll agree that you have a decent intuitive grasp of what is happening. We represent our beliefs with Gaussians, and our beliefs get better over time because more measurement means more data to work with. \"Measure twice, cut once!\"" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Relationship to the g-h Filter" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In the first chapter I stated that the Kalman filter is a form of g-h filter. However, we have been reasoning about the probability of Gaussians, and not used any of the reasoning or equations of the first chapter. A trivial amount of algebra will reveal the relationship, so let's do that now. It's not particularly illuminating algebra, so feel free to skip to the bottom to see the final equation that relates *g* to the variances.\n", - "\n", - "The equation for our estimate is:\n", - "\n", - "$$\n", - "\\mu_{x'}=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\n", - "$$\n", - "\n", - "which I will make more friendly for our eyes as:\n", - "\n", - "$$\n", - "\\mu_{x'}=\\frac{ya + xb} {a+b}\n", - "$$\n", - "\n", - "We can easily put this into the g-h form with the following algebra\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - "\\mu_{x'}&=(x-x) + \\frac{ya + xb} {a+b} \\\\\n", - "\\mu_{x'}&=x-\\frac{a+b}{a+b}x + \\frac{ya + xb} {a+b} \\\\ \n", - "\\mu_{x'}&=x +\\frac{-x(a+b) + xb+ya}{a+b} \\\\\n", - "\\mu_{x'}&=x+ \\frac{-xa+ya}{a+b} \\\\\n", - "\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x)\\\\\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "We are almost done, but recall that the variance of estimate is given by \n", - "\n", - "$${\\sigma_{x'}^2} = \\frac{1}{ \\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\\\\\n", - "= \\frac{1}{ \\frac{1}{a} + \\frac{1}{b}}\n", - "$$\n", - "\n", - "We can incorporate that term into our equation above by observing that\n", - "$$ \n", - "\\begin{aligned}\n", - "\\frac{a}{a+b} &= \\frac{a/a}{(a+b)/a} = \\frac{1}{(a+b)/a}\\\\\n", - " &= \\frac{1}{1 + \\frac{b}{a}} = \\frac{1}{\\frac{b}{b} + \\frac{b}{a}}\\\\\n", - " &= \\frac{1}{b}\\frac{1}{\\frac{1}{b} + \\frac{1}{a}} \\\\\n", - " &= \\frac{\\sigma^2_{x'}}{b}\n", - " \\end{aligned}\n", - "$$\n", - "\n", - "We can tie all of this together with\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - "\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x)\\\\\n", - "&= x + \\frac{\\sigma^2_{x'}}{b}(y-x) \\\\\n", - "&= x + g_n(y-x)\\\\\n", - "\\blacksquare\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "where\n", - "\n", - "$$g_n = \\frac{\\sigma^2_{x'}}{\\sigma^2_{y}}$$\n", - "\n", - "The end result is multipying the residual of the two measurements by a constant and adding to our previous value, which is the *g* equation for the g-h filter. *g* is the variance of the new estimate divided by the variance of the measurement. Of course in this case g is not truly a constant, as it varies with each time step as the variance changes, but it is truly the same formula. We can also derive the formula for *h* in the same way but I don't find this a particularly interesting derivation. The end result is\n", - "\n", - "$$h_n = \\frac{COV (x,\\dot{x})}{\\sigma^2_{y}}$$\n", - "\n", - "The takeaway point is that *g* and *h* are specified fully by the variance and covariances of the measurement and preditions at time *n*. In other words, we are just picking a point between the measurement and prediction by a scale factor determined by the quality of each of those two inputs. That is all the Kalman filter is. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#####Exercise:\n", - "Modify the values of `movement_error` and `sensor_error` and note the effect on the filter and on the variance. Which has a larger effect on the value that variance converges to. For example, which results in a smaller variance:\n", - "\n", - " movement_error = 40\n", - " sensor_error = 2\n", - " \n", - "or:\n", - "\n", - " movement_error = 2\n", - " sensor_error = 40 " - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Introduction to Designing a Filter" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "So far we have developed our filter based on the dog sensors introduced in the Discrete Bayesian filter chapter. We are used to this problem by now, and may feel ill-equipped to implement a Kalman filter for a different problem. To be honest, there is still quite a bit of information missing from this presentation. The next chapter will fill in the gaps. Still, lets get a feel for it by designing and implementing a Kalman filter for a thermometer. The sensor for the thermometer outputs a voltage that corresponds to the temperature that is being measured. We have read the manufacturer's specifications for the sensor, and it tells us that the sensor exhibits white noise with a standard deviation of 2.13.\n", - "\n", - "We do not have a real sensor to read, so we will simulate the sensor with the following function. We have hard-coded the voltage to 16.3 - obviously the voltage will differ based on the temperature, but that is not important to our filter design." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "temp_variance = 2.13**2\n", - "def volt():\n", - " return random.randn()*temp_variance + 16.3" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 19 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We generate white noise with a given variance using the equation `random.randn() * variance`. The specification gives us the standard deviation of the noise, not the variance, but recall that variance is just the square of the standard deviation. Hence we raise 2.13 to the second power.\n", - "\n", - "> **Sidebar**: spec sheets are just what they sound like - specifications. Any individual sensor will exhibit different performance based on normal manufacturing variations. Numbers given are often maximums - the spec is a guarantee that the performance will be at least that good. So, our sensor might have standard deviation of 1.8. If you buy an expensive piece of equipment it often comes with a sheet of paper displaying the test results of your specific item; this is usually very trustworthy. On the other hand, if this is a cheap sensor it is likely it received little to no testing prior to being sold. Manufacturers typically test a small subset of their output to verify that everything falls within the desired performance range. If you have a critical application you will need to read the specification sheet carefully to figure out exactly what they mean by their ranges. Do they guarantee their number is a maximum, or is it, say, the $3\\sigma$ error rate? Is every item tested? Is the variance normal, or some other distribution. Finally, manufacturing is not perfect. Your part might be defective and not match the performance on the sheet.\n", - "\n", - "> For example, I just randomly looked up a data sheet for an airflow sensor. There is a field *Repeatability*, with the value $\\pm 0.50\\%$. Is this a Gaussian? Is there a bias? For example, perhaps the repeatability is nearly 0.0% at low temperatures, and always nearly +0.50 at high temperatures. Data sheets for electrical components often contain a section of \"Typical Performance Characteristics\". These are used to capture information that cannot be easily conveyed in a table. For example, I am looking at a chart showing output voltage vs current for a LM555 timer. There are three curves showing the performance at different temperatures. The response is ideally linear, but all three lines are curved. This clarifies that errors in voltage outputs are probably not Gaussian - in this chip's case higher temperatures leads to lower voltage output, and the voltage output is quite nonlinear if the input current is very high. \n", - "\n", - "> As you might guess, modeling the performance of your sensors is one of the harder parts of creating good Kalman filter. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we need to write the Kalman filter processing loop. As with our previous problem, we need to perform a cycle of sensing and updating. The sensing step probably seems clear - call `volt()` to get the measurement, pass the result into `update()` function, but what about the update step? We do not have a sensor to detect 'movement' in the voltage, and for any small duration we expect the voltage to remain constant. How shall we handle this?\n", - "\n", - "As always, we will trust in the math. We have no movement, and no error associated with them, so we will just set both to zero. Let's see what happens. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_error = temp_variance\n", - "movement_error = 0\n", - "movement = 0\n", - "voltage = (25,1000) #who knows what the first value is?\n", - "\n", - "zs = []\n", - "ps = []\n", - "vs = []\n", - "N=50\n", - "\n", - "for i in range(N):\n", - " Z = volt()\n", - " zs.append(Z)\n", - " \n", - " voltage = update(voltage[0], voltage[1], Z, sensor_error)\n", - " ps.append(voltage[0])\n", - " vs.append(voltage[1])\n", - "\n", - " voltage = predict(voltage[0], voltage[1], movement, movement_error)\n", - "\n", - "plt.scatter(range(N), zs, marker='+', s=64, color='r', label='measurements')\n", - "p1, = plt.plot(ps, label='filter')\n", - "plt.legend(loc='best')\n", - "plt.xlim((0,N));plt.ylim((0,30))\n", - "plt.show()\n", - "plt.plot(vs)\n", - "plt.title('Variance')\n", - "plt.show()\n", - "print('Variance converges to',vs[-1])\n", - "print('Last voltage is',voltage[0])" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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KEh95pE8lND6fT22ujkAZnMvdKU9np1werzwdnXJ3dMrd4ZXb47/0dHTK5emU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\nxOMvf6yaxjbNyMvUlwtPDXG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LEV0AAACY46RB12azyWYLndbQ0CCHw9Hjxo8+jNaqQCAoi8XoY5kAAABA75w06EpSc3Oz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\n7vvuNNmtFj27fIu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- "text": [ - "" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Variance converges to 0.09072976736236911\n", - "Last voltage is 16.78247179353804\n" - ] - } - ], - "prompt_number": 20 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The first plot shows the individual sensor measurements marked with '+'s vs the filter output. Despite a lot of noise in the sensor we quickly discover the approximate voltage of the sensor. In the run I just completed at the time of authorship, the last voltage output from the filter is $16.213$, which is quite close to the $16.4$ used by the `volt()` function. On other runs I have gotten up to around $16.9$ as an output and also as low as 15.5 or so.\n", - "\n", - "The second plot shows how the variance converges over time. Compare this plot to the variance plot for the dog sensor. While this does converge to a very small value, it is much slower than the dog problem. The next section **Explaining the Results - Multi-Sensor Fusion** explains why this happens.\n", - "\n", - "##### Exercise(optional):\n", - "Write a function that runs the Kalman filter many times and record what value the voltage converges to each time. Plot this as a histogram. After 10,000 runs do the results look normally distributed? Does this match your intuition of what should happen?\n", - "\n", - "> use plt.hist(data,bins=100) to plot the histogram. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "#Your code here" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 21 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "######Solution\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_error = temp_variance\n", - "\n", - "def VKF():\n", - " voltage=(14,1000)\n", - " for i in range(N):\n", - " Z = volt()\n", - " voltage = update(voltage[0], voltage[1], Z, sensor_error)\n", - " return voltage[0]\n", - "\n", - "vs = []\n", - "for i in range (10000):\n", - " vs.append (VKF())\n", - "plt.hist(vs, bins=100, color='#e24a33') \n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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- "text": [ - "" - ] - } - ], - "prompt_number": 22 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "######Discussion\n", - "The results do in fact look like a normal distribution. Each voltage is Gaussian, and the **Central Limit Theorem** guarantees that a large number of Gaussians is normally distributed. We will discuss this more in a subsequent math chapter." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Explaining the Results - Multi-Sensor Fusion" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "So how does the Kalman filter do so well? I have glossed over one aspect of the filter as it becomes confusing to address too many points at the same time. We will return to the dog tracking problem. We used two sensors to track the dog - the RFID sensor that detects position, and the inertial tracker that tracked movement. However, we have focused all of our attention on the position sensor. Let's change focus and see how the filter performs if the inertial tracker is also noisy. This will provide us with an vital insight into the performance of Kalman filters." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_error = 30\n", - "movement_sensor = 30\n", - "pos = (0,500)\n", - "\n", - "dog = DogSensor(0, velocity=movement, noise=sensor_error)\n", - "\n", - "zs = []\n", - "ps = []\n", - "vs = []\n", - "\n", - "for i in range(100):\n", - " Z = dog.sense()\n", - " zs.append(Z)\n", - " \n", - " pos = update(pos[0], pos[1], Z, sensor_error)\n", - " ps.append(pos[0])\n", - " vs.append(pos[1])\n", - "\n", - " pos = predict(pos[0], pos[1], movement+ random.randn(), movement_error)\n", - "\n", - "plt.plot(ps, label='filter')\n", - "plt.plot(zs, linestyle='dashed', c='r', label='measurement')\n", - "plt.legend()\n", - "plt.show()\n", - "plt.plot(vs)\n", - "plt.title('Variance')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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JB8PQoah44glYW7SQeikkkhkMYHgevEoFyGRSr6busFrFPwqbawkJJb8D5MGDB2Pp0qXi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Fq/npUqepqQySC9dg3S69dtTi5LUzxqFDIPH4Z67FinT+txq2SGAZWT47AZ1Z0EjR+P0N69+SBX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\nK7Zfep2uYRj890e7+M2cdZw8c/kNd2WVTma+/w8Anv3VL+qOK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Y0CmDcEcbNmzQ+eefr6qqKuXn52vVqlXKyclRfn6+jh49evIgzM1yAAAAsKEzCsJ+v19P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\nmm3hO9IhhLd93mG747VaI6Z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- "text": [ - "" - ] - } - ], - "prompt_number": 23 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This result is worse than the example where only the measurement sensor was noisy. Instead of being mostly straight, this time the filter's output is distinctly jagged. But, it still mostly tracks the dog. What is happening here?\n", - "\n", - "This illustrates the effects of *multi-sensor fusion*. Suppose we get a position reading of -28.78 followed by 31.43. From that information alone it is impossible to tell if the dog is standing still during very noisy measurements, or perhaps sprinting from -29 to 31 and being accurately measured. But we have a second source of information, his velocity. Even when the velocity is also noisy, it constrains what our beliefs might be. For example, suppose that with the 31.43 position reading we get a velocity reading of 59. That matches the difference between the two positions quite well, so this will lead us to believe the RFID sensor and the velocity sensor. Now suppose we got a velocity reading of 1.7. This doesn't match our RFID reading very well - it suggests that the dog is standing still or moving slowly.\n", - "\n", - "When sensors measure different aspects of the system and they all agree we have strong evidence that the sensors are accurate. And when they do not agree it is a strong indication that one or more of them are inaccurate. \n", - "\n", - "We will formalize this mathematically in the next chapter; for now trust this intuitive explanation. We use this sort of reasoning every day in our lives. If one person tells us something that seems far fetched we are inclined to doubt them. But if several people independently relay the same information we attach higher credence to the data. If one person disagrees with several other people, we tend to distrust the outlier. If we know the people that might alter our belief. If a friend is inclined to practical jokes and tall tales we may put very little trust in what they say. If one lawyer and three lay people opine on some fact of law, and the lawyer disagrees with the three you'll probably lend more credence to what the lawyer says because of her expertise. In the next chapter we will learn how to mathematical model this sort of reasoning." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "More examples" - ] - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Example: Extreme Amounts of Noise" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "So I didn't put a lot of noise in the signal, and I also 'correctly guessed' that the dog was at position 0. How does the filter perform in real world conditions? Let's explore and find out. I will start by injecting a lot of noise in the RFID sensor. I will inject an extreme amount of noise - noise that apparently swamps the actual measurement. What does your intuition tell about how the filter will perform if the noise is allowed to be anywhere from -300 or 300. In other words, an actual position of 1.0 might be reported as 287.9, or -189.6, or any other number in that range. Think about it before you scroll down." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_error = 30000\n", - "movement_error = 2\n", - "pos = (0,500)\n", - "\n", - "dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n", - "\n", - "zs = []\n", - "ps = []\n", - "\n", - "for i in range(1000):\n", - " pos = predict(pos[0], pos[1], movement, movement_error)\n", - " \n", - " Z = dog.sense()\n", - " zs.append(Z)\n", - " \n", - " pos = update(pos[0], pos[1], Z, sensor_error)\n", - " ps.append(pos[0])\n", - "\n", - "\n", - "p1, = plt.plot(zs,c='r', linestyle='dashed', label='measurement')\n", - "p2, = plt.plot(ps, c='#004080', label='filter')\n", - "plt.legend(loc='best')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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FBA4HIESQUYJB0CbpN22KR7Pijk5wQtLu3u033vhoQf02GK6ePWFYvZofc0KY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Ue7Vvmcc+DZsAFZkyYhcMsttBEeUHUTiBOtOByqWiSz3qa9+CJsZvuJx4PYRRfxVV3oPRKp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- "text": [ - "" - ] - } - ], - "prompt_number": 24 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In this example the noise is extreme yet the filter still outputs a nearly straight line! This is an astonishing result! What do you think might be the cause of this performance? If you are not sure, don't worry, we will discuss it latter." - ] - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Example: Bad Initial Estimate" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "Now let's lets look at the results when we make a bad initial estimate of position. To avoid obscuring the results I'll reduce the sensor variance to 30, but set the initial position to 1000m. Can the filter recover from a 1000m initial error?" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_error = 30\n", - "movement_error = 2\n", - "pos = (1000,500)\n", - "\n", - "dog = DogSensor(0, velocity=movement, noise=sensor_error)\n", - "\n", - "zs = []\n", - "ps = []\n", - "\n", - "for i in range(100):\n", - " pos = predict(pos[0], pos[1], movement, movement_error)\n", - " \n", - " Z = dog.sense()\n", - " zs.append(Z)\n", - " \n", - " pos = update(pos[0], pos[1], Z, sensor_error)\n", - " ps.append(pos[0])\n", - "\n", - "plt.plot(ps, label='filter')\n", - "plt.plot(zs,c='r', linestyle='dashed', label='measurement')\n", - "plt.legend(loc='best')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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JDyIzv4Ttmao1ExE5lkXdfjuJXbvi/O9/AbDl51sckYi0dC0yQTYMg5O7qw5Z\nRETAnpGBUVpKZYcOABiaQRaRBmqRCTLASdXt3pQgi4gc2+z7qr4H9j/yCBlLl1Jy8cUWRyQiLZ3D\n6gB8NTBFCbKIyDHPND3LTJf37YsZEWFxQCLSGrTYGeTUjm0IctrZsnc/u3MKrQ5HREQsYBQWYisu\nxh0cjBkebnU4ItJKtNgEOcBh48y+xwHw0sc/WRyNiIhYwZaTgxkUhLttW62iJyKNpsUmyAC3X9AP\nw4A3v9zArix1sxAROdZUdurE3s2byVq0yOpQRKQVadEJcvf2MZz/h664Kt08+8EPVocjIiJWMAzM\n0FCroxCRVqRFJ8gAt13QD7vN4O1l6Wzdt9/qcERExCJGYSFxw4cTf9ppVociIi1ci0+QuyREcvGQ\nZCrdJs+8973V4YiIiEXM4GAcmzbh2LoVKiqsDkdEWrAWnyADTD6vLwF2G+9/s5mNu3KtDkdERKxg\nt2NGRgJg268riiLiu1aRILePC+fS01MwTfjbO/+zOhwREWkmttzcQ2aL3dHRVc9rNT0RaYBWkSAD\n3Dy2D0EBdhas/pU127KsDkdERJpBmzFjSOzUCfv27QC4o6IAJcgi0jCtJkFOiA7lirNOAOApzSKL\niLR+pok9IwPDNHHHxQG/zSAbSpBFpAFaTYIM8OdzTiQ0KIAvf9zJ6vQMq8MREZEmZOTnY5SV4Y6I\nwAwJASD/iSfYt3o1ZcOGWRuciLRorSpBjo0I5ppRqQA89c53FkcjIiJNyZ5RNRFS2bat5zl3UhLu\ndu3A6bQqLBFpBVpVggxwXVovIkOcfL1uDyvW7bY6HBERaSI1CbL7oARZRKQxtLoEOTI0kOvG9Abg\n4TdXUlKuXpgiIq2RUVyMOyrqkBlkEZHG0OoSZIA/juzJcXHhrNuew12vr8A0TatDEhGRRlY6ejT7\n1q0j/9lnrQ5FRFoZnxPkJ598klNPPZVzzjnH89yCBQsYOXIkI0eOZMmSJY0SoC/Cgp28dvtZBAc6\neGf5Jl77bJ1lsYiISBOztcq5HhGxkM+fKiNGjGDmzJmex+Xl5cyYMYO5c+cya9YsHnvssUYJ0Fcn\nHBfLM9cNBeDhN//L8rWqRxYRae0cmzcTP3AgbcaOtToUEWnBfE6Q+/btS1R1Q3aANWvW0K1bN2Ji\nYkhMTCQhIYENGzY0SpC+OmdgF246tw+VbpMb/u8LdmQesDQeERFpWmZQEI5du7Dv1qSIiPiu0a5L\nZWVlERcMI87pAAAgAElEQVQXx7x581i4cCFxcXFkZmY21vA+m3pRf07v04G8wjKufmYxxaUuq0MS\nEZEmooVCRKQxOBp7wAkTJgCwePFiDMPwuk1sbGxjH7ZOb913Iafd+gbrd+Ry97/+y+y7x9YamzS/\ngIAAoPnPC/FvOi/EG895ER2NsXUrZmIihIb+tkFMDKbTia20lNiQEAgOtihSaU76vBBvas4LXzRa\nghwfH09WVpbncc2MsjfTpk3z/P+QIUMYOnRoY4XhVVRYEPMfvIDTJr/BO8s2cOLxbblj/KAmPaaI\niDShrCycqamY0dGU79372/OGAbGxsHcv5OZCUpJ1MYpIs1u6dCnLli0DwG63M2TIEJ/GabQEuVev\nXmzatInc3FzKysrIyMggJSXF67Y33njjIY9zcnIaK4xaxYUaPH/9MK56ehEPzFpKVLCNC07t2uTH\nlSOr+cXfHOeBtBw6L8SbmvNi/4YNxAMVbdsedo7ERUYSsHcv+7dupSIoyIIopbnp80JqpKamkppa\ntapybGwsK1as8Gkcn2uQH3roISZMmMC2bdsYOnQoK1asYMqUKUycOJErr7ySe+65x9ehm8yI/h25\nY1x/TBNufmkJD87+FleF2+qwRESknuz79gFQmZBw2Gs5s2ezd+1aKmqZpBERORKfZ5AffPBBHnzw\nwcOeT0tLa1BATe3W8/oSFRrIX+f8l1c/XcuabVn8/eYzaRsdYnVoIiJylOzVN4F7W2ba3a5dc4cj\n0myc1eUDle3b427TBjMiwuKIWqdjrru6YRhcOaIn79x/NgnRIazamMGo+95j5Ya9R95ZRET8gi0j\nA0DLTMsxJ+Kpp2gzcSJtTzuN4E8+sTqcVuuYS5BrDOjWlk8fPZ9BPRLJzC/hokf/wz8W/qxlqUVE\nWgKHg8rERCo1WyzHEpeLgF9+8Ty0VZcaSeM7ZhNkgLjIEObdncb1Y3pT6Tb565z/cuMLX1JSVmF1\naCIiUofCm28m47vvKL78cqtDaXncboyiIqujEB84Nm7EKC31PLYrQW4yx3SCDOCw27j/koHMvOUM\nQoMC+Oi/W7no0U/I2l9sdWgiIiKNKvj990no1Yvw6dOtDkV84PzhBwDc1b2/7XtVHtpUjvkEucbZ\nA7vwyUNjad8mjB+2ZHHugx+xeU++1WGJiEg9BS5bRtvevYm+9lqrQ/E7lW3aYMvPx7lqldWhiA8C\nfvoJgNKRIwGwV9fiS+NTgnyQ5PbRfPzQWE7s0oYdWQWc++CHfLtev85ERFoS0+nEnpOD7aDFq6SK\nq39/TIeDgLVrMQoLrQ5H6ql84EBKxoyhZOxY3JGRuMPCrA6p1VKC/DvxUSG8c+/ZjOzfkf3F5Vzy\nxALe/3pzsx3fyM8n7LnnCH/00WY7ZmtnFBURdeON2LdssToUEWkG7uhoAGx5eRZH4l/s27fj2LSJ\nik6dMNxunP/7n9UhST2VXHQRea+8QtmZZ7Lvl1/Iee89q0NqtZQgexESFMA/Jp/JH0f2pLzCzU0v\nLeG5D35ong4XNhsR06cT9tpr4HI1/fGOARGPPELIhx8SNWUKYS++SNRNN2FT3ZZIkwtctIjw6dMb\n/077/Hwc69Zh5OZ6fVkJsnchc+YQl5ZGwOaqSR+VWYjUTglyLew2Gw9P+gMPXT4Iw4Dp87/jT899\nwfod3j+QG4sZEUFFx44YZWU4NOPZYM4VKwh94w3MgAD2P/44QZ9+Ssj77+PYscPq0ERavfAXXyT8\nuecI+uyzRh3Xtnw58SNGED15stfX3VFRVdvl54Nad3o4du4EoGTMGEynE6OgwOKIRPyXEuQjuGZU\nKq9OPosgp50Fq7dx5t3vcumTC1m+dneTzSi7evYEIGDt2iYZ/1hhFBYSNWUKAAWTJ1PRo4enZ6p9\nzx4rQxNp9QJ++gnnd9/hjoigZNy4xh28+gqQt2WmAXA6cYeGYlRWYhw40LjHbsHsu3YBUHTFFexd\nv54DDz9scUQi/ksJ8lEYNaATS54cx1UjTiA40MFXa3Yx4fEFjLz3fd77ejOuCnejHs+TIK9b16jj\nHmsiHnkEx65dlPfqReGf/wzwW4KsEguRJhX66qsAFE+ciFndkqqxGNU/cL0tM10jc8UK9mzZghkZ\n2ajHbsns1VfOKrp0gaAgi6MR8W9KkI/ScfERPHLFqax6biJTLxpAXGQw67bncPNLS/jD7fO487Xl\nzPlyPT9uyaK03LeFRkJnzsT5zTdU9OgBaAa5oSq6dsUdEUH+M89AQADwW4Jsa2EzyIFffqnG/tJi\n2DIyCP74Y0ybjaKrrmr08Y2aGeQ6EmR3fLySwIMYxcXYc3Iwnc46f1iIfzLy8oiaPJmQuXN/e7Ks\nDPu2bdi3b7cusFbMYXUALU1MeBC3nteX69J68f43m/n7f35m85585ny5wbONw27QLSmaXp3a0K9r\nPOMGdyM4sO4/atu+fUQ+/DDu4GAyly1j/4MPUt63b1O/nVat6JprKB4/HjM83PNcZWIi0LJmkIMW\nLCD6uutw9elD9jvvQGCg1SGJ1Cnwq68wXC5KRo+mskMHz/P2HTuqHhtGg8Y/mgRZDmUUFlI6dGjV\nA5vmxloa55o1hMyfj2PbNoonTgQg+JNPiL7lForHjiX/pZcsjrD1UYLsoyCng4nDUhg/pDur0/fx\n49Ys1v6aw9pfs9m8Zz/rd+Syfkcuby9L59n3f+Du8Sdxwaldsdm8fzEELl0KQNmpp7LVHka7q/+I\n02E/6ngcmzdj5OXhOumkRnl/rcXByTFAed++5E+fjis52aKI6se5fDnRf/4zhttN6fDhSo6lRSgZ\nPx7X737gR916KyHvvEP2u+9SfsopDRrfTEqioksXKpOSGjTOscQdH0/uW29ZHYb4KKB6Bb3yE0/0\nPFfzA1HLTTcNJcgNZLMZDExJZGBKoue54lIXv+zM5edt2cxbupG1v+Zw69+/4vVFa3nw0lMO2baG\nsehzAP52IIoHbv83vTu3YfYdo2gTGXzkIEyT+OqZgX3ff6/LZ3VwJyVRfOmlVodxVAJ+/JGYP/4R\no7ycwquvpvC226wOSeSoVfzuR2hNMhvyxhsNTpArXn6ZnJycBo0hYMvJwblqFeUnnoi7uvxM/FPN\nCnquPn08z9XcpHqsJshGbi5mVFSTXRHRdZYmEBIUwIBubblqRE8WTjufp/80lLZRIfy0NZsLpn3C\ntc9+zvbMA1RUuln0/Xb+NOMz3J8vAWCWUfUhtWZbNmMf+ogdmUe+A/vgdnCOzc23qIk0Hfv27cRc\ndhm2oiKKL7iAAw891ODL0iJWKr70UkybjeAFC7BlZzf6+KZpsn5H7uHdhdyNexN1axLxwAPEXHMN\nQYsXWx2KHIGzOkEuPyhBdteUDO7bd0y2M4yaOpW2J52E89tvm2R8JchNzGYzGD80mRUzLub2C/p5\n2sUNu2M+/W96i6tmLCJ7ydfEVJSwOzKeu+66mFXPT6Rnx1h+zTjA2Ic+Yt32umdKnN984/l/++7d\nTf2W/Ft5eav4oKhs146yYcMoPeMM8p9+WjWD0uJVJiVRdsYZGC4XIfPmNfr4r366ljPvfpc7Xl2O\naZqEvPUWCV27EvHAA41+rNai/OSTAS0Y4u9se/diz8jAHRlJZefOnufN0FDc4eEYZWUYx9iiOEZh\nIUFLlmDLyKCiU6cmOYZ/f+tWVhL06aetYgYgJCiAKRf2Z/nfLmbcad0or3CTfaCEru2iGDvxdHbe\nfT+hd9/OmJM7kxQbxrv3nc0fTkgkM7+EC6d9zLfra7+pzJ6VBcD+++6j5OKLm+st+aWwF14goWdP\nQmbNsjqUhgkIIP/558l95RVPBw5bZibhM2YQ/tRTFgcn4puiSZOAqhXdqKxstHEr3W5e+6yq68/c\nrzby6qdrMZ1ObCUlVYuFiFflAwcCELhyZZ0TC6EzZxL83nv1/y42zVYxYWE1MyqKnFmz2P/gg4dd\nSXSlplJ+4onYiostis4aQZ9/jlFaSvlJJ3lm0hubf9YgmyZBn31G+PTpBGzcSO7LL1N67rlNf1yX\nC6O4uGF9M91ujIKCWsdoFxvGc9cP49bz+lJc6qJnx1gMwwCGcfDpHR7iZGHOEvJ/XsaJKZdz6ZML\nefHPwxl9UudDxispq2DlmEv4ucsQIoMdjDPN6vGOTQHr12Pbvx8zLMzqUBrOZju0TZXLRfjTT+OO\niqLgL39p9SUX9hkzMDt1gmHDrA5FjoJ9927CnnuOoquvpiIlxes2ZcOGUd63L2WDBmGUlWGGhDTK\nsb9as4udWYVEhDg5UFzOw2+uZOiwcIah5aZrBH34Ie7ERMoHDPBckapITsYdFYV9717su3Yd0nGk\nhm3PHiKefBKjrAxXSgoVJ5xwdAcsKSFu5EjMyEiyP/xQV8EawAwOpuyss7y+lvPOO80cjX8I+uQT\nAErPPrvJjuFfCbJpErh8OeFPPonzxx8BqEhKAqezSQ9rFBQQ8uabhP3jHxiFhWQuX17VQ7Oe7Fu2\nEPWXv4DTSc68eXUmMF0SjpyEB6Vv5LicPUzt7uSerZX86bkvuO+Sk4kMCeT7LZn8sDmTjbvyqHT/\n9gvdDAnl4iEto0NDU3Bs3AiAq5YvaICgzz4jeP58SkeOpOSii5okDqOoiOC336Z09Gjcta32VU/u\ndu2ojI7GnpeHffduKtu3b5Rx/ZF961Yc995b9aCpy4ZMk6BFiyjv29enf/dSJWTWLELffBOjqIj8\nF1/0vpHNRvbHHzfsx92WLRiZmdhiY3HHxgLwxufrAbjp3BMpKq3guQ9+YNqn6UqQqxmFhcTceCNm\nUBB7D75PxWajfMAAgj7/HOeqVZR4SZDDn3kGo6yMknPOOfrkGAh57z0Cqu+Pca5cSfmgQQ1+H9Jy\n2DIysO/Zc1g3mzr3ycoi/Mknq35k13Gu1ZRXmIZBSVpaY4TrPZ4mG9kHgYsXEztxIs4ff6QyLo78\nRx4hc/lySkeNapLj2TIzCX/8cdqefDKR06Zh37ePAw88UP8vyYoKQl9+mfgRIwhctQrHxo2eJT0x\nTYI+/piYiROhrKxew9asqHdDBxtTLuiH2zR5+M2VTPnHMt78cgO/7MgFoGfHWEYN6AjAff/6hm37\n9tcv/taitBTHtm2YNhsVXbvWupl9506CFy70/AhrCqGvvELUffcRN3q0pz1PrUpKiHjwQYz9R/h7\nMwxcvXoBrX8RmcpOnTCrZ5yMJr50GDJ7NjFXX030ddc16XFaurBnniFk1iyv56lRXExodQuxoj/+\nse6BGnjlw/7Pf+IcPryqTAPYlVXAFz/uwOmwMWFod/5yYX9GDejIjsqq0iRycht0vNag5vuoIinp\nsD//krQ0isePp/K44w7bz7F5MyHz5mHa7Ry4446jP6BpelZSLPzjH5UcH4Oib7iB6BtuwMg9+n9/\nof/6F6Fz5xJ/1llQUlLrdrbMTMr79KF84MAmK68AP5tBLhs+nPK+fSkdNYqiq69utMtv3hgHDhB/\n6qmeup2yU06h8IYbKDvjjHqNY9+xg+gbb8RZnQQVX3QR+x98EDM6umqDykrCZ8wgYNMmQt94g6Jr\nrz3qsWsSZOfatdz+/J9IjA1l9hfrSYoNp1/XOPp1jadXpzaEBAVgmiY3/N+XfLxyKze/9BXvP3AO\nAY66f/8E/O9/2AoKKO/dGzMmpl7v2x85Nm/GcLtxHX98nSto1SwW0pSr6QV9+ikA9sxM2owbR97T\nT1M6duzhG5aVEXPttQQtWYJj2zZy33ijznFdqakELVtGwM8/N9kPR79gs2F26YKxeTP2XbsOaxnW\nmEKr69UDLb5RySgpwSgpwe2P/xZLSwl74QVspaWUjhp1WAlZ+BNPYMvPp7xvX1z9+jVpKL9fJGTO\nkg2YJow5uTOxEVVtMZ+/YTiTduyDVVCSnUtFpRuHvRHng9xuHFu2YBoGlXX8GPcX9p07AbyWUJSM\nH0/J+PFe9wufPh3D7abo0kupPP74oz5e4NKlBKSnU5mQwIH77vMtaD9l37Wr6tyrvjdEvDBNAn7+\nuSq/qkdpTdFllxH+zDMAhD/7LAV33+11u8ouXch5992qm/KbkF/NIBMQQPbHH1N4001NmhwDmBER\nlI4aRcno0WR99BE5775L2Zln1nt2I2TuXJw//EBlYiI5s2eT/+yzvyXHAA4HB+65B6j6Cz9k9uUI\nNzC4UlMBCPjlFwAmDkthwbTz+cfkM7nh7BMZmJJISFDVP1LDMHjij4M5PsJB+sadPPvB90eMPezV\nV4m99FKCPv+8Xu/ZX9n37MF0Oqno3r3O7WqWm26y1fRMk8Kbb6b44ospmjgRo7SUyIcfPnypaJeL\n6BtvJGjJEipjYzlw//1HHNpzTrTyGWQAqme0PFdjmkJlpaeHaEb1Yj1WCZk7lzZpaU3SAq2hAv/7\nX2ylpZSnph5WMmTk5xP22mtA1eqVTa0mQXa3bUt5RSVzl1SVVU0687dLsqFBATx793l0HvUg0QOn\n8MjclY0aQ8js2cQPG0b4//1fo47bVBw1CXI9yrKM4mIc6emYQUEUHNyDvbISR/V3Um2CP/wQgKIr\nr2zyEsnmFLh0KXEjRhDx8MNWh+LXbNnZ2IqLcUdFVfUpPkruhASyPvoI0zAI+/vfj3ieNfW55V8J\nMtSaoBolJTiXLavXHbG2nBxCZs+utUde/rPPkvfqq7j69/cpVICCv/yFA3/5C5lffEHZ6ad73abs\nrLMoGzQIW37+IR+ojvXraduvHxHTpnndr6JHD0ybDUd6OpSWHva6LTOToM8+87R3OW76Y2z+6D4m\nZa7h+Q9+ZNXGupuH19Tr1nZDTUtTNmIEezdtIn/69Dq38yTITTWDbBiUnn02+c88w/6nnmL/ww+T\n+9prmKGhBwVRSdSttxL86ae4IyPJmTuXim7djjh0+cCB5D/6KAVTpjRN7H7EbIYE2fn999j276ei\nU6d6zZA1haBPP8WekUFAE5b++Crwyy8BvH7GOX79lYrjjqO8Xz9Kxoxp+mAOmkFeuPpXsg+UkNI+\nmpOSD10gqUN8BDP+cg52h51/LFzLvK82NloIrt69AQhYs6bRxmxKnhlkL2UUtTFDQsj6/HOy33vP\ncxnbKCkh/rTTiDv77Dovnef/7W/kvvYaRS1kUaYjMk1CZ86s6k2/f39VO1WXq1kOHf7oo7Q5+2wC\nv/rK+wYuF45ffvGrVn2OX38FoKJjx3rv6+rfn6Irr8SoqCDqjjsatdtNfVmXIFdUHD6jVhvTJG7o\nUNpMnHh0C2GUlxN188207duXqLvuIvSf//S+nf3ISzkHLlpEYF1N1O12Cm+7re7OF4bBgepenKGv\nv+75sAr66ivsmZm13kRiBgeT8847ZHz/vdeSgaDPPyfm6quJmjoVAHdcHADjEmy4TZObX1rCgeJa\nLkGUl3suER5NYtZiOByHzuB74W7TBtPhwJ6T4/WHR6MyDIr++MdDVj8CCPn3vwn58EPcYWHkvPkm\nFdXlNEfiTkig+MorPV/QfqWR2zG6hw2j8qqrqOjSpVHHPZh92zbcQUGUnnGG5V1BKrp1w6j+d+lv\ngr74AoBSLwmyq08fMr/9turmu3pcdg5ctIg2I0cS/sQT9YrFqP5h605IYPYXVTfnXX7mCV6795zS\nI5HHrhwMwNTXljP11eXsyiqo1/G8cZ1wAmZAAI5NmzAKCxs8XlNzpaRQMmKEp2zvqDkcuA5a2tgM\nDqaiSxeMsjJC5s+vfT+7vaoUxx/LheqrtJSoyZOrrgK63RRMnkzeq682W4lF4MqVnhJOb2w5OcSf\ndRbRzXD15mjZaxJkH/sTF9x5J67u3Sm++GJLP5ctS5AjHnuMNuecg33btiNvbBiehuaBy5YdcfOg\nzz4j5L33qmbyTj+dUh/vcnSuXk3sVVcRfdNNODZt8mmMGq7evSk+/3wq27XDVt23OHBJ1ep5pXW0\nsSofOBB3mzbe46ueGS/7wx8AqKhuIH5KQDG9O7dhV3Yh98762uu+jm3bMCoqqOzYETP4KJazbk3s\ndvJefpnsd945qh9JTaF4/HiKrryS3DfeqNddvv4i6s9/pk1aGvGnnUbbvn1J6NqVdh06EHnnnQ0f\nvKQEW1YW7vHjqXj5ZcoHD274mLUd6uKL2bd2LQWTJzfZMY6Wq7qW1d9Ww7Rv3Yrj119xR0U1en2x\nc+3aOr/8D1NRgfsPf8A9YAAbiuDb9XsJCXRw4am11wFfenoKt57XF9OEN5dsYPCUt7nr9RXszql/\nYmsUFuJYtw6cTlw9emCYZosodyoZP568f/6TskZomVh8+eUAhM6ZU68ruvbt2wl/7LE6b77yRxFP\nPUXIO+/gDg4md+ZMCu64o/la1rlcBKxbB0B5LZMi7rg4TLu9asKnno0AmkrNDHKlDzPIAGZ4OFmL\nF1N8xRWWtge05MjB771H2MyZOLZswZ6RcVT7lJ12GnB0CXLI228DcOD++8mdPZuS887zKc7yAQMo\nOfdcbIWFxFx5JZFTp2LLzPRpLID9jzxC5pIluPr1wygqwrl6NabN5nlv9WKaBFYnyOWnnAL8liAH\n/Por/3fjcIIDHbz39Wbe+/rQL9zcglLWLlgOwEojihc//pGMvGKMFvbB1RClaWlVd1ZbdaOF3c7+\nRx/1NOo/kt3ZhTw6d2WdC8Y0p4ANG3D+9BOOrVurroKUlFB22mlV/ZkbKHDlShL69MFxwQWNEOlR\nCA72i5muCj9NkCvbtyf77bfZ//DDDf5BWVTqYu2v2Xz47Rb+vr3q0qlt3bqjT7QcDirefx/XihXM\n/nIDABec2pXwkLprEadeNIAl08dx/h+Op8LtZvYX6xl8+7+5d9bX7M09yiuZVJWaxI8YQfR11/1W\nZuGHJTG+CH3lFaKvvvqIXWNKzziDyoQEHFu3HrKK65FE33gj4S++SMj77zc01GZVcMstlA4bRvZH\nHzVpz11vHBs3YpSWUtGpU+2fUXa75+qxvQH5SWMqP/lkiiZNqmp3+u9/+zaIl8+awEWLiLzrrmYr\nbbKki0VUdbuY/Q895EnujqRsyBCgetbU5ao1sTEKC3GuWoXpcFBy/vkNC9QwyJ8xA8eWLQSsW4fj\n11+x79lDbnV7ofo6uFjd+fXXGC4X5f37H7EkwBv79u3Y9+6lMjrac1NazRKUjh076BofxsOXD+KO\nV5dzzz9XUOaqYM22bP67fi/pu/M5Lf9XdrftzbeOdsybvZTB906mXXkOH//zPc48qQtOhzUzqy1e\nZWWjzkqbpsnbyzbx4OxvKChx8dIna7js9BTumzjwiElBU8qfMQNMEzM8HHdYGGZ4eNWNtY1wOcxz\ntaY5+zybJrbcXGxZWZbV5HsS5AZerWp0Tiflp57q066FJeU8/+GP/Lg1iy179rMv76Bk1DS50RFE\ndF4eRdt2Etrl6Otji0rLmb88HTj05jyv3G6oqKBruyhe+PPp3DK2L8+8/z0fr9zKrMW/MPerjVx2\nRg9uHdvH0wWjNkHVtdjl/frhjo/HkZ5e6xW+lib4/fdxrllD8YoVlI0YUfuGDgfFl1xC+NNPEzpn\nzlGfG0VXX43zllsIffVViidOtLyk6WiZkZHkvvmm9xfd7iad4XT+9BMA5QeVuXhTmZiIfd8+7Pv2\nee1U0ijqyLt+r2zoUMoGDqTd8cdX5WLjxh3xe9G5fDmR991H6ahRtXavCHn7bYIXLqQiOblZygwt\nmUE2SkspuuSSqunzo+ROTMTVrRu2oiKc39feocEMCyNj9Wpy//UvTxP5hjBDQsh9/XUqkpJwde1a\nNYvSCBxbt2LabHWWV9TF+d//AtWzx9X/QM3gYCrataMyPh5bbi4Th3Vn9IBOFJS4+Ms/lvPG5+tJ\n351PUICdyj8M4sd7H6HHI1M55ZQeHF+cS9uCXD7860z63/QWD8z+lvRdLafBvm3vXmz79lm7rGll\nJfGnnELMpEmNUpeYmV/M1U8v5vZXllJQ4mJAt7YE2G3M+XIDw+98hy9+3HHEMezbtjXJjKSrTx9c\nfftS0bUr7oSEqhsQG+kLryZBNJsxUbXv3ElC797EWnBTUcQDDxAyZw5mZCSlQ4dWlYQ1cfui5pBz\noISLH/sPL378E1+v28O+vCKcDhvJSVGMGtCRP5/bh03RSQC8/PhblLmO/macfy9ZT0GJi35d4+nZ\nsfbP+fAnnyTxuOMIff11z3PJ7aN5+eYz+OKJCzl7YGfKXJW89ula/nDbv3n2/e8pLq3l5iu321MW\n935YZx6s6MCWOfOqvvxbgZoyxtirriL4CLO8RRMnUt6vX1XtfrXARYsI/fvfPZ2aft6WzZRXlnLN\nM4t58u3VzGtzAqWxcQRs3Ejg8uVN90aag9tNzKRJtO3du0n7tNfcj+A6UoJc3VnG1hSdmSoriRs6\nlMTk5PrdsxMURGVcHEZFxVFdeXds307A5s3Yq0tQf88oLCToyy+bfHGQQ2JqlqP8Tnn//ux/5JF6\nf6GWjhlDRXo6ZmBgnduZERGNUmtVo7J9ezJXrACHo9F+LRZdf33Vr+ijvUOzvLwq+at+75WdOlF8\n0UWU/e7Xe+Y333h+5RnA9GtOo6jUhc1mcEpKIqf0SOTELm0OmSG+cHA3DNu18NQT3J63hk/adOe1\nT9cy+/Nf+PihsaR28v8ZkrCXXybstdfYf//9FF1/vddt3G6TBau3kdqpDZ3aRjR6DM7vv8exZw84\nnYd2rPDBxyu3cvfrK8grLCMixMm0SX/gwsFd2bgrjykzlzLlPzM5eeHj3HnTE9x1zRlEh3nv+xz6\nr38RuGQJWZ99VmdvaH9SkyC7mzFBrkxKwgwMxL5vH0ZRUYP//o6Wbfduwl57DXdQECXnn09u9WIb\nTc0oKgLDaLJ2mruyCpj45EK27t1Px/hw/nr5IJKToukQF4b9oM9Q23eDYO4WbBs2cOvLX/HSTadj\ns9X9vWCaJv/4T9UkyaQze9S9bVAQhml6vRG6e/sYZt5yJuu25/DE26v58sedPPXO/5i1+Bduu6Af\nlz9bNQwAACAASURBVAxL8fSSr3S7Wffe54zKzmZ7UBRXLdgOxg4+WbmVWVNG0rXd0bey8lflJ58M\n1Yt7HOm72d2uXdVNmTVMk/Cnn8b588/8sr+Cv1R04ptffkvWFn5X9d+dEb14LOdL1tz+EI9NmEqw\n00Gl28Q0TdymSUhJIZd//T79926i4F+ziO7tpx2WbDZsWVnY8/II+N//KPelTPIoHLj/foouuQQz\nLKzO7Vypqdjy85vmc8tux6ioqLqBeNs2KnrU/W/uYJVJSdizsrDv3n3EBT3s1SumViYlHf6i203M\n1VdjlJVRdvLJjbY67ZFYkiDn/uMfnkSvPgrqs5JPY2uCfnt1dr44SMT99xM6ezZ5zz9P6bnnAlUz\nx17LU353CSQmPIi5dx/515Zx+SWYz85g2N71LHn+FB5dsYfPf9jBtLdWMu/uNK93iPuTgA1V9Yh1\nraD32LxVvPyfNUSHBfLRQ2OParnv+ghctAiA0rPO8nk2NbeglPv+9Q0ffls1czC0VxJ/u3YI7WKr\nPiBTOsTw4UNjcXzxLO0yc/l18bcMT8/jrotPIiw4gPyiMvIKyqr+W1jKjPkfkpSfiX3bNirr8cFm\nGdMkIL3q0rmZkoLxxReELV9O6ejRdf7d1pdj7VoCNm+mdNiwqtInu52KTp0I2LgRx9atnhULm1rw\nwoVAVfu05krKKSkhfsgQ3OHhVT+cfPgsrsuGnblc+uRC9uUVc8JxMcyZOpq20bUk4rfdwrKLJ/HK\nzFUUrNzK/7N3noFRlN/bvmZ7OklIIwRCIKH3XqV3ASkCgiCiUkQs/AVBFFRQlGanqvijKSrSe5Ve\nA0noCQmQ3nvZNu+H3awJSTabZEPx5fqiZGdnnt2dcp7znHPf7s62fDK2ndn7zcXbMQSGxlHFXsnz\nbc0rnOiNZW3m7KYb1nRl/ft9OX09ms9/O09gWAJzfjnF6j3BTB/cjDtRqWw9FcobV/bQF9jtUof2\nDaqRmpXHjfvJDPx4Gz9O60H3ZpW0tF1B5BcvIr99G3WbNmavobwOHQyNmP7+5BifM/no9SJXwxOQ\nSgRcHWxwcVRhoygQPpw6gyI4mGSlHd0DJeRKY7BXyRnTvR6NfatyJzqVO1EpHHCRMffeCTrH3OLa\n2RBilIZEhSDqGRd7la/uHsRdY8jIfvLpGsZsWGTS+n/SULdpgyIoCOX585UWIGOhEU3mO++QWYmN\nxlp/f2QREcju3ClbgFytGly5gjQqCk2rVma3zQ+QtcUEyNLISJSnDIID5RVdKA+PJUDWe3iUvtEz\nTIgODgjGbtbch25c1kLv6kpuv37Y7NhBy1MH+Hrym3R893dOXovmeHAkXZuUfvMXMjOx//57dD4+\n5HbvXqkWkA9Tmqbzr4eus2K3obA/JTOPD+ZtYm/aP8gcHUhZvdoqY1AVDJDLiFan57fjt1j8xyUS\n03OwVcr4eEw7xnavVyRYkEklOHVsDfdDecE2ixlpOcxYU3zz6liJE97Ec3r7P7StYIDsPGUKkoQE\n0hYsMF+nq9ejPHECbe3aZTImAIM5gc7DA1EqhWrVkH74IY6//YbO3d2qAbLdxo3Y/e9/ZLz7rqmx\nUOvnh/zWLaSPMEBW7d4NQM4jbP5RXLpkqle027iRrFdfLX5DY112WUrVLtyKZfyS/aRlq2lXz5Of\n3+uNk13JAbje25s63t6stavC2C/38dO+EKq52DF5QNH6QkliIjbbt3MwxrC/kV0CUCnMP8L0xv4O\ncwFyPh0aVGPnJ4PZcyGCRVsucDcmjfdW/3tdZbl7ESHUo8e7rzFk2ECyczW8s+o4u8+HM27JPuaO\nbsuk/o2fuGSCzc6d2K9dS9rcuWavIdHZmbgLFwzXXoEs/7V7Scz66SSBYYWXyW2UMlwdVLg6qli4\ndwXVgB88W+LsVoXX+jbipW71cCymTyKjhwthXrX4RHBAq9NTJTaSbt9/geetYADSqvnwWr3B/Kmv\nypkfj7LmnZ6FVh1KQvLXX+ibNwcLE0/msFu5Eptdu8h8440Sn7nqdu1g7VpTueN/DlFEcfEi6pYt\n0fj7ozp4sMzlevn3f5kx+DVHvi9Bvk9Bof3UqEHK8uXY7NljkH57iHM3Y1ApZDT1cyvT+ErjibKa\nfkbxPCr3tKwxY1CcOIGoVOJsr+Ktwc1YsPk8Czefp3Mj71JvUjZ//FHICEXTsKGh1vyVVyp13JLE\nRKSJiejt7YtdnjkUeJ+56wzd1gvHd+C347cJvRWOw5l/0FlJvUB69y7y0FD0Tk6mWj5LORb0gE83\nnuOWsea7fX0vlr7RhZruJZeB5J8Tk7xBPbAjey9EYKeSU8VeibO90vhfFY6/XIXDd7iy7zRVx4+k\ntlf5l4IV584hjYsrVRbQ8fPPsV+xgszJky1yByyIaGdHwpEjoNfjKggmsxCZNc1CRBGl0T0yt2dP\n05+1RqOQR6VDLImNNSjZKJVltrivCMoCygN2a9ca3M6KubZloaG4d+1KbvfuJK9fX+p+DwXeZ9K3\nh8hV6+jTsiY/TOteOMtohk4NvflmSlemfn+Ezzadw72KLUMLSLclpuUQtWEn/RZ/TBeX2tDkZcb2\nKH3CZwqQU1MtGocgCAxoU4veLWry+z+3+OvkHQK8nRnRJYCWddwRBIH8kM9WJWfV9B58vS2QJX9e\n4rNN57h+P4mvJnYuNXB/lOQb7VgyWS1YcpOVq2HpX5dYuy8EnV6kqqMN7lVsSM7IJSk9l5w8LZF5\nmcgf3KdfzDU0Einec97hTN/WptKU4tANGYwv4Gv8tyTaBveZYejc3Ej/6CNyhg7lrZg0Ds7bzv5L\n91i4+TwfjzHfzK/asQP5lCmIVauCsbGtIshv30YRGIjETC9J/n1efvmyoQTyP+QYCIbPVXXIENQt\nWpBllPaTW9BArNq3D/mVK+T27Yu6dWuyU1PRBASU+j5zATIYJDlzigmOT4REMWHZAZQyKbs/G2LV\n8kmrX8V79uzhm2++AeCDDz6gW7du1j5EsSguXEASF2fI3ll5yfBxky/unq+HWFFUO3cijY4mt3dv\nk/IFgLpDB+IuXjTVqk7o3ZCfD1zj+v1ktp4KZURn8ye57O5dwCAOLomLMyh/3C+9kayimLLHdesW\nKW0IDk9kyneH0Ysi777Qgld6N6R/m1oM+vhv1IIERXIy+qwsJBVc3paFhaF3cDAYKVjY6XsrMpnP\nNp7jaJDhAVbDzYEPR7dhQJtapWah8s8JRUgw475uUGInv210ezj8N37pCUz/8Rjb5g0y+/AqCSEt\nDWlcHHqVqtQHbc7AgdivWIHN77+T/v775at9zm88rQQ3PdnNm8iio9G5uRXqhNYGBKCpU+eRlTqo\n9u9HEEVyunUrtcbQmuRPAPLatCFl1aoS+yqURnMQfSkqOzq9nk1Hb/HhulPo9CKjngvgy4mdkUnL\ndp4Nbl+buNRsPtlwlvdWHSctK4/IxEz+CY7k+v1kPg0/Qj/ggp0n43o3tqhEKn/sQhkNgeQyCWO7\n12dsd/NBuKDTMVsZy0jvKJ5LrMlfJ0O5G5PG2nd74en8iEpmSiH/HlwWdYMDl+8xd91popIyEQSY\n0LsBM0e0NmWERVEkM0dDUkYuTmtWIzkHuUNfoO9Ay2QrC6KvVo3kX35B06QJoqMhuKlTrQpr3unF\nS1/uYdWeYGp5OvGymQlR/rNHsJJNe75Xgc6t5Iyk3tUVjb8/0gcPDLW5RjWpR0VodCqiKOLvXXYV\nLEuw/esvwCB3m28mJrHg+1Xt34/tli3ovL3Jfvlli0siEnfsQBoVVSa3x8NX7vP614fI0+gY1M4P\nHzfr3ketGiCr1WqWLl3KH3/8QV5eHuPGjXtkAbL9Dz+gOniQtE8+IesJcpSxBroaNdA7OiJNSEAS\nF1dqiYqQno4sPNwQRMmK/sS2W7agOnIEnY9PoQAZiaRQMKNSyJg5ohXvrDzOV39c5Pm2fmYzI5lT\np5LXq5fBttfdHeWZM5UnOVMAQaNBU79+kWXxqMRMxi/ZT3aelmGd6jBjmMHkwL2KLf+b2Z+YPV9Q\nMyeFH1btY9q7Qyu0NJrXqxexQUFI0tNL3TYuJZvlf19m45Gb6EURBxs5bw9pzoTeDS3OPGkbNEAU\nBMOSV15e4UmhVmv4LSUSU1a0iTqZK3cT+HrbZd4fbr4WrDjyG+d0tWuXKtejadoUdePGKIKDsdm9\nm5xhw8p8vHxEo9C81IIlOktRGbPHed27FwoOc4YNq9BYy0r2mDFo/fyKBOSqffuQ3bhB1uTJpZv4\n5OZiu2ULOYMHW9zTkLJqFemRkehdXc3uP1/SLLeE7LZeL7Lr/F2Wb73M7ShDhnba8035YGTrcl9L\nb/RrTFxKNit3BzH3138z3Sq5lF4YrI2HvfMS1af0JyWlZKvjfLT16xMdHl552T2JhCrvvkurzEz2\n7jrCmHWXCQxLoP/cbax6u2cR++vHgSmDbMG9ODopk3nrz7DnQgQAjXxd+fLVzjSrXThQFAQBB1uF\nQWrywxkk9O1a6kTKHMWZAXVsWI2vJnbmvdX/8OG6U9Rwc+C5JsVPzjPffBOHZcsQdLqi98NykK+6\noHd3N7td8vr16Dw8rH5+SaOiENLTDaVsxVxL9+PT6Tv3b9QaHV9M6MSY7pY1MyrOnsV+xQrS5s8v\n/Ox/GLUam+3bAcgePhxtQAAx164Vkqotcez37gFld9HTV61aJsnEvRfCmfLdETQ6PeN61mfh+I6l\nNviWFavKvAUFBeHv74+LiwteXl54enpy09g8ZU1stm3DefJk04UvSUhAeeQIolRKzuDBVj/eY0cQ\n0DRsiM7ZGcX58zhPmIBtSbqMgFvPnrj174+0hOxtfsbVkmWPoR3rUL+GC9FJWfxywHwGW+/lRV6X\nLoYZoEpFXrduJde8WdGWOK9rVxIOHSJt4ULT39Kz1YxbvI+41Gza1/diyetdCj20A6o7Y1vHF4Cz\nhy6xZp8VylcUihIvcFEUuXA7jje/P0Lbtzez/vANBAHG92zAqWUjmTKwaZmWZUU7OxK3bSP2ypUi\nDwObHTtw79wZmz//RBsQQNbLLyOOfxlBgG+3XeHiHcvMeQqSX3umscSWXBBMblu2FizNmyU/g2zF\nADk/M1pS4PfIkMlQd+5cxJ3OYdEiHJcsQWpBqYfD0qVUmT0bl0mTynRoXfXqZoNjk568RGLSoM9H\nrxfZde4uvWb/xZTvjnA7KhVvV3u+mdyV2aPalC841umQJCUB8OGoNkzs24gWddyZ9nxTfpvdn2ur\nXqZ1pkEVoUb/0pUuTEillbv0LZGYJuYNE+6x57MhtKvnSVxqNiMW7OLXQ9cRKyA9qTh50nKlo2IQ\n0tKQpKejt7VFX0w5WUa22tSM3f+jv2n79m/sMZZrzR/bjt2fDikSHBc9iICmVSvD5NnKjHyuLtMG\nNUOnF5n07SFuPih+UiTKZOi8DcGz9MGDCh9XakEGGYyTjko4v2zXr8e9Z08cvvyy2Nc/Xn+GnDwt\nOr3IzJ9O8NUfF5FdvYpq926zhl/2332H6tAhnN9+2+x5pTpyBElqKpr69dE2bAhyuUXBMRRw0Sun\nzbQlbDsdyqRvD6PR6Xm9XyM+f8X6wTFYOYOcmJiIm5sbv/32G05OTri5uREfH089K8s1qXbtwmbv\nXvI6dyZ7zBhs/v4bQacjt1cvk6PMf43kdesQ7eyw+eMPbIzNYNklaLbqatVCFhWFLDwcnV/hLm8h\nIwNZVBSiUmnRCSyVSJg7ug1jvtzHd9uvMKpr3RIlxSzFbu1alMePk7x2baWUw6i1Ol7/+iA3I1Pw\nr1aFte/2Ktb4xK52TQgOpHpeOp9uPEs1FzsGltIVX1Zy1Fq2nw7jl4PXCIkwBAASQaB/a1/eH96K\ngOrlz7qU1BVsu2kTsogIhJwc9C4upC1ahCcwZfM5ftwVxNsrjrF/4QvY21h+Y8+vPdNaEiADOUOG\n4PjppygvXEB240aZOp8LItaoQeaECeazHWUka/JktLVrFwn8nhS0deogv3MH+Z07aI215iWRX3Ov\nPHHCqqYFypMnETQa8lq3NhkZ6fUi+y5FsGzrZW7cNwQq1VztmD64OSOfCyi3uZD8wgVcR41C07Qp\nSVu3IpEIfPpy+0LbSKKikCYlGVQpKvHBWx40zZqhPHMGRVAQrr1789vsASzYfI61+0KY88sproQl\n8PmEjhbXY+cjv3iRqiNHom7enMQdO8r32+r1ZEydiqDRmDKREXHpbDh8gzM3YggKT0RfIICXSQX6\nt6rFvDHtTMo5jwshOxtJYiKzRrQiIi6NXefCGb9kP9vnDyI9S03IvSRCIhIJuZfEtXtJbMmQ0gMB\naXS0RcoPJaLTmUoJHpcJTL5jcHH9LAcu3+Pg5fvYq+RMH9KML7dc5Jttgfxf8Grck6KJP3So+Ptt\nXp6poVBx6RJ2v/5aYoOujbG8InvYMHR6PWdvxOLvXQX3KuZlIYXsbEOfilxeYi1xRfn9+C1mrPkH\nUYTpg5sxc0SrSmuMrZROglGjRgFw8ODBYgfuWkEDD0m/frB3Lw7nzmEzfTryrVsBkE6cWOF9P7EY\nP5csMBAAeY8eJX5WWf36cPIkTvHx6B7aRjBmAsV69XC1RE1EFBna1YXuB25yJDCCtQdusej17mUa\nekJqNlfvxhGTlEk11PT6+hvkKcm4v/Muuk0bkRtrdq3x2+n1Im8s283Ja9G4V7Fl5+ej8PUsfuYr\nfPQR6hkzaBKSyobfLzF9xTF8vNzo3ty3wuNIychl8e9nWLf/KskZhvrHqk42TOjbjNcHNKOGu3Ul\n5vIRQkNRnDmDaGuLzauvYuP4b8PCF2/05uT1WILuxvPFH4GsfLcMcjlffon69ddROjmhLOZ30ur0\n7Dxzm1y1jlqeVfD1dEH34YfonJxwat4cLKnrzc5GOHsWsX598PLi4u043KrYUnPFCuSA1VScx4yB\nMWN4/ObSxSNt3Nhwf4uMxLa0a+K99xBXrkR48ICq4eGIZWwQLQmJRILo44N0wABcXV1JSM1mwtKd\nHLocDoB3VQdmjWrP+N5NUFa0Ia1pUyS5uShu3sTVxaV4iUStFu1HH4FWi9yYsXtU93rJjz8ihIej\nnzixWPMaSadOsGIFttevozCO6ft3BtKxSS2mfrOXLf/cJjQmnc1zX6Cmh+XXvXzZMsP+e/fG1c2t\nfBMgV1cw7scVw31p6GebiDM6GsqkEtoEVKNL0xp0aVKD9g28sVM9/mYz4cIF5F26ILZogebUKdbP\nGUqfWZs5fzOaltOK1wofU38o6VIlK50CGF2Rc0OvRxMYCAkJuD5CJSYTiYnIg4IQlUrsBwzAvkDj\nZE6ehk82ngNg/itdmDakNW0a+DLm823c1CmpDiiSU3Eq5vMLx48jyc01uJ7WqIFN166oSvieJAMH\nok1KYmuN1nz+wVZCo1Ko5mrPoSVj8TPT6C0YjUpEX19cSylPKQ+rd102KcvMG9eZ2S+V7uIot7An\nqDisGiC7ubmRUMAFJSEhAbdiMrqfffaZ6f+7dOnCc889V6bj6I1Lo5KjRxEuX0YSHIzo4oK+X79y\njvzpQWKcWerNZL9E4+xZKEaSRTA2+okNzNuzSrZuRbpsGdrly6F1axa+2pX2b63jxx2XmPx8i2KD\nTlEUuRuTSmBoLFfD4gm6G0fw3Xiikwp3AjfzG8GRq7/ivGM72+p24tMeE2nd0IcPRrevUOAoiiL/\nt/IQGw6FYKOUsfWTESUGxwCisdHtrVYidzL1rNkdyOCPtvDz+88z4rnyS6KFhMfz4qdbuRtjqMts\n6e/JlMEtGd6lfqV3t0t++QUA/fDh4Fi4m1epkLFu5vO0f2sd6/YH0b9tHQZ1KL3MxvBmpen7Kogo\niuw+G8qHPx/j1oOkQq/ZKuX4eurxvbcHf28XJg9qSS0zv4cQHIyif3/0TZoya/KXLNlyFgdbBSe+\nHke9GpWXyTl/M5o5Px1lUHt/3nqh/PWzFWXf+TBCo5N5MyAAGSAY9aDNIgjoBw5EumIFkp070ZUz\nQBZOnUK2aBGa1avBywv96NGoR40CjYbT1yJ5+YvtRCVmUNXJhrljOjGhb9OKB8b5eHoiurkhJCTA\nvXvFZ4g9PNB9+CFQCfavcXFgY1PkeslH+uuvSK5eRd27NxQTIOuNJTKSS5cMZk7G82d094Y09K3K\ni59u5fKdWDq8tY7/fTCYHi18Sx2ScOQIkuPHEatUQTd9OvLevRGCg1GHh1fI8Gf22iPEpWTR0t+T\n+eO70L5h9TKtJD0qxIAABFGEkBDQaLBRyvlj3jC6vbeeuzGp1PRwolltD5rUdqdZbQ+a1vbgyJX7\nvLF0FzNWHKR7c188ytskKZEgBgSABSWIlYHk8GEEUUTfsSM8ZOTz1e9niIhNo3EtNyY/3xKAvm1q\nc3DxGB703wqp4Sz7+m/Gt+9CdTfD+Zyr1nLzfiLXsuzJemsRGYkpaLr1oKWkKq0ycnF2KHw+JWfk\nsEpVlxVew4jfZEjIKeRSopMy6T97M4eXjMW7qkOxYxfd3dF89x3IZKzYcYnbkUl8GSDHJvgK+j59\nSo47Clw3RV8SuXwnll/2XWXtnisALHq9G+8MK7kh9Pjx4/xjjJWkUildyrlaaNWndePGjblz5w7J\nycnk5eURFxdXbHnF1KlTC/07KSmpyDZmcXLC3ccH2YMHpMfHI1m1CklqKtmZmWAFi98nFWlUFB4R\nEegdHUn09oYSvjeluzuugObGDZIf2kZWty6q2bPRBASQZ+Z7d968GfnFi2QFBpLj50cNFzlDO9Zh\n66lQ5qw5xHdTDc2Xoihy7V4yu8/fZff5cMJi0orsy04lp0ENF6pXtSclM4/4VBdesn2VLafXMjzq\nCikHf2HSvYFsPBTM630b8eagZsXqZ5bGF79f4McdV1DIJPz0Ti9qVVVYfG59PKolep2Gn/aF8PIX\n27kbGc9rfc0vb4PRcOLaNfJ69kTv6sr2M2HMWPMPOXlaGtZ0ZdGrnWhRxzCTzspII6vMn6oMqNV4\n/PorAMnDhqEp5rN7OEiYM6oN89afYfLyPfh72JS6bFYSV+8m8Nmmc5y5Ycga+Ho40rCmKw8SMrif\nkEFqZh7X7yVy/V4iEMZPe66w6NVOvNCx+OVPm4sXUQDHNTYs2WJYCszIVjPkoy3s/mwIVczo6ZaE\nkJZmtnltyz+3mfXTCdRaPSeDH3AnJJTPmtkjUanQtGxZ5uMBOM6di6ZVK0M/RDE3fdnt2+irVDE1\nAOXkaZm34Qwbjxj6NW55aFkN6K9ds+j8VXTpQtUVKxB37SLJjFmA9P59Q11hw4ZFGi2dFy9GcfAg\nmk8/JX3BAsBwba/aE8znv51HpxdpHeDBird64OViR2ZGGta807rWq4cyIYGs06fJdSj+4Wva1pj1\nKstzQ8jJQZRIipR0SaOicDNK/aV/9JHB3bTAbyaJicHz6lX0NjYkNmxY/D3XwQHHiRPR1q1Ldnx8\nocZobycZuz4ZxFs/HOVoUCTPf/g7/Vr70q6eJ23qelK/hktR+UxRpMrsD1EAf7Xqw5z3/2Bv0G1q\np6aQfuJEkZp1Szl5LYp1+4NQyCQsfb0T/t5O5GVnkFd5TskVwt3XF1lEBGlnz6Jt0AAZcPDzF1Br\n9YWeD8pjx9DpvXi5Wxt+PxrC4csRvPn1LlZN71nyzq2MJC4O6f37aFq3rvC+quzejRzI6NiRrALn\nW3hsGkuN98VPX25HWuq/2t41XeTU6NUSfr4E0VF0mv4rbet5cuN+EmExaej0BevgbWDTvw2wfl5O\nNPNzo3ltNyLiM9h89CbZeVoAGvtWZcrAJjzXpDpjFu3lxp1o3pjyNcu/moCrYzE9DFIpOQMG8d7q\n4+z4/SAAw1OP0f3KMVIFgewSVq2dJ01CfuUKqcuWoTa6A0cnZbL1VCh/nrjDneh/ZRoXju/Ay13r\nmL3+GzVqRCNjeZqrqysnT54scVtzWDVAVigUzJgxg9GjRwMwZ84ca+7+XwSBvM6dkW3ahOLsWTLf\neqtyjvOEoThzBjDWJZlREtD6+RmUJIpZHtLWq0emBTXhWmPNZ758DsDMEa3Yde4uW0+F0r2pDzce\nJLP7fDgRcem8/eAMf8ZeYXWdztzp3p+GNV1pWNOVBjVcqOnuWGwBfc6prtiNG8d4zQMutvBidWAc\n3++8yqZjt5gxtAVjutcvVZJMfvUqkrQ0vo+E73ffQioRWPlWjxK7nUtCIhH4ZGw7vJxtWbD5PPPW\nnyEuJYvZI9uYLf63/f137H/+mbRp05jp043Vew1i98M61eHLVztjo6x8PVQhJwcRkCYmoqtWzSA/\nZCa4e7V3Qw4H3uefkCheXXaQ9TP7lKmu/EFCBot+v8A2o9tfFXsl777QgnE96xeqQ03PVnM/PoP7\nCen8fSqUPRcimPbjUY4GPWDh+I6GDvgC5AVfB+Bwjg2Otgp+fv95Fmw4yZWwOKZ8e5j1M/uWSTpM\nEhuLe48eZL/4IhkzZxZqStPq9CzcfN70e/VpWZNjQZEkbt+Hx+dbyOrWnbQNZW8wVJw5g/0vv6D/\n/XfyOnUqXMNo1Ep1nDcP5YkTJP/8M1fqtWLq94e5HZWKUi7FRiljU1Qe3QM60m54TyyZJqrbtSNl\n2TLyepoPCGw3bsTh++/JmDaNjNmzC72W8X//h2r/fuw2bCBr8mSSnd14b/Vx9l00dKRPHtCED140\nr29bETQNGqA8cQLZ9evQp49V9+08eTI2O3eSvHIluc8/X+g1++XLTcozVd5/H8XZs6R++63pddWx\nYwDkde5ccr+EIJD+6aclH99exa/v92HZ1st8/Xcgu8+Hs/u8oVTFXiWnVYAHrQM8qOXpxKXQeDh4\nmLVXA4mX2/JKrh9Z0an8o/KkNrHEHz6FczkC5By1llk/GYKE6UOaV5o0mDXRNGyILCICeUgIWmPm\nUaWQUagCRK83GBilp5MXFsaPb/ejxaS17Dpn+I4HtLFe70JJSCMi8OjYEZ2bG3GBgeV2Uc1HglL4\n2QAAIABJREFU06gR6rAw8gqsrIuiyEe/nkat1TOisz9t6ha1WrarbVD8aW6jJTYly+TGKhEE6lSr\nQn0fF+rXcMHT2ZZr95O5EhZPSEQSd2PSuBuTxtZT/644d21SnSkDm9CxQTXTitqm19sQ0KENmRIF\nnV082TJ3YJFEVlRiJq8uP0BIRBJ2Kjk6vZ7jqdAd843W0nv3kEVGolOp2HoqlC3/3ObktSjyy+Nd\nHVUM6VCHkV0CaFjz0ZXRWv3p3b9/f/o/AivArPHjDULUxdkt/0fJGTgQnbc3YjHSbQXR1alDvNGW\nsbxojc19BQNkHzcHXunVkNV7g5n241HT392cbHghQ02zsDgWvNic3Fcse8BpO3Yked06HBs14ts6\ndXj+3A0+23SW87fi+PDX0/x04BpzR7Whd8uaJS572/30E7Z//UVkwPMI3i35dkpX+rTyLddnFgSB\nKQOb4uZky4w1x/lxVxBxqdksff254gMDUTS55/1flB1rQ4KRSQXmj23PK70aPJKlesePPsJu3TpS\nv/2WnBdeIHHvXoTU1EI3aSEzE7vVq5GkpZH+ySdIJALLJz/HoHk7CAyLZ+inO9k4q1+pTTl5Gh3L\n/77Mqt1BqLV6lHIpE/s0ZNqgZsW6pTnaKmjk60ojX1f6tfJl87FbfLz+DH+dDOXi7Ti+f7O7Kbse\nHJ6IdO8pPIGEajXY+clg2jauTZPa7nSYto5/QqL4bNM5Pnmoeasg0vv3UZw7h7p5c3R16qA8fRoh\nIwP71atRHThA6pIlqNu3JzUrj6nfHeZ4cBQyqcCC8R15uUd9LtyK5av5huachEvBpKZmly27rtfj\n+MkngEHy8OEGnyrvvYeQk2OwTJVK+V+2I3M+3kauRkedalX4cVp37FRyXl68j9GyXnhet+XXiCQa\n+ZbyQFAoyBk5stTh5Vu1qtu2JSY5i5jkLJRyqSEwd/NB3n8gzrt3ov50Ef3sOnEvPgNHWwXLJz1H\n33JeU5aiadAAvb09Ql6e1fetN2akH3bTk4aFYbtlC6JUSvqcOdj/8EMRR0OlUeour3vZ+i4eRiqR\n8P7wVgzv5M/p6zGcvx3L+Zux3E/I4FhQJMeC/tX5lohuiA2HUsvTiakvdKBNXU/uLbgDsVe4smUf\n+l6D6dHMcq1YgOVbLxMRl07d6s68+XzTCn2WR4WmUSNsdu9GHhJSrEEEgDQ8HEl6ukFqzdubmsCc\nUW34cN0pPlx3ivb1vXBxsFr3QrHoatZEV7Uq0oQEpMU0xpeVrIkTyZo4sdDf9l2M4GhQJE62CuaO\nLr60QOvvT263bnTu8hxLAjojEQTq13DB39u5xAZRtVbHrQcpXA6L50pYAgqZhHE9GxQbhDr5eCE6\nOOKUnkbi7XDGLd7Hpln9TFbg52/F8vrXh0hMz8HXw5Gf3+tFUHgiV+ZdBCDj9t0i+8wnP3iesfcu\nG28YssUKmYReLWoyorM/XZv4VNrk3BxPjt1PGdE2alRqh/d/DpUKdfuSAwRrkh8gS+8WPqmnD2nG\n/ksR5Kp19G/jy4A2frSp64H7SINmYr5uraWoO3dGNC6ZtqjjztaPnmffxQgWbD7P3Zg0Xl1+kNpe\nTgxpX5vBHWoXcYLLuHgVWyDEzp3Fr3VmSIeK2xEP7+xPVScVr399iL9OhpKUnsvqt3tiZ7wRiKJI\ndp4WTWAQ1SIjSVDa81OyErcqNqya3oO29R5dY4fexQVBr0ceHEzOCy8YxveQHI8ok+GwbBlIJKR/\n+CEoFHg627F9/iDGfLmXW5EpDP5kB5tm9Ss+s6RWcys+k2k/HOW6Ub1gaMc6zBrRiupu5pfD8xHU\nasa5aWmz4AXe/OEIIRFJDPlkB/83vCW1varw9spjhKTFAjBj7hjsqxk+Qw13JzaMbsjF2YtJWnOa\n32u4MvK54msDlceOUWX2bLJHjCD166/JGToUbe3aVHnvPeQ3b1J1+HByvLwZ2moi5zIkuDqqWPN2\nT9Pv1bquJ19+MR59x2+pnp5I94/+4udZAy1WGrHZuhVFcDA6T0+yHpJdk8TEoNq/H0m2YT37km8j\n3vvDkL0e3bUun77c3vSg2TF/EBOXHeTcrViGfraTlW/1oHuzwhq2WdHx2LwygSNVajHTrT2dGlVj\n+uDm1KlWQkNqZqah8UcqZeZ1Db/+svmhZVeok+3LDQS8dm9D3qY6jRoEsPrtnmYdHa1FzuDB5Awd\najUVjoKU5Kan9/IiY+ZMJCkpZE2eTPaYMYgFyzu0WpOaQEUD5HxqeTpRy9PJpFsbk5zF+VuxXLgd\ny724DJr6udGhgRct6kws1K/Q4f3RcHwjLVMe0GjpAcu0b0URh0WLiJTbs/qKEkEQWPxa53KrjTxq\nNI0bo/P0NCtHqDC65qmbNjXVpo9vVY29p6py8k4i8zec4dsplezFIAio27TBZs8eFOfPk1PBAPlh\nsnM1fLzesHo888XWVHUq/vtQd+xIsrE8YbSF+1bIpDRxVdBpxTryevQwb3QlCOgD/OHiRTpJM/nj\ndhyvfX2QX2b04c8Td/hw3Sk0Oj2dG3mz4q3uONurqFvdhex2jeDWdu5fuoFjVl6RUjkhJwdpcjIa\niZRN15NxtFPxwcjWDG5fu1xlddbkqQ2Qn1G5FCqxKFBA72yv4vTyUUW2z9ee1JbBBac4BEGgX+ta\n9Ghegw2Hb/DNtiuExaSxdOtllm69TGPfqgzpUJvn2/lx4XoUrz4wLFUOnjiA0V3LLidYZdo0FJcu\nkbRxY6GZf9cmPvw5dyAvL97HsaBIOr73O3KZhMwcDZk5GvSiyJx7/7AQ2O7sT4sAT1a/3fORu2eZ\nXBbN2ZCrVOhq1EB27x6ye/dMUm1eLnb89dFAXllygIt34hjy6U7Wv9/XlNUFgypI+rCxNAy+QrX6\nQ8mq14xvJneldTFLfCUhSUjAvWtXEEXqXL7MjvmD+XLLBVbtCebLLYbsgiDqia5dH28xHfsGhQPg\n5i5y+kQcJ8TWjZY/n6B2NSda+RetZct3msytV5+k9BwycjRkOHqTueQn/P63hiZ/rScpJZPLaXoa\n1nLj53d7FQnw/Xw90Hp7o4iKRPHgAUM+2cFP7/WmfX3zkx4hJwfHRYsAiH9nBkfuJJGQFklmjprM\nXMM5o5i6hFE7fqLFnUDm2TfGwUbOlxM7M7h9Yf1YZ3sVm2f3Z8bq4/x9OoxXlu5n4SsdGdTOj4OX\n77Pr/F1sjhxh+7Ur1HJKJq55U/46GcrWU6E839aP6YObU79GYY2O3GMnEXQ6zjr58POZ+0glAk1q\nVUWj1ZOr0ZKr1pHsoGJLtaY0T4ticj0HXpg36NFZJpvpNLddvx75tWtkjxqFplmzMu/aFCA/lEEW\nbW3JnDbt338/XPsskxF/5AjKCxeKtbC3Bl4udgxuX7vIOVCEhg0RlUp89dkoNHnM/OkEUUmZvD+8\nZYkrVUJqKg7ff4+PXIWmwywm9m1Iy2KumyeVvK5dibt0yew28iuGpi1N06YoAfmAAXgfPsyPa/9H\nm3sp/HUylEHtatOzueXPJacPPkBx4QJp8+ahtrC5S922LTZ79qA8e5acUUWfjxXhm22BRCdl0di3\nKi/3KJ9krpCSYpJrfBibv//GbuNGbLZvR1QqyZowgcx33y12W01AAIqLF/miXVWO3rbheHAU3Wf9\nSUScoUzptb6N+OiltoVK4ca80ht+XYhHZjJvrDjGL+/1LlS2mB0aAcB9hSOuTnZsnNWv9FWzR8Sz\nAPkZxSK6uJDyww9oa9Y022EKgEaDNDoaURBKtSG2FIVMyqt9GvFyjwacvBbF9jNh7L0QQXBEIsER\niXy26Rx1c5KYqteR4uLGuBfKbnEKII2JQXb/vsHi8qGZf1M/N7bPG8TYr/aZbgD52ChlDEs1aANr\n+vThz7kDH0tmRmNcRZFfu2b2d9LWrm0IkMPCCmkZO9ur+G12fyZ9e4jDVx7w4ue7WftOT7o28SE6\nKZN3Vx1n1c1buGuyaNW+AT+8P7TMXe96Nze01aujCAlBdfAgPP88H49pR5fG3ryz8jgJaTl8MKot\ntZ5/g6Rixp9/TtXRZqDW6Hht+UH2fDbEVBKSmaPmzI0YOh0/R21g2I57HDux4aG9+OLV5m30CPRp\n78/yN54zZWyLjNe/DkRFMtpbxvxUNSM/300jX1ca+1alqZ8bTWq5Ube6s2nJLyNbzY3DF2mrk5Dm\nUp1G+zLR7dtX7L6XV3seqWd/mvh7sX9atxKzs0q5lO+mdqOGuyPfbAvkg59PMvfXU2h1hqzvghRD\nbbC0Qzv2zBnCpqM32fLPbXacvcuOs3fp07Im77zQHF8PJ1btCcLn63W8Bxx1qsmgdn7MGNay2Gyz\nJLEfjgsXMn5oG9SPKjguBdXevaiOHyevS5dyBcj5KyoPB8iWoPf2JqeSguMyoVAQf/QouurV+eT4\nHWb/cpJvtgUSlZRZYlZYZjTSuqtwxLuqAzNHlN1B87FiQYlafgZZ06wZSkA0ljVVT09k5ohWfLrx\nHLN+OsnRr4Zb3PgtCw1Fbsbg7J+QKL747TwezrbUre5CfR9nWtasT1tAcf68RcewlNDoVFbtMaw0\nfT6hY9GGTguQxMbi0aoV6latSPr77yLfa/bYsdj+8QeKwEDIzERiRugg3/jLMz6STR+MYsSCXUTE\npaOQSfjx+Tq8tO8nNOmXyXzzTdN7ZDWqEztiFD8Hp3Eo8D4/7LzKW4MN13FCWjbfLP2bn4E4Bxe2\nfjywyCrx4+TJuAM+45Fgt3Ilsjt3yB4/Hk2TJqVunzNkiEX7lUZHI+h06Dw9K278IYqGZibjfuQy\nCd2a+tCtqQ+LXtVy5OoDtp0O43DgfRokGBzhbJo1pmTvIPPkNzJKjfqND1PL04mjXw3nbkwa9io5\n9rYK7FVyZFIJyiM1yTpwgCFzJyI+pmVLvZcXOhcXpMnJSCMjS7ST1fr5wZEjJke8gtgoZfz0bm/e\nX/sPf5y4w/gl+5nYpxG/HbtFVmYO/jnJiILAW++PgHJKQuWMGIEiJATbP/80NUp1beLDiSUvkpCe\ng59nyUoTopMTent7VJmZ9KntxP676UxcfpDeLWtyIjiKS6Fx6LU6MqIMqwkhjp442ytxsDFY4Tra\nKrC3keNgo6BtPU/GdKtntj5c3bEjoq0tk8d2JjpMYO2+EK7eTeTq3UQ2GJUmlHIpDWq4IIqYzBZk\n9V7FU52JIJXQ0s8NXw9HHGwM54u9jWEMdio5VR1t6NzIu9SaOkEQmDmiFTXcHJj18wn0eujQwIsB\nbfx468d9cA/qvtiPPD83mvq58faQ5qzZfonLu0+x/xLsv3QPW6WM7Dwt4xUuXPapT6//G8/4YSU7\nCOqrViV1+XKz43qkiCLyoCAAi+5ZxaF3djb0bVTAkc4SVLt2YbN1KzkjR5Jr5UZDMNS6AozpXg8P\nZ1smf3eYP0/c4cz1GPq29qVvy5q0qetpyt4lB9/CDYhQVWHRq52eSDm3ipLXoQOiVIraeG6I+b0z\n9+7x2v+NYOfZcALD4lmw6RxfvdbZon1KjFK1xdlMHw+KZMKyA+RpdBAOBy8b3Golop6zjt7clXuz\nY8Vh3hjUosKNkBfvGJxXNTo9L3WtW2hlrywoT55EEEXDCklx9z2plNSlS3Hr0wdBoyF72LAS96X1\n90fn4YGoUtGwpiu/zenPmr0hjO/VgI4PrmGzdy+SjIxCATIqFfqvl+IfeB+W7OerPy7Soo47vh6O\njFq0h7saNy4N/4JfJ3XE/QkKjuFZgPzfJTcXeXAwkuxsUzes6sABlOfOkTtokFUPpfPxIfbChXJl\naAqiOHMGp48+IrdXLzJmzSryukoho3/rWvRvXYuMbDUZh46RvV+Npnnzch8z3+1HGh1d8rhkUur5\nFLWVyOve3Wq1ieVGENB7eCDk5SFJSCg5QDbawMpKsC+WyyQsn/QcVR1tWLE7yJS1mOCrQP6P3lA6\nY6YWsDRMznpHjyJJTDQ1sDnYKoqoWRTBuDIhuXmT7wfWocfmOwSFJxIUbmiokwgCQ9zAVq8l292T\nCxverFA2P7OADOW89vDu0BaERCSajhkUnkB4bDqBYYYHqUwq0NzPnfb1q9GhvhetAzxKzE5bjEaD\n/XffIbt/n1HLl9O5kTdKudRQf6jVYjfFmDkroFbiLdGw4qtJiHo978z9mZ+P3SE7T0u7ep688PHH\neJahLOZJQRoVhTQlBZ2zc7nLHHJ79yYmIqLC6gKlIQsNxWb/fnQ+PmUOkG3++gtJaipZY8ZYpHPc\ns3kN/po7kEnfHuJBQiY/7Qvhp30hVLFX0rN5Dfq2rEnutpPUBaS1ahapYf+v8PBzQjSWBkrv3UMq\nkbDsjS70+XArG4/eZHD72nRsWLq7m7SEALlgcDymez06NazGrcgUbj1I4caDZNq2fN2gunDyLr+d\nCmd4Z39mDG1hcZ+G3cqVSGNjyRgzhm+uZ7Lkz0vo9CJN/aoyZ3T5DYCURomzvM4lTxC0deuSvG4d\nkuRkk2JIceR160bc5cumfzep5WaSfJWe3GPYVwl9SD2b1+Ctwc34bvsVpn5/BIVcQnRSFg1rurJ+\nVr8Sa6sfJ88C5P8o0uho3IYMQevtTfz584ZMzK1bAGjq1rXuwSQS9NWqoa+gtaQolyO/cQNpVBSZ\nU6cWrQksgIOtAodBvUkd1LtCxzQFyCVkkJ8GUpcvx2b7drRm5PvyOnQgdcECs0vUgiAw96W2eDjb\n8uuh60zq34TXcsLgf5ZbTJeEvmpV8rp1Q3XoEDbbtpH12mtler/O2xv5zZu4pCTw6//1Yf6GM9T0\ncKRLI286NKiGS3I8mS6xiDY2Vi91cbRV0KFBNTo0+Pf8TsvKIyQiCZ1eT0t/D1MDp9WQybD/6Sck\nqamkz5mDd4GHtfzGDSQ5OWhr1UJfwAlLdHZGV7068hs3mF9Tx+RvR5OckYufp9NjMz8pE3o90vv3\nkUZGou7UCTDIOIKhxrTcAW6BZWnFuXNI4uPJHTDA6g2BmqYGdYj8MVs8vORknD7+GElqKrrq1S0O\nrpv6uXF62SgCw+LZf+ke+y/dIzQ6lT9P3OHPE3f4NsJQhtO8R8W1eZ8WCmaQAQKqOzN9SHOW/HmJ\neRvOsH/hC+bLFPLykKSlIcpkBltzI8eCHvDqsoPkaXSM61mfz1/pWOSaysnTcjsqhc3HbrH5mKHk\n6e9Tobzcoz7ThzTDzcm8Io7t5s3IQ0OZmViFFSmGXpbJA5ow68VWFt/TZDduIL9+HU3TpoZyCFE0\n2NADecZrqsSP3rVr6Qcwcw3Kwg0rePn9S8Xx/vCWXA6N59Q1Q0KqdYAHv/5fn2JVkJ4EngXI/1F0\nPj6IUqkhM5qTgyQtDUlqqsGgwBKL6ceAplUr8tq1Q3n2LLYbNpA1ZUqlH9OSDPKTjqZxYzSNG5vd\nRlenDtl1LFP4eL1fY17vZ9ifdN05RKm0wgEyQPbIkSCKaMvhUJU9ejS53bujqV+fgOrObPqgsJSk\nzs6H9HnzKjxGS3GyU1qUjSo3goC2dm0Uly4hu3MHdYEAWdOgAfEHDyJJTi7yttzevZHfuIFq/36c\nn3uuTPrWjxshNRWPjh3R29oSe+sWSCT/lleUcn5bhCjiOH8+iqAgUhcvJvullyq+zwKYAuTgYNBq\nCxmGmMPh88+RpKaS17kzub3LNuGXSARa+nvQ0t+DOaPaEBqdyv5LEey7eI+96Q3o0LEBNZ7rhKbM\nn+YJQRSRh4Qgu3GDnBEjSp0kiX5+RWRQpwxowm/HbnHjfjK/HbttVv1DmmhYldJXrWqaQFkSHIOh\nVK2psdxp8oAmLP3rEn+fDuXnA9fYfPwWr/VtxNhu9fBytSsSpEujopCHhpIhU7ImSYVrFRXfTO5K\nt6Zly/zbbtyI/S+/kDZ/Pto6dZCFhSGNjUVXtarZBIo1kEVEAKArzgnTiFQi4cc3u/PK0gP4uNmz\n9PUuFV9tq0SeBcj/VeRydD4+yCIikN27hzQ+HjB0oVb2UmNFyHzzTZRnz2K/ejVZEyZUyFbVEtTt\n2hF/+LApUH5GYbJfeYXsl16yij5tbv/+5Banka5WY7dhA5qAAFPmsMh7n0AbeWlYGHpPT0S7ylEu\n0fj7/xsgG+WbDAeWlrgMmtu7Nw7ffIPqwAHSFi58oq/1hxFdXNB5eiKNjUUaEYHOz4+sV15B07ix\nqUSoIqj27kURFITO3d0kiWhN9C4uaGvUQHb/PrI7d9DWL92uXn7xInabNyPK5aQuWFD67yWKSCMj\nDRnOYoyg6lSrQp1qzXjz+WbAYICnNzg24jpqlGkCUdxnLoSXFzFhYYUmJyqFjDmj2jD1+yN89cdF\nBrXzK7GsS+fpaSgXNDaqFQyOx/dswMJXOli0GuPr4ch3U7sxZWATFv9xiQOX7/Hd9it8t/0KUomA\np7Md3lXt8Ha1x9vVnqbH9/IacNjJl/ZNavDN5K54OJfd4VTvaSijksYaJDMlsbFofXxQt2xZKRKK\nBZEas/YllVjkU9XJhl2fDq7UsViLR6+8/IxHhsnsIzwcmbErV1uW8gqtFpcxY3Dv1KnSG1zyyevW\nDU2DBkjj47H9889KP57o6Ii2Xj1ExzJovarVlTegJxGFwmy5S0WRRUTg9NFHVJk5s9KOYXX0elym\nTMG9Y0dk5iT2KkB+x3hJdePFoWnSxBBkxsSYl/57QtEYA3/5dYOrot7Li9yBAy0KNs2i0+Hw1VcA\nZLz9tllt3YqQ30hoUZmFVksVo9ts5uTJ6CxY4bH/+ms82rXDbt26igzz6UEQ/pWyDA62aPviMveD\n2vnRyt+DxPQcvt9xpeT3S6Xoq1VDGxBQ7uAYAI1hWtKghiu/zOjN9vmD6N7UBzcnG3R6kaikTM7f\niuPv02F8v/MqTmcMdcJCrx5smtWvXMExGAJ8MATGAOpOnYg/e5bUJUvKtb+ykLpkCSnLlqErpsRC\nGhWF/fLl2P38c+EXRBFycyt9bOXlWYD8H8akZRweTs6QIST98gvZoy2VEAdkMuQ3byILD0caGVny\ndqJY8mtlRRDImDYNbc2a6J1KVjZ4bOj1uHfsiOvw4QgVbEp8hgHZ7dvAvwHhk4Dsxg1s160z6aw+\njPLQIYO0nlRqlexmceR/H/I7dyx/k0RCzoAB5PboAXq9ofH1ww9RnD5dKWO0Ng8HyNbC5o8/kN+5\ng87T0+qlFQXJnDqVxL//tqgRWpKWht7BAW316mS+/bZF+88PFhWBgRUa59NEISlLI7Jbt3BYuBCF\n0cilNARBYP7LBtfdNftCeJCQYXb7EyFR5Q6ObTdswKN9e1NGFaCVvwfrZ/blyo9jCftlAieXvsiW\nOQNYPuk5Zg5tRv9Mw7btpo8tpBFcVnTG8sn8DLIJa04I1WpkISFF7ima1q3JGTmy2MmnJDERxyVL\nsN28ufDfk5KoVrs2bhbqTT9qnpVY/IfRtGhB7v37aH180Lu7k1fG+jYwBNnS2Fhk4eEmmaGCCFlZ\neDZpgtbPj4QDB6yypJs7cKChiaa4Gj5RRH75MvYrV6Ju3ZrcXr2KnbFWFvKgIGTGeuWHHeueUT5k\nxgCwPLXJlYXNzp04fPMNGW+/XbSxURRx+PZbADInTbLuw6cAmqZNSV2woMyOoemffmr6f8f587Fb\ntw69kxPqDh2sPUSrY8oWFgiGrIHDN98AkPnaa6CoPLmz/DpkS9C7upL0559IYmIszmgXagTU6yt9\n2fxJwBQgF1gRUZ46hcOPPyJNSrLYzKN5bXeGdqzD1lOhLNx8npXTi5c7vHA7zqRWMa5n/bJljjE0\ngkpjYnBcsICUNWuKvK5SyEyOivlktj2C+ty5Yp+xZSG/BKVIgGxFZPfu4d6nD9oaNYg/c8ai9+Rr\n2T/c65NvMV1hedhK4r9/df1/TM6QISSvW2fSnS0PpjKNu8X7qEsfPEDIzUXIzbVevaNUWiQ4loaG\n4rB4Me6dOuE2aBA2e/bg9Mkn/15gjwjVwYMA5PXq9VTVd4Ih6+I8aRKOj7CZzSzGZcj8AFlTzkZA\n1c6dOCxcWGb1AHOYO+8Vp06hCAxE5+xM9tixVjvmw+jd3cmeMAF1639VCISMjDKt2CiNWZ68pyA4\nBkMwpG7e3JRJthbJa9aQunhxEQvwx44glEn9R+/hgbZaNSSZmWUqvXmayW/QLBgg56/sqMuojf3B\nyNaoFFJ2nrvLhVtFg8jg8ETGLd5HTp6WF7sEsHB88Q155kifMwe9jY3BetoosVYauurVyTGjP2wp\nOi8vcvr3r9SeDa2vL6JMZnj251jmQKB3cUFUqZCkpiIUMCLJf35XllNlRXkWID/DLPmBgrSkAPm+\nQSi9tML8CiGKuI4bh8PXXyOLiEDn4UHmG28Qv39/iU1d5T1OaagOHAAgt1cv6x33UaHTYbNrF8qj\nRy3aXBITgyQpyfrj0GqpMn06Hi1bImRmIs8vsSglQLZbuRLnyZNN51w+qr17cfjxR2Q3blhviGZ0\nox2++w6ArNdeQ7QtX61geXEdPRqPVq2QWVCCIKSkILt+HVGhMDTpPAXo/PxI3LXLoG9rxdItbaNG\nhtKKx5BxFbKzrbq//BUNuZkyC9WOHYbSmlOnrHrsx4HWz4/cHj3IGTzY1AsjL+CgVwRRRJKQYCrd\nKoi3qz2TBxiC6vkbzqLX/3uO3Y5M4aUv95KerWZAm1osfq1zucod9F5eZL71FgBO8+cbFE0eEaKd\nHSlr1pA+d27lHUQuR+vriyCKSC2dpAlCsYpRzwLkZzzVFGz0Kw7ZgwcAJRpUWAVBIHvsWLJHjiTx\nt9+Iu3CB9Hnzyrz0XBK269bh0bw59sZl85KQRkUhv34dvZ3dU5ORK4i2Vi1EQTBohGpK7213XLwY\nzyZNsN240boDkcmQRkYiTUpCtWcPOS+8QPbgwaXWIKuOHsVm584iQWv+crzWuDxvDQpNDPX6Qq9l\nvvkmud27k/XKK1Y7niUIOTkG85/4eIuuN+W5cwiiiLpFi0orA6k0RBH39u1xHTasUMZFH05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- "text": [ - "" - ] - } - ], - "prompt_number": 25 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Again the answer is yes! Because we are relatively sure about our belief in the sensor ($\\sigma=30$) even after the first step we have changed our belief in the first position from 1000 to somewhere around 60.0 or so. After another 5-10 measurements we have converged to the correct value! So this is how we get around the chicken and egg problem of initial guesses. In practice we would probably just assign the first measurement from the sensor as the initial value, but you can see it doesn't matter much if we wildly guess at the initial conditions - the Kalman filter still converges very quickly." - ] - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Example: Large Noise and Bad Initial Estimate" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "What about the worst of both worlds, large noise and a bad initial estimate?" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_error = 30000\n", - "movement_error = 2\n", - "pos = (1000,500)\n", - "\n", - "\n", - "dog = DogSensor(0, velocity=movement, noise=sensor_error) \n", - "zs = []\n", - "ps = []\n", - "\n", - "for i in range(1000):\n", - " pos = predict(pos[0], pos[1], movement, movement_error)\n", - " \n", - " Z = dog.sense()\n", - " zs.append(Z)\n", - " \n", - " pos = update(pos[0], pos[1], Z, sensor_error)\n", - " ps.append(pos[0])\n", - "\n", - "plt.plot(zs,c='r', linestyle='dashed', label='measurement')\n", - "plt.plot(ps, c='#004080', label='filter')\n", - "plt.legend(loc='best')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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HH3b5PTs72xHkqAEd+GL1Pt777g+ev7WvL2GLesZ+5WjfD4QA2S+Ee7JfCHeq2i+MRmNd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iaCIREEWqV60y/Fyor6e8Y0cSeXlUpO6azxKJ1ndgsXFjrZrfPXky4YsvplZZNJzvvIP9q68I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- "text": [ - "" - ] - } - ], - "prompt_number": 26 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This time the filter does struggle. Notice that the previous example only computed 100 updates, whereas this example uses 1000. By my eye it takes the filter 400 or so iterations to become reasonable accurate, but maybe over 600 before the results are good. Kalman filters are good, but we cannot expect miracles. If we have extremely noisy data and extremely bad initial conditions, this is as good as it gets.\n", - "\n", - "Finally, let's make the suggest change of making our initial position guess just be the first sensor measurement." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_error = 30000\n", - "movement_error = 2\n", - "pos = None\n", - "\n", - "dog = DogSensor(0, velocity=movement, noise=sensor_error)\n", - "\n", - "zs = []\n", - "ps = []\n", - "\n", - "for i in range(1000):\n", - " Z = dog.sense()\n", - " zs.append(Z)\n", - " if pos == None:\n", - " pos = (Z, 500)\n", - " \n", - " pos = update(pos[0], pos[1], Z, sensor_error)\n", - " ps.append(pos[0])\n", - "\n", - " pos = predict(pos[0], pos[1], movement, movement_error)\n", - "\n", - "plt.plot(zs,c='r', linestyle='dashed', label='measurement')\n", - "plt.plot(ps, c='#004080', label='filter')\n", - "plt.legend(loc='best')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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ZvinkiPElF4I5PuHllxEXgHEqnER/8w1ili6FrKio/ivREdwXAoClfXtYmjWD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\n1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HCOGydGfpgxRhwX8/ffI9CihchQYzAgYrNBkN6laft2eREoIPJJa2HltNqsIVQUrlcP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\nux+Jc2Kssok1zz0H34wZpNSXlcUW2JS33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XgZv6NdjIh4w4YElgLS4Z3xyCOEa9eCciXc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1xr/N9GERBxq0Ysm68eNRsrONU6dr4UK8/jAVFgd5BCjt2YdDkx6l3yvPYPXWGM9TFxEc0C2e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4M334zQDTdAPHaMJJuZJk4jNz4+NJVo1nLOhPk1+ixBQJ1GOcQrV1QCd9yBeg0GHiDkwvCg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- "text": [ - "" - ] - } - ], - "prompt_number": 27 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This simple change significantly improves the results. On some runs it takes 200 iterations or so to settle to a good solution, but other runs it converges very rapidly. This all depends on whether the initial measurement $Z$ had a small amount or large amount of noise. \n", - "\n", - "200 iterations may seem like a lot, but the amount of noise we are injecting is truly huge. In the real world we use sensors like thermometers, laser rangefinders, GPS satellites, computer vision, and so on. None have the enormous error as shown here. A reasonable value for the variance for a cheap thermometer might be 10, for example, and our code is using 30,000 for the variance. " - ] - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Exercise: Interactive Plots" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Implement the Kalman filter using IPython Notebook's animation features to allow you to modify the various constants in real time using sliders. Refer to the section **Interactive Gaussians** in the Gaussian chapter to see how to do this. You will use the `interact()` function to call a calculation and plotting function. Each parameter passed into `interact()` automatically gets a slider created for it. I have built the boilerplate for this; just fill in the required code." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from IPython.html.widgets import interact, interactive, fixed\n", - "import IPython.html.widgets as widgets\n", - "def plot_kalman_filter(start_pos, sensor_noise, movement, movement_noise, noise_scale):\n", - " # your code goes here\n", - " pass\n", - "\n", - "interact(plot_kalman_filter,\n", - " start_pos=(-10,10), \n", - " sensor_noise=widgets.IntSliderWidget(value=5,min=0,max=100), \n", - " movement=widgets.FloatSliderWidget(value=1,min=-2.,max=2.), \n", - " movement_noise=widgets.FloatSliderWidget(value=5,min=0,max=100.),\n", - " noise_scale=widgets.FloatSliderWidget(value=1,min=0,max=2.))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 28, - "text": [ - "" - ] - } - ], - "prompt_number": 28 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "######Solution\n", - "One possible solution follows." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "zs = np.zeros(100)\n", - "ps = np.zeros(100)\n", - "def plot_kalman_filter(start_pos, sensor_noise, movement, movement_noise,noise_scale):\n", - " dog = DogSensor(start_pos, velocity=movement, noise=sensor_noise)\n", - " random.seed(303)\n", - " pos = (0,100)\n", - "\n", - " for i in range(100):\n", - " Z = dog.sense() + random.randn()*noise_scale\n", - " zs[i] = Z\n", - "\n", - " pos = update(pos[0], pos[1], Z, sensor_error)\n", - " ps[i] = pos[0]\n", - "\n", - " pos = predict(pos[0], pos[1], movement + random.randn()*movement_noise, movement_noise)\n", - "\n", - " plt.plot(zs,c='r', linestyle='dashed', label='measurement')\n", - " plt.plot(ps, c='#004080', label='filter')\n", - " plt.legend(loc='best')\n", - " plt.show()\n", - "\n", - "interact(plot_kalman_filter,\n", - " start_pos=(-10,10), \n", - " sensor_noise=widgets.IntSliderWidget(value=5,min=0,max=100), \n", - " movement=widgets.FloatSliderWidget(value=1,min=-2.,max=2.), \n", - " movement_noise=widgets.FloatSliderWidget(value=2,min=0,max=100.),\n", - " noise_scale=widgets.FloatSliderWidget(value=1,min=0,max=20.))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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iIpWV203I1Kn4HDyIo3lzr+xO54yJIWH7di8EB85mzXA2a+aVukSK4/Mff2fL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\nvWULtG5d5caFlK2q+nkhZUvjQopis9lYvnw5dc+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MHz5cAbma+WzJTiZ8ugbjHEtM/KNd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\n/uQT8rp0KXZfIiIiIlJ6Ku3v9DNz8pgy6zcAJgztWPrhGPBcvpzw1q0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- "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 29, - "text": [ - "" - ] - } - ], - "prompt_number": 29 - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Exercise - Nonlinear Systems" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Our equations are linear: \n", - "$$\\begin{aligned}new\\_pos &= old\\_pos+dist\\_moved\\\\\n", - "new\\_position &= old\\_position*measurement\\end{aligned}$$\n", - "\n", - "Do you suppose that this filter works well or poorly with nonlinear systems?\n", - "\n", - "Implement a Kalman filter that uses the following equation to generate the measurement value for i in range(100):\n", - "\n", - " Z = math.sin(i/3.) * 2\n", - " \n", - "Adjust the variance and initial positions to see the effect. What is, for example, the result of a very bad initial guess?" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "#enter your code here." - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 30 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "###### Solution:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_error = 30\n", - "movement_error = 2\n", - "pos = (100,500)\n", - "\n", - "zs = []\n", - "ps = []\n", - "\n", - "\n", - "for i in range(100):\n", - " pos = predict(pos[0], pos[1], movement, movement_error)\n", - "\n", - " Z = math.sin(i/3.)*2\n", - " zs.append(Z)\n", - " \n", - " pos = update(pos[0], pos[1], Z, sensor_error)\n", - " ps.append(pos[0])\n", - "\n", - "plt.plot(zs,c='r', linestyle='dashed', label='input')\n", - "plt.plot(ps, c='#004080', label='filter')\n", - "plt.legend(loc='best')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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bdY7cJ5+0zRIZjVDZMcNEMlIqYV68GPnjxskdCTmJ+vhx6GJjYfXyQt7DD1f9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- "text": [ - "" - ] - } - ], - "prompt_number": 31 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "######Discussion\n", - "\n", - "Here we set a bad initial guess of 100. We can see that the filter never 'acquires' the signal. Note now the peak of the filter output always lags the peak of the signal by a small amount, and how the filtered signal does not come very close to capturing the high and low peaks of the input signal.\n", - "\n", - "If we recall the g-h filter chapter we can understand what is happening here. The structure of the g-h filter requires that the filter output chooses a value part way between the prediction and measurement. A varying signal like this one is always accelerating, whereas our process model assumes constant velocity, so the filter is mathematically guaranteed to always lag the input signal. \n", - "\n", - "Maybe we just didn't adjust things 'quite right'. After all, the output looks like a sin wave, it is just offset some. Let's test this assumption." - ] - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Exercise - Noisy Nonlinear Systems" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Implement the same system, but add noise to the measurement." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "#enter your code here" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 32 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "######Solution" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_error = 30\n", - "movement_error = 2\n", - "pos = (100,500)\n", - "\n", - "zs = []\n", - "ps = []\n", - "\n", - "for i in range(100):\n", - " pos = predict(pos[0], pos[1], movement, movement_error)\n", - "\n", - " Z = math.sin(i/3.)*2 + random.randn()*1.2\n", - " zs.append(Z)\n", - " \n", - " pos = update(pos[0], pos[1], Z, sensor_error)\n", - " ps.append(pos[0])\n", - "\n", - "p1, = plt.plot(zs,c='r', linestyle='dashed', label='measurement')\n", - "p2, = plt.plot(ps, c='#004080', label='filter')\n", - "plt.legend(loc='best')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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TbQkNJfOTT7AEBeG7fDn+//vfBcd5r1lD4KxZaAoLMYeHo1ayiFeTkUHQrFnW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Q8kIS2X1XsdCAhQqwudes7NM1rdAh7vfxfbqdmA8o4oZmfSI7oGdcL8iEvJZufJG04/flEUFcW8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\n/hP21NTqZHj6dBinT/f4GGv37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- "text": [ - "" - ] - } - ], - "prompt_number": 33 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "###### Discussion\n", - "This is terrible! The output is not at all like a sin wave, except in the grossest way. With linear systems we could add extreme amounts of noise to our signal and still extract a very accurate result, but here even modest noise creates a very bad result.\n", - "\n", - "Very shortly after practitioners began implementing Kalman filters they recognized the poor performance of them for nonlinear systems and began devising ways of dealing with it. Much of this book is devoted to this problem and its various solutions." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Summary" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This information in this chapter takes some time to assimilate. To truly understand this you will probably have to work through this chapter several times. I encourage you to change the various constants and observe the results. Convince yourself that Gaussians are a good representation of a unimodal belief of something like the position of a dog in a hallway. Then convince yourself that multiplying Gaussians truly does compute a new belief from your prior belief and the new measurement. Finally, convince yourself that if you are measuring movement, that adding the Gaussians correctly updates your belief. That is all the Kalman filter does. Even now I alternate between complacency and amazement at the results. \n", - "\n", - "If you understand this, you will be able to understand multidimensional Kalman filters and the various extensions that have been make on them. If you do not fully understand this, I strongly suggest rereading this chapter. Try implementing the filter from scratch, just by looking at the equations and reading the text. Change the constants. Maybe try to implement a different tracking problem, like tracking stock prices. Experimentation will build your intuition and understanding of how these marvelous filters work." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 33 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**author notes**:\n", - " clean up the code - same stuff duplicated over and over - write a 'clean implementation' at the end.\n", - " \n", - " " - ] - } - ], - "metadata": {} - } - ] -} \ No newline at end of file