diff --git a/11_Extended_Kalman_Filters.ipynb b/11_Extended_Kalman_Filters.ipynb index 36122c2..18b6423 100644 --- a/11_Extended_Kalman_Filters.ipynb +++ b/11_Extended_Kalman_Filters.ipynb @@ -109,7 +109,7 @@ " color: #1d3b84;\n", " font-size: 16pt;\n", " margin-bottom: 0em;\n", - " margin-top: 1.5em;\n", + " margin-top: 0.5em;\n", " display: block;\n", " white-space: nowrap;\n", " }\n", @@ -133,6 +133,11 @@ " overflow-y: scroll;\n", " max-height: 50000px;\n", " }\n", + " div.output_wrapper{\n", + " margin-top:0.2em;\n", + " margin-bottom:0.2em;\n", + "}\n", + "\n", " code{\n", " font-size: 70%;\n", " }\n", @@ -266,182 +271,30 @@ "\n", "**The Unscented Kalman filter (UKF) chapter is much further along. The UKF is almost always better performing than the Extended Kalman filter, and is much easier to implement, so if you have an urgent need for nonlinear Kalman filter I'll point you towards that chapter for now.**\n", "\n", - "The Kalman filter that we have developed to this point is extremely good, but it is also limited. Its derivation is in the linear space, and hence it only works for linear problems. Let's be a bit more rigorous here. You can, and we have in this book, apply the Kalman filter to nonlinear problems. For example, in the g-h filter chapter we explored using a g-h filter in a problem with constant acceleration. It 'worked', in that it remained numerically stable and the filtered output did track the input, but there was always a lag. It is easy to prove that there will always be a lag when $\\mathbf{\\ddot{x}}>0$. The filter no longer produces an optimal result. If we make our time step arbitrarily small we can still handle many problems, but typically we are using Kalman filters with physical sensors and solving real-time problems. Either fast enough sensors do not exist, are prohibitively expensive, or the computation time required is excessive. It is not a workable solution.\n", + "At this point in the book we have developed the theory for the linear Kalman filter. Then, in the last two chapters we broached the topic of using Kalman filters for nonlinear problems. I chose to start off with the Unscented Kalman filter, which probably felt like quite a departure from the linear Kalman filter math. It was also a departure from the historical development of the Kalman filter.\n", "\n", - "The early adopters of Kalman filters were the radar people, and this fact was not lost on them. Radar is inherently nonlinear. Radars measure the slant range to an object, and we are typically interested in the aircraft's position over the ground. We invoke Pythagoras and get the nonlinear equation:\n", - "$$x=\\sqrt{slant^2 - altitude^2}$$\n", + "Shortly after Dr. Kálmán published his paper on the Kalman filter people recognized that his theory was limited to linear problems and immediately began work on extending the theory to work with nonlinear problems. As I have said elsewhere the only equation we really know how to solve is $\\mathbf{Ax} = \\mathbf{b}$. That is a slight exaggeration. Many of us have spent years at school learning sophisticated tricks and techniques to handle equations that are not linear. Yet after all that work the vast majority of equations that arise from simple physical systems remain intractable. Certainly there is no way to find general analytic solutions to the Kalman filter equations for nonlinear systems. \n", "\n", - "So shortly after the Kalman filter was enthusiastically taken up by the radar industry people began working on how to extend the Kalman filter into nonlinear problems. It is still an area of ongoing research, and in the Unscented Kalman filter chapter we will implement a powerful, recent result of that research. But in this chapter we will cover the most common form, the Extended Kalman filter, or EKF. Today, most real world \"Kalman filters\" are actually EKFs. The Kalman filter in your car's and phone's GPS is almost certainly an EKF, for example. \n", + "In this chapter we will learn the Extended Kalman filter (EKF). The EKF handles nonlinearity by linearizing the system at the point of the current estimate, and then the usual Kalman filter is used to filter this linearized system. It was one of the very first techniques used for nonlinear problems, and it remains the most common technique. Most filters in real world use are EKFs. \n", "\n", - "With that said, there are new techniques that have been developed that both perform equal to or better than the EKF, and require much less math. The next chapter " + "The EKF provides significant mathematical challenges to the designer of the filter; this is the most challenging chapter of the book. To be honest, I do everything I can to avoid the EKF in favor of other techniques that have been developed to filter nonlinear problems. However, the topic is unavoidable; all classic papers and a majority of current papers in the field use the EKF. Even if you do not use the EKF in your own work you will need to be familiar with the topic to be able to read the literature. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## The Problem with Nonlinearity" + "## Linearizing the System Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "You may not realize it, but the only math you really know how to do is linear math. Equations of the form \n", - "$$ A\\mathbf{x}=\\mathbf{b}$$.\n", + "The extended Kalman filter (EKF) works by linearizing the system model for each update. For example, consider the problem of tracking a cannonball in flight. Obviously it follows a curved flight path. However, if our update rate is small enough, say 1/10 second, then the trajectory over that time is nearly linear. If we linearize that short segment we will get an answer very close to the actual value, and we can use that value to perform the prediction step of the filter. There are many ways to linearize a set of nonlinear differential equations, and the topic is somewhat beyond the scope of this book. In practice, a Taylor series approximation is frequently used with EKFs, and that is what we will use. \n", "\n", - "That may strike you as hyperbole. After all, in this book we have integrated a polynomial to get distance from velocity and time:\n", - " We know how to integrate a polynomial, for example, and so we are able to find the closed form equation for distance given velocity and time:\n", - "$$\\int{(vt+v_0)}\\,dt = \\frac{a}{2}t^2+v_0t+d_0$$\n", "\n", - "That's nonlinear. But it is also a very special form. You spent a lot of time, probably at least a year, learning how to integrate various terms, and you still can not integrate some arbitrary equation - no one can. We don't know how. If you took freshman Physics you perhaps remember homework involving sliding frictionless blocks on a plane and other toy problems. At the end of the course you were almost entirely unequipped to solve real world problems because the real world is nonlinear, and you were taught linear, closed forms of equations. It made the math tractable, but mostly useless. \n", - "\n", - "The mathematics of the Kalman filter is beautiful in part due to the Gaussian equation being so special. It is nonlinear, but when we add and multiply it using linear algebra we get another Gaussian equation as a result. That is very rare. $\\sin{x}*\\sin{y}$ does not yield a $\\sin(\\cdot)$ as an output.\n", - "\n", - "> If you are not well versed in signals and systems there is a perhaps startling fact that you should be aware of. A linear system is defined as a system whose output is linearly proportional to the sum of all its inputs. A consequence of this is that to be linear if the input is zero than the output must also be zero. Consider an audio amp - if a sing into a microphone, and you start talking, the output should be the sum of our voices (input) scaled by the amplifier gain. But if amplifier outputs a nonzero signal for a zero input the additive relationship no longer holds. This is because you can say $amp(roger) = amp(roger + 0)$ This clearly should give the same output, but if amp(0) is nonzero, then\n", - "\n", - "> $$\n", - "\\begin{aligned}\n", - "amp(roger) &= amp(roger + 0) \\\\\n", - "&= amp(roger) + amp(0) \\\\\n", - "&= amp(roger) + non\\_zero\\_value\n", - "\\end{aligned}\n", - "$$\n", - "\n", - ">which is clearly nonsense. Hence, an apparently linear equation such as\n", - "$$L(f(t)) = f(t) + 1$$\n", - "\n", - ">is not linear because $L(0) = 1$! Be careful!" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## The Effect of Nonlinear Transfer Functions on Gaussians" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Unfortunately Gaussians are not closed under an arbitrary nonlinear function. Recall the equations of the Kalman filter - at each step of its evolution we do things like pass the covariances through our process function to get the new covariance at time $k$. Our process function was always linear, so the output was always another Gaussian. Let's look at that on a graph. I will take an arbitrary Gaussian and pass it through the function $f(x) = 2x + 1$ and plot the result. We know how to do this analytically, but lets do this with sampling. I will generate 500,000 points on the Gaussian curve, pass it through the function, and then plot the results. I will do it this way because the next example will be nonlinear, and we will have no way to compute this analytically." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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dXW1jJHAy6gmd4cNzJxVP9qjSN1u5XE4Zs2/QGDNryuMeeu5gsvYPrGG3K4ap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\n4fuclZXUX6Oa/x4ARiM/257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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import numpy as np\n", - "from numpy.random import normal\n", - "import matplotlib.pyplot as plt\n", - "\n", - "data = normal(loc=0.0, scale=1, size=500000)\n", - "ys = 2*data + 1\n", - "\n", - "plt.hist(ys, 1000)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This is an unsurprising result. The result of passing the Gaussian through $f(x)=2x+1$ is another Gaussian centered around 1. Let's look at the input, transfer function, and output at once." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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zERFRR7E7rFi86k38vG+dX116Qiamjn4UMQYutEXnhol5CBEEAZ0SurZ5P7fb\nhTprDeos1aizNDxabPWwOa2wOxp+bE5rs41IIDmcNlQ4bUBt67ZXKdRQNQ4FUis1UCk10Gsi0Tmp\nO1LjMqBSqqFSaBoelWrYnGYoZCqIosjhNUREFHQnK47hvaUvNnsP2ZC+Y3D9lVOgkCsliIzOF0zM\nzwNyuQJRESZERZjOuN3kkQ/B5rCiqLwQZlstdufvgsNlRUxcFMzWOphtdbDYGh7NtjqYrXUdMh6+\nicNlh8NlR73V9w7m3Ue2nXG/j7b8ntQ3JO+/P1crNFAqVVArNFCrNNBrjd5hNwZdFGKNidBrDR32\nmoiI6Py0de9afLLyDThcdp9ytVKD8Vfff8bJIohai4n5BUaj0qJLchYAwF7ZMJSkpamQRFGE3WlD\nrbmqYarIxikj6yxVqDVX+5TVWqr8xtl1pKakHta272vQRcNkTGi4yVVrOOVm14iG5F6paZhXXtXc\no5q99UREFxCny4HP1/4bG39b5leXZOqEaWMeP6cpi4maw8ScWiQIQuP0ilrERyefcVtRFGG1m1Fv\nrYXVXt8wz7utHhZ7PSy2OpRUnsCJ8sOot9TA7rT59TgEU62lCrWWqnPaV6XUwKiPgVEf3fAYEQOD\nPgZGfQwidcaGnnuFqvFRDYfLzq81iYjCVHlNMd5bOg/HSwv86gb2yMOtefdCpVRLEBmdr5iYU0AI\ngtBwo6cmolXbe0QPnE477E5bQ6LutKHWUo1DJ/agpOo4HM6GHnGH09bw3GmDxWaGy+PssBtdW8Ph\ntKGsughl1UVt2u/jHxXeITc6td47LaWu2WkqI7yPTWPvOd0WEVFw7Tz0I/5v+SuwOiw+5Qq5Ejfn\n3o3BPa/mN6gUcEzMSRIyQQa1qmHxoyYpAHqk929xn6ZVyAYM6A+Hy9GYvDck9XanHU6XvTHJb0jk\nbQ5rw02xjUNxqurLUVpdFNQhN03cbhesbhesdjNq6ivavL9CrvTeKNsw3KZhZhudumEGHL02EjqN\nAXpNBCK0Bhj1DfccROqMkDGpJyJqNbfbhW82f4iVP3/pVxdrTMS0MY8hNa6LBJHRhYCJOYUdmUzu\nHWLTVm6PG+U1xaizVDcsytR4k6vZVgubwwK7wwa7yw6Hw9rw2Nijb3faYHNYJEnqgYZpK11uJyy2\nujbtJxNkSIxJQ0ZSFiJ0RmjVemhVOmgaH7Xq359r1Doo5aoOegVERKGvpr4S73/3EgqK8v3q+lw0\nCHdc8wBGWTH4AAAgAElEQVS0ar0EkdGFgok5XVDkMjkSolPO6UadpnH0NeZK1NRXNjyaK1Hb+LvZ\nVgeHy+HtuXc67bDarXB5Om5mm7PxiB4UVRSiqKKwVdvLZQooZCqoFGqsPhDjk8Rr1DpoVXpo1DoY\n9dGIMSTAZIhHpC6KX+cSUdjbd/RXfPD9AtSdNlOYTCbHdZdPRm7/sWzrqMMxMSdqpVPH0SeZOrVq\nn23btkEURfTr3xcOlx12hw1We33jlJQNN8aarbWw2OtPmbKyod5qN8PussHhsEGE2MGvroHb44Lb\n44LdZUGdrXU3yBp00eia2gtala5xznlN47AbNZSKpllu1FCrtNBrIqBVN4yhVypUvMgRkeQ8ogcr\ntn6GpZs/9mtrjREmTB31qHc2M6KOxsScqIMJggClQgWlQgW9JhJAXJv2F0URTrcDdoetcUx9402z\nDmvj7DenzEFvrUOtpRo19RWoNle2eejLuai1VGH7/vVt3k8hV0KniUBa/EXoktQDOk0ENE3Da1Q6\n73ODPoY3vxJRh6i31uI/y15GfuF2v7qsTv0wccRMROqMEkRGFyom5kQhThCEhhldFGoAbbtAWGz1\nKCjKR2l1EWx2C6wOc+OjBTa7GRaf3y1BnfHG5Xai1lyF3Ye3YffhlheVkgkyREWYEGNMQJwxCZf2\nyIW+8UZXrToCSgWnoySitjt8ch/eXzoP1afdkC9AwMjLbsOIgbfw5nkKOibmROcxnSYCvbpc2qpt\nm3rmf/xpMxwuGy7q1gVWuxk2hwVWuwU2hxlWuxkWmxnV9eWoqC1FefXJDp+T3iN6UFlXhsq6Mhw8\n/hs2717hU69SaqAQVFArtdhcuMQ71WR6Yjdkdx/KxJ2IfIiiiLU7vsGXGxbC43H71Om1Bkwe8RCy\n0vtJFB1d6JiYExGA33vmtaoIaFUR6JzY7az7OF1OFBTtQXV9RcOc8y67dxpLe+O0lU1lNrulccGp\nepjtdQGb4cbhtMEBGyyOWlSZS7zlm35bjq82LEJCdCqUyoYbWpUKNVQKFRQKFax2M6y2epjt9eia\ncjGu7DMaMYb4gMRERKHJarfg4x9ew46Dm/zqMpKyMGXUI4iOjJUgMqIGTMyJ6JwpFUp079S3zfuJ\noginy4ET5Udw4PgumK213uE0Nkfj0BqHBWZrHepPmyGhLcy2OhSc9J/27HSFxfux8ucvcde1f0Gf\niwad8/mIKHSdKDuC95bOa3aBuGEDrsPYnImQy5kWkbT4CSSioBMEASqlGhlJ3ZGR1P2M2zqcdhQU\n5ePXg5tRXV8Bs71h5hpL46w2HtETsLje/eZvmDRiJrKzhgbsmEQkvQMlO/DxluVwun2nr9WodLjj\nmgfRtyv/IKfQwMSciEKaSqlGVnq/Zsd8iqIIm8OKH7dugt1lRXpGGuqtNdh7dAd2HNwMh9PW5vN9\nsOwf+DF/FTondkOX5IsRHRmLqIjYc1rQioik5XDasfHA1zhU+qtfXWpcF0wd/SjiopIkiIyoeUzM\niShsCYIArVqHCE0UIhDlTd6zs4bi1rx7UVJ1HA6nDaVVRVi29VNU1pa26rj7jv6KfUf9L+QTR8zA\npVm5gXwJFzbOY99q2VIHEKZUAKYDKDfp8MmtfbGve8N9JDm9huOmoXdBqeBqxxRaQj4xP73dFltY\nZ6Wl9p3bn2n7bGzd2vw0daEZv/+lKbTeT24v3fbZfturlGqkxV8Ep8uJrqk9AVzjd5wHXr6+2eO/\nOuPLZsuVr96Knp2zodNEnCUe+MVDRNKJrbDgtv/+ihfmjMFtw+7DwB55UodE1CyZFCd94403kJGR\nAa1Wi+zsbGzYsEGKMIjoAmC21QbsWC6PK2irsIYrtu8UqmIrLHj4tpeYlFNIC3qP+SeffIIZM2bg\nzTffxBVXXIHXX38do0aNwp49e5CWlua3fWt7nNraM8XtG5aLD6V4zrZ9U7zZ2Wf/UjcU4+f2Hbf9\ntm3b4BE9sDl6w+aw4PDJvThWWoCq2lJU1JbigZf3ten4zfWka1Q6jBk8rXH11jPHc6Fqa/tOFGzJ\nselSh0B0RkFPzBcsWICpU6fiD3/4AwDgn//8J77//nu8+eabmDt3brDDIaIwUVR+BKu2L8FP+au9\nZdERsbC7GuZI94huwH9q4nZLje+C6y6fjK6pvSDnKoBn1Ob2nX/RtFpbOiYuRHuObMcHy/4Bi63O\np/yfM5ZIFBHRuQlqYu5wOLB9+3Y89thjPuXDhw/Hpk0dcEUlorBgc1hxsuIo8gu3o9ZcdcpCRXY4\nnXbYHBacKD/it19VfXlAzq+Uq5BoSsOIgbfCZIiHQR8DvTYSMkGS0X5hie07ScHjceO7Hxdj+U+f\n+Q0zi4mMkygqonMX1MS8vLwcbrcbCQkJPuXx8fEoLi4OZihE1E5ujxs2hwV2hw12pw0OZ8Oj3WmF\nw2n3e+5wWmF32hvKHLbGnm4zquor/Hq5OkKk1ohunfoiIToFcVHJiIqIgUEfA4M+GmqlpsPPf75j\n+07BVmuuxgff/x37j+/yq+vZORt3jpgO/OFdCSIjOnchPyvLmcZBh6JwixcIv5jDLV4g9GMWRREu\njxMutxMujwMutxPfrfoSzsbnLrejsb7hccfRtVKH3CyFTAmFXAWdKhKJxnQYdXGIUBuhVxsRoYny\n9oCLdUBVnRVVOAHgRNDjzMzMDPo5Q1Go/78IRXzPGpTUHMW6fZ/D6qz3KRcgoF96Lnol5yD/t31+\nc3nx/Ws7vmdt0972PaiJeWxsLORyOUpKSnzKS0pKkJTECf6JOoooivCIHrgbk+vD5Xvw85EfpA6r\nXfRqI67sdj0MWhMUMiXkMgUEzostGbbvFAyiKGL3ic34pXC139AVjVKPId1vQKKxszTBEQVAUBNz\nlUqFSy65BMuXL8dNN93kLV+xYgVuueWWZvcJlxtdwvHGnHCLOdziBdoXs9vtgtVhgdVuhs1hgdVu\ngc1haXx+apm58dEKh9PWMD7bZYfT5YDT+fvzQC5dH2hymQJRkSakxnVBZmovaFQ6KBVqqBQqqJQa\nqBRqqJSNPwo11CotVAq1d/9w+2zU1NRIHULAnc/teygIt894R7DY6vHhin/it8Kf/Oq6pvbClJEP\nw6CPPuMxLuT3r634mTs37W3fgz6U5aGHHsLEiRMxcOBA5OTk4K233kJxcTHuvffeYIdCJClRFOH2\nuLyJs8Npx4Hjv2HnoS04VLQHdodV6hDbJDW+CzRKLVRKDdSNP80+b0yq1SoNVAoNjBExMOiiIOOM\nJ2GP7Tt1lKMlB/H+0pdQUVviVzf80psxatB4zppE54WgJ+a33norKioq8Pzzz+PkyZPo3bs3li5d\nyjluKSyIooh6aw0qaktRWVuKOks1HKf1TJ/6WFFZBpfbiVUHPoLT6YDTZW/YvvFRDKFebKVcBZVK\nA3gEKOUqGCOjvMn0749q7+8KuQJWuxmZqb1xUUpPXhSJ7TsFnCiK2LhrGf637l243S6fOp06AhNH\nzEDPDPbo0vlDkps/77vvPtx3331SnJrIjyiKsDttsNjqYLbVw2ytRXlNMcprTqKytgz1tlqYrbUw\nW+tQb6uFx+Nu+0k6ftKRs5IJMigbh4JEaA0QIECricCgi4chu/tQyOUNzQG/vqT2YPtOgWJ3WLF4\n1Zv4ed86v7pOCZmYNvpRxBjiJYiMqOOE/KwsRM0RRRF1lmrYHNaGsdTuhl5op8vR2FvtaHz++zAR\ni70eFlv974+2OljsZljs9eeWbHcwAQI0Ki00aj20Kh00ah20Kn3jo+60ch20ar13PLZSofKOx1Yq\nVFAp1N7Em4go1J2sOIb3lr6IksrjfnVD+o7GdVdMhVKhlCAyoo7FKzVJyuNxo6ymGCWVx7xJtsNl\nh8vlbEy47d5Eu6S0GG6PCz8d/xYnyg6jzlItdfjtJpcpvImzUqGCUqFCanwXXNlnFNITu3GBGyK6\n4GzbuxaLV74Bh8vuU65WajD+6vsxoNsVEkVG1PGYmFNAOVx2lFadgN1haxxr3bSCY0Pvtd1pa3y0\n43hZAQqL98PpcrTtJBUdE3traVQ6xBjiEWOIR1SECWqlxie5PrXH+nBBIRQyJXr36uOdZUTZOMOI\nUqHiuGwiokZOlwOfr3sPG3d971eXZOqEaWMeR0J0igSREQUPE3NqNbvDimpzJarrylFdX4F6ay2s\n9npY7GZYbfWoqi9HQVG+1GGeE5VCDa0mAnp1BLSaCERHxCIuKgkmYwIMumhE6AzQawyI0BqgVKha\nfVxHVcN/sU4JXTsqdCKisFdRU4J/L30Rx0sL/OoG9sjDLXn3cIVeuiAwMb/AeDxumG11qLNU42T1\nYTjdDmCvuXH5dN+l1R1OG+osNaiub0jErXaz1OH7UCnUMOijG4eA/D4URKVQQSlXectVShWUcjW0\nGj106gjoNBHQayKhVUdAr4mAVh3BsYpERBLZVfATPlz+it81RiFX4ubcuzG459VcPIwuGEzMzxMe\njxtWhwXVdRUoqy5CeU0xasyVqLfUoM5SjTprDeotNai31flP0bdXmpib6LUGpJjSYYiIgUqhgsKb\nVDcm3HIllAoVjh87AblMgaxuPWDQRyMltjNvaCQiClNujxvfbPoQK3/+wq8u1piIqaMfQ1p8Fwki\nI5IOs5oQ5fa4UVC0B5W1pQ1DRU758fndVg+Lwxxyi9EYdNFIMnXyTs/XNEOISqH2lkXqjOiS3AMm\nQ0KrekO22Rum8evVhdP4ERGFs5r6Siz8bj4OFe3xq+tz0SDccc0D0Kr1EkRGJC0m5hKpNVdh37Gd\nEEUP6q21qLNUodZcjVpzFWotVaiqK4fNYZE6TB9ymQJRESbvT6QuClpNBHRqPbTq34eJxBoTz7os\nMhERXZj2H9uJRd/9HXVW36XLZTI5xl0+CXn9x3HoCl2wmJh3EJfbCavdArvTCpvDApvDCpvdApvD\ngq83fYiqujLJYtOpIxChMwJuGVRyDeLjEr3Lpjctk65WNfyuVUcgOjIWUREm6LUGTt9HRETnxCN6\nsGLrZ1i6ZbHfkEpjhAlTRz2KLslZEkVHFBqYmLeT3WFFraUaRyv24njlQWw4/D9U1JSgxlwZ9Fi0\nKh30WgNio5IQZ0xCdGQsInVRjT9GROqiEKE1QCFvuNGRKzwSEVEw1Ftr8Z9lLyO/cLtfXfdOfTFp\nxEOI1BkliIwotDAxbwWny4nKulIUlReiqPwIisqPoLjyOGrMlXA4bR12Xo1Kh+5pfWCMMEF7ynCR\npudatR46TcOjRqmFjHNiExFRiDl8ch8WLn0JVfXlPuUCBIy87DaMGHgLr19EjZiYNxJFEZV1pSgs\nPoCjJQdQVF6IGnMlasxVsNjqghJDkqkTxl0+CQZ9NAy6aETqjGysiIgoLImiiLU7vsGSDYvg9rh8\n6vRaAyaPeAhZ6f0kio4oNF2wibkoiqiuL8f2/Rtw8PhuFJYcQP1pN6K0hwChoSdbpYVGpWv80UKj\n1kGt1EKviUSkPgpalR4ymQxZnfrDoI8K2PmJiIikYrVb8PEPr2HHwU1+dRlJWZgy6hFER8ZKEBlR\naLsgEnOny4HymmKUVZ/EgeO7cPDEblTUlARk1hO5XAGDNgoyKGHUmpA3cAySTOmIMcR5x3ITERFd\nKE6UHcF7S+ehrLrIr27YgOswNmci16AgasF5/T+jqPwI3v3mb6isK4PH4z7n4wiCDAZdFBKiU5Ac\n27nxJx2xxkRo1XoIguC9kbJvV95ISUREF6Ytu1fi09VvN6wqfQqNSoc7rnkAfbsOligyovBwXiXm\nh0/uw+bfluOnvWugVmravIS8SqlBWvxFSE/IRKeEroiLSoJRH4MIrYFjvYmIiFrgcNnx2ep3sGXP\nSr+6lLgMTBv9GOKikiSIjCi8hH1i/suBTdiw8zscOL7Lp7w1SblSrkKMMR49O1+C7KyhSDalMwEn\nIiJqg9KqIry3dB6Kyo/41eX0ugY3Dr0LKoU6+IERhaGwTcw9Hjc+XfMvbNz1fav3SYu/CJ0SMtEt\nrQ8uSu6BSF0UVxcjIiI6R78c2ISPfngVdofVp1ypUOG2YfdhYI88iSIjCk9hmZjvO/orXv9iVqu2\njY9KhsmYiBEDb+WKYkRERAHgcjuxZMMirN3xjV9dfHQKpo1+DMmx6RJERhTegpqY5+bmYt26dT5l\nt99+Oz766KNW7X+y4ii+WP8+9hb+ctZtr7rkBoy9fCKXkCciCoL2tu8UPqrqyvD+0vk4UrzPr25A\ntytw+1V/hkallSAyovAX1MRcEARMmzYNc+fO9ZZptWf/z1tZW4oPvv8HCk7mn3XbP4x5nHd9ExEF\n2bm27xRe9hzZjv8s+wfMpy28J5cpcMOQabiyzygOESVqh6APZdFqtYiPj2/19naHFbPfv7vFemOE\nCZf1GIbLLh6GGEM85Lx5k4hIEm1t3yl8eDxufPfjJ1j+06cQIfrURUfGYdroR5Ge2E2i6IjOH0FP\nzBcvXozFixcjISEBo0aNwqxZsxAREdHi9k//+w/NlndO7I6bht6F9MTMjgqViIjaoK3tO4WHOks1\nFn2/APuP7fSr69k5G3eOmA69JlKCyIjOP0FNzCdMmIDOnTsjOTkZv/32G5544gns3LkTy5Yta3Gf\n5lbnjNRFYcatL3D8OBFRiDiX9p1C36ETu/H+d/NRa67yKRcEGa4dfAeuyr6B12KiABJEURTPvlnL\nnnrqKZ8xhc1Zs2YNhgwZ4le+bds2DBw4ED///DP69+/vLa+pqfE+f3rhZJ99Ls0YgaykbI5hI6Kw\nlZn5+zd9RqNRwkjOrKPb9wMHDgQuWAooURSx+8QW/FK4ym/oikapx5DuNyDR2Fma4Nog+9JLfX7f\ntnWrRJHQhaK97Xu7e8xnzpyJSZMmnXGbtLS0ZssHDBgAuVyOgwcP+jTcLUmK6oIeyZeedTsiImq/\nYLbvFDocLhs2HvgKxyr3+9UlGDrhyu43QKfi0BWijtDuxNxkMsFkMp3Tvrt27YLb7UZS0tmX6e3Z\nORt3jX0iZG/u3LZtGwAgOztb4khaL9xiDrd4AcYcLOEW86m9xqGso9v3cPn3CgXB+owfLTmI95e+\nhIraEr+6a7JvwujBE0L2Otwa/My1Xri1q6Give170MaYFxQU4MMPP8SYMWNgMpmwZ88ePPzwwxgw\nYAAuv/zys+7/h2sfD+vGgIjofNXe9p2kJ4oiNv22HJ+t/RfcbpdPnU4dgYkjZqBnBhM0oo4WtMRc\npVJh1apV+Oc//4n6+nqkpaXh2muvxaxZs1o1XlwhVwYhSiIiaqv2tu8kLbvDik9WvYVt+9b61XVK\nyMTU0Y/AZEiQIDKiC0/QEvPU1FSsWbPmnPYdM/iOwAZDREQB0572naRVXHkM//72RZRUHveru7LP\naFx/5VQoFewYIwqWoM9jfi6uyb5R6hCIiIjOK9v2rsXiVW/C4bT5lKuVGoy/+n4M6HaFRJERXbjC\nIjGXcWw5ERFRQDhdTnyx7t/YsOt7v7okUydMG/0YEmJSJYiMiEI+MTfooqUOgYiI6LxQUVOC95bO\nw7HSQ351l2bl4tZh90Kt1EgQGREBYZCY5/QaLnUIREREYW9XwU/4cPkrsNrNPuUKuRI35/4Rg3te\nw5t1iSQW8om5Rq2VOgQiIqKw5fa48c2mD7Hy5y/86mKNiZg6+jGkxXeRIDIiOl3IJ+YygePLiYiI\nzkVNfSUWfjcfh4r2+NX1uegyTLjmAejUERJERkTNCfnEPMYQJ3UIREREYWf/sZ1Y9N3fUWf1XYlQ\nJpNj3OWTkNd/HIeuEIWYkE/MRVGUOgQiIqKw4RE9WLH1f1i65WOIosenzhhhwtRRj6BLcg+JoiOi\nMwn5xNzldkodAhERUVgwW2vxn2UvY0/hdr+67p36YtKIhxCpM0oQGRG1Rsgn5jpNpNQhEBERhbwj\nxfvx/rfzUFVf7lMuQMDIy27DiIG3cF0QohAX8om5Vq2XOgQiIqKQJYoi1v36Lb5cvxBuj8unTq81\nYNKImeiR3l+i6IioLUI+MSciIqLmWe0WfLzyNew4sMmvLiMpC1NGPYLoyFgJIiOic8HEnIiIKAwV\nlR/Bv7+dh7LqIr+6vP7jMO7ySZDLeZknCif8H0tERBRmftyzEv9d/TacLodPuUalwx3XPIC+XQdL\nFBkRtQcTcyIiojDhcNnx2ep3sGXPSr+6lLgMTBv9GOKikiSIjIgCgYk5ERFRGKi1VuIfnzyOE+VH\n/OoG97wGN+XeBZVCHfzAiChgmJgTERGFuMLyfGw6+DWcbt+hK0qFCrcNuw8De+RJFBkRBVLIJ+ac\nLpGIiC5ULrcTX234AGv3fe1XFx+dgmmjH0VybOfgB0ZEHSLkE/OE6BSpQyAiIgq6qroyvL90Po4U\n7/OrG9DtCtx+1Z+hUWkliIyIOoosUAd65513kJeXh6ioKMhkMhw9etRvm6qqKkycOBFRUVGIiorC\npEmTUFNTE6gQiIioA7B9D778wl8w76OH/JJyuUyBm3PvxuSRDzMpJzoPBSwxt1qtGDlyJObMmdPi\nNhMmTMCOHTuwbNkyfP/999i+fTsmTpwYqBCIiKgDsH0PHo/HjW83f4S3vnwWZludT51ebcCMW+Zi\nSN/REARBogiJqCMFbCjL9OnTAQDbtm1rtj4/Px/Lli3Dxo0bcdlllwEA3n77bVx55ZXYv38/unXr\nFqhQiIgogNi+B0edpRqLvl+A/cd2+tWlRHfF5ZnjkJ7I95LofBa0MeabN29GREQEBg/+fdGDnJwc\n6PV6bN68mQ03EVGYYvvefodO7MHC7+ajxlzpUy4IMowZPAHRSGcvOdEFIGiJeXFxMeLi4nzKBEFA\nfHw8iouLgxUGEREFGNv3cyeKIlZtX4KvN34Aj+jxqYvURWHKqIeRmdq7xW8riOj8csbE/KmnnsLc\nuXPPeIA1a9ZgyJAhAQ3qVOFy81BmZiaA8IkXCL+Ywy1egDEHSzjGLDW276Eju2sesru2PA95TU0N\nP+Pnqrra93e+f63Gz5w0zpiYz5w5E5MmTTrjAdLS0lp1osTERJSVlfmUiaKI0tJSJCYmtuoYREQU\nGGzfiYhCzxkTc5PJBJPJFJATDR48GPX19di8ebN3HOLmzZthNpuRk5MTkHMQEVHrsH0nIgo9ARtj\nXlxcjOLiYuzfvx8AsHv3blRWViI9PR3R0dHo0aMHRo4ciXvuuQfvvPMORFHEPffcg7Fjx3q/Lmli\nNBoDFRYREbUT23ciouAQRFEUA3Gg2bNn49lnn204qCBAFEUIgoD333/f+3VpdXU1HnjgAXz11VcA\ngOuuuw6vvfYaDAZDIEIgIqIOwPadiCg4ApaYExERERHRuQvYyp9ERERn8s477yAvLw9RUVGQyWQ4\nevSo3zZVVVWYOHEioqKiEBUVhUmTJnFWiNPk5uZCJpP5/EyYMEHqsELSG2+8gYyMDGi1WmRnZ2PD\nhg1ShxTyZs+e7ff5Sk5OljqskLNu3TqMGzcOqampkMlkWLRokd82s2fPRkpKCnQ6HfLy8rBnz56z\nHpeJORERBYXVasXIkSMxZ86cFreZMGECduzYgWXLluH777/H9u3bMXHixCBGGfoEQcC0adO8Y/+L\ni4vx9ttvSx1WyPnkk08wY8YMPPXUU9ixYwdycnIwatQoHDt2TOrQQl5WVpbP52vXrl1ShxRyzGYz\n+vTpg1deeQVardZvAbAXX3wRCxYswGuvvYatW7ciPj4e11xzDerr6894XA5lISKioNq2bRsGDhyI\nI0eOoFOnTt7y/Px89OzZExs3bvTO7rJx40ZceeWV2Lt3L1cQbZSXl4devXrh1VdflTqUkHbZZZeh\nX79+Pn+0dOvWDTfffPNZ5/C/kM2ePRv/+9//mIy3QWRkJF5//XXvPTeiKCI5ORkPPvggnnjiCQCA\nzWZDfHw85s+fj7vvvrvFY7HHnIiIQsLmzZsRERHhTcoBICcnB3q9Hps3b5YwstCzePFixMXFoVev\nXnj00UfP2gt3oXE4HNi+fTuGDx/uUz58+HBs2rRJoqjCR0FBAVJSUtClSxeMHz8ehw8fljqksHL4\n8GGUlJT4fP40Gg2GDBly1s9fwKZLJCIiao/i4mLExcX5lAmCgPj4eBQXF0sUVeiZMGECOnfujOTk\nZPz222944oknsHPnTixbtkzq0EJGeXk53G43EhISfMr5WTq7QYMGYdGiRcjKykJJSQmef/555OTk\nYPfu3YiJiZE6vLDQ9Blr7vNXVFR0xn3ZY05EROfsqaee8rtR7PSfdevWSR1myGvL+/jHP/4R11xz\nDXr27InbbrsN//3vf7FixQr88ssvEr8KOh+MHDkSN998M3r16oWrrroK3377LTweT7M3N1LbnT4W\n/XTsMScionM2c+ZM77jKlqSlpbXqWImJiSgrK/MpE0URpaWlSExMPOcYw0F73scBAwZALpfj4MGD\n6N+/f0eEF3ZiY2Mhl8tRUlLiU15SUoKkpCSJogpPOp0OPXv2xMGDB6UOJWw0tVclJSVITU31lpeU\nlJy1LWNiTkRE58xkMsFkMgXkWIMHD0Z9fT02b97sHWe+efNmmM1m5OTkBOQcoao97+OuXbvgdruZ\ncJ5CpVLhkksuwfLly3HTTTd5y1esWIFbbrlFwsjCj81mQ35+PoYNGyZ1KGEjIyMDiYmJWL58OS65\n5BIADe/jhg0bMH/+/DPuy8SciIiComnqtf379wMAdu/ejcrKSqSnpyM6Oho9evTAyJEjcc899+Cd\nd96BKIq45557MHbsWGRmZkocfWgoKCjAhx9+iDFjxsBkMmHPnj14+OGHMWDAAFx++eVShxdSHnro\nIUycOBEDBw5ETk4O3nrrLRQXF+Pee++VOrSQ9sgjj2DcuHFIS0tDaWkpnnvuOVitVkyePFnq0EKK\n2WzGgQMHAAAejweFhYXYsWMHTCYT0tLSMGPGDMydOxdZWVnIzMzE888/j8jIyLOvOSASEREFwaxZ\ns5Gx/gYAAB7KSURBVERBEERBEESZTOZ9XLRokXebqqoq8c477xQNBoNoMBjEiRMnijU1NRJGHVqO\nHTsmDh06VDSZTKJarRa7du0qzpgxQ6yqqpI6tJD0xhtviJ07dxbVarWYnZ0trl+/XuqQQt7tt98u\nJicniyqVSkxJSRFvvvlmMT8/X+qwQs7q1av92jNBEMSpU6d6t5k9e7aYlJQkajQaMTc3V9y9e/dZ\nj8t5zImIiIiIQgBnZSEiIiIiCgFMzImIiIiIQgATcyIiIiKiEMDEnIiIiIgoBDAxJyIiIiIKAUzM\niYiIiIhCABNzIiIiIqIQwMSciIiIiCgEMDEnIiIiIgoBTMyJiIiIiEIAE3MiIiIiohDAxJyIiIiI\nKAQwMSciIiIiCgFMzImIiIiIQgATcyIiIiKiEMDEnIiIiIgoBDAxJyIiIiIKAUzMiYiIiIhCABNz\nIiIiIqIQwMSciIiIiCgEMDEnIiIiIgoBTMyJiIiIiEIAE3MiIiIiohDAxJyIiIgkc+TIEchkMkyd\nOlXqUIgkx8SciIiIJCcIgtQhnFXTHxF5eXlSh0LnKYXUARAREdGFKzU1FXv37oXRaJQ6lLNq+uMh\nHP6IoPDExJyIiIgko1Ao0K1bN6nDaBVRFKUOgc5zHMpCREREkmlujPmUKVMgk8mwdu1afPbZZxg4\ncCD0ej1MJhPGjx+PoqIiv+Pk5uZCJpPh8OHDmD9/Prp37w6tVotOnTrhkUceQX19vd8+ZxqWMnv2\nbMhkMqxbtw4AsHDhQnTp0gUAsGbNGshkMu/PnDlzAvFWELHHnIiIiKTX3PCQN954A1999RWuu+46\n5OXlYcuWLfjkk0/w66+/YseOHVCpVH77TJ8+HRs3bsRtt90Go9GIpUuXYsGCBdiwYQPWrVvnt09r\nh6X0798f06dPxyuvvILOnTtjypQp3rrc3Nw2vVailjAxJyIiopC0bNkybNu2DT179vSW3XHHHfj4\n44+xZMkS3HLLLX77bNmyBb/++itSU1MBAH/9619x0003YcmSJViwYAH+8pe/nFMsffv2xYwZM7yJ\n+TPPPHNuL4roDDiUhYiIiELSgw8+6JOUA8Af//hHAMDWrVub3Wf69OnepBxoGK7y4osvQhAEvPfe\ne+2Kh2PMqaMxMSciIqKQlJ2d7VfWlHRXVVU1u8/QoUP9yrp164b4+HgcOnQIZrM5sEESBRATcyIi\nIgpJUVFRfmUKRcMoXLfb3ew+CQkJZyyvra0NUHREgcfEnIiIiM4bJSUlZyw3GAw+5S6Xq9ntq6ur\nAxsYUSswMSciIqLzxpo1a/zK9u3bh5KSEnTt2hV6vd5bHh0djWPHjjV7nObGsMvlcgAt99YTtRcT\ncyIiIjpvvPLKKz7JttvtxuOPPw4APnOl4/+3d+fBWdV5vsc/JzsQspCFrIQAQZawJmxxAx0UN9oF\nl+Y2dNlzW5261Q5ucy81VklfbWvscbw6tl5ba9ph2u5RW6/TTtuyaOOwRSRhDwECISEhJCELDxCy\n59w/kMBJIMuTPM85z5P3qwrJ7/uc5ZPjKeqbX84iaf78+SotLdWXX35pqb/33nvKzc3t9ijF6Oho\nSbpmMw8MFI9LBAAAfuP666/XzJkz9dBDDykiIkJffvmlDhw4oLlz5+qZZ56xLPvcc89p/fr1uu++\n+/TQQw8pLi5O+fn5ys/P1913360//elPluXDw8OVk5Oj7du3a+nSpZo1a5aCg4N1880368Ybb/Tm\ntwk/xYw5AABwFMMw+vzin67rvf7661q9erU2bdqkN954Q2fOnNHTTz+tr7/+WsHBwZblFy5cqM8/\n/1wzZ87UJ598ovfff19RUVHasWOHsrKyrprht7/9re69917l5ubqF7/4hV544QVt2rTJ7e8VuJJh\n8lBOAADg4xYuXKjNmzerpKREY8aMsTsO4BZmzAEAgF9wZ5YdcBIacwAA4Be4CAC+jsYcAAD4PHev\nSwechGvMAQBe43K57I4AAF4RGRnZ73WYMQcAAAAcgMYcAAAAcABeMAQAsIU7v+YdqvLy8iRJ2dnZ\nNifxPRw793Dc3DPQy/WYMQcAAAAcgMYcAAAAcAAacwAAAMABaMwBAAAAB6AxBwAAAByAxhwAAABw\nABpzAADglxqbL+jMhRp1mB12RwH6hOeYAwAAv7N13zp9vOkdSVJiZLqyZs9WYCBtD5yNGXMAAOBX\n9h3b0dmUS9Ip13Ft3vtnGxMBfcOPjgAAwK/85s+/7Fb7bMtvVH/utK6fdrviohIVEBBoQzKgZ4Zp\nmqbdIQAAQ8OVr6suKiqyMQn8Vd7xjTpYsaPX5e6c/qhiRyZ7IRGGkoyMjM6vIyMj+70+l7IAAAC/\ncK6pvk9NuSTtKt3k4TRA/3EpCwDAFtnZ2XZH8Bl5eXmSOGa9+XLHR31ettJVoqysLBmG4cFEvotz\nzj1X/lbQHcyYAwAAn1dRU6oNO//Qr3XON571UBrAPTTmAADA53286R21t7dd8/P5U27tVvsq71NP\nRgL6jcYcAAD4tL1Hc1VcUXjNz3Mm3K3li3+mKWOzLPVNuz9XRU2Jh9MBfcc15gAAwKdt3bfOMk6N\nH6+nHvoHHSzZpYoTVYodmSRJmjZurg6W5FuW3Xdsh5Jix3orKtAjZswBAIDPKqsu1uGyvZbaknkP\nKygwWNPHz+tsyiUpJ/M2jUuabFn2aPkBr+QE+oLGHAAA+KSmlkb904fPdqtPTpt11eUNw9B/W/yk\npXakfL8uNJ/3SD6gv2jMAQCATyquOKgOs8NSi4tMVFBg8DXXiY1MUHR4rKX2/hf/6JF8QH/RmAMA\nAJ90+sypbrUJKZk9rmMYhjJSp1lqR8r3q+5s9aBmA9xBYw4AAHzSodI93Wp3zv9hr+vdmnW/ZWya\nHSroclMoYAcacwAA4HPqz9WooCTPUnv0zr9TZPioXtdNjEnVrVn3Wmr7jn07qPkAd/C4RACALS69\n8ht9xzG7bHfpJsvYkCFXdaPyXFc/Rl2PndE03DI+fGKv/rJlvSKGxQxuUB/HOdc/GRkZA1qfGXMA\nAOBzTtYfs4wzU3IUHhrZ5/Vjw5MUYFjboNLaQ4OSDXAXM+YAAFtkZ2fbHcFnXJq15Jhd1Nbeqt/l\n1lhqj9zxmEYO796Y93TsDtVt156i7Z3jRp3hGH+Pc849LpdrQOszYw4AAHxKZV2Z2jvaOsdR4TFX\nbcp70/VG0bKqowPOBgwEjTkAAPAp1fUVlnFS7Fi3thMflWR55nlD0zk1NJ4dSDRgQGjMAQCAT9mw\n8xPLOC4q0a3tBAQEdlv3WEWh27mAgaIxBwAAPqP+XI0qakosNXcbc+nirPmVvsr7f25vCxgoGnMA\nAOAziisOdqvFRrrfmI9LmmIZl1QeVll1sdvbAwaCxhwAAPiMyrrybrXxyVOusmTf3DjjDiXFpFlq\nhaW73N4eMBA05gAAwGdU1Vsb81tm/0ChwWFuby8oMFjXT19iqZ3g6SywCY05AADwGVVdZsynj58/\n4G2mjba+rbG0qmjA2wTcQWMOAAB8QkPjWZ2qPWGpjY5OHvB2k2LTLI9NdJ2v1ZnztQPeLtBfNOYA\nAMAnvPXZGss4fFikRgyLGPB2gwKDlRI3zlI7waw5bBBkdwAAwNB06ZXf6LuhfMzON7tUftr6tJQR\nwZF9Pia9LRdmWBv8HXu2qKWeNmkon3PuyMjI6H2hHjBjDgAAHK/m3MlutesSswdt+7Hh1ueZl9Ud\nkWmag7Z9oC/4URAAYIvs7MFrqvzdpVnLoXzM6vNOSIcvj1Pix+mB21fIMIwe1+vrsRtTn6StRX/s\nHJ+5cFoj4gI0ZWyW+6F9GOece1wu14DWZ8YcAAA4Xq3rlGU8Z9LCXpvy/oiLStSYLk9n2X5gw6Bt\nH+gLGnMAAOB4NWcqLePYyIRB3b5hGPrBDSsttcKS3WptaxnU/QA9oTEHAACOZpqmKro8JjEuKnHQ\n9zMhOVNR4TGd49b2Fh0/dbiHNYDBRWMOAAAc7eyFep1vvHztbnBQiOKjknpYwz2GYWhi6nRLjccm\nwptozAEAgKOVVR2zjJNi0hQQEOiRfaXGj7eMu75pFPAkGnMAAOBYpmnqL7v/aKmljp7gsf3Fd3mT\naGU9jTm8h8YcAAA41lf5n+lo+QFLbXzSFI/tL2FUimV8qvaE2tvbPLY/4Eo05gAAwLHyD/2XZRwc\nGKLrxszw2P6iwmM1cnhU57iltUmlVUc9tj/gSjTmAADAkUzTVI3L+pjEe296VOHDIjy2T8MwNDFl\nmqVWVL7PY/sDrkRjDgAAHOl8o0stbc2W2g3Tlnh8vxldnsxyuIzGHN4RZHcAAMDQdOmV3+i7oXbM\nTp+z3ngZPTxe+fn5bm2rP8euuck6Lqk4rJ07dw7qm0Z9xVA75wYqIyOj94V6wIw5AABwpHNNZyzj\n8LBor+w3PDRKwYGhneO2jlY1tpzzyr4xtDFjDgCwRXZ2tt0RfMalWcuhdsxqvyu2jCekXdfvY+Du\nsfvmaIrKqi8/Pz0xLU4ZXa4992dD9ZwbKJfL1ftCPWDGHAAAOFKNq8oyjolM8Nq+47q8WbSSFw3B\nC2jMAQCAI1XUlFjGsZGjvbbvxJgxlnFhyS6v7RtDF405AABwnFO1JyyXkkjS6C4v//GkzHTrJRwH\nS3fJ1VDntf1jaKIxBwAAjrO/+DvLeELyVMVEeG/GPCl2rOKjkzvHHR3t2nv0W6/tH0MTjTkAAHCU\nDrNDu49stdSyrrvJqxkMw9CcSQsttVO1J7yaAUMPjTkAAHCUYycP6mSX68snp832eo6k2DTLuKqe\nG0DhWTTmAADAUYrK9lvGM8bP16iIOK/nGH3FpSySVFlbJtM0vZ4DQweNOQAAcJSjJw9Yxpnj5tqS\nIyYyQSHBYZ3j840uVdaV2ZIFQwONOQAAcIzWtlaVVB6x1CakTLUlS2BAoCYkW/e9bf86W7JgaKAx\nBwAAjlFWfVRt7a2d4+jwWI0aGW9bnsz0OZZx7oGv1NzSaFMa+DsacwAA4Bhd37CZnjRJhmHYlEaa\nN+UWRYXHdI5b21t0sJSXDcEzguwOAAAYmvLy8uyO4HOGwjErKN1jGbdeMAfl+x7INhIjJujM+drO\n8Xd7t6rdFTrgTL5gKJxzgykjI2NA6zNjDgAAHONc0xnLODw0yqYkl40aYX2x0dlG3gAKz2DGHABg\ni+zs7N4XgqTLs5b+fszaO9r1+29fsdRmT5+r68bMcHubg3HsYisjtK3o885xqy74/f+LoXLODTaX\nyzWg9ZkxBwAAjnCodLflxs8AI0AJMak2JrooLirRMj7tOqWOjnab0sCf0ZgDAABH6PpmzbSEiYoc\nMcqmNJeNCBupEcMiOsft7W2qP1djYyL4KxpzAADgCHVnT1vGdr1Y6Grio5Is48Nle21KAn9GYw4A\nAByh9myVZTxqZJxNSbrr2pj/5/YPbEoCf0ZjDgAAbHfmfK2KyvZbaqMinNOYpyVMtIwbGs+qsfmC\nTWngr2jMAQCA7b7Y/ju1tDV3joODQpQYk2ZjIqu5kxd1q1V3uSYeGCgacwAAYLuub9NcOPMehYUM\nsylNdyHBoZo+fp6ldqzioE1p4K9ozAEAgK2aWhp17oL1xUJL5j1iU5pr6zqDv23fepmmaVMa+CMa\ncwAAYKtdR7ZYxnFRSQoOCrYpzbVlT7rZMj7tOtXthlVgIGjMAQCArb7O+8wyjotMsClJz0ZHJ2tC\n8lRL7Wh5gU1p4I+C7A4AABiaLr3yG33nj8esta1ZNa5KS22YET3o3+tgbW94gPWFR5vz1ymoMXJQ\ntu1E/njOeVJGRsaA1mfGHAAA2Kb6XLlMWa/TnpQ4x6Y0vUsdZX1s4skzx9TQ7LIpDfwNM+YAAFtk\nZ2fbHcFnXJq19MdjVrBus2W8YOpizZs7f9C2P9jHzjRN5ZWtV1Vd+ffjDjUH1+nm7FsHZftO4c/n\nnCe5XAP7IY0ZcwAAYIsLTee192iupTZ74g02pekbwzB00/Q7LbUj5fuvsTTQPzTmAADAFoWlu9TW\n3to5jokYrYzUaTYm6ptJabMs4+MVh9Ta1nqNpYG+ozEHAAC2OFV7wjKeMWG+AgzntyaxkQmKDo/t\nHLe2t6ik8rCNieAvnH/2AwAAv1RZV2YZd32Bj1MZhtFtZn/7gQ02pYE/oTEHAABeZ5qmyquLLbWE\nUSk2pem/jJRMyzj/8ObOG0IBd9GYAwAArztVW6q6c6c7x0GBwUqIGWNjov7JSOl+LXxuwVc2JIE/\noTEHAABet+/YDsv4utQZCg0OsylN/42KiO9WO1lz3IYk8Cc05gAAwKs6OtqVf3iLpTZt/Dyb0rjv\nb+59wTKuOF0i0zSvsTTQOxpzAADgVYWlu1VVf/l6bMMIUGa6c9/2eS0TU6crOCikc3yu0aWjJwts\nTARfR2MOAAC8qrB0l2WcNfFGRYyIsimN+wIDAjUxZbql9sct/2pPGPgFw+R3LgAAL7nyddVFRUU2\nJoGdPt/9a525cPnGz0WTH1LqqIk2JnLf8dMHtOXIf1hqj8x7ViFBvnO9PAZPRkZG59eRkZH9Xp8Z\ncwAA4DWt7S2WplySRkf4ztNYuhobO7VbraH5rA1J4A+C7A4AABiasrOz7Y7gM/Ly8iT5xzHbsvfP\nlnF8VJJy5t/gsf1549h9e2Kaisr3d46T00Zrytgsj+3PG/zpnPOmK38r6A5mzAEAgFd0dLTrD9+8\na6mlxI+zKc3giR4Zaxl/tuV9m5LA19GYAwAAj2tpbdaqNx/oVp898UYb0gyuro15VV25mlsabUoD\nX0ZjDgAAPC63YGO32vikKZrug88v72rauO7fw8EuT54B+oLGHAAAeNzVXld/w/Q7bEgy+MaMnqBh\nIcMttS9yf6/2jnabEsFX0ZgDAACPam9vs7xQ6JLMdP+5sXDlkqct4+r6k9px8Gub0sBX0ZgDAACP\nqqwrV3t7m6X2swdeVGjIMJsSDb4pY7M0Y8ICS+2zLe9bntYC9IbGHAAAeNR/7flPy3jq2GxlpEyz\nKY1nGIah+2/6awUHhnTWmlsa9ZsvfsmNoOgzGnMAAOAxxRWH9G2XSzrSE6+zKY1nRY+M1V05yy21\nhqZz2l203aZE8DU05gAAwGO+K/yLZRwcGKL5UxfblMbzFs36gTLT51hqh07stikNfA2NOQAA8AhX\nQ53yj2yx1P5qzgOKGBFlUyLPMwxDi+dYn9deXFFoUxr4GhpzAADgEZ98857l+urhYSO1OPt+GxN5\nR0rceAUFBneOz5yv1Z+2/87GRPAVhmmapt0hAABDg8vl6vy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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from nonlinear_plots import plot_transfer_func\n", - "\n", - "def g(x):\n", - " return 2*x + 1\n", - "\n", - "with book_format.figsize(y=5):\n", - " plot_transfer_func(data, g, lims=(-10, 10), num_bins=300)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The plot labeled 'input' is the histogram of the original data. This is passed through the transfer function $f(x)=2x+1$ which is displayed in the chart to the upper right. The red lines shows how one value, $x=0$ is passed through the function. Each value from input is passed through in the same way to the output function on the left. The output looks like a Gaussian, and is in fact a Gaussian. We can see that it is altered -the variance in the output is larger than the variance in the input, and the mean has been shifted from 0 to 1, which is what we would expect given the transfer function $f(x)=2x+1$ The $2x$ affects the variance, and the $+1$ shifts the mean.\n", - "\n", - "Now let's look at a nonlinear function and see how it affects the probability distribution." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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8VZ/FcRzkUgfIpQ5tbtfSLyljDDq9trEgr0WdusbseVMxbrFOUwutth5qnRqs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\niice/iOcHNSKZrMFtpwN4MRHIiIiuo3fDm9AVa1WVgv2j5A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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from nonlinear_plots import plot_transfer_func\n", - "\n", - "def g(x):\n", - " return (np.cos(4*(x/2 + 0.7)))*np.sin(0.3*x) - 1.6*x\n", - "\n", - "plot_transfer_func(data, g, lims=(-4, 4), num_bins=300)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This result may be somewhat surprising to you. The transfer function looks \"fairly\" linear - it is pretty close to a straight line, but the probability distribution of the output is completely different from a Gaussian. Recall the equations for multiplying two univariate Gaussians:\n", - "$$\\begin{aligned}\n", - "\\mu =\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\\mbox{, } \n", - "\\sigma = \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\n", - "\\end{aligned}$$\n", - "\n", - "These equations do not hold for non-Gaussians, and certainly do not hold for the probability distribution shown in the 'output' chart above. \n", - "\n", - "Think of what this implies for the Kalman filter algorithm of the previous chapter. All of the equations assume that a Gaussian passed through the process function results in another Gaussian. If this is not true then all of the assumptions and guarantees of the Kalman filter do not hold. Let's look at what happens when we pass the output back through the function again, simulating the next step time step of the Kalman filter." + "Consider the function $f(x)=x^2−2x$, which we have plotted below." ] }, { @@ -450,164 +303,12 @@ "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "image/png": 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+Brr6GuiMNY1LytegzliDOmMt9EYtDKb2jwPvKLFQihCv3lBIlJBJGopweWMx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\n5GAssomIiIiIHOz/A20f7l7OvBszAAAAAElFTkSuQmCC\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "y = g(data)\n", - "plot_transfer_func(y, g, lims=(-4, 4), num_bins=300)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As you can see the probability function is further distorted from the original Gaussian. However, the graph is still somewhat symmetric around $0$, let's see what the mean is." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "input mean, variance: 0.0006, 0.9957\n", - "output mean, variance: -0.0284, 2.2332\n" - ] - } - ], - "source": [ - "print('input mean, variance: %.4f, %.4f'% (np.average(data), np.std(data)**2))\n", - "print('output mean, variance: %.4f, %.4f'% (np.average(y), np.std(y)**2))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's compare that to the linear function that passes through (-2,3) and (2,-3), which is very close to the nonlinear function we have plotted. Using the equation of a line we have\n", - "$$m=\\frac{-3-3}{2-(-2)}=-1.5$$" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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k35ZV/93vfocvv/wShw8fRmRkpGM7LbvreVptVmiMDdAY6qAx1qPZUA+tqQkm\nqw4mq6Hfr+/FE0LAb3+IIBJIEeIThRBVFEReEgj4IvB5XnQjIIPGUF9WnfK757O0mhzLthutui7L\nqWSBiA9JRaRfHHg0/oaQbvUmv/dLJfu5557Dl19+iezsbIwZM6bDPkrCg4vdboPRqofRosXp64fQ\nqK+Gydr9YEpX48BB4CVyVMTbHkLHT5FABqlQDqnQG1KRHBKhHBKBNw3aJG4xlCvZlN8HF5u9FVfr\nzuF8xTFojPVdlpOJFIgNvgvRgRMh8KLZpgjpilsr2atWrcLWrVuRnZ2NmJgYp/03J+HBcvM5ebJt\nMGBycrKbI+m5/ozZzuwwW4wwmg0wWfQ3fhpgMOthMuthMOtwpaIQF68X9HlmFFeRS5RQePtCKfOF\nj7cvFDJf+CmDEBEYDX9VyB11VaHfi4ExGGMejHmuJwZzfvf036P+js/O7Ci8mof9+dtxpeJ8l+Uk\nIhmmjr8HMycuhFLmOyCx3QmKrW8otr7rTZ5zaZ/s3/72t/j000+xfft2KJVKVFdXAwDkcjlkMpkr\nL0XciMfxbgx0lAHw77KcztiC4rIzuFR2Fs26BpisRpgtbY/255ZWc7/GqjVqoDVqUFF31WmfRChF\ngG8YfOX+UMn94ato+xmsHgG1IpC6pxByE8rvgxuP42FcVArGRaWgtLoY+/O2o+DKMTBm71DOaNZj\n38mvkX1qB1LGzkJGYqabIiZk8HNpJfudd94Bx3HIyMjosH3dunVYs2aNKy9FBgFviQKJY6Yhccy0\nLsvY7DaYb1S4806dhKXVBIGC4VzJCbQYmmC2mGCyGJyWFHYFo8WA0upilFYXO+2TCKUI8R/ZNoPK\njRlTREIpxEJJ22uhFJXN5RDwRahpDIL4xj6hQEyVczIkUX4fOiKCxuDRhf8Pdc1VyM7fgeOFWU5T\nwtpsrTh2fh+Ond+HMFU04sOmgLEkym+E9IJLK9l2u737QoTchM/jt61EKfKGj7StVTw5ORlzk+/r\nUK7VZm1rAXc82rqomK0mGM16tBia0aJrRLO+oW3WE10jdAZNn7urGC2G236lerPdZzY5nnMcr0NF\nvL3yLRbJIBZKoJT5IjV+DlRyvz7FRYi7UH4fevx9gvHL2U9ifuoy5BTsQs6ZXdCbtE7lypsuobzp\nEi7WHUdGUibGR02mQZKE9EC/TuFHiKt48QXwkgggkyh6fIzN1ooWQ7Oj0t22qE89yutKUFpzCUaz\n6wdwMmYDKhGEAAAgAElEQVSH0ayH0axHUxdlDhXsxPzUZQhWh0Mpa+snLhZKXB4LIYT0hFyqxIIp\nyzAn+edl2xtaapzKXau+iH/t/Cv8fUKQPmkxJselQ0iDJAnpkksr2YcOHcLf/vY35Ofno7KyEps2\nbcKKFStceQlCeozP94JK7tdpq7Gd2dHUUodGbS0aW+rQqK1Dk7YOdU2VqKi/BpOl/6Yu1Ju0+OrA\n+x22CQViKGW+kEuUkEnkkEkU8BYr2n5K5PCWKCEReTsW/BELpRAJxTTHOBkwlN+HPqFAhBkJCzB1\n/N0ouHwUWXnbcb32slO5uuZKfJn9LnYd+xwzEhZg+oT5vWoAIWS4cGklW6/XY8KECVixYgWWL19O\nfbeIx+JxPKiVgVArA532McbQ2FKL6sayG91SjDCa9R26qZgsBtTW18BqM4PnxTm2WVv7ttS9xWpC\nXXMl6pore3wMBw4ioaStW8pNlW9viQIhfhEI849CWEAUZGJ5n2Ii5GaU34cPPo+PxDHTMCl6Ki5X\nnMM3WZtR0XTFqZzOqMGuY59j38lvkBqfgfRJSzrNqYQMVy6tZM+fPx/z588HADzyyCOuPDUhA4bj\nuC4r4DfrbJohm63VUTE3WQwwWgwwmQ0wWvQ4VLAL16svuWxaQwbmqNyj67UmEKAKxZJpKyAVeaPZ\nUAchXwxLq5m+5iW9Qvl9+OE4DtFh45ERtwxN+lrUmC8h72IObPbWDuUsrWYcKtiFnDM/YFJ0GmYn\nZmJE4Gg3RU2I56A+2YS4EJ/vBZlE0elXpyljZ6GqoQwnirJQr6mGRt+IFn0TNPpG2GytnZzNNWqb\nKvDBd6902PbVyTch4AshEcscA08dz8Vtr3k8HgJUoYiPTIZQQBVyQoYzlSwAc2cuwKK0h3Hw9Hf4\n6exep251jNmRX3wY+cWH2yrnSZmIjUikbz3IsEWVbEIGULA6HEumdezHyhiDwaxDi74JOmML9MYW\n6E1a6IyaG6/bnhvN+raW8Rut43c6x7jVZoFVb0GLvqshmj9LipkBlbcfxKIbs6aIZJCKZBALpZCK\n5fCWKCATe9OMA4QMcT7eaiyZ9gjmpTyAI+d+xIFT30Kjb3Qqd6n8LC6Vn0WwegQykpYiccw0ePEF\nboiYEPfpl2XVgbYFCt566y0sX768w3ZadpcQ17AzO6ytZlhtZlhsZsfzEyV7oDM3uyUmkZcEYoEU\nIoEUYoEMMqECKlkgVLJA+Ej9wOcNj7/rh/Ky6gDld/Izm92Ga/Vty7Y3G+q6LCcVyhEbcheiAydR\nVzUyqPUmvw+POx4hQxCP40EkkEAk6Dj9X6hqNKo111CtKYXerAFjdlhsJphbTbA4HkbYmevnPTa3\nGmFuNQLGBqd9XjwBIvzi4OcdAqGXGEIvEYR8MQReIgj5Igi8xPDiCeirZUIGET6Pj1EBCYjyn4CK\npis4X3EUNS2lTuUMFi3yru3DmbIcjAlKRGzwZEhFNCibDG1urWR76rr0t+psgJuno5j7n2fHm9Lp\n1vaYk5KSYLGaYDDrYDDpYTDrYLzxPOfMLpTVOs8kcKda7VZcqS3AldqCLsvwOB7szI6xEZPwb7Of\nhFoR6OGfc+dubtEdrjzt38vTf488Ob6expaCFGTiVyitvoSs/O04ffmo07LtVpsZ5yuO4kJVLpLH\nzsTsxEwEq8P7PTZ3oNj6xpNjA3qX310+hV/7V4R2ux2lpaU4ffo01Go1wsP7/p+IEOJaHNc2/Z9I\nKIFK7t9hX2p8BvQmLSrrr900faEBRrMBJov+xk8DDGY9TGaDo/+4Kxb3aW9dv1B6Cus3/TsWpC5D\nfW0TRF5iSK9xkIhkUEhV8FUEUIv3AKP8TnoqIigaKxf8HvWaamTnf4tjhfucpje12VtxvHA/jhfu\nR3xkMmYnZWJ0aDz9vyZDiksr2bm5uZg9ezaAtpv42rVrsXbtWjzyyCP43//9X1deihDSj2RiOaLD\nxvfqGJutFTpTC3SGFuiMGmgNzahpKkdF3TWUVhdDa+x96+6uY587nucUb3c8D1aPQOKY6Qj1i0SI\nXyRUcj+6Ofczyu+kt/yUQXgg/QnMT/0Vcs7sxqGCndAbW5zKnb92EuevnUREYDRmJy1Fwqi7aBA1\nGRJcWsmeNWsW7HbX9/MkhHg+Pt8LSpkvlDJfp33WVisKLh9Bed1VmCx6Ryt4+4wptU0VvbpWVcN1\n7Dz6f47XKm8/zJx0L8aNTIa/TwhVuPsB5XfSV94SBebf9W/ISMzE8aIsZOfvQL2m2qlcac0lbNq1\nEX7KIKRPWoy74jJo+lAyqNHAR0JIvxN4CZA8diaSx87sdP+pSz/ho91/7/NgzCZdPbbnbML2nE2Q\nieUI9otAgE8IAlQhCFSFIWZEAk0fRoibCQUiTJ8wH1PHzcOZK8exP28bSmucZ6Gp11Rj64H3sev4\nFkyfMB/TJyyAXDr0ZukhQ5/LK9lvv/02XnvtNVRXVyM+Ph5vvPEGpk2b5urLEEKGkEnRUzE6NB6X\nys+h1WaFxWpua+U261FafhWWVjMkMiG0hmZUNlx3Gkx1M71Ji8vl53C5/FyH7ffP/A2iw8YhQBVK\nFe4+ovxOXIHH42NidBoSRk/BlcpC7M/bhvNXTzqV0xtb8MPxL7A/bxvuistA+qTF8PcJdkPEhPSN\nSyvZX3zxBVavXo133nkH06ZNw1tvvYX58+ejsLCQBsYQQm5LLvVB4hjnCtutI82btHU4d/UkKutL\nUVF/FddrLsNut3V7/q8Pfui0bXzUZCyZtgIBqtA7jH7oo/xOXI3jOIwOjcfo0HhUNZQhO387ci8c\ndFq23dpqweEzu/HT2T1IGJWKjKRMRASNcVPUhPQcz5Une/3117Fy5Uo89thjiImJwT/+8Q8EBwfj\nnXfeceVlCCHDmEruj+kT5uPfZj+J3/3yr3ji3j/1+VxnS07g5Y9/i++PfAqtwT0L+AwWlN9JfwpW\nh+PBuc9i3cr3MSfpPkiEUqcyjNlx+vIR/P2L/4d/fPUnnL96Ev20nh4hLuGySrbFYkF+fj7mzZvX\nYfu8efNw5MgRV12GEEI62Hti652fI/cr/Pcnz6KxpesV64Yzyu9koCi9fbF42nKse/RDZE5fCR9v\ndaflLlecx3vfvoxvT72HyzUFaLVZBzhSQrrnsu4i9fX1sNlsCAwM7LA9ICAA1dXOo4gJIcQVbKz7\nriI9YTBpcfH6aUwZN9cl5xtK+pTfPWyGF89c1uJnnhyfO2KTAJh949GdevXn+HT5lwh78N8xdfzd\nkIhk/RwdIT3j1tlFbs3BubnOAx8AICWl8//iA12+vW+op8Rz+/LJyM096YjZ/fH0pHzH49wfT8/K\nd1WX8OT4b/698IR4bl8++bbl/+tXGzvd/uwbmZ1u/+fq7Z1u/483lkLXYHH6P9OX+Jup5wkhA8av\nwYBFHx/GXyIk2H1sC6IDExEbMhkykcLdoQFAp/dhT0Gx9V50dHSPy7qsku3n5wc+n4+ampoO22tq\nahAcTKOBCSGe7e7xy6GSBXZfcBii/E48nV+DAQBgtVlQWHkMRVUnMNIvHvGhU6CSBbg5OjJcccyF\nowZSU1ORkJCA9957z7FtzJgxeOCBB/Df//3fADqu+a5UDo55L2+d3WAwoJj732CLFxj6MVtbLdh9\nbAv25X3TZZkAnxBEh0/AtPF3I9gvAjzOpeO/AQzOPNedXud3H58Bj5EMb//xxpJOt8dFJGJ20lJE\nh40b0IWqPDnfUmx915v87tLuIr/73e/w61//GpMnT0ZaWhreffddVFdX48knn3TlZQghw1xx2Vmc\nuvQTtIamtpUjLQaYLEbUNVfe9jiO4+G/lv0dYqFkgCIdOnqd3z1s1gdPv3F7cnweG9stFWa5RAmt\nUeNUrLA0H4Wl+QgPGIWMpKVIGD0FfFq2nQwAl1ayf/nLX6KhoQEvv/wyqqqqMH78eOzatYvmUCWE\n9Jmd2WG06HCtuhiNLbXIObMbVyrO9+lcmdMfoQp2H1F+J55u7aPvI7foALLyd3T6B3dZ7RVs3v03\nqBWBSE9sW7ZdJBC7IVIyXLh84ONTTz2Fp556ytWnJYQMYbVNlbhWfRHNugZodI3Q6BvQrGtEs64e\nWn0zGBhwh2NgRoeNQ/qkxa4JeJii/E48mdBLhKnj78aU+Dk4W5KL/fnbcK3qolO5hpYafHXgA+w6\n1rZs+4yEBZBLqXsTcT23zi5CCBl+GGMwmvXQ6BtR1XAdB059h2vVzjdCV5o67m4sSnuoX69BCPEM\nPB4fCaNTkTA6FSWVRdiXtw3nSk44lTOYtNhz4ktk5W3H5Nh0pCcuQYAqxA0Rk6HKpZXs999/H59/\n/jlOnTqFlpYWXLt2DSNGjHDlJQghg0SzrgHHzu9DTVMFdAYNtEYNdEYNdMaWHi2D3h1/ZTAykpdC\nrQiEWCiBWCiFWCSFWCiF0Es0oAOchjrK7WSwigqJxRMhsahpLEdW/g6cuJANm+2WZdttFvx0bg+O\nnNuLCaPuwuykpRgZHOOmiMlQ4tJKttFoxD333IPMzEw899xzrjw1IcTN7HYbjBYDjGZ9h4fBrIfB\npG3r6qFvbOvuoWtAo9Z1qyeKvKTwUwXCR6aG0tsX4QGjkDJ2FoQCkcuuQbpGuZ0MdoG+YVg257dY\nMGUZDp3eicNnf4DRrO9QhoGh4MoxFFw5hqiQWGQkLUX8yOR+mYGIDA8urWSvWrUKgOdOIE4I6RlL\nqxml1cXIObMbpdWXYDTrYbIY+v26weoRuCsuAz7eaihlvvDxVuPyxavg87w8b2aDYYRyOxkqlDJf\n3Dv115ib8gscPf8jDpz6Dk2dNAiUVBahpLIIgaowzE5cguSxsyDwErghYjKYUZ9sQoYJxhisNgvM\nVgOu11yG3qSFztgCvbEFelMLdEYtdEYNapsqUNNYDjuz91ssIqEE3hIF/BRBCAsYiVC/kRgVGg+V\n3M+p7FVeWb/FQQgZnsRCCdInLcaMCQuQf+knZOVtQ0X9NadyNU3l+Hz/W9h59DPMnLgIUyfcDanI\ne+ADJoMSVbIJGeTsdhs0+iY0aevQ0FKLppZaaPRNNyrObZVonUkLvbEFrTZr20F5AxObryIAk2PT\nERk0Bt4SZdtDqoDQi7p5EELcj8/3QsrYmUiOmYGL1wuwP38bLl4vcCrXYmjCd0c+wd7crZgybh5m\nTbwXvgp/N0RMBpNuV3x88cUX8corr9z2JAcOHMCMGTMcr0+ePInJkyd3Ojjm5pVyLl261JeYCRnW\nWm1WaIwNaNJX42p9IWo0pbCzOx9I2BMCvghCLxGEfDGEXjc9+GJIhN6QCuVtD5EcEqEcAr5wQOLy\nNNHR0Y7nnrrio6tzO0D5nQys5JSUDq9P5ua65LyNumqcrzyGa3Xn26YP7QTH8TDSL+7Gsu2BLrku\nGRx6k9+7bcl+7rnnsHz58tuWocUICLlzdmaHpdV042GE0aqHwayFwdICvbkFBosWOlMTdGbnFc36\ng7fYB37eIYjynwB/eSgEXiIaADSEUG4npHO+3kGYPiYTkyLSUVRxHJdqTqHVbu1QhjE7SurOoaTu\nHIJ9ojAudAqClJE0qxHpoNtKtlqthlqt7peLD5aBTB67pOxtUMz9ryfxWlst0Ogb0axrQLO2vu3n\njVk4DCYdDGYdjCYdDAM0sJDH8SEWSKFS+sFbrIBMooC3RA6Z47kCSpkKIX6RkIhk/R5PTwy23wug\nY4uup+rP3A543r+Xp/8eeXJ8nhzbzfojvlnIgMGkw+GzP+Dg6e+hNTQ7lalqLkFVcwnC/KOQkZSJ\nidFTwefxPfpzo9j6rjf53aV9squrq1FdXY3i4mIAwPnz59HY2IiIiAioVCpXXoqQAWe322CyGNum\nrrPoUa25BkurGbbCFpgsBhjMerTom9Cs+7kyrTe2DEhsUrEcvgp/qOUBUCkCoPL2g7dUCW+JAjKx\nvO2nRIEzp8+C4ziPTV7EM1FuJ8OZVOyNeSm/QPqkxci90LZse21ThVO58roSfPTD6/jup08wa9Ji\niGzqYdtljrRxaSX73XffxV/+8hcAAMdxWLhwITiOw6ZNm7r9WpIQd2OMQaNvRGX9NdQ1V6FeU40G\nTQ0aWmrQpK3vuqX5wsDGyYGDrzIAQapwhAWMxKToaQjxi+jZsfRVJukDyu2EAAIvIdLGzUNq/Byc\nK8lFVt52lFQVOZVr1Nbhm0P/gtBLjJigJIyJHQWFjP4YHY5cWslet24d1q1b58pTEnJHrK1WaPQN\naNE3w2hu655huNE9w2j6+bXepEVNUwUMJq1b45UIpZCIvSEVe0MmlkPl7Qcfbz/4yNXw8W57+PkE\n0+wcZEBRbifkZzyOhwmj7sKEUXfhatUF7M/bjrNXjjsNkrS0mnC2/CcUbTqBybGzkJ6YiUBVqJui\nJu5AU/iRIcFiNeNq1QVcKj+H6sYyNGvr0aSr77T/3EDiOB4UMpWjgtz28IOPty9kYgWkYm9IRLK2\nn0IpeDy+W+MlhBDScyODx+I3i/6I2qaKtmXbi7J/nir1hlabFUfO/Yij5/ZhXFQKMpKWIiok1k0R\nk4Hkskp2U1MT1qxZg3379qG0tBR+fn5YtGgRXn75Zfj6+rrqMmQYabVZYTTfsoy3pe2n3qRDo6YG\ndZoq1DdXoUnXANaPi6e0EwklkAplkIhkaLXaIeSLERQQAolIBolICplYAR+5n6NCrZCpwKeKMxnk\nKL8TcnsBqlD8KuNpLEh9EDlndiKnYDcMZl2HMgwMZ0tO4GzJCYwMHouMpEyMi5pMszYNYS6rZFdW\nVqKyshKvvfYa4uLiUF5ejqeffhrLli3Dnj17XHUZMogZzQYUl52B3qS9UWm+0W3jxqOuoQaWVhN2\nnLbDaNbD0moe8BiFXiIE+0Ug2Dccfj7B8FMGQa0IhK8iADKxd4eWZk8fAU2Iq1B+J6RnFDIfLJzy\nEOYk348vd29CUeWxTqddvVp1AR9+/yoCfEKQnrgEk2PTIfCiQZJDjcsq2fHx8fj6668dr6OiovDa\na69h0aJF0Ol08PamZUiHMrPFiHpNNfQmHYxmXcefJh1qmytxqfzsgMfFgYNc5gMfmRpSiRxSkTek\nIhmkYjmkYhkkIu+2bWIZfLz9oFYGUqsCIbeg/E5I74gEYsSGpCAmOAleSgv25X2D8toSp3K1zZX4\nIusd7Dr2OWYkLMS0CfdAJpa7IWLSH/q1T7ZGo4FIJIJUKu3Py5ABYm21oEXfBI2+ERp9E1r0jdDo\nGnGt+iJKqi7Abh+YVQe74qcMwuiwcRgVEgc/ZSB85H5QynzhxRe4NS5ChiLK74R0j8fxkDhmGiZF\nT8Wl8rPYn7cdRaX5TuW0hmbsPPp/+PHk15gSPwezJt0LtYJWkhzsul1Wva+am5uRkpKChQsX4o03\n3nBsp2V3PZ/BokWjrhrNhjq0GBuhNTWixdgIo1XX/cEuxIGDwEvsvIw3v22bVCiHXOwLuUQFb5EP\nVaaJxxgMy6rfCcrvxBP017Lq/a1JX4vzFUdxtf58l2OJOHCIuLFsu9o7aIAjJLfj0mXVX3zxRbzy\nyiu3LXPgwAHMmDHD8Vqn0+Hee+9FeHg4Nm7c2N0lyACy2W0wWrQwtD/MLdBbtI7lu7WmJpis+n67\nPgcOQT6R8JEGQOQlhuBGhfnnyvPPlWovvpDmdSakH1F+J2TgqWQBmDZmCSZFzEJRZS4u1eTDarN0\nKMPAcK3+PK7Vn0eQMhLjQqcg2CeK7omDTLct2Q0NDWhoaLjtScLDwyGRSAC0JeAFCxaA4zjs3r3b\n6avEm1s6BksLz2AZ4MYYQ11zFZp19Th19iQM5hbIfCRty3jfWIGwP6e0UysC4eOthlTc3s/Z+6bn\nckjF3ogKHguRUNLp8YPlc2432OIFKOaBMljy3HDK757+e+TJ8XlsbLdWOPvni/k+6+nnZjDrcOTs\nXhw4/R1a9E1dlgvxi0RGUiYSo6eBz7+z3r4e+28Kz44N6F2e6/ZfSa1WQ61W9+jCWq0W8+fP7zIB\nE9dgjMFkMUBnbIHBpIXepEV1Yxm252x2Lnzddddtn/NZKVVB4e0LpcwXCpkKvnI/jA4dB7WS+o8R\nMphQfifE/aQib8xJvg8zJ96LvIuHkJW/HdWNZU7lKuuv4ZM9b+D7nz7FzEn3Im3cPIi7aLQinsFl\nAx+1Wi3mzZsHrVaL7du3Q6vVQqttWz1PrVZDIKD+sr1lt9tQXHYWZXUlaLixxHd9SzWatQ2w2Vv7\n7boCvhAhfhEI849CoG8Y/H2C4e8TArUi4I7/eiaEDD6U3wnpfwIvAVLjMzA5Lh2FV/OwP387rlSc\ndyrXpKvH9pxN2HP8C0ydMB8zJy6EUkbz1Xsil9WY8vLycPz4cXAchzFjxji2cxyH7OzsDn36hqsW\nfROqGq7DZDHCbDXCbDHCbDXdeG6CyWqExWq6sd+E2qYKl3fv4MBBLvWB0tsXPt5qKDusRNj2UCuD\naAEVQogD5XdCBg6P42FcVArGRaWgtLoY+/O2o+DKMadBkkaLAftOfo3sUzuQEjMTs5MyEeQb7qao\nSWdcVsmeNWsW7Pb+X3FvMLAzO5q19WjWNUKjb0SLvhHfH/kUZqtpQOOIC7kLMaPib1So25byVshU\nNAsHIaRXKL8T4h4RQWPw6ML/h7rmKmTn78DxwiynQZI2WyuOFe7HscL9GDcyBRlJmYgKiaNBkh6A\nvvt3EUurGddrLuNC6SkcO78fLYauBy+4glAghkwsb3tI5JCJFfCWyCEVyxHqFwlTIw98Hh/JiZ45\ncIAQQgghPePvE4xfzn4S81OXIefMLuQU7ILepHUqd+5qLs5dzUVE0BjMSVqK8VGTO6xUTAaWSyvZ\njz/+OLKzs1FZWQlvb2+kpaVhw4YNiI2NdeVlPIK11YKi0nxcqShESdUFlNeW9Es/aR6Pj4RRqYgM\njnEs8a1WBHQ5Q0e79tG5hBByp4ZTbifEk8mlSixIXYY5SffheOF+ZJ3agQZNjVO50upi/GvnX+Gv\nDG5btj0uHUIvkRsiHt5cWslOSUnBI488gvDwcDQ0NGDdunWYM2cOSktL4eU1NBrNtYZmHDj1HX46\ntxeGTv6K7KnkmJkQCcQQCSUdfzqet732VwVDKqIliwkh7jMccjshg4lQIML0hAWYOv5uFFw5hv15\n23G9xnkBqDpNFb7MfvfGsu0LMH3CfMgkCjdEPDy5NDs+8cQTjucjRozASy+9hIkTJ+Lq1asdVsjx\nVHZmh97YcmPp8Ca03Fg6/NK1i9AaG/FtwTto1t1+Ttl2Ar4Qgeow+MjUUMp8obwx5d2o0DgEqEL7\n+Z0QQojrDPbcTshQxePxMSl6KiaOTsPlinPYn7cdhdfynMrpjBrsOvY59p38BqnxGVB7jYRcrHJD\nxMNLvzVB6PV6bNq0CdHR0Rg5cmR/XabP7MyO81dP4nL5OdRrqtsezdVOAwp6Q60MRFRwLKLDxmNS\ndFq3XToIIWSw8fTcTshwxHEcosPGIzpsPKoariMrbztOXjzk1I3V0mrGoYJd4MBhhDoWAeE+GBE4\n2k1RD33drvjYW2+//Tb+8Ic/QK/XY9SoUdi9ezdGj/75H/DmlXIuXXL+aqO/McbQqK/BzoIP7/hc\nQi8JRvrHI0gRAX9FGKRCuQsiJIQMdje37nrayod91V1uB9yf38nwkpyS0uH1ydxcN0XimQzmFhRV\n5aK4Oh9Wm7nLckHKCMSHpiGElm3vkd7kd153J3vxxRfB4/Fu+zh06JCj/MMPP4zTp0/j4MGDiIuL\nw/z58x2LFriTpdWEw8U78MXxv99RBZsDB6XED+PDpuL+5GdxV9Q9iPCLpQo2IWRQGSq5nRDSOalI\ngaTIDNyf/CySIjO6rKdUa0qxv/BzfHf6A1ypPQOb3TbAkQ5d3bZkNzQ0oKHh9v2Qw8PDIZE4d42w\nWq1QqVR46623sGLFCgC9W/O9rxhjuHD9NM6WnEBjSy2atHWoaujZ+uJioRRKb18opKq2JcRlKmga\n9ZCJFEhLnokAVcigmGe6fXaR5OTBM4XfYIt5sMULUMwDZSDy3J1ydW4HPPt9e/rvkSfH57Gx3drq\n6tov5u+Yp31urTYr8i7mICt/+23rREpvNdIn3Ysp8fMgEUkHMMI2nva53ao3ea7bPtlqtRpqtbpP\ngdjtdjDG+n0RA8YYtAYNGlpqUNdciZyCXSjtZJRtV0QCMX5731/g7xMMmdj5L732f/AQvwiXxUwI\nIe40GHI7IcR1vPgC3BU3G5Nj07Hjxy9wvuIoalpKncppdA3YnrMZPxz/ElPH341ZE++F0puWbe8L\nlw18vHLlCr766ivMnTsXfn5+KC8vx6uvvgqxWIxFixa56jIdXLxegJ3HPsO1qou9PlYqlmPRlIcQ\nGzEJamVgP0RHCCGDnztyOyGk/3AchzDf0QjzHY2AcB/sz9uG05ePOi3bbrIYsD9vGw6c+g7JMTMw\nOykTweoRbop6cHJZJVskEuHgwYN4/fXX0dzcjMDAQMycORNHjx6Fv7+/qy7jUNNUgbe2re3VMQK+\nEHKZD2YkLMTsxCUuj4kQQoaagc7thJCBMyJwNFYu+D3qNdXIzv8Wxwr3wdp6y7Lt9lYcL8rC8aIs\nxEUmISNpKUaHxtMgyR5wWSU7LCwMu3btctXpOlVZX4qCy0dRVHoK16q7b70eFzUZKWNnQa0IgEru\nD2+Jgn4pCCGkFwYitxNC3MtPGYQH0p/A/NRfIefMbhwq2Am9scWpXOG1PBRey8OIwGhkJGUiYVQq\nLdt+Gx6/VJfdbkNe8WFk5W1DRf21bstHhcRiZHAMEsfMQHhAVP8HSAghhBAyBHhLFJh/178hIykT\nJwqzkZW/HfWaaqdy12suYdOu1+CnDEL6pMW4Ky4DQgEt234rl1eyGWNYsGAB9uzZg61bt+L+++/v\n87la9E1479uXUVZ7pduyo8PGYdGUhxEVMrbP1yOEENI1V+Z3QojnEnqJMG3CPUgbNxdnrhzH/vzt\nKLPT0YYAACAASURBVK0udipXr6nG1gPvY9fxLZg+YT6mT1gAudSzZhZyJ5dXsv/+97+Dz2/76qCv\nXTMsrWacv3oSm3a9dttyIX6RmJGwAIljpkNMqysSQki/ckV+J4QMHjweHxOj05AwegpKKguxL28b\nzl896VROb2zBD8e/wP68bbgrLgPpkxbD3yfYDRF7FpdWsnNzc/GPf/wDeXl5CAzs24wdVyrO48Od\nf+20LxAAxEYkYuLoKYiNTISPd9+mnyKEENI7rsjvhJDBieM4jAqNx6jQeFQ1lCErfztOXjjotGy7\ntdWCw2d246eze5AwKhUZSUsRERTdxVmHPpdVsrVaLR588EF88MEHfR5xzhjDm1/9qcv9y+9+Dslj\nZ/Y1REIIIX3givxOCBkagtXheGjus1g05SEcPP09fjr7A4wWQ4cyjNlx+vIRnL58BKND45GRtBSx\nkYngcd0uND6kdLviY0899NBD8PPzw5tvvgkA4PF4+Oqrr3Dfffd1KHfzSjmEEDLUedrKh31B+Z0Q\nQpzd0YqPL774Il555ZXbniA7OxvXr1/HmTNnHCsjttfbXVR/J4QQ4mKU3wkhpH/dtiW7oaEBDQ0N\ntz1BeHg4nn76aXz88cfg8X7+GsBms4HH4yEtLQ2HDh1ybKeWDkLIcOKpLdmU3wkh5M50l99d0l2k\nsrISzc3NjteMMYwfPx7/8z//gyVLliAyMvJOL0EIIcQNKL8TQkjfuGTgY0hICEJCQpy2h4eHUwIm\nhJBBjPI7IYT0zfAa5kkIIYQQQsgAcNnsIoQQQgghhJA21JJNCCGk3zDGMH/+fPB4PHz99dfuDsfh\n8ccfx+jRoyGVShEQEIDMzEwUFRW5Oyw0NTXh2WefRWxsLKRSKUaMGIGnn34ajY2N7g4NAPD+++8j\nPT0dPj4+4PF4uH79uttiefvttzFy5EhIJBIkJyfj8OHDbovlZocOHcLixYsRFhYGHo+Hjz76yN0h\nOWzYsAEpKSlQKpUICAjA4sWLcf78eXeHBQB46623kJCQAKVSCaVSibS0NOzatcvdYXVqw4YN4PF4\nePbZZ29bjirZhBBC+o2nLsWekpKCjz76CBcuXMCePXvAGMOcOXPQ2tra/cH9qLKyEpWVlXjttddw\n7tw5fPrppzh06BCWLVvm1rjaGY1G3HPPPVi/fr1b4/jiiy+wevVqvPjiizh9+jTS0tIwf/58lJWV\nuTUuANDr9ZgwYQLefPNNSCQSj/q9P3jwIJ555hkcPXoUWVlZ8PLywpw5c9DU1OTu0BAeHo6NGzfi\n1KlTyMvLw+zZs5GZmYmCggJ3h9bBsWPH8MEHH2DChAnd/9syQgghpB+cOHGChYeHs9raWsZxHPv6\n66/dHVKXCgoKGMdxrLi42N2hONm1axfj8XhMq9W6OxSH3NxcxnEcKy0tdcv1J0+ezJ544okO26Kj\no9nzzz///7d353FR1fv/wF/nDNuwDTAIqKzKYrgrkuJVsQLDcMssKy3t3rze1Cyrb1Z2vd7v9Vq2\n/PLen9bVW2qamcs3LROXryK4pqDgjrghLoCyDsM+c75/mHM9DijqMGeA1/Px4KG8zxl4ASJvznzO\n561Inoa4urpKy5cvVzpGg8rLyyWVSiVt2rRJ6Sj18vLykhYvXqx0DJOSkhKpY8eO0q5du6TY2Fhp\n2rRpdz2fV7KJiMjimtModr1ej6VLlyIsLAwhISFKxzFTWloKR0dHODs7Kx3FJtTU1ODw4cOIj4+X\n1ePj47Fv3z6FUjVPZWVlMBqN8PT0VDqKjMFgwOrVq1FVVYWBAwcqHcdk0qRJGDNmDAYNGtSogVwW\n2cKPiIjodpMnT8bQoUMxZMgQpaM0aNGiRXj33Xeh1+vRsWNHJCUlwc7Otn4slpSU4MMPP8SkSZNk\nA4Fasxs3bsBgMMDX11dW9/HxQV5enkKpmqfp06ejZ8+e6Nevn9JRAADHjh1Dv379UF1dDbVajTVr\n1iAiIkLpWACAJUuW4Pz581i1ahWAxi1/43csERE1yqxZsyCK4l1fUlJSsGLFChw9ehTz588HYL1R\n7I3Jd/uEynHjxiEjIwMpKSmIjIxEQkICdDqdTWQDgPLycgwbNsy0VrWpPEg2av5mzJiBffv2Yf36\n9TazbrxTp044evQoDh48iKlTp2Ls2LFIS0tTOhaysrLwwQcf4LvvvjPdYyJJ0j3/T+MWfkRE1ChN\nMYpdiXxqtdqsXltbC09PTyxcuBAvv/yy4tnKy8sxdOhQCIKApKSkJl0q8iCft7S0NERHR+PixYsI\nDAxssmz1qampgYuLC1avXo3Ro0eb6lOmTMHJkyeRnJxs1Tx34+bmhoULF+Kll15SOorMm2++iTVr\n1iA5ORnh4eFKx2lQXFwc/P39sXTpUkVzLFu2DK+88oqpwQZu/p8mCAJUKhX0ej3s7e3NHmdbz4sR\nEZHN0mq10Gq19zxv7ty5eOedd0yvS7+NYv/ss88wYsQIxfPVx2g0QpIkGI1GC6e66X6y6XQ6JCQk\nWKXBvt9stsDBwQG9e/fGtm3bZE329u3bMWbMGAWTNQ/Tp0/H2rVrbb7BBm42sk31PXk/Ro0ahejo\naNPrkiRh4sSJCA8Px/vvv19vgw2wySYiIguz9VHs586dw7p16xAXFwdvb29cvnwZH330EZycnJCY\nmKhoNp1Oh/j4eOh0OmzYsAE6nc60hEWr1Tb4w9xa8vLykJeXhzNnzgAATpw4gaKiIgQFBVn15rkZ\nM2Zg/PjxiI6ORkxMDL766ivk5eVh8uTJVsvQEL1ej+zsbAA3f3nLyclBRkYGtFotAgICFM02ZcoU\nrFy5Ehs2bIBGozGtYXdzc4OLi4ui2WbOnInExET4+/tDp9Nh1apVSElJwZYtWxTNBcC0d/ftnJ2d\n4enpicjIyIYf2KR7nRAREUmSTW3hl5ubKyUkJEg+Pj6Sg4ODFBAQII0bN07KyspSOpqUnJwsCYIg\niaIoCYJgehFFUUpJSVE6njR79mxZplt/KrFN3aJFi6Tg4GDJ0dFRioqKknbv3m31DPW59TW88+s4\nceJEpaPV+29LEARpzpw5SkeTJkyYIAUFBUmOjo6Sj4+PFBcXJ23btk3pWA1qzBZ+XJNNRERERGRh\n3F2EiIiIiMjC2GQTEREREVkYm2wiIiIiIgtjk01EREREZGFssomIiIiILIxNNhERERGRhbHJJiIi\nIiKyMDbZREREREQWxiabiIiIiMjC2GQTEREREVkYm2wiIiIiIgtjk01EREREZGFssomIiKhJXLx4\nEaIoYuLEiUpHIbI6NtlERETUpARBUDrCPd36hWDw4MFKR6EWwk7pAERERNQy+fv74/Tp09BoNEpH\nuadbvwg0h18IqHlgk01ERERNws7ODuHh4UrHaBRJkpSOQC0Ml4sQERFRk6hvTfaECRMgiiJSUlKw\nbt06REdHw8XFBVqtFs8//zyuXr1q9nZiY2MhiiIuXLiATz/9FBEREVCr1QgMDMTbb7+N8vJys8fc\nbenHX/7yF4iiiNTUVADAsmXL0KFDBwDArl27IIqi6WXOnDmW+FRQK8Qr2URERNSk6luCsWjRIvz0\n008YMWIEBg8ejAMHDuCHH35AZmYmMjIy4ODgYPaY6dOnY+/evXjuueeg0WiwefNmfP7559izZw9S\nU1PNHtPYpR89e/bE9OnTsWDBAgQHB2PChAmmY7Gxsff1sRLdwiabiIiIrG7r1q1IS0tD586dTbUX\nX3wR33//PTZu3IgxY8aYPebAgQPIzMyEv78/AGDu3LkYPXo0Nm7ciM8//xwzZ858oCzdu3fHG2+8\nYWqy//znPz/YB0V0Gy4XISIiIqt7/fXXZQ02ALz66qsAgEOHDtX7mOnTp5sabODmkpCPP/4YgiDg\nm2++eag8XJNNlsYmm4iIiKwuKirKrHargS4uLq73MYMGDTKrhYeHw8fHB+fOnYNer7dsSKKHwCab\niIiIrM7Dw8OsZmd3cxWrwWCo9zG+vr53rZeVlVkoHdHDY5NNREREzUJ+fv5d6+7u7rJ6XV1dveeX\nlJRYNhhRPdhkExERUbOwa9cus1pWVhby8/MRGhoKFxcXU93T0xO5ubn1vp361nyrVCoADV9FJ7pf\nbLKJiIioWViwYIGscTYYDHj33XcBQLYXNwD07dsXOTk5SEpKktWXLFmC/fv3m23v5+npCQANNuZE\n94tb+BEREVGz0L9/f/To0QPPPvss3N3dkZSUhOPHjyM6OhpvvfWW7Nx33nkHW7duxahRo/Dss8+i\nTZs2SE9PR3p6OhITE7Fp0ybZ+a6uroiJicG+ffswfPhw9OzZE/b29hg0aBAGDBhgzQ+TWgheySYi\nIiKrEQSh0UNi7nzcF198gffeew/JyclYsGABSkpKMGPGDOzYsQP29vay82NjY/HTTz+hR48eWLdu\nHZYuXQoPDw/8+uuv6N27d70ZVqxYgZEjR2L//v2YO3cuZs+ejeTk5Af+WKl1EyRuDElEREQ2LDY2\nFqmpqbh48SICAwOVjkPUKLySTURERDbvQa5+EymJTTYRERHZPD7xTs0Nb3wkIiKLKC0tVToCtVAG\ngwGCIKCsrIz/zshmaDSaux7nmmwiIrIINj9E1Jrcq8nmchEiIiIiIgvjchEiIrK4e13hsba0tDQA\nQFRUlMJJ6mfL+ZjtwTDbg7HlbMD9PWPHK9lERERERBbGJpuIiIiIyMLYZBMRERERWRibbCIiIiIi\nC2OTTURERM2GJEmorK7AjvQfcSQnGeVVJUpHIqoXdxchIiIim1dZrcf6lH8j8+x+VNdWmeqnr6VB\ncqnAo5GPwdnRVcGERHJssomIiMhmSZKE6yVXsXTzJ7hy46LZ8VpDNX5M/QY70zfg94kz4ePRDqX6\nYpzKSYenWxt0CuwBtaMLauqq4WDnaP0PgFotTnwkIiKLuH3/2OzsbAWTUEsgSRKO5u7GyasHUGuo\nscjbDPSKwMCIpyGKKou8PWp9wsLCTH/nxEciIiJqVmrqqrA3+ydk5qZarMEGgEtFWcjKS7fY2yO6\nGy4XISIii7O1aW22PkXOlvNZM9u1wlwk/fo9Tl5IR01ddZO8j5ySExg37E8QBKFJ3v4t/Jo+GFvO\nBtzfxEc22URERKSoorIC7Dm6BSmZm1BbV/+Vax/P9rBX2Zutyx776NvIyNuB0zlHGvW+CoqvYP73\nMxDkG4ZBPYahrTbgYeMT1YtNNhERESnmWmEuPlv9doNXrr01fpg84kP4eLaHrqIEf13+J1TXVAIA\ngrSPwMHOCZNHfIizl4/D0d4Jbb2DoK/UwcNVi8vXL2B9yhKcv3pK9javXL+AK9cv4Ej2Xrw99lO0\n8Wjb5B8ntT5ssomIiMjq8osuo6DkKtbvWlJvg+2idseAbgl4ovfTcLC/uSuIm7MHJjz5FrYdWgeN\nqxdCNX0AAKIgIjygm+mxDm43zw/w6YA3xszDhWtZ+H9r3jV7H5XVenz9y8eY8ezHpvdBZClssomI\niMhqjEYDvtk8H0fP/drgOc899if06xIHUTDfn6FzSBQ6h9xcr3tr/e69hLSNwDOxk7A9bT1Kywtl\nx67euIj//vY1TB4+C+3bhNzHR0J0d2yyiYiIyGqOZO9tsMEWBRFzJy2Hi5Obxd/vwO5DMbD7UOgq\nSrA2eTEyzu4zHSstL8THq95El5A+eCFuGlzV7hZ//9T6cAs/IiIisgqjZMSPqUsbPP7SkzOapMG+\nnZuzB16MmwY/L/MbHo9fOIQFa983rfkmehhssomIiKjJnco5gncWjUVZRXG9xzsF9USP0H5WyeLo\noMYfEmdC7ehidiy/+DKWJn2KOkOtVbJQy8WJj0REZBGc+EgNOXn1V6Rd2G5W9/cMw6MdE1BZUw6t\na9sm37v6TmWVhcjOz8D568dRWaOTHXN19MDAiKfh7dbOqpnItnHiIxEREdmEovI8pF/4X7O6AAFd\nA/rDxdEd3m7trN5gA4C7WovewY9jZM/JcHGUN0zl1SVIPrUGFXc030SNxRsfiYjI4mxtWputT5Gz\n5XwPk80oGbFg7fuQIH/SPDK4N2J7DEOnoB6KZbuTR1tnfLXhr7KslbXlOF6QitdGzlY0m6Ux24O7\nn4mPvJJNRERETeLEhTRcuHZaVhs/5E1MHvHhQzfYlvZIUE/8aeRseGv8ZPXTOUdw/urpBh5F1DA2\n2URERGRRBqMBB08lY8nPf5fVu4T0QZ9OgxRKdW+dgnpg1ksL0aHtI7L6F2tnIq8oV6FU1FyxySYi\nIiKL2rh7GVZuW2BWH9rveQXS3B9RVNWbc96K15H06w8wSkYFUlFzxCabiIiILCavKBcpmb+Y1UPb\nd4Z/mw4KJLp/Yf5dEegbJqtJkJB04Hv8vHeFQqmouWGTTURERBazad9KSPVc7R3ca4QCaR6MIAgY\nPegPcHJwNju28/BGXMo/q0Aqam7YZBMREZFFXLl+od6R6cP7v4SuHaIVSPTgQtpG4C8TF+O5x/4E\nRwe1qS5JRvyw80suG6F74hZ+RERE9FBq6qqxM30DNh/4XlYP8g3DjOfmK7IHtiU4O7mif9ch8HDV\n4l8//c1Uzy04hyNn9qJ3xAAF05Gt45VsIiIiemBFZdfxyfdvmTXYABDX55lm22DfrnNIFHqExshq\nv+z/DjW11QolouaAY9WJiMgiOFa9ddpybDkKysy3t3N38sKIXn9qEU02AJRVFmHj4S9lw2q8Xduh\nb8eh8HL1u8sjqSXhWHUiIiJqcjd0V+ptsAGge+CgFtNgA4C72gthfj1ltRvlV7Ep899Iv7gTvGZJ\nd+KabCIisjhbG4ls66OabTnf3bKt3LbXrBbbYxjCArpa5UZHa3/eOneNxD/WvY8rNy7K6ieu7IOz\nmwPGxU83/WLRXL+mSrPlbADHqhMREVETKyzLR/qZ3bLaH4fPwtODft/sdhJpLLWjMyaP/DPaeQeb\nHTt0ehe2H1pn/VBks9hkExER0X3bsHsZDIY60+tajS8eCe6lYCLr0Lh44e2xn2D8kDfh5uwhO/bL\n/lXcQ5tM2GQTERHRfTl2/iAyz+6X1Yb0eRai0DraCjuVPfp0GoQ3xsyDs5ObqS5BwpZff1AwGdkS\nrskmIiKie6qoLkd61m7k5p/FgZM7ZMcCfcMQHTlYoWTKaePRFi/GTcOSn/9uqh2/cIhXswkAm2wi\nIiK6B4PRgH+um2V2wx8AiIKIMbGTWs1V7Dt1CemDIL9w5OSdMdWWb/kcj0e8AAc7JwWTkdJa53cE\nERERNdqlwlP1NtgA8FTMOAT5hdV7rDUQBAEJj46V1a6XXEV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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "output mean, variance: -0.0009, 2.2404\n" - ] - } - ], - "source": [ - "def h(x):\n", - " return -1.5 * x\n", - "plot_transfer_func(data, h, lims=(-4, 4), num_bins=300)\n", - "out = h(data)\n", - "print ('output mean, variance: %.4f, %.4f' % (np.average(out), np.std(out)**2))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Although the shapes of the output are very different, the mean and variance of each are almost the same. This may lead us to reasoning that perhaps we can ignore this problem if the nonlinear equation is 'close to' linear. To test that, we can iterate several times and then compare the results." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "linear output mean, variance: -0.0533, 7449.9848\n", - "nonlinear output mean, variance: -1.9719, 26065.4836\n" - ] - } - ], - "source": [ - "out = h(data)\n", - "out2 = g(data)\n", - "\n", - "for i in range(10):\n", - " out = h(out)\n", - " out2 = g(out2)\n", - "print('linear output mean, variance: %.4f, %.4f' % \n", - " (np.average(out), np.std(out)**2))\n", - "print('nonlinear output mean, variance: %.4f, %.4f' % \n", - " (np.average(out2), np.std(out2)**2))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Unfortunately we can see that the nonlinear version is not stable. We have drifted significantly from the mean of 0, and the variance is half an order of magnitude larger. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## The Extended Kalman Filter" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The extended Kalman filter (EKF) works by linearizing the system model at each update. For example, consider the problem of tracking a cannonball in flight. Obviously it follows a curved flight path. However, if our update rate is small enough, say 1/10 second, then the trajectory over that time is nearly linear. If we linearize that short segment we will get an answer very close to the actual value, and we can use that value to perform the prediction step of the filter. There are many ways to linearize a set of nonlinear differential equations, and the topic is somewhat beyond the scope of this book. In practice, a Taylor series approximation is frequently used with EKFs, and that is what we will use. \n", - "\n", - "\n", - "Consider the function $f(x)=x^2−2x$, which we have plotted below." - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": { - "collapsed": false - }, "outputs": [ { "data": { "image/png": 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asdlslqurq0JCQq55PDw8XEVFRe0el52drW3btumBBx7Qxo0bdeHCBT355JOq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\nAAA4OUo7AAAA4OQo7QAAAICT+/8BQKWT/yXokOsAAAAASUVORK5CYII=\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -615,6 +316,9 @@ } ], "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", "xs = np.arange(0, 2, 0.01)\n", "ys = [x**2 - 2*x for x in xs]\n", "plt.plot (xs, ys)\n", @@ -633,7 +337,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 6, "metadata": { "collapsed": false }, @@ -642,7 +346,7 @@ "data": { "image/png": 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ZE56gtITh7SE9NW64ggNDPNg14Ns8EtorKyv1l7/8RUuXLtXpp58uSXr55ZeV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\n2/a8rlLV9ZWqqXO/bnY2ebt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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -675,7 +379,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 7, "metadata": { "collapsed": false }, @@ -684,7 +388,7 @@ "data": { "image/png": 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Lvk9xfrmaqi+YqksvLag8b0P6iMeYGcqnjZw7F/5/2qQgtAMAACwj4UhIXa5WtfV9FP/0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\nhjqdJyd9Ti2VmJj4GQhJ0rq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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -706,9 +410,16 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Here we can see that this linearization is much better. It is still exactly correct at $x=1.5$, but the errors are very small as x varies. Compare the tiny error at $x=1.4$ vs the very large error at $x=1.4$ in the previous plot. This does not constitute a formal proof of correctness, but this sort of geometric depiction should be fairly convincing. Certainly it is easy to see that in this case if the line had any other slope the errors would accumulate more quickly. \n", + "Here we can see that this linearization is much better. It is still exactly correct at $x=1.5$, but the errors are very small as x varies. Compare the tiny error at $x=1.4$ vs the very large error at $x=1.4$ in the previous plot. This does not constitute a formal proof of correctness, but this sort of geometric depiction should be fairly convincing. Certainly it is easy to see that in this case if the line had any other slope the errors would accumulate more quickly. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Linearizing the Kalman Filter\n", "\n", - "To implement the extended Kalman filter we will leave the linear equations as they are, and use partial derivatives to evaluate the system matrix $\\mathbf{F}$ and the measurement matrix $\\mathbf{H}$ at the state at time t ($\\mathbf{x}_t$). Since $\\mathbf{F}$ also depends on the control input vector $\\mathbf{u}$ we will need to include that term:\n", + "To implement the extended Kalman filter we will leave the linear equations as they are, and use partial derivatives to evaluate the system matrix $\\mathbf{F}$ and the measurement matrix $\\mathbf{H}$ at the state at time t ($\\mathbf{x}_t$). In other words we linearize the equations at time t by finding the slope (derivative) of the equations at that time. Since $\\mathbf{F}$ also depends on the control input vector $\\mathbf{u}$ we will need to include that term:\n", "\n", "$$\n", "\\begin{aligned}\n", @@ -718,19 +429,10 @@ "\\end{aligned}\n", "$$\n", "\n", - "All this means is that at each update step we compute $\\mathbf{F}$ as the partial derivative of our function $f()$ evaluated at x. \n", + "All this means is that at each update step we compute $\\mathbf{F}$ as the partial derivative of our function $f()$ evaluated at x. We then use a computational technique, such as Taylor expansion, to turn this into a set of linear equations.\n", "\n", - "We approximate the state transition function $\\mathbf{F}$ by using the Taylor-series expansion \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "** orphan text\n", - "This approach has many issues. First, of course, is the fact that the linearization does not produce an exact answer. More importantly, we are not linearizing the actual path, but our filter's estimation of the path. We linearize the estimation because it is statistically likely to be correct; but of course it is not required to be. So if the filter's output is bad that will cause us to linearize an incorrect estimate, which will almost certainly lead to an even worse estimate. In these cases the filter will quickly diverge. This is where the 'black art' of Kalman filter comes in. We are trying to linearize an estimate, and there is no guarantee that the filter will be stable. A vast amount of the literature on Kalman filters is devoted to this problem. Another issue is that we need to linearize the system using analytic methods. It may be difficult or impossible to find an analytic solution to some problems. In other cases we may be able to find the linearization, but the computation is very expensive. **\n", + "For nonlinear problems our function $f()$ is a set of differential equations. Modeling physical systems with differential equations is well outside the scope of this book. You will need to be reasonably well versed in this branch of applied mathematics to successfully implement the EKF for your problem. If you have not read it yet, please read the section **Modeling Dynamic Systems** in the **Kalman Filter Math** chapter as it contains the math that you will need to complete this chapter.\n", "\n", - "In the next chapter we will spend a lot of time on a new development, the unscented Kalman filter(UKF) which avoids many of these problems. I think that as it becomes better known it will supplant the EKF in most applications, though that is still an open question. Certainly research has shown that the UKF performs at least as well as, and often much better than the EKF. \n", "\n", "I think the easiest way to understand the EKF is to just start off with an example. Perhaps the reason for some of my mathematical choices will not be clear, but trust that the end result will be an EKF." ] @@ -753,7 +455,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 8, "metadata": { "collapsed": false }, @@ -762,7 +464,7 @@ "data": { "image/png": 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V7tdMn25ef+01M3rrckkNGkiffirVqiX99JM0fLhUo4Y0ZIgJuA0bSsOGmSkPkuTrK11/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\nBcqP9957T0FBQTp48KD27Nn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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -870,7 +572,7 @@ "\n", "$$ \\mathbf{x}=\\mathbf{Fx}$$\n", "\n", - "Solving an arbitrary set of differential equations is beyond the scope of this book, however most Kalman filters are amenable to Taylor-series expansion which I will briefly explain here without proof. \n", + "Solving an arbitrary set of differential equations is beyond the scope of this book, however most Kalman filters are amenable to Taylor-series expansion which I will briefly explain here without proof. The section **Modeling Dynamic Systems** in the **Kalman Filter Math** chapter contains much more information on this technique.\n", "\n", "Given the partial differential equation \n", "\n", @@ -889,7 +591,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "$\\Phi$ is our system matrix. We cannot use Greek symbols in Python, so the code uses the symbol `F` for $\\Phi$. This is admittedly confusing. In the math above $\\mathbf{F}$ represents the system of partial differential equations, and $\\Phi$ is the system matrix. In the Python the partial differential equations are not represented in the code, and the system matrix is `F`." + "We can then compute the system matrix by substituting $\\Phi$ in $x(t_k) = \\Phi(\\Delta t)x(t_{k-1})$. Thus, $\\Phi$ is our system matrix.\n", + "\n", + "We cannot use Greek symbols in Python, so the code uses the symbol `F` for $\\Phi$. This is admittedly confusing. In the math above $\\mathbf{F}$ represents the system of partial differential equations, and $\\Phi$ is the system matrix. In the Python the partial differential equations are not represented in the code, and the system matrix is `F`." ] }, { @@ -967,7 +671,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 9, "metadata": { "collapsed": false }, @@ -992,7 +696,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 10, "metadata": { "collapsed": false }, @@ -1015,7 +719,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 11, "metadata": { "collapsed": false }, @@ -1090,16 +794,16 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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KiIgInDlzBomJiQCAM2fOYOXKlSgrK0NwcLBYQ29vr/hvjibQbJefnw8AWLp0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\nrkJggg==\n", 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AC2jysc1m48c//jE//vGP+7s9IiIi8i0NDQ18tmYV7k1rqD6+l5CYHmJskRAG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\nIWqSk5MTAOi91zZsI+rKnJ2d4ebmxvstGdSyZcuwZ88eHD5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555Gamork5GQsWrQICxcuRHJyMl544QWsWbOmuXLT/wR4DdbaTr5ynMN3iIiI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\nHQeTtiHvsSU1h/qPq7XIB4ABPiN1KvQ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Dy+WCQCCAVCqNaPU+WygU6tCuNuH3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6tsrd7fV2C1HbvpyXjtq6Gh2lISIiIqKORu/Bu9wTGBiI9PR0GBoaYuLEiZgz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\n6bhcroiLMavVik6no6Ghgbq6Ourr66mrq6OpqSmiBj0YDB5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KcPr0abS0tMBgMKCqqgplZWXIz8/HkCFD8Mgjj2DcuHF46623ruUx9Av2GSAiIiIiX9dl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\nABERERGRlfofFqg2HR3o7zQAAAAASUVORK5CYII=\n", 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U1KCsrAx5eXkYPnw4HnnkEUyaNAmvvfba9TyGAcFhQkREREQ01PXaM/Dss8/i5z//OR54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\niGzU/wA9fyKMADA/5gAAAABJRU5ErkJggg==\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1214,7 +918,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 13, "metadata": { "collapsed": false }, @@ -1232,7 +936,7 @@ "⎣╲╱ x_alt + x_pos ╲╱ x_alt + x_pos ⎦" ] }, - "execution_count": 17, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" } @@ -1297,7 +1001,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 14, "metadata": { "collapsed": false }, @@ -1324,7 +1028,7 @@ "⎣ 2 ⎦" ] }, - "execution_count": 18, + "execution_count": 14, "metadata": {}, "output_type": "execute_result" } @@ -1357,16 +1061,16 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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jR+Pn54ebmxvdunXj8uXLBbZxwIABlofPBw4ciEajoU2bNoA53UOjyT8EO3Xq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\nAAAAAElFTkSuQmCC\n", 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Ma9GRsS0ahTmuhbnecosKLTh0+RAXrl/A4HJzdt2smjFlm+hbq2+hnetO9O/f32F5TqAX\nHh7OyJEjmT17NocPH6Zjx464urpy6tQpvv32W9566y0GDBhAy5Yt8fPz47nnnmP06NHodDrWrFlj\nt3HO8ePHadeuHf/+978JCQnB1dWVX375hT///JP333/fWm/IkCEMHz6cnj170r59ew4dOsSGDRso\nWbKkU2kbiqKwZMkSOnXqREhICM8//zzlypXj4sWL1uB+y5Ytt20nr3PlLu/fvz9r1qxh5MiRREVF\nWR9GPX78OKtXr2bNmjXW1GBnzxMWFgbAhAkT6Nu3L3q9nscee4yvvvqK+fPn0717dypVqkRaWhpL\nly5Fp9PRs2fP217Pw8DT0zPPn/PCvhG5q3XCs7Oz87xrjImJ4cKFCwQEBNzNKYQQQgjnmUyQnGx5\nJSVZ/puaCjod6PU3X66ujv+t1cIDtKW6VqNlRNgI1p9az/5L+0nOTMZF40KwTzBP1XiKkm72edhF\nyZmZ3VvX4v7oo49o0KABixYtYuLEieh0OgIDA+ndu7c1BcPHx4eff/6Zl19+mcmTJ+Pp6UmPHj0Y\nPnw4derUsbZVsWJF+vfvz+bNm1mxYgWKolC9enXrOuQ5IiIiOH36NEuWLGH9+vW0atWKjRs38thj\nj9ldQ17XFB4ezq5du3jrrbdYsGAB169fJyAggLCwMJuVUPJae9zZckVRWLt2LfPmzePzzz/n+++/\nx2g0UrlyZUaOHEnt2rVvM+L219CwYUNmzJjBggULeP7551FVlcjISNq0acPevXtZtWoVly9fpkSJ\nEjRo0ID58+dbA3dReBTVyUz91157jSeffJLy5cuTlJTEihUrmDVrFuvXr6d58+ZMnjyZnj17UqZM\nGc6cOcOECRO4cOECx44ds8nzyn0X4eXlVfhX9IiS2a+iIeNaNGRci85DM7YmE1y+DBcv2r4uXYKE\nBNsgO/e/b9k9scAUxRKUe3tDyZLW11VVJcvLi7K1a9uUW18eHk6fIj09vUg2PVFVlSxzFjqNzqlg\nWAhhL7+fz8KOYZ2eCb9y5Qr9+/fn8uXLeHl5UbduXdavX0+HDh1IT0/n6NGjfPnllyQkJBAQEEC7\ndu1Ys2ZNvg9aCCGEeMSoKsTFwblzltetQXbOKybGUvde9C893XIDcPmytfi2i+/6+EBQkONXYCAU\nw6SToii4aF2K/DxCiMLhdBDuKO87h8FgYP369YXSISGEEA+w69dvBth5vdLyX1bvgRQfb3nd2DTG\njrf3zaD87bchNLQ4eyeEuA/dVU64EEKIR1RiIuzdC7t3Q3Q0nDxpCbCvX7+3/dJoLKkhnp6W/3p4\ngJsbZGdDZubNV0aG/dcZGUU3+56QAAcPWl7DhkkQLoSQIFwIIcRtmExw5Ajs2WMJunfvhj//LNp0\nEUWBUqWgbFnbV0DAzRzsW4NtT08wGO7uwcrsbEs6Snw8XLtmfZ3dvx+XhATKurralHPtGly5Yhkj\nIYQoAAnChRBC3KSqcPbszWB7zx7Yt88SmBYWd3eoUMHyKl/ePtAuWxZKlwaXe5DfrNVa+ufubunb\nDTFVqgBQ1tEDr2azJX/8zBnHr7NnLbPtQgiRiwThQgjxKFNVSyrJxo2W186dcPXqnbfn6moJXnOC\nbEcvb+8HahnA29Jobt48NG9ufzx3kH76tOVBTSHEI0+CcCGEeNTExcHmzbBhgyXwPnu24G0oCoSE\nQOPG0KQJNGhgCS79/R+uALsw3BqkF+anCkKIB5YE4UII8bDLzLTMcOcE3Xv3FjyfOyDAEmw3aWIJ\nvBs1ghIliqa/QgjxCJAgXAghHjaqCseO3Qy6t26FW7b3zpebmyXIzgm4mzSxpJjc5Qy3qqociznG\n3ks3NhQKaERN/5p3tLFMQdoqjLpCCFHYJAgXQoiHgarCoUOUnzcPn02bLCt2OMvVFcLDoWNHaN8e\nate2bPNeiBLTE5kfPZ+4tDjcXSybuB2+chhfoy8jw0biZfC6cRm3D5idbasw6zbTNsNT71moYyKE\neLRJEC6EEA+yc+dgxQr48kv4/XfKOPu+OnUsQXeHDpYA3Gi8o9M7EzSrqsr86PmkZ6Xjob+5vbuH\n3oP0rHTmR89nQssJxKXGsXD3x8SnxmJQXFHN2Rw8uQN3nRuPVXoMD70HGo2WdcfXYTJnoVc0ZGUk\ng6Lgqigkm+KYFzWL4Y1fwKh3x6A38vGej8nIzsj3vIqi3LaPq8+vZlCVQXc0RkII4YgE4UII8aBJ\nTIQ1a2D5coiKci6/u0yZm0F3+/aWr++2G/nMHL/Q6AX0Gh2JyfEcuXCAmMtn0atazCYTapYJc1YW\narYZ1ZxNQlYW4w71Ijs7y9p27lW3E4G1Z/92qk/JwDt/jrQpU7Ray0ujRdFqrP++TjZfmj4muGQV\nEk1JXIu9gLvBE7NOZ6lz40ZCo2i4brrO6eTThBHm9PhIaosQIj8ShAshxIMgMxPWr7cE3j/8YNnd\nMT9GI7RubQm6O3a07NBYwNzr7OwsMkzppGemkWFKJ9OUZv13RmYa3x9bR2ZWBhqzmdSsBMxZJlRT\nFlez/mHSgUF2Nwf5bVaffeO/NwNmjU3wbDKbqOQdTFxqLMmZyaBagtwb/wBVtXytqujQ4qLoSElP\nQlXNqNnZqNnZDs+7N2Eze9ls/Tox1zFFp0Oj06HodJQwmdh3ZjMBhzzw9iyJt4cf3h5+uBtLoFE0\ndu3md4MypuEYJ0Zf5JgyZQrTpk3DbDbf667ckQMHDjBmzBgOHDhAamoqBw4c4LvvvrO7pjZt2qAo\nCpGRkcXavwsXLlClShV++eUX2rZtW6znLi7z589n1qxZnDx5Er1ef6+7YyVBuBBC3K9UFXbtsqSa\nfPONZWnB/Gi1JDRtSlznzlR68UXLhjPknzKSmp7MxdizXLp2loux/3Dp2lmuJlwkLTPFZmb6Trjo\n9Hh7lCRNzSSDLDQuLjdeOhStDs2NIBuNhqtp1yjtWQaNxj6gzbkGH9/K+FCVv+L+yvNhTlVVqexb\nmQF1B/DFoS84de2kJUC/EYir5mzLDHx2NubsLLxdPAn2DOSPy0dISk1EzcpGzTKhms2oWVlkZ1nG\nQAekZVxh9dZPbM6nKBpcXA34eZYiwKcC/t5lqFw2lG/P/ESGOdNhasvFpItUc6t2V2N7v1q2bBnP\nP/88u3btonHjxtby5ORkOnfuzO7du1m5ciXdu3cvULt38vDu/cBsNtO7d28A5s6di7u7O4GBgSiK\nYndNt5alpaUxc+ZM2rZtS+vWrYusj1OnTqVevXo2AXjOjU8OnU5HuXLleOKJJ5g2bRq+vr6Fdv4d\nO3bwn//8h/379+Pp6UnPnj2ZOXMm7jd+f+UnKCiIf/75x6582LBhLFy40Pr14MGDeeutt1i8eDGj\nR48utL7fLQnChRDifnP+PCxZAl98AX87kYYRFgb9+0Pv3pw6dw6ASjf+gOXMyMamXMNg1pKdns7+\nw1vQZakYsjVcT4nPs1mNosFVb8TVxYCrizHXvw1cTLlEclYqmhtBtEarRdG5WANtRaulin81BtQd\nwB9X/+Czg5/hnisgzS0pI4kgv2DSTbdfP7tRQCMOXzlsE9zmlpyZTKOyjezrOnjQNCkjiW4NniPE\nP8Tax5x2c4Jw843X5SsXCPGsRnn/MsQkXuF0zEmyMjNQzWYy01O5lH6GSzFnbrS8GhQFnbs7Lh6e\nuHh4oHVzQ1EUNIoGU/ajtcV9SkoKXbp0Yc+ePXcUgEPOpx4PnosXL3Lq1Ck++OADIiIirOUTJ05k\nwoQJNnVVVbUJwlNSUpg2bRoajabIgvCYmBg+//xzPvnkE4fH58+fj5eXFykpKWzatIkFCxawZ88e\ndu/eXSg3RgcPHuSxxx4jJCSEOXPmcP78ed5//31OnDjBhg0bbvt+RVGoW7cur776qk15tWq2N7kG\ng4HnnnuO999/n1GjRt03N3UShAshxP3AbIYtW2DBAku6SR7pE1bBwZbA+5lnoHr1m+XnzpFtzuL0\npeOcuXSc/zu6jszUFMwZGTZ51pk3Xi46PQG+FQkoGUhZv0DKlgyktE95/kk+z4ErB1EUxeHDll8c\n+uK2M9I5avrXxNfoS3pWul3qhlk14+fmR9eqXVl6aOltg+uaJW/fVs2SNZ0+b151FY0GRa9Ho9dj\nVs0YUvxoXbkrjRo1Ysb2GXj4VEWjaCwz6lkmzJkmsk2ZkGFCTU0jLTmRrORkspKTSQMUjQadhwcu\nHp5oqt0fAUBxyAnAd+/ezddff31HAfiD7OqN3WdL3LKmvlarRavVOtVGYd+AZGZmWs+/fPlyAJ5+\n+mmHdXv06EGpUqUAiIiIQKPR8M0337Bz506aO9odtoBef/11fHx82Lp1K56eltWHgoKCiIiI4P/+\n7//o3Llzvu9XVZWAgAD69et323P17t2b2bNns2XLFh577LG77nthcPy5nxBCiOIRHw9z50LNmpb8\n7e++yzsA9/GB4cNh+3b46y+YNg2qVyc+KYYDJ//H2m2f8cvhpXy9azZzV/2H7377jPT4OMw38sc1\nrq64eHlhLF0Gj8AgdJUqMKjnJF7p+x7PdBhN2wZdKVMqiAUHF/PFkS/5O/5v/or7i88OfsaM7TNI\nTL+ZMd0ooBEpprzXHs89I60oCiPDRmLQGUjKSEK9kb+dlJGEQWdgZNhIQkqF4Gv0xaza5/3mDpid\naSvnxqAw6/YK7IWiKByLOUZcWpw1qFe0WrSuBlw8PTH4+mHydce7eg28QkLxCAzC1c8PjV6PajZj\nun6d1IsXyE5NLfj3yQMoNTWVJ554gl27djkMwH/44Qf+9a9/UaFCBQwGA0FBQYwfP56M2z3vgCVQ\n69y5M1u3bqVRo0a4ublRu3ZttmzZAsC3335L7dq1MRqNNGzYkP3799u8//DhwwwaNIjKlStjNBrx\n9/enb9++nLvxSVKOZcuWodFo2LZtG+PGjcPf3x8PDw+6d+/OtWvX8u3jwIEDadTI8jMwaNAgNBoN\n7dq1AyzpHnmlXgGcOXPGGvxOnToVjUaDRqNh0KCbK/RcunSJIUOGUKZMGQwGAyEhISxatMimna1b\nt6LRaFixYgVTpkyhYsWKuLm5ceHCBQDWrVtHWFiY3U1CXlq2bAlgN0534vr162zatIl+/fpZA3CA\nAQMG4OHhwapVq5xqR1VVTCYTKbfZC6FBgwb4+vry3Xff3VW/C5NTM+Hz58/nk08+4cyZMwCEhoYy\nceJEunTpYq0zZcoUPv30U+Lj42nSpAnz588nJCSkSDothBAPvL17URcsQF35NZq0fNIw9Hr417+g\nf3/UTp04En+c7Se3kPzzevSZZmLjLpOYEmv3tjK+FcjSa0jVZqNzc0NrMKDc8kffRVXZf3k/tUrX\nApxfSlBRlALNMgN4GbyY0HICx64dY+/FG7npN2a2cwLhkWEjLakzqbHW8ydnJuPn5mcTMDvTVkHO\n60zdffv2Wf63XdprfdDSEQ+9B6qqkqZm4OHtjd7bG4DszEyykpMwJSXf9aZHD4KUlBSeeOIJdu7c\nmecM+LJlyzAajYwdOxYvLy927tzJ3LlzOXfuHF9//XW+7SuKwt9//02/fv0YNmwYAwYMYPbs2XTr\n1o0PP/yQyZMnW9MOpk+fTq9evTh58qQ18N20aRMnTpxg4MCBlC1bllOnTrFo0SL27NnD0aNHMd6y\nZOeLL76In58fU6dO5fTp08ybN49Ro0axcuXKPPs4fPhwqlSpwqRJkxg2bBjh4eGULl3a5hryUqpU\nKRYuXMiIESPo3r27dfwqV64MWGbYmzZtiqqqjBo1ilKlSrFp0yZeeOEFYmNjeeONN2zamz59Olqt\nlpdeeglVVfHw8MBkMhEdHc3QoUPzHevccuLAMresrpSYmIjJdPs0KxcXF7y8LGvzHzlyhKysLOuN\nSu469erV48CBA071KSoqCjc3N7Kzs6lYsSIvvvgiL774osO6DRo04H//+59T7RYHp4LwChUqMGvW\nLKpWrYrZbGbZsmU89dRTREdHU7duXWbOnMmcOXP4/PPPqVatGtOmTaNDhw4cP34cDw/HHy0KIcQj\nJy3N8oDlggUQHY0C5PlnODQURoyAZ54hxaBl17Et/N+KoWQmXberatC7ERxQg6Ay1TAlKZT0LEfz\npi1vmzLgecqDAAAgAElEQVRyq5xZXkcpIRpFQ2xqLMeuHSPEP8Q6c+xM0JxDURRC/EMI8Xc8QVOQ\ngPl2bRVH3byU8ywHYHODotXr0fr64eLjg0sB/y6O+eCpO+7L7Xw4dl2RtDto0CAuXryYbw74V199\nZRPsRkREULVqVSZOnMjs2bMpX758nu2rqsrJkyf57bffaNGiBQA1a9bk8ccf54UXXuDPP/8kMDAQ\nAG9vb4YNG0ZkZKQ1DWHEiBGMGzfOps2uXbvSokUL1q5dyzPPPGNzrGTJkjY5ymazmQ8//JCkpCSb\nWdzcmjZtik6nY9KkSTRr1swuZSK/NBM3Nzd69OjBiBEjqFOnjt17J06ciMlk4siRI/j5+QEwdOhQ\nhg4dyvTp0xk1apQ12AXLg7HHjh2zGe+//vqL9PR0KlWqlGc/YmNj0Wg0pKSksGXLFhYsWEBoaCit\nWrWyqdetWze2bduWZzs52rRpY/204tKlSwAEBATY1StTpgx//vnnbdurW7cu4eHhVK9enWvXrrFs\n2TLGjRvH+fPnee+99+zqBwcHO9XP4uJUEN61a1ebr99++20WLlzInj17qFOnDvPmzWPChAnWnKLP\nP/+cUqVKsWLFigLdYQkhxEPp5ElYtAiWLrWkn+QhW6fh9/CaHOrenF5D5nL0zF72bfuYP88eJNt8\nc6USrcGAzs0dnbsbGqMRN3cvhoe/jqIo7N2711qvIA8xgnOzvHsv7rUGqAUJmp1VGEFwUXJmTMPK\nhfGU51N53qDkBOkPs6tXr2IwGKhYsWKedXICQrPZTFJSEiaTiRYtWqCqKgcOHMg3CAeoXr26NQAH\nrKuxtG3b1hqA5y4/ffq03bnBEqBmZGRQtWpVvL292b9/v10QPnjwYJuvW7Zsydy5czl79iy1atXK\nt5+FTVVV1qxZQ48ePVBV1SYtpkOHDvz3v/9l9+7ddOzY0Vo+YMAAu9n92FjLJ2g+Pj55nis0NNTm\n6/bt27N8+XK7n+85c+aQkJBw277nPldammXRUldXV7t6BoPBejw/33//vc3XgwYNonPnznzwwQeM\nGTPG7vvPx8eHzMxMkpOT74tJ4gI/mJmdnc3q1atJT0+nVatWnD59mitXrtj8zzYYDLRq1YodO3ZI\nEC6EeDRlZ8OPP1pmvTduzLdqQmkv9j3ZkH2d6pLgopISG8OB/w4k68YqGoqioLgbcfMtiUsJLzS3\nrPQRlxZnnaHOraApI3fifg+aC5uzY6ooSp43KM7kPOdWVLPVRWnx4sW88sordO7cmaioKIfpqUeP\nHmX8+PFERUXZBVyJiYl29W91a4CVM/NboUIFh+XxuW6A4+Pjee2111izZo1NeV7ndhTM3dpmcYmJ\niSEhIYElS5awZMkSu+OKohATE2NTlpPG4kh+M/KrV6/Gx8eHmJgYPvroI6Kiovj999+t+eo5GjRo\nUMCruHkj5OjnIT09HTc3twK3CfDSSy/x66+/snXrVgYMGGBzLOdaH7jVUY4cOUKzZs3IyMjAaDSy\natUqqlevzo4dOwBs8pzAks908eLFwu2tEELcx1RV5fip3SQv+oDqKzfheTHvB7fMCvwVVoU9XRty\nLDSA9KRETJfPWjeVyQKCA2rQsHo4JzMv8E/yhTz/cNw6Q52joCkjBZ05fxQVZEwftRuU3KpXr86v\nv/5K27Zt6dixI7/99hvBwcHW44mJibRt2xZPT0+mT59OlSpVMBqNnD9/noEDBzq1MU9eq4vkVZ47\n2Pz3v//Njh07eOWVV6hfv741paRPnz4Oz+1Mm8Ulp3/9+vXj+eefd1jn1pueW2fBwZJiA/nfSISH\nh1sD7q5du1KnTh0GDx7M8ePHcXFxsdaLi4sjMzPztn3X6/XWNcZz0lBy0lJyu3TpEmXLlr1te47k\nfIIS52Bfhfj4eFxdXZ1ag7w4OB2E16hRg8OHD5OYmMjq1avp06fPbXd1ut2dRu6PTUXhkDEtGjKu\nReNhGtesk7+TsXQ2TbYdx5CR9yY3WV5e7G4Tyi/NSxPv7Yo2PQPl7M2Pyc1aHdmurvh7BxIe3B1M\ncP78Xi6mXsx3OUBNgoa9ppvjmXtsOxg6cDrrNMcSjgHQxLsJwYZgTh49addOamwqCeYEh7O8eo2e\nlDMp7D378Px/K6iccXV2TB0JDAzEYDAUaT/vB/Xq1eOnn36iY8eOdOjQgd9++80aeEVGRhIbG8va\ntWsJDw+3vmfjbT41Kgzx8fFs3ryZqVOn8uabb1rL09PTHQZu90peP+/+/v54enpiMpmsq63ciZyV\nUnKn6eTHaDQyZcoUnn32WZYuXWqT6dC9e/cC54TXqlULnU5HdHQ0ffr0sdbJzMzk4MGD9OzZs4BX\nZPH3jb0V/P397Y6dPn2amjXz//QvKSmJo0ePOjxWtWrVO+pTXpwOwl1cXKzJ+/Xr1yc6Opr58+cz\nadIkAK5cuWKTv3XlyhW7p2eFEOKhoqqU2LWLUitX4n3jU8G8JNeqxaUeT7OvTmkOxewlJT0e3Y2P\n4M0aLWaDK9muBlSdjtSsVNqWrGd9b02vmpxMOombzvHHs2nZadT0zvsPi6IoVPKsRCXPvB/AyqnX\nK7AXq8+u5rrpOkat0dp+CZcS1mX6hPNj+qhr0aIF3377Ld26daNjx45ERUXh6+trnVnOPetsNpuZ\nM2dOkffJ0bnBsqPl/bQpUE46xq03Blqtlp49e7J8+XIOHz5MnTp1bI7HxMQ4DEBvpdPpaNKkCdHR\n0U73qU+fPrzxxhvMmTOHiIgI6++DO8kJ9/Lyon379tblE3M+jfjyyy9JSUmhV69e1rpZWVmcOnUK\nb29va2wZHx9PiRIlbD6lMJlMvPvuu+j1eoc3KPv376dv375OX29Ru+PNerKzszGbzQQHB1OmTBk2\nbNhAw4YNAcvd5Pbt2x0+mZrbrcvSiDuXMzsjY1q4ZFyLxgM/rikplq3kP/gA8nmCP8tFy+H2tYns\nUA33anX5658jZJw7DFjWl3bx8cHg44vWaLT+MTOrZsu61C1vBrwN1Yac2n4qzzzk3PULY2zbNGtT\nqA9bPgwK83s2Pf32O4M+TDp16sTy5cvp27cvnTt3ZvPmzbRs2RI/Pz+ee+45Ro8ejU6nY82aNbdd\n67kwlChRgjZt2jBr1iwyMzOpWLEi27dvZ9u2bfj5+d3TQDz3uY1GI6GhoaxcuZJq1arh6+tLpUqV\naNy4Me+++y5bt26lWbNmREREEBISQnx8PAcPHmTdunVOPdQIllVNXn31VRITE21WU8mLVqtl7Nix\nvPzyy/zwww9069YNuLOccIB33nmH5s2b07p1a4YOHcqFCxd4//33eeyxx2yWwT5//jwhISE899xz\nLF26FLA8lPn222/Tq1cvgoKCiIuLY8WKFfz++++89dZbdquu7Nu3j/j4eJ56Kv/Vhjw9PfP8OXfm\nWYWCcCoIf+2113jyyScpX748SUlJrFixgqioKNavXw9Y1s+cPn06NWrUoGrVqrz99tt4eno6tYOR\nEEI8MP75Bz7+GD79FPKZ9ble0pPorg3Z2bIysVmpls1ZTu0BoFLZmrSo/TjB5UP55MCnlrxiLH98\n88rVvpPlAO/Go5zLLO6eo+/FXr16cf36dSIiIujWrRu//PILP//8My+//DKTJ0/G09OTHj16MHz4\ncLuZXUVRHC5ReTdWrFjB2LFjWbx4MSaTidatW7Nlyxbat2/v9Lmc7YOjenld061lS5YsYcyYMbz8\n8stkZGQwcOBAGjdujL+/P7t37+att95i3bp1LFy4EF9fX+v2787285lnnmH8+PF89913DBw4MN++\n5IiIiGDatGm899571iD8TtWvX59Nmzbx2muvMW7cODw9PXn++ed59913HdbP3ac6deoQGhrK8uXL\niYmJQa/XU69ePb755hubWfQcq1atomLFirRv3/6u+lyYFNWJW75BgwYRGRnJ5cuX8fLyom7durz6\n6qt06NDBWmfq1KksXryY+Ph4mjZtmudmPbnvIpy56xLOeeBnFu9TMq5F44EaV1WF//3PMuu9dq1l\ne/k8nK9Zjh1dG7CvZknSkxKtD1kqGg3+AUE832YsZUveXDpNVdUCzTg7U/+BGtsHSGHPhD8KOeHi\nwTB8+HAOHTrEzp0773VXikx6ejpBQUG8/vrrjBkz5rZ18/r5LOwY1qmZ8Jyp//xMnjyZyZMn33WH\nhBDivpCVBatWwfvvwy1bXtvQ6Uh4oj3Lwlz5p7Q7WSkpkGDJ4dS6uWHw9SPDTUf3RkNsAnAo+Iyz\nzFALIQrbpEmTqFKlCpGRkbRt2/Zed6dILFmyBIPBwIgRI+51V2zccU64EEI8lEwmWL4cpk+HU6fy\nrufnR/KAPmxrEcxv1w6Rkn7dkiuu0eDq44Orrx86NzfMqhlPneGu1+MWQoiiULZsWVJTU+91N4rU\nyJEjGTly5L3uhh0JwoUQAiAjw7Kj5bvvwtmzeVYzh4bwd6+O/FwJ/oo7DefPA1DGryKpbhpSDQpu\nxhIAJGUkFUnOthBCiAefBOFCiEdbaqrlQctZsyCPDcbMCpxoUoUzXR9jk2ccmdmnIQ4MejcaVm9F\ns9D2VChl2ZFOVhURQgjhDAnChRCPpqQkWLjQkvN99arDKtlaDftaVWNDm2CueumBy5ANlcuF0iy0\nPfWqNEfv4mrzHsnZFkII4QwJwoUQj5aEBMsyg3PnQh6742XptOwOr8yG8EDifS0bZig6HUoJD/7d\n/HmaV25VnD0WQgjxEJIgXAjxUFNVlWMxxzhybCs1v/qV0JVb0CYlO6xr0uv4X4sgNrWpxHUvy26R\nLiVK4Orrh0sJS573qeQzNEeCcCGEEHdHgnAhxEMrMT2RZb/OpM5XG3nqx0O4ppsc1jMZXdnWIpDN\nrSuR7OmKxtUVo68vrj6+aFxcrPXupy2thRBCPNgkCBdCPJTUK1f4c0wPRny/G31GlsM6GW6uRLYM\nZGvryqS5uxJYrgbp2ut4epd0+DBlcmYyjcrKJjhCCCHungThQoiHS0ICvPce6tw5NElNc1gl2V3P\n1taV2BZeiWxPd5rUbEeb+l3x9w5gxvYZpGelo2AbhJtVM35ufrLetxBCiEIhQbgQ4uGQkgIffmhZ\najAhAY2DKtc9XdnStgrbWwRhcjcQUKEaozu8hvuNdb0BRoaNZH70fGJTY/HQewCWGXBZ71sIIURh\ncvR3SgghHhwZGfDRR1C5Mrz+umUm/BYJXgbWPF2LqW92IKpLLVyqBONVoyZlA2vYBOAAXgYvJrSc\nwOAGg6nsW5nKvpUZ3GAwE1pOwMvgVVxXJYS4YcqUKWg0D264cuDAAcLDw/Hw8ECj0XDo0CGH19Sm\nTZt7sm38hQsXMBqNREZGFvu5i0KvXr3o3bv3ve6GUx7c72ohxKMtKws++wyqVYMxY+DKFbsqSR56\nvn26FtMmtmfHE/VwrV6VEtWq4+rrR0pWap753YqiEOIfwoC6AxhQdwAh/iEyAy6EE5YtW4ZGo2HP\nnj025cnJyYSHh6PX61m7dm2B231Qf/7MZjO9e/fmypUrzJ07l+XLlxMYGIiiKHbXdGtZWloaU6ZM\nISoqqkj7OHXqVOrVq2dzA5Bzk5Dz0uv1BAcHM2rUKOLyWNr1TmzYsIEhQ4ZQt25ddDodRqMxz7qq\nqjJr1iwqVaqE0Wikdu3afPXVV3b1Xn/9ddasWcPhw4cLrZ9FRdJRhBAPFDU7mwtL5uE5/T28zl52\nWCfVoGPzY1WJal0ZSpfEzb8Uuly/3CW/W4jik5KSQpcuXdizZw8rV66ke/fuBW7jQV2Z6OLFi5w6\ndYoPPviAiIgIa/nEiROZMGGCTV1VVW2C8JSUFKZNm4ZGo6F169ZF0r+YmBg+//xzPvnkE4fH58+f\nj5eXFykpKWzatIkFCxawZ88edu/eXSg3Rl9//TUrV66kfv36BAcHc+HChTzrvv7668ycOZOIiAga\nN27MunXrePbZZ1EUhX79+lnr1a9fn0aNGvHee+/xxRdf3HUfi5LMhAshHgyqSsp3q7haozzlh73i\nMADP0GvZ0L4qs97uBhMm8OLzH+MbXJU0TRaqqqKqKkkZSRh0BsnvFqIY5ATgu3fv5uuvv76jAPxB\ndvXGbrwlStimvWm1WvR6vVNtFPYNSGZmJtnZ2QAsX74cgKefftph3R49etCvXz8iIiL45ptv6N27\nN3v37mXnzp2F0pfp06eTlJTEjh07aNGiRZ7XeuHCBd5//31GjBjB4sWLGTx4MD/++CPh4eG8+uqr\n1uvJ0bt3b9auXUtSUlKh9LOoSBAuhLj/bd2K2qIF7t17U/qUffCdpdWwtVUl5r7TA82Md/nPqC/4\nV4tnKe8XKPndQtwjqampPPHEE+zatcthAP7DDz/wr3/9iwoVKmAwGAgKCmL8+PFkZGTctu2goCA6\nd+7M1q1badSoEW5ubtSuXZstW7YA8O2331K7dm2MRiMNGzZk//79Nu8/fPgwgwYNonLlyhiNRvz9\n/enbty/nzp2zqZeTXrNt2zbGjRuHv78/Hh4edO/enWvXruXbx4EDB9KokSXlbdCgQWg0Gtq1awfc\nPs/9zJkzlCpVCrCki+SkhQwaNMha59KlSwwZMoQyZcpgMBgICQlh0aJFNu1s3boVjUbDihUrmDJl\nChUrVsTNzc0647xu3TrCwsLsbhLy0rJlSwC7cbpTAQEB6HS3T8r4/vvvycrKYsSIETblI0aM4NKl\nS2zfvt2mvH379qSmpvLrr78WSj+LiqSjCCHuX3v2wBtvwKZNOJqzNiuwu0lFfn2yNgmVy/B8m9HU\nKVPXpk5OfneIf0jx9FkIQUpKCk888QQ7d+7McwZ82bJlGI1Gxo4di5eXFzt37mTu3LmcO3eOr7/+\nOt/2FUXh77//pl+/fgwbNowBAwYwe/ZsunXrxocffsjkyZMZNWoUiqIwffp0evXqxcmTJ62B76ZN\nmzhx4gQDBw6kbNmynDp1ikWLFrFnzx6OHj1ql5v84osv4ufnx9SpUzl9+jTz5s1j1KhRrFy5Ms8+\nDh8+nCpVqjBp0iSGDRtGeHg4pUuXtrmGvJQqVYqFCxcyYsQIunfvbh2/ypUrA5YZ9qZNm6KqKqNG\njaJUqVJs2rSJF154gdjYWN544w2b9qZPn45Wq+Wll15CVVU8PDwwmUxER0czdOjQfMc6tzNnzgBQ\npkwZm/LExERMJseboeXm4uKCl1fBJ0AOHDiAwWCgVq1aNuVhYWEAHDx40CZlJyQkBKPRyI4dO+jZ\ns2eBz1dcnA7CZ8yYwdq1azlx4gSurq40bdqUGTNmEBoaaq0zcOBAu/ybpk2bsmPHjsLrsRDi4ffX\nXzBhAqxenWeVffXL8Wu3OiTVqYre2xsv4OCVQ3ZBuBAPvKJMmyqiXOtBgwZx8eLFfHPAv/rqK5tg\nNyIigqpVqzJx4kRmz55N+fLl82xfVVVOnjzJb7/9RosWLQCoWbMmjz/+OC+88AJ//vkngYGBAHh7\nezNs2DAiIyN57LHHAMsM6rhx42za7Nq1Ky1atGDt2rU888wzNsdKlizJhg0brF+bzWY+/PBDkpKS\n8PT0dNjHpk2botPpmDRpEs2aNbPJW865hry4ubnRo0cPRowYQZ06dezeO3HiREwmE0eOHMHPzw+A\noUOHMnToUKZPn86oUaNsgt3k5GSOHTtmM95//fUX6enpVKpUKc9+xMbGotFoSElJYcuWLSxYsIDQ\n0FBatWplU69bt25s27Ytz3ZytGnTxvppRUFcunTJ5gYmR0BAAGDJvc9Np9NRoUIF/vjjjwKfqzg5\nHYRHRUUxatQowsLCMJvNTJo0ifbt2/PHH3/g4+MDWO7qOnTowJdffml9n7M5T0IIQVwcvP02fPwx\n5DGrcjS0NOu7NyCuUQ1cPD1xvRGgPKgPbgnxMLp69SoGg4GKFSvmWScnIDSbzSQlJWEymax5wQcO\nHMg3CAeoXr26NQAHaNy4MQBt27a1BuC5y0+fPm13brAEqBkZGVStWhVvb2/2799vF4QPHjzY5uuW\nLVsyd+5czp49azc7W9RUVWXNmjX06NEDVVVt0mI6dOjAf//7X3bv3k3Hjh2t5QMGDLCb3Y+NjQWw\nxnCO5J5oBUuax/Lly+1m8efMmUOCg+Vhb5XfufKTlpaGq6urXbnBYLAev5W3t/dtU4buNaeD8PXr\n19t8/eWXX+Ll5cWOHTt44oknAMs3hl6vt+YxCSGEUzIyYMECeOstiI93WOVklZL81Ks+15rXwcXD\ng1tv72VLeSHuH4sXL+aVV16hc+fOREVFERJinw529OhRxo8fT1RUlF0QlZiYeNtz3Brg58z8VqhQ\nwWF5fK7fLfHx8bz22musWbPGpjyvc996rpxg8tb3FoeYmBgSEhJYsmQJS5YssTuuKAoxMTE2ZTlp\nLI7kN4GxevVqfHx8iImJ4aOPPiIqKorff//dLs5r0KBBAa+iYIxGI+np6XblOWWOlja8dbWZ+9Ed\n54Rfv34ds9lsc1ejKArbt2+ndOnSeHt707p1a9555x38/f0LpbNCiIeMqsKaNfDaa/D33w6rnCvv\nzbEXehMyeDxpx1eizbL/RSxLDgpxf6levTq//vorbdu2pWPHjvz2228EBwdbjycmJtK2bVs8PT2Z\nPn06VapUwWg0cv78eQYOHIjZbL7tObRabYHKcweb//73v9mxYwevvPIK9evXt6aU9OnTx+G5nWmz\nuOT0r1+/fjz//PMO69x60+MoSC1ZsiSQ/41EeHi4NeDu2rUrderUYfDgwRw/fhwXFxdrvbi4ODIz\nM2/bd71ej6+v723r3SogIIDNmzfblV+6dAmAsmXL2h2Lj4/P9+bjfnDHQfjYsWOpX78+zZo1s5Z1\n6tSJHj16EBwczOnTp5k4cSLt2rVj3759DtNS9u7de6enF3mQMS0aMq6Fz+3QIa499wwl/zjh8Hi8\nt5Hofp1w6T0MXzc/Lv8TRzNtM1afX81103WMWssflbTsNEq4lKBXYC/27dtXnJdwX5Pv2aJRGOMa\nGBho/RjdKQ9oqlW9evX46aef6NixIx06dOC3336z5vBGRkYSGxvL2rVrCQ8Pt75n48aNRd6v+Ph4\nNm/ezNSpU3nzzTet5enp6YW6Ec3dymsW19/fH09PT0wmk3W1lTuRs1JK7jSd/BiNRqZMmcKzzz7L\n0qVLbR7o7N69e5HmhNevX58lS5Zw5MgRateubS3fvXs3YPleyy0rK4vz58/z5JNPFvhcSUlJHD16\n1OGxqlWrFri9/NxRED5u3Dh27NjB9u3bbb5Jcm8TGhoaSsOGDQkMDOTnn3/Ocw1KIcSjxfX8eUp/\nNI9SWxzvApfuquPA023IingJ3xK2H3l66j0ZVGUQp5NPcyzhGAA1vWsS7BF833/sKMSjqEWLFnz7\n7bd069aNjh07EhUVha+vr3VmOfess9lsZs6cOUXeJ0fnBpg7d+599WyJm5sbgN2NgVarpWfPnixf\nvpzDhw9Tp04dm+MxMTFOZSDodDqaNGlCdHS0033q06cPb7zxBnPmzCEiIsL6e7ewcsLz+j3erVs3\nXnrpJRYuXMiCBQsAy6cQixYtIiAgwLp0Yo4//viD9PR0mjdv7sxl3TMFDsJfeuklVq1aRWRkJEFB\nQfnWDQgIoHz58pw6dcrh8Zz1M8Xdy5mdkTEtXDKuhejGQ5fqxx+jOHjoMlujsKtdDXYNe4JxPWbl\nG1SHEVaUPX2gyfds0SjMcXWU2/ow69SpE8uXL6dv37507tyZzZs307JlS/z8/HjuuecYPXo0Op2O\nNWvWkJKSUuT9KVGiBG3atGHWrFlkZmZSsWJFtm/fzrZt2/Dz87ungXjucxuNRkJDQ1m5ciXVqlXD\n19eXSpUq0bhxY9599122bt1Ks2bNiIiIICQkhPj4eA4ePMi6descPqjoSLdu3Xj11VdJTEx0aulA\nrVbL2LFjefnll/nhhx/o1q0bcOc54YcPH+aHH36w/jsrK4t33nkHVVWpV6+edSa7XLlyvPjii8ye\nPZvs7GzCwsL4/vvv2b59O1988YVdutDGjRsxGo08/vjjBe6Tp6dnnj/nzjyrUBAF2qxn7NixfPPN\nN2zZsoVq1ardtn5MTAwXLlywfvwkhHgEZWTA3LlQpQrMneswAP+9QUXmfxLBxjf+zUVPM8euHbsH\nHRVCFAZHN9C9evVi8eLFREdH061bN9zc3Pj555+pUKECkydP5t1336Vu3boOtxlXFMWuzbv95GvF\nihU8+eSTLF68mPHjx5OYmMiWLVvw8PBw+lzO9sFRvbyu6dayJUuWEBQUxMsvv0y/fv2sm/H4+/uz\ne/duhgwZwrp16xg9ejTz5s3j6tWrdp8m5NfPZ555BkVR+O67727blxwRERF4eXnx3nvv5X3RTjpw\n4ACTJk1i0qRJHDp0iOzsbN58800mT57M2rVrbeq+++67zJgxg40bNzJq1CjOnDnDF198Qf/+/e3a\nXbVqFd27d89z+cj7haI6ecs3cuRIli9fzrp166hZ8+bDT56enri7u5OSksLkyZPp2bMnZcqU4cyZ\nM0yYMIELFy5w7Ngx3N3dAdu7iDtZsF04JrNfRUPG9S6oKnz7LfznP3k+dHk+qCQbX+jI2bCqud6m\nUtm3MgPqDiiunj5U5Hu2aBT2THiBcsKFKELDhw/n0KFDhbYV/b22f/9+wsLC2L9/P3XrFnzfiPx+\nPgs7hnU6HWXhwoUoimJd6D7HlClTmDRpElqtlqNHj/Lll1+SkJBAQEAA7dq1Y82aNdYAXAjxiNi3\nD8aMgTw26orzceO73mGc79UaVSO53EIIca9MmjSJKlWqEBkZSdu2be91d+7au+++S69eve4oAC9u\nTgfht1suyGAw2K0lLoR4uKmqyrGYY+y9ZJklbGysSvW5X6AsXuxwRQeTm4Gro55nYtVYXNxKUNZB\nAC7rfQshRPEpW7Ysqamp97obhWbVqlX3ugtOu+MlCoUQj7bE9ETmR88nLi0Od50bdTccpvyiDSiJ\n9qOvw5UAACAASURBVA8EmbUasocMxmXa25T198e4ciSZZvs1ZWW9byGEEI8KCcKFEAWmqirzo+eT\nnpVO5XMpdPlgNYFH/nFYN7tLJ7TvzUFz41kSBegV2IvVZ1eTlJGEh94DsMyA+7n5MTJspCw3KIQQ\n4qEnQbgQosCOxRwj5dolnlwRTeO1e9Ca7VNP0iqWw7j4v2g7dbI7lrPet3uQO3sv3njgrWwjapas\nKQG4EEKIR4IE4UKIglFVrn32Ef95bzklYpPtDpv0Wn7r15KLI/rTv7F9AJ5DURRC/EMI8Q/Js44Q\nQgjxsJIgXAjhvGPHYNQoWuWx7fDxplVZP7ozcQHeVHbVF3PnhBBCiAeHBOFCiNtLSbHsdvn++w43\n24kv7cX6UZ043qI6KArJGUmywokQ+VBVVVKvhLjPFPduqRKECyHypqqwbh3qiy+i/PMPt4YMWToN\nO3o357f+rTAZXABZ4USI29Hr9aSnp6PX6+222xZC3BvZ2dlkZmbi6upabOeUIFwI4dhff8Ho0fB/\n/2cXfAOYHmvLkufrcdJPwUOvA1WVFU6EcIJGo8FgMJCZmYnJwSdLj5KkpCQAp7cXT81M5VLKJbSK\n45uXbHM2AR4BuOndyDJncTHpIiazCY2qkJ2eDmYzaBTK+gXh5lqIGwkmJsKRI5CVZVvu5wchIVDM\nN1sFHVdheU7JYDAU698uCcKFEMDNjXf2n9lB7c9+pvbSX9Bk2q/lrZYtizJvHi49ezIMOHbtmKxw\nIkQBKYpSrDNu96ujR48C0KiRc+lrrq6uLDq0iPSsdDSKxuaYWTVj0BmY0HICAHO2z7GpZ87KIvnM\nabJSUlA0GkZ0m0yNioW0q6LBAFeuQKdOcOmS7bHmzeHHH8HXt3DO5YSCjqu4NzS3ryKEeNglpicy\nY/sMti2bQufu46m7eJ1dAK5qtfDyyyh//gm9eoGiWFc4GVB3AAPqDiDEP0QCcCFEkVEUhZFhIzHo\nDCRlJKGqKqqqkpSRhEFnsH4KdyzmGHFpcTaBukanw7NSZfTe3qhmM4vWTWX74fWFlwdcpw5s3w6V\nK9uW79gBrVvDxYuFcx7x0JCZcCEecaqq8tmm2XT6+Eca/HrYcZ1WrVDmz4datYq5d0IIYcvL4MWE\nlhPy/RRu76W9uLvYp5soGg3uFQNRXFzIiIlhVeQizl39i55thuKic7n7zlWqZAnEO3WCQ4f+v707\nD6uq2v84/j6HQUAUBUFxHnJAS1PRyszU0jJN65YNXjOHX1aSOTTScK1u5bV5EL1Nmg2a2WClppYz\nFy1Q0RA0zRFFHFBkns7+/XHi6PGgImxA4PN6Hp4H1l5nr28r6nzZZ63vOt0eF2d/Ir5sGbRtW/px\npEpQEi5SnRkGB2e+zgPhb+J7Ktvlcnrdmvw45jqufOIN2gd1qIAARURcleacAYvFgk9wQxrWa0bi\nn1tZv+0Xko7vZ8zAp/DzNWHJSIMGsHo1DB4M69adbt+3D669FhYvhquuKv04UulpOYpIdbV7NwX9\n+9E47CmXBNxmgejBoUz/7BF23NKdmKSNFRSkiMjFCw0OJSMv45zX03PTuanzP5h411Tq+tZj7+Ed\nvD7vMfYkbTcngDp17E+9Bw92bj9+HPr2hSVLzBlHKjUl4SLVTV4etmn/oaBDe9x+XeFy+UjzQGa9\nP5rFkwaS7etVAQGKiJROSGAI/t7+2Ayby7XCMqrtAtqRRg5NO3bH168epzJP8N43zxEVt9ycILy9\n4dtvYcwY5/bMTHtyPmeOOeNIpaXlKCLVSXQ0OSPvo0b8DpdL+R5urBlxPVF396DA43Q5rfTcdB28\nIyKVSuEGzojoCI5nHsfX0xfAUUZ1+BXD+c///kNKVgo1PWri3rQh1sQ8Ck6k8tWKGRxI/os7ev8f\n7m6lXCfu7g4ffQTBwfDyy6fbCwpg5Eg4fBiefBK0ob1aKtaT8KlTp9KtWzf8/PwICgpi8ODBbNu2\nzaXfCy+8QKNGjfDx8aFPnz7Ex8ebHrCIlEBaGtnjHsR29VVFJuB7O7dk+icPsm74dU4JuA7eEZHK\nqnAD55guY2jl34pW/q0Y02UMT1/7NF/88QXZ+dn4evpisViwWq3UadoCn8aNwWLhf3HLmP7tv0jL\nTC19IBYL/PvfMH26a7L99NMwaZK9frlUO8VKwtesWcMjjzzC+vXrWblyJe7u7tx4442cOHHC0Wfa\ntGm89dZbTJ8+nejoaIKCgujXrx/p6ellFryIXFj+wu/Iat0Cr5kfYrWdVYrL3x9mz6bu/zaS2bzR\neUt+iYhUNkWVUd1+bLtL+cJCXgH1cGvakJo+fuxOSuCdBeEcT002J5iwMPj6a/D0dG5/910YNgxy\ncswZRyqNYi1HWbp0qdPPn3/+OX5+fkRFRTFw4EAMw+Cdd94hPDyc22+/HYA5c+YQFBTE3LlzGTt2\nrPmRi8j5JSVxcvRw6ixdWfR/6P/8J7z1FgQF4QcXLPklIlIVnKt8YaHafvVo0rAjx3cmcPDYXt76\n+ikeGvIvmgS1LP3gd94J9erBkCFw6tTp9vnz4eRJ+P57+1pyqRZKtDHz1KlT2Gw26tatC8CePXtI\nTk6mf//+jj5eXl706tWLqKgocyIVkeKx2ch49w1yWrekztKVrtdbtIClS+GLLyAoyNGsg3dEROw8\na3jz6J2v0qZJR9IyT/LeN8+wY/+WC7+wOHr3hrVr7aUMz1RYTSUz05xx5JJXoiR8woQJdO7cmWuu\nuQaAw4cPA1C/fn2nfkFBQY5rIlI2DMMg/kg8n235jIXfvsLRK9tQc+IT1Mg4q+63m5t9A1BcHNx0\nU8UEKyJSwYpTvjC0YSjeNXx4aMjzdG1zHTl52fz3h38Ts32NOUF06gTr10ObNs7tv/4KAweClvJW\nCxbjIs9rnTx5Ml9//TWRkZE0b94cgKioKHr27Mn+/ftp3Lixo+/o0aNJSkri559/drSlpp7e5LBz\n585Shi9SvaXlprFg3wIysk5y+6IEBv24BfcC1/+kM0JC2Pvss2TppDYRqeYMw2D2rtnk2nJd1oXb\nDBueVk9GXTbK8UmgYRhs3LuC+EMbAOja/EY6NLralFjcU1JoExaGz65dTu1pV17JznfewVbz3Mtm\npPy1bt3a8b2fn1+p73dRT8InTZrE/PnzWblypSMBB2jw90cqycnOmxeSk5Md10TEXIZhsGDfAgL3\nHOLfLy7ltu9jXRLwAm9v9k+eTMLs2UrARUSwL70b2mwonlZPMvMzHZvRM/Mz8bR6MrTZUKeleBaL\nhdAWNxLa/EYANu79leg9v3CRzzCLlO/vz58zZ5J51hPxWrGxtBk/Hjc9Ea/Siv0kfMKECSxYsIBV\nq1bR9qw3c8MwaNSoEePHjyc8PByA7Oxs6tevzxtvvMEDDzzg6Hvmk3Az/ooQu5iYvzfThaqes5ku\n5XndlhjLvifG0n9BTJFPv7dd1RKPmR/QpvONFRDd+V3K81rZaW7Lhua1bFTkvBqGcc7N6IZhkHA0\ngZikv68FhxISGMKmP9fxxfL3KLDlE9rueob3exSr1e18wxRPSgr07w8bzzqduFs3+1rxv/fgFZd+\nX8uG2TlssaqjhIWF8cUXX7Bw4UL8/Pwc67xr1apFzZo1sVgsTJw4kVdffZV27drRunVrXn75ZWrV\nqsWwYcNKHaSIOEvdsJY6995Bh73HXK5l1PFh8YRb2NYrhFbWQ7Qp4vUiItVd4Wb09oHtndpTs1OJ\niI5wHOQDsDV5K/7e/oR1C+OhIc/z8aKpxGxfg6e7J3f3HVf6Tez+/vb14DfdBL//fro9OhpuvBGW\nL4eAgNKNIZecYi1HmTlzJunp6dxwww00bNjQ8fXmm286+jz55JNMmjSJsLAwunXrRnJyMsuXL6em\n1jOJmKYgN4e/woZTs2cfGhWRgMf16UDEp2HE9+6gE9hERC6SYRhEREc4HeRjsVjw9fQlOz+biOgI\n2jTpyINDnsfDzZOouF/4IXKOKUtTqFPHnmz/XfTCYdMmuOEGOHq09GPIJaVYT8JtxTzJacqUKUyZ\nMqVUAYlI0Q6tXoxl9Gha7Tnici2jjg+LJg4k4frTT3R03LyIyMVJOJpASlaK45j7M1ktVo5nHifh\nWALtG3Vg9MAn+WjRVFZuWoh3DR9u6n5X6QPw87MvPxk4ENatO92+ZQvccgusXAm1apV+HLkklKhE\noYiUn6yMU8T9320E3TiY4CIS8D96tydi9jinBFzHzYuIXLwLHeTj6+nrWEPeoUUoI26ahMViZfH6\nuayJXWROELVqwc8/2+uJOwUXA3fcAbm55owjFa5YT8JFpHycvRmo2Y5jtHpyKpfvc116QmAgGe+8\nwU9NEjmeeRzfvz8OTc9NJ8AnQMfNi4iUsS5tepKTm8W8FRF8u+ZjvDy9uar9DaW/cc2asHix/fCe\nFStOt//yC4wcaT9szarnqJWdknCRS4TTZiCbB90/Xs61C2NxLyhiOdjQoRARQc3AQMLPs8NfRESK\nLzQ4lK3JW4tcjgL2hxxdg7sSfyTeqXLKbdeNYuG62cz9NYIaHt5c2bpH6YPx8bEfY9+3r/0peKF5\n86B+fXjrLe39qeSUhItcAs7cDNR4ezL/eHMxTfefcO1Yrx7MmGFPwv92rh3+IiJycUICQ/D39ic7\nP7vIg3x8PHxYuH0hJ7JPuFRO6dP1NlZtXMicpW/h6eFF++ZdSh9QrVr2J+LXXgtnHujzzjsQHGw/\nBVkqLX2WIXIJSDiawImTyVwdsZhHJs8tMgFPHXwTxMc7JeAiImIei8VCWLcwvNy9SMtJcxzkk5aT\nRg23GlgsFnIKcoqsnBJvO8j1V95KgS2fTxb/h78OxpsTVFCQvWrK2YcfPvUUzJljzhhSIZSEi1wC\nNv70IY888jm3fLvJZflJhp8PX//rDn54aRgEBlZQhCIi1YOflx/hPcMZ02UMrfxb0cq/FWO6jOG2\ntreRmZfp8oQc7JVTUrJSaBdyNVd3uJG8/Fw+/PFlEo/uNieoFi3smzXProwyZgwsWWLOGFLulISL\nVKC09BP8NnYw9zz0Ps2KePod3yuEGbPHsa13hwqITkSkeipc5jei0whGdBpB+8D2bDy88YKVUzYm\nbeSevg9z5WU9yMrNZMb3L3LkxEFzgrrySvjhB/D0PN1WUGD/dHTDBnPGkHKlJFykgsStW0hyt/Zc\n9dFPeOQ7P/3OrO3Ngn/dydcv3kVG3Zqq+S0iUklYrW7cd9Mk2jW9kvSsVCK+m8KJNJMO2unTB778\n0nlDZmamva74jh3mjCHlRkm4SDlLy0xlVfhwWt50F5dtP+xyPb5XCBGfhrGtj/3pt2p+i4hUvNDg\nUDLyMs55/cyHJR7uHowZ9DQtgttxIv0YEd+/QFrmSXMCufNOmD7duS0lBQYMgORkc8aQcqEkXKQc\nbdm0nF19u9DnP1/ik5XndM3wq83Cf93FJ+E3k17Hx7EZyMvdSzW/RUQqWGHlFJvhWja2qIclNTy8\neHDwczSs15wjJw4yc+FLZOWcO4m/KOPGwfPPO7ft2QODBkGGSWNImVMSLlIO0jJTWfLawzS58TY6\n/1bERp0+fbD8EceQF75iTNf/c9oMFN4zHD8vv/IPWkREHM5XOeVcD0t8vHwZd9sLBPoFk3h0Nx/+\n+Aq5eTnmBPTiizB6tHNbTAzccw/k55szhpQp1QkXKWOx29aQ+lgYNy/fhtU466KnJ0ydChMngtWK\nBVTzW0TkElVYOeViDkirXbMOYf94kbcXhPPXoXhmLZ7GA7c+g5tbKVMwiwX++184eBCWLTvdvmgR\nTWvUYP9TT5Xu/lLmlISLmODs4+ZDg0NpUrMhv3z2Et1fmcWVB1NdX3TFFfajhzt2LOdoRUSkpEpy\nQJp/7SDCbn+Bd795lvh9m1gY+Sl3XP9/pQ/GwwMWLIBevSA21tEc9O235AYHQ7dupR9DyoyScJFS\ncjpu/u/yVVt2RnHt/A3cuvAPl8onAEyeDK+8Al5e5RytiIhUhAb+TRh767O8982zrIldRPMGbena\n9rrS37jwVM1rroH9+x3NjadPt7cNG1b6MaRMaE24SCmcedy8r6cvGAbu2/7kgee+4x/fbHFNwBs3\nhhUr4M03lYCLiFRBhmEQfySez7Z8xmdbPiP+SDyGYV+L2CK4Lbf3sq/jnrcigqTjB8wZtGFD+6E9\nfmftHxo1CtasMWcMMZ2ScJFSSDiaQEpWClaLlfzsLFp8tYLJT31Lux1F1IS95x7YuhX69i3/QEVE\npMylZqcyNXIqs2Jn8VfKX/yV8hezYmcxNXIqqdn2ZYnXdRxAaNvryc3LZtbiaWTnZpkzeIcO8P33\n9iUqhXJz4bbbYNs2c8YQUxU7CV+7di2DBw+mcePGWK1W5syZ43R95MiRWK1Wp68ePXqYHrDIpSQm\nKQYfdx+M/Qe5dco8Rn4URc1M59KDub4+9sMV5s2DunUrKFIRESlLZ38yarFYsFgs+Hr6kp2fTUR0\nBIZhYLFYuPuGhwkOaEryiUTm/vK+40l5qfXpA59+6tx28qQ9EU8tYm+SVKhiJ+EZGRl07NiRd999\nF29vb5ddwBaLhX79+nH48GHH15IlS0wPWORSkpebQ9Dy33h00lyu+t31Y8U9nZrx04KXtSZPRKSK\nO/OT0bNZLVaOZx4n4VgCYK8hPmbgU9Tw9CZ2VxSrN/9kXiDDhpEYFubctmsXjBwJZiX7YopiJ+ED\nBgzg5Zdf5o477sBqdX2ZYRh4enoSFBTk+KpTp46pwYpcShJ2/U6Lf73HuNeWE5CS6XStwN3K8gdv\nJOLV2wnpelMFRSgiIuUlJinGsTm/KL6evo6yhgBBdRsxvN+jAPwQ+Sl/HTRvycjh++/n6G23OTcu\nXGjfjySXDNPWhFssFiIjI6lfvz5t27Zl7NixHD1axLpYkUouLz+PZfNfw+vGm+m7NM6l9veR5oF8\nNPMBIu++Bv9agTpuXkREitTpsmu4oett2Awbs5e8wamME+bc2GJh/+OPQ9euzu1PPw3r1pkzhpSa\naUn4zTffzOeff87KlSt58803+f333+nbty+5ublmDSFS4ZJTEln0+O1cN+o5Wuxz/Z/l+juu4oP/\nPsDOJjV13LyISDUSGhxKRt65j4xPz00ntGGoS/ugHvdxWaMOnMo8weyf36CgwJzTLo0aNeCbb5z3\nIhUUwN13w+HDpowhpWMxSrAboFatWkRERDBixIhz9klKSqJZs2bMnz+f22+/3dGeesbGgJ07d17s\n0CIVwjAM/jrwG43ffpueka7HzucGBhL15FjWtLLvSg+pE0IL3xZKwEVEqgnDMJi9aza5tlyXdeE2\nw4an1ZNRl40q8n0hKzedRbEfk5WXzhWNe9K5WW/T4vKLjKT1pElObae6duXP6dPBXcfFXIzWrVs7\nvvc7uxxkCZRZicLg4GAaN27Mrl27ymoIkXKRnZfJ1pUfcN34Z4tMwE/27En83Ln49r6NgU0GMrDJ\nQFrWaqkEXESkGrFYLAxtNhRPqyeZ+ZkYhoFhGGTmZ+Jp9WRos6HnfF/w9vSlV1v7A8u4xP9x5JRJ\n9cOB1J49SRo1yqmt9saNNPrgA9PGkJIpsz+Bjh49ysGDBwkODj5nn9BQ149lpGRiYv4+Ll1zWmpn\nHkH/Z/xWLl8SyfCvY6iRW+Dc0cMDXnuNOhMmcKUS7oui39eyo7ktG5rXslEV57X3Nb1JOJbg2IQZ\n2jCUkHohxXgwE0qBVya/xnxL9L6lPDnsbbxr+JQoBpd5/egj2LcPVq509An+9FOC//EPuPXWEo1R\nHaWaXOax2El4RkaGY/mIzWZj3759xMbGEhAQgL+/P1OmTOHOO++kQYMG7N27l/DwcOrXr++0FEXk\nUld4BP3xzON4Jx5j8H9X0j0m0bVjq1bw1VdQhd44RESk9CwWC+0D29M+sL1T+5kPeMC+hjwk0Dk5\nv+Xqe9i+bzOJR3fz3ZqP+Wf/R80Jys0N5s6Fzp0hKel0+4gRsHEjtGxpzjhyUYq9HCU6OpouXbrQ\npUsXsrOzmTJlCl26dGHKlCm4ubkRFxfHkCFDaNu2LSNHjiQkJIT169dTs+a5y/WIXEoKD1rIyEgl\neN02Hg3/tugE/J57YNMmJeAiIlIsxTlJE8DdzYMRN0/Cw82T3xJWsnlnlHlB1K8PX39tT8gLnTwJ\nQ4dCTo5540ixFTsJ7927NzabDZvNRkFBgeP7WbNm4eXlxdKlS0lOTiYnJ4e9e/cya9YsGjVqVJax\ni5gq/kg8Rw/tofPHS5n4n18IOuq8yz23hjuH3n7J/jShdu0KilJERCqT4p6kWaiBfxNuu24kAPNX\nzOBk+nHzgunZE6ZNc27btAmef968MaTYymxjpkhlkpmTzk8/vM3IVxZx57dbcS+wOV0/0jyQD2f8\nH7/2aQZa/y0iIsV0MSdpFurZcQDtm3UhMyedL5e/h82wuby2xCZPhn/8w7ntjTdg1SrzxpBiURIu\n1d7uQwnMfeFexj41l05/uNZOXdu3HR/NfICjLYIqIDoREanMLvYkTbCvKx/Wbzw1vWuz48AW1sQu\nMi8giwU+/hiaNDndZhj29eEnTDosSIpFSbhUWwW2An6Omkv82DsZ9dpi/E9mOV3PrlmDD8b35Ysx\n15Hn5XHOgxZERETMYBgG8Ufi+WzLZyzc9RPXhQ4B4Kf/fc6hY3vNG6huXfjsM+dPdhMT4cEH7Qm5\nlAsl4VItpZw6wicfT6TFqIkMWhyPm835fzoH2zXkgw8fZOPVrQD7QQsBPgE6gl5ERC5KcU/SLGrz\n5spj6/GuF0h+QR5zlr5Fbp6JGyh794YnnnBuW7DAnpxLuVASLlXKmU8RPtvyGfFH4jn7UNhNf0by\n3bN3c89jH9Huz6Mu99hwT0/efX0oKcF1HAct6Ah6EREpiZDAEPy9/Ytc1134gKddQLtzbt70bFAf\ntxpeJB3fz1crZri8p5XKv/9tL1t4pkcegd2uB9OJ+XReqVQZhTW+U7JSHOvvtiZvxd/bn7BuYXhZ\nPfl25QcEvDWT0b/+ifXs/4/Vqwdz5nDVgAHU/vugBetJKyF1Qhja89wnnYmIiJyLxWIhrFuY4wwK\nX09fwP4EPMAngLBuYWw/tp2UrBTHtTO5ubljaRiI+4FkYnasoWn9y+jd2aQDdjw94csvoWtXyPp7\nSWZ6OgwfDmvX6lj7MqbZlSrh7BJQhQpLQL2zehq1dyQyaPrPtN51zPUGvXvDF19Ao0ZYwHHQQkye\nfbOMEnARESkpPy8/wnuGn/MkzR92/HDezZu1avlTt00wu+N/Z+G62TQKbEHrxpebE1xICLz5Jowb\nd7pt/Xp45RWYMsWcMaRIWo4iVcK5SkAZhkHO0aP4L1rDmOe/dk3ArVZ48UX49VdQXXsRESkjhSdp\njug0ghGdRtA+sP1FPeDxD2rMDV1vx2bY+HTJ65xIK+KBUkk99BAMGuTc9u9/w4YN5o0hLpSES5VQ\nVAkoW14e6bt2cd2c1YTNiKJ22lkbWho0gBUr4F//cj5BTEREpBwVd/PmoB7DadukE2lZqcxaPI28\n/DxzArBY4JNPIOiMUrwFBfDPf8KpU+aMIS6UhEuVlJuaSn7MFv7vrV8ZtGS76/rvvn0hNta+DEVE\nRKQCXWjzpr+3P4bN4Ms/vsSrSWN8a9ZhX/JOvl3zoXlBBAXB7NnObbt325+Sq2xhmVASLlVC4VME\nw2YjIzGRwJUxPDltBSHbjzh3tFjsT76XL4f69SsmWBERkTMUbt70cvciLScNwzAwDMPxfU5BDrO3\nzOavlL/Yn55IdqAvWCxExf1CVNxy8wK55RYIC3NumzcPPv3UvDHEQUm4VAkhgSHUtvqQ+ucOrl2w\ngUen/486qdlOfYx69WDpUvsacC0/ERGRS0jh5s0xXcbQyr8VrfxbMbrzaLzcvQCcShfW9quHT+PG\nACxY9SF7D/9pXiBvvAEdOzq3PfIIJCSYN4YASsKlivjzwFZsWxIYE7GW237c5nL4Tn6Pa7DExkL/\n/hUUoYiIyPmdvXnTgoUT2Sdcig4AePkHYK1TmwJbPp8snsapjJPmBOHlBV99BT4+p9syM+Gee06X\nMRRTKAmXSs0wDNbELmLRuxMZ/+oSrog77NrniSdwX71G1U9ERKRSKarowJlqN2mOr18AqenH+XTp\nGxTYCswZOCQEpk93btu6FR5/3Jz7C6AkXCqxvPw85v3yPkdefoYJ764hICXTuUPduvDjj1heew08\nPComSBERkTJisVho2b47tX3qsisxjkVRn5t385EjYdgw57YZM+C778wbo5pTEi6V0qmME3zwxROE\nPDWNod/+gXvBWTu3u3WDTZvgVpNOFRMRESlnxSld2KPFdYy65XGsFisrNi4kdmeUOYNbLDBzJrRq\n5dw+Zgzs22fOGNVcsZPwtWvXMnjwYBo3bozVamXOnDkufV544QUaNWqEj48Pffr0IT4+3tRgRQD2\nJ+/i89dHcdcTH9M59pBrh0cfhchIaN683GMTERExy4VKFwb4BBBSL4RWjTow5LqRAHz56/ukZpp0\nkE/t2vb14Wd+mnzyJNx7L+SZVKO8Git2Ep6RkUHHjh1599138fb2djnladq0abz11ltMnz6d6Oho\ngoKC6NevH+np6aYHLdVXdMJqNky6h7Gv/ETQsbOeDtSqBQsWwLvvgqdnxQQoIiJikvOVLvRy9yKs\nW5gjH+t95a10adOTnNwsVm//hryCXHOCCA2FadOc29av15H2JnAvbscBAwYwYMAAAEaOHOl0zTAM\n3nnnHcLDw7n99tsBmDNnDkFBQcydO5exY8eaF7FUWYZhkHA0gZikGMD+MVxIYAgWiwWbrYAlKz4m\n6JmXuSsm0fXFnTrBN9/AZZeVc9QiIiJlp7B0YcKxBGIO/f3+2DCUkHohTg9ELRYL994QxqFj+zic\ncoConYu4uvs1Lg9NS2TiRPsJ04sXn277z3+gXz/o06f096+mip2En8+ePXtITk6m/xnl37y8ulGM\nygAAIABJREFUvOjVqxdRUVFKwuWCUrNTiYiOICUrxbETfGvyVvy9/RndcSQr575G73/PomFSmuuL\nx46Fd94Bb+9yjlpERKTsFZYubB/Y3qm9qIdXowc+xetzJ7PveDyrN/9Eny6DzQjAfprmlVfCoUOF\ng8N998GWLRAQUPoxqiGLYVz8WaS1atUiIiKCESNGABAVFUXPnj3Zv38/jf8uHg8wevRoDh06xNKl\nSx1tqampju937txZmtilijAMg9m7ZpNry3WphWrk5dIp+i9Gzf6NmpnO688KvLzYFx5Oyi23lGe4\nIiIiFS4tN40F+xZwKu8U3m72h1BZBVnU9qhNj1qd+f2vxViw0P/y4dT3a2bKmLViYmgzbhyWM1LH\nE71789drr9kT9SqudevWju/9/PxKfb8yr45iyscgUqXtSdvDqbxTLgm4NTubW76PYdyMSJcEPKtF\nCxLmzFECLiIi1Y5hGCzYt4BcWy4+7j6OkzR93H3IteUSlbaZDg2vwcBg3Z8Lyck355CdtNBQDv/9\nALZQ3dWrqbdwoSn3r25MWY7SoEEDAJKTk52ehCcnJzuuFSU0NNSM4QWIifn7o6hKOKfxW+JpZWnl\n+IPNMAzyDyZx24xVdNtYxPrvu+/G+5NPuLzmuQ8wMEtlntdLmea17Ghuy4bmtWxoXksm/kg8Pid8\nCPIMKvL6rv27qFO/Gc1tKew9vIOdJ37j/psfM+fB6IcfwrZt8Pe/O4Dm77xD8xEjoG3b0t//Enbm\nag4zmPIkvEWLFjRo0IDly5c72rKzs4mMjKRHjx5mDCHVhGGz4bE5nofCv3ZNwC0W+0aQefOgHBJw\nERGRS9GFTtL0dvNme+oO7rtpIjU8vNj0ZyTR21ebM7inJ8yd6/w+nJlpL1uYk2POGNXERZUojI2N\nJTY2FpvNxr59+4iNjeXAgQNYLBYmTpzItGnT+P7774mLi2PkyJHUqlWLYWeftiRylsLDCGy5udRb\n8j8mTPmRJonOf20W1K5l35X91FPVYt2ZiIhIaQXWCeaO6x8AYMHqDzmemmzOjVu3hvffd27bvBme\ne86c+1cTxU7Co6Oj6dKlC126dCE7O5spU6bQpUsXpvxdJ/LJJ59k0qRJhIWF0a1bN5KTk1m+fDk1\n9cRSLiAkMATffHeu+ORnxr29ilrpzrVNjzULxPp7NPxdIlNERKQ6u9B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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1390,12 +1094,59 @@ "a_y = (0.0039 + \\frac{0.0058}{1+\\exp{[(v-35)/5]}})*v*v_y- g\n", "$$\n", "\n", - "These equations will be very unpleasant to work with while we develop this subject, so for now I will retreat to a simpler one dimensional problem using this simplified equation for acceleration that does not take the nonlinearity of the drag coefficient into account:\n", + "These equations will be *very* unpleasant to work with while we develop this subject, so for now I will retreat to a simpler one dimensional problem using this simplified equation for acceleration that does not take the nonlinearity of the drag coefficient into account:\n", "\n", "\n", "$$\\ddot{x} = \\frac{0.0034ge^{-x/20000}\\dot{x}^2}{2\\beta} - g$$\n", "\n", - "Here $\\beta$ is the ballistic coefficient, where a high number indicates a low drag." + "Here $\\beta$ is the ballistic coefficient, where a high number indicates a low drag.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is still nonlinear, so we need to linearize this equation at the current state point. If our state is position and velocity, we need an equation for some arbitrarily small change in $\\mathbf{x}$: $\\begin{bmatrix}\\Delta x \\\\ \\Delta \\dot{x}\\end{bmatrix}$, like so:\n", + "\n", + "$$ \\begin{bmatrix}\\Delta \\dot{x} \\\\ \\Delta \\ddot{x}\\end{bmatrix} = \n", + "\\begin{bmatrix}\n", + "\\frac{\\partial \\dot{x}}{\\partial x} & \\frac{\\partial \\dot{x}}{\\partial \\dot{x}} \\\\ \n", + "\\frac{\\partial \\ddot{x}}{\\partial x} & \\frac{\\partial \\ddot{x}}{\\partial \\dot{x}}\n", + "\\end{bmatrix}\n", + "\\begin{bmatrix}\\Delta x \\\\ \\Delta \\dot{x}\\end{bmatrix}$$\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from sympy.abc import *\n", + "from sympy import *\n", + "\n", + "init_printing(pretty_print=True, use_latex='mathjax')\n", + "\n", + "x1 = (0.0034*g*exp(-x/22000)*((x)**2))/(2*b) - g\n", + "\n", + "x2 = (a*g*exp(-x/c)*(Derivative(x)**2))/(2*b) - g\n", + "\n", + "pprint(x1)5\n", + "pprint(Derivative(x)*Derivative(x,n=2))\n", + "#pprint(diff(x2, x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "** orphan text\n", + "This approach has many issues. First, of course, is the fact that the linearization does not produce an exact answer. More importantly, we are not linearizing the actual path, but our filter's estimation of the path. We linearize the estimation because it is statistically likely to be correct; but of course it is not required to be. So if the filter's output is bad that will cause us to linearize an incorrect estimate, which will almost certainly lead to an even worse estimate. In these cases the filter will quickly diverge. This is where the 'black art' of Kalman filter comes in. We are trying to linearize an estimate, and there is no guarantee that the filter will be stable. A vast amount of the literature on Kalman filters is devoted to this problem. Another issue is that we need to linearize the system using analytic methods. It may be difficult or impossible to find an analytic solution to some problems. In other cases we may be able to find the linearization, but the computation is very expensive. **\n" ] } ],