{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## SYDE 556/750: Simulating Neurobiological Systems\n", "\n", "Accompanying Readings: Chapter 2" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## NEF Principle 1 - Representation\n", "\n", "- Activity of neurons change over time\n", "\n", "\n", "\n", "- This probably means something\n", "- Sometimes it seems pretty clear what it means" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "scrolled": true, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/jpeg": 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\n", "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import YouTubeVideo\n", "YouTubeVideo('KE952yueVLA', width=720, height=400, loop=1, autoplay=0)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/jpeg": 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\n", "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import YouTubeVideo\n", "YouTubeVideo('lfNVv0A8QvI', width=720, height=400, loop=1, autoplay=0) " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "- Some sort of mapping between neural activity and a state in the world\n", " - my location\n", " - head tilt\n", " - image\n", " - remembered location\n", " \n", "- Intuitively, we call this \"representation\"\n", " - In neuroscience, people talk about the 'neural code'\n", " - To formalize this notion, the NEF uses information theory (or coding theory)\n", "\n", "- Critical obvious difference between this and ANNs:\n", " - Time is an intrinsic part of the representation\n", " - We start by ignoring this, but it is a theoretica debt we have to repay" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Representation formalism\n", "\n", "- Value being represented: $x$\n", "- Neural activity: $a$\n", "- Neuron index: $i$\n", "\n", "### Encoding and decoding\n", "\n", "- Have to define both to define a code\n", "- Lossless code (e.g. Morse Code):\n", " - encoding: $a = f(x)$\n", " - decodng: $x = f^{-1}(a)$\n", "- Lossy code:\n", " - encoding: $a = f(x)$\n", " - decoding: $\\hat{x} = g(a) \\approx x$\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Distributed representation\n", "\n", "- Not just one neuron per $x$ value (or per $x$)\n", " - Many different $a$ values for a single $x$\n", "- Encoding: $a_i = f_i(x)$\n", "- Decoding: $\\hat{x} = g(a_0, a_1, a_2, a_3, ...)$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "## Example: binary representation\n", "\n", "Encoding (nonlinear):\n", "$$\n", "a_i = \\begin{cases}\n", " 1 &\\mbox{if } x \\mod {2^{i}} > 2^{i-1} \\\\ \n", " 0 &\\mbox{otherwise} \n", " \\end{cases}\n", "$$\n", "\n", "Decoding (linear):\n", "$$\n", "\\hat{x} = \\sum_i a_i 2^{i-1}\n", "$$\n", "\n", "--------------------\n", "\n", "Suppose: $x = 13$\n", "\n", "Encoding: \n", "$a_1 = 1$, $a_2 = 0$, $a_3 = 1$, $a_4 = 1$\n", "\n", "Decoding:\n", "$\\hat{x} = 1*1+0*2+1*4+1*8 = 13$\n", " " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Linear decoding\n", "\n", "- Write decoder as $\\hat{x} = \\sum_ia_i d_i$\n", "\n", "- Linear decoding is nice and simple\n", " - Works fine with non-linear encoding (!)\n", " \n", "- The NEF uses linear decoding, but what about the encoding?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Neuron encoding\n", "\n", "$a_i = f_i(x)$ \n", "\n", "- What do we know about neurons?\n", "\n", "\n", "\n", "- Firing rate goes up as total input current goes up\n", " - $a_i = G_i(J)$\n", " \n", "- What is $G_i$?\n", " - depends on how detailed a neuron model we want.\n", " \n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/jpeg": 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\n", "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import YouTubeVideo\n", "YouTubeVideo('hxdPdKbqm_I', width=720, height=400, loop=1, autoplay=0) " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Rectified Linear Neuron" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Rectified linear neuron\n", "%pylab inline\n", "import numpy\n", "import nengo\n", "\n", "n = nengo.neurons.RectifiedLinear()\n", "\n", "J = numpy.linspace(-1,10,100)\n", "\n", "plot(J, n.rates(J, gain=30, bias=-25))\n", "xlabel('J (current)')\n", "ylabel('$a$ (Hz)');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Leaky integrate-and-fire neuron\n", "\n", "$ a = {1 \\over {\\tau_{ref}-\\tau_{RC}ln(1-{1 \\over J})}}$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#assume %pylab inline has been run\n", "\n", "# Leaky integrate and fire\n", "import numpy\n", "import nengo\n", "\n", "n = nengo.neurons.LIFRate(tau_rc=0.02, tau_ref=0.002) #n is a Nengo LIF neuron, these are defaults\n", "\n", "J = numpy.linspace(-1,10,100)\n", "\n", "plot(J, n.rates(J, gain=1, bias=-2)) \n", "xlabel('J (current)')\n", "ylabel('$a$ (Hz)'); " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Response functions\n", "- These are called \"response functions\"\n", " - How much neural firing changes with change in current\n", " - Similar for many classes of cells (e.g. pyramidal cells - most of cortex)\n", " - This is the $G_i$ function in the NEF: it can be pretty much anything" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Tuning Curves\n", "- Neurons seem to be sensitive to particular values of $x$\n", " - How are neurons 'tuned' to a representation? or...\n", " \n", "- What's the mapping between $x$ and $a$?\n", " - Recall 'place cells', and 'edge detectors'\n", "\n", "- Sometimes they are fairly straight forward:\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- But not often:\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "\n", "- Is there a general form?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Tuning curves (cont.)\n", "- The NEF suggests that there is...\n", " - Something generic and simple\n", " - That covers all the above cases (and more)\n", "- Let's start with the simpler case:\n", "\n", "\n", "\n", "- Note that the experimenters are graphing $a$, as a function of $x$\n", " - $x$ is much easier to measure than $J$\n", " - So, there are two mappings of interest:\n", " 1. $x$->$J$\n", " 2. $J$->$a$ (response function)\n", " - Together these give the tuning curve\n", " \n", "- $x$ is the volume of the sound in this case\n", "\n", "- Any ideas?" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#assume this has been run\n", "#%pylab inline \n", "import numpy\n", "import nengo\n", "\n", "n = nengo.neurons.LIFRate() #n is a Nengo LIF neuron\n", "\n", "x = numpy.linspace(-100,0,100)\n", "\n", "plot(x, n.rates(x, gain=1, bias=50), 'b') # x*1+50\n", "plot(x, n.rates(x, gain=0.1, bias=10), 'r') # x*0.1+10\n", "plot(x, n.rates(x, gain=0.5, bias=5), 'g') # x*0.05+5\n", "plot(x, n.rates(x, gain=0.1, bias=4), 'c') #x*0.1+4))\n", "\n", "xlabel('x')\n", "ylabel('a');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "For mapping #1, the NEF uses a linear map:\n", "$ J = \\alpha x + J^{bias} $\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- But what about type (c) in this graph?\n", "\n", "\n", "\n", "- Easy enough:\n", "\n", "$ J = - \\alpha x + J^{bias} $\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- But what about type(b)? Or these ones?\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- There's usually some $x$ which gives a maximum firing rate\n", " - ...and thus a maximum $J$\n", "- Firing rate (and $J$) decrease as you get farther from the preferred $x$ value\n", " - So something like $J = \\alpha [sim(x, x_{pref})] + J^{bias}$\n", "- What sort of similarity measure? \n", "- Let's think about $x$ for a moment\n", " - $x$ can be anything... scalar, vector, etc.\n", " - Does thinking of it as a vector help?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# The Encoding Equation (i.e. Tuning Curves)\n", "\n", "- Here is the general form we use for everything (it has both 'mappings' in it)\n", "- $a_i = G_i[\\alpha_i x \\cdot e_i + J_i^{bias}] $\n", " - $\\alpha$ is a gain term (constrained to always be positive)\n", " - $J^{bias}$ is a constant bias term\n", " - $e$ is the *encoder*, or the *preferred direction vector*\n", " - $G$ is the neuron model\n", " - $i$ indexes the neuron\n", "- To simplify life, we always assume $e$ is of unit length\n", " - Otherwise we could combine $\\alpha$ and $e$\n", "- In the 1D case, $e$ is either +1 or -1\n", "- In higher dimensions, what happens?" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#assume this has been run\n", "#%pylab inline \n", "\n", "import numpy\n", "import nengo\n", "\n", "n = nengo.neurons.LIFRate()\n", "\n", "e = numpy.array([1.0, 1.0]) \n", "e = e/numpy.linalg.norm(e)\n", "\n", "a = numpy.linspace(-1,1,50)\n", "b = numpy.linspace(-1,1,50)\n", "\n", "X,Y = numpy.meshgrid(a, b)\n", "\n", "from mpl_toolkits.mplot3d.axes3d import Axes3D\n", "fig = figure()\n", "ax = fig.add_subplot(1, 1, 1, projection='3d')\n", "p = ax.plot_surface(X, Y, n.rates((X*e[0]+Y*e[1]), gain=1, bias=1.5), \n", " linewidth=0, cstride=1, rstride=1, cmap=pylab.cm.jet)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- But that's not how people normally plot it\n", "- It might not make sense to sample *every possible* x\n", "- Instead they might do some subset\n", " - For example, what if we just plot the points around the unit circle?" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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ce11Tz5S2HFQffrlwMpGhgdzz+i49K9oCbgeDiNiAR4ArgEnAYhGZ1M2iLxljZrhuj7vWjQd+AcwB8oBfiEicuzWpvlU3tnHvyt1MT4+x5qpaGg6qF/ERwfzwsvFsOFzFqh2lVpfjdzzRYsgDCowxh40xbcCLwKJ+rns5sMYYU2WMqQbWAAs8UJPqw+/XHKCmuZ0HvjjtzIa88CQNB9WLxXmZTBkZzf1v7qGh1W51OX7FE8EwEijq9LzYNe10XxSRHSKyQkQyznBd5UEF5Q08v+kYN+ZlMjE12tpiNBxUD2wBwn2LplBW18pD7x60uhy/4olg6O7n5uk7BVcBo40x04C1wFNnsK5zQZGlIpIvIvkVFRUDLlbBA2/tJSzIxvcvybG6FCcNB9WDWZlxXJ+bzhMfFlJQrhf2GSqeCIZiIKPT83SgpPMCxpiTxphW19O/ArP7u26n11hmjMk1xuQmJSV5oGz/tP5QJWv3lvPtC8eQGBlidTn/T8NB9eAnCyYQGmTj92sOWF2K3/BEMGwGckQkS0SCgRuAlZ0XEJHOV/5eCOx1PX4buExE4lwHnS9zTVODoKPD8N+r9zIyNoyvWXHAuS8aDqobCZEhfO2cLFbvPMGu47VWl+MX3A4GY4wduB3nF/pe4GVjzG4RuU9EFroW+56I7BaR7cD3gK+61q0C/gtnuGwG7nNNU4Ng1Y4Sdh2v40eXj/f8sBeeouGguvH1c7KICQviQW01DAmPnOBmjFkNrD5t2j2dHt8N3N3Duk8AT3iiDtWzjg7Dw+8VMG5EJAunp1ldTu/0JDh1mpiwIJael81v397P1mPVzMrUXu2DSYfE8BNr95ZxsLyB71w4lgCruqeeCW05qNN89ezRJEQE8/t3tNUw2DQY/IAxhkc+OERmfDhXTU3te4XhQsNBdRIREsi3LhjDhwWV5B/RPc6DSYPBD6w/dJLtRTV88/xsAm1e9ifXcFCd3Dgnk5iwIJ74qNDqUnyaDqLnBx55v4DkqBC+OGuQR08dLHrMQbmEBweyOC+TZesOUVzdRHrcEI7x5Ue87OejOlO7S2pZf+gkt56bNXx7IvWHthyUy83zRiEiPP2xXultsGgw+LgXNh0jJDCAL+VmWl2K+zQcFJAWG8YVU1J4YdMxGnUMpUGhweDDGlvt/OOTEq6alkpMuI/setFwUMDXzsmivsXOK1uLrS7FJ2kw+LA3dpTQ0GrnxjwfaC10puHg92ZlxjE9PYbnNhzT6zUMAg0GH/b8piLGjYhk9igfPBlIw8HvXZubwf6yevaU1lldis/RYPBRu0tq2V5Uw+K8zKG5ZKcVNBz82uemphJkE17betzqUnyOBoOPem3rcYJtAVwz08cvb6Hh4LfiIoK5cHwy/9hWgt3RYXU5PkWDwQcZY3hr1wnOzUkkNjzY6nIGn4aD3/rCrHQqG1r5sKDS6lJ8igaDD9peXMvxmmau9KbhL9yl4eCXLpyQRExYEK99oruTPEnPfPZBb+0sJcgmXDJxhNWlDC09Q9rvhATauHJqKq9vO06r3UFIoBefxDmMaIvBxxhjWL2rlPljE33n3IUzoS0Hv3PJxGSa2hxsKtSB9TxFg8HH7C6po6iqmSun+NFupNNpOPiVs8ckEhIYwHv7yq0uxWd4JBhEZIGI7BeRAhG5q5v5d4jIHhHZISLvisioTvMcIrLNdVt5+rrqzLy7txwRuGSSn+1GOp2Gg98IC7Yxb0wC72sweIzbwSAiNuAR4ApgErBYRCadttgnQK4xZhqwAvhNp3nNxpgZrttClFvWH6pkSloM8RF+0BupLxoOfuOiCckcOdnE4YoGq0vxCZ5oMeQBBcaYw8aYNuBFYFHnBYwx7xtjmlxPNwBeOv7z8Nbc5uCTYzWcPSbB6lKGDw0Hv3Dh+GQA3Z3kIZ4IhpFAUafnxa5pPfk68Fan56Eiki8iG0Tk6p5WEpGlruXyKyoq3KvYR+UfraLN0cE8DYauNBx8XkZ8OGOSIvhIz2fwCE90V+1uvIVuR7USkZuAXOD8TpMzjTElIpINvCciO40xhz7zgsYsA5YB5Obm6qhZ3fio4CSBAUJeVrzVpQw/2pXV5501Op5/7j6BMcZ3h4EZIp5oMRQDGZ2epwMlpy8kIpcAPwMWGmNaT003xpS47g8DHwAzPVCTX/r4UCUzM2MJD9bTU7qlLQefNiszjpqmdg5XNlpditfzRDBsBnJEJEtEgoEbgC69i0RkJvAYzlAo7zQ9TkRCXI8TgfnAHg/U5Hea2xzsPF7LnCzdjdQrDQefNcs1ivCWo9UWV+L93P5paYyxi8jtwNuADXjCGLNbRO4D8o0xK4HfApHAclcT75irB9JE4DER6cAZUg8YYzQYBmDviTo6DExNj7G6lOFPdyv5pOzECGLDg9h6tJrrczP6XkH1yCP7HIwxq4HVp027p9PjS3pYbz0w1RM1+LvdJc4x6aeM1GDoFw0HnxMQIMzKjNMWgwfozmgfsft4LbHhQaTFhFpdivfQcPA5MzJieW9fOY2tdiJC9OttoPST8xG7S+qYnBatvTHOlIaDTxk3IhKAQxUNTEuPtbga76VjJfmAdkcH+0/UMyVNdyMNiB6Q9hljk53BUFCuZ0C7Q1sMPqCwspE2RwcTU6OtLsV7acvBJ4xKiCAwQDikQ2O4RYPBBxw76RxtZFRCuMWVeDkNB68XZAtgVEK4thjcpMHgA4qrncGQEa/B4DYNB683NjlSg8FNGgw+oKi6mbAgGwk6oqpnaDh4tTFJkby7txxHh8EWoJ0xBkKDwQcUVTWRHhemPZI8ScPBa6XGhGLvMJxsbCU5SrtvD4QGgw8orm4mPS7M6jJ8j4aDV0qKCgGgol6DYaA0GHxAcXUTs13jxCgP03DwOkmuMCivb2WyxbV4Kw0GL2d3dFDXYtcrtg0mDQevktypxaAGRoPByzW02gGICdMvqkGl4eA1kjQY3KbB4OXqmp3BEK3BMPg0HLxCaJCNqNBADQY3aDB4uboW5/AN0aH6pxwSGg5eITo06NPWtDpz+m3i5WqbncGgu5KGkIbDsBcSGECrvcPqMryWRwbRE5EFIrJfRApE5K5u5oeIyEuu+RtFZHSneXe7pu8Xkcs9UY8/qXMFQ1SofjENKR14b1gLDgygtd1hdRley+0Wg4jYgEeAS3Fe/3mziKw87UpsXweqjTFjReQG4NfAl0RkEs5LgU4G0oC1IjLOGKN/0X5qczh/FYUE6UC5Q05bDsNWSJBNWwxu8MSupDygwBhzGEBEXgQW0fXazYuAX7oerwAeFudpuouAF40xrUChiBS4Xu9jD9Sl1ODTcBiWQgIDaNEWw4B5IhhGAkWdnhcDc3paxnWN6FogwTV9w2nrjvRATUoNHQ2HYWdTYZXVJXg1TwRDdwP0mH4u0591nS8gshRYCpCZmXkm9Sk1+E6Fw8svQ3OzBoPyap7YMV0MZHR6ng6U9LSMiAQCMUBVP9cFwBizzBiTa4zJTUpK8kDZSnnYHXfAunUQrRdMstrc7HjysuKtLsNreSIYNgM5IpIlIsE4DyavPG2ZlcAS1+NrgfeMMcY1/QZXr6UsIAfY5IGalLJGsA5NMhy0tHcQEqgdMgbK7V1JrmMGtwNvAzbgCWPMbhG5D8g3xqwE/gY84zq4XIUzPHAt9zLOA9V24DvaI+nMBAY4//G3O7QHhlKntNo7SAqyWV2G1/LICW7GmNXA6tOm3dPpcQtwXQ/r3g/c74k6/FF0mPNPWN+iZ3kqdUqr3aEtBjfoJ+flol0ntp060U0pBa3tHYQEaothoDQYvNypwfNOjZmklIKmNjthwfr1NlD6yXm5U4Pn1TZpMCgF0GbvoLqpnaRIvXrbQGkweLn/bzHoMQalACobnMNtJ0eHWFyJ99Jg8HJBtgAigm1UNbZZXYpSw8Kp6zAkRWowDJQGgw9Iiw2jpKbZ6jKUGhbK67XF4C4NBh+QER9OUbUGg1LQqcUQpcEwUBoMPiAjLoziqiacJ5Mr5d9O1LUgAom6K2nANBh8QHpcOPWt9k+v/6yUPztc0UB6XBhBNv16Gyj95HxARnwYAEXVTRZXopT1CsobGJsUaXUZXk2DwQekx4UDcKxKg0H5N0eHobCykbHJGgzu0GDwAWOTI7EFCPtK66wuRSlLHa9uptXeocHgJg0GHxAaZGNMUgS7SjQYlH8rqKgH0GBwkwaDj5icFsPuklqry1DKUgfLGgAYo8cY3KLB4CMmp0VTVtf6aR9upfzR9uIa0uPCiA3XCya5Q4PBR0xOiwHQVoPyW8YYthytZvaoOKtL8XpuBYOIxIvIGhE56Lr/zF9ERGaIyMcisltEdojIlzrNe1JECkVkm+s2w516/NmkNOd1hnfrcQblp47XNFNW16rB4AHuthjuAt41xuQA77qen64JuNkYMxlYAPxBRGI7zf+RMWaG67bNzXr8VkxYEDnJkWwsrLK6FKUssfVYDQCzMjUY3OVuMCwCnnI9fgq4+vQFjDEHjDEHXY9LgHIgyc33Vd04e0wCmwuraLPr9Z+V/9l6tJrwYBsTUqKsLsXruRsMI4wxpQCu++TeFhaRPCAYONRp8v2uXUwPiogObuKGs8cm0tzuYFtRjdWlKDXk8o9WMSMjlkAdCsNtfX6CIrJWRHZ1c1t0Jm8kIqnAM8AtxphTP2nvBiYAZwHxwE96WX+piOSLSH5FRcWZvLXfmJudQIDA+kOVVpei1JCqbGhld0kdc7MTrC7FJ/QZDMaYS4wxU7q5vQ6Uub7wT33xl3f3GiISDbwJ/KcxZkOn1y41Tq3A34G8XupYZozJNcbkJiXpnqjuxIQFMWVkDOsLTlpdilJD6oP9FRgDF03odaeF6id321wrgSWux0uA109fQESCgdeAp40xy0+bdypUBOfxiV1u1uP3zh6TyCdF1TS26kiryn+8v6+c5KgQJrt65yn3uBsMDwCXishB4FLXc0QkV0Qedy1zPXAe8NVuuqU+JyI7gZ1AIvArN+vxexeMT6LdYfjXAd3dpvxDu6ODdQcquHB8Ms7fmMpdge6sbIw5CVzczfR84FbX42eBZ3tY/yJ33l991lmj40mMDObNnaVcOTXV6nKUGnT5R6qpb7Vzoe5G8hg9fO9jbAHC5ZNTeH9fOc1tDqvLUWrQvbevjCCbcE5OotWl+AwNBh905dRUmtocujtJ+byODsMbO0o5NyeJyBC3doCoTjQYfNCcrHjiwoN4a1ep1aUoNag2HD5JaW0L18wcaXUpPkWDwQcF2gK4fHIK7+4tp6Vddycp3/XK1uNEhQRy6aQRVpfiUzQYfNSiGSNpaLXz5g5tNSjf1Nzm4J+7nJ0sQoNsVpfjUzQYfNTc7HiyEyN4YdMxq0tRalC8s+cEjW0Orpmlu5E8TYPBR4kIi/MyyT9azYGyeqvLUcrjVmwpZmRsGHmj460uxedoMPiwL85OJ9gWwPMbtdWgfEtBeQP/PljJl87KICBAT2rzNA0GHxYfEczlU1J4dWuxHoRWPuXJ9YUEBwbw5TmZVpfikzQYfNyNeZnUtdhZua3E6lKU8oiapjZe2XKcq2ekkRCpI/UPBg0GHzc3O56JqdE8uu4Qjg5jdTlKue3FzUU0tzu4ZX6W1aX4LA0GHycifOfCMRyuaOSd3SesLkcpt7Q7Onhq/RHOHpPAxFQdSXWwaDD4gSumpJKVGMEjHxRgjLYalPd6Y0cJpbUt2loYZBoMfsAWINx2fja7jtex7qBe3U15p3ZHB39Ye5CJqdFcrCOpDioNBj9xzcx0UmNCeeT9AqtLUWpAXtlSzNGTTfzwsnHaRXWQaTD4ieDAAJael82mwir+fVBHXVXepdXu4KF3DzIjI1Yv3zkE3AoGEYkXkTUictB1H9fDco5OV29b2Wl6lohsdK3/kusyoGqQ3Dgnk/S4MO5/c6/2UFJe5cVNRZTUtvDDy8brVdqGgLsthruAd40xOcC7rufdaTbGzHDdFnaa/mvgQdf61cDX3axH9SIk0MZPFkxg34l6XtlabHU5SvVLU5udh98vYE6RAimiAAATTElEQVRWPPPHJlhdjl9wNxgWAU+5Hj8FXN3fFcUZ+xcBKwayvhqYz01LZUZGLL97ez9NbXary1GqT39+/xAV9a386HJtLQwVd4NhhDGmFMB139POv1ARyReRDSJy6ss/Aagxxpz6dioGdJjEQSYi/PxzEymvb+Wv6wqtLkepXhVWNrJs3WGumTmSXB0sb8j0eS08EVkLpHQz62dn8D6ZxpgSEckG3hORnUBdN8v1uONbRJYCSwEyM3V8FHfMHhXPlVNTePRfh7j+rHRSY8KsLkmpzzDGcO+q3QQHBnD3FROsLsev9NliMMZcYoyZ0s3tdaBMRFIBXPflPbxGiev+MPABMBOoBGJF5FQ4pQM9DuhjjFlmjMk1xuQmJSWdwSaq7tx9xUQMhp//Y5ee9KaGpTV7yvhgfwU/uCSH5OhQq8vxK+7uSloJLHE9XgK8fvoCIhInIiGux4nAfGCPcX4bvQ9c29v6anBkxIdz56XjWbu3nDd36lXe1PDS3Obg3lV7GD8iiiVnj7a6HL/jbjA8AFwqIgeBS13PEZFcEXnctcxEIF9EtuMMggeMMXtc834C3CEiBTiPOfzNzXrUGbhl/mimpcfwy5W7qW5ss7ocpT71h7UHOF7TzL2LJhNk09Othpp4426E3Nxck5+fb3UZPmFPSR0LH/6Qq2eO5HfXTbe6HKXYePgkN/x1AzfmZXL/NVOtLseniMgWY0xuX8tpFPu5SWnRfPP8bFZsKWbdAT0jWlmrodXOncu3kxkfzk+vnGh1OX5Lg0Hx3YtyGJscyZ3Lt1PZ0Gp1OcqP/eqNPZTUNPO/100nIqTPTpNqkGgwKEKDbPxp8Uxqm9u58+XtdOhwGcoCa/eU8eLmIr55/hg9Z8FiGgwKgImp0fz8c5P414EKHv/wsNXlKD9zoraFu17dwYSUKH5wSY7V5fg9DQb1qZvmZHLFlBR+88/9fHKs2upylJ9os3fwree20NTm4E+LZxISaLO6JL+nwaA+JSI88IVpjIgO5bsvfEJtU7vVJSk/8F9v7OGTYzX89trp5IyIsrochQaDOk1MeBAPLZ5JWV0L33l+K+2ODqtLUj5sxZZintlwlKXnZXPVtFSry1EuGgzqM2aPiuP+a6byYUEl963a0/cKSg3AruO1/Oy1nczLTuDHl4+3uhzVifYHU926PjeDQ+UNPLbuMGOTI3VYAuVRZXUtfPOZLcRHBPOnG2cSqGc3DysaDKpHP14wgUMVjdy7ajejEyM4f5wOXqjcV9fSzpInNlHT1MZL35xHYmSI1SWp02hMqx7ZAoQ/3jCD8SnR3P7cVvad6G6kdKX6r9XuYOnT+RSUN/DoV2YzZWSM1SWpbmgwqF5FhATy+JJcIkICuenxTRyuaLC6JOWlOjoMd7y8nQ2Hq/jdddM5N0dboMOVBoPq08jYMJ69dQ7GGL78+EaKqpqsLkl5GWMMv3pzL2/uKOXuKyZw9Uy9WONwpsGg+mVsciTPfH0Oja12bvrbRsrqWqwuSXkJYwwPvLWPJz4q5Jb5o1l6XrbVJak+aDCofpuUFs1TX8ujsr6VLz++kZM64J7qw6mWwmPrDvOVuaP4+VWTEBGry1J90GBQZ2RmZhx/++pZFFU1ccOyDZyo1ZaD6p7zms17+NuHzpbCfYsmExCgoeAN3AoGEYkXkTUictB1H9fNMheKyLZOtxYRudo170kRKew0b4Y79aihMTc7gSdvyaO0toUv/mU9hZWNVpekhpmODsPPX9/Fk+uPcOs5WdzzOW0peBN3Wwx3Ae8aY3KAd13PuzDGvG+MmWGMmQFcBDQB73Ra5Een5htjtrlZjxoi88Yk8MI35tLc7uC6R9ez63it1SWpYaLN3sGdy7fz7IZjfPP8bH521UQNBS/jbjAsAp5yPX4KuLqP5a8F3jLGaLcWHzA1PYblt80jJNDG4mUb2Hj4pNUlKYvVNrVz8xMbee2T49x56TjuWjBBQ8ELuRsMI4wxpQCu++Q+lr8BeOG0afeLyA4ReVBEejwFUkSWiki+iORXVOglKIeLMUmRLL9tHsnRIdz8xCZe33bc6pKURYqqmvjCXz5i69Ea/vClGXz34hwNBS8lxvR+tS4RWQukdDPrZ8BTxpjYTstWG2M+c5zBNS8V2AGkGWPaO007AQQDy4BDxpj7+io6NzfX5Ofn97WYGkJVjW3c9swWNh2p4lsXjOGHl43Hpgca/ca2ohpufWoz7Q7DY1+ZzdzsBKtLUt0QkS3GmNy+lutzrCRjzCW9vEmZiKQaY0pdX/LlvbzU9cBrp0LB9dqlroetIvJ34Id91aOGp/iIYJ69dQ73rtrNXz44xL7SOv64eCbRoUFWl6YG2atbi/npaztJigrhxa/mMTY50uqSlJvc3ZW0EljierwEeL2XZRdz2m4kV5ggzvbm1cAuN+tRFgoODOD+a6byq6un8O+DlVz9yEcc0iE0fFZLu4O7X93BHS9vZ1p6LK9+a76Ggo9wNxgeAC4VkYPApa7niEiuiDx+aiERGQ1kAP86bf3nRGQnsBNIBH7lZj1qGLhp7iie/8Zcapvaufrhj/S4gw86UtnIF/68nhc2FfHtC8bw/K1zSIrSUVJ9RZ/HGIYjPcbgHY7XNPP9Fz4h/2g118wcyb2LJuuuJR/wz12l/Gj5DgIChAe/NJ2LJoywuiTVT/09xqBnPqtBMzI2jBeXzuWOS8excnsJV/7x3+QfqbK6LDVAtc3t/HjFdm57divZyZG8+b1zNBR8lAaDGlSBtgC+d3EOy2+bR4AI1z/2Mb9/Zz9tdr2WtDd5f385lz+4jhVbivnWBWNY/s15pMeFW12WGiQaDGpIzMqM483vncM1M9N56L0Crnro32wq1NbDcFfb3M6Plm/nlr9vJjoskNe+PZ+fLJhAcKB+dfgyPcaghty7e8u45/XdHK9p5vrcdO6+YiJxEcFWl6U6Mcbwz10nuHfVHioaWrnt/Gy+d3EOIYE2q0tTbvDYeQxKedrFE0cwb0wCf3z3II//u5C1e8v56ZUT+eKskXqm7DCwp6SO+97YzYbDVUxIiWLZzbOZlh7b94rKZ2iLQVlq34k6fvrqTrYeq2FmZiw/WTBBz5q1yMmGVn6/5gAvbDpGTFgQd142nhvOyiDQpruNfEV/WwwaDMpyHR2GFVuK+f2aA5yoa+HC8Un8eMEEJqZGW12aX2huc/DshqP86b2DNLY5uHneKH5w8ThiwrVrsa/RYFBep6XdwZPrj/Dn9wuob7Vz9YyR3HHpODLitffLYGhqs/PchmM8tu4wlQ2tnDcuiZ9fNZGcEVFWl6YGiQaD8lq1Te385V+H+PtHhTg6DAunp/GN87K1BeEhja12nt1wlGXrDnOysY35YxP4/sXjyMuKt7o0Ncg0GJTXO1HbwmPrDvHS5iKa2hycNy6Jb56XzdljEvQg9QCU1bXw/MZjPLPhKFWNbZybk8j3L84hd7QGgr/QYFA+o6apjec2HuPvHx2hsqGVyWnRfG1+FldOTSUsWLtP9sYYw6bCKp7++Chv7z6BwxguHJ/Mdy4cy+xR3Y6Qr3yYBoPyOS3tDl7fdpxl6w5zqKKRyJBAPj89letyM5iZEautiE5qm9pZtaOEZz4+yv6yemLCgrg+N52b5o5iVEKE1eUpi2gwKJ916lfwy/nFrN5ZSnO7g7HJkVw3O51FM0aSEhNqdYmWaGqzs2ZPGau2l/CvAxW0OwyT06K5ed4oFk4fqa0rpcGg/EN9Sztv7ijl5fwith6rAWB6egyXTU7h0kkjyEmO9OmWRGOrnQ8LKlm1vYR395bT3O4gJTqUz01L5fPT05iWHuPT26/OjAaD8juHKhr4564TvLOnjO1FzpAYnRDOZZNTOH9cEjMzYwkP9u6T/Ts6DHtK61h3sIJ1ByrYcrSadochLjyIK6emsnB6GmeNjidAL6uqujEkwSAi1wG/BCYCecaYbr+tRWQB8EfABjxujDl1QZ8s4EUgHtgKfMUY09bX+2owqL6U1bWwZk8Z7+wp4+NDlbQ7DIEBwtT0GPKy4pmTFc/sUfHEhA3vk7ha7Q72ldazo7iGLUer+bCgksoG53+RCSlRnD8uifPGJZGXFU+QnqGs+jBUwTAR6AAeA37YXTCIiA04gPMKb8XAZmCxMWaPiLwMvGqMeVFEHgW2G2P+0tf7ajCoM9HQaif/SBWbCp237cU1tDsMIjAmKZLxKVFMGBHF+JQoJqZGMzI2zJJf3LVN7RSebKSgvIEdxTVsL6phb2k9bQ7nEOWJkSHMH5vAeTlJnJuTSHK0fx5LUQM3JIPoGWP2ut6st8XygAJjzGHXsi8Ci0RkL3ARcKNruadwtj76DAalzkRkSCAXjE/mgvHJgLN30yfHathUWMXO47XsKK7hzR2lny4fEWwjOymS1JhQ0mLDSI0JJcX1eERUKJGhgYQH2wgJDOjX/vuODkN9i52qpjaqGp236sY2SmtbOHqykcKTjRypbKS6qb1LDVPTY7jlnNFMT49lekYsaTGherxADYmh2OE6Eijq9LwYmAMkADXGGHun6SOHoB7l50KDbMwbk8C8Mf8/WF9Dq50DZfXsP+G8Ha5s5MjJRj4+dJL6Vnu3r2MLEMKDbUQEBxIeYgMD9g6D3dGBvcPg6DDYOwwNrXYcHd23zNNiQhmVEMGCKalkJYYzOiGC7KQIshIjselxAmWRPoNBRNYCKd3M+pkx5vV+vEd3/7pNL9N7qmMpsBQgMzOzH2+rVP9FhgQyKzOOWZmfPemrvqWdE7UtlNS2UF7XQlObg8Y2O42tdhpbHTS12WlscxAgQmCAYAtw3gfaBJsIkaGBxIUHEx/x/7e48GCSokIIDdIupGr46TMYjDGXuPkexUBGp+fpQAlQCcSKSKCr1XBqek91LAOWgfMYg5s1KdVvUaFBRIUG6eByym8MRTeGzUCOiGSJSDBwA7DSOI96vw9c61puCdCfFohSSqlB5FYwiMg1IlIMzAPeFJG3XdPTRGQ1gKs1cDvwNrAXeNkYs9v1Ej8B7hCRApzHHP7mTj1KKaXcpye4KaWUn+hvd1U9I0YppVQXGgxKKaW60GBQSinVhQaDUkqpLjQYlFJKdeGVvZJEpAI46qGXS8R5sp0384VtAN/YDl/YBvCN7dBt+KxRxpikvhbyymDwJBHJ70/3reHMF7YBfGM7fGEbwDe2Q7dh4HRXklJKqS40GJRSSnWhweAamM/L+cI2gG9shy9sA/jGdug2DJDfH2NQSinVlbYYlFJKdeF3wSAi14nIbhHpEJEej/aLyBER2Ski20RkWI3YdwbbsEBE9otIgYjcNZQ19oeIxIvIGhE56Lr/7FVynMs5XH+HbSKycqjr7E5fn62IhIjIS675G0Vk9NBX2bt+bMNXRaSi02d/qxV19kZEnhCRchHZ1cN8EZGHXNu4Q0RmDXWN/dGP7bhARGo7/S3uGdSCjDF+dQMmAuOBD4DcXpY7AiRaXe9AtwGwAYeAbCAY2A5Msrr202r8DXCX6/FdwK97WK7B6lrP9LMFvg086np8A/CS1XUPYBu+Cjxsda19bMd5wCxgVw/zrwTewnnFyLnARqtrHuB2XAC8MVT1+F2LwRiz1xiz3+o63NHPbcgDCowxh40xbcCLwKLBr+6MLAKecj1+CrjawlrORH8+287btgK4WESG00WcveHfR5+MMeuAql4WWQQ8bZw24LxqZOrQVNd//diOIeV3wXAGDPCOiGxxXW/a24wEijo9L3ZNG05GGGNKAVz3yT0sFyoi+SKyQUSGQ3j057P9dBnjvFhVLc6LUQ0X/f338UXXLpgVIpLRzfzhzhv+H/TXPBHZLiJvicjkwXyjPq/57I1EZC2Q0s2snxlj+nv50PnGmBIRSQbWiMg+V6oPCQ9sQ3e/Toe8C1pv23EGL5Pp+ltkA++JyE5jzCHPVDgg/flsh8Xn34v+1LcKeMEY0yoit+FsAV006JV51nD/O/TXVpzDWTSIyJXAP4CcwXoznwwGY8wlHniNEtd9uYi8hrPpPWTB4IFtKAY6/8JLB0rcfM0z1tt2iEiZiKQaY0pdzfvyHl7j1N/isIh8AMzEuX/cKv35bE8tUywigUAMw2hXAf3YBmPMyU5P/wr8egjq8rRh8f/AXcaYuk6PV4vIn0Uk0RgzKGNB6a6kbohIhIhEnXoMXAZ021tgGNsM5IhIlogE4zwAOix69HSyEljierwE+ExLSETiRCTE9TgRmA/sGbIKu9efz7bztl0LvGdcRxGHiT634bR98QtxXrPd26wEbnb1TpoL1J7afelNRCTl1DEqEcnD+d19sve13GD10fihvgHX4PwV0QqUAW+7pqcBq12Ps3H20tgO7Ma5+8by2s9kG1zPrwQO4Px1Pay2wVVfAvAucNB1H++angs87np8NrDT9bfYCXzd6rp7+myB+4CFrsehwHKgANgEZFtd8wC24X9c//63A+8DE6yuuZtteAEoBdpd/ye+DtwG3OaaL8Ajrm3cSS89EYf5dtze6W+xATh7MOvRM5+VUkp1obuSlFJKdaHBoJRSqgsNBqWUUl1oMCillOpCg0EppVQXGgxKKaW60GBQSinVhQaDUkqpLv4PM2wPrX9jObcAAAAASUVORK5CYII=\n", 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import nengo\n", "import numpy\n", "\n", "n = nengo.neurons.LIFRate()\n", "\n", "theta = numpy.linspace(0, 2*numpy.pi, 100)\n", "x = numpy.array([numpy.cos(theta), numpy.sin(theta)])\n", "plot(x[0],x[1])\n", "axis('equal')\n", "\n", "e = numpy.array([-1.0, 1.0])\n", "e = e/numpy.linalg.norm(e)\n", "\n", "plot([0,e[0]], [0,e[1]],'r')\n", "\n", "gain = 1\n", "bias = 2.5\n", "\n", "figure()\n", "plot(theta, n.rates(numpy.dot(x.T, e), gain=gain, bias=bias))\n", "plot([numpy.arctan2(e[1],e[0])],0,'rv')\n", "xlabel('angle')\n", "ylabel('firing rate')\n", "xlim(0, 2*numpy.pi);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- That starts looking a lot more like the real data." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Notation\n", "\n", "- Encoding\n", " - $a_i = G_i[\\alpha_i x \\cdot e_i + J^{bias}_i]$\n", " \n", "- Decoding\n", " - $\\hat{x} = \\sum_i a_i d_i$\n", " \n", "- The textbook uses $\\phi$ for $d$ and $\\tilde \\phi$ for $e$\n", " - We're switching to $d$ (for decoder) and $e$ (for encoder)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Decoder\n", "\n", "- But where do we get $d_i$ from?\n", " - $\\hat{x}=\\sum a_i d_i$\n", " \n", "- Find the optimal $d_i$\n", " - How?\n", " - Math" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Solving for $d$\n", "\n", "- Minimize the average error over all $x$, i.e.,\n", "\n", "$ E = \\frac{1}{2}\\int_{-1}^1 (x-\\hat{x})^2 \\; dx $\n", "\n", "- Substitute for $\\hat{x}$:\n", "\n", "$ \n", "\\begin{align}\n", "E = \\frac{1}{2}\\int_{-1}^1 \\left(x-\\sum_i^N a_i d_i \\right)^2 \\; dx \n", "\\end{align}\n", "$\n", "\n", "- Take the derivative with respect to $d_i$:\n", "\n", "$\n", "\\begin{align}\n", "{{\\partial E} \\over {\\partial d_i}} &= {1 \\over 2} \\int_{-1}^1 2 \\left[ x-\\sum_j a_j d_j \\right] (-a_i) \\; dx \\\\\n", "{{\\partial E} \\over {\\partial d_i}} &= - \\int_{-1}^1 a_i x \\; dx + \\int_{-1}^1 \\sum_j a_j d_j a_i \\; dx \n", "\\end{align}\n", "$\n", "\n", "- At the minimum (i.e. smallest error), $ {{\\partial E} \\over {\\partial d_i}} = 0$\n", "\n", "$\n", "\\begin{align}\n", "\\int_{-1}^1 a_i x \\; dx &= \\int_{-1}^1 \\sum_j(a_j d_j a_i) \\; dx \\\\\n", "\\int_{-1}^1 a_i x \\; dx &= \\sum_j \\left(\\int_{-1}^1 a_i a_j \\; dx\\right)d_j \n", "\\end{align}\n", "$\n", "\n", "- That's a system of $N$ equations and $N$ unknowns\n", "- In fact, we can rewrite this in matrix form\n", " \n", "$ \\Upsilon = \\Gamma d $\n", "\n", "where\n", "\n", "$ \n", "\\begin{align}\n", "\\Upsilon_i &= {1 \\over 2} \\int_{-1}^1 a_i x \\;dx\\\\\n", "\\Gamma_{ij} &= {1 \\over 2} \\int_{-1}^1 a_i a_j \\;dx \n", "\\end{align}\n", "$\n", "\n", "- Do we have to do the integral over all $x$?\n", " - Approximate the integral by sampling over $x$\n", " - $S$ is the number of $x$ values to use ($S$ for samples) \n", "\n", "$ \n", "\\begin{align}\n", "\\sum_x a_i x / S &= \\sum_j \\left(\\sum_x a_i a_j /S \\right)d_j \\\\\n", "\\Upsilon &= \\Gamma d \n", "\\end{align}\n", "$\n", "\n", "where\n", "\n", "$\n", "\\begin{align}\n", "\\Upsilon_i &= \\sum_x a_i x / S \\\\\n", "\\Gamma_{ij} &= \\sum_x a_i a_j / S \n", "\\end{align}\n", "$\n", "\n", "- Notice that if $A$ is the matrix of activities (the firing rate for each neuron for each $x$ value), then $\\Gamma=A^T A / S$ and $\\Upsilon=A^T x / S$\n", "\n", "So given \n", "\n", "$ \\Upsilon = \\Gamma d $\n", "\n", "then\n", "\n", "$ d = \\Gamma^{-1} \\Upsilon $\n", "\n", "or, equivalently\n", "\n", "$ d_i = \\sum_j \\Gamma^{-1}_{ij} \\Upsilon_j $\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "\n", "
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It can be enabled with `nengo.rc.set('progress', 'progress_bar', 'nengo.utils.progress.TerminalProgressBar')`." ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "\n", " (function () {\n", " var root = document.getElementById('62f79b1f-6ee2-444f-afdb-4cfe7eba92e1');\n", " var text = root.getElementsByClassName('pb-text')[0];\n", " var fill = root.getElementsByClassName('pb-fill')[0];\n", "\n", " text.innerHTML = 'Build finished in 0:00:01.';\n", " \n", " fill.style.width = '100%';\n", " fill.style.animation = 'pb-fill-anim 2s linear infinite';\n", " fill.style.backgroundSize = '100px 100%';\n", " fill.style.backgroundImage = 'repeating-linear-gradient(' +\n", " '90deg, #bdd2e6, #edf2f8 40%, #bdd2e6 80%, #bdd2e6)';\n", " \n", " \n", " fill.style.animation = 'none';\n", " fill.style.backgroundImage = 'none';\n", " \n", " })();\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": 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A4flB6OiWQdjTELcDXIfC9C/B2rvZ51IWFlL03WpK1q1DKJVYzJyB9aLF6Lm0bBprUnQ++367QKl2CjVG2WhrazFs2DCCgoLQ19dv0Tllsq4quryKhy6kUq5SsaK7G6F2Fu0d0j+8vPkC605msG/pSNytb70+3K2SB6mboGXYMJVNXaMEU3u49zeY8Q0UXIKvg+HUamhm8tSxscH+xRfw3rMHy7lzKdu8haRJk8h5/XUUubm3HJt3gB3zXgmmp+sgLPMHYCLZc/DgQVasWEFUVBQqVZtVIZHJ7ih/5BYz40wiuloSYQG+HTI5pBZWse5kBvcNcbstyeFWdNkEIV2bIAAkCfrdC48fB7ehsH0p/DITypq/olrX3g6Hl5fjHb4Hi7tnUbpxE0kTJpL7zjsoCwtvKT5jc32mPNGXsff2xzDfD7vKgRjpmRIWFsZXX31FfHy8PONJJrsBlRC8kZjFk5fSGWBmzK4BfvQ0MWzvsBq1Yl8COtoSS8b4tHco/9BlE4TW9QniKjMn+NcmmPIxpB+HrwLh/O/Nbk0A6Do44Pjaa3jv3InZXaGU/PobieMnkP/xx7dUPVaSJHoNd+ae5YOws3VAXPKlu+0wVCo1v/32Gz/99BM5OTnNPp9M1hWUK1Xcfz6ZrzIKWOBsw/p+3li38ZagLZVUUMnms1k8EOjRbgX5bqbrJggjXQDE9QkCGloTgx6GxYfBphtsegR+fwCqim7pGnouzji9/Tbe28MwHTeOotXfkzRuPAUrv0BVUdHs81jYGTHz2QAGh3pRHKuLRV4AwwaOIjc3l2+++YbNmzdTXi5vUiSTpdXUEXo6gYMlFXzg58K7fi7oduD94lfuS0BfR5tHR3i1dyiN6roJ4kYtiGtZe8NDu2DsaxC3s6E1kRB+y9fS8/DA+cMP8Nq6BeOgIApXrSJp3HiKvv8edc3NF+v9Fa+2FoNDPZn5bABa2tokblczzHsqgYGBXLhwgZUrVxIREUF9ff0txyeT3QmOl1Yy6XQ8+fUK1vXz5gFnm/YO6aYS8yvYci6bB4a5Y2PSMSefdNkEIelpgZZ08wQBDVNehz8Djx4AI2v49e6G8Yn66lu+pr6vLy4rPsdjwwYM+vYl/8OPSJowkZK1axHNvLE7eJlzz/JBdB/myPm9OZRHW3H/PQ/h4+NDREQEK1eu5Ny5c6jV8t7Ysq5jXU4Rs88mYaWrw44BfgRbmrZ3SE36fF8iRrraLBrR/BmTt1vXTRBXSn6raxTNe4FDH3jkQMOq61Or4ZsRkH2mRdc27N0Lt+++xf3nn9B1dSX3jTdJmjyFsi1bEM2YoaRnoMOY+3sQsqg3ZYU17F6VSF/XEcyfPx9TU1P+/PNPVq9eTXp6eovik8k6C5UQvJmYzdOXMwi0MCYswBcvo475bfxa8XkVhJ3P5sFhHlgZ3/7NiJqryyYI4EqCuIW9GXQNYOLb8MAWqK+C1ePg4Iegbtm0U6NBg3D/9Rdcv/kaLVNTspe9QMr0GVTsP9CsGUre/nbc+/Jg7N1N2f/TJeL3VvLAvPnMmDGDiooK1qxZw4YNGygtLW1RfDJZR1alVLEwJoUvM/KZ72zDr329270Sa3N9vjcBYz0dHhneMcceruqyC+UA8ledRbpBye8m1ZQ0dDXFbGxYXDfzW7B0b3EsQq2mYtcuCj5fQX1aGob+/tgtfQajgU2uZUGtFkTvTuPkthRMLPQZv7AX1q6GHD58mKNHjwIwbNgwgoOD0dPruN9WZLLmyq1TcP/5ZGIra3jL15mFLi3bLrg9XMopZ9Lnh3hyjA9LJ3RrlxjkldTN0JyS3006/wdsf6bh5ymfQN/ZLT8XIBQKSjf9SeEXX6AsKMB45AjsnnkGg25Nf5ByU8oI/z6WiuI6Bk3xYMAkD8rLywgPDyc2NhZTU1PGjRtH3759O0SlSJmsJWIra7j/fDJlShXf9PJgnHXnKkOz+OfTHEks5PCyMZhfmU15u8krqZtBy+gWu5ga03d2w3RYu56w6WHY9CjUtnzKqaSri+U9c/Desxvbpc9Qc+YsKdNnkPXc89RnZt70tQ6e5tyzfDC+g+w4uS2FLZ+eQUcYMnv2bBYsWICJiQl//vkn33//PVlZLd9SVSZrL/uKypkanYAAtgb4drrkEJtdxq7YXB4K9my35HAr2qwFIUnSGiAUyBdC9L5y7EPgLqAeSAIWCCFKJUnyAC4BcVdeflwIsbipa7S2BVGyJZGacwU4vRrY4nP8RaWEQx9B5Ptg7gqzVoPr4NaftqyMotWrKf7pZ1CrsbxvLtaLF6NjaXnT110+nkPk2nh0dLQYO78HHn1sUKvVnDt3jr1791JVVYW/vz9jx47FxMSk1XHKZG3th6xClsdn0svEkJ/6euKo3/m6Sx/5KYrjyUUNrQfD9ksQHaEF8V8g5Lpj4UBvIURfIB548ZrHkoQQ/a/8aTI5aMLVQWqh1kCS1NaBUS/Agl2AgDUhEPF+iwew/zqtuTl2S5fivWc3ZtOmUvzzLySNn0Dh19+grr7xVNvuQx2Z8+JAjC312b7qPIc3JCDU4O/vz5NPPklgYCDnzp1j5cqVHDt2TK7vJOuwVELwWkIWL8ZnMtbajM3+Pp0yOcRklRF+MY+Hg73aNTncijZLEEKIg0Dxdcf2CCGu9ukcB1za6vrNoWWoAwJEnQZvjm5DGrqces+CiHfgx7tuqZ7Tjeja2+P0n//gtXULRkOGUPDZZyRNDKFk/e8IZePdZJYOxty9bAB9Rrlwbm8Gmz48TVlBNQYGBkycOJHHHnsMV1dXdu/ezVdffUViYmKr45TJNKlGpebR2FS+ySxgobMN/+3jiXEH2sPhVqzcn4CZgQ4Lgj3aO5Rma88xiIeAndf87ilJ0hlJkiIlSRp+oxdJkvSoJElRkiRFFRQUtCqAZq2mbgkDc5j1XUN12Oyz8HUQXN6hkVPr+/jguuoL3H/9BV0XF3Jfe43kadOpOND41FgdXW1G3OvHpEV9KCuoYf3bp0iIygPA1taWefPmMXfuXFQqFb/88gvr16+Xp8XKOoRihZI5Z5PYUVDGmz5OvO3ngnYnnVyRkFfB7tg85g/zwMygc7QeoI1nMV0ZWwi7OgZxzfHlwEBgphBCSJKkD5gIIYokSRoAbAZ6CSFuOtrb2jGImthCin6+hN2T/ug5t1E/fFESbFgAOedg8KMw/q2G9RQaIISgYu9eCj76mPq0NIwGD8buuecw7NO70eeXF9UQ/n0sucnl9B7hTNBsH3R0G76NKRQKjh07xsGDBwEYPnw4w4YNQ1e383yYZXeOtJo67juXTGZdPV/0cOeuDlim+1Y8s/4sO2NyOfLCmA6xMK4jjEE0SpKkB2kYvJ4nrmQnIUSdEKLoys+naRjA9murGFRqFREZESj1GspRNHs1dUtYe8PCcBj6BJz8tmFxXUG8Rk4tSRJm48fjFbYN+1depi4xkdTZs8la+iz1mf/s1jKzNmT60gD6j3cj5mAWGz9o6HIC0NXVZcSIESxZsgQ/Pz8OHDjAl19+SVxc3D/OI5O1pbPl1Uw5nUCxQsnv/bw7fXLIKK5my7ls7hvi1iGSw624rQlCkqQQYBkwVQhRfc1xW0mStK/87AX4AsltFUd0fjRP7n+Shw4+AsCZtNNUK269tlKz6ehDyDtw3x9QkQ3fjoQzv2rs9JKuLlbz5uG9ZzfWixdRsW8fyZMmkffBh6iuq/Kqra1F0CwfJj/el4qiWn5/+xSJp/P/etzCwoI5c+Zw//33o62tzdq1a/n1118pLi6+/rIymcaFF5Yx40wihtpabBvgyxCLzj/D7tuDyWhJdPhV041py2mua4FRgA2QB7xGw6wlfeBq3ezjQojFkiTNAt4ElIAKeE0Isa2pa7S0i0mhVnAq9xRHLh9k7p4gPnf4lQib0wQ7BzPOfRwjXUZiotdGH8yKXNj4MKQegn5zG/ad0NPsLlKK3FwKPl9B2ebNaJubY/PEE1jeew/Sdd1F5UU17P4ulvzUcvqMciFolg/auv/7zqBUKjlx4gSRkZGoVCqGDx9OUFCQ3O0kaxO/ZRfxbFwGvU0N+aWPF3b6nf9zll9RS/D7B5jp78x7s/q2dzh/kVdSN0GtVoJSIvvVo5QH6fCn7X72pe+joKYAPS09hjkPY4L7BEa5jsJUT8OVIdWqhhpOEe+BjS/M/i/Y99LsNYDaS5fIe/8Dqo8fR8/dHbvnnsVk7Ni/raJWKdUc+zOJc/sysHM3ZeIjvTGz+fvOW+Xl5ezevZvY2FgsLS2ZPHkyvr6+Go9X1jUJIfgsLY/3U3IZbWXK6l4enXam0vXe3XmJ7w4ms2/pKDxtOs52onKCuImamixOR9+Dm9vD8I075kEemE/yRC3UnM0/S3haOHvS9pBfnY+uli6BToF/JQtzfXPNvYHkyIbNiGrLYNIHEPBAw2ZFGiSEoDIigvwPP6I+ORmjQYOwW7YMw95/T0jJZwrY9+NFJC2JcQt64tHnn7X0k5KS2LFjB0VFRXTv3p2QkBAsLDp3/7CsfamE4OWELH7IKmS2gyWfdHPr0Bv83IqyagVB7+9ndHc7Vs5tRTmfNiAniJuoqkomLv5VSkqOoVtrg5PqQbxDF3FlGAQAtVBzofACe1L3EJ4WTk5VDjpaOgQ6BjLBYwKjXUdrJllU5jckieQI6DMbQj8Ffc3XshcKBaUbNlCwYiWq0lLMp0/H9umn0bW3++s5pfnV7Po2hqLMSgZO9mBQqCda1/1nVSqVHDt2jMjISCRJYuTIkQQGBqKtfWd845PdPrUqNUsupRFWUMYTbna87OV4R9UIW7kvgY/D49n51HB6OHaskiBygmiG4uIjXDr6OrVGyRgb++Lt9Qw2NuP/8SEVQhBTGMOetD3sSd1DdlW2ZpOFWgWHPmlYWGflDXN+AvueLT/fTagqKij8+muKf/oZSVcX64cXYr1gAVqGDd1KynoVkeviuXw0B5fulkxY2AtD03/OvCgtLWXnzp3ExcVhZ2fHlClTcHdveTVbWddSrlQx/0IKR0srecPHiUWudk2/qBOprlcS9N5+/N0sWTN/UHuH8w9ygmimvC/PUG55kkLPP6iuTsHMrD8+3s9haTm00ecLIYgtimV36u6/JYthTsOY6DGR0a6jWz5mkXIINjwEdRUNLYn+c1vxzm6uPj2d/A8/oiI8HB1HR+yWLsVsyuS/kuPFI9kcXBuPgYkuIY/2xsGr8QR4+fJldu7cSVlZGf7+/owfPx4jI6M2i1vW+eXVKbjvfBJxVbV83t2NWQ5W7R2Sxn1/OIW3wi6y8bFABrh3vPcnJ4hmKvwhBlWlAtsn+pCbu4nklM+pq8vF2nok3l7PYWra44avvbZlsTt1NzlVOehq6RLkFPRXy+KWZ0NV5MKGhZB2uGFMYtIHoGvY9OtaqOrkSfLee4+6i5cw7N8f++UvYdinYX+MgvQKdn17gcqSOoJn+9J7pHOjXQD19fVERkZy7Ngx9PX1mTBhAv3797+jugtkmpFWU8ecs0kUKJSs6e3BKKuO1fWiCfVKNSM+OIC7tRHrF2mgEGgb0FiCkCRJC+gHOAE1QKwQIk8jUbaSJhJE8brL1KVX4Ph8QzNQpaolM/MnUtO+QqmswMF+Gl5e/8bQ8OZlo4QQXCi8wO7U3exO3U1edR56WnoEOwcT4hnCSJeRGOk285u1SgkH3obDnzRsdTrnJ7BquznUQqWibPMW8j/9FFVhYcP4xDP/RtfOjrpqBeE/XCTtQhHdhjow6r5u6Og1Pt6Ql5fH9u3bSU9Px93dndDQUGxtO89GLrK2damyhnvPJVGvFvzaz4sAs44zq0eT1p9KZ9nGC/z00GBG+HXMz3+rE4QkSd40LGobByQABYABDSucq4FvgB+FEGpNBX2rNJEgSrYkUn2mAOfX/57pFYoy0tK+JiPzR4QQuLjMw8P9cfT0mm4uqoWa8wXn2ZW6iz2peyioKcBA24ARLiMI8QxhuPNwDHSaUW4jfnfD/hJCDdO/hB53tfRtNouqspKib76h+L8/NoxPLFr0EX47AAAgAElEQVSE1fwHkXT1OLUjlVNhKdi4mjBpUZ9/TIW9Sq1Wc/bsWfbs2UN9fT3Dhw8nODhYXjvRxUWVVTHvfDJG2lqs6+dNN2PNlJvpaNRqwbhPIzHS02bbkuAO24rWRIJYC3wFHBLXPUmSJHtgLlAihPhRA/G2iCYSRNmeVCoOZOD8djBSI9PramtzSElZQXbOBrS1jfBwX4yr63y0tZvX7aNSq4jOj2Z36m7C08Ipri3GSMeIUa6jmOQ5iWFOw9DTvsny+5I0+GM+ZEdD0NMw5pWG0uJtqD4tjbwPPqRy3z50XVywW/Y8puPGkXahiPAfLiJpwYSFvXDraX3Dc1RWVrJ7924uXLiAtbU1oaGheHp6tmncso4poricBRdScdDXYX0/b9wM9ds7pDaz71IeC3+M4vN7+zOtv3N7h3ND8hhEM1UcyqJsezJOrw5F6yY7PFVWJZCU9BGFhXvR13fAy/PfODrO+NvU2KYo1Uqi8qLYlbKLvel7Kasrw1TPlHFu4wjxDGGww2B0tBq5+SvrYOcyOP0DeAyHu38Ak7ZvulYdPUreu+9Sl5CI8bBA7Jcvp8bUkV3fXKAou4ohU70YEOJ+029JSUlJhIWFUVJSQr9+/ZgwYQLGxndm14Lsn7bll/L4xTT8jPVZ188bW707uyU599vjpBZVcfD50ehqd9wNOzU5BpEEfCiE+PqaY2FCiNDWh9k6mkgQVVF5lGyIx+G5gehYN90qKCk5SWLSe5SXn8PY2A8fn2VYW4285aakQqXgWM4xdqXsYn/GfqoUVVgZWDHefTyTPCfhb+ePlnTdB+zMrw37XxtaNYxLuLb99DmhVFKydh0FK1eirq7Gat48zB9dzMHNWSScysPb35YxD/ZAz+DGrRqFQsHBgwc5cuQIBgYGhISE0KdPnw7b/JZpxq/ZRTwXl8FAc2N+7uOJuW7btnzbW0xWGaErD/PipO4sGund3uHclCYTxGXgHA3jDouEEPWSJJ0RQrT70kBNJIia2CKKfr6I3ZL+6Lk0b3qqEIL8gp0kJX1ITU06lpaB+Pq8iKlpy8pl1KnqOJx5mB0pOziYeZBaVS0Oxg6EeIQQ4hlCT6ue/7uZ5pyH9f+C8myY9B4MXKjx1deNURYXU/DZ55T+8QfaVlbY/vsZUs0GcOzPJCwdjZn8WB/MbW8+CJ+Xl8fWrVvJysrCx8eH0NBQeSX2HerbjHxeTcxmtJUp3/f2xKgDf5vWlH+vP8ue2FyOvji2w+8Yp8kEES2ECJAk6XlgFjAH+FMIEaCZUFtOEwmiLqWMgm/OY7OwNwa+N9/n+XpqdT1ZWb+RkvoFCkUpDg7T8fZaioGBY4vjqVJUcSDjALtSdnEk6whKocTdzJ1JnpOY5DkJL3MvqClpGLxO2NNQ8C/00zadCnutmphY8v7zH2rOnsWgb19U858nYm8VABMf7o1rz5sP4qvVak6dOsXevXsBGDNmDEOGDEFL686/gXQF19ZVmmJrzlc93dHrAv+2uWW1BL+/n/sD3XntLs3XVdM0TSaIv1oLkiSNBVYBVkKIdl/6qIkEocitIu+zaKzu645R35b16ysU5aSlfUV6xn+RJAk314W4uy9CR6d1FWHL6soITwtnZ8pOTuWeQiDoYdWDyZ6TCXGfiMPpHxsK/jn2hXt+AQu3Vl2vuYQQlG/dSt5HH6EqLEJ3xr84pTeKkrxaAmf40H+8a5PdR6WlpWzfvp2EhAScnJyYOnUqDg4OtyV+WdsQQvBOcg4r0/O5296Sz7q7oXOH1FVqyns7L/PtwSQinxuNq1XHXyiqyQRx17WltyVJcgceFEK82fowW0cTCUJVVkfOuyexmOGDyZCWf/MHqKnJJCn5Y/LytqKra42X19M4Oc5Bq7GB51uUX53P7tTd7EjeQUxRDBISAfYBTDZyZ8LRH7DQ0mmoCus5otXXai5VZSWFX6yi+OefEWZWJI57gYwCA3wH2TP6/u7o3mC9xFVCCGJiYti5cye1tbUEBwczYsQIdHTu7L7qO5H6StG9NVmFPOBkzXt+Lmh1kTGmqjolge/uI9jXhi/nDWjvcJpFE9Ncb9qFJISIbmFsGqOJBKGuV5H96lHMQjwwG+WqkbjKy8+TkPAOpWWnMDb2xdfnJaytNXfjTi9PZ0fKDnak7CClLAUdSYdghZrJJYWMCnwOw2FP3ZZxiavqEhLIfes/VJ08SdbAfxFvEoitmymTH+uLiWXTUxqrq6vZtWsX58+fx9bWlqlTp+Lqqpl/C1nbUwnB0ssZrMstZrGrLa95O3WpCQg/Hk3lta2xbHxsGAPcb62bur1oIkEcuObXAUAUcPVfXQghxrQ6ylbSRIIQQpD18hFMgp2xmKS5efpCCAoK95CY+B41NelYW43Ax/clTIw1t4+CEIK4kji2J29nR/J28msKMFSrGatny+Sglwl0G9X4tNk2IISgfMcO8t//gFyVHRf7PoKeiQGTHu+Hg2fzChkmJCSwbds2ysvLGTp0KGPGjEFPr3Nt0djVKNSCJZfS2JJfylIPe571cOhSyUGlFoz+KAJrEz3+fDyovcNpNo2ug+gos5au19IEUVtVScSPq/H0H4h73/4UfxqDYU9rLGdqfhMctbqezMyfSUldiUpVjZPTvXh5PoWe3o0XmbWESq0iOjeK7cfeZ09ZHBXaWljpWxDiOZlQr1B62/S+Lf9xVZVVFH75JekbwrnQ61HqDC0ZfX8Pugc6Nev1tbW17N27l6ioKCwsLJg6dSpeXp1vq8auoF6t5rGLaWwvKOMVbyeecGv3YcnbbldMLot/Oc2X8wKY3Kd1XdS3k6YTRHRHmLV0vZYmiOz4y/z53uvUVlUiaWkR6rEYyVIH8zk+2Lp7tsmNtL6+mJTUFWRl/YaWliGenktwdXkQLS3Nf0Ouv7yDQzuXsN1In0hDA+qFEjdTN6Z4TWGK1xTczdq+LHdtfDzpb77PKcUgSi396DvAmKCFg/+xv8SNpKamsnXrVoqLixkwYADjx4/HwODOLM/QGdWp1TwSk8qeonLe8nHmEdeOWXOord391VFyy2uJeHYUOp1oKq+cIJqgVqnISYwn5UwUlmdMqKmtJDJ3PSaWVnj0H4iX/0Dc+vRHX8Olq6uqkkhIfIeioggMDd3x9XkJG5uxmk9KhQmwdi4VpansHfoAYeqyv2ZC9bXpyxSvKYR4hmBl0HaliIUQlG7eysHfLpFpPRgHg2ImLx+HoW3z1j4oFAoOHDjAsWPHMDU1ZerUqfj4+LRZvLLmqVWpWRiTyr7ict71c2GB8z93H+wKzqSXMOPLo7wS2pOFwZ2rjIwmxiBWAlcfvBdYd+3jQoj/a22QraWJMQiAwv/Goiippqh/KSlnokg9f4b6mmq0tHVw6dETz/4D8fQfhJWzi8Zu5EVFkcQnvE11dRJWlkH4+i7HxKSbRs79l5pS2PgwJIbDwIXkjniGnenhhCWHEV8Sj46kQ5BzEKFeoYxyHdW8AoItoCov5/jb6zlX6oFxXSHjQy1wnBXS7L/LjIwMtmzZQmFhIQEBAUyYMEFuTbSTGpWaBRdSiCip4MNuLtzv1DWTA8CS36KJjCvg2EtjMdHvXDPvNJEgHrzZC5tTpE+SpDVAKJAvhOh95ZgVsB7wAFKBOUKIEqnhbvE5MJmGVdvzm5oppakEUbw+jrrUMhyXDQZApVSSE3+Z5LNRpJyJojA9FQAzW3s8/QfiFTAQ11590dVrXdExtVpBVtavJKesQKmswNl5Ll6eTzerYmzzL6KCfW/Akc/BPRjm/AjGNsQVx7E9ZTvbk7eTX52Psa4x493HM9V7KgPsB/yzzIcGJO6MZt+feUjKOgZrHafnK4+h18xd6BQKBRERERw9ehRTU1PuuusufH01P2Yku7EqlYoHz6dwpLSST7q7MtdRs+NonUlOWQ3B7x/goSAPlk9pm90f21KHKNYnSdIIoBL46ZoE8QFQLIR4T5KkFwBLIcQySZImA0/SkCCGAJ8LIYbc7PyaShClW5Oois7D+fVhjT5eXlhAypkoks+cIj3mHMq6OnR09XDt3Rcv/0F4BQzCzLblA3QKRQnJKZ+TlfUb2trGeHn9G2en+zSyfuIv59bD1ifBxB7mrgWH3kDD4HZUXhTbkrYRnhZOtbIaR2NHQr1CCfUObVi5rUHFWRVs+/AY1dWCHolr6T17CFYLF6LVzNlKmZmZbNmyhYKCAvz9/Zk4caLcmrgNqpQq/nUhmROlVXzew43Zd+AucLfikz1xrDyQSOSzo3Gz7vgL466niRbEt8AKIURMI48ZA/cAdUKIX5sIxAMIuyZBxAGjhBA5kiQ5AhFCiG6SJH1z5ee11z/vRufWVIIoC0+jYl86zu80XvL7Wsr6ejIvXiD5SsIoy8sFwNrFDa8Bg/HyH4iTXw+0tJtf5fWqysp44hPeoqTkKMbGfvj5voKVVeNJq0WyTsO6eQ1bms5aDd0m/e3hGmUNB9IPsDV5K8eyj6EWanpb9+Yu77uY5DkJSwPNzPGuqaxnx8poctOq8UzZjp/WJRxffx3jIYOb9XqlUklERARHjhzBzMyMadOmyTOd2lCVSsW8c8mcLKtiVU93Zth3jrn+baVeqWbYe/vp42zGDwua95ntaDSRIPoDLwF9gBj+t2GQL2AGrAG+FkLUNRGIB39PEKVCCItrHi8RQlhKkhQGvCeEOHzl+D5gmRAi6rrzPQo8CuDm5jYgLS2tqffYpIrDWZSFNV3y+3pCCIqzM0k5E0XKmVNkXopFrVJhYGyCe78AvAMG4dF/AIamzd9W8er6iYSEd6itzcTWNgRfnxeb3NGu2cqzYe1cyDkH49+EYU82uqiusKaQHck72Ja8jcvFl9GRdBjuMpxp3tMY7jL85ntYNINKoSbi18tcPp6LQ0Us3c58i9X0qdg99yw6ls27AWVkZLB582aKiooYNGgQ48aNQ1//zt1roD1Uq9T863wyx0sr5eRwxdZz2fzf2jP8MH8Qo7t3zqm9miy1YQIMBBxp2HL0khAi7hYC8aB5CWI78O51CeJ5IcTpG51bUy2IqtN5lPzR/JLfN1JXXUXa+TMkR0eRcjaK6rJSJEkLp27d8QoYjFfAIKxd3Jo1OKtS1ZKevprUtK8BNe5uj+LuvqjZGxXdVH01bF4MF7dA/381FPvTufENP74knm1J2whLDqOwphBzfXNCPEKY6j2VPjYtL9sthCB6dxrHNydjbVBFj4i3MTTSxv6FZZjddVezzltfX8/+/fs5fvw4lpaWTJ8+HfdmjmvIbq5apeaB88kcLa1kZQ83ZnXxbqWrZn99lLzyOiKeHdXsadsdTYcYg7gSiAcdvIup5mIRRT/dWsnvpgi1mtzkBJKjo0iOPkl+ShLQMNDtFTAQ74DBuPTqi04TW3HW1maTmPg+eflhGBg44+u7HFubCa2fTaVWQ+R7EPk+uA1rKPZnfPNBR6VayfGc42xN2sr+9P3UqerwNPdkqvdUQr1CcTBuWbG9pOh8wn+4iJGRhH/6r+icOYTxsGE4vP4aem7NK0CYmprKli1bKCkpITAwkDFjxsjbnLZCjUrNgxeSOVRSyQp5zOEvl3LKmfT5IV6a3J1HR3TsPR9upiMniA+BomsGqa2EEM9LkjQFWML/BqlXCCFu2sGnqQRRl1pGwdctK/ndXBXFhQ0D3dGnSDt/FmV9Hbr6Brj39cd7wGA8/QdibHHja5eUnCAu/nWqquKxshqOn++rGBtroN/9wgbY/DiYOsB9v4Nd9+a9n/oK9qTuYWvSVqLzo5GQGOo4lGk+0xjjNgZDnVtr6eQml7Hjq/Oo1YJg71yk7z9AKJXYPPEE1gvmIzXjZl9XV0d4eDhRUVHY2toyc+ZMHB07z+rWjqJWpWb+hRQiSyr4rLsb9zjKyeGqFzddYFN0JideGouFUectA9MhEsSVfa1HATZAHvAasBn4HXAD0oHZQojiK9NcvwBCaJjmuuD68YfraSpBKPKqyPs0Gqu53THq1/YrQhX1dWTEnif59EmSok9RWVQIkoSjtx9eAwbjPWAwNm4e/2glqNXKK9NiP0WlqsXVdT6eHktaXVaczChYdx8oahp2qvMefUsvTy9PZ2vSVrYlbSO7KhtjXWNCPEKY7jOdfrb9mt3aKSuoIeyLc5QX1TBqmhOmW1dRER6Ofo8eOL71Foa9m1dnPyEhgS1btlBdXc2oUaMICgpCuwWTBrqiWpWaBTEpRBRXdPmprNcrq1Ew9J19hPZ15MPZ/do7nFbReIKQJMlYCFHV6sg0SFMJQlVeR847J7GY7oPJ0Nv7jVMIQUFaCkmnT5B8+iS5SQkAmNna4RUwGO+BQ3Dt2Rttnf99g66vLyQx6SNycv5AX88eH98XsbcLbV23U2kG/HYPFMbBlE9gwE2XwTRKLdSczjvN5sTNhKeFU6Oswd3MnWne07jL+65mdUHVVinY+fUFshNKGTLNC1/tBPLfegtlURFW8+dj++QStAybbp1UV1ezfft2YmNjcXFxYcaMGVhbyze7m6lXN6yQDi8q55NurtznJP99XWvN4RTeDLvItiXB9HFpXgHKjkqTg9TDgNWAiRDCTZKkfjRsPfq4ZkJtOU0lCKFQkfXKUcwmemA2un3LTFeWFJMcfYrk6JN/dUXpGRri0W8A3gOH4HnNrKiysrPExb9GRUUMlpaBdPN7HWPjVpSiqC2HP+ZD0j4IegrGvg4t3A2sSlFFeFo4mxM3czrvNBISgU6BTPeZzhi3Mehr33i2kUqhZv/Pl4g/mUePIEeCQx0p+uwzStevR9fFBYc3XsckqHmVMy9cuMD27dtRqVRMmDCBgQMHdqlqo82lVAsWX0wlrKCM9/xcmN9Fy2fciFotGPdJJGaGumx+ovNUbb0RTSaIE8DdwNZrdpaLuTqm0J40lSAAMl8+jMkwZywmd5yaKor6OtIvnGtoXUSfoqqkGEnSwrl7T7wHNLQuLBwcyMpaR1LyR6hUNbi5PoSHxxPo6Bi37KIqJex8DqLWQI+pMPPbVm9nmlGewdbkrWxJ3EJOVQ6meqZM9pzMDJ8Z9LTu2egNWwjByW0pRO1Ixa2XNRMf6YXifDS5r7xKfVoa5tOnY//CMrSbsad1eXk5W7ZsISkpCV9fX6ZNm4aJSSu75e4gaiH4v0vpbMgr4Q0fJxa5ds6pm23pUEIB939/kk/v6ccMfw1NOW9HGk0QQogh1209ek4I0e6dcJpMENlvn8CwuxWWszpm+QahVpOXnEjS6RMkRZ2g4Er5DysnF7wHDcW9f3cq2URu7kb09R3w9X0ZO9vm1zv6+8UEHFsFe14G5wCYuw5MWn/TUAs1J3JOsDlxM/vS91GnqsPHwofpPtO5y/uuRgsHxh7KIvK3OGxcTQld0g8DPTWFX35F0fffo21picMrr2A2cULT176yF3Z4eDh6enpMmzaNbt00XPuqExJC8FxcJr/kFPGCpwNPe8jbvjbmkZ+iiE4r4eiLY9DX6fzjWZpMEBuAT2gYQB4K/B8wUAhxryYCbQ1NJojcT06ja2eI9b86R12V8oJ8kk6fIDHqBJkXL6BWqTAyt8BrmAuGHidRqNOwthqBn9/rGBm1cF3ApbCGYn8mtjBvI9j6aS7++nJ2pexic+JmLhReQEfSYZTrKGb4zmCY07C/bXSUer6Q3d/FYGSux11P9sfC3ojaixfJXv4ydZcuYTpxIg6vvIyOTdPdIvn5+WzatInc3FwGDBjAxIkTu+ymREIIXknMYnVmIU+72/OClzzjqzFZpTUMf38/i0d683xI82b5dXSaTBA2NBTRG0fDjnJ7gP8TQhRrItDW0GSCyP/qHJKOhO0jfTVyvtuptqqSlLOnSYo6QcqZKOprq7DvV4HDwHwkbXB1egQfvyVoabVglXFWNPw2B1SKhhpO7hos/XFFYkkifyb+SVhyGMW1xdgZ2jHVZyozfGbgZtawDiI3pYztq86DgClP9MXByxyhUFD0/RoKV61Cy8gI+5dexGzq1CZbTUqlkgMHDnDkyBGsrKyYNWsWzs7OGn9fHZkQgreTc/giPZ9FLra87tO1tgm9FR/suszXkUkcWjYGZwsNLFTtADSZIIKEEEeaOtYeNJkgCv8bi6qsDvunOty2F7dEpVSQcTGGpKjjpMQcxKLHJSy9K1BWm2KudR/dA+7HwuEWvymWpMIvd0NpGsz4BnrPbJPYFSoFkZmRbErYxJHsI6iFmgH2A5jlO4tx7uOoKxJs++Ic1aV1THi4F55XpiTXJSWRs/xlas6exXjkCBzfeANdh6a7SlJTU9m0aROVlZWMHj2aoKAgtFo4KN/ZfJqay/spuTzgZM37fporY3+nqVOqGPbufgLcLfnugSbvp52GJhPEPzYL6igbCGkyQRSvj6MupQzHFzpn8a3GCCHIT0ki7twv1OhsRMe4muIEM2rTBuDVbyQ+gwKx8/Ru3s2hurihhlPGcZjwHwhc0mgNJ03Jq8pja9JW/kz8k4yKDEx1TZnsNZlQx2kk/FZLQXoFo+Z1p2dww1amQqWi5Ndfyf/0MyRtbexffAHzmTObfG81NTWEhYURGxuLu7s7M2fOxNy8c09hbMrqzAJeTsjibntLVvRwQ0tODje07Vw2T649w48PDWak352za54mivUFAsOAp4FPr3nIDJhxpw1Sl25Noup0Hs5vaL4LpSNQqWqJu/gROfk/oVZqkXXMhqJL5pha2+E9cAg+g4bi0qM32jo3KTGuqIU/H22o4TR4EYS8C1ptO2B3dW3FxoSN7E3bS52qjl5mvRlz+QEUafoMmebFgBD3vxJBfXo6OctfpvrUKYyHD8fxzTfQbWI1tRCCs2fPsmPHDrS1tZk6dSo9e3aOsahb9UduMU9eSmeSjTnf9fJAp5PWErpd7v/+BMkFVRx6fnSnrbvUGE0kiJE0rIJeDHx9zUMVwDYhRIIG4mwVTSaIWyn53ZlVVSVzOe5lSktPoIs3pbF9SDmRglJRj4GxCV4Bg/AZHIhH3wB0G9tnQa1umN10fBV0D20oG97KabDNVVZXxo6UHWxK2ER8YQJjk+/Hu8AfhyF6zHhgGFpX9gQWajUla9eS/9HHDa2JF5ZhPmtWk62JoqIiNm7cSHZ2NgEBAYSEhNxRA9i7CspYGJtCoLkJv/T1wqAT7aHcHjKKqxn+wQGeHufL0+M0N0GjI9BkF5O7EKL1NbXbgCYTRMWRLMq2JeP4ylC0je/sIm9CCHJzN5GQ+C5KZQUuTgsQpUNJjoom+fRJaqsq0dHTx72vP76DA/EaMBhDk+uKGB7/Cna9CG5DGwavDW9vGejYolg2xW0ib5+gR1YwOY6X8ZlhzFS//02Xrc/IaGhNnDyJcXAwjm+92WRr4upeE4cPH8ba2pq77777jqjndLikgnnnk+lpbMgf/b0xuQOmara1T8LjWbk/gcN30OD0VZpMELbA80AvGvaDAEAIMaa1QbaWJhNEVXQeJb/H4/DsQHRs7qwPw43U1xeTmPgeObkbMTRwo1v3t7AwG0rW5VgSTh4jMeo4lUWFSFpauPbsg8/gQHwGDcXU6sp00phN8OcisPKGf20E89s/E6iqvoqNv0dScdiADPNL7OvxEyM9h3O3390MdhiMJKBk3bqG1oSWFvbLl2M+fVqTrYmUlBQ2bdpEdXU1EyZMYPDgwZ12IDe6vIrZZ5NwMdBjs78Plrqda//k9qBSC4Lf34+fvSk/PnTnjEtepckEsYeGPaSfpaG76UGgQAixTBOBtoYmE0TNpSKKfryI3RP90XPVTMnvzqKk5DiX416mujoFB4fp+PosR0/PCiEEeUkJJEYdJ/7EUUqyMwFw9O2Gz6BAfIcMw7I6oWGXOgPzhiTRzGqwmnbxSDYHfrmMyrqSzX5fUCBycDV1ZZbvLKb5TMOssIacF1+iOioKk9GjcXzzDXRsbz7oWFVVxebNm0lISKBbt25MmzYNI6POtb3k5aoaZkQnYqajzZYAXxz07+zWsaYciMtnwQ+n+HJeAJP7dP4W5PU0mSBOCyEGSJJ0XgjR98qxSCHESA3F2mKaTBB/lfx+qDcGfl1v1yyVqo7UtFWkpX2Djo4Zvr7LcbD/+zftoswMEk4eJfHUMfKSEwGwcfPAt6c3vhnfY6NbgTTvd3C76VbibSblXAG7V8diaq2PyYxiNudsICovCh1Jh9Fuo7nbZyZ+exMp/PQztAwMcHj9NcwmTbrpOYUQHD9+nPDwcExMTJg5cyYeHh635w21UkZtPXedTkAg2Brgi7uhvNtecz32y2lOpBRz/MWx6OnceWM1mkwQx4UQQyVJ2g2sALKBDUKIdt8tQ5MJ4n8lv7th1K/r1qKprIzj0uXllJefwcpqON27vYWh4T8LGJYX5JNw8hgJJ4+SFXcRhMDCQImvSQG+M5bgMHZ+u3TJZMWXsP3L8xgY6zL1qf4U6+eyKX4TW5K2UFpXiouJC/cbj2bQ6uMoYy5hOikEh1dfbXKb0+zsbDZs2EBJSQkjR45kxIgRHXrNRFG9kmlnEsivV7DF35ceJl2j21QTCivrGPrOPuYP8+Dl0DtzNpsmE0QocAhwBVbSMM31DSHEVk0E2hqaTBCq8npy3jmBxXRvTIY6aeScnZUQKjKzfiUp6SOEUOHl9W9cXeajpdV433VVaQmJp46TcCySjIsXUAsJE1NDfIPH4Tc4CKfuPdBq4+mw18pPK2fbinNoaUtMfao/1s4m1Knq2Ju2lz/i/+B03mn00P5/9s4zPKpqbcP3nknvhfRKCOmE3nuTJl2pIuUIigUURexHj2JBUWxYQPhAaYI0KdJ7J6SHhAQSSO+9TmbW9yOABJIQkkkCYe7r8lL2zF57ReM8s97yvLwa4UrH3TFomZljv/gTjPrWfCguLS1l9+7dhISE4Orqyvjx4zE2fvjCkYVKJU8HXSW8oJhNbVvRzUxjTPgg/Hr8Kp/uieTAa31obfPw/WBYqNoAACAASURBVPdVB2oRCEmS5FTYanxT7ZuaEHUKhFCoSHz/FCZDXDDpX7sxl82dkpIkoq58SEbGIUyM/fH2/hwjo5oN7kqyUrj6y/NEx6QRV2yFUqnCwNQM987daN21J04+bWrutVATWUmF7Pw2kHKFiidfbout27/Nb9dyrrH5ymZ2Xt2JWUIur++WY5dShsFTY3B6+z1khjU74QYGBrJ79250dXUZN24crVo1+WH6NgqVYHroNY5m5fObnyvDrO7vdqvhX4SosPU2M9Dhr7nNsycK1HuCOCKEeLARY42EOgUCIPH9Uxh2t8NsuBpGeTYThBCkpe0m6spHlJfn4eoyF1fXuTX7OpWXwtY5lIX+zTXHZ4gusiM2MABFaQl6Rsa4d+6GR9eeOLdpW2kQkrrJyyhmx7dBFOWVMXxuG5y8KrvFlpSXcOD6Af4K34jXX4GMPCcotDJE96M38e//dI0hsrS0NP78808yMjLo27cvffv2bfKQkxCCeZE32JySzZeejkyz18x0eFAuxmXx1M9nWDLenwmdm3Y2TEOiToFYDJhSUcl0e6KcEOJSfTdZX9QtEEmfnkPPwxyLp5pXU4w6KCvLIjp6MSmp2zE0bI2312eYmrav/gaVEnYvgID/g44zUAz+jLjQYKLPnebqxXOUFReha2BIq45daN2tF67+7dFqgKa0wtxS/v4uiOzUIoY854dbu6orl6Kyojjy9w/4Lj+ERZ7gRP8WWL44l+GeozHUrvpEUVZWxp49ewgKCnooQk4fX03ixxtpLHS15fWWGtvuuvDG5mD2hiZz/t1BGOo233JgtZ4gqrgsmlsfBEDKNwFotdCnxbTmmZhSBxkZR4iMeo/S0lScnGbQym0Bcnk1pZ9CwKH/wcmvwWcMjFsBWjqUKxTcCA3iytlTxFw8Q2lhITr6+rh16IJHt564tuuIto76Km5KChXs+iGYtOv5DJ7lQ+tONtW+Nz87ldD3XsP8UCDXbGDFWEM6dRvDRM+JtDavelZIUFAQu3fvRkdHh/Hjx+Pm1vgn0F/j0/ggJonp9pZ8rjHfqxP5JQq6LD7E6Hb2fD7+0XN1fhDUPpNaXUiS5EnFaeQWbsAHgBkwG0i/ef0dIcSemtZSt0Ck/RyMJJOwmtO8fznqS3l5PjFXvyQxcR36+s54e32OuXkNpa2nv6+w52g1ACb8Drr/Jk2V5Qriw0KIOnuKmAtnKCnIR1tPH7cOnfHo1pOW7TqirVuF5ccDUlZSzu4fQ0iOyaH/NG+8e9Rc25534AAJ772LsqiQPwbI2dNeRQebjkz0nMhgl8FoyyuHxtLS0ti8eTPp6en079+f3r17N1rIaWdaDnPC4xhhZcqvvq7INeJQJ9afu8E720LZ9mIP2js371L3h1YgKj28IgmeCHQFZgIFQoivanu/ugUiY004ypxH3/K7scjOPsvly29TXHIDR4dptGq1sPpRp4F/wM5XwLEzTPkT9O9NnirLy4mPCOXK2ZPEnD9DcX4e2rp6FWLRvVe9xUJRpmTvTyHEX86m72QP/PrWPDqyPD2dpHfepfDECbI7tGLZEAWXScJCz4LxrcfztMfT2Bn9KzRlZWX8/fffhIaG4u7uzrhx4xq8se5cTgETgq/S1tiAP9u20vgr1YPRP5ykRKHin1d7N/sT2KMiEE8A/xVC9JQk6UOaWCCy/oyi9FrzsvxuaJTKIq5eXUp8whr09Bzw9voMC4tqqj8idsCW/4C1N0zbDoaW1a6rUipvi0X0+TMU5+VWiEXHLnh264Vr+7qFocoVSvatCCcuJIOeT7nTblDNFWtCCLLXrSftyy+RGRqSs2Aqv1tc5njCcQD6OfZjktckutl1Q5IkhBAEBASwd+9eDA0NmTBhAo6ODTPDOKaohJEB0Vhoa/F3x9ZYaCw06kxkSh5Dl53g/Sd9+E+vh2cufUPxqAjEKuCSEOKHmwIxA8gDLgKvCyGya7pf3QKR8/dVCi82X8vvhiQn5yIRlxdRXByHg/1k3N3fQkurivr76AOw6Rkwd60QCZP72xhUEotzp2+fLFp16lpxsmjb8YES3MpyFQdWRXD1UhpdR7nRabjrfe8pjY4mceGblEZGYjZpIqqXn2Xz9Z1sjd5Kdmk2riauTPScyGj30RjrGJOUlMSff/5JXl4eQ4YMUbuXU3qZghEB0RQqVezpqOmSri+f7rnMqpOxnH93EBaGzcfBtzrUmaSuanxYLhAqhEir4/6QJEmHiq5sXyFEqiRJNkAGIICPATshxKwq7psDzAFwdnbueP26+oxm8w5eJ+/gDRwW90KSN+8jZkOgVBZz7do33IhfhZ6ePd5en1d9mog9ARsmgaEVTN8JZrXvO1EplcSHhxJ19gTR589Qkp+Hjr4+rTp1w7N7L1z8O6Clff/SWZVSxeG1kUSdS6HjMBe6jnK77we4qqyM9GXfkrVqFTrurXBYuhTJ3ZX9cfvZGLmRkIwQ9LX0Gek2kslek3HQc2Dbtm1cuXIFX19fRo0aha5u/T/IC5VKxgdeJaqwmL/au9PBpOa+DQ01o1QJenx+iDYOZqyc3nymxtWEOgViN9AduFXN1A84C3gA/xNC/F7HDY4GXhJCPFHFa67ALiGEX01rqPsEUXAqkZzHxPK7IcnJDSAi4k2Ki+NwdJiGu/ub91Y6JVyEP8aBjhE8uxNauD/wc5Tl5cSHhxB15iQx509TUliAroEh7p274dmjD85+bWtsyhMqwdH1UUScTKLDEBe6jbm/SAAUnj5N4qJFqHLzsH7jDcynPYMkSYRnhrMxciN7ru2hTFVGF9suTPKchM4NHY4eOUqLFi2YOHEiLVrUvT9BKQSzwmI5kJHH6jYtGdKieU+/awxOxWQwdeU5fpzSgRH+zc+YryrUKRB/A88JIVJv/tkG+Al4Djh+vw/xGtbdCOwTQqy++Wc7IUTyzX9+DegqhJhU0xrqFojCwDSyN0Vh83pHtK0eLdfOhw2lspirV78iPuH/0Nd3xsf7S8zM7vp9TAmFtWNAksGz28HGt+7PK1dwIzSYqDMVJ4uy4iL0jE3w6NIDzx69cfTxq9LuQ6gExzZeIfx4Iu0HO9N9XO1GsJZnZZH8zrsUHD2KUd++2H32KVoWFY142SXZbIvZxqbITSQVJmFjYMMYizEUXixEqVQyduxYvL29H/hnFELwTnQiqxMz+LS1A7Mcm88IzKbkjc3B7AtL4cJ7g9DTfjzmZKhTIEKFEG3u+LNERXjJT5KkQCFEDd1S1a5pAMQDbkKI3JvXfgfaURFiigOevyUY1aFugSiOzCLz/8KxerEtus4malv3cSY7+xwRlxdRUpKAk9NMWrm9jlx+RyVS+hVYOxrKSypEwq7+k2zLFQrigi8Rdfo4Vy+eQ1FagoGpGR7deuHVow/2Hl5Id5SgCiE4vvEKYccSaTfIiR7j3WslErcT2EuWIDM1wf7zzzHq2fP260qVkuMJx1kfuZ6zyWcxVZoyMGcgUp5Er169GDBgwAOVwt7qdZjrZMV/3Rt/9kZzpLhMSefFBxnexpYlTzX5FOVGQ50CsRxwBjbfvDQeSAAWUhEGajIbDnULROn1PNJ/CqbFTF/0PC3uf4OGWlFeXkjM1S9ITFyHgUErfH2+wsTkjl6TrGuwZhSU5lUkrh3UV2asKC0hNvAikaePE3vpIuWKMowtrfDs0RuvHn2wbtnqdvXRiU3RhB5NoO1AJ3o+VTuRACiJiiLx9dcpi7mK5XP/wWr+fKS78iBXc66yIXIDu6J34ZHmgVu+G6Z2psycMhMz4/v7Je3PyGV6aCzDrSpmScuaeRlmY/F3cBKvbAhk/eyu9Gj1+FiTqFMgJCpEoScgASeBv0RTlj/dRN0CoUgrIvXrACwmeWLQ7vG1/G4oMrNOcvnyIsrK0nF1fRlXl7nIZDc/SLOvw5onoTgXpm0FR/UnC8uKi7h68RyRp48TF3wJlVKJma0dXj364NWzLxYOTpzcHE3I4QT8BzjS6+nWtRYJVXExqZ99Ts6ff6Lfti32S5ei43jvt/y8sjy2R2/nwOkDuCa5otBS4NzbmSldpmCmV7VQRBQUM/JSNK0MdNnW3h1D+eMRBmkM/vN/F4hIzuPUogHImvEs+rt5JMpc64u6BUKZX0by4nOYjW6FUffH2/K7oVAocrly5SNSUndgYuyPj89XGBredEPNiYc1I6EwA57ZUjHvuoEoLsgn+txpok4fIz48DCFUWDm74tmzLwU5zkSeLaRNP0d6T6y9SADk7d1L8vsfgCRh98knmAy5pwYDqAg/7Qnew7m955AUEiHWIbRv256p3lMrWXqklSoYFnAFFbC3o4dmIpwaySwopeunh/hP75a8PezBc0KPMuouc/0CsKbiBCFR4cXU5EF6dQuEKFeR+N4pTAa7YDJQY/ndkKSm7SEy8n1UqmLcWy3C0XEakiSDvKQKkchLhqmbwbXn/RerJ4U52USdOUHkqWMkR0cBYGTpSklRS9oM6Ef/aR0eSCTK4uNJXPA6JaGhmE2ehM1bbyGrpry1oKCAtRvWkpaYxlWzqwSbBdPFrgtTvafSxb43TwVdI7KwhB0d3PE31hROqJO1Z+L4YEc4/7zaGy/bJv84a1TUKRAxwEghxGV1bU5dqFsgABI/OI1hF1vMntRYfjc0paVpXI58m8zMo1iY98TbZwl6uraQn1KRk8i5AVM2gVvjTbfNTUsh8tRxIk8fJ+NGHCBhZutJt3HDaN2lOzr6tfuQFmVlpH2zjKzVq9H19MThm6/RrcbET6lUsm/fPs6fP4+ulS7HLI6RUJaE0vYNcnTa8JO3A2NsNSFPdTN2+SmKy5T882qfpt5Ko6NOgTglhGj4r3F1oCEEIvmL8+i6mmIxsebBOBrUgxCCpKSNXIlejEymg5fXYmysh0FBWkV1U1Zso4vELdJvxLF/xTZSYi6AKg8tHR3cOnbFu2dfWrbvWKtZFgXHjpH01tuoSkux++gjTEc+We17AwMD2bVrF0bGRoR0acveUgsMszdgU3KC8R7jmew1GXsjTehTHcRlFNLvq6O8NcyLF/o+PAOfGgt1CsS3gC2wHSi9dV0IsbW+m6wvDSEQqT8EIjfUpsXMOrV3aKgjRUWxhIcvIC8/BDvbcXh4fIBWaWlFuCkrtiLc1LJ3o+9LqARH1kUSfiwAS/tEcpKCKc7PQ8/QCI9uvfDu1Q8HL59KZbN3o0hJIfH1NygOCMBs4kRs3nm72pBTYmIiH+w7wu6WfgzVk3i1lWDd5XUcuH4AgIHOA3nW91naWj0+JZkNwbKDV/j2UDSnFg3A3uzxm9etToFYXcVlUZUNRmPTEAKRvioMVZECm5cfuL1DQz1RqRTExv1AXNxy9PQc8PX5CjMtl4rqppwbMHVLo+Qk7kaoBId/v0zkmRQ6j3TByj6byyePEn3hDOWlpRi3sMKrZ1+8e/XDytm16jUUCtK//ZbMlb+h6+2N47Jv0HFxued9QXlFjL4UjV1RHoMvHGZAnz707duX1KJUNkRtYEvUFvIV+bS1asuzPs8ywHkAWtXMCtdQNUII+n91FDtTfTbMabhCiIcZTRVTHcnaFEVpXC52izSOrk1FTm4A4eGvU1KSiKvrXFq2mIRs7WjITYRn/gKX7o2+J5VKcGhNBFfOpdJ9XCs6POGCoqSEmItnuXzyKHHBlxAqFVYuLfHu3R+vnn0wtri3rj7/yBGS3noblErsFi+uVOWUVqpgaMAVJGBPu1ac2f8PQUFBeHt7M2bMGHR1dSlSFLEtZht/RPxBQkECDkYOTPWeyrjW46qdfKehMoE3shm7/HSzHytaE/UWCEmS3hRCLJEk6XsqupsrIYSYV/9t1o+GEIicv69SeCEVh/9pHF2bkvLyAq5c+R/JKX9hYtIeP5e30d84pyKB/cxWcK5hQFEDoVKqOLg6guiLafSe6IF//39tvIvycok6fZzLJ49WVEJJEs6+/nj37k/rLj3QvWMuhCIxkYQFCygJDsF82jRsFr5BmZYWTwVeJaygiL87tMbP2AAhBGfPnmX//v1YW1szefJkzMwqeiWUKiVH44+yNmItl9IuYaRtxFMeTzHVeyq2hppxozXx3x1hbLgQz8X3BmGi93iWDatDIEYKIf6WJGl6Va8LIdbUc4/1piEEIu/wDfL2X8fh455I2prhK01NauouIqPeQwiBl/MCbP/+tiKBPW0bOHVu9P0olSr2/RpGbHAGA6d749X9XnO37JQkLp84yuUTR8hJTUZLW4dWnbri02cALv7tkWtpVVQ5LV1K1pq16LVrx3eLPmRDTjG/+Low2rryNLPo6Gi2bNmCXC5n4sSJuNwVmgrLCGNt+Fr2X9+PhMTQlkOZ7jsdLwuvBv138SiiUKro+ukhurtZ8uPUx3cwmFpCTDcnvn0uhFiozs2pi4YQiIJzyeRsi8Hu7S7ITTUe+w8DxcWJhEe8Rm5uALYWT+B54jRaBVnw7A612nLUlnKFkt0/hpAYlc2Q2X606lB1CaoQguToKCJOHCHqzAlK8vPQNzHFq2cffHoPwMbNnfx9+1i+6yDLxj/DXLmC//apWvQyMjLYsGED2dnZjBw5kvbt782RJRYk8kfEH2yN3kpReRHd7Loxw3cGPex7NPsJabXlcGQqs/7vIiue7cRgn+pnkzd31JmkPiyEGKC2namRhhCI4rAMMv+4jPW89ujYVzHwRkOToFKVE3f9J2Jjv0Nfxxbf8ExMc4pgxu56ucDWFUWpkp3fBpF2PY/hc/1x8at+Oh5UuM3GBgYQceIw1wLOoywvx8LBCWX/4Xxo5EjXmEj+t2wxNvPmYTn7uSqrooqLi9m8eTPXrl2jZ8+eDBw4sEqzv7yyPLZc2cK6iHWkFafR2rw1M3xnMMx12D2ztB83Xt0YyJGodC68Owgdrcc3QqBOgVgKtKbCrK/w1vXmWuZaei2X9F9DaPGcH3ruzXtw+aNITs5FwiMWUFqSjFsiuKQIpJn/1GmeRH0pLVKw/ZtAslOKGPlKWxw8avf7UlJQwJWzJzlx/hxftRuEQUkhb4Yfp1ViCqbHT2PWtx/2X3yO3OTe7l6lUsmePXsICAjA29ubsWPHolPNND2FUsHeuL2sDltNTE4MNgY2TPOZxvjW4zHSefy+/JSWK+n08UGG+tny5dOPd5lwbQWiNhJqAWQCA4CRN/+qvtvnEUdmWFEyqCosb+KdaKgKM7NOdOm8CyvroVx1UBHkLihbP7LC7K+R0TXQZtS8dphY6rF7eQipcXm1uk/PyIjW/Z9g2+BJaBsa8ZHIRZGWzLnsFA638+DU1QjOT3ya4sv3mhfI5XKefPJJhgwZwuXLl1m9ejV5eVU/V1uuzahWo9g6aivLBy7HxcSFry5+xRNbnuCbgG9IL0qv18//qHE6JpP80nKGtdEk8WuLpsz1LpQFZSR/ojHse9i53YF95X9olZbim6CPxYQDYNL4/80KskvZtjSA0uJyxi7ogKVDzd/OhRC8GhnPppQs/vB3Y5ClCUIIEiPDiTh+mKhTxygrLUVfUY5nh650eO55zG3v/bmioqL466+/0NXVZcqUKdjZ3X8aWlhGGKvDVnPwxkHkkpxRrUYxw3cGrqaudf3xHxkWbg7mn7AULr4/CF2tx9sRV1PmWkeEUpD47klMBjljMujeRiYNDxcFBVGEBs2mqDQB1wx9Wg4/iMy48cdG5qYXs/WrACRg3JsdMbGsvjv396QMFkYlsMDVhjdb3rtXRVkpVw4dIHDNSlJVCpAk7D288e03EM/uvdE1+LffISUlhfXr11NcXMz48ePx8qpd5VJ8XjxrItawLXobCpWCQS6DmOU3C78WzdNBQKFU0XnxQfp5WLFskqYJVh0C8aQQYtfjVuYKkPjRGQzaWWE+uvHj2hoeHKWyiKhLL5GcfxzTIm38em1Hz6zxSzwzEwvYtvQS+sY6jHujA/rG9+YGAm92Svc0N+IPfzfkNVQXibIyYj/+mIijB0lysCZfKNHS1sG9S3f8+g3G2c8fSSYjPz+fDRs2kJyczLBhw+jSpfZNnhnFGay/vJ6NkRvJV+TT1bYrs9rMortd92ZV+XQyOoNnfjvHz890ZKifJsSkDoH4XQgxTZKk+UKIb9W+QzXQUAKR8tVFtO0NsZzyeHnEP+qkBH9KZNpKZMjx9f8BS5shjb6HpJgcdn4bhKW9IaNfa4+O3r82GJll5TxxMQpJgv2dPLHQrp1FRs7WbSR/+CH5tlZkDe5HzOVQSgsLMba0wrfvAHz7DsLAwpK//vqLqKgounfvzuDBgx9onGlBWQFbrmzh94jfSStOw8fSh9ltZjPAeQAy6dGv9nlnWyjbAxO59P7gx2budE2oQyAigGHATqAfFXMgbiOEyKr/NutHQwlE2k/BSNoyrJ5rc/83a3ioKAxZQdj1Tygw0MLV5QXcWi2gop2n8YgNyWDvz6E4epox4qW2yLVkKIVgcvBVzuUWsrNDa9o+4GyH4tAwEubNQ5mVhdVH/yXdyoLwY4eICwkEIXD09sO33yDi8ou5GBCAj48PY8eORVv7wcpay5Rl7Lq2i99Cf+NG/g1amrZklt8sRriNQFv2aJbIKlWCrp8epGvLx7s57k7UIRDzgLmAG5BIZYEQQogmH5jQUAKRsSYcZU4pNvM1v0yPIsqLK4i68iHJtnqYm3XD13cZurpWjbqHy6eTOLw2ktadrBk8y5cv4lJYdj2Vrz2dmGJfc89EdZRnZZE4/1WKLlyomH392msU5GQTcfwwYUcPkJOSjLa+PiZtOhOXX4SjoyOTJ0/G0PDBPZqUKiUHrh9gZehKorKjsDO0Y7rvdMa1Hoe+1qPlfnruWiYTfz3L95PbM7KtpvAE1NsH8ZMQYq7advbvunFAPqAEyoUQnSRJsgA2Aa5AHDBBCJFd3RoNJRBZW65QeiUbu3ca3+9Hg5o48TVJYZ8T5WGGlq45vr7LsDBvXJO/S/uuc2bbVUqH2LLErIwpdhZ87VW/SYVCoSBl8WJyNm7CsG8fHL76Crmx8e0qqLAjB4k6e4JiHX1KHVqhr6fLlEmTcGxZt+9zQghOJJ7gt9DfuJR2CQs9C6b7Tmei58RHxhzww53hbDh/g4D3B2Okq3G+hUfAzfWmQHQSQmTccW0JkCWE+FySpLcAcyHEourWaCiByNkbS8GpxAo/pmaUqHusEAL2v0dB8E+EdnKliHxaub2Gi8sLFaNNG2ULgq3brrDAsBBHLW0O9fNFT66eZ2dv2EDK4k/RcXbGafmP6Li63n6ttKiIqDMnuHD0EAmiIizU2liPbk8MxbVtB2SyuoXcLqZcZEXoCk4nncZEx4RnvJ9hivcUTHVN1fEjNQgqlaDH54dp42jKimfv+3n42KDORrnGZDRwqzpqDTCmKTYhN9CGcoEoUzXF4zWoA0mCwR9j1HoinU9exUbLi6vXlhISOheFonYNbfVFIQQrnSVkWjKG7cnk+sU0ta1tPnkyzr/9hjIri9gJEyk4eer2a7oGBvgPHMJ/Pl7C1MmT0dXTI7pQwebvv2HFy//h1J9/kJuW8sDP7GTbiV8G/8KGERvoaNOR5cHLbzfdZRZnqu1nUydBCTmk5JUwTFO5VCeaUiAEsF+SpABJkubcvGYjhEgGuPn3JhnE+283taIpHq9BXchkMOp7tFoPx/fwCTyMRpGZeZQLF8dQUBDV4I//7FoygflFfOPjjJ+jCYfXXiYhqtqI6QNj2LULrls2o21rS/ycOWSt/Z27IwLuvn68NP9VrO1sKXHxRG7vwtmtm1j5ynNs/uQ9os6cQFn+YL/nfi38+G7Ad2wZuYU+jn1YHbaaoX8N5csLX5JRnHH/BRqRf8JS0JZLDPR+fI356kNThpjshRBJkiRZAweAV4CdQgizO96TLYQwv+u+OcAcAGdn547Xr6vfYqE4IpPMtRFYv9QOHSdjta+voZFRFMPvYyExgJynvyA0YwXl5Xl4e32Kre3oBnnkgYxcpoXGMt3eki88nSgtUvDXl5cozCll3MIOWKrRCFJVWEjim4soOHQI8ymTsXnnHSStyrH2kpISNm7cSFxcHH169kA/N5OwowfIS09D39gE336DaDPgCSzsHat5SvXE5sayMnQlu67tQlumzVMeTzHTdyY2hk37oSyEoPeSI7hbG/F/MzUDwO7koc9BVNqEJH0IFACzgX5CiGRJkuyAo0IIz+rua6gcROn1PNJ/CsZypi/6nhZqX19DE1CUBauGQEEqpdM2Epb6PTk553F0nEZr93eQyao2vKsLSSVlDLoYha2ONns6etzOO+RlFvPXFwHItCSeWtQJQzXayQuVqmK+xG+rMOzZE4dl3yA3rvzlpry8nG3bthEeHk737t0ZNGgg8aHBhBzax9WAc6iUShy9/WgzcAgeXXuiVY0JYHXcyLvBitAV/H31b2SSjHGtx/Fcm+eabIBRWGIuT35/ki/Gt2Fi5/oVBzQ3HmqBkCTJEJAJIfJv/vMB4H/AQCDzjiS1hRDizerWaSiBUGQUk/rVRcwneGDYQXM0bTZkX4ffBoNcB9XMvVxN/50b8b9hatqBNn7L1VIKW64SPBUUQ0hBMfs6etDaUK/S6+k38tm69BJm1vqMfb1DpUY6dZCzZQvJH36EjqsLTj/9hI5T5ZGaKpWKf/75h/Pnz9OmTRvGjBmDXC6nMCeb8GOHCD28j5yUZPSMjPHtO4A2A4di6fBgYzkT8hNYGbqSHVd3ADC+9fgmEYov90Xy87FrXHh3EBaG6vsC0Bx42AXCDdh2849awHohxGJJkiyBPwFn4AbwdE0NeQ0lEKricpI+OoPpCDeMezuofX0NTUhSEKweDpZuMHMvqTnHibi8CG1tU/zb/ISJiX+9lv/iWjLfXE/le29nnrat+vR5PSyT3ctDcPaxYPjcNsjUVNl0i8Kz50iYPx9JJsPxxx8w6FC5n0cIwYkTJzh8+DAeHh48/fTTtxvq7+y6JAAAIABJREFUhEpFfEQowQf/Ieb8GVTKchy9/fAfNJTWXXui9QCNd8kFyawIXcG2mG1ISLeFojFCT0IIBi49hp2ZHuue69bgz3vUeKgFQl00lEAIUWHYZ9zXCdMhrmpfX0MTE30Q1k8At34wZRP5RTGEhL5AWVkaXp6fYGc3vk7LnszO5+mgqzxta8533jUbPYafSOTouih8+zjQd7KH2supS2NjiX/hBcqTkrH79FNMR97r0H/hwgV2796Nq6srkydPRle3csirKDeHsKMHCTn0D7mpKegZm+DXbxBtBw3DzLb2hohJBUmsCF3B9ujtSJLEUx5P8Vyb57A2aLgalKiUfIYsO87HY/yY1k1junk3GoGoJ0mfnEXfxxLzca0bZH0NTcyltbDzFWj3DIz+AUV5DqFhr5CdfQZHx+m0dn8b2QNYS2SUlTPgQiSmWnL+6eiBYS3spM9si+HSvhv0nuiBf/8HTw7fj/LsbBLnzafowgWsFiyomFR3lxCFhISwbds27OzseOaZZzAwuNcCRKhUXA8LJuTgXmIunEWoVLj4t6ftE8Np1aELMnnt+ioSCxJZEbKCHTE7kEkyJnpN5D9+/8FSv26d5TWx7OAVvj0Uzbl3BmJtrHf/Gx4zNAJRT1K+CUC7hT6W03waZH0NDwFHPoVjX0C/d6DfIlSqcmKufk58/GrMzbrh5/c9Ojr3L1IQQjArLI5DmXns7eSBr1HtrCiESrD3l1DiQjMZ+XJbnHzUXxChKisj+e13yNu9G7PJk7B99917KpyioqL4888/sbCwYNq0aZhUMcnuFgVZmYQe2U/IoX0UZGZgZNkC/wFDaDNwCEbmtdt/Qn4Cv4T8ws6rO9GV6zLFawoz/WaqteFuxHcnMNCRs/mFHmpbszmhEYh6kvZLCCCwfv7xHk3YrBECtr8IwevhqdXgNw6A5OStREa9i46ONW39f8XIqNpCOgA2JGfyWmQ8H7Sy50XnBwublJWUs/XLAPKzSnlqUUfMbdVvXyFUKtK/+YbMFSsx6t8fh6VfIbvrpBAbG8uGDRswNDRk2rRpWFjU/GGvUiq5dukCwQf2EBd8CZlcjnvn7rQbMgJHb79ahczicuP4Kfgn9sbuxVDbkGd9nuUZn2cw1qlfaXlGQSmdPjnIwiGevNRfY9lfFRqBqCeZf0SgSCvGdkHHBllfw0NCeSmsHQ1JgTBzLzhUJHTz8kIIDnkepbIIP99ltGjRv8rbrxeXMvBCFG2M9dnSzr3G+Q7VkZdRzObPL6JnqM34NzuiZ9gwrqlZ69eT+sli9Hx9cfr5J7QsK4d2EhISWLduHXK5nOnTp2NlVbuqrpyUZIIO7CH8yAFKCguwdHSm3ZAn8endDx39+7vWRmdHszxoOQdvHMRU15RZfrOY7DW5zqaAO4ISmb8xiB0v9aStk9n9b3gM0QhEPcneFk1xWCb272sqIJo9BemwYgCoFDD78O2xpSUlyYSEPE9+wWVat34HJ8cZlb4ZK4VgfGAMYQXFHOnihZNe3Uspk6Jz2LEsEAcPM558ua3aK5tukX/4MIkLXkfLygqnX39Bt2XLSq+npqaydu1aAKZPn461de1PRIrSEiJPHydo327SYq+io6+PT5+BtB/6ZK0a8CIyI/gu8DtOJZ7CWt+a59s+z9jWYx/YZvyNzcEcvJxKwHuDkcs0XmpVoRGIepK7L478o/E4LO6FpPkla/6khsNvT4Cle8VJQqfim69SWUR4xOukp+/H3n4Snh4f3k5e/3A9lU+uJfOtlzMT7eqfP4g4lcSR3yPx7+9I74ke9V6vOoqDg4mf+yIIgdOvv6LfpvKY0fT0dNasWYNKpWL69OnY2DxYWaoQguToKIL27ybq9AlUynJc/NvTYdgoWrbriHSfQUYXUy7y7aVvCUoPwtnYmZfavcTQlkNrNbhICEG3zw7RydWCH6do7Pqr41E163tokBlqgwBRUt7UW9HQGNj4wviVkBwMOyo+PAHkcgPa+P2Ii8tckpI2EhQ8E4Uih/CCYr6ITWGElSkTbM3vs3jt8OlpT9uBToQcSSD8RKJa1qwK/bZtcd2wHpmBATemT6fw7LlKr1tZWTFjxgzkcjlr1qwhJeXBjP0kScLew4vhL7/OnOWr6TFhKpnx19n2xUesevV5AnZvp6SwoNr7O9l2Yu2wtfww4Af0tPRYdGIRE/6ewMnEk/d4Td1NdFoBqXml9Gnd4oH2rKFqNAJRDfKbcWClxrDv8cFzGAz6EMK3VVQ33USSZLi3egMf7y/JybnIqQsTeTEsBjNtOUs8nNTaw9BjXCucfS04vuEKKddy1bbu3ei4uOCyfj3aDvbEz55N3oEDlV5v0aIFM2bMQEtLizVr1pCUlFSn5xiamdN9/GSe+2EVI+a/iYGZOUfXruTXuTM4tOpnspOrFkJJkujr1JfNIzfzee/PKVQUMvfgXGYfmE14Zni1zzt+JR2AXq0bd0BUc0UTYqqGkivZZKwKw2puW3Rdqi/709DMuLOy6en/A9+xlV7OybnIwqCD/C2G8qs7jHJqp/YtlBQq2PzZBVRKwYR3OqNv3HA2EcqcHOKff4Hi0FDsPv4fZuMrNwlmZWWxZs0aSktLmTZtGg4O9XcWSL0WQ+A/u4g8dRSlUolb+050GD4aZ7+21YqtQqngzyt/8kvwL2SXZjOs5TDmtZ+Ho3Hl3Mb0VedJyC7i0Ov96r3P5owmxFRPZAYay+/HEkmCkcvAqRtsm1uRm7iDSLzYJYbyhOwUxlenkp5xSO1b0DPUZuicNhTnK9j/WzgqVcN9iZObmeG8ehWG3buT/O57ZP62qtLrFhYWzJgxAz09PdauXUtiYv1DXzZu7gx98VVm/7ia7uMnk3I1mi2fvMfahS8Tcmgf5WVl99yjLddmqvdU9ozbw+w2szly4wgjt4/ki/NfkF1SYaFeolByLjaT3prTg9rQCEQ1yG6GmDQC8RiipQsT1oKeCWyaBiUVA4ZKVSreiIrHQU+bZV2extCwNSEhL5CQuF7tW7ByNqbPZA8SIrO5sCtW7evficzAAKeflmM8bChpX35J2tKllWL95ubmzJgxA319ff744w9SU1PV8lxDM3N6PD2F2T+uZuiLryHJZBz49XtWvDyLM1s2UJR3b4jNSMeIeR3msXvcbka3Gs36yPWM2DqCNeFrOBebSolCRW9N/kFtaEJM1aAqU5L0wWlMh7li3PfB3Cw1NBPiTsGakeA1Aias5au4VL6KS2GdvxsDLU1QKosIDZtHZuYRXF3m4ub2uto9lQ6tvUzk6WRGvOSPa5uG/eATSiUpH39MzsZNmD87DZu3367082RlZbF69WpUKhWzZs3C0lK9FhlCCOLDQwnYvY1rly6gpa2DT98BdBwxptoy2ZjsGJYGLOVk4kmM5DZkxT9BwGuvYaTXML0kzQVNmWs9EUKQ+P5pjHrYYTa8bgPfNTQDTn0LBz4gevA3DFR0ZJiVKb/4ut5+WaUqJ+rKByQlbcLWdgzeXp+pdbZEeZmSLUsCKMgqYcI7nTFpUbfmsdoihCDt88/JWrMW8ylTsHn/vUoikZ6ezurVq9HS0mLWrFmYmTVMI1pmQjwBu7cRceIISoUCt45d6DxqPI5evlW+/1TiKV7Z9xEKeTIdbTqysPNCfC2rfq8GTQ6i3kiShNxQC1Whpsz1sabHPITXk7yZJkNfUvGxe+UkrUymhZfnYtzcFpCSsp2Q0LkolSVqe7yWjpyhc/wQKsE/v4ZRrlCqbe2qkCQJ67fewmLWLLLXryflo48Qqn9ns1tZWTFt2jTKyspYu3Yt+fn5DbIPS0cnnnh+HrN/WEW38ZNJuhLJpv8uYsP7C4m5eK7SngA8TTuRdeVl+pi/QGxuLJN2TeLdk+8+dCNQHzU0AlEDMgNtTQ7icUeS2NDjC86YteO92JVYK3KqeItES9eX8PJcTGbmMYKCZ1FeXn2d/4NiZm3AwBk+pN/I5+Sf0WpbtzokScJ64RtYzp5NzsZNpPz3v5U+kO3s7Jg6dSr5+fmsXbuWwsLCBtuLoZk5PSdMZc4Pq+g/43kKsjPZ8eXHrFn4MmFHD96ep30qJgOQ83yHqewau4uZfjPZE7uHJ7c9yZrwNShUmv+P64ImxFQD6b+FIkqVWL+o/lJGDY8G6WUKep+LxENbyfaDQ5E5dYZp20FWtcV1SspOIi6/gbGxH+3arkJbW30hmNNbYwjcf4Mhs/1w79hwsxRuIYQg/bvvyPzpZ0zHjsXuk4+R7rD2jo2NZd26dVhZWTF9+nT09BreVltZXs6VMyc4v/MvMm7EYWTZgk4jxrIh155DMdlcvMNeIy43ji8ufMHJxJO0NG3JW13eooe9xt0VNCEmtaA5QWj4KCaJQqWKL9t4IRuxFGKPw5HF1b7f1nYUbfyWU1BwmUuXplBamq62vXQb7Ya1izHH1kdRmFuqtnWrQ5IkrOfPp8UrL5O7bRvJ77yDUP4b4mrZsiUTJkwgNTWVTZs2UV7e8OFYuZYW3r378+yS7xn31oeYWdtydO0KzHcvYZi4jLK0+PZ7XU1dWT5wOd8P+B6FUsHzB57n1SOvkpCf0OD7bC5oBKIG5IbaKDU5iMeWY1n5bEnN5mVnazwN9aD9VOjwLJxYCteOVXufldUg2vqvpKj4BgGXJlFSUrcu5LuRyWUMnOGDolTJ0XVR97WdUBdWL72E1avzyd2xk5QPP6r0XA8PD0aNGkVsbCy7du1qtD1JkkTL9p2Y+OHn9Jj/X1K1W2AZcYAVL1WUyJYUFNx+Xz+nfmwfs5157edxOuk0Y3aMYWXoSk3YqRZoBKIGZAZaiJJyhFJ1/zdraFYUK1UsuhKPm74u813uMKsbtqTC0G/Hy1BafYLWwqIn7duvQaHI5GLABIqK1NPLYGFnSLcxbsSFZBB5Jlkta9aGFi+8gOULz5OzeTPpy76t9Fq7du3o27cvQUFBnDhxotH2dItwpSU7bZ9k8Nuf4eDtx+nN61jx8kxOblxLcUHFfyNduS6z/Wezc8xOejn04ttL3zLh7wkEpgU2+n4fJTQCUQO3m+WKNKeIx40fbqQSV1zGEk9H9O603tbWh9HLITceDnxQ4xpmph3p0H49KlUplwKfobhYPQZ8bQc4Yd/ajBN/RpOXWXz/G9SE1fz5mE2cSOYvv5D5f/9X6bV+/frh7+/P4cOHCQ0NbbQ9AZyIzqCVlSH+7dowZuF7PLvke1zbdeLc9s2sfPk/nN68jtKiikS6raEty/ov47v+31GgKODZvc/y0ZmPyC1tON+rR5lGFwhJkpwkSToiSdJlSZLCJUmaf/P6h5IkJUqSFHTzr+GNvbe7+VcgNEfRx4lsRTm/xKczwsqUXuZVTDdz7grdX4KLq+DqkRrXMjb2oX27tSiVRQQGPUNpaVq99yfJJAZO9wYBh9dGIhrQiqPScyUJ2w/ex3jIENI+/4Kc7dsrvTZq1ChcXFzYvn07169fb5Q9VWWvYeXSkpGvLmL6ku9xadOOM1s2sOLlWZzduomy4iIA+jv3Z8foHTzr8yxbo7cyavso9lzb02ghskeFpjhBlAOvCyG8gW7AS5Ik3Rr8/I0Qot3Nv/Y0wd4qITO46ehaoBGIx4mf49MpVKp4w9W2+jcNeA8sW8POV25bcVSHsbE37dquoqwsg8CgZ1Eosuu9R5MW+vR8yp3EqGxCjzVe0lWSy7H/cgkG3buR/O575B/5VyC1tLSYOHEiZmZmbNy4kczMzAbfT8D1bEoUKvp43Ntl3sLZlVGvv8Mzn3+Lg5cvpzb9zopXnuPC31tRlJVioG3Aws4L2ThiI/aG9iw6sYj5R+ZreifuoNEFQgiRLIS4dPOf84HLQP0tIhsAzQni8SOzrJyVCemMtDbD26iGrmVtfRjzE+Qlwv737ruuqWl7/P1/pbj4OoFBMykvr3+DmU8ve5x9LTmz9So5qUX1Xq+2yHR0cPz+B/S8vUl89TWK7ig1NzAwYOrUqUiSxLp16xq0RwIqwkvacomuLau3/bBp2Yqxb37AlMVLsXVz5/gfq1j96gtEHD+MUKnwtvTmj+F/8EanNziVeIqxO8ayL25fg+77UaFJcxCSJLkC7YFbE0teliQpRJKkVZIkqWcKSz2QG95ydNXkIB4Xfo5Po0ip4vWaTg+3cOoMPV6BS2sg5v6urhbm3W+XwAYHz0aprF/+QJIkBkzzQq4t4+D/RaBqxGIKuZEhTr/+gra9PfFzX6Qk6srt1ywsLJg0aRK5ubls2bIFlarh9nUiOp0OzuYY6mrd97127p6Mf+d/PP3+pxiYmrL3x6/5/e1XiQsJRC6TM913OptHbsbRyJE3jr3BwmMLySm5tzHycaLJBEKSJCPgL+BVIUQe8BPQCmgHJANLq7lvjiRJFyVJupierr4a86q4FWLS9EI8HmSUlfNbYgajrc0qylprQ793oIUn7JwHJfdPdLZo0R9fn6/JyQ0gJHQuKlX9+hkMzXTpM9mD1Ng8wo6rp5y2tmhZWOD820pkenokzpuHsuDf7nFnZ2eGDx9ObGws586dq2GVupNXoiAiOY8erR7MxNDZz5+pi79mxLyFlBUV8tfi99my+H3S4q7hZubG78N/55X2r3DwxkHG7hzL0fijDbL/R4EmEQhJkrSpEId1QoitAEKIVCGEUgihAlYAXaq6VwjxqxCikxCik5VVw/q+S1oyJF25JsT0mPBTfBrFShULanN6uIW2XkWoKT8J9r1bq1tsbEbg7fUpWVknCI9YWO/EaOtONti5mxK4/zrK8sYtyda2t8fh66WUxceT8sEHlX6WDh064OnpycGDB9VmEX4nIfG5CAEdXB68W12SyfDq2ZcZX/9Mv2efI/VqNL+/NZ+DK5dTXlTCHP85bByxEQs9C145/AqfnP2EMuW9cyqaO01RxSQBvwGXhRBf33Hd7o63jQXCGntvVSEz1HRTPw6klylYlZDBWBtzPGp7eriFY0foOR8Cf4frZ2p1i73907RyW0ha2m4SEv+ow47/RZIkOg5zpSC7lKhzDzY/Wh0YdO6M1bx55O3ZS86mPyvta+TIkejp6bF161a1d1oH3qhI9vs71t3OREtbm44jxvCf71fSYehIQg7+w6rXnif82CE8zD3YOGIj032msylqEzP/mUlKYeP/+21KmuIE0ROYBgy4q6R1iSRJoZIkhQD9gdeaYG/3IDPURqnpg2j2/HQjnVKVigWuNvd/c1X0eRPkOhBV++I7F5c5WFr2Jzr6U/Ly6/d9yNnHAitnYy79c71BJ9BVh+Wc2Rj27Enqp59Scvny7etGRkaMGjWK1NRUjhypuST4QQmKz8Hd2ghT/frPftAzNKL/jDk88/kyzGzt+Gf5N2z6cBE5iYm80fkNvun3DVdzr/L0309zOum0Gnb/aNAUVUwnhRCSEML/zpJWIcQ0IUSbm9dHCSEar020BuQGWpoTRDMnvUzB6sQMxtmY425QR8M5HQOw7wA3aneCAJAkGb4+X6KjY0FY2Cv1qmyqOEW4kJtezNWA+vdaPPDzZTLsl3yB3MyMxFdfq5SP8PT0pEOHDpw6dYq4uDi1PE8IQVB8Du2c1DuPwtrVjckfLeGJ5+eRmZjA74vmcXTtSvrY9GTjiI200G/BCwde4JfgX1CJ5u+woOmkvg+aEFPz58cbaZSqVLxW19PDLVy6Q1IglNW+5FRb2xw/328pKUnkcuS79cpHuLW1wtzWgIB/4hqtee5OtCwtcVj61c18xH8r/SxDhgzBwsKCbdu2UVJS/3kZCdnFZBaWqV0goELs2gx4glnf/Ixf/8EE7N7OH2+/hn6WknXD1zHCbQQ/BP3Ay4debvYd2BqBuA8aR9fmTVqpgjWJGYy3NadVXU8Pt3DuAapySHwwC3ozs064tVxAWtpuEpM21Pnxkkyi41AXMhMLiQtr+Ca1qvg3H7GHnD83376uq6vL2LFjycvLY+/evfV+zqWb+YeGEIhb6Bub8MScV3j6/U9RFBex4b3XiTxwgMU9F/Ne1/c4k3yGWftmNWuR0AjEfZAZaiMUKlRlDTvJS0PT8GN8GmVCsMDlASqXqsOpCyDVOlF9Jy4uc7C06EN09Mfk50fUeQutO9tgbKlHwN64JrONuJ2PWLyYksjI29ednJzo3bs3wcHBhIeH1+sZQfE56GnL8LKtwgpFzTj7+TNtyfe4tO3AkTUr2PHlx4y0H8rygcuJy41jzoE55Jc1zGS9pkYjEPdBrjHsa7YohWBLSjbDW5jR0kC3/gvqm4GNH1w/9cC3SpIMH5+v0NYyJzTslTpPpJPJZXQY4kJqbB6JUfW39KgLkkyG/ZdLkJmakLZkSaXX+vbti729PXv37q1XA11QfA7+DmZoyRvnI8zAxJQxC99nwMznuR4axNo3X8E+U59v+n/DlewrzD04l0JFw3aNNwUagbgPstvd1JowU3MjKK+ITEU5w61M1beoS3dIuADKB/990dGxxNd3GcXFN4iKqtkptia8uttiYKrDxb2NY5hXFVoWFpiNGUPh+Qso8/71qpLL5XTv3p2CggISEurmIVVariQ8MY92zg0XXqoKSZJoP3QkUz5Ziq6+AVsWv49hcDZf9vmSsIwwXjr0EsXljeeu2xhoBOI+aPyYmi8HMvOQS9DfQo1hCufuoCiC5JA63W5u3gVXl+dJSd1BcfGNOq2hpS2n/WBnEqOySbnWdPFxo/4DoLycgrtmRLi7uyOTyYiKiqrTupeT8ylTqmjfgPmHmrB2deOZz5bh3qkbR39fiVuWKZ/1/ozAtEDmH55PqbLhp/01FhqBuA8au43my/6MXLqYGmKmfX8fn1rjcnPm8Y2618rb208GIDWt7slcn1726BpqEfBP050i9Nv6I7ewoOBw5f4HfX19XFxc6iwQQbcS1I18grgTbT09hr/yOtYubuz+9ku66rbhfz3+x5nkMyw4ugBFHU6QDyMagbgPt08QGoFoViSUlBFRWMJgSzWGlwCMbcHCrU6J6lvo6ztgYtKWtLS6O97r6GnRdoATcSEZZCTULZ9RXyS5HKN+/Sg4fhyhqPz/j6enJxkZGXWyBA+Kz8HGRBc70xrcdhsBbV09Ri98F7m2NtuXfMwQu4G83+19jicc56MzHzXp3tSFRiDug0xfCyQ03dTNjIOZFXHxwZYm6l/cuUdFw1w9krDW1sPIzw+rc5gJoE0/R7T15ATub7pThPGA/qjy8ykKuFTpuqenJ0CdThGB8Tm0d2pys2cATFpYM+q1t8lNS2HP91/xVOvxTPOZxt/X/ia1UP3+U42NRiDugySTkOlruqmbG/szcmmpr4O7OqqX7salOxRnQcaV+7+3GqythgGQVo8wk56hNl7d7Yi5lEZxQdMYzRn26IGko0PBkcOVrpubm2Ntbf3AApFVWMb1zKImDS/djaOPHwNmPk9s4EVObfydSZ6TUAkVO6/ubOqt1RuNQNQCTTd186JQqeRUTgGDLU2p8I5UM87dK/5ejzyEvr4jJsb+9cpDAPj2tkdVLog83TQmczIDAwy6dyP/0OF7+jI8PT25ceMGRUW17zwPjq+Yz9CQDXJ1oe3g4fgPGsr5HVsoDI2ls21ntsVse+TtODQCUQs03dTNixNZBZSqBE+0aIDwElTkIIxs6pWHgFthplCKi+PrvIalvRF27qaEn0hsEvsNAOP+A1AkJFAWE1PpupeXF0IIoqOja71W4I1sZBL4O6o5d6QGBsx8HgcvH/b//B3D9HsRnx/PxZQH66p/2NAIRC2QGWprylybEQcyczGWy+hiatgwD5CkilPEAxj3VYW19a0wU/3Gs/v1cSA3vZiEJmqcM+rfD4D8u6qZ7OzsMDIyeqAwU2B8Dp62JhjoqLHyTE3ItbQZteAd9I1NyP3rDCZyY7bGbG3qbdULjUDUArmhNkrN2NFmgUoIDmbm0c/CBB1ZA/76u/SA3HjIqfu3f319J7WEmVq1t0bPSJvw44n1WqeuaNvYoOfnR8Fddt8ymQxPT09iYmJqNStCpRIEN4CDqzoxMDVj0OwXyU1J5smCDhyIO/BIezVpBKIWyAy1UBUpmszbRoP6CMkvJrWsvOHCS7e4nYdo+jCTXFuGd3c7rgVnUJjTNE1cRgP6UxwcTHlGRqXrnp6elJWV1coG/FpGIXkl5bR/iBLUVdGyXSecfP0xupCOKFWwJ7Z+J8CmRCMQtUBmoA1KgSjVGPY96hzIzEUGDLBoYIGw8QVdE7hev+Ey/4aZ6neK8Oltj1AJIk417tzqWxj37w9CUHDsWKXrLVu2RFtbu1ZhpqCbCeqm6qCuLZIk0WfqTMoKCumX7MbW6Ec3zKQRiFqgaZZrPhzIzKOTqSGWDR3DlsnBqWu9TxD6+k4YG7ept0CYWRvg5G1OxMkkVMrGr6zR9fJCy87unjyEtrY2rVq1Iioq6r4n9KD4bIx1tWhlZdSQW1ULtq1a49WzL45RghtJ0URk1t2htynRCEQtuCUQSo1APNKklCoIyS9umOa4qnDpDumRUJRVr2VsrIeRlx9CcXHdzO1u4dvHgYLsUq6H128/dUGSJIz796fw1ClUdw0M8vT0JC8vj+TkmodIBsXn0NbJDJmsAUqTG4Bek6YhCYmOMRaP7ClCIxC1QGZw09FV0039SHOre3pQYwmE8y1fpvrmIYYDkJZev1OEq38LDEx1mixZbTRgAKKkhMKzZytd9/DwAGruqi4uU3I5Of+hTlDfjam1Le2HPIlbvAEng/ZRUl7/SXqNjUYgaoFcE2JqFuzPyMVJTwcvw3pOjqstDh1ArlvvPERFmMmPtNT6JTvlchk+vey5Hp5JXkbj21IbdOmMzNDwHvM+Q0NDnJycahSIsKRclCrxSAkEQNdxE9HW08MrTJsD1w809XYemIdOICRJGipJUpQkSTGSJL3V1PsBTQ6iOVCsVHEiO5/BliYN0z1dFVq64NCx3icIqDhFqCPM5NPTHgmqtRYlAAAJs0lEQVSIONn4yWqZjg6GvXtTcOQI4i6fKk9PT1JSUsjNrbokNOjGzQ7qh7yC6W70jYzpPm4yTukG7Du2sam388A8VALx/+3de4wdZRnH8e9vt/S+SJcFLNCWNilolaQ0FbFGbhooJFLUKiUiRUsIKCbGmAjBP4zRIP5DYiTBahAvkSJVYlVILRQ0kYuUSLmUQJeCUqi9AKUQ22139/GPeVen2zm75+zOuWz7+ySbnfPOzDvPPjN73jPvzHlHUjtwG3ARMA+4XNK85kYFmtAO7fKX5cawv+1+l7390bjrDwNmfQS2bYT9o3va2AkDdzONspupo3Mis07vYtMj2+jrbfzF6o7zzqV35072DXrk6HCD9/3j1beY0TmJrql1GDurzhYs/iQ6ehIdj+7gn7tfaXY4NWmpBgI4E+iOiC0RsR9YBSxpckxISsNt+BrEWPXnXW8zub2NRdMafAfMzEXQ35s9ZW4UJk2aSUfHB0Z9NxNk36zeu2c/L2/cNfzCJZty9tnQ1sY76w8evK+rq4vOzs6KDcRT/9rN/BYZwbVW48aPZ9Fln6drzwR+98fbmx1OTdRKX/6StBRYHBFXp9dfAD4cEdcXLb9w4cLYsKH2sU7ue2UX122qbQjk4/ugHfA3Icam7ZPaWPBGLzc+3di+9zb6mdH/Gn200T/Kz2NvnvIXds1dy/h3jwNG103WH+2pjtb5/9+nA/ToAO0t97m1LOXmumfHTD694t4RrSvpyYhYONxyrTagSdFRf1BWJV0DXAMwc+bMEW2k46h2umo8CKf29TO1t3X+maw2J+7r48LtfeyZ0vhDfsL+dib3vzPqeibuOJUpHVuJttGfyfbHOPriqFHXMxKKgILerfHqp6d9L4fveXoQJTYS/Xsnl1ZXJa3WQGwFZuRenwwcdDUtIlYCKyE7gxjJRj520jSePGlsnq7aWLSoxLq+VmJdZkNrtXO5J4C5kmZLGg8sA8b+UzfMzMagljqDiIheSdcDa8m6/O+IiOeGWc3MzOqgpRoIgIi4Dxi7wx+amR0mWq2LyczMWoQbCDMzK+QGwszMCrmBMDOzQm4gzMysUEsNtVErSTuB2sbMOFgX0PgBaYbnuGrjuGrjuGpzOMY1KyKOG26hMd1AjJakDdWMR9Jojqs2jqs2jqs2R3Jc7mIyM7NCbiDMzKzQkd5ArGx2ABU4rto4rto4rtocsXEd0dcgzMyssiP9DMLMzCo4rBsISZ+V9JykfkkVr/ZLWizpBUndkm7Ilc+W9LikzZLuTkOQlxFXp6R1qd51kg55OIWk8yQ9lfvZJ+nSNO9OSS/n5s1vVFxpub7cttfkypuZr/mSHk37+2lJl+XmlZqvSsdLbv6E9Pd3p3yckpt3Yyp/QdKFo4ljBHF9XdKmlJ8HJc3KzSvcpw2K6ypJO3Pbvzo3b3na75slLW9wXLfmYnpR0u7cvHrm6w5JOyQ9W2G+JP0wxf20pAW5eeXmKyIO2x/g/cBpwMPAwgrLtAMvAXOA8cBGYF6a9xtgWZq+HbiupLh+ANyQpm8Abhlm+U7gTWByen0nsLQO+aoqLuDdCuVNyxdwKjA3TZ8IbAOOKTtfQx0vuWW+DNyeppcBd6fpeWn5CcDsVE97A+M6L3cMXTcQ11D7tEFxXQX8qGDdTmBL+j0tTU9rVFyDlv8q2eMH6pqvVPfZwALg2QrzLwbuJ3sC51nA4/XK12F9BhERz0dE8VPQ/+9MoDsitkTEfmAVsESSgPOB1Wm5nwOXlhTaklRftfUuBe6PiP+UtP1Kao3rf5qdr4h4MSI2p+nXgR3AsF8EGoHC42WIeFcDH0/5WQKsioieiHgZ6E71NSSuiHgodww9RvbExnqrJl+VXAisi4g3I+ItYB2wuElxXQ7cVdK2hxQRfyX7QFjJEuAXkXkMOEbSdOqQr8O6gajSScCruddbU9mxwO6I6B1UXoYTImIbQPp9/DDLL+PQg/N76fTyVkkTGhzXREkbJD020O1FC+VL0plknwpfyhWXla9Kx0vhMikfb5Plp5p16xlX3gqyT6EDivZpI+P6TNo/qyUNPHa4JfKVuuJmA+tzxfXKVzUqxV56vlrugUG1kvQA8N6CWTdFxO+rqaKgLIYoH3Vc1daR6pkOnE72lL0BNwL/JnsTXAl8E/hOA+OaGRGvS5oDrJf0DLCnYLlm5euXwPKI6E/FI85X0SYKygb/nXU5poZRdd2SrgAWAufkig/ZpxHxUtH6dYjrD8BdEdEj6Vqys6/zq1y3nnENWAasjoi+XFm98lWNhh1fY76BiIhPjLKKrcCM3OuTgdfJxjg5RtK49ClwoHzUcUnaLml6RGxLb2g7hqjqc8C9EXEgV/e2NNkj6WfANxoZV+rCISK2SHoYOAP4LU3Ol6SjgT8B30qn3gN1jzhfBSodL0XLbJU0DngPWZdBNevWMy4kfYKs0T0nInoGyivs0zLe8IaNKyLeyL38CXBLbt1zB637cAkxVRVXzjLgK/mCOuarGpViLz1f7mKCJ4C5yu7AGU92MKyJ7KrPQ2T9/wDLgWrOSKqxJtVXTb2H9H2mN8mBfv9LgcK7HeoRl6RpA100krqAjwKbmp2vtO/uJeubvWfQvDLzVXi8DBHvUmB9ys8aYJmyu5xmA3OBv48ilpriknQG8GPgkojYkSsv3KcNjGt67uUlwPNpei1wQYpvGnABB59J1zWuFNtpZBd8H82V1TNf1VgDXJnuZjoLeDt9CCo/X/W6Et8KP8CnyFrVHmA7sDaVnwjcl1vuYuBFsk8AN+XK55D9A3cD9wATSorrWOBBYHP63ZnKFwI/zS13CvAa0DZo/fXAM2RvdL8CpjYqLmBR2vbG9HtFK+QLuAI4ADyV+5lfj3wVHS9kXVaXpOmJ6e/vTvmYk1v3prTeC8BFJR/vw8X1QPo/GMjPmuH2aYPiuhl4Lm3/IeB9uXW/lPLYDXyxkXGl198Gvj9ovXrn6y6yu/AOkL1/rQCuBa5N8wXcluJ+htwdmmXny9+kNjOzQu5iMjOzQm4gzMyskBsIMzMr5AbCzMwKuYEwM7NCbiDMzKyQGwgzMyvkBsKsRJI+lAadmyhpirLnU3yw2XGZjYS/KGdWMknfJfs29SRga0Tc3OSQzEbEDYRZydLYPk8A+4BFcfAooGZjhruYzMrXCUwFOsjOJMzGJJ9BmJVM2TOKV5E9ZGZ6RFzf5JDMRmTMPw/CrJVIuhLojYhfS2oHHpF0fkSsH25ds1bjMwgzMyvkaxBmZlbIDYSZmRVyA2FmZoXcQJiZWSE3EGZmVsgNhJmZFXIDYWZmhdxAmJlZof8C6Pam0ETcUmsAAAAASUVORK5CYII=\n", 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\n", 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy\n", "import nengo\n", "from nengo.utils.ensemble import tuning_curves\n", "from nengo.dists import Uniform\n", "\n", "N = 10\n", "\n", "model = nengo.Network(label='Neurons')\n", "with model:\n", " neurons = nengo.Ensemble(N, dimensions=1, \n", " max_rates=Uniform(100,200)) #Defaults to LIF neurons, \n", " #with random gains and biases for\n", " #neurons between 100-200hz over -1,1\n", "\n", " connection = nengo.Connection(neurons, neurons, #This is just to generate the decoders\n", " solver=nengo.solvers.LstsqL2(reg=0)) #reg=0 means ignore noise\n", " \n", "sim = nengo.Simulator(model)\n", "\n", "d = sim.data[connection].weights.T\n", "\n", "x, A = tuning_curves(neurons, sim)\n", "\n", "xhat = numpy.dot(A, d)\n", "\n", "pyplot.plot(x, A)\n", "xlabel('x')\n", "ylabel('firing rate (Hz)')\n", "\n", "figure()\n", "plot(x, x)\n", "plot(x, xhat)\n", "xlabel('$x$')\n", "ylabel('$\\hat{x}$')\n", "ylim(-1, 1)\n", "xlim(-1, 1)\n", "\n", "figure()\n", "plot(x, xhat-x)\n", "xlabel('$x$')\n", "ylabel('$\\hat{x}-x$')\n", "xlim(-1, 1)\n", "\n", "print('RMSE', np.sqrt(np.average((x-xhat)**2)))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- What happens to the error with more or fewer neurons?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Noise\n", "\n", "- Neurons aren't perfect\n", " - Axonal jitter\n", " - Neurotransmitter vesicle release failure (~80%)\n", " - Amount of neurotransmitter per vesicle\n", " - Thermal noise\n", " - Ion channel noise (# of channels open and closed)\n", " - Network effects\n", " - More information: http://icwww.epfl.ch/~gerstner/SPNM/node33.html\n", "- How do we include this noise as well?\n", " - Make the neuron model more complicated\n", " - Simple approach: add gaussian random noise to $a_i$\n", " - Set noise standard deviation $\\sigma$ to 20% of maximum firing rate\n", " - Each $a_i$ value for each $x$ value gets a different noise value added to it\n", "- What effect does this have on decoding? " ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "RMSE 0.5075755918847665\n" ] }, { "data": { "image/png": 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FXFm7W1EiYYyBAKKU0lxou34NLC6Moz9FWCxkwkFAExBYnkB6aXQUc9WdZ+7uoqTfQS+KYk4TkNi4/v4B7ImleTmZ5anotdFVuqiqPBKK4zYaCJUUzuWWbsCclJKLhgqujIJxSjbV3QEP0mniVLLx9/ZMKM2mFYp/gC4gDSmVSpw8eZJYLIYMbCSverGrMwcyOZusVIzahdvv11xEXV3ahXl8dASsHp7de4Ez+0Mcef6SZoEA5aPPM9bZyX+Ew4yro9graTJPPz3retw+G0pZpZhtXEz4t4f/lrc/+nbSpTRKOIKptQU1cpZjufv4ycEbUdY+gDj9Q0ytreSqGWO+Du0Cv9QCIlUVZWwcS/V9sHR16+1MFknts9EtEI1jGe2u+0Bq+QpgF8KPJ1IklAp/uk77Lu1NLF3328F8ibxR0HaZsfUGnyYOJ8rlGc9RVcmZFczAAl1AGlIqlfjOd77DqVOnKJQEEiP20sUZ+zm8FiqmPEIIfNXGhbVA+lg0BU29BC9obUMO/miIsrsfLC7Kpw9zaU0PADHDeYzddtLP7EE2OClgsphwtkysoeQQoVyIf3j1H1AiEWItN/CdLyV5NvXbnDll4ILlQchGMHlt9TYmvs6qBbLEtSDKxASyXMZUt0C6UUIh1NK143a4HpBSUshWLRBdQAA4XhWQg8lrY6zrt8ejdFrNvL8zQJfVzAvx9JId+7nqsdYJ07TtAw4r9opk1DTTG3EpnqNQVlekAr2GLiANcLlc9aLAfEq7qDuyM1ufOz1WKsYCTrsbo1FL8XU6nXi9XkbTKiX3eoxxByPe0xTTFY4+NwYdN5IfOs9oVxfr1vQjVBMX/BnKmQy5Awcar2eOYkIpJeoFlV2RXTxx8Blett/Dy+JulKLC/b7P4/JZOX2pE4xWTOY8uVwGq9OJw6MF5qYKiJSS579zhpFTsRmvM19q6cl1F1ZXl5Y+PD6+6GP+PFIuFpCqisVuJzURplxaOvfI9YgqJcczeawGwfl8kWhp/q19loNgscyeWJp3t/sxCsGdPhcvJjKoSxQHeT6exlCo0GefHssQQtCHkYzLOKMW5HRwsgdWvKxQvMIY7aVgVQVECPFVIURYCHFsyraPCyFGhRCvVv+9dcpjfyKEOCeEOC2EuH8519bZ2cno6Ci5Wh+s0sX6bJAaNQvEYXXPeO5Y0UlQ3YLAwGsdP8XUW+DQjy9Sat7FhawJxWxmw/rtuFMDpJQsJ7dvJ/2TpxquZbZiwkqlwmOPPUZgJEBfpo+3XPhlEvYetreM8as3f4f1nSE23NrOpVNJsj1vw1wZo1As4vA0YXM6gekCMn4uyZFnRjj27OLveGs1IDUXlrlb+7mSbd3z6RJPf/0ExfzqXmSuhloAvX3dBpCSxPjYFZ7xs81QvkS2ovJgNSPp4Cq7sb4XjKEC727XXNev87mJlSuczC6sc3YjKlLyfCyNmCjQ6p6Z3r/DZkNajDwXnh4LqvXAWt/i5GMnLvLLh88tmaDNxmpbIF8H3tJg+/+WUu6o/vshgBBiC/AQsLX6nH8UQhgbPHdJ6OzsJB6Pk6gG7OyGxLQJhQAWu5GKKY/V4Jr+3GYvcbwcTTUDEHJfJHnjeYpZhdfCt3LO1YdFUfBaW7EWm9k0sJUTGzcwtH+/FigvpGDK3YPDbcFgFNPauhcKBb75zW/y6quvopbd2LKdFJzjdAa/QqXlGMb4WQisZ+Ot7UgJZ8WDmIwJigaBw+UmLrWTbWoM5Niz2kV+/Hxy0RklNQGpWSCW7m5t+wrGQQaPTHBqX5CxM/EVe82lpibsHQMbAd2NVYt/vK8jgFHAwdTqubGklHw3GONWr5O1Du3mrlarsXcJ3FhH03lSFRVDtEire2Z6fy0O8mR4emLP6VCGHr+db08k+Gksza+0+TAsczuTVRUQKeVzwHz9JQ8C35ZSFqWUg8A5YPdyra0eDK+6XhzG5AwByWazSFHBVLFPf65Lu/gOxQxk/ae4O5BnxHqctTtaOHzEzkX/GnqzSbJxzT321rc9gNNi4cWB9WSe/b/whc1w4Cv14wmDwOWzko5pFkgqleJrX/sag4OD3Lz19bRFd9K008OalhZe3XkDj0UPkYxdgMA6/B1OWta4OT3chskhKZmMjOfHeNeT7wUmL1TZZJHzhyM4PBZyqVJ9SuJCKY+OYvR6MVQtHFNbG5jNK5rKGx3R7t4ToZWfH10sFvnhD39Y7848H/78pT/n7w7/3fTjTLVAgPgyjh++HjiWzmESsMPjYKvLzoFZspBWgkOpHGdzRd7T4a9v67JZ6LdbeCF+9YH056siZIgVaWkgIDc0uxDpMvsus8LOBNN0dLv55Pkx7g14+HBX81Wv5UqstgUyG78rhDhSdXH5qtu6gEtT9hmpblsWOjo6AAhPBBECbE2+GQJS68IrStPNzA6TZrVkMxV6bvoOb/XkuFN9ju33STLEKJvNrC9HSMeKWJ0mPE0ufvFtbyPl9fL0o9+BUmZa516YHCwVCoX48pe/TDwe593vfA/B/SZCriFadll428AA9nweh9jB37r9EFgPwMbb2pkYzRPruYuiyUgoM4JilGAQdQE5+cI4akXy+vdoF6zx88lFvW/lsTEt7lFFGI2YOzpWtK37RE1Awit/l3r69Gn279/P4ODgvPZPl9I8cvYRHj7z8DSrr9bo0h1oxh1oITauWyAbHDasBgM3e5wcTudQ1NVp8fLtYAy7wcDbW5qmbX+dz81LicxVr+u5eJoeowlRUhsKSJfPjiFa4KxSJl+Ng5QUlXPRDMfbLHhMRr6wqefntpniPwHrgB3AOPD56vZG78aMT0oI8VEhxAEhxIFIZPHVoXa7Hb/fTywVwea2IDpumCEgtSaKam56oMuevYRXprEHTtPqHyFm3oCNEmeGf5WWbXsRqpEOZaI6B0QTn407drAhOs6r3rUMm9ZB9Nzkf1JKzG6V8cQQX/3qV1FVlQ9/+MNEjhooZio83/89Ag4/lmSSO/e+gFnYCOfezFGTVj0/cHMbwgDfqGymbDKyxdnNet96KhZBMZtFVSXHnx+le5OPtTtbsNiMVykgnSiKwpkzZ5BSYunuWrF2JlLKSQEJrbyA1IQjk5nfnegLoy+gSIVoIcqF5IX69mI1A8vqcOLr7Pq5t0COZ/Lc4NYs/Zu9TnIVlVPZlbcw8xWVR0NxfqHVi8s03YN+Z5OLdEXlSGbx512+orI/maUf7diNYiAOiwlvpkIF2F+1xIaiWQrrPUQNkr/dtIYWy8zOGcvBNScgUsqQlLIipVSBf2HSTTUC9EzZtRuYEVmUUn5JSnmzlPLmlstami+Urq4uUvkYDre5PhuE0uTJEY1GERgoJS7TtsRFvFLSveF5itKJbHk/nw1asTo20rn2cTYN7OesYTuZWH6yB9bEOd6U/AnObJZHeIDj4TJPPfUU//Zv/8Zf//Vfc2DscSKmo3g8Hn79138dY8nJsWdHCOwSTLhG8Nv8KOEwvkSCt25xESg289W9+1GlSlAdIeg/jzO+DoB1hRIbfBsoGCsUc1kuHp0gEy+y7a5uDAZB21ovwfMzCyevhJSS8ugY5s4uDh8+zLe+9S3Gx8cxd3WvmAsrHS1QyisYTQaSq2CBDA0NAfMXkGcuPYPdpF0Y9wf317fXBcTpxN/ZRWxs5Oe2qWKkVCZUUrjBpb1PuzwOAF5ZhTjIjyaSpCsq72n3z3jsTp8WB7kaN9YrySxFVdJalBgEs1aU9wkTQkqerc4q+u7wBJVeF+/0eXhjwLPo118o15yACCE6pvz5S0AtQ+sHwENCCKsQoh8YAPZf/vylpLOzk7Kax+RU67NBCJ+sPx6LxXDYXJQLknJpysyL+EVsgSweb5i8882s8a4jpRqIqR/i4sXtBDpPULxvH/niWU1A1Ao89jECvSq37H+FuGLme8U38OKLL5JOpxkYGGDHwO00RW/k/e/5NTweL89+6zQ2twXLbZql4Lf5USIRjD4fu50TtFmP0px08JX/fB/v/9H7ON92CFtRyyk3T4yywbeBvLFENpPk2LOjOJus9G3Xqunb13qJjmUXnMVUSSSQ+Tzmrk7OntX6cAWDQczd3VRiMdRlnIBYo2Z9rNnqJ5ssLWiS49WSSCSIx7XA/XwERFEV9o7u5d7ee+l0drJ/fPJ0rjW6tDqc+Dq6KeXzZBPXb1LA1XAsrVkaW6sCssZmocVi4uAqxEG+Mx6jx2bhjibXjMdaLGY2Om1XFJBIqcyeWIpSgzTb5+JpzEJgTZUJuKwYDY3dUL1NduwZhefiacLFMl9JJzGky/zllp6G+y8Xq53G++/AS8BGIcSIEOIjwGeFEEeFEEeANwJ/ACClPA58FzgBPAF8TEq5rJOKakWBiiVTnw1C8Ej98Wg0itet+UFzyckUW5kYoqnvNXI5D05xDz1u7UM9d+YCweEdOL/ox2jO03P3p3AEovDyP8OlfZjf+Rl6W1t54PRRPso3+ZMPvYXf/u3f5h3veAc7tu3CXPaSTyuc2DtG+GKaO39lPYlqDoImIBNaE8XoOT7qC9Pcf4y1rv1sNTfzqff9CSaTFhg3J5JstPgomVXisQmGT8TY+vpODEbtdOhY5wUJoQsLc2PVMq1EezsXLmjumFAoVE/lLY8tfyrqxKU0QsDanZr1mQyvnJujZn1YDJJM8soX+8Phw6RKKe7uuZvdHbvZH9QsRtAsEIvdjsFoxF8t+lwON9Zf7PsL/vylP1/y4y4ltQysmgUihOAWj3PFK9JHCiWei6d5d/vs2U2va3LxcjLbUBxAs9I/enyIh167wI4Xj/NnZ0fqBZKgBdB3eRwk0iVaXLM3WO1qslMJ5TmWyfMbx4coSsnakQLeFXJd1VjtLKz3Sik7pJRmKWW3lPIrUsoPSCm3SSm3SynfLqUcn7L/X0op10kpN0opf7Tc6+vo6AAJRZGqzwapxUFUVSUWi+HzaaZsNlGttFYrXDInsbojDA3diDFjod3RjlmYSVxK0Csl/iEDtoO3YTCVMBn3w9N/DhsegO3vxn3Pm/EcPkFLfgJzcqi+llotSORimn2PnqdrYxMbdrcRy8ewm+w4zI7JUbbRcxibB9jSpz337Y7b6fWvoblX86uKgpGN4XOUTCq5WBaDQbDlTk0sE4kEgR4HQiw8kF4TiKDZjKIoGI1GQqFQPZV3JWpBJkYyeFsdNHdrqY4rGUgfGhrCbjWxRh0iE5vZ+uZy9lzag9lg5o7OO9jdvptUKcXpmDZAqpjLYnVqd7n+Lu39W+pUXiklP7n4E14ae2lJj7vUHMvk6bFZ8Jonq7J3eZ0M5UtESo27NywH3w/GkEzWfjTidT4XeVXl8CzutR9OJHkpkeUjXc3c0eTiG6NR3vzKad78yin+7mKII+k8b/C7iWSKtM4xkrbbZ0dOaDeELyezNF/Kc2OT86r+f4vhmnNhXUsIacSoOMmWY/XZIDUBSafTKIpCS4uWKpetWiBqYpDBXiv5WC/jiS4ioQhGg5HNcjOUoTcaxdzdxa6OMEiBbeLfwWSFX/wbEAL3PfcAkBmxT87zYLIafd+j5ykXK7zhoY0IIYgVYvht2gmtRCKYmv2QGEbxr6Fc1Krnw+PHyOfz+Nq0u6aYdQfNZ5/GaLWi5kv072jB2WQlkUjw93//9/zHo9/H3+VctIAMplKYTCa2bNlCKBTCVM3KWolakImRDM09Lryt2t3qSsZBhoaG6G124iZLJj935biUkj2X9rC7fTdOs5Pd7VqorxYHKWSz2BzaBcHtb8ZksRJf4qaKoVyIWCFGMBukol67Y4ePZ/J166PGzdU4yKEVioNIKflOMMYdTS567bNf2G9vciGAvQ3cWEVV5RPnxtjktPGJ9V18+YZ+Xr1zK58a6MIkBH95YRyJVucRThXntkB8DkSyjN9o5B6/m9Tp+Iq2MKmhC0gD0qU0/+25/8aJkTOYyy6S2agWwGzfBqHjoFbqGVjtna0A5JKaBTI6/K8o9gqRo7+EwW9gdHQUKSXduW4qhgqtFwaxdHXj6t2MraBQrlyCBz4L7nZhc/0AAAAgAElEQVQALOvWYe5dQzrcNC0Ty+owYbIaKRUq7Lh3Df4O7eISLUQJ2AJaE8NIBJPLDEjibkHNw2e2JDhw4EDVhWUi6NsNQy/jl92glrjhLu0C/9xzz6EoCufOnYPmGKGhFOosozMbUR4dxeB0cn54mL6+Prq7u8nn8+QtFoTdvuyB9GKuTDpaoLnbhdlixOWzrlgtSDweJ5FI0N9kwEWWTFFFnaOVxGBqkOH0MHf33A1Am7ONPk9fXUCK2QxWl2aBCIMBX0fnks8FOTahhRcVqRDJL/08i6Ugq1Q4nyvOEJDtbgcmwaLrQSZKCudz8691OpTKMZgvNQyeT6XJbGKby87exMyCwn+5FGG4UOIT67swVWMbfrOJ/9Ldwo9v3sgzt2zkn7f0stNlZyLTuAakRrfPjgD+zOPj//X7Qa7cDJCp6ALSgLyS55XgK3z2uc9jKrsplgskk0lNQMpZiA3Wa0Dau1oxmATZZBFFyTIYfxQl0sWlVBMtnc1ks1kSiQT2mJ2QM4g6MqLVSXTuxFGokG8KwPb31F9bCIH77rvJjYEaPDttuydgw+23cfNb++rbaxZIJZEARcFk10QjZoxgMNhxONYT8Ku8/PLLZJMJLBY7cd9mUlk/7kwbUKa5z0Y0GuXw4cPccedxNm/Oc27iEMVylujo/L+g5bExCv39RKNRBgYGaKtOQQyHw5i7Outt3ZVZmkZeLbUAenO3m2w2i7fVsWIurFr8o89ZwEUOCXMWEz576VkA7uq+q75td/tuDgQPUFbLmoA4JgO1vs7uJa8FOR49Xv99NDPz2NdC1tfJbAEJ9RTeGnajgRtcDl5ZpID86dkR3n7o3LxrNp6KpjAKuL/5yhlOd/pcHEzm6jUaoAXO/+ZiiPsCHu7yN77Qb3bZeUebj2RBQVFlwyr0Gl0+7f1IJYucD2nn/UqNsZ2KLiANaHW08vm7Pk8mWcBU1j6U0dFRaN9GqMXCyIV/Jho9hclkwuPxaNXbyRKXLn2NsswydvRdhNwXGegdAOCFF16AMkTEELJYxNzdDevvxe7eSM5u1NxjU3DdfTeyIskeH4YpX+J7/8sW3v57OzBbJvPPY/kYfrt/chKhqTrFrngSX9MtOJ3rcLnzZDIZxhIpXG4nCAMv5n4NQ0Gr0RyMnGPPnj1YrQpG4yG6ew4jBKS9Zxg7N//Mn/LYGMFql+H169fT2qpZZ6FQqN7WPZuI8w8feYiz+1+c8fz8seP1/8diqAnIWPIcn/vc5zB5CytWCzI0NITD4aDFkMKF9hnMlYm159IeNvk30eGaTDrc3bGbnJLjRPSE5sJyTvq0/Z1dpMLhJRXf4xPHcVu083ssMz3B4V9HJ7j95ZOkldV1bdUC6Fsvs0AAbvE6eC2do7zAwj0pJXvjGaJlZd6B+KeiKW7xOGkym664750+NyUpp1lHn7kQpKCq/K/1nVd8fiStuT9bGtSA1PDYzHhsJkbiec6E0lhNBtb4HfP4nywtuoDMwk1tN/GOrl/BpDhBwNjYGDmXg+Ob3JzOPILJ/L/YdfN/cObsx2nqPUIuN8zF4X/Bm+8gN7GVkHuQW9bfgsFg4ODBgxjNRgx5LbBq7uoEmwf7podQKinK5ek1F45duzDYLWQuqpCdvKA2d7tpaps8SaSUdQtECVcFRMQoNLWQyw/h978Ou30NlUqI1tZmImUVd8CPJzXEBfk6DEbty/DamUMcPXqUXbu0YG2hcJ577llH2Zrg1SOH5v2elUdHGfF48Pv9BAIBHA4Hbre7moml1YKMnTmJUixy6sXnpz1Xzee5+MEPEvrc5xbwKU1nYiSD2aPw1J4nAYiolyjmFAqZ5Q20SikZHBykr68PQyF+RQGJF+K8Gnl1mvUBcEu7NkN+//h+irlMPYgO4O/sRkqVRHCMkqpe9QxuKSXHo8e5u/tuYKYF8koqy1C+xN9dvHIywHJyLJ3HZzLSZZ2ZXbTL4ySvSk4ssKDwfL7IRFlL7/7xxJXjfMFimaOZPG+eZ33FbV4nRjE5H+R4Js+3xqN8pKuFdY7ZRaFGOK251uZyYYEWBxlN5DkdyjDQ5po15Xc50QVkDrY5dyAwEDfHOTF4gqFLX0RIA7suuAmOvxEpOwgGH8U18Nc4N3+MSiWH+dxWAJSWNC3uFlpbW5FS0rO2h5akdjdXy0py2LVxt/n88LTXFRYLzl1bSY/ZkJGZbeRrpEopFKnUa0AATJUg8Q7tzt/nvxO7fQ1Sltl96wZKBhOK10d7SPOzd7m0u85zRwaxWq0MrK2Jk8DteY0maxtD8SP1eM9cVNJpSrkcY0IwMDBQ397W1lYXEDWTIXhSc5tcfO0QFWWyRiPz/PMcHPgNDg82Ldp1EhlOkfKcRiJRhEJKmQCWPxMrHo+TSqXo6+uDXOyKAvL86POoUuWNPW+ctt1v87PBt4GXx/ZRyuexOqZaINo5Ex8b5QfhBPcfOMNnLowv+r0aSY+QKqXY2baTFnvLDAG5lNdiel8aiTCyiiNkj2XybHXZG7bluNmrvT8LjYPsS2j7r7VbeXLiytMNn642VL1nngLiMhnZ6Xawtzrm9n+eHaXJbOQP+trm9fxJC2RuAen22RmJ5zgTXNkhUlPRBWQO8ukyZpsR6ZWkE+cZDz5Kl+N2PCNDXDjfg8n4e7zh9Qcwxj5D4uwvsHHDx4mOdlMy5ejp1k6WWi3JTdtvorV6s1PrVGuvCkguP3NYlfuNb6JSMFI4+MKs64sVptSAhLVW86biRWJNRszmAC7nhrpI9fbYEUqZsGqgPXqYLs6y2fIMFZsDJQG33347yRceBgXc51oIhx/ntp23gjTw8PcfmTMgDJr7KtLaQkXKGQISiUQwdGqumuDpkwhhoJjLMnZmsihz4olnGe90ca59C0f+8/iM41+JSkVlJHmajBLFuc1J0pIkU9De8OV2Y9XiH/39/ZCP4UJ7vUyycTX/nkt7aLG3sDmwecZju9t3c2JMqzWyuabEQKoTJGNjIwxVL+7/+2KITw8GFyUitfjHDYEb6HR1znBhjRRL3Fa9QP/VhdWZ5aKoklPZPFvdM91XAF1WM+0W84I78+5LZGixmPj17mbO54ucu0Iw/aloii6rmU3OK1sPNV7nc/NqOsfDoTgvJDL8YV/7vNxfMCkgc8VAQKsFGZrIEUwVViUDC3QBmZN8uoTDbeHBnQ+ytuckigR3/F5C6R4qqiQQCGAwWHA5dhE8/CDt/l9iPLeGoGuQjQGtDfeWLVvo6elh84bNrMnaKbgt9U61dvsa7XVyMwXE+ZZ3gJBkXpi92L4mIAF7ACUSweB2I4oRYuYEfv+dCGGov0YmfR5zLEQsl6fQ08Yt5ScJGEcptnRREWW2JBJkJo5hipuwPpagUsnh6z6GK7WOsfERXnpp7lqB8ugo4x0dmIxGent769vb2tpQVZWMx4MEwqPDDOy+HYPRxOBhbYCWWioxfGyEjOccJesFXvxRaMEpxOdOXCTjGKS7rZ90c5qUOUUpWwTD8gvI4OAgTqeT5uZmlGyaQ+mHsMgSmXh4xr6lSokXRl/grp67MIiZX7/d7buhWj0/1QKx2B24fH5iYyOMFUs0m018oDPA/7kY4pPnF26JHJs4hsVgYX3TerpcXdMsEEWVjBfL3Nrk4qPdLTwcivPqKrQNOZcvUFAl2xrEP0BLLNnldSzYAnkpkeE2r4v7m70APBGZ/VwrqirPxtO8OeBZUHPCO5tcVCT84elLbHDY+GDn/DvjhtNFHBYjTuvcgtPts1OqBuo3rEIAHXQBmZNcuoTdbWGg201r6yDnR7zE//CvOHVQa/lRa2Pl8Gp3CvFzgySUHoLuQTb7tbvL9evX85GPfASz2UxX2kSsafKkMBptWK3t5BtYIKZAM/Z2E5lXZ+/qGs1Hq+vQXFgmn5usw0iJHH7fnQBYrR0IYSKTOo8lHsFoMHBq/XqUdIWIsYWKy0u6dJ7Yxz9BpdeGp2sX5vMSm9JKKv8YTtlBs6ubn/70p4TDMy+INcqjY4x3dNDX04PZPOmvrmVixYxGCmYThUKBnq3b6d68hQuHXgEg++KLjPrbQYBZjmEXeZ744tEZA7RmQ1EUfvTk4wjVxFvue4CJ/AQpSwpRBmezgcQ8qtGf/ffTvPrU8BX3uxwpJUNDQ/T19SGEYDzu51D2lzFLGlajHwgeIKfk6rGHy9nVvguboiVJTLVAQMvEio+NMl4s02Uz85kN3fxaVzP/eCnMx8+NLUhEjkePs9G/EbPRTJeri1A2hKJqwhUslalI6LaZ+X9622g2m/j4udEVz8o6np49gF7jZo+T4UKJcHF+ca5LhRKjxTK3NTnpslnY5rLzZHR2N9bLiSy5ijpv91V9XV4nFiEoqJJPrO+sp+3Oh0h67hTeGt2+yfdFt0CuQfLpMg6PhWTqW6iqEe9L6xn1Q+iGfgBKn/4ElUwWZ1VALhwKAhB0D7EpsGnG8QLxCmOe6VktdntvQxcWgGtLK4XxPOVQ40DmNBdWJILJYyXm0y7efv8dABgMJmy2LnK5IYRaYUN/H4MeN6lsmZdMuxHlErccHEZxWVD8ZVztN2LpWYPriIdU+lW6NiXxFTZisVh45JFHUJTGvaUiIyNk3G4GNk93y2hWmoFIKkWqWcv6alu3nv6dtxAdGSYVCZN+8idMtGqinHU5uXH43ykVK/zoi0dRylfOAtqzZw+JdBRvZiOdfc2Ec2GSFu2u0uIrXzEGUiooHH9+jJcfu1AvCJ0vsViMdDqtua+kJJfTbhBExUY6M7MWYM/IHmxGG7d23NrweB6Lh/V27fyaaoGAFgeJjY8wWijRZbVgEIK/Guji17ub+eJIhD89O7+LvCpVTkRPsDWgxes6XZ1aLUhOi6PVYh49Ngtuk5E/6m9nXzLLE/MIOC8lx6ojbNfPEXi+pRYHmWc21UvVwPbt1V5W9zV7eCWZZWKWEblPRVNYDYLX+RZ2gbYbDTzQ4uUXW5oW3Nwwkm48SOpyupq0mKXbZqLDO3/32lKiC8gc5FIlbL5xwuHHSQyvI25u4dnf2MWP14NJKlQOnGXo3e/GnNbuzC+cKiNRKfiidDqnp+tJVcUZzTHqLpEtT57sDntvQwsEwL37BgAyzzzT8PFYIYZA0GRtQgmHMdklMZ8Fh70fm23y9R32XoolzUVxy66bkELw7Nq1jIguLBPjOAtw7vfvQkoFp2Mdnvvvw/j9UYQw4V27l+Rombe99RcZHx/nySefbLiWwWpdzNT4B4DJZKK5uZlQKEQm4EMALWv6WXuTlnF0/pV9pJ9+mnT1+6kIgTp6kjf+UhfhoRTPfuv0nBfF4eFhXnjhBQKWXrpaezEYDaRjE2w/oQmptOVJhnNzHiN4IYlUJUpZ5fCT87NCRtIjfP7A53nxmJaO3NfXB4UkOVVzi5QrTWQuG29aqz6/rfM2bKbZv/AbHVrXZHmZC8Pf2UUxm2WsUKKjmpUkhOCT67v4zZ4WvjI6wR+fGbniGNOh5BA5JcfW5kkBgclMrEtVAem2aZ1g39cRYMBh5ZPnx2ft8QSg5spLaqUcy+TZ5LRhnuPufZvbjkUIDiTn52Lbl8jgNRnr8Yz7m71I4KloY3F8KprijiYXDuPCL5Vf3NrHv9zQt+DnhdOFBVkgG9vcKzL7oxG6gMyCWlEpZMsYfN/BoJqoPO8g0dzMB37xz7AWrahOSe/dE1QmQkR//7cAiCUsZO2jrG9ZN+MDVcJhDBWVsFdwKT05F8tu76VUmkBRZt5BWbbuxOxUyDz144ZrjBViNFmbMAqjFgOxF4g3WfD7XzdtP7u9F0UNAZL27h7W2h1MBAK4lRz2WIjT/TYGW7W7T4ezH/d992FMVGgqbqVieQpEGa+pndtuu439+/dz8uTJGWsZVit4y2X8/pmVurVMrKTdgqciMVks+Dq6aGrr4NyzPyUm7SjmHC0+7UKWdrtpz5/l5rf1ceqlIEf3NC6gKxaLPPLII3i9XmzRPpq7XSiqgnUsT0/ITEkUyZFAKamTvcoaMHYmgRDQN2Dn2HOj87JCnhh6gq8f/zqP7n8UxaxwNHcUNRclW9GsLEPFRrow3Xo6Ez/DeHZ8VvdVjX5rtflmfmjadl9nN0WzlYwq6bRNtvkWQvDxdZ18bE0r3xiLXjGzqBZAr1kgXS6tE8FYVguk1yyQLqv2GiaD4H+u6+RCvsi/jjXOyFNzZcb/aj+F41fO2JsPUsqGLUwux2owsM1tn/eM9H2JLLd6nfVmiNtcdjqs5obv2YVckQv54oLdV1dLJD13G5MaTQ4zPoeZrZ0ru76pXFFAhBAGIcROIcTbhBBvEkLMLxftOqeQVbC4R1GMz+J4GjoCvShS4i17aRNtjIgIiY0t9H+oHWdvO6LaS+iS5yIbG7ivyqPaRTDcxHQBcVQD6fmZd76ieQBXZ4HsKwdRCzMzRWo1IGoqhSyVKLXEUA3g9985bT+7fQ1SFDDZJXaXm919vQhVZcuBI1ipkO0KkMlq3XOdjrXYtm3D1NGBY58JVaZwdb3KEy89y0T3BJ2dnTz22GP1tuUApVKJoMPBGlPjoF9bWxupVIoJqeJJZ5FSIoSgf+fNjF68wHD/FgBu2rELgHRzgNwrB9j9tn76tjez93tnGT09M57wyiuvEI/Hecs9v0ApKwl0u4kVYjhy2mldJEO66uaby401eiaOJ32RdRcfR61IDv/4ylZIJBfBaXLSV+kj7ojzX5/5rzz409/ilLEFh1PFpBopqZLylMK/PZf2AHBXz12zHLX6fhk1d97h1PQBZv7OLtIu7WLReVldhBCCP+prxwBXrBE5Hj2O3WRnrXctAB1OLUNuNK2doyMFLUhvn3LXfU/Aw+t9Lr4wFCRZnunuUWIFZFlFWeQo5MsZL5aJlStzxj9q3Oxx8lo6N6d1BBAqlrmQL3LblFbsQgjuC3h4JpamcFnbnppVspICUihXSBUUWj1XdkkJIfjub97OH9y7YQVW1phZBUQIsU4I8SW02eOfBt4L/A7wEyHEPiHEh4VokEbyM0IuVaJ5639C2YD31Va2/O7vAnDiX1/EkDeQtWT5u+51mCPP0/d/PoHVoN21Ra2TAfSp1PpAXW6BTNaCNHBj+dfh6iwii2Wy+/bNeDiaj06rQs+2pRBS4PPdNm2/WiaWp9OKMBjoWbeOtz/2AzbkEzhsJbyqHYMSxmRqwmz2aW1T7rsX+cgprJZOmje9wIUzQb524mu8853vRErJ97///Xo85MLp06hGI/2BQMP3shZIL5jMeNP5+nr7b7yJilQJ9rQiVCO7bt+O2Wym0N9P7sABhEFw74e34G2x89TXT8yIh4yPj+Pz+bBJraV+c4+LSD6CK68JmaJmyGRSSOSsmVjlUoXwUApv7DT22DAbb23j2POTVsjRo0d57LHHZrQlieQjdBu6qRQqfOj1H+Kzb/gsTmHmgmjmonGYjE0TvD/96Z/yqZc/xT+9+k88fuFxtjVvo9k+d0aOWigiBbwycXDadndzC1mv9h5fLiAANqOBfruVM1dISz02cYzN/s0YDVqw3mK00GpvrbuwRgrluvuqhhCCj6/vIl6u8DcNigsrqVJ17Uszf6VWgb7NfeXq6l1eJwVV1p8zG/uSWvzjtsu61t7f7CWvqvXCvxpPRVMMOKxzNk9caiYy1RqQeVggAANtbpocjYdOrQRzCcBfAP8GrJNS3i+lfL+U8p1Syu3Ag4AX+MBKLHI1SMRO4Ok5iOkFH2s++QWanK1YMHEufQkpJdtbN/N/s0OctNowHP03XK2aE78neIFN/pkWSKlqgSgtPoZTk3e4tYt7w0C6ux1HlwmD1UjmmT0zHq5XoVcvyOkOFY+xE5NpesCv9hquFu3jtm3ZQttb7qf7f/wGVqOCvSRpNioYrJNxE/d990GxTCBzI1bfcboqTiK5CDlzjgcffJDR0VGefvppAM4cO4ZRUejt7Wv4XtYERLXZ8eSL9a68gZKCsaKSsqm4TAEsFjOBQIBMIEDxzBkqiQQWu4k3vHcDmXiR489Nr1UIhUK0trYycanaA6vLRSQ3KSCynNOaQVpLs1ogwQtJVBV8ibMosRg3v7UPtSI59GPt8zh48CCHDx/mi1/8IiNTmkFO5CfoLGnv17r+dTzQ/wD/PvAh1ucdeNxWFJd2kR0bjvD4hcf5x9f+kaHUEPf33d9wHVMpZrMIm5kT8ZOkS5OBeIPBSKVT+yw7GggIwEanjdPZ2QVEURVOxU6xJbBl2vYud9c0F1aPbeZFaavLznva/XxlZGKGlVNJVwVkgUPIZuNYJo8ANs+j9uIWryYyjTrgTmVfIovDaGC7a7oo3elz4TQaeHJKkkBWqfBSIrvi7qvwPIsIrxVmFZDqrI7nZIOoWHXs7N9IKb+xvMtbPcYHP02lZKcj8D5M7RuZ+OIRmvEwZtDuLK0vDLI2E+AL3Wvh8Ddxt9gxKWnuOBGh39s/43jlkVFMLS10+Ncwkp68EJlMbszmAPnc0MxFCIGhdR3OfgeZPXtmBChjhRgBWwAlHEa1SzJ+Iz73zhmHqQmI3aeZ6AaHg87PfAbrztdjNSqYCwotZpWcmBQe+86dGFuasTxTQEpoWXMQf66Dw+HDbNmyhVtuuYWXXnqJ06dPc/7iRdpCIew9jaehud1uTAYD0ubEXShSrjZVzP30GbyKpGIStDVrfvhAIECy6grLHdLaqPRs8tO10cfBJ4bqEwYVRSEajWoCMpLG02zDYjcRzoVxVTOhTCXty2gNlGcdLDV2JgFSxZu8QCUWw9viYONt7Rx/boxsosjExARr1qxBCMFXv/pV9u3bp81dz0/gyXrwVFu3AIhCAlVp4ua+G/hgp3bh+9WmD/Pie1/k8AcOs/ehvXxwywcbrmMqhWwGm9ONKlUOhqZbIaWWDoSUtM8hIBdyxRnumBrnE+cpVorc0HzDtO21YkJVSkaKJbptjY//P9Z10Go18d7XznNmilDVLZClEpB0nn67dcbc8UZ0WC3c2eTia6MTc7qx9iUy7PY4Z6TUWg0G7va7eXIiVU9AeC6epizlqsQ/4GdAQGoIIc4LIX7rsm2PL9+SVp/E+RcpuV8jfvbNtL/5ISJfOoowG7E1Caieew6TiTfs9RAbghfJcWv7U6jiX9g4IlGHZ7bdLo+MYO7upsfTM82FBeBw9DaMgQAQWI+rI48SClGcErwuV8qkSqm6BVLcIEEI/K33zjiE0WhDyVuweC4LJPv7sRlVRDmH1whhZfJ0EAYDnnvvpfDEK5zLWPH276Uvt4lDYe2ift9999He3s7DDz9MslCgY3xc6/HVACEEFqkg3E0YpRYPkqpK+smfYOzWCi47W7UvaiAQIJnPo1qt5A5MXjxve3At+XSZI89o7+3ExARSStra2qozQDTxi+QiuAqagDiL2sVEOGZvqjh6cgJ35hJmc3Ukr6Jw8wN9qKpk3w/Pkslk2LBhA7/5m7/JwMAATzzxBN/97ndJZBKYEqZ6/QeAko5TlC4cfjftHZqffXyw2mLGYMJr9c4rW6aYy+Lx+LEarbw8/vK0x3JNARz5DMZZ5ndsdNpQ0fo9NeLyAHqNTmcnwWyQYLFAUZUzXFg1WixmvnfjeoxC8J7XzjNcfR21aoHIJXRhXd6Bdy5+d00r48UyD4caN/+MlxVOZgsz3Fc13tLsJVgqc6Rae/JUNIXbaGC3d+bo2uVkvlXo1wrziWGUgTcKIb4mhKidVV3LuKZVx9tzM/LQR7AM3Uvq22cw+qy0/vaNZEJDAJilkfd/4nOs2XYjdxwL8Gh4E+4Tf8N/3nABKSD5gx/MOGZ5dBRzVxc97h6CuSClyuTF3G5fM2stCIF1uLxjIATpPXvqm+tV6AYXuYOHKG0FY0Xi7bhnxiGklBSTZoz2yzJVjGYsDgdUtw9mp19k3ffdh6FYIjvsxOxIsNvm4VBIExCz2cy73vWu+r4dtXG6DZBSIlMJyiYThpZmSiMjFI4eRQkGybf3IpQyxqJWQxMIBJBSUr5pJ7kDB+rHaF/rpW97M4efHKaQLdeLGn3eAMlInuZu7Ys+MTGKUdUu0o6igZKlhGLKkorkZ8w2UcoVQhfTNCXO4n7TmwCoxON4W+xsuq2d4/u1gV4tLS3Y7XYeeugh7rvvPk6dOsXrL74eStX03Sq5hPb+OZpsOPwdICXRiQRKaWEdbYuZDHaXmx2tO+rzQWok7W7cmSSJULDhczdWXT6zubGOTxzHZXaxxrNm2vYuVxcVWeFoQntfG7mwavQ7rHz3xnXkKyrvfu08oWJ5SS2QZFlhuFC6YgbWVO72u7nBZecfh8MN05j3V6vVb2swyxzgzQEPBrTmilJKno6mucvvnjOFeDkIp4sIAX7n6sU1FsJ8BCQnpXwPcBJ4XgjRC6z+oIBlRFgsNJkf4GazF0uXi9bf3E66ECc7rFWFe6UDK1Z+5Y8/TuCunbSNuPmH4S1M2CxktvWSfOwHyCmmtFQUysEg5m5NQFSpTmsdYbf3USyOU6k0+NIH1mOyKdg2D5DZ82x9cywf5baTKht/5x/IPPMM5W2SprwNQ4P6gnIhTyFpQphn5rrb3D4MLu11j6SmV5oP97tI2WH30W5QvXR6TmA500q8oN3lBQIB3vnOd7K9WKLJ60UYGp9OyXAINZNClVDs66c8MkrqySeRJhNRWcKYLxE8+xoAzc1agLmweTOF48dRs5Oid+vb11LKKxz+yTDhcBiDwYAsWEFSF5BkRPs/eJp8mPOSpCVJrpxCVSWpyzKEQoMpVFXgzw/jeqPW2FCJaf+3XQ/0oRiy09YkhOCOO+7gLe9+C7L6Fejvn3RX5pLa8R0eC0ZvBzbKVCgxevb/Z+/Nw+O6y7vvz++cM/uu0b4vlrzFcRbbsZ0FEpYUaEmhQFtogbZ0ofShb6G0tG/fFh7o+3ah5XpKoS0FCjyUQoGWNmwNScjm2Inj2Ja8yZIlS9Y60oxmX885v/ePMwSh/LoAACAASURBVDPSWCNZaXAg8HyvS5fl0ZmZM2dmft/ffd/f733X74m1EfLlcbZ7GvcwEZ+gZK4quWKaHV86QWyD+egDbgea2IRAomfZHd69ro1KxQtyNmlFTBtFIBXs9Lr45xv7iRR1fvb0JWKZciTyHAjk1KlTPP744+tuP5u2zn0rCqwKhBC8q7uZsWyhbofdJ+NpHIrgpg2K8g02jQMBDw9EE5xJ51goll7w9BVYEUjYY0f7b/hOfhDYylkKACnlXwB/CPwX0Hk9T+oHjVIkS8t8mrgqaHzHHhS3jfGnn0ToRTwOFyHpwUgVURSVt77zg4zdYaOYc/GSk424XvuTlGZnyZ1YTb+UFhbBMKoRCFBfiZWvTW0BEN4GgO/mAfLDw+hLS+RHRym96w94z9dNlICf1s9/lGLAoIH6KaRMIk4xYUcqSQyjthbgCDbhCBaRCMbT8Wp7FIAvjn+Zk9ttNJ2YprPjdXg7Rnjp7Ks4cvxk9ZihoSFumZysNoish8WJMdS89byp9nZKMzOkHvguxh23UzRy+GxBZkfPkc+kCZeVXNn2DjAMsqdOVR+nsdPL4P4Whh++wvzcAo2NjcTnrF1/JYWVW7YiM+/kNKJoEFOipLJxJOa6OsjcWBykpH0ojK3VKvQbMev1B5pc+LsESIGN2oVMCSk81PEQB157gFAoVL09m7I2DZ6AA3yt+Eki1SLTZ56bN6KQSeN0e+j2daNLnYX0arQRMQW+TIKVDeaj2xVLiTVap8V50SgyujLKrsZd6/5W8YKMpy0/xLUIBCz10+du6GMiW+A3uyCrPjcV1smTJzlxorbGcy6d468vW6/3uUQgAD/VFKTbaedvpyPr6oXH4mlu9rlxbrIw39sY4Gw6z2dnrS7OW23fvhG+PTLP549epvQcpnpabUx+MK7y/w62QiB/XPlFSvkQcC/wt9ftjH4IYGt2c95tY6rZg1Ie3jR2/BjNPX285Sd/lv2lbdWQXREKv/SG9zPekSGYttH/2jejuN3E/+M/qo9XkfDaOzvrEojLXSaQOk0VabC0+t5Ba4Gc+R/vZvJ1r0eZnOGTP6Hg/d9/R67d2uE2ePbUfT3ZRIJC0iqKXl1rsTe04QwUEaIBA8Hoyihgpci+NfEt1HvuQGayBOd7EcLAMfA9Ln9Vr6kplObmNiWQhUtj2AxrFx0PBSnNzFC6coXlvVbBv6/nRqRpMjV8EqfTicfjIel0gqrWpLEADvxkH4Yumb0yT3NzM0szaRxuDW/IyhmXylLMYFnKmhdWS21Dy66rg8wML+BNzxC84wBquRCuR2PVv9uCOprh5uQDtcS+nFumqBYZ6qvV32cz1qLlDtjB24pPpFEdeaaeg7lOSlkdZ1tJM02lrM9FSjdImyZho7RhBAIbK7HGVsbQTX1d/QOg1dOKQHAlXyCgqfi3ULwGuLPBx9/v7OG8R/Dem11kC1tP1yUSiao8+nw6xzvOTHLP8VFOp7J8cFs7LRsIBTaCpgje2d3MiWSWY2saLKZ1g5FUrtq+ZCNUmit+cT7GTT43Tfbn9vxX48PfPM8f/8dZXvW/HufI+PKW7rO0RRf6Dws284HcIoS4BZit/F7+fxj4kS6iA8znDZzlHleZ+ApzF88zeOAwLd1tuHFUZYsAt7XdRktzF86SitPtw3fvvaS+/R3MnLULrJgIbR0dhJ1hXJprAy9InUK6uwFcDTjcK9ja28mNjBB685s59Te/yoM3K4Q9TcSXHsFWNPE07Kv7WrKJFYpJe93ncDb14AgWcUlrJz22Yo3R/bexf6NoFrn7de9G8fkwHjiHz3cDwR2Po8sS3/j4afKZEmaxiF4eWbsRIpPjNHX10NDQwIq9vLNVFKZVJ4phZ/dt+3F6fdXuvOFwmFgygXPXLnLHawkk2OJm8LYw+VKGoK+B5StpGju9CCHQTR01WcBmGHgMazF3pq2FRLjzNVJeQzdZvJIlmBjDc/vhKoEYsVUCiSdjBHwhJk7VTkms9IxqctfWfDJZDZC4vDZwh/GSQyoFEpEciaWttdrQS0UMXcdRjkCAqux7tmB95todtg0jELAI5HKuWDNSFVZnoF+twIKyF8TdzEJRbqjA2gj3Ol388Zk8x8Marzvk4nPTS9ecEmiaJslkkkXNzq+NWMTxSCzF7/S0cPzQLn69q/k5nUMFP9faQNim8bdTq+nY44kMJhvXPyrodzsYdDuQPH/zYDRdYDae41U3tFLUTd7yqad41z8/y1x8c6/KVl3oPyzYLAL5qzU/jwAfWfP/j1z3M/sBQkpJLlnC5bMWu0vPPAVSsu3AIRSvHcSqbLGC19/08wBk4nEC992HmcmQeuhhAEu2qijYWlsRQtDlq1Vi2WxBNM2/SSF9GyI2QdenPkX/N+6n9Y/+byK2LA7VgcfmIZU+jz+tIxrrO1KzifjGEUhzH45AEWfOMpONxkbRTZ0vXfgSB9sOsq1pB7577ib18MO0Nf00IS3Fszd+jFQ0z7c/+iiFf/p16zW019dVSNNkceISrQPbaGlpIVo2H7r27WM2Mo+tGKR1IETv3luYPHUCaZo0NjayvLyMe98+csPDmMXaa929z1LSxCZMYrNpGjut6CyWj9G0ouEulGj5GavAf8NYBqEIFF+hJgKJXE5imIJGJYa9txc1EABVRS+nsEqlEisrK4SCDWQTRYzS6mK8nFvGptjw22sXmWzBgctRRFEVUBS8diiYOhLJ1JkYW0GhPITK6fHQ6Gqs2WzM560orsvr3XQ++g6PCwmMXWUoPBs9S9ARXNenrYIObwcrhn1L6au1MJJFXjOv87l5lbac5PcvzXLn0+f5t8WVugXtK/kin5yc4/5dB/jyvpfxUCzJu8vE8fv9bVuem1EPLlXhHZ2NPBRLcr5sLDyWyKAJ2Be4tinxleUo5Pmmr4ZnrTrMWw/18sDv3MV7XjHEg+cXedlfPconHhmnUGdUsJSSpfTWOvH+sGAzH8jdlR/gkpTynjW33fMCnuMLjlLewNBN3GUCGTt+lGBLG41dPQhVoHhsmFcRSKDB2o1m4yu4D+xHa28jUU5jlWZn0VpaEOXdd7eve52U17VJU0XC2yB6CUd/H45y0Taai9LgbEBKnUxpHm9Gh/BA3btnEwmMgoqq+sheRSCKX0XRJEpcZ6hhiNGVUR6efpjF7CJv3vFmAHz33ouZTOK93Ago9DRN0tv4D8zNKDx2shMJ2JpD658YiC/OU8hmaOkfpKWlhZVsFt1mo3jPPRT1PD6tCU/AQf/N+8gm4ixMjBEOh8lmsyg37UUWi+RHalt6pPNWym7hTAG9ZNLYZe0sl7JLBDIqrpJOy8/8DAA7ZxQUt8CwZWtqILOj1oLesacNIQRCUVBDIYxyCqsyhbGprCxLx1cX4+XcMo2uxlpJrlEiW/Lgdq3WALwuOyYCX5PG1BbrIIWsFTE5PFZU1e3rZjplvWdz5Zbl/eEQ+VSSbLJ+A8CNlFhno2fZ3bh7Qylxm6edLF46Hc+RQMrR+G0BD59+Ostnu9txKwq/eW6Klx8f5YHlBE/F03z40hwvffoC+4+e4wPTyyTcXm6evsg3Bpr4g/42Qs+DONbilzoa8agKH5+2opBj8TQ3+tx41Gun5X6jq4k/H+rkpucgIa6HkZkEQsANHX6cNpV3v2yQB9/zEu4cbOQvvjPKy//6UT79xCTJ/KpAIpErUTLki0bCC1tvpnhdVFdCiM8IISJCiDNrbmsQQnxXCDFW/jdUvl0IIf5GCDEuhBgup9OuC0xTsvNwG03dXgrZDNMjp9l24FD1i6f67TUpLABP0FpAM4kVhKIQeO1ryRw5QikSoTgzi71jdYfe5etiJjWDsUbL73b11K+BAIT7ITUHhVWnbcWFns1OIDHwllxWuqsOMok4Tq8ft7t7HUlJ1crNymiO7aHtTCQm+Py5z9Ph7eCuzrus13b77ShOG/E/fC/e8RKH7DoJV4Rb9mQY526mu16BzVP/I7I4MQ5AS/+2qiPd+5lPEx2yuvZ2dVhpmt6bbkUIhUvPPL1aSO8uu/SvSmNFIhFsNht2zYpEwmUF1mJmEdXUcPl9+Lqs+6qGiq2YJG8mSa3kq5LaKydn8KRnabjzQPVxtYYG9BWLQJaXrevS2m6dc2qNgmspt0ST6yrJci5O1gjiWWMz8LmtRahp0MXsxZUtyXnzZdWZs9zKvdvfXU1hzRWKCGCoPBJ56XL9WTF9Lgc2IWoIJKfnuBS/VLf+UUGDpxtTcdJxjUFGV6MSjdua3Qjgbs3Jg/u383e7esiZJm8dmeS+k+P8/ZUIYZvGBwba+WzYxs8//SC3XT6Po/j96Z9VQdCm8QvtYf49ssJYJs/JZJaDW/RzNNltvK2jcUt+nc0wPJOgv9GDb006sKvBzSffuo/P/fIBWnxOPvSNcxz6fx/iT/7jDBNL6RedCx1+8N14Pwv8xFW3vR94SEo5CDxU/j/Aq4DB8s+vAX93vU7K6bFxz1t30rmjgYlnj2MaOtv2H6r+XfXZMZK1Rq0qgcQtGWjgtfeBaZL8xjerHpAKOn2dlMwSkexqntbl7iGXn8E063SNLSuxiE1Ub6oQSHr6WwB4+1+34evJJlZwB4LlKKc2AtGxWm6Yi0m2N2xHN3VOL53m53f8fLVXkqKY+LdnyOsO7A84cDhg6OQsgY/9Hs2RZ7jU/1oS8fptJBYmxlFtNsKd3TQ3W3ntFVXl0qVJVN1J10Cr9fp9fnr33szwQ98h4LfSB/FiEcfg4LpCeiQSobm5mX339uD02mhotRbb5bHzSKEQGNiGqmm4/AHSHhvhqTlyxQwmOomlHIZhEpkrEkxcwnNwdS6HGm6oRiBLS0sIIejots4vFVsfgdQgFyNjhnD7Vhdfb/l1hDrtGCVzQznvld/6Leb/5AOApcACcJSHSXX5uphJz6CbOnOFEs12jY4B6/OwODle9/FsimDA7aghkNHYKIY0NiUQh9MSeHjFc5s+aCQLIEBrsgjTzOsoQvC6lhCPHdjJ3+3q4R9393Lujj187eZt/EZ3M4FMsuLJXddn7PuBX+9sQkHwrvNTFKXc0EB4vTA8E+fGzmDdv71kqImvvvMw9//WHdy7u5UvPj3NPX/1KO/+F0vd+CNBIEKIj5V3/H8DdFZ+X3Pb84aU8jHg6uTwfUClRcrngJ9ec/vnpYVjQFAI0fb9OI/NMP70UTzBEO2D26u3qX7HugjEHbByp5lyl1pHfx/OvTcS/9rX0BcXsXWuKp8r6pr1hXSTfL5ObrtCINHVBaNKIBe+AAZ8/buFDWcxZBMJ3IEALlc3+fwsprmaZinqsxgFhWKiwJCrvJhrLn5620+vPsDotznmbeb8T9zNjf98kpLpYPgNgtb/+QEO7Qe7zPDE92Td549MjNPc04+qaYRCIWw2G/Pz80xNTWErBmnuXc01H7jvjeSSCeZPn0AIYdVB9u8j9+yzyDWDrCo9sG59VS9v+/8Oo9qsj7F+1PoCth2wuhF7giHizT56xy2SNLQs8UiWpekUuqnQHCigBq0v+Xcmv0PKLao1kOXlZYLBIKEmayFPxVY3DMu55XUFdJmJkjODlgKrDG/QIhmnr4RqU+rKeaVpkn3yaJUkqwTitp63x9+DbuosZBaYz5doc9hxeX0Emluq0V09XK3Eqs5Ar1NAr56LzSJ4zdhavaYCM1VC8dpQ3OUZLGu8IDbFIpKfag7WKLsSiTV9pzLPbSTtVtDutPP6lhDDKaun1oHAC0cgi8k8kVSBGzsDmx63pzPAX//sTRx5/z389ssGWU4XUIQVqbxYsFkE8gxwovzzvjW/V36uF1qklPMA5X8rcowOYG3hYIY6jnghxK8JIZ4RQjyztLR09Z+fE0rFApOnTjCw77Yak5zis2GmS0hjdcFUNRsun78agQAE7ruP4qVLIGVNBFJXyruZEqss5SVmOaOllMRyMRoyUVJmhGLKzeLEZRYuXaz7OrKJOO5AyGrrLnUKhfnq33L5yxSSDoqGjZ5CAb/dz30D9xFwrPnwj3yFpaKfKxMzoNoRwdtpbygxd1c3ne9/H4cbv8rcoofxZ2qNiNI0WZwcp7nfIkBFUWhububMmTOU9KJFIN2r/bc6du6mbWgHJ775dUKhENFoFPe+fZjZLPnzFwBIp9Nks1mam5sRQqDZVhcl7Zx1PZtutdRonmCIotdLIG7t/HUtQyKSY2bE8hl03WKRuilNPnj0g5wxrmCUjYRLS0s0NTWh2hTcAXs1AikZJeKFOGFXbefhfCyOiYY7uPrl94as9Fc2GaFjKFRXzluam8PMZilOTyN1nXxmtYgOq5+V6dQ0s4UiHeWUSEvftg0jELAIZDpfJGNYabMzy2docjXR7N5Y3VRULDLVCxsX6OvBSBZQ/Q4UlxV9bcVMmEwmqx6a6xGBALyr23qtu7zO51WYf64YnrHI8VoEUkGzz8nvvGKII++/h4ff+1I6gs+v/vJCYrMi+uc2+3khT7KMeknJeo0ePyml3Cel3Ne0QWuNrWJ65BSlQp7BA4drblf9lvvZzKyvg9QQyKtfDeX54LbOVQJpdbeiKVq1OAqrBFJXiWX3gK8dohaBZEoZimaR8OQRUj4n6UXrOUafXO/qBYtAPIFgtaniWpLKZifQ0x4KpooWu8TXXvs13rf/fWvuHMMYfZB0yYZeKhK5fImh7rejChib+QIIwc6uKZq8EY58daza7BBgZWGOYi5Ha5lAwOrMmyvLm5uC7dhdq19sIQQH7nsjyaVFHIpVyHaVyaCyQ6+0MGlubia2cpSRM+/GMHLIYhHHorX4BpqshcMTCCJKkostOTRdR7hzxBezzJy4gjuzQPglVtv7y4nLpEtpFh15zFQKPZ8nGo1WHei+Bme1BrKcs2ojV9dAsjHLgOcJrxKiI9SORon0yjI9NzTUlfMWRi3fDaUSpdlZCplKEb1cAylLea8krzBfKFW78Db3byOxuEA+XT91WCmkj5Ud4hUH+mZImi4wCyRzG3tM6sFIFlF9dhRnmUC2YCZMJBJWK36n87oRyJDHyft6W3nnf1MS/N/F8EwcVRHsatsagVTg0FR6G1/YVNvzxWYprE8KIerGu0IIjxDil4UQb7kO57RYSU2V/61sa2eAte1eO4E5riPGnj6Kw+2ha3etQU8tq7OulvK6gyEy8dXwXw0G8b30pYBlIqzerqh0ejtrIhC7vRFVdW9SSB+oprCqs9BzS5RsJrmoA3cgyMVjR2paqADopRKFbAa3P1D1m1RIyjCyFAoLmIUABdMO0TFaPa3Y1TUqnHNfJ1VUqGSn5kYv0Nd8O3O6A5JHAVDCvdzV9GUyiSInvr16/msL6BVUCuk200tH7/q5GAO37Cfc2U1mfpZoNIra1Iitp5vs01ZPqAqBtLS0cGn8L4hEvsn4pT8n++xJikJBamB3uavvh5nO8/BNgkA8jqmlWFnIsBgxCWUu47rxRgBGli2V16xmtU6PTk1hGEZVgeVrcJIuRyBLubIH5CoCyayU+2CFV9Vowt+KlyzpZJzu3VbEcnm4NgopXFyNGguTk+QzaTSHA1WziKLJ3YRTdXIxOUvaMGkvK6Qq13SjNNaONUqsZDHJZGKyOsJ2I8wXdRxmnPnMc/taGakiqt+OsCmgKZi5a4sFEokEgUAAj8dz3QgE4L19rbyhtb645HpheCbBYLMXl31rZswXMzZLYX0C+GMhxHkhxFeEEJ8oq6YeB54EfMBXr8M5/SfwtvLvbwP+Y83tby2rsQ4CiUqq63rANAwunXia/lv2V7/MFaj++gRiRSC1hdLG33wnobe8Ba21teb2Tl9nTVt3IQQuV8+mXpBKBBKNW+qbYLu1iBTibm5/0y+Qii4xNzZac7dswjofdzCIw9GCEPZqBJLNllU8pQYKig+Wx9Y/7/BXSLpXCWBu9BwACfsu/CRIJs9AqJfW4hPsONjCqQenq36LxYkxNJudcOdq474FxUofablATf2jeh0Uhf2v/RkKy4vouk4qlcL38peTfuQR8ufPE4lEcLvdGOYkydQwLlcPMzP/m/mTXyDjsCHXhP+eYAipG4z0qPjyOfIyxfxkAl1qtLQIRDk6rBDIstOSVEauWMReE4Gs5JGmrEYgje5a8ssmy32wGtcUTn1teMmQzmQJNrtp6vZx9vHZmlpRfvQiajmVU5y8TCGbwelZVQwpQqHL38VYyopsK4OkqgSyQRqr1+XAoQguZHKcWbJEjnub9tY9toIr+SI+ka3p03YtSMPEzJRQypsqxaXV1EDqQdd10uk0fr8ft9t9XQnkhYaUkpHZxJbTVy92bJbCOiWlfBOwH/g48DjWIv4OKeVeKeX/klJee3j0JhBC/AtwFNguhJgRQvwK1vTDVwghxoBXlP8P8C1gAmtC4j9iTUe8bpi9cJZ8Ksm2A4fW/U2pEEgdKW82vlKzQDh37qT1//mjdY0Gu3xdTKema47d3AsyALkYZGPEnv0n67EHLQmqx7uD7YfvQrXZGD36WM3dqgQSCCGEisvVWSWQTNZSdSmyhYJwwfJVNZT4FZh+kkSjpVRqG9rB7MXzSClpbn4NuoSx6c9DqA+MIode5kazKTz+rxeRUrJwaZymvn4UVSVbyvKhox/iT878CSk1iyPXTEtffbPWjttfgtdl7aCXl5dp/PVfRw2FWPjTP60qsOZmv4iiuLj1li/jdm9jpv0B0iGBtsYAVlHGOXQV0erGUEykKJvx9vdWjxtZHkFTNBJuK0u6tGCRXDUCCTsxdUk2VawSSIM9QDq9er2yKaN8ndcoaNyNVgRSbnl+4z2drCxkuXJ+NUotXLyI69ZbUINBipOTFDIZHO7aNEa3r5upnLXIVgjkWoV0VQi2lZVYp5dOIxDsaVzf6ubBBx/kwQcfBKxBUmHNZC699QjESJdArm6qFJd6zRRWKmVFeoFA4EeOQGZWcsQyRfZsoMD6UcM1ZbxSyrSU8hEp5b9IKb8upRy91n22ivLQqjYppU1K2Sml/LSUMiqlfJmUcrD8b6x8rJRSvktKOSCl3COlfOZaj/98MPb0UTSbnb69t677m+q11XWje4Ih9FKRYu7aX4guXxeZUoaVwmrNxO3qJpebQco6KYCKEmvsu0QnLIe7UPOUshrtA7fgcLvpu2kfF48dwVzjL8kmywTit3ZELlf3agSSmQAENtFMwdAgNgnGqrGJM1aAmXT1I4TC9oN3klmJkVyKcFPb7YzkVFaWv4MZtNJzbn2GAz/Vz/TZGJOnIkQuT9DSt42RpRHe9I038ZWLX+EX9/wi0taAZroJd9TX5quaxq13W3NNJs6dRfX7afq/fpvsMydYnJujudnLwuJ/0tryUzgcTWwP/x6GW6f1JVE8a8bqVgik0QywuNOqTehaBlc2QvM91sagYBS4GLvI7e23kyzXv5djMbxeL06nE879J76F/wIsL8hSbgmBIB/9Bk8f/0nyeSsIzqbBphSwO9cUaxUFn02SLs8lGby1BZffzvDDVuRp5vMUL1/GObQde18fxXIKy+mtvS7dvm4WCtai3LbGJX7tQrqrSiADwQG89trHXVpa4siRIxw7doyVbI5YyaDdobKYXazpALwZKobaKoE4tWsW0SsKrB9FAhkpO9D3/rhHID/OkFIyfvwYPXtvxuZc3xlTqIrlRt/ATJheubYMslIc/fvTf1/1g7hcPUhZJJ+vM+uhQiDffh+xckotlxglF3XQscPqrrr90B1kVmLMXjhXvVu2nFLzlOWqFQKRUpLNTuB0duJwByjoAswSrKyJgIa/Al23kUwX8YbD1VrQ3Og5tgW3MVLwIcwMy2p5RvbKJDe8tINQm4dH/+UpSvkc57Qr/OK3f5GiUeTT936a9+57L+2ZARK+CKq28cdv372vRpgmo6efhW/+LkHjPzH27qVkmvi9I5hmno7OcgnuqQVc39YIbUvR1LU6ArbyfrTSwFSD9cXWtQwNpTlsPVY96ELsArrUubf3XhJlAomm09X0FUf/Fu+YFfGlYnmWskuEnCGi0e8hpUEsdgSATE7FbVu/EHqdGjlDQdd1VJvCDXe2M3UmSnwxS+HSJTBNHEND2Pv6KFyuH4F0+bsoqUEE0LqmwV+lkJ5Lp6iH7W4ns4USp6KjddNXjz32GFJKdF3nyYsWEfW63ZjSZDGzfu55PVQ2UeqaFNa1CCSZtAQHlRRWJpPZUIL+YsPwTAKbKtje6rv2wT8C+D8EUgfJpUXy6VSNefBqWGbC+gSSjdefirYWB9sP8hO9P8GXR7/MvV+7lz94/A+IlL93udzl9XcI9oBQIZ8g1nkzQbuPYmnaIpDtFoH033oAze6oUWNlKiks/yqBGEaGUilKNjuJx92Hw+OlUChZhfJouQ6yeBYiZ2HPG0kuRQg0tdDY1YPN6WL24gUUoeALHiBtaswnHwVFg5XLqKrCXT87SHLJSo99OfFtXt3+U/zTwX+mMzPE5OklXPEQM64xcvrGjeXsThc+t4uVeILlE99CXHoQ+Yu/AEj01Dfx+/fi91kaj/Sjj6KfbSOz6MIffIx8eTiVu/x+hA0fc8U53DYbqjHLQA9Vp3GlwaDtiSsMxVvQNYWVYtFKXxklmD+Nr2TVnlKxPNFclA5XiETCGqwVW7EIJJt34Haud1R7y270dFkttfuuDhRVMPy9GQqjVgrMsX0Ie18vxtIy+XQSh6c2Uujx9WCqDQQ1WTPgqFIHiUxcqnsNK0qsuAysI5Dl5WXOnDnDoUOH8Hg8HL9sbRx2eK1rttU6iFF2T6t+K3UnXNo1U1hXRyCmaVIoPK9s+A8NRmbj7Gj149hiN+MXO7ZMIEKIF5e+7Hkg0NzKb37qi+w4fNeGx9RvZ2KpPTJbIBCH6uAvX/KXfON13+Dntv8cD08/zLsf/xAAJ2cfwJRXzRDQ7BDqBV87sVAXA24PCAPVbK+mp+xOF/237OfiU0cwy/r/XDKOzeGsRlJrlVjZ3CRu1kBanwAAIABJREFUdz8OtwfDMNClsloHGf5Xi7B2v47E0iL+xiYUVaVtcHu1kH5T862cyEA09hhmoBNikximwUPG/aQ5CYqfnzv7F3R89W6+/uER/u0vT/CtvxuBksKMf4yJxASboaO3F+lw8vQVD+g5EmqeQGARw7VCq+tVAJi5HNmnniI20MbUw+0IITl//v1IKXF6vCiqRkB3MZ+Zp6WjA4dnhcHXr86NH14aptnVzMWHv0f/vJeVBi9FygX0xTOg53EoWexOQbqcwtrlBjBxu/uIxY4gpUm26MbtWp969JbTURUC8QQcDO5r4cLRedIXLiGcTuzd3dUeZ4V0qqaIDpbx1FAb8ItagrpWIX2H13rPdVvHOgJ57LHH0DSN22+/nZ07d3Jh2frM7glaktet1kGMZBEEKF4rMlKc1y6iJxIJXC4XD88+zOm4NUjsRyGNZZqS4ZkfnwI6bG0m+mEhxDmsiYQIIfYKIT5x3c/sBwzNbkezb9xUTtm0ncnWJ9B1+br4/QO/z4NvfJB33PQ+dCl4+NKX+NKFL60/+L6Pw5u/RKyYoLfcryjUeFPNIdsP30kumeDK2ZHqubiDqwW9ihckHn8Gw8hWCQSg6GyxCMQ0YeSrsO1lGI4g6WgUf7Mlv+3YvpPl6SkK2Sy3ttzKbFFBSp18UzuX45d4+3fezt8c/Ssc+SiN/Tey/9X93PHGQV7+S7v4qf+xlzf94X5e9ofdXA4PV1vHb4TmllZMm53zqRYSRQeR2Sm6uycQWYH8R8t1njl2DFksEmlyU0za6el+D7HY48zMfgEhBJ5gCHdRJVPKEPRpxO027CsPVZ/jzPIZ9np2Usrn8ORVFhut1ENTUxPMrvplfV7TSmHllujV0mhakJ7uX6dUipJOj5LVfXjq9APzBqyaTDq5+pm48Z5OSgWDsQkTx7ZtCFXF3tuLBAr5fNUDUr0O7makFsYua1NV1yqkdzvtaOiozj56A73V25eXlxkZGWH//v14vV527dpFwuZAA3YH21CEsvUIJFlE8doR5chIKUcgm6Wkkskkfr+fz579LA/OWwX860Ug7/vKaT7+vY3rRN9PTMWypPL6/yGQq/BRrCFSUQAp5Wlg4635jwlUv32dG93h8aBqWo0XZKvw2X287Ya34/f00+Ny8/CVh9cf1HMI2vYSzUXpNEuYBnT03V5zSN/N+7A5XVU1luVCXyUQp7MLEDwVOY+JwO3uqy5Yed8ALI/DlWOQnIE9byIdW0ZKE3/ZnNc+tBMpTebHR9kd3k3MsEj2fneRN9hiTCQmeE/wbQgTXvG2+7jttf3sfVkX229rpXt3mKZuH4OdfThUB+Mrm3+xraaKAml38Ey8l2hinkBwknDhFjLf+R6Zo0dJP/oowu0mphoU7ZL+/l+hoeFOxsf/jHx+Dk8wiC1nvUc2NU4JG/EJi3wShQTTqWmGpCUC0NIGS36rENLY2AgzJ6A8ItjnypKK5VnJRWmSC4TDd9IQvhOA5YWHKUo3bu/6tIW33KU5HV1VnDf3+GkbCDBp9mMftFrw27q70TVrU3B1BCIQmFoYSus7K2xWSFeEwGFEcLi314ywrUQfhw9bBtmenh6yHh9Bo4RDtdPibiE6P0n22ZN1H3ctzLIHpPqcLg1MkJs0jkwkEvj8Pi6uXGTZsFRt14NApJR858wC/3W2/vz47zeGZ6xNwp6OHw8FFmwxhSWlvHrW6tbHjv2IQvXb17nRhRBlM+G1U1gbwe3upc2hcSpyioJRPy8cy8cIGSkKKw46d95Y8zeb3cHArQcYe/oohq6TTSaq9Q8AVXVwxXaA306/nVPcgtvTX+38WvB0WhHI8L+CzQM7Xk2ibNwLNFkRSNvgDhCCudHz2FU7jQGrDnHEnOVQNsfX7/0c3ss5vKEG2rZtpx5URaU/0M9YfPMIpFLIbm3zcj7ZjBacQAiTgXv+J7auLhb+9E9JP/oYnkOHKCbTlLwKQgiGBv8Y08yztPwg7mAIkbEURSVpqZ8WIxEoZqr1j7Zi+fqUDNI+PzZdx+fzwewz0HcXqHZ8tjjJaI4WrYQmc4QbXoLT0YrbvY3lJYus1/bBqsATtjoQpFdqF/8bDgTJ2RtYbrLeP8Vuh05rTsfVRfSkbmAKB8U6LUY2K6SniimM/AQ5ZdWJfXX0AaCqKqVgA850glKpRLu3ncGvHGf67W9HGpt/1Y3kVQRScaNvYiZMJBLghJJZoqha35/rQSAr2RKpgs7YYhrzGgOuKvjeaITb/+xhUvmtqdDWYngmgUNTGGrZWuffHwVshUCuCCEOA1IIYRdC/C7ldNaPM9Ryx8yrC+neYMPzIhCXqwe3TFMw8pyOnF73d93UiRfieLQkpXQAf3lhX4vth+8in04xPXKq2sZkLc6qljhgSenGYW/BXklhudosr8nIV2DHa8DuIblkqXEqz+Nwu2nq6mHuovURuKP7laQNhdeEevibyDLBRIzLp55l24HD67wvazEYGrxmBNKglc15bd1kFQctbePYtBvwhnbQ8v7fpzh+CX1+Hu9L7kJJFsBvFaw9nn5czm5i0cfxBEOUUlZ7kFTxEho6o7IHZo4zvDyMQOBJrxam864AvmQSkU9YZNp5AAKdeJUFSnmTPQ6BRBAuRx8NDYdJ5YcRSqmmD1YFWqANFznSidqotE1bxJGPMZ5cff9keaqj4yoZb2UOSCo7ua42tlkhfWR5BLU4Q0o6SJSsusTV0UcFSbsTTy7DpUuX6PC0030+hiwW0a/RT67SxqQCcY1+WIVCgXw+T1q1akIF1dokXQ8CmYpa73uuZDB7jUmAFTx2cYnZeI6RmfqzVjbDyEyC3e1+tE3mrr9QSNz/DeJf//p1f56tvNLfAN6F1bhwBriJ62ziezFgIzf6845AXD0gi4RUhWPzx9b9PV6I4xESm6OIy95fd25B795bcLg9nD/yKLlksqYGAnBGWmmTlNaLEKLauC9vL0tXi2nYY030SyxFEELBt8Zf0b59F/NjFzBNg7fueiudDbcSdmoIYPKZI+il4rr+YVdjMDhIJBchUdj4i+pcOIGXNGZDF76+PE5nhhbPSwHw3nMPnvIi6LnzTuxpE1toVTrZEL6Tlfgx3EEfhVQah7CzmJ/nZucsw+wkefEIZ5bP0B/oJxNZgvJ1NB0+/PEE5oTVpoXOWyHQhc+wVEq7nSaaawB7+Vo1NNyBpIgrfAlPvSl2vjZ8ZKpF9AqKYxfpnH2UhQWT5Zny38ptXhyuWiKqEIhZXKwZAQCbF9KHl4bRSlYx/GK2UDf6ACiaJlFDEtKLnDt3jm1pL+G4FUGU5jdu9lBxodemsKw03kaF9IqEN2JG8Nq82GyWp+p6EMh0bPUxLy7WlzpfjdEF67jKRMGtwjAlZ+YSG7Zwf6ER/cxnSPz7DweBbJdSvkVK2SKlbJZS/gKw83qf2A87NnajB7dEIKZpcP6JR6pqqQoqTRX3hXt4auGpdfeL5qIMSGuxa2iuP1NLs9nYtv8gF489gZRmVaUFkDNMzpasvHxCsbrhV1ImBa18nDsMA3cDlqTZ2xCuaefSvn0nxVyO5ekpK23nGSBbsvLMY8NncPn8dO7cvO/StpC18G1aSJ86QlikSBQVWnetUCi46JWW0k0IQftf/Dmdf/cJ8i47qiFwh1d7HoUb7sQwsjiCK0hp0q21MV9Y4VCPC4nCU+emObN8hhsab2Blfo6Wvm1IRQXViT+ZRL9QJpD2WyDYha80hmpP0eEsEAiu1p1CwQMgFdwt52vbmFTgKbvRrxovW7g4RldxFM2mMPw9K0Nslklay9UeO18mEMWIrZ9kuUkh/fTSafrLC/poJr9h9DFXKCGBoYYQo6Oj9FxYXTz1hdr6wWhslA8f+zCZUgYjVT6veimsDaS8FQnvVHGKHQ076A/2Y2jGdWnpPhVdSyD1m05ejQqBjDxHArm0lCZbNH4oCuh6LEbh/Hk8hza2IXy/sBUC+dgWb/uxwsZu9AZyqSSGvrmU8cqZEb71sY8w+mRt65GKSuqmYDtnl8+SLtZ+8GP5GNsMi0C6yot8PWw/dCdGyfqCuwOrDf5OJDMUpYIqdeLCWrCqBCKd4AzCnjeBahFGcilSLaBX0LHd2j/MXbRarHvcA5T0ODlvIxOTEQb2HUS5xvjQwaA1kXDTOsj0URp9DlLpy/gaF4nM9iJmV8fbao2N+O6+mysz1mMEm1f7jYVChxBCQ7qsfl9tMsS8LNHQ3seuBpOnkw0ks0luaNhNfHGezp27MZ3Wzt+fTGJMnITGIXAFIdiDrzCKp/UcQkB7y72r56D5UHLdeFrO4gzXtngHQFHxaiapQu1GoTA6im+gk+0HW7n49CK5dBEzaEUwYrm24eJs3ppEqBhxppJTZI8fZ+yee4h+6lOYxaJVSJ+ovY6mNBleGmZ/uBu3qnBqeaVu9LEwkeDUJSu9dmt3J4VCAX0sRrwcBJXmVwnkfPQ8v/LAr/Dl0S/zwOUHqirEigcEuGZL9wqBXMxdZFd4F/2BfvJK/jqlsLK0+B20+p2MbSECWUoViGaKCMFzTmE91xbu1xPZY1bmwnP4B0ggQohDQoj3Ak1CiPes+fkA8OPhktkEm7rRpSS3wbzqCmJz1k5y4mRtRxanswNNC9KtRjGkwYnF2tErsXyMLk1Symq09G3cHK97z004vVZKZ20N5ImVNCqwh9NETWsh0RwOFFWlkMvCbzwBL/9A9fjE0mK1PXoF/qYWPKGGqh/E7bHmlUw42imWJEO3bZK+Mg144qM0GxKf3bdxHSQThaULhJvbCAaHAUFkoo2Z8yPrDp2fs/wkTa2rTRs1zUsgcCtFrHNsKdqY11Ro3MbhW3dTwkFfqo9tWhdGqURDRyf2BosA/Mkk+vQF6LBayRPowq3E8bQNUyg5aA7tr31J8QGcDdMY9vozJ7wOhXRJVKWt0jAojI/jGNrOjXd3YZRMzj4+h+6xVm2xUOsCny+UaLFr2BWF6dQ0iW9+E31+gchH/oqJV7+GgG6SiCzWFNKnklMki0luat7LkNvJMwsRVFVdF308/q9jPHrUKs7v6+3G4XAwlzc4vl1guOyUFqwU1vnoeX71u7+KW3PT7G7mu1PfrX72VZ8dKSXnn3iEYrk93kYEUklhJUSCneGd9Af7yYgMqczWUkzPBdOxDD0NHgZbvFyMXPvxK9HHHdsamY5lSWS3XkgfmYnjsav0Nf7gC+iZo0dRfD6cuzfPAnw/sFkEYge8gIbVebfykwTecN3P7EWAzdzo10pjrSxYuenLp5+t6V2lKBrd3b+MkT5Jv1NdVweJ5WM0unVksRFF2ZjHVU1jsNwI0hVY3RU9vpLiJr+bm1tuJaLbkFIihMDh9lizKIJdYLOkq4au13hAKhBC0D60g9lRq5DucQ8AMCNV7KpJ1w2bdH2dOQ4PfgDxxF8xGBzcOAKZtlJIDT27aGyaYmWlDTMpmLoSs0hoDZYWLDJub++ruT3ccCeF0iSaSyeUMVjSNIqhXjpuejmKNsdgYhB/2oq0Qm0dCG8ApIknk8FIpKz6B1jXREg8rWdZiQ0gRO3XprC4DSEkK+n6slevy4khFfJ5KzVVnJpGFgo4hoZoaPfQtTPEmUdmKEoJUiKv1M7jmCsUaXPY6fR1ciV5hezRY3jvuovuz3waxeOBf/0aAFce+m71PqeXLAHG3qa99NkE06ayLvqQUhJfyDCv6wigy+NkW2Mjs62tDPdr5Bo86PMLnI+e5x0PvAO35uYz936GV/e9mqPzR8msWGSg+u0sX5niWx/7CGePWB4buUkKy+ayIYVkV3gXA4EBCmqBZDpZ9/jng6lolu6wm8FmH+ORayuxLixY5/CGWy1Z93NJY52eSbC7I4CqrK9JPl/oeoYTJ36OVOrsNY+VUpI58iSeg7chrpEF+H5gs268j0opPwgclFJ+cM3PX0spN9df/pigvht9awQSn7cIJJ9OsTBeezm7Ot+KpgX4mbB9XR1keXkWT6CExzV0zfO79TWv44a7X0Gwxap1pHSDU6ksd4R8dPvayZmSpG4txg63h0K2Ng99tQdkLTq27yK5tEg6FsXpbEcIOwlyDHijbNLiCjn5GFfanJTOfplBfx/jK+P1TWdTT4LqwNvThMuVJhbtpNnv4HLSt65rcHIpQsFm0B7urrm94tPwdabxpq33adHpBU8jc8FJXIaL82ctEgy1dWDaHSh6EUVKCgUVOsoEEugi6dPQHBmykfUdbVOLvciSndjKEaSUPBRNYqx5TV6fFVlUCumVGSCO7dZ7eOM9XWQSRSKXl7EhKF2+XPP484US7U4b3b5uElcuUZyawn3oIJ7Dh+n7t68x9DvvAeDiR/6S2ff9HmY2y+ml0/hsPvoCfdgW58g6nOzcf6DmcbPJIsW8QcwhaLVZEU5PPE7JbqfQvZ1kwEZyZpJ3PPAOPDYPn7n3M3T6OnlFzyvQTZ3LM5dAAcVjY668mYhMTSAc6qYpLN2u49Jc9Ph6GAgOUFSK5LJbU0ltFbmiQSRVoDvkYrDZTb5kMrOy+XNcWEjR6HXwkiGrRrhVAikZJufmk9etgWIud5l44jjzC/9+7XO5coXS3Bzugwevy7lcja3UQLJCiL8UQnxLCPFw5ee6n9mLAHXd6KGtRyA9N96MEAqTp2rTWJrmo7v7V+hQouTTF4jmVnPi+swoiioJt6zvEnw1wp1d3Psbv41aNqgdi6cxJNwR9FYn2y0UrS+6w7OeQJJLtR6QtWgfqtRBziOEik1pRfPlGfQuQeJq29AqUnPf5eKgl+mmEoO5FKlSisVsncZ9009C535KpuXViMU66d+xg1jRTfLCkZpDs9EYaZdBg7N2cJDPuwubLUywN48zaeXY5woxSmaJE94IQl1hdHoGzenCEwxRkApKPkdeg6TugJbyPDV/B9EGB1IKCrM3czWyeRci3kYs9gSPr6R5y/AEj8ZWUyZef7nJZsL6TBQujoKi4BiwIree3WGCLW4iU0vYNRvFNQQipWS2UKLdYaPb303wjHVtKwVSoaq0vuUX8Dc2k79hJ8n77yf+1a8yvDTMnqY95HN5cuUZMXNK7VybRMS6Jgm3QouwdqsNx5/BZhg0G91Mu7IkrlzCa/NWyQNgT+MeWj2tRCLzVRd6Rda9NDW5aUPFZDJJSk2xs2EnqqLS4e1A13SMooFxDc/Jc8F0LIvqGeMrkXfyZOKTwLWVWKMLKXa2+Qi67XQ3uBmZ3VpHiYuLKYq6ed1auJdKFpHFYk9c89jMk1bk7jm0uQry+4WtEMg/AxeAPuCDwGXg+HU8pxcN6rnRKwXrzQjE0HUSkUVaB4ZoG9rB5Mn1nem7Ot+KUL3cGyjx9MLT1dudSStf3dH30ud8vk/E0zgUwb6Ah9YKgZQVPtUU1hokygRSz2vS3NePZrNXF45CwokzWKTXu2K1ha8HvUgiU96ptngZuGxFVxdXrppDUkjB/GnoOUQs9gj5fCOGEWDXnVbxeupkbVRWiqcoeRU0pbYGIYRCuOFOvB1p1JS1WM5n5rkUv0RemPRpz5It6Tjae9B1nbyuo+RzRH0qGQJVIQGqRrTJTTQVQiTDGKVVL4ZpSnJFF/ZUG7ncNI8tW5FlRXoL4A1akt+KGz1/8SL23l6Ucn8yoQj23tNJPp1GdXgozc9jltNdSd0gW55E2O3rZmiigAgGcAwO1rzW1oFB4prA3ttL4rFHGY+Ps7dpL8ePH8eftD6Lo5laddfKQplAPAphXaCvrFAaGaHX7ca74mXKlcOfkXz6Zf9QJQ/rugpe3v1ySsk8wmtd88rnIDY7g3AomPn1ZCClJJFIEDEj7ApbDUBVRcXnsWp1lRTf80W2lOWjJ/8Md/enSesrPLH4bYSa3rQOYpiSi4sptrdY57KnI1AtjF8L1QJ6x/WJQEq69fiZzFh1fMBGyBw9itbair2v97qcy9XYCoGEpZSfBkrltNYvAy9MfPRDjnpudM1mw+nxbtrOJLm0iDRNQm3t9N+8j8WJ8XWEo2k+errfwQ0uk7Oz36re7pcJTFPgD1w7hXU1jqyk2ef34FKVKoHMF6xzr5fCSi4tghA1HpDqa9dstG4bYnb0PNI0iU1lsftLqKoJK5frn8DcsyTL/aKyDpPOuLXojMevKqRfeRqkSalzL4nEM8CNdHZ20tQ7gMchmZpYrRFIKRGJAtK/vu0+WGks1VFCcVjpo/n0fHUC4Uv0C6h6kbTbTzRqRXlKIceKV6NYWt2tF4rLJN2SSylLJZWOry50+XQJiYK3YDnOj8asx4kU1xBIxY0esyKtwuhFHEO179/2g20IUUQXXpCS4pTlO6kQUZvDRre3iz2XJaWbd6wzaTb3byMRWUQ7dJDc8WdQiwa7Q7t56qmnuLm7kya7xievLLG4htjii1mEppB0KwRzpqXekZIb9u5FlARa23YUCc2Z9eKAV/a+klDJR8yWIJuIE1+Yp21oB1Ka6EKvG4Fks1lryqSSYmd41QkQLvcL+34osU5GTvKG+9/Akcj9FKN38A8v+xy6qdPQeoqxTaS8U9EMBd2stmHf0xlgZiXHSqa44X0qGJ5J4Hdq9ITXG0m/H9BLq5FQZXxAPUjDIHvsGJ5Dh+r6w64HtkIglU/cvBDiNUKIm7Hmkf/YYyM3+rXMhCvl+kewtZ2+my2lz+SpE+uO6+l6O0Vs+NOPAlDK5/G5cuTybhRl40aP9RAr6ZxJ57gjZBVRW8pzJRYLm6ewrvaArEX70A4ik5eYPjNMasFECEnW49qYQC4/TtKn4ffeAChkm9y0KI71XpCpJ0GoRN15pDQ4eNuv8uY3vxkhBL2dIaaWJKZuXfNcKomiyxoT4VqEG+6wfmkp0qR5mM/Mc2b5DEFHkA53K9ryAmnD5ORJqwCuFPOkXBpmdjWqjEUtqfWFnHUdUtFVAskkrBSmz96AYmtnJGe9L0vF1QXUFW5HRSediGFmMpSuXMG5fZVAlpaWOHfhDDJgIy28LIc6SI2NIaWsEkiH007HCjSkYWlX27rXWTEU5rb1IQpFdl6RiDlBNpvljttv59O7e5kvlnjDqXEi5ceML2YRXS5MReBL6qSPHEHx+9l5993YbDZ291gdj/U6ZsK9TXtpNEJcNq5Uxyjf9MrXAFA0cnWNhBUFVlbLsqthV/X21qAlv44lrU2XkSyQPRVZd//NUDAK/PWJv+Zt334bpjS50/tH2BM/zf72GzjQegB8xxhd3DiiuFBWYO1otTYJe8rRxFbqICOzcW7sDF63RbukW9dN04LEYo9veFz+/AWMROIFke9WsBUC+bAQIgC8F/hd4FPA71zXs3qRYCM3uje0fjb6WlQIJNTWTlNPH55QQ900lqb5KHjvYsCeYXzhIebHR3GFCxSUxnXHXgtHVqzd1x3lhdalKoQ0lfniZims9RLetWjfvgvTMHjiS5+jlLJ2X9mmFlipn8IqTT1K1q3R2PxKgsH9RNpDbMumGY9dNeRy+qjVNDJxFJutgW/Mn+XjIx8HoGf3LvKGRuTUI8BqncYTrq1/VGC3N0KuAUd7njZXI3OZOYaXhrmh8QaS4f3Y4svYNY2nn7bShEoxT9GuomZWd+rR6KMI6WBCWkXYVCxP/tw5rvzGO5n7xy9Yz6PrLPleQxFrt742AhH+drxkSaUSFMYssqxEIIlEgk996lP8+7//O4nGRjJdXh669w4+/swzfOhDH+Jrj1jk1eaw4TltyZXHt63Ofa+gQiAJhw1dU7hrNsCp46fo6Oigp6eHA0EvX7yxn9lCiZ85Nc5SsUQ8kqPUZj2Wa6lYVu8cxO5yMTQ0xPjyMhIoLaxvRigM8OsezhZHmT4/jKJqDN52GLvLTS6fqmskrHhADLtR0x24uyx+uLx82bq+T8wS+9IoRmZrMlrd1Hnbt9/GP535J14/+Hq+9tqvkUn00h12I4TgjdvfSFEsM5E+gbGBEuvCQgpFwGCzB/IJbmjfGoEk8yUuzKeuq/9DL8VRFDuN4ZeWhRpm3eMyR58EwPMCFdDhGgQihFCBQSllQkp5Rkp5t5TyVinlf75A5/dDjY3c6O5AaNMU1srCHA63B5fPjxCCvpv2MTV8sq75cGf/b5IxYHzio0ycexK7R0eu+fJtFU+spPCoCjf5VsPsVoeNhTUprFIhX+OMt0yE6+sfFbQP7QBg4dIYLV2WNyIb8NePQPQiybi1yw/4b6K5+VVk1Ax7ZI6JxAS6WX7tegFmnkH2HGQ5+iiB0O184vTf89mzn2Uhs0DPQWvU7dTTVlQWi5Sjueb1u/IKbJkmXM15ulwtTMQnmEhMsKdxDyuubQhpsru3DSkloVAImwKmzYYzVURKiWnqRGOPY4g2UnZrMUnFCiS/9S3Sjz5K9ElrsNTyP3yHkw9ZUWd/Pk5krfPc02S50TN58lUF1naklNx///2Ypskv/dIv4Zu5REvBTmClj/0FnR07djCVSqNgRYz5p44TC2pccK6PbquO9OnLXOxWaUk2EovFOHz4cHVnfDDo5Qt7+pnJl3jDyXHmk3ly4f+fvfcOs+us7v0/e++zT69zypzpRZpRsyzJkixbsmzccAHDDaYmARISEm5yyQ0JIaQBv5B7w3PTCKSSyyWUOIDBwSaAKe5Flqxm9VEZTa+n97Pb+/tjn2maGUkG27n8flnPc56ZObP3Pu/eZ+93vWut7/e77HvYMV5Gn5zEt8dm2be1tVGu1dBVdQmZcM7MBqptRk4zcPJFmnvWoDpdJLp7KZYzK6aw5hxIW6xtSb1qbdx2fuMZu76njdjRgJm9uprI+dx5BsfP8JEdH+ETuz+BT/UxkqnMp5Ru77gdnxJGCr7AWHblNNnAVIHumA/32YfhLzYQku39r0QofPz0DIYluH3D6gutn9R0PYfDEaYpuhddz64K563s24errw9HPP6qjeVSu6wDEXZz7je9RmP5qbPL9UYv57Kr9kTITU0QTrbOP9i923ZQr5SZbDC7F1vhJpiwAAAgAElEQVR/dAv7ayHU2mky+e8A4A2uf9ljfS5X4oaQf0lHu6RLnZfJmJN0n0tjWaZJMZ26bATiCQRparWzmWt33IzLlaTsc0BmCC4994nDFHy2cwoGryURvwuQ6I360YTJSNHu0874YTDr5JOtGEaOETNExahgCYuHzj2Et+c6Eu4KQ2fslfzUxBAAsebVs6q+gh9JgbWqxGx1FktYtoSJsCO5PW06iqIQj8fxqzo4XDgMgVUuUygcxTDy5OR2LNnE4xN2BDJwFte6dQQ/8KsAdL53L+d7b6FFjNM+e4LJ6ZmF719W8CsGpZpOfeAssteL2trKkSNHOH/+PHfccQdtra1QzNK3tg1nvQPvqMq9995LyeUlJCwcwqJ84ABT62OMlsZWPM/mnrWMXzjDiz0mI81dRIJBNmxYqjq0O+LnK9f2MFzV+OLNfkYD9hTgy5voqh/fHhu9E2pwh6rNzRhTy1NYc/e87rEoj0zSus6+J+PdPRRyM4i6ibhktZ/P57Eki77mpQCAtc0NQcj8DMK00MftaNnIXJ0DOTp6kLc81UrscMPxWIKxbIXOJh+VIzOYQ2Vua78PxX+G/SMrd28cmCqyPhmAiaOglyE/xua20BUjkO+dmKQ56GJbR+Sy2/0kphsFVDVEU8R27iuhsaxajcrBQ69p+gquLoX1vCRJfyNJ0l5Jkq6be73qI/spsMux0Y16Hb22Mu48OzlBpKV1/u/OzVuRFYXBo8vTWJIkYQVvoWbIBLptBxMMbFy23eVssq5xvlKfr3/MWdKlLtRA5uRMGmmsYjqFsKzLRiAAbes3Iskya7bvwuddQ0XVQCtC5ZIIbOgZCgEVr7sbhyOAy5UgHNqBN2qnUM5d+IG93bBdJEy5skiSg2+OnWZteC172vbwzXPfxEDQlXQxMVNGq1ZITY1Rd5gko6s7kHBRx9Rk4iwoy14Tu4ZsUcOtGMRyR3nnO9/JbXt2EpRLCMUuyJdmxpmZfRRJUphUkqhCEPTpFNM16gMDuNf1U8nXcEplmu65meOxDjY5Jgi3mKQcLrL/8sD85/ldEiXd5oC4+vspFIt8//vfp6uri507d1Iv25NmtC1KRC0y5FiP1+PFDEXwVEtUT53Gyuepbu1jpDCy4uIk0Z6kkkoz3JYgE42y1edDXkEReU8kwJ/5o2T9Ct8wK0QkGdUEvWczznb7OoYbApz1lhb0ieUOxGo4kPW+biRTEGtAkhPda6jp9j10KZlwMj1JRamwKbaUIe1xejBlk1wxhz5VQTRQblcbgZw5dwjVlDn/2BNUS0UmclV0U7DG7yLzjbMUnxzlFza/A4DvDC3nUlQ0g+FMhXXNi6Ln0jTXtocYz1XJrFJIL9cNnhyY5e5NSeQVCIQ1o7ZqS4aXY4aew+EI4XLF8fs3kF5UB8lMjFMrl6geOYLQNLyvgf7VYrsaB7Ib2AT8MfAXjdefv5qD+mmyFdnokdVb2xq6TjE1Szi54EBcXi9t6zetWAcB2JHcw9jJMLIiKJgS0UDPitutZgv1j0sciFNlRtMxLLHgQBoRyIKM++VD8xvf9rO89Q8+iTcYwuvtpSxyCFhWBxFDz5APuQmFF9YeicQ9GGRpVkzOn/t3+82RfRDfQCq/D6dvI4dSp7m/737e3v92ZiozPD32NN39vVhCYvTkMfKz05Q9JnHv6mG7vzpOadyLl1FA0O5vp8ndZDvykAuGn6evr4+kMUpArWNadrH8wsgXGR39As2JNzItJGKmScBdojhbxpiZwdW/jkq+hlfOMqBEyRkmO4MqPsc4Nbebob/6NLVTtpSK3+2kYipUzp3D2d/PI488gmVZvPnNb0aW5fnr7vb72dCjU3HHubjvIlWvH3e5yOiz9qTh3LmdilEhXUsvO8/mkD2JJc0NuDSNrpOnVr0mazIm73i2iEuS6Ggg8syNC0TD+QgkFluxBjKXtm2zbEczFrBX/4nuXnRrZTmT2cwsVUd1HsK72CSnRLlSRhttMNJl6aojkKkhO6rQqlUOf/fheRXe9bMamAIjXaM/2oWjvpEThR+im0trK2enSwiBjcDK2eg3SrNcc4VC+pMDs9QNi7uvWTl9+qEnP8TvPPU7V3UOlzPdyKOq9nVuarqJfP4whlHGskz+9Q9/mxe++a82/8PhwLtj5xWO9sraFR1Io+5x6eu212JwPw22Iht9jguSXe5A8tNTCGEtiUDA7iSYGhmikFrefyF+waRyKEbdUBjXJKLuFUT7LmPPZEuEHQqb/EuLr0mXigXM6vqyFFb+MiTCxRZoitHZkC7x+noxRQ3NKS+tgxgatZmD6A6LYHChBW88YfM6bvbJnMuehWoWRvZT7d5CuXyWgbobp+zkvjX3cXP7zSS8CR48+yCtW27AIZkMH3jSJhF6DeKeVRyIoeGrDFMY8yPLeeIOweaYzSbPTk0QaU7ak0Z+HMYOEXDU0TWT8i6TrPk1jvnfz8PuDzFbyxATMgFlllJOQyDhWreOStHEp2Q50NAV2xvvISjsyb3Q3sH4h34Ls1TG7/MCEpV6nfPJZi5cuMCdd95JU5O92JiL/Fw+H2u2N+OqZzn6+BhZScZfr3H63Dmca9fQ2m2v3kcKI8tOtSUkMFwuQmaCzQ4H9X37EKuIeuanK2yqSHx7ex9/bBRAWGitC8gwn8+Hw+GgEgquiMIyC5o9e8zmqXgtnsg9z+ipDKFEK3oDuHmpAymXytQcNXrDvQgh+JvHz/HpH9k1IafbiV7TqQ7nkf0qaovvqhxISSthzOTBqbB2540c/u4jXBxPIQGRs42ifa6GMC261DvQyPPY6GNLjjHQkDBZnwwsiUDmHcjYyoCY752YJOpzcn3PygCO0+nTPDP+DGX9J1MaNvQ8qsNGh0Wb9iKETi53gOzEBLVyifT4GOV9+/Bs2YLi913haK+s/cd3PlnFJEkakiTpuCRJRyVJOth4r0mSpB9KknSu8fPVSzxepckr6mHZq4VyfrkDmdPAiiSXOpDeBpx36KWlcN56pcLJb32bTFDm07MqD2adRNxXf9pCCJ7NFtkT8SNfAjOcZ6PXjWUprHkOSOzqEV9zmlhlj7KUTDhxhILHnlSCwYUOim5XklDoOq4JyJx3yPCDPwKtSDpuT8bfmjjP67tfT8gVwiE7eEvfW3hu/Dmmox10ePMMHX8JI1dckYU+b9mLeJQ6xVH7/K71ylzfcj16rUYpnSLS3agnjeyD8YMEImHCa3Lk321ileI8r97PZ0bSjNU0YoqbAONYFmjOgJ3CKgm8co79dQfNTgebE9sIY0840kd/D210lOlPfhJ/Q1I/09TEs5kM3d3d7NixY36YtUYKy+3z417TS9v4U1yctahYgg6vi0FJwnv9LjoDNmJpvma0yErlYQotcbBMdu68HqtYpHrs2MqXZbpCuNnLtQEvvQeew13PUHEtXENJkgiFQlTcbsx8Hqu6NB1rFjQUv5PJ8wOo7TEOXDjMI585ytkDKbyNviiLkViWZWFVLbx+Lw7JwacePcOf/+Asf/fEBcp1A5/Ph9N0Uh3O4uwI4GhyY2avnP45kT5BpKjib0ly41vfhVatMP78D7hBdkCujqsvDBaYuTrb4zcg9AhfP/P1Jcc4M1XEoyp0ejSoNaKN8gxBt0pPzLciobCmmzx+ZobXb0quqH9V0e0o0bCMFfv6vBzTjTyORgQSCu1All2kM8/M94DJT05QO3nyNZFvv9T+r3UgDbtVCLFVCDH3pH0UeEwI0Qc81vj7P9RsNrq2pGDovYweVm7SRpqEL4lAmto6CMYTy9JY+//ta1TyOdQ7NjJpyGhyEJfi4mptuKYxXtfn4buLbYGNrq2Qwro8B2Ql83ptVd5KU2RpBDL0DPmAiiy58PuXAgASiXsJyWUqboXqURsSm5InsRwxhmpV7u+7f37b+/vuR5Ikvpk5SlewRDZTBM1EBF3LWOjzlj6PIgkUEUFoYX6uaxtv6XvLgiPvuw6cAbv2Mn4IaV2ArlsnkAcVioe6Gazai4NhaS1xZ5CAYUNptUQ3SixGuarglbPsL+nsCvsZzspoc3yRNX3Efu3XyD/8MAzZk9DBnTsQkjSfupqzuRqIy+tHbW2hPX2QcoN0uU51UAgEqG25lhZ/C4qkLItAXpp9ifcO/wiHO4GaS+O8ZiMoCqVnVuYN5BoOBKD83HP4HTUKmaWpnVAoRKkxxkuRWGZRQ3hlSpk0fZu2I6rK/HEDrXbUuritbbFYREIi1hTjr354ln98apBdPU1opsVz51NEAhE8phs5Y+LsCKA0uTGytWWF+Evt2MwxwkWVtp5+Et29rNlxA9LJp3mX4kT2qQRutms6RrrG+mQILXs9L06/yGB+cP4YA1NF+pMB5PzQwoFLdgS+uS3EiRVSWE+fnaWimdxzTXLZ/wDGFgEdnhlbnbtxJbMsHdMsozZ69SiKi3D4ejKZZ+d7wBRSNmDjtS6gw//9DuRSezPwxcbvXwT+y3/gWIBFbPTSwsPn8QeQFceKDiQ7OYE7EKTu8vCrJ4dINQhn83De4y9hNPp45KYmOfzdh9l0y+3s3GZnDVddaa9iz87VP8LLZaZb5tnoy1NYhdmZyyKwVjKXK4mieCmHgojMMNWBjF3sHXqWQlOQQHAT8iV6TDYaC671mgyqDsxIJ9nSEU7XVLqDPWxfpPmV9CXZ27aXf7vwMG3dC6k1NXIZCe2UjdbyhZvQcy2UCodB6OTmHEhbB3TuglMPM+vOM9N2lvK0h/pXQ5QyBcYbKLWsaydRT5xA3QYymJ0b0OsmhqFQCimM13WuD/n45uExpjP2AmK6Xif2Xz+Ad+dOKg/Zk0jd7eb1r389kcjSKLK2KIUlyTK+tjgOj50K2zA5iWQJBl0uVFmlzd8231hKCMGXTn6JX/jeL9CRWYuMwJmeYuT8GTxbtlB+Zjlip17RqRZ1ws1ejEyG2qlThJt95GerS4rzoVCIQiMFdikSyyrU0bCjkhu230UTdgoxN1Ml3Gkz72uZhYn33KT9PWRrQT7z+HneubODL/3S9fhdDp4YmCUeiuOybPCCsyOAI+IGUyxLD19qp0aO4NYVWrttZNeN978Tv6WyVVfw7WjmB8ee4pgyjJGu0tfsR8/tRJEcPDjw4Pz1OzNVZH3zovSV0w8luwa4uS3ERL5GqrQ0Gnr0xBQhj8qNa1ZOJ48VbQfS5m/jmbFnVkVkXsmMhoyJQ13gmUSb9lKpXGB23I4uTdNED/jxbF4u9Plq2xUdiCRJb1nhdbskSa8e8Nk2AfxAkqRDkiT9SuO9ZiHEJEDj57IxSJL0K5IkHZQk6eDsFfo5vxI21w96saiiJMt4w+EVayDZqQkiyRYO5Ms8PJPj2eyCPk/Pth3otSrjZ2yc91Nf+Tyy4uCmd77HZtMCUc/Lq388my3S7HSw1rs8aomqDhySrYfl8nhBkuYnsvwVOCArmSRJeL09VDwKpYku0l84Se30LNbYfooek2Bwucy7292Ky7eBrV6Dc94QmTXrsSyNJzMZ3tr/1mXs3rf1v41UNcWxzma0iJ+XNuzAt1IjpzlLnwNfAl9TjPJECMuqcvbsJ5nOPEB8c5qKeIqJjjAjkTLHNwQIuHoY/F4HJaebWcu+ZjeFXFhqMwX/FvyW7Xj0RDeVvD25nU/Yt+GuoI9/PzbBWLoZSZhMlKeRFIXWP/8zPEIgWRbJSpHt25cKYVZMi7FKDVOWcftsZ+js6aFi2qmw0KFjNFcrnD5vrzg7gh3z/T4+9OSH+LODf8YtTbeQLHVxPS8RlgpcPPg8vpv2UDt5EiOzFBGXm7Yn/kizd158r2l9O/WKQb28kHYKh8NUNA1TlpdHIAWNUi2Lw+Ui2bOWbSE7SZCfrRBbY3fVLE4uPH8DkzZZ9OlBJ/df187//JnNuBwKe/tiPDkwQ8AXQBYyOgZqux8pYEc05mXqIEIIxi/aNZRYRzcAiZ41RKM3IwlQrgnw0qnjDDpmMNI1+poDCNNPj+cGHr7wMFWjymypTqas0d/s4/jkQf42HOKP2zox5iKQ9uWFdM2w+OHpae7c2Iy6Sv/zOQfyrvXvYqY6w0B2YMXtrmRzQopzEQjYhXSAmnliXmnb2rIZSb36bMErZVcTgfwSNvv85xqvfwJ+C3hOkqR3v4pj2yOEuA64B/h1SZJuvpqdhBCfE0LsEELsiL8GhJq5bmzL6iChyKo1kEiydV7EcLi6sF/npmtRHA4uHjnIyImXOP/iC+z6mbfjb4oS9UTZEt9Cd7D7qsdm1z9K3BQJrCizIEsSzU6VKU1HkmWcbg9apdzggMwSjL38NYLXu4aKWqdStifJ8lNnKTnrWJK1ogMBaE++iQ6nYHjbG0l1d2KiMqq7eNOa5RSkm9puIulL8qDIc/barfzglv+CK962+oBS5yHWhy8UJjfswO1uY3ziX9Hc36dt9wwXLv4Jp80nObfGj79isW3nv+JwBKh5PWQaeef7owZYNV5yb4OKhsOoUA80U2l856eirQQUGT1XZzRT5UKulyAFxsuNCTQU4tytN+AePUsyO7YMWvu2A0/xy6Fe/vL9/w9bD5zljhcH+NCt9/H4unYkS8DpEfqboqRSKWZmZljji7HGPMU7vv02nhp9ig/v+DC7yzeiorM3MkOPP8PwyZO4b7wBGv0hFltu2l4khJu9lB5/HDkUIra52/7f7ALRbg6JVfF65xtLAQjDwqoYZHNTtKzpR3E42OSza1v5VIWm7i4sYVGeXbj/95+zJ/o9a7byv9567Tzs9dZ1CSbzNQqGfU1G3bOcfP5xHvzrjwOX54JMlieR07YzjHXaTitdqLHeu57J6iD7nv0epmmSk0ro6Sp+l4O2sIeAfjNFrchD5x7iqye/g7vlQT4/+ov87Pgj/EMkxIOUGKilANjUGlzWofC5CymKNWPV9BXAaHGUgBrgDb22vMvTY0+vuu3lTDfsRcQcCgvA5+vHoUTxJrOs2WRfd6P35SEzXym7GgdiARuEEPcLIe4HNgJ1YBfwu6/WwIQQE42fM8C/AdcD05IktQA0fr48wZxXweTAymx0X2S5HpZetwu34ZbWeQLfcG0hclHdbto3bmbw8Is8+cV/IhhPsP0NC1m6z935Of7whj+86rGdKddI6QZ7LpPisdnoC2TCeqVMKZNucEBevgPxeXupUaIudaIEZWrDFjm/nXYLLUJgLbbmxL0AWPoZUrnnOV2TubXzzhXBAoqscH/f/bxQGqIYtc/LdTlmfvocRNfgDUcopQvsvvEpbrv1HDNPvZn082/mppv2s/v6H3LjoRI7ZvtQXVEC0Ria00nOb0dgYZHCVTnAfitJruTHXctQVQLzOljHgq3sCPn47rFJVEXC6WolSJHpWpns5DgP/NGHOX9xkFAtw7ReX5LOMM0a52oy/dY5XndiH/fEQ7S4VNJ+P3mfh54Zg7oaZdMuOwI9efIkm8sF7ghWaRcWX7j7C9wRvoNTp09zI4fw9+6k15fB0HVSkkCJRCg/uzQHn52uIMkSYt+PGH3iRxivv51w0r6W+ZmFYvmcA6m1tizpjT53r6fSI7Q22hu3qY1eLJbEkfEBDDTqjej6Ky8Mk8qmMCSTv3zXDUuKzq9bby/yzqbsY552DjI2/G0ie5/DlLXLckGOpY4RKTpxBvx4GyCF6cPTRCUHE/4Mx/bZnCIDi8ysnQ5cm/AzM9vGmtAaPnXgU/zTwCdwBE5yffJ6/pQEX9XtifqkqIBpEGgU0hdHII8en8LvcnBT3+oAk7HSGO2BdmKeGJuim35sB2LoDR2sRSksSZJQrXUE2iq0NmT467GXl9p+pexqHEi3EGJxw4YZoF8IkWFBaPEVNUmSfJIkBeZ+B14PnAAeAd7b2Oy9wMOvxue/HFMCDQz9Smz07KWpA/shjCQXHMhQdel+vdt2kJ0cZ3ZkiJt/7n04nAuiiV7Vi1O5ehHFQ40eGLtXqH/M2WI2utvro1Yuk29wQK4E4V3JvD4biaX5Joi+rgwIMuFeVLUJt3tlsp/H005BamINg2jaDC+VBff337/itgBv6XsLiqRwKtgAIqirRJqVDFTSEO3DF45g6jr1ShlJksmOTxFO9OByxvD4e/Hu/gPk3b8BQCAWR3c4yISSRB1QrM/iLj9DRch8N3oz7lqWiuagUtCoOCXOu6LsCvr4zvFJbu6LszYRwGkYzGgmX/m9D1HKpLn/o59gb79OqWrMFz8BpjL7KRDiWg5x18WX+LN1HXz52l6+E3fzjY/+V97zRJqKv5X4jTfS1dXFqVOnSDSEJH937c+zNbGVxx57DK/byY0chq49dPjyOBSZoaOH8O3eTenZ5xDWgn5SbrpCICAx9bE/4lB/J4+NDCCsAkgLPUIe2D/Cbz5kRw215uYlKay5e72qF+f7wuiVheP/xeOfwZBNjGKNmUKNP/72SfySieKVUR1Lu+QlAm42t4UYHLU/96I6ie48iL+tTLH1wGUjkOOzx2kqOWnu7F1482iKaSxa7ruZ2qLOkal8GiEE/c1+BmfL/P6uP+D9m9/PTtcf4p78Ez5925/zxlyajaG1hBU3J1xOqNhRyLVtofkIxDAtfnBqits3JHA5Vu/4N1Ycm5fA39u+l2Ozx8jWLt8jaCXTG0q8i1NYALVUFIfbRJo8iMu0KJmvylR8RbsaB/KMJEn/LknSeyVJmpu0n25M7FfXceXlWzPwrCRJLwEHgO8IIR4FPgXcKUnSOeDOxt//oSYpMrJ/ZTZ6tVBY0q42Ny+i2LYohbW0ODenztu2fhP9N+z5icY2UdeQgDbX6k4n6VSZbgj/Ob0+tEp5XqAwmPgxUlhu+2EW/n04GcDjeJGir0IwcO1l1Uot7zZ8soUQUHB0sjO5OiEq4U1wc/stZJ12CsGQV4E1pxuyFbG+JZ0ia6US1WKBSMui1Nee34AN9wEQjMbRBEw3tRBX6qSqKZz1s3S4Vf6t7/V45QLFrEYlrzEes88pXLeYzNe4b0srCb8Td7FMTviJdjfx7k/9Nd1bt9O7YS0SgvMvLsA6z8zaqLuYNIMntvA4Ont6kABvaZJa81pkj4eNGzcyOztLWbch0mZtnAsXLjA4OMje9c240SC+DtXfREezi4tHD+LbexNmOk39zIJMTnasgHP0FNNdrdQQmLrOY5//LP6wi/ysHYE8MTDDsVkNSZKoRiJLUljzDsQs0dK3DoB6WUdR7fEnjHay5BF1i88/cQZTSeMxXPgDKy9kbl0Xx0rZtZdpJYW7yV54ZVofw7hMBHJi5jiRkpN4l52+0VNVQtNVHkFjy45tOJriODR7/4xVxCpq9DUH0AyLmGMDv3HdbzAz28qGZNhuk5wfRYp0s8nfyUmnc76Qfk1biKlCjZlijf0XM2Qr+mXTV5awGC+NzzuQm9tuRiB4bmJ1KfbVbC6FVX06h5FeiA5nB+woNq8dxu/xUZhZoSnba2BX40B+HfhnYCuwDfgS8OtCiLIQ4tZXY1BCiEEhxJbGa5MQ4n803k8LIW4XQvQ1fq6uWPga2ops9FAEISyqhYVez3PQ0XCydV4Fd6KuU1+0Ooy0tHHnr3yQe379Qz+xPPRM3SDmdCzRv7rUki6VgmFRNk1cPh+1Spn8zFwfkJdfQ5KnwyAkrOAxOPEQLse30LxTeCp9l90vkbgbgGFN5t6+dyBLl78171n7NoRsw1BrYrk6LWCnr2A+AgGo5LJkp2wo9aVcnDkLRGNohsF4ooWgniFVTdHkDvP2ZBMvdl1DPaKjVQ1yUyUm4xZOLM4NpHE5ZG7pDdLywpcIzcySJ8wtv3z3fCrQ07WVdm+e8/sXUkpnM40iMLN4IwurSCUYRIlG8Vamqbjt72Hjxo2AoO60C7SV6kUee+wxQqEQOxKNfYPtEOmiJ1IjOzmB3mdHhKUGGssolMhNlfBUZxjt76GptZ3bfvEDjJw4hiROzDuQUxMFBDJen5+yz4+xKAKZWyy5YgE8AZvzUSvrhBNeHE6Zn4m/nbJawym7+f4LT7BzXRWP4SHetPL9dOv6BGuEXUsMOHI43CbVtA89fJFy7eyK++iWzsjoWWRzof5R3j+JCez3yzgkQV2SkYo5PIpKVi7bjPRGw6hzMyVMS3BuumQ3kSqMg2VApJtN4X4uOFWqefs6X9voNHhiPM/3TkziURVu6V99cTVTmUG3dNr9tgPZFNtEk7tpPo2Vzx9hdPSLq+6/2OZSWJUn86S+cBKroiMsi+lzE4hanGpniVA0Np81eK3tapjoQgjxDSHEh4QQv9n4/cfDpP1/1FZko6/Q2jY7OYE3FMbl9TJV1wk5FAQwWlu677W330UosfoK52ptStNJOi+PzFjcmdDdkHQvzM7gjzTh+DFQHfWjBdRaDC2ch4nD1ENnQBI4zl0+Hdaf2MOTRQdPFlcuni8bd2ihnlJIr9KlLXUOZAdEupZEINlFkeBKFojFqbo85ANBvKUJZquzxDwx7g94ELLMi+vsyWP6Yp7huMoWucwPTkxz67oE+x/4PNLkeUbqrRiSymRpkZxIcjNrA2nSExNkJ8epVIaY0OzFQ5QUztDS1bazpxtvdZqKrqLXTQKBAF1tESTV3i6nnWNiYoLXve51qKUxUFzgi0G4ix6XfY6jw4O4Nmyg/MwzCNPkwkc+jiWr+Pf2Mzs+ynX3volr77ibrmu3kR75AZmJSXIVjfGc7UicXj9lp4pVLmMW7ZqGUahjCZNY30LhtlY2cPtVQnEvZk6hu20tquwi6vw2TdGzuC03HfGOFa/3te1htsj2IqDPbzvCgPh5hKGQDj+KMJbLl5/Pnsebt9+PdXQhdIvKoWmOeyEY8zIzM4NlCdrbO7DyObJSicyZYfoSdhR0brrI0OImUnMQ3kg31yS2YEoSZ1J2O+W5QvrR0TyPnpjm1vVxPM7V01dzEOuOgH2+siRzU9tNPDf+HLqpM3D2E5w7/6mrgvbqRg4FPxIyRrZG+iunSY+NodequLt1tdUAACAASURBVOtr0HoFwfZmiqnUimrer7ZdLYz3nCRJeUmSCpIkFSVJKlxpv/8/2cps9Dk5k4UgaU6Ft2ya5A2T60M292K4enms+49r03WdZtflncBiLshCCmv6ZUN4ASzNpHo8hUfpouK1o55iqz1JO861oI2v3hEu4U3wTK2F5ua7iXmuzH4faaQAZatCKp8BfQXhyvR5iHSDouINR5AlBeUFndqZDJIkE2pe2UkHojGyjS55nsxFUpUUcU+c5OhFtpw9xeNr+xFArmwwGvHRb5SZLda5xTnBySd/RHzPvUw3EObD+UXdFpuvYW3ALuaef/EF0umnSBNDAoK1PA7/0uvj7l+HH3vSzk3bNYKeqE2YVMpJDHmSWCzKli1bID8GoXaQJAh3Eq4P09TazuCRg/hvuonK0aNMffKTzDZ6iswWz+L2B9h4821IksTrf/WDSLJEOfVdXrqQmh+D4vIxNyq9IWlSnc5RM8vzBXSwIxC3z0Eo4SE/WyUQiaHKbmJlicNjdvQTjawMt5YtwVqhIAkHzcEC1ZyTTTe8HW24g0LLPurp5bpfx1PHiRTt1GysvYvK8VmsisFDQqMz6mViwnagb/zlD9CzcT05qcLRh7/Lvi9/jm6/rX810GgitaEluMSBbGq1+2mczNnRj8/lYE3cz1cPjJAq1VfVvpqzOQjv4jbAe9v3UtAKHB19iGLxBEJoGMble7SDLWOiGD6UiIumt/ZTH8xTfMROYYaLnaBAoB+EsCimU1c42itvV5PC+l/Am4QQISFEUAgREEIEX+2B/TTZSmx03wps9EshvDc0ittD1Z9csXMlm9J0mp2rMLQbNheBTNd13D4f9UqF3MzUyyYRAtROpRGaiT+6joqjjgDyTQE87m4cUoDyC6v3c5YkiS/f82U+fuPHr+qzRhpO9zafk0lHGA7+n+Ubpc9D1E6duX1+ugKb8My6iF2I0d28edUIKxCNkWn0MfdMn2W2OkvUE6U+cJa7Xnia0UCCsaiD8SYHpiyjpIrEpQrpR79Ccm0/19z3NtDs2tdEJYthNLSQvE0EYwkSYYftQDJPkXX0kHSqGFkF2bW0pBj/779B3ydtMb5sA3rbJNnT+VS2DVkxeN3rttiw4DkHAhDpAkunZ9N6xk4dx3nD9WAY5L76Nbj5DVhmnvHTh7n2jrtRXTZ5LxhLsPmOd2IZoxx/9NH5MViql6KmYUnSPBKrNlOgapRoW+RA6hUdt08lFPeQT1U5m6+gKm42Gb1EhP0sBIMrTxv6ZBmHAA2FcDDDbMpNuLWN8oUOhKPO5PhyBd1js8dIVHyEEklUt5vyC5PIUTePV2t0NdkOxO1209TUxMYdOxGSINy+hmM/epR7znyR0vHnOD2Zx2PVCJYmGTh4iP3pTn7wtW9x7BvfIWFYnCiPz3/eta1BNhVNvIrMbesv/2yMFkdRJIWkb2GBsrt1t60gsCh1pWlXnvB1I49c9+LsCODdliBweyfqmMzGpj2ExzxIdZBjds0yP7Nc9PLVtqtxINNCiNOv+kh+ik0JLGejXypnolUrlLMZIosgvFsCHjyyND8ZzpkQ4sdmrs6ZbglSmnHFCGQuxTVZ13F5ffZKJjX7Y0Ug5cMzKGEXgZYNWJJJzSVTUEuEQlvxbktQOTqzYqOhOesIdhBwrtya9lIbrmpEVQf9sVYmPM2IZ/8KtEWidZZpF9Fja+ffWhfeSd1RpUqR7Z470MZWXgH6ozGyoRiyaeIeP0e6libuiVM/e5ZbTx/FY1Y51utkJO5AEoKLZzO8ufA0lmVx7wc/TGvEj1S30ys5EaRQOLpw8ORm1gZzTA6eIpN5gbyjh1anQi3rBHXpSlsJhYhvW4skQXbKjkBMbRTLVJlqsN1bWhqPcH4MQo0UUdiuCfR0xzENg5QCSiSCb88erC03IcyjSLLE1rvesOTztt55N7Kji9rhf6ejkSaryy4sIai53fNILLNQpy5V53vBCCGolQ1cDQdiGYIXR/OokgNSOT662VYcmoMFX2r1ETuhoQZSKA6T4aKDycoU7kAfrnw3k/mvL3sejqeOEy97iXV2YxY0tJEitfX2NemMepmcnKS11e65k2iAQSyPh5//1KeRIwk2XXgU6wsf5ZeHv8CDH/sw//7YBZ6d6eLM88/w0g+/x9aim5P1he/jTlQ+iZf3JyP4XZdflI2Vxkj6kqiLVBeCziA3JDYR0M7i89mLmqtyILUsctWLs91+LoJ3dDIrj7M5dBPWKHjGg1TNo4Cwa5evsV2NAzkoSdLXJEl612I2+qs+sp8iW2htu4jT4XTh8vrmyYTZBoolvCgCaXGpdHpcDC3iggjDYvJPD1A59JNRXGY1HQFXrIH4HQp+RWZKs1NYc/ZyOSBmUaN+Lot3WwKfz0ZiZTbtQrOKBENb8N3QgtAtyodemZt8uFany+Ok1a1Sl1RSmg4vfn5hg/womPX5CEQbKRJSYkwoF3l65htYDovUF06iLyLOzZnqdFGIJYnm0wRLGoZlEPfGqZ0dINKe5I2zT3Gqw8lgUqWnOIN/4iKe1EVu+8VfJZJsJeZ3ojQikDxhcvnDCwdPbmat4xz+ljJC1EmJJpoViXrOhZAqaNpSJ+JQFQIxD7mpClbNoCaPopgtVCoNkl9lEAwNilOLIpBuANojFqrbw8XjR+n99iN0/MPfk57MYlSPs+7GvQSalqYKQwkPqu9OBHBH6gkCLoVyo7hd8fvnkViyJqMEnEgNQqRWs5tHuX0q4YQNbChUGylGU6I6a0NgV4tAtNEictBJMjaJEDCgy1zIXyDW30to9HVUxUVy+QWNuKJWZDhzEWfeIN7ZRW3YPv6Fir0Qaw+7mJ6epqXFTjVFo1EkJFLFDInuXrre8zv8IH47p4MbSG26izd9+A94z64aH7xL5h2fsIGdvdUAQ6JGUSsihGDDqJ0ivSl4ZbXb8eL4fP1jsd0ZcaNIgkiLzb/W9Cs7EK2WRTF8ODsaCysheH7iW1TdFaTAXlLZN6Lp07ijOtMXV2409mra1TiQIFDB5mLc13i98dUc1E+brUYm9IYj83Im89pLiyKQpEul2+NcUgMxMjWsgkZxYHne9+XYlLbwGVeylgaZ0O1beDheLgekcnQWBHi3Jea5IJMNOexQcCvOVj/OTjuN9UpgMEaqGp1uJ+0NiPJE773w3F8vRCHpRu0hZjuQ0vMTGJLO6cl9FMopCtvsFXbq8ycw8stTiNlInGguTbBijzXmtlNYrg0becf0o9RUmdG4yob0BTZmTrJ21x423XI7AA5FJuZ2IguoqD3k84sUlpObiTlLxPp0TNPBtO6gGZNazj6Pcnl5x7xI0kt2qoI2XrL5NaFNvH3rzyEZbsrFC1CcAMSCAwm1AxJKYYyuzVu5eOQQSjSKpKpMX3gBYWlcd++bl32OQ1XwR+OkfXvxZ4bYVTpGvtBoMNaapDI+TimVxim5cMcXoolaI/J2+xwEYnZKLNT4XpyKm5mpSbxeL+qlKcO63XhMGy3i7AjQHBmlXIww6TG4kLtA67oNyGPrkE0v4+P/Mr/bidQJQmUHCEG0o4vi2SyWEFw8Y6cAfWYZy7JobbVRdqqqEvEGyZhFrIrOumSIAX8/j0duIrn7bvp23kjcuIgz3jMfVcVq9oR9Kn2K+tksjnQNAXSLKyMj50iEi82yDKLaSQZqMsfL9v126WJhJTOMArLhQ629CJUM2akJatUSF8MZKkJmXWEnQkiEuuucePIUX/3kAQ49OjSPpnu17WpQWL+4wut9r8XgflpsVTmTcHg+hTWH/AknW5iq6wQdMj5FodvtYriqzU+qpSk7xz1yOk1F+/FRFTONToNXSmHBAhvd5V3A6b9cDkjl8DRqux814cWpRnE4guTzB5EkJ36/zRXw3diKkapSP/+T0YcMSzBW1+jyuGh12+c3vvV9NvHrwD/ZG6UaDiS6FrOgUT2eIh/IUszbq77QmiSx912DVTVIff4EZnkh/WgJQdoXIlxIE2oEKPGihFUs4t6wmd2V88QaveS9Q0NYngB3/coHl8CuW0JunKagrHaTzx/B7g4NJDcjSRDqKDIxlaQuBHHLoJa176FyZVHRvWGRZi+5mQqV4SkMd5ZgbD2t7a04y0kqxUE7fQULDsThgkAL5Ibp2baDYnqW9Ogw9ZpGJXuQYKKX5JqVYdWOoBPZuQlf70Y2jD1N2zN2VHc0GuSbw6f48n//IACBjoX7o15pOJCn/4jzL30XHUFvxI5E3KqPXDa7cvrq6+/B/Pt7MdM1HB0qAd8U2XwLRjjAYH6Q5Np+qvU6vukbmJl5dD7lczx1nHCjgB7v7KY+XKRogTZVI+Z0UMzY0fucAwGIN8XJSiWMTI21iYX7fH1LoOHIUhDpRnW7CcTiuGr2YupE6gTFp8aQvTLG+CG0i5ef9Mt6mUwtMw/hnbNU+jFMfZaTeoKnJg8D0hVTWEIIDAo4HQHkr90Pf7uLiae+AcDACZmB8dN4rTDe8hoS/VUCTRqqS+GFbw3ylT/ax7c/e/Syx38lbFUHIknSRxo/PytJ0mcufb3qI/spsjk2+jIyYShCJb8QgfgjTTjdnga81n4AOj1OqpbFTMNZpBr54IQh+O0HjmBeQc56NZuPQK6QwgJodqqNGoj90L9cDog+VUafLOPblmjsLuFt9AYJBDYiy/bk6L0mhuxzULpMMf1qbLyuYQrocjtpnYtAAt2w5nY7CqkXbQ6IKwS+OKX9kyAEtfYFJxFuacPZ5if6no0YmSrpfz6JVbcn+am6jqY4CBUyhBoBTXjUTpO41q9DDrVzx+wYkmURHRtlwzs/gNu/lCSXCLiRNYuinMA0S5RKDT5DuItKMAjuMmOz9gTXpNfQSw4kyUVlhQgk3OzF1C1y47bIpj/cjxJ04qwkqdQG7WZYsOBAwC6k50bo2WZrkg0eOciJx59FWHn6b7x71Wtbd0tEhMId/+13mdz+Do713o3T4SDmC3FN1eTGO+3WsLF1iyG8DSmcwkkCz3+Ksgq+Rnor2txBuVJd7kAmj8GFx9Fy9kRdi59Hki1yuRYcVisXchdweb2YLpPQxVsQQmdiwp48j88ep7seQ1YchJpbIFMlawgkATsUNxMTE3g8HsLhMNMz3yWb3U9zspmCVKU6XcTnctAesWHDdhOpRhfCRuqvqbWdUhnadZ3UhVHqg3nUeAkrP4Koy0v6nFxqKyGwAMbGvoLb1UpL4i72TxzAoUau6EAMowiShdNlPz85PcFz3x8CFLb2OVl7+DOE70vgT29DCabxKzr3f2Q77/mfu9n9lrW09b/67ZIuF4HMFc4PAodWeP2nNWyuN/pKrW1L2YUIZK4HyERNn4fPdnvsm2OOkV5poG0cSAyeSfGn3/3x8AvTdR0ZiF0BhQV2Cmta01EbDsQfjrwsDkj5yAzIEp4tC07H1+gNslhAUVJlfDuS1E6lV0wbXa3NgQ46PU6iqoJblhivaXDr70M1Awc+Z3NAYmsRpqB8YBJ3fwRXg0QmKw6CDaFN95ow0XetRxsrMvu5Y+hTZQYb30UonyJYt6+fZ9he1br6+iDcybsvfIV3f/Pvuc41yj133rRsjMmQC7NqkBX2Z86nsSSJdKc9uczq9jVqqlcACY+rm3JlpRSWPclWynZ04vWuRQm6cJZbqJtTmLlGb4vgIl5LuAuywwSaYsS7e7l45CDHHvs2khxk/Z4FhYPcdweZ+ouDpB84TeGJUdS6ThMSrUE/7v6tTDjXEvaFUbwtbOj6ZWJnbM0lNeadP8acA3HLRfqMs7Q26RTy9nvhaBt1IZbJ17Pvb0H1oUXeAJgUjaexLIlCPk41F+VC7gIFrYAa9+IrdxEO7mJ84gEsy+BY6hjJaoBoWzsUDBRDoAdUiir0VqT5AjrAwMDHOHfuf9Dc2QISzIzbQIC+hB+vU6Ej4l1oY9sAHzS1tZPJVdlU0+g704zkVhD1c5gF21HXBiaWfUdzNudAFtdAyuXzZLPP09b2s9zc8Tq6Ul0UCuKKDqTWUBN3qRIXazt4cOZPqBpVmlwa6w7/PpIi4du+hs473gXAhp4E5dMzBJrcbHt9J9fd1XXZ478StqoDEUJ8W5IkBbhGCPHFS1+v+sh+ykwJrswF0WtVtFp1HsILdnQw50C6PPYKeqhBJrQyNdLYCJ5fWJPgfz97kS/vG3rZ45nSdOJOB8pVsNmTLhVDQNllTwovB4ElLEH1yAzudREU/yLdroYDCV2iwOu7PgkCqsd/fMz6cONadXlcSJJEq8vJRF2H9h2w9k54/rMwcwqifVRPpLCKOv7drfPQ6nBzElleIIJ5NsWI/vxGzFyd6c8e4eRRO0KK5NKodQVJuHnxsUNUowkeH61QdCcZHEvTmR9jU5e0oqR3c8CNUTFI6RJOZ5zcojpIOiTjrVpI3dsACBTsRYbXt2bFCCSS9OKWQFfHkHDg8XTaEUjZholWSmfBGwWnd9FOXTa72tDo3baDsTMnyYydQ3Fto6khnGhpJuV9k2AJtLEShe8PcVvO4K6QSuYvDvPzR4v8c82DJwMlYWEWJgjclqT5N69DjS981pwEfNXhJEuQPscpsg0NK9kfAEkmsljGpDABJ74B170bzXczqjxKevI7lGf9WJYK+V50y+CXvv9LOFrtwnvAvJ1abZxzE98iU8vgyZpEO7rmkXRys5eTioEnrzEzM0Nrayu12ji6nqVYOklT3P6+Z6bthcAHblnDx9640VYFXsQBAWhq7UDXTa7Lxdme24iyPYI+chE0m9NVfGJp07fFNtdIanEEMjb2FSTJSWvr29mZ3EmylqRec1GtXh4oUxu3HZVl6nwv91GCMQ+ykqFjx43UCw6cvjrS936bULwHRcQoxA+T/fIAleOzPD/xPM9PPH/Z478SdtkaiLATt9svt81/mm1yYAU2emPCyk6MUy3kCSdbMYVgZpED6XA7kViIQNxFnWOKheRSuCse4o4NCT7+yEmeOLP6zVZ4YpTZ/318yXtTV0EinLO5sWQVe7W9EgKrPpin8KNhCk+OUnxmnNK+CcoHpig+PoJZ0PBuW7pPJLILVW0iHNm15H1H1IMSdKKNXplEtZoNV+s4JGhtjLvVpdoRCMCtv2f3Vi/PQmwtpecncMQ8uPoi89DqSOtyBrpnU5TmD12HZ2OUgaEcLlPQqqlIpozHbMU7PsRRNc77v3SQv3mhwkgxwNpQhvAqkvfNITdoJmndwB/cMR+BmGaNrJIimq5jJhI4tRoTL9oaSYFAP7X6xAJvpGFuv0rc50DzTeJRO5FlB5JDxi3sSapSHVmavoLGalpAfpSerTtACGTFRbB5O6qroeB6LovQLcI/00fLR3aS/NgNfEKqcaxiYiS9VCJOPkONwIY2So4a1f1/h6tdR00uRSLNRSBHjARnOt9JuLiPWoNhX2s4V4e+KOI88DkQFuL6X0Wb1JE7oKyWKE7aTsZjNLPH/zsM5Yf4UumbABiDbTidcUZGv4xTlzALFWKd3VQvFjCFwEx6OaUamGoJy7JoaWmhUFxo52uaL6EgM5uzFy67eqO88/qGgnB2yE53euz7Y66Qfk3pHizJZLAvhTY0hHtjN8KsUzuzegQyWhwl6AwSdNqOzzCKTE49RHPzvTidUdyKm4geQdfd1OtL+xWVc1mef/BfMLSG1lgDlptOKQgUdt+fQK9Vad58A5rViqu3Gw5/CekfbiIo91OLnsGIaWQeOMNLjz7D3x39u1XH+UrZ1aCwjkiS9IgkSe/+TxgvFAyTmrlcWsERdWOkqkvJhCFbQ2euQVSkpZVZzcAUC+golyzT6lLtQrpuEtAEZZ+K2uLDmCzz1+/cxoaWIP/tgcOcmlgqAJAu1fne8UkuPDtKZTC3BN00Xb+yjMmczW03bQhCzUla1vYv+b8QgszXByj8aITCo0PkvzNI7uELZB86R+FHI8g+Fc+GpSzjUGgbN+99EbdrOdvb2RH4yRxITaPD7ZyPrlrdqh2BALRth347x6+xHm2kiO+GFiRZmnfoq0mYKH4n4Xet51jSSVvZ4u629xLovZPH7/wsbcVZ7rpvD//2a7vp9vmRENwUGSQSW5nN3hx0I9UtO5b0X0+tNk6tPkU29wIWBtGsRkGVCZYLTJ09g9Pjxe+3C9uVyuCSY0mSRLNfpe6bwBdcKH57GhLqFXNmgQMyZ+HG5JgbpqVvHYFYHH90J00tC6mk6ok0steBq8euT4xWNJ60NC5qFqnOINO3tfF1NJSmELploasq+tRyslotV0SVKpwQ3Rjb30fImbHPW5HI6VWwTOqpxgKoXrJJn+vfiGElETWD2mYFJIniuB3VbEy4OH2xlX+48x847rZZ15nBSZrlXciVE2zJLRTQq0N58qag5neQVgRE7MintbWVYuE4kuTE5UqSzjxBkztEurICgCM7ZEdsjfsp2t6BS/YQFnt5PHiAl2rH0YaHcXZ3o/gFwvBQv7A8UoSlKrwAk1PfwjTLtLe/x/6obBbZlNE0D7qxVMrvxBM/ZN83/pXnv/GAfakytoOZmooTdU9RStttjBPtXWijYzhvvA/eZ5M+mw//CNkhmF6/D/f6Ju47u5u3TN72iiAeL2dX40CagDRwG/8J4+VnjpzjI2dHl72vJn2Iurmkf4EvYueLx043HMgiGfeWRdFBl8dGYhlpe18RduJs9aNPlvGqCv/nF3YS9Ki8759f5FtHxvn4wye466+eZvuf/Ijf+pfDRMoGigUzswsr12nNuCoILyzVw3rfp/+Rbfcs1aLSx0qYuTqRt/bR9sndtH7iRlr+cBfJ37ue5O/sIPnb25HUq++O7OwMYGZqmKUfT8JluFqny73QYbHN5WSqrmPMOe/bPwYtWymNdiA5ZXw77JRcIBqlbf1GerauHFRP5Kr87D+9wEnTwFAkJioXaO55A4V/OQ8WBDZt4NpWP9nRCdb40/hVDdm7cqEyGXQjNbggmrfRbCl/mHT6KWTZTbggmNQMko3L5vL55uHPK9VBQg4D3TuDL7BAjFQDIVQtSoXi8ggk0sh/50aQFYX3ffofEcqN833QhWFRPZ3GvSGKpNgT56mJAoYEzoBKfqZK1N9AF6p2wbns86FPLAdA1NIp3HKRY6KXpngroS12b25LgdlKBpewGD52xN746ANQy8PuD6KN2IuIkv8kwlRg1h7H+piLwdkyHrOPv3zDp9GERmk6g/6NR0CC3Q2hzWhbJ2K2StYUpFX7u3dHdSRLRTKcFIrHCfjXE4vdTjb7PLFQkIxVROjm0hOYcyAN84bCrI/uQpac7G/ez8XBo1jlMs6uLlx9SZRgG7mHv73sOoCdwpqrf1iWxdjYlwkENs+ncicbcjC67kKijmku8JBGTtioqYOPPMTk/8vee4dJeld3vp83Vk5dqatzT0/O0miUBhSREcEEc5EAL7ZZsC9gzLW9mLXXu97Hi+3rxddmbWMbFq/BcL1EE0SSCAIhhEajGU3OHae7q6pDdXflevP9463QPd0zGtnAvezVeR4986i6uurtN/y+v3PO93y/Fy+ild1sKb80wFBylrnxUSRFIWjaYNt4No3AwO3wrqfoHnktliZSXfgCwQcsvhV5mr5GyvV1/QnGizTeFxC243CpqvHI/Aolc+1NqGTctN7Idxbx1o53ppmBRLoz5Jr0z9WL+5BPZbKh0Wh6MahJP0omgKNbWEsN0mEv/+OXD1JuGPzmZ0/w+WMzpCNe3v/gNj73mr3IuA/eD0+5u0PdtikYJukbzEBSqoKA2zcRRWmdCnDt9CJIAr6dcQRFQvTKSEEVOeJBjvsQ/S9MdLE1FKXPXFsb63pxpa4z4Ov0W3q9KjYd5hnpXVi/+G1q5yr4b04jepv6UbLCm/7wgwzsXu+M+J1zczz4337AqWwRISDzuh3dnKw9zuWpL2EVFTw7X4dn61YuH3maeqXG3lhzJ+7b2MgnHfa0p9Gr8iCi6KW4coxC4QlisTuQ4tuYsVWGo+7u3xsI4vcNIgjSuj6IYztI4iwIDqo81H5diqio1QxVr70eQMK9rpBkk2Gk18FoWG0A0caLOA0L3+5O5nguV0QWBbrSfooLdRLNnpYmuLMdtXB4nTc6gLZSxCtUOGMP0R32ErznVxAxMK0GC/Vl0qkUsxfOspKbhcN/C30Hof9W9OkygkdipfEs2lKMdFhFwmQ4oKNKIp8/Ns2u+C5suUrMifFoIYBYhnhIQ/X58NkBBMuhIonM1DVUScQUS8hGkNHn5iiVThMK7yERvxfLqpHMrFAVNCq5VVmIbcPKlXb/A8AxbEaC+1nSzpPw11gedZ9fdWgIz1AcQQ1Qfuz7azxWACzbcmXcmxTeK5//LLXaGH29HePWfD6PKIosN2ndrVkQQ9eYvXie3fc+QCAa5emPfQpLdJ8PUw8x1F9lbmKU5OAw1pR7TT2b3Q0HnhDS6z5CYz6Glawy+8kH+VDmU8z9nINwHSXuH0e8SON9AbGgmxiOQ8N2+Or82lRY6Q6A4Or6tMIXCiOIIvVSkVA8iaJ6Ns5AvB4WdJNs07Qm2hdC6XHrwXrOvYl29oT5ynsO8cV338nJ//xzfPLf3sq779nMYL2zxXjuvJvytijBN5qByKJAUpXbE/Krw3Ec6qcX8G6OvmCguFYovSEQ+BeVsYqGybJpMejrZCCtXkh2lapx9UgeLIfgnRtLtq8O07J53xdO0hP18dFfuw0bGPF7CcW6mCqexMw/g7rl5VjVIKe+8yjhZIqhcHPn6N8YQCI+BdVyr82i6RAO72Nu/hvU61PE43dT7b6JJcnP9p4Mg6FdZLybEEUVn29wXQZiLtYxfS4DyKx1ym9S2INSTlPzyTjhq8pyouSCSpNh1LKxjTUBpH5mEUGV8G7uZFBnsyU2p4LtuZNWBlJxXCC52liqFY2KhiTrNKQwXQEVMbmZiL/KklnCsE227dsPgsC5L/13WJ6AO94DuNdfGNCp1cZYGpdJ3XQfnmKr2QAAIABJREFUfhrYV47wwK40jz43jvX5X8FrjhFQIsTLIdQxAV+yQbx/EKO5ARGTfqaW6gzEVApLi0T8cSbOnMKyKoRDe4jF7kAUvfhibmkwP7mqh1GZA7OxBkBqx+ZQ8HC+9Cy7bBFf3n3W1eEhlG73/Nl1mfqxtWTUudocpm3SF+rDMWzm7C8h6UFC2Y63TS6XI5FIYMru891ouKW97MXzWIbBllvv5GW/+h6kFQFbqYGt4HXqJHu9zE+MkR7ejDY6BoKAOrzWxlbQtiN6baaHtoAA/c981AXIn2BcLwNp6VC/SONtRqvOLgCfz6+tX4qqhBz3oa8CEEEU232QWFNWIa8ZKIJAXOnQa1tMrMuFKkvY9KXdgTxEASPb+bzNqRA3D8TWsH60qRLI7v9ns2VWajpzzeO80SY6rHUmXB3GbAVrWcO35/kVcm80RI+Ekg78iwDkSouB5e1kIK1hwtb1cSyb6uEcns1R9zw+TxyfXmGlZvDe+7fQ8LjncsTvIZRKUVcl6kf+Eacxx9IXLlO4OMne+x9EiDZ3/NfIQARBINM8rnnNIBK5GV13F4tE/G6yqZsBGLBNbk28km3mzVhlHb9/07ppdH26jBbI4TgC9aVO076VgViygH7VHArQpvJCR0srmva7zLlzBbzbY2tKj+eyJXb2hImm/NTLBl4HVEmkoAnIsky9q2vjHkgdDFkiHfG0s9dIb4J5wZ2G3rRlKwO79nLuyFGcyABsfzWOaWPkqzT6XM+W8rSP5I4D+P0BaoVZ3pU+z8es/4h47iv4h/oIyFGidgxlTESJmCT7QugzZQzHIdAfZGqpxkjQxHEcNm0dpN5wl69weC+S5CUWuwNTdDWj5mZXyelcxcByLIfyk7PoQZ2ZSo7tZY2eJQdHkVEymTaBQEoMUXxkbRlr9QxIZXSCSvIEgdnbKH19pj2omsvlEOp+wtN7AFgouKB25cxJREmib8cuRg7cyvDATejyCqbmZVB9jqITQq/XSW/ajD4+htLbi+j1rvl+n3ITjg0rQ+7fMtB7O4g3Xlr+l8T1Pv3h5r/RF2m8bmSb5adXJ6McLlbXuQkqmcCaEhZ0RBWjTQpvTjNIe2TEVWWi1m56tqEzg81gPICgiCgp35qM5upwbAd9qoS3OTAUceDb5+bapZznU+JdHRmP0gae1VE/s+jOeOzcWIr7XxqtRvoLbfK1ZF8GfSpHJpb4rc+eYGLaJRfMNMGlcWEZq6QTvOP5sw+Axy/MI4sCL9mSYLzmXtNNfg/h7h4aioxjm4i+C1iGwZ2p17Hrrvs7TWrftYe1MgEvou2woJtEI27fxe8fxucbYDa2HYDYyVlEUUJEovTtKQKBzdTrk9h251roM2X0cA6zFqc419lRurMgbhO/Km9gaRod6GQg83UkWSTY5UWfLGFXDHy7O5uChbLGfFljZyZMJOn2PEqLDeJBlaWqQSQSoRYKYuauKmFVCzRMHyVJpTvcWdAiAxkWhQaiI5CMd7FrzwjFusBs/8Mgye59bTlUgqcRCFAveEgNbcKfHKQqhtn95LsZFuf4UPIDKHvuRBFVKo6MMNVkCkZnqU+WWDEduvpCTC/VyMhuD/GmO7bh7ZoEx9MeaE0k7kM3soR8FRYKq9hPbQBxd/P1s4tYSw3Y7Z6D+GKFniWBaiqEIEmIfgUxrOLZcoDSo49ia5or3Lk4ysylrwHQ/8SHmHzk90C0uHy6jF03KH59nHK5TLVapT4nQ8nty03kTwIugHRv3obqczc8SX8fDXkZs2HR7znKXNF9TtKbNqONjaOOrLLxbZ3zxCCVnB+pdoaAEiB2z++vvyd+zHE9ADkgCMIg8G8FQYgJgtC1+r+f+JH9fzCyDfchfe9gqpmFrPU4VroDWIUGttaZVG0zf1ozIJpBZpXPObg9EIB5bLKCQyrkAoqSCWJkO32CHy6XOVXuNN2MuRqOZuHb2QUCDHpUHjubb5eibrSEBS4Tq91DaIbjONROL+IZiWB7JPQNjH2+ubDCm0+O8Z1C6QWBgdofwqmbmIsvTLOnlYEkRInf/MxxvnR8lnd94iii6fCdiUWKNYPaqQVEv4x3+41N4j5+fp6DQ12EvQrjdY2YLNGlyISTKWxRRJdE1C09HFv5NnFPBvNHKxBtsp6uUcICl8or6TbzupuBCIJEPO6aeM4E3N+PXnTw35wieEeG6rN5PHofjmNSr19pf44+XcaI5LG1XpZXbVCkiIpaczPbmrOB33Zs0KUz6zVW5mpEUj5EUaB+dhFkAe+2zrGfy7kgvLMnTCTlLp7FhTrxoEqhohGJRKiqKsb8PI7V6f852eNoToA8ftKrASTpY0WsEHN8yBe/ypb6D1BEizN5997WZ8o4OJTsYzi1XmSPl2h3hkAoTC3QB4OH+Nz+T/DXM5soNbNCM5SkWg5jmwKyOoG1UGPFcphxTCqaScSpEAgE6O5PEu6ZQS8PUv3al6g+8W0S8XsA6E0uslheVT1YngSEdg+penQOKeohctC9PtXlOgNFhXxXZ6lUugNIkT7scpnK974HH74FPnyA6ROfQHYcfE+eozg0j1ROkcuVmMk+Qe25ea4cc7MtoR5Axr1uheVJGtUKc2Oj7d6c3TCxChqO38JsOCxU5phbrCEpCl2ZXvSJCTwjHTJF+5yn0pSmgvhZYVc4/a92NL2RuB6AfAR4FNjO+vLVtSdp/heOrKbjEQV2B328JBbk8/mlNYtmp5HeWeTbw2tN6mheN9Yt7DFFJiKJzKsCFb/kDjcBSk8Aq6RjVXRsx+HXzk7ygbFO/Vafch96z3AE0S+zO+bnB5cXma5pSAJrymTPF90ehSVjLUXZyFWxCg38e5K88/9+jrd87PA6aZVPZgt8b6nMvzk1zoPHLvGtxeINAYk60Gykv8Ay1lRzgf/od0fJlRp8+ldv5y/ftB+v6XAkX+KuP/kOxdML1IfDCBsM+F0dsyt1Ls6V2x4PYzWNTf6mvWrc3aE3VJlZ0WaicBJ7m0LlqSz1erMRf40SFkA65MFuWMzrJooS4cDNn2XT8Hvd77UVRMchUXcI39tP+P4BRJ+M/WxTVLGpieWYNnqujKZmkRlsG0uBm4HIjRiiJVFrTK4/gOiQ++/KFVbmasTSfrendaaAd0sM0dMZpmxRxHdlIoQTLoCszNdIBD0sVnSi0SgVQQDTxFzs6EFpk6cAkVEzSCbSAZBw0ktZqhC3IziP/wnKpUfYOpLk0rNHMBoN9OkyVmIJzchTyQZJDgwhihJ+v5+aIcDbvsH9L70Lx4HvZpuDlmqM+f5+avM+dHkOwYZly+Gvj07S3+VD1VeaE+g2cnCSSr6fyx/8O668673oj58gGNhGNDFDQVtFeV+ZcgkHsgezqLmK0jeniKYziKJAoSqSKBiMBqvt31G6/Vg1ASmZovjFz8HSOBx8BzPbfo6bq2myFxW05DTW5DC9vhIn9Oewq/NM/MBtxifiSV7ymt2YhopZW2Lm3Bkcx2awCSD6TAUcMKQGWGGOLGYYO3uR5OAw9twcjq7j2SgDSaYpTrnP1b7nFw3+scT1JtH/ynGcHcA/OI6zyXGc4VX/rT/6/x9EVnMHAAVB4KHuLqYaOkeKnR1hG0Byq5lY7gIT6+7BcZz2Z1wd/bLCrE/EinSaw0om2P68E+UaS4bFaK1TNtOnSohBBanLixhQGfKq6KbNqYUKaVVZUyZ7vmgbS63KQuqnF0EEdUcXh8cLHJ1a5n8+M9X+uWE7PFOs8ks9cf5iWz/LhsUvnZ7g5ccu8djzAImc8iOo0gsGkCsNnYQk8Y9PT/JLtw9yx0ic1+7v5Y6eKJsGIvzGUArVhvefneb4lQ125VfF480BzXubADJeXw0grtxJXZG5MHqBSLqbvl+8BaU/xNK57Zi3/wmErm093B3x4jSsdmkwErkJWXYf8OlKg2TDJux7rs1kC98/gHDR/Xmt6tbGjVwVQ13AEXR8vhGK83WsJsgLXglRMPFo0XWzI0CbmmosTFFcqBPLBNyeVlFbU74CNwPpjfqI+BVUr4w/rFCcmSce8LQzkJplYYniGiZWY9rV+Co48poMRPJZGKJBwgnhLLkEgF2v+RWMRp3Lzz6NPlNBG3J7PXNndJKDbgnJ7/fTaDSwLIuBuJ87NsX51AW3ZxGQI8yaGo1ZDzVfFVvSKHllzi5UeN/LRlhcXKSnp4dqdRRooC0PkQ0dQMBh9n2/Q7DQhxK4giFVqZSamf3yZLv/UXtuDhwIHEgjyTLRWIhC3Y9k2kxF9XaPQ0kHwHQIP/gGKj86gqkJsPdhFspF3vHpJbS73L5ncTLGvliOmmOyNPtNFo0SXsvH7jsH2HprN4YeQHE0pk6fQPZ4yGx1RUdb0/WWWCHm78IjWazMzXUa6IC6aQMASXWjl1SWqzKD4r9OsPRG40ZovO/6aRzIz0JkG0ZbvO+ViQh+SVxTxpKiHgSvhJHrlJ0Gdu+lf9deot3dlC2bmmVvWFoacARm/CJqs3wAqwApW+XxgntT5TSDapNCrE2V8AyGEQQBKagQdgQSQZXRcv2GKbytyKyaBYEW+2oRz6YoVxo6Fc0koEp88NGLzJfdWvOJco2aZXN3V4i39MR56rYdfGh7PyXT4pdPT3DPsxf57QtX+PDUHN9cWOFitYHWZIUIooDaF3zBADJZ15jPV+gOe/mdB7e3X+/1KizZFq/3+hCCCqOqwKcOT13nk9z43oV5BuN+RpIBqqZFTjMY8a3NQJZScWYvX2Dv/Q8iqjLxN28HUaJw+U6ul2ylmrMg8/r6/sTUfIVMwyFk/X3bjjdwewa1qwtZj1OtuBmIfqWEHnCzznBkC7btUF50z78gCEjiMp5GN7XqxPoDaGo7LYzO4dgOqaFws6cFvh1rM6ez2SI7ezp+HRE5T/HMUXp9GosVvS2GWAv41zCxGjn3HNcFh+5VGUi54ZaJ4nYYO7gZ9j5E3y33EE6mOf/972Mu1KjETqHIScpzJqkhd0H0N/XY6nX3nDx0sI/LyzVsRyMiRbAdG2dKARHKkVHOmzo3D0S5KSHgOE5zAt1VZQibEeZTt5A6UCGwJYHx4SdAsInFsuQnmwKUTQBxHIfa0TnU4Qhy3H0Gu9JJljT3eHIxOFNwPdJbjXTfzXeBaVGe9uHEt/Lgpy4RWm5Qv83At7QNOxRlOG65hmD37GDeWaHbCTEy4EPxSFh2AI9aY/TEUfq270KS3WdQny5j+WVEpUpMaXDfiPuMZLZsQx93AcQzMrLucnuDQRSfj1zeR8DKYhg/eefxn2yL/n+xyGp6mzIakCVelYzwyMIy9daOUBBQugNrMpCB3ft46A/+BElWNqTwtiJVc8j6BIKrZCKkgIIU8aDnKjy+VGpfrLG65pa2lhqoQ+5DL4ZUnKrBAzu7KRgmyRdQvgLagNM6RnOuhrlYx7cnwekmvfj/euM+NNPmA19zBR6fWi4jAHc0rXkVUeDNmTg/vHUHf7l9gC5F4tuFEn80nuNtZya5+8gFhp44xe2Hz3GyXEPtD2HkqjjGjVENLcdhqqZTWdb4wGt3r3GG62mW4JYvLePfk+DVN/XwjdM5ivUNmsvNqOsWT40ucu+2FIIgMFFvNdDdhdAfjiBKMldCPkRJZvc9LwNA7vISefkQxmzluj2c7uY0esmy28AJYFV0srpBr2SiCDMw755PQRKJvGoTarmb8sIFwC1nGF1ulhTvdi1k230Q20Jy5lBrfdQbM1jWVQKVwRTIXuaaZkipwRD1MwU8m9ZSsmu6ycRilV0tAKkWiDROUzRS3FL9AbplozSl/qv+QNtYiso8WqWBIBps6TlKuPFHVKpunT8/lwcHupwgzhv/GX7+LxFEkV1330d1dAFLqlIUjuAVbgYEkoNrAaRWc0t1D+7KEPLI6LUlIqoLeuq4AI7AcugyM7bJ779qZ9sD3Z1AP4MkBelbOkPdl6Sy9dX0HZyka+AuhJpEV3yW/JWsC9zlHMQG0adKmIVGe+gUoKunl6LtxQYWEypnF90SlMuQBMQonpSf4kyU7Mc/yb5LOtPvugVNySLP7CY62Id38Cb6IwZjE6PUZIMuy0/pH5/BsR08gQSK2qBYLK2ZTTKmy6xgIikaQbPI9pEu3vLHf872Q3ejjY0jJ5NI1zDnUrvCLE8HELApLD2x4Xt+nPEigNxgWI5DXjfaAALwULqLkmnz2GKx/ZrLxKqtkTRpRf46AJJc0TFFAX/Ct+Z1pSfA/FyV46Uar2ya+IzVNLSmC5s66N5IUkDBKuu8Ync3liphXcc6dqO4OgOpnVoAwdWIOjVTxKuIPLAzzbvvHeGrJ7P84NICT61U2Bn00nUVWMmiwMOZLr500xZOH9rNpZfu4dEDW/nbnYP89lCaqbrO44WSO1BoOejZGxsofHp2BVuAvV0BXrZzreBjT5PWOy87+PcledPBARqGzSMnr61b9PT4Ipppd/ofTQDZ3CxhCaJIOJHEti0233oH/iYlGzrn3bjOsafDnrY3+uIqb5fikzPMeQSGepvU23xHx8y7LYZPHqJuTGJWdPTpMmZyAUWJk+xxG68tSi7lPBKLKNV+wKZen1x7AIIA0QHm5mRCcS9qwyUtXF2+upAv4ziwM9NclI79AxFxlprdxbb8YwDYcnNhj0Yxc3kcx6E0+RVy2ypsfs37eOimT2BUHmNq8u8Al67qF4MoSNiOz/UoAXbedT9dnm7K6Wdx0ClN9oIgkBwYAtYDiE+V+Pn9PdjFPAFP01u9IqFW+mjELtM/HOHAYIxcLkcwGCQcDrsT6L4Reha+jWCbTMVeh2iu0P+OuwgWeumKZZk9cQJWmooSsSGqR+cQVGkNXb2rfwQHgXrIR/fAjnYGIigictyHMVcjvNmhnofShz/CkzsFlNu8CLZMeTxKon8Q+m9lxHOFwopbUgrKJjgRFv7u66QSm1CUBrbHR99OV63AKrqbw1zVzeDkWhlCGTKbtyHJMtr4GOoG2Ucr7LAHYzaAJEdZXHz8mu/7ccXPHIAIgvCgIAgXBUEYFQThd39a3zuvG1hOZ6ECOBQL0utR1pSx1EzQnSBfJWnSitYU+kYA0l1wfyYE1v5MyQR4Ch0HeHtfEgEYrTXQp8ogi6jNgUMxpOBoFvt6I6CKLCyut2pthV0zmP/ISRqXOscdkSV8otBmYtXPLOIZjiAFVU7PrrCrJ4Isibzz7hGGEwF+/5EzHClWuTO6wfzBVRGWJfaH/fxCOsbvDGfo96pcrDZeUCPdth3+y3fdevu7bl0vU93bPKfzcRV1IMzu3jA7M2E+c+TKuve24vEL8/hVids2uTvbFoV3aNWQYquMtff+l6/5XSXpA0lYM/dzdbT0sKAz3GlVDa4cy2OKAv3daVBDawBEEARi2/Zjyw0Wv3nENeAKZAkENuPxK/jDKsutRnpxBkkoIK+4BI1abeMy1txKjPRwmPqZgrspuIqS3Wqg7+wJu/a4R/6eYMYFaM/iFfqEBWq4vb9GKs6872mOPPtqnp3/U6q9y1Ryu/mrI79OJvMW5he+iWGskM/niTYZalZtlQ9LupvexDZWMk9iVDKc+848se4elOZMQwtAqtXOeX14SwipkkcWg3T19JMJD+Ff3gKxUd76gMuWymaz9PT0YNs6lco5wnUZsdIgVhpjZikGia0Ixz9B/8v+DxS1QUUcZfEjHwXADg5SP7WIb28CUe0QC7qG3RJpIxFiV3I35wrnsGx3Q6B0BzDyFSKpWXeAeLCbv3+FgFR5jsDCPubL8yT6B6DvIJtDBWyv+3cd+O3/DUebRZv04y9FURQd2+unVnLBu/UsFAX371cqRQi7GwfHcdBHx/Bs0P9oRT3gEKwppFOvRPgpLO8/UwDSlJf/G+AVwE7gzYIg7PxpfHeuSeFdnYGIgsAb0jG+v1Tio4cnefRMfsNGeitau/uN+hODTQCpyWsb32pPkKcSMl2iyG2RAP1etZmBlFD7ggjNIcKWlHqh4gLXxEwRYwPRRwA9V0WfLLH4ybNtEBEEgXTTmdCYq2LOu+Ury3Y4M1tiT9Oe1qtI/NHrdjNlmWi2w6Fo6EZO35rYGvBysdpACnuQIjemzPuZZ6c5V3IXzn1d60Er07yVl0bCCKKAIAi8+dZ+zmZLnJktrnu/4zh878IChzYn8MjuojFW0+j1KPhXsbdSwyMkhzYxsGvvmt8XZBEl5b/unI5XkQg3iQwLTWCu/HCWrOxmp30+D3TvXgMgAOGMe0sXJ07j4NAQrhBo6mTFuv2stEpYxWkkoYBaacq6b9BIr/q2UjGipJv9D3UgjBReSyM/my0R8Sn0Rn1w7stQyRPYd597vFaC14k/ZLlmEgqFEPcvMr/3DIKgsK04SOBHryP3zK+SNfbS3/cWbFtn6srnKJVKJLrczE5bWVtaC4VktK4xlkd3YuqLBOMdGZarMxCAzVoBp1ZAROSt//m/4Ultw7eyFUHR6FN/hKZpLCwskMlkqFYvY9s64VwW3ewibs+xlK3S2P0OmD1KwkniOAJKT5aFz38L24J6rgtHtwgcWJvVdvU3Z0PCHnbFd1E360wUXZBWugNYSxqSBwb+4Jc5+fuvYzDsYDsrhHK3s9CYJt4/CH23IIpBbF8XomUTiUUJPRDHWhrFPOk+n1LEw6kn3Aa9S28GM+CWHRXdaPu8mPPzribX5mtnIEueOrIt0J/+LXbt+vNrvu/HFT9TAALcCow6jjPuOI4OfAZYb+78E4hZbT2AXJ4rkz9XwAI+cHyK93/hJGLS58p0bLCwZDWDLkXCexW91K6b9JdtRNth9qqGq9Tt53Bc4iWCiigIjPg9jFYbGLMVPEOdOqjYzFxyRRdAGhWDw+Mb229aTTMnKai6IHLRTZe7VRdA6qcX3Z3q7gRjCxXqhsXevo6j3KHNCbbuTIDjkPoXuO5uC3gZq2mYtnNDyrxzpQb/5zfP09sTQoI2kWF1REfdzyhkOiXA1+zvxSOLfHqDLOTSXIXZlTr3b+9Mdq9mYLXi7re+nV/8479A2GCiV+kJXreEBa7OGLgyOHbNoPKjLEtb3HPZ61Ggew/MnVkjOeEPuBx/PZrHUotYTplAcyAu2h1gOV9zGW7NDES0fKhykuoGADJnuOq9qaCFkauu0b5qxblciZ2ZsKuo9vTfQGIroV23A1CM3s7rpR+yUNaIRv34R0bxjnm49eCX6RvPostbMCVIRz2EQjsIh/aSzX4WcOjpc2efaqv8ua2KTrXrsPvZ53Qcu4jZ6GxCNgIQY2ICu+oKC06MLlHz9SIsDgFQyj3K7KzbEO/r66NUcsE4NHUeQw+RCrv3etb3cpB9KMc/h1DbRDQ+Q1VWaRRD1M7WkePedj+xFaos4zFMKorAgfQBREHkC5ddV8SWpInhDBC45xVMyCvcERKRrABycQueSABfMATeCBfEh7C8AYR6ierKMqFDt1I//NcITtOIKwSFS0WW81X0K2VKDiRHmjL4puPaEwN6UwHYs+naAJJX3FJZcX7umu/5ccbPGoD0AqulcGear7VDEIRfEwThqCAIRxcW1urt/2uiVX5KyjJfPZnl4Y8+zQMf+gGPHp4hbkB0a5RSw2S8WEdObDxBnr+GxLq5WEcCQrrTNktqxVnZYdkj8pKyu2vd7PcwXtNwbKddhweQQu6imq+6D4zPgm+eWS87YVg23z3i7nbGHuhFSflZ/NQ5GheXyDTlTGqnF1GHwkghlVPNBvpqAAHwZQLIFZMPfvXcC54m3xbwojsOkw0NtT/8vMq8f/GtS2imzdbhKL1eFWUDgTjr9CJxwyHn6fws4lN41Z4Mj5zIrvOXv5q+6ziOOwPiWwsggiAgyRsTEpRMALtirPOBWR29TUCa1w3KP5zF0SyWt7u9lD6v6gKIXoGVyfbvtDzlhZ1VxIPu9WyBSiztR6uZnJtYgeIMoqfpIyMObFjCmqt0I2ISmHOfBd+utf0P07K5kCu5DfQrhyF3Am5/F4EmE6kaP8SImEPJP0cqdQFZbRD4io2zNA3lHA05jSbSnkLv6XkYw5gkFFpkaJtbamwsdzIQbaZMsedHaHPdVJtqs8XFYJuaLMsyHo9nDYBoExPYhrswfv7xMVRvmkolBvUgK5VTzMw0JUT6+iiVTyELXnx1E2NFJ9nrRVZEZid12PMGOPV5QtYBgsFliv0BKpVtaONF/AfWD97pM7MEGzplBPpCfbxx6xv5zIXPMLYy1mZimc4wJLaSL0+y06MRzB+koC242QeuWsTZ8h3YCkj1GuPPPYsUieDduYP86LPuF3mq3B5yuPyNSbTpMku6RWKgOQtm2BB2gVgbczcIG82AgHsPTwkucJTm1z/7P4n4WQOQjQYb1qxejuP8d8dxbnEc55Zk8sZ9vZ8vZjUDryjwnk8e4zc+fZxssc7vvmI7T//effy7nb0sig52SObZyaUNJU2gCSAb9D/MgrtDiyIweZU8yneXywgO3Dbrvj7i91JzHOY9AurAqgwk2GyC19zF7K6BLr51dm7N4F++2OAtHzvMxOQKJRy+PlUg+Y49bRBJVq1mCauGv9loPT2zQkCVGE50ykYNy+ZUtc6hWJDD40t88bnZGz6PVc3kE4+5vYxL1QZqf1M08jrKvM9OLnHvtiQFx27rhq0Oq2qgjS6TkeR1el5vunWAsmbyjdNrH6jHL8yxqyfcnl1YMiyKpsXIVRnI9eJ65cpWZEIeRNNmvuFmH95dcXIKhGWRkCy5AALr+iAB/wiaP4t4k5tRdjIQd+f7a397mLHRC0jNuSGv3U+tNr4OzOcLAeLyFJWLZYS0H7lrrX7SxGIVzbTd/sfhv3WlWfa+CUWV8AYUaupmGigMZr+C1/cDiitplDER8+wPANCEKFU6FN50+tU4jsrg4BWS/TEMx8Eode7ppSvPYgTyVC90fE0sJ8XshU4/zu/3rwEQfXwCNRXCAQJLGkFPiCVHRq13UxSXmJmZJpFI4PP5KJfOEG6o2N4LFAW7AAAgAElEQVQ+rFIFb38v3SMRZi+twC1vB6NKT8Mt+TUOqjTsO0AA/83rXTj1qUkCmkHRFHEch1/f/+v4FT//9ch/RYx6EEQDQ90Lig+vdglFsAln72C6cN7tfwCzl1dYNhwQIKiIjB51s6/A7bezMOfe84raYEku0X2xAIbNiuUQ7W72WlZlINr4GGI4jJTYWJdusb7Ioureiy9mIBvHDLDaOacPuDbN5scY2YZBUpZ5dmKJ99y7mSfedy/vvHuEeNDDa1MxFEFAHQpzdHK5WR9tYDfW7npzurFh+aU+V8XGIakqbb/vVjy+VGKPLRKcqeLYTpshNNPrQ1rVcJdaAKK7Yo0/vyPNYkXj2JT7YD41usir/upJzmZL3N8bpeER+cGlRQSf7IJIOkDg+CKa41BSaDN1Ts0W2dUbQVq16z9aqqLZDm/f3sNNA1H+9NELN5yFnJxe4ewlt2R2sdroKPNe2ZizXtNNJgpVdmTCTNX1NT4g7fN3ZhFs6At7mW2sBZCDQzE2JQJrmukrNZ1jU8tt9hXQ9kFvUXhvJNQ2gFwb/FrDhLliHadh4d+fZKah09e6D5I7QJDW9UH8gc1Uq6NUa6NIUhBP05irpaabckS0whXGdAkE8Gg9mGYJw+iULR3bYT5nk1HGsZcU/mFumbd87DCfOXKFleZGoyVhsi+4Ahe+Bgfe1rbGDcQ8VMoOh+XbSKrfRxCKTE3tpeH10jj+FAgiNcNLxbHbGYgsB1lZ3kI0dhnHqWIJAmalc02yS4+ApdDz5CLBaAwVARmFy8c6jpvrAWQcdXgIKyBzN242uGw5hJxhNBXm82fp6+vDsjQq1YuE5hcwEi8FQOnrp3drlEK2QiO6BzL76Zo5hlYPIu1apHCwwMrNjzGz8nGmrnyMK9MfZ27+G+73Tk4RbOjojkh1eYmYN8av7/91ns49zROzTyBLWQxhM6ZtMiLN45hRfMtbmKtMtDOQ809lwecu6pu7/Vw5dQKj0cB/x+0s4J5nVanz+fgTFEwH23EQe4PQlHKXLQGCLrjpo2N4RkauKVEyXZ7GkhyUUIDiwosAslE8C2wRBGFYEAQVeBPwyE/ji3OajtqcV3jjLX1tuRGAuCpzfzyElfZypJmBwFpvEMN2WLyGyVM5W2Ueh6GAlxXTYsVwgaegmxwv1bjH68PRbcylBpuaC+hMZu1CJygSgkdi3jBJqTL370ijSiLfOJ3jr797mX/zP56hK6DyyHsOkUREiniYXakzsVhF9Csk376bTJNhtjwcQop4MC2bc9kSe3vXlq+eWq4gArfHgrzxQD8LZY3ppRvTtDqbLSFYDj7T4WK18bzKvBebFNNN6SAFw9wwA6mfWkBO+OiN+JjV9DVgJggCDx/s5+jUMqPz7nc8cWkB2+mUrwDGau5Of8R34xmI6FeQoh707LUzkFSTiTXXLC16BiPMajq9LTaf4oXUDrj0mCvK14xAYATDKFAsPkcg0Fk08oaBgcPL++MMKcs8s+yjIgsozUZ6dVUZ68pUEb1hE1MMBASGb0qTKzb43S+e5uAff4e3f+JZvnBsBlUWGRr/nyCIcPAd7d8PxTxUljWOhO8j3yfgYYBiMU0tHKZ+4gwkt1OrWjQEp53JNRoNpqb6EQSD/NxXcWQRu0kpr1dqVKNPoeR2MXxwF/e9493cPLSF5OJJxo/PYzW11lYDiKPr6DMzqJuG8af8JBBxgKLpEFe2N0/hDP39/VQq53Eck3BJQ/e6RASlr4+erTFwIHt5BQ6+HaX0LLXcHuRQhaUd32Iu/mnGxv+M0dE/5fLlP+LMmd+gVDqFPjlJuPmYL026WfND2x5iU2QTf/bsB5Hsixhaipnls2z1WASX7sCJiOh2g0T/IFrNYOz4Av6MjReNXbESpqEzeeo5yl1RdBQwJVSvRpElzoYkvlMyyexPYZgryI6MEExD02paG99YRLF9vcvuJimUTL2YgWwUjuOYwHuAx4DzwOccxzn70/jurGZQK+mMJAMMxtcLzdwfD1OXBKZ1g+Wge8FXlzbmdAOHjSm8xmKNaWx2Rdy6c6sP8sSyy8i4v9vlvxvZComijt90uBJb/zlSUGHOdifdgx6Zl25J8IkfTfLn377Ea/f18JX3HGJzKoRV1OjqdktHT15269CiX2Hrg+7NWTnglv4uz1fQTJs9V/U/frRSYW/IT1iW2uysM9n1TKeN4mzrfWWDS1V30VYHQujTlQ1nZ87n3EU/1OWem4GrAMQq62jjRXx7E/R5VaqWvc7s6w0H+pBFgc8ccdtn37swTzygsq+vM9cxXnN91vu96wHqeqFkAtctYXWHXW/0BcNC6vIihVVmG0YHQABe8luQPwXPfKT9UsDv9jzK5bPt8hXAl05mWZYcUraD3yoxsnkbVwyTqcvuPdkyozqfK/EH//AcACFvArB5y+t28Pi/u5uvvuclvO3QMOdyJZ68vMjNaRnp+Kdg5+sg0mkpBmNeKssNpD4NzSORWYgAAvqWLdTG5iGzH61qUBdol7Dy+TzlcgJFGSKb/Qx4JBzdwnEcTj7+z9hqhcDxELG3/hJbDt7B3gdeSSp/FL1uMX3OzUxXA4g+PQ2WhWd4GDnmfoeuCIh6iYCWRjBFIuH5Zv+jNYEewNDc86H295EeDCMpIrOXlmH3G5C9DYTJe/nRk29l5Ot/ze4zv8k9d5/j7rtOcejOHyKKXrK5L6BPTRHrcsvES5MX3estKrz/4PuZrsxwwp/DNhRmpr6IKEB8/CVUvW7mEO8b4NKROSzDxlQqZHwGffoZvIEgY0efYeaSOzwqVUWCQZuwHka9qUZDEBjel8A0isiW2C5fWSsrWIXCdRvo0+VpJEEi0d33IoBcKxzH+YbjOFsdxxlxHOePfxrfadoOec2gsFhbU/ZYHXfFXCaJHfdwrFBB8MprMpDcNRRyHcdBLroy7jcn3c9o9UEeL5ToUiQODMRcb5BcFeNKhYGqzeQGG2UxqDIvdKRSHjrYj0+R+OPX7+ZDD+/Hr8o4po1dMYik/AzG/Tx5uUM0yLT6ASn339PtBnpnoa1ZNs+VahyKuQC0tTuILAqc3oAqu1Gcbc4c6Csal1cxsZyG2e4FrY7zuRIhr0xDdbeCV5ew6qcXwQH/vuQ6X5BWJIIeHtiZ5ovHZ6nrFt+/tMDd25JrynJjdY0hnwf5BTq4KZkA5kJtvU1qM1rOhEuig2cwTMW0WDEt+lbfB7vfAFtfAd/9gCvMB/j9nZ1mq4Fu2w5fPj6LHFGpLrgL7KEDN5HoDiAuhbFshWJljC8+N8Pr//YpInUHySPiVwdRlCyiR0YQBPb0RfgPr9zBU//+Pv75XXfyNzvPgVaC29+95tiDXR60WoPt4UfQSwF6Lx4BQO/P0FgAM74HS7NpCE5bSNG1bBXoyTxMuXwWM34F2YHifJ1i6WtIeoiuYhTf7l0A+Pbvp2v5AqpkcfnoXPNv97fnQPQJN6NShze1+zdFRyBQncXMz2PWEkQi8ySTScrFkyiGg2foQYzZLGIohBSJICki3ZsibgaiBhBueoiEY2MLDsXGRRpHjiBJHmQ5gNebIZV8kLm5R2jMjBPpyaAIFkszk+3zcqj3EPeEt/DpiAt4jZUnWGx48ZV6WdRmiKTSKB4vZ5/MEu/zU1hepDsRRSpcYHjfPsaOHWHy1HEi/iBiwSTgM4kYEcbSx/jlP7mTWHcAwyyubaCPX7+BDjBdmqY70E0snaFcWMC2Nr4nf5zxMwcg/2/EvG5gA3bN5L7t65tt4Hp6DHpVhKSXo1PL63am15IxsWsmiumwIMPuqLtrulJ31Xe/t1Tm3q4wsiq53iDZCtpUiSHNYdxcz58VgwoLotOeM3n5rm7O/uHL+cXbBtslEKvkZjdSxMNLtyR4eqzQlmlvAc90sw9zanaFkEdmsKtjynS0WMVwHA41Bwg9ssTWdGjDWYuro65bjC1UODgUQ6y47o5TDa1jcbtBGet8rsSO7nDHSOqqDKR2agE57UdJB+ht9hVmGutZUQ8f7GepqvPBxy6wUjPWbARsx+Fspc7wCyhftULtCbrKqXMbD252h71EdZuaLGAMBplpsvn6VmcgggCv+nOQFHjkveA4+Hx9iKL7nlYGcni8QK7YYGhThNKyiekoEO5leDjGgOIhV03wvTNH+e3PnWRfX5TbIkEyQ2H0Wjcqp7lauEsUBQ70h4mf+Tj03wZ9a73ig1EPkaHDeMUFvjH2Mrx2FZ8i0gjIOLZAacXNjOtip4SVy+UIhUIMDj6MKHqodn8fRYDvf+YYcvoEodytdL3hFe3vkBMJPH09dNvTTJxcxNQtQqEQpmlSLpfRxlsAMoTUzEDmqiZhZwUzm2O50oc/UMRauUxp6RnCJQNh+6vRZ2dQ+jrzJb1boyzOVGhUDTjwNpK4mUIpZVI/eRK70Rn8zWTegGmWqXTn8GwaoctTY+kqH5Tf8Q4x6s1Sj4whME11cRsIMLVwlnj/IDPnlynMVhg8GMSyLDIDmwGHzYNRGpUyV06fYGDnbqQyyE4JxVY4lz1HIOreg4ZRRNH1DoCMutpo6gYy7q2YLk/TH+onnExjCSIrPwUm1osAcgPR2tH6bbhl6NoeE3d3hbC7PByZXEZtMrFaZZn8Bl7oQFtLyQirBGSJhCIzWdc4Wa5TMEzu63IXVyUTdAcAp0psUlVmGnpbg6sVelCmLAtrvkO8akdtNRkxLoAkqeoWzzVVaz2iyO2RAB+fXWReMzg9U2R3b2TNZzy1UkEW4LZIp4y3pzfC2ezz+4FcyJewHXjjgX6EZmP1YrVxTWVe23a4kC+zIxNiqq4TlkWicmdS2Cxq6JMl/HvdklvvNTIQgJduSdIb9fHxpyaRRIGXbukw9B6ZX2GyrvPaVHTd7z1frBa83CjiQQ/DTTwr9frbTf7eq0tlkV544L/A5JPw3D8iCFI7C2kNEX7x+Cwhj8ytN3cDAjPaXoj0IUU8yIZNT9dWujx5/ve7NvGJX7qFYq5GX8qHY8t4OA3NWYo1cekx12b29vWaqYGoTHzHN9DNzXx14V7Mri1EKFMV3c1Lccq9dx1FJNQ89/l8nu7ubhQlQir5CsrhHyDJGpXG4yCZhMa3En75/Wu+x3fTfhITT2BoFlNnC4w0pTouXbqEPj6OnEohBYOucoFPZk6ziHp1anNzZBebgpfj/0RVzxKuASP3YUzPoK4BkFV9kNR2MrESggOV/gSOYVA/caL93ljsdjxSmtodNurmbXSpNZYW1jqQDixN81oM8sNfwTY99GdfiZz2s5CbINE/yPFvT+GPqHgSzY3jjttAEBnyLSIp7rkavus+pIaKgJuVz8/P0zBdIDONJWTNgFCGE/Mn+NrjHwGvB6UpZ7NRTFemGQgNEEmlaWSG+KfPfu4FU+xfaLwIIDcQM80d+a3dkTV2slfHXbEQlihwrtHATHhxdNt1N8PNQDyiQGzVAggdAJGbGlhDPrWtFSUA9zRrsEpPALukYy7W2RLz48A6ym+h2XtJX2NuAVYNEUZU7hyJI4nCmjLWn23rp27bvP/iNOdy5XXzH08tl9kf8hNY9Xfs7g2zVNXJFtfLt6yOVvnqzs1xepvHeLHauKYy78xynYpmthlYA17PGgZK/Yy7IPr2uWCQUhVkYWMAkUSBN97iLii3DMaI+NyH2LAd/nQix86Al19I35gB1ZrPjXkRPFLbu36j791ruvfMclBhtpkd9W7QC+PAr8DQS+Fb/wlKWfz+EQRBxevtp65bfPN0jlfs6WbzviR+r86Z+oMQyrQnywejW0n7C/z7B0dYnnU3L4mmNIcqnm+7EwKwOAqP/gf48jsh0g/bf37d4Wjid1GDC2j1NwMihU2vJ2LkKFarKBGR0oVJAPxNBqBhGO2JcHBnQmyxTqP7WSJDh1EqaYL+rQhX3Z++/fsJTx3F65cYPTpPKpUiGo1y4cIF9ImJtve3kvTTePUIVRtiXQL5aoVyKQ42TK88CgKEQ3twFB/G7OyaDCQ95PZBspfceZLYr76deCzIsqqAJFF95pn2ewVBJK7dgr7NwR5J0eVpUC7X0RurSqzz53lr1wha8hTy7O1sLo3gJEVsy8ITSDN9fpm99/YxN59HURTiPYOQ2ok6/xwDu/chCCL9u/fiifThyA3AJqgFOVdwrXgNfQXFtPlkY5q3Pfo2pCt5VtKBDQdaAYpakaJWpD/Uj616sYIRUuHQT9xU6kUAuYE4vuAubA+OXN8X/CWxICJgdnkYxa0/tibS86u8RFaHsVDHwiHcHEwa8nmYbGg8vlRif8hPvGlL2/IGAdjaFL1b7Q0CsOh3L2fKufZNYxU7JayQV+HmgWi7kQ6wJeDld4a6ebRQopHwrGmgV02LE+Uah2Jr5Ut2tRrpz1PGWi2Zsbs7jKJZaxrpVyvztiimOzJhrjS0deUrbbyIFPeiNMFXEgTSameRvjreeEs/qizyit0dD49/yhWYrOv83qbMC/JPaYUgrldgvjr2aU05E9NkpqEjC9fwqxcEeM1fgWXA136bwf63s33bHyKKMt86l6eqW7z+pj4kSWRn72WmtJspLRtI4c4siINFvT7N3IR77nw1AykoIgsLUBiFs1+Gf/x5+PABOPJRGLkP3vLZNtOnFY5jMVf4GI3lPoTKQQDGel5FlDJFy4Nvc4rKqEtKCDUBbG5uri2pDhCNHsTLAIXhr+NPXiKSO0To0J51f7b/ppsQHZuBpMbkqUUMzWLbtm2Mj49TvXIFddNw+72F2QqCKBDLBJkDbFsmqPspii59OTT0WsyFBRxNQ+nrEALcPkiY2cvNeZNIH+neQRYKBby7dlF75siaY4pMu9MCBe9xusLutVrONuedGiUoTrPYVUdAZnjiF1BsmYrHPef5SRnFI7H7rl7y+TzpdBpRFKHvIMwc4yUPv5Wfe+d78QaC+Lu3gwiRsEhYD3Ny4SSO42BYZZ5QffxZ9jvc1XcXgyUv49FrD6y2vEr6w/2cGx0DOpuHn2S8CCA3EMfmS2DZPLh14wZ6K6KKzJ6gDyfh5XCx5oqsNXemuWtMoZdzFXI49CdcABnwuSyd46Ua98U7C3WrVIIksH3QFalrUU9bsdC0/kxcR17EKmoIqkv5Bbe0c3q2yFK1c3O+sz9Fvyhh7IzQn+4A1zPFKqbDOgHFHd1hRAHOPg+AnMsW2dXj+pfszISxSgbnm9pdGynzns+VEAXYkg5ypaEzsKrs4zgO+qTrh7I6er0qs9rGD1pv1McP338vb71jCICqZfEXk3lujwR4WXxjeewbCaXHBZCNWGRW1WBbzX19XjeZ1QwyHhXpWmDVtQnu+49w6ZuEr1ymp+chAL743Cy9UR+3DbvXflf4KQTg7JOzSBH3vHh0t15eqV5kbqJEqMuLla10JDq+/G74/C/D0gTc95/gt87BGz8B6V3rDmNu/hvU65OUJ16LWHdBPeskiMQS6KiIe/eiNdy/KxJd3UCnDSCCIJDyvgYj4Nbiw7k78G7wDHm2bEHw++muXsA0bKZOF9i+fTuWZZH1+/EMdxrHhdkK0ZQPb083hWiUeCxGl9ftC3g0G8/2N2I0J9PV/v4139O7NdbpgwCpVIrl5WXUWw9SP30ae9XsCaPLeCc85AuPEGuyLpdmmyIYCxfQFIG8fYmU+ipk3d1ALTRmEESRmfMOOw/1oHgl8vl8+3zQfytoRVIBvW0NENxyEwBJVSNhJTgxf4ILiycAm/OSzPt2/ArvTv0qj9/zSi52J5kqbexx06LwptU0J0+exKfVaSxtULL8MceLAHIDMVZu4DMhEXr+IbN742Hs/6e99w6TpLwP/D9vdVd17p6enMOm2chm0gYQCIHJSTqQlW1FFH7Wz2dJJ5/Pls8n2/fzz/fYls+W7yyd7ccCSSCBJJAMAkySkGAX2F3YYdPsTs4zPaFzvfdHVff0zHRP2knA+3meeaan4ltv19S3vjmk81zHEM4yT7a9bVeBToTJ/gnaMam3HdWNHhcSMIFri3NKldi9QYwaPz63k2qXPkMD6bNfIsvihftrpCMJHCEjqwkd2liKlPDc6cmbzakJ9g6Z4NT42xzb7/PDY+hCsD80NYzZYzjYWB6YNRIrmTZ5o3s023NiW3UQMZbk9ETMjsSaWo0ULAHSVOpjRJrETUlDjpM71R/FHE/iapxqYqtx6dne9fkoD7qz0Vf/0NZHbyLF76+vvihVX6/yIeP5KzAnzkcIJyRISW88SUcskd98lcvln4aavfDY78H4AL2RGM+e6uP23dVZf5Q/dpKmsnZef64L6bG+eNdYI7peTG/vY/S2Rqit9ZMeSeBqKraivDZcC/c+AF94FQ7/LgTyB4QADPQ/jWGUoSUOkB6385LG4pRvvgKA72tVtNWXYIoUZXbZk66uLjweT7b5FEBF4BYwHbh76tFT5TjLvDPOJZxOPJdcgu+NZ/CFDE691EN9fT1uXaejtiZrwgJLgJTU+HFWVjBQUkJ1MERR+WEAgukgeIuzAiTXhAWWIx0JXactM1ZFhXX9E5s3QzLJxNGjk99bayuh9gZisXaodiOEZLDTOi69r9NW48EkTX3Nx6xzVfro7TqHy1cKwskl19YyNDREPB6nstLWeGsvtX63TWo7nlorXyUQ7cEb9/Ji54t87gnrmO8bGuWmuvfx4IMPknY6McM7eLr16bzfV9uoJdwGTg+QSCSodOsrkkyoBMgc9I7GGJb5uwjm41DYD0JwdDyKo8JHsmsMafcSyRfCq40kaMNq3wnQYL9lF+sOdgan/rOF795I0S2Wg3G918WZaQKk1yEx0hL/eOHwvfRIPFv+AqwQ3aDbybNvTq0b1nYhwvrhNA/3DfNon/UP9/zQGHuC3inVajNsqwlyvLNwB7QzfWMkUibbqkP29iG0sRQp4HwsjiNoWEl5rZNC6I3uSNb/kTs3AIlW61zTC+BVuw264knMOZyHg8kU37jQyw2lQfaFZub1LAQjp/XwdBLnIwgBImHSHUvQFktMjcDKh+aAW//GMpX88NM88eJRTAl37LYfiKYJkQ62bx4iNp7k3PEBhNuBjKSpqLiJvr4nGB8dpNI2vRiNIXj//fCb34PmG6zjz0Fk9BjB4CX4wx6iIwncukb/WJz1132MO67ZjytUzLn1AQbLXsTRd4yBgYHs23auMDbcYWpe/SwVp38bozaAcOQX1J7du4ifPMm6S4q5cGKQdELS4PHSWV2N3mhldSdiKSL9MUpq/IwFg8TdbiqcDkJN70WYECo5YG2XESA1U8rkUd4YxOHU6Dhl3c/l5ZY2NFJSAk7nFDNW4vx5wlgtiHvDUYpcKQZsDSTV+xod1R7Ky64nULsFHALX+hD9F1pJJYvYsLecYImH7m5L88pqICXrwVMM7ZPncRmWWdwzcA4hBVpUY1exVealIenhX+//PiIW4+pIBCceXv31q3nn70LkAmXuMo6+dJT6+nquuuNurrzr3lm/46VACZA5ePpkH9LtYFPQM/fGwL6QDwOIFRkMeB2kh+IMjMWJm3JmCO9oEmdK0iUkVaGME916uL+rODjDzOHeGM6GvK73ujkTjU2JsujDpCwukeOF38DTI/Ep5bwdmuDgxlKePdWfPVYsmaale5SbfT62+z186c12LkTjvDY6UbD/x/bqEH2jcXoj+R3pJzqsB35GA6kOuQkkrfO12H4Q14YiYmdGkKZkNJakbTA6VYDkaCDx1gia14mzbOr3Uu3SSUg5pYFTPv7qfA/jaZMvrysc1TJf9EpvwQrM8dYI42EXxNOcn4jTnUjOLUAAKrbCdX8Epx/nfc/fxLdD32RD2koSZLwP0glqN/gpqvBy7N87cARdpCMJqirvRMoEgdqXCZkmwtCyhf/mSyo1xsTEWQKBHXYyYdzujZ5AaBo7D9/Exz/+cTb0FuOKhhhta+Gv//qv6ezsnHzbtomdPIa/bzfu8XqM2sKl/727dkE6TV1whHTK5NyrfTREoyRcLk73T/DaU208+j9fA6Ckxke3HcZeHo9j+Gq57PKfUnfZXwKQbGvHWV6O5poalu3UHVSuC2Yd6UVFRei6Tt/wMJ7t25n4lfVgT0cipAcHcdevp6LiFnr1XsLeEQY7LMHUOfFLUk5BQ8Mn0QwH5Z/aiedQhZ28V8Lu66w6WF1dXWialhVUCGH5Qdp+nR2TYQsQd9LS9L/Y/EW+tO9zADyf2s/Q8DAHX3qZA7/3ezgrnXjbvfQNzSwS2zbaRnOqmeHhYS6//HIad+6hcdfeGdstNUqAzMHjJ3vApbE1PL9/QpemcWnQh1ni4qRp3eTtdjZ15bQ6WJkIrHhAz5pVyg0nn6gt4+O1sxeC3OB1EUmZ9CcnH5Q9qTSlCUl6LL8AkWlJejQxRQMByw/SHYlxutfyP5zsHiVlSnbXFvE/NtcxlEzx/tfOYkI2gXA6GWd7oYz0E50R3LrGujJrfyEE20OWhpVxpLs3FiGjKZIdY5zstuZsa1WQ87E4Aqh1TwrgxPkIRmNohukp83DuyBOJlaE9luBbHf28t7KYzb75vRjMhtAdlrlyWml3mTJJdIxiVvsQCZM3JmKk5WS48ZxccR9n7n2Wf0pdx4HUr+DvD8O3b4ZX/sU6b1Et2w/X0HMuYnWhjCQIBHYg0rWEGn+BYzCOUR8s+NZfiNHR1wFJMLAdf9hFIpqiwqPTNzap8QohEK4aKnrKuPHm93L11VdTXl7O5s2bpxxr7PHHsp+N2sLNxzw7rZau/o5jBIrdHPv3DgbbQiAFP/7XZ3n2gVOMDyfY9e466rYU0zk0hDOZJNBvOc99/o1omp1D0d4+w3yVoXpTmL62UeITyezDvaenB+9llxE9fhxzfJzEecvPYDQ2Ul31XkyRpqgpwnB3J6lklAu+HopSxQSDVo8Yoy7AQF8nICmpa6CsPoBpmpw7d46ysjKcuVFndZdCfwtELWe+0xlECB1djyKA4lQxZtq6j1qjFex56WW2fRctrS4AACAASURBVPjD6JWVXHnVlWhS46GfPTTjutpH2ynvKycUCtHc3FxwnpcaJUBmIZ5K8+yFQRBiZtz+LFxXHkL6dH42Zr2RdtgP5urpOSB25rUonnyICSH42sYadgVn2opzydRsyvWD9CSSlKfBLFBe3BxLgEkeAWK9BT1jR2NlfBk7aovYHvDyufoKTk/EcWmCfcH8gnRLVRAh4Fh7fjPWic4RNlcGp2R/X1IZRERTWUe6a72VhxE7NZTtkrelKsiFqNWL3rBDGNNjVjizq3Gm4zszx50FHOkAf9HajZTwH5sqC26zUPQq/wwTVqJjDFISd1MQ4iZDdt5OTZ6CmoX47mkH/838MKOffhWuszPVf/41a2Wols1XVOLUNUbGEpgjcatrYO8hvGWnmBhpnVLyf76MjlqtWwO2AAGo0nUGppXcnzCCOJPjVHWd5+qrr+Yzn/kM9fX12fWpoSFGn30q+/dsGoijqAhj3Tpirxxl4/5yes5FaDM34k940UoivP+PLuM3/+hyDty9EafhoL29ndLxcdLdM5PlEu3tGHX5BUjGD9J52rrHy8vL6e3txbN/H6RSTBw5QqK11RpvQwOBwA58jkq0dXESDifnTnyTuAGN3qumHPf1Z6wyKruu24WUkp/85Cd0dHSwb9++qQOos/0g7S8B1v+7YZSgVfkIJpP09PTQes6a/7pz3Wz3+wjfew8AhzYdoi3URldLF/39kz7LaCpKfDiOGBZceumlOBzLH32VQQmQWfjVuUEm7Le3fA7wQmTKmjwViyE8TjqGLUEx3QeS7I+SRBKqnF1Y5CNTdjzXD9IdT1IuNcwCJqxUTg5ILrVhL+vKfNl8kGPtw5T4DKrt8hT/T2MFW31uDhT5ZzTDyuB3OWkq9eXVQKSUvJ7pOZHDtpogYizFcbvToMNvoFf7iJ0a5o2uCGGvTonf4Jmh0SkCNev/yPNwzFQ7LhTK2zIe44GuQT5aUzo/U9I80at8pIfjmDntWzPjLN5UjEhM+qXm+zKSNiU/fKWDq5vLKC4thwOftxzgd/1vuPLzULYFl1dn06UV9PRGSY8mMJMmPcetyJ5I1QszotTmQ2T0GC5XJS5XGX47+7vE4WBgfKrPLSYNnKkJ9DeO5z/Oj34E0TEQIDxOHCWzB6F4du8i+sor7P2NRm65bxuHXvgSe8MwHouQ0nL6g8Tj9PT0UAGkpmWIy0SCVHc3ek1+AVLRZPlBOu1OnBUVFUxMTCCbm5G6zpGfnucnP9dIGAH0+nqEEFQHryJVDGyv5VT7P+EdS1NcOZlNL6XkzJGTIBxsObCZp556ipdffpmDBw+yf//+qQOo3mMVrcxxpBtGCdQECPb2cv78eU6csNbt+MUxqr72NYQtEHSHTvG2YlIixRNPPJHdv320nQ2RDWhOjT179sw6x0uNEiCz8OTJXhxeS/2crj3Mxmafm6AQRAIO0qVuOicSCGa2so32jNOJSV2e4oxzUes2cGuC03Yo71gqzVjapFxzFDRhmTllTKZzeGMZvzw7QCyZ5rX2EXbUTpqHXJrGj/du4n9vb5qxXy47akJ5Q3nbBqOMxlJZB3qGbdUhxFiS8/EEKTsE1rUxTOJChLMdI2ypCvLc8Bi9idSUJL94a8TqB18z0yRSrDtwayKvCUtKyZ+e7cLn0Ph8Q+EIpMWQ6U2fW/8s3jqCs9RDUakXIzXpq6otcC8lUiZD4wnahyZo6R7ley+10ROJTzrPwSp3suNueM8fZ3M3tl9Vy0RKgoTB1hEmhsK4YzuIVL2AXjd3z/rpjI4eJxDYDpDVQEJSY2AsgZkTqpxOSGIOQTQneimDlJLhBx/CvX0bmsdptV+eI9LNs2sX6eFhZFcb5a4RHKkYmzZYIbonT57MbtfZ2Wnlm/h8JKdpIMmuLpCyoAnLqTuoaApa/UGYdKR3Dw7TcunnODZQzVDMw/lt70MzLEFfWXErmLCp+Xlc3mFa2vYw7J4MEW57Y5CJ4S6CpdW89PLLPPPMM+zevZtrr7125gBcfitsuj1XgJRihh2EBgeJxWJ4jCQkoey6/binmaMONh3kZOgkJ0+e5Lxtajvde5q6sTqatjTh8Vy8SXYhKAFSACklP3+jl4Za6w1uISYsIQRXBP2YJS46XYLuZJISTcM5LTAo3muF8Oar7jsXmhA0eSYjsXrsVrgVurOgCWtSA5kpQA5tLCWWNHnuVD+nesdmlHD3OjQ8s2Thg+VI7xyJMTA29U01U4F3ugayrtSHEU1nI7EA3BuKIC3x9FgO9Ad7hgg5HVPyNOLnIxh1k/3gcxFCUOMyZoTyJkyT/9jSzmP9I3y2viKboLlUZPJ0MqXdpZQkLkQwGqy8l7D9Fhl2OqZk8SfTJp/855fY+NVH2fT7j7H7jx/n4J89xfX/4xm+/NAxirw6126ZPf+orD6Ayw4mGLDfrMNDh0j6ehhLLKxYdSo1ysTEWYK2APEVuUCALy1ImZJIzryKhEnM4yZ27BhmfJp28vrrxFtaCN15B4Gr6wgcnBoRlQ/vbktzir7yKgm7BlZx8yaqq6tpaWnJbpfpQFhTVkaqtxeZzNH62jI5IPkFCNh1sdpGiUdT2VDen3/3CJ36etad+xH1kZdpC+5ioMMyPRtFmxgfLCMQGCQxbnChZzP/8K8/pK3Niso6+m8XQA7gbqjnscceo7m5mZtvvrmwwKy7zDJhpaw5M/RS0kacip5eQkJQM3ABRxTKPnjXjF0P1hzkdPA0mlvj8ccfR0pJy6stOHBw8IqDc87xUqMESAHO9I1zYXCC0lIvPodGYI6H53RurCoCw8H3vSZ9bo3SoSRdf/oiw4+dI9k7gTQzIbyTOSALJTeUtyduOdMrXTrp8WTeGjjpkQQ4BZp35sPz8nUl6A7BN585S9qUbJ8mQObDthrrIT89nPdEZwSHJmiunGoDdzo01tkmp4wj3dUYQjoEO9Ma6yoD/KRvhFvLi3DZ/g8zkbb7wRceX7Vbn+ID6UskufuVM/xL1wBfaKjgsw2zP5AXgyNgoPn1rB/EylNJZU1Ipbo159NfRL7+6El+dqKHu/fW8bvv2cQf3LyVP7/rEv7m/bv51kf388h9B3Hrc9u0G/Zb19T6Yg+G24H/zC6ENOjq/sGCrsNyoEMgaGWMO5wa3oCBy46Y67dfDtIpE6cJseIiZDJJ7MRUQTXy0A8QhkHoppsIHK7F3Vw857mNdevQgkGiR4+SaLUEiKuxkebmZtrb2xkdtQIr2traKCkpwV9TA1KS6p1sRlUoBySXmk1hpJ0PMtaXRpMGkYkhrrnGoPH8T2l47QF0Lc0LD1oFDCdw09ptJVvWDgbxnGshHYvy7W9/m5/94FnaXu8i4YKzEwnq6+u5++67Z/dDbHyP1ca49Vnruo1SEqkhaqoqueG738ORimDINFpZw4xdy7xlbCrdRE9VD+3t7Rw7dozh08P0+/ppqp7dQrAcKAFSgKfsntmGX6c6TwmSubjKTgL8t3ScoTofNWU+jLogY8+20/P/v0zvN15BS8uLEiAbvG7Ox+IkTHNSA/EYkJbI6MwwViuE15X3WnwuJ3vqw/yq1QonzC3hPl8yJqrpJU1OdI6wocyf90G4u9gysZy0BYjQNUbL3OzHSZ9PI2qa3J1jvkq0jYIpZ+R/5FLtMrJFC1+JTHD9S29ybDTK329r4CvrqgpngV8kVgVm6611ep5KtV2GJTeS7IdHO/jH58/xkSsb+fqdO/jsNRv52MEm3re/jpsvqeZdzeXZ/KC5qL/MCghID8dpqPGhTRgUG1fR0/NjTLNwQMF0sj01bA0ELDOWI2b5cPptR3p8wrq/zCrrDT565Eh2ezORIPLjHxN497U4QvN/ERGahmfnTqKvvEL87FmcVVVoPl82qujNN99ESkl7u9VASq+0QrCTOX6QZEc7Qtdxlhd+SahoCqI5BS8/1soP/uIILuknUCNpvnUfQtfRU+Nsb5zgwuuDnD8+wLlz5xgcrKV64FK2dXZxcKsf58mjhDwefvHqz0lWnSFau4GQ38+9996Lrs9h7m66CnQfnLQ6HxpGCVIm8BzYDek0WpUPAxMC1Xl3P1R7iOd4jpLSEh5++GFIQLR6fg3dlholQArw85M9bK4MMGiaC4qayVDp0ilHo98t6IwnqS31UfqhrVR95TJCNzZl+0f0eR14FlmzZr3XRVrC+WiC7ky5+IBlnsrnB7GSCAtfy+FNVuhwWcBFRXDhpc1DHp2GEm8eATLTgZ5hZ3UIoileGZr0HZzxajTh4PmxcercxpTM90RrxGrhWl9YgNS4dXoSSR7oGuT2o6fQBPxozwZuK194scSFoFf7SfZMINPmjDyVep81n5l76UTnCF9+6DUubSrmqzdtuehzGyE3UoBbg6qAdY6qurtIpYYZGHh63scZjRzD5arK5icA+IvdpMcy2eiWABkYtJzavvIijMZGJo5M+kHGnnyS9MgIoTvuXPB1eHbtJH7qFLHXjuFqagQsR3dRUREtLS0MDg4yMTFBbW1ttjJtsmvSD5Joa0evrs46nvPhNBxUNoXoPhuhojHItv0bGBweAMPIhhNvu6yEULmH579/ijOnz+ASaTb1nkeLj3DZNQdp2LyV5JEX8MTCjIgBRDrFe++8Y34+CN0NG66BlsdAyslckBuuxH/NNYgyB3oK8Jbk3f1w7WFMTEp3lpJOp4m6opTU5N92uVECJA8j0SS/brV6ZnfGE1TNN25/GleGfJhhF8OpdDaKyxEwCByupeJ39vIH9Q6S5Yt3euVGYnUnkng0jZDPeniY+QRIZGYOSC6H7RLnl9TMzK+YL9urQ1MisfpG4/SOxtlaQIBsqw6ijaV4Y2zyDeqFdIJ+Q/D82AR3V4SnFDmMt46gV/jQPIV9GDUuAwl84eQFdge9/HRvM9sDi9PyFoJR5YO0JNUXtfJUbP8HQH3AjdYd5Qq/l6HxBJ/855cp8hh84/17Zq3wPF+EJtACBgG3g2KnQAsalNZdjWGU0tX9w3kfJzJ6fIr2AZYGkhhNgJw0YXX1WgIkHHbj2bOH6JEjWbPp8IMP4aysxHflFQu+Du/u3SAlidZWDLsGlhAiW1zxnN1gqra2Ft1OWpyigcySA5LL/psauezWJm79wi5qaqtIpVIMDg7ivewyADzrm7jyzg0Mdo9z8vU3afJO4OizzHRa5TYqNtwFpoPw2BtsKvIT7D5PdUPj/C+0+SYY7YTOo5PCusJL3d9+g5SIoQs3FKi8u71kO0WuIo7JYxw4eIAj4SPUherybrvcKAGSByklX7xuE9fvqKIvkVpQBFYut9eWgB0GPD2EVwjBGyNR6hZpvgLLhAVweiJGTzxJpcuJM5jRQKaaLaQpZ5Qxmc626iA764p4z7bFRyhtrwnRNhhlxA5nnXSg5zdlbK4MoI0n6UimSNsPoKcHx3mkRscE7qqc1BpkWpI4Pzqr+Qpgi9+al4/WlPLdnRsoXWKHeSEyjvTYqWFS/dEpYcaVITfGq4M04eDz9x+lNxLn7z64l7LAwjW9gucPu2lcF0Lrj+JqCOJw6FRU3Ep//5Mkk8Nz7p9KjRKNtmb9Hxn8YTepuIkbsgESvXYOU1mJB+/ePaSHh0mcO0eyp4fx558ndPtts2oBhXBfcomVsQ1TamA1NzeTSqV47rnnMAyD8vJyNJ8PLRQi1T1NgMziQM9Qu7mYfTc24XBOZor39vZS/KEPUv3f/xyjro6mnaWUbdCZiI/REJz8/20brOH4MyOsv+w3Ge1rp+uX/05FVVXBUut52XS9Fc7b8mhWgCSSVm5HiiROR+HoOYfm4EDNAZ7rfI6N+zfS7emmLqAEyJqhyGtw37s2EC52I5nMLVgoh4oDCPuhWDXtGLFkmu5IjIbixddhCjodlBlOzkTjdMeTVBg6mt2bYboGYk4kIS1xBgtfi6YJHr7vAP9hf33BbeZie9aRbgmOTA+QQhqI13BSjoO0sPqbDI0n6BqN8dM6g22jZjZhEqwQWZlI500gzGVP0MeJA9v5+qZa9AW2qL0YnKVecArGX7QeaLnjrLQ79v3nHx7n2VP9fO22beyqW7ifaTYcQYNE1zjp4XhWeFVV3o6USXp6H51z/4idQBgMTBcgk+a3PvvFZHDIEiDV5T48u63cg+iRI4z88GEwTYruuGNx1+D349q0CQBXThn3hoYG3G43w8PD1NTUWOXRAb2ykmSnNd/psTHSw8NTGknNh7IyS/Pu7e3FEQoRusXqjSKEoGyHdf+MjVpjino28sR32ghXernpvlvYd8udIK0M9AXhLYb6K+Dko+iGZX5KJPoxzQRpzUTXZ783DtccZig+xGOtVqb/agmQlXk1e4uSaUy0WA3E53RQIx20C5Pf+vtfUmwKQh6dkEfHpWtICQ3zdJIWYr0dytuXSHJJwIvm1UHM1EBy+4AsJ9tzHOkHNpTyemeE+mJvtoFTPrb6PXRiRWKFRlKYPidnPYLffSNOsnvCMg1hlS+BmQUU87HUYbrzQTjs3iDtY+AQGDWTUWeZlq9HLgzz/svquefSxQvpQjiCRjZ4IhP95fdvxefbRHfXQ9TWvH/W/UcjlgM9MMOEZY29WtezGsjIcBwNS4AYgTCOcJiJl48QPXIEz769GA0LfKDm4Nm1i3hLC8a6yTLuDoeDjRs3cuzYMepyyrTrVVXZXJD5RGDlwzAMiouL6emZWb22Z7Adt9PHqbMN7C+u5LnhzxCfSHHL53eiGw4O3vMhkrEYmw8cXviFNt8I//ZVjLERQCORGCCZtF68nK7Zew8dqDmAJjS+1/I9AOoDS38/zQelgcxCpo959UVkLL+vvhQH8MGdNbyruZz1ZX50h8bQeJLmigB7Gy7OsbvB67ZMWIkUlYZu2cJ9+gwNJD1LDshSEvYZ1BR5sqG8J+weILOxv8x60L4yPM7rXRHS1V4cwHu6U8QzDYCw/B+OkAtn0dxl9VeLTGVeozaA0Cf/vcqDLnSHYHd9Ef/llq3Lcu7Mdyt0Db3aErpCCKoqb2ckcpSJidZZ94+MHsftrsEwpobcZjSQUoeTAbtvzPhoAhNJIGC1BvDs3k3kscdInD9P0Z0z8xcWQvjeeyj57d/CWTHVlJqps5UrQJxVldls9EkBsvC38YqKCnpzwoEB0uk0ra2tbNqyEYdD8MPBP+b8UCNX3rWeUrssi8Pp5N2//Rlqt2zPd9jZ2XwjAKLlZ+h6mESin9S4fQ3u2UPNQ64QO8t20hftw+P0UOqZXeAsF0oDmYVMOYzFaiAAv7O+ivfWlNDkXZ4H93qvi0E7oivT5c7h12dEYeX2Ql9uttcEOd4xwmgsSevABHfvnf2NcE9NCE4Nc2RwjLquKNR4ubo4SHlRitjpYQKHa5FSEm+N4GpaeH7KSpLxg0zXklxOB/d/4nI2lAVwOZenVlGmyrJRF0DkOOYrKm/j9Jn/TlfXg6xf//8W3H909NgM7QPAFzIQAorQOGJrIPHxFIZDZIMEvHv3MPbkkwivl+D177mo63Bv3ox7WlFGgC1btvCBD3wg2zMdQK+sIj0ygjkxMZlEWDt30uJ0ysvLOXnyJMlkMhuG29HRQTweZ/OWTdTH+njx2VIa62PsuHphGk5BitdB2RZoeRTXllISiX6SI2et6/LmD+HN5VDNIY72HqU2ULvsrWsLoTSQWeiMJwk4NAIX8Q+va2LZhAdMRmLBpKNe8xtW4cQc0iMJ0ETWR7KcbK8Oca5/nF+ds3JKCjnQM2ytsiKxTk3E+XVkgrTLwd2VYdwbwiTOjSCTJumhOGYkMaf/Y7Ux6q03U/f6mTbsvQ3FhLzLN/+Z1rbTa4S5XZWUll5DR+f9pNPxfLuSTI4QjV6Y4f8A0Bwa3pALvzkZxpuMpjD1yYdWxg8SvOEGNN/F9VcphKZpbNiwYcrDMhvK291Nsr0dLRBAW0DuSYaKigqklPT1TZZKP3PmDEIImpqa2HXnpRzedYprP7F/aR/Wm2+E8y9gOEMkEgOkxqzyJE7/3CapQ7WHAKjzr47/A9agABFC/KEQokMI8Yr9c2POuq8IIU4LIVqEENcv91i64smLMl+tBJlILIAK2+6v5dNARuI4AgZiBZzKmSz2771kvRHOZcIq8bvwJyW9Mk2rB3QJ15eGcG0sQiZN4ucjxLP+j7WtgRi1ASq+uBfXxqV1kM8HvdKLXuXDs32mOaOu7qMkk4P09Dycd9/cCrz58IdduJOSsXiKWDINCRPNPfli5blkB+EPfZDST3x8Ca5k/mRDeTu7SLS3odcu7m08E4mV6wc5c+YM1dXVeDwenB4POz71Sdyls7dZWDDNN4FMo0fjlgYybvVd10Pr5tgRmsPNbC/ZzqVVly7tmBbAWjVh/aWU8v/LXSCE2ArcA2wDqoEnhBCbpJSF2+9dJB3xxEWZr1aCereBLgRJKXNMWPk0kNmTCJeSjAB54o0eSv0uyoNz+ywaDZ3XhMCs9HCFy4XXoWGuC4EmiJ8ewoymEG4HesXy53NcLHr56oxR8+pUfCF/NdZw0eX4/Zu50PYtqqreO+MhmxEgwWAhAeKmfzAKArpGYjiSEr148vEhnE4q/9N/WqIrmT/OKsvUk+ruItneMSVyayEUFxfjdDqzfpBoNEpHRweHDh1asrHmpXo3+CsxhntJBkZImpYA00Mb5txVCMF3bv7O8o5vDtacBjILtwH3SynjUspzwGlgWUVvZyy55gWIUxM02mUyKo2MCUtHJkzMnBLi6ZHZkwiXkkwme8qUc2ofGS4pss0emuB9lZYTV3M5MeoDxE4NW/6PhuCKaFBvR4QQ1NV9lPHxNxkaemHGesuBXouu5w/q8Be7MMdTIOH1zghuCZ4VMIfOhV5RDkKQ7Oy0kwgXZ87RNI2ysrKsBtLa2oqUcoq/ZVnQNGj+DYy+C6TTE8QT1vmd7tXJLF8oa1WAfFYI8ZoQ4h+FEJk7ugZoy9mm3V62LMRNq9vfYnNAVpL1Xhc+h4bf9tU4puWCSDl3EuFSkwnnna8AOVhpbSdiae5smDTBuDeGSXaOkeqZmFf4rqIwFeW3oOslXGj71ox1o5Hjef0fGQJhNzIlcUsrss4tBf5ZcopWCqHrOMvKiB47jozH0RfhQM+QaS4FlvnKMAxqFxgSvCg234QRs2rBjaf7caYFQqxcU6iLYVUEiBDiCSHE8Tw/twH/E1gP7AK6gL/I7JbnUDNKzgohPiGEeEkI8VKuQ2yhZGtLLbKMyUrykZpSvtg42V1P81v/2JlcEBlLI5PmipmwYNKMNZcDPcPemjBaf4yaoeSUKCXXxqLst7yY5kiKSRwOF7W1H2Bg4CnGx89mlyeTw0RjFwr6P8Au6w4EpOBE+wgGgqLQ2gindlZVZos5LjSJMJeKigrGxsYYHx/nzJkzNDY2rkx3v6bDGNKa3wltHKdc+8+cDKsiQKSU75ZSbs/z87CUskdKmZZSmsA/MGmmagdy9dNaoDPPsb8ppdwnpdyXyTBdDJkkwsUUUlxpri4Ocl/9ZNz4dA1kpXJAcrmquYxSv8G+xvnludSGPVSdHOU699QIHqMmgHA7wCHQZ2mJqpgftTXvRwiDtvZvZ5eNjlo1noLBwhqIv9gWIKbgjN22uKR4ZZsXFUKvqsYct4px6nWLj0jKONJbWloYGhpafvNVBqcLo8LqXBjVU+hibczrfFhzJiwhRFXOn3cAmX6ZjwD3CCFcQogmYCPwq+n7LxWdS5ADslpM10BWQ4DsqQ/z0u9fl83AngshBN/91BV86YapHdiEQ+DZXop7YxhtkVWLFZMYRimVlbfS1fVQtj5WJJuBvq3gfoFMa1vhIGa3TC4qWrn7aTYykVgAes3iTViZ5lK/+MUvAFZOgABG0w3WByHQHW+dF6U1J0CAPxdCHBNCvAa8C/gdACnlCeC7wOvAT4H7ljMC62LLmKwmDp+tgYxmNJBMGZO1rU2tL/NT5J05xuK7N1H6kcIPN8XCqKv7KKYZpaPzAcDqAeJx189af8kTNNA0QbnTiVta1uS14EQH0KssAeIsL0dzLV6o+f1+PB4PfX19BINBSkpWzpFtbLot+9mpr+1Q9VzWnACRUn5QSrlDSnmJlPJWKWVXzro/kVKul1I2SykfW85xdMaThKa1H32rIHQN4XZg2m+KqZE4CKuUvEIR8G8mHL6C9vZ/wjSTVg/0AuG7GTRN4C0yCKPhMa1lLt/aECDOKstosdAaWNMRQmS1kPXr169odrfmr8Bp2gUi56iDtZZYcwJkrdD5FsgBmQ2H35hiwtL8+pTyFop3NvV1HyMe76aj835isfYZPUDyEQi78Zsiq4G414gA0bMC5OKDMjN+kJU0X2UwHJYGqHur5thy7aCeKAXojCWzTaDeimh+nXTGhDVHIynFO4+SkqvxeBo5c8bK1w3MEsKbwR924UlKPGtUgFxMBFaGpqYm3G4369bNnQm+1BhB65zOYOOKn3uxrNVM9FWnM55kV3DtZz0XwuHXSdpd49IjcZwlb53IDsXyI4RGXd1HePPNPwQKlzDJxR9244ibeHRAEziNtfH+6SwtpfK//AH+q6++6GNt2bKFzZs3r0pxQsNlaT+6c+XL4CyWtXEHrDFiaZOB5OI7Ea4FrIKKk070te5AV6w8VZV34nQG8Xga0PW5c2x8YRfChHBaw+F2rFoF2HyE7703q4lcLKt1XYbdWEp/CznRlQaSh9F0ml0BL+u9ayNRajE4/DrmRAozmkLGUsqEpZiB0+ljy5Y/zZOOm59MKG95WuDyqUfHUmPolgBxOpUAeUtTZuj8dN+m1R7GRZHJBUl0jgHgVAJEkYfysvkXtc4kE4aktmZyQN5OZHqjv5XCeJUAeZuSyUZPdlgCRJmwFBdLprUtgNun7qelprTsOhqibfh9G1d7KPNG+UDepmQaRyWyAkS9MSouDo9fR3Na/gFlwlp6XEYpGzb83lumkCIoAfK2xWGbsLIaSFAJEMXFITSBMl1N/QAACRVJREFU3zZdrZUQXsXqogTI2xQtYP2Dp/qjaF4nQldfteLiyZixlABRgBIgb1uE4QCn9fUq85ViqfCHlQaimEQJkLcpQoisI10JEMVSkdFAlA9EAUqAvK3R7OKJKgJLsVQoDUSRixIgb2MyZd2VA12xVJQ1BHA4NUJlqjSOQuWBvK3RlAlLscRUNoX45F9dhdDWThkTxeqhNJC3MQ5lwlIsA0p4KDIoAfI2RvMpDUShUCwfyoT1NsazoxRzPImzVNmrFQrF0qMEyNsYZ8hF6PrG1R6GQqF4m6JMWAqFQqFYFEqAKBQKhWJRKAGiUCgUikWhBIhCoVAoFsWqCBAhxHuFECeEEKYQYt+0dV8RQpwWQrQIIa7PWX6Dvey0EOLLKz9qhUKhUOSyWhrIceBO4JnchUKIrcA9wDbgBuBvhRAOYXVY+QbwG8BW4F57W4VCoVCsEqsSxiulfAOsirHTuA24X0oZB84JIU4Dl9rrTkspz9r73W9v+/rKjFihUCgU01lrPpAaoC3n73Z7WaHlCoVCoVgllk0DEUI8AVTmWfVVKeXDhXbLs0ySX9DJAuf9BPAJ+88xIUTLXGOdhVKg/yL2Xy7UuBaGGtfCUONaGG/HcTXMZ6NlEyBSyncvYrd2oC7n71qg0/5caPn0834T+OYizj0DIcRLUsp9c2+5sqhxLQw1roWhxrUw3snjWmsmrEeAe4QQLiFEE7AR+BXwa2CjEKJJCGFgOdofWcVxKhQKxTueVXGiCyHuAP4aKAN+IoR4RUp5vZTyhBDiu1jO8RRwn5Qybe/zWeBngAP4RynlidUYu0KhUCgsVisK6wfADwqs+xPgT/IsfxR4dJmHNp0lMYUtA2pcC0ONa2GocS2Md+y4hJR5fdEKhUKhUMzKWvOBKBQKheItwjtegMxWVmXadnlLqdiO/ReFEKeEEA/YTv6lGFexEOJx+7iPCyHCebZ5lxDilZyfmBDidnvdt4UQ53LW7VqpcdnbpXPO/UjO8tWcr11CiF/Y3/drQoj/kLNuyeZrrrI7dpDIA/b6F4UQjTnr8pbyWQrmMa4vCiFet+fm50KIhpx1eb/PFRzbR4QQfTlj+O2cdR+2v/dTQogPr+CY/jJnPG8KIYZz1i3bfAkh/lEI0SuEOF5gvRBC/JU97teEEHty1i3tXEkp39E/wBagGXga2FdgGwdwBlgHGMCrwFZ73XeBe+zPfwd8eonG9efAl+3PXwb+bI7ti4FBwGv//W3g7mWYr3mNCxgrsHzV5gvYBGy0P1cDXUDRUs7XbPdKzjafAf7O/nwP8ID9eau9vQtoso/jWKL5mc+43pVz/3w6M67Zvs8VHNtHgL/Js28xcNb+HbY/h1diTNO2/xxWcM9KzNdhYA9wvMD6G4HHsPLqLgdeXK65esdrIFLKN6SUcyUbXopdSkVKmQDuB24TQgjgGuD79nb/B7h9iYZ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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#Have to run previous python cell first\n", "A_noisy = A + numpy.random.normal(scale=0.2*numpy.max(A), size=A.shape)\n", "\n", "xhat = numpy.dot(A_noisy, d)\n", "\n", "pyplot.plot(x, A_noisy)\n", "xlabel('x')\n", "ylabel('firing rate (Hz)')\n", "\n", "figure()\n", "plot(x, x)\n", "plot(x, xhat)\n", "xlabel('$x$')\n", "ylabel('$\\hat{x}$')\n", "ylim(-1, 1)\n", "xlim(-1, 1)\n", "\n", "print('RMSE', np.sqrt(np.average((x-xhat)**2)))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- What if we just increase the number of neurons? Will it help?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Taking noise into account\n", "\n", "- Include noise while solving for decoders\n", "\n", " - Introduce noise term $\\eta$\n", "\n", "$ \n", "\\begin{align}\n", "\\hat{x} &= \\sum_i(a_i+\\eta)d_i \\\\\n", "E &= {1 \\over 2} \\int_{-1}^1 (x-\\hat{x})^2 \\;dx d\\eta\\\\\n", " &= {1 \\over 2} \\int_{-1}^1 \\left(x-\\sum_i(a_i+\\eta)d_i\\right)^2 \\;dx d\\eta\\\\\n", " &= {1 \\over 2} \\int_{-1}^1 \\left(x-\\sum_i a_i d_i - \\sum \\eta d_i \\right)^2 \\;dx d\\eta\n", "\\end{align}\n", "$\n", "- Assume noise is gaussian, independent, mean zero, and has the same variance for each neuron\n", " - $\\eta = \\mathcal{N}(0, \\sigma)$\n", " - All the noise cross-terms disappear (independent)\n", "\n", "$ \n", "\\begin{align}\n", "E &= {1 \\over 2} \\int_{-1}^1 \\left(x-\\sum_i a_i d_i \\right)^2 \\;dx + \\sum_{i,j} d_i d_j <\\eta_i \\eta_j>_\\eta \\\\\n", " &= {1 \\over 2} \\int_{-1}^1 \\left(x-\\sum_i a_i d_i \\right)^2 \\;dx + \\sum_{i} d_i d_i <\\eta_i \\eta_i>_\\eta \n", "\\end{align}\n", "$\n", "\n", "- Since the average of $\\eta_i \\eta_i$ noise is its variance (since the mean is zero), $\\sigma^2$, we get\n", " \n", "$ \n", "\\begin{align}\n", "E = {1 \\over 2} \\int_{-1}^1 \\left(x-\\sum_i a_i d_i \\right)^2 \\;dx + \\sigma^2 \\sum_i d_i^2 \n", "\\end{align}\n", "$\n", "\n", "- The practical result is that, when computing the decoder, we get\n", "\n", "$ \n", "\\begin{align}\n", "\\Gamma_{ij} = \\sum_x a_i a_j / S + \\sigma^2 \\delta_{ij}\n", "\\end{align}\n", "$\n", "\n", "\n", "- Where $\\delta_{ij}$ is the Kronecker delta: http://en.wikipedia.org/wiki/Kronecker_delta\n", " \n", "- To simplfy computing this using matrices, this can be written as $\\Gamma=A^T A /S + \\sigma^2 I$\n", "\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "\n", "
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It can be enabled with `nengo.rc.set('progress', 'progress_bar', 'nengo.utils.progress.TerminalProgressBar')`." ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "\n", " (function () {\n", " var root = document.getElementById('781686b9-5652-456e-a9c4-e3c0098f403d');\n", " var text = root.getElementsByClassName('pb-text')[0];\n", " var fill = root.getElementsByClassName('pb-fill')[0];\n", "\n", " text.innerHTML = 'Build finished in 0:00:01.';\n", " \n", " fill.style.width = '100%';\n", " fill.style.animation = 'pb-fill-anim 2s linear infinite';\n", " fill.style.backgroundSize = '100px 100%';\n", " fill.style.backgroundImage = 'repeating-linear-gradient(' +\n", " '90deg, #bdd2e6, #edf2f8 40%, #bdd2e6 80%, #bdd2e6)';\n", " \n", " \n", " fill.style.animation = 'none';\n", " fill.style.backgroundImage = 'none';\n", " \n", " })();\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "RMSE 0.059589387758251525\n" ] }, { "data": { "image/png": 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\n", 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"text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy\n", "import nengo\n", "from nengo.utils.ensemble import tuning_curves\n", "from nengo.dists import Uniform\n", "\n", "N = 100\n", "\n", "model = nengo.Network(label='Neurons')\n", "with model:\n", " neurons = nengo.Ensemble(N, dimensions=1, \n", " max_rates=Uniform(100,200)) #Defaults to LIF neurons, \n", " #with random gains and biases for\n", " #neurons between 100-200hz over -1,1\n", " \n", " connection = nengo.Connection(neurons, neurons, #This is just to generate the decoders\n", " solver=nengo.solvers.LstsqNoise(noise=0.2)) #Add noise ###NEW\n", " \n", "sim = nengo.Simulator(model)\n", "\n", "d = sim.data[connection].weights.T\n", "\n", "x, A = tuning_curves(neurons, sim)\n", "\n", "A_noisy = A + numpy.random.normal(scale=0.2*numpy.max(A), size=A.shape)\n", "\n", "xhat = numpy.dot(A_noisy, d)\n", "\n", "pyplot.plot(x, A_noisy)\n", "xlabel('x')\n", "ylabel('firing rate (Hz)')\n", "\n", "figure()\n", "plot(x, x)\n", "plot(x, xhat)\n", "xlabel('$x$')\n", "ylabel('$\\hat{x}$')\n", "ylim(-1, 1)\n", "xlim(-1, 1)\n", "\n", "print('RMSE', np.sqrt(np.average((x-xhat)**2)))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Number of neurons\n", "\n", "- What happens to the error with more neurons?\n", " - Note that the error has two parts:\n", " \n", "$ \n", "\\begin{align}\n", "E = {1 \\over 2} \\int_{-1}^1 \\left(x-\\sum_i a_i d_i \\right)^2 \\;dx + \\sigma^2 \\sum_i d_i^2 \n", "\\end{align}\n", "$ \n", "\n", "- Error due to static distortion (i.e. the error introduced by the decoders themselves)\n", " - This is present regardless of noise\n", " \n", "$ \n", "\\begin{align}\n", "E_{distortion} = {1 \\over 2} \\int_{-1}^1 \\left(x-\\sum_i a_i d_i \\right)^2 dx \n", "\\end{align}\n", "$ \n", "\n", "\n", "- Error due to noise\n", " \n", "$\n", "\\begin{align}\n", "E_{noise} = \\sigma^2 \\sum_i d_i^2 \n", "\\end{align}\n", "$ \n", " \n", "- What do these look like as number of neurons $N$ increases? " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "- Noise error is proportional to $1/N$\n", "- Distortion error is proportional to $1/N^2$\n", "- Remember this error $E$ is defined as\n", "\n", "$ E = {1 \\over 2} \\int_{-1}^1 (x-\\hat{x})^2 dx $\n", "\n", "- So that's actually a squared error term\n", "\n", "- Also, as number of neurons is greater than 100 or so, the error is dominated by the noise term ($1/N$)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Examples\n", "\n", "- Methodology for building models with the Neural Engineering Framework (outlined in Chapter 1)\n", " 1. System Description: Describe the system of interest in terms of the neural data, architecture, computations, representations, etc. (e.g. response functions, tuning curves, etc.)\n", " 2. Design Specification: Add additional performance constraints (e.g. bandwidth, noise, SNR, dynamic range, stability, etc.)\n", " 3. Implement the model: Employ the NEF principles given the System Description and Design Specification" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Example 1: Horizontal Eye Control (1D)\n", "\n", "From http://www.nature.com/nrn/journal/v3/n12/full/nrn986.html\n", "\n", "\n", "\n", "There are also neurons whose response goes the other way. All of the neurons are directly connected to the muscle controlling the horizontal direction of the eye, and that's the only thing that muscle does, so we're pretty sure this is what's being repreesnted.\n", "\n", "- System Description\n", "\n", " - We've only done the first NEF principle, so that's all we'll worry about\n", " - What is being represented?\n", " - $x$ is the horizontal position\n", " - Tuning curves: extremely linear (high $\\tau_{RC}$, low $\\tau_{ref}$)\n", " - some have $e=1$, some have $e=-1$\n", " - these are often called \"on\" and \"off\" neurons, respectively\n", " - Firing rates of up to 300Hz\n", " \n", "- Design Specification\n", " - Range of values for $x$: -60 degrees to +60 degrees\n", " - Normal levels of noise: $\\sigma$ is 20% of maximum firing rate\n", " - the book goes a bit higher, with $\\sigma^2=0.1$, meaning that $\\sigma = \\sqrt{0.1} \\approx 0.32$ times the maximum firing rate\n", "\n", "- Implementation\n", " - Examine the tuning curves\n", " - Then use principle 1" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "\n", "
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It can be enabled with `nengo.rc.set('progress', 'progress_bar', 'nengo.utils.progress.TerminalProgressBar')`." ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "\n", " (function () {\n", " var root = document.getElementById('656ed93e-40fe-46d5-8677-8bfd95fa97f0');\n", " var text = root.getElementsByClassName('pb-text')[0];\n", " var fill = root.getElementsByClassName('pb-fill')[0];\n", "\n", " text.innerHTML = 'Build finished in 0:00:01.';\n", " \n", " fill.style.width = '100%';\n", " fill.style.animation = 'pb-fill-anim 2s linear infinite';\n", " fill.style.backgroundSize = '100px 100%';\n", " fill.style.backgroundImage = 'repeating-linear-gradient(' +\n", " '90deg, #bdd2e6, #edf2f8 40%, #bdd2e6 80%, #bdd2e6)';\n", " \n", " \n", " fill.style.animation = 'none';\n", " fill.style.backgroundImage = 'none';\n", " \n", " })();\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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ulZTxTHgsSUolE/iSvlpB084rkPToKP3ICIQkSXbAYWCeEGKzJEkeQBYggDno3FDjJUn6Cjh5m0D8KYTYdNt6E4AJAN7e3s2SkpL0trFMreHnk0l8eSCW/FIVI5rV4q2e9ajmYHXf9wohSPvf/8jbuIkan32GY/9+AGi1gh3LIkmJzuWpt5pS3dfxrmtotBq2xW1jScQSckpzeKruU0xpMgVXa1e9vzcZGZl7oEiGra9CwmGo001X13DbqaGwsJBTp04RFhaGUqmkQYMGdOjQAS8v3XWFOdns/GoR1y5EUb9tR3q89CqWNrYGMe9sVgFjIuNQagTTVN9RzzaM1m13Y2nhpte6j4RASJJkDmwHdgshPr/D6z7AdiFE4IN2Md2JvGIVXx6IYdXJRMxNTXi5Ux1e6uB330C2UCq5Nv4FSqKiqP3zaqyDgwEoLVLx2/zTaNSCEe+1uO+goUJlIcujlrPm0hqszax5OfhlRjUcJfd3kpExNELA2TWw611AQK95/8pQKigo4MSJE4SHh6NSqQgICKBDhw5Ur/53Ykn82dPs+moxKmUZXcdNJLBzD4O5if+MvM6kzAxclIL5ZqcwM1tEQKPFVK8+UO+1H7pASLqf0iogRwjxxi3Pewoh0sq/ngq0EkKMlCQpAFjL30Hq/UBdYwSp70dSdhGf7LzCzgvpVHew4p1e9XmqiRcm9whkq3NzSRw+Am1ZKb4bNmDuqWsDnpVSwKYFZ3Cvbc+gqU0wNb1/DUR8XjwLTy/k+PXj+Dn6Mb3FdNp6tTXY9ycj80STn6ara4jZAz4dYNBX4Fz775fz8zl+/DhnzpxBo9EQFBREhw4d/jGgR6NWcXTtT5zZsRV3bx/6vTEdV69aBjFPW6pmxb5oZlmXUb8UvqtrRnLq07i4tKdx0HKDCNCjIBDtgaPAeXRprgDvAaOAEHQupkRg4i2C8T4wHlADbwghdt5rD2PXQYQl5DB3xyWiUvII9HLgg36NaO13d7dPWUwMiSNHYV7bG581azCxsQEg+nQ6e3+4RFCXmnR8umIFMkIIjqQcYcHpBSQXJNOlVhemtZhGTfs7p9rJyMhUgPMbdZ1X1WXQ/SPd+M/y5BKFQsHx48eJiIhACEFwcDDt27fH1fWff/OKG+ls/2IBN+JjCOnVn05jxmNmYZgxxCUxOXxyKoHlNU3poDFjZbu6RF8eS2HhZVq32o2lpYdB9nnoAvEgeBCFclqtYFtkKgt2XSEtr5Q+gdV5t09DvF1t7nh94eHDJL8yCfvu3f+R2XRsYwyR+5LpPrYh9VtXfMiQUqNk9aXVfBf1HRqthvFB4xkfOF5Oi5WRqQzFOTphuLgZaraAwd+Cmz+gE4ajR49y9uxZAJo0aUL79u1xdnb+1zLRp46x+9ulSCYSvV55g7ot2hjEPG2Zhuyd8XxQkMvWmhYMt7fj86Z1SE9dQ3T0RzRssIAaNYYZZC+QBcLglCg1fH80nm8OxaHRCsa19+G1Lv7YW/07PpD9009kfPLPzCatRsu2pedIj89n6DvNcPeu3IChG0U3WHRmETsTdlLDtgbvtHiHbt7d5LRYGZn7EbNPF4guztLNamj3BpiakZuby7Fjxzh79iySJP0lDE7lc19uRa1Ucmj1CiL3/omnf336vT4Nx2qGuZsvS8jj+qZo3vGWOO5uxhu13JlepwalpamEhvXG0bEZIcE/GvRvXRYII3Ejv5SFu66yKSIFV1sL3upZn6db1PpHod2tmU1eiz/HoU8fAEoKlGz4+DSSJDH8veZY21X+WHo6/TQfh35MrCKW1p6tebflu/g5+Rns+5OR+c+gLII9H0D4SnBvCEOWg2cwubm5HD16lHPnziFJEk2bNqV9+/Y4Ot450zAn9Trbv/iEzKQEmg8YQvuRz2Fqpn+fU6HSkrcnkeTQVN5oYcNlOxM+qVeT57zcEEIQGfUCCsVpWrXchbX13VPlq4IsEEYmKkXBnO2XOJ2YS4Pq9swc0Ii2df5OPRNKJUnPj6X0yhV8fl2LVQNdwVxGUj6bP43Aq54T/V4Lvmfg+26otWrWX13PV2e/okRdwrMBz/Jy45exMb+z20tG5okjOQw2T4DcRGj7GnT5gNzCkkoJA8Dl44fZ+90yTM3N6TNpKn5NWxjEPGVKATkbokkqKGFKO3tumMPyAB96uelsuXFjOxcuvk7duh/gXWucQfa8FVkgHgBCCHZeSGfejstcV5TQO6A67/X9Oz6hzswkYdhwJFNTfDZtxKzcp3nx6HUO/XKVFv19adn/7l0h70d2STZfRHzB77G/U82mGtNaTKNn7Z6y20nmyUWjgsML4ehnut5Jg79F4RTwV4yhosKgcyl9T+TendSo34j+r0/D3lW/2gMAodFScDCZ/APJxFazYEoTa5Qm8HNjP1o46monVKo8Tp7qgZVVDVo034QkyTOpq8TDFoiblKo0rDgaz1cH49AIwUsdfJnU2R9bSzNdz6bRo7Fu0gTvFd8jmZsjhGD/qstcDU1nwGvBeAfoVxB3LuMc80LncSXnis7t1Opd/Bxlt5PME0ZWLGx+CVIjIGQ0eW3f52jYWSIiIiosDACK9DT+WPwJGYlxtBg4lHZPP2sQl5Iqo5icDVdRpRRyqYUrr7mrsTUz5ddgPxrY/p10cvnyu6Slb6JF89+xt2+k9753QhaIh0B6XikLd11h89nrVLO3ZHrvBjzVxIuCP7aROn0GzmPGUP2D9wFQKTVsWhBOkULJiPdbYO9y/6rte6HRatgQvYEvI76kRFPCc42eY2LjibLbSea/jxC6OMOeD8DMkvxuCzl6w/avdNWmTZvSoUOH+woDQHTocXZ/swQTExN6v/omdZq1NIB5gqKTaSj+TMDEwoTTfb2YUpRLLSsL1gXXoabV37HI3NxQIs4+Q23vCfj7T9d777shC8RDJOJaLrP+uERksoKQWk7MGhhA9TXfkrNqFZ7z5uE0dAgAihvFbJh/GhdPW556q+m/Or9WheySbBafWczWuK142noyveV0utbqKrudZP6bFGbA1tcgZjcF3j045jqS8KjLCCEICQmhY8eOd8xKuh2NWsWRNT8SsXMb1f3rMeCNGTi46z8qWJNfRs5v0ZTFKLCq78yuTu5MS0ojxMGGn4P8cLX4+2Si0ZQRdrofQquhVas/MTU1Xiq7LBAPGa1WsOXsdebvvEJWYRlPN/HkpR1LUZ+N0LXjCNENDIo7m8Gu5RcI6lyTjiMNN2XqbMZZ5pyaQ0xuDB1rdmRGyxnUsjdMpaeMzCPB1V2w9VWKSlUcrz2ZsOQyNBoNwcHBdOrU6Y51DHciPyuT7Ys/IS32Kk37DKTjmHGYmunf3qY4KpPcLbGg1uLQ15cfPU34OCGdLi72rAj0wfa2caNx8YtJTFxGSMgqXF30nx1xL2SBeEQoKFWx7EAsK48n4KYp5avjX2KHBt+NGzH30N2h3Cyi6/lCAHVbGCa3GkClVbH28lq+Pvc1GqHhpaCXGBc4DgtTw1R9ysg8FFQlsOd/lJxezQnb3oQq66FUqWncuDGdOnX6V+XzvUiMjGDHl5+hUano9fLr1G+j/weztkSNYlscxWczMK9lj/PwunySn8fXyRkM8XBmSQNvzG/LXiwsjCbs9EA8PPoR0GiR3jbcD1kgHjHiMwuZvf0SCaejWHLkS0zq1ido/RokCws0Gi1bF58lM7mQ4dOb41LDMJ0gb5JelM6npz9lT9IefBx8eL/1+7T2bG3QPWRkHgjp5yn7bSKnsm05YdqWMo1EQEAAnTt3/kevpPshtFpObV7PiY1rcfWqxcC33sOlhv5tbMriFeRsiEaTX4ZDV29sOtdiWmwKa9NyGOflxry6Xpjc5u4VQsuZiKcpLk6gdavdWFgYv4uzLBCPKAeu3GDHktW8eHAl55r3pMOX86npbEORooz188Kwtrdg2IzmmFdhFOr9OH79OPNC55FckEw/v3683fxt3Kz1T92TkTE6Wi2qE18Ttn8rx0QzSrCifv36dOnS5R/dVStCSUE+O5ctIuHcGRp26EKPF1/F3Eq/JBGh1pK/L4mCwymYuVjhMrIBwsuWSZeS2JGZx9TaHkzzrX7HWGDK9bVcvfo/GjX8FE/PIXrZUVFkgXiEKVNrOPT6+3jv38riFs8Q8PxIJnbyIyNGwR9fRtKwrSddn21onL01Zaw4v4Ifzv+AlZkVbzR9g2H1hmEi6R8gl5ExBmrFdSLWfMiRLCcKsaOOjzdduvekZs3K3/Gnx0azbfF8ihW5dH5+AsE99J/iqMosJmfdVVTXC7FtUR3H/n6UmML4C4kczi1gtn8NJtS6c8Bbqczi5Kme2Nk1oGmTXx5YMoksEI84QqUi5rmxlJ6/wOsdXkPtW4eZ/QOwiy4kYlcS3cc1on6ryt0ZVYb4vHjmnZpHWHoYjd0bM7P1TOq7GGYCloyMIdBqtUTtWcuh0HMohB3eLpZ0HTgKHx+fKq0XtX83B1Z+g42TMwOmzsDTX7/fdyEERWHp5G2PRzI3wXlIXawD3chVqRkdFc+5/GI+b1CLkZ53dxldujSN9BvbaNVyO7a2/nrZUxlkgXgMUGdlkTBkKGUmZrzX6y2i8gRd6rnRM8OE/LRiRrzbHOfqho1H3IoQgu3x2/ks/DPyyvIY03AMk0ImybUTMg8VrVbL5YvnOfjnZrJKJDzN8ujWeyB1mnWu0h22WqnkwI/fcv7AHmo3bkLfyW9j43D/moh7oSlSkbsphtJL2VjWdcJleD1MHSzJKFMxIjKO+OIylgfUpo/73VNscxWniYgYSe3ar+Bf52297KksskA8JhSfPUvSc89j06YNe0e/wxcH4rBQahlfZI2rmzXDZzTHzAjxiFvJK8tj8ZnFbIrZRA3bGrzf+n061uxo1D1lZG5HCEFsbCwH9uwkLTMHN7Lp6m9LwxEfIllUrSYgPyuDbYvmcyM+hlZPjaDtiNGYmOj391Qam0vO+mi0xSoce/ti164GkolESqmSEefiSCtTsTrIlw4ud+/YrNWqCDs9AI2mmNatdhu15uFOyALxGJGzdi03Zs/B7dVXEc+/yMd/XibydDrDiixxDHRmzGtNHogdETcimHVyFvF58fSs3ZMZLWfgblPxzBAZmapy7do19u/fT1JSEk7k09k8ksZPvYlJo35VXjPp/Dl2LFmIRq2i96tv6j27Qai15O1NovBICmbu1riMbIBFDTsA4ovLGH4ulgKNhl8a1/mrr9Jdbbv2PbGxn9A4aDnu7t31sqsqyALxGCGEIG3Gu+Rt3Uqt5d9i16kTp+KzWbciiro5gnh/K6aMC6a2q/HcTTdRaVSsvLCS76K+w9LUkjeayUFsGeNx48YN9u/fT3R0NLZmGjqpD9O0tiNmQ5eDQ40qrSmE4PS2TRz7dTUuXjUNksKqyiohZ90VVCmF2LaqjmM/P0zKT/aXC0t4OjIOtRCsC65DY/t7u2hLS1M5FdoLZ+c2BDf+Ti+7qoosEI8Z2tJSEkeOQpWWht/mTZh7eVGmVPPD7FDKskv51UnJmO7+TOzkh6WZcV1OAIl5icw9NZfQ9FBC3EP4qO1H1HGqY/R9ZZ4McnJyOHToEFFRUVhamNHOJIrWpQex6DINOrwJVXQDqUpL2fXtEqJPHqVe6/b0euV1LKyq7r4RQlB8JgPFtlgwNcFlqC4QfZNz+cWMiozDwkRiQ4g/9W3vny4bdf5VsrMP0brVLqytH053A1kgHkOUSUkkDB2GhZ8fPmt+RrKwoCCnlF/nhJFvKvjatJDa7rbMHhRAh7rGd/0IIdgWt41Pwz+lSFXEi0Ev8lLQS3IltkyVKSws5MiRI4SHh2NiYkKrWha0S1yCjb0jDP0BalfdDaS4kc7Wz+aSnXyN9qOeo8XAoXqljWpL1eRuiaUkMhMLX0dcRtbHzNHyr9dDFYWMjorHydyUjSH++Fhb3mM1HVnZh4iMfIE6fm/h4zOpyrbpiywQjyn5e/Zwfcrr/+j8Gn8uk53fnsetmRvfKLJJzC6mf2NP/te/ER4O+hX4VISc0hwWnl7Ijvgd+DpmFoANAAAgAElEQVT68lGbj2jq0dTo+8r8dygtLeXkyZOcOHECtVpN08YBdCrYikP8NqjfFwZ9BTYuVV4/MTKCHUsWAtDv9Wn4BOv3+6lMLiD71ytoFKU4dKuNfZdaSLe0xziaU8Bz5xOoYWnOhpA6eFnd/6ZJoyklNLQPkokZrVpux8Tk/oJiLGSBeIy5MX8+OatW4/XFYhx69wbg0NqrXDxynV6TgvgzU8Gyg7FYmJowtUc9nm9TGzNT48cIjl0/xpyTc0gtSmV4veFMbTYVe4vKzdaWebJQq9WEh4dz5MgRiouLadSoEV0buuK2d7KuE2vPOdDqZajinf6t8QbXWt4MevsDnDyqXj8ktILCY9fJ25WIqb0FLqPqY+nzz5TYA9n5jL+QgI+1Jb+F1MHdomKN/eLjl5CQuJQmIatxcWlXZRsNgSwQjzFCqSTp2ecoi43FZ+NvWPr6olJq+G1+OKVFKkZ+0JJMlYoPt13k0NVMAmo4MO+pIEJq3b+tsb4Uq4r56txXrLm8BlcrVz5o/QFdvbsafV+ZxwutVsuFCxc4cOAACoUCX19funftilfSRtg/B5y8YfiPUKPqGXr/iDe06UDvl1/Xq2WGplBJzoZoyqJzsQpwxWVoXUxs/vnhvycrjxcvJFLP1or1wXX+0a77XpSUpHAqtCdubt0JClxaZRsNhSwQjzmqtDQSnhqCWbVq+Kxfh4m1NdnXC/ltfjg1GzjT79XGAOy8kM6sPy6SUVDGs61r83av+jhY6d+q+H5czLrIzBMzic6NppdPL2a0nCH3dZIBIDY2ln379pGenk716tXp3r07dao7If3+MsTuhUaDYeCXYOVQ5T3yMzP4/bO5ZCYl0GHU83rHG0pjFeSsv4K2RI1Tfz9sW3n+a73tGQpevpRIoJ0N64L9cDKv+JQ5XWD6MG1a78HKqmrZWYZEFoj/AIVHj5I8YSKOTz1FjY/nARB1MIWj66NpP6IuwV11GRAFpSoW7Ylm9clEXO0s+V//Rgxo/O9fcEOj0qr48cKPfBv5LdZm1kxvOZ0BfgPk4URPKKmpqezbt4/4+HicnJzo2rUrgYGBmKSEwcbxUJQJvedD8xeq7FICSLl0gW2L56NVq+n3+jR8Q5pVeS2hFeTvv0bBgWuYuVnj8kxDLDz/nU6+5UYur11Ooqm9Lb8E++FQiUzCnJzjnD33HH5+b+Lr82qVbTUkskD8R8hYsoTsb779axKdEII/vznPtUvZDJ/RHLeaf8cAzqfk8d6W85y/nkeHum7MHRz4QGon4hXxfHjiQ85lnqNtjbbMbDMTLzsvo+8r82iQm5vLgQMHOH/+PNbW1nTs2JEWLVpgZmICJ5bC/tnlLqWfoEaIXntF7v2TAz8ux9HDk8HvfKBXfYMmv4ycdVcpi8/Dpmk1nAb7/1XbcCvr03KYeuUarZxs+TnID7tKiMPfFdOl5RXTDy8wfSsPXSAkSaoFrAaqA1rgOyHEEkmSXID1gA+QCIwQQuRKutvOJUBfoBgYK4SIuNceT4JACI2Ga+NfoCQyEt+Nv2Hp709JoZJ1c8KwtDZj+Hst/tEaXKMV/Hwykc/2RKPSaHm9e11e6uCHuZGD2FqhZd2VdSyJWIJA8EbTNxjZYKRcYPcfpri4mKNHjxIWFoYkSbRu3Zr27dtjZWUFxTmw5WWI2V3uUloKVlXvf6RRqzj403dE7t2Jb5Pm9JvyDpY2Vb/5KY3OJWf9VYRSg9Ngf2yb3XlQ19q0bN66kkwHZzt+CvLDppJ/R8nJPxEdM4fGQd/i7t6jyvYamkdBIDwBTyFEhCRJ9sAZYDAwFsgRQnwiSdIMwFkIMV2SpL7AZHQC0QpYIoRoda89ngSBAFBlZJAw+CnMXF3w2bABE2trkq/ksG3JORq1r0GX0Q3+9Z70vFI+3HaB3RdvUN/Dno+HBNGsdsVGMOpDamEqs0/O5njqcZpWa8rsdrOp7VDb6PvKPDhUKhWnT5/myJEjlJaW0qRJE7p06YKDQ3lM4foZ2DAWCtKg18fQ8iW9XErF+Xn88fl8Ui5foMWgYbQf+WyV+ykJjdDNbTiUjFk1G1yfaYC5x52F5pfUbN66mkwXF3tWBvpiXUlxUCqzOXmqGw4OIYQE//hIuV4fukD8ayNJ2gosK//XWQiRVi4ih4QQ9SVJWl7+9a/l11+9ed3d1nxSBALK4xEvTcBp+HA858wG4MTmWM7uuUbfV4LwDb5z4dyei+l8uO0i6fmljG7lzTu9GuBobdwgthCCrXFbWRi2EKVWyeQmkxnTcAymejZJk3m43J6Z5O/vT48ePfDwKL/7FgJOr4Bd74K9J4z4CbyqHh8AyLqWyJaFcyhW5NJz4mQaduhS5bU0+WVkr72CMjFfN7dhgN8dXUoAa1KzeftqMl3LxcGqCifwy5ffJS19M61a7nigrbwrwiMlEJIk+QBHgEDgmhDC6ZbXcoUQzpIkbQc+EUIcK39+PzBdCBF+21oTgAkA3t7ezZKSkoxu/6NCxqJFZH+/Aq/PF+HQty8atZaNC8IpUpQx8n+tsHG4c7FOYZmaRXuusupEIm52lswaGEDvwDtPtzKovcUZzDk5h0MphwhyC2JOuzlyu47HlMTERPbs2UNqairVq1enZ8+e+Pn5/X1BWSH8MQUubIK6veCpb/UqfAOIOxPGjqWfYmFtzaC339drfkNpTC45664iVBqcn6qLTZM7D/AB+Dk1i3euptDNxYEfAn2qJA75+VGcDh+Cd63x1K37XpXtNhYGEwhJkkyAYKAGUAJcFELcqIQhdsBhYJ4QYrMkSYq7CMQOYP5tAjFNCHHmbms/SScI0A0ZSnr2OcpiYvDdshkLb2+yUwv57eNwajV0pu+kxvf80I9KUTBj03kupeXTo5EHcwYFUt3RuJXYQgh2Juxkfth8ilRFvBL8CuMCx2FmUvEUQZmHR1ZWFnv37uXq1as4ODjQrVs3goKCMDG55UMz4zJseA6yY6HrB9BuKphUPfYkhCD8j80cWfsTHr51GPTOB9i7VC2F+h9ZStVscB3dEPNqd2+mt/p6FtOideKwMsgHyyp8H0JoOXNmBCWlybRpvQ8zs0evmFRvgZAkqQ4wHegOxACZgBVQD10QeTmwSgihvYcR5sB2YLcQ4vPy5/5yHckupsqjun6d+KeGYOHtjc/aX5AsLIjcn8yx32LoPLo+AR3unT2k1mj54VgCi/dFY2ZiwvQ+DRjd0hsTE+OeJrJLspkXOo+9SXsJcA1gbru5+Ds/Wsdumb8pKiri8OHDhIeHY2ZmRocOHWjdujXm5re5J89vhG2TwcIOhv0AvvrNEVGrVOz7fhkXD++nXuv29J70BuaWVbuJ0RQqdVlKsYp7Zind5KfrWcyITqG7q+7kUBVxAEhL28Kly2/TsOECangOq9IaxsYQAvEr8A1wVNx2kSRJHsAoIFcIseou75eAVegC0m/c8vynQPYtQWoXIcQ0SZL6Aa/xd5B6qRCi5b2MfxIFAv7u1+Ty/PN4vDsDoRVsW3qO9Pg8nn6/JU4e958Il5RdxPtbLnAsNovmtZ2ZPySIuh7Gv9PZnbibeafmUagqZFLIJMYGjJVPE48QKpWK0NBQjh49ilKppFmzZnTu3Bk7O7t/XqhWwp4PIGw5eLfRpbDa6zcitzhPwdZFH5N69RJthj1Dm2GjquwGLUvII3utrvDNeVAdbJp73HOtVdezmB6dQk9XB77XQxzU6iJOnuqOlZUnzZttRHpEs/geegxCkqT2wFHgPLo0V4D3gFBgA+ANXAOGCyFyygVlGdAb3Qll3O3xh9t5UgUCIH32HHLXrqXmN19j36ULhbmlrJsThpOHDUPebopJBfymQgg2R1xnzo5LFJWpebWLP5M6+2NhZtxfavk08eghhODixYvs27cPhUJBvXr16NGjB+7ud0h+yE+FDc9DShi0fhV6zAJT/RIfdMHo2RTn5dF70lTqt2lf5e+j8Oh18nYlYOZijcszfw/1uRs3s5V6uDqwQg9xAIiP/4KExC9p3uw3HB0f3YaWhoxBxAGfCiG+veW57UKI/vqbqR9PskBoy8pIHDkKdVoavlu3Yu5RjZjwG+xZcZEW/X1p2d+3wmtlF5Yxe/sltp5LpZ6HHQuGNqaJt/FTYuXTxKNBSkoKu3fvJjk5GQ8PD3r16vXPAPStJBzRVUUri2HQMggcovf+CefOsP2LTzC3tGLwtJlUr1O3SutoS9Xk/hZNycVsrANccR5eDxOre/8+rUvLZuoVXSrrj0G+eolDaWkaJ091x82t2yPRb+leGFIgrgCR6O7qJwohlJIknRVCPJg5mPfgSRYIgLL4eBKGDMWmaRNqrViBZGLC3pUXiQnPYMg7TanuW7nCpANXbvD+lguk55cyrq0vb/eqh00Fm5FVlZzSHOaemsvepL00dmvM3PZz8XWsuLjJVB2FQsH+/fs5f/48tra2dOvWjZCQkH8GoG8iBBxfAvtngas/PL0G3KueVXSTs7u3c/DH73Dzrs3gaTNxcKvanBNVehHZay6jzinBsY8vdu297uue2piew+TL1+jobM+qoKqlst7KxUtvk5Gxg9at9mJtrd8EO2NjSIGIEEI0lSRpGjAUGAFsEUI89PPTky4QALkbNpA+80OqTZuG6/hxlBWrWDcnDFNzE55+vyXmlpWrPSgoVbFw11V+PpVETWdrPhnSmPZ1jduETwjBrsRdzAudR6m6lClNpjCm0Ri5CttIlJWVcfz4cU6cOAFAmzZtaN++PZaWd2kDUVYAv78Cl//QVUUPWgaW+sWrtBoNB1d9z7nd2/Fr2oJ+r0+r8uS3oogbKLbEIlmZ4fpMAywrcGO05UYur15Koo2THT83rnyF9O3o0lqforb3RPz9p+m11oPAkALx12lBkqRuwFfoAst3TyR+QMgCoftwvT5lCgWHDuOz7lesAwJIuZrL1sVnCepck44j61Vp3dD4bN7dfJ74rCKGN6vJB/0a4Whj3AK7zOJMZp2cxeGUwzTzaMacdnOoZf9wRjL+F9FqtURFRbFv3z4KCwsJDAyke/fuODndo018VgysGw3ZMdBjNrR5Ta+qaICy4mJ2LFlAwrkzNOs3mI5jxlWpMlqotSj+iKMoNB0LX0dcn2mAqf39B/dsy1DwyqVEWjjoGu/ZmupXwCmEICJiFEXFcbRtc+CRTGu9HUMKxAAhxB+3PK4NPC+EmK2/mfohC4QOdW4uCYOfwsTGBt9NGzGxseHo+miiDqYw6I0QajaoWsFSqUrDkv0xfHckHldbC+Y9FUSPRnfuWWMoblZhLwhbgEZoeLv52wyvN/yRalPwOHLt2jV27dpFamoqXl5e9O7dm1q17iO+V/6ELRN1AehhP4JfJ73tyM/KYMuC2WSnXKP7C5No3L13ldZRK8rI/uUyquQC7DrWxLGXD5Lp/X9HdmYqePFiIs0cbPm1sR+2BpjvnpGxm/MXJlG//hxqej2j93oPAkOkud7ThXS/RnoPAlkg/qbo1CmujRuva8UxexYqpYb1c8PQqgUj/9cSC+uqxxLOp+TxzsZIrqQXMCikBh8OCMDF1rhzqdOL0pl5fCYn007SrkY7ZrWdhYetccXpv4hCoWDfvn1cuHABe3t7unfv/u9Ct9vRauHQfDiyEDxDdPEGJ/1PcjfiY9mycDaq0lIGvPkuPo2rFsYsjVOQs/YKQqXFZUQ9rAMr5gLdn53P2PMJBNlbsz64DvYGEAettoxTob0xMbGkZYvtmDwmSRaGEIiDtzxsBoQDNyVaCCEe+hgxWSD+ScZnn5G94ge8vlyKQ48epMXlseWzMzRsV4MuY/7d0K8yKNVavjkUx7KDMThYmTN7UCB9g4zbrkMIwfqr61kUvggLUws+aP0BfXz7GG2//xJKpZLjx49z/PhxANq1a0e7du2wsLiPsJcoYPNLELMHQkZDv0VgXrXYwK3EnQljx5KFWNnbM2T6h7h5+1R6jb9SWHcmYOZmjeuzje5ZFX0rx3ILGBMVT10bKzaG1MGxEsN+7sW1az8QE/sxIcE/4uqqX5Hgg8SgdRCPStbS7cgC8U+EUkniqGdQpaTgu20r5h4enNgUy9m91+g/OZjaAa5673ElPZ9pG6OISsmjd0B15gwOxN3euD3uE/MSef/Y+0RlRdHbpzfvt3ofJyvjj1d9HBFCcOHCBfbu3Ut+fn7F4gw3ybgC60aBIhn6fKL3YJ+bnN31Bwd/+p5qvn4MnjYTO+fKuzy1ZWpyN8ZQcj4L68DyFFbLin3In84r4unIOGpaWrCliX+Fx4TeD6Uyh5OnuuLo0ISQkB8NsuaDwtACEfEoZC3djiwQ/6YsPoGEoUOxDg7Ge+UPaDSCDR+HoyxRM2pmSywNEGhWa7R8f1TXrsPWwpRZgwKNPsFOrVWz8sJKvjn3Dc5WzsxqO4sONTsYbb/HkdTUVHbu3ElycjLVq1enT58+1K5dwVbrl7fr4g3mNjBiNdRuo7c9Wq2Gwz+vJOLPrfg1a0n/KdOqNDNalVlM9s+XUGeW4NjbF7uO909hvUlkQTHDzsbibmHOlib+eFgaLtHiavRHpKT8QquWO7Czq1oyyMOiogIh5xH+x7D088XjvXcpPnWKnNWrMTM3pfvYhhTnKzm6IcYge5iZmvBK5zr8OaU93q62TPn1LK+siSCzoMwg699xTxMzJjSewNp+a3G0dGTS/knMPTWXEnWJ0fZ8XCgsLGTr1q1899135OTkMHDgQCZMmFAxcdBq4eB8WD8a3OrBhEMGEQdVWSl/fP4JEX9upUmfAQx6+/0qiUPJ5Wwylp1DW6TC7YUg7DvVrLA4XC4sYeS5OBzNTfktpI5BxaG4OIHr19fi5TXysROHynCvGMSXwM0XRwLrbn1dCDHFuKbdH/kEcWeEEKS8+hpFx47hu2kjlnXrErotnvA/E+85O6IqqDVaVhxL4PO90dhYmDJrYAADg2sY9TRRpiljacRSVl9ajY+DD/M7zCfQLdBo+z2qaDQawsLCOHToECqVilatWtGpUyfdRLeKUJqvm/p2dQcEj4L+X4C5/t19i/Pz+H3hbNJio+ny3Is07Tuo0msIraDgwDXy913D3MsO1zENMXOuuG1xxaUMPhuLKRJbm/pT29qwbtDz518jO+cwbdocxNLCuHVCxsAQQern7/XGuzXpe5DIAnF31NnZxA8YiJmHB77r16E1MdPNjshT8szMVljZGbamITajgLd+iyIyWUGvAA/mDg4yemwiNC2U94+9T3ZJNhODJ/Ji0ItPTKuOuLg4du7cSVZWFnXq1KF379537pt0N7Lj4NdRuhbdveZBq5cNEm9QpKexaf5MCrOz6Tv5beq2alvpNbSlanI2RFN6KRubJtVwHuKPZF7xjKPkUiWDImIo0wp+b+JPXVvDtrTPyztH+Jmh+PpMwc/vdYOu/aB46M36HgSyQNybggMHSJn0Kq4TJlDtzalkpRTy2/zT+DevRo9xAQbf79bThJ2lGXMGBdKvsafB97mVvLI85oXOY2fCThq7N+aT9p9Qy+G/W1yXm5vL7t27uXLlCs7OzvTq1Yv69etX7sQWux82jgPJVNeF1QD1DQBpsVfZsmA2Qqtl8LSZeNVvWOk1VJnFZK++hDq7BMe+fti1q9xpNFOpYmBEDDkqDZub+BNgp38G1q0IIYg4+wxFRTeL4u7dCPBRRe8YhCRJ30mSdMdzuyRJtpIkjZckabQ+RsoYF/uuXXEcNpTsFSsojojAraYdzXrXJjr0Bonnswy+n5mpCS93qsOOye2p6WzNq2sjmPzrWXKLlAbf6yaOlo4s7LiQBR0WkJCXwNA/hrI5ZjOP843PnVCpVBw8eJCvvvqKuLg4unbtyqRJk2jQoEHFP0CFgFPfwC/DwMELJhw0mDjEhoeyYdZ7WFhZMWrOp1USh5IrObp4Q3F5vKEC/ZRuRaFS8/S5ONLL1PzS2M/g4gCQnX0IhSIMX9/Jj604VIZ7uZhC0LXnDgIu8PfAoLqAA7AS+FYIYbzI5H2QTxD3R1NYRMLgwSBJ+G7ZAlbWbPj4NGXFakZ92ApLPQro7oVao6ubWHogBicbC+Y/FUR3I1dhpxel8/6x9wlLD6O7d3c+bPPhY58OK4TgypUr7N69G4VCQUBAAD179sTRsXKNGFGXwY634OzPUL8fDFmudz+lm0Tu/ZP9P3xLNd86PDV9JrZOlesELISg4FAK+XsSMfe0xfXZRpWKNwAUaTQ8fS6OqIISfm7sRycXw7e7EEJDaFh/tNoyWrfajYmJcVvPGBNDttqwA5oDnuhGjl4WQlw1iJV6IgtExSg+c4akMc/iNGwYnnNmcyMxn00Lwg1SQHc/Lqbm8dYGXRX20KY1mTmgEY7WxvvD0gotqy6uYunZpbhYujC3/Vza1NA/K+dhkJWVxa5du4iNjcXd3Z2+ffvi61uFTreFGbD+WUg+BR3fgc7v6TUS9CZCCI6vX0PolvX4NW1B/9enVzpTSavUkLsxmpKoLKyD3XEeWveeU9/uRJlWy3NRCRzNLeD7QB/6uRvnpiAtbROXLk8jMGApHh79jLLHg0KOQcj8g4xFi8j+fgU1v/4a+65d/iqgG/hGCLWq2KupoijVWr48EMPXh+KoZm/Jp8OCjd4h9nL2ZaYfnU5CXgLPN3qeKU2nYGFq3PYghqKsrIyjR49y4sQJzM3N6dy5My1btsS0Kk3l0qJ0wejibBj8FQQONYiNWo2Gvd8v48LBvQR26UmPl17FpJL2qRWlZK++hCqtCIdePpVKYf1rDa1g4qVEdmTm8UWDWoz01L8Y9E5oNGWcPNUNSwt3mjff/Nj3BpMFQuYfaJVKEkc8jTozE78/toGdI+vmhiG0gpH/a1XptuBV4VyygjfXnyM+q4ixbX2Y3rsB1pW8W6wMJeoSFoUvYv3V9dR3rs+Cjguo41THaPvpixCCS5cusXv3bvLz8wkODqZ79+7Y21fRXXJpm674zdoZRv4CNQzTDEFVWsr2JQuIjzhN66GjaDv8mUp/YJYl5JG95jJCrcVlVAOsq3CTohWCqVeSWZ+ewxx/L16qZbj07dtJuvY9sbGf0KTJGlycH88T6a3IAiHzL0qjo0kcOgy7bt2o+cViUmMUbFkUQeOuNekw4sEU+5QoNSzYdYWfTiTi52bLohHBRp9edzj5MDNPzKRYVcw7Ld55JLvDZmVl8eeffxIfH4+Hhwf9+vXD29u7aosJAUcXwYE54NUcRq4Fe8PEf4rz8/h9wWzS42Lo9sLLBPfoW+k1CkPTUGyNw8zFCtfnKt5P6VaEEHwUl8ry5Eze8vHgHV/jZcupVHmcONkFR8cQQoJXGm2fB4nBK6klSbLVzySZh41VvXq4TZ5Mwa5d5O/cSY26TgR18iLqYAppcXkPxAZrC1M+GhjALy+2olSlYeg3J1i05ypKtfb+b64inWp1YtPATTT1aMqcU3OYemgqilKF0farDEqlkv379/P1119z/fp1+vTpw4QJE6ouDqpS2DxBJw5Bw2HsDoOJQ17GDdZ9OJ2MpHgGvDmj0uIgNALFtjgUW2Kx9Hei2qshVRIHgK+uZbA8OZPxXm687VO9SmtUlKSk5ajV+dTxe8eo+zyKVCRI3RZYAdgJIbwlSQpGN3p00oMw8F7IJ4jKI9RqEp8ZjeraNfy2/4HWzolfZ4diZm7K0x+0wKwSBUn6kl+qYta2S2yKSCHQy4Evng7Bv5rxhq1ohZafL/3MFxFf4GLlwvz282np2dJo+92Lm9lJu3btIi8vj8aNG9OjR4+qu5NAF4xeNxpSwqDrB9DhbYMUvwFkJiWwaf6HqJVlDJ42k5oNKldHoy1Wkf3rFcpiFNi198Kxry+SSdVsW5uWzZtXkhlczYmvG9XGxIinQd2c6W5Uq9aHgEaLjLbPg8aQJ4jFQC8gG0AIEQk8Pn1tZf6BZGZGjY/noS0uJn3WLMwtTekypgGKG8WE70h8oLY4WJmzaEQw345pxvXcEvotPcZPxxPQao3j9jSRTHg+4Hl+6fsLNmY2vLjnRZZGLEWlVRllv7uRk5PD2rVrWb9+PZaWlowdO5YhQ4boJw7pF+D7rpB+Hoav0mUrGeiDM+XyBdZ/NANJkhg5a2GlxUGVWUzG15GUxefhPLQuTv39qiwOuzLzePtKMp2d7Vna0Nuo4gCQkLgMIbT4+U416j6PKhVyMQkhkm97SmMEW2QeEJb+/ri/PoWCvfvI3/En3o1cadC6Omf3XCP7euEDt6d3YHV2T+1I2zqufPTHJZ7/MYz0vFKj7dfItRHr+69nsP9gvj//PWN3jiWlIMVo+91ErVZz+PBhvv76a5KSkujZsycTJ07Ex8dHv4Wjd8PKXqBVw/idEDDYIPYCxJ0JZdO8mdg4OTNqzqe41apgd9hySmNyyfgqEm2JCveXgrBtUXV30ElFIRMvJRJsb8MPgT5YGCBV914UFyeRlrYRL6+RWFvXNOpejyoV+Qknl7uZhCRJFpIkvQ1cNrJdMkbGZexYrIODSZ8zB1VGBm2H+WNhY8bBNVcQRrqDvxfV7K1YObYFcwcH8n/2zjusqev/468btkyRIQgyFFzgHmjRtlorat3WvQfuTq2t3bbWrm9dte5ZrLsOnHXvrYBbkY3sFfZIzu8PsD9bAQMkgDav58kTuZzc8wkm933P+ayrYSl0W3ia/UExGpuvhl4N5r4yl59e/YmQtBAG+Q/icNhhjc0XEhLCsmXLOHHiBO7u7kybNo0OHTqUL3T1aS4uh81DoFZ9mHhCbZFKALdPHWPPz/Oo5ejEkK9/wMyqbG3oM84/JnHdLXQt9LGZ1gID5zIm9z1tS0Y2o4JCqGuoj5+aWoU+j9CwxUiSLs5OVb6bXmWoIhCTgWlAHSAKaA78d/9iLwmSjg528+cjcnKI/fIrDI318H7bjbhQObdOR1eNTZLECC8n9r/jjbOVMdP+uM77WwOQ52huC8jH2YftvblXRcQAACAASURBVLbjYu7CzFMz+frC12otIZ6ens6OHTvYuHEjSqWS4cOHM2jQoLJnQv8bRQEcmAWHZkODHjD2AJipL5Lniv+fHPptAY5NmjLoi3nUMFPdXqEQpOwJJnXvIwwbWGI9pRm6luUvmBeencuQwEeY6uqwuVk9tTX8KY2MzIfExu7BwWEkBgZlE8aXCVUEooEQYrgQwlYIYSOEGAE8t9CKJElrJUmKlyTp1lPHvpIkKVqSpICiR4+nfveJJEnBkiTdlySpW/nejpayYODqgvV775Fx4gTyvXtxb2uLY6OaXNj9iIyUKquggqu1CTsmt+fdLm7sDXxMj0VnuBqWrLH5HEwdWN99PeM8xrHjwQ6G7R9GcEpwhc6pVCq5fPkyv/76K3fv3uXVV19l6tSpuLm5VdzgHHnhquHySugwAwb9DvrqCTIUQnB60zpO+63F3cubfrO/RN9I9UgjZU4BietvkXkhBpNXHag1srHKnd+KIzGvgKGBIeQrBZub1cPBsHKSHUNCFqKjY4yz06RKma+6okoU0zPd5FTpMCdJUicgA9gohPAoOvYVkCGE+PlfYxsDm4G2gD1wFHAXQpTq69BGMVUcoVAQPnIUucHBuPrvJUtmyua5l3FqUovukz2r2jyuhafw/tYAolKymPZ6fd7p4oaejub2ns9Hn+eTs5+QmZ/J7LazGeg2sMw5EzExMezbt4/o6GhcXFzo2bMnVlZqyhxPjYQ/BkPCvcJ+0a3Hque8FHaAO7JyKbdO/EWzrt3pPG4yMpnqWzkFSdkkbrhDQWI2NfvVr5C/AQrrKw288Yi7mdlsb16fNuaVE2kvT7/FlSt9Xuhy3s9DHdVc20uS9CFgLUnSB089vgKe+6kRQpwGVL3t6wNsEULkCiFCgWAKxUKLhpF0dLD/bh4iL4/YL7/CzMqItm+5EBKQQEhAQlWbRyunmhx4tyP9Wzqw5HgwA5dfICwxU2PzdajTgZ29d9LKthVzL8zlo9MfkZGnmuM+NzeXQ4cOsXLlSlJTU+nfvz+jRo1SnzhEX4fVXSAtCkbsUKs4KAry2b/oJ26d+Auv/oPpMn5qmcQhNyyN+N8CUKTnYTXeo8LiUKAUTLodTmB6FssaO1WaOACEhPyCrq4FdeuOq7Q5qyul3YrpAyaALmD61EMODKzAnNMlSQoq2oJ6kkJbB3g6Uiqq6JiWSkDf2Rnrd94h4+RJ5AcO0OwNR2rVMeH0lgfkZRdUtXmYGOjy89vNWDqsJWGJmfRYfIZtVyI1VtLbysiKZW8s492W73Ik/AiD9w3mTtKdUl9z9+5dli5dysWLF2nVqhXTp0+nadOm6svYvn8Q1vcEXQMY/xfU66ye81JYOmP3j9/w4OJZXh05nlcGjyyT3ZnX40hYdROZkR42U5thWK9ixfKEEHz0IJKjSXLmuzvQXUPF94ojNfUqSUmncHLyRVdXczk5LwqqbDE5CSHCy3VySXIG9j21xWQLJFLYyvQbwE4IMU6SpKXABSGEX9G4NcABIcTOYs7pC/gC1K1bt1V4eLlM0/IvREEBYUOHkR8VheuB/SSl6rDjx6t4vupApyHVp+duTFo2H24L5PyjJHp62vFdP0/Ma2iuOuz1uOvMOj2LlJwUZraeydCGQ/9x8UxLS+PgwYPcu3cPGxsbevXqhaOjmhsWXVpZ6Iy2aw7DtoKJ+pymOZkZ7PphLjEP7tHVdzqend9U+bVCCORHI0g/FoG+izlWIxshU8P/xY+hMfwSFsf7TrbMdtVsw6mnKWwGNJysrEd0aH8CHZ3yZXm/CKgzUS5LkqSfJEk6IEnS8SeP8hglhIgTQiiEEEpgFf+/jRQFPP2tcgAel3COlUKI1kKI1mVqsailVCRdXezmfYsiI4O47+Zj62KG52sO3DwVRWxI5ZThUAU7cyP8xrfj4+4NOXw7lu6LTnMpJElj87W0bcmOXjtob9+e+Zfn88HJD5DnyVEqlVy8eJGlS5cSHBzMG2+8waRJk9QrDkoFHJoDB2eBe3cYs0+t4pCVlsq2uXOIDX7AW+99VDZxKFCSsvU+6cciqNHKFuvxHmoRh98fJ/JLWBxDalvykYtmS2j8m5SU86SmXsLZaepLLQ5lQRWB2ATcA1yAr4Ew4Ep5JpMk6enbgX4UNiIC2AsMkSTJQJIkFwqbEl0uzxxayo+huztWvr7I/f1JP3kSrz6umFgYcHLTPZQKzdVKKisymcTkV+uxc0oH9HVlDF11kf/9dZ98DdlY07AmSzovYWbrmZyMPMmYbWNYsnwJhw4dom7dukybNg1vb++K5zQ8TV4WbBsFF5cW9oserL5IJQB5YjxbvpxNyuNo+n30Oe5e3iq/VpGZT8Lqm2QFJGD2phM1B7oh6VY8cOCvxDRm34+is6UpPzVwrNSCikIIHoX8D0MDe+rUGVJp81Z3VPlfrSWEWAPkCyFOCSHGAV7Pe5EkSZuBC0ADSZKiJEkaD/woSdJNSZKCgNeB9wGEELeBbcAd4BAw7XkRTFo0g9UkXwzc6hP75VfoFOTQcZA7SdGZBJ3QfKZxWWnmaMH+dzoyoMiBPWjFBSKSsjQyl0ySMdRtKB+afYhnsCcxSTHUbl+bYcOGUbOmmqvRZiTAhl5wbz/4fA/df4AyOIyfR0rsY7Z8OZustFQGfvoNzs1bqfzagsRsEpYFkheZjuWQBph1rquWC3mAPItJt8PxNDVilYczeuUsxVFeEpOOI5cH4uIyA5nMoFLnrs6o4oO4KITwkiTpMLCYwq2fHUKIKi+srw1z1QzZQUGEDRmKxaC3qf3ll+xfGsTjh6kM+8oLk5rV88uzN/Axn+66iRAwr58HfZqrN8YhODiYffv2kZqaikdzD04ZnuJk3EnedHqTrzt8jYm+mvoTJwbDpgGQHgcDVkGjXuo575PTR4az49vPUCoUDPj0G2xdVP8a54alkbSx0Flfa1TjCmVGP01Edi49rz/EUCbjQCs3rPUrt5WnEIIrV/pQoEjHq90RZDLNJ+JVNer0QXwrSZI58CEwk8LKrv/NylX/EYyaNsVy1ChSt2wl68oVOg52R6kUnNvxsKpNK5Hezew58E5HGtQ25d0tAczaHkhWXsUjsDIzM/nzzz/x8/NDR0eHMWPGMLDvQBZ1W8T7rd7nWMQxBu8bzL3kexV/E5FXYE1XyE2H0f5qF4e4kGC2fv0JSBKDv/q+TOKQFZRAwuqbyGroYT21udrEITW/gOFBIeQpBZuaula6OEDh6iE94zbOztP+E+JQFkpdQUiSpAO8I4RYUHkmqY52BaE5lNnZhPTuAzIJ1z17uHYshsv+ofR6pxl1G2umraM6KFAoWXj0IUtPBuNiZcySoS1oYl/2i5kQgsDAQA4fPkxubi7e3t507NgRPb1/XsCux11n1qlZpOam8nG7j8uVWAfAvQOwYxyY1oYRO6GWehfo0ffv8uf8LzE0MeHtz+ZhUVu16CAhBBlnokk7EIq+sxm1RjZGx1g9F/FcpZIhgY+4lpbFlmb16FBTTauwMiCE4MrVvhTky/Hy+m+sHkBNK4giP0BvtVml5YVBZmSE3TffkB8eQcKSJbR80wlzGyNOb35AQX71dQ/p6siY2a0Bm8a3IyOngH5Lz7PuXGiZciZSUlLw8/Nj9+7d1KpVi8mTJ9O5c+dnxAEKo5y2995O69qtmXthLp+e/ZSs/DL6Qa6shq3DwaYRjD+idnGIuBXIznmfY2xhweCvvlddHJSFDX7SDoRi1NQK6/GeahMHIQQf3IvkQmomCxvVrRJxAEhKOkF6+i2cnaf+Z8ShLKjig5gHmANbgb9TWIUQ1zVr2vPRriA0T8znn5P65y5cdmwnQdiyd3EAbXu50KanS1Wb9lySMnKZtSOI4/fieaORDT8NbEZN45Jr+SiVSi5dusTx48eRJIkuXbrQpk0bZCqUlVYKJSuCVrAsYBn1LOrxy2u/4GL+nL+REHBsLpz9Bdy6wdvr1BqpBBBy/Qp7f/mOmrXtGfjZtxhbqOZQV+YpSN58j5y7yZh0qoO5T/kb/BTH9yExLAyP4xMXO951Vk/Hu7JSuHroR35+Ku29jiCTVf72VlWhtp7UkiSdKOawEEKoL5WznGgFQvMoUlN51PMt9Oztcd6ymb/W3SU0IJGhX7bF3Lr6x4oLIVh7LozvD97FysSAxUNb0MbZ8plxcXFx7N27l+joaNzc3OjZsycWFmXP4D0ffZ7ZZ2aTr8xnboe5vOlcQm6BIh/2zoDAzdByNPT8BXTUewf78NJ59i36AWsnFwbMmYuRqZlKr1Ok55G44Tb50RlY9KqHSQd7tdr1x+MkPrgfyXA7S36u5HDWp0lMPEFg0AQaNvyOOvaDq8SGqkJtAlGd0QpE5ZDmv4/Hs2Zh+9lnGLw1kE1fXcSunjlvTW9WZV/usnIzKo3pm68TlZLNB13dmfJqPWQyiYKCAs6cOcOZM2cwNDTEx8cHT0/PCr2v2MxYPjz1IUEJQYxoNIIPWn+A3tN3p7kZhTkOj47Ba3Pg1Y/U1v3tCffOn+bAkp+pXc+N/p98jaGxals4+QlZJK67jTI9D8shDTFqol5/05nkdIYGPaJjTVM2erpWejjrE4QQXL02gLy8pKLVQ+VUia0uaAVCi9oQQhA5YSLZAQG4HtjPnVt5nN3+EB9fD+q1fHFq5afn5PPJnzfZFxRDRzcrPupozekjB0lISMDT0xMfHx+MjdWzxZOvyOd/1/7HprubaG7dnJ9f/RlbY1vITIRNb0NMALy1EFqNVst8T3PnzAkOLV2AfYNG9P9Y9XLduRFyktbfBkmi1ujGGNRVbcWhKg8zc+h5/QH2Bvr4t3TDtBKa/pREYtJJAgPH07DBvP9kYpxWILSolbzISEJ69cakozf2Cxexbf5VcjPzGfaVF3oGVfdFLytCCP64GIr/wb9oIIvFsIYJA/r2xt1dM/WmDoUe4ovzX2Cka8TPLWfS5uCXII+GgeugYY/nn6CM3DpxhMMrFuPY2JN+H32BnqFqjXqy7yaR/Mc9ZGb6WI/1QNfKSK12JeUV0OPaAzIVSg62dsexkvo6FEfh6mEgebnxtG9/7D+3egD15kFo0YK+oyNW06aSfuQomSdP8OoQdzJScrl2MKyqTSsT4eHhJF72p6Esllg9O9aluLMvTKDQUJtVHxcftvTcgpmOARPPfcJ6KR0xcrdGxCHwyEEOL1+Ek2dz+s1WXRwyL8eStPEOurY1sJnSTO3ikKtUMu5WKHF5+WzwdKlScQBITj6DXB6Ak/OU/6Q4lIXnesUkSepfzOE04KYQIl79JmmprtQaMwa5/z5iv/kW1337cG9ny42jETR6xa7aO6xzcnI4evQoV69epWbNmowePRrbOo58vvs2i48HcyUshUVDm2NjWv7WmCXhmhLN5uC7fGFpzv/MDAkK3c439k0x1lNfxNL1g/6cWL8C15Zt6PX+J+jqP//CJ4Qg/VgE8qMRGLjXpNbwRsjUvBoUQvDhvUgupWWyookTrSqxr0NJ9oSELsbAwA57u4p0LfhvoMoKYjyF2dPDix6rgA+Ac5IkjdSgbVqqGZKeHnZzv6YgLo6ExYvo0K8+Ojoyzm6vWHtOTRMcHMxvv/3G1atX8fLyYsqUKbi4uFBDX5f/DWrGjwObciMyhR6LznL+UaJ6J7+zF/z6Y2Jqz/8GHeTDVh9yLOIYQ/cPJSQ1RC1TXNu/mxPrV1C/TXt6fzhHNXFQCFJ3BSM/WliN1Wp0Y7WLA8CC8Dh2xKXwsUtt+tiouWZVOUhOPotcfqMo70G7engeqgiEEmgkhBgghBgANAZygXbAbE0ap6X6YdS8OTWHDiHFbxOyyIe07uFMWFAi4bc0V3K7vOTk5LBnzx78/PzQ19dn/Pjx+Pj4oP+vC+ig1o7smeaNuZEuI1ZfYvGxh+rZcrq2AbaPLuzjMPYgkoUjYzzGsKrrKtJy0xi6fyhHwo9UaIqr+3ZxcuNq3Nu9wlvvzUZH9/mx/Mo8BUl+d8i8HIvp646F1Vg10MZ1d1wKP4bG8nbtmrzrVDW5Dv8mNOxXDAxqY283oKpNeSFQ5VPhLISIe+rneAr7RScD+ZoxS0t1xvr999GtVYuYL7+g6Wv2WNjW4My2Byjyq09J8AcPHrB06VICAgLw9vZ+bq+GBrVN2Tvdm97N7PnlyAPGrLtMYkZu+SYXAs4uAP93Cju/jdoNNf4/96KtXVu2vrWV+jXr88HJD1h4bSEKZdmz06/6/8mp39fg7uVNj3dmoaP7/DwKZVY+iWtukXMvGYs+9TDv5qyRUOXr8kzevReBl7lxleY6PE1K6hXS0q7iVNdXW7FVRVQRiDOSJO2TJGm0JEmjgT3AaUmSjIFUzZqnpTqiY2qK7adzyL1zF/n2bXgPciMtPpvA45HPf7GGyc7OZvfu3fzxxx8YGhoyYcIE3njjjWLLZPwbYwNdFgxuzvz+nlwKTabn4jNcCVO1rXoRQsBfn8HRr8BjIAzZXGx2dG3j2qzrto633d9mza01TD02lbRc1RszXfH/k1N+a3Fv35GeKoqDIi2X+BVB5EWlYzm0ISbt1ZsA94THOXmMuRmKrb4eazxcMFAhE70yCA9fhp6eJfb2g6ralBcGVTKpJWAA8AogAWeBnaIaxMdqw1yrDiEEkeMnkB0URL2DBzi8PYbo+ykM/9oLY4uquTt78OAB/v7+ZGRk4O3tzauvvoquChfO4rjzWM7UTdeITMnmY5+GTOjo8vy7YEVB4aohYBO09QWfH0CFi+POBzuZd2keNjVsWPT6IhpYNih1/OU9Ozjzx3oatO9IjxkzkanQqCg/IYvENbdQZhVQa1RjDOtrps9zlkJJ3+sPeZSdy/5WbjQ0Vm9EVHlJT7/N5Su9qef6Ic7OU6vanCpHbWGuopAdQoj3hRDvFf27ysVBS9UiSRK2n3+GyM0l7qef8H67PkqF4Pyfle+wfnrVYGRkxMSJE+nSpUu5xQGgsb0Ze2d407WRLfMO3GWy3zXkOaXsqObnwLaRheLw2hzo/qNK4gAwwH0A633Wk6/MZ8SBEewP2V/i2L/FoUMnlcUhLzKdhOWBiHwl1r6eGhMHIQTv3o3gZkY2yxo7VRtxAAgLX46Ojgl16oyoalNeKJ77CZYkqb8kSQ8lSUqTJEkuSVK6JEnyyjBOS/XGwMUFywnjke/1Rzf0Fs27OvLgchyPgytv5zE4OJhly5YRGBhIx44d8fX1xd5ePVsnZoZ6LBvRks96NuLY3Xh6LTnL7cfFbAPlpsOmgXD/IPT4GV6bXebSGU2tm7L1ra00rtWYj898zE9XfqJA+c9+Fk/EoeErr9Jj+ocqiUPOgxQSVgUh6etgPaUZ+g6mZbKrLPwSFod/Qiqf1bPnTSv19ItQB5mZIcTHH8TBYSR6eurNDn/ZUeUW50egtxDCXAhhJoQwFUJo/8paALDy9UWvTh1i586lZZc6mNQ04MzWByg1lHj2hJycHPbu3ft3hNKECRMqvGooDkmSmNDRlS2+XuTkK+j323m2Xon4/wFZybChN4Sfh/6roO3Ecs9lZWTF6jdXM7ThUDbe2ciUo1NIzSkU26v7dv29cug+7QOVxCErKIHEDbfRtTTCZkpz9NScAPc0e+NT+SmsMGJpqqO1xuYpD+ERK5DJ9KnrOKaqTXnhUMUHcU4I8Uol2VMmtD6I6kH68RNETZ2KzayZJDd7i79W3+a14Q1o0lG9bT+fEBISwp49e5DL5XTo0IHXXntNJSd0RUnMyOW9LQGcDU5kUGsH5nauheHmgZAcAoM2QIPuaptr18NdfHPxG2xq2PAeA7m9bTfuXt70fGeWSuKQcTmG1F3B6Nc1w2pME2RGmut1EJSeRZ/rD2liYsSO5vUx1EDIbHnJyXnM+QuvU6fOMBq4f1nV5lQbVPVBqPKpuSpJ0lZgN4X5DwAIIf6sgH1aXiJMO7+OSefOJCz9Ddf9PbCrZ86lvSG4tbZFX40Xpry8PI4ePcrly5epVasW48aNKzV0Vd1YmRiwYVxbFhx5wO6T50m58z22OunIRuwEl45qnaufWz9cLVxZuHoWtwN2Y+5RT2Wfg/xkJPJDYRg2qInl8EbI9DVXKys+N58xN0Ox1NNlnadLtRIHgPCI1QA41S3/yu6/jCr/m2ZAFvAm0Kvo8ZYmjdLy4mE7Zw4olcR//wOvvO1Gdno+1w6Fq+38kZGRLF++nMuXL9OuXbvn5jVoCh2ZxMwWgqMW32GkzGBkwWeczCs96qjcBDzGI0CfVEddljgcZ9nN5ShFybkmQghSD4YiPxSGUTNrao1srFFxyFMqmXA7jJT8AjZ4ulRJP+nSyMtL5PHjrdSu3RdDQ82E9L7sPPf2TggxtjIM0fJio+9QB6vJk0hYuAjHgQNp4FWbgGMRNOloj1kF9r4LCgo4efIk586dw8zMjNGjR+PiUoXd7KKvg98ADHX0SRrqT9LBDMauv8K7Xdx4p7MbMjX1N7h5/C+Orl6KS4vWdH9vFtK1H1gRtIL7KfeZ7z0fE/1/9ncQysLSGZlXYjH2ssOidz21doArjk8fRnM5LZPljZ3wMK1+tbgiI9ejVObiVHdSVZvywlKiD0KSpI+EED9KkrQEeGaQEOIdTRv3PLQ+iOqFMi+P0N59EEKJzcbtbJ53HScPK3x8Pcp1vtjYWHbt2kVcXBwtWrSgW7duGKpYoVQjhF8o7OVQoyaM2guWLmTnKfh0903+vB7Naw2sWTi4ORY1Klbj5/apYxxathDnpi3oM/MzdPX1EUKw+d5mfrzyIy7mLix+fTGOZoUrKFGgJHnrfbJvJmLa2RGzrk4az1zeEJ3I7AdRzKhrw6f1qt/deUFBOmfPeVPLsiOenr9WtTnVDnXkQdwter4KXCvmoUXLP5Dp62P7+Wfkh0eQt3sLLbs58eh6PI8fli3sValUcubMGVauXElmZiZDhw6lT58+VSsOj06AX38wtYWxh8CycBVjpK/D/95uxrd9PTgXnEjvX89x53H5o8DvnT/N4WWLqNukKb1nfvp34T1JkhjWaBgruq4gITuBoQeGcinmEso8BYkb75B9MxHzni6Yv6mZ0hlPczE1g08fRtHZ0pSPXe00Old5iYrahEKRgZPz5Ko25YWm1CgmSZJ0gO+FELMqzyTV0a4gqidRM2aQcfYcTnv2sW1ZKEam+rz9cWuVtjySk5PZtWsXkZGRNG7cmJ49e6qty1u5uX+osEVorfqFdZVMiu+idz0ihSl+10jLzueHAU3p07xsUVwPr1zA/5f52Ls3YsAnX5fYzyFSHsmM4zOIS4lldeq3mMcbULO/G8Ztapf5rZWV6Jw8ul19gJmuDgdbuWGup7noqPKiUORy7nxHTE0b06L5+qo2p1qilkxqIYQCaFVOA9ZKkhQvSdKtp45ZSpJ0pCjx7ogkSTWLjkuSJC2WJClYkqQgSZJalmdOLdUDm9mzQaEgefECvPrWIyEinfuXYkt9jRCCa9eusWzZMuLj4+nXrx9vv/121YvD7V2wdTjYNoYx+0oUB4CWdWviP8ObpnUseHdLAHP975CvUK2AYWjANfYv/IHarm70m/1lqc1+HM0c2fjaehbHfIJxnC4nWt1Gv6V6e0cXR7ZCydhboeQolaz3dKmW4gAQG7uL/PwknJy0voeKokoU0w1JkvZKkjSyKKu6fwlNhP7NesDnX8c+Bo4JIdyAY0U/A3QH3IoevsAylazXUi3Rd3Cg1oTxyPftw0EnChtnMy7ufkReTkGx4zMyMti8eTP+/v44ODgwdepUmjVrVvUVQAP+gB3jwKENjNrzj4qsJWFjasimie0Y08GZtedCGbH6EgnppVeFjbgVxN6f52HpUJf+n3yNQY3SHb4KeR5Z6x5hl1WLi94h/Ji5lIlHJpKSk1Kmt1cWhBDMuh9JUHo2Sxs74W5chdt9pSCEkojINZiaelDTwquqzXnhUUUgLIEkoDNlCHMVQpwG/l0Ksw+woejfG4C+Tx3fWFT36SJgIUlS9dzc1KIStSZORNfOjrh53+E9wJXMtDxu/BXxzLh79+7x22+/ERISgo+PDyNHjsTcvBqUabiyBnZPAZdOMGInGKpuk56OjK96N2HB4GYERKbSa8lZAiKL98NE37/L7h/nYm5bm4GffoOhiUmx455QkJxD/IpAFCk5WI31YMhb4/i+4/fcTLjJ0P1DeZT6qExvU1VWRSWwIy6Fj1xq060aldH4N4mJx8jKCqFu3QlVf4PxEqBKsb6xxTzGlXM+WyFETNF5Y4An6/U6wNO1oqOKjml5QZEZGWH70Sxy797F8NoR3FrbcONIBOnJOQDk5uayZ88etmzZgpmZGb6+vnh5eSGrDqWhLy6H/R+Auw8M3VpsuW5V6NfCgZ1TOqCrIzFoxQW2X/1nOfTYRw/5c/6XmFhaMvCzb6lhVvqFNz8hi4QVgSgzC7Ca4IlhvcKiez1de7LOZx25ilxGHBjBmagz5bK3JM6nZPD1o8f4WJnxXjVp/FMS4RGrMTSsg421+rLa/8uU+G2UJOmjouclRf6BfzzUbEdxUl+s91ySJF9Jkq5KknQ1ISFBzWZoUSemPj7UaNOGhIULadvFGgRc2hvyd9LbjRs38Pb2ZsKECdjYlLy3X6mcWwyHZkPDt2DQ76BXsa0Ujzrm7J3uTWunmszaEcRXe2+Tr1CSGBHGzu++wNDElIGfzcOkZunbV/mxmSSsCEIoBNaTmmJQ95/l0JpaN2Vzz804mDow/fh0/O74oY6iyzG5efjeDsPZ0IAljZyQVeO78rS0G6SlXcXRcSwyWfX0j7xolPZXvFP0rM4woThJkuyEEDFFW0jxRcejgKfTYh2Ax8WdQAixElgJhVFMarRNi5qRJAnbzz4ltF9/cvxW4fH6IM5fOMu58EjMzMwYO3YsTk5OVW3m/3P6Jzj+LTTpV1h4T0c9mcGWxvpsHNeW+QfvseZsKCGPwvG6+wc6enq8ycnseAAAIABJREFU/fk8zKxKL26XF51B4pqboCvDeoInejbF+yhqG9dmg88G5pydww9XfuBR2iPmtJuDnqx87yNXqWTCrTCylEp2etbHVFdzWdnqIDxiNbq6ZtjbaRsCqYvSBGIwsA+wEEIsUtN8e4HRwPdFz3ueOj5dkqQtFPa6TnuyFaXlxcawQQNqDhlChL8/t8zMyDJJxlLPEd8pw6s2r+FphICT8+HUD9B0MPT5DXTUeweqqyPj87ca09BUwa2V35Eq8un84ddY2JYempobISdx7S1khrpYT/REt1bpWek19Grwy2u/8OuNX1l1cxUR8gh+ee0XzA3K7jf44mE01+RZrGriTINq6pR+QlZWGAkJh3FymoyubhVHvr1ElLbh20qSJCdgnCRJNYtCVP9+PO/EkiRtBi4ADSRJipIkaTyFwtBVkqSHQNeinwEOACFAMLAK0LZ8ekkQQhDdpTN/vdmV5MQE2jR4DZ0IF+JDMqvatEKEgGNfF4pD8xHQd5naxeEJWfI0MnYvpaZOPmfr9Wf0rgh234gucXxuaBqJq28hM9bDelLT54rDE2SSjHdavsN33t9xI/4Gww8MJ1xetrpYW2KS2PA4iWl1behlo5kGQ+okInIdkqSHo8OoqjblpaK0b8Jy4BDgSmHm9NObj6LoeIkIIYaW8KsuxYwVwLRSLdXywpGVlYW/vz93797FwcyMFpu34Or1CslWZpz/8xGODS01Xi+oVJ70j77wK7QaAz0XqNwFrqzkZGawc94XyBMTGDjna0Y4ujF103Xe2xrA3Vg5H3VriM5Tf4uchykkbbyDjoUB1hM90TErexvXXvV64WDqwLvH32X4geEseG0BbWq3ee7rgtKzmP0gCm8LEz5xqf7BhHl5ycTE7MCudl8MDKqJL+slocRvgxBisRCiEbBWCOEqhHB56lGqOGjREhoayrJly7h//z5vvPEGY99/n5p165L0y8+07VmXpKgMHlwuPXlOowgBh+cUikObifDWQo2JQ35ODru+/5rEyHB6fzgHh0YeWJkY4De+HcPb1WXFqRAmbLjyd0vT7HvJhY1+ahliPalpucThCS1sWrCpxyYsDS3xPeLL7uDdpY5Pzi9g3K1QrPR0Wd7EGd2qFHAViYr2Q6nMoW7d8VVtykuHKmGuUyrDEC0vBwUFBRw5coQNGzb83enN29sbHT09bD+eTX50NJY3D2LjZMrFPSEU5Csq30gh4NAncPE3aDcZevxU5hahqlKQn8+e/80j5uF9er4zE5fm/1+YQF9Xxrx+nnzT14MzDxPpt/QcoRejSfr9Dnq2xlhNbIqOScUK/0Fh5vXv3X+nlU0rPj/3OYuvLy62bLhCCKbdCSchr4A1Hi5Y6Vf/SCCFIoeoqN+xqtUZY+P6VW3OS0c1CDrX8rKQlJTEmjVrOHfuHK1atWLSpEn/6A9t3L49Jq+/TvKKFbR9w4aMlFyCTkRVrpFPxOHSMmg3BXy+15g4KJUKDi75mfCgG7w5aQbuXt7Fjhvp5YTfhHY0kCtg9yNyahpgPcETHWP19VcwNzBnWddlDHAbwKqbq5h5aiY5BTn/GLMwLI4Tyel861aH5mbVr3x3ccTE/kl+fjJ1606oalNeSrQCoaXCCCG4ceMGy5cvJyUlhcGDB9OrVy/09Z+9+7WZNQtlbi76+9bh5FmLawfDycnIryxD4dDHheLgNRV85mtMHIQQHFuzjAeXzvHqyPF4vN611PFNM5V8kq9PhB70S4xn7dUIteQxPI2eTI8v23/JB60+4Gj4UcYdHkdSdhIAJ5Pl/FzUU3qEnebrOqkDIRRERKzBzLQpFhZtq9qclxKtQGipEDk5OezcuZM9e/Zgb2/PlClTaNSoUYnjDVxdqDl0KKnbt9OyuS75OQVcPRSmeUOFgIOz4dJy8JoG3b7TmDgAnNvqR9DRQ7Tt+zat3+pX6tiswASSN9/DwNGMVjPb4u1Rm2/332X2ziDyClQr9qcqkiQx1mMsv7z2Cw9THjL8wHAuJAQz9U44DYwN+cHd8YUpUZGYeILs7DDq1h3/wtj8oqEVCC3l5klG9O3bt+ncuTOjR49WqY6S9bSpyExNKVjzCw3b23HzZBTyxGzNGSoEHPwILq+A9tOh2zyNisO1/bu5tGsrnl264T2k9LDLrIB4krfcQ9/JDKtxHpiYG7J0WEve6VyfbVejGLH6EkkZpRf7Kw9vOL3B2m5rySrIY8j1ILIVBazxcKZGNespXRqRUesxMKiNtXW3qjblpeXF+TRoqTYolUpOnz7N2rVrARg3bhydOnVSuY6SjoUF1tOmknn+PE2s45BJEpf2hmjG2CfbSpdXForDm99qVBxunzrGyY2rcWvXgTcmTC31zjbzWhzJW+9j4GKO1VgPZAaFmcoymcQHbzZgydAWBEal0mfpOe7HpqvdVk9rT1p5/EauvisGCb9xJ+aI2ufQFBkZ90lJuYCDwyhk5cwU1/J8tAKhpUzI5XJ+//13jh8/TpMmTZg8eTKOjo7Pf+G/qDl0KPrOzmQs+QnPV+15cCWOpOgM9RorBBz+9P+3lTQsDo+uXeLw8kXU9WhGjxmzkMlKLk2ReS2OlB0PMKhnQa0xTZDpPzu2VzN7tk1qT16Bkv6/nePY3Ti12rs3PpXN8TmMsjOjg6mCOWfnsDxwudp9H5ogMnI9MpkhdewHV7UpLzVagdCiMg8fPmT58uVERUXRp08fBgwYUO5yGZKeHjYffUReSAiuGVcxMNLl4h41riKEgCNfwMWl0HaSxreVou7eYt+CH7B1qUefmZ+iq1fyXW3m9afEYVTjYsXhCc0cLdg73RtXaxMmbLzKilOP1HIBD87K4f17EbQ2q8G37s6seGMFvVx7sTRgKZ+f+5x8ZSUFDpSDvLxkYuP2YFe7H3p61T/L+0VGKxBanktBQQGHDx9m06ZNmJqa4uvrS4sWLSrsGDR5/TVqeHkhX76EZp1sCAtKJCa4bP2ri0UIODYXzi+G1uOh+w8aFYfEiDB2//QNptY29Pv4K/SNSg4RzbwRT8r2Bxi4mj9XHJ5Q29yQbZPa08PTjvkH71XYeZ2lKCzCZyCTWNHEGX2ZDD0dPeZ5z2NKsynsebSH6cemk5Gn5hWdmnj8eAtKZS4OjqOr2pSXHq1AaCmV5ORk1q5dy4ULF2jTpg0TJkzA2rr06qOqIkkSth/PRpGWhv3dfRiZ6XNxT0jF75BPzoezvxSWz+jxs0bFQZ4Yz875X6Knb8DAOXNL7emQdSOelG33C8VhdPHbSiVhpK/DkiEteKeLG9uuRjFq7SVSs/LKZfPnD6O4l5nD0kZO1DH8/1BkSZKY2nwqczvM5VLMJcYeHkt8VnwpZ6p8lMp8oqL8sKzpjYmxW1Wb89KjFQgtJXLr1i2WL19OcnIygwcPpmfPnuiVsnVSHgwbNsS8fz/S/9hIiw4WPH6YSsSdfzciLAMnfygsvNdihEZrKwFkp8vZOe8L8nNy6D9nLmbWJdcBygqIJ3lboUO6rOLwBJlM4oOu7iwc3Jzr4an0++08IQllu8vfGZvMpphk3qlrw+u1zIod08+tH792+ZUIeQQjDozQWJe68hAff5DcvDgcHcdUtSn/CbQCoeUZ8vPz8ff3Z8eOHdjY2DB58uRScxsqivWMGaCjg9XZ3zGzMuTi7kcIZTlWEWcXwMnvoNkw6LVEo+KQn5vDrh++Ji0hjr6zPse6rnOJY7MC4v+OVirJIV0W+raow2bfdsiz8+n323nOP0pU6XXBWTnMehBFO3NjPnpOET7vOt6s81lHvjKfkQdHciX2SoVsVheRURuoUcOFWrVerWpT/hNoBULLP0hISGDVqlVcu3aNV155hbFjx2JhoVlHoF7t2liOGkXGvr00b2FAYmQGwdfLuLVxcRkc/Qo8BkKfXzUqDkqFgn0LfyA2+CE9Z8zCobFHiWOzghLUKg5PaOVkye5pr2BjasCoNZfZeuXZft9Pk61Q4nsrDEOZxLLGTioV4WtcqzF+PfywMrJi0pFJHAo9pBbby0ta2g3k8gAcHEYjSdpLV2Wg/Str+ZvAwEBWrlxJRkYGw4cPp2vXrujoVE4XsVoTJ6BjYYHpvqVY2hlz2T8UpUJFR+zVdYW5Do16Qb8VUEp4aUURQnBk1a+EXL9Cl/GTcWvXocSx2bcS/06CK++2Umk4WtZg59QOdKhvxeydN5l/8C7KElZeXwZHcyczhyWNnLA3VL0AYB2TOvze/Xc8rTyZdXoWG25vUJf5ZSYycj26uqbY1e5fZTb819AKhBby8vLYvXs3u3btws7OjsmTJ+PmVrkOQB1TU6ymTiH7wgWaueWSGpfFvQsqlAMP2Az73ge3N2HAWo01+3nC+W1+3DpxBK8BQ2nWtUeJ47LvJpG0+R76DqZYjW3ydxKcujEz1GPt6NaM8CosGz5983Vy/lUhd3dcChuLmv90KcHvUBrmBuasfHMlXZ268vPVn/n5ys/FVoPVJDk5McQnHMLebpC2Y1wlohWI/zhPtpQCAgLo1KkTo0ePxsys7BcRdVBzyBD0HB0x2LYAWxdTruwPLb0c+K2dsGcquHSCQb+DbsVLY5dG0NFDXPxzKx6vv0mHt4eVOC7nQQpJfnfRszMuypDWrGjp6sj4po8Hn/VsxMFbsQxZeZHEovIcIVm5zLwfSRszYz6uQPMfAx0Dfur0E0MaDGHDnQ18cuYT8hWVlysRFb0JIZQ4OIystDm1aAXiP82TLaXMzExGjBhB586dK21LqTgkfX1s3n+PvHv38LCKJSMll1unSmjJeW8/7JwIju1g6GbQ02zP5EfXLnN09W+4NG9VagmNnOBUEjfeQc+mBtbjPJAZVU5PBUmSmNDRlWXDW3EvVk6/385xJ1bOpNth6EkSy5o4oVfB5j86Mh3mtJvDuy3f5UDoAaYem1opuRIKRQ6PH2/B2voNjIzKnrWvpfxoBeI/SH5+Pnv37v3HllL9+tWj2Yqpjw+GHh7o+C3AoYE51w6Fk5dT8M9BwUdh+xiwbw7DtoG+ZrccYoMfsG/RD1g7u/DW+x+jo1v8RT83JI2kok5wVhM8kdWo/BpBPh612erbnuw8JT2P3ORmRjaLGtXFoQx+h9KQJIkJnhP45pVvuBJ7hXGHx5GYrVoUVXmJi/MnPz8FR4cxGp1Hy7NoBeI/RmJiIqtXr+b69et4e3tX6ZZScUgyGTYzZ1IQE0ND6Q45GfncPPlUU6Hw87BlBFg1gBE7wVCztqfGxbLrx7nUMLOg/8dfoW9oVOy43Ag5ietvF/aQVnOzn7LSzNGCD0c0JdvBGL2IDOTh6i/017d+X5Z0XkKYPIwRB0YQLg9X+xxQGBQQFf07xsbu2p4PVYBWIP5D3L59m5UrVyKXyxk2bBhvvPFGlW4plYSxVzuMX+0Em5ZQt4EZN45EkJddANHXYdMgMHeAkbvAqKZG7ciSp/Hn/C9QKhQMmPM1xhbFz5cXnUHi2lvomOphPdETHVPN+kKeR2xuPt9ExdGwhiHeBXrM3B7IoqMP1V6Er6NDx8KS4flZjDo4ittJt9V6fgC5PJD09Ns41Bmh7flQBWgF4j9AQUEBBw8eZPv27VhbWzNp0iTc3d2r2qxSsfnwQ5SZmdSXXyA3s4Ag/+vgN6BQFEbtARP1lPsoify8XHb/9A3yxAT6zvocS3uH4sfFZZK49iYyQ12sJnqiY2agUbueh0IIpt8JJ1shWOXhzIbRbRjQ0oEFRx/w0Y4g8lUNHVYRDysPNnbfiKGOIeMOjeNSzCW1nj8q+nd0dEyoXbuPWs+rRTW0AvGSk5aWxvr167l06RLt2rWrlMQ3dWDo7o55375IO1fj5KpDwMl4cjGH0XvAvI5G5xZKJQeX/I+Yh/fpMWMmdRo2LnZcQWI2CatvgUzCeoInuhaadZSrwm8R8ZxNzWCeex3cjA3R15Xx89tNebeLG9uvRTFu/RXSc9QbfeRs7szG7huxN7FnytEp/BX2l1rOm5eXTFzcAexq90NX10Qt59RSNrQC8RITHBzMihUriI+PZ+DAgXTv3h3dEhys1RHraVNBCFwvzyNXWYNAp5Vg6arxeU9tWsfDy+d5beQE3Nu9UuyYgpQcElbfBIWyUBysivdNVCbX0jL5PjSGPjYWDK1t+fdxSZJ4v6s7Pw5syoVHSby9/AIxaert4GdrbMt6n/V4WHkw89RMtt3fVuFzxsRsR4g86tQpOaRYi2bRCsRLiFKp5OTJk/j5+WFsbIyvry8eHiWXg6iu6JnrY9EIpNsRODsVEHgxm5xMzcbeB/x1gGv7dtG821u07NG72DEKeR6Jq2+izCnAarwnerZVn7glL1Aw+U449gb6/OjuUOx+/aDWjqwd04aolGz6LT3P3Ri5Wm0wNzBnRdcVdHLoxDcXv2FZ4LJy+z2EUBAV/QcWFu0wMane26EvM1UiEJIkhUmSdFOSpABJkq4WHbOUJOmIJEkPi54164F8ScnKymLTpk2cPHmSpk2bMnHiRKysrKrarLKTkwZ+/bFyj0cyMMQl9ix5OQoCjpZec6gihNy4wvG1y3Ft2YbXx0ws9iKryMwnYfVNFOl5WI31QL9O1W99CCGYdT+Sx7l5LGvshLleyavETu7WbJvUHoFg0PILnA9Wb4iqka4RC15fQO96vfkt4DfmX55frqzrpKTT5ORE4eAwQq32aSkbVbmCeF0I0VwI0bro54+BY0IIN+BY0c9aykB0dDQrVqwgLCyMt956i379+qGvX7URNeUiPxs2D4X4O+iO2ojl2LFIh7fjUt+AoONRZGeUrw9CacSHhbBv4Y9YO7nQ892Pim0XqswpIHHtLQqSc6g1ugkGTtUjPHhbbAp74lP5yNmO1ubPX800tjdj19RXsLMwZPS6y+wNfKxWe/Rkenz7yreMaTKGzfc2M+fsnDJ3qIuK9kNf3wZrq65qtU1L2ahOW0x9gCeVwDYAfavQlheOa9eusXbtWoQQjBs3jtatW7+YYYGKAtg+tjDfod8KcH+TWmPHIjM3x+nBLvLzFAQcUe8qIj0pkV3ff4WhsQn9Zn9RbK6DyFeQuOE2+TGZ1BrRCMN61cPRH5ady5yHUbS3MGa6U8n9KP6NvYUR2yd1oEXdmryz+QarTqux3SuFfo8PWn3Auy3fZX/Ift4/8T45BTkqvTY7O4KkpFPUsR+CTFZ1+SRaqk4gBPCXJEnXJEnyLTpmK4SIASh6LvbTLkmSryRJVyVJupqQkFBJ5lZf8vPz2bNnD/7+/jg5OTFp0iTq1NFslI/GUCph73R4cBB6/ASeAwHQMTPDauIEZKf34+qqS9CJKLLk6llF5GVnseuHr8nLyabfx19iYlnrmTGiQEmS313ywuRYDnbHqKFlMWeqfAqUhSGtOhIsaeSEThlvCMxr6LFxXFt6eNZm3oG7zPW/U2I12PLwJOv6c6/POR11mslHJ5Oe9/ykvajoP5AkGfZ1BqvNFi3lo6oE4hUhREugOzBNkqROqr5QCLFSCNFaCNFaXa0vX1RSUlJYs2YNN27coFOnTowYMQJj46p3mJYLIeCvTyFwM7z+KbSd+I9f1xw+HF1raxwDt6DIV3Ljr4pn7j7p65AYGU6v9z8ptumPUAqStz8g534KFn3rU6OZ6nfpmmZheBxX5Vn86O5Y7lIahno6/Dq0JWNfcWbtuVBmbLnxTDXYijKowSB+7PQjgfGBjD88nqTspBLHFtZd2o6VVVcMDWqr1Q4tZadKBEII8bjoOR7YBbQF4iRJsgMoeq5ezXCrGU9CWFNTUxk6dCidO3dGpsEmORrnzM9w8TdoNwU6zXrm1zIjI6ymTkHn6glcnSRunYqu8Cri5O+rCQ24xhvjp+LcrOUzvxdCkLonmOzABMy7O2PSrvzVUNXNtbRMFoTHMtC2Jn1tKxbPIZNJfPFWYz7t0Yj9QTGMXnuZtGz1Rov5uPiwuPNiQtNCGXNoDDEZMcWOi4/fT0FBqtY5XU2o9CuKJEnGkiSZPvk38CZwC9gLjC4aNhrYU9m2vQgIITh9+jR+fn6YmZnh6+tLgwYNqtqsinFlDRz/FpoOgW7fQQlbJRYDBqDn6EidKxtRFCgr5IsIOLyfGwf9adWzL03f8Cl2jPxQGJmXYjF9zRHTV6tPFdGMAgVT74RjZ6DHd+7FZ3iXFUmSmNjJlUVDmnM9IoXBKy4QL1fNZ6AqHR06sqLrCpKykxh1aBRhaWHPjImK3kSNGvWoaeGl1rm1lI+quOW0Bc5KkhQIXAb2CyEOAd8DXSVJegh0LfpZy1Pk5OSwdetWjh8/joeHBxMmTMDSsnrsh5eb27th/4fg7vPcVqGSvj7W78xA9/ZFnOwV3DwdXa6IprDA6xxfvwLXlm3oNGJssWPkJyNJPxWFsZcdZt2cyjyHJvnsYTSROXksbeSEma56a2n1aV6HtWPaEJGcRf9l5wlJUG8575a2LVnrs5Y8RR5jDo3hfvL9v38nlwchlwfiUGf4ixlg8RJS6QIhhAgRQjQrejQRQswrOp4khOgihHArek6ubNuqM08a+9y/f59u3boxYMCAFzOE9WlCT8OfE6GuF7y9HnSeH7Fi1qMHBm5u1Lm0noJcBUHHo577mqdJiorAf8H3WDnUpec7s4oNZ828HIv8UBhGzayx6F2vWl2s/ONT2RKbzDtOtrSz0EwORkc3a7b4epGdp2Dg8gsERqaq9fwNLRuyzmcdOjIdxh0eR1BCEADR0ZuRyYyws9O2FK0uvMCb1v8d7ty5w6pVq8jJyWH06NG0b9++Wl20ykVMIGweBpb1ihr+qFaqQtLRwfq9dzEIvo6jTT5BxyPJzVJtvzxLnsauH75GV1+fvrO/QN+oxjNjsm8lkrLrIQbuNbF82x2pgk121ElMbh6z7kfS3LQGHzpr1oHb1MGCHVM6UENfh6GrLnL6gXojBl3NXdnYfSNm+mZM/Gsil6NPERe/j9q2vdDVNVXrXFrKj1YgqjFKpZJjx46xbds2rK2t8fX1xdnZuarNqjjJoeA3EIwsYOSfZS7bbdK5M4aNG+NwdSN5OQqCTjx/FVGQn8/e/80jIyWZvrM+x8zq2WiknEephX2kHU2pNaIRkm71+XoIIXjvbiS5SsHSxnUr3B1OFVysjPlzSgecahkzbv0V9gSU0N2vnNQxqcOG7huwM7Zjw6XpKBRZ2NtrQ1urE9XnG6DlH2RnZ7N582bOnDlDixYtGDt2LObm5lVtVsXJiIff+4EyH0b8CWb2ZT6FJElYzZiOUch16ljlEXg88tmuc08hhODIyiVE37uDz9T3sXN71qmfF51B0sY76NYywmpME2T61atPxrroRE6lpPNVfXvq1ai8qrE2ZoZsneRFK6eavLslgHXnQtV7/ho2rPNZR0dTeJwn42JyrFrPr6ViaAWiGhIfH8+qVat49OgRPXv2pHfv3i9UFdYSyU2HTQMhPRaGbQfr8hdhM3ntNQw9PXG85kduZkHJvauBK3t3cuf0cdoPHEbDDs+m3OQnZpO49hYyI12sxntUSavQ0niUlcM3jx7zuqUpo+yfTeTTNGaGemwY15ZuTWz52v8Ov/x1X63Nh3Tyo7HWySJScuajM7PZ+2iv2s6tpWJoBaKacffuXVavXk1ubi6jR4+mTZs2L76/AaAgD7aOgNhbMGgjOLap0OkkScL6nRnUCL2GXc08Ao5GkJ/7bILXo2uXObN5A+7tO9J+4NBnfq+Q55K45iYgsBrvga551Tb8+TcFSsGMuxEYyGQsaFi3yj4Lhno6LB3WksGtHVl8PJjPdt9Coaas68ePtyKTGTC940ba1m7Lp2c/ZfuD7Wo5t5aKoRWIaoJSqeTEiRNs3boVKysrfH19cXKqXuGV5UaphD1TIeRkYSir+5tqOa2xtzdGzZvjELCJ7PR8bp/55yoiMTKcA0t+wsbZFZ8p7z5zcVVmF5Cw5hbKzAKsxnqgZ/2s07qq+TUijuvyLL53d6C2QdWubHR1ZHw/wJNJr7qy6VIE7265QV5BxTrUKRRZxMbuxcamO2Y17Pi1y690cujE3Atz8bvjpybLtZQXrUBUA3Jzc9m6dSunTp2iefPmL4+/4QnHvoKb26HLF9Bcfc1fnvgiTEOvYmOey40jERQUlYnITpez+6dv0NU3oM/Mz9Az+Oe+vchXkrjxNgWJ2dQa1Qh9h+oXOROUnsXPYbH0tbGocLa0upAkiU+6N+KT7g3ZFxTD+A1XyMor2f/zPOLiDqBQZFDHvnB1Z6BjwMLXFtLVqSs/XPmB1TdXq8t0LeVAKxBVTHJyMqtXr+bBgwf4+PjQp08f9PSq1x54hbi0Es4tgtbjwfsDtZ/euEMHjFq1om7gFrLS8rh7LgZFQQH7Fn5PRlIifWZ+hpnVP2t2CaUgees98kLlWA5yx7B+9bj4Pk2OQsn0OxHU0tNlvpqypdXJpFfr8eOAppwLTmTYqkukZJav7En04y3UqFEfc/NWfx/T09Hjx04/0sOlB4uuL2JpwFK1+jy0qI5WIKqQR48esXLlStLT0xk5ciReXl4vh7/hCXf2wsGPoEHPwuqsGnhvkiRhPWMGpmGXsTLN5frhcE6sX0nErSC6+s7A3r3hP8YLIUj1f0T2rSTM33KtVsX3nub70BgeZOWwoGFdapbSAKgqGdTGkWUjWnEnRs6QlRfLXJojI+M+cvkN6tgPfuZzryvT5Tvv7+hXvx/LA5ez4NoCrUhUAVqBqAKEEFy8eBE/Pz9MTU3x9fXF1VXzvZYrlYiLhVnSDq1hwGooJmNZXRh7tcO4bdv/a+/M46Oqzj7+fRKSsCRAFvYtIJsQkB0VKxSpgFqwIjXWyr6rfUFLQa3vxxcLVt/WvlrbArWCSoUggqBsYgSUCgrIHkDCkgCTAAlLQsg2mfP+MRccYLLPTCbh+X4+85k7555z7m+ee2aee8695zw02xfHxdTt7Nmwhh4/f4SOfe+7KW/mppNkbU0h9N5TclfBAAATkElEQVSmhN3jn8uif3PhMvNOnmNk40j6R/pHUKLCGNixIQtG9eTkhSs8OncrJ89fKXHZ07YliATTsKH70C+BAYG8fPfLxLaLZcGBBby+/XV1Ej5GHYSPsdvtrFy5knXr1tG2bduqsZ7SjaQdgcWxULsJPB4Hwd6/+VvvmadxnNuD/cqXBNe6jT6xI27Kk7UjlYz1SdTsWp86g6K9rqksZNkL+K9DybSoEcx/ty79HJGKoE/rKP49rjeXsvMZPncriWeLj/lQUJBDauon1K93P8HBhbf/AAnghd4v8GSHJ1l0cBGzv51dphCmStlQB+FDLl++zMKFC9m9ezf33nsvjz32GCEh/vVYZbnJPAOLHoGAavDrj6GWb57bt7dswe7WTaleEIAEDSJp3/VLeWUfOs+F5UcIaVOX8GFt/GoJDVdeOZbCqZw83mzfnFqB/jVZryi6Ng8nbuKdFBjD8Llb2XfqUpH5z55bh92eQeMmscXWLSJM7zGd0TGjiTscxyvbXlEn4SPUQfiIlJQU5s+fT2pqKsOHD6/88RvckZcFH/4SstLhV0shoqVPDpufl8vKP83GBAfT88hxwqoH8P26pGvDEXknMzn/74MENQr1uyU0XNlyIZOFp9OY0LSe1xbi8ybtG9bmo4l3UTO4Go//cxvfHis8MJDt9BJq1GhR4mW9RYRp3aYxvtN4lv2wjJe/eZkCh2cDGyk345+/lCpGQkIC7777LgBjxoyhY8eOFazICzgKYNlYSN0LwxdAk5sD8HgDYwwb5v2VsyeO8cDUGTTo0pVmx9dyNimTU4cvYE/PJm3hAQLCgp1LaIT45w3fy/YCph5KplWNEGa08p/ARKUlOqoWyybfRYPaIYx49zs2Hr457ldW1lEuXtpOYzc3p4tCRHim6zNMuWMKKxJX8NJ/XlIn4WXUQXgRYwybN29m6dKlNGjQgPHjx9O4ceUYVy4VxsC6mc5Y0oNfh7YDfXbonas/4eCWTfQZ/gS3de9F1OTJ1E+Mp3pQAXvWnCBtwQEwhqjRHQkM89/l0WcdtXE6J583b29OzcDK/bNsVKcGSyfeRev6oUx4fwdr910fPc5mi0OkGo0aDSt13SLC5C6TebrL03x67FNe2PICdkfZ52EoRVO5W6Ifk5eXx7Jly9i4cSOdO3dm5MiRhIX532Qsj7Dt7/DdfLj7mZtiSXuTpL27+WrRAtr0upvev/glADV79yK0S2ea2zbT3JaJ/UIOkSM6+OUs6at8dT6T923pTGxWj551KmlM8RuIDA3hw/F30qlJHZ768HuWf+9ccTc//xKnbXHUqzeQkOCoMtc/8Y6JTO02lTXH1/D818+rk/AS/tnfruRkZGSwZMkSbDYbAwYMoE+fPlVrfoMrCatg/Ytw+xAYMMtnh714JpXP3nyNiCZNGTRlKmLdzxERIidNwvGv3QQFCsmRNWga7b+z0jPtBUw7lEzrmiHMaFl5h5bcUadGEB+M7c2493bw3Ed7yM4v4O76qygouEx09JRy1z+201gCJZA/7/wzgjDnJ3OoFqB/aZ5ErelhbDYbixcvJicnh9jYWNq3b198ocrKqR0/znV4ZH6R4UI9SV5ONiv/9AeMcTB0+u9vCvxjv9iY4EZgS09kV0YLOpy5Qt0G/tmD+J9EGym5+XzarQ01KvnQkjtqhVRjweieTF60k1dW7eCt+/5Fg6gBhIV65ncxKmYUBsMbO98AUCfhYapei6xAEhISWLBgASLC2LFjq7ZzOH8cPnwMwhrC40tKHBGuvBhjWD/3LdJPJvPQb35HeMPr7+lkbjlN1jc2gpsXELLtHwSKYdfnST7RVlo2nc9gUUo6k5rVp3sVGVpyR/WgQOY92YOJPfYSSCbfnfu5Rye8jY4ZzbPdn2XtibW88LXek/Ak6mo9gDGGLVu2EB8fT5MmTYiNja269xsAsi86H2d12OGJZVCr7GPJpWXnZyv4YevX3PP4SKK7dL9uX/b+NC6tPkaNjpGE/6o9lz9vQpOLuzm0LYCeD7UiNNx/5pyk59mZdugkbWqG8LuW3g0f6g8ESh7do9Ziy7qD2ZuE9LzDzBjUzmNDr6NjRgNoT8LDaA+inNjtdj755BPi4+OJiYlh1KhRVds5FOTD0hHOHkTsvyGqjc8OffLAXr76cCGte95Fr6GPXrcvNzmD9CWHCW4WRkRsOwICA4iaNIkmCSswDgd74pN9prM4HMbwm4PJpOfZ+XuHFlSvgkNLN2KzxZGfn879vWbwq97Nmbv5KLM+S/B4T2Ja92nak/Ag6mLLQVZWFnFxcSQnJ9OvXz/69u1bdW9Gg/Nx1tXPwfHN8PA/IPoenx06Mz2NT//vNcIbNmbQlGnX2dl+Pof09xMIrB1M5IgOSJBzBnLY/T+jztt/pWHWIQ58XY3ug6OpXqviV8qde/Ic8eczmNOmCZ3C/PPeiCdxOPJISp5P3To9iYjozeyHDSHVAljwnxPkFziYNSSGAA/NbB8TMwbAubgfhld/8qr2JMpB1b908RJpaWm88847nD59mmHDhtGvX7+q7RwAtr4N37/nXLbbg3EdisOen8+nb7yKPS+PIc+9SEjNH/9UHdl20hbux9gNUaM6Ehj641wHCQggauIkmh1YTn6unXXz9pF7Jd9nut2x81IWc47ZeLBeHUY38d3QXEWSkrqC3NxUoqOfApxPmv33Qx2Y2LcVi7Yl8/zyfR6LTgdOJ/Fs92dZd2IdM76aQb6jYs95ZUYdRBk4fvz4tbCgo0aNolOnThUtyfscWg2fvwQdhkL/l3x66E3vzScl8TCDpkwlsmmza+nG7iB9UQL29Bwin7ydoPo3X43XfmAwEVFBdL60gZSjl/j4f78nIz3bl/KvcSHfzoQDJ2gcEswb7ZpV/QsKwOGwk3RiLrXDOhMR8WOPU0SYOag9v+nfmrgdJ5n+0R7sBZ5bX2l0zGh+2+O3fJ70uTqJcuB3DkJEBonIYRFJFJGZFa3nRnbt2sUHH3xAaGgo48aNo1mzZsUXquzYdsPH46BxV3h4rs8eZwXYv+kL9mxYS88hw2jbu8+1dGMMF1Ykknv0EuGPtKH6bXXdlpfAQCInTCBq10r6hO8n60I2H7+2k3PJxa846kmMMUw7lMzZPDvzOkZTx09jPHiaM2c/Izsnmejop25yiCLCs/e347mftWX5rtNMjdtNvgedxMiOI5neYzobkjYwffN08gvUSZQWv3IQIhII/A0YDHQAHheRDhWryonD4SA+Pp6VK1fSokULxo4dW/WW6XZHhs25dHeNCOfjrD5YuhvAOBycPLCXL975G81j7uCeG5bvztx0kis7zxB2X3NqdW9QZF11hvycOo88QtDyuXT99o+QlcnyP+0kaX/hi8l5mndOpbEuLYOXbmtE19pV/74DgDEOTpz4O6Gh7YmK6l9ovmfua8MLDzhDmI5ZuJ11+1O5nOuZG8wjOo5gZq+ZxCfH89zm59RJlBJ/u4zpBSQaY44BiMgSYCiQ4EsRDoeDzMxMzp8/f+116tQpkpKS6NatGw8++CCBlWgp5hJjz4Nzh5wL7qXsgZS9kLrPGQluzHoIK/qPuDzk5+aQevQItsMHsf1wENvhg+RkXSYssh6DJz6H3XaF/LRs7OeuYD+XTfa+NGp2rU/tAc2LrVuCgmg8ZzZRE8aTNm8+1da+wt6Yiax+u4B7HmpE54e8ew2yO+MKs47aGBhVm/FN6xVfoIpw9tx6rlw5SkzHtxAp+lp0wr23USMokNfXHebrI2kEBQq9W0by0/b16d++Pi2jyj5P5InbnyBAApjz7RymbZrGG/3eIDjQf9fl8ifEnyI0icijwCBjzDjr85NAb2PM0+7y9+jRw+zYsaPUx/nrR2+yILx1ofvdWUQAQaj6o8aF4e1v7mp1+fGt0JMhZY/pYAymoACHESsMqnd/AxekLjXIYVbGbEJNySOuVXYCa2ZQkB3GmdVTwZR8sMJhnI8COwzXHoMVxANN0GG9qgb22qeZ/NbvylRWRHYaY3oUl8/fehDumsB1v14RmQBMAGjevPirR3fUqRZCw/y0IkUEIIi51ZzC1R+h77+xiCABAdY4tXV8Y0kKEAgQJND57ilMQQF5l3Px4AM0bmlu0hic+TWh+TWBW2N4CaAgsx55x3pSO7jsw0V2h4Ncu4N8u8MjbtxBHg7yPFBTxVOttvd7Qf7Wg7gLeNkYM9D6/DyAMeZVd/nL2oNQFEW5lSlpD8KvblID24E2ItJSRIKBWGBVBWtSFEW5JfGrISZjjF1EngbWA4HAu8aYAxUsS1EU5ZbErxwEgDFmDbCmonUoiqLc6vjbEJOiKIriJ6iDUBRFUdyiDkJRFEVxizoIRVEUxS3qIBRFURS3+NVEudIiIueAsgYcjgIKn05dcfirLvBfbaqrdKiu0lEVdbUwxhS7MFildhDlQUR2lGQmoa/xV13gv9pUV+lQXaXjVtalQ0yKoiiKW9RBKIqiKG65lR3E/IoWUAj+qgv8V5vqKh2qq3Tcsrpu2XsQiqIoStHcyj0IRVEUpQiqtIMQkeEickBEHCJS6N1+ERkkIodFJFFEZrqktxSRb0XkiIjEWUuQe0JXhIhssOrdICLhbvL8VER2u7xyRORha99CETnusq+Lr3RZ+Qpcjr3KJb0i7dVFRLZa53uviDzmss+j9iqsvbjsD7G+f6Jlj2iXfc9b6YdFZGB5dJRB17MikmDZJ15EWrjsc3tOfaRrlIicczn+OJd9I63zfkRERvpY119cNP0gIhdd9nnTXu+KyFkR2V/IfhGRtyzde0Wkm8s+z9rLGFNlX8DtQDtgE9CjkDyBwFGgFRAM7AE6WPuWArHW9lxgsod0vQ7MtLZnAq8Vkz8COA/UtD4vBB71gr1KpAu4XEh6hdkLaAu0sbYbAylAXU/bq6j24pJnCjDX2o4F4qztDlb+EKClVU+gD3X91KUNTb6qq6hz6iNdo4C33ZSNAI5Z7+HWdrivdN2Q/xmc4Qe8ai+r7nuBbsD+QvY/AKzFGXrxTuBbb9mrSvcgjDEHjTGHi8nWC0g0xhwzxuQBS4ChIiJAf2CZle894GEPSRtq1VfSeh8F1hrj9YDGpdV1jYq2lzHmB2PMEWvbBpwFip0IVAbctpci9C4D7rPsMxRYYozJNcYcBxKt+nyiyxiz0aUNbQOaeujY5dJVBAOBDcaY88aYC8AGYFAF6XocWOyhYxeJMeYrnBeEhTEUeN842QbUFZFGeMFeVdpBlJAmwEmXz6estEjgojHGfkO6J2hgjEkBsN7rF5M/lpsb52yre/kXEQnxsa7qIrJDRLZdHfbCj+wlIr1wXhUedUn2lL0Kay9u81j2uITTPiUp601drozFeRV6FXfn1Je6hlnnZ5mINCtlWW/qwhqKawl86ZLsLXuVhMK0e9xefhcwqLSIyBdAQze7XjTGrCxJFW7STBHp5dZV0jqsehoBnXBG2bvK80Aqzj/B+cAMYJYPdTU3xthEpBXwpYjsAzLc5Ksoe30AjDTGOKzkMtvL3SHcpN34Pb3SpoqhxHWLyK+BHkBfl+Sbzqkx5qi78l7Q9Smw2BiTKyKTcPa++pewrDd1XSUWWGaMKXBJ85a9SoLP2leldxDGmAHlrOIU0Mzlc1PAhnONk7oiUs26CryaXm5dInJGRBoZY1KsP7SzRVT1S2CFMSbfpe4UazNXRBYAv/WlLmsIB2PMMRHZBHQFPqaC7SUitYHVwO+trvfVustsLzcU1l7c5TklItWAOjiHDEpS1pu6EJEBOJ1uX2NM7tX0Qs6pJ/7witVljEl3+fhP4DWXsv1uKLvJA5pKpMuFWOAp1wQv2qskFKbd4/bSISbYDrQR5xM4wTgbwyrjvOuzEef4P8BIoCQ9kpKwyqqvJPXeNPZp/UleHfd/GHD7tIM3dIlI+NUhGhGJAvoACRVtL+vcrcA5NvvRDfs8aS+37aUIvY8CX1r2WQXEivMpp5ZAG+C7cmgplS4R6QrMA4YYY866pLs9pz7U1cjl4xDgoLW9Hrjf0hcO3M/1PWmv6rK0tcN5w3erS5o37VUSVgEjrKeZ7gQuWRdBnreXt+7E+8ML+AVOr5oLnAHWW+mNgTUu+R4AfsB5BfCiS3ornD/gROAjIMRDuiKBeOCI9R5hpfcA3nHJFw2cBgJuKP8lsA/nH90iINRXuoC7rWPvsd7H+oO9gF8D+cBul1cXb9jLXXvBOWQ1xNqubn3/RMserVzKvmiVOwwM9nB7L07XF9bv4Kp9VhV3Tn2k61XggHX8jUB7l7JjLDsmAqN9qcv6/DLwxxvKedtei3E+hZeP8/9rLDAJmGTtF+Bvlu59uDyh6Wl76UxqRVEUxS06xKQoiqK4RR2EoiiK4hZ1EIqiKIpb1EEoiqIoblEHoSiKorhFHYSiKIriFnUQiqIoilvUQSiKBxGRntaic9VFpJY441PEVLQuRSkLOlFOUTyMiPwB52zqGsApY8yrFSxJUcqEOghF8TDW2j7bgRzgbnP9KqCKUmnQISZF8TwRQCgQhrMnoSiVEu1BKIqHEWeM4iU4g8w0MsY8XcGSFKVMVPp4EIriT4jICMBujPlQRAKBb0SkvzHmy+LKKoq/oT0IRVEUxS16D0JRFEVxizoIRVEUxS3qIBRFURS3qINQFEVR3KIOQlEURXGLOghFURTFLeogFEVRFLeog1AURVHc8v8jBMdC18IFwgAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#%pylab inline\n", "import numpy\n", "import nengo\n", "from nengo.utils.ensemble import tuning_curves\n", "from nengo.dists import Uniform\n", "\n", "N = 10\n", "tau_rc = 20\n", "tau_ref = .001\n", "lif_model = nengo.LIFRate(tau_rc=tau_rc, tau_ref=tau_ref)\n", "\n", "model = nengo.Network(label='Neurons')\n", "with model:\n", " neurons = nengo.Ensemble(N, dimensions=1, \n", " max_rates = Uniform(250,300),\n", " neuron_type = lif_model) \n", "sim = nengo.Simulator(model)\n", "\n", "x, A = tuning_curves(neurons, sim)\n", "\n", "plot(x, A)\n", "xlabel('x')\n", "ylabel('firing rate (Hz)');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- How good is the representation?" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ 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It can be enabled with `nengo.rc.set('progress', 'progress_bar', 'nengo.utils.progress.TerminalProgressBar')`." ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "\n", " (function () {\n", " var root = document.getElementById('55e1a23e-d602-4ee3-ba9a-c4ef1afe77ab');\n", " var text = root.getElementsByClassName('pb-text')[0];\n", " var fill = root.getElementsByClassName('pb-fill')[0];\n", "\n", " text.innerHTML = 'Build finished in 0:00:01.';\n", " \n", " fill.style.width = '100%';\n", " fill.style.animation = 'pb-fill-anim 2s linear infinite';\n", " fill.style.backgroundSize = '100px 100%';\n", " fill.style.backgroundImage = 'repeating-linear-gradient(' +\n", " '90deg, #bdd2e6, #edf2f8 40%, #bdd2e6 80%, #bdd2e6)';\n", " \n", " \n", " fill.style.animation = 'none';\n", " fill.style.backgroundImage = 'none';\n", " \n", " })();\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "RMSE with 10 neurons is 0.151211\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#Have to run previous code cell first\n", "noise = 0.2\n", "\n", "with model:\n", " connection = nengo.Connection(neurons, neurons, #This is just to generate the decoders\n", " solver=nengo.solvers.LstsqNoise(noise=0.2)) #Add noise ###NEW\n", " \n", "sim = nengo.Simulator(model)\n", "\n", "d = sim.data[connection].weights.T\n", "x, A = tuning_curves(neurons, sim)\n", "A_noisy = A + numpy.random.normal(scale=noise*numpy.max(A), size=A.shape)\n", "xhat = numpy.dot(A_noisy, d)\n", "\n", "print('RMSE with %d neurons is %g'%(N, np.sqrt(np.average((x-xhat)**2))))\n", "\n", "figure()\n", "plot(x, x)\n", "plot(x, xhat)\n", "xlabel('$x$')\n", "ylabel('$\\hat{x}$')\n", "ylim(-1, 1)\n", "xlim(-1, 1);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Possible questions\n", " - How many neurons do we need for a particular level of accuracy?\n", " - What happens with different firing rates?\n", " - What happens with different distributions of x-intercepts?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Example 2: Arm Movements (2D)\n", "\n", "- [Georgopoulos et al., 1982. \"On the relations between the direction of two-dimensional arm movements and cell discharge in primate motor cortex.\"](http://www.ncbi.nlm.nih.gov/pubmed/7143039)\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- System Description\n", "\n", " - What is being represented?\n", " - $x$ is the hand position\n", " - Note that this is *different* from what Georgopoulos talks about in this initial paper\n", " - Initial paper only looks at those 8 positions, so it only talks about direction of movement (angle but not magnitude)\n", " - More recent work in the same area shows the cells do respond to both (Fu et al, 1993; Messier and Kalaska, 2000)\n", " - Bell-shaped tuning curves\n", " - Encoders: randomly distributed around the unit circle\n", " - Firing rates of up to 60Hz\n", " \n", "- Design Specification\n", " - Range of values for $x$: Anywhere within a unit circle (or perhaps some other radius)\n", " - Normal levels of noise: $\\sigma$ is 20% of maximum firing rate\n", " - the book goes a bit higher, with $\\sigma^2=0.1$, meaning that $\\sigma = \\sqrt{0.1} \\approx 0.32$ times the maximum \n", "- Implementation\n", " - Examine the tuning curves" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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QpUgA+nfvymePGciDb21gx/66oMsRCY2sCYJ3N1fzyqodzJ4xTBvSZ7F//MRI6mNx7nltbdCliIRG1vxFvOOVNXTNz+WSqUODLkUCNLK8G6eN7cP9b67X3sYiSVkRBNuqa3li4WYurBhE96L8oMuRgM2eMYwd++t5atGWoEsRCYWsCILfvbaWxrhz6QnDgy5FQuCEI8o4ok83/ufVtbh70OWIBC7jg6C2Icb9c9dz5vh+DO1dHHQ5EgJmxuzpQ1m8aS/z12uJapGMD4KnFm1h78EGvjxdYwPygc9NHkRJYR53a9BYJPOD4L656xhRVsx0LS4nzRQX5nHhsYP58+ItbKuuDbockUBldBAs3VLN/PV7+OJxQ3QBmfydL08fSsyd++auD7oUkUBldBDcP3c9BXk5nD95UNClSAgN7V3MKWP6cP/c9TTE4kGXIxKYlIPAzCI10nqgrpFH3t7Ep4/qT8/igqDLkZC6eOoQduyvY87yqqBLEQlMm0FgZjPM7F1gafLjSWZ2a9or+5ieWLiZ/XWNXDJtSNClSIidPKacsm6F/LFyQ9CliAQmlRbBz4AzgZ0A7r4QOCmdRXWE++auZ0zfEiYP6Rl0KRJi+bk5nD95IH9btp2qfVp/SLJTSl1D7v7Rf5dCfW3+4o17WbxpL5dM0yCxtO2CikE0xp1H394UdCkigUglCDaY2QzAzazAzL5DspsorP709kYKcnM49+iBQZciEXBEnxImD+nBHys36EpjyUqpBME/AVcCA4GNwNHA19NZ1MfRGIvzxMLNnDq2D927al0hSc2FFYNZuX0/CzfuDboUkU6XShCMcfdL3L2vu/dx91nAuHQX1l6vrt7Jjv31nHeMWgOSurMn9qdLfo4GjSUrpRIEv0jx2IeY2V1mtt3MljQ79kMz22RmC5K3mYdTbCoefXsTpV3yOGVseUc/tGSwki75zDyqP08s2MzB+lAPgYl0uLyWPmFm04EZQLmZfavZp0qB3BQe+3fAL4F7PnL8Z+7+08OsMyU19Y08885Wzj16AIV5qZQo8oELpgzmT/M38dzSbdrFTrJKay2CAqAbibAoaXarBj7f1gO7+0vArg6oMWXPvruNmvqYBomlXaYO70V5SSF/WaJ9CiS7tNgicPc5wBwz+527r+vA57zKzL4MVALfdvfdHfXAj769iQHduzB1WK+OekjJIrk5xllH9uOPlRuoqW+kqKDFXw+RjJLKGEGNmf2Xmf3ZzP7WdGvn8/0aGEli5tEW4KaWTjSzy82s0swqq6ravvx/x/46Xlq5g3OOHkhOjq4dkPY568j+1DbEeVFLTkgWSSUI7gOWAcOBfwfWAm+158ncfZu7x9w9DvwWmNrKube7e4W7V5SXtz3w+9SiLcTizmc1W0g+hqnDe1HWrYCnFqt7SLJHKkHQ293vBBrcfY67XwpMa8+TmVn/Zh9+FljS0rmH66nFWxjTt4Qx/Uo66iElC+XmGGdO6Mfflm7X7CHJGqkEQUPy7RYzO9vMjgHaXNfZzB4AXgfGmNlGM7sMuNHMFpvZIuAU4JvtLby5PTX1zFu3m9PH9+2Ih5Msd/ZR/TnYEGPOiu1BlyLSKVIZDfuxmXUHvk3i+oFSUvgD7u4XH+LwnYdXXmpeXF5FLO6cNq5POh5esszU4b3oVVzAU4u38qkj+7d9B5GIazUIzCwXGOXuTwJ7SfwXHzrPLd1GWbdCJg3qEXQpkgHycnM4c0I/HluwidqGGF3ydU2KZLZWu4bcPQac00m1tEtDLM6cFVWcOrZcs4Wkw8w8qh819THmrNDsIcl8qYwRvGZmvzSzE81sctMt7ZWl6K33drGvtpHTxml8QDrO9BG96VmUzzNLtgZdikjapTJGMCP59vpmxxw4tePLOXzPLd1OQV4OJ44qC7oUySB5uTmcOKqcl1ftwN21r4VktDaDwN1DOS4A4O48v2wbM0b21lWg0uFOOKKMxxduZsW2/ZqWLBkt5c3rw2h11X7W7axRt5CkxfHJVuYrq3YEXIlIekU6CJ5bmpjnfdpYTRuVjjewR1dGlBXzykoNGEtmi3QQPL90GxMGlDKgR9egS5EMdfwRZcx9bxf1jfGgSxFJmzY71s3sc4c4vBdY7O6BXXpZXdvAvHW7ueqUI4IqQbLA8UeUce8b61iwYQ9Th2tVW8lMqYywXgZMB15Ifnwy8AYw2syud/d701Rbq95ev4e4w3Ejegfx9JIlpo/sTY7BKyurFASSsVLpGooD49z9fHc/HxgP1AHHAf+SzuJaM2/dbnIMJg3W1cSSPt275jNxUA8NGEtGSyUIhrn7tmYfbwdGu/suPliQrtPNX7ebsf1K6VaoaaOSXiccUcbCjXuprg3s5S6SVqkEwctm9qSZzTaz2cBjwEtmVgzsSW95hxaLO2+v303FsJ5BPL1kmRNGlRGLO2+s3hl0KSJpkUoQXEliI/qjgWNIbEZ/pbsfCOpis+Vb93GgPsaUoQoCSb9jhvSga34ur6p7SDJUKlcWO/D/k7dQmLc+sc3x5CEKAkm/wrxcpg7vxcsKAslQbbYIzOxzZrbSzPaaWbWZ7TOz6s4oriXz1+2mT0khg3rq+gHpHNNH9mZN1QF2HagPuhSRDpdK19CNwDnu3t3dS929xN1L011Ya+at282UoT21EJh0mnH9Ey/5ZVsD/R9IJC1SCYJt7r407ZWkaPu+WtbvqtH4gHSqsclF55Zv3RdwJSIdL5W5l5Vm9iDwKInrBwBw9z+lrapWzF+XmKg0WUEgnahPSSE9ivIVBJKRUgmCUqAGOKPZMQeCCYL1uynIy2HCgEB7pyTLmBlj+pawTEEgGSiVWUNf7YxCUjVv3W4mDuxOYZ72kZXONbZfCQ/N20g87toWVTJKi0FgZv/H3W80s1+QaAF8iLtfndbKDqG2IcbijXv56vHDOvupRRjTr5Sa+hgbdx9kSO+ioMsR6TCttQiaBogrO6OQVLyzeS/1sbjGByQQTbuULdtarSCQjNJiELj7E2aWCxzp7t/txJpa9O7mxNS9iYO6B1yJZKMxzWYOnTGhX8DViHScVqePunsMmNJJtbRpf10MgB5dCwKuRLJRt8I8BvfqyrJtGjCWzJLKrKG3zexx4CHgQNPBIKaPHmxIBEGX/EhvrCYRNqZvqaaQSsZJJQh6ATuBU5sdC2T66MH6Rrrm5+qKYgnM2H4lvLB8O3WNMc1ck4wRqemjBxtidC3QL58EZ0y/EmJxZ9X2/UwYoLEqyQxpmz5qZncBnwa2u/uRyWO9gAeBYcBa4EJ3351qsQfr43TNVxBIcJovNaEgkEzRWmf7u8m3lcC8Q9za8jvgUx85di3wvLuPAp5Pfpyygw2NahFIoIaVFVOQm6NxAskorXUNfQF4Eujh7rcc7gO7+0tmNuwjh88FTk6+fzfwIoex7/HB+hhFCgIJUH5uDiP7dNNSE5JRWmsRTDGzocClZtbTzHo1v7Xz+fq6+xaA5Ns+h3PnmvoYXdQ1JAEb269ELQLJKK0FwW3A08BY/r5bKO1XG5vZ5WZWaWaVVVVVQGKJCY0RSNDG9Ctha3Ute2u0mb1khhaDwN1/7u7jgLvcfYS7D292G9HO59tmZv0Bkm+3t/L8t7t7hbtXlJeXA4lZQ+oakqA1X2pCJBO0eWWWu1/Rgc/3ODA7+f5s4LHDuXNNvVoEErzRfRNBsLrqQBtnikRD2i7RNbMHgNeBMWa20cwuA/4TON3MVgKnJz9OWW1DjC5qEUjAenTNB2BfrbqGJDOkcmVxu7j7xS186rT2PubB+hhFahFIwJpapTX1sYArEekYkVm0x92p0ZXFEgI5OUZRQS419Y1BlyLSISITBHWNcdxREEgoFBXkcUAtAskQkQmCg8lfOg0WSxgUF+ZSU6cWgWSG6ARBg4JAwkMtAskk0QsCdQ1JCBRrjEAySHSCQF1DEiJFhXkcqFOLQDJDdIJALQIJEbUIJJNEJwiSLQItMSFhUFSgFoFkjsgEQdPFO1p9VMKguFAtAskckQmCWs0akhDRrCHJJJEJgqYxgqKCtK2KIZKy4oJc6hvjNMTiQZci8rFFJghqNGtIQqSoMPEPidYbkkwQmSCo1awhCZGmSQsaJ5BMEJkgqKlvJDfHyM+1oEsReT8INHNIMkFkguBgfZyu+bmYKQgkeMUFTV1DahFI9EUnCLQEtYRIUaFaBJI5ohME9Y0aKJbQUItAMkl0gqBB+xVLeBQ3tQg0a0gyQISCIK6uIQmNputZtCeBZILoBIG6hiREmrqG1CKQTBCdIGiIacE5CY2m1qlaBJIJIhMENfUxuigIJCQK8nIoyM1Ri0AyQmSCoLZeg8USLkWFuRzUrCHJAJEJAnUNSdgUawVSyRCRCYIatQgkZIq0S5lkiMgEQV1jXJvSSKho32LJFJEIgrg7oG0qJVy0b7FkiogEQeKtLiiTMNG+xZIpohEEySTQGIGEifYtlkwRyL6PZrYW2AfEgEZ3r2jtfLUIJIy0b7FkiiA3AD7F3XekcqK7WgQSPsUFubqyWDJCNLqGmoJALQIJkaLCPGoaYu93XYpEVVBB4MBfzWyemV3e1snvdw2pRSAhUlyQizvUNqp7SKItqK6h4919s5n1AZ41s2Xu/lLzE5IBcTlAn0HD6IpaBBIuRYXJFUjrYu8vSy0SRYG0CNx9c/LtduARYOohzrnd3SvcvaJbSQkARfn6ZZPwKG5agVQzhyTiOj0IzKzYzEqa3gfOAJa0dp+mrqEuBZEY0pAs0dQK0LUEEnVB/IvdF3jEzJqe/353f7q1O/j7VxarRSDhUaQWgWSITv/L6u5rgEmHc5+4J5ouXfLUIpDw0L7Fkiki8Zc1HncKcnPIy41EuZIltG+xZIpI/GWNu2vGkISO9i2WTBGRINA1BBI+RYUaI5DMEJEgUItAwqdYs4YkQ0QiCFwtAgmhLvk5mKlFINEXiSBQi0DCyMwS+xarRSARF5kg0O5kEkbat1gyQUSCAO1XLKFUXKg9CST6ohEEcdcYgYRSUUEuB9UikIiLRhCoa0hCSmMEkgkiEgTqGpJwKtK+xZIBIhEErllDElLF2rdYMkA0ggAoUotAQqhI+xZLBohEEIB2J5Nw0qwhyQQKApGPQdcRSCaIThCoa0hCqLgwj4aYU98YD7oUkXZTEIh8DNqlTDJBdIJAXUMSQtqTQDJBdIJALQIJoff3JNDMIYmw6ASBWgQSQmoRSCaITBBoiQkJo/fHCNQikAiLTBBoiQkJoyK1CCQDRCYImn7hRMJE+xZLJohMEGiwWMJI+xZLJohMEBTmRaZUySJqEUgmiMRf1xwzcnIs6DJE/k7TYohqEUiURSIITBkgIZWXm0NhXo5aBBJpkQiCHCWBhFhiBVIFgURXIEFgZp8ys+VmtsrMrm3rfPUKSZgl9iRQ15BEV6cHgZnlAr8CzgLGAxeb2fjW7qMWgYRZYpcytQgkuoJoEUwFVrn7GnevB/4AnNvaHRQEEmaJfYvVIpDoCuIqrYHAhmYfbwSOa+0O6hqSMCsuyOOttbs4/eY5QZci0i5BBMGh/qz7351kdjlwOUDvgcPTXZNIu31p+lBKu+rKdwmf51I8z9z/7m9wWpnZdOCH7n5m8uPvAbj7T1q6T0VFhVdWVnZShSIimcHM5rl7RVvnBTFG8BYwysyGm1kBcBHweAB1iIgIAXQNuXujmV0FPAPkAne5+zudXYeIiCQE0rHp7n8G/hzEc4uIyIdF4spiERFJHwWBiEiWUxCIiGQ5BYGISJZTEIiIZLlOv6CsPcysCljXiU9ZBuzoxOfrKFGtG6Jbe1TrhujWHtW6ofNrH+ru5W2dFIkg6GxmVpnK1XhhE9W6Ibq1R7VuiG7tUa0bwlu7uoZERLKcgkBEJMspCA7t9qALaKeo1g3RrT2qdUN0a49q3RDS2jVGICKS5dQiEBHJclkdBGZ2gZm9Y2ZxM6todnyYmR00swXJ223NPjfFzBab2Soz+7lZMPtotlR78nPfS9a33MzObHb8U8ljq8zs2s6v+sPM7IdmtqnZ93n8bYusAAAE8UlEQVRms88d8msIk7B9P1tjZmuTr9sFZlaZPNbLzJ41s5XJtz2DrhPAzO4ys+1mtqTZsUPWagk/T/4MFpnZ5JDVHY3XuLtn7Q0YB4wBXgQqmh0fBixp4T5vAtNJ7LT2F+CskNU+HlgIFALDgdUklvvOTb4/AihInjM+4O//D4HvHOL4Ib+GoF8vH6kxdN/PNupdC5R95NiNwLXJ968Fbgi6zmQtJwGTm/8OtlQrMDP5e2jANGBuyOqOxGs8q1sE7r7U3Zener6Z9QdK3f11T/w07wHOS1uBrWil9nOBP7h7nbu/B6wCpiZvq9x9jbvXA39InhtGLX0NYRKl72dLzgXuTr5/NwG9lj/K3V8Cdn3kcEu1ngvc4wlvAD2Sv6edroW6WxKq13hWB0EbhpvZ22Y2x8xOTB4bCGxsds7G5LEwGQhsaPZxU40tHQ/aVckm/V3NuibCWmtzUaixOQf+ambzkvuBA/R19y0Aybd9AquubS3VGoWfQ+hf4xm/47aZPQf0O8SnrnP3x1q42xZgiLvvNLMpwKNmNoFE8/Oj0jbtqp21t1TjoUI/7VPGWvsagF8DP0rW8SPgJuBSOvn73E5RqLG54919s5n1AZ41s2VBF9RBwv5ziMRrPOODwN0/2Y771AF1yffnmdlqYDSJ1B7U7NRBwOaOqLOFOg67dhI1Dm72cfMaWzqeNql+DWb2W+DJ5IetfQ1hEYUa3+fum5Nvt5vZIyS6IbaZWX9335LsTtkeaJGta6nWUP8c3H1b0/thfo2ra+gQzKzczHKT748ARgFrkk3SfWY2LTlb6MtAS/+ZB+Vx4CIzKzSz4SRqfxN4CxhlZsPNrAC4KHluYD7Sl/tZoGm2RUtfQ5iE7vvZEjMrNrOSpveBM0h8rx8HZidPm034XsvNtVTr48CXk7OHpgF7m7qQwiAyr/GgRqnDcCPxg9lI4r//bcAzyePnA++QGNWfD3ym2X0qSPwwVwO/JHlRXlhqT37uumR9y2k2q4nEDIsVyc9dF4Lv/73AYmARiV+M/m19DWG6he372UqdI5Kv5YXJ1/V1yeO9geeBlcm3vYKuNVnXAyS6ZxuSr/HLWqqVRBfLr5I/g8U0m0EXkroj8RrXlcUiIllOXUMiIllOQSAikuUUBCIiWU5BICKS5RQEIiJZTkEg0sEssXrtkrbPFAkHBYGISJZTEIg0Y2aPJhdme6dpcTYz229m/2FmC83sDTPrmzw+MvnxW2Z2vZntP8Tj5ZrZfyXPWWRm/9jZX5NIWxQEIh92qbtPIXEF+dVm1hsoBt5w90nAS8DXkufeAtzi7sfS8joxl5FY9uBY4Fjga8klBURCQ0Eg8mFXm9lC4A0Si4KNAur5YLGweSQ2LoLEBkUPJd+/v4XHO4PEWjgLgLkklkoY1fFli7Rfxq8+KpIqMzsZ+CQw3d1rzOxFoAvQ4B+sxRLj8H5vDPiGuz/TkbWKdCS1CEQ+0B3YnQyBsSS2PmzNGyQWKITE6qOH8gxwhZnlA5jZ6OQKoCKhoSAQ+cDTQJ6ZLSKxicgbbZx/DfAtM3sT6A/sPcQ5dwDvAvOTU0p/g1riEjJafVSkncysCDjo7m5mFwEXu3vU9i0W0X8mIh/DFOCXyU2K9pDYglAkctQiEBHJchojEBHJcgoCEZEspyAQEclyCgIRkSynIBARyXIKAhGRLPe/qguokuLioZYAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy\n", "import nengo\n", "\n", "n = nengo.neurons.LIFRate() \n", "\n", "theta = numpy.linspace(-numpy.pi, numpy.pi, 100)\n", "x = numpy.array([numpy.sin(theta), numpy.cos(theta)])\n", "\n", "e = numpy.array([-1.0, 0]) \n", "\n", "plot(theta*180/numpy.pi, n.rates(numpy.dot(x.T, e), bias=1., gain=0.2)) #bias 1->1.5\n", "xlabel('angle')\n", "ylabel('firing rate')\n", "xlim(-180, 180)\n", "show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Does it match empirical data?\n", " - When tuning curves are plotted just considering $\\theta$, they are fit by $a_i=b_0+b_1cos(\\theta-\\theta_e)$ \n", " - Where $\\theta_e$ is the angle for the encoder $e_i$ and $b_0$ and $b_1$ are constants\n", " \n", "- Interestingly, Georgopoulos suggests doing linear decoding:\n", " - $\\hat{x}=\\sum_i a_i e_i$\n", " - This gives a somewhat decent estimate of the direction of movement (but a terrible estimate of magnitude)\n", " " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Higher-dimensional Tuning\n", "- Note that there can be different ways of organizing the representation of a higher dimensional space\n", "\n", "\n", "\n", "- Here, the neurons respond to angular velocity. This is a 3D vector. \n", "- But, instead of randomly distributing encoders around the 3D space, they are aligned with a major axis\n", " - encoders are chosen from [1,0,0], [-1,0,0], [0,1,0], [0,-1,0], [0,0,1], [0,0,-1]\n", "- This can affect on the representation\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Administrative Notes\n", "\n", "- Assignment 1 has been posted \n", " - [HTML](http://nbviewer.ipython.org/github/celiasmith/syde556/blob/master/Assignment%201.ipynb)\n", "- Due: January 28th at midnight\n", "- Total marks: 20 (20% of final grade)\n", "- Late penalty: 1 mark per day\n", "- It is recommended that you use Python.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.6" }, "livereveal": { "scroll": true, "start_slideshow_at": "selected" } }, "nbformat": 4, "nbformat_minor": 1 }