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Created March 29, 2014 18:04
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{
"metadata": {
"name": "MKL"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Multiple Kernel Learning"
]
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"By Saurabh Mahindre - <a href=\"https://github.com/Saurabh7\">github.com/Saurabh7</a>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This notebook is about multiple kernel learning in shogun. We will see how to construct a combined kernel, determine optimal kernel weights using MKL and use them for [classification](http://en.wikipedia.org/wiki/Statistical_classification)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# import all shogun classes\n",
"from modshogun import *"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Introduction"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<em>Multiple kernel learning</em> (MKL) is about using a combined kernel i.e. a kernel consisting of a linear combination of arbitrary kernels over different domains. The coefficients or weights of the linear combination can be learned as well.\n",
"\n",
"[Kernel based methods](http://en.wikipedia.org/wiki/Kernel_methods) such as support vector machines (SVMs) employ a so-called kernel function $k(x_{i},x_{j})$ which intuitively computes the similarity between two examples $x_{i}$ and $x_{j}$. </br>\n",
"Selecting the kernel function\n",
"$k()$ and its parameters is an important issue in training. Kernels designed by humans usually capture one aspect of data. Choosing one kernel means to select exactly one such aspect. Which means combining such aspects is often better than selecting.\n",
"\n",
"In shogun the [CMKL](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CMKL.html) is the base class for MKL. We can do classifications: [binary](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CMKLClassification.html), [one-class](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CMKLOneClass.html), [multiclass](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CMKLMulticlass.html) and regression too: [regression](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CMKLRegression.html)"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Mathematical formulation (skip if you just want code examples)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"</br>In a SVM, defined as:\n",
"$$f({\\bf x})=\\text{sign} \\left(\\sum_{i=0}^{N-1} \\alpha_i k({\\bf x}, {\\bf x_i})+b\\right)$$</br>\n",
"where ${\\bf x_i},{i = 1,...,N}$ are labeled training examples ($y_i \\in {\u00b11}$).\n",
"\n",
"One could make a combination of kernels like:\n",
"$${\\bf k}(x_i,x_j)=\\sum_{k=0}^{K} \\beta_k {\\bf k_k}(x_i, x_j)$$\n",
"where $\\beta_k > 0$ and $\\sum_{k=0}^{K} \\beta_k = 1$\n",
"\n",
"In the multiple kernel learning problem for binary classification one is given $N$ data points ($x_i, y_i$ )\n",
" ($y_i \\in {\u00b11}$), where $x_i$ is translated via $K$ mappings $\\phi_k(x) \\rightarrow R^{D_k} $, $k=1,...,K$ , from the input into $K$ feature spaces $(\\phi_1(x_i),...,\\phi_K(x_i))$ where $D_k$ denotes dimensionality of the $k$-th feature space.\n",
"\n",
"In MKL $\\alpha_i$,$\\beta$ and bias are determined by solving the following optimization program. For details see [1].\n",
"\n",
"$$\\mbox{min} \\hspace{4mm} \\gamma-\\sum_{i=1}^N\\alpha_i$$\n",
"$$ \\mbox{w.r.t.} \\hspace{4mm} \\gamma\\in R, \\alpha\\in R^N \\nonumber$$\n",
"$$\\mbox {s.t.} \\hspace{4mm} {\\bf 0}\\leq\\alpha\\leq{\\bf 1}C,\\;\\;\\sum_{i=1}^N \\alpha_i y_i=0 \\nonumber$$\n",
"$$ {\\frac{1}{2}\\sum_{i,j=1}^N \\alpha_i \\alpha_j y_i y_j \\leq \\gamma}, \\forall k=1,\\ldots,K\\nonumber\\\\\n",
"$$\n",
"\n",
"\n",
"Here C is a pre-specified regularization parameter.\n",
"Within shogun this optimization problem is solved using [semi-infinite programming](http://en.wikipedia.org/wiki/Semi-infinite_programming). For 1-norm MKL one of the two approaches described in [1] is used.\n",
"The first approach (also called the wrapper algorithm) wraps around a single kernel SVMs, alternatingly solving for $\\alpha$ and $\\beta$. It is using a traditional SVM to generate new violated constraints and thus requires a single kernel SVM and any of the SVMs contained in shogun can be used. In the MKL step either a linear program is solved via [glpk](http://en.wikipedia.org/wiki/GNU_Linear_Programming_Kit) or cplex or analytically or a newton (for norms>1) step is performed.\n",
"\n",
"The second much faster but also more memory demanding approach performing interleaved optimization, is integrated into the chunking-based [SVMlight](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CSVMLight.html).\n",
"\n"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Using a Combined kernel"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Shogun provides an easy way to make combination of kernels using the [CombinedKernel](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CCombinedKernel.html) class, to which we can append any [kernel](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CKernel.html) from the many options shogun provides. It is especially useful to combine kernels working on different domains and to combine kernels looking at independent features and requires [CombinedFeatures](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CCombinedFeatures.html) to be used. Similarly the CombinedFeatures is used to combine a number of feature objects into a single CombinedFeatures object"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"kernel = CombinedKernel()"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Prediction on toy data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In order to see the prediction capabilities, let us generate some data using the [GMM](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CGMM.html) class. The data is sampled by setting means ([GMM notebook](http://www.shogun-toolbox.org/static/notebook/current/GMM.html)) such that it sufficiently covers X-Y grid and is not too easy to classify."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"num=30;\n",
"num_components=4\n",
"means=zeros((num_components, 2))\n",
"means[0]=[-1,1]\n",
"means[1]=[2,-1.5]\n",
"means[2]=[-1,-3]\n",
"means[3]=[2,1]\n",
"\n",
"covs=array([[1.0,0.0],[0.0,1.0]])\n",
"\n",
"gmm=GMM(num_components)\n",
"[gmm.set_nth_mean(means[i], i) for i in range(num_components)]\n",
"[gmm.set_nth_cov(covs,i) for i in range(num_components)]\n",
"gmm.set_coef(array([1.0,0.0,0.0,0.0]))\n",
"xntr=array([gmm.sample() for i in xrange(num)]).T\n",
"xnte=array([gmm.sample() for i in xrange(5000)]).T\n",
"gmm.set_coef(array([0.0,1.0,0.0,0.0]))\n",
"xntr1=array([gmm.sample() for i in xrange(num)]).T\n",
"xnte1=array([gmm.sample() for i in xrange(5000)]).T\n",
"gmm.set_coef(array([0.0,0.0,1.0,0.0]))\n",
"xptr=array([gmm.sample() for i in xrange(num)]).T\n",
"xpte=array([gmm.sample() for i in xrange(5000)]).T\n",
"gmm.set_coef(array([0.0,0.0,0.0,1.0]))\n",
"xptr1=array([gmm.sample() for i in xrange(num)]).T\n",
"xpte1=array([gmm.sample() for i in xrange(5000)]).T\n",
"traindata=concatenate((xntr,xntr1,xptr,xptr1), axis=1)\n",
"trainlab=concatenate((-ones(2*num), ones(2*num)))\n",
"\n",
"testdata=concatenate((xnte,xnte1,xpte,xpte1), axis=1)\n",
"testlab=concatenate((-ones(10000), ones(10000)))\n",
"\n",
"#convert to shogun features and generate labels for data\n",
"feats_train=RealFeatures(traindata) \n",
"labels=BinaryLabels(trainlab) "
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"_=jet()\n",
"figure(figsize(18,5))\n",
"subplot(121)\n",
"# plot train data\n",
"_=scatter(traindata[0,:], traindata[1,:], c=trainlab, s=100)\n",
"title('Toy data for classification')\n",
"axis('equal')\n",
"colors=[\"blue\",\"blue\",\"red\",\"red\"]\n",
"# a tool for visualisation\n",
"from matplotlib.patches import Ellipse\n",
"def get_gaussian_ellipse_artist(mean, cov, nstd=1.96, color=\"red\", linewidth=3):\n",
" vals, vecs = eigh(cov)\n",
" order = vals.argsort()[::-1]\n",
" vals, vecs = vals[order], vecs[:, order] \n",
" theta = numpy.degrees(arctan2(*vecs[:, 0][::-1]))\n",
" width, height = 2 * nstd * sqrt(vals)\n",
" e = Ellipse(xy=mean, width=width, height=height, angle=theta, \\\n",
" edgecolor=color, fill=False, linewidth=linewidth)\n",
" \n",
" return e\n",
"for i in range(num_components):\n",
" gca().add_artist(get_gaussian_ellipse_artist(means[i], covs, color=colors[i]))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
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qWU/wgEBq1oQjR+TBxpkvPprghg0xXL3Kq3p9QkqW28AxtRpV2bLsP3Ik25Kt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CBTxotq1aBIEdu2x0YcHR3RZeA8Iyn/06mB3jExrPzf/wgNtZSvLGM0Gg063T0WLDDlv169Gn77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\n"
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Generating Kernel weights"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Just to help us visualize let's use two gaussian kernels ([CGaussianKernel](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CGaussianKernel.html)) with considerably different widths. As required in MKL, we need to append them to the Combined kernel. To generate the optimal weights (i.e $\\beta$s in the above equation), training of [MKL](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CMKLClassification.html) is required. This generates the weights as seen in this example."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"width0=0.5\n",
"kernel0=GaussianKernel(feats_train, feats_train, width0)\n",
"\n",
"width1=25\n",
"kernel1=GaussianKernel(feats_train, feats_train, width1)\n",
"\n",
"#combine kernels\n",
"kernel.append_kernel(kernel0) \n",
"kernel.append_kernel(kernel1)\n",
"kernel.init(feats_train, feats_train)\n",
"\n",
"mkl = MKLClassification()\n",
"#set the norm, weights sum to 1.\n",
"mkl.set_mkl_norm(1) \n",
"mkl.set_C(1, 1)\n",
"mkl.set_kernel(kernel)\n",
"mkl.set_labels(labels)\n",
"\n",
"#train to get weights\n",
"mkl.train() \n",
"\n",
"w=kernel.get_subkernel_weights()\n",
"print w"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[ 9.99664617e-01 3.35382730e-04]\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Binary classification using MKL"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now with the data ready and training done, we can do the binary classification. The weights generated can be intuitively understood. We will see that on plotting individual subkernels outputs and outputs of the MKL classification. To apply on test features, we need to reinitialize the kernel with `kernel.init` and pass the test features. After that its just a matter of doing `mkl.apply` to generate outputs. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"size=100\n",
"x1=linspace(-5, 5, size)\n",
"x2=linspace(-5, 5, size)\n",
"x, y=meshgrid(x1, x2)\n",
"#Generate X-Y grid test data\n",
"grid=RealFeatures(array((ravel(x), ravel(y))))\n",
"\n",
"kernel0t=GaussianKernel(feats_train, grid, width0)\n",
"kernel1t=GaussianKernel(feats_train, grid, width1)\n",
"\n",
"kernelt=CombinedKernel()\n",
"kernelt.append_kernel(kernel0t)\n",
"kernelt.append_kernel(kernel1t)\n",
"#initailize with test grid\n",
"kernelt.init(feats_train, grid)\n",
"\n",
"mkl.set_kernel(kernelt)\n",
"#prediction\n",
"grid_out=mkl.apply() \n",
"\n",
"z=grid_out.get_values().reshape((size, size))\n",
"\n",
"figure(figsize=(10,5))\n",
"title(\"Classification using MKL\")\n",
"c=pcolor(x, y, z)\n",
"_=contour(x, y, z, linewidths=1, colors='black', hold=True)\n",
"_=colorbar(c)\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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fhU8/h07t4Z0XoFsntMdCE1JCP8EwWyBLxEzGiKxvsxH/ZjI7zLYJltQiIxdw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Lip3VveoR51ReWsGjCP8XlvhWdi21ZC+kCIklXCiuCYwdBz4dOboTwfYtu3qKZ5/AmYx59w8L33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\ngpoO/B/wB8Zdc1XJfir5BM4aI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VGP2N8/pOKg7hzqOYbER18j+58Lnl5WCcd9Sp6qQmra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\nRqPRaDQap6MNDI1Go9FoNE7n/wHgSQ7cz0uZdQAAAABJRU5ErkJggg==\n"
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To justify the weights, lets train and compare two subkernels with the MKL classification output. Training MKL classifier with a single kernel appended to a combined kernel makes no sense and is just like normal single kernel based classification, but let's do it for comparison."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"z=grid_out.get_labels().reshape((size, size))\n",
"\n",
"# MKL\n",
"figure(figsize=(20,5))\n",
"subplot(131, title=\"Multiple Kernels combined\")\n",
"c=pcolor(x, y, z)\n",
"_=contour(x, y, z, linewidths=1, colors='black', hold=True)\n",
"_=colorbar(c)\n",
"\n",
"comb_ker0=CombinedKernel()\n",
"comb_ker0.append_kernel(kernel0)\n",
"comb_ker0.init(feats_train, feats_train)\n",
"mkl.set_kernel(comb_ker0)\n",
"mkl.train()\n",
"comb_ker0t=CombinedKernel()\n",
"comb_ker0t.append_kernel(kernel0)\n",
"comb_ker0t.init(feats_train, grid)\n",
"mkl.set_kernel(comb_ker0t)\n",
"out0=mkl.apply()\n",
"\n",
"# subkernel 1\n",
"z=out0.get_labels().reshape((size, size)) \n",
"subplot(132, title=\"Kernel 1\")\n",
"c=pcolor(x, y, z)\n",
"_=contour(x, y, z, linewidths=1, colors='black', hold=True)\n",
"_=colorbar(c)\n",
"\n",
"comb_ker1=CombinedKernel()\n",
"comb_ker1.append_kernel(kernel1)\n",
"comb_ker1.init(feats_train, feats_train)\n",
"mkl.set_kernel(comb_ker1)\n",
"mkl.train()\n",
"comb_ker1t=CombinedKernel()\n",
"comb_ker1t.append_kernel(kernel1)\n",
"comb_ker1t.init(feats_train, grid)\n",
"mkl.set_kernel(comb_ker1t)\n",
"out1=mkl.apply()\n",
"\n",
"# subkernel 2\n",
"z=out1.get_labels().reshape((size, size)) \n",
"subplot(133, title=\"kernel 2\")\n",
"c=pcolor(x, y, z)\n",
"_=contour(x, y, z, linewidths=1, colors='black', hold=True)\n",
"_=colorbar(c)\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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PpNgOQERExO22ADPCHhkBdLMSS2LZbDsAERFxjNYA7MJcPBFJZirkiIh7pTZi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\ngg==\n"
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we can see the multiple kernel output seems just about right. Kernel 1 gives a sort of overfitting output while the kernel 2 seems not so accurate. The kernel weights are hence so adjusted to get a refined output. We can have a look at the errors by these subkernels to have more food for thought. Most of the time, the MKL error is lesser as it incorporates aspects of both kernels. One of them is strict while other is lenient, MKL finds a balance between those."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"kernelt.init(feats_train, RealFeatures(testdata))\n",
"mkl.set_kernel(kernelt)\n",
"out=mkl.apply()\n",
"\n",
"evaluator=ErrorRateMeasure()\n",
"print \"Test error is %2.2f%% :MKL\" % (100*evaluator.evaluate(out,BinaryLabels(testlab)))\n",
"\n",
"\n",
"comb_ker0t.init(feats_train,RealFeatures(testdata)) \n",
"mkl.set_kernel(comb_ker0t)\n",
"out=mkl.apply()\n",
"\n",
"evaluator=ErrorRateMeasure()\n",
"print \"Test error is %2.2f%% :Subkernel1\"% (100*evaluator.evaluate(out,BinaryLabels(testlab)))\n",
"\n",
"comb_ker1t.init(feats_train, RealFeatures(testdata))\n",
"mkl.set_kernel(comb_ker1t)\n",
"out=mkl.apply()\n",
"\n",
"evaluator=ErrorRateMeasure()\n",
"print \"Test error is %2.2f%% :subkernel2\" % (100*evaluator.evaluate(out,BinaryLabels(testlab)))\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Test error is 13.55% :MKL\n",
"Test error is 29.09% :Subkernel1"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Test error is 16.26% :subkernel2"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"MKL for knowledge discovery:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"MKL can recover information about the problem at hand. Let us see this with a binary classification problem. The task is to separate two concentric classes shaped like circles. By varying the distance between the boundary of the circles we can control the separability of the problem. Starting with an almost non-separable scenario, the data quickly becomes separable as the distance between the circles increases."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def circle(x, radius, neg):\n",
" y=sqrt(square(radius)-square(x))\n",
" if neg:\n",
" return[x, -y]\n",
" else:\n",
" return [x,y]\n",
" \n",
"def get_circle(radius):\n",
" neg=False\n",
" range0=linspace(-radius,radius,100)\n",
" pos_a=array([circle(i, radius, neg) for i in range0]).T\n",
" neg=True\n",
" neg_a=array([circle(i, radius, neg) for i in range0]).T\n",
" c=concatenate((neg_a,pos_a), axis=1)\n",
" return c\n",
"\n",
"def get_data(r1, r2):\n",
" c1=get_circle(r1)\n",
" c2=get_circle(r2)\n",
" c=concatenate((c1, c2), axis=1)\n",
" feats_tr=RealFeatures(c)\n",
" return c, feats_tr\n",
"\n",
"l=concatenate((-ones(200),ones(200)))\n",
"lab=BinaryLabels(l)\n",
"\n",
"#get two circles with radius 2 and 4\n",
"c, feats_tr=get_data(2,4)\n",
"c1, feats_tr1=get_data(2,3)\n",
"_=gray()\n",
"figure(figsize=(10,5))\n",
"subplot(121)\n",
"title(\"Circles with different separation\")\n",
"p=scatter(c[0,:], c[1,:], c=lab)\n",
"subplot(122)\n",
"q=scatter(c1[0,:], c1[1,:], c=lab)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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54YsvvkDHjh2xZs0aKBQKDB8+HNbW1hg3bhw6duwodfQyp6yM+5s3b6JPnz5Q\nKpVQKpXw9/fHmDFjXlumrNRSHiQmJuLo0aOYM2cOYmNj0bRpU1y4cAHr16/HsmXLMHToUKxduxZB\nQUEICgrC1q1bC5vetWvXFu41ev78OdTV1VG9enW4uLigbt26qFGjBurVqwctLa0S/cMoPz8faWlp\nuHbtGiIjI3Hv3j1cvnwZjx49gkwmg56eHho0aFA4V+KWLVvg7++PiIgIeHh4YNeuXZg3bx5atmyJ\nBQsW4Pjx49izZw8AoHHjxpgwYQI8PT0/26MJUhANVBn013k5hw4dgra2NtauXYvFixejVatWaN26\nNZo2bQp3d3fk5OQgIiICo0ePRt++fWFpaSl19DIlLi4OGzduxKJFiyCXywv32BkbG8Pf3x+urq4I\nDAyElZUVpk+fjrZt22Ly5MliHqliKE/jvjzVUlrdvXsXa9euxaZNm6CqqoqBAwfixx9/REhICAIC\nAhAcHIxmzZrh3LlzaN68OQYOHIgbN24gNDQUhoaGSExMhJ2dHerVqwcfHx94eHiUiukEHj16hF9/\n/RWHDx9GZGQknj9/DlVVVbRp0wbXr19H7969kZCQAC0tLchkMtjZ2WHNmjXYvn07/Pz8kJOTA4VC\ngczMTIwcORKBgYGloq7yTjRQZcypU6fQs2dPqKurY9u2bZg2bRpGjhwJW1tbtGrVCl26dEFSUhJO\nnDiBcePGoV+/fjAxMZE6dpmWkJCADRs2YP78+TA3N0fLli1hYGCA58+fY8mSJfDx8UFycjKsrKxw\n7tw5bNy4Ee3atZM6dplQnsZ9eaqltLl48SIWLlyIkydPomLFipg3bx769++PuLg42Nra4smTJ3Bx\nccGUKVPw8OFDbNmyBVWrVsXNmzdhamoKNzc39OrVCy4uLjAwMJC6nPeKiYnBb7/9hm3btuHKlStQ\nKpXIzs5G165doa2tjZSUFLi7u+PWrVvIzc3FoEGD4O3tDR8fHzx58gS3bt1C7969MWbMGFhZWUld\nTrkl5oEqI549e8aGDRtSV1eXwcHBdHJy4pUrV3j48GGamppywYIF/N///sdKlSpx/PjxfPbsmdSR\ny524uDhOnjyZ+vr6bNKkCceOHcsNGzawWbNmLCgo4Nq1a6mlpcUKFSrQxcWFUVFRUkcu9crTuC9P\ntZQW58+fZ5s2bainp0d7e3vu27ePlSpVYnJyMg0NDXnlyhUGBgayWbNmnD17Ns3NzamqqkoHBwfO\nnTuXN27hCvvhAAAgAElEQVTckLqED6ZUKnnmzBkOGzaMxsbG1NLSooeHBwMDA9muXTvu27ePvr6+\nXLVqFYODg2lmZsZ58+bR29ubRkZG7NevH6Ojo6Uuo1wq6pgXDZREFAoFf/zxR9ra2nLcuHE0MzNj\nTEwM586dy3r16vH06dOcMmUK9fX12bt3b/7xxx9SRy73Hj16xMDAQOrq6tLPz4+jR4/mxYsXaWFh\nwfv37zMuLo5NmjShjY0NlyxZQoVCIXXkUqs8jfvyVIvUrl27xrZt21JPT481a9bkrl27aG9vzz/+\n+IONGzfm/PnzGRwcTLlcTl9fX5qZmbFGjRqcOHEiU1NTpY7/Ud2/f5/9+vWjqakpHRwc6OPjQ3d3\nd4aHh7NevXo8efIkFy1axOrVq3Pt2rVs1aoV5XI5Bw0axJcvX0odv1wRDVQplpaWxsDAQNavX59a\nWlpMSUmhn58fBw8ezNzcXE6aNIlyuZyurq48ffq01HE/O+fOnWODBg1obGzMKVOmcPDgwUxNTWXV\nqlUZFBTEbdu2sX79+uzWrRtTUlKkjlsqladxX55qkcqTJ08YEBBAXV1duri4cN26dWzYsCHDwsI4\ncOBAdu3alVevXqWDgwONjIyopaXFzp078+TJk5/dFQMyMzO5fft2urq6Uk9Pj+7u7qxWrRojIyNp\naWnJ27dvc/z48XRxceGGDRvYvHlzmpiYcPLkyczIyJA6frkgGqhS6vz58zQxMaG6ujrj4uJYrVo1\nHj16lImJiWzZsiXV1NSoqanJJUuWSB31s7dq1arCS8Vs3bqVrVu3JkkuWbKEBgYGdHBwoLGxMc+c\nOSNt0FKoPI378lTLp5aens4ZM2bQwMCA9evX5/fff09fX1/u2LGDCxcuZL169Xj27Fl6e3uzQoUK\nNDIy4uzZs5mYmCh1dMkplUo+efKEffv2pba2Np2dnWlkZMTHjx9TU1OTL1++5NChQ+nq6soff/yR\n7u7utLKy4pYtW8Te8Q8kGqhSJj8/n/Pnz6eenh4PHDhATU1NJiUl8fTp05TL5Wzbti2dnJzo4+PD\n3NxcqeMK/yc/P5+dO3emtbU1W7VqxZs3b9LMzIzR0dFMS0tjz549aWRkxDlz5ojrXf1NeRr35amW\nT0WpVPLUqVOsXLkya9SowWHDhvHrr7/m8uXLuWfPHtrY2PDgwYPs06cPDQwMWKNGDe7YsUPq2KVW\nQUEBp06dSnNzc9avX58VKlTgs2fPqKWlxeTkZI4cOZK1atXi+PHj6ejoyGbNmvHOnTtSxy6zijrm\nxSyBn0i/fv1w6NAh5OXloX379ggMDISfnx/y8/PRv39/nD9/HlOnTsXBgwdRoUIFqeMK/0dNTQ27\nd+/GkiVLEBkZidmzZ6N+/fowMzNDq1atoKqqiqVLlyIsLAw9e/aUOq4gSC4vLw+9e/dGz549Ua1a\nNfj6+kIul8Pf3x+zZs2CQqHAV199hf79++P333/HmjVrcPfuXXTv3l3q6KWWqqoqpk+fjpiYGHTo\n0AGmpqbo3r071NTUkJaWhg0bNiAiIgJ6enpISUkBAHh4eGDRokVQKpUSpy/HPnIj99n/9Xb9+nVW\nrVqVGhoaTE9Pp4WFBY8ePcq8vDyOGTOGcrmc3t7evH//vtRRhfd4/PgxfXx8aGBgwODgYH7xxRdU\nKpX89ddfaWdnRxUVFTo4OPDKlStSR5VceRr35amWj2337t2sWLEi7e3tOX36dI4ePZq//fYbjY2N\nGRwczIULF9LCwoI1atTghg0bpI5bZuXm5nLixIk0MzNju3btWLlyZT58+JDGxsZ88eIFd+3aRV1d\n3cL3ojx8avFTKuqYFw3UR3T9+nWamZlxxYoV1NXVZV5eHiMiImhiYsLq1avTwMCAc+bMkTqmUEyL\nFi2ijo4Oa9asyeTkZJqamvLAgQNUKpVcvHgxDQ0NefnyZaljSqo8jfvyVMvHEhcXx44dO1JHR4eT\nJk1iv379eOXKFZqYmDAsLIzbtm2jjY0NLS0tOXv2bHGOTglJTU1l3759qaenx0GDBrFx48Z88OAB\njY2NGRkZyTt37tDNzY1yuZzjx48Xp4cUkWigJLZixQoaGhrS3NycSqWS7dq1Y/fu3Xn69GmOHj2a\nlpaW4hh1GXb//n06ODiwd+/edHZ2Jkn+9NNPNDY2poeHB01MTLhw4UKJU0qnPI378lTLx3D69Gna\n2NjQ19eXbdu25eXLl2lhYcGHDx9y3759tLCwYKVKlejv78/09HSp45ZLjx49oru7OytWrMhZs2ax\nY8eOfP78Oc3MzLh06VKGhobS2dmZjRo1Ekc7ikA0UBJRKBRcsWIFtbW1+fvvv1NXV5cxMTHMzMzk\nt99+SyMjI/r6+jImJkbqqMIHevHiBTt37kxdXV3ev3+fenp6fPjwIUlyw4YN1NLS4sKFC1lQUCBx\n0k+vPI378lRLSZs3bx5NTU1Zo0YN/vbbb7S1tWVKSgpXr17NihUrUltbmzVq1BC/tD+Ro0ePUldX\nlyYmJlyxYgV79OjBnJwcenh4sEmTJuzatSvlcjlPnTolddRSTTRQElAqlfT392fNmjVZo0YNkn8e\n7rGysmL37t3p4ODAUaNGSZxSKGmTJ0+mpaUl7e3tC+/XqFGDEyZMYMOGDdm1a9fPbi6b8jTuy1Mt\nJSUmJoZNmjShpqYmjx07xmrVqrGgoIAjR46knZ0dW7RoQSMjI65atUocrvvE8vLyOGDAAMrlcrZs\n2bJw0k2FQsE1a9bQxMSEmpqa7NevH7Ozs6WOWyqJBuoTy8rK4ogRI2hmZsbnz59TLpcXzg+0evVq\namtr88CBA9KGFD6a48ePF55crq2tzfj4eCqVSq5bt47GxsYcPHjwZzXJXXka9+WplpJw7do12tvb\nc/DgwaxSpQoLCgrYrFkzdu3alRs2bKCbmxtdXV3F1RMkFhISQktLSzZs2JBjx47l0aNHaWtry+vX\nr/OPP/5gnTp12Lx5c8bGxkodtdQp6pgXFxMuAQUFBWjRogUUCgWysrJw9epVhIaG4quvvkJBQQFU\nVFSwY8cOtGzZUuqowkcUHh6OLl26QKFQICkpCePGjUNISAgCAwNx9uxZPHv2DOHh4Z/FNBXladyX\np1o+1I4dOzBs2DBkZ2cjPj4e1atXx6xZs9ClSxcMGjQIx44dw9ChQzFp0iSoq6tLHfez9+rVKwwd\nOhRnzpyBj48PHB0dERAQgEaNGqFOnTpQU1NDREQEQkNDUbNmTanjlhriYsKfSGZmJr/55htWr16d\nycnJtLS05E8//cQXL15w1qxZdHBw+Kz2PHzusrOz6ejoyEmTJlFTU5MJCQkk//x4t5WVFfv27cu0\ntDSJU3585Wncl6da/qu8vDxOmDCBWlpa/O2331ixYkVGR0fz+vXrdHR0pEwmo6WlJc+fPy91VOEN\nfvrpJ2pqarJ3794cOXIkR4wYQZJct24dq1WrRisrK27evFnilKVHUce82AP1AXJzc9GsWTOoqPw5\nH+m5c+dw69YtDBgwANevX4eLiws2b94Me3t7iZMKn1JMTAwCAgLw66+/IjMzEz/88AO2bNmC/v37\n4+LFi3j06BHOnTsHLS0tqaN+NOVp3JenWv4Lkhg0aBAePHiAiIgI5OTkYNmyZVi+fDnat2+PX3/9\nFVZWVggODi78WSiUPomJiWjUqBEAYPz48dDQ0MDUqVOxZs0aKBQK9OvXDzNmzEDfvn0lTio9sQfq\nI8vPz+eYMWPo4uLCpKQk2tjYcMGCBYyMjOTgwYPp4eHx2Z04LLyuVatW7Nu3LzU1NQvPM7h27Rqr\nVKnCYcOGles5WcrTuC9PtRTXq1ev2KhRo8I9Tl5eXhw/fjxzcnK4YsUKVqpUiT/88MNn+UnTsig5\nOZn+/v50cnJiy5YtuWfPHqakpLB58+bU19enpqYmBwwY8Nm/n0Ud8+LPhf+goKAA7dq1w8GDByGX\ny2FgYIDQ0FCEhobCw8MDKSkp2LdvH2QymdRRBQnt2rULSqUS+fn5kMvl2LNnD1q3bo1mzZrh6tWr\n8Pb2Rl5entQxBeGNUlNT0a1bN9SrVw9GRkZISkrC9u3bcenSJVSqVAlTp07Fli1bMGbMGKiqqkod\nVygCfX19bNq0CX5+frh8+TKSkpIwduxY2NnZISEhAXfv3sW5c+cwYsQIFBQUSB231BOH8P6DdevW\nYc2aNdi/fz9cXFwwffp0NG7cGIsWLcKzZ89w/PhxqSMKpUinTp2gra2NU6dO4cCBA3Bzc0N2djY8\nPDwQEBCAoUOHSh2xxJWncV+eaimqqKgoeHl5IT09HREREQgLC8OCBQswYsQI3Lt3D4cOHcKVK1dg\nbGwsdVThPzp//jw6duwIHR0d7NixAxoaGmjdujVq1qyJ2NhYWFtb4/Dhw9DQ0JA66idX1DEv9kAV\n08SJEzFs2DBUrlwZFhYWOHnyJHbs2AF3d3fk5+dj586dUkcUSpnNmzdDQ0MDCQkJqF27Nh4+fIja\ntWsjISEBU6ZMwYgRIz67X9BC6RUfH48ePXogMDAQ9erVQ0hICAYPHowFCxZg6dKluH//Pi5evCia\npzKucePGOH78ODQ1NXHy5EkMGTIEs2bNQkhICHbs2IFnz55h4MCByM3NlTpqqSX2QBXD8ePHERQU\nhI0bN8LX1xf79u1DvXr18N133+Hy5cs4c+aM1BGFUszHxwdVqlTB1atX0bVrV4wYMQKpqalo2rQp\nZsyYgY4dO0odscSUp3Ffnmp5n6dPn6JJkyZQVVXFL7/8AmNjY7Rs2RJ2dnaIi4uDnZ3dZ7tXorx6\n+vQpmjVrhpSUFFy9ehU3b97EgAED0KFDB9y5cweqqqo4derUZ/WeF3XMiwaqiC5cuIDAwEC0aNEC\nP/74Iw4dOoTBgwcjLi4OzZo1w5YtW2BmZiZ1TKEUS0hIQEBAAE6fPo2YmBgYGRlh/vz5+Omnn6Ch\noYHVq1fDw8ND6pgloryMe6B81fIuKSkp6NSpEzw8PJCamoqXL19i8+bNePHiBXx8fNC8eXMsWrQI\nampqUkcVSlhaWho6dOiA2rVr49ChQ9i8eTOaNm2KS5cuwd/fHy1atMCyZcs+m3PdRANVgu7evQsP\nDw/07t0bJ0+exG+//QYdHR388ssvmD9/Pq5fvy51RKEMadiwIfr164dnz57h2LFjmD9/PmJiYhAU\nFISQkBDUqVNH6ogfrDyM+7+Up1reJj4+Ho0aNQJJ/PDDD2jdujV69OiBM2fOID8/H3369MHKlSs/\nm1+gn6NXr16hc+fOuHjxIuLj43HgwAFMmDAB7dq1w7Vr12Bubo79+/d/Ft8DooEqIUqlEsOGDUOF\nChWwcOFCDBs2DLt374aBgQHS0tJw5MgR1K1bV+qYQhly+/ZttGnTBhkZGTh79ixq1aqFzMxMDB48\nGOrq6li7dm2Zn0+nrI/7vytPtbxJQUEBAgICoK+vjxo1amDr1q3Yv38/VFRU0L59e/j6+mLy5MlS\nxxQ+AZJo27YtbG1tsXXrVly8eBGOjo64d+8efHx8MHz4cAwfPlzqmB+dOIm8BBQUFKBr167Yvn07\nkpKSIJPJsHz5cqxcuRKpqam4e/euaJ6EYqtZsyZu374NIyMjpKWlISoqCnXr1kVkZCRCQkLg6+sr\npjcQPonc3Fy0adMG4eHhqFOnDoYMGYJmzZqhatWqsLGxQZMmTTBhwgSpYwqfiEwmwy+//IKnT58i\nKysL1atXx7Zt2+Dh4YEqVarg+++/x6RJk6SOWXp82HRT7/cJVvHRrFq1is2bN+fTp09paWnJUaNG\ncfXq1XRwcODKlSuljieUcevXr6etrS1dXFw4Y8YMkn9O0Orj48NFixZJnO7DlOVx/0/lqZZ/Wrx4\nMb29vbllyxY6Ojry8ePHTExMpLe3N8eNGyd1PEFCjRo14tixY6mrq8tbt26RJOPj42lmZsarV69K\nnO7jKuqYF3ug3iImJgZbtmyBt7c3bG1tceHCBSQlJWHKlCmYP38+Bg8eLHVEoYzr27cvli9fjufP\nn6NDhw4AgJs3byI/Px/btm3DkydPJE5Y/sXExKBZs2aoWbMmatWqhWXLlkkd6ZNZunQpxo8fD09P\nT/Tq1QsBAQFwdnaGmZkZbGxsMGPGDKkjfjIkkZOTg7i4ODx48AA3b95EZGQkbt26hSdPniA+Pv6z\nm1hy9+7diIiIgEwmQ82aNREREYEvvvgCGRkZaNGiBU6fPi11RMmJc6DeICoqCu7u7qhVqxYSEhIQ\nHh4ObW1tTJkyBbdu3cL+/fuljiiUIz179oS5uTl8fX3h5+eHwYMHIyMjA9u2bUNERASqVq0qdcRi\nKyvjPi4uDnFxcahbty4yMjLg4uKC/fv3w9HRsXCZslJLcYSFhSEwMBDjxo3DypUrcebMGRgaGmLU\nqFGIjY3F7t27pY5Y4nJzc3Ht2jWcP38e4eHhuHv3Ll6+fIns7GwoFIoiv46amhq0tbVhaWmJ2rVr\n48svv0SjRo1QvXr1cneCdUFBARwcHDBr1iyMGTMGmzZtQuvWrXH69Gl89dVXuHfvHgwNDaWOWeLE\ntfA+wJgxYzhmzBgqFAoOGjSIenp6NDU1ZZ06dfjs2TOp4wnlzMuXL1m/fn3K5XL+8ssvhY9PnTqV\nQ4YMkTDZf1cWxz1JdujQgSEhIa89VlZreZvY2Fi6urpy2LBhVCqVnDRpErW0tFixYkU2btyY8fHx\nUkcsEfHx8Vy9ejVbtGhBbW1tAvioN5lMRiMjI3bt2pX79+9nZmam1JugRFy5coWmpqa0s7MjSSYl\nJXHYsGG0tLRk3759mZ2dLXHCklfUMS8aqH+4ePEia9WqxcWLFxc+dujQITo5OTE/P1/CZEJ5VlBQ\nwAYNGvD06dMkydDQUDZu3JiOjo48d+6cxOmKr6yNe5J88uQJbWxsmJ6e/trjZbGWt0lKSqKdnR3b\nt2/PBg0aMC8vjyS5e/duVqlSpUxfAF2pVPL69escOHAg9fT0PnrDVJSblZUVp0yZwri4OKk3zwd5\n/vw59fX1ef/+fdarV48DBw7k/v372alTJ7Zr165Mf9+8SVHHvJgR7W8uX76Mtm3bws/PD/PmzUOd\nOnVgaGiI2bNno2fPnmICOeGjUVVVxVdffYXRo0ejf//+mDZtGmbOnAmFQoFOnTph7969aNKkidQx\ny62MjAx07doVS5cuhba29r+e/+677wr/7+XlBS8vr08XrgTt2bMHTk5O2Lt3L/z8/ODs7AwTExPc\nvHkTwcHBZfIC6FFRUfjuu++wa9cuZGVlSR3nNbGxsZg5cyZmzpwJU1NTDBkyBEOGDIG+vr7U0YrF\n3Nwc06dPR8OGDWFsbIzVq1dDJpPB1dUVTk5OePjwYZk81eAvYWFhCAsLK/4XfuRGrkz99davX7/C\nTz9t376dVapUoVwu53fffUeFQiFxOqG8UyqVnDNnDk1NTblly5bCx1euXMmePXtKmKz4ytK4z8vL\nY6tWrV7b6/x3ZamWd1m3bh21tLT45ZdfkiQVCgUPHTpENTU1Pn78WOJ0xaNQKLh7925WrlxZ8r1M\nxb3JZDI2adKEly5dKnN7bjZs2MDatWtTqVRy+fLl1NPTo6WlJU1NTfnbb79JHa/EFHXMi5PI/8/t\n27cREBCAr7/+Gt9++y0A4PDhw1i8eDFCQ0MlTid8Ttq1a4eAgAB069YNd+7cwejRoxEVFYVt27aV\nmVnKy8q4J4k+ffrAyMgIixcvfuMyZaWWd3nw4AEaN26MI0eOwM/PD/7+/nB1dcWSJUtQpUoVrFmz\nRuqIRZKfn4958+Zhzpw5yMnJ+aDXUlNTg6GhIaysrGBnZwdLS0tYWFhAX18fWlpaAP48iTo7OxtJ\nSUl48eIFoqOj8fTpUzx//hxpaWlQKpUflMHc3BxLly6Fn5/fB73Op5Kbm4uGDRuiWrVqCAsLw6VL\nl2Bra4v9+/dj6NChiI6OLpN7Mf9JnEReDFevXqVcLqe/vz8NDQ25detW7tu3j/b29q+d1CsIn0Jw\ncDCtra25cOFC6uvrc9KkSZw2bRrlcjkvXLggdbwiKQvjniQjIiIok8lYp04d1q1bl3Xr1uWxY8de\nW6as1PI2SqWSEyZMKNzzFB0dza+//ppyuZzjxo0rE+d2ZmZmctKkSVRXV/9Pe320tLTYpEkTzp49\nm9euXSuxmjMzMxkeHs6goCDWqlWLampq/ymfvr4+t2zZwoKCghLJ9TElJiayZcuWbNu2LUkyJyeH\n69evp4aGBk+ePClxupJR1DEvGiiSPXv25NKlS0mSJ06coLOzM+3t7bl161aJkwmfqz179tDBwYEL\nFiwofOynn35i586dJUxVdGVh3BdVWa/l22+/ZdWqVWloaFj4KeILFy7QwMCAOTk5Eqd7N6VSycWL\nF1NDQ6NYDYmKigpdXFy4fPlyJiQkfNLMDx8+5Pjx42lra1vsRsrU1PRfnwItjS5dukRra2vGxsay\nadOmbNasGYcMGUIzM7NysdNBNFBFlJuby+bNm3P79u2Fj+3Zs4ft2rWTMJUgkH5+foXnQhUUFHDR\nokVs2LBhqf+lR5b+cV8cZbmW+/fv09TUlGlpaZw/fz7lcjlr1apFQ0NDHjp0SOp473T16lWampoW\nqwFxdnbmvn37Ss2enLS0NC5fvpw2NjbFqqN+/fp8+fKl1PHfafr06dTR0aGbm1vhuVzXrl2jiYmJ\nxMk+nGigiiAhIYHOzs60tramhYUFw8PDGRERwWrVqnHTpk1SxxM+c7t27aK9vT1PnDhBNzc3WlhY\n0NHRkbVq1Sr1H4suzeO+uMpqLQqFgpMmTWLNmjULH3v8+DFtbW0ZGhoqYbJ3S0tLo7e3d7EOf82Z\nM4cpKSlSR3+n6Oho9unThxUqVChybdOmTSs1zeCbTJs2jf379yf553x2kyZNYoUKFXjq1CmJk30Y\n0UAVwcCBAzl06FAqlUquWbOGFhYWtLGx4apVq6SOJggk//zklKWlJX18fFhQUEClUskxY8awd+/e\nUkd7p9I87ourrNbyzTff0MXFhXK5nD///DOTk5O5cuVK2tnZMSsrS+p4b7Rz584iNxj29vY8cuRI\nmfskW05ODlesWEFdXd0iH9a7ceOG1LHf6ObNm5TL5Txw4ADt7OzYr18/zps3j5aWlq99krisEQ1U\nEXh5eb3WKW/fvp1du3aVMJEg/Ju/vz/Xr19feP/cuXN0dXWVMNH7leZxX1xlsZa4uDjq6+szLS2N\nN27cYL169VihQgXWrl2bd+/elTrev2RmZrJjx45FaiicnJzKzcVst23bRn19/SKd0zVjxoxS2Swe\nPHiQhoaG/Oqrrwof+/XXX1m1alUJU32Yoo75z/ZiwmfOnEFKSgo2b94MpVKJ/Px87Ny5E7Vq1ZI6\nmiC8platWti1axdyc3Nx7949DB06FFlZWTh58qTU0YRSKiIiAhoaGtDW1kbt2rVx9epV1K9fH0uX\nLkWNGjWkjveaGzduwNra+r3XGDU2NkZoaChu376NevXqfaJ0H1ePHj2QkJCAlStXQkND463LKZVK\nTJ06FW5ubkhJSfmECd/P19cXw4cPh62tLQAgNTUVERERiI+Px6NHjyRO95F9aKcWHR1NLy8vOjk5\nsWbNmoWfZituJ/cpHTx4kGZmZpw3bx6rVKlCIyMjmpmZsW3btuXyuj6fgkKhYHR0NK9cucITJ05w\n79693LdvH0+cOMFLly4xKiqqVB/LL81yc3PZuXNnGhkZsWLFipw8eTKXL19OCwsL7tq1S+p4b1Qa\nx/1/VdZqWbVqFS0sLGhlZcWgoCDeuXOHCxYsoK2tLdPS0qSO95q1a9dSRUXlnXtf1NXVuXTp0lK5\n96Uk5eTksG/fvu/dG6Wtrc3Lly9LHfc1v//+O42NjfnLL7/QwcGBrVu3Zp8+fSiXy8vkBJtFHfMf\n/JPhxYsX/P3330mS6enprFatGu/cuVPsIJ+Sp6cn9+3bR/LPX/xDhw5lQEBAuR+gJeH58+dcvHgx\nW7duTTMzs/80L4uamhpNTU3p7e3NhQsXMiYmRuqySj2lUslBgwZx/PjxhY8dP3681B7KK43j/r8q\nS7Xk5eWxYsWKfPjwIePi4ti5c2caGBiwYcOGfPDggdTxCimVSg4ePJgymeydPyu+/PLLTz4NgdQi\nIyNpYWHxzu2iqqrKjRs3Sh31NSdOnKC1tTUDAgIKH9uyZQu9vLwkTPXfFHXMf/AhPDMzM9StWxcA\noK2tDUdHRzx//vxDX/ajys3NhZ6eHgBARUUFlStXhpaWVrmYQbWkpaSkYN68eahevTpUVFRgYWGB\nESNG4Pjx44iLi0N+fn6xX7OgoAAvX77EiRMnMGrUKFhbW0NFRQVVqlTBrFmzkJCQ8BEqKdtkMhk0\nNTULv28BQE9PD3l5eRKmEkqbzMxMyGQyODg4wNTUFMHBwWjevDmCgoJQpUoVqeMBABQKBb788kus\nWrXqrbM9q6mpYc+ePQgJCYGRkdEnTiitOnXqIDo6GpMnT37rMgqFAoGBgZg+ffonTPZurVq1gq+v\n72uHV6tXr474+HgJU31kJdm1velq5iW8ig8WHBzMBg0asEqVKgwNDWVwcDBNTU155swZqaOVGmlp\naZwyZUqRTm78WDddXV1OmDCh1H80+VO6cOECTUxMuGvXLm7atInm5uZs0KABd+zYIXW0fylt4/5D\nlJVaYmJi2KBBA2pra3Pq1KnMysriqVOnKJfL+eTJE6njkSQzMjJYtWrVd479WrVqiXH/f27dukUd\nHZ13bq9+/fqVmqMne/fuZdWqVXn37l0OGjSIampqVFdXZ+/evcvE/HV/KeqYL7GfDOnp6XRxcSk8\nNPb3INOmTSu8SdmobNiwgXZ2dly/fj07duxIQ0NDuru7l/oJ5T4FpVLJkJAQOjo6StY0ve1WtWpV\nHj16tNT8kJDSiRMn6O7uTm1tbc6cOZObNm1ilSpVJJ9648yZM6+N87LSdBRFWamladOmnDZtGqOi\norZkLHAAACAASURBVOjq6kpVVVVaW1uXmjl5Xr58STMzs3eO9cmTJ0sds9TJzs6mh4fHO7dby5Yt\nS80leRYtWkRtbW3WrVuXycnJzMzMZNu2bTlx4kSpoxXZJ22g3nU189L0w6du3boMCwsrvD9hwgSO\nGzdOwkTSUygU/Pnnn4s8J4mUt0qVKnHlypWf/cno06dPZ1BQUOH9ixcvsnr16hIm+rfSNO4/VFmo\nRalUUk1N7bW/8gcNGsTly5dLmOr/e/XqFY2Njd86tlVUVMRRgPeYMWPGO38+NmnShHl5eVLHJEl2\n69bttUuhhYSE0NPTU7pAxVTUMa+GD0QS/fr1g5OTE4KCgj705T4qhULx2kdFNTQ0kJGRIWEi6ZDE\n9u3bMXDgQGRmZv7n19HS0oKFhQWqVq0KBwcHWFtbw9jYGBUr/j/2zjusqev/4+8kzBBAIEwBcYEM\nxQEiLkCruItatTir1r2r1tqqqFVx19FqtbXuvdpaXF/5ilvUunGjqOBgieyR5PP7g5/5liYoArkn\nCff1PHme3hPqeZ3knpvPPfeczxEDAHJzc5GamoqkpCTEx8fj4cOHSEpKQm5u7kfXlZOTg9GjR2Py\n5MlYs2YNBg0aVCXnrf37PDYxMYFcLmdoxMOaV69ewdraGrGxsWjdujWKiopw9epVtG/fnrUaMjIy\n4OPjg5SUFLXvSyQS3LhxA7Vq1eLYTLeYOXMmmjZtio4dO6qdO3bu3Dl06NABJ06cYH5ddHJywsWL\nF9G3b19kZmZi48aNICLk5OTAzMyMqVulUtFI7UO7mVdCFZVCWloajRw5kjw9PSkqKoo2bNhAUqlU\nuYKwKnHlypWP3mMKABkZGVFgYCD99NNP9OLFiwp7vHr1itatW0ctWrT4qO0N3r2kUimdP3++Ej4R\n3SIuLo6kUimtW7eODh8+THXr1qUvvvhCq1YraUu/rwy0vS2xsbFkZ2dHAQEBJJFIKCwsjHx9fal7\n9+7MR2uzs7Pfu6mus7MzvXnzhqmjrnH9+vX3Xi/79u3LfLpDcnIyubu7U6tWrZSrQFu2bEleXl5a\ndZ0qjbL2+SqRifzmzZvk5OREQUFB5ODgQDVq1KCuXbvS2bNnWatxSnZ29kftMQWAzM3NacKECcpd\n3DXJy5cvaerUqWRpaflRjsHBwfT27VuN+2kTsbGx1K1bN3J1daUaNWpQmzZtyMHBQWsyNGtDv68s\ntL0tTZo0US4kuHfvHnl5edGECRNILpcz9crLy6P69euX2m/r1avH590rJ/fv3yexWFzqZzt69GjW\nipSZmUlt2rQpMfdpzJgxJaYfaCt8APUPWrRoQb/88gsRFc/XCgoKol9//ZWxFbccOnSozKM8AoGA\nunXrxnTlztOnT6lXr14fTLL37mVgYKC1SSU1xfbt26lZs2bKeS/btm2jxo0bM7YqRhv6fWWh7W2x\ns7MrcYMzY8YMioiIYCf0/3Ts2LHUPE/169fXmvk6ukp8fHypK/SEQiEtWbKEtSKFhITQsWPHlMe7\ndu2inj17MjQqG2Xt81ViK5fHjx8jNDQUAGBoaIg2bdrg8ePHjK24QaFQIDw8HF27dv1gziAjIyPM\nnj0bubm5+OOPP+Dm5saNpBpcXV2xZ88e5OXlITIy8r3bHADFuaV69+6N7t27QyaTcWTJlsePHyM4\nOFj52bRv377KnNc8xeTl5cHT0xPLly+HQqHAixcvsHv3bgQEBDD1mjFjBo4ePap2ro6npycuX74M\nQ0NDBmb6Q61atRAXF6ecb/pPFAoFpk+fjmPHjjEw+x8BAQFYs2YN8vPzkZqaiqVLl8LV1RUKhYKp\nV6Wh2ThOO+7eOnfuTDNmzCCFQkGpqalUv3592rdvH2stjZOYmEh2dnZlGr2JjIzUmmWw6pDJZPTD\nDz+UKfO5jY2N1uS90SRRUVHk7u5OycnJpFAoaN68edSmTRvWWkSkHf2+stDWtjx79ow8PDzIy8uL\nrKysyNTUlExNTSkyMpKp1/Hjx0vtmzVr1qxyj9s1zf3798nY2Fjt521iYkIJCQnM3PLy8qhXr15k\nYmJCZmZm5OHhQW5ubtSlSxcqKChg5vUhytrn9T6ASkhIoJ9++onc3d3J0dGRJBIJff3118wn2Wma\n6OhoMjAw+GCw8cUXX+jUPISCggIaMWLEB9slEono8OHDrHU1zqxZs0gikZCjoyO5ubnRypUrKT4+\nnrUW835fmWhrW7p3706zZ88mouJ91EJCQmjZsmVMneLj40v9MbexsaG0tDSmfvrKpUuXSr3eV69e\nnfligrCwMJo5cyYRFU+j6dChAy1fvpyp0/soa5/X60d4MTEx8PPzw8mTJ2Fqaop69erh8ePHWLRo\nEfNlnppk/fr1aNu27XsfZbm6uuLp06fYuHEjTExMOLSrGEZGRvj555/x4sUL1K5du9S/k8vl6NSp\nE1avXs2hHffMmTMHCQkJaNiwISwsLHD27FkEBATg+PHjrNV4NMz9+/fRvXt3AMUpWcLCwhAfH8/M\nJzc3F+3atUNBQYHKeyYmJoiNjYW1tTUDM/3H398fW7ZsgYGBamaipKQkDBkyhIHV/4iPj1eeq4aG\nhujSpQvu3bvH1Kky0OsAatSoUdi0aRP27t2LK1euQC6XM38mrGnmzJmDESNGfPBvEhIS4OrqypFV\n5ePo6IhHjx5h8eLF7w2Gx48fj2+++YZDM+45efIk0tLScOXKFezZswe7d+/+4DnAo/t4e3tjx44d\nICLk5eXh4MGD8Pb2ZuYzceJEJCQkqH3v1KlT773h4ak44eHhmDlzptrr4a5du7Bv3z4GVsV4e3tj\n586dICLk5+fjwIED8PHxYeZTaWh0HIzYDn+bm5tTenq68njy5Mm0cOFCZj6aZvLkyR9MSXDv3j3W\nmpVOfHz8B/ft04ZlvZpixYoVNGbMGOVxXl4eGRoaMn1MzbLfVzba2Jbz58/TF198QU5OTlSrVi2y\nt7envn37MntUExUVpXbFrEAgULtDBY9mUCgU1LVrV7XXQLFYzGxu6KtXr6hRo0ZUu3ZtqlatGnl6\netJXX31Fz549Y+LzIcra5/V6BKp58+ZYtGgRiAgJCQnYu3cvmjVrxlpLI0ybNg3Lli0r9f3GjRsj\nJSUFHh4eHFpxQ61atfD69Ws0b9681L9Zs2YNxo8fz6EVdzRr1gwHDx7Ew4cPQURYtGgRAgMD9fox\ndVXm5MmT+PTTT+Ht7Y3hw4cjPT0dGzZswLZt2yASiTj3ISL0799fZWWVUChEu3bttH6HCn1CIBDg\n999/h1QqVXkvNzcXw4YNY2AF2Nvb49KlS/jiiy9gYWGBMWPGQCgUIjAwEC9fvmTiVCloMoojYnv3\n9vLlS2revLlydYq27AtV2SxZsuS9oy/Dhg1jrcgZEydOfO9nMWfOHNaKGuGXX34hMzMzMjU1JT8/\nP3r+/DlTH5b9vrLRtrZ06tSJtm7dqjxesmQJDR06lImLQqGgfv36qe1rDg4OfJZxRty8eVPtpHKh\nUEgbNmxg5lW3bl26ePGi8nj48OFa+VSorH1eL0egiAhr167F+PHj0ahRI1y7dg2ZmZkYO3Ysa7VK\n5+DBg5g6dWqp7//www9Yv349h0Zs+VB7IyIisH37dg6NuOHLL7/E27dvcevWLQQGBuKrr77CqlWr\n9CffCo+SgoICWFlZKY+trKyQn5/PxOXOnTvYu3evSrmRkRH27t2LatWqMbDiqV+/PmbOnKkyqVyh\nUGD8+PFq83NxgTadu5WCRsM4YnP3Nn36dPLz86MdO3bQtGnTqEaNGnq5fPby5cvvHW3ZuHEja0Vm\n7N69+72fzZkzZ1grVjoZGRlUp04d+uqrr2jHjh0UGBjIbNsEFv1eU2hbW3777Tdyd3en6OhoioqK\nourVq9Nff/3FuUdubi7VqVOnSo306hIymYxatWqlVU8lpk+fTi1atKBz587Rjh07SCqV0s2bN5m4\nvI+y9nm9C6AUCgWZmZnRy5cvlWU9e/ZkOmypCZKTk9+bVHLz5s2sFZmzb9++Uj8fAwMDSkxMZK1Y\nqezcuZM6deqkPE5LSyMjIyMmCVK1LeioCNrUloKCAjp16hRNnjyZAgICqEWLFrR7924mLmvXrlWb\n88nBwYFyc3OZOPGU5Pbt22RqaqryHZmYmNCdO3c495HJZDR37lzy8/Ojli1b0tKlS+nvv//WuryM\nZe3zevkIT6FQwMjISHlsbGwMuVzO0KhyISL4+fmhqKhI7ftr167FwIEDObbSPnr27IlNmzapfU8m\nk8Hf31+vtn2Ry+Ultrx51weI0XC9LjBkyBDY29ujfv36rFU+yNu3b9GyZUtMmDABp0+fRnZ2Ng4c\nOIDevXtz7pKRkYG5c+eq5HwSCoU4c+YMTE1NOXfiUcXb2xurVq1SWVCSn5+PyZMnc35tEIlEmDlz\nJlavXo0HDx4gKioKPXr0wPDhw3XzOqXBII6I2Ny9jR49WrmJ4eLFi8nR0bHEiJSuM3r06FJHVt5l\ne+X5HwsXLiz18+rXrx9rvUojJSWFnJ2daf78+XT8+HEKDQ2lwYMHM3Fh0e/Lw+nTp+nq1avk4+NT\n6t9oS1umTJlCQ4YMIYVCQQqFgr766iv68ssvmbgMGjRIZZKySCQqMQLKox3k5+er3dJLLBbT9u3b\nmTh5eHjQgQMHiIgoJyeHGjRoQH/++ScTF3WUtc/r5QjUypUr0aZNGyxatAh///03YmJi4ODgwFqr\nUoiOjsaaNWvUvhcWFoa5c+dybKT9TJs2Df3791f73vbt23Ho0CGOjTSDVCrFqVOnEBcXh8jISAQE\nBODnn39mraXVtGrVqsSkVm3m3aboAoEAAoEAoaGhTDKPy2QyHDlyRGX01srKSi8XaOg6xsbGOHny\nJITCkj/3ubm52LVrFxOnx48fo0OHDgAAsViM1q1bM82iX14E/x9taa4CgUA3h+a0kNzcXNja2iI3\nN1flPTc3Nzx8+FBtKn+e4se6np6eePDggcp7xsbGSE5OhoWFBQMz/USX+n1CQgK6du2KW7duqX1f\nIBAgIiJCeRwcHIzg4GCO7P7HvHnzcPHiRezfvx8ikQgDBw6Ek5MTli5dyqnHoEGDsH379hLTIoyN\njTF58mTMnz+fUxeeshMQEIBLly6VKDMyMsIvv/zC+ZSPgIAA9O/fH+PGjcPLly/RokUL/Pbbb0z6\nFVC87VtMTIzyeM6cOWW7fmluEKwYDqpQkp2dTWPGjKFGjRpRp06dKC4ujrO6uaBnz55qH0MZGhpS\nUlISaz2tJzU1tdSNTkNDQ7VuImNFuH//PnXt2pUaNmxII0aMoMzMTE7r57LfV5QnT57oxCO8goIC\n6tmzJ1lbW5OtrS2FhoZSdnY2pw75+fkkEolU+k/t2rUpJyeHUxeej+P+/ftkYmKi8t15enpy7vLg\nwQOqW7cuubi4kEQiocjISM4d3kdZ+7xePcIbOHAgUlNTsW7dOnTq1Alt27bF69evWWtVCrGxsThw\n4IBKuUAgwJ49e+Dk5MTASrewsbEp9XHd8ePHcfLkSY6NNEN6ejratm2LkJAQ/PLLL8jLy0OfPn1Y\na/FUkHe5lW7fvo2rV6/iyJEjMDMz49Th7NmzKgtyTE1N8f3330MsFnPqwvNxuLu7Izw8XKX8yZMn\neP78OacudevWxZ07d3Dq1Ck8f/5cd/cr1XAgx9ndW15eHhkbG1N+fr6yrEePHrRjxw5O6tck+fn5\n5OTkpPeToLlixIgRaj9LqVSqF3fRBw4coA4dOiiPi4qKSCKRUEZGBmcOXPX7ykAXRqD27t1LTZo0\nIW9vb/r+++9JLpdz7pCYmEgSiUSl39jZ2fEZx3WEK1euqIxCCYVCqlu3LpMR+Ldv39LgwYPJw8OD\nQkJC6Pr165w7qKOsfV5vRqDe7QGVmZkJoHjpdnp6eoll3brK9u3b8eLFC5Vyc3NzrFu3joGRbrNy\n5Uq1GZJTU1OxYcMGBkaVi4mJCTIyMpTP8LOysiCTyWBoaMjYTPsIDw9H8+bN8eDBA7i4uGDjxo2s\nlVSIjo7G+PHjERkZic2bN+PQoUNYtGgR5x4XL15UmYgsFArxn//8h884riM0adIEERERJfZMVCgU\nePbsGVJSUjj3eTcitn//fvTr1w+hoaF49eoV5x7lRqNhHHF79zZ9+nRq2LAhrVmzhgYNGkS+vr46\nP6KQlpZGYrFY5a5PIBDQkSNHWOvpLGfOnFE7CmViYkKvXr1irVch8vPzqWnTptS3b19as2YN+fv7\nc56RnMt+r2lYt2X06NG0fPly5fH58+epcePGnHt88803JBAIVOZf/nPUn0f7OXXqlNqRxNOnT3Pq\nkZOTQyYmJiUS/Xbv3p127drFqYc6ytrn9WYECgDmz5+PiRMn4tq1a3Bzc8OpU6d0/rn8li1b1K66\na9WqFUJDQxkY6QctW7ZEx44dVcrz8/Px66+/MjCqPIyNjREdHQ0PDw9cu3YNI0aMwPLly1lr8ZQT\nsVhc4q789evXnF/Xjhw5gpUrV5ZYmWRoaIgFCxboxSh/VaJly5Zo3bq1ymhip06dkJiYyJmHoaEh\niAhpaWkAip8asTi3KwKfxkCLef36NWrVqqUSQIlEIjx79oyfOF5B0tPTYWdnpzIp1sTEBA8fPoSz\nszMjM91Hn/o967YkJCQgMDAQffv2hY2NDVauXIlNmzapvQHQFAMHDsTWrVtLlDk7O3M++ZincsjN\nzYW5uXmJzcYlEgnWrl1bas48TRAREYH9+/dj8ODBuHjxIp4/f45Tp04xD8rL2uf1agRK3zhy5IjK\nVgkAMHbsWD54qgSsra3Vrv4oKirCH3/8wcCIh0cVNzc3XLx4EaampkhPT8fvv//OafAEFK8A/Pd2\nIPb29pw68FQexsbGJeZBAcUJUv+5BRoXzJ49G7NmzcKzZ8/g7++P6Oho5sHTx8CPQGkpGRkZqFmz\nJjIyMkqUGxgYIDk5WWeyJ2s7ubm5sLS0VMmqbG5ujsePH0MqlTIy0230qd/rU1vKw7Vr1xAUFISs\nrCxlmampKaKiohASEsLQjKcizJs3D/Pnz0d+fj6A4gUBtWrVwuXLl6v8ooAqNQKVn5+P7777Du3b\nt8eXX36pW7P4S+HixYsoLCxUKf/222/54KkSEYvFWLhwoUq5XC7H2bNnGRhVLikpKRg5ciTat2+P\nadOmqZ1Px8PzPgYOHFgieDIwMMCkSZP44EnHmTFjBho2bKgcWXy3Gm/OnDmMzXQHvQigBgwYgNu3\nb2PSpEmwsbFBUFAQsrOzWWuVGyLCihUrVH7sDAwMMGHCBEZW+suoUaNUhrNzc3OxfPlynR55yMvL\nQ5s2bWBqaopJkybhyZMn6N27t063qaohk8lw4sQJHDhwgNmNYVJSkorTv+cN8ugmOTk5Ja4HhYWF\nare74oJ79+5h7969+Pvvv5nUXx50PoDKyMjA0aNHsWfPHnTs2BGLFi2Co6MjTp8+zVqt3MTGxuLM\nmTMq5QMHDoS1tTUDI/1GLBZj9OjRKuVXr14tsT+SrnHx4kWIxWIsX74cHTt2xPbt23Hx4kW8fPmS\ntRpPGSgsLETnzp0xdepUbNy4Eb6+vkx+XPz8/ErssWlmZoZmzZpx7sFT+bRq1QomJibKY1NTUyb7\n0W3atAlBQUHYuXMnunfvjlmzZnHuUB50PoB696zy3WoCIoJMJlOZ8KhLPHv2rMTqCKB4yee8efMY\nGek/c+fOVTupMiEhgY1QJSAQCEqMFCgUCigUCpXlyzzaycaNG0FEuHLlCg4dOoRly5ZhzJgxnDr8\n/fffuHHjhnKOoEgkwvjx4xEWFsapB49mWLJkCVq2bKm8JuTn52Pv3r2cJtXMzs7GhAkTcObMGRw4\ncADXrl3Dr7/+iri4OM4cyovOX0ktLS0RFhaG7t27Y9++fRg/fjwyMjIQFBTEWq1cFBUVlZjY9w47\nOzt+1YsGsbS0hKura4mygoICLFq0SO1KSF0gMDAQCoUCI0eOxP79+9GrVy+EhITw55GO8OzZM7Ro\n0UIZ2Ldu3ZrTtAF5eXlo164dkpOTlWWmpqaYMmUKZw48mkUsFmPGjBnKlW9EhOvXr6N3796cOSQn\nJ6NatWpwd3cHULxnqZeXF6c5qcqLzgdQQPGdWuvWrbFt2zYIhUKdTqAZHR2Nx48fq5QfPnyYHznQ\nIAKBAEePHlUpT0pKwuHDhxkYVZx3CTXNzMywdetW+Pn5YceOHTo9OluVCAgIwM6dO/Hq1SsoFAqs\nXLkSTZs25az+x48fq6xOFYlEOjEywFN2zp07V2LBUlFREWJjYzmr39nZGXK5HPv37wdQPIXlxo0b\n8PHx4cyhvBh8+E+0H0NDQ3z77besNSqF7OxslR84Q0ND1KhRg5FR1cHV1RUikajEYy8i0ukFCVZW\nVnwWch2lW7duuHHjBmrVqgVDQ0PUr18fBw4c4Kx+W1tblZXAhYWFcHBw4MyBR/M4OjrC2Ni4xKIl\nLtO3GBkZ4ffff0ePHj0wbNgwAMDmzZtRvXp1zhzKCz+koWUkJCSUWDJsaGiIhg0bwtLSkqFV1cDE\nxAQtWrQoseluTk6O2hFBHh4umDlzJtLT0/HkyROcOXMGdnZ2nNVtZ2eHiIgIiMVimJmZwczMDGPG\njEHdunU5c+DRPP369UODBg0gkUggkUggFouxadMmTh38/PyQkJCAe/fuITk5GV27duW0/vLCJ9LU\nIm7evInAwMASdwImJiZITEyEjY0NQ7OqQ0ZGBpydnZGTk6MsE4vFiImJgb+/P0Mz3UKf+r0+teVj\nkMvlOHHiBC5dugRjY2M0b94cLVu2ZK3FowFkMhmioqJw/fp1mJubo3Xr1vDz82OtxYyy9nm9eISn\nL1y/fl1lnpNMJiuxzJRHs0gkErXJJq9du8YHUDxVBrlcjtDQUMTGxipXcx46dIi1Fo+GMDAwQFxc\nHBYvXgyhUAiFQoGvv/4aERERrNW0Gv4RnhZRo0YNlajX1NRUZyfE6yIGBgYqmd6FQiE/B42nSrFn\nzx5cvHgR2dnZyMrKQm5uLgYMGMBai0dDvHjxAt9//z1yc3ORnZ2N3NxcLFy4EM+ePWOtptXwAZQW\n0ahRI3h5ecHAwABisRhisRi7du3iV01xzO7du2FmZgaxWAwDAwPUqlWL09VPPDysSUpKQlFRUYmy\n1NRURjY8mubly5cqGwkbGxvzSXc/AB9AaQl5eXnw9/fHzZs3IZPJIJPJMGrUKHTq1Im1WpXjk08+\nwVdffQW5XA6ZTIZ79+6hSZMmOr0aj4fnY2jWrFmJ7OMikQiNGjViaMSjSd7lYPonCoUCHh4eDGx0\nBz6A0hIOHTqEFy9eKJM2FhYWYvXq1SoZyXk0DxFh2bJlJb6L5ORkZZ4SHh59p2XLlli8eDGMjIxg\nYGAAT09PTlMo8HCLubk5jhw5AmtraxgaGsLKygpRUVGoVq0aazWthp9EriXk5uaqzH+Sy+WQy+V8\nAk0G/Dv/jUKhUDu5nIdHXxkzZgxGjBiBvLw8mJubs9bh0TDNmzdHamoqMjMzYWFhwU8dKQP8L7OW\n0LZt2xInrLGxMT755JMSOYl4uEEgEKBLly4lVj8KhUK0b9+eoRUPD/cYGBjwwVMVQiAQwNLSkg+e\nyggfQGkJLi4uiImJQePGjeHk5IRevXph3759rLWqLNu3b0d4eDiqV6+Ohg0b4sSJE6hduzZrLR4e\nHh4eLYFPpMnDw1Pp6FO/16e28PDwfJiy9nl+BIqHh4eHh4eH5yPhAygeHh4eHh4eno+ED6B4eHh4\neHh4eD4SPoDi4eHh4eHh4flIKhxAHT16FPXq1UPdunWxaNGiynD6KNavX4++ffsiMjJSp5NOFhYW\nYtq0aejXrx8OHjzIWofn//nrr78wYMAATJ06VefzQC1btgx9+/bFjz/+yFpFq2B9DVNHfn4+pk6d\nin79+jHZxDcuLg5ffvklhg0bhvj4eM7r52HHf/7zHwwYMACTJk1CZmYm5/WvWLECffv2xcqVKzmv\n+6OhCiCTyah27dr05MkTKiwsJF9fX7pz506Jv6lgFe/l008/JalUSgMHDiRXV1dq0qSJxurSJHl5\neVStWjUCoHxNmTKFtVaVZ+bMmSW+E4lEQjk5Oay1ykVgYCBVr16dBg4cSPb29tS+fXuN1qfJfl+Z\nsL6GqSMnJ4ecnJzI19eX+vfvTxKJhL777jvO6o+OjiaBQKA87wUCAV2+fJmz+nnYsXjx4hLXPBMT\nE3rz5g1n9bdu3ZocHR1p4MCB5OjoSCEhIZzV/U/K2ucrdGU4f/48hYaGKo8jIyMpMjKyXCIfy+PH\nj8nY2JgSExOJiCgzM5NsbGxo//79GqlPk0yZMqXESfvuxcOWf/6IvHuNHDmStdZHc/z4cbKwsKD0\n9HQiInr16hWZmprSjRs3NFanrpy/LK9hpTF27Fjy8/MjmUxGRERnz54liUTCWf2Ojo4q532dOnU4\nq5+HHQYGBirffXh4OCd1vzvPU1NTiYgoJSWFzMzM6OLFi5zU/0/K2ucrtJVLUlISXFxclMfOzs6I\njY1V+bvZs2cr/zs4OBjBwcEVqRYA8PjxY1haWqJ69eoAivfyqVmzJh49elThf5trnj9/rrZcJpOV\n2NCTh1tITR6QpKQkBiYV49GjR3BxcYGVlRUAwN7eHra2tnj06BEaNGhQKXXExMQgJiamUv4tLmF5\nDSuNxMRENG7cGCKRCADQqFEj5OXlaay+f6PusU16ejpn9fOwQyaTqZS9ePGCk7ofPXoER0dH2NjY\nAACkUikcHBzw8OFDBAQEaLTucl+/KhKl7du3j7788kvl8datW2ns2LHliuQ+lqysLJJIJLR+/XqS\nyWQUFRVFYrFYZfhdF9i9e7dK1G9mZsZaq8pjaWmp8r389ttvrLU+moSEBBKLxXTgwAGSyWS0ZcsW\nMjMzo7S0NI3Vqal+X9mwvIaVxtatW8nS0pKuX79OhYWFNHHiRKpevTpn9QcFBamc92FhYZzV3sXm\nHgAAIABJREFUz8MOW1tble/+hx9+4KTupKQkEovFtGfPHpLJZLRr1y4yMzOjly9fclL/Pylrn6/Q\nleHChQslhr8XLFhACxcuLJdIefjzzz/JysqKBAIBSSQSWr16tcbq0jTjx49XnrBisZiuXbvGWqnK\nc+fOHZJIJMrvZdiwYayVys2GDRvI3NycBAIBWVpa0u7duzVan64EUKyvYaUxevRoMjExIaFQSE5O\nTnT79m3O6s7Ly6M6deooz/v69etTUVERZ/XzsOPx48cl5uN+/vnnnNa/efNmsrS0VF6ntm3bxmn9\n7yhrn6/QVi4ymQweHh6Ijo6Gk5MTmjZtip07d8LT01P5N1xsg1BYWAgjIyON1sEV+tQWfaGwsBAG\nBgYQCnU/6wdX55eubH+iLdcwdSgUCshkMmbXg3ePc/hpBFUP1tc81r+DZe3zFeoZBgYG+PHHHxEa\nGgq5XI6hQ4eWuPBwhT4FHPrUFn1Bn74TfWpLZaAt1zB1CIVCpt8XHzhVXVhfJ1jXX1b4zYR5eHgq\nHX3q9/rUFh4eng/DbybMw8PDw8PDw6Mh+ACKh4eHh4eHh+cj4QMoLeP+/fs4deoU0tLSWKtUed68\neYNTp07hzp07rFV4eHh4eLQMPoDSIiZOnIhGjRrh008/Rc2aNXH27FnWSlWWS5cuwc3NDZ9++in8\n/PwwfPhwfh4MDw8PD48SfhK5lnDq1Cl07twZOTk5yjJbW1skJycztKq6uLi4IDExUXlsZmaGvXv3\nomPHjgytdAd96vf61BYeHp4Pw08i1zEePnyo8oWlpqaisLCQkVHVhYhUti+QyWR4+PAhIyMeHu7J\nz8/Hpk2bsGzZMly9epW1Do+GISJERUVhyZIlOHToEH/TUAb4RB9ago+Pj0pZ9erVdSYfhj4hEAhQ\nq1YtxMfHKy8iBgYGqF+/PmMzHh5uyM/PR0BAAOLj41FYWAhDQ0Ns2rQJvXr1Yq3GoyHGjRuHTZs2\noaCgAMbGxujXrx/WrVvHWkur4UegtIRmzZrhu+++g5GREQwMDGBgYIAuXbqo3dyRR7PI5XJ07txZ\n+T0YGRlh0qRJCAkJYa3Gw8MJu3btQnx8PHJyclBUVITc3FyMHj2atRaPhnj69Ck2bNiAnJwcyGQy\n5OTkYOvWrYiPj2etptXwAZQWMWbMGFSrVg1EBJlMhi1btmDw4MGstaoco0aNwi+//IKioiIoFApI\nJBJMnDiRtRYPD2ekp6ejqKioRFlmZiYjGx5Nk56ervK0w9DQkF8N/gH4AEqLOH78OPLy8iCXywEA\nubm52LlzJz8PikMUCgU2btyI3Nxc5XFBQQGioqIYm/HwcEdISAhEIpHy2MjICMHBweyEeDSKh4cH\njI2NIRAIlGWGhobw8vJiaKX98AGUFqFu0h4/kY97+O+Bp6rTqFEjbN26Fba2tjA2NkZISAh2797N\nWotHQ4jFYsTExMDDwwNGRkZwd3fHyZMnIZFIWKtpNXwApUW0b98eZmZmJe4CBAIBTpw4wdCqanHy\n5EmVz9/U1BSdO3dmaMXDwz09e/bEvXv30LNnTzx9+hRDhw7Fq1evWGvxaIArV65g5MiREAqF+Prr\nrxEXF8cvmikDfB4oLSMqKgqffvqp8jEeUJyD6O3btyWG1HkqHyKCtbU1MjIylGUikQg7d+7kVx99\nJPrU71m2JTMzE1u3bkVmZiY6dOiARo0acVa3XC5H48aNce/ePRQWFsLAwAAuLi64c+cOTExMOPPg\n0SyPHj1Cw4YNlTkIxWIxhgwZgtWrV3PqERUVhWvXrqFWrVr4/PPPIRSyG9+pcnmgFAoFXr9+rfPz\nhbKysiAWi0uUFRQUlPhR59EMeXl5KhNlTUxMkJ2dzciocigqKsLr169LBOU82s/bt2/RrFkzxMTE\nIC0tDaGhoZzOxYuPj1emMQCKc6Glpqbi+vXrnDnwaJ6DBw+W+N3Mzc3F5s2bOXWYNWsWJk+ejJyc\nHKxevRr9+/fXiRswvQigbty4gdq1a8Pb2xt2dnbYu3cva6VyU79+fZXVLzKZjPMTuiqyZcsWlU5L\nRPD19WVkVHH+/PNP2Nvbw9vbG25ubrh8+TJrJZ4ysmHDBjRs2BB79+7F0qVLsW3bNnzzzTec1W9o\naAiFQlGijIj43HR6hqGhocpoj4EBdyki37x5gxUrVuDMmTOIjIxETEwMLl26hCtXrnDmUF50PoBS\nKBQICwvDvHnzkJqaipiYGIwZM0Zn81d4e3tj7NixKuXffPMN8vLyGBhVDWQyGSZMmKASQA0aNAiN\nGzdmZFUxnj9/jqFDh+LYsWNITU3FihUr0L17d50fpa0qvHnzBnXq1FEe161bl9ORaDc3NwQFBcHU\n1BRA8eNsGxsb1KhRgzMHHs0TEBAAkUiknPspFovx7bffclb/27dvYWFhAalUCgAwNjaGq6urTjx1\n0fkAKjk5GdnZ2ejXrx8AoGHDhggMDMSNGzcYm5WfFi1awNzcvESZTCbDrVu3GBnpP+/mefwTiUSC\nVq1aMTKqOLdv30ajRo3g7+8PoHhSsFAoRFJSEmMznrIQGhqKX3/9FRcuXMDLly8xZcoUTvdiFAgE\n+OOPP9CrVy+IRCLlNIlGjRrpxI8bz4e5evUq2rVrh4KCAgDFo1GRkZGYMmUKZw4uLi6oVq0aFi5c\niJSUFGzbtg13797ViRtXnQ+grK2tUVhYiJs3bwIAMjIycP36dbi6ujI2Kz/+/v4q81WICL169eLn\nsWgAIkL37t1VyuVyOZo1a8bAqHJwcXHB7du3lcnw7t27h7dv38LOzo6xGU9ZaNmyJZYtW4b+/fuj\nQYMGqFatGlasWMGpg5GREU6fPg25XA4iQn5+PpKTk7FhwwZOPXg0w9SpU5GTk6P8fuVyOeeDDyKR\nCFFRUThx4gTc3d2xYsUKREVFwcbGhlOP8qDze+EZGRlh/fr1+OSTT9C8eXNcv34dvXv3hp+fH2u1\nclO9enXMnDkT3377bYlHSklJSbh7967affN4yk9CQgIeP35cokwgEGDKlCmoWbMmI6uK4+Pjgy+/\n/BINGzZEkyZNcP78eaxatQpmZmas1XjKSHh4OMLDw5k6/HthRUFBAdLT0xnZ8FQm//4eFQoFUlNT\nOfeoUaMGoqOjOa+3ouj8CBQA9OnTB+fPn0f//v2xd+9eLFmyhLVShWnTpo1y7sE75HI5BgwYoDKx\nk6f8EBH69++v8pmKxWK0bduWkVXlMXfuXPzxxx/o378/zpw5g0GDBrFW4tExunbtqpK24Pbt2yqL\nXXh0i+TkZJVHsWKxmE/Z8hHweaC0FCJCSEgITp06VaJcJBLh8uXLnOaD0WcePHgAT09PlQCqadOm\nuHjxYomkmjxlR5/6vT61pTzk5eWhQ4cOOH36tLLM1NQUY8aM0Yub1aqKv78/rl27VmJayDfffIPI\nyEiGVtpBlcsDpW8IBALMnz8fxsbGJcrlcjnCw8P5uVCVgEKhQK9evVSCJxMTE8yfP58Pnni0hh9+\n+AG2trYwNzfHsGHDlJN+ucDU1BTOzs4lyvLy8vD7779z5sBTueTl5akETxKJBJ6enpx6JCUloW3b\ntjA1NUXt2rV1btcNvQyg9CW4CAgIULtk+MGDB/zmtpXAyZMn1a5sdHBwQOvWrRkYVT760heqMvv3\n78fatWtx7tw5PHnyBC9evMCMGTM4dbC3t1fJDZSWlsbPhdJRHj58qHYqiJWVFacePXv2RPPmzZGS\nkoJ169YhPDwcT5484dShQpCG4aAKJU+fPqXAwEASiUTk4OBAf/75J2d1a4qzZ8+SgYEBASjxMjc3\np+zsbNZ6Okt+fj5Vq1ZN5XM1MDCgY8eOsdarMEePHqXq1auTUCgkf39/io+P57R+Lvu9pmHdlpEj\nR9KqVauUx5cvXyZfX19OHV68eEFSqVSlr/j7+5NCoeDUhadipKSkqFz7hEIhNW/enIqKijjzyMrK\nIlNT0xLnT+/evWn79u2cOZRGWfu8Xo1AffbZZ+jUqRPy8/Nx4MABDBkyBA8ePGCtVSECAwPh5eWl\nUp6VlYXp06czMNIP5syZozaXTe3atdGmTRsGRpVHQkIC+vfvj+3bt6OgoAB9+vRBt27dqvQ8Hl3G\nxsYGd+7cUR7fuXOH8yXejo6OWLJkSYkpBTKZDNevX8ebN284deGpGOfPn1cZmRYIBNi3bx+nGchN\nTU0hFAqVSa9lMhnu37+vE+kLlGg2juPu7i07O5uMjY1LRLPh4eG0efNmTurXJHfu3CGRSKQyWiIU\nCunvv/9mradz3LlzhwQCgcrnKRKJ9OLz3LNnD4WFhSmPFQoFWVpaUkpKCmcOXPV7LmDdlpSUFKpT\npw717NmThg8fTlKplGJjYzn3OH78OEkkEpV+s3LlSs5deMqHXC6nTz75RO3IO4snGj///DNVr16d\nxo0bR4GBgdStWzeSy+Wce/ybsvZ5vRmBMjU1hbGxMe7evQsAKCwsRFxcHOzt7RmbVRxPT0/07t1b\npVyhUCA0NBT5+fkMrHSToqIitG3bVu1oTKdOnXQi++2HsLe3x927d5XnRXx8PGQyGSwsLBibaRd7\n9+6Ft7c3RCIRrl69ylqnVKRSKS5fvozQ0FD4+Pjg4sWLaNq0KecewcHB8PDwUCmfPn26MpExj3az\nbt06nDt3rkSZSCTC2LFjmeSHGzFiBPbu3Qs3NzdMmDABBw4cUNmXT5vRqzQGW7duxdSpU9G1a1dc\nvXoVtWrVwu7du3XqCymNzMxM2Nvbqw2W+vfvj61btzKw0j1GjRqFn3/+WaXcyMgISUlJyv2YdBki\nwsCBA3Hr1i34+/sjKioKc+bMwbBhwzhz0IWl//fu3YNQKMSIESOwbNmyUoNnbWpLfHw8tm7dqlyN\nq+7xviZJSUmBg4NDiQnIIpEIs2bNwqxZszh14fl4WrdujTNnzpQos7W1xevXrzlfdXz8+HFER0dD\nKpVixIgRWnWDVyXTGAwYMABHjhxBkyZNEBERoTfBEwBYWFhg06ZNat/btm0btm3bxq2QDnLw4EG1\nwRMArFmzRi+CJ6C482/ZsgXz5s1DkyZN8Oeff3IaPOkK9erVg7u7O2uNMnP37l0EBgYiOzsbMpkM\nQUFBnO9YL5VKVUYq5HI5IiMjtXoUjwdYu3YtLly4UKJMKBTC19eX8+Bp3bp1GDZsGCwsLHD16lW0\natUKOTk5nDpUBno1AvVPCgsL8fTpU9jY2MDa2prz+jUBESEoKEjlDgIovgu8du0a6tevz8BM+3n4\n8CE8PT3VLuv38/NDbGys3gTbb968QWpqKmrUqAEjIyMmDto0avMhQkJCPjgCFRERoTwODg5GcHAw\nR3b/Y+jQoXB3d8e0adMAFP8IHT9+HPv37+fU4+jRo+jcubPKMvhu3brhjz/+4NSFp+zY2dkhJSWl\nRJmZmRlu3brF+ZZVdnZ2iImJgZeXF4gIXbp0Qa9evfDFF19w6vGOmJgYxMTEKI/nzJlTpuuXzu+F\np467d++ic+fOICKkpaXhu+++U150dBmBQIDDhw9DKpWqJNKTy+UIDAzEs2fP9CZgrCyysrLUbtAM\nFO8+fuzYMb0JnlatWoUZM2ZAKpVCLpfj0KFDaNCgAWstZrRr1w6vXr1SKV+wYAG6du1a5n9n9uzZ\nlWhVPrKzs0sktHR2dkZWVhbnHh06dICXlxdu375dojwqKgr//e9/dX4Vqz4SGRmpEjwBwOjRo5ns\n9/nPc1kgEMDZ2RnZ2dmce7zj3zdFc+bMKdv/WMmT11XgoAoVfH19ad26dURElJSURDVq1KDTp09z\n7qEpTp48qbKK4t2revXqVFBQwFpRaygqKqKaNWuW+nn99ddfrBUrjcuXL1P16tXp2bNnRES0efNm\n8vDwYOLCot+Xl+Dg4PeuvtSWtuzYsYPq1q1LsbGxdPXqVWrQoAGtWbOGicumTZvIyMhIpT85Ojoy\n8eEpneTkZDI0NFT5rkxNTen27dtMnMLDw6lPnz708OFDOnjwIEmlUrp37x4TF3WUtc/rx233P1Ao\nFLh16xYGDx4MAHByckKHDh1w48YNxmaVR3BwcKkTNpOSktC4cWN+w2EUnwsBAQGlZradNGkSOnfu\nzLGV5rh58ybatm0LFxcXAMVzAuPj4/lVmmWAdOBxY3h4OCZNmoRBgwahd+/eaNOmDVq1asWkrw8a\nNEht33n58iVWrlzJuQ+PehQKBfr27auy8bNIJMKyZcvg7e3NuVNeXh7GjBkDoHiEeP78+di3b5/a\nFZ5aj2bjODZ3b7Vr11ZmIc/KyiIvLy86cuQI5x6aJjAwsNSRlYYNG2pFPg1WyOXyD34++pZBOSYm\nhurUqUMZGRlERPSf//yHnJycmLSTRb//WA4cOEDOzs5kYmJC9vb21KFDB7V/p21tSU9Pp4CAAKpT\npw7VqFGD2rdvT7m5uZx7nDx5kkxNTVX6lqGhIT19+pRzHx5VNm/erHak0NzcnFJTUzn3efToEdWu\nXZt8fHzI3t6ehg4dqpW/U2Xt83oZQJ07d47s7OwoKCiInJ2dafTo0Xr3Y0lEVFBQQPb29qUGCd7e\n3iSTyVhrco5MJqMmTZqU+rlYW1tTXl4ea02NMHnyZHJycqLg4GCytbWlkydPMvHQtqCjImhbW0aM\nGEEjR44khUJBRUVF1LNnT4qIiGDiMnXqVLV9zMfHh59KwJinT5+qTXwKgNmUljZt2tDSpUuJqDj5\ntb+/P23bto2Jy/soa5/X21V4qampuHHjBlJTU/H8+XNYW1sjPDwcpqamnLtoktTUVLi6uiIvL0/t\n+y4uLrhz5w4kEgnHZmzIy8uDj48PHj9+rPZ9Y2NjJCQkwMHBgWMzzVJQUIBdu3YhJSUFzs7OkEql\naNCgAezs7Jj46NIqvA+hbW0JCgpCRESEcrL2zp07cfDgQezZs4dzlzdv3sDFxUVlCbqBgQG++eYb\nfP/995w78RTTokULnD9/XqXc19cX169fZ2BUPKUmNjZWOc1g7ty5KCgowPz585n4lEaVzAP1T6RS\nKTIzMzF+/Hg8f/4ce/fuRXBwcKmBhq4ilUpx586dUvcwev78ORwdHUsNKPSJD7XVwMAAt27d0svg\nqV27dti2bRsSExMxceJEpKSkMAueeDSLp6cn9u3bByKCTCbDgQMHOE+o+Q4rKyv8/vvvKuUymQyL\nFi3CqVOnGFjxLFy4UCXnEwCYmJjg4MGDDIyKeXfuAkBOTg6ioqKYnbuVgqaGwN7BQRWlUrNmTTpz\n5gwRFe8H1rFjR/r111+Z+WiSBw8ekIGBQamPrQQCAR06dIi1psY4fvy42v0C372EQiHFxcWx1tQI\n27Zto5CQEOVj6itXrpCDgwNTJ5b9vrLRtrakpaWRv78/ubu7k4ODA9WsWZMmT55MT548YeYUEhKi\ndn9JKysrSk9PZ+ZVFbl9+7ba78LQ0JDmz5/PzOv06dM0cOBAsrOzI29vb3JwcKAhQ4bo9BwovR2B\nAoD09HR4enoCKB6Sq1evHtLS0hhbaYa6devi7t27pSZOJCJ07doVffv2VZsPSVdRKBQYOnQo2rdv\nX2q7RCIR4uLidPtO5z2kp6ejXr16ymzCnp6eSE9P16rHTjyVh7W1Nc6fP4/Ro0eDiDBq1CgIhUIE\nBgYiISGBidPu3btRrVo1lfI3b97weaE4JDU1Fc2aNVPb9/39/ZnlQ/zrr7/Qq1cv+Pj4oH///nj5\n8iW2b9+OX3/9Vbdz8GkwiCMitndvvXr1osGDB1N6ejpduHCB7O3t6fLly8x8uOD58+dkZmZW6kgM\nALKxsdGqnBvl5fHjx2RnZ/fetpqamjK9M+eCmzdvkq2tLZ0+fZrevHlDo0aNoi5dujB1YtnvKxtt\nbUtAQABFRUUpj6dMmULffPMNM58///xT7YovADR+/HhmXlWF/Px88vT0VPv5i8ViSkhIYObWvHlz\n5cp4IqJvvvmGpkyZwsznQ5S1z+tw6PdhfvnlF2RlZcHV1RVhYWFo0aIFoqOj9XYUCijOTpyUlFQi\nY/G/SUtLQ7169TBo0CAUFhZyaFc5FBUVYeTIkahVqxaSk5NL/Tt7e3skJibCzc2NOzmOycjIwNGj\nRxEUFITw8HC4uLggKSkJmzdvZq3Go2Hy8vJK7N9oa2vLdI5n165dMXr0aLXvrV69Gj/88APHRlUH\nhUKBHj164O7du2rf/+OPP1CjRg2Orf7Hv89VqVSqH/ORNRzIacXd2759+8jBwYEiIiLoiy++oNq1\nazPJgcElhYWF1K5du/eOzgAgIyMj2rx5s06keVAoFLRr1y4yMTH5YLtatWql98uoMzIyqF69etS/\nf3+aM2cOOTk5ac2SYG3o95WFtrZl/vz55O/vT7GxsbRixQqSSCQ0adIkyszMZOZUUFBAPj4+avuk\nSCSinTt3MnPTZ4YNG0ZCoVDt3NexY8cydXv8+DF17tyZGjRoQBcvXqSoqChycHBglmKlLJS1z1eJ\nAMrLy6vElzVw4EBavHgxOyEOWbBgwQeDDfz/ZM+DBw9qZSClUCjo8OHDJJVKy9SWWbNmsVbmhNWr\nV1OvXr2UxxcvXiQ3NzeGRv9DG/p9ZaGtbZHL5bRgwQJyc3MjCwsLmjRpEnXv3p18fHyYBlHZ2dml\n5h8SiUTKhT08lcPSpUvVThoHQE2aNGF6TX83vWDkyJEUEBBAVlZW1LhxYzp48CAzp7LAB1D/wMXF\nhR49eqQ8njFjRpX5kSUq3iPN3Ny8TMGHRCKhVatWacXoTWFhIf38889kaWlZJnexWEznz59nrc0Z\nCxYsoK+++kp5nJSURFKplKHR/9CGfl9ZaHtbPD096cSJE8rjzz77jFauXMnQiOjvv/8udVWsSCSi\n2NhYpn76wo8//ljq9dDW1pZSUlKY+v37XIyIiKBhw4YxNCobZe3zej0H6h2ffvopxo0bh4cPH+Lo\n0aNYs2YNmjZtylqLM/z8/JCeno7PP//8g3+bnZ2N8ePHw8TEBF26dEFcXBwHhiW5f/8+wsLCYGJi\ngpEjR+Lt27cf/H/CwsLw5s0bBAYGcmCoHTRt2hRbtmzBkSNH8OjRI4wZMwaffvopay0ejnnz5g3c\n3d2Vx+7u7sjIyGBoBDRu3Bh79+6FSCRSeU8ul6N58+Y4d+4cAzP9Yf78+Rg7dqza90xMTBAbG1ti\n3hEL3rx5g7p16yqPteHcrFQ0HMhpxd1bfn4+jRs3jlxcXMja2pocHR2pWrVqNHz4cK3MQaFJrly5\nQra2tmUa0Xn3MjIyoi5dutB//vMfjWwNI5PJ6OTJkxQWFkbGxsYf5WZtbU3nzp2rdCdtRqFQ0Pjx\n48nS0pKkUinZ2NiQi4sLjRw5ksmeaOrQhn5fWWh7WwYPHky9e/emZ8+e0ZAhQ8jGxoZCQkLo9u3b\nrNVo0aJFaufm4P9HorT9UY62Mnny5FIf2xkYGNCFCxdYK9Iff/xB9erVI19fX4qPj6e7d++Sj48P\nbdiwgbXaBylrn68SAdQ7evXqRVOmTCGFQkGZmZnUrFkznfgyKxuFQkE//fTTexNvvu9laWlJ7du3\np9WrV1NcXNxHBaFyuZzu3btHa9asoY4dO1K1atXK5WBgYEDLli3TyjlbmmbHjh3UuHFjysjIIIVC\nQTNnzmSetuDfaFO/ryja3pbs7GwaNGgQWVhYUMuWLenkyZO0cuVKsre3p8TERNZ69O2335baj4VC\nIf3444+sFXUGhUJBffv2LTV4EggEFB0dzVqTjh07Ro6OjrRnzx7q06cPicVikkqlFBkZqRPXbE4C\nqClTplC9evWoQYMG1L17d+Uu8OUR4QJ3d/cS2aiXLVtG48aNY2jElvz8fJo6dep7M3h/bFBjZmZG\n1tbWZG9vT/b29mRtbU0SiYQMDQ0rpQ6hUEjjxo3TmpEWFkybNo3mzZunPH78+DG5uLgwNFJFm/p9\nRdGFtigUCjI1NaW0tDRl2YABA2jdunUMrf7H9OnTS+3TAoGAJkyYoBM/rCzJzc2l5s2bv/dz/Ouv\nv1hrEhFRv379aP369crj33//ndq1a8fQ6OMoa5+v0Byo9u3bIy4uDjdu3IC7uzsiIyMr8s9pnNq1\na+Pw4cMAivNS7N+/HxYWFlU2Y7OxsTEWL16MnJwczJ07FyYmJhX692QyGXJycpCeno7Xr1/j9evX\nSE9PR3Z2NoqKiirsOmPGDGRnZ2PVqlV6tyl0WSEimJub4/jx48ocXocPH0adOnUYm/GwxsDAALm5\nuQCAW7duIS4uDvfv39eK69uCBQswZswYZbb8f0JEWLlyJdq0aaP05ylJfHw83Nzc1G4ODBTvtrBz\n50507tyZYzNV8vLy8Pr16xIbTOfm5pa6X6tOU1kR24EDB6hfv37ljuS44NGjR1SzZk3y8/MjKysr\ncnZ2JicnJwoLC9OKVWeseZcuwMvLq1JGiyrj5eHhQb///nuVm6umjqKiIvr888/J3t6epFIpOTk5\nUfPmzcnFxYXu3r3LWq8E2tTvK4qutCUiIoJ8fX1p+PDhZGVlRT169CBPT08aPHiw1ozuvG/uDlA8\np/HmzZusNbWK7du3v3e6hTbNJXv79i01atSImjRpQubm5rR06VL68ccfyd7eno4ePcpar8yUtc9X\n2pWhS5cutH37drUiERERyhfr5FmZmZnUoUMH5ZBxQUEBdejQgZYuXcrUS9vIz8+n1atXU40aNTgP\nmlxcXGj58uVV+jGdOn788UcKCQmhvLw8kslk9MUXX1BQUBC9ffuWtRqdPHmyRD/XlaCjLOhKWxQK\nBa1fv55MTEyUUxVyc3PJw8ODYmJiGNv9j6VLl37wMf3ChQu1JuhjRX5+PvXp0+e9AaehoaFWTBh/\nx/fff0/9+vUjhUJBly9fpuDgYKpZsybz3/2PpdICqE8++YR8fHxUXv/c12bevHnUo0ePColwSZMm\nTejixYvK4/Xr19PgwYMZGmk3crmcoqOjqWfPnmVOZvkxLysrKwoLC6Njx47xI03vYfS0xtUAAAAg\nAElEQVTo0SVyqty4cYO8vLwYGpWONvb78qJLbXnz5g1JJBLlcVJSErVu3Zp5Xqh/c/jw4VJX5717\nNW7cmJKTk1mrMuHSpUtkY2Pz3s/H0tKyRH5D1igUCurTp0+Jc+369evk7e3N0Kp8cDYCtXHjRmre\nvDnl5eVVSIRL+vbtS19//TUpFAqKjY2lunXrUnBwsNY9BtFmUlJSaMeOHTRq1Chq2bIlubq6koWF\nBRkbG5NIJCKhUEhCoZBEIhEZGRmRhYUFubi4UIsWLWjEiBG0ZcsWevXqFetm6AwPHz6ktm3bUlBQ\nkPJxc0RERKk3LqzRxn5fXnSpLQqFgry9vWnlypW0Z88esrKyIl9fX7KxsaFVq1ax1ivB3bt3S81Y\n/s/RqKq0Sq+wsJD69+//wZtOLy8vrRh5fodcLqe+ffuSVCqlOnXq0MuXLyk/P5/69u1LI0aMYK33\n0XASQB05coS8vLzem+1UGy8+L1++pPr165ObmxuZmZnRnDlz6LvvviOpVMo/f+fROu7du0e2trY0\ndepU8vX1JalUSl5eXuTp6UnPnz9nracWbez35UXX2vLgwQPy8fEhY2NjunbtGhERPX36lGxtbbVq\nxIKIKCsri3x9fT8YMNjb29Pp06dZ62oMhUJBGzZsICMjow9+FiNGjNC6x5tbtmyhwMBAys3NpYiI\nCDIyMiIDAwPq3r07ZWVlsdb7aDgJoOrUqUOurq7UsGFDatiwIY0aNarcIlyTn59PISEh9NtvvynL\nFi1aREOGDGFoxcOjypgxY2j27NlEVHyhXbx4MTVt2rTUUV9tQFv7fXnQxbbcv3+fatWqpTy+fPky\neXl50Zo1axhalc6sWbPK9Li/devWWnvTUF7OnTtHzs7OH2y7SCSiY8eOsdZVQS6XU//+/Utsj/bs\n2TOytbVlaFUxytrnK5TG4OHDh3j69CmuXbuGa9euYc2aNRX55zjF2NgYIpEIdnZ2AICioiLk5OQg\nMTGxwkvueXgqC5lMhsTEROV5KhAI0KRJExgaGlY47QSP/uLi4oLMzEzExMRgwYIFCAsLg5ubG77/\n/nv88MMPrPVUmDNnDq5duwYLC4v3/t3p06fh4uKCkJAQPHz4kCM7zRAdHY1atWqhRYsWSExMfO/f\nenl54dWrV2jfvj1HdmVDoVCgT58+OHXqFHbt2qXcpmXbtm3w9fVlbMcBGg7ktPrubd26deTl5UXH\njh0jHx8fcnV1JQ8PD/L396f09HTWejxVnMzMTGWaAhsbGzp+/DhduHCBfH19acWKFaz13os29/uP\nRVfbcuLECbKysiKJRKKcb/j8+XOqVq0avXz5krGdegoKCqhPnz5lXoDSuHFjOnv2rNY90iqNwsJC\n2r59O1WvXr1M7ROJRLR8+XLW2qVy4MAB8vPzo/z8fJo0aRJZWlqSvb09eXp6UkJCAmu9clPWPl+l\nAyiFQkGrVq0iJycn5dJLhUJBw4cPr9IZynm0g6+//poGDhxIcrmcduzYQa6urlS9enVasmSJ1v9g\naHO//1h0uS3R0dHUpEkTIirO0TN9+nRydHSkyZMnU1FREWO70rlw4QLZ29uXOZCytramuXPnqt0N\nQxtISEiggQMHlmmO07tX06ZN6cWLF6zVSyUtLY3atm1LQ4cOVZY9efKERCKRzudVLGufr9AjPF1H\nIBBg3LhxaNy4MT777DNlltzmzZvjxo0bWpHBl6dqQkS4efMmunbtCqFQiPDwcKxfvx716tXDlClT\n1GZ05uH5N40aNcKzZ88QFRWFtm3bIjExEYsWLcK1a9fw5ZdfstYrlWbNmiEpKQnz5s2DSCT64N+n\np6dj1qxZqFatGjw8PLB27VpkZmZyYFo6iYmJ+O6772BnZwc3Nzds2bJFuXvA+7CwsMD+/fsRGxsL\nR0dHDkw/ntzcXAQFBcHc3ByHDh3Co0ePQETYtm0bAgMDYWRkxFqRGzQZxRHpxt3b9OnTqXfv3pSb\nm0u9evUiS0tLsrGxoeDgYK1aKspTNcjOzqb27duTpaUlderUiQoLC0kmk9HAgQNp4sSJrPXKhC70\n+7Ki622JiYkhKysr8vDwUI5cvn79msRisU7kWcrOzqaBAwe+N6FkaS9bW1saNGgQnT59mmQymUY9\ns7KyaN++fdStWzcyMzP7aFcTExNasWKFxj0rg71791Lr1q2VyVvNzMzIyMiIGjduTE+fPmWtV2HK\n2uf5AIqIcnJyqH379mRlZUWtW7dWZnoePHgwjR49mrUeTxVj8uTJFB4eTpmZmRQaGko2NjZkb29P\nwcHBlJmZyVqvTOhCvy/LZuhEutGWD3H48GFq1aoVERH9/PPPJJFIyNLSktzc3EpssK7NJCcnU//+\n/csVSL17WVhYULNmzWjy5Ml0+PBhevr06Ucn7y0sLKS4uDhlHjxvb28yNjYut5ORkRFFRERQYWGh\nhj65yuXgwYMkFouV5xNRcZBrbGxM2dnZDM0qDz6A+kgUCgV169aNtmzZQkREMpmM1q5dSz4+Pnpz\nUvBoP7m5uRQQEEBHjhwhouLz8scff6RPPvlEp7K060K/P378uPIznTZtGk2bNk3t3+lCWz5EVlYW\n1alTh4YNG0b29vbKfFDvFtLoEllZWTR27NgKBS3/fgmFQjI2NiZzc3PlPpPVq1cnBwcHsra2JolE\nQoaGhpVWHwCysbGhtWvXavVctH+TmJhINjY29N///pdcXV1p3rx5FBMTQz169KDPPvuMtV6lUdY+\nX6XnQP0TgUCABg0a4OjRo8jNzUWHDh2wePFiCAQCNGzYEM+ePWOtyKPnvHjxAo0bN0ZSUhL+/PNP\n5Ry8q1evwtfXF0Ih310rk3bt2ik/04CAgA8uJddlJBIJTp48iZs3b6J169aoXbs27ty5g//+9794\n8eIFIiMjoVAoWGuWCYlEgtWrV+Pt27fYtGkT3NzcKvxvKhQKFBQUICsrC6mpqXjx4gWSkpLw6tUr\npKenIzs7u1LS2wgEAvj7++PkyZNISUnByJEjYWBgUOF/lwsyMzMxduxY1K5dGyEhIYiJicHNmzfx\n2WefwcrKClu2bGGtyD2ajeN06+4tKyuLWrRoQQ4ODhQaGqp8Fv39999r7ZYZPPpD37596dtvv6WU\nlBRq0KABeXp6Ur169cjf319rVxeVhi71e6LSN0Mn0r22vI/o6Ghyd3enO3fukL29PS1dupSioqIo\nMDCw1BE4XeD58+c0adKkD+4fx+pVu3ZtWrVqlc7143fIZDJq2bIl9ejRg6RSqTINRlxcHFlaWurM\n1IKyUtY+rxuhL0dIJBLExMSgd+/e+OSTTyASifDixQs8e/YM58+fx5kzZ9CqVSvWmjx6yIULF3Dh\nwgWMHj0aUqkUly5dwuzZs3H16lUcOnSo6qxqqWTatWuHV69eqZQvWLAAXbt2BQDMnz8fRkZG6Nu3\nb6n/zuzZs5X/HRwcjODg4MpW5YSQkBC0a9cOLVq0QNeuXTF58mS8efMGoaGhWLRoEfr06YNGjRqx\n1vxonJ2dsXz5cixfvhzJycnYsGEDtmzZggcPHjAZWTMyMkJAQACGDBmC3r17QywWc+5Qmfzyyy94\n8uQJTp06hcWLF6NRo0aoU6cO7t69i9WrV8Pc3Jy1YoWIiYlBTEzMx/+PGg7kdPLu7aeffqLWrVtT\nfHw8OTs708iRI2nBggXk4OBA+/fvZ63Ho2dERUWRnZ0dBQYG0uDBg0kul1NeXh61a9eOli5dylqv\nXOhKv//QZuhEutOWj2Hq1Kk0YMAASktLo7p169Lnn39OkyZNIltbW+X8O31AJpPR9evXKSIigvz8\n/D64eXF5XgKBgGxsbKh9+/a0YsUKevZ/7d15WM5p+z/wd4t2lbu7fS9RaRUilRIiExnZMphhLFPW\nCcmM7VEiHJZmLK0qY8s6tpS0mAwRRZZCjXYqRov2+/z9Mb/peL7PPPNMoT51u17/qOY+5nqfOa7L\n+dmuT2Eh12V/VBs3biQ9PT1SU1Nru18rOzub1NXV6fz58xyn6xztnfMi///DnUZERKTH7afU2tqK\nefPmIS4uDjNnzkRoaCgAICEhAatWrUJ2djbHCRlhMmzYMPj7+8PR0RETJkzAkydP0NTUhLFjx+Lw\n4cM95h6Jf9cT5n18fDx8fX2RmpoKPp//t5/rCbV0VHl5OWxsbGBiYgINDQ3ExMSgrq4OAQEBOHr0\nKG7dugVVVVWuY3YKIkJxcTFu376N7OxsPHv2DAUFBaisrER1dTWamprQ0tLS9nlxcXFIS0tDQUEB\nqqqqMDAwgImJCczMzDB48GAoKSlxWE3nysjIgJOTE/Lz8zFnzhwoKChgypQpOH36NMrKypCUlNSu\nfbp6mvbOedZA/Q8+Pj5QVVXF+vXrsW/fPqxevRoNDQ0YNWoUjhw5Ah6Px3VEpgd7+/YtZs2ahbS0\nNCQmJmLw4MEQCAT4/vvvUV5ejoiIiB67YWZPmPdGRkZoampqm8fDhg37r+/z7Am1vI+CggJMnjwZ\nHh4eWLJkCRwcHKCqqgpJSUncu3cP165dg4mJCdcxGY7ExcVh0aJFEAgEeP36Nerr6xEUFITDhw/D\n1tYW4eHhkJOT4zpmp2AN1Efw66+/YtKkSVi+fDl+/PFHpKSkQEdHB8uWLUNFRQXi4uK4jsj0YLNn\nz4a4uDh0dHRw5coV7Nu3D5WVlZgzZw5++uknODs7cx3xvfXkef+fhKmW/5SamgovLy+MGTMGYmJi\nCA8Px++//47ly5fj/v37uHr1KjtQ/AQ9ffoUNjY2SElJwbx58zBhwgR88803SEpKgq+vLx48eABl\nZWWuY3aads/5j3nd8L/pgiE61blz50hDQ4P8/f2JiKi0tJQWLlxIPB6PYmNju/07yZju6fjx46Sk\npETPnj2jlpYW2rBhA2lpaZGuri7FxcVxHe+D9fR5/++EqZb/5qeffiIVFRU6ePAgFRcXk76+Prm5\nudGoUaNIR0dHKHaWZtrvypUrpKSkROLi4iQQCKi4uJhcXV1JTk6O+vbtS3fu3OE6Yqdr75xnDVQ7\nHDhwgMaNG0evXr0iXV1dWr58OYWHh5OpqSkFBQVxHY/pYXbv3k39+vWjfv360fHjx4nojw0zJ02a\nRLt27eI43cchDPP+T8JUy9+JjIwka2trmj17Nq1Zs4aIiHJzc2nkyJE0ePDgbv1SW+bjuXv3Lqmq\nqlJiYiLZ2NhQUFAQCQQCunv3LikrK/eYXes/VHvnPLuE1w4NDQ0YM2YMSktLYWlpiVOnTkEgECAq\nKgrLly/H7du3YWxszHVMpgd4+vQphg8fjmvXrqGmpgYTJ07EiBEjUFJSgtbWViQnJ/f4R54B4Zj3\nfxKmWv4OEeG7777D/v37ERERAW1tbbi5uWH69Omorq5GUlISbty4AR0dHa6jMp3k8uXLmDNnDmpq\nalBeXo43b97A09MT2dnZkJKSQmRkJKZMmcJ1zC7R3jnPtjZuBykpKVy9ehVOTk5QUFCAQCDAtGnT\nsHfvXowaNQqOjo44e/Ys1zGZbu7SpUuws7NDY2Mj5OTkMGzYMNy+fRu///47DA0NkZqaKhTNE9Pz\niIiIYMuWLVizZg327NmDdevWISgoCCEhIRg9ejR4PB4+++wzZGVlcR2V6QSnTp3C3LlzER0djREj\nRiAwMBDa2to4cuQIVFRUEB8f/8k0Tx3SWafA/tQFQ3SZgoICUlZWpm+++YYsLCyosbGRiIhOnjxJ\nCgoK9PLlS44TMt1VZWUlqaurU0pKCq1atYrs7e0pNTWVwsPDic/nU15eHtcRPyphmvfCVMs/aWlp\nIW9vb1JUVKRr167Rvn37yMjIiI4fP067d+8mJSUlysnJ4Tom8xHFxsaSrq4uqaurU25uLpWXl9OI\nESNIXFycpKWlKSwsjOuIXa69c541UB2UlZVF5ubm5OXlRUR/bDKmoqJCZmZmxOfz6erVqxwnZLqb\ntLQ04vP5JCYmRu/evaOWlhbavHkz6evrk6WlJWVkZHAd8aMTpnkvTLW0V0BAANnZ2ZGpqSmlp6dT\nVVUVjRs3jsTExEhOTo4iIiK4jsh8oJaWFlq8eDEpKirS5cuXycfHh9zd3amwsJBu3LhB6urqlJyc\nzHVMTrR3zrNLeB1kaWmJw4cP4+rVqzhy5AgiIiKQk5ODBw8e4IcffoCnpydevXrFdUymm6iqqsK0\nadMQExMDR0dHBAYGQkREBJ6enmhoaEBYWBgGDx7MdUyG+T/WrFkDR0dHlJWVQUREBPPnz4eenh7q\n6upw5MgR+Pr6Ijg4uMe8gJj5v6qrqzF79mzcvXsX/fv3h4iICHbs2AENDQ1YWlpi4sSJ2L59e499\nZVGX6eRGTmiP3o4cOULS0tI0btw4IiLatWsXKSkpkbGxMSkpKdHFixc5Tshw7erVq6SkpERiYmIk\nEAiopKSEhg8fTuLi4iQjI0NRUVFcR+w0wjTvhamWjvrhhx+of//+JC8vTy9fvqSTJ0+SsrIyzZgx\ng8zMzMjDw6PtpetMz/Dq1Svq168f6erq0vnz5ykmJob09PTo+PHjdPDgQeLz+UJ5Vrwj2jvnWQP1\nAe7du0fq6up09epVUlVVbXsHUnR0NMnJyVF2djbHCRmuPHr0iPr06UPXrl0jIyMjOnLkCBERFRcX\nk6amJt28eZPjhJ1LmOa9MNXSUQKBgA4dOkR8Pp/i4+NJWVmZMjIyqLKykqZOnUqKiopkZWVF9+/f\n5zoq0w6nTp0iDQ0NWrhwIc2ePZs2b95MRETHjh0jc3NzMjY2pvT0dI5Tco81UF0kJCSEZGRkyN7e\nnoiItmzZQhoaGuTs7EzKysqf5A14n7qYmBhSUlIiWVlZIvpjbxUtLS3S1tam3r1799gXBHeEMM17\nYarlff25uaKoqCg1NTXRiBEjyMfHh3Jzc2nVqlUkLy9PJ06cYBsLd1MNDQ20YcMG4vP55OrqSlFR\nUZSfn0+ampo0efJkcnNzI21tbaF7EfL7Yg1UF7p16xbx+XxKSkoiZWVlKi8vJ4FAQLt27SJJSUkK\nDQ2l1tZWrmMynUwgEFB0dDTJyMhQTk4Oqaurt13Kzc3NJT6fTykpKRyn7BrCNO+FqZYP8eTJEzI2\nNqaVK1eSvLw8tba2UmBgIOnp6dGcOXPI0NCQFi9ezHVM5j+8e/eOhg0bRnp6erRlyxYKDQ2lQYMG\n0atXryg/P58sLCzIzc2NKisruY7abbAGqouFhYWRrKwsWVpaEhHR/PnzycbGhtavX082NjY0b948\ndnQm5BYvXkympqakpqZGRES//PILqaqqkp6eHsnLy1NISAjHCbuOMM17YarlQxUVFZGtrS316tWL\nHj16RAoKClRWVkapqamkrq5OYmJipKOj80m87qMnOHz4MElJSZGjoyOtX7+eFi9eTAKBgPz8/EhS\nUpLExcVp9uzZ1NDQwHXUboU1UBx4+PAh8Xg8OnHiBKmoqFBNTQ29fv2a5syZQzwej9zd3am4uJjr\nmMxHVl5eTpMmTSI5OTmqqKggTU1NOnXqFBERpaamkqKiIt29e5fjlF1LmOa9MNXysfj5+ZGRkRHp\n6upSZWUlKSsrU3x8PBUXF5OLiwvx+XxatWoV1dfXcx31k1RSUkITJkwgRUVFWrJkCfn5+VFJSQlp\naWnRN998Q5s2bSIVFRU6c+YM11G7pfbOebaNwUdkamqK2NhYfP3115CSkoKMjAzc3d0hJSWFixcv\nwsTEBPb29igtLeU6KvORvHr1Ck5OTlBUVISKigr4fD7OnDmDZcuWQUFBAe7u7oiKioK1tTXXURnm\nowkKCsK6detQW1uL4OBgGBkZwc7ODs7OzhgyZAgiIyNx5coV2NjYICUlheu4nwyBQICIiAgMHDgQ\njY2N8PDwwNSpU3H48GG8efMGaWlpuH37No4ePYqzZ8/Cw8OD68g9Wyc3cp/k0VtNTQ3p6+uTv78/\nqaurU2trK12/fp1UVVVJU1OTevfuTeHh4VzHZD5QbGwsycrKkr6+PjU0NFD//v0pKCiIiouLae/e\nvaSpqUmvX7/mOiYnhGneC1MtH9v9+/epX79+JC8vT0ePHiVnZ2dqbGwke3t7GjduHPn5+ZGysjIt\nXLiQvZC4kz18+JBGjhxJRkZGNHz4cDp37hwNHDiQGhsbKSIighQVFUlMTIzGjx9PVVVVXMft1to7\n59kZqE4gJyeHxMREpKamoqamBnV1dZgyZQqioqJQVFQEf39/rFq1CosXL8bbt2+5jst0UE1NDVas\nWAEfHx/ExsZCREQEYmJiuHz5MhITE9GvX7+2zVb79OnDdVyG6TTm5ubIzc3F4sWLsXz5clRXV+Ps\n2bMQFRXFuXPn8OTJE/D5fDx69AgDBgzAoUOH0NDQwHVsofLmzRv4+/vDwcEBDx8+xNatWyEqKorx\n48dDX18fQ4YMwc8//wxxcXHExcXhwoUL4PF4XMcWCiL/v9vqvAE+gTeZ/x0iwsyZM1FUVITHjx+j\nsrISq1evxrVr1zB//nxcv34dmZmZSExMhJaWFtdxmXZ4+fIlXF1dwePx0NLSgpSUFIwfPx4SEhKY\nMGECTp48CSkpKZw+fRoiIiJcx+WMMM17YaqlMyUlJWHevHnQ09ODlpYWXF1dERoaisTERHz55ZdI\nTU2FlJQUREVFERkZCQcHB4iKsmP499XQ0IAjR45g5cqVaGhoQGRkJPbs2YOkpCQMGTIEzs7OsLe3\nx9atWyErK4uIiAj079+f69g9QrvnfGedAvtTFwzRrTU3N1NwcDDJyspSWloaSUpKUmVlJT18+JD0\n9PRIVVWVZGVlKTg4mOuozD/Yu3cvSUtLk5mZGeXm5pKysjIVFhZSQ0ND2zulAgICqKmpieuonBOm\neS9MtXS2yspKmjNnDvXu3ZtmzZpFfn5+dODAARoxYgRVV1fT5MmTSUlJiZSVlcna2poyMzPZ08kd\n1NDQ0LYhpoyMDEVERJCxsTG9ffuWtLS0KDQ0lHJycsjR0ZHU1NQoMDCQmpubuY7do7R3zrMGqotc\nuHCBlJSUqFevXtTQ0EDm5uYUFhZGLS0ttGbNGlJWVqaRI0eyHX27ocePH5OLiwvxeDwKCwujMWPG\nEBHR7t27ic/nk4WFBSkpKbU9eccI17wXplq6SlJSEunp6ZGamhrNnz+ftm/fTtu2baOxY8dSZWUl\njRw5klRUVIjP59PgwYMpPT2dvRLmH9TW1tKxY8dIV1eXFBQUaM+ePcTn86m2tpZUVVXp4sWLlJOT\nQ5aWliQtLU2Ojo6Un5/PdeweiTVQ3VBZWRk5OTmRp6cniYqKUktLC/n6+pK9vT0lJibS2rVrSU5O\njnbs2EHv3r3jOu4nr76+nvbs2UM8Ho+mT59OM2bMoNevX5OOjg5t27aNbt26RZMmTaLBgwdTSUkJ\n13G7FWGa98JUS1fbtm0b9erVi2xsbGjGjBkUFRVFK1eupJkzZ1JRURGZmJhQ//79SVNTk8zNzenk\nyZPU2NjIdexupaKigvbs2UMaGhqkoqJC27dvJ1FRUWpsbCQVFRVKTExs23NOTk6O+vTpQ/Hx8VzH\n7tFYA9VN1dXV0ZIlS0hBQYEuXLhAPB6PioqKKCEhgfh8Ps2dO5ecnJzI1NSUcnJy2OltjuTm5pK1\ntTUZGxvT1KlTKS0tjQwMDOjNmzf07NkzcnR0pD59+tCiRYuourqa67jdjjDNe2GqhQu1tbU0depU\nUlBQIHd3dxozZgxduHCBZsyYQf7+/nT79m1SUVEhNzc3MjIyIh0dHQoICKA3b95wHZ1Tubm55OPj\nQzwej3R0dGjLli2koKBAlZWVpKenRz///DMlJyeTsrIyGRgYkLy8PAUEBLDLdR8Ba6C6uevXr5Oy\nsjLJysrS06dPydzcnC5evEjFxcVkZmZG2traxOPxaNasWezUdhdqbW2lBQsWkJycHI0YMYLCwsLI\n09OTiIhWrVpFampqZG1t3fbqHua/E6Z5L0y1cEUgEND9+/fJ1taWVFRUaM6cOWRjY0M3b94kOzs7\nio2NpcjISNLS0qL169eTubk5qaiokIeHB2VlZX0yB5ItLS10/vx5srOzIzk5OTIzM6Nt27ZR3759\n6fHjxzRkyBAKDw+nX375hVRUVNpuH/jiiy+orKyM6/hCo71znj0CwRF7e3s8fPgQ06ZNw8SJE1FW\nVgZzc3P4+Phg0qRJyM3Nxbhx43D06FH07t0bAQEB7EmgTrZ9+3bIysri+vXrWLVqFQYPHoxJkybh\n9u3bWL16NSwsLKCoqAhTU1Pk5ORg5MiRXEdmmB5BREQE5ubmSE9Px7Fjx5CZmYmSkhJERUWhtLQU\nQ4cOxbp16/Dzzz+joKAAOjo62Lp1KzIyMjBo0CD06dMH3377LW7evMl1KR9da2srLl68iOnTp0NG\nRgZeXl6QkJDApk2b0Lt3bwwbNgzm5uY4fPgwwsPDsWHDBixYsABEBG1tbVy/fh2xsbFQU1PjupRP\nDtvGgGNEhOjoaAQFBWHgwIG4ffs2Lly4gLCwMDx79gyxsbEICAhAWFgY5OXl4e/vj0WLFnEdW6hE\nRkZi/fr1EBUVhbu7O9TU1DB69GhMmjQJFy9eRO/evTFlyhS8e/cOK1euxPz58z/pLQraQ5jmvTDV\n0l00NzcjNTUVvr6+KC0txfjx43H27Fk8evQI+vr6qKiogLW1Nb777jtUVFRg7969sLS0REZGBvh8\nPhwdHTFv3jyYm5tDRkaG63I6rKqqCrdu3UJkZCR+/fVX9OrVCwDg4OAAGxsbpKamwsvLC7du3UJ+\nfj527NiBiRMnoqqqCu/evYODgwOCgoIwYMAAthZ1gvbOedZAdRPV1dWYN28erly5glWrVuHs2bPY\nv38/fv31V8TExCAqKgonTpzAgQMHwOfzsXLlSnz99ddcx+7RYmNj8a9//Qs1NTUYMWIEhg4dCh6P\nh4MHDyIpKQmnT5/GkiVLUFNTAzc3Nxw6dIhtjNlOwjTvhamW7qa1tRV3797F6paRxuUAABgTSURB\nVNWrcefOHdjb2yM5ORl37tzBqFGjkJWVBRMTE9y9excTJkzA6NGj0dLSgoiICPTp0wd1dXWws7OD\ni4sL3NzcYGho2NaMdCe1tbXIy8vDyZMnkZycjAcPHkBERASurq4oLy/HsGHDwOPxUFJSAg0NDWhq\namLr1q0IDQ1FYGAgkpKSAAAzZ87Epk2boKury3FFwo01UD1UQUEBxowZg5qaGmzcuBEnTpyAn58f\nXr9+jXXr1iE8PBxXr17FgQMHwOPxsGTJEixevJgdhXTAwYMHERwcjLq6OgwaNAjjx49HVVUV8vLy\ncOjQIcyePRtJSUlQUFBAU1MTrly5AiMjI65j9yjCNO+FqZburLKyEmvXrsXZs2ehoqKCgoICHD16\nFGvXrsX+/fuxYsUKREREYOzYsbhy5Qo8PDzg7u6Op0+fIjU1FbKyshAVFYWxsTGsrKzg5OQEJycn\nKCgodOn6SEQoLCxEeno6EhIS8ODBA+Tl5UFSUhJmZmZ48OAB1q5dixs3bsDW1hYvX76ElpYW0tLS\nsGnTJri4uMDX1xdZWVm4cuUKFBQU4O3tjeXLl0NCQqLL6viUtXfOs3uguhl9fX3cv38fO3bswLp1\n61BUVISioiIcO3YMW7ZsQXV1NWJiYnD8+HF4enpiw4YNUFdXh7+/PxobG7mO3201NTVhw4YNUFZW\nRkBAAAwNDbFt2zb07dsXRUVFWLJkCbKysuDq6oqmpiY0NjZi9erVePDgAWuehNS6detgaWkJKysr\nuLi4oKioiOtInzQ+n4/Q0FCUl5dj8eLFsLCwwFdffYXi4mJcv34dTU1NePToEezt7ZGZmQlra2s4\nOjqipKQE8fHxICL4+fmhsLAQaWlpWLFiBVRUVCAtLQ1LS0tMmDABfn5+CAsLQ1paGvLz81FXVweB\nQNChnM3Nzairq8ODBw+QmJiI/fv3Y+HChXBzc4ORkRF69eoFU1NTfP/993jx4gUKCgqwe/duKCoq\nYtmyZRg2bBg0NDTQ2NgIOzs7nDhxAqNGjcLLly8xb948mJqaYtu2baivr8fx48fx22+/YfXq1ax5\n6obYGahurLi4GPv378e+ffugq6uLBQsW4MaNG3B2doaamhp8fHxw7NgxnDlzBrt374ZAIICLiws2\nbtwIa2trSEpKcl0Cp5qampCVlYWAgAAkJCTAyMgIfD4fS5Yswfnz52FmZobJkyfDzs4OHh4ekJaW\nRmhoKL755hv4+Piw0+QfoCfM+5qaGvTu3RsAEBISguzsbISHh//lcz2hFmF1//59nD59GqGhoaip\nqcGwYcOQk5PTdobGwMAAAoEA7969g4KCAqqrq1FbWwttbW0kJiZi6tSp2LZtG2bOnIn9+/dj+PDh\nuH79Ovr06YM3b97g3bt3kJWVBRFBTk4OEhISEBMTg4SEBAQCAURERNDc3IyGhgY0NzejqakJtbW1\nkJKSgoyMDOrq6mBqaorS0lLo6+vD0NAQycnJ2LdvHzw9PXHz5k1MnjwZR48exVdffYVjx45h9OjR\nSE5Ohru7Oz777DPU1NQgNjYWAoEA/fr1g4+PDyZMmMBe78UhdgZKCGhpaSEwMBC//PILBg0ahLVr\n1+LZs2d49eoVzp8/D19fX5SXl+PMmTPIzc3F3LlzcfPmTUyfPh26urr417/+hYcPH3JdRpd78uQJ\nAgICYGRkhAkTJoCIYGNjgz179oDP56OiogLLly/H1q1bERkZiS+++ALR0dGoqqpCeno6goODWfP0\nCfizeQL+uEeFz+dzmIb5bywsLLBx40aUlJTg6dOnsLGxgYqKCjZv3oyzZ8/i+fPnuHLlCgQCAVpb\nW1FUVAQHBwckJydjzZo1iImJQUREBC5fvoyYmBgUFRUhJCQECgoKWLduHUxMTLB48WJoaGjAy8sL\nRNR2s7aHhwdevXqFGTNmoLm5GfPnz4euri58fHzg7u4Oe3t7bN68Ga2trfjpp5+Ql5eHzZs3o6Sk\nBMOHDwcAqKqqoqqqCgDQq1cvhIeHY/LkyRg6dCjExcURFRWF58+fY/v27fj999/x8OFDeHt7s+ap\nh2ANVA8wYMAAhIeHIzU1Ff3798fWrVuRk5OD3377DWlpaZg/fz5u3bqFO3fu4Pnz59DT04OBgQGy\ns7Nhb2+P4cOHY8eOHaipqeG6lE5TV1eH3bt3Y+jQobC1tUV0dDS++uorqKqqYtOmTVBUVMSLFy+w\ncuVKfP/99zh37hw8PT2xe/dulJaWIi0tDYcOHYKFhQXXpTBd6LvvvoOOjg6io6OxZs0aruMwf0NE\nRARqamoICgpCVlYWMjMzsW/fPrx58wZlZWU4fPgwdu7ciaamJuzbtw99+vRBdnY2iAhiYmKoqKiA\nubk5njx5grFjx+Lp06eYMmUKKisr8fnnn0NERARjxoyBlpYWBg8e3HaZzdPTEwCwaNEiVFRUYMGC\nBSgsLMSkSZNQWVkJCwuLtjGUlZWRk5ODwYMH48CBA5gxYwZmzpyJuXPnYtSoUWhubkZ0dDSSkpIw\nduxY7Ny5E3l5eUhOTsbSpUshKyvL8W+Z6Sh2Ca8HevLkCXbt2oW4uDj069cPWlpaMDU1hYiICAwN\nDREdHY2jR49i0KBB+PLLL9HY2IiQkBA0NzdDS0sLs2fPhqurK+zs7Lgu5YPcunUL8fHxOHr0KF68\neIG+ffuirq4O+/fvx6JFi5CYmAhvb29MnToVZmZmcHd3x5w5c/DixQskJiZiypQpWLZsGczMzLgu\nReh0l3k/evRolJeX/+XnW7Zsgbu7e9v3W7duRW5uLqKiov7yWREREWzYsKHt+z9vTma6ByLCgwcP\ncPv2bSQkJCA7Oxv5+fkQFxfHgAED8PLlS/Tr1w8qKip4+PAhlixZgpUrV+L8+fNwc3NDQkICpkyZ\ngkOHDsHX1xfr1q3Dvn37MH36dMTHx8POzg7Z2dkwNDREQUEBtLW18fTpU5iYmCAtLQ1ubm4IDQ2F\nl5cX9uzZAycnJ/zyyy+ora2FiIgIzMzMYGZmhgkTJsDKygp6enpc/8qY/5CSkoKUlJS27zdt2sSe\nwhN2paWlCAsLQ2RkJGRlZSEhIYGpU6eioqIClpaWuHDhArZs2QJ7e3tcunQJISEhuHPnDkxMTJCc\nnAxJSUkYGxtjypQpGDp0KKytrbku6X+6f/8+fv31V5w+fRpZWVlobW2FjIwM5s+fj507dyInJwfW\n1tZ48OABvvzyS4wcORJjxoyBq6srhg8fjpKSErx48QILFizA/Pnzoa2tzXVJQqunzfvCwkK4ubkh\nJyfnL/+tp9XC/HFGurS0FMnJycjIyEB+fj5evHiBwsJCSEpKQlFREdXV1dDV1UVNTQ3k5eUhJyeH\nqqoqGBsbIzs7G3Z2dkhLS4ODgwPS0tIwcOBAZGVlQVlZGRUVFWhoaAAAvH37Fr169YKBgQE0NDRg\naWkJCwsLjBw5EsrKyt1yWwXmf2PbGHxC6uvrcebMGRw8eBAPHz5Ea2srVqxYgQcPHsDDwwPnz5/H\nsmXLMHv2bKSnp2PIkCFYunQpXr58iUOHDmHAgAHIzs6GmJgYNDQ0MHr0aAwcOBCOjo7g8/ldfjN6\nU1MTKioqkJ6ejjt37iAlJQUFBQVobW2FtLQ0Jk6ciOjoaNy+fRsWFhZoamoCj8fDw4cPsWLFCigo\nKMDX1xdjx46FuLg4amtroauri6VLl8LDw4OdKu8CPWHeP336tO0Jy5CQEGRkZCA2NvYvn+sJtTDt\nQ0Sor69Hbm4uXr9+jeLiYhQWFqK5uRkFBQWQlJREeXk5ZGVl8fbtWygqKqKurg5qamogIqirq6N3\n797Q1NSEjo4OeDwe+vfvDzExMbaVjBDpsgZq586dWLVqFSorK8Hj8d47CPPhiAi5ubk4fvw4QkJC\n8O7dO0yePBkZGRkIDAxEZGQk/Pz8sGbNGsTFxcHS0hJZWVkYP348Pv/8c9TX1+PYsWNwcHDAhQsX\nQEQQCATQ0dEBn8+HhYUFdHR0YGpqClVVVejr60NaWrrDOwHX19ejrq4OhYWFKC8vx6NHj1BUVISc\nnByUlJS0HSWqqqri9evXWLRoEfbs2YOEhAS4u7vjyZMn0NXVxdu3b6GqqopLly7h1KlTSElJwdKl\nS7F161Y8evQI8vLy8Pb2hpeXF0xMTNgC14V6wrz39PREbm4uxMTEYGhoiP3790NFReUvn+sJtTAM\n8/G0d86Lf8ggRUVFSExMZE8sdRMiIiIwNjbGhg0bsGHDBuTn52Pz5s1oaWmBn58fKioqMG7cOFRU\nVKCwsBB6enqor69HTU0NfH19oa6ujry8PIwYMQI7d+5Eeno6SktLMWjQIISFhaFv374ICAiArq4u\nSkpKUF9fD1HRP55D6NWrF+Tl5UFEkJWVRUtLC3r16oWmpqa2o77Gxsa2R4KlpaUhJSUFIkL//v3x\n6NEjzJ07F1lZWYiKioKfnx/Cw8OxePFiTJs2DSdOnED//v1RX18PAOjbty+CgoLw448/Yty4cbC3\nt0dJSQnWr18POzs7nDp1iu3fxPxPJ0+e5DoCwzA92Ac9hfftt98iODj4Y2VhPjIDAwNERUXh2bNn\nOHDgALy9vREcHIzy8nL4+voiPz8fmZmZePv2LUpKSiArKwtpaWmUl5fjyy+/xE8//YS4uDgcOnQI\nly5dwqNHj7Bz506YmZlhxowZWLp0Kezs7ODv7w9tbW0sXLgQYmJimDlzJurr69v+XLBgAcTFxds2\n/dy3bx+MjIwQHBwMMzMzeHt7w97eHnZ2dhg+fDj4fD50dXXB5/NRWVkJNTU1VFdXIzU1FfPnz4ez\nszPGjRuHH3/8ETNmzICEhAT69u2LsLAw5OXlISYmhjVPDMMwTKd670t4586dQ0pKCnbt2gV9fX1k\nZmayS3g9RFNTE8LDw5GSkoKkpCQ0NzdDU1MTtbW1+Prrr7F7927Ex8fD2dkZBQUFMDQ0RFFREfr3\n79+2NcLly5cxffp0HDhwAKtXr8batWvxww8/YNasWTh79ixcXFxw8+ZNWFhY4Pnz59DQ0Gi72VJS\nUhJVVVUwMDBAZmYmxo0bh/3792Pbtm2YNGkSUlNTYWdnhx07duD8+fPIz8/HwIEDceTIEbS0tEBc\nXByurq5wdHTEggULPvkNQ7sjYZr3wlQLwzD/7KNcwvu7R4ADAwMRFBSEhISEtp/9r8E2btzY9jV7\nBJh7EhIS8Pb2hre3N4gIr1+/Rnx8PK5fv464uDg0NDRg1KhR0NHRgZOTEywsLODj4wNTU1OEh4dD\nR0cHKSkp4PF4yM3NhaysLMrKyiAlJYU3b960/SknJ4eysrK2zw0ZMgRxcXH49ttvsWzZMkRHR2P9\n+vVwc3Nr23Xd0tIStra2MDAwgLe3d1tzR0QICQnB+PHjwePx2i4dMt3Dfz4GzDAMI+ze6wxUTk4O\nXFxc2m4eLi4uhqamJjIyMv5yEyY7euuZCgoKcO/ePWRmZuL58+d4/PgxiouL0draCgkJCdTV1cHE\nxARPnjzByJEjkZKSAk9PT5w+fRqzZs1CbGws5syZg5iYGEyZMgXnz5+HtbU1nj59CiKCuLg4fvvt\nN/Tu3Rutra0QERGBuro6zMzMoK+vj0GDBsHKygqGhoZc/yqY9yBM816YamEY5p916TYG7BLep6Ol\npQWFhYVoamrCkydP8Pvvv6OyshKvX7/Gu3fvUFNTg9bWVrS0tAAAxMTEIC4uDjk5OcjIyEBJSQk8\nHg99+vSBsbExJCQkoKurC3HxD3qegelmhGneC1MtDMP8sy55Cu/fB2M+DeLi4jAwMAAAGBsbc5yG\nYRiGYbjBNtJkGOajE6Z5L0y1MAzzz9o759mduAzDMAzDMB3EGiiGYRiGYZgOYg0UwzAMwzBMB7EG\nimEYhmEYpoNYA8UwDMMwDNNBrIFiGIZhGIbpINZAMQzDMAzDdBBroBiGYRiGYTqINVAMwzAMwzAd\nxBoohmEYhmGYDmINFMMwDMMwTAexBophGIZhGKaDWAPFMAzDMAzTQayBYhiGYRiG6SDWQDEMwzAM\nw3QQa6AYhmEYhmE6iDVQDMMwDMMwHcQaKIZhGIZhmA5iDRTDMAzDMEwHCU0DlZKSwnWEj0JY6gBY\nLd2RsNTxMe3cuROioqJ4/fo111H+guu/r095/E+5dq7H57r29mINVDcjLHUArJbuSFjq+FiKioqQ\nmJgIXV1drqP8V1z/fX3K43/KtXM9Pte1t5fQNFAMwzAd9e233yI4OJjrGAzD9ECsgWIY5pN07tw5\naGlpwcLCgusoDMP0QCJERJ06gIhIZ/7vGYbppjp5aWmX0aNHo7y8/C8/DwwMxJYtW5CQkAB5eXno\n6+vjzp07UFJS+stn2RrGMJ+e9qxfnd5AMQzDdDc5OTlwcXGBjIwMAKC4uBiamprIyMiAiooKx+kY\nhukJWAPFMMwnT19fH5mZmeDxeFxHYRimh2D3QDEM88ljl+kYhukooWuguvOeLu21atUqmJiYwNLS\nEp9//jnevn3LdaQOi4+Ph7GxMYyMjLBt2zau47yXoqIiODs7Y8CAATAzM8PevXu5jvTBWltbYW1t\nDXd3d66jdCv5+fn/ePaJq7Vl3bp1sLS0hJWVFVxcXFBUVNSl43O5HsXFxWHAgAEQExPD3bt3u2xc\nLtevuXPnQlVVFebm5l06LsD9mtfQ0ABbW1tYWVnB1NQU/v7+XTr+n9q9TpIQKSwsJFdXV9LT06Oq\nqiqu47y3hIQEam1tJSIiPz8/8vPz4zhRx7S0tJChoSEVFBRQU1MTWVpa0qNHj7iO1WFlZWV07949\nIiKqqamhfv369cg6/t3OnTvJy8uL3N3duY7So3C5tlRXV7d9vXfvXpo3b16Xjs/levT48WPKzc0l\nJycnyszM7JIxuV6/0tLS6O7du2RmZtZlY/6pO6x5dXV1RETU3NxMtra2dP369S4dn6j966RQnYES\nlj1dRo8eDVHRP/5qbG1tUVxczHGijsnIyEDfvn2hp6eHXr16Yfr06Th37hzXsTpMTU0NVlZWAAA5\nOTmYmJigtLSU41Tvr7i4GJcuXcLXX3/dLZ6Q60m4XFt69+7d9nVtbS34fH6Xjs/lemRsbIx+/fp1\n2XgA9+uXg4MD+vTp02Xj/bvusOb9+WBHU1MTWltbu/y+xI6sk0LTQAnrni6RkZFwc3PjOkaHlJSU\nQFtbu+17LS0tlJSUcJjow/3222+4d+8ebG1tuY7y3lasWIHt27e3/WPItE93WFu+++476OjoIDo6\nGmvWrOEsR09cjzpKGNev98HVmicQCGBlZQVVVVU4OzvD1NS0S8fvyDop3gV5Ppr/tadLUFAQEhIS\n2n7W3Y+w/66WLVu2tF13DQwMhISEBLy8vLo63gcRthtya2tr4enpiT179kBOTo7rOO/lwoULUFFR\ngbW1dY95TUJX4npt+af1IDAwEIGBgdi6dStWrFiBqKioLh0f6Lz1qD1jdyVhW7/eB5drnqioKLKy\nsvD27Vu4uroiJSUFTk5OXTJ2R9fJHtVAJSYm/tef5+TkoKCgAJaWlgD+OAVnY2PTrfd0+bta/nTo\n0CFcunQJSUlJXZTo49HU1Pw/N7oWFRVBS0uLw0Tvr7m5GZMnT8YXX3wBDw8PruO8txs3buDnn3/G\npUuX0NDQgOrqasyePRsxMTFcR+sWuF5b/mk9+JOXl1ennAHicj1qb+1dRZjWr/fRXdY8BQUFjB8/\nHnfu3OmyBqrD62QX3I/V5Xr6TeSXL18mU1NTqqio4DrKe2lubiYDAwMqKCigxsbGHnsTuUAgoFmz\nZtHy5cu5jvJRpaSk0GeffcZ1jB6Ji7UlLy+v7eu9e/fSF1980aXjd4f1yMnJie7cudMlY3WH9aug\noICTm8i5XvMqKirozZs3RET07t07cnBwoKtXr3KSpT3rpFDeDNHTT8EuWbIEtbW1GD16NKytreHt\n7c11pA4RFxfHDz/8AFdXV5iammLatGkwMTHhOlaHpaen4/Dhw0hOToa1tTWsra0RHx/PdayPoqfP\nEa5w8Xvz9/eHubk5rKyskJKSgp07d3bp+FyuR2fOnIG2tjZu3ryJ8ePHY9y4cZ0+Jtfr14wZM2Bn\nZ4e8vDxoa2t/9Mu1/wvXa15ZWRlGjhwJKysr2Nrawt3dHS4uLl02/n/6p/nOdiJnGIZhGIbpIKE8\nA8UwDMMwDNOZWAPFMAzDMAzTQayBYhiGYRiG6SDWQDEMwzAMw3QQa6AYhmEYhmE6iDVQDMMwDMMw\nHfT/AAAEpXfiwGc+AAAAAElFTkSuQmCC\n"
}
],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"These are the type of circles we want to distinguish between. We can try classification with a constant separation between the circles first."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def train_mkl(circles, feats_tr):\n",
" #Four kernels with different widths \n",
" kernel0=GaussianKernel(feats_tr, feats_tr, 1) \n",
" kernel1=GaussianKernel(feats_tr, feats_tr, 5)\n",
" kernel2=GaussianKernel(feats_tr, feats_tr, 7)\n",
" kernel3=GaussianKernel(feats_tr, feats_tr, 10)\n",
" kernel = CombinedKernel()\n",
" kernel.append_kernel(kernel0)\n",
" kernel.append_kernel(kernel1)\n",
" kernel.append_kernel(kernel2)\n",
" kernel.append_kernel(kernel3)\n",
" \n",
" kernel.init(feats_tr, feats_tr)\n",
" mkl = MKLClassification()\n",
" mkl.set_mkl_norm(1)\n",
" mkl.set_C(1, 1)\n",
" mkl.set_kernel(kernel)\n",
" mkl.set_labels(lab)\n",
" \n",
" mkl.train()\n",
" \n",
" w=kernel.get_subkernel_weights()\n",
" return w, mkl\n",
"\n",
"def test_mkl(mkl, grid):\n",
" kernel0t=GaussianKernel(feats_tr, grid, 1)\n",
" kernel1t=GaussianKernel(feats_tr, grid, 5)\n",
" kernel2t=GaussianKernel(feats_tr, grid, 7)\n",
" kernel3t=GaussianKernel(feats_tr, grid, 10)\n",
" kernelt = CombinedKernel()\n",
" kernelt.append_kernel(kernel0t)\n",
" kernelt.append_kernel(kernel1t)\n",
" kernelt.append_kernel(kernel2t)\n",
" kernelt.append_kernel(kernel3t)\n",
" kernelt.init(feats_tr, grid)\n",
" mkl.set_kernel(kernelt)\n",
" out=mkl.apply()\n",
" return out\n",
"\n",
"size=50\n",
"x1=linspace(-10, 10, size)\n",
"x2=linspace(-10, 10, size)\n",
"x, y=meshgrid(x1, x2)\n",
"grid=RealFeatures(array((ravel(x), ravel(y))))\n",
"\n",
"\n",
"w, mkl=train_mkl(c, feats_tr)\n",
"print w\n",
"out=test_mkl(mkl,grid)\n",
"\n",
"z=out.get_values().reshape((size, size))\n",
"\n",
"figure(figsize=(5,5))\n",
"c=pcolor(x, y, z)\n",
"_=contour(x, y, z, linewidths=1, colors='black', hold=True)\n",
"title('classification with constant separation')\n",
"_=colorbar(c)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[ 3.70179551e-05 6.14303709e-01 3.83958304e-01 1.70096833e-03]\n"
]
},
{
"output_type": "display_data",
"png": 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6+rLzXjsg3t7eCAsLwxdffKFuUzQGbRW7l6Ibq0oePXqEPXv2ICYmRt2msKiI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\nIKgF/w8KXbsaNzC3wAAAAABJRU5ErkJggg==\n"
}
],
"prompt_number": 10
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we can see the MKL classifier classifies them as expected. Now let's vary the separation and see how it affects the weights.The choice of the kernel width of the Gaussian kernel used for classification is expected to depend on the separation distance of the learning problem. An increased distance between the circles will correspond to a larger optimal kernel width. This effect should be visible in the results of the MKL, where we used MKL-SVMs with four kernels with different widths (1,5,7,10). "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"range1=linspace(5.5,7.5,50)\n",
"x=linspace(1.5,3.5,50)\n",
"temp=[]\n",
"\n",
"for i in range1:\n",
" #vary separation between circles\n",
" c, feats=get_data(4,i) \n",
" w, mkl=train_mkl(c, feats)\n",
" temp.append(w)\n",
"y=array([temp[i] for i in range(0,50)]).T\n"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"figure(figsize=(20,5))\n",
"_=plot(x, y[0,:], color='k', linewidth=2)\n",
"_=plot(x, y[1,:], color='r', linewidth=2)\n",
"_=plot(x, y[2,:], color='g', linewidth=2)\n",
"_=plot(x, y[3,:], color='y', linewidth=2)\n",
"title(\"Comparison between kernel widths and weights\")\n",
"ylabel(\"Weight\")\n",
"xlabel(\"Distance between circles\")\n",
"_=legend([\"1\",\"5\",\"7\",\"10\"])\n",
" "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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WNXRviB7BPdAzuCcaV3/8KAl7K3t0CuiETgGdAAC5mlycuH0CB2P15dLRm0dx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\nljl2xAAAAABJRU5ErkJggg==\n"
}
],
"prompt_number": 12
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the above plot we see the kernel weightings obtained for the four kernels. Every line shows one weighting. The courses of the kernel weightings reflect the development of the learning problem: as long as the problem is difficult the best separation can be obtained when using the kernel with smallest width. The low width kernel looses importance when the distance between the circle increases and larger kernel widths obtain a larger weight in MKL. Increasing the distance between the circles, kernels with greater widths are used. "
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Multiclass classification using MKL"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"MKL can be used for multiclass classification using the [MKLMulticlass](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CMKLMulticlass.html) class. It is based on the GMNPSVM Multiclass SVM. Its termination criterion is set by `set_mkl_epsilon(float64_t eps )` and the maximal number of MKL iterations is set by `set_max_num_mkliters(int32_t maxnum)`.\n",
"\n",
"To see this in action let us compare it to the normal [GMNPSVM](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CGMNPSVM.html) example as in the [KNN notebook](http://www.shogun-toolbox.org/static/notebook/current/KNN.html#Comparison-to-Multiclass-Support-Vector-Machines), just to see how MKL fares in object recognition. We use the USPS digit recognition dataset."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from scipy.io import loadmat, savemat\n",
"from numpy import random\n",
"from os import path\n",
"\n",
"mat = loadmat('../../../data/multiclass/usps.mat')\n",
"Xall = mat['data']\n",
"Yall = np.array(mat['label'].squeeze(), dtype=np.double)\n",
"\n",
"# map from 1..10 to 0..9, since shogun\n",
"# requires multiclass labels to be\n",
"# 0, 1, ..., K-1\n",
"Yall = Yall - 1\n",
"\n",
"random.seed(0)\n",
"\n",
"subset = random.permutation(len(Yall))\n",
"\n",
"Xtrain = Xall[:, subset[:5000]]\n",
"Ytrain = Yall[subset[:5000]]\n",
"\n",
"Nsplit = 2\n",
"all_ks = range(1, 21)\n",
"\n",
"print Xall.shape\n",
"print Xtrain.shape"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(256, 9298)\n",
"(256, 5000)\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's plot five of the examples to get a feel of the dataset."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def plot_example(dat, lab):\n",
" for i in xrange(5):\n",
" ax=subplot(1,5,i+1)\n",
" title(int(lab[i]))\n",
" ax.imshow(dat[:,i].reshape((16,16)), interpolation='nearest')\n",
" ax.set_xticks([])\n",
" ax.set_yticks([])\n",
" \n",
" \n",
"_=figure(figsize=(17,6))\n",
"gray()\n",
"plot_example(Xtrain, Ytrain)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAA8MAAAC/CAYAAADafQ4RAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n"
}
],
"prompt_number": 14
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We combine a Gaussian kernel and a [PolyKernel](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CPolyKernel.html). To test, examples not included in training data are used."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"labels = MulticlassLabels(Ytrain)\n",
"feats = RealFeatures(Xtrain) \n",
"Xrem=Xall[:,subset[6000:]]\n",
"Yrem=Yall[subset[6000:]]\n",
"\n",
"#test features not used in training\n",
"feats_rem=RealFeatures(Xrem) \n",
"labels_rem=MulticlassLabels(Yrem)\n",
"\n",
"kernel = CombinedKernel()\n",
"feats_train = CombinedFeatures()\n",
"feats_test = CombinedFeatures()\n",
"\n",
"#append gaussian kernel\n",
"subkernel = GaussianKernel(10,80) \n",
"feats_train.append_feature_obj(feats)\n",
"feats_test.append_feature_obj(feats_rem)\n",
"kernel.append_kernel(subkernel)\n",
"\n",
"#append PolyKernel\n",
"feats = RealFeatures(Xtrain)\n",
"subkernel = PolyKernel(10,2) \n",
"feats_train.append_feature_obj(feats)\n",
"feats_test.append_feature_obj(feats_rem)\n",
"kernel.append_kernel(subkernel)\n",
"\n",
"kernel.init(feats_train, feats_train)\n",
"\n",
"mkl = MKLMulticlass(1.2, kernel, labels)\n",
"\n",
"mkl.set_epsilon(1e-2)\n",
"mkl.set_mkl_epsilon(0.001)\n",
"mkl.set_mkl_norm(2)\n",
"\n",
"mkl.train()\n",
"\n",
"#initialize with test features\n",
"kernel.init(feats_train, feats_test) \n",
"\n",
"out = mkl.apply()\n",
"evaluator = MulticlassAccuracy()\n",
"accuracy = evaluator.evaluate(out, labels_rem)\n",
"print \"Accuracy = %2.2f%%\" % (100*accuracy)\n",
"\n",
"idx=np.where(out.get_labels() != Yrem)[0]\n",
"Xbad=Xrem[:,idx]\n",
"Ybad=Yrem[idx]\n",
"_=figure(figsize=(17,6))\n",
"gray()\n",
"plot_example(Xbad, Ybad)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Accuracy = 97.70%\n"
]
},
{
"output_type": "display_data",
"png": 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}
],
"prompt_number": 15
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The misclassified examples are surely pretty tough to predict. As seen from the accuracy MKL seems to work a shade better in this case. One could try this out with more and different types of kernels too."
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"References:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[1] Soeren Sonnenburg, Gunnar Raetsch, Christin Schaefer, and Bernhard Schoelkopf. Large Scale Multiple Kernel Learning. Journal of Machine Learning Research, 7:1531-1565, July 2006.\n",
"\n",
"[2]F. R. Bach, G. R. G. Lanckriet, and M. I. Jordan. Multiple kernel learning, conic duality, and\n",
"the SMO algorithm. In C. E. Brodley, editor, Twenty-first international conference on Machine\n",
"learning. ACM, 2004\n",
"\n",
"[3] Kernel Methods for Object Recognition , Christoph H. Lampert"
]
}
],
"metadata": {}
}
]
}
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