{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Coregionalized Regression Model (vector-valued regression)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### updated: 17th June 2015" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### by Ricardo Andrade-Pacheco" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This tutorial will focus on the use and kernel selection of the $\\color{firebrick}{\\textbf{coregionalized regression}}$ model in GPy." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Setup" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first thing to do is to set the plots to be interactive and to import GPy." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline\n", "import pylab as pb\n", "pylab.ion()\n", "import GPy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For this example we will generate an artificial dataset." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#This functions generate data corresponding to two outputs\n", "f_output1 = lambda x: 4. * np.cos(x/5.) - .4*x - 35. + np.random.rand(x.size)[:,None] * 2.\n", "f_output2 = lambda x: 6. * np.cos(x/5.) + .2*x + 35. + np.random.rand(x.size)[:,None] * 8.\n", "\n", "\n", "#{X,Y} training set for each output\n", "X1 = np.random.rand(100)[:,None]; X1=X1*75\n", "X2 = np.random.rand(100)[:,None]; X2=X2*70 + 30\n", "Y1 = f_output1(X1)\n", "Y2 = f_output2(X2)\n", "#{X,Y} test set for each output\n", "Xt1 = np.random.rand(100)[:,None]*100\n", "Xt2 = np.random.rand(100)[:,None]*100\n", "Yt1 = f_output1(Xt1)\n", "Yt2 = f_output2(Xt2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our two datasets look like this:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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tmUxGpVJJJy5dkkol/U9/8ifKZrNVx/zc9LTe7uvTL/zoR8EOxiQAANY5QjKA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\nXczX1tuabds8kapIkQG0ZneH/f39SF3u6enpZvyNKuwWcnR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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xlim = (0,100); ylim = (0,50)\n", "fig = pb.figure(figsize=(12,8))\n", "ax1 = fig.add_subplot(211)\n", "ax1.set_xlim(xlim)\n", "ax1.set_title('Output 1')\n", "ax1.plot(X1[:,:1],Y1,'kx',mew=1.5,label='Train set')\n", "ax1.plot(Xt1[:,:1],Yt1,'rx',mew=1.5,label='Test set')\n", "ax1.legend()\n", "ax2 = fig.add_subplot(212)\n", "ax2.set_xlim(xlim)\n", "ax2.set_title('Output 2')\n", "ax2.plot(X2[:,:1],Y2,'kx',mew=1.5,label='Train set')\n", "ax2.plot(Xt2[:,:1],Yt2,'rx',mew=1.5,label='Test set')\n", "ax2.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will also define a function that will be used later for plotting our results." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def plot_2outputs(m,xlim,ylim):\n", " fig = pb.figure(figsize=(12,8))\n", " #Output 1\n", " ax1 = fig.add_subplot(211)\n", " ax1.set_xlim(xlim)\n", " ax1.set_title('Output 1')\n", " m.plot(plot_limits=xlim,fixed_inputs=[(1,0)],which_data_rows=slice(0,100),ax=ax1)\n", " ax1.plot(Xt1[:,:1],Yt1,'rx',mew=1.5)\n", " #Output 2\n", " ax2 = fig.add_subplot(212)\n", " ax2.set_xlim(xlim)\n", " ax2.set_title('Output 2')\n", " m.plot(plot_limits=xlim,fixed_inputs=[(1,1)],which_data_rows=slice(100,200),ax=ax2)\n", " ax2.plot(Xt2[:,:1],Yt2,'rx',mew=1.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Covariance kernel" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The coregionalized regression model relies on the use of \n", "$\\color{firebrick}{\\textbf{multiple output kernels}}$ or $\\color{firebrick}{\\textbf{vector-valued kernels}}$\n", "[(Álvarez, Rosasco and Lawrence, 2012)](http://www.nowpublishers.com/articles/foundations-and-trends-in-machine-learning/MAL-036;jsessionid=0659F0627887C5F2742261E8D6D1FBF7), of the following form:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\n", "\\begin{align*}\n", "{\\bf B}\\otimes{\\bf K} =\n", "\\left(\\begin{array}{ccc}\n", "B_{1,1}\\times{\\bf K}({\\bf X}_{1},{\\bf X}_{1}) & \\ldots & B_{1,D}\\times{\\bf K}({\\bf X}_{1},{\\bf X}_{D})\\\\\n", "\\vdots & \\ddots & \\vdots\\\\\n", "B_{D,1}\\times{\\bf K}({\\bf X}_{D},{\\bf X}_{1}) & \\ldots & B_{D,D}\\times{\\bf K}({\\bf X}_{D},{\\bf X}_{D})\n", "\\end{array}\\right)\n", "\\end{align*}\n", "$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the expression above, ${\\bf K}$ is a kernel function, ${\\bf B}$ is a regarded as the coregionalization matrix, and ${\\bf X}_i$ represents the inputs corresponding to the $i$-th output.\n", "\n", "Notice that if $B_{i,j} = 0$ for $i \\neq j$, then all the outputs are being considered as independent of each other. \n", "\n", "To ensure that the multiple output kernel is a valid kernel, we need the $\\bf K$ and ${\\bf B}$ to be to be valid. If $\\bf K$ is already a valid kernel, we just need to ensure that ${\\bf B}$ is positive definite. The last is achieved by defining ${\\bf B} = {\\bf W}{\\bf W}^\\top + {\\boldsymbol \\kappa}{\\bf I}$, for some matrix $\\bf W$ and vector ${\\boldsymbol \\kappa}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In GPy, a multiple output kernel is defined in the following way:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " \u001b[1mB_K. \u001b[0;0m | value | constraints | priors\n", " \u001b[1mrbf.variance \u001b[0;0m | 1.0 | +ve | \n", " \u001b[1mrbf.lengthscale\u001b[0;0m | 1.0 | +ve | \n", " \u001b[1mcoregion.W \u001b[0;0m | (2, 1) | | \n", " \u001b[1mcoregion.kappa \u001b[0;0m | (2,) | +ve | \n" ] } ], "source": [ "import GPy\n", "K=GPy.kern.RBF(1)\n", "B = GPy.kern.Coregionalize(input_dim=1,output_dim=2) \n", "multkernel = K.prod(B,name='B.K')\n", "print multkernel" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The components of the kernel can be accessed as follows:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "W matrix\n", " \u001b[1mindex\u001b[0;0m | B_K.coregion.W | constraints | priors\n", " \u001b[1m[0 0]\u001b[0;0m | 0.67770340 | | \n", " \u001b[1m[1 0]\u001b[0;0m | -0.00412505 | | \n", "\n", "kappa vector\n", " \u001b[1mindex\u001b[0;0m | B_K.coregion.kappa | constraints | priors\n", " \u001b[1m[0] \u001b[0;0m | 0.50000000 | +ve | \n", " \u001b[1m[1] \u001b[0;0m | 0.50000000 | +ve | \n", "\n", "B matrix\n", "[[ 0.9592819 -0.00279556]\n", " [-0.00279556 0.50001702]]\n" ] } ], "source": [ "#Components of B\n", "print 'W matrix\\n',B.W\n", "print '\\nkappa vector\\n',B.kappa\n", "print '\\nB matrix\\n',B.B" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have built a function called $\\color{firebrick}{\\textbf{ICM}}$ that deals with the steps of defining two kernels and multiplying them together. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " \u001b[1mICM. \u001b[0;0m | value | constraints | priors\n", " \u001b[1mrbf.variance \u001b[0;0m | 1.0 | +ve | \n", " \u001b[1mrbf.lengthscale\u001b[0;0m | 1.0 | +ve | \n", " \u001b[1mB.W \u001b[0;0m | (2, 1) | | \n", " \u001b[1mB.kappa \u001b[0;0m | (2,) | +ve | \n" ] } ], "source": [ "icm = GPy.util.multioutput.ICM(input_dim=1,num_outputs=2,kernel=GPy.kern.RBF(1))\n", "print icm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we will show how to add different kernels together to model the data in our example." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Using the GPy's Coregionalized Regression Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once we have defined an appropiate kernel for our model, its use is straightforward. In the next example we will use a\n", "$\\color{firebrick}{\\textbf{Matern-3/2 kernel}}$ as $\\bf K$." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Name : gp\n", "Objective : 376.744145175\n", "Number of Parameters : 8\n", "Number of Optimization Parameters : 7\n", "Updates : True\n", "Parameters:\n", " \u001b[1mgp. \u001b[0;0m | value | constraints | priors\n", " \u001b[1mICM.Mat32.variance \u001b[0;0m | 1.0 | fixed +ve | \n", " \u001b[1mICM.Mat32.lengthscale \u001b[0;0m | 178.415052332 | +ve | \n", " \u001b[1mICM.B.W \u001b[0;0m | (2, 1) | | \n", " \u001b[1mICM.B.kappa \u001b[0;0m | (2,) | +ve | \n", " \u001b[1mmixed_noise.Gaussian_noise_0.variance\u001b[0;0m | 0.352294081182 | +ve | \n", " \u001b[1mmixed_noise.Gaussian_noise_1.variance\u001b[0;0m | 5.06765701728 | +ve | \n" ] }, { "data": { "image/png": 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YpAW3NmzKxs3byTh6Ar3Rn6DQCHRGP4ptF5gpUSmeXzuLuO3LAUhqEMvoVr19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\nIqaEi7d8tONYotEYtVUB6sJVRdvOZFBZf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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "K = GPy.kern.Matern32(1)\n", "icm = GPy.util.multioutput.ICM(input_dim=1,num_outputs=2,kernel=K)\n", "\n", "m = GPy.models.GPCoregionalizedRegression([X1,X2],[Y1,Y2],kernel=icm)\n", "m['.*Mat32.var'].constrain_fixed(1.) #For this kernel, B.kappa encodes the variance now.\n", "m.optimize()\n", "print m\n", "plot_2outputs(m,xlim=(0,100),ylim=(-20,60))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that the there are two parameters for the $\\color{firebrick}{\\textbf{noise variance}}$. Each one corresponds to the noise of each output." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But what is the advantage of this model? Well, the fit of a non-coregionalized model (i.e., two independent models) would look like this:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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43T+F0B2ri+59ctMeDPlpLi/GRgEwr2I9NrfrRHjzBrg4GnBxNJCfm8nsGV+x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Mh4Lr1pPDljJ/DEN9+ywqgjwbdd+YhROAYMrvKaLS8vZ/IH74Ddyo6rribcZqXd/r1kN2lKyFvv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\nJuHqwJ+KioqKispfBPUbv5Hwe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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "K = GPy.kern.Matern32(1)\n", "\n", "m1 = GPy.models.GPRegression(X1,Y1,kernel=K.copy())\n", "m1.optimize()\n", "m2 = GPy.models.GPRegression(X2,Y2,kernel=K.copy())\n", "m2.optimize()\n", "fig = pb.figure(figsize=(12,8))\n", "#Output 1\n", "ax1 = fig.add_subplot(211)\n", "m1.plot(plot_limits=xlim,ax=ax1)\n", "ax1.plot(Xt1[:,:1],Yt1,'rx',mew=1.5)\n", "ax1.set_title('Output 1')\n", "#Output 2\n", "ax2 = fig.add_subplot(212)\n", "m2.plot(plot_limits=xlim,ax=ax2)\n", "ax2.plot(Xt2[:,:1],Yt2,'rx',mew=1.5)\n", "ax2.set_title('Output 2')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The coregionalized model shares information across outputs, but the independent models cannot do that. In the regions where there is no training data specific to an output the independent models tend to return to the prior assumptions.\n", "In this case, where both outputs have associated patterns, the fit is better with the coregionalized model." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\color{firebrick}{\\textbf{Can we improve the fit in the coregionalization?}}$\n", "Yes, we will have a look at that in the next section." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Kernel Selection" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The data from both outputs is not centered on zero. A way of dealing with outputs of different means or magnitudes is using a \n", "$\\color{firebrick}{\\textbf{bias kernel}}$.\n", "\n", "This kernel is just changing the mean (constant) of the Gaussian Process being fitted. There is no need to assume any sort of correlation between both means, so we can define ${\\bf W} = {\\bf 0}$." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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HABsXLwR31tTj22Yh/J1zueK6PzGsoSFs7hzyIwcX1g37nlyLguIzOX7suDe7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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "kernel = GPy.util.multioutput.ICM(input_dim=1,num_outputs=2,kernel=GPy.kern.Bias(input_dim=1))\n", "m = GPy.models.GPCoregionalizedRegression(X_list=[X1,X2],Y_list=[Y1,Y2],kernel=kernel)\n", "m['.*bias.var'].constrain_fixed(1) #B.kappa now encodes the variance.\n", "m['.*W'].constrain_fixed(0)\n", "m.optimize()\n", "plot_2outputs(m,xlim=(-20,120),ylim=(0,60))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At the moment, our model is only able to explain the mean of the data. However we can notice that there is a deacreasing trend in the first output and and increasent trend in the second one. In this case we can model such a trend with a \n", "$\\color{firebrick}{\\textbf{linear kernel}}$.\n", "\n", "Since the linear kernel only fits a line with constant slope along the output space, there is no need to assume any correlation between outputs." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We could define our new multiple output kernel as follows:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "${\\bf K}_{ICM} = {\\bf B} \\otimes ( {\\bf K}_{Bias} + {\\bf K}_{Linear} )$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, we can also define a more general kernel of the following form:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "${\\bf K}_{LCM} = {\\bf B}_1 \\otimes {\\bf K}_{Bias} + {\\bf B}_2 \\otimes {\\bf K}_{Linear}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "GPy has also a function which saves some steps in the definition of \n", "$\\color{firebrick}{\\textbf{LCM}}$ kernels." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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X/INtm7/jpYoA5Z4SfrF6Ob/JW8ebKTVcMeMvlHp97CnUpyLq0xHLOFDkpbCk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\neJrtiYcV9z0QW26yZ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DCsE/EC2wJ2zrhMIW2cBD6wb1cAn0L2//ZiPvATrfUZ\npVQF8AVk23cE8Z83w7A+bxTyGdRutCYyOZ52qzjHNf/F/7sx6WEiJtqXX2AduCAHa7vRyEEr70M7\noLX+ld2YprG8zRKX2b78kvp9PQ/4E7L/txta6zP2/xuxvmNl22cY29c/Rin1ZYhZZhI+b+QzKHMk\nb/90RCZnbHJgS7HFxHL79iQs39UYrfUK2wv3uuxM6cdOLDmA1SwiUYEZxj5o12Dt3wXAF7TWm+R9\nEHoK9r7ufL5/K+4+2f8zjP1degAocLazbHtBaBmdQjiLmBAEQRAEQRA6O51COAuCIAiCIAhCZ6dT\npGoIgiAIgiAIQmdHhLMgCIIgCIIgNAMRzoIgCIIgCILQDEQ4C4IgCIIgCEIzEOEsCIIgCIIgCM1A\nhLMgCIIgCIIgNAMRzoIgCIIgCILQDP4/D8miwtXBihkAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "K1 = GPy.kern.Bias(1)\n", "K2 = GPy.kern.Linear(1)\n", "lcm = GPy.util.multioutput.LCM(input_dim=1,num_outputs=2,kernels_list=[K1,K2])\n", "\n", "m = GPy.models.GPCoregionalizedRegression([X1,X2],[Y1,Y2],kernel=lcm)\n", "m['.*bias.var'].constrain_fixed(1.)\n", "m['.*W'].constrain_fixed(0)\n", "m['.*linear.var'].constrain_fixed(1.)\n", "m.optimize()\n", "plot_2outputs(m,xlim=(-20,120),ylim=(0,60))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we will model the variation along the trend defined by the linear component. We will do this with a Matern-3/2 kernel." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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JoJGblU5QgA/lypTCy8OMl4cZbw8zXlYzNc8Uh3j37vfXKkOFF1vi5WnBy2oi\n+L11AOw0WajltAMUfFjqmLWdnv0HUaJkSXRdR8XGEjJ5CxlVa1Bt/y5ymzzAyYwqVDt2gF8q1Gd9\nSF0sSmHxKYEDeGnsz1iNGkmJiew/NQl/cw7z5nyN2WygZ89nSMlycDolG7NR4e9tI8DHdvt+GyGE\nEEL8Q5JxLuqu1Grsww8ZphRvvvUWL774Ipqmc2jiZGq98S7dej7j7sqRH+w4nBq7j5zjt90n+X3v\nSc6l5lyS8VzQ4BFwZtN2+8/E+Jdgd99+vPzKK4Di9OnTLF78I05NZ/+nozhVrxHly5Xju+/mM+D5\nfrxW4y7Mjz6MxWz8V/Wyf5UtvhKH04Xd4WL4iNF88ukY2rfvwJFjx9m9Zw9hedmssnnS9vG2lClT\nmvFfjGOFTVHrwF52mm3UcuQCcLpcFfZVrMVDq79jbu02uDSdyPilzK7RGlBE7ro0C2yxmPD3tuLn\nbSU9+TSH9u3CZc8myN+b0ycS0Zy5VKtckV07t/JoRGt27djC/r27AOjUKZKXX36ZS1qYX1SPnBHV\nD6BgOfWDEdhWLqd4xyfYUeUuah/YS7RPAFWrVKXZlo1ktnkE79jFnJr1HXlhrQuywra4ZeQ2b4n/\n268X1DlnRzzKuw3vY8bXc3j4ic5kOG3sSjhNQOmq2DXTRbej42POI+LBOtSrWoIqIYEY88/rcDrJ\nzXNgMSqy0pLYNeJDIqdOgfMfnrp0IWT3buncIYQQ4pYiGefb2eVBiVLw1lt0TUwEpS4EnSWC6dr1\naUqU9ONcWjaZOTm4dIXNaqFO5WDqVA6m1/9qc/RUOjsPneWXuwZhmmmg/ebFgDtQjG7cBUuyiw+n\nryf97BEsWibLFs7h7dpVef/MMaLXZfD2nhL07t2LIScT8XlvCPGfxzArLYsunbpgNML0aVN59NFH\nKVuqJAajwmw0YjYbsa5cDq3DUQaFQSkU8Mubb/PW119z8vRZQDFuwgRyHIr+/Z/H7tT44+RJFi1a\nRPcez+DSYOM7b1LlhZfoX6Uqp7t1Z8GCBTTPzaKqpyeTzxwl2rcYcxKTuS+iC5ODvqPWtlWsLFOL\nFn/sLHj7VvpUZHTlx3k5KYvIHbEALGncltWPR9F23qcF+5X1sfPpc/dSLqR0Qe3v6dOnmTv3NF5e\nXvTs2ZOpU6eSmZlJixZh/P57KD169GD06E/zA2eFpkGe3YmW31UDwLZyBT7R40nu2Yezbw7FoMDl\ncuEfPZ6LNXHsAAAgAElEQVTsps3JadGKaZ170OeHhYx67Cl2lytP/5hoJnfuwaNffIFz+XJUi5ZY\ndHcXD13TyXqoGZrDjtPlKrj/3FJleOLJdnj7+NCzZ08Apk6dSkTEg9iVB5/FzGPPsTRsgeXIdNqY\n9/M+5v28D38fK/dWL03jmqWpUbEYPl4enD59moXP9WfomuXEbY/nLS9vNqxbTcvFiwlZt07a3gkh\nhLhjSMb5NpbncJKUlkNWrhOnS8diMWEx539W0nX83nwN3xh3hvKb6g8y4p5uGCwefzqPKy+Ll36d\nRtdD65laujqlSwYRvmUtG+5vxtL/PcH4CROpU6c2FSpUZMGCBfTv34+ePZ9B13Vcmo41bhmlOz9F\nyrN9iX/uRWJjY3klYQ+BUybxSv37mZmUijIo2rfvQGCAH4888gilS5Vi6tQpjBs3nk6dIrnr0AH6\nzJ3J3hq1uGvXTr6tVJP0LDs9T+0nrmQ1wk65B+rNrhkO4M4i392a+qf2Ui3ZPcgusXQlQk4cYnfb\nLnh7Wig3ewoAGb2fA6WumAVOHvoxTk0raD2n6zpoOgaD+xOrQeX/NChioqP59NNP6dG9K0rXiYmZ\nxJAhg3lt0CvutnNGhclgwLh82V9OWPJPM/GX18Jruo5h7Fhy+vbj7Dsf4nDpOJwaulKYTSZmfT2j\n4H116YoFyzdyb4vHyVKBnEnJLjitt4eZAFMm/qZ0Fs+dzBdaDu2PJRDtE0hAQADtjx3C+fwLmMaO\nufAsQgghRBH3XzLOEjjfIZwujdSMXNKz7djtToLff5vAKRM53aUHh48cofHaVaxq0JjOmQqLXynq\nNm5BUJkq7Dp0CqduvOKAtlGNOuJl1cnNOEda0ilceRk0rHs3ke0eI9DXk0BfG5npycT+tJiXDu3F\nJ3o8C6tU59SpU0RlpFwYjJcfdBUrVoxz587Rq08/cp1G7q7TiOU//8qWnfswWX0YemwT7eJXFgx8\nAwqWZ9cIBzQid7nrkaeVqUFNKzRM2MVOi42sRvfS+NfV2GvUwrLLnYHOiOqHrlPw4SGpZxTn3vkQ\no0FRfOhb+E2eSNKcb6FNG6z55ShGo6GgDOZy/zjgvV6ucaZBu8NFZo6d/YeOsGDRT3Tr3hOr1cRX\nM2fw8MOPEBwczJiJM1i0agclq95DjstScAmj0kg7tp1Bm+bx7Dn3e5/eux9p9zclp3kYQX4eBPp6\nuItSZNZCIYQQRZgEzuKfyQ+0MqOe4/TbH2B3aJT44C0Cp0yiY3AIP3t406lTJP7+/owfP4GI/7Xj\n6MkUuq2Po+eJPQB8WzeC4Q07XUOmUUdz5OFhMTBw/Sza71wBwFdV7mdE3bYogxGT2YyGEYPJijL9\nxUQtlwXv500JDiWmTgN6bogjKsPdpm9PjVpU37WT7IhHGflQS1q2jqD6uNEETnH3w059tg9pQz/C\najYS8M4bWCeMQ/txMYZHHi641i0VAP6LabftDhepmTlk5jjJc7gwmox4WM2MHj2aWbNmY/IKokmr\nDhj8KnL4ZNqf3v/46rWpuWcHGVH9OPPOMBx2B2WGvY1PzEQp3xBCCFFkSY2z+GfatIElS/AOD8c7\nP9AaWj6E3yyelO3YiScMJqbP+Jpu3brT97nn6PVMT/zfeh2fE3s43aUHnp6ePBU9nkBjKl1zrZg8\n/SldrhLBpSuwPyGR8pWqY/UKIDkjl5w8JwazjTxNd2eu8xmt3lj9ShUEehfncDVHLt42A15WOLx/\nF3dXLY/V4GTtz8uwZB/jcpVCgum5fjlRman8EdkND5sH1adOIjM8gnMx0+ltNeNpNeEx/nP0dm1R\nSuEfHo7/+SBz3Ofw2KMYLg70lLq1Ar8r1cL/zf1bzEaCA7wJDnAPEkzPziM5LYecXAc6BpxZSYR4\npuLvdZhf137Dp5qTDvs2XlIOc6RkKBWix+Ny6RiNCp+YiST17ENG7XspmefA9nPcPw7ohRBCiKJK\nAuc71WWBS8+e3TCZLgw2DCnmSYeOHQksVgLX4iXuAW3P9CH57Q9INRhJjt9F83WrefWxDixGsX3T\nT4T3e476ISE8/HDTglnzXC4Xn4weQ52YcUSmnOLbSjVJSU2lV/xSilky6ZlnAl1Dc9nRnHZ0Zx6g\n06lTJJ06dWbJkiz34DZd54/fFtB4255LumTk3l2Tpps30BQ427kbATHRWM0m8LXhPWYM3jt/u/RZ\nIyL+/F7cakFyIVBK4edlY9yY0Uz69H2eH/AiTixMmTqDHj168nGTWnSYMpH03v1YX7om+FXCOM1A\nhx1LWFW+Ps2+nADA6e5R2D8ehQE4MGkatQZGYe/XH/PnY/noo494ISEBnylTJCMthBDiliSlGuLa\n5JcCaDrYHU4OHjrCpmHDaDpiNC5N58spUwmPeJgSwcEYDEaUQWE0KGbOnM7eUSOZcyaxoKb53nvv\n5esAL3yixxMT2YOvU9LZs2cPoAgqVowmTZqwaNGP9Ordm66du2AwgM8vKyndtQMLjGbauhysqlOH\nbdu38yJA27awYAH89NOFwFgym//Kleq023WIxOYdiFq6lJwWLbHZ3OU0eXkOjk77BvuPPxGxYQEA\nc2qGs+aZV3nkvsqsXPQ1Vcd+QlRGCnF1GhK/cysDNRcMGOD+vVzpQ4wQQghRyKTGWRQZTpeG0+nC\n7nThcGocO3ac+d99x8AqlclpFsakmGgee6wtpUqUwLYqjjEHDvHp6E9p164dBw/uZ9NvGxgy+HVM\nBkXXrp2pUL5cQc3z2ZkziTl2jCH160N4OB999BG9y5WjeJcuEiTfIJnZeZxLyyHX7sJsNhH83hv4\nRI8nMfJZDp9K46Gf5xf0wPY0O6i4cirT9q0pOH5euVAee7gN1onjmdO9O/e///5Nm0hHCCHEnUkC\nZ3HLummdKMR/omk6md8vwLfdEyQ/04eMYZ+4p3J/7RWKT5vEkCfeYEWxu0HTmPndEO5K+QOAnWYr\ntRx5xNVtROtdu3j/3Td54403bvLTCCGEuJNI4CyEuDliY8lrHsbplGyycp1YLCZ81/xMRtOWDBv7\nFc2/m03nfb9c0kJwp8VGyxLl6dCxE/379yM4wItA3z/3DxdCCCEKw38JnK/ckFYIIa5FmzZYrWbK\nlfTjrvKB+HqYSG7yIE6nk8ZHNtJ53y9MKRHK7wHlCg6pZc/lEf8KYDDi5eVBUkYeiTPmkpSWffXr\nCCGEEEWABM5CiOtCKUXxAC+qlQuiZICNbaVDeLpYCKFlitPl4Fq+DK5IXMm7AHj9jz2sOxnMSx9M\nI/DtwYR0f5q8H5ew71gSZ1IykW+fhBBCFEUSOAshrjtfLxuvD+zNYw+3oNmWjST17MPcxo2JcWYA\nUC35GKNWTeKpFYsImuqelMbhcOHp6UFGrsbeY8mcOpeBpuUH0LGx7k4p5+m6e50QQghxAxVK4KyU\n+jj/Z++L1j2llAq7eJ0Q4vYVEhJC5+nTYMkSfCd9QczE8QR0fYZoL38Amh3bTOSu/Cnca7Smy+8u\nvnruTY4mnsDby4McF+w7mkTakLfdreteeskdMOu6ezkiQoJnIYQQN1RhTYDSWyn1JNAHQClVH0DX\n9TilVKhSqp6u61sL6dpCiKKkTRvMQEhJPyxaBgOVmcZmK7UdeQDE27yZ+uCT1EvYypDYz5izdw9r\nB73L4w9WoeLH7+ATPZ6MVhH4jBmDS9MxGhSMGQMDB7pnJRRCCCFukELpqqGUekrX9W8vej0cWKbr\n+kqlVBhQX9f1kZcdI101hLiNDRs2jDfffJNVdevSdNu2S7ZF+wTwfrk6jDUaeGLHSmbXDMeoFB12\nxnKmexR5I0bh99br+MaMB8D5/AuYxo65MJW3EEIIcY2KYleNwPyyjFfzX/sDyRdtDyqk6wohiqiu\nXbsyu1u3gqD5tyZNSOveA4CojBTuP3OQXx5uyvHOzxIZv5QOO2OZXTOcx6wPMWb+ZjJy7AXnSs+2\nc+iPFLJy8m7GowghhLhDFUqphq7rMQBKqVb5GWaAv43s33333YLlZs2a0axZs8K4PSHETRASEkLH\nyEiYMQMGDOCezz5j2LBheAIvAvc1aczQr2bzdPkSlM0/pkwxb3RNo8GEjygTv5S4B5+gUpkAKkyZ\nhNlk5PibH2BQWdizk1nw7VyZSEcIIcSfrFq1ilWrVl2Xc/2rUo2rDPBL1nX9W6VUFJCUv/wqkApU\nApbn1zi3AypKqYYQd6jYWHdtslLumSNnzCiYRv23Bx7k3vXrSOrZB7PJiG/MeFLCIgiIW8Lc2m0Y\neU9nAIbGzydiwwJOz/4ee8vWRMd8ydgxn9G5wxNYDC7GjPmMDz/8UGYlFEII8SdFaubA/AzzJl3X\n0/Jrm+fgzjY31HU9Jj+YXq7r+rbLjpPAWYg7WWysu1PGwIE4Rn7CyXOZeL05mKCpk0gd/DbHo15k\nycbD/LT+EJnZdpoc38HRevfTz+MUv5rzOHXyJAsWLsSe52Boozr0/XYOZpPxZj+VEEKIIqZIBc7g\nHhyYv1hR1/VP8tf1BhKA0POlHJcdI4GzEHe6i7LRAA6Hk5T5C0i6rxk2qwWTyUiu3cmwcd+w7Zid\nB88dZWzsSGZVb8EXNe7h8NalvHfmCFEZKUzp2pu7X3qJejWqYLUUVgMhIYQQt5oiFzj/GxI4CyGu\nxuXSOJ2SRXqWHYvVjNlk5JNRo1m4cjvvp56hy/41zK4Zjq5pdNq9nMkBpXjTx49+/fvRoWNnzAYI\nDvDE18t2sx9FCCHETfZfAmdJwwghijyj0UDpYj6UDNQ5l5ZFcnoumgbZp3fziq4TWLsJkTvyJ1Op\nGc6kxl2omHuKhg89ipeHhWnTptE8rDUligfh722lmJ8XBoP6U4YbXYelS6FNm5v4tEIIIYoqCZyF\nELcMg0ERHODN5AljGf/Zx/R+biBGk4Xj0WMK9nFknEV3OXF5lOLdKevwNOaRuH0NLg06+3vzRXI6\nHSM7UWzdKoI7tye7dWs8z89A+NJL7slVliyR4FkIIcSfSOAshLjldO3aFYAhgwfjfGEg5owUVjVo\nwv79+4g6uoWyO6Lp41MDn3INybZ6E1TzMewbd1P1+2GE+BUnJj0VXdN51myl1rJlOP7XFnPlUJmR\n8HZ1tW8WQL5xEEL8I4U1AYoQQhSakJAQ3njjDdSyZZjHfwEDB1J+3iyOvjyI5J59aLF5Pe1z9/PH\nL1+QFL8IT2MeK4KqM7tmOL3TzlJ39g+Ejx9LLUce9pq1MS9eBGPGkN3mEfJGjHQHUrGx7kAqNtad\ngda0C+uWLHEvi+suMTGRYcOGoWkaLpfGq6+9zqBXXyPP7iTX7mDo+8M4cOgw2bl2snLsZGbnkZmd\nR/YPC8nIzCEzO499BxIYOvRD8hYu4sTUaRARQXqvXuiaxrAPPySjVy93B5eICPe3DLru/uell9zr\n5HcrhLgKyTgLIW5dbdq4g9jwcCoqxYfvDkFzaUy35zF+xRq6du+OyQizZn1Ch54DWNX9FZgO3ePd\n2caDQWXJrVCdmvE7APCMXczUXs/TqGEDag7sg/bYYxgWLnRfq25d2LYNHnsMzq+7E0s6/q4u/KLt\nmqbjcDrRfoolu3kYDocLu1ND13U0QNP0gmVdd//PtGnzmRQ9k8Qk96yQ8+b9iEInBy9AcW7GFF7c\nvp/Xhwxh2dKlgE6vxMNUmDiGc81akjT9G76a9yNlP/kUa0YSP1WpgdM7gL5TphC3NR7/fXvxyU4n\n/dk+KAU+Y8bgdGkYDQo1dqx84yCE+EvSVUMIcdtJTExk5syZ9O3/IufScpj+1dc80fZ//LT4R0p/\nPJxeyScu2X9vQFnuSjkOQLRPAKfefJeBB/fiN3kCudVrYNuzy71jsWJw7px7ecAA+OyzCwHk7ex8\nMLx0qTsjO2CAO1Bu0wb9xRdRY8eS8e0P5OY5Kd6pHRmtI/hj4nQ0pSj5/lsETplE0qtvkjFoMEaD\nAXQd28rl5Ia1vsLFdEaPHs2sWbMBiIyMBGD27Nk0z8lkzplEon0CmN+sFdu37+D9lNNEZaTwu8VG\nI3su9pq1ybvvAXyix7PTbKWWI49B9RpT9eA+ojJSAMiI6kfqByPQNB2/N1/D/8sJAKQ804eUoR9h\nMRvw8bLiZbNgMsoXs0LcbqSrhhBCXOR8KQdAoJ8nb7zUh1NJWTyz9XfKJp8gI6of+uHD+C5fAsBd\nKceZXaM1OhC1axmrdE/Ovjccg0HhEz3+wonzg+bcvv0wfjKKU8ePM3PmzNt3qu/zpSkPP4w+YAD2\n4SPIbRGG39ixMHYsGa0i8Fm+hD8iu5FzbzMsZiPZEY/is+RHKjW/l9zWbfCZMgmAoJEfYjQoMl4Z\njP9br+ETPZ7DU+dy+t6HyMxxkJXrICvHTlaOg8Rsf/yrtECZrPx+3IyPXwDF63VglzIyZ28cUXtW\n47nvJNiK0yVjL19XfYhJTbsybcEwQuN3YInfwYGgEGolJTIz9B7WVmlDzXNZkB84p2XmkZ6Vh4+n\nBaPxwv93mkxGzBYLGnAmLQ9nUjYGwGwy4Gkx4udtw2Y1oe6ED0tCiCuSwFkIcdvz8rBSKf5nmDOT\n9F59+WPIe1gtZjzuq4f56GEAnNkpjGn2HBtC6rA+wQPbh4t5f99pml3hfLkOjZMn0tjw1lA+XLQY\n341b2FehHF+M/ZTQ/fvpOG3ajXy8/+x8hn7IkCFoPy3hw81b6VayFBX6PEvaM1EYWkXgM3Ys+oqV\n+O2OLzjOZ/kSd4a+bkN6Ws0AnJkyi5L31MJ29DDmmAmcKV+V4KP7AfD/+AN2f7uMkIO/MbtmOKN/\nzYN1K65wR4H4VmwCgB1IsoNH8SoAjLq/IrrRRpf4C+0HP2vcBXTYWLwqoWfcv88qSYnMrtGasY27\n8PLGr4lM3Mnsmu4SjMhZX7Jm+3HMJkW77bH8GtYeH08LtaPHk2t3ceTlV1kSu4SePXsCMHXqVMLD\nI/APCETTNMxGAzaLAX9vG14eFgmkhbiDSOAshLgz5NdD+4aH463p5PR/AfPRw+yuXou1x48Tdfh3\nygaa6GULJdRyN8+snkOz+KXsCwyhWnIiAHme3lizM/H/ciKWPxKpHruYVsElKbvwW54uXo64evfS\nYvp0pjpNNBsxEpPRQPTE8XTp9DQVypfDZDRgzP/q/+JgFW5MtlrXdZwujSNHj/HV17Pp9/wL5Nld\nPNv3ZTb+/jvev8cz4IfZlPAJYsrgtxnU+zn8YtxlDMmBQQTmB80HffyonJEGQEjlWpwt2YjhMzdw\n4lwmp5IyGeBTjUiOAhB8dD/7AstRLfkYAPflB82f3dcVXw8LXh5mvDwseNnMeHmYMehOTv5xlCb3\n1MfDYmL6tCmcOH4MXXPS7KEH2br5d7JO7ip4pqwT8fieXUnkmqVEJp8g664aeO11b3/YnohfySQe\njl/Khpbt2P30i2yN34e3zUTkpsWAO/AeXfExAF6ueY7IaZMYdtqH5TZfth2fircpj+WL5gDQs+cz\nBdd1aTp/JGejuTKxmAx4WE0E+tiw5X+AEELcniRwFkLcOfIHsBmWL8Vr0ngYOBDV93kOz/mOpGMJ\nNJ86iaHP1qVRLag6bimH7mlOtd9+BigI/hK9ixGSeQ7P2MWklihL2dPH2WmxEZabQYutx9hwf1MG\nr/mVTl98ga7D7DnfgMWbzl264LlyBVlNm2MwKKZNm8u4z6Px+W07u8uHMmPmdDIdRvr26YtS7tJp\ng8EdZBsAS9xyclu0zB90p4GuY1kZBzrkNg/jxKlTLFy4kN69emH9OY4vEo7wyCP/o3iJYHRNdzeO\nwF3b99U3i4iZOofUHBcGBTt27aJxk8Z8uGUrNp8A+mQkkXF0P07twriTwOSkguXKGWnMrtEalCJy\n61JSR77LD427APDyhq+I3L2Mo6VCKX8yAYBqycdIrliNwMP73L+Ge0O5//22KMPV6ofvy/+ps2d9\nILM2u7PL/uYGjEo7RMuk40T7BFCsWDF6HT7AkxmJBCafIOuu6njt3UVG7+ewrv8Vv/gdNNsSx9k5\n31OmRSuilILH64H+NGdWLicz24HPXQ155kwGiWcy+Kn8ALaG1mdtiRp4AIk57rso2+xFNpz1IGn2\nb1QLCeTuisXwNOQSG/tTQVY6esoUwsJaU7xYMaxmIz6eFvy8rZhNRvdJZLIdIW4LMjhQCHFnuiyQ\ncTicpH+3kHNNmqIMRvx/XUVei1bYVi4nK8fB2lI1yF74I3NNFXjrh+E0O7YVgH1B5aiW5M6mzqjY\niCn3P4JuTydh73ZcuRk8Et6C//u/t7DFLad4xycKBqbFx+8kqVN7upw6TsfgEPZUrMzw4R9Rs2Yt\nwJ0dPv+fRNvKZZSIfJL03v1Ief9jlAL/t1/HN7/+OiOqH59Wuotx48YzN9ifpps20DE4hP/971Ee\n+mjkJcGae1Beq4IBeEarN23+145cl4nft+/FZPPjg+NbeWpnnPv5LsoWH/cuTtnMswDMqdmK6Pvb\n02PpJLod2cyqj2II8vOgVr8u2GvWxhK/A3vNWljidxa85Rm9nwPlrhs//z44NR2XS0PTNDTd3WUD\nTcdggGnTpjFu3Dg6R0YCOie/jOaHzCRW1m3AvAdbMG36DFZUr8z9G38ls11HvOfPIb1XX1LeG4am\n6wQ/2wWvpUtInP4NWU3D0FEYDAqj0YjZZHTPHnkZXddJSs9h9PjpbNyRgNWvNF5B5XDplwb5JoNG\nxulDVC8fiJ85h0XzZ9C/33MFWWm7w4nd4eTcmdPkvDaQ1j8vRx8wgI+Cg+napQshAwfCggV3ZmcW\nIW6y/zI4UAJnIYS4TFZOHklpueTkOcFgwMN2oY5V1zTMg16m1MwYAPb4l6Z6qrtLx+ya4Yxu3OXS\nThu6ToCvB4E+VqJWTqXFmu/Y1CaSo0cO8dTe35gSHMq7pSqjOfOoXfMuXhv0MivjltGje3dMRsW0\nadN4OOJhqn0+qiDgBC4s6zo+MRNIebYvW7ftoMXmdUwOKkNG09a89N1U9j3ZjZ+7vUJaVh6Noz+i\n6ervGdFtKIs8ypLtUBiMl5UW6Lo7a5xfQ3xeQlBpQpPcz7m2RFkeOH2cs3O+Z8LRRDr6+eDxVAf3\nfY0ajv/w98mrUQvrrp1ktAzHZ4X7XBmtIjj95UyKv/cWfl9O5Oys+Witw7GajZjNxoJSFtNVylkG\nDx5MlYQEnv3mG1DKXd7SpQshu3e7g8+/yeq6XBp2h4tcu5McuxO7w4XD5Q7cUQqjyYjFZGL69KmM\nGzeeTp3cHT1mzZpDt179qdGwGXuPJhN/+Bynk7MueX+MSqNetdLUrRJM3SolKBXkhVKKXwYPovOX\nE0gMLknImVOMs3nzhL8PpU+dhLZt4fvv74zOLEIUIRI4CyFEIcnKySMpPZc8uwunS6fUB2/j/+UE\nVje4l8Ad26jlyON4cEn2lA2l1ZZ1TCtbixF1H8XsFYTFyx/dYL0weOyyoPSKgfZldM2J2WTE02rh\nuV+m0W6buxPI3FrhfHpfNzRd58VfZxC5a9ml54SCaxUMistfvviauiMHe3YKzpxUqpYvxQfHNlJz\n4VecfrAFJdasBNz1zfPzXERlpf4/e3ceH2V57///dc2elSSsyqIEtypKZdHT1io7gqj1CCoutVRZ\nxPO15/gttZvn8KvWirbaFTVY1yq4YL/1WGSLYF1wQVCEWhdAAYUASSbb7HNfvz9mMiQQIIEEAnk/\nHw8eM3PP3MuEgbxz5XN9LgCu6tKT8RdfzDl3/AonmerL7HIZ3MbgdRs6/e7XFMz+JdEZN8N99+NZ\nuhj33Lmp/tfpvtvtrUwhnkgSisapDcXYvOVLXnxpIdd993rcHjfzn/4LF100nu7du2devytYx6/n\n/IXV//oKf1EfvNlFjY7XvTCbU3rlEd7xKVe8/CTD3luZaY8HEDm9P1/8fTl+v4eCHD/5uYEmR8BF\npPWpHZ2ISBvJyfKTk+UHIPn3hbj//ABvnPstfvfRp7wQj2ZGEuf0PZlNeYVM3fohi2JBlmflMmnS\nJDoVFHDeBaNw+3MprwpzWtliSDemcMJBQjs+weXLwhfIoajrcSSSllA4StKxGJcb4/KQcKA6FCOe\ncDLXNeCrj0gkkgAM3P6vzHY3DtnuKJXlO3li+JUc1zmHSa++AMCHl1zLwn5fp2z5kyRjIS67eAxu\nHObPT01+G5s1mP4v/oWaqTOI3XkP25csouBX/x9F6z9kKlA5eSrhoSMo3rSJ/hMu4/jCLHxeDz6v\nu/EX7e47Yeh5+OtHf8ePh4suahyW21FoBvB63HTyuOmUE6Bn13y+MfBrJJMOoUiMGydfTySWpK4u\nDMbg9Xr4378+w7IX5qZHpYM8s+AvjJt4AzndT2HtZzsoqwxRVhkC8ln19encEoTrNqzMnC9+3vlk\n52SBMeyqjbEtGMLrcpEd8NA5Pwu/T9+eRdoj/csUEWkm90Xj4OWX6XP66Qz+y19IDvg6RUOH8ZPz\nh/K7f33KwCHnsXjNe6zw5TKg/9eZN/9Zbpo+ldNO6gPWMuTBX5H3v6lgunz5cq759G188Z384dQz\n+fjdT+h57rn86U9/bLQAyFWTruamGTfT5X9+Qpd1i6mYPI3sd97k1PUf8vpb9wLgL99M3Wlf48PO\n3bjijaWM/ebJ3D/kNMaNu4BT/7AKXk1d/4k98uniryNameoS8vE/17H2w3VMvHISjuPwk3nz8V17\nI+fffgeeZAIzZjTmjVdgfapOuTA/i8LrJnJXc0oL9gzGxrS7sHwgbreLvJwAeTmBzLZoPEF1bZTR\nI0cQDke57rvfw+fzUFhYyLhxo+jevTtJx7Lhy0re/7SM5xa+ScKVzznBLzPH+KRzH04pmcPb7/+L\nrk/Pp6hTNk8/9STjxl2Ex9eVz8tqMNYS8Lnp3CmQ+cFNRI48lWqIiByi+lrca6+9lieffBJr4Yqr\nJvGXp+dz2WUT6Ny1O75XltLjmolU3jCNHbffyYfr/4nnlul8Z8NHbH78WW566WWmTZ3Ce++t4sEH\nHoXGppkAACAASURBVGTSpKswBp5+eh73jRzKNX9+IDOhDmvpPuJb+NJLhcf6n0VZ6Rs4NjVpsNPc\nOXz5xHNkv1pK4Z8fpOL708BC0aMPMScrn7VTZgCWRx95mPO++W/87a8L8Hnd/Pree3a3xLMW/uu/\n4He/Sy1DDbvv33+/6nLT4okk1XVRakIxonEHC/h83nQ3Dcsdv7iD7/z5AcaFqtnQpRere3yNieuW\nZiaV3nLhTNaeeBpfffIO44cO4AfTvpsp2bDWEo7EwHEI+D10UYgWaRWqcRYRORrsMXktmUiSXLSI\n5MjRJJKpiWqbt2zl+ecWMO2mm7CO5cGSh7jkkkvp+9E6IkNHYI0Bayn675+Q/+fUqnzVN06n6o5f\n4fa4cQNZr5bidrnI+fdLSfzH/4H778fjdlFz443kPfIIduFCuPDC/feOXrQotbx2fVCG3UFanSD2\nKRZPEqwNUxtOMPfhR9j4p9/xzI7NrD35NEZFLDNuvpmp6z/kuCfn8ug5l/DH/pc1mqBZkOtn0Kk9\nGHRaDwac1I0sf+oXw9ZaItE41kmSE/DQrTB37xIZEWmWdhecjTEDgb5AkbV2bnrb5UAQKK7ftsc+\nCs4iIgfSkpHgQ+0drN7Dh2TLli08+tiT3HTSqQS/NZRHn3iS8eMvonfP4wm8spS7PviQefOfw190\nAgO+OZa4vwe7qsKZ/X0eFwNP7cE3z+zJoFN7ZEJ00nGIRGJ4XFCUn0VhXkCrF4q0QHsMzs9aa68w\nxswElgEG6GutXWCMmQKsstau2WMfBWcRkQPRSPBRK5l0qKqLUl0X5aG5j/DwI49yzaQrMiU5M2bM\nYPjYy1n18XZWfbSNT7dWZnp5+7xurnW+oGjiZQw6rUdq8qC1uJcsovq8oeRmeehelLt7wRUR2ad2\nFZyNMRNIheR7G2y7G1hirX3FGDMCGNjw+fRrFJxFRJpDI8FHvfrR6MlTbyYcTfLoE09yycUX0avn\n8ZnXlFeFWbnuS9748EuK3ljO7xfdy7wzxvCn86/n3DOO5/+89jgnPvMoO+f/lbphIwmHY/g8hh5F\n2aqFFtmP9hac707ffQYYaa291xjzIPCgtfb9dHAeZa398R77KTiLiEiHFE8kqawJUxOKE0taPB43\nAd/u2ufo317kpBtTC7LMO2MMx9XsZOjm1QD87Wd/oPiGq+nx9qt8vnkzs95dw32//jVdOmUx6YrL\nuOOOOzj33HOPyPsSaY/aYx/nXdbaNcaYkenaZkiVa+zXrFmzMveHDh3K0KFD2+bqRERE2hGvx023\nwly6FYLjWKprIwTrooSjSdweN1mXXEzNlJvIm/sAk9bvXtXx48Le3Lktnx9ecjVnrltMVyCvW28m\nf/97lFdWUbZtOz+5/RcMP/+b1NRU8x//8R9NTwYVOYatWLGCFStWtMqxDmrEOV2nvKeKdA3zTGBj\ng3rmfunnl1prS5sq5UgfUyPOIiIiDVhrqQlFqaiOEInEOfHiEQTSfbXrbTm+H72/2gCkRqPvH3QJ\nuz79B+dseIvlgSxOPvU01n24jlBwJ49f8R0mPf7YEXgncqyx1hJPOCSSSSKxJPF4klgiiXUsDuBY\ni7VgUy9utK8xBmNSt670Y5cL/F4Pfp8bn8eN1+PG7Xa1ybUf9hHnprpiNPA8MCF9vwB4B9gEDAZK\nSXXbWHow5xUREelIjDHk5wTIz/Zj//M/MXuEZiATmt8bO4nHT/93bHWU8Z368Psdz/Boz9P5yYZN\n+H0eXu11HAOeeJyKcZdQMPEyXAbVxst+JZIOsXiCcDRBXSRO0rEkHUsikepZbozBuAxuVyrketxe\njBvcpP60hGMtNVGHylAiFb4dB4PF5TZ4XAaPMXi8brJ9Hvy+1IqlbRWs96fVSzWstZuMMcF0iUZR\n/ciyMWZwur45aK19v7XPKyIicsxatAjz+9+n7t9yC9ZazB/+0Oglp/QuxH72V3aVxXnrlPOZ138M\nk9ctxv+1kXSt3sCAzZuI9T+LqvNHsGNzOb3v/h9yHpqjbixCPJEkEo1TF44Tiad6yieTDg4Gt9vg\ncbvxeb143Kng6G+DuafGGLzpkeZ9iTkOodo4yWSEpGNxNQjWbmPweFwEfB4CPk/6WK5Wb9XYJjXO\nDUakFzSxrbQtzikiInLMqv/mf8stcP/9mP/8z8xTTnExro0bySuZw8yvD+Gaihryuxp+7POQOOkb\nXPfRMgD+VdSH09atJfent9HF5yanZA4Vk6eROOdbdLVWvaA7gNRCOglqwlHCkQTxpCWRTI0euz1u\nfF4Pbq+PBmvytCtulwu3z8W+4mvCsQRDCZI1MRzHwVqLy4DLZXCnw7VxHdrnXCsHioiIHA3q2xAu\nXpzq5Q1w6aXwwgupXt7pEenfX3oFd6xZhwuHB9xJ/n3TpwDMO2M0YDKTC3dNnkZ49m+IJZLE43E6\n5wXoWphzJN6ZtIFk0iEUiVEbjqdqkJNOapTW5cLr9XTont99uua0n3Z0B0vBWUREpJkWLUpNuLrw\nwtRotLWwaBEWuHXJEn73uz/we6+f/4iFqJ5yE8YY8krmsKVnP3p/maqJfvasC/nsh7P4zgWnkJft\nJxZPEI/H6VaQTVF+1pF9f9IijmMJRWJUh2JEYkkSCYeEtakSC58Ht+vw1wK3ZwrOIiIiwl133cXP\nfvYzHvzOd5j2//4fvwV2/s9dXPvdGym+dCT+dWvZOWwMHyZyGP7aC8zrP4YHLvgeF593Mhd/qx85\nWT4isThOIkG3gmwKFaDbHWst0ViC6lCUUCRBLOGQcBSSW+JQgnNb9XEWERGRw+y6664DYOpPfoJd\ntIjQ6tVM/+61HL/2Xdzr1lI9aix1Tz7DyS4Xm39QyKR5f2Zlr7N4Npbk729u4NJvn8xF3ywmOzuL\nXTVRdlaF6dopSwH6CEokHWrrolSHYqmQnHQwLjc+rxuP10dWO61HPlZpxFlERKQjWLSIxMhRfLWr\nltpogpyAn+wVy1jTbyDzln7Euk27AMjL9nHZ+Scz9t+K8fs8RKIxnGSSrirhOCyisQRVdRHqwqnR\nZIfUAjk+r0cTOFuJSjVERESk2eKJJF/trCEcd8jO8mOM4cMNO3l66T/5eHMFAAW5fv79glMYfU5f\nfF53poSjINdP14IcXIfYnUBSItE4wZoIoViSWDwJxoXP17En77U1BWcRERFpsWgswZadNSQtZAf8\nWGtZ8+kO5i39Jxu+DAIQ8Dh8d9zZjBh8An958nFGj76QgoJCcrI8dC/MxedVwGuJWDxJsDZMbTiR\nCsouF36fF88RWMyjo1JwFhERkYNWF47y1a46cLkI+H1Ya3n3X9uZ88zrVMdS06H8rjhffbiE6y75\nJjfe8H2SjkM4HCX5twU8W7mLWbf/GGMMv7rrLqb06UPXdL11R+c4lpq6KMHaCNG4QxLw+7yHZUQ5\nULqEyPBRu/uAW0vglaVERoxu83O3ZwrOIiIicsiqaiOUVdRh3G4Cfh+O4/Dz2SV8uM2FN7crkCrh\nGPtvxYw5ty/d3nqVrlddxkN5Ray54WZIRvnaH3/ND6yTWpEQUr2nGwS3jrDMdygSo6I6TCTmEHcc\nvB4Pfl/bzeJrKiDn3TebgrvvoGbqDIJ33gNAwc9/RF7JHHbO/2uT4TlQugRg97GsJVC6BO8Ha6i5\n9bZjJoCrq4aIiIgcsk65ATrlBqisDrMjGMLldtPFX8e2N+eT3eN0+pw9lmAtzFv2EV88Np/c71zM\nzdfeyLS/PEzJn/9Ir0SccdahYvI04uU1dL/2Cuwtt2B++9vUCf7rv+B3vzvmlvmOxhIEayLURuLE\n4g4ud2rk3h8wtMHq1I0ESpfQ9arLmgzIobHjySuZk3ltXskcaqbOSAXjfRwHSB3rjtmp48x9AADf\nB2sof3w+gdIlBJYv2x3Ah486qkN0Syk4i4iISCOF+akWdLf/f7/ikUcf57vfvR6PG55++tdcMfkW\nCtd8yi9evo95W9Zy6bnXcEvxh0zd+DYAH558GgWzfw0YKm+YTuHvf0+wLorH7SK35AH4wQ9So9BH\nKcexhKNxquqihKMJ4gknU6fs8/vxtSAp72ukuCWju5Hho6iZOqPJgBy8YzbJ22/LPJcJ13t05wiU\nLiEybCQ1U24ib+4D5JXMIbD4ZbxfbAIg1v8ssl9+Ca6/KnWbPlZk2EgKfjaTvLkP7HMU+1ij4Cwi\nIiJNmvr9a8nyWqbd/J/sDIbIzSvg0kvG0H3GtZRufYtJ7y3GJpMMqtqW2WdVyPDZ3MeYPvX71P7q\n13jcLgrSwa3i+9PY8Z8/x/NlEJ/HRV62j+wsL35v+4wjiaRDOBKjLhwnEk8SS6SWrXanFxtpaVBu\nqKmR4s7pYFo/ugv7Lq9oGLrr998rIB/MdVhL3sMPZkJzZvS5QQAHwHEajUh3FO3zkyoiIiJHXO/e\nvfnpT38KQOdO2dx6843srAoTisR5adQYNnz8T6Z+tAyAz7qeyLvdTmXy+sXMn/d3fpN7BqPP6ct5\nDY7n9bjJyckCYwiULqH8vGGUBSNgHdwG8l9fTnzkKLL8XrL8qZZsbT2JLp5IEk8kicSShCIxkklL\n3LEkEg4OBo871R7O3WCxkUxorddgVLi5E/KaGinOfvmlzOhu8uc/Apour2gq7PrffL3xG7M2E3Zr\nps7IHAtoNOq853X433qjWV+3vIcfzNzfV/nHsUjBWURERJqlvoTjf35xFw/PfZjXuneH2lTbul0n\nn0DgV3/glZ//mKtee4E3F55J1dy15K9bzOpxk+jZNY/u6XAWGT6KrlddRqCJutwd8/9K5beHs6sm\ninUs1rG4DLjcBpcxuF0GFxBYXkpsxAg8bjfGGIyx+EpLiY0cCYB1wLGWRNLBWsBafMuXUXf+cCyQ\ndCxO0pL72nLqho1MLVnt9eDypuqS/fsYSd5fTXHwx7c3f0LevkaK9xjdbaq8olHYtRb/yjfwrVtL\nrP9ZRL95Hnklc3Bv2Uz2yy/tNfqcVzKHyPBRu6+liesAiJ1xJr71H5JXMgf/m6/jW7c2FcAt5M1t\n8Lr+ZxG8Y3aj6zuWu3koOIuIiEiL3Pi9a7lo8d/5+ptvUjtmLB9U1fKtN1+l5qnfEnz+cT576Qq+\n/ckOJi6+l3n9x3Df8eMAuPMbZYwpmUPFN4fusy43OnwUfmPYX0QJlC6h6zUTqJ46g4pf3I21lqLb\nb6PTww+w/akFhNOhzWVcuNxuTGafiS3qMtGU/dUUxwecnXnc8Dkg1VHkANxbNu/1OveWzXu/sImw\nG+t/FmWlb2TCan2Qb1gvHbzznsaheR/nifU/i7Jlr6cC/NwH8K1bS2js+FSo/9nMRvv51q2l4Oc/\nIvjLezO/SdjXDxYNv85Ha7hWcBYREZEW6f3Pf9L7zTfhBz8g9/77GRxPUH3zLeSXzCE0bCRccjH/\nBpQN6EWg15mc98GXvPPRNn5+xgT+3ukU3n0rztmnXsYP/r2WUw8wca0p9eE1v2QO9a/Oe/iBVHgd\nNQZPE8fYc5QWY1KBd8pNzX7f9WFvfzXFDSfY1auZctPeZRzWZgJlzdQZmRFi/xnFuMt3UTPlJvwr\n38hMyit/fP5+vzbRb3wr9Xw6VDcZkI3Ze1v6OrJffonQ2PFAqmSk4L9/nDlOfTu6QOmSTIlGaOx4\nkr37kFcyh7y5D6TON3LMfn+wqC/naG64bo9aPTgbYwYCq4CN6U1LrbU3GWMuB4JAsbV2bmufV0RE\nRA6TCy9MtZRL92j2+7z4S+aQ+M54ooPPo64uTCDgh1FjGAwM/trxhKNx3lq/jdc+6I7z2Q7e/Wg7\nqz8p49T0Ib/YXk2yOkxRp+xGp9rXyOQ+w+u+wqUxRIaPygQ9SAVajKHrVZcdMLA1Cnt3zG70XGa0\nNh1a60snIF3KcOc9BF5Z2igsBl5Zmrn2yLCRqYB6zll4v9hE/IS+YEym/CL75Zeoazgau0foznwd\n6keimwrI+3pf6etoGGKT6WNnwvDIMZn31+hrnVZ/7oZfg8x29v67aU64bq/aYsS50FrrAjDGnA0E\n02Eaa22pMabYGHO2tXZNG5xbREREDoc9+zAbg+eii+gDJJMO28prqK2L4vf78HjcZPm9DBvYh2ED\n+1BZHYYf/ICz1i1mXv9UKJv04l+Yt3En/zvh/zDk9OMZfFoPTln/Nl0n7Xtksin1QTvwytLdI5z1\n960l1v+sTKgNLFmE94tNuwPbfsoFGoa9+ppfoNFkvvr65PrnIF3KcPttBO+YvVdYhN2j0RjD9nfW\n0vWiEQRWvYO3QUu5wPJljTtqNBF2oYn65WaIjBid6cd8oJKOlrx2v5oRrturVg/O1trSBg8HW2vn\nGmOmAUvS2zYCIwEFZxERkWOQ2+2iV7dOOI5lR0UtwbowPr8XrycVO4579zW6vvQUNVNn0P+2X7Dq\n4+288qscJr32Ait7ncXTXw7g6aX/JD/by+0XXM7QkjnUReJkB7yZwBgoXULe3AcajbjWlzuExo5P\nTYybchPurVsabQOIn9AX7xeb8H6xiWTnLgR/cTdwgHKBdNirPwekQm/wznsyk/mShUW7g2C6BKS+\nbGO/JR4NRmvjAwcTWPVOo/O2WYBtcLw93+s++0Yf6LX7Gg2HNgvGh7Neus1qnI0xI4Bn0g8LgIoG\nT3duq/OKiIhI++ByGXp0yaNbkWVnZR2VtWG8Pi80CH4FxjBySF9Y8ARfLbmGC3qfRdZH23j/0x1U\nVEeYefJ3uLW8lklPpKo8Xxs2gVDPMxnzPzdRPWUGVXuMuNYH5Fj/szIlGcnOXTJhN3ZGf3zr12X2\ncZfvovP3JpHsc0KzygWSvfvsfrBHTXG9mik3pSbL1V9Xc3odtzBwtiTsHk7NGg1vxXB9uOul23Jy\n4Kg9Rp8P+FWYNWtW5v7QoUMZOnRo61+ViIiIHFYul6F751y6FeWwKxiivCZM5NvDCDQMSMaQHHMh\n5wDnnH481lq2ldfy4Wc7Oe7T3WUZW3fWcN+WXP5+4UxWe86muOQ1TupdyMkTb2HgkG8TuHg8Rf/d\neLEOd/kuYv3PItGzF9mLFwI0aq2WvejvmW37DG4HCHv1AW2vkeBf3ktkxOjUDwn72b81yy+OpOaM\nhrdqqUkz6qVXvvEPVr7xWmu8PYxtRnuUvXYyZkoTmyustQsavGaJtXZ0+v7dpCYJlhpjJgB9rbX3\nNtzZGGMP5lpERETk6FNRHWZXVRiMi6yAr+kXNQir1VNmUB2K0euph3n1gsu595yrKQuG99rF53Hx\n09XzuejtF/d57oYLh3Qf8a1MTfL+gvOhjmw2Z/+jtUXbwWjV99rgcwIHrpfu0zUHa+1B1YwcVHA+\n4EGNKQYebBCcz2Z3vfNMUiH6/T32UXAWERHpYKrrIpRVhnCsISvgw+yxkMb+wuaOf7uAz7ZW8tnW\nIJ9urWDDl5V8f+mfmbRuMR937sOp5aluFxWBPIoiNQC8fco5zJ38C4o6ZTHxbw8wZPF8tnxzBLGe\nven33GNsveZGtt/+S7ICqdULPW5X5pqaCnveZUuoPn840bhDLJ5ahTAaTxKJJojU38ZSf7q//Q8+\nPv2czPZYPMnJ697mn18bklqQpf5POg+5XQa324XbZfC4XLjdBvcet163C7/PQ5bPg9/nxu/zEPC5\n8XtTt4H044DfS26WF4/bdbj+ag+fJoJzZNjIzKTL+tfUB/P2GJz7Aj+y1t7UYNsUUhMDm2xHp+As\nIiLScYUjMbZX1BGOO2Rn+XG7UgGvJSOT9UF7x9DRdFuxhHdHXUGP9e/R+6sNbM3rRq+aHQDM6z+G\nlT3P5PeLf51aoOXfrgXg1rf+wqR1i7nlwpms7D2g0bFdLpNawdCY9EqFEEs4OM7RlV2y/R5ys33k\nZfvIzaq/9aZus33kZ/soys+iKD9AUX6ALL/3SF/y/u2nhKZhrXnDH7i6XXVZ+wrOB0PBWUREROKJ\nJGUVtdSEEvj8Xnzelk3HatiODqDrVZcRGjuenY88DYtexr1sKb2eepgldzxITSjO6r5fpyYcJxxN\nEI7EOfWjd1jZawDhaGpb8gDB2OUy+DxufB4XPq8782f3aG+DkV+/h4DXQ8CfeuzzulOjyi5Xellx\nFy5jcLlSmS6ZdEg6lmTSIeFYHMchkbS7tzsOsYRDNJYgEksSjSWIxpJE4qnbcPpxNJYgFE1QF47R\n0pyf5fdQlBegKD+LLgVZHNcll+M753Jc5xx6dM4ly39k19Lb328lgEZhuv41fbrlKjiLiIjIscNx\nLLuq6qisiWJc7n3XQR/AodbSWmuxNnXrWItj67dZvB73UVX64DiWcDROTShGTTh1WxuKpW7Dqdvq\nuhgV1WEqqiNUVIeJJZz9HrMgz8/xnXPp3S2fE3rkc8JxnTixR/5hHane199xw0VmGtY9t7tSjYOh\n4CwiIiJNqa6LsDMYJpawBAK+oyqsHs2stdRF4pRXpUL0jsoQ28pr2VZey/byOrZX1BFvIlgbA726\n5nFK7yJO6VPIGX27cFzn3Eb164fh4vc5YVDBWURERI558USSHZV11ITjuF1uAgc5Ci2tI+lYyqvC\nfLWrli1l1Xy+vYrPt1Wxuax6rxKXovwAZxZ3ZcDJ3Rh4Snfyc/xtd2H7qHtWqYaIiIh0SFV1EXYF\nw0QTDlnpZb2lfYjFk2zaFuSTLZX864ty1m/cRXUolnneGDildxFDvtaDb53Zi+5FOa16/gN1Y9Hk\nQBEREemQEkmH8mCIqlAUi4uA35eZXCftg+NYtuyoZu2Gnaz5pIx1G3eRSO4u8Ti1TxHnndWLb53Z\nk4K8QKucc3+17SrVEBERkQ4vEo2zsypEXSSBSS+scljraqVZwtEEH3y2g7fWf8U7//yKSCwJgMvA\nWSd149sDenHu6ceTHWibCYYKziIiIiIN1IWjlFdFCEcTGHdqARCF6PYnEkuw6qPt/OODLaz5pCxT\nG+33ujlvQC9Gn9OXk3oWtOrfnYKziIiIyD5kQnQ8gbUGv1+dOdqjmlCUleu+4h/vb+Gfn5dntvc9\nrhOjz+nLtwf0apVRaAVnERERkWaIxhNUVoWpjSSIJx08Xg8BXztfHa8D+nJnDUvf/ZzlqzdTk55Y\nGPC5Oe+s9Ch0r8KDPraCs4iIiEgLOY6lJhSlqjZKJJ4k6YDP52nxaoXSdmLxJG+t/4ql737O+k27\nMtuLjy9g1JATOf/rvVq82IqCs4iIiMghSiQdauqiVIdiRONJEo7F43Hj93rVqaMd2LqjhqXvbmL5\n6s3UhuMABHwezv96L8acW0zf4zo16zgKziIiIiKtLJl0qIvEqK6LEo07qVXyjMHj8eD3aVT6SInF\nk6xc/xVL39nUqBb6lN6FjDm3L988sxd+7777eis4i4iIiBwG0XiC2lCMunCcWMJJ9SM2Bo/Hjdfj\n0cj0YbalrJol73zO8jWbCUVSo9A5AS/DBvVh9JC+9OqWt9c+Cs4iIiIiR0gsniQcjVMTihJLWBJJ\nh2TSYtwuPG43Pq9brfDaWDSW4PW1W1n8zud8trUys71/3y6MPrcv555+PF5PqpOKgrOIiIhIO2Kt\nJRZPUheJUxuOEU84JJKWpLWpMO3z4HapJV5b2PBlJUve+Zx/vL+FaDy1uEqnHD8jBp/AqCEnMuTU\nbgrOIiIiIu1dMukQjsapDcUIx5KpQG01CbEt1EXi/OP9LSx+exOby6qB1Arc75Zc276CszHmciAI\nFFtr5+5r2x77KDiLiIhIh5NMOoQiMarSkxBjcQfjduH3ebVQSyuw1vLx5goWv7OJNz/8kpUPXN1+\ngrMx5uz0Ra4xxowAKtJPFVtrFxhjpgCrrLVr9thPwVlEREQEiETjBGsihGJJYvEkuBSkW0N1XZT+\nJxYddHBuq6/+7PRtcTogXwnUV2pvBEa20XlFREREjnoBv5ceXfIoPr6A007ozIndcslyW2LRKHV1\nYcKRKI6jAceWys/xH9L+rd6EMD3SvMkYUwFMSW8uYPfIM0Dn1j6viIiIyLEq4PfSI71CnrWWUCRG\nZU2EcMQhnnTweT34tXR4m2v14GyMKQA+IxWa5xpjVtc/daB9Z82albk/dOhQhg4d2tqXJyIiInJU\nM8aQk+UnJys1eppMr3gYrIsSjSWxLhcBv1ddO9JWvvEPVr7xWqsc66BqnNN1ynuqSNcwzwQestZW\np2ucB5IaYV5qrS01xkwA+lpr793jmKpxFhERETlEkWicipoIoUiCWNLB5/VqpcMGDqWP80F9FZvq\nirHH89Xp21JjTDGwDBgMlAJ9gaUHc14RERER2b+A38vx6bKORNKhqjZCsDZKPOHg8rjJ8vuO8BUe\nvdqqHd1MUpMAixq0o5uS3qZ2dCIiIiKHmbWW6lCUyuoIkVgSl9tFwO/rcKsaauVAEREREWmR2lCU\niuoI4WgCXC6yAh0jRB/2Ug0RERERObrlZvvJzU5NMKwLRymvihCKJjBuF1mBQ2vbdqxScBYRERHp\n4Bp26agNRdlVFSYcTeLxeQiozV2GgrOIiIiIZNSPRFtrqaqJUF4TIZpwyPL78HjcR/ryjijVOIuI\niIjIfiWSDuXBEFWhKBY3WQHvUVsPrcmBIiIiInJY1IWj7AyGCceS+P0+vEfZKLQmB4qIiIjIYVFf\nD51MOuwKhgiGwriMm0Dg2O8PrRFnERERETkkVbURdgZDJBzIzvK36zIOjTiLiIiIyBHTKTdAp9wA\nkWicbeW1hOOWnCw/Llf7DdAHQyPOIiIiItKqYvEk28prqYsmyMkKtKsArcmBIiIiItLuxBNJvtpV\nSyiaJLudjEArOIuIiIhIuxWLJ/lyZzWRhCU3O3BEr0XBWURERETavXAkxtadNeByE/AfmS4cCs4i\nIiIictSoqomwrbIOn8+L13N4e1UcSnB2tfbFiIiIiIjsT6e8AKf2LiLbY6itC+M4R8fgqYKziIiI\niBx2xhh6dMmj3/EFJOIxItHYkb6kA1JwFhEREZEjxud1069nIV3y/NTWhUkknSN9Sfuk4CwiMaLM\nhAAAIABJREFUIiIiR1xhfhan9CrEbZOEwtEjfTlNapPJgcaYmcBGoMhaOze97XIgCBTXb9tjH00O\nFBERERGq6yJ8uauOgN+Hx+Nu1WO3q8mBxpiRANbaBUA/Y0xfY8zA9LbS9GvObu3zioiIiMixIT8n\nNXnQjdOuRp/bolRjJLAhfX9D+vEVpEabITUSPbINzisiIiIixwiXy9CnRyeOK8xqN7XPbRGcy4HO\n6fuFQD+gAKho8JrOe+4kIiIiIrKn/NzU6LPLJgmFj2znjbboOP08MC19v5jUqHNBc3acNWtW5v7Q\noUMZOnRoK1+aiIiIiBxtXC7DCT06UVUb4avyOrKy/LhdzRv/XfnGP1j5xmutch0HNTnQGDOlic0V\n6brmhjXMVwLvAkOApdbaUmPMBKCvtfbePY6pyYEiIiIisl/JpMMX26tI4iLg97Z4/0OZHHhQI85N\ndcWolw7Ng621c40x06y1C4wxG4HBQCnQF1h6MOcVERERkY7N7XZR3LOQiuowZZUhsrMCuFwHlYNb\nrNVrnK21a4CKdPu5BxtswxgzAghaa99v7fOKiIiISMdRlJ/FST0LiMeiRGPxw3LONunjfDBUqiEi\nIiIiB6OsvJby2ih5OVkHfG276uMsIiIiInI4de+cS3GPfEKhMPFEos3Oo+AsIiIiIke9gN/LKb2L\n8LksdaFIm5xDwVlEREREjgnGGHp160TPLjnU1oZIOq27aIqCs4iIiIgcU/Ky/ZzSuwibiBOJtt7E\nQQVnERERETnmuN0u+h5fSOc8H7W1YVqjCUVbrBwoIiIiItIuFOVnkZvl4/NtQdzeli+Y0pBGnEVE\nRETkmObzujmlT2eyvIe2UIr6OIuIiIhIh2GMUR9nEREREZG2pOAsIiIiItIMCs4iIiIiIs2g4Cwi\nIiIi0gwKziIiIiIizaDgLCIiIiLSDArOIiIiIiLN0CrB2Rgze4/HlxtjRhhjpuxvm4iIiIjI0eKQ\ng7MxZipweYPHAwGstaXpx2c3te1Qzysdw4oVK470JUg7pM+FNEWfC2mKPhfSmg45OFtrS4CNDTZd\nAVSm728ERqa3BffYJnJA+g9PmqLPhTRFnwtpij4X0praosa5AKho8LjzPraJiIiIiBw12mpy4EGt\n/y0iIiIi0l4Za+3+X9D0ZL4Ka+2CBq9ZYq0dnb5/N7DUWltqjLkcKCY1wly/bQLQ11p77x7n2f+F\niIiIiIi0AmvtQQ3yeppx4LktPOYzwGCglFRoXkpqBLp+W9/0tj3Po1FqEREREWm3WqOrxgRgsDHm\nRgBr7Zr09hFA0Fr7flPbDvW8IiIiIiKH0wFLNURE2gtjzMz6Mq90KVgQKD6I34yJiEgHYIyZba29\nrcHjvb53tOT7yRFfOVALo0hDxpgp6T93N9imz4hgjBkJjErfV294wRgzMP3/gxbbkgwtwib12mKt\nkSManPXNTxpKl/IsS/+0V5z+T+5s0GdEAGj467Er2btfvHQ8P05PVC/QYlsCmb/zjenPwMb050Lf\nRzqotlhr5EiPODf1BqTjKmb3Z2Bj+vGVaPGcDs8Yc3b9N720Tqg3fIeWnl/zLoC19t70XBp9TxGA\n2enb4vTnQj9oS71DXmvkSAdnLYwiGdbauQ1qiwYCq0h9RsobvEyfkY6pqIlt6sTTsQ0GOqdHFGem\nt+l7SgeXDsqbjDEV7P4s6HMhDR3S944jHZxB3/xkD+lft75X340FfUY6tCZGmyH1W4j6MF1I4x+u\npOPY1aBrU30do/6/6MCMMQXAZ8AUYK4xpm/9U0fuqqQdafi9o35grkXfTw7Yx7mN6ZufNGWEtfYn\n6fv6jEixMaZ+IaWidH1iw37xTfaGl2NeObApfT8IDEH/X0gqMD9kra02xgSBCehzIbsd1FojDR3p\nEednSF046JufkJoB26Dd2Aj0GenwrLUL0hPALKnaZqve8AI8z+7/GwqAd9D/FwJYa6vTt6WkQrM+\nFx1UW6w1csT7OKdbw2xEvVg7vHS7sWdJ1aIVAROsta/oMyIiTUn/31ABDK7/LZX+v5B0zftGoKhB\nn159LqRVHPHgLCIiIiJyNDjSpRoiIiIiIkcFBWcRERERkWZQcBYRERERaQYFZxERERGRZlBwFhER\nERFpBgVnEREREZFmUHAWEREREWkGBWcRERERkWZQcBYRERERaQYFZxERERGRZlBwFhERERFpBgVn\nEREREZFmUHAWEREREWkGBWcRERERkWZQcBYROUyMMVONMe8ZYxxjzGfGmLtbsK/TCudv8hjGmJEN\nrmuJMabvoZ5LRORYpOAsInIYGGNmA3cDvwQKgInAQGPMqiN8XQXAkgbXtRp47khek4hIe6XgLCLS\nxowxxcBMYKC19gVrbbW1do21djRQYIyZYoxpFKLTo8BL0veXpm/LjTGXG2MeMsY8lx4hXlU/Qtzc\nY+xxeSOB9+qvi1S4H9hmXwwRkaOYgrOISNsbCSy11n7exHMPAaMAu6+drbWj0redAQNMARaTGiFe\nRTNGiPc4RsPtz6evr95gYMOBjici0hF5jvQFiIh0AMXApn08twm4soXHe89a+3D6/vT0yHP+wV6c\ntbYKwBgzASgBJhzssUREjmUKziIibW8DqZrmphTT8hHePUP4xvRxDkq6zvk5UiPYw6217x/ssURE\njmUq1RARaXulwMh9dKuYBixtYnvBfo63Z0guJhWeW3KMhkqBVdbaIQrNIiL7puAsItLGrLUbgXuA\n99KT+wrSE/mWAp+lyy6qSHXZ6JseAf7Jfg45MD2hsMAY8xCp0o1qINiCYwCZ8gwLlBhjiuv/HOJb\nFhE5Jik4i4gcBtbaHwO3kQqzFcCzpCb2TUw/v5FUffEG4F3gLhpPGHw+3YfZAstITSisINUBoyXH\nSO5xaYPTx9gAfJb+82lrvGcRkWONsXafE7kP/qDGXE5q5KPYWjt3X9tERKRl0iPEV1hrrzjS1yIi\n0tG0+uRAY8zZwEZr7RpjTP1jAKy1pelfA55trV3T2ucWEREREWkrbVWqMTt9W5wOyFcCleltG2nc\nM1RERJrPsp+ezyIi0nZaPTing/ImY0wFqfo7SM3srmjwss577SgiIgdkrV1grW1p32cREWkFrR6c\n0zO5PyO1stXcBu2XTGufS0RERETkcGmLBVCmAA9Za6uNMUFSK1AFgaL084VA+Z47GWP0q0cRERER\naXPW2oMa0G2TlQPT/UQzkwFJtU4aTKrJfl+abvZPW3T4kKPbrFmzmDVr1pG+DGln9LmQpuhzIU3R\n50L2ZMzBF0G0enC21t5rjJlJahJgUYN2dIONMSOAoFamEhEREZGjTVuNON/bxLb63s2lbXFOERER\nEZG2pJUDpV0bOnTokb4EaYf0uZCm6HMhTdHnQlpTm6wceDCMMba9XIuIiIiIHJuMMe1rcqCIiIiI\ntJ1DmeDWkbT2oKyCs4iIiMhRSL+p37+2+OFCNc4iIiIiIs2g4CwiIiIi0gwKziIiIiIizaDgLCIi\nIiKtJhgM4nK5mD59+l7PTZw4EZfr6I2fakcnIiIicpRJt1Q70pfRpGAwSFFREYWFhZSXlzd6rrCw\nkOrqapLJZJtfx76+RofSju7ojfwiIiIi0m4NHjyYNWvWZB4vW7aMUaNGNQqzy5Yto1+/frhcLkaP\nHk1VVVXmuZKSEoqKinC5XAwePJhNmzYBsHHjRgYNGsS9995LUVERJ510UqPztCWNOIuIiIgcZQ40\n4jxk6lOtdq53S65p0evrR5xLSkpYtWoVDz74IADTp09n1KhRTJw4EcdxCAaDFBcXs2DBAgYNGsSP\nfvQjKioqePbZZzPHWLNmDSeeeCJTpkyhuLiYu+++m40bN3LSSSdxzz338MMf/pDp06ezceNGlixZ\n0ug6NOIsIiIiIkeFiRMn8uyzz2YeP/vss1x++eWNHo8cOZJhw4aRn5/Pgw8+yLJlywAoKCigsrKS\nAQMG0KlTJwoLCwkGg5l9CwoK+OEPfwjAtGnTqKioOCzvSQugiIiIiBxjWjpK3BY6deqUKdcoLy9n\nyJAhjZ7fsGEDzz//PEVFRZltDRctueuuuygtLc08X1xcnHmu4T6Hs2JBwVlERERE2sTEiROZP38+\nVVVVTJs2rdFzJ510EhMmTGg0Kl1fq/z8889TWlrKK6+8Qn5+PiUlJaxevfqwXntTVKohIiIiIm1i\n4sSJlJSUsGzZMkaOHLnXc8uWLaO0tJRgMMi0adP48Y9/DEBlZSVFRUXk5+cTDAYpKSk5bOUY+6Pg\nLCIiIiKtqr7koqCggH79+tGvXz/y8/P3eu65555j2rRpFBUV8fnnn/Pcc88BMGXKFCBVkjFq1Chm\nz57NsmXLeOWVVxodY8/ztfn7ai+dLNRVQ0RERKR52nMf5/ZCXTVERERERI4QBWcRERERkWZQcBYR\nERERaQa1oxMRERGRY9KmbUGstVgLjrU4zqHVhSs4i4iIiMgxyeP1terxVKohIiIiIsekQOkSaNhZ\n4xA7kSg4i4iIiMgxqetVl1Hw8x+lArO1qfuHQKUaIiIiItJqXK7G47IDBw5k7ty5nH322c3e33Gc\nVrmWmqkzyCuZk3nc8P7B0IiziIiISAexfft2rrjiCnbu3Im1lv/+7//OrNbXmlavXk0wGGTjxo1c\neeWVDBo0iE2bNrX6eQ4keOc9mfCcVzKHmqkzDul4Cs4iIiIix4gXX3yR++67D4DKykpuuOEGKisr\nM89/8skn/O///i/Dhw9n+vTp3HHHHZllrOuVlZURjUYBsNayefPmFl9HQUEB+fn5nHjiicycOZOp\nU6cye/bszPMlJSUUFRXhcrkYPHhwJlSPGjUKgM6dO+/3dUdMqkXHkf+TuhQREREROZB95abrrrvO\nAvanP/2pHThwoPX5fHbFihWNXrNs2TILWMBeeumlNplMZp4Lh8P2lFNOsRdddJGNRCJ25syZtlOn\nTnbjxo3NvjZjjN20adNe5xw0aJC11trKykprjLHvv/++DQaDduLEifa2225rtH9zXncggK0bO95a\nsNVTZ9jqqTOsTb9ve5B5VTXOIiIiIkeJUDjGzmBon88/8sgjlJWVcddddwGwcOFCLrjggszz1lqW\nL1+eefzZZ59RXl5O165dAQgEAtx6661Mnz6dQCAAwIwZMzjxxBMP6boLCwvZuHEjkBqNrqyspFOn\nTpnngsHgXvs093X7k/3yS4TGjid45z27Nx5CnbNKNURERETasUTSoay8lk+2lLNlVwjj8e7ztTU1\nNZSVlWUer1+/vtHzL7zwAr/85S+58cYbWbJkCRs2bOD6669v9JqpU6eSn5+fefyb3/wGY8whvYeK\nigqKi4szj++66y4GDx7M6NGj91t+0dzX7Uto7HjKH5sHxoAxjQP0QdCIs4iIiEg7VBOKsrMyRDTp\nEPD5yMrKOuA+11xzDR999BEvvvgiTz31FDNnzuTUU0/l4osvBuA73/kOjz32GNdddx0ul4uFCxfS\np0+fzP7WWm677Taqq6vxeDwkEgkmTJjAggUL8Pv9B/1ennvuOYYMGQLA888/T2lpKa+88gr5+fmU\nlJSwevXqvfZp7uv254N753I8ZvdI8SH+AKDgLCIiHdeiRTBmzO5vptbC4sVw4YVH9rqkw3Icy87K\nOoKhKMa4yQr42ff48t7uuecevvzyS8aMGcPYsWP59re/zdixYzPPu93uRiPMw4YNa7R/NBpl5cqV\nzJgxgz/+8Y+UlJQwe/Zsdu3aRc+ePZt9HZWVlRQUFFBRUcHzzz/Pww8/zIYNGzLPFRUVkZ+fTzAY\npKSkpNFodMNjNOd1+3PLb5eRHfBS3LOAk3oVcnKvwhbtvydjD3EFlSYPasxAoC9QZK2dm952ORAE\niuu37bGPbYtrERERadKiRTB2LPaWW0j8+jc4jsX1f2/F+6c/Urvg/xEdMQrHsVgsNt1S1lqLMQbj\nAoPB5TK4jcHlNrhdLtwug8vlSm13mUP+9bZ0HNFYgu0VdYSiCfx+H16Pe7+v79M1h7bKTeFwmEAg\nkPn8hkIhsrOzm73/nn2cBw0axNy5c/n617+e2TZ69GhWrVpFv379uPvuu5k4cSLPP/88w4cP54or\nrmDBggUkk8n9vu5AjDG8cPY47ho0KfXDsbV8Y+ta/rDoXqy1B/WPs62C87PW2iuMMTOBZYAB+lpr\nFxhjpgCrrLVr9thHwVlERNpENJ4gHI4TiiWIx5MkrSWRdOgy62cUPfIQNaPHEe/Vm6JHHqLyhumU\nz/oV2f94hcjwURjIjEgbA2Xby3j55YV89/rrsRYef/xxRo+5kG5du6YXJ3NwUvP2cZl0aWU6YBtD\n+tbg8bjwul34vG68Hhced+pWYbtjqQlFKasMEU9asgN+XK7m/f23ZXA+VhhjsMDGPz/DmpMGcsKv\nbmfwovkYOOjg3OqlGsaYCcC7ANbae9Pb7gaWpF+yERgJrGnyACIiIocgEo1THYoSiiSIJxySjsW4\nXLjdbrweNy6vGxfgBeru/g2BbV+S9/JLQGqVsdo7ZtP99tvIK5nDzvl/JTJidKPjL178Mg888ABV\nVanZ/U8/PQ+P2zB58vdbdJ1xxxJJOCRDCRzrYJ1UuyuXAZfL4DIGj9tFwOsmK+Ahy+894CikHD0q\nq8Os++RzFi9ZyrSpN+AHHn30UcaNu4ju3bsf6cs7pnR9+1VGv/0qeYvmpxZAOYSuGm1R4zwYwBhz\nNjAyHZ4LgIoGr+ncBucVEZEOxlpLXThGVV2UcDRJIumAy4XP68Hr9eFuRnFosvfuiVH+N1+n4Oc/\nIm/uA9RMncEXZ5zFwkcfYfLkyUAq2IwdO47KykqefnoeAFdfPSnzfEu4XAaXy33AMBxKOFRXRUkk\nQuBYPB4XPrchN9tHbrYPv1fTlY4GW7Zs4YknnmTKTbdQURPhqafnEQnX8sQTT1JXWwWQ+Uy19Icw\n2beGS27XTJ2R6qrRzoIzwC5r7RpjzMh0bTOkyjX2a9asWZn7Q4cOZejQoW1zdSIictSKRONU1EQI\nRxPEEg4ut4uAz4c/4KG5c/4DpUuIDBtJQXpkuWbKTQSWLMK3bi2+dWupmXITwTvvYeFjj/KnP83h\n9ddf5/TTz2DevHn87W8vMmjQwMyx6ur23VP3YJWVlbFw4d+ZPHkyHrfhySee3GskMhhKsKs6inUc\nfF43OX4PBXkB/D4F6fbGWkvJI0/xhwcfpawmiduVCskzZtzE1VdPOuQfwmT/VqT/RFe9Q+SeXx7S\nsdriX1c5UN9oLwgMSd8WpbcVpl+zl4bBWUREBCCeSFJVG6UmFCMaT4LLRcDvxef34zuI7liB0iV0\nveoyQmPHk/3yS9RMuQkweL/Y3SPWvXULAJMnT+b111/ngw/W8sEHa+nSpQtbt25l69atnHrqqXz8\n8cf87W9/o1evnq06Srhw4d/505/mZJZKbmok0uf14Gsw2hyKJ6ncXoPBEvC6KMgPkJ/tV830EWSt\nZWewjorqKNdPuYnaaHyvkHz//fc3+3h1kThvrN3Kq2u2tNUlH3PySuYwaOoMBqXv1ww+h98ewvHa\nIjg/D0xI3y8A3iEVpAcDpaS6bSxtg/OKiMgxwFpLTShKsCZKJJ4kadMh0efD4zv040eGj8r8+jY0\ndjxgyJub/lXujdNxf7mV7JdfIvnzHxG8czann34GH3ywFoBdu3bRr18xGzZs5OOPP2bSpEkUFhYw\nbtxFe52n4agxtKx+dfLkyS0uB/F43OS+Wkpk+CgwhrJghG07ayl8cwWBS8crRB9G1lp2VNRRURvF\n7/eSk5NFaqXnxh599FGefnoeV189CUj9gFRYWNjoByRrLf/cVM6y9z5n5bqviMWTh+ttHBMy5Rlp\neYdQpgFtEJyttZuMMcF0iUZRgwmCg40xI4Cgtfb91j6viIgcvaLxBJVVYerS5Rduj5uAz0vWflZI\nKysr49lnnyEnJ4fJkyfz6KOPUltby5VXXrX/cNpg9bCG30RrptxE8Jf3ApD8+Y/IK5nDi0nLvGUr\nMqPLAFVV1Q0Pxfe//32aqkZszqhxc61fv57t27ezcOFCampqMQZyc3MZN+4iXn55IePGXcQJ6z6g\n61WXZYJCls9LwS9+Rl7JHLY++Rzbvj2MbL+HrgXZZAVa0hlYmstxLDsqagnWxfD5veTm7F6wpKmQ\nfP313+Xmm2dkfigqLCzM/BBWXhVm+ZrNLH/vC7aV12WO07+4C8MGnsD1c9EPQs0QvPOeTFec4J33\npH6wvOqygz5emxRCNejTvKCJbaVtcU4RETl6OI6lpi5KsDZCJO6AMfh8LSu/WLjw7zz++BMAlJa+\nkgm2eXl5LQ6nobHjm/wGe2r/AZxbE+btt99m0qRJLF++nO3btzNgwFmcccYZTY4Q1juYUeN6DUPW\n+vXr+eCDtdx44xS2b9/e6HVvvPFGZjR88vcmN5oIBWRG1e3oC8lxubDW8sWOGnJfXYZ33Di6FGTj\ndjfuuSstl0w6bK+opboujj/gS48wN1YfiPcMyQ1/yPve9ybzwWc7eWTJSt771/ZUW0Mg4HEYf95p\nDB90Ai+/+Cyn9zyFd9dtPOjfaOzJWkskGsNJpurlc7M8dMoNtPuJp8mkQ7A2QmVNhFjSEjhQ/2tj\n9uqS01Jt0sf5YKiPs4jIsS0WT1JZHaY2EieWcPB4PQR8+x9R3n8wsPzmN/cxb968zD6TJk3i//7f\nW2k4AtzwONZaSh5+jOtXvcXJLzzFR5ddRyzuMOClp3hjxETmj59ObThOPOkQTzgkkg6RaIya2joC\nWTkkEknq6mroXNgJv89HdVUlhYUFZAV8BHwesgNecgJecrJSt2+98Q/eXvk6TiLCyGHf5obvXUe4\nrprXVizlhu83/b7Kysp45pn55ObmMnnyZB555FFWrFjBRx991OTX6eqrJ3Hrren3bG2qK0g6PGfq\nuBv8urr++W1PLSD4rQsIeF10LcgmN/vgl1PuqKLxBNvLU4uWBAJ+PAf5Q0g4GmfF6i0sfGsDX+6s\nBcDjNgw+7Ticyo95/rE/cPXVVwGpkerUKPWh1dQnkg7RaAyXgYDXTVF+gJws31E7ip1MOpRXhwjW\nRnGsi+z9vJd0D+z20cdZREQEUu23Hn38SSZPuZlwNMFjT/6FSy4eT8/jj2vWqPKhlDpYaymrDPH5\ntir+tmgFq9d9xSsbnyHieDln82ZOXvQU8/qP4b7OqdGnW/vvYlLpczzjPZF1vQc0cUQ34ZpI6q4r\nwM6qKBAFPFSX1e7zOr6x5Uu6nHkpGMPaKvjBb0v5xta1rOw9gEU/W4DXJKkqr+Wdr1Zw5tdOpig/\ni0/Wv8fil/7BRaPP5zf33c/8efMYMOCsA3/BmrC2uoYz/n/2zjs+ijp/4+/Zvtlskg2EhBKq0gWV\nIigldAjYPSUgakCD4O+4w7vzPBWv2PVEwSNoEIKnEs87PT3pSFNUehcISklCSUjPZvvOzO+P2d1k\nQ0ICBASd5/XKK5vNTtnZ2Znn+/k+n+d5ZBrWjHS+P3CAdm3bYv1gMfa06fhHjCIyQCxOlbiQiyuJ\nNhtoarNcMAH8paDc4aaozIVPlDGbjERa6h4AmtauDunOAZBlTOvW4B42klNFlazYfJT1O3JwevwA\nxEaZGH1Te4b3aUtMpBHoi8Fb2CjOG16fH6/Xj04DVrOeFs2jrviqckOh1WpoZoukmS0St8dHQakT\nRwNTGM8HasVZhQoVKlQ0Kjw+P0VlTt5KX8DCzEVMTBmPIDSsUlazOvz2bWNZeOoMCIJSWZ05E9O6\nL3EPG0lm5iLmzVMqqx07dyGnwIkptjXXXtcfFxbsTm+t29AKEuPsR8i5/masFiNREUasEXq6HtpG\nxaBhRJr11dL8qn6CqX5+UalE+wMV6WB12uP143D7cLr9ONxeojeu4aG3/sjGwXfz4dg0juee4rHv\n/sPtO5YxY/Qf+K5Wgh4OWZbRSG5cFUVEGSXycw/hqyzEV1GA5HfTs2cP9uzZy+zhSQx68dUwe70T\n326iy/f72Ni7H8gyg3dsAao1S9VSjfP7RVweL0adhqYxZqItpoZ85L8I+PwihWVOKpxetBotJlP9\nnaquTz6m46OpgWP+CpmZmUzdt5P4Dxbzj0de5D2qPMS7tGlCcv/23NStRY2Bi8zs2bPDiHNohqEB\nUMiyD71WIMpiIDYq4hczMBJFicJSB+VOLxpd1QyXWnFWoUJFvcjLy+P999/nT3/6EwAvvfQSkyZN\nIjEx8SfeMxU/BwSnScsrvfhlMJsMPPbYo3g8zvOqlFWvMnc68gMvbv6KtlYbs2zxARmCQgxPffgJ\n1/QYwKC7NFT4I7D7jcS3lgA44wTwMqzwAMX9B9PEquO7Dcs5emAXA4tzKOzTm1EvvEhCQkL4xod1\nadyDMqgjdk8OgzPSubGTIsOw7liGc8w4NNdZOPHpbDSGCEaNuZWHmjXhcLd+FJU7KSxzsnv/D5TY\nvWhNVmStGZMtES8Q27lNaPUWvci1HeIZbV7GxIVv4TyVV2WvJwh0+X4fe6/tzODtm1lujmzQLut0\nWqw6RZ9bUOYmv8iB+RfcUChJMqV2V0BDq5zXlgjl+JyrkhzER+V2Eqw20jLS2blzJy1zThNfmENW\n91G8Jydi0GsY2DOR5P7tadci5qztm9auZn5OXlVToSxzeuECMuvQ1QdRnSzHRJqwNYv8RWrZtVoN\nCU2tJAAlFS6KypwImourPqvEWYWKnztWroRRo/hm1iyefu89Cs+coXNODk9/9hntDx9m/OLFYa+r\nfhNg1SoYPfon23UVVz7sTg+FpU48fgmDQY/JXL1Cef6ziGENdbKMxmojzV5Kp06d+CEjA2vJSdbc\nfAd//tpN7+NLON6qBwgCAhJRBh8p8mm2NbHRN2cfUz5LZ3PRt/ylSXMO7drFP/Dyq9NHGb/Zy3PP\nPce8efMa70DUhlrcO4Ka466bvmH8Y78FoMu8lxlkL6XLR//FPVKppO9fns6ECSlIcjEtqvc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EOGY1qvpKXVZ6Flf/yPVCx5n9a5x9k4VnnN4NOnyG3dFuF3T4ZVoqqvo76KVX3NUWJi67OWD5Jv\nQJFwVLMcG+KqZH0doQzVG468ksTxM5UIsoxJryEmykRUhPGim5p+iQgm+jncPiRZwGQyYIlQBiTB\nGYVprVvhHjqczMWKa0N8s2ZnnW9BwhbS2EbGIje5DnHFah4uPqFYxvW7n6RTu2jTLJKUdZ8w/JlH\ncQ/tqqyrtbKunO49WT1lGgOfexn5jTdBEJhli0caM46E9teyZEkWQ1yVvBEgzbXNhgTPKeeQEZz4\n57+xD0xC6/Zg0GnwvPIKnluTSRw3ViEjzVYQNWoUUcFz5625MG4s2ktERARBQKcVFO2uHszUMvhb\nuRIWvgO/+Q2xb7yBLMuId96J6X//I27zBioGDqHo2eepGJDEjQOHUun0oNNpefDB1HCCdZ6o7fs8\nc+bdHD1VztrtOXy15wRHTpZx5GQZi5fvo1/3lgzr1YZu7ZqSmppKSUkpWVlZIdI8fvx4Jea8oKDB\nVecrHScL7Xy1O4+v95wgv8QRer5tvIVDm7+g8Mg2ZMlPkyZNQhKOhr53SZJxuT3otQIJNjNRakLj\nVQOVOKtQ8RNCkmRKKpRUKlEGs8lIk83riZv0K2Vqcchw4lLuCumTCz/6b6gRqC69nmndGuJyj3Oi\nWQKDt28GFDeB1rnHKWygZ+15oVqTTK36aAizHMvMXESXeW/yhr2Ud+6dxLP1aEW1Gk3IQxaUNLNT\nRQ4MOg1REQZsUWa1wfAccLg8FFe4cXtFJBlMJkNYo18Qy5cv48DfXyXuTB4be/dj3pkykOWQFVr1\n8y0+Pp4HHkxl+6ECVm89xs6cGKTjeWDrgu+OpzDeOo4M54/c8O5s7I9MozBNqQzX1JouX76MeV9u\noGfhI+zZo0h8el7fkz9v2U5PtxKXvd4cyTv3TiL5+VfCZkNcQ0dQdksSosOFXqvBZNAQfdc4WpiN\n4YTytnFVj6/E6t3o0YpdY2A6XhAEtJ99BqtWETV6NFHB1036FS1Reh1cHh92pwePR4n6RtBgNOov\n+nsgCAIdWtro0NLGg8nXseX7U6zbkcPeI4V8tTuPr3bn0TTGTN8uzSnzmkHQgKykNe7atZPs7MMI\ngvDTVp3rux7VM+AuKnPy3fen+Gp3HkdOloWet1lNDOjZiqTrE/n7C09x5oetAEoBoEjmn/98X6m4\nP5R6zsKGX5Rwuz1EGLS0ax6lugxdhVA/MRUqfgIEHQtcXhF9jbS1msb6QdLs7d4D09rVWBfMP6de\nL7h8q2oav1Zn8lnXdwiHDG0pWbGP7bu/xxrTDL+swesT8flFPD4x8FjC5xcB0Gg0aDVKB7zf58Xt\njuea0X9EJ0h8efg0R178mHsp4/6MdA7f/SD505+iZZyiRA1JNKq9H6fTyZDDhxloL6XikWlY/BIP\nPvgAffr05asnf8+gl5QbW2ZmJsljkmnz/V7cw0aGeQObjQYwKFX3ikFDKawoQ68VsJh0NIkyYzT8\nsi9rflGivNJNucOL1yciBGQYZnN4ZbmmVj01NZXZJSWhxr6Pe/fjxgBprn6+FZW7WLv9OGu351BU\n7gJAqxG4uVsLhvVuQ48OtyvadLkH9n2blfM4IKWoua6aVc+UlBQef3wm//d/v2bLli0hKcizS7Io\nWLyYifc/gMfrQ6/VIAwZQotIExaz4eqffTgPQm/QK4FD0ZFV1wyP10+Z3Y3Do3zmGq0Wk1F/zuNS\nX7OjUa9l0PWJDLo+kYISB+t35rJuRw5FZS6Wf3cUaE6rpJlIlaexn/mRo6dy6NGzR70WfQ1FQ+Ks\na12uDoeRugJfREnm6KkydhzKZ9uh0xw7VR76X4RRR7/uLRjUM5Fu7ePQBgZknTp1YsuWrQxxVfLR\nmTwyrDaW3JxE6kMP1dmI6BdF3C4vURY9ia3UkJKrGb/sO4wKFZcR1R0LZATMJgOW2jSltWj0guQ5\n2DB0rspJUbmLw7sOMqzG8wUOPZnL9weWM4K9vLbFw/dZlAhwaECD1mDBK4EXMMW24XQlzKEZW0f/\nge9sPWDeBjQCxNuGMyotEZ+2DR2PFtFjwBCsGenEf7CYeFDCIHbu5P4dW/hwyjRKPljMxIXz2bhn\nF58NH8OSJVmM/N8nxG3aQNmTs4h5+blao20J3JxMa1fjSBrG8QJ7SNLRbOvXmG6/td73eLVDFCUq\nXV7KKz24fSKnThewfv2X/F/bxJDkok+fvmzbuoVpbRJZlpNHevp8Tpw4icUSUU2rnhqSSgCkbd8M\n2zdjT5tO8d9eYVd2Pqu3Hmdndj5SwDglIdbCiL5tGXJDa2JqpnFdgNY02Iz37LPPsnz5MiY98CBu\ntw+TKYKRw4fRxKLHqsYInwWjQUd8E0X2FPR1L7V7cHpFEDSYTWeT6Jpym3NppuNjLYwf3oV7h3bm\nhxOlbNzxI1/vOoYDExpbO2y2dgDYEXnp/c10bx9H17ZNaZMQFSKIQSeKugbH1VFfnHVO9551pjjW\n5zAiSjK5BRUcyilm35FC9h0pxOH2VW3boCXFn0OTe++kV5fmGPXas0j7vffex+7du1m/Zy8ZAU1+\n+4I8JQ67xuDQ6/Pj8/qwRRpp0zr2ouQ1Kq4MqMRZhYpLDKfLS2GZs5ofbuNq2URJ5lBOMTuz89l5\nuIAW275m7rb1ZDdpTadixQ7ukK0VKd+vZq0xgo3WWFrE20idlMKenVu5887bMeq1fPbpfxg1cgQt\nmidg0Ck3O0mWESXlR5IkRAn8fhG7y4fd4aHC6aW43EVhWXt6lzo5XVTJ6RIHp0ucLCYRVh8AQJAl\n/pXQnnb5SuRs7N7dXOd182n7axn44isAfLr+S+7avpns7Gw+7tRJsctLm4595hNoS4rr7JIP3mRN\n1W6y0c88gSkjnbzF/0IaOZLYKBPWn4mG0C9KOJxeyh0ePD4RnySj1+swGfSYdXq+2riW7NmvhUku\nbrppO+NW/o84eynx904C4PPPPweqtOrVK5CdvlwBAZnP4bxSPp3+MqtjO0NAs9uvS3MmirnETxxx\nUUSgtqqnNSqGlJQJTEiZiFkLLZpH8dKzv7vIo/bLgSAIWC1V57vD5aG43I3D40ej0yozNlQ1vgXR\nEHmFRiPQqXUsnVr3Je3OvszLyOTjL76iS+8hlPtMeCQ92w7ms+2gEjij12lo2zyaa1rasK3JYuZH\n81m/ezf/GzE6bHBcszpbfZbq+wMH6Na1aygERtetR52NysnJY8MI9cJFi7jhpiQqfXpyfC04snAT\n2bnFeHxS2PtqGm2kVyelcbVPzm5aTHwSu5wbcmupWUVesWI5e/fuA0Hgg36DYPNXpO3eDru3h8i+\ny+tDEkWaWE00TbBe/bMiKkJQibMKFReLlStD+kQAZBlx+QqK+g+i3OFBQkOEqeGOBTU1ekFrKm/3\nHnj634I1Ix0Z2Db1Sb7ec5Jv9p+gzO4JLV7Q/kZ2dbuZG77/lmP3phJtNdJ54dssN0fyRdEhKBYY\n2z+FnAPfsmTRfBzFuRw/fow9e/Zi0kkIgajk+Ph4tFBbOxNNY+refZ9f5GRhJcfzy/khr5TDucXc\n8ck82uUfDZH567xuDkYn8ETLm0l6LR2L1stHfi1FgepNsNIZrE6eq3KZ060HRwYk0S/wv+8PHAgl\nwpE8FgE4XermZJEDk0GLLdKE1WK8aio/bo+PCqcHpzuQeCaBXq/FoNdh0umpORyoTXJxg81ClL2U\nDKuNP2/eRqfOncOCHYBQPPZvfzxI1PbNfH79cJx+LSkrsugF3NRrLDl/eo6kG9vQ9uVZCpFoEV33\n1HkDtKbJyWORZZn7Uu5HFkVMBiP33jGGjq1salW5kWAxG7GYjWFuPV6/jKkBSX51WlAGGuDuuT2Z\nCL1MaqoyGJuX8R4tr+1FXrGXQznFnC528ENeKT/klUJkXxK6jyJlxypOO80MiG5Fv01fsm3UeHaY\n2mPbd5LoSCORZgMRJh2Op5+n7PsD9Nu0AYLpi7n5TFu+nPvvn8SxvHw+/mwlGp2J0XdPJrdcz6sL\nl7P34FG+Pr4Et6jH5Y9m2Y97znpfflcZzWN0ROtdbFzxMbdOnkDqHYqrithxVJi07Njx46Hryfyc\nPJILCkhOHovdbicyMpLUhx7i1F23wjcblXWLEi6Xm7iYCGxRjRMqo+LKgkqcVag4H9QkyStWQHIy\n/OY38MYblDvcyL+dSczCd5A+/ATzyPNvPArTgg4ZjjUjPSTVOP37Zzh6upyeGel8nmvhu8SegDJl\n3qdrc3p1jOfGoztpnv4t9rTp6J5/FQcyG9av5a6jPzDE7eDU9b3Iyspi+vRpTJiQEqrWdOrUidLS\nMrKysti+fQfz5v0DOPtmWR/0Oi1tm0fTtnk0STe0VirC+1dy9FcPceRIXqgK3qU8n+SIZnxX3grR\nU0ls17G0LtgKu74GFALcsgHbW75iOfNy85Uo44x0+gGbByTRMkDOBAgLYNj/Yx5Lv1jKw1MeItKs\nY0H6Wzz44CQSExPPXnktgyJWrbokDWWyLOP1iVS6vDhcPrx+Cb8ogUaDQa9Df45o4LNQi+RiY+9+\nzDpTBoJAdnY2KSkpCEKVtnV48j1cWygRtWC+4orR+350WoEWsRYGf/Upt+1Yhn11G1jdMF/cc2lN\nHYOHUTogiaioaCY/9ABNosxEmAy89Jf6Ld5UXBgEQSDaaiLaasLnFzlT6sDu8IRVoWviXBaUcHbV\n+rG0h8KWr3R52bH/GKu/2k6zxI68o/0VsiQx4cAaAOU8SxwLy/advXFZ5vFyI/0Cf550RdF65GMs\n+1Fg2V+WAl1oMaALAAfsgF15nTWxF2UB5YWgkYm3RdCmeTRtE6Jp1yKajok2Mhek1x2dXm2gHp+R\nHpKWfRYbz5L0+Ur6X+pkZsz4TWhw2PqbjZRMnooggG3h29gijWqy388YKnFWoaKhWLkSxowJkeTQ\ncwBz5lBS4UbQCNgWvoM9bTr+EaMuaDM1NXqFH/2Xb5u1Z89bmazc4seXMIb+o1tyoHNvxl3fmoE9\nE7mmZUxoKtB/zeiw5TMzM5nn17K93yASkoazPiuLm266ieTksSxZ8mFou9nZ2WRnZ9OzZw+2bNmi\neOhy9s3yQt9P3NrVtN+5ls0Dkrjmmo40XZzBgJxv+DquLTpTFM+e2M/o/V/zr+tGY9SK3LFpDfm/\nfxzfa6+HJcRBeOUyNTWV0pISsue9yeDANrt17UqwH75mk9HaNSs5Nu8N/uGuRJJgyZKPcIhGpk19\nmKgIA5YIgxLKUNvnPXOmktq1YsVFkeegM4LD7cPjFfGJEqIkI2g06HVaor5ajxmq9luWMX25qt7E\nMaBOyUV2djYTHvstDqeLzz//HJsthl+Nv59yIYG9Fc34Ys5aoCnfjf4DOdffzAN92pJ0YxtiLHdQ\nuPb+UOAINMwXt+Z57PX5yfvTX4kZkIR21Eg6RJkx6Bs3/EJFw6DXaWkZp/h1lNvdFJY78UuKq0/1\nmZj6LCjrQ6TZwNH937AqK52ePXtwcPceKkvPhP4fF+Fj/LAulDo8lNndlFV6cLp9ON0+pny5kF/t\nX0VWd+U6OmH/KgRB4M2bJwEyPo8TnSDjcdmRfG6iInQkjxzCnp2b2bppHT5nCffcNorf/24mnJ09\neF7Izs5myZkyJkycEPb+9WtWhbzBLf+YqzQmR5rUZL+fOVTirEJFQzFqlEKi5sxBlGRcHh+RGfMp\nSU1Dp9MRu+DizParI0iODuYU8+mJSHas3QdNe4NfxGZw8b+iwzzUvDWTx4475/JwdhNQbKwtpAVc\nsiSLlJQUdu7cGZq679q1G127drvgm2VdCLqBtHz+VVzA5h8Pc++mDZT06IDHrSNl/yo+7TmC1/tO\nRJbB5deQ8s8MPjzuYOJXH3J8/GT468uhKfwq147h3PHlCgYHpAjB9DkgZOdXveo588ghrGfyGL9w\nAevNkdx/fwrTH3sUECh2+Dhd5kID6K/rS9NHHiVqzhx8flFxGHlrrnIOjKp7UCQHdOH+gFOJ2+PH\n4xMRZRmfKCGJip+1VqfFoNOhM2jDLsRBzTZUC5J55olQVHRdNoTBafUxY5KRJduTYW0AACAASURB\nVIlRX3xKv+2b2TwgiYT4eNI++Rf2kgJOz3oBTXRbTtGGKS+txC9GAJVEGHXc0qMVQx8dTMdEW5gm\n0z1sJKb1X573Z24fPBSPy41eIxATacLWLBLtpF+d93pUXDoEq9Aen+Ij73D40el1GA2NEzgUIt8f\nLuG50gLS7KVUpE3nwIEDDN+0jpvWLzrremlau5q411eweUASv83NISUlheamclK2r0K6qT2dZv6B\nZcuWhmbIAPrffjv+01vZ+N93qmnml9AkNiZs0F9vdHoNidHOnTuVWRvgoKyQbpfbiySJRI0cgbh0\nGVHJY9Rkv18QrnzifBmnSlWoOBckGUr/8gIauxvbW3OJRCE2jkBCXmNBlmV2Hi7g0w2HOZhTDCgW\nVE20JWxf8z65rnImTEhhyuSGkdm6moCChFqW5VCluW3bdmRlZdGzZ49Gez9wdvURQDd/IR+++XfG\nvvwaAB9Gm+j029+zKNLGrh8K2HxdS3Z+eQMbErqzJaIF30X2wPLiCm7oGE+ve37NwFuS0AwbyVdP\n/p6JASnCweFjmLUki88Dmuea1n6gEO6Nvfux/oxSk+585IdQOItBr8Og04Y66Mtf+DuSLBATkK2U\npE7lzG+fQcgrCXjuAnKghhWMXSYY16xBoxHQ6bTodHqK69GLho7V0BHYH5mGdcH8s2LMzyWPqD6t\n3vnID/T7ZiMHu11Hy0++wOnxc0gy0jkjnaxdhey4/nagGEGA669txpAbW9O3awvFQaAmztMX1+8X\ncXt86LUQbTHSJk51wbgaYNTraB0fjSzLlNrdlFS4WLT4fZYs+ahuknkeGOJ2kGYvZWPvfrR//hVa\nImAPnFc1beKC14vY0lIeq6gkdfJk+N3jfPjkH+jTpy/m+HgEQSArK4u/3dSbQ+2vYUnWRzzwwCQe\nmz6NaW0ScQ8bUatTSH1uItUlRm906My8lev4uHc/0rZv5t533yXdZObJ3/26yg6wZuLkleANruKS\n4ooizrIsh3eeXsKp0kaBSup/Eah0eigqd+Hyihj0OprpqpELWT6njOB8qs6SJLP5+1P8Z0M2x08r\nVnEWk54x/dsztn97FmbMY4urfgu5hiJIqAsKCgKhBcqNJD8/P8xD92JultVRs0oan5BA/Mt/D/09\nqNrjpBtak3RDa/z39WFoTjHbD11Dy0P5nCyqZNPeE2zae4K3BOiYt5HOA1JY4BMY9drLPK7RYIuN\nRTcmmcKAzVWQaAY/l80Dkrg3N58JEyfQ+cgPTP34fTafyqPlp0pceFgH/dARIe9WUJryLBbzBc0m\n1KcXDUEQKHtBGUxYF8wPI83nOqdqTqs3HzCc2zZ9ybp7HuTprnfjjx3Oa22+J23bvynrch2Rd95O\n/+4taBoTcc79bogvrizLOF1eNIJElNlAq6bRitxFxVUHQRCIjTITG2Xm4Ym3I4guHkh9BAmBmJiY\n8475DlV4pzzCO0d+4NnN23hs8WJSUyeH2cTVho7TJjMzbTplMoDAbToN1kdTKQzsR4fsA0wMRLbb\npk8jOXksnd56HesfZ1D40X9rvWbV5yZSfZA/pqAAj18mYeIESjZ/RY8fDvHgg+PDPLRV/PJwRRHn\nQ3ml6DUCJoOGmEgTlpEjEQJT4yHMmVPvVOllwZVO6lVcFHx+kcIyJ3anFwQNEWYjkbq6K28NNduv\nDcEK85LVBzgWIMw2q4lbB1zDyD5tiTDpycxcdO7pxYtAzRtJ0EO3If6ulxo6rYbu7ePo3j6Oh5Kv\n43RxJTsO5bM9O58Dx4o4lFPCoZwSMN7Mf//+Jb06xdP75mRsTeLqPPbt2rblsVvvUqpYsszmU3mK\n9d0zT6DNyyVixdJQY2bM038ISUzgwgdFprWrSX3ooSpiK8v8rV8fkhspLAICwSc+E9HXDsHctAPP\nRTbDUaYl5etPmVHqoEmUmaScHRQ+NJWUVx9v8P6fyxe3fOAQfJUuLCYdbeMjMRkbZ3pfxZWB9u3a\n8sKfnwQUd5fUBx/A5fHjdHkwGvVoNfXPJNSs8BYEZlqAc2r265otCs66xAsC8S+9hl0rYM1IZ2ba\ndHjr7MCe84Usy0oipdNNfNMmPDVzqpJc2uYunrmgNar4uUGQ5fMXyl8KCIIg5xYqWfCSJOPxehFF\nCb1GIP65p7EueFt5YZCo/tSeiLJcRZRvvx3atIG5Af3j7NmwerVKnq9CVDjcFJbVbtd0TlP+rE9x\nDw8M5hqYcAVw4FgRH64+EJJkxEaZ+NWQzgy5sXVY41R9tlANgd8v4vX7kSUZWZLRaBRfVk1AciAE\nHCjq+mZJKDcVWVb8nSUp8BgBrUZAq9Wi12kvm82b0+1j749n2J6dz45DBZQ7qiz5TAYt118bT5/O\nCYz9eA5NFr0TRn7DqrfVpAighM0UrP1GiS5PuQsgRBzrSgU7F6qfN8/GxrNkSVZI61nremQ5RNiD\n+1Nb1VmWZU4W2tl/tIi9RwrZfvAkfqnq2Euil+ZWmZePraf7/z44a/kLhSTJON0edAI0iTZjs5pU\nj9pfGDxeP8UVLpxuPz5RQhfwEW901Phu1nr+NuQ19UCSZNweH0iiYlkZZSLqZ+L7rqJ2CMo19IIu\nXFdUxTkIjUbAbDIqf8gyMlXkpazSTUVBOdFWE1bzT+jFKggKgT9+HAJBAsyYoZDmxx9XK89XESRJ\nprDUQZnTgyBoMJuMGIxnv66+RKoQGuB8cORkGUvWHGDX4QIArBEG7k7qyKib2teqMz3fsAJZlnF7\nfYh+EZ1WE4qkjo+xoNdpG3UaXRQlvD4Rj9ePw+PD65VCLhEajRIPrLsE0/YRJj39urekX/eWSJLM\nkZOl7MguCMXmbv7+FMLKFTyw8h1W33wHP45Jo2+X5iQ6ncSHZgRGkJm5iKlOJ9bAeg3794Zp1kPV\nq4BNVUNnEoKoXjnrYrXxcadODM49RIbVRn5OHjVrzqZ1a0KkuWZzoDUjnW9a9mClrRPfHyuirNJT\nbUmBSL3IkL4dubFTPNs2LuPWscnEvfJ12PozMxeRPHbcWYOu+gZnHq8Pv89PhElH++ZRGPVX5O1D\nxWWA0aCjRVPlGyNJMnanJ5Rc6Q8E8hj1uit6QOXx+vD6/Oi1GswGDYlxEUSYGui1r+IXjSvzyhes\n2AUrPAuqpsZjMtLRaLXkz3qek0UOdBoBg06DxaTHGmG4/FOFbdpUPf7qK6UKPbf+znsVPz08Pj8F\nxQ4cHj9Go4EIc/1m9WcRpgaQ5OrIL67kw9UH+GbfSQDMRh23DbiGW2+5hgjTxZ27kiTj8ngRkDDr\ndcTHXJ7BpVarwaxVYn1jqDqGsizj8foD4R1evD4JCdDrdRgamXRpNALXJsZybWIs44d3obDMybaD\np9l6MI7fCgLftLwOlu8nc/l+rFGDadfzDML2bCJ37aVr+pvE20uxp03H6XAQ/+F7YXro0vEPsG1x\nZiCSGubnniC5oKDh1f4A4XY6naR9sDgU7pLfoTPJtbiiBAdoTrePPdf04scNh/mx811E3xGDw+3n\nuxORcEI5f2KsRrq3i6Nbu6bc0LEZzWyW0Hp6dkhVrp8fLA5zG0mw2lgOpE6eErbd2jTYsixz3/iJ\naEPV5agrmgypuPzQaASiI00h3W8oAt7hweOT8PklNFoNWq0yiG7w+dOQptQGNq76/CI+nx9JktBp\nNRh1GppGGrBarGrjqorzxpVFnAOykeAXoezJWbU2pURlpOOpUfWxe0SKKyuRA18Mg1bAbNIRaTZg\nMujDyUNjNPUFpRpz5yqV5q++gt27lZ8ZM64MOYmKWmF3ejhT6sQnyphNRiItl36wVeHw8O/12aza\nchS/KGPQaRjTvz13DupIlKWW8vZ5wO32IkoiEUYdbZtdOTpTQRAwGfVh++P1iVQ4PNidXjw+EUGj\nxWjUNUgreT6Ii4kguX8Hkvt3wJHSl76HC9h64DQ7Dxdg94CleTe+K2tJ36NbSLOX8mWfITTrdgOf\nuZzcqf+I63xKJXfvnj0snT+fLVu31t/UVw8iIsKb8FJTJ4ckFyUVbnILKsgtqODoyTJ+PAmni73w\nzXfV3lQ3YiKN3NKuaUD33ZQWTSNrJSIFBQVkv/EaExfOpyJtOv85XcSePXt5LpDMWNgmEXeNZcKa\nCwUNd951D6mTJhHfJFLxp1WhogHQajVhRBqUIoXL5aPS7cXrk/FLVbaMgkZAq9Gi1WrCpXENaEoN\nvqbikekU/vlFREnC5xeJzUin7JbBeIaOQK8ViDTpsMZEYjJe2VVwFVcHrqirYZMHxyO2Sgw149hn\nKilS9sf/eO6pccC6cW3YFDqyjLRiFScGDcEvSmgFAZ1WwLpxHc0m3oPvsf9D8+abymjzQpr6Vq2q\nalScPVtZx+7dyv9ychrleKhoXJRUuCgqd0FQjnEZtunxiSz79kc+3XAYp8ePIMCQG1uTMrxLvW4G\n54IkyThdbvRagWYxEVdNl7dBr6VpTETovbvcPkrsLpxunzKgMDR+NdpiNjCwZyIDeybi80ucyfoP\n/Ra8xoedh/DmgMnM0Jvof2Ifw3/zCK6ON3Gdz8NqWwtyBYG0kpOMt1n4c8r4C/e1rlYVOz3pEVwe\nH+0z0tl7pJB3klLJPWPH4fadtZhBp6FdixiuTbRxTUsb17Sy0byJpUE3/uXLl3Hgi6VU3ns/B23x\n7Fm1HoB1JgvymHEkDzu7cUqUJDxeEafDgauiGJNkJzEhWiUaKi4axoB0I6ZGBLXPL+Lzi3i9iue5\nx+9TejAA+8DB+N7/GFfSMGSvF2SZglnPYR+YhHvgYASfF+egJM58+B+8w4YRY9Jj0GkwpL+FfM/t\nJI4Z89O8WRU/e1xRxDlihWIHZX9kmqLrC9h8+a6/sYoo1zI1fq6mLW2N5hvPiNGUPzyN6Hn/oMSp\n3KxiM9+h4uFHcfa6GbPDjdmgrz/RavRohWiPHKlomoOV55wcRfM8c6Zadb4CENQvlzo86HQ6zObL\nQzBFSWbjrlyyvjxIcbkLgBs6xjNpVDfaNo++iPVKuNweIgw6OrSIueqT18wmPS0DEhW/KFFmd1Ph\n9OL1ieeMAr5Q6HUaVvvs7LXaSDu0HteZw2jNUaScPMjGtr0YfHiLEgPc734ALJs/ICUjnYhxv8bW\neRSix06BO5Jv951Uqul6LYKgfN6iJOPxiThcXiqdPioCMxsJW7/iiX+mK+s1DgIjPN79NClr/82/\n9G05mNiTSLOe1vFRtI6Pom3zaK5tZSMxPiqsAnc+mNa6FXFn8shYsYysQPT2x81iGLz9EOM3bKAg\nM5PU1MmKFt7jQ5ZE/pm5gPmzn+e3v/k1AG+++SbNmsXx1FNPNc7BV6GiBoL9FhF1XZbvryUsp+Zz\nE+4++zUqaVZxCXFJXTUEQfiDLMuvBR7fDZQB7WVZXlDLa0N74u3eA8/NA87ufq8Ldeic6ly2ji5c\nUZbx+UVEvwiyjFYjoNdpMOm1WC1GzEb92XpR1ZbuioRflMgvtlPp8mM0GdBpLw/BlGWZXT+c4f2V\n+8nJrwCgXYtoHhjdnZ7XNLvg9QYrzBaTjuZNIn/2HrmyLFPh9FBW4cbtk5ARMJkaZn9VHwoKCli2\n9AuS/pPF4EAi2Kru1/PNxFRa7D/M33Mrada2OxpzLG5Rz80n9/FdYs+L2mb/vD1sad2TuJgI4mwR\nJNgiuPnUfoQxY2gdH0VMpLFxK7uyxNHkEQzevpkMq42mcU256+gPoVCHoSNG0TS2CWaDlqYxZixm\nI3l5ebz//vv86U9/AuCll15i0qRJJCYmNt5+qVChQsUVgItx1bhkxFkQhOHAE7IsjxQE4UagnSzL\nnwiC8AiwXZblXTVeL1c8Mg3jd9802PA/DOewpDGtXR0u45AkmjyUUlXhrmc7flHC5/PjF8VQM2KE\nSUe0xaRo/9QglCr8xMfC4/OTX1SJwytiNhkvuGJ3IThysoz3V+5n75FCAJrGmJk4oisDeyZecIOe\nEizhwazX0CLO+rMnzHWhuv2VV5QwGvQXJenIXLSQhOf/TJpd0S1nWG3MssUzctRI9u7dR35+PtOm\nTWPHzt0MHXMHh4+domev/hSXu9i++3uaNmsOGh1urx8ArUYTGmhHRhiINBmIjNATFxNBM1sEzWwW\nmkSZGr0R6axrW6Cxen7uCeb9Y16gyqwMDr69eTCxH/4Hk1Gn2G1FNDJZV6FChYqrBFeqHV11Rn4f\nsCrw+CgwHNhVc4Gy518lZtYfQ8RZm5d70TtxloxDlokfdguG/XtxjhmHmNi63lADnVaDThs+ZVzp\nESmttCNLEoYe/Yj9z2eYbx+H0aBX1jFqlEIir2Ty3Ngkt7bq+513KtKVYPX9EhFph8vD6RIn/kDD\nn9Vy+WyFzpQ6yVpzgI278wAl7e/uIZ1I7tf+oqQUbo8XAZl2CVG/+Oas6vZXoihR7lDsr4INhqba\nZoPqgiwzdd/OkJMGQFpGOu07dGDiqtUgCHTq1ImysjK2bvmOPr1v4KlfVzUCPjDmukZ/fxeCc0nU\nxr+diTx9Gj0OH4AAce50TVtiW8ciNHIjpgoVKlT8knBJ7saCINwgy/JaQRCCZqjRQEm1lzSpbbnq\n0cXBBC/xmScuWKoBUPbcK2HpQ9q8XAz79+Lt3oPixVmh9Z5P0hsQ5oVrWruamPF3UTJ5KseffQGj\nXkPz52dhnD+v8eQal4PkXqzEZNQoZX3BpMegx/X114MkKT9Bj+vly5X3cpHHpqzCRWG5Cwkl3e/i\n/CnOD5UuL59syGbZt0fxi4qbS3L/9tyd1AlrxIUTd78o4nZ7aR5rIcZ6dTT9XU5otZpQJDAoDYbF\nFU5cLhGfpJDsc1WjTevWEPfB4rO69YdnpDOkWSLrzZFkZ2eTnZ19/o2ADUBdVeLzsTWEupPVSiZP\nRR41lpkvPEvUoneQZ8xAEASazJkDthi190KFChUqLgKXqowVW8tz9V6pa1rPiAEyXB+hrc+2Jvhc\n8AbjHDNOIc2BysuFhBpUR/AGFpuRHiLTxox0ilOnUtKtL+Yz5disJiW280JwOUguXHyceTAUJrgu\nUEjz7t0wdmzV4xkzlPc0dy489xw8/fR5DQgkSaawzEGZw4Og0V62hr8gvD6RFZuP8smGbCpdSoPp\nwJ6tmDiya5iP7oWg0unGatLSJjH2pwv3ucpgNulpZVIaLoMNhuUOj+IfW0uDYW1BNs/FtyK3WSLx\nqQ/TaddOsrMP17qti01wPGf65Ef/VfavoaQ64A8tihIxgWubI20alrlziF2/Ft59G37zG4TgdxKU\n7+Xo0Vf2TJgKFSpUXMFodOIcrDbXeLqMKjJtA4prW7ZBqWy1oN5Etxo6bjGxdXjF5TxDLM5C4AYG\nhGmsnc+/ikkQECWZk8VOJLESvU6DxajDFmVu+PT75SK5FxpnXls1PIhBg2DgQHjrLYU0X3+98vzc\nuUpU+axZUFR09oBg+fKqzugAmfYMG05BsQOnx4/BqG9QYEljQpZlvt13kn+u/J7CMicA3ds35cEx\n3enQ0nZR6/b6/Ig+H+3io64YH+arETqtJmR3V73B0OUTFRtCowGN5uzvuwysN0fS48D3IdLcpUsX\nlizJwmazhTybawsJgYZ7OtdVJQ7OlJ2LVAf32evz4/P50QBGnYDZUCUHspgNYNBVuf5U/16+8YZK\nmlWoUKHiInEpKs7tBUFojyLHiBUE4QbgX0BvYC3QDlhT24Iv7tgGO7YB0P+WgfS/ZVCDCW2diW4N\nTBa6lAiLEAdcokRZvh1kCYNeS6RZR3Skqe4I28YkuQ1FQ6Uh1avhQT/ruXOV/91+u/I4SJahKiQm\n+PqgdCOI4OOAPlyWZTz/NwPT/Hmcee9j5NHJWC5DYElNHD9dzsKle/n+WBEAreOjeGB0N27oGH9R\nDVayLONwuomNNBLfvFYFk4oLhCAIRFtMRFuUGQm3x0dRee2SjhkzZuD3+0NEOCUlhccfn8nixYtJ\nTh4bWmdYSAgX4OlcxyA7+FxtpLpsyqMU3jQQndONQa8hJsKANcKCQRfwoJ8/T/k+QdX3J0iSa2xb\nJc0qVKj4JWLDhg1s2LChUdbV6MRZluVPAALuGdHKU/JuQRB6C4IwDCiTZXl3bcs+/sTTjb07DUof\numicJznXaTXoIqqIdKVHpMRegSDLGPRaLPUR6cZAMPlwzhyF4LZpU3XTHTlSkVY0RBpSvRoe1DSD\nIseYPRt691aI8m23QW5uVUiMLNc+IJgxQ/k9dy4VTi9+USY28x3luI5JRnOZtZl2p4esNQdZvfUY\nkgzWCAMTRnRleJ+2aC9SSuHx+pBF/8/Cj/lqgMmop1WzKklHaYULu0vxjEajCZsoEQSFeJ9vOuDF\nQAbyZ70QSj4DqHjkUYTXZ9MxohaHmJUrq2aeVDmGChUqVNSJpKQkkpKSQn//9a9/veB1XTJmFvBq\nXlDjb1CqzpcN9co4GgEXS86rNxpCDccOvRaLQUuTvz6N7h9v1V5ZaiiZrF5FDiYf9uunkN0ZM5Sf\nOXPg2LHwbQQf1yYNqYv8vvmmso0gaW7bFv73vyqd89y5yrKzZ4etzu7ycurpvxFX6SX23beV587H\nlrCRIEoya7YeY8maA1S6fGg0AmP7tee+4Z2JNF+cY4csyzhcbppYjTSzXXgYiooLh06rIc5mIS6g\nsPnrcy8y/x9zSJ2SBho9Hyz5mKjoGB6eMiVsuczMTJYsyWLChBSAs6Qc9UKWiX76CawLlCY+ZIjN\nSEcSJewvvESc1YC1WgR7VIQRIk21n/uqHEOFChUqLjt+ER5Xdco4GnH9jUnOaxJpefVKdP94i5LU\nqZT+/lmMeg3NfH4M51NZqtlgOGqUUmn+/PMqScWMGVXPBSu/FyINCb4meGOXZUhOrpJnrFoVIu7e\nH49gWLaUktSpIAjELnibFoIGtD9dY9zhvBLe/mw3x0+XA3Bd+zgmj+tBm4Soi153UMvcvnn0pZ1R\nUHFemPzQJPRaQuEfLWxG7rh1NLLfh0+UEEUZSZYZnDQMj0/igUmT0GgEoqJjGDFyNF6f4ucsyyDJ\nMrIsIcsgSzICMhqNgEYQsH61lqgF6XimPYbljTeUmYYoE9Fz5hB9923K9+KtuQ0fIKtyDBUqVKi4\nrLikyYHnA0EQ5NxCx0+9G1csqltYSZKMx+vFuHYNniHD0es0mA1aLGY9ZpOh9tCP6tKM6jfl2rTG\ndT1X8+a9cmVV5PicOeGR48Hq9OjRyjIrV+JJGorri+WUDUjC6xOJmTObZrNfrLUZCmhYCmQjwuXx\nsWT1QZZvPoIsQ1xMBKnJ3bmpW4tGCYqodLqxRehJCPgRq7j6oIQhiUiyjF+U8ItS2P8FQUCnFdBp\nNWg1GuV3bRKL2voHQE0hVaFChYrLgCsyOfB8oRLnC0OQUIuyjNfrx+8XsW5ci2fYCPRaAaNei9mk\nx2TQoddq0PyuFjIMVTdoCNMZn0Wyg+Q5WMGuWaGeOxf/uFvRLf0CgPKHH6Vg1vOIkkz8c88Qu+id\nMIeAmp62pi9XEZdyV73OAo2N7YdOk/H5HorKXWg0ArcPuIZ7h3ZulOARMeDL3Cbeitl0+YJZVFyF\nUFNIVahQoeKS40pNDlTRyKiPZJqNemKeezqMZLoliYpyD5LkQhJFEircIV/AcoeH8lOlxPzlaaLe\nfRvH1OkIQETAFcM5dTqOZ59HRsbi8mKZM4czNw3EPWQ4co+biHn4UaLffRv7yGR8djexmRmUTJ5K\n4Z9fwDp+A5FfrSM6Ix1NwC/bukhp8nMPHRF6TzWJsHv4qEuuSa+OUrubhUv38u2+kwB0aBnD9Dtv\noF2LmEZZv9OtxGV3ah2rxhurqB+q9EKFChUqrmioxPkqQW3BCab1XwLU6gkbJKdajQazUVPl/BF0\nqACiM9LRnzxBxIqlVKRNp/gvL4MsEyvKRL87n/KBQ3F7lRkJ599ewTF0JJ5hIxFQ0mwqXvw7Go0m\nTFrheP5VIgQBcdQYykeORqAW2616COSl1qSD0qC3bmcu/9/evcbIddZ3HP89c5/Z2Z2Zvdp78WXt\nNSFAEjsOJYRAwXZaEAFETFDpCypKoDdRqVIgSOVVRRWIhKpWLRcLCVVqaSjXNkVVHIdVaZBI4jgk\nqUNIcO5x4tjejXd35lzmnKcv9qwzttf2rjOzc/t+pNGcOTtzzmP5aM5vn32e//Od/3pUC46vdDKu\nT+y5XB+4dvLcP61fgjC0KlccjQ70qJBn9T8AADoBwblNXHDhBGsvGk4vVPlj9rYvae6vvqBE9JlT\nf3uHvN03qLrrhjMuELdBwyTW2slTjr7+o4d08IlXJEnbt43osx++8g2v+rfE9XwZG2pqvLT8eHMA\nANCWCM7t4nwLJ/zNV1T80hcu+vFVVf5YSQ/vxWpXS01feGY59z3ygr75k4c1X/HVk0nqj2+8Qu+5\naqJuwyjmFioa7KPMHAAAnYjg3OaKf/159e77+orCaT2HQFysdvXSdkMXnlmFubKrff/xiP73kRck\nSVdNDevPPrpDg4X6LNtdDQJ5jqfJdSyZDQBAp6KqRru4QA/v3C1/qtkv3yHpjVWgOHvyoaxV5t79\n5z3Oxd6/2uM1ysEnXtY//vAhzc65Sifj+qMPvE03vH1T3XqZyxVP2ZTRxHAfEwABAGhxlKPrAstN\nDlw2JF9iOF3x8dtIxfX1nZ8+pv0PPCNJumxjvz6392qtG8jX5fjWWi0sOFo/0KNiLxMAAQBoBwTn\nLtHQHtzz9Gg3Y7nrevi/I8f1Dz84qGMzZSXiMX1iz5t147umFI/V59/h+VWFVV+b1hfPWOURAAC0\nNoIz6qMmPEsrLx/XSjw/0L/sP6y77ntK1kqbRwv63N6ddVkue0m54qonHdP4MBMAAQBoNyyAAkh6\n+qVZ/d33HtTzx+YUixnt/d1t2vvey5RM1Kck3NLQjNFBajMDANCNCM5YdLHyci3c6xyEVj/5+ZP6\nt3sOqxpYjQ7m9Zcfu1pTE/0X//AKVYNAvutpy1hRqSRDMwAA6EYEZ0i6x/BmzAAAEepJREFUeHm5\nVp0ceGxmQX//7wd1+JkTkqTf/53N+uT736p0qn6XtuP6SselTRMsmw0AQDdjjDNOa5XycSthrdXP\nHnpO377rEVXcqoq9af3FR3dox5vW1fU882VHg71pDdVpVUEAANBcTA5EV3lt3tU3fnxIvzx8VJL0\njreM6k8+cpX6etJ1O0cYWpUrjiaG88pn63dcAADQXEwORNd48Ncv659++JBm513l0gl9+kNX1nXJ\nbEkKgkCe62nrGKXmAADA6wjOaAtlx9c///djuvv+ZyRJl28a0Oc+tlPDpVxdz+N6vmI21BTjmQEA\nwFkIzmh59z9+VN/6ycM6ecpZXMzkhst143Vb67aYyZJyxVNvNq7RQeozAwCAcxGc0bJm5hx9+z8f\n0S8ee1GStHW8pD//6HZtXFf/YDtfdjRSzKq/L1v3YwMAgM5AcEbLsdbq3oPP6js/fUwLjq9MKq4/\n2HO5PnDtlrr3MkvS3HxFE8N59eaYBAgAAM6P4IyW8tLxeX3jx4f02JHjkqTt20b02Q9fqeEGlIML\nQ6uFsqPJ9X3KpJN1Pz4AAOgsBGe0hLLj6/vTT+iu+55SNbDqy6X0qQ9eoeuvHG/IJL1qEMp3XW2b\nKCkRr8+S3AAAoLMRnNFUQWj1s4ee1b/efViz864k6b07NuiT739rXesy16oGgQLf19bxfsUaMPQD\nAAB0JoIzmsJaq18ePqrv7j+s54/NSZLetKFfn/rgFZoaLzXsvK7nK2GstoyVKDcHAABWheCMNWWt\n1a+eOqbv7n9cT74wI0kaLuX0hzdcrndd0ZhhGUsc11c2KY0PFxt2DgAA0LkIzlgT1lo98OuX9f2f\nPaGnosBc6Enr5vddpt3XbFIy0dhxxhXHUyGb0MhAvqHnAQAAnYvgjIZy/UA//9Xzuuu+3+q5V05J\nkvp6UvrQu7bq/e/Yomy68ZdguexooC+twWL9K3MAAIDuQXBGQxybKeueB5/R3b98WqfKniSpvy+j\nj1w/pT3XbFI6tTaX3vyCo/X9ORV7M2tyPgAA0LkIzqgbzw90/+GjuufgM3r0t6/K2sX9k6NF3Xjd\nFr3zbeMNH5JRa36+ovGhvHobVJ0DAAB0F4Iz3rAjL83qwIPP6n8efl4Lji9JSiZiesdbRvV7b9+s\nN28aWPMKFnPzFW0a6VUum1rT8wIAgM5FcMYleen4nH7x6Eu679EX9OzLp07vnxwtatfOjbr+ynHl\nmxBarbWaX6hocn2B1QABAEBdNSQ4G2NuiTa3WGtvi/bdJGlW0qS1dl8jzovGWgrLv3jsRT1z9LXT\n+/PZpN5z1Qa97+oN2jzavFJvYWhVLjvaOlZSKhlvWjsAAEBnqntwNsbsknSPtfZpY8z3otcnJcla\ne8AYM2mM2W6tPVTvc6O+gtDqqRdmdOg3r+j+x4+eEZZz6YSuuXy9rnvbmK7cOqxkorlBNQytKhVH\nW8eLTW8LAADoTI3ocZ6MHvskHYm290jaH/38iKTdkgjOLWh2ztGhJ4/p0G9e0cNPvqL5in/6Z7lM\nUm9/8zq9s0XC8pIgDOVWXE2NlxSPr93kQwAA0F3qHpzPGoaxQ9Kdkq6WdKJm/0C9z4vVs9bq5ZML\n+s3zM3ry+ZN6/NkTevql1854z0h/j3ZsG9H2bSO6cutQy4TlJdVqoKrvaWqiX7EYS2gDAIDGadjk\nQGPMDkkHrbWHoooKF001X/vql09vX3vd9br2unc3qnldJwitXp1Z0Auvzuu3L87oyedn9OQLM5qL\naiwvSSViesvkUBSWh7V+IL/mFTFWqhoECqq+towRmgEAwPKmp6c1PT1dl2MZu1Rst86MMbdaa++I\ntm+XtD8a47xX0ualn9W83z736kJD2tItKq6vmTlHM6dcvTyzoKPH5/Xiq3N66fi8jp5YUDUIz/lM\noSetqYmStk30a2qipMs2DijdBhPr/GpVCgJtHi22bLAHAACtxxgja+0lhYdGVdX4TE1o3qXF4Ro7\nJR2QtFmvj3fuemFo5Qeh/GogvxpGj2g7COX5gSqurwWnqrLj1zyqmqt4mp1zFsPynCPHCy54roFC\nVmODeW1aX9DUeElTE/0aKmbbLnh6flVxhdo0Vmp2UwAAQBdpRFWN3ZJuN8Z8XlK/pL3RcI2dUYie\ntdY+XO/zNpJfDTU772i+7Gm+4mu+4kUPX/NlT44XnBl8g2VCcBSEzw7IQVi/Hv9UMq5Sb0al3rSG\nCjmNDuU1Ntir0aG81g/klU23f9lu1/OViksbRppX9g4AAHSnhg3VWK1mDtUIglAnTjk6NrOgYzPl\n6PH69slTFdUx354jmYgpGY8pmYgvbifO3M6lk8plksplEtFzUj3ppHqyySgoZ1TqyyiXTrRd7/Fq\nOK6vXMpobKiv2U0BAABtquWGarQavxroxClHJ2YrOv5auSYcLwbk469VLtjzGzNSf19GvbmU8tmU\nerJJ9UbP+VxK2VTi3MB7viB81v5EPNbRY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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "K1 = GPy.kern.Bias(1)\n", "K2 = GPy.kern.Linear(1)\n", "K3 = GPy.kern.Matern32(1)\n", "lcm = GPy.util.multioutput.LCM(input_dim=1,num_outputs=2,kernels_list=[K1,K2,K3])\n", "\n", "m = GPy.models.GPCoregionalizedRegression([X1,X2],[Y1,Y2],kernel=lcm)\n", "m['.*ICM.*var'].unconstrain()\n", "m['.*ICM0.*var'].constrain_fixed(1.)\n", "m['.*ICM0.*W'].constrain_fixed(0)\n", "m['.*ICM1.*var'].constrain_fixed(1.)\n", "m['.*ICM1.*W'].constrain_fixed(0)\n", "m.optimize()\n", "plot_2outputs(m,xlim=(0,100),ylim=(-20,60))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Prediction at new input values" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Behind the scenes, this model is using an extended input space with an additional dimension that points at the output each data point belongs to. To make use of the prediction function of GPy, this model needs the input array to have the extended format." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For example if we want to make predictions in the region 100 to 100 for the second output, we need to define the new inputs as follows:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[100 1]\n", " [101 1]\n", " [102 1]\n", " [103 1]\n", " [104 1]\n", " [105 1]\n", " [106 1]\n", " [107 1]\n", " [108 1]\n", " [109 1]]\n" ] } ], "source": [ "newX = np.arange(100,110)[:,None]\n", "newX = np.hstack([newX,np.ones_like(newX)])\n", "print newX" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\color{firebrick}{\\textbf{Note:}}$ remember that Python starts counting from zero, so input 1 is actually the second input." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also need to pass another output to the predict function. This is an array that tells which $\\color{firebrick}{\\textbf{noise model}}$ is associated to each point to be predicted. This is a dictionary constructed as follows:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [], "source": [ "noise_dict = {'output_index':newX[:,1:].astype(int)}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The astype(int) function is to ensure that the values of the dictionary are integers, otherwise the Python complains when using them as indices. Then prediction is command can then be called this way:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(array([[ 61.6493168 ],\n", " [ 60.97078391],\n", " [ 60.29634431],\n", " [ 59.62608188],\n", " [ 58.96007595],\n", " [ 58.29840145],\n", " [ 57.64112904],\n", " [ 56.98832524],\n", " [ 56.34005258],\n", " [ 55.6963697 ]]), array([[ 10.03066081],\n", " [ 13.9122405 ],\n", " [ 19.37464407],\n", " [ 26.60289973],\n", " [ 35.75497252],\n", " [ 46.96392513],\n", " [ 60.33994173],\n", " [ 75.97221989],\n", " [ 93.93074111],\n", " [ 114.26792495]]))" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m.predict(newX,Y_metadata=noise_dict)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\color{firebrick}{\\textbf{Why we need the output_index if we already extend the input space?}}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the case of the coregionalized model, each output is automatically assigned a specific Gaussian noise parameter. However, GPy is flexible enough to do more crazy stuff. Think about using an heteroscedastic noise model for each output... Not straightforward, at the moment, but the pieces are in place to handle it." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can even use different models, not only Gaussian noise. For example, Bernoulli noise or Poisson noise... but that is part of a future notebook. " ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.11" } }, "nbformat": 4, "nbformat_minor": 0 }