Skip to content

Instantly share code, notes, and snippets.

@aasensio
Last active December 17, 2015 12:39
Show Gist options
  • Save aasensio/5611861 to your computer and use it in GitHub Desktop.
Save aasensio/5611861 to your computer and use it in GitHub Desktop.
Bayesian Linear Regression
{
"metadata": {
"name": "Bayesian linear regression"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Bayesian linear regression"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Initial steps"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Some initial imports to make our code work. It uses NumPy, Matplotlib and emcee."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"import matplotlib.pylab as plt\n",
"import emcee\n",
"import random\n",
"import IPython"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Define our fake \"observations\", which is obtained from a linear function $y=1.2x+0.5$ with Gaussian noise with $\\sigma=0.5$ and a few outliers added."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"nPoints = 30\n",
"sigmaNoise = 0.5\n",
"xTrend = np.linspace(0,5,num=nPoints)\n",
"yTrend = 1.2 * xTrend + 0.5 + sigmaNoise*np.random.randn(nPoints)\n",
"xOutliers = np.asarray([1,1,4.2])\n",
"yOutliers = np.asarray([8,6,3])\n",
"xObs = np.append(xTrend, xOutliers)\n",
"yObs = np.append(yTrend, yOutliers)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plot the initial data."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.plot(xTrend, yTrend, marker='.',color='k',linestyle='none')\n",
"plt.plot(xOutliers, yOutliers, marker='o',color='r',linestyle='none')\n",
"plt.xlabel('x')\n",
"plt.ylabel('y')\n",
"plt.savefig('originalData.png',format='png',dpi=600)\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAEKCAYAAAD+XoUoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nh5hsu1YAAAAASUVORK5CYII=\n"
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Standard regression"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We want to do the full sampling of the likelihood (equivalent to a sampling of the posterior distribution with flat priors). Let's define a class which returns the $\\log \\mathcal{L}=-\\chi^2/2$."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"class linearFit:\n",
" def __init__(self, x, y, sigma):\n",
" self.x = x\n",
" self.y = y\n",
" self.sigma = sigma\n",
" \n",
" def logPosterior(self, x):\n",
" model = x[1]+x[0]*self.x\n",
" return -0.5 * np.sum((model-self.y)**2 / self.sigma**2)\n",
" \n",
" def __call__(self, x):\n",
" return self.logPosterior(x)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First do the Bayesian inference without taking into account the outliers. To this end, we use the sampling package emcee (https://github.com/dfm/emcee)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mcmcLinear = linearFit(xTrend, yTrend, sigmaNoise)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ndim, nwalkers = 2, 10\n",
"pInit = [1.0,1.0]\n",
"p0 = emcee.utils.sample_ball(pInit, 0.1*np.ones(ndim), nwalkers)\n",
"\n",
"sampler = emcee.EnsembleSampler(nwalkers, ndim, mcmcLinear)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Do an initial short sampling to avoid the transitory called the \"burn-in\". Then, do the final sampling."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"pos, prob, state = sampler.run_mcmc(p0, 100)\n",
"sampler.reset()\n",
"pos, prob, state = sampler.run_mcmc(pos, 1000)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Do some plots."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig = plt.figure(figsize=(8,6))\n",
"labels = ['b','m']\n",
"values = [1.2, 0.5]\n",
"loop = 1\n",
"for i in range(2):\n",
" plt.subplot(2,2,loop)\n",
" plt.plot(sampler.flatchain[:,i],marker='.',linestyle='none')\n",
" plt.xlabel('Iteration')\n",
" plt.ylabel(labels[i])\n",
" loop += 1\n",
"for i in range(2):\n",
" plt.subplot(2,2,loop)\n",
" plt.hist(sampler.flatchain[:,i])\n",
" plt.xlabel(labels[i])\n",
" plt.ylabel('Frequency')\n",
" plt.axvline(values[i], color='red', linewidth=4)\n",
" loop += 1\n",
"plt.tight_layout()\n",
"plt.savefig('mcmcNoOutlier.png',format='png')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAjkAAAGqCAYAAADp8VUdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n"
}
],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plot the original observations and a sample of the straight lines from the likelihood."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.plot(xTrend, yTrend, marker='.',color='k',linestyle='none')\n",
"plt.plot(xTrend, 1.2*xTrend+0.5)\n",
"samples = range(nwalkers*1000)\n",
"random.shuffle(samples)\n",
"for i in range(10):\n",
" plt.plot(xTrend, sampler.flatchain[samples[i],1]+sampler.flatchain[samples[i],0]*xTrend, color='r')\n",
"plt.xlabel('x')\n",
"plt.ylabel('y')\n",
"plt.savefig('fitNoOutlier.png',format='png',dpi=600)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAEKCAYAAAD+XoUoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niAZ9pZTKRf4PjxFmB1tXesUAAAAASUVORK5CYII=\n"
}
],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now do the same but including the outliers. Since the fit is not robust to ouliers, the fit will not be good. The reason is: 1) the model is not good for the ouliers, 2) the assumption of Gaussian noise with fixed variance is not correct."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mcmcLinear = linearFit(xObs, yObs, sigmaNoise)\n",
"ndim, nwalkers = 2, 10\n",
"pInit = [1.0,1.0]\n",
"p0 = emcee.utils.sample_ball(pInit, 0.1*np.ones(ndim), nwalkers)\n",
"\n",
"sampler = emcee.EnsembleSampler(nwalkers, ndim, mcmcLinear)\n",
"pos, prob, state = sampler.run_mcmc(p0, 100)\n",
"sampler.reset()\n",
"pos, prob, state = sampler.run_mcmc(pos, 1000)\n",
"\n",
"fig = plt.figure(figsize=(8,6))\n",
"labels = ['b','m']\n",
"values = [1.2, 0.5]\n",
"loop = 1\n",
"for i in range(2):\n",
" plt.subplot(2,2,loop)\n",
" plt.plot(sampler.flatchain[:,i],marker='.',linestyle='none')\n",
" plt.xlabel('Iteration')\n",
" plt.ylabel(labels[i])\n",
" loop += 1\n",
"for i in range(2):\n",
" plt.subplot(2,2,loop)\n",
" plt.hist(sampler.flatchain[:,i])\n",
" plt.xlabel(labels[i])\n",
" plt.ylabel('Frequency')\n",
" plt.axvline(values[i], color='red', linewidth=4)\n",
" loop += 1\n",
"plt.tight_layout()\n",
"plt.savefig('mcmcWithOutliers.png',format='png')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAjkAAAGqCAYAAADp8VUdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIiLSpf8HjLzDoBWF5C8AAAAASUVORK5CYII=\n"
}
],
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.plot(xObs, yObs, marker='.',color='k',linestyle='none')\n",
"plt.plot(xTrend, 1.2*xTrend+0.5)\n",
"plt.xlim([0,5])\n",
"plt.ylim([-2,9])\n",
"samples = range(nwalkers*1000)\n",
"random.shuffle(samples)\n",
"for i in range(10):\n",
" plt.plot(xTrend, sampler.flatchain[samples[i],1]+sampler.flatchain[samples[i],0]*xTrend, color='r')\n",
"plt.xlabel('x')\n",
"plt.ylabel('y')\n",
"plt.savefig('fitWithOutliers.png',format='png',dpi=600)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAEGCAYAAACJnEVTAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n"
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Modeling the outliers"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If we want to have a robust fit, we have to model the outliers. We model them as coming from a broad Gaussian distribution and we let the method infer the value of the mean and variance of the distribution. Each point has a probability $P_\\mathrm{bad}$ of being an outlier."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"class linearFitWithOutliers:\n",
" def __init__(self, x, y, sigma):\n",
" self.x = x\n",
" self.y = y\n",
" self.sigma = sigma\n",
" self.nObs = x.size\n",
" \n",
" def logPrior(self,x):\n",
" if (x[2] < 0.0 or x[2] > 1.0 or x[4] <= 0.0):\n",
" return -np.inf\n",
" else:\n",
" return 1.0 / x[4]\n",
" \n",
" def logLikelihood(self,x):\n",
" PBad = x[2]\n",
" YBad = x[3]\n",
" VBad = x[4]\n",
" model = x[0]*self.x+x[1]\n",
" termBad = PBad * np.exp(-0.5 * (YBad-self.y)**2 / VBad**2) / (VBad*np.sqrt(2.0*np.pi))\n",
" termNoBad = (1.0-PBad) * np.exp(-0.5 * (model-self.y)**2 / self.sigma**2) / (self.sigma*np.sqrt(2.0*np.pi)) \n",
" \n",
" return np.sum(np.log(termBad+termNoBad))\n",
" \n",
" def logPosterior(self, x):\n",
" t1 = self.logPrior(x)\n",
" if np.isinf(t1):\n",
" return t1\n",
" \n",
" t2 = self.logLikelihood(x)\n",
" \n",
" return t1 + t2\n",
" \n",
" def __call__(self, x):\n",
" return self.logPosterior(x)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 29
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mcmcLinearOutlier = linearFitWithOutliers(xObs, yObs, sigmaNoise)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 30
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ndim, nwalkers = 5, 10\n",
"pInit = [1.0,1.0,0.5,np.mean(yObs),np.std(yObs)]\n",
"p0 = emcee.utils.sample_ball(pInit, 0.1*np.ones(ndim), nwalkers)\n",
"\n",
"sampler = emcee.EnsembleSampler(nwalkers, ndim, mcmcLinearOutlier)\n",
"pos, prob, state = sampler.run_mcmc(p0, 300)\n",
"sampler.reset()\n",
"pos, prob, state = sampler.run_mcmc(pos, 1000)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 31
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"loop = 1\n",
"fig = plt.figure(figsize=(16, 6))\n",
"labels = ['b','m','Pbad','Ybad','Vbad']\n",
"values = [1.2, 0.5]\n",
"for i in range(5):\n",
" plt.subplot(2,5,loop)\n",
" plt.plot(sampler.flatchain[:,i],marker='.',linestyle='none')\n",
" plt.ylabel(labels[i])\n",
" plt.xlabel('Iteration')\n",
" loop += 1\n",
"for i in range(5):\n",
" plt.subplot(2,5,loop)\n",
" plt.hist(sampler.flatchain[:,i])\n",
" plt.xlabel(labels[i])\n",
" plt.ylabel('Frequency')\n",
" loop += 1\n",
"plt.tight_layout()\n",
"plt.savefig('mcmcWithOutliersRobust.png',format='png')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAABHkAAAGqCAYAAACf/pj+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsnXl8FUW693/nZCEJS8KSBEjYl4QlhGACKKBRCAjI4kgU\nvKOImMwFuY7vOOpcr77AMCM4w507zigu8w7i1UEFZhRQk3HByKohAYwaRxAThEhQJBFZhJDU+0dR\n6eo+3X36LH22PN/Ppz7nnO7qquo6Vd1VTz31PA7GGANBEARBEARBEARBEAQR1jiDXQCCIAiCIAiC\nIAiCIAjCd0jIQxAEQRAEQRAEQRAEEQGQkIcgCIIgCIIgCIIgCCICICEPQRAEQRAEQRAEQRBEBEBC\nHoIgCIIgCIIgCIIgiAiAhDwEQRAEQRAEQRAEQRARQFCFPHfeeSdSU1ORlZVlGKesrAw5OTkYPnw4\n8vPzA1c4gmiDuOuTf/vb35CdnY0RI0Zg3LhxqKqqCnAJCaJtUVpaiszMTAwaNAiPPfaYy/mysjIk\nJiYiJycHOTk5+M1vfhOEUhJEZKL3Tjx16hQKCgowePBgTJ48GY2Nja3nVq5ciUGDBiEzMxNvvfVW\nMIpMEBFNY2Mj5syZgyFDhmDo0KH48MMPqU8ShA5BFfIsWLAApaWlhucbGxtx9913Y+vWrfjkk0+w\nadOmAJaOINoe7vpk//79sX37dlRVVeGRRx5BcXFxAEtHEG2L5uZmLFmyBKWlpaiursZLL72Ezz77\nzCXeNddcg/3792P//v14+OGHg1BSgohM9N6Jq1atQkFBAQ4ePIiJEydi1apVAIDq6mq88sorqK6u\nRmlpKRYvXoyWlpZgFJsgIpaf//znmDZtGj777DNUVVUhMzOT+iRB6BAdzMwnTJiA2tpaw/Pr16/H\nTTfdhPT0dABAt27ddOM5HA47ikcQHsEYC3YRfMZdn7zyyitbv48ZMwbHjh1ziUP9kQgFIqE/lpeX\nY+DAgejbty8AYO7cudi8eTOGDBmiiufuXqlPEsEmXPuj3jtxy5YteP/99wEA8+fPR35+PlatWoXN\nmzdj3rx5iImJQd++fTFw4ECUl5dj7NixquupPxLBJlz74/fff48dO3bg+eefBwBER0cjMTHRpz5J\n/ZEINnb1x5C2yXPo0CGcOnUK1157LXJzc/HCCy8YxmWMBS0sXbqU8m/D+TMWni9LX/nrX/+KadOm\n6Z5r6+0h2GWwO/+MDIbERIZu3Rhqa0Pv/iOFuro69OrVq/V3eno66urqVHEcDgd2796N7OxsTJs2\nDdXV1bppRXJ7pPxDO/9I48SJE0hNTQUApKam4sSJEwCAr7/+unVREtDvr4K23B4o/+DmH87U1NQg\nOTkZCxYswKhRo1BUVISzZ8/63Cfbcnug/IObv50EVZPHHU1NTdi3bx/effddnDt3DldeeSXGjh2L\nQYMGBbtoBNGmee+997B27Vrs2rUr2EUhgkB9PfD99/z7+PHA0aPBLU+kYmWFcdSoUTh69CgSEhJQ\nUlKC2bNn4+DBgwEoHUEQDofDtJ+SlgBB+I9Lly5h3759eOKJJ5CXl4d77723dWuWgPokQXBCWpOn\nV69emDx5MuLj49G1a1dcffXV+Oijj4JdLIJo01RVVaGoqAhbtmxB586dg10cIgjExPBPpxMYOBCQ\nbBwSfiQtLQ1HJQna0aNHVauSANCxY0ckJCQAAKZOnYqmpiacOnUqoOUkiLZEamoq6uvrAQDHjx9H\nSkoKANf+euzYMaSlpQWljAQRiaSnpyM9PR15eXkAgDlz5mDfvn3o3r079UmC0BDSQp5Zs2Zh586d\naG5uxrlz5/Dhhx9i6NChwS6WC8H2+kX5Bzf/tsRXX32Fn/zkJ3jxxRcxcODAYBdHl1BoD8Eug935\nV1QA7doBLS1AWRmgtb8d7PuPFHJzc3Ho0CHU1tbi4sWLeOWVVzBz5kxVnBMnTrSq/JaXl4Mxhi5d\nugSjuIYEuz1Q/sHNP9KYOXNmq02Q559/HrNnz249/vLLL+PixYuoqanBoUOHMHr06GAWVZdgtwfK\nP7j5hzPdu3dHr169WrVV33nnHQwbNgwzZswI2z4Z7PZA+Qc3fztxMLs3hJkwb948vP/++zh58iRS\nU1OxfPlyNDU1AQB+9rOfAQBWr16N5557Dk6nE0VFRbjnnntc0nE4HLbvayMIMyKlDbrrk3fddRde\nffVV9O7dGwAQExOD8vJyVRqRUheEOdOmASUlQF4e8NZbQFJSsEukEEltsKSkBPfeey+am5uxcOFC\n/Od//ieeeeYZALxPPvnkk3jqqacQHR2NhIQE/OEPf9A19Bop9UGEH+Hc/rTvxF//+teYNWsWbr75\nZnz11Vfo27cvNmzYgKTLD8BHH30Ua9euRXR0NB5//HFMmTLFJc1wrg8i/An39vfRRx/hrrvuwsWL\nFzFgwAA899xzaG5u9rpPhnt9EOGNne0vqEIef0EdlAg21AYVqC7aBo2NXIPn2WdDS8ADUBvUQvVB\nBBNqf2qoPohgQu1PDdUHEUxIyOMG6qBEsKE2qEB1QQQbaoNqqD6IYELtTw3VBxFMqP2pofoggomd\n7S+kbfIQBEEQ7snM5No0ycnAkSPBLo3/KS4G8vP5FjEy8kwQBEEQBEEQxpCQhyAIIsypqeEuzU+e\nBK66Sn0uEgRABw8C77/PbQBpjTwTBEEQBEEQBKFAQh6CIIgwp6VF+T5ypPpcfb0iABo/PrDl8heX\nPYQjL4/bACIIgiAIgiAIQh8S8hAEQYQRepo548bxz6ws4G9/U8ePieGfCQnAzp2BK6c/OXQIiI4G\nDh/mAivCc2jLG0EQBEEQRNuAhDwEQYQckbDFyC70NHNeew0oLAS2b3f1dFVRAaSnA9XVQJ8+gS+v\nP/j2W+DSJeDUqfDVRgo2tOWNIAiCIAiibUBCHoIgQo5I2GJkF3qaOUlJwIYN+q7M+/QBjh4NXwEP\nEBnaSMGGtrwRBEEQRGRAi6GEO0jIQxBEyEGTemNCRTMnkNt/Jk0CYmO5gCIx0d68IpX167m211tv\n6QsDCYIgCIIID8wcbhAEADiYXc7ZA4idPuYJwgrUBhX8URdHjnANnp07w1sDJZLJz+fbfwAuPNiw\nwb68evYEjh/n32fPBl591Tw+9Uc1VB9EMKH2p4bqgwgm1P7UhGt9xMTwbewAX2x7443glofwDjvb\nH2nyEAQRckTCFqNIJ5Dbf378UfkehmMxgiAIgiAIv2HmcIMggAgU8pAHEYIIPahf+g9P6zIpiXum\nio0FPv7Yf+UI5PafK67gnzk5wLp19uZFEARBEAQRypg53CAIIAK3awVyCwFBCMJV3dMO9OqC+qX/\n8LQunU5F+yUuDjh/3tbi2UJjIxduPfustcEM9Uc1VB9EMKH2p4bqgwgm1P7UUH0QwYS2a3kAeRAh\nCO+58847kZqaiqysLMM499xzDwYNGoTs7Gzs37/fUrrUL/3Hrl3K95//3H18+d0Rrsb5zLyHEQRB\nEARBtCVIQ55wR8QJeciDCEF4z4IFC1BaWmp4/s0338QXX3yBQ4cO4dlnn8WiRYsspUv90n+0tCjf\nCwqM44kBgExUlC1Fsh1yFUoQBEEQBME5eJBrdZeU8PEeQWiJOCEPrfgShPdMmDABnTt3Njy/ZcsW\nzJ8/HwAwZswYNDY24sSJE27T9aZf0sReHyGocTqBDz80jicGADKffup5fkarRQ6HEjZt8jxdT6iv\nV1yFjh9vb14EQRAEQRChDGnIE+6IDnYB7rzzTrzxxhtISUnBxzpWQcvKyjBr1iz0798fAHDTTTfh\n4YcfDnQxCYIAUFdXh169erX+Tk9Px7Fjx5CamqqKt2zZstbv+fn5yNeqlFhATOwBPrE/etSbEvtG\nZiYvR0wMUFERGt6+KiuBMWO4gMdkV13rACAqCmhu5r937/Y8v61beR0AwB13cGN/WgoL7fV6FRPD\nPxMSgJ07Xc+XlZWhrKzMvgIQBEEQBEGECOvXe2arkGh7BF3Is2DBAvzHf/wHbr/9dsM411xzDbZs\n2RLAUhEEYYTWQJjD4XCJIwt5kpKAM2e45kllpblgQsbdxN4d3uYr8/nnyvfRowELSku2k5UFnDvn\nPp4YADzyCNfC2bnTOyHVxYvKd52/GgBfSbKTigou6DO6B60gcfny5fYWiCAIgiAIIkg88ADwzTfA\nrbfy8R4JeggtQd+u5W57COA6qSQIIjikpaXhqKRSc+zYMaSlpZlec+YM1yRpauIaKFapqADS04Hq\nau+EE97ma8Q33/ieRiAZO5bbQLruOu8FPAAwahT/zMkBnntOOR4tLREkJ3tfTiv06cM1uUJBk4og\nzCBjmARBEITdkE0ewh1B1+Rxh8PhwO7du5GdnY20tDSsXr0aQ4cOdYnnj+0hBGGVtro9ZObMmXji\niScwd+5cfPDBB0hKSnLZqqXF6eTCFnc2ZGTkbVLe4k2+ZljVJpJdlpeUANdf73veMsXF/OWekGC+\neiNrIQ0ZwjWR3F2jR1oaF+J07ao+fumS8v3HH62nRxCRjGwLq7iY2yIjCIIgCH9CNnkIdzhYCKjJ\n1NbWYsaMGbo2eX744QdERUUhISEBJSUl+PnPf46DBw+q4tjpY54grBApbXDevHl4//33cfLkSaSm\npmL58uVoamoCAPzsZz8DACxZsgSlpaVo3749nnvuOYwSqh6X0dbFxx9bsyEjk5Sk2ONxOICaGs+1\nOLzJV8uuXcDVVwPbtwPjxlm7RrulyZ/NQkwaRd2I/HbscC2fXA6HQylHYaFnE8+ePYHjx/n32bOB\nV191TT8uDjh/3nqadhMp/dFfUH0EjmnTuHA3L4+8CQqo/amh+iCCSbi3v759+6JTp06IiopCTEwM\nysvLcerUKdxyyy04cuQI+vbtiw0bNiDp8sN35cqVWLt2LaKiovCnP/0JkydPVqUXrvXR2Eg2eSIB\nO9tfyAt5tPTr1w+VlZXo0qVL67Fw7aBE5EBtUMEfdREfr9YOSU8PjuFlb5CFH+PHcwGMv8jPd/WY\nBShaS0blEIiJZ9++1uwVadOYNUsxvCyfs0NjSY/YWL79zkiwJaD+qIbqI3DQwNsVan9qqD6IQGBk\nlzDc25/ePPCBBx5At27d8MADD+Cxxx5DQ0MDVq1aherqatx6663Yu3cv6urqMGnSJBw8eBBOp2Kt\nJNzrgwhv7Gx/QbfJ444TJ0603nx5eTkYY6qOTRBE5NGxo/I9Kso7w8vBIjZW+b5mjffp6LkoF+q5\nnTurhSzbt6uvNZpcCvfr33+v2CvyxGjy2bOKnZEOHZTjRUX68f1tn+SyUhkY4xpWBBFqJCVxTTkS\n8BAEEUz8bZcwlNBOirds2YL58+cDAObPn4/XLq9Gbd68GfPmzUNMTAz69u2LgQMHory8PODlJYhg\nEHSbPPL2kF69erlsD9m0aROeeuopREdHIyEhAS+//HKQS0wQhKd46or89Gnl+9VXh5fB3bg4xSPV\ntGn+0UASLsrXr+f2cUT9OJ36W8nk7VwyH3zgaqDPk8noO+8oW8bi4vgg0sz72euvK1u9FixQtnp5\ni7ztTCvYIohQwB9e/QiCIHylpUX5/vbbwSuHv3E4HJg0aRKioqLws5/9DEVFRThx4kSrfcjU1FSc\nuOwK9euvv8bYsWNbr01PT0ddXZ1LmmTXlQgUgbTpGnQhz0svvWR6/u6778bdd98doNIQBGEH9fWK\n4GH8ePeCj/h44MIF/r1TJ3vL5m+EgMfpBN580z9pbtzIP5OSuJBDbM2Ki7NuK0jw7LNcWNPQwK83\nM0rdsSPwww+KcEU28Pfdd/zz3Dngs8/0BXHyljt/aKPu2OG5jSSCCCRi9by5ma+enzsX7BIRBNEW\nueIKvqgGAI8/HjnvzF27dqFHjx749ttvUVBQgMzMTNV5h8MBh95+dem8FlnIQxB2ohUiLl++3La8\nQn67FkEQ4U1mplqz5NgxZfuREbm5/DMnB1i3zrai2UJ2Nv9saQFWrPA+HSHY2bgRmDOHfy8uVtve\nyczU3woVbSK+f+cdYP9+bufoX/8y15KaPp1vP7vqKm50WTYkKwttpk5VX1dczMvQ0KCU0x//47hx\n/P4jZbAaSMi1d2AQph785dWPIAjCG5KT+WekeV/q0aMHACA5ORk33ngjysvLkZqaivr6egDA8ePH\nkZKSAgBIS0vDUWlV8dixY0hLSwt8oQkiCJCQhyAI24iNVbvyFhQWml+3cSO3+XL4MDBoEHDkiH/K\nE4iJ7tdf88/EROD3v/c+nTlzuCBFCHgA7p5ZZv9+bvR41Cj1fe3bp0w2tRQWcsHO0aPut8EdP841\nk3bt4lvtjLZ2CaGc4PXX1cKo2lrzbWGZmfx8crL//utIoLS0FJmZmRg0aBAee+wxw3h79+5FdHQ0\n/vGPfxjGEa69S0pct+wR/qOykmsiHjhAW7Uinb59+2LEiBHIycnB6NGjAQCnTp1CQUEBBg8ejMmT\nJ6ORJKpEkEhO5iExMdgl8R/nzp3DDz/8AAA4e/Ys3nrrLWRlZWHmzJl4/vnnAQDPP/88Zs+eDQCY\nOXMmXn75ZVy8eBE1NTU4dOhQa18liEiHhDwEQdiGMJSrRWipGDF2LN/2cPo0cPIk4K93ciAmumK7\n1vffAz//ue/pJSVxrZjYWLXgRBinzsvjbs7l+8rKUhtGlnFX9zLC0LO4zunkAh8tBw6ohWbyNi2A\naw+ZIbbznTzJt/N5QqRqqDQ3N2PJkiUoLS1FdXU1XnrpJXz22We68R588EFcf/31ph4axH8Zaau6\noUZWFt+iRQKeyMfhcKCsrAz79+9vNea6atUqFBQU4ODBg5g4cSJWrVoV5FISbZX//V/g22/5+3fm\nzGCXxj+cOHECEyZMwMiRIzFmzBjccMMNmDx5Mn71q1/h7bffxuDBg7Ft2zb86le/AgAMHToUN998\nM4YOHYqpU6dizZo1plu5CCKSCAkX6r5C7u+IYENtUEGuC6fT1RbLihXAww8bX19cDPzlL67H/VG9\n06ZxQYhwJW6HB5yoKMXg4eTJwD//6Vt60dFqGzxTpnAbOVVVwFdfcZtFI0YAZWXKfT3wgH4drlsH\nXHZAgeJiLvRKSOAGnfXqorGRrwReuqQcczqBhQtd0y8s5AaZAaCgQC3Ykc9pSUpStvPFxbnfQqZF\ndisv8omE/rhnzx4sX74cpaWlANA6WRSDV8Ef//hHxMbGYu/evbjhhhtw0003uaTlcDjQ0MDItTcR\nFCKhP+rRr18/VFRUoGvXrq3HMjMz8f7777duH8nPz8e//vUv1XWRWh9EaKGVZYgmR+1PDdUHEUzs\nbH9BN7xMEETk0qsXF0TILF1qLuTRbkkCgF/8wj/lWb8etk90ZY8We/f6np7TyYU8TidQXq5oCCQl\nceHLqVO8zgoLlftau1Y/rTfeUIQ8QqsJUDxmaRGGnmWuvhrYutU1rqwdot3yfu21xvd35ozynTFX\nAY87z2yRqqFSV1eHXr16tf5OT0/HhxojL3V1ddi8eTO2bduGvXv3mq5Q/vGPyzB0KPDHP5L3EMJe\nAuk9JJh44uVHC3nzIQJHGa69tgxkW5gg2hYk5CEIwjb0XHknJXENESMhi7xFSPCHPwD33OO7K/Wk\nJGONEjsQhod9obKSe+n58EP1FpCYGP6ZkADs3q2uG3lbl8zGjdzo9Zw5xsIRWcMnJUWdVp8+3A16\nly7qdDt2VP+ftbXq84sXA4sW6ZdJFiK9+67r+UOHFMHZlVcqNo8EKSmRZ3cA0PcAouXee+/FqlWr\nWleCzFaDyHsIESgC6T0kmPji5Yf6IxE48vHee/nYto3/itT+SBCEGrLJQxCEbQhBhMypU+b2cNav\n1z/uqa0Wh0MJv/mNZ9fqpTFsmLndF2E8WHu9r2htfAgbPd99x+t39GhXAYeZdy1h9Hr9ev79rbe4\nDSRh+PjjjxX7PloX8KdOccGdVpaQl6f+vX27+reZ1pTcRh591PW8rBlVX6/YJ/r4Y36stlaxOxBJ\nBoW1XkGOHj2K9PR0VZzKykrMnTsX/fr1w9///ncsXrwYW7ZsCXRRCaJN4omXH4IIJiUlwS4BQRCB\nhoQ8BEHYRkWF/nEzg8QPPOB6rF07YOdO78vxyCPeXyuorjY32CyMB9vNmTNcu4Yxbti6rAy45Rbl\nfHGxWjCiRRheFlpNSUlqw8f79/PzeXmKO3jBDz9wT1paIZLG5ISLEEgr9JGRNYXefddViCYLiBjj\n8ZuauEcxgHtgA3z3ZhZq5Obm4tChQ6itrcXFixfxyiuvYKbGeuaXX36Jmpoa1NTUYM6cOXjqqadc\n4hAE4X889fJDEIFGfk8LRw0EQbQdSMhDEIRtGG2vuu4642v0bPLk5fm2VWvFCu+v1ZbDyO6LntZS\n587+yVdGzzW6sK0D8PozE/JcXnxWIW/96tGDDw4PH+bb5LScPMldtMt8/TXw3/9tnKdZ/UdFKd8v\nXHAVoh04oH+dMAYt2sX33wP332+cT7gRHR2NJ554AlOmTMHQoUNxyy23YMiQIXjmmWfwzDPPBLt4\nBNGm8dTLD0EEGtlhwvjx+p4xCYKIXMi7VoBxZ0SUCE/CqQ2aUVpainvvvRfNzc2466678OCDD6rO\nnzx5Ej/96U9RX1+PS5cu4Ze//CXuuOMOVRy5LoqLuQaO1vNzbCyf0OshPGDJxMUB5897di+/+Q3X\n4HHnzcsM2bMVwLdf7dgBjBvHfyclcc0apxPYsgUoKgKOHVPie+tdKzMT+Pxz/j0mhtvlycpSe6KS\nSUjg8WJigOHDuXaPGUVF3HjyxYtcI+YPf+D1vnMn194ReYjdQfI9lZQA11/vWjcAt0GUlKTepjZ4\nMLcnZLRla+xYfl5QVaW2PWR0z6tXA/fdp+8xLVL6o7+g+iCCCbU/NVQfRCDQbhcXThyo/amh+iCC\niZ3tL+I0eYqLuUtdM9sZwUTeFuGpjRGCsJPm5mYsWbIEpaWlqK6uxksvvYTPNNKZJ554Ajk5OThw\n4ADKyspw33334ZK8XKTh4EFXAQ/A+6gRycmux1591eJNSDz8MN/e462AB3DViGGMe5cSiK1TTU3A\nDTcAAwaoB1Z62j1WuGzSAQBPe8wYJT89oqOV54qeJpSWgwd5HqdOcVs2K1YAR49yobOs1fP992oB\nT1SUYr9Hz7jzv/0b/+zQQTl25oy5TR6tEedp09S/T592vSYhgRuPBnh7iUTDywRBEAThL8y2TRME\nEXlEnJBHuAU2s50RTOQJlC82RgjC35SXl2PgwIHo27cvYmJiMHfuXGzevFkVp0ePHjh9edZ9+vRp\ndO3aFdEmVn6//NL1mNMJvPKKcTn+9jfXY0VFlm7BLZ4KgfWE62+8oXwXW6ecTiAnhz975Gu8FfJo\nr3v7bXV+MmvWcM0oQPG0ZUb37ur0c3L4daJetm3jGjzV1dzgs0xzM9Crl7HtIbG1Ki5OKe/gweZ1\nnZKiCMbcPRdFvHPnFCH5kSORaXiZIAiCUBDODZKT+XOfsE50tKKBTBBE2yDihDxGboFDhYoKZQJF\nW7WIUKKurg69evVq/Z2eno66ujpVnKKiInz66afo2bMnsrOz8fjjj+umtWzZsssuYpcBKFOdS042\n1+zQas84na5enrzFH0LgtWuV75WVQHw8F27o2Y5xZ3PTaNBaUaEWxIhqrqx0TWPrVrVgpk8ffWGQ\noL4eeO89/t3hAP78Z+6hStTLrFlcI2nRIldtnbg447RjYxUBU0EB/2xp4VvHNDv6VNTWKoKx/HzX\n56LsnEbEk4VBXJBYhnbtliEtbRm5JjaAJkgEQYQzpAnvPcOHh+buBoIg7CPihDzvvMM/KyqATz8N\nbln06NNH2RZBEKGEw4K/70cffRQjR47E119/jQMHDuDuu+9u9TAiU1a2DOXly5CRsQxAvurcE0+Y\n56FVDGpp4XZihMtsM4R7cdnFtoyvQmDtdVlZQO/ewIQJaiOHAjPhBqAetGZk8G1OiYncg5VYdZPz\nlG3VCEpK+Har9u15PcXF6Wsg6cEYF8jI9dKzpyLw0fLjj4rWkJaLF5Xn2muvqc+ZNS05b60Wl8MB\nnDjheo0sJO/dGwDyceHCMtTVkZDHCJogBY7iYsVOVrduJFQjCH9AmvDec+AAcPPNwS4F4S9o0Yaw\nQsQJeZqa+KfWdgZBEOakpaXh6NGjrb+PHj2KdGF59zK7d+9GYWEhAGDAgAHo168fPhcWgiWEkKB9\ne9d8CguBTZuMyzFjhusxxhS7NGbINnL04n/xBR8ofvml5+7Ohccp7XVmrtOFu3IjxKDV6eSGqM+e\n5TZoTp7kxoiTk7nnqhtuMN5iJoRAohwXLrgX8sgaOp06cds83bvz8nbqpKSrdz8VFfpCG/mYeA4L\nfvYz47KsX8/rdu9e7o0sJsZcoJeQwIVgYmAjlzcUtTdDBZogBYbiYmDDBm4o/tIl4LvvSKhGEP6A\nNOE9Q7vte8eO4JSD8D/yok3fvuQ5jdAn4oQ88kSDjIwRhHVyc3Nx6NAh1NbW4uLFi3jllVcwc+ZM\nVZzMzEy8c1ld7sSJE/j888/Rv39/3fSio41dZ1+WE+nyj3/oH5c9MBkh28hJTXVd6fjmGy6AsDrx\n6thR+X7pEheGyNcZeX4CuEBEGAc2Qgxa9QTSTU3c1kxdHX+Bl5ToawYlJACjR1sXWsXH87REXZ04\nweu2vp4PFu65h/8/b72lvm7QIGDSJK4tpId8XAheBFOnGttCSklRa0FdumQu0Dt3TtF8mjYNeOop\npbxm2wDbOpMmcS2svDwyUm0nBw+q+6KdQjVazSXaEqQJ7xna7d1ipwMR/mgFeKTUQOgRVCHPnXfe\nidTUVGTp7UGQ2Lt3L6Kjo/EPo9mfxI4dfPKyc2foGBlzt4WEIEKB6OhoPPHEE5gyZQqGDh2KW265\nBUOGDMEzzzyDZ555BgDw0EMPoaKiAtnZ2Zg0aRJ+97vfoYvWPdJlLl0yFgi403DRkpiov1VJi9Ag\naWnhtl7ESseoUfy4kTaDkUFm7U407XV6gpWYGL5lat4891s1xKB13z7Xc0LwIQuu9TRo3n8fOHTI\nOA8tTicSQN2EAAAgAElEQVQXpImJvizIAoDp07kmQlKS+l4PHeL19P33+ppCH32kfNdq8gij1Hq2\nkLRxAUWgZ2Zb6MIFJT1RXsKY48f5lrr33ycD1XYith926gT06GGv1gFtwSMIwog//1k9Zli5Mnhl\nIfxLRYX6Nyk1EHo4mF3O2S2wY8cOdOjQAbfffjs+NpB+NDc3o6CgAAkJCViwYAFuuukmlzh2+pj3\nB9HRyvaI+HhXjzVE+BPqbTCQcNs+DE4nH2DoudqurTWe+BjZb3FXvcXFwF/+YnyeMWDgQL5VKykJ\n2L9fKUN+Pp/8AlwrZMMG/bJoyy2fj47Wt8uTns4FOWbIzwgjcnL4vnorzcyoLIKoKCW/1FS13Zt1\n64D585XfMTFKWjNnAlu2GKe7eDHw5JNcOCPK6XAAXbvyiWhenqvGjbaOr72WG5IGuGBcTwgkExvL\nBT4y1B/VOBwOTJ3KUFKi/x8Q/iMxkW+5jI7mwlsrwmlvSU7m/SohIbS3sFB/VEP14R1JSXxLttPJ\ntVTs7FuRgDyuAYAuXbgWM7U/NeFaHx068C3+DgdfZKP+EJ7Y2f6CqskzYcIEdO7c2TTOn//8Z8yZ\nMwfJycmm8YQ3n2XLlqGsrMyPpfQdeQvJjz/yDulw8MG2rDVAqtfhQ1lZmarNEa60tBgLLq68Uv+4\nkVFfKxw8aHxOaA59+SUXPjQ0AGPHKuetGmQ2m0TpCVWsbtUw01gRdO1qTcAzdKirdo7MihXq/+Xb\nb9XnFy1Svmdmqu/LTMADcHfuWhjjE9H0dGvCBXmLX1qaeVyAC4FIU9I969fTtrZAcPYs/3S37dAf\nkI0Soi1x+rRic2/06GCXJvQR4xoBedeKLH78kX9atVlJtD2i3UcJHnV1ddi8eTO2bduGvXv3mnr/\nCaWJtryKXVLCVxzGjOFbEEaMUOJVVChbDQC1Adfx492v/hP+pbiYCwoSEviEyGwilJ+fj/z8/Nbf\ny5cvt7+AYYaZNomRsMKd1oYZ2gFNVhaf9BvZxpEfJ+vX8///2WeN//cJE6yXJSaGC2t377Y2+aqs\n5FvbzIQ4ZvvpO3TgK5wDB3JB1ebN+vF69wYefhh45BF1WWVNmIICvgKYkMC3+HiCEFZddZXaEKAw\npmxFuHDNNfz5l5DAbSCZ0a4d34LU3MzD6NHc4C3hSlKS8q4h7EPuw2+/bW9eYrunEUITzuHgW9lD\nZQs7QXiD3LeGDw9eOcKFlBT17zfeCE45CHtwOvm4x+m0ZrOSaHuEtOHle++9F6tWrWpVZQoXdTq5\nmFOn8snmuXOuqnQOh+tkCyDvJ8Hi4EFjuyGE55htFzLyrmXmatud94D169W/P/6Yb0u69VZFw0Pu\nmxcuKCtbYgKsFUJ068Y/o6L4ZMnIw5WWpiZuqHjRImvxs7KA6693Pe5wqF3Ky9pHguho4JNP+Pcv\nvgCef944z6NHXbWltFud9uxR+oFYKbJKSwv/1GrUDBmiH19P6NPcrOSvJ7BJTOT3kJoKfP65+j/1\nRBBHEHaQk6N8f/zx4JUDIG+jROSitUkCkP1LLbW16t9PPx2UYhA2UVnJTYAcOEBbtQh9QlrIU1lZ\niblz56Jfv374+9//jsWLF2OLu/0CNuLNdqqSEuNzjPFJo4BUr4OL1S07hDUSEowNLBt5nTJz8elu\nkmIkMDByp37qFHDLLeZpZmQo6XzwgasAUGxP0tumJAQVch83Y/16LkySYUwtLFu61FUQtnUr0K+f\ntTySkly1pWQvDSNGKNtNoqONNYKMEMJpkYagqkpfcOrOI5jQQpCZPJnbDDp5Un3fHTqY22QiiEAg\nVs9D4T1C3kaJSEVvQejMGfN3fltDKwg7fTo45SDswUiBgCAEQTW8DAC1tbWYMWOGoeFlwYIFCzBj\nxgz85Cc/cTkXKKNZsrtkM2OqpaVcg6ekxHV1Xn4xOZ3cRogQ6GRm8i1bMTH84UyCnsDS2Oh+y44R\n4Wq4zQ4cDgfS0xl27uRtWG8wJgzx6l+vf7xbN1f7MWbXOp1cs8TpVFY6tGlHR5tvEZs2jffjmBhF\n4NCxI18pNCq/HlabhjDaaoS4J29p185Vc+f664F33+Vtfu9eLjjxtimL6/QMJut5PDTT3BJl++c/\nlXQ7d+Y2h/bu5du0tMyeDbz6KvVHLVQfgUNu06tXA/fdx797sh3YX+zaxYXj27cHd6sWtT81VB/e\nIfctrYMAQHnvyO/8toxsOgLgXj/Pn6f2pyVc6yMY7xTC/0Ss4eV58+bhqquuwueff45evXph7dq1\nKnfN3mDkCtkfmG2nktVE09L4g1Vv+4VMSwu3jyEgd6jBxWjLDuE5R48qQko9o8JaTQ+ZaB1LYe3a\n6atnA+o+L7NggXtVVmGA2Oi58cUXvN8LwQpjXAjjiYDHyMi0jHh+uFtp83U1Pi/PVbDyzjt8YPzt\nt0Dfvt4LeKKjFQ3HykrX8+PH87bgbtudTFmZujwNDfx6PQEPYN6u2jp2vhsJfX75S+V7MLYDjxvH\nn3Fki4eINGQHAYJ27finFUcGbQHtu/yFF4JTDsIeyMQE4Y6ga/L4A1kKZuQK2R8cOcInKkJDQUaW\nmEdFKYZDtdJVvZVrcV24uEMlXAnXlQA70NZFz56uBnz1tNwEWi0Qp5OvRr/6qr4ATi99QWKiWjNO\nqylz3XVci8XouSFr73lLVZX7FUUrLtSjonh5vvvO8zI4HN4LbzxBaDhmZnJ7OXoIY4FW3KMLg9JW\nadeOC8s7d6b+KONwOBAfz1ptHE2fDrz+enDLFKkYafIIrcC26MKe3o9qIq0+5Pdk587A/v32jF/l\nvuVOUz4mxngxoK0QE6Pe7i3qJBLaX3NzM3Jzc5Geno6tW7fi1KlTuOWWW3DkyBH07dsXGzZsQNLl\nh+zKlSuxdu1aREVF4U9/+hMmT56sSitc66Mtv1MiiYjV5LEDO+2qCE8Wei8v+f9paTGWrmqFPL17\nK98nTeITn7w8PhklAktsLP9/PNU2IIwpLtYXwCxYYHyNduLf0sI1OmbO1I9vZhxYaMZddRX/3aGD\nci4hAVi7VvkOuD43fvjBOG2tNy8jzGzyOJ28zbkT8AA8jjcCHiAwAh5Zw7G+3jheSoq+bSA9PBHw\nAHwrGq1o6SPX9/79wStHpCMbNpfnEuTCnrALb+xF+hP5Od3QwDVC7RhDyVq+Cxeax/XFU2ekINvb\nAyKrTh5//HEMHTq01evyqlWrUFBQgIMHD2LixIlYtWoVAKC6uhqvvPIKqqurUVpaisWLF6PFlz3v\nIQS9Uwh3RJyQ59Ah/iI4fNj3FXiZ4mI+GRPhqafU54U6tKzR43AAX3+tqMdrV9NjY4FevXgYP553\n1IsXuYCIJiqBhzyR+A8hLDPaYuWN0MHIKPMVVyh5GjFsGP+UDfWeOwcUFfHvRi9L7VhANoycn+/e\npgxg7CkvKSkwwhdPEQJmrRFoM2JjuWFqIQDXDi5lxLZUK0ycaL0MADccHWxjt6GK3JbJlbp9yNoD\nubnKdzu2A9MWPALgWpNiQWP06MDnrzdntmMMJWultG/v+fXBFoYFGrP3cDhz7NgxvPnmm7jrrrta\nNSC2bNmC+ZeNNM2fPx+vvfYaAGDz5s2YN28eYmJi0LdvXwwcOBDl5eUuaS5btqw1lJWVBexefIFM\nTIQnZWVlqvZmKywCkG8jMZExPnViLD3df3lcc42SrggyDQ2MFRYy1rUrPxcVxYP2Gjnk5Ogfz8vj\n6dlJURG/p6lT7c8rXHA4lP9g507Pro2QruQXAJi2e4CxggKz6/VDp06M1da6xp8/X/3f6YXJk3nc\n9HTXc1FRjMXEMFZVZb0soo9262aer1lbcvd8CMXQoYPxucJC5d5qaxlr106pKzmeu/9K+994Ur6e\nPZU2SCho+2T37sEuUeSibZN6zyx/IY9L5P4XalB/VOPv+tC2uY0b/Zq8W3Jzrb/3vEXveV9SopyX\nx/4iaHE6lXM9eljPOyODp9+tm+f9OTHRfIxhF3rv2Y4d+blw749z5sxh+/btY2VlZeyGG25gjDGW\nlJTUer6lpaX195IlS9iLL77Yem7hwoVs06ZNqvTCvT6I8MbO9hdRmjyZmcoKcXy88Qq6jKyds2mT\ncTyt6ql2FUFIVCsrldV9d1swPvrI9VhSUmC2avnTYFekrCbu2MG1T/S8ABH+RV6Rs8rp08q2K5na\nWj6EMeOTT/in3lZLT12uxsUpGj8FBepzOTmu8ceP11dd1xqHdDiCY3A9Ls73uO3bA7//vfK7Tx/u\nnj452fV5Jm9ncYcnWtVOJzB4cHg/g4jwR2s43s4+bbY9PVLey4TnFBYGNr8DB1yPvfee/flOnap8\nt6IdKr9PhH0yK8iaUqNGWb8OULt1HzkycGYB9MZEZtvPw4XXX38dKSkpyMnJATMY+DkcjtZtXEbn\nCaItEFFCHtkOxPnz3I6HJ5i9GLUCG+HFRTuQ6tOHP1yt2NjQ8yLU2Mi93di9XevLL/lnYqJ6cibw\n5EUUyhbePRnokicS/5KRYXxuzx5raTgc6n4ycqRrHDHR0fYn8Ts+Hti9m3//6it1HLElyekEPvzQ\nNW09Lx2XLgGDBnF1b+22l6NH9e9DT3W9Rw/1b8aArVu5zZpAYmbTSIuR+vfZs8D996uPvf0299j1\nzjvq41oX7ma4E97JCNtNofYMCjXi4vjWOsIe9u1TvjudwJtv2peXmU2GUH4vE/bibqut0bjIW8Gg\n3qLNI49Yv94XPv7Yu3ONjUBpqef5nTrlWXx5LtDS4rlZALIVqWb37t3YsmUL+vXrh3nz5mHbtm24\n7bbbkJqaivrLk8Djx48j5fJAKi0tDUelgdmxY8eQlpYWlLITRMCxTUcogIjb0Ns6YX6dOrRrZz3u\nyJH8uKwunZzMtz8ZbSW4/nprWw582a5ldRvWuHHmat5yeZxO8zzFPQdim5mnBEqdPUK6kl8AwAoL\neVsw2m5jtl1LVjOOiVFft2aNa3yxVbKhgbH8fB5vxAiuGt2+PWNjxyr9QW73ckhL01fHNuunKSnW\ntxHl5+vVkzp06aLcT3KycVoDB1rPN5AhKkpRRy8q0o/jyVYtgLGsLM/ii2cQ9Uc1AFj37nyLgp3b\nhwjO2LGBee+YEez3snh28z5P/VHG1/rQjvOsPBt/+lM5fyVMmMCPabc7jR/vyf3oB0+Qr1u40Hoe\n7sLs2eZpeFq2hATXYw89ZDz2Niub3rjA3X27Qztm0r5/eZqR0R/l7Vr3338/W7VqFWOMsZUrV7IH\nH3yQMcbYp59+yrKzs9mFCxfYl19+yfr3789aWlpU6URKfRDhiZ3tLyJatqigfv3UD7ShQ42vMXoQ\nGuehDnFx/LgYSEVHmz/MU1P19wxrg5iseotVoYa7AaAn9mnkSXaoEaiBbqS8JEpKSlhGRgYbOHBg\n6wtTy3vvvcdGjhzJhg0bxq655hqX83JdVFUxFh/PP+PilIGG2d50d4IALUVFPI/oaMY6d2Zs+nT+\nX2dkqIVMhYXWBoWyLS+zeOJ+rIROnVz35WvjiME2Y/q2gwDGVq/m9+rtgNfT0L69Z/FjY3n5tTbM\nunVT2oEn6cXFMTZtmmfXrFgROf3RX1B9BI6iIv4cArjdvWC9F4P9Xlb3S2p/MoCr3TrZvoz765WQ\nkeH7c371av33rjfl8eR62daNu2t9ub916/TT6N1bSV/Pdo4Q3HiT5/XXu7+2a1fXxSWrAjyHg4/N\nPf3/S0oipz+WlZWxGTNmMMYY++6779jEiRPZoEGDWEFBAWuQHny//e1v2YABA1hGRgYrLS11SSdS\n6oMIT0jI4wZRQbJRNTFBML7GNQijZFbii5eAGEiJQZ1RMJOuiyAmSFYwWjWwKtRwNwDcuZPXpzsB\njz8NOHuSltW4ngx0tYMeT4iEl8SlS5fYgAEDWE1NDbt48SLLzs5m1dXVqjgNDQ1s6NCh7OjRo4wx\nxr799luXdIzqolMnpX7NjKJ37Gjcb6KjXeNrB6fduvHjslA1Jsb6iqesLWQ2wLIqsOjQQS1sio/n\naRs9E7TPMTkUFXmuDeNLEMaTPQmMmWs0ehLWrPF2EhP+/dGfUH0EBq1gOSXFXiGLrC3jb0O3vqJ+\nTlH7k9ET8uiF9u2Nrg9MMC6/tWAkuLJyreg3dr/v9IRMnizg+CuIcUFg8jP5c9sgVB9EMLGz/Tku\nZxDWOBwOMMZc3BkXFPC96nrIrs4Bbr9D7JXVz0P5fvPNwCuvuOaltT3hKWbl1RIdrez1la9rbOT7\nqp991je3epmZfE8/AHTuzO0M6Bmtzc/n+/4BoHt34LPPvM83IUExhjdtGvDGG9biTp8OvP66d3nK\naNuPlZ6hXMPbYDizZ88eLF++HKWXN6qvWrUKAPCrX/2qNc6aNWtQX1+PX//614bpOBwOLF26FACw\nYgXQ0pIPhyMfiYm8fSYkANXV+u0J4MZ6T57kdgX27+dusQUlJcD112vzc02joYHbzZHTycqy5vIc\nUP77qChj479VVeqymRETw58vTic3UulJWWSuuUbpb3aTkMANW/7979avEf9PYyN/Hnhif8cIUXfm\nlF0OguVh3x/9iXhHEvaSlORqALaw0D6X9fIzxOm0ZgswUOzaxW2ObN8OjB9P7U+GG34Nv/qIivKt\njXXtCnz3nf/KQ3gL9UcZej8SwcTO9hdRhpdlY3MdOpgPrHbsUL6vXu1+EiEbdd2wwdUA2pEj1sup\nR2wsN1QqPH3913+pz2sN4skTT/leHngA+OYb4NZbffOoUV+vyPxPnTL2ECKM3oprzAw8ujPqJ/8H\nb76p1IWecTw57v79+vllZvJBd3Ky+/9HW+7Vq83jRyJ1dXXo1atX6+/09HTU1dWp4hw6dAinTp3C\ntddei9zcXLzwwgu6aS1fvgzLly9DS8syAPlgjP/n6enmAh4AqKjg/a19e+C669Tnpk61ZoDwxht5\nOunpwOHDXKjiDWYCSz0j0Dk5+saJKyu5AWgh4PGG1avV/c1uzp3jQlurrFihCOCSkvwj4Nm40YqA\nBwDyASwDsAypqct8z5gIK0LFk5Re39d6vfInspBn+3bX806n+XvUTsiRQeThqxCRBDwEQRCBI6KE\nPMIrTXQ096aTlGQ80R83ThFi3Hef+7S1nnu0VvG/+cZaGfW89QDAxYvq348+qv6t9ZQhyuN0AuXl\nxvGsoDdA1g5WX35Z/1p5sq11o6zFXdmEq2XtRFZ2kymQvSIZDV7r6xW3l+7c2AqtJcGcOebxIxEr\nbiWbmpqwb98+vPnmm/jnP/+JFStW4NChQ5bSb98eOH6ca9iYeb347W95vzx9mv93WhhT9z891+dl\nZVyQNHUqMH++Z5O/zp31v2vR0/DZv991IHzllVywc+6c9wIegAtz337b8+vceVoxo7pa+T5ihHF9\nlJQADz/sPr116zzL31MNCKfTuzoKZUpLS5GZmYlBgwbhscceczm/efNmZGdnIycnB1dccQW2bdsW\nhFIGl1DxJFVR4XrM1wUXM6ZP559jxgDDhrmelxcH9d6jhD2467MEQRAEYTu2bQQLIOI29DxGyfYt\nevRQrtEzsmaGdl+wdv+7v/fMPvSQOn2trR3ZoK2MMJQaHW3tvhjTN9ZcW6u+Z2FDRWsDQFsvsrFn\nrd0cd/aCamt5PrW16jS1+7q1Njq6dFHyUHv0MK5PLVobImY2Y2QiaY/znj172JQpU1p/P/rooy7G\nl1etWsWWLl3a+nvhwoVs48aNqjiA2t6AXlsxs5cl27Qwsk8jtwkjWzvatAoKrPW9nTuNvUN5E4ye\nMZ6mY+SpzF0QtomcTrXXH0/Dxo363snk/0I2gi3HkT30eZKn3jPGnY0GbmA7/PsjY9bsZJ05c6b1\ne1VVFRswYIBLOpFSH0YE25OUjFGbtIPu3ZU8Zs0yL4undub8SaS3PxkrfVb7jrQrZGSI/CIztG/P\nx3/BLkf4BQShZ4Qu4VofsuFy8poZvtjZ/sKzZWsQFdSrF3+AJSYqDV5+sHXvrlyjZwjVDHliIRt/\nteIxy8yQqlHQTgqtGhCW0xAGaN1hNEAWxugSEvTrU3tfCQnq67XCI0+MIHMPAPqG+4zqXLjPNgpm\nyEaBnU5e/1YEgZH00mxqamL9+/dnNTU17MKFC7qD088++4xNnDiRXbp0iZ09e5YNHz6cffrpp6o4\n8gB2xQrluNyHunY1bgfyfxYbq/9fTp+uviY72zWOtp1Y7Yfp6d571LASRJu2K329YFSPngY9g8rt\n2un/d/4IDodnZXc4IsuF+u7du1WC15UrV7KVK1eaxh8zZozL8XCuDytG9m+/nbHkZMYmTVLiBGsA\nrBVw2ulhS85H9s6ndz6YTSCc25+nWOmzVoQ8ni4kijGTCLm5yrW5ucqxQL53PA3R0Yxde61n9cKY\n+t7bteNx0tPtFQAx5rogKYd16/yX18KFrseGDrV27c03C4+TcoC/mntEEK71If+nKSnBLg3hLSTk\ncYOZJo/swUaeqIvjYkLvPg/XBzhj5qvrvkzmZMGTJ16n9F5EesgD4KoqfeGLrFkj0LpW1+Ynx/Vm\nddXKwFzP3ab4L43qMzPTvAza/3H6dPeCQLV3pIjoSuzNN99kgwcPZgMGDGCPPvooY4yxp59+mj39\n9NOtcX7/+9+zoUOHsuHDh7PHH3/cJQ3tAFYIycaPV9ex3sozv14JRto3CQlKfNllsRy0Gh9WPNyJ\nfuup63BPgzeCX1+CvOLvbSgpYWz+fOPzVuvX7sCfS/BntwgaGzduZHfddVfr7xdeeIEtWbLEJd6r\nr77KMjMzWWJiIvvwww9dzgNgS5cuZV27LmXt2i1liYnvhc3Kn56mqYz2/xdxZCGvVc1Mf1BVpe7f\nRs85f6C9d0/P28V7773Hli5d2hoipT9awUqfFf1RhPfee0813hDjS5n0dPV/OX68Xt78nEa5VoXr\nhF8/yNrgRnF69vT+Od2uHRdAiN/ywo1YECwp4X1p3Tp9zXUZvfGqUdn1xq6e3J8saFqzRj+OjHbs\n4y706+fq4VZPe18IsYS3TyHsWr1afa3cHzt1alv90QrhWh/Ber4T/oWEPG4QFSSECh07Kit68vYE\neYBotN3JOA/9DqU3sRk8WC1Q0J7v0MH8Aa8VPMmD3O7dzYUVcjpG7isZ834ArH3xaMsup+WJ5g5j\nrnVpVC6j1ZOdO/U1OkSYNs04b+2ku2dP94JAdfoR0ZX8gt4qZXy8q9Bl9mz964WwduhQxgYNMv4/\nBf4QYMghLk6t2RUJoXNnVw0DT0L79lzoGUj37YD7Z6Ve4H0Z+o0rzNi0aZMlIY9g+/btbPDgwS7H\nAbDERP0tuKGOu8UC7f8v4uhpotqFdiHGm23T3iDfd2Ki+fk1a+wrhzsipT9awUqf1asPT8ekvlJV\npW4fixcbj9mMhB21tYwNGcK/x8eba7Zog6wBaidC8AUoW8cZU8aK/frpb/kW/4N2+7ieJpH2+vx8\n1/OFhVz4Ivpiba16nDF0qOcaf56OsQVtqT9aIVzrQ25zeu2SCA8iWsizYMEClpKSwoYPH657/rXX\nXmMjRoxgI0eOZKNGjWLvvvuuSxxRQfPnqwUFhYX+G2xpXwBipUX7ooyK4sdkjRRPV+0LCtR5a1dw\nzPb3T5nC41xxhfmD39sBsHYwq/fSN4rrDrO03MW9+WZ+XG87iQg9exqnd8UV6hd5bS1jN93Ev48f\nr78FQD3hDXpXChn0hDzyQEs7GdMiD1zMtuoIfFHJnjbNtX9NnmysLeZN8NaWTigFo3vwRXBkJaSk\neH5NJGnyWLGTpaV///7s5MmTqmPaPhkIwYe/cDeRke9L1oAwWtm3A622kTx5s1OYJt+7bPdKILQM\ngingYSxy+qMVrPTZUKkPq4Ilo3FVba1r/7T6nJ482f77M8Os3LL9KqvPkTFj+LUZGZ4JXbwV1PhC\nqLS/UCEc6yMjQ5nfmmnuEaFPRAt5tm/fzvbt22co5PHEqKQ80Orc2bpmiBXkdLQaCFrVz549zW31\nmG1riIri9krEC6WoSD1g7NzZVbgid3B3qu0C+cUlCyvMtH/00td76Qvi45XjZlo0ArkcGzeaC4n0\n6q6hgdtm0DvXrp35S1oexCQl8bhy+YUqsbHQIehdKWQw0uTRHrOWln5ISFC09SZNsj6w1PbDsWNd\nB7AbNzI2d653aUZiSEoKfhk8CVygCHsbeYCwYifriy++YC0tLYwxxiorK1n//v1d0pH7ZEpK+Ah4\nrGC0RcXTRQZf0GobadujXQQqH1+JlP5oBSt9Ntzqo6FB/x3epYtrXG0cob0iB2E7LZSwstXNjGAI\na7wl3Nqf3YRjfQRrOzLhfyJayMMYYzU1NYZCHhkzo5Jaj0tGe269VWmT09BbMfP3REUY0ZK3ooh9\nt3r56ZXDbPXOLG+r9aCnnSFry8hCG9notZVy7NxpLiTSu6aw0HzrjhmyZy7x0JSvTU529eqlDiHR\nlUICPSHPQw+pf+fmeqfdpQ2zZjE2cKD+OaP/y4rBQjPDy4HesuRpMNpqlpnpXXq+eOQKXoDt7TxQ\nuLOT9dhjj7Fhw4axkSNHsvHjx7Py8nKXNOQ+2a5deExEfMXqgoc/kCd4es8du4RqVt6xoUAk9Ucr\n6PVZmXCsDz3Pinq3oScs0V4TqK1ahD7h2P7sJBzrI5DbkQl7sbP9OS5nEFRqa2sxY8YMfPzxx7rn\nX3vtNfznf/4njh8/jrfeegujR49WnXc4HGjXbikuXBBH8pGeno+6usvDfQmnE2hu9qx8mZnA558r\nv0tKgOuvd03XnzUZEwNcvAi0a8c/5eOJicDJk8qxxESgsZF/dzjU6RiVSRtP0KUL8N13xuUyuk4w\nfTrw+uuucYcPB/T+XqP0HA4gKgq4dIn/7tkTqKszvq5zZ+DLL4EBA4BTp1zT27kTGDfOuNx6//HU\nqcrv6GigfXvg++/FkbLLQbAcIdCVQgKHwwHAtS60dVpYCGzY4C4t8/OzZwPvvSf/L+prtX9Jp07A\n+VUIol4AACAASURBVPNAUxNvX3rPgoQEfr6pyTzvcMHhAHbsAH77W/4fhBN6/6G1axzUHyW0fdJK\n3wsXkpKAM2f4O7iyEsjK4senTePtPS8PeOstHi8QaN/ZAJCeDhw96v+85OdjSgpw4oT/8/AHDgf1\nR5lwrA/Rn2TcjRcF2vf4ihXAww/7r2yEZ4Rj+7OTcKyPI0eA8eP53KZPn2CXhvAFO9uf05ZU/czs\n2bPx2WefYevWrbjtttt043TsuAwAD05nPt58k09stGzf7nn+9fXq37NmAQUFimDFU9xNXAE+YAVc\nB4tNTWoBDwCMGKGfxkMPWStPbCz/jIkB9u2zdo1Rvi++qB/3k0/U+Tkcyj3qERenCHji4oDdu83L\n0tDAB/GjRrmecyfgAdQCHgC48Ub170uXgB9+kI/kY/HiZQCWYc2aZeaJEwC4YFQIefLygGefdX+N\nmLAZsXWrvoAH0BcOnD7N+1B8PDBhgv51585FjoAHAObM4e3/0CF70l+xwp50Ae8E52E2Vgs4Doe1\nvhcunDnDhbVNTcCYMcrxXbv4vR44YI+ARaa4GMjP5xNh7TsbAH7zG3vzB8zfp97gcChh2DDvxztE\nZPDFF67HrI4xtTzyiG9lIYi2Tp8+/L1GAh7CjLDQ5JEZMGAAysvL0bVr19ZjDocDtbUMffsq8a67\nDnj3XbVAxeHgWh5JSerjs2cDr75qnGdysqtgBVCvhnbtqq9B4i1VVXyCa0UgFBuLVi0mOb6Z1tJ/\n/zfwy18Cq1fzSaCRRLi4GDh4kGs3rF/PNWaM0Go4yWUR2kZJScaTclmzIjpaEfIAris/evXCGDB4\nsPFkNiGBh4oK5T5jY/Un9NdeyzVEBDExXDBw+rRyTF6dDceVALvQ0+R56CGuSdLYqG5Da9YAixYZ\np6W3emiFjh21Qjk1JSXA2LHm7TkSSEoCamr4p1nf8xbR533RZOzWTf/56i3Z2cBHH1F/lJH7pBWh\ntxmZmXzhIyZG/SwNFlFRQEsL/z52LG+TSUn8HSLeJ/HxXHhrF/n5wPvvm8exoznK78F164D58+1J\nG+B1u2ePt2nZ3x+zTFYEHA4HqqqqbM3fE8JxvGA0FrVyG9prZS1tIvCEQvubMWNG63dteRwOB7Zs\n2RKwsoRCfRBtlzatyXP48OHWm993Wc1EFvAIsrPVv7dtc13ZYowLLbS89pp5GSoqXI9FRalXI86c\nMU/DE6KizM9r70sW5MgvUzOtpfvu4/Xx+edAv37AsWP8c9cudbyDB/ngtaREv+7kel+71ji/ESN4\n2cwmmfJ9iEG7wMrKz65dagFP+/bq8+fO8cnkyJHKMSONjcRE5X9wOPg2AKHxJDh2TFnpJMxZuZKr\nl44dqz6+eLH5devXe5efnoBH/p9+8pPAbd8IJKmp6t9ZWfw+i4uBs2f5sago1//BW0Sf9+X95E8B\nDwB89JF/0/OVrKwswzDCSA3TBhwOLtwZNsy3dOrr+XP85Em+OGA3suan9v0EADk5yvcPPlDeU+I9\n6XQCH35obxkTEvhnt2765wOxTfKOO1yPuas7T/jgA9+ut5utW7di69atmDp1KqZOnYr169fjb3/7\nG6ZNm4ap8j5hwm+sW2ctXnS0+vd11/m9KESYcd999+G+++5D//79ER8fj+LiYhQVFaFDhw7o379/\nsItHEJGBbdZ+LDJ37lzWo0cPFhMTw9LT09lf//pXn4xKehvMMPKU1a2bEsfM1bM3IT5e3Jtn5Rcu\n9WQjzWZojcjKRqWLirg3L4CxnBxXryGTJinnAW64WM5TjqvnUUzP64II2jpfsUJdLr1rPHFVb3T/\nADdQ29DAWN++/HfnztywWW2tWZpB70ohg1F/1BqzBty79vVnn5JDVhb3iJOba18ewQhal+Zxcbwe\nZSO0Zt79PAnCk5BRf/Sm3OL55Uvg7t5hezu3Sk1NDaupqWH3338/u//++1lVVRX76KOP2AMPPMAe\neOCBgJRB2yd98cQUaIOPcrn1nB7I3vHEe4ox6+6hZTzxNCkjDC/rGaft2NG+epLzkd0+653Xqzsz\nhPt1f7SZQPbH7Oxsl2MjR44MWP5WCKXnk1W07fqhh6xfW1WlXDd0aNsw/B7KhFL7GzVqlKVjdhJK\n9UG0PexsfxHRsvUmlZ66/TVPXz84HIqbVn9MmvQGVGYTIhHk8Quf4PAgBEV6GE30fvELJY7sqUp4\ntyopsTYZs+KBKCHBWl3066cuu1F9G3lU04ZBgxS3ujt38sGv1uPSxo36LgqN042IruQX9PpjXJy+\nkMx9WvaGlBTGZs+2P59gBTHB1bqJ90dYt46nbebRztNyCgGC7wH2NG4fCObkU69Pesu8edw7Tn5+\nYCZr8rtEzzvm/PmMde3qu2t4Pa9YnmLUz+xycSvnoSfEcVd37vDVrbRSzsD1xxEjRrAdO3a0/t65\nc6du3wsmofh8cod2zDh+vGf9f9AgnkbXruQNKNiEUvvLzMxkX3zxRevvw4cPs8zMzICWIZTqwypF\nRXzs1aULX3AnwWn4QkIeN2gHsJ06udO6YC7xzdM3DnYIeACuGaSXd2wsH1zLx+QVR6uDOrO8BbJm\nzOTJ7q/zNHTpYi2ew6EeFBgNpKuq1EIud6GwkAtyoqL0hVLaFWsjjS7usjoiupJf0JtQGrUf92lR\n8CUI5s/3nwaPNn1PNOj0ghAc+zdAtz0Fk2BOPv2pyRNI1+SMKQsK0dH6Wjnyszs/XzkuFmCEQN8d\n2ue7J5o8goYGxmbNcm2PgdDk0ZZXvh8hkPUl/bFjfSln4PpjRUUFy8rKYr1792a9e/dmI0aMYJWV\nlQHL3wqh+Hxyh3ZxEWBs+nTr1+stmhHBIZTaX0lJCevVqxe7+uqr2dVXX8169+7NSktLA1qGUKoP\nq2jnnrNmBbtEhLeQkMcN2gFs9+7iuPvgTsDjLh07VsgBPiHTy7tzZy611ZtsMaZeCZ892/N7Ettn\ntFswPKlTvdChg2/10bMnzz8jQwhVXEN8vGdCHrNw5ZV8YJ6ergzQtWnL6srh+JKwCz0hj3gBaduE\nu8mP2DJHwX3QasF07qzUox3CaDHp8yUNMTH1f33A7+3aV4I5+ZT7pK9aGeKdJ7br2Y077VT5f5e1\nWWQNM/H8ycjgk81u3VyfPXL/8VYowpjru1O8U43yFsJXh8NzbRt5m3hMjDpd7fvKG6GVtl95gnxf\nweiPDQ0NrLGxMeD5WiEUn0/u0HuHiHGZFXxti4T/CLX2d/78ebZ//3524MAB9uOPPwY8/1CrDyto\n555m8z0itLGz/YWEdy1f0Xrzyc0F9u5Ve9cAgJQU4MQJT9M2P9/QwNP1t8tl4THLqlFf8S/KnkYK\nCoC33tKPHxeneOQStG/PjQlrvY8B3NvUtm3m5YmPB/73f4FbbuFGn/1plNNK/itWAL/+tff/RXw8\ncP48N0C9bx/wwANqz2La/9nhAHbs4MZMyTq/grY/ZmZyryxJScDzz6sNhMoeyvTw1rtWOBEXB/z4\no+/ptGun7tO5ucDbb/N6792b17Pswc4XoqOBb7/Vf1ZocTiU55PM6tXcALyII2jfXjES7T2h2x8b\nGxvhcDiQmJgYsDwdDgcSEhiqq333hmWnRyctxcXAX/6i/NZ6cNSWJz9f8Yooe7wUHjRlD3PaZ8+R\nI8ZeJt0hexwbOFBtpFh44TTK26pHTD1iYtReiozSFTQ0eGZwXk5j5Ehg/37vrg10f3z99ddRXV2N\nH6UH6//9v/83YPm7IxzHC9r25HBwz41W+4o8NrXb2x1hTqi1v48//ri1vzouN7Tbb789YPmHWn1Y\nobERyMgAvvmGOx/Yti0ynYm0BWxtf7aJjwIIoG9vQDb25nR6ZoBRSds8MKavWaMNnhoUFWXVO5eX\nZ7zCJq/ema2y6KneAor6vd45d1oyWsOP8rmOHb1ZjXe9F1/SMAoxMepVXKGCLG8DSEriRjXj4tTX\nipXjYHSl8vJyNnv2bDZy5Eg2fPhwNnz4cJaVleVTmiUlJSwjI4MNHDiQrVq1yjTvqKgo9ve//93l\nnLY/atVIPTHcasf/HWqhd2+uFWNH2qI/6xmE9TUIrNjf0gaHQ60FIoy8jhvH2JgxvpWL2/oCC0W2\nbt3KHnvsMbZ8+fLWEAjkPum7fRX9dmAH2neO3jYP0V4yMtRtSryXZWPM8tZCPa0ZT7d4CYy28o4Y\noaRj9NyT4y9caD1P7f0Iu2dCY8jseWAF7bWebrFRPxcC1x+Li4vZbbfdxtLS0tiyZcvYsGHD2J13\n3hmw/K0Qqs8nM7TtISXFs+uFZpe3Y3HCf4RS+1u6dCnLz89nycnJ7I477mCpqanspptuMox//vx5\nNnr0aJadnc2GDBnCfvWrXzHGGPvuu+/YpEmT2KBBg1hBQQFrkB7gjz76KBs4cCDLyMhg//znP13S\nDKX68ARh8J/s8YQ3dra/8GzZGrSTSlkVVJ4wxMZ6vjfeykTHDlsXotPOnOk+bk6OfnnNBvN66Tid\n3Die0QDRSvCk7jwJQn3e3/UM6Auv1q3Tjzt9uvq38LAWjJfEoEGD2ObNm9nhw4dbPfjU1NR4nd6l\nS5fYgAEDWE1NDbt48SLLzs5m1dXVuvGuvfZaNn36dLZp0yaX83pC13XrFENxiYnccKuVgZ43/6eR\nADOUQ5cu3CClL2noCZI7dOBtVGvHy9cgP1u8TUNPvdgTI87mwiV40vQDQjAnn9o+6VtaSpAF+2Zb\noYyQ3zXCi6FRXoB+ukYD3YED+bOgSxflOnmrr57Qwlt7Q0Z2qWSbJQMG8DYrl0fvHq1SVKTuA2JL\ntdH729PtdVbq3gzh1IA7RAhcfxw+fDhjjLUuePzwww9s3LhxAcvfCqH4fHKHtj14uqXRG293hD2E\nUvsbNmwYu3TpEhsxYgRjjLH6+no2ceJE02vOnj3LGGOsqamJjRkzhu3YsYPdf//97LHHHmOMMbZq\n1Sr24IMPMsYY+/TTT1l2dja7ePEiq6mpYQMGDGDNzc2q9EKpPoi2R9gIec6dO8dWr17NZs+ezW68\n8Ub2hz/8gZ0/f96fWegiD2C1Lx7thM/qapQVr1lmHrDk4I1hUjHAtGJLQ7ZDYHTctc7sCfLqqL/T\ntrPc3oabb1baYKC56qqr/Jre7t272ZQpU1p/r1y5kq1cudIl3v/8z/+wJ598kt1xxx2WhTyAqzaJ\nlUmUp/9HSgpjPXoEv10EIjid6udbTAxj115rHP+66/yTr9btvbfpCI99Mr4acVYC3DeuABPMyafc\nJxMSfPPGER+v1LP8PpXtw1i11aEV1Gmvk9t3bq5+mYXx/JgY9QRSa+hVaytHuwii9a7lid0Qd5qq\na9YYG56V461YYT1P7dhAvHu1trkSEriwydP/W04jPt4349GB7I95eXmMMcbGjBnDjh07xs6fP88G\nDBgQsPytEIrPJ3ckJ7u2ayI8CaX2l5ubyxjjbtMbGxtZS0sLGzx4sKVrz549y3Jzc9knn3zCMjIy\nWH19PWOMsePHj7OMjAzGGNfikbXSp0yZwvbs2aNKJ5Tqg2h72Nn+ov259ev2229Hp06dcM8994Ax\nhvXr1+O2227Dxo0b/ZmNKXfeCRQVAZWVQFaWer86wPfbW+H//b/LUwUT/s//AebMcZ9WUpJiG8Aq\nv/89/0xIcB+3Sxf942+84Vme7rBiO+Tqq72z+WHVVoi/bIr4iw0bgFdeCU7eS5cuxcKFCzFp0iTE\nxsYC4Hs7f/KTn3iVXl1dHXr16tX6Oz09HR9++KFLnM2bN2Pbtm3Yu3dv6/5pV5ZJ3/MB5OPwYeVI\nVBTfQ3zkiO82QgRxccDEicBLL/knvVDg2mu5fSttmx82jD/LOndWjjU1KfZI9Ni2zTyv2Fjg4kXz\nOJ07cztJ/uByk1XhdCp2Gzyj7HLgdWZWD8EiPj4eAJCQkIC6ujp07doV9fX1AS/HuXPAO+9wezcb\nNnh+ffv23HZZQoL6fSr/byNHWktL+47NyVH/3rePp9XSAlRU6Jf5zBneP5qbgTFjFFsfMTH8U5RT\nazvollvU/Ur7V0yfbv1d064d8MMPxucXL1Zsmsj1VlzM7WV99RXw0EPAww9by0+kIzNxIr+Higpu\nW+j0aR7OnQM++shzew2yja/z53maZvbTQoUZM2agoaEB999/P0aNGgWHw4GioqJgFyvs0b4b1qwJ\nTjmIyCIvLw8NDQ0oKipCbm4u2rdvj6uuusr0mpaWFowaNQqHDx/GokWLMGzYMJw4cQKpqakAgNTU\nVJy4bID166+/xtixY1uvTU9PR11dnUuay5Yta/2en5+P/Px832+OIHQoKytDWVlZYDLzp8RoyJAh\nlo75G8BVc0B44fB25cHKavG8edY0bdq18/xcYaG1MkRHG6t+XxaQe31/ntyHCMLjjnbV1NcgTM34\naq/DvuDXrmSJW2+9lV1xxRXs9ttvZ3fccUdr8JZNmzaxu+66q/X3Cy+8wJYsWaKKM2fOHPbBBx8w\nxhibP3++ZU2evDzeTrVbitxp1lmp+zVrFC9odniRCkQw2mKWluZ67LrrlFV5T/Jw5+GuttZaOtr/\nTGunymrQ0yzwdcua6IbB6I/u+PWvf81OnTrFNm3axFJSUlhqaip7+OGHA5K3Xp/0VpNn7lyutXPN\nNeo0RN/LyrKetrsyabdC69nRkePk5ir2dGTviHpbmLRpaTVgPPF0ZbXvOJ3G7+vLCiiWaWhQa08B\nfNwgtJBFvURF8feyp3aGtNuYPdXkke0bBas//vjjjyHpYSsUn0/u0PYPPU93RHgQqu2vpqaGffTR\nR5bjNzY2sjFjxrBt27axpKQk1bnOl92LLlmyhL344outxxcuXOhiSzJU64NoG9jZ/vyqyTNq1Cjs\n2bMHV155JQDggw8+wBVXXOHPLCzz9tv252FVY0DrxUoQHc29gI0Y4Xpu+nTAigKUVlNJpqLC+FxM\njOdeqIzuQ6a2ln8ePOhZ2u74/HP+aaS15Cne3H+oUVFRgX/9618m2jSekZaWhqPSUu3Ro0eRnp6u\nilNZWYm5c+cCAE6ePImSkhLExMRg5syZpmlv3Mg1drRek6xq1plx991cg2zRImX1Phj4omXWpQvX\nBDh/Xn1cZ8EJu3YBt97KPb6ZUVXFV/KvvpprA119tXHcX/zCXKNK1rB5+WX1uQ4dvPMO9l//BTz5\npPpYZSX3bseY5+kB3KNYqPLII48AAG666SbccMMN+PHHHwPqYUuLt544jh/nq/rvv6/WrHntNf77\n2We9S3v8eNfrtM/oiRNd21plJdcAam5W3nk33si1ucTj7MwZ/fuQqajg7efUKd5fxo2zXnYr2ogJ\nCTD1brZ3r/X8iov5O7ZLF0UDKSoKeOQR4D/+g/83APdilJ2tePvyRHtL6+lrxQqu4WyVgweVcgSS\n8+fPY82aNdi5cyccDgcmTJiARYsWIS4uLvCFiSC0479AjLGJyIcxhn/84x+q/jpCb1KkQ2JiIqZP\nn47Kykqkpqaivr4e3bt3x/Hjx5GSkgLAdVx77NgxpKWl2XIvgcTpVMZJel4nCQKAf8RHwrNPZmYm\nczgcrHfv3qxPnz7M4XCwzMxMf2RhCnRWKQsKxDnPVy/tMKRsZ5DtGMjHtd6uZJKS7CnLddfx9Pnq\nnfXAPeIoQc+oakwMX10tKPCtjPb8v/C+AXvJHXfcwT755BO/pdfU1MT69+/Pampq2IULFwwNL8v5\nW/GuBRh7bXPXHz39H8xs0ngTSkqsxRNGY73Jw+HghpEbGoyNCQtNH9lmTWGh4pVKz5aNtm7d2Q1p\naLBWXq3dlNpa758nVv9zcZ9W6pLfR+D7ozuCZbOOMdc+aWavzR3i2e6pIV89jDxjCbT9wenUN/Cs\nZ7BbjmP0zPcnZobAtRo8AjmOJ4ZsjTQWo6KUZ4Xw7OXt/yV7J9XWlxUvZEJrk5cncP1xzpw57M47\n72Tbtm1j7777Llu4cCGbM2dOwPK3Qig+n9yhbd9ar5lE+BBK7e/f//3fWUFBAVu7di3761//yqZM\nmcIWLVpkGP/bb79t9Zx17tw5NmHCBPbOO++w+++/v9X2zsqVK10ML1+4cIF9+eWXrH///qylpUWV\nZijVh1XsfJcRgcXO9ueXlGXPPtpQ64u1PovoTSpjYsQ5dTDbwqSkF/xgdVIDqD14aM+1b+9qlNIX\n71nuQteuPI+GBteBdZcu1tJISDAeMBttwwt+gP8atEUyMjJYdHQ0GzRokN9cqL/55pts8ODBbMCA\nAezRRx9ljDH29NNPs6efftolrlUhj+wu20pdyhPQFSs8+x+sbCn0JHjiqatbN/979srK4sKcqiq+\n9UR4yZInbHre4QBuhFrEsbJ9cvx4xn7xC/1zcn8UAnR1W/T83hYv1m+DvtYZ3+oa+P7ojmBOPrV9\nsl0779OaP58bYfXFeLOgUyfetsT7SQgPjJ7/Tqe+AWPtu0Xuhw4HF9bKBqMB313Jy2RkmAt51qzR\nF4wIL46eeioSghuzPHv25OXq1Ilv6/LGq5GcnnAywJg1L2Tq93/g+mOwzAZ4Qig+n9yhbWuTJwe7\nRIS3hFL7y8jIUHm7am5ubjWarEdVVRXLyclh2dnZLCsri/3ud79jjHEX6hMnTtR1of7b3/6WDRgw\ngGVkZLDS0lKXNEOpPqwi90VPnAQQoUfIC3mCjZ6Qp107PqjSs0PhPr3gB6uTRafTs4mcu9V8X4OY\noBcV2SNMMnebHJzAJxiwr4EbYCRYDTYAVO3XG49rrmlaC+7szoRjkCdneu6izTTTxGqrVVtFjPFJ\nvFkcPUG5p9pxZraYPBGUaYXhnTqFriZPMCef2nekmZanO4wm+PKz2eqgUy5TXJz7dlpSotgGSUhQ\ntGNkTdA+fVyv69SJx9u4kf/2p4CHMWvvOm/ds+shngPaPIQgS9SNkUcvq8hpd+umHLeiHRQsIc+/\n/du/sd27d7f+3rNnD/vpT38asPytEIrPJ3doba/16BHsEhHeEkrtb/r06apxa01NDZsur1wHgFCq\nD6sILXMS8IQ/drY/v9rkCSVaWoCPP3bdi79unftrk5KAxkZbimUZM1s7Mi0tvLxJScD337uPb+YB\nxFP0bJAkJADJycDAga7l+elPgRdf9C1Pxny73g727QP69g18vn2DkalFevbkHmMSEwGNWR+3OJ3e\n53vmTGTYW5KRPQYlJaltaiQlmd+r7NHHCvI+byMqKly9onla33V13LaQnt2Tffv4PXfqBFx2kOGC\nwwHs2MFtl8mcPq32OBZKhJLNul/+ErjvPu+uFW0pL4/b3xHI7WbqVM+f1Z06cVs4ZkybpqT7/PNK\nGxT9A+Bty+FQ53/6NP+cM8eed4iezR8tRvXmjW0F8RzQmmM7f557rcvL489e+X2vtaXlKd99p3xf\nv97c/pJcLiteOf1BVlYWAODSpUsYN24cevXqBYfDga+++goZGRn2FyDC0f6Hl6vbMpmZ3H5UTAx/\nh/jLqyYRnsyYMQMAcPr0aQwZMgSjR4+Gw+FAeXk58vLygly60Of660NzPkSEFhEr5GlqAvbv59/j\n4/ngZ906Vzeqehw4YDxp92UCOWAAcPgwT+PSJf910Px8ZRAbSLQCHoeDD3bPnNF3Ge+rgIcIH776\nin9+/z0X+BUUuDcUDLga+xQGRq2yYgU3PuopPXsCX3/t+XWeIrsl1qN9e1fj1MKLvaiLhARel0lJ\n5pPLlBTguef49/XrrQk/rD6TrrpKMQpdXGztGm0+V1+tb6g6K4tPVI0EPACfOI4bZ02wHWxCcfL5\n0EPeX+tugg9wYYWnPPkkUFjoms6sWYr7Zrl9al2gC/QWSLKz/z97Zx5fVXH3/8+9WQgBkkuAJJAg\nSxISAiEEiUQNGoEAIiKtBsFWESn40lq1C8rj8/grrZWlYlu7ULWlolJFYkWtkrg8GiEiqKxW9CG2\nCYYlKJAIuBBI5vfHODlz5ux3P5d5v17zuveeZWbO3Jkzc77nuyjjxeulzprFh1ReMLFypTMhWHKy\n+QuUNWvodei1mz/CMaP7IgvHzpxi82Htp08HWlut8zaCi0KsETabEQ4BD0BDI//pT39CXFwciHz6\nCTqi4LR7d2fnt7Qo9+vycsUpuuTc5JNPPsF1112H8ePHw+PxqMZssIKJSCTnPCHTEQojgNZcKy6O\nmjmIpg12CHb4b5Z8Puo/x66DU7cmr9d9zqsDSdTpJ0LTuV2I3ngE9M0LmG8QcTszp3AaEt0fnzj3\n3EPLCrUpYPfu+s5MAcXsQTQ3S0+n58XHq6+NmXuYjbPx48X/xb/Uu7d222WXKfmKvk7sJrMQ1UZ+\nhgB6f2EmbMb5R894ZL7pmpqaIuKzjhD9MemPPx3RLIn/D/1RHxf/V34MsryNxiXbr+cPSuw/en1U\nbHqr/WaI4aXFZLcN7Lad0X2ROWBn9xMn9RAR/2ve4bqV42X+vCFDwjMe169fT/Ly8sivfvUr0t7e\nHvLyAiGa7k92SUxU/tOCAuf3Dz0zS0lkiIb+99vf/paUlZWR8847jyxatIjs2LEjYnWJhvZwClv7\neTzmaylJ9BPK/heAYURwuOmmm5CRkdH1tlPk73//O4qLizFq1ChcfPHF2LNnj618Ozpo2O31652H\nczXSHAhUuNzWBuze7X/oWrfQ2Rkac5mUFPqGNdrwN2z2uURKitpEgWEUNpi90bdrZsSwa+bIs3Qp\n1YZLSXF+LmD8RjMuTv37ueeMVdx37qRvNkXNnNZWqoV49qxybby5x/btxvVyGp7e6Pr13v7v3q18\n93esm5nx6ZnspaXRtt61y9xUID7K9FMzMjLw3HPP4de//jVeeeUVZGdnY/DgwRg8eDAGRdBm4cYb\nnZ8jak5dconynamPOwnlys+pmzZREzyvF5gxA/jv/1abZzG8Xtq3makfCyEuHsPz9dfaY8rLzetm\ntZ8nEPPuKVPo5/nnq7VlzDC6L06fTq99506qQSmyf7/9eon3osOHqYkloIRHr6nRavKJvwsL95FK\n2gAAIABJREFU7ZcZCFVVVdixYwe++OILjB07FitXrsSDDz6IBx98EL/5zW/CU4kYhh9T553nfB37\n/vv0nr93rzTVkgB33nkn3nnnHbz11ltIS0vDTTfdhPz8fPziF7/APifq2+cobN1FiHoelkh4Ii7k\nmTdvHmpraw33Dx06FJs2bcKePXtw7733YqED24CqKjoR9evnbHHDFjIiGzfSPDMz7eclYvTgNXAg\n/XSyQD7XOHGCqvRffHHgArdgIj7MS7ScPk3H4qhRyrb6euOH9epq+vnUU1oTDjP8EQL27k0fWPw1\n/dF7gBw6VLsI/u53jfM4e5b6oRERBSjdu1NTpuuuow+WRUX65wH0gZnHasw884z+dr0HSt4c01/h\n2EUXGe8zEl599JG6z+jdT6PNH9PcuXOxfft2FBUVYePGjfipv85wgkww7qG8Dx2fjwrYEhOpPzyA\nPhh6PDTV1lK/HPyczIQ6TGhz8cVUaP7uu4oQgadvX7qf9+WUkKCtF2+mZISZj5pu3ZwJSc2EywkJ\n5kIg1obbt1O/dXYQTV89HmDPHnoP6+yk9eF96DCcCK5EQRn/MPH++/QzPl5rHis+n738sv0yAyUh\nIQE9e/bEN998g5MnT+LUqVM4deoUTgbTGeE5Cm92x/5/JwwaRF9kSAGPhGfw4MFYvHgxdu7ciXXr\n1mHDhg0YPnx4pKsV9fDzd0qKs2dcyTlEyHSEHNDY2EhGjhxpedzx48dJVlaWZjt0VNHFxEJ724Gp\nPIuJRarp0cM/84Tycr7O+qrz/fv7l/e5kAYNIuTiiyNfDzFRMwXY72Axjt547NOH9nG96FCEUJMp\ndqxe5Bu7/4WeOZSeuRFLPl/ww64D9PqamtTbWJhkveO9XkKuvto8z1Gj1P2fmWyx+1F8PC3D69VX\n3xXzE03bRBOXn/yERuQRr4MlhtF+q2QVQEPPZEsvQpA4FlkfjBb4ue3MmTNk9OjRYa+D3pj0x1yL\nnxvFsN/8/9W9OytXnexGe+LHJDPXSkzUN/MQI0bGxZmb+xmVP2GCMi6chhu3Kks0nTQ6Nz3dvzJZ\nVEsW9UovJSU5M5MZPFibB7uvpKQYt6N+HUI/Hmtqasjw4cPJXXfdRb788suQlxcI0XR/sov4n0qT\nK/cSTf3vzJkz5IUXXiBz5swh6enp5NprryXPP/98WOsQTe1hl/p69XjkzWkl7iKU/S8qerZdIc8D\nDzxAFixYoNlOF7A/59Kbpg8lIvn5dPHZty+duIz8XIwZQ48PxN+MUmft9lCEHI9UCsWDM5/i4mjo\n8nHjInWNbxLW37zenxM3ThKhAoDuQ5bok6dHD/sLRbv/i+h7Iz7e3NeOxxOasOt69fZ49K8lKYkK\neHifB3y68kpC+vUjZNIkmgDF54aZ/7CyMvWDvLif+VBhqahI+V5YaN7+cXH2/x92XYWFyrZevaz/\ne/E+q+fLYcECQkaOpPtZeGyaomc8ikKdaBDy5OX5J+ThhaiiLwD2fxn5TDIKf67n38XnU86rrFSE\njXqI9xpx8cvqyt8HvF5tfryfGyOBkhFO7glm5/bubb9M8b7m8Zi/gEpLs5+33jXx/7WZf5XWVkLO\nO088P/Tjsby8nPzrX/8KeTnBIJruT3YR+1tmZqRrJPGXaOh/r7zyCpk3bx5JT08n06dPJ3//+9/J\nyZMnI1KXaGgPfxDXexJ3IoU8hJA33niDDB8+nBw/flyzz44mj1kb8g8TAwYYO0dledgpC6BvOsVt\nbBHLb1u5km6z8/bRLcmsDWMzwZ+uH5MA6HpgYn3ayBFo375287SXVq40Fpb4k5KSrI8RhSW8AEQ8\nVty2ahXdpudIlT1E8/uuukqtCWWl+ce0ffTqMmCAWguCCWbZf8UjClz69fPv/+EF2UwzUo8FC+hD\nKUBIcTGtq95DN982aiFi9IxHr9dLevbs2ZXi4uK6vvfq1SssddCbI/m+4SwvdR9l7NmjOBdniM6Y\nm5q0Ahvj/5Dmf/XVihAoJYWOr4QEpRyxb2ZmWjtgT03VXpeogWKmaWTWJkb3iNRUbd31zrXLwIH+\n3dPsOuoUz+PrrPc/8vD/KR3zoR+PnZ2dIS8jWETT/cku4piyO3dLoo9o6H+XXXYZefTRR8mxY8ci\nXZWoaA9/4Mcj0+aUuI9zXsize/dukpOTQxoaGnT3Byrk4Y9JS6MLlH79jBeGZpoBycn008g048IL\n6XaWP6/NEEsRqaqqtA+/oUijRkX+Wml/MOlg5xgAusyy5sxRtFD0hDz8Q6IZTiJf6Y1df1NNjdKP\neRMFliZPZtes3SZu79mTtgET/vLmLuIDpsejPAyyfXrCFzNTNDECiihErqxUv5HnoxGK2o2i0Hba\nNPE/d56Ki43/bz2hFxOGG/UL9f0mdsZjTU0Nyc/PJ7m5uWT58uWa/WvXriWjRo0iRUVF5KKLLiK7\nd+/WHCPOkXp9yS58Pvn5ynariEt6LFig9OGSErv3WpqYSdiePVoTazv3Cx5Ri5bXRrKD2Ti87z56\nDD/+vF79Fz6iCZwZgQiz7TwQiOckJSn7xPuDiHZcxs54JISQn//85yQrK4uMHj2ajB49mmzcuLFr\n39KlS0lubi7Jz88nr7zyiu75bmwPsT+wyJgS9+HG/hdK3Nge4vOik7lDEl2c00Ke/fv3k5ycHPLO\nO+8Ynm9HyGO2qLG7MGKLGasFZEKCcqzR4pJfoDFbSr3FqhuS2B78A0Sk6xaOtGoVIW6cJEIF3xZ8\n37jsMuPxYAXT6rBKPl9wNXkARdjC3l7zk2taGn2oLSujv0eMMDeR4v1y8bS2Ur9F4vHduxv7MSJE\nMd8CqLlSfT1t8wkTtMeLec+cafxGXnzovfpqRchVWKjNm/+fx45V6mzVtkYY+RYRMc47Nsbj2bNn\nSU5ODmlsbCTt7e2kuLiY7N27V3XMli1bSFtbGyGECoTGjRunyYefIydP9l/AQ/PS/09EjRwjeGEQ\n72Pqqqvsj0kmhGHChrQ0RbhbWmpPA4/v80bmpXYxE/KwtYe4KGc+qdiLIcCZ9pCVthKfVq3SD09v\nRlaWOg8j4bWo1Sfup2ua2BiPjCVLlpAHH3xQs/3DDz8kxcXFpL29nTQ2NpKcnBzS0dGhOc6N7SH2\nKad+qyTRgxv7XyhxY3vorRUl7iSmhTyzZ88m/fv3JwkJCSQ7O5usXr2aPPzww+Thhx8mhBAyf/58\nkpaW1vXGpLS0VJOHHSGPXceHdh5I2Ntvs8QEN+J2psnDb+Mf/JxoLERLEuvMq9dHoj7i4nf06NCW\nF4uL2EBgbSH6i9Hr28yMwwomjLDyW9XUFBrfVvwEaiWI5R1H612zkdmGOF7saBOIAiCz8/l6JySY\nP+iLD73iNYtvjcrL6XYrIRef9DRz+Ouyc7zx/TI2xuOWLVvIlClTun4vW7aMLFu2zPB4O8EJnGrb\naPNSUkmJst1M44yHFwYxH1qpqfYceDNhRa9edB7mBSeZmcpY0NO6E1NGhv412R17PLywVUwpKfra\ncMzJMj/WjIQvepozov8xs8ScsRs5ZddDvI/y9ysxbxFRoBQr45GxZMkSslLnhrR06VKVtt2UKVN0\nX1C6sT34/9zni3RtJIHgxv4XStzYHvx49Hik0NXNhLL/xQcnRpf/PP3006b7//rXv+Kvf/1rwOU0\nNAR2Ph8mmA8fbERJCf286CJgyxb6ffBgGoZdhA9HSYjfVQwJCQnWIYnFOv/jH6Grjx0mTABefVX5\nfegQ0KePfkjZYLBpk7PQtOcCBQXaULpiP8nPB6ZOtZff/fcDOTn0+/btwKlT2mNSUmh41tJS4PXX\nlW2EAHwE3V69gKQk4PPPaRhKO2Puz39Wvouhp0tLgffeU35XVSl5bt6s7hvV1cDs2TQMdEcHDX/+\n1Vd031NPAQsXAnfcAVRWAtu2GYeYZ/h8wPr1+vs6O4ELLlBCvPNhpRct0oZ45xGv8aKL1CGlb7wR\nmDtX+f3Pf9K6P/qoeb59+wJHj9Lv27YZH6eXh17kcbF9Y42DBw9i4MCBXb+zs7OxzaThVq9ejWnT\nphnsXYLERBqaHKjAwoUVhn3HDK9X6UsDBijb336b9ptdu2ioZKN+kJxMP0tLaV7bttHQ34sWAatW\nAbfealz2j36kjGcxKnZ7u3JfSEy0vg4+rHlcHB2PjM5OYNIk4Kqr6H0sOZmOT6NrysoyLufECXqv\na29Xbz9+HJg2DejeXan37Nm07URaWmgbAbS/Nzcr49oOmzYp4entIrbvmTPq+xXjb3/Tnvv739fh\nRz+qQ2IiMHmy/TLdxB/+8Ac88cQTGDt2LB588EH4fD4cOnQIZWVlXcdkZ2fj4MGDuucvWbKk63tF\nRQUqKipCXOPgwYdTl0Q/dXV1qKuri3Q1JEGkRw/gyy/p9379rNeKknOUkImPwghgrclTWWl2vr3E\nsHKQzPvZEZ2mMvRUp/Pz7dclXMmNmkWiaU9Ghr5mQKCJfysaI0OJEBK4DxAAhto0fH/i1f8JMdZw\nIUTfR4uYWLSP1lb1G36xD69ZQ8gNNzjz3cP7DmL9y+OheYgaCMyZMiF0TPNaMFVV+lGI/PFnws5j\n16c3VvmQzOI+M/j2Ky8nJDdXfa7dAFGiBhDL145PGKP2F2Gae+rrj43x+Oyzz5If/OAHXb+ffPJJ\nctttt+ke6yQ4QbB88vBaqHoh1EXy86lmS2Kisb8ps3Eomjzp+bEbP96eVhB/j9EbO0lJ9k3QnGjV\niImZl+pFqmIw7WGPh7afE7PuHj2M76tm6GlDsfmOL9/ov1bPAe4bj5MmTSIjR47UpBdeeIEcOXKE\ndHZ2ks7OTvLf//3f5KabbiKEEHLbbbeRtWvXduUxf/588o9//EOTtxvbg401qTXgftzY/0KJG9uD\nBcpwqnUqiT5C2f/c17N1sCPkMQovZxaCmE/z5yvn6Pn8EH0AsAWhkQo7739j5ky6LZZCqAcj1dcH\nx+SLOYn151w7/wkN3Yzgd+wIEAwfIAB0TRpXrVKb0jGTRobZQ6KdfsAmOlFYOnas9lg7Jpd8mjBB\nqUtTkzLBAnSs83Xnr4vvP8xESi8Kkd2HSREr4Rf/0Mhv797dPER0RQU9btQoWmdxHLB7lhVifRIT\njf0L8Yj3ZTMTE749lXNiYzy+8847KnMt0RyE4SQ4gddLQ6ibOc41g/9feOGbnvBShO9H7GFxyBDq\nm8fpvT4+np6vJ6xtaiJk3Djz842uia8bi2DFzMmMCORlSGoqPb+83HhcMHNVO2ZoZikhwf7/rHeP\n1JtLCwvVwmkmsGb9gfocio3xqAfvU1I0p5wyZQrZunWr5hw3tofevCVxJ27sf6HEje3B/EA6XTNK\nog8p5LHAjpDHqA3taAjwAh5C1IOLJX7xxR6MCKGf/CKWbecFRcwBI//gGEvJ6QKYD/Ha2mrtYNIs\n/6KiwJxA2697TAyloPgAAUCamqiwg2+/K65QhJt6b63NHhLtOPJl/q6CLSwVo1QRon344zUK2Him\nbaGkWbOM292OPxM+L+b3x+zBmDlt1jsfMHfyKt63eKG06HfHDLFMM41KHv6+nJbmT3mxMR7PnDlD\nhg4dShobG8np06d1ha5OgxPs2aPv+N8u/P/JO93VewgUoyzpCQ4CEVykpupr82Rnm4cYF0Ooi/tr\naqiwgs/bTLDpxAmyWTJyzM6w41DaLDkJszt7tnb+Y36M9PKuqqICdlHTORYDExw6dKjr+29+8xsy\nZ84cQojiePn06dPkP//5Dxk6dKhuaHc3tkd+Ph0PCQn0JUAgztslkcWN/S+UuLE97PrAk0Q/Ushj\ngR0hj5G6v93FEe9M1c4bR96hLL+dOYDmH0SZGZee8ChUycrkLNKJx6que/bQBxVxOx9hKJR1pSGx\nhUq7lOrqatvmIYQQ8sADD5AFCxaotgEgP//5zwnA0ptdY5A9NOg5XLbzppCFyTYytSJE+yDp86l/\nezz2x1pCghL+Xbk+daqqIqR/f/q9Z09j7RmzLjJ3rjrUvB56efEPl/RhSls3vfMTE601ONg1AdS0\nbsAAKsBysqDgy0xKotdpxyxNvMfymlR6vPnmm0Kfi43xSAghGzduJMOGDSM5OTlk6dKlhBDid3CC\nyy5jv5U0apSz+jgx2xD7ox0zKj75KwBqalJH7hKTGBFK7xgxpDtvbi1iZz7t0cNe3c2w0k6ySnad\nLhOi/4KDOdwVt/fura/xp6TYGY+EEHL99deToqIiMmrUKHLVVVeRlpaWrn33338/ycnJIfn5+aS2\ntlb3fDe2h/jfSu0B9+LG/hdK3NgeZlFXJe5CCnkssCPkMVrcOFkgMW64gUb34PfpmYQYlUGIEo2j\npEQZpFbCIxqlIvbTmjVq/yx2/hc9szv+raXdsv3RAqEaJtwf7mKC4QOEtYXYTvxDQ1JSYPU06heE\n0DfQ/Lbycjp2EhOptlzPnrRveDyE/OQn9Bg9AYn4HyvXp06treqHPF5bhT9O1AjksWOuxefFhM5G\n7QsQMmiQsXDKjtkGHxb6qqv88xvEa4zU19s3S9PzoWUHKnCNnfEYLPg5kglKnbYte5PPn2clfOOP\nvfVWus3JCwYzDRmWDx+CHKDam1b5pqUZ19MomQlI7JwvhiQ3SnrCVzYfGp0zc6a53zknUbWsrklv\nH4uoqXf8fffJ8SjixvbgX57w2uoS9+HG/hdKZHtIIokU8lhgJeQx8sdDz7WXeE0eOyZeffvql5GS\nQrfpSWFbW/X9/fALTLv1dWu65x57gh2W2JtkPceX/KJW71y28A2kvmyxEyuTRDB8gBgJefiUkODc\nFwiPXh9hb5n1xidfnpHvHz1BLaBVh9Ub6/zvxETlWL5fmmkCODXX0rsfTJigCKvGjNHmwx/Lh482\nQhRE++M3iP+fBgxwpmIstrNd6PGxMR6DhdUcaeeBTU8AzmvI6gkB9f5DJ/d3q8R8S/lzrpnGHaAV\nhhk5GLbj109PsKZ37wCoqRkfMn3OHOv84+O1AQf4xDuDt99ntImtg8S+IGpL8ok6aZbjkceN7cFM\nsJ1qc0qiDzf2v1Dixvbg54hA1tKSyCOFPBZYLWDN3mDZ8bnCC3hoeeZJVGPn91m9QeffnouLYztl\nRypFKgoXu7mJ2++5x/o/Yw8k/DbxrbBVSk+PLSFPMHyAsLZYudK87USfMPw+9tbfCOYYWK8vGGnE\ndeumjrzFfP+wh1Pxv2f+L5iDV716GiUG/+Bl5tODF/oaRRnj82daaszsTM9vkAi7tyQl2VsUiIJo\nf2zARV9FTlSM+evVM+8zIhZ9gASK1RxpR2inJ5AwEqSzFyv8tgEDqMPnnj2Dc+9nvqH8PZ+//+jN\nX/fcox8FUyQzUz9/JkxmfdduvUShVbCEYk418fRMYlk/cSJYoy9S5HjkcWN78II9cU6UuAs39r9Q\n4sb24McjW9tK3IkU8lhgtYDl36yLiGZXYmI+DNTl6Sf+bZaReUe3bsZ1MXsjaFS2x0MXgcFy/Cgm\nOwvM++5zthB1Ev7VKrGFurhdfIgNRduwNG2aOycJIwL1AcLaQuzPffuahwsW23XlSuM6trbSqC4A\n1Y7j82ptpVozev2sqkrr+8eOZh7/Fr+4WN2PReEQ/zCoZ5ZphZGmkd4DpxOhCYvQ4+9bH39swMUo\nXU6w2xf0z42d8RgMrOZIO0I09ia/rEzf/EfMU2+bWbLjVJhf2CoCdm2aNcs8H/5FjNncxQukjARh\nRgET6uvVghU7bRAX57zd7CRmlspSSor1eBR9GllpNE6YoF2HsHErx6MaN7aHaC5opNkmiX7c2P9C\niRvbQ3zpYjfiqST6kEIeC6wWsB6PfWemRonX5tHbP2qU8kAnLob4hY/Z2w+jh00rs6NIJ6dvZp04\njzRTAweMNXnMtESCnai2RkwMpaDA2kLsz3v2mAsa9NrWX/TezHu9+hoyVg9gYrQvJuzYs0e5lvp6\n/QdffwQjRlHGjMoIF/6oB4vX70SbIJC+IMejGqs50k7UJfb/s3P4KIi0DCWxSHdO7qOisKV3b/W2\n7t21GnxUwK6frLRLmdDGbt30+nx+vvE52dlq5+V2Xm7ExdExz9e9Rw9a/uTJhMyYEbyXJGbaW6KA\nng9ioPd/s+vTm9urq+V4FHFje4jj04l2pSS6cGP/Y3z66aekoqKCFBYWkhEjRpCHHnqIEELIsWPH\nyKRJk0heXh6prKwkrdwNa+nSpSQ3N5fk5+eTV155RZOnG9tjyBD1eDRzByCJbqSQxwIAXW/njRY0\nRlJOJ4siq3Oqq/Uf6OxEDSJE/2GzrMz87ZmdFEgkrWBE4RJvRk7Snj3m+9lCQxQ0hVOTR/ocUMPa\nQuzPViYhZmNOxMikySivmTONNWTMwrN36xZ+tXS794tQI7Yx/4BvFn7dDCd+ffj/QWryBIaVkOe+\n+6zz0PPJwwuHRo+m2+LjqaaInnmX3bkiM5OWl5qqFnhcdZX6t15URTvJ51PmVbumxnr91chRP9NU\n5AUydstJTKTCHHE709oNxpxl9uKLEO28LzrK16tHYaGxVpMcj2rc2B7iWszfOUASedzY/xiHDx8m\nO3fuJIQQcvLkSTJs2DCyd+9esmjRIrJixQpCCCHLly8nd999NyGEkA8//JAUFxeT9vZ20tjYSHJy\nckhHR4cqTze2hzj3SL887iWU/c+LGOEPfwAuuMB4f3t7YPnfd5/yvaZG/5iqKqC6GujdG/jzn5Xt\nRUXAV1/RTzOeekq7betWYOFC5/Xl6dMHqK93fl51NbBzZ2BlA0Bbm//n8u2ux+WX08+kJGVbfT0w\naJD6uOpq/+tgxd/+Frq83cxTTwGZmfR7aSnw6KPmx/fqZT/vU6eAjg7gzBlg9Ghg2jTjflZdDWzY\nAHR2Kttee035ftddwGefac9LTqb9asIEYP9++3ULFLv3C6csXAhUVJi3FQ/fxuPGAV98oez77W/9\nK/Ott5R9s2aZn1taSj+HDQPmz7dXnsQ/7r3X+piEBO22l19Wvp86BcTH0z5z4gRw9Kj2+LFjzcto\nbKRL1q+/pv3tiy++FREAGDUK8PmUY71eoLYW8His687j8wG7dil5bd5sfU5Kiv79S2yT8nJgwABg\n7146B7G6A+rvZng8wIsvarcTQsdiMLCqS0eH+nfPnurfevXYuxc4fTqwekmil6IioG9f+j052b81\npUQSKJmZmRg9ejQAoGfPnhg+fDgOHjyIF198EXPnzgUAzJ07F88//zwA4IUXXsCcOXOQkJCAwYMH\nIzc3F++++64m3yVLlnSlurq6sF2Pv4hzz6JFkamHxDl1dXWq/hZSQiY+CiMALDVOysv1zzWKemH2\nxpIQ+6G9ncLUu9n1iKZfRtG3+DR+vCLlZU5W7UQA4ROv+RSMN4f+Jqv/h73hb2qiau1lZcamIMxs\nzuNR3jKLb1fNtMGMEj0nJoZSUGBtwY8Ru6rdfLuKDs+NjmOJf9PO+k1Njb5JBX+s3ht2po3Afvv7\n1tKfsOOhgteiycx0Zi5FTS6M74d2ytTTlnJyrhPkeFQDmGvyzJ9vnUdTk1ZTw8j3HKDVBikoIGTu\nXPq/snuDE4f9iYnaCFJGGnhmSe++YnWOkS890QGxmDdvqm2k9aNXP6fX5E8yG1PisVdcoTbXdFLO\nmjVyPIq4tT0C9esmiQ7c2v9EGhsbyXnnnUdOnDhBfCy8KiGks7Oz6/dtt91G1q5d27Vv/vz55Nln\nn1Xl48b2EKMuRsqMXxI4oex/7uvZOlgtYAHzhxI7CxXRAbOVeZg/IUsJoaGNWR4DBmgfxOwssGpq\ntJOxHeEFUy0XncQGupg0ij5iN913n73/lX+oqKzUti2LRMRfqz+JmSWwfKgac0wMpaDA2sLu+ONh\nDzhmAh5CtOZ5CQnGQgvx4crjoQIcZoqk9x/37auMNT0n0XYJRFARbJyaz4nmbfy5FRXOyoyLI6RP\nH+19ys65TqJ5MeR4VGNnjrQiP1/fwT/zzSNuHzxYPT6zsgKfS/jUq5f/4dNFrF6eiGbT6rZVJ7MQ\n8naSPy8anKa4OPN7mnj8mjX2hVRioi+u5Hjkke0hiSSx0P9OnjxJxowZQzZs2EAIISohDyGE9O7d\nmxCiL+T5xz/+oTrWje0hHaHHDqHsfzFjrhUfTz+NVLc3bTI+l6mgmvGtFiAAoKAAGD8e6NFDfUz3\n7vRz1Srgllus89SjtVX5fvgwkJ4OfPCBUq4ddehp04DiYnp+Xh4930zNm5k6MXOWjAxg5kyaT2Ki\nf9fB09IS2PlmpgTsfy0oUKuY82YhjN696WdpKVX116OsDMjOpir3ANCtm/aY3bup+r7XS8sPtllN\nrMCPRbPxx3PNNXTKuuYa8+N48zyvF9i+XW3KwSOqtW7eDHz5pWKKpMfRozSlpyumF2b4fPQelJio\njFcAeP99+hkfb88kJpQ4NZ9jY8TrBbZtoyZbAJCfT83f7JaZkEDb+tgxIC2Nbq+pAaZOtT63qgp4\n9VXj/1YSPhoagLNntdsJAS65RLu9qYl+9uxJx9nBg87KS00133/yJJ3fnLJmjfq3z2dtzr11K/C9\n79nLv6YmMBPr117TmkfZwWhO06OjA5g3z/7xN96omGsmJxsfFxen3fbVV/bLkUgkEivOnDmDq6++\nGtdffz1mzpwJAMjIyEDLtw8bhw8fRnp6OgAgKysLzc3NXeceOHAAWVlZ4a90kBFNardti0w9JFFO\nyMRHYQQAOf98JfKM3tskJ2+trN7+mb3RCvxatImpitsx1QK0b1vtnheNyUrjhml86P0nInykH6Zh\nUVionFtQoLyBFaPIGJU/bRr732JiKAUF1hZ6Ib+DRVMT1RDr399ay6ZXL21/sevAVE8DSc8Ey8ip\nczBMvoKJk2hfogNofyKFERIcjSinyPGoBgDp2dN/R/pGocr58b1yZeTnCzvJ38iLAwYYta068Zpn\n/tSvqkqJ1BnK5K92s5H2lMej1pZVJwSnI8cIbmyPaDI9lgSGG/sfo7Ozk1x//fXkzjvaxXoPAAAg\nAElEQVTvVG1ftGgRWb58OSGEkGXLlmkcL58+fZr85z//IUOHDiWdnZ2qc93YHvxz3ujRcky6mVD2\nP/f1bB0ARRW9qor6obFa2KnPt068+Yhe/iwFfi3axIQ8dhdvxhEu7CW2UCstte8zYdo0Z/4V7KaS\nEutjCNGasSUkmLcz/8Cq9/DK8rMSMvXvz/6bmBhKQYG1Bd9Ods21ggXfF/n/kAlgrMwtWdIzKdIz\nweLLMAorvWZNyC87KuFNR/0Jw+4PcjyqYXMkWxh27059mNm9D1dV0YhUevt4071A7/fx8f5F5XKS\nRIFzIOfqnR+IqfOIEcqcpLc/mHOskeDd7CUWm1f1hIUej36EUJrkeORxY3tEk+mxJDDc2P8Ymzdv\nJh6PhxQXF5PRo0eT0aNHk5qaGnLs2DEyceJE3RDq999/P8nJySH5+fmktrZWk6cb22PPHvW6U45J\n9xLTQp558+aR9PR0MnLkSN39H330ESkrKyPdunUjKw3i6LIFLHuDJi4wmPNhI6wWTqJ/EKNF6KxZ\n/rYCfy3GizE7CzePRxvqUs95sajJwG4WPh89nwk9jDSjxEQIITk5wVuA8onXhjAqW+/tYiCwB9OK\nCtLVt/T6Sb9+rM9FfChFDeHQ5LGugzYx/0lWx/FJb+LU8xVz/vn65wSzT8YCwQjDbgc5HtXwL0JY\nciJMaW1VwpvzadSo4PpvS00N3TzCUrdu/vvN0RNWm41xf+r3/e8H1pZ6zqjFF1PJyfZ9DPGJCar1\n5sL6ejONLzkeedzYHrzmgHTy6m7c2P9CiVvbIxC/hZLoIZT9L+I+eebNm4fa2lrD/X369MEf/vAH\n/OxnPzPNh/fdINqFf/ONeR3GjDHet2aN1j8IH4qZJ5BQ4Qw9e/eHHrJ//saN1EcMC/Ou5/siPZ36\nV2B+LpKSFB8AbW00VO2sWXT/xRcrYcrNqKgA/v1ve3UsLdX3dWPEnj3Wx4i+GcaPt5+/HoMGAc3N\n1PcI61vM7xPP558HHuI+Vtm8mfqJqK+n/ShcFBSofzNfWXo+K0T/HGI+en5r9HzFfGv+berrJtA+\nGW54P0PXXOMs/LoRzD+SDMEbfkR/dXohzvVobaV94fhx7b5evYDrrgvO3AdQvy+ffx6cvIw4fVrt\nN8eJ/xs7vsXi4rS+uZywdq32HmaXYcP07z8TJwKFhcrvr77yb9666Sb6SYh6e1kZvcffdZfWB5od\nn4eS6If/zysrI1cPiURCkX4LJVZEXMgzfvx49GYecXXo168fxo4diwRx5SBQWLgEv/sdizlfp9lf\nXm58LntA0+Pvf9duY0Ih8aHRrnNZM0QnhSNGWDtI5Zk/n35OnUonZSbgqa9XHriPHKFCjF27qJPh\njz/WOliuqqKfBQXA22+bO2BOS9N3dGxESwtdFNplyhR9h46A8qAoOtBlD/b+UlBAb5p5ecADD9Dv\n27fTfEtKANrHliApaQmGDl0SWGExysUXU+dw4RTwAGpH32lpilPVs2cV58GMuXOVB6qBAwHmjy8+\nHli/Xn/i9Pm0+4wm27Fj6eewYcCLLwZ2XeHm1CnFOfWGDXSMB+pU9v336T3HjjNrSXDZvdv6mKoq\nrQ4G68/iFNytG50b+D6hJwh3yokTgedhBS+M5Z24W3H4sHabODd1dtIxc8EFNACCU8rK/A9WsG+f\nEmCAZ+dO5V4E0Dr74wjeaI2zdSv97//yF+1cbFeYKIlueEevQ4YET7ArkUj8Q28tKpGoCJmOkAMa\nGxsNzbUYS5YsMTXX4hHNlQBzcy0zp5LMH454fFWVNiQwc2yZkKA1C7GLWL5TVfiyMv/KFc2dvF56\nHbzTWubrp6xMCXVdU0NI797O1Mmd+lzg6yCqhxu1TXq6f+3A4G1dmd8dxsCBdHt8vPI/R8lQigoi\n3Raio18jfzkMNp5FE8ZgmBP566w4GmDt4fUSUl7uLrXgSPfBaAOwDqFuZYYxe7bxecx3lZP7eqTS\nzJnqPuw0DDvvT2rBAuPjKitpOf740RHXFoGk+Hj9a0xLM+or+qlnT+XandcDwenIMYIb20P8T6UP\nEPfixv4XStzaHtIZemwQyv4XcU2eUFBUpH6jWFFh/tbYTAp66aXabXfdBXz2GTBypHr7V18pb75F\njQF/uOce5xLarVv9e8MyaBBQXU2/e73K28iTJ+m25GSmwULLYOFXL79cHfbdDkxzgv1HzESN5S/C\n6sCTmmquIWJkUsfXwecD+vUDcnOV7/v3a88nRH0uMyc4exZYvNi8HEn4mTSJap6VltJ+wvcr0fSx\noAAYPBh4803tG+hgmBO5+U0L01zbtQv45z/DrxacmEhNjLxeqjEiCT0TJhjvY/ODHtOmBb8uoeKX\nv1T3YacaZUePKprB+/YZH5eSAsycCVx0kfM6WpmYO+HsWf1r1DO/A7RmfQDV4jp1il67P9cjiS2M\nzAIlEkl4KCigmpNMw/r73490jSTRSEwKeQBFAFBURE0N/GHECOCZZ7Tb9+2jA0s0UWKCAa8X2LbN\nvzJ5li5V/2Z+dgB93z2MWbP8K++aa6hAg6mfe720TI+H+jHYupVuT03V929ihHjsf/5D1X3HjaNC\nov796SLy00/t5ymaDohmAlZCnpYW6v/h6FFaH/adLd55f0Xsuhlnzyrfd+2yX+dzkUg8qFdXUxOt\nt96iY8HMXw7fD8Q8gmFOtHBhcHzZRIKiIiq4LiqKjLCKCd0IAS65JHzlnsvoPeADtB/z5hoihND+\n7Y95Uri54ILA8zhwgLaVmQncSy/Re5DT+15qqmJiGkrS0rTbCgq0a4tevdS/9UzWJLEPW3+OH0/X\nt258cSGRxAqiSe/OnZGphyS6cY2Qh4jqFBYwAcwHHwCvv+5fmfX1+hMZWwSVlqq3FxUpb76Livwr\nk2flSvXvqVOBpiYq0DDzfbB5c2Dl8m/wn3uOLuD5Bf4XXzjzm8ALXJKTgS1bgPPOU/w5fPopfaA7\ndkz/fD2NCrF8cSFqpV3EO4BlPgx4Z7C8vyLxYT81VX0tsURtbS0KCgqQl5eHFStW6B5z++23Iy8v\nD8XFxdhpMbNE4kGd76ubNpk7p+P7waRJ9HtZmfI9UJhAOFBfNucivMAhGP7OJNb88IfKd49HSXZe\nlCxcCAwYELq6BQvmAJ13LO4vbW36jpuTk4ELL6TfxXWCFe3tWq3CQDByZzh0qHZbYyPw5ZfK7/h4\nuobitWadLMXi450dL4lemJ/HTZukgEciiTT8fT0pKfaeRSRBImSGYDaZPXs26d+/P0lISCDZ2dlk\n9erV5OGHHyYPP/wwIYSQw4cPk+zsbJKSkkJ8Ph8ZOHAgOXnypCoPvcsQ7YetEI83823D+9nw+ejx\n3bub+/2xi1gPj0frJ4EPQ6yX/PEHZGTbeeml2vxLS9V+ctLSzOtTU6McHx9PyODBip+CXr0ISUyk\n371eGqJVPF8vjHu/fur6T5qkLdMMFiK9qUn93Q56x0fBUAqYs2fPkpycHNLY2Eja29tJcXEx2bt3\nr+qYl19+mVx++eWEEEK2bt1Kxo0bp8mHb4tIhFHn+0FiIh0vRr6y+P+S7+vB8jcgQ1z6T309vSf4\n029iYTwGE8CeTx6+2Zz4XOnVy9y3XTQlf0KnO00+H73XVFURkpcXunISEggZMMD8GHbPi4sz/q+N\n/vPMTLo9kGtg/U+iINtDEklk/1PjxvZoaqL35/79g/PsKYkcoex/7uvZOoRCyDNzpr2yL75YOScY\nD4ai81eAPujwmDkuvu8+/8o1esBlD6keDxWcMOGW6NzWqD6s7noLTJZ4IVFVlX4e4rbJk9X1nztX\nLVAIpVPA/HwqOOAdcLpxkhDZsmULmTJlStfvZcuWkWXLlqmOufnmm8m6deu6fufn55OWlhbVMXxb\nTJ9O/49x48In5OD7y5496r7XvbvxeaEQyLjZ8bKbiYXxGEwAkORkQoqK7D2U03OUFB9vfZ6egD4a\nU0qKEkQglKl3b207Bjt166a8JBFT9+70/sde4Ij7y8v1+ok6KYEF/EtsPSLHoxrZHpJIIvufGje2\nB/+8k5IiBT1uJpT9zzXmWoGwZo3zcx57zN5xKSn0U8/fhz8wUymel19Wvvt8ilkTK5vHn7CogNoE\njb8OZupy/DhV12V+OeyEQvZ4FJ81zC+P16sO8TpqlBKS3qgN7ZhqrF1Lb3cAbZdgOQXU8ynD+3Fh\nPnxigYMHD2LgwIFdv7Ozs3Hw4EHLYw4cOKDJa8mSJViyZAk++GAJgDps2xY+c6Vdu+gY2rOHmk3y\nfc/MV1a/fjQxc7xg4GbHy7xzcuaQPJw48WdUV1fX1eeWLFkSjuq5jr176b20qsr4mPvuU77PnKl8\nWvk4A4AbbwyoekExcbbDiRPUx1yoaW0N7T3P6wXee8/4v/n6azq/1tVp/QcC1Jk6b5J3/fXaY+67\nL7BrEP0KSiQSiSRw2PMOQOe0WHoWkQSRkImPwggAjakRe6u4Zo3dPJTUq5d9qWio3tQXFyv1YVop\noplWt27U1ITfZmWmZESg16GnqVNZqezfs0d5s9jURFXMr7iClieW3aOHkkffvnSbmDdTI2eI+4Ml\n1ebzZFpJeiG5Y2EoPfvss+QHP/hB1+8nn3yS3Hbbbapjpk+fTuo5+5mJEyeS7du3q47h2yIazJX4\nvmdGKMy13AyvITBgQHDydBLyM5D/IxbGYzDh2yM/31z7Qv98mZymNWv8C5/uJNXX62vp+JtETeKa\nGnrv9Ccvj4fXBELoO7mLkO0hiSSy/6lxY3vw99pu3aQmj5sJZf+LGU0e0bnp3Lm0+8+da+98PnLV\nyZP2paKDB1PnxOnp1EFhsGAOLHntllOn1Me89x7Qo4eihbNmDdW28QenGgfiW3YxUkdpKc2PwUfq\nGTQIOHiQRh/x+bRlf/21ct7zz+uXn5trXr9Aw7wyLQYeplHUo4eybfbswMqJJrKystDc3Nz1u7m5\nGdnZ2abHHDhwAFlZWYZ5mjk9Dhd83zODj4Jzxx2hrZMb4CP8DBsWnDydOKI20i6U+E9BAfB//2e8\nn0WikwTGmjXKGiSUXHKJ8RzJGDeOauONG2d+nNer1Qq64gr1fOyEfv3Cp50lkUgk5xJ81OLTp50F\nw5GcO8SMkAdQPww4DV08Y4byPSlJP6KTHqdO0Wg+Z85YL6LswIQL27bRBRb/cMwP6upquoBqaaEP\nsADwP/8TePl2ER/WPv9c2devn/8P9QsXqhfGTIjCC+EA6xD1mZnOy+ZhJlmM+nolwki3bvSTj8YV\nC4wdOxYNDQ1oampCe3s7nnnmGczgBwaAGTNm4IknngAAbN26FT6fDxkZGYZ5uslcie93lZWRq0e0\nwN9v9u0LTp5OBDfRICCMNcwEPADw+OPhqUc04vVSE89gYPflEkAjTU6e7F85aWnmYyM3l65nPv/c\nes5cvFg95gF7QiqPBygs1N9mZ+0lcQdO19QSiSR0iAL5YDx/SmKPmBHyiA8DTkMX8yFLv/nGfrl2\n/X3YhQkXjh8Hdu9WL+CYv549e4BrrqHb+BDQ4RQ4mD2snTzp/0PZvn3KwjIuTrkmUUNJDDE7dqz6\n944d/pXPYH2ALfz5ELJ2/BG5kfj4ePzxj3/ElClTUFhYiGuvvRbDhw/HI488gkceeQQAMG3aNAwd\nOhS5ubm4+eabsWrVqgjX2hqvV/E7UVtrfhz7DMZYdjvs3uL1mrebE5wIbtwkIIwVvvvd4OcZFxf8\nPAPF49Fu6+ykPmwCpazM2fGffkr9gPXv77yslSvpp55/PgD45BNlrrZi6VK6xuCxI+QpK6Nzvnhe\nXV34/LBJQg+/ph4+XAp6JJJIEh+v/v3cc5GphyTKCZkhWBjRuwynvkBE2/nsbHtl2/X3YRcxapUV\nc+ZQe8yKivD6PBH96LDoK7wdvj/wPobKytTXJPo7EOtjtt8pZWVKXqI/ED2/IjEylIJCtLWF6CvC\niGCPZbczbpzxGIh2oq0PBkJNTQ3Jz88nubm5ZPny5Zr9H330ESkrKyPdunUjK1eu1M2DtYcdHy/6\n5yspJSW0fmbY/BeKfDMzQ+snJzNTPWdZhTdnKZA6EULIpEnG+82iX/JJL+JYjx6EnHee9bkZGdpt\nCQnujz65fv16UlhYSLxer8b33NKlS0lubi7Jz88nr7zyStf2999/n4wcOZLk5uaS22+/XTdfN7YH\nW1Oz5LY5QaLgxv4XStzYHnv2qMej3WdWSfQRyv4XM5o8Ik5V/TdvVr470Yqx6+/DLk61RA4dovaY\n4X5rJr5l7+ign4RQfzv+wl/z1q3qa+JVwvmIYwBw113qN5bifqewCGB6mkpOtcQk0YNo9scT7LHs\ndpifLekTJ3J0dHTgtttuQ21tLfbu3Yunn34aH330keqYPn364A9/+AN+9rOfBVzeAw9YH2PmoyU/\nP+AqAFBMkINBQQH1cdfUROtOSPDyFmlpAV5/Xfn92Wf2zvO3TkyR8n//1/iYRYvs5aUXcezLL+k1\nmZGeDhw5ot1+5gz1WainNeUWioqKsGHDBlxyySWq7Xv37sUzzzyDvXv3ora2FrfeeivIt3/iLbfc\ngtWrV6OhoQENDQ2oDZYaZIR56inFDF7OCRJJZCkqAvr2pd9jzXWEJHjErJDHqar/xRfTRWCkzXAG\nDQKam+2XHw7npHZssflF6uWX+x96mVc7LylRXxNrE71r/ec/lQcDny/wtjATEkqHsO6CCXZqavx3\nTH4uEoqQ8hJnvPvuu8jNzcXgwYORkJCA2bNn44UXXlAd069fP4wdOxYJzL4uAOw8kIumsjxWPn9C\nSc+e2m2TJwPvvENfPAwaZC90uuiXxiksRH1iInD2bGB5WfGTn9BPIyHRqFGBzVFer7kAql8/IC9P\nf5/e/+E2CgoKMEzH6/wLL7yAOXPmICEhAYMHD0Zubi62bduGw4cP4+TJk7jgggsAADfccAOet/KM\n7RIGD6ZCS48H+O1vpRmtRBJpYtV1RKyycCF9fkxIoAI6p8/H/hBvfci5AxOwuImnnqId59FHQzfp\nMs0VgJbFR83So0cPxWlxebmzNv3kE2pr6vVSJ6D8NZldKx8J6OKLA28LJiTUIxxtLgmMhQtpv01O\npv9XKN/exyr791OHra+/bm/cS4LPwYMHMXDgwK7f2dnZ2Oanw6glS5YgIYEJaSq+TQrdugGPPaZ/\nrs8XXB8cepGcAqVbN20EytRU9T26uNjc31ZSEnD4MJ1D9u4NrD5mwjARf9tj/HjjfZMnA888E9gc\n1dlJ29XoWs6eNfIHVIdTp+r8LzjKOXToEMo450vZ2dk4ePAgEhISVBEps7KycNBAtXnJkiVd3ysq\nKlBRURGq6gaFU6eUPlpZGVxtO0loqaurQ11dXaSrIQkiPh8dk16vjKzlFvbtUzShjx1z/nzsD1LI\nE2UkJtIFlcdDTch4h796mAkjgoUdzZWaGqrBU1MDfOc7dJvXC2zc6Kyszz5T3n6WllJVcbZINbvW\nMWPow2hJCbB2rbMynRKONpcEhlPBpESLDCkfeTxBtHVZsmQJ5s2jJlV6Gi2nTxsLBETHuoGyaxdw\n0UVaoYwZcXGKWbAeohDK4wHuvVe9TXQsLDJhAm0Ds3KssDIJ/de/1ELnuDj/BV5Mkyc5WfvQzQRc\ngZgUr1oF/PCHxvtbW6k2j5YKjBpVgRtuAKgV4S/8r0SIqaysRIuOTdrSpUtx5ZVXhqxcXsjjBrxe\nOi5kYAL3IQoRf/GL6B2PEnuwyM4dHTSylhS6Rj+8SxF/no/9IWbNtfyBhS/3x8woWLA3ZoQAghl4\nxLDj3+i554BLLwV+/3tgxAi6rbMTuO8++t1u2/Jhy0+fVi9QzczGqqtpHd94Q2rXnOssXKiEQhZN\n/iT24R88ZUj5yJCVlYVm7lVPc3OzSlPAKfffb2yyxHww6RGI0EMkNZUKO4qLnZ3Xp4+RQIEiCkoI\noXMFj5n5lM8H/P3v9LuVHxojqqsVk1C9KFsNDer5KT4e2LnTf03Dyy+nn+ICnzfTCuSlx09/an3M\nE0/ob1+7lp4f7VqUr732Gj744ANNMhPwiOPywIEDyM7ORlZWFg4cOKDanpWVFdL6hwsW3XXXLum3\nTiKJNDIarPt46illncU/H4cSKeThYOHLjx6lalSRgH9xu2lTZOogUlZGBTx5ecYCGt4ZMdNO5jV/\nGhqUtr3wQvtl8w/oa9cqZXzve+rjZLhlCWPfPvqGGQDOO0/2CX9hoa/lIiJyjB07Fg0NDWhqakJ7\nezueeeYZzJgxQ/dYYuNpet8+433Hj/tbS2cwQT4z8ykttXfeu+8CY8ca7xcvPynJmTPKtjalbv64\nN2ptBa65RvldU6MNH//kk1SoM2AAMHAgfQN7993Oy2Kw9QK/bvB66TzJ7ntOzMZEXntNCULgFFHA\n5nb48TVjxgysW7cO7e3taGxsRENDAy644AJkZmYiJSUF27ZtAyEETz75JGbOnBnBWgcPGZhAEg3c\ndNNNyMjIQBHXEY8fP47KykoMGzYMkydPRhv3FnjZsmXIy8tDQUEBXn311UhUOSRs307v+z16UA3U\nSCkmSOzj89E5HwijT9eQxe0KI8G6DKfhy0NBfT0hXq9xKNtIkJpqHaaPD1nf1KQOr06INsysEfxx\nYhh0Psxs//6BX1cwiZGhFBQi3RZ8X+T7oMQZbg4pH+k+GEw2btxIhg0bRnJycsjSpUsJIYQ8/PDD\n5OGHHyaEEHL48GGSnZ1NUlJSiM/nIwMHDiQnT55U5cHaQwyDzKf5843rwB/Xs2dgYcbZ/NraqswT\nds7Lzzffn5JCSGIiDd2dkaE/h8fHm+fB5remJpqPk+uaNcu83QA6h11+Ob3m7t3Vdfe3PQlR6ur1\nasdrIP/VVVfZD8EuJr793Toen3vuOZKdnU2SkpJIRkYGmTp1ate++++/n+Tk5JD8/HxSW1vbtZ2F\nUM/JySE/+tGPdPN1a3tIYgM3979NmzaRHTt2kJEjR3ZtW7RoEVmxYgUhhJDly5eTu+++mxBCyIcf\nfkiKi4tJe3s7aWxsJDk5OaSjo0OTp1vbw86zmSR6WLCAkPR0Ol9feqnyfBLK/uf5tgBX4/F4EIzL\n2L+favDU10tP5Tz9+lENnORkYy/ubW2KM+K77lI7vfX56NvAtjb6dvXjj43b99lnqdlVdbX6rShA\n364ydftp0wIPkx5MgtUHY4FItwXfF6UWz7lJpPtgtMHao63NWDOjWze1DzT1+f6VW1oKvPeefn6N\njco8YJV/WRmde6wcTO7ZY65pYFUOO98qqpQRra3q9jMqr6oK2LBBmc8yM/0zEVu5kppEXX01NZkG\n6Dy5fbvSDoG4dbriChoMwWnUtIQEdTAEOR7VyPaQRBK397+mpiZceeWV+OCDDwDQKHhvvfUWMjIy\n0NLSgoqKCnz88cdYtmwZvF4v7v5WXXLq1KlYsmSJymk64N72sPNsFmuIQVXctMZPTlYcLwN0fn3p\npdD2P2muxeE0fPm5gp0wfby5FG+6xXzq7NpF8zAT8ABUsEOIVsADKE6oi4oU3wkSiYg03ZNI9DEb\nE6IPNEZBgf/l7d6tv50Q6njZTr0AYOtW9eLIiJISY79tdmA28v6ut+w4OWZq2qmp9HdyMr0+f2CO\npY8dU7adOaOohAfKV1/5J3y67DL66fEEJmSSSCQSK44cOYKMjAwAQEZGBo4cOQKARsHjfdixKHh6\nLFmypCu5JRLZuRhCXe/50i0oa5g6AEuwadOSkDvgj3h0rZtuugkvv/wy0tPTu6SyIrfffjtqamqQ\nnJyMNWvWoKSkJMy1PLdxGlpeLxpXMMLTP/+81NCQSCSSYOHxKAKNhAR9G3FRi2PgQPv3cl6bQ4R3\nojx2LI2OaEZBAWCwRABAr6WjQ4mql50NHDjgbK4IJIqc16uN5sWHRo+Lo86jq6tpnbZvV2sOx8eb\nO4YW8XgUX1l81A6A+tIJBlu2AL16OT/vq6/8E7JJJBJJIHg8HtOolEb73Bbtjo/EfODAuSPk+fe/\n6WdqKvDAA5Gti/9UAKjABx/Q/y2U0e4irskzb9481NbWGu7fuHEjPvnkEzQ0NODRRx/FLbfcEsba\nSfzBTjQuf5AaGhKJRBIYXm7Wj//2NU9cHBU62Lm3OhXWGzkx5rV8qqvV+2bN0h7/wQfmWiGi1tCX\nXzp/08eiyLEIWU7o7ASmTFFv4+vb0QF89hmQm0vbPS+PhlBli3OjoGlM40ekTx/FJOupp9RmeA89\npHwXnT874dJL6dtip9TXx57jZYlEEp0wMy0AOHz4MNLT0wHoR8GLlWh3fCTm8vJzR6jO5ssvvgAW\nLYpsXQKhT5/wCOYiLuQZP348epuEb3jxxRcxd+5cAMC4cePQ1tbWpYoniU6kMEYikUiiEz7U+Pnn\nU+HCv/9tP2oOi4plh+pqKjwygpnziOZK69drBToXXqgIpfQQ/fVkZTmPXsH82tgxDdPj2DH1YltP\nQHP2LBX4nDkDXHCBsp1FBBT54gsqGBLhTbJ8PiVkuxi1o6PDfv1F/t//838h+s47wOTJ/pctkUgk\ndpgxYwYef/xxAMDjjz/eFdHOKApeLOI20yV/4aNyhiU6VYgYMiQ8grmIm2tZcfDgQQwcOLDrd3Z2\nNg4cONBlf8ngVe0qKipQUVERphpKzkXq6upcY7drl+PHj+Paa6/F/v37MXjwYKxfvx4+QVLX3NyM\nG264AZ999hk8Hg8WLlyI22+/PUI1lkgkTuFNtHbtci7QsHJ+zLN+PU1WXH65+ndKCnDypPJ74ECq\n9VJcDHz6qX4e48dTnzr33guMHAls3uz8RcONN1JtG3998rS308U2u+YdO4DBg42PHz+efi5cSDWP\njPjkE/Vvj4f6UGprU67xqaeCb85cWQl8843+vh49zOt8zz3A0qXBqYdEIpEAwJw5c/DWW2/h6NGj\nGDhwIH75y19i8eLFmDVrFlavXt21dgWAwsJCzJo1C4WFhYiPj8eqVatMTbncRNOn5OkAACAASURB\nVFmZ8nKkpMTdAg8nhGKeiwTvvw9873uhDyAUFdG1RE/pPFdeeSUWL16Mi7/1ujtp0iT8+te/xpgx\nY7qOcatndEnsEAt98K677kLfvn1x1113YcWKFWhtbcXy5ctVx7S0tKClpQWjR4/GqVOncP755+P5\n55/H8OHDu46JhbaQuBvZB9Xw7cGvcfWiGIrU1mqFMHapr6cO863W1TU1wH/9FxU6JSVpBQssH5+P\narboMWEC8L//S333tLRQM7H331droljVo1s3Kjzxl9JSrZmyUfsVFgJvv02P9fe5o6rKWojmb95e\nL/0/Ro3S319Z6cT3jxyPPPL+JIkksv+pcVt7FBQAhw/TFy7x8fSlyI4d545fHrcizsUZGXStck5H\n14plm0qJJJrgTSPnzp2L559/XnNMZmYmRo8eDQDo2bMnhg8fjkOHDoW1nhKJxH94Hy1VVdQB8v79\nxsfrCShER79GjB9PtU3q69XbvV5g1Sr6vaaG+sB5801an/JybT7MV46Rf59Bg4B//IMKTP7v/6gg\n6OhRbV579pjXN5CYDh6Pvh+6qVPVi7vLLqPXyQQ8gXDTTcr3hQsDiywm8vLL5iZ8e/aYO2W2a/4n\nkUgkEvs0NCgatWfPAseP68+bkugmHEplUW+uNWPGDPzxj3/E7NmzsXXrVvh8Po2plkQiCRyjMJRG\nNDU1YefOnRinE69Xmk9Kwkksmk+GCq9X7afl6FFqUrRnj/rB3OcDTp3Sz+Orr6gvn7Y242MAavbE\nzJdaW4ERI+gbyAsvBObMAfg4CsyXW1sbfcPFInPxUaTef5/6sTlxAnj4YWpe5fNRJ8aAti6icMlK\n8LBrFxU6+aO5RAgVLukJbi6+mNZlxAjq9ydYauZXXKH8lyy0LKA2GYuL888vz4IF1Mm2UXscOWJ+\nHf/6l/MyJRKJRGIO71cPoC9dxLkuVlm4kM51ycnUdMvNJluiL8JQEHFzLd6+MiMjA7/4xS9w5lu3\n4TfffDMA4LbbbkNtbS169OiBxx57TGWqBbhP1U4Se7ilD1ZWVnZFIeC5//77MXfuXLRy3j/T0tJw\n/Phx3XxOnTqFiooK/M///E+XkzuGW9pCErvIPqiGb48PPqBOe5OS1M5+k5LU/nni442FA4WFwIcf\nUi2go0fNy25tVRZiFRWKIIL5BvJ4qP+cby2yAVDNIibMefddfeHMwoXAmjVKlJGrrqJ+e9hvpiGk\nbQvjujJB1wcfGJspmZGdrR99rK3N3I/As89S7R49WDvx4dgZa9YA3ypfYto0es2iyRgLtesU3pTP\nqM306mRwFXI8csj7kySSyP6nxm3tERen3HeTkoCPPz53TLX4uejCC4EtWyJXF6fwdVeba4eu/0Vc\nyBMM3DZAJbFHLPTBgoIC1NXVITMzE4cPH8Zll12Gjz/+WHPcmTNnMH36dFx++eW48847NftjoS0k\n7kb2QTV67bF/v9op8OTJwCuvKL+thAOEaPMQ+f73gSefVH7zgoj33lO2i9pFZn51AEVThffPM3Mm\n8MtfUgHWtm3GWjtGAgu+rv6qUTc1aevKNKK8XhppzKhec+YA69aZ5+/zqU2xunVT/BcZCZLMhHVW\nsC5j1B4VFYCRAt2ECTTELdUCkuORR96fJJFE9j81bmuP5GT6Qob5TYuUaazVPB0KxLmIf4kU7Yh1\nr6ykL2TOaZ88EokkPBiFoeQhhGD+/PkoLCzUFfBIJJLohoUtHzxYMXMaMQJ45hn1cdu3A927G+dR\nUaE2t9Jj7Vr176eeohorr76q3s77CQLowtHIrw5A1bVFB8w330wXu1995d+i97PPnJ8jorfIPXFC\nP2Q6z8KFVPhlhehrh3cSzczdnC547fpX0uPgQf3tOTnUR9LUqcBPfuJ//hKJRCJRw+77nZ1U4zQ1\n1dq3XiiwmqfDgZtCx4s+BTdtCn2ZUsgjkUgAAIsXL8Zrr72GYcOG4Y033sDixYsBAIcOHcIVV1wB\nAHj77bexdu1avPnmmygpKUFJSQlqa2sjWW2JROInDQ1U6FJfrxUOMIGJHj17UrMrK8GE+OaKF0Tw\n+7ZvVx/HFkNxcdQESnQmrCeY+PYW5TdGC6577gksX/4F3YUX6h+jJ7Syg9fGCs7qmL17nZfLMBKM\n/fvfitnagw/6n79EIpFI1IgmsidOUEHL2LHhrQebpyPpEyjQeT8cFBTQNY+orGP00ieYSCGPxC+C\nHcnDCjZIIiGtPldIS0vD66+/jn379uHVV1+F79unvgEDBuDll18GAJSXl6OzsxO7du3Czp07sXPn\nTkzVc3whkUiinksvpQ/q113n7D5+8iT9LC01N22aNMl43+7dVFNIdPgMUNXv7Gya/9atVJi0cKEy\nD2zbpl3c/eIX9uquJ5jyeKjvH8aaNcrn55/by9eI1FT97zz+atPYeRMoCtBEjFTsWRsYUV1tHO0M\noP+dRCKRSMKDlX+8YMPm6b17I+cT6MYbI1OuE5jG09mz6u0ffhj6sqVPHolfMJtQgAp6vpUBhAyf\nT3nTaeTcMpLIPqjAt0UsecKXuAc5HtXw7fH443RhtGYN8NhjiiPkqiolIpP6XO226mp67KOPUgHN\ngQP65dbXqx0qO8XrVd5+iVGeMjJohCceu3+5eE16giajY83QK7+yEnj9dRqe/Y039O+BbW1A797q\nbcnJdPEs+jzKzKSLRp+P+mOws7g2uwbm/FqE9/egtz87m/6/ubl08ZqbC3zyibI/MVExK5DjUY1s\nD0kkkf1Pjdvaw+h+np6unRNDuQaPBp88cXFa4Um0YRa4oKND+uSRRCG8Q85du0JfXjSoBUqcw8L6\nsjfxEokkssydSx/s585VNEhKS6nAxi7r1ytmV6KAhzcPqqw0ziMxkS5+vF4aZUIPft0jau4cO6b+\nXV1tXW89amrUAh5eazQlxX4+RvNSdTUVoBkJeAD97a++ql00FxQoJnRtbfb8IFgJqYz2d3ZSJ9aA\nvgBs3Tpav88/p9cn5lNRYa98iUQikQTO669rt730krIGnzcvuOU1NCg+eYxMkUNNID7lIo1d7eNA\nkEIeiV8wtfPk5PCEsIsGtUCJc/x9iJRIJKGFd/b73nvGqsPMOXO3bvTTaiwzfwFeLzWrMoK9KCAE\nuOQS/WN4AYFomhQXp5iDjR5tbhomwq5bL8w670ySmaUZkZxMr9NMY8mOQ+TERO22736Xfq5cqWz7\n+GMaqQug5W7caF4/K6x8Kr32Gv0PPvhAu2/WLFrv3r2pIKuhQb2fr7dEIpFIQsvPfqbdxqIvAvY1\nXe3C+wbiywknVnN0NHPvvaEvQwp5JH6xfXt4hS6DBlETLSngcRd8NB1pqiWRRA/79ql/GwlamPr3\n2bM0zLrZWO7WjQoOune3Du1qJsBhbN6sFqLExyvn8oKpXbucvaWcOpUuePXcifFao1YkJVF160BM\n0gD9UPXMPPmnP1WuG1A0pTo7gfvuc1bOqlXAlCn0+/nnA2Vl5sc/9JDxvpEj9evNmDbNWd0kEolE\n4j/M9JrnxAnl+6JF9DMUPlVbW4OTj1N69oxMucFg1arQlyGFPBK/kEIXiR38DesrkUhCiyjEMBK0\nfPkl/ezooEIXvShcjIkTqeDEThhzUYCjx/z5QK9ewMyZ1OH+jh1UgLR7N83/8GHlWCO/QE7htUbF\na+WFLQBw/HhwytQzaeIdF/Oas8xEy652JDNjq66mIe/ZG9ft2+li38zM7Y47nNcboMIvZr4WjoWs\nRCKRnOtkZGi38do7zHw6FCZckTLLZZqtbuS//iv0ZUjHyxJJEJB9UEG2hSTSyD6oRq892tqA73yH\nCnc2bTIWtPDOj/UEMtOm0cVir17Uh0t1dfCEulYO98WFZbD/8v37gREjaJABMWwtQLV+2tsDL+ft\nt7X+dRISaOQzn4/Wo7yctn9qKhXOPPqof+3M/q/SUrVWlt4ivXt3+v8zQR9PYiLwwgtqZ9gAkJZG\nhXH8CyA5HtXI9pBEEtn/1LitPawc6esdwzvSj4tT5rPKSjoPBFqPNWuon79Qo3ft0f7XWQc+CF3/\nk0IeiSQIyD6oINtCEmlkH1QTSHuUllLtFkA/AldbGzBsmBJq3ChKlz/060d947BIU6LmKL94Ki2l\nvnmCHUmkokJRg4+LoxpNjLQ0rQPoQBAXgzNnAhs2BC9/gP5fekIivYXonj3U+fTo0fpq/VVVWk2g\n7t0V59BK3nI88sj2kEQS2f/UuK09jIQGHo8ivNE7hgli+H0eD9DY6J9VBp9PUpIScTmUSCGPM6S5\nlkQikUgk5xh8FKn9+7X7PR6amIDHyDzI5wPGjjU/xl+sHO7z9vhZWaGJ5sfM2hISgJ071fu++MK8\nDZ0SF6f+HYp1n10T2vp6+tZ30CDqb+Hqq9X7hwzR/6/NnG1LJBKJJDT06WO+/8YbtcJ6QuxFabQi\nOTl4/n2M8EqJhWNkk0kkEolEco7BR5Gys8gzc7gcKgfrVr7fmK+alBTgd78LTTQ/dm2ffUaFHmlp\ndDszZWJteNFFgZWzcCHVmGGUlNA3r5GCN8tbuFAbnrexUftfp6Za+2KSSCSSc5lQOD4GtD7jjMoW\nYf7TAuH4cWr+HSy8XuVFU20t3RaMlx6hansjzLR4wiIYC232EolEIpFIog0+ipSdRd6VVxrvi5SD\n9cGD6eeJEzRySCiETeK17dhBtYs++kh9XElJYOXs20edIQM0/zfeiJzDejG0+r59im8kBnOonJJC\nP7t1ow6xJRKJRGLMX/6iaJyazatOefZZ+mmkxRoXp//yY8wY55qoemXU1al/MyGNxwP8+c/O8ucF\nOqLfNxEndV+7Vmn7nJzwCXv0+Oorql0VSqRPHokkCMg+qCDbQhJpZB9Uo9cevDNfPU0ZIx8t0aSp\nYeREOFxcdhld2I4aRReOgZQf6WupraWL6ZoabWh5Vjce5gjbqh8BcjyKyPaQRBLZ/9SEuz2cBAzw\n+WgEKa+XvgQoKjLWDhkwADh40Fx7ZNIkrVYmAGRmqqNVWmFUBn8tgQRG4M8dPZrOi3/5i/6x7LpF\nFi7U+ugzaxu9uS9QrKKOJSUB33wjffJENXWi+FKWf06VL4kuoqE/RLoO53r5EmusTKH0YL53nBKq\n/mBXcydU5W/YQMu3EvDYKT9UJm92y586lS7C9Ra5rG7M5wOv/eVPP5JElkjfn2X5kS1fYp9gmfcw\nAYPeQ79Zfzhxgjr7P3MGuOACum3PHmouLGrgDh1qPXfoCXiAOpw5Y36eU/Su0+MBfvhD5XdiImuT\nOrz9tnFe//qXsYAHoA6fxf9m4UK1xpS5NlAdAGuNoVDwzTehzV8KeYJApG/YsvzIli+JLqKhP0S6\nDud6+ZLAyc/XbrN6K2VEqPqDXTMxN5QfSpO3QK+f1W37dnNH2BJ3EOn7syw/suVLrGECGV5QMGSI\n+bEeD/CDH6h/ezzAgw9qzV15LrusrutY0eyXV/D45hvg7bepNs9XX6n9pgE0UIFZOcbUobXV+Jp+\n9SvtdiP27zcPerBqlZKHIliqQ3k51VbSE/acPWte+9ZWoHdvdZ1FodDWrWY51HV94/Ng5m+AIpDi\nfQWJyUk7hYuIC3lqa2tRUFCAvLw8rFixQrO/tbUV3/nOd1BcXIxx48bhww8/jEAtJZLY5vjx46is\nrMSwYcMwefJktJm8sujo6EBJSQmuDKYxsUQi0WA1PwLA7bffjry8PBQXF2OnGP4pAD7+WB29CgDu\nvz9o2UtcyLmmtVNdXY0RI0YgLi4OO3bs6Nre1NSE7t27o6SkBCUlJbj11lu79m3fvh1FRUXIy8vD\nHXfcEYlqSyQSAau5VHxg10NvWSweu3q19pif/cx+PXftMq9Hebnx/kC0Qjo7jfO99177QovBg821\nbsxgkb5CJRxxmm9VlVYgZWZV5aSdwkVEhTwdHR247bbbUFtbi7179+Lpp5/GR4I3w6VLl2LMmDHY\nvXs3nnjiCTlpSiQhYPny5aisrMS+ffswceJELF++3PDYhx56CIWFhfBE051MIokx7MyPGzduxCef\nfIKGhgY8+uijuOWWW4Jah5Mn1b+dLFYlErdTVFSEDRs24JJLLtHsy83Nxc6dO7Fz506sYl6oAdxy\nyy1YvXo1Ghoa0NDQgFoWGkYikUQEO3OpXewIgySSqIFEkC1btpApU6Z0/V62bBlZtmyZ6pgrrriC\nbN68uet3Tk4O+eyzz1THAJBJpognN5Ofn09aWloIIYQcPnyY5Ofn6x7X3NxMJk6cSN544w0yffp0\n3WMi/T/IJBPg7vFIiL358eabbybr1q3r+s2PY55I/xcyyeRmKioqyPbt27t+NzY2kpEjR2qOO3To\nECkoKOj6/fTTT5Obb75Zc1yk/wuZZDqXsJpLI/1fyCRTqIhHBDl48CAGDhzY9Ts7Oxvbtm1THVNc\nXIznnnsO5eXlePfdd7F//34cOHAA/fr16zqGSC/xEklAHDlyBBkZGQCAjIwMHDlyRPe4H//4x3jg\ngQdw4sQJw7zkeJRIAsfO/Kh3zIEDB7rGMkOOSYkkuDQ2NqKkpASpqan41a9+hfLychw8eBDZ2dld\nx2RlZeGgTtgXOR4lkvBhNZfK8SiJVSIq5LFj7rF48WLccccdKCkpQVFREUpKShAXFxeG2kkksUVl\nZSVaWlo02+8XHG14PB7dsfnSSy8hPT0dJSUl0nGgRBJi7JpDigtUaUYpkdjHaF5cunSpod+5AQMG\noLm5Gb1798aOHTswc+ZM6S9SIolS5JwoOVeJqJAnKysLzc3NXb+bm5tVb0EAoFevXvjb3/7W9XvI\nkCEYOnRo2OookcQKr732muG+jIwMtLS0IDMzE4cPH0Z6errmmC1btuDFF1/Exo0b8c033+DEiRO4\n4YYb8MQTT4Sy2hLJOYmd+VE85sCBA8jKygpbHSUSt2M2LxqRmJiIxMREAMCYMWOQk5ODhoYGZGVl\n4cCBA13HyfEokUQeO3OpRBKLRNTx8tixY9HQ0ICmpia0t7fjmWeewYwZM1THfPHFF2hvbwcA/OUv\nf8Gll16KnmLID4lEEhAzZszA448/DgB4/PHHMXPmTM0xS5cuRXNzMxobG7Fu3TpMmDBBCngkkhBh\nZ36cMWNG1xjcunUrfD6fxlRLIpEEDq8xd/ToUXR0dAAA/vOf/6ChoQFDhw5F//79kZKSgm3btoEQ\ngieffFJ3LpVIJOHDzlwqkcQiEdXkiY+Pxx//+EdMmTIFHR0dmD9/PoYPH45HHnkEAHDzzTdj7969\nuPHGG+HxeDBy5Eis1otPJ5FIAmLx4sWYNWsWVq9ejcGDB2P9+vUAgEOHDmHBggV4+eWXNedIFViJ\nJHTYmR+nTZuGjRs3Ijc3Fz169MBjjz0W4VpLJLHDhg0bcPvtt+Po0aO44oorUFJSgpqaGrz11lv4\n+c9/joSEBHi9XjzyyCPw+XwAgFWrVuHGG2/E119/jWnTpmHq1KkRvgqJ5NzGaC6VSGIdD5EepyQS\niUQikUgkEolEIpFIXE9EzbUkEolEIpFIJBKJRCKRSCTBwfVCntraWhQUFCAvLw8rVqwIWr7Nzc24\n7LLLMGLECIwcORK///3vAQDHjx9HZWUlhg0bhsmTJ6Otra3rnGXLliEvLw8FBQV49dVXu7Zv374d\nRUVFyMvLwx133OGoHh0dHSgpKemK8hDO8tva2nDNNddg+PDhKCwsxLZt28Ja/rJlyzBixAgUFRXh\nuuuuw+nTp0Na/k033YSMjAwUFRV1bQtmeadPn8a1116LvLw8lJWVYf/+/bbbwi3I8SjHY7DKl+Mx\nOIRiTMrxKMcjIMejP8jxGLry5ZiUY9IpsbxmleNRjkcQF3P27FmSk5NDGhsbSXt7OykuLiZ79+4N\nSt6HDx8mO3fuJIQQcvLkSTJs2DCyd+9esmjRIrJixQpCCCHLly8nd999NyGEkA8//JAUFxeT9vZ2\n0tjYSHJyckhnZychhJDS0lKybds2Qgghl19+OampqbFdjwcffJBcd9115MorrySEkLCWf8MNN5DV\nq1cTQgg5c+YMaWtrC1v5jY2NZMiQIeSbb74hhBAya9YssmbNmpCWv2nTJrJjxw4ycuTIrm3BLO9P\nf/oTueWWWwghhKxbt45ce+21lu3gJuR4lONRjsfoIlRjUo5HOR4JkePRKXI8hrZ8OSblmHRCrK9Z\n5XiU49HVQp4tW7aQKVOmdP1etmwZWbZsWUjKuuqqq8hrr71G8vPzSUtLCyGEDuL8/HxCCCFLly4l\ny5cv7zp+ypQp5J133iGHDh0iBQUFXduffvppcvPNN9sqs7m5mUycOJG88cYbZPr06YQQErby29ra\nyJAhQzTbw1X+sWPHyLBhw8jx48fJmTNnyPTp08mrr74a8vIbGxtVAzSY5U2ZMoVs3bqVEEJveH37\n9rVsBzchx6Mcj3I8RhfhGpNyPJKwli/HozuR4zF05csxGfzrjfUxGctrVjke5XgkhBBXm2sdPHgQ\nAwcO7PqdnZ2NgwcPBr2cpqYm7Ny5E+PGjcORI0e6QtRmZGTgyJEjAGgUouzsbE1dxO1ZWVm26/jj\nH/8YDzzwALxe5W8KV/mNjY3o168f5s2bhzFjxmDBggX48ssvw1Z+WloafvrTn+K8887DgAED4PP5\nUFlZGdb2B4Lb3nx/jY+PR2pqKo4fP267LtGOHI9yPMrxGF2EY0zK8SjHYzDKk+MxOJyL4xGQY5Ih\nx6R9YnnNKsejHI+Ay33yhCOE86lTp3D11VfjoYceQq9evTTlh6oOL730EtLT01FSUgJiEAAtlOWf\nPXsWO3bswK233oodO3agR48eWL58edjK//e//43f/e53aGpqwqFDh3Dq1CmsXbs2bOXrEe7y3IYc\nj3I8yvEYXYS6feR4lOMxUuW5ETkeQ3f9ckxqkWPSnFhds8rxKMcjw9VCnqysLDQ3N3f9bm5uVknA\nAuXMmTO4+uqrcf3112PmzJkAqCSupaUFAHD48GGkp6fr1uXAgQPIzs5GVlYWDhw4oNqelZVlWfaW\nLVvw4osvYsiQIZgzZw7eeOMNXH/99WErPzs7G9nZ2SgtLQUAXHPNNdixYwcyMzPDUv7777+Piy66\nCH369EF8fDy++93v4p133glb+YxgtDfrk1lZWfj0008B0BvgF198gbS0NNt1iXbkeJTjUY7H6CKU\nY1KORzke5Xh0hhyPoeuPckxS5Ji0T6yuWeV4lOOR4Wohz9ixY9HQ0ICmpia0t7fjmWeewYwZM4KS\nNyEE8+fPR2FhIe68886u7TNmzMDjjz8OAHj88ce7Bu6MGTOwbt06tLe3o7GxEQ0NDbjggguQmZmJ\nlJQUbNu2DYQQPPnkk13nmLF06VI0NzejsbER69atw4QJE/Dkk0+GrfzMzEwMHDgQ+/btAwC8/vrr\nGDFiBK688sqwlF9QUICtW7fi66+/BiEEr7/+OgoLC8NWPiMY7X3VVVdp8nr22WcxceJE2/VwA3I8\nyvEox2N0EaoxKcejHI8sXzke7SPHY+j6oxyT6MpXjkl7xOqaVY5HOR67sPTaE+Vs3LiRDBs2jOTk\n5JClS5cGLd/NmzcTj8dDiouLyejRo8no0aNJTU0NOXbsGJk4cSLJy8sjlZWVpLW1teuc+++/n+Tk\n5JD8/HxSW1vbtf39998nI0eOJDk5OeRHP/qR47rU1dV1eUcPZ/m7du0iY8eOJaNGjSLf+c53SFtb\nW1jLX7FiBSksLCQjR44kN9xwA2lvbw9p+bNnzyb9+/cnCQkJJDs7m/ztb38LannffPMNqaqqIrm5\nuWTcuHGksbHRdlu4BTke5XgMVvlyPAaHUIxJOR7leJTj0T/keAxd+XJMyjHplFhfs8rxeG6PRw8h\nBgZ7EolEIpFIJBKJ5P+zd/dhUVyH/sC/o+wvLyqoaViS3cS1AYIrCOvLiqY2axVfyA0lNSHFRPCt\n7YPPrSaxRmtvIuQ2gmm8qdrwNM1DWqJt0Jt7IzZXqUnrGjUVDWJjRSNJIIEViRaJGDEonN8fxNEV\nkN1lZnZ29/t5nn0eGXbOOTt7vnuW48wZIiKigBHQl2sREREREREREVEnTvIQEREREREREQUBTvIQ\nEREREREREQUBTvIQEREREREREQUBTvIEqIEDBwIAPvvsM7zxxhuKlr169Wq3n++77z5FyycKNswj\nkX4wj0T6wTwS6QfzGDo4yROgJEkCANTU1OBPf/qTV/tevnz5hr/Pz893+3nfvn3eNY4oxDCPRPrB\nPBLpB/NIpB/MY+jgJE+AW7FiBfbs2QObzYZ169aho6MDy5Ytg91uR2JiIn73u98BAJxOJyZNmoTv\nf//7iI+PBwCkp6dj7NixiI+Px6uvviqX19raCpvNhjlz5gC4OusrhMCyZcuQkJCAUaNGYcuWLXLZ\nDocDjzzyCEaMGIHHH39c68NApAvMI5F+MI9E+sE8EukH8xgCBAWkgQMHCiGEcDqd4t/+7d/k7a+8\n8or45S9/KYQQ4uLFi2Ls2LGipqZG7Nq1SwwYMEDU1tbKz21qahJCCHHhwgURHx8v/3yl7OvrevPN\nN0VKSoro6OgQjY2N4u677xYNDQ1i165dIiIiQrhcLtHR0SEmTJgg9u7dq96LJ9IZ5pFIP5hHIv1g\nHon0g3kMHTyTJ8AJIdx+3rlzJ15//XXYbDYkJyejqakJH3/8MQDAbrdj2LBh8nPXrVuHpKQkTJgw\nAXV1daiurr5hXXv37sXs2bMhSRIiIyNx//334+DBg5AkCXa7HXfeeSckSUJSUhJqa2sVf61Eesc8\nEukH80ikH8wjkX4wj8EvzN8NIOX95je/QUpKits2p9OJAQMGuP3817/+Ffv378fNN9+MyZMn4+LF\nizcsV5KkLh8KV67tvOmmm+Rt/fv37/W6TaJQwTwS6QfzSKQfzCORfjCPwYVn8gS4QYMGoaWlRf55\n+vTpKCwslENy4sQJXLhwoct+586dw5AhQ3DzzTfj+PHj2L9/v/w7g8HQamJTdQAAIABJREFUbcgm\nTZqEzZs3o6OjA6dPn8Z7770Hu93eJbhEoYp5JNIP5pFIP5hHIv1gHoMfz+QJUFdmQBMTE9G/f38k\nJSVh3rx5WLx4MWprazF69GgIIRAZGYm33noLkiTJ+wDAjBkz8Nvf/hZWqxX33nsvJkyYIP/uxz/+\nMUaNGoUxY8Zg48aN8n4PPfQQ/v73vyMxMRGSJOFXv/oVIiMjcezYMbeyr20fUShgHon0g3kk0g/m\nkUg/mMfQIQlOoxERERERERERBTxerkVEREREREREFAQ4yUNEREREREREFAQ4yUNEREREREREFAQ4\nyUNEREREREREFAQ4yUNEREREREREFAQ4yUNEREREREREFAQ4yUNEREREREREFARUm+S5ePEixo8f\nj6SkJFitVvz85z8HAOTm5sJsNsNms8Fms2HHjh3yPvn5+YiJiUFcXBx27twpb6+oqEBCQgJiYmKw\nZMkStZpMFLR6ymNTUxNSUlIQGxuLadOmobm5Wd6HeSRSB8dHIu3Nnz8fRqMRCQkJ8jYlx8Cvv/4a\njz76KGJiYpCcnIzPPvtMmxdGFKCYSSIVCRV99dVXQgghLl26JMaPHy/27NkjcnNzxdq1a7s89+jR\noyIxMVG0tbWJmpoacc8994iOjg4hhBDjxo0T5eXlQgghZs6cKXbs2KFms4mCUnd5XLZsmVizZo0Q\nQoiCggKxfPlyIQTzSKQ2jo9E2nrvvffEoUOHRHx8vLxNyTHw5ZdfFjk5OUIIIUpKSsSjjz6q2Wsj\nCkTMJJF6VL1c69ZbbwUAtLW1ob29HUOGDLkysdTluaWlpcjMzITBYIDFYkF0dDTKy8vR0NCAlpYW\n2O12AEBWVha2bt2qZrOJglJ3edy2bRuys7MBANnZ2XK2mEcidXF8JNLWpEmT5JxdoeQYeG1Zs2bN\nwl//+letXhpRQGImidQTpmbhHR0dGD16ND755BPk5ORg5MiRePPNN7Fhwwa8/vrrGDt2LNauXYvB\ngwfj5MmTSE5Olvc1m81wuVwwGAwwm83ydpPJBJfL5VaPJElqvgwij3T3x5medJfHxsZGGI1GAIDR\naERjYyMAMI8U8AIxj2qMjwAzSf6n1zwqOQa6XC7cddddAICwsDBERESgqakJQ4cOdauTeSR/02se\nAe0zyTySv6mVR1XP5OnXrx8OHz6M+vp6vPfee3A6ncjJyUFNTQ0OHz6MO+64A0uXLlWkLiGEKo9V\nq1axbJbd6yMQXJ/HXbt2uf1ekiTFBjs9v29q9AO9tzHUygsEWo6PgHpjpD/eX9YfWPUHCiXHwN6E\ncn9g/f6tP5Bolclge++17GOsq28PNWlyd62IiAg88MAD+OCDDxAZGSmHduHChThw4ACAzpnXuro6\neZ/6+nqYzWaYTCbU19e7bTeZTFo0mygoXcljRUUFjEYjTp06BQBoaGhAZGQkAOaRSCscH4n8R4kx\n8MpZBCaTCZ9//jkA4PLly/jyyy+7nMVDRDfGTBIpQ7VJnjNnzsgrore2tuKdd96BzWaTgwsAb731\nlryielpaGkpKStDW1oaamhpUV1fDbrcjKioK4eHhKC8vhxACGzduRHp6ulrNJgpKPeUxLS0NxcXF\nAIDi4mI5W8wjkXo4PhLpgxJj4Pe///0uZb355puYMmWKf14UUQDzRyY/+ugjnx4ff/yx6mdjEPlK\ntTV5GhoakJ2djY6ODnR0dGDOnDmYMmUKsrKycPjwYUiShOHDh+OVV14BAFitVmRkZMBqtSIsLAyF\nhYXyKXqFhYWYO3cuWltbkZqaihkzZqjV7C4cDgfLZtkBr6c82mw2ZGRkoKioCBaLBVu2bAGgrzwq\n/b6p0Q/03sZQK0/vgmV89JS/31/W79/69SIzMxO7d+/GmTNncNddd+G5557DihUrFBsDFyxYgDlz\n5iAmJga33XYbSkpK/PZab8Tf/YH1+7d+PdFLJkeNmoCbbrrd6/a3tn6Gv/99L8aOHevR87V677Xs\nY6xLvyQRBFOQkiRxJpX8in3wKh6LGwsPH4qWlrM+7Tto0BCcO9ekcIuCD/ugOx4P8if2P3c8HuRP\n7H/uOi+RXgkhnvd634iIidi+/UVMnDhRhZZRKFAzj6reXYuIiNx1TvD49oHe0sK7QBARERERUc80\nWXiZiIiIiIiIiIjUxUkeIiIiIiIKSuHhQ+U7F/b2CA/n3ZeIKPDxci0iIiIiIgpK3lwmzcuiiSgY\n8EweIiIiIiIiIqIgwEkeIiIiIiIiIqIgwEkeIiIiIiIiIqIgwEkeIiIiIiIiIqIgwEmeIOLN3QN4\nFwGiQBTmdcaZcyIiIiKi0MG7awURb+4ecHUf3kWAKHBchrcZB5hzIiIiIqJQwTN5iIiIiIiIiIiC\nACd5iIiISHG+XELMSwyJiIiI+oaXaxEREZHifLmE+Oq+vMSQiIiIyBc8k4eIiIiIiIiIKAhwkoeI\niIiIiIiIKAhwkoeIiIiIiIiIKAioNslz8eJFjB8/HklJSbBarfj5z38OAGhqakJKSgpiY2Mxbdo0\nNDc3y/vk5+cjJiYGcXFx2Llzp7y9oqICCQkJiImJwZIlS9RqMhERkeo4PhIRERGRWlSb5Ln55pux\na9cuHD58GB9++CF27dqFvXv3oqCgACkpKThx4gSmTJmCgoICAEBVVRU2b96MqqoqlJWVYdGiRRCi\nc8HGnJwcFBUVobq6GtXV1SgrK1Or2URERKri+EhEREREalH17lq33norAKCtrQ3t7e0YMmQItm3b\nht27dwMAsrOz4XA4UFBQgNLSUmRmZsJgMMBisSA6Ohrl5eUYNmwYWlpaYLfbAQBZWVnYunUrZsyY\n4VZXbm6u/G+HwwGHw6HmS6MQ53Q64XQ6/d0MIgpQWo6PAMdI0g7HRyIiIv9SdZKno6MDo0ePxief\nfIKcnByMHDkSjY2NMBqNAACj0YjGxkYAwMmTJ5GcnCzvazab4XK5YDAYYDab5e0mkwkul6tLXdd+\ngSVS2/V/JOXl5fmvMUQUcLQcHwGOkaQdjo9ERET+perCy/369cPhw4dRX1+P9957D7t27XL7vSRJ\nkCRJzSYQEYC6ujpMnjwZI0eORHx8PNavXw+g8w8/s9kMm80Gm82GHTt2yPtwDRAi9XB8JCIiIiI1\naHJ3rYiICDzwwAOoqKiA0WjEqVOnAAANDQ2IjIwE0Pk/kHV1dfI+9fX1MJvNMJlMqK+vd9tuMpm0\naDZR0DAYDHjppZdw9OhR7N+/Hy+//DKOHTsGSZLw1FNPobKyEpWVlZg5cyYArgFCpBWOj0RERESk\nJNUmec6cOSPfGaS1tRXvvPMObDYb0tLSUFxcDAAoLi5Geno6ACAtLQ0lJSVoa2tDTU0NqqurYbfb\nERUVhfDwcJSXl0MIgY0bN8r7EJFnoqKikJSUBAAYOHAgRowYIV/WcWXy5lo9rQHS0NDQ7Rog18vN\nzZUfXJuB1OZ0Ot36nN5xfCQiIiIitai2Jk9DQwOys7PR0dGBjo4OzJkzB1OmTIHNZkNGRgaKiopg\nsViwZcsWAIDVakVGRgasVivCwsJQWFgon6peWFiIuXPnorW1Fampqd0uKklEnqmtrUVlZSWSk5Ox\nb98+bNiwAa+//jrGjh2LtWvXYvDgwVwjiwJKoK0BwvGRiIiIiNQiie7+Gz/ASJLU7dkIoabzS7+3\nx4HHTgmB0gfPnz8Ph8OB//iP/0B6ejq++OIL3H777QCAZ555Bg0NDSgqKsJPf/pTJCcn47HHHgMA\nLFy4EDNnzoTFYsGKFSvwzjvvAAD27NmDF154AX/+85/lOgLlWPiLbzmV9/Zx39B6T9gH3fnrePS1\nr/M9DA7MozseD+1591kU3O8P+5+7zvXvVkKI573eNyJiIrZvfxETJ05UoWUUCtTMoyZr8hCR/126\ndAmzZs3C448/Ll/SERkZKS/wunDhQhw4cAAA1wAhIqLQkZ+fj5EjRyIhIQGzZ8/G119/jaamJqSk\npCA2NhbTpk2TL7G88nzemIBIHcwjUd9xkocoBAghsGDBAlitVjzxxBPy9oaGBvnfb731FhISEgBw\nDRAiIgoNtbW1ePXVV3Ho0CEcOXIE7e3tKCkpQUFBAVJSUnDixAlMmTIFBQUFAHhjAiI1MY9EyuAk\nD1EI2LdvHzZt2oRdu3a53S59+fLlGDVqFBITE7F792689NJLANzXAJk5c2aXNUAWLlyImJgYREdH\ncw0QIiIKWOHh4TAYDLhw4QIuX76MCxcu4M4778S2bduQnZ0NAMjOzpZvMtDXGxMQUc+YRyJlqLbw\nMhHpx3e+8x10dHR02X7llundWblyJVauXNll+5gxY3DkyBFF20dEROQPQ4cOxdKlS3H33Xfjlltu\nwfTp05GSkoLGxkYYjUYAgNFoRGNjIwD0+cYEgPvNCa5fOJ5ISU6nM6DucuqPPAqxB0DuNz85vnkQ\nKU/LPHKSh4iIiIhC0ieffIJf//rXqK2tRUREBB555BFs2rTJ7TlX1q5TCu9ASVoJtLtP+iOPkjQJ\nQuQqVh5RT7TMIy/XIiIiIqKQ9MEHH2DixIm47bbbEBYWhh/84Af4+9//jqioKJw6dQpA5/p1kZGR\nAHhjAiI1MY9EyuAkDxERERGFpLi4OOzfvx+tra0QQuDdd9+F1WrFgw8+iOLiYgBAcXGxfJMB3piA\nSD3MI5EyeLkWEREREYWkxMREZGVlYezYsejXrx9Gjx6NH//4x2hpaUFGRgaKiopgsViwZcsWAO43\nJggLC+tyY4K5c+eitbUVqampvDEBkZeYRyJlSOLKfeYCmCRJCIKX0WedH2reHgceOyWwD17FY3Fj\nvuVU3tvHfUPrPWEfdOev49HXvs73MDgwj+54PLTn3WdRcL8/7H/uOtf3WQkhnvd634iIidi+/UVM\nnDhRhZZRKFAzj7xci4iIiIiIiIgoCHCSh4iIiIiIiIgoCHCSh4iIiIiIiIgoCHCSh4iIiIiIiIgo\nCHCSh4iIiIiIiIgoCHCSh4iIiIiIiIgoCKg2yVNXV4fJkydj5MiRiI+Px/r16wEAubm5MJvNsNls\nsNls2LFjh7xPfn4+YmJiEBcXh507d8rbKyoqkJCQgJiYGCxZskStJhMREamO4yMRERERqSVMrYIN\nBgNeeuklJCUl4fz58xgzZgxSUlIgSRKeeuopPPXUU27Pr6qqwubNm1FVVQWXy4WpU6eiuroakiQh\nJycHRUVFsNvtSE1NRVlZGWbMmKFW04mIiFTD8ZGIiIiI1KLamTxRUVFISkoCAAwcOBAjRoyAy+UC\nAAghujy/tLQUmZmZMBgMsFgsiI6ORnl5ORoaGtDS0gK73Q4AyMrKwtatW9Vqtm6Ehw+FJElePYiI\nSP84PhIRERGRWlQ7k+datbW1qKysRHJyMvbt24cNGzbg9ddfx9ixY7F27VoMHjwYJ0+eRHJysryP\n2WyGy+WCwWCA2WyWt5tMJvnL8LVyc3PlfzscDjgcDjVfkupaWs4C6Ppl/8Y40aMVp9MJp9Pp72YQ\nUYDTYnwEgm+MJP3i+EhERORfqk/ynD9/Hg8//DDWrVuHgQMHIicnB88++ywA4JlnnsHSpUtRVFTU\n53qu/QJLpLbr/0jKy8vzX2OIKCBpNT4CHCNJOxwfiYiI/EvVu2tdunQJs2bNwuOPP4709HQAQGRk\npHx50cKFC3HgwAEAnf8DWVdXJ+9bX18Ps9kMk8mE+vp6t+0mk0nNZhMREamK4yMRERERqUG1SR4h\nBBYsWACr1YonnnhC3t7Q0CD/+6233kJCQgIAIC0tDSUlJWhra0NNTQ2qq6tht9sRFRWF8PBwlJeX\nQwiBjRs3yl+IiYiIAg3HRyIiIiJSi2qXa+3btw+bNm3CqFGjYLPZAACrV6/GG2+8gcOHD0OSJAwf\nPhyvvPIKAMBqtSIjIwNWqxVhYWEoLCyUFxMuLCzE3Llz0draitTUVN45hIiIAhbHR0+E+XxDgUGD\nhuDcuSaF20NEREQUGCTR3a08AowkSd3ekSSQdX659WXhZe/3CbZj5w9674N1dXXIysrCF198AUmS\n8OMf/xiLFy9GU1MTHn30UXz22WewWCzYsmULBg8eDADIz8/Ha6+9hv79+2P9+vWYNm0aAKCiogJz\n587FxYsXkZqainXr1rnVpfdj4W++ZVve28d9Q+s9YR9056/j4Z++3rkv33/9YB7d8Xhoz7vPouB+\nf9j/3HVeIr0SQjzv9b4REROxffuLmDhxogoto1CgZh5VXZOHiPTBYDDgpZdewtGjR7F//368/PLL\nOHbsGAoKCpCSkoITJ05gypQpKCgoAABUVVVh8+bNqKqqQllZGRYtWiR/COXk5KCoqAjV1dWorq5G\nWVmZP18aERERERERfYOTPEQhICoqCklJSQCAgQMHYsSIEXC5XNi2bRuys7MBANnZ2di6dSsAoLS0\nFJmZmTAYDLBYLIiOjkZ5eTkaGhrQ0tICu90OAMjKypL3IaLgEx4+VF4M2tsHEREREWlP9VuoE5G+\n1NbWorKyEuPHj0djYyOMRiMAwGg0orGxEQBw8uRJJCcny/uYzWa4XC4YDAaYzWZ5u8lkgsvl6lLH\ntbdrvv52ukRKczqdcDqd/m5GUGppOYu+XXJFRERERFriJA9RCDl//jxmzZqFdevWYdCgQW6/U/J/\n36+d5CFS2/UTiXl5ef5rDBERERGRH/FyLaIQcenSJcyaNQtz5syRb7NsNBpx6tQpAJ23b46MjATQ\neYZOXV2dvG99fT3MZjNMJhPq6+vdtptMJg1fBREREREREfWEkzxEIUAIgQULFsBqteKJJ56Qt6el\npaG4uBgAUFxcLE/+pKWloaSkBG1tbaipqUF1dTXsdjuioqIQHh6O8vJyCCGwceNGeR8iIiIiIiLy\nL16uRRQC9u3bh02bNmHUqFGw2WwAOm+RvmLFCmRkZKCoqEi+hToAWK1WZGRkwGq1IiwsDIWFhfKl\nXIWFhZg7dy5aW1uRmpqKGTNm+O11ERERERER0VWS6OXm7EeOHEFCQoJW7fGJmveY95fOP6i9fU2+\n7GMAcNmrPQYNGoJz55q8rCe4adUHmcfA51u25b193De03hPm0V1fjod/+mvf9w2l/q53SucxUHLX\nE46R2vPucyy43x81+l8gZ7JzPcqVEOJ5r/eNiJiI7dtfxMSJE1VoGYUCNceDXi/XysnJwbhx41BY\nWIgvv/xSlUaQP11G58Dn+aPzbivkD8wjkX4wj0TaY+6I9IWZJNKfXid59u7diz/+8Y/4/PPPMXr0\naGRmZmLnzp1atI2IrsM8EukH80ikPeaOSF+YSSL96fVyrSsuX76MrVu3YvHixYiIiEBHRwdWr16N\nWbNmqd3GXgXjqa/aXa7l2z7Bdrz7Sus+yDwGLl6upT7m0R0v1yJ/UiuPes9dTzhGao+Xa12lZv8L\nxEzyci3yJ79ervWPf/wDTz75JEaMGIG//e1vePvtt3Hs2DHs2rULTz75pCqNIqLuMY9E+sE8EmlP\njdw1Nzfj4YcfxogRI2C1WlFeXo6mpiakpKQgNjYW06ZNQ3Nzs/z8/Px8xMTEIC4uzu2MhYqKCiQk\nJCAmJgZLlizp82slCgTMJJEOiV5897vfFcXFxeKrr77q8rvi4uLedteEBy8j4AAQgPDyod0+5E6r\nY8I8Bj7fMteXvAoBhHm38NY1j0GDhvj7kHmNeXTXl+Phn/7a931JP5R+P9TIXVZWligqKhJCCHHp\n0iXR3Nwsli1bJtasWSOEEKKgoEAsX75cCCHE0aNHRWJiomhraxM1NTXinnvuER0dHUIIIcaNGyfK\ny8uFEELMnDlT7Nixo0td7J/a8+7zJLjfHzVeXyBnEoCQpJU+jTURERPEvn37fHp9REKo+3nT6+Va\n58+fxy233IL+/fsDANrb23Hx4kUMGDCgzxNMSgnGU195uVZg0aoPMo+Bz1+Xa/WlzkB7P5lHd7xc\ni/xJ6Twqnbsvv/wSNpsNn376qdv2uLg47N69G0ajEadOnYLD4cDx48eRn5+Pfv36Yfny5QCAGTNm\nIDc3F8OGDcP3vvc9HDt2DABQUlICp9OJ3/72t27lSpKEVatWyT87HA44HA6f2k6eCeXLtZxOJ5xO\np/xzXl6e4q8vkDPZ2TcmAfjeN1sc3zx6x8u1yFta5PGKsN6eMHXqVLz77rsYOHAgAODChQuYPn06\n3n//fVUaREQ9Yx6J9IN5JNKe0rmrqanB7bffjnnz5uEf//gHxowZg1//+tdobGyE0WgEABiNRjQ2\nNgIATp48ieTkZHl/s9kMl8sFg8EAs9ksbzeZTHC5XN3WmZub61Nbibx1/SRiXl6e4nUEeiYlaRKE\nyPWprUTe0CKPV/S6Js/Fixfl0ALAoEGDcOHCBdUaREQ9Yx6J9IN5JNKe0rm7fPkyDh06hEWLFuHQ\noUMYMGAACgoK3J7TuTir5HMdRMGMmSTSn14neQYMGICKigr55w8++AC33HJLrwXX1dVh8uTJGDly\nJOLj47F+/XoA4KJZRH3gax6JSHkcH4m0p/Q4aDabYTabMW7cOADAww8/jEOHDiEqKgqnTp0CADQ0\nNCAyMhJA59kAdXV18v719fUwm80wmUyor693224ymXxuF1GgYCaJdKi3RXsOHDggvv3tb4v77rtP\n3HfffeLb3/62OHjwYK+L/TQ0NIjKykohhBAtLS0iNjZWVFVVqbZoVrCBT4tOcuFlf9HqmPiaRy2x\nf9yYb5nr62K0obWIrd7zqOX4KETfjod/+mvo9dlgpvT7ocY4OGnSJPHRRx8JIYRYtWqVWLZsmVi2\nbJkoKCgQQgiRn5/fJY9ff/21+PTTT8W3v/1tOY92u13s379fdHR0cOFlHfHu8yS43x81Xl8gZxLg\nwsvkP2p+3vS6Js+4ceNw7NgxfPTRR5AkCffeey8MBkOvk0dRUVGIiooCAAwcOBAjRoyAy+XCtm3b\nsHv3bgBAdnY2HA4HCgoKUFpaiszMTBgMBlgsFkRHR6O8vBzDhg1DS0sL7HY7ACArKwtbt27FjBkz\n3Oq79vpmLmJHart+4Syt+JpHIlJeoIyPAMdI0o7a46Ma4+CGDRvw2GOPoa2tDffccw9+//vfo729\nHRkZGSgqKoLFYsGWLVsAAFarFRkZGbBarQgLC0NhYaF82UhhYSHmzp2L1tZWpKamdptFomDDTBLp\nT6931wKA999/HzU1Nbh8+bIcmqysLI8rqa2txf33349//vOfuPvuu3H27FkAgBACQ4cOxdmzZ/HT\nn/4UycnJeOyxxwAACxcuxMyZM2GxWLBixQq88847AIA9e/bghRdewJ///OerLyII7+bDu2sFFi37\nYF/zqLZgzKOSeHct9QVSHtUeHwHeXYv8S4086n0cvBGOkdoL5btrXU+t/heomexc22clhHje6315\ndy3qKzXHg17P5Hn88cfx6aefIikpSb41HuB5cM+fP49Zs2Zh3bp1GDRokNvvuGgWkXf6mkciUg7H\nRyLtcRwk0hdmkkh/ep3kqaioQFVVlU9fNi9duoRZs2Zhzpw5SE9PB9B5y7tTp04hKiqKi2YReakv\neSQiZXF8JNIex0EifWEmifSn17trxcfHo6GhweuChRBYsGABrFYrnnjiCXl7WloaiouLAQDFxcXy\nl9u0tDSUlJSgra0NNTU1qK6uht1uR1RUFMLDw1FeXg4hBDZu3CjvQxRqfM0jESmP4yOR9jgOEukL\nM0mkP72eyXP69GlYrVbY7XbcdNNNADpPI9+2bdsN99u3bx82bdqEUaNGwWazAei8BeyKFSu4aBaR\nj3zNIxEpj+MjkfY4DhLpCzNJpD+9Lrx85Q4J1y4MJEkS7r//ftUb56lgXMSOCy8HFq36IPMY+Ljw\nsvqYR3dceJn8Sek8BkruesIxUntcePkqNfpfIGeSCy+TP/l14WWHw4Ha2lp8/PHHmDp1Ki5cuIDL\nly+r0hgiujHmkUg/mEci7TF3RPrCTBLpT69r8vzud7/DI488gp/85CcAOhd2fOihh1RvGBF1xTwS\n6QfzSKQ95o5IX5hJIv3pdZLn5Zdfxt69exEeHg4AiI2NxRdffKF6w4ioK+aRSD+YRyLtMXdE+sJM\nEulPr5M8N910k7yIFgBcvnyZt8gj8hNf8zh//nwYjUYkJCTI23Jzc2E2m2Gz2WCz2bBjxw75d/n5\n+YiJiUFcXBx27twpb6+oqEBCQgJiYmKwZMkShV4VUWDi+EikPeaOSF+YSSL96XWS5/7778fzzz+P\nCxcu4J133sEjjzyCBx98UIu2EdF1fM3jvHnzUFZW5rZNkiQ89dRTqKysRGVlJWbOnAkAqKqqwubN\nm1FVVYWysjIsWrRIXhQsJycHRUVFqK6uRnV1dZcyiUIJx0ci7TF3RPrCTBLpT69312pvb0dRUZH8\nv/nTp0/HwoULdTVDG4x3KuDdtQKLVn2wL3msra3Fgw8+iCNHjgAA8vLyMHDgQCxdutTtefn5+ejX\nrx+WL18OAJgxYwZyc3MxbNgwfO9738OxY8cAACUlJXA6nfjtb3/rtr8kSVi1apX8s8PhgMPh8Pk1\nBxveXUt5TqdTvrsH0Nm39Z5HLfHuWuRPSo+PgZK7ngTjd1a94921rlKj/wVyJnl3LfInNceDXid5\nAkEwDpic5AksgdAHu5vk+f3vf4+IiAiMHTsWa9euxeDBg/HTn/4UycnJeOyxxwAACxcuxMyZM2Gx\nWLBixQq88847AIA9e/bghRdewJ///Ge3egLhWPgTJ3nUxz7ojpM85E/MozseD+1xkucq9j93nOQh\nf/LrLdSHDx/ebYM+/fRTVRpERD1TMo85OTl49tlnAQDPPPMMli5diqKioj63kShUcHwk0h5zR6Qv\nzCSR/vQ6yXPw4EH53xcvXsSbb76Jf/3rX6o2ioi6p2QeIyMj5X8vXLhQvn7aZDKhrq5O/l19fT3M\nZjNMJhPq6+vdtptMJp/qJgoGHB+JtMfcEekLM0mkPz5drjV69Ggxx9A2AAAgAElEQVQcOnRIjfb4\nJBhPPeTlWoHFn33Q0zxef7lWQ0MD7rjjDgDASy+9hIMHD+JPf/oTqqqqMHv2bBw4cAAulwtTp07F\nxx9/DEmSMH78eKxfvx52ux0PPPAAFi9ejBkzZrjVE4x5VBIv11JfIORRS7xci/xJizzqMXc94Rip\nPV6udZVW/S9QMsnLtcif/Hq5VkVFhbxwVkdHBz744AO0t7er0hgiujFf85iZmYndu3fjzJkzuOuu\nu5CXlwen04nDhw9DkiQMHz4cr7zyCgDAarUiIyMDVqsVYWFhKCwslOssLCzE3Llz0draitTU1C4T\nPEShhOMjkfaYOyJ9YSaJ9KfXM3kcDocc3LCwMFgsFvzsZz/Dvffeq0kDPRGM/yvCM3kCi1Z9kHkM\nfDyTR33MozueyUP+pHQeAyV3PeEYqT2eyXOVGv0vkDPJM3nIn3h3rV4E44DJSZ7AEox90Fc8FjfG\nSR71sQ+64yQP+RPz6I7HQ3uc5LmK/c8dJ3nIn/x6udbatWvl2dkrrjRGkiQ89dRTqjSMiLpiHon0\ng3kk0h5zR6QvzCSR/ni0Js/BgweRlpYGIQTefvttjBs3DrGxsVq0j4iuwTwS6QfzSKQ95o5IX5hJ\nIh0SvfjOd74jzp07J/987tw58Z3vfKe33cS8efNEZGSkiI+Pl7etWrVKmEwmkZSUJJKSksT27dvl\n361evVpER0eLe++9V/zlL3+Rt3/wwQciPj5eREdHi8WLF3dblwcvI+AAEIDw8qHdPuROq2Piax61\nxP5xY75lri957XudgUbvedRyfBSib8fDP/019PpsMFP6/QiEcfBG2D+1593nSXC/P2q8vkDOJAAh\nSSt9GmsiIiaIffv2+fslUABT8/OmX2+TQF988QUMBoP8s8FgwBdffNHr5NG8efNQVlbmtu3KKXuV\nlZWorKzEzJkzAQBVVVXYvHkzqqqqUFZWhkWLFqHzdQM5OTkoKipCdXU1qquru5RJFEp8zSMRKY/j\nI5H2OA4S6QszSaQ/vV6ulZWVBbvdjh/84AcQQmDr1q3Izs7uteBJkyahtra2y/YrX06vVVpaiszM\nTBgMBlgsFkRHR6O8vBzDhg1DS0sL7Ha73JatW7fyts0UsnzNIxEpj+MjkfY4DhLpCzNJpD+9TvL8\n4he/wIwZM7B3714AwB/+8AfYbDafK9ywYQNef/11jB07FmvXrsXgwYNx8uRJJCcny88xm81wuVww\nGAwwm83ydpPJBJfL1W25ubm58r8dDgccDofPbSTqjdPphNPp1LxepfNIRL4LlPER4BhJ2lF7fOQ4\nSKQvzCSR/vQ6yQMAFy5cwKBBgzB//nycPn0aNTU1GD58uNeV5eTk4NlnnwUAPPPMM1i6dCmKioq8\nLqc7136BJVLb9X8k5eXlaVa3Unkkor4LhPER4BhJ2tFifOQ4SKQvzCSRvvS6Jk9ubi5eeOEFFBQU\nAADa2trw+OOP+1RZZGQkJEmCJElYuHAhDhw4AKDzfyDr6urk59XX18NsNsNkMqG+vt5tu8lk8qlu\nomCgZB6JqG84PhJpT61xsL29HTabDQ8++CAAoKmpCSkpKYiNjcW0adPQ3NwsPzc/Px8xMTGIi4vD\nzp075e0VFRVISEhATEwMlixZ0uc2EQUCNTLJPBL1Ta+TPG+99RZKS0sxYMAAAJ1fOFtaWnyqrKGh\nwa3chIQEAEBaWhpKSkrQ1taGmpoaVFdXw263IyoqCuHh4SgvL4cQAhs3bkR6erpPdRMFAyXzSER9\nw/GRSHtqjYPr1q2D1WqFJEkAgIKCAqSkpODEiROYMmWK/AcsF0MncqdGJplHor7p9XKtm266Cf36\nXZ0L+uqrrzwqODMzE7t378aZM2dw1113IS8vD06nE4cPH4YkSRg+fDheeeUVAIDVakVGRgasVivC\nwsJQWFgoh7qwsBBz585Fa2srUlNTuagkhTRf80hEyuP4SKQ9NcbB+vp6bN++Hb/4xS/wX//1XwCA\nbdu2Yffu3QCA7OxsOBwOFBQUKLIYOtfIIq1osYak0pnUOo9C7AGQ+81Pjm8eRMrTck3XXid5Hnnk\nEfzkJz9Bc3Mzfve73+G1117DwoULey34jTfe6LJt/vz5PT5/5cqVWLlyZZftY8aMwZEjR3qtjygU\n+JpHIlIex0ci7akxDj755JP41a9+hXPnzsnbGhsbYTQaAQBGoxGNjY0AoPjNQojUpMUaWUpnUus8\nStIkCJHrc3uJPKXlmq43nOQRQuDRRx/F8ePHMWjQIJw4cQL/+Z//iZSUFNUaRETdYx71JTx8KFpa\nzvq7GeQnzCOR9tTI3dtvv43IyEjYbLYe/4f1ynpZRORO6Uwyj0TK6PVMntTUVPzzn//EtGnTtGgP\nEd0A86gfnRM8woc9+cUkWDCPRNpTOnfvv/8+tm3bhu3bt+PixYs4d+4c5syZA6PRiFOnTiEqKgoN\nDQ2IjIwEwMXQia6nZCaZRyJl3HDhZUmSMGbMGPkuH0TkP8wjkX4wj0TaUyN3q1evRl1dHWpqalBS\nUoLvfe972LhxI9LS0lBcXAwAKC4ulhc252LoRFcpnUnmkUgZvZ7Js3//fmzatAnDhg2TV02XJAkf\nfvih6o0jInfMI5F+MI9E2lM7d1cuA1mxYgUyMjJQVFQEi8WCLVu2AOBi6ETXUzOTzCORbyRx5T5z\n1/n8889x9913o7a2FpIk4fqnWSwWLdrnke7aF+g6P6C8fU3a7RNsx7uv1O6DzKP++JZRwLfM9XXf\nvtUZaO8n8+iuL8fD934O+Kevd+4baH02mCmVx0DLXU9CZYzUE+8+x4L7/VGy/wVDJjvX91kJIZ73\net+IiInYvv1FTJw4UYWWUShQczzocZLHZrOhsrISADBr1iz8z//8jyoNUEIwDpic5AksavdB5lF/\nOMmjX8yjO07ykD8plcdAy11PQmWM1BNO8lylZP8Lhkxykof8Sc3x4IZr8lzx6aefqlI5EXmPeSTS\nD+aRSHvMHZG+MJNE+uLRJA8RBbb58+fDaDQiISFB3tbU1ISUlBTExsZi2rRpaG5uln+Xn5+PmJgY\nxMXFYefOnfL2iooKJCQkICYmBkuWLNH0NRAREREREdGN9Xi5Vv/+/XHrrbcCAFpbW3HLLbdc3UmS\ncO7cOW1a6IFgPPWVl2sFFrX7YF/zuGfPHgwcOBBZWVk4cuQIAODpp5/Gt771LTz99NNYs2YNzp49\ni4KCAlRVVWH27Nk4ePAgXC4Xpk6diurqakiSBLvdjt/85jew2+1ITU3F4sWLuyxkF4x57A4v19Iv\nvedRa7xci/xJqTwGWu56EipjpJ7wcq2rlOx/wZBJXq5F/qTmeNDj3bXa29tVqZCIvNfXPE6aNAm1\ntbVu27Zt24bdu3cDALKzs+FwOFBQUIDS0lJkZmbCYDDAYrEgOjoa5eXlGDZsGFpaWmC32wEAWVlZ\n2Lp1K+9WQCGH4yOR9pg7In1hJon0q9dbqBNRcGpsbITRaAQAGI1GNDY2AgBOnjyJ5ORk+Xlmsxku\nlwsGgwFms1nebjKZ4HK5ui07NzdX/rfD4YDD4VD+BRB9w+l0wul0+rsZRERERER+x0keIvrmdFVJ\nsfKuneQhUtv1E4l5eXn+awwRERERkR9x4WWiEGU0GnHq1CkAQENDAyIjIwF0nqFTV1cnP6++vh5m\nsxkmkwn19fVu200mk7aNJiIiIiIioh5xkocoRKWlpaG4uBgAUFxcjPT0dHl7SUkJ2traUFNTg+rq\natjtdkRFRSE8PBzl5eUQQmDjxo3yPkREREREROR/vFyLKARkZmZi9+7dOHPmDO666y4899xzWLFi\nBTIyMlBUVASLxYItW7YAAKxWKzIyMmC1WhEWFobCwkL5Uq7CwkLMnTsXra2tSE1N5aLLRERERERE\nOqLamTzz58+H0WhEQkKCvK2pqQkpKSmIjY3FtGnT0NzcLP8uPz8fMTExiIuLw86dO+XtFRUVSEhI\nQExMDJYsWaJWc1UVHj5UXvPE0weRkt544w2cPHkSbW1tqKurw7x58zB06FC8++67OHHiBHbu3InB\ngwfLz1+5ciU+/vhjHD9+HNOnT5e3jxkzBkeOHMHHH3+M9evX++OlEAU8jo9EREREpBbVJnnmzZuH\nsrIyt20FBQVISUnBiRMnMGXKFBQUFAAAqqqqsHnzZlRVVaGsrAyLFi2S7xmfk5ODoqIiVFdXo7q6\nukuZgaCl5SwA4eWDiIiCEcdHIiIiIlKLapM8kyZNwpAhQ9y2bdu2DdnZ2QCA7OxsbN26FQBQWlqK\nzMxMGAwGWCwWREdHo7y8HA0NDWhpaYHdbgcAZGVlyfsQEREFIo6PRERERKQWTdfkaWxshNFoBNB5\nZ5/GxkYAwMmTJ5GcnCw/z2w2w+VywWAwwGw2y9tNJhNcLle3ZV97y+brb6dLpDSn0wmn0+nvZhBR\nkFBzfARCbYwM8/my50GDhuDcuSaF2xNaOD4SERH5l98WXlZ67Zlrv8ASqe36P5Ly8vL81xgiCipq\nrM0WWmPkZfh62XNLC9fE6yuOj0RERP6l6S3UjUYjTp06BQBoaGhAZGQkgM7/gayrq5OfV19fD7PZ\nDJPJhPr6erftJpNJyyYTERGpjuMjERERESlB00metLQ0FBcXAwCKi4uRnp4uby8pKUFbWxtqampQ\nXV0Nu92OqKgohIeHo7y8HEIIbNy4Ud6HiIgoWHB8JCIiIiIlqHa5VmZmJnbv3o0zZ87grrvuwnPP\nPYcVK1YgIyMDRUVFsFgs2LJlCwDAarUiIyMDVqsVYWFhKCwslE9VLywsxNy5c9Ha2orU1FTMmDFD\nrSYTERGpjuMjEREREalFElfuxRrAJEmCnl9G5xdyb9un7330fLz9Qe99UEuhcix8yzXgW+b6um9f\n6jSgc40T7/hzAdtQ6YOe6svx8L2fA/7p633fl31HWcyjOx4P7Xn3ORbc7w/7n7vONfBWQojnvd43\nImIitm9/ERMnTlShZRQK1Myj3xZeJiKiQODbIrZcwJaIiIiISHuarslDRERERERERETq4CQPERER\nEREREVEQ4CQPEREREREREVEQ4CQPEREREREREVEQ4CQPEREREREREVEQ4CQPEREREYWkuro6TJ48\nGSNHjkR8fDzWr18PAGhqakJKSgpiY2Mxbdo0NDc3y/vk5+cjJiYGcXFx2Llzp7y9oqICCQkJiImJ\nwZIlSzR/LUTBgJkk6jtO8pAPwiBJkleP8PCh/m40ERERkRuDwYCXXnoJR48exf79+/Hyyy/j2LFj\nKCgoQEpKCk6cOIEpU6agoKAAAFBVVYXNmzejqqoKZWVlWLRoEYQQAICcnBwUFRWhuroa1dXVKCsr\n8+dLIwpIzCRR33GSh3xwGYDw6tHSctY/TSUiIiLqQVRUFJKSkgAAAwcOxIgRI+ByubBt2zZkZ2cD\nALKzs7F161YAQGlpKTIzM2EwGGCxWBAdHY3y8nI0NDSgpaUFdrsdAJCVlSXvQ0SeYyaJ+i7M3w0g\nIiIiIvK32tpaVFZWYvz48WhsbITRaAQAGI1GNDY2AgBOnjyJ5ORkeR+z2QyXywWDwQCz2SxvN5lM\ncLlc3daTm5sr/9vhcMDhcCj/YogAOJ1OOJ1OfzfDZ1pkUog9AHK/+cnxzYNIeVrmkZM8RERERBTS\nzp8/j1mzZmHdunUYNGiQ2++uXHqulGsneYjUdP0kYl5env8a4yWtMilJkyBEriJlEd2Ilnnk5VpE\nREREFLIuXbqEWbNmYc6cOUhPTwfQeabAqVOnAAANDQ2IjIwE0Hk2QF1dnbxvfX09zGYzTCYT6uvr\n3babTCYNXwVR8GAmifqGkzxEIc5isWDUqFGw2Wzydcu+3MGAiIgo0AghsGDBAlitVjzxxBPy9rS0\nNBQXFwMAiouL5T8009LSUFJSgra2NtTU1KC6uhp2ux1RUVEIDw9HeXk5hBDYuHGjvA8ReY6ZJOo7\nSVxZfjyASZIEPb+MztMJvW1f8O2j5/eor/TeB29k+PDhqKiowNChV++A9vTTT+Nb3/oWnn76aaxZ\nswZnz55FQUEBqqqqMHv2bBw8eBAulwtTp07FiRMn0K/f1fniQD4W3vAt14Bv+enrvv6p01/9IFT6\noKf6cjx87+eAf/pd3/dl31GW3vO4d+9efPe738WoUaPkyz/y8/Nht9uRkZGBzz//HBaLBVu2bMHg\nwYMBAKtXr8Zrr72GsLAwrFu3DtOnTwfQebvmuXPnorW1FampqfKtn6+l9+MRjLz7HAvu9ycQ+p+W\nmey87GslhHje63ZGREzE9u0vYuLEiX18xRSq1MwjJ3k0wEmezn30/B71ld774I0MHz4cH3zwAW67\n7TZ5W1xcHHbv3i2fGutwOHD8+HHk5+ejX79+WL58OQBgxowZyM3NdVvwTpIkrFq1Sv45WBeV5CRP\n7/tplYnrF7LLy8sL2DyqgZM83u3LvqOsQB4f1cDjoT1O8lzF/ueOkzzkT2rmkQsvE4U4SZIwdepU\n9O/fHz/5yU/wox/9yOs7GFyPi0qSlgJ5YUkiIiIiIiX5ZU0ergFCpB/79u1DZWUlduzYgZdffhl7\n9uxx+31vdzBQ8o4jRMQxkoiIiIh855czeSRJgtPpdFsDpKCgACkpKfIaIAUFBfIaIJs3b0ZVVVWP\na4AQke/uuOMOAMDtt9+Ohx56CAcOHJAv04qKiur1Dga8UwGRstQYIw8ePIjLly9r/VKIiIiISGN+\nu1zr+uvPtm3bht27dwMAsrOz4XA4UFBQgNLSUmRmZsJgMMBisSA6OhoHDhxwu2QEcL88JFjXACH9\nuH4NkEB14cIFtLe3Y9CgQfjqq6+wc+dOrFq1Sr6DwfLly7vcwWD27Nl46qmn4HK55DsYEJGylB4j\nk5Pvg8HQeQlmWFg4wsLCtXkhFHKCZXwkIiIKVH47k4drgFAgC5Y1QBobG/HQQw8BAC5fvozHHnsM\n06ZNw9ixY5GRkYGioiL5DgYAYLVakZGRAavVirCwMBQWFvJyLSKFqTFGDhqUgC+/rAAAfP21V63x\n+XVQaAqW8ZGIiChQ+WWSZ9++fbjjjjtw+vRppKSkIC4uzu33XAOESBvDhw/H4cOHu2wfOnQo3n33\n3W73WblyJVauXKl204hCFsdIIiIiIvKVXxa2udEaIAC4BggREYUsjpFERERE5CvNJ3kuXLiAlpYW\nAJDXAElISJDXAAHQZQ2QkpIStLW1oaamhmuAEBFR0OIY6W9h8plS3j7Cw4f2XjwRERGRyjS/XItr\ngBAREXWPY6S/XQYgen1Wd1paeNyJiIjI/yRx/S08ApAkSV3uRKInnV+4vW1f8O2j5/eor/TeB7UU\nSMciPHwoWlrO9qEEX16nL/np677+qdNf/SCQ+qAWJElCRMRoeeFlL/eG9n0ncPdlv+uKeXTH46E9\n776HB/f7w/7nrvNMzJUQ4nmv942ImIjt21/ExIkTVWgZhQI18+i3W6gTEflb5wRPX/4YJCIiIiIi\n0g+/LLxMRERERERERETK4iQPEREREREREVEQ4CQPEREREREREVEQ4CQPEREREREREVEQ4CQPERER\nEREREVEQ4CQPEREREREREVEQ4CQPERGpIAySJPn0CA8f6u/GExEREREFpDB/N4CIiILRZQDCpz1b\nWiRlm0JEREREFCJ4Jg8RERERERERURDgJA8RERERERERURDgJI+XwsOHer2+BBERERERERGR2jjJ\n46WWlrPoXGfCmwf5sggrF18lIiIiIiIi8hwXXiaNeL8IKxdfJSKiwBHm89m7gwYNwblzTQq3h4i8\n51mOmVki0jOeydMLp9OpZukBWraanOqVrOp7SWpR+n1Tpx8oXabS5SnNqfPySF+cIVL/lf/MuP6x\nq4ftVx+dZwmrg2MfXcvf/cHf9ff+edBTjpXJrP9fP/mLVu+9ln2MdelXwEzylJWVIS4uDjExMViz\nZo1m9XKSR2tO9UoOgsDqhZZ55CSPHjl1Xl5o8df46Dkn6/dn7Rz7NKX3PPq7P/i7fuYx9Oglk5zk\nYV1aCohJnvb2dvz7v/87ysrKUFVVhTfeeAPHjh3zd7OIQpIe8+jNguh5eXlcFJ2Chh7zSL7wft06\nrl2nP8yjtjwd+yl0qZnJL788hPvuu8/r75/83CYtBMQkz4EDBxAdHQ2LxQKDwYAf/vCHKC0t9Xez\nSHVcrFmP9JhH7xZEX3XNv0mf+Aevp/SYR/KFZ5eIaHmZF3mPebyx8PChbv/R0vPj/3n0me/52K8G\nz8apUByX9ETdTH4N7z6zO79/trS0+PQdp6/9yZc7RLMfBy5JCKH7v3TefPNN/OUvf8Grr74KANi0\naRPKy8uxYcMGAOAsPelCAERJEcwjBQLmcYP8HGaS/I15ZB5JP0IljwC/s5L+qZXHgLi7Vm8BDKUP\nKyJ/Yx6J9MOTL6jMJJE2mEcifeF3VgpVAXG5lslkQl1dnfxzXV0dzGazH1tEFLqYRyL9YB6J9IN5\nJNIXZpJCVUBM8owdOxbV1dWora1FW1sbNm/ejLS0NH83iygkMY9E+sE8EukH80ikL8wkhaqAuFwr\nLCwMv/nNbzB9+nS0t7djwYIFGDFihL+bRRSSmEci/WAeifSDeSTSF2aSQlVALLxMREREREREREQ3\nFhCXaxERERERERER0Y0F1CRPWVkZ4uLiEBMTgzVr1nT5/dmzZ/HQQw8hMTER48ePx9GjRz0ue/78\n+TAajUhISOjxOYsXL0ZMTAwSExNRWVmpWNnHjx/HhAkTcPPNN2Pt2rWKlfvHP/4RiYmJGDVqFO67\n7z58+OGHipVdWlqKxMRE2Gw2jBkzBn/7298UK/uKgwcPIiwsDP/7v/+rWNlOpxMRERGw2Wyw2Wz4\n5S9/qWi7nU4nbDYb4uPj4XA4PC470DU1NSElJQWxsbGYNm0ampube3xue3s7bDYbHnzwwT6VV1dX\nh8mTJ2PkyJGIj4/H+vXruzynt88MwLtc91aet5nzpH2A51nwpDxv+mhv5Z05cwYzZsxAUlIS4uPj\n8Yc//KHHspT+jFXz8y9QKd3fla7f17FOqfrV7hO91d+XcVOJ+q/wZWxVov6+jL+B6L//+78xcuRI\n9O/fH4cOHZK319bW4pZbbpGPw6JFi+TfVVRUICEhATExMViyZIlqbQCA/Px8xMTEIC4uDjt37lSt\nDVfk5ubCbDbLr3vHjh29tkVpnmZESRaLBaNGjYLNZoPdbgfg3Xcmb3U3Nt6oPq2OvR4p3R+0OvY9\nff9Vo66LFy9i/PjxSEpKgtVqxc9//nPV6gK6/o2gVj3e5rIvdTU3N+Phhx/GiBEjYLVaUV5erk0m\nRYC4fPmyuOeee0RNTY1oa2sTiYmJoqqqyu05P/vZz8Rzzz0nhBDi+PHjYsqUKR6X/95774lDhw6J\n+Pj4bn//f//3f2LmzJlCCCH2798vxo8fr1jZX3zxhTh48KD4xS9+IV588UXFyn3//fdFc3OzEEKI\nHTt2KNrm8+fPy//+8MMPxT333KNY2UJ0vt+TJ08WDzzwgHjzzTcVK3vXrl3iwQcf9Lg8b8o+e/as\nsFqtoq6uTgghxOnTp32qJxAtW7ZMrFmzRgghREFBgVi+fHmPz127dq2YPXv2Dd8HT8praGgQlZWV\nQgghWlpaRGxsrNtngiefGd7k2pPyvMmcJ+VdeZ4nWfCkPG/6qCflrVq1SqxYsUIua+jQoeLSpUvd\nlqf0Z6yan3+BSOn+rkb9vo51StWvZp/wpP6+jJtK1H/leb6MrUrU35fxNxAdO3ZMfPTRR8LhcIiK\nigp5e01NTY+fW+PGjRPl5eVCCCFmzpwpduzYoUobjh49KhITE0VbW5uoqakR99xzj+jo6FClDVfk\n5uaKtWvXdtneXVva29sVqfNanmZEaRaLRfzrX/9y2+bNdyZvdTc29lSfVsdej9ToD1od+56+/6r1\nPn/11VdCCCEuXbokxo8fL/bs2aNaXdf/jaBWPd7ksq91ZWVliaKiIiFE5zFsbm7WJJMBcybPgQMH\nEB0dDYvFAoPBgB/+8IcoLS11e86xY8cwefJkAMC9996L2tpanD592qPyJ02ahCFDhvT4+23btiE7\nOxsAMH78eDQ3N6OxsVGRsm+//XaMHTsWBoPBo/I8LXfChAmIiIiQ21xfX69Y2QMGDJD/ff78eXzr\nW99SrGwA2LBhAx5++GHcfvvtHpfradnCx2Woeiv7T3/6E2bNmiXfmtGbYxLors1HdnY2tm7d2u3z\n6uvrsX37dixcuPCG74Mn5UVFRSEpKQkAMHDgQIwYMQInT56Uf+/JZ4Y3ufakPG8y50l5gOdZ8KQ8\nb/qoJ+XdcccdOHfuHADg3LlzuO222xAW1v16/kp/xqr5+ReIlO7vatTv61inVP1q9glP6u/LuKlE\n/YDvY6tS9fs6/gaiuLg4xMbGevz8hoYGtLS0yP+rnJWV1eNY2tc2lJaWIjMzEwaDARaLBdHR0Sgv\nL1elDdfq7v3vri0HDhxQrM4rPO2jarj+dXv6nckX3Y2NPdWn1bHXIzX6g1bHvrvvvy6XS7X3+dZb\nbwUAtLW1ob29HUOGDFGlru7+RlCz73qay77U9eWXX2LPnj2YP38+gM6FwCMiIjTJZMBM8rhcLtx1\n113yz2azGS6Xy+05iYmJ8unHBw4cwGeffabYl7ju6g+kPxqKioqQmpqqaJlbt27FiBEjMHPmzG4v\nlfGVy+VCaWkpcnJyAACSJClWtiRJeP/995GYmIjU1FRUVVUpVnZ1dTWampowefJkjB07Fhs3blSs\nbL1rbGyE0WgEABiNxh7/cHzyySfxq1/9Cv363fijx9PyrqitrUVlZSXGjx8vb/PkM8ObXHtS3rV6\ny5yn7fM0C56U500f9aS8H/3oRzh69CjuvPNOJCYmYt26dT2W1xs1P2PV+PzTG6X7uxr1q0npfKpV\nv5rjppKfJ2rUr+b4G2hqampgs9ngcDiwd+9eAJ3H8MoEPPB37j8AAA3RSURBVACYTCbVMnTy5Em3\nuq68X9dvV7oNGzZsQGJiIhYsWCBfntBTW5Tmr88oSZIwdepUjB07Fq+++ioA77/j9FVP9Wl17PVI\nq/6g9rG/9vuvWnV1dHQgKSkJRqNRvkxMjbq6+xtBrdfkTS77UldNTQ1uv/12zJs3D6NHj8aPfvQj\nfPXVV5pkMiBuoQ549mVkxYoVWLJkCWw2GxISEmCz2dC/f3/F2nD9jJ+SX5DUtGvXLrz22mvYt2+f\nouWmp6cjPT0de/bswZw5c/DRRx8pUu4TTzyBgoICSJIEIYSi//M3evRo1NXV4dZbb8WOHTuQnp6O\nEydOKFL2pUuXcOjQIfz1r3/FhQsXMGHCBCQnJyMmJkaR8v0tJSUFp06d6rL9+eefd/tZkqRus/H2\n228jMjISNpsNTqcT+/fv73Y9FU/Lu+L8+fN4+OGHsW7dOgwcONBtP094mmtv8u5J5jwpz5sseFKe\nN33Uk/JWr16NpKQkOJ1OfPLJJ0hJScE//vEPDBo0qNd9u6PGZ6xan396o3R/V6t+tSidT7XqV2vc\nVPrzRI361Rx//aWncXH16tU9rjt35513oq6uDkOGDMGhQ4eQnp7u1RqSSrRBLTf6npCTk4Nnn30W\nAPDMM89g6dKlKCoq6rYcNT5P/PUZtW/fPtxxxx04ffo0UlJSEBcX16VdWratt/r8/VmuFX+8TqWP\n/fnz5zFr1iysW7euy/cuJevq168fDh8+jC+//BLTp0/Hrl27FK/r+r8Reirn/7d3/zFR138cwJ+H\nXzCswGEL3R0LuAXI/eLEoyyuVdamiRbRDy65GTNrgm3Zsn/8Q6up2a/VBo25qVsbJVm2NQK05mjl\nj4AThUmyhK4spTELSIFbN17fPxg3UE7uuM/nTo7n46/7wb1e78/xfr3fn3vvc+9T6phCrctAc3m9\nXpw6dQoVFRWw2Wy+eViNXNeaMYs8Wq0WFy5c8N2/cOHChJUuALj99tuxb98+3/20tDSkp6erkv+P\nP/6AVqtVJLaa2trasGHDBjQ0NEz5Nabpstvt8Hq9uHz5MhYsWBByPJfLheLiYgCjG7vW19cjNjYW\na9asCTn2+EFw5cqVKCsrw99//42kpKSQY6ekpOCOO+5AfHw84uPj8cADD+DMmTNRs8jz7bff+n0u\nOTkZPT09WLhwIS5duoQ777zzur85fvw4vv76a9TV1WF4eBiDg4OwWq345JNPphUPGF20KCoqQklJ\nCZ544okJzwUyZgRT14HEAwKvuUDiBVMLgcQLpo8GEu/48ePYunUrAECv1yMtLQ2dnZ1YunSp3+P2\nR40xNhzj381C6f6uRn41KV2fauUfo/S8qfR4okZ+NeffSLnRvOhPXFwc4uLiAIwufOn1evzyyy/Q\narUTrqwLtD6n04bJxgKdTjftNgTblhdeeMG3ABWu8+tIjVGLFi0CMPp11cLCQjQ1NQV8jqMUf/lm\n6mcbJYSrP6j13o+d/zqdTt/5r9r/58TERKxatQoul0vxXNd+RhgYGIDT6VTtmIKpy1By6XQ66HQ6\n2Gw2AMBTTz2FXbt2YeHCherX5LR28omA//77T9LT0+XXX38Vj8cz6QZZfX194vF4RERkz549sm7d\nuqBy3GgzvPEbVp44cSLoDRtvFHvMtm3bgt6M8kZxf/vtN9Hr9XLixImgYgYS+/z5875N+lwul6Sn\npysWe7znn39evvzyS8Vi9/T0+Nr9008/yV133aVY7J9//lmWL18uXq9Xrl69KkajUc6ePRtU/Jlq\ny5Yt8vbbb4uIyK5du6bcRLCxsVEKCgpCijcyMiJOp1NeeeWVSWMEMmYEU9eBxAum5gKJN95UtRBI\nvGD6aCDxNm/eLNu3bxeR0drSarXXbWQ3ntJjrJrj30yjdH9XI/+Y6cx1SuRXs08Ekj/UeTPU/ONN\nZ24NNX+o8+9M9eCDD0pLS4vvfm9vr3i9XhER6erqEq1WK//884+IiOTl5cnJkydlZGRE0U2Pr23D\n2OaeHo9Huru7JT093fe/UasNFy9e9N3+4IMPxOFwTNkWJQVbI0q4evWqDAwMiMjoxuv33XefHD58\nOOhzpmBdOzf6yxeu9/5mpFZ/CMd77+/8V41cvb29vvFpcHBQ7Ha7fPfdd6r2qfGfEdTIE2xdhnpM\ndrtdOjs7RWT0/GfLli1hqckZs8gjIlJXVycZGRmi1+tl586dIiJSVVUlVVVVIjL6yxkZGRmSmZkp\nRUVFvl/RCERxcbEsWrRIYmNjRafTyd69eyfEFhEpLy8XvV4vZrN5wq8UhBr70qVLotPpJCEhQebP\nny8pKSny77//hhx3/fr1kpSUJDk5OZKTkyM2m02xNu/evVsMBoPk5ORIfn6+NDU1KRZ7vGBPRKeK\nXVFRIQaDQSwWiyxbtiyok/1A2v3uu+9Kdna2GI1G+eijjwKOPdNdvnxZli9fLnfffbc8+uijvgnh\nzz//lMcee+y6v29sbLzhr6wEEu+HH34QjUYjFovF18evPRmdaswQCa6up4oXbM0F0r4xgdRCIPGC\n6aNTxevt7ZWCggIxm81iNBqlurrabyylx1g1x7+ZSun+rnT+6c51SuVXu09MlT+UeVOJ/OMpvcgT\nSP5Q5t+Z6NChQ6LT6eSWW26R5ORkWbFihYiIfPHFF75+sGTJEqmtrfW9pqWlRYxGo+j1enn55ZdV\na4OIyI4dO0Sv10tmZqY0NDSo1oYxTqdTTCaTmM1mefzxx6Wnp2fKtihtsj6qpu7ubrFYLGKxWMRg\nMPhy+jvHUcK1c+O+fftumC9c7/3NSOn+EK733t/5rxq52traxGq1isViEZPJJO+8846I3LgPh9qn\nxn9GUCPPdOoylGM6ffq0LF26VMxmsxQWFkpfX19YalIjMot+6oCIiIiIiIiIKErNmF/XIiIiIiIi\nIiIi/7jIQ0REREREREQUBbjIQ0REREREREQUBbjIQ0REREREREQUBbjIM4u53W6YTKZIN4No1nO7\n3cjKykJpaSkyMzOxdu1aHDlyBPfffz8yMjLQ3Nwc6SYSRZU5c+bAarXCZDLhmWeewdDQUMhzIudU\noukREdjtdjQ0NPgeO3jwIFauXMmaJAqjhx9+GEeOHJnw2IcffojFixdj9erV047b2NgY0uspeFzk\nISK6CXR1deG1117DuXPn0NnZiZqaGhw7dgzvvfcedu7cGenmEUWVefPmobW1Fe3t7YiLi0NVVRU0\nGk2km0U0K2k0GlRVVeHVV1+Fx+PBlStXsHXrVlRWVka6aUSzisPhwIEDByY8VlNTg+eeey5CLaLp\n4iLPLOf1elFSUoLs7Gw8/fTTGBoainSTiGaltLQ0GAwGaDQaGAwGPPLIIwAAo9EIt9sd2cYRRbH8\n/HycP38egP858a233kJeXh5MJhNeeukl32tdLhcsFgtycnLw8ccfR6T9RNHAYDBg9erV2L17N958\n802sW7cOc+bMYU0ShVFRURG++eYbeL1eAKNXw128eBF2ux39/f0oKChAVlYWNm7cCBEBAJSVlcFm\ns8FoNGL79u2+WA0NDVi8eDFyc3Px1VdfReJwZjUu8sxynZ2dKC8vR0dHBxISEjghEkXI3Llzfbdj\nYmIQFxfnuz022RKRsrxeL+rr62E2myEifufETZs2oampCe3t7RgaGkJtbS0AoLS0FJWVlTh9+nQk\nD4MoKmzbtg3V1dU4fPgwXn/9ddYkUZglJSUhLy8PdXV1AIADBw7g2WefhUajQXNzMyoqKtDR0YGu\nri4cOnQIALBjxw40NzfjzJkz+P7779He3o7h4WG8+OKLqK2thcvlQk9PD6+WDTMu8sxyKSkpWLZs\nGQCgpKQEP/74Y4RbREREpK6hoSFYrVbYbDakpqZi/fr1APzPiUePHsW9994Ls9mMo0ePoqOjA319\nfejv70d+fj4AwOl0RuZgiKLEvHnzUFxcDKfTidjYWACsSaJwG/+VrZqaGjgcDogI8vLykJqaipiY\nGDgcDl8t1tTUIDc3F0uWLMHZs2fR0dGBc+fOIS0tDXq9HsBo7Y5d+UPh8b9IN4Aia/yqqohwlZUo\nQq6tvfH3WZdEyoqPj0dra+t1j082J3o8HpSVleHUqVPQarV44403MDw8fF1d8gSWKHQxMTF+5z/W\nJJH61qxZg82bN6O1tRWDg4OwWq1obGyctBbdbjfef/99tLS0IDExEaWlpazFmwSv5Jnlfv/9d5w8\neRIA8Omnn8Jut0e4RUSzT2pqKtra2nz39+/fjyeffHLS54hIPZPNiWMnrAsWLMCVK1dw8OBBAEBi\nYiLmz5+PY8eOAQCqq6sj1m6iaMWaJAqv2267DQ899BBKS0snbLjc1NQEt9uNkZERfP7557Db7RgY\nGMCtt96KhIQE/PXXX6ivr4dGo0FWVhbcbje6u7sBAJ999lmkDmfW4iLPLKbRaJCZmYnKykpkZ2ej\nv78fGzdujHSziIiIVDXZ1XH+5sTExERs2LABRqMRK1aswD333ON7zf79+1FeXg6r1eo3LhEFZ3wd\nsSaJws/hcKC9vR0OhwPAaB3ZbDZs2rQJ2dnZSE9PR2FhIcxmM6xWK7KysrB27VrfVyXnzp2LPXv2\nYNWqVcjNzUVycjJrMcw0wuuniIiIiIiIiIhmPF7JQ0REREREREQUBbjIQ0REREREREQUBbjIQ0RE\nREREREQUBbjIQ0REREREREQUBbjIQ0REREREREQUBbjIQ0REREREREQUBf4PogGS0rJwhskAAAAA\nSUVORK5CYII=\n"
}
],
"prompt_number": 32
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.plot(xObs, yObs, marker='.',color='k',linestyle='none')\n",
"plt.plot(xTrend, 1.2*xTrend+0.5)\n",
"plt.xlim([0,5])\n",
"plt.ylim([-2,9])\n",
"samples = range(nwalkers*1000)\n",
"random.shuffle(samples)\n",
"for i in range(10):\n",
" plt.plot(xTrend, sampler.flatchain[samples[i],1]+sampler.flatchain[samples[i],0]*xTrend, color='r')\n",
"plt.xlabel('x')\n",
"plt.ylabel('y')\n",
"plt.savefig('fitWithOutlierRobust.png',format='png',dpi=600)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAEGCAYAAACJnEVTAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n"
}
],
"prompt_number": 33
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x = np.linspace(-10,15,200)\n",
"ygood = np.exp(-(x-3)**2/(2*0.3)**2)\n",
"ybad = np.exp(-(x-3)**2/(2*3.5)**2)\n",
"mixture = 0.5*ygood + 0.5*ybad\n",
"mixture2 = 0.1*ygood + 0.9*ybad\n",
"mixture3 = 0.9*ygood + 0.1*ybad\n",
"plt.plot(x,mixture,color='black')\n",
"plt.plot(x,mixture2,color='red')\n",
"plt.plot(x,mixture3,color='blue')\n",
"plt.savefig('mixture.png',format='png',dpi=600)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAD/CAYAAAAOoUbCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCCbqDAaDoUX8H3wDHa2g19yAAAAAAElFTkSuQmCC\n"
}
],
"prompt_number": 28
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"p0"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 18,
"text": [
"array([[ 1.0606031 , 0.96452018, 0.38858442, 3.66446217, 1.83950851],\n",
" [ 1.17178078, 1.00183944, 0.52318631, 3.49389418, 1.96699147],\n",
" [ 1.0914209 , 0.7740165 , 0.50393537, 3.60355444, 1.89598058],\n",
" [ 0.8890157 , 1.19624651, 0.58164677, 3.49458174, 1.92106043],\n",
" [ 1.05740291, 1.01445692, 0.56420445, 3.6915332 , 1.91198091],\n",
" [ 0.88978303, 1.04389486, 0.41624164, 3.83019303, 1.98656303],\n",
" [ 0.98005343, 1.03333391, 0.52895837, 3.65626186, 2.00356688],\n",
" [ 1.26836094, 0.91330453, 0.49677357, 3.68169779, 1.91491127],\n",
" [ 1.12691196, 0.96759283, 0.48695862, 3.79897006, 2.10925723],\n",
" [ 0.93223683, 0.98288492, 0.50528861, 3.62586051, 1.94518346]])"
]
}
],
"prompt_number": 18
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 18
}
],
"metadata": {}
}
]
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment