{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## 高斯分布\n", "高斯分布,也称为正态分布,广泛应用于连续型随机变量分布的模型中。\n", "对于一元变量x的情形,高斯分布可以写成如下的形式:\n", "$$\\mathcal{N}(x|\\mu,\\sigma^2)=\\frac{1}{(2\\pi\\sigma^2)^{1/2}}exp\\{-\\frac{1}{2\\sigma^2}(x-\\mu)^2\\}$$\n", "其中$\\mu$是均值,$\\sigma^2$是方差。\n", "\n", "对于D维向量$\\textbf{x}$,多元高斯分布的形式为:\n", "$$\\mathcal{N}(\\textbf{x}|\\textbf{$\\mu$},\\Sigma)=\\frac{1}{(2\\pi)^{D/2}|\\Sigma|^{1/2}}exp\\{-\\frac{1}{2}(\\textbf{x}-\\textbf{$\\mu$})^T\\Sigma^{-1}(\\textbf{x}-\\textbf{$\\mu$})\\}$$\n", "其中,$\\textbf{$\\mu$}$是一个D维均值向量,$\\Sigma$是一个D*D的协方差矩阵,$|\\Sigma|$是$\\Sigma$的行列式。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "高斯分布有着优良的性质,便于推导,很多时候会得到解析解。 一元高斯分布是个钟形癿曲线,大部分都集中在均值附近,朝两边癿概率呈指数衰减,这个可以用契比雪夫不等式来说明,偏离均值超过3个标准差的概率就非常低。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. 拉普拉斯中心极限定理\n", "\n", "拉普拉斯提出的中心极限定理(central limit theorem)告诉我们,对于某些温和的情况,一组随机变量之和(当然也是随机变量)的概率分布随着和式中项的数量的增加而逐渐趋向高斯分布。\n", "\n", "**下面的代码说明,多个均匀分布之和的均值的概率分布,随着N的增加,分布趋向于高斯分布**" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from scipy.stats import uniform\n", "from scipy.stats import binom\n", "from scipy.stats import norm as norm_dist" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def uniform_central_limit(n, length):\n", " \"\"\"\n", " @param:\n", " n:计算rv的n次平均值, length:平均随机变量的样本数\n", " @return:\n", " rv_mean: 长度为length的数组,它是平均随机变量的样本\n", " gaussian: 对data进行拟合所得到的高斯分布\n", " \"\"\"\n", " rv_mean = np.zeros(length)\n", " for i in xrange(n):\n", " rv = uniform.rvs(size=length)\n", " rv_mean = rv_mean + rv\n", " rv_mean = rv_mean / n\n", " gaussian_params = norm_dist.fit(rv_mean)\n", " gaussian = norm_dist(gaussian_params[0], gaussian_params[1])\n", " return rv_mean, gaussian" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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xZqMxZlUOP08yxvxljFmZtT0c6YwSBaZMgZ493e1XX4VmzfzmiSfGwLBh0LYt\nbN8ODRvCunW+U0mUUVETIMfyG/NpwNFsYTZN6MEwtLimxLuXuINn6E0i6UyjFefzhe9IEjyjgfp5\n7LPMWnth1vZkJEJJFFm2DDp2dNfT9O8PN9/sO1H8KVYMxoyBunXht9+gfn3YvNl3KokicV3UBGlY\nyWHs4C0acSrr+JjqtGMiGRQP6XOIRKsHeZrxtKccO5hHQ05mve9IEiDW2veArXnspm+IJHurV0Pz\n5rB3L/To4aYYFj9KloQZM+Dcc+G776BJE7f4qUg+xHVRE5RhJQnAFNpwMZ/zI/+iCXPY5dZWFxHA\nUowujOId6nICvzKfBhyR52dYkX0sUMsY86UxZp4xpqrvQBIQv/4KDRrAn3+6wmbwYDcUSvw5/HCY\nPx8qVYIPP4QbbnCTCIjkIc6LmiCwjAAaZk1hW58F/M4xvkOJBM5eStKS6aziHKqympk0pwR7fMeS\n6PA5UMlaez4wFJjpOY8EwY4d0LgxrF8PNWrA+PGQkOA7lQCceCIsWOAKnJkz1Xsm+aLxTZ49zJN0\nBXZTisbMZQ2n+44kElh/cQQNmceH1KQO7/IGnWjPBKy+n5FcWGu3H3B7vjHmJWPMUdbaLYfum5yc\nvO92UlISSUlJEckoEZaR4Va1//xzqFLFrY9SpozvVHKgqlVh+nS49lq3ls1pp7kZ0iTmpKSkkBKC\nqbyNtbkPozLG1AcG40ZJvWatHXDIzw8HxgGVcEXSQGvtmGzasUUdspWYeC9paYMIzdAvE4J2itZG\nJ8Ywhs5kAK2YwSyae80T2nYMef1u5asVE7rXFJw8Qfp3ClU7kc1yLl/xPrUpz3ae4z4e4DmvecLf\nRmjbsdbG3PgaY0xlYI619txsfnYssMlaa40x1YEp1trK2exnQ3GckChwzz3wwgtw1FFuiNMZZxSq\nmdBdXxtLx5nQvCf7/hbHjIHOnV0v2ty5bgIBiWnGFO48levXm8aYBGAYblaZqkA7Y8xZh+x2B/C1\ntfYCIAl43hijHqA81GMRI+kKwJ0QgoJGJH6s4jxaMp00inM/A+mRNe2zxCdjzETgA+BMY8wGY0wX\nY0w3Y0y3rF1aA6uMMV/gvqRr6yurBMDLL7uCJjHR9QQUsqDZLxjX5wZLCN+Tm26Chx/evzjnqmxn\nbhfJc8xGdWCNtXadtTYNmAQcOnF7JlA+63Z5YLO1Nj20MWPL+XzBNFqRSDoDeICXfAeKE1pIMba8\nzdV0YRQaSVejAAAgAElEQVQAL9KL5szwnEh8sda2s9aeYK0tYa2tZK0dZa19xVr7StbPh1trz7HW\nXmCtrWWt/ch3ZvFk0SI3wxm4tWjq1PGbR/LniSf2r2HTpAls2uQ7kQRQXkXNicCGA+7/lPXYgYYB\nVY0xvwBfAr1CFy/2VOJ/zKMh5djBBNrRl/6+I8WRUC3GKEExjo48xJMUwzKB9tTkA9+RRCSovv3W\nfdOfkQF9+rgeAIkOxsCoUXDppW5ih5YtYY8mipGD5VXU5OdTXH3gc2vtCcAFwHBjTLkiJ4tBR7CV\nBdTnBH5lKUl0ZnRMX+CsnhGJhKd5kFfpSmlSmU1TTud735FEJGi2bHHf8P/1l/tA/NRTvhNJQZUu\n7WZCO+kkWL4cbr3VLZYqkiWva19+xk0A8LdKuN6aA90ErrvBWvujMWYtcCbw6T+bSz7gdlLWFh9K\nkspMmlOV1XzN2bRgBnsp6TtWmIXqokWR3Bhu5yVO5GcaMY8F1KcmoMEJf0vJ2kTiVFqa66FZswbO\nPx/GjnWr10v0Oe44N1Nd7dru37FqVU33LPvkOvtZ1gX/3wFXAb8AnwDtrLWrD9jnJWCjtfbxrBlm\nPgPOO3SqzHie/cyQyUTacT1T+JkTqMFH/HRQrRikWUtC1U6QsgStnSBlCVU7/rMcxg6WUpdqfMoK\noC7b2UlZb3lC20Zo24nF2c9CQbOfRY+C9OQPAXoCG4FqHDymvqj/3sGZETNIx5kIzKA6Y4brcTPG\nFTmNGxfx+SRIwjL7WdYF/z2AhcA3wGRr7epDZpXph1up+StgCfBAdnP/x7PnuJ/rmcI2ytGA+YcU\nNCISCjspS2Pm8iP/ohowmetJQHOWiMSuvK+D7Mor9AT2UIIWLGeDrpGMDS1aQL9+bvhZ+/awenXe\n/4/EvDzXqQnZE8VpT00vBjOYu0mjOA2Yz9tcHaYsQWsnSFmC1k6QsoSqneBkOZ3v+YAzqQC8xs10\nZSSFH8YYW+/N3+2opyZ76qmJHvnpIanNe7zDlSSSTifGMJZOh7ainprAZsnHv421cP318OabbgHV\nTz6BI48s4vNKEISlp0aKpjVvMoh7AOjM6BwKGhEJpR84g8bAbkpxC6/zKE/4jiQiEXYSG5hKaxJJ\n53nuyaagkahnDIweDRdc4K6XatsW0tU7H89U1IRJbd7j33SkGJbePMN4OviOJBI3PgbaMokMivE4\nyXThdd+RRCRCSrOLmTTnWDaxiHr0ZoDvSBIuhx3mZkSrWNGtQdSnj+9E4pGKmjCoyn+YTVNKsYdh\n3MGzPOA7kkjcmU0z7mA4AK/QjYa85TmRiISfZSRduZjP+ZF/ZX25kddErxLVTjkFpk2D4sXh+edh\nwgTficQTFTUhdiI/sYD6HMmfTKcFvXgRTUss4scr3MaTPERxMphCG6rxie9IIhJG9zCIG5jAdsrS\nlNls5SjfkSQSLr8cXnzR3b75Zvj8c795xAsVNSF0OH8ynwZU4ife5zJuYDyZJPiOJRLXHqEfY+jE\nYeziLRpRhR98RxKRMLiKJftGRtzIWL7hbM+JJKK6d3cFTWqqmx3t9999J5IIU1ETIn8vrnkuX/MN\nZ9GU2aRS2ncsEcHQlZEs4Foq8gcLqM8xbPQdSkRC6BTWMYm2JJBJPx5mJi18R5JIMwaGD4caNeB/\n/3MLrqal+U4lEaSiJgSKkcG/6UgSy/iZE6jPAnV5iwRIOom0ZioruITT+C/zaEhZtvuOJSIhUJpd\nzKAFFdjMWzQkmWTfkcSXkiXd9TXHHQcpKfCArmmOJypqiszyIr24jqn8RXkaMJ8NnOw7lIgcYidl\nacRbrOE0LuZzptGKRPb6jiUiReImBriQL/ie0zXsW+CEE2DqVEhMhMGDYdw434kkQlTUFFFf+tOD\n4eyhBM2YxSrO8x1JRHLwO8dwLQvZyDFcw2JG0xlDpu9YIlJIdzF438QALZjBXxzhO5IEwWWX7Z84\n4NZbYeVKv3kkIlTUFMFNwNM8RCaGGxjPMpI8JxKRvPyX02jIPLZTlhuYwEDuIzQrcYtIJCWxlOe4\nH4CbGFOoiQGMMUXaJMBuuw26dIHdu93EAX/84TuRhJmKmkJqzBxGZt3uyVCm0dprHhHJv8+5mJZM\nZy+J3MML3MdA35FEpABOAiZzPcXJoD99mE6rQrZki7hJYP09cUC1arB+PbRrBxkZvlNJGKmoKYRa\nLGcKbSgOPMlDvMQdviOJSAEtoR43MhaA53iAG3nDcyIRyZfUVKYBx/A7C7mGh3nSdyIJqlKl3MQB\nFSvCkiXw0EO+E0kYqagpoLP5mrk0pjSpvIpbA0NEotNk2nInbtz169xMQ97ynEhEcmUt3HEH1YG1\nVKY9EzQxgOSuUiWYMgUSEmDAAFfkSExSUVMAJ7OehVzLkfzJDJpzOwAaUysSzYZyJ0/Tl+Jk8CbX\nUYvlviOJSE5GjoRRo9gNtGAGWzjadyIJk6Je73TQVrcud2cNPdveujVVdd1UTFJRk08V2cQiruFE\nfiGFOrRjIhqZKRIbHuIpRnILZdjNXBpzDqt8RxKRQ330EfToAUBX4Esu8JtHwiwU1zvtvz+YTCbS\nlnLADM6gPH/msw2JFipq8qEc25hPA87ke77gfJoxiz2U8h1LRELG0J0RTKcFR/InC7mWyqz1HUpE\n/rZxI7Rq5VaIv/NOxvvOI1HIcAuv8RXncibf8wadNKV/jFFRk4eSpDKLZlzM5/xAFa5lIds43Hcs\nEQmxDIrTngm8Q11O4FcWU49jfIcSEVfItGkDv/wCl18OAzVboRTOLg6jBTPYyhE0ZxYP8rTvSBJC\nKmpykUA6E2lHXVL4heO5hkVs4ljfsUQkTPZQiubM5DMuogo/shA4nD99xxKJb/ffD+++61aKnzLF\nrRQvUkj/5bSsCSYMT/Ao9ZnvO5KEiIqaHBgyGUlXWjCTrRzBNSxiHaf6jiUiYbad8jRgPt9xBhcA\nb9GIMuz0HUskPo0b51aGT0yEqVPhuON8J5IYsIAGPMbjFMMygfb8ix99R5IQyLOoMcbUN8Z8a4z5\nwRjTO4d9kowxK40xXxtjUkKeMuIsL3A3nRnDTsrQkHn8h3N8hxKRCPmdY6jHYv4HXMYHTKMViez1\nHUskvnzxBdx6q7s9dCjUrOk3j8SUp3iIWTTNmtG2hb68igG5FjXGmARgGFAfqAq0M8acdcg+RwDD\ngSbW2nOA1mHKGjGP8Ti9GMIeStCcmXyEDqQi8WYDJ1MP2ERF6rOQcXSgmOY8FImMLVugRQvYvRu6\ndNlf3IiEiKUYNzKW7ziD81jFa9yCZjyLbnn11FQH1lhr11lr04BJQLND9mkPTLPW/gRgrf0j9DEj\n5y5eIJnHyaAYbZnEEur5jiQinnwP1GcBf1GeNrzJSLpqthyRcMvIgLZtYd06qFYNhg8HrRciYbCN\nw2nBDLZTlnZM4m5e8B1JiiCvouZEYMMB93/KeuxApwNHGWOWGmM+NcZ0DGXASOrKq7zAPQB0YRQz\naeE5kYj4tpKLaMRb7KI0XRjNC9yNvs0TCaOHHoLFi6FiRbf6eyktoSDhs5qqdOINAJ7jfuryjudE\nUlh5FTX5OXMnAhcBDYFrgUeMMacXNViktWc8L3MbAD0Zwlg6eU4kIkGxnNpZ61OVoBdD6McjviOJ\nxKYpU2DAAEhIcLcrVfKdSOLADFryNH1JIJPJXM/JrPcdSQqheB4//xk48IhSCddbc6ANwB/W2t3A\nbmPMu8D5wA//bC75gNtJWZt/zZnBG3SiGJY+9GcYPX1HEpGAWUI9rmcyU2nNwzzFDsoygD6+Y+VD\nStYWu4wxo4BGwCZr7bk57DMEaADsAm6y1q6MYETJj1WroHNnd/v55yEpyWsciS+P0I+L+Jz6LGQ6\nLanN+6T6DiUFY63NccMVPT8ClYESwBfAWYfs83/AEiABKAOsAqpm05YFW6QtMfEeG4p23ObauZb5\ndg+J1oLtx0OFaiNUWWKrnSBlCVo7Qcqi11TQdtozzmZgrAV7J4Oj8jXldtyPxg24HLgQWJXDzxsC\n87JuXwp8lMN+VjzZssXa005zv6QdOlibmZnr7sE5bsVSG0HK4qeNI9ls1/Ava8GOpYPVMcGPwp6n\nch1+Zq1NB3oAC4FvgMnW2tXGmG7GmG5Z+3wLLAC+Aj4GRlprv8m7nPKvLu8wgxaUII3B9OIR+vmO\nJCIBN4EbuJVXAXiRu+iadVv8sda+B2zNZZem4AbNW2s/Bo4wxmgl5aDIyIB27eDHH+HCC+GVVzQx\ngHixlaNozkx2UoaOjKOX70BSIHmuU2OtnW+tPdNaW8Va2z/rsVesta8csM9Aa+3Z1tpzrbVDwhk4\nVGoDc2hCaVJ5mW5ZM17oICoieXudW+jBUABe5jY6MtZzIslDdpPenOQpixzqoYdg4UKoUAFmzIAy\nZXwnkjj2NedyE2MAGAiwdKnPOFIAeRY1sehSPmIecBi7GM1N3M5LqKARkYIYTg/u51mKYRlNZ9oy\n0Xckyd2hB3nrJYVgjNm3XW8MDBhAOpD0xx+YypUP+nlOm0g4TeU6+tPHXXh+3XWwdq3vSJIPeU0U\nEHMu5lMWUJ9ywATacQuvkccoPBGRbA3kfkqRSj8eZRwdyCCBN2njO5b806GT3pyU9dg/JCcn77ud\nlJREki5WDxPLeXzJaGoCu7mbISwr0CQ9KmwkvB7mSc7nGRpu3gzNm8MHH8Bhh/mOFZNSUlJISUkp\ncjvGXY8TfsYYW9QvxhIT7yUtbRCFbeciPmMJV3MkfzIVaEsaGUWq60yhs8R+O0HKErR2gpQlVO0E\nKUvk20nmMR7jCdJJ4HomM51W3rLkpx1rbcx9IjTGVAbm2GxmPzPGNAR6WGsbGmNqAIOttTWy2c9G\n6pwYz4wxVGATK6hGZdYzmpvowigKVqgE5bgVS20EKUsw2jgcw5+nnw4//OB6bCZP1vVeEWBM4c5T\ncdNFcSGfs5h6HMmfTKcF7aCIBY2IiJNMMk/xIMXJYBJtac4M35HiijFmIvABcKYxZoMxpsshE9rM\nA/5rjFkDvALc7jFu3EsEptKayqznY6rTnRGo50WC6C+A2bOhfHl4803o3993JMlFXPTUXMBK3uYq\njmIrM2lGG6aQRskCt/NPQfpmJGjtBClL0NoJUpZQtROkLL7asTxDH3rzLGkUpw1TmEkLT1lybycW\ne2pCQT01kTHCGLoDv3A8l/Apv3JCIVoJynErltoIUpbgtGGthblzoWlT99CsWdCkSRHbldyopyYH\nF/L5voJmNk2yCpoSvmOJSMwx9OEZBvAAiaQzhTa0ZJrvUCIhlZ+L+HPbbssqaFIpSXNmFrKgEYmw\nxo3hqafccjbt28PXX/tOJNmI6aLmElYcVNBcx5sqaEQkjFxh8wy9SSSdyVx/0NU1IrHBFmqrw1KG\nZg377spIVlA98tFFCqtPH2jbFnbscL02f/zhO5EcImaLmup8vG9SgBk0pzVT2UtJ37FEJOYZ+tI/\nazrQDCYB1zPJdygRr05jDdNoRSLpDATG0dF3JJF82dfTWKwYpSdNYgXA2rWkVKxIiXz2UEpkxGRR\nU4vlLKYeh7ONqbTSkDMRiTDDgzydNXkAjOcGLdApcas8fzGbphzNFubSiN6+A4kUyP7exlQszfmJ\nXzieJGAotwKZ5N5LKZESc0VNXd5hEddQnu1Mpg3tmEg6ib5jiUjcMTzMkzwKJJDJGG7iFkb6DiUS\nUQmkM4m2VGU1X3M27ZlApu9QIkXwCyfSnJmkUpJuvEpPhvqOJFliqqipz3zeohGHsYs3uJEbGK+C\nRkQ8MvQDevMMxbCM5FbuYJjvUCIRM5D7aMACfqcCTZjDdsr7jiRSZCuoTmdGA/ACd9OAeZ4TCcRQ\nUdOcGcyiGaVJ5WW60ZnRWodGRALhWXpzFy8AMIye9EFrHUjs685L3MWL7CWRVkxjHaf6jiQSMpNo\nx2Mkk0Amk2jLOazyHSnuxURR04F/8ybXUYI0XuAuujMCGxsvTURixIvcxa28QiaG/jzI0/RF460l\nVl3LAoZwJ+BmOnuPKzwnEgm9J3iUCbSjPNuZQxOOYaPvSHEt6j/538Ew/s2NFCeDfjzMPQxCKxOL\nSBCN5NasYbEJ9OUZhtIToysMJMaczddMoQ3FyeApHmQsnXxHEgkTQxdG8SE1qMx6ZtGMUuz2HSpu\nRXFRY3mQpxhGTwDuZSCP0g8VNCISZJNoR0umk0pJejCcN+hEcdJ8xxIJiWPYyFwaU57tTOE6HqGf\n70giYbWHUjRnJus4hRp8zDg66MsqT6KyqDFk8jz38hQPk4nhFkYyiHt9xxIRyZc5NKURb7GdsnRk\nHDNoQWl2+Y4lUiRl2MlcGlOZ9XzEpXTiDQ0Fl7iwiWNpyDz+5HBaMZ1necB3pLgUdUebRGAsN3IP\nL7CXRNoyide5xXcsEZECeYeruJJ3+IOjacxbLOIajmCr71gihfL31M3V+JT/cirNmEUqpX3HEomY\n1VSlJdNJozj38Tzdecl3pLgTVUVNGZvGbKAD49lOWRoyjzdp4zuWiEihfEo1avM+/6MStVnOu1zB\nCfzsO5ZIAVmGcCdNmMtmjqIB89nEsb5DiUTcUq7kFl4DYCg9acwcz4niS9QUNRX4nYUZb1If2ERF\n6rKUt7nadywRkSL5jv/jMpbzDWdxLl/zITU5i298x5IYZIwp8pad+xjI7YwglZI0Yxbfc2aEX5lI\ncIylE4/zKAlkMpnrqe47UBzJs6gxxtQ3xnxrjPnBGNM7l/2qGWPSjTEtQxsR/sWPfEAtLrW/sQ6o\nzft8xiWhfhoRES9+ohK1eZ/l1OJkNvA+tbmM933Hkphki7gd7AbG8VzW9QM3Mpbl1A77KxAJumSS\nGUVnyrCbtwC+/953pLiQa1FjjEkAhgH1gapAO2PMWTnsNwBYQIinH6vGJ3xITU5nDSs5hprAD5wR\nyqcQEfFuK0dxNUuYQXOOYitLuJqWTPMdSyRH17CQ0XQG4G4GaTi4yD6GbrzCPBpQAaB+ffjtN9+h\nYl5ePTXVgTXW2nXW2jRgEtAsm/16AlOB30MZrjFzWEpdjuF3FnAtVxVvg34lRCRWpVKa1kxlBLdR\nij28yXXczSC0SKcEzSWsYBqtSCSdZ7mfwdztO5JIoKSTSBumsAJg7Vpo2BC2bfMdK6blVdScCGw4\n4P5PWY/tY4w5EVfojMh6KCRn354MYSbNOYxdjKIzTZjDDlMiFE2LiARWJgnczkv05hmKYRnEvQyl\nJwm+g4lkqcIPvEUjyrKTsXSkD8/4jiQSSDspSyOA006DlSuhWTNITfUdK2blVdTkp0AZDPSx1lrc\n0LMiDT9LIJ0h9GQIvUggk0d5nJt5nXQSi9KsiEgUMTxLb65n0r5FOmcCZdnuO5jEuROBxdTbN4Li\nZl7XWjQiufgdYPFiOP54SEmBdu0gPd1zqthUPI+f/wxUOuB+JVxvzYEuBiZlzYpSAWhgjEmz1s7+\nZ3PJB9xOytr2K8t2JtKOxrzFHkrQmdFMpH2eL0JEJBZN4Xp+5kRm0YzGbOF9atOU2fyPUwrQSkrW\nJlI0R/MHi4DKrOdDatCaqfrCUSQ/Tj0VFi6EK66AmTOhWzd47TXIYUZBKRzjOlhy+KExxYHvgKuA\nX4BPgHbW2tU57D8amGOtnZ7Nz2xuHT+VWctsmnIuX/MHR9Ocmf+YRSUx8V7S0kI1vtyEoJ1QtBGr\n7QQpS9DaCVKWULUTpCxBa6fobZzGGuZyOv8HbOQYmjOTj6hZ6DzWWp1Js2GMsbmdE6Od+/KxcK+v\nHNt4hyu5hM9YxTnUYRlbOaqwSQqdQ22Es40gZYmtNvYdVz74AK6+GnbvhnvugYEDVdhkw5jCnady\n7TO21qYDPYCFwDfAZGvtamNMN2NMt8JF/afLeZcVVONcvuYbzqIGH2laSBGRLD9ShZrAYq7mWDax\nlLrcwDjfsSROlGI3s2jGJXzGj8A1LCpCQSMSx2rVgmnTIDERBg2C5OR8/W+hWGMqt7WmYkWuPTUh\nfaIcempuYSQvcTuJpDOPBrRjIts4PNs21FMTTe0EKUvQ2glSllC1E6QsQWsndFmKs5fB3MUdvATA\nQO6lD8+QkedI4oPbUU9N9tRT808l2MMsmlGfhfzC8dTmV9YG4m9CbYS+jSBlia02/nFcmTYN2rSB\nzEwYMAAeeCD3ForQy5pnlgAKS09NOCWylxHcxkhuJZF0BnIvTZiTY0EjIhLv0kmkB8PpzkukUZz7\neJ55NORItviOJjEokb28yXXUZyGbqMjVLGGt71AisaBVKxgzxt3u3RuGD/caJ1Z4KWqO41eWUpfb\neIVUStKJMdzPQDI1aamISJ5epjtX8TabqMg1LOYTqnMOq3zHkhiSQDoTaE9T5rA5a2HY1VT1HUsk\ndnTsCCOyVkPp0QNefdVvnhgQ8aKmJh/wGRdzGR+wgZOozfuMpVOkY4iIRLX3uIJL+JTPuIgq/MjH\nXEp7xvuOJTEggXTGciOtmcafHM41LGIV5/mOJRK1crzGpXt37vp7p27duCUOr4MJpYgWNb0YzDLq\ncAK/sowruJjP+IxLIhlBRCRmbOBkLuc93uBGyrCb8XTgRe4kkb2+o0mUSiCdcXSgPRPZTlnqs4DP\nudh3LJEoZ3PcXsRyD88D8BrQmdez2U/yI6JFzWDu3nf9zNUs4XeOieTTi4jEnN2U4SbGcBsj2Esi\ndzKUFJI4iQ2+o0mUKU4aE2hPWyazjXJcwyI+pobvWCIx7wXu4V4GAvAat9CF1z0nik4RLWq2UY5W\nTOV+BmrBLhGRkDG8wm1cznts4CRq8SEruZAGzPMdTKJEcdKYSDva8CZ/UZ56LC7CWkgiUlCDuJf7\neZZiWF7nFm5HkwcUVESLmkv4lOm0iuRTiojEjU+4lAtZyXzqU4HNzKMR/elDcdJ8R5MAK8VuptNy\n3zU09VjMJ1zqO5ZI3BnI/dzNIACG02PfsDTJn4gWNT9wRiSfTkQk7mymAo14iz70J50E+jCAZdTh\nFNb5jiYBdBg7eItGNGEuf3A0V/E2K6juO5ZI3BrM3XTPWovsee7jYfp5ThQ9vK1TIyIi4WEpxgD6\nUJel+4ajfcn5XM8k39HCxhhT3xjzrTHmB2NM72x+nmSM+csYszJre9hHziA5gq0sph5XspRfOY46\nLNOkACIB8DLduYnRZFCMfjzKc4AmDMibihoRkRj1PpdzPl8ynRYczjYm0c53pLAwxiQAw4D6QFWg\nnTHmrGx2XWatvTBrezKiIQPmeH4hhSRq8hHrOIXLeY9vONt3LBHJ8gY30Z4JWQstw2g6k0C671iB\npqJGRCSGbeUoWjGNbrzMbkr5jhMu1YE11tp11to0YBLQLJv9onLBhxzXuCjg9rcz+I4PqMX5fMW3\nnMnlvMePVPH4CkUkO1O4nsbMZSdwE28wjVaUYrfvWIGlokZEJOYZXqUbl/Cp7yDhciIcNIf1T1mP\nHcgCtYwxXxpj5hljqkYsXUjkvM5F/jeozscs5zIqs56PuJTavM9PVIrwaxGR/FrEtVwFbOFImjGb\nRVzDkWzxHSuQVNSIiMSJGB5elJ/B5p8Dlay15wNDgZnhjRQ8DYF3uDJrZrwGXMXbbKaC71gikoeP\ngct5j584kct5nw+oRWXW+o4VOMV9BxARESmin+Gg7oZKuN6afay12w+4Pd8Y85Ix5ihr7UFfeSYn\nJ++7nZSURFJSUjjyRtwdDONFIIFdjKETXRmp9eJEosg3nE0NPmIeDTmPVXxEDRozl0+p5jtakaWk\npJCSklLkdoy1kZlNwRhjizpzQ2LivaSlDSI0M0CYELQTijZitZ0gZQlaO0HKEqp2gpQlaO0EKYtr\nx1obldeW5MQYUxz4DrgK+AX4BGhnrV19wD7HApustdYYUx2YYq2tfEg7NlLnxIJw18MULlcxMhjE\nPfRiCADJPMbjPEbhLy8Kyt+E2gh9G0HKojZyaqM8fzGV1tRjCTspQwfGMZMW+W4niMe4QxlTuPOU\nhp+JiEhUs9amAz2AhcA3wGRr7WpjTDdjTLes3VoDq4wxXwCDgbZ+0kZOObYxk+b0Ygh7SaQj8DjJ\nROl8CSICbONwGvEWo7mJw9jFDFrSl6fRlM/qqQlAG7HaTpCyBK2dIGUJVTtByhK0doKUxbUTaz01\noRJLPTWnsYZZNONsvmEzR9GCGbxHnQK3k00atRGzbQQpi9rIuw3LAzxLf/pSDMsE2nEzr5NK6Tza\nKbpwHyfVUyMiIiLUYxErqMbZfMN/qMqlfMx7XOE7loiElOFZetOcmWynLO2ZyDLqcNJBE0Fmp+iz\nKAaVihoREZGYYLmP55hPA47kT2bSjBp8pDVoRGLYHJpSiw9YS2Wqs4LPuYi6vOM7lhf5KmqMMfWN\nMd8aY34w/8/encdHVd3/H399CCAgKCqKyiLuIoqiiCiowZVFFpe6Va21rdSl9atV+61dxNYu+vNr\n/brUotYF7dcNFEFRQSWgIBEEQQQRRIqgqIggAkogn98fdyaEkEkmyZ25d2bez8djnJnMzZm3w2RO\nPjnnnmP262oe/2Fi7f85ZjbFzLqGH1VERESqsyOreY4z+H/cQBHl/JHfcybP8i2too4mIhk2l0Pp\nzgxe4VR2ZSUTOIXruY24j6yErdaixsyKgHuAvsDBwPlm1rnKYYuB4929K/An4P6wg4qIiMi2ujGT\nmRzBEJ7na1oziOe5iT/imowhUjBWsQv9Gcef+B1FlHMbv2Y0Qwpqo850PvF6AIvcfYm7lwFPAoMr\nH+Dub7n7msTdUqB9uDFFRERka86V3MNUjmUfPuYdjuBI3mEsg6IOJiIRKKeIP/AnBiX+wDGYMbzL\n4fTizaijZUU6RU072Oqso2WJr6XyE2BcQ0KJiIhIam34kjEM4h5+QTO+558MpRdT+Jh9oo4mIhEb\nyyC6MYtpHE1HPqGEYm7kz3k/dpvO/1/aE/LMrA9wKbDNeTciIiLScCczgdkcxkBe4GtaczbPcDn/\n5HWc46wAACAASURBVHuaRR1NRGLiP3TiON7gVm6gMZv5M7+jBNibxVFHy5jGaRyzHOhQ6X4HgtGa\nrSQWB3gA6OvuX1ff1LBKt4sTFxERyZySxEVy3fZ8y23cwBXcB8AkjudCHmfZVl20iEhgE034b27l\ndU7kES7hOFYwm8P4L+7kIS4l3zbirXXzTTNrDCwATgI+Bd4Gznf3+ZWO6Qi8Dlzo7tNStKPNNwuq\nnThliVs7ccoSVjtxyhK3duKUJWhHm29WL86bbx7HJB7mx+zLYjbShGEM41Z+TTlFdWmJeLyf1UY8\n24hTFrURdhs78xX/pA0/SNx/gQFczn31+KOI5e7mm+6+CbgKeAWYBzzl7vPNbKiZDU0c9gdgJ+A+\nM5tlZm/XNYiIiIhU8c033A2UUMy+LGYWh9OdGfyVG+tY0IhIIVvFLpwDXMhjrGZHTudF3qcLlzEc\nozzqeKGodaQmtCfSSE2BtROnLHFrJ05ZwmonTlni1k6csgTtaKSmerEbqXnuObjqKvj0U8pozF/5\nDbfwO8poWs8G4/J+VhvxbCNOWdRG+G1saWdPlvMPrmAwYwAo4QR+zj9ZwEFptZGzIzUiIiJSP2ZW\n58veZow2gzPPhE8/ZRpwBDO5iT82oKAREQl8SjuGMJpzeIov2JViJjGHrvyF39CCdVHHqzcVNSIi\nIhnlaV2as45h/IF5NGMI8A2tuJJ76EWwY7iISHiMZziHzsznAX5KU8r4DX9jHgdzJqMIZ2Qou1TU\niIiIRMgo5xyeYj6duYk/0pzveJwf0pn5/IMr82S2u4jE0Sp24TIeoCdvMZNu7MVSRnE2JRRzBO9E\nHa9OVNSIiIhE5ARKmEZPnuI89mIpszic3rzBRTzOpzXucy0iEp5SenIU07mCe1nJLpzAZKZzFA9z\nCe35ZKtj6zOttuolE1TUiIiIZNnhzGIsp1NCH3ownU/Zg59xP92ZwRR6Rx1PRApQOUXcxxXsxyJu\n51dsojGX8CiL2I87uIZd+SJxZHpTalNfMkNFjYiISJYcwnuM5CxmcQSn8yJracnv+SP7s5AH+ZmW\naRaRyK2hNddzO52Zz5Ocy3Zs5BruZDH7cAuwCyujjlgtFTUiIiIZ1p3pPMPZvEdXzuJZNtCM/+Fa\n9mMRt/B71rN91BFFRLaymH05nycrRpZbso7fAkvoxG1cT1tWRB1xKypqREREMsGdk4AJnMx0enA2\no/iepvwvv2QfFnMd/8MXtI06pYhIjWZzOIMYyzFMZRzQknVcz+0soRP38XMOYEHUEQEVNSIiIuHa\nsAEefBAOO4xXgZN5jbW05DaupxNL+C/+lxXsEXVKEZE6mcYxDACOZAbPcgbN+J6fM5wFHMQYBtKH\n14lyKWjL1u7JZuYN/R9t0uRXlJXdQX7tmpuv7cQpS9zaiVOWsNqJU5a4tROnLEE79dmpuRCYmTeo\nT1y0CB54IChoVq0CYAVwN7fwD65gNTvVNxnxeQ+pjfxtI05Z1Eb4bYSf5SDm81/cycWMoDnfATCP\nzvyTnzOCi1lD65Rt1PRZa1a/fkpFTeRt5Gs7ccoSt3bilCWsduKUJW7txClL0I6KmurVq6j57jsY\nPRruvx8mTtzy9e7d4eqraXrRRZTl1XtIbeRvG3HKojbCbyNzWdrwJZdzHz/nn+zJZwCsowVPcS4P\n82PepHfi+7a0oaJGRU0OtROnLHFrJ05ZwmonTlni1k6csgTtqKipXtpFTXk5vPkmPPYYPPMMrFkT\nfL15czj3XBg6FI4+Gir2Y8in95DayN824pRFbYTfRuazNKaMQYzhcu7jZF6r+PpH7MOj/Ij/4wI+\nYj9U1KCiJrfaiVOWuLUTpyxhtROnLHFrJ05ZgnZU1FSvxqLGHd5+OyhinnkGli7d8tgRR8BPfgIX\nXACtt55uoaJGbeROG3HKojbCbyO7WfbnQ37Eo1zMCDqwrOLr0+nOE8zgjqVLoUOH6p9BRU2dE4XQ\nTpzeZHFrJ05Z4tZOnLKE1U6cssStnThlCdpRUVO9ykXNN998w6dLltBixgxalpTQ6tVXafLZZxXH\nlu2+O98MHMiaQYPYuN9+Kdvs3Lkz+fUeUhv520acsqiN8NuIJksjNnMSr3ERjzGE0bTi2y0Pdu8O\ngwfDkCHQpQtY0DWpqKl7ohDaidObLG7txClL3NqJU5aw2olTlri1E6csQTsqaqpnZu5Ll8KECSy9\n/352LC1lx0qPL7fGPN+4Fc81bsnbRc1xq/ll3Lx5A+vXLyW/3kNqI3/biFMWtRF+G9FnacYG+jOO\n8zibH7RoAevXb3lwr72gXz/o1w8bPFhFTR0ThdBOnN5kcWsnTlni1k6csoTVTpyyxK2dOGUJ2lFR\nUz0z26ZHnEsXxjKQMQyilKPxOu2EUAr0JL/eQ2ojf9uIUxa1EX4bccpi+Pr18OqrwUIrY8bAypVb\nP0M9+qnGDUwlIiKSP1q2hBNPZMbOO3PpMyt5b93YqBOJiOSf5s1h4MDgsnkzvPMOvPRScCktrVeT\n2nxTREQkadUqeP55Fp56KksatYw6jYhI/isqgh494KabYNq0ejejokZERCSpSZOoE4iISD3UWtSY\nWV8z+8DMFprZr1Mcc1fi8dlm1i38mCIiItVTPyUiIjUWNWZWBNwD9AUOBs43s85VjukP7Ofu+wOX\nAfdlKKuIiMhW1E9lS0nUAWKsJOoAMVYSdYAYK4k6QN6pbaSmB7DI3Ze4exnwJDC4yjGDgEcB3L0U\naG1mbUNPKiIisi31U1lREnWAGCuJOkCMlUQdIMZKog6Qd2oratoBn1S6vyzxtdqOad/waCIiIrVS\nPyUiIrUu6ZzuQtRV15JO8X2Pp9lc9crL5zXo+0VEJO+E3E9tUVa2hIb1W4sa8L0iIlIXtRU1y4EO\nle53IPgLV03HtE98rRoX1S1dFZs3J2+FtW9cGO3EKUvc2olTlri1E6csYbUTpyxxaydOWfJOqP2U\nWdXXuP7Li1ZqNSZtNLSdm0NoI4wccWvjZra8NlHmiMN7pLo26vvaxOU1yWQbdXlt4vrvW88Wtvms\nbbjaipoZwP5m1gn4FDgXOL/KMWOAq4AnzawnsNrdP6/akHawFhGRDFA/JSIiNRc17r7JzK4CXgGK\ngH+5+3wzG5p4fLi7jzOz/ma2CFgH/DjjqUVERFA/JSIiAXNPdzqyiIiIiIhI/NS6+WZdaRO01Gp7\nbczsh4nXZI6ZTTGzrlHkjEI675vEcUeZ2SYzOzOb+aKU5s9UsZnNMrO5ZlaS5YiRSeNnakczG2tm\n7yZem0siiJl1ZvaQmX1uZu/VcExBfg6D+qmaqJ9KTf1UauqnUlM/Vb2M9FPuHtqFYOh/EdAJaAK8\nC3Suckx/YFzi9tHAtDAzxPWS5mtzDLBj4nZfvTbVHvc68AJwVtS54/LaAK2B94H2ifttos4do9fm\nRuCvydcF+ApoHHX2LLw2xwHdgPdSPF6Qn8N1eN8U5Oujfqphr02l49RPqZ+qy2ujfqr6x+v8ORz2\nSI02QUut1tfG3d9y9zWJu6UUzj4K6bxvAH4BjAS+zGa4iKXz2lwAjHL3ZQDuvjLLGaOSzmtTDuyQ\nuL0D8JW7b8pixki4+xvA1zUcUqifw6B+qibqp1JTP5Wa+qnU1E+lkIl+KuyiRpugpZbOa1PZT4Bx\nGU0UH7W+NmbWjuCD4L7ElwrlZLB03jf7Azub2UQzm2FmDVs7PXek89rcAxxsZp8Cs4Grs5Qt7gr1\ncxjUT9VE/VRq6qdSUz+Vmvqp+qvz53BtSzrXVcY2QcsDaf8/mlkf4FKgV+bixEo6r82dwH+7u1uw\nuHmhLL2azmvTBDgCOAloAbxlZtPcfWFGk0UvndemLzDT3fuY2b7ABDM7zN3XZjhbLijEz2FQP1UT\n9VOpqZ9KTf1UauqnGqZOn8NhFzUhb9aZV9J5bUicdPkA0NfdaxqWyyfpvDZHEuwxAcGc035mVubu\nY7ITMTLpvDafACvdfQOwwcwmA4cB+d5ZpPPaXAL8FcDdPzKzj4EDCfY2KWSF+jkM6qdqon4qNfVT\nqamfSk39VP3V+XM47OlnFZugmVlTgk3Qqv4wjwEuBrAaNkHLQ7W+NmbWEXgWuNDdF0WQMSq1vjbu\nvo+77+3uexPMV768ADoKSO9n6nmgt5kVmVkLghPq5mU5ZxTSeW2WAicDJObiHggszmrKeCrUz2FQ\nP1UT9VOpqZ9KTf1Uauqn6q/On8OhjtS4NkFLKZ3XBvgDsBNwX+IvPWXu3iOqzNmS5mtTkNL8mfrA\nzF4G5hCccPiAu+d9Z5Hm++ZPwCNmNodgGPsGd18VWegsMbMngBOANmb2CXATwfSPgv4cBvVTNVE/\nlZr6qdTUT6Wmfiq1TPRT2nxTRERERERyWuibb4qIiIiIiGSTihoREREREclpKmpERERERCSnqagR\nEREREZGcpqJGRERERERymooaERERERHJaSpqREREREQkp6moERERERGRnKaiRkREREREcpqKGhER\nERERyWkqakREREREJKepqBERERERkZymokZERERERHKaihqROjCzJmY20sw+NrNyMzuhmmNuNbOV\nicvfosgpIiKFycx6mtkEM/vKzL4ws6fNbPcqx6ifkryjokak7iYDFwIrAK/8gJkNBQYDXROXgYmv\niYiIZENr4J/AXonLWuDh5IPqpyRfqaiRgmJmS8zsV2Y228xWm9mTZrZdut/v7mXufpe7TwE2V3PI\nj4Db3f1Td/8UuB24JJz0IiKS70Lop15291Hu/q27bwDuBXpVOkT9lOQlFTVSaBz4AXAasDfBX6ku\nMbMOic7j6xSX89Js/2BgdqX7c4Auof4fiIhIPgu7nzoemFvpvvopyUuNow4gEoG73H0FgJmNBQ53\n9+EEQ/YN1RJYU+n+N4mviYiIpCuUfsrMugK/BwZV+rL6KclLGqmRQrSi0u0NhPth/i2wQ6X7Oya+\nJiIikq4G91Nmth8wDvhlYsp0kvopyUsqakSAxLD+t2a2NsXl/DSbeh84vNL9w9h62F9ERKTO6tJP\nmdlewATgj+7+7ypNqZ+SvKTpZyKAu39Cmn8JS5ywaYm725lZM3f/LnF/BHCtmY1LHHMt8L9h5xUR\nkcKSbj9lZu2A14F73P3+ag5RPyV5SUWNFDqnyrLMaVgAdEx83yuAm9ne7r7U3Yeb2T7Ae4ljH0jR\nqYiIiKSjrv3UTwkWGBhmZsOSbbj7Dokb6qckL5l77T8nZlYEzACWufvAKo8VA88DixNfGuXut4Sc\nU0REpN7M7EDgyUpf2gf4vbvfFVEkEREJUbojNVcD84BWKR6f5O6DUjwmIiISKXdfAHQDMLNGwHLg\nuUhDiYhIaGpdKMDM2gP9gQfZch7BNoeFGUpERCSDTgY+SpyjICIieSCd1c/+DlwPlKd43IFjEzvf\njjOzg0NLJyIiEr7zgP+LOoSIiISnxqLGzE4HvnD3WaQejZkJdHD3w4C7gdHhRhQREQmHmTUFBgLP\nRJ1FRETCU+NCAWb2F+AiYBPQjGCzplHufnEN3/MxcKS7r6ry9bquMCUiIhng7gU7ZdjMBgOXu3vf\nah5TPyUiEgP16adqHKlx9xvdvYO7700wXP961YLGzNqamSVu9yAolFZV0xzurks1l5tuuinyDHG9\n5Nprk3inp3lp2M9Err02et/E4yKcDzyR6sGo/33ietHPlF4bvTZ6bbJ1qa+67lPjAGY2NPHhPxw4\nG7jczDYB6wmKHxERkVgxs+0JFgn4WdRZREQkXGkXNe4+CZiUuD280tfvBe4NP5qIiEh43H0d0Cbq\nHCIiEr50Vj+TDCsuLo46QmzptUlNr01qem1EwqWfqdT02qSm1yY1vTbhq3GhgFCfyMyz9VwiUQlO\nL0v3fW4NmjsqUh9mhhfwQgE1UT8lIhK9+vZTGqkREREREZGcVteFAkQKy4wZ8K9/QePG0LlzcDn0\nUGijafkiIiIicaGiRqQqd3jlFbjtNpg4cdvHi4pg2DC48UZopMFOERERkajpnBqRyr7/Hs48E8aN\nC+63agU/+xnssQfMnx9cpk0LCp8BA+Cxx2CnnSq+XefUSNzpnJrU1E9JrkpsF5iS3teSS+rbT6mo\nEUnatAnOOQeeew523hluuAGGDoXWrbc+btw4uPBC+Ppr2HtvGDUKunUDVNRI/KmoSU39lOSqmvse\n9TWSW1TUiDREeTlcckkw8tK6NUyaBF27pj5+yRI4+2x4553g+Hffhb32UlEjsaeiJjX1U5KrVNRI\nPtHqZyL15Q5XXx0UNNtvH4zE1FTQAHTqBG++Cf36werVcMEFUFaWlbgiIiIisjUVNSL33w/33ANN\nm8Lo0XDMMel9X7NmMGIEtGsHU6cGiweIiIiISNZp+pkUts8/hwMPhDVr4N//DkZc6mryZOjTB9w5\n2Z3XNP1MYkzTz1JTPyW5StPPJJ9o+plIfVx3XVDQ9OsH559fvzaOPx5uugnceRzYjc9DjSgiIiIi\nNUurqDGzIjObZWZjUzx+l5ktNLPZZtYt3IgiGTJxIjz+eDCN7J57oJYlMWv029/CCSewO3AbN4QW\nUURERERql+5IzdXAPKoZ2zSz/sB+7r4/cBlwX3jxRDJk40a44org9m9/C/vs07D2iorgoYfYCFzE\nYxzM+w2OKCIiIiLpqbWoMbP2QH/gQaC6P2UPAh4FcPdSoLWZtQ0zpEjobr8dPvggOJ/m+uvDaXOf\nfXgAaITzJ34fTpsiIiIiUqt0Rmr+DlwPlKd4vB3wSaX7y4D2Dcwlkjlffgm33BLc/sc/YLvtQmv6\nFmA9zTmT5+jO9NDaFREREZHUaixqzOx04At3n0X1ozQVh1a5r2U2JL7uvhs2bOAFwE46CTOr9ZKu\nFcBd/BKAv3BjZvKLiIjUQRj9m0jcNa7l8WOBQYnzZpoBO5jZCHe/uNIxy4EOle63T3xtG8Mq7eNR\nXFxMcXFxPSKLNMDatcGiAMDfgPTq77p96N/GDfycf3IKr9KH15nIiXVNKRKakpISSkpKoo4hIpFK\nvdyzSL5Ie58aMzsBuM7dB1b5en/gKnfvb2Y9gTvdvWc136/1/yV6d9wBv/oV9OqFTZlCukVNHX5O\nAOdG/syf+R2l9KAn06i+49DeAZJ92qcmNfVTkquq7lPTjA18R/Pko2gPG8kl2dqnxhNPNtTMhgK4\n+zhgsZktAoYDV9Q1hEhWbNwYFDUA//3fGX2q/+VqPmc3juZtTmBSRp9LRNJjZq3NbKSZzTezeYk/\nxInkjSOZwcucxgZa8DCXsAsro44kkjVpj9Q0+In0FzCJ2sMPw6WXQpcuMGcOVlREpkZqAG5iGMO4\nmZGcxQ8Y2aB2RcJSyCM1ZvYoMMndHzKzxsD27r6m0uPqpyQnHWjGnzmLsxm11ddXsgvX8hWPUY5m\nDEiuyNZIjUhuKi+HW28Nbv/619Ao82/9+7mMMhozhNG0Y1nGn09EUjOzHYHj3P0hAHffVLmgEclZ\nCxYwEzibUWygGbdxPT0o5XX60IavGAGMYRCN2Bx1UpGMUlEjhWHMGFiwADp2hPPOy8pTfsaejOIs\nGrOZoQzPynOKSEp7A1+a2cNmNtPMHjCzFlGHEklXqtXLJhx0ENsDLzCAffmIX3Mb0+nBSbzGj3iE\nVcBAXuAn/Cvq/wWRjFJRI4UhseIZ114LTZpk7Wnv5UoALuN+mvJ91p5XRLbRGDgC+Ie7HwGsAzJ7\ncp1I6Hyryzk8ySnAV8AlPMJn7FnpWGMEP+LyxL1b+B07oMFJyV+1Lekskvs+/hheew2aNYMf/Sir\nT/0mvZlNVw5jDmcxiie4IKvPLyIVlgHL3D25K+5IqilqtPWA5IpWfMPfuQaAXwNf0aba454GrqI3\nx/Emv+dPXM/t2Qspkoawth7QQgGS/37/e7jlFrjwQnjssYovV10CM7X6LRSQ9FMe4AEuYyrH0Iup\n9WpXJCwFvlDAZOCn7v6hmQ0Dmrv7rys9rn5KYqtq/3IH13ANd/IWPenFNLyGZZu78Q4z6M5miujC\n+yzkgIrH9J6XuKlvP6WiRvLb5s3QqRMsWwYTJ0Klv7pmq6hpwTqW047WrOFIZjCTI+vcrkhYCryo\nOQx4EGgKfAT8WKufSa6o3L8cxru8k+hLjuQdZtONmjfYdB7gp/yUfzGW0xnE2IrH9J6XuNHqZyLV\nGT8+KGj23RdOOCGSCOvZnoe4FIAr+EckGUQE3H22ux/l7oe5+5la/Uxy1V+4kSLKuZtfMJvD0/qe\n3/JnvqEVA3mBU3klwwlFsk9FjeS3fyVWe/nJT8Ci++P0cIYC8AOeoRkbIsshIiK5rR3L6MvLfE9T\n/sTv0/6+L2jLLfwOgF9za6biiURGRY3kry++CJZybtQo6wsEVPUhB/I2R7EDaxnEmEiziIhI7rqY\nETTCeZ7BrGKXOn3vcIbyHdtRTAkdWJqhhCLRUFEj+euxx6CsDPr3hz33rP34TMfhIgAu5PGIk4iI\nSG5yfszDADzMj+v83d+wI6MZQiOcH/LvsMOJREpFjeQn962nnsXAU5zLJoroy8u04cuo44iISI7p\nxRT2ZxHL2ZPxnFqvNkZwMRCM+IjkExU1kp9mzID586FtWxgwIOo0AHzJbrxMX5qwiXN5Kuo4IiKS\nY5KjNCO4mHKK6tXGeE7lc3ajMx/QPcxwIhFTUSP56ckng+vzzoMmTaLNUsnjXAhoCpqIiNRNC+Ac\nngbgES6pdzubacy/+SFAYsxGJD/UWtSYWTMzKzWzd81sbmLDsqrHFJvZGjOblbj8LiNpRdJRXg5P\nBx/8nHtutFmqGMMgvqEVPSll/6jDiIhIzjgbaMW3TOUYPuTABrWVnIJ2PsDGjQ3OJhIHtRY17v4d\n0MfdDwcOB/qa2dHVHDrJ3bslLreEHVQkbVOnBnvTdOwIPXuG0qSZpXWpzQZaMIqzABJ/JxMREald\nclmA+iwQUNVsDmMOh9IG4KWXGtyeSBykNf3M3dcnbjYFmgDl1RxWkDtUS7yYGXcfdxwA/2/pUqxR\no3oXIFvzNC+12zIFjWBBAxERkZosXkwxsJ7mPEUYMxCsYrSGEVowQPJDWkWNmTUys3eBz4Hx7j69\nyiEOHGtms81snJkdHHZQkXQ0As5mdwCeYjoNLUAyoYRilrMn+wJMmxZZDhERyRGjRwdXDGEtO4TS\n5P9xAZsBxo6FVatCaVMkSumO1JQnpp+1B442sy5VDpkJdHD3w4C7gdHhxhRJz/HAHqxgEfvyDkdG\nHada5RRt+UvbyJHRhhERkfgbNw6AsQwMrcnP2JOJEOznpilokgca1+Vgd19jZhOBvsD7lb6+ttLt\nl8zsH2a2s7tvVfoPGzas4nZxcTHFxcX1jC1SvfMS10HREN8ZkaM4i2v5O4waBbffDnWeDieSnpKS\nEkpKSqKOISL19e23MHkym6Hee9Ok8iJwMgRFzQ91pqfkNvNa5vSbWRtgk7uvNrPmwCvA39x9XKVj\n2gJfuLubWQ/gaXfvVKUdr+25RBqkrIyVTZvSBujKbN6jay3fYKQ3DS3d49I/1ihnGUXsCcGeOkfG\nc1RJ8o+Z4e6qoquhfkpi6fnnYcgQpgC9U/YvNfU9qR87EOMDgDZt4PPPoZF2+pDo1befSufduwfw\nupnNBt4mOKdmnJkNNbOhiWPOBt5LnHdzJ1v+YC6SPa+/ThtgPgfxHodGnaZGTiOeS94ZNSrKKCIi\nEmeJqWfjajmsPhYA7LUXrFwJ77yTgWcQyZ50lnR+z92PcPfD3P3Q5HLN7j7c3Ycnbt/r7oe4++Hu\nfqy76+xnyb6nngquYj71LKmilBk5UqugiYjIttwzWtQA0K9fcK3zaiTHaZxR8sOmTcEQPfA050Qc\nJj2TAXbZBRYuhLlzo44jIiJxM3dusO/a7rvzbqaeo2/f4PrllzP1DCJZoaJG8sObb8KqVSwA5tM5\n6jRp2QwwZEhwR1PQRESkqsQoTcVoSiaceCI0aQKlpVraWXKaihrJDxVr+EMuTD2rcNZZwbWKGhER\nqSpZ1PTvn7nnaNUKjjsOysthwoTMPY9IhqmokdznXqWoySEnnQQ77hhMMfjww6jTiIhIXKxeDVOm\nQFERnHJKZp8rOQVN59VIDlNRI7lv9mz4z3+gbVtKo85SV02bwsDEZmoarRHJKDNbYmZzzGyWmb0d\ndR6RGk2YAJs3Q+/ewR+/Mik5ve3ll4MRG5EcpKJGcl9ilIbBg9PeTSYuzIwhjz8OwIwbb8TMqr2I\nSCgcKHb3bu7eI+owIjXKxtSzpC5doF27YK+a2bMz/3wiGaCiRnJfsqhJnnSfU5xXWM96mtMdaMcn\nBL93Vb6ISIj0VwKJP3d45ZXgdiYXCUgy09LOkvNU1Ehu+/jj4K9KLVsGK7jkoO9oznhOBeB0Xog4\njUhec+BVM5thZj+LOoxISgsXwmefwW67wSGHZOc5K09BE8lBKmoktyX2pqF/f9huu2izNMBYgvNq\nBjI24iQiea2Xu3cD+gFXmtlxUQcSqdakScH18ccHoyjZ0KdP8FylpbBhQ3aeUyREjaMOINIgOT31\nbIsXOJ1yjJN4jRasYz3bRx1JJO+4+2eJ6y/N7DmgB/BG5WOGDRtWcbu4uJji4uIsJhRJSBY1J5yQ\nvefcaSfo2jWY/VBaCnrvS5aUlJRQUlLS4HbMPTtz9s3Ms/VcUiBWroS2bYPlLr/8EnbcMXFSfbrv\ns3SPzUSb2x77Fj3pSSlDeI7nGbLVcfrZkbCYGe5ecOeVmFkLoMjd15rZ9sB44GZ3H1/pGPVTEj13\n6NgRli2DOXPg0EMBaunf6v/YVu/5q6+Gu+6Cm2+GP/yhXvFFGqq+/ZSmn0nuevHFYOnJ4uLML3eZ\nBWMYBMAgxkScRCQvtQXeMLN3gVLghcoFjUhsfPxxUNDsskuwKlk2HX98cD15cnafVyQEKmokd72Q\nOKl+8OBoc4QkeV7N6bxAIzZHnEYkv7j7x+5+eOJyiLv/NepMItWqfD5Noyz/mpYsaqZOhY0b+YMC\nuAAAIABJREFUs/vcIg1U40+LmTUzs1Ize9fM5prZsBTH3WVmC81stpl1y0hSkco2btyy3OWAAdFm\nCclcDuFjOrEbX9ID7QsoIlKQojifJmnXXaFz52ChgHfeyf7zizRAjUWNu38H9HH3w4HDgb5mdnTl\nY8ysP7Cfu+8PXAbcl6mwIhXeeAPWrg2G5jt1ijpNSKxiCppWQRMRKVBRFjWVnzeZQyRH1Dqu6e7r\nEzebAk2A8iqHDAIeTRxbCrQ2s7ZhhhTZRnLq2emnR5sjZMkpaDqvRkSkAP3nP7BkCbRuXbFAQNYl\npqCN+81vMLMaLyJxUmtRY2aNEidWfg6Md/fpVQ5pB3xS6f4yoH14EUWqcIexiZGMPCtqJnM8a9iB\nQ3ifvVkcdRwREcmm5OjIcccFK3tGIVHU9AaKKCNYOa26i0i8pDNSU56YftYeONrMqluKo2q5rne7\nZM6HH8JHH8HOO0PPnlGnCVUZTXmZvoCmoImIFJyop54BtGsH++7LDsBhzI4uh0gdpb35pruvMbOJ\nQF/g/UoPLQc6VLrfPvG1bWhTMwnFiy8G1/36QeP82z/2BU7nXJ6mP+O4i6ujjiM5LqxNzUQkC+JQ\n1EAwWvPRRxzPZGZyZLRZRNJU4+abZtYG2OTuq82sOfAK8Dd3H1fpmP7AVe7e38x6Ane6+zZ/Ptem\nZhKaE0+EiRPhiSfgvPO2eiiXN99MasOXfE5bymjCLnzFOlpp800JTaFuvpkO9VMSqeXLoX17aNUK\nVq3a5o92mdp8szoXE5wsPZrBnMHolN+rnxfJhExtvrkH8LqZzQbeJjinZpyZDTWzoQCJAmexmS0C\nhgNX1DWESNpWrw5WPisqgtNOizpNRqxkV0o5mu3YyEm8FnUcERHJhuQoTe/eWZ6FsO35MpMT53Qe\nxxvYNutDicRTjT817v4ecEQ1Xx9e5f5VIecSqd748bBpUzA0vtNOUafJmBcZwDFMYwAvah00EZFC\nMGVKcJ3cADNCS+jEUqAjq+jC+8wlopXYROogy1vVijRQni7lXNU4+gPQn3G1HCkiInlh6tTgulev\naHMAYExO3Dq+4pZIvKmokdyxeTOMS/ySP2BAtFkybBbd+JQ9aM9yukYdRkREMmvtWpgzJ5h21r17\n1GkASIwbcQxvRZpDJF0qaiR3TJ8OX30Fe+8NnTtHnSbDrGK0Jr/LNxERobQUysvhiCOgefOo0wCQ\nGDfi2IpbIvGmokZyR3KUpn9/KICdjF9MlDMqakRE8lxy6tmxx0abo5K5wFpasg8f05YVUccRqZWK\nGomMmaV9AbYuagrAq5zMRprQE4IRKhERyU+JouYHd95Zcz+YReVAKUcDmoImuUFFjURs26Ukt70A\nK1bAO+9As2ZQIJu2fksrJnM8RQCvvBJ1HBERyYTycngrKBqC/9bQF2bZVIKRI01Bk1ygokZyw8sv\nB9cnnggtWkSbJYuSU9B48cVog4iISGbMmwfffAMdO7I86ixVqKiRXKKiRnJDgU09S6ooal5+OVj9\nTURE8ksMz6dJmhZMgKY7M2jK9xGnEamZihqJvcYQbLoJ0K9flFGybiH7swhg1apgdRwREckvMS5q\n1tCa9zmY7dhIN2ZFHUekRipqJPaOBVizhvmA7btv7QsK5BXbsv3mOG3EKSKSd2Jc1ICmoEnuUFEj\nsZeccDaOa0lrUYE8U1HKvPRSlDFE8oKZFZnZLDMbG3UWEb78EhYuDM4V7RrPrZZV1EiuUFEjsbel\nqCms82mSJkGwGdvMmfDZZ1HHEcl1VwPzyNe/gkhuSax6Ro8e0KRJtFlSSBY1vZiCfmwkzlTUSKx1\nYCmHEmwA9ia9o44Tie8gWPUNtqwCJyJ1ZmbtCf5O8iCQj/NVJdckp5716hVtjhp8yAF8xc7swQr2\n4j9RxxFJqdaixsw6mNlEM3vfzOaa2S+rOabYzNYkhvRnmdnvMhNXCk0/gilXwUaU20WcJkLJVd90\nXo1IQ/wduJ5gX0GR6MX8fJqA8RbHANqEU+ItnZGaMuAad+8C9ASuNLPO1Rw3yd27JS63hJpSClb/\nxBklhTr1rEJy1bfx46GsLNosIjnIzE4HvnD3WWiURuJg40aYPj243bNntFlqofNqJBc0ru0Ad18B\nrEjc/tbM5gN7AvOrHKpOQkLVlO85mVcBFTXsvTd07gzz5wd/2TvhhKgTieSaY4FBZtYfaAbsYGYj\n3P3iygcNGzas4nZxcTHFxcXZzCiFZPZs+O47OOgg2HnnqNPUSEWNZFJJSQklJSUNbsfc0z/py8w6\nEZy33MXdv6309ROAZ4FlwHLgOnefV+V7vS7PJfkvWII59XviFMYzntN4F+iW9smJNbdZv2Mz0Wbd\nnt/d4brr4H/+B264AW69Nc3nENmameHuBf1HqESfdZ27D6zydfVTkj133QVXXw0//jE89BBQW78Y\n3WMtWMcadgRgR9awnu2p6JtEQlbffirthQLMrCUwEri6ckGTMBPo4O6HAXcDo+saRKSqLVPPBNB5\nNSLh0m9jEq3kymcxn3oGsJ7tmUNXGrOZ7syIOo5ItWqdfgZgZk2AUcDj7r5NweLuayvdfsnM/mFm\nO7v7qsrHaVhf6kJFTRW9e0PLljB3LixdCh07Rp1IckBYw/r5xN0nkVgtXSQy06YF18ccE22ONL3F\nMRzBLI7hLSajKdASP7VOP7NgLPRR4Ct3vybFMW0JTsB0M+sBPO3unaoco2F92UpNw+z7sZCFHMAq\ndmI3vmazpp8FN888E557Dv75Txg6NM3nEdlC089SUz8lWbNiBeyxB7RqBV9/DUVFQHynnwFcyGM8\nxsWMZjBnMBpNP5NMyeT0s17AhUCfSks29zOzoWaW/K3qbOA9M3sXuBM4r65BRCpLLuX8CqexOeIs\nsZKcgvbii9HmEBGR+kuO0vToUVHQxN3WyzqrmJH4SWf1szeppfhx93uBe8MKJTKA4Jf2YNWzJ6MN\nEyfJpZ1fey1YNadZs2jziIhI3SXPp8mRqWcAH7EvX9KGtnxBJ5awJOpAIlWkvVCASLa0YB3FlFCO\n8TJ9o44TL+3aweGHw/r1MEmnBIiI5KTkSE0OLBKwhTGNIK824ZQ4UlEjsXMir7MdG3mbHqxk16jj\nxM+AAcG1pqCJiOSesrKc2XSzqq2noInEi4oaiZ0tq54V+IabqVQuanSSpohIbpkzBzZsgP33h112\niTpNnSSLmp5MiziJyLZU1EjMuIqa2vToEXSEixfDggVRpxERkbrIsaWcK5vOUWymEYfzLjqjU+JG\nRY3EShfeZy+W8jm7MZMjoo4TT0VF0DdxrpGmoImI5JYc2nSzqnW05D0OpQmb6B51GJEqVNRIrJzO\nCwC8yABcb8/UdF6NiEhuyuGRGqBisYDcK8kk3+m3RomVZFHzAqdHnCRezGyry84XXMBmoGziRHas\n8piIiMTUF1/ARx/B9tvDIYdEnaZetiwWIBIvKmokNnZhJcfwFhtpwgROiTpOzPhWl69xptKbJsDJ\njKz0mIiIxFZylOaoo6BxrVsFxtJWRY0Wq5EYUVEjsdGXlyminBKK+ZZWUceJvRcJpqAlNyoVEZGY\ny/GpZwAL2Z+v2Jk9AJYujTqOSAUVNRIbmnpWN8mipj/jMMojTiMiIrXK4UUCttiyCWfF/49IDKio\nkVhoTBl9eRnY8su61Gwuh/AfOrI7n3Mk70QdR0REalJWxrqSEgDaDB68zbmSuXROZHIKmooaiRMV\nNRILvZhCa9Ywj84sZt+o4+QIqxjVGsjYiLOIiEiN5sxhe2ABB/BVlfMkc+28yKkcG9xQUSMxoqJG\nYkFTz+pnLAMBFTUiIrE3dWpwlSwIctjb9GAzwKxZsH591HFEgDSKGjPrYGYTzex9M5trZr9Mcdxd\nZrbQzGabWbfwo0o+U1FTPxPpw1pa0o136YBO2BQRia08KmrW0ZLZAJs2wfTpUccRAdIbqSkDrnH3\nLgR7LV1pZp0rH2Bm/YH93H1/4DLgvtCTSt7aj4UcxAK+pnVefNhn00a2YzynAlsKQxERiaE8KmoA\nplbcmFrTYSJZU2tR4+4r3P3dxO1vgfnAnlUOGwQ8mjimFGhtZm1Dzip5Krkk8Uv0YzO5uW5/lMYw\nCIBBjIk4iYiIVGvZMli6lNXAfDrXenguUFEjcVOnc2rMrBPQDSit8lA74JNK95cB7RsSTApH8pdx\nrXpWP+PoTzlGHybSMuowIjFlZs3MrNTM3k1MpR4WdSYpIIkT6t8CPE9OZ96qqNEmnBIDaf9kmVlL\nYCRwdWLEZptDqtzXO1xqtROrOJ7JbKKIcfSPOk5OWsmuTOVYtmNjYiKaiFTl7t8Bfdz9cOBwoK+Z\nHR1xLCkUFVPP8sd/APbYA1atggULoo4jkt5cHzNrAowCHnf30dUcshzoUOl++8TXtjJs2LCK28XF\nxRQXF9chquSjAbxIYzbzKiexmp2ijpOzxjKQ3kxJTEQT2aKkpISSxN4Yhc7dk8s0NQWagHatlSxJ\nFDV5twByr14wcmTw/3fQQVGnkQJnXsuQoQW7QT0KfOXu16Q4pj9wlbv3N7OewJ3u3rPKMV7bc0lh\nMTOe4SzOZhS/4C7u4RepjiT9gb9MHBv/5z+I+cznYFYCbTZtgqKiNDNIoTEz3D13dvkLkZk1AmYC\n+wL3uPtvqjyufkrCt2ED7LADlJezQ3k5a2v8PK/p8z5OjwWP+x13wLXXwk9+Ag8+WMOxIumrbz+V\nzvSzXsCFQB8zm5W49DOzoWY2FMDdxwGLzWwRMBy4oq5BpPBsB/TlZWDLye5SPx9wEIvYlzagzdBE\nUnD38sT0s/bA0WbWJepMUgBmzAiWPj70UNZGnSVsxyZWctNiARIDtU4/c/c3SW+VtKtCSSQF4ySg\nJeuYSTeWslfUcXKcMYZBXMvfYexY6N076kAiseXua8xsItAXeL/yY5omLaFL/sJ/7LEwe3a0WcLW\nrRtstx3Mnx+cW7PzzlEnkhwU1jTpWqefhUXD+lLV/WZcBtzEMP7ITTUcGf/pX3F4/hMooYQ+cMAB\n8MEHYAU5w0hqUajTz8ysDbDJ3VebWXPgFeBviZkGyWPUT0n4Bg+GMWPgscewiy6itild8Zlilsb0\nM3c47jh480144QUYoFVMpeEyOf1MJHzl5RUTzkYzJNIo+eJNevMVwIcfBn81E5HK9gBeN7PZwNvA\n+MoFjUhGuG89UpOPNAVNYkI7HUo0SkvZHVjCXsyha9Rp8sJmGvM8cCnAs8/CwQdHnEgkPtz9PeCI\nqHNIgVm0CFauhLZtYe+9o06TGSpqJCY0UiPReP754IrBbLvFkdTXsxU3nq3pMBERyYY33wyujz02\nf6cEJ4uat9+GsrJos0hBU1Ej0RgdbHekqWfhehWgZUuYNQs+/jjqOCIihW3y5OD6hBOizZFJu+4K\n++8P69cHfY9IRFTUSPYtWAALFrAKeIPjok6TV76HLSdqjq5un1wREcmaZFFz/PHR5si04xJ9+Rtv\nRJtDCpqKGsm+UaMAeIHgPBAJ2RlnBNeagiYiEp1ly2Dx4mDjza55fu5ociRq0qRoc0hBU1Ej2ffM\nM8FVxDHyVv/+0LQpTJkCK1ZEnUZEpDAlRy169YKiomizZFpyJOqNN6C8PNosUrBU1Eh2LVoE774L\nrVoxIeos+apVKzj11GAp0cSCDCIikmWFMvUMoFMn6NgRVq+GuXOjTiMFSkWNZNfIkcH1oEHB+R+S\nGWeeGVxrCpqISDQKqaiBLf+fmoImEVFRI9mVLGrOPjvaHPlu4MBgusPrr8PXX0edRkSksKxcCfPm\nQbNm0L171GmyI1nUJIs5kSxTUSPZs3gxvPNOsOTwaadFnSa/tWkTnLi5aROMHRt1GhGRwpLcn+aY\nY4JzHAtBcrGAyZOD6c8iWaaiRrInOUozcCA0bx5tlkKQHA176qloc4iIFJpCm3oGwV41bdvCF18E\nWzeIZFmtRY2ZPWRmn5vZeykeLzazNWY2K3H5XfgxJS9o6ll2nXVWMAVt/Hj46quo04iIFI5kUXNc\nAe3FZrb1aI1IlqUzUvMw0LeWYya5e7fE5ZYQckm+WbIEpk+H7beHfv2iTlMYdtsNTjopmIKmBQNE\nRLLjm29g1ixo3Bh69ow6TXZpsQCJUK1Fjbu/AdR2prGFE0fyVmLDTQYM0NSzbDrvvOD6ySejzSEi\nUiimTg32aunePfhDXiGpXNTovBrJsjDOqXHgWDObbWbjzOzgENqUfJPYcJMf/CDaHIXmjDOgSROY\nOBE++yzqNCIi+a8Qz6dJ6tIFdt4Zli8PZmiIZFEYRc1MoIO7HwbcDYwOoU3JJ4sWQWlpsOpZ//5R\npyksrVsH0/3ct5zTJCIimVPIRU2jRlvOI9IUNMky8zSGB82sEzDW3Q9N49iPgSPdfVWVr/tNN91U\ncb+4uJji4uI6xpW4M9t2JuIfgJuBR4FLtnk0neFpS/O4TB2ba8+/tfOAJ4ApQO8qj6Xz8y+5raSk\nhJKSkor7N998M+6uKcPVMDPXz4Q0yNq1lO2wAwbsAnxT7UE1vcdq+ryP02PB49X+vNxxB/zqV3DJ\nJfDwwzV8v0j1zKxe/VSDixozawt84e5uZj2Ap929UzXHqbMoAEFRU/nf2VnAgRzAQk7lFSZwauWj\nyc+iIl7Pvz3f8gW70YIN7MUSlrJXxbH6mSw89e0sCoH6KWmwF16AgQOZyjH0Ymo1B9ReKMSncKln\nUTNzJhx5JHTsGExBq+aPnSI1qW8/lc6Szk8AU4EDzewTM7vUzIaa2dDEIWcD75nZu8CdBH8YFgHg\nKKZzAAv5jN15nROjjlOQ1tGSsQwE4ByejjiNiEgemzABgFc5OeIg2WFm21waHXkkXwIsXcoBjRpV\ne4xIJqSz+tn57r6nuzd19w7u/pC7D3f34YnH73X3Q9z9cHc/1t2nZT625IoLeRyAJzifzTSOOE3h\nejLxt4bzeSLiJCIieSxR1EzglIiDZItvc3Gc1xKPnsrd1RwjkhlhLBQgUq3GlHEewVLCj3NhxGkK\n20v0YzU7cgSzOJj3o44jEgkz62BmE83sfTOba2a/jDqT5JHly2H+fL4FSjk66jSRGp+4PoUJkeaQ\nwqKiRjLmZF5lN75kHp2ZRbeo4xS072nGU5wLwCU8Em0YkeiUAde4exegJ3ClmXWOOJPki1dfBaAE\nKKNppFGilixl+jCRxpRFmkUKh4oayZjk1LN/80O0P2v0HubHAFzEYxSxKeI0Itnn7ivc/d3E7W+B\n+cCe0aaSvJEoajQ2AcuADziQHVjL0ZRGHUcKhIoayYiWrOUMngPg/7gg4jQCwXSIDziQ3fmc03gl\n6jgikUqs6tkN9BuXhMC9oqh5NeIocTE+sdqppqBJtqiokYw4g+dowQbeoDdL2DvqOAKA8Uhip6Af\no70DpHCZWUtgJHB1YsRGpGHmzoUVK2DPPZkXdZaYSC6WcGrFGTYimaXlqCQjfsqDAIzg4oiTSGWP\ncRF/5rcMYgw7Rx1GJAJm1gQYBTzu7qOrPj5s2LCK29okWtKWGKXh5JNhxIhos8RECcWU0ZgevM2O\nrGYNraOOJDFVdZPo+kpr880waFOzwmBmHMh8PqAz37I9e/AZ39Iq1dEUwuaXcXv+cfSjHy9zFXCP\nfiYLTiFvvmnBBhmPAl+5+zXVPK5+Suqnf3946SUYMQK7+GIasqFlfDbYbHjWSRzP8bzBGTzLaM6o\neEw/Z1KTjG2+KVJXyVGaJzi/hoJGorJlCppIwekFXAj0MbNZiUvfqENJjvv+e5g0Kbh9cmFsupku\nTUGTbNJIjYRqOzOW0YZdWUkPSplOjxqOLsyRkqiffzu+4zP2YCdWw+zZ0LVrmm1LPijkkZraqJ+S\nepk0CYqLoUsXmDuXYEBQIzXg9KCUUnqyiH3Zn0UVj+nnTGqikRqJhSHArqxkNl2ZzlFRx5FqfE8z\nnuD84M5DD0UbRkQk140bF1yfemq0OWJoBt35mtbsx0fszeKo40ieU1EjofpZ4voBfob2pomvB/lp\ncOORR2DdukiziIjktOefD64HDYo2RwyVU8RrnARAf8ZFnEbynYoaCc9HH3EysIFmiQ03Ja5mcQRT\nAdasgX//O+o4IiI5xcyChXHMYMECvgIa9+mTmHomlY0hKPYG83zESSTfqaiR8DwYLBDwNOewmp0i\nDiO1ubfixr3BxnEiIlIHzmBuBeBFLmIzTvrnPxaOFxnAJooopoTWfB11HMljtRY1ZvaQmX1uZu/V\ncMxdZrbQzGabWbdwI0pO2LgxmMpEcuqZxN1IgF13hTlzYMqUqOOIiOSc5OhDcjRCtrWKXZjM8TRh\nk6agSUalM1LzMJByyUsz6w/s5+77A5cB94WUTXLJ00/DihXMBabQK+o0koaNAD9LFKD33lvToSIi\nUsVufM4xvMX3NOUVTos6TqyNZggAQ9hmv1uR0NRa1Lj7G1DjeOEggs3McPdSoLWZtQ0nnuQEd/j7\n3wG4E9ACATlk6FBo1AhGjoTPPos6jYhIzjidF2iE8xonaU+2WjzPYAD68RLbRZxF8lcY59S0Az6p\ndH8Z0D6EdiVXTJ4MM2fCrruiU85zTMeOMHgwbNoEDzwQdRoRkZyRnHqW/IVdUlvKXsykGy1Zl1gL\nTSR8YS0UUPVP8zpTrpDccUdwffnlfBdtEqmPK68MrocPh7KyaLOIiOSA5sApTABgLAOjDZMjtkxB\nE8mMxiG0sRzoUOl++8TXtjFs2LCK28XFxRQXF4fw9BKphQth7Fho2hSuuAL++MeoE0ldnXgidO4M\n8+fDk0/CRRdFnUhCVFJSQklJSdQxRPLKKUBzvqOUHnzGnlHHyQnPcQZ/5KZgSYXNm6GoKOpIkmfM\n01jK1cw6AWPd/dBqHusPXOXu/c2sJ3Cnu/es5jhP57kkx1x1VXCS+aWXwr/+lVijP91/53SPzUSb\nen4wKn4mH344+Dc8+GB4773gPBvJS2aGu+vEt2qon5J0PWTGpcCN/Jm/cmOVR2v6HK7tM7q+35vt\nx+rzvc4i9mNfFsObb0IvLSok1atvP5XOks5PAFOBA83sEzO71MyGmtlQAHcfByw2s0XAcOCKuoaQ\nHPX118EvwwD/9V/RZpGG+eEPoX17mDcvGHkTEZHqbdpUMeFM59PUhVVMQWO0VkGT8KWz+tn57r6n\nuzd19w7u/pC7D3f34ZWOucrd93P3w9x9ZmYjS2wMHw7r18Mpp8Ch2wziSS5p2hSuuy64/Ze/aDNO\nEZFUxo9nV+ADDmQeB0edJqdUFDXPPqt+RkIXxjk1kueCKWVb2x74GNgVOG3CBMZXc4zEX+V/2xbA\nf4A2b7/NiY0aMbHScZqSIyKS8NhjAIzgYrSFQd1M5ViWA+0WL4apUzUFTUKlifOSJt/qchV/ZVfg\nLXoynvJKj0lu2fJvuh7nTv4EwG84Gf2biohUsWZNxdSpx7kw4jC5p5wiHk/eefTRKKNIHkproYBQ\nnkgnYOasqif/t2QtS+jELqziVF5hAqdWPprwT2rP3xP14/b8rfmapXSkFd9yFG8zg6PYakEByXla\nKCA19VNSq3/9C376UyYCJ8bi5PuoHqv/93bGmAewww6wYgU0b17Dc0ghythCASJV/YK72YVVvEkv\nJnBK1HEkRKvZifu4HIDfJ0ZtREQkYcSI4CriGLlsPsBRR8E332jBAAmVihqpkx1Yw3XcDsBN3Izm\nE+efO7iWdbRgEGM5lilRxxERiYclS2DyZGjenFFRZ8l1P/pRcK0paBIiFTVSJ7/kLnbmayZxPK9z\nYtRxJAM+Z3f+h18B8P+4PuI0IiIx8XjibJAhQ1gbbZLcd9550KQJTJgAn34adRrJEzqnRmqVPKem\nNV/zMXvTmjWcQAmTOaG6o8nlc0r0/IGWrOUj9mU3vuRM4Fn97OaNQj6nxsweAgYAX6TYTFr9lFSo\nuvLnAuAAoC/wChCn81Ry6ZyaivM0zz4bRo2CW2+FG26o4Xmk0OicGsm4YQyjNWt4jRNTFDSSL76l\nFTdzEwB/BSgrizSPSEgeJvidVCRNwSqQR/MWBwCfsTuvos/DUCSnoD3yiPaskVCoqJG0HMz7XMm9\nbKYR13JH1HEkC+7nMhayHwdCsOKPSI5z9zeAr6POIbnnJwSfgf+fvTuPj6ss+z/+udJ0L4VS6EIp\nSzc2oVCkIFuDoNaC6CMg9EFZ9BEV4VEUBVwguP0eRBCQRUBBUEqRigpYQRQCWKBFukL3QuneUgrd\n0zTJ9fvjzEymIZNMMmfmnJn5vl+v6ZyZOTnn6nll5s41931f9wT+mwYt8ZczM6PzmWeyDmDePI6p\nqMDMWlwXTyRbSmokK7fyDSpp4Nd8ldmMjDocKYB6OnNN0E8D1dWwZUuk8YiIRGFv1vEFggU37+XL\nEUdTKpx6nD9wBQBf42K0LprkSkmNtOm/gNP4F++yJ9fyo6jDkQL6E2fxCsDatdy4226pb9Jau4mI\nlJJLuZNu7OAJzmABB0cdTkm5k0tpxPg8f2AgKhgguVEfqrRu+/bUYLMf8mM20DfScKTQjMuAqVTw\nLeBhXmUGo1rdX6SYVVdXp7arqqqoqqqKLBaJXje283XuAEhVhZTwLGEYj/FZzuZP/C+3cU3UAUkk\nampqqKmpyfk4qn4mrfvRj+C665jFERzNa1mMJS6N6l86/6773cQVfItfMp2jGM20Vn4PElVtJLbK\nufoZgJkdADyh6mfSFjPjy9zNPXyF1xjFh/kPTV/cxK+iWDFVP0t/bTRTmcpxvM/uDGYjm/UeLHt5\nrX5mZmPNbL6ZLTKzq1p4vcrMNprZjMTtB+0NRGJo9mz46U+BYH0aTY4sX9fyI5ayP6OYwTe5Jepw\nRDrEzB4GXgJGmNlyM7s46pgkvgxShXGCXpqy/S4gr6ZxLM9zMnuwUTOWJCdt9tSYWSeC8uynASuB\nV4Hx7j4vbZ8q4FvufmYrx9E3YMVkxw4YPRpmz+Yu4NIy76nQ+Z1PMpnJnM42unMYb7CGikmMAAAg\nAElEQVSUA1vcV+/zeCv3nprWqJ2SdGeY8SSwnH0ZwpvU0znt1Xj3fuT/tXCPezpP8iSfYhmwX11d\nsDCnlK189tSMBha7+1J33wlMBD7dUgztPbnEWHV10FMzdChXRh2LxMLfGcfDnEcPtnMPl2A0Rh2S\niEjeJGfQ3Mo3miU0ErbJjGMuh7AfwCOPRB2OFKlskppBwPK0xysSz6Vz4Hgzm2Vmk83s0LAClAhM\nmQI//zlUVMCDD7It6ngkNr7JLaynLx/jn3yXn0cdjohIfkyZwinAJnZTGecCcCr4RfIr1J//XItx\nSodkk9Rk85s1HRjs7iOBXwF/ySkqic6WLcEqv42NcNVVcPzxUUckMbKO/lzIAwD8hB9wIi9GHJGI\nSMgaG+GKYP2UW/kGm9g94oDKw0Ocz0qAOXNgwoSow5EilM3M75XA4LTHgwl6a1LcfXPa9t/N7E4z\n29PdN6Tvp1KZMecOF18MS5bAyJHBEDSRZiZzOjfwXa7i50zkPI5kJuvZO+qwJIOwSmWKlI2HHoJX\nX2UVcAMfqI0keVJHV74P/A7gu9+FT38aevWKNigpKtkUCqgkKBRwKrAKmMYHCwX0B9a5u5vZaOCP\n7n5As+NoAmbc/fjHcO210Ls3TJ0KBweLjAULKkY/UV3nj8/5K9nJc5zCiUzhKT7BOCbjVKBCAfGn\nQgGZqZ0Stm6Fgw6ClSu5CHigiCff5/e1/BzXMBqPOQZefRW+971UBVYpL3krFODu9cBlwNPAXOAR\nd59nZl8xs68kdjsbmGNmM4FbgPPaG4hE7M9/DhIaM5g4MZXQiLSkns6M52HW05exPM2P+WHUIYmI\n5O4Xv4CVK2HUKB6MOpYy5AC33ho8uOkmePPNKMORIqPFNyWocnb88cE3VDfeCFfuWu9MPTU6f6b9\nPs7T/I3TqaSBy/gVd3C5empiTj01mamdKnMrV8KIEbBtG7zwAnbyyZRC70exxeru8IUvwB/+AP/1\nX/DYY63EIKWoo+2UkpoyZmbsD7wA7Af8Hrgg497x/KNa54/+/BdxP/fzRRoxzsP5o97nsaakJjO1\nU2XMHcaPD8oJn302PPpoG1/oFVeiUEyxunuQYB50UPBl6zPPwGmntRKHlJp8rlMjJWo/oIb92Q+Y\nwvF8me0EHzTNbyKZ/Y6LuYafUYHze4Dnnos6JBGRrJgZZsbFFRXwyCNsBYZMmpRIaCQygwYFc2oA\n/ud/YMOG1vcXQUlN+Vq2jOeAA3ibVziWT/J3dtAt6qikSP0fV3Mbl9MV4Mwz4dlnow5JRCQrh/AG\nt9MDgEv5HW/pC71IJRPNLt//PlMB3n6bJ/r2pUKJprRBSU05WrYMTjmFIcBURvMJnmYzvaOOSoqa\n8U1uCXpqtmyBT34SJk2KOigRkVZ1Ax7hXHqyjQf5Ag9yYdQhSSKp3IlzLm+xgT58Cvh21GFJ7Cmp\nKTcvvQTHHANvvsmrwCd4WguLSSiciuDPgcsvh7o6+Nzn4K67og5LRCSjW4DDeZ0FjOBS7ow6HGnm\nbQ7ggkQduv8H8KIWfJbMlNSUk/vvh1NOgXXr4KMf5ePARvaIOiopIalynD/9aTDx9tJLg2p6O3dG\nHZqIyK5uv52vALV05VweYSta6DGO/sYZ3MB3g9XizzsPli+POiSJKVU/Kwc7dsDVV8MttwSPL78c\nbroJ69KFUqi+pfPH7fyBLwG/BiqBV4DxwNJme+szofBU/SwztVOlJ9OE/68CyX7kL/Eb7uNLLf00\npVJRrNhjrWQn/6ILJwMceGBQkGb//VuJTYqZqp9Jy6ZNg6OPDhKazp3hnnvgttuCbZG8CMZD/xZn\nDP9mGYM5DphJb87hkdTrIiKFsWtFz0v4dSqhuQwyJDQSJ/V05tMQDJ9/6y0YM0YLc8oHKKkpVbW1\ncNVV8JGPwBtvBAuKPf88fPnLUUcmZeQlTuBIZvJnPsPubOKPnMvjfIqhLI46NBEpQ1/lLu7mqwD8\nL7dyR8TxSPbeh2DNmuOOg7ffDhKbxWpLpImGn5WYSjMuBK4jWIemAbgZuBaobfEnSnH4k84fv/M7\nX+Mu/o+r6c1mdtCFm6njms2boZfGsReShp9lpnaq9CQX0OzFZu7kUr7AHwC4gpu5hSso5yFdub0W\nTTzuDps2wbhxMGUK9OkD994LZ53VSpxSbDT8rNzV18PEibwB/JYgoZnFERzPK3wXp1aLakqkjLu4\nlBEs5H4uoit1XANwwAFQXQ3r10cbnoiUrFG8xnRG8QX+wFZ6cBH3JxIaKUq9e8NTT8Hpp8N778HZ\nZ8OXvhQsJyBlTT01xW7lSvjNb4JvKlauBGARw7iWH/EI5+Kt5q3l1FOg88fp/KOZyi85juOTT3Tv\nDl/8YjA88ogjQIus5Y16ajJTO1V85syZw80330lj4wdf61lby/5//B1X0Jku7GQWR3AeE5nPIWl7\nqfejmGLd5f3pDnfcEVTY3LEDhg6Fm24KFoBWG1LUOtpOtZnUmNlYglLunYDfuPsNLexzG/BJYBtw\nkbvPaGEfNRZheecdePxx+POfg28rGhqC50eM4JKFC7mfOurJphBA+f5RrfPH4/z+/PNwww0weXLT\n0x/6EHz+83DuuUFPjoSqnJOattoztVPF529/+xtnn30VtbVfTz3Xm+18i39xBf+iNzsAuJ2vcyW/\nYAfdmh1BiUJxxfpBhwITgJHJJ448MhgBoOSmaHW4nXL3jDeCD/7FwAFAZ2AmcEizfcYBkxPbxwKv\nZDiWS8uee+651nfYutX92Wfdr7/e/eST3Ssq3IPvKNwrK93PPtv9n/90b2xMjCvzLG/Z7puPY2a7\n73MRnz/q/39r+z1X9P//lNmz3b/2Nfe+fXfdacQIvw38DPA+tDiG8gO3rN5TZSxxjSi3W5btWc7X\nt1TF9T315JNP+u67j/NO7PRP8Hd/gC/4JnqlPkMmg3+YaR38zMr2tedCOmZY8RTitWx/tvm1yU88\nXaj1y8BXpj35Bvj3wYfR1DbESVzfU3HQ0XaqrTk1o4HF7r7U3XcCEyGoqpfmTOCBRGswFdjDzPq3\ncVxJU1NTE2y4w9q18MILcPvtcMklcOyxsMce8NGPwnXXBa916gSf+AT8+tewYgU8+iicemqJfiNR\nE3UAMVYTdQDhOfxwuPNOWLUq6IU891zYfXdYuJDLgSeADcAihjKB8/g2N3I6TzCURXRiJzSbJ5Z6\nT4k0yaY9kwxi955yh7lzGfzUU9y9bSar2Ien+CQX8Ht2YwvPcgon8hjjgP9wTJ6Dqcnz8YtZTUHO\nUkdXbgeGsJ3LuY1VDORQ4CfAIuA1CNbre+KJ2MzhjN17qgRUtvH6ICB96dYVBL0xbe2zL7A25+hK\nQUNDMHlt82bYsCF1m/mPf7BpwQJ6bd7Mu2+9xbq77mKP996jSwsrr7sZHHUUdtJJcNJJ8LGPBX/w\niRS5TAvjQfC1+mjg48BpnMAopjOMJQxjCeOZmNpvB11Yxn4sY7/gg+gHP4DXXoOHH4a994a+fYP3\nS/JW2dbHnpSobNoziQv3oN1cuxZWrw5uS5fCggUwfz7Mmwfvv88RwBGJH1nACB7ifCbw3yxhGLAy\nuvglEjvoxu1czt18hdP4J+cxkc/wF0axORjqnLAEmA8sTNzuevJJ6N8fBgyAfv2gS5eI/geSi7Za\nd2/j9aTmf5m0/HNXX53l4bLknvlxptdSvZhk6sWExsamW0ND033yVl8PO3c23erqgtuOHbB9O2zb\nFtxv3Rpst+DItO3HgX6J7XfpxhL2YA57MYt+zGYvZvgfeeeVV+iiN5mUnMwfMQ3Ay8DLGNfzbzpR\nz2G8wTG8ypHM5CAWcBAL2I/lDGcxw5Nr3/z0p8H9U0+1fOCuXaFHD+jZM7jv2hW6dQvuu3QJFqZN\n3ldWBj2jyfuKig/ezJru02/Q8n3zRC79cUn2tsZGdu1Z2O1UqXjxxaBdS0pvR5P3mdrS9PazoWHX\n9jPZbiZvmzfDxo3BLTlfNJOBA1k1bBi/fPUdnq59kDl8iKY/R2rJtJCBlL6ddOHvjOPvjKMrtXyU\n7pzINRzPS4xmGkPZzlDg9OQPnHHGrgfo3r3pi7CePYPHyVvnzk3tRLJtSLYPnTplbhOatwdTpuz6\nntLnf85aLRRgZscB1e4+NvH4GqDR0yZXmtmvgRp3n5h4PB8Y4+5rmx0r2wRJRETyyMuwUECW7Zna\nKRGRGOhIO9VWT81/gOFmdgCwCjgXGN9sn8eBy4CJiUbj/eYJTUeDExERCUmb7ZnaKRGR4tVqUuPu\n9WZ2GfA0wRD337r7PDP7SuL1u919spmNM7PFwFbg4rxHLSIi0g6Z2rOIwxIRkZAUbPFNERERERGR\nfGirpHO7mdlYM5tvZovM7KoM+9yWeH2WmR0Vdgxx1da1MbPzE9dktplNMbMjWjpOKcrm9yax3zFm\nVm9mny1kfFHK8j1VZWYzzOx1M6spcIiRyeI9tbuZPWFmMxPX5qIIwiw4M7vPzNaa2ZxW9inLz2FQ\nO9UatVOZqZ3KTO1UZmqnWpaXdqoji9tkuhHiYp2ldsvy2nwE2D2xPVbXpsX9ngWeBM6KOu64XBtg\nD+ANYN/E472ijjtG1+Z7wP9LXhfgXaAy6tgLcG1OAo4C5mR4vSw/h9vxe1OW10ftVG7XJm0/tVNq\np9pzbdROtfx6uz+Hw+6p0WKdmbV5bdz9ZXffmHg4lWC9n3KQ7aJ4lwOTgHcKGVzEsrk2/w38yd1X\nALh7PFYWy79srk0j0Dux3Rt4193rCxhjJNz9ReC9VnYp189hUDvVGrVTmamdykztVGZqpzLIRzsV\ndlLT0uJmg7LYpxw+FLO5Num+BEzOa0Tx0ea1MbNBBB8EdyWeKpfJYNn83gwH9jSz58zsP2b2hYJF\nF61srs3twKFmtgqYBXyjQLHFXbl+DoPaqdaoncpM7VRmaqcyUzvVce3+HA57ae1wF+ssLVn/H83s\nFOCLwAn5CydWsrk2twBXu7ubmfHB36FSlc216QyMAk4FegAvm9kr7r4or5FFL5trMxaY7u6nmNlQ\n4BkzG+num/McWzEox89hUDvVGrVTmamdykztVGZqp3LTrs/hsJOalcDgtMeDCTKr1vbZN/Fcqcvm\n2pCYdHkvMNbdW+uWKyXZXJujCdZCgmDM6SfNbKe7P16YECOTzbVZDqx39+3AdjN7ARgJlHpjkc21\nuQj4fwDuvsTM3gIOIlizpJyV6+cwqJ1qjdqpzNROZaZ2KjO1Ux3X7s/hsIefpRY3M7MuBIubNX8z\nPw5cAKkVnltcrLMEtXltzGw/4DHg8+6+OIIYo9LmtXH3Ie5+oLsfSDBe+Wtl0FBAdu+pvwInmlkn\nM+tBMKFuboHjjEI212YZcBpAYizuQcCbBY0ynsr1cxjUTrVG7VRmaqcyUzuVmdqpjmv353CoPTWu\nxTozyubaANcCfYC7Et/07HT30VHFXChZXpuylOV7ar6ZPQXMJphweK+7l3xjkeXvzY+B35nZbIJu\n7O+6+4bIgi4QM3sYGAPsZWbLgesIhn+U9ecwqJ1qjdqpzNROZaZ2KjO1U5nlo53S4psiIiIiIlLU\nQl98U0REREREpJCU1IiIiIiISFFTUiMiIiIiIkVNSY2IiIiIiBQ1JTUiIiIiIlLUlNSIiIiIiEhR\nU1IjIiIiIiJFTUmNiIiIiIgUNSU1IiIiIiJS1JTUiIiIiIhIUVNSIyIiIiIiRU1JjYiIiIiIFDUl\nNSIiIiIiUtSU1Ii0g5kdYGaNZrY57fb9ZvvcYGbrE7f/iypWEREpfWbW2cwmmdlbifZpTAv7ZGyX\nEu3ac2a21czmmdmphYteJDyVUQcgUqR6u7s3f9LMvgJ8Gjgi8dQzZvaWu99d0OhERKScvAD8EngU\n2KVtyqJdehiYAowFTgcmmdlwd19fkMhFQqKeGikrZrbUzL5tZrPM7H0zm2hmXTtwqEzvnQuBX7j7\nKndfBfwCuKij8YqISGnLtV1y953ufpu7TwEaWtglY7tkZiOAo4Dr3H2Huz8GzAbOyvX/JVJoSmqk\n3DhwDvAJ4ECCb64uMrPBicbkvQy385od520zW25m95lZ37TnDwVmpT2eDRyWz/+QiIgUtbDapUxa\na5cOA950961pr89C7ZYUIQ0/k3J0m7uvATCzJ4AjE93we2Txs+8AHwZmAnsBdwAPEXTbA/QCNqbt\nvynxnIiISCa5tEttaa1dav5a8vVBIZxXpKCU1Eg5WpO2vR3YJ9sfTHybNT3xcJ2ZXQasNrOeide2\nAL3TfmT3xHMiIiKZdLhdykJr7VLz1yBIpDaFeH6RgtDwMxEg0c2/pVlVs/Tb+DYOkXwvvQEcmfb8\nSOD1vAQtIiIlK4R2Kam1dukNYIiZ9Wr2+hu5/w9ECks9NSKAuy8ni2FiZjaaoKt+EdAHuA14zt03\nJ3Z5EPiWmU0GDPgWcGteghYRkZKVbbsEkCgsYImHXc2sm7vXJh5nbJfcfaGZzQSuM7MfAuOADwF/\nCu9/IlIYSmqk3DnNyl+2YQjwM6AfQff8P4DUt2XufreZDQHmJJ66193vCSlWEREpfe1tlwAWAPsl\nfu5pwM3sQHdflkW7dB7wO2AD8DZwlru/m8t/QCQK1sJSG5l3NruPoIb5Onc/PPHcjcAZQB2wBLjY\n3ZtPOhMREcm7ltqptNe+DdwI7OXuG6KIT0RE8qO9c2rup6nKU9I/gMPcfSSwELgmjMBEREQ6oKV2\nCjMbDHyM4JtoEREpMe1Katz9ReC9Zs894+6NiYdTgX1Dik1ERKRdWmqnEm4GvlvgcEREpEDCrn72\nRWByyMcUERHpMDP7NLDC3WdHHYuIiORHaIUCzOz7QJ27TwjrmCIiIrkwsx7A9wiGnqWejigcERHJ\nk1CSGjO7iKAM4Kmt7NPeSh4iIpIH7l5Of9QPBQ4AZpkZBEOkXzOz0e6+Ln1HtVMiIvHQkXYq5+Fn\nZjYW+A7w6bSa6C1yd91auF133XWRxxDXm66Nro2uTbi3cuPuc9y9v7sf6O4HAiuAUd4soUnbX7cW\nbnpP6dro2ujaFOrWUe1KaszsYeAl4CAzW25mXwR+RbA41DNmNsPM7uxwNCIiIjlIa6dGJNqpi5vt\nUn6ZnYhIGWjX8DN3H9/C0/eFFIuIiEhOMrRT6a8PKVQsIiJSOGFXP5MOqKqqijqE2NK1yUzXJjNd\nG5Fw6T2Vma5NZro2menahM9yGbvWrhOZeaHOJSIiLTMzvLwKBWRN7ZSISPQ62k6pp0ZERERERIqa\nkhoRERGRYrd9O/z+93DiidCtGzz7bNQRiRSUkhoRERGRYuUO114LgwbBBRfAlCmwYwc89ljUkYkU\nlJIaERERkWK1YAH8+Mfw3ntw9NFw6aXB87NmRRuXSIEpqREREREpVm+8EdyPHQv/+Q/88IfB49mz\ng14ckTKhpEZERESkWM2dG9wffnhwP2AA9OsHmzbB229HF5dIgSmpERERESlW8+YF94cc0vTcEUcE\n97NnFz4ekYgoqREREREpVsmk5tBDm54bOTK417waKSNKakRERESKUUMDzJ8fbB98cNPz6qmRMqSk\nRkRERKQYvf021NbCPvvA7rs3PZ9MatRTI2VESY2IiIhIMUoWCUgfegbB/JrKSli8GLZuLXxcIhFQ\nUiMiIiJSjFoqEgDQtWswHM0dXn+98HGJREBJjUgGZtbirb37iIiI5EWmnhpoKhageTVSJpTUiLTK\nm906uo+IiEjIMvXUgObVSNlRUiMiIiJSbNzVUyOSpjLqAERERESknVatgs2boW9frF+/XV5y913L\nOruDhkZLiVNPjYiIiEixSfbSpIaeNRsCPWAA7L03bNwIy5YVOjqRglNSIyIiJcXM7jOztWY2J+25\nG81snpnNMrPHzGz31o4hEkfpBWn+9+MfD55sYeiZmWEVFfzznXeCJxJD0FTURkqZkhoRESk19wNj\nmz33D+Awdx8JLASuKXhUIqEIemSS/TPfvOeejPvM4lvBw12KBaiojZQmJTUiIlJS3P1F4L1mzz3j\n7o2Jh1OBfQsemEiIkv0zc3k64z6zSZtXI1LilNSIiEi5+SIwOeogRHKR7KmZRwvlnBNSSY3KOksZ\nUFIjIiJlw8y+D9S5+4SoYxHpqL6spx+wmV6saKXTcS6HUg+waBFs316o8EQi0a6SzmZ2H3A6sM7d\nD088tyfwCLA/sBT4nLu/H3KcIiIiOTGzi4BxwKmZ9qmurk5tV1VVUVVVle+wRNrtEIJFN4NemswT\n/uvoykpgf/egBLRIDNXU1FBTU5Pzccw9+8liZnYSsAV4MC2p+Tmw3t1/bmZXAX3c/eoWftbbcy6R\nqAWVYZr/zhrpv8fZ7CMSJ2aGu5d82SMzOwB4Iq2tGgvcBIxx9/UZfkbtlMRass25hLu5m6/yABdw\nEQ8QJDbJ391d26UpGMcDPP88NmbMLvvp913iqKPtVLuGn7U0+RI4E3ggsf0A8Jn2BiEiIhIWM3sY\neAk4yMyWm9kXgV8BvYBnzGyGmd0ZaZAiOUj21Mzlg+Wcm0v1z6inRkpcu4afZdDf3dcmttcC/UM4\npoiISIe4+/gWnr6v4IGI5MlBLABgPge3ue/K1MbK1nYTKXphJDUp7u5mpr5MKSnDWcj+vE13ttMd\n4Mkn4fTTQQuXiYhIBAYlUpVl7NfmvuqpkXIRRlKz1swGuPsaMxsIrMu0oyZgSrE5gllMZxSdaGx6\n8lOfggkTYHxLXwaLxEtYEzBFJD4GshqA1Qxsc1/11Ei5aFehAGhx8uXPgXfd/QYzuxrYQ4UCpBSY\nGTdxBd/ilyxgBAsZwR48yUkAH/84PP20CgVI0SmXQgEdoXZK4s7M6EItO+hGPdCVehrpRGuFAk7B\neBbgpJOwF19EhQIk7jraTrW3+tnDwBhgL4L5M9cCfwX+COxHKyWd1VhIselkxnIGsg+rOZZXmMax\n9MHY0LkzNDTAypXYwIEoqZFioqQmM7VTEndmxn4s5W0OYAUwuMVEZtekZgTGAmAJMAxQUiNx19F2\nql3DzzJMvgQ4rb0nFom7k4F9WM0ShjCN0UCi9N+4cfDXv8Ijj0QZnoiIlKGmoWfZSc6k2YduQG0+\nQhKJhXaVdBYpJ8kMfiLnscviZuefH9z/4Q+FDklERMrcPok0Jdtp/1uATexGd2rpk7eoRKKnpEak\nJXV1nJ3YnMB/7/raGWdA797wn/8wouCBiYhIOWtvUgOwkkGJnxUpXUpqRFry9NPsCczmcOZy2K6v\nde8OZ50FwPmFj0xERMpYe4efAaxKpDOD8hCPSFwoqRFpycMPB3dkmEaWGIIW/KuJliIiUhi59NQo\nqZFSpqRGJMHMMDN6mrE1kdQE82laUFUF++zDUOBYphYsRhERKW8afibSMiU1IrtwzmQCPYGXgKUc\n2PJunTqlFt/8PCoYICIihaHhZyItU1Ij0sx5TARgQls7Joagnc0kNARNREQKQT01Ii1TUiOyC+dk\nXgCCVWVbdeSRrAcGsJZ9WZHvwEREpMx1AfbiXerpxDvt+Dn11Eg5UFIjkmZ/3qYP77OWfm2nKWZM\nT2yOSm2JiIjkx4DE/RoGtGt8gHpqpBwoqRFJk0xOZnBUVvsrqRERkUJJJiWr2pmerGEAjRj9gU7U\nhx6XSBwoqRFJcxQzACU1IiISP8lUZjUD2/Vz9XRmHf3oBPRnbehxicSBkhqRNMnkZDqjstpfSY2I\niBRKMpVpb08NpK9VszLEiETiQ0mNSJr29tS8CWykN4NYRX/W5DEyEREpdx0dfpb+M0pqpFQpqRFJ\n6A/sw2o20ps3GZLVzzhNCVAyIRIREcmHjg4/g/RiAe0pBi1SPJTUiCQk+2ZmciTejrdGcqiahqCJ\nRM/M7jOztWY2J+25Pc3sGTNbaGb/MLM9ooxRpKNyGX6mnhopdUpqRBKSs2iynU+TpKRGJFbuB8Y2\ne+5q4Bl3HwH8K/FYpOjkMvxMPTVS6pTUiCQke2qynU+TlNxfSY1I9Nz9ReC9Zk+fCTyQ2H4A+ExB\ngxIJSRjDz9RTI6VKSY1IQkd7ahZwENvozoEspQ8bwg9MRHLV392TdWzXEkyhEykuO3bQF6inE++w\nd7t/PNm7o54aKVVKakQA3nuPIcB2ujGfg9v1ow1UMouRgIoFiMSduzu0azF2kXhYvTq4Y2C75n0m\nqadGSl1l1AGIxMLMmQDM5ggaOvC2mM4oPsIrjGI6z4Ydm4jkaq2ZDXD3NWY2EFiXacfq6urUdlVV\nFVVVVfmPTiQbaUlNR2xgT2qBPdhID7ayLcTQRHJRU1NDTU1NzsdRUiMCMKN969M0p2IBIrH2OHAh\ncEPi/i+ZdkxPakRiZVUwbKwjRQICxipgCMEQtMVhxSWSo+ZfIF1//fUdOo6Gn4kATA+SESU1IsXN\nzB4GXgIOMrPlZnYx8H/Ax8xsIfDRxGOR4pJzUkNq4Jnm1UgpUk+NCKR6atpbJCDpDQ6jjs4cxEJ2\nCzMuEWkXdx+f4aXTChqISNhyHH4GpFIZzauRUqSeGpFt22D+fOqBORze5u5mlrol7aRL6mdH5itO\nEREpXyH21CipkVIUWlJjZleY2etmNsfMJphZ17COLZJXs2dDYyNzgR10y+IHPO3WJNnLc3TY8YmI\niISQ1CR7ajT8TEpRKEmNmQ0CLgeOdvfDgU7AeWEcWyTvEpXPci3GPJsjADgsx+OIiIh8QIjDz5TU\nSCkKc05NJdDDzBqAHqC+TSkS8+cDMDfHwyzgIIDEvyIiIiEKoadmTeK+P2tb3U+kGIXSU+PuK4Gb\ngGUEXwS87+7/DOPYInm3YEFwl+thEunMiByPIyIisovaWtiwgZ3Aevbq8GGSqYySGilFYQ0/6wOc\nCRwA7AP0MrPzwzi2SN4tXBjc5XiY5QxmG90ZALBxY65RiYiIBNYEfSxrAM/hT7dkKjMg1WcjUjrC\nGn52GvCWu78LYGaPAccDD6XvpJWaJXZ27IClS6GigiWNjTkdyqlgEcMZyeyg93nXNlIAACAASURB\nVGf06HBiFMlBWCs1i0iEUkPPcrMB2EklfXifLjkHJRIvYSU1bwPHmVl3oJYgyZnWfCet1Cyxs3gx\nNDbC0KHULVmS8+EWcJCSGomVsFZqFpEIpYoE5MaBdfRjEKvol3NQIvES1pyaacAkYDowO/H0PWEc\nWySvEvNpOCic6f3JeTWp44qIiOQqbfhZrtbSHyDxr0jpCG2dGnevdvdD3P1wd7/Q3XeGdWyRvFFS\nIyIicbc2mA0TxvT+ZFIzIIRjicRJaEmNSFFSUiMiInEXYlKzJpHOqKdGSo2SGilvicpnoSc1ixYF\nc3VERERylRh+FmZPjZIaKTVKaqS8JXtURoSzusxmegcTOWtrYdmyUI4pIiJlLtFTozk1IpkpqZHy\ntX49bNgAvXrBwIGhHTY18ExD0EREJAx5GH6mOTVSapTUSPlKn09jFt5hmx9fRESko9w1/EwkC0pq\npHyFXCQgddjmxxcREemozZuDIc09erAlhMMpqZFSpaRGylfIRQKSlNSIiEhoEkPP6B9OGqKSzlKq\nlNRI+VJPjYiIxF1i6FlYSc0G9mQnlfQB2LEjlGOKxIGSGilfeUpqlgJ07gwrVsDWraEeW0REykyy\np2ZAOH0rTgXr6Bc8WLculGOKxIGSGilP9fWweHGwPXx4qIduABg2LHiQHOImIpEzsyvM7HUzm2Nm\nE8ysa9QxibQp5OFn0DQELXVskRKgpEbK09KlsHMn7Lsv9OwZ/vGTvT8agiYSC2Y2CLgcONrdDwc6\nAedFG5VIFkIefgZpSc2aMFa+EYmHyqgDEIlEnoaepSipEYmjSqCHmTUAPYCVEccj0raQh59B01o1\n6qmRUqKeGilPeap8lnTxDTcAMKG6GgtxDRwR6Rh3XwncBCwDVgHvu/s/o41KJAsafiaSFSU1Up7y\n3FOzkH8Hh2dUXo4vIu1jZn2AM4EDgH2AXmZ2fqRBiWRh6uOPA3DCWWeFdkwNP5NSpOFnUp7ynNQs\nIDjuCFQoQCQmTgPecvd3AczsMeB44KH0naqrq1PbVVVVVFVVFS5CkRYk+2fWsBgYFsoxNfxM4qSm\npoaampqcj2Punns02ZzIzAt1LpE27bMPrF4Nb70FBxwAkBgmlv472vxxS89l3mc9fenLBgYBK/W7\nLzFhZrh72Y2JNLPRwH3AMUAt8DtgmrvfkbaP2imJF3e2V1TQHejFZrayG01tjmWx3fJrp/Asz3Iq\njBkDIfwxKRKmjrZTGn4m5Wfz5iCh6doVBg/O22kWMgII63s1EcmFu08DJgHTgdmJp++JLiKRLGza\nRHdgKz3YSq/QDqs5NVKKlNRI+VmyJLgfOhQ6dcrbaRYn0hklNSLx4O7V7n6Iux/u7he6+86oYxJp\nVSLpSA0XC+uwmlMjJUhJjZSfRYuC+2H5TTcWESzqGe7SniIiUjYSSU0qCQnJBvZkJ8D778OOHaEe\nWyQqSmqk/CxeHNwPz2+6oZ4aERHJSaInJeykxqlgXfLBunWt7SpSNJTUSPlJ9NR89aabMLPULfTT\nqKdGRERykafhZwCp2TQagiYlQkmNlJ9ET80i/klQESZ5C/k06T01qqgkIiLtlafhZwCpVEbFAqRE\nKKmR8pPoqVmc54Fh79OH9fSlJwTV1kRERNojT8PPgmMmN5TUSGkILakxsz3MbJKZzTOzuWZ2XFjH\nFgnNli2wZg21wHLyV845KZU4JefxiIiIZKsQw8+U1EiJCLOn5lZgsrsfAhwBzAvx2CLhSCQXbxJM\nlMy35LyaVMU1ERGRbOVx+Jnm1EipqQzjIGa2O3CSu18I4O71wMYwji0SqtR8msJIJTXqqRERkfbK\n4/AzzamRUhPWV9UHAu+Y2f1mNt3M7jWzHiEdWyQ8ieSiUClGaviZempERKQ93AvTU6OkRkpEWElN\nJTAKuNPdRwFbgatDOrZIeBLJhXpqREQk1jZtgh072AJspVfoh1dSI6UmlOFnwApghbu/mng8iRaS\nmurq6tR2VVUVVVVVIZ1eJEtR9dQsXhx865aH9XBEWlNTU0NNTU3UYYhIe6WGnuXp8M3OI1LszENa\nP8PMXgD+x90Xmlk10N3dr0p73cM6l0iH7bMPrF7N/sCyD6xNY+y6Xk3zxx3b5x2MvQBWrYKBAzse\nu0gIzAx3V3bdArVTEisvvABjxjAFODHVpqS3L9lsZ37NMBorK6G+HmproWvX/Pw/RNqpo+1UmOWf\nLgceMrNZBNXPfhbisUVyt3VrsF5Mly6sKOBpU71CmlcjIiLZSs2nyQ8HVtbXAzC4W7c8nUWkcEJL\natx9lrsf4+4j3f2z7q7qZxIvyXktQ4fSWMDTplIZzasREZFs5Xn4GcAaRgHkYRUckcLL/0IdInGR\nTCqGDSvsaZMb6qkREZFspRbezJ/VBEOiNTBaSoGSGikfyaRi+PDCnja5oZ4aERHJVp6HnwGsYh+A\nxL8ixU1JjZQP9dSIiEixKMDwMyU1UkqU1Ej5iENPjSoriYhINgow/ExJjZSSsNapEYktS6wNswIY\nBBzwsY8V9PzvA+y5J2zYEHzzprLOIiLSFg0/E2kX9dRIWejBFgYBO+jCcuoLH0Cyd0jzakQiY2Z7\nmNkkM5tnZnPN7LioYxJpUWNjsLYZsDqPp1FSI6VESY2UhaEsAeBNhtBIp4Kf/w9TpwJw8cknY2ap\n3iMRKahbgcnufgjBemrzIo5HpGXr1weLYu65J7V5PI2SGiklSmqkLAxPzGxZRGHn0yQtojoRxzXs\nutKziBSCme0OnOTu9wG4e73WU5PYWrkyuN8nv+nGO+xNAxX0A6iry+u5RPJNSY2UhWGJGmSLKWzl\ns6TkeYejCmgiETkQeMfM7jez6WZ2r5n1iDookRYlk5pBg/J6mkY6sSa59OaafJYkEMk/JTVSFkaw\nEIguqVnIiF3iEJGCqwRGAXe6+yhgK3B1tCGJZFCgpAaahqAl5/CIFCtVP5OycBALAFjAQZGcP3ne\n4SzCaNQANJHCWwGscPdXE48n0UJSU11dndquqqqiqqqqELGJ7CqZYOR5+BkoqZHo1dTUUFNTk/Nx\nlNRIWYg6qdlMb1YzgIGsYTDLWRZJFCLly93XmNlyMxvh7guB04A3mu+XntSIREY9NVJGmn+BdP31\n13foOBp+JiWvD7A369lCT1aS/wYik2RClUywRKTgLgceMrNZBNXPfhZxPCItU1Ij0m5KaqTkJftm\ngnkt0ZVSTs6rUVIjEg13n+Xux7j7SHf/rKqfSWwlEwwlNSJZU1IjJS+Z1EQ19CxJPTUiIpKVApV0\nBiU1UjqU1EjJU1IjIiJFo7YW3n0XKiuhX7+8n05JjZQKJTVS8pTUiIhI0Vi9OrgfOBAq8v9nWiqp\nSZ5XpEgpqZGSF5ek5i0OpI7O7MdytOKfiIi0qIBDzwDepS91ABs2BL1EIkVKSY2UtoaG1HKbyYn6\nkYVCJUsYChDREqAiIhJ7Bax8BuBUkOqjUW+NFDElNVLali6lK7CCQWylV9TRpA1BExERaUEBK5+l\nTtn83CJFSEmNlLYF0S662VxTWWcREZEWFLinBpTUSGlQUiOlLWZJjXpqRESkVQWeUwNKaqQ0KKmR\n0qakRkREiol6akQ6REmNlLY4JzXukcYiIiIxpDk1Ih0SalJjZp3MbIaZPRHmcUU6LGZJzXr2YgN9\n6A2wZk3U4YiISJy4p3pqdjv4YMysIKdN1TxTUiNFLOyemm8AcwF9BS3R27QJVq+mFljGflFHk2BN\nCdYCLcIpIiJp3nsPamvZBGzBKdSfU+qpkVIQWlJjZvsC44DfAIX5akGkNQsXArAIaKRTtLGkSa2X\no6RGRETSJZKKlYU+bbPzixSjMHtqfgl8B2gM8ZgiHZcaehYv6qkREZEWJYaeFTq1eA+ga9dghMOW\nLQU+u0g4QklqzOwMYJ27z0C9NBIXSmpERKSYJJKaQvfUAE0lpFevbn0/kZiqDOk4xwNnmtk4oBvQ\n28wedPcL0neqrq5ObVdVVVFVVRXS6UVaEPekJjE8TiSfampqqKmpiToMEclGRMPPgCCpeeutIIbh\nw6OIQCQn5iGXlTWzMcCV7v6pZs972OcSadWRR8KsWRwLTPvAZEvjgxMwmz+Xn326Uss2ulPRqRNs\n2wZdumTzvxEJhZnh7upRb4HaKYnc174Gv/41lwF3pNqN9DakvdvZ/4yfcw48+ihMmADjx4f1PxJp\nt462U/lap0atgkSrsTHVExK3npoddGMpQEMDLFkScTQiIhIbEc2pAZqGn6lYgBSp0JMad3/e3c8M\n+7gi7bJiBWzfDv36sTHqWFqQSrTmzo0yDBERiZOoh5+lxSBSbPLVUyMSrddfD+4PPTTaODKYk9qY\n09puIiJSTuJQKEBJjRQpJTVSmmbPDu5Hjow2jgxmpzZmt7abiITMzDqZ2QwzeyLqWER2sXMnrF0L\nZqyN4vzJpGZlJCmVSM6U1EhpmjUruD/iiGjjyGBWckNJjUihfQOYi+Z+StysWQPu0L8/9VGcf/Dg\n4H7ZsijOLpIzJTVSmpLJQkyTmgUAnTsHhQK00JlIQZjZvsA44DdoTTWJm+Swr0GDIjl9lxEjaAAa\n3n4b6uoiiUEkF0pqpPTU1gZr1FRUwGGHRR1Ni3YCHHJI8CA5/0dE8u2XwHeAxqgDEfmA5LCviJKa\nnTjL2Z9OAEuXRhKDSC6U1EjpmTcvKJc8YgR07x51NJkle5E0BE0k78zsDGCdu89AvTQSR8mkJjm3\nJQJLGBpsvPlmZDGIdFRl1AGIhC7m82lSlNSIFNLxwJlmNg7oBvQ2swfd/YL0naqrq1PbVVVVVFVV\nFTJGKWfJ3pH99osshCUM5VSe1RpqUlA1NTXU1NTkfBwlNVJ6Yl75LEVJjUjBuPv3gO8BmNkY4Mrm\nCQ3smtSIFNTixcH98OGRhfAmQ4INJTVSQM2/QLr++us7dBwNP5PSE/MiASnpSY2rEJNIgelNJ/Gy\naFFwP2xYZCGkhp8pqZEipKRGSot78Qw/GzAA9toLNm6E5cujjkakbLj78+5+ZtRxiKQ0NDQlEkpq\nRDpESY2UljVrYP162GOPppr7cWWmIWgiIsL+lZVQV8cqwHbbLbI4dikUoBEEUmSU1EhpSR96ZkVQ\n4EhJjYhI2UvOolnMSUQ5MnITu7MeYPv24EtCkSKipEZKSyI5+NULL2BmWNwTGyU1IiJlLzngbBHR\nFQlIShVz1hA0KTJKaqS0JJKD2dxD8G1XzLvPldSIiJS9pp6a6ObTJKVSGSU1UmSU1EhpSRQJmE3M\niwQkHXooVFTAggVQWxt1NCIiEoE49dSkUhktwClFRkmNlI66Opg3j0bgdT4UdTTZ6d4dRoyAxkaY\nOzfqaEREJALqqRHJnZIaKR3z50N9PYuBbfSMOprsJYegzZkTbRwiIlJ4DQ3JmmNKakRyoKRGSkdq\nPk2R0bwaEZHytWIFXYHVDGArvaKORoUCpGgpqZHSkZpPU2SU1IiIlK9Fi4K7GMynAVgF0LUrvPMO\nbN4cdTgiWVNSI6WjWJOakSOD+9deC+bWiIhI+Vi8OLiLwdAzSNQMHTIkeKBiAVJElNRIaWhogFde\nAeDViEPJVnIdHdt/f1YAvPdeMC9IRETKR8x6agAYmpjloyFoUkSU1EhpmDMn6CY/8MCg67woeOr2\nb84Nnvr3v6MMSERECi3RUxPHpOY7Z53V9AVc3BezlrKnpEZKQzIZOOmkaOPooCmcEGwoqRERKS+J\nnpq4DD8DUklN8G8RLGQtgpIaKRXJZODEE6ONo4P+TSLuKVOiDURERAqnoSE1xCtWSU1iTs2QiMMQ\naY9QkhozG2xmz5nZG2b2upn9bxjHFcmKO7z4YrBdpEnNHA5nEwSTMlcVzwA6ERHJwYoVUFfHaohF\nOeeUXXpqRIpDWD01O4Er3P0w4Djg62Z2SEjHFmnd0qVBItC3Lxx8cNTRdEgDlbycfKDeGhGR8pAq\nEhAzBx4IZuwPVLIz6mhEshJKUuPua9x9ZmJ7CzAP2CeMY4u0KTn07IQToIgnMqZSGc2rEREpD6ly\nzjHTtSvsuy+VwH4sizoakayEPqfGzA4AjgKmhn1skRYVeZGApFQqo54aEZHyENOeGjPjueXLARiC\n1qqR4hBqUmNmvYBJwDcSPTYi+VfkRQKSpgJ06gQzZmgVZxGRchDXnhqcxfwPAAej9dOkOFSGdSAz\n6wz8CfiDu/+lpX2qq6tT21VVVVRVVYV1eilX774Lc+dCt24walTU0eRkGwT/h1dfhalT4bTTog5J\nSkBNTQ01NTVRhxELZjYYeBDoR1Cj9h53vy3aqKSsxbSnBuA1jubL/IbRTIs6FJGsmHvutcctWJHp\nAeBdd78iwz4exrlEdvH44/DpT8OYMZD4wy34dUz/XWv+ONvnCrlP8Jx/85twyy1QXQ3XXYdI2MwM\ndy/eyWc5MLMBwAB3n5kYWfAa8Bl3n5d4Xe2UFE5DA/ToAXV19AK2Zmw3ctnu+M8fxXSmczQLGc5B\nLAQMvT+kEDraToU1/OwE4PPAKWY2I3EbG9KxRTIrkaFnKcn/h4oFiIRORW0kVubPh7o62HdftkYd\nSwvmcDjbgREsog8bog5HpE1hVT/7t7tXuPuR7n5U4vZUGMcWac1LN94IwCd++lPMLNFLU8ROOCG4\nf/llqK+PNhaREqaiNhK5l14K7o8/Pto4MqinM9MT28fwaqSxiGQj9OpnIgWzfTsfBhqo4GU2EnSd\nF3nX+IABMGwYbN0Ks2ZFHY1ISVJRG4mFZKXL5JdZMZTM+I9V7i9FILRCASIFN20aXYAZHMFmekcd\nTXhOOCGoiFNTA0cfHXU0IiWlraI2KmgjBRPznhpoSmpULEDyKayCNqEUCsjqRJqAKWH79rfh5pu5\nmSv4NjenvVDEhQLcYeJEGD8+SG40t0ZCVuaFAlotaqN2Sgpm3Tro35+twB5AMNg4XoUCAA7AeAt4\nh73ox3oVCpCCiLpQgEhhucOjjwIwibMjDiY8ZsZu48ezHYKhCStXRh2SSClRURuJh0QvzVROoT7G\nw6aXAuvYm71ZzwERxyLSFiU1UpymToXly1kBvMJxUUcTImcLzlN8Jnj42GPRhiNSQlTURmIjkdS8\nRHyHniVN5ViAxL8i8aWkRopTopfmUcBL8Nf4Uc4JNiZNijYQEREJTbJK55RE5c4pxLdIQNI0RgNK\naiT+Su+vQSl97qk/9h+NOJR8eZIzqAV48UVYvTrqcEREJCRdqOXDdAGKY6RBsqdmdMRxiLRFSY0U\nFTPj2IoKWLYsMfSsNG2mN09DkMD9+c9RhyMiIiE5mtfoSh2vA+/TJ+pw2vQqxwAwCmDnzkhjEWmN\nkhopOp/jWwBM4hsxnl6Zu9TAMw1BExEpGccTzKeZEnEc2XqfPixgBN0BZs+OOhyRjJTUSNE5m+TQ\ns3MijiS/Hgfo3Bmefz4o/ykiIkXvhEQ681LEcbRHcgga07RejcSXkhopKqOB/VnGCgbxMh+JOpy8\n2gTw8Y9DY6OGoImIlIhi66mBpmIBTJ3a+o4iEVJSI0Ul2TczibNLsurZB5ydWIPn0VItiSAiUj6G\nAv1Zxzr2ZknUwbRDqqdGSY3EWBn8VSglo66OcxObpT70LKnPxRdTBzT8618MSZQCFRGR4pQs4FwM\npZzTzWIkWwDmz4eFC6MOR6RFSmqkeNx/P4OBuRxS8kPPkt7HmcCFdAJ+wMVRhyMiIjmoStwXw6Kb\n6XbShT8mH9x3X5ShiGRk7oWpH2VmXqhzSQmqrYXhw2HFCj7HIzzK5xIvGHygBlrz57LZp6M/l//z\nD2Ux8zkYgINpYLHeR5IDM8Pd1eXXArVTklfvv8/WPn3oCRzCXOZzKE2f+a21G7lsh3es47FgHtCA\nAbBsWVDIRiQPOtpOqadGisNvfgMrVjCbYD5NOVnCMB7kAipp4AdRByMiIh1z//30BP7JqcznkKij\nabeXAA4+GNasgcmTow5H5AOU1Ej8bd8OP/sZANdBeRQIaOYn/ICdVPIFgEWLog5HRETao7ER7rgD\ngF9xecTB5OBLXwruf/vbaOMQaUH5/XUoRcMSE+Ov6NEDVq9mOvCXqIOKyFsM4YHE3JoHR4xIXRsV\nDhARKQJPPQVLlrAUeJIzoo6m4y64ACorg56aVauijkZkF0pqJNZ6sIWr6QfAtTwRcTTRCnpr4Hwq\nGMF8PjgnR0REYun22wG4E2ikU7Sx5KJfPzjzTGhogAceiDoakV2oUIDElplxI9/mSm5iKqM5jlcI\n8vDCTtQvzD7Z/dzdGJcAz3IKn+Bp6umC3lfSHioUkJnaKcmLxYuDQjfdutG3tpYNBZzcH+6xgo+N\nTwKTgUXA8MZG0IgBCVlH26nKfAQj0l6PPvooDQ0Nuzx3EXAlN1FPJ77NTSQ/UMtZNXAm/fkoz3Er\n3+DrUQckIiKtS8ylYfx4Ntx/f7Sx5Mx5mgZWsD/DWQkvvABjxkQdlAignhqJia5de9ClyzjMgjz7\n2B0z+VvdAroAl3A393JJYs9oe0ricP7jeIkaquhKHV8H7tD7StpBPTWZqZ2SMNTV1TV9SbdxI90O\nPhjbuBFeew07+mgK27sS5rGat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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(14,12))\n", "x = np.linspace(0,1,100)\n", "for i, n in enumerate([1,2,10,20,50,100]):\n", " ax = fig.add_subplot(3,2,i+1)\n", " data, gaussian = uniform_central_limit(n, 1000)\n", " ax.hist(data, bins=20, normed=True)\n", " plt.plot(x, gaussian.pdf(x), \"r\", lw=2)\n", " plt.title(\"n=%d\" % n)\n", " \n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. 高斯分布的几何形式" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "高斯对于x的依赖体现在二次型$\\Delta^2=(\\textbf{x}-\\textbf{$\\mu$})^T\\Sigma^{-1}(\\textbf{x}-\\textbf{$\\mu$})$上。$\\Delta$被称为$\\textbf{$\\mu$}$和$\\textbf{x}$之间的马氏距离(Mahalanobis distance)。当$\\Sigma$是单位矩阵时,就变成了欧式距离。对于x空间中这个二次型事常数的曲面,高斯分布也是常数。\n", "\n", "现在考虑协方差矩阵的特征向量方程$$\\Sigma\\textbf{$\\mu$}_i=\\lambda_i\\textbf{$\\mu$}_i$$\n", "其中$i=1,...,D$。\n", "\n", "**由于$\\Sigma$是实对称矩阵,因此它的特征值也是实数,并且特征向量可以被选成是单位正交的。**\n", "\n", "协方差矩阵可以表示成特征向量的展开形式$$\\Sigma=\\sum_\\limits{i=1}^D\\lambda_i\\textbf{u}_i\\textbf{u}_i^T$$\n", "协方差矩阵的逆矩阵可以表示为$$\\Sigma^{-1}=\\sum_\\limits{i=1}^D\\frac{1}{\\lambda_i}\\textbf{u}_i\\textbf{u}_i^T$$" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "于是二次型就变成了$$\\Delta^2=\\sum_\\limits{i=1}^D\\frac{y_i^2}{\\lambda_i}$$\n", "其中定义$y_i=\\textbf{u}_i^T(\\textbf{x}-\\textbf{$\\mu$})$。\n", "\n", "我们把$\\{y_i\\}$表示成单位正交向量$\\textbf{u}_i$关于原始的$x_i$坐标经过平移和旋转后形成的新的坐标系。\n", "\n", "定义$\\textbf{y}=(y_1,...,y_D)^T$,我们有$$\\textbf{y}=\\textbf{U}(\\textbf{x}-\\textbf{$\\mu$})$$\n", "其中$\\textbf{U}$是一个矩阵,它的行是向量$\\textbf{u}_i^T$。\n", "\n", "**如果所有的特征值$\\lambda_i$都是正数,那么这些曲面表示椭球面,椭球中心位于$\\textbf{$\\mu$}$,椭球的轴的方向沿着$\\textbf{u}_i$,沿着轴向的缩放因子为$\\lambda_i^{\\frac{1}{2}}$。如下图所示:**\n", "\n", "![](http://research.microsoft.com/en-us/um/people/cmbishop/prml/prmlfigs-jpg/Figure2.7.jpg)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 高斯分布的局限" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "高斯分布的局限主要体现在其**自由参数的数量和单峰分布**上。\n", "\n", "对于一般的协方差矩阵,其参数的总数随着维度D的增长呈平方的方式增长,为了简化参数,可以将协方差矩阵约束成对角矩阵或者各向同性协方差矩阵(正比于单位矩阵),这样虽然限制了概率分布的自由度的数量,并且很容易求协方差矩阵的逆矩阵,但却**大大限制了概率密度的形式,限制了描述模型中相关性的能力**。\n", "\n", "高斯分布本质上是单峰的(只有一个最大值),而不能很好近似多峰分布。后面,我们会引入潜在变量来解决这一问题。**通过引入离散型潜在变量,相当多的多峰分布可以使用混合高斯分布来描述;通过引入连续型潜在变量可以产生出一种模型,该模型的自由参数可以被控制成与数据空间的维度D无关,同时仍然允许模型描述数据集里主要的相关性关系。**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###不同形式的协方差矩阵对应的概率密度曲线" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import matplotlib.mlab as mlab\n", "from mpl_toolkits.mplot3d import Axes3D" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def plot_2d_normal(mux, muy, sigmaxx, sigmayy, sigmaxy):\n", " fig = plt.figure(figsize=(8,6))\n", " ax = fig.add_subplot()\n", " x = np.arange(0, 5, 0.1)\n", " y = np.arange(0, 5, 0.1)\n", " x, y = np.meshgrid(x, y)\n", " z = mlab.bivariate_normal(x, y, sigmaxx, sigmayy, mux, muy, sigmaxy)\n", " ret = plt.contourf(x, y, z, cmap=plt.get_cmap('coolwarm'))\n", " fig.colorbar(ret, shrink=0.5, aspect=5)\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**下面是一般形式的协方差矩阵对应的密度轮廓线,协方差矩阵有D(D+1)/2个独立参数,参数的总数随着D以平方的方式增长,大矩阵计算和求逆困难。**" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_2d_normal(2.5, 2.5, 1.0, 1.0, 0.8)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**下面协方差矩阵是对角矩阵的情况,椭圆的轮廓线与坐标轴对齐。概率密度模型中有总数为2D个独立参数。**" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_2d_normal(2.5, 2.5, 1.0, 0.6, 0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**下面协方差矩阵正比于单位矩阵,该协方差矩阵又被称为各向同性协方差矩阵,轮廓线是同心圆。这使得模型有D+1个独立的参数。**" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ERHy4Snsq7dO0/RLbT0h6TtIXI+Joled1iaHZS1Lc50RgLqbu5VfHBlFd37PURleQtoi4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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_2d_normal(2.5, 2.5, 1.0, 1.0, 0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##参考资料\n", "[漫谈正态分布的生成](http://cos.name/tag/%E4%B8%AD%E5%BF%83%E6%9E%81%E9%99%90%E5%AE%9A%E7%90%86/)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.5" } }, "nbformat": 4, "nbformat_minor": 0 }