{ "cells": [ { "cell_type": "code", "execution_count": 76, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import scipy.stats as sps\n", "import matplotlib.pyplot as plt\n", "from scipy.misc import logsumexp\n", "#%matplotlib qt5\n", "%matplotlib inline\n", "plt.rcParams.update({'figure.figsize': (10.0, 6.0), 'font.size': 18})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gaussian distribution \n", "* probability density finction\n", "\n", "$$\n", "\\large\n", "\\DeclareMathOperator{\\Norm}{\\mathcal{N}}\n", "\\DeclareMathOperator{\\Gam}{Gam}\n", "\\DeclareMathOperator{\\e}{exp}\n", "p(x \\mid \\mu, \\sigma^2) = \\Norm(x \\mid \\mu, \\sigma^2) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\e\\left\\{ \\frac{-(x - \\mu)^2}{2\\sigma^2} \\right\\}\n", "$$\n", "\n", "* Maximum likelihood estimate of Gaussian density paramters \n", "\n", "$$\n", "\\large\n", "\\begin{align}\n", "\\mu &= \\frac{1}{N} \\sum_i x_i \\\\\n", "\\sigma^2 &= \\frac{1}{N} \\sum_i x_i^2\n", "\\end{align}\n", "$$" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmMAAAFxCAYAAAA/Pq9wAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XmY3Fd95/v3qX2v6qWqF3W3WvtmybIt23jBYLMFQoAA\nIawJYQJJJoEYLrmTZZJw75Bwb3JNCAk8GUjIDANkgMQOcSCADcYrXiRZ1r5vvVdVL7Xvde4fv6rq\nru6q6pKQJbv7+3oePa3+bXV++qOej875nnOU1hohhBBCCHFtmK51A4QQQgghVjMJY0IIIYQQ15CE\nMSGEEEKIa0jCmBBCCCHENSRhTAghhBDiGpIwJoQQQghxDUkYE0IIIYS4hiSMCSGEEEJcQxLGhBBC\nCCGuIQljQgghhBDXkOVaN+BSdHd36+Hh4WvdDCGEEEKIZe3bty+qtQ4ud93LKowNDw+zd+/ea90M\nIYQQQohlKaUutHOdDFMKIYQQQlxDEsaEEEIIIa4hCWNCCCGEENeQhDEhhBBCiGuorTCmlDIppT6u\nlDqulMoqpUaUUvcppdztfpBSyqKU+phSar9SKqWUilX+/huX33whhBBCiJe3dmdT/hXwMeAB4D5g\nW+X3G5RSr9Val1vdrJSyAf8G3A18Hfi7ymdvAtZeXtOFEEIIIV7+lg1jSqkdwEeB+7XW71hw/Bzw\neeDdwDeWecwfA68FXqe1fuTymyuEEEIIsbK0M0z5HkABn1t0/MtAGnh/q5srQ5m/C3xHa/2IMngv\np7FCCCGEECtNO2HsZqAMPLvwoNY6CxyonG/llYAX2KeU+msgDsSVUhGl1J8rpV5WC88KIYQQQlxJ\n7QShfiCqtc41ODcG3K6Usmmt803u31L5eS+QB/5PYBp4H/AHwBrgVy+p1UIIIYQQK0Q7YcwFNApi\nANkF1zQLY9UhyU5gh9b6ROX3bymlHgF+RSn1/2itjzW6WSn1EeAjAENDQ200VwghhBDi5aOdYco0\nYG9yzrHgmmYylZ9PLwhiVV+t/Hx1s5u11l/SWu/RWu8JBpfda1MIIS6L1poDI3NcnG71dSaEEFde\nOz1j48B2pZS9wVDlGowhzGa9YgCjlZ+TDc5NVH52tNEOIYR4UZTKmt/++n6+f2QSk4L/9rbreN+t\nsuqOEOLqaKdn7LnKdbcsPKiUcgC7gb3L3F8t/B9ocK56LNxGO4QQ4kXxj0+e4/tHJvnYazZx1+Yg\nf/KdI5ycSlzrZgkhVol2wtg3AY1RgL/QhzFqxb5ePaCU6lNKbVVKuarHtNbngCeBW5RSNy641lx5\nRhH44WW/gRBC/Awy+RJ/+8hpXrU5yMdfu4nPvms3LquZv/3x6WvdNCHEKrFsGNNaHwK+ALxdKXW/\nUurXlVL3AZ8FHqV+wdfPAMdY1IuGsWhsGnhYKfUppdRHK/feAvy51vriz/4qQghx6X5wZJK5dIHf\nfNUGlFJ0um2846YBvn94kulks7lLQghx5bS7Ufi9wCeBHRjB7N3A3wBvXm4rJACt9fPA7cATlWf9\nJeAGfk1r/aeX0W4hhLgi/nnfKIOdTm5d11k79t5bh8iXyty/f6x2bDI1yV/v/2u+euSr5EutymSF\nEOLStLXgqta6hLEn5X3LXPdB4INNzh0E3nJpzRNCiBdPNJnjyTNRPnrPJkwmVTu+ucfLjn4fDx2d\n4sN3rSeSjvC+776PcMYob3164mn+9jV/i0m1+/9ZIYRoTr5JhBCr1hOnomgNr9vWs+Tc3VtC7Ls4\nSyxd4PPPf5653Bzf/oVv8we3/AGPjz3Od05/5xq0WAixEkkYE0KsWo+fitLhsrKj37fk3N1bg5TK\nmgcOH+DBMw/yri3vYmvnVt6z9T3s6NrBVw5/Ba31NWi1EGKlkTAmhFiVtNY8firCHRu764Yoq3YP\nduBzWLj/9D+jlOI/7fxPACileO+293I+fp7nJp+72s0WQqxAEsaEEKvSuWiKcCLHHRu7G543mxQ3\nrvVzIfsUd/bfSbdz/rrXr309PpuPfzn1L1eruUKIFUzCmBBiVTowMgfAjUPNNwBZ0xumbJ7jrv7X\n1h13WBzcPXg3j489TrFcfFHbKYRY+SSMCSFWpecvzuGxW9gY8jS9Jms9hNZmPPr6JefuGriLRD7B\nC5EXXsxmCiFWAQljQohV6fmRWXYN+DE3qBerGskcpJwZ4ujo0sVfb+u/DYuy8Ojooy9mM4UQq4CE\nMSHEqpMtlDg+keCGoUDTa2K5GMdnjhFQ2zg8Flty3mvzcn3oep6deLbB3UII0T4JY0KIVefkVIJi\nWXNdv7/pNXun9qLRbPHfyNGJeMNrbgzdyPGZ46QL6RerqUKIVUDCmBBi1Tk+mQBgS6+36TXPTz2P\nzWTjFWt2MxXPEW2wT+Xu0G5KusSh6KEXra1CiJVPwpgQYtU5OZnAYTWxtsvd9JpD0UNs7drKzjVd\nABxr0Dt2ffB6FIrnw8+/aG0VQqx8EsaEEKvOiakEm0LepsX7xXKRYzPH2Nm9k+19xur8R8eXhjG/\n3c+GwAYORA68qO0VQqxsEsaEEKvO8ckEm3uaD1GemTtDppjhuu7rCLhs9PkdtaHNxbZ3befY9DHZ\nGkkIcdkkjAkhVpWZVJ5IIsfWFvVih6OHAdjZvROAjSEPZyLJhtdu79rOTHaGSCZy5RsrhFgVJIwJ\nIVaVE20U75+YPYHL4mLQOwjAhqCHM+Fkw96vrZ1bATg+c/xFaK0QYjWQMCaEWFVOTBq1X616xk7P\nnWZjx0ZMyviK3BB0k8qXmIovnVFZDWPHpo+9CK0VQqwGEsaEEKvKiakkAZeVoNfe8LzWmlOzp9gU\n2FQ7tqGyZVKjoUq31c1a31qOzUgYE0JcHgljQohV5Vw0yfpuN0o1nkk5nZ1mLjfHpo75MLYx2DyM\nAWwKbOLM3Jkr31ghxKogYUwIsaqcj6YZ7m6+vtjJ2ZMAbAxsrB0Leu147RbOhBuHsXX+dYwkRiiU\nCle2sUKIVUHCmBBi1cjkS0zGs6xrsdjr6dnTAHU9Y0op1oc8nG7SM7Y+sJ6SLnEhfuHKNlgIsSpI\nGBNCrBrnp1MALXvGTs+dptPRSaejs+74hqCbM+FUw3s2+DcAcCYmQ5VCiEsnYUwIsWqcjxphal2L\nMLa4eL9qQ9DDZDxLMldccm7YP4xCcTZ29so1VgixakgYE0KsGuen0wCs7XI1PF/WZc7EzrCxY+OS\nc+srAe7C9NLeMafFSb+nn3Nz565ga4UQq4WEMSHEqnE+mqLbY8PrsDY8H06HyRQzrPOtW3JusNMI\ncCMz6Yb3rvevl2FKIcRlkTAmhFg1zk2nGG5RvF8twB/yDS05N1TpTbvYJIxtCGzgfOw8pXLpCrRU\nCLGaSBgTQqwa56OplsX71TC21rd2yTmfw0rAZW0axtb715Mv5xlLjl2ZxgohVg0JY0KIVSGVKxJO\n5FoW748kRrCZbPS6exueH+p0cWG6cRhb5zeGNs/Hz//MbRVCrC4SxoQQq0K1R2uos3HxPhg9Y4Pe\nwdqelIsNdrqa1owNeAcAI9AJIcSlkDAmhFgVxmYzAAx0OJteczF+seEQZdVQp4vR2Qylsl5yrsvR\nhdPilDAmhLhkEsaEEKvC2Fw1jDVf1mIkMbJsGCuWNROxzJJzSikGvYMSxoQQl0zCmBBiVRidTWO3\nmOj22Bqen0xNki/nG86krKoOcTYr4h/yDkkYE0JcMgljQohVYWwuw5oOJ0qphudbzaSsGlpmrbFB\n7yCjiVFZ3kIIcUkkjAkhVoXR2QxrAq3rxcDo3Wqmz+/AbFJNe8YGvAMUygXC6fDP1lghxKoiYUwI\nsSqMzWZaFu+PJEZwmB2EXKGm11jMJvoDDi7OLK0ZA6NnrPosIYRol4QxIcSKl8mXmE7lmxbvA4yn\nxun39DccxtRaM37yOOcO7GPAa2FiTsKYEOLKsVzrBgghxIttbM4YVmw1TDmWHKPP07fkeCGf47t/\n/Rec2fsMALvdnfxo6C0Nn9Hr7sViskgYE0JckrZ6xpRSJqXUx5VSx5VSWaXUiFLqPqVU86Ws6+//\niVJKN/mz52d7BSGEaG20jTXGxpPjrHGvWXL80a/+A2f2Pctd7/s13vp7f4y5lOPm098hm8kuudZi\nsrDGs0bCmBDikrTbM/ZXwMeAB4D7gG2V329QSr1Wa11u4xlR4OMNjp9tsw1CCHFZqmuMrWkSxtKF\nNHO5Ofo9/XXHR48e5oWHvsdNP/82bn7LOwDofOMHUQ98gZ988xv83Ac/tORZA54BRpOjV/gNhBAr\n2bJhTCm1A/gocL/W+h0Ljp8DPg+8G/hGG5+V0lp/7XIbKoQQl2t0NoPVrAh5HQ3PjyfHAVjjqe8Z\ne+rbX8fT2cUdv/z+2rF1N9zEMz/ciPlH3+PV73wXDo+n7p4+Tx9Hp49e4TcQQqxk7QxTvgdQwOcW\nHf8ykAbev+SOJirDnT7VbKEfIYR4EYzNZujzOzGbGn/1jKeMMLawZ2zi9AlGjh7ipje9FavdQfbo\nUeIPPUS/yrE3cCOlfJYDP/j3Jc/qd/czm5slU2xc5C+EEIu1E8ZuBsrAswsPaq2zwIHK+XasAZJA\nDEgqpe5XSm29hLYKIcRlGZ1NL1u8D/Vh7ODD38fqcLLz7tcx+ek/49zb38HYRz+Gfs8vsnY2inlw\nK4ce+SG6XF+l0evuBWAiNfEivIkQYiVqJ4z1A1Gtda7BuTGgWynVeH+ReeeAvwB+Dfgl4IvAG4Fn\nlFI7L6G9QghxycbmWq8xNp4cx2620+XoAqCYz3Py6SfZfOvtxL/yj8x+7Wt0/MoHWPv1r2EbHOSP\nnvsqBf9a4pEwo8eP1D2rGugmkhLGhBDtaSeMuYBGQQwgu+CaprTWv6a1/iOt9Te11v+stf494PWA\nB/hsq3uVUh9RSu1VSu2NRCJtNFcIIebliiXCiVzT4n2oLGvh7qutMXZ2/7PkM2k2rN1A9L9/Cf9b\n30LvH/4hrptuYvCLX6BssbDr0YewOpwce/yRumf1u40wVh36FEKI5bQTxtKAvck5x4JrLonW+nHg\nMeBupVTTb0mt9Ze01nu01nuCweClfowQYpWbmMuides1xiaSE3XF+6efexqn14ft37+P2eOh5w/+\noHbO2t/PT+96B0OjpxgaWMuZfc/WDVUGXUHMyiw9Y0KItrUTxsYxhiIbBbI1GEOY+cv8/POAGei4\nzPuFEKKliZjRgd/fIoxVV98HKJdKnDuwj6ENm0k/8ggdH/gA5kCg7vroXT9H2N1J59mLpGNzTJ49\nVTtnMVkIuUJSMyaEaFs7Yey5ynW3LDyolHIAu4G9P8PnbwKKwMzP8AwhhGhqKm6EsV5/42Ut0oU0\nM9mZWhgbP3WcbDJBMDqHstvpeN97l9zT0+Xl34Zvw3/wCMpk4uy+uvlN9Ln7astlCCHEctoJY98E\nNHDvouMfxqgV+3r1gFKqTym1VSnlWnDMr5QyL36oUurngTuAhyozM4UQ4oqbrIYxX+MwVu3BqtZ6\nnT+wH2Uy4XnyGbyvfS2WjqUd92sCTh4euhmbyUy3w835g8/Xne/39EvPmBCibcsu+qq1PqSU+gLw\nO0qp+4HvMb8C/6PUL/j6GeBXgbuBn1SO3Q18Vin1IMZq+0WMXrb3Y6zKvzjkCSHEFTMZy+J1WHDb\nG3/dLV7WYvTYIbq7gpieP4X/bW9teE9/wEnM7iG35zYCU2c5nU2Rz6SxOY3/h/a5+winwxTLRSwm\n2QJYCNFaW3tTYgSmTwI7gC9grLr/N8Cb29gK6QTGUOabgT/DmD15J/B3wG6t9cnLaLcQQrRlMpZt\n2isG9avvF/I5Jk+fpCtbxNzRgfu22xre01cZ8py8/jYC4Wl0ucz4iWPz5z19lHSJSFpmgAshltfW\nf9m01iWMPSnvW+a6DwIfXHTsGPCuy2ueEEL8bCbi2ab1YmAU71tNVrqcXYwdO0KpWMR76iyeV78a\nZWn8Fdnrd6AUnFy/m3vyJRSKkWOHGd59E1C/vEWfp+/Kv5QQYkVpt2dMCCFelqaW6RmbTE3S6+7F\npEyMHj0MQCA6g+eeu5veYzWb6PE6uJhT+G69lUCxXLsXqAUwKeIXQrRDwpgQYsXKp/JsTZS4vmRC\nl3TDa6ZSU/S4egAYPXaYDqcbq8mM5/bbWz671+9gKp7Fc+cddMzMMXnmJIWcMVmgz22EMSniF0K0\nQ8KYEGJFyp2PEf7/9vFp7eTVB+YIf/EApcTSJRGn0lP0uHsoFYuMnzpOZyqL8/pdmNzuls/v8dmZ\njGVx33knncks5VKJydNGCazT4qTD3iE9Y0KItkgYE0KsOIXJFNGvHKZoN/HbpJi4s5diOE3k7w+h\nC6XadWVdNsKYq4fp0YsUczm8oxO4b7l12c/o9Rk9Y7b16+ny+gGYPHu6dr7P08dkavLKv5wQYsWR\nMCaEWFF0qczMt0+irGZO39PPC5Rw3hCi6/3bKE6lif3gQu3amewMxXKRXncvU5Ug5U9lcd26fBgL\n+RzEs0WyhTKdN9+MszjfMwbGUKUMUwoh2iFhTAixoqT2TVEYSxJ46wZGC0XAqO9ybOnEfWsvyafG\nKEYzgDFECdDj6mHq7CmsZjNuFM7d1y/7OT2VSQFT8SzOG2/Cn8wwefL4/HlXD+F0+Eq/nhBiBZIw\nJoRYMXSpTOKREawDHpw7u5mM57CZTXS6bAD4XrMWTCbiP74IUBtG7HH3MHnmFIFCGdfu3Zjsjbbi\nrVedoTkZz+K66Ub86RzxmSiZRByAkCtEspAkVUi9GK8qhFhBJIwJIVaMzOFpSrM5fPcMoZRiMpYh\n5LNjMikAzD4bnlt7SR+IUErkmUoZPWNBaxeRC+fwRmdx3XxzW5/V4zMCW7VurLOy0n51uDPkChm/\nV3rfhBCiGQljQogVI/XsBOYOO46tnYDRa9W3aMFX9yv6oKxJ7Z1iKj2F1WSlGI5RLpXwp7M4d+9u\n67N6Ks8Nx3Mok4merduNzzxzCoBed69xXoYqhRDLkDAmhFgRitMZcmdiuPf0oio9YVPxXK22q8oa\ndGFf7yf13CSTyUlCrhCRc2cA8KdzOHde19bnee0WnFZzbSNy/549uLN5Jo4fAeZ7xiSMCSGWI2FM\nCLEipA8a+0C6bjIWcNVaMxHLNFx933VjD6WZLJapklFof+4sNmXC19+PORBo6/OUUrWFXwFcN9yA\nL5MjctYIdrVhypQMUwohWpMwJoRYETIHo9iGvFgCRi1XPGMsO9FoX0rn9k4wK9aP99Dr7iVy8Rze\nbB7Xzl2X9Jkhr70WxhzbtuHNFkgkYuTSaZwWJz6bT2rGhBDLkjAmhHjZK0YzFCZSOHcGa8cm4sby\nFY3CmMllxb4xwO7pTYScIaIXzuOJJ3Hu2nlJn2v0jOWMZ7rddAaMWrXoiLGWWcgVkmFKIcSyJIwJ\nIV5esjF44nPwLx+GJz8PhQyZ4zMAOHd01S6bjBk9Vs02CS9vctBT6GLtdCeFfA5fNo9z16X1jPX4\nHEzGs2ht7HsZ3LgJgOjFc8Z5d4/0jAkhliVhTAjx8hE5CV94BTz8p3DhKXjoj+HvXknu6ASWbieW\nzvngVR0+bNQzBjCzxug567voAcBbKGHftu2SmhPy2skXy8QyBQC6dl2PpVRi6vgxQBZ+FUK0x3Kt\nGyCEEG1JTcNX3wLlEvz6j2BgD5x5BP3NX2d0Os7xPSE6ozHu7vRhNSkmKj1jIW/jMDZhjjBrixKY\nMjYE7+ofWHax10gkwr59+4jH42zYsIGQ15gsMBXPEXDZcO7ciffb/4tIZVukkCvEdGaaQrmA1WS9\nUv8SQogVRsKYEOLl4d/vhVQUPvwj6KtsV7Thbv777V/jM0UHOXMRDp1jvdPO3183zFQ8S7fHhs3S\neABgKj1FxHOCt828Gm/JhGdr616xgwcP8q//+q+YTCbcbjdHjx6lI9SHlV4m41m29HpxbN2KL5tn\nPDKF1poeVw8aTTQdpc/Td6X/RYQQK4QMUwohXvrOPwHH/g1e/fvzQQz4+9EIn9JObp4p8h/7fod/\nXKPIlMu84/nTnE5nl6wxttBUaooD3hOYMDOgerBv3dr02jNnzvDAAw8wODjIvffey7333svb3/52\nYtEp7raeZjJmDHma3G4CHj+FUpFENCKr8Ash2iJhTAjx0qY1PPwp8K2B2367dvhgIs2nTo9xd0zz\nN7Nmbihc5I3P/yX/esNGlIK9nWaCLcJYOB0mHJijpIuEnMM4tjUOY9lslu985zt0dXXx3ve+F4/H\ng1KKXbt28YY3vol+c4ILRw/Urg8ODgEQuXieHldlGFPCmBCiBQljQoiXtotPw+hz8MpPgNUJQFlr\n/o/jI3RZLPzXfUncG7vh1t+AYw+yNnGW+7YMknGaiXbbmj42nAnTW/Izk5vA7x7CvmVLw+see+wx\n4vE4b3vb27Avqim7Zc9NTNBB6sJBkskkAN2VbZGmz52phTEp4hdCtCJhTAjx0vb0F8ERgOvfWzv0\nYGSOQ8kM/8Xlx18A27APbv1NMNtg71d4fZcfUzTLYZdmrlBs+NhoOkoo4yGSHcXhHcTk9i25JpFI\n8Oyzz7Jr1y4GBgaWnFdKMeXdDOUSjz/+OAC+7TuwFYpEjh/Db/djM9kkjAkhWpIwJoR46UpG4Ph3\n4cZfAZsLMLY5uu/cFFvcDn4uXASTwjboBXcXbH8bvPC/mZ6bwXIyTlbB/xybbvjocCaMP2khmhlF\nmczkLyaWXPP0009TKpV41ate1bSJ/o4uZuy97N+/n3Q6jX3zZjy5AjNjIyiljLXGZEskIUQLEsaE\nEC9dRx4AXYLr31M79NhskpPpLL8zFKJ4Po51jQeTzWycvOmDkIuTO/hvmBIFdlhtfGUsQr5crnts\ntpglkU/gnCuRSp4HNPnzsbprCoUC+/fvZ+vWrXR1ddFMj8/O0VJv7Xprfx/eYpm52Axaa0KukNSM\nCSFakjAmhHjpOvQt6LkOerbXDv3DaIQuq4Vf6PSRH01gX7tgeHHoNvD24zj1IADv6gowlS/yvUh9\n0IpkjE3FTeEk9nQCk7tM7ny87prDhw+TyWS45ZZbWjaxx+fgXMrC2uFh9u3bB0oRCHSQL5VIx+Zk\n4VchxLIkjAkhXppmzhqF+zt/qXYoki/wo5k47+nrRE2koaixr1sQxkwm2PGLdE48hpc0Pxfy02+3\n8s9Ts3WPjmaiKA2FuRSebAHbkIf8xTi6pGvXHDx4kM7OToaHh1s2s8fnoKxh/ZYdzM7OMjo6Suea\nQQCmx0ZqYay6ZZIQQiwmYUwI8dJ05AHj58531g49GJ6jpOEdPR21Gi/b0KLC+x2/iLlc4LWmffT4\nHPxiTwePzMSJ5ucL+cPpMO6MhXK5jCdfwLG9H50vU4ykAaNw//z581x33XUopVo2s7qWmTs0hMVi\n4eDBg3RvMXryoieOEXKFyJfzzOXmfqZ/DiHEyiVhTAjx0nTyB9C3G/zzsxgfmJpjq9vBNo+T/FgC\ns9+G2bto+YqBPcxZe3ib7RkcVjPv7OmgpOE74fnesWgmij9pbEASCHRiHw4AkB8xAt6RI0fQWrNz\n585lmxnyGstdzOVg69atHD58GP91OzGXykROHKPHLWuNCSFakzAmhHjpSU0bQ5Sb31A7dDGT47l4\ninf0dABQGE1iXeNdeq9S7Hfdzq0chkKWbR4nOzwO7l8wVBlOh+lMGT1anWuHsXQ5UQ4z+VEjjB06\ndIje3l6CweCyTQ1Wwlg4kWPnzp1kMhkmnA7cuTwzIyO1VfilbkwI0YyEMSHES8/ph0GXYdN8GPtu\npQj/LaEA5WyRYjSDbcDT8Pafqt04yMPFpwB4czDAvniacK4AGD1jvWkPtmIJ3+YtKJPCNuAlP5ok\nHo8zNjbGjh072mpqt8cIY5FEjvXr12O1Wjk9Po4XE3OxGUJOCWNCiNYkjAkhXnpO/QDcQei/oXbo\n4ek429wO1jrt5MeM1e5tAw16xoCf5DZTUFY4/SMAXt/tN54xY8yYDKfDdMUsuLN57Bs2Vp7loTCR\n4tTxkwBs3ry5rabaLCY63TbCiSxWq5UNGzZw8uRJ/P4A6WIBn3ID8zM4hRBiMQljQoiXlnLJCFGb\nXm/MjgTixRLPxJK8tsso1i+MGmHMumZpz5jWmosJxYj3hloY2+520G+38nDUCGORdARHUuPJFbBv\n3ABUgl1Zc+LIcXw+H6FQqO0mBz12IokcYIS4eDyOtd+YUZmYnKLD3kEkLWFMCNGYhDEhxEvL5EHI\nzsH6u2uHHp1JUNTwmkoYy48lMHfYMbutS26PZ4vkimXCoTshcgxioyileG2Xj5/MJsiWysTmolAE\nd66Abd06AKyDXkqUOTd6gU2bNi07i3KhkM9OuBLGNm3aBEAy2AtA9Pgxul3d0jMmhGhKwpgQ4qXl\nnLHHI8N31g49PB0nYDGzx2cM+eVHk02HKKs9VOmhyhZGZ38CGEOV6VKZR2dmUHMZAPw+PyaHUchv\n9tkIu5IUSoW2hyirFvaMeb1e+vv7mbIYuwJMnzpByBkimo5e0jOFEKuHhDEhxEvL+SegayP4+gBj\n2PHHM3Fe1enFYlKU0wVKM9mGQ5QA4UQWAEffDnB1wQWjiP/2gAebUjwcmcabNnrUOiqLs4Kx6feY\new4TJtZVesvaFfQZYay6sOuGDRuYjCewFUvMjl6k29lNOCMF/EKIxiSMCSFeOkpFIzwNv7J26GQ6\nRyRf5FUdRk/YfPF+4zBW7aEK+R3G9kgXngTAZTZxk9/FT2NpY40xrencVN8DNlGeIaR9WM1Lhz9b\nCXrs5Etl4hljYdl169ahtcbs8BKbjhJ0BZnJzFDW5WWeJIRYjSSMCSFeOiZegHwC1s2HsSdnjbW/\n7ugwwldhIgWAta91GAt6HbD2Dpg9D7ExAO4MeDmTBV/KhzNfxLlxU+2+bDZLODVDX6mDYjR9Sc0O\nVVbhr/bKDQ4OYjabKXd0EU8nCTqDFHWR2exsq8cIIVaptsKYUsqklPq4Uuq4UiqrlBpRSt2nVGXO\n9iVSSn1TKaWVUocv534hxAp1vlIvtna+XuzJuSRr7FaGHMZK+4WJFGafrWHxPhiLr9osJnwOCwzf\nYRysDFXXAPkKAAAgAElEQVS+ssODRpHybsGVL2BfN1y778KFC2g0feUOCuOpS2p2cMFaYwBWq5XB\nwUEy/g7yaDqVMfFAiviFEI202zP2V8BngaPAR4FvAx8DHlRKXVLvmlLqzcA7gcyl3CeEWAVGn4PO\n9eA1thAqa81P55Lc0eGpzW4sTKaw9jX/f2A4niXktRvX91wHdj9ceAKA3T4XVkpM9GzCnStgXbu2\ndt/58+cxm82ElJ/8xKWFsZBvfhX+quHhYVJWK9pkxjVtLDYry1sIIRpZNkgppXZgBLD7tdZv11p/\nWWv9CeATwN3Au9v9MKWUB/gi8AVAqlmFEPO0hpFnYeCW2qETqSwzhRJ3BIx6MV0qUwinsfa2CGOJ\nXG2/SExmGLoVLvwUAJvJRI+eYqR/Ax6TGUtHR+2+c+fOMTg4iLPHS2EieUlNr26JFFkQxoxJAIqi\ny4vpnLEvZTQjMyqFEEu106v1HkABn1t0/MtAGnj/JXzenwFm4L9ewj1CiNVg7iKkwjCwp3boyTkj\nFFXrxYqRDJR0yzAWSeQIeR3zBwZugehJyBrbKQUS55ju7MHUN78BeTabZXJykuHhYax9nlpdWru8\ndgsOq6lWMwbQ39+PSSlKLg/5ixOAbIkkhGjM0sY1NwNl4NmFB7XWWaXUgcr5ZSmlbgF+B3iP1jp+\nKQsqCiFWgdHnjJ+D8z1je2Mp+u1WBqr1YpPV4v3WPWOvWN81f2DgJkDD2H7YcDe+8Enw3cH41uvh\noYdg/35Gy8Ysx8GBAawWJ+l9U5QSecxeW1tNV0oR9NrresasVit9fX1MJWLEJibwr/dLzZgQoqF2\nesb6gajWOtfg3BjQrZRq+Y2llLIAfw/8UGv9rUtpoFLqI0qpvUqpvZGIfJEJsWKNPAtWF4TmN+je\nG09xk28+eBUmUmBWWLqdDR+RLZSIZQrzw5QA/TcaP8f2AhAYOYEqlzg7m4TXvx5+//cZ/f73QWvW\n/OqvYs1F5j+rTVpren3mupoxgMGhIUouD7G5WYLOoAxTCiEaaieMuYBGQQwgu+CaVn4P2Aj8dpvt\nqtFaf0lrvUdrvScYDF7q7UKIl4vR54zgZDY67KdyBUazBfb4579eCpMprEEXytL4qyuarKwx5lsQ\nxpwB6N4Mo3vJlXJ0RbL0RCc4tGZo/qMHBgiFwzieegrbu98EQH58+bqxVOosBw/9Nj95dDu/uflD\nvLn/95mc/Lfa4q+Dg4Nok4lZk4luZ7cU8AshGmonjKUBe5NzjgXXNKSU2gj8CfBnWuuzl9Y8IcSq\nUMgYe1IOzlc97I0bPVN7FvaMLTeTsrbG2KKvrDV7YHQvkce/jz9lYd3oOQ5u3kbRH6D8kY8wun49\nA+PjAJiiE5iTUYonJ1o2ORL5Ic8+92ZmZ5+iv++XuZB7F6VSmSNHP86xY/+FcrnA4KCxwn/W6SZk\n7pRhSiFEQ+2EsXGMochGgWwNxhBmvsX99wEzwANKqY3VPxj1arbK732X3HIhxMox8QKUizCwIIzF\nUtiU4jqvMSRZThcoxfJYe5t3xIfjlZ6xhQX8YNSNpaNE/9tHseetbLp4hrTTxfGnn2P6058mazYz\n8KEPQZ/xVWSJnKXw/CnINR4UmJ5+nEOHP4rHs41X3PoDtmz5FCnbh/iTp36PwaHfYWLyXzhx4k/w\ner04FZRcHvoiJiKZSK3XTAghqtoJY89Vrrtl4UGllAPYDexd5v61GHVnR4BTC/6sATZV/v7lS2q1\nEGJlGanMD1qwrMW+eJpdXid2k/E1VSvebzmT0qicCDXqGQMm/BlM2syOsycBeM4bYHR0FIDB22+H\n734XnE6s0fMUXSH0p/6vJZ+RzY5z+Mi9uFzruWH3/8BuDxmf6bOjMeHq+g2G1/5nxie+xfj4/6bX\n76fk9BCYyFEsF5nLzV3qv44QYoVrJ4x9E9DAvYuOfxijVuzr1QNKqT6l1Fal1ML/un4S+KUGfyLA\nSOXvn7ncFxBCrADjz4N/EDxGXWi+XOaFRJqb/AuHKI1qiOWWtVAKOt2L5hSN5aCgmQoZS2SsU5oe\nm4W9sRQjIyM4HA66urrghhvgL/8Sa/Qc2uqg9A/fgDNn6h518uT/TbmcY9fOL2KxeGvHq0Oj4USO\n9es/TkfH7Zw6/ecMb+pAW20QNoKiDFUKIRZbNoxprQ9hLNL6dqXU/UqpX1dK3YexIv+jwDcWXP4Z\n4BgLetG01g9rrf958R+MOrN45fcnr+RLCSFeZiZegL7ra78eTmbIlXX9TMpwGmU3Y/I1n7wdTuTo\nctuxmBd8tWkNn/gkjJeYcRvP696+kz1+N8/FUoyOjjIwMICp0gPHb/0Wlt7KPpi+fvjDP6w9Khp9\nhEj0Idat+ygu17q6z64OjRqB0MT2bf8vWmuc3Y8BkEoby2dE0zKjUghRr92tjO7F6OHagRHM3g38\nDfBmrXX5RWqbEGI1yMZg5gz0764d2h83esH2+OY72YvhNNYeF63WKKxbfb/qscfgiSdgvES2bDyv\na9NmbvC6uJjNc3FmloGB+QVgMZmw/tHvAlDoXgff/jacOEG5XOTkqU/jcm1gaPDXlnz2wp4xAIej\nn+G1v0Ei9Sg+zyQpbXzdhjOy8KsQol5bYUxrXdJa36e13qK1tmut12itP6G1Ti667oNaa6W1/kkb\nzxzWWl93me0WQqwUk4eMn33zYexAPE2PzUK/Y74XrBBOYwm2XkUnnMjWL2sB8JlKFcRkGZW048gX\ncW3YyPVe41kRb4D+/v66W0x33YapkKDYNWz0rP3FXxAOf49M5jwbN3wSk2lp71yX24ZS9VsiDQ39\nOlZrF8NDB8nYjJ4zWWtMCLHYJW3yLYQQV9z4AePngmHKg4kMu7zzwaucLlBOFrD2tA5jkUSOoGdB\nGHv+efjBD4y/T2nMWRvOfAHb2rXsrMzSjHiWhjEAa5+XQvcwAPpr/4vzpz+P272J7u7XNvxsi9lE\nl9tem0QAYDY7GRr8EP7uKWzBLH48siWSEGIJCWNCiGtr4gXw9oPHmJWYKpU4nc6yyzu/yn4hbAxb\nWkLNw1iprIkm8/U9Y1/84vzfX/U2TAUrzkIR28AAAauF7lKB2Y4gHo9nyfOsW/ophtajUURvspLK\nn2N47W+hVPOvzcVbIgEMDLwPXbQyOHyM7bFe6RkTQiwhYUwIcW1NvFBXL3YkkaEMtWFEmA9j1hZh\nbCaVp1TW82uMJRLwT/9UO5/+rd9Alc3YTEWU1QpAKDlH1Bto+DxLyIU22yj5exl9qw/7jCbU/XMt\nXyXktS/ZEsli8WJL76G7e4R1KZeswi+EWELCmBDi2sklIXqyfogymQGoG6YshjMoqwlzoNlmIPO1\nWrXV9//pnyBV2V9y+3YurOkApbCbc6A1uVwOX3SKWYuN6XxxyfOqQ6KJPduYudlF/4NzmH7wcMvX\nadQzBrBx+AMopVnTNS1LWwghlpAwJoS4dqYOA7queP+FRJqQzUKv3Vo7ZhTvO1GmVjMpFy34+uUF\na0l/5COMjxu7sblsGZi7wOTkJMGksQDrwcTSHd2qvXAT7+6Fkqb/e3H40pdavk6oEsbK5fpV9nt3\n3MPcdJDuNaNE02FZhV8IUUfCmBDi2mmjeB8qy1q0GKKE+SUlQl4HnDoFeyubg9hs8IEPEDl3GoAO\nVwYmXmBiYoLuhBHGXmgQxkwuK8prJjJ0jO5n0jiiJfiP/4CZmaZtCHrtFMuauUyh/llWK9Nn+rE7\nM6yzZonn4y3fRQixukgYE0JcO5OHwB0En7EnZKpU4lSqvni/nCtSmsthaWMmJVSGKb/1rfkTb3wj\ndHaSPH8BU1kTcmVh4iATExN0OR2sd9o5mMg0fGZu+DRFS4y+s73GgUIBHnigaRuq9WrhBTMqq4oX\nAxQKNm51InVjQog6EsaEENfO1GHomV9u8Ggyu6R4vxg2gpJ1mTXGIokcXrsFp80M3/zm/Il3vQuA\nXGQGZ75A5+AATLzA+Pg4fX197PI6G/aMAcS7f4qp6KRz1/vnDy6YFLBYtV6tUd1Yl8XOdHSIHa48\n4dRoy3cRQqwuEsaEENdGqQiR49Czo3aoGooaLmuxTM9YOJEl6LPDsWNwqLKQrMMBv/ALxsfFMzjz\nRexbric/cYRoNEpfXx87vS7GcgVmC/VF/KVSjjnrk3imboI3vBOqK/8/8ghMTjZsQ7VeLRxfGsZ6\nO7uJhNdiM2vmZh5v+S5CiNVFwpgQ4tqYOQvFbF3P2JFkhi6rhV7bfPF+MZwGs8LS6Wz0lJpwvLIV\n0sIhyje9CbzGZt6lfBkLJUyDuwinSmit6evrY4fHUfvshaanf0KJFL7JV1A0++Guu4wT5XLTocpa\nz1iyQc/YumHiU35yORvF+E9bvosQYnWRMCaEuDamDhs/F/SMHUlm2OFx1O0/WQinsXQ7UebmMynB\nCEBBr6M+jP3yLwOQS6coozDZTRDazhRB46N7etjuNkLe0UVhLBL5IRZLANfMNoqRNLzznfMnH3yw\nYRvcdgtum7lhz1jX1u2YclmikSGc+dOUSo3r1IQQq4+EMSHEtRE+CsoMwS0AFMuak6ks2z31PWDt\nzKTUWhs9Y6UMHD1qHHQ64ed/HoBYeAoAk88JPdcxRTc2syIQCBCyW+m2WjiSnC+6L5cLRKcfobv7\nbkw2G4VopjbcCcCPfwzJuq15a4Jee8Oesc5t2zFn08zMDGOixMzMk63/fYQQq4aEMSHEtTF1BLo3\ng8UY2jubyZEt67owpotlijNZLMHWQ5TJXJFMoUTo4un5g695DbjdAERHzwNgDXWCJ8SUqY8eRx6T\nyfgK3OFxcmxBz1gsto9iMUaw+3VYgk6KkQysXQu7dhkX5HLw0EMN2xLyOgjHl86mtPv82DNpYrEe\n8mULkWjrBWSFEKuHhDEhxLUxdRh6ttd+rQ4T7lgQxoozWdBgWWYmZXWNseDBvfMHK71iAOPHDwLg\nGh5EA5O6mx7ml5fY7nFwIp2lWFmsNRJ9GJPJRmfnnVi7K2EM6nvHmgxVNusZA/AVCmhtYjzVQTT6\nI7QutXwvIcTqIGFMCHH1ZWMwd7GuXuxoMoNFwUbX/JZH1RBk7W7dM1ZdSiK0b0Fh/JveVPvrzPmz\nWEolfBs3E4vFyGkLPZnTRjE+RgDMlTWnM1m01kQiD9PRcTsWixtL0EUplqOcL8Fb3jL//H//dygt\nDVNBr51Ig5oxgIDTiSrkGZvuplCYIR5/oeV7CSFWBwljQoirL3zM+Fk3kzLLJpcDu2n+a6kYNcKY\nZZkwVlt9fy5sHNi5E4aGaucT0SiufJGOjduYmjLqx3rK4zB7DpjvjTuazJJKnSKbHaG7+zXGZ1eG\nSIvRDOzZA72VBWAjEXjmmSVtCXrtJHJFMvmlQc3X1Y0plyExNYRSFiLRH7V8LyHE6iBhTAhx9TWY\nSXkslakbogQoRNKYPFZMTkvLx1VrtILJWePAgiFKgGwihb1QINi/cT6METUmEQAbXQ5sSnEkmSEa\n/bHxrGoYqwTBYiQDJlP9s7///SVtCbVY+DXQP4Apl8GZ68Luvo6ohDEhBBLGhBDXwtQRcPjBtwaA\n2UKR8VyBbYtnUkYzy/aKgRF8bKUCgWzCOLAgMGmtyRWLlE1FOp2dTE5O0hEIYKcIU0YYs5oUm90O\njiYzTM88hsezHbu9B1gYxiqr9L/hDfMf3KCIv7rWWKMtkTrWbcCcTWPCTJZNlV648WXfTwixskkY\nE0JcfVNHjCHKynpiR2rF+466y9oOY6NhgslZFEAgAK94Re1cam4WjaLoAJMyMTU1RU9vL3Sum++h\nwyjiP5JIE4vtp6vzztpxk82MOWCnUC3iv+ee+dX4n30W5ubq2lLdn7Lhlkjbd2DKGc+ZjHcByBIX\nQggJY0KIq6xcNnqkFg5RVtb4qi7AClDOFCknC1iXWdYCIDwWJpiaMX65+26wzA9rxqYmACj5beTz\neWZmZujp6TE+vzJMWf3scKHEnHbSuSCMgVE3Vq1fo6sLbrpp/l0eeaTu2pCv2jPWYJhy3XrM2Qzo\nMlNhEzZbiGnZGkmIVU/CmBDi6oqNQD4BofllLY4kM3RbLYTsC7ZBqhXvt17WAiASz87Xi91zT925\nmdPG2mPlkI9IJILWmt7eXgjtMLZkyhvDj9V6tRG1Cb9/T90zrEEXxUgGrY2lL3jd6+ZPLhqq7HTZ\nsJhUw2FKk9mMG7Bk0yRnU3R23sHs7FNoXV72HYUQK5eEMSHE1RU5YfwMbasdOtqoeL8axpbrGSuV\nCJethFKVMPaa19SdnjtrhDHzcC+TlQ2+jZ6x7aDLxmblUFtsNuy8E7PZXvcMS9CJzpcox/PGgRZh\nzGRSdHvsDbdEAvDYnVgyaYqxIl2dr6RQmCWRONL6HYUQK5qEMSHE1RWpLGuxaBukbYvrxSJpUGDp\ndCx+Qp38vv3MOr2EkjPQ1wdbt9adnxkbwV4oYls3zNTUFDabjUAgML+sRmWo0l0OE9AzTFm2s1i1\nbq1WN3b77eCq9NidPg3nz9ddH/LZGw5TAnj9AVQuiylvwuG4wWjjzBMt31EIsbJJGBNCXF2RE+Dp\nBWcHAOezxjZI29xLZ1KaOx0oS+uvqeiPjJqrYGq2vri+Ym46jDNfxDe0gXA4TDAYNLZB6hgGi6O2\n5tnMzJMMMMKFUnDJZ1R3AChGKzMq7Xa46675Cxb1joW8zcOYP9QLBWMIMxbTeDzbJIwJscpJGBNC\nXF3hY7VeMYATKSOYbHEv7hnLLLvyPkD42QMAhJKzS4YoAZKpJCZdoNvbQyQSIRQKGSdMZujeVBs2\nnZl9irXmCKezinK1NqzC7LOhrKb5bZGg/rMefbTu+qDXTqRBzRhAx9BaTDnjXDgcprPzDuZi+ymV\nGl8vhFj5JIwJIa4erY3ws6BerBrGNrntCy7T7S1rkcsRPnUegFBqZknxfqlYJFsqUbAU8Ss/qVSK\nYHBBz1dwG0SOo7Vmbu5ZNrvsZMplRrL5uucok8LS7ZwfpgR41avm//7oo8a7VR/rdTCdylMsLS3M\n79i0BVXMo8sFxibH6AjcitZ5YvHnW7+rEGLFkjAmhLh6YiNQSC3pGRty2HCbzbVjpXgeXSgvX7z/\nzDOErR4Agt0+WLu27nQiGgGlSDuKqJQxfFkfxrZAbIRM7Bi53CS7AsYitMdTS3upLCHX/PIWADfc\nAB7jsxkdrasbC3ntaA3RZH2oA+jeth0FmPIpJqYmKjM3TczNPtv6XYUQK5aEMSHE1VOdSRms7xlr\nNEQJy+9JyY9/TMTdgdJlum+/ecnp2YvnAYh5S2TnjIBVG6YECBrF/nNj3wVgd6Wo/0SjMNbtpDSb\nRRcqvV0WC9xxx/wFjz1W+2uoxSr8zo5OzGWNLZ1iNjqL1erD693G7NzSfS6FEKuDhDEhxNUTrp9J\nWShrzqRzS8NYbVmLZdYYe/xxwp4OOtNxrHe/esnpmRPGshXpkJNIJILdbsfn881fUBkunZ39KVZr\nJ73eTayxWxv2jFmDTtBQnG4xVFl9rM94n0bLWyilcJnN2DIZ8tk8yWSSQOBW4vEDlMuNi/6FECub\nhDEhxNUTOQGeHnB1AnAuk6OgNZuX9IylUVYTZq+t+bMKBXj6aSLuTmMm5Z13Lrlk7uIFlNYUhjqJ\nRCIEg0HUwtmWHcNgtjOXO0UgcAtKKba6nRxPZpY8q7ZH5cKhyoUzKheGsepm4ckmy1u4PJgz80X8\nHYFbKJdzxOIHm7+vEGLFkjAmhLh6IvUzKU82m0lZKd5XpvplKuo8/zyk00TcHQRLWRgYWHLJ3NQE\nznwR8+Ca2rIWdUxmMr3ryao0HR23ArDV4+B0OkexXD+jsrbW2MIwdvPN4Ki0/exZo3YM6PZUhimb\nLPzq7+ymXCwAEIlECARuBhRzszJUKcRqJGFMCHF1VGdSLqoXU8AmV30YK0QzyxfvP26sLxb2dBDy\nN14YNhGbxVYs4PP2kU6nl4YxYK7H2LC7I2CEsS1uB3mtOZepD1ImhwWT11a/vIXNBrfdNv97pW7M\nZjHR6bY1rBkDCPQPUNYlMJUIh8NYrQE8ni3MzUkRvxCrkYQxIcTVERuFfLJ+JmXamEnpMs9/Feli\nmdJMdvni/SeeoIwyesb6uhteksxmKJuK+At+YFHxfsWsV2MplHFb+gDYWumla1bEXzdMCfV1Y4uK\n+Jst/NoxvA4FqFKacDgMQCBwC3Ox/ZTLhcbvK4RYsSSMCSGujgZ7UjacSTmTBb1M8b7W8MQTzDm9\nFM0WQpuHl1ySz2bIocnZijizRrBr1DM2a4rSESugpk8BsNHlQNF4eQtr0Dm/Cn9Vk7qxYIsw1rnN\n2HLJnIkTDofRWtMRuJVyOUMicaj5ewshViQJY0KIq6OyIXd1OYlCWXO20UzKyjBgy9X3T5yAaJSw\n29hSKbRxaMklsfExABKuAiRZOpMSyOYmyZamCcQKtbDoMpsYdto4nmpcxF9OFSmnF/ReveIVYLUa\nfz9+HKJR4zW9diLxJqvwr1tvvGMiQS6XI5FIVOrGYFbWGxNi1WkrjCmlTEqpjyuljiulskqpEaXU\nfUopdxv3WpVSf6eU2qeUiiqlckqpc0qpbyqlbvjZX0EI8bIQOQbuYG0m5dnKTMqmy1q0CmO1ejHj\nWUGvfckl08eNZTSivhKFeGHpTEogHnsBAH9SzYdFYKvb2XSYEhYV8TudcOON878//TQAIa+DSDKH\nXrS1EoDN4cRa1jgSRi9bOBzGZuvC5VpPLL6/+XsLIVakdnvG/gr4LHAU+CjwbeBjwINKqeWeYQP2\nAE8Cnwb+M/BV4DbgGaXUPS3uFUKsFJETtV4xaL4nZSGSxuSxYnJamj/rCWNj7Ui1Z8y3tIB/9uwZ\nACa6iiRmEw2HKGPx51HKhtexDsLzYWyL28HZTI5cuX47o+qkgroifoDbb5//+1NPGW3y2imUNLPp\nxjVgDqsZa2WSQLVuzO+/iVhsf8MAJ4RYuZYNY0qpHRgB7H6t9du11l/WWn8C+ARwN/DuVvdrrVNa\n6z1a649prT+ntf4HrfWfArcCCvjkz/4aQoiXtNpMyoVhLIMJo0Zrobb2pFwwkxLm1/VaaG58FHOp\nzEyng0w607B4Px5/Aa93O6bKHpVVW90OShrOputrviwdDjCxtIh/YRj76U+NNvmar8IP4HK7oQQ2\nh22+iN9/I4XCLJnM+RYvL4RYadrpGXsPRmj63KLjXwbSwPsv87PDQBbouMz7hRAvF/FxyMUhVN8z\nttZpw2mu/xpaNoxNTMC5cwCE/SFcNjNu+9JetHg0grNQxOMbBJYW75fLReLxg/h9u42QOHcB8ilg\nvrducRG/spiwdDiWhrGFy1s8+ywUCoS8zVfhB/AFQ2RtFhwuE5FIBAC/3xjunIvta/7+QogVp50w\ndjNQBuqqSrXWWeBA5fyylFJmpVS3UqpXKXUz8A3AA3zv0poshHjZiVS3QaoPY4uHKMvZIuVkoXUY\ne2Z+YdTI4PqGvWIAiWQcC2VCugdYuqxFKnWCcjmLz3f9fLuiJwHY4LJjUU02DA+6lg5TrlkDQ5VJ\nBOk0HDy4YH/KxmEsuHYDWinM+SThcJhyuYzLtR6LxU9sTsKYEKtJO2GsH4hqrRt9o4wB3UqpFnuW\n1GwDIsAERrB7A/CZyh8hxEq2aIPwfLnMuUyOLe760FXtcbK2WvB1QRgLd/XVeqAW0lqTLBYoW0r4\ni37sdjter7fumli8Urzvv2E+jFXqxmwmE+udDk40mVFZnM6gF63Qv3iosjpMGWkSxkKbjOUtTPEZ\nCoUCsVgMpUz4/TcQiz/f/P2FECtOO2HMBTTbvTa74JrlnANeB/w88LvAScAPNP5vbYVS6iNKqb1K\nqb3VrnwhxMtM+Bi4usFtrHZ/Jp2jqBtvgwTLzKRc2DPm8DWcSZmOxygpSNkL2DP2JjMpn8dq7cLh\nGIDOdWCy1tWNbXE7GveMdTvRhTKleL7+xMKhyqeewmWz4LFbmtaMdW41AqB5ZgZYWMR/I6nUKQqF\nWPN/AyHEitJOGEvTPDA5FlzTUqWQ/2Gt9fe01p8H7sEIZ/+yzH1fqkwA2NNoNpQQ4mUgcmLJYq/Q\naCZlBhRYOpuEsVIJnntu/rFlS8MwNnvmNADTrhymlKlh8X4sfgC/f7cR0sxW6N60pIj/QiZPutRs\nRuWir70mMyqbDVP6Qr2gNZZpI4wtrhuT3jEhVo92wtg4xlBko0C2BmMIM9/gXEta6yRwP/AGpdSG\nS71fCPEyobURchZug5TKYgI2OOu/VorRDOaAHfX/s/emsZFl6Xnmc+6NfWWQjOCeZO4bc+nKrLVr\n6aXU6pa7pXFD8shjwdIMJBnQyJ6WMPNrjMFg/gjzoy0btmBAgqBZ3IYlW62RWnK31GtV1165b8yF\nZJJM7kvs+3LP/DixMoJJZiazKjN1HiBB8t4b98aJRrNefuf93s++xa+miQlIpwHIjoySLln17cBm\noreqGWMhgVW02sz7pVKCbHZamfdrhA+3VcYkcCfbWtmqhdG2mfhPnVKZYwCzs7C4WA1+7SzGTJsN\nOxIjW8bv9zcqY4FTCGGSSOi8MY3m7ws7EWMfV697ofmgEMIFnAbOPcLza3/+dj/CPTQazZNMakl1\nUjaZ929n84y5nbg2d1JubNNJ2ewXe1GNIQr7OlTGZmYAiId86ppNYixZ9YsFAqcaB8NHITYLRVXx\nOrzFjEoj4EDYjXYxZrfDC02/Jt9/n0jAteU2pXqJiZQG4XC4XhkzTQ8+31Ft4tdo/h6xEzH2p4AE\nvrHp+G+gvGLfqh0QQgwIIY4IITxNx8KdgmGFEP3ALwFp4PpDvHeNRvM0sLqzTkopJeW1bcTYR42m\n7rWTZ4DOga+JlSUc5QpFjzLtb96mVOZ9QSBwsnEwfBiQUJ1RudftxCFEmxgTQnQeGA5tvrGwb+tt\nSgCH30PBZiPo97C2toZVDZkNBp8jkbyMZZW3fK1Go3l2uE/EtUJKeVUI8QfAbwshvo2KojiKSuB/\nC5Fxs+sAACAASURBVBVRUeP3gF9FhcH+pHrsnwDfEEL8BcrEXwQOVa8LAb8updzWc6bRaJ5S6p2U\nSowVqp2UXw13tVxmpUvIQmXnlbH9x+BKsWO0RTIexVWx8FQCOJyOtk7KZPIiXu9BbDZ1PJMoMDM7\nwkrifyT7J0tIn8TX7WJ42OBGov3Xky3spjifbn9/m3xjkZ//LbLFCulCGV+HLDR3pId4LIOtkKJc\nLhOPx+nu7iYYfI75+f+HdOYmAf/41p+HRqN5JthWjFX5BjAD/CaqG3Id+LfA/yaltO7zOoCfosYh\nfRUYQI1HWgF+APwbKeV7D/62NRrNU8PaBHh6wKe2CqeyBSr36aTcckB4JgNXr6rvhWC1bxiY7mjg\nT+eyuEwIloL0RfpaOimllCQSl4mEv0RiLceHfzXN1PlVLEviMl7AnyoAJVZnU7jLDi72Fvnh1Rs8\n/w/2Eqi+N1uvm9zVdWTZQtiaCv/NlbELF4i4TQBWk3l8YV/b++waHWPp1hzW6qK6bnWV7u5uuoKq\n6peIn9diTKP5e8COxJiUsgJ8s/rvftf9GvBrm46d5+FT+jUazdPO2m3obTXvw0PEWpw/D7VZkceO\nsVYS2AxBt6c15tCyKmRlBYfLIFgKtvnFcrkZyuU4sXvDvPUHHyJMwYnPD3P0lQG6v/0FRPgg/PK3\nkFKydOUe/y4a5foPVpk8t8qLv7CPU18YwRb2gIRyNI890pTs09sLBw7A5CQUi0RW7gEq+HVfBzEW\nPjrOxN+9TWVxDlwDrK2tceTIEZzOAZyOPhLJS4zwq9t/xhqN5qlmp4PCNRqN5sGpdVI2jUG6nclj\nCpVy30x5PQemwAy1e8CAli1KXnyR1VSBXp8Tw9iUH7a8jBSCrN+GvWJvE2Mb68oYf/0HAcZO9vBP\n/veXePWXDtIz5ENEDtc9bkIInhsMAHD2fznF8JEQ7/6XSf72j64hAkoAtiXxQ4uJP3JH2WG38o2N\nHVQNBKXVVQKBQN3EL4QgEDxFMnmp82eh0WieKbQY02g0j4/0KuTjbeb9vW4nTqP1109pPYet24XY\nJK7qNIuxF15gNVXouEW5cUMJoGjADrSa93OpIlfe+SFWycmLX3mdn/2NcXyhpnuEj0DsLpRaq3dz\nhsXP/dZJPvuLB5i+tMb3/lSZ/MvrHeyuL75Y/zZyUTUcrCY7d1T29g4ipEUhmSUcDtfjLQACgdPk\ncnOUSrHOn4dGo3lm0GJMo9E8Pmq5Xb2H6oc6dVLCDgaEb66MJfMdzfuxKSWUNjxKjNUqY4Vcmb/8\nN5fAeQuv5wQnPz/alspP+DBICzZUaOyY24nTUB2VQghOv7mHL/+zE6wspCkKKCx3EGNNlbHgh+/g\nsBmspTtXxoQQGMKiXCgTDodZX19vdFRWYzdqY5s0Gs2zixZjGo3m8VEdvF2rjOUrqpPykGdTrIUl\nVcbYVjMpFxdhfl597/HA+DhrqULHWIv4vTmQkozTgbAL/H4/lZLFd//9FeLLMVyheSKDz3d+Tq2C\nVxWRphAc8Dhb4i32nQ7z5X92glRJsn59A2tTQj+nT6vMMUDcuUPYY98y+BVAOAVFYRDu7qZcLhOL\nqUqY338CMEgmtBjTaJ51tBjTaDSPj7Wb4AyCvx+AqVwBi3bzfiVRgLLcujLWlC/GmTMUEGxkivR3\nEGPJ9VVc5QpOAni6lLn+R/9hgoXbcV757wRQaU3eb6bnAAijEccBHPa627LG9p7sxT8WwJYv89M/\nu4OUTUPDXS6Vxl8lQuG+WWPC7yLnsNFVHTxe843ZbF583oPaN6bR/D1AizGNRvP4WLultv6q24Hb\ndlL2bCHGNm1RrlXFTV+HUUipVBKXMAiUAnT1dHHjnUVuf7jCC1/bS3B4DoBAcAsxZndB977WsUge\nFwuFEulypeXS8IkeXIbg5lsL3Hx/qfU+zb6xTPy+KfxmX4iyaeJaV36xVt/YKRLJK61iT6PRPHNo\nMabRaB4fHWZS2rbqpATsW21TbhJjK1VDfF+wvTKWLhawedw4LSdBVy8//dM77DnWzdmvjJFMXMLl\nGsbp6N36PYePbKqMqWfc3lQdq1Xx9u718/Z/uk1sOdM42eQbC6/O37cy5h4dAiA2dbOloxKUGCuX\n4+RyM1u/X41G89SjxZhGo3k8ZKOQWdskxnJqzNCmTsryWg7hMDD8js13gUoFPv648fOLL7JS9WD1\n+VvFWLGQJ29AKaCS9WMXTFw+O2/+D8cQhiCRvLT1FmWN8GGITkG5CDTE2M1sZzF29rOD2Owmf/fH\n16mUrPp7rBGZuU08W6KwqbJWI7h/PwDrs9NEIpHWyli1gqdN/BrNs40WYxqN5vGwaQwS3KeTsjog\nvK27EWBiAtLV0UP9/TA83KiMbdqmjN9WDQPZgPKKFdbtfPGfHsXtc1AorFAoLG29RVkjfASsMkSn\nAdjjduAy2mdU2nrcIMDMlfnCrx5l/V6ac9+bUScPHoRgEIDIqmo8WNuiOjY4fACA5OpKW0elz3sQ\n0/Ro35hG84yjxZhGo3k81HxX1cpYrmIxkyt2FGOl+8VabNqiRAiWk3nspqDb21pJ27ipAlszDj/C\nMhl/eYyRY90AJKqCZkeVsab3bwrBQY+rbZtS2AzMkIvyWpa9J3s59GIfF743y8ZCGgyjvlUZSUeB\nrYNf+0NDCFkhm84QiUSoVCr1jkohTPz+E7qjUqN5xtFiTKPRPB7WboHdC4FhACazeSRwaJMYk2WL\nSjS/s07K6vbfarJAxO9qq6TFZ1U1q1wOYVguPvuLB+vnkolLCOHA7z92//fdcxAQbb6xzZUxUFuV\nNb/bq790EIfbxo//w00sSzbEWCZWf8+diHgiWEaZfKlMb0+PurZpqzIYOEUqPUGlsrXvTKPRPN1o\nMabRaB4P67eg96CqEnGfTspoHuR9ZlJurowBK8k8/R3M+/HFRZBgmWVK3QWc7sb43UTyEn7/UQyj\nvQOzBYcHQqOtHZVeF4uFEslNvi97VYxJKXH7HLz2jw6ycjfJjXcW6++1L7VRf8+d8Nq9FJ0WObtJ\nqCouW038p5GyRDp94/7vW6PRPLVoMabRaB4Pa7fa/GI2AfvcnTspO4qxTAauXlXfCwFnzwKwnMx3\njLWIR6NIRw/SKOMcalTNLKtMMnmVwHZblDV22lEZdiOLFlZKmf0PPt/HwIEgH31nmsLJMwD0ZBPY\nKyWWYx3S+quUgnbydjtieYlgMLjJxF9L4te+MY3mWUWLMY1Gs/vkk5BcaIu12Od2tXdS1mItOomx\n8+ehambn2DEIqMHdq8kCfR0CXzcKEukKAdAT7qkfz2RuY1m57f1iNcKHYeMOVMpAQ4y1mfir77lU\nHRguhODVXzpILl3i/LksjI5iIImkY6zMLW/5uEpfAMsQxG/dJhwOt1TGXM5+nM5+kskrO3vvGo3m\nqUOLMY1Gs/tsGoMESsgc8XWeSWl4bBjVWZItbBoODpAulEkXym1ibH0+TUEWsFW3Jgf7Buvn6ub9\n7Topa4SPQKUIsRkARlwO3IbRLsaquWg1QQkQGQ1w5OUBLv/oHvGX3gSgL73B8srWA79te/oAiE5P\nEolEWF9fp1JpbIkGAqd0R6VG8wyjxZhGo9l9NnVSZisWc/kihz2dxdiD+sWgPdbi3T+7ArKA6RMU\njALDvcP1c8nEJez2blyukZ29/00dlYYQHPQ628SYGXCCzaC8lms5/tIv7MOwGbw/9HMA9Kc2WE6X\ntnxc16B6r/HFe4TD4ZaOSlAm/lxujmIxurP3r9Foniq0GNNoNLvP2i0wnRAaA+BOtZPykWMtaBZj\njXstTcaZu6FGHeWdDpL2JH3evvr5WthrxxyzTvQeqq6j1cS/WYwJQ2DvdbVUxgC8QSfPfWkP05ku\nVnsP0ZfeYIUOgbZV+vr3gJTEN9aIRCLA5rFIqqKX1OGvGs0ziRZjGo1m91mrdVKawNadlFahgpUs\n1rf7WlhchHkVmIrHA+PjQLsYk1LywV9OYzfjSCAvbKQcKSJuJWpKpSTZ7NT2Ya/NOP0QHGk18Xtc\nLBdLJErllkttYU+bGAM49YURnB4bH77w39Of2iBjc5Ja61zZGggOgaiQyWbo7VWjmpp9Y37/OGBo\nMabRPKNoMabRaHafTTMpb6bzOIRg7+ZOyo37dFI254udOQM25QWrj0KqirF7N6Is3okT9i4jbXYs\nKah4KthN5UGrCZgdm/drhA+3Vcags4m/HM0hK1bLcYfbxnM/O8rcyAuEhFrf8vsXOj6qz9NHyVYm\nC9hKJYLBYIsYs9m8+HyHdEelRvOMosWYRqPZXYpZiM+1mff3e5zYjNZtwnqsRU8HMdZhixJUZczn\ntOFz2pBS8uFfTePvcWHPzSPsSuw5go0tQSVgBIHAyQdbR/iIakSwlJG+LsY6zai0qnlpmzjxuWHc\nMkd++FUAli9NdHxUn6ePjKtEzmGnNDfXNqMSaib+K0gpH2wdGo3miUeLMY1Gs7ts3AFkw3cF3Mrm\nONJpJuXafSpj9xFjNfP+vYkoq7Mpzn5ljFQyjunyAuDv9tevTyYv4fUewGZrHNsR4cNQzithCQy7\nHHjMDh2V1fe+2cQPYHeanNmTJdV7iJGSwfLUvY6PCjqDJAOSvN0kd3eGcDjMxsZGS0dlMHCacjlB\nLjfzYOvQaDRPPFqMaTSa3WXTgPBMucJ8vtR5QPh6DjPowHCYrScqFfj448bP1VgLUNuUtS3K89+d\nxRdycvilftLFHHh8FM0ikS7lF5NSkkxe3nnYazO1yl51PYYQHPK0m/jtHeItmjn+D47gzkZ5qWBj\nZTkKHSpbQgjyfV4Qgtjk7fqMymi04TELBKrhrwm9VanRPGtoMabRaHaXtZtg2KB7H9DY1usoxja2\n6KScmIB0Wn3f3w8jjUiK5USe/oCLxck4i3finH5zD8gyGQFlj5eEPUG/tx+AXG6WUin24H4x2HFH\npeGxY3hsW4ox24ljnL71V4yVTdbtEVhY6HxdvxpoHptTlTFoNfF7vQcwTa828Ws0zyBajGk0mt1l\n7RZ07web8m01OinbRdeWGWObtyirkRRSSlZTeSIBF+e/O4vLZ+fYa4PEJiawhCBvs6tYC4+KtWiE\nvX7mwdfh7gL/YJsYWy2WiW3uqGwaGN6GaTLuW6EkK9jCJ1vX1kSwTwnIxMpyXYw1+8aEMAn4T2gT\nv0bzDKLFmEaj2V3WbrWNQXIZglF3a85WJVPCypa376Rs8ovFsiVKFUm4BHPXNzj1xRHsDpP1G9eQ\nNjsVBElHkohHbVMmE5cwTS9e74GHW8sDdFSWOnjGajie/wxr+QW6HGFi713reE1PeBCkJJWI43A4\n6OrqaqmMAQSCp0mnb1KpFB5uPRqN5olEizGNRrN7lAsQnW4TYwc8LsxNgavlNTU42xb2tN9nC/P+\nckKJIPNWCofL5MTnVHJ9bHoKy6lE3ebKWMB/AiE2edJ2SvgIrN2uz8fcUoyFPVipIlah3HaL2hqs\n9WtUBFxc8HW8pN/bj2WUSJcKyGKxY0dlMHAKKUuk09cfbj0ajeaJRIsxjUaze2xMgay0z6S8Tyel\nfXPgayYDV6+q74WAs2frp1ZSeYIVQWYqxfgbwzircyjjSwtIh3pGrTJWqeRJpyceLOx1M+HDUMpA\nUoXPDjnt+O7XUbneHm8BwAsvEE4ucdVR5pZ/nPRapu2Sfk8/eUeZrN2ktLTUsaOy1oiQ0L4xjeaZ\nQosxjUaze2yaSZksV1gsdO6kLK1lwSYwQ5vOnT9fr0Rx7BgEAvVTK4k8zxVsCEPUq2IAiVgU4fSA\nA1xuFx67h1TqGlKWH868X2NTR6UQgkMdTPyNjsps5/sMDTFgVvjIWUEKgyt/fqXtkj5vHylvmZzD\nTnFOzai0LKulo9LpjOB0DpDUHZUazTOFFmMajWb3WL8NwoAe5dG6vcUYJIDyag57rxuxKQi2ZYuy\nKdICYHE9y8miyf4zYXyhRpp/Kp/FcnspeUoNv1i1evRQsRY1Ng0Mr62lrTLW4wLROWusRv9IH0lT\nElq+zI2raUqFSsv5iCfCWrBMyWaSmprsOKMSVN6YroxpNM8WWoxpNJrdY+0mdI2CXVWKtppJCcoz\n9iB+MYDMRBwHgs+8uad+zCqXSQtJyekk5UjVB4QnkpdwuYZwOsMPvx5PN3gjrWLM42K9VGaj2PCH\nCbuJGXRS2qqjEug7oqI+nMvnKVRMbn2w1HK+x9XDekhVBKNTtzvOqAQIBE+Rz9+jWNx4+HVpNJon\nCi3GNBrN7rF6s80v5jYMRlytnZSybFGO5jsPCN9CjFkVC89sjphXEBltbF0mbt+m7HRhCYN1c51+\nj4qISCYuPVpVrEb4cOvA8C1N/PeJtwD6n1fjmGJWlkhqlss/mkdajQBY0zCx9ap1xefncTgchEKh\nDmOR1Jp03phG8+ygxZhGo9kdykU1CqnvWP3QzUyOg14nxuZOyo0cSLBHNlXGFhdhXpnl8XhgfLx+\navrSOq6iJLWnVcBtXL9a76RcYok+Tx+Fwgr5wuLD5YttJnxEibFqcv79ZlSW13Jbzo4MvXwWR7nI\nqr+HUx9/i/hKlrkb0ZZrfNV8sXh0XT06HG6vjPnHEcLUeWMazTOEFmMajWZ32JgEqwyRhhjbqpOy\ntFqdSbl5m7I5X+zMGbDZ6j9e+uEcCUPi29c6YzI6PUnFocRYwp4g4ok0wl6rI4QeifBhKCQhpbYV\nB5x2/Ft0VMpCBStd6ngb4ffTV0yx7Oth/9RbeN1w+UetsyrDgT4wKqTyWWSpRCQSYWNjg3K5sSVq\nmm683sPaxK/RPENoMabRaHaH1Rvqa+QoAPFSmZViuXPyfi1jbHPg61b5YncTrEwnOecsMdDV+pr4\nwjyW04XT46RkKgN/MnEZIez4fMcffV31jkrlGxNCVE38rVuS9qqwvK+J3y5Z8vdgWmXGXQvcuxEl\nutiIuejz9FGwl8nYbZQWFjp2VIISmYnkZaS0Hn19Go3mU0eLMY1GszusTqiZlD0Hge3M+znMoBPD\nuSmMdYtOymtvLWA6DK46KgwEW8VYIrYBTjfOoOquHPAOkEhewu87imk6eWQ2xVvAFh2VvfcfGA7Q\nH/Kw4u8B4Pid72HaDa78uFEd6/f2E/MWyTrtFGdnO86oBOUbq1TSZLPTD78ujUbzxKDFmEaj2R1W\nJ1SkRdtMys4ZY7bIpqpYpQIff9z4+aWXAMinS0yeWyVwpIuSgIGu1vslcxkqTjfSq7xa/d4wqdTV\nRwt7bcbbC+7utniLaKnCWrGxJWl2OcEU9+2oHByOsOTvxULg/uAtDr/Qx60Plsln1H0GfYOsdZUo\n2kxSdxodlW0m/qDaftW+MY3m2WBHYkwIYQghfkcIcVMIkRdC3BNCfFMI4d3Ba0NCiP9JCPF31dfl\nhBC3hBB/KIQYefQlaDSaJ4LVG/UtSlBizGsaDDvtLZdJKVXG2Ga/2I0bkE6r7wcHYViFut78YIlK\n2aK8V10/2FQZk5UKSZsdaRhknVkCjgCysEilkiUY2AXzPqgpADUTf5Xa1mtzdUwYAluPu74F24nB\nA8MUbQ42PEFYWGD8mINyyeLWB8uAquqtdSl/2MbknXpH5ebKmNezH9P06Y5KjeYZYaeVsd8H/hVw\nA/jnwH8G/gXwHSHEdvd4EfgmIIF/B/w28F+BXwGuCiGO3ee1Go3maaCYgdhMi3n/ZibPYa8LsamT\n0koWkcVKe6zFBx80vn/pJRACKSXX3l5gYH+QVUNiGoKwvynsdWqKolf9Tbhh26huUV4EILAb5v0a\n4cOq8lftlDzkVe/hQeMtBrvVXMrFgNp+DM9doX9fgGtvLyClpN/bT9KrxFh8UXWVdppRKYRBIHCS\nZEKLMY3mWWBbMSaEOI4SYN+WUn5dSvlHUsrfBX4X+Dzwy9vc4iZwWEr5s1LK/1NK+cdSyt8Bfh4I\nAv/Hoy1Bo9F86qzdBGS9MialZCKT41gH835pbYtOys1iDJi/FSOxmuP460MsJnL0+Z2YTYn9G9eu\nUHGq+yywwIBvgGTyMnZ7N273HnaN8BHIxyGtRFG/w07A1t5Rae91U47mkZXO8RYDQbXFuhRQ2498\n+CHjbwwTX8kyfytGj6uHgk+trzneIhqNtnRUgjLxpzM3qVS2Fn8ajebpYCeVsX8MCOBfbzr+R0AW\nVeHaEinljJRyqsPxHwBRYLz9VRqN5qlidUJ9rVbGVoploqUKR32dk/cB7Js9Y81irNpJef3tBVxe\nO/ufC7OcyLd1Ukan7mC53AQ8HhZyC6oylrhIIHCqrSL3SNSy01avA9WOSo+7Pu6phq3XDRVJJd55\nYPhQ9f0vVCtjfPQR+58L4/LaufbWAkIIIsEBDBPShQJWPk8kEsGyLDY2WhP3A4HTSFkhlbq+e+vU\naDSfCjsRY88DFvBR80EpZR64VD3/wAghgoAfWHmY12s0mieI1QmwuSA0BsCNtKrWHPN1irXIIZwm\nhr8plT+RgImqoDNNOHOGTKLA3UvrHHllAJvdZCmRr1eWasTm57GcbnoG+kiVUgy6u8hmp3Yn7LWZ\nSDUiY6UhfGodlc0hr7Wt19JqZ99Yl8eO2yZYDKi5k3z8MTYDjn52gLuX10nHCvR7+ym5JBmnneLc\n3NYdldUGBW3i12iefnYixgaBdSllocO5BaBXCOHocG47/lfADvzfD/FajUbzJLF6Q/mqDBVVURNj\nR7fqpAy7WytXH39c92Nx8iR4vUy8u4hlSY6/OoiUksV4rl2MxTawHC68Pco3NmBTz901834Nbw/4\n+mHlRv3QYa+LWLnCWtOMytpEgfIWYkwIwWDIw2Kk2ruUTsPEBMdfG0JKyY13Fhj0DhL3lsg67BRn\nZujt7UUI0eYbczp6cbmGtIlfo3kG2IkY8wCdhBhAvumaHSOE+EXgfwa+B/zJNtf+phDinBDi3Oa/\nDDUazRPC6kSLeX8ik2fIaafLbmu7tGMn5Sa/mGVJrv90kZGjIbr6PMSyJQplqy1jLFqpqG7Haii/\n31oHlLl91+k7DivX6j/WtmAnmrYqDY8dw++gtHKfjsoud0OMAXz0EcGwm9HjPVx/Z5F+1wD3AhmK\ndpP05CR2u53u7u42MQaqSUEn8Ws0Tz87EWNZYKvkRFfTNTtCCPFzwLeA88B/K7ca5FZFSvmHUsqz\nUsqztXK9RqN5gshG1aigJjF2I53jaIctSqtQoZIotGeMbRJjs9c2SMcKHH99CIDFuKp4DTZljMlS\niZRL/Zx1ql9BZmEWn+8QNptvV5bWQt8xFW9RUZWw2hbs9fSmJP4+z5bblKCiORY9ocaBatDt+OtD\nZBNFupaHiQZU7lh06o56dF8fy8vLbfcKBk6TLyxSKOg/VDWap5mdiLFF1FZkJ0E2hNrCLO7kYUKI\nLwPfBq4DX5JSJnf8TjUazZNJLQy1KsaKlsWdbJ5jnZL3qyKlpTImZdsYpOtvL+ANOhg7qboOlxOq\n+tTfVBlL37lDwePDANaNdeyGST5zY/e3KGv0jUOlAFHVj9RttzHgtNe3ZGvYIx7KK1mk1fnvzMEu\nN2vSTsGsVg2ra98z3oO/20X5mr8ebxFbXACgv7+feDxOPt/aGFCL70hq35hG81SzEzH2cfW6F5oP\nCiFcwGng3E4eVBVi/x8q6uJNKWXswd6qRqN5Itk0k3IyW6AsO5v3a9t3tr4mMTY9DesqxoFQiGRo\nmNnrGxx9dRDTVL+iFhPVyliTZ2z18kUsl5ug28Vydpljvm7K5dTuJe9vplb5a9qqPOZ1t1XGbH0e\nZMmiEu/s7qhV95ZrHZVXr0Img2EIjr8+SOquhUk3UB31hKqMAaystPY7+f3jCGEjoX1jGs1TzU7E\n2J+iAlu/sen4b6C8Yt+qHRBCDAghjgghWgwhQogvAX8B3AK+KKVsnXqr0WieXlYnwBmEwCDQZN7v\nJMZWM2AKbN1N5zZFWlx/bxkBHPvsYP3wQiyHw2bQ62sU6Ndu38JyuukfHGQ5s8zRahBrMPDcLi6u\nifBhEGaLif+4z8WdbJ6C1RjYba8Kza22KuvxFuNn1QHLggsXADj6yiCGTXBk/bPYbAbpSolKKkV/\nfz/QLsZM04XPd1hXxjSap5xtxZiU8irwB8DXhRDfFkL8uhDim6hE/reA/9h0+e8BEzRV0YQQZ4G/\nRGWV/QnwFSHErzT/273laDSaT5yVGxA5ooz0wI10HocQ7He3OxvKK1nsYQ/CbOqkbBJjlRdfZuLd\nRcZO9uLvblTB5mM5hrvcGE2Br6sri0ibnZH9B1hML7LHUcZmC+Lx7H0MiwRsTug92BJvccznpizh\nTpOJv95RuYWJf7AqxhbHm0RjdavSE3Cw/zMRDq+/gPTY1MDwmVkCgQAul6tNjIHKG0smryJl5ZGX\nqNFoPh12Og7pG6jux+MoYfbLwL8FviqltO73QlSoqwvVBPD7wP/b4Z9Go3kakVKJk77j9UMTmRyH\nvS5sRnvoamkl27pFCS1ibHrkJXKpUt24X2M+lmUo1FppW8urbcBIf4S13Bo9xAkGT+9u2Otm+o7X\ng1+hsRV7o2NHZabjLfprKfx7DjUONn0G468P4Si7KTgCZKrxFkKI+5r4K5U0mczkIy1No9F8euxI\njEkpK1LKb0opD0spnVLKISnl70op05uu+zUppZBS/qTp2P9VPbblv11ek0aj+aSIz0EhocztVVQn\nZbt53yqUqcQL9W08AHI5uNTYYru+0UWg18Weo90tr12I5xhuEmNSShI2ZYAXfoGTCk4r+vjM+zUi\nx9Sa86r3aJ/bicsQD9RR6bKb9PocLPY0tmF5//16ztrAgSDFYArKwxTtNtKTqqOyv7+f1dVVLKv1\n799awG0icWFXlqjRaD55dloZ02g0mnZqZvZ+leu1XiyzUix3nklZ3bZrEWMXL0J15mL0M2+wMJ3m\n+GtDiKaqWq5YYT1dZDjUeF15fZ2cx4tDWsQqMfY4lEAJBh+TX6xGTXRWxz/ZDMFhr6tzR+XqxDsa\n3AAAIABJREFU/TsqFww3+KsBaYuLMDsLqGBYjsVxl0YB2Ji6rR7d10epVCIabbXcut1j2O3dxBPn\nd2WJGo3mk0eLMY1G8/AsXwNEfXbjzcx9xiDVOym9jYNN23PXn/tFDFNw5OWBltctxNXrmitj0SuX\nqbg8BJ1OFjOLjDktQDyesNdm+to7Ko/7VEdly1ikPg+yeJ+OyqCbxUS+PhAdgPfeq38bOeWgYldZ\naRsL8wBbmviFEHQFz5DQYkyjeWrRYkyj0Tw8y1egex84lMBqdFJ2GIO0kgWbga3JmF8TYyWbk1vO\nw+x/LoIn0Dpd7V5M3bNZjK1cv4rldBHp62c+Nc+Yw8LjPYDN5t/V5bURHAFnoM3EHy1VWGkei7Rd\nR2XIzUIsh3zls42D775b/3akd4ipyBRgEEtnkOUy4XAYIURHE3+w6wy53ByF4vojLlCj0XwaaDGm\n0WgenpVr0N/sF8sTdtgIO+xtl5ZWs9jD7sYWpJT1atDk/s9RqJiMvz7Y9rqFqhgb6mpsU87fmwNh\nMHrkCPPJe+x1Sroe9xYlqI7RyLFGthqqMgatSfzbdVSOhNzkShXWz77cONhUGRv2DXO9/12EEWLD\n201pfh673U5vb29nE3917bo6ptE8nWgxptFoHo58EmIz0H+ifuh6OtfRLwZQXsm0+sXm5mBBJcxf\nG/9vCPV7GDjQ1fa6+VgOuymI+BtRGStp1Ts0euAA6ewkLsN6/Ob9Gn3HVZxHdVuyNmmg2Te2XUfl\nSLf6HO7tPwZG9dfwlSuQSgEw6Btk3TeP4fKTdtrJT02rR/f1dY638I9jGA4ScS3GNJqnES3GNBrN\nw1HbqutTYqxoWdzM5Dnh7zCTMl+mkii2+sXeeQeAtd6DrPYeYvyNoY6xFPOxLEObMsbihoGwLHp7\ne7EVlPG91lX42Ok7pjpIE/fUc+02hl32B+qorIuxgoATVTFrWfW8MZfNRdgdphgxsMhw76J6Vn9/\nP4lEglyu9VmG4cTvP0Fcd1RqNE8lWoxpNJqHo95JqbYpb2XylKTsKMY6dlJWPVLXjn0VGxUOv9jf\n8THzsVxLJ6VVKJB1eXBVypRkibARpyzceDz7d2NV29Ov5kGydKV+qGbib+Z+HZUj1fXMx3Lw2c6+\nsWH/MMtDG4DFxJSqBG41FgmgK3iGVOoalUq+7ZxGo3my0WJMo9E8HMtXwdUFARXQejWlxMgJn6ft\n0nInMfbOOxQcXm4f+CIHxwycnnafGSjBUhshBJC5fZuSx0uX08FiZpG9DgtcBx5v2GszfcdBGKp5\nocoxr5upbIFcpZEBVu+oTLR3VLodJr0+J3MbWXjllcaJJt/YkG+IOZcy5C/lDXKp4n3FWDB4BilL\nJFNXH3mJGo3mk0WLMY1G83CsXFN+saoIupLO4TMNxtyOtktLKxmE3cAMVTsp43G4do3bB9+kbHcz\n/gvH214DkC9VWE8XWjopZy6cA9NGf1+Ee7FrhO2SwCdh3q/h8EDPwbbKmAXcbB6LVOuo3MrE3+3m\nXizbWhl7/32oqLFGw/5hpk1l1resBBPvLeL3+/F4PNuY+PVWpUbztKHFmEajeXCsijKxN5n3r6Wy\njPvcGB0qVLUxSPVOyvffR0rJtaNfJZyZJ3K08xblQrwaa9E0WHxmWpnZ9544yXpURWMM9b6xK8va\nMQOnYOly/cfa1uzVVEN42fuVP660tIWJP+RRYmx0FAaq2WqpFFxXXrxh3zAlm4XL5cKWn+H6T+6B\nhIGBAZaWltru53B04/Hs0x2VGs1TiBZjGo3mwdmYgnKunkhfkZLr6Rwn/e1blFJKSkvpujgB4N13\nWe47TrRnH+PBtS0fM98h1mI5lQQpOXjqNMXMdYoWDPW8vNUtHg8DJyG1CGn13ve4HHTZTK6kmjoq\nXTbMkJPSUrrjLfZ0e1iM5ylbsqNvbMintn9doQBGcYlkrMS9m1EGBgZYXV2lVCq13TMYPEMicaEl\ngFaj0Tz5aDGm0WgenJpfqmren8wWyFmS8U6dlKkiVqaMY6C1k/La8Z/HUUhz8NU9Wz5mPqYqTc1D\nwuMIbIU8bq8PR2mOFcuLabZvjT5WBqom/mVVHRNCcNLv5kqqdUvSPuDbujLW7aZiSZYS+Y6+sWH/\nMACVfj8Fs4TDLHP97UUGBwexLIvV1dW2e3YFn6NUipHNTj/qCjUazSeIFmMajebBWboEpgPCRwG1\nRQlwosMYpOKiEiP2QV/1QJHc5ZtM7nudw3e+j/31z7a9psbcRhaHadAfUF6zSqFAzu3Ba5Upl1ME\nZJK02XmL87FS255t8o2d9HuYyOQpNA3ytg94Ka/nkKVK2y1qHZX3otmOlbGIJ4LdsJPqNqmYBkPm\nJHevrBP09gCwuLjYds9g8Aygw181mqcNLcY0Gs2Ds3hJbVHaVEXqSjqHyxAc9HQYg1StDNlrlbGL\nF5kY/RyW6eB44iIMtqfu15jdyDLS7cases3Wr13Dsjvo9nqJxy9gCBDug7u8uB3gDkHXaItv7KTf\nQ0lKJtINE79jwAsSSsvtJv561lgsC6dPg6v62d29C0tLGMJgyDfEmke91rf2EVJK5q9kcLvdHX1j\nHs8+7PaQHhqu0TxlaDGm0WgeDMtSImTwdP3Q1VSOYz43NqODeX8pjRlyYrhsAMh33uX6sa8yuHiJ\nntN77/uomY0MYz2N7c3b584BMLxnlJXou1Qkn1zy/mYGTrbEW5yqbtE2b1XWBGinrcqBoAvTENyL\n5sDhgBdeaJz86U8BGPIPcc+u4i1yazPsOdrNxLtLDAwMdKyMCSEIBs8Qj3/86OvTaDSfGFqMaTSa\nByN2FwpJGFBiTErJtbTqpOxEaSmDfcBX/3nu4zmSgUHGb3wHXn11y8dIKZndyDLaJMbuzd9T5v0X\nnmcj9iELJYPBwL5dWtgDMnAKotOQTwCdTfxmyIVwmBQ7mPhtpsFgl0tVxgDeaOoIfestQHVU3q0s\nYrfZScoKR075yMQLeMwuVldXKZfLbfcNdb1ILjdLvtAef6HRaJ5MtBjTaDQPxuJF9XVQVaTm8kWS\nZatjJ6VVrFBezzW2KKXkWm4IdzbKvrvvtHqlNrGWKpArVRjtadx3rZBHFAv07RujmL3FdMGoG90/\ncWpJ/MtqEkEnE78wBPYB733jLeaiHcTYT34CKDGWKqXo6u0l7XLQJ5bxhZxkl0wsy+oY/hoKvQhA\nPPbRIy5Qo9F8UmgxptFoHozFi2A6IaLM+5dq5v0OnZTllSxI6p2UyQ+uMtP/GY5P/A1mKAjHjm35\nmNmqSGkWYymbHWchR744hZAlpgsGe/xbd2M+Vuodldub+EvLmY5xEyMhjzLwA7z8MtirUwhu3IDV\nVUYDowA4hvtIuRwU79zm2KuDxO+q7eBOvjGf7wg2W4BY/IPdWKVGo/kE0GJMo9E8GIuXVKSFqYTD\nxWQWpyE46m0379e252qVsev/9SZCSo5N/I2qBBlb/wqaWVfVpJpnLLG2RtnhJCAgFlMDtTPmAC5b\n+3M/Efx94OtTn0eVTiZ++4AXma9QibWPRRrr9bKeLpLKl8DjafWNvf02o0ElxooDXko2k/iN6xx9\nZRBTurCbji18YyZdXc/XPyONRvPko8WYRqPZOTXz/kDDvH8xmeWEz42jg7AqLWUQThMz5KJSsphY\n8TI2+wH+zBp87nP3fdTsRhbTEPWMsbvnVIdgf1cXsfgHRC03Yf8nNBx8Kwafa2zb8uAm/r29quo3\nu1G9vvkzeestRnwjGMIg5isCsHZ3Cl/Iyb5TYYyCj8WFdjEGNd/YjPaNaTRPCVqMaTSanROdhmKq\n7hcrW5IrqSyfCbT7xQBKixns/V6EIZi6uErOcDN+46/Uye3EWDTLUJcbu6l+TU3dvAFSMnp4P/H4\nOW7nqG/jfWoMnYH12/c18dv7vSDomMS/t1c1NkxXq4CbfWN2086Qb4h5dxyA2MYaslRi/LUhjLx3\nSxN/l/aNaTRPFVqMaTSanVM376vK2M1MjpwleS7gbbtUWpLScgb7oDp37bt3CCQWGJk/Dz09cLzz\ncPAasxuZFr/YYjSKUcgSOu7HsnLcyFUYC4ztzroelqHnAFn/XIQQnPJ76j46AMNhYutxd6yM1dZ3\nd6167pVXwKYiQLh2DdbXGQ2MMlOcx+P2kHSYFGdmGD4SIujuxpJWx6Hhft9RbDY/sbjeqtRonga0\nGNNoNDtn6RLYXBA+AsDFqujoVBmrxPLIQgX7gJeNhTRLSyXGb3wHgdzWLyal5O56I2PMsiziCMxs\nBss5BwgmC+YTUBl7Tn2dP1c/9FzAw0QmR6bSSN23D3gpdhBjLrvJUJebmY3qOa+3zTc2FhhjNjlL\nz+AwKZeT/K3bCENw8gX1v8HtG+2jj5Rv7AXiWoxpNE8FWoxpNJqds3hRJe83mfe77SajrvbZkMUF\ntS3nGPRx7a0FTFnm6K2/VSe32aKMZ0uk8uV65Wh9fZ2KaeItF0mmPqZiHyBriU+/MuYOQc8BWLhQ\nP3Qm6KUi4XKyaatyyEclmsfKtg/33tvrbWxTQlve2GhglFw5h3fvHtIuO7mbNwH4zOf3Y1Qc3Lo2\n1fGthbpeJJu9S6HQHn+h0WieLLQY02g0O6NSVp2Dg43E+wvJLKf9HoRoT94vLqTBFMguJ7c+XObg\n7Du4Ckl1cgd+MaAe+Hrvxg0AIj4nicQFYiKCzbAx4BvYhYU9IkNnYeEcVKMrnqtWCc8nGwLLMay8\nYTWB2sxYr4e7a+lG9EXzZ/OTn9Srf1bEi2UYRG+qz8LtcxDyR1iPrVAqtM++rPnGdFelRvPko8WY\nRqPZGWsTUMrAiNpGS5cr3MrkO/rFAErzKewDXm5+pMTC+IU/Uyd26BcDGKt5qm5ch0qF4aMeLKvA\n3aKDEf8INsO2S4t7BIbOQHoFkgsAdNtt7HM7W8VYdUh6cb6ziT+ZLxOrVc1eeQVMU31/5QpjVhCA\nZEAJrrX5ufprDx7ZS8XMc/W9mbb71nxj8bg28Ws0TzpajGk0mp0xX513OPw8AJdTWSSd/WLSkhQX\n0jgGfVz98Tz97ix9a7fUyW38YgB31zMI0RimPb+2hpnP4N1vAQYXU5lP3y9WY/iM+rrQGM59Jujh\nfDJbr3YZHju2Hhel+VTby/f1KjF7d70q1Hw+eP75+vm+D67jNJ0sOVXHZiKXoZJQ3x89dQCA8z+9\n0RYqW/ONRWPv7cIiNRrN40SLMY1GszPufQyeXgiNAcovBp3FWDmaR+YrJIUgsZbj5MKPGye/+MVt\nHzW5mmY45MZlNymVSiQsiZnLUHHO4vcfZzK58On7xWr0jYPpaDHxnwl4WSuWmcsX68fsw/4ttilr\nYqzRgdn8GRk/+CF7AnuYzc0T7Oom6XaQn5gAYHBwECEE0eQqi7fjbffuDr1CLjdLLnfvkZep0Wge\nH1qMaTSanTH/saqKVf1hF1NZxtwOuu3tW4W1CtCtyTi+Lgf7vvfHjZNf+tK2j5pay3AgrLb2lpeX\nkULgrqRJZ6/h8J2gaBWfnMqYzQn9J1tM/GerAvVCsiGwHEM+KvEClXSx5eXDITc2QzQqYwA/8zON\n77//fcYCY8wkZ+g7cIik20n++nUA7HY7/f39WK4Ul3/ULri6u18DIBp955GXqdFoHh9ajGk0mu3J\nRmHjDoyo7TMpJecT2S39YsV5Zd6fnEoyPlbGTKltNcbGYP/9U/MtSzK9lmZ/VYzNTU4CMDSYQcoS\nKZuaRfnEiDFQvrHFi2ApX9cRrxu3YezIxG83DUa6Pdxt7qh8+WUVcwEwPc1oJcB8ap7IocPkHHYS\nVxrzMEdGRig70kxfWSO+mm25t8ezD6dzgGj03d1crUaj2WW0GNNoNNtT80NV/WJz+SLLxRIvBrcS\nYylyDhPTbnD83luNE1/6Ur2ytuWj4jkKZYv9ESVeZm7eRBTzdO8vYhhu5koqRmNvcO8jLmoXGTqj\nmhtW1fahzRCcDrg5l2gaizToU0n8HU383tZtSoejpatybDpOWZaRfdVq4eSt+rnh4WEqVhnLnuXq\nj+db7iuEoLv7VaKxd5GyveNSo9E8GWgxptFotmf+YxCGmsUIfJhQVZwXOoixmnl/OVnk0Ev9uH74\n3cbJ5u23LZhcU2LlQMSHlJJ7q6uY2TS2yAah0EtMJmYIOoP0uHp2YWG7RLXDlHuNGImzAS/X0lly\nFQsAw2XD1uum2MHEr8RYGstqMuE3fVYH3rsNQCyoRh/FkgkqKXWf4eFhAEIHYOK9JQq51vFIPd2v\nUi4nSSavPuIiNRrN40KLMY1Gsz33PoLIcXCqysxH8QxBm8lhr6vt0vJaFkoWsaLFqTMB+LjahWkY\n8IUvbPuoqVUlxvaHfUSjUfJS4jHWqBjr9HS/ylR8iv3B/R2zzT41QmPgH4C59+uHzgS8lCVcbRqN\n5Bj2U5xPtXU+Hoz4yJcs5mONoNhmb92+v34fgWCmOI/PHyDhdpC/rvLGQqEQHo8He3eeUqHCxLut\nw8NDoVcAQTT6091br0aj2VW0GNNoNPfHqqhtypFG3MKHiTTPB70YHQRRfkYFuzrHAnRffx8sVRni\n7Fno7t72cVNraUIeO91eB3NzKlOru1ulyIe6X2MyPsmBrgOPuqrdRQjY8xLMfVA/dLZaNaxVEQEc\ne/xYqRKVWKHl5Yf6/QDcWmmqmh05AkNDALjX44zYw0zGJunb32riF0KwZ88eVjYWGTzYxZUfzWNV\nq3EADkc3fv9x7RvTaJ5gtBjTaDT3Z/kqFJIw+lkANopl7mQLW/rF1i+sUrQkh39mD3z/+40TO+ii\nBJhazXCg6hebnZzEKJfo3ZPB5Roig49UMcW+rn2PtqbHwZ6XIXEP4qqrsddh45DHxfvxhkfMsScA\nQHEu2fLSg9X13m4WY0K0fGb7EzYm45P0HzpCxuUgda2x7Tg6OkosFuPAKyFS0Tx3L6+33L+7+zUS\nyYuUy+1bpBqN5tNHizGNRnN/ZquhoXteBuBc8j5+MSkpzSVJ2QxGj/fA3/5t4+QO/GKgPGO1TsrZ\nu3cxc0lcAym6u19jKqHmMD5xlTFQlTFo8Y291OXlo0SGctULZu/3IhwGhdlWMeZ32RnqcreKMWj1\njd1cZy45R2hUdZOu3L5ZPzc6qjpLpTdFoNfFpR/MtWyF9nS/ipRlYrFG5U6j0Tw57EiMCSEMIcTv\nCCFuCiHyQoh7QohvCiE6/2nc/vp/JIT4EyHEZSFESQghhRBjj/LGNRrNJ8Tsu8oTFVRbZh/GMziE\n4JS/Pex19vwqHgm+wyHErZswM6NO+P3w0kvbPmo9XSCaKXIg4iOdThPLZgl4lhBmiZ7u15iKKzG2\nv+v+8RifCn3j4PA3xCvwcpePdMXiekZ5wYQplG9srr1CdajPx63lTcfffLPefXrwo2nKskyhV3WT\nRhMxKmlVdevv78fhcDA7O8vpN/ewPJ1kaTJRv00w+Bym6WN9/Ue7umSNRrM77LQy9vvAvwJuAP8c\n+M/AvwC+I4TYyT1+C/hlIAdMPcT71Gg0nwZSKnFR3aIE5Rc7HfDgMtv/rz/9d7MADLwyCN/5TuPE\nz/6simvYhpoYOdIf4N49td0X6l0CTEKhV5iKT9Hl7HqyOilrGKbqqmzyjb3Upf5efT/WtFU5GqC0\nlMYqtkZNHOrzM72Wodzk9yIcrovY/fNK0M1bq3g8XhJuJ/mraqvSMAz27NnD7OwsR14ZwO23c/57\ns423Zjjo6Xmd9Y2fIGXT/TUazRPBtkJKCHEcJcC+LaX8upTyj6SUvwv8LvB5lMjajn8K+KWULwE/\neJQ3rNFoPkHWbkEuCqOvAGo4+OVUlpc6bFEuTyeQq1mkANdoAP76rxsnv/a1HT3uZk2MDfiZmZlB\nVCqEhmOEul7Abg8wGZ9kX3Dfk9VJ2cyel2H1BuRiAAw4HYy5HXyQaBVjWFC811oFO9Tnp1ixmNlo\nDW6tfXZ7l4rYLJRv7OAR4h4nuUuX6peNjY2xvr5OoZjj5BdGmLu+wXpTjEZvzxcoFldJpa7t9qo1\nGs0jspOq1j8GBPCvNx3/IyAL/Mp2N5BSzkkpy9tdp9FonjBmqx14VTH2QSJDWcJrIX/bpRf+dpZe\nh4G934uRisN71e06IeArX9nR424uJen1Oej1OZm+cwe/XMIVKtAb/iKWtJiKT3EwdHBXlvZYGH0Z\nkC3VsZe7fHwYz2BVPVyOEfXZbTbxH652VLb5xr76VQDsFcnoSpHJ6G0Gj42TcTmIXWgMJ6/5xubm\n5jjxxhB2l8mFpupYT88bgKG3KjWaJ5CdiLHnAQv4qPmglDIPXKqe12g0zyKz76n8rJBKu38nlsJp\niHpsQ43oUoaZy+uEbAbOsQB897uNSIuXX1bbbTvg1kqKw/1+0uk0a9EoXd0q2iLc+0UW0gukS2mO\ndB/ZvfXtNkNnweaCu2/XD70U9BErV7iVyQNgeu3Ywm6Ks62ia3/YhxAdxNj4OFSF1oG5HJMr1xk8\neBiA5Tu3kNXPeWBgALvdzuzsLE6PnfHXhpg8v0piTVXaHI5ugsHPsL6hxZhG86SxEzE2CKxLKQsd\nzi0AvUKI7c0gGo3m6UJKVRnb83LdRP5uLM3ZgBf3Jr/Yxe/PEXIaGJbEORpo9YtVKzvbUbEkt1dS\nHO4LcPfuXQC6+1awiSHc7j3ciqoRQE+0GLO7VFfldGME1Csh1Rn6zibfWHEuiWxK3Hc7TEa7Pe1i\nTIj6Z7h/Ic98aZ3g6AhCCKKyQrHaJGGz2RgZGal/dqfeHEGYgovfbwwQ7+39IqnUdfKF5V1dtkaj\neTR2IsY8QCchBpBvuuaxIIT4TSHEOSHEubW1tcf1GI1Gs5n125Bagr2vAxAtlbmWzvFqVVzUSK7n\nuP3BMscOBAFwDHvge99rXLBDv9hcNEu+ZHGk38/du3dxiiy+vjTh8JsATEQnMITxZMZaNLP3DVi9\nDmn1+2rE5WCf28lbsYbIcu4NYmXLlFZa/WEH+/ztHZVQ/wwPzeeRAmayc/T0DxL3ushdbPjG9u3b\nx+rqKqlUCm/QyZGXB7j53hKZhPoV3tvzeQA21n+8q0vWaDSPxk7EWBZwbnHO1XTNY0FK+YdSyrNS\nyrPhHW51aDSaXWCq+h/s/eo/4O/F0kja/WLnvzuDMAR9bhu2Hhe2Kx9BsuqHGh2F48d39Lhby+o1\nRwb83J2eJuy+gzBgaOTn1fnoLfYG9uKytY9geqLY94b6erdRHXu928978TTF6paic78SroWpeMtL\nD/f5mdnIki9tGur9xhvg9XJsRv39OzHxEwaPnyDudZG9eLF+2f79KvJjenoagM/8zB4sS3Lx79R2\nr9d7EJdrRPvGNJonjJ2IsUXUVmQnQTaE2sIs7u7b0mg0nzrTP1FesdAYAO/E03hNoyVfLLme4+b7\nyxx7dYDKfArn/i74i79o3ONrX6tvcW7HxFIKISDiqBCLx+kKL2IVnAQCJwG4Gb3J4e7Du7W6x8fA\naXAGW8TYGyEf2YrFuYT6u9XW5cLsdlGYTrS8dHwoQMWS9a7SOi4XfOlL9EdLdKXKTFz/MYOHjlI2\nDFavNMRYX18fHo+HqSmVINQV8XD4xT6uvb1AJlFACEG494tEY+/oNH6N5gliJ2Ls4+p1LzQfFEK4\ngNPAucfwvjQazadJpQQz79SrYqDM+y8GvdiNhriqVcVOnuxF5is49wbgz/+8cZ+vf33Hj7y2kOBA\n2Mfi/CxCVAgMRHGJkwhhEMvHWMmuPNl+sRqGCWOvtpj4PxvyYwp4u3mrcl+Qwt1Ei2/s+KCqmF1b\naBVpAHz96wjg2EyOG+kpBg6qz2J1fY1KtRJpGAb79u1jenq6nsB/9ufGsCqy3lkZiXwFyyqyrrcq\nNZonhp2IsT8FJPCNTcd/A+UV+1btgBBiQAhxRAjx2DxkGo3mE2D+HBRTsE+JsdlcgclsgS/0BOqX\n1Ktirw1irqlAUufGbVhaUheEw/Daazt+5NWFBCeGgkxOThIO3sN0WAyN/SIAt2JPgXm/mX1vQGwG\nYkoABWwmn/F7eCvaJMb2dyFzZUrLjUHiwyE3Qbed64sdxNjXvgYOB0dn89zpsfClEjhdbmIeJ9kL\nF+qX7d+/n3Q6zerqKgDBsIcjL/dz/aeLpGMFgsHncDr7WVn9m8ezdo1G88BsK8aklFeBPwC+LoT4\nthDi14UQ30Ql8r8F/Memy38PmKC9iva6EOJfCiH+JXC2evi3m45pNJoniekfgzBgrxJTP9xQlZcv\ndjfE2PnvzSIMwXNfGqUwHccWdmP+dVNV7B/+Q7DZdvS41WSe1VSB4wN+pqam6Ou6QzlvMnpAGdcn\nNiaAp0mMfU59nfph/dAb3X4up7LESypy0bmv5htrCC8hBONDAa4ttGaQARAMwpe/zNHZHGWbwdRf\n/QlDR48T9bnJfthIHtq3Tw1Rr21VApz9yhjSklz43gxCGETCX+b/Z++846sqsgf+nVeSl/LSeycB\nQui9CSIgKGLBglh3bbv2tur+1HVXXN3iuruWLZbVtawVxYodREAE6ZBQQkjvvb+8vDa/P+5LAV5I\nAqGEzJfP/Twyd+bMnDvv3nfuzJkzNTVr1VSlQnGK0NPtkO4B7gdGoBlmVwD/AM6XPdtbYw7wuPuY\n4k67r1OaQqE4lcheDTHjwCcYgFXVjST7eDPIV3MdrS1rZu+PpQyfGYNfgBeteQ2acdF5inLx4h5X\nl+6elov1smC3N2OOrsBRHo3eoNWXXpVOrH8swabgPlLwOBM2FIISYP837Umzgs24gLXuEBeGQG8M\noSZacw524h8ZG0hmWSM2h4dH6+LF7U78e3Z+Q8KosVi8jVT91BFkNjAwkLCwsIOMsYAwH4adEc3u\n9SU01lg7TVUqR36F4lSgR8aYlNIppfyblDJVSuktpYyVUv5KStl0SL7rpJRCSvn9IelL3ekejz7U\nR6FQHCuWGijeCilzAGhxulhf18jc0I5VlD99koPBqGPigiRsxY3IVifezgooKtIyhIYDgzFyAAAg\nAElEQVRqKwB7SHpxPUKAq66UkOAS9EYXgb4dU5zpVemMDhvdN/qdCISAIedoTvx2zXgaH+BHkEHP\nt9UdI2HeyUGa35izw29sZEwgNqfr8HhjABdcQFw9mC1O9ugriTcHAVBaWoSzrsOoGzJkCHl5ebS2\ndkQlmrggCYBNK3I7TVV+0ZdaKxSKo6SnI2MKhWKgkPUtSCcM1bYw+rGuCatLMsc9RVmWU0/29krG\nzU/AN8CL1v21IMB73ccdMhYtAqOxx1WmF2nO+3k5B4gJycHRoidx9OUAVFoqKWsuY2TYyL7T8UQw\n9BywW7SFEIBBJzg7NIBV1Q043c713kODkFYntsKOacmRsdr0pUe/scBAxLnnMjy3hfRkX8LXrcfb\nZKLaz4RlS8daqtTUVJxO50GjY+YQE6PPimPfhlKqiy1qqlKhOIVQxphCoTiY/V+Cf6Q2TYnmL+aj\nE0wL8kdKyYaPsvExGxkzNx6AlsxavOL80b/zeoeMK67oVZXpxfWMjjBSVVWMOayY+twAolM0/7D0\nqnQARof3o5Ex0FZUGnwgq2Oqcn5YIDV2J1vqNad905Bg0IF1X217nsQQX8wmAzsKPRhjAIsXMybb\nwv54Ey0fvkfc8NHUmH1p7uQ3Fh8fj8lkIjMz86CiExYk4e1jYMNHB4iIPA+Xy0Zl5co+VFqhUBwN\nyhhTKBQdOGyQtVIb1dHpkFKysrqBM4LNmPQ68jOqKcmqY9LCQXiZDDibbNiLGjHpqqBth4yYGJg9\n+8j1dKK0voWKxlYSjQ2EhRWgM7rQ1Q7G4KXtspZelY5BGPqP834bRh9t94Ksr7WtpYDZIWaMQvB1\nlTsUhcmAV2IA1sya9mI6nWBcQjDbC2o9iuXCCxlT4MCpF+y25JAQEo7Fy0DVpg6/Mb1ez5AhQ8jK\nysLl6vA9M/kZmbAgiYLdNTQUJ2IyxVFW9rGnWhQKxQlEGWMKhaKD/B+0kBap5wGwu6mFAquNBWGB\nuJwuNnyUTWC4D8NnxgBgzaoDCaYNn3bIuPpq0Ot7XOXWfM3oMDSWEhOVQ2u9kbjUjv0s0yvTGRI8\n5NSPvO+JofO1EBdVWQCYDXqmB/kf5DdmSg3BXtqMs6Ejdvb4hCAyyxtptNoPlxkQwJg0zZ9vZ4oP\ncbsyACitKMVRXd2eLTU1FYvFQlGbH5+bUWfFYg4xseGjHKIiF1FTux6rtaSvNFYoFEeBMsYUCkUH\nmV+BwaTtrwisqKxHL+DcsEAy1hZTU9LM9EsGo3dvFG7dV4POz4Dx/Vc6ZFx7ba+q3JJXS6BR0li9\nF//AMmr2BzJo4lQAHC4HGdUZjAob1Tf6nWiGnqt97uvYOH1+WABZllayLZpjv2motkLUur9jdGx8\nQjBSwo7Cg1dathF41Y0klbayc7Av4cs+wNvkQ7W/D80//tieZ/Dgweh0usOmKg1GPVMXJVNV2ISl\ndCYgKSv7pC+0VSgUR4kyxhQKhYaUkPmlFujVyxcpJSsq65gW6I9vq4tNn+USnxbMoLFhWnaXpDWr\nFpOuGmHVgr4yZgyM6p3htDW/lqmhVsLCDyAENOeEEZGkxcrKrM2k2d7MhMgJfarqCSMwDmInwp4O\nY2d+mOag/0WlNjpmjPZDF+CFNbNjWnJsQhBCwLZ8z8YY8+YxpgR2pvhCRQWJEdFUBfrTuPr79iwm\nk4mkpCT27dvXHo2/jSETI4kcFMDmT1oIME+ktGz5YXkUCsWJQxljCoVCo2Qb1BfAsIUAZFqsHLC0\ncn5EEBs/zsZudTLj8qEI916TtsJGXBYHpo2dpih7OSpmsTnYU9pAnKgmKjKX5iIfoqJGIXTao2lr\n2VaA/muMAYxYBKU7oSYXgHiTF+MDfPm0QjO0hBCYhgZj3V+LdMcWCzAZGRphZltXfmN6PWOiJ1Ab\nYKAg0ovkvEJa9TpKNm9EOhwdVY8YQXV1NWVlZQcVFzrBrCtTaWmy01wyA4sll4aG7YfWolAoThDK\nGFMoFBoZH4LOCGmav9bnFfUIYLJVx54fSxk1J46QaL/27C0ZVaAD07fvaAleXvCzn/Wqyh2Fdehc\ndszswOTTQNX+IJJndsQn21q+lXhzPJF+kces3kkj7ULtc0+Ho/yiiCDSm1o44J6q9BkZhmx1Ys3u\nGAkbnxjMtoJaXC7PI1YT598IwOZhfgz68lsAyoSkZceOjqrT0tDpdGRkZBxWPjzBzMiZsexbmYxO\nmCguWXZseioUiqNGGWMKhQJcLs0YG3x2e9T9FZV1TA70Y88HOfiYvZi8cFB7diklLelVmFqL0bW6\nYz9fcom2H2Uv2JpXS7yunqiofbiseupyAkh2+4u5pIutFVv796gYQHAixIyH3R3G2AURQQjgk3LN\n+DINDkJ462lJr2rPMykpmEarg71lHrZGApLGzyW8WbApzQ/f5mYiTb5UBvrRtGZNex5fX19SUlLI\nyMjwOA055aJkjN4BtFTMoLz8U+z2LsJpKBSK44oyxhQKBRRuhMYSGHkpAHuaWtjbbGVCnaQ8t4Ez\nLh2Ml0/HPpP2oiacda34rH2vQ8Ytt/S62g051UwMLCYstJCGDH/CgqPwC9KMwey6bOpb65kYObEb\nKf2AEYugdEf7VGW0txdTg/z4uKIWKSXCoMNneCjWPdVIpzZVOS0lFIAN2dUeRQohmOSfxqY0PySQ\nkpVDna831d9/f3DVI0ZQX19/2KpK0EJdTLs4hZLt03C5WiktXX5YHoVCcfxRxphCoYCM5VqA0lQt\n6v57ZTUYBZi/KCNhRChDJx88TWhJrwIkPunugKHDhsGZZ/aqSqvdSUZ+OcPCNyN0kpKsMIbMOKv9\n/OayzUA/9xdrY/gi7TPjg/akiyKCybK0sre5Y6rSZXG0bxweHehDcpgfP3ZhjAFMmXgJ1YFGcmK8\nSd6nhc8oqirDXlzcnmfYsGHo9XqPU5UAadOiCQkbhbVmMIWFb9Kz7YYVCkVfoowxhWKg47Rrq/1S\nzwVvf+wuyfKyWkbWga9dMuuqDqd9aJuirMRUntExRfnLX2r7MfaCLXm1JFJGVHQWzgJ/bA1epEyb\n0X5+Q8kG4s3xxJnj+kTNk0pwIiTOgB1vtweAPT88CIOAZWVaSAvT0CCEl17zxXMzfXAoP+VUY3d6\nNpAmxU8H4Kc0PyJqG/B1uqgI8KPhm2/b85hMJoYOHUpGRgZOp/MwGUInmHNtGnXZs7G25lNd80Of\nqa1QKHqGMsYUioHO/q+huRJGLwFgdU0DVXYHQ3Y1Mm1RCgGhPgdltxc34axtxWfr51qC2Qw33NDr\natdlVXJm9Ga8vS3UbfbB39eP8ETNL83mtPFT2U+cEXPGsel2KjHuaqjJgYINAIR5GTgnLJBlZTW0\nulwIox5TWggtu6vapyqnp4TRbHOSXuzZlyvOP44Y7wh+GuGPAAbnFVIZ6EfNVwdvAD5u3Diam5sP\niznWRlCkL8MnXIajJYB9GS/0nc4KhaJHKGNMoRjobHsdzNEweB4Ab+dX4tvqYqa/H6NmxR6W3bK9\nAlwOfLLWaQm//CUEBva62h2ZOaTGb0dagiiqDCF1xlntI3DbK7bT4mhhRuyMbqT0I4ZfBF7+sP2t\n9qSro0OpsTv5qkoztnzHhONqdrTvVTk1WfMbW59Vdbg8NL+xMxJnsXF0EDaDILWwFKcQFOblYCvq\nmKpMSUnBbDazbdu2Lps3Zk4K9urzaHX+REXpji7zKRSKvkcZYwrFQKa+CA6shLFXg95AhdXGyrpG\nRhfZOefnaQjdwVOP0uHCsqUEn/1r0VkbtW2P7rqr19XWNNuI53v8/OtwrjMhhY602fPaz68vXo9R\nZ2RS1KRjVvGUwctPc+Tf/RG4p3dnhZiJ9Tbydol7qjI1BJ3ZSPMWLS5YiJ8Xo+MCWZ1Z0aXYWXGz\nsBhcbEn1Ja6yBh9rK6VB/jR+/VV7Hr1ez7hx4zhw4AB1dZ4Dyep0gilz78BpN7F9w9PILkJqKBSK\nvkcZYwrFQGb7myBdMF4L1vqXtTk4dILbRsQeNj0J2vZHrlbwTf9SS1iyBBISel3tt+lFTE1cj8Nu\npnS3FwH+AUQMSmk/v654HeMjx+Nr9D06vU5Vxl4D9mbY/SEAeiG4MjqUNbWN5Le0IvQC3/GRWDNr\ncDZqe1XOHRbJ9sI6qppaPYqcHD0Zb703a88fjk5KhhaVUhngR/WKFQflGzduHADbt3cd3DU8Nhqz\n1yL0AevZunJTX2isUCh6gDLGFIqBisupGWPJsyE4ifz9tXzisDDSIpg39fDpSYDm1VnoGqsw5W7R\nEh544Kiq3r/7fYKDyvHLH0y1ry/DZs1pn6IsbCjkQN0BZsbOPCrZpzQJUyFiBGx8od2R/8roEHTA\n68Xaqkm/CZHgck8HA3PTIpASvtvneXTMx+DDlOgprBnpiwSGFZTi1AkKSouw7tnTni84OJiUlBS2\nbduGo1OU/kMZN+0OEHryC16gPNdzjDOFQtG3KGNMoRio7P0M6gth0o0017fyzIpMGn10/GpcwkGr\nJ9tw1FmxFtnwy/gSIZ1w6aUwdmyvq7W02hkW8gmtNj/qP6wAIRhx9oL2898WaCsB5yXO60pE/0UI\nmHorVOyG3LUAxJq8WBgexP9Kqmh0ODFG+OKVYKZ5SxlSSkbEBBAdaGLV3vIuxc6Km0WRs5qcs8cR\nW1VDYJOFotAA6j786KB8U6ZMobGxkd27d3cpy2SKJiZqCYFJ61n19iqszfa+0V2hUHSJMsYUioGI\nlLD+WQhJxjn4XL7+TwY/JBiINxo5NzrIY5Hmj7aBlPht/0QzKpYuPaqqv/nhVUICy3FVTKXQ20R0\nbAIhMR0jcd/mfcvI0JHE+McclfxTnlGLwTcUNj7fnnRbQgSNThdvl7pHxyZF4ahooTW7HiEEc4ZF\nsC6rCqv98NAUALPjZ6MTOr66+SwEMDK3kGp/H0pXfIqrtWN6c8iQIYSHh7N+/fojbgyeMvhOdHoj\nPrHv880ru3F1EVpDoVD0DcoYUygGIvnrtY3Bp93B+g9z2VjfTGGogZuTItB5GBWTNgfNGQ2YstZj\naKzQfMVGjux1tS6XEyyvYmkxE/pVDc0mL0ZfeEn7+ZKmEjKqM5iXdBqOirVhNMHEG2H/V1CdDcC4\nAF+mBvrxUmEldpfEd2wEOn8jTeu0qPnnjozCYnOyuoupynDfcCZFTuIr/X7krDMZnlcEUlLgraex\nU8wxIQTTp0+noqKC7OzsLpvo7R1OQsL1BCRsoqJ4Fxs+zunDC6BQKA5FGWMKxUBk/XPgG8bOutmk\nry5i24wgwr0MXB0d6jG75ZWvcBn98N/2IRgMRz0qtmPXS5j9KigqPYu8qkqMegOpUzvCV3yT9w0A\n8xJOY2MMYNJNoPeCH/7ennRbQgTFrXY+rahFGHX4T43GmlmLvcLC9JQwwvy9+XhHcZciFwxaQF5D\nPnsfvZWAFitJZZUUhZip+ve/DxoFGzVqFP7+/qxfv/6ITUxM+AUGg5nksz5hx7f5ZG4sPXa9FQqF\nR5QxplAMNEp3QtbX5MU+wPoP87BPDSXDy8Xt8RH46A9/JMimZhozWjCWZeJdsA3uvBNSU3tdrc1W\nT0XFv6mtj2DUZgelQf6MPOtsjCaTVo+UfHzgY0aHjSY+IP6Y1TylMUfCxOthxzvto2NnhwaQ5mfi\nr3ll2F0Sv6nRYNDR9EMxep3ggjHRrN5XSb3Fsw/X2YlnY9AZ+NJcDBdfzPisPKxeRnJrK2npFF/M\nYDAwffp0cnNzyc3N7bKJRmMgycn3Ir13kDh5H9+9sY+CPV1vzaRQKI4eZYwpFAONVY9TxgS+/mkY\nYfFmfhjtS5jRwM9iwzxmb/nTazjMUQRs+B8iPBx+97ujqnbnricw6C38uP9cKrN2ghBMWHRZ+/ld\nVbvIrs/m4iEXH5X8fseMX2mjY2ueBEAnBA8lR5PbYuOd0mr0/l74TYigeVs5zoZWFo2NxeZ08WWG\n5xGqQO9AZsbO5LPsz7D/9UmS6psIaWgiLyyQ6kcfPSjvpEmTMJvNrFq16oi+Y7ExV+Hvn0bg0LcJ\njtXz1YsZVOSrFZYKRV+jjDGFYiCR/yOVe7P5rPoh/AK9Cbg2mR/qm7kjIQJfT6NiW7fRUG7GUJWL\naf86eOIJCPLs4H8k6ut3UV//EYWlw5iR20RhsD/Jo8YRGBHVnuejrI/wMfhwbtK5x6Riv8EcCZN/\nAbuWQcU+AOaFBjA50I+/5ZVhcbowz4oHCQ3fFTI6LpDkcD/e21LYpcjFQxdTba1mlS4b8fDDjN+f\nS72fifySIlp/6JiWNBqNnHXWWRQVFXW5RRKATmcgdehSbLYyRl+0BpOfkRX/3ElNaXPfXQeFQqGM\nMYViwOByUf3xM3xa+xhe/j4svGcsfyypJMnHi+vjPIyK2WxYfvcijrBBBKx/HTHjDLjppl5X63S2\nsn3HXdhsPnyxex7GzI3YDXqmLLmmPU+jrZEvc79kfuJ8/L38j0XL/sUZ94C3Gb5+GKRECMFvkqMp\ntzl4sbACQ4gJv0lRNG8qw1lj5dqpiWwvqGNXkeco+tNjphPrH8uyzGVw//0M13vj22IlKyqEqjvv\nBFfHqsixY8cSGhrKypUrjxh3LChoIjExSyiteJ3ZNzlBCD5+ejs1JcogUyj6CmWMKRQDhPJv3uXj\nfVehM/lw0b3jWd7SxH6LlUdTYvDWHf4ocC19nIak+RhL9uCT9yP897/gIV93ZGU9hdNZyPb9szk/\nL4vcEH+Sho0kekiH39kH+z/A4rBwZdqVx6Rjv8MvFGY/DNmrtLhvwJQgfxaGB/Jsfjl5La0EzIkH\nnaD+m3wunRCHr5eeNzbkexSn1+m5bOhlbC7bzIGWIoz//S9T9mVTY/YlVydpffzxjrx6PfPnz6eq\nqooNGzYcsZlDBj+MyRRHYdnvuPCeVATw8dPbqC5p6rNLoVAMZJQxplAMAIp25vPJJ0F4ebm45MEz\naAww8KecUs4KNnNumIdNvj//nKa1RTjNEQStfh7xxz/CkCG9rre65geKil+jtGQI6/JGEFS2E7tB\nz4yfd4yw2Z123tzzJlOipjAidMQxaNlPmfQLiBwJXz0ENm206YkhsRiE4P8yi9CZvTDPiqNlZyVe\nxc1cMj6WT3eWUNnoeXukS4dcio/Bh1cyXoEZMxi9aDF+LVb2R4VQ9sp/kZs3t+dNTU0lLS2NNWvW\nUFNT02UTDQZ/hg9/ihZrIRV1T3HRvWMROsFHf91GSZbnUTqFQtFzlDGmUJzmZP5UxooX92PWV3DJ\nHYMJCPfh15mFSOAvqXGHR9vPy8N+x4M0TL0Gnz3f4p0WcVSbgbe0FLFr1x1YLIGsL7yA6/Z8Q05Y\nIIPHTiQyeXB7vhU5K6hoqeD6kdcfo6b9FL0BzvsrNBTBqt8DEO3txcPJ0aypbeSD8loCzopDH+xN\n3afZ3DA1EYfTxUtrPccJCzYFs3joYr7I/YKChgIMjz/OGXUWav19yIqJoGnx5VDREa9swYIF6HQ6\nVqxYgcvVdXDX4KBJJCXdTmnZcizOT7j0gQn4mL349NkdHNja9UbmCoWie5QxplCcprhckh+XH2Dl\nq3uIMuzh4kV1+A0ZzX+Lq1hd08jDydEk+HgfXKimBrnwfGqn34ywWwnauxzeegv0+l7V7XS2sHPX\nLdjtrWTlLKQ2swkH1eiMBmb/4vb2fK3OVp7f+TzDQ4czPWZ6X6jdP0mcBlNugZ9egP1arLWfx4Yx\nOdCPh/YXkWd3EHRhCo5yC6G7alg0Npb/bcynotHqUdx1I67DIAy8tOsl8PZm5H9eJbK+kczoEIoM\nBlyXXQZWrWxAQADz588nJyen2+nK5EF3Exp6FvuzHsdl2M2lD0wgPMHM1//JYNNnOUhX1yszFQpF\n1yhjTKE4DbE02Fjxz51s/7aAkf6ruGDk55hm38GuRguPHShhXmgANx4ayqKlBS66iMaAsdjixxC0\n5nn0b7wM4eG9qtvlspOefjtNTfvI3DeTjfXDuTb7c8qD/JlyyRUEhHXIe2vvW5Q2l3LfhPs87oc5\noDj7MW268uNbobEcvRA8PzwRoxD8cnceYmgwvuMjaPy+kLvSYrA7Jf9e7Xl0LNw3nCXDlvBp9qfs\nqd6DSE1l7pXXYTUaSE+MoiIzE668EtyO+xMmTCAtLY2VK1dSWNj1ak0hdIwY/jQmUww7d92MQ+Rx\n0T1jSZ0axebP81jxr11qL0uF4ihQxphCcZqRv7uadx//iZKsWs6K/YhZ4W+jv/wVyhyS69NzCfMy\n8GzaIZuBWyxw8cW05tbRMPNGfPasxPfXV8O0ab2qW0oXe/b+muqaNRzImoIt6HzOXrOc7Ag/wqPj\nmLRocXveSkslL+96mTPjzmRy9OS+Ur//YjTBpa9ofmPvXQP2FmJNXjyblkB6UwsP7i8i8IJk9AHe\neH+Rx3Xu0bE9JZ7jft0y5haCTcH86ac/IaUk+ufXMzEqnsKwQDIT4mj+5hu44QZwOBBCcOGFFxIY\nGMj7779PQ0PXscSMxgDGjX0Nnc7Ijh3XYXeWMvfnacy6KpWifTW898QmCvd07X+mUCgORxljCsVp\ngrXZzur/7WXFP3biazayeOSbjHC9BZe9QpN/DNfsyqHO4eSNUYMIMRo6CjY2woIFODbsoPriJ9DX\nlxE8MxhxVe9WNrpcdnbv+RXl5Z+SlzsWv8CLKF3xI97e1bi8jCy8/zfoDVq9Ukp+v/H32Fw27p94\nf19ehv5NxDC4+AUo2gQf3QIuF/PDArkvKZJ3y2r4a2kVoVen4WyycVMNhJqM/ObjdFwepgcDvAK4\ne/zd7KjcwQdZHwBwxlPPEmrwIj0+nKyEBOzvvAOXXw5WKz4+PixZsgSr1cqbb75JS0tLl8308Ulg\n7NjXcDotbNt+FS0teYw8M5ZLfz0Bo7eeT5/bwdp3MrFZuw6ZoVAoOlDGmELRz5EuSeZPZby9dCN7\nN5Qx7uw4Lhv6MqGlH8CFz9GUOIufpeeyt7mF/4xIYqTZt6NwdjZMn45z0w6qLnsSqTcSFlmI7oF7\netUGh6OZXem3UF7+GXm54xDiPPbuqmNq5Xqqzb7M/cUdhMZ1bHG0ImcF3xd+z53j7mRQ4KC+uhSn\nByMWwbzHYc/H8MX94HJxf1IUV0eH8HR+Oa9jJfjiITjzGngpPJQdBXW80IUz/6LBi5gSPYWnNj9F\nXn0eBm9vLnjyGaTRwJbBseTGx+P85BOYPx/Ky4mOjmbJkiVUVVXx7rvv0trqecUmgNl/GOPG/Q+n\ns4UtWy+noWEXEYkBXP7wJMbMjSd9bTFv/W4jmRtLjxjlX6FQKGNMoejXFO6pYdmfNrPy1T2YQ0ws\nfmA0022/w7DvfZj3e+pGXsHlO7P5qb6Jf6QlMic0oKPwp5/CxIm4DuRTdcXfcQTHEhpRhPH3v+5V\nGyyWXLZsvZTq6rVkZU1FiPNwNAcw+cfXyQ8PZNy88xg1Z357/r3Ve/n9ht8zPmI816RdcwTJA5jp\nd8L0u2DLK/DpHQiXkyeHxrMwPJDfHijm3yEuzOckEJbfzHMhITz99X425x0+NagTOv5wxh/w0nvx\nwNoHsNgthMYlsPCB31Lva2JjaiL5cXG4fvgBxo2DtWtJSUnh4osvpqCggNdff53m5q6DuwaYRzJx\nwjL0eh+2bruCktIPMHjpmbF4CJf9eiL+wd6sfG0vHz61jZKs2uN5xRSKfo3oT28sEydOlFu2bDnZ\nzVAoTipSSgr21LD9m3yKM+swh5qYcmEyQ1NdiOXXQ+FPsPCv7Bt+NTdl5FHQYuPFEYksCHdvY1RT\nA/feC2+8gSMolqrL/owjMJqwQdWYbr+8V+0oK/uIzP2P4XRI0tOnERg4lXARhP3Vv5ETFcTQCVNY\neP/D6HTaasyy5jJ+9uXPcEkX757/LmE+nvfDVABSwpq/wPd/hMHz4JKXcJiCuT+zkHfLargyKoQH\nC5zYVxexxejiz0Ybb906jZTww3cwWFe0jju/u5PpMdN5bs5zGHQGdq36mm9f+gcR9c2csS+XxMJC\n9FJqYUyeeIJ9RUW8//77BAUFsWTJEiIiIrpsqs1WRUbG3dTWbSQ6+jKGDnkEg8GMdEn2bSxlw8c5\ntDTYiB0axKSFg4gZGqQWbCgGBEKIrVLKid3mU8aYQtE/sFkdHNhSwc7vCqkpacYv0Itx8xMZeWYs\n+oI18OEvwGZBXvhP3gubxUP7i/E36HhxeBLTg/3BZoMXXoDHHoOaGqyDJlFzwe9A6AidF4L3wqk9\nbovFks/+rMeorl5Da2s8O3dMYvjwGZgPlFH1xVsUhgWQPGYiF/76kXY/sbLmMm74+gZqrbW8cs4r\nDA8dfrwu1enF5lfgy/+DgGi47FVk7AT+klvG0/nlpPmZeNrmS+iKfLJ1Lv7p5+Rvt0whMdTvMDHL\nMpfx+MbHmZc4jz/P/DNeei92fPMFq175N0HNVqbtzyclvwBvmw3i4uDRR8mbPZtly5djt9s577zz\nGDt2bJdGlMvlIDf3GfLyX8TbO4KhQ39HeNh8hBDYbU72rCth29f5WBpshCeYGXlmLEMmRWL07l3Y\nFIWiP9GnxpgQQgfcDdwMJAGVwDLgd1LKHm1QJoQ4D3gEGAO0AquAX0spc3tSHpQxphh4OJ0uSjLr\nyPypjOztFThsLkJj/Rg7L4EhEyPRW6vh29/CzncgLJXsi17jwWov1tU2MTXQjxdGJBFltcCLL8Kz\nz0JJCS4vP+pn30rz2Asx2GsIu3UyhsHRPWpPa2s5efkvUlz8NlLqyMsdR1lZGmfPmEndS29QWJ9P\nvZ+J0XPP4+ybbkG4t0/aWbmTe1ffS4ujhRfmvcCY8DHH87KdfhRtgWU/h4ZibXPxOY/wXbPgjr35\nNDpc/MLXnyu+KkdncfC6l4NF149lwqCQw8S8uedNntz8JJOjJvPkmU8S5hNG1qYf+eKZJ9G12hhV\nUM7YrBwC6+sRAEOH0nD33Xzo7U1eYSHJycksWLCA8COEO2lo2MXevQ/S1JxJYE9wz+YAAB3mSURB\nVOAEUpLvJyhoEkIIHDYn+zaWkbGmiOriZrx8DKSMD2fIhEhiU4PQedisXqHoz/S1MfYscBfwEfAl\nkAbcCawDzpZSdh22WSt/CfABsBP4DxAI3AM4gYlSypJuG4EyxhQDA0uDjaLMGvJ2VpG/uwZbiwMv\nk57BkyJJmxZN5KAAhKUaNvwTNv0HHK1kn/Ewz0YtYnllA746Hb9JCOfajK3o33oLPvkEWlqQBi+a\nxi2iceo1uHwC8I9pJfC2sxHGI/8ASilpaNxFUeEblFd8jpROaqqHsz8rlbiY4YxuaOLApx9QGOwH\negPzbruXUWeeBWhbHb2c8TIv7XqJSN9Inp39LKkhqUesT9EF1gb47gnY9BKYAmH6HVSOvZHfFzfy\nflktEQY9V5Y4uXRXI+VOJ6VjQ7nokuF4ex088vRZ9mc8tuExzF5mHpn6CHPi51BTXMjnTz9JZVE+\nkXVNjM4rYUhBIT7uwLCugAC23HADq0JCsLlcjBkzhhkzZhAW5nma2eVyUFr6Pjm5z2KzVWI2jyQh\n/gbCw89BrzdpU9zZ9exeV0LOzkrsVic+ZiMJI0JJGB5C3LAQfAO8jvslVSiON31mjAkhRgDpwEdS\nyks7pd8JPAdcLaV8+wjljUAe4ABGSCmb3Oljga3AK1LKX3arEcoYU5x+OB0uasuaqSpsojS7npKs\nOurKLQD4mI0kjQojaXQY8cNDMOockLsOdr4Nez+jTnizavSdvBu1gHXNLkxIflZWwB3LXifiqy/B\nakUCjrAkmkcuwDJqAS7fILyN9QTeMB0vDyMnbbhcDhobM6iqXk15+We0tOQjpTcVFUMoyB9MgG8i\nQxubqFm7klKzNw69HlPiCK799QMEhIVhc9r4MvdLXtz1IoWNhSxIWsDDUx4myBR0gq7saUzpTlj9\nJ9j/JRh8YMQifhp2LU9ZI/ihrhlfBGeW2LikyE54vQM5Joxx8wbhE+LTLmJ/7X7+b+3/caDuAFOi\np3DjyBuZFD6BLZ9+yKYP38VhtxNV18TQkkqG5Bdhbm5CJyVNfn6smzuXrWPG4NDpSAoJYezUqaSN\nGYO3t/dhTXU6Wygt+4jCwlexWHLQ6/0JDz+biPBzCQqagtEYgMPmJH93NdlbKyjYW0NrsxYOIzTW\nn8jkACKTtCM42g+dTvmZKfoXfWmMPQH8BjhTSrmuU7oJqAbWSCnPO0L5s4Fv0aY0Hz/k3CpgIhAm\npew2bLMyxhT9EemSNNW10ljdQn2llYbqFhoqW6gubqa2rBmXU7sHvXwMRA8OJGZwEDFDgoiINaIr\nT9emqA6sobZkO9t9ktgaNIYNgVP5yZyMU6cjrqqCaz5ZxlVffExEbTVOv1BssSNojRtNy+DpOIPj\nwOXEJ8CC/+JJeKcePMUkpaS1tZTGpr00Ne0jf/+PSK90XK5mpBQ0NcVSWhrHFz7ncX5uFqbsLFrr\nKmj09QYpcQYlMPfmWxkxZijZn27hE/k0X9jLqW+tZ1jIMO4adxcz42YCcM/Xe3jmnOFs+iyH5qq3\nmJ1kgNkPtbflqdxSHhgUTcWLO4m4eQw5Oc/yYHkyy6ZdoBkgsx/i6W/3c69hOY9VjODRJRfy4/tv\nMX3x1Tz97X4Arti0k+jpB6jMMBN+5x2sf/kOrMkGdjlv45p933BrhD+/0hlZFjCOZ87R/NZWr16N\nq/5d5i56kcs3fMalX69nydI/a41a/Scuqp3CG+YUftj2LjPGX0HgvERWv/o4q+qKiZk9mrTloXiP\ndlAo1lDkU8V9Cz9s1+nSVRksnzuSyn/8k/dn6rht7G1s+iyH8u/+xwVPP8ref+2gNmI30xdf3d6W\nQf99lc2pk1n8yB3k5DxLcvLd5OQ8y1tvV/LbR57QBJfuhC2vQsZy1gWnEut3gFr/K3gz7Gw+dYbS\nLAX+dhfTqpxMqHES6YRh0YEMHRuJT2IgTqOL9/a9x8vpL1NtrWZw0GDmJ85netBEqldtYfd3X2Nz\nODDZHETWN5FQUU18WSUhDQ3YvLzYNmECO8aMoTYkBJ3LRXxzM8leXsSGhBAdH49fYiJERUFQENLs\nT23DJsrLV1BR+RUORwOgw2weQXDQZPz9h+Hvn4aPTzI1xa0U7KmhZH8tFfmNtFo048xg1BEY6Utw\nlC/Bkb4ERfkSEOqDf7A3vgFeaopTcUrSU2PM0F0GYBLgAjZ1TpRSWoUQO9znuysP4GnTs43AHGAo\nsLsHbTl+lJTAP/5xeLonY7UrA7aneY+1vKrruNclARc6nOhwocMlBU50OIUeOwbsGLFjwCba/m/E\nLoxYMdIifGgRJu3ARIvwwSU6fiiEdOFHM0GymghRgT9l+IpSDPYaagqNFNf5sCvTTLV/AIWmKHJ9\n48gNv5mK+FAAdC4nwwqLuHn9SuZk5jKyuhkZEIV9wVKKg2NwBgQidXYkFoyGagxjShATImjR2alr\nXUHr3hpaWkqwWkuw28pwuiqBjgCfFpuZ+soY6mqjaKgJx1DTiqG+ms0/G8FZX7xDk5Q4fP1oHhxP\ngnkF+TPH85fSP3BgzwE+2f0My1MzmZO8gIsHX8zUmKnoOun+rpeNZ4DNn+dRGeVkdv5fDzLG/pZX\nzgODorHlahHgc/OeY61Yrp1c82eY/RDPrsriXtOfeX7WGh4FNnzwDtMXX82zq7IAWEwUrLmJqndj\nCL/zDqzJXwLw7Kp5nPvxv/jh+XeY9sIjvHvLCJ5x17tmzRpmnrkSgLXWeKbszej4Tqz5Mz/NWkPj\n1wVsNrUwZlUBgfMSWZPvxEAUz+98nlsqn8X6wd8Ze/NeDp24W6/TjImqf/2L5wMM3Db2NjZ/nsec\n79+Fpx/FXNjIF2vfaTfG1qxZQ9TmzRTYaoA7yM17juTku8nNew6n49oOwdFj4IJn4Jw/YvthFLno\nmbvtIybsfJ4ndCa+DZ/Jd1FzWB02mm+jtRWWepeVhMxcYnZIwludhMmhnOf9V5w+NZQ37uPbLTtY\nIb9DZ3Aw6LI44qu80WeUU1hmID88CEak4GOzY25pxWyxMmr9Ghw+ftRERlERFc1qsxmam2HfPsyb\nNhFSU0NwbS1B9fWY7XZ89HoSDAHIeG9aB7XSOGg/hdEZSIN23wmXwNTsjXezNyl+JkYk+eC0mWmy\nhdBoD6O5JYSazFDydwfjdHohnUaky4iQAh/Rir+w4qOzYRJ2vIUdbxx4CzsmYccoHBiFEwNODMKJ\nAZf704lBuNAJiQ7JMS/y7KtVomq16YnhN78B/8NXIJ9oemKMxQBVUkpP0f+KgelCCC8ppe0I5dvy\neioPEMvJNsYqKnhwkB9rBx28wkvS8xvCU17PZoBnmdJj8jHK9JjWM52OXfeONCFkl/lObJs80fdt\nOrweLcUl9Njwxk4gDpHYrexAWUukq4JUmcGZ9jKSXTkkuXLxibBCBDTOkWwULnQ6J0LnRKfrwn3z\nwMF/2u1etLb60Wr1o7U1AUtzAJY6P6y13rgsLvRWC3prI16tlRikA5tRu73XjywnP9qGzegCsgF/\nQorWkhqcytVpV8NuWFdQhO/1T3Wrm6KP8OoUxPe+fVBXgF/pDhaV7GBR1Xpk2dsUtrSQ7hXNTv+R\n7PcZToEpmvSgQBqMbX5ZEe7jzHZRmwFdoMQ7CbxcEqNLopOgk9qnQCIO+1vicv9z4sIlJC60o0ta\nJDqdC73OgV7vRJicCF/3d1oc/H0W7XJcgNV9uM+0P0CNaD9tPl09VNvTJV3d/YqBwMKdW/iNxXJK\nGGM9mabMBoxSygQP594ArgWCpZR1XZR/BbgBSJFS5hxy7gbgFeBiKeXHXZT/JfBLgISEhAn5+fnd\nKnVU7NjBb378lA0pQ3pcRHi4lYXH63lomuj0UOlpPd3X7amew9LlkWQeiYPze8zrQaWu9Oyp6dib\nB6VHnWRPrlNX8vA4enYsbddJF0ZpxygdeEk7Rmlv//SWNvxdzfi7mjE7tU+ddAJSky5l2/+0nzcp\nkVLicoHLqcPl0g7p0uFy6nE5BdIpcNl0OFr1OFv1uKw6HDY90iFBOpDSiQsneuLxcqUgMILOFyF8\nETpfvpljYFNkzGF6LCn6H3cXvEakw4nDdiWNzqsOy2PWv03g2QncY7uId70Of1ebkLePSfn72Jw4\njK1Jwzxe1UMZWprB/uiRh6VflJHFb4uj2v+uSvmI6pRP2v9ezuV8KJZ0KXeYzGCfOFyuJ9ra3UZC\n4k4SE3cdlKer+s7MaGHW7hZSTTqGmToc67cacthu6FhY7klmZ/LzR6OTkvikdI/nByXdRXLy3R0J\nUoK1HizVYKmBllqkpZrKxkYKmlspbXZR22qg3ulNkzRik3psGGgVRqxCj0Wnp1WnwykETgQuBFLo\nkG4jqONTeznpuOs6jB4X2vdXCs2Ucgnpzu/+hgva/25HSBAuhHAhddqnEC53unYI3P9HIoRst786\naj5E3kF/d3mJTwD9J6zU6cq8HTt46Pr74Agx9I6VvvQZSwcipJSRHs4tAxYD3l2NjAkh/gHcAQyX\nUu495NxtwL+Ac6SU33TX2OPqM1ZeDv/9r+dznoaLuxpC7mneYy2v6jp129Wb8t7e2mEyHXy0pQcG\nQlAQ6E6cP8y/bvmO21+Yc1h61OodlM0ee3Di0kBYWt/+Z9GD64gznX9QmicZ/7rlOyqj1rKUpw/K\n23a+6MF1xP15Jqu+S+FqsVyr111X0oOfk2e6iqhZayibPZa/LTmf+95bQdKDnwPwAwHEmc5n77sx\npO3by6rvUgC48Zvn+PLj+5n9/Ds88MIjPHXLE+36LF26lJln/o+5c7KJWr2DB154hPveW9GuY9Ss\nNWz5upGXTau4yTqXuD/PZOnSpQAsH7ScWzY8i7VWm6YEmDsn+zCd9g5L4/KHDKT/PJ1/3fIdc76/\nnbR9eyl6cB3v5T7ZXt/SpUtZ8u57fDEmhfveW8Gq71KYOyebVd+lsG7tte31dqZNx871nlI4ndoe\nqHV12mdr68GH1ap92mya4ehy9exwOvumfX0Vb/NUk6PonrvuAr/D4/L1FX3pM1YCDBdCeHuYqoxF\nm8LsaoqyrXxb3r2HnIt1f3qawjyxREbCQw91n0+hUCgUvUOv114qgtRqWoXCEz0xxjYD84HJaHHF\ngPbVlGOBtT0oDzANWHnIualAA7C/J41VKBTHn0kLkzym35d02OA4zHrwoD/NcxPA8ODh+dxcYfNq\nr6O5aj0kHZy3rQ6vQdoemoOS7uLM8kJgbHtdd88dAoYHubWiABjLtMuu7EgH9Jt2wvQHCQs1A2DK\nWYA12cDdc4cQFns7Myp2MO2yK9vbAjBr1ixc9aUAnGkqJC6t05TlrAeZUluDeW4Kk7b5YD5D89iY\nlahnVV0xt465lbQDlXjPvZLCGm015dxOOp3h0h6zYbffzq1jdO36H/C5gjSgMd7MtAlXHtQWn+wc\nElInt1+Dts8ff6z0eF29bNcSOzS4y+uuUChObXoyTTkKLVhrV3HGrpVSvulOi0YL6FogpbS404xA\nPmDn4DhjY4BtwKtSypt60lgV2kKhUCgUCkV/oafTlN06okgp09H8ui4RQnwohLhJCPE34O/AGqBz\nwNc/oU1FTu5U3o62lVI8sE4IcZsQ4kHgG7RtlR7tuVoKhUKhUCgUpxc9maYEbeuiPLRVjQuBKuAf\naIFcj7gVEoCU8n0hRAva3pR/pWNvyv+TUp58fzGFQqFQKBSKk0SP9qY8VVDTlAqFQqFQKPoLfTZN\nqVAoFAqFQqE4fihjTKFQKBQKheIkoowxhUKhUCgUipOIMsYUCoVCoVAoTiLKGFMoFAqFQqE4iShj\nTKFQKBQKheIkoowxhUKhUCgUipNIv4ozJoSoRNta6XgShhbUdqAykPUfyLrDwNZf6T5wGcj6D2Td\n4cTonyilDO8uU78yxk4EQogtPQnQdroykPUfyLrDwNZf6T4wdYeBrf9A1h1OLf3VNKVCoVAoFArF\nSUQZYwqFQqFQKBQnEWWMHc5LJ7sBJ5mBrP9A1h0Gtv5K94HLQNZ/IOsOp5D+ymdMoVAoFAqF4iSi\nRsYUCoVCoVAoTiLKGFMoFAqFQqE4iQwYY0wIcbMQ4i0hxD4hhFMIccT5WSFEjBDiDSFEpRCiRQix\nRQixuJd1egshfi+EyBVCtAohsoUQjwghjMemzbEjhLhOCCG7OWJ7IOe1I5S/7ETocjQIIfKO0O6w\nXsiZIoRYKYRoFEI0CCG+EkKMPZ5tPxaEELFCiIeEEGuEEKVCiGYhxG4hxFNCiNBeyDml+10IoRNC\n3Ou+361CiEIhxN+EEH69kHGeEOJH9zWqEUK8L4QYdDzbfawIIYa6nzkb3c+uRiHEDiHEb3qquxDi\n+yP07SkRBuBIHKHtTb2Q0R/7fmk3z3N7D2Sc8n3vfn69L4TIcbcrr5v8qUKIj4UQte7+XCeEmNPL\nOgOFEP8QQhS7nye7hRC3CiHEMSnTCUNfCeoHPASEAtsBPyCuq4xCiBDgByAC+DtQBFwFLBNC3CCl\nfLWHdb4HXAT8F9gATAMeBwYD1x2VFn3HWuBaD+nRwF+A7VLK4l7I8yRr09E07ASyD/iDh/TGnhQW\nQkwFvgeKgd+5k+8A1gkhpksp0/uikX3MBcBS4HPgKTRdJwP3AFcIISZJKct6Ie9U7fengbuAj4C/\nAWnuv8cJIc6WUrqOVFgIcQnwAbATeAAIRLtG64UQE6WUJcez8cfADcDtwKfAW4AdmA08AVwuhJgq\npWzpgZwq4F4P6Tl91dDjzDoOd87u1hiBft33HwIHPKSPRtPjsx7KOdX7/o9ADbANCDpSRiFECvAj\n4ED7XasHfgF8LYRYIKVc2V1lQggv4FtgHPAPYC+wAPg3EIn2PD12pJQD4gCSAJ37/ys01bvM+xdA\nAhd0StOj/chUA/49qO88t4y/HZL+N3f69JN9Tbpo90Pu9t3ew/yvHelanqoHkAd8f4wyNgENQGyn\ntFh32jcnW8cu2jwCiPKQfpO73//a3/vdraMLWH5I+p1uHa/qprwRzcDO73yvA2MBJ/DSydbxCG2f\nCAR6SH/CrfsdPZDxPZB3snU5hmsggdeOsmy/7fsj6PSi+5osPB36Hkju9P+MI7UXWObut7Gd0vzd\n/ZuJexFjN/Xd5r5+dx6SvhywoUXYP2a9Bsw0pZQyT3bzNtyJq4BsKWX7m4SU0olmFYegGVo9kQHw\nzCHpbX9f08O2nDDcQ643AC1ob9W9KiuECBBC9KvvlBDCIIQIOIpyg4FJwPuy0wii+//vA2cLIaL6\nrqV9g5Ryt/Q88vWe+3Nkb+Sdov1+JSA4/N77D2Ch+3tvFhADvCylbJ/aklLuQPuxWiJOAVcDT0gp\nt0gp6z2c6nX/uqd6A/pyKuZEIoTwEkL497JYv+17T7inpq9Am935qhflTtm+l1L2aITOrfuFaC/d\nOzqVbwJeBoaiPcO74yq058Z/Dkl/Bs14X9KT9nTHqfQAPSUQQkSjjW5s9HC6La0nHTgJKJZSFnZO\ndP9d0kMZJ5pZaFOoy6WUdb0sW+8+WoQQ3wohpvR56/qeKWg3Wb0Qok4I8boQIqaHZdv6b4OHcxvR\njIEJfdDGE0XbtH15L8udiv0+CW1k7KDpUimlFdhB9/ded30bgPYg70/0tn9jgSa0vm0SQnwohBh2\nXFp2fLgM7d5uFEJUuP19AntQ7nTr+8VobX7NPaDQE/p737cxGvCm676Ebp4F7pfM8WhuO9ZDTm9C\nGzHrk9/ygeQz1lPafow9+Uu1pXXr2O6Ws6eLc8UcwWftJHKj+/PlXpQpQ/PP2Qo0A2PQ/CvWCSHO\nkz2Ykz9J7EbTcy/a281ZaFN1c4UQk2X3fiF99T05VXjM/fl6D/Ofyv0eA1RJKVs9nCsGpgshvKSU\ntiOUb8vrqTxofbv72Jp5YhBC6IHfovnNvN2DIrnAemAX2hTPFDRfyLlCiBny1PSF7MwmtNHpA2iG\nyHlo7Z/l9uU8kiP/adX3aM90iea33BP6e993pi+e0cGAjycZUspWIURVD2T0iH5ljAkhgtAe+D3l\nOSllTS+r8XV/enqQWw/J050cTzLa5PRERrf01TVxy7kUOCClXNNTYVLKBw9J+lgI8TbaCMTzwJBe\ntK1XHIvuUsqFh5x7VwixFm169jE0J88j0Vffk6OiL+8FIcR9aG/QL0kpv+uJsJPZ7z2gu3uvLU9X\nxthJ7dvjwDNoi4cellJmdpdZSnn9IUkfCCE+RZum+zswr89b2IdIKQ8dnX1DCLELbbHO3XhetNPG\nadP3QohUYAawSkqZ25My/b3vD6Ev+vJIMtrk9Mn3oV8ZY2grJx7tRf430VZd9AaL+9PbwznTIXm6\nk+NJRpucnsjoCX11Ta5CewN45VgbJKXMEkIsA64TQgyVUu4/Vpld0KffBynl20KIPwCHGmqe6Kvv\nydHSJ7oLIW5CW1X5Odob8FFzAvu9OyxoK6E90ZO+Odl922cIIR5H69eXpJR/Olo5Usp17peV2UII\nH9mzFZmnEk+h3S8LObIxdtr0PUc303EY/bjv+6IvjySjTU6ffB/6lc+Y2wlf9OLwtMy3O9qmpzwN\nPbal9STkQ0kXMtrk9CZsRJf04TW5EW0a47W+aBfaakWAHsfs6i3H6fuQ18M299X35KjoC92FEDeg\nLf//BrhUStmjpf/dkOf+PG793gNKgDAhhKcHaCzaFGZXo2Jt5dvyeioPx7Fv+wohxFLgEeBV4JY+\nEJmHtqo8uA9knVDc3+0Suv9eni59bwB+hrb6/6M+EJlH/+v7vujLWrQFbYfJcD9fwnogo0f0K2Ps\nRCClLEW7uFM9nG5L29IDUZuBWCFEfOdE998xPZRxQhBakNLxwOddrLQ7GtqmqXrrEH6yGUzP2rzZ\n/TnNw7mpaH4aW/uqUX2N2xB7GVgJLOrCv+poOBX6fTPas21y50QhhAktREF39153fdsAnKxRvx7h\nNsQeRfMBvElK2RebEA9Be2Hr7WzDScfd93F0/73s933v5gK0GFhv9tG93R/7Ph1terGrvoRungXu\nCAzb0OITHvpyNxltoVbf/Jb3NAbG6XTQfZyxp+g6zlgtYD4k/zAg5ZC0hRw5ztiMk30dOrXpn4fq\n6yFPmFvPwE5pfoDJQ95xaDfBnpOtWxe6hHSRfrv7Ovy7O93d6ZvRHs4xndJi3GkrT7aeR9D/OjTn\n3JWATzd5+12/A6M4cpyxazqlRbv18+2UZkR7qz401tQY93V7+WT3YTf6/86t5xu4Yyt2kc+T7oGA\n3kPetufZFydbv250D+0ive2Z/uvTue87tXeFW99Rp3Pf032csffd/TamU1pbnLH9dIoz5u77YUDC\nITLafhc8xRmzA0l9osvJvpgnsNMuQBuyfwQt8rrs9Pcdh+QNRRuWbURz5v4lsNpd5kYPsqWnLwRa\nxGOJNgJxo/tTAv872dejUxtNaAZmsacbsVO+pe62X9cpbSxQiuaw/SvgZrSoxFa0efRTxuA8RJd7\n0N6annLfaHejDeVLtBVY4d3p7k6fjmZ8ZLtl3uP+f1Pnm/9UOtDi7jjdff4LtJhbnY9Fp0O/o8UE\nlGhRyW9Cewmyozki6zrle82d76xDyi9GM+i2owV9fBBtVKWMTkF+T7WDjh+OfLRpqkP7d96RdAcW\noUVaf9Z9X9yONrrmBCqBoSdbx270fxotlMEf0aZm7we+c+u5kU4vH6db33dqfwzaKNZPR8jTb/se\nbdePtt/ucvezrO3vaw/JOxhtNK/c3Y+3ufvVAZxzSN4k9zX5/pB0L7TRL7v7OXKT+7kigcf7TK+T\nfWFPYAe2ffk8HXke8scC/0PbGsKKNlS5pAvZXckwoUW+zkP70c5BW2JuPNnXo1Mbr3K3/w/d5FvK\n4T/KUe5rtA9tNMgOFLhv4GEnW7cj6HIG2nYxBWj+AFa0EBd/BoJ6onunc9OAVWgGWCPwNTD+ZOvY\ng37s0b3QX/sdbST7PrQo261oLxt/55DdM+jiB9l97ny0H3AL2gP/Aw4ZAT/Vjm6ecwf90HjSHW3b\nqGV0vFS0vWz8i/5hiPx/O/dugzAMRQH0sQEjMAw9U7BEtmIHZmADqGnoU/gVKEIk3RXoHCldlMR+\ntnTzcU49B+89r181VvhOtXia+2+1f7v2qdt13jBOfq72NW6oVsf3ol2Xqnp2Pa9Vdfyw3+HLMfY1\n3iA9ul9uNRbGrP7Bf+u26xMBABDgA34AgCBhDAAgSBgDAAgSxgAAgoQxAIAgYQwAIEgYAwAIEsYA\nAIKEMQCAIGEMACBoBvHdVVzxzITdAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot gaussian distribution\n", "mu = 0 # mean\n", "sigma = 1 # standard deviation (std)\n", "t = np.linspace(-10,10,1000)\n", "plt.clf()\n", "plt.plot(t, sps.norm.pdf(t, mu, sigma), 'r',lw=3)\n", "\n", "# Genereate data from this distribution and plot corresponding ML estimated distribution\n", "# Repeat few times to see different model estimates for the different training data sets\n", "N=10 # number of training observations\n", "for i in range(10):\n", " x = sps.norm.rvs(mu, sigma, N)\n", " p=plt.plot(t, sps.norm.pdf(t, np.mean(x), np.std(x)))\n", " plt.plot(x, np.zeros_like(x), '+', color=p[0].get_color())\n" ] } ], "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": "2.7.13" } }, "nbformat": 4, "nbformat_minor": 2 }