{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Fitting a model to data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this recipe we will demonstrate how to fit a simple model, namely a line, to some data. Although this example is simple, it illustrates what is the proper way of fitting our models to data and infering the parameters of the models." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us first import the main packages that we will use:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# show plots inline in the notebook\n", "%matplotlib inline\n", "\n", "import numpy as np\n", "\n", "import matplotlib.pyplot as plt\n", "\n", "from IPython.display import display, Math\n", "\n", "import zeus" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The generative probabilistic model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to create our *synthetic* data we need to construct a *generative probabilistic model*.\n", "\n", "We start by defining the *straight line* model and also setting the *true values* of the model parameters:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# define the model function\n", "def straight_line(x, m, c):\n", " ''' A straight line model: y = m*x + c '''\n", " return m*x + c\n", "\n", "# set the true values of the model parameters for creating the data\n", "m_true = 3.5 # gradient of the line\n", "c_true = 1.2 # y-intercept of the line\n", "\n", "# Set the x-coordinates of the data points\n", "M = 70 # Number of data points\n", "x = np.sort(10.0 * np.random.rand(M)) # their x-coordinates" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are now ready to generate the synthetic data. To this end, we evaluate the model function at the *true values* of *m (slope)* and *c (y-intercept)* and we add some random *Gaussian* noise of known amplitude *sigma*." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# create the data - the model plus Gaussian noise\n", "sigma = 3.0 # standard deviation of the noise\n", "data = straight_line(x, m_true, c_true) + sigma * np.random.randn(M)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also plot the generative model and the data:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
", "image/svg+xml": "\n\n\n\n \n \n \n \n 2020-09-24T10:04:58.954564\n image/svg+xml\n \n \n Matplotlib v3.3.1, https://matplotlib.org/\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n 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}, "metadata": { "needs_background": "light" } } ], "source": [ "plt.figure(figsize=(9,6))\n", "plt.errorbar(x, data, yerr=sigma, fmt=\"o\", label='data')\n", "plt.plot(x, straight_line(x, m_true, c_true), '-', lw=2, label='model')\n", "plt.legend()\n", "plt.xlabel(r'$x$')\n", "plt.ylabel(r'$y$')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The likelihood, prior, and posterior distributions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first step to solve a problem is generally to write down the prior and likelihood functions. An important benefit of MCMC is that none of these probability densities need to be normalised.\n", "\n", "Here we'll start with the natural logarithm of the prior probability: " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def logprior(theta):\n", " ''' The natural logarithm of the prior probability. '''\n", "\n", " lp = 0.\n", "\n", " # unpack the model parameters from the tuple\n", " m, c = theta\n", "\n", " # uniform prior on c\n", " cmin = -10. # lower range of prior\n", " cmax = 10. # upper range of prior\n", "\n", " # set prior to 1 (log prior to 0) if in the range and zero (-inf) outside the range \n", " lp = 0. if cmin < c < cmax else -np.inf\n", "\n", " # Gaussian prior on m\n", " mmu = 3. # mean of the Gaussian prior\n", " msigma = 10. # standard deviation of the Gaussian prior\n", " lp -= 0.5*((m - mmu)/msigma)**2\n", "\n", " return lp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We assume that the likelihood is *Gaussian (Normal)*:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def loglike(theta, data, sigma, x):\n", " '''The natural logarithm of the likelihood.'''\n", " \n", " # unpack the model parameters\n", " m, c = theta\n", "\n", " # evaluate the model\n", " md = straight_line(x, m, c)\n", "\n", " # return the log likelihood\n", " return -0.5 * np.sum(((md - data)/sigma)**2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The log posterior is just the sum of the log prior and the log likelihood probability density functions:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def logpost(theta, data, sigma, x):\n", " '''The natural logarithm of the posterior.'''\n", " \n", " return logprior(theta) + loglike(theta, data, sigma, x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sampling the posterior using *zeus*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We initialize and run zeus to sample from the posterior distribution. Thin only takes a few lines of code." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "tags": [] }, "outputs": [ { "output_type": "stream", "name": "stderr", "text": "Initialising ensemble of 10 walkers...\nSampling progress : 100%|██████████| 2000/2000 [00:08<00:00, 237.71it/s, nexp=0.8, ncon=1.4]\nSummary\n-------\nNumber of Generations: 2000\nNumber of Parameters: 2\nNumber of Walkers: 10\nNumber of Tuning Generations: 24\nScale Factor: 3.03521\nMean Integrated Autocorrelation Time: 3.02\nEffective Sample Size: 6629.56\nNumber of Log Probability Evaluations: 104165\nEffective Samples per Log Probability Evaluation: 0.063645\n" } ], "source": [ "ndim = 2 # Number of parameters/dimensions (e.g. m and c)\n", "nwalkers = 10 # Number of walkers to use. It should be at least twice the number of dimensions.\n", "nsteps = 2000 # Number of steps/iterations.\n", "\n", "start = 0.01 * np.random.randn(nwalkers, ndim) # Initial positions of the walkers.\n", "\n", "sampler = zeus.EnsembleSampler(nwalkers, ndim, logpost, args=[data, sigma, x]) # Initialise the sampler\n", "sampler.run_mcmc(start, nsteps) # Run sampling\n", "sampler.summary # Print summary diagnostics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lets plot the chains. We can see that the burn-in phase is very brief." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
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Zsi3+7d4cY1MlfN/F8zpoWgaATdPmTLPLaFhHbNZYW1hifM8+Htw/wM1b/4FWJ8bk/p9D63Q58NiTuEhsbe+iu12ikkpGCQPg9ZookcxbYdi0O9fQwwd47Y8+z0S9QrJcRZ9+AG0whuu1MX2f1zoyj2cSRCRAlvE8g93yV8hnn+ZWZZlXz57FTEzyqUfex5DhoSYUdr/yNeKFLNb8PPGnniK0dy8b3Q0GY4Oo8r3mfcUw+Z+uv4jvmfzXUx9DBSqGzaZnMiHuEI/Pommp7xRbv9Nm+dobdPpdBicOszTfpLl4l0unD+OE4vybiRKJkODMmze5vCPYk1wkY7xKOv5BBg+fIpXJ0W2d5872G3zF3Ude89mXmWVoYxOzXEUrXUSPxvBTTzAYP0BC0pDCGoomI1wfa6lFaCpFv7mKev4PMOvDtFQde0TjaxWFR0YKTE8fQ1QXcQtF5FCIN9o+17oG09EwnyxmvrMtQggkSaLx9S/zR50GzaOPcq2TwhKCiCyz1Le43jGYWTVQamdwjausJT9I2VQ5+fghZCHQdR3DMFhbW6PZbGIYBreaICFxJAt2v48h+px58U9IEuWRySOEBwYI7d2L8AWyImP2uqzPX8NNwoBu0W0nsE2LiWMn0HT9bdW23q/ztfkv8GhpP19fyGIbHZ7aV2T/xBDUFrEvfpZbjTDhIx7KwIcJRSbBrVDQCwinz7ndV7neWeOBxFGiZoiZvQcJCZvtK1+nqL6GbV3ld7/xKcaldYbzGUoz+4hGx7+z/mrXIhPRkPG5tt0l0rBprRsceLJIr9cjk8nQ6dwgGh5DcaIoCR0hBNvtHc5v3uRDM48hCQlN075T/nbfpbbZpbQnRftLX8StVHG2tnDiOktf/hrCT1DY+gapj3wYFPWtfecBMpa9i0wIyl068QS+HEJSe6x2VhhJjCJ5KZAgLmQkGRQ8umd2uLHd4cqAjqO5HNqb5GQ2jfB9ekLh116/jpsLcTRfZFWSyaoKvzCcR1Xk78T8nWZE+HStDo3f+R2i9RrejW/Qn36YamaQav9eAiEcVhgoXiQSHsaKneCFtRfoOyavWcP0wpv8wugYALZZQbnxJbZtjYuhGa4lCvxf907imyb28jL67Cx/eH4Nag2Oqykaq/PoiRSxgUHiukxGjzB5ehQpdK+t293dRVVVTOs5VDlBpLWX/3ytwuVshv/vyXG2Llzj0Mkj9NuChQtlZk8OkC7FEULwrc0GRrfNqW98ifTHPoo+fq8O2K7P85fuoHgWTjXH1Z7Npx7ai3lnntLUHsKJe22FaZosLS3h2A4bixW0GGj2LtTXqTcznP7ZTzBQLFI366y31xnvZ9jovkDLshHhA3SVPAeiJXI7dSLHjyMtv4zvC6Sn/j2W67NS6zFbTCDEvWtpnutS31ynMD75VrvqI8sytm0TCn23jwTwLY+rX17AlyWe/cfH8DwTkFCUEK+cucLFtRs88dhxDg/PUK58mZu1Lb5kn+Cf7tmPvtZjo7mAY/d5/PHHkWQJX/ioskrv9dcxzl8g/alPwuAAqqSC4N48vsP29mcBSCaPIkkSzm4Pq1ynHPtjcrn3kUodeVucS5UuxWSYsGpjGGs0mhcRvTaFoWeIJiexPAtJwJYDf3h7Cf3WOR7yzzP9wX9HX8kymFSo1l6ib6wjSRvE4/soG/c+JG11dhmMlHAX53E8lc71eRoL6/Qe+CDjRwa4fuMq40M5kvkG6cxD7DgywyHtbXUf7pX77tICmwt3ePXKIgKBbCfZ3brNZtNnYGKMJ973OOXFNZJDYYz+XRbbs5x//TJJ5wwHDz8FNwRWuItTTDM+epKdWp+HHxxC+AJJljC3mni7Ju6+FFWzzGC8yELfB6NHfX0JV8vx9OE9341t+yoiWqK/JqPENay4xY3XXsWxXK601xHFJoOjj1Pu3qAVKlAXGe46eQa1EP9oYvD7tvGd9O0+//3sZ8gmsnz8yEdxnBobG7/HysoQlpvhQx94GtuyeOXLXyAZUZAlgec+zNDMPnoti/+8vovkC35hS2A4DRZe/12M+S9R/MgnKIRiDEczxMLjKIqC4zt84dbn8S81SekxXpk8RCyZIiYkFElg9Dt0PvsVuo1VLtfmSap1Bh8eRlNb3LW7ZIeOkrd2eHPd4PWlVX6hOMjyrsQDyTC7iV8nqhZobZzCWm8xkZyDu3WwfG4VNc4tv87V3gJ7H/27yKEEb+68yVhijKH4EAJBp+XxP7++RLTgEUsqDIejzCy8dXGyegfj3AKRbJS5tSYVPU/tqymyT/4cUjj+fWVa7VfR1BSfu7TF5PI2J589RDgeZeVKFTXUYSi0QTU+i6Q2WVv6OrmBx/lMP81Uo8IHZveQzWbZ7pp8a7fBM6MF0kYXIQRKOo208SZrL3yR3MkP0R89zvLqGicO7cdtLtA07xIPjRLJHPzuhXnfxzIMnLcuyty8s8hnlzeZw+OnP/1xJPne9x9c22Zpp8yktIt06xv0Ch9ALZSISWXa1xusNPsoDz/M/pEM9luJzHLbomu5zJUSlC2HV5c2+EzzBvtyc3wwn3pbmSydfZPGlTL2jMn4M0fYaZlUOhb78mGUkI7XcRC+oLvUxs9FcHZ69+L/dt9q9nnxygpH902Si+hYfZduv8b6rXPkCznyA4cJpWIoqowQPrJ8r+/onT3HVzwZpV7jwzOTLAOZWIKsiGNrgsuvLZCdHmZmJEbdbxNJJNC3fCRd4WZC5rlqixMxl8WdrzKbncXe7nCkNEVuZB+3DZMvlps8rUVIl20Gh2KEi9Hvfr7crGKv9fEdH3NYolY2wBcgSxjGOtu3Ncyux4HTw/faIF/gtXfRL/0mTvFZDGMAqRgiOZqjXa0Qz2SRlT91/v8WIQTrqyvEbvw3ctF7+3Q7PMcyAzx48kEU9W9vGkS6X1/jPHHihDh//vx9WfeP0m/9548ioxA3BYoqOFOYYbExy0B6nPfbF9iNLOL0HmW1UODf7E+y1D7HZzZjHLHyfPyBR5HkEGe/9PtklCrmRoFQ6FWc4i6tlRE8PUpjcorpwSZ/3J6hnxvH6QvGerfIrBo0/H1sDtU44m3z5Ng6qytN1jpTpPZUcWNdXjY+TXZDxo6vIdk9JpoOHzj4NO1qCNEymCkOQHiXcuIuGzvH2ai6bOgej07HSX7zj7hecVgdzrI5OEjJ2qGdTtJXE1TcOFlrgZLTJWSk+GCryvO+S7wwhtZU2eebjIYMjJ7FtmWguwkq/UWk5El2JzLou+tk8hlq/Q1a+9aZq+7QqR9HSr3OrjPC7Kn/C2/YDWo7C4TCGp/SF5iwElTrC0TtfeStEsaJOf5fl+5Q3F4jyRZjmSFW02Gaap/j2SVSvTHa3ia3nRxbxhj5IYOOPMDhRhu9+jKP63NIydNE8gNsRf6YcnWB3fop8oURHEvixegQG0vXkJH4ydouvlLmhdIsW3qRk70qH+6W+IO4TMOq88y1l8hNhDg8u4eNW1+hVYojVWbRvFEkOU8vnOb5UpODyTa5tS7KQIbG12qkpy/iZS3stVFi3SHemJJZ3C9xNJPl/b7Mws1x/HiEvb5EJGbSzQ2wXVvA9hy663cZHtvDymYTu6eSSmtEqxUeeuQ06ZNzlFeWCLU7WIsNFrwe7S2DZbeIdXiQX3x4jM/98v+D85khIsVBPv3IQXq3L/PCYowtJcMzjesUsyC5PYimuWqtMnV7mEJkEm0yzc1zv82NkMK1A0fQFJ2RpRVSpHjq4LOMmJ9lg2UWNgbpT57iWfc6sl3jTsVHXlNpKnOMhj2Swwm2U4vI4ZuQTjIyPk45+ov8yZ01diq7/A+Ki7BKUL3NNf8lRqYfoZbYQn1T5fLwBHvqgkHTpTuWpZmf5zFsEvUi8VMfxe0plLe/SKN+ld5d+NDpcb5kQXlB4sXMLKrv80yrxqkPn6K1/iK+ucOeqX9BKiLxH9fuctu6g1CTjJ9ZZKShsDc0gzzs0FB/H0VVWFs9QD0j84HZOYTks7j7VSpyk7Cq8ncGf5Klc1fZtUc5+hOnGdk3y/bOS6y1rvHZnX20NpqEfZ/DtuCwn8DQ2sRnL3I3Psuy/gyH+lU+3Pgy/uzPUC9fptE9j97bzzcvrLBTanMtP0demeDhjs3p9AjzX/sMyZhPLJJGsoqs7h9mfXSZ42P7SSw30AZsPrum8FoHhBvmI4cnebqp80f1GrXMAh9LXOGF1iBPFPYyrm+Sik1z6dXP02/XkbAxGsOsi2ls2+bqSB6vVGLIsSlUv8hhp0JTAVfpMaKHuKt8iDuhMaalbY4UbvBGJcZN8sgaOL7O3qVdjscy9ENvohsqXys+RSys8kuWw+baDNEH0thdmcG6RS/j8x9r2xzZ2iRBnuFOly9HNjDGosjCJmMlmdloYIg29fEhxNxprL5BNO7z9zWNTrVB2ZS5yhCnrBU6tdf5Rm4Iq+shR7L0pBinmwqXCymOCouP6eNsX3iDG50LXNn7OFo0hO2UeTybJxSL3WvsfR9RnkcqjnLR2oNdXiReO4fcNNCTCp2kgfA89rZ9juqH8OJT3NaLGIcKhNbmUawmN7e/SSTTZrq3n0Y4zk53iWN7P8TQwBDFwWnCqQRfXHyNK899hpRfY774GKNmlydi5xhUUqSLxzHKFq9vLxBJt3j90C+hhotM1F+G+RBb6g757Oukc4NEa0Oc4SEGwjFmrAWubq0xkbhIWFOwzAiJXo+4EqIwkWb42P/K721dYqSdw9xwOJF4juFMgi9eFcirDoUTj2Fxg62mSVyp4amvo4ePkDA+Sn5QQ9tV+SO9zbxu8iG3RyYk4Wk1Vutd9o7PEalHSCol9j08xMZv/S5GfR1H8mh0otimjECQVu4iH36a2Ucfwcgtcf7Wfyc9cIxoeZnOXZPl7RxvjB2DUJTjRofB1hJmokLBgA1zDyMjUUT3Ao7fYdr/GJvSCDt5h3Lia9yQx5jc8iiaFtcLEXw1ii55eL6g0XdRZcHpTopjqspuZZn9H/4offU6y65NZ+EOtdsVOr7OgzsrhPLDWPu7bPdT+MlH0coL+IrDyPAOVWmHsnEYw25zQ0uwldzPnsQw/3hkhkuVGuz+LvrtG3wtdAo3nuaBTJqfzu4lUi/TuHuHr8VP0HN2kLYWCVfr5OU8Q9Eh+gMpvpz3SYci/DOnz8s9GTUsUHtrrMpdDhTuEPUMNq+P8dXMMM0Dj/Bh2WJ053kyyRGi+mm2z15kNB4ivV9lOZ7mP2w2SLshjm6vMppWuDGxh4+NZ7mz/ByF7mv0LsW4OPhT7MRihBIWH7l9g2G/xtQ//ueoQ2PcunWL7e1tHMujvNomkUziaZ/H6PaQ78wg6yrbTynEohbUOjiGxF1tkgdqS1yMZKkaPuFOiveZbR4ZH6axdImO1yF05KfplUpcPfNl3KkR9oSPYeouWbapn11AmZxkfDxHp96mkBlkt7ZJsdFgcDxOat8o1fXP0lpus7WTZyc8xexEmK7zCpbZJxH+KPPfegNJybIzU6S7P8up8pe41osyb++jOHIIravSdhqclFeJJtpstkyG8zn+3qO/yO7v/C5meZfw6ZP8cegGT5sPId/qgnKN2EyFdjaGjIRxPcfY+D68Gy6V8Bm2w1fo2Tonp/8euekHcKQ+v/7cDlJdYmwmwwPSdVZrr7DtbpLf2qETmaA39nfox84R2n2N0N5/wxvbfRpLy4R6NaZaKuHJxzgx/SoV38VoFDk8VqeQfYTPby5ydauK7MZ4YrdGo9YhbpuY4UkqRhgRjzKVjuIaTdLZCqE9Fc75h9iNH2YgN8zHaw16rU2WR6KMeddZnq+yupxifmIQy+6xVzcYM67yenKKZDnMschVCntUopsPoobOYKZDlLvHcZ8/Syfcxk0eIp2d4KVkjIgWxo6Cq3T43x/6CHculIkN3GJ78fNclya4GBsmqgsKyQEi0b2sLC0TXn8doUj8zLMfxFvZJjU/T3SrjFqaJDH1NK68i+FHuXTmdbqWwUCqSTdyFT+uosdsdq2TvBxLY0nDDLQiPLW3yCdmStTv3MUfsCjseR8rHY9ts8uhjWuIW1WcUY/nqy0+rw/iux4f66c5MimTGLrNzTsLLK9Nc/yJT3Lh5hW0jVXmsjdQ4i5+/tP4xTzh63H+UHdRWxY/v+XituosG6/izZpUj48y0D5LjAx+70O0jRZT8gCVyga/nZaJqBk8T1CIJhm3VyibZebWQsy2BMJ0uMmLpIarhEMeYiDHeTeLUyhyWozxZm2WpmsjRw30RIFfWN9gM/0F2k6bF9SfxFHCZPxBfooUklzgl/tb2LHLxIXBP599ANeS+cbLL5I8XiBdKNHoN9AvHuIr0QpD8S6xWAjMHg+dP8eRo5/mzqXniWtj+OOz3Fi8SEvsMl5ZY/TofhInH8XsRMkX4cpGH33U53bzBrvdvfRWw+S4g5B9xkbfT6l1AaP3HC+KaRBDTOm3ieguKanDl42PkEyl+NeTRUZ3Yvy73iLXKPO0LvHoy19GFxmm3v9huvYyv7riM+V7TCQktNYmh973MS698SvI0QahUIS29AxT0SjR0cMoXpnfW5lH9gvMLHfZHRnnulElK0l8IhXhkY9/FM/z+L3//iecsxPkjS6PG00iRpYGFU6f3GLtQpELhkNXt3jimQd4sT2Iu9YjnuvSThb51JEBfueNP+aOqeNGIqQHdf63gyfwtSLdvknUd7n1+W/SWLJQI0nGD+e4sFulEsly+PwXOPKRo7yxM0zyTpt2UWEt22HIzLFm2Rw+MkwzlGLl3K/TquhEph9nLlIgT4hG7Rye+jkkfCxrhmx3mo7WR1b6JDoVRLFI73aNLx8bQfFifMLL8QeyTMoX7I82mW+ZPNb7Joo9x4gXpRbfYH0iR3Z9hoF4nl9Lt2nq44z1z3LY+hMUzWJ0d4BwLEFhyOLV3hTn3UcZ8/NMb20wLEcYHi5wpjTPbGGI5ZVXWO3l2Vc5Sn3nGk7+KmXto3gxiw/MXKW7PoJmPsSpT0zjI/jcy9foXvkKs0M+eNMYnRCN7hYTWZ2WEqaxrVEci5EaCHHgifezdudrpItHkLUUTtvjpeefo9M6i5HZ5NF0ls93j1CPjfEfPvJBVPnH/0YmSZIuCCFOfN/0IMHz7vzWr36cqKyTtjUU4Av5g/Q7IOwZcoYg5C7RDqXZHhrlfdEzlLsuq+oAjqTx4J0+w90I7tA5LmaLlPUxBq0OB9s3MCthotkK56OPEA457IQK6HhAFx2L8e4iFxNPITcKPGCcZSD8ErKlY0byLCdHsSNNVmqHObiTYjLzHF/MHsbuxBiUezztXqfWG2Utfopw5BpDVo1vJffQbubwvBC+6nB4ZZnBeo9buSi1vSq+oiP3U7yfNa6oLXYSRTR0rMYIk22LhmrgKCF8JY4bMnlq4wJhp00kX0W09tLtzvJmKcpWJkRI9EmHVtjbb3AlM85Ub53hrTZLIypr6j7MZgYt0QLFIGrHkFBJ7fi0R21iVpi8bSPVKlxI78cTHs+0P49bivJm9BiyqzDau8NDUh8HjS/op1BaCrFwEzcj0cCk4NQZ9mwW9DGevdNBL65xV+3zuvogctRlsmVTDSeI7GrsRKMcrmyzp3CGb6Yep9fLMcUaPSdPV43Qj/SxTI9wR+bhpok3vMndUIKOn+OYt8RAq8dW9yFulLI4Sh3bdRjc3OD9Uh01X6Gh9OnbCv5OitdGHkTJ20R0weO9C/yJ8gQiZPFzS30+H59irNtDba2wWCzRjKoc3blFzt/G7kiEMzKJhEty7f30Dmqod+sUuh02Eg221SHWSxbjTpewOMmurjLfW8MMKRDRiGTbPFZ/jZvKOK3IMKrrIPfaTKz08JI9suldvPJRhoxxHDVJu/llvjk3B1qacKyD0rdIb9UYLtmU+vM4vsK8OEnfiNMrjXJy403STYPBfI12wscRMZaVEaoZaEppbNklEQuTbMdZ9UJopkG+UqeXP8x46Bw56xYuOcY3B7iSLbNY2ofsqIQ6KZyYh5noIlkeIysWq4URdC1CUjvHTPsmaxszOBPjzCiv4HgOX1WeJiYiPOW+iSOGyepXwYfE9klkEeYLI2HGI8vcjBRpbKYoEONTd8s4apn+9C12Qll23SGWtRKFTptHuYgZ26DZj6BVHiOiCqqmhep6aEmJ2IE8cnWZckTmqnQc3Qxhyj6+4ZLSJPZprzJoL3Mndpwd8WFOri+Sjp7heirDrHuTmCeRYISbKwVqM0vMx46Cq6MqLk8tWAzZ1/n6SAFTmiGnNdiNZtF6CpqVQU3fJk6NbTHBw9d8rgxqLCsxjodvc1edQmht9knzzGvHkD2X8e48e9w6mhNBUi3acoyW5XBWfAg97KAnGtgI7EqBk6HXGLPWKWthVqLjFJ06l+OP4bZBlztoSRfPlZDwmemWWY0Mk6wJ4tEIdxItnm3M82LmBIqQ+VT7LFvzh2j1a+QmwTGHaKkDXBoI4foeIJEw+9jpXRRdoAodSZYZ6ZQpNTzO5AbJySal7hLXspO8z1xCVdrclMZYkA+h2y32+RusJwcwDBWrr6HGHJ5tvcmbhX3ErB6PL4JhRulMvcGb0Z+AdpRGqszDnbuIiY/RQGFkdZNzuomX6zG62WVoWaYtC1rhEI1xi3o2huK5JF2XJ6tl5PVDfH4mgSn1mdpaY604g6aVmbbmyV1eJ7JHI5KU8WQfRTnBvLmPDxtVfnuPT9s2GF+vsJAbR9MMRq3bPN69Qq2Xx5IVQnEbV5J4YeCn0LolHl66wt1Mju2xHqojONW8zE5yglW9iOdqxNqCTqjHKHdJ0aMrYswZG+i+DKrMrvMkr+SypKwhfnLZxNBeQogm7W6OmK7iSnm+mRW0wjGeUL5J3jR4sfh+FCeDaFuUdJtybIAdp8dR8wpOM0xNj7BX3iXSihNTStiZJo1OkUpyi4Tbxa+XuJgfYbLfxxIgSzKHy2XsiShS6QIbVoRF6QhpbDzXw67ksLJtQpqMMOOoHUhZPUZbHW4NjJBK3SYiGbS0JMduhvCdNEZ6h1bJZjWcZ6K3Q/FGmucODpLs+Yy4DW6kh4jEtkEI3PoQB+tNIrsbhDtNtqYrJMoNikaWM3sOU01kydQ6fKLdw5+5QluGF61HGZLi9LQ68bDFjLFA0jG4ET8AWoiF7jSOZiK7UWJ6H6Ft0sWjYeeIkiAT6fGJxg36fYPWzhCunacp13GlFuGygTf+MFY4wuGOwZdmfRzJ50M3G3xhZhxV7jMnbnIzPsSIuYESjrLWK9HqKqhaksNunVjqJqNumd7mwyimjy/3qIccXioM4RMlIukM9DqU1ChLqTgTtS4HEl8mEjbwF3S+mvxpnKyHFGuTKmu8b7HN8ohJdU8SWQ1jrumIVh1FTbOVd3GiHSTh8/TWRczaGN84nkeoLpOtXeqhIsLTkesTyOlVSjvXaboPshPp4NkKIV/mibU1lFASwnAlFWcxWyDmSaTSFXxXUFhVWRlIIMUbjFk6B7dDGJ6B7jjsGVgknlzGlz1eso5yLTqEJCnkzQ1U0accHqbbGsZx+kSTNmHNwohEGOpvUZEy+N04cl9GyzbpOkVCsV1O175Bv/sYhCDddtBWNknJUBvaoJkcJdWdw+k6RH0brfgcodQcNW0D9dokpVSMSErmhYRL2l4hJtXZVsaZ7RuENJcuGsvWk+QYY0A8jxnfImaphFbn+NoBnYoqcbK8REKdZyVxnFp4CrMp0zZDKNkeh9wV9rgbmJpMb+MIU6lbNNQYb3qT7GQh0m1Dp4Ajx4n5bYa3O5ydHCeixPhA9QZKocGrqVke7L7Ohdg+LC1O3B8jU+mQlNvcyXnM9LcIW1tc0E/Tt+NoUhndiDGWucWmlqFlZNmnXmWPs4FaD+Gn+siyji3ytBbTvDY7TryXRUv2caIthJXCDd371ttw5zAbIYlHG18hp1b5av4BdL9JV9FI+SojjQaX5AFwYhSlLqXKOXqhDI58gN14iicWrjM1VqOXcnGbLq2tAQwpx2B2BVtbpK9CUk7whv4020YTQyoRNQ10Ncyji3doqirW4RVqsQm27Rl8dYdH1q4w50T41mCSpNrnvPsIBgoRX+O0fIvJ0E12HYtOQ+Oue4RGqoQih3kwPc9kf5PnN6foZ/qcDm3zsvQBwr08H7i7QCQOjexFBrOHsfRVGr0VJF+iXjlARwqT6/q8OT5GBRMjAiFZJ9+PM1DrUWxsExMuGV9Hs/sYpZeoxFSy20Ve2P84rp3HSuxQoI7i2ey0skRzHiEZnuhdItZvsqa6XEx+CF+SkPoZDuz0uDwQx/QVtNQ20OfJ9hvs6CMsySWm+g32OD7dUBU8h1cjDxKRYkTUAQyxwtONMwg5z7KaY6rVpd4NU/FHSSjzXBp4BD9d4SeMF1n0TnIjVEKL9HBUDWQH0SoieS5ytIYiZCCKotp4wqPnKPhOCDnaIgIUjF3WpXEsL83DG+cR4aPcTIRo2nWitsaDtRdIu9uURZFaKsOd9AE0NBRZZbTS4lDpdXa0OCPGKhsDB7jRP8D+yi0GzCmi6df5k+GjxC0JtZenF3GI1jsYkTBKT+Lv7U9y8VaP1yQNjRCa7nLMukS2FiHSHmAstoRR6LFRL2K14uxxw/TdEKYvGI9JtIduo0d6/H5mHzG3Rcna5UZ0hk9G13hefoJqv8mxzgq30iMcaq6S3R7juVIcyalxonyNbDzKejGN68d5YDnOK9M7rOgplG6RiKPSEVUGYk3G5jfRdx28XArR0xjTQ7iFHruD21wO7UNVshysNZgyqnQ2FwlNePRUmbWdae4cGsGXZeT2MHKigW1FCceaCBvG+1ukPQgDfcnnenKEIxsuhq1wdrhE2NSJ2As8Ef46rV6OYrdAVuuwmRUs+lmWtTFG3R4l2WBHHmBPDeqhIpdyfUIhAzyJyYpgvF7h9kifHXkcz4nzdOwsXUdldHUC3dM5m+5yPR0H10NzIyS1KB1b5rT8DYZdly/oT+GpCh+bb9MvSEw9OM1G5bPcLMfwtg+S7rZ4fWKQGfM6mdQCPUIsaoc52W3xD3/p/xkkeP4q/G1J8Pyn//F/ZGhmlYjpoCphPp8/QbHt0ervoa7L2LKHLASaBtP6JTb0Ak4vhxpr4+MR9UwmjEUuxWeQ8VDVKL4PEjJR16CnhvCFhyRJPN68wc3oKK4sE3E6bEdHcO0wimpRtMrU1QiuGsPtZghrfRTF40T9Nllli1fi09S1LLKsk3HbtJQ4LhKyUPE9DVkz8YSEwEE4aSQfTmyW2fRiVPfYOAqMWDVO9u/Sp8/N2H6acondbhxdl5i0dzHNNK2wjJ20Kbhtcit1wkXBhjxC1S8inCh21EH1TfRYG8+O4Hth1EgTkFA8QdFt0OgMY2RtfFfD72RxFRnZBz21jdB8dCGh+DadxgQ+Pqf9M2yFFBqRIeS+Sld3KcotynKRfitP3LIZMDts7nFxfRvJB03WEEDUsxCyh4dCDwVZklEkBYTHwTW4lBpkvL5DamCRpcgstvCxlT5CyOiShpAkhO/RqRcIyxFC6U184aKh4MsSjm/imTEkL8Vp8RJnkwdRXItPVc5j+wnOZPZQjQgsWUarZ8klqjTUBAIZSbgIWfBwc4lzkT2EFMHJ2jleyp0EdPaaS0zWryELQU4v0tN8draOcnZ8CDXSY3//JhuRHBVpAEWzGbIqDJZd5iMPYfoWfUViuLNJdUJmX2+ZphpnO1SgYHWp6nGcXhYt1sSVPRQnjDCSjOh3SFtN5pMTzJnbDFltno+NgeTiKjqSD7KkgJPA7KRJEsGKlikqGzzdvIOr+FyPDHEnOo7rSMiejlBqSMiElCiuIiH5HnG7g+WX8EImlhtC1fuo9SHM1C6K4t37UOw6pN0GQo1SFwUarSiS55CPbuGHNRTXw9OigAaKjy5kMMKYsiCit3DlEB9ovwGehYzMbW0/O+E0H6ld4nP5k5i9DDg6T66ss72vxVIkh5DAkyQQ4NXgE7yEQOALH2PjKHfVMDeHR0j7dR4Tz+HvPs6re7OkpA2aThLLzuGLe+UUTnSR9T57+yushQax63s4ZK0ipRa4HN/LULfMSfs2vgyGrPBi+hF8AY803uTV1ANEhUfaddkJRQCZkA+6cPGEwJJVXGQkQ2JYaXO6dYWu6vG89H4S8W0aegbXV5GtCKGoiYmLbajIkkKyphPTdCr5Bsgu8XaSYfUaNS1F3GqwEBtHQ2PE3mJdLyCj4kuAEIyYW6yGi3i+TMyBY+48ebPCtfhBtv0R7DAI1WRfb5WbkXEcW+Zj3TN0lQhvJI8jJBBCRjJS+JE2ru9j90OEQi4hzWHvbge/nuLmRAIl2ibiq1iyyyOti7gIXk8eRUHBl3w0X8HGRVKU77lvWyC7GhomP1k9z8vp/XRll8c6V/C9MLuhEOfjJymUHXZKHpJn4/s6shMF4aJFLDxFQ0IgPBXHyKBGegi1h+PHoBdD00wioSauF8JWbASCkBDIkkLM69FSY6iOj6QIHtlYJ5Qu81LqcUxHQlItwj6Yso8ECO59pblnhjlYvcVaMc+D3RtkfJeuEuabsdP4TpiH/Ne5GN+HhITAR/NlXFlQsFZphItEXIek02Y9VERIMiCRdnsca18mIQRrapxLqUM4jTEeqN1mPHMRGRnP1ZBVm/XePi4lp0FW0JJ1dN8DId+LUAKQQAhMLISiA8p3yjvpNMl5fZbDQ/RNlXDIBFnBc6MYnQQCh5AfIu4oOEofL2kR0ZuIpkZXDJJSbUSsho2EQouoL5G0m8z396NGe4R0GckNIestPDuBFjHB84laLoNmg8VUHg+YsrZ5ZFnlt0YOMdpZIe63uBp/gGj63rNKPDOBrJnEyyr7NuvEXBctbbEd17mUzGNYOgKVbNjhQV5lPVRkVxlFlnws2UcIn4JVZsTa5kbiBJIEcjeDG6/gIZHt2MyJeV5J7kcJhYlaBj0pQsmucqJzk35lAq2ZwSkuIMV26SsZzqQfxcfheGeJK+lJQHCgUuZGoYQnPGSh4fRTIEmEYg3iXofYWoKtWB4/ZiJHm8yaKxSsNg5wPnUET4BhaCiSwohSw1BjCE+jrysg2TzcvkKiY0PY5mvx93PUX8EXsKCO4bfyGLKHnttGAFa9BAjUSI+o3kcWBoascbBzjeXwPpoh8BWPsKvhOxEmln3u5Evo8RqPNl9h2JXZDSdZ1uNshAcY3RXs2egjZhe4EZ6mQhFfklBC925LsGslJkSdeHiDO/EBMjsKal9nstNkfOgiutXGDGX5fP5hPFx8fBRfQ5Y8on6PthoHIRizdvCR2QwNIICI0+PhtQpO2ECN1tiITLIYHkYWCjISjuSzp3ybqYrOcmI/66N9InaPg5sVLkf200ypPOxco9nbQ3mgQQeNjFCJeX3WwnF6jSj79CssRUbJWTVOtq4xnznGpjyO1cmgJ2ogCeR6mpLhs5kSKOk6D7YukOqXmU8/Sl2L4Usq+GFctY8jCY7urqJuxthJFulG+rSGv327pwSeh2kk8EUYhI3t+0h4xKMqH+09x4I+wN3ENFHXoiOSTLirmLLOlp4m6Xg4coTR/gb1cBxDiXK8c4Os2+PL4SfRIhZClvEsHRGyeKZ1hpuhMcpqmiebt3g+exyBgisLvF4CLdLmQ40X2dSLXI7NIkkyoptHU2X8SA3ZFbgaPN14E39pklx6GynW5su549idIUhXiTtNCrsSi8kJ3LDN6f4bLIdGiQuDuNfmfGwGrzvEtLrAqLGKIlvMx/dQVzN4rokna+QXe1RyM2T7PrUI6LldVKGQMbap6jmyXp+8JLiphpEVDbUfIW1bbCtp5HCXtGOSlnaZXG3wSvo04WQHQ1VRQjau79DZjRHOOTxmvMkbsaNEGlMcWX2ZTNpByexg6EkuRafpijBJv01TS6H5Kk4rhRN2ickWo+55wuUQl1KP4ksqectnoFthvNXDkCTuHHYoOyVkI46Oii3JxOliZJrE/B59OYSQJJxulFPOiwz7PW5G9rAo7+V4+zJXc0dwRA98m7ntLbyizkJ4FCG5SK6JJsXxJMGg1WLWWEH1TF5KP4bXy9D1dRQhmLaW2C5lsCSbpN+mrcRxewm0WBuQEMAz9a/yevo0HTkOSPiuDiETBZXB3iYgGDVr3E7tw5BSWPggW+zr1ejIETbcFF60+536LPuCkJ1AllwevrzLN0fH0Qs2T9Y/S1SOsqaneSN8BNDwnDCSGyaWqaN4KomKhZqpUJNLyJLLtLXFoL3DC/H38ZBxk6YkUYmmeKB9DVvAC5EPIns6thtGjdc4aF7lWmyaaWuNY+Yu3XaBtLCw4x3m5SnCa3n2tDvIRCnHHfRknUpRZTVSwlQk9vbukHYdLoaPcbL5Gi8VDoIWAmRkT+B5DrP2CndiMwA83rzAtegMLS2JJwker5/hevIgnhTGEz4h36KihAl7Nj+1vo6/dhBDE1wYzNPMN3ETBqasEaqOoUZ3ybLB0f4CnojxevogaWuTij6Er0ZwJPCFw/7eEvPxPSAAfBxPJlofRtJtJN/HS9cJtTTqfoZkyMTQ+ih6n7zTYrt9AEn45HsdVmIKmYSDplmoro+QHXqKjCwpCF/Bd1VCqoUng+8rILlv3boloTs6QjWxJZAAxZOw/T6+IgEySDKqpOC5MkIxUSUVRch4EuSacOq6zZVRmc6wiUEauTZML7qGFgdZ8gEJT3gMmNs80L7BT/38Z1CT338r4Y+bH5Tg+dt789lfE1ncSxQYsolQJGxZQ9PKdJMhhJUAV0I1I7iaw4I+gN/PsH+txY3hNErEpuJDIz6LZebR42WEBBBBUW1MWeVU8yXeSD2I7AuMpRJuKU9bTtJSIKsusq99lYp+jLv+fpRQlQP1BhcZxlIdNNVCCTVwe0lQJtCiHp7rs9uZRIvvMG4vseEdR3JDHGjeppCt01NDnEseQPYl7kzoFNwKSZHn0cY1ZKlLb3cMtznAU3IaZ/Q83ygMsB4pkm6VmXVugOnzh4mH6Sh5qnuzIAmE5JG2lznWXUIx4VvpYwgk7E4CTzaIq21GTcHY6jDDQ7cRsRW2rDTfVI/gKhK+cJlstEiwRVxZ4ErqIVxJZVi/Q0tTuaztQZI0hjptlGaadslhV1NwbBcJGZQYw80yG1YETQWxncTTEzjROsQE3/7oN2ZXONq9xZejz+DpLVDLeHYKU1PZCQ+TdFuYahi7k+bYrQUiEZnyXIiqkkcixkCrjhqrsK0XcCUJ10hTks6yGxpHETK5Sod97hrX0+O8GD9KmXFQXXylgi8LRMJkxNxkzTpNJOyix+p4rsJyOIWHg+3FeXngYUJWCMlXWQ9PUYg3EbhciR2gpYbpZVVkqYEl+ZxXR0i4febsW9S8PDU1ysaQiuqtcuyGR9S1yUyd5zXnALeUGdAdBuwaJ7s3eTF5Ci1cZn9vBceTKetJFnWV7VCGDWUAzXPYaywj4SG7R8FXUCQPV+6h6AJNtSDSwxImSbVCWcpyJ5ohKgzuREfxeoJoNYIxEGXSu8WWO0dHJElEtjGsNF5MMOFssKpk8XoxFN3CSVdQ5Xv7y/d9Tu7cIK2WEUoYmwEuRw+jqj0+VH2dRWuWa6kJVBSyzi7b/WlktUlEMunLEqaIgitxPTyO3lNYShXxJZvRxjKt7RZ+voeedLE7Wc7N+BAqIPDx2wX6nkcutYWZ1Tnv7GPAMVH9Hp2ZNmVpgKjnI4UFUqfE6nQLWdcx/TQFc4PpSgM57qA6JjGpwtej7+OWOIQqt7FUi6s5BUnai1oboOFN0dkqog69QjVRQJXCOJ5JurNLyFIwUgkMSWKssU2x7tB1o0znz9LzJV4JvY94N4JQVfZoV6koHSICCrEVNvQiqiRQDJ94q0NCrDHYcRC7E6ynhqlHdCTFRnRzPCydYcDawu5ZHKjOEBrYoa9F2Q0NsmgdJCV3cFUHz1PJ+2X2G9tEhUPaNFAqeVK5Looik/TbbKoemuIjhExVyyC7Fo6ZoCcr1PU0nuyT7glaEQU1ssPB1nW2ouOU1HVuqrNkUJg2c+y01pm626EeE2jJIQousL2H2MAOedWirBbwzTgZsc5h5xIGWbrRCFfjA8gohGRB2pAx14YJ6Sm2tAlaap2EXMEjjAIMKLuUxSDCkgmHQFJdhOZR7K3SjI5gKBF8+iixPpKq8qHqBfpbx3huOIvv6PQxUDWFRFunpzXwYkmyVoNUfxcjdAQ/bIGdYNPJc0eTkKUOnmKD8DGbMR5uLnBzuEjVLTFVtbidynAzewRNadLSB9DWVJxUlFDKwtP6XGQWzbM5snuVs7kHkUIeaivEXPcuiUaIjirQihuU9QKmF0ZWHWrOKC8ks+y3l1gJlVB9Dx8bc7jGplvAkmPMtZep+R53hhOEpQ6u5OFLgqZZJNTrMZTcQkiCTTGA4uqcdi9xMzpNhxymDFYvghczaUgJFASxUJ99rSq64aCmDG5Gpqg6JSKWj9A2CKUtLEXHdGM4Io8qJB5d7FAfWKOZUZjrLRNZ34sxMo8Vh83wACEsHnQW2HQHabRjFEN3WU4W6IQS2HqerGOw3U2wnk5zfaSFltglL22giz7h2A6S7zFhV1gOg+9btDMp1mMuM+Iuz6ceQMInhMV4dxvL0KnHU7whHUNCQn9rRBPhe3SbKQxZYyeZRcZCkVSi0XVKVo2mGmcPt4n3Q3zEXmMwDk1J8KXuJDviEMLZwR6ssTXmshA5hOwewfATqIoBwuNWehiEiiR53Mnn8fGwOwLfSSHrIXwkpF6G/f5ZCimLqxxmKZIAV2XdO81KcpeuAToO49Y2y9EiOjJ7uxUua2mEKqHi4QKvqqdJezJeZAe0NpHmKkotRG82japbHOsucF3sQfcdnixfZWFEYTWUJW93Ody9zDfSJ7mcPIAuNELCZ6zTZFcfYk+tQaIbYjtlk+1AUrXxlBBjwiHnbWESZ62UYyWbRYkk0HyY9rY40LzKulZkJT5MO+Rw3L1OvN2hpmvspoaR9ChD2gp9yUOvT3IxcRxDiXNM+xqm4VHqhBmLN/A1ia+kH8J1NfY21rC6CslSl7oWZU9jhQxREopFzZeZMVZZ9/fiRSwyrkFZj2KnEryay2JgIiQJMxLnwriKJbVRFIWr3ihYBQrOLo7i01HDVBWdkUaLm16BO85juEqPeijChUyStpRlr7GFE12iouQotiwqdoqVpIbtGejtJKZIkZMc6o1pNMmklVFRwy0EPk43yzV5BLXk0lJ9HLeH7nXQZAm/O4warTEZWiXjdeg5DgupSTRFEPZDnJUPoht9fB/qXgHdSDEkXSXar7CdfwBDi+HZIRqNORoZmNLuMOY6mJJMPNymp8UodTsgtdkWMVYiw6yFRvB6Mb6ljuGKBq4dZVhZZTvqk3HaSALY7tDKpIhn62jxKr4sk3RbGEacOWuJXNtmx4mzWx8hlbrGk60LOGKBZWOY1UiO1WGQvQayJlFxUyzZ40huHDXWQMh99GSVNTIsyAeRLR9VKTNnLHOdQ6jROifyNzmbklATBiNeiHi/gyvrHDQXWcHiRniSHTuK39UJJxuUpDKPOLf5QuQkLjYNKUVHVzmS2kJO+uzzN7mg5fF8CRmJZLGHhMyNyAEUBYzsNpfSMZK+jyOPYigatifhNSTcfIyILyNJApFuMtdfZF9rE1Nx8JIK1xBoRLBDgnm9QLJvszvo0lATSE4ESwFXSLiyx3i1SkMqIpIS+AqZHY8VXWWnPcJoeon18CCpWhux6WMX+nhIjFubDLBFqJdnISwBGofMbeqOz2Y6znooymb4GGojTrcT5cBOlYbsUc4Pcz08yeCOQPMN2pkQcqxHLrRLx4/hI6FKsCSepdUukWmsITk+hfI6/r4Oi+kpRpp3KK6qtAuCk85ZROcIXx8ZIqI5HDfuIPsam7U5vjyRJBq2ABlJlXFUi8Od28RmynxQ2uCF0FHOFD6IJ0LEJJOQJONJNvEQKI6P5Cs4jQI9SUNSdQpen5BrsqTMcSM2hd1LYWyFGM5dZNKOoMoaIUnmlHeD+WiBiC9zxKySs6tcj89w03wQL71OTl9nRUqyFN2HK6u48SRvdIoc06+QokFXDTEfmSPcVfGkPgm3io5O28pzSX0K4fdJVGOUZR9X2Gi6xM34FFFfxpc83kwcx5UE6VqLZTHMt5IPE5El5rotxpqbSNEqi1qG65FjnB1qMxm+zk1/H8spk6HQLnUpg9ceQJdCFHodlvIF1rRJFN1EFoKuP4sumdDPoXgyptQmWrH4pPEanys8hCQEviLT1V3iFoy1fXZDbTrpGCF2Odq9wbrIsCaVqFjj5PuCTlhnJ5Ek5Dn07RBe2CbiDGIYFgPlm5RzWfaENim5fSIe3I2mcWRB2K6x6D5AJN5lX+8WbS9F2xmmWeziyBquk2dwo4+p9tByDR5q7PBc6SC2pOIBRbdBWctQTQm2ptpsDwwiVJWpzirD2mVqSpxVMYjlh5BkFRWZmd4KQhW4mvy3Ognyt3nb/lpISEiAq0BPFzh4JCWTo84dOo7LgO8Sa2R5aWycrqbiNUIk7C2G7Qo1VUHvGTTjs9hKisnuXdYTGhU5xlB0kJ8Ofx0t1qG7fRNpZ4iiHeGCLGPEdWKezLRtMaB7FG6EOanJ6JOHOHg0SfeNK9yK6aC26VeTyK0JppNpLiUFDy7exbd2wblNPh/mwPAad8ceI/GmjL52jJDb5knpGjuhHNcOFDC0NIm+xuDOCUIK1KseCPD1FVpbeQ5mJMrdKYb7m2RFCKmVI5fPoKttVLdHVY1wNFwh5W4Q9eukXJ0PN14EbZA/kXIcuPsGE/E1JgtPEiZFJnqafnEeVe6QtRIYhs/h8gL5xDSmUceO9pm211nW96Mmysw0bnNTfICQmuNgP8cuGjG/yZ7+JpndHZbih5iubOC0bzGzdIh2JEkznMLTFdpmGEw4oV4iKvkU7CqhXoSUZdMoCKRSg/Bug5V0kjgGBWUFM7SXoUqYnICOmWCsClqpxoNLPnp8mX6rxt1cGEWzqGAx0ZGZyS3hNfv0jYNMxedY7Qrqqk5X6xBRM0SE4APua2DY+D3BkKhiixyWHEbrJ1iT0sQkg9FuF5IWg3eX2ekmWHlsiov5RyhIBaI02HJ6OL5A8iQebVwjHKogKz5jdppzjTz1CQdfkZkwrmEqMul4jgRhjnducMEcwShBrqywsTXDibSDfnCVR52j1KwdevEms+Vz3ExNs9QrYsoevtciLEX4ZCPEZatHrG/hR1LsDAhCWpntiIOPxKnKyzyvfJQL8hNEBnYR/T5H2huMSqNUehnSToKSiHEuHSGyYdJORdAiDqPqKuPNee6WHyfbrBFOtKlFx1gjwrR1m8L6ALrTwJ1qM6ZHmG6/BFKCjPkwyUXB6NwrdOQMkXUZNTVOTb/DgazCb8RPINkK/YrPtjaHKaKIHsRjt5loG4TyeUpembY0QCRRo6PK4Fo8UX2Z59WfIWx02VvfplUo0k2nWMpOoPU9uq6NJ7tE/SphVG7HD7Ktg5Bgxu8xaZQppByEqiPiCURmgH+VTPDq0gpRtczltENfDuM5OfQ45A2XN0vjGHYOzc4SbXuc3iojbc+gHChgezFG2jvk3Dy+K9Cq11lwk7TjE+y7fI1EYgI5ViIy6OFHIiRiOnNUCRsuEcmgt6ExpRaweg6x5hAjXoLDdp9z0RoXh0tEDI+SWCGUALM6S6iwDyVeYa7bZ80cJUqIqMiTU84QWehRyDRoek9zyv0mTeERcmawd8MkEykOShU2B3wkB9qGTkNLILs9hO9id8dx7f14fcH+8gZ+1CMUu4hWTjCi2qyHS0xnZxg7ZdNKLJPb2MbqCSZsi6Filq1uhV2tSrKxh9mOzN5Bn+EOtKw4Ufc4ObdBqLjI1WwRH4VWZ4jk+jw7NRklV0IdzvFm6Gd4ar2Mn+yiKR1G9R1u29PErGFCRouOlgR9i1mnyYXeHkjBTH+LWKdGVw+TviUzvcdkt9pmot0ntr9Ib7NHqmVwY2yHBRFjwt0m31Wgm2HGaPDa6DRrpVso3RBxS6eWsOiZRY4v3aVnpSi0HPxCkwfNBEtJCIsUuurSc2YY7Eko0T6yK/Bkh1S1yeRSA90P88jadfxYBt008aojGDL00hkMJ8R41+BapkhY0ci4Oo6IspBxUX3BvnadvquwlJjAUzVky2JFG8AWBRRX4pRzhx3abGlFYnoep7fN8N019KyJKzWYbCZJjfY5ZF5jQDzB1cwoO4pMyylQN5qcaG5SNAT7NtucO/Uks1qZsHOJVzNhEr0CmmVhqmF0q0nFTPLwxg5506CHg1LLMBcaJ2s+g+Jv0cmnOdo5x5R7lZCcIGnP8aHRn+YlbYlm+S7H5aucTT6AqiR4f6fFl7UMrUyE2yGNWNMgtxVBDPaQVQdNjvF4YhOpepfB3jrLmf008hNcbYVRJTi90uJOIs0022QTJltGhsXKKCW1ha5EeX22RGmtw/vXzrI0vI9FfGKuwVCvR1ZpIFswm6szNFFE7k2i3NiLu7tLPJTmJ9w1zr5vmjelYXYaN1Ach6hvELJCZNoqMzWJs0NjqEkHzY4S8vuYCY108wqJu9tI4zXmZJkVdZdlo0jbnqCo3eKU8yqp3jiL2hGiUoLomgpmj5K9xUxMpZfLYiYM0p6L1S7iWF3+7oZAj6rcTOu8HDLRjATH9W2iLY22mcDTNBQ/xJzfolg7g6/qDI2nMByL28Yopl3CqtZJetBMhtnr1Tli3EQXKm3FIWUcw1AsHjDPMWKO0x+KYEgy9fYj1Gs19qY36AwP4MUcorZBOD7Og2GPoeIoh8OnqRhXqRlXSHSa+J1hns6W+Yo2DJ06N+1BypbACSdZS4YJdaqEywZRq8t4JEykHmVrLMHTvavodw+hpp9is1PhsHeDmmYQjoeRorfwpSKp+gCemWRG2eLSzDAT/Sp1aQzTL9EXVdBsjpY3uFIYxpd0jvdvEIspLBijjC9eJTu9AArURB47cot46zD7J2a4FtGodNfxDBVduDzq3iApXybSTdDT17GMLA9OfZLf2r4GVgctomBszXItdJRmUmfKkaj6YYStEnd32I2YeKpCth5mdmWFw1YH1U7zcrxIUwszt97hYOIWCjKiUaId99FCOdJ3VeYTeSzFIB7dIYvCsD3NsBnF7OuM3VJY3h/Ct9Jsaxqy6ZNoHQVJRdITRDUbQ4kxUE9TVL7Idv5hrlnThH2ZdFMQ9UPklmUydhkjXyM2VKckd2mIPSAiHCqXuakV0ZJNJo1FCncWGdqCMBrJdA6fFIYbZn0xy0jxNjm1zZTpYTeO8M2oy2CzwYUDLvPaAZwK5HrbWCJN0ukwqJW5Ix0jOVTicCJC7/oWR5pFGgN5oo0N8l6Px7uvE4rrmD0Dz9dx6wdRS2Fyi2HcsTy2pLC3XmVOvktY32R48Cgf6byG07S4bc9xe2SI80PH0ZQuYQWO1s9QU8bZ1cfIuFVqShy3FSMd82jGTUwvjG/ZDFS6zLUEXUlBq9ZRal1uFB9DHugw0rxNdrtNsztLbHSRhKbxCfurLK0Mc3t0AmJZ7uxTcHSZuOeRC6fIr27wYqlAcqgE228QtzIYnSFKtsOh1g67Uzp+5AhquoSvxUl0bSaLk9BZpK/4TBiLeFEZrbuFrT5BWnRIrsWQ1RDdiILaSrKT0jFR753v9e4QlWL0R6PEwwZPum0qTZlkWJBkA61Tob49w44ucXtmkE1phLgZIbsrEFM5rITOwPIap/u3SbZDHJzZz5nqNu2mStj2kMM+cl4j13mYWq/PgJEgJ83i2DUe9b5OXUkRqQwTEQdxzHXkUJ0BuUXdHcNUkshqjEjPIGLWOCrVWU63iblbvDy2l0JLoElRQmKdYek27sAHoR6hKlrITh80gY6L3x1C1DxOH2pzfCKMunuDSGmQm68eIWcnaEdibMYPsdGbQ8TXUGXIajpt38DRotxOjyKLMSQ7Bl2Zw4tNnNht1EIDpzaKn4KqliJR13hodYfbMZOEsUt3MEEtFCchLI527tCTfUKuiXurj5o8QEWMY4djJKujRLsHEa1NUqESoaLCYjKMXbgLdBj0m3zUOMcF4yFe94uMtSs4ShrDzeC5MTy5QVp1OLRm07I2OBBaYDH2CFuKwO5OEBLbnOY2hjVM9Og+mpu36Rk1dCvB3js7nJ/bQ0wbZEzLUtWmaHhZThQm+Ptuk/8oeghF5mhVwcukkNQkbU1Fy4NfuYq2cYVJkWRMKgESB1IOpneFanuTK6Vp7JiEHqqjrk7xIXsYo3uZ7X4Es5jkYafARr+M3YozZkTIlCyqSpSTd7YJ+XupzoTQwg2uDWdA8jjRvEzaqZFKpkl2NDpGiFo2w3TLZTB2hYSqgJLG6DYIR6L3M4XwVypI8LxLsvj2UOmwEh8FHYbtNPGKhG1fpVhU0eYcmqkm1/RZ3HifXrbGkNQmlDoAepH9MZPEjkphax+3jOtcnXyInxyf5KTaoLFZ55FTP8ktZnl52eTRaYWvV+5SnJ/n0emn2Hvy3/JfP3cTWyT5R09OER2KcWrNQDM26Soq5mSaopvnAW+MQ22dzXSJYr6KNvYgV/QVJEkiw13c05McFM+yffEOg51dZF1mODbO2YhPpF1kenwTUWuRSuXxDu/h5spNTmQOMfjxv8dTfYFbPYiy/AbFj72Ph4dLGJ06l+42cf11NpvfxM+OcXpgGmunjBeP4MU/zVM5B8l9g/iT/w6lMI29ehVl+mF2mj7FzHFutbK8//E4Y5pEvezyxW9AP/NZJnJlhP4kh/QidySbX+o7pBOzZLQ2ZjjLrHuB4UGV+Mn3M1B8iMVXznLlYoRj2CzutPnW/jHCYYePDo9xffMWc70aUctHiblIiZOk4mN0Qw3CiQWeiVzhq85RVEdl//jH+WdTB3C++By1yQnkU0/SFJuMrH2NeHacaL5HRilxRH+a7KlBQrkiS1fOk5/U8Q2Z0MAhxG6HR+bLeJuX+H39BmSO8FhzlHT0NH57nX65y+qzj6BoKmW7w8iOYL1WIyPpHJ8cIOq5uM4OA0mZfZHjXMbiCbvL49ENfo0QX+r6HN6oYB7dT7q7yaip8fBwkqlHj/DNRo/nNxoMeeuoe1Ryep0hO81g8kF6yTpTZwy2ttfZmI7wsdkw6Q/8B3pnzmPfbBKOhnD9NUarOr8dH8GzbLr9GWZH4+zN6OxV08h9nyubCY44Lmkxz+85E0RrFUTrMJPpcYon9+AO+GyW3yA80uVTloWjpPGz/xK1GOWTosOvfqXLrhqmSJyhnV3MSJgP5ztcVD7M00/uYXChQ//Wt1jqG6gj00yKIkZSQTo5TXety+DIfuL7D/LHn3+JeB/mBufInBygeOBRlu+o6HqNUk2j3slQ0GRE2aWYLXI8FueSP4Q+vkNC7fAR703czevcjQ1zdc8ptPoVJAVmnTZaUWF63qJ7fB/d3B0ez5+kvW7Q68Ml5xJJr4xRP0E5XWQit81wo8Hh8EE6/RZu5SiWFIax2zz9/p8nGh9i7tQ6Wzt/xETHZdE5REsLM9y8xUedVf7rUomGHkEzYMTxeOb9B9GP/RzarbPU22CvthhT5tj/4F7+y/xXKItNPjX9YWJbK2zfaNE2JazwDFN76oyNzaEu5MnfvcGme5OJ6f18+JP/km63x8ZLO9jLO8iayaMPHudar4G6K1Aqn0LXWzz8zPsYP3SUxYsH4NZt9rRdbk/u4dn9g5jdKjnRJCNOMXRoD72qSv78NXKpFLkTJaTSB+jF28TrX0TrdvmNraNI6iqhKCiobClDqMRI9ZuYqsWxJ0+hOkepXbtGKp5jdM8hUiMTNLnDRbuBcWoAeWWFmROnGBl+mJFGnUg+y05VJrdzmz2ZO2wNf5LcSBRVg4VvXEDWmmRjTfChNPcAI3Ibub7B0RNDjCkl3uwbzJciZEM2cX2DwV6aT5dlDk4OYI4d4Irr4K36nNLeT0RANbzAJ/acoHVnifO9u5iqTcnR2de9wqBc4IFP/0PqX56nsXSDPdJDrMpnqY7InD74KcbvJDDXauhZmUIoweFzL5BxwpSTe3hT7+INDOOmpxio1hjtGoSPnOJ/PapSWehz1dnLckZFmYW7K5fYnzBJ9y8zW4sQL4yyIJkgWuiiw6P//N9z5rOf5W5jCUkvERtOMF2a4kGjSXqkxL6h47ie4PeqZ4hs3+GEucm1oRZ+Zh+2lGJ3V8I1HA77JSZSBczFeYr7qjxz+F+j9+p85cotqjP7cHsySq6KfSjHUOZn6dzaJKFm+QePPYQTjvJyucvS8h32mzbRUJKN6SP8809/EEXyuXXrf0dUu2zHIkTWalzXZzlZL3Pgxm1O5gvckTVK02MsOWHMvQfRQiGOqge4G5d5+XNRVLXK4U89xcnSCbRQmJ/1D3Jn5zE2F7/KqZ7H3GAMbfrvcEhY3Nj4E1w/gnIOLL1AJDrKWGmIg6OPMhVqsfD8c/TVOZ4uwfXCHjYXV3iitUH2iV/kYLNG0XoIB5P8ap9uf5XJpMmzv/BPeUaW2RhZ4JHTT2JlMvz+K/8LTi/MXOEAux0Pq59mphQhN75LLvcYTq7D5ktbJELbxAeijB2d4blqi1AuQ2L9DxlqbZAXDxAbnaCcTLCv5TAe3qav+Dz6yGE+tyjhxWc5ud/ksYeOIpVvUDY8fne1z/5ChiOteaTXbpHVkzw7e4yt9W1m8ybm3CNU765TaDf4p0urtEtNRG6Wv5PNMHV9iWh8AoDDYyGGh+YwXY+PH5+jdemrvGQYHNZaVCyd0fLHSMpnkIf3kRis0d+KkrXSHOm4KHaJ6arMvuFRol9fJJY4jBQt8PH/4dM4DYverR0ulMp0LyiECUHIx1b7RLM5JvdOsaZ0Ubs9CgMJnjl4irFYgU7nOpnMQwz0DtBonkPnp4kpY+g5hT2dHebrdd68sEJZjMFcjoG0ziygXzR5eDKMMnCI8OvnmfU1Njf71M0w+/7hT7Gv6rD+9Zep9FbQ5U0SkQQtyaWzk0dVM5QGJni/oXD6yaepOwqqovJUeYNRRWJx/lW6Zov9idtYg4NE4p/mZKyFaq3R3h7ADsk0VIutcI6h+F5+cSjPB3s+i4Nx0lsp8qkUws2wJb/JptEgbIaJx2c5/cwM9qLG4rnfZXFuH625GYxqnaQPp6IKfaPGhG9Q7wvcWJhpJggjeNbaIhHOk/7JDzB7x8eOKayfX2Oot58wk6BL/FLFJaOH8XWZ33ANLuVMYrLOzx5+EG9zkMOD/3euNw1WVpfZNXYZ67nY6SEGIhJ7MjKR5lEmxqNMJi+yYaucePg4rfZhbv/+K9R0ieP9CI95Oq+OZ0jcPsdwIce+X/z/UNvqUQlVOTw1w8XX3+Dm5UWscBqnrzBaPUu0qpPIjyFpYI9MkA7FcZZkItUaytxTHDoyR8QuERs7zIOZKM2NJh8YTvLHuw26O1t88OWvEz16mHDpKba/Nk8paTAegScfOES//iUiMxn2ZvfSqZW4vVChGdX48EM/jXvj96mUR9jzxAgblkMv1SI3PcRX610+MjFMSA4hhfdT6M7Qz/fpLZYZaYapqir+YJFeZ4SKeITB/G+yP6bxilNgqD3E9GaZHVnndLTI5yNRQskYpzNbHF9X4dYKF/o9hot51sqjHJk+wMgDKjd+72Va7TiZ44cIW8OI6HlotsiN3uaDAze4UXwM0Y+jx6J8MN8i0tjLQqvHT7c2EHKbSD9OeSLL7ZEJJh2PozNZ1nMlQukM5zrzZMwWT09O8ODoFMvP/Tqb6w5ubA0vl8OpyPxSfZty+w6WpZHP6JzohtjsNxk5+hgvrq3hSRof+sg/wEo41LqbPNbfJW1ALyJR3H+EWn8v0a+9yd6wz1wpzJNvvkRn7yEyD/8cn0nV2YitMFaIMvbMUyS/vkZYazL9j/8d9uuvcvtLv4Xa2ODDfp9oei/90QhT+x5FKSucD4eRMqOMbb+MvD5AdHSG9z/+Pl7848ss95eZ0tI8IZcwEg4nTh9g93dewNqp0fGSjNUUhv/pv+GfDY7xh6//N1Y9l2TjFrtKjH/60EeR5TTfePkMQ5UW1YIDVYPU9iRGBGY/+kvY/jrdwUuk0yfQQ1FKZ67ze+EmbFYYtMaIOgUOHhggtLtLOvYSZ/o6W9IIycw449ljmG/cRY65iOw0ir6NnSsSCSVpR0ym6hpTRw+TsLcIR0uc3HuMK5d/i6QYoacdJlv4Jp3lOsutUY70dri9Zz/rQ7MUHIVO2CfbKvJgIsLJlMPnIwN4sSHszioTYZ3Z0n6ObIT4WLrIwtXb9PthxgaKzA2M8Mu92/Q9i2z0BpEquCsVPmgtED/1Phb82wxJxxgf05h+5jGU3i6mfYPP1Xq4+mHy802SO20OzHyI6cijHHusRHR7m78/OkKy5TB1c4WtpsNBz+XQ3gKx2RSi69CJu1za49OQ6jx6u83OksagViK57yDJ94/x3H/6n5FybaShWfrmvyecEyQHksTXpxnPRjh0ehjjSoXUuWs4Zh+5NMbfHT/LrfUtvNhJnv3UR6l0W7heDcmPMl5tMqIkUPQthmfGkMxZZi+cZbuX5amJa2zG0tTcFPrAPyaZHbxPmYO/HsEzeN6lX/23/xP5uTs4ks0buUN4aox/0jpALDtAcjqJEtql4V2iYTZIhpIMj/0Srt1DF3DL2CQXzrHeWedg/iBJPclytYdhe+wpxInoytuGbPV9QdXu8ms3/oCM2+WfnfyXyLLC5fUmw+kIhcR3hwoVQnClcgWA2cwsmqXQ67vYfY/8aBxJkrA8i0vlS+TDeaJalFJ0kPZuj3S0iR8fZGNzk7IWZiCdYiwSovlHf4SczZF48n04no2m6G8bblJ4PpLy9gdWeV6f3/nWr9MRD/CvnnwAXAvUMKhv3SveXIPkMMjvPMTd92oYTb565f+GIkyk7EeZyc7y2tZr/MN9/wDr5XtDg0qajDRr0fLOksk8TCw2hRACz3FQFIXfPbvGQs9keibD3x0r0nd63H3zFQYu7RB/7CB2Js/z69tcj0Y4pT7PvojMctNFhB7j8bkHieoqwr83FKIky/R6y9xZ+SzKTgVpZ5cB/xSFn/zHyFHtHbfBt1yM87vISod6qUY/NcB0ahq/5+CbDmougiTLrJs2BVVBWuuyHYKKZbO/GCUSiXDxv/0WlqLw6M/+Am7HguoG6sof4CLx+USWLcnmFw/+AlrfIHTxvyBLEhz9WUR6nOfnv8TN6y+wN1Vi1HApbEXJ/dwvIqdS1P5//wdvrtQJ//wv8NT+AdCj9K9eZff1z9JJLtK1enTXEwwlTuA8/hS1zXlOzo6QHJmDaPbe/jYduq9s4tJmwz7H5PBR6l6Y2+E875stoCkSZzbPkNGSHOw1YewhUL9bb3/77CpXax3+VTLB3a1LKAmJ933wJxCSjCxLdM5s4ncMUo+l8Yji97poxeI7lnVzZ5t4Nof61jDU1dqLtFtXMH2ZSvgkx0on0e42sTe6xB8cREnqOI4DgOZbNL/8HM7mFs2f+jS3rr2M1b2KNnaSZ45+kLAa/s5x9rYhlX0Xz+thb0vUFMHwUBJFknDrJvPfWGKlY2EfyHJsOseeQvw7y+h0b6DIEeTwJN/c2eHxza+TLEzTN7L0XnsNP5YmfngfkdlZJO3tdetPx/BtlUqFnZ0dQiEfpOcZLD1LIrEf+8yvcLN8l9mP/L8J67Hvif3e81QcIfjl1V0KksyzhEkVFMKx796nfPfca1STeV50wvyz2SFS2neP3W/HIZobCBFBzuS+81q/v4ljN/mdtSh12eWpgo6sJHl9dxtp7Q6xq9uoap/ZkeK3RzJl7NBRRuYOfDdG4bPaWuXCxjk+sPdDpEJvH3IUzwXhva1Ofdvn169xudUiFtvD3xtII5sV8plhnL7PzY02X1wrI8uwdyDB05duYck5hn72KJJyLxinYuD3Xda7O+SHCqRSaaR+A7t8g81vXiVu3OtLteFh0p/6JF7Xxmvb2OsdtiNVEnsKlGIlFs7vUH/zZWqlPhN5h4mR99F76VXCU1O86Thsd2yi44dZ3u0itR0+8vgYe0tJAG51+3yx0gQgrao8HfOZSiSxt8oIx8EaGCAhukieCdkpjHaLXr/DTrlBt9vFNE0AHnvsMbTvqUdu3cQzW9jyIqbUQY2f4F+f2+VxuceHC6NsLBp0OlUe/vgc0VgSx3G4s3uHiYEJ2v02K70VTpROoMkarm3juS6h6NuvjF1bb/L8zV3+zoNjDKYiAFhWBaO/Qq12hnqzh5N9iofHH0SWZbxuF0lVkcNhPP/e04hk+d6+aPUdvnB+iWcPDZFPJ75vX78T37cQwkcIDbdtoUdDyOF717gcz+cr17Y5OZFlKB1BCIHrOCiui/zWdgghcLZ6CF1mo1VD0wVjY2NvW4cQguevPo9dtomqUebm5iiVSm/vJ10Xt1zGvHULfXISfWKCr1RbjId1Bu0rLG6+ziVL4+cP/UOWzzdRkzrDjSZS8w6xn/ggLQvKHZPpgfgPHO7ZbTSQYzFkXf/OtOpGl6VLZYb3ptFf+AbCrRI//QihPXuo/9ZvI1yN9M/8LPpQ8h2XaRjLyHKIcGgQhMDHwXX7bGzU6ckKU40eC+fn2UwpfPinP0nvzm1W1suM7JslNTSA8AX44t6tFg2Tu9f+N9woCD5EtjDE6PgwfbfPb17/TQB+fv/Pk9B/uH377bL/7a0apu/z80N5IvK950JJsozbaOCsrdF9+RUoDVL49E++VScE5bPfIJ7wYWQcT0+j+Amcnodp2SD5DI4WebneYd20+bmhHML3Ma9eZVONU4w67EZijBVG6Pc6bKyvo9Y8mjsGLzVWcVWZaEjjX3z0WYw3d78v5v7cmxjVs4xHn8IvPICWHUAIwa9c+RWEgJ+Y/UVUSeHuxQuMloqMxS2UaB7//H9hJ1TgD3unQQh+7vZz6KOjpD/xie8s2+l0sC5fQZ8YR2+9iSjfxqqlkfZ/CDlnUJv/Con0CLHjP/v2mGyX/3LuDfR+hDm9wP+fvf+OkiS7Dzvf7w2X3lZmlvftvZseD8wMvCNAkJQoiiIpktLTPlIitfvO7kq7Z6Wjt2efnvZJOpK4WklLUUuKTiQBCI4YmDEY29O+e9pXd3lfWeld2Pv+qMJgBmMwgx6gZrrv55w+nRURGfHLuHEjbvwi4kasI9n3wX5Ki03ygwl08/Wdki5euIz/0iq5Rw/wXL1B8Cd/wI7uBKP/r99+zXSu63H+uVucNL6LiLt0LTQ4Phei97FPYm0bZ/H6VbL9A8wvlGlee5bRDzxGOjfwhuUdSEk7CIhtvh458AOqxRYLq9Pk8jl6enrAboBuvdLefH7hecJGmKPdR9/2duX7HRbnv8Xs5Ro9Ax+kZ0cB0zKZWm2yUuswnlkjbjmkUoeQUmJfv47faqPt2c3vLJXpMg1+dSCPdBzc1TXMnm6c2Tlmzy/SSg1x8EODVFeXCAKHZH6AoOlSW1nna3P/FKs9z/DQLvqTo0RD20mkdtNq3yKTeQA8j9If/Gek6xA5dAh59CjXWg47Y2EShs7FeotVx+O5pYs4TpHf3vUghWge3DZTl08ztfYCVmSdbGyUHaN/jdUv/BdmFq+S6x1j9LOfYKXUpGfbfoqz00QSSZK5PDNtmz9bLvGz4SZ9hsZCHYaGhtB1naC50U+WfuvryOIt2PFRxOAxWm6LZxaeIWWlONJ9BEvbKAshBO16jQtf+n20doXR+z7D5OQNzFCIwx//zCvt4KWOgzV9nVKpytjYGCMjIzSrNuGYiW5oeI6PbmoIIXAbDVpL85jxLvzpSeL3HUcIwUJjgS/f/DK23eCDQx/mSO+RV8p3pdrmW5enqaw3SM5Mc9/PfJSdva9tV1TX2lx7bo61+ksktYDR1BihoQHy+0doL6yy5P4JCzfKaO5Rjn/4k1gRg86tysaX+8MEQZtoNMOJ9To3q1UedH2Gtw3SbDVxXZdsNvvabe7yX7D6B39MKzxO+IEP4QwPEh/extRCA2+5hXZimZ5CjN6H+ih2h/njlTKSgI/lMxxMvPa4GwQBmqYhpeTvXXiRiDvJnojHjswO/Beuogcmhz/5OaxQFNnxMZKbbSfPgWf/OQCte38Le/oUya4eAjGIMDWMTPh1dUX6Ac5cHT0dwki/fjzVeVg8T9D/EIQTaJZOx/V5fv5FhO6jd/Yws97krx8forbWJpmPoOsa0pe0SiU6rSbZoUF8v8HK7BKtapzth/vwpcQJJHYQkDYNXNvHbrnEN2OU5Xn8cA4jEsb3bRynSCTS//Z2AO8DqpPlH5N//g//V1LbpkiLFk8mHiKnhfj1HccZ2ncA2Djhq1Reot64QhA4jI78xm0tT0rJl25+iT1de9iV3fVu/IQfu99/YZpa2+Xvfmj7bc1HSsmZ5RMs1CZYcxx2ZXdxce0if+fg30G2fLSw/roE0w8KAontBUSsN08oSSlZd31yloGUAba9TCjU+4aNaSkl1eoZ/EYN+dwssb1Hiezff1u/84fxXBfPtgnH498LApYvQrQLN9FN22uTtJIQ+PDdf7YxzcP/LRghvMCj4TSIiAiG6+HOzRLevRuA1pkzGF1dWCMjrywrcByaL5+hvPwMZncf3vNrZO+5j+j99+M4DqHQ60+kg5YLmnjl5OmdCIKN/ZGmCZaXl7Ftm+Hh4VfGSy9ABhLtLcrvzedt43kNfL9NKJRH00JILyBouejJN/gd7TbO7BzhnTvwPA9N09Buo8d9v+VScXy63ujA9xaklK+cqPyopPQRYnOd2XVolyE99KbTz7Ztuizjlcbzu6np+xhCENr8PVJKpO8zeekq5eICPb19NCplIokkIwcOv6vLrnk+Nc9nIGy9btyfzBWZd11+pacL6/kltIhB4qG31wiQQUDQatM+f57QtnHMnp43ndZueyxfmWcgcg29ezt0jb8yrl6vo2kagW7xu89OAfAzRwYY6tpotAWbJ7FrjstnCxl2xN7etvS9JGCpVKLdbtPf/8N/12suLvgBnhtg/Qh1+nuCQNJ2fWKh18+j1Zqh2bxOV9cH0bTX18X3k1arxUsvvUQsFuP48ePvyjy/1057s4TO253H+kKTbF+M2pe+iLu4RPyRR4js34c9MUHgOET27v3hM3qL+Us3eNv75mLxKWq1i4yM/Aaa9v1touk2qdpV+uJ97zgGbzNJrb/JevLrdYSmocVibzj+3SKl5OLMGis3LxGPRrj/vvtonVtFi5kYuQh61CDo+OiZEEFgo+uvrccrzRXCRvj1CezvaZXAjHCr4pMMm3RZIHQdYbxJ/ZQSFs9tfO4/svF3eRqSfW+YDH/173i721zQ8RAhHSEEzvwCQaNOeNfr26iBDPjqra8ikTwy8AjpcPptzX+rBYF8JcH8dtlBQCAh8kPapW+k3F6jUrtEb/og4VD2DaeRmxekfvCiz6s13DYTlVkO53e+MqxYLHLx4gly+XW2b/sQkcgA7tISlb/4AtboKKlPf+pN59f0/bduF7QrcPWrsOtTr1z4eyuB7yO0jQSN73kA6D+wHXc6HZrNJl1dXW80i7el5baYrc+yM7PzDbfps7NlLF1jX/+b1DnefD9cKr3AyswcsfAHGNr9LtwV4jms/fP/DSIZ8n/vt14zKggki6eW6dqRJZIJIaXkbK2FqQn2xyNvWV8XG4t8+daXub/3fg4VDuG0W5SXFimMjr/x9577l5DbCbs+efu/6W16J/scZYNK8Pw4SMnP/4c/JZIr8qnGCR63Ps+oIfn7H/sI0WTqByb1kdJH015/YnGn8wOJlBLjRzjIvZEr61d4eu5pAHpiPXx+++fflfnekZrr4NsbDbl3gdr5Kneqpu9TcX36wxbuShM9HUYLvfsJrrer2nJ57maRD+0uEH7VXVJuIJnrOIxGLFUX36Pm5ubIZDLE4+/NN3R45TK1b3yD5Cc+gZHJbEkMUkqkdN73Cb234m2esBpvlnhRlC0gpcR1XUzTfM0xxCuVEJaF/h7db91NvHKZoNnEGnjjO9h+VO/GxQLlvUW9RevHwXc3XwgoEGENI56mOx56XXIHQAj9+1fQ7zK6tvEKvHfL7uxuYmaMil1hW3rbuzbfO1LsR7/i8UbUQUG5U8V0/ZUrk2b3j/cK/9uRipp86sDrrwaammAseueeFN8JBgcHtzqEt2RkMmR/4Re2NAYhBELc2duxSuwo70VCCCzr9RebjewPv+NG+ckwMhn4MSTfVRv+7vFDb6kQQgwKIZ4SQlwRQlwWQvzWG0zziBCiKoQ4v/nvf/nxhPveEngddCEQAr6ZeAA9GmV0+46tDuuOJ4RgODnMwfxBYubWn4gpiqIoiqIoiqIoylZ7O5cXPOC/k1KeFUIkgDNCiG9LKa/8wHTPSik//e6H+N4VeJ2Nl6R7YfwATCD+Bn2SKIqiKIqiKIqiKIqi/Dj90Dt4pJRLUsqzm5/rwFXgzul++jYEXoeE7SBqWcarG8+serfREaqiKIqiKIqiKIqiKMqP4h1lI4QQI8Bh4KU3GH2/EOKCEOIbQog3fBWDEOJvCyFOCyFOr62tvfNo32MCAE0nbXfYFjgcjIU5nFSPDCmKoiiKoiiKoiiK8pP1thM8Qog48AXgt6WUtR8YfRYYllIeBP4N8F/faB5Syv8gpTwmpTyWz+d/xJDfO4JYDmmESYowfd0Ffv3YQaLv0puiFEVRFEVRFEVRFEVR3q63lY0QQphsJHf+SEr5xR8cL6WsSSkbm5//EjCFELl3NdL3IC/wkBISWGwbG0NTj2cpiqIoiqIoiqIoirIF3s5btATwH4GrUsp/8SbT9GxOhxDi+OZ819/NQN+L/CBASokgwIqqR7MURVEURVEURVEURdkab+ctWg8CfwN4WQhxfnPYPwSGAKSU/w74WeC/EUJ4QBv4eSmlfPfDfW8JggApBJqESDK51eEoiqIoiqIoiqIoinKX+qEJHinlc4D4IdP8DvA771ZQ7xd+4BMIgYYkrO7gURRFURRFURRFURRli6hOY27Dxh08GhogVP87iqIoiqIoiqIoiqJskbfziJbyJnzpI2IpUuH4VoeiKIqiKIqiKIqiKMpdTN12chtCWoSwGSUSjm51KIqiKIqiKIqiKIqi3MVUguc2RM04ESNMWLe2OhRFURRFURRFURRFUe5iKsFzG/xAggRdV6tRURRFURRFURRFUZStozITt2EjwSPRtbd8yZiiKIqiKIqiKIqiKMqPlUrw3AZPSoQE3VAJHkVRFEVRFEVRFEVRto5K8NyGINj4X93BoyiKoiiKoiiKoijKVlIJntvgBYHqg0dRFEVRFEVRFEVRlC2nMhO3wfMDBKCpBI+iKIqiKIqiKIqiKFtIZSZug+9sPKOl+uBRFEVRFEVRFEVRFGUrqQTPbfD8jQSPoasEj6IoiqIoiqIoiqIoW0cleG6D5UtGOxA3zK0ORVEURVEURVEURVGUu5ix1QG8n/Vko/z0tgKp3vhWh6IoiqIoiqIoiqIoyl1MJXhuQygVovuBvq0OQ1EURVEURVEURVGUu5x6REtRFEVRFEVRFEVRFOV9Tkgpt2bBQqwBM1uy8HdfDihudRDKT5Qq87uTKve7kyr3u5Mq97uTKve7kyr3u5Mq97vTnVLuw1LK/A8O3LIEz51ECHFaSnlsq+NQfnJUmd+dVLnfnVS5351Uud+dVLnfnVS5351Uud+d7vRyV49oKYqiKIqiKIqiKIqivM+pBI+iKIqiKIqiKIqiKMr7nErwvDv+w1YHoPzEqTK/O6lyvzupcr87qXK/O6lyvzupcr87qXK/O93R5a764FEURVEURVEURVEURXmfU3fwKIqiKIqiKIqiKIqivM+pBI+iKIqiKIqiKIqiKMr7nErw3AYhxMeFENeFEDeFEP/jVsejvHuEEINCiKeEEFeEEJeFEL+1OfwfCyEWhBDnN/998lXf+Qeb28J1IcTHti565XYIIaaFEC9vlu/pzWFZIcS3hRATm/9nNocLIcS/3iz3i0KII1sbvfKjEELsfFWdPi+EqAkhflvV9zuPEOL3hBCrQohLrxr2juu3EOKXN6efEEL88lb8FuXteZMy/9+FENc2y/VLQoj05vARIUT7VXX+373qO0c3jw03N7cLsQU/R3mb3qTc3/E+XbX131/epNz/y6vKfFoIcX5zuKrvd4i3OG+7K4/vqg+eH5EQQgduAB8B5oFTwF+TUl7Z0sCUd4UQohfolVKeFUIkgDPA54C/AjSklP+/H5h+D/AnwHGgD/gOsENK6f9EA1dumxBiGjgmpSy+atg/A0pSyn+62cDLSCn/h83G4d8FPgncC/wrKeW9WxG38u7Y3LcvsFGefxNV3+8oQogPAA3gD6SU+zaHvaP6LYTIAqeBY4Bk4/hwVEpZ3oKfpPwQb1LmHwWelFJ6Qoj/L8BmmY8AX/vedD8wn5PA3wNeAv4S+NdSym/8hH6G8g69Sbn/Y97BPn1ztGrrv4+8Ubn/wPh/DlSllP9E1fc7x1uct/0Kd+HxXd3B86M7DtyUUk5KKR3gT4HPbnFMyrtESrkkpTy7+bkOXAX63+IrnwX+VEppSymngJtsbCPKneGzwO9vfv59Ng4a3xv+B3LDCSC9eZBR3r8+BNySUs68xTSqvr9PSSmfAUo/MPid1u+PAd+WUpY2G33fBj7+Yw9e+ZG8UZlLKb8lpfQ2/zwBDLzVPDbLPSmlPCE3roz+Ad/fTpT3oDep62/mzfbpqq3/PvNW5b55F85fYSOZ96ZUfX//eYvztrvy+K4SPD+6fmDuVX/P89YJAOV9ajPDf5iNLD7Ab27ezvd737vVD7U93Ekk8C0hxBkhxN/eHNYtpVza/LwMdG9+VuV+5/l5Xtv4U/X9zvdO67cq/zvLrwKvvjI/KoQ4J4T4rhDi4c1h/WyU8/eoMn//eif7dFXX7ywPAytSyolXDVP1/Q7zA+dtd+XxXSV4FOUtCCHiwBeA35ZS1oD/ExgHDgFLwD/fuuiUH5OHpJRHgE8Av7F5u+8rNq/mqGdb70BCCAv4KeDPNwep+n6XUfX77iKE+J8AD/ijzUFLwJCU8jDw3wJ/LIRIblV8yrtO7dPvbn+N117AUfX9DvMG522vuJuO7yrB86NbAAZf9ffA5jDlDiGEMNnYSfyRlPKLAFLKFSmlL6UMgP+L7z+WobaHO4SUcmHz/1XgS2yU8cr3Hr3a/H91c3JV7neWTwBnpZQroOr7XeSd1m9V/ncAIcSvAJ8G/vpmw5/NR3TWNz+fAW6x0RfLAq99jEuV+fvQj7BPV3X9DiGEMIDPA//le8NUfb+zvNF5G3fp8V0leH50p4DtQojRzau+Pw98ZYtjUt4lm8/p/kfgqpTyX7xq+Kv7V/lp4Hu99H8F+HkhREgIMQpsB07+pOJV3h1CiNhm52wIIWLAR9ko468A3+tJ/5eBL29+/grwS5u98d/HRsd9SyjvV6+5uqfq+13jndbvbwIfFUJkNh/x+OjmMOV9QgjxceC/B35KStl61fD8ZkfrCCHG2Kjbk5vlXhNC3LfZPvglvr+dKO8TP8I+XbX17xwfBq5JKV959ErV9zvHm523cZce342tDuD9avPNC7/JRqHrwO9JKS9vcVjKu+dB4G8AL4vN1ykC/xD4a0KIQ2zc4jcN/D8ApJSXhRB/Blxh43bv31Bv1Hlf6ga+tHGcwAD+WEr5uBDiFPBnQohfA2bY6KQPNt6s8Ek2OmRssfHWJeV9aDOh9xE26/Smf6bq+51FCPEnwCNATggxD/wj4J/yDuq3lLIkhPh/s3HyB/BPpJRvtzNX5SfsTcr8HwAh4Nub+/sTUsq/A3wA+CdCCBcIgL/zqrL9fwL/NxBho88e9Uad97A3KfdH3uk+XbX131/eqNyllP+R1/evB6q+30ne7Lztrjy+q9ekK4qiKIqiKIqiKIqivM+pR7QURVEURVEURVEURVHe51SCR1EURVEURVEURVEU5X1OJXgURVEURVEURVEURVHe51SCR1EURVEURVEURVEU5X1OJXgURVEURVEURVEURVHe51SCR1EURVEURVEURVEU5X1OJXgURVEURVEURVEURVHe51SCR1EURVEURVEURVEU5X1OJXgURVEURVEURVEURVHe51SCR1EURVEURVEURVEU5X1OJXgURVEURVEURVEURVHe54ytWnAul5MjIyNbtXhFURRFURRFURRFUZT3nTNnzhSllPkfHL5lCZ6RkRFOnz69VYtXFEVRFEVRFEVRFEV53xFCzLzRcPWI1m3w/TaNxnU8r7HVoSiKoiiKoiiKoiiKchdTCZ7b4LoVVlcfx3HWtjoURVEURVEURVEURVHuYirBcxuE2Fh9UsotjkRRFEVRFEVRFEVRlLuZSvDclu+tvmBLo1AURVEURVEURVEU5e6mEjy3QwgAJOoOHkVRFEVRFEVRFEVRto5K8NwGwUaCB6nu4FEURVEURVEURVEUZeuoBM9teKUPHnUHj6IoiqIoiqIoiqIoW0gleG5DEAi8ICAI1B08iqIoiqIoiqIoiqJsHZXguQ1rDZvT02WWq62tDkVRFEVRFEVRFEVRlLuYSvDcBk3TAfBVHzyKoiiKoiiKoiiKomwhleC5DbJUIjk7QbBe3OpQFEVRFEVRFEVRFEW5i6kEz23QDQPD7iBbza0ORVEURVEURVEURVGUu5hK8NwGI5YAIOioPngURVEURVEURVEURdk6KsFzG3yh4+gCp1Hf6lAURVEURVEURVEURbmLqQTPbXA9h7auYatHtBRFURRFURRFURRF2UIqwXMbDMNEahqBrR7RUhRFURRFURRFURRl66gEz22wDAs0jcB1tjoURVEURVEURVEURVHuYirBcxsMw0AKQeC6Wx2KoiiKoiiKoiiKoih3MZXguQ2WaSKFhvQcpJRbHY6iKIqiKIqiKIqiKHcpleC5DYFjEwQBXuCB5211OIqiKIqiKIqiKIqi3KVUguc2eJ0WgePg+h6BbW91OIqiKIqiKIqiKIqi3KXeVoJHCDEthHhZCHFeCHH6DcYLIcS/FkLcFEJcFEIcefdDfe/RNA2EIABkp7PV4SiKoiiKoiiKoiiKcpcy3sG0j0opi28y7hPA9s1/9wL/5+b/dzShaUgEgZAEHXUHj6IoiqIoiqIoiqIoW+PdekTrs8AfyA0ngLQQovddmvd7lhACITQkAdJRr0pXFEVRFEVRFEVRFGVrvN0EjwS+JYQ4I4T4228wvh+Ye9Xf85vDXkMI8beFEKeFEKfX1tbeebTvNUIgEUgk0lOvSlcURVEURVEURVEUZWu83QTPQ1LKI2w8ivUbQogP/CgLk1L+BynlMSnlsXw+/6PM4j1FCIFAQwL4/laHoyiKoiiKoiiKoijKXeptJXiklAub/68CXwKO/8AkC8Dgq/4e2Bx2RxNis5NlESA9leBRFEVRFEVRFEVRFGVr/NAEjxAiJoRIfO8z8FHg0g9M9hXglzbfpnUfUJVSLr3r0b7HCE0g0RCGQ+CqPngURVEURVEURVEURdkab+ctWt3Al4QQ35v+j6WUjwsh/g6AlPLfAX8JfBK4CbSAv/njCfe9RmAYDnq4Q8udIsZd8XZ4RVEURVEURVEURVHeY35ogkdKOQkcfIPh/+5VnyXwG+9uaO99QhMgNnqgLjtnycnPIYS+1WEpiqIoiqIoiqIoinKXebdek35XEkKAHeAEFoHfoVw5udUhKYqiKIqiKIqiKIpyF1IJntsghLZx+w6ADPC9xpbGoyiKoiiKoiiKoijK3UkleG7HRr9ESAGBH1Ccr+M56m1aiqIoiqIoiqIoiqL8ZKkEz20QQuAFNp50aTQkpaUG6wvNrQ5LURRFURRFURRFUZS7jErw3IaN16RvPKNVr7ewG+toutjiqBTlziKlZLm5jBd4Wx2KoiiKoijKj12pU+Ly+uW3nKZev0yns/gTikhRfjyCQOIH8odPqLxtKsFzG4TYWH0SqNaKNNunabWnf2zLu9xo88dL68x3nLc1fcX1cILgR15eEAQUi0WazXfvrqTAD/D9gEa5Q+C/vdg8r4GUbzxt3anjB2/+WFzVsXl+bZ7FjkMg33jnIaXE+yH9JzmOg+e9ewmGSwtVTk2X3rX5baUnZp7g/Or5H9v8LxUv8cWJL/KNqW/82JbxdsggQL7RNlRbhFP/Ec7/MTz7L+D64/AW26S7uopXujPK/v0mkBIpJdNtmwv1FiX3ndXpZrP5ru4HfpJqtRov35rl2nJtq0N5nc6NG7grK1sdxg8VOM4b7wPegBu4FNvFNx3f9gO892iD1vMDHO9Hbzv8SAIf3ua6fa+Sm/uXn7QgcF5pI5U6Jb5666s4/ttrJ74TTqdNvVTE6bTf9XnfrkajwZUrVwhuo837XuEFkobn88WJL/Ldue8S/ED7V0rJ2tp3qNUusrb2HRYX/5wgsN9ynkHLpXVxDa/4/bKTUlJyPdx3uB/qNBo0K2VWpm4RbLZ1nrq+yrevvPf34T8o6HToXLnyY6+3dc+n/A7bG7BRRvZsjcDeWM9By8Utvvfq3+3601Nz/Nunbm51GHeUH/qadOXNic0+eJASxwvQAkmj8jJ4O8AIveF3Wq0pwuFBNO37qz7oeAQtDyMbBjZ3ntUy2b6BV5bR8QMeX6sSIJls2TQrNufnynz+yACm/to83UYjw+H/mi8R1jT+1kCesP7Oc3mlUomXX34ZgOPHjxOLxTZ2Nl6ApQscx8EyDDRdf6U/oqDZpP7EE8Q/8AG0WIzOyjrBwizF0QwLk22sUgLflwggnNXoPRQm4gp8R5Iq9LwS/4lqk6ShU7Wb9FT/CCF0wuF+CoWPo+sRAPzA5z9f+c+Mpcb4+OjH8UodXLMEhk8o1ItE8PziCZ4rlYlGRni0Z5wHMwlorML8adjxcdA0KpWXKJdfYmjoVzGMxCu//1arw+lqi89mopw5fRrHdRkeHmZkZARN21if15ZrWLrGWD7+jtbts985j253OPrrH0EI8Uo5l12PtKEjhKDTcAnFjO9vZ8Dq6iq1Wo1t27ZtTF8uE4/FMS3zLZdXXWsTTVqYIR2Apttkvj7PjsyO18wfoF4qYlphOo06yXwBTdeRvsQvdzByEU5NFklELMazFk3Z4VrpGkIIDhUOgWeD0EA36bg+YXNjeWdny1xZrPHJbo1E1EJPd9G5Xia8M4MWMl4p96vNDtujYUzt+zHdqt4CYK4+R8ttETWjb39Fd6pgxUHbiOPaYo2X1xr8zP5eNO31d9tJKal6PnFdR2MjeatvTvfsF/8NodQAxx77HG67TTi+WeaV2Y1t6nsWz0HvQUj2vj6ca9eof/s76MkE2V/+5deM8wKJ8QMxuW4Zw0jjS5+VlRUIoL+//5Xxfq2GFo/jTE1hDQ4iLOsNf9OTq7MU22X+6siht7HSNpOeroNhWtSKbeavLbGyM0M+EmZ/YmP9r9Vtzs9VONQXor1ymXzffiKJJABBYNNqzVIjTSoUJWbGcB2bZqmEiKxiGDFisW1vHYTnwPSzBJn9oHsQirOytEp+cBjDfO323vR8nq802BOPMBB+/Tpw5heoF9f4vVQ3D6TjvFDZSOgaQvBLfTkyAYjWIqI6jRx8iKDjocdfOx/XdTl58iTd3d1s27ELTYDxqv1qaWmB5Zs32Hn8fjQr9Lp65Xsumr5Rn91OBwAzHH7Ddb/aWqUQLfDi5Dod1+ehbXksQwOnBTcepxnqo5Vpks08iK6/dh7lTpnZ+ix7snsw9e+vpwvnz3Fp/mn89D3s+PgnkFKiv43jgmv72C2XeOb1sf5g3G7gYumvX/+vZt+8SevMWZKf+hR6JISzNk318W8igMLf+7s/NJ4fRgYS+1YFP5AspgyKTZcjw2lCxsY+wA8kz98sEsuH2Z2MMdnqkDB0hiNvfMz+Hq9cpvyHf0j8+EHM7ffQ1lwWV5aIx+NYlkUQnCSZ3I9h9TJXn+Px6cdZ8aL8N/t+jp5w7Pszqq/ghRL8zkKVffEIn8inX7Oc71xZwfV8huoQSUpC0RCaNEg1XQAiB3KvbFtSSoQQ2PYKQuhYVo4XbhVZ8D0+v61As9EgkUgQeJLFWxX6xtPo5kaZB1JutF1u3CC0bRvC+H6b5ItnF1istvnNR8apOD5dkY3t6Ae3add1sW2bVrNNq93E8nSsxRbNuMvgoT2vHCc3Yg2Yn/8DpPTp6flpLCv72hX83X8GPftg92d+SAm/PaeenEKPGBy5f/A1w6ttl1LTYaQrihACxyni+R4TboI98SimJlhdXcVxHAYGBl7zXb9axZmfJ7x9+xvua9fWvknHXmJo8G9u/GY/IHB8Wv4tIuFBDCP2uu+8mm2vIoSGZeVeM9wNJJOVKubKPKOFKKJr7JVxtfolimtPADA09Gs8v/A8c/U5ZmozbM9s//48Vldpnz5N/EMfQhoGCwsLDAwMvKb98WaklNTX13j8K9/A6diM5Td+R3rnPjQrxK5du141rU+17bNSa1H3rrGjaw+dFUkqVCKUyeIbCTzHJxT9/r5JegGB7aPHXt+OCYLgTWMMHB+ha0gCzp48iRsEpOMRurqTWFYWN9ioMxUPvlGscTwVY3c88pa/9dVWmivoQicXzSFlQKN5g7lZD88LOHDgAADTF89RW1sl8H123Pcg0WQKgOfLddZdn09nEvidFld+53/D+uhj7DzyITTx+v1usV3EXiiS7ennyzWHOdsh6jkIAbZvoy+vI7w25bkLtFuL+OMu9fIMbdPCSvRh26vYei9XKzXu7UrjTNUwMiHaoRksM4tcNGnN1iGQ6OkQSMlNx+ULS8v02JP88p4PIoT+yj7l1U6u1egIKAc+g2EL8eLTtGtVaBaxtnWR6emldHGR9cgo7C68cj7wZmodh4gUmJv7Fc/xEZpANzYvmktJq7VGOJxlwfYId9p0pZLouv7mM62vwNJ5GHkIudlG/P5+0keIN/5u69Rp2ufP44bDnKq1GU4lGB8dev2E7QpMfBt2fQqsjfn7lQoBAj2ZfMP25PdIKfmnEzdIhVL892N9rxlXXlpg5sw5xo7eS7I3/7rvBnWXzvUyfqlD9FCBxguLSAmpjwy/Mo3rBxiaeM1xQUreOibPoxRIzEaDRCKOKyW6rqPrG9tAo+EQipgb7Y7vfccPQAiqvs8z5QaPZqKsNucYSY7Q9trErY02cdsPeLZc54PZBEbAK+X6PX7doXFiidiRAkbXRn1cqXVeGW+3PXw3IJp81T42CGDxLDK3G4wIwngH57RSws0nIL8T6st4iUGIdb2uHXmnUQmed8HGY1oS32nx1Rsv8G+nbe7b8xgfHjL41s0vEAr62DWwm93ZAvNLX+ZsuZ+P7v4k2VgM3/W4+PUX6TbjBO48VnSC6flLNPydWIkcQ/fdTzhR5FprAMcPEwQuS2uLnDq7ii5T/F67zScPZshUz1O9cprJ8FHsrnkc+xxu8rdwlqr8y8VJBivzHI3rDO//JNdPraJpsC0XwciGsGMeC9c6JIcTVD2f7T1xSt/+Fi/Ml2jl4qxLydJTzzKVyrMgTRqOzocr58nV59G9gA90+1ydFGQ/9jk633yWjJQ4M3+ILS0mm3l6jTXOvDRJQx6gJ7ebmVLArp4Ep6+cJS2+xXAjRGnhINm9Dh2tm127P8N311aollaxIvBLMcBv01idwHK7SaX2osXjfPP5F/BLda4Un6VnfxpjrcxS7DzDgxaJ5P18a/Ecq+t1Kn4v4dRlLqIx2Oxi9oUvcE/Ex5kfJ7S7nyaTdJoNllcXaNQgHo9zwYzx5LVJ3MV5dpSXqIZMVnMFnr94kw+2Aw4HYZ46eYkr1VUGCEh/6gDJ/CDrT/451fE1MtPbMfbeh+ebSCKs+jfp8xeJ5w9Apo/Uyeskkpc4/6UvEci/Qm8+wXwhwRc703wsl+R4cjdXnikTz4YZP1LAtDQQcPnyxu26UQ0CM8Sll69RXbTZdXCM4UKMVH//Kw11KSX4Pl4guPbCAjfbNt0Hcnxod4GTp77KzYXr1A9/lmPbDhEEAWevrjF1o0RP5wy6sXFgKIxug5EswQurROpJojsjLP7h77NAi//j+BE8r0S4U8SIpllO1+gufhHaZS4XPst3Zjr84nCVhGVy5XoHZ77CC19Y51Bvi8yjn6e8PEMr+CNENKArdz+1yBG+vlohaQf88lgereJQXSmxWpwlnctR9iu8fOp56tU8Y+V54n4UeXSMauQiw9kDmIGOltlozNvtGvXyPP5Lf0b3/oco5o8wfa7I7zYaaGh0lxZ5+JGj2PYapbVr5AsPYIYMTlQafHN1gaiA1KUV3BtX6R65nw89NkQ9OE2p9BJ/9EdrdImAD//Mr1B2Na69PImU8+SMMPszO3GqJUq31uk+1LN58rXK3MKfUTQ+yXdPnGW/FOxo+egn5pGDBkF4npXA4muNPD9fSDFYuwnde2m15lha/iJp8TBPXb3IjeoaN7N7eLAl+GRVkixYXPtPv0chEcbSddzkGPqHj3PBO8OxnqNEXZNQLMqTpSr/9uoFpC94sHsnPY7GieUqJ/UinzOeI5w4RiG1C8+rEgoVWJp8masvfI2q3yCf3svCShynuMiZ9n4a8R5+sSdGp3YR79JFZp00s+GrjMWrzL78AI3x44wUkuitr3Fupc4X/TEM3SYbGuLRqZsUiGJHniIIZ5iN7GBHYj97tQwdM0/3jgydchvnzCqRe3t48sYFdk9eJLK2xkobzhemOJvaRd+Jpzg8dB/Z5fOs9cUIF/q5oA3S9n1m2g6/3t9Fp9lA6CZTVZexfIyZx/+E3+vKEu/q4wVnO21f4/5MirPNNterDfaerxLMvcCSd5lLzLCS6+fe3d1Efcng4CCrq6vMz8+D26JeLfN/vzBF2+7wcHwZWWtTFy0uXH+RtJUicvkqqXiK2E99jmrZI9Mfp7I4z8RLz7EWWWMk0YD6DqrNDuG9YxzecRxd1zcS5cDN4g0ef+r3SSU8VvkFkpUbGCsG9+w5SLhToj49xfmllwnv9HhpJIUZGUU0zzDqj2G2VrjQ/ApLZoFrZ18kcAY5eOwgO9witTNfoDc/Rac9zb/+o2lGmqfJ52KMH32MntGfpu22MX2dF6YqHMi0iAmbP77YYmi1TTTRTfcBnWq5TDaTZGX1L8hlH6Tg7cYaS1NbanK2OskTcxP82qFjhKVJX18fq+urJGIJ6qsO81cqHP7IMPXvfAfpOJT/8D+zurzEzLyHpnkMajeIT/004e5uZEiyVD5FKpSlXp2BtTb6pM1L0T7ccIqhZIsb/i36smlSlTSt8DA9ro5bnsQvQGa6wKWFBjO9FnZkmq8vW3wsWsDEZtH1+O5KA2uiBtECVjJPx7b5WxGTgUwWz2+THh/HD3x86TNXn2Nu6TqxLz7FQKdB5+krTC89zbQ7TjjXh3SaBMJhcOgWS+XztJOP8fzcSaqdgCvGAP/H9Dz/aMcOao5LUHkaeeqbnGukaeT2cqWrh0903Yu7vELjmWcpfeCjXJhYQExN4Ohx6reuEe/qwxocYCGmMxRP80gWVlouyVyUq5cvEonFicafICiX0W7s4GvNMNd37KNHc2ifOsuug3uQfpbVU7PoxQQ9x4dpdGz+91MTtDo+f/XqSUbuWaWxazfDuSzXFhfwFp6mt9LiP/3pAtc1k4d2RChcO8fuo3vJ7L4f2LjYcPnyZQJfsnSrQjIXIWKcpFO5RWP2KINTUwx+6ABlp8y5mRfZWdZZjjWhuMB8qMaCleEeO8bDEysU/vavgpSUr50kMvgIxQ48c/4qjx4aJeRHMSwd6dW4eeIkux56GEydWq1GLpdjaWmJQsTCikbQYilsexlvcYXyzQpSJuH+QRqNCQI/wKCbp/7imywuXSXy0CEeOPwA7tzv8eJaiafs43x02wNErzfpiBn6QpJoIkRTbJx4DCYHaTzzDM70DGgak4WAUXMYqgEYa2ixgEbj+ubxp4EVjtE6u0qzMktl6LtodLNt5y+90m6cWW9y4kaR49u6yItVltaeZrWxQLo0S7TwEIP7foGJ0mVEY4Vm14N84dotmlMX2Tv9bcbv+3nszFHuHVplfvUJOl5ALm7RsZewfRvXD3hxehqtrJN66s+p6V2srDQplwxqN59j970FlhemmX75afKji2ipz3JFZvlAoYusodFpNgjHE7juOitLHW6cOclSp8PVSoWMZRKt3mItEsJ8epmugQTx5Bqzz8/SdyBEtXONaftRlp58gVT9ZYrjh8k2u7gUiVJMhhiLjLIkWvzmp+6htNgkmvaZPfUkfi3BubEEjl5lZ9cObrlxakuLOBOnqOnd/M8/+ymcThujPgenvwLDH6C92osWNqjlaixfuIJdb9O58jyt5EW6BnZT1RdYSBxm2umiZY0xdVPnt+8/TPpNLojJIMBdXETvSvHyrWv8lxuniGo6v3bks1jhIrXGEywuVZgvH2HH7r2szM3w4gvP05t0MUIBxdkBBvfuZ+lmha+triOaLtsmpmkGdRarNdyXvs5T+gT9ps/eVB9R7X66urrodFp85cxfMLcIhXCOS9E0XYVuLF1DOB4zV68Q/sYz1IpLnPGuUUhX6F6yiA8kONHsUOhaoiv9AF+5VmJmfoZyyOJKbJBfumyznvxXaIbOybkPonk+Y+4+RpfWiVoxTmV8bqw8zmpQZ717CM+K8vjzv0//7qOMZ7bRdtvUJ9P8s8kp+rvqpJM6160o90zewsp2EZQXWLtexajNEcy6mNopLv2jf8XuX/1fCPp3IaXEsiwqLYeoBSeWTxAK7eALLyyx/9YUo/eOcfDgHq48dQNPnMBuTVLOfYTubIna6nex4vfxX73tFNwOv7pzlJ5ojq8Vl/jzpRX+/oEddJ17nngQInPsOPryWb72xafYvnuBifwhvIULfPrzf4Py5T9grnmRQriXzOAvoMW7ME0T37G5NHEDIxCkpc6ZmSWeWV6j3/f4W4koVm4jybowNcs3L89yX6pJZmmZ5sUX6GQke7vnWXvS5nzRZuW+I/zMo3tZ9Sychstix6HYcPipQ32cLpb4wsUJlqLr9KUHgNcmeBZOXqZ+2WFmbYK9v5DlzGKFSwtVHpZFxu45wNJSg+ZimVDVxoiYmFJSb9aJd2yEZXHlxmkef2aSow89zNHuDJXlFnXnOsVLXyCUCpPKfJpUqg8ZtdE0QcjzCee7aX/lK/xOOEKAyW/3F/ia49KthTkg81xuLiNvnUL0PsDxQpjrYpr4vm0UrsUwpM5TgxqnGx7zqxcwq19H12FgMs1QT56RvYc46cc410pRn6mTn66yI5cgsy3DWqJCT6yb8tKLSPppnV7mVqJItbgOYggRliyvfIPpkz1opDj+mY1E9kqtQ2f2HMNrT2PfKLHS6KET9ek7NMjy5A3iXaOkcnEC3yGe7XrN+g38gBMvPEdo/gW6u56i14jyTKePS06W3/j0p9CNOzcNIrbidlKAY8eOydOnT2/Jst9Nv/8ffgoLg7RtoAnJt3K7mK0PkNa6ODZ5ATk4TTn4MOcK/fzdnqsstpb4rl0gui74VHKUTKqfySt/gZsqs7i+l+3hk4RZpLTYTUCJ2fhuxvo9vhnbj6Ob0LHoNSYZLha56R5hOaRxX+kiB3dOUSw3qXj9RHp9qtGAZ5Yepqs2QDR1gXVN4pYzfMjx6NMlWiPJ8PgxHP8ZGvFJXmztYXV5hKLpUtDq7J9+iZWqzkwhRWW0BweHuGWA0Jh3JJFwDaRJtJXlI/Mlnk1JiGTQgyhDzTKHO6tY9WVq8QqN5UE016OU72emN0GsvkAuuUzYczk1kufw+nWs8iBu13VusItG7AhOKMBzypgC9splDsz6uPEVKvZ2hktZVgej/JEbItKos98+Qz4b5dn0NoS02S7Os9OOoWsuJ/RB1urjRHKruKEEmeoiA95V9pJhVd/HbjHCsvk1luwlrpSOkx3KkSglOadbrLVqGELn4aV58umrfD1/PzU/z/H1ZXZWMzzdk6IpqwwvXKFXdLgnJuiYN5hIZWmWhtjtAXaaYmicbw4GdCVdzCs36fVr9KxESe68Sl23aS4XSBR7eGpbitq4w2h3N49UL3By7gE6GY0PL5pcw8EIxRCpNpVOjYX6Kts1qJZ9pOgiEWugV1c5nL2fnb/6GFe+9FWs5QbtisZNVnACHSfWR+XwIR4dTfGlP/w3TPSPEKRS7B+FkWtP8GJ7DyupEfaWZhijRKS5TkeP0NbWyM7uojs8ht2bZ+7673Ex1c2tsV1EdJOuYpGe1RqH9z6EWH6cdu4Gi9d6aA/sZlcsQbp4nmKxRlcnxHJygFyQwA1JakM3qBPgJKLsGBuk7HyMb04u4jVWOTS/gN9zjOHgBHXjEjExDvE2y4tRbowMYbbSGI4glNSpJ1e5b/VlYtVdODsOobUjeO3/hOEtUr41wsHjA1x1J2ivR/nL0IOE/ICPVmdJ79+Osf5NQkaEfOiv09Vc5V/qbVqZFRp6iPTJRQacXu6r6LSiHZzhJzE0k1vL9zDRFeWIXmZMm2cueom5TpKEyPFI5H4mz1zHtrL07hthx0ceZHLyq6w5LR5fHYOahJCFbHscLVbosqZI9N5kOnuEmcjn2L18mQ9pL1L3exCtZWrRdeLBHp5/ucX66E1ezhxEbxQoCJdPV3vxr/wFazFJOzJCX9TgSu8QnUSdPUEa3ZuD2CJPt/dSX8wwk44wkrd4bLXG83qYduYWx+Jnebp+mEPGOgfkHEkrydrCGq4bEAl85koxLun30rYitJIeQVYnveyxxz9Hr5ymYRk4uk9KwHPJv4LjxZHBKg9nLnC2MUBdWghhEAgYmvXpszoUE0scbDb4WuGDWJbOr7SvM3fpCCtdHtlogvGqx3Vd4y8zgnirhSkijKyvczVVxO7yCek6ATGOTawR1ODqUBZj2z5SpSWWwg3+GuB3Wtyo2VyO38fwzAl6umqczQ1Qqrn4JAiEwUNLZS4O5RhsOPxipIfpyzMspU5wuveTWIHBSrDCp2Mh0j1DtACzXGauOEm726JT7kNfXsKvz2LYbbyCxtxQmohbZ0e7zH31UdzKdr7bm2Myq7Pt1nlavT1UiucYZJJsLUkpZRCOt4gwymj6EJH0EDtG+vl3lTNMXXiBweUFXhx4kHBY49PuV9jTqdGwx6iLPKvaTUzT5akdv0rI6OHeiSssr3vcGGzSxyT7jDXq+ggv8SjC0+hqLrIkOuw3nqcg2vhNn5irE0UjlDTQe/9HfrezwHAtzQOrgt7sV8iEQpx42cWsFjB3D7DUucHNIML+8ElMo8Za4ijt5oNka4vsMLbx590Gi5Q4ujZPUjeo1SfwfY18tIdMqI+e3CiF/i4mv/0XNNwK7YbLeriXLh/agUPIqBJJZNl57BDVrm9waWGJtfQBBleWqNR0rlXGaGQzmEaYtBNwYGGeqL9Owna4FukhM7xOVM7ScXX2z+6hGD/ASq7JUvo000YvhUWH7LrN+T09hPwwEcOj4wmaQR2hS1L1Xj6yMM+K3WQsk2V15xWmG032TvpcdLNMFYa4//olukJpoocXqAYWV1uH2N+pUA2ajHQt0aKOvdyLm/e4ldrDeTdPMhLjQ4kxbtg13MZzGMV5zhl7CAuL/bE0H69JTHuBYqXFDXmUhnYT2S4TXlxlILqNbKSAzCb4SrZDRIO/sVTivyaTmJ5Hr3aLC1mDI8FlrFCIWwu7ORuOExTGebTTZsz4EtHwAJHmZ5i+eZkBDIzIIk8O9HJSxohIkx3FIsPRCCd6Czzqr5KVX8fSa7SeTvL8yM9RSkXREg0eu7LCnlqbno/1Yh95hJnFReorJeqr66zULbRYjGrkBTynw8D1ML4XZuKDETyjSV+1TFHLsUyOvmpAKdqhWmkh7UGyTonhVh1RtRnRS7jxfTBS4OryVW70jjKqF6gmfAZai0SvN5jL5+npFxQqYVIiRsNpkq6sMpitkDrsYJcvMzcXZtmNcSO2mx3NCXxjmaKexvcfoDi7hJfM0skZrPSEeLR6khtugSV7ABKDhKQksF16rSv0Bs8h5w/SX8jwwUc+R+0Lf0a1WKY+nuDKNov9i2N4ExXi3hza6Ak623fhEtD8ts5QYjcpdG4ln2BVruHpMKqNsv3wz1H35zh5bp5g7R60bf0csF5irnUa217ALEtWwiOcj+xhe+I6qeZZiplHmOkMUp2vUddjjFeWGe5Ks6NnnjXhIVe2saMwQZQRvlF2uRa06WqUGFv3uZQZY7iyStzJMBGJkTYTjOBh6jU6GZd4/GVeih2krA0yVDjIwWtT+M4K3+4T3OtfRKzd5Hrpw1wu5Ik4TbKmYId/isuRQaqtbh7Tv0Ui7JCe34fMXMDPxGiU9yJP3+RSd4xK6hD5cIS5eEBEy9CJrIDu8ZvDn2FyrkEm+Cadyhm+kzhA2QghdEkuFMXyCswV26RXr2KZFj1HMiSmyiSnPDzC9Np1CgeOo8Vv0J7vYermNC3pU0iv0oxOYFuSgh7h5vp+TqTidPQuQn6U8Rh8KlKmdnUJsXeGrn0/x/n2AJeKE3zu0jOM+t1cj05xPZ7mG5HjtJAcL2o81udRGJ/h4o2rdFYKuOl7eFlqJGoVPpw5h2k5XHQPUEvHOFLJ8Hh0DL1s81dvNbCcOrfkOYxdUN2mkVq7hGNbyOqjtOsNukSYlu7whXwURBJDM+gWCfbcXGTNn6a7bbHNTyDaNWYj3yXaW8LUYDa7iyl7G6s9Ue5pl1hsj1JsRYnka5jhMJ9fmaZsnmOlU+JU+hc37q6mj58u+syF+3k2WMHPTBCiw+c0ieFH+a8Nmz3RNsZAGqRN+5zgdLJALuIRSYRxG0UemD3HSGic5WKVTHCQ2WSctfoibXuFsGfAQIudQ2GqlR2sd7VoN10m+7JkghnWiyME9RjE55AEGMEuesyrxDuzvKgP43lJBo1rxK0wfa05XnAfQcRyfN5e4x5G+cdamTm9wr61Kh+59U0adpz4rl3MWx2el4OkpMZeKhgVmx1jNmutswggSHUx4TzAnuISqbEHCLxz/IVmYtQjdFVylFJJ1tvrpJHskAG/+Td/kaX5Kf71179LzRrAcNocr8ySrUfRkezdNcPCms6NUhZbtukbTrAYHCAoO4wnlpkb7ufBfJvfXTjPuojjyTCRtM//sGOIRvgIV6dmGHBhYvZlsnMeejvNch4q5UWEbnCsfIuu7XUudx5lcDXKhcE1rqZaRKpjBHoIM2FjSp3ojSdoe5JE7/2YtRD3DHSzsHANr+drlEQXHgUGV9JIW8O1p4mHizQjEZYX8lx8oAcCi9HaCBOhDoEwiaRW0VoOD5XOkXM8okaIVrjN9dQI0bkCUSPKF3oknrWNvvXnuS/6JJrfYKjajxkKk+1p80R5kFP+YUb1JEeqNwn8LMOJXi5lS9hZm4lmh4ob4vh0hsLqJLX+00zKD9MJG3x0/DpBJUxi8TH2faqfBdfgd//yCVLlSaI9UZrJ/SSXyqS9W4xGAi66g7TbGQa8Cj3bo9zzmc9y9sX/Gdxd+M0BYn6KJ+anEY3n0Pum6Y1mONX5AEG2n//PZz6Dpb2DO4Heo4QQZ6SUx143XCV4bs+//V9/nUJ3jZStoyH4Su4Qes3Fcw7gaTpOUCJq29QL3RwMn2Te1ymLBEIz2LVSItXQyGQu8ETyALaRwMRkW2sepxkia5U5ndoOCAwEQ5111i0DiUt3e4EbycO45W4GxQ122s/SJko1OsrN6Ah5/xZrznYevOmR73mG76TGWZUFQmGDT5RfZEHr5Zx1mFC4TLfTYDGUoNkI4dsRMCz6S1WOzpc4m9Eo7fKQholfz/NzvMSCWOOF5HHCQYh2qYe4J9Ho0BImgRZGj5e5Z/0yqXKFWFcD2xnimnuAm9kUjuVj0SQcKxHyBR1TJ+y1GayWmU5EcLQu7EoBM7mGL13irTyBsGj6GpHkAnHXALNDtNRhUhvHBz5mf5m1ZIKJ+C6ka9HTnuUYRWokeVreQ7TpktZarPUFdGQLPQhISXBElHsmK/j5FSqmxjlrHN0IyAQebWHRO2cxFU+zo7jMSO4kL6Tup2OHkdEmwtHQhYk0XVxH0qplGOoI/MIKTSEQ6Gi6Qd6eZ6m+G6knILyCp+skqiU+558DTWPNcChpoDmS08YnsDI2gQ5HWtc4Gd1BIASfnC3xZGwXGcr0TV3n1Ph2AiPCnsplRvWr+DVIpmIEpk5n+mFeTktyRpSjq9e42Vfl5dAhKjmbPe1lCjdHudbVR1FUqBrg6ZJErsI91bPMmd0Uw4MYvo8t26Tm0+hdS4TNOkGzH609xLi7it2Z5YXRXro8yIsFJs0swmmRNTv0tRaxRZgb+lHsehgRzxBvzHGoOc2+xCI1XaNk6JyP7aRkxrB8H9dvgRkiJGO4ukS3Jclajaa5nWRkmm57knUzz+BMP0v5G8xlRtC0ALNiEVgR3HgLzzUQywHlRAbDMomFZthXvcRCbZxqdoAd+kU86XOdXWhYHJXn6ZBjm38NH4/oWp6ytpMTfSb3tK/wYnIPtbUMCRHiU5MraIkJLo2arJtxHM2gEqQxVn0+Zn0XqdeQgYY782FWjRZz6RSZ2hrp2Crd+g6WEzUa4SrX9H2EvRRVz8ZwwYz6FKwZDjXOcjO6h9X2wxxeXiaae54nu/ZxtHaKYa+JKTIsr6WYGDFYCPVTcCqsGRkOVFYY8kr8ZfcuNC9ECInUNXzPBy+BH6rgiw4Jx+TDtxZZ7m7yVHAvO+I3mA/14gc+BbtOOZ7GCySmW2NbZ4FkOUGgCxbyBk6gsdA4gJkoIiwHL/Cw6xn2WNfY2Z7mRHyMkplHA/wght+WaIaNYQYE6PS7KxyrTvBS+gh2M4IbSlKLl3igNsHpxF7wfT5dPUFpdgcLSdBzgrI3QMcrUI+28DxwfQNL+JjJNXrsKiuij5Bl4xg+25p1boYSbG/eIuGVOJ06yL7mFCLkMCeGqRhxkCYhYeNrGoFj0G6YhFINfrp0kmcyB9D9BvcurNNsddEZmOR0/IOE10wq3SW2NW4xG/sorhYiXOngJ5YILI9ox2fbVJNlo4f1WAQ3t44XEhiugY5kR3uZ6HyWkyNxpBbQ3SqyZgxixsp026vE5krEch6Dso5rCCajB5hpbWOfc5OJXJwmAcm6TTUSQ2gewqnz0eXnWQgXKGhFLGFhaxpPJD+D38rwofKznM6O00p66AEMNlcpRVOUDRMhBEbdxIs0SLgVpLCoGQkeqJwj4zfQhcGcN8yZ7lHM6iifmizSCD1PJN7CqXdjJWp469v46kAeoeuMxCYY6VS5kNiB0DSCusCIBUhMKl6LQbGCVtOZifcyKFbpqTZJuSbTGUFpvY9ar0NONgkqeaaMDJHAQRAFKTm4vMLKoEEqeoUqEeZb+8kaHiLUwKvkaGcXMIWJ54SwazGE7pPvuFTCGczUDLoQBLpOtBinZ90hbi6y0B+mZMTZ1pnnyMtD/P7OAulykazd4Hr/DmKJWYSUOJUe4kGHXddvEWt2qIUqxKplwkaO5/YeoBTRCaTFx0srFLpP0tLgO3wa0wAn3MbUPA40rtBrF3k2/UGkpuHV8rhWHdfXMHRJQZth3ozgaRZmECOsudzbuEHWXaY5swdqBpXIOkasjFa1uTT2KVqmxiNzyzyzz8LTfO6/2OH5nQU0q82gu8Sc1Q1CYmg+nmtRryQwNIv+oIiXqXCkeQl9vQ8R+CynI0xqBRa8CEKPEDclGa9B0o6zkI4w0Fxlr/40YREgWoKvhn6Ogegy1VAYuxWhf9FkJR5Q66thGJLOag9Wp4NhmmiZNWzNByQfKL2AUxvmmfE8vg6JjoOrx4nVTJp2P0ZqgQNLJwg5+zmdFdT9EIYQHJ0ukfFNzFSd86k+bkULWFIQT68QIAnPp6ilQY+VsITB8esBXsfGEmGGB08SsRcJdIMvZz5GybA2X4ERoEsHTwvh1LMg2oRiTXSp4WsGEg8kjC418H2wCitMGLvQdJsj1cssWeM4piBzdpHhWohICIq7V3Fqeax6HgeTSlywO/wMIWec+dwC7Uo3hZhHRNf5dnyArsYC4+5VXkrey976DXqcOuVonnPmfaTXU2TC1xGxMqm1NENzg3zhsMSN1Dm2eol0MMNE6h7Ww73gWrQaEchUSAdt7q29RL2Twi1tpxCf5lp3lglzmEDvgOvgV/IIIkhhky2uM5fLETHifKr+XSr5gHOxXexq3OJGuB9PD6HbSaK2TcFpsNAVYaQ9R0fzmLLGCFd1esVNJr19dKdnqOhRmu0Eo/pNdts3aQYGLS1Mv9dmPjTAvD3GalJHa2aJxMrk/XkWrW4CIQCJUR2lKWE0dIV+b5kzye1sa9/Eb0SIRBy67TLfjB/Abxaw4hXumX2GRrObl/uPI4TGB4unyHY1CHQPP2hxyxukU9/B9uhl4lyhpWm0wr2cjR+m02zRkhlSqw06qR4emlpkKi6o7GjTMaLYTRPDanKgMU2vD9/OjDHgV5h2duN1NHzTZKe8wjZ/mlbIxV8LOGfejxOPIrQw4UyV/a0pzsz3YeZaPCwu8oz+KInmKPdPnkKkBKLnAmF3D5VIlZJm02uXmGOUFa2b7iWDM33dhAOPamKdXL1Oh3E8qXNsYZlsu0yIEMKzEaOXOBceZHC+nwtDvQReFCe+TihUJuU2WAviGJaGFfjcVztF3uswa8U5m7yXbmeFZbmNVL3MSlzg+BkS8TVsTbLLvs6s0Y/0o/R5FfZUlwnRoGp4PJN6CNNP4bdzSGuVR9rfZSGynalwkv2tq9Q7WRbt7XRHLnA9vh9htfhE7Zu8HDvKnNaLpnlITUfqPrTSaKKONDySfoeOkUITgo50CQgw3AiB0UEEAUbQpq2F8XyT3c3rrDr345oBYnmReixDtzbFsc63Kbe6WQn3czlzCA0dXwuRbrY4mj7JrcgwB1cuMNMzxs3OMH3eAjuXDJL5m3w1fy+9nRZVLY1teexam2Q6nKfW7GZPYDNhZGgZLj3+POV4miPueXqqgs7KOEPGCn7POquNFO21PsaaLsgUNd0nYUmC/HVK3T5PJfYx2J4n4zS4mNjFo50zPB69j8AIyLg1mlqWfGeVsaLGM4U+AqPFx8tPsWKOMZEYxRQuj83NcaI3xqKZRZcGWjtC22uQjZQ5en2O2NwArdA6ttGDF3XIDM5yOZ1j2tlBMuoyai+ztzGLW6qx2pVHExVKzT4mhrfhCgl2FCPUwfXCWEYLPwA9cIi1kjgRQDj4Gowsuaz7MarJLhw/IB6a5l7vJNeqDxB1BdudNV4qhGjGQ0jNostrYQhYDqWJtjVaMoGt2xihOkJoGO0YiaDKetQANEQ7TU94CjfwSNYt4tUY87E1VrJpCIAggiVM2q7JgHWLvOszFerD1TQeuV6jVdcRfS5uYYnL3iisDSBrc6z39ZELr5BkGVf61KwMH5q5yM/91h+ghd/60ez3A5Xg+TH5N//d/0Tvrgn0Vh3divP13AMUag2W5RDNIIoUAhBoRocR6wbLVo7UXJJqbxssDz/wydkrLOu9GEYT3Yiz0Z+aAOmTcGsbVzUkPDi/xM1cjqaTJmLUqMSjaH6HQA/hOSEwO2hCp1PqJRytYFkdjtXPkvUbPBfZSz2cxhcC6VkIw8GXPpoXxWum6I5MoGkBq1YG0BEBDDaqaG2dpa4osaDEgfYNYm1Bp2PQTqYJdJOToRxOOMKe9jSZmg9am5eyuzGEQWK9CWnJukghAoN81SUUqjFv5jDCLezaxi2QVnIdgUa6bXLIucB6O8tCJskqWZxWBgQIKTCTq0S1VWwtC1Iii3kcU5IPryJkHVMLoTUiLMY19JCP9HScaoG4EzBYLTG5y8WXHqKhEdCFESshhEAKCQhMr8Oos8JEZBhfehyb9zgTH6a/torXs0LV7MXFwZE+VtsnY7rYpklDC9MqdaMJg3BmASkDdGEgpYYrG+BbCC/Fp1vf4HRiL2tGkk+vn6bZGOfJgUF8q4ovfMxKilFrlltyHN3y0fQOAsmexixXQn0YeohBe4Y5axApBAm/yb1LT2MIBze6g5qhs1YfZKIvgab5mF4N20iiIZFCkHMqRP02q+5BvJZGst1gXL/GmcF+cp0qgQ5rZoZ7a1c4mdyLDHTCokMgAjpBHL8TwYxW2daa5VZ0iIfql0h6bb6ePoAeBLiaRiADNGEg/BhuLY+BjkguYegdPlq6sLF9xPdR1JM4jRimoWNay7h+FMswkbqHRGL5HZAxPN3HbiexonW0eg4vXkIIHxePvF2iz57HMxNcM/dRb8QIyyZ79O+yam2npicwjBC+kASBQRSBaJs0DIkeaoMUPFY/jeF1WA4VuBEexnA6fLx0li/1PoTjx/EbKfYUF5kbs3C1gMAP4WoSQ3fQ3Q6P1c4Tkg6BDGitjXNF6+NWrhsjXufjjW+yZB9noi9KIH3MeguvnseOpUm2miQyqxStBOG2TycukcV+ekIzmNY689og2Zrk/tolSK9SNmOcTB3FCwI+svJtvpP7IGghDClwtQAhQbRD7PcvUTGSzIa78e0oWltnhznFvtZ1HC3gOf1B3ISNrYdwvQiBEyYWaQAdGuUcmrAIApMEklashhmqsae5Rt6Zom6midsNvtV1GEOY+G6YiN4hEAIfEMJnX/MWF6Lj+IHOznKNcf0S4cDhUnQbt/Rx9JBDQMBwe5Epq5t2K8xnvGcpm2nOx3YhACkEmhR4+EgZEHVs2qEQYamxe75NZMHl/Ngg9bRDxrNoGw4fWDmHSNR5MnUPCEHghTB1m/7OLOtWYaORKAIEglCgE/UdPr1+mudTu1gwkny89jS+sFjQ45yNH2OoWGOmYIHnIvAQcuOW/phsgRGmpUfwZYB0wxghly6niFXKMWn1YVhN9FgJIXR83yWQAaZmEgscsm6FhVB+4yRHGjx42aYzOsXL8T10AhuBJOxbJGSRkpnB93WCwKDTiZP2l2gnBfc1rtLj1ijrKZ5LHEFoPrGgSUuPkndKrFkZjEDDRWdf4wS2lUP3IYTDhdhGnxwCAULQ35rnQHOO87FhFsJdOJUhDjvnGDWuI9HRkBuJUXM/s6FBAqlDpI4eCAxHR5guUkAQ6OgBGKJOw4xjSLFR7wjAd0gEDg0zief7WNrGeuzIKNVWHjeAqG+S8KARq0BIolsuwVqaQI+R91oE6XlqZpjD1ZO4WpqUs843rccw4w00oWFIHYGP08xgxutIXCxfkvSbrJtpHE8y4i/x8Poaf5K/j+3NSWJ+lVPWQ4QTGx0hy0AHzcOvp9m/uEg+KDE/EGc1EqcqTCib1ImRiLukzVVqRgzLF2gIbM2n3bYQRgdLs9FECKHpmO0UXqSMj2S0UmRHcJNzie2EIkmSzSKXQv0kbIdHGifxml247TjrBQ9Nq1EKdTMT2UjE7m3PcS06Akj6nVXmrTxe4CGdFL6dQggIp5bZ27pBYj7BhfhuamkXPVQl7gVk5TqulCxFeiGQeDLAQLDTWWPeKuALC1cPCGRAX6vE0LRE9M3zXPwgB+xJEnabl5J7kHaaQPjokToAobUkdkgi4y3CwO7mFc7Ft9Nnz7EUGsHTXAI8or6F0THZed3hpeEhzGiFDze+TVZqmIFF3QjxeHYvoYbB+GyH+vgqM6E+Un6HLrfMrcjGYw12pcCDzRkKoZs83rUHu5HGdyPcv3iL4Z4LxF2H+VAfTyYOIcwmvvSI2xa9coWMX+dMYgdCBjxSOYUtQpxP7KClhRhozHF02cGPdbCtdWwjzfOpgwipoaNhaz67GlfprbuciD5KkChjawGH61c5qx9ChB3ybot2fZBOZg0vcIloYURg05AxGtUoyUQR3/KJem3uqV3hfPogTT+D48Qwo1Wkb+DUu9ClJBA+ZqLMve3TZJ0S5+UnsKMdOmEdhIYvHFwBXas6/YseF3uyVMyAeLaMITQCN4ZhdHA8HV/qCDp4gUDDJxnSub96mkUjwY3YdqQXhXaM/fpLIAMuxAYxRQg8i4FinVIeQtLj3toFNASPJx4iCIFAQ/MlrubzcPMCL0X34mAw3iwzGetCSEmggW+HiRh1Plp+nlUtwjOhBwhFHIQbxwi5ePj4noWlN/hY8SSNmSPEQuvEu2e4EB9g0d6Dm2riigDTEUgZxgnZHKtf4XxkB0Y7So85xa1QDzhpQqEW0YYk3W6ynDNwhYnveQhdMDa1zGT3HjTp4UgLK1FGAEcqN5mKDlA3IkTxWfcEhgVJ1+dAc5pnIvvBcJG+QUZb557pBb6Vepjd8StMRHJIsdHPS7saJZLqsKs1xbXICF6jmyOrz5CJebRiBmtWmtlwL3YrhBXpoEsNQ+g02zF0q8mB5hR55zrN2hDPpj+AJkwsYaK7dY7MzVOPWlzdpeG0UtAJY0qTji7pa5RZzmpY0SoCgeeGaFSj3Mt3GRclTiQPUOoUOL52ntOj+3ECh4RTZv/iTfx8ntPJcXQhEL5LsHnHreZ7ZPwW2xo1ToZ2E62aNHWTjmkSd9p4CYGLixmrAhC4FprpbB5dBJ9YfZbvdN1PR0aQMsBpxwilSmjCYLx2nWyzTiqQFFO9VOUotyIhdL3FJ0tXqWkRZlu9TBRA1+TGBVMJmjCIBB0+NDHP2dQ2Vno1DtcvE/fq1I0oL0a3b5w6eWFC7TQiWUJvZHFsDTM9jy6iG4nioM2wPcc57uOD3ksIe4l6tIt+p0gAPJO+h3qQIujEiUXXOF4/y1PJg+iBwc/WT9OSLoYvqFthTsd3Yizn6a3UGPRKeIk6MtPkdHIfLgae8NnTvEzW93hJ/wAHmlc5UchjEMZDw/ddpPDpCdYpWz0EmmRbc4G5UAFHM/F8GO5MUgsXSPsuca9C2i1zITJIS0/y+eWLdOb3sWLFOTXQjUyuo4fa+H6YWLmPuDmJDJfZZS+yHOpnJlzAkx4hX0MaOkGg44kOR2sXKFl5psJ9gMT2dCLlfnQEmpT4uQVcaeC1I4TCLQLDReKj+xbtavdGuyIIaEubaMIlHGpi2mFc10VaVVwrhC4MQGIFOq4IkAJ86aMLHV0KjEAggXZgoJs2QgrcwCGQGlIKNEPS51ZYNrIEwkNDbM4TfDvGhy+2eWFbGjtTIuo4RCtdFLNlMAw0KQjERif4o41rbGtN8Vd/7cvod3CC5859+OwnRBMbPfDYIfA1D0foJKx12iGBL+I4jmB8xmK2J8yclUavdjNQW6QZTtOIaThOHTfcR8fLEQl7+Ph4MkMs1CarrXNQPsmL/mO0/AT+coS2l6CU6UJ3uhhvnWF38xJG9QGu6f04hTIPF9f5klGnHtNBlxiBjb0+hpXcjkw2yNXatJY6JM1p+rV51uW9zOfT9E8U6Y2DlrrBtJVnIjzMXDyGEYeM7/Op8gqOHmN1YQCzE2NoNkJ94BqlgSIX9DHSgcd2KnhNi+fzJmFpUclv9BsT1W22Vc8xIkpEbZ1njZ2siDzSE0i7yHhwmp2tQXJzO0js7IH+MnNui6/LXnyh0VVZYlvdJ5W7jBde5ELqfhpagu70ZXyvTc0aQXpjbCu3kI0Ea7E6WtBGtOuIYICs4zFQWmCyMoYekoSaORwd6h7EUxsHeEs6jNsLjFfXmWntpZkq07am6dgpViIGjpFm2F1gwczjNvIcu/QyiBD1Aw5uIsK+YodUp0jHmOFccgdo0KmlOVz/Jlfy9xMxBO6aSb4pWMyl+VL0k/hxk7AM0EWNFFVi4QZdzSIT9h60qIVILuG34lzVRwlcB69tMZkaomsNRMugNpDg5Z6HsMyAFa2LDgF+GpAB3c48npQk7XlG3QqXxAGW42F8I0JYn2bPtRoZK0FqaJad7Q6X5GGsUJNBe4VYUTDu1eg2i2x3HKq+Ti3c4UVjP64UXAv2YzQCUs4qptBIrucoaxGQAX6oA2GPqO6gpZeQUmNH6yIX9f2cZw/x6BwlM0b/3DKxag8TYwPs804x0znKsp4mF8xTDvLI1DoHxQIrvsmi3YMZXkfGl9GFQbB5XXbkaoWu7mWEUeSQKDJrFugYEY5UBKWGzdXBgHWZYrw2z2p1F/P9NjtEiQtaCumFkE6YJ+L34DbTaIaN1KrsK8/SWtfRemxCpo4XD7ie9rGCgLDfpNkq4HQCepO3KIWSPJG5l6QGEbdDKatjazoJr0ZEc3DNYZZTAZKAMAZ9wTLHgpv4nocelrQdj/OdB5kJJbCo4sYrrIYNAr8fo96FQ5gJN0Go/BLrmTFMIoQrHtpyBK2dws6k8AKHvavXiNWjmP4ayf5ljPUWzUiS4ZpLPZNmODNNVW8SEQHdoVkm9GEMAf3L06SqIaLdU6RXsvTWDGaTWW4kNEphn1gtyieDryOtDq0OdJ/fQXJfif2dWV72jyKdMFa0jRupE2p4DAW3GHTK9DtnEbJFeeUQQSyPZ3boCTdZCLsgBZ7QKFppdN8mcMN00GmKLK4X4tBClXbKQ7cWGK3P0woPIbU1Ztx9DBTijCe7uLlwndGJNTTRwe/djeFbVNdzRNN5djbbXEyP0NUQDLUn6Qk67JazGOkG/zW/DyFMAlcntGaxcKUfbc823EQP10yL8fZ1pIgTFgG9kWlm/f2IRopQzEfYEWS8Sn/1OtPR/aBraL6N0DtYSD48P0O73s3kIKSrMcL1MpVEhm3FGrNdSziJPGmnTHK9xHpkP5F4kabXzfmCR9UfRHg10Nq4boiuySbb2z5LPQ1uJrfxyHybb3eHaFrdJGhQM7vQb/YRzyWJJAJsEdDSQ8RLLbYv3sTJ78NNRehe7NBVdUg1cpTDYayeWxRkg0WtdyOBYncxraVYzvdjej6RwCfmtZjPxZkTx9ADk92lC6yEE8wm8pjSoyOaBNKnYQ9As8Rj7Vm0VIVTxm5yFcHh8GmWwgXa1QEuZ/pxOmH0UInVIEnea+DqYR69OcOaJujOX2UmlOVlaw/hWgJCt8jEQjSEwLWTWL7JaKnItqJNLVnH6lon5wwQnu2mun2Rh8SzTDs50qLD/k6FSn0HKy1JNnSOtUyI67E9CCPDofoCF+uDzA908Ze5FJrRIKOvo+seocQKmi/5ROMqX03tJeKs04oYzO4QhJptpuJDmNLBkBrbozfJ2CWumLsoBwlMKdECA1drEdgaqeUq9VSUIK3j46NLQY+4zkBtAS1sENXLaK1uPrMyhFGYp2qOUZ2sMlMYoxQ0me8JWLByBELgOHGkHWGovsRSVONaYhTaSQytw0qoD9Ovk7hWwrMEdiFKzZKkVkLErTrp7BJ7zRVOh/cSeHFMZ4ySsUK55pK16xyXZ3k6cQhTM+lzWszJLtygQZdv4lkeC84OZrMaGFniskm+uUB7LYdbsNGtBo+Wz3BN7yUc+BxuTXIzKrgoR8j6bfqdVSa8PmbC/YSlYLS9zqDd5Hp0iGOrJZoiwa71VQbrPpGUgSdCmI0D2ME029tz3EiOcnlXBEQfhoBhUeOIe5MD7XlmrV6WYpId4hpB1WRn5CpXIgeIah6lkQ49tqS5OMZLfYfxfI37K9/CKpUoOBqp7SkauoFnRtHX0ohWDrcteLDvLNVQmGzTxdBdMkjaQQicBr3LOss9kl5njYVQF1OhfdyIungUkUKgI7gS3UnCWyWCpKYniNYa7Deu0BYec5ExkEUOrPi8HP0AHXGEqlNBygrPxPuJOTaPNE+ha5IlPUVhzabWeZgXcwYtv0G8rNNxhpDtOCvpDKmyTTUTJhRbw5ABjXoGw0hT6QPfrjBYXEOKDmvxboxWHiJlHnKeI+o7mHaDrxXuJ2EJtGaYp6L3E2/W0ERAXYSJGAn6Oh2M5hyXGUDGdTw3xqSWw6vDLjlNl0jQ0DyiZoe6FmN4rUFSzHI+PcY1axBHGHiNFEvtXoTXZrhYJpe8xYn8KCOdBVzh05iJ0umPIgwXy2xgSo+jjZOUl3oZqa8wGopzwwlR9zL4zgLbm5Mcdeco+zmejdxHYLQJuWWccJgZs59yNY8pNaruHsKhVZLGCrUgQzk5Rj3cQTglHlq/wdOJY2jRJY4kJoiJBmZQJyQ1EsUy7aCPdGgFvRTwfOIYVS+K5ku6krOMOCvs1MrUOlfxqHNd2081liDW1SGeqZHpeOQ6c6yGuxHodMVLtIkyoe0CbPTkGudiQ1hSw/RjG3fy1VxSS6t4wy6e3oMwIBQq88D6KVLNCDIeI5RdZV99Ea+TY6YrRtUQlLs0VvtqSJFGGFGSzRarcRMsg3RzlZXwEB5pEo7H6GKV5wthiqVx9ufblK0sXet15LqONVSlo8cYtyeJRppEGxpBdA/SdPnQwhQLZh/Xe2J4WKyHLJba2/AdjaG1m1iGSb0wxlpU5/61Eo7n0k67hBIVhlprTMtBZqIFjJDLU+Gfwy2HyC1epbtdItIK0AqLrA1nGLq+SJ/by2S8TEHOUlhLMLF9mGhYp1CHLA0yxYDriR5CsQqpoErNSJH1GuxrTuAX2uwRqyxyHy9aR9EME8uyMVyJLWySpo5IVAmkTj0wiBFBF3G67RV67ApnQge57IeQQcDqrMZgb4le20XXTHQCPlq/zOVonKxRob9t0LYDhBfHa+b4UiFHqrGCY3i0zDCmplPr9ZmNFriWNehxdHyRpambDM5KXKNIJryEJdNUZYLnQsfRWnX2T9V5MReiu7RGqS9GOZUiFARE3TbLoT7ifof09C3Ox44yGx7D9AN2r4VIr4QJ96yzrVbmTGY7Xxs4zOHkFeaCEfR4g4P1q7ws7qPVyJCVkrAdMJ3JMRfsxQyXNu6GruWQepm+MixovTRFHXc5xfHsJKtmhlyzzkR6BNds0l9cp7/us+QvMNXTjxl3+Kn6CS6ZvVyKjSLrffzUfINne1M0hcNoM2AplMG2LDQri6s7jF64RSVqcCQ7S49mEgiTut6hqoew2pN8zf/rhLta3F97gvb6MHFnL8VtUxQ7/cxYQzw8XaYql/GzLY6UBV/cDbZpMGTPkWqEuZzuB6vO6UNt2qYPEra3XmYo1MZp6VyMbGdVyxJvDmDEFthpryJCIWrtMplwz9YlEH7MVILnNm3kqjeUImF83SOnGYy1b9JpFek1w1jdYb6TGWU60kel6dM0TpCPGQg9gZ3MYYaHSFQsRuarnOnOU4wkeCh/hF/k39MKJcnXl2jNmdR79iBG4wTCI1rucFDL0j96L/MnutirRTkc3Uffr41w6Y+/ymlf4ogW62t95N1e7mmEubZmkVpYJ5n06WgaxvB+8hkPI94gVugjOTFO5dYCY62XGAz7PHPvdoJQQKPYS6yYJe9HSLsSOy5pe9/FqKS4d/ceNHc/fU6bXPIamd4P8onCCH7lCu0lh+WYz2hXBd1M0rWyjGjAJ4LTOJV7Od+Bbbe+S89Ail27t1PUdDJ776eon2bAtOkP9jC23GQk5RBJHeDU1UVMo8gefYYL2kdJUCK6dJ2CzCJ6+nlUN5iLZVgXLo/aFwk5OuXuTxO9cp6FziyPTaVZNzNc6wYrrKO5Os3VMJ8XT5LBR8oKJiOENZ+mrhHd6bJtYYJboREiSAZSNr2axfZlm0o6xprRw0DLoS86xVj7EEbuFq7bYa/rYvUI2rko7ekPcKS7SP3WDRKH/xaHYilyc0uU6fBSuIEM5TnY1thn3oJODXvNZD7TxJWSRbeLjBujEnjkhMe9so6z0KRneoHpTpqrueOsxfoZ1RN8Tqzwp+0Odduhr1ikENfoCl0nYmgc8HZRqTVZjyaxgzCH2s+g9ZqEQilymonVnMdo5WhGs3QttFhzw+ywdPKP7GPvVI5y8QpOoUHPrZOsuCN8y+2mhUPgBiTMLH9fmjxbniFkS6rhXhrJDl2xCZ4MjSCkz0BrhSlxnMXULsJ9BzCXrtOzK+DhSgOtpdMyPs/BSIyzyTrrl9ZZy+cJywQDTp1ku8zQjRJu8gjZsYCucIaVpXkS8hpJrYvC/ABz4VXC/Q676iUS9NA18kvUnzvLzr4zOLUQ6ZUQ9/zUw6xc+l36xy1m/F3IjoUzW4VGD8IIUWgKRGKNNAXCAykO+RPcYpzAdKnHY2jNGsdKL/Kc7CHrr7H39AVKo3tgt4ev7aTekei+g+G7pCkS0MXl8H2Uo+vknCLHAkku6GDFNVyvBxEKGNi5l0/t/ChXTj+BbszztVqamaBANtWHFq6wb73NU8kwbeNR0lqa3LLkl9vXKQ98gLPJBPNelPH6OrncIZLjBa5e/3NeNkfI7j1A76kXCRkjRDsWnpsj1m0y3FcgVo7SfW2ZmL7EcifH/t2HqbdGMdGIhjR2ujotr8Gtrn6S622cVoZ42sYQD3H4H3yWm8/9R7aVTYoiRS1VIFkIkwl9m8yFebKZHLLrV+i2/hXeah8DMkHYNIh13cN65Cblgk2mVeFMdZiO5YPfRDcdqOxD80YJtTqkOmUyvVnc5iJ2qY+Brj1cqjlkdt1LfvsiE12zRG4VadNkKJOkd7SbUnudlZiO7w6zs9Ph5xNzTIv7CFIJEs4ozakVRP4KRiyCDARBYi+x2aexZRzTluT70ixbDzCwfAQrWEY3lhnxOyw1IhyudFNveJzszmC6JY47l5ASJiIaP1+6wnIZVq0W9Vmfw/tLlOarDNVD7P31z1B94gztasBMvMqNiMeAmGIk2cOolyB8cZGn7x0lSF1kx9VpEqbGqVyWlpcl7tZptVNk1gXHKwsMZMY4YNbByeLEQ3iVIfKRBheSTYzAJry2zOjiPMM1k6IVY397Dj0cpjfbxUqlh9VgnWaoi1qnh21WNzHXp6QVeEyLUYlkeSbVwnINPrb0Ei8n29xIdOGYMbTqOi+l7yXECPlamyPOszTNRW6FjjGYDJiuTbBkt9HbCbqDy/QyikhEiDYcDuYHGU9343cVeLHoMbc2w7aFKkcqTbSmS/7Xf5tRYWPe+BfciELY0AnVw9SkyXBjiuJqP/cX10CLUA+3aZsF7N5j5NZDJLc38Q4eJfzyl+lZWyY+NMTQ6M/yyd57uNGq8NzpFP3+N7A7i3RHcjw2OITv6MzENUJaN90vzNFVGULumsWKhEindjKWMHjk1PNIO0ozX2G6934mVtLkgxoPrubpuD4JLYxVKJCr1phc0unvzDF89AiPb9tJ+MYUP9u6yGL3bi62X6TmdTHe1nAjHcr13Yyli4zv305I30f9hTCV6SRRPeBvpjye+NhDrDmHmZs9TdCosMOZJFYtIGpdpFoFyPfhpZroQmNXOMSsm8ALJombggOfOMie5aeYqlX5065Blpv3sM0/yVixQb5xhvnsg5SMFvdNSRqpbqKlNoPiIUIrLquDSyQ6Ni4RDi8s8RG7h1jIYiHp8O8zMTwny8+Npqgu9rEWbhNYCUJ+mF2VbWSjJ/ETeQr7c5RW1vHdLJ1OkvqsR1ciympXmkcq8wzpa+huksPdMYLYvXTcKt7gl8gt7MTVLTqaZFpqOJ0x8voKt7pMXGFySK4yMPZhjiVcnEqMY2O/zuLCX9Is36KxGCeqbeenj8ex7BALZZ+V1R5u6f3IkShONEZ6bYFULYyV6KfbspATUdLjWULFNay57aQ++hjz124SmnqZICEJdVUwohfw6cVY2k297ZOPVujEBthrGpTMPWTSIebXJumXJQZmqpzaFiPj1dmvLeCwnbVWjP7SEkaQIhVrYlU9at1zCHmYX+zbxUJI57KzSGxhmJ2ZNKOdF1nIrlOqmwy5TURkjCM//VGefe5ZBqemqN6zm4WFMS537SPwYDyTohq4CLeA6y1jJ20y7UmiC33sWiuxL2sQT2R4stZDzdBITC0ynHUJ2zmoHObBaIzukEV8os1/6c6yGhWk4kUeznjkLvfSZ93HZPMAfYsJro1YeH6MsGlhYJMItlG2BwjlsoxGTjAhk4zoA0S100xUu5gJxshLwdGFNkHEwpy6RiidwMkd5LHmMq2IRrL/1+jWFvng/CKnIzsx9GXGWlcwTtY45LoYQL2/l95sN+1yk5uTFl35Msl+yXAjxiNduzkd0+HGGpcOacy3A+KTZXZM3aDVO0rE6aavvcazsWG296X45b3HmPnmv2d7Po+GRbAOEUz6q8tkR8cR1Wu03Sw5bwyiMdqNCJGMhaPpPFBuMG7O4UTn6Un/DLua30ZbbhN2VrmQ6eU7g/fjSJdGPMtI/UUG7QoXIwfpd5ZZbrh4rSS7DZPzBRMv8Oh2ptjTyrOvanC+UcdvtjBWAlbHxv//7d15cBzXfeDx7+ueewYzwGCGuAECIA7ehHiL4qWTkmVJViRFim3Z8cpOnDiJK9lkN96t3VSyW+scTjZxqtaxY2/sKtuJHUex17cUOdZhURJFUbxJkCBI3Dfmvnr67R8YSbxFiqQgAL9PFQqDNz2N1/3r18dvut8j0R6naeB5csMVZNxLKXN24/XlWKZf4uR0GS1FD0er19Jd7SFg+NloJijTYbK5afY5UriXdODu/gW12SIj3kWEKNDoznKippLi6lX0OpfhiSWosTRbV6yg8shPyOULBD0TZANe7ESGxpM2DidMTUQpc7hZ4zRxJAwmy8s57FRkMIhmJ6j1mXy/2sNys0iXjtM9ZVNlhDBdKZxnEvjGx2l0jTBREyVdcKPtKgyCnF4TouAtsD5eR+sLJ6hwBel64AHSRw4yeOwUPnOK1mMeVK0Ht6cLq2ASqnDTEllKPDfMTuufSMYCTGe2UL9oJ+OHjjLt6KVxNIXHGeFYZTlhZyUtvUM4M8PUW0V6ygZJNeXRXdtJ95ziDOU4nQcpBnq4vfNWTo3UMXRqgLDhA7cfv7ZwDGzAnhhgxaMbWFGdIjuwh3B4FYeeaWLzsUkO1rvI2y5yqUUUwt34HQ6CeAjrHl731qEdJqOORXjz9XjGc9TFRsgFp7ACBaxhjRG2KHqdVCegxlZsG+nF5UxRb/p4OTtKmXKxPtUN5jjZdJ7xExFq7Cle3LyLtF6E3+GjMqCwJ9fQGSgjbo/Srcs4GczhKDhpIMOOigIbx4b4UQaa05B0hegpNlDpcnLGowgYirsP7WWsOEadA1a5PAz4ChhGA87pRu4tTOHatIXHIxFOPvtddrvjTBlRmvoz9PlNOgJLaQ23EAtXszc1yYc6l7G9Os6ekdMUXGUsj1XwfmcY7UmRyBZJVbgZXFtDPjOEp2cVjmQYn+Fj5coIOnSc7qdPkVkdR5d5mA4/TtofojkdJjrVyLTt5EMtUYKmxcDwaexsAU9xhC3mKQ7qKM19ERpr1zBc7QfzDNlYFlcWdqWexXSBpyJMcaiZutEKPJXlfMB/mrzjIFPeECndgtO8/KiGc50keK6R0jOPYGnD5LSvEeUwaMk2oifasX19VLnHMDqCLNVnaHVlsBfvJJS4hWJ6lKGyRdganGaBNR0NRBIdRE4cpNezlEcX19Lk/g2yk6/TVXMnIwUvPeNpFgdzfL57D8uzB9ix7eNU1NTyC45TX+6laWMDSike2L6JmxMjvKonsatq6PCupSXRwJLpArHKPIvbIdT4KCfTvewe2k2lsgjUN7B2xa30vtDHqnInmcp2olOaH/tcrKqvYuU2N7Hv/4BgwIv/wfs40JthdeVKgqtvYqcGK7ec3Il+/B2NfNBlAltIZgukM/08/er/Jedaws47fwXrxM/Q9esgtJHbfHnsF3IY6x9DlVVTnhxGB2pwpmto9TZjJzVLV3spc5hkUwXSrsfosT6Lz5dkU9hkRcUDvHgqwGNl2/AMRCBcoNV0staZIVfbTHlkPeGypUyuChHt9tDsifCvx9KkFoWp8mt+b81G9g3tJfBKAxXWNGXlK4m726kwy8j6s5ieY9zZWuAHEwlUPsDa5X/A2sZK0uFXyBc68ay5ifHEcV4/OIZn8Rk8jjxBxxKiLY/hXxVBuU0SS8fxV5RjbJ8ZHtkaz1BfCEP/HjodBzkTbeP97h34csspOCeg1UGws4NDOYtdKo/vcIo905Pk7DQdLS1Ey8ro/srf0d5WwV2bbubwcJxVsQEa3INEvE7+PJ7D7/ZS3bGEqsQymiZO0VLnor3jbvpsN5/f/UNcmRy+eosqG+rjzfh3PELANUH9ky+zJ6bpX9vBQ+uqUEvfTzL9EsZQETs7humbpH7SyZpgK+miQtNFa7WDhqW1VFffBfkiRw7F8EzkIKWwcincvUlcsU20r+ti59ZmCp40z4XOUEkDXZ449pJW7GAbpt/JlmKBzxoR3OkUd5qasrE05aEkqz62jQP5Bta3R9AvDGEXKihEvWQLdQQmp1h6++2YkQip6Sn8ZUEMp5Op1V1Mv1zD0tt3EKmuxXC5GGrYSibTx/p4gkPZZu6ra8V3PI0jEKJzSSV93s1kxgfxmZqtxaPkf36IU8rimY3bUImfgulmmZGlY+16WjbdgtnYwrh1kq5oF8ZUARvF8eR+sqke0qdXcDTgZWWHSVnBT33KZt/up8iPtTFY6SbaPMGKDbdiGC5W7fwAff0JHrXdFCsf4rt9fWwa62draIrl420MjU+TncpTqzI0PHIvrQ0NNCXHMWyDkyd6qVA1NHZGiAxUM5g6zfvaN+O775c48NoRBvqHwbeChvoBamvWEskso2rgq7w4mWPTbTvYsP5eAIaPThLrGcURLPLwyibO9J6GqSLh/ieorM/QvnETLq+PwN2/yetP/ZBQzuLkogAfXNNIBXcTajZxpqMEogGs/P8g99J3CTQ14tvYjq5YQrPaQO3wd7DSmgMnF+NyjFFWnsCbiXJqegpnwc2ioRhZsmxraaeYqCcZmsTj9fPJO9+PMgym82N0eyMc3GVjdPfQseVeFldvIJ/NEIpWkZzKYw0fJ+yPU129CZfHRClFcngSUPyg72fYdpFF0SWsrvSSeukXbL1nE8lkGd/sHeNQJbgDS6ixI1RN5XgkV8HiXatwLYlwd65Ias9+gv6PY6X72FEbZ+3d/wvVs5ej3U8zMDaOP1vGamOEUIOH6o4WAikf8cPd1AQ34bOeh1VLWVPzII5/OwXZCZzGMBVlAW6rD+AdTHFfwuD5KPTXtqCbV+MdGsAYzRK+uYvPrAqTi+V5bijBy+1Fhk2Fe6iXLa4Jli0vI/xSDUamSG9zA1V2H2ZqhIZH/iNHXnyeA4OvEXG0orxFyj3lLNE2XauWE6qsBgU3T3eS3P8SoWgjlb5xllYGCQQ7+PujOfyTI7xflROMtnHm0GlW3trJr6z/NcbHRvhGsY/OLavp658kVjFMY3UrW2o/RfzYKXKZNFs3bkErxdpUlkR8MbF9jRzPu6hrreKuFTMjzLkq72DR2AmGC1ky3ad4JbyOteE7cKgkq5tMTjm9NG7s4tRkjmg0QrnHSaWtOJLKcuhkkvZmuHnbehb5FgGwkiArl36MWOx+jEycMq8LQnUsBeLx/RQKSbL1tzJ1aARnMENlrZ+GquVUq838+9A2/MUUv7y2nB6Hn1P6KOusOGV33otR1IRSRbLHpxj1ZRnJ7aG8oYGb73+YtbYm3rGZ6EMfpYUir/90mrpUkJqmVnI5zbKOauobyvEERwgEOrD908SeGUQlY7iaGnm4LsKX+jXr27azbPyLjJyZxqhbzJY7dnJsXx41mWaraZHJTtK0azVPndEMxcJ84K73UV0RgM6NVNngHc6xojaEO/9hEk89zZKGRvytLaROn8G9Aqa8DfQfbiJkx9h26Dj2eAT3xh3c07CE+L8OYqecGBVRuna18BeVlTjsIsFQOXTtYsQyWD3wXWJZD23191NfWE/G48dV1k/S4aY9q3gsl+PgiI9mbfCp++7ntb/6LCk6WNTcwpqH70VbNoWhJHWVzZx69gSq0E/OUyCfC+CviLJl+y9Rmejn+OABTH+UjQ2LqfXXYFWtweksp6n5QVKLThJcvxIwUErx21ozmY3xyqETjOU8HDZc+EIubg9tI32si1V1foJVi0k/8wzWwCDhQpgBX4z2HTfRtnE148fXoV98mqDfibvqJkY8QTL+ekKqHp8vRKMdZ9f9Ozk1NAXA5zauwJtO0f21r1P2WoKlbSkO1XayvuNR0qNniAUrSZ9Ik4n7iHuHiSV2YgejLF9WzdKeJJuN1bib3DhME23fiiOwn0WxIax0OU7PepYvruDv6u7i63t7mXTmqViyg8R0AhWLsdQs0pY/RmNFhJGhDLu91ZjBHTjDFrccG8XlMIg8/AkeGMuhTZuBV00qjwVx1rdA7QjL7CRm0odesRK3uYenPIpmp5f3r7wXOgJEAjexMmdxaGSYw/ueomMMgmW1VEU9bF8SYupEnta1i7ijci0oB25XOVbhYcxvfZ/BwSHWxDwsWX0T/2wUiQwdobnMwbKPfJRcysLpc+B0GAy0DrH73w6SC0yC9tA4kiFS2ULLiq046qs53XcGQ2lGh/yET6fp3PwhVt1yDwZeDNPBPaZC3wU7tWZvPMV0Y4bN9bX421opeMIc+elRosYA9QEnjRXlNK5bC/4oj1Z0YGcKfPO1DJZH8UDXRzH69zKVDBNpCDOV0+QT49xa08zPxvu4q7IBnV4PpsI5rclmBxhXo7RONRMNl1OsiXJssBKdN/CHsnTVO+nw3IU3oXDu/hkTJqzcuZ1YHkyXkw/XOQn3TZHZsxdPKIjvVC9HRyvoaL6Ztbc38vzXc+SrE9TdcitqaiNjw68zXfYsVS19RBtqWFE5TDHhxREqp9OXIezrYmiRnw17f4E6mgR/hIntN/Gcp4wd5QGW2inGM5qU6WAoMU6wwub+dWtpLqujucLm+L4DjLlS+CoCFCdMPtnexsT+ZzntOENZ9WKWVJfxmuHgwV3bePkXzxGIRll17x9xUhcZHOzllukD1DjLyEe9LF2/ibztxvYdoyHohsxeMocPobpaCW97H08e2I2deIkKv4uNjbdRuXYnykoQ7rqFmxrrKUv9NfbYOK3+CDpSjWUoNt9zP3rM4mQqxaRnEeHhM2SHyljSVMXWrWvZUxbBTScbW+vxThsEwyZVTZX0/ugFJvceJ1dexTZdQ8cvfwLlcvHPviNUpCZIjGXR/p080LEL3emgp/EMuQO1vOJtx+4dp2I6iXHrI9Rv3optZ9CNH8Iw3GSLcbz7zvBa/iD+iRRdU3UErGa2/tJ64q/tx647TuvJ/SStOtrWPEhVVSOJnxwh4YlgLe5kIv40i256H30TPvp1nOXDDrbfeTujsQEmp8fZsmEL6048i09F6XGEica/zOQLe8moEG5vgK1ek+SKVhyHM/S6iiweMWkI+llV3c4rNQYHHS1kpgdYWbmYZQ012FNxVlRW0rP/MMVkgXvb6whFo/zu4d2kCkmS99bijlVg7j3FotAE2+5+lPHuPkLZII42P5UtTZCepLnZx+KcxUhkJ3r3D+iyx6mKtuF3OFiypYaliQxdQR9Gew0fGKwilsixsixJpKkc77JKdNHGNqEv3kzaTtNy8jCZ4X7M4ArcjcvwtO5ismEjjYNPE4pWoGIr8ddC1031DO2pZF1nBYuaguQHk9ivFJkaHqB62x3ULx5g8b7XSdatZ9sjN2Mk0oznOwCTWz0+UkM7GR85RPu6dsrcDcSf/zaTZgtNjbXEPGuYyp6iofFXcZRGLp2vpA+ea/SF3/uvRDq7scwiL1SswO9w8lHPFlrXbMAZ9ZHNDjI4+G00GoWipeV33vxsxsrgMT3EcjFC7tBMfzCleCilLvr/8sU8X9r/97gdLp5Y+QQAqZyFx2liGud+Jp6P4zJceBweYGbYbG1rDPOtXsNjuRgBZwDTuHBDz+fzFJTCZTpwGopcdzfK5cLV1HTF60drzRee/gk5Gvj0Hcuv+HMXk7WyfOO1P8FdHEeFttMZ7mT30G6eWPkE1v5pzLAHbdk46kxS+R78vhYcjrJz5nFkKE73eIoli0MsK/Nha5vE5Bjq9V58Xe0YwSDdg0P8wjbY4R+n3JFjOnaEYPkuKkOLLrKOJhkY+AaFsTHU4WnCng1UPvrBS68PW5PvS2D6DXTIwDZM3KZ7Ju4a1HkxtLMWOQPyRU3IO9MPyPDJbqaGBlh6y46ZeWYTqFe+CJ4QPfU3cSI3zh1Nd6AKGXjhr2dmtP4JCEQ5Ez/DyydeolXVUZfNoPYcofLjT2B4PIx9/m8ZiWcJ/8Ynqa2YyWznT59m5CdfYzp4FKtokTlVTWt0GWUf/jA9J0/S2dmJw/nWkKNaazL7x1BeRcrop6K6DQvFhGVQE/KglGI8M47TcBLSgCd0zvJ2j8Q5OpbitqCf3UdeRrlMdu7c+db6Hkhipwp42isuv7FcRDLVzejojzEMF6HwTsoDbVijaXKn4vjXVaEc5/amn977GqkXXiD8iY/Tc6aHbHYQf10LzRWLL9k+z44bhsJwzbQrO1dk6JUhDsTTrLq5gbDfhcf5VpsrFnMoBUq56M/kqJ88hCpvpFh0kT10CCMYwrNsKeoqevzP5XIkk0nKyvzE47sJBlficlXCqeewe59Hbf9PF52f1pq/6B1mW0UZ6/w+TOe508RGhym6ffRYirXhwMXXhdZwXvnMvs3m+ak0Wdtmc3mAjG2zf2oao/8gI88eR7stmqLlb36m6+778AbObcOFYoGTsZO0lbdddL91KWeS4/x4bArLDPGxugies/aD2UKRv9rbi3KZbKsOseyVPmzTS/h9bW/V355po+lsGrfbjcPhmFnOfJL0wePkTp7EGhnFs2I5ZaVtVhdsCiMpiiGF0+/BYTgY7olx5ue7qYocI1K/CG/n/WQPH8bV1MS+3l6KyoG/upmnDo+A1nzgpnoWR2ba41i+wD8MzPQZs6bMx/ZwGS7DwM7nwbYxPB6wbdA2mA601iilmJycJJfLMTg4SDweZ/v27RgXib1t58nnx3E6F/GNk+OsrfDQFgowMZAiHcvTsiZ6XjzB1jbJQpKQO3TB/M42Gs/ycu8kdyyrwu14K275/CRDw9+haKWpqXkQr7fhbWNZtDVHhuIsqwliGJdvi1eqZyxJfYUPl+PSbUwXbTAUlmVhWRZer/fC+fT3cOr4KVxOF5s3b57ZTi6iMDKKWRbA8Pk4nckRcph49TTTyROczhmsq15HbCSDy+vAGcuicsM42zre8fKl43kO/ryfzptrKPy/f8FOTBHYsR1PZyfjX/g7lM9P5eMfQTkvs/yl7emc+abTGIaBI5Zh6lgf2doQDUuaZo4F8Rhuf+CCoWh1UXPi8OcwPCbVtY/j8ZRjmiZaa57pe4bR9CgPtT2E07z4cNaXsieWIm9rNpf7L6innc2SePrfcESj+DdueOuN+OBMewnVX7CsWmsMw6A/mydZLNLpn4m3nZsZohjeOlfTWhOLxXAZTqaGp/n6i/vAzlJf4eOX77qd5PODABgeB8ox8xljdYFU/DAR/1qUPwKlNvlk95N4HB52Ld6FUoq+vj6CwSAhvwcMBxz5HoQa+GJPBdEyN3dm+3BEIrjb2s5ZBmtqCtPvR02dgOM/ophzotY+juGy4MC3oX491J/bdYPWmsFYdmbZkxYqr6luCVK0bBzOi+9v8+k0mYOTBJZXMVW0GP7CF4lGQlR97KMXTDs8MMV3hv4R5dC0e5tYP1FOYNlyzPJy8pk0TreHYsGiMD2BO1p10f3U5UxNTeHxeC7aNodTw7hNNxWeKz9/0FqTTJ5m5ESKurY2vIGZuOesIulckaDHRuvCm+ea2rbBssDp5N8nE5hKsS187jHMTqdJjMQoOANE6s99T9sa2yry42Nfwoq/TGvNJhoq1+PxNOB0lmNZcVyuSrTWpF98ETubw7duLWYwSN623xwVKFUskrM1r4we5cXR4/z+irvwO2eOI32nT9N98incnhO0LN5Gdc3dxH/6U8YO7KFsUR1VH/wglq1xOF0z/RcZCsMwSRWLPD0R545wEK/SZPMFPB7PuW3t1LPQ+wJ0vg9qVqG1pj/RT9AdvOAYYReLnHr5WZyGTe1N2zhzYB9Ot5uG5atm1rFtkynaJIaHOHHiBJs2bbpoXM+PF7aNnUhglpe/Wfba6Gu8NPwSD7c/TMQbeXP6nFXk8GCcX5wYx0gm+JU7Vr55rv0GK19k6OQ0ZuY0LqUI1Ddh+nw4/R60LnL69JfoOzqM07qdDfdswTAUxXgetMYMvdXHy1i+wFSuQIvXhcPhOGcfc46h/Yz95Z/CoqVUfPLTaJcTp8tNKmeRmswy9J1uoisiVG+uIeNQfKlvDIXi0ZowVe5L7zO/2vMSw9P7WR1uYHPNZmLdp+k/coAN9z+Mo7Q/O2tFwr9/dub1zj+EzBSYLrThBaVQ5sWPu3a+iHIYF1zLzLxZhMQQBOvOOT8cTg1TsAvY+TCJrMWKutAFx5qZ61cbo5SUyWcs8lmLQIXnksu7UEgnyzfIZ/7n/8a9eJQV1mmecr2fGofm19dtoKq59c1pCoVpcrkRClacivL11/w/j00eoyZQQ9AVvOZ5vRuODsfJ5It0NV79Rfn5EvkEe0f2cmjiEOXuchL5BJ9Y9Ym3veC+kSwribYsrONncDY04Ki49uW8+krkwXSee1GtNez/FlgZ6Hr8zZPHt97WYFmoUoKmOD2N8vkwztvR29ks6TOHcFRG0YMxzIoKXPXnngzfCNlslmKxiN8/O7dRvnGioOZ5lv+9IpfNkIpNUxGtIj4+ijJMgpHo23/wKl3sIhVgbzzFwUSGR6vCZH7Wh3txEE/b1bVla2oKMxB4s01d9P/bmkwij8+YAk85OC88QbFtzZOvDXBmMs2jGxqoCb11UvtaPM1L00keqg4TcV3dTbiFQoFisYjH8946KbLtAvn8GB5P7WxX5ZpZlsVzzz1HXV0d7e3ts12di0o+9xyZfa9TdvtteJYuxc5m0VYRM/Du7Wuz2SGSySNUVu6c1eP3jVKwipzqOYlpmrS2tlIYTmFWeFAu47otr1W0MZS6siRnPjUzTLbz8hfI14MuFtGFwkzC+SKOTx0HoK28bV7G/nrRuohS137+YWuNcdZ6TqfTnDjRzaIqJ4uiSzAMF3Y2S/yHP8LVUI9v/TVcp9g2jB6C6FIwr99DIrZtX3Wy73yWbeEwLl6nRLaA0zTO+eLtSuVyIySnYng8TfjLr0+nvfEf/5hc9wmiv/WpC97LpvK4vM43232qWMShFO63WT9ZK8urI6/SWt5Ktb8arTVFyzrnS9pzDO4DXxjKG691ccQNJAmeG8Eu8tiXvoUnMs77Mi/xI+dDtCmL33/wfkzH1X3zJK7cRGaC7/d8n1Qhxfrq9ayvvvakmRBCvEHbemb0vlm8+LBtTf9UhoawVy6C5phcLofT6bzmC5IbRVsW2cOH8SxdetlkpBBCiNlxqS+jhDibjKJ1A2gr9+YNEwOBOpz+CEtqI5LcucEqvZU8vuxxLNu66lu4hRDi7Vz09uJ3mWEoGit9s10N8Q643e/toVeVw4F31arZroYQQohLkOSOuBZv+/WSUqpBKfUzpdRhpdQhpdTvXGSaHUqpmFJqX+nnv92Y6r632FYWA4WhFAddizEdJlU34JECcSGllCR3hBBCCCGEEEKIkiu5g8cCfk9rvVcpVQa8qpR6Smt9+LzpntNa33v9q/jeZRfzeKwihVSUcm1hedWFHVUJIYQQQgghhBBC3GBveweP1npIa7239DoBHAHqbnTF5gLbyuKyi1TGi7RnZu7kCTrlqTchhBBCCCGEEEK8u66qB0Cl1GKgC3jpIm9vVkq9rpT6kVLqouNhK6U+oZTao5TaMzY2dvW1fY+xXQG06cZEUaNsnmiqZpn/vTU6iRBCCCGEEEIIIea/K07wKKUCwHeAT2ut4+e9vRdo0lqvBj4P/OvF5qG1/qLWep3Wel00Ovf7qik6PWjDQaXysayzndXNTdIplhBCCCGEEEIIId51V5TgUUo5mUnufF1r/S/nv6+1jmutk6XXPwScSqnIda3pe1DRLoLWuFGEK+f94gohhBBCCCGEEOI96kpG0VLAl4EjWuu/vMQ01aXpUEptKM134npW9L3I1hobUIDHH5jt6gghhBBCCCGEEGKBupIegbcAHwYOKKX2lco+AzQCaK2/ADwEfFIpZQEZ4FGttb7+1X1vKdpFtFIYgDcYnO3qCCGEEEIIIYQQYoF62wSP1vp5Zm5Sudw0fwv87fWq1FxRtItoFAYap1s6VxZCCCGEEEIIIcTskDG9r4Ft22iXFxfmbFdFCCGEEEIIIYQQC5gkeK6BVSyCx0eZLzTbVRFCCCGEEEIIIcQCdsXDpIsLVbojlLtCBJze2a6KEEIIIYQQQgghFjBJ8FwDrQwMFKYpq1EIIYQQQgghhBCzRzIT18AqDRQmCR4hhBBCCCGEEELMJslMXINiUaO0xjAvO8iYEEIIIYQQQgghxA0lCZ5rUESDBofcwSOEEEIIIYQQQohZJJmJa1C0ZxI8ptzBI4QQQgghhBBCiFkkCZ5rYBVtFMgjWkIIIYQQQgghhJhVkuC5BkVrppNleURLCCGEEEIIIYQQs0kyE9egWCgCYDhkNQohhBBCCCGEEGL2SGbiGliF0h08hqxGIYQQQgghhBBCzB7JTFyDCmBXHKrdjtmuihBCCCGEEEIIIRYwyUxcg0hjiG2PLcdwm7NdFSGEEEIIIYQQQixgkuC5BspUmH7nbFdDCCGEEEIIIYQQC5w8oiWEEEIIIYQQQggxxymt9ez8Y6XGgNOz8s+vvwgwPtuVEO8qifnCJHFfmCTuC5PEfWGSuC9MEveFSeK+MM2XuDdpraPnF85agmc+UUrt0Vqvm+16iHePxHxhkrgvTBL3hUnivjBJ3BcmifvCJHFfmOZ73OURLSGEEEIIIYQQQog5ThI8QgghhBBCCCGEEHOcJHiujy/OdgXEu05ivjBJ3BcmifvCJHFfmCTuC5PEfWGSuC9M8zru0gePEEIIIYQQQgghxBwnd/AIIYQQQgghhBBCzHGS4BFCCCGEEEIIIYSY4yTBcw2UUruUUseUUieUUv95tusjrh+lVINS6mdKqcNKqUNKqd8plf+RUmpAKbWv9HPPWZ/5w9K2cEwpddfs1V5cC6VUr1LqQCm+e0plYaXUU0qp7tLvilK5Ukr9TSnu+5VSN81u7cU7oZTqOKtN71NKxZVSn5b2Pv8opb6ilBpVSh08q+yq27dS6iOl6buVUh+ZjWURV+YSMf9zpdTRUlyfVEqVl8oXK6UyZ7X5L5z1mbWlY8OJ0nahZmFxxBW6RNyvep8u5/pzyyXi/k9nxbxXKbWvVC7tfZ64zHXbgjy+Sx8875BSygSOA3cA/cArwGNa68OzWjFxXSilaoAarfVepVQZ8CrwAPAIkNRa/8V50y8DvglsAGqBp4F2rXXxXa24uGZKqV5gndZ6/KyyPwMmtdafLZ3gVWit/1Pp5PC3gHuAjcBfa603zka9xfVR2rcPMBPPX0Xa+7yilNoGJIGvaa1XlMquqn0rpcLAHmAdoJk5PqzVWk/NwiKJt3GJmN8JPKO1tpRSfwpQivli4PtvTHfefF4Gfht4Cfgh8Dda6x+9S4shrtIl4v5HXMU+vfS2nOvPIReL+3nvfw6Iaa3/WNr7/HGZ67aPsgCP73IHzzu3ATihte7RWueBfwTun+U6ietEaz2ktd5bep0AjgB1l/nI/cA/aq1zWutTwAlmthExP9wPfLX0+qvMHDTeKP+anrEbKC8dZMTcdRtwUmt9+jLTSHufo7TWzwKT5xVfbfu+C3hKaz1ZOul7Cth1wysv3pGLxVxr/VOttVX6czdQf7l5lOIe1Frv1jPfjH6Nt7YT8R50ibZ+KZfap8u5/hxzubiX7sJ5hJlk3iVJe597LnPdtiCP75LgeefqgL6z/u7n8gkAMUeVMvxdzGTxAT5Vup3vK2/c6odsD/OJBn6qlHpVKfWJUlmV1nqo9HoYqCq9lrjPP49y7smftPf572rbt8R/fvkYcPY3881KqdeUUj9XSm0tldUxE+c3SMznrqvZp0tbn1+2AiNa6+6zyqS9zzPnXbctyOO7JHiEuAylVAD4DvBprXUc+D9AK7AGGAI+N3u1EzfILVrrm4C7gd8s3e77ptK3OfJs6zyklHIB9wHfLhVJe19gpH0vLEqp/wJYwNdLRUNAo9a6C/hd4BtKqeBs1U9cd7JPX9ge49wvcKS9zzMXuW5700I6vkuC550bABrO+ru+VCbmCaWUk5mdxNe11v8CoLUe0VoXtdY28CXeeixDtod5Qms9UPo9CjzJTIxH3nj0qvR7tDS5xH1+uRvYq7UeAWnvC8jVtm+J/zyglPoocC/wwdKJP6VHdCZKr18FTjLTF8sA5z7GJTGfg97BPl3a+jyhlHIADwL/9EaZtPf55WLXbSzQ47skeN65V4A2pVRz6VvfR4HvzXKdxHVSek73y8ARrfVfnlV+dv8qHwDe6KX/e8CjSim3UqoZaANefrfqK64PpZS/1DkbSik/cCczMf4e8EZP+h8Bvlt6/T3g8VJv/JuY6bhvCDFXnfPtnrT3BeNq2/dPgDuVUhWlRzzuLJWJOUIptQv4A+A+rXX6rPJoqaN1lFItzLTtnlLc40qpTaXzg8d5azsRc8Q72KfLuf78cTtwVGv95qNX0t7nj0tdt7FAj++O2a7AXFUaeeFTzATdBL6itT40y9US188W4MPAAVUaThH4DPCYUmoNM7f49QK/BqC1PqSU+hZwmJnbvX9TRtSZk6qAJ2eOEziAb2itf6yUegX4llLqPwCnmemkD2ZGVriHmQ4Z08yMuiTmoFJC7w5Kbbrkz6S9zy9KqW8CO4CIUqof+O/AZ7mK9q21nlRK/QkzF38Af6y1vtLOXMW77BIx/0PADTxV2t/v1lr/OrAN+GOlVAGwgV8/K7a/AfwD4GWmzx4ZUec97BJx33G1+3Q5159bLhZ3rfWXubB/PZD2Pp9c6rptQR7fZZh0IYQQQgghhBBCiDlOHtESQgghhBBCCCGEmOMkwSOEEEIIIYQQQggxx0mCRwghhBBCCCGEEGKOkwSPEEIIIYQQQgghxBwnCR4hhBBCCCGEEEKIOU4SPEIIIYQQQgghhBBznCR4hBBCCCGEEEIIIea4/w8+hoENcNDOXAAAAABJRU5ErkJggg==\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "plt.figure(figsize=(16,1.5*ndim))\n", "for n in range(ndim):\n", " plt.subplot2grid((ndim, 1), (n, 0))\n", " plt.plot(sampler.get_chain()[:,:,0], alpha=0.5)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We discard the first half of the chain elements, thin the samples by a factor of 10, and flatten the resulted chain. We then proceed to plot the marginal posterior distributions:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "# flatten the chains, thin them by a factor of 10, and remove the burn-in (first half of the chain)\n", "chain = sampler.get_chain(flat=True, discard=nsteps//2, thin=10)\n", "\n", "# plot marginal posterior distributions\n", "fig, axes = zeus.cornerplot(chain, labels=['m', 'c'], truth=[m_true, c_true]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now lets plot the projection of our results into the space of the observed data. The easiest way to do this is to randomly select 100 samples from the chain and plot the respective models on top the data points." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "inds = np.random.randint(len(chain), size=100)\n", "plt.figure(figsize=(9,6))\n", "for ind in inds:\n", " sample = chain[ind]\n", " plt.plot(x, np.dot(np.vander(x, 2), sample[:2]), \"C1\", alpha=0.1)\n", "plt.errorbar(x, data, yerr=sigma, fmt=\"o\")\n", "plt.plot(x, straight_line(x,m_true,c_true), 'k', label=\"truth\")\n", "plt.legend(fontsize=14)\n", "plt.xlim(0, 10)\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And finally we will print the *maximum a posteriori (MAP)* estimate along with the *1-sigma* uncertainty for the model parameters:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "", "text/latex": "$\\displaystyle \\mathrm{m} = 3.467_{-0.138}^{0.122}$" }, "metadata": {} }, { "output_type": "display_data", "data": { "text/plain": "", "text/latex": "$\\displaystyle \\mathrm{c} = 1.032_{-0.643}^{0.672}$" }, "metadata": {} } ], "source": [ "labels=['m','c']\n", "for i in range(ndim):\n", " mcmc = np.percentile(chain[:, i], [16, 50, 84])\n", " q = np.diff(mcmc)\n", " txt = \"\\mathrm{{{3}}} = {0:.3f}_{{-{1:.3f}}}^{{{2:.3f}}}\"\n", " txt = txt.format(mcmc[1], q[0], q[1], labels[i])\n", " display(Math(txt))" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.6-final" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }