{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Model Checking\n", "\n", "After running an MCMC simulation, sample returns a MultiTrace object containing the samples for all the stochastic and deterministic random variables. The final step in Bayesian computation is model checking, in order to ensure that inferences derived from your sample are valid. There are two components to model checking:\n", "\n", "1. Convergence diagnostics\n", "2. Goodness of fit\n", "\n", "Convergence diagnostics are intended to detect lack of convergence in the Markov chain Monte Carlo sample; it is used to ensure that you have not halted your sampling too early. However, a converged model is not guaranteed to be a good model. The second component of model checking, goodness of fit, is used to check the internal validity of the model, by comparing predictions from the model to the data used to fit the model. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Convergence Diagnostics\n", "\n", "Valid inferences from sequences of MCMC samples are based on the\n", "assumption that the samples are derived from the true posterior\n", "distribution of interest. Theory guarantees this condition as the number\n", "of iterations approaches infinity. It is important, therefore, to\n", "determine the **minimum number of samples** required to ensure a reasonable\n", "approximation to the target posterior density. Unfortunately, no\n", "universal threshold exists across all problems, so convergence must be\n", "assessed independently each time MCMC estimation is performed. The\n", "procedures for verifying convergence are collectively known as\n", "*convergence diagnostics*.\n", "\n", "One approach to analyzing convergence is **analytical**, whereby the\n", "variance of the sample at different sections of the chain are compared\n", "to that of the limiting distribution. These methods use distance metrics\n", "to analyze convergence, or place theoretical bounds on the sample\n", "variance, and though they are promising, they are generally difficult to\n", "use and are not prominent in the MCMC literature. More common is a\n", "**statistical** approach to assessing convergence. With this approach,\n", "rather than considering the properties of the theoretical target\n", "distribution, only the statistical properties of the observed chain are\n", "analyzed. Reliance on the sample alone restricts such convergence\n", "criteria to **heuristics**. As a result, convergence cannot be guaranteed.\n", "Although evidence for lack of convergence using statistical convergence\n", "diagnostics will correctly imply lack of convergence in the chain, the\n", "absence of such evidence will not *guarantee* convergence in the chain.\n", "Nevertheless, negative results for one or more criteria may provide some\n", "measure of assurance to users that their sample will provide valid\n", "inferences.\n", "\n", "For most simple models, convergence will occur quickly, sometimes within\n", "a the first several hundred iterations, after which all remaining\n", "samples of the chain may be used to calculate posterior quantities. For\n", "more complex models, convergence requires a significantly longer burn-in\n", "period; sometimes orders of magnitude more samples are needed.\n", "Frequently, lack of convergence will be caused by **poor mixing**. \n", "Recall that *mixing* refers to the degree to which the Markov\n", "chain explores the support of the posterior distribution. Poor mixing\n", "may stem from inappropriate proposals (if one is using the\n", "Metropolis-Hastings sampler) or from attempting to estimate models with\n", "highly correlated variables." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import seaborn as sns; sns.set_context('notebook')\n", "import warnings\n", "warnings.filterwarnings(\"ignore\", module=\"mkl_fft\")\n", "warnings.filterwarnings(\"ignore\", module=\"matplotlib\")" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from pymc3 import Normal, Binomial, sample, Model\n", "from pymc3.math import invlogit\n", "\n", "# Samples for each dose level\n", "n = 5 * np.ones(4, dtype=int)\n", "# Log-dose\n", "dose = np.array([-.86, -.3, -.05, .73])\n", "deaths = np.array([0, 1, 3, 5])\n", "\n", "with Model() as bioassay_model:\n", "\n", " # Logit-linear model parameters\n", " alpha = Normal('alpha', 0, sd=100)\n", " beta = Normal('beta', 0, sd=100)\n", "\n", " # Calculate probabilities of death\n", " theta = invlogit(alpha + beta * dose)\n", "\n", " # Data likelihood\n", " obs_deaths = Binomial('obs_deaths', n=n, p=theta, observed=deaths)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (2 chains in 2 jobs)\n", "NUTS: [beta, alpha]\n", "Sampling 2 chains: 100%|██████████| 3000/3000 [00:03<00:00, 958.04draws/s] \n", "There was 1 divergence after tuning. Increase target_accept or reparameterize.\n", "The number of effective samples is smaller than 25% for some parameters.\n" ] } ], "source": [ "with bioassay_model:\n", " bioassay_trace = sample(1000, cores=2)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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QxyzSr8EynVoP05qBIZYePfIxLFDj/RjxA48O8xVh7HseJnqxbf/6LKHgRIzSI5NuKpkzuXNLD0OpwLFMsc6MSQ87O+v3npKOsyIOM/oX8NWOXgTLdULt6WXPbNirjttwjjWdO3aybmYk+yGlHJFSfltK+WJU8e+lwENCiANCiP8jhNAd4zTHFOPpPDf+4Gnu2trLp69Zz7fedAZ1939SNe+ta1OO1StvguixkfNblqo6eOtP4aUfg00/VMeWjfPqs5dx61+/kIGJHO/8/lM6kqU5oZFSGlLKiHNvSCkbpJRXTLcPlqYCUmIYyjia0Uz34ezK26Xz10J1sJzh6RRBZuU9emLfMBs7ZujQDO+Bg0+wcf8I92zrK7+Mdx1N/ts4lspTnR1icGjAe25zT5r9Q4HI0tgB6Ns6szH2PKciVwAxR0Ti4BP+8JwWCEJO30nN5C32DCSwbIlEeum0M/1k2rakuTZGxBAz+1y7aZRyeo6SW8ZQcLzBZEmbmkkY3A277p7+8rPMjHUVhRCvEkL8CHgYGADeBdyIkqe9d1ZHp9HMIYdG0rzpO0+wpWucb73jBXzo9Djiey+DZ38ML/kIfPBhWHnhPI9yljAMuOpzSgCj81H44dUwfohL17bxo/deSm88w3t+9LQXjtdoNJojIhDBcvwrLFtCakTVtczlrr0/Fmo60QKNYcV7wDrKvwHBCNY0oxrFDCVzDCayUy7XNZpmpGgicVoTi2a+/NOWzRP7hknmTBYPP03t6E5/TBmLbT1xf+HuTdNPNXQZ3Q/jh9R5qXWaCFf7ysHSiQYJx1mJmKkpI79dY2l29U1wcCSFlBBxHawZXpK2VFElY6azBG5fvEk+m+UUDd3o94yUEge2K5XKeWImIhdfE0J0A98CdgPnSSmvllL+XEq5AaW0pHuAaI4JtnSN88ZbHmckmedn77uY68duhR9eBWYO3v17uPqLM1K4OWa46Ea48beQ6FNO1sBOLl3bxi3vvIgdvRN8+o7nj0iuVaM5lhBCdAkhDk11m+9xHps43yO25RlhUqJqqzofmf5mup7Bfv5X7BtMYNvT+26yA87dQmRBRrAyY3Bo48yjLEdKUBCignMwnMyxfyjJ3oFEyWsz+b167tAYj+0dKuvgxzNlImmeEmZ5o344mWcomWNPmXGJ2fwdDW4r4JAK3AiWGt/y/oeh48FJN+V+NgqWREq8yY+yCpyTDkliCFVFOKNDlf73wlSLgC9YYzoRrMM6q/Gew1nriJmJTHsN8EYp5TPlXpRSFoQQl8zOsDSauWPD3iE++NNnWdxYxa03nMTaP98IXU/CeW+F674GtS3zPcS55ZSXwXvvg5+9CX50Lfzl7Vx55gv55NXr+er97VywuoUPvOzU+R6lRnM0+Kv5HsBcky1Y5Eyb5tqjLM7jGae+g2UdjtE5fpCRZI4dvRPYEtYta6y4qGts+/7VHDtYrkNQ1zaj1VxjfkG1ySg4M/2F9KxszrIlUkqiUzWgDUbMrNJIUcGyeXzfsPf4jKL3P18hopEtWIyk8qxqCfdnao7vgs54yfKP7Bni+gtWFj07TUfdcXCC76aYZgrc9AioagYiMm6KoOE4XdMRTXGXkbgpguo6PJwIllp3hs6Z66zONLrsaeYcxmf60EY47y0zX+8ImYmD9a9A6JMnhGgFaqWUvQBSyt2zODaNZta5b3s/H/3FZk5dUs8vXmPR+qtrlfTpm74P598w38M7eiw7G953P9z6Rvjp6+GGn/KhV1zF9p44/3rvLs5a0cTlZ+iuDJrjGynlDEIpCxyroNJ/V18KNU3e0w+3D5IzbV5/4aqjOx7PkJKeg3WkNVjpfHmj9eBIiiWNfsbBpBGs2XRq3GhBsfFm5lQqVAXFWTnSweJMH2LtdbM3liPFjYzMkkrufdv7iRhwzbkrJl8w5IiUvl9jqfLped4aFS6pjftHmMgUWHbeipCTV5Ufp1wHMtdw7x3P8MyBUV5zznJqpujl5kZ/DDs8RrWt2Yxg2aHPk48rcqHO4XQubU/Ez3Y3JRBIDgynODiS5ppzl09vSLifa8E0A8vemupukhTBwN+GlWMkmfP2sTBj0uWZSQ3W74DVRc+tRne51xwj3PFsNx/6+bOcs7KR375gC623vxlqmpWQxYnkXLm0nqycrCXr4JfvQGz7FV996wWctqSBj/5yM0MJLXqhObEQQlwohPiIEOJzQojPu7f5Hte0SPSpNK/BXaGn50LWOGdajKcnN3yDppBrABqJw0vVcSM9JX37+rdjJ4fZ0jXOY3v9KIfvX5U59iJjOZEt0DM+yyqqu34Pe+4v+1LetGmO76Q6N4KRGwfgzi09ZdPMjipuqp4xk3n38owkc5i2Pb1rL1iDVeb9yhYm30YlByvnXCtmkfXvRn1cYo7zdVJbHQC7+iac/VqhXm4ugxPZEtVBo6jvlWRyZb/+eLZyD0opYWBnuFmxlOFzUzSB4H2+puNgOfe2lNhS1UcKoSKBOXP6UTfLlk4NVuWo0lgqz7MHR8OvTzXJkkvArt9Tm+qhPnmA5b1/5MldnYwVfd88umco9JkvYaJ3uocyZ8zEwVovpQx1BnMenzm7Q9JoZp8fPd7JJ3+1lZee2srtq++g9qHPwpnXKedq6Ql8CTcsgXffDSe9GH7zARqe/wm3vPMikjmTf/zNNl2PpTlhEEJ8EHgcuBL4DHAe8Ang9Pkc15RYpjImCkev1cIT+0Z4ZM8UQhWB744oyoiu6X36sPZn2crAHE8X1ckM7fb6ZeVM20/oysZVjUel76/A8090jLDpwKjax2xiZlXfoiKypoUUKkokbNP7jnUN+zkll6xc++I+76q8HQGpmUhpB8dT5v0qTgHsGEqyPSAeUSkqGjGUeVv8vsoKZq8bZXVV6pRTH45gJbIFNu4fYWu3cowpimB5zostKzpYUkqe6hwJpT2GSI/A4E6lIBgYdTkHy92He1/pCi5Ytp8+6zwXTfXT2PUgAhlKLZzub75EnTMhRMX9PtU5QvdYJvweTpUaONKBNLNUFeLUZNU5ippp/3127sbSeUZSk0wC52cn1fVImImDNSiECP3QOI9nWexfo5ldvvtIB5/7/U5ee1YzP67/D2Kbf6Qky9/601AqzQlLTRO88w5Ydw3c83HOOHQbn37Nev60a4A7nu2e79FpNEeLTwPXSCnfCGSc+7cAC1Pr28XMKOnm1Nwq8wWZyKpTMpnoxFOdwwwlVb2I4cywH26KoGVLGpIHyq4vpaQ+eYCm0a1MZAoI26Sm888qfW8aDpZLIjvDt7mCslxo2/lUyb5yhbCh7DoAc16PlU/DnvtgYEf5191I0iQRrJFkblpKs+77FJuq/gqKHKxS47s4qrK9J05HQP7clpLadC+16Z7Q9Rh1wjl/2jWADJxniiJY7lhLri1JiciFu41ENlzzZBTVjk3m7rjDSFVId/UmSoLjlLLoOipOgbW9xYoxLZs/bOtjR+9EaJmawS0Y+QQRKx9KLZzuPIN0o18UOWWB99MTcwmlZE6xAzPgNHnXg6B5fCeLhp+Zfr3XAqhvnImD9d/Ar4UQrxVCnC2EeB1wB/CDuRmaRnPk3PLwPm6+dzc3nNvIfxT+mciee5WQxVWfU9LlGkWsBm74Kay7Fu75BO+rfpDL1rbx+d/vnP30GY1mYbLUUcQFsIUQhpTyXuB18zmoqXFlwI5+tHnvYLJs5EdKSTpncnBEzSLHcmoe1lt0hnU+li1pju8qsjH9GfmW8R3Up7qImCmEtJQJlo1T2Zjzn6+Oqt+B/ExTKbvL6n2V9nUqchrC6VI2toSm8V1U58dmtv+ZkhpU9/lU+dddB6vIAUlkC14622P7hvnjzoHiNUuYkcaItAJOXekKhSmaU9sS2kY30za6JZQOaATy5XKm7UUIi1MEK9X2KEO+KBWvgoiEIYvf88oiF64jV9H8d521YO/NYA2W+zhw7yoWloi72DampcbRPZZ2huZ+bgRIMAw77P5M83vEtpUPYxiB/VoF2PFbleJI8OzNIEVQ2s6KEjc2JoWgIdlJTXbw8L/m5uH7cSYW5s3Az4CvAc8AX3Ue3zwH49JojphvP7SPr9zXzg3nNfPl9D8j+rYqJ+KyD8z30BYm0Wq44Sew7lqMP3yC767fjCUln75jq04V1JwIdAsh1jp/7wFeL4S4Apiq2GiBMPPPqGVLukYPP5Vmd/9EuJmqgy3D46kd3AKAWe308onVT28HTpqPa5SGVAhlqWWsUqWk/31VMYLlG6uH22jVVduTxdGF4qa0djjiY4cOwcaWksbkfpYOPcGc4qZMVVU4965hX+QQPrh7kPt39ANOn6VpMKNIpW0Gms+Wrldc71RCMHgSTEsNOFipnOlFvYodLF95ssyYg9eRlP5chrdr9VckEMHa3T9B93i6Yoqg52BV8rDcbYWkxSukCHqPbRqqIr4j44577wMYO8MyCZ4Yoa2WNmw7lMIXPAvbe+LhCdbshHeMqbzpyLQHUgTda31od+hYQ6d2ysbSbvqjxI3MhdzRSpHjqVjIDpaU0pZSflVKeaaUst65/5qUC7aTn+YE5j8f3MtX72/nhvNb+XL2i4j+rfDWn8DZ18/30BY20WrlhK6/jrZH/pEfnbOVx/eN8Jvn5qePhEZzFPkKcJbz9+dRE4gPAp+btxFNBzG9CFa5dL7tPXGeOzQ2Y0GbYHPRcilFVlENigAaEp0YXvQkvNKB4RR3bukpHWP7H9TSzrFFcnGePej2SgrXlIBysISUgTFNP0XwcNIXC5bNs4fG2D8w7j9ZbAAW1TwFZ/Or+p/DduTRK0Y0xrumNCqDUabKg3VTzyrsyTV8K5l0iQGW9z9MbXrq3wLf953GObUDEawy70EwQrqq+x4a43u8xxPZQkj8wCz413HwGs1UODfB97wkQ7BokiDs4ITvg9GqZM5kJGUWrVu6n4qS6u71Ekw7LBG5KIpgYWO4nwcp8ZQZ86WTH+7+R1IFCpaNwCr7Oqh6t00HnM/b2EHY+wAkBmjvV4IsQqgcwZLImaycskjflvLHHTg2L8ZWZgPCPtyM7QXsYAEIIdYLIW4QQrwveJurwWk0h8MtD+/jaw/s4W0XLObLhZsR3U/Bm3+gRC00UxOtUs7o+ut44a5/4ZNLnuaL9+xkdAq5XI3mWEZK+WMnJRDnvhVolVJ+Z35HNhWuoTa5AVHuVVflzW3iOV2Cxms0UmQoFjLYTm8jKSLgFME3x3ci7PKOnJu+VagwDvfZZYMbGO49oB6ULexXs9698UxoGQBitbDiwsByYWbuXwkvrbB7NGDIOqIb/oYrG7CYeUTXk87WwucxZ1rI0U7oegq6n1a1KfFuSAw46Y8OtsVTm57mT9sDjk8hoxQlg5hZ0gWTeCX1xwoRLG83GbVPJXM+OTPKeLDNgINVum+vRs2JjjQl9nqvPbR70BecACxTGd9jqTyDCb9fVEjNMOTsBP4uPobi8Tipa03ju6gfU0qdtlTPF6cDSmGEI1iB/VSKYEkpebpzlIlsufcnmK6oHmfyFum8Ot7aTD81hdHAuNWyPePpkgiz5/QKQTpveT20Sl4vxr2eAteeW4NlFzlWwVHPlCc7huiLZyk+Xv/Pw+wvNg+xoGk7WEKIm4CtKFWlGwO3475Ro+bY4ZdPH+Ir97Xz+vOX86+RWxCdj8IbvgPnvHG+h3Zs4TpZp7+aDye/xRX5DfzLH3ZNvZ5Gc4wihPimEOJS97GUMi+lLJ0CXmhMs5h7sgjNVPbwwESWR/YMeQZpUA46FqhltWzJwNO/RnY+ijLVDFi8rnQ/RTt00/Qq+nmBxaNmsuKgVQQLjHJ1adWNk0b7jmR+e9KmsoEIVsGy2doVdlBk0hEnCZzTgmXzp80ddG9zSgILGRjpgENPwoENsPeP/snq20rL+A5imUF/A+33wr4/h8dh5dnZO8HmQ6NqO/sf9l4aTmRIjDiy1hUuBjc9s1xUoZgplyiqQwvWYD3RMRwSsfD36zsCraNb/cbIwTE69UYb94e119IBVcOg5l0wYFocPS1J/bQtL52zfmKfM1rJqp77aEh2hrcnIkUOlv+3nR5H2IWS+FUqb9EXz/DcgZHSaKS0Qx+ObL7Ajv2HiJn+eWodfCowbrVsXzzgyE6SAAAgAElEQVTrqSL6x+WfCVtKIpNEsEK4qZWBY1Ey7YEmxcFjziUOq/G3ZVsMJrLqOivjFBUnzQ0msowknYmb9Cj0O2LnpR7slPuebWYSwfoYcJmU8oVSylcGblfO1eA0mplw/45+bvrtNl6+bgn/tvRejJ2/g6s+Dxe8fb6HdmwSrYIbbkWseRHfiH2b4c2/54mOSfpOaDTHNgK4Uwix1+mDtX6+BzQ9XKdh5v2CPH/DfWK0s6zhuvnQOOPpvNfoN6h458145xJ0dnbQNZZmeLBXGUhCOMbzJHUu+A5bpUha2PYNR+yC21RGrR2IqhWlaYnSc+UteRgGmGdPT3bupe2l+O0fShXVu0jvfQlGBS1bEiuMMxqMNhXXdrlOnaO6tmg0IOtdbjzB2pd4N6T87/JdT/+R9n5HJn50f1nJ/2mr2BcyxIa2g7Sc0iVZ3mEARlN5pUjp1WDZDCVyIRl2N4IVjLTUpbuxD5TWrNlWeD/RQoqImSGRC6aV+QeyZyhd5tng47AjWJIJV5RG6F6/ssS4Dzgl+//E4uFnSux/9zMgpB1yMP0d+ft5cPcA7PtjeP3QohWux5EOhJkNHZnB1JGdfYNJxjLuOfQdH/cjNZjI8odtfRQsi5xp0TOehl4/FdCb3Alcc7Yt2dk7QcGy2bB3iI6hJMO7H6c6N+ot4zrDoc9XUcrtxo4RHnMl7w8+DkPtpZMLoSM+eszEwcoAu+dqIBrNkfDU/hE+8ovNnL+6hf96wX4ij30VLvwreMlH5ntoxzZVdfCXv0QsO5fvVf07t9/xyxk1I9RojhWklH8HrAY+BKwBnhRCPCuE+Pj8jmwKip2GXPmGteUiWCHnwsxBz7Ow++6S5WqrlAGccmbDI4EQlmd477mf6m5l9BYs26mVEMiA7HelhCzXuXCNaVtKBiayWI7BGqqV8WbSi2bHne3WRIPy1sXGY+V0yhn7VwED2ZgsgjW6H3bdBRN9ZV+uFFk07ELRoCoY7UFZ9ckOwqvpkZiWTSHg6NVm+sPLdjykIibdmzAsZZD7Yn6Tn6hEfyeRkb00xfdgS8ldW3u5f0e/crIOPakiDM7Y9w8nVYPlCjVYUkrijmFf3MzXLpSKs7gRLHczywYeZnn/g6EIVmN1VO2vro1MwPEqfh+UoxJOTQstY1slZ2LCkW9XvbYqpLjZUJUfo/j9dFNEhbTK14x5To1ElpmIEEZArKXM9RgxU9C7mbo+1YvOcD5HxdfucDLHjt546LkdvXG2dKnn5NgBVvXcS8RMYUnpfXYLlk0mW6BjKEVfPMtwpozj1vOs9+dIKs/ewQS7+xKMpvJs7x7lwL5gC4GAUxmcEJE25BJEC6qes2XseRoSHc6LjqNenB4LCz6C9VngP4QQK4QQRvA2V4PTaKbDzt4J3v+TTZzUVsdPrxZU3/1ROPml8NpvLIheCMc8Nc0YN/4Ws2kNX0h/kd/dXWqAaTTHA46Y0x+llO8DzkX1efzqPA9rergGRHZcNR8uZMoqdkkpGXZSakIZc8FajKImna6UuRvBqooI6pMHwFHBc3G3Z9uSukwvEhhJW4HC+nzZKJWbZWjaKi2rZyxD11iaMbexcFlHo9RgWtZQRVtdrHJKUpFzFiT0VMdDKiVvmmTyeT8CVvybM6b6d+3tPFh67IEsNKNoNSFtgnG2ghRe/zG1rutgBRoDT6bQ5jhYQkq2dI+ztXucLV3j5SN3hTRM9GCPdtIyriS3LS86VNlQtW3JUwfHGUxkS2Tnc7mCipwNtYOU4f0KP4IF0Dy+g/6D7TzU7qc9BlMEgZDj7h1iheMPOpOmZVOI1HKw0AxIr7YLWS6KGY5g9TqKehJUrWGlsJ7wlR/cVMNMwWQ0lceVpSi+TNxro2y6qZTqvTWiHBxJla2Dcx006S5fbhsokYiqiEFNlTp/QQfLsHL0brydA929JX3hhLSUc5dT0bWIlSVqOHt1ZOQNO+v1SXt+qIwyYcMSf3vOR9F1JqNmUeQ8kKIZTOsU0oI997Ns4GFqUz3Up7poju9WapOx2pLj9R8v4Bos4MfAB4BuVOPFAmCy0Jswao5r+uIZ3vOjp2moifKzd5xG011/DY3L4YZbw30kNEdG/SLq3383uVgzV2/+EL17p1AC0miOQYQQDUKIvxJC3IOSajeBd8/zsKbA9WoChllmFHbfE6qzcR2hzuEUj+8bZmAiS2gWPehgFRkjruR11oleN2R7aRnfQePEvnCKXsDBcp+QdYtD20rlzBLjRxRFsIYcB9CdHS9bOu8asAHjyxA2IvRMsYNVOZ3SW2t4H6RHoHdzyTJFG/OO3cql2Nk3ETIKg4ym8hyayLNvUBmnQSW0cqICUroGrf/czt4EewYSvmy5XcYQL0kjdDZgB/so+Rs9OJJiPF1qwhUweKh9kGTWV8OzHQGJyWqwVPqjej1ihdMMpRUwoKVNIeicCAOEYHefipI0JA/Qve0Rr6EvlEawukbLpDFarvBJeIzuvgwhyBZMtvVM0DPhpLs6jpstiyT0kUVBKJvO4YBMfZk0ysABeU6BLcG2LXb0TrB/OMlEpoAsil7lTZsHdw2A9NU3Q9EyM6sc5GgNw6k8rWNbS/bolUJWSBH0e0qpj4EblQ46rjXZQaoxaUx2llwXQpp0Dqe8a15IyZq2OhCwvP9hVvXci7n/scD+Ag6Ws85zh8Zp759ASul9p7gqkMXXiwg5t8EIoL/dtjHfDnnmT7fTl6tWD+p9Ry6wkTLPzS0zcbBOcW6nBm7uY43mqJPOm3zgp5tI5y1+/J5LWP7g30N6WMmM1y+a7+EdfzStRN54JxYRan75FuT4ofkekUYzawghfgX0Ax8E7gZOllJeJ6X82fyObAo8pyFgcLvyzI7iV+PEXkTno2DbXhRqfPsD2Nt+rVaVhA32IgPNNTyzBWeW3YkUNCX2Ut3zlLec6xCZgQiSUdMY2lY5+9xdL5EtIANRsf3DSXpTIlSoL4ochVBsS9oYItgHK3gcknLRL88pdJ+aSkY6sKK7m7bRLcphLef04KZUKnOrOjsUMj49XzSwvO0Y2sFz5SrGeedClokoWQVGU3k2HRwllTORGRVNCkl+FxmalpRYRnXouYkc5C1JX9w3et3oUEmEZf8j4PwWFKxSRT0XM1gfNbIv3N9KGEgEA+MTRAulujLLmmpK6twO5RtKlrMss+Q58A385cNPUJMdJGvaXgTMre2SyLBTI73/AEgVqft1DY54cuUAUkSwRZRU/UmhK9OWkkRg3d54BkRYMzJTsFg28Agr+v7kOTxbu8a9FFkObVTXcjT8PgVxjXm7gjiEH1ETgKChWh2/q/gZy8eJWFmnQbMM1QqCcqhG03nvjKxfWktzbQyB8JyjYGpj8DqQKCcymcmRyJkMJnJ+wL3gOrrFY/bd0JCzhk0656qU+i5MrDDBaNJx4lNDZPv3hJWPF3IES0p5UEp5EOgC8u5j5zmN5qhi25JP3L6VHb0TfOsdF7K+40eqR8Nr/gVWXjj1BjSHxZKTz2TDi/6LqJki9cPrQ0WrGs0xzibgbCnly6SU35FSHiMXd5mojNMQNFNwpK0n9kBqkMTAPrKbb2PR8CYSo/0IbBoS+9ncNRZOL5MW3WNpLyXKTV9yZcmllNS5KUbJXn8kzlDcSFTEzoXEG6CoWbBDzJnN3tE7wcHhcDPbQ2MZCrFGkg2nqH24hpvnRPnLVqUHqUn1TpIi6IwlU5piJZ26r57xaTReHt0P6dFQpCRvSj8K6Ownb0meOzRGJm95467JDvn7JHCuDKFU0KyCcgWl5YhgSBB+CuE+VwChTApoOpNmtyN5P5EtMLD5HjZ2jPDnHd2+PHjROTEtiTSiZGpX+ONyUvaC6WajCXVeajN9nrAGUkJqCLpUXU/BkmUMZcXuvgnfqRraHepv9XjHCO1949Snulg28EjJui88pY1zV5Q6VMVIZ1yVgmxeap0Q2I6D5To0o6k8I0nfIFfH7h/Lju4xr9GylJL23lFySV+QAaBv5VWMt5xblCIIE0XRIOmY3q4DYFo2UTOFYee982dJyf7hlJfemDMtBtKVozBB4ZnyzoTv9gkBUUc9sDZxgFXGGEsHH6NpYo+qsZbS+6wXb9NLacWNCvqLBJsSB68DKeHQaNrbRt60J0/HDO7IeU1iIBAYZo6djiCLGQ1fE4bw19l5oJv9wwFnfSHXYAkhWoQQ/wNkgX3Oc9cLIb44V4PTaCrxzT/v5d7t/dx07VlcWdcJf/48nP0GuPT98z20457XXX01n2/8J2KJHqxb31yxqF6jOZaQUn5ZSnnshWW9EIw/YxwfH6Z3POMJBIAyX0bbNwJQkx3wnm+OO+0XAimCA/EMzx4c4xmnyahpBepJACltXC2J4USO8USK4WTOqwNxhXCsSI3KWApl+EhcY6p3PENfPEMsIEyRzJWp/cAg3nI2IJQgw1C7t42gXVad6qZmYr/v+IwdQErJgZGUml13Z7y7nykxuCTBHjxT4NRnBTeRMy3SuRybDo4yklHHP5ZTEQUlO10+uuKeq1jUgI4HofNRxMAOT/o7a1qQGSdStH527yMMPndX6Pg37Bn00iulhJwTHcjlc4ylfJGLIHnTBilVNGD5eWqJMvVNvcFeX7t+rxrPBh285KATwXKb4Kr9NCQ6aIrvJp7OsaV7XKVSEk6BK0hK5MSDCCG88zey6OKKy1X1KRGF2nQvjRN7SxfwdimwCUewAJ7q9OXdi0UumvqfYHn/w95m6gtjLBvcQGgFJ9XRr4hSxzmRKUrdFIJMwWLD3iHi6ULomgtGfuKZAs93qyj07v4Eu4dLe2RZkRpnk34UuFyqqh+pU86P6ywadoFLRFi/ThB2sBrje6jL9Hrrg68+aBQXDxYdR1VuFDLjoehmLCqmdLCCWxXSBgFVUQNhV45KBScPSsVjFrCDBXwXiAMnA+4RbgTeNp2VhRDrhBAbhRB7nPszyizzWSHEDiHEVke96TUzGJ/mBOGh3YN86897ecvFq3n/pW3w6/dDyxq4/lta1OIoEI0YvOOtb+d/5T+K6N8Gv3ynP6Op0WiOMk5anmV6RsXe/fvpjWeUmefV4UxhYjgGWM60eO5gQMK7b8Krk3CDDlJKz6Ar2JLH2nvZP1pq/A0uvbzEkDIDkYtnDozydOdoSCyg2pFYL8RUaqEyrgQrW2rBiLDISDtKdEr+O5QiSLD6BUiPkM5bDCdz7BlIEjLbnOP1xAGkbxSatu2lSG3tGufRPX7UaSSZYzSVUyl4RSd01GluO+gEwVwBBVsGDWd/JYmkUBwpyIwhhkt7DubS4YmsXf0THBoYCW2vxOB0DtewC3gi40WDzpmWk4IlYMl6aFim3qOi31J3/J7r0P0MBOuiOh8NGdFC2lRnh2mO76Yx0YHhGMauCEI4A63y77Z7nUWd6ES2ZimAckCLjsW9/ltHNquobYClAxsInSvv+Mp/KozRvaHJw+JIbG3OF+Boq68qSmMT3nux60AXA90dxCJG+HWHvBWWZRcVGv8WLNtzprx1Y81etNE9joNupCjg/Aq7wKLBjd6+m8d3EpnUVgqnCAabOxePs/i8eK8718GSoY1E9//Z+XzZFGKNiPploX5W0UKSRSO+wqAInD9/RIZqbBw8rqJ9FpJDFGMtv8DZwMJ2sF4FfFRK2YcXOZZDwNJprv9d4NtSynXAt4HvlVnmaeBSKeUFwPuA24QQtWWW05yg9Ixn+Pvbt3DWiia++IZzEfffBBM98OYfQk3zfA/vhOHik1tZdsnr+bT5Qeh8RDm5FeoPNBrN3LPl0GiofxC4BqcyVHrjWU89sJimeLsymPHrf1wOjvgpe66xZ0ubYBWJEiAolWuQIuKILQeiFZaKmNC/jdaRzSAltsQzQN0UQstwZuaxcE2p+ppqb0sHR1Js742TCNZnCUHQpwQ/aGVaVthpKEqvk4Hj3tWX4PnucXCiX2OBflSP7RtmT/8Eu/onSOWDwiAS2zEqbaemyTUybSkx7AI1mX4akgcC6wTlz/GN2iKfKZUzS2qbPEn7QNG/KHLeQBnCjYkOb5ui6F3KFmyEG8ECEIaXymdL34j1DergIIqk021/8AKL5vhO77WoGRYxsGSRQ1KG2nQPpy2pB6ClxgCE/4YCi0Xce7MjhpjUho4VJrwjl0J4jkl51T6L2OA2pcjpUBUJjFGG1zuprY6qgAOlaqyc67j9AZom9hS97v9dHACKWJUjqGakruS5XHWbug866tIK1d3VZvyItURQlRur6BgBVGdHiA48X/a1hCub77x/kTIRLCkioWiSJSXjmTwCC9uIIWN1SFuqi1taKu00gFIn9NdXn0tBzBDhCFaorlJNQhRHruxobWDZo8tMHKw4EJIDEkKcBJRv7hBebilwEfAL56lfABcJIUJSH1LK+6WUbgL086gzV6JW4KQrrg3eUP1LNMcxedPmwz9/DtOS3PLOi6jpuB+2/Bwu/zisvmS+h3fC8ZlrzuTB6lfxo4YPqj4v93x8XmaJNJoTGhGcDZfQeor3WDlLjqhFpjTC5NKW3u9vDoERMM6CtR2NA5tgYIcyMIN9oOwCgtK6CikiJV8Jg4mcqnMaaqcu08vK3vuo7XuaRpmiZWw7Hb0qeiYN1wAO1H4YhmcmxdPKWZyIBaSfnVolWeSggJPmGOwqM9ETHiu+0ez1+guch2Cz3KipIg79E8HUroKnYperU/VMVuMq7/WIlfVm6VP1J/n7dQar0sHG2XRwNCQrPpzKE88UKqYY2sGZ/mCKlA0gaI7vojo3ggRsESPsvUlGUjmQNhFXhk646VsiVCclcJ3FQPqVFb6mgtebkHbIyC52HEIRrArdftpGt3iOQBQbW0RCryufRTn7BoKcaXPnlp4SV795fAdhWQnh1UEFJxMWD22kIdGp0uncTQjX8ffXLtjhPmKGEOEaKJRQRHis/usy5GAJWrL+tSjKNP51rxE7Eha5MKP1jLechxmpY0lDdXCF0HtTouhoRCYLGmLIAlXjHdSme6jODoe23elMuLjjLBcJs0UUIU1PSGPfYJKR8TgRK4ckohoxm2lW9dzLqp77qMoXTQzhpxGDeo+kMKiviWIElDKFLL0mwO/XB4H3bYFHsH4A/FoI8UrAEEK8GPgJKjI1FWuAHinVJ8+573Wer8S7gA4pZXeZ1z4GdBbdNpRZTnMccfO9u9nSNc5X3nI+p9Rm4PcfVTnjL//MfA/thKSlrop/vPZMPjf8Cnae9gF49sfw4Bfme1gazWEjhFgkhLhRCPFp5/FKIcTCnrwLGDhmpBaaVwVqoWyM6USWA8aHRIbkj4PmUyzVS7JrG6lcASGgqcYRCrALCCkx65c5Rrw/tnIy5MPjE/4i0iaW6qUxsY/61EGqc46DVc6YFlEvTdE1vLMNq+ldeXVotMF9us5Aom51+Gj6wlLXbgpT6DkzS7SQoDbdw95HbwMzXzSDHjhU6RvdhWgdqXVvYF/GL8Kvzvn1PbYRc8bpjy/ozLhKjwCDiSy98YxXQzPWekFov4lMwXcWAsb5QCKLadtEzbR3fLYRKzI0bRJZE4GN7Z4bYXheaSg6ZlsqJQ3pGbByrEjjLDlAfaorcE6CMuv+ectbtq+Qh4qqTDStpxy1I7uUmJK0oOiaqI5EENJmTVsthiFIUF92Gw3JAxhGyGRXRr5zYuodwZbq3CjN8Z0YVs5f1nH0rTL92yZHOv+r9yYaiIAFI3aGlaNtfNukW3KjU+514zpr8ZazQQisaC1VUYOljdVKMObQRl9JFIhYOT+9F4FVPXW2j2nZtI1uYfHwU6Gxe+N23lujjBdhR6ox7Ly3T1tKVvT9maiZQgoDW4ajjcGa0Fz1Iue14HUqvfRfI+Soy5JrwpaSXY4IRr6q1b+uF7iD9WXgdlR6Xwz4b+BO4N9ne1BCiJcDXwDeUWGRb+LLxru3K2Z7HJqFw73b+vjvxzt5z0vWct25y+HujykJ4jd+T/e7mkfefNFqLl3byjv3X0Xu/HfBhq/Dxm/P97A0mhnj/O60A+8EPus8fQbwnXkb1AyRRoSBtPAMotFUPmTYViIkZl5khxT3Ut3dP6GiE8AiZ2Y7YucBSaG6hUzdivAKZewaIcONZi1bUuVEhbxi/MAsvxRCRQmMiDdAt8i+fyKPdAxPQaB3VkDFrWf1X5CuX1OxRtew8khkSbqY2beTZQOP0ja6hUI2BYV0xT5QVfk41QcfVseDwe7+REi2OnxKAsc2TbtP2CZmpI5cdasnUw2wvWfcO1dC2py6qJ6aqDI6swH1QlDiFcXiAbYjiOCPSSAtk6iZxgyk/NVEJOefoiJy6bxFPGfz5I69oYa0vXueJUiwnsh19ACe7x73hFPUggIzWpr+BlAb36v6udlW6JoAJbBw/fkrWdpYgyHAmmQywRDCuxYlAts53raxLdTEIqGan2WDG3wn3dlnpZ7CMcNA4Ds9UcNACkGtI9ziThSERh64DrtGJvyIaQVSeRMz1hTa1kTT+nBES6j/vKNwlB0BDDvsYEkRoaE6RlXjEta0lj/vbu+wlc21LG+qKXndi2CVSREsxJo4pTnCWSsaS16TIoLTT7wsY60XkKlqDX3O1HXkpIIGvs9Uamt4/8H3aWjpS9h0YJyhRJausVRJhH2umYlMu5RSflNKebaUsl5KeZbzeDoj7gJWCaGuDud+pfN8CCcy9jPgDVLK9gpjGZdSHgjeUA2QNcchh0bSfPqO57lgTQs3XXcW7PydUjF65U2w7Jz5Ht4JjWEIvviG80jkLP6f9T4463q4/ybY8oupV9ZoFhbfBN4mpbwG1WAY4Cngsvkb0syQIsq2gWyooH5aDpYNO3rjjKXzAYlzZfT5PaWk95qQFgK/obC7D1uWmhQSJzqEoDbmF+QH5dpNKYjh9NaaaGdxQ3VRBEs5WBgRz1+rSve7wwou5rcFcx2sEhmMAFaButFtrOj7I0airySCZU34FRBVETeyU97kaRt5zpOztxFKinoKE0vK8oZ7UO7axZAFEAbRaDV7B33xhVg+HkixU67DmrZaT8I6WAcmi1LXXCNWIAMRLIEwMzTHd6pz5yyzqDaCEVWRnq6xNO2DGWJmivaBhLf9qvxYaMzBiFowSgFK0j24ZLHz1FwbY3VrLUsaHSfCtkqimobAE9oQ+O0EwmNQxxURgaoeEd5fNCIqysvTulbtvswbtbK5lgvWtCCE8BrnttbFuGztYk5qq/P2BWG1vYiVo3V0C8I26R6dvC2AqG7iwPLXMLTscv/4Ren5Es5NOimcI4F6S8M2Q58DgcQwDM5f1Ui9k8ZXydFqqIn66aPB/TnObLkUwbbWVpbXG9TaqZLX7EgVnYPjFSuilMPk7M+t87LzIKVKAQ6pCFqY0XDU0lU/HGs9H4BUweLgaJp9AxNFaZxzz0xk2q+sdJtqXSnlILAFPyL1DmCzI5IR3MelwG3AW6SUz03/MDTHK5Yt+fjtW0DAt//yBaqPxR8+BSsuhBd/ZL6HpwHWL2/kry8/hV8+28vGF9wMp7wc7vwwtN8730PTaGbCWinln52/3d//PFCqWb3QcKM2IgqR6tBMbVO8vaj+pBSJJGnHeN4+1TtwV5TAFV5oqzW8v12jPeo4chGnLsIO7CddpzIry03BSpRTN95yDma0noKoIiqkN07DmY0PHKAXwTJtSddomqoxpWwWnMEW+Kl2Q05Po0JNoIy72MDaeSe18U61z+wohu3UdTWtA8Aq+MZcQ01UGXkVDHGB7fU1SmRN1eC3kkEXeH4ms+oSKGCEDMWolQ5EsFQUzhACK1LtSXKDE9EL9GdSOIIjKJEL23br1ErHJKRJJOqnf6pzFaz5Cq+zurUWKdxUyFJTM+gMSSE8g90lYgiWN9X6YgzSKqm3kWYOkspxE5GoW3gWorXeiW6GDl2EaqpiEQHFtU8SDgwniVvVcPqrGF16Ga11VYFJgnBapyuCIYQgFjXws+qc50OiMHnq0j3UZnqJlKm5cj87ANGaOvKWcqi8CFaJgyXUP+cYe8YyXq2UOvd24Dw6+xNG6HxVR8u7A240tBj3O6BUpl2wfNlKACLJ/pL1bKMKpO2lma5dVJzWKZAIDCuH4eyjLt1d0qYAVJpiIdbofV4BT5XT+/4R6uu7KbawUwR/WHS7C7gPVZs1Hf4W+IgQYg/wEecxQog/CCFchYJbgFrge0KILc7tvBmMUXOc8d1HOth0cIwvvP5cVrfWwQOfVc0Yr/8PiCx8u+dE4WOvXsfaRXV8+nftpN74E1hxPvzqPXDwifkemkYzXXaWaQ3yamDyAokFgFvTIY0o0agRSr+qKsQdA7KUiUa/W8p4y7mka5Z7qXURK0PEzFCfPEDzxB5W9Dzg1Ri5xlVrXZWqi3AcE0sKkg2nYEVqiDef6YxNzZ0X+xqmZSNFlFz1YiJWxmt8qhDKWQxQW2WAYVCwbAYSWcZSpYqIQihVPFD9uQCySy5wtlhmEPguwlCiQE12GFtEyVe1AIR6AalUOqtiimBom47xW0kdr9z+vf2IGJmaZeUXFiq1LVpk1PqRHRuBjRDCq9cxnAhPIdYEFKuzWRCSFwcQoaiau7whLYxIlIFlLysZli1liZvQVBPDsHNkapZ5Ywky0XBqYBy213vLdWBKVO5ss0QMo6pvE/Q4c/GR6hKFRPCN3JDIBJCz/cdrF9WXvK8FWzKcyvPUwTg7xyIUZKTk8gkq1kUjRQ6PCG+vnK8dMbMYlKYHBp2nXOs6P93Veb54AsK9zlQWZFhiHZTjbUupPnNSKgVAYXhRarWNUgSi4neHm6JbOxT+esxXtSDrlR6esAsl69lGjHjLOQxn1XYX1YdLPCKRCBE7S9RKe98r3njKDMWwzVCT7IJtk65dySonIudK29dHKvdZmytmkiJ4SvAGNANfAv5zmuvvllK+UEq5zrlvd56/Tkq5yfn7UinlEinlhYHbgv9x08wN23vifOOPe//lRUkAACAASURBVPiL81fw+gtXQsdDsOVn8NKPKgNes2CorYrw1bdeQPdYhi8/1APv/DU0r4H/ebvqWaPRLHw+AfxcCPEToFYI8T3gx8Cn5nVU08CNHEkRIWIIBlsuILf0Bd7rQePS7S8FYAXqXvJVzZhGFfnlar2omWbx8NO0jO9gRa4zZNxEAkpetTHDq5vqGc9ixhroX/Eqrz5ESpjIFMLyyVIZQhJBLK+ksKOGL1ld7Aw11VZx2pIGxtLlokfBCJbwtmEYgqFk1qu1sR05+BKccWVMGyFNbKPKm/XuGA4015XARC+LRp4ps5EKYwoYyq6iWjHFYxpru4BE0+nqtSInM+o0hy0UreQZ2E5tnIE/c2/YOaSIML7i8sCBKCJW3ldpFIaKyIhwE1ghTRYNPY3AJhqNYcZK62pMW4YiWOesbPIdJGFAmcbFfbW+cy+kTbZ2GSOLLvEM+pCsOZRNEQw5gtFqLzojhUEh1kSmdrlS1kQ1MvbrqgJpaKhawpevCwtWeymmIsLewQQZU6o0w8A+zcA23FS7eKbgOC/OdtzxlXMOpFk2IpqvUiIU8eazsGqXeL3jgscfimAJA0MI7zMfev8cRb58VQtbu+OIzKhSFRQi1Fy82MNa3VrHqYvrK6bVufV11XFfgTRdt4rhxZeoWklAWKXpyZZRjR2pon/Fq9QyRduPGIJYQaWdttTGWOzUeYqSqLY/cNvwnbRU0+mMLXoBtVVqDOo1EfrOOlrMJIIVwlEC/BLw6dkbjkajyBYsPnbbFhY1VPGlN5yLKGTg938Hbadp1cAFyqVr23jvS07hpxsP8kS/hBt/C9UNcOubYHT/1BvQaOYRKeWTwAXADpSIUydwmZRyOhb1vOL1EjaiZAs26bqVRBaf6hke+WY/WuD2aAIV5VjeVKPUtiI1yglpUhLihp0nYqn6kFMWN4RMm6CSV7rgCykU14WAaiZcTuyhYEkQvvhBxBCeESqE7yCAMvaEEORlOAqh9hlwsIRfS5LOmxwcSZPI+5bjw3tHQ3Lrwe1EC0nq0j1OKlapITeazrN312bPyXFx+xCFtulGsALnoyqQgpWrXuTtu7hvjxltqFi75RrjIYEIwoa3wAahIgVuClu+qpWDYznnuPx13TQ/w3E4TFs1dQ5uvSo/Tk1OVXOISAwhBJna5aH9D8SzoeOojUU9B0uKCGcsa5w0TdW9frK1y7zarJKUNdtPEVzZrHobhdIrYzX+HiRka5YgRbTk/XbPUsjjcaM6wd152xbevVF0brLNp3l/NzoOVs5U/dYiIujMlW/IK6TpL+ewprWO2uZl9K68imTjqUQM4TuvwdTSoFCK0//NVTy0JQwse4UTCVVprXakWqUC50yqM4PKCQy2dCjysJY31dBaX1lAzL0WgwqD6bpVSKPK6UdnIIp6nwmEP6lTSXAm8JlZ0ljt1bIta6ouewUJaYcipM+bSpz8pLY6dc6FwDKqiNrHkIPlcBUliasazZFz87272TeY5GtvvYCWuip46EswfhCu/xbEdO/phcqnXrNepQre8TwTNcuVk2WbcOsbIVGaj63RLCSklD1Syq9IKT8spby5QpuQBYefQhQl7TS/baiOkq9qBcBsPolszTLGWi8Ipa9ZkWpiEcNLIwOwHJUxwy4oCfWIoZyDChGsltoqT9zANfouPrmVk0tqK9QmUvUnqzQmJ/0uU6eM9YghPCNcOVi+eRJxohlnrPCjDME5em85QxCNGJ4xa0Vq6U/5Sybsap5ILg/1r3Kpy/Q65zDCooZS1TRwohPFzzWfXWbJUlPQFR5JNJxKPuCUBdObpDAwY/WByFd5I7RE+l4oiQMhbQxsFZwwYl6qmG+AipLeVEJKYhHlVBZMqfZZJtInEE6kRKWTBhlNKZU6L+K26HSoafKOKRYxWNJYaqy3eQa8v0M3DTVWHMHKTXiOZItTV+VFsJadA1V1XgRLoARGIlambASmJHWzqGcXwLBTwyc9R9EI+QRtdVWcdvLJcNqVsOYyomdcycmL6rnopFZwIqmGlfMckebaWKkKol3ANguhuq7GmiiXn3USV56zhqvOXkbEULVeoQkO16HyCNYuAlJixuopOJGwmICXnBbuF4cwYPm5npPlStVPF7cvWnDiwE2tFY4gjWGq74mgM1gsSlFMJFosZCK45OQ2VrX40fbweZQlzpohBA3VUV53wUpa6qqwIjVE7coNnOeKmYhcdAkhDgVuw8CvgH+Yu+FpTkQ27B3ix08c4D0vWcsVZyyBnmfhyVvg4vfA2sunXF8zf9RWRfj6DRfQF89y02+2IRevg3feAckhFcnKjE29EY3mKCGEuFUI8dOpbvM9zimx3dQo3zhpqokRbz6LkbaLMOraGFl8Cen61b5xKQQvXbcKCSEHy5bKIHefc52VkIEn/eVPXVLPqpZab5ugIk6nL22gBKH6D5m2ZCydB4RXqxU1fKNRFKnKuQ5WY9tSf1sBwQJvOcfClE564mjbhSQDPaUQgkTT6SSzygndP5wsja4Jg5a6cEPXyXDH6RqOESFCRrmLm/JWqFvGK9a5xyEJZ066759a/6RF9aTr/GbFlVHCAK6jIBChWf1IzI9aBu8Nu0BdupdYRGAZ1eQsC4RRNpVSBbmijsCCf52taK6hYEtyBQvbqKJn1bWw4gKM2mbvHCh/oIyjs1KltLkRrItPbsVyVf/KyH+7zadd5TovytS0yol8+KqHCKEcGOdg1i0NpDYWO13SLokkFazi2IERikKtaq2lpioGdW3QchLUL+bCNS2saasDIYgWEqzo+xOGnefkRXXUVUVJr30N4y2+8rFhFyiYZmi7wohAJEpDdZS6KqXgZxU5fxFRHMFSUvHuZlS9XeBwpYVhGOH3wL02nXNaE4twycml0ViXs1c0qR5b7tgzY9B+H9WOQ5RoPN1rl2AIQETAiXRna5RzN9F4mldrB75TF3yvjeIoeKwO3JouZzHXkVPHVnqxvvT0xZ5jLaXEjtQs+BTBvwJuDNyuAVZKKRf+j4/mmCGeLvCpXz3PaUvq+YdrzwSrAHd9FOqXwlWfn+/haabBxSe38fGr1nH3833cvqkLVl8Mb/85jOyFn1yvREo0moXBPqBjGrcFTbbgSFUHVN6a62KYsXqydSvChepeBMuguamRvGmTqfVFFZ7vGsc2YiyuDc+KF0cC3PQhQ4iyjUiDz+SqlYFk1fkOUqZg0VTr1zsFpaCLI1hRt7i/ZQ2jrRcyuPRyv6+PM66hJS9GrnkJrL8OOzb5LLnrnbmqf21FqVAiYPCFGieX25IzNi9VUIBvWvnbiUUMJZ1ev0QpEqJ8gbDxHBYzaKqtIrf8EqaFEI6b5USwAuM2ndRK1wlzMewCzfGdVEUM7EiNiiqK8s2h1QpRDBF25F3HsXMkhTQiNNVVKwfDceokjmFfJhgXjYYd2da6Kixn3GWyTbnklMVcccYSzyExhIClZ0N1I4ZhYEiThmSne0JA2l7qW01VIDLinHPXuUfaiHRI1Pr/t3fe4XFVZ8L/vfdOH5VRb5Ys2ZIlWcLYBmyKwWCKTQtL2IQSQjYJyZJddjffJmyyyWaBfE/KRzZLlk2DLKQRSCMQWAg9hNAD2DRjGzDGveMi2Sozc74/zp2ZO6MZSbYljcr5Pc88c+feO/e+99x23vO2JDFbW06UWLpYcTK1vbYaZv9Tf5rSZDnrLWqfxuJjjqK5ooDysA871kv4wEbSdMmMNrFF0uLbYnYAy9Jp4VNWYkcaFWd75SJ2VZ2QLo+T1CJxi6UNmWSx8HWH67Vly6UMhXweqhOumWLr50FfF5YIc+oiaVZBSSj7joK1r7iVrdVL2FecKiYd9NrJQZiO2lThY49tp2/H44fKDrfExMXLrrLjEgfnklyIhHwD7ueY7UurnzVWDNsmqJT602gKYjAAXHffG+zo6uWWK07Uxf+evBG2vQ4X/wICQ1cfN4wPrlo8k2fe2cm1977B/IYSWmaeBpfcCb+8DH56Plzx++SolMGQL5RS1+dbhpFgn+O6FgoE2IfuqLpjWNydPXctHSybvdPPYs/7KYtUX0zHNCTSIrstWHHLT9CKclRd9mexu6itu9+2s2IhAGfNrmbXMzoTfnHQS3l1Edu2JiwWru2IMLe+lPXOWEwiFbRtWxwM12HFelxKgOD3WPRSihWpAJ+P/lgMX1Lq7GTGPqUfSKqT1xOsYm9xGzVbHh2wms+2iHnC7Kg4kT5fMeHuDQgDY7BCvoRikp5iXdf4dTs7JiyRCVfJoRLsk1xfWzQUVjyGiCQtBTPKC3jWrnd2kMgiqPeZUEY8tkXM9rHvYJT9/fE0V0jbEmJxRaywFkJliOxJO7luFzElHk6Y4bhx2k6KdrHJ4pQHQLCiga4NTewvbE7uKy5eLHqTSombsN9POOwD26IuEiQS8kKVdtFMJFYo3vums18LQSUzkbszL3qc2MKklU/Fsbe+mravPZEODgariTtZ6JRY2CLUl4bYsPuAHlTIpgUC9O5Lt8A5k7Yl2B4vkZAPr22xs3sfnmgXEkgpw/GGdC8dyyItK+DOsuMo6XuT0+fNAn8h7+3q1teZgIWi31fsHFc/LpWERCKMGErfTwnZsxzDnkgH1NVD7VxY+fukUp44pD5fBCF1jWjjc1rqSYj1pfZueZPtmKCswI93n963z7YoCfl4/0AffbEYe6pPxYr30zQtBBXVkJEsQ4mdukcc2bZWL0GJTeaTSQEHQ3VEKwYfKBkNDsVFcHK4UhjGLQ++voW7l2/i6tOamTMtAjvfgj/dALMvgPbz8i2e4RCwLeHGD88l7PPwd794mf09/dByBlz2S9j1NvzkPOjanm8xDYY0nNqOPxKR+53v0/Mt03CIK33PFRfqEeHSsC9rUD3oEfBpJaFkeuTWaZXJTlaTkzVMYWM7MRYpCxZE7QBZPLfSChAnyKYaBH02bdXafSkeV04wfELBSnWpdYiIq0PsWMg8VkJxSSlAcUtnGAQIeBMFShOWoOxtoEh3Aev1V7gWxtOVIFfSi8yR8VlV2u2sz1+SbMOEOrqgqZR+bzFdBY20tc5OJfAg1e2NZfriJdtRT8SBqqJUxzSeSCDgki25VdExWL59a5PrAoR8NnMaq2mpLOT4GWVZs9Z5LCHmCfPW9v28tnlf2rLEddRTsxC8gaR73r7CFqhoI+iK3SkKB/TAKCStHwmLWrZT4fd6mTb7BOJ2yhqaTC+f7ULzp9xOa4qDBL2pffdG049LiYWoGA1lQTze1P1wIFhLZMZClnZUk+wCx/qzyCdpSkHc8uL32JSEfMyZFkkmUMhKPMPtL801b2BdqcSh7i9sRoLp7n2ZsWhRXxGq+Uzwu7M5JuxpznWfYd214n3aZdL5HfTaKdkzFKyQz8PMiqLkAEzChRBABUvZVHcO/d7CtEP32BZzpkXSYsncyVKypekXQbtWAhTWUF8aoiTko7ooSMwTpt8XQRXV6ph7jz4PxSEfpSFfMubQkYrjGkuJeYLEbd/AU6Kgz1+GKpk+QIbR5lBcBPcAfwXYwEbnvxc48yeMK4VhfLJjfy9fuvt1jqor5uolzTqm4PdXgzcAZ38r3+IZDoPKogA3XTqPtTu7+ewvV+jOxMwl8JHf6IQlty2F3e8OvSGDYQwQkX8GfgnsBu4HdgF3iMjnhvn/WSLyrIiscb5bhv7XyBCNx/FYFparA+oesa8sSrkdRT1BqosCzCzVnVqfR48eA1QXB2iuKEBZNh4nJiXVoRd6AxXZkwa4FIOiYKqwazYSMRsxlR5v4bEE5XSkdN/V1UF1itAmY6xcGQZjniAtVYUs7agmlBGo73PWb60upDCQvqzflYmvq6AxtS8UluW2ytgUh7RrVFoHEh23kq7IOt1cES2rCHsjHUhxbfJ4om53L6XSbDt7I+16vu0nZgeIVh1NR21R0mK4q2x+sjOuz2/q3CixCPTswNO1BfGFk3EqtiXUlxczu7YI8RfiibpSzzvEK9qT05kxMLYIB0LTkucz0TT7i2fhrzsaX+2cpBJgu93bvEFHYfLnzCBoW5KmsNtWSsHKWn4pWJJ1OwAHo7pd3XFCfgsqCgLMPeWC5Lz9hTNpndFAwJuygmgFyzk/SZfADEVIrGTq79S8XAqWvl4TST/SVksqnq5ZiXghZEBbTS8LURxMV1BmVaXHN3aFG/TASIFOmJJS3NOvzd6olivos10WrPRjml1TROe0iOtvA49ZiT0gy2NZWTnexDwFtJ2f8kbNolQCUL8AOi+CxpPw2RYzKwrSLKJJ6T1+aFyEr6YzOeDgtmC5Bz4y2y9h6c4W0zfaHIqCNQs4Vyn1EaXUl5RSlwPnAq1KqesTn9ER0zCZUUrxpbtfo6s3yn9++Gj9sH7hFtjwHCz7f1CYo+iiYdxzUnM5154/m8dWbeeGh1bpmU2nwBX36oQXt54FW17Jr5AGg+ZzwBKl1BeUUt9XSn0RWOLMHw4/BL6nlJoFfA+4eZTkHEA8rrAFGqorKAv7aSwPp1kAKgsDnN2pO1/93tyu1pYI7TWFLJxZgVd07yjRMekp72Bf0axUx7fQSdVte5MFarsKGljUPLjrb6Igq0pL660Vla7KY/SWBERcBWczC5Y6nbze0lZOnKn3F/AO7MQtaCrn7M4a2qqLnOxuOPtOWbD8HpvZs1roDuvR9NLKOhrLUx1YJRaddRFmVRWmZVpLdHrTC9gmUs1L0tqmxbUI+WwUwvSyULLD7Y6t2V06l+6EoicWW2tOx19aj2VJUikFcZJoWAS9NjPKAsn9xsWjs+YBTD/RZRl0WQlLGphdXUR9SYh+T+oYS4pT1pBMa0PiOkqqci5toTDggco2eqedBEA00pT6Y2Q671efRFfBdITsaco9lqTHKklq/1b9ceDLiKXz5752a50sc4nrq702Qnu1c4zeULIN4rY/qdQlE0XE+tLrdpG95EDSmpTD+pPE0SwSteDS+vaWBcESYjVzU/NSjTtAZ/N7bGqK0zMnZw5yRH1F0PnX4Nft1d2XqG/ltpylklyEfHZSCSSUXv9rAK5Bm3hJoz48sdNiJgEompb+2+NLKuNl4UGSxgzIAJhjvcJq8IWSsWa51Jdc/7dzKcOjyKEoWMcDz2XMex44Icu6BsOw+e1LG3lk5TauOauVlqpCbdV47HpoPhOOviTf4hmOkCtOaOTy4xu4+U9r+e1LTtbr+uPgEw+B7YMfn6uLSBsM+eftjN9ryZq0Oh0RqQTmA3c6s+4E5otIRcZ6ERFpdH+AjJ7JoRGLK/b3RrEtIeDzsqilPGtR20Sii35fMZQ2gdNZ0nI531pGfF4fVoaLYCxcCSJEQ5XaZafhRDjqryFciVKKPZHZNFcVJzuhufozQa+NINQUB1Gu/QLYtlMcFyHmLCwMeCCWKoi6sEl3CDfXLcNXexQVhQM7bwnnpKKQNzki7nG5WvVG4/TH4sQsP63VhYQDPvaUHMXW6iW0zDkJ2+UWdSA0DY9tU3TMxUSnL0oeQ4uTlS7RMS8KerHq5hO3vCix8diS6giLhceyWDijgvaaIkSEuOVLs2YBnN6eGkw8qbk8TWlsry7ipJYqRITtlYs4WNZBWdNc/B4bQSUzuMV9hVhBbYHoCVSlWePwFxEKePHZFrvLUskzgqX1yemDkkqHDboANKRugsTxTisJMr1MrxsqrWVz7VL6gy7lWgQVLAOxUGhLaVdBE1url7DFKTJriVBXEnT9JWXBEncR3MIaKG9Jmc+yUFMc5NjppTSWhSkL+6gtLcJvO1JbHhJXWZqbpVja+uFW4BuOpzs8fUCtL69t6eveX4hLI8opT2JfSSpd6fybT0eVpWpoiSfVBtksLcMxvogMrI+WvoJFQ5m2Xge9HijXcW9proZNp0BDRpe+dh5UdULHhcQdBXqA8ml5sp6bYG0nzZ3HJy2waVbpHGKmuVZmPkS8YRCwYwfp9xZgi7C/cGZ6UeqMvxxwsogGMq2PY8ChJL5fDnxdRP5dKXVQRILA9cCK0RHNMBXYtOcgX71vJQuaSvnEoiY9tHjvP2iT8vnfyf2WNkworj2/g3d3dvOFu16lKODhrI5qqGiFKx+B2y/Sn2XfgAWfNufckC+uA24VkevQbvD1wFeAa0VSPQqlsgSx6HU3KaWDkJRSMRHZ7Mx3pyf7LHDtSAp9sD9GLK5S7jk5SOus1B0z+EYtDxLr0wkHEq44lg+IcqDuRGh0pXO2bJ2swbJzx5248NgWx0zX1qT3HSVKkvtIpTmLKthRcTylB15OC3J3K1S53X4GdjTdLpO90Rjrdx9gR/USvG2pzIYxTxDLtiDmskolsq9ZFlYWb4qm8jCrtu7j5OZyPHYlf3itBmJxPJawpK2S97v70JEUYHtTHe6t1YvZHo9StHd1VhkzLT5hvweCXqCHqLeQ3qIKsHY5yTriKZcpy0p2yHeVHwudrjTvtgdalhLr7iO6PlUE1vKHAF1Co8tbQrTsOMp2/cWRKd3imHDBq4uEkuetLhLknR1dA1woIyEv3X1R4rXzKNj2Knv9bWlWH9vSrpRnd9Yk67cVFhSjuiCtp1zSCMVDpatXyXZq8hdAUS00ngLvv6vjiGYuYc+eN9LeL0s7a2HdWojq62vOtAjS2sgDfQOVdksE2s7V/3/9d3pmLguWgzgDBvHihmQyjuQyt+S+MLAXJVbaNZDctzOvosDP/OnZ3SRFZEBq+URMZGWhzuxYUVyoMzNDaoDFdimBvvBAq2GgOJlgzF08Og1X7GUa1Z1EgGgsTlnYz7SSIK9s3JN9XYdcsaMABHXsW3e4HmV5iXVcxNLG9NTymc+d8gI/2/b1JAtBjyWHYsH6G+AkYK+IbAP2AouAj42CXIYpQDyuuOY3rxBXim9/6Gj9snzpJ7Duz3DW/4XiIxrYNYwjvLbFzR89VsfY3bGcP61x+pxFtdqS1XIW/OFf4N6rITr29SoMBrRL36XAaqALWAV8BLgFnZIr6nwfCd8BmjI+Jx/JBgMei5bKAupLQgOWTSsJDigg6k6akGCAMtTXrd23VH8yjbhyssJldqIRG4XSRW7TRp9zCOxa4He2VRTUMoYLdUfOdhIIxOyQthxEU0VC3f3PbJ1RgM7OucyuLtKuYQ5uZSzRJnHLiwSKBvzf3XFWYietcomOrjsBYWt1IefPqU1ayBJGKdvSxU7rS0MpBdHVmVWWj5jHdc4y6qWmHZnL4pJI5uDzWFpxUApRCn+vTrlo9+7NGieXxF+AN1iYezlQXNXArrJj6fOVJNstcVwhp6Pqrh9WEvZxWlslLRm1z+bWR1jYVEa4tBZ/+zLOOzr1Tj96WiS5bZ/HIuLEAc6ddxxHHbsYSmekWmEIRUavk3FdWjYUVOg4H4BgJOWCmSChTGzRdgJf04k5Xclaqwtd52EIuZzlBf36nHj3D6xXLiLE7CAKC5W8TiXruUvcVyG/J6srbIKm8jAzXO6tqDjNFQW6SG88qt+zAzbutv4M3s6JW8jKdNl1YuPmN5RQFwkOiHf02BaLWsppLB+kfIJzLnLeAwC2l8D8i6lo0DGDmYlN3DImOHZ6CUs7qge/J0aJQ0nTvg44UUTqgVpgi1Jq/WgJZpj83Pb0uzzzzi6+8cGj9Eto70Z4+CvQtFgXFTZMKgr8Hn768QVc+qPn+PTPXuTHHz9Ox08EiuCSO+CJb8CTN8D2N+GiW7Ubk8EwdhzJBbcBqBMR27Fe2ej35Ab3SkqpPSTMGQ5H+uL32BbFQV/WZcdML02LdTq7syanUpJG34Hket2Bamich/egFzg4sINnWZSEfUh3nJpISnkbdCTaIeTzcEZ7KaHV2kWqpaaEg5sLKA56KY6EafeWULclmFYbyN1enhwuY4V17VDXnjbP3XFuKA3x5tZ9WeNsnL1QWxxk896DOj230xaWCFFPAYqD2gIfLHWawCWTLUTjGbIljJ6egcrt9LIQO5z+d3o8krv9BK2BpbY5Z1oE9uzRid1VnD5fBF/fnrSsb7nw2QOPe0Z5AWt36gQYYZ+H7aFqrHgfdmwNxFNp7ZvKwry3q5vygvRrrigwMFOcx7aoLk4ds20Jc+sjeJw069mwbQu7ujV95nDukbKZWonYvjLnKouay9nR5RrA8xVopdelAGfb1UnN5ZQXuK1aGYpWJi1nQc8+6rr/xN6DfYSbTxywigBbq08FFKWBXUD2uC/IUlg5Bx7boqO2KHkeLRVNidh3QGfkc4o7ZyVXMorE4kQsX6wnfYHjVlgc9HJsY+5ixaBLNTy8citNmcpW8xm6ftiBoQdp2qp1evpsg0WZmT49toVn7L0D9b4PZWURKQNOBWqUUjeISC1gKaUGqucGwyCs2LCH//fgKs6cXcUlx9XrIcH7/kmbmj9wk3ETm6QUh7z8/JMLuOSW5/ibH/+FGz88l3Pn1OhRtCVfhuqjdPbIHy6Cc74FR19qrgXDmKCUeu8I/rtdRFagLWC3O9/LlVLZq5eOIW6FxJfDjTCxSrL7Figm7Nej73VlxVBYxYywwhJdByj9zzYhr4fTW8vB1cke3l0r2vXNEcDvsfE7lgxEZxUjtER3DLOQiAEaDm4lKJkNLkNh2bLXcZsToTaSULA8SWXTEthZfhzdHoHq5qz7Oam5nO37etLdFyONuoNb0TZg/WBNK2x8m95AWboF0H2qxEoWiz1hZhkey1H6LJt4HMSOs6fqRHz73qNneuuAfQzYp8/m6GkR1qpT8DuxeVVF/mTH3LaERc3lbH9vJ9audKtdccjLBXOHctfLTao47jDIVaup/QPw5r06NiuBZWs3vEhDTktMWYGfMreiJAItZ+q23bMeQuWICKe2VmIJPL5KlxLJmSAhl4LuLwR/IaXtp1DatS2Vjtz9V0n9PxZpYldZPFmQO5OEhTeR7XMwLEtorynizS37EBVL3f+JZBWu2K9hH49bZmB/4QzAVTcsy8BBLoI+O/v1Y3vB9iIHUq6rmVUMVpKQ7AAAHatJREFUEgS8NufNqU27x05uqeBAXzSn4p4Phq1gichi4C7gRbSr4A1AC/B54PxRkc4wKdl7sJ+r73iZysIA3/rrOfoB8NJP4O1HddZAV/C1YfJRVuDn1397Ap/62Yv8/R0vs3lPO1ee3KSvg9kf0CNsd/8t3PMZWPMQnH2DySRpGHVEpBj4R2AekObrpJTK4lszgKuAn4rIv6MDWq4YcSFHiUT9qGRHsnYe3j3vcez0UnAygFmWMKOiYOCfE+5NVnp3Ive4iAxcqXHRgP8nO3vhgVnOGsvCVBUFtHJ2GFi187A3P8U0l1tlU3k4Naou6TImY8QQYp4Q0UHctAr8Hgoy28myoLoz6/qB4ko2TTsXSHdjTHcRTCkalYWuzmzSPVPh9wfYXzgzLWlBpquWm8byMI3lKYXPrYjbllAa9lFaXcgWp9jzUNaTUcEbgN59KQtgAo9PW4ky44UgLevd8PbhdMgrUxbPzLToA2pyDXfQr3hazlAHt1tuOOinJyOphptIyMcZ7VXDvt4by8KOguW47Va2Q0V77j94AtoNdwjrZ2IAIOYJ6zjOTS85BzNyg6BuC3lfFhfABJnxl6Vh3wDrVb45lKfTd4CLlVKPicj7zrzngQUjL5ZhsqKU4ot3vcrWvT38+qoTtN/1zrfgwX+FGafqJAeGSU9J2MftVy7kn3+9gq898CZvb+/i2g/M1nVsIvXwsfvg6e/AH78B7zwOp30ZjrtSB2kbDKPDb9B1Hu8GDg6x7gCUUquAhSMt1LConZfmRneozJkWoaIgQEmig2J7dGcrHhu681Q2U69TOuMw9uxsuzBL53KQ0fSj6yM5lw2L8mbmLctugRqMhNdfZlzbkeC1LNpritjf4yR5CHjY3xNNH73PdQ4SHWIVT6bNTqx6envVgFpFg5FZjyqxsYTilQ/9ikR2vf4st2O22LlRYkAyFV8YDu5huHbabKTlnIkEeXGI9Q9lMCF5+lRUJ1rwFw2agZHm0+HAriHv9fR086Pjd1ca9rGkrZINuw/q5BwTmEN5SjQqpR5zphO3Wt8hbsMwxbn1qXf5w+tb+dez23Rdkmgf3HWl7hz81Q8HfwgYJhUBr813L53Pt8tX8/0n3uHF93Zz06Xz6Kgt1g/vkz8H7RfAA5+HB78Ay2+HM6/XxYqN26Bh5DkeKFNKHWkii7FnMLefYeC1LRoy3e3EBmJDJxgQybp/EaGhNETI52HV1n3p62ebHrCB8fcu8HtsFjaVURIeGG90uHhsYVZVyup0VF2El957X9cqShAshf1bBrZJImZGJGl9TChE2VL1D4ZbifBksaTlRcGqbNcWrKLaPOw8xYC4xemLoHuHtqSNECe3VAy90jBJWJrilg+sA0O78HmDw0oqlhYv6j0EV89DpDDgZXbtyN1j+eJQnmArRWRpxrwzgNdGUB7DJOZPa3bw9QfeZFlHNZ862Rnt/OPXdAafD3wXimoG34Bh0mFZwjVL27j9kwvZ3xPlwu89w02PvUVPIkNVeTN89G748M+gZw/c/kH4ybnw3rP5FdwwGXkKGMSPZoqRdNk7/MGMeQ0lOvva4TAOFKzZtUXJQsYJqosDrsK/R443I+FERaGfZZ3V6fPrF2gPj0wrpYpRGvLR7y1Kq2V2OLg7z0UJFzmlUkWR86Fh+Qu0deUIrLMjIkamJdAb0J4WR0Dm2MJIurgltr23uB1P/UKdTXEESNMzA7mLPhs0hzLE8Tngf0XkfiAoIjejY68uGBXJDJOKtTu6uPqOl5lVVci3P3y09mle+wQ8/V86Y2D7efkW0ZBHTmou58HPnsJXfv86//nIGn794gb+7dz2VHrV2RfArGXw0k/hz/8BP16mRxFP+Ds9f5TcFQxTir8BHhCR54Ft7gVKqa/mRaJ8YqWsIyPLMLc3CgrW4lkVaQWHB6XlTELRXkIF48BNyfZCOEsChHAlTW1zqS9r5S8buoHDP12JznMi/ipBcdALPTrz4lRlNFJ856oTd6ic1lZJd280bZ6I0FFbjN9j4RvB85bWDsZdf0gOJU37cyIyB7gcuA2dfnaBySBoGIq9B/q58mcv4rUtfnTFsdqXeM8G+O0noHwWLP16vkU0jANKwz6+d9l8PrJwJ9ffu5Krbn+Zo+qK+dvFM1jWUY3H44eFn4Z5l8OLt8HzP4RfXgYlTXDcJ2HOxVBQOfSODIbsfA1dGHgd4A7wyIdzVP6RgZn2Rn4fY+siGBlGFrYkozxCH/Z56O6LDr3iYFgWUjsXL+D16DilXJnXhiJZ58qXPljl99ic0lIB4yyBwFhwXGMp0djo3P4jpbMVBbxZU+Q3Vx5iso9hMJwKD4YUw1KwnJoejwFLlVI3jK5IhsnEwb4Yn/zpX9iw+wA//+RCneK3/yD86nJdUfySO7JnAjJMWU6cWc79/7iI3760kZufXMvVdyynvjTIpQsauGj+NKqKQnDi1bDwKlh1Hzz3A3j43+CRa3XK3bmXaatWnt1KDBOOS4BZSqkt+RZkXJCMhx3hXtWA+k651su/i+BocmprBdHD1YaykHAp7B8k89pgFPo91EWCzHK7dE7xWNfacZTyezwwnNp2hhTDUrCcwolNHFrMlmGK0x+L8/d3vMxL69/ne5fN5/gZZTpS9n//WcddXXKnjrExGDLw2BaXLGjgQ8fW88jKbdz21Lvc8OBq/uOh1Zwyq4JzOmtY0l5JeceF0HEh7FgNK+6AV38Fax7UleXbz4e282HGYqNsGYbDWmDiJbgYbUazUzXYtid5wqORLoCaSMQQjR+egmVZMmSRWMPIYWUkJZkIDBC1fFb2DI8G4NBisK4HfiAi1wIbcblNKJVZpMAw1YnHFV/47as8vmo7X7uwk3OOchJYPH8zvHIHLP4CtJ2TXyEN4x7bEpZ1VrOss5p3d3bz25c2cM/yzfzL6lcRgWMaSjiro4rT2+uYccZ1yOn/Dmv/CCvuhNfvhpd/Br4CbdlqO0/XThnD9L6GCcXPgXtF5L8ZGIP1eH5EyieS8T3S282x7dp5sO2NEd7n5CeRNdCe5IrpZCFx5VcXDb9Ib74ZYMGqmZMfQSYIh6Jg/Y/zfQUp5UqcaRNhbkjSH4tzzW9e4Z4Vm/ncmbP4yMLpesEbd8ODX4TWc2DxF/MrpGHC0VQe5pqlbXz+rFbe2LyPR1Zu4+GV2/j6A6v4+gOrmF4W4rTWSpa0Hc2CC04jIFF490l48z5Y/YC+/iwvNJ0CrWdrZatker4PyzB++HvnOzMoVAGHU+RpcjDWrnplM4847fxUZHpZCNsSppWMoFtbXnKzTw0sS1jSVqlrP04QjIvgoTHkmRWRaqXUVqBpDOQxTHB6+mP8w53LeWTlNq5Z2srfn+a4AK79E/zu01C/EC66ddK7fxhGDxGhs66Yzrpi/s+Zs9j4/gH+uGo7j6/azp0vrOcnz6wj6LU5qbmcJW2tnLZ4ETXn3QgbXoBV/wur7te1tQAqZ8OspdCyFKYdZzIjTWGUUuYd5yaZ93sUY7BMh23EEBEd4zyS+B1rf8i4Do4GhVmSU4xnzN16aAynN7EGKFJKvQcgIr9TSn1wdMUyTET2Huzn737xEk+/vYuvXtDBFSc06gWbV+hsb2XNcNkvwTd1070aRp5pJSE+ekIjHz2hkYN9MZ5du5PHV23nj6t28Oib2tOrvaaI01orWNL2Oead8X+x338H1jyk47We+W946kYdt9V8pla4mk/Xvw2GKc9odqtMl21cEy7TCYP8I5+RzjDxsEwawUNiOApWZoueOgpyGCY4a3d0ceXPXmT9rgN8+0NHc9ExTlXwzSvg5xfqSvSX32U6rYZRJeizWdJWxZK2KpRSvLW9i8cd69bNT67l+0+8QyTkZUlbJUs7/ppTLvsMwdh+eOdxrXC9/Qi89mudorrhBK1szVqqg3nNaPukRkSKgOuAxUA5rnefUqohT2LlkZGzYIkISrkjC5ILjnjbhlHGKFcGw2ExHAXLOOEaBuXJNTu4+o6X8dgWv7hyIQtnlOkF7z0Dd1yi64l87PdQVJtfQQ1TChFhVlUhs6oKuWrxTPYe6OfPb+/gsTe38+jKbfzu5U0EvBantFSwtGMBpy87j0jAhk0vacvWmofgka/oT0kTtJ2rE2XULzCFjScn3wemAV8FbkfXfLwGuCufQuWdEVCClnVUo7J2JYyCZTBMJNpriqgYD8W3JwDDUbA8InIaqSdh5u8pmmHJ0BeN85+PrOHmJ9+htaqQH11xbMoHfPkv4L5/gpJG+OjdEKnPq6wGQ3HIy3lzajlvTi39sTgvvLubh97YysNv6GQZtiUsbCrlrNlVnHnMNdSd/u+6IPZbD8HqP8ALt8Cz34VQObQu08rWjFPBa2qlTBLOAtqVUrtEJKaU+r2IvAjcB9yYZ9nygKMQyZEPJvg8rphbY7UyGCYss6oKh17JAAxPwdoO3Ob6vSvj99TOsDRFWbuji3/65Qpe27SXSxfU85XzZutsOPEYPHodPHOT7nx+6CfGLdAw7vDaFic1l3NScznXf6CDVzfu5eGVW3nojW1cd99KrrtvJUfVFXPW7CqWdl5My7GfRHr3w9uP6iQZK++F5beDN6TjtVrP1a6EJhh8ImMBe53pLhGJAFuAqVmsL+HSN5rWWqNsGQyGScqQCpZSqnEM5DBMEPqicX7057Xc9NhbBH02P7z8GJZ1VuuF+7fBPZ+Bdx6D466EZd8Ee2JlyTFMPUSEo+sjHF0f4Zqlbbyzo4tHVm7joTe28u1H1vDtR9bQWBZiaUc1Z3WcyrwPXogV74f3ntLK1qoHdCp4sWH6idqVsPUckwJ+4vEKOv7qMeDPwPeALnSipylIQsEa6cyaQ9TBMhgMhkmAyUlsGDbPrd3FV+55nbe2d3F2ZzXXfaCDqqKAHul89Vfw0JegrxvOuxGO/US+xTUYDouZFQXMXFzAVYtnsn1fDw879bZue/pdbn5yLeUFfs6cXcWStg4WnHYyxWd/C7Ys14rWqvt1rbcHvwjVR2k3wtZz9LQZrR/vfIpUj/8fgW8CEXTtx6mHiuvvEXARTCPWl5o2sYwGg2GSYhQsw5Cs2rqPGx5czeOrtlMXCXLrx47l9PYqvXD7m3D/5+C9p6HuGLjg+1DZll+BDYYRorIowOXHT+fy46ez92A/T6zezsNvbOPeFZu484X1iEB7dRELZ5SysOlKjjrm89TGNiOrHWXriW/CE9+A4gYnSca5Ojuhqbc17lBKrXVN7wA+mUdx8s9ouQhGD+rv8hbj4WAwGCYt5i1vyMnrm/Zyy5Nrue/VzRT4PfzLslY+fmITQZ8NO9+GZ/4LVtwB/kI4/79g3hWmgLBh0lIc9HLB3DoumFtHbzTGivV7eG7tbp5/dxd3PL+eHz+9DoCSkJfOugV01J5JR1svR3U9Q822P+J78Tbk+R/omMRZy7SyNXMJ+ML5PbApjogcA/QqpV53flcA3wE6gWeBzyuluvIoYn4YNQXLsWAFTbyiwWCYvBgFy5BGfyzOE6t38NNn1vHU2zsJ+2w+ffIMPnPqTCIBD6x/Fl64WQf5e/xwzMfh1H/VBQkNhimC32OzcEaZU5Kghd5ojDc279OfTXt5ffNebn1qLf0xBTQAH6PC/xHOD7/JabzA/Nf+l/ArdxITL7tL5tBVvZBo/Yn4m44nEolQ6PcgxqVwrPgOcD3wuvP7f4Ba4BbgUuAG4O/yI1oeSboIjvCgWbRHf3sCI7tdg8FgGEcYBctALK5YsWEPD7y2hXuWb2JXdx9VRX6+eHYblx5bS/Hu1+HP18Mbd8O+TeAvhpP/GRZeBQWV+RbfYMg7fo/N/IYS5jekMmb2x+JsfP8g63Z2s25XN+t2drNhbx03dp3M++oA07tf4cT4yyzc+Sadu36AvfL79Cub11UTr6kZvOubxaZQO92FTZQUBKmNBJlWEqQuEmRaSYi6kiAFfvMIHwHa0UktcDIHng10KqXWiMi9wDNMRQWLLIWBR4Kao2HrqybjpsFgmNSYt/MUJBZXvLV9PyvW7+GFd3fzxJod7O7uw2sL57YW8tHGXubaq7DX3wo3PQW9+3QmqeYz4IzrofVsU93dYBgCr23RVB6mqTyXC+CZHOiLsqurjzfe34V67zn8m5+lesfLdOz/M77Yw7AfDnYFWCvTWR2t4u1YDU+rGtaqWjapcnyhQkfhClIXCTGtxJku0UpYcdDEuAwDD5DIvHA8sFUptQZAKbXBUbqmHqUzYOtrI29pCpXqEh4Gg8EwiRkzBUtEZgE/BcrQtbSuUEq9lbGODdwELEMPn31TKfU/YyXjRCceVxzoj9HdG2V/T5Su3ig79/eyo6uXrXt7WLerm/Xb97B75xZC/Xuok520+XfyneJ9tJbvpLx3I/badyER6l3SCB0XwozFMOM0M+JoMIwwIZ+HUKlHF+ieWQ98SC+Ix2DnW7B5OcHNL9Ox/U1m73oL2f9k2v97CLN7Xynb9pawob+I3fEQqwnxkgrSRZCYJ0xhOERxQYhwMEAwECAcChAOBikMBQkHAwR8HnzBQryVLQS8NkGvjdeWqeSi+Aa64X8NXAI8mlggInWkamNNLSpa9cdgMBgMh8xYWrB+CHxPKXW7iFwO3AwsyVjnI+iiji1oRWy5iDyqlFo36tJtfAl+9ymdSlksQJy0ys7v5DRDLM/2f9GBwpYHLK+etr3Ob9cnx7zN+/u5a/lW+pVNPxZxBbaKYasotopiqSge9HSAXsLSS4gewvRQJL3U0MPJ0k2pdBGiR5fT9DvHrYADhRBohJqjYN5l2oWjeg4U1Yx6sxsMhixYts7GWdkGcy8FHEet3v2w622dZGbfRgL7t1K7fwu1+7cyd/96VM8+pHcfkoifATjgfAbh2dhsLu3/t+RvEfBYgiWivy39PauqkF/97Qkjfrh55gvAfSLyQyAGLHItuxh4Oi9SGQwGg2HCMiYKlohUAvOBM51ZdwLfFZEKJx1ugouBHyml4sAOEbkHPbL4rYztRdD1SdxMB9i4cePhCblzD3hmpjInqTjEFVoDUc585bilK71cuZYlp+Pod7TKWB6HWD+oGMSjeoQ67duZVjGIOb9VNCne+UOIH0eI4yHmCRKzA8Q8AZQnhOUL4fGX0RuOsD0UgUBEZzELRKCwBiL1ECgeWKNndy/sXnd4bWkwGEaREig6Tn+yoRT0H9Q16fq6nedOP8RiqFg/vX19dPX0cOBgDwd6eonG4nRbYf5POEJPNE5vNEZvf4yY0lbxmPOJK0VpuId169YdtuSu5/O4KYCklHpKRBqAWcAapdR+1+L7gV+Osgg2HMG7y2AwGAyjyuG8u8bKglUPbFJKxQCUUjER2ezMdytYDcB7rt/rnXUy+SxwbbYdnXzyySMi8MTl/XwLYDAYJjHXj8xmaoB3RmZTR46jVL2UZf7qMdh9DZh3l8FgMEwAhv3umqhJLr4D/CRjng+YgXaG+RNwMjBehwSnobNWGRkPn/EuHxgZRwoj48gwHmS00S+ov+Rp/+ORv6DPyRa0+8PhMB7Obb4xbaAx7aAx7aAx7aA50nY45HfXWClYG4A6EbEd65WNrjOyIWO99WhXv8QBZFq0AFBK7QH2ZNnPGhFpdKY3jkns1mHgCh43Mh4m410+MDKOFEbGkWEcyThuLFfjAaVUL/DUkWxjHJ3bvGHaQGPaQWPaQWPaQTNC7XBI764RriCYHaXUdmAFumgjzvfyjPgrgN8AnxIRS0QqgL8C7hoLGQ0Gg8FgMBgMBoPhSBkTBcvhKuAfRGQN8A/Ob0TkARE51lnn5+gk4W8BzwFfVUqtzbYxg8FgMBgMBoPBYBhvjFkMllJqFbAwy/xzXNMx4DNjJZPBYDAYDAaDwWAwjCRjacEaK/agE11li9EaLxgZj5zxLh8YGUcKI+PIMBFkNBwe5tyaNkhg2kFj2kFj2kEz5u0gKlH3yWAwGAwGg8FgMBgMR8RktGAZDAaDwWAwGAwGQ14wCpbBYDAYDAaDwWAwjBBGwTIYDAaDwWAwGAyGEWLSKlgi8mUReVVElovIChG5ON8yZSIi3xORVSLyiog87UpXP24QkcuddoyKyNX5lieBiMwSkWdFZI3z3ZJvmdyIyH+IyLsiokSkM9/yZENEypwyCaudc/w7p/7cuEFE7nHuj+Ui8mcRmZtvmXIhIteO1/MtIuucZ80K57M03zIZRobx/iwcKQZ7XonI8c5zYo2IPCwila7/5Vw2kcl83ky1NhCRgIj8QETeEpHXROQWZ37O+2Ey3isicp6rn/uqiHzQmT+p2yFXH+twj3tU2kQpNSk/QLFruhbYB5TkW64MGc8DvK7pd/ItUxYZO4HZwM+Aq/Mtj0uux4HLnenLgcfzLVOGfIuAemAd0JlveXLIWAqc6vr9LeDWfMuVIaP7Pr4AeDnfMuWQcz7wB+C98Xi+x/N1aD5HfG7H9bNwBI8z6/MKEOBtYJEz/9+A25zpnMsm8ifzeTNF2+Am4EZSydqqnO+c98Nku1ecc/t+4tkOzAH2o40nk7odcvWxDve4R6NN8t5IY3QiZgF7gbJ8yzKIjGVAL2DlW5Yc8v2EcaJgAZXoVJu289t2flfkW7Yssk6Yji1wEfBovuUYRL4rgBfzLUcWufzAs0DTeD3f41Uu8zni8zphnoWjcOwXAY8CxwGvu+aXA13OdM5lE/WT7XkzBdugwLnOCzLm57wfJuO9glawdgEnOb9PAdZMpXZwv9sO97hHq03GrNBwPhCRq4DPorXcTyilduVZpMG4GrhfKRXPtyATgHpgk9KFqVFKxURkszN/R14lm6CIiIUu8n1vvmXJRET+BzgL/TJZlmdxsvFV4Hal1Lsikm9ZBuMXogV8CviSUmqq10WZDEzJZ2HG86oBbckBQCm1U0QsESkdbJlSavdYyz1CZHveTLU2mIlWLK4VkdOALrRl7iC57wcZZNmEvFeUUkpEPgz8XkS6gULgXAZ/Lky6dnBxuMc9Km0yYWOwRORlEdmZ42MDKKV+qJRqA44HviwiZeNNRme9S4DL0C+MMWW4MhomPf+Nfkl9N9+CZKKUulIp1QB8Ce0WNG4QkRPQI8Tfz7csQ3CyUupotKzCODzPBsMhMG6fV6PJBHrejDYeYAawXCl1LPAF4Hdoy9aUQUQ8wL8CFyilpgPnA79iirXDeGXCWrCUUvMPYd3XHG30VOCuURNq4H6HlFFELgS+BpyulNo2+lKlcyjtOI7YANSJiO2MNNjoOLsNeZZrQiIi/wG0AOePZwuqUurnInKLiJSNI2v0YqANSIwmTwMeEpGPK6UezqtkLpRSG5zvXhH5PuPQUmk4LKbcszDzeSUi64HpruXl6MH93YMtG2u5R4iszxt0PNJUaQPQFrkocCeAUup5EdmJtmDluh9kkGUTlblArVLqaQCl1NOOJauHqdUOCQZ7Hg523KPSJhPWgjUUItLumm4C5gEr8yfRQETkPOA/gaVKqXV5FmfCoJTaDqwALnVmXYoeyZro5u0xR0S+BhwD/JVSqjff8rgRkQIRqXf9Ph/Y7XzGBUqpbyqlapVSjUqpRmAj+n4eN8qViIRFpNiZFuAS9P1jmOBMtWdhjufVS0BQRBY5v68Cfj2MZROOXM8btGV/SrQBaDdH4I/AmaAzwKHjaNaQ436YpPfKRmCaiLRCst9bDbzF1GoHYPDn4eEuOxJ5EtlXJh0i8mugA+gHYsANSqlf5VeqdERkB9BHuo/n6eNodB4RuRT98C5By9oNnKWUyquyKiJtwE8dud4HrlBKrc6nTG5E5Cbgg+iH3U5gl1KqI79SpSMiHcDr6JfSQWf2u0qpC/MnVQoRqQJ+D4TR9/Bu4PNKqZfzKtggiMg64Dyl1Ov5liWBiMxAW+5t57MS+Eel1Ja8CmYYEcb7s3CkGOx5JSInAjcDAXTQ++UJj5DBlk103M+bqdYGznPtNnSCsH7gy0qpPwx2P0zGe0VEPgJ8EUh4n1yrlLpnsrdDrj7W4R73aLTJpFWwDAaDwWAwGAwGg2GsmbQuggaDwWAwGAwGg8Ew1hgFy2AwGAwGg8FgMBhGCKNgGQwGg8FgMBgMBsMIYRQsg8FgMBgMBoPBYBghjIJlMBgMBoPBYDAYDCOEUbAMBoPBYDAYDAaDYYQwCpbBYDAYDAaDwWAwjBD/H9beEyviuXZjAAAAAElFTkSuQmCC\n", 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