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@fonnesbeck
Created October 25, 2015 21:08
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{
"metadata": {
"kernelspec": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"display_name": "IPython (Python 2)",
"language": "python",
"name": "python2"
},
"name": "",
"signature": "sha256:d0ff3775ccd1b7845a3cd87dd8eb4803d77a41e4d1c8b13033e649cf5f5dcb04"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Answer all questions and submit them either as an IPython notebook, LaTeX document, or Markdown document. Each question is worth 25 points."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Question 1\n",
"\n",
"The data below provides counts of a flour beetle (Tribolium confusum) population at various points in time:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"days = 0,8,28,41,63,79,97,117,135,154\n",
"beetles = 2,47,192,256,768,896,1120,896,1184,1024\n",
"\n",
"plt.plot(days, beetles)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 1,
"text": [
"[<matplotlib.lines.Line2D at 0x112dca150>]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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tJ50rmFK7yMbUJ3+PBzxwbPDus5kjiYwUrRiWxirK6hnAJ4DNgJ2Ddz/Pm0hk9GjFsDRS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\ngma+9td/HUHzcm7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"text": [
"<matplotlib.figure.Figure at 0x1114d8c50>"
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"An elementary model for population growth is the logistic model:\n",
"\n",
"$$\\frac{dN}{dt} = rN\\left(1 - \\frac{N}{K}\\right)$$\n",
"\n",
"where $N$ is population size, $t$ is time, $r$ is a growth rate parameter, and $K$ is a parameter that represents the population carrying capacity of the environment. The solution to this differential equation is given by: \n",
"\n",
"$$N_t = f(t) = \\frac{KN_0}{N_0 + (K - N_0)\\exp(-rt)}$$\n",
"\n",
"where $N_t$ denotes the population size at time $t$. \n",
"\n",
"1. Fit the logistic growth model to the flour beetle data using the Newton\u2013Raphson approach to minimize the sum of squared errors between model predictions and observed counts.\n",
"\n",
"2. In many population modeling applications, an assumption of lognormality is adopted. The simplest assumption would be that the $\\log(N_t)$ are independent and normally distributed with mean $\\log[f(t)]$ and variance $\\sigma^2$. Find the MLEs under this assumption, and provide estimates of standard errors and correlation between them."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solution to part 1\n",
"\n",
"Here's an arbitrary (non-optimal) solution, which we can use as a starting point to improve:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"K0, r0 = 1000, 0.1\n",
"\n",
"logistic = lambda t, K, r, N0=1.: K*N0 / (N0 + (K-N0) * np.exp(-r*t))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"times = np.arange(160)\n",
"plt.plot(times, logistic(times, K0, r0))\n",
"plt.plot(days, beetles, 'r.')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 3,
"text": [
"[<matplotlib.lines.Line2D at 0x1114bbd10>]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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uHM32KN15G3B5maV/iB1EpC6m0gm8DbgAeEx4PgfYYmYrw/M7w5h1GN8whdeWhgkTxS0G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\nBEREGkxFQESkwVQEREQa7P8BXThffRi+OWcAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x1114bbe10>"
]
}
],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def mse(params):\n",
" K, r = params\n",
" return np.mean([(logistic(t, K, r) - y)**2 for t,y in zip(days, beetles)])"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mse([1000, 0.1])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 5,
"text": [
"34826.299294607059"
]
}
],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from scipy.optimize import fmin_l_bfgs_b\n",
"\n",
"opt = fmin_l_bfgs_b(mse, (1000, 0.1), approx_grad=True)\n",
"opt"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 6,
"text": [
"(array([ 1.02870213e+03, 1.30426903e-01]),\n",
" 9427.6719301474641,\n",
" {'funcalls': 120,\n",
" 'grad': array([ 5.45696821e-04, 7.27413862e-01]),\n",
" 'nit': 23,\n",
" 'task': 'CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH',\n",
" 'warnflag': 0})"
]
}
],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"K_opt, r_opt = opt[0]\n",
"\n",
"plt.plot(times, logistic(times, K_opt, r_opt))\n",
"plt.plot(days, beetles, 'r.')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 7,
"text": [
"[<matplotlib.lines.Line2D at 0x113d43510>]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAEBCAYAAACe6Rn8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nICJSYyoCIiI1piIgIlJjKgIiIjX2/+Mm83atWo5cAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x113d437d0>"
]
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solution to part 2"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"data = np.c_[days, beetles]\n",
"data"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 42,
"text": [
"array([[ 0, 2],\n",
" [ 8, 47],\n",
" [ 28, 192],\n",
" [ 41, 256],\n",
" [ 63, 768],\n",
" [ 79, 896],\n",
" [ 97, 1120],\n",
" [ 117, 896],\n",
" [ 135, 1184],\n",
" [ 154, 1024]])"
]
}
],
"prompt_number": 42
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Similar to part 1, but with a likelihood such as this:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from scipy.stats.distributions import norm\n",
"\n",
"logistic = lambda t, K, r, N0=1.: K*N0 / (N0 + (K-N0) * np.exp(-r*t))\n",
"\n",
"def likelihood(params, data=data):\n",
" K, r, s = params\n",
" return -np.sum(norm.logpdf(y, logistic(t, K, r), s) for t,y in data)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 43
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from scipy.optimize import minimize\n",
"\n",
"opt_mle = minimize(likelihood, (1000, 0.1, 1), method='Nelder-Mead')"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 82
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"min_func = lambda s: minimize(likelihood, (1000, 0.1, 1), args=s, method='Nelder-Mead')"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 49
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def bootstrap(data, nsamples, f):\n",
" boot_samples = data[np.random.randint(len(data), size=(nsamples, len(data)))]\n",
" return [f(s)['x'] for s in boot_samples]"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 52
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"estimates = bootstrap(data, 100, min_func)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 56
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"np.std(estimates, 0)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 64,
"text": [
"array([ 6.57049020e+01, 4.01655756e-02, 1.84341579e+01])"
]
}
],
"prompt_number": 64
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"np.corrcoef(np.array(estimates).T[:-1])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 79,
"text": [
"array([[ 1. , -0.30679739],\n",
" [-0.30679739, 1. ]])"
]
}
],
"prompt_number": 79
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"K_opt, r_opt = opt_mle['x'][:-1]\n",
"\n",
"plt.plot(times, logistic(times, K_opt, r_opt))\n",
"plt.plot(days, beetles, 'r.')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 86,
"text": [
"[<matplotlib.lines.Line2D at 0x1143b2390>]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": [
"<matplotlib.figure.Figure at 0x1143b2590>"
]
}
],
"prompt_number": 86
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Question 2\n",
"\n",
"1. Implement simulated annealing for minimizing the AIC for the baseball salary regression problem. Model your algorithm on the example given in class. \n",
"\n",
" 1. Compare the effects of different cooling schedules (different temperatures and different durations at each temperature). \n",
" 2. Compare the effect of a proposal distribution that is discrete uniform over 2-neighborhoods versus one that is discrete uniform over 3-neighborhoods.\n",
"\n",
"2. Implement a genetic algorithm for minimizing the AIC for the baseball salary regression problem. Model your algorithm on Example 3.5. \n",
"\n",
" 1. Compare the effects of using different mutation rates. \n",
" 2. Compare the effects of using different generation sizes. \n",
" 3. Instead of the selection mechanism used in the class example, try using independent selection of both parents with probabilities proportional to their fitness.\n",
"\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import pandas as pd\n",
"\n",
"baseball = pd.read_table('../data/textbook/baseball.dat', sep='\\s+')\n",
"\n",
"logsalary = baseball.salary.apply(np.log)\n",
"predictors = baseball.ix[:, 'average':]\n",
"nrows, ncols = predictors.shape"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 113
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# n * ln(SSE/n) - k * ln(n)\n",
"aic = lambda g: g.nobs * np.log((g.resid**2).sum()/g.nobs) + 2*len(g.beta)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 114
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This works best if you write a function:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"periods = 15\n",
"period_lengths = [60]*(periods/3) + [120]*(periods/3) + [220]*(periods/3)\n",
"tau_start = 10\n",
"cooling_schedule = [tau_start * 0.9**i for i in range(periods)]\n",
"\n",
"def anneal(periods, period_lengths, cooling_schedule, nbrhd=1):\n",
" \n",
" aic_values = []\n",
" tau = cooling_schedule\n",
" \n",
" solution_current = solution_best = np.random.binomial(1, 0.5, ncols).astype(bool)\n",
" solution_vars = predictors[predictors.columns[solution_current]]\n",
" g = pd.ols(y=logsalary, x=solution_vars)\n",
" aic_best = aic(g)\n",
" aic_values.append(aic_best)\n",
" \n",
" for j in range(periods):\n",
" \n",
" for i in range(period_lengths[j]):\n",
" \n",
" solution_step = solution_current.copy()\n",
" \n",
" flip = np.random.randint(0, ncols, nbrhd)\n",
" solution_step[flip] = solution_current[flip] - True\n",
" solution_vars = predictors[predictors.columns[solution_step]]\n",
" g = pd.ols(y=logsalary, x=solution_vars)\n",
" aic_step = aic(g)\n",
" alpha = min(1, np.exp((aic_values[-1] - aic_step)/tau[j]))\n",
" \n",
" if ((aic_step < aic_values[-1]) or (random.uniform() < alpha)):\n",
" # Accept proposed solution\n",
" solution_current = solution_step.copy()\n",
" aic_values.append(aic_step)\n",
" if aic_step < aic_best:\n",
" # Replace previous best with this one\n",
" aic_best = aic_step\n",
" solution_best = solution_step.copy()\n",
" else:\n",
" # Retain current solution\n",
" aic_values.append(aic_values[-1])\n",
" \n",
" return solution_best, aic_values"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 116
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solution to 1(A)"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Schedule 1: cooling = [60]*(periods/3) + [120]*(periods/3) + [220]*(periods/3)\n",
"solution1, aic1 = anneal(periods, period_lengths, cooling_schedule)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 117
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"periods2 = 2000\n",
"period_lengths2 = [1]*periods2\n",
"cooling_schedule2 = [tau_start * 0.999**i for i in range(periods2)]\n",
"\n",
"solution2, aic2 = anneal(periods2, period_lengths2, cooling_schedule2)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 118
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def plot_aic(aic_values, solution_best):\n",
" plt.plot(aic_values)\n",
" xlim(0, len(aic_values))\n",
" xlabel('Iteration'); ylabel('AIC')\n",
" aic_best = np.min(aic_values)\n",
" print('Best AIC: {0}\\nBest solution: {1}\\nDiscovered at iteration {2}'.format(aic_best, \n",
" np.where(solution_best==True),\n",
" np.where(aic_values==aic_best)[0][0]))\n",
" plt.plot(np.where(aic_values==aic_best)[0][0], aic_best, 'ro')"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 119
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot_aic(aic1, solution1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Best AIC: -416.611888647\n",
"Best solution: (array([ 2, 5, 7, 9, 12, 13, 19, 20, 21, 23, 24]),)\n",
"Discovered at iteration 1984\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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3KEkDgnhwYjR9g7xJmRiNWgUqlYojHx3CUGchbVcxabuKz37WhL6s/b6UKwcG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\n40fUFFzzhAAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x112d71090>"
]
}
],
"prompt_number": 120
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot_aic(aic2, solution2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Best AIC: -416.087321595\n",
"Best solution: (array([ 2, 5, 7, 9, 11, 12, 13, 14, 19, 20, 21]),)\n",
"Discovered at iteration 1748\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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9UGC/Eo8lZMQkGaVB41FKiiGUZlSXoKm7w2Q6s9IfC4ykqMmDv//Y7rwWjYZq\nbGkuSEdJ9+uLyyh3KAOXiatHFQ4OOTOW191axeRwyK/3owGAC2oq8MLuJtNnRIUXq9FYTWhO13GD\noiSr/vSz3HmiK4sz9o9slJNDbRFHU6/X3LepDg99bjJCfi4IhyopTWfNzc147bXXbN977bXXTFFg\ngxE6MamFG5Od/oC6mnZK9FMUBav/ehhX/fZD03aq/Tx6+RTc8Klx2okym5RTQeWErDnInRz71gmJ\nagHpot6sviQ7bYmSrjAmYGgVCVkxR3BZ9mKJSzLCxT49x0mWgXCxD5+uqdD6CjFHamHQJkGjBwMo\nuOczNbh4UoVpeybISB4zDfbwwiJ1sK0PsURmTv7vvvSJ3rBtoPFBQzeaumPpd+QMWlIKmo0bN6K3\n194H0NfXh40bN+ZlUIWCah2qg5n10ZhnjwYmc5+NJkvICpq6k7PDJW3yP2dcGSo0TSeXMV5U05AV\nI2enosiHoM/8cWbjowEMgUiPtzYTs9s3FfRyvTFJy6Nx3ocSlxT4NXOV3uJBE1KiQJAw1YtTzyk6\naDSjSgK4e+HE9APVaOs1f6aqIDPvQ4VxIX0fHzQY2pObaDKrUI14WBkiHdyFNLRJKWh2796Niy++\n2Pa9BQsWYOfOnXkZVCGonTMaQVoZwBLGzH7prRMMm8yZkBXbVtCSbAgkNlTazmSUDXRyS8gKEpIC\nv0Cw4vOTMWmE2b5Fi4TKusnMfLwTxCJoUuHWbwWopXYUB9OZVTOKM8+WaBqNzAga9h4UqJ+fXyAY\nXx7ElJEhowacZvYqDohJgtiOQ219+Ma63aZt6jnM4+uMqtpBISPPuiJquwL1uun3tyriiQHcP8er\nCD5OYUj5y+vp6UFlZaXte2VlZY7azmDghvnj9FWpQGgIrfoe60C2Tok3UVMY1NL0dmarBOOj0TPK\nbXSaA63ZPT9WM6EaDXWYszyiRY/ppjZGQKXC6JuTfixuhCeb02IXDEAATBkVMm2LSzL8jGlTUhQt\nNNrckpueX20fQPDrr8/AZ6eGmUWDwnwG6f1hERuTlBF9aNCjJc0WMvn12V0n9UZ6bjQp6z4DuWQO\n77gwtEkpaMaMGYP6+nrb9w4fPozRo0fnY0wFR1+V28xCVgExf4JRV+37fz5o679hI9T8AsGEiiCq\nS/3wCQRnVhVrl1Lwzy/sSzrWDRJj4pNkVaOxhvxa92/tjSMmG879VLAaTWWRDxNHODeEyzQYgC3n\nQhlfEUwlVEX9AAAgAElEQVQqIZOQFaMWnZYcSTUXkRCTsLSa41iBwgo2uz42Vux8TqywMl0EhTWd\nsUmtCRcagHVBMZD75/Dw66FNSkFz8cUX4+c//zna2tpM29va2vDUU09hwYIFeR1coRC1elq2kUqW\n+aWCCfM9diqKXVoZG8dzCwS/unoGzhhZDFEgeHzxmVpJleSkTrckLBqNT9NonJAVoHbdbrxzWC1H\n8y9/rEt5fsNHownhFHOAG9MZWw5GgZL0pQuIgn5P//zCXvzHliMmH43aj0Yx+WKsgoa9f6L5dACY\nTHVunjaNQIwkZDzxt6P6+a23Se/BC5PP6NKAq4n5vWOdptf9LX2UT7jpbGiTMrz58ssvx8GDB3Hn\nnXdi6tSpqKioQEdHB/bv34/zzjsPX/rSlwo1zrwiWAo1st956+Rkl09ihS0rbwf1BwVEktWPn/qB\nJRp1JhItU91+/0yLeLItp0UhtRbgxu1Ej/+wsRvRhGLycwFA0Edw9JSanHugtQ89MQkLJ4/QfTS0\nejONLosmZBxs7dO1SxmKyYfClodxjnKzhwqlk11R/OHjFnz7gglo7IphTFnA9sa9WIlbfVRuGcga\nzQCWgZwckHLWFAQBd955J/bu3Ys9e/agtbUVkyZNwje+8Q1Mnz69UGPMLTazzukjQo5mFbo765tJ\nh4LkKCXzOdUVekAU0BvPvHi/KRhAlhnNyP5Mma4W2ag2kaQuHjmmNJj2fDT66bda6R+rRlNTWYRX\nPmlDuxbtlZAV1UejCxq1ejPVaKaMCplaHlg1GrqN/rWWwEkF3devqTb/tf0E3jlyCueOL7O9p6ik\n4JOWXkwbVZzyvLmgyCfg0jNGYHdjd1Jb6vU7GvG5qWGMKjEEIk28pXTHBmZ4M8BNZ0MdVwmb06dP\nH7yCJQ0vLT0HPkE1m+lOa5tgAOsqPB12zn9KQlYQiRsCItPcDsNHAyRkrZKw7OzodvMbfnr7CRzp\nULUK2t5A72iZggqXGh6L1d8xpiyIMWUB3RFPTYJGeLNR7ZkQgmK/CDaAyto4TWBMZ6ZgAJLcx8YK\n3Zf6jI6fiupjYGGf6fFT0YIImlljSnDRpArsbepJ0oR//d4JiALB12cbflPr597SM3AbtXHL2dAm\n5SyxYcMGPb+EnRzoxEgIwTXXXJPfEeYZGvJqjmJi91Dv260/pbUnjs5I+ha///LHOvTEJZvrGTR2\nRbHug5OYO74Ml2gtCtixSppG4xcIYooCJxf/nqYe/d9jygJo7IolTc7PME3TemISYpKsaRBmM83/\n7mvF87ub8NRXzwIA3WGfCuvtWR/ll6aPxJsH23VBo2o0RjAAoRoNVG2Itg3Qz2+j0RgRhOa2D2kn\nNO39qKYybKnv0I9lYZ9JoSphq2Hzaqkdu+oO1lFYd4kNYNMZZ2iTUtC0trYmrT5ZoSMP4Lj8TCGM\nXZ+dGe3aL6eidv3u9DsBuvYAOJu29rf24eVPWvHyJ604Z1wpRoT8prFQH40oEDU+1GGIrG2eToqS\nrECwERLU13Pfpv34yqwqiARgDS7vH+80VV12M8lab4/VDi+ZXInKkB9FPkHXpCRN0NDwZpHenmLk\nI7Efh2zxibFfWVk2zJh25sxDbX0IF/t1zYya5KKWMGfr7+CMkUY4duEEjfpZW4MhKEmCRruX6lK/\nWkppAJqnFBsrAmfokVLQ3H777bbbDx8+jLfeegtbtmzJy6C8gDrowfwt9hsu5unV+TGN3PipsY4a\nEDtB//VgBxbPrAIANGkmENbEFCXJvp4Fp1di86EO7D5pRMZRU5ikAH6bawZEgqik4KOTPVg8o0oT\nYsaka82bcSdozCNjfTR07guKhqBRoGa++xmNRlEUXQsTiDWCyqxxs72FZMuYrc/o1uf34vzTyrHi\nH87Qxqputwoaq0w+v6bCeK9ANdAlRY0wFIlZaBzTAimswpDuUhrw4fzTyvVndqQ9gpoUIeuFxDbS\nkzPkcP0T6ezsxJ/+9Cfce++9uPfee3HgwAHccMMN+RxbQTHqeyn66mrSiJC+TKT+glwSFAl8KZzt\n7AT97hGjU+azO08CMCoDqO2Nk89DJ6Pndxu1yqhg6I7aO4b9oqA63EeG9NBg9rTWCdeVoEm6hnEM\n1bYCPoL/3afWzlMUVeMbXaYGGtBw8FQajWBRaXQfjWxU0nYaKZukqQsai7e9J5a8GPiFZj4shH9B\nkhWciiQgCmrCKito39XC1q1VKoyACEXXglp6YrjpuT35H7BL2Lp9nKFLSo0mkUjgvffew5tvvomd\nO3diwoQJ+PSnP43m5mbcddddjlUDBivUbPT//lKPKSNDePjyKWjvU7WHdKvWTNoIUESBQBCcEy3Z\nyZT+s5MpjEhNZ35RACHGRBiXZEiKupoPiMRkmy/SfFLP7jyJ2y88DQBMBQ2jkoy7FtTg7foOPUeH\nHR7VDt440KbfQzqsq9UA8zAjCUkf1+sH2vV7jSUUlJezvV8UPWFTEMxC2BpOTsObD7b24eipqOmz\nswu8MD9najoz75cqIrEQU+SGnSdx7FRU89GYK3DXt5uDOCh08q4ZUQSfoIaFD7TpnI6RazRDm5SC\n5uabb0ZFRQUWLlyIJUuW6B0uX375ZceS94MZ9pZCfrU2Fo0eSzehJrIUNKpwc9BomGmBRkHVM/4R\nNeqMLUGjbv+3Nw5j54kuzKguQUAUEJMMIUQbd7EcaDUyzuOSgiKfAEnWCluKZkE4Qqu19exOtdCm\ni1iAZNMZ86BplQJTHTJFMbVaUF1Qit5qQQAxlSyRLfXTCFQh+5MtR0zXc4o6swotIHnStjuOPov/\n++pB/PDzk3EBY07LNc096mIg4Ev20ciKgtGlgeQxK8D8CWW475JJeO5DtbWCb4D9bu1y1zhDj5Tr\n9IkTJ6KlpQV1dXXYv38/+vrs+7oPFQiMelD050h/l+nK4WeTeGlEENm/z54yrgVesLLsz3WtiEla\nZQAAdDqsb+9DV1SCgmQB+blpahvsMqZ/ToelfHzQJ6C9L44TXTGT9gGoxSkBw5Tk5q6t+7CP8tq5\nYwAYmhbdn1bABlRBEU0YYjdd1BnRwst6NSFmegY2AzaZ4bS/vXGLqczmuNKgDxfUqEmjuy0VIpp7\nYvj5348nH5Ql9A6CogCRGG0S/n7kFF7b346SgIAjHRH8gWnpIENBkU9U/TpaxetMg1vyDX3e3HQ2\ntEmp0Tz00ENoamrCX//6V/zud7/Df/7nf+Kcc85BJBJBIpHb5K+XXnoJzzzzDH75y1+itFTtjrhp\n0ya8/vrrEEURN9xwg57Lc+zYMaxduxaxWAzz5s1DbW1tTsZACEEkToslmr/4qXwRqnlKRgkya9zU\nEUmYWkhbYTdTXwYdxejSAF75RDNfEeowNx8va4UoWcaUBTF7TClOqzScwQmLPyLoE7C/tQ/7W/tw\n0cQK0yRwUNN+zh5bipN1bUnXPNzeh5uf24tXbzrX9j5Y/nTDOXpi5NRRxQCM/kaSwvhWiFpVgCII\nZh9NRGs+R1H9VcazYn00dkMxTXLaP2lYs2VzEk6a/dv1p7Dxwybccv54hyMzg14n4BNMRUV3nlCf\nS7FfxJsHO/DmwQ5cOUMNGjnWEdVNrT6B6IsPIDtTbz5o6aEVxj0eCCevpPVwV1dX42tf+xoef/xx\nLF++HOXl5SCE4J577sFvf/vbnAyipaUFu3btwqhRo/Rtx44dwxtvvIFVq1Zh2bJlWLNmjT5prlmz\nBjfeeCNWr16N+vp67NixIyfjIDAcw3Ty0TUahx/lf1w5DeVBX9Z1pFiTlxV2AqTnpxNOkd/46Aix\nL0EjK6pgsVJV6jeVjLeOnRWqAZ9gmmTZpEogeQI+0qEmOO5iOk86ha6y1zk9bIQLKwo1Caqvrdqk\nqrAY5zzcHkHQonmZ/EraW07VH8yBBeqL3Y09pn2c7sFpqs6mwVoqDI3GnEdDv5fFjElUVhQcPxXF\nb7af0GvxBUSC/S29+gMYKHXP/vV/DwDI/fPiDCwyCqWaPn06vv3tb+Opp57CjTfeiKNHj+ZkEE8/\n/TSuvfZa07Zt27bhoosugs/nQ3V1NcaMGYO6ujq0t7cjEolgypQpAICFCxdi69atORkHYcJm6e9Q\nXxU7CBpRIPCJJOs6UtTRbQe7lY7rIy1U2Tqx2s14smKYnx7+4hR9uxq1ZOxnLR/PCgC/paimrKiT\nnR6pZRk6zQ9i/T7WOc0qNK3XJMRITqSvWezMjVOZzHzrR5Uu6sxkhnPYZ6yNwLa7Vr6gzyDoE3Qf\nzYq/HNIDOVgT5+7GbtzwP+be3jWVRWpFBe31QBE0+sJlYAyHkyeyitkNBAK4+OKL8b3vfa/fA9i2\nbRvC4TAmTpxo2t7e3o6RI0fqr0eOHIm2tja0t7cjHA7r28PhcFJ16WxhtQJJ99Wov3An0xkB0NgV\nw483H8nqmmJKjcb4N+2O+NTWBgDqCpVFAEladcuysZpna3VZ+7lYhSR7qzKSBV6RX0Rcojkv5mOp\nqSaV4LW2BKBjoiiAJRjAcq8W4cy2FADUSbm5O4bDmtBL56NhN9nJ/Ge/OQsLT3eKsLT/XqSbN2VF\nwXUbPkqzl0FMi4LziwICIsHDbx7G5kMd+FAznfUxPiW7njr6I6TBDi46dBYCo1cRlzRDGVe1zvrL\nihUr0NHRkbS9trYWL774Ih544AF9m5dfOMJMYHQirgj5UDtntG20FmBMM9RWPrGySJ/g3F0zRdQZ\ns73Lkvdi1bBYExx9R4aSZHYqC6jO4eOnjDFaV7c1jP/m7NEleP94p2nfIp9R1t/p02Insv2WBm9x\nm4oS1twaWTZHnQFqBBV9zT4yGoZNKQ34cOwU035bb0hjbwJjkx+t7993yUS9IoMd2QZxJSQFJ7tj\nSWN3gg1O+PYFE3T/XItWiJQ9h50MoXlW9P5+ubUB910y0fPoUbbKNmfoUhBBs3z5ctvtR44cQVNT\nE+655x4Aap+b+++/Hz/60Y8QDofR2mo4h1tbWzFy5MgkDaa1tdWk4fQHtvw6/eL7BIIb5ruv3KyG\nRLuLxvq/nz0d0YScVqM5s6oYB1v7TOGrtqY8q49GBvzMJ7zpxjnwCQTFARHNTO4MK3QANbT7v74+\nA0t+97Fq+zdN6rIqaNLYOtjcHascHV0awOmWzHTr/cQkQ0jS9y7V6r0RG42GPX5secA08epttWEf\n3szOy+xYv3nuGFw2JfV3y8kkkG69RH0s0YQMn8MihmXaqGL8TUvMLAmIqCjy4RQTLTh/Qjn+flRd\nENiWp9EsoPSd1w+046tnV5tMjl5Ax8OjzoY2BSqeYU9NTQ2eeuoprFmzBmvWrEE4HMbDDz+MyspK\nzJ8/H2+//TYSiQSamprQ2NiIKVOmoLKyEqFQCHV1dVAUBZs3b8Z5552Xk/H4BMPXYle00A3tfXGM\nKHYnv2nDtXQajUgIgj7BtKqttFRNtutPpsA8AdPJd9KIkMm01d6XHEFIgw1CfnMwQFxStLFopjOH\nxxRLOAcblAZ9+JmWVU+x1uH6oKFLrz9GQ591wUMMm/7qtw7j538/bsoPEQVi0qjYxmd242W3scNw\n5X9Js49TiPPX/1utiReJyzjQ2ovP/+KDlOcRBIIvzzCCZaxaUFWpoXU51UFTFOu9ej+50zD5U5EE\nN58NYQqi0biFVeMnTJiASy+9FPfddx9EUcRtt92mv3/bbbdh7dq1iEajmDdvHubMmeP+Iim+zKKQ\nuZPUuhKPS4opIszxOKLWT/uwsdsxp4FuJUQ1LdHkxupSvznBEaozuLU3juaemD7J0n4yVoI+80Rs\nZz2hE1mRT0gyU9W3O+dT0V3ZcGM3gRKVIT+qS/1o6lZNQWePKcU0re01fZ6sz4ZOSq/WtZnGS/9N\n/RQzR5eYTGd2mCdc499W35AdTvvQsziFOFPtNJKQ9XtOBVtKBzDf7z9MC+PCiYYPye77RFsnsLea\nidns45M9mDG6xPX+bpkcDuFgWx+e2tqAuKTgn84dk/NrcLxnQAmaJ554wvT68ssvx+WXX56034QJ\nE7By5cqsrpFqzvMLgj4pplpcFfvVFf3ji6dh0ogi/Oyq6XjwFTVM063N/cHLTseIkB9+QXAUbrrP\nRTsdLfcvK8kCrrzIh7KgiG+u/4g5XsEVZ43CpyeaM9YDomAqsWJn06f3UFnkN2k01ppf1udEBUDE\nQaO5/xJz0AelJCDimW/Mwt8Od+ChPx8yaRPFfrNpyS4k3KS5EaJrXo9dMdX2eizWummUQkSURRKS\nrrHFJDkpQdbYTzYtLtjvmFXY2X6fNL8W64NyU9WBjuu7L32Cl781x5XwzYQin6D7NTPxbXIGF56a\nzrwgVal0USC6ozrVGjxcrJopzqwqASEEZUFRN7XFZaO8fSpGlwa0azprUWvfOQZAjShr70vg4TcP\nq9dg/BeXMn1qrJOUrKhjvXz6KNP2gCjgYJuhlditgGkiZVmRaJRyVxSTX0Cwca5ToUW1LzpeyqI0\nPg+6MmcfIe0UeVLzK9GOmywmn4z277KAaFq1s6azPU09pvuisGftiqbvK+T0UbttHRBNGPlCx5kA\nBittfXGEQ8a6kD3/F84cadrX7vskwOyjyQS9o2seYpAVKKaW3ZyhyYDSaApBKt+LGvZLX7n/UfkE\nov8IE5KcthkYmzXPalFOWBeRAZGALm6/xbSYtk5uiqLY/ngnh4tMAsPumfgEgldvOle1ndPzwezk\nt7tLei72uoks+haZyv5r/+7RJn7WR0Nho9boc7CLzKOC8f/84RMs1nwepqKaioLpVcXY29ybcuLX\nz+nyfpyIJCRd+KUqC9MXl1HCBA3Q1f9z151tKifkdB6135LFdJZm9J+09CLkE/BJixo1GJNkBHz9\nW5t2RRMoCYj6Z6oowISKIPa39qUt88QZvAw7QZPKBaMGA6R2cgPJpgq/KCAmqf1SJCWzRlg+kdhO\nDGxehPV0EyqC+iTKDsV63YNtEVtTR2nQB59AdFNNqgmOPVpR1LEQqBO9XeXphKxgwemVet4P3ZYp\n1nteMm+snstiV7bHLyablZIEjSXqbL+WVGqtmxbSTHWuxu0wOTode7i9z/Q5RRKyPsGmWgQ5mWRL\nbCLWjp2KIqj1FbpqllqOhoBkFAwQl2R858V9lm3902i6ogl89bcf4t7PTMRnp6qarQI1ou7Ngx05\nN8txBg7DznSW7sf80UnVD5LqJ2X9OYT8AmKSjGhCbaucbqXI4hNIUmZ+U3cMi/9rl/7a+gNUYDj5\n2ffsNCknmZeQFexoUMvEpCuwqFfYhXrvP9cixqg5xnpeNc/GKFXDCh23WFe33zx3jF6fzc5HY2c6\na+i00UgUowCmXeVgBcYzcyNonH5ATs/05uf24tbn9+qvE5Kif/6pcigTkpL0+Y4I+Wwn599/3Iyo\nJhTOqlYd+ITQMG7GN5fit8AOf6RmKu5vK2hqTmUDURQF8GmLhDy0fOIMEIbdR5vKR3OkI4IXPlKr\n36aMtLT8tgVCUBIQcSqSSGs2s+IXiMmfASRXDp49tjTpOD0Ci9lmt+J1WiXOGlOCv+xX+7+kmj/Y\n+mC0w2W15l8ShOS8FFlWEPIb5sAfvnYIbx1KTtZNhz9FAyAaEv6FX36AYi0ija2UQJ/NP0wz+4MI\nUVfl//LHOgDGRGvWcnrRrQU8uKlw7LQITyWk2AlbUhTD7JriGLdBJknjY8epqPdKz5Pq9ti3WrWk\n0DcPtmd8fRajCoB5GzV7ctPZ0GXYCZpUk+pXtFbJ6bj/kolY8fnJpm1BUUB7XwIhF6HNLJUhH450\nREyTjHWCq51jDvlUmKgzwZSY6F6j+fJZVZAVBXFJ1uuT2aE60I0JghBjoiJ0o0ZMkhHTNJrGrhhe\nq2vDO0xnULc8sGgSrp/nHOYqCqp5SFZg3wpAY7RNfbL1Oxv1f9OJzyrTzh6jCnY3Go2T9uq2DH9C\nVvQAlNTatmzjg0t/furrIlDvVy20GsCM6pKUiy67nBa7LqOZoPv6rGZPh1JDnKHD8BM0KX5cC0+v\n1COcUnHGyGJTz3hAVfu7oomkUNx0jCoJYETIh1NM0iRrQvnJl6fZHmea7DXsyqs4/Xj9WufNvc3m\n8jCzxphzJVinvKw1H6PzXW/c3LHxil/vxDuHT6HIJ6ClN45H3jpse+10fGbyCLWNtgMEBMctZjE3\ni30Co80BAPTGNCHF3KMkq89m9Zem4F6HUGzTOV1oNH87bGh0QYvGm5CNaK5UwQcJ2SbYI+3ojPHp\nTd+0gwTBvemM0t/6aKwJlr2O3ndo2M1Gw4dh99GmcoCKTGUAp7LwTghE7fdh55xNR2lARHfMEDTs\nJOWUJDemTDNfMXOP3a05TYQBUQ186I5KKPYLKNcE7GNXJAs2BcCbWptlQohJ+NhdsyhDYZspdkLF\njV/M6tuhworVhiQtMXL22DKMK7ev2OyGQ0z4+LajRq04es6rZlXh8ukjIcmGj+anbztXQ0/Iclb9\nY9hcVZpHQ6AK11TavZ1GY+3gmSl2PjHAMAly09nQZdgJmsumhLGIyT1h8YtGi9xMA6UIgL1NvVkJ\nGmsjL7uVpvUnuPD0SowpC5jCTbttTBtOGk1AVP0oPTEJF9RUOGaJC0R14q58ox5xyT5c2ordMzhj\nZAhzmQrS/UGw80W5+iYT24KeVkGTiS/EbteOvjgamVpy7Kd5VNNaqkoCehVtNya6bH001NxFSxSp\nwQ7ENheJxe6dfgsa0N+WOcqP+jX9Gfo3OYOHYSdo5owrw/2XTrJ9zycwvdgzFDQnumL4/cfNunM6\nEwSYV3l25r0vnWUkXZ4eDoEQgqevmWlK0mzpSS5l4jQ3BUQ1Uq4rmkBZUDS1UnZib3NPkkCye0zj\nygK48VNjTduWX3Y6VjE9cfqD3UgFNxoN7EN02QRba4HO9OdMNmF+c8NHONxu+L2obGvojOrfL1Eg\nEIn6fXMTNsz256FYtY5/vXRS0ufYoZtkiZFHQ1S/VCrTmd1b2SZsrvnbMSx/5YDt4k2G8QwzNTtz\nBg/DTtCkwtoTJRuyMW8QYu4lY7fCvfOi0wAAs0aX4FaH9sB2V07no+mJqea+uxfW4Aefm5y0HytY\nHnzlYMpwaYpPICYfy7cvGN8vM5QVO43GjdWFbWzH0tob1ydttg+OG+yuSwXHpyaUAwAS2rmX/s5o\nRuYTjE6ZcVnB+DTPh0b8Uf5xZpXespkyaUQRyovUyXrKSPX5s60WTnTF8MttDZqfjaTU2u1MzNn+\nJt462K5Wllbouc0ntfZW4gw9uKBh8DH2l2zLYZwzNnPzkGDxHTR2xWz3+8eZVfjq2dUZTYROUXAB\nkSCWkNETk1AcEHHOuLKkmmhAsvCyvqYTdEefoU2JAjHV5cq17d3u9t1GLNkJmva+BN7WSvCrPpp+\nDU/njosmqNeU5KSILZGoz6mxK4aEJGO+JpTeO9aZdB5AS5ZlPsrbPj0B188za42EqFpHkU/AsoU1\n6jb9TfXP1qOdIAA+bOzGcx82OY7dTqj0L4tG7Y9kPY+sKBhV4sfXzq7O2C/aH3pjEla9UW+qkMHJ\nH1zQMFgrAGdDNqsztTyI8drJKXzbpyfgoklOnR6hTyZ0Jf21s6v1LPfkcQqIa/6BVLXZkgSNg+ms\nl8kFCoiCyYSTjZaXCjuhYr3Edy6cgMumJPvinJIO9fYQNtFdqSjXWhlICvCHj5tN7/k1yfD24VN4\n4m/mz1QUCEI+AW29cSS03CMAeGVfK+yQFCWteZBArbUX9AlGiRftPfZYQtTcLdqszw72+0gDT7Kt\n4k8/LiMYgPHRaOMRSfbnz4aWnjheP9Cu18/j5BcuaBh8Nkl/meJUfTcVTj1pllhWrG750RfOwOIZ\nVfjCtJGO+1AfTVonc7rHoA2b9StVl/oRFPMnaOw0JLYrKABcOaMKYy15NASqdmFHSUBALCHj46bu\njMZ7QY0q1Dd+2IQn/nbM9BzoI4hLCtp6zStngRDUjCiCor1PBbOdWRBQNd50AQ8EanAB+xXUW5Iz\np3Wj/NGv4+ovTcUlk6nA7p8ksAtvVhTtK1bgiDO9eC7vgVMQhl2ts1TYlTHpzzncQmD+8c0bX4av\nnl2tm1Pcws5Dt184IeW+fpGgrTeBxq4YpqXosmi9G6upQYGaqMmW0Qn5RQR9hqnIaXLPFusz/tMN\n56SsJEAhDiG948oD8AsCdpzowsG2CKZk0HXSOpZOpuU2+551HvUJBH4t6iwuGz2MnL4+isVHYwtR\nNZpSLdAASG41oe2WFgUKRhb7MXtsKWaPLcXUUcV4fX9b+gNtx26ck32tbjPq5xVyzqea7XBqIR2T\nZOxs6Mb8CWUFb+HNNRqGXJjOfCLJeHFm1WhikpKVCc7NZEspCYgYXRrA9uNdKYWq0xeS1r9SoCZq\nsnkjAlHbKVNy/Vu2hsG6XRTQvWZacpPGlgUhKQpikoJPT6xIKXiTxmJRM2IJVqNxHpcgGB1dE4xG\n44SspF/0Exh5QKdVqtqcrtGkPjTt9ayLoWywChx1mxoGl4vzZwL11Q1lhaYnJuGnW47i+mc/wgu7\nm7DnZA8eeOUAmm2iU/PNgBE0L730Eq655hp0dxt2402bNuHuu+/Gfffdh717jUKEDz30EL773e/i\n3nvvxb333ovOTnsHaqaY+8wXUKOx2KdjkpyR0KBkkocgCgRfOks1raUas9M7a79yJr5z4QR93Gzv\nFqLlaeQL631meq37L5mEV286V68gLGph7Znm0ADJhUzZ7Hmnc1177hicOapED6dPyEbDs26HHjiS\noqT9TtKgElEwkmppTpNd24VU6CYtCsleENDL0Sdj1WgISX3+T1p6sfR3Hzm8mx1GlfahK2ke+vNB\n/HFvCxq7Ynjy3ePo0WooWmspFoIBYTpraWnBrl27MGqUkSty7NgxvPHGG1i1ahXa2tqwYsUK/PSn\nP9Uz0++8805Mnpwcjtsf2BXot84bl2JPZ7IVNKwKH5fcNU+zUhb0ob3PfRRNiRYokFLQOLw1IuRH\nZVQt4XQAACAASURBVMin/1Cz6TmTLVQInzEyhAOtzm2lk9DuhQoHKspFJnEyY0Fj2X/Fa4dM780a\nXYLdJ3tMk+vVs9UgjZbeGCRZwdFTUZx3GsGsMSWYNSa5gCpgtGhIDdHvBwCe+cZMXfNkD3Xlo4HZ\nVEfUjVlBv5O9WuSdSdBomhOxvsFwoKUXDZ25ddqf1NpnF+5bW3jY5oYAdD+htYhvIRgQGs3TTz+N\na6+91rRt27ZtuOiii+Dz+VBdXY0xY8agrq6uIOOpqSzCueOyy2L32fRoSYcAgrv/VIcNWsHHbBtM\nrfriGfjl185yvX+pVnYmpeksxfEERi5Gf3uVZAIVwreeP97URC4d9F6ocKDPWCQEJzqj6IwkMvbN\nWbUrth0x0WdQc14KncD9goC4LKOpO4aqEj9mji51LJEkK0pauzp9m2o+1aUB275FblAspjPBkuuV\nDdS8yk5ztCSOXovNhtJg7tfD246q4exWjaaxK32zu8GCtUIHjWbt80Cj8VzQbNu2DeFwGBMnTjRt\nb29vx8iRRtTUyJEj0d5ulClfs2YNli1bhueeey7nY8qmUdd3NOf7pBFFafZMhv6gD7SoP8S4pGRV\njmNUSUDv2eIG+kVMrdE4vycKRvRORppFP9HLymcoFKijnt7vjfPH4vHF0+ATgJ9vbcCT7x6HL8MZ\nOV3JIZr1zn6l6LBDfgF1LX1o70uguswoSWOH7EKjoW/bWV3ZQ1td2Ohlq+kM2fsz/ALBtFHFTNUN\ncwkagZCUwQD5KE1Dhf37x7v0bfuae3D9sx87HTLoCFq+COGQD3PHl3kSAFEQ09mKFSvQ0ZHck6S2\nthYvvvgiHnjgAX2bG5vpHXfcgXA4jObmZjz22GOoqqrCwoULczZetyXeWa6ckZyp7RZ9AtH+xiU5\nqzDpTKGTZDDL9rzUmQ2o0WgTRxSZSq/kC/psMvWjfWbyCLywu1kXNKVBH86s8pkEVqams4Ao4Ouz\nq/G7XfbJj/Rskqzg0jNG4I0D7fokxy4KgqKg+oocIvRkFz4a+rbdPbDbWnrdOIPNGhTblyhTJEUx\nlXeSLaYzL6BjWbfjJJbOV83kv9ja4M1g8kTAZ/4e+MTUAj2fFETQLF++3Hb7kSNH0NTUhHvuuQcA\n0NbWhvvvvx8/+tGPEA6H0dpqJK+1trYiHFadt/RvVVUVFixYgP3793suaPoD/UHTCSiWpY8mU0o1\nQeOmh860UcWISzIOMYLEL6i5OIBqhz9jZKgggiZbcxD1V1gnYnYCzyasPZVwKtHMkzFJxqzRJZqg\nSd6vyCfAJwCRuIIj7RHIUDBpRAh/rmvFRRMrXUadkaT7oZQGfbj3MxP11g3jyoP2HUg1rBpUfyYo\nWVG1ErvflR7eTAobamw3llQJrPnkk5ZeVJX4caQ9gnOyNNnbYV1A+gRBWzAUXtJ4ajqrqanBU089\nhTVr1mDNmjUIh8N4+OGHUVlZifnz5+Ptt99GIpFAU1MTGhsbMWXKFMiyrEeZ9fb2Ytu2baipqcnp\nuLIxnbFkHt6sHae9ztZHkylUown53BUztE7CPq1eGgA098QQKsCYWVJVH7aDCnLrfZg1mszHQVsR\nz7Jp6XC3VgomkpB1n5idOdIvEvi0Ipv3v7wf9/xpPwDg0beO4JfbGpJqndmh+2gcBN+UUSF9TD/+\n8lRUFDmvM61CJdsJivqczBqNObyZNj+PJmQ9GizfWAuKehl99p0X9+Ha9R/hnk37c3peajq7apZq\nafELajTokNVo3ML+ACdMmIBLL70U9913H0RRxG233QZCCKLRKFauXAlJkhAKhTB37lwsWrQop+NI\nVdU2H9CVqEDUL3y2UWeZUl7kw6gSP0YUu/saJAkageil4+OSopcqsUI1iVyT8ZTk8Ln2x3QGADOq\niyEQ+wm+LOjDyGI/ogkZpQHn50wIgU8UIMkKWnvipin9pT0tCIrEdf09J0FDy9CMLw/qlSGcsEad\nZQvVjARiaDSmygCg4c0EGz9sQmNXFP/3s7mJJn1hdxOefPe4bcCIVaPxOnEznocB0I+PFmylprMh\n66NxyxNPPGF6ffnll+Pyyy83bSsqKsKqVavyOo5Cm850jUZb0TpNWrkmIApYVzvL9f5Wk4yf8dEA\naudR64/6pvPG4UKbYp25IFONxmnv/prO5o4vx8vfOhe3v7jX9n1RUENKK4p8ePIrZzqeh6767cYp\nI33+Cx26ky+H1Xj8IkkZKZicsJndSljWEkhFwT5JkgYd0EvV59D0+uS7xx3fY2Xs09tP4OvnjGbe\nc67gfaQjgtKAiHCeFk+5hP48yrSoPR/VaIab6Wyg0l/TWabQH7RAVM2gEGazbLBqeqrpzPjFWuMX\nbj5vHD4/NZy3chfWZMl0OH2qrCkn24oQAHD59FG226tLAuiKSvAJBGeMdK46IDLmJesw3DSdowLG\naSJhgwX82rWcwqmtCZvZBgNIiqJrNLRvGj3Pq5+0qiWNCJIi3OzHlLvfJftd3tfcC0krbOoXSEpN\n76aNe/Cj1+tzNo580tobx8ovnKE3HAyKQsF9YZSBOaN5TOEFjfEzi0lyQcxmmaJASdL0/IzpDEie\npK+ePRqVofys/H7x1bMwo9q+zbUjDh8rO+n0R5N08lGVFRkrylT4BEObttNK0mk0lSH1OhGHTph6\nsIBWOSCVVqOazizbstFoFLVQKE2KVc+j/t18yIhEtVZ4trtuup9lXUsvuqPuEpZN/ZO0tuZ+gaCs\nSLTtVGsajwcaQTYcbo9gZLEf5Zomfe8lEzXzfOHHwgWNDYWW+PRDEAjR6pwNzI/FKoB9gmCaqPqj\nDWRKzYiijDUlR42GmZf7I+Sd7p8KDScNrCxo5DPFHTQap20sbhM69YRVUbB1vh/tiODFj8wtD9RD\nsgsGUFtHG9+fNw+24/ipiNoMDeaK57ZmQyU5iMCO21/ch5//PX2IcktPDPuae/XXkbiMH285Cp9I\nEBAFvLi7OcXRqoY60DnSEUHIL6C6VB3rGSOLUV0aUBNjPZA0A3NG85Bc5IZleoo+bQVKdNPZwNNo\nAGDqqGKcVmGU3veJxOTELIRfqT84jS5XGo2TIKGKjp0gmhwO4Z8vmKBf2yjrn7xvf02QVkETS8i2\nq/dNe1vwyidtGFlsTKhsFYhMoMEAIiF6p9Gm7jh++34jgj4BL14/GyUBkdFobEKgk/M8HYm6iFr7\n7fuNmF5lmDD3NffgncOn4BMIrjxrlEkI2ZEuSXcgcNPGPeiLJ1tHvAoG4ILGgheT5Zxxan0rAUQz\nnQ3Mj+W7F5+GJ/7RcGZbv8QRD2ooZcKlU0bgrotPS9rOmgT7M5mzguSZb8zU/02/U3aC5j+vmq4X\n92RDgPPxNaSnpOOpDPls857oMzi/hmlTkeV4ZFnTaCzJqHuaeqAwbbOpWc8+EELTaFxeb6tWXsaJ\n7piEr51drb+m0ZI+QcAZo4rTpicU2rSeKbsbjXwg63w2LPNoBiK5MP+cX1OBqVrOghtoHssf97ag\nrTeel5IbucAvCqaOndZnRfNEBipVJQF80cZhn84k4xb2eRQzSbC66Sytj8YQNP1Z8BAHqWDUWFP/\nTg6HsPzVg0l9Zui1i5nPmiB7H41I1P/Y7qbNPWpnUUPQqKT00biY4PsSMh585WDKyFH2ugBwsE0V\ntn6BmD4D53sa2ILm1U+Mz9P6PfIqj4YLGgu50GiuOWc01vzjdNf7sxm82493oc1ViRDvsZqKzqzK\n0Dk/QKAT8NfOrsZsh+rJbmAFid+mw6gbQUMnyK6ohA8bs8tUTxd1Zh3PXoupiA6TNRER9CfqTA2r\n7YtLOGes+nzViDfGVJ3i0egl0lJc59gpVVjQysROAREAkHCoJSgyguZEZxQfNHSZ3jcqlXsnaBRF\nwfFTqQt/JlJIEm46GyAU0qFNYZtebfywCW0ZlPr3Ei+eVT6g93HL+eMxeaR7TdSKU+KnPrGn0VTV\nSc54ve6DxqzG4bSap1enY7NqExSqgYWZRF5qcumKJvC3w8l1C52QFQWCoJ6zNy7rOR0ALT1jHsPJ\n7lhSgILiIhjgw8YeANAXaWyF4pNd5hYDCVmGTyBJrc79ohEd99TW47jPkqlPFbJowjtBs7e5Fzf8\nT+rCn6k62grcdDYw8MJHk21RS69hw23DLqsLDERGhHIzdta3xn6P3JrO1DwaY5KISjL8IsFnJldm\nNI7TKuwreBPLOPQxWoZFV/vm86iJNO8d68JDfz7k2nykBgMQPWm1jDGvss+IHcLHJ3tM53hGE7j7\nmnv1njZWIppgof4WVkv7uEk9nyQrqGvpxQcN3fAJBP+ysAZL5o01xkMIRKLu12NzHSrAU+XZ5JOE\nrLhqp51K4yK8BM3AINvOmv2B9ovPuJHXAODXV8/AofY+zBufu2KAhea6uWMdky0zIV1Uero8GKt/\nIJZQqx5n+o10KvljDQZwEnySrOCf5oxGMWs6U+WMPtlKsgJBVENlW3vjGOUQ8kvDmxWoIbdsnydT\nDo/2bCZUBJMmymOaqeh7Lx8AAIwuDeC3TLAFoJrKRoR82K6V/Y8m1EoMk8NFulD82jMf6gLEpy0K\nTqsMIigSRDVzGv0M7OZqOq5dHhXf3NHQhd9/3JJ2v7ikoCwomrreUgTCTWcDAi9NZ6UBEadVBPGt\nT2XX3TOfOK2CxlcEcfGkSlOQwGAj4BMwtjyYfsc0UI3m4knmkjtuv1LWfjRRSTXxZBoJd4ZDIAo9\nMxU0Tosqu06jNBiAhoJTGdHQGcM/rf/IuY+OrN7/h9rkvHimvUBnhWC6efBkd3K3zY9O9uj+HwB4\n98gpnIokEBAFXdCwWgq9v4Wnj8DG62br1/YJBJKi2H7f6T1m4qORZCVl3sq2o+7a0CuKgqMd7srz\nJGQFdy2owf9ce3bSe2opIW468xwvTGe0pXKRT0BUkhEYoFFnnNTQ7879l04ybXfbjE60+GgOt0cg\nksw0mpe/NQcLTx9h+57V3EUnW+v5E7KS5E+iMonVaAAgklAnb6eikJLWR4e+P6GiCH+84Zyk/dim\ndNlEdUmyggXMfb91UPUjBX0CZAX49vN7AECvJsEKUvpPv1bBICErekg1S5Mm4NwsRt880I49TT34\n4q924KU99lpIQlbwwCuqlnZmlXNpIgBo7I7hF9vc9ctJyApKAqJtdW5CvGlfzQWNBS/cJadVBvGb\nr89AwCcgEpcHfOIjxx5fGpNUOvxCcmitWgjR/TlSmeesWgftjmo9orErhsois/lNTdhUkgQNDVl2\n7gyqJJlr7DSpuhbVpzIi5DNpE28caE/a14kimx9vQCT4978e0UOYb9c64ZoFjeGz0gubamNgAxM6\nIgnUVBa5Krq78o16/Po9VTC8dbAD33lxX9I+7Hkeu2Jqys85lpAxptRdRYKE7Fz9nRCgM5IoWDsG\nChc0FryY5AkhGFcehE8giCTkIRPNNdwwiqNm9/lZgwHotowbHDnARnwB9lFUh9r68NdDHUnBHdRH\nk7AImtVaIzVWQH7+Fx/oDnNZ0cxhNtUXfnX1Wfo2GpYsEnMFgn97ox4AklbnL+xuwud/8YH+36G2\nPtvfjfX3TJv8sRob3cWn12RTO8YCwO5GIzBBkhVUl/oRlxX857vHkq5lhc7lHzZ245OW5GoDVHN7\nfPE07Rk5n4vm/jhNDT987RCOaMm3dqZPigCCX793Aht2nkw7/lzCBY0FL4IBKGrlWOcS5ZyhjV2y\nICFZJ+UnURIQTW0c6HkrmKg7GtXlVJ2CCieaq3FUc9Rbx00Fh6RVBrBTAojN/oKD6SxsiQw8YQlZ\n7ogk9GCMK6aPwndtKkAAhtbDTsRGh1v19y/Jih6AwI5F1RTU459PUw8NSN9uRFbUxN4zq0r0PCUn\n/4mkaFW3tZu0nntLfQfeO676e+IOeUKAsWaJ2uQZRRMyNu1tcV2YNBO4oLHgpTZBvxxeCjtO9pQF\nRVNFgEwRBYKYJUejsStmCgnOB6xPkPpSzh5rTlylwQCyRaOhWCszxxmNRjWdJU+gbJDD/ZdOxKov\nngEB9oEnRZbn2m5JavYLRP/dhPwCyjUNyHouO0HDjocKe/o2e3iqPjV2WNtqHGozR5Sy5yNa4VEn\n2UT3pd8Fu/Brev+pNBo6piKfAEVRsPlQB1q1Z7m3qQc/2XIUu7JMFE7FgBE0L730Eq655hp0d6s3\n2d3djR/84Ae4/vrr8atf/cq077Fjx/C9730Pd999N9avX5/TcXipTdCQS67RDE5CfhEvLkl2dLvF\nJxDbIpfXzx2L33x9Rn+GlpK/HzEin+KSgnnjy5KjzpiETcDcOAxgTGqMOe72F/fi2V0nHTUa9hqT\nRoQwd3w5CCG2jnhrrtlbh8xJo3Fm0vYxZijruj2QQtDQ7RIT3twbk0wVATLx4VqLczZ0mjP6adUE\nipq1r+AnW47gUc0k+ZE26VPhseLzavfR453J1QHo/dOEVDt0n5oC9MZlrPjLIdSu242tR0/hQy1/\nKR+VDwaEoGlpacGuXbswapQR+uj3+3HNNdfguuuuS9p/zZo1uPHGG7F69WrU19djx44dORvL1bOr\ncf3cMTk7XyZQjYb7aIYWmYQ3s/z4y1PxyrfmoDggYlwOwq+doAmNgPNqmICgrqUPz+5qAgD89O2j\naO8ztIrOCBVA6iT13zsaUdfSh3cPn4IgALPHlmJy2Ai7/sXXztJL2LMIxNy2gcI6+q+w5DydWVWs\n+4IAGiJt1rDOP00tEJoqYCOakE3N5wDg/71ej831qlCTFGdNIR0VRT7b9tGshUvQBOQr+1rx57o2\nKIqCu/5Yh0hC1j+XM0YWY9aYEltnPr3/uKToi1YrtPp6QlZM59h+rEs3mSVSdF7NlgEhaJ5++mlc\ne+21pm3BYBDTp0+H32+Ofmlvb0ckEsGUKVMAAAsXLsTWrVtzNpbzTqvAtXPHpt8xDxgZ255cnpMn\nLpsSxsovnJF2PzpR0LlsTGkwb91JAcMspJrFNJOXLJvqtOmwEyIBPmjown9sOapv+/6fDwIwBM1r\ndW36NURCcP8lE01trGscQr7ZEimsv4IVNPQ5UeFBTUYiEz1mbZZGKwZQDUKwERgxyYj4ZE2gtIRN\nQlbP/eurz8K48sx60gR9yf436r+iCFCFGf3M6e6SrJj29QuCrpl0RxO6X40KLckmPJ0yc7RWa06S\nYc2XpXLHKVS9P3g+pW3btg3hcBgTJ050tX9bWxvC4bD+OhwOo60tfVmGwQDXaIYmQZ+A+RPK0+5H\nP3f6Oy9UFW+2ve+HJ7ptFzrsSGgLBDaz/zxt0qeTadAS1UWIu8RTwpjZ2Im5yGf4qay/E2ulg6oS\nP9PDhgpQ41w/+Nxk0/gA4J8vGI+rZlXr51MAzJ9gVDFY+fohvLC7CaJAUBwQ0RPLLDw4IAqm6tWA\nUQeOogZCGM+a3n9ckvUcHvVcRmfU65/9GP/npU9MzyGewkcze2wpbvv0BCRkc8dcgRDdf+PUdbU/\nFKQEzYoVK9DRkVyIr7a2Fi+++CIeeOABfZsXWasDBZ++ouWCZjhi/dwLVQNPjXaUERJEvFrXhqXz\nkjV6dt6iHTFZQUArQ9DJKiqZJzG3sIEDpnbL2gAmjijC6WFVG6Lh2nQSDgUEPHfd2SgNiHjvmFqK\nhk4nrAb16Ynmyg0A8JVZRn+aoE9AX1wyBeW8qSWAzhhdghK/6FhzjT0HG9nV0BnFY5uP4AtnGoU8\nVdOZOZ9HUQxJowsaWcEz7zfq/YH8ItFzoLpjklHxQTuX2qXX+Zn7BIJtx7owY7S52rqkCah8+GgK\nImiWL19uu/3IkSNoamrCPffcA0DVVu6//36sXLkSFRXJXwYgWYNpbW01aTiDGb/ANZrhzqdrKvDO\nEbVxV74rRNBFnV9UW3KH/GrE1oLTUxfxpBoFOyFRu76dfyWTdRPbL4VdWRcHVOH21FfP0sv3f25a\nGF+bXY1bnlOz/quYemvzJ5RhXe1MvKCFIVfaZMk78bOrpiMhK7jthb3qNbcaGfmfmlCOgE9AXFaw\n+q3D+MqsKpwxMjmr33rLdnN3kulM0yzpFupDoV13abM2n0BMfhT6OdJ8pbgkp2wHv/D0Svz9yCns\naDCiyzZ+2IS548tQ5BNSVn/OFk+LatbU1OCpp57SX99+++14+OGHUVrq3BNkxIgRCIVCqKurw5Qp\nU7B582Z88YtfLMRw845PTB0Rwxn6sJNyPv0zgKGZiIJRIkaS7aMe2e+kodEYExJdYSdkRS9SSbk+\nA58nG+LL1jT70vRR+PJZVQCMBVnQJ6CmsgiTRhSZTGuA+uxGlQRw46fG4bp5Y9HaE8eoEvtio1Zo\nkML/b+/eg5us0z2Af9/cmrZpkqZX7YXalkLRo4WyVegUaiswoOAqAlNkQTqISkHPMHKsAyrCUmCX\nMqwFdpFFEVAOHmbEw5FlcdvFRcC1DJei1aUXkNa1lDa90ibN5T1/JO/bJE3SpG0ubZ/PX+bNm/T3\nvsQ8+d2ex959sHyPHxrvIfGXQLuBxtHIjNFipRmXNYHToTVg4cfX+wwd6g0sNDojf41iocDuPMrm\n0pvYOOMBh23nyKUiJKgCrYbjAODnNi2CJUJ06Yz4n4o7yEkeuh/wfpW92fZ/rIKCAnR3d0Ov16O8\nvBwbNmxATEwMVq1ahb1790Kr1SI9PR1paWk+avHQ4vfRUKAZtbh/+gdCXcuPNhivTInF8sn3Ie+T\n71DT3IWwIIVpv4adAGc59NS7jNYUVF56LBbf3zH9Or70c7tVkAHcGwK0TPr41xvNCA0UoaVbD6lY\ngNBA05c8F/S4gLNr3jiHm1qF5t3+MYoAfJL3kMvtALiAaj1Exv3tMysmYv8/f3a4QsvR4BOX9Row\nVRm1nbfJTVbhS/NCCq7UQY/BCLX5HgDmoTOL11n2LCvv3HPam+GIBUyfTZt6I4somQR/+Vczmrt0\nUAWJYT9rnvv8KtDs3r3b6vGePXvsnhcbG4uioiJvNMmruP9xKNCMXtyPrX3zU/s5c/CkIgGk5oUK\n3GiJw+XN5nZZTqLXtWqhNbDm4RYWjZ09+MPXdXgiORR/q+7NUebOBmSG6d2LU93UjUfjFDh9o9kq\ndxf3g4z7QrWX42wo9JfSRmTRE7TFssCf56dCazCiVt2N4n/cBmC6Nq5P1NKtQ4RNL8uyqummv90E\nAPxkztrMXadYILBammwZaP51t8tpdVHL6/jevG9m3oRw/G9lE/RGFpNiQvj6P5fq2zGj/zUsLvH5\nqjPSqzd9u48bQnxmqIqwucNUL6Z3x7+zoVvL3gr3hRYsEUKjN+IH834crufBceeHk5CxzouWYs5q\nLLL4lc73aHzwP4rlvREJGYdpZowsi/sVARgbHoRZKWHYNTcFgHVGhR4D2yezt71b1a0zIl4p5e+j\nbY/GsgnXful0qRy5WMDw+dy4/OA6gxFJYYE4vuQ/8GpmHH5qca0sgSso0PgRhVQEsZBxuMeAjHwv\nZsTg8KIH+z9xCDEWmyS55I2uiggWQxUkQnOXjg88ti93a18YAzTd0/Ft4ZJgiq16EqZjHl8sYWcA\nzLZHc/deD2b++YrVORq90WpSHzCtVgsJEFoFGp2d1WEChsHqqbFIsigprtEZrH58ioUMepysDHsy\nNczhc3zbzW+46OFIfhVfl860iEAuFeHBqOAhXX3mV0Nno93kWDm+WD4y5pvIwASIBIgKcW8z4GCZ\nUsT07qtwJ9DkpUVDJhGiutl6eMiSO4tbpCIBn3vLNAfUNy0T15Oxu7F0CKVGBKOx03pbhuW1iAUM\n2jXWczgavRHzDl4D0He1nZCxqaBq6Ls5VsCY6hdZzv28/+2/kWwReMQCxunKMFfmxLjriFNK8cRY\nFeKVUoiFDJLNCxtsMyQMFvVoiEtG7+6mkU9oXunV37CZpZcejQFgCgy2gUksYDBzbO+KJXfmaMaG\nB/IlBvRG07JeW1wbPd2jKXw8AX/JT+MzEACAyOJahAIGDR3WOccsJ9htW8dV7+T02MmyzCX2vKez\nDmCW99jIWqcNAoC0+3uHy1yZs+KWe4uFAggYBg9FyzAuItiq+upACtA5QoGGuCSA8uKMWIx5k6SB\nZe2mZnEmPSbE6kvwlcdi8OsHI/D0gxH8MXd6SFKRED/e7cJfbzTjdqsG8oC+gy62mQA8hVuxxv29\njDg5ZBaZtFMignDTPI/BzStZDo3ZrqLt0hlw8ac2/rG9/S4CxnRd3PAh3xaL9xofGcQv3ggJEGLL\nrCSrfULRIf3nxeP2Sjm6hUO9cZO+PUi/dv96HNZNdy1FEBl+uOzKztLLc/jNhOZJndAgMf8r/8MF\nE/DMQ5EIDRJbfYG5FWjEAjR09PDDcKGBYqsaOoBFCWovZdDgftj/dlaS1VDXg1Ey/jr5PS9Ovpyz\nk0Jx3SIFv726MUJzj8ZSdIjE6ligWMgPdWr0RqRGBvH3Yt6EcJcSsHLnO+q0DHWgoTka0q+UcOf1\nzMnwxjDA0asN+KnFfpVK23MB61379noY3KbEeKXUreXHEpu/L7NTiydYIsTRxe7tiRmMYCf1gCRC\nAZ9dWSzsW4PG0sT7Q/APi/IGtj2atVnxmHh/CLpshs0EDGO1oEIiNC1N/sPXdeasAQL+B8Bv3Ngc\nW/J0ChJCA+0+JxD0LQUxGBRoCBnl2jR61LVpcayiETKJa0XWuIqYgP1Awx17d0aiWz0ay6zDU+IV\nVvtKLIUFubbLfyi8lhmHl81zUrYCRKZAw6XwcVZV03aC3TYnGZcHrVOrR0acHCnhQWBhKhtgu9oN\nMGXQfiN7DCRCAd9TCnQjqI+LCHb4HFeXZ6jQ0BkhhGev8Jo9lnMCfI0Xiy9N7j8D3aw46o/plwJE\nvRU7+z5nau+6L6rwS7vW6XCT7Ze3adVZ3+uVBYjw21lJWJp+H6JDJGiyqSaqNVdh1eh7X8/VA5IM\n0eZVmqMhhPjccw9H4v9eMFUTtdej4fJyOeqROGL5y304JDHnhr669Uacv9XqtBdg++Vt2kfjCeHs\n2AAADvdJREFU/CuYWwSQdl9vyYJx5k2s3ToDxOY9RVoD63BifyCENivkBouGzggZ5Vz95bry0Ri+\npyJgGH7pMXfMMkiEBYtxYunDbpc64OZ2Vk+NxdhhMDfIzT9NTwyFzsg6ndcQutijsX4N+Pe3fJ/J\nsSG4VN/BD72tfDRmSJd7iwUMPlv6ML67NjTViynQEDLKuTrpy6Wpt8WtYLId9gpyszdjad6EiP5P\n8gNbZyfju4ZO1Kq7oTOwTnsBQsY20Ljeo7EdguxNw2M67ujfZqAYhhnSwEVDZ4SMcrdbB5/T6syK\niX45v+JpCqkImQlKc/4xI7R6Ix4IleIP81L6nGt/6Mz5PQs319ixHYK80WTK7BziZEWcP6FAQ8go\nxyVXBPruZvc2XyTKHApigQA9RhbdOiMiZRKkRvZd0RUoFuDHu124YZH+v780OhOignFmxcQ+K/fU\nXaZ/swdU9pcn+xsKNISMcr+dlcj/t69LVNwXEoAPF0zwaRsGgsuo/M6XtfhnXbvdcxJCpXgwKpgv\n6GbaRzOw+x0eJEaiavgk36U5GkJGuYy43rLp/tChiFH0v7Pd38gkQvy73ZT3LMFB0TqGYRAeJIbB\naCq3XKvWDLiWzrbZycOq9+c3gebkyZM4cuQIDhw4AJlMhs7OThQXF6OmpgbZ2dnIz8/nz924cSNa\nW1shkZjGLzds2AC5fIgq9BAyCm2fk4w3TlW7neuMmESHBODyzx0AgPedFK0TmOdp/vvaHYgEjEvp\nYuyJ90IF1qHkF4GmqakJFRUVCA8P54+JxWIsWrQIdXV1qKurszqfYRi8+uqrSExMtH0rQsgATLzf\ntE9DTIFmQCZEBeOxeDm+uW1/2IzDZXDW6IxYln6f1/K1+ZpfzNEcOnQIS5YssToWEBCA8ePHQyz2\nXqoJQkaz/5o+Bv+ZFe/rZgxb97mQNZlb4qxn3SswN9z5vEdTXl4OlUqFMWPcyw68Z88eAMDUqVMx\nf/58TzSNkFHlCYsaMsR9rqTb4ZY4u1P7ZyTwSqDZvHkzWltb+xzPy8vDiRMnsH79ev4Y60LagzVr\n1kClUuHu3bvYuXMnIiIiMG3atCFtMyGEuMNZkkoOlx1Ab2T9YuGFt3gl0Lz11lt2j9++fRuNjY1Y\nt24dAECtVqOwsBBFRUVQKBR2XwMAKpXpl1dERASysrJQXV1NgYYQ4lNTxij61M6xJRSYMjxTj8aL\n4uPjsX//fv5xQUEBtm/fDplM5vA1RqMRnZ2dkMvl6OrqQnl5OTIzM73RXEIIGbALZ87gu9+9B5FW\ni26RBAG/WQ6Mf87XzfIKn8/RWLJdgVFQUIDu7m7o9XqUl5djw4YNCA8PR1FREQwGAwIDAzFp0iTk\n5OT4qMWEENK/C2fO4Nybb+Ljmzf5Y681/4wLsXJMnTnThy3zDoZ1ZVJkmCstLcWkSZN83QxCyCi1\nbf58bP/73/scL8zJwRvHj/ugRa65fPkycnNzB/0+frG8mRBCRjKRVmv3uFAz+ISmwwEFGkII8TB9\ngP09Ngbp8NrhP1AUaAghxMOmvfQSCh94wOrYGwkJyFq50kct8i6/WgxACCEjETfhX/j++xBqNDBI\npZi2cuWoWAgAUKAhhBCvmDpz5qgJLLZo6IwQQohHUaAhhBDiURRoCCGEeBQFGkIIIR5FgYYQQohH\nUaAhhBDiURRoCCGEeBQFGkIIIR5FgYYQQohHUaAhhBDiUX6TgubkyZM4cuQIDhw4AJlMhoqKCnzy\nySfQ6/WIjIzEvHnzMH78eABAfX099u7di56eHqSnpyMvL8/HrSeEEOKIX/RompqaUFFRgfDwcP6Y\nXC5HYWEhduzYgaeeego7d+7kn9uzZw/y8/OxY8cO3Lp1C1evXvVFswkhhLjALwLNoUOHsGTJEqtj\nCQkJUCqVAIDU1FTodDro9Xq0tLRAo9EgOTkZADBt2jR8++23Xm8zIYQQ1/g80JSXl0OlUmHMmDEO\nzzl//jxSUlIgEomgVquhUqn451QqFdRqtTeaSgghZAC8MkezefNmtLa29jmel5eHEydOYP369fwx\nlmWtzqmrq8OxY8fw1ltvebydhBBChp5XAo2jIHH79m00NjZi3bp1AAC1Wo3CwkIUFRVBoVCgubkZ\nO3bswJo1axAZGQmgbw+mubnZqodjj1KpxOXLl4foagghZHTgpi8Gy6erzuLj47F//37+cUFBAbZv\n3w6ZTIZ79+5h27ZteP7555GSksKfExoaisDAQFRVVSE5ORnnzp3D7Nmznf6d9PR0j10DIYQQ5/xm\nebOt06dPo6GhAcePH8fx48cBABs2bIBcLseqVauwd+9eaLVapKenIy0tzcetJYQQ4gjD2k6KEEII\nIUPI56vOCCGEjGwUaAghhHiU387RDIXKykp89NFHMBgMyM3N7XfRADEpKChAYGAgBAIBhEIhtm7d\niu7ubpSUlKCxsRFRUVFYs2YNpFIpAODUqVMoKyuDUCjE8uXL+VRBo9HevXtx5coVyOVyFBcXA8CA\n7h2lWTKxdz8//fRTlJWVQS6XAzBtk5g4cSIAup/ONDU1Yc+ePWhra4NcLkd2djays7O98/lkRyiD\nwcCuXr2avXPnDqvT6djXX3+draur83WzhoVVq1axHR0dVscOHz7MnjhxgmVZlv3ss8/YI0eOsCzL\nsnV1dezrr7/O6nQ69s6dO+zq1atZg8Hg9Tb7i8rKSra2tpZdu3Ytf8yde2c0GlmWZdnCwkK2qqqK\nZVmWLSoqYq9cueLlK/EP9u7np59+yp48ebLPuXQ/nWtpaWFv3rzJsizLtrW1sStWrGDr6uq88vkc\nsUNn1dXViI6ORmRkJEQiETIzM3Hp0iVfN2vYYG3WiFy6dAnTp08HAGRnZ6O8vByAKbNDZmYmRCIR\nIiMjER0djerqaq+311+kpqYiODjY6pg7966qqorSLFmwdz+Bvp9PgO5nf5RKJRISEgCYckkmJSVB\nrVZ75fM5YofO1Go1wsLC+McqlWpUfwG6g2EYbNq0CQzDYObMmXjiiSfQ1tbGb95SKBRoa2sDALS0\ntGDs2LH8a8PCwiglkA13751IJKI0S/04ffo0ysrKkJKSgqVLlyI4OJjupxsaGhpQX1+PlJQUr3w+\nR2ygIQO3efNmhIaGor6+Hlu3bkVMTIzV8wzDOH19f8+PZnRvBm/mzJl47rnn0N3djcOHD+PQoUN4\n5ZVXfN2sYUOj0WDXrl1YtmwZPxfD8dTnc8QOnalUKjQ3N/OPXUlVQ0xCQ0MBALGxscjIyEB1dTUU\nCgWfr66lpQUKhQIA3WdXuHPvwsLCBpRmaTRRKBRgGAZBQUGYNWsWP1JB97N/er0excXFyMrKwq9+\n9SsA3vl8jthAk5SUhIaGBjQ2NkKv1+PChQuYPHmyr5vl97RaLbq7uwEA7e3tuHLlCuLj4zF58mSc\nPXsWAPDVV1/xH9LJkyfj/Pnz0Ov1aGxsRENDAz92S0zcvXdKpZJPs8SyLM6dO4eMjAwfXoF/aWlp\nAQAYDAZ8/fXXiI+PB0D3sz8sy+JPf/oTYmNj8eSTT/LHvfH5HNGZASorK3Hw4EF+efOcOXN83SS/\n19jYiN///vcAgJCQEEyZMgUzZszodwlkaWkpvwQyNTXVl5fgU7t27cIPP/yAjo4OKBQKLFy4EI89\n9pjb945bPsqlWVq8eLEvL8tnuPvZ3t4OpVKJBQsWoLKyErdu3YJIJEJqaiqefvppfo6B7qdjP/74\nI9555x3Ex8fzQ2SLFy/GuHHjPP75HNGBhhBCiO+N2KEzQggh/oECDSGEEI+iQEMIIcSjKNAQQgjx\nKAo0hBBCPIoCDSGEEI+iQEOIH1u6dCkaGxt93QxCBoUCDSFOFBQU4Pr16zh79izefvttj/6tjRs3\noqyszOrYoUOHEBkZ6dG/S4inUaAhxAsMBkO/51DCTTJSUWYAQpwoKCjA3LlzcfjwYRgMBkgkEgiF\nQnz44YfQ6XQ4evQovvnmG+h0OmRkZGDZsmWQSCT4/vvvUVJSgmeffRZffPEFxo4di+XLl6OkpATV\n1dUwGAwYN24cVq5cCZVKhaNHj+Lzzz+HUCiEUChEdnY28vPzsWjRIrz33nuIiopCV1cXPvjgA1y9\nehUBAQHIzc3FM888A4ZhcPbsWZSWluKRRx7Bl19+CbFYjBUrViAtLc3Xt5AQKhNASH9iY2Px4osv\noqysDJs2beKPf/zxx6irq8Obb74JsViMffv24fjx43zep7a2NtTU1ODdd99FUFAQenp6kJOTg7Vr\n10KtVuPAgQM4cOAA1q1bh7y8PNy4cQNZWVnIycmx244PPvgAnZ2d2L17Nzo6OrBp0yYolUr+/Jqa\nGjzyyCMoLi7GqVOn8Mc//hH79u3z/A0ipB80dEZIP+x1+lmWRWlpKRYuXIi4uDhER0dj9uzZuHDh\nAn+O0WjEggULoFQqIZFIIJPJkJGRAYlEgujoaMydOxeVlZUutcFoNOLChQuYPXs2pFIpIiIikJmZ\niXPnzvHnBAQE4Nlnn4VMJsOMGTPQ2trKF7EixJeoR0NIP+zNnbS3t6Onpwfbtm3jj7EsaxWUFAoF\nwsPD+cdarRYfffQRrl27hs7OTgCmIlQsy/Y7P9Pe3g6DwYDExET+WGJiIi5evMg/jouLg0Bg+u3I\n1RTSaDR8fRFCfIUCDSEusgwiISEhkEgkWL9+vcP6O0Kh0OrxyZMnUVVVhS1btkCpVKKiogJbtmxx\nKdDI5XIIhULU1NTw8y41NTWjtoAXGV5o6IwQFyiVSjQ0NECj0QAABAIBcnNzcezYMdTW1sJoNEKt\nVuPatWsO30MqlSIoKAhisRj19fX4/PPPrZ5XKBSora21O1QnEAgwZcoUnDlzBhqNBnfv3sXFixeR\nlZU1tBdKiAdQoCHEBQ899BCSkpLw8ssvY8WKFQCA559/HomJidi5cyeWL1+OzZs345dffnH4Hjk5\nOVCpVHjttddQUlKCxx9/3Or5OXPm4Pr163jhhRdw8ODBPq/Pz89HYGAgVq9ejbfffhvTp0+3eg9a\nHk38FS1vJoQQ4lHUoyGEEOJRFGgIIYR4FAUaQgghHkWBhhBCiEdRoCGEEOJRFGgIIYR4FAUaQggh\nHkWBhhBCiEdRoCGEEOJR/w+Pxjo460ShRgAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x11389a650>"
]
}
],
"prompt_number": 121
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solution to 1(B)"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"solution_n2, aic_n2 = anneal(periods, period_lengths, cooling_schedule, nbrhd=2)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 122
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"solution_n3, aic_n3 = anneal(periods, period_lengths, cooling_schedule, nbrhd=3)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 123
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solution to 2(A)"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def calculate_fitness(aic_values):\n",
" P = len(aic_values)\n",
" aic_rank = (-aic_values).argsort().argsort()+1.\n",
" return 2.*aic_rank/(P*(P+1.))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 158
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def run_ga(pop_size=20, iterations=100, mutation_rate=0.05):\n",
"\n",
" aic_best = []\n",
" best_solution = []\n",
" aic_history = []\n",
" \n",
" # Initialize genotype\n",
" current_gen = np.random.binomial(1, 0.5, pop_size*ncols).reshape((pop_size, ncols))\n",
"\n",
" for i in range(iterations):\n",
" \n",
" # Get phenotype\n",
" current_phe = [predictors[predictors.columns[g.astype(bool)]] for g in current_gen]\n",
" # Calculate AIC\n",
" current_aic = np.array([aic(pd.ols(y=logsalary, x=x)) for x in current_phe])\n",
" # Get lowest AIC\n",
" aic_best.append(current_aic[np.argmin(current_aic)])\n",
" best_solution.append(current_gen[np.argmin(current_aic)])\n",
" \n",
" # Calculate fitness according to AIC rank\n",
" fitness = calculate_fitness(current_aic)\n",
" \n",
" # Choose first parents according to fitness\n",
" moms = np.random.choice(range(pop_size), size=pop_size/2, p=fitness)\n",
" # Choose second parents randomly\n",
" dads = np.random.choice(range(pop_size), size=pop_size/2)\n",
" \n",
" next_gen = []\n",
" for x,y in zip(current_gen[moms], current_gen[dads]):\n",
" # Crossover\n",
" cross = np.random.randint(0, ncols)\n",
" child1 = np.r_[x[:cross], y[cross:]]\n",
" child2 = np.r_[y[:cross], x[cross:]]\n",
" # Mutate\n",
" m1 = np.random.binomial(1, mutation_rate, size=ncols).astype(bool)\n",
" child1[m1] = abs(child1[m1]-1)\n",
" m2 = np.random.binomial(1, mutation_rate, size=ncols)\n",
" child2[m2] = abs(child1[m2]-1)\n",
" next_gen += [child1, child2]\n",
" \n",
" # Increment generation\n",
" current_gen = np.array(next_gen)\n",
" # Store AIC values\n",
" aic_history.append(current_aic)\n",
" \n",
" aic_best_min = np.min(aic_best)\n",
" \n",
" fig, axes = plt.subplots(nrows=1, ncols=2)\n",
" \n",
" \n",
" print('Best AIC: {0}\\nBest solution: {1}\\nDiscovered at iteration {2}'.format(aic_best_min, \n",
" np.where(best_solution[np.where(aic_history==aic_best_min)[0][0]]),\n",
" np.where(aic_history==aic_best_min)[0][0]))\n",
" axes[0].plot(aic_best, 'r-')\n",
" axes[0].set_xlim(0, len(aic_best))\n",
" axes[0].set_xlabel('Iteration')\n",
" axes[0].set_ylabel('AIC')\n",
" \n",
" for i,x in enumerate(aic_history):\n",
" axes[1].plot(np.ones(len(x))*i, -x, 'r.', alpha=0.3)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 332
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"run_ga()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Best AIC: -415.262574256\n",
"Best solution: (array([ 0, 2, 5, 6, 7, 9, 12, 13, 14, 15, 21, 23, 24, 25]),)\n",
"Discovered at iteration 74\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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sMMvLVfzqvfcSVgu9UDknAf01a9ZQl6Tw46233sqrr77Kd77zndg2eQ7iGsLr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\nQUfERRAEQQg6Ii6CIAhC0Pl/zb8iPkMvHqAAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x114eccbd0>"
]
}
],
"prompt_number": 333
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"run_ga(mutation_rate=0.1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Best AIC: -414.924853731\n",
"Best solution: (array([ 2, 3, 7, 9, 12, 13, 14, 15, 16, 17, 19, 21, 23, 24, 25]),)\n",
"Discovered at iteration 60\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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wQtzPPot99tkYBw4golHsQIBoVRVGd3eqKojHMJxJ1+8nsmqV+jsrS8V33G7C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\nUc9fuHAhCxcujOeUANBKS0VhVbsdvahI1ifrIYHnpxw9ijliBGZSUky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iKPPjcom/QVXF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"text": [
"<matplotlib.figure.Figure at 0x1150df190>"
]
}
],
"prompt_number": 290
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"run_ga(mutation_rate=0.001)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Best AIC: -408.88454751\n",
"Best solution: (array([ 1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 19, 22, 24,\n",
" 26]),)\n",
"Discovered at iteration 40\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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Hv/76a7Zv386HH37o18I0DrKz2dfi9BbVeYuKwnj4sPdnuedFCCHa7az3cykv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\nF13XA37tbdu2sXXrVurq6hg0aBC33no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"text": [
"<matplotlib.figure.Figure at 0x1150e45d0>"
]
}
],
"prompt_number": 291
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solution to 2(B)"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"run_ga(pop_size=100, mutation_rate=0.05)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Best AIC: -418.947211437\n",
"Best solution: (array([ 1, 2, 5, 7, 9, 12, 13, 14, 15, 23, 24, 25]),)\n",
"Discovered at iteration 30\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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cLAtr8mRV7tupRNU4dQrj00+RCQmnuw/3MnfQFzo/rZ+vnky/eB3naY4pHiNG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\nKKTyMU1NGAcPIlNSMMvLCWt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wOAj80z/h+eUvsRYswGhtjZU0W3PmYBw6BMEgdkGB8oAy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"text": [
"<matplotlib.figure.Figure at 0x11511ebd0>"
]
}
],
"prompt_number": 292
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"run_ga(pop_size=10, mutation_rate=0.05)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Best AIC: -413.821090366\n",
"Best solution: (array([ 2, 7, 9, 12, 13, 14, 15, 20, 21, 23, 24, 26]),)\n",
"Discovered at iteration 46\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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AAw/w+OOPs2zZMjZt2sTRo0dZs2YNo0aN4oknniAvL481a9YAUFZWxqZNm3jk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\ngg==\n",
"text": [
"<matplotlib.figure.Figure at 0x1164c5050>"
]
}
],
"prompt_number": 293
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solution to 2(C)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Change selection of `dads` to include fitness-based probabilities."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def run_ga2(pop_size=20, iterations=100, mutation_rate=0.2):\n",
"\n",
" aic_best = []\n",
" best_solution = []\n",
" aic_history = []\n",
" \n",
" # Initialize genotype\n",
" current_gen = np.random.binomial(1, 0.5, pop_size*ncols).reshape((pop_size, ncols))\n",
"\n",
" for i in range(iterations):\n",
" \n",
" # Get phenotype\n",
" current_phe = [predictors[predictors.columns[g.astype(bool)]] for g in current_gen]\n",
" # Calculate AIC\n",
" current_aic = np.array([aic(pd.ols(y=logsalary, x=x)) for x in current_phe])\n",
" # Get lowest AIC\n",
" aic_best.append(current_aic[np.argmin(current_aic)])\n",
" best_solution.append(current_gen[np.argmin(current_aic)])\n",
" \n",
" # Calculate fitness according to AIC rank\n",
" fitness = calculate_fitness(current_aic)\n",
" \n",
" # Choose first parents according to fitness\n",
" moms = np.random.choice(range(pop_size), size=pop_size/2, p=fitness)\n",
" # Choose second parents randomly\n",
" dads = np.random.choice(range(pop_size), size=pop_size/2, p=fitness)\n",
" \n",
" next_gen = []\n",
" for x,y in zip(current_gen[moms], current_gen[dads]):\n",
" # Crossover\n",
" cross = np.random.randint(0, ncols)\n",
" child1 = np.r_[x[:cross], y[cross:]]\n",
" child2 = np.r_[y[:cross], x[cross:]]\n",
" # Mutate\n",
" m1 = np.random.binomial(1, mutation_rate, size=ncols).astype(bool)\n",
" child1[m1] = abs(child1[m1]-1)\n",
" m2 = np.random.binomial(1, mutation_rate, size=ncols)\n",
" child2[m2] = abs(child1[m2]-1)\n",
" next_gen += [child1, child2]\n",
" \n",
" # Increment generation\n",
" current_gen = np.array(next_gen)\n",
" # Store AIC values\n",
" aic_history.append(current_aic)\n",
" \n",
" aic_best_min = np.min(aic_best)\n",
" \n",
" fig, axes = plt.subplots(nrows=1, ncols=2)\n",
" \n",
" \n",
" print('Best AIC: {0}\\nBest solution: {1}\\nDiscovered at iteration {2}'.format(aic_best_min, \n",
" np.where(best_solution[np.where(aic_history==aic_best_min)[0][0]]),\n",
" np.where(aic_history==aic_best_min)[0][0]))\n",
" axes[0].plot(aic_best, 'r-')\n",
" axes[0].set_xlim(0, len(aic_best))\n",
" axes[0].set_xlabel('Iteration')\n",
" axes[0].set_ylabel('AIC')\n",
" \n",
" for i,x in enumerate(aic_history):\n",
" axes[1].plot(np.ones(len(x))*i, -x, 'r.', alpha=0.3)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 294
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"run_ga2(pop_size=20, mutation_rate=0.05)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Best AIC: -418.947211437\n",
"Best solution: (array([ 1, 2, 5, 7, 9, 12, 13, 14, 15, 23, 24, 25]),)\n",
"Discovered at iteration 57\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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CAjBixAhiYmI4duwYUkreeustZnW11+LzKXHRo/Q1Q4iW2L+or1fltB6PmkIk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\nQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x118f42550>"
]
}
],
"prompt_number": 295
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Question 3\n",
"\n",
"Use the combinatorial optimization method of your choice to obtain a solution to the traveling salesman problem for the Brazilian cities described in the lecture notes, using minimum total distance as the criterion. Use the the first city listed in the dataset as \"home\" (*i.e.* the trip must start and end there. I will award 5 bonus points to the best solution!"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def parse_latlon(x):\n",
" d, m, s = map(float, x.split(':'))\n",
" ms = m/60. + s/3600.\n",
" if d<0:\n",
" return d - ms\n",
" return d + ms\n",
"\n",
"cities = pd.read_csv('../data/brasil_capitals.txt', \n",
" names=['city','lat','lon'])[['lat','lon']].applymap(parse_latlon).values"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 47
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ncities = len(cities)\n",
"periods = 60\n",
"cooling = [60]*(periods/3) + [120]*(periods/3) + [220]*(periods/3)\n",
"tau_start = 50\n",
"tau = [tau_start]*periods\n",
"#switches = [4]*(periods/3) + [3]*(periods/3) + [2]*(periods/3)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 300
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from scipy.spatial.distance import euclidean\n",
"\n",
"# Calculate total distance among consecutive cities\n",
"distance = lambda s: int(np.sum([euclidean(c1,c2) for c1,c2 in zip(cities[s][:-1], cities[s][1:])]))\n",
"\n",
"solution_current = solution_best = np.concatenate([[0], np.random.permutation(range(1, len(cities))), [0]])\n",
"distance_best = distance(solution_current)\n",
"distance_values = [distance_best]\n",
"\n",
"# Cooling schedule\n",
"tau = [tau_start * 0.9**i for i in range(periods)]"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 301
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"for j in range(periods):\n",
" \n",
" for i in range(cooling[j]):\n",
" \n",
" solution_step = solution_current.copy()\n",
" switch = np.random.randint(1, ncities, 2)\n",
" solution_step[switch] = solution_step[switch[::-1]]\n",
" d = distance(solution_step)\n",
" alpha = min(1, np.exp((distance_values[-1] - d)/tau[j]))\n",
" if ((d < distance_values[-1]) or (random.uniform() < alpha)):\n",
" # Accept proposed solution\n",
" solution_current = solution_step.copy()\n",
" distance_values.append(d)\n",
" if d < distance_best:\n",
" # Replace previous best with this one\n",
" distance_best = d\n",
" solution_best = solution_step.copy()\n",
" else:\n",
" # Retain current solution\n",
" distance_values.append(distance_values[-1])"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 302
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.plot(distance_values)\n",
"xlim(0, len(distance_values))\n",
"xlabel('Iteration'); ylabel('Distance')\n",
"print('Shortest Distance: {0}\\nBest solution: {1}\\nDiscovered at iteration {2}'.format(distance_best, \n",
" solution_best,\n",
" distance_values.index(distance_best)))\n",
"plt.plot(distance_values.index(distance_best), distance_best, 'ro')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Shortest Distance: 134\n",
"Best solution: [ 0 1 2 3 6 5 7 8 9 11 14 13 16 17 23 25 24 21 19 18 22 20 15 12 10\n",
" 4 0]\n",
"Discovered at iteration 3556\n"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 303,
"text": [
"[<matplotlib.lines.Line2D at 0x1270d44d0>]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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IA0ilpdtL21q25ZYpI0hPjOLVA+f8Krlic6jotAphWg3Nra0cfwf1hRCiK5JM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\n",
"text": [
"<matplotlib.figure.Figure at 0x1270d4510>"
]
}
],
"prompt_number": 303
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from mpl_toolkits.basemap import Basemap\n",
"\n",
"xmin, xmax, ymin, ymax = -70.0, -20.0, -40.0, 10.0\n",
"\n",
"fig = plt.figure(figsize=(11.7,8.3))\n",
"bm = Basemap(projection='merc', \\\n",
" llcrnrlon=xmin, llcrnrlat=ymin, \\\n",
" urcrnrlon=xmax, urcrnrlat=ymax, \\\n",
" lon_0=0.5*(xmax + xmin), lat_0=0.5*(ymax + ymin), \\\n",
" resolution='l', area_thresh=1000000)\n",
" \n",
"bm.drawcoastlines(linewidth=1.5)\n",
"bm.bluemarble()\n",
"bm.drawcountries(linewidth=2)\n",
"bm.drawstates(linewidth=1)\n",
"\n",
"for i,c in enumerate(cities):\n",
" pty = 'r.'\n",
" if not i:\n",
" pty = 'co'\n",
" bm.plot(-c[0], c[1], pty, latlon=True)\n",
" _x, _y = bm(-cities[i][0], cities[i][1])\n",
" plt.text(_x, _y, repr(int(i)), fontsize=9, color='yellow')\n",
" \n",
"xx, yy = cities[solution_best].T\n",
"bm.plot(-xx, yy, 'y--',latlon=True)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 305,
"text": [
"[<matplotlib.lines.Line2D at 0x1333b8050>]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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tV5/myrii88pTFARtA9G8wFTz4HVYqafkHnKgyBZLdf7sA/YnF1Ct8JFKlcxv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N9H9TFTeAB9BxoQ1p5+X4irTCgDM3wUmAPm8291+CjnxHqzgSCeDBIsYUIjIfva8wWraqUClfRW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ZIBYHLce38srTpQVuMADBAWouMPUYWk3MreyZQsLfo8p+F6BSi5v0dxAtT4Fp4yj/NDp9pTBG\nRJuV5LABaOaeg2uayTlRGxD23BCy22Qw27alGLUtHydeTTZ4IUcsWfmD3piSHABlhOiRa7rWt5e9\nHN7wBvi6r4d/XMG3P1IRCqGETytQTnH2omFxJAv87auuh5aNhXP3FyijCXrMlkoLerJb0lV6iEi9\nCzRHgQuPiWRXv5gHoIelez8ThaJdDsZ2upsjoWTm1MA01akY3CeYNJemSLQ41LRpPerZJ6wPUPTQ\ndghgtDSf9TEXNeeOHVJgW5aSmzTa4F1I3PnB4VnxXhke4mIiUFmblH3quqbPEevV6F0rhba2h3ml\n84DIZukoKIAt5HE5vNFK8+CHC2IQdYiiMEk8OSRZuUDosl6rFFzbQpAH7z2t95x5sGTv2ZaHXz4h\npGa50nRYDP2Va5oPPmX4sj/f8C/eJg6mVjExUDVWG7yTAmFtNM3Scbwv0Ojxfsf9D00pdzRt64iJ\nWLFcynN483pLcXZCDEryyhqqylJbK6UHUbo0qMkxuJpKX6LQJbo4xvvbTKaO8uFKBBA+8F6ufeC9\nPPiZr0c/+MVgazCB1735mzi8PeUr//x7+Lavfz/f9t1/Dqsr0ArXNEyqEuqKvSs3qCeVKOtnODPG\ngbCUnkcdQyINqVy1IIuf1mgjBKhqUrJcHuOjlFCJ4ySOkdwNI4Y1FbX3XnV2ykJqOpwsn8wlK8Y1\ndP1jr9JnARnPqXqPfQzYb3EMZ64YvJMw66d7W4cgxz+fr7GCTzbKu8d95nunNCiTIPFcmsFdw+V7\nKllIbezwLvQGT9vB8YrJKA2jGu5pMVHUZzRFNdR6SMJfPji+yCZLiqkBhlKqINN/M+TRb2kR1trQ\ntr6HYusdySXODzpcZ9i6AKZIWD9BVCAYotPlsqW0pv/bhyBSaE7a9QxEia7P3cUY8Z0n+og7tjTk\nc7NkIsV0RzM7q6EwfNFf8PzozxiOzij+xk7AGI3GEFNbEqU1IQq7tapKds9NOT5sadol02kNKvml\nPRVaouoYBxKJMaaXyAJojgLVzAiLdE1INnHNVj09mnUyDQAAIABJREFUrTi6ITmm7QsFkdjDptnh\ncD4z4xKsK8E6Vg9NXZVCclkM3qN0U++w1lKWBa136f7mRSnStkJiMkanVExMEZ7u1W20VkkKj6QA\n41Ho0WcU3VLyntXUMJ1OcK7rWZ5lWdA08v5YraefuulvaVoplHOtCwpl6ZyjW8L+tY5zD4sj4Tp5\nCIKJLJs2RZkDE05phdGKWCThhEAfrW1fqtm9v0rXUdO13RDJCujBv/w3E/7nbz3kV35Dc/OWGKyg\nAl0IoANFUWCUtNe68tQ+9cxSlpoLF0um2wIXFlWBDxHnAtVU5kw5sSlP31fay31WoIwj+g5TlLRq\nC2MUy+M9lCmwSqM6Tes0wWjOPzZjZ2/O/l7k2ff/OmeOnuHMK/8inb/A4a1zqKD4V7/yOv6bN/4q\nqqxRCImpXR5zcOsa7dEetqxAl6K+MeAHyXHOnSwg59I8SuTHkFwkKacdgVs3b+KaJabaRmnd94kE\nie6UttKh3ZSgpEGsBJSOwiTSRruUZ19pgpZWN0pH0DY56q4XDRGjeQK0HG0b3olDDrBPlfRnMMzD\nP+3bp3YOqxH05k1KXLQywsFQOSUmDnVcibZObvdk9GwioBylerpiojj3UEXuoae1HpEJkqZmmsAx\nxr5wMeeEwqhIeGBIqt77lxKJgeAirXdSW5EciSXqutGymGglNXLt0jM7Z5nsRvavdLQLz61PeIpK\ns3PBYuuQ6MUJzgOq0ibvTkt9UFQSwQD7lx2mCGzdp1OrmqSZqRXaW24/20lEsraVE83WfWWCsyJv\n+4UksRWEEu+d1LBJ2YNQ7aNW0hNKaxrfEmxHWZR4pZOeZ46WSF6FGCyj5BoEHzE2kW+UYr7n2L20\n2kxzzN6UOZkKPXPfwUR+rLaH7sreR3TMHQMySTwtTDrXJOlU1pAo3Ek7r48mexg40raSU/M+pMJv\ngdaslTngfZKqUmJ0Bm8RtFFJtFmiQvknve5yX7AmlVtMtwuKwtJ1TZ9vc6lvIvh+vmWUwlrTN9WN\nMeK6FqNhNpvJ8VvNzZuHzM6WGKtxbqhd6lqPD45IENktq1PtohjnGBxlIQt755yURoRI66V1T1UV\nvYB7CAL/++C5cVPz8+8o+at/xfO9P1ABA/nLJoQihMDlpw6oJoaz9xeEqDBK4xQUhcEYQSO0IJZM\ntkoRg2g7SivUoxBEh1EXljZp2SqroSnRCqZ1hY6B24f7zENH0AprhFBQny2Znum4ec2y9/Gn+e4r\nP8zLZ5alOsff+qyv5bNed5Wb+zOopugYoGtkTlrL9oVLSYA9QdDpfufsWzRqgIWJoLREzE46uRhj\nKeoa1zlCu6Aoa7nu2hKDS+U+0mMPbQnRUNTbGFvRhSXRe4geqyq2ZhWF0Vy/eoWopE+cL2bYaktq\nWVWgnR8SXYuPDSoRZ8bC7ytYe3rGVH49R4/9R3PecNXg/UltL2T0ddp2ks36qe0DRlFojKgQ+zQG\nMZJrcaVS7wUweqZULI9cX7tlqyQsnVQNQsolhZC93JG25Nqgtda9ll4+IZWik/EFMkb36h6rFyDt\ntb+OmWihqGaaYiYTXBnNmYcKunng6IanawI3L7fUM005lWPZoqCcSJJcBdmhqPYLCWB+y+M68eab\npwOzs4bZWY2xhuWRZz9JdU13oJzlPJCM21ZZEzDnwDL5QAR4Q/JefdKTkzyDnJY2hmWzgBR1Gs2g\nVJ7zkj3z1aZoN0OXYojahey3nK4ZvDx54mrUnCOlsw+KrmFITgApz5kdEKXB6OxlR9CRLNSc9+06\nl0on8v0cFBe61uN0qoeLCpdxKhTDrR7uRRD8kxjFsTFaxmKtTs6WHxlAWRwzJK8K+buspI2NUiZ1\nR+j6a5GjOq1UX6rQ92A0AmM516XSEdHZnJ6xSRA3JKUZuZbeBUypKcoywZTpugKoQHQOj0JHmQWd\ny4K6Ct96TGIxaqWk7U4Qq/5zby/5B3/vmFc82fFHHzJola+NaKx2bcfRfsdjr9ilaRYEUxCUxiiw\nWhytwohj5Xzg/AMlz3yw5frHlrz4yW3JWaqQkINS7rc1qAB1mDMtpniv0JMttIJufpuQyi9qDMui\nYFoUmItQ6QVPPNvwBU84+L5n+dXlW3n78cv4W9/zX+BNIc9ADNiqop7OMDESVcSjib6T1kfJmxGm\no8FWJnV6kHqtydYOR4cH+LZla/cMdT3l9u1boB3BtRS2oqinLOcH+DS9jLH4oNGlHHe2fZYuNMzn\nxxwfHlAaTevg6HAft2zRlaWsCuLWBUy9w+7OlPb4iJuNoyxr2sUR0bUpuyStjzL6kefWiUAnDqSV\n4bWT5Jb/WKO8dQM4BD7j79ydfQmgggidC0lfdFxjTAbvLnm9e4M3dexhzdm5gsluWix09sKGg6yz\ndiKpBk3r3uMZPJ31CSLebZkIASLOOzD2hu/mvNIqjh5TdCZgfyognirOv8hyeKOjOQosj+WfbAMb\ncutcSYyO473Qk3fWt+PbiZWpBq257QuWesf0Rp6RAZIxKpSWUgaVEu69oDXphwKUQJ7T6UScAEoh\n2KQcVN/qKNLnFDN7LO9XzsUQCSz3HZMzJ29vjvqUCkMhrRKlEuc8ukgdn72ix9qUiEQXWoGSPKvR\nGh8CzkmdWz59yX1afOgYanNjP25JNxuJHFMLEdEBjmmuJgPSDVqJEZX2pVKbnJyLk8jTmGIwoi5Q\n7SpCq+i6iA+isFJV8vnl0Typc+QoTUFMkmJN2xfNi1FpKauS1jkWy5bgoGsCupBxoMHjKEaXuTCG\nUlu5dkn1RmkhW2SSjJBaPNoEyrJM0Lmn1hVdUALbxqHovvWaf/L9FTduyrwWpqLGe2i7lsVhJ+kD\nAG0wEXRwFKYgOuEMGm0plEKpjqrWbO0UzI8dR0euZ7iG1PC1KkRUIMRILAqiNfjQ4ZrAfHFMDHKP\nz24pXvOKJa9+jePFL/L8/e8+Q9BT1JGH33X8zmvh21+vKV96H09dtQIV+20UFaaMqOmcrhF4WgWp\nkVNeDeuGUgRtmG3vUs+2mS8brC4oC8Xe4Q2qWYk1FTpoSt1y++AZ6skWLlja/Ru0TUNZVYAV3qSW\nCDyEhrbZQ7W3afduExctYbbDsjPSosZI7iZ4j17uM6sV3cEN9m/dIDQd1bkHqKstlvM9Ylzgm2O0\nX1uqc2DHOKI73SAOZLBPt8EbR10v5LHWo7mc3ognznWdKDP8PiA68rqM8XS2aUyC1m50QaULxJ22\ne2siO7oR3SIw2Un1c1olkeEhgliv+ZAoTPevnZgZ/cUBUEmBnX5/sqrTQxz5e/17/cUYmEdjbyoK\nIsKZ+2uhqi883RIW+wNhw7vI/rWh9xoKikpa3EymlnIiEls3r7R0S3kgtYEz91tMXazAZOsRqxjI\nXATPiWuVP6u11K4t5ssUvYxIEKjR9Rz22+tcjmsFFUQnNWQ7l8rhlFa+N0j5FEWRxJY7fIg9tKeS\ncVF9rWS6pynCcBnGHivZpIgtaU4jj/mQLxxPcqVEXHZM8+6PsTK5Vd+1Q2sISq5JSPk8rfP5KDon\najJn7psxXzQ0y47pTCLIrnMoouQTFw6jhUUIq6QbyY/KxKmqGm2UwNBYrn9izvRMgbIB70KKgBVV\nZYkxUJYTYoy0TYOxarhuxB7+BxG4zi26ZO5ImU82whpF1NC6HJEGPvYJqW9UMRe/u771yq0rDVvn\nLMumEQRDqwTTmiF1EDxoLa2NQuDCpRmfeOqA5dxx/tIO82ZJdB0h+t4B0SlXaKxFBzicH9N1LZ/3\nOseXfGHDIw95PvD+gnf91oTv/5GCI2dwdHzjw4Z/eDnyd89vs+X3+Lov+2Xe98yz/N+/+gYOlwkR\nQHQ7HQ1RdQTXotCEaHokUMhSivl8zsH+EWcuXsQ7x8HeEV2zoDDQLeYoa5nv3wYdiNGhohHi0nQC\nCKSryNcvsJwfcrR/i9jcJEYoqmlqRisCEcYaFJGu69DhmL32mOX8NqayaDtheXyE0QatIsvFMcE1\naGX7Fa1fo/rf8lo0OMafqtj089/WjdNqHvFThyJXvzc2XKYX919lpJ9kiKrR73lsJyPDjUfN6xvm\nrudwT0ZvMjO4RpiA7cLTzGGybdcMESsLc3/g8eKf4JqVQSsSU0/yNVqJIkYIOZdz8jv0hImhqDqT\nIcYXp2fmmeFzxcTglqsXf7zNzhqmuzYRN2R/noApDOcfqWmXHcGBrSLGGpwf8pPji/2ZTzqWjeIj\nH9O9rJjWw5jkHmcihqKwFUSV2J8j1Q3vCSH/fdLwrV/zGGC+76i2zNCCZzS5MlnHmBFdPx3TWpMK\n0ANKFaj0IGdDmHN04+ssPJfQQ63yudDfslw/NzZkpzG6ToNEBpZmHq9H6dgbXKWEoKJTcts7RdfO\nISp85ymrEu9aysJSWE20iOCwkVyoGJwBmodcDiNF9WVZ8NR7Djj3YMVkV5jC3uQxiTdbFIU81Eph\nC70iuKCQzgTCcBVlH5UgZCIURUnwHhccAXlOcuPPgYCUZmMvyiyR2N6zHdMdS709KmXQ0nUk182G\nkMtFoCpKQohsbVuCD+IgLZfkDgPOOYGCozBXLRbXttCLDgfaTvGL/27CRz5YUoaKqAJN5+miJ6jI\nvLJ865OWST3ht965x5veBF/3jR/jH73lf+PH3/7l/NofvZJoHKq0lMwILPFcJ+CJwZCE9mVN0Fpa\nQSnF8ugA33a0x3uY4IjLJZ2GRdvRzo8pqwITQSGF7CvzLgLByRiTgpK1BSJkLZHtbLZF8J795TFJ\nYpvoGplvpHKg0NB1ERe1FPKHBcbaNYiOu+ToRs7f6HMvZJR3r6zJ8RryQuTf1oOe8TFWg5TVz9/p\n93vZNq0vp213byJr4fZzDp+k/Ca7lnIq2md+tADmg41Puh94ZMWjX39fJfXvvk4u1VX1kQFhBRpI\niNTGEz9pgIbwOi8iy6NVozfdNRS1RhcRW9r+Ycs5JTleKsQvRDUlRqmJWodzAba34Jv+esdbf7BY\nocXLApbYlznjl9iIiqRCErPo8RC9DZNm82TJf8vnAos9x5mHqn5Mce26Z6mtbPBCiH1z02zUeiWb\nEPrIc7jXQw42ly70/xIJ46TXtjqGTMZYf+20c8uf8X5gAGcWa4445ZwM7WKJTvVghwfHnDu/1de1\naaWpq5LF4ZwQwVjdoxFt21AUBbYwaCJFURNVZDl3AoGfFXSjqip8SPCXll6Pcn/zTxlzjsSUln8a\nhdUGIj35atxU1gdHiBIVhgTdaCOflw4smXovOev5jVRPeZ8luIHBa5QIAuQo00eP1UWqDwxYU7A1\nnXDp0oJl63Cdw1ZlusZSvvHgg4FzZxwf+0iF7xxKB3FKHbzv/ZJHnmiNtgofRRmodR3RBgqrmExr\nlvMDHv2MCXs3Pd/zv8z55VdP+eZvfTsvf/Qpvv8Xv5ygRBuWQuM7RReEXam0FdWV5IiUiZXrlnPa\n5QITkmFWiug9wTsm0xlaO6LPuUC9Mqd6Jzrl0HV/URFYXyuskTqvGFyC5ZJQOQFTWKknVhqDS3W+\njqhzSdMYUjt90c0oysnn+SQM+EJsdzNkL1z+cDDkA7Arrw8O5eo37sUgfzJjXHeuT9vuoU4v7VDD\n9kVLNbXiNKUJNdavHB84/8xNN2U7GWEJc06gqxgD1hY9caA/iShsrn6RTA/0CjZ8ipeQF8i8iGut\nmZ61uGXsjV8x1SgjME72suX4q3lDUftXK4tv3GCI3vzVHb/1e4Y//IB45Jmok42SLPiaqioxRqK7\npmn63Gi+foPc1kk4Nx8rG9V8HZaHAVtpbGn6h1oxmjhRjyJKSfCXZdVDnBmClrqX7AHqnrSRyUq5\nfk+c5tiPRUigQ6Qt57xaMrFePjHWRx3g3rHA7PBZmQ5RMoNJsgykeLwsNV3X0rUdRim8UjTLDtd5\nJlOJ6uqywkdPXZccL5aEAC4GqqqkruskmgzGWlzXETU899Qxu/dVQCT4jqKUKNorUWHx3qe5KYtf\nhqalzjJCkIbJOkXRIIbFey+tewavTDq6x4DrOgpbSHYil6eogIsik2a0xtaa471Up5eul02RXoai\nTU+AEgGDEKTc4fgYZrOKGzfmXHxwBgRe/Gjgc17Z8drPnlMWkV//rSmXn7I43dF6TxeEaeq6TuoX\nC2nO60PApRo2rSWC7DrY3d5Bh0O2JprDs1P+8L0HvPmvznnll7yaIk7pVE00e6iqBbeFjhORToup\nW0Lw6Chws3cdVilMVaZaYIFfXXCoosDoAu9bog4QhZEZezIV9MoqwfftgvLzpozwB27euEroWmLb\noCYVOa2gk2CGwiR0K8nUEfsSlGENyAsPo19OhzLjCAb9D709nygv6ySP95N3l/up3qsRO7F+bwgs\n7uW7p213NXq2Evp6PTOpyFsPOZikYDVEREOyfn1hzgMew2x5kFJnJWodw+K+GiGNYa6M9Y4XxbEM\n1Thi0KlD8xiGraaGedKwnO5KvZKow6T1IcbUGy5T6D1lWVIURerDlg3DsLjnhe7zXxd4yWOR//Z/\n1P21EAM6RKmruTTXR2O9o5CMyzgXun7z8zVZhcAi89sdswun31YZZ0zEG4X33RCVpHxc3hRJRiuS\nHnj63EXOU0oJQ9Kt8INhX23ay8p92fRef8wN97CfJ0ntvW/mGnPbIkEJjo/nKDR1XeJ8hGVDiCL8\n3LaRaV3gvMNaIZt0KZ9GENH0shQRSVGYFy9//zkxWJce2RpFuzFFiJGua3ujnssujDF4N5xbCEH0\nN6PkTPN9XoeLyU5cSOeY8mnRk4hDQmI5sxv5L7+i4Qd/TDo4uAW87nPhu75jQec07/73hu/53poI\nUqeWyj9MMsi57+XlZ/aZbZUc3D7mrd/b4lzk995T8oM/OuHy5ZK6LCmjk6hWRULuxOFkrrSuIzjP\n0i+JKmC1FAkXtoBY4L2lLGYE5bj44H3szgre9+7r/PtfegdPfMmDKPUELpZEvUM5bYiFk1IE52Qy\nhUDwHdE7ohJ4OCpNtFK3GrRFFR4LImjtReTUdQvCcn8wJtmRGwvG9ko9kejdkBzSCl2VvaMQlcJF\ngdZJqZaYkB/QxFTErDYatoFJOLTCGkV5KpO3XnhYM293i/KeJ5q58Zjr69VJx/V0xGrTPjdFq+OU\nzroW7922uxq9cw9PEKMR00M5WpBGn1u3xpkCnx/u8WeGE5K6ity/sbDy0HTd0INqWBzXF8PVcZ7u\nHcSVhSVHjtW2AqWZ7g5aiwNDMoIS+FYpKSHIhsj1+pOrEZnWmt2dyJu/tuMfvdWwXA43RYYyhPw5\nkmmalqHwXvef2RQ9r163YRufa3MsXnE5GfJJmyaYD0Hqk2DQmgwD/DyO1PO/daZs3tb7aI2v86rh\nWr1hm/oZrmP6Y9Qg7X2FhANJX7QT7U3JJQZMKXCiLQ3eR9quxRSWGC2FtbRNR5eKv0MAZURiz9qU\nfw2Gq08vaBbCBn7Jq85gU061aZfp/MbjN6mJbkSK7QdC05hpGqNAl1lurZfuS9cjE2sADJLfjkFy\na3VR4pTQ+g8OIy96OPJFfzbytmekXu67/oeWr//bM/YPakqt2JpogoKwSLWcRu5zhnj3bywoS8P2\ndsli6flf/9kWl6+K2otJJRVu2aEKQCu66HEx0rpOpAKBxnV0KLxQLwUy9A4fFUErFsuAScSCwjjO\nb0/6/oHP/t7PcO7xV2G3X0ss7sNWgWLiODosibYABa5tiZ3GK43B4ruO4B0OhbVTyskEbTwhOILT\naBcIQcg8gT0pDlIpd5ojquTY5sc8v67kpiZFmBHCoDK6oJN2Z5ZDg6AiYKBnja88GeQ65Tx3x8/H\nOq3++cKMn8r3x5CsnG7ex/hsVmHYTcfbZJTuFJ19Krm70xzkceBzr9vdO6cn3cBxYfbwJhsPuvp3\n1txc7dAQe48L0JlYIXVXeSFcJU3kfamVe5KjpH6/8WTEtz62aKDcNlLEmsbhUwguxjo1Uc37SfkK\nUZNIRkrkXfrF3RjDA5ciP/tLhg8/ZUm2ZG1MA9mAVOydr+Mm49RDK72HOhiPTbnTRSpTGL+3acLF\nBJdmg5cLyMfe0/j3TQ7FOvR4Lw/d2JD2JCOtNz5A46h3+M4gwWatTqSbgTijVK6B7DC2ZDaZsJgv\nsIU0bG26lkikc0IYyQQdPXrg3VLz7EcOOXOx5PwDBTu7E3ESgsM7R1lUOO9xXSp8jgalLDF0tD4g\n0nDZ0Rk2rW2+c0jnFqEUZigy69EaY7F1wXK5lHNP/R2N0thC2kehLD/2U4pv/OtL/u1PRb7g8wVO\n/Mff1bC33/HPf3yLZz8xlfxg61Da8xkvXfDZr1ryzl+f8uyzkyTRJb0bjdVcvkKif0NZFCgnrZqc\ndzgiDQFHTEXpGdoWXcw2RAxKFE1S3N92giBoJSVLfn+PsztbvP71j3DluSM+/MHbPPMHv41S7+Li\nK/8sr/3Ci7zxP3kHP/72v8Bv/tErZUE2FltNcF2DAdp2iQqeqqgoyx1sWaFsi/cdoQXfQnQLoGVx\nnMQUVNIPUlnFiGT4FKnPkHAGMtQpN6tHL8QNHSIyHVMhdH4vDs5qnr9pJg/R4oZIaBSGDpGfLIZ3\nfY7Wt+drMPOWhUY+meNtXF/u4pznzz3f7TSH+W7b3XN6ab1NwiF9ZBKJoo03Or9NC7FKMOH4u2K4\nJHkfY0QbRVGI9FSG2TLsGdUqWzAfexyFSPR2Mv8jXxp+HS+wmc6dDY5IUgUxvjpJeUlVMSEIZCfP\nxRBhjI1DjJEPfEjzgQ/lrgX5+sk+x/zlzJA02q4YjE1GR86hD8FWT4hhknXLQHBSJH/aRMy5pxhD\ngufUyMGIJz4PqzWHwzjzv3zuI695owOkTux7NYpf3X/eckTUa58K51w8dyXX1nVZw3PQWjRFQGuB\nbqpJhUqRSNbnE4FpjzYmabtKNHbz2Tm3ry15+Mltykqgy5DKCbTWGB9Q2lCkCKzrpAFy24k6SIb5\ns1j2ChydctRFMXY0xg9uimBBYE0lRe0ukyS8kLkmVY11jk983PO+P2x54xs99a7lsRe1/OWv3mZn\nB77zv9/jm7+54BWv8HzGk8d8xpNLnr1i+YN3W/b2hDgzm5V84hN72NKgbDIQxhA6T8BR64KyLph3\nCxauxRlwmXCmcrlJkPHpUuC9kHJmpkhpSM3CNdRlQShLjkPLhe1tXvLQDttmxq35Hs9cPuLa+9/F\ne8+9gX96+Ab+2le8gy/6rPfwQz//ZVw/vEAMEWssViuq2RYRD8oQmeKCdK5QCkxZiWapDpSxJlQV\ni+O5dEvRorIUkuOcH6McuakoMGSe8yqk50+LeLmKiRwTA9K4Nvf8TCU5vSHN8zelHji5DQYu/d3n\n9HL4ueFLd9lOMzSfzJbn60kDzR0HtcmQbdrPC23wxsd44SO91IMq9JBN8lI5eZJjLHd1MR/+ZXgK\nNUBAkmOgr7MaTmiYWJkwkuWIdF8QLYPqjzW8lPavhgBJ5c+S9A8z0SSpuhidmHtC9fatiAmTxr1i\nBNI+hwu+atilxk0ixjwWo5NmpB/g2/FNFAOpV26mUkDUo2u52aAt9hyT3VVYc8z8XMW9xaEInqHp\n7MigDtp1WXhgIJeEMDZUo4VibeKNj5ej9Pzw5PueDfEY3h2gyzzvwsgga4IKafxybwJSvpBVYoxJ\nKjhKE2NHYVIRO0pyTWiigqqSfGVhLEZXPPPhPZYLxxOvOoc2AikKQ9Am7dUs49UJ+aewuNbRNh3O\nZ4TAJI1RlyTNSkJY9nlPnZwpIUUMBq+Heh1gs8MjcmVE6KKncW3S2FR03mGU4t/8/Dbf8S17vOPX\nAr/3bsOVK54rz8FkCn/mzxzy5JMd73vfhLe9bZtb+6Su8Iq6KlA6UFeWtvHUhaivFFajMFhVUBYV\n1ggS0gaPi9JlItP7Q/SpS4XFI7CoigqjLGVREhHCy8yWGDS+azHVjNZFmuaI/cURzz47p6oM3aHj\nmXf9Ah/9f1t+5+fP8V/911t811/7IX72t7+It/3GXyRERRc7lG7QdJjgUaHE6oLO1HQEvCowVgyU\nMZZissvxvJG1YpTDjmk1UXnO94BTTPJ9qZ4sJkKMj+QOD/2alH1RuWuyi/FzGePQxih9R8XBEMrP\ndbam+pQMXv/t9YV/RX9ytEYh5TMoRQiO3KOSlDrwPrC2oxPH2mRsTjM8L4SBW48S14ODTfDqnbZ7\nqNNbJY/kqE0iMbUiKTbOT6xfmL4Dcvay0ntVVSK5Dmljssmoyg4YTba0z76/3ii66mHQ1bPox0G6\naaN72/cJtBLRtd4TvMKlMg1rrUxkRjc8T/nRBc+LVR/x5CEpLRqa3ieVmVWHYYhmTo53PbIbDMdw\nTN8GumVg+2IxGsdmiHKYIKPmumvjWXU5V+su++AzRXirY6E/Rj/afh6cAvP0Y0qR2OizY1anRPig\nrU2MxpgYkUoEpKNAnkVpCLFE1HlE4qmwYsCMKdg/nBNCZHuroqgLumXkI++/SVUbHn3pFrNplchK\nnq7zhKYDKrJCkLUWozVGGVrTyRqospHNPflMqllMaEBIY9XDlR17qrkXnjWiBoOKvYJ/QAx641sK\nW+C8iH67GLl9UND9iOKrDpZ89lvggvGEHYVzinf+xhne+U5PYUrariP4lhBEoFpFqMuSCxdm7O0v\nOD7s2N6dUGgrBiAgxk8XTGvF4WKeojvpqK58SAo5OkXdUsAfYiQag0VRWkulDFZpSm1pYodBcf3m\nPh/5wC2CjzzwoinTmeZ4H27daDhzZsKN67f5vn94i1/+zPN8/uf+Gge//16Ob10BpGWTdx3V9i7V\n9hmqnYeoH3w1qtjFR0M0HXQeRY02NdqUBDfH6uG5yc+TTkYvO2357bFaUv59cKiHZ2fTM3ni9x4C\niWn9WBWpWMNEeEE3BbkGcMhapmhOiYNGyA2nh2e5P/e7RI53MzIvhLE7bV/PN2q8p+L01UVvNYpb\nX7zHeZjxlhcxa4ckvk2dDdq2FQX6qFaiE5n5wAjEAAAgAElEQVQYm4+7vqD372+4abmI+aSHkiax\nypGfSQutECNCUigRD38VktBDIdTaua4xlxDITRbSkyyj9WLv9W1de3Td4wFRl5ns2tTPz6/cr03b\n2KCsQxGrY9mc1xtf703b+mfH12P4fX2Mce3nyX1qpcgCpVoryrLA+yTRFklkjZDgafHobYKr875N\n6nlojObgZsPHP7RPURuqSdK79IOhLWyRhMgN1gyOlPT7E/FoGDORc3SdugF4MTKFtb3ySvakMzs0\n3wdjDFFlx3A8d3XSX5X2WNJXkr6e76FfUHz+MsB3wS//6Jx3Hxr+9392pr8mPsGtRYjUkwneBbq2\npdCaszs1V68d0bYe7yqsFci9azqO/TGuKMDGlL8WuCJEyWv191NJ+YUSvBltRNLOKk1ZWiwKHSGo\ngsViwVMfukU9M9z/6AznHZN6yn0Xpjz8cItpFQ+fXfKJ68dcfuqAf3vVsjy42l+LnXMa9IRmcczR\n1T0OLn8M+9Hf5eLLXkN93+t5yYsbvvNv/mvwkcLMefxFhzz4stfIPE4rw8qMG0dj6uSztl5qcE8L\n7Hif+VkadWEfH/f5bHeCD9Mr8rmV7whELmL3nnx+d0s3nGZ0xmvwpzL2F9IwfjLbXY3eagSw+hrx\nJMQJ65MnsxFHBkZJxJgN3mAMVo8l0dJJY5ffG1/84fPrEyr3nlstbs9wZb5xNqsqRA3R4H2Xip3l\nGKLsn8kucuxL9wU++5WBn3u76febPwskZRkROM7j3UTXH49tEzw8Ps91AxKDsDbPPlKd2Ef+7irU\nuAp32n5BPumkDG2MTk7uMcN0433YsG2CI4bav08OHrGjVlBG0aveSK1nJfWP7TLljZMMmTI9aeXK\n0/vceq6hmhjOnK/Zv91w6+qtfo4++HhNXYthC87jokCTuZA/OE9d1cwmgUUrZSe50FxF6JoWpRQu\neKwpiAiUrDdEsVVdJ9FrETwQUktARZ06jqjUTWSoCtVG4P1Fsufv+RnDW949Y15aZtMJxiiKwuBa\nR5ciybZtIUq9oFaK2VaFc4IwuC4wnUl/PlsUlOkcVUJ2pNWSOHxYg+4VU6R43nuP1YaqKMF74QIU\nAqNFJDbauyWM2EuPTWh8hwJc9Mznc2ZVzXLhiUXBix8/iy0DMbYoJhwfBqItUEVJcAFd7ONrxe1n\nZty6fMyV9/w2T3zeo3z4o5/DX/k7X008vsmXft4f8PrXPkvw3fBg5mcjkktYV14/bTvtWT05N0eR\nYQ97DIZlE9rx6dpizBHeGJ1JYwxBcqNZ83b0XG5aXzc9g39S5/Hp2D5pqtCmk12PVsYXL5cuKCXK\n7ePXxu2Isue/CZZbf31cDjE+7nghGY93dTyZmZmiwmSEvQ+jdjji5Q/tbeS70vkhGy/4hrd0mNRP\nTqlhcuRoS9RM3EbvKW9jY7juOJz0PE86H/O9jnI66JWu0+BX6sBYNVanORPjv9ev5/qW31+Xoxvf\nt1zHuH4dxuPMkeUA3ybZNqN7ubTsLIliTcR1juhD33XBGE1ZFhSFSHDVVUVVllRVlRoFC/NwOqk5\nuDnU1x0dNFx8qOKhx2Y8+uQ2O2crrn+iZTl3I7jSJEECieCc8zRNgzGarcmEaV1RWmkPZFJTS5Xq\n4bpWZN7EakguNTOBM6lJHAwRmg497ARlVVJWFZ3zyWgN197HwBut4V+Vmjc9NuO4MFhj8Umzc/0e\n5IhGa+lEYqxlOi0oS01ZmZ6AY40iBi/tmMqCoixW5ykDRJvuZg/76gj4mLQ7lTTeVeJ0PPP0MZce\nngjJRWtMUSQZP81y3rBQe7idA+JsycLPUVjqYptLly6xvTNDF4oLFzre8rUts7Li7O4FvuA1L8YY\nxdU//hV0XIDXhDDnq//yM/zznzwnY8qtxFbm7cna4fU5fdp8P+VJGOP7/WuKk8/YC7Gtr40bPoEs\n7wPKkaXVtAGlZWyborixsbuTA7u+VtzLdqe18E9qu+dIbz3CGL+/DnWteg6JXWUH46eU5EfG+xQC\nx0mDF9Yu0rD4reYN+4k6ukeyj6HBaCLvIfJCQMK6jTEED867PupYv9lCTEmeboQ3fKnHe/i5d0j9\nVl60xwv0oBl5EgIeX8d173GTJ7lpgsQQaQ4DOw8UK/teL+pfv5/iiJ4Oq66PYdM4Np3Hytg2zJFN\n23jhzM6PnIPqe+cJy1XOp0s5UaMVrvPS8cHkrhwe17WkYA1ipPFODF6UmlClFJOq5FWfez/NouX4\nuGH/VsezTy14+PEZZWl54NGKm1fnXP7onGrS8OKXnGMyk0Lkru3wKslTpSgzJgPinKNIAg65ganG\n0LYd2o9gfWPwnbxnrU1yfjn9k0hISpoKt02b1LhS2iBdLa0UN58T9Zi//fgUHT07RU1dVQgbVerT\nQnJIWu9oW+mIYcq670m4WHQ8/OItqWu0VmDiCJWxMga5NSv3VSslz1JUcq4hUtoCQsCkvor5s4um\nwWjN5cuHTCaWM+cnNMFTlNLCyDdSCmStoWaGKiyxU5gmUtopEzOBxlNFx6I95PpyyQc/pvh733TE\nL/7qM/z+O7Z5/JEpH3zqOltHv0/QL2NaLnnisWN+/bdfTFUkwhyDAIRKzw4b5u2d5vEdPjX6R3IK\nIqtkkj/p7c7QoRqBYqc9m3c9wsgejNfy/79v91CyMCiDwCr8tv4wwEm4M0aJqApbYK009Awjoeqx\n6kgmA6zsMw5w0HrUNx5jf9FVPnZIUYHtqe7D+Ib8TJbRGu9DHgzVn19+aLIxfOShwH/6lxzf/l1C\nwlGaPlcZI3jnVybBvTgO68bkNKMy/n1x4ClqjSnubIDGRmdMkR+PaRNEuen39f2Ox7V+nPVo7l68\nZ4msrHSq7o8jsGLnHCEGXJfaIinpWBBCk0pNJM/XOUfXNkyrCmVSv0fAaGnVE2MkRIWtLGeqku3d\nwLVnj7j81DFPvqoGH7hwX8X5CzXXn1vw9Edu8xmvvEDwIansmKT0AyipVSMKc1AaJg+ogzUGvKLt\nHBohS8nQFVYpQhd64070GG0JQQgyIdcfRinHqMpS5iuB/etLumXkgcdEQixGpDZOa0prhLDiIy76\nVKpie/btcrlEhUjTyv0pK0uIXgrnlaIwlqosiSGw7BqJFbw8x0KsEYYzSiUDKLJ2hRIJtK5tcV1H\nY62owWjL5cuHvOrV92MrTW0tkUizbNCRAXHxBbSWSheoMjC1BksndZe0VFaxaFt+9tfgN/54mze9\nYc4XvOYm//JfGD74MVhc+yOKC0/wn3/FJ/h/fv4htBHh+BA8WhmCStJkwfekkjvP6zvX/K7M+Zig\n51G0N3o6WFks/wS2u4tXD07m89meT7T2H8pI3ltrIU7m9vqf6xykE9GMF/Vzo6W4dM0oZijQGLvy\n3XXPIXvJm8aVoyr5e1XrLYTQF57LeHIOTzxdYVQGrLEnF/G1HCOAMZFveEvHj/+04cZNhdYRraXb\ndpNau0jN4Gq0N97v+PzHYxq/D6tSbZtg2+WBY+u+4oRc2fj768YmG+ZNRm7d8N/rhF6/XzHGHrZb\nf3+4X6fBvKlVkB4RYNI9Dd6D0qn0Q+DoLkrLoMmkQludSgY8dV0NTpRSPXQn8HUiTSktubEWDm63\nVLUotnRt2+c6ds+U3Lq2gCh9HUWaTWr4BHq1eOeIKImSAFMUdM4LYSBKVKFTrV3WarSJ4NQFB1Hj\nO0+qrsBQoAuL75bCuUswtfce1zqMNXRNYPtcSSD3XISm64RNXFdiYNMxbFGkwnlxBvOzVtUyR5fz\nAKbtlV+8Ebjfak1lC5a+6/vzaE3KCSWVGaUEzjUKvCT66smE1hgW7RIXYDlvmW2XFJUQcXTScS2V\nllxdVChr2NqqOTjapwnH1LWFspSKuKjonOKoCQRVglfcuHKOf/IjW3zhKw/5yq854st+GZ54+sPE\nvZ9m+mUHvPnvvpKoNRiJRkPXCbqRn+kYiPHkc3mnOT6eq+PX1cigxfwMjQh1Q8HVC7+dhtZEINff\nbwY/9R3HdC8Gabze/GmJ8uBeuiyssSnzazCcdP63ySjl18bF3HBy0YXVC7i+gK8vxJuM8Dhi0zor\ndnjGQs7rk1sWVlIkKAYrQ5ixjwiHsc6mkXe/V/Hvfl1azkQ1jH8Y7MkarNOM+TCGzcni04xPN5ei\nflutsiPHhmWTwRuP9TT4dNN12jTm9eONP3OnyG5dlX7duZG/48o9zRG8oM+KGJN0mDFYI3m3zEar\nqwrvvJQWZMWTbICREpSma3Guo7SBZhlol45HXr6LaztKU6CU1I1aC84HlouGsiyoqwneORrfSBss\nK0bPaIUpLCidNCM9XdsNiw9SulAYy6SqMBpc8ITW42OAoHFdWhwVUm6htCyYIfSLqWYwLnIdBR4t\nCoNN59q2Hb5tmVYTaSQbcv2aQMWFsWiEZPPEk5f40Aev8sjj2xKlKoVzHQvvqKyVaCmmGlMd0UaI\nPXJ/pDt8TH2ASmupK4FYQ4wsjw8pJhW3bx4z25UIPHovcHSMUu4UAlEbooJm2eAbR11XWFvSOmmF\ntGg6rt0+YJGeyVIrStuidcfv/qHhnb9Z88PHC74Y4NzHuaULLt98hNmZBXRLfLMAlZr3Jv6GPOWj\nNegOa/bd4PsMZYrDO0R6sZ9xn57tzoZa1rNcpizMnRyonL59MsbrT5OhG2/3lNProcweEszeTCoc\njyP2Xcpx5P/1iy8x9cgSdlru2p1honVJmcFIDDd3KJpW+f9k4PG0qKmPbIDc7UDmaC6E1n2yOS+2\nCC1VWrn0U0T2v7cf+fGf1hSFkAH6QvPgJE+g8tdPQpp5O82gnJzDmw1hjJH5nmN6ZsidjPcz/tzY\nIbkbRDm+5vJ3/s/KF/qBhij+vhrD36x+JxJTU04hgISYnQHoW0iR70/qym40PkjEBpmZOb7b8lsI\nqddhKglRKlLVFX19XiHSXxk6JxMujEF3KsFcBYvjNmluSgF7jKL0QRQ1kKoyuBZKm6FwMT4ahQow\nKUpcDHQuEQWUlb51zuMSMUqrSFlX7M6mIn8XvHRPV6pna4q8rQi6d60b7iMSKRptkmC0kpY8Hsok\npZZmACGKse68R0dNLJM+qjGElNMTIkuQkoHZlNlWwc1rcx54aIuQlGxCUiDynRTIF8YSokOljg+5\n359WCuVjnyfzXs4ZJRHqwe2G4/2WCw+UtK5DR8WksqKkkp6vw4Mlsy1PqS0lBrfsWLpIVVREI01k\nCR2lVShtKYhg96mmBqMmVGYGs2tw3PHuKzO+5m9+FUrPJZpzEe8ipiwJXSB2cl9XDFS6divPavY+\nVhzEsYM7+m4qXqdfw+LaZ//j3e4E/36aj5x+fvLHvbvRy3p1rEKZydRIQrs3eLF/r/f+dSQqWShC\nFJUSFfQq+ysK4SWXB4zzd2NgoH+01WA8SfsRbdBkiNXQVdxaK1TwEPq6qsgq2zC3XBkW65HBIrPd\nBk3QLEsl8NXYQIus2ekR1vD3yTzd6rE3fS6/1y1Svmhycr9jpmTu8pCPsQplxhV7plQWj5ZFN0ZF\n1KIvOaBA2fCMxtfvT9Rk8kdD8jLlPqWatFQCIdUigXoiPdxyMbhScvww6r+lFDgXUhSkUUUU5yL1\n7Qsu4INLzkzAmIJZrVG2PpGLjpFeuWV3NoPplMViSTPvOHuhoppqWtdgtMVoQ4GUO5SlYX7cUlap\n+4VS1EWNRjGxJTE6DpYNXfDYosQ5T10UbFclBCHllFZTV3WqIdQ4FyFoOqVAWVwy8DmHrpTqc5Eq\nqQ/5EFO/OdiaFVy7MufBBw22siyalrbz+AhWKwpdoLQlBrDGiqqKdyilWcQgCipW5vW5+yZ84qm9\n5JgGotZ4FF2I/Vouks8SrfroexanipHKSNlLrnFs25Znnt7j2tVjvIu85BXnmMwsTSOtnPYPFxwf\nevZuLTg6EkbqEy89w/0XS7oQkqPgqQpNEzq60BFVYk+bIqkCKcqiYKpr2sbw9192jqu/d5VvPrOL\nn85ojq9gjhaUztAETWcKIi0spXtDVCqppiSiS4qEegcZlaIjn56T5Ayq2K8LvRMePTquC0wP2/Mx\nB5uQsfV1YVPEpVCydm/a5ynHej6R271+9zSUKzvmd2Osp1d6pOhTMbb3kNNL9SVAXCvWlIdkGGw+\ngbzoF0UhjTHDKNoIUuyqRoZlHfFeifRGUdgmCv56DqtXshjBi5tyVHeCE0F6dQUVVoxnNDFFI4au\na9KoVyHddZhx4xUdwZybYMXTcmriFGiaw47JrkQsud1R/ux6f731nOIqLDycD4AxqZ4t3Z/eb+0f\nPFiPPsfHyMe21vZ0fGk4u9r+SM7F0LYOUqRWV5VAZwGaRYuxiqqWRriuCyxCh3MBgnQKEDmy0A8n\nhtCLlkvuaSh1yLnW/Pe468HN6wsObre8+KVnqKqKdtmI76aS4Q6RqtK0jSz0RRLpVhERUo5Ja9M6\ndBTFHRUVVVGIeowSMfW2a2lSrjCGKLqRahBuDinHFGPsex2u5kDzvA84Fymmmqo2fPSDezz0+DY+\nSm7QaIF9C2MxVow3MeLaRorczTC3jNIE59iaFjgX8V2kmqT5niBHXRhi2/1/7L15jCVZdt73u0ss\n771caq/qrum9p7tnY3OG5Ixo0h6JIk3BtEkIMqiBCJCUJS9cZEmWBYGEZQi0LC+QZdN/yNpNj01a\nMGxBtECZNknLC01S4nAZztKc6Z6ll+rqWjMrM997EXE3/3FuxIv3MrOqZuXAcACFqnr5MuLGjRv3\nnPOd73wHpTRWKVzyojYjjBrKusaqFeIQU2J+0PLW9TlXn6jRVjOZWaxS6LLm2qsH7N0+ZGe35MLF\nKW97bIvPvLzPzs42ymh8F1HWoAvL/tEhdVlRT6cEDR3iOKUYKCrLweGcUCgIJXeXSz4E8NabvO25\nBmvP4tSCwgYKaqK1YDyhqEhB9FsNKSe9cm+80epWvTHMJnBgY/bv5CAWnzKU+ZWJdH7vIqmv/DFG\n52A9bQYnOf3jz9Zrwb+Q48FGT43/Uuufp+NFyv0gexipcx0M7Wdk05Z82WqT7pdWf571y6vVxrZh\ntMab6fjaYyO5Sag4dnv5ev33ho2GlfFWikENo980h8BQrc/BSTnQkyK9/lgZutNzYOPzhS4ROpg+\nKpJjY6WXzUVy0tzINdfncLzoBjhYpQxdj1mZxxfh+nk3RZRXEVb/R+aWtXVSloVoZsaARlHXFUVp\n0JkV623AddIXT9ZPjuiz8dI5SrVao7MgsQvS8HQYv/ymdBVH5PO6zrNcBMpas3OmIoZIWZaQFCnE\nLEMFZVXQLMVA9w5cSokUIk0XMVETNdiyEJa6i7i2odKWoqrw3pGSyt3Ss2ZsLgdIfbeNLOnVr6H+\n6J2u3ononRVtNBeu1ty53nDvbsf5SzUuQ5EpRLrYUVsRR1g2zWCcFRIhudZlEW6Zo+nEMj901JXc\nf4gCQYcUSLlRr48B5x1lZnZWZSmMUh/QRqStiqLgpc/dYnvbUpQaU2Tv3RhcI3JjTz2zze7ujOgj\nL33yNlfftsOZXWnq65OowmA0XRd487U7HNxrufrUDF0pJpMJBotXjoShi4kYOlQhz6qqQDU3qcun\ncMVb+BhQlJS2ROsIW9AmjV+2RNPvL2pl2pJAroMBVL1ohThY8u+Q12BvBO9fy/qVONRobX+tHZvO\n+0k/H/97k4OwaQxP+t0vZb4fLDidek3IHgYYR1ZmbdDjF1YpoTEPea7eeI7OcTKB4eTjpO+eFvqv\nxp6GDWPze6ffbx+BZVJEnfiBDwX+3s/Iz3uFFfnuesrrQQvwtNzeevR1fC7GD3qx75mMegCO5/x+\nRn1zbpRaKcf0cGhfiN1LZWm1Dg9ujumkZzZetL2kW9/LTam8a+Q1YIyhrmv5PHqCE8HxqqqFzp9z\nSIXWTKoC33lC9rZUxh6MUUzqksJOKAqbG8EGnJNNSiTDhLwxHmkCPv2JuygN9cTgnMMojU9JcmGD\n0Da0jaeqjUB/MKwPHz0hJgpliSjQQqohgIrS7TtqNQgzW2NxXu4zAmHs4SpQMbL58vdOVghy5yYr\nGWkUpjDUlUdFxbSs8UqK4Lsg4tCLxUJKD1RGLhDIe7FYYHW/mScmkwkxKiaTEh8iOtejKiBm54H+\n3ynlru7Smqtr2mGOrVY0ruXwUEpIjo48jz+7hSkib7x+xN1bLU8+dYYzuxXExM0bc2azkseu7kKE\n2XQCDcJcjZHPfmqPra2SK1e2ePXle1y8OqGdJ+rSEnTAq4SzSfKOJH7f77d8//d6fuwnfovJky/y\nZ/+tN/jOf+EG3hf8jQ+/g3/8iwU6RFCZqa30kIOWTmFSzkBi6BKxor0wGLgh3ZMyHPzA8oAv7TjN\ngf5aMninGaOHMcz9Xu69HzgS/eeb39u83v0Ic6cdD+6cbnuJreMD19qsulhv0NPHsFd+XCeeX/XY\nKetQ3OpBjwwpfcSQsrY5w3flH2T9wlWkOYYRNw3lSdHh8F0E3vqBDwXKUuFc6i8xbEanheEnlSls\nGtzjRmRjTkZz0N+/d5FuEZidt8fGe1JUt1kkvzpkXo8JOqe0NmeR9fOeVn6x+TzH95jSiq0pVHmJ\nRKRFUGS5bLDWUpWWsiikn2LwuVt1RJcW5wLWaiBI9/YsEG4Lw9Z0wnRSDko5KqdiBvg8e/EkqfNL\nOW95dLjE+8g7Xjwv962N5HpiXxivc9F4om0CZ89OsFoavaY8t9PplLZdEmKUIsAkJQmTsoQuoBDS\niY+RLr/QITchTihU7ktHkgg0sKr50oi49vD886ZQJCiNkQ4eStMuAzvbBUVSzCYzQgwctYm267Iz\nkQG6nG8Vgk6kzAo1PnhCSjgXaJqAKiJWi95sMnIN5z0+CryrcwG6QtO14vzZUozUvGmIMTLbtkxm\nlqI0fP7ThwSf2N6xPP/OM0ynktfUGPb3G554bBdiIgZPaStmVU0AAtIRYme74OrVHaqq5Ppb+/gg\n4gMxJekQEpcCL6bEdRN54s9DwR0eubTgu7/zNt/2R9/PuYnmZz/8q/yDf/QeVPQo71DKkFSBUj0Z\nCyEXZYWY1R8j3IGYcnqn381ERQcVT5Q1+1KO09CU09IeXwvG77TI8wsJBOLI4D3M9WA9qnzY4yHY\nm1IT5bLQ7fii48aw44Gs/X8waquoaBOmzJ+ubfKrmxobiuMexeY1+9qrXlPyfonRk4zs4GUDL74r\n8uK7A3/hJ6YovaIkj8e3mot0Ksx40njHzsEmvDl+iONzNfcC1ZYR5h4c+/5J14X1shGR7LInjm8l\nCJ5zHkWxNk8nRbXrkf86aWYcCa4gWhBYPLcB6jdzo6jLAmPkmtZqIUGliLUaayyzrS1pM9O1kCJV\naRCfLAriRG7KSkQj57XG4p3HxW4o0F7MW669dsTOrtSPgtTYtbmAvCil24Bzjhgji4VjWmuM0qRM\nZEhK7qkqK2L0RJ3rB30UJZYYqQoraIciQ7MrB6CuSpQxdN6TnMCmRa5NtIWsXUIkuIiLkem0Yjop\nKJUUtduyYnHUMp97Xnh2m8oWFEbjYqDUmmgtoXO0vsGWpeRZU0JZgWWD9yijSERidDz73Fk+95k9\nzJ7ikce3KIyic43UFuaC/t7YD2Qbs2LlKi2MUt8mlvPA0y+cx1jNxSszfOdJSQhHi+WCuppglGE+\ndzRNR9sUbM1qXOMoqwKrwCVYzB23bzU8+2TF44/XTLbF2VUFeOXovMZFhdYehQen+PTLc154ds5B\n6JjUCWUCFy54mqVhWk1wocUFh9EFmCworoEUib5XY9I51JNefFrn1qFSnyHGr1/IsJEN/PIfm0jQ\nST/7ah8n7eEPO5bT7qOfxdMg0dOc7C90Dh5KkUU2pnAixNgfJyUhx98dNjxgKB3I3x8Xd/bHONIb\nH6dBlJtjGUc/65HHcaWUzXEqpdjZVvzwH+/4m/9tzXyxmvCxiv7g9Z0C85001tNCdImk1qXDNj28\ndu7Zvryug2iMGUS7NxfGirTBGunleM5tFZnHzEKLKaDiyjhuKrlsztlmxDi+VxmbGM0hT4oaxAGU\nUhRGk4pi0NVMqY/s8xpIiUldkRL4QuS/tFEU1lBaqUXz3pNiRBspNTBZgYQ8ruWy5fZbLXu3G85d\nLLn86FTmSamhvU8/pyoprDa0TsprZnUlospKDItRiq7tqMqCuqrxKeFCJKRcfxYiqSyo6ylt1zEr\ni8wS7lnMhhDFOE+qiqIsabomF8Yr7rzVsr/XYgspj3mzOeSRR3fYnZXsL1qWzYK9e0seu3qGlCJN\nsySWBVoJW7NSGm1F6ssnUSKJIeSGrEjxP6Cio7YF2+en7MwmfP61u7z68gHPPH+BolI4PMYYqmw0\nvffEJKUfw/NNfiB2yDpK+ODQRgS7q6rE564SNvdya5YN29slb91ccveuRG/796T/3ROPn+OJx7eo\na8tzz5yn7VqahcOHgMm1sd45ghNpuKRFcIBQ8pGPwHvfm/jZ33qLf/hLb+fzv/zL1JXnuz/0PlQS\n5MrMSopYChtYgdGRrl2KGEBKmYSuhZmdIfqU/+7JLAN7vSfDfAWN3uZxmnP71T6+0Ajry3cdyZc9\nTLrqpOOBRi8EoWhrJRqTcs2x9M46fHhsoKmHBAHG3v94Y1T0zQw3N+7TsNtTw3zdj3s9yuvhufH/\nN683hvB+8EOO3/gdw29/PIpA8ANgvdW9nA5h9p/1G+u6CLMa5uek7w/jCytDVRTFwJR0biUyfNL4\n1o2wwIvj5rSre4CiMOKUqPsvrAdFlin1ebFed1WKnEMmgxhtSUipg7GWRdMQQ6Ioy1xsDSlJvzzv\nIwopPykKi9E57xohRoXKBCmtNVZJxBeQTgspwZuvHbF3u+XspQnPvucMpe1ZqyvDbI1edRdAIMem\nCcym0nUgGYvzDkgYW6BUkI7etsAkIVSgFKiEthptjWz2KmIwlFYYlW3X0nZOmLIpUWhN8h6rNElp\nrl2bkxI8/8JZlJKGtt7DtTePuLe3YOMSr2AAACAASURBVDYtmU0Lzpw9w2xqaXNTWat6o+OxymKM\niLpHH8GO2i1pmT9bGHRdU2VB6YLEC09d4HeaG7iFY1paUs7Haq2xWmdVHJkzP+jnihFFKW5fX7C1\nW4JWEq0mqWkMfUIiSicJWxleeP48KkQ+99ohj1za5p/7hjNgLD//v7/EZCqlKmUtpJa2dTgCkSJL\nlwnhyqTM2NUFxAkf+/iCP/unA7/20f+NP/CBLd7zXT/ILH2Sn/vwR3jfB38f3nQoWlKn8cEJTBk9\nsVuQokcbS5/HI+dwUw9l9j1BSZBrQb9SrM3x8bUAX341j9NQvNXnOc+a1gOO3sY8yAF5MHszkVly\ngTUVjcyqHEdNJ+d9GIlGr8Nww00gMNa64HRmErIyICdBcpuGRaX1858W/o4jwfHYi6KgqgreeHPB\nz/8T2ag3dezW1VbkPAP5Q58Sum8Y1x4mWs3H6VFg///Z+ZLDmy32UY2t9ECosZlG33XdseiwH28P\nbfYRd3+pcdSqtaIoCowGYzwxibTa6E6O3dt4vOPovb+u5OJyTtIHoorDWfr77yPdECLOidSY8x1F\nIYZtPp+TknT1rkuN0RB8pK5LIBGCpzCFKI4YA6pXQxHDdnDQcG+v48l3bFFPK7Q2WHoSkMKaQoSk\nQ0SXmuTFU4spceduw9aswHWNRDylJXVRNGRJBK9xiUH5Quf3oiwkylJa41pPJKcCXEeTSyi0VoQ4\n6h4PzOeeo6OOd7/rkhjYJESYutQ8//bzlGYl/+VjYtl2JCTy8lF6pMWUSN4Re2c0SUcKW1iU8Dik\nvs4aqrKiMJZmucQmaFzg8Kjjhad2iFrhe0ZuiMP6iikNRk6IBxEVRZFm71bH0+/ZlXc+BQwa5x3J\nSsf6FAP4iDKl1DlOKj7wvvMSYRlN5x1ndis+97l7PPf8BUypaVxHIGHKAm3lGbQHR6Qg/RG1bFKE\npDloZsznB+h2j4Ojixh7jnt7Bd6DSZE2OGJqUY0m0cnYU5CuA0rRGzOpv5V6wJjiEPEN8GbPOF/5\n71+W42Hzdb/XhvCLgRUf5ljfz8WAjYOqsiwxpsB5UT1aD4Q4to+edDw4p6fF05FGkuvFszKs9ais\n31jHN6BT6rkqmcSwgq76XEGvhSgDF5hNq3UWm+QXj7MQe6sPmY6e67nIOoc9qWEwiLE3tipHPNnA\nKJVlpQI/+7+YoSynL3jvn4MZT6rSG4b+eO2dNj3+n8SBUAlbiBBv38poFUSfHllVM4O6XLH/Zsv5\nJybD2I3WQnrwDh+SvLapLzaXMQGDYe7nm+FZ5tZPRuM7hyoLgguk/p6izN2gvKPyc9dI3iP1+b7j\nOcYQevWVHrdPWXkkF6QCnYt0vhExaMA76YGmvJzLR9EXVTGRYoFWJeBp59LapygNURuiSvgcoaIN\nwYehZg4SVWmyaHOkMCY3XlGY4NmyFlNaqRMMkc4nXnnlLtYqHn9iF6MSpdVMqopSaxbLBlISWDPm\nfnrGyHQg+UitE65tEIG0SOsblBIaP+TNdMhrJm7eOOLmrSVPPrkjxJOUI+4oXRwKW/T6D6KYEgJW\na8jtl4ILWZi6om1alq1czxpDbTRWaQorNZE+Bo6WHSkpJjs11hqa1vHa9XtcujAhloaoQGfINqRI\nQGGsRUWBS42GoixofRZydpHpzOIXia2JISElD8GA1VIugU7oUtZVFxOEAN5lZRdH9I4XnjuLNZK7\nXnYNgYQuJL9WTQ2JQBs9sQBlG0Cjk0GZFuc8xY/Cfww89bE3+Qf/5X/HolnwH/21C0SOKGMkuIKo\nFSoKlJyUAWRviUSp30sRpSJEg45CUlI9ZJUjQFTuDEN6gJLlF3b8Xhu0r9wxjshY25vkSDnAkHIQ\nnbfmqJTA2MoSihnlbIvl/h7oJNF58si+q4gYlC7uO4qHEpx2zuWIY50e3ye45QZk8GO69drD2/je\numEgw6Bp/NVcsDuG7HriTG/5Gf3JuRjFGtS3usZxyLHPLSm9DuOJuHGfhzoZ4hPPXA2tW8b3Nv4O\nMHQY6RlhUjCsSTEQw/o998cYzh2PuZwaTKFxTcRsidGUWrcS7xw+tIMRWzW93dBETRmOyo10+2uI\nqkbCWkNZljQuDBG9PKBVq6dIRBp99+dYV3gZz9em7iqMiuj7m8+GUOdLkZ0hpRQGLYY3O0GioSj1\nbbaQpqgRiWBlrdoe9QcSRSkNWKuyYrlYSNG2WsF2KUneripLnAs4H7l7Z07bBh57fJe260hGs7O9\nw/b2Nq5zxLjPsm2ZTSe46AaIuS7r4d5tUbDMxlFbTVlKsX1UWZLNS3eE5bLj5ZfvsbtT8cxTu+ye\nmbFslgDYoiDmQo0eDrfG0pOBZM7U6v1RSlinWlFOJtKz0mhsUQhoZwxN12W2YaJzjnv37jGpK1CK\nm3eWvOedl6lKy7KTKN8Yg3deurYryX+6rmN3d5uqKPCL5YD6XH50i9c/d0BdW6Y7Jb5bIUTDXKPw\nuZypayM3b0ixelVopnWN0pqiKNFGUSlF6BpiDHQ+0LhWYFlthICiFFkICaM1u+cmvPPVBd/qgX/7\niI9efozvO/de2htvYAsy3ApJidJKYoQqaWGR9i2oYl++kKNW6YDuB4b4asf6/6qR+nIf4whu/P/x\nV3K41iOJ9A6yfBSCx3eSRlA613yPaqYf5kk8lNHryxJ6YzNAdSM4a9jQ+vFmrUM4Ode1eZ/jv3vI\noE8W958dMwymjw7F2wrRrxbp6Lrr19owYKN76PNsoc9b3OdcQ4Q68vBOu55Eqrn0AyUwX4a1+uhr\n/LjGkPFJkK6tFMtDT721yuf1veaSWs9d9ucZj63Xv+yj7dE3AWHqWtsX9Y8WqMpQNPljtbmI1+/5\npOvfF6Ie4a5iiGQNjaPCoizFRipFUVfSugeNVtKxQDqB5+ayWnJ01986YGsrs0IzBOp9IALaaqKP\nlLbIRiVSWMPVR3Y4PGp56ZN7nDs/4Zmnttm7d4/D+YLSWorpBFNW2NIQloGqqjDasFwsB8jWew9K\nU5QlJrf7iTmnFXzH/l7DwWHHwUHH+fMVTz9+YTBaRhuZ6UTW3cxF+f1a9ys2dQ9fA/gQmC8b0FLI\n7pyjqgpcMgTnKI2lMIaYInVZSo7PGpq2oW09dWV54817TGYWHwKt86AgBpUbvnbsXphgtGZxtCBW\nhWiQKihLy+xSRdcm3npjzuNvl5rPqqxyBCxkI5/AKMNrn91nOXdUteX6tSMee2KL+nJFWRS52F2j\ncqlEckLEiUDjPQmRRgNFiopm4fHLxNZWQVdo8JHr/8GE5//YLf7P5Vv8Gz/8GB9/qQJEZEDjVkiG\nEvUhY2TOU+jXnALCkMNL5JZEavzm9xvTcbH9///4Yg4lSAl9TWwuuUmSV42uo0PQJSEXrXZORSKp\nJBH6fY6HMnqrqGNdEmnQMRg1S4wpjaJBgSrHm/hwa2qF1Y4NqAx+FX0NhJRRHqrPYfRlCV32SEWG\nbH2TPWnD3YRHe6WLoigGA6K1GcY3hnTHBn4QS964r9NyiQJj+RFce5wAtPl7JxnSGKCbB7rGU1Qr\nQozWAidu5vXGhuW4s7KKBKXvWH9fWSEk5RySPBjG3od4wNnL4ThbtUcH+jncjLzXov0ohKmeGEVK\ng0c9QNJGDG+IIphgrTD5Ou+xSOTjfcSqTBbSmmbpuXl9wTtevCCbqVZ0OcoIKVEaK41Pc7udXluz\nKg3veOdlPvKRN9AGXEg431GGxNFiibVLqqrGzVuMAWsKqqqWNR8jxlq6pqMqK1F50RIh3blzwL2j\njvm8Y/9ex/nzE86erblwviaGyGxrJtFLv1aiGG+ZH0EJeiMn45UcW0yiJqO1pmm7LOiepHmz0bI2\nkPfTFlYgZMSg+tz/8bW3jggRfEjc22+kTjNFbGFQSG4xJXj1U3vsnC05f6kS1itQ13UW0oZb1494\n+rmzWG3wBLq2Q1uNLYw0j47w+qsHFKXm7U/tYrRm73bHq5875MxuiZ5OKZSQtA4XR4QYRKYuWebN\nUsoHkK4Ub35iju8iRaUxVvHWcs73lfDXz8HVf2nGH/7RH+H53Y/xk//JL/IHv+fdJDxaBVTy+GQE\nzdGyk0kkXrCYH2bi1ICDsNIVVoJwZAdQ3o3f20jvpFQIfC3CpP37LP87edyZJ5EyECXfzHtXhJgI\nXYfqBS9YoUanOeGbx0MosuQNawSDnRaxwfFWRCcRK4b8zsg4bBrGPvIaCyj3x/jzlcbjqgbqpHON\nxzB44YiBjTHwI38i8XO/YLh2XQ+0+R5yO8l4yHkZDP5JbZXGhI7++iexUFWOzTcN9Dq0u7of30i9\n3uKuY/uyQhmDDwGtFcYaCKvnI7k6sz72/DYn0vAshkWV69C0Gp74YBzHh8zbqFh3Dck+XhZyMqy9\nUY8Ys0C4MYRMjdfZAOoceTvvsZMKIvgYIUm03OezDIbCrEo19vcWVLVhMrGkJAattBaldO5YICo0\nqlc50VKU7rqWLiaeePIMb1474LXXDnnbY1v4lDc5bXFeSDcpG6HlcknTNFTVhEJbtI2UZYXSipu3\n9nnp07chwWxWUteW55/bZvfMNvP5XOBL7zk8PGQ2mzGdTjOBJ2VhZCgyU9dnUpLJz71zTliVGaKe\nVKJy44MDpZnYAoUipIRBavTKoqCwFg24tsFaQ4qJJx87x8ULFUeLJU3XEfNz9UGM66SuefTRHa69\nccCrLx/xzPO7lKXCAM1iwZvXGmbbBTu7tRjYLLcWgicoMKriM5+6Qz0zPPL4FsZqrr96xP7thguX\nJkLwCpGubWmbhq5zJA1d2xK1kJ1SJpAt9h2mgCsvTERmLGkW9xzXXjnib38QvvuVq8Soefm1i7z9\n2SWmLmkbB6lDp4DCDKLoIOo93jti33swO1fy70zISpE4FKlLeYNKKxb7V/s4zeB9rR6be99JyI/8\ncPhWDpySEI7QoKOIOciSzyjaw/NoHyrSU3nDOWmwm4btxHze5g1l4oNSamAe9vBM722fJGA9pu73\nMOT4OqJcoYbvruXuRgavP19vTL/jg5HHriZu3Fxt8GqAaI9HJcM8MKo7G23eYwMohuF+kebxKHht\nrjaO5kCKircuFNx9vcG1AVWrfK2UW76wNl8nLqzUX3PdqOrRM7HGiIpJvtuY83orOEGJAVArR6Y/\nz8qpOd3IjefW5OdSFIVE3Nkx6X9urZUNyTtUEvgLZKMigdFWjJ4yGKWGZ3jpyhZ7dxpe//wBTz5z\nVrg/RtodpZAgl+RIjiwOpCVjDIWG82cLZhPLSy/dZm+v5fz5KQqBDa3VpBCkxjDPYQ9Xd12H834g\nYH3yd2/zyOUpTz5xkc452s6htOHo6EjmAaTYWymO5nN0/ncfIdd1jfeeruvwMeQWSEBMlNmolbak\ncx1WKzSawkhdZqUtRVFQG1GdUQlUlBozYwyOvpNIys5gxaSeUFQVPYzfLFu6zkGAQiuefvIsb14/\n5NXPHPK+9z5K27a88qkDnBct1Dde22cx91y4NKGqDcHB/u0lt68veeTJbc5fmRG9NAb2XeTqE9tc\nPD8R+FkbJpMpIXi0tbTRMz86xKWAc7D35pJ2EfBt5PwTJSRxGFCWcqJ5+3OKj30i8VdevM60WvDe\nZz7PhXOOC5dLXn/do43odtK3REpZezd46GUXo0R6KeeSjcmdLrxIvZncFiumCMmjvkz27sthOL/2\nIrz1Y9OZXz8kQbfaZTb3jJS7ZPhsCBF4OvUSAelBgd7DRXpDdJCOG7zVYDa+f8J5+u+mFAmBtQhE\nNotVZCQWfD3yCWFFd88g6LBJ0UNip41/9P9+MzXGcOmC54/+Ycdf/msz2i6snf2kezlmSPW6kR1r\nfR7/nZMg3gEtPHGuxodrAvO7jrNvq9FGMT1TsNgLFI/YAWQxGznGk0g2CiVEFNbnBRhILM612MLS\nOXnJ0WR0opcSyPef/z+OUtfvX8oCTiqIH0fRPaTZZRKS+NEMkXyvPVkWmqKQ5sDGaEgW37nMxhRD\npnINX1JgCsPz77rA7/zGDS5enLJ7ZkJwjugTxITFEIO0iJL3RcoItJaC+Rgik7rk6afO8vIrd9jZ\nrplOSiBmtMGv5dSMkVzYtCo5XMzpvGM+95Sl4ZEr2zRNQ+ccxlq870iJVaG3Xsk0hJQ1XhNM6hpt\nDM3REcu2wxYFlS1IvQB3TEL2CSm3ANJS+6cEuiVGfNdKnV1M+M6JY2NFj7Mvs5nUhs+9eoed7ZIz\nZ2WsEZFoKyaGUIpDGHKboksXKrrG8YmP3xQSye6Ep54+w7VrhxweNhit+fwr96Q7BjDdMjzzzjNs\n7U7Fac09BUOIuC5kQXBRvhGoNPKxj7/JvXtLnMtRl1EEl3jyvWeIqstMajHyKkHben7oTyZ+7he2\n+Mmf+Rb+qx/7n9i/C2/dnLE3P4+uNSwC0beQBD4WDc5E3x7LFAXBSb2jONFQFOUq1aIUZVUSvMM1\n0qB2XfX/q3vcj8PwtXScGDhsjjnJDtNH2uN0Wf/NGMURl/NJzjXlIEU9RG714Y3ehsEbb+TDaEcx\nwOrv41GGUiu1kDFlfzhXH00kNXzWG4xVbdeqTCGl1UDGkWG/0Y7r6noygRTten7oX3P8w39c8vrr\nKyMnzPzx/aweWP93Dy+ZLDV1mpJKbxA3w/rVIYZvHLWeFuW180C1bTLlPTHZMSz3Ha6NFHWvcrMu\nFzY+xvO3it5X0GWMgWRN7gogRdPDmOgjXzVcQyWhE4vjsRrzmMEr8K8+9d7WPL48vjAWEdCrZr11\nVVCWlsIaQsgvgzX43A6oLKRWLeToVGWjZXNhdlEYuqbJMGEQA2lNdq70AB36TCSJbZtzWZpprbhy\nZYvPvLLHiy8+wtFhx+3b97i717C7XfD0k7sM0LqCRdNQ1zUxwNHRgu3tUiDERC7cjhgrZRMheLQ2\n4ghm5ZOQozqtNT4GmrbFeS/0bSXGses6cXSMoSxKUhQ40YyQkel0Ig1jvaNpW0pbMJlOgT59IN3n\nY4o8+bYz3Dvs2NtvObO7RQops2kTJq2aLZMEKi11wROPb3Pt2hFaaR5/VJitVx/dZtEWgGZnt2Q6\nM/gQmW4VKCsMa+mxGLlzvWEx9zzy6ERqRJHx37x1yMufvUXTOp5+YQdKKSW5d6dldq5EVwmdjERc\nIUnJRIKiUpQVzPcX/MKvvIP/+Zdf5Nve+VtUNqLKKZVKaDStb1HhUCTGoieGbLiSbEQpinBAzE2H\nOtcI7Jml17RReB9ZCfJ/ZY7T942Tj5P26K+1YzMIWftZnyFNYjt653fzOymJtF1KuQysL0BSY8Ws\nk48HGr0BDozrEymDXf/3KgztYcjh1kZwl3jh4x5s499dz5mt61mGzKqSPbHXq+yvv9Kv7NHFk6C0\n3gAe3Oz4nn854Br48N/pSMkN95xiYudKQVmvjNVmg8N+c7asy52Nob3NMWxCv5vfOw3q7I9yopnf\nGfVaM4rpuYLFHcfuVaGc9575eO768a6exnrOrz9kjj1KGal/KwrKoiAEkdjq4VCGZ5+hBNWf57gg\nQB+xj52CMfQ8vv76mliHleu6ZjapKYwfNvoUI1ZpqqpCKZENM4XGJ2FAojLFOSicD1SVyItprVE5\nv6cRlqjK148piQgziUobdJKoq7QFl84rjg47fv3XX6cqDRfO17z7HRf4xO/e4Wju2JqJxqUyWl7d\nBBCZLzwXzk1X+e4gxc9WW1zoIVDIrzNtT8wqJOcWY0RGJCooznvRzoyJM9s7Uvuavye+L1ijCSlC\n8HSuI4aAy0a0spXQBUIkBCG2yDsbaFtHcbZmPl+gED3N5KNs8FGiUg2U2qKMAm15++NC1ElKQZL2\nQ5K6MFy6NJUuE4XFp0jbdXTeSb7PGJpFpCwN115bcOnsNt47qrLkk596i3NnK556ahunPYvgiSqw\nc6WCrA1rc0PgmGJGHMSQP1/AX+0S7/6x/5xXL5/j5l3Ln/lL34qyBVWxTaE1dAuadn+Vu85OW/AO\nEQ7PeaT+85i7TSRhdjvXElyLVPur4zvzV/G43x7ztXQ8VAonqywJ8LKefhn94nAurfWgg6u1zozv\n+9/7QwhO5wnVir6XmNJKipWzd9VTq/sXF0aMTbJY63izR4kEVVrhr33fhJPyYwJ3qdwdHYRsIb81\nnjyVkogUx976H4fSfubvLXjXC4Gf/En41d8q+Dt/X/M3/27gXe9IHB7Cj/67FTfedBzcdJx5RAqJ\n+70eJQXsRknOp+1aYpfvX2VRos1ojxEjcXhmx2vaeoR29bsrTHt4WBOTa1TyL5CodgyLfU+3CFQz\nmdPISukkZki4sAXOSZfqXk1jnMRXeeGgRHNQo/FOtBpTEi3JITLM0GhMuQO16qPu1eY7GEi5IUn2\npxHPLWWyTILSippK0zR5A8sGW8tcK0CnQNsuoLLYiEAfwVEU0tNN5Mj8cE6S9H9DwY23jtg9UxFT\nIvvp1EVJ6Iuq8724JH59SAnfNaiiwmLQtsjq+4rHH5/hugmTSgrdq7rC+1tszyoRNojCVhR9TanN\nWyw8s6uG5XLJdDbFOWlJFL206qnLgrqqWCyXOB+IGNB61dYnKVGq0ZaqKmiaRhyz7W2qqiS4TohM\nOQLMBZSopAhdoDQGFyFpkdiKaCIRrQSO7UlJe/sdh3PH9qyCFKVTezLUZUkySZr+GoM2Bu87Cqux\nBpxSLNsWpSPG9s/U5v6GUv9YlhWLtiEkicKjEh3Od73nCskpfuM3XsctA6YwvPK52ywbx2SrwunA\n0jlcDOjCYLAYowhpSYoWHy14hzWWGC1XrsypL8O3fCph/+CSX7m4xR9/7FtJ0WNsg1WAVURjSdr2\nu46s65gjt7X3tZcfy05cJm95j9CoSYA4OapHu1LKkOf4FVaDYT3pOC1VlCGuYxHffRGThzjGqM9p\n1z9pjKf9/EE/G1939Z9h8199N+8b2T0efX9IeMivAglDSlLr27dBe5gZeHgiC/k59jBjXxGoetp7\nP/ERpTLdf+Tdr0dAK3gt5o1U6bys1CkPIMNCYv/1yiQM0eMGcXhkfCT6k1zAv/lDim/5gOKJpxQf\n/aTmD327oao83/Ohin/1exw//Cdb/sO/WjLdhYMbHbtXq+wNpnz5RFGU1LXUEzWNeK79IBOrSEb1\nc8Vm1Lc+9jzLx++ZVaQE0C4CxUSL0VrdIvWOoZvLz/qH3+eYCitdBkRirRTIJiWiSsPC78fSjyMl\n0T2sTB+1S1QUewcnz0PGIfJ99JJtahR9r6K//gVOeY1ohoIXlJLGpjEGKZzOGodFUTCpJqgU8a5j\n2TR0XhFDYFpWFLbIotJx5ZQFgSjRisIUhBS5faPhmed2CT5QlOXg3QuRSaGV5JBjEl6eqA/J+TyR\nApuVdBRlWTCppOO40Ya2iZSFRJ1d1w1RdIyimHI0d1kEWprbamMwpiCl3DVeK7a3Zly5dIm3bt3i\n9v4BSmnmy4bkg/QRVAK/eh/osvGNIRF9YBkWxCCi0D0UbKzofLrO5XwlVLakzMSW5Xwh2qZWCrpj\ngpu3D/mtl27w7rdfoK5sJkRpiLJGrNZMJzVLF2g7J++5VZIfpcLaghA7MejBs701ZVrXEGExXxJc\nRmyirB3Jfcv+Ma0rLp6b8psfv0lKUFWap5/bRk8si66ldR26lG7tRWmBiA8ZePRS1dV1LRrFd39n\nS/czYBv46PYVfvTK13N0eJfJZIb2VhonaIjKo7SRqE5lp25Ysf2bIA6S7DnZ0c4OlSzvnjQmhdL9\nGtd9n77hrV6hKw86TuNLbLLD72fkTov4xmjbqkxplO64z3hOGtPmNU/73tiwro0576vrG7ceHL2V\n4zy+TyU2AoNSUqO7Qq4EilYPMGsPNHqLfc/0jB0ip/VJTIOxW4/0VhOxCVeOP4/ZEx98qlFpxKDY\nsfZgewoxWYEre2hrDoNMmowpDdFZtwgc3nYs7xnKDypspairive/b8n/+kvyYv/8L2p+4PuklGGy\nawgucnSzY+dKKSyuJHmSuigxKGxVoo1FLZe0TiCb9Qd9vAZxcw435+SkhdUvym7eUU7NsRdDW0Vo\nV9caOwIhhLXyDgVoa3Id12oMKkevAxwagjR1JK2UKdaS9SMYU/Uv5TqBZXz+YcxDFCdq+z0JxHlp\nrCpLKYmDk6Nn5zqmk5qiKvDRk1W3CT7fW0zSADYmdJI1kFLCKMXtOx2TqWVrq0IhebCyKOgAlyJG\nWaHyG0uhNIvlkhShsCVaGZIPOOeGTa0voQgpcXfviMN5oGl9llsTqG22tUXTtpjCcu3abS5enFDP\npiht2NsXYkdVVVKLpBVH8yM++/k5RVVTliWHiyPaZUNZFJlVKOs+jLq5x2xkq9wN3XUOZQzGFqQo\nmZEYc2PgXIMoeXAhs3RtC9Gwv9/x+TfvcePOEe9/z9s4f3bCsm2FnZ+jjOizk6ICBI8BUAkVPaUx\nQgrK76FRBq0TdVFTFROW80XGW2Vz0kljU5JifmOoigKl4dm3n2Nnv8LpiClEzUYiHI01JXVd41yH\n6zpC9AQipC5HXgqtAsks+NjHFP/pP4K/e/Gd/Lln/nlu7L9FUVlCSARvCDqR4pKuOcDkLWLNYe73\njdUyh2T6hTysYVtaQeKCHzpW5PoFiZBzUXUCVvnuLx1yPC0N9KAobzONsBaQDOIjD/f7Jx33M4ir\nsY0RLPKeoofPVY9UyImyU9GnlfooL+/v2qKVIBcp+GxL+rVw/7E+0Oi5JnL71YbZuYJ626yVDaz+\nToIC9EH+KaHuQGLJFO/YF66PztVDpqt7H0VCilMfrnSTFomnlCEq1UOgCdqjyGTLsnPeUk4lj5BS\n4sxu5OBA7ungEM7srq4xu1BwcL1j742WybZltmWpi5LCWJzr8MGjipLpbAbLJW3XbaidrN/Dityx\nTjbpSQcPgha6RWDnkWpwfLRS0qLGKrrUDjAVaZSL7a8JQz2ZjgFtVmzTfoxD09/ssUYlQsPSdkfn\naC+tR9FItHD8efWzwIAO9FtGEb9g7QAAIABJREFU/2FvhEMMA1Mw5Yh+ML4p0jlHXVcURYEO4t1D\nxJjcI05pevKv0gZrFW3bsFh0XHt9n6ee2YVs2FS+p6gAbUBp5kcLjC4oipIUJTLXZLKJ1qiR0xCd\nUP5fe2POchnY3al58rEdhM1p6LuJOu9YNC3791quvm2LzgVS8rnvnMkpgoTSQvKwRknXhTyXk4k0\nrTWqX/cMCiIpiVEQrUGhz4v3m+dbabrO0zlPYSzlpMJqaJqWqpICdu8cn31jjzduHHL5/Bbf9v6n\nObMzk6jKSKQSQsCFSAoO7508ZyVF4IdHkWllODurofV0XuBStKK0FdOqpl00tIuWqqxQtmDeLEgx\nURmJOrU1LJsl9aRGFZZiKhFtVVfYouDo8BCUOBoxOKw1dK0TZyQWhOhQKWJMiVKexjs+/FOB3ctP\n8SPv/l7axR20rihtQddGlJZcKClSTHYwKRC8yyzY0Ypds3urSGMF40NZT4hBnIfsG4hxU9JqKbsm\nqEyEWXsf7nOcFB2dlgu7X6R3+v47KieCtWDmeLPpk8d20rGZlhp/vhpnn//sf74inQxRnUorO9Kj\nX8bk6FoPSJNWFqXtsNdJRw9JBqYvVZHl3NUJ3SJwcLtlue/ZvlRRTc2GNiSgRbw3JaR3V1a2WLt5\nxhOzejhD/ilGQoonLI3eC1g97D4iHPeLM1rTeJeT0PICKWRzqaaGdhGYTGqq0qFVghjZv6fY3ZWr\n7GzD/r3hkgBsXy4IbaQ9itzcWzKZes6dV1Q1tE1LypCZ0kqULnJfNhDPegXppbU/q07fJy/uTU8u\nuCQRSLmZK0jSZieIEdwkBg33kp0sU9hjYznpJdG5nEQYr1aUP+IoN9cTezai+HUoIl9+iPjHz1IW\njs5GZa20Qq1+p2s7jDHM53OqqmQ2qzHWilBRkEUetbQf0klTWWEZeh+4dWtOUSi2Z9UATfcP1gfJ\nR4YgzMhJNVrPUQSWlV5pg6YktYJtt8SgODjs+OA3v50YOpxzhOxQFIXooE7ihLc+f5czZ2qsEWKN\nvJxyn9YYfEoDHBlCxPkWF/MIU6KwJsO/0OWaNhflOQeliEbTBi9NZa2svdB5FJoYHFVZURWF5Pqi\nMBOtEuHmT3z2Dkfzlm984TJ1aSgLzXKxICpp/+RyR/UOIQO55LFa89btlhu3FkzqgsWi4/3vucrl\nc1OUqaWXYIzYspL1EwJFuU30kYNFI90mQkBbRVlPqOsarRJRKZz3FLoXxra41lMozaVLl3DBc3Bw\ngDGWoAM+KKSdlAACKSaSjdy7JQ7f2cc+QFIN7bKhsjOqoiB0h/hwBClglULZLTx7I3Wp0WadRoau\nZ3Sq1SeohOs6lNZUkxrvA8YWlGVJSpH50YF0YR+E7TcinC/yqHLd5Libyhd7jIMNWEV/PYw/PsbI\n0fC7J53vtOv0/+6d49TvYT3pJO/TSgxWUn1gINHeCorNKRIgZvg9WxP6mr2H0cd5KCJLNbOcn2ja\neeDwZsvcKnYu1phyBR+mjNXLhsixva+HV3oYrRio/iHXKZn8/9Vmv9n/TuD0vFHmiLIYdfcui4Iu\nxMxzI2Og4BqYlR0//ScU5z56yNnb8EuXRCvx//lV+K4/FPn5X7B8++/3/MqvSV5kTECxtWYytdRF\nzfLQcefWEW0bqCeKYitinJNlnXNtxhhSiJRVhdGaebNcQZF6fXLGC2pzcfX3DVKjF0PKkktmrXhf\nWtwkgovY0qwIR2Mjyqp0Qmu1du1+/nqlmr443XmH0YbpZCKw30DPVgMEuW64V4o4fSPY4b7kZoY1\n0jMWY4Yhq6oaGLHOtwLr5ULqqizwXYtzjmYpEOakqlDa0LmOoDSLxVKEvKMiWnmh7951PPbYlhBd\nEKMkjokjmdXclFb0KK3WNFHaRGm7irz7xrtVJZJivpUNbTE/oCiKLIummEwmOC8b9MFRy63bS55/\n7myODoR1vGIBC2lCawtJVGC887ReIP6qKnN/P03b5HKFKNGcVwkVPMqATglTVXgiLoYMRUcmZYnR\nQv/v2hajs2OZIv/so9e4s79EK8Xn3zrgicvbaJPhZhJxgDZh6VqS76hLzbwJXL8x5+u/7lFKE2kX\njo984k3O7U5459svYY1ie6dmUpe0zmOszF/jHMvlAucDOiZmW1vsbm/hoyc4T4cwPneLGuUDBJgU\nFWprRlXXKGukoW/X5XUo74jRuUg8gOvg6FZicv4ixdbTNH5JuziktpZu3tDMD1AmYa0gQm1zRPTr\nSk8rZ3oUSeVuCymlrK0u1s91S1ZIhiaWkRgDznUURQkh0LWLIcef4vE0x+b+eNrn/XvqnMM7d8xg\nPcx5TvrZ5j4zhjk3o8n7EVUedN1j10w9nNn/bkatlCZpRSLK/kHvMCBIk8n7ikqgDD2ArBSDatHm\nfZ10PEQTWS/GSivqHcNkd0pzELh7bUE50czOa6pJOZILO9nr11pnFY00DNQYkYCSzTYeG+zYAKxF\niimhjZb8RfaUlYKmaVD0SdrIY1cC73t34APfFLl8CXZ+Dd7/vQHzjfDYZMmz77B87/cHvuMPwM/+\n9w0Hh4of/nfsEFVq+uvLRu2TZ+tcxdbZisP9Q44OPQe3nLwHaxF134NuuTkNJMBWGt9uhOAP4bhN\nz1m0Xa87jFE6hRe1Yu+Nlq2LlmpWnDyXo5cW0siDWp/7kPN5SieCEuinLAq8EkHjmJSQRTYjyvyc\n+mhzDO8Kwzd/YFaQRkppMCp17kKQtBGoMkMXCnKReM3wLEJgNq0FgvVBWvGgiMEzbxNvXjukLA07\nW7UYO2MopMuqvDhaXjSrFOXWFiY3h9EadBx1k0iJIF2ECcFjjeXOQcv2diXOQTbi29vbFEXB0dER\ni+WSV1875G1XtylLUe7wPg5SX8RIs1wK7EdfjiNsyQGaRhG9J2mbN4VMqNCKHiZyzmNUouug0AZi\nYlqWTKqKaVVJvWKUEhZ53opb+wvmS8c3vOMi2hhev37IP3vpBi8+f4XzZ6akLNouj0mi/EVzyKc/\n1dK5yCNXdphtlxwdHGBL+Fe+453cvXPEJ165iXMBHxKPXT3L62/u883f+DjOLVksFmij2Kpqjuae\nwyZwTkldqIgOROoMXe9MtnBEZmd3iYXmzv4eQSXu3t3j6HDJ4b2I7xKTbUFuFvsOW+VefQF2n/h6\nvK7x80N8c0CrW5Gs6iKKgmpq6dw9uuVN9KD8REalxi9yv3hzA1nVU1oS/Xa8glA0oUuEFkBJm6so\n7wc6a9hqtb4PnBo1rRNWBsc2iuC20pbN/p5fbNT3IPLJgwzd/Y6THPc+/yqfDd8kRk8YIrt+fgGt\nBdJMSbgTyq5JjqUkxi7GsEKSsgLS/Y6HYG9mWCu3oUkpUe8YLm/PmN/t2Hu9Y7oLu5eqHEkE8n6I\nQnq09RGady4bLrnp6VSklRaLxXBzinXseTwO8YylbiHEgM55oZjCIFOVlCFFxeUznj//o4Ff+3XF\nT/+PNW/emPC3XjnEHHl+u1L8sUcm+O0Z21tLfvwvdZAZVzEKm2sTnw4pSr+6LC1FCbNzFl0m2kVg\nes4M3zdaVDIkBxald1c21tIOI54sETZGJDcW3ZhlNR6b1kI/375U0s0jh7c62qPE9sUS9IippUcQ\nK6mnzR6DWMcsMYV0NZDvZIWcKOzJ/MtrHufxl0itTtQ7Q1kia9g6+ugvCIykk6hyaCvRcq/QUZUl\nJMV8sRTIDoElGyc94UprIIgix6ufO+Dc+ZpHH9mSSKxz6EJyLv0YNRIlqZSY1hNShLbrMEbuEQUu\nQ4fGZkgYuHt3wbXrh3zD1z2aYUiJ7I+Ojoa5XTbi0F28OB1mMkSfDZ5EtoWx6ARlVeS+ijkCtooU\nM9QTg0BOOZ9trIUUiRFMEkahNRqrFNOqJBpp46P6HnX5efoQeO3GATf3Ftw7anjhyfMUVUFS8MwT\n56jrA67fPmR3u8o9/jTBh6x0ozCpRKmO7/rOd3Dz5m2axQLfOaZbW9RVzdNvszz+yA57B/f4p79z\ng4+99CbTackb1w84e67i7IXzRJdYHC346Es3ZP61OC7nz02FbVoW1EWFUppufsibt26y8B3zdknr\nOpwLvPWZjmrLYEvNh//Gkvd+PfzXP13wi7+k+ezvtvwPv6R47oX/g+//8Sf4v/5JIPklyi5FaSUW\n1FVNci3N0R7EJaRyWMarCKRHJ5D3dROxgiG1skq4ZFUQrSVq956iKnGZgGELKx0i0kpq8WGPYb3q\n+7M1v9hjLaLr96cNw/fFXOPkvN66wUupF+RYpT4ygJRthjQoTmRnUfW2Q5HUqoehVuQIERIaa7/E\nfnor6G21OPoNeHZOMzs7YXE3cv3lOVtnS+ptPegiko1YD7f15zMZWmrblq7rGAtF91OzmXTtf3cM\nc0ovuUQIEuWlDhYHjq4JNAeGP/3jNdOtSYbdAn/qsYq/8kbkL1wouRsDsxCY1DXGGtrODTAVSura\n0kDnz90UtM41Sp6AbGzR+9zTTe7JWktZlATnCN5LnVmvzajECRhbt/4FOskzGv+7F9UeG6gxJAqw\ndbZmsl2xd33OYt+xc1F6u42JCUNOcXSu02CPoWmvVjkyl5Y8Kjs0SY0hilVkt3msJ7N73H1VvqKV\nQN4a6Y3nXEvIzsX21pYosHQisFZUE6qywALzxRJyNGKNoV10XHv9kAsXa85fmA2O9TH0ISWSDySt\n0LleNOSOBkpJ41O00KGVXve8b95aYozi7v6cq5d3aJsWjB7YlEVZMJkUhMgKos25B6MN0k9RIgvp\nyqCyfqYlBA9KmuGSIs4Hmq7N5JwC30WIgVKLzFhdlUzqktKYbEQlOtSaLNEm72xZWN64ccgTj57h\n656/ggteaixRBAXTacXh7SPJmYBIgNnEJ1++SVVZnAs888R5ZkXJpCw5mi/F2CuBXk2hMFaa+z79\nti0uX9rmaNnx2rU9Xn0DvvkDT9AuWz760m22tyoOj1o+/fnbdF3gkaMzfNOLj+OdY+/wgBbE0AXH\n0nckLTnbO9cckx3DuasTok78xf8MPvgBzTe9N/BHvtvxZ34RPvSnvoG//O+3tKHFtfewOoJTRB8w\nGtrmFq5dklIrsOgJ61RtfJqG4hpZOipDED1JTg0/kLRK0lJPXJaVMCSDp6oqFvPDtXf1CzEi4/3v\nS83lbR7ruf/jsOmXYlDvd70BQWMF+45zn/1VV+9wLhvJRs9ag46J4LrhvEkpFBr/AEW4hzJ6PcOm\nz9MorYbGjVondi6XzM4WzPc8t19bYivNdLfAVqKArXSurMtG02hDWVZZXNbSNC0hq7ifHHn09X+y\nWdSTyPu+LvFNXx958d2BP/cXC159JdAtItNty7lHtigrC1qEYtvWE4IjFgX/+mULEYqiwMcoMUdK\nQtZou+xsJKqywHUdLvdYEyjWDg/CGAsktFG4btXKRhtN17VDhKWUQueuDeJN9RO7vgjGC6GPrGLP\niO0JOeQ1qdRgwHrPJ0ZRz7dFwfaFkruvN5y5pKXrglq1fEpROqKrTEqJkmhag156iDgQ8T5QFnYV\nqSrZvFNcjZPsFI3M9mjFDmHeyoPMeL4gSZGktEA2ShQ1rDU47yirghQDbdNRZTKNtUJqKbSw/KZT\nUTrxnePNGweUpebC5a2coxRNUh8DJurBCBETyko0HlXCuy6ThAoIlmUXJPJSMjdGC6Ekhsg7X7jA\n/t6ST392j8eunMm1a060OssCFOzsTGhbLxBwioTg2JptZaZfxGhLUVi0Vkzqmv17hyyXS+lKrpOo\nl3ifiSGIGAKKqizASY7TGMV0WjOtK1Lw6JgotMFUE2xhcMFx/c4RewdLqtLQOs/2zOY8X0U5qTjq\nFriuo5gY9u41vPzaXZ68uoWOmvnC0Xae3a2Cxy9v8+TjFwje88ily9y9d0DXSm3q3f1D2onFmgKl\nC7Zm29jKYWykqrd4/Y0jjg4dH/nNN3jmyXM89+wlDg+PKIsS5zy//tvX+c2Pv86zj5/hoDniwDUo\nW9GEQNM5SJrbry8JAS4+atHW4KPn9l2F1pEXnnX84F/ROCri9AMk/m+69gDXzbFGdFkVlmY5J6ZO\nIPJQ4dtcU5lrQnNo17+IHHtR84JOqJFCoSziwUHPhpAUKYyicR0+OI6aRQ4R03B6tWZ0cz7rRBJf\nHwWt5/y/Usboiz1OIuJtnn9svIUEl1alZznYWKvu6FmeKYKOoEQ4QGuDNQUQ8TgSvfPaK/N8iezN\nFXbd/0tniTqRUkpZHUOpxPaFgrNXpty9ccDhHVH/mO5a6h3L3/+plve8M/K3fsryX/z1xB/5Fzt+\n4Pscbav42Cc1/95P2GFCxhPnfZQ6IBX5lm8OfPsHPc89E3np05p/+hHF3/5vLHfvQjuPnHtbRVkp\nqsrkPIqjbVPGw8k9xCzKQDAKbTPEmOu9dE5Yay2zb8sC30jLHmtNxtIFvnRO6vlMCc1hpA+uyb8v\nxiSrtHgJ41czOTrSCoIUKFgozjpfQ0S25TetEgaXG7oPhCHHoDQYrVA6oUuotgw3PnOALQ1bl0pm\nWzVlXdF1DSQoK8mf+RDw3uFyPZ/qxXdTQheWwkhROrlvWmEs3nViuHSu3SKzrRAKfb6xtcyHypAF\n2TjGPo8iwDwxeUIEW2jKsiSmxNbWTOA8H3CuoSgKZrbEN0s677CxkDxHgr1bc7o28uSTZ+hVNUJw\nEBHDn9eT0gZFxPuUXw4RjQ4+UJZQVhMmRaRxjl5U2mR1lNJqrNY8cmmbm7cW7N1b8sjlHWleGxIx\nBZQxtK6hrg2Hhy3bW1achlxg3ztbsfNMJkZyiyZRlGBTpKxqFl3gcL6QDlG6ICnN/KBjPm84M6u4\ncu4Mh4sFvmv5f5l782Bbs/Os77emb9j7DHfqe3uSuiVZg2XZikVsQ4zAmGKQy+CQGBU4FQJxhZBg\nSMCEFJBQhXESMEVIAlQwwTEVTIYKYAgpG8uxjbGA4FGy1GiwelJ33+57b997z7D3/r5vjfnjXd/e\n59y+Pci0I62qrj7nnj1801rvep/3eZ9nRBRXKFogYq346Seuc7wZGUbPtctLXj4KfMW7r7Fc9lIb\nzKDIXLy4YD1a1DjxVe9/mI9/7AXe/Y4HaJ3i6eePeOTBQx5/+KBuOC3LZc8wbDg5uoMyFuM6VusN\nY7a01tEYV9V+Ck1jsE1hs/H89M8+w9d+zeM8cGWPzemKg719qafuO37t13X80595iqeevcXVh3pu\n3hhwjcG2hnHw+CGzfEBz5fEGZYy0ImlNg+XL3rrm6Ah+/mcyB1/+dYzqIqokWN2msRcJfkRZS5gC\ntu2wqsUZzXo4lQ2UrrNnDlx1/p4FL5WaA+Nu8p4NiaKqoc/s7zIkz7Q5oaRRFnGj2Er1ldpDqYCs\n0dbiXEvOhTCNdT6dWyB2/1ezf+f50sibHQDfrPFq6BXs9Hnlb/MbQPrwXlnykTuVgQTFUqJCGYd2\nhRB1NY+tDPZ07zU8P96A4PT2aHYnUc54xGnxozNGE6MHModXFvQHnjAWNseJ9TMDv/8/tPyWD2ke\neURO8ud/seP//AeGnOF7vmviG3994h//lGRPpRROXw6MpwltwFihem/uKn7kRzV/6X/suHMjsjkS\nRptSsLhosM7U3bwEuhjzORbh2fpYCBlrztNzjdGknGhaxyxo3bZNrWfpLVN0sxkrPJfRBmKYXSJ2\nO7/thkXJ63bXs97orYLNLui1bYupLtZai8P69ibUgNv3PXG1opSMa9zOMUJpmkYWHa1b7MOG6DPr\nu5HN7SBGqU6MPEMI+ByqGLNFGYMuRfQqixigWmNkogKqZBElnoO3YtaWYxYFl2srGeT8kG63SjUb\nVeiq6rJ7oFXN8sQItRBCIlUNzGEzAplF1wqLT6lK9tj1NaZSOD0+5ubNNYt9S9s3xOrIYJRQ903N\nZHMpqJLJSolod23UFkkz0YUcfWDyCWubrZ+f1iKb54yRnvlSePjaHp/87C3GKfLQtT1KKSx6R8qJ\nzThy+ZLjmWeO+ar3PYC1VurOrcUaywzkbKaR49WJ6E22DdpaUs5VZiyjjWYcEi8frfFTom00z764\n4vqtDZOPLBeOd7/9EhcOejSKKUb+yROf58J+x/vf/RDOgjKFWISsMYaRGCJt20BuULHBT57Nak2Y\nNH3nODoeeOHGiqOTDV//NW/BGcO4EUFvowwpJJxrODi8yHozVrFq6Yudle6btiUpyDHyyEP7nK48\nrTVYbenanqZp2V8umUJgT2u+/te8g5u3T3nyqdvsH3ZcuNKyGQLNsrC4qClFYZTDqEYW/RyweeL9\n74OPfhTay4/SPfZbSHlNHE/JK0PJAosPk0BS1jjIgc16TUq+miWfhd3PhbJz4/VgxXsZ2AAhSAYy\nu7DcO092CMi8IRRG7z2ffOY76oTZ/ut5yPOLHfheixRzbxnmfu/ZvfnM36nnXTcepbKVUkpgqILg\nCtt0lZEur8vE1zzWN6y9uTsZgdvOum0bs2uCDiGwWFis7ZiMp9/T5OS4cSuyvhMYDxRh0Lx4w2FM\nIufAnbuKK5cBlfmyt2salfgnzyWuPC4GnLP1yic+Gzm5PeE3I67XHFxrqUpCuE7XmtOOVj+7N1DO\nw7SoUmtwtYZhbYWnTK0TWgqKcfRos2MYWmtgW4uq9SijMFaRfEG3ZWu6ubtm97u55+n8cp0Rv7h6\nU0vtZTkjuIbSmqOjI1BgndluPKy1aKW2kFmalVdINFctt18YOH5J9BpzKqQkOLr0Gqu6WZXgpI1C\nm4Q2CmuFXWutIlnZESutMNptM1JR/N+V9pXKVb2G7XkxX60aMHc6nPVaKtDKCB5f8pYtOYwTVoPq\n+4o4SZDe31syTr5CQgofE8MmcemBFoyheHGJsE42KgqFqvdRFuhc62ty7sY4/tu/csy73hX4gb/V\n8L3f2/E1X5v5Q9+xoqC5edPy3/3FS0zDnJ3CQw8ssbrw5HMn3L478IGvfBifgjgFaEP3cMvNWzdR\nxdBaK+eIYhxHQsyVZSZK/a5pMW1H6xrW64HJTzLHlObOyyu0gsce3advLTkJXL631/DizRUf/9Qt\nrl5e0jWWF26c8GWPXuadj18kUt0irGNcryhK0SwaelPdDCpD1GnL1QeusjrecOHA8/nrx7z90Yt8\n8F9/RDZ6qmetDXHysKwbr66ncY6jeHpOTKKpKjMxiOdfSJG3ve0C16+v+Ml/9jkuHHS88+0PcGnf\ns1mvpR7btcScOTjseNd7H2QMgczI5QdbNuOGcYiEICQenTTTaiL5iX/jN2auX4eXX4bLX/17iCkz\n3X2ZOKwpwRH9QIyJME1VI9QybE4J04Ayc8vIDgE4Ozfv//Nrj3uDYkq1cepcPQ5ZuOcprSqDNYat\nDusOCjofhHfB8ks/w7t3vDpn4NXOZ7c2737aZeEFYWwaa3BtIwIPwSPyl6+UbLt3vCHtzbMHL0ru\n6dzO5uxuw1pT2ZSGtrOklGhazXK/44G3epp+YnUnsLp9xMFlx3u/qvBNvznzt/43xV/9Ho+f4Ad/\nsHDp4QWuUeQEKUhaH6bMpYeWhBhYvRzwm8T+5aY2984prTpn07PFyuuCOy+yRovZ6Gwzo9ipmMwU\n/rYGQamLWbwPiCxOYWezA8Zpkle4dvdv92Mrvdo1ldfnOlHkFs8ZnGRbs1VSZfMZhUZctM1WraBK\nC0kahrOG4D2UwpWHHdZZDg4OKDmxGQdyFteKMAm0qRDZtZSyiIkXRQmJEAo+ixZnTjNULP9JfZea\nXSrpG6uXYBdQVVXjB63rsVcILBuFMWCr4PSi6zk9PSWERNs25BiIURzJsxOYsIRQpccyfjOgbWAY\npFm3mEzWsFgsmIYRhcipSS1zR4DKFEjS7K2UomkavuvPHvCBrx64ejWhtOYXfkHx+37fRfq+5cMf\nPuGbvmnFP/wHl4W4pDWqaB558BLPvTTy8LVDkagrSurTORGToAkH+70QonKixIDKmb5tUNox+pG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heWjZCwUMQxst5sZBHWWliRSleVIZERRCmmIL2Hw2qFTwljxXdQ5YxxItzgR9nIjUXaTKjM\n4UyBCjEeHx+zaFqSzjSd3UJ0ymhS1bQMKRJS4uCa5cVPTzz/mRUXHmjpDxOJCbOO/JnvTvzl738v\nLxx9JTeeu04IE90StPKYsI8pkOMJhUIsPZqJ2YxYqUpSqWUEVaqm49lFbpv03SdLmCGe+cf7LM6v\ntszu0IydXu4OfrtP7fBepLWuuynG7dpkrWOapnNEmfsc9Bs4ujd3nA1c99b83nDLgrz7vj+e/adS\nqoC7UhjXYHvH5CexTlOvdk1kvEEZMvkmrfSZGp90wW/T89kHqWLXpYgFRojwhx/r+PPXA9/1zkOu\n/6Tn+/5m5oO/Fl5+UbDY/tCyvCifdT/68KxyrpnJKLC5K+/dv9DQOmEBNhZCTjSNqU3pqgYQRfCZ\nlCQD1aVg9ew0rQgF0A6jpP9B5cKy6zHKkMmQM43TxAIoR8yJYfDkGoiaptmatRojfXClFNbrtXx/\nlaSaa42SIc+bgur8TSRFL02zzmGNFLu9F8dtZRoonhIrhGQtTjmUc0gj9hzowadEShlrxNtrClIP\n2t8/IA0TWtvaP5RROdPU7LdpW8mgcpHPVoZcF0TnDBe6A0IQpp11ItPVto4YFTFGjjYTHoNulkS/\nEmiXAlpqZ/vLBQtrcKrQtg2n6wE/CSPWmgZrFIeLJY01W8udXDIJzdoHjLFMwVOUmI8+e+M2Vx/q\nhaRA1YdV1V8uV9UcJSiE1kU2OShUUWjj8N6j0HQfyOg/A8v/F/7poeU/e/wAtOZv/52WrmtwFHSM\nLNpEq1sarQkavCq4RY8/GXjXW6/wjkcucvvOipdurwH49OdO2F8O9H3Lo2+9xGazoiAMZ/QuiI+T\nwMypLsiRgrWO1TDy4q0Vj75lj5gKOms6JyLZPichjZXM5AesURzsL2mdoW33uHxpybRaU0IimQll\nFUN1IVfOobQmFMkyY6oF85Tpug6fEneGFaEIc3hhejrXYLEVTkoY5/DTRIiBSEErQU9yhTxjSXSN\nWAcpJwSn1clISoXGOCYfwEamMqKttE74Yrn2vshwI3DzuciFVcfePvwX/3ni7//Qozw5fQu3p+cp\n6UhMfvUDpDABkaIipVgoCVXGmsVVqKsYUG4LkRUiRc+i8AqFkddVH7ZZtIBsoQT5Xe1eXWBnCVeX\nqdcLK3NValceOb/G7cb9FmxBj0pJxJgBu7VPe+0vLWeSh/n/9373m1C8fK1DOFeveyPj3mD9ynPU\nJEA2hiVGbGfp2w4/RbQSFvVrjdcPelsZzVJ3OLWYqBTiElyVPJhbAmboU042l8TLMfIdjy8o68jz\nnzmhFPiJn4Rmqbn4qMO1ppJYzu8OzrEWAaUVYYqc3o7kCLZR7F8S6acYgjAVjcGHUA1ALTmVCuvN\nLBg5j5l4E1PGh4gRYy76zm5dsrEKqy2pJEIUSSk3N25TMA5SLBIoSmGxEIHhEALzzFDo+v1niq11\nkpRa+/LeYwxCoS7CxPRJMgPnBG6Vmpyk76ZqPc7ZowRTyUQn78lq1nARR22gElVWuKIwytAZR1uz\nS7FYa8WCxokqvK2Gq/O96PqecZpIpdA0rZBTlGTDwQfargMfGadp65gxn6MxBnIi+In1lOgbJ430\niHpCzLEGXFk4rRaFBbQWmnzJWCSLmKZA8IE8iftH39sKIcvf+66T7L16g3nvaazdbjKgbtq0bFaU\nUqinFWYsPLGw/NlH97aZfs6Z3/PvvMzpieapz/bcfL6ttliOFCaapmWcAlOcMKal6xuuXV1w+XLL\n5YstH/v0y1w4tNy6vebpZwJXrkiDfd/3xCj3RWvN5H2FrqSNxhpDCJHnnztmf9/RdW6LTpQCBxd6\n4hhIBULItZ7b0rU9fd+xPjpmGAM5R8Yp4pyTulgMrDZr+m5BYwwmCVHIWo3VstHw3uNrCaUg66b3\nHk3GT16e/0ZUTozRdP0+UwxVGUdTcibkiEb69VRJlKBxxpCjom00mCJizMWQaKoVmMLmQkkt3YOa\nvis895lT/vB/DJ/8JPzU07+LMq5JLz1HY7taK53hybp4lzMkhvo/WffV9lxKfSZnm6X7LY9z/+jM\nJJRgdf8F+Isx5h7A+WjuDw2qM4S/+e+/cgHu3DHMPAT92sbYv+xRy04g9zZ4TwhHpCCIxL9yTe/s\nON9MPZNYBNrUtUYiE1PqXaoYYjQ0xjKtCy9+7ohSoDvQ7D1gqt273Jx5gXzwWuaxR+FnfuHenjc4\nuT3iNwXj5AYeXOoZ/bR19lZKS21nzkLrw0sG7xNaCwnDNo1ki+sRX4NFVx2lSxE2Y06RlJOgSCXV\n+pfGGOj7htVKdvPWKYaVQFQ5Z4ZhrDR8gVZjlIl5NrOD87BECIGm6WnbjpTiTomFvHV1mL0GQQgY\nAnPY7bXJWhiI2hiBoLTBuQYfAqjMFDxWGZQx0gOXRP1kb7ng6OiIvUVP3wjNf4aBjbXCNvSezTCK\nGLQPTARSLsRccHbCaluVcRTGWKyVYJPmY8uJ/b4VvcimYa/rxHsuJXo6TJLVyCi9zcZAc3R8wmYc\nkDaLBW3TSqYZIkc3Jx64trd1QJg3Mmi1VY6ZtVwL0rKyzawrjDxfu0+lhvxI4b/RVziNgeQnSg0+\nH/nIkvd9uefXfcOKhx+5y0vXlzz1mZ5f+Ok9Vqs1pm2wjSOpTCLjU+aJz97mxVtr3v7YAVevHnLh\nYuAXn3iRvQMJYKP3EkiMnKlrG1LK3Lm5IadC40Zu3xnoe8OVa0tSSnTVH28MkUtNj2kzKiWsS+iS\naJuWrut46aUbnAwDTdfSOI0pCtdoIqCTuGbMdWWjRPXHaENjDMMwMGmFz4ViFH4Y2V90svE9s3gp\nJfC2KY6j42O0k8y67xoaa1hNG1KcCL6w7DsaY+hsy/KK4jNP3GY9jSjlSFFj245SIql4bFQ0tIwn\nibs3PN/+7bC3B//9//7raA7h7vNP02wzh9kWKFexg3md2C145zbRdS1RSmGcJUWpMZPvF8zKPf/2\n2nDZr/S4N1O6l03/Gu/klYHuVzaze7Xxpga/OYAXUFU7V3DrN3afXjfo5Ry3Bzxf+KaR3bUs6EoY\nb7lgTMfh4T45Z8ZN4LnPHFHuucbtUnNwrRE0JZ2xiqgyHotF4Xd8c+TD/yb83X9o+ec/I+zU9e2M\n32QuPdoxrANhlIbpi8u9bauC975qYs7N3LVYXGnBMWZiHPFefNHiXDAuBT96jBaYRiwvRExb690N\nm01wnVHsdQ7vI4cPOF58+g4PPr5P20v2guLM5mBm350vTO/u3zyJhQwwZwCqLrrOWppKWpiJQ/Nn\n+xiQxnW5Rgph9GktGVSYvJxe1ZdURuNDwk8ntMbSdgLx9X2HcQ3BjzWLhdVqU+tVoiepgGEYUdZV\nkVgx11TK4GMieamRpXovSuFMkBd/vr22xxrH6elpFchOOGOY/MiiX+KUkl4bpWqvZYO1YkETQqaU\niFbiJpDShr2DjlmlPdb6zWYaxYAUYU1a56oFidQpS87bTH2uU59Olv/7y1o2ty1OFfwQavtA4fp1\nx9GdJR/9x5ELe5qveB889MiI0ZZLh/scr08x1tA5x+3bp/zcJ19ib+l4/3suynWpwtUXL3Xcurnh\n0bccCDpiRDYvp8itGytu3RhYLB2tM0w+ce3qkuWeYzONIrK+11ZBhcLxyYnoeFpN3zicaVh0DdkH\nwjCxv+ixTUOrNTplqfujaJ00RFMUi65j2gzYDJ21NNbhbWDwI2OKDEOk61pcdV6PIWx319ZailIE\nP6K1oeQs1k4lMY0bDIVl32OcwHCnx4HcwtHxAArG4Gk7h1KWHJD6KhOJwjgtufF8YLPaoPYf5a/9\n+IfQXeL0+hMoHcm6x1Y4f87w8pla/0xc2wWJs0FNVURKoWZfNqWEnFUE3iyznnC5N/B9cccbr4fN\nf5/NnOcA+cqyUX3lm358c939V4pcs723M15cpISCKuzsil59vH6fXi6gd7R7hbhcz71v844rhAAI\nPBJD5MWn1nIsdrdT2bvicJ0mxXmxny/WbiF/5vOWP/FnNV/9VYVv/ebAt/52+D/+juaH/6/E3uUG\nZcrWkdkP0vQpwsxpG+SE5k9d1ITqXSQqVHcEWfzn14nKSmLYTBjTYZ2peok1BdUKq6xkgUqkui5c\nOMD7iE+Zktfc/PwpVx7tkQm3q4XOkOS5jcOZezJnz9MkcKb4qmVaZ3FG2jXEBFVT0Ew+bHVAc80k\nJdgIYzGGSOMsTSMmosoaQkq4tieGUPUkNUkpNlOgbSzjyQkXLxxKoHENKSZs09IYzXqzEUulAm1n\npQXhjKNDyqVaMklQF9FrvVWUmUN9DJ6UG5RqMFZcBLz3aOvkeaqs2+gTGo2ycw2mCtDWxm2nLZGy\nFT2IVes0xLC9xkknXNtCEeun2e1AlQJGarnyvMq4/bKueq1noHnEnBYrDgJaacap8PGf11x/9hp9\nn2ibpvbFZY5PNzz5wnP8+//ekuvPLLl+PRMQApQqhcuXWp58cuTF6yseeHAP5zRxjDz/7CkpZR5/\n/JC9ZY/RmlKf5UiprgjS/pJyqfXoQr9oWa9OKDqz3Dtg0TpOjk443NsjCWyCyRmrpIE8FOibFpNW\nDEOgNRbVtDS9pm9ahmlDTIGsoGgwTq7TXKfOMUovYUqsTldERJS7FHDOkkKg0bXTUmu6vicDt15a\n89wzJ9t687W3OZqloeRQGbdgckCbzGZK3HpmRfSZK+/7Fn74F9/DePeE1csv0jZxWzJIKVRR4UzJ\n6QzRZAdzwgxnnsn8EAZvLpGdOISqAQJxIElzHXAOevN/uyxyXmu/WON+ZJFXvuY1CC4zE/9NzmDP\nZ9a/0mM+9rqe1pIF5ezf7j9eN+jdfGrCtaKvGL3QaZVeY6zGNpq2s1in6Q4anHOMQ+D29TVhyhgH\nl9/SiT5jhSDOwLEVW1dQRDEDJDuIsfDxTxp+8QnL41dHfue/lfj4LxrGLDi866RONq4DJ3cGXK+q\nuHQmF7YP83wT5hhIUZRU0CVtJ5DWksXkkmialrbtSTlAlgkV6zE2VrI4rRTKGsiBpjGYYjm4MDGs\nPHdvjhxcsVXVX1fYdbfr2h1P2WZC87/Ja0UBo+9EDV7kVAXidF1DKhpfiQKlyILoWjHvXa1WxCgW\nN5pC4wzFaEYv7gSl2vaEYcQZy1ghaGKgcZY7Jyfb5vZcmasma5QWs9Fcs5Nlv+D45JS+7TDWshnH\nmn2KLuacwc2BP+eMVgXXWLQxJGpTeYoM44R24uum2wZdxNJp0S85HaZqwQO69jtSHSf0vGHSmuQD\n47ShlIKb2bZFMtQUI5SMrRCn3fa3qS00nHPmJ39iibVVZLzeB/FMFq3MFCLLvsMAylk2wyAtIMhk\n6/sGtWfpOs1b3lr4TR+6jZ8Un/l0w2c+rfjcLzUU1fD4Y3vcvjvx1C/dRWupB3ed5ZFHOvrWSfaS\nsjTWW4MPtXeTWTOUGixEbedgr+fC/j5NIz2SPnhhizpLDhGrFXttgzaK7AMxZva7joXrKUoTrMEZ\nU1tzQBkl5qceCOIF6b1HOXFRt8aKEXSt/RUl1y9GCRZd19G1LSerUzSaXBKrE88jbzng8OKCk/WK\n0kSKAqvAlUTysvm8dR2O7mS0s1x+/+/BLB7h5IXPMq2PyFYzWYv1GR2L+B1SM7tSkGbtQibL/kjt\n5vxuralojVIoZaVmqQoULWpBIhkkwVTVkg1KWtfr56ka95Q6K1d2NqP8/3ecVXR65dglAPMGvN7m\n84f8OsH71ZRXXu+4Xu+1Z8tkX/g4g5Qx++zJTZLzfRNqemG6ByvPEH0m+sy4kpqVegn6/aY2kMo4\nuOaYDWbmC3F2od9ZetTDL7MxrN2+/mMf0zz5+SWmq/XDIotef2DYHCVWxxPLutiKu+4OipTv2O2K\nzn5vzpLxKORh1kqkp8YxiikmIgXmqpLJHBylPcJirCWHUKnymYtXNbdeSNx+vtYKznwfSnHwgMN1\nrzSCPfv73DgdosdPwphcdC2lyLWYpiBO5sA0DbRtS2Mbcokc7ktjNEpUKER7c9ra9wTvKblw9fIl\nwugZQhBY8VCsY2IU3coQJ7m/RbM+PUUpIdO0bYv3E4vlksuXLnB0dEwKfkscsMZWPU6ZSWeJSGIH\nY1HKMPnI/nLJyfEJGZiGkf3DQ8ZpZL/vyTELfJe11FGrbBNJHC0MirHu7HMOFJLY9cS4RSPGIObE\ny36B0YYwTcIutHabFVN2ddWUsjR3uwZrLEbHuoEwUKn1Y4j0jWM9TfR9x3J/n1DdEE6OT/nIP3+O\nd7z1Kv/ixy7z0R/xdHtHPP7ugV//G1Zce6jlx39sQdNorl3reeDaEj9FjBGPPF3x4Pk8KZWKjdoK\nYwfvMU6a3Y2ujhzKgcpshoHVZuB0s6EUw4ULB/VZTQQdUTHjpwmUWBCppBhC5O5mjVos0U2LNqJj\nuNmcMCRpRRIoUPrdmqbBYLDG4GOgNz2rSeqtzrU0nUIrzcWLF7BNw+mwkWb4vcLzzx7TLyyu0UxK\nCFKKRIpS/15vLEd3JPN+4Fd/G3q6wNHzn6Dou9A4cUPxAWJDTopauIdyJisrs71X3ka73ZwvdU2Q\nzLUggu6z/9pciy45k4sgVrNn3lw+kIU11/l0P/ufLx0oFKio1wz3zuuN/E1KLl/cY/7CGJ3nx73b\nDFXPsaC3YvavNV436F15vCP5wrhODMcSEA4etJAF+x5PJfCVwjbgtUvD8qJAmXMnyrw4lnsOamaC\n6ln1XqmqfRi58fRK+tbavOsJzGJlFKbC5cuQm3k3o2VOb3c2Z5vpd0FFWKcKPU8OdoosuUShyuMY\nNhPOCvuyZCE/z3JeWmlC8OSScEaz3OvJJ4krDxfabom1DT5EhmEk5UIYMscveQmmjcJ1in7fbW1H\nZlhN1zYCa5ycS45oo9jvl0Q/EQvEKdU+10LbWLQScem+a9nvL7MeBlCarrW0ztDlzGacCFPGGUuj\nDXsXDlGnpzRGQ0iEHKpyyc7+RyuHDyLnhcqEOGCNZr1e07cdzgi0aKyh2taRqW0DqV57Le0Dyggs\nG9pMDp5hvUEBbWj20nQAACAASURBVLdgOj3h+GRF19p6zpJ15zNbU3GgFzd7pxQpDjhnUEUcx4va\nkVTke4UMkynVUsltZc+Mlv7ATIVpa3uHUrVnDTDJ0NTnZJ5iuQhxh1wIMRGCZIR7e/v8i088y0MP\n7POV73yA05M1wzhy+8Tw3EsH/MhHJmJK9I3oqMbanGwXLY88oji56xhWHnLBjxPLfiE1tCpPJ5sq\nMNZRsjBOfUjEmEi6cLIZSTlzcHiJWycjmyEQ1Yr9ztECSYFVor0pbu4NJSlOp2MCiWJkjhpnUSkL\n0ck5/DCS0Ji2J4TAOmUOlgdn6tuGxrZM3hNSZNHtkVLm5s1bZOS5mKaR5V7LlWuKZ568y1veeYDR\njWRUJKyCoBTXnxXZwbf9mm9kE/c5efGX6JuRgUJGo6aMigllElEjKMyc5RW29bydnuZurdlCkjWw\nzS4kOc0kJ1XnNIRxkr7TM+WIXSYiz2IuaSuJNUOFX0yo89XHeVWnXfY1Q7owG3O/2ePVsrd7Wab/\nSmou9RbMAU+g2syZW/6q4w0osihMb3CtYVonUiiEobB3oUWpQtOL510KhWap6fZEzXwLgW+LiyJw\nPKuDz5+ttRaTTaReEGPC+0xOihQy197RV1HRHf01p0wYMr/9d8GHvinwgz9k+PGPWmKswtbnrmU5\ns6s5c8G12gouGCNOCyUVxnFi8h6jM9Y0UiNrhF0XQsAag9VmW7Pq+5YGyTR61FZf0djq2ZYyemmw\nndgPRZ+ZVhlKZHlRWJJnb37OMoGtM9VcMhGmhPcTfsqkpNBW3MVVvcmmqlY2nfjxrYeRzWaDNYbF\ncomPsnuNfiLFgLIWnYvUeKwiJsM4eoy1+JhQaPwUsJXFaW3Den3KVDJ+MsRpou0acb3fhHO1sJSk\nqfrskA2LIiSRQTtY7mGtYW9vj1SE/NL3lqZ1ZJVZrwYyBmUsuUpeLboGSmax6FmtAhcvtqJ8o6SR\nGmRjZY3ZPivzhLfWbmtNzlpC9Fslnt0GKTMOA7ZpBGpPeeuwIXCnkvphzoS5TpgCq7sTTz53l9/w\nNW/h6PiEyQf6vSUqRVbTRDbQdQta6ViEJAai2ji+8Rtu8/73B55+yvEvP+H41Kda1qdSdxJ5OgdG\nIG1T2cApQ4mJ9TgR4sQwjSht2KRjhqyYlEWHjFGeZtGRqP2YtV/OaFNlxTTZK0KKmK6laIUfPW0v\nCi4UaBthNDd9jy5sRRa01ow+bOdyjgInkwVRWA8bTNfQLpdCRrrmmYbI6sjTX1qQSiVZKMXJqTz7\nv/cPXOF97/scf/rPdXgKRTt09LhUKLEj05I4BUZydpJtlbMGsLv5jmIHTW7Xseq/mAXVmP+gtUEr\nIRTlIkFfM3+eMAJn7kEpihTv0er8kgx4wJz1bjFN2AW885nfmzXeSBB709Vj1IzSlu1W5PVO7PXh\nTSXyVdpoLlztuXN9w+ZupNuv2oXA3gMNoLaKJPkctABGz04AdUGsJ964piqFRLHWqNBOmhSb4yiQ\nfajpeFLnoFIUfP/3wxNPGn7n78j829888YM/ZPnRfwwxVQmwIgLB205SxXaXVhBJM2s1uURCFmkw\ngTxl4SGLp5lRBsj4VKn6KcjCWDIhBTSKvmkqbAC6sYhlXWK9HojKiLpJX7C9RhsJ2vkMw0zL8kTr\nWqk7lNpkrUUwVyGLuR8GShL3imGYpNfOFELMpCxK/Z11bLycT0yRrmk5VWsShdsnJ6yHkUYp1usV\nxhguXr5CSYjPW0o0nWO9XkMWqNmqQmslS4kpczpOjHkWy6410TzXZ+Vya6Vrtga6Qkdx43EY4uDJ\nznDXH9FYiyoJk8TsNJNQDvw4YE2HdoYGJ5mYtpyuJk5PPQ8/ug9FiD655EpQAm2MEBJyRhu77b/U\nFXKOKVSZOakJzkXvnMWU18wEJEQiympbF9ZK5gLW40QBDg8OuXnrJkZrDvaWnN69w9WLFzhdr9Ex\ncq3v8NrQuIbj9UCrNY01+JQYg+cHfmCPH/x7ine/2/Pe93p+04cG/HTM9/y5S4xennHjHMoHQook\npWh1pm86itKMEXyUa4ApGMCpjA5gm57NMNE0mqZygWyBkpJ41hVRo5nI3NysSaUwxETbOvy0Yab4\nW61oq7ntNHmUtoyTZJdFF5zVRCI+jCjXotsOm2SxDdOEdZbF0mEbWJ2O7O8tiO3IiY3om4o7z098\n8Bs6ftuHBr7zv3o/MR3jmh6dDRQx8s16BDVbawGlllBq0JthTrGVEfPjolNtR7A1/GVy8ZSU0SRK\nFbww1S0iZYUy+1iriXESUYq5SR0lJJ1SCGlNKmH7N5Wrsov+0op+gpjXft1tkNuRd+bfzwbB1//M\nVw9Y94MUX/na+zfe/3KGKjOhqOZ68xL/Cuj5leMN1PR2PTDNUuE6TRgzw1Fkccmh1Xnbobk3ags1\nyUcIbGjM9ryVEgsbn2pjrobNaWJ9N6C0Yu9Cw+WHlpSaps8klVKzimah8evMx38envx8w9seK3z4\nWzK/6RsS3/mnzxY6dz5qiiqBpxW5qK2E10yCEK/AnQOD94HuoCWnqo+Yc63nyWKpjJHWkEpxFlcG\nS0oiDN04R+4z6zFX1RU5rugz2p7PPHMu2Jr5Uq9jygVrDeO0IaXE5AVaMUYYfcYKy7TrF5Ai4zht\nr7dQ/g3Hxyu0NezvH+DHCWMcfhxZdC0XL1wQ7D9nnHWEMNA1DQrFhf0Djo7usuwX7B8c4L3n9tFd\ngYarya6PCac1i37BVAWIxVvPbO+ZrvWDoqBpWi4fHFBUwSeBxZq2pTBxcnpEU1o613D54iWee+HF\nbdbeOge1ZePu0UDX2QoFFyFt6V2tVCBVU410RVE/J5FYm+d7yglm+bwiiMMDVzN376iaKChpptZU\nvc4KkQHUYD5ME4sYuXL5gIO9Uz72mRt89bsfpnXgg+PixUOMtpzcOcIoxd5yyemwwbQNBI+PkaI0\nPlh+7mczP/szBsWChx4uTEEUTaSOXNDOELxAvi0WKNJTN06kGoxzkszHKCpRx7EZ1qzXhfZgSWsM\n0UemKRKVqc9Wg7WWcRgIKZKNYpik79VZTVGZEGfNUY12rm40xDzZNQ0hBpyxtI007q/Xg2SySljV\nsunRLPYbNqsNT3/uNpffsUfKgZefTTz+OHznH4l89/d9I9dvTuLKUHstZ4CmECk5VahXoZWwsWVO\n7/iZ56BILTA3tZE7pQwq19iUt8Fgli2c77JSGtcuKCSCHym1/zcnIZVRN0USZPN20/elFfJk3AvR\nniXSfaGfMb/v3vd+IVnbq7/2C7t66r6/nbE0ep1a5Rvo09s1Qiql2LviuPv8xPoo0uwbmjO2PmfH\n2Qs8F4vnizZLcu12DhJYV3cCFx7qcJ2qHnciH0Yp27YDpQSq6A8NfpOZVonkM0+rlr/wVxuWi7T9\nvPnUZw8ra8WrLuZYW3pyhWukdqIqVGOMputarFFM00TbzmSWmZBTlfsrhXvOYGMUqnmhBn8tbMyQ\nc1VUyYQpkXzh4IzOqFKKokSncgpRPPQ0hM2Ic2K3YxuLzZ79gyXR++pzaGuzdWGaxHBVWGfyGK2P\nTiiAySLe3Na2hb1+yaJt6Lqepm0YhpHgA13TorXC+8B6PdJ1PX7yrNdr1sOGmXU6u1fYWnv1XjYO\nonJRzj1ypUgflTWGIUzcPr6LtoaQw1aGy1JY7B+wHlaUCE63HOzv1wVHbIWMa7DacO3aBa6/tMJ7\nsTMqRY6jVDJIiUkCL/MkFTakiPxmStFCGKlmwDGLp9l3/vE7/Ik/flXsm2aSi9LVWzBjG2GGphhJ\ntfl9tVnTtQ1f8Z6rPPX0Hf7+TzxB5wzvedtlHjGKtl2wPDwUks9mpGw2DMNAyOL5GGIkBOnDs0Y0\nXm/dMSirUCkTcyRMAWctX/bOwu/9d0/57Gc6nvqlJZ/4ZCZWr8RZ33WmqWcyGz9WRqqBXGuuGULJ\nFGPZTBOjkmwv5UIsicZ1+BJBF0xjsI2tm0a9ZWDnHGnbhpCCsDCdIyvp2Q1hJ6RQdwjkAuM0slhq\nHnvHPjduD9z49AlKw8EBfPd3w//6Q7+GT31G0BxjWvmetKvPnbXrUrKDPmcfU0G73TO3rbepV8B7\nRRWEIlTIWdqAJDBLYMwlQKkbdmXQdTMsPpwCyZbKOK9nWL/zi0cKea1xvxra/YLXq41z/Is6x+qH\nvWn1uTdjvOI4X2O8YUWW+aRso2iXmmmd2dwO2AfNK07+3n6NLZ5eawLbBXIWaK6QFAqMrRlYFPkk\noPaBKcQtQYgI1hq4qjm+MRF9wa8ybhk5Xc0Z1K6ArbQi5UCJopIfk4jiKiTFd65lb7FAawg+YK2p\nUlFCeW+7lhg8Jdem6TO7vd3kU1tJsVzboWfPR2PEYkkrmE4y7dJUB4id6j/U64DGR9nVaq1qE7As\nfBpotMI0jvU6EELCWsfRyem2xig2SjJRbdMKVJdlgRzDgMpgO/nMrus5PTmt9czI3nKB0ZrctaRl\nx8nGsxkGTk5OpNevcVVibFfHE2WTMw+UNbvMet5pAjEGmqajaMV6s8Y0sujfvnuHyxcvsLdYYpoG\nnSH4SN92pFwwrmEV1ugCfhzRVVR8bkovSYBIKczLRqSktG0pyClthcVtbZaWAxcafs6aojXTqOgX\nsFrJkyOZorxQKQW5ME3SQmCdIwbPyXpFLgv6tuF9777K1UtLfu5fviROHk2HD4HNemC5WOJTxFjD\nZhAptylIlqtUhixQu9YabYyQWHQtByDr9jPPWr7vbx7y/i8P/LrfcMyHvy3w5JOWj/5Ux8c/0YKS\nORGDCD+P3rO/aLGuqu/EBGi00ww540smpMJqM2xZsjFHMOA62ZBNMRCKlM+csTS2wdSmbmMNRZXq\nBBHrxkM2eSmLAlAqGaMhxIImkOKS/spEu+gJdzO/6gMTP/upL+P/+aePMK2fRpcLFK3ZNhhvSV4C\nYert83Z2UStnp7v8UJ+PQoXcsQKBlsLco1ayNASp6v+pFKQcyUVhaSnaYLXDLfeEtDaN6BLlGqVc\nCSy5tkm8gkhwbvyr0fN/eeONfNcbfc3Z4/9SzGi/0PGGrIXOjpwze5cd02ZiWmf8kLCtOve6sxdp\nDm5nHQjOKgVorQlD4vYLG/p9S9e7qji/U0WnzOFBzb9QcsScwdHXdwIXls1WDktV3DGL5wT/5R8L\nfPZJw4/+uONkPffrAEkWC9dYbK3xlSyQR6wNsJthI4udMRQFPkaclV2wcyLrNI2TuJfXMsDMJsrs\nIFljDE2fiWOu8Jz8rcjFkgBV/edmG5xxqhqNpVodIWxGZ6VfbJomUsq0bUdMEb+ZaFu5XjFGtNK0\nrqGxFoOSdoX1mktXr5JjpP3/qHvToNv2vL7r8x/XWns/wxnu2AM9ENI0Q4goVZpKIlEDaZBEE/LG\nKjVRi64y4ptQvoip0kItx2CJVtQqQ6W0EkxKUAjGICAQwcIJApJ0uqGhxzue84x7WOs/+uL3X2vv\nc+65957bfQFdVafOec6z99prr+H/m76Ds4z7wOlqRec81omU3PVuSymVfhiIOZJDxVhHrmIQuiQv\nqqmbcMggK4fKX+yRFAjlXHRRS0ElWPU9KSW22y3TKHJmKmXsfK61wlXQ1OZ7V8kxtPZuU9dYbjr5\nfGcstvNoFFZrSorCr1PC0ws546wkFylJoqWUYrPVrFaZ7faQaGl18I6c2+O1FrI6cOemJK7Xylr+\n7qcf8Nz9NXfPOq5urumGFQm43e9BKVzXUXfbZb5YilBilFLkmEgxkqepWUYVnGoOGdqwHyde+rzj\n+uWB//3nHN1QeP+HNnKNvMNYi3OecT8SYpROQckieqAUp8OKplrMbtpSjQgyXN/e4ozCdEYI+lQJ\ngDERK3jrmPWWjbaNiykBJaS4aO+mVmmOYWKcRvZBzHGNgpQzmkIiQLJYtjy8NfzUz57yy9vvYLf5\nFYx28iw1RSVFIZckAbAZh0pLcyaj01qb9SjgHSmx1ANSe5a1m6F9pRTRp63tWVcVbYTfNVezVKny\nrPHUqgghUZWgr0s0UBwQoQRmV5EnbV8qLP+3YnskEVVPN8t7/Pjf3NXh/z/bO6r05gpNGcVwbthf\nZbYPI2cvuje0N0uphE1mvE64XtOfGXxvl/0cl9raCD/t/BnbZL9EQiw3pNi8wNaScZ0XbUljcSeV\n/sMdL/3GrbT4bjO2N2grwUQWRpkp/Nd/zfMnvqPyff/OyE/9bceP/0zPfj9XCIX9OIrQcS1Ya9hv\nRsYptNamxjmzzNKKLgI9101ItxS870gqEULEGCfivVN8xDldKcXq3PLgck9NCttJgDkEaWTBmlvB\nyPGs1iv2+z2nvSenJC7iIZBibiARUepXWto1Y1N3kRmWoBBDLty/c5fR7kQNPyVqKeQUGYZBXMFz\nQjuLqnC6WhP3AqAoWQJeRbo6RhkSCauFbL4AcmRQgtNGWlAIF9JUxdnpKfvdHqisug5KYeV6kk6L\nSW9ulevKey4vHtINw2KyW9rcNdVM1xk2t4Hzu2KDRK3E2BIRpUTp34hwuCoFpWWeV9KsbCPJ+szt\nVEax22lOzzQXV1Zsp6xZ5nvz2pBa96HWirEW33VL4sGw4qMfvsevf+6KX/z7r/ONX/ccDy6vyLlw\ncnKKNZrNZrs4QQzDIHO9du5ylSDnjDh7iOO9WDGlmKjGkkMCI632hw937Ke7TNNEmPbUcRRgmNbk\nHPmDfzCiyPzmpwYuXwGNlXtSw3YcRSQgSyLqOg9G5qy51IVnqpsSjDOOVr6Tk+jQKtvkBymkLFqv\nNJ+3Zi7UujuliRdYotng4sC0gTAm7n/kH2X74NOokkCtgD1KuVbNzbzcRoZ5JODNLUXaNTpUd4+s\nWZIuLa7yVhvmoYdzjpJFJEHWmtj2qGTmWypKBeo+oLRolFqrcf2aqjw5TegaUQlKCrzZdlwpvevI\nxXe4vTWZ/a3f89u5fTkcvqfZntJaqD5y4UoprO86xttMmgrTNtOfHHZVcuH6pYgfDCfPOeJOeGqu\nT6zuOHxvHtmfsVLlaASibpUGXchRpI9oWbZthqAlyw04OwysTi2728T2YQIS/bmhPzdLu8t7z8NL\nxQ/8Vctz9wPf9ocn/sN/45a/8eMDP/GzBzqCs0Kmn2JiGoO0J6dI37mG6srLMYM8CKVGNJppCozj\nBChCzOQimbCsmIfqVinF+q7j+sHI3Rd7IQEv85KyGEzqo0xsGsUYcxyFcmCto+8HtHFttmdIrc3o\nvWccR6yRBEKwZ5JU7HYbTvpBdBdvbzFK4/sOasF5z2YjfClrjVguhciUonx2DOhm+UOVGRTtOOf2\ns1KH2st7v0h9qSremOvViv1+h0ZxdnLG6cmaKQQubi4YY2TVrTlZrShh4uz0hFjFAV1bRy6Z1D5n\nmhLPPLtiaT1Cm9tpckzYRmWoWSpdo4VyMDvZz60zaa3LHHK30wyrRM4WQYTKNbbmsJjPfE7JdgsL\nACqL/dPrlztyrnztV96nVlivBZ6fmu3U3L7MDd3YOS9dgyaA0BuZG6acJZDqglmtqKrQ+45IFM9F\n5HNrFik0YwybmxsJ9tZileLiwvB7f2/gW7/1immET/69HZ/6RM9nPr9mipEpS4O/6z2npyeEMhFH\nqVpzbly0Kt6YRml63+GNJ2URTQg5kmshFDnHSrXZrTVYZVk5A0qz20+EEIVUoww57Xn4usL2A/bu\n+7j97C+izUooFDmicUCRaquIXJjQE0qjwlSWAcbSUZoH+EfAMHlQF/H0aRLTXE1DFpdCN/TU6pjG\nHXPOPlf1tdku5XHb5lfi2qGNw3YObTx5uqUqC2oOmIdtDnAH/VkWXujv9Pzr3doOgemQtL9b+/1S\nlGCednt77c03QfxorVjftWweJPaXmX4tlg5KKfZXBb8ynDzjKLng7lhW55b9beLm1QnrNatzh+lo\ni75mtbbEsXJyxwkPqLXtZgkvYwyDE3WGXMUKxRtDzIXnXhjYrDLXlyMxFMbrTEmVk3uerncNSSqB\n7bXXLX/lr3f82I9PnJ8lYghtgA21uZ+neZZSpSJAG7R2iJILQEOnlkoIsYn4tiwxN8+rpkFZ6wHJ\nKkLHitW54tVPb+GFo9y0NCRhszzSzWRWLa0jCS5emQWgoI1tljMJXZIs6qXidBOq9uK1Z7WGUkgx\nELSis5rTk6FJviWRt6qltdUy5NaGTBlrHGPYSlWYpacvMlkC6jgW065VJKJqQ7nOSik1y4ynG/rG\nUZP5ZBynhdcXQ0L1ksWLGLFnHybG2PhgWRwYNBJ0clPfmZMEuY9kwe6MgxaktJUKtvOdnOZ2vAUx\nF50X0FdeNov+pjCx2qyygXC0UqLL2FqouTbKhhblkpdevWU/Rj72+7+KcdoSakUZy7gTD7lSsvDj\nsgRa1VxAyjRRWuIzxUDMkZQz4zQKGT8JWrPvvBCoY6IUpFKMgRRl3nvn/Izt7ZauXcNP/v2eT//6\nCX8tB158PvLRrx755m/Z8AM/YFubU0jyxihSmhjDrgX1mftpl/axURqjRMQ8x4DxTnwOW1IiQ7GK\nbYLWtRH/retmr1pROBodlxeJFCvPf+SbuXn4CaEFdY6qEiT5WwTso8DPZ0rCDK/n0YAnQJdHKygZ\nF8gjOQOr5qRFNQ4mtUpQy4mcIqgDD9gYRVWZkkOr+BS2k9FKqYmT03tYbbh+EJniZo6Uj6yPcyI7\nu6TMxtK1FEE//3+o7fmlbMeB6d2MSV8OOvRpt6dqbz4edec/3alhfy2E9fEmM9yxxH0m7DJ339cf\nZngACoYzS39qCNvC7UNpG6zvAAOMu8T53X5xo9ZKif07LOg8NwMSrBdiu5LF19fK/WcdqxPN5z69\nASBsC1sVWZ10LcNK4jTgO0qKPIyKq6uBvqtsd/s2p2itGmPaAtfktUplux8xGpzVjbrgFnDOFGQe\n5ZxUYDGmNu+RIGpAUIFIkDdWEGNWHTy9Zq6JqqKpOZ9xrTWGmRhcSY2PB0KqF6qFaCFqrRn6gRgC\n+3GPVpXOOaFCtAy1c9Ku7b1nP47i3D4MhJjQMxG6IWedteyjPPhaa+GMNQHkWmThOL75Z+JyrbXZ\nJfk2AwrsY2CiiOu3gu1uC/1A62e3BSG1FpZusliaHETGrCJScdTKauXY7yLrE7c8FLpVmcqANRIM\nc5a5rLOGFAWgpJQgDVVzNJ9CoNbCj/5oL4olts21kFlUVYLiK0nQvXOVUJqUmbQ/DSFk7pz2zBVg\nzgW8pRZFLokQpAU+jwgqsN/vqbWy2+1E5ks3yoU22OpE7eRGULUAVYnGYEwJqywxCUe0lMJJv8Kh\n8M7RJc9YMlkpcjZ88VXL5z5n+MmfFHUcaxQ0p3YwaJ35uo9mPvmbil0A5zwqK6zSmCpgIeMVRitS\nbN2D+aFWiqJmKo8lpgmtNf/V9+/56Ec2/MB/Y/hP/wvH4DPf82cCn/pk5fu+D977jQP56iV0f07R\nBZ00qmpKnahkoSVQm6C03Guqedo92sZ8clI+R8cQD4FLui3zvaRJeZLWsdIiKt66SJJvFmJOSKe3\nUFIlAzUkqurw1hFLohTxGjw+huOujlLi9jHbbM1enb/Trc6n3Z4UnI+/57v9HZ5Er/htr/TmA6lt\nCCwHIfY1KitW9yy3r0a2F6K4Pm0SJ884ZuXX2gbH0voSr7ruVOFXUJNhcxHZPAxYo1itW0ZN08lT\n0pZzxokKRsnUIkRpkMxzNrCNOYOuPPshz+3DxHhTCLvM9nJifS62LOM2srvao4F+DXfvO3KS1p7O\nEvA6r/nj3x74iZ+xXFwCShFjbhw8A1hqTcSYl3kjyALZ9X4J0DEXaomgDErXhVdGnavXVikY4fvN\npoK5FlxzAsilNOUQacE5beidX8xR0xQeyYDnam6mg6QYsUqBMaQc2U8jaeiw6xNykXaU73u00aTt\nhFJNcLoinmpKYZ3nznrN1eZGnOYbX7IksWfKJVJiblWXXrLq+fpRK7XpV+YwsV6di90NUnB4bznT\na3IM9N6zGobFfVtpkYBLSaovq0UCbhgs1zeTyIzRWsFHY8VcKsroVnkWvLKEEJd5WsqJnAqmka5j\nTMQkvLiqpD0v7gJSzadmilprbY7xMt/T1pJTpCICDq88uCF/1XOsVmvCZss4jlBl3tV7v0jtpZTZ\nT0HOjxaVFGl9ivxYrpVYqxj2dh3aWFEJUiJCnkuBktnu9nSuo9eWnDNnp6eoIlSHFCLdei3O6jFR\nxfIOqw1hDK1KlYr2/By+7Vsj/9KLe37tNyy/+knHL/2KZnOzwmqFs45xmqip4LqOVOUYtNGSuJXK\nOO7JbqCqjqpH/ty/1fGP/EOKZ5+JmJr5rj+defnlwsc+pvj8ywOXr32WlT0lCGMeVTpqCVTmxCdD\nafZBdQar1KM/LGvScuHbNoOMqBJkUCJHJzNcqXBV0+ZVWoItKFFmUUdgmNbGVk1VSmtDqYnx9iEj\nGmoAZQ+CCI+oTc3dj4PU11KbvssL+W9lK7B9wiM/zeAu+ezSkohjrIZ6w3se2dtR0HxDW/jwIcu+\nan18j7Mt8PH7Km/1mcfbU7U3DydS5JGWBQEwp5bxOhPHwrRJ9OcWN+glqxIE5uFCdJ3AvZWxmMGw\nOpFq8eYyCMBgdhgvdZl11FrpnG2lUGmwZjGKNcaSXCWlSE4C2T+9WymhEsbK5Ssjl6+Mb+hA3F5C\nnLas7hh856VyCwGjIkMHf+F7R37+/3D86I9rHjyoGNMBhpgrKUnf07RD6vtBpItUpZQAVFLMpJCE\n62QMnbbUnETVXmsUG3mWq4B+qlFLYlC1aPyphlCsVdrJK+d45s5Z065URNXU4Y18BkmoHtXKgzyr\n3ztr6bs1N7WQC2x3I7ZALAXvoebEuh9QubKLkc1+onpHNUIwnkaZzdXWnhElDhH5VvNDvcxC2j2L\n2AlpFNpJa0eVSthuef7+fbKViuN06PD7QtCGOklW7nzHdrdlDAlVNJ115IZfKFSmmLFeN81QJ1qf\nuWCtb4g9B49omAAAIABJREFUQ0FTKGjjBJpuLRihSVQlc1dVIKbcVNPUYb7a2lGlFHwDKtXWAXBe\nWlNKa0nCaqXznheeH6BU/tbP/zrf/gd+F2erE/pSeHhzwxgixWpKSY3WElvVKOhIETTIVGsoKlGa\nOLh14oaexrBUskZrpjiy7s+xfiADY0hNiSeisqBVO2swCPijltiuF+ymkQQoozEacq188bXMv/+f\nDKyGyke/OvO1Xx35tn8s8/98IvNjP3JfWulochWD46Kkc1Kbb2ceHUnfgNakZNFu4uULTynSmfkT\nfzThXaUW+Cs/9F6+96Ovo7UjOYVpZgm5BhRJnNaX6o6WzDTh63oAyx23N1GP/x8oVZa+m1LzLLpC\nTZQcW4Vq2vPVPkgjmsKIE4P8nFsQNtKKJQN74cg6SygD6IRSceGvtv4r0Ja+ZfT1W1vZfakB7y2D\npgJBwh6//ngtnX93HHTenAf4NPSN2ubuy/RWzejb+RPbTQMsWpLURXiLtzkNT43elEBnca6h6YoM\nmKd9II7ywet7Dr9usyhaS0xpajmAG5yTQfs81C2lUFXFeY1ztvHTDJ0SQeZSBcWolPDrFHIjzW0d\nVTLWiFXIDBjorGP1wcrmMnBzGUixLBfJ9lI9hl3h6rWJ7a3COuH6DaeO9R3LD/53lh/9W5mP/ROB\nf+/P7/iF/8vwYz+hubiUgDz7yZmsWa06aAK7xrSW2Ri53ewb2hP2ux3rvpcW7zDw2U8/pBtMQzeq\nQ5XUWkaqArkuYJ1aKlOZdR9FGuzk1LLZ7YkU0NLSi7ngTNdMQzUYtZCFO+twraJY+U7IxCXjq5dz\no0Uhx3mPV3Cx3bAbJUDkUtBWXApiFN3KnJK0OVEHcei5NaGFwJuBTEFnhfcdYRwJIXJzcyOybSgR\nedYy46rt3D68uIBlbicJlG0z1For203k/JmOnAtVC/k8RxHettYtHDtnbaNMSFU7TRPaGGYj3nk2\nNM8EnRPUrbLtHm6BRmvdWr4zgbkswS63mR+18OKzay6vAqthRUyZaRzpO0/X90zNLX3uu80uIMZo\nvHfkYrneb6UCrmCVYRj6RgfLxFoYTs8IcWouJIJAzDkTx4nqLDFnvFL0fcd2ExjHcQHbqKKoNVNy\naehLQWEfb7e3mf/zFw2/+HcE/HH3zNMZKy3ALLY71jmMKYSsoBapir3FFEMKI5/9lYjtFe/7+hPQ\ngfe/L/MV7618z/dU/uJ/7vin/9m7fO+ff4Bza5TKiOPBQUdzXlHrUXV3PMN7EkfvDf9XDy4JUGmy\npZRlTqtIJR99/wMw6bDP1k5XhdpUf+YCQEBnGYtBqyIiFylBTrAoUc1tutbifJpF9svYvpSA94Zz\n2pK54winlnby8f4f+zbt1++U/P7Eilcd/64dQVsfQQqEw8cff4Y+/PzmDBLgKdGbM2x8RjbFBi5I\nObG9aNZCGoZTu7hhz/ZAtVaRyaISYoRcjojUjpwy1w82vPcDJ5SSBTmm5QtoJWg3gQwnUgp0zqOo\njNOe9WqF0nD3/JyLqws6b1FV4YzAs909xZ17PRVFztJyjDWQqyJuC5sHE3FfiXsJZnGcOD0XEebr\n68x/+8Md/+P/XPi2b8m894XEwwtB1wEUrTHWsFoNSGUXoFb2IWKcKKDs94EYisDOc8Jby4NXt4QQ\nOX9WzuecCCrA1MMsQAO99Qyu5/rqit5Y0SdVkqXP9AqlIUwCaAAYt1tOTk7o+4HdKMTjEBWbuuV8\nvULlyuA8IQUskKOg71KpWOukxTommWFpWQSMVRhrGKcRtJbAkjJVKUo5vvVUc6KGoubMWnhPJut2\n40p73Hcdp6enXFxcYLW0eI0Rc9mu79ns9ljrqM081ncWjNARrNOEMXNy1tEPHR7NyZ17jOMkMxyt\nRRi4zc4OmeNxq57FeLYUoQjM/991HbvdDkDk3loFOKMHaXO5GEJT+ZGH9+WHG1585oT9dkOqldub\nW07v3WO7Hxell67rjkyPJYDmIvNe7Tzb29ul8l77XgJVMoxTZEyTtOdah2M/3ojmqFbEIvtzvZeq\ntgqNoxpNynN7TygbsYi2rPamzbFiAzwZnHUibpALcTT0TuGNnPu+k+fxY9/xKl/xwS1/9+9ZfvkT\nmk++tMPtVmxfB2ok7SuvfDLCtwS+/msSf/SPab77uxV/8S9/BGXPQWmM9pQyyj08qzjU0uhJB4kx\nWdseE3lum8TEo6ZXbe0AkH0qSSwVVSozBVOjo9RcqUXQ4VYL2Km0neYjayXQ9P2qCRPI/Ssz20BK\noQG2NFMqh4BRDoFTnm01Px1vt9x+SdvjgeOdkOEfCTxHievx+98gOPIEpOaimPMm73/S5z7xWI/i\na52THnXsnCOt/YNn3tGxPOXpfSoZslnmaF6Q5y949VIgjfJJ5892Ag03Cu8lw04pY7XBVLkPjGqO\n2qVgm+Hn9YMR3xuGlRyKMQfu2qzIUlKmpCQu2FQ++OEPs7nZcHl5ifOOadqLd5zW+CZuTC5SZVYx\nlzTeUGOGYiiponvF2Xt6wm1EW03YJeK+8uClLS9+4JyT9SlaC9jgh37EtoozLyffOYd3lt1ux8nJ\nimHoubm6puSMSx5j4PR0RcqZmBKSSRY2t4H1mWuzIb1cY6WaDVOV6k/mVIK8vHsm/mgPrq+4vrnh\n/vkdwjSRwkR/crJoXjpjsc6gq1RtxlpSSYSS6IwnpczZ+gQD9FYti0ZJuQFvAs73OO8ZuogqpZmX\nCqjAGkOuApqRxdFSU6VkfXjA5wxNHXJDjXwX1xwqTk5P2W23hP0eg0I5ySal0pLc3jTLoFKqmN22\n7LFqxb1n13zu0xf0g+V8JUjeadzLDFNbMlJ5GmMkh29tSOeEkiKUBalcVJu9WAvPPBP5wkt6UV4x\n6tDmPH4gawvmtlWSnfdMtxtKLjzc7Js1k+KZ+/d4cHPLPgRK1cRU0CZLgOfg7yaI38RUapvdWjrn\nRDzAO1gNuMETojhhrNcn3G5u29x3RmHKAh9LIu2kPZpSolS5z1AsCVvMkVSlCpH7TaO1iB7IvSCC\nA1orYoysViumEJimkULlB/96zzMvFL7uazPf8UcCH38h82uf3vDv/ttynvo7H2S8+gwPvwg/9EPw\n2c/3fM3vWfF13/A5/tWPv8QLz038pe//Jf7Uv/I1Epxos6HS2lZzpSZPxHIfHc/wHufk1WYttCyi\nDZhWa6XoplTke0IMzHJ0miQBqQowqblryuflIqR1GmK2zXnFCq0FMKWgJFIolGbgXEvzqlMtAWyh\n7re2sXl8Hp4+sB6DEoGFDz3/bqZm1aXF/ObAlbkgevxYjnnZjwe4Jx6rUm+o5EoWLAcV4dU+8RDm\na/do4H7S9o7Qm6od0GwzPwe8Zz4w0K+EYzerTVTAW4NCt7YOAuNvbclpmii5cnsVWJ1KiyuEQNd1\nS3U5l8ldqwqurh4SQySlxPpkzeXlBQq4ub6i5EzvnAApasUoRdf3VKQtWltmUIN4Zmml0RbcXY/V\noM56Xv3sLdMu85lPXKAU3Ht+zXDWnBY0izv7jADsXOSF5zVTEGrAyclJ4xAK4jPmTJ0yOIvRhoev\nbrm9iTxz0jV9QsmcjdEin9UUMfwsICwNP9brFWGaUFoxtQDVdz1GK3KcBJLvPKen55ALm5sNftWh\nSmuvOIOyll2YBN1nrSBRjaGkQqm5SVFpchzJKTN0HQbY7vb0q4HbzZYY49LPN9qgKvTGU3WzllEH\nWbXOeqAI4V1QO/SrFaoUtpsNBgGUKGOJUZCpWosUm2qBTyFC5KaRpGuVqq0bDGf3O64fjrz3+VNR\nX3ENUapAaaFTCH/ucA/nJCCPGSSj22pkjGG1Knz84xf8uX/97sI7dPYgZD27wocwopBqcFZTSUFm\nRB94cc1nXtrzv/7S5/hD3/RhbnZ7EWzOUhXXdm9apTDei0BAFePkiiQHzjosIgBQUmIqmawKoUQy\nhb4b2O52xNYRCU3UeQyBwVvhMmrFMKzYxkgu0A2diI3PGrRaeHW5nVPdaAq6oRidtYQpMKaJZDRZ\nQQjSISlUqoXPvuz47Guev/m3V7jTLV//Xs/19Q0A/9l0wcf+Szj9ffB6r/iGb+r4J/+Zr8DYHu9X\n/J2f/t/4U3/ma1FVQEA0kQBRLmqLWxWpLzX/W67iYX2rh+sK9chL7/A7am6BXRL3fhCz3LzwbWdU\nZhaJQdWshJoohKq1aY4K6EnmikpmjgCLalOeO6nLhz++nNe57frbMNf7UoAy7zRYHtOUaq2UXA6n\n/Qn7elLL84nH2pL+R98LLJXkk2Ja4w1r06rQLzPoPSI7U2fRXgj7Q+PUei3cNMRhYwoBrTTOOoQL\n1UACRlNTbHMBw+YqUEpt9j5l+fISOKXCA0Gcdc6xXq2ZzMTN1XWjB/RYawmbgPdeWlRZ5l8UAQpU\noO/d0gUptTLGfQNhyHzQoHFec/89HZevBVKQ3v/DV7bYC8Vw4jBG4TrN6R0hA4cQ+OD7E9/9XTs+\n9enIT/z0mgcPuqNWsATI1SDmna+/suP2IvHc+3v6QTQs55aXmOYGkZ4yBuc9037H7DeYc+bq6lLm\nCqUQpsj6ZMXZak2/HjC3G1IWdZVpH8AYaXkl0cbYjyNnayF7X283mFK5d36KN6LTWUthP0mlZ61r\n16OSxknaqCmL7qc15CxZ7Ljf0fc9K9+himcq0lZ0TqDr1mpWfUfOSVpGpWknGk1OYtFkGiBqDiLC\nqdLkkjDWk7KQnXNMS0sRY8m5cnMx8aGvukPOhVTEVbzrvKAfm2PFDBcXMNU8p5OFzRgZlMcUcc6x\n3VZWq4I2CpSc84P+5kEp59isNscoiNaURCXIOlZDh9ZCWfF9j8+ZMWamKInfftwvyiky856PU/iK\nxoiVj3OGm6tbUNANnpQirm9E9NsNIRdc17d5VYPj1zbXbs4AxhhSrlJ5GitWP9qwHno20yhSXAoU\nQsA31rJarXFW5ngpJrJRZAXVGmIUBDVFoaymKqgUdrean/+FNfv9De5+z1ftIu/5uJy3nxqe4zvv\nfpDurENXAyXxDd/8TSgVWUTej/U056yK2uxjyiGMLFX20QJ13AYttaXjdVkktZpl8RL7/W5BWR5U\nkEQ3UJuGypEdHa2bx6L4h0pz+bl1NLTSLVE7RGSlwHpJcJeA/tuwfSkB782quEdyiTqj9w+6sEvd\nfRS83uzz30zC7BGOZa2PBcLDbO/Nthk0CeVtXwtPEfTCPmF8g/OWTNwXdlfilD5f3xDE4XtuQWkU\n2gp7ZSFkFo0p4lRgjcz79rvI6tRw59mBWjPGKlBiYwIZ58WNIcSRnCN379zh8vKSaZqYpgljLOM4\nMQzDoj0pQsQVbTUxS7trPg+KyuAs0Xu2uwY0qeCdOI+XUtHv0YyjtHJ3l5kUKrcXB5mh9UmHVgXv\nHJ/7gudf+zfhD/3+wL/8L17x6d8w/C8/e87lZUdWBxcJTeX64cjpfbBOPN90VZBkMY/jBFScFm7U\nuutJ+73YCCkI407mgm2gXrJIbg2dp3eemyouANvNDtv17HY7aRnmvDiL317f0HeOVApTnDjPq4Vr\nNqvPjFPgrBcuWQ4Rrx0hR/b7kTBOaGu5d37GfpzEI7Aht7z3TNPEejW0lh/UkrAKjILb7Qa0wRpp\nwTprWa0Grq+u8G5YMr6UK+MUBJ7vBUwRguiDaqTaME0LEmAYzAJqqqWSiI1UXxdyPO1hzuUwc8g5\n4bsVNUyUatq8GGJUrNea/SjgmZQTGpmX1Vox2tB52a+q0spNUdCYg7P0/ZpPffYVPvb7vpKUK1e3\nt5i+Bx1IOdA1xw3V6Cu1FFKbV2mFUE5CwJ6L/dLqZM04jqScWa/WzfE7o40R1SIl9j7jbo/VMIaJ\nzogMXMgStFKFEgJW6WXh7buOMUWmEKlUjIbaeKxd10k3poKyhqohlsSUIiElQkqYqvHGL4GW2PHa\nFx8A0Pv3kCmw/wz/d3fOn33vP4gPa1TdQd1JBcVhhvdo8j+3Mg9/P/LbN7TPytHcbzYRned6Wfai\nABpobgx431G0pmZBoEr3SqH0PP/Th45F29sSSOfjBtTyz9bZUodjm+9n23lWq56b69AE9Z8uGL2T\nmdyXsr0V9+5pXn/scMFRoHsa/t7j/LvHX/f4/PDonW9xfAeZymWY+hbb2wa9m1cjttN0J7C/kvbW\ncG7xK8PlF8dmYHwYhM6zqdDg7FpJ6y5ThfiJwmnL9YMdm8vIM+/t2wxLL/qU8vzXRfUkp0QqkYcP\nL5uyglvaXcIZlHaitK8is2x6TpI9l0n4aDPMvvcWXfsGQADvfMvWkNlYb8k1cb7SxG1FVcPNgxGA\ni9f2fMUH70qLNkxENP/TT/b8zM8p/vE/kPiuf+GSv/SXPa89sIIqLIUYM2EqPHvipYWYDyom80W3\naHrnGbqONE2s+56h6wXajsJpLQjOXIkhkkPEoqgpc7Jes9tPdF72b4wWObeqWLueEMamKFI5Oz0l\nTpYQRs5Xa9FzBLqhZ6IwToHT1YBVmt0+4YxjLIHTk1Oc9+LUXcU8VNprEyjFsO4JcSSEineO3jtK\nCijgdL0ipcww9FhjGMc9YRy5f/cu1lqmaWygJdhvb8FYwn5azo0xhjhN0tuPaU76McpgjaGzDq0U\nYxB0Jkj1PCNjoeVnap7YiGVUqUUCaQOqbLeK3kdubrUENlplR10qs7KALESZRmkjC2Zzp797NvCb\nL13zkQ89w+n5ObtGhDfWo7QBYnO1FyS0awAxgN5CKEZQl97LLMhKdZ9jpvcdxnlu65bjbFZp1aTL\nCn7VLcdH+74hRMo8n8yJUjTWGEoJVDKd76hK5vEhRlIUHp4gkmWul2KilqZ8Q8v0s8zLw3ZifxNZ\n332B5z7wT/HPXV/yH08/yZ/9im/iYsrij1cMpTppKdd0VPlIYKoc5nnHC9wxovLxluah+pIOk+xj\nfv3B8qcu66AmTqN0HnJuy4SRDoWV7ktp82sZKrbWHbSq8ziwyRxUdqyX42H+VCUmulf7vbzmTaqc\nt9rebT7fvD0psDxNe/MRwMsT9vV4xfakY39SVdd+OH7RI8fzVCLXqrbWtCQxb7W9bdA7f69obI43\nieHc4oa5LXAo5OXgD+gaow/tSm1ps4PazCEhxcLlayNn9y3rUy/O18v5bBBVxLixziofWtpJppHj\n5hZTbW2vmgslJkrzqU0zOq5kjCqYaJidg721R/wrsdVJ7YEenON6u2sBGPyJcNKs77h4aeLmYuIL\n6oJ793vGkKiN3Lq7jPzgX6389z/sufdsQOvA7L93czlxeu5Zn6xQ2ovjeddJC621WkxRnA5rSopY\nY+m8SK5N457OWs5P7uND5tUHF4vsWec8WIUKhaHvuTusef3yisF3WKtRpeKVph/WhDChqGxubzlZ\nr7hzssJqSyoycwqjEOW32w01RVauw1mHVxKkT++ccX17i1Zweuec7XaDtZZ9qljnJRAjoBNjhSOn\nlMFZQcE5axi6ju1mI8r9SuyG5plfiJFU2sxYHVQ3tJIWJIg1UMyZl1+6ZX3q2hxF7gHhzBVxrK8s\nc4GZ9zmLKM/3wCySfdyuvL2F1SpTH4iaizXSJlT1OEnRC7hLGQdGNF5zylzdbNnsJt7z3CkpZ156\n9TXcakWIIhG320dRyel7vHNNp/JR80ujPEUh93sWqoUzhr4T+kKMUQJuE+GehQBE1VxhvaNGcW/Q\nk1SE/apj3G6p+UAjmtvFYlYsz6wIKxRCk1uz2jKv/945cpbzHFNAVd30aBMPPiPneHv5ClkpLtjx\nz3/wG6klo0zA5AzFovCAZOSH2DZTQNITq7tle8N/H2gn7adHXjSDSWBuh0rzsRaxotKoJkSuGkZB\nQCp1aY8dAti8IM/NLdUC9eykwhEI7Rh1qlBLAv7Y4f2Ob29EZL5V+5DleVQcBTTVsgk1q5oe9vM4\nKAYerWDfqhp87NN5mhOnlAhEPM3L356ygKI/dajztjiUg2nqPF+eH8IFgdXaNapWapjQTZ1lNazJ\ntXLxyp7+zDLcd1Qn2XJnpAoj03rwtQUNs1RG1ggKTXhjciMZI+2IGEec11hkMahKvNhiFADAlIVK\nIKrxVhwKUISmLmGMzPY6bcgVYoFkVBsPVE7vngCai5f2XD0MXD18c2X1q+vMi19xTt85Ll7b8drL\nG+6/z7EdA5RJpMBK5rTrGHcTORWULXiviaUwaM2dVU+thd6uGGMg1SIVQmsT3m43PH/vDilE1taj\nnGM/jey3N0RtUFHAHTkXTNV0vWfabkVfcwzc1EroMrlmsgZywWmH0Z7bmIkOXlg7ckjcW/foWlBp\nQlMY9zvOz84oMdErgb1fjHtsBactZBEOKBWs68jjhC1gcmHtO2Yd1FnM2LkO22Vupi3aKcosQ6Xk\n+pc2OykFrm737DaBr/3ofVyVKmeXJlGHqVBTQilJjEJTdpk1RqVqE2SsUYWQEookepzG8tnPmSYH\np9rcR4KJQ9PZrol7a1GhqYVQRR9SGQWm8PrVnufur/mG3/0epilw7/wMv1qhr2/Yp4DxFm3NIu5g\n5kBchFKQW0vOGMs0BdEoVXPHo2CMQumK10qMdTHgNNkUtIXe2VZ9OUJSWOWpJVKnEaMqxVT8sCLm\njPUDtlRCKNQMfdexcl46GCS2aWIsGW802ruWWASmOMr1MJqcK7ko7j6neP3z0D//QYq6xuSXKek+\ntlqiHclonB7JtakFUZbEph7JuUE+7hs+us3ty1qZjVtbHffI62tTTkU1l4xal0C1ID5VRRkous3f\ntWLcSydHqdp8FiVKCcd9RmQ2ArRSCB2itXebM4WqMk4vcRICvIaZA7islHUWlZfjVG0WKEIe8u8l\nus7zxKY/qtreshIN33m+Nidy73R7J+/R6lg+Tc8nu53ZR6u3N/uMJ9nPveFnNScycwSb/5Tlurcz\n15KaNpNtXF+UJvPWleHbozdrXYiZuUFHFbB5KNma7ZSI+jYElgwVpXrxXYdtw/JSCzEVlBGnb7lY\nlTjJ/CZVGocpLgjJ45M1IybRMnSej6fruobak+ovtbZojFEU60smZxGxNbiGMpQTJrMcGc5PIbIa\nVljr6IaesNu1mfohgzu7vybnwvVr05JNKA1ukOomjpk0VXY3kU//6oPGb1O8+JWnfOcfG/ldH5r4\noR+BV15ZtTaRphsUcQpYJ8g9XCJmmZ2kKM7iruu43e6YxonedpClOjNWKB3jZsvzzzzLGBP7/Z4x\nC8ncevEmFI3NiXt377Lb7ejWK2oITOOEQgJVLYndbk/nhJ6xvbnli7e3nJ2cSlJTC8o69psb4m5H\nSJGaKivvMVrT915OhhIzUtEpNYRpFIFfbZlywhhNGNMyK9HWMMWJasTDrWRxSc+5gZHc4T4IIfLg\n5R0f/NA91qsBRWEaJzKVaitWabS1GH1A/h4bF5cmhF1rZcqZVMRc1Xdim/TD/8MdSqmC2ix1Aa8Y\nbdnt9g3yX2UmqzNd56Wlrw0hJq5vd7z/ubsopdlst+SS2dzeEsLEer2m1uZB1xC+vs0t4yTO88Y4\nUg5iAZQSNYpyi1uvZMmuijBFQVgaS0oiBZaAKUT2NVKyFtCLdQx9T9yMmAY68dZJm7hU3NC12Wvj\nl7VKxCihlxhEh3JssnbOuaVj83iWniaZwYfbK1ISlHPrGi6z9NLE3Guti+3Ul719mbtQtQqxvHFN\ntRHfyvZb+YgjFZhlkZ+/GCK1p4yMGYwVIBdOM01KhKyRz5hfjz4I89daKLXVhcoIxaECRjUgkoC8\nZvBNqYJCr/XRL/9utkDfbKZ2/H9fbtv1zZCcb/u+5V8NZXv8nnk9Vo8G4Sdtb1/ppQJalBjEfVm4\nRDNqtzs1y4fKBXq0baSNIcbQgg2UqbK/TjzzQfFUUwZyiowk8rwoPfJNDxYdyjdLoqYZaK0VmoP3\ni+P0PLzWRjOlSCrSfsilMkXxnCvM5OJM1ZJZKy0csJAEkVebYsaMnry+uGXaFcI2Y71ife5Z3+ka\nwCQvaL8wJqabwrQp5FTJqXLx0pa/8TdX/MPfNPLxPx24vLrkJ37qjE98UvzvfN9RSyTEgLdObIli\noFbJY9I+sNtPGDRea3KRanc77ckhUErh+vIKULx471n244jxwlf74vW12Pwk2IVApMogv0iVNFvu\nGNVIuqVw2vcMXccUA5swMvhezomC1GyIpikydEMDddTm+q7oOi+wfiVC26UWqlHt3CY67TBOgkeK\niTQlhmGgAp3v8F0PGEoeUUaLAHkWmsblxZ6uN5yeOmIIaC3X2TbvO1CNptDamC05UlovAtRoxTRO\nDdpvxOi1yImeEWmlPTbCMZbGjWmo1JJi278ELkneJWLc3Abuf2RNqZXnX3yRB5eX3O52eHcQxu77\nfuH9bbdbqFUUhVqA3u8nlNEtqbEYJTSOUkGXisK0ubZi8I6qK7oqkrHEJG7gtRbCuGPAc7patQQB\nLq6uyCmjjWa32VBTYrAOpy26FkqM5JSYwigoWwq5tXYFBVpxriO35194cIqUJLPuVmcoHDkZ/DyL\nJMtzXspjge64QqvMbaM38vLa74/fB2+7MD/NplqlWaoYBlttFt5mzYKo1VYcO3JOS7CbSetGO6E0\nNGFy4TUGakmH79cqQ6UMxnZoa8SdpAWxuR1nvGd9ciL2SzPiOQam/a7tSz5zbrQq5srp6dRPnnZ7\ns329G5/xZvs4bn+qg5TO46/iDVWzvKllLPN1mU2r33x726BnqygU5JoWtFap4FaKfF0ZbzPdSi/D\nxxkKXKsot6QkmXZusmPeeVlwi0ZbGXJ7Z6m5ihTWzMdonz97mJVWzak2nJ/nMNM04ZzDeofCikwU\ncluIKodp66Eg5azSIl4dklQrStoXxlqZpVSZMVhjmcbAtMmErcCm+xPN+Yse4+TzrdUCLJnCovrh\nOkP/vEU9p7l5MLG/yexuEw9e2fOzP2f45V99ln/g92z5zj9+xc2N5i98/wmnZ88w7jZorej7njEX\npiDLTEATAAAgAElEQVQ+a9Y5ri6vSanitSGFgFYV5yXzTqXS9wO1FLz1WKC0GyCnxPnJCdtJpKs6\n59lst1zXW858h+874hQOvoTWsNluRW8wZzCazvVstzvOvcdYS+d7rLHEGgWEUUXY2nnXvA8Tq+bR\nF2MQ404jWpiV2iD1wsXxncM714BQivWwYpxC05KcpdkO/X/RvoQY5Ji1EiQsWjOOI24WQ21dhMUR\noc1ZTAMyxZSIVaOtJFH7/QalFNYIgMU2aybn5V4vrRoqbYHMMeOclcIWQXcqpfHecL3dc37Sc3Vz\nw2a/J+SE9cLpm6ZJEJspLff23MGQ4CzGt7lWtHWtvSn3pxD7FXWKWGXw1mGtIqXQftdztQvsY8Jb\nWRxiDJz2Z6gkqjt3T0+52W4oRjFNIlkmBsiG8/UaUxWUyqqu2aXAmCNZiWTaFAM5luU51y0A5FS4\nvRDXj5P3fB3b3Q6lZkm5PK/5spgVCW6HUVs9LFyPbU8b1I6D5DvealOTahYnCtXUeEZmzKYkViLK\ngJoXaI1WIhSulBYxBORclpxxVmg1yjqUrpTcEmsrc+iqRKJPPlzal7Wtj2jVZuyjdNlmyccWDJRS\nOKMXgedS8qOUjy9ze1rk6JfDBXzSPG9BdXIc8o5/kpumchAHPwilHL2uvv1Q722D3gvPPMOrrz+U\noEULOkrjesV4U8hTJQWwXh16y1X4cDlFuWGKRHDrHONNxq80GFnY7pyd8cLzL/D5L3xR7HGUwju/\n+LWFGB85wUIIZlksZrNSrdUCoqDCbhxJuVJVYZwiWrOgN3MpjDEw6z3Ukig0Mnmq7G4C+00mTnKs\nq/sG34sl0HwsuRSmKWCVWc5xVaJ6IZ5Zmrsv9AwniYuXJjZXkZM7MjD/5V894+d/QfOVH84UZXj9\n4gH3T07Y7/bcOTllt9uxWq2oKJzr0WqDooocVE3Y3uO8gDpSyXRaUVNTcjEG4w23mw2baZRMNCW6\nfsCgsEUxbnek/URImaH3JCrGWercdus6api42e1JU6CExOXFBcN6Lar6MXLS9Zyt1qia2KVIilJx\nD75HiM9gjcwlY6lM40huC/RJa9dZJWAbYyz7KZBKXbhxtjlNKABjyCVijCJMMPRN/Ue1atWKbqZR\nmjgFqS6g6VvqZeHIbZaIVpAVudSm/iMISmudIGBLXeyT5uOZxrHxR8VDcL3uoVRySaJ+ozUvPnfC\nF1654bSD3V4k24wTUFJMTWIPs3A5Z47mrBy0GYUzyOwVqEWU22pN55xUZsbQDZ3Mu3VFe0/VsBkD\nGy2LdKqZUiJDtxIgUYx0nRNlnUbXyN4LIMo5TvoBU5XQVLynQ3Oz2ZByJNlWeShROKGBgASIUinp\nsMBsXv011PlKAkIDFmjlqTW290jQm5MQeWgO/LVaZyWWt94eWeCfOP57ygV5FsRHxi05Z/abraxB\nw5rdbieApQb8EfRtmw9WSZAPf9eGjJVzTykiyp/FDLvmSglJWp1tbimHqEV5KEe2tzey75TA6MXG\nS5R3BOhj2nz6UA2XL3mm96Tt7RCYx+3Pdxr4Ht/3k3/3+P5aQgHQ6CTUowZmPdxHtSiUFgDdW21v\nG/TidsfKe5JS7ENEEGYyPO9WmmlbmG4T+twIyKTmZQY3H5m1llykRRXGTH9qmheeIUwTX/zCF6j1\nMOgsiCVMOmqJqJbV51IahFiyzWE1EEJkipHBdiggxSQtPueJKYt8kzFi0Bpl8Fn1gbsFsLmJjDeJ\nuC90K8PJPY/yB6KkSBDVZR6omwQUiLxVKmIDlOrBNFKBtMOYVT9WjWtmOLtzzmc+v2e722CtI4RA\nzVGUL0pms9ksOo21FPquozdGNC0B13n2456uH0BpTGfICAn3er9jnya01aQKq/WKwfd436FPi7R9\ndeFme8tuNE2hRrLRGCP3hw5tLYPvKDFyenoqGp2lctr1KAUrP9BZAec4a+j7HmMNMUyt1SuO7vPQ\nv+86akNwroYeSlnk5iqtXTuOWOOa7xxLS5yc5Z5L4lPXeS/tuCLVcG7nVyEegzRJrllOTCm1qKco\npcSWqdCuq8IYJwa1mkcQgdRKbQjbkkt7jcE5L4LnTRXFKgFOPf/sCZ/+3Bf56IfuMYXAiy++SEG4\nh7MQQYhhmefND3pOWboiQSpGrWdEpXgaWq1IYYKUsTkzrHrpWlgBw8QY6IzC1iwIz5zRCCAjZeFL\noqT1Zq2j6zqZJ9baAEcFVRXaiWVSQTiEVhu080xIp8daea3MSDNKGbreAgICMSenhDzROyuSXLmS\nk8Jh0EjgLKqhvhfZscNac7zcPbq4PrnhtVAXHgt8x8TmJ20HtGwBzJKoS2AXwMs4NgS36cgpNcEH\nUWrJFEyr7KS9WNqq1fiWbY3IJUEzwhbvQql4VWvjLRJoQEVeU6ExIATU1/Q5lu+fS+LQ5nzz7/hu\nbMdB6knBbzmCowruaSvOpw+Wcs+0dzHzIt+ACEWeI23FGPmttrcNes/dv8cuRG73IxUIOVMQKHWa\nJGhMu8L6jj20PdRMX5CHp5aKtWbRQFTa4LsO70Qtfp7FzarxtUqoSyWjFKLw4RwlZ1JMUl21+zTE\nSC4tsDmDN3aBq8eQkO66iCQbIwt8bFqiYayMt4lpk7Gdpj+13HnBNTdpsZyZ26jzSZ+rTLkckiWW\no98zLxjWompldystlPvPn7T3VJETmyZyjiIxFsRQt/crcsl87NsnXn3Z8Wuf0ljjm29dFX+xWdM2\niylpUYpEJWcBvqSSiDWjvG0+gKIe47VFO4cqmTTuGDWcnp1RZxfpBvzRWrHb7VkNK9a9Bufprae4\nzH4ccd7SdZ6aEgbDqvMo07XWZpVWZhE0ZFUa43zj4Sl0q2xKqTJXSwnjPKUmtlNgzAmdC75UAaOU\ngnUi/0QyvP7ajq/+mvvUkjHWoJA5biqFlFpgzAVvZ5kxEYuWgCiLY4mBOI0Mwwkpl6b3Idft5MRx\n/07ki19o+pvI8uK8p9pCKZW+c+SSmMbAycmKlKQCjbngvOZkcHzulRt+9wdfxHvPZrOR89uCp/US\nfG9ubhiGAYDQzkUpmt2Y8L2l66SjoQFrNL21KJPplLQNtbNgtNAHlKZ3mt5ZdmmkoOh8D0rakuKE\nVdhPo4DG2rV21jGl2CqwKtJwSYSXdatS43xdFRjX6A4aSpoBFYXh1LC/zXTPvI96ozFFqBCCzNQt\nuBz51HEExhDNOdQy03vr7V0cX8nVfcMCeghGStUmnebZ73ZNKlDWtlzj4sOnGj9QzUou80JcgWXB\n1mI2K1Oco/9vr2uT5EfFnJ8005x/encqu/l7f6kqLo8DXJ60z8f3/5af99hI73AKNQuSW89nYK6W\nDz/Xkqlvw+t726B3droi3dxio2alOkxKTCGSszhpALjuUXmmVFqvXKnl5i4lS/ISRLhYG9tQU2JP\n4p1bWpUpybytIK2voiAU4dNV1VCkDbmptczocqmiH5klA3XOsxulrTLPgxTS/su5cPF58e/rTw13\n3u9xnTg0zO7JxxfmOHNcqun2D4lFqV2cgwyRrkAB5zVhX9huRu6/eI/dbotqqNG+7+WBV4qTkxOh\nbaTI5z+n+daPbfnDf2THz/30Ob/6K73Mp5DFxzW5ra7v2E6i2DFO49J2NcYwDAO+byT+GBnDyDjt\nWPcDJ+s1KzcTlBtU2nuMtqJtGhNhDML7UqJAb7QSUeIcUcqxWq0oKdF7T6USU8QYg+0HtHPcbLbE\nkslhJKcJZ0WNZQoBlCLkzBQzNU1sxz27aaKoircelAQ/YVLM4ClwTnP3fEUYR5zqReg5xdbeNm0+\n5doCNMvZifCys3ZRQum8xxstTuVYxkkqoGfvRf7kn7zgP/oP7sn82WhO+qFB9CV5KLngnKeUxG43\nYltLXVEJIfLhD5zxiV+/JMTCV77vDGMNzlk8LDO9XAWEtaCPXeHias/nX9pQCsQkQJXVynGycnzN\nh59lNUilT87c7vdc3dySFZwOPaZWvNV45yibDcZYbHMaSW3In2uhWksq4i6QcyGrSNHybAgyUzRU\nldb0Q081mmnao1prsxThchorVXEKmZwK41bKkTQlnD2FKbVlSCqp2sAstYEO5mA5z/VmWsE7iWcH\nUvM7eNPj+1j+Pgoj9fDbWisxBJKxdP3AsPLcXF+Ra1P+YJbiKo/sTUFr4UqSvKwVzEh26VQdvvSc\nXj0eyg4VTn3i/79729MEvncMFHqLduabzw4fvROWc6IEtKZbYiajqdngtx7eU1UDEr359vbk9NM1\nyhjGKBB81Tgsl0c8tdW5OpBkEfxMPcrsRA2kMG2rwII7WSCsllZpyYVUo3wzxQJEQInShG69cauU\nOHunBFUdbH4awTuXgq6qwbVXxLxtiiMSKK0S5nrNkqHd/4BfADIz8GGpUHn058MlOBrENt1DrWhE\n+DIbxgsfUFvOzv9f9t4s2Lb8vu/6/Ke11h7OdIe+PbfcraElRZLlCSfyFGRTCVSAPKQChDxRvBAC\nMaHALhJDKAwUUBDHsR1TYMrhwY79AOVSqoKD7JgkMpIdWbHaakmtoVutvt13POPea/hPPPz+a+19\n7tiSWraTYlWdvn3O3nvtvdfw/03foWZ1HDg97MlZgCptuy5ADDWpzpydnhKrmuB7PvfZhle+uMO7\n3xP43n/xmO/78BH/8O/v8ZnP7FAZUYoHUcXv2lYWrlktC8gQqFwlgAxr6fuenb0lOSW6dUsyMqzP\nUVYfH6WajkMs2qgJpyzOVfS5l8p2nJtl4bH1Q0/wAzNXkbNoPPqUhXqgFX0IdEOgHYIAibJHW4vV\n0AYvvMOY0LaiC5GVj3jkOGI1rq5JQ2mnBaGcxKRxTtpLlXNSyY2JVkooY4R/Zlzp72+1hIqzR13X\naKVoZjNSynTrNaCwRjGfNfS9Zz5PW12KiE6Rqqpp247aVcQUcdaRcpmtGEUqItZ9P+Cs4lvf8wi/\n+U9e4/FLDXu7S3wJ9COht6lrabGGQN9Hvvjl26zbwJOPLtjbr0EpTlYtQ5+4fqPl9uGKHWsws5kc\nr95z2nvWQ+B01XNhZ0HMUvHmnLHKijVQgqAyzpmNmkwUClLwHX2OoDUJRVPVkowW+cC6ruliKLZH\naexSS9U9zsG08GTreUV3NqDMnDQorC7nIEcZdCO+ebJ4jy3BzVL+9VrufEMgFoBzVVXaktcqGp6K\nouYipPwQArNZw+nJMdrqydMzpe2W+NgiP09SH38bF+rpOytIW5y0OB2L+38z/XUer3tt3wgA5l6v\nHau/+wXQce28F21hs2PFJAWnmChpFL1cslBgyPncsRjns5Mryn22NyE4nVguK57Qlzk+ben6yFe+\nckLXymI539MFaaZxWuOUyP6sfUdbxG8rbcTF2hZx2SRw9ahkMKuVojEikZSLukHKmX4YCGU2VFUO\n28zIGTwJZ0vlQ8I1NamT4BdQkAIoTczFoBIJnkaLePLqNOAamc+MHMSUpGU7nkxZoAqfcLSzGFMO\ntbnIlTLkPIr8Fv5RzsWM1GAaTdVohi5x89oRl64sqJwlxUDnRQvQWU23HqicY7lc4tctta15/ZVd\nfv5nZjz3vGf/wgDOcNb19L6XyspaTO3QZKrKFVqHQodUfAt78RDrBlKKzBdLXIFMp+CFoK9khmGM\nRitomrq4H0CtXTFhledoa8U3sCze6xRQZ76AKjSxqNavVmtSFjPTLnictszqmRixpsTQDzKMzhnf\ndeQUcUYxn80koBTqgLS65YLvh4hz8tlHjs5QfB21Eu6nsWIdRDGkHQEGsfBGNzxTTfAddVXT9j1a\nGYYhcnKqWCzSdDM57WjbjkWRvdM2YyuHNoocRWUmpYCranISeTijNWdrz3JRsbezgBipKpE0UyWZ\nSjESQuLV1064ebvjicd3ePZbalRSWCcI5N15Q6ozV6+uuXJhl9V6jU6gjJD+G+OoljVD33F8ckLe\n3UHbCq3tZqasJDBkJQkBWbohcegxCHpWG03oPW3w2JxIo0JKMnS+x2dBOJtio5Sy3Cd+iMSQMRi0\nUWhXg95BpzURRcqhSOhBKhVRyrm4IZQ2yFQPjpnunYvVJjDk7TJo/HPezOK2/z7eo9t/kpdvVwRj\n0Nzaqdo8e2Od6EEJl++sXyO6i+N7iKdmGvryAbdrxw1BY1z/pZIcaQaJaZQ4fcI3G4C+lue+Ndub\nCY7bnbF7B0S9wUfkBwWnrUBWugPkSA6DpCMpIFX2iOYEtLhjbEjt998eGvRiDKAVe8uaRVNzfBZZ\nr79MVVkuXarpU09fRHBzzuzO52J5cxbosvCGUkygwa+TSFTFJL1+U9y6zfYHFR5VKoEjZ0FgKpiQ\nnDknsA6fAhRppZglA4/B04eeqp5RN04AMaE4Q4QICdqViGinuNH3PEdoVKN+Q8EMmcIAKe3a7bGq\nUlnI9jDpjIpqR2LdtxIIopxEowUYkYvsE2NASZA03D47xpqDsggHmnpOyJrffUGzHhT1wrPyHe3Q\n4aoKM3Miv5USC9ugM4Qw4H1Ca0Pd1KIuESRBCV6QhjEESJHKibiws05EH5TA6ZNKtGFNpTTaVYQs\n86ixWkmlQtQ5U2uZw+7sisdbziJyrY2h2Vly0q5RQQb/KkkObYv8k9WGC8sFq6HHxyCWOsjcmELa\nHTPD27dXLJcyNzZWQAWhXA+1q6XKUYqYJajFFNGlCpt4nkrOTYoCZhLuoRFkpQoigwbsLC1+MFgs\nxjXCT9XShYgpkAc5f6okPykWtClQVw5FZN2Ki4C4t8tn1WS0sbz82hEvf/WYSxfnvP99j+CcIcRA\n8CKUrLWmNiIs0FSGFDN1PScby8lq4IUv3SJl2FlUHOxWzGYNSWt8TMUFI4KTFVUX7qUvUmiypCiS\n0fKakAgIlSTKRUxKmWFo6YaegGhwaiMWW1qJMHnwEWMsOSt877HLyyjlSL4jVE6+hzKMrvVjXCNT\npMA2v8vqL084X/WpaeY3vmAcmU3gk2kb24XjgGFTkW6ekqdm0liN3XebYmEENsLYmVKxJ0nutRmF\nvDeC5neuuWNc1uPn2tr/JuDduf3+BLW3kth+v/3eCUpKU0V993uPnYANxVxNnb+xbSmz03EfqSQS\nY2P5zrno3dvDFVmSIQ4Z5QYg8A8/8QUAHn3kMvNZ5NZpj06iwqA1JKUFUr5eo5JYamQtQqDVzHB2\ny+NaRbPYAERSSmDEZmXd9qLGoZRYEGHJOYqtSZDsSBtF1/XiC2dGtZhE5cpCltKE3HPOEsIwgWiM\nNuK6vXTTe9+rHC+NWfmv2ihWUEA2CqkAx4OvgKpyOCdITO9lJpmjInhxH3eNIWWNMdWU7Qwh0LU9\nqUDwb52ecXF3n7N+YHV4iHYFzh8TsesYfC+fucwcnn/Hms9+vqLrelGFoEDhtQCDRvmtUS8SmGye\n0Bo/iIh4ipkQPXVTobNBo/EpEsJQWraK5EUnc141chxyxhlHGwK+65k3DWEYmBknLfF+IHsxEh6r\n7aEo/hsUuchxVZXDqdFVQVQsjBEqiFagtePoqOfJJy5JS9zogro09H2PddVUxWUURoXp+IyBxxhZ\ncrQ2DENHzJlZvaCpMyG2xOgJIbNaaXZ2FWcnDqssoq5yJgEvy7w0jzqXxnJ42vPJT7/Ge955mcv7\nNbYAcwQlKu/tYyDExBDgd373q9SV4QPvvYI24mDQ9rEEAlVk0DLKGFylmc8cf//jX+Jgt2FRW67e\nWvHYxRnLRcOqHfj0S7d4+sl9nnh8JqCWgio22RTll0I5YGsh0nKFxxgKMABQiZBkwQghydzKWCq9\nke9KBXHrBy9KJCWJ8F3C6rUEOOMwWqhBWY30hvOWO9MNdu6We3CrbLtymH5XYxjctE2nqvDO9+N+\nf3vYlqcqbvwIgkoWIfwYfNE9Lc9+a5E2f2i2ewXHO8/Jm3n9SPNQU0LysDni5inbPPBpQVabJ46U\nmofF8YcGvcpYnM5kOj7/yg1OzgYWs4oPvv9ZVmcn5By4tVrTx0TUitO+JZEFTVeAISgpZau5Yc9W\nHF+XmZSby8IsC5vozoUoROCqrslKkGqD9+WLyU2cihq7LgfdFV6f0gqdRf1g4kUp0ewMUTKxmCJh\nSNh6E3TvfcLUJnm8g/w53TpbN+NYTZjC5dFGmoLtWj67qzU5i14hZJwa9f1Epd8HkaryIXLz7EQk\nuLTGKQgx46qGEDq8D0KqThljIj/wPT1/9k+v+eivz/nEb80AJZ9BKc7W62mQ3hcjX+dcUfjI9EEs\novq2p1u3Ra5qtAtyJGkWS/vQe3w/cOngArOqIRTCe0qKHkVlrFj2GPHnOztdERSoonzifSiwNUor\nvMD2jSYNvaAIYQpeEigFyHR42DGfO5rG4Qzi8VeSlRgTSQWZq2gjgI0oxzwlqJ0rjglyHlOODAV0\nk2IghiDjgkKe/8JLFZlIjBpXi+GotJJNkdQrCN6cCcPAteunXL4w4wsv36Z9ZMnF/ciXXj3miSs7\n1E3FECLeR45WAy9+8SZXLi146sk9fEysuw5fvncGjLZAZHShMcbwzrftoxKs+8zRSct3ve9xcrHK\nWcxhZ6n44qvHnK4HHn9siTJ2olnksmKMSc+IrpbrPaE0AnhJmaquWHc9Q/SEokdrjcMYkTVTWea6\nxlgmwXk1Vs0Q1qdYqxiUReXyHtpIGcxGoP6+21gg3afo2QQ+hSD5Nqal8rptbc3pP9MCOL12u1Vz\n59vcK2BNFcrmPq+ccIhjLthffXcwvX+L783D+t/s9o0ATL5Z273nenKlb0jl49+2PpOCrMzW0RzP\naQmaSk1t87ElvgEiFXTsN9rezLS4yhD6SIry9J1lzYU92F9e5PT4mFXvaduWaCzrrscPg3AmshK2\nrBJEZ4wRUxnmu5bQJdzcbHQ1YyLGhLVCol13IxpRZKWqypFDLjeALsP5YhGiRfWl73tEmFUI7niP\nD5Jt5xwYr3ZjFb6LuEbf9wIYL+M7g91GrX+Ey44qMeNMUapbQWdtTnwYEtbpIk+ppGWUFN4Hmqam\nUo7ZXEAq67W0d3VSDEMQ7lU7UFWG5c4c4xxoabX+zM/t88wTPX/yBzt+6MMt/+A3lnz8E3NOVy0x\nRPb298o81UwKJyEEOu/56b95xPPvCvydX1zykz+h+NAfgx//b9/gK68IrP5n/9ZFXvp8JW4XSjN3\nNbb4+Skl7a4hiinwuuswhUg9qlLknLCA1gbKBFYc591UhaHEuX3oO5Qy6CyUjqEPXLu2JsXMyWnP\ns8/uYLTMgAUtK204bSyptMayEgECq6SCbZqKDfNTJNHG6se5aqJ5NJXDWEsIgV/6pX0UYDR0vVAJ\ntJUkIcZYSMeKk5OBGMWmavAD3/mBx3jx8zd54+aK1dqzs9wv8nSKj/3TqzireeyRHZ5+8qCgjeVa\nH7xQBKqqIpHwKZCLu8hyNmPoO5y27O/WXNxrWOcs3n9REKvzheOD79vnhc9d44XPXOPCxTkXL85J\n0U8LrNCFhA82BhdVWvHj3O9svZb2aJl0xYy4mkQIMWCMwpRjYJ0tCjMCxtm5WHF6a6B2irWtcUaU\nWrIFnQZyNGyDWWRduRcIRU0z8rvuxK11Xb7XGPjGx8YW6XZQm8qArf3J/fug4HfXls9zN4deui2b\n/YwKI1s7zNzxud+6Odxbrb7ytWxvNmjfO+DDpmK+3z6K4spoAl261EqNijdb3M6p5S082fGYj52N\n+20P1940kgEbW/HMlQv8k89d540bp/zWJ1/i6Su7dKszDBmLNBliVpAEcalL2yybvKEzhEB5yjTM\nNNZOBF5RKpKgYguhOCN9YKvVZDVkSrAcs/0QAnXdyGJMgePnVIAzQvTN5cA1u4bT657dRxzNwm3Q\neg85mTJHKI3PLS7IlFlkGGVxtFacHUeOr0vVEUJmuZyRkhCRcw4y30xSfdWNK61Sw+AQDzYtZrMp\nRBrXSIu0cpv0FWhD4otftvzs/7bPc29TfPiPH2NM5lf/b4erpYWrjcEpJQoi4zHO8J//Fzt83/cq\nLl30VE2NcYp//I9m/Fd/bYkCLl1csnCaoAPZZvpW6BFDOQdtO+BTRlktmpbB45VU27apBfQSKYoT\nsnjmnFmv1yzrGVFlyCLSK9WYpo+RszPPKy+f8tjjO8SYeOrJi1R1oU64RroIJagaq1ivWmnpWcN8\nsYDomTUOZ82kqLERnRYVn5yzXG8p0Li5eAWmzMnZKX/rZ1c8/+7E3/nFOT//c0ucc/xLf+KMf/Pf\nOmK10vzyLzb8T39jxay2HJ/1PPbIAnLg297/OCEEfu9z12k7z9UbZ3zltROeemyPxx/bBcQIN5b2\nbcqRpmmEhF9mX957TIbZcge0EgCJNiQyZ6sVqyjekCFG8RJ0DltZnnl6h7NV4PqNFTdvrLlwoWF/\n3zEMiduHLSknFkuNjoK2rWsB/YjzfCwGzOO8NqCNmC+HEDaVU6bIr0kFPPS+cDLH1lWLqRfYHAlD\nK2MNrSBLF2dcwM7fZWMw2A4am/bVGEwm0YDNUA8wqClMjyqpm7lQuWvLz/lAKo4GD0b5bd/322vD\nOBsdkcP366edc3a4a39v6q3v2t6KgPegfTysZfmw93/QOpo3M6LyBtN/puO0mdeKrZcuVfQGJ7RJ\nNMh5Y5231dJ+2CF6aNA7Po24qqGyluUefPi7nuXvfewlXvjcdRZ1xXJnwUnXYRFCd7aabGU2EVNR\npcubYSTIzGIcZsZyw0MZcOaxNNaTNQyUQEhxXGBDkcgKlDXEQQjCs8LTSilRuwqttDh951QG77DY\nt1inOX59oH7OnTth8vnGmcHWMJa7LwhdTooCUY7PgoKsmwVt19E0cIy0FavaYK0iJV0ANJmxAwSx\nqHGA7zusgbqqJhdro8SJoe06hjAqetRiuaT0NP/6whczV69eIcSB2VzMSE/PTqkrUapRWW5Y6ywm\nG65fl3afUoqmmaFUx3d/d8fP/M+e3/h1y2/8vQUpGWJxe2hmMwkWOeKHVmSSrCOQWa3XWKNoXCva\nJEMAACAASURBVEUm4fuOpIQfNkK7By/zxRyK910UWSyramKINHXNOg688sop73znBfb3G5mVOke7\nXqMpCMwsZGvUiMCVBaxpKlQWbU9ThMJlcA4g6iTaWlxVESPMrGXWNDR1jTaGvpdW7o/92IIPfQge\ne0x86Z56uuUHf6jn3/139hk6xevXOh5/dIf3PHuZbvBYq1i1LX3f03YD1262zGeWfgjs7dY89eQ+\nKSW6TtrTrq6onJOrKgSZE5LxxdDXFrk8ZxzKWvmuOZE0WG2LD19DCiKJRoYcIzs7Nc3C4fvIrZst\nL710jDGa5Y6jayNDb7n86Ky0t9V0TYcQxX9SjWLsCmsljGRlSaQyRwWjDV3X0w9+k1DkcaDlsbMF\neXUq+0Wq6zIZZ9NyHAPRdvWzCVLng8L2ClZeMxLm87jfNDmXi9mrLlXl9rYtVjzu6+vfNu24h8+y\nvplzvrd6/19v63OqfM/v7Pzv+V7V8F17KrtJFBD35vuNlTWKjL6roh+BLA87Jw8Neq++dsito55L\nl/Z47m2XOO366bF1G7h0ULG7mIMeOFytSCrIEN5acsm0c8oyxymKK8oG4pCJPk0nbaqcygU/+ukB\nRVW+RhXitRBlRemeUkGOSvWpICN9mQNqJXw+H4SvpxRSEexa1keB0CeqmZnMXM9v5SbNG4HU8V+D\nmob5cookuxz8QFULUKVZKA6uNBxe6/B95OSwY3evhpzxfYezNXUh5fdeqqjKVVRVhXWWwXtxJkfm\nO82ixnuZMclx23ivWV3UbdIoZSU8otliydnpGYtZjbEBZ5vpOJMdvl8TgqASX3qp4c/+mSeonOIv\n/oe3WR3d5td+VRZJYw3rrsVWTtpdzsk8LgmB+ezsjNmsxhlRoskZuqFHWZE2G7wnI8mOSJ4Z6rqi\n7XsgC3cwZ27fXrO3VzGfqcmxXDRVTZm/6dI2Fk1X3w9AoqkdTWVZr9c0lWEYhBc5DH6aac1mM2az\nGcZoTk/OJGCOs6SUpGoyiqtXRQKP4tP14R/s6XvFX/8bx7z4e5af+AnF776w5v3veowaacdaY2T2\nnOGpJ3Z5+oldBi9qKUPwrE5Pp26HVoL2tNayblup/nLCKI1xjrpYRo1KICllqsZhinh2GAacViwX\n82LuKtdeSjKjbWaWZ57Z4/HHF2ijmC1mHB0e85VXzvBfjTzx1M45gEiMGa0sMXpyaYWL6o1FoRlC\nQGvRJ+37ntWqJRbT5XFmCKC1x9Zz8kr0KzFFfxMtVCSlENGS89n9vbbt1tZ9wSyMqOsS+NjqcI7U\ngK2ZkUKT76JFvLntYTO6r6cq+ka3u8Uz/oC3Oz7H10d2L9Xa2I4ij5WBjMpgK1huKuk8efxptH5w\nWHswthN45avXeOWNW3zqxVf42Cc/z2+/cBWA97/9ES7vw8npMVoJQnp31qBLxjoEUU+xzgqXpbSX\njDE0s5pmx9AdFYRdGZxnNhfQmA3KDEbAEWNVMyJ4xtnYMPipddqXfvuofUnOGAV1vdE6HInbrtH0\n63DXyRFyOtNQ9JxMURau0Tbqc/QSnJCcSrFYLHDOceFKw96Fipzhyy8e0q0GKlvTVHOccVjtGDoh\nX8ekUUpg4DEIOd5YJ7Y8WWyQqsphijuAtZZ+6MlZgl1ETYCVoZd/+75nMZvxzDOZH/3RW3z/9x8x\nazJOKyprhDqB0EAOD3tiVvQ9fORXGj70Az3RKNo4sBo6WbxXK3GpKH5/Sm2I+dZajFYYramsFbcC\nY88lNnXd0DSNOB14L1w3NnJ1IcDOomYxn4tpqsoMQyetvKqGckxEnFp0T5tmVrhwmXlT4Zylrhuc\nq9jb3WfWzKmrBqOt6LT2A+PcIBVE6cnxCYeHZ/RDJkTNMCT6zjP0gYODwGKR+Et/cZ+vfrXi3/sL\nwoFbt2v6ocd7T9M0cj3oxFOPLUubB7SR95zPaiongT7FiB96KmdxxTPNFtBHXTmcFUmxrm2lmreO\ntvcCPIpJzGKziDU0TsAmVZmTqoLMHIaBGEM5pkKif+qZJd4nvvLysVRqMdH7MCbPgMxMSaLdOXph\nGiXm0eJNmCfHDmsqnGsYof/Bt+SSZOYiySWYF1USsY0Q8IMC3rjJfafPLe4jiGb8PW/9fVw3xln7\n3cvb+b9t1pl7/775rGP3TE0/+c6/P/R7vHXb/T7nH+S2OfbqAZ9PnfuRc3b+Rys5Q6IAVZS+EN6s\nKT9KU+wv1GiDUTo+Dm3d5DN6v+2hQW//8j7ZwpASX7l6LC2bZcN3vvcx9i/ssNyZM28aLh5cYG9n\nB40sCCEKuomCaBwNOMfFevdiTQrg240c0ZiXjWPjEKT6CsVtQSEtRTMqcSC2NiluzEFDCJycntK2\nLSPgJOUsclFGT0EKwDUa3yaqqmI2mwkCtJwwre6HNtuQKuUkFQscLa0xq0WuqmtFvslZxxNPHzCb\ni93I0e1eNEGL8HUMmeATIUFS0naSbpZAvVFKEHlG2ly5LDqxiN0664A82dNY6wjeM/Q9TFMO+PKX\n4Kd/6oDLlyM//Jev8qMfuMpPfuka//bNljpDCJ5mVpCmleV7v9/z+nVLIJN1keYt/DutpLJRGeLg\nxfjVGBEoRlFbcSpYzhfkmBiK/ZNz1eRXJq0xRd3UWGux1nJ03HF42LG3W0sOV4ATzjoqW5U5mMyh\nyGJ51RXdSu/9JJcWCmldKTW1FGPM9P1A1/Z0bUfbtXRdR87g+57Xr6/5py/e5MbtE6w94/B2x+2j\nnk+98AYvfbHlIx+BlBy//tEZ3/ptLbs7FV3fMwzDRFER7VK7Aaq4iowkWbPZjJ2dHawRYeF2veb0\n5IS2XYvLRxiwWiyEcpSEauh7+q6jXa8Kp1Bhi+SZ1Qbf96xXZwxdhx96QVmyyaBtqbJPTk7kutbw\n7DsuAJrTY5ntynhBWpmjTqm1lvlshi1gsaoSh3t5XJd7WRXAjyS1AH7oQVvx4QuhaNwGKC10XboT\n5Ta6R3vrfgv5HcFpAq0gM0O1WUS3A5NsmyVuDJDT+9wn7p5bsLf3d7+f+33qc4/dXan+87zdv8pV\nD/l58LGRil0V3uzmnOfS1tTKkB8S1h7a3lzMGmZVzVkHOUn10MwrDqNjvthlvRoYssVHw/6yoe1X\n3Do9AyBl4XoZmzFKCWk9hmnGt3ux4vjmgHHS/pSh+GjfIu3NcQBO0qAiKNHQVFoRY1HiJ2FshasV\nvlcMKdOnSHe6krmYEmK0sw0kj/cDxmlmS8PxtYGh65gta4YhbAkQy+wRJXMJhWS8KLF0MQa0SpJ9\nGE3IIkYLCp1kxmSyQuAAifnC0q4DacikLqIrTd8OZKXwwUMHzbwuGoUJVYSJNY7U95icReNRQeMc\nFk1TVXRpwGupQLXJIkflo7h5h0C93CkJQuD2bcsv/kLD5cuRH/nwdZ795cTeATw+izz3vshvftzx\nr/+pY/xg+fxnK37qZxuZ3/mA1ZahH6SNnGRWJy06zSw3ZB9Z2qYIRUPvEyp54VZmhVO2EPUTPkfq\nWU1UktgYwObMrZsr3vHsBS4fLAQ1qTQzVxdYfMQoUE4RYyIH4T6ShP+XlcYrK0IJXuGc+OMlrWm9\nJ2TIKeGURkUxp3VW1Eu6ocfHxNOP7fL936v47u9ZcXxzjwuPRD70nfvcfH3Nd/7RG/yfv3zK93yo\n4sUXam7ebnnu6R3hgZYqNinwREwlNAA7KurHhI0alaFp5vjU0vsOnTM7+/sMfUvfdRgtRHRrKxF1\nMEYCR+hxwbDjpKWLNvgcSM7ijSEbSK4m+4EwBKwzJCUan30UJwpfqAXZR2YzR9dFFikz+Mz6sEMb\nxe6FhpwE0KKLoIHShcuqCmnYgNMaW0lypnUiqBpYMwvXqIabvBFvkrRlZ6jx6YSw3CFri80D4eY1\nKqVkDSAXNZaEmNqJf8H5JVKzST9L73KazW2JWqjMaFOUVdFkpCTQWTPWZpvKTJXAm7f2+/W3I+98\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e1GRypkDfxShWqlOpYGMQgFS24hSQY5KkSStu3dLkPKCUtDXFIVxhTOaP/rGBn/7JfVDS\nMvUxTBWH957j0wGtFQf7y8m9YzQwFjBPKqo3qiT9ZQYZ0waQ4yOuqhj8QF1VYmybM1pbsXsqxHOV\nmZSGyJmsJfgYiiST0tJpcMLRFB/IDfAqJAHupCyo2Vic5c1Y3WSpMMdzqMr3HKk9xCKxV5LolDM3\n3jiTbNxGCg0UaytB9VrL6rTHznepLj7HgKeKM1w6Zeiu051BSLcI7Snh7BCtEikGoTahp2prHMXk\n0gkYF7NtDMgIerkXmeiewe9r2r42xZa3au515z7/sG1vBsV5v+PwptqiZfQxCkhMF95WSzpNWpqb\nal+yo1G+LxSRdouxjg0Q5t7bQ4PeydkKEEserTQ2B55/ap+Ly4qP/D8vAdKefM87n+GpRy9SuUw7\ndKx78MZz+WABaY/bxyes+wFdWWpnCVHaLLM5HN4cUWXFs8splpccvs2sbofNcDVl6l3N3kUzURai\nFkscqQ4iQ5+wzhDipgnSdj2zyrFqW/Z292hchc4RU9XMq4rYrqmcDOpjDAKWKPMEpZTIaRU1jZSL\n91jO54jyxgoHSeZQpT0VZeHWWRGz4tG3LelaybhnO7a4l1OyUMlqYpl5kYvhbin3+65o8ihZaGPK\nYESpZQhCtfA5gU9FkUDmQjFlumGQhVHLYifCARqL4umn1zz5JHzsN+cCqim8uto6fIrkmCBJi8xa\nK8cZETGWSaigDZUR37hMhCSJkiqB0lip6JVSXH3jDGsM3/0dj02Z9ygWnpKV6jdtZiRj2xgErBNK\nBVdulyIaLXM8Zy0p9ihtwSRyDkJnyEqOV048+aTnbc+u+fKXZmTgX/julk//7gylaqo6TrMvqcLl\nJv3yV45425O7E+Cp67oJaNIPA8Q42XsJl1RQtz6EQqkpTgcxTeAiVW5sZUZdUGl7OuOkmk2JnCKj\nhnwulV8sFZv3XkSdt9CGo0hCTBnL2H6VxTnFcVYt1XLOEVtoMTJ33iRh0lKV6mjoEkc3ey4/WYtQ\nwjhj1gpjHf0w4LvE8tHHiLlBkahipju+ya3bX4B0gdl8gWJAOY1OipglKxfDaAlmo1nweD/owgfs\nuyCz75KUjVXyfUElD1vQHrhN9cS5v/z/2723r6X9OT5/ai3nAkC7Q6Jy07pU0/UwVn4U6yCjLSiD\nCHkI1SXGsWsB1nyDPD254oQLX1uLUwGdMjdunMrNZRR//Lue47knD6hVZqZnuKpmMdNUqzOu3Tzm\n8oUDjNFcvXadtm2pZjV15fB+YLGshazdJ+qFHMDgk5Bel1DNpf2hjcJUYkILaspuQ4zixADkrBlW\nntkTlcwMlaj+oxAF+WHg8OiIhYaZE4rCI5cukm5muuDJaLSBygkZ1/eeGIKoZVjFUCDomCxam4j4\nUYjiFiAO4sWJHYHt5zKf0yjR36yK5BkSMKoinxZKSis3f57QfCAms2+8dka7iuLUQFksgRh8QdQW\noWClMUqEqilBL5fKKZBJSj6zUcisUlu+73tO+c2PL6Saqy0qZbq+Y9V3GDTzuqbverJL8l21wlhN\nlCuS4ANDBtfMqF1FzhHfebQVYEpKUfiDIfLa1RP+yLsv4YsDu7W2WCp5sfDJ+hw9BGTG6owtMzwm\n018hycsCrZUQu1V29OV4SNtRkJKzZcf3fO+a/b3MzetqMsX98A+d8pFf2WGkFng/FNk7QcbGmDg5\nG3jk0mICFGmtGYaBqhIAidFlfpeFlhFjRJvzt9bYjjNGgqZ18rnkOtVonUHrDfE+JXo/kLW0Fo02\noBUpCOgp5kSFxseA93GqmkVIORc5OplFhYIundUNOUoyZVD4WPQzEQTwuCgpOa0cH3kOb/RcuFKz\n3JvJvRnjBDfJCoZOKBez3SuQHM5k/PoWxzevo42m2a3IoZxHnRm6gFIWtAU0SWXIfqroxuNbOScc\nweKaspk5lgU2nz+2W798A5FqU1Oemz3d+R5v8fbNqBq/Gdu9KruHEcnvtY8xUOpiBXbuNZR2dwE6\nClK8KGCliNaglJFqToFSktSK8Lhi455+/+2hQc9ahzEOkib4AasUx2ctX3jtCICL+0se1EVcHwAA\nIABJREFUuzjHt2tZKIKmmc3ROuNswhrh8hzs7XHr1m3qpiZmsW0RRF3i4qU5r758wu7S4eqaNg/E\nlCdvvaykzUJKWOXEqy7Jl8wlY44h4tcJbRXoLMNQijGnAnJCG8vJ2YpX+47HH7nEfL5gZz6Hi5c4\nPDniZLVCVRajFLO6YWe25PDwiN4P0hpE4PqVE0uYXMrxNI7Vy6wl5TxZxyiVUOXkydhJFR1DhQFR\nos+gKbJmRVVcIV5nMURWZ552JfzFgwtN6TcKSETpUT9R5LRmVbN16+ZSScQJpZqKUHNKieQjL71k\n2NmJ7O1Gjo4F2OK0RikjKjVKs2xmpOCFnuFMQWEmcWL3AWukoqN875iCIAZDkDZwkoX12s2OWWPZ\nWdbSg1eSkAz9QEiippJSkpbe1gB79FPMWWaorqqgzIXIUlVJlSmD8a7rAIUzjrqy/GX9BrO/sObR\nlxUfWzfcuKmoa00zC7zjnZ7f+eSMFCUIj1lmiEKvaKqKb3/fFX73xRuklHj68d0pGA4+lDMvrTg/\nDFTaUTfN5OeYc54US3KWY6aVKgCpWETZyzwuZkilvQlChahrAa8ggK2uFT3PZj7DGPClQBNwD1ir\n0UaSLmuscAKdiJdTQEACNpI2slBupOWtjJpam8Enbr3RceXpObOl+CEOw1CAOPJ5nDWoZIGB2cEV\nQqpQ2XN8/AZGZeazfWKOZK3R2hExaFtjlC6zGgUkCvVSEnkt9KbBd6RhkDaHcWRl0NoWL81Y7hG1\nFfw2ek732ko9fN/HH7TlO/6dOm+q7O8euzz3p3NvKy/Odzy8HXD/sGx3z+DuDnZ3/nu/145/u1el\nbozIiI0BUWZyRtZNrQtiPojoQKEuZDQqj9KVUhiM6M70jc70dMmAyYlBQbde83c//iWOzwbqyvD+\ntx+wP69ZnbWcdB11A3omsOZFnlHXHf06cXZ8yqW9PYyrOTk7JQ4DRY0WUwSk96oZ+/t7+Jy4fnjI\n6VocrtFW5kchoVSintlCORM9Tqs0IUPbRZqFKaaxcnOLMG6pwJAW35nO3Og7vuXgAnPraIxlZg2+\n6wQMMzM4bcg+0Djh1EUgFzV8Yyw65fIeUj3pMvwas245yVL9OWdJadTDLHMKpYhQSOylpaM3PlIA\nSidMhuhlf8ulpVIaoiJpaWuHHErwkPaeVKBCpwg5YJQh5KJ0E2T4p5RETWscMcFnXrS8/dkzfuu3\nd6ism6SdVMiolElDT1VmWP3QkxRUVQ0+MHMWa8QQNvQD2liMdvRdRy7nJWX4yqsr1uvA8+842Gpz\nJDQao9Q0V5QqWE0BenLZyOIGbyPYDChDzgqHIUdxawtCLKOytcxRS0ja+46e9+3A8u2Zp2Ydz773\nNv/lX32U7/uBNR/7R3NEJisXyyUJaMY68e5LmeXM8cH3XuGTL7zBM4/vYq2jH8QvUmarAsAJQUAk\nbd8WOow4tRulsU4zDAKwGmk3oy1NyomQAi6P4ug91jlmdSXSbUoAMj5GSUBLcI7BE3wkFTPTXCp5\nrTQ5BWIKNFYMllOIE6BGaYVVmhwjKkvXIZcxni5JknEFnLKoSutUgERkyKXjkXKgPRtQxmDmj0J0\nZDXgU8+scZhkwRgCMnt31S5mbskI/UTlhI49KkvwTMUfT+Q/e7LKGOvQpkG7JdrNCL5HpbXYViXp\niqiJ/pCnQJTz+QAn5qMlsnJ3S+4cbWG7VFTjkd16LttP2bzPuYrt3O7HaTdsB+eschHGHjE1D7c3\n+/3cHoTu/Ebmj0opYgIKd1kpkQ8LMUjlPwK9lC7/K0pAZBFJSOMxV0pGIVmjdJGQ1Iq7HTbObw8P\nelqLOG5V4azjE1+4zfHZwKW9GX/+T32AxXyG7yOzZk7bdqzXa9q2pZlX0pIAfL9mbznHulpmW48+\nwquvX+X28RFZZUKxVJnNapaLOcbJFxi61wno4lAsi2QKntAnXO2KGam0g4zR1DNDdxaZKyVeaoUM\nrdFolamcQSlpO56enHI8P0YtFvi+p57NOLh4gePTE1zxKUsJgtHs7+xw1nXkvkdpg3UWlRJJlyZl\nFsHkEAoYgE1WYwuQgVzI+Jv5LFOnJks7k0xpUQlE3miDcpqqTkBHCNJKdEZmI5QshyzwfIVUk6Jq\no4pp6qbV50tAobTalIbkI59+wfEd3xZ44YWGjAB2Us5izVTaZjlnys5KJeCRjpwALMIwyOytzAxT\nimQlfnCf+fwRe7sVH3z/I8yampG/Jhlv0dgMUvVMpsJhY7OTy/yUDCkIDN9aU6qCJFxWU5CTxZXB\n+41weTxSrH4cXv2E4z/+I5dZOYMh83d/ZV4EvIsWaLnmR2ECV9WTYe7OQnQnj056FgsnLfVQyLBK\nU+ksQtpeRJ6NtaTBQ6mKhz5OmWzTNFRVVeTPCt3FWNSI+M1C7dFak3LEZLFXiiEQSNMseUyectr4\nUo7XlSlcTVUSQKUK+CrGkkGrqaJMpfJQShK51aFnfVxcSqy4Wmgtxs2iM1osohIMbcItd0g6k+nI\nDBhnSbG07HNGKyOOC8ZhqloSNGUwCkyO+L4lDq0kHylMCvtaO7Q2WNdg61rEhHUkD5rkhdeoSou9\nDAPHZZU/+IrpD8Nn+Ma3NxvcvtZgrZSawFohhHGML/W70mhlpY3JCL4awUl6Ky/JU3w0I/hKruQH\nvvdDg15lLVlJy+jWcc+nXroBwL/8ve+iLnwqZ2sxCQ1i0OkHz/psxWJnzt5yzmrVEUJP73uqesbj\njzwFOZKj57Xrp1y73vHo5SUxDFgytdYcLBbUzzzNGzdvcdb3JBQhSqaWIuRkRKdy66Jf7DlOb3ra\nY0+11Cik0tIq4yzs7cwYho7eR+bzGTdu3eTo8Db7+3voRY1tLPtmD6tE/WJ3Z4m1htliATdvkqNU\nUCYL7D+VCi4nQd/lmM8pCUBJGnxP8GPAk5My/qsUE0rNaIU2jpwLmi95alszX9TAqVSRUeaDKspA\n16Dpy1wHLbWNUZuLKoYwtTlFRUNapsIHi+QY+dznKv7cv9FiLfR9LALaiso5TAaTMlYVt+6Sfaks\nXC+tFTlG6kaqK2crCZiVKwtuxvvEc2/bZ7TWUUoV5+2+ELJlATXGTiiuc6o9qoB8QsAWgv2kfKJk\nNpV9lvlATOQsYtgZ+duP/84l/pMvHfPfv3efoa5wStH3AylFVmtPM2uIpcLrfY9CU1UObcT8VkAt\nmd1lxeFxx85OPQkzhyCC59nmiWphnTvn/NE0Ir2nkODV1DUpZ7q2xTg3CXhnsrQndVXUd8p3bgxV\nbYnREXtBoHovM9BYqsUpyOnCVVKAFn+8GAV0M5qGg8zj1ChrpxXC7zOsDyOr48DBozPmS4syqVgX\nJVCmzCIFYBWjAMcWFy+StSHSknKHrRviGRgjogA6abCSEIUsWf1ssSsWSzrjhpqzk0zs2+J5Wdr8\nWd5HYmAQ37+hJQ0t5CCV4ta9tt2G/FrrkIfN1R5Modhksv88EdW/WZtSG3eM8SiN3TGUBiPjFa3F\nTWTTOdu8fqzYJ4VVpabrUukHH/uHBz3n6IfAxz71VT79xesAfOAdV7hyYRfr3MZWBwqROhNCuVhD\nYm+5JMTE6ckZIQjS5tprLxNjwpFY1EK4fvLRBRf392hXZ1RKs7SORVVjgNdv3qT1A3FIjELqvvMF\nECBmnJUTcvKFJxNntz2r256DpyrqymF0RpNwBuY7C45OVoTgi4CxYcieWye3ISZqW7NoalaHJywv\nXKRpGtquY9k05Jw4OVvR9T3aiWBxzhoVA8RAVjKbGYEQUuUOjDYro9LAprdd0JlZNBdzObEjJk8h\nwIFQlFJiQlQvMpikimGmZM1BO4YccdYAYjiqSqk9aomKVFZk8AM6i/vFfFETY83f/Kk5KstsLufM\nbDbDe08/DFRQ2pbCgTPGYI2TCltnbNWI1JmxoMRdW9pkmes3TljMN1YfsThDjoorlEs35YRKm/mk\nL+4ZxspsUciqAvCwBSA0+AEFMjdKpSosbfAx4MSU6Izix955INVKucHGKscPAzYllB71LUtbM0f6\nvsOZ/4+8N42VLD3v+37vcpba7t779OwznOGQQ0ojUSRlW3tkJ1ai5EMQC07iIICBIEAQAwkQBAkg\nQ0oMJB+CwECExAjyJY4BI0AsWHJkWYpEkSK1cR9yNs7a09PL9N2r6mzvkg/Pe07d3nvIIeVEB+jp\n6XvrVp176tT7vM//+S/iELN/ULG7X3HhTMl8Pgelk3jeYu0qOimmN9FajTEyI23bdsjPGxip1pLb\nDJtZSSt33TC7s9YQk/YuTzEpx8fH6b4SM2uRwghEGmJPYlHgA16F9L4HXL+4pMQT3S/uMRU+Lcxj\nnTYZTdWycbpkfacUI4BO5DYynxbIvu80q7nkB2brFwl6LOMGrclHM+pGg27BhIRgiHOObNA9RJEH\nNV2Lil6MBOqKkOa5KvYVWrxKu67B+Y7YNSjvhplw1LcUJL67ove9HYL40G/A79Nx/n+BuNLfpyeP\nDwpp3knsPvw/aYSSrkVfQ1ApiDvPxdjeeaAfGcW+wRtgsnjy3gcpmve5tvctev/8S69RNy2vvrMH\nwAvPnucTT+3QuA7tFCbphqyxTCZjqqoSZ5IIrhMXjc3pGBuESu9CxNgcZWVmsb255Hhxmas3Fowy\ncXFwTYUpCjJTMC0yzp/e4sb+PhotdlRNI52V1rStsPCUtpigKMc542nB8V7L0ZWa8eM53nUYm7w1\nvexcfQSTZzjvqbsO5aMsQtbQVDWZNXgvnYVvO4osY23tHLPpnIPjI44WSzxiASWLpE5Yvx5cNPqI\nGB8EUhLzY7nk/cIrAuJE6khEECmEARciWolmUGmBsQ4PW7LNDJtrfOfoQiAmQpCLXrr/GDBKduRo\nIXQIHBUFNkMiaoq+cIfA5cuBPBMh+iC+jwHvPG0M2NThxQTldr4lS7/Lslmk2RT4tiXL5fUWVc1b\nlw74oefPietK10ESyetUBBRSCOOwcKgEZWqiiclEu0g2ZoEYRahu9MqA1ibHGYwgEiGRQXwqmgPN\nPpFjXDJzFhseRec81ib9XiLyEIUoUdc1xmZ84+X3eerRdfJc5ATGWOFfnCASxdizVQO+87RtTVEU\nGC1wn/deWIkhDsWk1xz2ptq9FEKKtpChuuCpqioJ+I3sflOR7ckyPSwscG8EzU2ddUT+7RIpKMQg\nj1Er6W+MgWresXZG5ro2Bcf2aATEwf7Oh0j0FmgoZo8SwoioPbL7KNFZKkC6FXlDFJoRMY3JXMS1\nDa6rib4hNBUqtDIDTf3bICmPkYhD45JMxw4Tsp5percq94MtLv3I4U56vzvM/e748//yHN+vrjVG\nWZdWs/0EsQdBFJSKCBsTQuwI0RGjS+cUib0PJ6v1KIYAxiQt671f/75F7/T2Op//8neGf3/00R3G\nZUnXOvBe6P3J8ijLxMDXdx0xeqw2lHnBdDwiOrGjMjYDLTq6aSksvJ21gqt7S0ZlRmFy8IHF/Ahl\nDDozlEZxam3CbJrROsf7u3u0aRfbeZn3LV1DtWyxWiBNU4je78blinOPTFHK07SeItNkRYHyEW3U\nkOUWoji4dDSMTC5WS01N8JK4jRKywsZsJvqrEPERmqZN8x/pcnwU8X1M4ucYUi6AUtgiT9qqXt+S\n5rBECD4x2tIuPXVxvfh8NLYs5x17uw37ew3TiWVzQ4qL05EmOKJNcoZ+gUIYoCCuJjFJJYoUqUOQ\nFG4S3Z8Q8UrcZJZ1BUYW2DzN6px3jMbSdY2KEUQoypz5cp66wk4e14g27dLlOefOTJmMV7BlRLqL\nPKVEdM6dWLTjAG3lhR2Kv3dtKowxueKcIPsohQ8e13iKsmRUSiyRjwHlHS69Jiceb7QYOWsNyqx0\nQyCw63g0GhbVa9fnvPbtq5zaHnH2zBrOOQpjqGphe8Yo5BFjxEpteVRRFsWwoSHBi6gM5yLWirQk\nOE+WZtceaJtmgHyU0slWDaqmpmlajM7QShifTcoL1FpLR+0lhksRJXEkCHGpT7qAVdDvykWG1SxE\nScJABLo6SFK9EUJMkdvBwqzfkUcvQdGDtWBXY2MmZvEmkuVgZiWuBd/JBkMHT3QOrSOx8zTNkqZa\niF7WRCyOQCIfxb5bS6xoJZ8ho9Tgh0uIK/DkQRflYT383jqtOxWDm4tZb3x8j4Kh7t4F3vPnvk/H\n3Ugr99Phfa+CernfgZg8cZR83usgDj0+dBAcJHJKNBFF0f+0/FFKELAURPs9z/Q+9bGLnNks+Y3P\nv8zhvOG1S3t8+uMXxc4ySNupjewIR+Mi2RVlWKUpyxKtQRtYm04oRyUExdtX3+d3//g7vHdjzub6\niE985BxvXnmd9ck0hacGRuOScjRibU30UQdHh7ReMnTXxiXzuuXytetkWU7nRT+mUIROMuVAjPeb\nRaSqHLNpSdtJF+WCEh2dMpIP58JgFKyUxnWOpmupXEduclBQL2um62vgI7PZGotaAjy1tlgr0Oqi\nrsQ7UimiMeR5zmQy4eDoiLYV1l4X/UBYQSVYL3VJ/Q2mrCbGPm1C4bqW7bMlG92Iw72axXHL8dyx\nqBybm5ZoxIUky0z6HRKFV35LmQMqhdUZBvHXNCbBAFGyDlWCw4y1QlyIMivUMZAXOYW1LJfLISXc\nexGhd05Tjsdk3mPblvliSdMI7FjVjvNnp0J8cSvxc5ZlwyIKDJpL1f87WdT1pB+fPDiV1ieuVxTi\nA33sU5oBBYlzqpt6IOBoYySqJ6VX5LnMIpu2ZVlVdEHmbwoSrCJ0/KqqePvSHtoonnx0c/D97O/3\nnr4fU1JGnkykY0p07xcSn+J8lILlsiYER1kWklHYtRRlic0s82U9CNBD7MRizEXyXGaALgTaTgpQ\nHxDrYw/tpBGDNrLBIA5d4ElR8MCGJYCWObMPLpGIZLG4/PKcj312Qj8r6c0BBJYtqKoaRcDmyUR9\n8R7F9sfQ3hKVaO90YbFmRsBDgpsxhqZtqBdH+HZJbhUxdgQX5Pm0TsEwPTGlJ9oICqBUhiQzSL6f\n+OQmZmUq5P1ydxPRZxhk3nc9/FCOQUqh7l64lJzkgxfs7/NxN3lC//etxfh7KXZ9d0ZcMbRVikbj\nJHIS4qrgqb57Fq/dSL+xX4WKk77Cfc7tvkWvbV1i2MiLXtmds762NvhJBu9w3tE0DUtrybMsQRSy\nT9NKE7xja2MDZQy/9YVv8jt/8h1++OmzPP/Uaf7kW+/xzz7/ChdPz8iNxuuI0jYVBU9dL8mM5tTG\njOCgcR7LhOveYU7vMK9a5lVFE4WYEbQhKDGljiEy3lEcL2pal1iPRqEyI5qwzmEiZEZTFBlo8S50\nrqMYjcBYGtfRNC1rkymguPH+Lk5FMe7VZmAMeu/xTujjIDdF20qHsvLGTKnnLgzzz/6xQrsJyQoq\nDAuUWGLJIpBNDKcmJVttydVLc7omsHvDMdu25IXE8eiIyC0Qx30hScg8rjRFkjTEQSumEV2USitG\nT4RwRHwiB9dNg0FiekSM79BKktIjiqZqsLllXtVoY8iKIlHkk22YsUTf3ZSaHmOCT9OQWsVA58Pg\n3NI79hht0FYPhe6kuFUl4o5Ckip84zG9xZjSoufznunU0XUK38mGxsWIzRTGaEZlQdP55J1pRGgf\nQGUB5zwb6zmX3lvwrVd2+fhHz5HnUiz738OHFqsZcg+NsajklJPnko04Kkc0PiRmp0CcIUSqqsJY\nIwkHKZXDBzn33nFQro6maZu0qOuB8NPD4n26hBiEy70lbN6VWL7v8oL3q4KcFiCZzWpMprn4sTGX\nX6rYf3/J9umRwM9Jjyn6SIVLDFWBoqBbXEarYyKbCTZ1RKPResTYGFTnaZslXVuhMIyMwTcFTXUo\nMHbK6VMmo8/ti4j8Qzgihl6sHIOH0IDyAvGmcNs45NPdbkF2J0jxQb92r+Omhf9ER9SjBncraD3p\nQv7BnRq+D/14kN/tTnO8uz3X3YrenX7+rgUybVh6Jrc8OKzc4JRBqSyZfPT3nHgFSfxL7z4Fq4vY\nf+/ux32L3v/8f36R42U7/Pvda4ccHs2ZjEu2traEqbmc03Yd82XNH3zlFfYPlxit2Fkb81c//QzT\nacGVG8f849/5GiFE/pN/5y9RZBDRnD+9xf/1ey9St16G9kbQ3M47UJG2ayizEdNRSbdc4OuGiYUC\nz3htyvZmzsHRnHm1pG4a9hY13keauWd6ukxdk6dpAq1yKAW2NJRlgfaOBoXOLHo0Ht402VhqlnVF\nmeW0bcuBPwKE9t95J7Bj06a5SaBuXILw4lCwQghD4oLk4fVMo/TmpB16DzX2O9HbNETyZZEBEAlG\nsflQzvyGY3noqI4Do41sgAaNUoQgmXV5nosptg+SNZh2wESIwaNsNnQHSitm65GDI5VmTKCDZMI1\nXSvzP2R35kOQWZ7RoDXdXGAsyQUUg4LtzZa9/Yqzp2fye4SQwl7l7944ub/uQ/eEvCYhCkydIK1B\nvJqgZpLvpFIMzNoYnTBVM5lLOuf4iZ884MqVgm9+vcSgcW1L23SJBJXy7IwltzlNV+GjJyQG5/mz\nMy5e2OSr37jGteuHnNouU0hrYrGmLjnLJPLIOzd0tjGKQLwL3UD+0KoQx0mFGOam6+m8o05pIZIl\nGMT3NCWS9HB37z/q0gZLpVmwS4kMfSqHNeJ2EeAmiLM3xc5yEfhG8fiSsGYfUNqxczHn8mtHECI7\npycC0XtPW4vXrms90SuOdhu0VXSLPRRzFGsJnncEMggWrQt0FshMhirGRN+gQ0foFmircM2S6BvZ\nFMU034Gk15LPiTIZNhtjdIZ3Db4NeKcgEZjkFjo5R0vg6HdBGPnuSSYr787Vc8hW9jajazk7+mnq\nD+r4IMSUu4nOv9cOb1UwU+E/uUFQCoVBWYNSeYrXCkQ6xKjIS04qMpq62S91xYj/nju9vuA99/hp\nDuc1714/4sU3rvPRR7dS3IsMy/eOan7991/iyUdO81M/9hGWy4pvv36F/+4f/j4//cNP8cVvvcXP\nffqj/Oynn6HzHcfzY5S1rG+t8Qs/8TS/+fnv8JVXLvPxx3donAMipiypqwrfOIITP74qwLxqCShy\nY8gzy3SU411LkVkaF7lyZc54LSOzQtsPyiQfTCPGy5Wn8Q2qsNTaM5mMKfKCtqpE+4WibVq0gqVz\nslNvGtrOUdUSjuq9hHtOplMODg4krTyzZEkkGVnRrn2QeYSysktxMQw78whE71MsT7op4mqe0WuW\nBOZLGDYKowzTDc3y0BG8EFTQEafBpJy3IrOUxhKdJyozzEAk6VtJ2CyrjMDxyPF3/tOr/PIvn0Vh\nKFAJgkXmp12HsKuM5BOqgE0eiW3X0NU1xhjKQnwtt7fGfOPbV2k6J+HBMFh1uZSqro0hKoHleh2g\n0nrIunMxEFJSQw8JhbiKXtJKoQJJLmEprAUTV8n1VmONbAR6z5YQPMuuw3hx/TFoIcMo0EY0hMdt\nTWwjs8kUfGBZtZxeHyWCi3TENjMpesmkzlm6kyzLcG1H9GAziwsdsasxKmUceg/WYPJMXHVQGMzA\noFQxkls5n8IYfIh4beicQOMyE/YoJVFM4suZFgIj8LVPukOtxKUlhiBEriAOOc6LFlTuJkEDlJK7\nbrYdKaeGd185psw14zVPdCUhaPAOq4VQdbTbaykntORoI0HDKuTiXauS7EKLpjWzFps62hAnMNmh\nPj6kO7iKaW6g6PBqdU4gdmXGlIzG60wmM47236eq99H0m9OkUedOjVW/+J34xm1uHXfuTG4uEPdb\n6IWdE08+nUr/GP59y3PKoJnBVQrpcW9+rQ+nBXzQDk5OU93x/299vvs95l7nogYYOiFdKCHgKYha\nJ5axkNZkw+aJwUGypCM06X4/AWkib624ttz7eICUBTHw/GufeZpvv3mVd68f8bVX3uPiTiknWQde\nv3zI//Nnb/IzP/oEn3zmIcpyRNc5zu9Meer8df7oW5eomo7PPv8Y1mYczecoo9nc2qTznslkwk9/\n6in+93/2FZ597BSFlRDS197a5dV39jAaPvn0KU5tb4jBcoruWS7nBBZ0rUuLW8Y1t0ABW5uFQHFA\njIo2ab9cl3L8Oo8zipDJzqKnt5PMibPc0tUSxbO5tU3jvWQBGkOmM3SQD93R8VGCOhO9Vosgm5jS\nAJTYqJkU5OmT+Lxn1sU0JxK5lTAXY4iJ2afBsCIt6FXRizFg0jw3+IhV4lWoM5mRWaNTCncU144Q\nhR6PSpmG8jxt1wnsqxRHR7C3a3nkkZa33x6hEhwbQhBhu5JzcskI2RbZQKEv0twpBIE/M2spxznW\nag6PaqYTm2Kb5JbUSlwZYhRBdH+uPdzRX58wEIFW7izWCnjufUf0co55kQu0HsEj8ymLFAyFwHeu\nc+KsoxTKyIIa2gatI8E5FnVNL4TXSMCqcx3NMlAWGdPxiKprMDZtVoLHGkOR53RdR7VcyvvjV/KF\nuq7xIYjxthZJiNaGpWuoqxbnHbPxhN5LtN/9Z0bIRa7tRNydMim9CyK3sTrN7hg6Zx+jmFRH2Tz0\nsz3630lrrE3z0EQawqfu2fdLheFor0WbwHhmOD5usaPVxs1FRwiKxllkKwSbz/8CUWUEAkQDAxwZ\nIbms9It7jJoYDV5lmNwyXTMcH1+naecUuU1LkhTfHpEwRjGZFPjQsDi8gasr8qJIz59g+dQt9Mso\nN/29WmBPfk2IU3de81ZQ5QMskCcL3Ik6228ye4ehE+yWBzq/m7/+wY7vRnN4pwJ2t4L53RS7k/+/\nKnwnukoSzSBEoklvPiF57SbIUpHmgS1R2WFkEmL/DOp+6OYD5OnllqYV0sSzj53lc199hxsHC/63\n3/wmW+sjNNA5z7/1U8/y0JkNvHccHx0AGqsVj188y/ZsRNN59g4OyUcFddswnU25cuUqPkoS9Ppa\nyaPnN/nnf/QGO+sTjhY1znteePYse0cVn/vqZX7kWcfOeo5O2qiyLFgsFuLzmRm3Y1aCAAAgAElE\nQVRi6Gjqjo21krNb69g8F9iz7agqYQpq7YUxGYUAoSLUy4pSKVSI5GVJ4xyubmS2Bly/scv+/oG8\nbp4TnBtcS7okEyBZqWk0ahBTJh1eotNK0RCrsYiSXQ0MriIhRrwTSrnNLJYUt5FCQeUG6eOPwGYZ\n4/Wc5WHL0X7HxplcSB/aUNgCFYUBiU6MPJsRvScmAo01RsyptYIoReXlVwo+8kzDW2+PBBrVepU8\nkMglOi2gIQS6VgTrWolfad02dK6jbVpym7GxVnBjd0mRjwjGUBZlEsxrisJS92G+UUJUQ0hWZErk\nMOJZmqjuCFMzSxZhWglU6XpT8CwDrXCBNHeU2ZgE4kbR8MUIRmOUbExEdyZEDZmHSUeZZRmdczRd\nx2RS0nae3cNjypG96ZqUY/HZDIEkeA/EopQCo8W8oUgiepTCq2Q1qQzeySy16xxW22FGHrViNJqI\n/AJwncyGSfrBSBDbJZ1GINHLZqmHzU8QVpRSlGUpgcas0AWlSJsrzY1LFceHHdaqIUNPkAiYbmh8\nNHS+IhpDR8XermJ+vaFcP83pT/wVOjsFbILs7rwYSskzOKxIj6LCRg+xolnuEnSNU+NEUOhHXV46\n887z/rUFzfExvm1SfIwaRgknX1H9uZBDeijw5OJ+hy7z5E981zDqh3s8SNf2Qb9+v8fcNr5JsGcP\nT2qlEXVLKnaq98TtC7Ccc8+Mj8NzJJPqELjXcd+i17SOjdmIcS6LwV/77Ef4p3/wbZrOs39U8Vc/\n8wQPn1tnNpnILt91hCRgVkBelGxsbXB8eMiNGzfY3t5kNhH/wszkvPXGm6xtrHP52i5vvbfPp567\nyGyUY7Xm4tl1Kldz+vSEza0RX/zyZR4+O+XJi2uMx2O894xGJc6H4f+fenibP/r6uzx+cZPSKjoN\ntrCUdkznPPPFgtaLB6cIfyNt2zI+dYpRWXJweEjTtoSohEUXAkUAneVCzPAJJtKGrmvx9JlpgBJy\nhu7Fz7F31jfDQtRrqWTBY/i6aIdVYtMJ8cArWfxFF5V0Zir5aKpIjJ6N0wXLw5blYUsxVWS5uF7U\nsSVa0EjH50OQYu08PjiKwg6BrQQl8z2leOnlgl/8xSN+67dTNluiFfTWcD4Irq77+ZqX5AvvfRJ2\nC/TZdR2ByPUbSx55eJ0QlcCIWZa6OUcMiE9mEIeVaOxNAm5jTMo41P1tPuzoe2KGTTpD05toI52c\nNZkUMaXTbE+Khg+iZ5SUchGX6xQOrI0eBPbOOQm99YEb+xKCfLzoyDLoomTCWWMhkUdClHBLow0k\nEk3wnqLIUVqkLCjEGk+JiUGWZTRVLW4uUczDFZ5xOSYEn1LtxfTdh96AWw2mzL30xSQ3F2kmkgQD\nBkkDajXfGqzaEvstdAHvpEu5+OSM2UZJUeaE4Ni9uuTdN+a09Yj1bXCh5vjIc3zdM955hDOf/Ldp\ndUYPSPY6yzvBgTqKvioqQ0Cho8P4ObuXXyN2x6jMEJRCI7FHMvFPnX7sCMGBaslGOQZBH1S6FjHc\n4rX4IRa+By9Oq8IHpHlV6liJd3yeH3Thu1sBupcs4W7n/UFe40G+NxyxNyDvLf5O6PlU+twj9pJE\nT3BJkpRkWvoBXuKB4M0feeYCx/M5WZ7x+ENbfPr5h/jcl9/m7FbJxTNrtE1LV4zoXDdYA+V5hjVG\ncthMhmsa5sdzQhtYW18jECmyEefPnMXFQJ0c651zbE8mbG9MiVoRWiFNTMaaz37yHH/6ravsHi55\n4bnzjJLXobEpQgcoMs2Z7QlvvXvAE49uJAGyeDWOxyO00SzrjjYtKEQxtZUE8kDnRAflfMQoGfbP\nl5XARyHSxQ6UwIUhIjv3IJBpv8uMCb50zq3esBSKOpAxemeLaCQx+6SrByu6ue01dQjMIzePvC8h\nBLLCYHOFayP7lxs2L1hc9LSxlcXYB0ZFKbqRRA7IckuMnsxK4e2iF09zrXnjLcPWpmM0amiaIi3m\nkiAuLile0u57ir7UX0jnZpLXow+BNjF+19Yymal2HctlhUlzwH4DYJURpl4Q2M2ohE+EmPR0Qtbo\nkqUayYdTKel2+yJ4shsNPiS4WXOwD8uliNDb4HEqCgxtNLbMk8m/xBBJUoFN8gTHe1cWXLu25JnH\nd7hwZppMGTpsXlDmuSxsWgu7NeshMUEVXNehQsRmOW2fdEFPVBGB/Ww6Hd7fTEfILVlmJLgZEYFn\nWcZsNhI2sIpYZVksF6T4EOmItfyRzme1UEm4sRug4hhlDhpiJDSeS29UrG+VNLXHNYHgQvL9VOyc\nK5mdGnH1zYpLL8/ZOpdxcNVjRyNOP/9LNHpKC2S0Q+G728KmoxSCoBwaj40LDq+9znL/MuNxQetN\ngkZvWWAFRxZT8rzA+5NzsltgPCXX48Pu9D5o4VtNmUB0RyuT67s9zwcDCz/Ycb9CdD9N3veqxftA\nR5RY6pDW81T5pIvTQBr7RJ/sySKkDCoxpUbQtnsd9y16L3zkIT7xxFkgUrc1RV7w8Nkt4G2OqyiC\ndBSdF2+8zFq2trfEQ5BItaiYjKao6ZR2WXG0vw8hMJqMKTJLnuUcH+xxemvMc0+e4kvffJfcaCal\nZbK2xmK+IFohonTec+7UhGvvz/mzb13hR59/mKZpB0r20bJCRcNTj53lC19+nbOnJqADUYn58rLp\n8KkNlogjWQxMcu+4evWqBJBGBRG6JOgtyzLF5HhUMMM8RGLuUyt94rPYM/cGH0QiPsj1EaTTJPhI\nFmVtetupleF0D5X0Dh09MxRWXU5fNPpDm3403icTgNI6hcgqbCY/k+VWBN2VWF+NykJmakrMor/w\nxZLZzFM3DIW7h/P6uWPvPak1Imp3YiuWZzmRliyzGBMZjSzf+OYNNjYKtjdL8lLYi3meD9fJGPGn\n6s25+8U5z/Oh+A83rF2J7dGJoKFUmneJAD+mzEXRuTl+/3c26GLg2u6ca+8foTPF2tqY5XFLnhum\n05x66dneLrGZIkdxvOx44zu7ZJnm+ee2mY3ydA8E0dUleUjnXJoDr7SE3ovRdO9ikmUZTS1J81Xb\nUOQ5o9EI5YMYPSQY1RoGwkMP9ZRljvdCIpKZsJcO3CYSy3A/aHGtCUGyKptG7onMntgMyOJlM0vw\ngePjyHSWsXMq5/zFWbI9TDNJYwg4cut47NHTHKxb3njtgNDB5lPPENSEoJVMzeO9BMEqLUQI89Iv\nKQo4vvEGe5deQoVAE9Yw+VriOa70nCqq9Nw6bRjFYz/0fX/s+/9+rNZ7MT5YEfmu5Qn3fL6+0115\n7Q7QHHeH3W6lsHxYxwcpWB9mcftuOlj5GTdcx36uG1Wy90tEviDmy+l8VzC+RHiplaXZXY77Fr2/\n+a//FNeuvUfXSlp0DIEnHj7LZJQzXzbsHVWcP7PN9qnTrG9s0NQ1h/t7ohLTMB6PIQQm4zGjCw+J\nuwnQtDW6sDSukhiTLvL+3oKf/dRj/NDTF6jrlus33mcynlA7R6EVTZHx8huXyTND23V85Zvv8OjF\nDQCqqk7LvSeoirM7Y77z9j7nThdMN2bkRcnxYkHjwqAz80OB0bRNy3Q6Y7GsCD4mJqVAuk3TpLBD\nKZ59qyXzNiCegB8hWYnF4c3ofR6zPBuCUJXRSXcWThQxhlmF/CwDJCXkDpUgMCUdlpLAXdfK4888\nPsG1nq4S+7S8sBijybJsSD2vqorlckmZG9bX1rDWitt9orIbpfmnvyHCZGOam37OpsLYn29VVdi4\nosm7riMaYRZaoylGOZ/45Jim9rz55gE3diu2tscSv1NXsoPXGoMiapXCeKEPyvExDEG8RMnR01rY\nrdgVVHxyc+B7wpHSVE2LMYr5suHFV/bJrGIyzajqwPK4YzzJ8C5y/VpFDJGrV+dsbJYYq7hxveLs\n+TFnT48otBFxuO/ICzEraJoaUiBr1CrNEj3eSRHuCTsmFb6iKDhuKrmPtHTDhdIykwuSuaeUuAKp\npPtzCeamZ64SMVbj2k6yKAGFbJp0yuzrtXq9hKKHQPvvZZlIW7Iso2sq5scd07klKsgLseHrug7n\nWkwuY9IYHKPSMp7lHO3VrF/4IRoUkRajWlRMpJLbl7H0t4Dk9fKY/auvM5tEjt59BaM8o+k6Wk/x\nlMTYopQ4N/Xz8D5IWYl1kcwt1b2jY4ZXHxbe288tJrj5QzlSxbq5kztJp/+Ld9za1Z7U1976uDs/\ngawBsmU6OSdVw5odT37NyJxYJT/Wex33LXp129B1julsRts21HXNWp7z9COn+erL7/L+YcuPf/ZJ\nFssabQs2tmfsnDlDW1fMjw7wTS1GsjFii1zYTFaxbGvm8wWH9REbG1scHc2JMXK8bKmcY9k1NG1H\nqNtBo2RCZDrO+KFnz9O0ji9/6z3OnxLI6/K1JbuHkvH38Dk4tVlSN5739xzTNSUO7T7gA7TeY5Tk\n7Fkr85CucwQnxAyiUOiV1sTkAhJcgih0smyKwkcjJoPc1AEppQZdVP+mds5hrE2BiCIQjijx5lSk\nBSsVWZXMdrXArdHLW9s/d2+86pO8YXkkBIV8bCQpIAZGk5KiKEQXl26Ltq1TlltkfTZjMinJsxxC\nQNHPFSPOtRJtEyNBrXRHvRhabuAASFdWNTWZTUU1xTgpZMjs+oBZC03Tcf78DG11Qink9zRa0jKE\n6drPP6Tz8y6s4MqYTLn9atNxcmMRQmC5bMgyTesjb76zx3vXFjz2yBrXri85f3bMhXMzjNYUeYlX\nXgg3bceoLIkRFlXDO+8cUi8dTz27ycb6mAzJniPlJ/bEGxVBpU5LJY1jf/1l8yV/8izHakPTVClF\nQ+F8S2FyRnlOkVmijiy7BqMgGrnvmlY6tRDFP9RogyLjqFlKekaMiZAli4M50fWH4IeIK237NIhe\nRxqwmbgPnb0wxnlP2wXKpP/rIcqYiCx13dIuDnFdEJREa8hOEfGYwWMycL8KEpQmKwtGo4zFjUti\nljBeB13iXR9fBDfn4AmVQcVAUL092Yku71Z48y7HyYd832ZoUYG6FcI8+bv8xTvuB5vK924lAN3h\neRioK+m/CQpT6VOmEvlFaaLS973k9y16o9GY9c1NfFezsbHJwcE+S2145tGzfPXld3nz8h6ndnZY\nc5GskKys8WhE21aMxmP2rl8VwodzRJzoK5RhtD7m2pVd7CTHjsW0+cc/+RC//vuvUY4MZzZGoDXb\n65tkxlJVNc3Brvh1+sDGOOOZR7d48fU9OhfYWit44dkdWhd59e0DppOCvYOKna0pisjx4RF152ic\nE2q1l5lclslFM9qgQhwYnVmC1sT6SqjaqCRDSEVB2ZOuKvqmHd9N7gypaLheUKSkiKOU6Km0TsLx\ngFLSovcFhtt2S/K29xBAfSxwUDE1w6InnaUQTJqmwaAYjUqs7VibzcizTOKQnBM/QyKuFXgyJpNm\ng0ZZNTyfsA9Jc1fppEIQQ+SemBETAcRoiTEySqVkBmG2Xnr3iN29JeOR4aHz6xRZmvlmGT6Ca7sU\nY6OGzUNEJdPoIJo6tZpVARwdNxwfNxwcN9SNZ74Q+ciprZKPf3Sbl17ZY2Oz5OzZqQAmnSezKVgY\njXcRX0sa+fp4xNNP5kSlaJ0E8Or0WROYVSQtIQZhi0aVZB2rImGsGuBxxQqCLjKx6Kq8xCktl3PK\nAMo7OhVZ1ktMkZNnOYGeBCVz4SzPEHq9o3MdOrND9JDce7LQtm0rUCaiz+vne/092Xd63nsJZ7VW\nrkGnhm7de09MnSYqEkNGVF42QFqhtKGNOdGI3s4GJTPSm1aa28ksbeokTVTYmJGNThFVRhstGNCq\nlhiRWw/l6UXMUcu9EU+klZz8bPz5Hip9/m9mIv5FLXwn7807sTXvfvRpFauvqFv/T5FGS2IDqJRB\n3Fs08T7zPHiAojddW0PhuXGj4vDwQCA153hoZ4pS8Oa77/POpXfZ2jlNNJbJdMrb775LkVtya8lH\nI1pXUy8rvA8s5secuXCO0fqY8XKPw+URjWs4c+oMNjvgp3/sMb709Xf5o2XLz3zqUdYmgdA0xM5x\nbmcbF97n81+7BMAv/OUnWB9bruzVnNoo2dpaZ7Gc8+lPPsy1G8dsrxe8e+0Y15W4tk06vIBcI4PS\ncegsBiZdEBcNDWkWGJMIWg8fvr7zUWlmBkBvXKxWnVEfzqmtIdDLBOSSR1RKQuCmuVxINlS9js7a\nE27iw64o7aIidJX8bDG2kAgwIQtoI27/TVOTWUvmLWuzGVlmRcuVvO/oobgTi6IsYel7Rg8f4qFb\noBcGK6wWhqMPkiPnXDskN8RefB8DL/zIBY6Pao6Oaw4PGv70y1d49OF1LpwdE7UhKjNIAfpDdIxe\nGIaJQGNTagJIwfvat69zanPEbFLwzBNTFCnXsczAGMpJjtIxZbdpcmWh89iE/Zda0pidD8wPjxlN\nprTOU82X2NkEF0VjJ+9Ruk7pWqgQyfM0n40hvXeJ9u8lWquqKoLzjCYlqMhsOqOqKqIXKDM6jzNp\nRhklab1zXuaZQeYZ3nuqZokI0hEINC0m1mYDaarfCGhkNtebTOvkzDPMmtWqcM82Cq5cOmb79HiQ\nPXgvJupKGXzQKCuzaFnDNUFZogrQGRQGTHtLjTvZ6cjfQauUgwmGDLzFUeKMBmqsbsVeMWQMsKCK\nEANRifdijAGCRpFxp+PkUjrM++6ywPbM6g/3WBW+m772F6DonVzD+mNgEp8ogCf/Pik/WB13Llon\n36oYJTQ7jU6RYPB0HrLi3vNc71v0ru0eEHyg8QqlM46OD9B1xZlz59lcm7B3uOCLX/oyn3juCfKi\n5LEnniSLnktvXOL8+fNszWaEqsLnTrafRqOCol202NGIY7fP3B/x5PoFiq7mwukpv/Tzz/EHX3mH\nZRXYXhe9EmSE4PnXPvs0n/vq22xvjplMxrRdx2xWpFDSCkVkbTZC6cCyrrl8XXFtd4nOPV4polGY\nlIhglWJWTrBRyy5ZATrKZ00FApLmDdIRihPIymZsqECAc8nBHtnxhyCzG6UUwbtkl6VEZJyYKjFG\nyQOjH/UnCrrSklgdumGzGPonjmkBt4ZmLpCULRTCnk/woJGuUROY5jlFljGdlGgLPnQCe4YUyREt\nIRVYsSIjhZM6XFCU5GiPSAKIdG2Dsb17iFyCPDcEL2EfmbZYZWiDwGHDzNJHttbHzEYZD52dcXRU\n8+bbx7x3Zc4Tj2+wNsvl+lhYVNWwmCsk1sgamXUuE7HGKM23Xtvl4QtTHr24jU6+jDFEVCYRVip6\nZmXBZNxQ15G2CrQEnNJEJ1BdsCJEL4scnVmqainkIg1d01AWubBrjcwS7AmYOeqItYUQaeip9RGC\nvFUp15tgFFYLg1G1nrGyMDHYlEoSu45cGQKGupFkcqW1XHOl6XzAK0vVOEKK9lE2idm9JN0nh3Fx\nhjGiz8yynKwwFFmG945gLK4T4sn+bs17lxYoBdO1DKUlvT5GkafoKI2XcyHlNxp010j3aVtM0MQM\n2thhYupu0zGkYJ+Ym+mQi3OOP8bHOUaVAlkSMXiyzhIDkgVIGh2QjIUjkBIne5cjNSymPcsvopIf\naIxR2KJxxaKMvaKrbxY+zIKn4Lb5neo3jgmdiSe6PtVbcKXzSMS4EFfL9YMwRu+lsfsgpJS7MkpV\nP1ELtzxm5XO6ehI1XNRbxe93mu/d/P2wKo6xRyakmIG8dwOSljYWchv4pOcj+bQOi+k9j/vbkB3P\nsVoxGU/wTUWR5yitWcwXLCuZO7x26QaPP3wKU9XcuLHLaDzm2Y8+R56XlEbhGpnTueDI85LgIi44\nLJaNyQbvv3+Do/qIxWIhWH9RsjUrefvKPj/y7AVCTNEmIVIYyQDLjFyU2WzKMpEssiyDZcViPh8K\n0PZWxuUrFdtnM+pWFpNRErcXJiPXAsPpKPMXpywtnUCR8eZ5mkqT9Z5ochP0OCzyqUPqb5hb7r1V\nJMzNN4lWAmnptGUJaQFS8oChyJ5MEe4aP/y8PAcD2aT/4E+nU6bjERBpulZE7jotIGlR6nPZZF65\nEjD//M9U/NlXDM1CWJBapdy61O0ooG7qIRfP+Y6ecmGNgeTbmVmbZpkS+xRiYDrN+eFPnmVvv+aV\n124wKi2PPLKOzeU6BWKSQ6h0ryuUYUhTuH59Tp5pLpxfJ8RA17UCq6p+o+GHD9VP/uwBb72e87U/\nG8t5EGTzkpIfslQkrLVY0+ECbK6tEwhYu0pqV8agjBYLtraVIkFinwaZ1wpRyYs3K/JaxmhUDLRd\nBzFitCXL5HPUh8uWRYFLXqHpjgLS7BOBSnWCvkkxQqKT9KLZ66UdaqVrslYc6J3rUlaZIs8L2qZl\nfb0kRLh6ecGpsyUQ6DrpVEUbHPFRcbxwWNPJblql9yFIEfQqopQnnlhGIgwLWK9VlS1dQEVP9B2+\na8nKUUo6SfdhJH0e7rVirUrYzcfJRfT2nxoW2Q+9s/tgx33X4x9AU3hrobypI+5nttxaNNUtm4R+\n3Vr9u0e4bv/Z1WvdtxAPa+dNLzOMC+KwmCa2cD9OSib1so+4s9fpyeO+AGjwDpsZcYVwncwLAN92\nfPb5iwC8+Pp1vvSNtwnBc+XKVY6Ol2xunSIfTbhyZY+oCtbWd8iygiKTnTE+MjYjCpcT5o5RMRJi\nBZIh99TFLfaOKl78zlV0cvPvnGO+mNN2jqZ1AmPllrXZhFFZMh1PmIxH9I521mjWZyVlqTnedxzd\n8BzfcBxdr8kw5Gi6ukEHsMqwMd1gbTyjtDmZNuQ2o8jyYaZltE7mzHKz9MzBmEgWJ9t2YdE5+tyv\nnuI/5JqhBinCcPPFOCxy0Us3ljaLkIgGRtsENXbUc1kguzpQFjlZbsgzEV0HL+G64/E4eS4KnNW/\njgsyr9RGkhx6QXzbSk5cXo54+GLgySfERkvbDJNlKG3Te+HFC1LJ+wIklqgZfsciy8mMUOvbtk2/\nJ8P8KITAzvaYz3zqIpubI7754vu88vI+Bwee3omQxFiNfeEnUlUtu7tLNjdFdykLtcgGupQy39/2\nIUHaIQrVXelVUeyTyFHCvJRwWdHvOSfzs/lySVXXQy6fD2HQISqjaV0nEGYMKK1w3g3sVlLobSoF\nFFnGqCwZjQqKMgcVqeuaxVLM0rWVoqp0z0r1mCQjyIwmH2bIcdj8CJRusDZL11UlR5sVfd/7IPBk\nWiiUMqBh58wYYzTz425Y/MRUop/lWsrxDB8DrWuGjYQJDhsjOkR0kF12/2fo7IaVS0JBTezQviV0\nDSp4mWGnjZPUPDW8aTHefdlafS91eel+XkFl//+HEvvjw5AY9M+hk87z9uKkEiXLnPijb/nazT93\nJ0jzTsdtELRaMdj7IiZnIAYVShmUsigl4xDRaFm0sgKzoyGuAmbvdty30+u6BmKOIpJnFt8kMW5m\neeGZC1gT+Rd//BZf/NpbHC9q/pUf/wSTyRSlc77z6qsoH1jf2KSat+TFCLoWGgfOszZZw2SW0YWM\n07MtYufZ39/n6o0j3rkqXnxf+OY7PPv4aUbliOADRVGwvTHhq69cg+j5xEcfxtiMuqopR+UQ7TNf\nLsmznPX1kq3NikvvVmS5ZjzLaStH6MQBhKAIPtK4lq7sUtHRMtfroT7XYaxNjDgpRDr14P1HzFqL\nASF0xDRb6wtZbzztHN5FmtbhCyVm3arHL5NOL7mF9AVSKTGoHhaE9Hq+jVSJxHLq4piIE3mCKWnq\nmiLLmU2mAmt5JbMRTjh1aC0Zf/ghSLRnHxIj0XW8+FLGc890fP1rIidwraf1QujJjU0mxRHSPI8Q\nkuu9LLxFUQhCEDzLZSXpFAkTNUkKgRP92kMPrbFzeszefsXubsW77xwxXcvZ3hmzsz3GqECMimvX\nl7zz9hE72yWnTpX4lHhhjBE2Y7IxGz5EIBld6QMYFZJ8oU4ECCcHHZ0IOLovel7ev6woaTvJCPTO\nEZV4iOZ5LpFITUXoxJ5N7kGRsPQyE2tNcopI9wLJkSauBPX9PDMEPyBhMUZ815I86sRkOfokW1l5\nk/Ybqv66ay3rgU5+sCEIq9Z1nhg9eV6ggsaHjocfn/Lmq0fM1leZeZ1zSXMYGI00Vo9oGoixQynQ\nVKn7nMBNcoV4EkFERZ+IX5HY1bhqjq+T9CUm+U2ffXliVNAf94L3TsoRVozOcGIh/SDPsTp+oELs\nD+H4Xs731t//Vhjybh3b6iG3X787Fbs7QZx3Ogby3uorq8KnNNA3CQZPSHPwMDDZFQyfs3sd9y16\n45EkHUQnDExrDE3bEVNH9smPnGdUFPzGF17lm69d5czZCzzxdMT7yGOPP8m3v/lNms6xtr6B9wW7\n166goswJ2sUSbWA9G+ES9PPia9f54xcv8dwTZ3nh2fOcP7VOVbU0TcN4NKIcl3zm+RHg+eqrN7i2\nX/GxJ09TtR1bsyWTyRjXdWijKXWOQzEeF2zvOLQxdCHp4JQeyCZt5yhyy+F8zmQsA33vvNDAtUGr\nZAmVdh+DCkuvdjYqLeYJOERrTd101POOpnbUi0BduX70csdDKVmossKwdaZkNBWszwSJWvED/BWp\nDpLbyXbB+rYYHosGVsl71NQYpSmsLGYmOXNoo2malHAegsCqISaMPM0OlSz233jR8G/+qwvatoGo\nsYV0bnIOYp2GjoNgXK6Z3LhlWRJjZLlcCuElF9ag855MrQp6TB8GKbiejc2C9a2CGOBwv2H3RsXb\nbxxw8eF1Tu+MeeedIz7+8VPMpsWgzYs91Acpo2/1wRs65yCQnUnwJsjmLSrZ2CilB9/JUTaSGXHb\nkGnDKC+SJMCR2Vw2BUFmjdpotColzy94lJYC7NoWEIuwzIorRw95n5QPOO+GpHvnfXLpCckiLvA/\n/P09nv6I5x/9HyP+wf8ypigUv/orNRfOeY6OFb/693LeucTw+3ofpDs04i0qNnPgCHgn6SBt6wjR\nkxWGLDcDxN3v0F0nptI6BMYZlJOc4DtQySpNCZwalCKQYWIzLDTqZAFMw3XXRJsAACAASURBVOi2\naaCpCIsjfNNSjEoSr5R+avTB+jOZz928iP7gOrzvlil6r+71+33c6TXuxX69lYG66uJuetRNm4/7\nvd7dZQu3dHy3PV7OQTx+zaBxllmMrMcxZX8+CEHpvkVvNpuxXCxY1Eu0Nugsp2raQVQbOsfzH3mI\n6WTCP/4XX+d3Pv9lzp45zQ+98GNMNzaZjkq+/uU/phgZHnroDFs7O8z3D9m/vos/apmuTdEqcuXa\nIb/5ua/x3vtH/Hu/8KOc2l6XWUoItG1HneZR1liWdc2PPneBzbURX/rGe/z2l94ExILs3/jpZ3He\n4VLCtY+yozeZ7MR9mzR2RqOMwbuONjgKXdB6R6wW0jXESJkVOF+JjszotIu2aNXDZnFQKAUfaRrH\nctGyWHRUC4d3d6lwKjlpxfSnN3WJ4H3ELx3vvTlnPMs4fWGCygTulDvOE11kcSAsx51TBbm1g5uJ\nc55yMsY7R1UvaRCGX5YKUw/jOS8dXlARnYqcD1IUjRXB8+Fx5ODI8PijgTfeMuIHmRK2Q4LQrJZl\nSynpfEKCOn1IwZAK6QjNqjPxSYQuOH1cwcFBWIut6zBas7VTcvbcjKbq+NaL17ly5ZjNjZLxaOUy\nEmJMnWrqMpQYevfdnu93nv28MgZ0X6SDJ7g4wHIhnYdzjizLmIwmuLZFxUimZIZlkgUaOoifZC8s\nD4a660BJOkM/u80zS5FlKUNPUdc1XeexNsN5L68dxbQ9ajE30AmGDjHw3/7KOp/6TGBzSwhEP/cT\nnv19zX/5X8/4qb/S8rf+3Yr/6pct0FEWI4yW9APV31DpHgtpvtqbectsWkFcwfVAEvhrvJcNLm2D\ni5GgWpo6kE1HBEoMOUFBUC0mOnrNKkoNdnsgTjJt0xLriuroCGyOsgUkw2+JiznxwbjluH3xjDev\nvMMc7NYC+IPr2O6lQ7vXkcrIh306tx13Lya3H7d2aB/kWp6E3E++7m0Srlte68GvXQ9sS7VTKgg7\njB7i7lfj77HTu3D+AkdHh1x1LdE11NUSZQxVXYMpyXMZKq7PRulFYXt9ytp0giJy4/2rZLnCu5Yv\n/uEXOXf+PGVW0vhIXbe8+NpLfOPt93nn6j6fePo8P/fpp8nLDKWkW1gslyityIuMLniMsozKEh8c\nH3l0h4dOjVHWcjyv+Se//zrvXjtifWqpqyX52NL5SN00Ykqcy5BeSAtGgkYRIkATZGbpgpAMrNbC\nEEuLRL8498SSrvEsFi3zRcdy0dK2dy5wWaEZTSzjaUYxMphccfXtBVmpmGxlwxDWO49GY7XleLdl\n73rF8rjjrZcPmKxb1s/kUpCA5bEwwtY2cqYT0ckFFHXbkNmMGANZJpKRxWJB0zbS5SlhjXWdE9Gz\nMSKER3b64u2pBqapUfDyKznPPFPz1jsCZQbvyIoCYxS+6SBqoo8oY9DaSKhsjElbJ5Bu6ztJHHBi\n4G0SPCjGAEl4bhQWS5ZnoEiLM8QQyDLFQw/NePXVfcpTZlhkejhPJXgyRJ/g2ZXuzBjD4aFhuVSD\nXV1RFEQkiNV1rdSw9MGzyS1FJeeXLHl79l2JTbuVrhVxOyoK41Cn3Dvf0SXiS5Hn2DSjM0pT1w3O\ni+C6dQ5S7JSPyU9eaZZVlYpljlKaq9dJtmbQesfxIrI2C3jfsbbecnwsO92QIB4p2GLb5J3oI/s/\nSqe4IteRFxlZZnn1xT1G45yiKPBeNh3WGnGfsTk2RObtMcs64rrI2s4FImIgrgl45phgki2chN+2\nTZPmQwJHjcoSZRSFOcOxagnOE7xJ19gR1Sr54eTRy3aGhTKuooD6gjEwOGNifA62gD+4ondnKv79\njz/v6eODF5u7mw/0TxHj7dfhTpBm/7V7wZ2r87q5A/RR1gqCMOtvOr+UorJKJ7z7cd+i17YdoDBZ\nTutaxrMZaEtzdIzNcrSC3d0j/uFvfwPnpbX8R//kt/n6S6+zuTEltAt+/IXnODjYI0bD9vY59vaO\n+PY7+3zhz16krio+/dGH+Pf/+o+RlzkHR4fENNPa3tlhrW05ODiUTaGP1HWF1QqrNVub0g02XUdZ\nZJzZHvO1l6/ys599gi4c0i7mmHwkHWKe4aKXINcoGYF9V9B2HU0bsYmG37Y1tijTjKXXDCWBufdc\nvTxnd7e6/WJmmtHYUo4Mk2lBMTIJxpPAQ3HaV2ycKrh+aUmzDGxdlFA8lTqmoD1rZ3Km2xm7VyoW\nBx2LQ8fi0LG+k7N1dszVvUMAzp4do0LEaEXjPAZDnuV0QUgmMQSUlWLlg5frqgy51kl/liWnmdSt\nxuTOkoqo1Zo//NJEZjNa5o99hzudTIm2I8Q+rFScVlTSjPW2bD6le/cenk3TYK2hLMvhxjcp5bvX\nm+EDmV4xZvvF7/TpCY89ukU//ol9cngCnJWSlAQXQrJ4i8So+K3fmgqEaITer71Ba5uy9cTI1gex\nRNNZRoiBuqkpsmJIQ/dpQ+d68pKSdbXzktQefcS5lPIQ1KqLj8LErVLChVJKLMsSacanIFttrWx8\njEhz6kYs4ALQuI7OB+q25Ut/lPM3/4bjD3/vmGUFv/CLpRRmZKPQNC1ZNsK73trOACFt9iSCy1iZ\nQd+4tiSEyOnzK6i4n0OWZYlznjZC46fsv3cEOEZnnsNjUKEWSU1s0Cbj8OCAtpXP4tb2tpg9JPg6\nhIA1GSoboYspqC4RFVzKUOwHgf3g4MRKettxYrd/S5f3QUHS/viw53gPMr8ajj/vynffo+/04k1f\nkf85CY/eXvRvne/d+vX7XqO0gVnpo1M3FwMJ12RgcqZYoRgDg2jvLscDpSwcHR2LY3+/a9SiHWo7\nB0bz1VevcDivmZQZ//l/8PN0Mee1S9d57a1LXL1+wB/8yUv81AtP8tGPPcfvfvHb/MZvf44nH7vI\nX//JHyPvDpmWFqsVo6KgG49pXAdacXR8TNM0ydGlwyc2d93UlEXG9evXKIocm2UcHB3z7GM7fO7L\n77Coaoy2OGC+WIgriU0K/vQ7xBAIXYfEVERGRc721hb1smIxX4qLd3pTQnL776GbvT0peJNxxnSW\nMZrkjEbic+njyprq5JvbiykjUIwMZx4bceX1CtdEslIEzSc/AFlhOffYGstFw+7lJc0icHij5Wi3\nlaKdKdZmheTvBYE/FdA24sQ/kDl0z4KS83EEtDKp6OuhizDGkOU5WZ7hgginc6M4OhSGVmalKykK\nSWgIvkMr0TQaLcnjw02sxQkGkwJ008KntWY2myVyh5UClEgcvvNp06GINtmNsYKOui5gk0NMCNKt\n9uG0RVEkaFM2Lcac6MyVOpFFmAg0IdD5NsGaabOBbNhccBRZBkGzqJbkoUjwoE9UZ5nDRRJaoKKw\nIwnYLKduO1rnE5s3QTs9nzjGNEtWaJPROY8LEQ/kSuQW8r6l+bCxQ3fTWy/90t9o+NZL8Lf/4zX+\n8o83/De/0vF3/rMCEC9U36fPq173Ke+91FqfbMjE4eb6lSUPPzEhy8wAO1triQR0p/gH/9Ocjzzd\n8T/+fcOv/l3PI89/ll/7e3/KQ2d/l2vXSv7D/+InON4f0+p96rqiGI2ZTdeJMdLUFUU5xmiLR+z/\nosmZbu5QHxzRugadFi5xqfwwVv9401/3O76fpJUHK3z/0lc8OdTK+g9YFbsTDZm6pdA8SNG/8/W/\nucsbHqdW8+IYhcjVv25vSK3QKJNhe93TXY77Fj3XOQkf1RqTF0QieWnY2FK0ywU60zx8Zo0/+bZi\nUXd86auv8cmnH+Ijj5zhP/rbf4tz587zG//37/J3//tf4zf/8CV+8i99hn/4v/4aH3v2Kf74D36X\n3/utX09i6MBisWRvbx8fI9O1NY6qI2yWs39wyHy+oKlaMqvZWJtSloWkQP+/1L1psGVZdtf328MZ\n7vRe5suXWZlZ89DV1a2eUbdGGoHQgFpCDEJhkACH7UCAAtkQNv4AJgIiZIMBEUbIRgY7whqs8BAY\n0GANbUk0knoq9aTuqq55zKzMfPnmO52zJ39Y+5x7X1ZmZVZHqyVORFVm3nffnc65e+31X/8BRdMs\nOTxuePyJ13jXo3cxzq4aPs9WZIZmsomvRPy4VmKQlEoi8G0di+mcwlrOnzvH8dGxGAFrkz2lMyv0\nWIpOUWgefug06C7+SU5JFwaKEvgsofq5Ukz0mVDGaCZbBdM9x9bFLNXQORiTJJCfAl3AmftqmkXg\n6IrDLXPH4RJPP7XPww+OhfySQ09djMQsdi0KyTprglu7ZgW+1EkRoliyKVTPeg0p0roWa002NJaZ\nXFLwyCNL/ubfOCZ42Nub8y/++TY7O4a/9td2eeQtjvnC8vd/+AwHR1lnl5+xaRtSSFSVZMyZquyL\n4LJpKIqObt9R2OUzE8hSLn/nAsaIBdqVqzNeeUW63eHQsrVVoVRgPK4YjUYCVzeeGBN1bbOrjczL\nCitONYtccLuNjdIrK6PWeVwreYDEzECUbx+Nk0gqlRIuiLeoNdIFtyGSoqfItxXW9nMuSS0viNB3\nfNoYjBY9pcrsTcnzFY3d3355yt2zhsF7Gn5ly9IGi1aJazsKayx7e5G6yukOSn6nLAvpurPJuWzY\n5HPVRhOjIyXLct6K7rXWoq80BrzGt2KsbUr4m3/b8tYHHRfOB86987v59u/SvPCq53v+5h/iL33o\nE/zVP/c4/+jH/ihtmDEYCqISvAcVRdqj5HvjvcP7gFseU9AQfJIcxRBIqcv/E3hXdQvf6xbNzCpe\nu2Ud2qS/evLP8qw0qXzr+hiwq43q9WXn9cvwG5XjG++d1m5PnHz0G//d3XqzVxARtkBvg7N6rpRu\n9iJ/F4/XP9nrSC2Kjtp34j63hy9vVvjW/p3TKU4ca8gPdJrUHLKdC+/tOv7bFr2iNJy/cB4fA7PZ\nDO9bBnWJ1oZ5u8QAb3n4In/g2hGf+J1X+MQXXuKt5zd55Kvez8WH3kkxPsV3/0f38Q3f/J0sFkse\nfvhhyqLAJM8DDz/CPffdy/H+NRbLFu/nHB/OKMoKX0UOD2bM5jtMF3Mhl2hNyh1KiglNwRPPvcZn\nnrnK0dzxzrfcxb0XT7O3f5jlDQOO5mItRoalOmisjRGdDBpDxJKSJQQJpIxhLh+o1uiYUFG+xCFG\nrl+fAbC9PSBpVsa+emW0rLXOCw/4hMBoJGnLU6LI8odTZ0peeWoK5wpsJSkMcq4N3occOSTwQjUo\nOPuQYee5Ja6RdIijo5aXXprxlkfP0LQtHmF5gsyi+vTs7LYhhV/hW4+KMm9JRuQnxsoF5nyb0QJZ\nDNEiCkfBleuav/xDG4TW8h3f5vjuP3nApz9dUtWJH/zBs3zoQw3f+2eP+PEf38y+mQLbKm0otME7\nx3AwkC47dRExOVg0iYOKaB5FVN1JDDCaxgkV/1Offo2iMDz2tm1Go4LLl47Z229YLjxF6WibQ7yX\nTUVKMJ5YrNVcOD9hY1TLptXLQikzRiRPMSS0jnidmE2XzKcN9djijxoWU8/58xMKFHVRSipEErRA\ntENyfuvCkKIiBE9dFVIMcycXstdrx5SU6yZiUESV8G6JDwItF9pQlwPuWxzxrn+4JPxhuO+s41u+\n0/PT/3vJh77D8b1/+oCjI8WP/A9DCguJwGBgKaxEIEWlsvF07JnFeXWiaTwvPTtje6tGJUXQAZ8i\nlgHJSYpDObR87rePeeQeGJ15EHvX1/Lud/1rfuNjE8LulN/47fP86N/5FD/yP3qKshZGbJLdeMyw\nZfAtaC+2aGnObHYdFTyVHlLWQ6Yu4ZMj+iUmaXQyKF2glJE8ROcga8AkZy1mtyS9Ii3EnB8ooY70\ncsSkhOQQxcxCd3Wom1bQFb31gpJ/prr3AlFFsVxLK+g19Z10t5WKq0q6/kDcquNZu63Tp+TnSNGA\nDqAauS0aNDUxSreeVOBmxfONjnV48c10tyfYkzd5yls90vrc7o1uv+PP5pZHp9OMxORPPMcbHbct\nejEIhjqZTPIOumN4SQKAQ/Evf+Y3OTieMxqUvO3eM5T1gJASbQi42ZRRVXF2+4x8ORJEhDY/2jwN\npqIaThiNKvZ2dynLkrIsOD48JAVP2y7xrmWx8FR1zXLZMjMa5wt++he/wP3nx7z3sfPce/E0SWn2\nD5e0raMcDHEpibNKT04QKy1bCBxX17VAb8FijVD660yt11qstjq9XYoQA8xnHms1W1tDkSf0G7CT\n+HUnXIds4RVX2rHYpSsYxcaZkmamGYwL2rbtBdMx0c8UZVa1SmeX54Oy1JhsdhxShoo6R5I1QXhZ\nlv28JqXEcDQkNCLuF2q8J0RyHE1meQZP1SWXh4iPgWs7CZ0StYWDvcTpU473vDvysY8OSTHyW781\n4Lv++BExjCmMFTsrrfFeaPCL5VJy6DJbUGmdO2IPMVBaI5FPmbrvfOhhx+ATR9OWBx/Y5OzZMZ03\n6H33S7RUiCJVWC4dVkcGwyHeRV69dMi1KzPuOhdznqf8Xq5Uwkhtlrz64jQ77SjaxjMeF1y7uqCo\nNIXVvPjcPg89eEqE+Bl2VEZJ4U6iuxMHFyvGylq6xuAj3rV9LFSnhfQ+C/BVys2gQWkJJ/YhcHh0\nyKFz8APwO6cUf/f9FeU2nD8Hv/zLhjPb8Nprhi9+sQAlkLVC0IytLce99zZcvRbY3YPZrMyzaZl7\nzI9bRhPL1rkaQklJSVANUTWEnEVosbn7DhTjbSDxkcfP821f/2l+4cN38Wf+2BW2Nh1JeXwQGY0i\n5WIbsxGwwlQiXaFpqaKhqgtUoZjHJdqOUW2J8YfU6phoNVHXoEGFIJu1vMYrDEQL0csGVuWvQmYe\ni2GdSFJyaZLviSb/K611ArlLIHQWCPm7yYm/y8PXqHgyJkiR1rgdabWhyI++TpvvvourPrRbqFlr\nlWL/uzGFnPUsMDNJCxaj5H7yLr+ird4dHetkv1sVnfVxzx05tLyJo5dA3UFhvwMiS0tZlZSFQZEo\nrc3DRGlcmrbl4HgOwIXtDd792D2cvXCBqh6glKIqxdHfaIGv2taLmh6FsjWPvfN97F19meVsF3N0\nTK2EYt+6VuJYjGZQl6RFFId5EoumYedwyca44g++7z6KakDUmr39fY6OpyyXDVFrojLCYMsNr8rX\nZ4qJFDxWyzwqpoBrWygKZjOXX3fZnxibSRxPPX0NgPFYImGg/zr1RwdzdrqxhGw4bSHaNB+DfF+0\nwBgbZyouPTdlvJ0fT0kulEY8DMtS8Onu8WLo4Di4cHHEmTOiEev1bkGsszpyQ0fE6XLUOhcYjEap\nAtG3mNUFgyzgAgWK1MAHcZGsC4WmYFQnfuAvTfn7/+0Wf+Z7jzk6kvZ5dqyYjGXhN0bmRJKVB6q0\nGDvKNmvZQzEvUN0F63xAS8R2b/uVQqQoSryP3Pfgac7fNe7hsETqNwkghB47KgVHjhFj4N57JhBn\naON48qkdNsY113ZmLJYSIbU2hmS8UeJc5My5AdtnB9jKEIlEF3n52WNevXTMPRfHmSVrQeWuNENS\nysjszgeRfygFRonPaxu8aOislWvfCLvRByl0Yl8W8c4RczL037ir4u9eS/ytUwOOXyxon3UZSTBU\ndYnN3bkia04zdL4xgfe9x3H6lGNrKzEaLtjfV/zK/2f4f/51wWzqGG8WOG0ooqEgoZKi1ZGgE7as\n0Bh8C7YqQQ9QKvCrHzvLfac3+Ln/9dd49qUxl68O8KnJ3WR37QqaoRDXIGGoKogtZVEBJT44om2p\nBpHFtGFQjNFRgS0JppYOx3h0UULw+fFywQqO1C4IbgkxkIKUr5RWMVo92KakWKY1sD0ZJR0VoHuK\nO9yyw0grp4+UfUEzvk2X+Sb3W4fiVP/3bixy499XBS/1d1cokhZj+4TN3aUkB8gmMT/nV5CZun68\nUQe1bjh9p5KIL/dxpyL42xNZUmQxF5slUiKGgLWG8WjEgIRViq3NMXuHUx66e5vv+o5v54mnX+Ds\nubPUZcnlS68ysJa77joPMeRFNcgX1VZ8zTd8kM9/6qO88tyCsqrQWjMaDmjbhsIIjb5xiVgVzNoW\nY4XSvmwcZSFfKNGWiVnw/v4hKWmJIgoxFwT6a1gjvpddHppSorvqxMI6D00b11Laoi98l68es1g4\njFE8dP8WeQMJazsc6DZwJ214bCZrRIRkEFTOUFaawdhQDQzHey0bZyq8k3zAlDsCpdbp97pneZ7a\nqjhz15CUsjVWjCwbsRBTuXvqGHlt2/b+oToXW1MYrFI0bZtJKCDal5Uzgta635F+6FsXgOa3Pnqa\nH/57O/z0T21y6dWKo6MZg0GLMWPq2nE8lTTzGCPBewqtMw4vCEHnmKKNESi5g4dzVJHAgDk1PUUu\nXT5k7/qCtg1MNoXZKGbeHUQi7vs6W3eVhSVkD8mOMfqDP6j58IePeP65gmuLGd5H3vnuszkOKOKy\nZZs2Ur5sbzMXqAc1yUTGGw2ujfgkIvTgpbO22mKCwJuVLfPrD0JMIhG1y16m2e4tJdCaGEFpsTSD\nTiaiOX1ac+89kS9+wbLQib9+QYOSjls7RVTdhqlbhFbmAB3k99wLBc+9UIkRtYJmvoC4ZDQRiGw8\nKaiGlsYltHZ8yzfP+bZvn7O7r9nZU+ztOb72cmDjycA2Nb+aEuDwrefHfuKt/G8/c4b//Ac+wWee\n2CTgZaaCbABVVxCyO0qz9DgfsSZQ1ANUHKJZoJUjNgeEZoravJukxiRtMErCdMEBAmmTNFoVKF2Q\nYks732U5n5J8g9KGFBwqysZM5WoXlUblwpRSp3EVCDGjvJBM3xFywrOxfycoHVApgsqORmoNI83v\nVSebC6/8bu+LmvKKo+XxY0ZaThS8jBT0NBBt0UYi2qIPa3Ig+T6p34M+72Yi9i9Jl/hl7u5u9vh3\nctwe3vQtrm3Q2lAYzfRwTj0QxwpbVhAje4dTAK4fNWyfPUv7xNOcPr0J3nG0f52lVmyMBwxHm2xO\nNnARloslKI3zga2z57j+2hDvcuJ2WQqVOVsyyRyuEz7KvGlzXHJtb8b167uMNhzVoBbauTFoVYC1\nHB4csFw22KrMQ/ycbq7ANZHXXpty/fqcd73zQt41yyEuFqsd1XTWcunyEQBveWg7eyCK0BtOQpmo\nlc5t9SEmkpKCLxFF+b1o8fPcPFtx/dUFk1NCaIG8a1nbsBhjcMGzeb5k96WG/esNG6eXTDZLifbJ\n7NqizFlreW5m8lywm+c557C2Etal0WgvLjBSJITSX5aSb9i5dBil+brf8pz6sy1/431zfurXNvjo\nbw4wWvO5z9b8wQ8u+Ohvwdd87YJPf6pceTTmIpdiEMmLa1dauTXbLACdu57ZcsbGxgYxJZ59ZpfZ\ntOW+h7bYPD1AEfGxi9DpFpZIjD53sDLH6gpeSqIXHAwtd9874IGdmi/8zg5b2wOKSiB6lEIFheq9\nUQOtdxRWSzCuc5AUrk2MRiVlXbNsFjjvsGWRP2OL0UKAKQqLtkW2sPNSBGMAjcgSQoSQo3r6TqPz\nXo38+T8345VXSp78gs0BspoUlUB+WmA82cDQL/DdNdiRgwTJW2X57Vx1TDYrilCydbbI166QhKJa\n8vMf9nzkt0acOh05c9Zx992w8X2BD3496PcveWD4cd7y2FX+zj9+mB/5p4+zMUr85ifP8Q/++aMk\nFTA9GaV7TzK/FLRYM6hqzGBCWVRM9/ZJvqFIBW3rqMenKUYDMENMtCTXQowoIyblYlCRhEhnKmw9\nQJtIQOObBWQ/T6JYrMmmzxC1RTzdIwRHjC0EvzavSzJRzYbXqstxy7hl10xFPOhM9urLopQeyXHL\nyEwXqEjKEDr5ulaUhcV7J2HYfc2TgndiaqUUuhowmWyilGUxX9Iul0w2htgicbR/De/mJ8eHb/J4\ns0XrjQreOkx5a8uyW0OdX84C+GYe6w46PfH8865BRTE2JkaIkbIqSd5z//ktXrqyx+eeepmf/L9+\nFp2WXL92mcFwzPxgFzsZ8exTX2C+dHzjB/8IRTHA1BanDK88/xwvPvMEJJhsjEneE1xL08yFCBK8\nwJUpCQHGSrL0sNb4kJg3gbES/VdVCcEmaU1UZH1eKRBLvtis0YzGJdf3GgaDiq0zAz71mUtv8GGu\nNmbnz03Y2hwA0l31GXsnPq60WnyQDmB1ocsFrlkt2t55hmNhfM6PHcNJ0WvclFLYohCn/CiFrB4X\nbJwLHF3z7F5bsHV2TGxaEfCXHVVXJhVdkGhRFP2MoZvtkQIxGVmkdefm4nsfxxQjrXdCGNKai59J\nnPnrsPXtkf/4qw755u+a8+wzFf/8x7b5hm9s+Kf/bIfZTPHDP7xNtqyBKGkaxtrs4KJy8bU9OxNE\n8K2VmBGgxUrrhef2aRrP299zIYutYyYW5M80w8gqE1ZctsiLcWX+nciWX0phLdQDzYW7h4w3ShTC\neFUhZsG4bHZsoTGmJEYRmOtsMj6elFx+5YiqNgxGRhLgjeTEx1aKb8oXjFwXQk5IKpGSdDDaaJxb\nrDqClIkuMUCCP/iNLeNx4sO/OsEYGcxLrJbB6lJmgl6kHT0yoVdykJi76BAi2qyuxXpg8iag6K+B\nFANaebxyLKOiOa44OHa88PKSxz9X8Md+RLqPT29c5Pvf+xc5pGXvtWf5kz/w7ahWfFOVdRIwm913\neg1VSpl1K5W5MAMmownT2T7Hh69ST7YZDM4xGFlgQdQNIU4lHio1+LDALxfMl8d451G6pCjHlPWE\nycYmRT2gCkIuIzq8K4iuhSQQN8pAMUGrSAothCWq1cS0EOQ0u/dEU0ijpWVgLz6gJhe8DKErSNn+\nSkyxNSiL1gVKG3HA8UsIzQn/0A5yjTHiFbi26b/zXae4KngdSpRybFRJigZVKobVgPGpIdODHYIP\noApQYa1bvPNjvVh9KR3bujfmjQXvRmjxZrO9mzm0/F4cty160+Mj6rqmsBbvHEYp5oslwQfa6DAK\nvu+b38svfPJpPvP0K/zoT/0S3/+h9/HZ3/44v/PpzxJQvOd97+HJAmA2cAAAIABJREFUJ55kZ2ef\nt731LZw7fzdH+we0yxmvvvAUy9kho9pw8fwF2mbO3vUdJuMRSSV0sPgE7WIhfodGSBnHB0dAEucK\nhJpdFgWDwYDjeYMLifl8Iaw0UxEy9Vyh2DxVcmqz6E/Sqc1Ta7T57kIQc9+miTz19C5GK+67ezN7\nPdITY9QaXCGQ5Fr6gpKZoTbmhIOAzie94y+C4tR2zfFuy3ijzCbUCHQaI1GJaJwk0UPVoAA808OW\nppUMN60MqJwubuTi7EyPrbV9NyddkOSvlaXk53Ui0LIqRe+XL9iY4RvnHcsID/5x+Nw7Lb/+5yvu\nfrDhx39sG1D8kx85JZ9JjoAqi1JeO5G6qHK+WiK4lNMIulDWDCcn2dmnCGVR8PzzuzRNy1vffo4Y\nW2ZTR13XAmP3MK3Oi6uwKElkWyw5D9podFqRCGIMOOc4f3Hcd0EC5Sq0UWQ7Vpm7GS2BuM5l1q/n\n7F1DUopcevWIR956Wsymc3OQMkSVYmKxbCEnNcQUUCYvhF1H21mMdQka+b2cPRP40HfM+NEf3SJ6\neSxlNNWgRjSWCvyqg+ugzc6JJeVNRIySAKFNylKNiPeJyWYlmlYr5CLXztDKyRKgaowZiKG1Lrjy\niuf7lOYnzjzMf/mu76HRlnZ3hxBVlucEtIrEpPsONeWNcNfBdIbsKDHpUe0uBy8/zej0XYy37mc0\nOAvuiP3XXmA226GwAxQK305plzOCb1DEHOdUk0yLb5bMjpcECtrlHKMVm5MxrjUsZwofHMpKMoQa\nnsZazexoH7eUkGBiQml5rVqB1rV8z6IDpKOXzUsHgyrAyuYkaYqypqpHUvRMBUinF5p92lmTv90Z\nUqUTUacsXepgSYHFVTfKS6n/zECRgudwf5+6HFENB0wPrrOYXSUtp1JYMrnoK3XcSXG6WaG7XSf3\n5e703sxx26KnNaToSYLQUBUlzgUWTcP0cI/JsMa7wNe98yE+8/QraK3wbs7VV19kPm144JFH2d15\njeef+yIqaZ576vNcu/wqOzs77O1eZWDh9LgWLVcKWReVGNQ1i7bhaD6nzTOg+XRGWYjP5NUDx5nN\nAZuTAc55qrpi+9QZDg6vsnSJg4NDnPcks9qhdVAfaKKKeCdQmbaSZKCS7i/ElFkvnX5NLLrEPb9z\n5xfhcZ5F5flb6kglefHt4M5uTtfFd+gMs4YoRen0dsHulSXXXpmzeabEVJ1bifSG1tpMYjmZbfXy\nMwdceGAkzjlJrZLcyZvuDkbpZ1xJoFyV7bEy4SQleV/CAZGYnBQzzKMUf+uRU/w3Lx7z3w9O0/5c\nidEJ34pm0RQWHwKNc1S1WHwVpkDboi9IKUWxJguaZduSUqKuK4nxcS0pthgtyRbTacuFuycC5yUo\ny4L9/X0mkwlVXcn8r1tUSVJktM6ZcUIxjyqKk7+Sz6QsSmGm5u7cOUfHAE25eBplephUK9G1Bech\nBVIQUbfORarbpRdFgVfZZzVKZJNrBOY0hZU1TilMPmkmd6MprbIQLfDnv++ID//ymN1rBSHHI5ES\nOtu7OR8yQUj3cH93HazgdZ27vLyZQeDdxcxz4d6RpD1o2fSYQlOWA4o0AB9R2qNsxbVLnub4mPHb\nv4m/cs83EfEUyxnH+/vU46FsIlWU95OE4CFSgpQX9th3mErJdeaaJQdH1/B+wfbkLFU1IrkDrjz9\nUZrlaxhjaWYN3rWgFoJamJwfqIxo7bwjMadZBHy0uYAJOiLfa9FMjodjRhubMNxAkWgWM1y7JKkS\nXRRkOSiFFsSBGIlujm8T0Xf2c6uORSeBL0WzKcHTw9GYpMR4X0KmO9/HbtaXU97z/C+E0G/uVqSV\ndehw9afSAR0dg4FFm0Dwc4gLUPL9NlHTkbi+1OPNFps3lhjcvIDdSTf3e1X47kCyECjrAVVVMT3e\nZb5sUcZSlSV+UDNbLtHK8PRLAhE+ev85Hri4zeJ4xl2nN7n7rjNcee1VZkf7vP+rP4DF89LzTxFj\n5PSoZOfKq1ScYnxqi92dayxmM6w1jEYD9o8PWTYtMUNZVVXJhxkTz1065G0PbEmntrHB1vY2L738\nItd3d3FJUZQFCUVdD2idXJhGGwH+lOyclZEdue7tl6IMlFPqNXg+s5JiWrmc9MJf1nLN8oXY7dzj\n2t91Hor74MUDtCOm5MWT3BHe/9YtDvfmXHlpxsVHxiirJKU8z9equiKGxGhDAeIKMz1scU5IC5Wp\nMLogEvrnlrlZ7BdG3RW6FPDZVNhaw2IhKRcqiUBeJ7Hnil6gtwOd+FuPbqFSpEbkG6gcD6MlJFVp\nxYXzU6bHcHw4xCCbpKZp8CnmMammKAqWy6VAcV7IJylLY2JILBee8aSirIq+Mz175jTLpmXv8IDR\ncJSF36l/jynJhiRmwwGNfPGqsmJ6XNC2eTPQwZCp6zpNvwnpZmDSPUFZWFROG08Rrr02ZfvsSODE\nKPPItm0pC5nhlYM6z/CgKGtMYWh9i8oblU7flaIj+dXs69w52N0t+dhvTlDEfkFXRoHSvYE6+XV2\n51LmeioTWYRIoZQSyNoo2ralbWShvfLqjLsfmFCohDaAKoiqoIiWr33vAR/5WMvlF8WdZ3LvH6C+\n5xtJtkH5xPxon8oaynLAIjZEFbJWTssSknzX1AnokaSLFQarZjGb4ZrAaHKB+eEBi+MdwuIK851n\nMbZGlRMCgbIuRNgak7A5kxY2Y5A/VdKoGDAqW9+FRFKWxdyxmM0wRYlrW3Z3d4l2wGTzFEVpGQ7H\nYjsXImVZo5WhbZ2YvvsGRUAHRwhtZkvSox8qOUFzALds2F8esL97CV1KEbXW4hvZsIteUM5fZz+o\nEPg+dYS61bivW2FXf00R5Vu0VcyPdvG+BXeM0k4MDKKsfWmNf/CVOm4227vZcSei9Dtxa/ndPG5b\n9Kz1OLfA2hpjR3g8o3pAAi7v7PK//JtPnrj/F1+4yk/OFvzF73gf06Njnnjqizz02Nv51m/9djbG\nG+zuXOWFZ58j+JbJaMipyRDvPVcuX2Y5n+HahoR4Hw6HQ976lod5+fJljqZTIpHCGrCK3YMFG0PN\nC5ePWbywx2MPL4nK8sq1KXVVUA8NdV2xmLfs7zQMx5byVJE7rkgMERccrcomwoD3WeejyBFmkbbt\nErjBRXF3ab3MDyLQpagbrftkgS7ORuY2AnUYrdDZYNnkdPOYQl5oAynBoLZU50e4xnPpmSkbZ0pO\n3VVJ8dECb4YQJXG7VPhWnjuSKOpCUg4iqLBagZRW1HWZoa4MPWmFzvE+PnhSQmQBzhGczxpFSEGs\nt4rCohIE7yi0oV2Kf6bVFhc90Xka39K0DRcvRr71m4+5dHnOJz4+4oXnLVhDdB5VGIF/U2LhlzSh\nocyEhZTAhSXXri4oK0NdW1SSBAVlhRBTFpakIt41knGoJXVDaaF6Q96QhJCFxzLT+9lfmGSqfxCd\nXBBzb4VaKx5dxl3e4aNoYpJopnyOZlPHhXtU7hghOiEItY3IXJomRxRpRds2lKqWDtBoou6IJxnU\nzuzOFBPXrit+8qdHWCSyp5NzkGmGPWykgChJ7Suto8oQatY7KnGfb9vIay9PWSwC5y7UHB04poct\no0nWDyqDtp4/96eOuefulp/7ebnOJ/d+NZPHvg2VSoyb4+bHHB8fUdlSIH0lMzOJFUp5DrZyLUl5\nM5HyTBclpu2FKUnB00yv08x3wR1TjTYpzZCQ5LymGAQY1ULTR3WPK51x9AoVEkYJXOiixy3J51NM\nJGLrZSPjI4uDJb4sKMuCCsBqhnWibebMlkeo0ohZefJEterYOranSv3WtgMU5NUowAdSXOCWQEgo\nY+k9IUmr+54g+OTmL3fF/SxvreNRyRNcJPqWROwdevoNk+7Qmzd33EoU/mbhyxsf62aPcavH/FLm\niL8b3eBti17CEQJZX2cpByOqkQS6bm+d5j/5zg/w3Ks7fPyJV/iub3iM//djT3Pp2hGfe/46D10Y\ncfb8edqlY7855PjwiJ1rV5kdHxK9Yzk9xKrzgBLbp8xANFYc6+fzOafPbDGsK1RKLJYNiUC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K6haQXFGGycJ2mV524KcW6xaNugjaVtnTAi8bn4snZu1o9ul97pEFfQYV/C1E2HgvRBu1ohJs9S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D39NNbvIMYjWKxRy/JxQ5GPHG2J6hEaq16hlMJ1YzUpyjm8b7BGGKTLrPmpvkw1XlRl+USo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\n2uEx27Ewnm1ZDT2fnXxiMObANI4UlOH56ycnfPLoVHMrJ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2yTRfCuveRVX3TW25My5/g0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oUI1eRUVFRcXRoBq9ioqKioqjQTV6FRUVFRVHg78Al7h/aG2tLRIAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x127105ad0>"
]
}
],
"prompt_number": 305
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Question 4\n",
"\n",
"Suppose $y$ has a binomial distribution with parameters $n$ and $p$, and we are interested in the log-odds value $\\theta = \\log(p/(1 \u2212 p))$. Our prior for $\\theta$ is that $\\theta \\sim N(\\mu, \\sigma^2)$. It follows that the posterior density of $\\theta$ is given, up to a proportionality constant, by:\n",
"\n",
"$$g(\\theta | y) \\propto \\frac{\\exp(y\\theta)}{(1 + exp(\\theta))^n} \\exp\\left[\\frac{-(\\theta \u2212 \\mu)^2}{2\\sigma^2}\\right]$$\n",
"\n",
"For example, suppose we are interested in learning about the probability that a possibly-biased coin lands heads when tossed. *A priori* we believe that the coin is fair, so we assign $\\theta$ a $N(0,.25)$ prior. We toss the coin $n = 5$ times and obtain $y = 5$ heads.\n",
"\n",
"1. Using a normal approximation to the posterior density, compute the probability that the coin is biased toward heads (i.e., that \u03b8 is positive).\n",
"2. Using the prior density as a proposal density, design a rejection algorithm for sampling from the posterior distribution. Using simulated draws from your algorithm, approximate the probability that the coin is biased toward heads.\n",
"3. Using the prior density as a proposal density, simulate values from the posterior distribution using the SIR algorithm. Approximate the probability that the coin is biased toward heads."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solution to Part 1"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def logodds_post(theta, n=5, y=5, mu=0, sigma2=0.25):\n",
" \n",
" lpost = y*theta - n*np.log(1. + np.exp(theta))\n",
" lpost -= (theta - mu)**2 / (2*sigma2)\n",
" \n",
" return lpost"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 296
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"logodds_post_min = lambda *args: -logodds_post(*args)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 297
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from scipy.optimize import fmin_bfgs\n",
"\n",
"opt = fmin_bfgs(logodds_post_min, 1., full_output=True)\n",
"mode, var = opt[0], opt[3]\n",
"mode, var"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Optimization terminated successfully.\n",
" Current function value: 2.869167\n",
" Iterations: 3\n",
" Function evaluations: 15\n",
" Gradient evaluations: 5\n"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 298,
"text": [
"(array([ 0.47831325]), array([[ 0.19307885]]))"
]
}
],
"prompt_number": 298
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Probability that coin is biased:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from scipy.stats.distributions import norm\n",
"\n",
"1. - norm.cdf(0, loc=mode[0], scale=np.sqrt(var[0][0]))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 299,
"text": [
"0.8618219756399822"
]
}
],
"prompt_number": 299
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solution to Part 2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First need to calculate scaling constant `C`:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def calc_diff(theta):\n",
" \n",
" return logodds_post(theta) - norm.logpdf(theta, loc=0, scale=0.25)\n",
"\n",
"calc_diff_min = lambda *args: -calc_diff(*args)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 300
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"opt = fmin_bfgs(calc_diff_min, \n",
" 1, \n",
" full_output=True)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Warning: Desired error not necessarily achieved due to precision loss.\n",
" Current function value: -3.966336\n",
" Iterations: 0\n",
" Function evaluations: 57\n",
" Gradient evaluations: 17\n"
]
}
],
"prompt_number": 301
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"c = opt[1]\n",
"c"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 302,
"text": [
"array([-3.96633573])"
]
}
],
"prompt_number": 302
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def reject(n, c, mu=0, s=0.25):\n",
" \n",
" k = len(mode)\n",
" \n",
" # Draw samples from g(theta)\n",
" theta = norm.rvs(loc=mu, scale=s, size=n)\n",
" \n",
" # Calculate probability under g(theta)\n",
" gvals = norm.logpdf(theta, loc=mu, scale=np.sqrt(s))\n",
"\n",
" # Calculate probability under f(theta)\n",
" fvals = np.array([logodds_post(t) for t in theta])\n",
" \n",
" # Calculate acceptance probability\n",
" p = np.exp(fvals - gvals + c)\n",
" \n",
" return theta[np.random.random(n) < p]"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 306
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"nsamples = 1000000\n",
"samples = reject(nsamples, c)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 307
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"np.mean(samples>0)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 308,
"text": [
"0.72345679012345676"
]
}
],
"prompt_number": 308
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solution to Part 3"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"n = 100000\n",
"mu, s = mode[0], var[0][0]\n",
"theta = norm.rvs(loc=mu, scale=np.sqrt(s), size=n)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 317
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"f_theta = np.array([logodds_post(t) for t in theta])"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 318
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"q_theta = norm.logpdf(theta, loc=mu, scale=np.sqrt(s))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 319
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Importance weights"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"w = np.exp(f_theta - q_theta - max(f_theta - q_theta))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 320
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"p_sir = w/w.sum()"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 321
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"theta_sir = theta[np.random.choice(range(len(theta)), size=10000, p=p_sir)]"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 322
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.hist(theta_sir)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 323,
"text": [
"(array([ 6., 32., 314., 1304., 2769., 3037., 1818., 595.,\n",
" 115., 10.]),\n",
" array([-1.40089395, -1.03821797, -0.675542 , -0.31286602, 0.04980996,\n",
" 0.41248593, 0.77516191, 1.13783788, 1.50051386, 1.86318984,\n",
" 2.22586581]),\n",
" <a list of 10 Patch objects>)"
]
},
{
"metadata": {},
"output_type": "display_data",
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H+fPncTgcVFVV0dTUBIDP56O+vp6WlhbsdjuhUAibzQZAKBQiEokwOTlJIBDQHUMiInli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\n",
"text": [
"<matplotlib.figure.Figure at 0x1151076d0>"
]
}
],
"prompt_number": 323
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"np.mean(theta_sir>0)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 324,
"text": [
"0.86140000000000005"
]
}
],
"prompt_number": 324
}
],
"metadata": {}
}
]
}
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