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@ChadFulton
Last active August 25, 2017 23:00
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Markov Switching Model - Mixture of Gammas
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"\n",
"import numpy as np\n",
"import pandas as pd\n",
"import statsmodels.api as sm\n",
"import matplotlib.pyplot as plt\n",
"\n",
"from scipy.stats import gamma\n",
"import scipy.special as sc\n",
"from scipy import optimize\n",
"from statsmodels.tsa.regime_switching import markov_switching\n",
"\n",
"np.set_printoptions(suppress=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simulate some data from a mixture of two Gammas"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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XVa5vH3/5XSo3kQNEZJWqdkdZNk3O/rMA3i8ib5BaVPUhAOtSfF6uSjOI07Jb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\nKQb7REREREQlxWCfiIiIiKik/j9IBv8L84j4QAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10f207490>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"np.random.seed(1234)\n",
"\n",
"# Set the simulation parameters\n",
"nobs = 200\n",
"obs = np.arange(nobs)\n",
"k0, theta0 = (1., 2.)\n",
"k1, theta1 = (7.5, 1.)\n",
"\n",
"# Construct the regime index\n",
"ix = np.random.random(size=nobs)\n",
"ix = ix > np.median(ix)\n",
"\n",
"# Construct the simulated values\n",
"endog = np.zeros((nobs, 1))\n",
"endog[ix] = theta0 * gamma.rvs(k0, size=(nobs // 2, 1))\n",
"endog[~ix] = theta1 * gamma.rvs(k1, size=(nobs // 2, 1))\n",
"\n",
"# Plot the regimes / observed data\n",
"fig, ax = plt.subplots(figsize=(13, 4))\n",
"ax.scatter(obs[ix], endog[ix, 0], color='C0', marker='x', label=r'$k=0$')\n",
"ax.scatter(obs[~ix], endog[~ix, 0], color='C1', marker='^', label=r'$k=1$')\n",
"ax.legend()\n",
"ax.set(title='Simulated data from mixture of Gammas: regimes denoted $k = 0, 1$');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Construct the model class"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"class MarkovSwitchingGamma(markov_switching.MarkovSwitching):\n",
" def __init__(self, endog, k_regimes, order=0, exog_tvtp=None, exog=None, dates=None,\n",
" freq=None, missing='none'):\n",
"\n",
" # Initialize the base model\n",
" super(MarkovSwitchingGamma, self).__init__(\n",
" endog, k_regimes, order=order, exog_tvtp=exog_tvtp, exog=exog,\n",
" dates=dates, freq=freq, missing=missing)\n",
"\n",
" # Setup the additional parameters\n",
" self.parameters['shape'] = 1\n",
" self.parameters['scale'] = 1\n",
" \n",
" def predict_conditional(self, params):\n",
" params = np.array(params, ndmin=1)\n",
" \n",
" # Get parameters in each regime\n",
" k = np.reshape(params[self.parameters['shape']], (self.k_regimes, 1))\n",
" theta = np.reshape(params[self.parameters['scale']], (self.k_regimes, 1))\n",
" \n",
" # Means (k_regimes, 1)\n",
" predict = np.repeat(k * theta, self.nobs, axis=1)\n",
"\n",
" return predict[:, None, :]\n",
"\n",
" def _conditional_likelihoods(self, params):\n",
" \"\"\"\n",
" Compute likelihoods conditional on the current period's regime\n",
" \"\"\"\n",
" \n",
" # Get parameters in each regime\n",
" k = np.reshape(params[self.parameters['shape']], (self.k_regimes, 1))\n",
" theta = np.reshape(params[self.parameters['scale']], (self.k_regimes, 1))\n",
" \n",
" # Get the scaled data by regimes (self.k_regimes x nobs)\n",
" endog = np.repeat(self.endog[None, :], self.k_regimes, axis=0) / theta\n",
"\n",
" # Compute the conditional likelihoods (self.k_regimes x nobs)\n",
" # conditional_likelihoods = alpha**beta * endog**(alpha - 1) * np.exp(- beta * endog) / gamma_fn(alpha)\n",
" conditional_likelihoods = endog**(k - 1) * np.exp(- endog) / (theta * sc.gamma(k))\n",
" \n",
" # Repeat across an additional prepended self.k_regimes dimension\n",
" # (the filter requires at least two self.k_regimes dimensions)\n",
" conditional_likelihoods = np.repeat(conditional_likelihoods[:, None, :],\n",
" self.k_regimes, axis=1)\n",
"\n",
" return conditional_likelihoods\n",
" \n",
" def transform_params(self, unconstrained):\n",
" # Inherited parameters\n",
" constrained = super(MarkovSwitchingGamma, self).transform_params(\n",
" unconstrained)\n",
"\n",
" # Force shape, scale to be positive\n",
" constrained[self.parameters['shape']] = (\n",
" unconstrained[self.parameters['shape']]**2)\n",
" constrained[self.parameters['scale']] = (\n",
" unconstrained[self.parameters['scale']]**2)\n",
"\n",
" return constrained\n",
"\n",
" def untransform_params(self, constrained):\n",
" # Inherited parameters\n",
" unconstrained = super(MarkovSwitchingGamma, self).untransform_params(\n",
" constrained)\n",
"\n",
" # Force shape, scale to be positive\n",
" unconstrained[self.parameters['shape']] = (\n",
" constrained[self.parameters['shape']]**0.5)\n",
" unconstrained[self.parameters['scale']] = (\n",
" constrained[self.parameters['scale']]**0.5)\n",
"\n",
" return unconstrained\n",
" \n",
" @property\n",
" def start_params(self):\n",
" # Inherited parameters\n",
" params = markov_switching.MarkovSwitching.start_params.fget(self)\n",
" \n",
" params[self.parameters['shape']] = 0.5\n",
" params[self.parameters['scale']] = 0.5\n",
" \n",
" return params\n",
" \n",
" @property\n",
" def param_names(self):\n",
" # Inherited parameters\n",
" param_names = np.array(\n",
" markov_switching.MarkovSwitching.param_names.fget(self),\n",
" dtype=object)\n",
" \n",
" shape_names = ['shape[%d]' % i for i in range(self.k_regimes)]\n",
" scale_names = ['scale[%d]' % i for i in range(self.k_regimes)]\n",
" \n",
" param_names[self.parameters['shape']] = shape_names\n",
" param_names[self.parameters['scale']] = scale_names\n",
" \n",
" \n",
" return param_names.tolist()\n",
" \n",
" def _em_iteration(self, params0):\n",
" # Inherited parameters\n",
" result, params1 = super(MarkovSwitchingGamma, self)._em_iteration(params0)\n",
"\n",
" tmp = result.smoothed_marginal_probabilities\n",
"\n",
" # Shape\n",
" shape = np.zeros(self.k_regimes)\n",
" scale = np.zeros(self.k_regimes)\n",
" for i in range(self.k_regimes):\n",
" y = tmp[i] * self.endog\n",
" ybar = np.sum(y)\n",
" pibar = np.sum(tmp[i])\n",
" \n",
" s = np.log(ybar / pibar) - np.sum(tmp[i] * np.log(self.endog)) / pibar\n",
" func = lambda a: np.log(a) - sc.digamma(a) - s\n",
" aest = (3-s + np.sqrt((s-3)**2 + 24*s)) / (12*s)\n",
" xa = aest*(1-0.4)\n",
" xb = aest*(1+0.4)\n",
" shape[i] = optimize.brentq(func, xa, xb, disp=0)\n",
" \n",
" scale[i] = ybar / (pibar * shape[i])\n",
"\n",
" params1[self.parameters['shape']] = shape\n",
" params1[self.parameters['scale']] = scale\n",
"\n",
" return result, params1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Create and fit the model"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Markov Switching Model Results \n",
"================================================================================\n",
"Dep. Variable: y No. Observations: 200\n",
"Model: MarkovSwitchingGamma Log Likelihood -498.430\n",
"Date: Fri, 25 Aug 2017 AIC 1008.860\n",
"Time: 18:57:44 BIC 1028.650\n",
"Sample: 0 HQIC 1016.869\n",
" - 200 \n",
"Covariance Type: approx \n",
" Regime 0 parameters \n",
"==============================================================================\n",
" coef std err z P>|z| [0.025 0.975]\n",
"------------------------------------------------------------------------------\n",
"shape 0.9357 0.123 7.604 0.000 0.694 1.177\n",
"scale 2.8865 0.995 2.901 0.004 0.936 4.837\n",
" Regime 1 parameters \n",
"==============================================================================\n",
" coef std err z P>|z| [0.025 0.975]\n",
"------------------------------------------------------------------------------\n",
"shape 8.7396 2.895 3.018 0.003 3.065 14.415\n",
"scale 0.8932 0.271 3.291 0.001 0.361 1.425\n",
" Regime transition parameters \n",
"==============================================================================\n",
" coef std err z P>|z| [0.025 0.975]\n",
"------------------------------------------------------------------------------\n",
"p[0->0] 0.5942 0.108 5.490 0.000 0.382 0.806\n",
"p[1->0] 0.5688 0.127 4.477 0.000 0.320 0.818\n",
"==============================================================================\n",
"\n",
"Warnings:\n",
"[1] Covariance matrix calculated using numerical differentiation.\n"
]
}
],
"source": [
"mod = MarkovSwitchingGamma(endog, k_regimes=2)\n",
"res = mod.fit(search_reps=10)\n",
"print(res.summary())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Classification\n",
"\n",
"For example, classify the data into regimes according to whether or which regime has greater than 50% smoothed marginal probability.\n",
"\n",
"The plot shows that the model only misclassifies a few data points. In the plot below, the opacity of the correctly classified points is lower to highlight the misclassified data points."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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gbty4kYULF7Jnzx5Gjx494vkkeuo77TOp/YalgEBEREREsqH+ZnlHDlYugxtxlGDdunVc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\nRK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10f489910>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Classify the data based on the smoothed marginal probabilities\n",
"smoothed_ix = res.smoothed_marginal_probabilities[:, 0] > 0.5\n",
"\n",
"# Plot the regimes / observed data + classification\n",
"fig, ax = plt.subplots(figsize=(13, 4))\n",
"\n",
"label_00 = False\n",
"label_01 = False\n",
"label_10 = False\n",
"label_11 = False\n",
"for i in range(mod.nobs):\n",
" color = 'C0' if ix[i] else 'C1'\n",
" marker = 'x' if smoothed_ix[i] else '^'\n",
" if (ix[i] and smoothed_ix[i]) or (not ix[i] and not smoothed_ix[i]):\n",
" alpha = 0.2\n",
" else:\n",
" alpha = 1\n",
"\n",
" label = None\n",
" if ix[i] and smoothed_ix[i] and not label_00:\n",
" label = '$k = 0, \\hat k = 0$'\n",
" label_00 = True\n",
" elif not ix[i] and smoothed_ix[i] and not label_01:\n",
" label = '$k = 0, \\hat k = 1$'\n",
" label_01 = True\n",
" elif ix[i] and not smoothed_ix[i] and not label_10:\n",
" label = '$k = 1, \\hat k = 0$'\n",
" label_10 = True\n",
" elif not ix[i] and not smoothed_ix[i] and not label_11:\n",
" label = '$k = 1, \\hat k = 1$'\n",
" label_11 = True\n",
"\n",
" ax.scatter(i, endog[i, 0], c=color, marker=marker, label=label, alpha=alpha)\n",
"\n",
"ax.legend()\n",
"ax.set(title='Classified data from mixture of Gammas: regimes denoted $k = 0, 1$; classifications $\\hat k = 0, 1$');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Predicted values"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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8vgEA8Ol/XohBPmeVR0RUkqAkwxdf0XaKQp9YGZQUqyv72r24FoWXamCcoFIX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pdXYN+dZc05z32X7uPliy/n3uObBF5hrIxH/62Ymo5BaSWbH3CiSIZm9rV29V+8+gDT+RRH9g5n\nvLZiBULRJmMUY8ZWN6vSBY79k6qQmgLk0HRo3bYRhk8xVYq71Gqt7UY0ueYL01iiMHZDbbg1pNdt\n+qJjw64iA+UIBKNTaRrsF6zR+t6MUYilO1o7nx3TnRO69zLJHK7b6xhYCJmN9ejJMA3BUk4x3/1e\n+44fqqKlxD0uWvNIc4y1aaDsOi1hkbNycXdL93K58WjGOF2OwESHesdRhdamHbO2u4nXXTXPjftH\nu+FkjALBiALbZGw6G8ggw3yx93srZ0aDfT02FgqTg33tIKJZHlCSnrf81Vv47InPjnyektNksAyL\ntCiMbMiWjLURrjOxbtfXnZMje81UMW7Ep2U8ATYpY2tmH8DVTeo63YxOyihMXF+QDF3/E3d3jZhF\nvQH3p96TrJ36N6oXyZVVdifZFTgqrs2mRjPdM3GzvOHrd0CLnNkFgFcvRW4tCQBiksfbJWDrec8w\nwJWtoU3ctEOKHQwe7t2wibnFgU0TKpf6upHXI+eoSZh9AMNq9zD7/d9T1yGrd096z13v4Xce/J2x\n76HDZZOC2Vsns1jOEHrFmPTqebwfIkw1BpOuQhVrAZHeHGtP3AmbIEUsuwSYyuUgzGyb2ZdSsumu\nIL0K18yp72uzszlQLKrvUbJx5E6iHdSRQa7H9KCYKoIUeOH2xqVLnYzo+tHPZBYQIuBCY52vnv8q\nADkrF7sIJiMIAz78yIf54c/8cFyzoK0ptwqNIbScb7GcxT7/Q9hn3zOQ+U7GUjmLlPDgmc34IK5x\nyYZdVeYUxvAxqmWPw8B+KTUdH5r1AaTep5w43zqPJCRvLJJNmeyfmkNKg0stdW8uRvars5m9yDA1\n1n78+RIveLBfsqYIjWaPveKwaHkNCHOYhqCQNjGDeTxpc655juXs9TQ6PqFf5NKY1L/WAFfS3cUs\nY5nIIDuSidcgW+vhlqdyPPDLt/O6q4Y7LxTSatIMA9dSKkY7axZiwFnt1CP/8ojl6S/WSo0udNIt\n3svpUnyC1uy7lvMsFqYHCvOSEYQB7aBB6C4MvE/VrSGDPCJqOFQb4bWvXXwq6TGA0iwgRQc/9ONu\npFlzCzY0oyvxezX7Iixx84HZkc4/+6cXETI7lNkP6HUWqKQWIbURuyL1hxuEmJaqpVCFZ8p//bI1\n1Qq6xW0zkVXiersWOXzYPZ0dn63ImAXkBMC45m4iwuJA9qYcbbwbncHxobsiTk9ovQmwXJlBhhZn\nE8z+I2uP4IVe3AJ+WHhhGxM1VjNmocfadlRcaqjrq4wC+9G6YCekCsr5ysGOmu6EQjlijQv9ehrY\n6r4eysqzOJHkqD882SIlCuSsHEKmYscs3RSnf+zotUVv0NoycTZXIS3ycdE8TAb2u/VOg2DfCRyk\n8Hq6+Grd/lxCAmmJywv21fonh3b+zVpZLFmkI3sJIdXluUVqi0zjfF6BqX7g0fYnZPYjsC+sFi3X\nH2iap0NJPEUPa+2HPseqx3i6+vTY99CfJzBqlKze61koZXHdAmtD3N3cIERYugi9O1en0osYqc2x\nXvtu2MIg19NjoJxNQZDfNrO/6WziSxdLznJ4Vu1Jq20N9gM82UnIeNSBcjfRCRpYFHqypYYwMMlu\na1xKKQlokjO7c24+Olwer57jq+e+ymx2lpsWbxoq4/mDR/6A37r/t3jd8uv4y+/7S2BruY8OfXhf\nKqrvbbGcAZkCmY6NSIbFYqRO6Hghh+ciO9xoD1ppb/bUqw2SkJqI6675+hA5neniK93Qq18VoIm4\nuYwyEJkrZpF+MT4wnKldRIZprlmcQwb5WKnwfI4XPNivZKYRZov6EGumZNhBI+5yKYSILesA3KYq\nSJFBKa7mHhb6RJ3UDxuGKhIb1VRo064igyzlbBdYjpKqgGqeImRmKNh3AgdEQM4qxprgmlPHC2R8\ngu53p9EL7zCGREuAKuluWlP7dXdlT9NkjCLBCLCvALwkdNThJQn2604dglyc1diK2R/VPRIgHzEB\nLa+F46tupP1Fkf3RtUXtLhQr7TVcp8Brrxq9se6bLiC9uQGv/Y4fFUEnFq7p9BLC8FgZYW/q+iGG\nacdgTVucXi4Zj+q7oFixuYgF2ejUaLhNhBhMnz4bkTUUMN7KEq7lV0kxeD2VuAhrcGNvelWQKfKp\n8UAqGQulLNIvxSwPwOMbqlnLuA3Qo42FSqFnjUJP07pRoWtbpnO9khddU6MzdLoeoJQuxYcbXZga\nCpusMX4s6+9RM5HVTg0pBaV0keyYPgXjwqd7yLAoxJ0m234DpIg/gw5ddKy/Jy1hmi9MkTaKSOHF\nDZfafhMZ5simRm9R+vVbQ8wNhsmj3vXKfbz/B46wVOmupSkmq62YNDQ5Ux7RxC0jZnFFL1i3fRtJ\nQFqM/w4Xirqjee84b4fq563AfiyrMlqRjCdq8Nc3xw1hqFqiBNhcbasmktpSc1xsdjZB+Mxk+8B+\nOYP0S0ML310/RFhqbCZtcmcyexBWnYYz6GAUPzdsY9HXgTprEfiFbWutNas9nV6IwevF5nrc1A6I\n3XiAXY2dUIZRXcng925NWPOjQzWoa1Gwut/l3qix1snqWe69cC+37r2VpfzS0O7gR1eP8qKpF/HB\nN3yQ/aX9ZMzMxF3ENZCejbL7iwnzkPFgv/u4Q/ORxC7ag1aamwqXjDyQ9hIH0CVT5/JdsK9xSb87\nod6bdRPM6bwyI9mMmimebVxEemWuWSwjg/zYpqDPl3jBg/3pzAxChFyoj0/TdIJWzNpB90RYyVR4\n6qw6mUu/MNazf81egzDPUqkXUI8rEluzN5BDir3GhSlzQ1OAegMsWEWmEydePwzjItB+Zn8+mjgb\nQxqPaa1eOVMe0Bg33K7sKWcWR+qXNfMSM/uJQ0XTU52DdcORsWBfGgO+3snIWd20nxMx+zlrPLM/\nlRlkBdbaa0i/OGCrl4x9Mzk8e2bAa19nN5L3eCajFuQT1eEOCcpnv3tAULr6y9dUqxM0Y1ZMez1X\nO9WuNeNzwOznLCVL2eozdcIqGWPwejTDuzmkl0M7qGHJ0ZaUw2KhpEDJRkJu8Pj61mDfpws6lBd+\nh2CLjKEG+zozpiNn5UAa8aHdCdsgU6TNdAw0YvlKlK0bF10mUm2eDVf5uufTFnmrNFEWIhle6BEK\nh0wEVFKiiBN1d+0ESpLS3811KvqeVqPPrBn5+cJULKnT467tNyDIkhvD7HfNCAaZ/Rh0J8bvQinL\nu2852PO4tDFZvcikod+30levoCNnzOKLPhlOBFgyxvjvcKmo1uJ+4NEJqxhktzzQxmSI2YpZU4EY\natmaMQo9rPXFdq9Lybg4VVOAeS670PP7hVIGGRRpePWBjqQKTKu9Iwn257NLCCE52xgtKfFokRK9\nDmHlbEoxstsE+xeb6nPuKexhppBDBjnWIpY5mQnR8ymcoC5nVLS8FiCHykkV2J98Tqqu1a3YhQjg\nipIqCP/KhS9TdarcunwreXOadXt9wOzifOu8ao4nBEII5nPzEx3sIGp4GWZJmWpPXEzUE44yzAB6\nDt2HIxmP3oPW7E28vgNWMsoa7Dt9YD/MMF/ozvmYEOiTSZ9pnIEww76yGqOmIbBkmYanxsul9gqh\nX+aaxRIyyH9HuPFMjiC/E6K5AheOwoWH4OJR2DzFrX6LzxWBj/9TOPhauOYOOPBaSGUhDCFiXFWX\ny2gi+Q7fyzH+h4SbPMHhEx/mpctH+JTtsBG0cL72ITKeDftvgStuBlPd5jV7jdArslTJQODB2fvg\nzNc5FG6QaV+C370V9r8abv5xWDwCaN16Xmn6Ag9OfBme/jv1/1ZWXafbhsYFaFwEe4PlrM1+7x74\n7zfC1W9Wrzd7ZQyGCqkS+VQagjTiwj+Q/uPP8RrL4H4iUCClukcP/DE/eeab3DMLG//wX+HBv4bD\n3wVXfQ/kZ2J5y3Suy3QcqH0RPvwFClJgyCyGIShYRQgcvL/6SVJSwkvfBYe+CwwjPkSE3jTIFNXa\nafj674Np0fY2kcF+FqdmOAPUT90DD98FyzfBkX8Kec10bUBYYCqfgTBQ9/X43VA7o+5J4yJv79R4\naAYaf/o2DqaWyBgNCma0ObotePjj8OCfqu/bTIGR4iY/gDJMP/a78NifwPVvY8NeIwwOU8hY4DTh\nxD2w9hR0auo/p8EPbDZ4MjjJ3a0W3p2/QGrxCCy8GDPyPI5ZisYlXrX2Nf4GWP3S++DQbbD3Rtjz\nUsipRc8LJJg25Uj6VU4VyZs13vLYz4O9H276l7D8chiT7RkXbtjCiu7DTASMrjv525Qdl3tmoGxE\nzEz9PBz9S3jsU+rnwgIU5wGh5lXzEnSqYGbUmLRy0b/Rf6lc918poXkRGpegtcrLjQ6PF8D87ZfC\nnhvg5n8Nh7974DN5NJgyo0JfpxnNhc/xutMPQxEyRz8Ej/wZXPdWeNm/gOI8nbBOWksqAg9OfQWe\nvBNOfw38jvpd6IEwwUyDmWbeTHFzuMFa/Rz8xY/A/lt4fPUoEDULalyEzVOQKcL8dWAoUBvQJi/U\nmMybeYRhE/7JD2BmK/CKfxWP+WRo6dGcZvYvPgIPfRRx7n5KIuSG2qfhd/6OvekpLqaiZlCRvGz/\ng7+CfExgGm3yRgR2nAYc/V/w0J+BvQnCAMOkbAB5+Lf8IXz47/ByKUSYIZcyI3cfB/djP0baMOFl\nPzL0WpPRjIpiNVDJiyxWeBo+8v0s+zXORNdKGMDJf4Cj/4t/duIbfHgGOvf+Ftz/UYqhBdKklM6R\nNfIgof7Zn2PO6eD7a4jwsJLxeDY89mk1/loravyEASUZQAleufJh+NBfwfVvh5veA4U5Vpo62xfd\n1+ppdV/OfAOyFcjPQm6KV3Qe4bN5F+/3Xk+qsg9e8WNw+I1jP/u40GA/BtYbJ+DRv4LzD0Knxi2t\n03whF8DHfkzN9eWbqOeKPfeS+gX41p/DM58Htwm+A36H+f+fvfeOl+Qqz/y/VdXVXZ3DzXeSZjSj\niDIWQthkIRDBBhsMNtEBG9j1endtg9Ma7LUNLHgDP8AmRy02IAyIJAkQVhiFUUAozkiaGc2dO3Nj\n386hwvn9cepUp+q+PaOxMQvv53M/gju3Q1Wd8Jz3fd7n0QRk4YJH3w2fuwbOfQWc9WLalIhpPsBx\nbTh6Fzz2fbkGVhbBP2/mdR1y8Av1L/JbZoFPRGDVSMhDmRDwxF65Bh65nfl4i7xxHPGBp6Kd+UKO\nz54OyIRL025glRagWYbZ8yDSm709uCFVyGYTU+A6UHoCDu/loodu5HfFnXwSWLv295gt7IYtT4Xt\nl/kVzK7MvhCwdD8XLt/JV4D6D94Bu54D8xf2rI8gD7BJX3UJ14ZHvsWLf/T33C2O8PhaBK75Hcjv\ngDNfBHMXjlwrVWZ/e3aeXEwn4kapr9xH5rvv4JfNVb6DD/Z98PkM4w7EZ1+Btvv5cl9LjO/noQBk\nQmXjq8tw/zVw6CZ2tI6heUfgA5fIuXjpb8P02UPfq9KSYD+gsjbLnL1yO4aAu45/BzSYP7jAX915\nEDEnWH34a8w6LqRnYevPcax6jKfOPFW+tr7OtGGxsnYA9l8HngMTp8PkGaH3ru50WA94HrPrd/A+\n8++ZpsjMzTfA1G4539Yfh5WHYe1xcNtM6AbfitUoeknOvOMSmNzF2dUohqchHvs65zW+yzMjGnfS\ntWcuPwz3fJa3Hf4B35uG8q3/B+74Auy5gtX6UXDTFBJmgK+MxbuJeTp7Nr4NH/kBnPFCuPj1HNw4\njNueYD4fl+vL8kOcLmqs2sfh/76GWvsgGWeeM2eSGG6MRvM43PAuef3n/CLMnn/Se+6PK366wP7H\nr4DiIfm/8zthYjfpVhw4ypKZ4ux7Pgd3fpSvZAvs1KJcWFoBIdU3Mtu2sttega++DR7+Jm9trENm\nmqfpRS7RvwArsD2d5F1MsH79nzLn+qodsawEyJl5ltf2scO1efWjfwh33S0XcmD79CyHiMmJd8/n\nYN/H5UFh17Oprj/Cds/j6Q+8C777XWisg5mQoMlugtOQwCozB+k5mD6bSOkhlnSq98YAACAASURB\nVHQNJnfBHf8At30Qdj+fUl5aSF+wdhM7v3cdM6KOUbwXxBTnm0vcJ9LE/vENUDkKx38EEYt8+hwA\n1utrcOxx+OHVEhhtfzoZLQoanL7/i8Tu+Ttinsdk8wFwZkhrq5xumnD1q7ly5T4eyhlU9n+TggDu\n+wJkt8M5L2PD55u+QdzEd12b9Xs+Davyd/aOrbyYIq/d+P94fQ5K9/0j1F2493PwrbfDGVfC7Pms\nL99OznF45cK74f23QW1FgpzktLyn2S0IkQYWKGe3YBx7DG9CcO7hr8AXl+HR70KrBNPnyI3Ec8Bz\n0Fo2lrufNSsPWgrve39F6bRtvMBr8azbfhOuvUsCRQA9AlYOYikmPINz7BbfQ+fIfZ9nl2/o8fFo\nlNcwS2bvh+H2z8GB63keHn922jaWqkfghnd2xmp+J8xfxBVLKe5KLJHeEPDNPyRz+FqiMZ256v3w\nozvg7s/A9Llw1lWgqyyKv7v30GK6/nfwe8Gsu5+G4cB1f0b2ka9BBuKN/cRcE4iS+cpbIX8mLNwJ\nwoOtl4KVkYfLYz+Ub5OegdQMTO4Bt90Zl3YD6usSVKvfOS35+Sn/2cyci1Y+iqctUZq7iMITN8PD\n18LEHrmoRiRodN02QqvwjPq98NHnyc/2bIimiRbOIeZB0c+Gc8M74Xt/DWe9mLx3kElbg0+9RB70\nWyV56Nh+GcQyEuDrEXltbhtcG81tky2W2a/bsPwgxf3f5PiOrZhCsFx8FN5/ZudeWlk5V2fPJ8kK\nO2wbvv0nXH7kS+zLxmisH8S0a/DQ12Bit7ymQA9fIBalxN35j3wKbr5FHrJ1E7Y9DcszWDYsSM6R\nK9/HNk3Op9OKj0AKzPL9NCNpvLzg8sUvwRcXZSKgXZUgbP5CeV3CI+21ofUAx7QkNIqI5jJnGRHO\nvOn3eFbpXu7J6lQfv5ECAn70Rchth7NfBtGknEvCg40jsP4YrD9OJRKBgslzqj+AL+3n/Or9PGHq\nUG6Qi5QwWxp8+Ofl4bmyCLEMZv5CNHGIDd2A6hIT7jEKiQT6P72O163ez59NQOXx74GRwslp/Ap3\nEPvqm+HR6+VBOn+aPFxpOug6Uc3ArN/DUbMgD17ffRfc+Ldw9ssoReTWdtnyt+BTn4BDN8lbPnW2\nHIe1NWhXOCc7wTcTSSrxHIUnbpNjL38anPUSOVb9AzxmXD5rKyvHpBB980yAEKzXZE/Hi9a+Ch/5\nOwnyQT77xAQ5ktT1MtWFfaQeuAaAsmXB3DS/UvsGfP4meb3Ck4eB1Kz8vIhFVrhQu5Mj0QKsHoCv\nvhWujXL61DxGS8DfnSsPQ25b3qP5i2D75T4o0Ug6Lcz6Ptpag1/Q72efaXB3MwaffLGcz+uPQTQN\nu55FrP4oS7qLl96BsfdDHM8koCCB5Mr/PpdtvjcKEUsC9rkL5IF/7VGcxgLkE/zaTb8GN3bUq3JW\nHktMAw3WHv0Os5Wr5T+YCbbNPI3Lo0XuFxrxq39VAsLyAk83DNi+hdXyY3DDjZ15l9shx/fkmeQ4\nxpydhO/8Kdz/ZagcIx+fxbDSbNCCw7fCj/4JfvAeOa7PvAoCk73eytvC8l5MD97x+H9i4uFFzp1M\n4W4cJ7V2Oy+LunyHaTLf+mNS0QKaEFxi/gjWcvDYd+GGv5CJhskzGSdKPmXk+e274HO/LA9owoWJ\n3SRjGsf1iFwHFSY47RdkQpJBkGlulNGMFmct3QQfez4c+yG73DYzW7ewaBqc3ba5+Ka38964xX9g\nmpV//h1mfbPIcsSium2aLY/dBLddCMWDTE1N8HAsCle/svMhySn5+VNnyTHvry255oMIrQXf/CN4\n5JukSkd4gZ7gsJjBfPDLcg6BHJP50+Q1mRaa57K6ukRWL2M++m344Qp7gMK2eVqNJ0jWozzTXONO\n8mSueYtM8BzdB3oEK3kuEQElzZNj99vvYHVuhp0ixesO/TG85x7wq4T5bVtoCcDIyfXhB+9lYcdO\nzrcNXnvXq+AHB0F4PCuf5dPxDN7Kw5TSNr8u7ub8qy/ilUmd77XjcOv/kdd90/uhcLpMLlz6Zj/p\n9e8/frrA/gvfDbG03Aj9krL98F1w+xu54+w38+w3vZTaYzfwl7f/Kc82J7jwvNdKUOI5bDz8ESa9\nlsww7X4eX+G5vO+uPP/xeWfyhu/+kFvfNMMX//kfgX9h7Q3/zNzUeTLr++gNMsNy8AesT6U427Up\nNBtw/q/C6c+BHc/g9s+8Hc98BF53jQRH934e9n0CbvxbqlvnuVC0mD/yGJz1IpnN2f18mTUFOfj6\nTpjrn/51qs4G/NoXZBbyrk/DXZ+kdfRmmJ3m4sWvk9CS2IVJHp15Kqsv+ChXf/JNJLT9aMfuldd8\n1fvgvFdy74E64s6Xc2j3i+DZ/01uXo98Ew58B621ArkoWx/8PCRmMHMW16Wexh/+5ie471MvId5e\nhWP3YsYngRKrb/oWhfzpckO953Nw24dZT8VhssDvaN/nDncrxZmz4TUfwLYb1L7zGjKe4Oza7Vjp\nAutnvwyu+N+w9IDM8v3oS/DwtRTnZjhDCM4ofh/OulIu5nuuCJ4xwI++cwMc/8+sX/YW7hbn4N58\nFUZiqwT6e66Q2eTtl/Xcy/X1OvVrXsChqUvgF/+O8uLduNe/gfO8Zay2C5e9RT6LLRdDNBW8tl5r\n8573fYwkH+aJV3+GXemdsPwQH7/mU8BDZKqr0DgCT38bdyavRDzyX3jkzBfCG35fgtjFe+TPwj6u\nKj3Be1JbyBx/AIq3k951ARV3mfef+2Xe+cJdcP+X5PP9l/9xgpNBftfM3DSFtoC9HyKz/VLgKF+Y\n+W1qjTTwD2R2PReWD8Av/Fe44DUyw3OKY/W6j8CxD3D4me+iMDUHD/4z3PFRuOl9wd9s6Dpix1a2\nOGVIbIfLfhf2XAnbnsaR5SaNb17F4dnL4CXvg5VH4K5PwQ//L2IywXxbBz0H57xUjo1dz5YgdkTs\n+/s/pqpfS+ttt/HQ49fBrX/Cz5kFbnWK1F/4NyQKeySQfeJWOLwX9n8bbfsWzqyvwO370GYvANZ4\n4jVf4ymT87IicsdH5UbRFUYhRzydYut9H5Tr0gvfA+e9EpITlD/xYh6K5eB1n+fOj7+cpDgGi3eT\nyswAG3zn3Hcxd+nz4NoXQmweHvueBBs/91sD1Z6U58BnL+KfeDrvesv7WfjHlyKKy6QXbyaW2wqU\nOfRrX6Mwu0fOz7s/A7d9SG7oKtLzUNgFZ76IcrsItR9yTmM/PPYQ7uTpPC6qeG+7jTs+eiV7oh54\nBmS3wpV/DWe+iEcOVnFveglPbH8OXPFX7PvMq6F9ABb2kdAzQJPKKz+Ot+3ZVD53MTU3j3bgejk/\nL3mDrLj2Zdy9Tz6Du+Lnwxs/KLN++z4BP/wCbdOBqQkufOIrkNkOz/lTOP9VEmyocB2u++I/QOvv\nqfzSBygkZuGhr8OdH4fbPiz3inhO/tduSNDS2Ogc8NECIK3udTmdgkKGpx//uqzOvuC/ywNeTpoL\nPXbNx6Dyvzn+xq+w28zCsXspH/gqrPyA85r74XgMnvH7cNFrB+ZaQgj49EXckno6/O7fwtG74f4v\nUz5yLTuwYNdTITkpn/3OZ/Zkv/1vS/6fnsdNnMWnFl7EFB9mm1WCSkkevJ/5B/K7RpM0v/TbPL52\niOLLr2ZSFDl+w3+E8sMAHN/5dLad9gK5vh65XVYE7vyofI+J3RxMpME9TOuct8CkX0XZcTluYQ/v\n/+uPkuBDrP3qp2DyQllpe/S7xB6+julYg7xnoYkWbLsUTn87j+sXI+59Lfee+2pe/bQ3y8Pw4r1y\nnTx2Lzz4VaLb5tnVWIa9d8v1+CX/k31cyHVfez8x7Tu0fm8fsWZV7lsPfU2OkSESoksz00xHYrip\neZrzz2Jx4R7MfIwHX3I1f/DZdwPfJIOGXjpCPGPySfEs3vTWT5IsPgR3f1buS/d/OfS9+6MUt2B2\nmhdWbgB7Fn7+9+G8V8H0WSz937dwpPag3MNra3DPZ3xMcFPoe0X9Q9FMswiJrXDpmynteAFHvvd+\nDPMgl1/0Zn5zJYXZ2gfsZfkF74Qdz4f1x1k88A1Y+wFzxQWYvYD2Ba8lurGf5erdiN+8AU3X5Z57\n6GY4dIusVAXjX8eanWS7AO75rNxDn/9OfvlbKUp2hDve/jxZYaytyjmgcIsfH/n47UQNnY+/8eeg\nVWFhcZGl697KI3N7+Pb2P+PDN/45BneRLB4EMwVX/g2c9yqu3Vei/djrKZ75fPj5v4SlB1i9/rfY\nVioy3XgMzvsVia+2X876P72eO+OT8KbPwvrjuPs+xeLiNbzCtXGz58JFr4DZ87jz9r042jc48sZ/\npv2Vl3C3uBzOKvD4wf0UjSXEHx1C82w5hu7/Mtz8P+Va+xMSP11g/8wXDfxqq8/ZWmusgxnnjkQK\nB8HR9BQ8788BqUTQ2v/33Jd9ObztLwGo334Y7677+fp9i2ydnSFz5jNZtB4H/oU1TciF9pxflD/I\nbvnlz13K46Wn8rpX/U2PFKGhJWgr3miiAJf/R3j6fwDhsXb15fxz5UJe8/q/5YLtISXCkFKS5KHK\nciTpWXj22+FZf8TB+66Be9/J3md+hdmnXMLy1a8ihYftelQNjVR0Bv6g10xjIuniuUmpca7rsPUS\n+fO8P2fvN94Hq5+m9bYDkMthf/pKKq7kAlZwqemnw3/9PI9e90U49pcsN5ucYVpyIp73KwBs3PcR\nuOcDXFb/GJb9OZJWDCZOp+x3xf+j+4uc9tzfpP7AG1gzE6Abkuoxd77cSIXH8jUv5YljOb76gnfz\nqkvDHftUGXC9UULXZbm4fsbr4DfeFPr3ALGIjnDj0iQHWPMbkN7b+i0ue/1bOX9rOC83nzCJC9nA\nfbh6BHY8Fye7g6+Le4nzEOlfvRryuwFwH1zCs/Ms1Y/LZ3/6c+SPH2/8xK2s628hffnvwyW/T/qB\nz8C+/0HNa8gM+1N/Q/54LkHGp3tMbFJqvOejVzCf3A6/+3EyPiCsuHVani8Ne+XfQnLQT+BURsqn\ngG00K2DulOXwC17tX5OMw0sPw3Wv5rHdfwAvel3P6xNRG+FaHVWWqTPhhX+L+/z/zrHP/hwTUy+E\nX/mbE/pOuegEFaSc28Mt2ahWi74MnE+zdPZV7Mz6LpEXvgYA4TpsfPYS7p78dXjbX7Hw/X+Ehb+h\n2KrIzOz5r5I/fc/ph1/9L9RW72Tx9/cxn+vlHRsksH3edENzsPXT4A9uI7p2GK59CRWvyXpTXvPR\nnb8Bv/P6odcT0SOYWpy2XkcAFTyOOaez8Obvs3D/t+HQO1ltNeVm3DU/ZQbPz352Ae3y4q1w/e9w\n7a738sKXv4LKV/8Ct/h1yk0bW2/RTj4FXvXBnu+QijXBiweSmxtoVJiDP7iWb33lOij/V8qeTdWV\nPN3reT788V+PfE4GCdpKjGD6LLjqvfCi9/DALf8Aj32QH738Dradu2vIiyMkfGnOarsKmVjn2kOS\nKOPEwZvei3js89z4krv5pYsGzefyUV/Pu3qU3dt2w54rKGs1WPkBnzzt73naq18w9L01TcMQSamg\npWmw9RLElos5+snryaSfDb/03k2/X87KsdasABo1XSOR3wOv/eTA3yXNFJrRoNF2oTDL8ew8evkx\nPGyWL/o12PVi+Yfn/pL8b9f9euTaP8RbWqP1jHfAbKcfwASyZgEbn19tZeSefOaLuG33Ml+/4S3s\nyenwii8Gr4k8voawcyzVF/318bnyR4XnsfipSzkw81J467uDMZo+shFINm80N5hJzsDFr5M//cpn\nXc/5wJdfyeEljyeu+hgXbMty7IO/Qd47QtuDoh7BArKv+ypYBSKffx4lQ8NxhTyo+2OPTYQGVJQO\nfgtufgef2P0pPvArV/V8j5jepeaVnICf/8/yEDjkvb9x503w8H/Avvyv4MKXApBwPbzrPoYBzFsX\n87/KNTQjQ4q9rKQm5Do5dSaL8Rh8/we4V3yMdz6c4svfX6CZXMGaaVGbOVvq/m+5RFLk/HuO1jng\n3v+JK0jrW+BPPxV8n/wte9EbtvybRGEoven/vPoidHXdsTTJ6Z14XoKqXcZxPTaMCJPRDNp/urnn\ndcloDeHGA6dtZs5lRdd5pP1MnvW8P+dVvh8RSB+XQFq4sIvly9+C8+Wv8JnGq3nDa99OfkKOk+j9\nS9CAB9ceBGAp/nS0X/o9fvi//gzBV6nogoxVgEveKH8axYED9b/n+Klv0N2alYoBijuuXOa6LaVV\n01i3nJpysH18pcblp8v3mBphB1536rS9Jp6T6WlMAXxN7lZv04ymYePRdOt4bpJ0fHhXe39Ew5RA\nNI0NX70jZ+WxzAi4Fk2niuNJNZ6whtWpdBThJkMbdGt2BeFFyMVlVjuqJQMFB0fUiPlNg6oxb7k2\n2NFebBbRRAwhpFuvaj5TMpuWniIZiyDCZNQ0DXSDUquI56TIjOj879hml4Neg0xIY1p3xCIGwrNo\nOHKhULJcwkmRig0/J2uaxrbcFBGSgfxmj4xYV7ORZRp4do6VxvHQ92p5Nmhe8Br13wFHYt2QG52u\ndxbiMcCK0BrE/ecU0SPowqLhVoLG0H8LNR7V7zHQYKsbwc+RsgTc08mJ/pcTjxoILz7gVbFcr6Lp\nNrkTkN1UMeEriaw0Vnho7SEmYrPsfSjqv+9gk2LDa4PmETNSoOukTeW+GXZNneekJCZTIQ34phbH\n9Z2FHeqBNKNqRK85VYo+RUwZ8YyKqJ5E02XTcNORm2XcNALjNNUs3BOa1vm+XaHWxHQ0DZom/R90\nh4WNEppRHzAJA0jFIgg3Hih2tUUt0JZXKmCVdiVoulPut6MiVDpT0yg2pSHfdFezXlgkfG32blWP\n4LpPItYaRYSbIN9l3NUdk5ZsmjxUPhL8rudebhIRUrS8TkNyqVn3G/jH44rnrTyOb6CI0RiQfFWR\nMtNoekOqvADHa8dxGtLBO7RJt+t+rTVXEHY2VMRgynen7vejUTr7/fLJ0Yg0VVxphq+PTddFM1rS\nT6FrjGasCMKVz3bAI0aN55D1crW5hGfn2JKPE4sYGCRpuuWeZlH1nCxDOlm3u5XRuufLJj8lW7lE\n5wfGWzySAr3ZK8k84r1XfIWrma710TR0DGceS8txcGESXYPT8tMg9J5nqPoU3vrpQ1x9+xM8ZUsW\n4chxEfqs1T3zw6U+0GT828/cxVufs3kVOJ+Mku0aJykrEiTYlM5+2hwco4moAW4ncdB221LQw0mT\nifeOu6ie7FE2WqhKbOe1C8xkO/NUebHcvyrB/nRCJoJVQqDUL+38EwT04Wdgn3zcQjgJNlpFhBDc\nfFSeICt2JWigURtBt/HNVLozSJ5+upxgynkzzFgrMLJw0z06z0AgX1ftc4JUnx806I4ZlhEuZagm\nRs7KEDN1hBen4dVwfMWXhDG42UwkYwgnSbk9CARqThXhWYEWdqxLws/V6li6fD+lNLIWAiaKLamd\nHjV0Ceh9XXS14ceNNKmYgXDjbITo7NueLb+HmyQbH9xcVGRiSYTQ2GiVAinN/g7//ohGdHkg8oGv\nOsRtBvYBtuYTaPY0h8qHAAJtf+gF0DFTR9h5VpvHQqUnm04v6D5ZK/WwsH2FiUSks1BLMFGlLapo\nGIEb479mdKQkB9V0VCyU5aazJT098G+WaYBrDaiyLPgHhG51j3FjJil5mCv1FR5af4iMvgPPluM4\nTKUiSAj4m56qVpRGXBPI5jbhxklGw8B+MlCx8rQGUU0dnuVnNJxaYGgzzqHM0lNgNHA8QcOrghcn\nZhqBWZOS0h0nlI+G+lzVCHtg7bgEnyHSk90bOUidfuVinY51xoC6l7ExwH50iEThRqssJYs3SZKo\nQ8YA2D/JKDZlRjk3ZC3KxQoIL8rhUkeWt9wuI4RGdgywH9XTPWB/sSLHeG5csB/LYyNfP8pHQ5r3\ntak2pRTqYu04TnMaXcQ2VeQptdcQTmYAdAFMp1PoIj4gvymlN6sDfhixiIHXzrPWPBb6WauNjuhE\nd6QtE+HIsTWusVbLbVFzN8DJM+Pv75aexqFF3W6h6Q1iRhzT742KG2o+nZwMskpsFeKDFeK4kUTT\nBOX2eOv8uq8DP9/nFJ5uPZ+ft97HDQ+ucenOAufM5dC9TI+s5tHqUXSibM1OcesfP5e/ecV5CEfe\nz1Fuu6C8e+oDvhJXnDPDL164Zazv3h2moWMIKePb9qU3w/bppJ84UHtGJxGXJhPvXUtjfdLCKpGb\nM2eJRTpqX3MpubfcvyLB/nxKVuGSpjIM/cmW3/ypB/tS5z5FxS7yROUJjlaPctncZUDnBKh0oTMh\nYF/X4NKdcqGdy6QRXixUR1j9Lh3JYxq9t11JrvUbP6hMtnB67bQ3C8tIguYGmtUqym2ZiU/H4j5F\nxaLldmTYkuZgdjAbN9G8JDV3EAg0HAkY1PWoSWV7NkJrBXKXAZgI0aotNosIN8lczkI4SRpODdu1\nu5QK0kFmvxKyIQf3aBOwn4yZ4FmUWhUq/qEqOwbYF148cJJUC4rnpjY9fG0vJGg1JjhUOgQo194G\nhmZiRTqVHcvfzFpeM1Teqyk6ZkrQGYPDfBlOJMrNJpreDjSLQQLMtqgFhkmjPB1OVWSVeVlzuJP1\nUlXOn63ZQbAfN+VhsP8AdNQH+5PxEwf7W9Nyod+/fpDD5cO0anMjs11q7qox3znAjHbnbrhVdJHo\nMdVREdUTeMgDoqc1iPrrRMSIINwYDbca2MArA7hRETOSaHqDaruBK9q+aZU+4H49TqgqjMoMK0O2\n/WuH5O9DQKTK7Cuw74jONSXNOMKLUGyVO1KUm8iJgszauSESheVWCcaQLFYJnFFj70Si1JJGgMMk\nBy3TwGsXeirHpWYZvBiJ6OZrfFxPdzLzwGJVjsVCbLDiFRZ5K4/tS6RqeiOoePaHGk9rjTJtt81G\nax3hZNG83FBJRk94fOPxb7BhL6J7uVBDtKl0DNz0QPW7ZbtoRm3AK0UmQwpUnQ3q9uChTiWQUtF+\nsN+V2R9TI/14TVYPMuYUEX9PU0o5xVYRzWiQ6gK1cUNSnZyTlEFeqW8g3Jh0++0LlYApNsY7hG74\nB5r5dC/Yz1oxHjja5MBylSvPnWU+Z+HYaZZrXZn96jE0N89ZsxkmUzGycRPPX+vC3Ha7o+k2QXN6\n9pAnG1E9Scur+bLT4dWnRFSu+WqtUPjKc9MDOMAyUnhdTIcjlSMgdObTvfRURel+pCh7U3bmZRVO\nrWU/A/v/D4Qh0tTdUpDVf+lOyVdVC7Kin+S6wKHKzj9lSzYYXNKMJ8VSLQTsN5Xhw6DxidrUKn3G\nD2pw6SJJLDL+o1JmUdU+s5lKuxxk4iX/U3LZ2o4LeqPHbVKFrmtYepaWV8ETvRmMpltD9zoLldLr\nDsrS/gIwnVLGXIMLV7FZxLUTbMnFg8W52CoGNJ6UmQlO8VV78PWKXiScVE85cOCe+ICw3CoH75Mf\nstGpMHQNTVgBpWWtuYaGge7FR+p/g6+135xgpbFCtV31tf0HzY8sU0c4EigdrQ1qSbf76DTqvy3v\nyYP9lZp/j7s2SummWsOlFmio/2uHAhyjsqsr9XWE0NmWGQQ10YiOJuIDRnJqHs6EUH82i225aYTQ\nuPmopPUdXSqAiGKQYKk2CHYUNSzhU+E6brGjQWTLqw6lq0jeblOCHM3p0WFX3hxBtW4MsK/AiaIW\nCc8iaugdH4sQn4JhUWyUEUInFZPZU2XIdsjPWIdlK5M+3arpVgPXbnVNll9p3Gh2MvtWSKWxPyw9\nGap1XrXLCC++aZIk7dOfiiHuyycTVbuEcJLkhlAKJW2vwGLXXN/wDwjxkOpOfyQiaTytS/9egf1N\nDLVUyMx+DbQWmu4EHhX9oahdxWY5GO+encWzM6Fg/18W/oVXfv2VvOOmd5DQZkm1nh36vlPpGE47\nOVD9rto1NN2h0Hcwj/k0HoDF6uLA+63X/aq72b+uGkQ0nx44ZmZf0Vmm4x0QqCpUG80SGI2eCkIi\n8Ac5ucz+eqOIcOOkQ8aoAvvjVtvKtqSt9c+7TDzC/iW5V1x57ixz2TiuneZY1xq2WFvEbmbZUZBz\nOWNFEPYIGk9XrNblvd2MEnsiEdPTuDRp+tWUsMRBMhZBeJ3EgQL7wkkNgP24kQS9iev3gC1UFzC8\nAvPZ3nV3a6aA8AxqThnPSbAlJ68p73tm/NSDfU3TDE3T7tE07dpT8YV+HBHVMjS8Mrcu3sq29Hbe\nfY0/KHywvxK4XHYGnWUa7JpKcuW5nYVhOhPDGwb2fWfd2WRIZrLPUEZFkN020ieUYVWAo3/zrtrV\nIJsHYBBHIKjaVTSjOVAKVZGMZBF4AzSLlldF7zIaS0RSoDfY8Csh6rSfi8cRnimzbX0RCvabxeDa\ns7GMzAh6CepOdeDAEYB9N0lmRBZP8rotKnYluM+bgX0AQyRoizpCCNYaa8S0DMlYdNPnsS2fwGtL\nKsjhyuGgetJNmQFIxCJ4bbmZHasOlqrbPqjvB/vtEIfkEw3F0e5eqONGGo+apGFt4jB8qkI9h/7D\naXesN9cQTopCKhxERZDPqXt8LNfk2JhLjweEumMmnUC4SR5cvxeAWlXO84iXC90AlcGcmkOqWtE/\np/uj7VdQwkIBYWVo1G2cpXlxml4tqFLlRhjKqZBgvxkcTKJ+5aaQSCC8CKUhh62W2+JPbvqToP8E\nFECVplwA00kJ0hZrkos+EQL2I4ZORCRpeVUaTgM0Nyj/W6aBcC1KXZn9+BiZfctIQoghmDTlSkhu\n74hIRVOS3ncCB51RUXfL4CVID6H5WaaOaBc4Vjsa0PaKTXUvR39XgKSZQRj1gMutnEBnEzOjXhZE\nzq/A6FEJtofReIIep2YpGH/CzmG3erPCIN1X3/bdt1G367znF97D2eIvKES3DbwnyF4310mx3Oc0\nr8woJ+O9B/NoN9ivhYB9RScLOewqita4mX21/iozKuiYo5XbGwP88aT5ovdsSgAAIABJREFU5AwO\ni80NhBdefVI9OBubVAZVVOwNNC8xYGSngO/5W7PM5+LM5yyE3UfjqSzitHNs9xtVI4ZOKpokQnxT\nsL9U9U3koqfOfLHjdl/xqWbDM/tNt4bruUEyNYyzr5KYan85WjmK08ozl+2tqEz6pm/yfTKBw+9E\nfLSp509KnIrM/n8CHjoF7/NjC8vI0hbr3Hn8TnYlL2axKIiIdEDjWWsobl3vgL7hPz+Ltz6704Qy\nlY4hnFQoZ3+1sQrCYD49SClIGENoPP5JMnmCJbKEn+VY78tW1ewKdHHsFchYri+haV5oUx0QNDiu\n97kDt0WvTXnSTKNpggPr8r5l/Q0j4NeFgIliS9J4tuT7MvutEgjZ+KfK/wJvABAqO3TNG82jV5n9\nml2l7tM9lIvwqJDXJ6g7ddaaa0TJbMrXB9hWSOC1JNg/VDokOal6Y4DbmE+YIzNXio/cz9nvz2Kf\nTKzV1YGqM66TkTSeXvddWf9twH46lkB4BtURwLjULoI7/BlHtCQgfFdKGWoebsmcuA7ylO+i6wqX\nhJFDOBku2JZDuJnQDVDRQJRjYyIaQ3jmyAOM7dl4tIjp4fdZgXs1Lrob6HXitL06FbuCEDrp6Gj3\nVFCZyEaQBFDzPxmNILwuNaO+eGD1Ab7++Ne5/vD1we9KrTK4nQrXTMo3uGtLwKRs7/vD1JMIvCA7\nrGhPlqmDv0aodXBY8qHnmsx0KGWx6VUxSGx6KI+bstFvM7rVOCGEoOlViGop9BBaFvi0PXuCttcK\nspHllqy4blYtBMhEc2iaS7Ehx/ndK3txmzPMJMfM7Ps0GT3q00qHZGTVXldqlQN6i+dkce0MK43V\nIEsK8MMV6bfx2as+y1W7rqLccIb2LExnrNA9UvWEKcd2FXHTQLTl2OqmPqnY6KOTdUfGsoiQHDuz\nf7S6iBAaO/Pzwe/U/arYJTSj0dO3J83obOp2c6z3749SSzrEh4H9ZEQ1+I8HMOtOGUMMriOqsqWS\nknPZOMLJULXLtNwWdbtOqb2BsPNsK3TWkGzcJKblew4FYRGY14Uc7k82FN6pOhXZRB6W2Y9KTAAS\nN6m5pLkpUn0VMnVwUlWSI5UF7FaeuT6hFNmfKOeDcDLM+mB/MpFFCG3AufonLZ4U2Nc0bSvwYuBj\np+br/HgiaWTxtCYNp0G16IN3p8OrVINElbtV6LrWs5lMpy2Em5bApC+W6yt4TorZbAg/zwzP7Cuw\nnzZPbCIp0N7P95ONrJ0NOuqDjGU/cxPW9Q5Q8Be8Yp/1uC1qRLTOAqEA6f51mQHM+5M0FVU0nN7r\nq9t1Wm4L4SaZz8YRTodjWWqVwLNIW9GAsw+Dp2u1kKci2ZEbezwqM4c1p0Ldrga9C5uFur5Ku8Ja\nYw1DjAf2txcSePYEoHGo7IN9oxEs4ioS0QiWkSSixUMzV0oyTNFCEmYChEZbnAKw74/rgtWdrUqj\nGQ2/CnHqSrOjQlE4+i3Nu6PqFImQGfqMY3rnOakotooIL8Js+sSzTgrsA0TdbWwvJDhnLo3TyobS\nGFS2XFGiZMO5JQ/YQ6LThB4O9hW4V2A/0fV3hkhgezWq7QrCtbDGyAonImk0oxVsWjF/bCf8Bvia\nE/5dDxQPALC/uD/4XaVdkQA1KreQOT+JUfXkWjIzRGpPXataWxUH2vKVryrtSnDQT0bGOMAYitvc\nuy60vCrRMWhoMVN+7qlo0K07dQQuCWN4EiFlRfAUePWTSeV2Wa7LYzxDRa9ZrK5SapU4ULoPp3r2\nWK8FggZYldkf1titKjPlLrAv7CzCyeIKp0ed7dGNRylYBSZ9KlGxbg/tWZhKyXlVcyo9B7SyLdfx\nqb5xk4pFiJDGwORodZDmWApc3AfneMaKYIjU2Jn9h9ceQ9g5tuc77zXlH1or7fJAs2gqaO4+uYNi\nxZYVnTCqWTpo8B/vvZteCZPB9Vplua88V1Z+5nJWDx9fUZc8O8/2PrBveNlNM/srPo1nIuT+n2wo\nHFK2l9E0L3SMyjXLxwTtEmuNNaJamrRlDRy0U/7rV2sl6nadYmsdYReY65M6zsZNcOU97FZNzCVi\nCDfOSn1QkfAnKZ5sZv9/AX8EnBxp7d9JKDBt6iZ3PSIXm1YzF2xIG80SwouQj4/efKYzMrNfd8vY\ngfGKjGPVFYSTDk6L3aHKTGE0Hk2YpK3NN73e61FShr0bYNNVNB4f7Pub/VJTgon0EN6vyrasNzqD\nXQiBI+qBQgh06CAHN2QpX/FBkzFfGrEvy6kOM8JJkk2YxI1OM1SpLXmsqVhEcn39U3w/lUhuOtrQ\ncrSKuCm/Q8OpUnelilB3J/6wUNdXaVdkU5mXHksZKR412JpLYzHJ4dLhgLMflq0sJGJYTIRn9n0+\nssoY65qOQQKnX27wJEI1ZHZvlOloFk1z0SKlU9p0NSpiEaWmMxzsN70SMW34M1bZ8e45VGpvINwk\n6dj4ze0qcnETXHn9pdI0l+4skE9EaTVTrDXXemVy6YCOjP98Y35zd21EZl8BzGEZbEX5UhtyNwXM\nII5NXR6QvPhYYzkZvJ8cZzEfKEcNHc2fG2GhQL4C/QAVu9yzlkzEUwgvgqPJTOBMKlyWrh/sK858\nzPQ9LXyanSbixMdoWE355mirXWDfEx4OdWLjcP4jenDIeLKhkiHJECUiFflEFM/uzVRX/Xs5TmZf\nJV6OVda55egteHg41bMDOtVmkYspGo/MhA4D+1N+03bFrnC8dhzdSxLVrVAu96PFR9mT24Pjetxx\ncJ2lcnM42O+iSnTvJ1Xbl47s62nTNI18IoalTYWuj+URlMy0JcUlxs3sP7L+MG5znvlcZ49W9LS1\nZnGgWVStj6NUxEZFza4Ee1x/KFrSuGC/LSrE9MF78OLz5/jdZ53O7mn5fpPJGIbnS2HXl4N7Kpwc\nW7rArwS+2U0bdBXrYXJIJe9kQu3lJcdvmA5T44lKzj7I+7/aWMUkGyrSoVSuVhsbPbKb832ZfV3X\nMJGfHSUfrG2ZuAlugrXGeOPo32ucNNjXNO0lwLIQ4q5N/u7Nmqbt0zRt38rK6IHz44pcTE7oHclz\nqTQMnnvWNE6rwGLtGI7nBJmX5CYZ3XQsQkQooN07MJbrEuzPhID9lCllIfsbdIutIrpIkj0BJR7o\nlK36F4qmW/MbdOVjVzSNlYYEE5kh4E5xnpdqndJry20h+poGFbfuqD+h1AIQMXR0L07DHbw+IChl\nqhJpsVlko1nC8+95xNCDLN1AZr9ZJCKS5OLhutYq4r48Y9Ot0XSq4FqYxuZ9EEoWtdwus9ZYG0t2\nU8We6RTCnurJ7IdRpfLJKIZXCN3MPOpEiGPoHSBgkMDhyWf2FUDtzsoo7qWmu0NpXac6pAxsx8+g\nP4QQtEWZhDEC7BuDeulVewPdG06pGBWyMV2O33pllkt3Figko7h2Bk94A4pb5basFiWicn4r2dZR\nBxj1XVNDKigK3B+t+Jn9ribEiCYPfHWninCtsRr41aHiWN2nBfnzX9M0dJGgOUTh6cCGBPmHSoew\nXZnEqNlVRFejumHo4CVAl/8+mw4H+6pa9ERZgX0552VmX1Z3ym3ZXKvWqVGhsoDrXVVMCdxFTyVk\nWKhegVMB9tXaFCY7qiKfMBF2HtC6wH4FvPE4+4oetVxb58aFG0kYWbzGtrFeCx0Z2gDsD1Ekm0zK\nz6m2KxyvH8dzcpw1l8ZzeuVnPeFxYOMAiytZLvnvN/Cqf9hLo+3y1B3hlZ2pdAzPUeCrM4eqjl9l\nDFHOKiSjmGIiNLOv6Ff5eFhWO4LnJsZqrKzbdZYaC3itObbmO6B3MplCeCZrjVU0vd2TVEqPIRk8\nLIQQNNyK36A7uJ+ovXTccelQxQoB+z93WoF3vOis4P/rusakJWmNy43lIJEwGZvtUU/Kxk1cO81y\nYzlUElqFYj1MJ0+d5rxKElYcOcbCDqSKfgdyHV1trKJ7mQHZTej0n6w3SsGc80Iy+wAJQ477rNmh\nk+XiJsJNhKoJ/iTFk8nsPwN4maZph4AvAM/VNO1z/X8khPiIEOKpQoinTk2dOHf23yLUAmhXz2Ai\nGeWVl2xFtAt4wuV47bivYhPfFORpmhaYm/RzEteba3hOmunMICi1zAh4sYFFY6O1AUNO/qNCZR+6\nwb4QgpYnjXQsPwuoOMFKwzg7pGF1iw/2FyudxTmQGuxqolM8zxX//aaSndN+hOQAz1wdiDw3RcYy\nySqOpQ/2u7MecWVs0R4E+5pIhWo6d4cyXrJFUzbRifhYTc/qMHOsdgzbs3Ht5NjPY/d0ilq1wKHy\nIZqODXqzh/OpopCMgpMPpfG4Wj2QJ1RhaslQbfETDTXeJrueU3eG7N/CUAs6TsXDwGbdqSM0m0x0\nePZIeUR0g/2GWyYSUtoeNzIR2UzvNrfwtJ0FcoloUALvL29XfN61At1RP2PcGOGHoO5/2JiATjVn\nwT8Edh++oloCFx/se+OCffl+SzXVA9Dtr5CkGaLwJIRg//oBhJPEEQ6Plx4HOv4A3QBBF3KcymbT\n8EZqda1P+KZSCtTEzA7NrtyW/QDjVCtUNXK93lkX1H0dh/Pfccl+8upWClQqz4GwyCWiICIkjQkW\nqgs0nSaOsMem8Siay3JtlZuP3sxM5EJMw5BryBihMvvaJpn9dFQmoGpOlcXqMZxWRpot2Z2sMEiK\nWcNpcGAhxTN2T/ChX7+Ye/7bFfzyJYPuwSCpNaaQn9ktv1lzNsCL9cgSqygko2AXgqxsd0hTuljo\neEvHTFw7EWoI2R/7i/sRCD+z3wGBuYQpTSXbcs50V0EDed2TOCjWnToerp/oClHjMS3ZxzSCBqjC\n9Vw8rUYyMh6VZs7Xj1+pr8gDlDDYnuuVoczGTdqtFI7njKyMbLRKCKExtYl53YmEopAFmf2QMarr\nWlDNVWCfENlN6KgoFpvlAOwLu8B0ehCLpU15aJmwOlg164P9n9oGXSHEHwshtgohTgNeDXxPCPHa\nU/bN/g1jV+Ys2sWn8dCBM3jx+XOyudLu8Cpr/sY2DsibsAZddF3PpeaUEE4qNLPf4Y0Ommp5QxaD\nUZGKxhFC78kKNN0mHg4G8SDTqTKHay05qYZ11M9mUwg3xrHqINi3ugCDWghL9hLCM3v0g009SVuE\nN9eqzH4mHkH3UhRbxUDtQ91zRXXqn3DrzXUIkdvqj1hEB0/e+6q70iMZOipU9UPp5dvt5KYVHhV7\nptM4zUkaToOj1cNomghVFsgnotitHJV2ZSCTI7rkCVWYPtB7slFpVxDCIG913r8bqGxGjTpVETXk\ns2l64dekDs6jjINSIX0vTa9MVDt5sH9a7JnUDr2F6fgc2wsJCklzqCRdxa6Aa8mMPoqzP/wAA52D\na27IfVbg/JgP9tPdYF9Pgiao2Ksysz9Oc6efBV9qLKIJk4TZWYtMPcSJFqk9XnOq2OXzAZnll1lJ\nWVHopp5EfDdczRtOO1Rj6qh/TUpFSDXoesJlub6M61hjgd9s4L7cWRfUfR2VYVdhmQZ4oysw44YC\nRYURzprRiE4qFiGhTXOkciQ4nI4L9qd9sH/X6s1U2hWOHdvFs86YGntNMg2TqJ5Ej8hD6LAGXU3T\nAmrX8dpxPDvLeVuyCDeJjhFk9h/deBQAtzXDX7z0XK46b27kfqVpWpBc606INbwyuOGVmHwyit3O\nS3flvt4K6eIeToFKWxHsdpyN5sbI7DTAQ+tSYyStbe+hROUSUYSboOrKPTLfndmPKRWxE8/sq4Nh\nhGSwZnRH1JA0wH6jzbAotUugibF7+7ZmJ0BEJGe/egzNzXFaoffeZxMm9Yacz6OoPOV2GbzNzetO\nJCYSGXnQdP3M/pDqU5AAbEnOvmsnQ/sflBzpRrPMQnWBCAmmkrkBvyOAQkwehLakOoZg2YQE+2HG\noj9J8TOdfWAikaJ1/OW4dopfvHCeLbl4p4mqsiA3gjFoPNCxXO5eyNab6wg8dC9DIUR/WRlc9btt\nbrQ2cOzwMt+osMwIwu1tOlMgqFc9x1e/aftg3wpf+CeTkme52nVN6r27ecSKDtIWg4ejmJbCpdnD\ndQ7AvpMkbZlkLBPNkw1VZcXZ969d8SPDwL7jJDfN7GuahumDkbq3is64YF++RjnhNpvjV1pOn07h\nteV4eKwsXfnCAHQhGaVek9fXTeWR7oSNAbUWUwvXFj/RqPkUkO5xPdnVhD4MhJ7qkDSS+FA50UVf\nEi/Mo0JFwuzte/GEh02J+Ajqz2YxnUrhNXbwtJ0TaJomN/4+GoMKRWuJGn4/jJ/ZH+V0rADqMGMj\nBe7XmisIoZOMdsas6repumsILz5WZl81D680j6GJ3qx8TEvi+BKz3aH4+k7lPHQM9hf303JbuMIB\nrxegqv4Wg1FgX36H4z6VKG91SW/6h/HF6iJeVwVyVGT9w0K3zHBHtnc8sC/c+FAK2YmEcjGd2sTE\nLZcwMcUkC5WFoAoh3DgJc/N1RTVCP7BxKxHNZGX5NF56wfwmr+oN1UCsC4uIPvwzNZGg6q7J7LmT\n4/SpFJYZwdI78rNBH0d7hokxqwtqj+ym8ZScwxheuB9GIRGlUR9cH6GzhoUZeGXiJu12grbXllKv\nI+KR9UcwRIpt2d57mUtIJ15b8xMOXXNVVdD76bfjhBqjymW+PxQNcFSDvwolGaroyJvFfC7u+yUs\ns1A9it3K9jTngsrs+y66I5p0q21fUegk+qKGRS5ugRej5ff/DKs+KeyxWFuk6TZpt8KTfvl4GiE0\nSi2Z2Y+ICeaz4WvUmelLqR16C7vze4Lfqcx+3Tk18rw/rjglYF8IcaMQ4iWn4r1+HKEGyJZcnIu3\n58klTCytgIbBQmWBpltFE4nQE3h/bEnL0n93Zl8tahmzEMofVqXkARpPcwPXSYzVENr/fnhWT1ZA\ngaBuSogViaJ5Fi2vjhDaUBfOiVQU4STZ6OpDUO/XzTee7Crl9TceBUZfXd9po7WBhu6r7kTIxE1c\nJ8Fac83nIncOWOmYhS5ioTQeuxXfNLPffe0CdyQg6Q7lWaA0xuvN8Q9fu6dTHa39mnTly4VkKQrJ\nKDV/M1McSgDbFWghEphRLdnjCHiyUbMrPfKJ0Eu96pea/dcMKSUZDrhuOXo7Qmjszpwz9PXpvsz+\nw+sPIzSbQmTnSX8n5ZKtHLILiSjCTWJokXCw353ZVw7VXm1oVnEt8O8Iz8hZZhThRREIn5ffeU5q\nTAg8NM8iMkZfgsqQ1Z0qmpfoee6WkQLNo+70HiIVX99tzpPQ5jlQPNCTje45MPjAJcJwrnwulkEI\nXVZLPZOMJQG+WgNB+YFYY3H2lZJUqbsxu6UOUeOAfXkoa3n1gabrE42lahEhNGbSozOs+UQUbGm4\nt9yQQEp4cazo5tebT1gIN4YrHArG2ViROM8/ezyNfRUK7G+2BhoiTtmVOv6enWU+ZzGRjGGKfDD+\nD2wcIK5NMpXMBq6zm8VMOoXmxYM9crG6SFUsEG2Hz+9CMkq16veDVXp5+w2fxhY2VrpddDdr0n1o\n/SF0ewvbC71V1Jyf1UWTGiTdB0gF/PuFJ8YJNUaHUc1UsqA2xiH0lqO3A7ArPXx97I75XBzPSbNY\nWWKhsoiw84HGvopMvFPFHCW/WQvofKcubyyfWwKhteV3GQL2k1ELnSgHNw4CMhEXhgNSMRO8GJV2\nmaPVo7I5NzfIsACYSFl4jR09QioS7CexRWtA4vcnKX6W2acjT/WyC+dl+VLTmM8liDHJQnVhpMtl\nf8xlsgjPZKmL8qLA/jCXw1iX7JwKIQQldWo+QRpPVPFQ7dFgP2bqIPxB7VnEjPBM2kQqiucmKdud\nMlbgkttVBk7HoghXAiThxnsOKeoU3l1tWG+uE9XSWGYE09DJWBEcO8GRyhEf4CRIxeR3SsYMNJHs\nyew7nkOpXcJ1kmOB/W46TGRMsB83YyDMAOx7dmrsknk2bjKVmEInxpG6LBOHAZB8MoqwfRfdriY0\naRfeHJBmlM6qTx7sN9wqiHjPAXS6S/ouzBjpXyskNakdNIB2x97FvXiNbcxnhmeukjETuubQrYu3\nArDNuuCkv5OSXnuaD/bzySigkTQKA9kuxZ3vpvHgxfFwhm4Q640SwouSs8I3HnVgAMCL9yQbug+A\nuthcTx46lBf5fpac/34o/n5/wmF/cT/pyBR4Fqa7hQPFA8E97qfxqL6JUZKXciO3/NfHifvZbMtX\ny+p8v3hotnbgmqwEQug9vGllgjjO+I1FjOD7dHs0nEys1NfBs8gnwp+nilzCxPErxw+vyyRAt0HZ\nqJAyxH6v1fJunnf2zNjrUfAePrd7szUwoiVo4gM9J8tMxiKfNNG7JBkf3XgU05sPpacOC6nIkw72\nxZsWbpLfy3lK6N8XklHcPrlSFU23BkOqQGnLDOQZR8lv2p7NgeIBGtUZtuV770kuHg3uN/QCT8mr\nj5wUjafbIT4s1OF3HHrZrYt7cVvTzCbnNv1bQBprORkWqgsUW6t4fRr7oJpS5XwOkxpW0XDH87M4\nkeh+bgg9YCD0RzIWQReJoI+o3Qqv8CsDrrIP9pv13IChlooJ37RxNtvh88dNA11sPo7+vcfPwD5w\nznyGF583x2sv2xH8bks+geYUeKL8BA6NscH+tG+stVjtgAG1qM0lwxuUY6Ys2XUb8FTsCp7wG3hO\ncDGXh4dYT9NZ4ErZDfYjnY524cZDOWzq70zSPWWscp+uOCgte38S9fEolVFGN9jfaG1gaungMJO2\nTNrteACOZFO0/LdkLAJeb/UjkO50xwP73QDJ1MYD+7GI4XNXG+joCHf8Bl2QvP2IO8VqS2bICiFg\nX2aMU0T1aI+LrlLw6VcVkVlY+0lnGVpeDUP03oeJRBLhyev7twT7iu/dXxIvtUrs33gQp7ZnqJwf\nKNO0DnXtlqO3IFrzTCVOXhTg5Rdt4aOvfyp7ZuQYz1gRDF0jpuUHwH7Dl7VVCk+KmgTDnYE3fOfU\nYWBNZfeAAcWdRFdjfGTMsZw0kwgh38Pry8qrnph+TvSB4gFyxnb5HVqzLNWXggOpJuI9ilbJiK+s\nM0IFJ+XPY3lNHQUapYqjYlwpSkVZrPSAfd+NdQw5QOXxAJ1rv3f5Xt61910Dbt2bxVqjiHCSsgl3\nROQTUZp1uQ48uCbpfeNer2noQU9EaW0PLz3/xCg8ACm/lyG6yZ7WvedNWDOYhk4hGcO1MyzVlrA9\nm4Olg3jN2RMD+ykLp51ktS4z+zcdvQnTm6QQC2/qLSSjcj8xEgOKPC2vhtaXsFCRGTOzf7B0ENuz\nsRvzbCv0gsBoRA/on9DLHzd9Xv3J9HuofWxY1jpqGH6D/+j3bjpNfrR6N251z9gV57lsHGFnWG36\nZml2LpTGg4iQMkfLb7a8arB2n6rIxDuGWQbDhTQSUQPdSwQHQOEOuueCEuewWG4eoeW2aDcHDbVU\nnDaRRNNg52RnDdM0LZAFH0fZ6d9r/AzsIzegD/76xT06s1tyFq1mPmhAsoa4XPbHdMZCuCmWa4OZ\n/a2Z8HJrmCa3OkEOc9gbFdGQrIDaDGNdG7EqYcvPiRMZIUUZN7K0RLnL4l0uVt20lERXdi7Sd9oP\nkykrNosYXiq4vkw8gud0Fg7hJkj6mf1ULIJw4j00nm7O/zhgv7u/YHyw32nsTUezgH7CYL9Vn0D4\nVhRh1Jh80gQ08rGZHkWeht1G09s9kovQqVA8WbnAllcbyO4lrY5+cTel5187Ag56X0PaHcfvQODh\n1vYEtJqwsEwDz6fC1ewa9yzfS7sy+jWbRdoyueKczpyVmt8mpggB+05NZsu7ALm6t8MMmzZaStI3\nHORFDb1zGO+qGkCvko45ZpXK7KLKeI7Vkw1NhRzGbdfmUOkQCU2CsEZNUhTvWpJqyzE91TPHlXlN\nfIS+fcoyg+8gPKsD9ru+G8j1KDYGNSAeNaBv7VxvlBButEcgYFhYviQvdObTh+79EF/a/yX2Lu7d\n9PXdsdHaQLgJ8iMOpSDlN8sVuQ48sPoAIIG1MaZErOFN4Da2kjSmePaZJ36YVY2c0U32tO7DwHxa\nzoNCQnK5606dB1YfwPEcarVJZkJU5oaFMqxbrq/QdJrcfux2WuUzOW9L+HpT8CtqE9bcAGe/LepD\n6UhpywyMGvulsLtDVVe85vxAZh/A6jJJ665kRwxN7rObAPKwCKhmQxTGVFVvVM8PwN3Ld9P22ji1\nM3pUhEbFfDYeqIoBRMXEQL+F2k8zkYmRYL8tqgMCEk820l1rhDHiIJGMysSBOpQLJ00mBCslfFPP\nldYhwJfdHJLZv/z0CW5++3PZOdn7ucN6Bn+S4mdgf0jMZ+PUa9nAHGuYy2V/TKdjeE6qR+7reG0Z\n4VrMZcM3QVVKrjvVYOB2Z61PVHpTAdTuhUJtZIkesG/gOj7Y94Zn9gHSZhaBG2Rei83ygAttxDfn\nAQYqIRlf6acbTBRbRfCSQWY/012+o5f3n4xFcJ14z2TrqPmMB/a73Wv75SyHRawru5qJyubVE3ke\nu6dTtJsd+lYY2FeyeVlzpmczW/cbOFXGVEU8hBJ1MmGL2sChR1V7hGeSPUEztycTSie//wBz6+Kt\nRPU4bmMb0+nh2UPlkFxqlbnj2B24wsGtnRFQcU5V5BNRcLMs1ZaCg2/bbWOLluTsd1Hhut2Xw6Li\n+3cMO8xHI1pPZr/7vbsPgOOOZdPoHFwdp+N+C90ygp0x9XjpcRzhYLpSmaJUlg2UCuz3f66a4/3j\ntTtSsa7qX5cCTcTQMbqa5iUPe5zMvlo7u5yTmxsIb7zeGqV6AvI5Hase47ZjtwHwxf1f3PT13aFE\nBXKbKJPkk1Eq9ShJMxlkJeOR8fYXgHz916gfeRMvOHdmrHvUHyqz39/43x8KxGlumq05+UwLyRj1\nunydospVy5PMjJib/THtG2utN9fZt7SPptukWT6DC7eFA9+8XynJRqZ7Mvue8LBFfSgdSXG/YXRG\n9uH1h4loMbz25ACdBbrGsxfD1Dv7TETXfe+WEwf7G60N8KJkhxzxpf0xAAAgAElEQVRIo8EePvq9\n9y7uxSCCW9/Jjonx1utMPEKUzr2eT80PZM/VfpowCkFfSX8oY81xE6HjRtqKIPzq1aiqQSImEzwA\nhibXlTAcEPeb/z1kT47XLjA3hLOvaVpP0leFUvb6WWb//8GYz8URdocjPI5mM8BMxkI4acp2B+wf\nrazgOemhC6IClAJB3ZYNch132ZPl7PeWABXgSEY7EzMW0fGcDpgY1eSX9YGuAtgbrXKo5JnuL7z9\nG4kyytjoA+vCTQan8UzcRDhdr+uiOCRjEWy7F+yvt9b9754Kldzqj0Q0AT6NYdxsRMw0gnuUivhg\n/wQqLd1NukLoZGODC6NSaIprkz0NuhtNpRfe+xp1YHsymX21UJshC7UukgPNl//aEfPNy7ppPEII\n9i7uZcZ8CoYeGan2kfB9FErtCrcs3kJMt3DrO0Idq59M5BNR3HaGptsMgHHAYe/j1ZtDqhUqqr5s\n4FAaj9GhtvS/d4/mvj7eJh/RtU5m3+3N7Gf8xsNylzeHas4VbanBbbcypMw0D6zJbHS3xwZ05nh6\nhPNyKtaf2e9cezdoGHf8qY28u4opKybjrZu6rgVgsdqu8rXHvoZAEGlcyI1HbtzUQbQ7ao783Oym\nmX2ZqZ5NyENUhDgJc/w1PhvLgJvkZSeowqNCHcosY/QaqA4grt+cC1BImjQb8ve3HL0FXTPw2tPM\nnMChWmX2G26N6w9fT0SL4dZ3cf7W8IZqxaOO6xLsq0O27LEQQVWwP7Jx2cejoW+a2c9HtqNpeijQ\nU025eh/lUR0UhzlPj4pSqzRyjKo93BHhfUwqbl28lYnIWSTM+NhqSJqmdXTkhcZp2cFxpECzpeWH\nzoGaXQPNG1nJO5lIRSNBRXNUBT4ZjQTJypSZB/RQGo+ha13PTkM4OeaHZPaHRc6XpP4Z2P9/MOa7\n5DdheCNNf+QTJrqXouGWcT0XgKXaMsJJD80yxsxOuV4BBwVqT4bGow4Pba8RfIdKuwLCJNFlWtLd\nFCfc+Mgy8lxC9jN86+C3AEnHEa6F1acNrSgF/bxdxVVXCiSu51JqlXDtzvX1Z/ZNLRVUG1RGsNQu\nBYu9slsfm8ZjRtB8HvVmG52KWETH8wFX3HdUPTEaT0d+E89C1wenXN5fpKNigvXmeteBT46BfvCk\nFteN5smXFJUDshVy6ImIHLiZsWkFpyKskAPMkcoRjlaPkvbOYSoVG+mEq+gYlXaFW47ewvbE+UBk\naLn2ZCOfHJSkU5z8bjUe6FCThh3K6o5UQ0oOaczs5uzT995xMxb0VoybWTONDlWmH0znYx1L+f+/\nvTMPk6M6z/17aunqfXp2aTQzmkWjDSEJkIQAIzBgtmDwisEx3rAdHJPEsW8cOyGJ7TzxknjNjZ/s\n3BsvGJOAYzvXmCUxYDA7lkD7Lo2W2Zfu6X0594+qU13dXdVd1dPdMyOdnx8ea2q6q2uqq0595zvv\n936MQ9OHIAkSkjFmiUjQ6x/UXWu8RdnoFf4e0JyITk+v5TH4lMIxx9j5VZFkiMgX+NvRsLNajXjB\nKuasluWzd58au2T/5MhP0C6tx8zp65ClWfz48I9t7QNQm7gh5zOVEhhhtSdtbrWgUoTXlsc+I+CW\n0eyVccUqayvacrDETaXrhq1mZ1NN6NaC4BafonfRfWPiDXR6ugEqOS7QzWlJnV8c+wVahPUIKh70\ntZqPyex8uWgr4pm4rr83M50woj5XBHjEgGWQRinF/qn9UHI9WB50mzruhRT1fBUH+0zGY9aMrhJq\nD50yq3pi/t63svYcj43j4PRBKJm16G1xViTb6VMleTQTRF9raWzDgmaJNmEyMWnqVMWSHT6bsZFd\nBIHoErJyxf5eRUQ6rV6XPlH9jqziADah9wotkIjsWN7ZogX7XMZzDtLd7EEunff9tdtNlBACn9gM\nCqpLeaYTk6CZgKWukbnxAPkbKC/jqSLYl/NL5SwQCafCIEUt6N0Gt49Kjh6rmtYhHb4Q//LGv2A4\nMqwOtCYPZCbf8UqFs/0mjxc0J2FSCybCqTAoKFIpj+7Rqxbm5Adun2EfPkUCsl5kchndM5kN+jRr\nbrlVjEcWdZmR3QDJGOwrgvqQcxLst/oVBEX1oW7VbEgWBfU7zqoD1khULZya1TusFp5Ltjozk6he\nxqMXbJvIB1oS74Q0eVfV+64Gj2ZxasyCM5kAEmtMO08XvF+buE7Gx3Bq7hQ6JNWFp9L7nNLsdSEa\nU4+VBfv5zH5RsK8FIVZyK1bUay3jEQqy4C6DzI7V+QD2J66SSPKON0V2eSGP2shmKlYY7Pc39WM2\nntMD2E5PHwBAoC545cJzu8LfhbkDX8BAcJ3lMajSinwRv7HGwS2LeUmGhZ1iMew8JA3BfjQd0c6r\nvWw5W4V8avgpDEeG0UKvAE23ode7EQ8ffNhWoW4ym0SGJqEIgYpBF5OlhGR1xUSg3oJJTyX+4Loh\nfPM9m8vKLsvRpOnEi8foYtiKIs006XrwFp8Mqum9KSjaXOrEzskKWptf0Z1eYpkY0pE12NQTspzM\nK5KojrkZNfnG7Df1OjSLsZyN0y5iHeyfiZ5BJBVBOr4c3SYSHiDflKlYUsKC/eLO8HaYSsyUvfdl\nMb8KZ7UyyORm8dnBkgLbSvQG1Wsva2K7CajZ8IAigeSakKO5gr5BDDau+W2qHpzg1p29ymv2WWbf\nrT2brVb4WeJFoe3oDLodJ7JavD4gJ/PM/rlIZ9ANQt36zNKs86kVIUVdIrvh4Rvw9p+8HdOpUdCM\nHx0WA2KxxzRQ6EHv1FrNmBVg+4ukIiVNcBRDZp85h1jR5nchOXoLBCLiyy9+GZF0GDTnLgn2WYBT\nPAD4tMw8ayTEllWTSU9hZj/DGvO4EXDngwm/ki8cZbPr6cQ0FOIHIaKtCRGrygdQUvRqhVpPoX6u\nC0Htb3H2faxub0cuHdBXFcxQ7eUK7Tetgn3W22B6Hpl9sxoORtDVBi9x5t09X3wmdQi/PvNrrPCv\nwGykybS1uRGvptnPaYXQSmYdWnyumkuRmn0uRObUBwcL9vVjznoKA3LBWm6VzqWRponybjwGjT3N\nFsp4FMNEnU2UKqFm9pksqLDrbsCtelHPGAroD80cwlBoCLOxNFZ1qH9Ls6QGdwK8JedWvQelspNh\no4ynuIhfkQW92NKujEcQCMSihmyxbMRRksQteQAQ/HL4l6rN35zaLbg5swNnomfyk84yMEMFrw1J\nAwv2/YJ6jwnUa2sVg7G1rwVXr+mw/fpilvm6QHMiWpTyMiA2zuTSIUOwr1oRMx27j/QAgKMCXZck\nICDlNeNnzvZZSngYLT4Xskk1GcLGR3bfWU12JVGAzyVCQsBSxrN/Ui3OnZ3pMC3OBYB2rdFgcSGw\nLKgTzVQu5ti5aUaX8Zhfo4QQSKRwtb+YX5/5NZrdzTg73uw42O9pbgbNKqDpkGmdAqBm93NlvPbz\nzetqm9kH8hPRcnJbr8v4bNaCfYvVPL3HTqalqjquJo+MXNbLrTfPRVySgI6AAjdRA/dmBw2GVnou\nQXP0A3jf+veh298Nv7gcYmqNpYWmMbNvlPHIxAePLDvO4Mgi0YMEtr9IKoKSxjxyfpJRvERZTJtf\nAc004V39d+NXp3+FE3OH1KX2okYwLGNe3KqeBessgGVZ+UQyn4ELuCWAuiASGSL1Fcgb/Eq+2Io5\n8kwlpiCTIAKKVFbiwfDIInIZ9e/12syGskIpABBoIH+cDljV6Uc2NgApY/1wbfa6kIir54zp9iMp\n5nhUeC71wDhZvWZfr+Ewye75FclR8FELvJIPoEQ/rnQujZdGXsLlXZdjPJxEe4UCQI9hNavb341I\nJFRzvT6g1lekUqwLrLoCwzJvNOcusKJUJAWgoqn1JnOlEuCzvL+NPvu0yOlHvy4psR/sC4UyngKP\nfJd6f7HVotnkLEaiI1jdvBoz8TQG29VrzgM1uCNFiQMgX8tSbjLsU0TderPYDcYtiXrND83Z66AL\nqJOGDJK6mUIiW9o0rBweSYYItWbqhr4bMBFRZYJjI0NocbfgPw7+R9n3h1NhPHnySQD54tdyMFmK\nAq2WJ+eBx4bHfq1o9bRh7tCfYtB3cdnXBbQgjhYE+9pYLamr3lK2C4ok2FpZLTgGt/r+Fd5+ZFIh\nbOqu0IjM50JMGx9ZUTMbK8pd/wG3DJH6rYP96f0QiICJ6eYS201Gu7cJlBZacALqRJPkPKDIOe7R\nELZRV8IksWYynhzN4fkzz+Pitm1IpGG7OJfR1eRB4uw7kJrcYTlRCHllpFPqPVrsPhZOhfHIIVXi\n1uxuLnnvfGHSVaWMMYrac0Ir0KVNcMtCQXxjhE0aknFr281yNHldoFkvJuLlm7MtZho3wixBukIe\nnE02g4rDCDlwJlkW9OE3JzfhU5e8BQBw7wOvYY8UtlzeVeT8Q302OYtMLqMGsvA7DiwBLSuAvF6Y\nUopwKoxsUVtxRRL1QLacxRUADGgP+1WeG7G6+TEcnD5o6pjhk7QGRO7C1ufsxjwaPoCHDjyU78KZ\n8el/ozrwEbiFILLZws7Bxht7Mj6JRCaByfgkROqvWBDH8LhU9yGJEnhl+9abbCIm5AKqz7qNTspG\nVrX7kXjxDixvsx64WnwujIQ9kJol7JncgydPPInfTKgZxWBR5sTjUpu5zCZnLbuzWnEqcgrPn30e\nj594HEBhnwTG+q6gaaFTPXHLEhBXEElFkKM5vD7+OqLpKLYt2477o6mKmX23K79KdcWKK/DrFxNV\nDeqVCHlV/+mgK4TR6Kje2A1Q3XcKMtWSCBGqHSj7nuKZOEZjo9g9sVs97jKZK6WMZp+tBtKcArfN\nQFESSd7jvqhplc+Vvz8fPfaoHjh3+waQzcXQ366tuKW1xj05Dzzuwnt//fIg7tjag8sGC+99Iz5X\nftJenLVzywKEnAeSqABUstVRFlCL+FIAvvHKN7B3ci9ySMNVZAtaDkUWIFIvsiSOt616G/79F6MQ\nCHB4LI7fufxW/PDA9/Dg/gfR4e1Aq6cV0XQUpyKnMBwZxhsTb2Dn2E5kaRZCzo92pXLHZlajI2S1\n85T1wONpXN5NFgQg5y1Y2TFjpW8tEqO/BXd6gy7javGp96FHaAFwDOl4h7oK7rCpUoe/DePUhS7X\nJdgPWDrxMFq8Msbncgi1h3AqcgqxdEwvHDVLWDCCHgm5rBfTySN69j1Hc4ikIphOTuO10dewwrcS\nszmXddDrcyE9swWh4MaS37Ek2WxyFv4Kq8UZmsFcak79Lx2uuPokES8yAEajam8LNja6JTdGoiOY\nTEyiT5uwWWXnrVgeciMT2QRCVMmyGU0eGdF4APCqjbUopaCg+NmRn+Ebr34DM4kZpKauQM/AgKPP\ntkNAk02Xk9uqmX0tOZAJlJ1wsvqT8FwQXf3O67hYF91D0wfxHwf/A+tb12MoNARZbOxzcj7wYL8M\nXSEPDg6vR0aRHEk3OgJuTEVTSGVycEkCxsLJssGK0f7tvufuw33P3QcACJLV8FYR7AN57fyHH/uw\nvi2X2VyQ7XLLAmimssUVAAy0++CSBBw4G8Wfbf8z3PXoXaBZX0n2rEveitcPfQKdlxd28/MrEjKR\nDUgEn8VfvvCX+naazU9oXJIAjyxCIU2I5ZQCOYDf0Dnynifv0bc30y22A1PVi90LmvVCkeydV8Vw\njmgmCL8iOX6wDXX6AZACiUcxzV4X9p8No6u7C48cegSPHHoEAgRk5lbD5yocnFQ5hhcPHf4+Hjr8\nfUfHwljmXYb09HZ0dZYO1J+7yVpzXS/UAlsvHtj/AB7Y/wAAQCACBvybALxSsQBQzeyr39PlXZfj\nkXACm3tr3yeA2aQ2u9rx8KGH8fChh/XfKUXL/IokQKA+PHTwITx08CHT/XkFazmGmtlnshZvwfXD\nfqdey/YCRVVjzK5lb4Em3quIyMYGMeJ9Dp955jP69nalD8BetPkVhLwywjERK/wrMDpRmjl3yyK+\n8s7SgMiIIBC40ar97YUdkdXkgw9uLWiyK8FSSAtSAB7c/yDWt65Hr3gzZjLbbb0X0FYUqA99TQEM\nBTcgljqDbf0teOnYFC7wXw9FfAh/9eJflbzPJbgwEBrAhzZ8CDu6d+AT909iWX/lolmfS4RLFJBO\nhSARCdmM11b33FohS+r4ZZUFZfgVF9JTV6K/Mz9xavLIIARwoRUeyYNwJIjOoPNC/mUBP44P/y94\nlQEsC85ZSlwZLT4FB0fnsHKgp+S+K2eeEXDLmNZsPjd917yb9vb2G7EX1gFzs9eF5Mg70BEqvVdF\nqj6TbnrkprLHbwbNBMpm9l3EjwygxwNmNOECAKew0qK42Qq2UrM86La8Dpo8MkbH3JB8Er704pfw\npRe/pP9uU/smfGHbt/DBfzyDQB0SQ53ulXj19FXoGdpi+Rpj4iCXLh/sN0ndOJX1Izm3orrMvkdG\nJrIW0aan8IXnvwAAkAQJD9/6MAaaaj/ZqQc82C/DipAH0dc3ANjgqCiTFQX+bNcZXDnUhpFwomzm\nQnXj8eGa1t/D2p4siPa/J15tQtqh7aa+T9qNVcpduGqtmvVIZXP49k+KC3RFZON98My+F1J6ddn9\nyaKANZ0B7D0bxuc6LsV7e7+EfzoYK1nK97lk5BI9JefLr0hIT12JP7r2E7h0NcHuyd04NjGDr+4r\nHPCCHglrpQ9hz2wUvuWFmf1cshO3rPgEBjpEtUMpEfDIs022bDcBNROQmtyBTPhCKCvsBUiKJCIz\ntx73brgP+w93wa84X8ZjemczpwdGq9+FqVgK37788zgePo51Letw7EwAv/fA7pJJgiwSJM6+Ax+5\nVqrYrbOYkDuE7cu3Y7m3B2v/7DEENtXWraZaFElAZvzt+P2b85PigaYBxBPqz3Y0+9noEG5b8Slc\n2vkmTEWfwPI6yHjY+X77ynuRkQ+Bav97fj/FHrHUmi8Uux3vvjyrb5NFGZ3eTizzLcPfPjaFiTK2\nmS5RQDY6CPf0nYjEVxYW/4oiUhPXgIhzUC6wFxTLgoB0eBMGWptxINNcktlPjt2Mr17zR1jXm8TB\n6YPq50ANyEMeGa0+FyajSXz5LV/G3f/nDbg7qpN6+Ugfxo98CquWDRZsd8sCArEbcNGyG/FDwLaM\nJ5DbhD78Bf7lzpvhlb24+/++DConbB+PWxbRlnwPvrpjC8bnUgCAt6zrxEvHpnB20odn73wWU/Ep\nTCYmMRGfgEfyoCfQgw5vBwSS/07C8cds3Y+EEIS8MiIxim9f82384fdG4V7WONmcpDmClRuPAOhj\nu7FZkygQhDwyesVb8MfX3oE/+t4cNqywL3FltAcUTM2EsJvGsKmn8vtbfDImo0l8Z+tn8OLZF+ES\nXXCJLnzt/40jMFAu2JcQi16B398xiAzNO8oEXUGElBBCSgj7jrfgCRy11Owz2ZWZ3E5MrcY693tx\n1ZrKiQVCCAKuAIKuIPaeSuPv9wtlM/tuoRW90odxy+YWBF1BBFwBCERAIpNAIptAm6cNr+zzQCAw\ntQwtB7OeLLci0OSREY5n8ZUdX8HRmaP69r6mPtzQdwMOjMwBOGMpT54PQY8LqfGbELygxfI1XkVE\nLtGNDw59Fi/vWYmgu0wyzdWFyO77QCmqcmhr8shIT78Jf/P2P0TfsgT2Tu3F3sm96PH3ON7XQsGD\n/TIYbyAnwf6GriYokoBP//sufduNG5ZZvp4FcwPuN+Pjm4b07Y8991zVN5IiSugSrsfHN28GAEzO\nJfHN1JOFMh5ZACAgPXMJvDZs6tYvD+LJfepyXqe8ATS7tyS7x1ZAir3o2fZYKovuQB+6A914ITcJ\n4IUCq7qgW4aQ7kEiNl1wztUuowTr/Tfhro0r9e0PPP40ejpsynhkETTdimy6tWyW3YgiCQCVsb3j\nary297DjBmeA6lThV6SyD9dmrwuJdA4bWi7G1mVbAQDHTqsNtlxSYeZMFgVko2vxrsEdGOqszglh\nJqYGNY3W5luhSALis0O4Z+PNBSsnj+9RdfF23HhAJaz1X4PJOfWh7sT72y4ss98irsbbN12jbz96\ncBcOSRMFr3VJAsTEGnx881Wm+0onn4dfsZZhqdeLiMTMJQAyJTKeXKoDQIetTrOAmlUXqAISvRhA\npOC7Z118U2kRa1rWYE3LGgDAs4fUvynkdaHVr2BiLoWLOi5DKjZW9bXjVySMhjtKHGjcsohcqg0t\nUicEcqSg/qEcXpcLYqZHl+ZFEhnLQj0z3LIAEu3H+tb1ePGo6jqybnkQK0Ie7Do1A1kYQKevE50+\n66L1VCaHuWRGDwwr0ex1YTqWwo7uHUjEf+HIjWe+9LV68cHL+7BjqPwqBPt+izuztvhcSMQD2NJ5\nMUbDj+Hadc7vs3a/gmQmh+OTMdy+tXLA1OJTkEjnsCZ0ITZ3bNa3f/nBx8q6NgXdMo5N+PHRjR+1\nfM0zu/bpNXpmhLSMsWwyfrsED/rlW/DxzRdW/BuMzIyfAOjussG+SxTQRnfgAxdcYvmaHz+3E8ub\nPBUnbsV4XCI6AoouzzWjySNjNp7GDX3mqxZzSXWcddJ3xi7svJSrV1Rr+gg2N1+H/4kfxLJgGRmP\nLIEpXqvN7ANAOJFBb7AXvcFe3Nh3o+P9LCQ82C+DcZBzIuO5sLsJu/7ieuw5M4vfnJzB/pFI2QYo\nkihAEghS2WzB9kgi48i/2IgiC0hm8g4B8bS6b0+xZh/qTdvmr+ymsL4riB+9MoyxSFLfX/FSO8sG\nmWX2ASCSzGdXIonSwSLokRFJZBBNZuBXxJL3R5OFfr+z8bTt4rBCJyL7mX0ASGoP82oGNkIILqig\ng2eFb1OxFFZosp10Vv3+igc89nM660yvbySWUr+/RgYZ5WD64VQ2V7CsPBZJAkDZ7rkA9H4PiXQW\nZ2dVa9Z6aPZZA7SpaGGjm1Q2V/LAdUkCUllrl45oMos2v3UmmO0vmsyAEBQ0vSsO/O0iiYJ+3xmD\nJFYMH00V3l8zcXVSGPLKaPO7cGBErQGKp7PzCvYB9QFsxC2LSKRzSKRzqk2uTbmcWxKRSOfHznAi\n7UjDrEgikhn1/eNz6vXWHlCwsbsJr5+y53g1G1evB7vBfsgrYyaWBqUUsXS2ofehJAr4/K0XVHwd\nGy+Ls8YtPhemoilEkhnE09mqCuGNk/fNFYpz1c8sHR8B9X4vdx0G3JJ+vVsxPB1Dd8hjafLAVmvM\nJp+yQPRx2gmRhHq9MNtpM1ySgFSm/L5PTEYdO/Ewvnf3pXrDMjOCHhmpTA6JdNZUUjennVenTT/t\nwFbrXWUm/CxBEUtlEU6ksbpM4st4f1l1zy0HizHYfb4U4cF+GboMF4XTjK5bFnHJyhZcstJ6GcqI\nIglIpgtv7LlkpqpMMqBmBYwDRULbtzHIZTdwOksh2ch0r+9Sl0v3ngkjkc5CIKWBhlc2D/bdsgCB\nFAbr+oBnGCwCbgljYXUyYZxgeWSx5P2As2DfOGDZzuxr50vN3GUdu04w/u69F6OcYRCz45uOpvSH\nq3WwTwp+Xw0s2HfSzKeesOsomSkN9glB2aAYyE9iY6ksRsKqhKMewX7ALUEg6vdkJJXJlVxTxfdg\nMdFkpqyLhiQQEALkqHp+Cot/jcG+/e9QFoh+3xnf5zU8OI1Mx7Qg1iOj1adgMjqJdJYim6NVXzts\nwlya2ReQSGcRtwgurPC4RIxF8g/hSCLjyNhAkQV9fBwLs8mlgo3dITy6ewTT0ZReVGvFrD4psier\na/a6cGR8DslMDpTar09oJN4ywf6xiShGZ9X7rJpeFu2G5NKGCrabQH58nJorHB8zOVr23AXcMiIJ\ndVJlNXk8ORWrKGcBzCfVkiggU1Wwn4EkkLKrEpWSBQBwciqOa9dWZ8O6Zln5VWFjgGt2jqe0MbDa\nZ2I5WExQLrPP6lxiqQxmY+XjAHYtyyJBm8/59XouBPvcerMMK6rM7FeDIosFmXiAPbSq1OwX7S9h\nkok3Dl52lszXaoPD3rNhxFNZ0+ybVzG33yOEwKdIiCbzwUREzwwUynhYsGacMBBC4HNJ+tIh+5tS\nmZztAl1vUY8BO+SD0CzmEumqZVXtAQWtZVZPmDxk0hBEprTMvXVmfz7Bvnoerbq3Nhr2fRgztAAw\nHkmg1adUnIzKogBZJIinsxjRgpBqV8XKIQhEl2AYYcX4Ripl5iIVJvOE5Iu6zfbNcJLZlyVBv4eK\nJ7+SQAruLwCY1f7OoEdGq9+FmVjaMFmo7vHB/ubiYF/RMvRWmUQrPNqKACOcSNuu4wHU88Ay+2OR\npFpr4ZWxSQtCd52q7K398zdUuZndLHezT8Z0LI34IlthM3JBVxPee2kvdqxuL9iuZvbTGNUmRtVk\n9lkH08F2n63vimWgpwz3XcJktbqYoEdCOksLro9ihqfilrabgHqvNXnkkpUoQC16T+ecr7BGEmkE\n3OXNHuwkCybmkqZNsWoBW6WyCnCPT0YhCsRxvYAd7Mt41DgiksyU7VzNEhPLmty2bLqLccsCXJJw\nfgb7hJAeQsgvCSF7CSF7CCF/UMsDWww0eWR9EK42w24XRRL0Bw4A5HK0atmIvj9D4GQ2MBofqJKN\nGyDgltHb4sXeM2F1Gd/kAVXufPmVwmA9n9k3yngkPWNQvA91spB/P7vxbMt4jBMd25r9IhlPna4D\nljk0ZozZQF8c6J2LMh43m1QVPZQrOVkV7EMWEU9lcXY2Ab8i1WV5GVAfgiXBvpWMp8LDutL1xPZZ\nHFgbP8tJYCwJAlhsYrx/CSHwukTEioL9mVgaHlmEWxb1yeqZmUTJ+53AEgHF71dkAYlMDsl0zrbM\njr2PBc1s3HSU2Tesqo5FEmgPKCCE6BnnSlKeJ/eO4ptPHsRtm7uwtc+e53jI68JMLIWYjYB1oXDL\nIr709gv1RASjxadOdplcrppJNZPlbapgucnQM/vRpL6NBfDlsuNsDGDPmmLCiTRm42nL4lzGP79/\nCz5yZamtqixUn9mvND5VyuwPT8cAoGoZTyUqZbOPTkTR0w5hMhIAACAASURBVOy8XsAOwTJ1Egw2\nfoxFkqAUZZN+7DlXTXEuoI6PasHyeRjsA8gA+DSldD2A7QA+QQhZX5vDWhwQkp+1NibYz9/Yc1rm\ntdxstdL+jANFfmA0163bkfEAapHu3rNhy6X2gTbVjrO4qAsoDdYjCbXo0CgnMGZ5Sot8xYKVgbDD\nYN/qby+HMbMfTWbrtsLT6mMPs3wQyTL3Zm48xt9XQ3yxyXjk/KTKyGgkYVsm4NGC/dFwoqouiXZh\nmmUjSTMZjyQgafEdZXMUsVTl64ldf8X7Nt4zTgJj4wqeu+hB6lckRItkPDPxtJ7ha9Ou0dMzapBR\nbYAasMjsuyURqUzOcT2Ax5CZPzAaAaUoCVDL4ZZFJJhmP5JEmza5DLplDLT78HqZzP7hsQg++aOd\nuKAriK++c6PtOoMWrwuZHMW4VpOyWO5DOzR7XcjmKA6Pqc3iqgn2gx4Jb9vchXde3G3r9S2+0loZ\ns9Xqks/RniFhi2B/eEq9livVeGzrbzF9pskSqSrpYkdqVimzf2JSPXanDbXsogf7MfNzd2w8iv42\nZ5afdtHtuMsoDlySAJco4Ky2klsu2GdN6+Yj7WzyqHU2S5Wqg31K6VlK6WvavyMA9gFYUasDWyx0\nhVRrq3LZg1qgSGJBVpMVv1Q7ySiuATAr0DVa29l1vljfFcTxySgm5lKmD+RLB1qx5ws3mD5sizP7\n4UTp0pvxhi0OhIrfzzIO1ch47Gr2WdYinqq+QNcOQbesasENGeN0hmn2S914gPkF+6wQsdmhdWe9\nYEFtsYzHSWbf6xIRT6uZ/Xp0z2U0e10lg76ZjEfRHtZmjc9YIWyl+1u2kPEoVcp4JO1akgRSMsH3\nKpIu72LMGLSwLLN/alrN6FYb7Pv0YL+0QBew1ghbwVZ0AOArj+5H0C3hbZvtP4rckqjXIYxHCq+3\nTd0h7Dpl3rxuNp7GR7/7KtyygH+8a4ujY2YTqDMz6rlspM/+fGGSmr1nwwi6paomKoQQfOuOi3DF\nqsp9CQB1fBQFUrDyaS/Yz7uomDE8pZ7/Spl9KyRBqLpAt2KwX2FlkE1U6p3ZnzHJZlNKcWwiiv4y\njSLnQ0ivkyh/bXlcIs5q91BZzb48v8w+2/95KeMxQgjpA3ARgBdNfvcxQsgrhJBXxsfHa/FxDWVl\nqxfNXpfjRkpOUd1zzPTs1UkRipcA8wNjoU6fqXfKaeOMrF8eBKXAzpPTloO8tauBrGeyADbgFf59\nBZn9Wst4qnLjUV/HgnCjQ1AtYVpwY8Y4nEhDFglEwSrYr17Gc3IypuotLbonNhpjgS4jm6OYmEtW\ndOJhuGVR1+zXM7Nf/D0BFgW6kvX3FLVpW8f2UV6z76RAV32fWYDkcxWunAFq4SkLTFmQx4J9dx0K\ndAHVFtZJcsWjfe/PHBzH0wfH8XvXDFUsqDXCxoJkJouxkmC/CeORpF5HxKCU4tMP7cKp6Rj+/n2X\nONYts0k2C/YXo4zHCnbs+85G6lIXY4Y6PsoFNU1WjnBGWEBt5cgz34BZFgkyVWf25yfjOTEZQ9Dt\nvNeKXcrJeEY1Ew3WWbvW9Lf58Nfv2oi3rLe2uwXUMYtl9u0U6HZV4cTDCHlk3bBgKTLvYJ8Q4gfw\nMIBPUkrDxb+nlP4TpXQLpXRLe3t76Q4WOfdeswr3f3Br3T+nRMaTVC+q6jX7YsHkwSwLQgjRAwXW\naKUSzJEnnMg4dpDY3BPCgdGIvixotpRp9Mc2C/bNMvvVaPZdos0CXe09k3Ms2K9fe+zmInnIaydn\ncOGKppKJZi1kPMcno1gR8tie5NUbty7jyV+zk9EkctS+24fHJWIukcH4XLIuTjyMZp9Lt01kWGn2\n2e+KYcF+JRmPVYHufDP7Zvdui8+lW50yZmJphDxqMMFcLE5N10nGo+1vJpa23VALUL/3HAX+8r/2\noqfFg/dfvrLym4yfq52/uUQGU9GUXjwKAJt7VQ3+9184UfCe+587jif3jeKzN63D1j57jmtGmjUr\nydMs2F9CMp5W7TqYmEvWdVJdTLPXVZTZV++r8gW6WmbfIiM7PB1DwC2hyaZlajGSICCTq1Kzb+Pe\nL5fZPzkVq1txLpBPNJoF+0cnVAnXQJ1kPIQQ3L6lp+L46FUkjGoT8XKF3p55avYBVep1YjJqusq3\nFJjXk54QIkMN9H9AKX2kNoe0uOgIuG0XEc0HNTg3OkqUOtU4wSUWynisljxZBs2ujGd5k1vP9Dl9\n2F820ApKgRePqY1rzJYyA2Uy+6qmuPpgfz6a/UmtMKxeMh5A1fGyYD+RzuL1UzPY2l8aSNRCxnNy\nKlY3rWc1mGX28zaI9gIKr0vE8HQM2Ryta8ax2Ssjlc0V6NtN3XjEvG1rMUwGZGcp37iv4u2AM82+\npGf2S9+zstVX8jCbiaf1wDTokSAJpGYyHk+RdIVdAzPxtKNVA/a+Q2Nz+OMb1zpa6QDy48IpLfA2\nXm+bupvwzou78Z1fHsF3fnkYAPD6qRl85dF9uG5dJz58RZ+jz2KElnJm35cfb+3em7WgxecqcOOJ\nm6xWF2Mns1+thAdQC0hTVWX2ayPjqZeEB1C7JQfckulE6eh4FADqptm3i88lIqM5DpSbsF3U04y3\nbe7Ctiom5ozBDn+BtfNSYz5uPATAvwLYRyn9Ru0O6fyk2I2HafarLtCVrQp0zQv97BboEkKwfrma\n3Xf6gNrcG4IiCXjh6BQAlt0olvEYu+aWFujOJUw0+zbPkSIJumzJrmZfElSpU94hqH4PZdWOT/2c\n35ycQTpLcalJsM++q2qWjxknJhdbsK9l9g2a/bGIMx9vjyzqmdJ6Z/aBQuekdNZMxqM1CjN5YB/S\nihtXlelgqe7DQsYjGjP7DmQ8krWMp7/Nh1gqq9dzUEo1/2r17yWEoNXvygf71cp4WGa/JPGg/pzN\nUceZfQC4qDeE37pwuePjYZ/LJB1GGQ8hBH/9ro142+Yu/M1jB/DNJw7i3gd+g3a/gq+9235BbjFM\nCsMkCIvFFcsOrQaf8mVNzj3Lq6W4MN6OZj+ga/atMvvlbTcrIQvEsRsPpcwxyoaMxzB2DE/F9PEt\nm6MYno6ht6W+wbaVTv3YRBRuWahrbZQdjLUu5eKAJq+Mb91xUdUrOIBqEwsAR8aiVe9jIZlPZv8K\nAHcBuIYQslP77+YaHdd5hyIXZuL17rJVykaKC3QrZvYdeM/qwb7DB5QiibhkZTOeP8oy+2YyHmOB\nbuH+/Ypc5MajWhc6maiwCYrdbCiTOjVCxtPiU3S3iZeOTYEQmDZlY6swlRquWDETS2E2nsbKOj8o\nnOCWy2X27VtvsqR0Xd14WAO0WKFNqqWMxyTY3382DJ9LrKj1zst4Cu8FSRT0Wg5HPvsCk/GYZfbV\nyR9z+Yins0hlcwVdYdv8ii6lqzYbzWQyLUWN0ozH5ESz3xFwQyDAfb+1rqrgm52/k9rfXTy5FAWC\nr717E966qQvf/u9DOD0Tx9/eedG8tNJNHhmEGAt0l06w73GJ+vfTKM0+oE6ynRbo+lxqM0Yz681M\nNocTk/MrMpWq0OxPx9LI0crdlovdvH7ne6/i+m88jf/ZP4qRcALpLK1rZh9Qj9Eq2O9r9VXlWV9L\nWIwgkPo7JrLEzJHxubp+Tr2o+uxQSp8FsLDf9DlEsYyHafarlvEUFffE01lIAinRaLOBUrIp4wHy\nuv1quj5eNtCKrz9xENPRlGl2I98mWyjJWPoVEalsTg+snHTPZXhcIqKprO3MPqBODFhGqXgCUkta\ntMw+pRQvH5/C2mVB07/PNU8ZDwvm6qn3dIpuvWmYoDL9eLvNYN8YfNbVjUeTMUxFbQb72cKiVwDY\nPxLBmmWBig9LKxkP2xbPZR1l9tl9bhao97Wqk79jE1Fs7WvRpUYhwzVobAxXbdfXzT0h/Ph3L8fm\nInmkMZvvZCJx7doOvPC5a9FR5XeuZ/a1WgSz600SBXzz9k3oDChYvSyALfOQAwDqBKLJI2NCSyJU\nW+y8ULR4XTgzm2iojKdV8/fP5SgEgeR7x5Q5d4QQrYtuqYznxFQM6SzFUMd8gn0BaYea/TdOq30b\n2HPUCqObVzSVxb6RMGRBwEf+7RXcuqkLQP1sNxnlMvvrlpfvwNsIWGY/6JHrbqLSHlAQUKQlG+wv\njuo8TomMJ5LIQCDVZ3wUSUQ2R/UlxkQ6Z/pwZlktJ4WabJCq5tguG2wFADx/dNK0+Q372SyoZrIe\nVtw4G6+seyzGrWf2nWmCmWa/WHZUS5h/9VQ0hVdPTGObRYOe+cp4TmhyBRbcLQZ0681MoYwn5JVt\nB7PsenSJgiOfdac0m2T2k2YFumLpagWgLuOrwX75hz2QPy9m2Xu2OuXMZ99axtPd7IEkEJyYVJep\n9WDfmNk3nNdqZTyEEFzU21zycDbek04mEoJAqg701c9Vz8nwVByEqKsXZkiigPtuWY/bt/RU/VlG\njLa3S0mzD+RXZRpdoJujefkmawxY3C+iGCvd+aFRNWgb6qw+2HeJguNxeNfwDAgBLlzRVH7fBjev\n3adnQSnwzfdsxrXrOvGfO88AqJ/tJsMs2E9nczg5FVtwvT6QjxOcJv2qgRCCgQ4/D/Y586PYjSeS\nUCUq1c5W2UDB9pnIZE2XxtkD1kmwP9juR7NXrip7urE7BI8s4sm9owBKVy7csghFEkwLYVmwz2QE\n4Soy+8aA0C6K5sMN1LlAVwukfnVoAvF0Ftv6W01fN18Zz0ktmKv3g8IJbpPM/mg4iU4HmUOWHe1s\nUuqa5WnRNfvqQ5BSilQmV9KVWbGQ8YyGk5iNp21lxqw0+0D+GnbkxqNLf0qDS0kU0N3swXFt5Wcm\nrk5mmGYfyNtvApWDLKcY/4569zUp/Fz1XJyciqHF62qYQxWbRMli6YrrYodNVDpt1tPUAnbtsSLd\nZw6Ooz2gVJRTBS0y+4fHIgDU51m1SAJxvMK6a3gGg+1+W5p9QB3nWWO37QMt+If3XYJ7rhrE1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uafZCIECOosSNp96wSUijg/33X7Zy0d7fnNpw9RpVzvjAiyfR5JHR5p//tW0seL98sA0AIAoE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\ngg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10fc7e5d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Plot the actual data and the predicted data\n",
"fig, ax = plt.subplots(figsize=(13, 4))\n",
"ax.plot(endog, label='Data')\n",
"ax.plot(res.predict(probabilities='predicted'), label='Predicted (one step ahead)')\n",
"ax.plot(res.predict(probabilities='filtered'), label='Predicted (contemporaneous)')\n",
"ax.legend();"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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