{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# A Primer on Bayesian Methods for Multilevel Modeling"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Hierarchical or multilevel modeling is a generalization of regression modeling.\n",
"\n",
"*Multilevel models* are regression models in which the constituent model parameters are given **probability models**. This implies that model parameters are allowed to **vary by group**.\n",
"\n",
"Observational units are often naturally **clustered**. Clustering induces dependence between observations, despite random sampling of clusters and random sampling within clusters.\n",
"\n",
"A *hierarchical model* is a particular multilevel model where parameters are nested within one another.\n",
"\n",
"Some multilevel structures are not hierarchical. \n",
"\n",
"* e.g. \"country\" and \"year\" are not nested, but may represent separate, but overlapping, clusters of parameters\n",
"\n",
"We will motivate this topic using an environmental epidemiology example."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example: Radon contamination (Gelman and Hill 2006)\n",
"\n",
"Radon is a radioactive gas that enters homes through contact points with the ground. It is a carcinogen that is the primary cause of lung cancer in non-smokers. Radon levels vary greatly from household to household.\n",
"\n",
"\n",
"\n",
"The EPA did a study of radon levels in 80,000 houses. Two important predictors:\n",
"\n",
"* measurement in basement or first floor (radon higher in basements)\n",
"* county uranium level (positive correlation with radon levels)\n",
"\n",
"We will focus on modeling radon levels in Minnesota.\n",
"\n",
"The hierarchy in this example is households within county. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Data organization"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, we import the data from a local file, and extract Minnesota's data."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns; sns.set_context('notebook')\n",
"import warnings\n",
"warnings.filterwarnings(\"ignore\", module=\"mkl_fft\")\n",
"warnings.filterwarnings(\"ignore\", module=\"matplotlib\")\n",
"\n",
"# Import radon data\n",
"srrs2 = pd.read_csv('../data/srrs2.dat')\n",
"srrs2.columns = srrs2.columns.map(str.strip)\n",
"srrs_mn = srrs2[srrs2.state=='MN'].copy()\n",
"\n",
"RANDOM_SEEDS = [20090425, 19700903]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, obtain the county-level predictor, uranium, by combining two variables."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"srrs_mn['fips'] = srrs_mn.stfips*1000 + srrs_mn.cntyfips\n",
"cty = pd.read_csv('../data/cty.dat')\n",
"cty_mn = cty[cty.st=='MN'].copy()\n",
"cty_mn['fips'] = 1000*cty_mn.stfips + cty_mn.ctfips"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Use the `merge` method to combine home- and county-level information in a single DataFrame."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"srrs_mn = srrs_mn.merge(cty_mn[['fips', 'Uppm']], on='fips')\n",
"srrs_mn = srrs_mn.drop_duplicates(subset='idnum')\n",
"u = np.log(srrs_mn.Uppm)\n",
"\n",
"n = len(srrs_mn)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"order = unpooled_estimates.sort_values().index\n",
"\n",
"plt.scatter(range(len(unpooled_estimates)), unpooled_estimates[order])\n",
"for i, m, se in zip(range(len(unpooled_estimates)), unpooled_estimates[order], unpooled_se[order]):\n",
" plt.plot([i,i], [m-se, m+se], 'b-')\n",
"plt.xlim(-1,86); plt.ylim(-1,4)\n",
"plt.ylabel('Radon estimate');plt.xlabel('Ordered county');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here are visual comparisons between the pooled and unpooled estimates for a subset of counties representing a range of sample sizes."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"sample_counties = ('LAC QUI PARLE', 'AITKIN', 'KOOCHICHING', \n",
" 'DOUGLAS', 'CLAY', 'STEARNS', 'RAMSEY', 'ST LOUIS')\n",
"\n",
"fig, axes = plt.subplots(2, 4, figsize=(12, 6), sharey=True, sharex=True)\n",
"axes = axes.ravel()\n",
"m = unpooled_trace['β1'].mean()\n",
"for i,c in enumerate(sample_counties):\n",
" y = srrs_mn.log_radon[srrs_mn.county==c]\n",
" x = srrs_mn.floor[srrs_mn.county==c]\n",
" axes[i].scatter(x + np.random.randn(len(x))*0.01, y, alpha=0.4)\n",
" \n",
" # No pooling model\n",
" b = unpooled_estimates[c]\n",
" \n",
" # Plot both models and data\n",
" xvals = np.linspace(-0.2, 1.2)\n",
" axes[i].plot(xvals, m*xvals+b)\n",
" axes[i].plot(xvals, m0*xvals+b0, 'r--')\n",
" axes[i].set_xticks([0,1])\n",
" axes[i].set_xticklabels(['basement', 'floor'])\n",
" axes[i].set_ylim(-1, 3)\n",
" axes[i].set_title(c)\n",
" if not i%2:\n",
" axes[i].set_ylabel('log radon level')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Neither of these models are satisfactory:\n",
"\n",
"* if we are trying to identify high-radon counties, pooling is useless\n",
"* we do not trust extreme unpooled estimates produced by models using few observations"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Multilevel and hierarchical models\n",
"\n",
"When we pool our data, we imply that they are sampled from the same model. This ignores any variation among sampling units (other than sampling variance):\n",
"\n",
"\n",
"\n",
"When we analyze data unpooled, we imply that they are sampled independently from separate models. At the opposite extreme from the pooled case, this approach claims that differences between sampling units are to large to combine them:\n",
"\n",
"\n",
"\n",
"In a hierarchical model, parameters are viewed as a sample from a population distribution of parameters. Thus, we view them as being neither entirely different or exactly the same. This is ***parital pooling***.\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can use PyMC to easily specify multilevel models, and fit them using Markov chain Monte Carlo."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Partial pooling model\n",
"\n",
"The simplest partial pooling model for the household radon dataset is one which simply estimates radon levels, without any predictors at any level. A partial pooling model represents a compromise between the pooled and unpooled extremes, approximately a weighted average (based on sample size) of the unpooled county estimates and the pooled estimates.\n",
"\n",
"$$\\hat{\\alpha} \\approx \\frac{(n_j/\\sigma_y^2)\\bar{y}_j + (1/\\sigma_{\\alpha}^2)\\bar{y}}{(n_j/\\sigma_y^2) + (1/\\sigma_{\\alpha}^2)}$$\n",
"\n",
"Estimates for counties with smaller sample sizes will shrink towards the state-wide average.\n",
"\n",
"Estimates for counties with larger sample sizes will be closer to the unpooled county estimates."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"with Model() as partial_pooling:\n",
" \n",
" # Priors\n",
" μ_a = Normal('μ_a', mu=0., sd=1e5)\n",
" σ_a = HalfCauchy('σ_a', 5)\n",
" \n",
" # Random intercepts\n",
" a = Normal('a', mu=μ_a, sd=σ_a, shape=counties)\n",
" \n",
" # Model error\n",
" σ_y = HalfCauchy('σ_y',5)\n",
" \n",
" # Expected value\n",
" y_hat = a[county]\n",
" \n",
" # Data likelihood\n",
" y_like = Normal('y_like', mu=y_hat, sd=σ_y, observed=log_radon)\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (2 chains in 2 jobs)\n",
"NUTS: [σ_y, a, σ_a, μ_a]\n",
"Sampling 2 chains: 100%|██████████| 3000/3000 [00:20<00:00, 144.12draws/s]\n",
"The number of effective samples is smaller than 25% for some parameters.\n"
]
}
],
"source": [
"with partial_pooling:\n",
" partial_pooling_trace = sample(1000, cores=2, random_seed=RANDOM_SEEDS)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"sample_trace = partial_pooling_trace['a']\n",
"\n",
"fig, axes = plt.subplots(1, 2, figsize=(14,6), sharex=True, sharey=True)\n",
"samples, counties = sample_trace.shape\n",
"jitter = np.random.normal(scale=0.1, size=counties)\n",
"\n",
"n_county = srrs_mn.groupby('county')['idnum'].count()\n",
"unpooled_means = srrs_mn.groupby('county')['log_radon'].mean()\n",
"unpooled_sd = srrs_mn.groupby('county')['log_radon'].std()\n",
"unpooled = pd.DataFrame({'n':n_county, 'm':unpooled_means, 'sd':unpooled_sd})\n",
"unpooled['se'] = unpooled.sd/np.sqrt(unpooled.n)\n",
"\n",
"axes[0].plot(unpooled.n + jitter, unpooled.m, 'b.')\n",
"for j, row in zip(jitter, unpooled.iterrows()):\n",
" name, dat = row\n",
" axes[0].plot([dat.n+j,dat.n+j], [dat.m-dat.se, dat.m+dat.se], 'b-')\n",
"axes[0].set_xscale('log')\n",
"axes[0].hlines(sample_trace.mean(), 0.9, 100, linestyles='--')\n",
"\n",
" \n",
"samples, counties = sample_trace.shape\n",
"means = sample_trace.mean(axis=0)\n",
"sd = sample_trace.std(axis=0)\n",
"axes[1].scatter(n_county.values + jitter, means)\n",
"axes[1].set_xscale('log')\n",
"axes[1].set_xlim(1,100)\n",
"axes[1].set_ylim(0, 3)\n",
"axes[1].hlines(sample_trace.mean(), 0.9, 100, linestyles='--')\n",
"for j,n,m,s in zip(jitter, n_county.values, means, sd):\n",
" axes[1].plot([n+j]*2, [m-s, m+s], 'b-')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice the difference between the unpooled and partially-pooled estimates, particularly at smaller sample sizes. The former are both more extreme and more imprecise."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Varying intercept model\n",
"\n",
"This model allows intercepts to vary across county, according to a random effect.\n",
"\n",
"$$y_i = \\alpha_{j[i]} + \\beta x_{i} + \\epsilon_i$$\n",
"\n",
"where\n",
"\n",
"$$\\epsilon_i \\sim N(0, \\sigma_y^2)$$\n",
"\n",
"and the intercept random effect:\n",
"\n",
"$$\\alpha_{j[i]} \\sim N(\\mu_{\\alpha}, \\sigma_{\\alpha}^2)$$\n",
"\n",
"As with the the “no-pooling” model, we set a separate intercept for each county, but rather than fitting separate least squares regression models for each county, multilevel modeling **shares strength** among counties, allowing for more reasonable inference in counties with little data."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"with Model() as varying_intercept:\n",
" \n",
" # Priors\n",
" μ_a = Normal('μ_a', mu=0., tau=0.0001)\n",
" σ_a = HalfCauchy('σ_a', 5)\n",
" \n",
" \n",
" # Random intercepts\n",
" a = Normal('a', mu=μ_a, sd=σ_a, shape=counties)\n",
" # Common slope\n",
" b = Normal('b', mu=0., sd=1e5)\n",
" \n",
" # Model error\n",
" sd_y = HalfCauchy('sd_y', 5)\n",
" \n",
" # Expected value\n",
" y_hat = a[county] + b * floor_measure\n",
" \n",
" # Data likelihood\n",
" y_like = Normal('y_like', mu=y_hat, sd=sd_y, observed=log_radon)\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (2 chains in 2 jobs)\n",
"NUTS: [sd_y, b, a, σ_a, μ_a]\n",
"Sampling 2 chains: 100%|██████████| 3000/3000 [00:12<00:00, 247.41draws/s]\n"
]
}
],
"source": [
"with varying_intercept:\n",
" varying_intercept_trace = sample(1000, cores=2, random_seed=RANDOM_SEEDS)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plot_posterior(varying_intercept_trace, varnames=['σ_a', 'b']);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The estimate for the `floor` coefficient is approximately -0.66, which can be interpreted as houses without basements having about half ($\\exp(-0.66) = 0.52$) the radon levels of those with basements, after accounting for county."
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"xvals = np.arange(2)\n",
"bp = varying_intercept_trace[a].mean(axis=0)\n",
"mp = varying_intercept_trace[b].mean()\n",
"for bi in bp:\n",
" plt.plot(xvals, mp*xvals + bi, 'bo-', alpha=0.4)\n",
"plt.xlim(-0.1,1.1);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It is easy to show that the partial pooling model provides more objectively reasonable estimates than either the pooled or unpooled models, at least for counties with small sample sizes."
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/fonnesbeck/anaconda3/envs/dev/lib/python3.6/site-packages/pandas/core/series.py:851: FutureWarning: \n",
"Passing list-likes to .loc or [] with any missing label will raise\n",
"KeyError in the future, you can use .reindex() as an alternative.\n",
"\n",
"See the documentation here:\n",
"https://pandas.pydata.org/pandas-docs/stable/indexing.html#deprecate-loc-reindex-listlike\n",
" return self.loc[key]\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, axes = plt.subplots(2, 4, figsize=(12, 6), sharey=True, sharex=True)\n",
"axes = axes.ravel()\n",
"for i,c in enumerate(sample_counties):\n",
" \n",
" # Plot county data\n",
" y = srrs_mn.log_radon[srrs_mn.county==c]\n",
" x = srrs_mn.floor[srrs_mn.county==c]\n",
" axes[i].scatter(x + np.random.randn(len(x))*0.01, y, alpha=0.4)\n",
" \n",
" # No pooling model\n",
" m,b = unpooled_estimates[['floor', c]]\n",
" \n",
" xvals = np.linspace(-0.2, 1.2)\n",
" # Unpooled estimate\n",
" axes[i].plot(xvals, m*xvals+b)\n",
" # Pooled estimate\n",
" axes[i].plot(xvals, m0*xvals+b0, 'r--')\n",
" # Partial pooling esimate\n",
" axes[i].plot(xvals, mp*xvals+bp[county_lookup[c]], 'k:')\n",
" axes[i].set_xticks([0,1])\n",
" axes[i].set_xticklabels(['basement', 'floor'])\n",
" axes[i].set_ylim(-1, 3)\n",
" axes[i].set_title(c)\n",
" if not i%2:\n",
" axes[i].set_ylabel('log radon level')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Varying slope model\n",
"\n",
"Alternatively, we can posit a model that allows the counties to vary according to how the location of measurement (basement or floor) influences the radon reading.\n",
"\n",
"$$y_i = \\alpha + \\beta_{j[i]} x_{i} + \\epsilon_i$$\n"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [],
"source": [
"with Model() as varying_slope:\n",
" \n",
" # Priors\n",
" μ_b = Normal('μ_b', mu=0., sd=1e5)\n",
" σ_b = HalfCauchy('σ_b', 5)\n",
" \n",
" # Common intercepts\n",
" a = Normal('a', mu=0., sd=1e5)\n",
" # Random slopes\n",
" b = Normal('b', mu=μ_b, sd=σ_b, shape=counties)\n",
" \n",
" # Model error\n",
" σ_y = HalfCauchy('σ_y',5)\n",
" \n",
" # Expected value\n",
" y_hat = a + b[county] * floor_measure\n",
" \n",
" # Data likelihood\n",
" y_like = Normal('y_like', mu=y_hat, sd=σ_y, observed=log_radon)\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (2 chains in 2 jobs)\n",
"NUTS: [σ_y, b, a, σ_b, μ_b]\n",
"Sampling 2 chains: 100%|██████████| 4000/4000 [00:20<00:00, 197.72draws/s]\n",
"The estimated number of effective samples is smaller than 200 for some parameters.\n"
]
}
],
"source": [
"with varying_slope:\n",
" varying_slope_trace = sample(1000, tune=1000, cores=2, random_seed=RANDOM_SEEDS)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"xvals = np.arange(2)\n",
"b = varying_slope_trace['a'].mean()\n",
"m = varying_slope_trace['b'].mean(axis=0)\n",
"for mi in m:\n",
" plt.plot(xvals, mi*xvals + b, 'bo-', alpha=0.4)\n",
"plt.xlim(-0.2, 1.2);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Non-centered Parameterization\n",
"\n",
"The partial pooling models specified above uses a **centered** parameterization of the slope random effect. That is, the individual county effects are distributed around a county mean, with a spread controlled by the hierarchical standard deviation parameter. As the preceding plot reveals, this constraint serves to **shrink** county estimates toward the overall mean, to a degree proportional to the county sample size. This is exactly what we want, and the model appears to fit well--the Gelman-Rubin statistics are exactly 1.\n",
"\n",
"But, on closer inspection, there are signs of trouble. Specifically, let's look at the trace of the random effects, and their corresponding standard deviation:"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, axs = plt.subplots(nrows=2)\n",
"axs[0].plot(varying_slope_trace.get_values('σ_b', chains=0), alpha=.5);\n",
"axs[0].set(ylabel='σ_b');\n",
"axs[1].plot(varying_slope_trace.get_values('b', chains=0), alpha=.05);\n",
"axs[1].set(ylabel='b');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice that when the chain reaches the lower end of the parameter space for $\\sigma_b$, it appears to get \"stuck\" and the entire sampler, including the random slopes `b`, mixes poorly. \n",
"\n",
"Jointly plotting the random effect variance and one of the individual random slopes demonstrates what is going on."
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x = pd.Series(varying_slope_trace['b'][:, 10], name='slope')\n",
"y = pd.Series(varying_slope_trace['σ_b'], name='slope group variance')\n",
"\n",
"jp = sns.jointplot(x, y, ylim=(0, .7), stat_func=None)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"When the group variance is small, this implies that the individual random slopes are themselves close to the group mean. This results in a *funnel*-shaped relationship between the samples of group variance and any of the slopes (particularly those with a smaller sample size). \n",
"\n",
"In itself, this is not a problem, since this is the behavior we expect. However, if the sampler is tuned for the wider (unconstrained) part of the parameter space, it has trouble in the areas of higher curvature. The consequence of this is that the neighborhood close to the lower bound of $\\sigma_b$ is sampled poorly; indeed, in our chain it is not sampled at all below 0.1. The result of this will be biased inference.\n",
"\n",
"Now that we've spotted the problem, what can we do about it? The best way to deal with this issue is to reparameterize our model. Notice the random slopes in this version:"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [],
"source": [
"from pymc3 import Deterministic\n",
"\n",
"with Model() as varying_slope_noncentered:\n",
" \n",
" # Priors\n",
" μ_b = Normal('μ_b', mu=0., sd=1e5)\n",
" σ_b = HalfCauchy('σ_b', 5)\n",
" \n",
" # Common intercepts\n",
" a = Normal('a', mu=0., sd=1e5)\n",
" \n",
" # Non-centered random slopes\n",
" # Centered: b = Normal('b', μ_b, sd=σ_b, shape=counties)\n",
" υ = Normal('υ', mu=0, sd=1, shape=counties)\n",
" b = Deterministic(\"b\", μ_b + υ * σ_b)\n",
" \n",
" # Model error\n",
" σ_y = HalfCauchy('σ_y',5)\n",
" \n",
" # Expected value\n",
" y_hat = a + b[county] * floor_measure\n",
" \n",
" # Data likelihood\n",
" y_like = Normal('y_like', mu=y_hat, sd=σ_y, observed=log_radon)\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is a **non-centered** parameterization. By this, we mean that the random deviates are no longer explicitly modeled as being centered on $\\mu_b$. Instead, they are independent standard normals $\\upsilon$, which are then scaled by the appropriate value of $\\sigma_b$, before being location-transformed by the mean.\n",
"\n",
"This model samples much better."
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (2 chains in 2 jobs)\n",
"NUTS: [σ_y, υ, a, σ_b, μ_b]\n",
"Sampling 2 chains: 100%|██████████| 4000/4000 [00:20<00:00, 193.45draws/s]\n",
"The number of effective samples is smaller than 25% for some parameters.\n"
]
}
],
"source": [
"with varying_slope_noncentered:\n",
" noncentered_trace = sample(1000, tune=1000, cores=2, random_seed=RANDOM_SEEDS)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice that the bottlenecks in the traces are gone."
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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S08kc3uyYwCce2o21q+pDXjPg2hVgERBkHBBT/oQpl9d8CVQWsPDd07a2kBcsgl9MhszHMxHPYnQug7e7p6THcHjZvc9osShbsDDG1gD4ZdjO92EALxDRTPBRKx+veg9Uq7HY58noJgamU9i6urG6ApYJFyheP5F33e386BPuz2qQh6YW75cKYQbhxfcKyMlEeRFUXNCKpgaOV+hoWuE+8OvWOT3fd04VmyZ4tJxfXqynjxX8MN2OCcbr3Obl4BoSF2QyNMawf1MLOsbiZWkL3rr/QAgK6Z1KliFYHBOY039XO2iyiBCRiI2sYeJ07wzamupCnYe3O1lI/EKYpsc9UX1EhG+UyHLtZaloLmX5WBhjHwDQC+Dfw3aefxpAD2Ps52pftOWF92UB/EeNXROJkrZhsX387Op4TUxjqZxRFPLaN5XEF17vKtrulz3AO3ucH1cYhZYuR9g08+5t1d2AlCdiqlxl8sWLtqtPFg3nLZoojLlfpD6gow+L3zilMJnWKhL8XojI7oi1gsO/3Ov3TaWK2svr1yZCR1TxtlUYlFSHX06+Ez3TON4znZ8bwq/tt4ZN0L2oRX8tCmZZcI538ON3zSBTXTmWg/mk3Nb+OdhO8/uJ6LeI6AEA/w52ipYbGt4mxI53IpEtiqzJ6Caebx/G8+eCQ4DFRq6x2oxEnnyjG8+ccI/GjnROIqObmPGU0/DxKXid0S9eHIVhWvmOP50zS4a9VuRjkewXTiG0d0p6BXlIbZKbrbavbXLOxk0NBYo1lsK5uc+jLkCwhBWaDMzHx2MfnzOs/FwWv3Py+8AHPXJLmNycIu7Lw7hFws6jsWrQCfKJuUDB5OSFPxcxvP2N6xP4ytEeaRuVtUvTEUTe96MS+KPrnUzi71+9XnJSq987HxQUJHvuixEIVK5g2QbgWc+27wPYUpviLE0GZ1L4zMsdGJj2d6DlTWFC6xydy+CrR3td+/HfS/kGxEbOGKvZCER8IdM507ccpuWe2cuRLSxlErnK98Nzw4EhlaUauuxX2TFhcj/xl5lriPx7WIWFjw5bGqKu48VRsDenl8YYVtXb+/O5K3UBgQJhF+tiTC4PuZYirlvjd4tfumRrXrwdWEShOx5xr6b6iLR8gG2CslymOrn51PtZ8vrCfs+3l56bxZ9dYZAE9DnzO7ivSgwtlmkRL1wYwVeO9uDVK6Wj1EqX2y7PVSf6rFQfMOojeIJM7EGh7wtJuYLl6wA+5dn2SWf7ioXbxf1GRoAwbyFk+olSe4kvG2PV+y5kprenjvXmTRpiU7UswvCs3ai9nUKYTmhkLoO3u6d9fxff3+PdU3ijwzWdCUclq+JJR9ZlmLN4583PE9b/JS7SNSssJCZS7COgolFlXcAoM+yMfI3JBeKQM+dD9Dnxer5yeQzfPF7QUnlWXN7ZvnplHMd7/J+ViNgmG6PFggWw79PnX+tyPdMTnvMXTGGFbWHalbiLTLvIGiZevjyWD2fn5j5TsCLw4870z2AinnVNApWVQZZapVz8NPRS1tHvnBqUBgDJjsvoJi4OzUnNi/OdzFRGSec9Y+wwCuXUAHySMfZ/ARgCsB3AZgBvz1sJlwn8ZSk1sbHU6OzS8Bx2rmt2NXIGVrWP5YtvdBVt8/PzXBZCeIsbpdy+690tyHQg1u0tZ4XMu3asQVtTFIyxokmOQOXh17y0Xg0qrFDiRU3nzCLtk+N95oZJRdu4BiMj7GCkVEiteE3ezrxrtPNOSWyHFwbn8MDeQuak/GU8xXL5lXzKx03B5wZn8cgtmwCgaAVQWVQYUelnIl5Ttu+ZvllcHJpDa2MUa5rr8vdDvL/ecov99nwFXpqW7dPyljlMfx/RijN2+w2KXr48hscf2CW9fp18HDBvhIkK+7Ln+5fmoyDLHZmPJWg/GRndxEuXxrC+pR4bWxo8xxUOHJxJYfuaptqmyhZOJdqkw2QAsByHsEigT0Gy7StHe/DBWzfjnTtWy4+RmsLC0+8xY4Y9ll83EzCp0yt8Tav4fqxt9o+YCmsK8jOFyZCdUTctIWOCWyMOdU6XIJCXmbcX8ef6qObSpp49M4hPPbK/KC2OVuKpiNFfsj15PUbnMp4lvYvLzeeFuJJ5VjiyH5hO4aZ1ze6ySoS8t8xhBJlMYwl678tK4DqPlBQsRPRUOSdkjH2eiP648iItP0joWEt1xGFU/kTWKBrFiod959Qg3ndwA961a135hS2TUPNSqLgjCzL9+L3AI3Npf8Ei2RbGnMUYw3QyV2TPlh3aPZHAxtYGtDYWwlN5UWUhsXwk6h1LmETwuk0iEYZbt7biykhxsoiwHZpd38rnp3zuZ4V07O/Y1pZfSdKL3xXE2eayZs4gb/+b2xpd9z9nWBiYTrlS9oe5A6XuEy+3N2WQVzNyHSNUttIO+LunB/GnHzro2ib6zTrHE9i5vrlIILxwYQQ3bylMPpZFq8nSQgW1AJ5/TbRGLIYpbD5Sujw+D+dccsQzej4BnmhuOHy9+GWdSebwyuUxWBZJR3QcbgvP6la+gQDAbDpXZOsd8YRYXhmJ1SwDrNiWvR2FrEOWOYCD+nz/hJLM1+kv61RWN5een8Ag1yK5D0nkOUnuJ35VmbWKP3/vi2tY5LLr83Lcu1s+EDjePR1qQTeG8k14he+FDfVRDXfuWFM4r89JxVOkc6ZLKJ7uk/tlZIJljeQ5ef2Vtjk1uAOcSdrrwXSOJ6SCiJtV/QZ3jLGiEX2tlH5vmiJRsLx8eQz/dLgncNBpmBZ+emm0aLusfEGh8qNzxZF5i5F3cD4ESw3tM0sTIsKXD/fkM7aKk+1kjtiXLo/iwtAcRmOZQPXXb8W6rG7hTY+DmzthOS9eHJVmgK2WMKMdEjSWfELEgH7SP6Gk/6JOg9PFadzLCdOVIUvwmPCEoRY00eIKccHiFXrt/bPQTXLNY9IYC5wN/80TxZPyvJTXCbrLJLa7uggre/Kud46KTDAzJu/Ewmm9VNI0xKOkro0GT+wM0my818joVk1WqPzpJXe7lfUDQemH/Bb0kz2nIFOYNGvACtFYFsGit7BwMxVPTV0fCfaM8YZgWuFDO0tRKpFj2fgUK8ysaBLCjR+7/ya0NkYDBZLfT4z5Z7Udmk3jukdrCxOlywLmAImp3P2eS1C035cP9+DycMz3HokhxuKkRBlTIVZy1Fj4xXW9RRLTy2vM7Ujm2tJ3Tw/iy4e7izJXA+FDoisVLLowF6oUfhoLx29hMLGdct7smMCTb3SHum4QYx4LQq3S+ctkSNCYwLu8A7ByNJYVTdYwXaPakbl0ySzGfKRqWJTvcDO6+zzlCpxaL+zjd/WhWXdHLyumRcCPztsLEzHYo+Gg+vgKlhLdJl8WuHDdcPcszPLO8vj/wka/l/NM/4zvb2IAg2kRolp1rxtj7gmSQYLKWx8xICOquc+Typn51EE8dY2XrF66o7RIruGGeU6GWVpjEc/nbV+i1uEXQGNr1vPXybod9uGOKfXee9/z9x3cEKixyOq+5H0sjLE7GGMNpXarojxLDp7enPP517rw1Fu9+e/fOjFQFE7ppRBP7355XhVMV+WOKqpZ60WGX9vzhv76LTHLNzPGMwX4X8u3oylZJfcOFhH2blyFjz+4y/8IVnjh+SRHGbISicUMej4WEVZL8lGJAQylNBYvD+4rXjjVe3TQgObly6MuZ7CY1ysiidgTTV2yppUzS2vIz7cPS7WFMIJFt6yi+S5exGJ5TykuZucXvm2Rfzv3mq7ed3CjfEcfElkDb14vmKvD5j8rlZBTnNC8f1ML3rVrXeBrIqv7ctBYzgJ4lDH2F4yxJxlj/5UxdtCzzzdqVLYlwVy6tP21VN4vPlI1LXKlkig14SuIWq9Emsjq+cW4ROHBO0zLIjz9dp90HQqxHgy2IA22c4e3J4t4f7YsQl1Ew6oAgQEUXiyv/wQo1DXsmuxFx8PWiGRCw6uxlCNYZPt6NwUVTzfJtSaL2EHJBiVSjU0Qt6VW/QRs4ST6rXi2ijBNO6tbONkrFywbWuxQbfF5eJ+NaEr0m3A6Ec/4aginPNe+bVsbtpSZ+LVLMv9qbYkAk9evjWMmmQv1/vNdgl4T2YROP9PgfFKuYGEAngJwEMAUgHcAOM0Ye5TvQESfrF3xFh9x1OmXYZjnk/rVu7ZJf+f9i2mRy67Pc0rppiUdVWxq81cO/Top19yAEq1VPMcPz43kI6JE8zCvf9awMBnPSkdE7jkRtpklaJT0+rWJIk0QKB6Rr22uw4dv2+L7u0XObPSAF42BBZoC/uFnnUjlDLnG4n9aYSdCRrfQWFf8KjUJs9J2rmsuK/GlbF/GmCuVTKkOw6+D5ecWOz0/IWpZ5FomoRTnPZGJl0diocy8lwMc2zvW2nNExDblzWwdZlQ+k9J9tRlv9oFSwRYyRL8nv58y7VDk/OAcfnxhJNwgxtmnXDN4GFNwranE6PthIvoYEf0/RPQYgF8F8Fc1LteSQbSL+3VQfNErP1MLt4l67Z8RxpDKGfjczzqlM+O3rWnyLZdf4xLNci9LosQ2ttrCqncy6fsyGpIUGEFteUBwuGsMjo/Ff38AeEMyh6J/OpXXKqIawyfeswfv2Nbmew6LyOkAApqxT6QSx7QIA9Np14vNNdAwpmmCPW+iUTK1mbeHDa0NiEY0MMbwvoMbSp/UB8bciR5LdUZ+Dnf+LMWBhXgmXRAiL10ewxOvdYYWLF6ISBohyIVas5Nz7PKwv2ApDMCK6xvUPqpBY/LB23jMP9GmeI94kwsjnAjFbU3WnjiyM/7rd+3w3V8W0TjflCtYUgCOebYdBuBfq2WO204u34c3Hr/Z5vlJdp7jIxrzDTEuhV9Hz5dXBdwva0tDFHs3rsofN5X0j0Li7bClIRpqtCmGQtvO+/CT2URKZcf1Oi25YJHnUypsCzOaFYvLJ9iFcfQSAZPxrEs74XhnYwPhV3aUdaJhIsdEcoYVOHNb87lH3OxFVAiRDWMKk2Facs0vEtGwqiGCR++Ua/kivJjegdma5rr8QKnWaKz8kGyxDfH3Joz5MyIJdrl755qi/fIz+J1TtjZG8fO3bcbjD+yStjVO2JRBtaRcwXINwH/wbPsz2L6XFYm4YJKfacm7mJMX3mi8nW1EY8EjwYD2EGZSm4jmRALxKvi1d8si6KaFhjoNO9Y2Fa0QKdLaKNHQHI1lPrRvqSnMpwXfv8eejKiVMMsBxQKksHSu/X1Vg//okfsuvI70fZta8pqsSNjOqhbhqn6ChZdBLIt4j7jWK7bNsGuteOHpfhrrIti3qaVwPdPCjrXNRaluHrllU36JAg73CXlNf6mcWfPoSI6mMZfg9cN/jRz7M4zGIgt2kT033eCCxf6tPqrhtm2rSwrX5eC8/xMA/5ExNsQYO84YGwHwCQB/WPOSLRFEYeH3gPh2v9EJP8w7Kolo4VZBlKGXOYJksBtwKQ3EJFuw1Dumm3zZJSJL1qAZs1/KoLTpfD/A33woK2WR854Ka517I8Pu37se9VENZ/pmcLrPXuD01+/Zjl+RLEdMnmghXna+ra2x9Az/27etxuMP7MKtW23TjMYK81gM1xySkqdyjqm+M8iZlnSww7eITvxLw7EiASpmlPCmSQkLDw1uiGr48G2b89tNsgWbV/hGNYY2z4CF30evcMsZVk2jI70DpTDn/oNDe31+Ca+x2AOxwvN+cN96qcDkpk3+S9ia12pOTTmUJViI6DCAvQA+BuB/AfgNALcR0fV5KNuSQDRv+Zmt8us9CI866rJfc40FWCcs36oxVrGJoX86JV05b3SuEPkiqsfcbGRZhIl4Fq9fmyg6FrCFpG7a0VZMEEQyeSQ1s6B4YbL5CqMnKrz861v8R21cq9i6ugkHNrcW/e6d38B9aXxbqagzAGioi2Bja0M+io6B5TuqhDA3JOwIO+yExFu2FNeHkzUs6fV4mxN/ujg0F1i2Sn0s3RPJfOZi8fyxtG5nAPC0Ie9+QCEIomixNvhrrJWwvsWtPYUZBPgJHz6uCiNY7Pes8P3unWukx+WXuODXDNmWKh0UVEPZj4WI0kT0OhH9CxG9RUShSs0YO8gYO8YY63A+D0j2+a+MsUuMsXOMsdOMsQ8Lv32NMTbIGGt3/v5zuWWvhDCqLNf52wMTAAAgAElEQVRYxOfsnnVtfx65PukK+wzKjQWUtvF7Jy9yuE1VnFtBZHf6BASuo22RvW56NMJcTviwsoFQbAqTah/C9cLinUBpWhS6o26qj+Sj92TI5qzwOnhH1YwBDZ4oML6P2FxanFT5m9sK0YRBTlmRsPvx6r9ze3HyzpxhSf1+fOVCb+cV9CwMi7CmuU6q8ZXCInmUVVRSNplvg0fcpT2pVx6+eWNNTWFezTSMKSzqkx6H38sw/UdEc/tYNMZcAmvbGrv9cM2DnzJszWVh0PPNQs68/yKAJ4joIOyljJ+U7HMCwH1EdCeA3wfwbcaYaHD9GyK6y/n7y/kvcrgXXCpYhJfGawriSfma6iKBI9M1AanWAf+OgKd4F383HbNRKXOr4YSX1kU0RxBxjaX4QNm5LIvsnFEBcw6AwqjLrziyqslMYUHvrVjmIHMWeUQ49xHz4xs8bYCBFS10xZ+32BlpGsPvPrjLFYYe5K+xz8Pw87dtxkOSCZJy7OvJ+tesYQV2jgc92lsy6z9GNCxCc30Eu9avClmuAh1jcScsnGG/4GfhnSc3HwJ2J+vVQhqico3l7p1ry5obVIpSgmTXetsCcOjABnz8wV34N+/ZjbqI5hpkXHfm8fCmFwmhUnkHYt6AlCZngMKTmPopLL9+z/aic29f27QoefMXRLAwxjYBuAfAM86mZwDcwxhzTW8lop8SEV844zzstybsG8avtYYxtlv8QxVRa7JoH99rC2OIoHQgPC1771TSlTrcy903FUeGiIgRYCLcFk1UGNHzTriUj2U8lkFGN1EXYS4VXXaU7FwN0QjqI5rLBxR0yXI0Frd5jRwTi39nIMrs4HXCi4WwfT37e6NEY3nXrrWubbwj8F5lQ0uDa3DS7FnwyzvDXjcJt21bHbiejQzpbHnDkt583iZul2g5fpjOWi5hFATpYExohxz+//5NBWHFw9VFGvIai8QU5tn3li2tLg2xHLxV89463hfURTSsb2nID/zE9tHrrPNSjsbizWenMbi06whj+NMPHcy3Od7PeDV4mdBvbYgum3kslXATgCFuNnM+h53tfnwcQBcRifm1/0/G2AXG2A8YY7f6HPcnAHo8f4crLbh3FMPVUhliGxeFiffB8j5jaCaNLp+lT1sbo9JOU4xXF8Nz66OFkRPP60RUMCPwTtgvFxTnh+dGMJnIoSEacY2kZP2/VyjcddMaNNVH0FgXcS2MJTPpBS0f4IcsU0HQeyuWTzQtvGf/Btdz9Drv86Yw59PbUWoMuPOmNdi7sfhF5s/MrwNuDfDX3Lq1Fb9xT3ljoKCOPqOb0oFLXbT8Uf5MSgconI9IppXx5yRb5VI8J5OYwjTGikyPHG9KfgLw0ft3FmljYbDnGW0UJuW6Gyfv7L3v8317Cssh8GCJl5xsx2H8G96F8pgnqMHbxstxsUQj2rKYeb8gMMbeD+D/BfCYsPk/A9hPRO8E8D0ALzLGZOrEZwHs8fwdqqY8dwkx5UF2evE5/7Jgi/aGKXtHGrKXRjZivW/3usB4db7qJHfOWlQo7zu3r8a1Uf9JaF42tDQAzN8UduvWNtzrWWiMv+QNdRpyRiFbrUx48DkJ5STfdGkVJSLxvIgWiXfvWefSOEzbe190Hf7pfT782fDiiJMeS73sQeaWX7h9K3auL36+H39wFx69cxs+9ch+rG6qw12CJsvPxrWzrasb8bsP7gqcMFepX2JoNu1quXxyoxevViZe0+V7c/4XJ7jKfCwMBXOYl/Wr6l33nEcqVmIiY7A1UT7p0ts0eRi09/bdtq2g+dVFNFebTkrSCP3+e/a4vpsSxVLUsG/2BGjkBy+SOnzs/p34V3cXTGJRja1ojWUAwHYuCJzPbc52F4yxB2HnG/sIEV3j24loiIgs5/+vA2iBxMRFRLNE1Cv+ARj07lcOj9y8Cb9wuz2K2bY63Gz4HWub8aF32OGVsgcrNk5ZyK3MdPPeA/6ztokof4w4byaqMfz7nzuAQwc24M4SpjWRtqao7WORaCwfvX8nfuH2LbhpXbOrk+MdbkM0AiL5pDpeb1lH46qP0NN/8NbNRfsWJouFFCye/cRJY6bl9rJwocVNYlGN4c6bVuc7Ui6s+X7isgnzMa9ifUsD9m9qQX1Uw++/dw/eLYyQef25Yzca0bChpQE3rWv2zVNVjcldrJ5fXd+z3z+BpunK6uAMDoS2HmHFPhbGmDRlDv+Nm5t2b2jGvc6AoSLB4jlEvE337l6Lmze34tE7t7kWSfMS1RjiPvkAOd4F6kzLKhYswk3wZpbg77d3sT8A2NTWiN0bCpp0RGPLYuZ9RRDROIB2FDSQxwCcJSJXzCtj7D4A3wbwr4nojOe37cL/HwZgAhjCAnHr1jZ88uF9gfZbxoCP3L0d9+0uTM4Din0sBHc0k9cBCACbWsuzE1tUcBSKGVOZ4whkjOHAJu/Ix/98UU1zpb8XayDeg13CCJur740ek5yoaXzglk0AHI0I/p2cOBq+ZWurs6/oY7E/K/XdirH99jo5hd+8EyQZY/jALZvzQjSfrdrZQTQtlVueDS0N+PBtW1yjzFLk/Tms0GHzkOg9GwrPQ8xT5WdK8uINufUi+llk7efg5lZpeDbfV/R7NTnPWPRDyMKNgzQWoDBIaGusywtafk57EmG4tC9eSwIP7330zm04dGBjPvggSGh5TU+P3LIJt21rw8fu3+naT0xwOTybwVWPNUEcbHoHmeXMpOcay0Iv9rWQprA/AvBpxlgHgE8738EYe4Exdq+zz+cBNAF4Uggrfqfz21OOf+UcgP8C4FeJqPql38qgsS4S2KgYY9izYVVes+Dvh1dj4aG/nAhj+OOH9+c76bt3rsEjN7vTdktnuQtw7YT/zxFfUm/ZGRgevVMePmqv2SFqLPKGKZo9uMbCfRLczyIeWh/VsH1NU37RMz/nvShYZdqNzD4fhPcy4rwMw7KkUWF5c5tzDd5hcoHJhZMY4FFwrPrDn+XH7t+J/Zta8I5tba5RZil4nSNCJ7+mqQ5/cGgP7tlZMPHx9nDr1jb88cP788IrKIw9jD2e19Gvr5LN7eDPjguuB/aux/171rvqAzgz3r2ChcFXYxERR/Dc5Li2uR4/LyQyDcIrVJNOeHOpSD4A+Llb7QFTVHNnerDTrmxBm2dZhcfevROffHhfvq6XPLnSuK+Sn1PEL8OHjGhEA9HCz74vPfOrRhDRVQD3S7b/kvD/fQHHf3CeilYWftFFsv4tL1g8IcV8wph3P97Idq5rzsf479mwCrppSTMnN+Qd8/aImwuOFy+O4tatbY7GUti/SLAwYP0q+cTCiPOCF2beyxGdp9xE1OCZKS0eqzF7UpxJBS3h3t1rcap3xnVebnoE5HNeuLYgE/SfemQ/AHu0+NrVcacM7hrs29iCw9ftRJj2IlOyqDC38OJaFk+UyaOUWoVQ5jBy7jfvvQl9U0lsqjB6iXc0D+5bj5iz+Bl5ymGX212mFkegBQ1eeQfknQ0uwrdLlyFA8BICH3BG8DxjsVgfwBZKsoA4rrFENP8UPWLYMj9nORqkd7LpmqZ6jMeyoTIv7N/UglevjIMAjyPe/SliD1QBy8e/31inIaObRffz4YOb0D3RE1iee3atxZqmuvyg1rAIAUpfzVkwwbJS8NNYZCNnvq1IYwG3jbs7R34KcfePBJhI+MhRlpconTNhWe4Xq1hj8Q/3jUaYZx6LvAxixJRXYykkMxReNNhRcYZe6My9Zo49G1a5zsvvi1gGsty/iXABd9dNaxBL6zjdN1NU/rVCBgTDY+MuRIXZ37mJe5PjGN7pBFC0NkYRzxgus0UYDWp1Ux3uCLDTcx69c6t0+WVNs8NPAeQFpwy+Lv31sTg+fNuWUGXjbbWpXkMya+LmLa2+Ye0yvIMmDtfG6yKaS6gAbh8Ln28lwlDwsUQj/oJF9Pfxupbj8vJe94Pv2IS7dq4JlXmBX4+IXOXj76jfvY9oGnSfRdT4ebw+ltXNdbh/7zrUB4Skv99ZqOyck/dtoR34SrCUiV+Kdlmz4du86TC8ZiXe6B4+uAkam3D5LYIoCKLi0ft3Tw+gsS7ielm8KrWm+U+YjGi2Ad8OxS04t+/fu05+AJBv6HlTmKOxuF40J+rHJMpnWPZqgcVpPuxj5tI5zKV0rG6uC20K4yl0ZILx1q1tuDISg266nffeqLB80kaN4ZMP78vf50fv3IbxWDYwUrAa9m8KHzIbZEPnNvkwo3fu6G2siyCZrSzJo8wUFjQnS2yXW9oaMenNcs0Kg4+g8oj1KwSyhCmxnIZoBNsDlq5wFVEYFIrtnZfJr9xB81zyfkRJ83poX7jlF7jZNZbWA1dQrTVLMtx4KeOnsQSZwrwQ3B0BV+FXN9fh0Tu3hZ4c5zURiUJvMpHLp1fxK3tzfSTvQPXCnfeAe55HUPAC72Cb6+w5MDxHljhaWtNcZ68waRG+ebwfAFDneXNkt1hjwJWROL5ytMdV51IdH6+zrH/5hdu3YN2qetuvINFYZOa2xrpI/vk010eLfCN8saewzvJq4SGwGwJypeVNrZIb+/6bN7qyCfNJkzyzgLh4FUf0F2xotSeA8hDaW7a0Fj2TLasbpelbON42KvOxNHgi8WSIg6hSUYcijz+wC//20J7SOwZQ8DuRR7CUb5LjlOtHlMFN3dMBy2TMB0pjKRO/EYYs7NU3FFZo7IcObCiKUw+Ld/Kid2RDRK7OxFv29S0NaGmI4n0HN+BNz8JbEa0QI0PCNYKaOHcqahpDS2MUsYyOjG5iNmU36nt2rcWGlgZEmNuc4dVYvNE5ALB5dSOGhAXFCkn+3Pt5Q2x5mYJMfsXOe27+sz/Lea+536WpbmFerYObW7HtfU2Bo9GCv6HQ+XHu2Wnb4vm9fd+BjXjP/g14vn0YgB023+3JNdXSEEHMScj6sXfvhGER6qNa3jznpZTW4G2X3vvNUNCCw64lXxhQlN6/Fmu68CpY5E5nVPCxyBtR0Oqm79m/AS9fHgudN05GW1MUhw5sKHuZ5WpRgqVMytJYfM4hmk7CzsOQ4fV/eM10lsfeLZb9/TdvxDscTYk7J7nPwD5XIfOsaAoLKq84Km1rjCKWNvC1t3rzne1ux8RnO++F40p0LPx8Ymy5bB7Lpz+wv6h8XLvwG+nWaXZ4qPh+50wLGd3M+zfKSc3OtbMwkUS1opSJg5UYNYvtQtMYNBSizURBLeskNY2hvsp8Xd53SvaO5TWWkLataL7turfftq0Nl4ZjaK6PIJUzi6K1KkUU2pbH9BtEW2OdNFUNYGuP5aTdkcEYy+cYW0iUKaxMfDUWiRiRjZLv3rkGH3zH5qrnYQCFl0bmY+HbvekyOPfsXJsfCYlaDZ9n0hDVBFNbOI1FpK2pDnNp3fXS8PJFGPO8fMBv3ReU3afYHCAzE0QjWtE9KCVYIpqtsYjP6mz/LL7weldFpoh371mHe3atzQvtxYQPYPi9Fk2bIrL6BY20y10DpdTu3msUm8JYvq3K3jMZMu0MKJj6VjfV4Tfu2YHfKdHuwuLysZTh2Pm1u7b5ZjBYzijBUiblaCzeyWCP3rkND9+8qewoIj+8K1N6hZ4doVP6/LyjsIhw501r8KcfOuis0e6cRzAohC3u6qa6onBUrlFFnHBjjkXA9jVNhZQZkvMVCxa+PbgcpQRLNMIc530x+dDbMqR/Y10E7z+4MdCnsFA8fv8uAIWOrvA83YR9pkHO5CDKSTQKSHJjoSAkw2qCeee9ZzsPud63qQU71zeHivgKA584qpsWfnJhFEBx6pb6qIYH9rqzEqxqiOLQAfectZWAMoWVidhR/+mHDuLVK2M4Pzgn7QzFzuzWrW2ulOH8l2oES2GGvf3pFXp2duPS5/EbyTJhOwWM3h9/YFdRTiRZ7D8vn+aZi8Cvu2/jKgzNpKUdXZE2ZoXTJnikml+4JZGdzLNvqnjNivF4xrlG4CWWLM1OJ1zQjuUVkUU6is5oL+W2WT6hNAjRDyAT5FygvGf/Brx4cdT12461TZhNuRfhyzvvnee+d+MqdE8k0dZYhz96/75QEy7LRWPupca9t5XPr/Iitu1K/a1LDSVYqoS/BLKXLcxs10rkym/fdxOeax/ON2K/Tt+0KJTpgL8ARSNZ51OMCpOxsbWhyAHa1iTJf+YxhfFJeDvyyf34Ff1NM5y8mapEr8/r5pcviUfLHO+eLvqt08k8HZROZClTFF7u3ERvsETQkgIy9m1sKXLoBxEmw6/oB/C2Y4L9DHhwwIsXR3Fgc2GQ9pv3Fpuz8j4W5/uv3LEtn/jULxKyWjTmHsCEzVcmKre/9M7yF1JbiijBUiXcjCQ1hbnMPe6euZCHqvxrblvThDt3rMaJ3mnn3PZ27whpJqVLl+L1wl8AbxkLi3EVR7mUQpbhNpKPGrPvzYaWBrQ2RvPmiLxYCaOxhDSFcdv8zVvkPg9xdrpXeCazJt57YMO8zVOZb/jz46PgiMZw6MAG7PGESMvC20Wz2ea2RozFMvkO+fbtq7F/U0vRypp+bCkzw0Cp837qkf0l1zkptOnC94g2vwMExlheeAEInMAoUk7ur+WCEiwVsLa5Dns22iOmoAYu5vTxa2SVmsIYY3kTVZCT2Tu/4ZFbNuVDRTkRj9mgUDb706LyswlL03pwH4tTdsO03BFJXEhLzhfGeS+jLqLhjx/ZVzRXhiOa+2Ts39gi/2GZ4K27LEJI1jb5stYNUQ2/de8OnBucwz5h/ZmwIbCPvXsn1q4qL/Jq6+pGPP7ALvzg7BASWaPIHBdG0PstvDafcB8LJ6yfjWt0d5WRfXypowRLBXxCcMrxte1lHe6tW9rw+rUJ5AzLdxRWuWCxP4nETrZ4P+91ZY2Xh1x613rhL2ciY5QdFSbPF+U2xWQNqyizrf1ZfGyReaSMiK0gU1YpjWe5aiucMGY8WVLD9+7fgB1rm/PpV7wrZoZlfUt9BathMmxsbUBDnYZEtvT+MtY212NzWyPu3rlwnbXGWF77ENfoKQVfR8mrSS5nlGCpkvxa55IOStMYHti7Hm92TORTi3Aa6zSkcmbFjmFxyWHkzWrFJwvTMTbWRfBv3rO7qBPincpoLJMfwYaVgzJNjgsbbiaz6y8IlgCx5T0dHxjW2rHuNYktd8ESBtkgIBrRXMEmlVLN4/m1u7ajczxelFwzDE31EXzUk6p+vtFYITs0X7Y4DDeta8YnH95X1UTIpYYSLFXCR3t+L9DdN63BxpaGopUBm5wJWpVOkBRt4AV/Q2WCBZC/CDxyxl6IyDGFlTmPQITXVVwCQOzU8pMwJeeTzdHxu045bGhpcC3fu3V1Yz55IxBuzfLlTjWTdOfz3Kub6vCuXQs/ua9SNMHHUu5cn5UkVAA1j6VquH3a7wXSNCZdbrbQkCpz3BX8HxRoCqtmxM1fjjc7JvPCqxqNhSMKMTGqKyigwTcqrMpO8eec1SkBu8xNnqCD+ex0lxLvO7ghcDnjSrkB5HIeJoQbV7KC5UpCCZYqieYFS3nH3bHDSfZX8Uil4HS2BG3io/fvxC++s7CWSdjIFBniy8FfmLD1DNpPnCAqlo9Hh60PSKgI2P6VWNqeN1PuZD0vXsEbNtJppfGuXeuKfGzVEHbVxpXEulV1+ZRIN7pgUaawKuETt/aVGT10y5Y27FzX7Fp9sBxE57040t/c1ojNbY3Ys2EVJuLZqlRscbTO5+SENYWVGukf3NyKjrG4SwDt39SCTzy0W5q/ybtG/fBsGqub6mqaCpwxt2B5aF/x2u2KcHzw1s14+OZNN4zGB9iZhHsnUwCUYFGCpUo2tjTgEw/tdq2kGBbZXI+w5GfLg6STBRuikaIFlaphxslQXGk/8XsP7XZ99wYzcNb6bBdn9n/trV7EMwb2blxV846LBzBsbmvE/XuVYKmUWiSnXG6I0W9KsCiqgjHm2xnO63WdT9sUZv8/n235dN+M67rl4hUk5coDMWKNmxtq7fBkjOUnAcoyBygUQYjzbSq1RKwUbkyD8gpADDc+2jnp2jaf+K2gWTEhYxce2LsO9+52z6UIWjWxHH7+toIDn3cINTq14kbCef3WraqvWXLL5cqNXftljJime8JZynUhOkMxVLga8hpXyP2jETsz7FxaR3N9BD2TKdxZo5nKPOWIOJF1pYV/Kuafe3auRSJj4P03r7xsxeWyYIKFMXYQwFMA1gOYAvBxIrru2ScC4O8B/ALsPudviOjLpX67EeH23IHp1IJdc31LfVkp5D/x0G70TCWxSxJt1CosLhaWuoiGX7ljW+j9w8LNdLs3NGPX+mYcOrCh6gWWFDcejXUR/PxtW0rveAOwkBrLFwE8QUTfYIw9DuBJAB/w7PMxAPsBHIAtgM4yxl4hot4Sv91w8GCBU73TYMzOijqfy4/u3bgKv1xm5tW1q+p9/U+3bm1FY522JNJYMMbwh+/fi7qItmgr7ikUK4kF8bEwxjYBuAfAM86mZwDcwxjz6oy/DeBLRGQR0QSAHwD4zRC/iddawxjbLf4BqP3Mr0VmdVMdNMYwk9KxdXUjDobIYlwNUU2r6eJVjDHs3diyZMJRm+ujZee0UigUchbqTboJwBARmQDgfA4720V2AugTvvcL+wT9JvInAHo8f4erLP+So7Eugvv2rEVrYxR33VRZgsAwfPT+ndi+pknZjRUKRWhWovP+swC+5tm2AytQuDy0bwMe2hc+i2olbG5rLLkevUKhUIgslGAZALCdMRYhItNxxG9ztov0A9gF4KTzXdRSgn7LQ0SzAGbFbUvF3KJQKBQ3AgtiCiOicQDtAB5zNj0G4KzjKxH5DoB/xxjTHP/LRwA8G+I3hUKhUCwRFtIU9kcAnmKM/TmAGQAfBwDG2AsA/pyITgF4GsD9AHgY8v8gom7n/6DfShEBgMHBwaoroVAoFDcKQp9Z1sQuVqvZy0sZxth7sQJ9LAqFQrFAHCKiI2F3vlEESwOA+wCMADDLPJw7/g8BuFFUHlXnGwNV5xuDauocAbAVwEkiCr1Q9EqMCivCuSGhpa2I4PgfvFEmY6o6qzqvVFSdK6pzV7kHqBlhCoVCoagpSrAoFAqFoqYowaJQKBSKmqIES2lmAfx3eCZdrnBUnW8MVJ1vDBa8zjdEVJhCoVAoFg6lsSgUCoWipijBolAoFIqaogRLCRhjBxljxxhjHc7ngcUuU7UwxtYzxl5gjF1jjJ1njH2Pr43DGHuAMXbOqe9Lzlo6KPXbcoEx9heMMWKM3e58X7H1ZYw1Msa+wBi7zhi7wBj7R2e7b5te7u2dMfYrjLGzjLF2p23/urN9xdSZMfZ3jLEesR072yuq47zUn4jUX8AfgJ8BeNz5/3EAP1vsMtWgTusAPCx8/1sA/wR7KfpOAO91tv8XAF9x/vf9bbn8wV5s7iews2LffgPU9+8BfAYFX+pm59O3TS/n9u48sxkAtzvf7wAQhz2AXjF1BvBe2GtR9fK6VvNc56P+i36TlvIfgE2wIykizveI833jYpetxvX8DQCvwE57c1HYvgFAwvnf97fl8AegAcAxAHv4C7nC69vitNUWz3bfNr3c27sjWKYAvMf5/j4AHSu1zqJgqbSO81X/GyKlSxUUrXzJGOMrX3pT/i9LGGMagE8CeB6eNW6IaNJZpmBd0G9ENL3Q5a6A/wHgG0TUI6S4WMn13Qe7k/0LxtgjABKwta40/Ns0C/htybd3IiLG2G8BeI4xlgTQCuCXEfweL+s6C1Rax3mpv/KxKP4BdqfzucUuyHzBGHsQtgby+cUuywISBbAX9rpH9wL4TwC+B1uTWZEwxqIA/m8Av0ZEuwA8CuDbWMF1XqoojSWYsCtfLksYY38H4ACAR4nIYozxVTr57xtgDwSng35b6HJXwPsB3AKAays7APwUtg9iJdYXsLUtA8AzAEBExxljk7A1Fr82zQJ+Ww7cBWAbER0FACI66mguGazcOnOC+qqgOs5L/ZXGEgCFX/ly2cEY+0sA7wLwESqkwz4NoInZ69cA9uJs/xLityUNEf0NEW0jot1EtBt26vAPww5aWHH1BWzTHYDXAHwIsCN/YNvTO+DTpldAex8EsIMxdjMAMMZuBbAF9uKAK7XOAIL7qkp/q7ZA6i/YQXYLgOOwX8jjAG5e7DLVoE63ASAA15xG1Q7g+85vDwG4APtlfBlOJFGp35bTH9xOzxVbX9imsNedOpwB8IvOdt82vdzbO4CPOfU95/x9ZKXVGbamPQhbIx0FcKmaOs5H/W+IlC6suoW+FAqF4kZFLfQVwH1QSxMrFApFpRxCGYsl3iiCZQQADh8+jB07dix2WRQKhWJZMDg4iEOHDgFOHxqWG0WwmACwY8cO7N69e5GLolAoFMuOslwIKipMoVAoFDVFCRaFohYMngKGTi92KRSKJcGNYgpTKOaX6y/bn9vftbjlUCiWAEpjUSgUCkVNUYJFsSIwifDjiVnM6MZiF6WY5CRw/RXgBpgzpphnZvqA1NLPKqQEi2JFMJDJ4XIijZenYotdlGIufBcYPAlkZhe7JIrlTvs3geNPLnYpSqIEi2JFYDnKwKI06FKaCPFITRa4m0KxUlCCRbEiMJ3OPcIWofM29ZA7KlOYogosa7FLEBolWBQrAv7KLYpOQCVeeK7RLKOOQbEEMUOn6lp0VLixYkVgOZ23thgaCygfNLA2aDdrCQYWKJYPZm6xSxAapbEoVgTcyMQbNBHhykgMhrkAWgIRLifTuJxMB5eOClkxYhkd/VOp+S+bYuVgKMGiUCwoBR+L/b1vKoUXL47iSOfkAly9lPOem8IKguXpY3149szgPJZJseKwwvryFh8lWBQrAq6XcFNY1rC3JLO1X36nYi1IMIXlDOVvUZSJtXyWklKCRbEi4OHG3MNCjhZRa5fL8Gwa//CzTvRNJQsbZeHGiQmgx7MEUCknv0IRxDJqP0qwKJY0U0MJGHrpkRoRwciZ0OY5ond41qqUJJAAACAASURBVPaj9Ln8I5KLtn8D6D0C6Fkg5wihZTTiVCxBlGBRKKonk9DRdWYc3e0TJfdNpXSM9cYwM5wsuW/NkWks3OxlZjEez+BY9xT0ZeR8VSxBlGBRKKrHcuxb2WTpMN1sxtYGcinbwUke01it4KY1tyiRqUnOjqaOgWlby8nllo/zdcGIjQCZJZiGZymiBItC4SaXNqCX6UhnTuukEMkbTdM9j8WycojHL8Mwq9Ng3uqaxI/ODwtlYMVlkpUvL4GMvL+HllHHsCCYOnD6a3b+K0VplpEpVQmW+cI0lkY228ycPSpcZNpf6cfZl/rKOoY5nXOY/thwZrVHNPuYTGYYhhFHInGtvIJ6ON49jetjiYIGVLbGYuYDC8gs7hjCCM1akTMsmNYSaJMcbi5Mz0h/Ng0DF19/Bak5lbwTgNJYbggGTwGJcflvRg5482+BnjcL36e6Kr9W71Hg6P+u7Nhjn7dHhUuES4eHyj4mTOfLd+GCJa9f1CgszAoqAxFAzP4rOlDPl98qd8RpWfbAoEY88VonfnC2/PtfK0a65hCfzhQ2nPsW0HfUd//45ARiE2PoaVcrcwJwTbBd6ijBUglE9oqBp74q/53n9Bk5Z392vAic/xcgOVXZ9XreBHK1n6VNREieHIU+vnAzwJOz5ec7KjVQM2azSF6ZtiezzFNGF284s1dJaRvei7bhPYUNXKBZBkzTQmNiENGOHxWdVyavchkDhm7i+qlX8Jmnn4Wejlddfk7/9OLN9j9x9Aze/Ml5TCedIIbZ/uCHuyjpeeRkDROfebkDnePVPwvTMJBNhTPRDl27gtM//oH9xXOvyCKM9cTyvsilhBIslcBVeN+XojCbAgCQcgTKEksip0+kke2dQ/p8cdSVlTGQOjcB8pvIl0sC/W/Pr7nPshAZOILY0GjgbvqVq2hJdoFMC1rE3RmxGkkarrHkzXNw+1iSpoakGXFdGQAMPYd0bA6tsS5YsbGi88ruXvvL/Tj/s0EcuT4OiwiJZI2FgZErIyOzP/F4HKlU+LLF0zO4MHAdT73V62whkEkgnwmn+Xu9BEzKs05QyPGe6hfZunbscEFYlKDv/JmCEBI03uzMMK4/+QfofesNjPUsveAHJVgqgSeDYz63L2+IX/wXIohU+zhykymk4sUNM3NtGvpYAsakO/+VGc9h7uU+WO3PAV2vAXHBf5MYr2kGX0qOY7p7BpkLJ2EGzHaP9n4HO2dfAUgwfdX41nujzNy+ewvPxZrwXKypsNEph2nqsBzfCllWUZvw6zSNnImpZA7Ds2mkQ8zjKQf9jb/Bqe//HiZSpcO4gzh16hSOHz8een8ictWfLIIZy0IfTuS3GdMZGHP2AKwgWJaPb0Hk6sAETnYVm8tnR4crO6Fw71L97aBsGzB7AdYSzOKgBEslcMGilbp9Xo/vEhM0BMzNjWOyvxepmNuWr/U+j4aBL4LVueuY67OFkBVzOgP+0qemoR/5R1x95hnMTdRmhD2Ss5CbScKKp4ASaVQsAqbjWeiOWYBqLFnMgGdHAAzDgK7ryHpH8EIaF8syXW3AsiyYAYI4kbFHyTnDwuTIHLJpt5ZBlj0ptFxiuRhIz+D00Nmyj62GkeQIMpYwiOG+J71wD5Knx5A84WioHsV/oeg+exLjvd1F2w0iV1l+MjGL47OJov04X3jxDL75+rn898nRBL7/7Ssw9QoFgeBjSfbHkZ2+G9HsVjBt6ZgMOUqwVAI3I2g+qw7wzqNMQTJ8fcbl3DQTCWTS2XmTR1nKIW46gsJwzxXR5pwXy2PnzpvGop7t2TjmLg6iLtaPmRG5YCEiTM7OwJRER8l4biaGDCyQbsIK0oQYMGY2YnwmjStDs/jO5z6DwYuXYMxkYKVqM3ekYAqzv4vPxCSyvxPQfZqP4J3Rtmnkha9lWS7zaX9/H144fxlJw30/BjM5nJhLggBoyCCTHcSLz7+KV55/C4Dtpzozl8RnXurAiRd7y66Lrteh68r9GH5BR2yqOCOzkcuh8+TbMPRiQTbcPgYzU3n6f4MK5mDSc9BnU8hNyv0WzLEILLTGMtrZgc6Tx1zbkoaJE3MJdKcL5b+YSOPy5XEYYkCCB7HdvnRyGEcnYxhO8PDzMl9ssjA8l8ZcWsdQt4bLuUbkzKYi8y/HNHQMXr1ka8oLjBIslcAFC4v47ECez3AMXp3BlaO2mkxEGP7KU/jsV17BselVAOwRb9mN0TKL7OlWzoSVM/H91I/x49Yj8hrw6xg+HTMRzGQSiWPH7HQqE5PInB+Gdr7L14E+MDqKnu4RXLje4Vtc0zCQnHXCT53OGgDIkNS75zDw2l8DADKW/SxM00QulcJwuz1SpFShEySTQGU6OtMdR5A6/wIsR2PiPhvxLKZlQjcA3Sx+4qauIza1G5Op/SDLzAuW0YG3oI2/jZ/OJvDdMXe4bVdiFnMZ20wVxRzis68BAGZmpzA1nMDFN4dw5dQwtNEEchaV3SYmEk1IoQ4T5iwyieLnO9J5DeO9XRjpuOLaPtQzg68f78PxtwZc27snEvjMyx1IB2hPsjKaV49Dj88h13cGADAwnUJa0EwzCUfghKzeXErHF9/owpxsMBEiIi82mcbsmD0oSlgx9I8X2mnSKde4Z5LrlqEUkqeLfWecrG6hc9zWauIZHVZKh275axjjM/24fvTvgKx9TNRIoiljm5tJNzDc1YYrA0mMZg2cRhSn0pZv5GPP26fQc+wkpgb7S1W95ijBUgl5U1hBYzGm0rCcFysWv4SR2Tlkjcps40bORGI6jWcTrTBnZ9CRaASRhbef/Rb6LrSXd7KRs8DA265N8TcGEX9jECl9EhEEO/5I94xoGRCdOQzW/wayV68ie7UDlMsBRNDBcLJxDeZ8XuJMzh7txRP+ETGdJ9/GuZdfQHdXFyjJ9yOc+kk3UjFPSpR+u17TGQMDGQsWEaLcXMBfNuGdi/2sH6l2nxBxH/SxDhizozD1nOu0rn1yBeFViBqzOyI9ayBnNWAqtwuj0+sL2svcAAgEspKIe9rJVKIT8fSQsPBkoWfNJHSY0xmsuTyMuqkxuy2G6Hh5x05EiI1mUd88iU2bjiKb60Zs0u1r0TRHSHu0WO7AHk0Jz4EIFzo6MZPKoX1APh/FIsIbU3FMRBsw1dwkHGrBRBbRhnFYFuG7pwfxoxF7zoqRy+Ha8beQTaUwNTQgPa+XS939SHe8gSu9g0BysuDvS00Db/xPYPRi4doWYWY06RJ4V4+NoMMxw/1kPIUvvWRriIiPARNdMGayIHGSLxE2TV8FYv4+k4lEFj9sH4KVNaBPZ2BlTVhZI3+8iJlI4vL/9x8QO/aqPWl0ogNbpt/AhthpEBGG+lLQE82g2DpknAnBOQK0CINhEV6diiFlWuia7ULaSCN1ZQz6aKzoOS4ESrCUSfsr/eg87Tis+SzvrInkmXFkLtvRX0Mjb+DKQA+uDHG/RXk20GvHR3H58BASlmMKgP0iNGbHMNbdKT1mePg7GBj8etH2zkQjjqW2SY+JJi+jgQZhJXL+Pomc11TCUDf2HFh6AkSErBPpZuqESVhIWo04L1nwajqrI2ly9cP/fsQn7Y7/mVdPY+LCVYAsWNlZZFPXMTchX0hrKjOD5voBEOmIOAn0GQO03DhgFo65kLuC/rFeGDMzSJ0ONzeCCMgRw7DQudF4H2Yunsh/H7x2DbLe3UonkB3sBCMLJhi6xzfihQtD+OZxewQZIR2peAdmJ9wjSoMIc4aJLAqdGDe1gWBHUZk5aAQwywiUK4ZFyFlWPlza1C1kYwlE62NotFIYvnoS7c8+j1y6cJ+0qFyw8E6Ym/SNnInIyFXs7/0WZgev4aVL8pH7W7MJpE58Dc25ceiCP6CXTMxQA3TSYFoW5sZHMZayR+qZXA7HZmZxoa8PvaOjmNaLO8fY5Lh78uRMLwCAjV8GTnwJ6HWySycnQbCQ7HsB5Aw8RrvncP3kmNRsG8mOY5WWgJl0tJNTX0HdlZ/Y9yQuaCx9R9EQHwami/0xAGBlTDRkLWybyCL+5lBeW46khoCeI0XvnBWbQzbLkO3OgFKTwMVnwWCBLIIeyyLm+NzqsqvBjAiIgAjsGKKryTTOxJJ4dXwcV1//n/hPX3oaE2MnEI2dXZSoOiVYSkBEMCwj/3ByaQMpPhfD2WbGsrDIQjxmq+6WYcHKmUjPuDvCnJ5DIuHv7OMkZ7Ou6CrTMpFKp7Bx7iQoncbEP3wO+ph75J3JDEPPFY8Yfxjfj7dT26XXsYgAKwskJ4rnXvGIN8NjP2aApk8BqXFMZ6ZxdfoqdEtHLjUJgyWRMzcjd7F4pvQrY7N4O2E4p/AXLIbBkJyrg5U1kJ7LAroOylmYufSmRFvgHd0ULGMN6lgaEcdZHrUyAOnQ0oWotROZM/hJ6lXMPPNdzD73KsyMu26Tg3Gc+GE3coIPwTIJuqWhs/M6MHgKWi6OSN9ZmENX8/vEp4oXEyMCkqd+gtyxbwGwO/acCXQOz2B02tYSGVmAZWF62M5IYFgGvnbxa8g4ZhfS46g34iDTRGI6hbRgtsq7qRgDiGBZFnRdR9owMShEWX11aBL/u28s336ZxpCyongluQ+ZjIVE/zSMmSyMZMF3EInWOXX3ChZ+SftBTPTHYU6OgQhoseK+46cZ3cTWAYZ9SQ2aoAEnYb9fGdJgWibSgzOYGOlDX98FJLNJZLKjmISBjmgTvtRvt/fh2TRmHY1p5Nm/RPc//3WhfPmb42hUjqAB05DNjiERv4a5mK3xZx0TqS4x301pF7FxzaXChsQYtNgATEMHOQMXIkLGTIEClpvOzmQRzZpoTTj9hyNYtIx88TmTCDNxwMyk0dvbi6lpe6BqzuZw6ukrGOoomN4tPWqXRY/Csii/HhFyCaTH09CnJ/FqLIpZfXEygCjBUoKjvUfxd0f+DoarAXl8KBahd3oAZzrbkZiYg2VYGJ24C3Mxt3P/wvkLOHnypO+1kidOItvTa5/SNGESAxEwNzmF8bExJOZmsLrzezAtIHvtqu95ZHQcOYye06dc20bSwKy5CrByoJTHzMTq7Rp6TWEcAjJmBgSnA2IWGAwYTEfWlDszyTRhTo9CD5j7MDVUj9hUg+MbsaChCSbqMJ2JFHdcROhP1YNiO9CQ3octcQ1aVgdZFPgu5XqnYcZzYB6f5kS/M1oWOnCytiBq3QTKxIHrL2N15w+wdaodLbNX8p315us/wio4nYXT6fYPxJDIEBIJHYCtsVxGC9Knf4zek46JBQwHEj0wHc0knoujabITlp62y5aNIadrSM+lAKbDyJn5lpdOMpBuIJ1MY3jkebx99Ns4cuQIPnOqB//9WGc+Mi8ydgHbRk7kNZZEPI5RKwrGCL3ZLYCeLprRrTnRjpYnyEI3LXQmMkg5gs8yCZGMASb4RYgIg1enXWbLDfVRRNLNmLHqEDMa8tsZEaKmCZgWLAuI6BFEshrGJ/ugZ502YpqYSUdwZcQWxi8efhOvvPA0ACA60oWm0QtFz9eIE2KdNxX8aYzBMg0wEMjiSUrdwRgiPzB68ZJR0FCtwcswJoaRSseRTDimOgKuxk9gzogh4+Mb59efGUljaLgQdWk63S5ZhNeujucnjI4nsliXbUFvw2rbZBmz62wSQTcITTnN1lgNCybp9jM0GjAbz6JzeBoz05NgmgYLDKYFTLIWHKZdSmNZiqSTaUxNTSGjC50lWTD0HAxDx2xmFqZhomnwn7Fp4Gt49kevI5WpQxIaphMbXOfKZu1z6LruG+VkTEyAdAud12dwQV+DkfQqsDl7dm0uoyOXimEg2QpE3IED1y9N4+q54pFQfK4OmZSG9OFxzD7XBTNWGJlejr8Tl1N3IwENVzyz78kRLMxrCmOAbrbCMNpw1LgZF83dtnzVk1idm8EqI43s6Cgmuj1zJOJjqMvMwAKQmfGfZJYxCLO6iSRZMLM6GOqhRVqQ1bUiTac7UYdnhtpwOb0BDPVoNBjWTKewbiYNSux2ysuQMi389fUhvJgGrhuFKCOiEI5vagKDhmTMfnbG4Ago3YZ4MpU3FfUlLDROJbF6ZhJvtJ9H79XLyE6MQ0MOOc0AEUM/a8EQawRyY4jqU3YWGGLYGxvERCxuO77jozhw7Aq2zyTQPJeDbhImkqswcHEanZlJxPSCRmpYFgbnsjjR1Y/pS4fRcuwLyI1dRsfVSfT2z6F7zBaSQ6cv4PSp4bwZJRaPw7QawUAwiZCbuwRKuE05ZBIa4g2wPPNnhuYymDRNXJ112koyAUqnUZ/UkdZNzCRzsCzC8ZNn8dMXClFVFhHG4xbazbWYyq4CQIi92o/mXIvdyTqdpWblkAPhHDNhOO1uv7UDd2W3YWoug+lEFqeunUAu/SoAYGpTL6Zbe5G+ZueDM5NppK6PITWYw9j0BKycs5poSkeiuxe5eBoD0534hzNPQM9lofVddYd/T0yhsf9tTFIGRkEHgJU28n4u0wlm0YlgmBpezW7CV2cbA9oP0JtJYbBnBKZhwsjlYDqm4JlkDu0Ds3i+fQiwLDSd/S500tGqt6Fj8DZMzm1GOmdiJJ3DFfMqelkPyLRwUY9g1CJolMFqdhV9PzuD8dM/RLLvLEAEZmqIONWaZi0qKmwp0lhnN5rk4CzMBB+FEYavXsGFM6/hn1/4jxjouAAzNYHx6CSOp47h9akWXKKN6I9kpOkWjhw5gq4uO3eYrut47bXX/n/23iRIsuw60/vOfYMP4R5TZkTlnJVVqAkFFAZWAxwaAhvqXkjdbdJSvZKZVtq0rLfaaCGZ9ULWC5lMVIsyo7UEiWSrRQJGgGwABEnMKKBQVagpKyvHiIx58tn9TXc4WjzPyMwCQbYoAGqY8Zp5RoZnRrzn7717zzn//5//srX1EGfXwjHwAQ0w8zGH5TU0gLUwi1J+98I5Nkzy2O98dSPw+l/CcapCVUWU/Qk2L5j+8GEXe9AInPCN4T2+cffksS13h5rx5uxNRv0PKkqEgX2eWXWGreJXGJQfxluHOAsoC77gieoexbt/9thPeVeCLdm3bTaub56+f290jzdf/9IpLLWTW46sJy9y0lCShUGd0av/iYrlq+Mef5Ztcz15CP3EfsbArqPB8KniLVp+xl5W8tWv32PzcIXvHa5SDg6ZTjJuTXL+xeaj+P1PDzK97W28c4RZk9vNEzbJTgl964Wr+/e4unOXxlHgK3/wPabZAd9emvGNtQExnin1/TqvR1yzNyGLUSfM9n+F5ZOYwnqO9vr8q/HnYPIUZ6cr5K5DJYsc7jzFbki5bSGvHJu9GUMXuKcRN3yEefvbJMUEBncp58HggUJrb+YZ5BP+1Xc3aqNODQxDg1I8mZkximGcPS73DQclzUkT80hrk6qydfc+m1KyS329ioNdmlubZP0ek0HB0daY3jhn662vsnX7oWBEgW/lbYx4YlNhXU7wgcy1uNW8RCUxITgSNyHRks7+FtVm/YwshgV+6BJOtib84NXr+KLgzmCVKs94Z3iF2+1LHL+3AcDW4ZBMYm7d3eTG/Rv0BjWpPj3Y4PZIYese5Xd+h96915m89QPim68TNh9ylisbf0B3989puIinIsPZhYeqMK+PL5VelbxIGIXkr5RDBwm8Sx2I82GPKp9Qzqs2eZDgAPiS8XTEHhc55FN4DfQna+STEa1wwrvmLW40bhGFkpsh4ihACGNUA3n/PjrocTKOqcqC3eNVuu5hha8/A5eF/7fjbwPLXzMacQOCsP+tPcbfnS+yITCdOm4Purx19yJVOWHIlNxUVIzZfNugQRhrxA/u/eX+YEdHNWZcliXkA/Z/9GVAUQ3Moh+xfuWL5N5RukClDYILvG8ucNNcJATP1gekzh9oap6fphK81oStVUr3uJlihaW0sLnQp5rVVdHRpKDMLJt7GUtbQ8bfeMTf6vgmx9WEA1mmDBBIcLGjKgqKwz4z30R8k4Yv6e08LinOy5yXb/2Al/beYuQenvsX3/5dfuet/4mNr//PAGznE+7lQ85XwoUKCh0y5YSkKtAP9E9sVAWl9xwkAwiCscL9ENNgjTXt0ChSzmTbjKYll7dvY3wgCSWv9EbcHexwa1gvqA8kpHd//CMGvb/cPka8ZTrsccclvBZ/gp52cUUBqkwx1LPYUMy6vFou8KXiBb69kPBuKyHVwI7pMI0MRpQPsQ1OmAXPbrHK4tigwB+/c4hXpaDBctVBvNByLdKqRWeckpUFGyczShcIoaZ+rVdadgoayLMpS72K9aPylCcqyoqqcvjC1XCYKmNJ0GIV8QmDxHDc6FA+IqN9YLEij4gs8knOzq03uXR4i8Z7f0I2HqHDNkV8ht3xkMh64r7l89+7Rxj18fsPqyANAa+eShRvhkzcLgpMNKIUGEeG4BUNAaOOp+/9iN0v/gX53nNkFqowo9Hvc33/bQL18/z+d/6CV8Yv8fr4V9navA3A9+NltppPYqt1cjoMhjv1YzupKJ2wN2uCHfOk7mDtAGxOtnXnoX/d7VuUd464tv0f8CJNzoebbL33DoUtH2uQzSvPDzd6PDtZQyVQlT9dWekoyaRWN9qsYqaWygdm3vMIMwKq5B58ehFLSr8qCNayVN7h7NEhUVViK0sWKnqRI/cFk6ogc4rzno1Zi+NRwnubBxz4LqoVpvJ1VR3+NrD8ezeaSZPGaJHuwf+Gv/3bXB/NuD/N+NLwKn8wvczt9IBxKLBFwaXbTX59+CxX8+t0tJ7Y39nc+wkgNwTl8NaMbFLVUMzRDSQfEBQG5ZBj+SbeB2wQCjVMtYM7uUoAPEqWV0QfgMI0FzR//DjOeoajRXrTNQgDxtWM//uNh/uwT42lkgBi2d65z+e/8l1+9wdbXH//iGJ8wNQ0kQf+ZraAd7/A6O4f8HZVcGib4GOiap3sJOftGwOOzUd4Mr3Ni9E7xIPH4RWxOWmIWK3yx1Rhrx68zpbrcWvzfYIqVTEDD6jSCHMprQjLLcWNHuduikrwPiDiqXwD4yHpKU6FFOWp4hiOYzg85CNb1znfn5LYCKeBMnjCbJvzg98hzPds2dL7fHn2r5nYn2zYc2HArd4Gm2W9wIxliaKaohpwxiNzyVYZYGwd78cFy7MrnD/4NRqhTUMDqtDjDBN3CS2VnndMTCDy0D/p4QclBLAi5BhQpVVWrAzGLGV9Jn5KlPdZO3yPzmRM6gxLRYLX+RLlc1ZGDgL88Vv7vLs7ohhawnjev1M68AHnF8A1ac4u44yyzgXCnLy3xxl56XmlgOqRattVDnUFa67HRXNMb/s+Z5MDVhv7VJIBBRVKdXDEkumxGB5CocPZIZWZa9w0sDH+Y8blGBciVFYoJSI4h3cVnaikEse9wwpbFtxzEWPNaObHDKrhPL0PVPcfqPoMrNe9WKU1GN+mMlC1KjbG9Rw5mPao1DNxMQPf5SRaq8Uxs2P6tzYeOm6LpWh7DrTDnx58mtts8p2vf41pNmC/mhDZXYpsxj//wg/44nfe5uxkvZ57Qbm+95Mu1KVzNLRi3Vp2RgWzEDDSpO+hZx3BWp762r+huVebcRp54BohFBphqwrtefzIcG5vH1VlEtXrSuaEPDQJKiz413CuwoaALStM8Bj1oAs4v0A++ik86c9x/G1g+WuGm4HtlRxUM0I54cZgys3RjKNRg/YsoOoZRhV2T2iMISlyjMQshhQxMd/Y+cmKJes7hluBN766iaqyrw0ObMpXGl1mcUYjZFTekJgJNYHdwLsl5qssZaiY/fXiMnwVcNJAgWm0QD/pMBw8VElFOAyBEatY5xnPCfwf3d7gy0nKv1xcY5jPJaQaOM6Eeyc3KcTzTb1MihCj+K2MP5st8431y3TO3MEBzfB4r8oDLiNf6DNd2nl4LfIM6yOONgZ8/v274A1RWCIuVhDXxkdnwQQWrpxgeRyW2x1PKIIj84ZQCuIcjSlkdoGGGVH4ZczUMzm4zSfte3woN3xoX/AaExMwRd0A6Mt60vaP3ieZVUzsT2agF/U5Or1fO0XLBrLKf/97/5oiL1nSwUObfmrxjxrhyujDvFDVsEc6KxArDP1lvHsO3ApLg5TmbJFk5vj6l79CvpkT5kH3SGqIrV3miBouD/s8d7RLtfcerpiQuIzzVZNVl1AkBmSJqEhor32fJgVVv88r1/dJXINF1yQZ7HG8sY0OSwoiFEHV8FQ0YIEW+StHhNyRvXnMm3cH3LPw/vQRZaK1eHUEIxRxynRQcqVZC0jUxSxXEVsXU6r7G5yLjlmOhozmpPTSzuvzJ1cxCCv5Nif9fYIajBqMNnj3R18lLnYJruCkmTFseA4jw+2oLsWNVDyKhZbDmk+USmnOMrwPOOdAD5E4R+OSsnDcfn+bv5i+yptpTuljBrLCiayTu5z3V7pYtIY4XWB2acCNa4rrFExV6alnfzxgYs/wp80uI+kh1Yh7h3vMRrdxKqD1JnN/9uebHI8fT3z+E/kjPi4/puObzEwGmtIkJoRluuUFrv/uHzLOeiy99yZoeAzpbS7vEpLx/HkQIlMQM0G2doiyrLaXAVRj4vuHfHb3e4iz9Hd3afgOsTaIcQRN2Lrxl6vQfp7jbwPLXzMG97YZDZWRK6jGW/zacY8zwxbn4mP+04VXadiK95xFpYYmvPfM20+INUaTh9CKukDIHNE4sBCE4JVBUbFweI0vHl2mPzshqVZYLgZUD+a0BEBxVCjrfMd9nNv2DjuzxxfZUHToZmcp7j6U+gYbCER4ifhao0m8sg08hJMSl9D2LcZynqrKSOZF0MbE8Q6X2XfPchyvAlAWJf/rNwNv7qwgvslOOIvOp0J+3CMUGeXaDBaGFKFC+ADurPUfM6koSntqF+JViK0hrwzHd29z1p1hzXZpqCWyi4RkDURBPE4e75MoSECEsQkEq0SuwqBsScShyFwJFdi//X3SruWFeIu/e+8dHEqO4cb+g8Y2QTUQ+jOaex8IKqeelgJlQnD1zbWkWSFs5AAAIABJREFUjIoZOxs32ZxGdeA0DqT2AzMFdF0CGteNkPNfZzVhQRfJrOcszxKpod132NGI8gNYvQ8CQef8FVwe9TiqKhSLM45IwRjhJpc4SPcIskM0XOOcDSTVdXbeeRMJETZEhNvfIxv1mRQjSo1AIahQEfhu+j7/R+/PCT7Un6PwtUGkgp9Zqp0Jg3/zFZquIEosoSXkk4pxska2kiAH17jaUy719ylsHQitN/yL//PH3Lx+xPLumwQU8QETFOuF2f4xBJjZZ5iEJ9n+0QEvp2/wcvodXOdDBJrErgBSFmhivaExM6zPLmFCoLc3wRMRTkr8a2N++7c+Tz56HZURDodiIKvY/N//GcOte4wGFk4s1iUUZZtkuMqqOU/fFezdusHBF76JNhv80L9IY2ZBlf3JhwmzNYbSxs8fhN+wr/OR6itYucvtPKkfbA38ysYd/Lc+4L2myhPRLlWU0/MxKp5FJ3h7iR/aCyz09hkVU1BFvWc2KE8fuPNLOSuXDkg4h9CgY07omB2+0bhCaseImUv3VelP2nT3M/7z8k/Ip1NEV0j8OpglFOH99366M8DPa/xSBRYReVZEXhGRW/Ovz/y8j7m40sEmEYpSBGVqc+5beLI5ReJFmq01wsEWX2+9zJ1oGec9PEL0qSpBayjC7k8pdyesvH3IemYxkSEfVvSHTeJpG1sExvkquwefJHcekXrpVgSnsBbfZ80c086Ezds5k/sPF0FTNmhNz3L8nbeZzlVXrvJEpoWhwTQK9Js5Z2cj3LwD/vnJNZ4srpGo0FS4O9wElHtjh1EFgWBqEtgVJVWRc5I1Ed8ixZLgiLEMr3+DqaSUxDi1eNsjfEDfr9MAzvGU7vD3/Gt847tfmP9DnfXhDUwV0ZrkPjQRHuglC8ziMwQEqx+YIGoQhTx0uRE1SU1MI6Q44K4owU7w1jPOY/IlwxN+hRCtEJxlpAmv34/IqwkCOOvwqnWjXv/xclABQ6DQB+1FBjC43HH71R+QZ3MC1zg62ifNx4Q8xtoVIt95KAkQsGIQUWywRJIiRBiEw2xIL3IYDYgGomApjeI1IkhCgwYiQj7r0V7exy+dAAFRR39ymdWjZWJfIN6AWK6t/5ArzS/iNaLQhD1/BlVL5SqWqlUulSnqAndHz/KiuUG7eI39rTFf+fEeoarQstZFHX75Dne/cAuOd/iP26/SxJJKiaJM5SyH+QsEnyCqLIRjrsgTJK7D2C7gi4zb2yPcUaChFUsnPT4zep8rgybvTRVVgwtLjMILDPZbOImwJuJyt+K5vX1+9d5rdEOHBsv0qpTl7TUSt0KqTbzLCKR4wPnAtMhIrII2KTTlprnEMtskfkhaNLlufoOQK1Rgph1skWBMm/5cTi+b1+fJoVANc5ZGyii/yoEYFCVgME45p8c8W23X194J7dBjgfucc18nvfH7j1kGqdTy8AhDQpOIHqscYdQTYclKYVZ6ssrjnWVs583GanhQGgsxk/QZYoXFUNKOSnS9IDlTJ6yiShCDcAaTO877fYxrzuHmWtn5rjwu9PlFjF+qwAL8L8BvqeqzwG8Bv/3zPmDrsMdZTTDNKXekieWIioLYtJi0umSNi5yUKVNN2E0Wsc4i+sA8D7rViGA9+b0BhIDmFePNNzDbbxLPKsZHGd9BcbYOIrmAr9rEYcICOSpCKQGrQlDBhQYXJtcoj+GtHz3cDbBllSubP2TnjVd5+0/rLuFyZmkmbRbSDgBvVefoXNtkNjman1+962EcoGmFuFD0uI86iwkpaISVucqomHFkLTOtJ99no1e4YnZZi++wHN3As0qgzaBaowwrTMzjSoJaXBBOj/uj4zq7O7MHS0dnEIVow+BCjArsmZQ+LcZRg4OVNdDwmDQ4yzJiHzAoU7cCEiEoA0KdRGpFM2qjTvFvbmCC4rWLpus1H6LgbcH28E2O8mPUe1zVYLF6kSJ/vKenIAET+ENZ5cd+BVWDaIS6Dvv3N5CJgbk55/fdWSJXwxp2DjYiNb+SYLEYDI5YZgiKSETqI1wQEKUpTdbGu1zo38apYdFktBJLQw1pSJlMN2o2RwMItCQm8RGBJYgWIDgCFe+U51mQPo56iUpaM0xnH5NURHjSUJP0VmsfuoWQ8eXXd/nyyR43e3dJfR+yIT+6fcJbJ1Py+CbJ8oC2FKSFZTLtU1Yx5SQ6XUREDeIDeZWiKpQ2J6gyqjqY+rbwfDzkqQzuTB15kDlEZmiPhjhtEDTBRx7F4aJAmU7IFJw28Dal6wtCfpaWDngiXyfxTxCA2fiARoih8hTaoGqAdse0mhOmuoQT6MsiuU2IsgbWxtw3y+TReZ4evIKdHdX3SQwhxPzDmzf4e9s7FBKYklAS0yZQmByH0vYFWrUY+2VcmrOlMw41PGxtC2H+yRTBMI1KfNwnaEISV0RmiJOImW1zvz9DvaewY1QFcQ0qdWRi6Sfr7LeeJXCBl6pjPtW9iZcFJLIoSqQReesFChvxw+NnuXB4Qlot0KwW6kAp0P//wVX/lyawiMg68Eng9+dv/T7wSRFZ+3ket6o8xtSlMRJY7P5f3Fi8jhFPIOKl4x7FqF4kYt9mlZwktEBjvGvxid43KWcT8uNvMZ1skU1m9FDu2wmMMrL39zHeYYJDEQ5MTGUjLrx7RLsqaKijRkQs3wvPETTBYCgD3O895DEWqglJNSM63Dx1D97cqaGeAJj2MXE6oplOOZq9weHmHZQEFcX4Jquuy2HrElffP4Jhj6XyaZrFM3x3pV5kZ9MhXR9QTehrigCF1HKCSeypl5fA9vRz9NxHyT9g5R2rx8wXfbwhPlrFB894fIXD6uNkIrisIpGKVTlhUVIWWCCVkgu9I6w/YvLI7odVVdWVIIHUJUTi6upOazwvxnA/6dIyXRZHEdEjmWRCQWIKIh9I7RHfvPt7uNJxtmzQzfr44pHehvnSUBlDndvOAUAFocFhb3Da8CbW89nGKzyXbCF4jAuEwrAabfJc4w7/KP0GCzJhZAKIR2ILCCHuAIKTBhkrNG39OWMfeEL6iHgaVEQ+cCbqEY9nhLmdB0BKrSpLmxkCxAFkugiDJeYxlCwSvDqixgST5LTLDLLqFOIJruJoXKDBY3OLDYHZwQbVsE9zeMK4uYuGwOpkwsfe3eW96zdwJ4LMAojQwPKyfZflcsqgOkNZtTDHJVs/vIt1E/qlxZ33mNQRAalOqMRgCMQaiEPBpPo4uf0Ie2mXYOqupbEEJiKkUSAKGetyzNWwR0TBukx5QmAiCZNIcWoxLpA0K2QO9SXiSULAYfhh88N8P/8wApykfV554rtcSqbEsoZzghXlP+JHXDQDPmSP+NT2JiMnfEk/yaF9klhrWDon8LnyOmf8MRrAG+GPzKf4fnWBWtmpfG/rew8BUI3JTMVmWlAiOBMoRAkelu0UPxvhsj5JMZpX4crtskMpFkuMSoP3eYk9e/ExG5hFmbJuLVa6DKNVChFC2SBIPQ88gahZEPjp7gA/r/FLE1iAy8Cuzs1+5l/35u+fDhFZFpEnH30Bl/6mBz3xjRr/mOOgl/cHXN7tE+MA4fmwS0VFc9HQCc/Q6C8TxFCFNnFosdMckI1POCkn9Pqb5JMeiCeI5559m9n27bpPIyjO1D0zvdEC6cxwrX9IJEKEo/IGpwa8zoNQYFo+wpdQITisU7bv1/zL53cfVjSRFpTRjG9FI3Ynu2wONzAhIvEpGkU0kwx2Kq7591hQCxqDQma6AISymmfK8HahVL6kMarNJ0VTCj8j+Aqv9SKnNn3sOhqFWOrzbQxLQnZIIGC1U0NuEkjGYy5H9zlrjlmRHl4hdZYlZsz2It4ZPOSViqJAFVLXpSNTWlEPJx4rDiMWQw1DvGHa9JY+DMgpz+OjiCBwnoS37v8m0/4xzjoWi4pWVTEoaiisOpzV8tbFAya2TVR2+cfpH/GbYcRT1UXwjsgWKM25WCmwZMZ8JL3Lp8we7UFJY1Jh4iOuJDuUvstSvsb3zRmeye5yebSHQ+klDaqQYLxFgp3bxStN+9D7zMXLaHuFc7M9Fu7epzUaoKHA+IJ25hBWGUw+RltznpZN1gwsmXVMEBLn6c0WqIjAeFYnY1YmPT569zoxjkYWaI4cm6MJi1KrsqZBcb4iGMOs06RfKYd2mXZhEYWrb71TL3ICYGhSsSJjIvI6kJknMFlGfLCLnR1gg3J2OiBxMyJnuRJvEc3NNwXBqkMl1Hxaw54uhYUmJKosiZJogajSJDCVBqsyYy2a8LXWp5lMcyo3Q0zCA+m39Q3G2iYLS7Ss5RP3b9MoAt1+h8HsW3RHGaM4w3qPRTihhY0i/k5a98WctD/L1WyJC8cnLGUl6TwMmxCjCO1qjGbKbrlGqYvccJdB4d7RLT7/tf8RJ7ZOQBQU5cnhIot5TkrtyGFCxZkw4VJRsnHju5ytjmiRE0LF9ewcO9Uyh/FVdtpX+VR8goQWcW5ZP6kFQR/z73OZAwyeKQ1Ww5TDZJH5RSU0RzQ7I0zy77YN8s9y/DIFln/X8c+AjQ+8vvNX/sRfMZyP+cS710nupWhc4dKI5XxCFGo7E6PCYmtKM2pRxQ1CKCGqMOKoNIIYhuNDDpIF3m6tk4YeGoEYxbojRsk9tDkiNKd0QlrnwyoYVxI0JqUglTGD9B6rfWF975BmNgGU8Mh+GR+LXqPb2KdnHObmXWZvvAFFefpgX9QDLvlD3h/9BnleEB0MadkOLQqSyKHRlCdGA47EYcQTBSXxBvU1Plvk9TG9Ct3mIe29jCRXUgd5skAIgWf2Pa2jijITCikZ/9t/e7proNHAshnOO4MjrsV7hBAQ6WJCxPTSkNTP5lWN8in3LSImpGJJ1bFuc8b2IfcRfOBK/iIrxTmMaxNE6SUTSlNixBFRMS6fwWnEG90lRCIeVBsqNQRjfMR/+MM7LL9dUJYVWtbcy+3dE0LlyV47QJMZVdFgNy7oVDGV83RDk8h7GoMxoimaPE1IlnChwmuFIJw3D/gvZZ8ULwYflhCUJMScHYyICDyf3mTF9GlPL5IWsCAR0TywxCEgD9Q/JkEXrnIwXIfmlNXGJlF7zPpwm9XNfTbCJznIn6SldYW5qFMiVc5EqzzVgM/qaxAE8YbOeIaG2uwyFDnGgyk7fPjuPaIyJ0MZ4AnVPufcTeAV/m0nYxx5VA1H8fPcWzw5VY3rozuphpKAkkcJXgRvGmTxOUxc8PT2Lou3J2jwTEKHZFbS7M2wauinjTrwByUgDKNmrYOYZ+gd3yVyJc2TCfFkD6IHXGZEJYuEKVw6LHjx8FUiVxBCQunb9MoOTx0cc3E0oqkNrp0oR1UCbsjZ0QmuEvq2ZPvsIWX0IPdIAINKxAvDbS4dH/PpW5vEWhGFhMR2SYuzYGqUocy7mNkYVYOqctjb5albM3YbOWNT8UTo8zHucWk0ZSkfEGoQlMy2eIGUrgTye4Gm5CzIhDTkfPrNd7Fjwcc5rbhf182hwfJWj2u7O1TqubJ9n85gisw7Yj6ys8l6v4eqoCqsZUsslIsEkzMqf1IO/fMcv0yBZRu4KPUKwfzrhfn7j47/Abj2gddn/qYHPRxMUVlirC+RV9fod5dJqIjJMKVl6WBAiw7d/DKgeCIkmfKU2WBFx1gn/Pigya38N1GN6dgF8vZz5EYIZYFd7GFMBTiKyNOupiTeYpynVVVc7d1laCyv2+dYnLZZkggvFapCeMRmxljLfutl+sk5slDy3vf/mOYj2Oon8lv8/dff4eKh5dXyLN/UVSI8T0X7fC5+j6YL7LoJb2GQJCNuzmhIxFP5SwCU8w2OPHraMSwIzamjoRFnwhLL+Uptq1864qiiuHMPtRZXVEQaUcVNVBQJkI+vcpKdENGimzTZiJ/BrG0DSpJXdDdPuNy/x7oOQATjlbx6qHibHB2zqENS2yIu1zA+IQ2GgKISiDXFhzZR0WW1HOCj6LThr16/IsR7JERc3JsxG4/RvKQz6jEdTwlTSwhKx5UslC2CCTTzA9rvGSTUHIuN1lmQISFaxi9cq09sHgiykJ5+772jZqYCgiHRlIvaZ5kaQl2J+miIWAwdEEFUa87JfdBsQOjYHGLPXtycy3drkYcVM7dpqQGyZPwsPsSIBj6evsE5OSGarjCbLeIBr4HcB4LrUIUzWL2IUZgs3OGofQfvCg61w8kTt3l1bYtELMMInLlEnpyn17pyelY6dxVAhSaHPLO+Qac7RSXgcNilIzphVAtC5s9NbBzNUQ35ZRpzd6GFBGgfVyz0soeAjypBBKMGvIAEWuMpoRnz4OoEIkrTAFsH9bQqa34wGLp7My4Oxlyyq5yLx4xUORbPTtJBCNxY2OW9eMYXZk/iSfEhZuV2VqvKiEjwSOlpTIV2Hoh9Y578gUqgWWY8c7DBJ2//mHg6I688jdt3+dD+IZvNCW8tzliVMcbVQhNVJdgmmemg3QN2Q5upmbIxGeBDzZssxRMi02Wh3ySeQ5kudCiK5+u/mxUiGyNRQAVEPKgQqbI6GOI1JWgDowndagUC5O4X28vySxNYVPUIeBP4J/O3/gnwY1U9/sD/G6rq5qMvYIe/4ciqWgNedzkv13+XNrlZZG3ziKWTEa34gNwkYBRHlyVfZ9YrTNga/wbp6AyXzBYfKXu8JRdwagiSMjqcwYGtG5qIWBHl7PSAznhG7hucnRxx9eQ+T+YRa/YCKo5gOnxy7z6ZH2HnluEalKFrYDEM6fDFlef5qtzi7N7xHK4IZJMXGSYv8pm9OxxKmz2T1ryQxJyVCZN4BSSw25wRLZ3UHEDkaZbnAKiqHDFKrAEpa9moQTA2UB5Nacy7z5W6IljJW0yGHQiBbFSwKqtMO5+YO+MKM5/xxff+iGv5JZ7KLiJlxE6cgFrwdeNohGchqyeEDzG708XT+zLe3qHBjEjqDD0qLvLcTHiaLbzAajRAXODCyQ6fPfkuVZyCKlFSYZrnCAufQPBETklmsHdvu1bwaEBmGTbPeOvwx6g4mlPBT5ZYyDLG6cvEZWCJDE/MgUk5Sbp4ArNGEyc11+RNjMyhHVUh1OQSMQYjCYnWFjhI3VhpJCKS5LRLWoCG90ThofEkQOKULDnHsu2evldGy3WgRLGaIEDkHfcHz3PGLTIpPorThA+FDSIHqKEZSqJ0gat+kcx9hIBQRZZpa8ywe4JD2Axn+J67xFW7g5WEUMWsjqaAMtVzdRCszx6gZnrSjEJiriV7JKEkYcZAoS9NjHiQWiM1Xr7NTOrPmk4rjHhkvq1Ce1ihps7qF6TDaLEJAco5hLQ8muHMw6xpjYx00eGN1n5yCknwLIYpM3MVE11kNV6ial3ivN7H+AG3khfRRpcbxUt8y3wIoYAQMZ3+Kiedz6CnSirF+wASc/k44+zNE4r8GtP8RbyBl3be5dx0BBITCvjanR8QHdzFzzOCiIj9VkFrZDEhBhuI8owFd0jCLXR5hWHzOSTLafjm/GcCZfoMyck68biiMczxfhnvu1hpIelVLowv4qTe20aMx6QJ06VfZcYZAGJXYeYeYQu+xf7G7b9ynftZj1+awDIf/yXwT0XkFvBP59//XMd4NiDMO+ejiceUnue2B5x5/wDjAoPGywyrc8yiJt5AEo24Ot2neTIjCh6D4R06aG9C1/Uoqk7dQ4DhtfgSb4wusnZ8zCdvv4UJgaZYzjDioszjpThC64g7YggCLjK41jnSfI9eNO9uD0oepRhTq2lEYnYOj3jmve+TAi0fY3WZLL7IE8yw5gxBBRMCG+2M+82MmvoWvGnWSfecoc7m1ullNqa44mh2S1SFihXCfPKF3oQrSS0UmDMslAqDrIAQamfZ+SI7Tp5BVDiv+/i3l4k1BgwmxLQatRPww81HHgxBVCgPF7j7Wr1ZU5VndA9LUluSFlPa02POV1s01SI4GnaVqHQYlFXTx84rBgBtrCGRJ3IW0YjIKd/ZPyRIQFHO2Vvc+5P/ho17Eca1UV0iqjrEziMKzUnFs+MdLkfnEX8RVbBJRdXpkjdSkiilYdogNeSJCkED7UlJLDm6cHS6AJqq7ntJTYskghduf5MYiwDPHO3RHeWoQJh3ZcfOM0xfwLp1mtS817j5LA/ojjqwK0snI+LjGYnUPI3TDldkl5e4SdtUNIIl7l6DeN5/ZSIyk2LmycHSYo6rpSi1bUmUojauA6HxRCLII4kEQBDwy3fo3JmyfqtHxy1SsErPt7ESExAO258jyy9Qss1J0yNRwEjgTNQ8Lc+CqdWyq1HJWQfPTaBTjElcnb5n0TmimUfmDWMdf45Vs8RTjfssSsY6Yz6s+/ig5PFT+PhJIhvjNWatN+Qz790iRG2QZdpDx0JzAApjlmkc18HupPMZhLpI2ls8S0jWePrwAPUtKFcIvglGETEsMyISSyEpB3d/zGzjDi5JsFFEXK0RhYCxgVhjojjiSrXL0/d3ACVIE5NEtNfexM8DpwBOIoIK0WiGCRYXQRknBDEsknGtOGDSeokHyrNz6ZjUeHxyBiuBM4MdLvYPuJQdc3HYp4p/yjbqP6fxiz3a/8ehqu8Dn/5FHlOiQIcpBUo89cRVG2OaeFMwanyMIC2eO3TU5t3zyd/3ILUv1Uq7oBpnLOxNiBYrLtm7qFkCMajGJN7x3P42VlKaWrDEFDUNJuklcGCaGZpOWZ0ZgtQSRm8M7UoI8Vw27OvJCWBwmGSdX/e/yvvNQMulqDwu/T03LGmZiNjX68T9pqMYdlH6BNfi0vF9ZmXMweKTbMQTMpsxmAwRK/xj+yp9v8gg+QTRPOn2akiNxUrd7+GJmElE6gNlUbBx5w6xOhpSMYsvE+kWpllSVR4e+GxJg1TqiKYi5PHy6fkqgqJ8dGOXH3/+93j65X9OuXPEEwdDPp29z3KpZMnTJLagaLaJ54qsKHvYrR3UzasDmXMCiqkCbYRIE8YnE16I+yybKVF1jNsw3Mr/Ie1mhwuTA2ZxGxNqbMpHhgRP1BqxgMFqRogscXIWo0MiKVmWCSV1tedRGqWS9GcsuBlp4yxH7c8C0JgWdVVzpqJT9Wi1eqTRgJm2KEgRqWqlFw5LhPHuVA7WzvK6d1Sg1v4JgsFgalUagSvR4420VzhCokX63UXSUFeDwcSE0nBhfMJs8TKxX2GpWGEnXuVd0+RSucK58Uuov8e5qM+BrtPSEpU6w37gWOScoX/Y5mwyQvAs6JixWWToUowGnCRYiTH9FT58XJAtJqgDESUOntiHeaAyRMCaDHk2bHFdnqEyjnaUICKM0hcJJ4ZGWlF1U7K0pGoMaWRTRNZRhBZgNUYBkVpppVJfnbPS5ykOmFbLdFYHEKWoGtLKETDEUk8MDYYghiS9jCRLBOcYNp6Ya+cF9R5MRKO9jo/WMK5k/eZ7jMsS85Fz+GhMZ/oiq/2ScRxYdFMKk9KmohVG8y3Dlch74uOKmTuHUYNF61YDzPyZhSCCKPioXrI7o4JgGlS6TCQBJKJjClbjPm1zE0ydUDQmGQvZEfe8/EIXzl+2iuUXPhbKDdo65xekxSB+mWr5owxaz+HNvBQNMV2dcUZHKMLA1B5C/cRx3LpLc1591CaIMyQuKMWwGHUgXsIHgwRIQvEgB2SYPo/FoNEaiV3gwnC35i/wtMXRwaD5fJtXW3tMAaiZ8eT0SzTfvc5+2gWUSjzG1guPlS7/aOsP+Whxs4adgKXxSzw7zPnMxptM1PL8zj3+we5fsDI7YisJfHvzTxnNhlgjrNyf8uTWybwxS3AmquW2QTGEUxVTrsLUdXjtu+9w5wfv8oQc18Q8oEQIMJwOaNoKMYFh84CbrXskEiMI48aH6jAtpuZYLCTOsjWuUU0/6eMbVzmfrLMcFaw8YsVrCCTjsu5LmL+XHrYIoa5IWlphCLzs73BV91ijZH3/hGUzBYHE5hz4JV6wb9L1MxJKzhZ9FkyBi2rXWC+GRTflSnufs80ZYb6db2RqKXbpzs7vZd2QjyqYQMtVGK3vRWkUL/XCosbTCgW2+XGGiaVKc0TiU46lJQUpnvjBLpwoi5PZ6TGaofYr6z4iil6iJnYfqBojDeCpF0sjLJPV1YakLOYpRj3nqoxuEC7rMauMsFFMWp4DBKmewUpME0eqrXl1Wt/PegilbSCRYoxnOT1mOT7En0QEjbCm5p2CALpIUj5MeJpmRJo/dA+PDajENEKJSSsaa/tkzemDwyAixDaQTisk5Kh4nDkttdEQsS8xJ6nFiGNJMzCONJmyLif8HbnDha0DPvXeTT717nus9TNs/pHHJ7/Uv03iMxgxRDpXc6nSHuR85P4W1eozFPEZBGU9SijuTnBUvHh4l5VhXe0nru4nqVt+58kngNbVqneG0f02R1I/IyIQUWLNmHIujEgyy+LRhCDRvIKtg54zjVoB9mCPF0mpAiSmdr8YxwEXOW7cu84vcvxMA4uIpCLy34rIbRGZzb/+dyLyV2xY8O/3GMYr+EesNow3ZI0UmzzE+xXDZXdw+l3JUwBkxmO8IQpzqa7AenQEKHFjnTXXoSUXcQjtUJIEW2dYc9UIxmOTJ1kq14jxNKWkSUmHKS9GLXTaqMnAqkLnzWZqcq4NKjIWCElA2yMkLonyWto5bnwc8AT1dMho5Y4kpLTLDDWKKxMWDTSl4h9k3+A/43vYu68yLWZYEZy08aaF+FqJosC48Sztfl5PXqnPP1fDO8aw/e1XaB8MkUf6SEZ8jBKhtb3NxekBbc04N71GqvkpDARgjSGYuqJpZIHFzJP7WkKdz/q4pFlfy+BPA1qSVaxPDjHq8ZFQJgmH3c+RheeRaU5EoE1JV3PObg/wCHn6Uc6GuJ6sxjA7J4SzExaGE873axeDRTPDPILrA6z5HkES0lxpUgfpYvY86fGEMqtV8ALELcdJK2GnYQl4LugxCuSRMo49inKeA866AWpqaWh4WIqAKGLqoB2JnO7g+GCRilQxKFaSh1szM2d9VWn2Mxb7tq7k5lustEIBps5E7weYAAAgAElEQVSCk8Ihoc7oI60lAcYql48OWZ3MuLKZ113tIsySK0xiyxnTPj3Wg4pYiFCaHLT/PllyhQTDkjiS6VUWFiN8+vT8rJWi8WmMrwUAAWVy7mvY+fVdnw35kNlARebPTd1kGGWPODAjxEBSBp4YZI8AnXU08HmX8uATqEBs7Jz0biGmA0kLO/wUz5oRT3NAJIHF6UPOSkSpjDBIfC02iRSSktC8jIjSmFU1H9RqU0YJztQowrn4mKE7T5KU5JspL9zKHmiN699rAulcSJ3iMF7myWLgRCNCVMPFiQRsNHe8mCMRSeEQhCC1RZOezpJ6tXigzPPRMguD2fwYFV6UKvWce/sXG1h+1lDYvwSeA/4r4D5wFfivgYvAf/EzPtYvZDx7cEg0zxwDBrXCio5xomTG0wpx3S37YA1wAeZ7hp89ET6evkS3zBi1UprRffD1RHEm50K8jcbQ7XRIzQpCbZXhRfCidOMRTR2xOJ0QS2AkFVZrnHsxG/F0u1k7q37p86eKp7pqgKy1x97lNhePznHJ1fxHLJ5KI2y0gtLlfLFNUUJ3DN448vYxv7ZzwrD5Ms3q25iiJEsWMdtv0T9ao2G6nLR+ve4852Hm7E2TYGp1ThNAhDyO2XOBq/kmk94dJPnN02uayRny6IR4VCFG6WY5J52Y2A3mDrgPg1AQQYnJ0g/RLZS14gbee2bTGdO0jxFYftD/AKR5RdsEkBqS89EScQhMIkcVQ7uqIZm66bGe5jNzlpazeNPExgmTZInF/hhvkppPMjEERc2DCmJOWdtAtOAgKygjR5NAlMekPUfjEcVeXDiG/RYtA6UE2lrMr9z8CgosjwZIFfCnyb9yRgYkYinlQaUn9Ft/97RHRwVsVBerbmrxC128N/MAOD/ToARRMvdhVrbfRGeWk4U6e9ZYEAfptCQO9WdbmniWpoGmU7wxfOawwnihO/WQRlipRRUqD3sjnKkVT2X1LCIJyoBB+gKC0ppOuOI6bHWuYcwuoiMeSIir+CLNeYLiNGEaCUs+IkQFuGZd2Ya6+jk/XqNRHp5eh3pBrZ81EaFll9FgUFO7TKTDinYUmLbmS5wIQRpkjZdwlLRmGS4+S6JDzjLmxDRh7khuRHFRqOXMUlcZ1sQ0pQ7AkdYQrpH49F7WfIkQVQ2mjSUWNAc8y6N650pECRKIKWo5MJDsLMP/w96bxVqWnfd9v2+ttYczn3PnqeauHqrnbpqkKFIyJVm2NThS4lF6sY0AcWIjw4NjwG95SoIgL8lLgCAPSYDkwXAejDgRBJiySFNkc2yyu8meqqq7uqZbdz7zHtZaeVj7DLeaUscWxThAf42uO52999pr+Obv/yVCkwkPVYQyg/nzZ5Tpjeo9q7OmY5CQTmwlrK14jyNY+jN3r1NuDi+TSo4cfLxd+J8l/bQFy28B17z3s7f4kYi8BrzP/08FS/v6CvpohEdhJWjPTgxDneEQEvHgNTqfaRg6YMdWOF/dYkqzTBnHO2RRk3p+RodTTkyD0xR6ZYpEKzgHkyjEFwba4fBclCkjQGcOZUqcVN32CAw3nlqsdXz15ne46CM8ioaMibTgJebSwT3WD/dpM8SJwisB7+knz1LrTzgzjmC0eryUROlnaGDBBVNb5RZzank4ntDZn9CUHgBWNIhHLWTLnATBinBcn3C78zovvXOKi6dAvtDcnEPEMdFbdDzUsgztgiYrxRRVlpQVREvI0VcM44ucrTVYkQ3uv3ObMxFKZbGisVEcKjCrFIRUZVTdfnHiyXQICCPQZMqkwuuyqoZyoUr7aFKQNz9HP/IMDmrs5e8FpmU9oqQSKjJnig5FNC5RZZtyZjlgqY2njOPG3PIUoHkvQ5kuRaqJBUrxeL2wfkSBK4RSKVyFV4V46npMbkLgO/IlzaphlKuSGZp+Sk1KCuVRlGhnYQLxIMdU+nvfTOkqh/aaY3uRYe1dEoFYFvAjVjwiERFSxfHCSiY+52J2l2m0Q31sSUYLqBsRe64lMRJSpDt+GPYHQi6WosiIfczWyT38UgV4CPh7CgnWyO69NTyeXOCjSEBN6JUG5aE9naK9Q4kN4Y35GBx4TU0KmpRgvxyKLJd2Y9ieVZqBMLeywrxbnAMrMWkmSD1cEz4/s8eDsrbizub3VC6sUZMS5TOWqRHFDGgTRwXwiObQVsk/Ql+He/ZKgxdhGAWrNleWXDJOis/PLZoZlapONJsvCT2QqhlkpEsER80l5KqGrtbFijBSBY3q3Z2oj3UD/bOmn7ZgeQjUgWXxWAMe/OSP/9tPoygHE1POG2vNGEvYtGNVsh8JO8cls0C0zDQOL3ivKcQQUyC5oVStIBig2vcOEY/Tiut5iZVZaiqc1l7BYPG6JFMGX3FLL2B9yLH//X/yv7MuBdm0gxWFFyGPXwU8rz78fYwa4VSIbuglCTBDaZr91GXIsShKHFaEcXyZsexzkj0F2QaRbhF5KCWan2wnnr7OaZSmipowP8DT/QOyCw0iOWAsz2OWhI+bZrxl7rKmX4DSoWXKkw8z3t4s8aMRZyYCLC2borQj9QVTGxNJSYLwL/+7/5KJ2sXLMdBirDsAFBIYVVOkOlCeoVq4T8TDVHnGqkTEU6bPo+1HOPHUp45pGjTL1oMxd1d3WVcW44U1dxYspyVNUmuHtR7yDggo5QKasnKcpdfxHrRyOK+wuoNIDSgpxdPPM1qqmn0llWDwjFRZifkwl1YtPNVWFNq78F4q+NdFynNCfX3/BCcuMDIfXFRTmzEwno5VDHSDQr1CbD1eK5KiYOBixqYkdQo3y5ElKC4TZSnEEVe1MZlYkup7pjmlaNRj3vTlPeYGQ0odFAltRzhtgwGAq3BaF3ZvnO/M8Uin5kW8HFHGT5OMMi6P79GMRkRYSvFoH4SSqBJxs30XqoRmLsRMQymCdh6RmVdRiCjOCyagNFdYYYAdh3c71bA8sS1/vnJdgFLBVDpIlU7ugVMzpbjyPvXDC5S1HfzydRIgZtTi6XgMkZScKIiyI1QOkZR4UXN3eK6FyIbYixNHHoX3LZf2ovEliKJUEHmHlSCEy8plVpgrTPzPto7lTy1YROSXln78X4HfE5H/nlA7cgH4+8D/8qd9zv9XVE4KvERzWPxlRgXBP7z+KKdQzDeNQID0Fkenb4mnGeGvilI38XgaMqEcQfMsC/5ibTGDEX2z0FgsAmIYqwIn5zWOgJJV8v3Xf8D60RUw0LaVuKgOzDT5VTZcydQHmAtZPvSiWO4AUWiIdI5YIRfHNN5mqNZojC3aRdgl/uGroKatajAybak7Q8XPQGDlZIN/7+g2I/08XnWIbMlEC4lX5FLywhtbPKgNKFBophigd/gCfRUFjfycs61K95YJD5VGDQumKy1WOAHxWAmumL4OjDcVRSmO/LE5Ew+TuZtIyMSCCfhOUodoyQXXmqRM1RSF0LIVpppaWKKZOAqTh6y76holUIij0BFT22JDH+NLOE2eA91FVB98TmvgFlo0MNVlgKKTanJn45Uw6Kxi8B0761QJqc5RUqFASdBopRJOgtD2EVBQHwUFwlYCSfCMdYHRKVKCGeUUylPiMBTkKJTyZN5TzLX/ZYVk9q9nqBwNt0DOjbKSEl0FqQHvKleVI6YI2UvzhHRZamzl8bKIWTq1ipNdtPMo60hMjkwhE2GkPHUHia+SOlSoY48zT20czmgphqHKwQtR7smUJ3YKW1nBHhircG+RJoUOwXeTBZimUjx6vpkh8Yszf2bKSkmDEkfbaUSCspIpgy0vUxvbEEyXRdxmRkHhCV+tGFIJd2tWsEBaHAU6CEgPU2WpW4WZWvq6ZCqahl/cDSDTJQ00pVWU1d4P7TEWzQBzlXxsLH+W9NOwWP6nn/C7f/zYz/8B8F//FJ71M6cfDy7xXFwyVMXHWv8+TlIVjEFg3OCIc89ElYgzCEkIKkvILGkOHZn2WGUDK620QaV8aPBT+UutqCUREKhQjqnA+tHiYLv5QZU5M86VwVea6CwO5PH0q050ErxjgcnO7i2OTJkKd8lh1SL3ohQHXjAfGxEocRQS4hFWPwX6qfnfpircd9bIyukrbObB5RViNo7de90lYcLc7ZS6WwzUM4xU8G3/8KnPsXV6ADTPCcvZO59JidMLt9V8fH/CAnopKWTJihsH37k7x1SDT1svjU1UgV5qEz1SFu+ESZzhvMYbcJaq5p75/ZWatUSYva3MvwuV5n5eV5M9JiALZUgGBVPxDFVOx3lSv8+ogsSb9X+Z/f94ho7HU4olUwlTCckShYDoRVxoFjRGFiEveWzNH09jN5NgCYZrqrRu8SFRgFkrBnXuHH18RTxeKngXcSCKGgdYOvNYUylglKoy1DIQTe9oKQMws/O9AFAqT+kVXnmmldqSi+U4apCZax8bia8Y/+wWhTg0gvIyB+0s5xmOlZh1b9I7e45J/ePn4vzbCSfaUaafQRC05CHLy7wC1nOiIxJUAI6U4P1YnInF3CwrXYVyiNdExnLqHZYQB3NLT53En8C8fsr0pxYs3vsrP42B/NtKG/5DUDtzk/ePJc+8kHLZEhAVrivFEVWCwwFx1ckrtLUNm8Yu+YeV+Cqj5PwzRYX8l+InHMlgTT0O9rxkpeDJTYFYHRovCefeS+xrTNpfpNYvGamSVBTFY48Zq6DVtW1EpCwi4b6FsgwrYeUq8L1lKiomlCl77m/Gz5imnJs3p5inUBtGTNWCuT53ewGkIDPXx9I0zRjq4kPhF+fdf0t/nrkzlrTUx8njGUuwHFIfXFG5xER4JrLkbps/v9LLRXioV7HeYx4b15z5zS4Sz0k74riRcvXBkIdJnbgC6VTiwYJFMYwb9LKPOFI9HEIkobtgpGcu2OCay6sbq6WxQWVxip/HhsIccK4twbm5qb7X9hbI9Yo1h/m04tBeGOmS1GkSFa4pykpJqgLMM5o2FNNRMVdyjFgGS4I5SKXZOD2YksjneO3mzLwQ8KpkBuoiKlg/ASMLXJ4RSpVk7oIaK4cWyAnpvC4CyXsMyOmi5wkp1glZoqhnNoxdW6bVvHS9Qbk7OLUMZxMAVPEeUzpaH28++pOpWvNSGUQKvBcGOhQSz872zKLLlWekisrFHnOmi7lEk8eE+wKnwaGq4txMIk7Mz7bv/ad1LJ9AunafKZZhW//JHxQ4Ezs/rDPmMjvMlhEjZTkxNmSczH5vFozOLhVEwUwjPL9xhJDGbP84DvgYTSXEcESCJp+LYzK3VmZa90wlHeEriCsRlgK5f+wrA0GwLDP+mdY655t/shL3E8mphS0ykPKc5bBMQWNTDNUic+onjdNXPnYP5BLNlQDIWebvH7uQsI6ZsuTVfOSV+y2X6JwwBNDuPQptMNpXVQseEzm0dhX4pczXeFpTHGxFVYwmjHzYVBRK4yIBs8tULwpFMxEOVhSWgn5Vha3E42dZYnhU5bLTylOFHyjFM9IfZyzTJUvoaFN/bALEh2QBUR5RHiVj9GPzPFIlUxW05Ila1GkUS3sn1yVKPA93Iu6sCoOenj+qrNJkZ+sRMp3UfNxDKXEUVYKBx+qwhoVY+qpkqvRcaZntZ2VvI4Q5NezPx5MtufZmVokHJuIoNRxFLYSlzDyYr3m4oUf04GPzONEWpc5blYpBde4qBe6xazwzob1scYfvH9/rE+0rIQJIMr+nqtyyToe7ZyyfVzuf00IMjdrPltV/Klg+gW5OV5mKw1WH/2MzVjFQb05DPr6UOAS7tNGUeLy7R1kFVl11zbCpGbUWN1Tan0s1XN5ep70/XrBNmnFgTI8110LC4bSJR+lPzgqZPXsWS5gJSTvTKOenwzPUGaUs0o6XNVthsenVUje85VvcvrTADl2+dkZFFFxZBY4TyXF4Hm1GWHM+VgQL5jQb28dIfCVYgqjP3J35Oyl7j+N2jQ+2L88P7PJ8xLyO1i4UM5qZRfqT10j8CO3355XwfSnDYReLqByrNLmJ0T7Anh+v6vCeVe+aLBWM9qgI+r2PH82xKnkUGaYqJ1sKDD/SnhOtsXjyWDjraaay0F77bY2VsLdEoEyEgdh5ijrAw/V35kJptiZS9biZxZVQ/hyHnBXlzWJZDs+pKjmRkokqsXiydOHG9Sq4x0bN80kJ4aue36uooIJCgN9zxpBMgqVxsB5xfztmtppnala/EsZgim8gLDK1ZKkGTVyVUyRB0ZidGe9eI3Nfo2DMqP3xbouz87BvzDkrD4KXwM3E+tLmidwPid1rc6+Ae2w5M7GMTMFp1Uoil6BgnPX0uSdodxORBV8ojJ6vCVTZm7aKGy0Jc6lcYqI83sBK7fhj7/VnSZ8Klk8iXw9fBCL3Paz8cK5RKfHU7FdI3e8zMPX5JVZCjcvskGoELSNM+e35Z+regQarl3zBSy4BJ4qJsvR1gfKDebdj475PZL9C5H7AV5/9kNH6AVH7lHhpKQsxc/eJxXNiSkb+jfl9pyqhEEOeLLz+ojzKC4U6L8CsRCj3NrF/g7j8CuKPw2FR06qz+D5GwqYt1PlDOei+g0KRSzo/xDMtbrBTubMENCcsy4bjnuGk95iXVgDxDFaEeks43Ermu3f5IJZiFp8nMAXlpzgVpLkojzEZVjSaIyR9xGmvRhZVwU3xDJuah5sRo/U22j/C+Eco5RkvMUTxJ2E+OSKr3SdLhaqi5Jz7ciIuQL5UDg4nQiaH1RpVgmpmGYlQxoPwVT0uPgMNpcad3SaFLJI8Hqw0+BevJny4JpyuGEZNzQ/3WvPMoWFLMe6oUCynIo5XDaUM5wz/pFnjw2aPvFq/QUdTikdVLr4FM50HWxb7dskyDZ84r5uf9jQHm4bDzcV6eiVz4eKr/VAmS/tu5uKplAHtbzLoaPJU4cyCSTuRj1nuWpdotZyyW6BVlXihQtfNTCXkFQqA9vfR/hTPFAQOVuw55W6ZrH8LZHje/JhPg2dCwt2tLlHrFsKQec47kMfn56VQ7pyCMupqTjY0o6ZmumRdKM7mnxq2VLXPqmf6/rzJXF/OpynPni2AV7cZR11+lvSpYPkE8nE4ECGWfsp7FxR3WhXgoj9EKFHBab3YABKKonIVkauYW5s9PtjsIj7kwltReKU4My2ypQ1XsmjMZZeWRrv36JtmeJ4/DEJMjjlcafOf/Vf/I/1VxWDVcLgRxppFEZlOsMmsFvkR2t9Fu5vBPy6CVr56pwCTUZBwoNb5aO32ufefpClnroFdLxFn55Fc8SOc+w7GvsmM4bilMZfxkO8+1eS1ly/iytcw5bfm53HUVtxL1ymVqQ74LBWy0txbQVv1wKQb3kmLY0uVXC8KjrcN0+gSpVqsDcBEEkrOC8bYfg9jv8k0VUsRljKkbCvF0ZMNNr1gFBj3AbH9No/2bmPWf8Sb12a6cGABy1pnRh/n30K77+FUUXm3QkfNx+Niy6Lvw90WmYoplwT4zJXhgSI5DinjOqAUUzHeGYXfCfs9wdi3w9qpkOAxrQtllY6axXr+3DPdmI/guJ0GIau/P7/no5WEzHtyvk3OW9U8ecQvucq2XgPv5+62hXvsMStbhKlKmGpPv1bDGuiv3CUyQWipqgjRq1PEnwatWmB/q879nXh+D6s097bmlRjcvvoak7UYo9yStq4p2efm9lKMS0qomKwHav72PBU+FxPANEUodBhPlo65/UQ8n6v3eh/rVQBQVbsfM1XR3LILLq7gnpudi3v1iKOnM378fA2palJO1xRHvbgan6fQ0bk5M+4Wp52ILA3W/cnqYm/Mwl6jpqLf1UG4JEHAqKWqjsf9Eefqa/xHDJNPYyz/VtF2sRsQX0X43ufrfLjb4EcXOzzYignVtMLQrOCYaUKVGR+OJhbNsJ7yxhVdVegHTC3l92nYDodJl7t7KeL+kMIsAAPFfXfu8tH+kNtbb+Cj15nqFCuaE9XDikFEiOMaZ60GRSL86DPf4+1rfY66U1Qj3G/m8jD+Fsp9HSr02DL9V8w0bIfm7mYLFyvELzbsYS/hH/y9X8JFN8iIlmJAFsURIpbLxbuUHM5dAV7g9l6Duv5lfu3OEe1kB3GLJl33L76Nw7HfbHG/16JQmlI0E0k57YR3Eg23LinudRxHa5qk/BYKIR4V/IP//L/g1fhb4L6C9h+FtGcVUrxLfd5yE3+CkGOVLGnTi6SIjjmjRs61yR1cfJM0P2PaOOB4/CUu2w/IVDzPrxm1+5z1NA92Ix5sG4RjKvAtghfChJ8RvPccrZuFG5GFFv7G800+3GkyY2YzbTak5U7CvpnNpQHj3p3fw1dApPgSYcok1TxcT8hl1rFzEd2bifvlMeAMHgfezuVfqRVlFOPJgVPy5B0ATroW7e5j3NucrOdAwDa7u9pmotOfxH8rfEbBSza3yJ7GU6sSV0rxQUBVMP8z0iqqrEqIXU6hIrJIz4X5QSOG9BBFqPkSFRS3+70BD3bfQOZ1GnYuEJXvE6vWfJyFMogkKImZdFvsd5t8cM1wtBlxby/muPl97q3f47C5gD8plGGqEwqJlmJ1i/UUgSIWhqqBRVF6+NboswzSGAhZkgdmg6mOebQe8WAn5uFmSiEG494itl/h0e4dOl5z0dYYtd+fz0qmYg7ThfLUX/0B1ghHG4ZxlDCssAqDQJqPCgGMW/CSexspaxtP8bOkTwXLJ1DT76MRrAlmu3UFkjiIPTUdse5q+LJNgIwQRkn82B0cw17MVf8q046qPAeClndoxQGb6jhu80fPXeBbL6xV13ggI3LfJ+ZNTqIOhYJ/8gvP8I3ndri/WefbL1xgaxoEQKe1wkFU5cxHY+7ufMSHT3+Dpg9ODLVUaxA7EwSJN3iKOcbQ3Y0m715aYU8ZjP3mInaC0EiE1b0LnKkW5dyPvNCRNDnfe/ku1t/EuLeZ1DTHPmXfGFrJV1ndvIUTMO5NIvsaee2AxMRc2N/nrb19vv78JgftBpZ7aOVJXM7IxFAFiu9eTnj956Y80A3uTnoopXip/5CurCG+5KwVoqNaeabNhZvS8gFFZdWU6YOQIfR46rbOsVtvom4I71+0/PBlw+mkx5XjQ+qHCZEr5u6WUfM+RxsP8QoO1gzDJ3LEKTy6ygyvrAz7DTyHPGj2yGauOULM6PbWmxSJx5oKXNCVsOQbj/wIKwpXyYIiEsQNETckKt/k4dob3Nl8n8ydcmra3Ov18MaR64gzs1w3IQy7Y5T/Ci7K57tqlqsaMgtnn4RCNMEecZVA8JxFKca9gXF32NYhtbvAM2jEoI7n185IuQ/nTwFwXqG854I/xFfCbVq/H9bhY2JJMMpVrkvLtB06h+5vGW4+GVOgcOkRF22E05tMdQoI9y8phtMmxn4XY3/ARGlmwj1PhAfxJtY4+l3NmzcMPlmj6wSfaPZX67hqj926Uucbr3YRoB85cF9H3FGAcUKqrDHC/FRULiXe5CR4LWid8yBdw4rirPI+ibcMVIM8VvOWAIWMOTUTchVxumLIN/6I2vbrdFSBrazZu6vf5Q8+u86oOWR/9xZ2KR3cziFdgzVz70I8V2pnzwR4tBnzgwsrXHvyM/ws6VPB8gl0cSQUuPkm8iLkohGBaL2GUENQTCsfcWFUqIStyDMgiwQrEe892+LehRQnwWmi6iEAW2rLvfWUs3bC3a1GCEaLJXX3ifw+db1JFPAmeLBR462nVtj0Oc0ioCav9daIJMQIXFUo1+OUIu6Sx4qzbtBsYmsZFAU694h13Eu2GKsaD3st7qw+xIui2RpyvOFIy69h3OtM43ehuUXSbpGUBZOq0KruQXvBOYUvI+rxgB8+NQFynClxHsp8ws3Or3Icf4Hdson2D1D0QQRNQXP6HYq0E4r7BJQ0g1WH57g+ns8g3oeeIspiVSPM2b/zO0xVivcF05ri/l7MB7ttJmnVQRHFnrtFmgnaOrZVyKCy/gNm7NDjKcTQtlM2L7QoUbgip9Oss3rlDs3uKrrQTKsWtAFuo7pWOZSCyDq8KE7WDNp9FKxDb4ntG4zSIZ6bAEgV4M5MAd7NNV/NAkAzWDrBYhmZGo82DSerGvHHRPZbRPKQ8cqIceME8Q7vDdZHVTZRwDSbB7695YOtNv/8y9cWzkEfko+Tcgo+J1PBtVJ3Y9YGC0VhVl2f6A3OaGJYZ4WFaw2gWYZaEamSCMQdIbbKtfUh1jRKqziGnvIoCWnwtuq/PoN0mZGzMwiVIN5GDc+kvs/t7Q85Xgt4fB9E2+QSI1JHELx7yNppzP14LSRXRBWWmNdV5N/z5mcu8Z0XR7y3rflg13L3yQj3wmhR01VZgPvJ6nw0veIIIcfYH4L/o/kYZ2t2sK456RlO179brVrwCviqfvVvX9kH8bz7tOH+hYjIevJZ0g7h7DtusVn0uZHDk7bBMzdTlHh6rqSvG/zo4hqvP7tCaevcevYHjDv3mEY/OQFnlvGI/SrmMTfsWdQkUw12ao8rvH+29Klg+QRy9SZZJ6oK7oIupLxhqBvcra1yL1lF2zF3txLubqaURlV9yoPjJXUZZ1oxkIzfflTjSlly2jN8dKVG1Cz46OoR71x4k1wHzei43qCQaO7nXvMtIgyXfDBlBZDpCom1Ffw6rKwuBAuV225vlLATfUTa66DSAHni0FgFedRh2GkxVGD9XQZRnaYd8OzDBHGWu5cMijGaIWp6Ctd+iXq7SepyrFPc220w2PJs+4ieM/SfWOVa/xL3tuq883TMtO7o9E+5NNynuXGVovskrkpkiFzINCpKQ1M/iZEtUKoSthGaUCx51LkPPuiHhSjMZEpatMhqAWSw/dzLTGwDKOZ1EmUU8NASr1gvC+z2M3hbJ3cxkygI5tTl89oZD4iCdGJo1hRnJ9s8GK3zVKPHZ25MWbv4DLYS1E6ESHJmR0Yzpt8zkArHqxFlJDhVgFO88fQaHzxrubP1PqmKSVkUmHoVYGeKGVSX93MY9IGpsd/oc9Q5xKMYJxG2qj/QDv7ws19g5OvsuY9Q3uN9ANN0LjD92FvOTHL46MwAACAASURBVJN+vIcSjcQ9nkrWAxzPTCA6x87UUZMJkS+YphoDHOYdbKFxpWbLpaw4hTGKfu0KouqYuSDwjGsDOpMzpjphqoIw8RLcgDMsq+88pzjq1IJLS5t5Dxy/lOK8HCLvJ9/GJ7eCXSfgnTDQh0ySKSBo50jKkoeNlSqzUoARTgtJOeX/+IWr/NOffwLlPdNZgNs7NuIDjruOt9f3iTLPG6ME0zrBRVOEMO+FRJRLRcBOhTjo3QsJ/cYCwXkGfjmtCWerA/Z3J0zqlqPNeyhfMEoNXntW1lpoW4Y46uoPCHa/YKM+6zbGC6yWd2lITNN5vvRAeGv7Ca5l9+nY4EIsjcKp8yWpQ1ObcYBKmShZpE57PtrTM/D86j9hotOAED6e8rOkTwXLJ9DR7jpJIzDtthtRSI3mNEHrNR7V28jYoQltUcd1zYN1i7DA5Rl0DLlPsEoHWBCBUUvzbvN5vrcx4oq5TapaROWfg6yLKxMeXrjAiqrxZA65ilCArSwi7x3GtUPmTHU0N1bWeXRpn9bqDym8RuV/mf2jv0Aj6nMv3sH5FrPNmJSwe7xPY6K4ubvDd67HfOv6TdAxn5u+RGwUn58aVq2w4uvE1oM2JI02QsGwJ7jYUtQDYMSH3V1+tPIE5ckT2KmmSB3i4dJRh52dFbYuNlm9nKCcELsS4x1WbNAUt3cQXcOhKQRK7XDIwi1TFbg9iDvsT9YYuga9J54EoJv2KKVG7Ft4CRhQDTup0JDBO8Mt2eVMppyqxrxfikJouUlw68SKWq6oscna2ue5+mCLGx9eoFP7HHtf+G+opTHOG8ZVFl04wQEWs2lPmSYDrlzscCIdTkynKjQVJmnMJPUgFUOJY0Awlftw3RVVMewshuaxogOT667waCVA6w1NnY9WH1UaMYzUVXJ3kYYbY5zF+xMKXXBYG+CdIfaL+qGmdDGmS8N6hs1N2iRExWsUJhQTFpXXRLuAUxaXPebWWJmhvEfUgHEtQgRMNa/aOzp2iJd9GuXvkdpH4EGJ4jDZCPucAokAiThqCf/3+i/g8xp4hVVDni6PuOIfsWpDgDkuv0kyHqBa3wnIwYHjgzWM5z2P2lzMSrwO5+jHNx7w/ssH4DWrR1fpNF5mGiW8+9kpBxcHpMUdzro/JpYMg8a5iMZpzomBfza6jo0nCMIH8QXeTrdZtCIWRnXFSNe42drha69uMqxrbu82GEc1jjt1Vtdf57D3PbTKufn8NznduMUfPXuVhys1NlzJpd3f5pH0AutPTjnovoVxBSq+T+IdmJJhS82D+w+zZ7hd2wOdoP355JML/TOsrTq14shrD/DANP4A5pmGvsqu9GjxGHEMTMJERRXsEtil2rmfBX0qWD6BThOhVjXgSiUntZrU9oh1j3HLYrCURlEbHZEUYw7rhww7s6yUB9y84mlmIxAoVYn4AN3iRTOoCReKAb8yPeXi7RbiYgRNGTeIUJg5cxWeHJ+wc/ddirEFu8GJ2p+PsdfbwiQntOt1bmTPMa6vkrz8Re426pzqFkOzQdMbtq3G2NCFT08dSWG4v97AKiHxlmaesVJklJ0uHSs4b3FR2JD1Voc/fKnHo16NQhxvN3Z5u3mJR3EXa4SyHs+9vuJhZZLxd2qnAdI8aaKsm1sKh3GTiWg2V2o8dfAIsZ4HnRoPuzVON37EuPfdgPJbmfVWNIVP6HTf53f/wy8BEEUrWBM04cgHK0TUGcNUU8SKMonZrwmWKbENCAFhfAovitiWGF/wwjDn5S/9u7Trm1itESNoVaNWu0g3jRFnKMXw/k6LV3LLZZuy5mKeLSM+P16lHlnWz4bUXYb2ZXDxOF8hKgjff/UZDrdDH3LlHVen92gF5C4g6JwTSQK0jQgXlzCdOmWfonGHEBQRhmmH1LyEEs/9PQ0UvL13myzOkCIiElMx/1CoOC1Sdr79NqWa0Nz6Ie9fH/PNa+/QbfweReTw3qJ9Ti4WU6T83md3+YNXN1jLP+Li6VeJslP+xWdv8MGTW0S+yhTDU/NTRCw179EUGF9yuqo5uXAR7Sx1O+a6c9TlGt2ky4vjdxAXVcjEDvpDUj+k5m7TLL6Ooc9qv2AZuab0CmtgqJp8WL/MQfQbFHFCqT2nXRiu3iI6XQ0JEV7jIoMo8FKS1xXfeWXAd3YT2m7IE8UB69OM2HkcwkflKoqQuemmNZT3RFYqy1F4sB3xjVc2uLWxThkpbl8OzcK+8uo2rz2b8kzxIbE7I/ahz9Iv5SsMuy9Rs44NE3NxpU6kyoC4kUXk7oz7m1/jNB2y1/4G+cr3eeNlQ14rwZUkk4RfsQMK10FsWpnSgnhP6+A93kuucltdwecRuvVdRu3b1KNgyYkPXr/Y5bSkT831QTsUQiHf5J2ND2jm51E9fhb0qWD5BFq1F6i5PLi0kg5xLmjTINk6oqwVuNSTpx5rNZMiZuusTb9XdYuLD/A+pts/YffRA4YyRkvArOqU6+zafXZPhfTHV1k5CPm1D1cOiLfexQbFHItC5ynrpx3yXOFLQVTGydkWl+4Hv3Wj1qQQzw87T2EPVviPywf8w1/+ItMoAX2HrHeP9Y2UlnMkzmMbCS4OnehmQOipz1ixDeR4jYf1Fe4/2+W1554JgVqgUWsFjb3Cn2+7MxTQLhJWyw+RNKOfJJjoiJac8sT4Nttp0LQS0yBOSyLnGauIQ91hkke8/B/9XS4/+D61wQQrU+5upZxkEfc6FnuuosyzNZpy0Wriqr+GiFAXh3hL3XusFBzUP6TOmLxrKeuKenwP5ToMGtuhYNWD8gUOhfWGljU0vCbtNKjFKfV6TqcxInXB3VarhbznZGrxrqB0PWwUUfcalbW5cfwI78c4m1AbabCK0nsODZylFkQzrpt5jY74AZmtUypN3Z1RqpIcg1lSEhpjuwAz9VWtRpVwoNUGLVWyIYLv9Pm/fv4qpVFs2F/kqfHzcxyretlHvKcphzx4ImEkx0QoRm2hN5zgvWV/D4bdrzGpe6Z5nbI0DGuaB402K9MD2tkRIoo8jbi7lUK+iLEInq4NzjVVtSrQTjja7qFtQPku8xgRhUGI3fHc73WmO0RHikd+g/bEEfsTUptzedrl145KJk04qsfYqnDL2YixbTMdtUFnNNyISOXkKmfSzMlMwm8e1kkkgHIGtAqFQbE1jUIzLVXSdCWuobHKhOZuzbs4SgbNDG09jSLHASKGUnJO2orSW4yAvaTJ196jNrrNWv8RNZfz7KhAYQFH6S1OKerllG4CjahBETewpWFaxggK5QTVHbO/MWGzeYLgKWMFoxoH10/43F/8BX7g/xoDv4EVRb9+xpOTD7h0VJCriAkNfvPdAOg5ad0JmZ2lzOfV5ZqH5UVS9ybDxpQ7G4bSaZpln73hGb1a79+UBf4b0aeC5ROo3VxdJKmK4srBI/76Gz/i5bsxtWHI8rDaop0jdTGXxhcpfMTpiuLWlV1AmJbRvMFXLdpnR8dsHl+n5fqkylEO2giedfsqF/1L2PqUuJdRakWuDMpqDpPe3M3hY8uv7b/L3/j1vw+AiUJ5pFMTrtpH/Oozm7SbLfRWwrRxhriSaFe4fWOXHz+3i13ZIJUShcVSMhFLEsG1rTqv3vg8u4Mzvtl7mnfMBRprQfTU0wYx4ZAAtNQAl4fA8brPuTf4gPpoxH3dJHbfp+snyMu/w5NPPsn29jbD6y0uF5auC1pW3GgSbW4QauuDqlpzGbXhB9zJrlFmhAC1E9w05jfe3aRlNs6tzXsvvsjxTndeeFlYjXhPJjDSJddOe3zUvURDMiT6kEb5OpH7oNLeFGWxi21co3PlFZK4RqwznDP0qniV6nWCA9EegrcMtWF18JB22Q8AkzbHKcuo1iWnjvPB968Izc8SsxGYXWVBaP8a+aTN8GQHZT3Ge7SDtfI+IXCvcTMYaQFvFStFzplrsjJ5iYZq0IsLNgnFt428oOYvg1d86eFd6kozTHN6vs9ofZ/x2gn7vS1ax/cZ6QnaedqZYb9zlZFvcO9qjmWCy2s0MOBAFwUHwxaTUURpDGlWpz15C4mKgCgMKGu4UBZ4LFls0U5QXvOX790kLkpcodDHdTxCpxwgPie3Aw71Cvt6jbQWegepYCIAMOomtGolk47jrKXBQ1z9zdkEMWNq9RCtcNYwzqNKMUp4euJ5ZfQaF/M7CJ6hGvCZwSpZtMIgM9jiiHsrBVI/oWczpnkdH/V578p3KBNDMamjreVC8iJts4nynq3pLTonD2n6MVpFpMTE5YRsGjMeJewMQbvK6hynjJIpRe81mptQj+q06y8yUjUemQ3KqM00Tzmd9hibmIPBGkosHz3RwV7oUW42aNXrDHWHcbYdlr9yYa1MYHt4yubwjLRYQOZYZfD+FPEeXTikEKxLcOUY7f4ld3pd/tnPP4nWU5IYbly4+qfmhf869Klg+QRav1Jnu/sN8tY7mOEGv/S2sOfqbBwZZjmhqtQoPN3pgJabMHUxp0kNazTOO1Q54p5dY191+EbaJS+ukBpFHj+PjxVl9AZxOeXXbkY882iEf/caZrAefO46YiwRg7iq7BfPwCfcTbok24HRJlqzW97hc+OvsSp90r0XAOgkawy26jSyCYX0sK02V1rPgzJYSXjp7geE+t+IKI2ovfQS6bMv0qtBHmucgagegsdxnJDqdI7APGwlxN0J2QXhpPMK14qnAeFM1enbiHqrhzR77O7u8vTTT/MH6vMca03qLYnE7Gy/GObORWhfBDdLL+HSc9ukZUZv8LCCJleUZU5MxI2d84JlXO9yfGmHWemKtoZx2eSDuMt367B+8kM2an3itM5x/Bw9OaQnceWT9tQZ8NyXvoyJItIowpvQ4nXW+jftrjCUE3L3EbfWv83hW6uko3uspW8RmYc0bU4jTfANoW+nTBGUg17eZzJeQ8oa2JJCQrfByBdEtk49E5ouIRKLN8fUx5YGP2awcxfPzHK9x7E55tqPP89H2y9yf+8XaU0LrCiecRmfj+v81QeXePVohcvHR+SRoRY5rtUSrtW/zTQtUK7Os8/8CmvmPiuDEpRhTbV4o/FznLCG9o5R5wck6W1+Ln7ExYd32Xn0kJOoQy4R72/sYKTHVnSVZi1l3Rnw4PI6TkqUGnG0koXYida0hmskhaaeCVcf9bk4HLFuD4i0Y5yMwHt2xili9DztW2yEL4UUzf0kZSwGvGcc7c9jSwElGa6tlrRlgohic1y5drzHuDFrpwe09TF9Y7ijhK+vDhmrlFFqoO5Z4T1q5ZRrn11nyxyiESKneObsjMbIUaQGTcl2foTGkUUFuckZ2BaZRGhxOO+CMC0M2uYhSceH5Alr1tjbafCr134HgGZzg1vRDg7FlALlNOXxFsXNizQGEzQe5RJev/63+MrFv4FRAS3DT7t4G+A1RQnfutJgexrTynL0MJ8ruUWUELk71Mf/HGNDJkhpIrQYjIOQPCSM6dC7EKOTn3brrT+ZPhUsn0A7z92gEZ3gGjfR6j7ti1vIC6+gqgOgxNOhw88dd3jmrEYWT3DOI86RTKCdFazU+yi3z/cbX2CYNtntlUTG86D8LPuPbnDU+xHbN/43ZPo/c1y+TbcY0s0JcRnR5GLJWobSh8bDcQrdjR69nV0AREfcuPtNzu5HfDv+K6i1ywBcsY5Jv0VjMibysDkV+r/yVzCNPi7JMaLRZRPJDLOeUlGaQBSzyUf4zkNWK7iWNK7z6vETxPkq4hVpDpuNAaWBtW4b31ojiwweYeO0FZILokVe/UdljHKalp3ykha+0KzawOoatTynpTx/bQXa3To7p8d84Z0B1u5yYBq0szXazYTV2vmeEl6tEinFloWaE9I8ZNMVKAqtefvPt8ieXeN3/9N/yP7eFXpRj0aUoOQQ5T6kyW3kpd8N720iJj4hLxqsXQnjvr5ykZt7hofrEd36y6jsFCUl3fgm7dEEJZpGp0c7qtMuJ0RZTuwKnKRM7Bqjsz2mZyktO0CR0nAgpRD7AhFNGZ0wbH+dto649LzhQluz5lcwKiFaWeel+x0uH8ZcH/e5JBbjSx5FQxSWFZvTdpbfOqpzmTaP1lfxIiS+5HRrizw29NMd/t5Lf5O/vb1OrBxfHnR4NXuWi9OIek3hY0UR54zbp6zqMXtHYxrZGNeIONhrM2rW8Eazv3qdKysrqJLQohnwVTfLwzXH6bqhiDXtjWClWDHE1rMV10NarxKGjUPudke8+Jbi3hMN8AExwLmSk5anU6tjD+qUVlE4OK69TmQtER7jDd47VppXiXWNz8b7PDeZZTkJyoPRmj3lOBnEHCcRolRwp4lCK4WIImmv8Llrr7LxfIsr4y3Wsi0ulytoD7GBKWPWs/eCsiXgtOLJo5Rb+TVO/Qql07SmGSqyiBLOojoNH8A7VazZSvZITcgu226sEAPNIkNQdLC8MOmxM96glo1IiwLJNN9cazCKOpi4BgIm2aM5Lli3fRDLStbiyeEuP3/wJMmkGxCdxTMwHVIU71+vAvvGYETYHvdBoDsahHM1zUnWFmjMPyv6VLB8Al1sNdA4REqMKdF7HXrXnsEog+3X8WNNmjS5GjVJvLAhSSgMs46osETWcUNd4qLucCHe4enoBvW6Yb024a9f6/Ebe8/zd0+2+fdLQz021IY3eeH+h0heR/AoC0mqKJ54hCZmfZTzzPgNfvPJ50nqoaYDHfGvmnv8n+ku5tozc437meYFfv321+jsB0RWM+lCFLH1VIPx0zkPbjyFcZpatsqXan8BgPbKHt3LN7BFxO70LepxeEacxNwYp9RogNdYY3lNv8JH0kaLsEpJbHM2iyldW0fVUsQstKRdm6IQIg/b8Xs0qpaSYgyiPHtqwl6yxpdqO2wWU+rjLFQzR5dIXUm0vVPVRyxI4g4idXaab3G19VWcV3PQQScxqB187ylaV1/mgnoEPsQJrNPE7lZA6jUhhqS0xoiga0M6W8EqExHubRt+cLXG3cYqN7+cchivk48ThsMVxp11VFpHXRiRqQPeujDhzZ0N6k64drALGMpC03RDVuwZeQRqepfeozE9l/Kcd3zxzLMxLsDn5OWYdmHZjF4gVg2UdfhI2C7OMApEFMpEFMbjFRiEGhHN+jaHnZRYwCvFOI14yX+fP3/jKiJCdOHPkaZ1Vtaukqzs8MWjmM9mK9haxHrcZqiEiIjPv7/HZ95fg6wBytI8Kpg0uzQv/zq9L/wjOnYI3tMvD+fllUosHQvOnLFWb3K61WAaQyMekShhpXXKquoTxaG1893ygM2GpTQl+JK7e55yQ3h4/RJ51KXME0oVRJfyHuMFM2s4IIYk6eEkppBdStdBEJSBtNfhlaZnslpABJE0GBOSJowIojROa7z35GxRy2K23UUaUuepyFLTJQ1irljHlo9CkoJMePn4gLXsiHjseerBkLY9ZZoYrDa8kmzzimvTb3W4VJxxvZXOK0Z7IuycnVErBth4ymfNl7hYXkCbVZQkDFyTE6c4qml2RBMJPKiXNH2dIqqBTBiaIVJftMHYKQfovIbyjofbF3h0scZKkmCjhIQarXqN+qrmpFMySaAzGfPE2TP89vXf/lNywX99+lSw/L8gAbwX2tLj8//Jf0vvuT1EhLKcgmgaUR1EUC4m1cJTwxq9IhSBOWUxStOTLk93NDeudBEl1IxlIzY0ooj25vNw+ee4sfkiD/ZWEPcWI91h/9IWZ6qFUULLFLSKMc8cHvKPDwbsUD83xiyJ0Knjt/7StfnvlEpoOEUygeY7z8LJBVCKKGoRxzXy3jpNr7gwWmev9jQAUdRja/fvMHYJgqEum+FetZT42S9Spg3QHmcsvqZoqpQn1q7TqWXUbJ8oElR7hdrzL5wb33O7MVoCmtiZv8ZfeuJvVZMb0qC1jxAnXP3SP+LL0+dYFDV7yvqARC9aIi8WRkAUcXLGSCWIn6FCqaqcL+KkeAaA/ZbCFauIjWmOM9oyYtkAEhGekAkXygdVHVKg0HFF6McrZO0Y0iaTaZfCNOdMZOf6HsPmm3TKNg+3UlSSUMZCmk1AHMZ7xHsKr9FuhCofsuoj2o1bdJxDZx2UXGL7wy7Zww4xEbHXiC3RaY7djkFpdq3jihoGq2ASNONSNDu2xlnXUaMka4zBa3o64y9eCEgO9ed+A9rbSJTS+sWXKTod1kyLXzYNnm+0+Ju9nydKUppFk1ZWR1yN/uE6f/XuQ/6HF57l6e1NTL1FfiUibVg2RjGD1hb7e2BrnivR9/hV9WPS/6e9M4+R5DoP+++9uqu6+r7m6rlnd2f2Xi6XS+5yRfGQKMq6KFKWJVFOZCOS5cRKgsAwkMBwAAMBYiRBTidBHCMIkCg+AseODTuJDkoyLVsiKVGUKMokl+Qud5d7zM7RMz3T3fXyR1XPdM+9u7N3/YDGTL+q6n5f9av3vfe9732f5pGWyUhhKbr74M3CGJeaB8nrPlrdImFN4k4cwzFmkWXBe2smoz8qorolu1OPoQKLRdOhqTQarcirrRRpAjKuyXDJ50VzkAYaPYs6umHQZT6MvfBBdFwMDYqH9hAkQsWy0PCjlhSST1WYmH0bK6jTyyKGLrCUh8InqI3RM59Db9p0WWcxVMCDF59lv/E8NX+RvJL8v/wo3yiPkUoDhoYna/xt/yvYsrM7NaK0yHg10jILwESQIqFpBNocVfcS9y80GBAalumQ5RVOGhdwGjmq3rskDJNj5S+GAyIlWKhN0qSJCmBscZHuRI5cI9rX1TB4/+RRqv0fYdLr40LWRqoAKQSGtjpi8/UmVixbQMrQHjyaCG389kiGV+zTSC00BxjZJDgZhNJILHaT1jQGmw0sOcCB+e6lFh3GwBIIU6K5GqOjo+EBvwtx3+cZ+wf/iM8+8xn27nwI1xnn6/0fZM5wANkWzr21+WtF/gcBFe8Sfdk2hZMdDE8VIBoGsquLpyLX1wM9aU4IRV4KHC2DebgLZyIX1dPBwMBsOLhy51Ldg64BdMMOAziKJoGWJik8hveM0/QmaWoN9EBRXCN/3N8cmUZPNQhcQU/6KDkn+i5DkmwYYViTQIGTYffgLjRpoDUbCKXIzM6gI1GG1/GZPSkHw7UQMqAhJN5CA6eZREkDISTfvfQklh2aC109xwW3ylxDYrAINJk1OjXVQduhezhPV1Q3gGSQItV0OSDOIzUtrJfUEELDFEkMkQ/bhxCk5wwq1Tx9pTINW2f8te9z/MfPYrizOPpbCD2DFAJo8HKllxldIjQDkcgiz+2HhsXi+TKtsD8QoGl1PEtyXrvMeP0c+5MX0C5JGpfTNIUNQmNXzuNzmdfo63+JhN4kXc1iSpOUGab7LeVSZFLh/7rn8uoDDdAVpiYo6zaPfPKzlMYnqGoWDamRNA103cQ0Xe4pF/hIKYM0PU72dvOOaeE3BcXucS502SjdQHOrXEz2IAojGFoBv24gxg8zMwj7+97DgcS97KpO0n/5HDNJF90wEdQwrTl8p0LTSxC4Frbp0/TOcyl5mqaSBNNnkAtnuCjn0EwDO5FcujcKwdC77+PI5ROkuwco9h6B4AAF3cOVBkldo5yu8fy7B8lpPlndohjt/u/PuZRo8LNvfZOkm8BO2mT9HItTvVya3MOFVw9SXfDDdBeLHrOqyaylePgMvHfKZMbdwbnsMOONc/wwPcK5RJGcPtfRljKeGQ7iNIOxkXF000CaEs+yUFUHbd4kt5BH5sfCeH+Gw2eSit7gEvWUzVRg4Mo8hwfLXDDOUF08jWoqGnKOdH2SJ6dnuOfibqr1HKDQUQwVXiDh2NREBmUYeI0mg7XzyJvQzceKZQuYhsZTdXhi9L1LZe87tpNiIoWXSlDq6kaZPqbTxPbnmdZsLhhpTif6caSOXTmDsObQneUw9bqvY9vLu31bixw7u+7BtJJICbZQ6BKshM+D/e/BDiKzzVYrvvvjnPH3Mmc3mPWmqA15DCR99rz3few/9gjHzSL75Ql2jezAztiY3eHoJ5VKIYSOoWlodrQHIwoQ6Hth55jWBESbyoSh4VSK1JXBSMMii4+WXhGme/QxsCUqIXny2GeXihtJh7Ly2Wk5kftmaOL56948Lm8xceYUPZMpAr2EVu7q+EhNgtQN0AMWhYbZmGQ22aQhw4XLI4NZ7hsK65/ApJbQaJj10LCiFmmuuJE9Tz/MvQf20B5NTEhJtj7PPqaYGBnBieRKuFkKhU9i9XwJGf12rXQ4tmaREgZOo06yWSNZOYv1YIHhj38RJZuk5mFKTzJn5mj2DyAHBpG1WQxDostF1GwJaj5CNTH0RUxdY17UQqcD5zBVPAgcdK2ObS9gF1yGhYahC4LL+9CEQym9C00uK/iuVLjRsCdts+gGNI0wPI1CIU2LB/aMciGjMecI3Fw4OOnNWR334WyiyKzUwbGpHBppZc7mz8UBzpgVkAaD3Q5mXw17924A0naanJbi/Wd+RK4W5QRRgjM9eeZdi1p3Dy+dGEAZofkxJapM5s4jdcmCDMjMngMEhq2T9MdbtSFjzWIoiY6O1HSGDx7m8IeeJJ0aIJsawNZtxtIHSNtVlLDptlxsLWCnF96HhtaLbmqgG3jJfmzpkpUeJeGRWwioLrqhSdkrMGOkCNw0gzWBiWRfYTe7UwfRdItLiQI/yuxeDpoW/U3aOpapk9BtjlWORccEmqaTVAHNeZNEtEetdaGvG9iqilSCvmmbCeu9CCFQRsCFYo2ZrgyVSQe9CW6tSDa5n2mjQqAMMnKGnsxPEJrGohcOImwl0KRG1s5yo7mxrgK3KY4hkMJE2/czS2X+iRPIVJnZygB7HnuIU7/5XzhbtznwyXs4/ZuvML2YWVIARmoOfex1eiv3MDdrsrO4H2FurB4svUldzVHv8ziS7qe/ey+uslCiSaKUQt8x1nF+M7BZFTxb0xnpzjJ7uUE19Q61rjAnup8LTSSl0vtJnzrTFnw7JJlM0uUpTtcFZhQKRTMku0/08hfTVfKBBWXtZAAAGOhJREFUT9bWeLF1gdTwe/bgvHye08ka3Z//Oxg9KxRL76FwFC5FuCcmonLgOPPV05TrL1EYHwgLgybeYJLZ2ZMUpk0WGklUeQqjK9/xkaXBNLV5j3q9gKztYt/5Wc6XX+CVYABdtxBCRDMEcJN9TPck8SanEICBIuWuiJ+064Pw1l9Aqm+pyEulqV+u8R5zjj+XheV0yaaGyj0IholhWBiWje26mI4LTYUrQBoa1a4caU0gDJPi2G5OnJKIwhRD0zV8X0Pmk3SXdxOkh5l97g8Jas9yXuzAnDNREjS0JdfTdK6XSQ3+3L+XIQzy5yW57Azpxwfhqzpa7SDS7UEYP8BKdsqWOvEL7D9/Eqfo82fvQGOuC9Wcg2gSaHXtJJtpMDUTYHb1crwxg96z7KIqECjPBqFwTAu7v4wx40F1cSlRmdGfYSiRxdItMj0VLr7+etgxNlqh8ls5WASURzkvT3PY9vhU7iFSEw9S/cZvMTHVww+cLqRxAV3XWAhMgqaJCEySqf1kMt3Uxdf5+coZvnz6TbLz3aGjiJQYlg1OBmoXeaD7AV5XHuf1vybl7uNk0KQrtY+jaY9DKZezzjQ1MUl9II2Z1jmwaPGtMzp9tQYDC2/xXeMiTqOXbGKQbGqe2YJHM/8KtWF76Y6Uvfs4Md9gaOprUGBpbbN1v6SpoRk6lWQFvyAx330TuEwlyDM7dZHdXorvAL0ZF4RECnDlAjsaz9GV17jPfRqAuu7RxIQgxfjMHONTHqJSQs4IhlNFflT9Kvs1ENkB/A89w+zX/j1i7ifsaQqKXT+g5JW40cSKZQvYmsDWBEJffliFafKFA7sQB3ahGTp9v/Cz9AUB0rYpOxeZqme5PDzAG337eGbha3ynXmPf8A6E3cXMs6eQ2sapjm3CgIHv5gYY+NzPL5UrITF37oGh+zvOH1WfQgWrcy5kPZPM3mNolSEOHNrfcUy2RrQr1y7aCj1jWQm4SRM7egAGvBovRg+SEDpJRzBceIliKo29o3dNmZoDHtrphY4yz/DQ3TSZ0VE0P5xdqEYTYQhqyVNI0UOgpUh96jOYXYWOaz9RKXC+VuL86xVSRol8t2RIv8y3J36A1Hz6O27EINVSkvOZAUZensS40CAwVzR/OwVj7+so0nQDzdJx9NZOtCi6QNRJhvnWJVLTkJpGWSVRwqPv3Jv8WBN0lYYxjQsIKdEtnb29BQIU/XMTnL8UpghIPf44KeCdV1wmz6dYsKosikV8awrf7maOS6STZxnd/wQn597mNbeL3oU5dgtzSXECaALOpkyG6w64K1JueXkcb1kx16d3UJ8Zwxy8sPz7egnmq5MI04O+e1FtuW0szcLNDdG038HwwvwlwtQRDUXd0TD8LqzREql7UuQYpVqtwuuvUywWUfWwXSpNhulqFPzivY/RfLkGZ+ZJJlK4hkuVMOSOIW2sZB7Ns6hNL5KYtNkVhsUK6+kOUlRJdvbbLEzPIEgs1XNvYS8X5i8ghCDvu/RUjnN0Xx/z1cN8on8vQggsIZjOOMxdTqEVDvHkYJ6CkeXer/4p1abBlJDsEYNYkUFSExoLukF9TGMynVq+XzLDx9Q5GvUzvCFKCAxaU5akGYZdKpNjIjfBXxlvIKUGSkNHsbvqkEmbPHO0n7RrQmMO115EIXizz2Zm/AmOzkqELnDyXSw2Ay56PeRefZk5x0MfHcSVOR69NMme0yY9lTQMPojjJkFI+jL3Upz+MprodNG/UcSKZQssJtOY0yvH9ZA2lm+fbDNr5RLnKVg1ers/St13yI79NI+d2QnJHoLFlv/9ig9TnQUWUDf68ZzlNRNhRort/l9cVRe9fGDd+gsrwX0PPrrmsZGExXcISKzwc6+nzhJMWmhu58LfnrTLuVmLdMoHO4V0m6AZ9BYqFLIGx4fWD8+tjY4QjHUGwztw4ACLizNUq39AMrlvqbw7SFFsS7+rZ1KsJKFrJHJFZj2f+fkCmjtF8uARjOo3l2aLO8qhYjSkHgYu1CQ7LJN3rYDk+EPr1rVFcXCI4NQUVtTJNowApEDzLaz+JGafjzwZHtNpUlI+Y4k9pD96jP4//B1GP/RZXnjxP9JsBGhCYkXh46ud3T4AI/c9wBszP0RIQWDMM1hMkc+XOWVfxMLFdE0KKlwzyjoTWNZzGOXoYiHRhGLakTzb8z4+k53CMHKrvgPg8cHHuZB/jXPTTbz+NicLO02qbLH/w09R+53fw941vnRIkxqP73w/f/jq1+jrL4K6jBCQcG26DI+s7Xd8h+d5PPRQeH8vRoolYzSpqQaGYZBQ8+BYBL06THTORPf7H+fc/FtU5+YpM45/aQDPWfYI9P1xeqrjPN1ziXff6Ou4tuSVmK3PIhAcqmTCxf6Cx7jo/I6crnPKKjJiWZS9MqoZIEwXXVwmDLylQTNAL5aAt5G6wfOlPrREDwUWOd/2+ykBQlPIwETPhv1Aj9vDvvouevRMqMxcA63QQM7MUF900GcB3SGXWA4eq+uK/spf8EfdH2Ki9xh+KRxIOfMu5lyTEeGFa0xCUto/AMph4RtNsg0dMXQc9v00Wq3OweQn8G0d/9RXMfWbs9oRK5YtUN37ONX6PFsNinBq7Blqcwt8oJBmOOeBbcHgg1v+Pmf/Pua+9xK+HU6Rl5Cyw2Opnc8dH1zpjbs5hmR/yuXw7hzeCsXSnYI3G6epdHfu2N3/YA/vnNyDk82gnw0IgjpCSBJOF5/e8QDl8gfW/brE4gQL+pmOsnQ6DaSBTmX5SH2UV61LnExb1KwymrbOA1Icxxj6BPpr0+zaM8lMLgfVcP3l7z66bC7stU3O0cQiIJFaxLHy2B/69Ka3yPJ8sI0oum8Y60rI0AnDHgtbhBQS6bokcjmGTYuBe+7BKBYp3HucoG0WKUUrQhgM7itw8ZudMiVzORzPor+RY5ppdMPCIKB8/y5EsIN8ZYDs65c44D9NvtuhWQUvFaV4lpKS3aA/kLh+hl2liQ7TTDuDqUFSwwH29I8oD/cslY8lbBqBjV/uIvELX0CsmFX3d3fz9EcfJ59Pwcu/iyEEecthPGcwZ63veeQ/8jBzp58ln1qgdinAcRwojcMbzyJNDTYwC2fqeRbUGiHfhcDVFf7oEDKxPOhQrQynCKQUjBQTq68FysUirnaJ5HDUvqVAZAqo+XNwSQfRwLv3XozJMpx9G9OQ+OkESc/hwzOnCIJZwAUVIJMVZMIk038Eo7jsYJJQLq34xPse7mNq/vssvjEPboFg4QIqtbNDHghnjWk3ja0ZiFbis2Iov/9DA7O2QDrQ0TwLLZlgIYhSdMjVFpCutMM6TeC6EyuWraBb4WuLzBYPcm5ynuOuTd+KTX0iSkOrpcPGYpS7aJw9h3ScpXMSx49jHz0Kv/fHy7MUYLF3/Y1OSfvKXQrt4TTS1jG7Vj98Dx34NQ5Mvkp/T2fmOSdhMrw7NMMd6f9tRBCFNddshoZ+acPvc+sjuPWRTeuVfOIDzP7wh+jn/pL+9DTPDhxEinU6HyHQEr0MmS8jATtyrfTNzhG0KSVTpRSJuQbW+Tp0W2Bt4TeNZhhG9P26Fq5j2W1mNE1q6JkMVmGYnZ/4YsflUhpLk1NdaHiUaFKnUPFxV6yDJKLf8Iv1ec5eeg2EjwR6ej+J5eeXFIUQAr3okjoM2BNL9Rz2Fvj8wcqSB9hGWK5HZWIPtrfcEebbNrSuVCotiqVoeKUCfil5DOl389Lli2HROoMes68P87GjiO98kzCLbxCuhWQH4dIbnZ/vW6higvmgQOPiJPXpDNbsWool+j1yuY5ns+yVeX3qdVLW6hluO/LenydtuksdshACszfF/GIe3gKi5/HgwYN876++h9Chy8wxkN+P3Ptx5Ow5+N5/h6CJlh6iP70XWXygQ5mniiUqA4NL791DB6m//RYyXaYR+OC3z7bC6xy3G9ux0ddo76K7gmHYSC+5vEesGeW2j977ls6h/gwT3UneOX2TtAqxYrkurDdSBBC6JHFfF9INb713/1HsXTtXeVHpus4Du3cyVm5bV1ivc73aeuoSq3/tTiiTvodMeuOsc+PFRZrNBVjDrLMWKrGIWKuTWIE1NIQYGODNbwcEb76LSJeRm35FtIAsBOO58dDG3YYmJA1TJ2glQlrhrr3+x7Y+N+yAHFPgWTq6t9wJu5Eb9HpVnPcNrMkFpKGTE2uvP0EYmufoUA5lV5n57klgD+gmppFpUyptFxxom3GVJuD082Q8my2x+Q3dGBVgCRc0F7i4+fkHPk3yne9wNpjDK0V2/8p9oWLxQ2+/7N/4WbLNJloqxSnVRV13mTpvoRsG3kovw6XInp3F+wr7whnZJooFf/WCthAgUzkW7ruXJ4YH6BqdIOWlMPMmShkcGfo5EomxUOYoxxFB2I40w2fl9CCZL5LILHtkGV1d5L/wBUb+8mVe+crX1+wn8l4vmcwRRrw1Bj2WzoyzB40spUiRqKUZy3Jw1gfHwj7jnY3vwHUlVizXgaWglWsP4ND8NicATUPP59c875GJsTXLbx0is8MW59vpo7uozryx+YmEpozT5cOodJMvpFPrm8II0xq1Rp560MQzPLQVpoHWCDBodUhbVSwAhkOy/xiH/TTpPp3506/jppfXL05UTvDut18kJ9buzBY8nSlHInUNUj0wPwlAIptnsbacuwcjyj1SGsPx92HNWpjdD6zfkNoZeRQGji1FEtiM1sy5fa0v/eTHUIuLa1+wkiW768ZOKEsYDsf8HrRBjZFctH8rMwAP/crSKVqic+asWpXTdTTDWLoNYXNbu80JITZXKuuhhZlMleOQMpKUvfLSISEEqVSb84sW3edWO9JWWCZaptM1fjstbSI0gZF3Vx1LaJK/N1BGW+uZShnMMIqjuxApFnfXEI3XXsLs674SSa87sWLZAqXSTzE399oVX6fWdre6anLD3aEZ4QpIZPPMXrqw+YlXwbJ0W1QsmUOkM4e2dG7rE3VHJ9/lb3gusDRiMyLTQDPoVBytNRJHuwrF0nsP2sgjHBaCqXPnuNTTR6qw7G1jaRZDWs+6l4feVUFozjv4zFJ5ptyN7bRdZ7pw7Eug2/S/NshicwbNWnuNYBVSgultfl6LlmIJln9Fo/sKOqfW/RXQ7QumAhGunWyAJw0eGX4C5NbMtnrUec5ndcxKkkzJJZG16RnLwPdbv+P2PWNig8HLKqJBwNL3b1GhAwhTwxpIIt2178OaSgUIpELo4WbclleinnTIvmfnkumuncyhx5ifObnlem0nt41iEUL8G+BhYAGYBX5JKfWdG/HdnjeE52097PRSPu3t1Sv8rXs+T3CFimX3Q4+ggm2uSIslAbfflnvFi45LiiUccQd03iddSnptk1LTDkebfteqj1iLj4x8hLn63NIINJVM4fb0YmTSm1y5jBKtjbGdQlUqP4eUK0wexnIHIV092k27/Z49rY5JNa+ybSy1Q0k5ISmP7th8zeqhX9nyQ/HU2FPM1ec4U9L4xslZhCbRDMn4A5HyM2xYmLm6uq9HZB4UYa7fTc6NZmrpCvQchNKeLX+Narmst7cHzQzNe8PvXXX+Zyc+S61R48JbkXGrPSPakoJf3UZ6Rj7D5oJcH24bxQL8CfAlpVRdCPFB4MvA8CbX3BR296R48+IcucTWRzFb4Wp20EqpXbf4CkJq0YbB66BYor/D7hadJoxwbUF3czB7gW6vc/StR5ucleFC3xEob60j6E6sHsUbxpU5Skz4Pu/MBST1zsdN1zeeYWhZG//B3tBzKmLb7nQ0Y1HNq8ws2FIsrYXzNbyS1mSLI4ZCFHyxPwXPvf3q6hP2PAXv/girVkRLb92xZiPMPh9On0NJta4jwio0Y9XeJwjdrQF8f4PZdvu9kBLe88trnuYZHp7hYfqC7/eXKNttpnPL7/zb8fE3L7DKbaNYlFJ/1Pb2OaBXCCHVldqGbgBjJZ+xR7dgvrnN6Sp/jGr1J2ja9jzY7Ugh+HxfEUdu8eEwE7DzQ4ihAZ5e2Ldq8T5vGrxKuEBOuhJ2CDeIpGHjuAtLO+i3ihACaXc+ogcqGWYXGhzqv7aMgHrWZvHtGbSrHfy0HrvKEUgUt6yotw07BZX72KKrwpYwKz6ynkC90Pk7fXzs40wvTK++YN8nwFi9TgKQzWY5cuTImubBpRnLFU7LHcth9/BR9FTb8zZwDPwyZG9sIq/NuG0Uywp+EfjfaykVIURrY0Q767vixFw1ppnDNNfehLcd+PoWR8GtfsAvg9TIO6udIYZci1nfxRMKLi5C7+Grq9RV2DnL5Q8zM/NDNG2L6yUbYOqSh3dde4gOo+jin+icDV0Vug2Dx6+5PrcCQoi2zn759y26RYruGjvYN+nMXXdtpZPu6oYXoDS0uet9Oy2TtjDa97ZpUNixzhU3j1tGsQghngfW26hRUmF+V4QQPw38DLDejsMvAb+6/TWMuVXp351DapJUYePF40Rrb8ZDf/8G1GoZw8iQzT5wRdd4h8uoWuM61SjkmpTKxMfgnefBvX4Di5vBlc4irgbbS3D/U5+68gtbisW+xsHADeCWUSxKqYObnSOE+Cjw68DDSqlz65z2L4DfXlHWC3zjmioYc8tiuQYjh25OTKQWiUxuW5ea9LRFGNjnFsXLwejaYYK2m88dH6S6cH2V7Eq22/FmO9ALLvZwCrOy+QbYm80to1g2I1qw/2fAo0qpk+udp5S6DJ0Be2/EKCTmbmG1qQRg7yPvv/FVuUtI2sZVRZa4Jm5BzSKkwBraujfizeS2USzAfwYWgd9tUxQPK6W2sO03JiYmZnPylQGmL7xLZc++zU+OWZfbRrEopQqbnxUTc52JZ793NJquM3rv/ZufGLMhcQbJmJir4RY0lcTE3CrEiiXmrkLT13YBjYmJ2T5uG1NYTMy10tf3DFJe65a62BQWE7MZsWKJuWswjGvbrQ4sBxu8gvw8MTF3G7FiiYm5EroOhOsr3eungo6JuduJFUtMzJUgJfRunAAtJuZuJ168j4mJiYnZVu6WGYsGcOrUqZtdj5iYmJjbhrY+84oClIkt5x24jRFCHCOOFRYTExNztRxXSn1zqyffLYrFAg4DZ4AryEkLLAewPA7cLVOeWOa7g1jmu4NrkVkDuoC/UkotbPWiu8IUFt2QLWvbdtrikp3aKPjlnUQscyzznUos81XJ/NqVXhAv3sfExMTEbCuxYomJiYmJ2VZixRITExMTs63EimVzLgO/xorkYXc4scx3B7HMdwc3XOa7wissJiYmJubGEc9YYmJiYmK2lVixxMTExMRsK7Fi2QQhxJgQ4jkhxKvR39GbXadrRQiRE0L8sRDix0KI7wshfl8IUYiO3SeE+F4k758JIYpt16177HZBCPGrQgglhNgdvb9j5RVC2EKIfyeE+IkQ4iUhxH+Iytdt07d7exdCfFAI8YIQ4sWobX8sKr9jZBZC/IYQ4o32dhyVX5WM10V+pVT82uAFfAX4dPT/p4Gv3Ow6bYNMWeA9be//KfCfCLNY/TVwLCr/h8BvRf+ve+x2eQEHgT8B3gR23wXy/kvgn7O8llqK/q7bpm/n9h79ZpPA7uj9XmCGcAB9x8gMHAP6gJMtWa/ld70e8t/0m3Qrv4AioSeFFr3XoveFm123bZbzSeD/Eoa9+UFbeR6Yjf5f99jt8AIs4DlgsPVA3uHyJqK2mlhRvm6bvt3be6RYLgIPRO8fBF69U2VuVyxXK+P1kv+uCOlyDfQBp5VSTQClVFMI8U5Ufv6m1mybEEJI4AvA/wIqhKN5AJRSF4QQUgiR3eiYUurSja73VfCPgf+qlHqjLcTFnSzvMGEn+6tCiIeAWcJZ1zzrt2mxwbFbvr0rpZQQ4mngD4QQVcAHnmDj5/i2lrmNq5Xxusgfr7HE/CvCTudf3+yKXC+EEEcJZyD/9mbX5QaiA0PAC0qpe4BfBn6fcCZzRyKE0IFfAT6slOoHfgr4MnewzLcq8YxlY94GeoQQWqTJNaA7Kr/tEUL8BjAK/JRSKhBCvAX0tx3PEw4EL2107EbX+yo4AewEWrOVXuBPCdcg7kR5IZxtNYD/BqCU+rYQ4gLhjGW9Ni02OHY7sB/oVkp9C0Ap9a1o5lLjzpW5xUZ91UYyXhf54xnLBiil3gVeBD4ZFX2ScAR4O02R10QI8evAIeAjajkc9ncBR4T5awA+D/yPLRy7pVFK/ROlVLdSakApNUAYOvx9hE4Ld5y8EJrugK8Cj0Lo+UNoT3+Vddr0HdDeTwG9QogdAEKIXUAZ+Al3rszAxn3V1R671grFr40XyHYC3yZ8IL8N7LjZddoGmSYABfw4alQvAv8zOnY/8BLhw/h/iDyJNjt2O73oXPS8Y+UlNIV9LZLheeDxqHzdNn27t3fgU5G834teH7nTZCacaZ8inJGeBV6+Fhmvh/xxSJeYmJiYmG0lNoXFxMTExGwrsWKJiYmJidlWYsUSExMTE7OtxIolJiYmJmZbiRVLTExMTMy2EiuWmJiYmJhtJVYsMTExMTHbSqxYYmJiYmK2lf8PJ39r+qxIB8kAAAAASUVORK5CYII=\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, axs = plt.subplots(nrows=2)\n",
"axs[0].plot(noncentered_trace.get_values('σ_b', chains=0), alpha=.5);\n",
"axs[0].set(ylabel='σ_b');\n",
"axs[1].plot(noncentered_trace.get_values('b', chains=0), alpha=.5);\n",
"axs[1].set(ylabel='b');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And, we are now fully exploring the support of the posterior."
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"xvals = np.arange(2)\n",
"b = varying_intercept_slope_trace['a'].mean(axis=0)\n",
"m = varying_intercept_slope_trace['b'].mean(axis=0)\n",
"for bi,mi in zip(b,m):\n",
" plt.plot(xvals, mi*xvals + bi, 'bo-', alpha=0.4)\n",
"plt.xlim(-0.1, 1.1);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise\n",
"\n",
"Reparameterize the `varying_intercept_slope` model to be non-centered, and compare the resulting parameter estimates."
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [],
"source": [
"# Write your answer here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Adding group-level predictors\n",
"\n",
"A primary strength of multilevel models is the ability to handle predictors on multiple levels simultaneously. If we consider the varying-intercepts model above:\n",
"\n",
"$$y_i = \\alpha_{j[i]} + \\beta x_{i} + \\epsilon_i$$\n",
"\n",
"we may, instead of a simple random effect to describe variation in the expected radon value, specify another regression model with a county-level covariate. Here, we use the county uranium reading $u_j$, which is thought to be related to radon levels:\n",
"\n",
"$$\\alpha_j = \\gamma_0 + \\gamma_1 u_j + \\zeta_j$$\n",
"\n",
"$$\\zeta_j \\sim N(0, \\sigma_{\\alpha}^2)$$\n",
"\n",
"Thus, we are now incorporating a house-level predictor (floor or basement) as well as a county-level predictor (uranium).\n",
"\n",
"Note that the model has both indicator variables for each county, plus a county-level covariate. In classical regression, this would result in collinearity. In a multilevel model, the partial pooling of the intercepts towards the expected value of the group-level linear model avoids this.\n",
"\n",
"Group-level predictors also serve to reduce group-level variation $\\sigma_{\\alpha}$. An important implication of this is that the group-level estimate induces stronger pooling."
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [],
"source": [
"from pymc3 import Deterministic\n",
"\n",
"with Model() as hierarchical_intercept:\n",
" \n",
" # Priors\n",
" σ_a = HalfCauchy('σ_a', 5)\n",
" \n",
" # County uranium model\n",
" γ_0 = Normal('γ_0', mu=0., sd=1e5)\n",
" γ_1 = Normal('γ_1', mu=0., sd=1e5)\n",
" \n",
" \n",
" # Uranium model for intercept\n",
" μ_a = γ_0 + γ_1*u\n",
" # County variation not explained by uranium\n",
" ϵ_a = Normal('ϵ_a', mu=0, sd=1, shape=counties)\n",
" a = Deterministic('a', μ_a + σ_a*ϵ_a[county])\n",
" \n",
" # Common slope\n",
" b = Normal('b', mu=0., sd=1e5)\n",
" \n",
" # Model error\n",
" σ_y = Uniform('σ_y', lower=0, upper=100)\n",
" \n",
" # Expected value\n",
" y_hat = a + b * floor_measure\n",
" \n",
" # Data likelihood\n",
" y_like = Normal('y_like', mu=y_hat, sd=σ_y, observed=log_radon)\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (2 chains in 2 jobs)\n",
"NUTS: [σ_y, b, ϵ_a, γ_1, γ_0, σ_a]\n",
"Sampling 2 chains: 100%|██████████| 4000/4000 [00:28<00:00, 140.82draws/s]\n"
]
}
],
"source": [
"with hierarchical_intercept:\n",
" hierarchical_intercept_trace = sample(1000, tune=1000, cores=2, random_seed=RANDOM_SEEDS)"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"a_means = hierarchical_intercept_trace['a'].mean(axis=0)\n",
"plt.scatter(u, a_means)\n",
"g0 = hierarchical_intercept_trace['γ_0'].mean()\n",
"g1 = hierarchical_intercept_trace['γ_1'].mean()\n",
"xvals = np.linspace(-1, 0.8)\n",
"plt.plot(xvals, g0+g1*xvals, 'k--')\n",
"plt.xlim(-1, 0.8)\n",
"\n",
"a_se = hierarchical_intercept_trace['a'].std(axis=0)\n",
"for ui, m, se in zip(u, a_means, a_se):\n",
" plt.plot([ui,ui], [m-se, m+se], 'b-')\n",
"plt.xlabel('County-level uranium'); plt.ylabel('Intercept estimate');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The standard errors on the intercepts are narrower than for the partial-pooling model without a county-level covariate."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Correlations among levels\n",
"\n",
"In some instances, having predictors at multiple levels can reveal correlation between individual-level variables and group residuals. We can account for this by including the average of the individual predictors as a covariate in the model for the group intercept.\n",
"\n",
"$$\\alpha_j = \\gamma_0 + \\gamma_1 u_j + \\gamma_2 \\bar{x} + \\zeta_j$$\n",
"\n",
"These are broadly referred to as ***contextual effects***."
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {},
"outputs": [],
"source": [
"# Create new variable for mean of floor across counties\n",
"xbar = srrs_mn.groupby('county')['floor'].mean().rename(county_lookup).values"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [],
"source": [
"with Model() as contextual_effect:\n",
" \n",
" # Priors\n",
" σ_a = HalfCauchy('σ_a', 5)\n",
" \n",
" # County uranium model for slope\n",
" γ = Normal('γ', mu=0., sd=1e5, shape=3)\n",
" \n",
" # Uranium model for intercept\n",
" μ_a = Deterministic('μ_a', γ[0] + γ[1]*u.values + γ[2]*xbar[county])\n",
"\n",
" # County variation not explained by uranium\n",
" ϵ_a = Normal('ϵ_a', mu=0, sd=1, shape=counties)\n",
" a = Deterministic('a', μ_a + σ_a*ϵ_a[county])\n",
"\n",
" # Common slope\n",
" b = Normal('b', mu=0., sd=1e15)\n",
" \n",
" # Model error\n",
" σ_y = Uniform('σ_y', lower=0, upper=100)\n",
" \n",
" # Expected value\n",
" y_hat = a + b * floor_measure\n",
" \n",
" # Data likelihood\n",
" y_like = Normal('y_like', mu=y_hat, sd=σ_y, observed=log_radon)\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (2 chains in 2 jobs)\n",
"NUTS: [σ_y, b, ϵ_a, γ, σ_a]\n",
"Sampling 2 chains: 100%|██████████| 4000/4000 [00:32<00:00, 124.40draws/s]\n",
"The acceptance probability does not match the target. It is 0.7084623255238152, but should be close to 0.8. Try to increase the number of tuning steps.\n"
]
}
],
"source": [
"with contextual_effect:\n",
" contextual_effect_trace = sample(1000, tune=1000, cores=2, random_seed=RANDOM_SEEDS)"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
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