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Density Estimation with Dirichlet Process Mixtures using PyMC3
{
"cells": [
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"cell_type": "markdown",
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"source": [
"---\n",
"title: Density Estimation with Dirichlet Process Mixtures using PyMC3\n",
"tags: PyMC3, Dirichlet Processes, Bayesian Nonparametric Statistics, Bayesian Statistics, Nonparametric Statistics\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I have been intrigued by the flexibility of [nonparametric statistics](https://en.wikipedia.org/wiki/Nonparametric_statistics) for many years. As I have developed an understanding and appreciation of Bayesian modeling both personally and professionally over the last two or three years, I naturally developed an interest in Bayesian nonparametric statistics. I am pleased to begin a planned series of posts on Bayesian nonparametrics with this post on Dirichlet process mixtures for density estimation.\n",
"\n",
"##### Dirichlet processes\n",
"\n",
"The [Dirichlet process](https://en.wikipedia.org/wiki/Dirichlet_process) is a flexible probability distribution over the space of distributions. Most generally, a probability distribution, $P$, on a set $\\Omega$ is a [measure](https://en.wikipedia.org/wiki/Measure_(mathematics%29) that assigns measure one to the entire space ($P(\\Omega) = 1$). A Dirichlet process $P \\sim \\textrm{DP}(\\alpha, P_0)$ is a measure that has the property that, for every finite [disjoint](https://en.wikipedia.org/wiki/Disjoint_sets) partition $S_1, \\ldots, S_n$ of $\\Omega$,\n",
"\n",
"$$(P(S_1), \\ldots, P(S_n)) \\sim \\textrm{Dir}(\\alpha P_0(S_1), \\ldots, \\alpha P_0(S_n)).$$\n",
"\n",
"Here $P_0$ is the base probability measure on the space $\\Omega$. The precision parameter $\\alpha > 0$ controls how close samples from the Dirichlet process are to the base measure, $P_0$. As $\\alpha \\to \\infty$, samples from the Dirichlet process approach the base measure $P_0$.\n",
"\n",
"Dirichlet processes have several properties that make then quite suitable to [MCMC](https://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo) simulation.\n",
"\n",
"1. The posterior given [i.i.d.](https://en.wikipedia.org/wiki/Independent_and_identically_distributed_random_variables) observations $\\omega_1, \\ldots, \\omega_n$ from a Dirichlet process $P \\sim \\textrm{DP}(\\alpha, P_0)$ is also a Dirichlet process with\n",
"\n",
" $$P\\ |\\ \\omega_1, \\ldots, \\omega_n \\sim \\textrm{DP}\\left(\\alpha + n, \\frac{\\alpha}{\\alpha + n} P_0 + \\frac{1}{\\alpha + n} \\sum_{i = 1}^n \\delta_{\\omega_i}\\right),$$\n",
" \n",
" where $\\delta$ is the [Dirac delta measure](https://en.wikipedia.org/wiki/Dirac_delta_function)\n",
" \n",
" $$\\begin{align*}\n",
" \\delta_{\\omega}(S)\n",
" & = \\begin{cases}\n",
" 1 & \\textrm{if } \\omega \\in S \\\\\n",
" 0 & \\textrm{if } \\omega \\not \\in S\n",
" \\end{cases}\n",
" \\end{align*}.$$\n",
"\n",
"2. The posterior predictive distribution of a new observation is a compromise between the base measure and the observations,\n",
"\n",
" $$\\omega\\ |\\ \\omega_1, \\ldots, \\omega_n \\sim \\frac{\\alpha}{\\alpha + n} P_0 + \\frac{1}{\\alpha + n} \\sum_{i = 1}^n \\delta_{\\omega_i}.$$\n",
"\n",
" We see that the prior precision $\\alpha$ can naturally be interpreted as a prior sample size. The form of this posterior predictive distribution also lends itself to Gibbs sampling.\n",
" \n",
"2. Samples, $P \\sim \\textrm{DP}(\\alpha, P_0)$, from a Dirichlet process are discrete with probability one. That is, there are elements $\\omega_1, \\omega_2, \\ldots$ in $\\Omega$ and weights $w_1, w_2, \\ldots$ with $\\sum_{i = 1}^{\\infty} w_i = 1$ such that\n",
"\n",
" $$P = \\sum_{i = 1}^\\infty w_i \\delta_{\\omega_i}.$$\n",
"\n",
"3. The [stick-breaking process](https://en.wikipedia.org/wiki/Dirichlet_process#The_stick-breaking_process) gives an explicit construction of the weights $w_i$ and samples $\\omega_i$ above that is straightforward to sample from. If $\\beta_1, \\beta_2, \\ldots \\sim \\textrm{Beta}(1, \\alpha)$, then $w_i = \\beta_i \\prod_{j = 1}^{j - 1} (1 - \\beta_j)$. The relationship between this representation and stick breaking may be illustrated as follows:\n",
" 1. Start with a stick of length one.\n",
" 2. Break the stick into two portions, the first of proportion $w_1 = \\beta_1$ and the second of proportion $1 - w_1$.\n",
" 3. Further break the second portion into two portions, the first of proportion $\\beta_2$ and the second of proportion $1 - \\beta_2$. The length of the first portion of this stick is $\\beta_2 (1 - \\beta_1)$; the length of the second portion is $(1 - \\beta_1) (1 - \\beta_2)$.\n",
" 4. Continue breaking the second portion from the previous break in this manner forever. If $\\omega_1, \\omega_2, \\ldots \\sim P_0$, then\n",
"\n",
" $$P = \\sum_{i = 1}^\\infty w_i \\delta_{\\omega_i} \\sim \\textrm{DP}(\\alpha, P_0).$$\n",
"\n",
"We can use the stick-breaking process above to easily sample from a Dirichlet process in Python. For this example, $\\alpha = 2$ and the base distribution is $N(0, 1)$."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from __future__ import division"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Couldn't import dot_parser, loading of dot files will not be possible.\n"
]
}
],
"source": [
"from matplotlib import pyplot as plt\n",
"import numpy as np\n",
"import pymc3 as pm\n",
"import scipy as sp\n",
"import seaborn as sns\n",
"from statsmodels.datasets import get_rdataset\n",
"from theano import tensor as T"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"blue = sns.color_palette()[0]"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"np.random.seed(462233) # from random.org"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"N = 20\n",
"K = 30\n",
"\n",
"alpha = 2.\n",
"P0 = sp.stats.norm"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We draw and plot samples from the stick-breaking process."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"beta = sp.stats.beta.rvs(1, alpha, size=(N, K))\n",
"w = np.empty_like(beta)\n",
"w[:, 0] = beta[:, 0]\n",
"w[:, 1:] = beta[:, 1:] * (1 - beta[:, :-1]).cumprod(axis=1)\n",
"\n",
"omega = P0.rvs(size=(N, K))\n",
"\n",
"x_plot = np.linspace(-3, 3, 200)\n",
"\n",
"sample_cdfs = (w[..., np.newaxis] * np.less.outer(omega, x_plot)).sum(axis=1)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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dXfD5fGhp2R93c00driIIAnw+H3Q63XDgl2Rxxtcl6O7uBM/zaGiYGeNWdrud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Uv7TOdg5+ZZuOYtSZIjrReVsZ1rTq9V6dL+G2jioxeu//iPp/DrXz+HD3zgQ7j55s8b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\nAoFQAPx/h1tnxKHL0EAAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fabde8836d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"ax.plot(x_plot, sample_cdfs[0], c='gray', alpha=0.75,\n",
" label='DP sample CDFs');\n",
"ax.plot(x_plot, sample_cdfs[1:].T, c='gray', alpha=0.75);\n",
"ax.plot(x_plot, P0.cdf(x_plot), c='k', label='Base CDF');\n",
"\n",
"ax.set_title(r'$\\alpha = {}$'.format(alpha));\n",
"ax.legend(loc=2);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As stated above, as $\\alpha \\to \\infty$, samples from the Dirichlet process converge to the base distribution."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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kZ0QENQzDdDyzDuxknE4XGzZcNKOwkCwrNDXtJi8vQG3tmddNkCQoL59nvU6l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r3s3bsPSZLI5TIAdddggeBGEW9jAsEdwFwd5vWl6VajnR6Ph1wuBywfGdV1jZGRQQBHMH7963/J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"text/plain": [
"<matplotlib.figure.Figure at 0x7fabde5c05d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, (l_ax, r_ax) = plt.subplots(ncols=2, sharex=True, sharey=True, figsize=(16, 6))\n",
"\n",
"K = 50\n",
"alpha = 10.\n",
"\n",
"beta = sp.stats.beta.rvs(1, alpha, size=(N, K))\n",
"w = np.empty_like(beta)\n",
"w[:, 0] = beta[:, 0]\n",
"w[:, 1:] = beta[:, 1:] * (1 - beta[:, :-1]).cumprod(axis=1)\n",
"\n",
"omega = P0.rvs(size=(N, K))\n",
"\n",
"sample_cdfs = (w[..., np.newaxis] * np.less.outer(omega, x_plot)).sum(axis=1)\n",
"\n",
"l_ax.plot(x_plot, sample_cdfs[0], c='gray', alpha=0.75,\n",
" label='DP sample CDFs');\n",
"l_ax.plot(x_plot, sample_cdfs[1:].T, c='gray', alpha=0.75);\n",
"l_ax.plot(x_plot, P0.cdf(x_plot), c='k', label='Base CDF');\n",
"\n",
"l_ax.set_title(r'$\\alpha = {}$'.format(alpha));\n",
"l_ax.legend(loc=2);\n",
"\n",
"K = 200\n",
"alpha = 50.\n",
"\n",
"beta = sp.stats.beta.rvs(1, alpha, size=(N, K))\n",
"w = np.empty_like(beta)\n",
"w[:, 0] = beta[:, 0]\n",
"w[:, 1:] = beta[:, 1:] * (1 - beta[:, :-1]).cumprod(axis=1)\n",
"\n",
"omega = P0.rvs(size=(N, K))\n",
"\n",
"sample_cdfs = (w[..., np.newaxis] * np.less.outer(omega, x_plot)).sum(axis=1)\n",
"\n",
"r_ax.plot(x_plot, sample_cdfs[0], c='gray', alpha=0.75,\n",
" label='DP sample CDFs');\n",
"r_ax.plot(x_plot, sample_cdfs[1:].T, c='gray', alpha=0.75);\n",
"r_ax.plot(x_plot, P0.cdf(x_plot), c='k', label='Base CDF');\n",
"\n",
"r_ax.set_title(r'$\\alpha = {}$'.format(alpha));\n",
"r_ax.legend(loc=2);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Dirichlet process mixtures\n",
"\n",
"For the task of density estimation, the (almost sure) discreteness of samples from the Dirichlet process is a significant drawback. This problem can be solved with another level of indirection by using Dirichlet process mixtures for density estimation. A Dirichlet process mixture uses component densities from a parametric family $\\mathcal{F} = \\{f_{\\theta}\\ |\\ \\theta \\in \\Theta\\}$ and represents the mixture weights as a Dirichlet process. If $P_0$ is a probability measure on the parameter space $\\Theta$, a Dirichlet process mixture is the hierarchical model\n",
"\n",
"$$\n",
"\\begin{align*}\n",
" x_i\\ |\\ \\theta_i\n",
" & \\sim f_{\\theta_i} \\\\\n",
" \\theta_1, \\ldots, \\theta_n\n",
" & \\sim P \\\\\n",
" P\n",
" & \\sim \\textrm{DP}(\\alpha, P_0).\n",
"\\end{align*}\n",
"$$\n",
"\n",
"To illustrate this model, we simulate draws from a Dirichlet process mixture with $\\alpha = 2$, $\\theta \\sim N(0, 1)$, $x\\ |\\ \\theta \\sim N(\\theta, (0.3)^2)$."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"N = 5\n",
"K = 30\n",
"\n",
"alpha = 2\n",
"P0 = sp.stats.norm\n",
"f = lambda x, theta: sp.stats.norm.pdf(x, theta, 0.3)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"beta = sp.stats.beta.rvs(1, alpha, size=(N, K))\n",
"w = np.empty_like(beta)\n",
"w[:, 0] = beta[:, 0]\n",
"w[:, 1:] = beta[:, 1:] * (1 - beta[:, :-1]).cumprod(axis=1)\n",
"\n",
"theta = P0.rvs(size=(N, K))\n",
"\n",
"dpm_pdf_components = f(x_plot[np.newaxis, np.newaxis, :], theta[..., np.newaxis])\n",
"dpm_pdfs = (w[..., np.newaxis] * dpm_pdf_components).sum(axis=1)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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V3G4PotFwT8+rsg8bFKqkHyhUT5lkMg6e59u+2kspGsdqTtcS8IMHD8BxHGZm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\nCeQPZjEZwrrIhfkAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fabded36e90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"ax.plot(x_plot, dpm_pdfs.T, c='gray');\n",
"\n",
"ax.set_yticklabels([]);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now focus on a single mixture and decompose it into its individual (weighted) mixture components."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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GiRNHoaGhgTfeeBstLc1oXxvYeaFgSkoSfvvtV4jFIixd+iI0NTURFRWOVateREtLC/7z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\n3Lmr1gyqrhIXF0eNGo40a9YgRe3Lli2bKcrKVapUhcDAAN6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f0tDQEBsbG6Fl/BRd+6Iv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\nREOIRlVERERERERDiEZVREREREREQ/wP81JGAkLfE90AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fabdcbfe190>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"ix = 1\n",
"\n",
"ax.plot(x_plot, dpm_pdfs[ix], c='k', label='Density');\n",
"ax.plot(x_plot, (w[..., np.newaxis] * dpm_pdf_components)[ix, 0],\n",
" '--', c='k', label='Mixture components (weighted)');\n",
"ax.plot(x_plot, (w[..., np.newaxis] * dpm_pdf_components)[ix].T,\n",
" '--', c='k');\n",
"\n",
"ax.set_yticklabels([]);\n",
"ax.legend(loc=1);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Sampling from these stochastic processes is fun, but these ideas become truly useful when we fit them to data. The discreteness of samples and the stick-breaking representation of the Dirichlet process lend themselves nicely to Markov chain Monte Carlo simulation of posterior distributions. We will perform this sampling using [`pymc3`](https://pymc-devs.github.io/pymc3/).\n",
"\n",
"Our first example uses a Dirichlet process mixture to estimate the density of waiting times between eruptions of the [Old Faithful](https://en.wikipedia.org/wiki/Old_Faithful) geyser in [Yellowstone National Park](https://en.wikipedia.org/wiki/Yellowstone_National_Park)."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"old_faithful_df = get_rdataset('faithful', cache=True).data[['waiting']]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For convenience in specifying the prior, we standardize the waiting time between eruptions."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"old_faithful_df['std_waiting'] = (old_faithful_df.waiting - old_faithful_df.waiting.mean()) / old_faithful_df.waiting.std()"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>waiting</th>\n",
" <th>std_waiting</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>79</td>\n",
" <td>0.596025</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>54</td>\n",
" <td>-1.242890</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>74</td>\n",
" <td>0.228242</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>62</td>\n",
" <td>-0.654437</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>85</td>\n",
" <td>1.037364</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" waiting std_waiting\n",
"0 79 0.596025\n",
"1 54 -1.242890\n",
"2 74 0.228242\n",
"3 62 -0.654437\n",
"4 85 1.037364"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"old_faithful_df.head()"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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OM2DAAGOMMb///rtp27ZtlvsLMxal7vD7U089pTFjxkiSqlatqvj4+GyPMWXg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\nAwBgEYQ6AAAWQagDAGARhDoAABbx/2BFFcwgjeMiAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fabde7e0250>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"n_bins = 20\n",
"ax.hist(old_faithful_df.std_waiting, bins=n_bins, color=blue, lw=0, alpha=0.5);\n",
"\n",
"ax.set_xlabel('Standardized waiting time between eruptions');\n",
"ax.set_ylabel('Number of eruptions');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Observant readers will have noted that we have not been continuing the stick-breaking process indefinitely as indicated by its definition, but rather have been truncating this process after a finite number of breaks. Obviously, when computing with Dirichlet processes, it is necessary to only store a finite number of its point masses and weights in memory. This restriction is not terribly onerous, since with a finite number of observations, it seems quite likely that the number of mixture components that contribute non-neglible mass to the mixture will grow slower than the number of samples. This intuition can be formalized to show that the (expected) number of components that contribute non-negligible mass to the mixture approaches $\\alpha \\log N$, where $N$ is the sample size.\n",
"\n",
"There are various clever [Gibbs sampling](https://en.wikipedia.org/wiki/Gibbs_sampling) techniques for Dirichlet processes that allow the number of components stored to grow as needed. [Stochastic memoization](http://danroy.org/papers/RoyManGooTen-ICMLNPB-2008.pdf) is another powerful technique for simulating Dirichlet processes while only storing finitely many components in memory. In this introductory post, we take the much less sophistocated approach of simple truncating the Dirichlet process components that are stored after a fixed number, $K$, of components. Importantly, this approach is compatible with some of `pymc3`'s (current) technical limitations. [Ohlssen, et al.](http://fisher.osu.edu/~schroeder.9/AMIS900/Ohlssen2006.pdf) provide justification for truncation, showing that $K > 5 \\alpha + 2$ is most likely sufficient to capture almost all of the mixture weights ($\\sum_{i = 1}^{K} w_i > 0.99$). We can practically verify the suitability of our truncated approximation to the Dirichlet process by checking the number of components that contribute non-negligible mass to the mixture. If, in our simulations, all components contribute non-negligible mass to the mixture, we have truncated our Dirichlet process too early.\n",
"\n",
"Our Dirichlet process mixture model for the standardized waiting times is\n",
"\n",
"$$\n",
"\\begin{align*}\n",
" x_i\\ |\\ \\mu_i, \\lambda_i, \\tau_i\n",
" & \\sim N\\left(\\mu, (\\lambda_i \\tau_i)^{-1}\\right) \\\\\n",
" \\mu_i\\ |\\ \\lambda_i, \\tau_i\n",
" & \\sim N\\left(0, (\\lambda_i \\tau_i)^{-1}\\right) \\\\\n",
" (\\lambda_1, \\tau_1), (\\lambda_2, \\tau_2), \\ldots\n",
" & \\sim P \\\\\n",
" P\n",
" & \\sim \\textrm{DP}(\\alpha, U(0, 5) \\times \\textrm{Gamma}(1, 1)) \\\\\n",
" \\alpha\n",
" & \\sim \\textrm{Gamma}(1, 1).\n",
"\\end{align*}\n",
"$$\n",
"\n",
"Note that instead of fixing a value of $\\alpha$, as in our previous simulations, we specify a prior on $\\alpha$, so that we may learn its posterior distribution from the observations. This model is therefore actually a mixture of Dirichlet process mixtures, since each fixed value of $\\alpha$ results in a Dirichlet process mixture.\n",
"\n",
"We now construct this model using `pymc3`."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"N = old_faithful_df.shape[0]\n",
"\n",
"K = 30"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Applied log-transform to alpha and added transformed alpha_log to model.\n",
"Applied logodds-transform to beta and added transformed beta_logodds to model.\n",
"Applied log-transform to tau and added transformed tau_log to model.\n",
"Applied interval-transform to lambda and added transformed lambda_interval to model.\n"
]
}
],
"source": [
"with pm.Model() as model:\n",
" alpha = pm.Gamma('alpha', 1., 1.)\n",
" beta = pm.Beta('beta', 1., alpha, shape=K)\n",
" w = pm.Deterministic('w', beta * T.concatenate([[1], T.extra_ops.cumprod(1 - beta)[:-1]]))\n",
" component = pm.Categorical('component', w, shape=N)\n",
"\n",
" tau = pm.Gamma('tau', 1., 1., shape=K)\n",
" lambda_ = pm.Uniform('lambda', 0, 5, shape=K)\n",
" mu = pm.Normal('mu', 0, lambda_ * tau, shape=K)\n",
" obs = pm.Normal('obs', mu[component], lambda_[component] * tau[component],\n",
" observed=old_faithful_df.std_waiting.values)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We sample from the posterior distribution 20,000 times, burn the first 10,000 samples, and thin to every tenth sample."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 20000 of 20000 complete in 139.3 sec"
]
}
],
"source": [
"with model:\n",
" step1 = pm.Metropolis(vars=[alpha, beta, w, lambda_, tau, mu, obs])\n",
" step2 = pm.ElemwiseCategoricalStep([component], np.arange(K))\n",
" \n",
" trace_ = pm.sample(20000, [step1, step2])\n",
"\n",
"trace = trace_[10000::10]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The posterior distribution of $\\alpha$ is concentrated between 0.4 and 1.75."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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Fajs6QmclOI7DuveO4MCpFlw7PR+LfjS6D1oXmf0nm/GX949AJZdgxeIpCbOW0cxNdKiP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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fabde7e0510>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.traceplot(trace, varnames=['alpha']);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To verify that our truncation point is not biasing our results, we plot the distribution of the number of mixture components used."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"n_components_used = np.apply_along_axis(lambda x: np.unique(x).size, 1, trace['component'])"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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mpurLL79UUFCQYmNj9fnnn+upp56SJN10002aMGHCOdtERER4s0QAAGzD68EO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\nLvzszFUCAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fabbd08eed0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"bins = np.arange(n_components_used.min(), n_components_used.max() + 1)\n",
"ax.hist(n_components_used + 1, bins=bins, normed=True, lw=0, alpha=0.75);\n",
"\n",
"ax.set_xticks(bins + 0.5);\n",
"ax.set_xticklabels(bins);\n",
"ax.set_xlim(bins.min(), bins.max() + 1);\n",
"ax.set_xlabel('Number of mixture components used');\n",
"\n",
"ax.set_ylabel('Posterior probability');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that the vast majority of samples use five mixture components, and the largest number of mixture components used by any sample is eight. Since we truncated our Dirichlet process mixture at thirty components, we can be quite sure that truncation did not bias our results.\n",
"\n",
"We now compute and plot our posterior density estimate."
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"post_pdf_contribs = sp.stats.norm.pdf(np.atleast_3d(x_plot),\n",
" trace['mu'][:, np.newaxis, :],\n",
" 1. / np.sqrt(trace['lambda'] * trace['tau'])[:, np.newaxis, :])\n",
"post_pdfs = (trace['w'][:, np.newaxis, :] * post_pdf_contribs).sum(axis=-1)\n",
"\n",
"post_pdf_low, post_pdf_high = np.percentile(post_pdfs, [2.5, 97.5], axis=0)"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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GgrIQYl7E43FnOhns/cpggaKBZUIyAO5i2l55lkAgwHHHn0hhgRv8DXYSWGCb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\nx30gAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fabbcfa3d10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"n_bins = 20\n",
"ax.hist(old_faithful_df.std_waiting.values, bins=n_bins, normed=True,\n",
" color=blue, lw=0, alpha=0.5);\n",
"\n",
"ax.fill_between(x_plot, post_pdf_low, post_pdf_high,\n",
" color='gray', alpha=0.45);\n",
"ax.plot(x_plot, post_pdfs[0],\n",
" c='gray', label='Posterior sample densities');\n",
"ax.plot(x_plot, post_pdfs[::100].T, c='gray');\n",
"ax.plot(x_plot, post_pdfs.mean(axis=0),\n",
" c='k', label='Posterior expected density');\n",
"\n",
"ax.set_xlabel('Standardized waiting time between eruptions');\n",
"\n",
"ax.set_yticklabels([]);\n",
"ax.set_ylabel('Density');\n",
"\n",
"ax.legend(loc=2);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As above, we can decompose this density estimate into its (weighted) mixture components."
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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4+AdRVlaJvrqandvW4eXjj49/sMXngSv/G1Lbhqd3O1xcPdiVEn/Bdl1cdOc9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\nIAiChfg/iuztr2jkjFYAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fabbd097f90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"n_bins = 20\n",
"ax.hist(old_faithful_df.std_waiting.values, bins=n_bins, normed=True,\n",
" color=blue, lw=0, alpha=0.5);\n",
"\n",
"ax.plot(x_plot, post_pdfs.mean(axis=0),\n",
" c='k', label='Posterior expected density');\n",
"ax.plot(x_plot, (trace['w'][:, np.newaxis, :] * post_pdf_contribs).mean(axis=0)[:, 0],\n",
" '--', c='k', label='Posterior expected mixture\\ncomponents\\n(weighted)');\n",
"ax.plot(x_plot, (trace['w'][:, np.newaxis, :] * post_pdf_contribs).mean(axis=0),\n",
" '--', c='k');\n",
"\n",
"ax.set_xlabel('Standardized waiting time between eruptions');\n",
"\n",
"ax.set_yticklabels([]);\n",
"ax.set_ylabel('Density');\n",
"\n",
"ax.legend(loc=2);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Dirichlet process mixture model is incredibly flexible in terms of the family of parametric component distributions $\\{f_{\\theta}\\ |\\ f_{\\theta} \\in \\Theta\\}$. We illustrate this flexibility below by using Poisson component distributions to estimate the density of sunspots per year."
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"sunspot_df = get_rdataset('sunspot.year', cache=True).data"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>time</th>\n",
" <th>sunspot.year</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>1700</td>\n",
" <td>5</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>1701</td>\n",
" <td>11</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>1702</td>\n",
" <td>16</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>1703</td>\n",
" <td>23</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>1704</td>\n",
" <td>36</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" time sunspot.year\n",
"0 1700 5\n",
"1 1701 11\n",
"2 1702 16\n",
"3 1703 23\n",
"4 1704 36"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sunspot_df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For this problem, the model is\n",
"\n",
"$$\n",
"\\begin{align*}\n",
" x_i\\ |\\ \\lambda_i\n",
" & \\sim \\textrm{Poisson}(\\lambda_i) \\\\\n",
" \\lambda_1, \\lambda_2, \\ldots\n",
" & \\sim P \\\\\n",
" P\n",
" & \\sim \\textrm{DP}(\\alpha, U(0, 300)) \\\\\n",
" \\alpha\n",
" & \\sim \\textrm{Gamma}(1, 1).\n",
"\\end{align*}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"N = sunspot_df.shape[0]\n",
"\n",
"K = 30"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Applied log-transform to alpha and added transformed alpha_log to model.\n",
"Applied logodds-transform to beta and added transformed beta_logodds to model.\n",
"Applied interval-transform to mu and added transformed mu_interval to model.\n"
]
}
],
"source": [
"with pm.Model() as model:\n",
" alpha = pm.Gamma('alpha', 1., 1.)\n",
" beta = pm.Beta('beta', 1, alpha, shape=K)\n",
" w = pm.Deterministic('beta', beta * T.concatenate([[1], T.extra_ops.cumprod(1 - beta[:-1])]))\n",
" component = pm.Categorical('component', w, shape=N)\n",
" \n",
" mu = pm.Uniform('mu', 0., 300., shape=K)\n",
" obs = pm.Poisson('obs', mu[component], observed=sunspot_df['sunspot.year'])"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 20000 of 20000 complete in 111.9 sec"
]
}
],
"source": [
"with model:\n",
" step1 = pm.Metropolis(vars=[alpha, beta, w, mu, obs])\n",
" step2 = pm.ElemwiseCategoricalStep([component], np.arange(K))\n",
" \n",
" trace_ = pm.sample(20000, [step1, step2])"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"trace = trace_[10000::10]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For the sunspot model, the posterior distribution of $\\alpha$ is concentrated between one and three, indicating that we should expect more components to contribute non-negligible amounts to the mixture than for the Old Faithful waiting time model."
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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yWRxstPs8AokFcq3bdU0aJwRPGDjl8ZbH048iJSGom3tdUxcuaYyYXpQGiUiA\nxHYDLDYnkhLjmb7knWZQLDFYCbI4KHsTEnVbnDD2WsgSk+KQIItjlCm5LA7SOCGUShksLkBncviM\nz1tums+HvNvtMpeamsAoCF0WB8wOGgIBL6Jrru6xwUnxEC9x19DiCQVIkkv6fd+cLjpAdp5IgLZu\nq89xKQopkuUS5l74j8uD2epAgjwOMoMdZgeNOIkAqakJkLf2MOfQmR2wOgGR0Pca2B0u/HCyFWkp\n8Sgc5VsDLEltZFwRo8EFtTFASR7I3wm2c3XozLDTFBo1Jsybmj1gslzpcFKoKioqsHjxYhQXF8Pl\ncuHUqVN46KGHwrZTqVTQaDTMtlqthlLpTmyQnJyMrKwsZGe7b+asWbNQV1cXVqEaiQUxYzXms406\n/GVrFQxmO2ZMUOHehQWIlwiHxDUeicVP8zIT8csbJmBBWTb++Z8LOF6nwW/+8G/MmZyJW+eNgTw+\ndN234chIvM8jdcyxgM93T1rtdjtomkZxcTFeeOEFTm2/++47vPXWW9i8eTMSEnytFDfffDPz99y5\nc1FbW8tJoRpp9zVSYvXs63vcShOfdkFvcE/QOzp60GWwMvs8//vTrtYzlhLPMZoOA8Qi9qQUZ867\ns7m1tHZDLhVB32OBxeaAiAJqHE40qQ2gQcNqD1x0blPrQfUuRmt1RuZ8AtAQUe7zy2Vx0PeY4bA5\n0NHRg06tkXUMHR09cDhdOHxWzXymVvcwVpmuLhP0PWYIeDy0tHbBYLYDcHtHhMLdzgK9123iuVz9\nvm8Op4uR39OX9/3xoOk0wGG1+3zecqkbYr8aW6ebuqHvMSNFLoG+xwK7VYB2dY/POTzXQMjn+cjf\nbbRB32N2t4/3tdDo9WaYbdFTqNgYqN+JYN83XY814F6MZKL1fuKkUN1xxx2YPXs2Tp06BYqi8NRT\nTyEjIyNsu9mzZ2PTpk1YunQpqqurkZaWhvh49+oMn89HdnY2GhsbkZubi+rqaixZsqR/oyFwgqZp\n7D3Wgi27zwEAli8swDVTMol72RBhVLoM/337JJxp0GHLv2rx7xOtOFyjxu3X5GPulMxhV1eEQIgV\n+fn5+Pvf/45p06Zh5cqVyMvLg8FgCNvOYDDg5ZdfxnvvvQeZTBaw7/7778fmzZshFotx+PBhLFy4\nMFZDIATB7nChSW1AllIaMJkO1cYbLq5qTqcLPD9rEpfaQZ4YG2+Xv3MtXZzkBPxc/kJg8Cv8602r\nxjcBgos6OshCAAAgAElEQVSmcfRsB3gUBWVvUXmHy8Wk9AbQp9pb0fD4Y3NNZE+yEXis1e4M+gx4\nDvWPmQt1HrvD6fW3C91GK1MOZiTMg5wRuCwSuMPpW2W1WnH69GkYDAbQNI3vv/8eAHD77beHbFda\nWoqioiJUVFSAz+dj/fr12Lp1K2QyGcrLy7F27Vo8+eSToGka48ePx/z58/s/IkJInC4XPthVi73H\nW5EQJ8SDtxSjIPfKdikbrkwYlYwNK6djz9EWfP6fC/jb12dxqEaNlYsLSS0wAgHAM888g+7ubshk\nMmzfvh1arRa/+tWvwrbbsWMHurq68OijjzLJKGbOnInx48ejvLwcCxcuxJ133gmpVIoJEyYQhWoQ\naFIboO4ywWJzYOJoBesxDqcLpy9qL2/3Kik8r+Qi4XA4afh7AlZf0IHPpzBlbGrQdh6FiC0pRSjs\nDifsDtqnLhbdG8/jDUW5r4HOYEUwAgvOupWqYAkVAN96XB66DVaIhHzEiQUxS5XOdQ6v7bX4eUNz\nUD4pKvAcwRYfvRXvs406GCx28Hk8JMvEMU8VPxRgewYi78MFu8NFMkB7welKrFq1CjwezyezEhBe\noQIQEMxbUFDA/J2bmxsy/S0hutjsTrzxz2ocr9MgR5WAh28rIRPzIY6Az8P103MwrVCF//dVDU7W\nd+LpzT/izmvHYh6xKhJGOEuXLsXNN9+MG264ATfddFNE7ZYuXRp0//Lly7F8+fJoiEjoI55V9FBB\n/d0Gm0+NoL6g6baApmnkpnnF2DidsDvdyon3pNzlEwfu+Yv7b7CLBo7Uuq1FST61l9iPb9GEt7Z6\nc6T2svsf11eDwWzHmUYd4kQCTB6bytRuioTaJrdlbnxOEut+F02zJnJgU3jZ0rWHmv7TXpbCYJZF\n/0+9rYMGi9sV0tbrojkSXqk+NdD8nnGunKjrhM3hxPRCFfgk6yEAjgqVw+HwyfJHGH6YLA78+dOT\nONvUhQmjkvHQrSURm/0Jg0eyTIxHbp+EH6rasGX3Ofzt67M4Wd+JlYsLfdIAEwgjiSeeeAI7d+7E\nLbfcgsLCQtx8882YP38+k0CJMPwJNZkOsMTQYfaz4FFa0hSBxW8tVifivYq0ek9EnbS/hSqyVX8f\nCxWLrJ706cFwueiQk3+ui22e2Combog1lXloWbQ9FtbPuwxW6Hqs6DbYmJpcgDs9vM3h4mzVC3Wc\nt8tfMDdKp8vFWjzZG8/lGmqLlJpuMy5e6kFJfgpn11cA0JtsiOu9t/54P1suFw0eP/Ix23rdJp1O\nGnyiTwEAOF2GsWPHMnU+ImXjxo2oqKjAXXfdhVOnTvnsmz9/Pu655x4sX74c9957L9RqdZBeCP1B\nb7ThpQ+P4mxTF8rGK/HoHZOJMjUMoSgKs0sy8OwvrsKEUck4XqfB+nd+9HF5IRBGEmVlZfif//kf\nfPvtt1ixYgW+++47zJ07d7DFIkQBLpYSfyUmnIIVCrbJuN3pCnqM0WxHZ7clstTiXgc5vPumadQ0\n+s6xvBUQNsIlTgh29bR6C9q1pojbRUKXwQqH04WaRh3adaaAsZw834maRh2nWDUgtLLK7KMCa3J5\n96/VW5hrztZbpFYaVVKgAh4L6lq64XC5oOlmV1qDcfqiFkfOtLPu81bm++v+R8r1XYbTrLqtrQ0L\nFixAfn4+k1UJAD744IOQ7Q4dOoSGhgZUVlaivr4e69at87F0kWr0sUdvsuHlD4+hRWPE3MkZuHdh\nYchVGsLQJ1kmxm8qpuCrg43Y+u/zeLXyOBbPGoWfzckjpnfCiEOv12P37t346quv0NTUhDvvvHOw\nRSJEg8vZHoLiPxf0V4oiCb1nT5AQXGFr15nQrjNB2Ls8767bRIVUErz3+FuoIuXU+c4+tAJaO92J\nLCgeBVVSXKCy0s/pQbfRhppGHWRx4a3EUQjlYa4dhcD75b1Z19oNqUSIkjEprBc8UssUf4DnUTwK\nYa1sXPF+jjt0ZmT3oRabB65K8UiAk0J133339anz/fv3o7y8HIA7G5Ner4fRaIRUerkgHalGHzsM\nZjterTyOFo0R15Vl4+7ycUPOnE3oGzyKwuKZo1CYm4w3v6jCl/sbcK65G7+6qQjJMnH4DgiEK4BV\nq1bh3LlzuP7663H//fdj6tSpgy0SIUqwFsz1I5jC46JpmCyOgP05ygQ0dbDHJbG5B/p/xJZYgbFi\n0W4XvJBTGq993haqwZgFnW/tZk32wGYZjEQ+T7r4HnPw7IRMvxw1qpAuf73/s7n8+bczWuwwWx1o\n8cuO6G7f+z8niQZeodIbbWho78GYDDlUyW7rmN5kA4+iIi7O6/2sN2sM/VOohvAUvttow5kGLXKU\nCchS9n2MXOG0nD1jxgyYTCbU1tZixowZSE9Px/Tp08O202g0UCguZ+dJTk72qUsFuKvR33333fj9\n738foeiEUJgsdrz6j+NoUhtwTWkWUaauUMZkyrFhxQyUFShR29SF/333R1QTF0DCCOHee+/Fnj17\n8PTTTxNl6kqjDxYq78ldY3tPQFuhkB/Uis+e1juMS6H3sYjMbcynrxhMSrl0eaFNj4Z23zpE/Z0m\ndEbgmsYlxg0IVKq974tPUoqA5yGw/+oL2qhYVfpjKVLrgrtcBsOT7bFVc7nt6YtaVF1wWyrNVgeT\nWCMcAQsFLNfJZneivrU7ZFIYd180c3z1BS0TkzdYtGlNjEvrmQb3XCjYIkq04WShevnll9HQ0IDW\n1lbcc8892LZtG7RaLZ5++umITub/cPelGv1IrEQf6ZjNVgde3HIMDW09uH5GLh66Y8qwdPMj95o7\nG345C9v/cwHvbKvC7/9xHHeWF6BiQcGAr6L1BXKfCX0lXCF4wvDFYykJafDxt0h4Hc3jUQETRQpu\npYdt2hmsJpI3oWpH0QivjARrHQtPHa51rgLacZDFRdNwOFwQ+SVJOHNRi+4QdbMC+gkjo8eFki09\n/OUN939dRmtAbDjbUNiyDQY7NhT9ebeqdWbGyhQK1usT5LQn6t3GipkT08ML4N8tHdhvY7sBGr0Z\nDocrZGkdj4gtGiN6zDbUNnVh6nhlWBFOne+EkM9D4ajolu252KYHwJ5khqZpNLYbkJokgVQSmVWP\nC5wUqkOHDuGjjz5i0sg++OCDqKioCNtOpVL5WKTUajWUyssXui/V6EdaVedIK8s7nC786ZOTONuo\nw6yidNx5bT46OwdGO48mkY77SqC/Y55ZqERaYhn+v8+rUPmvszh+th2/uqkIiQlD1wWQ3OeRwVBU\nIF966SUcPXoUTqcT9913H66//npm3w8//IDXXnsNfD4fc+fOxerVqwdR0pEJl/pOoSb/bMoNRQF8\nPgW2hXx2lz+/zHshFACb3eleuAxhJAimOHlSd4ciSSpGlzF4TSp/uFp//GFVLP22G9p60K4zoTgv\nxcfdLBJlCggfQ8XjUXC6Au1J3mPz7uOS9rIrH03TEVmizFYHdD2hr69CJmEyGrItUhfkJONsU/gE\nblyl8sS7ecOmxzmckRXq9X82XDQNnp9Gxe/N/NdjsjPncLrogEyDnmc60sfNyOGZ7w9s3zVdjxWX\ntEZc0hq5KZ4RwsnlTyx2T8g8LmNOpxNOZ3jT4uzZs/H1118DAKqrq5GWlob4eLfWaDAYcM8998Bq\ndT/Ahw8fxrhx4yIfAYHBRdN4d8cZVF3QYlJ+Cv7rhsI+1RcgDF/yMuTYsHI6SseloqaxCxvePUSy\nABIIfhw8eBB1dXWorKzEX//6Vzz//PM++5977jls2rQJH374Ib7//nvU19cPkqSEUPhn4fOGR1EB\nChAFKqhlQa0LrH/k33soS5LV7mTih2JBblpkMSB9Vai4zPbbe13WugzWflnXwlmomFvFJcufH6cb\ndGEVJG+aNQacbdLBESJdvbcSxTa1Egq4JYUKJnOLxogm9eUFcDZ3O7uDRnOHwef+eh+nN0am1Lrl\nCfzMk2zFY9E7fk6DY+c6WNxgIz7dgMB27bxFbwuR6bKvcLr7U6dOxVNPPQW1Wo13330X99xzD2bM\nmBG2XWlpKYqKilBRUYHnn38e69evx9atW7F7924kJCQw1eiXLVsGhUJBqtH3k4/31GF/dTvyM+V4\n4GfFJOPbCEUqEeKhW0tQcd04GHsTk3yytz7iVSwCYahTU1ODW2+9FT/96U8BAH/5y19w4sSJsO2m\nT5+OP/7xjwAAuVwOs9nMTBSampqQlJSEtLQ0UBSFefPm4cCBA7EbBCEM7DM2l4tmLQLrgaKogFpO\nFBU89oWtllLA5HEQU0xHGgMdS5c/z2TbZudeS6ov5/IsCAd4qHl9EKyPHpOtT0plKAXRe4GabbGa\nqxegi0aA8u2iaTSpe9CiMcBmd8JF07DaAhV0u9OJ5g6DTxp178UAT5HlUARmQwx/nTyKVX2LnjWG\nbahl+7OxKFTet+ximx7mfhYF94eTy9+vf/1rfPXVV5BIJGhra8PKlSvDuuZ5eOyxx3y2CwoKmL9J\nNfro8fWPjfj6xyZkpMTjkTsmR1QAjnDlQVEUFkzPwdisRLz1RTV2HGjAmQYdfnXTRE6+2wTCcOCZ\nZ57B888/j+eeew4AsHjxYjz11FNhC9HzeDzExcUBAD7++GPMmzePmbD6J1NSKBRoamqK0QgIwQjn\n8neuOfTEkccDTH4TJoqiwI9AMfGc22C2w+WimWK+fYXLpJOrlcOb5AQxk7TAQ3+VPx/8k3sI+LA7\nXbA7nH23hCG8QuXwjCFEsokgIVExkcn70WFTcLkqvRabA8fOdUAeL8LE0e7fGu8xNXUYYDQ7YLIG\nd4vzfkq8XR3dmSYDx9CsNoCigCxlQmBMGiep3Wj0ZqSnXJ5DuFy+2bqHik8Ul/paRrM9qjVZOfXU\n1NSEoqIiFBUV+XyWk5MTNUEIfedwjRoffVuHpAQRHls6JeIUmoQrlzGZbhfAv++qxf7qNmx49xDu\num4c5kzKIFkfCcMegUCAwsJCZjsvLw8CAfcX5O7du/HZZ59h8+bNQY+JxKVpKMaKDTW4XqNuqxMm\nOw0Bn8fa5nRTN+SyuKDtJXFimOwWn2NSUxNgdtJwcfTeSE6Oh1Ipw+mjzQCA/OxEyA19j/0w2emQ\nMgNARqqU1V0pNTUBcnVgTA0AZGfI4byk9/nMCYQ9lz9KpQxteiscftNiuVTkcw9SdGYIDDbIEsRI\nTZVB3tq3mFC5PA7WEF6SPMqdWCSp9z54sNgcqGszQC6Lg0DAgyNMJrpQjM9NRq1XUWWRkAexnb2/\nFIUUZof790ChkELe5WvVVKQEv0fBSE1NAEVRsDtckMvc19HqBAQiAeSi4L9lCfI4yHvY3ftSUmWQ\ny9zPg1Ipg1Zvgb73QifaXZAnxvl8BxQKKeIlQpxt0CIlMQ6pSXEw2F1MG6VSBrmsmzk+OVkKeW+2\nQVliHM40uhc35LI4iEV85l7Z7E5QlFsB98fTX7R/Mz39JifHQ669bLlLTU0AzedD3n154UGWGBfV\n83N68/z85z9nJl82mw1arRbjxo3D559/Hrbtxo0bceLECVAUhbVr16KkpCTgmFdffRXHjx/H+++/\nH6H4hPqWbvx1+2mIRHw8esdkpCSSIskEX+LEAvzyxokoHqPA33edxXs7a3DkbAdWLCokNasIwxqB\nQICmpibm/bRv3z7OCtB3332Ht956C5s3b0ZCwuX4FJVKhY6ODma7vb0dKpWKU58jLdlIpESSkKVL\nZ4K+xww+j8fahnY60RMiCYLdaofZ5muh0nYa0KM3Q2/gFlvTruahtU0PfY97YqbR8Jm/Y0a6jPUc\nnZ2GoOfWxwuiIld9QycuNgcmVXA5HD73QK+3QG+0gnY4ceKMvc/n5tMuTvdCqxVA7KXjWXrvq77H\nzChdfaVLJ/KRX8DjMe5tUonQJ3lCt/jy/e/Q9Pi0k4gEMPWYI74W9Q1aJEpFaOkIfn/ZOF4T/Ni9\nPzbAZLVDLotDR0cPDpxuY/ZV9ZghixP51An75uBFZKUmoEXjjt+aOTEdnZ1GRp6TNW0+sp09r2G2\n6y66oPdKliIW8plnxXNetgQQzHWM8m+mp9/zjVofmdUdPdB0W3w+02j4EFPRU+o4KVTffvutz/a5\nc+fwySefhG136NAhNDQ0oLKyEvX19Vi3bl2AK0Z9fT0OHz4MoZBYVSJF3WXGnz49CaeTxoO3lCA3\njayOEoIzqygdBTlJeHdnDU6d78TTbx/EXeXjcHVxOrFWEYYlv/3tb7F69WpcuHABZWVlyMrKwosv\nvhi2ncFgwMsvv4z33nsPMpnv72ZWVhaMRiNaW1uhUqmwd+9evPrqq7EaAqEXh9MFTbcFqYkSCPiX\nV8/ZFGSD2R5WcWaNlaIoZKRKoTNYoUqKh7ordGC6f5a1SLzoEuNFEWe9AwBpEA8TtoK7HqJVHuNs\nYxA3Sr9xe05ntNg5FfANRrgaR8zpaeB8qx4CPgWTxYF4yeWpazhlSioRgkdRrHJKJULw+b7WSm9X\nMYHfdfXe9H8Wxmcn9ek9eqZBi4mjFFGtlRTKVRAALCyxWR5lyoPHPZUC5ZMoA4DP96Y7gsyTA4l/\n0gm73YXzrd0+nzV1GOCiB1ih8mfcuHGorq4Oe9z+/ftRXl4OAMjPz4der4fRaIRUKmWOefHFF/Gb\n3/wGf/rTn/oiyojFaLHjDx+dQI/JjuULCzApP2WwRSIMAxRyCR5bOhn7jrfiH9/WYfOXZ/D9qUtY\nvrAAGSnS8B0QCEOIwsJCpi6iSCTysTSFYseOHejq6sKjjz4KmqZBURRmzpyJ8ePHo7y8HBs2bGDi\nf5csWYJRo0bFchhXJFa7E6ABsYhbPG+T2oB2nQlmqwN5GfKgx9kdLqaYaSjY0jJTFCCPF2HGhDT0\nmOxhFSp/uMYlTR2nhIDPw4817RH1DwCpiexueqG8FIMpYZHiDFajKUAWt+LQH8sQwC1dvOf83veq\ny2jl7M4oFvIxPicJ9S3d6Oj2teqMz05irF2Xz3V5TP7KlreS7h+L569LeadYDwfXgrx9gW3hwc4h\nSzeXxB9ccThdPoskvueho7ag26wOrpQ2a9j3tWgMiFZJeE4KlScbkoe2tjbo9fogR19Go9GguLiY\n2U5OToZGo2EUqq1bt2LWrFnIyMiIROYRj8Ppwl8+O4U2rQk/nZGLa0uzBlskwjCCoihcU5qF4jEK\nbPnXORyv02DDOz9i0VWjcMOsUQHFGgmEocbjjz8e8iX80ksvhWy/dOlSLF26NOj+adOmhU1sMRJx\n0TTnUhzHzrndJrnWe/EkkLCEybzVn9TkHsl5FBW2CC8bJo4KQH9+Q4PJFep551EUspUJaI6ilcOb\naNQd5lEU4iUCGMyRx6D1JzW7Rwlit1giZDVmf8uf9z1QyMXItl2+5v79R1KypsvQdytfOPpy6fQm\nG7oiSDnvDZsltcdkB49HIVEq6pXJK0sgopPIgqbpoEoTEOUkLUHgpFDx+b4/DgUFBXj00UcjPpn3\nRezu7sY///lPvPPOO2htbeX8hRmJQb/eY6ZpGn/8xzHUNHZhVkkGHrhjStA0sMOdkX6vB+Jcz+Qr\ncaDqEt7cegrbfriIA2faseKGiZgzJWvA3ADJfSZEytVXXz3YIgwpjBY7NF0W5KYlxOx7a7I4cPK8\nBjnKBGQpI6uJ5OF8SzdcdgczsdJ0mxEvFqCh3XA5HorytX74Tw0iXc0fk5kY4OoD+E7iMhRSn0xp\nweiLC18kJErFQe9fOLe+2JbFuHwTqi50sipF4SwyY7MSYXO4IlKoxmTIcf6Svl8KnUexYS30jNCT\neU9x28t9ebX1U2IDbk8EX0ONPnZxef4WOC7Ut3TD6uif1UzjVdLAU+x44mgF5PEiH4uny0WDx+//\nb1a4ZyQaiwLh4KRQPfDAA6xfcleveZgXxBatUqmg0WiYbbVaDaVSCQA4cOAAOjs7cffdd8NqtaKp\nqQkvvPACnnzyyZCyjLSgX/8g3u0/XMQ3h5qQlyHDvQvGo7MzNitSg00kwctXCoM15rHpMjzzXzOw\nff9F/OtQE17++xFs3VOHiuvGYUxmcNebaEDu88gg2grkLbfcwvxdW1uLuro6UBSFgoICjBkzJqrn\nijYmiwM0aEgl0YsbPnXe7QInixdCIY9NYiJPWu6mDkOfFCqz1YEmtTvQfebEdDicLtS1BCo6/vin\nGo/UQuU90fXuyXtO4z9xDt1fYBKERKkYY7MScaRWHZFs3ogEfIzLTgy6P5yFytGbfU4iFMBij259\nHc9wXS46qEIkFPDCnjtSXV/Sm9I6UusCBYp5bjzTUzaLEUWFlimS8jP+9ycSC1Usqb4YmGQkHN7f\nMXca9gga9w67jmUR4/RFLSbnp/q4AffH+uhNOLfEYOeRxYuicn6Ao0I1efJkOFl8Lj2+j2fOnGFt\nN3v2bGzatAlLly5FdXU10tLSEB/vzl+/cOFCppBvS0sLnnrqqbDK1EjnxzPt+Ozf55EiF+O/b5tE\nak0RokacWIA7rhmLeVOy8PGeOhw524Fn/3YY0wqUuHVePtIVpHYVYejx4osv4ptvvkFJSQlcLhde\nffVVLFmypE8eFAPFyfPuRUaurnCRwKX2ylAh2CTZMw0NNj8KN7n2ztIGBJ/Yen8cSVIHhVwCjV8s\nTopc3Kf6Ub59SILGmXBBlRwHjd6MHFUCLlzS+1yD/uK54mFrNHldRo91yYOrD7EynqO5WA+9KR6j\nYBYZPC5o7M8BFVImhVwCp4vm5Erp6WZ8dhL0Jhv4XoaGyfmpOFGvCdIytjhdLlZFVyTgI1kmRrsu\nsjjC/mKxOX3mrkdqO5Aqj0NigggUFTyGMBzh9DK2Qr/uhn06HSucFKoHH3wQY8eOxezZs0FRFPbs\n2YP6+no8/PDDIduVlpaiqKgIFRUV4PP5WL9+PbZu3QqZTMYkqyBwo7apC29vPwOJiI9Hbp+MxASS\n7poQfVRJcXjwlhKcbdTh4731OHy2A0drNZgzOQM3zc4jadYJQ4qDBw/iyy+/ZLLE2mw2VFRUDGmF\nio1QQduRMFTUKZ/Cq0HiroLJyhT0DXJEMH0qRS5BilyCOLHAZ/LKD2ai8iIShUrAZs2KQFHwV/j6\n0IUPEpEAQiEPYhEfV01IA0VRaGjvAaLpAcjhwXK5fJUWAZ+HzBQpkynRRbO4xfUi5PNZEyX01X2V\nR1EBlkSK5eThLFQ8Cr6xaSEO9siqkEugkEt8EiT0V9nuL6zujlRkFrhoQdN0gJVZozczbo/hFCpd\njxUCPgUBn+dTlDechcpkcSuUcSKBTzkFWz9dG73hpFAdOHAADzzwALO9ePFi3HvvvZxO4MmU5KGg\noCDgmKysLPztb3/j1N9IpE1rwp8/PQmXi8bq20uQreqb/zqBwJWC3GSsW16Go7Ud+HTfeew73oof\nqtpwbWkWFs8aBXkUzeQEQl9JTU31KeQrFAqRnZ09iBJxx6NotGiMaFL3YEJu8pBeKItkaus9uXE4\nXBAJ+YEryEHmP91Gd5xSpBaqcdlJ7vP5xRJ5T6S9W3r3r5BLfKwpoeCzhDh4PhmfnRQ2plkk5MFl\nowMmgFxiob1d2TwU5ym84oTY44UiyTjHBg0aZqsjpIwuF+2TiZCme92pehUqmqaDhofweHBXIu5F\nFi9CXrqMc5p6/xg4t6Lk66sWTPRQ6ei5PPXjs5NgtDgCFg283UgFfB6USXHo6IpxDbMgsCkbFPqW\nmKW/1DYHSc3PAZqmmXgsAD6/meFcB2nQkMWLAhSqaMZWcVKourq6sG/fPkybNg0AcPjwYeh0kftl\nEiKn22DFax8dh9HiwMpFhSjOI+nRCQMDRVEoK1BhyrhUfH+qDdu+v4Bdh5qw73grrp+ejZ/OyEV8\nFONACIRISU5Oxm233YaZM2eCpmkcOnQIubm5TGbaRx55ZJAlDI7TSYPiA22dbpcbbY+1TwqVj8tO\nDCOvI5l8eRtgqi9oMWVcakBwfLAVZRdN48DpNsSL2acnwSxXHgImtjwKY7MSodaZIYtn/70S8MPH\n/1w+Nkh2A4BT/JrZ6sTU8amobe72KUzMZsXLTk3wyVxWOi4VFrsTpy9qmc/YrGtiIZ+xApSOVcJF\n0xEpVP4KmNXuxIl6DVRJwV2/+XwKPIevLMkyMUalydCptyBFLkGPiT3+yqPUiAV8xIkFGJudCAGf\nxzmrYpoizleh8lKTmFiqPsRQ+e8TsliR3RapwLb+Vqm8DPngKVQs1kqKik2cl8XmwKXOyFw0uWKz\n+w6kx2T3UqjCtxfyeQH3NFoxXABHhep3v/sdXnjhBfz6178GAIwfPx4bNmzgdIKNGzfixIkToCgK\na9euRUlJCbPvo48+wqeffgo+n4/CwkKsX7++D0O4crHanXjxw4Po6LJgydWjMWdy5mCLRBiB8Hk8\nzJ2ciVlF6fj3iVZs/+Eitv/QgG+PtGDhVbm4flo2JKI+lbQjEPpFTk4OcnJymO1rrrmGc9uamho8\n/PDDWLFiBZYtW+azb/78+cjMzARFuWMsXnnlFahUqmiJDQBMAgNB76o923vd4XSh22CDQs6e/c3h\ndOGCl2XF7nDBZLFHbaGjo8uMZJk4YndEb2XJ6nCiucOIFo3Bp3ZQuHmMKUj69HDt2CbB0sS4AFci\njyLimVRKRHxOChWbAhPayuELDRpCAR9FoxU4cLotqNwAIE8QAV6hNyIh3ycle2aKlPW5yM9KZNLW\nRzpxTpKKg7qC6YIoZQqZBJmpUlxoDbTyZaRImRqHQa1EvZ8nxAsZS2PvHk4yS0QCzJyYzlxPb0XJ\n87ywud1RoEK6e/pftoQ4IfLS5ZBLw3to+Ctfg5mkgk1p8I95iyYN7X1PuuS2dPoKdvqiFi4Xjdy0\n4MmNGjmcU8DnBRSTHnAL1aRJk7Bly5aIC3AdOnQIDQ0NqKysRH19PdatW8fU9rBYLNi5cyc+/PBD\n8Hg8/PznP8fx48cxZcqUvo3kCsPhdOGNz6twtkGHWUVpuGVO3mCLRBjhCAU8XFeWjZ9MysC3R5qx\n41XpGNsAACAASURBVEADtv77PHYfbsINs0bj2tJMCAUkUQph4HjooYf61M5sNuPFF1/E7NmzWfdT\nFIW3334bEklsMuZ544mnoUHD5aJxSWtCcoIY8RIB6lu6oTNYMYZOhCopMLbAfzLQ1GFAU4cBMyak\n9XsC16414UKbHskJYhTkJkfU1t8tr4WlPkw4S5M3doeLmRD79z2tQOWTjMN/jhIsfiVOLEBBTjLi\nJe5pUH6WHGqdGWqdOWTKaLbfuGjMlZNYrJOee5goZbdcJgQp6OuvEEXyLJisDuaa+BMvFrCmjs9I\niYdYyA/rtuh9b2TxIvSYbEhXxENvdFui/J/nvl5Xdzvfxqy1wajQrpb+zxJFAWkcEzQJep8772s/\nKk3WL2UjFMV5KUELXjtcLsSJBMhKlTLZ9yiK4pRptL9FfSPF6aVQedyi9b3PXLAU8DUNOnQZw9fN\nEvAp+FcXiOb4OC071dTU4NZbb8WiRYsAAK+//jpOnDgRtt3+/fuZ5BP5+fnQ6/UwGt2mQIlEgnff\nfRc8Hg9msxkGgwGpqal9HccVBU3T+H9f1eBEfSdKxyuxcvGEAasJRCCEQyzkY9HMUXjpgavxs5/k\nweF0ofKbc3jqrQP47kQrnFHMLkUghOLNN9/E9OnTMWHCBEyYMAGFhYWYMGFC2HZisRhvvvlm0HcO\nTdNRdQXhBA00qQ1oUvcwCognnih4sVt2GaMhu8dC1JdCrOEmKXaHM6KVYe905B7lacIoBcrGKyHg\n8wIUiAmjFMzfod6dybLL1hihgI8sZQLG5SRBIgy+1symoPU19bJnsj2tQOUTYO85v6Q30cSEUZEp\ntN7QiCzpRqgg/WB1uDzXOJziFi8RIEkqRo4yAUWjFZg5MR2j0+Ve1qTIn1s2N0TKq3Czp0uxkM1C\nFfraePZ4FNdIan5KJUKMzUzEpPzLYRoeSx3gduf0RhAkvgwAclThy04EU6490ICP5ZpHUYzFjY1U\neRxrrHRcjL1RPPMHh9OFH8+0o94r/brBHPg7aLU5OSlTAMDn8zAqTYbs1ARkKNz3Ipo/85wUqmee\neQbPP/88U0Nq0aJF2LhxY9h2Go0GCsXlH7bk5GSfulQA8NZbb2HBggVYtGjRsAkmjjWf7juP70+1\nIS9DhqdWzIhK9icCIdrEiQW46Sd5ePH+q/HTGbnQG+14d2cN1m/+EcdqOwZ+QkoYcXz++ef4/PPP\nUVVVhaqqKlRXV6OqqipsOx6PB5Eo9CR4w4YNuPvuu/H73/8+WuJCbwxeGLaj28zEgfSY7GjVGBnF\nJJhSEOwrFo2vnkdxubxaHL6N5zsfLn27zmCLeGVY02XGgdNtTGyPVCIIahFPlIqQmSLlNBH1JyFO\niCnjUiHks/ct8lOoZk5M73MWt7ICJaYVqALe8RNGJTPKYiiFkMtCK4XIFAEAEZfJ8HSfpZSGPE7A\n56FwVHJAHTN/5cf/czayVAmYkJuMnCBJujyKkqcPoYCPUWkyHwXC49LrIV4s9FGmPfuKRiswvVAV\nsdU3NSkuqDu81E8BCl1nLKLTsssil/hcT88zG8ziRvHYZYp1pl+PBdrcu6DjHXdm91P2aYBTSnsP\nAj4FkZCPbFUC4nqtsOEU0UjgpGoKBAIUFhYy23l5eT6ZlbjCNsG67777sGLFCvziF79AWVkZSktL\nQ/YR7QKRQ43P99Vhx4EGZCml+N39sxEnFiDuCh9zMK70e83GcByzEsCDuQrcubAQH+46i90/NuDP\nn53CxDwFVt5YhEKv1WLW9sNwzP1lJI45FowbNw7p6engB5n89pVHHnkEc+bMQVJSElavXo1du3Zh\nwYIFIdv0mGy4oDZiQp4iwGJhMNtR16RDt8HmE0cUii6zgzlWoZCyPjMWqwPytsAJRUpKAruLUwSo\ne2ywudxWBaVSBqODRnfvCjGbLDa7E/tPXcKoDDkUyVLIO9kD8OWyOAjFQvAEPM7XwiOP9/EqpQz8\nEIuN/f2OJbYZYGMpIpyRnuhzzUOdZ9woO9q1gXV+wsmWnZUUcr9c5l61T0qKhzLIhPjaGRIYTDak\n91pFFv1EirrmLrR3hq87lJWZhPYeG3pCLAB4k5oqYxSEJq0ZDocLaWkyJMu4ucwm68zgCWyQy8Q+\n18bucEHefjnBQW66DI1tbpc5p9OFgjxfC7PnuqhUcsgT43GhtRvjc5OZ74JSKYPF5kBnr4uh51ye\ndjOK0hEnFsBmd8LhdMUk6ZLnXEplApKS43HmgjvBiFjEh9XGbh1MSUmAzsRupc5IlTLfUU/fvudz\nf2fychWQiPmQq93XM02ZEDB+bxTJUlhsDtB+lrPUlAQYbLHzQhHHi5GUGAeBWBjwGyKViuCkLstj\ntLvgcoHz70hWRiLzTKamJiA5KR6pLK7UfYWzQtXU1MRoq/v27eO0+qxSqXwsUmq1mrFydXV1oba2\nFjNmzIBIJMLcuXNx9OjRsApVR0ds/E+HAnuOteD9r88iKUGER26bBJvZBiSIr+gxB0OplI24cV8J\nY664Nh9zS9Lx6b56HDunweN/+g7TClW4/Zp81hiQK2HMkTJSxxwLbrrpJtx4440oLi72Uaq4eFCE\n4uabb2b+njt3Lmpra8MqVJc0RrRretCpNWJa4eUEFgazPWhsA1d0Ej6kAvf7t7nDAFm8CAaTDQnx\nIuh7AhWXS23dEAn5Qb0brHYn2rUmZCndSQ14FAWH04XGdgOylFKIhXxotUbojVY47UJ0dPTgVG07\n057t+dXqLdD3mHGqxwxlUhyrXHKZ+3O2fZHS2WmIqSt8jz4wlkoWL0Jnp4GRX8DjhfwuJ8cLcK4h\ncKyh2nD5fbBZ7LDYHe5rwFK/yQPf71wp8UI0NttCxoh55GtT93B23+7sNMDU67KYmxKHboMNDosd\nHRyz9HV3m91xMk5nwNi9nxU6JQ4uuwMGix3J8sC5kedYjaYHPIpCmlyM7i5fBdLhdDHHedp7trt0\nRhi8vjPGfqSaD4bnXNpOI/h8itmWiASsMUJ8Hg86nTHod2Z8pgwCyj0W/2M83zcA6O4ywiTgMduJ\ncYKA8XsjFfJgtNiZ+CUPujhBVL6/wbjYDByqamXdZ7Pag8ZRccFmtvk8k0IA3V2mqL2fONmpn3ji\nCaxevRpHjx5FWVkZXn31VTz99NNh282ePRtff/01AKC6uhppaWmIj3evpjidTqxduxZms/vGnDx5\nEnl5Izfxwn9OXsL7X5+FPF6Ix+8qjarWTCAMJJmpUjx82yQ8uWwqxmTKcbhGjf/56wF8tKeOcxpc\nAoELL774IhYvXozp06dj6tSpzL/+YDAYcM8998BqdfvlHz58GOPGjQvbTiJyK3T+RVv7q0wBbreX\nqvOdMFsdaO4w4EyDFk29/7Nx8nwnjtZ2BO3vXHMXWjuNqG/R48cz7WjVGNHSYYS6y4RzTe46MeF0\nFTbrjbe8sWYw4orFfi6GU8aFjvuOVWa3orxk5KpkSEnse9IUj2ubMikO+ZmJAfvzMrhPMr2HKREJ\nOCdu8OCx6IZLkiARCTAq3S3XKJbYn8wUKRIkwpDXPZT740CHV3jHIwUTSx4ffDxJUu4ZOPl+7qNC\nr/T/nngibyiKPQkg22fKxLiIMl1e7iuwTbA6c4C7pl1/iHWmRU4WqqSkJGzbtg1arRYikQgJCdwK\ny5aWlqKoqAgVFRXg8/lYv349tm7dCplMhvLycjz00ENYvnw541I4f/78fg1muHLgdBve3XkGUokA\naypKfQIXCYThyvicJKxbXoYfz6jxyd46fHWw8f9v78yjo6ryff8959RcqUpVpYaQBJIQIIRREBUI\nJEingUZc+i4oXgUXthd7Adq61BYeINznWzaKNKzuR/dFL+h9wm3TImKj3Rdsrw+7kSFBMDIISEAI\nCRkqCRmqKjWe90elKlWVmpPKUPl91spKVe0z/PbeZ9i/vX8Djn13G/+jaCSKJ2fEbNdPEIGMGDEi\nrkh/FRUV2LhxI5qamsBxHEpLS7F48WJkZWWhpKQE8+fPx9KlSyGXy1FQUID58+fHdPwOmwM8D79A\nA4DbR8NsjX1SwWp3wmp3dpstDkcwH6WbdW2wOVzeQBMef6Sb9W3evE82hwu3G00wd7hngnm+exLa\nlnYrvr/ZjOG6FK8/TE8Sdg5IohhN9pd/s1DAIUMb5zihsw4KmRBjdSqIhVy3ZMgAoO0MNe8b2j3k\nIXs4UM3UySGXCIJGOpwyWge7wwWJyL3iKhSIMH1cOlJTxGiw+N8P4cJqewg2qJ40Mg2OaLMI9xCD\nWoa6ZjNkEgFYlsHoTBUEAhZVAdH/ctKVcLp4GNTuFT9fPHnGhEECbYRCwDF+dfdNUK1KEfnl8XKX\nM0H7NfCnyXlaiEUcRhhS8E3nJI6AZcEDEVc4dSop6gNXEMMoTYGTVQONqBSql19+GXv37vULMBEt\nL774ot/3/Px87+eHH34YDz/8cMzHTCZOXazD7k+/h0QkwEuP3YWsEA6WBDEYYRgG940zYMpoLf52\nugqfnbiBvUcu4/+duYV//slo8iUiesTkyZPxu9/9DlOnTvUz+ZsxY0bE/T799NOQ5cuXL8fy5ctj\nksV3OPbtVbep+/Rx6X7bKGTxKVQefHNOxYrLxaMmTMJNT1Q/m8PpF9qZ57v7Pze1uVfvbjeauwUY\n8IUBE1N49IFEPDPuwZCKBLD0wEyp1/HpDk/ABN+Bc6Y29jFIT+fGWIYJmRRZLORC5sXqLfoyQX3u\nMCWy0xVe5cazyujUyr2TEuoUsV9gEN/Jx/zhaqRIhbjdaIp68n2EXuGnQAHuRMxdn7srZjKJMKoI\nn55JI9Zn9XZSXhqa26y4Xhv+eRVMD7cHUe57g3BRFHvtHNFslJubi1deeQVTpkyBUNh14S1ZsiTi\nvuES+548eRI7duwAx3HIzc3F66+/HkcVBi//+K4G//HXS5CIObz46GTkhAhfSRCDHZGQwwMzclA4\ncRg+/uoavj53G2+VfotjF+rwcGEOdGTiSsRBeXm533/APTiMpFAlhCB6Q6D5Sn8m94wUeS8UFpsD\nd9qCr4w5XC7UNpm9q1mBcCwT9cw/yzB9nvMmLEG6Kp7um5SXBp4Hyi7VRd64L/Gpi++APTBq3rhs\nDdrMNlSFiaZGaV1iI9hzQKOU4N6xBjS1dXRbqfNVWD1R9qJZjfMQbDXTN1y8x1wZAPIyUmGxOqBK\nEQU13Y3mGcayDHRqKVw8j6r69pjua5u95wqVrz/ahNw02B2ukLnVepOwZ7h06RLGjh0Lu90OjuPw\n1VdfQa3uyocQSaEKl9gXcIelff/992EwGPD888/j73//O4qKinpYpcHBl2duYd/nVyCXuFemSJki\nhgKqFDF+/kAB5t6diT9+8QNOnLuN8ot1WHDfcDwwPQdiESUGJqJn79693X7z+O32NcEGDdYAP6P+\nHHeG802IxA/V/uZ8vnX9McwsdLT5iQC3H01LlPlk+oLgFn/uX+8eo4taQfXNiQS4/U0GBD7ih+sf\npVwEpVwEh5PvZhZG9C4sy0Ab5PpIhMLqa67q+1mbKul2PolIAKGAhU4ljSogncdccFiaHHVNFnTY\ng0+4OF080pQSNLZ2Bf/oqVlfukYGg1qGikq3lYBIwPZqaPRwhFWofv3rX+P999/3Rkx68sknsWvX\nrqgPHiqxr1zu1pYPHDjg9cfSaDS4cyfJbLCDwPM8Dp+6if1HK6GUi/DyUjLzI4YeOelK/M8npuL7\nW63Yc+g8Pjt+A1+fq8WSOXmYPs5AM55EVNTU1GDfvn1obm4GANhsNpw6dSpmn6dEYQlIyNvXfoM8\nz4NhGNgdTlyt6R4aOV6Md6KLfua5jUVCDrnDlGAEHC6GiBDWYXXAoJbFlKizvxAKOMQ7RBuZMTgn\nT7PTFWhq6/CbJFDIRGgz2wadP+ykkWlxr9j2B9G2b6pcDIvV4U3OLBSwuGtU8MApgUr0uBwNXC7e\n793ru834HLfLT11zl8+TKEQeON9jZKcrcLmqOeh2TqcL+SPUENW29UhZH6aRe/cPXJzoy6FEWKPC\nnibmjJTY16NM1dfX4/jx4yguLu7R+QY6LhePP37xA/YfrYRaIcbax6eQMkUMWRiGQfHULPx65XQs\nmpmDdosd//7pRfx63zc98hUhhg5r166FSqXCt99+iwkTJqCpqQlvvvlmv8jiyY/jS6BC1dcTBZ6V\npPPXm9AWQ0CLSETrF+VZFWPgTrabEySanHdb3u1fold3zdBrU6UxJ5ntLfySoHb65/VG9w2YyaI4\nxPAdYOcOU2Jcthr3jjX0qylrPMgkwm654gYy0eqrBdlqTB2jg6Yz15JIyHVLLKySu00GA5NRK2Wi\n7kFBPOf1ud19r99JeWkRZVIrxEGjCAJdiZx9/bnioSfRLnuTsApV4I3fUwUr2P6NjY1YtWoV/vVf\n/xWpqaEftoMdm92Jf/vkPP77m1vI1MqxYfndFM2PIOBOaPhPRSPx+r/ch2lj9aisbsX//r+nseez\ni2huG9gz1UT/wnEcnnnmGWi1WjzxxBPYtWtXUDPA/sIcoFApZX3n/A4AV2+1oMPm6GZ62Fd4fDM8\nQ4lwA0NPRDCVomtQxzDdZ5z7Drew7sHp4FnNiJqAKo3JUqEgQhJ2Tz9qFBIY1DJ3DrNBtjo1GIlV\nCfdsHswMOX+Eyq0ER9FvaZ2BQgyarkkO372ijXIZyofKoxOka2RQ+yhzoyMkto4Gj5LflxMYMXlp\nxSpYuMS+gDvfx8qVK/HSSy9F7UQ8GKOCtbRb8VZpGb7/sQkT87RY/9S9Mdl0DsY69wZDsd5Duc46\nnQKbR+tx7qoR73xyDl+fr8XpKw14ZO5oPDxnVMIjPfUlQ7GfE4HFYkF1dTUYhkFVVRUyMjJQWxs5\nzDPg9hF+7rnnsGLFCjzxxBN+ZcePH/cGTCoqKsLq1avjks/XNwBwm0jdNUqLxlYrquojJ3eenKeF\n08XHncuqud2KlsreW5kSsGzUPg4ZaXKfFbrugxuJUAC70+VVpDyDLpZhkJOuxI+1rd4BnQdPyOm+\nwCMqz/PewdlgW4mJhVBR9nzx9F9PJ9eJ2Ij1svPeZ0G6KdCnLxxqhRjT8vV+ihMXRhEbrlf45beK\nhOdJIuBY5I9Qe0P0a5RioDq6Y+hU0qD1mTJaiw6bs09TG4RVqM6ePYs5c+Z4vzc2NmLOnDleu+yj\nR4+GPXhhYSF27tyJRx99tFtiXwB444038NRTT6GwsDBqgSNlEB9o3Kxrw/85cA6NrR24t0CPpx8Y\nB0t7Byzt0dmgR5M1PRkZivWmOrtJTxVj4/K7cezcbXz8VSX2Hb6Evx6/jn8qGonp49MH/aBmqPZz\nIli5ciXKy8vx9NNP46GHHgLHcVi0aFHE/SwWC958882Q757XX38d7777LvR6PZYtW4b58+cjLy8v\nbjlTpEJkdFokSEQCcGx0So6AY8HzXQpMPHmsejNynlDAwmGLrFCJhRxGGBS4fNPtO+F7y3r8boSd\nzuLGVrdPVf7wroBX6RoZtKmSboMhSR8GrUnXyFBZ0wKdSgqJiENVfXv8uZ8GInE8Rg0aGa7VtAQN\nnEAkjt5coYqVwHtQpRBDmyr1M831kBni/gi5QhXgxzYuRwO73RVTffMyUmHq6P5MFAo4CEP4eCWK\nsArV4cOHe3TwcIl9Z82ahUOHDuHmzZv48MMPwTAMHnzwQTzyyCM9OudAouz7Orz7l+9hc7jw8Oxc\nLJqZM+gHgwTRF7Asg6LJGbhnrB6fnfgRfyu/hd2ffY/Py6uw9P5RKMiJPScekXx4gh4BQFlZGUwm\nU1Sm42KxGG+//TbeeeedbmVVVVVQqVQwGAwAgOLiYpw8ebJHCtWEXH9fg3CvASHHwe50gmUYCDgG\nLlfXxuNy1Dh9uT5uOeJh7Ag1LnUqRtHO9nqSBHvGUb7VlYoEaDPb0GFzoCBbDblUAG2qtJtPh++5\n0pQStLTbIOzD2WadSgqNUuzN35M/Qh1hj/BkaVNiSsSaKFJkQlhbnZCKYg8jrVdJoVGI+y2h8VAl\n3KpQMFJl7pDniVB8WYbBqMzY3HNC6XWBcUGUPn5tnueg5/dYkpr3F2HvqMzMzB6fIFxi3++++67H\nxx+IOJwufPz3azh86iYkIg7PLZ6IKaN1kXckCMIPqViAR+aMwv1TMvHx36/h5IU6vFX6LSaM1GBx\nUR6y08l0bijS3t6O/fv346mnngIAlJaW4oMPPkB2djY2bdoErTZ4ZCsPLMtCJArulB4YTEmj0aCq\nqipuWUcGCcTAhdGoxEIWdqfTG3rY19ch3EA2XSNDbZO/OZzvoETAsmBZxhsBLBy+pn2+k4DRjus8\nSohnvOQ74zwsTYb6O2Z3clOWicqXeHSW26ciWF6cRBKYDLUnDJQAVLnDlFCniKGJ05GflKm+R8Cx\nGJ+jgShKs3etSgqJWIDszFQ0NobOH9ZXeCZYAglnOjo+V+1NkJ6plaP1pluhCmb2G6vCmSjozuhl\nGu5Y8MZ/nsHhUzdhUEux4clppEwRRA/RpkrxzIPjsWnFNBRkq3H+WhP+13+U498+Od9tEEkkP5s2\nbfL6516/fh3bt2/H2rVrUVhY2OsJ4nvqLyII8rLnwilGaTIIWNab7DqaMf2kkWndfGCkIgEmj+pa\nGUuRCjF1jM6bSykcvkkwfRU6SYiBUSDefYIsUUnFAkwflx7X7Dl57vQcAcdCq5KStcwgQyETxeRH\nnCIVDpiAIelpMm/kQQAQd5rihXu0+kUn9LlWg61SS0QC5GWkYnJe+Im0RJPw1MFbtmxBRUUFGIbB\n+vXrMXHiRG+ZzWbDq6++isrKSnz00UeJFiXhnL5Uj/f+6xIsVgemjzdg+bx8SKN8AREEEZmcdCV+\n9c9TcOHHJnz8VSXKL9Xj9OV6TB+XjgcLc/otxDLRt1RVVWH79u0A3Il8FyxYgJkzZwIAPvvssx4d\nW6/Xo6Ghwfu9rq4Oer0+qn2Viu5Kgk6n6KbsCCRC3A6Ry6lglB5j83R+AQCU1W1QK8XQ6RRQKrry\nSbEsgxkTh0HAsWhpt0LZ6F7BuXusHimd5jNZLVa0mmxQKtz7KxTd81EJBCwcji7fqAydHGhw53XR\n6xRQGt2TFlkZqRidk4bvPDPHuhRUN3SfAVerZdDpFKhp7gDPcVCliP2Cz8SLg2FhbLP1+DgDnWSu\nW29C7RSZAdNGAgEu/dgEADCkyVDXaIZYxIWVz/Osy8vWoLrJ/WxLVcnQanWvsrMM0yvPld4ioaP9\n8vJy3LhxA6WlpaisrMSGDRtQWlrqLd+6dSsmTZqEysrKRIqRcNotdvzxiys4eaEOIiGLny8sQOHE\n9IGTb4IgkozxORqMy1bjzJUG/PnYdZy4UIuTF2tx3zgDHpiRE9I5lkgOfIMblZWVYcmSJd7vPX3u\nZmZmwmQyoaamBnq9HkePHsVvfvObqPZtDZK0tqnJBGdAIIl2i927bf5wNexOF651Jt4NFrBkbJYS\nLMOgoaEN2hQhrnXmaRs7Qo3mzoSW5g6H95gWkxWWzuS4bW0daDVZ4bI70NAgCSqjRChAh70rxHum\nRurdrqmp3fu5pVkEQar7GOoUMawdtqDHE3NAg1SA5hYz2sw2ME4nGhraehyQpanZ7D1fsgZ2GYpB\na+KB2ikyA6mNjHcs3ntXwjFobbNAyHFh5ctLT4Hd4YLR2A6zyQqHy4VGIeM9zl2jtL1Sv95SxhKq\nUJ04ccLrNJyXl4fW1laYTCbI5e7BzksvvYSmpiYcPHgwkWIklDNXGvD+kctoNdmQO0yBf1k0jvJL\nEUQfwDAM7s7XY8oYHc5eacCfj/2IkxfqcPJCHSbnpeFn07MxOiuVJjaSEKfTicbGRphMJpw9exY7\nduwA4PatMpsjm4BWVFRg48aNaGpqAsdxKC0txeLFi5GVlYWSkhJs3rzZ6/+7aNEiZGdnxy1rsMvP\n1+Zf3Zl3SSxgQ0al8jXP0qtl6LA5UdNoglzSlX5DJhFguF6BVLm/b5gn2IPdETo6n4BjALvbnGZc\njsYvmp6fD1WnX9d9Be6AHU2t4fPEpXZG9FMGJgyNF7qXCWJQ4ms6nSIVoP4Ouj2rAhELOa+ZY9eK\nfVd5YNLi/iah0hiNRkyYMMH7Xa1Ww2g0ehUqqXTwht5sbOnAn778AacvN0DAsXhkTh7m3Tu8V51Y\nCYKIDOujWFX8YMR/nbqJispGVFQ2YmSGEj+ZmoVpY/XdoogRg5eVK1di4cKF6OjowLPPPovU1FR0\ndHTg8ccfx9KlSyPuP3nyZHz66achy6dNm+ZnTRErE3LTvLmjgvmqBHOiTo1B6RhhUGC4PqXbZEGw\nlVlR53VvDROMQiISoL3DDpZhvGbqE3LTIBSwfn4Yns+e84by0fAMejJ0cijlIih6KaGxVinBnTYr\nmfYSxCDDVxHSqaQQCjgo5dE/FzRKMeqazX7+nQONPpUsGZLB2exOHC67ib+euAGbw4W8TCV+vrCA\nVqUIop9hGQZTxugwZYwOP9y6g8OnbuLbH4z495qLKP3yBxRNzkDx5AxoVYN3IodwU1xcjGPHjsFq\ntSIlxR09TSKR4JVXXsGsWbP6WbrOFZ9OgukcveEsHu3Kq14tRU2jCaOCRBv0HivIXIMn+bzveztQ\n7pD16NyFZRgoI8xCxwLLMhgzXNVrxyMIom/wrHorZSIwDONdmY+WbIMCGoUYSrkINQ2mARmgJqEK\nlV6v90ZiAoD6+nrodD2LeNdfjmdOpwtfnb2F/zxyGfVNZqgVYqxZNA5zpg5PeCSVgeBs1x8MxXpT\nnXvvmDOnDEdtowl/Pf4j/nbqBv5ywv03aZQWP7lnOGZOzIg6alki5CN6hlAohFDoP8PZn8qURun2\nLcodpvQzRQmm+HAsA5GAg0bZS6ZwYZCI3FH1PCikIrRZbJAIBRALWRg0MjS3hzbd85U/cGXNt2r3\nFRhQf8eCG7VtGKalFSSCILpQpYhRMEINuTS+1WqWZbyr+HeN7t9ofqFI6GiisLAQO3fuxKOP5HWb\n0AAAD89JREFUPooLFy7AYDD4ORMD7tmvWFau+trBzuXiUfZ9Hf789Y+oazJDwDFYcO8IPFiYA6lY\nkPAY/wPJqbAvGYr1pjr3PhyAB6ePwPy7M1H2fT2+Pncb31014rurRvzho+8wKS8N94zVY2JeWkwh\naXvCUO3nZGfiKC0MSlE3BSrYQhLDMJg6pn/SaeSPUKHdYofKx8TQ2OKOOBhpcjDQfNH3G8MwMKhl\nMKhJmSIIojuxmDWHY6D6RSdUoZoyZQrGjx+Pxx57DBzHYdOmTTh48CAUCgVKSkrw1FNPoba2Frdv\n38aDDz6IFStWYPHixYkUKWosVgeOnbuN//7mFuqbLeBYBnPuysADM3KQFmdCPIIg+geRkMOsScMw\na9Iw1N+x4Pi52zh5sQ7ll+pRfqkeIqE7ceKkvDRMDJLThyCiIdiLfqDl+xFwrJ8yBQBOl3tSM1KC\nzECFi3yGCYIg3CTc3sUTKclDfn6+9/N7772X6NPHBM/zuFnXjmPnbuPrc7fRYXNCwLEomjwMi2bk\nkO8FQSQBepUUD88eiYdm5aKqvr0zl1UDzv5gxNkf3CbKWTo5xo5QI3+ECmOGq6CQ9Z4fCDG0GKiz\nqb64olWoAoplEgGydCkRo3URBEEkOwM3XEYfUttkRvn3dTh5sQ63G90hd9UKMRZOz0bRXRlQ0mCK\nIJIOhmEwwqDACIMCi4vzUNdkxnfXGnGushGXq+7gVoMJX3xzCwBg0MiQO0yB3HQlcoYpkKVLoaTd\nRFQMAn0KEjGHNgtC+jdkalPQ1NoBAdd9RSpLl5Jo8QiCIAY8CR8RbNmyBRUVFWAYBuvXr8fEiRO9\nZcePH8eOHTvAcRyKioqwevXqRIsDwG3O98OtFpzrHDzV33EnCRNwLKbl6zB9fDom5aUFfXkQBJGc\nGDQy/FQjw0+nDYfd4cL12624fLMZV6ru4NrtNm+OKw8apRiZ2hSka2TQq6XQqaTQqSTQKCQQi/rG\nH4uIn3Dvprlz5yIjIwMM4867tG3bNuj1+rjOM9BM/oKRk66AQiqELoQVxnB9CobrSXEiCIIIRUIV\nqvLycty4cQOlpaWorKzEhg0b/HJ7vP7663j33Xeh1+uxbNkyzJ8/H3l5eQmRpbK6BV+fr8XVWy2o\nbmj3hlyUiDhMHaPDXaO0mDpGN6Bj3BME0TcIBSzGDFd5QzS7eB71zRZcr2nFjbo2VBtNqG5od0/K\nXGvstr9ULIBaIUaqXIQUqRApMiFSJEJIxQLotXI4bA6IhRxEQg4iAQth5x/HsRByLDiWAccxYBkG\nAo4Bx7JgmMFhPjYYiPRuYhgGu3fvhkQSvy9d7jAl2sz2hEeB7Q04loWegkkQBEHETUK1hxMnTqCk\npAQAkJeXh9bWVphMJsjlclRVVUGlUsFgcGdcLy4uxsmTJxOmUP3py6u4Wt0CUedAaVRWKsbnaDAq\nK5VWogiCCAvLMEjXyJCukWHGhK4Q1O0WO+qbLai/Y0ZDswUNLR2402ZFc7sVd9qsqDGaelUOjmU6\nlS0WAo6BwOe/kGMhFLIQCbhOZY11Z5oXcZCI3L9JRAJIRJ3/xZz3s1Tk3k4s5IbE8zDcuwmIPfps\nMNwR73osKkEQBDEISKhCZTQaMWHCBO93tVoNo9EIuVwOo9EIjUbjLdNoNKiqqkqYLKsenoA77VYM\n16cMiQEDQRCJJ0UqRIpUiJEZyqDlDqcLJosdbRY7TBY7LFYnhGIB6oztsNqdsNldsHX+d7hccDhd\ncDh5OJ0uOF2898/l/eyC08m7t/HZ3mK1w+50wW53wdVDRUDAuXMkiYSszwoa511FE3IsuE4ljmMZ\nsCwDQed/ju36bYQhBfcWGHokS6II927ysHnzZty6dQvTpk3rFlyJIAiCIHzpU/u2cDN+PZ0NjIRa\nIY45MzNBEERPEHAsUlPEfvk3Ep2HyuF0wWZ3dSpsTljtTnTYPH+OkJ+ttq5tPYqe1e5Em9kOh9MF\nu8MVkxwpUiHuGasfFGaKge+f559/HrNnz4ZKpcLq1avx+eefY968ef0kHUEQBDHQSahCpdfrYTQa\nvd/r6+uh0+m8ZQ0NDd6yurq6qJx+h0KCyECGYp2BoVlvqvPQYCjWeSAR7t0EAA899JD3c1FREa5c\nuRKVQkX9Ghlqo8hQG0UHtVNkqI36joTavhUWFuLIkSMAgAsXLsBgMEAmczu+ZmZmwmQyoaamBg6H\nA0ePHsWsWbMSKQ5BEARBhH03tbe3Y9myZbBarQCA06dPY/To0f0mK0EQBDHwYfgE29pt374dZWVl\n4DgOmzZtwsWLF6FQKFBSUoLTp09j27ZtAIAFCxZgxYoViRSFIAiCIACEfzft3bsXBw4cgFwuR0FB\nATZu3Njf4hIEQRADmIQrVARBEARBEARBEMkKhbsjCIIgCIIgCIKIE1KoCIIgCIIgCIIg4oQUKoIg\nCIIgCIIgiDjp0zxUsbBlyxZUVFSAYRisX78eEydO9JbNnTsXGRkZYBgGDMNg27ZtUYVcH+hcunQJ\nzz33HFasWIEnnnjCr+z48ePYsWMHOI5DUVERVq9e3U9S9i7h6pys/bx161acOXMGTqcTzzzzDH76\n0596y5K1n8PVORn7uaOjA+vWrUNjYyNsNhtWrVqFOXPmeMuTtZ8j1TsZ+zrcu2ooEnivT5w4Eb/6\n1a/A8zx0Oh22bt0KoVCIQ4cO4f333wfHcXjkkUewZMmS/ha9T7FarVi0aBHWrFmD6dOnUxsF4dCh\nQ9izZw8EAgF++ctfIj8/n9rJB7PZjLVr16KlpQV2ux1r1qzBqFGjqI06CRxf1tbWRt02DocD69at\nQ01NDTiOw5YtW5CVlRX+hPwApKysjP/FL37B8zzPX716lV+6dKlf+dy5c3mLxdIfoiUMs9nMr1ix\ngt+8eTO/b9++buULFy7ka2treZfLxT/++OP81atX+0HK3iVSnZOxn0+ePMmvXLmS53meb25u5ufM\nmeNXnoz9HKnOydjPf/nLX/jdu3fzPM/z1dXV/Lx58/zKk7GfeT5yvZOtryO9q4Yawe71devW8YcP\nH+Z5nue3b9/Of/DBB7zZbObnz5/Pt7e38x0dHfyiRYv4lpaW/hS9z9m+fTu/ZMkS/uDBg/y6dev4\nI0eOeH+nNnJfP/PmzePNZjPf0NDAv/rqq9ROAezbt4/fvn07z/M8X1dXxy9YsIDut06CjS9juX4O\nHjzIv/baazzP8/yxY8f4F154IeI5B6TJ34kTJ1BSUgIAyMvLQ2trK0wmk7ec5/lume0HO2KxGG+/\n/Ta0Wm23sqqqKqhUKhgMBjAMg+LiYpw8ebIfpOxdwtUZSM5+vueee/Db3/4WAKBUKmGxWLx1TNZ+\nDldnIDn7eeHChXj66acBADU1NRg2bJi3LFn7GQhfbyD5+jrSu2qoEXivm81mlJeXY+7cuQCA+++/\nH8ePH0dFRQUmTZoEuVwOsViMqVOn4syZM/0pep9y7do1XL9+HcXFxeB5HuXl5bj//vsBUBt5OH78\nOAoLCyGVSqHVavHaa6+hrKyM2skHjUaD5uZmAEBLSws0Gg3db50EG19Ge/188803fs/2mTNnRtVe\nA9Lkz2g0YsKECd7varUaRqMRcrnc+9vmzZtx69YtTJs2DS+++GJ/iNmrsCwLkUgUtMxoNEKj0Xi/\nazQaVFVV9ZVoCSNcnT0kYz9LpVIAwP79+1FcXAyGYQAkdz+HqrOHZOtnD4899hjq6+uxa9cu72/J\n2s++BKu3h2Tq62jeVUMJ33v9o48+wpw5c3Ds2DEIhUIAQFpaGurr69HY2NjtHmhoaOgXmfuDrVu3\nYtOmTfj4448BABaLhdoogOrqalgsFqxatQptbW1Ys2YNOjo6qJ18+NnPfoaDBw9i3rx5aGtrw9tv\nv41Vq1ZRGyH4+DKW+8z3Pc0wDFiWhcPhgEAQWm0akApVIIEzms8//zxmz54NlUqF1atX4/PPP8e8\nefP6Sbq+J5lmeMORzP38xRdf4OOPP8aePXtCbpNs/Ryqzsncz6Wlpbh06RJefvllHDp0KOg2ydbP\nQOh6J3NfA8nZl/HwxRdf4MCBA9izZ49f/4Zqn6HUbp988gnuueceZGRkBC2nNnLD8zzu3LmD3//+\n96iursaTTz7ZzbIh1H5DhUOHDiE9PR3vvPMOLl++jA0bNviVUxuFJta2cblcEY85IE3+9Ho9jEaj\n93t9fT10Op33+0MPPQSNRgOWZVFUVIQrV670h5h9hl6v95tNqKurG/SO3NGQrP38j3/8A++88w52\n796NlJQU7+/J3M+h6gwkZz+fP38et2/fBgCMHTsWTqcTTU1NAJK7n8PVG0i+vo70rhqKBN7rcrkc\nNpsNgPtaNxgMSX0PROKrr77C4cOHsXTpUnz00Uf4wx/+AJlMRm0UgFarxZQpU8CyLIYPHw65XE7X\nUgBnzpzB7NmzAQD5+fmoq6uDVCqlNgpBtNeP53fPs93hcABA2NUpYIAqVIWFhThy5AgA4MKFCzAY\nDJDJZACA9vZ2LFu2DFarFQBw+vRpjB49ut9k7QsyMzNhMplQU1MDh8OBo0ePYtasWf0tVkJJ1n5u\nb2/HW2+9hV27dkGhUPiVJWs/h6tzsvbz6dOn8d577wFwm4VZLBav+UCy9jMQvt7J2Nfh3lVDkWD3\n+owZM7xtdOTIEcyePRuTJk3C+fPn0d7eDpPJhLNnz+Luu+/uT9H7jB07dmD//v3405/+hCVLlmDN\nmjWYMWMGDh8+DIDayENhYSFOnToFnufR3NwMs9lM7RRAdnY2vv32WwBuE0mZTIaZM2dSG4UglmdR\nYWGhtx2//PJL3HfffRGPz/ADdO1v+/btKCsrA8dx2LRpEy5evAiFQoGSkhLs3bsXBw4cgFwuR0FB\nATZu3Njf4vaYiooKbNy4EU1NTeA4DqmpqVi8eDGysrJQUlKC06dPY9u2bQCABQsWYMWKFf0rcC8Q\nqc7J2M8ffvghdu7ciZycHPA8D4ZhMH36dIwZMyZp+zlSnZOxn61WK9avX4/a2lpYrVY8++yzaG5u\n9j7DkrGfgcj1Tsa+DnxX5efn97dI/Uawe/3NN9/Ehg0bYLPZkJGRgS1btoDjOHz++efYvXs3WJbF\n8uXL8cADD/S3+H3Ozp07kZWVhVmzZuGVV16hNgrgww8/xP79+8EwDFavXo0JEyZQO/lgNpuxfv16\nNDY2wul04oUXXkBubi7Wrl075Nso2Phyz549WLduXVRt43K5sGHDBty4cQNisRhvvPEGDAZD2HMO\nWIWKIAiCIAiCIAhioDMgTf4IgiAIgiAIgiAGA6RQEQRBEARBEARBxAkpVARBEARBEARBEHFCChVB\nEARBEARBEESckEJFEARBEARBEAQRJ6RQEQRBEARBEARBxAkpVARBEARBEARBEHFCChVBEARBEARB\nEESc/H/GaTioXJAE1QAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fabeadb8910>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.traceplot(trace, varnames=['alpha']);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Indeed, we see that there are (on average) about ten to fifteen components used by this model."
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"n_components_used = np.apply_along_axis(lambda x: np.unique(x).size, 1, trace['component'])"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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znMQW0YWN/i5sVvb35LCrLJnnpPNpi50zzwEAYCMEOwAANkKwAwBgIwQ7AAA2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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fabbf9d59d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"bins = np.arange(n_components_used.min(), n_components_used.max() + 1)\n",
"ax.hist(n_components_used + 1, bins=bins, normed=True, lw=0, alpha=0.75);\n",
"\n",
"ax.set_xticks(bins + 0.5);\n",
"ax.set_xticklabels(bins);\n",
"ax.set_xlim(bins.min(), bins.max() + 1);\n",
"ax.set_xlabel('Number of mixture components used');\n",
"\n",
"ax.set_ylabel('Posterior probability');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now calculate and plot the fitted density estimate."
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"x_plot = np.arange(250)"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"post_pmf_contribs = sp.stats.poisson.pmf(np.atleast_3d(x_plot),\n",
" trace['mu'][:, np.newaxis, :])\n",
"post_pmfs = (trace['beta'][:, np.newaxis, :] * post_pmf_contribs).sum(axis=-1)\n",
"\n",
"post_pmf_low, post_pmf_high = np.percentile(post_pmfs, [2.5, 97.5], axis=0)"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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TRN6pO33fC049RI4wFlAVttA0jVQqVSTqTp95QRAEQfAbw17UnTXu\n4vC7va+qKuKK+s6kHU5XmK5Td1rEep06SsMgRJAMVVVVFURdnLogCILgT4a9qOdyeUHOi613Els0\nGnXX1lNJ251rGB6nXgcUO3UAQ4XRyboz1Z2BMfb3iFMXBEEQ/MmwF/VUyp6i5nXqYIv6uHETXaee\nSvQAtlN3x65W50XdSmNREHUnWS4SsWeqp9OFSW25nCTKCYIgCP5k2Iu6I7jFiXI2oVCISH5SWyrR\nA5aFwiIejxMOV6EH7GN1MragKwXgJstVVVXl69p73XNalikheEEQBMGX+EDU7TaupYlyDlVOE5lE\nLwrvMBdb7LEsNLKuS4dipw7Q1dXt7rNFXULwgiAIgv/wgaj37dQBIvnRqulkLwrT7fvuzFrXyaAA\nUxVE3cj/XBgI0+PuU4qicLwgCIIg+IVhL+qZTPGaeqlTD1c7Tr0HhUkqlcKyLKrzTt3NfPc4dTM/\nnK4q79S94XdN093vFARBEAQ/4QNRt0W5OFGuQFXeqafiPWgYxGJ2H/jqqL3dyXzPqXJRj+SduvMZ\nsOvfc7nhv6Yej8fYvHnj3r4MQRAEYRgx7OepO665NPxumiaapqHpIcLhMOmEHX7v6OgAoGFME2AP\ncoFip47SMNHc8LuTLe8w3NfUd+xoZ/PmjZimRSRSTVNT896+JEEQBGEYMOyduuPQS8PvTlMaE43q\n6mpSyR6U5RH1prEAaJb9Oe+auv25gCvqzqhWB+cFYjiSSCTYtGkjSil0XWPr1s1uNEMQBEHYt/GB\nqFcOvztu2kK3680TvWDl2LFjBwBjGm1R17GPMygO2/cn6sO1/7tlWWzYsBZNU0XbP/hg0166IkEQ\nBGE44QNRr+zUnXVvC41oNIqRy5JO9NDR0YGu69TVNwK2U7ewxd+LpQqinkqlivYN1zr1lpZtbomf\nl66unWVLCIIgCMK+x7AXdaeFa/mauv27qXQmTJgAwLbN79HR0UFDQwNKt8PtGjk7MU4Vu1uvUy8X\n9eEZft+5sxNNK/8r0zSNbdu27IUrEgRBEIYTw17US526I+oFp64zefJkANasWkE6naaxsREzf2uu\nqJfQn6gPx+z3eDxOMtm3G+/u7qro4gVBEIR9h2Ev6o5DLw2/F9bUNSZMmICm66x5+w0AGhsb7XC7\nZaJhYKpg2XlNpRMO253l0um0m3jnPfdwoqOjDV3X+9yvaRqdnTv24BUJgiAIww3fiXohUa7g1EOh\nEGPHH+CKse3UdbR8klxfTj0QsP833MevWpZFd/fOfo9RShXV2wuCIAj7HsNe1B2hzuVy6Lrurik7\nwmvmE+AmTj7Y/UxjYyOWGljUgT5mqptFzn1vE4v1ui81/ZFIxNyxtIIgCMK+hw9E3RbbbDabd+mq\naLul7FvYf/JU9zOuU7ecZLpdE/XhNqmtp6e739C7Qy6XIxbrHfA4QRAEYWTiG1HP5XIEAgE3id1x\n0k6p2oT9DwClqK2tJRwOYxWF3yutqReLupNl7zAYZ7ynGGy5mq7rA4bpBUEQhJHLsG8T64STDcPI\ni7oGmG6DGCf8Xh0JM/PkM6it1vPbAwRIuT+X4mwLh8OYpkkymWDUqHrATjpLp9NUV1cP6b0Nlv6y\n3kuJxeJDeCWCIAjCcMZXoh4Oh9E0hWF4E+XsYIPC4FMnnkwAWwBNdPR8+N0YIPwO9vjV/fYbD9ii\nns0Oj0lt6XSaTCZDIDBw+B0gkYhjGMagwvWCIAjCyGJQ4ff58+czZ84czj33XN56662ifcuWLeOc\nc85hzpw5PPTQQ+72d999l1NPPZVf/OIX7rYbb7yRz33uc1x44YVceOGF/M///M+A3+0VdU3TUPn4\ne2n4XWGiKKyDmwT6Db/bQ12UK+o9Pd1Fu4fLmnp39050fVdWSSx27uwcsusRBEEQhi8DOvUVK1aw\nadMmFi9ezLp167j55ptZvHixu3/evHk88cQTNDc3c/7553P66aczfvx47rrrLo4//viy81177bXM\nnDlz0BfoFXVd110xN4x8drpSWCiUZaBwhB5AQyM/zKWP2/Q2oOnt7SnaN1yGuiQSCfdFZjBomkZv\nbw+NjU1DeFWCIAjCcGRAC7h8+XJmzZoFwNSpU+np6SEet9dtt2zZQn19PWPHjkUpxcyZM3nllVcI\nh8M8+uijNDY2fugLdETdNE10XXfF1jt0xa5JN4qcOpqGZuUq9n13z10k6sVZ48PFqScSu75GLhnw\ngiAI+yYDirrTS91h9OjR7njT0n0NDQ20tbWhaRqhUKjsXABPPfUUX/nKV7jmmmvo6uoa8AIty3Hm\nxevEXidtoaMw0CiuLe+r77uDSaGrXLmo732nbpomqVRy4ANLyGRSu5RcJwiCIIwMdjlRrr/mJgM1\nPvn85z9PfX09hx56KI899hgPPvggt95664DfaZomlmUVibppGkSjYXQ9iWXoaFbxTHFd19ByOUwV\n6nNN2jKCrlNPJOJEo2F3X3V1kKam2gGvbSjp7u4mEgm6rXEHTxjLStGUnyk/GPb2ve4LyDMeeuQZ\n7xnkOQ9fBlSL5uZm15kDtLW10dTU5O5rb29397W2ttLc3NznuY499lj351NOOYU77rhjwAu0LMsN\nhXtFPZPJEI+n7e5vlkYQ7wuFwsjl0DDIEiisv5dgeMLvsViceLyQ8Z7LKdrb924Ye9u27aTTBun0\nri8FbN3aRnV1w8AHYv8HurfvdaQjz3jokWe8Z5DnPPR8mJemAcPvxx9/PC+88AIAq1evZuzYsW79\n9oQJE4jH42zbto1cLsfSpUv51Kc+1ee5rrzySt577z3ATsA75JBDBrzAvkTdMAw3MmCpklnpqH5b\nxDqYnpnqpeHq4RB+T6X++RB66eQ5QRAEYeQzoFOfMWMG06dPZ86cOei6zm233cZzzz1HbW0ts2bN\n4vbbb+fqq68G4Mwzz2Ty5MmsXLmSW265hc7OTnRdZ/HixTz11FOcd9553HjjjUSjUaLRKHfeeeeA\nF+gV9dJZ4nZCmF4k3Ao7+31Qoo5X1IvXrodD9nsy2bcwt7Rso6OjnVQqxeTJB9LUVBwhyWQyUq8u\nCIKwjzGoxVpHtB2mTZvm/nzMMccUlbgBHH300fzud78rO88nPvEJnn322V26QMuiolMHp7a8oawO\n3UJ5+r5XqFF3j9P7FHXDsNfxd6WcbHfiJMlVygeIxWKsX7/W/X3jxvU0NIwpeT4WsVgPo0aN3gNX\nKwiCIAwHhn3vd6gcfgdIp20nW94xTkMfoEbd3lfIfi8PV5t71a3H471A5cTD7du3AnDYYUcwceL+\nZLMZWlq2FR2j6zrxuGTAC4Ig7EsMe1G3LMttOFMu6nbGe6lw22vqtqgblbrJ5TFVgFAohFKqTNQt\ni7IhL3uS3t7eiqHzTCZDR0cbVVUR6utHM378/uh6gK1bt5S9hPwz5XCCIAiCfxn2og59h98zGTtb\nvbwNrELPl7gZqnK9POTr25VyJ7V50TSNVGrv9X8vXQ5waG3djmVZjBs3AaUUgUCA8eMnkMvl2LGj\nvehYJ5IhCIIg7BuMDFFXpU7d2yK2glN3utTlO805ou5EBMAZ6pIp/+weoq/M946ONjRNp7m5UIM+\nZozdua+7u7iZTyqVGrB3gCAIgjByGPai3ldJG+RnnlumK9yOfFlo6FYWC1UcmrdssdY0Pf9rsaiX\ntobdW2VtdpJceZQgm82QTCapq6srehaRSDXBYIju7q4iETcMQ9y6IAjCPsSwF3UoDG/RNK1M2HWy\n5WvqSkMnY6+ne7LXNU2jujrqlsZZaFjYM9Wz2azr/Avfu3f6v9uleuUOu6fHHjpTW1tXtF0pxahR\no8hmsyQSBYev61rZoBpBEARh5OILUXeGt+i6jq4HsKvRbXQy+UltBSzLTpQrDb1ruo4ClJb/fF7w\nCzPVi8ev7kr2++4Mc/f29lRMknMEuq5uVNk+p3TNG4JXSvW5Ni8IgiCMPHwh6t7weyAQKJrPolkZ\nsEy81eQWCgUYJTXqWl7MldI8x2oeUS9ek96V8PvmzRtpa2sd9PH90VfWek9PN0opamrKWwiOGlUP\n2PPXvUj4XRAEYd9hlwe67A2c8HtB1JXrjHWybve4Ukw8me8W7lq6pik7uq3sF4BIJAJAV1exIA42\n/G5ZFt3dO+ns7KCqqqqikx4MC375BgCxeNydTlf4EpPxZoxotKaii6+qqqKqqoqenu6ipjnSLlYQ\nBGHfYVg7dScbvd/wu5VxRb2091uxUy9MedM0HSsfsLfQPaJe7NQHG37v7NxBLpdDKcW6dWt4++23\n+OCDzYP6bCmWZWGZ5S8TIeJYllW2nu6lrm4UhmEUzWB32sUKgiAII59hLeqOqJaH34vX1J2WsA7O\nCrvhdepKoeU/pynNfQGw0FxRdxLRHMwK4lqJzs4ON/lOKbvUrq2tpWyNfjD0JcAhKwZUXk93iEZr\nAIjH456tVj7xThAEQRjp+FrUlVJoVqXwe74O3ePUNc86ulK45zA9/d97e4vFbzBOPZlMVsww1zSN\nLVs2FNW+DwbDMIoy9h0Clp3V7l1Pb2trZdmyl3jjjRWkUklX1L1OXdf1ot8FQRCEkYtPRL18TR0g\nFArZTr1E1DXs470tYksnvDnJct7we6mjdYa69EUymWDNmnfKzu2QzWbZunXXwvB9vQQErRS6rhMK\n2dGH3t5e1q61x9imUkneeGOF29Y2Ho8VfVbW1QVBEPYNhrWoOw7dCYM7depOFnsgEEQnh24V92hX\nrqgXwu9uGVvJ75bSPKJe6mj7HupiGAZr1rzbrxNXStHe3r5LGehGpZC/ZaKToro6ilIK0zRZvXol\nAPX1o9119s2bNxIOVxGPx4teRqQHvCAIwr7BsBb1bNYWa0dYC07dvuxAwE7eD1AsWgrDbgHrhNyt\n4vA7VA6/lzrc/oa6bN++dVAJaJqm2LJlcG7dTpIrjwwESKOwXbxhGLS3t2KaJsFgkEMPnc706UcB\nkEgkiEQi5HJZMplCi1spaxMEQdg3GNai7oimd01d1wOuU7cz4SFsFSekaeSKQu+WJ/PdoSDqAdep\ne7uxgTPUpdzlmqbJjh3tg5613tPTlZ/93j+5SnXxlkWtYY9ajcdjrFnzHtu22b/vt9/4fNtbzU2g\nc7riedfRDSMnwi4IgrAPMKxF3XHo3tGrXqdeV1dHQjVge/NCyb2GWTSdTVGoUXe35c9hEnCdeiVR\nr9SRbfv2bbuUAKdpGps3bxyw65xhmGV1edVWO1XYLwSRSDWdnR0kk/Z1jhs3wT3ugAOm5O/Bvl5v\n1EHTdGkXKwiCsA/gC1Evd+pO+ZiiWz+QVv1o2rXDi1rFGoTdn5XSyhLKNU0DCyzs81VVVVUU8EpO\nvbu7c9Au3SGbzbB165Z+jykrobMsqs12976mTTuMQMCOQFRVVbnLD2BnxQeDIZzMf29ZW6V58YIg\nCMLIw3eiHgjorqA6WfGW0rG0wqS2XrUfvdp49zylSXIAuqZhYWHkx7ZWGr8K5ZnjhmH8UwJpJ821\n9lsmZxrF3x2yYgRJYaFhohOJVLsvJx98sJXNm4vX6uvr693vKs0PSKf33mx4QRAEYc8wrEW90pp6\nIBBwQ+l9NYeJ6ROwPDPWS5PkIO/eUVj5sH0kEiGZTJaJbjqdLgqbl/aH31VaWrZV3J7LZctaw1Zb\n7fa1YpIjkhfrOL/97W9ZtOhBLr30G/z+98+719fYWJixnkoli15QMhlx6oIgCCOdYS3qpU7dLmkL\noOta0fYClUPilULlStmHOwl1kUiEbDZbFoIvnUkei/X2WZc+EEopOjs7Kq6t79y5s+j6NStLlbWT\nLGEUkFVV9Pb28Mwzz/CPf/yD5uZmqqqqWLjwPn7zm2cBGDXKTpZzzu+NKIhTFwRBGPkMa1Gv5NSV\nUq6olot65UQ01YcIK5Q7nrWvoS66rhW1jy1NpttVcrkcO3a0l23v6ekueicJWb15Ma+2P6civPrq\nK6xdu5YpU6Zw8cUXc9ttd1BdHeVXv3qaTCaDpmmEw4VcAiehDuwMeKdEUBAEQRiZ+E7UoZDJXjbJ\nDChz61Z5Nzn3SKUgv8/JgC8tPbNnkify32cVCeU/g6ZptLa2FLl1y7KIx4u72YWtnvzl2/eaI8zz\nz/8OgHPO+VJ+GULx2c9+ls7OTpYu/SsAtbWF3vDeqINSmvSAFwRBGOEMa1EvDb872d6F8LtH1PPr\nx1aJqFtY6P2Jeh7HqVcawuLUfsdivYMe8tIf6XSqKBO+t7enzEWHrF5MdLc7XntbO6tXr2bixImc\neOJJRKM1xGK9nHXWF9A0jSVL/gPLsmhqanbPkUoVXkDs8rwP90IiCIIgDG+GtagXnLpTp26LeuVE\nOTMv5yXtYFF9ht+9hxYmtZWLeiqVxDAM2tpaKs4y31U0TaO9vdXNUN+5s7PovLqVJkCGjKolYKWx\ngLf+/kcATjjhRILBILW1tViWRTQaZebMk9iwYT0rV/4fo0bVu+cpzQ9wXk4EQRCEkYlPRN127IGA\nnv8zULQfQMd2uhbl7WD7qij3Tntzwu/d3eVNWrLZLG+++cagusINFqUUa9a8R0dHO7FY8XeGLDtM\nnla16KTJmUE2vvsKkUiEo48+GsDt997b28Ppp38GgOXLl/HbFT1uI57u3jhLXi3878kXt++26xcE\nQRCGH8Na1PsKvzsNWLxOXcfudV4m6hVq1N19FETdceq9veXCrWma/XKwiw1nBsZi06YNpFLFDtpZ\nT89SjU6OD1raifd2c8ghh9DQMAbwinovRxxxJOFwmL/97WWajTfdJQgNA+WZNb+rY2AFQRAEfzGs\nRd0RodJEObtzWvGauoZ9TKmoV6pRd1GVRD3W9/FDgK5rbo4AAJZFyOrFIOiK83vvvgvAtGnTaGxs\nAiAcriIQCNLb20Mmk+aAAw6gra2NnV29BCiszwcolLWZljmoITSCIAiCPxnWol6a/e449VDIcepe\nUbeFzKSkx3t/Tj0v6ppWGL9a2oltT6ORRSdHRkUJYDv4Ne++ha4HmDp1KtXVUcC+9traOjKZNBs3\nrmfq1KkA/N/6OFki7vkCVkHUFZBI7N37EwRBEIYO34i6M40MCk7dG37X8mFmq2zEat+3qCBf8uYd\nv1o6U33PErTsDPWsqkYnTWdnJzvatjJlyoFUV1cXlefV1tYCdnLfjBkzANi85h90q/3dY7yijlIV\nZsYLgiAIIwXfiLrTeAYKjt1b663c8LvHqVt9l7NBoSmNrnud+t4t+wpatuhmiRKw0qxbtw6AQw45\nhHC4quhYZ10d4KijZjBx4kS2rnuTlFXltuFxku4cJANeEARh5OILUTdNMy/q9uU6btU0C6Kuk0+q\n8+f/1PkAACAASURBVIxgBdVvCZqm7KEumqYTCoWGRS13EI9Tt9Js2rQJgAMPPNANvTs4CYOaplFf\nP5qPfvRjZDNJOravd9vfBigua5O56oIgCCOXYS3qmWwh+90WZ0UsZRJL5RvNeDrKVXLqTtZ6Xzjr\n7U4UwBm/uteSySyLoJUgRwhLBdCtFJs2baY6WsOYMWPc3u4OPT32cBknM/+ww6YD0LblPTLYoXmF\nBZ5lCukBLwiCMHIJDHzI3mNbux06dkS9OwUvvJnEMi3GofD2eldW3tV7p7Pp/b+zqHxRW0s3RIDq\n6moSiQS/e60LQxVC3V/8l2if59idOElySVWPsgx6drbR29vDYYdPRynF6NENRcfv3NkJ2M8nl8ty\n2GGHAdC65T1Sx36KarMTBYStbtLYn81kMpim+U8PpREEQRCGL8P7/9nza+ZOolyhBZxV1g5Wy7dT\ndcLOWKBr/Xd/s028cl8EotEoiUQClUv2+7mhwl1PV9XoZNzQ++RJ+2MBoVBhWIthGHR3d7kh+Hg8\nzrhx46mqrqNty7ukqXNfeSJWp/u53dG/XhAEQRieDGtRd8LrjlMv1KDbc1MVgJnLb3F6vztO3XIT\n6vpDKeWWwdXU1ACQSezYTXewa7iZ70SL1tMnT56MWRJU6eraiWVZbgZ8IpFAKUXz/tPo7Woj4RkQ\nEyLmviDpukZvrwx2EQRBGIkMb1E3K4u6pqnCzxSLuuPUldIGFWJWSrkvAtGoHWZPxTr7+8iQUZQk\nR5rNmzcTDkcYO3YsOcJFxzqh9zFjGgFIJGyXP3b/aQC0ffAeZv4Z6RhuwpxSSpLlBEEQRijDW9Qr\nOXXLLkWzXMGym86UivqgB6+oQsa849STsT3v1K2SJLlUdxudnZ1MnDQZTdPcuerOsTt3dhIIBBkz\nxu4w54h68/6HAva6uuF5EQhbhfa3mUxmT9ySIAiCsIcZ5qJuh4ydkjbncnVN9/Q3d1qiWvYasuZM\nchvcrSmlsFSxU0/GunbL9e8KmUwanZwr3ts2261hJ0+ebO9XhZr0ZDJJNpuhvr4eXdeJRCIkEnEs\ny6J5wsGgFG1b3iNL4UUgZBU6yYlTFwRBGJkMc1E3sSyr4NSVBljouu6Glgvhd8v7QfRBrKfbn1Nu\nGVzBqe95UY/FbNHNKvvF4oONawCYPGkiFpCmIOrO0Jm6OrvErbo6imEYZDJpQlXVjG7an/ata8nk\nRd0iL+r5l6R0Or1Hh7skk0na29uKmgUJgiAIu59hXdJmWaYrPraQ29Ktabq7Dq67U8g8gqH6bzrj\nxXbq9guC49QTsd03YnWwxGJ28lqWarAstmxaTyAQYML4cYACT+TBGQHrFfUdOzpYt24Njbkk4/Zr\n5u22zbTtTDB6tJNWaObX1WsAk3g8VtSRbqjYsGEdO3fayxnbt3/A6NFjGDduwqCSGAVBEIRdY1j/\nP6vj0sEJp9tCrRRYSrfX18l5PlEY0DLoIamKsuz3RLwXLBP6m/BWwpJX+++pPlCtuzNIJquqySR2\n0tbWyuQDphIIBMg5ZXp5enp6CAQCRCK2E3ca7HR17SQATNyvgbffhK7t72GNbnSfhR2Cb0LXA8Ri\nvUMq6gt++QbpTIZMOk3RX4bVC2zkS8fXEwwGOeigaYPPfxAEQRD6ZViH3/GIuhN+t0vLCyFzDQNM\np5zNEfXBi4Qdfi926rFYzJ3Pvrvo7e3hgw82k81my/ZZlkUsFnOT5No2rwJg/8kHApDzNMJJp9Ok\n0ylqa+tQSmEYOVpatgFQU1NLiz6D6nEfs79z28qiev7idfWh7SxnGGa5oIMTNiCXy5JIxFm79n0J\nywuCIOwmhrWoW6ZZLOqe+nRL5UvXMNDI5fvLafmmM4O/LbukzZn+FiQcDhOPx9GtcvH9Zwmb3axe\n/SabN2/kjTdedUXYIZ1Ok8tl3SS57RttUZ80eRJg1607lK6nb9iwzs1m13UdlMaoCUcA0NKy3c01\nMFGErJgroKnU0CbLpTOpckEvQSlFPN7L5s0bh/RaBEEQ9hWGt6hT4tSdy1XKFXUNw82At1BYg2w6\n46CUwrIKzj4aje5Wpx60Yow27Ulr48dPRCnF+vVr6e3tcY8phN5t8d626V00TWP/iRMASKlCz/ee\nHvtzdXWj6O7uoq2tlWi0hlAoRDJp16JXVddRM6qR7S1tHl1V6GTdzPd0eui65qVSKYzc4Prna5rG\njh3ttLe3Dtn1CIIg7CsMb1EvDb/nL1eBW7qmLNPNgAcNbZBNZxyUpoEqpNnV1NSQSCTA3D1ONmq2\norCYNu1wDjhgCtOmHQ7A+vVrXNfsTZLLZlK0bdvEuHHjqArpWECOiHu+3t5ulFJEozV88MFmAKZM\nOYiqqog9VjVf2z9m3FTisR63e5zj2J2XiWw2W3EpYHfQ0rJtQJfuRdM0Pvhgs/tyIwiCIPxzDEr9\n5s+fz5w5czj33HN56623ivYtW7aMc845hzlz5vDQQw+52999911OPfVUfvGLX7jbWlpauOCCCzj/\n/PP5zne+M7CoWFZR9ruFhjN0zdLsxip2k1f7PCb6Lg8q0ZTCsgrr8dFoFMuyyMR37tJ5KqGsHFVW\nN1ki1NePBmDUqHqamsYSj8fZvt0Ow3uT5Fq3vIdpmm59uoXmZr4bhkE8HqemppZ4PEZ3dxf19aOp\nra1zk+YC2GvlY8bZ6/GbWhxHXvwCoWmaO+Vtd2IYBl1du96RTylFS8v23X49giAI+xIDKuCKFSvY\ntGkTixcvZu7cucybN69o/7x581i0aBFPP/00f/vb31i3bh3JZJK77rqL448/vujYhQsXcsEFF/DU\nU08xadIklixZ0u93W1bxmrqdpZ5Xdb0g6ipf1mbtoksHu52s/aJgf87JgE/HOnbpPJWIWJ0oLJLa\nmKIRsAccMAVd19m6dTOGYRCL9RIOV2GpgLuevv/kA1CAQcj9nCPINTW1rkufONFed49EbDcfsOwI\nQ+O4KQBsae3GAnemnePc7dnxuz8E39Ky7Z9OfOvp6d57Y28FQRBGAAMq4PLly5k1axYAU6dOpaen\nh3jcLt/asmUL9fX1jB07FvX/s/fm0XHd153n5/d7r3YsVdgXAiAJ7qtIal+o1drdihxLIztKJ04m\nM3OSE/fEzkzHcWInnXZ8Tnc8mUzsdNyT8YzddiLbstWWYsmSLMuWLJKiuO8LdmKvwo7a33u/+eNV\nPaBQAAiuhqT3OScnFqregkce3nfv/d7vFYK7776bffv24fP5+PrXv05VVVXBufbv38+9994LwL33\n3suePXsWvXZx+V2bKetqtiJcYNkKeOxd6uKSg/rMWWC2/3vUMWu5XIJWDAUkReHKVI/HQ21tPdls\nloGBPgzDcF4mBrtOAoKm5rzyfab0ng/qHo+HsbFRysrKHMGc329/T6MwqEcHu53jTXTi8Wmn+pFK\nXd2gbpoG0ejQojvsF0e5vXUXFxeXK+CiETAWi1FRMROUIpEIsVhs3s8qKioYHh5GSonX6y06VyqV\nwuOxBW6VlZVEo9HFLz5nTl0h87vZEMI+vx2O7UzdUtplzTwLUewql5iewsPis+eLoaskHpKkRTmW\n8BR9Xl/fmCs52yX4UKgU08gydOEsNTXVBAL2S0talDrH5LPsiQlbAZ/P0mF2pm6X30vCNXh9QUaH\nupwXFoHt0Jf3ib/aCvje3gtXNJ4mhHAW1bi4uLi4XDqXLJRb7B/tS/kHfSnfnVf9nk8CpcyVldVM\nUEe7pHG2PLPH2vKZejweL5jrnn3fqVSSqanJRUvF+WNTIjzv5z6fj6qqamccraSkhGh/G6aRoaWl\nxdkPn2ZG+T49bZvOTEyMUVJSSnl5ZNb57JeAfPldCEFFbQsTsX4y2bxPvpU7j/1ykE6nr1q5O5PJ\nMDISu4Is3SaRSDj35+Li4uJyaVx09qumpsbJzAGGh4eprq52PpudbQ8NDVFTU7PguYLBIJlMBq/X\ne9HvAkXmM0LT0XQNj6fwtvPBCs2L11ucFV8M3aOhDB3UTKY+PT2Nj2lSmiQUsvv36XSagwcPOe2H\n6upqtm/fjhACTSssZfssO6ibWimanDnHbFpbVxONDgNQU1PJUM9LQH6Ji72gRnj8aIBUGTKZDD6f\nD8MwaG1dTUmJv+B8wWAQK5FG0+wXlMr6VQz2nGYwNsmq+pDzPpRKJQiFfJimiddr5X6XUq6Ejo4O\nSkp8TlCf+zzmMt/zyBOPj7JqVcMV3c9y5EqfscvFcZ/x9cF9zsuXiwb1O+64g69+9as8/fTTnDx5\nktraWoJBW2nd2NhIPB6nv7+fmpoafv7zn/OVr3xlwXPddtttvPrqq3z0ox/l1Vdf5a677lr02nN7\n6qYpQFpks3Zm7s3Jv4Syv2OhO59dCpapHKvYfKY+FU/isaYxDZN43M5oT5w4SjweJxKpIJ1OE41G\n6enpo6qqGsMwGY/2onu8lEZq0a1pLDQylheURTxe7OAmhCc3J68YGZmgr/0YYAd1WySnY5p20NWt\nmew6GAwRDJYVndPr9SMTCSwjgxI6kRpbQd8/PMqq+pAjmBsbG3eO7ekZpKKigmj08rNjpRSdnRcK\nlsTk73sh5nseeaamhgiFKigp+eD8w1FdXXpFz9jl4rjP+PrgPudrz5W8NF00qO/YsYPNmzfzzDPP\noGkaX/jCF3jhhRcoLS3lgQce4Itf/CKf+cxnAHj88cdpaWnh6NGj/Nmf/Rmjo6NomsZzzz3Ht7/9\nbf7wD/+Qf//v/z3f/e53aWho4Mknn7zoDTo9dU0rWGpikwvqeaGcKO7jLwkhnKBeWmo/zPGJKSQm\nOkksK8jZs6eIx6epqamltXUdqVSKo0cP0tHRRldXF9/7u/+L8VgfQkpuf/i3eeCmJtIyDIuUo9Pp\ntNOG6OrqoL/zBFU19c49zN6H7lUz/f0VK5rmLXMHAgHGx+2xtiw6lXUrARgaiqJocr6XTCYwTQNN\n06+KWG50dIRs1nAqBFeKlJL+/l7Wrdt4Vc7n4uLi8mFhSdZr+aCdZ/369c7/vvHGG3nuuecKPt++\nfTsvvfTSvOf6xje+seSbU0phzppTBxyhHNjhXGILwACQlxfUhcARynk8HsrLyxkbtVsOZeYF2tpi\njI+PEQ5HWL16LUIIAoEAK1a0cObMSf7xH/+R6XiClZtuY6j7NO+8/A3U+O3c+vCnFr3ubDX7oUMH\nMI0MrWvWORl1RhTvQ/f5/FRWVs97vtljbVkRIlJrZ+ojQz3AzjnXnqa8PHxVgvrISPSqBfQ8U1OT\nTqvGxcXFxWVpLGtHOeYI5YDCzFcU7lTPj7ldKvb61RnVfGVlJdOT40xm/fiYJhaLEgqVsH79poI5\n+NraOn7yk58wOTnJTQ/8Jg998k/52O//LRVVtezZs4eunt5Fr5v3ca+ra6CtrQ2AtWtanc8zeeW7\nUo4Sv6mpeUExmjPWllPA+/whSsI1jA51kX8dyt9/3lkulbqy3erZbPaShG2alaDU7KGv74Lt3LcA\nUkpHb+Di4uLisjSWd1Cf3VOXsyxi8zhB3bKzWy3A5SAQWGrmUeTH9HrGAozJ1dTU1LFx45aicbkT\nJ45z7NgxGhoauOG2RwAoKa/i8Sc+DsCbP/oGprGwa97k5CRCCBoaVtDR0YHX62Vlsy0QU8wo3/1q\nBIH9YlNVtbC40MnUmRlVq6xbSXJ6nKnpnC+8337xGR0dyX1DOX7yl8Pw8BLn0pWi1LxAtXWaEhWl\nu7uTI0cO0Nd3Yd6vCyGuieOdi4uLyweZ5b1PHbCKMvVZXxA65GxR46IGcQmLXGaTn4HPU1lZCcD4\naD+VDas5Ohrh6GgWKAzQP/n29wF49NFHCcppEgRAWaxqqmbHjbdy+MA+ju/5ETfs/njRNU3TIB6f\nprS0jOHhIaLRKOvXr0fX9Zyhq7A1BEpRavUBUFtbv6hjntfrQyGcsTaAitoWus/sZ2B4hLKSRvIP\nMD+rrmkaExMTBIMV853yokxOji8pqJdb3QTVCArIEAIUHhJ0dXdysifOlNZUdMyv7TLdEryLi4vL\nJfD+ydTn6annM3ULSVw2XcoOkQKElI5BC8wE9YlY/0KHMD0epefse1Q3trJixQr81ggV5jkqzTMI\n4M77n8QXKOHwW8+TThbPu+eNZMrKynn33X0ArFy7Jfc7gokHoUwiVjt6rr1QXb34CKAQAgM/GmnH\nDa+iznamGxyyM/NsNmtb7lqW4zm/WBl8MdLpNMnkxQ16PNYUgVxAHxOrGNE3MKJvZEraW+hCahjd\nKj6PW4J3cXFxuTSWd1CHeXrqM58pPYwCJmUTmufS59PzSCFgTk8dYGKkb8FjTh98DaUsNt30KCY6\nXuL41BRe7DJ3ecBg9523kUnFOfJ2scf95KTdTy8tLeP1119DSknz+tuczzWyVJsn8KsJLOyXjmBw\nZq+6Uion6osUZO+G8OW+bb8IVNauBGBw2Bb+GYZBaWkZAAMD9u93uUE9Gh1Cyos4+FkWFVY7AkiI\nStLaTEUgLutIEUEAFVZ7kS2vW4J3cXFxuTSWdVCf7SgnnX72TFQ3S9cR1W8kKSrRLrP0DoU2sQDh\ncBghJRMj828Ns0yTMwdew+sP0brlTiSGrVYn6Kxw1ciy86Y7KCkp4eTeFwsMfGBGqDY0NMT58+e4\n5ZbbKC+bFbSRCBRxKhFYZAkWlLk1TWPDhi2sWtVKff0KZy7cJOcsl+url1c2oOkeokN9KOwlOTU1\ntQCOJWsymbxksZxlWbP68gtTovqRmJjoTMqW3MEGVcZJ6oyD+BlD5Z5XyBosOj6RiNsrZV1cXFxc\nLsqyDuoo5hlpK0RoGgiBfgVBHShQv0tNIxKuYCI2f6Z+oe0QialR1m6/h0pP1LmnjCjDmiVTmPRt\n5s57HiSbzfAP//D3zs8ty2JqapJgMMhrr70KwGOPPWaXzbG1BFG5iSH9BlKyEgFkRWjW8YqWltXO\nM6murnEMgQxhz7Zrub661DQi1U2MDc+Yw+Qz9Ww2Szw+jVKKePzSzCT6+i5gmhcx+lGKkLIdBydk\ni/3nZCWotY7jmSXmyz+/EjVQlK1LKRkedpe8uLi4uCyF5R3U5460KYpEWbZFq3bZ/fSZExW+FFRW\nRkglJufth58/8iYA62641xF/KcCrppAYzpx5GX203PQMdXV1/PKXb3PihL1WdXJyAsuy8Hr9vPnm\nG1RX17Br103oKu1k+lZu5t5Lftf6TFAPhyOUlxd6yjc2NmOaFobIe8DPZLcVtSsxjQwjo/aO+Hg8\njsdjn39oaBBN0y5JAZ/JZIjFhi8qkAtaw0gsTHTbiMeyqLTOzkwrAAYBMvhRgEQRNAt76HYJ/vLV\n+S4uLi4fJpZ5UJ/lKJfr3S4U1K8UJWYehWB2X71QLJdOxek6/S7hqkZW1pciUJh4MQjgIZ4LVF4U\n4FfjIHzc/9gnAPi7v/sK6XSa0Zyxzauv/oREIsEjjzyKlBKdlCOSy+NVOXvY3My6ZamC7Wx5ysrK\n8Hg8GHPK7wAVOWe5wSE7ax4dHXVWtsZiw1iWdUkb23p7e4r+HGyr2xidnW309HTht8bszBscQVy5\n1e349Ft4SItSdFJ4SDmOfmX0FmXryWSCdPrqbpRzcXFx+SDyvgnqduBWRbarUtPw6JcvknOYsx41\nP6s+VwHfeXIvppFh7Q33EiSX+coaMmJmYUqaMCY+BHZJuXzl7ezYsYPu7m7+/M//lP7+fk6dOsUr\nr7xMS8tKfv3XnyKbzSJyebqzQ10pPCpOFj8qV0moqKhccMQrFCpBoWGhFWTqM3ax9suEPUpnvyQY\nhsHIyMiSneUSiQTj44XrUScmxjl4cD9nz55iYKCf3t4eIlYHGiYW0tY8mAkC5Hr4lDOsbWFUW0dM\n24BCIjGd7L3c7Co4v6a5JXgXFxeXpbCs59Rh9py6jjVP+d1zhb10B1H4fpPfIDfYc4q1N9zj/Dxf\nel+7dTc6/SggQTUhZsrGhgwySQkVVgdBFWNaNPLss79JMpnkyJHDHDlyGLCNYP78z79IIBBw1PAA\nGeyA6yGOxCKZy9J/8G6cUIlA7jk076+QyWYBgYEPD0k74xWCipwCfmjYvsd0OlWwLKW3txefrwTL\nshadgwfo6+sp+M7gYD+dne2APUdfXV2DUhbHTp5Ew8KW/GWpUO25KoTGuLbaed6GCDKqraXSPEve\nyz/AKBNWS8F18yOALi4uLi4L8/7K1MWcOfWriBCFs+pNTU0ES8roOPFLRxAWG+igv/MYDau2UhUJ\nILB3uFda5yhVM6K6rAiQlhEsJBIDzUrS1NTMU089xV133cWKFSu46aab+Mu//I80N9vBK5mcyZST\nuR3seb/3jLDXweq6bo/fLUD+BccQfmw9v72rPVASxh8qZ3jIVpebpkEoZJ9TSo1YLEYiEWdiYvHx\nsampyYL+9tDQAB0dbWiazqZNW2ltXUtZWTklJaVO31yiqDDPoZFBATGxvugFKitKSIgap1IhgJBV\nOHmQTLoqeBcXF5eLsewz9XxQF3kx3LWJ6bmxNgnMqO03bt7OwXffprftMC3rb+LIW88DsP2uXyeo\n7FK2holGHIt8nmkvVDFEkLQoJaAmKFX9lJdvxe8PcP/99yOl5Oabby/IePMObwqwpN0Xz/fTM6IU\nFHgu4qyW1xeYyg/Kvg9T2DvOK2pb6O84RjqdxufzoWkaoVCJc93BwX7q6xuJRBZ2lhsc7HcWt4yO\njtDefh5d97B163YCgZnlMwMD/Y62ICPKGGzfz4EDB2hv76C0ooG6lVu48b5P4AuUOMdMyXoCZgyB\nZbctGMSy1jjPKG9E09hY7Dzn4uLi4mLzPsrU7fePa5apS4lCc9TnCsG2rVsBaDv6c8ZjfbSf+CVV\n9atpWrvTCbgWkphcj52T2oE9bHXit0aZFg0owKdsj/f82FlpaXlRmTtffjfy61aVwqumMfBhCY8t\npFuCIFDTNOcc+RE5mN1Xt3vThmFQUlKKUgq/308sNkwsFnWe91xSqaQzWz81Ncm5c6eRUrJx4+aC\ngA4wOGhn2QlRxS/e3su3vvUtTp06hccXZCzay4m9L/LDf/gjYgMdzjFK6EzJBudPV2Kb2+QRQjjX\nd3FxcXGZn/dZUBeLrSe/IjQpHQU22EG9qbGasoo6Ok/t4+VvfhGUYsfdT6NZGWfd64RsQQmJzGWY\n+WPDVid6TtUtsYjFhp1tZvPNd+fL7+k5/fR8lq57llZU0fSZoD7bA74yZxc7nOurj4yMOH31SCSC\nUoqeng5isfltWQcH+5FSkkwmOH36BJZlsW7dRmfmPU8qlSSTsUfz3v7Fm7z70+9QVlbG7/zO7/CH\nf/Q5PvVnz7Hj7qeZHBvkpX/6XIEQMSmqZj1F6O0tXPaSSMQxFlmQ4+Li4vJh530W1K8dUkos9II6\ngBSCjTvvwzQyJKfHWLfjflZuupVS1ef001Migk8VirhSogKFRtjqxMQumbe3n8c0Tfx+P9PTUwXW\nrEopLMv+PZPS3pXut8Zz57JHz7yepS010aRe5CoHUFVvr3TNZ+oTE6MFYrmSklJisShtbWeLzpnN\nZhkbGyWdTnHy5HEMw6C1dS0VFZVF3x0asrP0to5e3vvZvxAOR/jUpz5FXfNafCJOSE5z80d+k3s+\n9u/IpBO89i9fJpux71MJjSRVzrnS6VRBH10IQTQaXdJzcHFxcfkwsuyDumHYWa3UvUtb8XmZ2DvV\nZ14c8mX4m+54iKc//TV++/PPce+v/69IIfFjB9wEFSAEHlW4jESSZURbi4XH8YI3TZPy8rAzYz48\nPGOJmh8nU9jKeZTCr8axkKRFGVLTlvy7CwFC92DicfaqA4SrVyA1ncFBO6jH43GCwSBSSqampmht\nXYsQgtOnTxZl6z09XWQyGU6ePE4mk6a5eSW1tfVF11ZKMTw8TDqd5qUXX0BIyVNPfZxwJMK4WI0C\n2wpWKdbvfIBNtzzK6FAXe17+J+ccca1waU13d+es3004O+hdXFxcXIpZ9kG92Pv92jE7qOfL614t\nQ6SmGS03C+9X40gUCnshCYBHJVC5HN/Eg1fFMQgyrG1hXDY7qvpIpIKqqhp0XScaHXJsW4dyqvR8\n+V8nhU6atCgDsbRe+myktEvwGhlQOeGf7qGippmBgQFM0ySTSSOEoKSklOnpafx+P42NTWQyaf71\nX19wRsimpibp6eni2LFDpFJJGhub5jW/Abs8ns1m+NnPfsbk+Ai33XE3jY2NGPgwtSBpEcZLwlH1\n3/7I/0hF3UrOHHiVaN95+/kJPxlmevSxWGFmPj09vWDf38XFxeXDzrIP6oZh5MbZtCLjmauNYnZQ\nt3vjAWuW0YpSlFj9OVtYYVu5KguNtBOQsyKIxLQDqpAkZTXTws5qz3f188KBJBNmhGw2y8v7B/jB\n/jjd/XbgymKbzvhVvvQeBqXQL3EDnZQSU/gRgD5bLFffimFkicViTmDMl+Cnp6dpamqhoWEFiUSc\nf/7nb/DCC9/lhz98jtOn7ZL7ypWtNDevXPC60egw4+PjHDhwgLKKOu69+w4ApkSDfQ1pL5IJKfsl\nRtM93P7o7wGw58f/NyrnJBcXM9m6Uorx8THnv4WAkZHC5TguLi4uLjbLPqibpplzk7tWuvcZlJwJ\nnvbWtRI8JNGV3f8OqBienJVr3o7VQzJ3XwoLSQZ7TGt2ST4uauxRN1JgGSSk3TcOqWGwLCfwJkS1\nXXq37M1laVGOEBLtIoYwc9F1nSyFi10AqhpWAzA4mKsMWNasoD6FEIKWllWsWrUGr9fLwEAfiUSc\ncDjCli3baWhoXLANYJfeB3nrrbcwTZPb7vkoHl23f4/cutWsKCFNCX41ia7slkPj6m2s3HQbgz2n\naT/xSwDSMuy0P8BeHpPHXcfq4uLisjDvm6CukNdsRj2PmrPUJStscVrQGkEok9Jclg52wAWc4CSw\nMPGRkfbilYI+u5RksG1kw6rLmWH3qSnKrB7n18rKUrxqCg9J0qIcJXQ0/dLbDpqUWPnFLgVj8rCL\n+QAAIABJREFUbbYCPh/Uk8lEQVAHO2jW1zewY8dN3Hjjrdx8821s2rS1SOU+l6mpSYaHhzl8+DCN\njY3s3GJfK199yJOQdhYesGay7Vsf+hRCSg69+RzKslBCIzurBD/XFGdqatItwbu4uLjMw7IP6oZh\noOt6br/4NS6/y0KFuVT2hrGAGqHCPI+G4fTOE8JWfntyWbxEYQg/Rm6nev7necblytySlwmklXGW\nnARzfugWtvq+1LKd6aZkgz3Kdpmqf0uzg2LBWFv9KoQQTlAfGYnh8/nwer3z2rB6vd4lTx3EYlHe\neecdlFI8++y/xSttN7vZpXSw1fwmOkE14vT7yyvrWbPtbsaGe+g+uz93XHXBcfklOHkGBws9+V1c\nXFxc3gdBfSZT1655pi5kYe9aJ01SVCIx8RInTQkCleun51ecJp3s3cCHEhoGfjwkCraNWdJPhhJ7\nYYnqJitCzvkAsgTxqzG8JEiKCIYIAuqy98QrGUBBgQLe6wvS0NDI4OAgSikmJ21TnLKyMjKZNJlM\n5vKupRQ9PV0cPXqUiooKtm3b7rjrpcQchzohnWea1w4A7Nj9cQAO/+L7KKVIycLj+vp6Z04hhLNd\nzsXFxcVlhvdNULfQrnmmLqSv4L81MkzJBkblGoa0baREGAFkc/10lMJDEisnsDNzJe+sCOXy7sJ1\nofls3acmqTROO7vSwe63h61OFLksHS5plG0uUtMx8Rbdw5o1a0kmk4yNjZFK2dWEsjK7tJ4vwV8q\nExNjvPfeexiGwUMPPczAgB2ATbwwjx4grynIW+0CRGqaWbnxVoZ7zzHQeQKEJBCYKd3PvTfLshgY\ncLN1FxcXl9ks+6A+U36/1jI5QJvJ1O1lJCYISVqWYwkPAWWXytO5hSuSbG5lqN33NmYFdaBoft2S\nPiblCgC8JHIvCHlLVwODAKNyrfNyoMnLH+PTdB0DPxoGQs30nzds2ADYm9myWdudLRy2f5+LLXRZ\niMHBQfbv34/H4+Hxx/8N09P2y0qC+X3kTeEnTQk+NVVQSdh+18cAOLHvJQCqqgpV8GNjM5MIQghG\nRlwjGhcXF5fZLPugPqN+v/bld8TcUreCWSVeD3apfTrXJ873zWeX3wEyIpj7vDCoAyRkLcNyMxmC\nTIk6MjnB3bhsJqZtJCPLnEtrVzCbnx9rg0JnuQ0bNgJ2UM+PkIXDYaSUBaNjS8U0TfbufYeJiQl2\n7tzpZNf2HH/tgsclc+V1v5q5Zm3TBqrqV9N15l2mJ2LU1TUUHDMw0Ffw39lspmBrnIuLi8uHnfdF\nUNd1HUtc+/I7Ysb/XeWuli+R61Yi10/XQNrBX8+5xUlMTHRHPW8QQCGKxHJ5LOlnRN/ItNbonCMl\nKorm8C+3nw72+4+Z6/vPzobXrFmLruv09dkBMpvNomkaZWXlJJMJ0ulLW286Pj7KgQMHAHjwwYcc\nAZtCOs9pPlIikvMBGHG0B0IINt/yGMqyOP3eT/B4PAUvNrN3zoP90jNXQOfi4uLyYWZZB3XTNFFK\nzYy0XQcU+qyt3jM7zYPKLvVmcqV1AI/KB3XD8Vu3D5VkCeAh6Si8F0JXSQy8KFGYlUspr9gW15KB\n3DVmMnWfz8fq1a0MDg5iGIZjCRsORwC7P34pnDt3jra2NhobG9m8eSujoyPAzGKahVBCJy3K8ZBy\nXmwAWrftxhco4fR7r5LJZJz7AruPPlelPzfQu7i4uHyYWfZBHbhu6ncAa04J3osdRHzKDh75UTaw\ng7qFtM1oRKHILitCCGwh3UJIlbV76SJQ/Jl25X80Kj/WNkcst2HDBkzTZHBwkNFRu0+dD56XUoI3\nDIM333wDpRS7du0iFCpxvPqncxa6i5HMKeNnu/Z5vH7W73yAZHycffv2FJXg+/t7C/7bLsG7gd3F\nxcUFlnlQzweI6zWnDqCEB4FtJqOwM/WQOYBGFoUgTTj3RQuNlLOFLS+Sy7OQWG42eeMaY45By5X2\n0/MIPYhCFJTfobCvnkjY9xcIBPF6vYyPjzm99osxNDTI4cOH8Xq93Hbb7QVOb4YsuejxKVGOhWYL\nEGddc8OuBwF45ZWXKS8PFxwzt5KgaZprG+vi4uKSY1kH9YJMXVx7RznA6QML7BKyAEpVPwKYFA3O\niFbeHtZRvlMY1PNl+nz5fj7yn80u6dsodP3S/N7nQ9N0DHx2pj4raG7cuAmwg3p+P7kQgnA4gmEY\nTE1dXHymlOLtt3/BxMQEW7dupba2jv5+u0/v9xdXHuZFSFIijEa24DlFapqoa97IoUMHGRwcLBht\nMwyDZLJQqzA2NnrZM/YuLi4uHyTeP0EdyXWJ6rNc5aZEPSp3VRMPCW2mpJzPsp3tbHPK7yY+DLz4\n1GRBQJ2NlykUkBGFWa0QEnkVltcIITCFH4mFxHB+3tDQSFlZGT09PQUGLpWVtotbNDpcdK65TE9P\nsWfPOwDs3LmTcDjiZP3V1Qur3ufilODVaMHPN9z4EEopXn31Fee+8sw2ogGQUtDb27Pka7q4uLh8\nUFnWQX12+R0hr0uijpjJkDVhMSUasZCMytUFX/M4nu+mvQedwqCOEGREGdJ+HSi+jrJyK1oDRZ7z\nV6OfnsfMieW0WX11IQTbtt3A5OQko6Ojzlx5OBzB4/EyMhK9qFvbuXNnOHv2LPX19bS0tCCldMr2\n9fUNix47m4woxcRjj7bNEhWu3nIHwWCIV199peglYWxspOg84+Njzl56FxcXlw8ryzqoF2bq1yWk\nFwRYSZa4VseQvqOoR6yrhG3DSsbuq4viR5kWtgLcp4rL2V7iCBQZUawSvxLTmbkoRwFf2FffuXMn\nAB0dHfT322NoQgiqq2swDKPA6GUu6XSan/70dZRS7Ny5k0ikwhll0zTt0kbxhCApKpCYjhgRbMHc\nfffdRywW49ixo8hZznTZbLao3C6lcB3mXFxcPvS8f4K6uvIRr6Uwe/2qRnaBL9mqdhMfGmaRSC5P\nWpTZYjtrnqCe6yGn55TeUQrtCubTi25Vt/v1s8faAHbssIN6Z2cnY2Mz4rPqattYJxodWvCcFy50\ncfDgQbxeL1u3biUcjjhitbKy8ku+x7wRzdwS/COPPAbAK6/8uGhL3FwVPNjZuru9zcXF5cPMsg7q\nBeV3xPUJ6rMzdTV/UM/bw+aV7ybzB3UldLIE8TJdYNUK4FX2qFxxpi6uivLdwWOfX58zWtfQ0EhF\nRQWdnZ3E4zMK/VCohFAoxOjoSMHP86TTKfbu3cv4+DgbNm3H7/fzy3YPmZzl7PmJKn6wf2HF/3wY\nBMjix68mEGqm97927TrWrFnDvn178XgK2xvzK94Vg4MDl3RtFxcXlw8SyzqoF5bfKXJcuxaoWT11\nuUCmnu+nWyLv+e6b93tgZ+sCCkrLdj99muw8/XRN065qo0FILyYe556dnwvBzp27SCaT9PYWZr3N\nzfYu9M7OtoLxNqUUXV2dHDxoO8jduGs7WYLoKuFsZcvKxU1n5r9JQVJWIlAFtrFgZ+uWZTnXzJNO\np5yXvtm/03z9dhcXF5cPC8s6qBfNqV/HoG6vLZ0/qOt54Vsu3jlz5vn4N0vsnpSVKKDEGnRU8EEV\nRaBIiTml6qs0nz4XUwTQyBZVC3btugmw++qze9SRSAWRSAWTkxMFS1P6+3vp6enizJmzVNQ00rSi\nkbQoo0TZpfoiseAlMJ8RDcB9992Pz+fj1VdfcXa7i5x+Yb6sPJNJO652v2qmp6c4evQQP/7xf+dr\nX/sa3/zm1/ne977NG2/8hK6udnd1rIuLy1Xn6jVvrwFzhXLXQyo3kzmLi2bqEvv+DOEHBV6vF4/X\nSzw+M3NtCj8pESGgxvCpSdKUUmINYSHnWXii8Hi9XG1MGQJzMleCn+lN79y5EyEEZ86cYXBwgObm\nFuezlStbGR8f49y5M0xPT2OaJkNDAxw/fhzLMrlh120IIUjLMoKmHdQTVM699JKxhJe0KMGnptFU\n2hkRDIVK2L37Hl5//VVisREikXJUTiUfiw2xYkVTwXmklAwNDVBRcfn3cqVMTk7w3nt7OX/+jBO4\nA4EAHo+XsbERYrFhzp49RWlpGXfddS8rV7b+yu7VxcXlg8X7KKjL61J+R3hQyNzqlqydXc+5bt4e\nViONiY4lPGiajs9nByKvx2tnvrnDpmUdAXOMUqsPnyhBI8u0qJ1nlE27KvPpc1F6CMxisVwkUsGa\nNWs4f/487e3nCoJ6IBBg06attLWddURpUmocOHAQ3eNlx9YN9vS78uaeFiRk4Tx58Y2Q+yb2K9qc\nXzUpKvGpafxqlLiod37+yCOP8vrrr3Lo0CHuv/9e5+eJRALLsgqU8fmfj42NEonMv/r1WmFZFkeO\nHODAgX0YhkE4HGHbtp20tKxm9eoGotEpLMtiZCTKyZPHOXPmJC+//CPWr9/E3Xc/cEULfFxcXFxg\nmZffSyubAXs3+PUovQMgBJb056xiFYI5auqcPaxBAI2M7SSnwOuZ6cV7fT6EnLlfQwRJiXI8JAmp\n6PxZugJduzb/qCvd7nPP7asD3HXXPQC89957RZ+Vl4e54YYbaW1dy6ZNW5maihOLRdm46z5Kg/ZC\nlvyim4ttZQN7/r4kVEIoVILHU+yYlxJhFIKgVWgbu3nzFpqamtm3bw/JZM4fIFeCn0+lr2l2tn49\nmZ6e4sUXv8++fb/E4/Fw//0P84lP/DZbtmyntHRGZyClpLq6lnvueYCnn/4NampqOXv2FC+99APS\n6dQiV3BxcXG5OMs6qGez9my1nuszX58CPCjpR+QyyrljbXrOHtYU3twilwBSyoIsSwDBQLDgfsfl\nKkZlKxOymVFtLZaYG9QUHs/VL73DrLG2eZbLPPLIo2iaxrFjx+Y9VtM0amvrKS8P8/3vfxcpJbfc\nehdgB+Fgbgwtw+Je7wJBIBBESokmJX6/n2AgVPCMlNBJiXL0OZvbhBA88sijZLNZTp8+A9hz6cCC\nwTuRSNDefn7JPvaXg2VZZDJpzp07zXPPfZP+/j6qq2u58877luSqV1FRxZNP/g+0tq5jYKCPF198\n3rW7dXFxuSKWd1DP2EHdFo8Vl2uvFfmVpVA81uYo33OPzsA/b9YppSQYnAnsSmikZZiErCY7dzYd\n26ddymv0CwodE29R+R2gvLyctWvXMjw8zIkTxxc8xb59e+jq6uSee+6jNqznltuUObqDKbHwVjY7\noAeKWguaJgt83cEuwQP2nvVZPPDAg+i6zsGDB1FKOa2ZeDw+r+BMSsHExBhtbWevemC/cKGLQ4cO\ncPjwe/zsZ6/xxhs/IZPJsGpVK2vWrCMen6Krq52TJ49fdJWtpuk8+OBjbNy4hWh0mFdffcmdtXdx\ncblslnUTL5uxg1DejOU6xXSUnJk7n5upO/awuUBhisCCGbbMZaTJZHLxm1dcE4HcbEwZxGuNk81m\ni15CbrrpJs6cOcN3vvPf+PKX/1PRsZlMhq9//b8gpeTJJz/GyMiwnVGruDPKZmjzjLIpu+QeDAQX\nbJ9omobX6yWTtjUIaVHmbG5TSjnHhcNhbr/9Dt566xf09fWxYsUKNE3HNG33u8rKqqJzSyn51s+G\n0N6KEQgE5/0j+N8/ufNij87Bsix6eroYHY0hpWRgYJDOznY0TWP9+k0Fu9+llBhGhra28/h8Xl48\nnEbTPAv+NfjjZx4gHo/T09PJO+/8nN2771/yfbm4uLjkWdaZeiZtlyJ17frsUs9jabMydQrLoTq2\nPWx+QYrylCyq39N13Q7YiySLUko811gkpTS7OpBfujKbW2+9lYaGBg4ePMDZs2eKPv/ud/+F/v5+\nnnzy1ykpsUv5KRGmVNmlb4P5X0iEEIsG9Dxej2/mO0KSFBVoFFvVPvzwowAcPnwYwGl5DAz0LXxy\nAaZhkkjEyWQzC+3WWZB0Os3g4ACdne0cO3aI0dEYQgguXOims7Mdj8fDli3bCwL6bDRNYhgGmXSa\nZCKx4PWllDz00ONUVFRx4sRR2tvPXdqNuri4uLDMg7ph2AFV0/Xr1k+Hwky9oGStFB5l28PqpLHQ\n0L1z16YW45sjnCu8GPOW7682Vs5Zbva4XZ7Vq1fz4IP2DvP/+l//saBcffr0KZ577p+prKzk2Wf/\nLcPDQygEKRHGm5vXj4t5+scK/IHAkgSOQlDw4pOQdtY9dw59585d1NbWcvz4cdLptLM2dnp66iIX\nsLPsdCpNPDFdZFozl/z62Y6O85w4cZSBgV6njC6EoLu7kwsXuvH5fGzZcgOh0Ew7JZPJMDw8REdH\nG+3t5+np6WJy0jYeMk1z0et7PB4efPAxdF3nzTdfc45zcXFxWSrLOqjne+ryGqnCF8LKBXVFoWJc\nJ4XEJCOCaKQxRHBJZjEC8Pv8865gFUJc89I7gKUtHNTLyspYuXIl69at4/jxY3zpS/8hN2u9nz/5\nk/8N0zT59Kf/CNO0d5mnRBgsg/yAWlIUl751j8cROC4Fr9frvAAYIkiGEOPjowWKcDubfZRMJsOJ\nEycwTRNd13NjYvPZxs5B2K54yWSSVDpVVDyZmprgzJlTHD16kHPnTjE5OYGmzZgeKaVobz9Pf38v\ngUCALVtucDQB2WyGjo7zHDiwj7a2swwO9jM0NEBvbw8nThylMnMcnxpHWRbJZJJkKjlvr7+iopLd\nu+8nk8nw5puvXVOhn4uLywePJUXLL3/5yxw9ehQhBH/6p3/K1q1bnc/27NnD3/7t36JpGrt37+b3\nf//3i475/Oc/z5YtW/jc5z7HiRMniETsUuXv/u7vcvfddy943WzOT/x6l98Ruu0spwx0Us6suie3\nhMXCVr5b2sWz9Dy6rqPpOqZhzvwuCjzehfusVxMlA1hozprVufj9AZ544gmef/4HvPXWL3jrrV8A\nds/785//Arfddjvnz9ul+YSootzqs9X/6DBnThyFM7O/VAT2i0A2N9+fkFV4rThDQ4M0N690vvfQ\nQw/z7W9/k0OHDrFr1y4CgRBTUxP09V2Yt6++0MWymSymaXL+/FlSqSSGkUUpCym1eV/ULMvi/Pkz\njIzECIVK2LRpi6OlmJgY4+zZ0xiGgd8foLa2jvLyMFJKUqkUo6MxhoaHqbDaSYoI43IlRtYgbsTx\n+/1F8+nr12+ivf083d0dnD59gk2bthbdj4uLi8t8XDSov/fee3R3d/Pcc8/R3t7O5z//eZ577jnn\n8y996Ut84xvfoKamhmeffZaHHnqI0dHRBY/54z/+40UD+WyMrF1+l7rnupbfwc7WpTmFgJzJjN/Z\nrOa4wXrCl3TOgD9IOpO2Axd22dnrvXxr1UtCCEwZIpmcxDTNosBVVVVNKpXk2Wd/g3Pn2jhz5jT1\n9Q3cf/8DbN9+A9lsllgsit8fIJMtJUI7MKNWn43u8VyWiY7P63WeTUpE0LRehoYGWbGi2TGYqa6u\n5qabbubdd/cxODhIMGi/WE1PT81rRLPw87ADdTw+lXs8AiHmryyYpsnZs6cYHx+jrKyMDRu2OIF4\ncLCfjo42hBCsXLmaurqGgnsIBkNUVFRyeqya0mwnATWGZmYY01qx8JBMJvHOeQESQnD33ffz3HO9\n7NnzC1paVhWU+F1cXFwW4qL/Au7du5cHHngAgNbWViYnJ53tXRcuXCAcDlNbW5v7h+hu9u7du+gx\nl0K+Z6pr+vXN1MExoIGZErxXTdt99Fyf3dIvbc2oEOD3+SgpKcHr8+H1+a+LSV6evAnNfCX4uroG\nwM7Mn3ji1/jP//n/4DOf+WO2b78BsIOXUora2jqwDAQWCpimvvBECnyX+aIihED32MFSCXs+PpvN\nEIsNF3xvtmAukYg7VYH8TveriWFkOXXqOOPjY4TDETZu3OoE9KGhATo62vB4PGzevI2GhhULvlSY\nMsCIto6EqMBLnIjZZnvxC8ik0wwNDRZ8v6SklFtvvYtMJsPevW9f9d/LxcXlg8lFg3osFqOiYsZu\nMxKJEIvF5v2soqKCaDQ678/zx3z729/mt37rt/jsZz/L+Pj4otfOl9+169xTB7tcnUdXKaTKopMh\nQwgvCSzhKRDUXQpCCHxeb4EL3fXA0m3f9/lK8F6v1wlI3d0dBbPfqVSSvr4LeDweamvrCatuu/2A\nDrMz/pzo70rm7b1en1MKqa9vQAhBX19vQW/5lltuJRKJcPToUTKZjGMHOzBwdYN6JpPmxIljTE1N\nUllZzYYNm50KRyw2THv7eXTdw+bN25e2R15IJuRKEqISLwkiVjsoCwT09/cU6QI2bdpKdXUN586d\nXlzh7+Li4pLjkoVyiwl3FvosHyCeeOIJPvvZz/LNb36T9evX8/d///eLXiuvEpbXWf0OM2I5sJ3Y\n8qV3I7fxzNLLr48X/VXEzI21neoe4wf7487/feetcX6wP05C2Z+n02le3d9tf/7uNHsOn8OyLIbN\nRn50KI0fW5WdmCuQE5feS5+LJiWabgdOn89PVVU1yWSC8fEZExdd13nssY+SSqU4cuQIhmHay2XS\nKZLJxBVdP08ymeD48SMkEnHq6hpYt26D89IzPT1FW9s5NE1j8+atBIPBpZ9YCCZkCylRjk9NUWr1\n5X4s6e7uLMjYpZTceed9ALz99puuaM7FxeWiXDQFrqmpcbJsgOHhYaqrq53PotGZ1ZxDQ0PU1NTg\n8XjmPaalZWZhyP33389f/MVfLHrtmfK7F3SJx1N4u16vvb3tWiAogyQoBB5SKJFrHwhhZ5LeSNH9\nLHv0MtSUhpcEmlb4Pqdpkrhowpc9CUCZ1YcuTHQVx6cmyIhSsnoVAWvcMZxJeRrQch7sKIXP78fr\nvfLqQ0gGmZ6eJhTy0dq6mmh0mP7+CzQ21jlK9GeeeZrvfvdf2Lt3L7fccgtVVVVEo1EuXOhix44d\ns36vYmvcgmuFil9CJiYmOHHiKNlsltbWVlatWuVcN5PJcPbsKSzL4oYbbqC6eqnb4JIFz3xKtaJn\nT1GihjEoIxSqyF17GI/HYu3atTmf+PW0tW3l+PHjDA52sW3btiVe78NJdfU8JkguVx33OS9fLhqV\n7rjjDr761a/y9NNPc/LkSWpra53MpLGxkXg8Tn9/PzU1Nfz85z/nK1/5CqOjo/Me8+lPf5o/+IM/\nYP369bz33nusW7du0WubuUxd6B4M0yKbLZzvFSiy2WtkqalCaDKEtOJoKonPzGAh0YWdLWVEKVZ2\n8Xnn5YimlaCZE1hGFpUThmmaxDQtTPxY6GgYWEDItMvZaVHKuFyJZSlCxgUATDwYll2EB1vyIIVe\n9Gd0uQgk8XgaKb1UVFQxOhqjt7efigq7OuD1Btm9+27eeOOnnDhxgqeeeoZoNMrIyAhTU0knqzbN\nxXeWx+Ppgv+OxaK0tZ3FsixWr15DbW0DiYQt3lNKcfr0CdLpNM3NKwkGy4qOX4zCexGMydVUmacp\nMzoZHa10qhzd3X309Q2zcuVqSkvL2L79Zk6ePMkbb/yMmprmJY1Rfhipri4lGr2IZ4HLFeM+52vP\nlbw0XTSo79ixg82bN/PMM8+gaRpf+MIXeOGFFygtLeWBBx7gi1/8Ip/5zGcAePzxx2lpaaGlpaXo\nGIDf+I3f4HOf+xyhUIhQKMRf//VfL3ptp/yuXX/1O0KQ9a3AnzwLgIZJyrcaT3YIhcTS3p9qZEsv\nRzcn8Kpp0qK4D5wQVZSqQUw8TMsqTLykRASEwGtNoGMHsbiYtWZV2Yr3q9mN8Hg8mKaFpkmam1cy\nOhqju7uLSKTSyZo/+clneeONn/LLX/6Sj3zkQfx+P6lUir6+CzQ1tVzkCoUopejt7eHChW40TWPD\nhs1FO9n7+/scwVxjY9MCZ1o6hggwIZsIWz20t59n48bNORW+wDQN2trO0tCwgtraerZs2c6xY4c5\nefIY27btuPjJXVxcPpQsqX6cD9p51q9f7/zvG2+8sWDEbaFjAG655RZ++MMfLvnmDHMmqF/vmA5g\neGtQyTYEJgoNpfnR0nEMvRLEsvbtWRBTD0O6B6+aIk1xUJ8W9ZSoQXTSZAiRlTNvjGGry/ljSMtC\nW9SrPZqnezx4PLYeIxgMUltbx9DQIIODA9TX20r9pqZmtm3bxrFjx/jFL37OY499lHPnztDX10tj\nY9OSx9tM06St7RwjI1F8Ph8bNmwhFCr0IIjHp+np6cTj8VBVVUNXVzupVApd1wkEgtTVNVzWPvSk\nqCIgxhgfHyUaHaKmZmYxjhCC3t4LKKXYtesWTp8+ycGD+9iwYTPe62BY5OLi8v5jWUcm0zDsUqPQ\nrn+mDiA0Mr4mFCAw8SXPo4B0YPX1v5erhKmXoRCO8K8IKUmKSgRQYbVBTuRYavagYaCALH5MMUtI\nqF/9DXMCCIdnJiiamlrQNI3u7k5SqRmXuWee+QRCCF5//XVCoVI8Hg+WZdLff2FJ14nHpzl69BAj\nI1FKS8vYtm1HUUC3LItz586glCKbzdLWdpaBgX7GxkaJRofp6eli//49HDy4n4mJxSc6in9RWzgn\npUZXV4cz8ZFH0yQDA70kkyluuGEXyWSSo0cPXto1XFxcPjQs76CeM0mxfoXL5LL+FlLBTYC9hjXr\nbURdgpPcskPoWFopHuL2nPQ8TIhmDDxILGqs41QZJylR0dzLDaTkTLBFcc2yxpqaWmdywuv1sWpV\nK5Zl0t5+zlGCb926nW3btjE8PMxLL/2IlStbAejt7Z13JevMfSsCVpRjxw6TSiWpr29k8+ZtRRv3\nLMvi2LHDBap6r9dLJFKZK43XEQqVOOr7kyePceLE0YWvrSw0lbZH2XKYwkdTUzOGYXDhQnfRIUJI\neno6WL9+E4FAkCNHDpBIXB2Vv4uLyweLZR3UjVymbiF/JeV3wHZi89aQ9dZhCR8Z/8pf0Y1cPUw9\njIBFs/URuR6FQMOw1f9AFnt2PylmSu+6rl8z4ZbfHyhwUquuriUSqWBiYtwJfj6fnwceeAApJc8/\n/z1KS8ucbL27u3P+X09liFgdhK0ep3++alVrUbk+kYhz4MA+Z7NdSUkpO3fexI033srNGFFgAAAg\nAElEQVTGjZtZuXI1ra3r2L59J7fccodj4GP75u91jkskEpQYPdQYx6g3D1NjnqDOPEy1cZISawCp\nstTXN+L3Bxgc7F/QqOnChW527bqFbDbLoUPvXtnDdXFx+UCyzIO6vbBDcf3n1OeSDm4gUXYryOtr\nGHMtMHXb3tarFlawWtLHoLyBUdnKtKghKjbgIUWWwEzpXVFkcXq1qaiodLJeIQRr1qzD7/fT29vD\ny/u6+MH+OKK0ldtvv53x8XH+8m/+iUGzBQX0D/QhrcIte0FrmGrzJH41TpoStm/fWSSIAzuAHjly\n0BFrrlq1mm3bduD3B4q+C/ZM+erVa9i58yY8Hi+maXLkyEHOnTvNkSMHCJpDCCzSooykqCBDCZIM\npVY/NeZxBgb6WbnSbut0drbNO5OeyaQJhUKUlpZx8uSxi2+nc3Fx+dCxrIO6adqZumKZjPC8z8xm\nFiLfV/dxkaAgJWkZZkprwiuSCBSpWQI53aOjLdVr/TKpqqopcBT0eLw5q1YPYauHErOflAyze/du\nysrKOPLOj4iOxkmLUgRQabWBUnitSSrNM5RbFwDBuGxhVFuHz1foCmgYBkeOHCwog9fW1lFfv2JJ\n9+v3B9i162YCAXvsMxaL4vV6mdBbGdK2MaqtZVxbxai+nmFtGxOyCQuN7u4O+vouUF4eZnJyYt6t\nc0IIxsfHWbduI6ZpcvCgm627uLgUssyDem61JvoHJqAuC4SOqYfxqASatbQ566BlB5mkyPXTFXg9\n134ZjRCCcLhQaR8IBNi8eSsGXkrVAKVWH7rXx8MPP4xpmvzs+a8Qs1aiAJ00teZRKq3zeEmQFBVE\ntc0kZVXR36lYLFZQNge7vJ/v0y9GKpWip6eHY8eOsm/fXjo62pmenkYpRSaTISsCRRMTSmgkZA1R\nbTOVlVVMTU2SSCQQQtDV1YFpFmseNE3i8XgoLS3j9OkT7s51FxeXApa1JdpMT31Z3+b7EsNTjW6M\n4VdjpJi/pJxHV0m8xEmJMkxhB3JN04pc6a4VtbV1jIxEC3reoVAJMW0jYasLv7ID26ZNm9i61XZf\nO/Pm11hx327Anlww8DKmrcYQxSJHW91+mtHREcDOti3LIpNJs3bt+nk1A3ZGf5h9+/Zw7Ngxenq6\n5xXHBYNBe1f9+uNUbnkK3Vd8fSV01q3byIUL3fT29iClJJNJMzDQx4oVzUXfl1JSV9fA+fNnOHBg\nH/fd99ASn6SLi8sHnWUdLfPqdyW15V1SeB9ieKpRyfMEGCNFw6LfDVq2FbDj9a7Acx3npP3+ACUl\npQUZNNjBcExbg0fFKTF78TPNY489xoULF3jn7Tepa2yhdcN2/GocnQwRs5MxuQpD2oFVWhna2/sZ\nHh50etiNjU1ksxmGh4dobGwqWtTS39/Hiy/+iDfe+Kkzvubz+dm0aTP19fZWOaUUJSVljI+Pce7c\nWU6dOsWpU6fwv/JjNtz8ONvv/Bj+YKFjlBCC5uaV6LpOV1cHAL29PdTW1hUp8sFeldvb28PZs6fY\ntetmyssjRd9xcXH58LHsg7otlNMcFzGXq4T0YOoRPMYompXEZP5SulAmATWKiYe0sAV2Uko8l2G0\nciVUV9fS2dk2r6FMVoQY09ZSax7B5/fz1FNP8f/+f9/ivz//HR771CZaVrQSsTrQSVNtnUFZ+b9L\niqEh+38FAgHWrdtIKpXi7NlThEIlBa50p0+f4vvf/x7vvPM2SinKy8t54oknufPOu9i8eQtKKY4d\nO0w6nWLNmnWOiYxSio6ODr7zz9/i8KFDHHnreU69+zK77v8kW259HCkLqwANDSuwLIuenq7c/++m\ntXVt0e8shKCpqYVz506zf/9ePvKRR6/Og3ZxcXlfs6yDulIqJ5STbk/9GmB4a9CNUYKMk6F23u8E\nVRSJyZSocZbZ+PzXvpc+l0ikgr4+n7PkpwghSYswATVGY2MjH3vqk3z/uW/yyrf+go984nOsWLWN\nsOrBqyaR5HvVgtLSUlasaCYSqSCTSXPy5DGklKxduwGAd975Jc8//z1OnjwBwJo1a3nqqae5887d\neHKrcy3L4tSp46TTKVasaC5yhWttbWXnw3/A7t3HOfDee7z19jvsffmfaDv6c+79+GeIVBdazjY2\nNpFMJolGhxgaGqChodER3s2msrKKYDDE+fNn2LHjJqqqqou+4+Li8uFiWQd1wOlnupn61cfwVKGE\njt8YRIhKlCz86yCUQYk1gIVGXNpBX9O1y7JDvRpUVlYxONi/4N+FlIgQUGMoYOO6Fh742B/wxgv/\nhVe++UVueei32XLrR5F6YWZ8x1a7FG9ZFmfOnMIwDKqqavjXf32RH//4JQYGBgB7h/vHP/4027Zt\nL7p+T08Xk5MTVFRULeg5b8hSUt4Wbrvdw7bt23nxtX2cO/o2P/yHP+KOx/8XuPkJ57v2i8Bapqcn\nSSaTnD17mhtu2FV0Trtk38KZM6f42c9+wkMPfZTy8vCSn6eLi8sHj2Uf1G31u/wVT6l/QBE6GV8z\nvlQHZXKYiTm99VJrAInFhFzhbHSbOwJ2PamtrWdoaGDBz1Oi3DYqQiFR3LKlnkD4r3jtn7/M3lf+\nH84eeoMduz9Oy8Zb8Hhnfg+lFKdOHefAgffo6Ojg8OHDZLNZvF4vDz/8KKVrH6WitoW2NLS9N+Pk\nJpRJidVHiYrmxs1Geffdd/B6vQQCISKRCiorq5yMPq7V4zWnKQnBM08+yJ71t/HWi1/jFy/8HZWi\nj9/7vf/ZeYmVUrJp0zYOHdpPIhFneHiwoAKQJxKptEWDsSjHjx+mpWU1K1Y0uy/BLi4fUpZ9UNc0\nDaXc8vu1IutrxJvpI2AOMi0rMKUd7PzWGEE1jIGXhKgGBf5A4JrPpS+GlJLKyipisej8QUtIUiJC\nUI3kxtkyrGuqIfzpr/Hua9/i7KHXeeP7f4Pu8RKuWkGwrJIDLyj6+noZGhqaJZZbwUc/+m/4yEce\norS0lB/sLxToSZUlZA3mWhPKuTefz5+zi00zNjbC2NgInZ1t1NU1IFU1JhpjopUadRwNg5s21VC9\n4v/klf/2H/jhD59nYKCfP/mTzxMI2NMIPp+P5uYWuru76Ohoo6KiEl0vND/KC+xOnz5Bb28PwWCI\ndDrNmjWLrzV2cXH5YPL+COpC/Mod5T6wCA0jtAbP1EmqrLNM0ITEoMzqRSEZ11YDEp/Pd93FcfPR\n0LCCWKzYmCVPUlYSNEcw8aCTpUQNYwU93POxT3PDXR/j/NGf031mP2PRXmIDHfRgB8+WlhZuvvkW\nbr/9TjZs2Dj/hjelCKoopVYfEguV+zu5YkUzTU0tBS8aqVSKkZEog4P9DAz0UcEgk3IFSVFJTK6n\nxjqJl2nqy8v5tf/pP3H05b9h7949fOYz/46/+qsvOf3xxsZmBgcHSadTnDlzis2btxW90ITDEUpL\nyxgdHXEmBIaGBqmtLc7sXVxcPtj86v+Vvgja/9/emQfJddX3/nPOXXpfpmdpzYxmsUYayZZkWxZO\nTIyxDY4NCRQvDksSY3A9QvICiYG4ICYkLMkDCgPmUXFVEh6mXhleIGBTeVDEFjg8EZ43eZGFZEmW\nRsuMRtLsS0/v3fee98ft6ZnR9IxG0gwej8+n6lZ3361P/+bO/d5zzm8xKylitaavGK6/mXy5hC93\nlDrXy5eukKTszbgiQtD2/9pi0s+HYZjU1SWYmBirub1ImDI2slJRDiDqnsZQRWRDM9fe8l6uffMd\nWE4KX74Hv1EiGo2xbdv8Yi6zkapI3O3Fp1K4GOREnICaIC+i8wQdwO/309raRnNzK4ODZzl24gRx\ntxe/mGRCdjIpO4i5vUTUaQq+y/n857/IP/zD13n00Z/wl3/5Ue6776usW+eJ8ubNl/OrX+0llZpk\naGiAZLJ5zndNe8IfPLifvr6TXHHFds6cOUU4HJlXcU6j0axtVsedehFMwwCh59RXmrKvhVx4B0Vf\nG/lAN9nI6zCDSYKB4KoR9Gm8sK/5udEBEIKcSCBxKRJGAC4GITVMk7OfxvIBmpz9NNBDxO/1sq+8\ncseigu53x2h0DuJTKfIiypjswq8mcTCZlJ2Lzl9LKWlubmXM3kaBMH41Qb1zmKKIkBexSirbI0gp\n+ehH/5I773w/AwNnueeej3L6dD/gFZKpr/dyBBw/3kM+n5v3PbFYnGg0xsTEOFNTKYQQHDv2MoVC\nft6+Go1m7bK67tY1MEwTUHpO/deAa0YpBroo+1pQxvwQqtWCV/o0seD2rGxEARIHBxOBw5RYRxk/\nAgdQZEU9I8Zmuro2LVhlrlwuceTIocrohWJStjMuNhBzTyFQTMoOXLG0Aj+u8DFmdJMWTVjkqXcO\nk2YdDhYSh5de+hVCCO688/184AMfZHh4iHvu+Rh9fV4O+s7OLoQQKKU4evTwvIIv03PrAL29J1BK\nVevAa2HXaF47rH5RNwzQM+qac2htbYMFOuuusCmIOBY50mIdAgioCUaNbobMqxgyr2LS6KQkwrVP\nAExMjPPii88zMjJMkRAjxuVkZSNRdQaLHBnRQEFeYPiYEEwZbUxKz2+hXvUwIdpQwNRUiv5+T8Df\n854/5M/+7MOMjY1yzz0f4/jxY/h8PpqbWwGYmprizJn+eaePRmPU1SVIpSarKW8dp8zhwy8xPl57\nukKj0awtVr2oe8Pvr3QrNKsN27YxLXNBYc8Iz9HMJktaJDHJk3COItT8IimzKZdLHDt2lIMH91Mq\nlWhr62DU2Iwj/PjcCUJqiDJ+puTSqrbVIiubmJCXIXCoU72khTd33tfXW009+3u/9/vcfffHmJyc\n4OMfv4cjR46wfn17tWJdb+8JMpn0vHN3dGyobD9ezUWvlOLECe83DQ0NXHS7NRrN6keoWoWbVwlC\nCN705jfTffPHCIfn96psy6BYWvwmrTk/lmVSKpVf6WZcMEopMpkMqpayK0WDcxCTPMNyK2E1QFCN\nUsbHRI1eulAOQTVCyB3AoEwJf6U3X8kTr4o0OgcRuIwYWyiLmemJ3/+N8zuj/dvzORxnbsEXvztK\n3D2JwiARjzExMYYQgp07fxO7klv/pz99jPvv/wqBQIBb7vgsG9bXEXO9XnqJACPGlmr1t+l2HD/e\nw8DAGTo7u2hpaZ3znY7jkkyuq1ko5lJxHIdisUCpVCIUCi84rQFw37+8sOi5PvFH11zw9zc2Rhge\n1jXmVxpt55WnsTFy/p0WYNV7v5uL3Bg0r22EENi2TaFQmD+aIwRp2Uyde4KwGvDmv12TkBqkwXmZ\nIkGKIgIITHLYagqJi4skJVvIiORMqVSliLsnkThMyrY5gn4p5GU9kyjibi+ZzBQ+n59CIc++fc+z\nc+dvIqXk1lvfgmXZfOlLX+An/+tveet7/5ar2m0MiljkiLhnmDLmjhq0tXUwPDxIf38vjY1N1eQ3\n4JVuHRoaoFgs0tHROadWPXiZ9fr7+zh06AAjI0NksxnK5XJ1Dl9KiW3bRCIxkskk7e0b8Pn8ZDJp\nUqlJXNetuL8ILMvE+8N48/uGYWDbNvX1ns+DHoDTaJafVS/qhqGLuWgWxrZtyuUyjjt/xCYv6ihx\nloAaJc06poz15FWMiHsWW01hq5nscGV8ZGSCjGhCibn/FmE1gE9NkRdxLxHPMpKTDQgUsVIfliUw\nDINSqcS+fc9z1VU7kVJy881vwrIs/vvn/55Hv/05jD+8m6s3hHGRhNQgeRWfM/JgWRbr13fQ23uc\n/v4+Lrtsbj14KSWTk+Ps3z9ZHQHLZrMcPXqY4eHBeSVkhRBIKavOd/l8nnw+z/DwIAcO/ArLsmlu\nbqWlpRVzVhrec8/jOA65XI6+vpNk0nlM08QwTQzDQOr/cY1mWVj9om6aWtQ1i+IPBMjWGoYXginZ\nQsI9TtQ9zbjRRUlEGDMiCFXGxPMKd7GqdeLPxedOEnbP4GAxITtWJAojKxu5qt0ruWrbPlzXJZfL\nsX//i2zffjVSSt7whhu47Y8+xU+/+wV+9L//B9a738vWzZ0oIO6cYMS4Ys45m5tbGBg4w8DAGZLJ\nZoLBuaMLQghc1+HIkUOcPn2KUmmmUI5l2SQSCRobkwSDIYQQc4bSi8UCw8NDjI2Nkk5PUSoV6es7\nwalTJ2lubqW9vbN28p4KUkoUilK5RKlUQqGQQmIYBoZpYplLiyjQaDTzWf2ibph6nE6zKFII/H4/\nuVxu3rVSEHGKlfhwvztGXnqhcEqYlFjY+x3AVDni7nFAMG50zevBLyctLespl8v09/fh9/vJ5/Nk\nMmn279/L9u07kFLSvvl1vOXOz7DrO3/PI//6bfj929my9SpMikTdfmBG2KWUdHZu4OWXD3L8+NE5\nmehc1+X06VOcOdOP4zjV/ROJetrbL8PvXzy/v237aG1t8yIQgMHBs/T391EoFDhzpp+BgTNs3NhN\nXV092WyGQiFPsVhCKRcpJaZpYSnPJ8DLQSFQykGV8zglBwc4eHA/l122sZoyV6PRLI1VL+rmdEY5\njWYRTNPEsiyvxzn7chGCCaODRucgMbePoogsKbbcUAUSzlEkLuPysqrD3FKYHqb2SgebSOklT1JK\nLZodsa2tg3K5zMDAGYLBINlslkwmwwsv7OHKKz3HsfVdV/E77/8cj377czz88MP8TjbLNdf+FkE1\nwtjYKIlEffV8iUQ9dXX1jI+PMjw8SENDE6dO9XL27Onq0LhlWbS3d87LUnchJJPNJJPNjI+PcfTo\nYcrlMkeOHF70mAa8wAUXE4FC4Mwxy+7dh9i9+2f4/QEaG5vo6urWIq/RLIFV7f0eDAZ5313/Favj\n7TV7D9r7fXl4tXq/n4tSkMmm5yVmAQi6g8TcfoqEGDM2VavO1cJQeeqdIxiUSMlWMnLxHOr/Zacf\nvz9ANBrDsiwsy8K2ffj9gaqT2td+8CsKxRLFYpFSsThP2Kc915VS9PS8zPDwEOFwhGw2U3E+k4yK\nDgqVkYah/iM8+tDnyGdTXPf63+K3f/sWfLaPq6++BtuemUooFPLs3fscSqk5drFtm87ODTQ0NC1u\n1CXgui7Dw0MMDJypGWaXSNTT2NgECNLpKcbHx8hkM/OebRxMSgRxhI/OBkmhkCebzVIue1MD0wl2\ntm27mvb2+Zn8tFf2rwdt55VnzXq/f+ITn8AVJuN6Tl2zBIQAv6/2MHxWNGGLLAE1Rp17jHHZVVPY\nfe5E1dN9QUGvaKNhGBiGwebNW2uGXJ6LFAK/z4dpGOTz+ZqheEIINm7cjOM4jI2NEo/Xkc/nyOfz\n1KkTlNxBxuVlNK3v5vf+21fZ9dCnefqpJxkbn+Sdt7+DI0cOsXWrV/M9k0lz8uTxOQ5rtm2zYcNG\nEomG87b3fLiuy9DQAKdPn/IiEIC6Om8uPhwOc+TIYdLpqUqhmSxCCHI5zzmxTICcTFAkjKHyBBnH\nVin8pCgrH4lEV3XUIZfLMT4+xsjIEL29J+jtPUEiUc91191AR8dl2udGo5nFqu6pf+5zn6OMyWTw\nWnz2fEcm3VNfHtZKT32aaS9rpdRccVeKOvc4fjWBg8WUbKEgYigklsoSUoP41SQKwaRsJyfPEb5K\nHJZt2di2fUFicq6Np53hXNetPRyvXBJuDz41RU4kKCubMAOVADFwsMmJOiZzBj/71/voPdFDU7KZ\nd73zduoaW5E41SFthVegR+LS1dV9ydXblFKMjAzT23ucYrGIlJKmpnW0tq7H55s7otbXd4L+/lPV\nz7FYHR0dnew6ON+RzlB5Qu4gQTWCACKRKJ2dG4hEotV90mkvm97IyDAALS2tXHfdDaxb1zKvB3m+\nWHi4uHj41zq6p77yXEpP3fjsZz/72eVryvLyi1/8gjIWJaulZiILw5A4CxX20CwZw5Dzwo9ezUgp\nsSwL13XniqYQ5EUchMSnUgTUBGE1WE1MY1KgSIhxo4uijHnHKIWoeGbbtk3AH/D8PC6wd3iujYUQ\nWJbtzSs7Ts04+7yIY6spr/cq/IyKjZiigEkeAwcfGaLmFNu3XUEmk6Hn6BH27t1LJOSnpTmJEgZ5\nEWNMbiIrmwiqEVKTYyQSDXNi1y+ETCbDkSOHOHv2NEopmptb6e6+nIaGRsxZpXnL5TK9vcc5c+Y0\nQDUkrlDIY1k2Z9LzfRSUMCnIODmRoK3OZXJygqGhAQqFAtForBIj76O+vpFEooFCwfPCP3ToAFNT\nKbq6LqNYnLHxE/vPnvf3XL/94n0JXquEQj6y2eIr3Yw1TShUOxpnKax6US/hp+xrxpBa1FeKtSbq\nMC2aFkIKTzSns50IQVFEyIkErjBRSMrCR0HEmJItpGULLhZSGpiWid8fwO/zYVnWJeVMqGVjIaYd\n/Gwcp4xyzxlZEJK8iOOrDEubosSE7CQtmnGED4F3PikFmzd309TYSE9PDwcPHmRoaIj4xlso+jtQ\nwkAJAwc/fneMyckJmpqSi4adncu0SPf0HKFQKJBI1LNly1YaGprmPHArpRgdHeHQoZeYnJzA7w/Q\n3X05GzZsqsyRZ0ilJvG5KXIkaoYIKmHyxqtaiUZjZDJpJibGGR4exO8PEAh4oXm2bdPY2EQsFied\nTnP27Gn27dtHJBKlrs4btteivjJoUV951rioh3B962regLSoLw9rUdSnMQyj0iOuXCcKhJAoTAqE\nyIsEeVFPQcZwpR/LtPD5/d7ct2kuW1KUxWw83WufN7IAICQ5UYet0vhJYZMlL+soyTA5WU9WJsnI\nZtJiHW0NNldvv5z+s6Mc73mZQ889js+2SDRvQkpJWQToTkrGx8fI5XLU1zec9yFFKcXw8CCHD7/E\n5OQkfr+fTZu20NbWgXlOPHkul+Po0cOcPn0KpVza2jro7t5CIBBECEF9fQOBQICxsVEMioTUMAWi\nNaMRrmi18fv9NDWtQwjBxMQ4IyND5HI5YrEYsvKQ7/N5+0gpGR0d4ejRlxkbG2X9+jaeOTRy3r+L\nFvULR4v6yrOmRb1IEOVP1rz5aFFfHtayqIMnmqZpVufCpxfLsrF9Pnw+Hz7b5xWJMc0L6sEulfPZ\nWABmrSkDqAh7AoscfpXCVikKIj7X0U8IiiJMnZ3mqquuRAbXcerEIY4feo6efbuxfAHijW381rZ1\npFKTTEyM4zjOoiVs0+kpjhw5xMDAGcALudu0acu8RDbTqWWPHDlEPp8jHq/j8su31XxoCAZDNDYm\n6T87hEGZoBrBxZiXi/+KVrvyswSxWJxEomFWr32IYDCE3x+o7hONxli/voXx8QkGB89y+PBB8oRQ\ncvGYey3qF44W9ZXnUkR91TvKTbAeI9ZVU9S1o9zysNYc5VYjS7WxAvK5HOVyef48u1LE3F6CahQH\ni3FjwzwxDLjDxN0+igQZzUj2/uL7PP/88ziOgz8Y5W2/cxtveMMNFY/6HO3tnfOKuxSLXoa4oaFB\nAOrrG+js3DDPCS6VSnHkyMscOLCPoaEhpqamKBZLZDIZ0ukppqamSKe9EEMhRDVXfzxeh2tGiYUt\nGhNRmpJJ6pIbMJpej1FxiK1VJEcpRX9/H6dOeSVqm5tb6ei4rPoQFgr5SKfz1X0UULDbKAcum8nj\nfw7aUe7C0Y5yK8+lOMqtelEfFx1YsctqbteivjxoUV95LsTG5xP2kBog4nq957RsJi2aZ+amZwl/\nViQoE0BNHOSZPc/xwgt7yee8OPJYLE57exvJZJIrrtjKli1bCYdDjIwMMzg4gFJebHw8XofjuIyN\njXH27BnOnDlTeT1NOj0/Jt37rRbRaJRIJEooFJrzQJ7L5ZiYGGd8fAL3nHz9hmGSbN9C64ar+aO3\n/QZbtlxe00F2amqKnp7D5HI5AoEg3d1bCIXChEI+MhkvtC6VmuTFA4cwKVISYfLhKxDG/EI8WtQv\nHC3qK8/aFnW5AStau0ykFvXlQYv6ynMxNi4UChRrJKoBsN0UcfckBiVKBEjJ9RRlJfRLudQ7R7DJ\nMCWacYRNzO2jXC4xlZripZcO8uKLLzA6OnpRv8U0TeLxOHV1dSST6+ju3kx7ewfJ5DqSyeSSYvYf\nfjpFOTtEaug4E2d7GBs6wen+fgYHB6v7BINBtm7dytVX72Dbtu2Ew2H8/gCRSBTTNOnrO8nAwBmE\nELS1ddLd3TVnWPiHz6SIub0E1DgukrTVhQi2zHnI0KJ+4WhRX3nWrKg/8D+/y0uDQcKReM3tWtSX\nBy3qK8/F2rhULlPI5+fH3ANClYm6pwlU4roLhMnKJvIihsSh3jmMSZFJ2UZJBKlzjmFQJhyO0Nm5\ngcHBAV58cS/Hjx8jlUpRKBQ8/wKfH9d1CYXCxGJRIpEY0WgUn8/CdR2CwSB+f4D29g4aG2v7u5yL\n4zikUpNMTk4wOTlBOpOuGZ6fyWQ42dvLyRMnOHz4MFNTnnj4/X62b9/Ojh07aGlpwbJsIpEotm0z\nOjpMqVQiHo+zYUN3NfvkI3syoBQBNUbU7UPikhUJcnYXli+AlFKL+kWgRX3lWbOi/vDjB/mPPScI\nh2o/+WtRXx60qK88l2Jjpbx0r/Py2lcwVZaIexq/SgHgIimKKGVsgmoUiUNGNFIiSEgNYZGbc7yD\niYOFTQ6FYEo2kxVe+lhbTRFQ4/jVOAKFi0FariMjmhacp55utEUGn0phu1PYZBCVCASFoESQkghS\nEgHKIoiDhYtF2D1LWJ1F4FWLsywfTz31BLt372Z8fAyA9evXc/XVO7jiisurTnumaVIul5FSsmHD\nRhobk/zw2ZnSuobKE3dOYJOljI8JeRnKivHJO6/Ftu2L+ru8VtGivvKsaVH/+Z6ThEK1i2loUV8e\ntKivPMth42KpSCFfWLAgjKHyBN1h/GoSk8Ki5/JKy8yIbBk/CoFJDjkrge30V5XxkZWNZEVD7bz5\nysUii63SlVr1aWQljl4BJYIURZSCiFAU4UUfCCx3iiZ6KjnvBd3dlxOP1/Hss3t47LF/55lnnsZx\nHCzLYufO17Fz504aGurnjBiEwxF6sp0oOUuwlUvEPUtIDQAwJVv57Ws7iccTrCnP5JEAABEnSURB\nVFvXTGiBzoNmLlrUV561LerPniQU1KK+kmhRX3mWy8Zlx6GQz+Gem6hmNkphUMRUOQwKGKpY7bEX\nCTEp2ymLACY5Aq6Xc90kXxVhmMnVA1DGK1NbFn5cYQICgYtUZUwK1e+Z3ZwyfgoiUhHxyAWXrX3H\nNT7273+xmis+Go2xZctWTNNkfHyMxx//GY8++u/VFLRtbe3cfPNNbNjQBdWHFcgTJSXbceVMiNBs\nf4RoNEZXVze27SMcDpFINNDQ0KTzyS+CFvWVZ02L+v99rpdgYL7XKmhRXy60qK88y2ljhedEV6va\n20IIVabOOYaPNA4WE7JjJhUueOlwcRAoFF4v2q8m8KsJbDWFZOH/MxeDMgFKIkBRhJdc3nYxpkPa\nentPcPq0J9xCCDZs2FgtE6uUYv/+X/GTn/yYX/7yPymXy9i2zfXXv4Ft27ZRl6hDCm88okCUtNFM\niRAIgVDlihPdhFervr2T5ubWarnccDhCLBajvr5RC/w5aFFfeda0qO9+rm/BGspa1JcHLeorz0rY\n2HUV+UIep1boWy2UIqwGCLtnEEC+khq3LGo/NM8+zqCIoYoIylXhd4WJgw8Xs2a6V+9YF0nZW1QZ\ngVsZ9p/uTUtvEQYuBg42CDknTj2fz3Po0IFqr93n89PdvZlIZOahZGJigt27H+ff/u3/VPPNJ5Lt\nXLvzGnZcuaXqPFfCT0YmyYkEILixK8fx4z2UyyUikSgbNmysDsO7rott+6irq6e+vqFm+efXIlrU\nV541Leq/eP7Ugv9MWtSXBy3qK89K2rjsOJTLJVzHy0bnKheBWFDoTZUl6pzChxdnXhBhcqKevIhf\n8DA5SiEpVYb7CxiqgEHBe08Rg9IF/x4Hk2jITyAQIBgMVZYgo6Mj9PX1opQ3TRAOR+juvrx6fwiF\nfExN5Xjxxb385Cc/5oknnsB1HUzLZvv2K3ndzh20tLYi8JwJs6KRN+5oR0qDEyd6GB310squW9dC\nW1tHteiNUspL3lMJp0sk6udUjnutoUV95VnTov6fL/Tj89VOmadFfXnQor7y/Dpt7CpVFXnHdb2C\nNtOz5NNCrxS2ShFWg/jUzA26hJ+yCFDGXyl4Y+C50nk9bKHKGBURl6qESaHqcDeb6fKwjvB68tOL\nwqjsLZiemxeVMrESpzoiYIki596aLMsiHI5QLBbJZGYS34RCYTZs6GLduqZq8hmAb/9HP4ef/xmH\nnttFemIIgOS6ZrZv28oVW7eSqKsDvBrw69a1oJTi5Mnj5PM5TNOkra2DZLJ5Xtpgx3GxLKsq8LFY\n7ZDbtYoW9ZVnTYv6L/eeXjDkRIv68qBFfeV5JW08Xd7VcRxc1xN65TpV0TQo4lfj+FQKS2XmOMwt\nhlspAFsWduXVh4O3lLEQQiKkQM56lYaBIaW3bSYJntcbdr32KeVyxxsbSKdTTExMkkpNksmkSaen\nKBYX9ur3+Xwkk+toaWlDSunFqQOu69Dfs5dDzz5G38vPVTPZtbS0sHXrVrZu3Uo8Hse2fTQ1JVHK\n5ezZs7iug23brF/fXi0aM88Grotp2kQiEcLhMJFIFMuya2bCWytoUV951rSoP7Hv7Jw6zbPRor48\naFFfeVajjZVSM0P3rotyFcp1kBQxKSCVgxAueH30yvy3gSMsHOxKWJxAylniLQTSkBjSREixVD++\necxOCuO6LhMT42QyacbHxxgcPEs6PUXv2QkssvNGCqZHCTKinqxYB7PEOJ9NcfLg0xw78P84fXwf\nqlJkJ5lM0rVxIxu7umhvb8cxoyhMgjJdnVtvbm6hqWndgrXolVKUy45nA2lgWV6FQK+AkI9AIEA0\nGsM0rQt2vrvvX164oP1rsVyJdrSorzyXIuoXOIH260esQMUsjUZTKflqmlizHpqVUrhKoSrV4hyv\nGz0zFC5AIjCEwDBNr8b8CrdTSkkiUU8iUU9bWwel0jaGhgZ48dGTuOUyNmlsd4oA49XQOpMiMXWW\nqDqLcr04/JyIIf2NbHndrWx53a3kMpOcPPg0J1/6JadPvsTg4CBPPvEEpmmyfv162tvbq4sQgt7e\nE/T1naShoZFksplIJDpHnL0SujO2dBwHx/EK5wCVCnwKKQWGYWAYFpZlVSoGWhiGiWka+Hw+LMsr\n/WsYxopUDdSsXVa1qNuWtWz1rDUazfkRwhNsVrGQWJZFa2sboeBwpXccpODUUxQdFItFLCdFhCEs\nMl48PQqbHLbKEVMDKNfzund8Ji07LuM3rrmcfFFxqvc4vUf3cfrkYU6e7OXkyZPV74xEIiSTyerS\n2NhIQ0MDzc0t1Nc3UleXOK/4SimrZvXaXaRcLpLLZar7KKWqUxDgVbYzDINMJlcZ+RAV14jKfVF4\nf7Ppz0JK73tmTW9oXlssSdS/+MUvsm/fPoQQ/PVf/zXbt2+vbnvyySf52te+hmEYvPGNb+RDH/rQ\ngscMDAzw8Y9/HKUUjY2N3HfffQsOZQEYpqljRDUazYJ4vWOrspgUS2VcJ0K63OTN0ZcdfM4wQUax\nyFec8qiIfRGLIqgpwhY0bIyyY+MNwA3kcjlO9fdzqq+PgYEBBgcH6enpoaenZ873+3w+4vE48Xic\nWCxGOBwmGAwSCoUIh8OEQiH8fj9+vx/LsjFNoyLuBqZpYlkWpjndY/fh9/vw+QLYtj3nIcFVLouk\nCphBgZqeGJGiWvIW4PjxowghkVJUX6U0K68GPp+NbfuxLBPD0PfeVyvnFfVnn32W3t5evve973Hs\n2DE+9alP8b3vfa+6/fOf/zzf+ta3aGpq4r3vfS+33XYbY2NjNY/5+te/zp133smtt97K1772NR55\n5BH+4A/+YEV/oEajee0gAMOQGMZMxIyrwmSdNs9RsOwgSlP4mMDHFBb5eYl1FOAPBNi0aRPdmzZV\nzqrIZrMMDQ0xMDDA2NgYExMTTExMMDY2Nqe63IJtEwKfz4dt29VX2/ac6kzTXHSRholp2kjTxjB9\nSNOPMAMIO4g0g2CFkGYQw/ZjmjaGZWOYNlIaVXFOpSYXbNv0CIHrqmoP3ztOYpqy0g4LKQ1GR8Nk\nMqXKA4lZeUCYu0xPG0hpVNfph4RfD+cV9aeeeopbbrkFgK6uLlKpFJlMhlAoxKlTp4jH4ySTSQBu\nvPFGnnrqKcbGxuYdk06n2bNnD3/3d38HwM0338y3vvUtLeoajWZFkUIgTQvLtMAHihCO00C67OC4\nDjhlpJvBUlksspgqX0mbOy32nj9BMBiks7OTjRs3Yts+bNuHZZk4jks6PcXg4CDj4+NMTaXIZrNk\nMhkymQyFQqFaRnf6fTqdplAo4LpLizS4WIQQVUH+rjXzkDAtyNOvCy3nbl/s8+z3hmHME3Hv4WXm\ne2ePUky3cWbduZ/tGutm3tf6vtcq5xX1kZERtm3bVv1cV1fHyMgIoVCIkZEREolEdVsikeDUqVOM\nj4/POSaRSDAyMkI+n68Ot9fX1zM8PLycv0Wj0WjOiwBMw8Q0ZjkIEsV1XPKug3JdlFIot8Bt2yzS\n6SkymQzFYr4qzvl8nmw2M+e8dXVx6uouLGbdqYQalsvlmsti26aXUqm05HXFYpFsNltdt5Kc74Fg\nujd/7mutdYvtMz3FMHe0wKhOK5w7iuAt01MQxjmfp6clZo8sCISg+nkmHFOcs23uflJKlKKybnp/\niRCzR0MkSonqPm94w81s2XL5Jdn9gh3lFouAW2hbrfVLiaSLh3001S2cwtK2JP1D6QW3azQazVKY\nGbaf7ezm57rrZsLAnEr433RvO5fLkctlyOfzFIsFCoV8tTdeKhWrouxW4u+d6Yx/1RwByivMgxdd\n4N0Sp1/nUijXul+Kyvz5TAEeVVlLZT2VYMTp3zgbz1nv/A8Jsz8vtu18++ZyuV/Lw8SrmWQyyf79\nRy/pHOcV9aamJkZGRqqfh4aGaGxsrG6b3dseHBykqakJy7LmHdPU1EQwGKRYLGLbdnXfxbj+qhau\nv6rlgn+URqNZ+3z5Ize+0k24JNTsUEHmd3Smh+bP1wFa6Bznvq+1LPRdM174M6+zt53v+5fSkVvo\ndwkh5m2rtW4pTB9zIccvZd/p3vhyp3kJBAKXFKMOSxD166+/ngceeIB3v/vdvPTSSySTSYJBr/fc\n2tpKJpPhzJkzNDU1sXv3br761a8yNjY255hpQX/961/Prl27ePvb386uXbu44YYbLqnxGo1G82pl\ntmd6LdZyVjrNyrGkjHL3338/e/bswTAMPv3pT3Pw4EEikQi33HILzz33HF/5ylcAeMtb3sJdd91V\n85jNmzczPDzMX/3VX1EsFmlpaeGLX/yivnA1Go1Go1kmVnWaWI1Go9FoNEtn9aaN0mg0Go1Gc0Fo\nUddoNBqNZo2gRV2j0Wg0mjXCqi3osli+ec3Fs2fPHj7ykY+wadMmlFJs3ryZP/7jP76gnPya2hw+\nfJi/+Iu/4K677uKOO+5YsNbBj370Ix566CEMw+Bd73oX73znO1/ppr+qONfOn/zkJzlw4AB1dXUA\nfOADH+DGG2/Udr4E7rvvPl544QUcx+FP/uRP2L59u76Wl5lzbfzzn/98ea5jtQrZs2eP+tM//VOl\nlFI9PT3qPe95zyvcorXDM888o+6+++456+699161a9cupZRS999/v/rud7/7SjTtVU02m1V33XWX\n+sxnPqO+853vKKVq2zWbzarbbrtNpdNplc/n1dve9jY1OTn5Sjb9VcVCdt69e/e8/bSdL46nn35a\nffCDH1RKKTU+Pq5uuukmde+996rHHntMKaWv5eVgIRsvx3W8KoffF8o3r1ke1DkBD3v27OHmm28G\nvJz8Tz755CvRrFc1Pp+Pf/7nf6ahoaG6rpZd9+3bx5VXXkkoFMLn83HNNdfwwgsvvFLNftVRy861\n0Ha+eK699lq+/vWvAxCNRslmszz77LO86U1vAvS1vBzUsvF0kp/ZXIyNV6Won5tTfjrfvGZ5OHbs\nGB/60Ie44447ePLJJ3VO/mVASolt23PW5XK5OXYdGhpidHR0Xr0Ebe+lU8vOAN/5znd4//vfzz33\n3MP4+HjNuhTazktDSkkgEADg4Ycf5qabbtLX8jIz28Y/+MEPuOmmm5BSLst1vGrn1Gdz7tOL5uLp\n6Ojgz//8z3nrW9/KqVOneN/73jcnF7O29cqwkF21vS+dd7zjHcTjcbZs2cI3vvENHnjgAXbs2DFn\nH23nC+fxxx/nkUce4cEHH+TWW2+trtfX8vLx+OOP88Mf/pAHH3yQAwcOLMt1vCp76ovlm9dcGslk\nkre+9a0AtLW10dDQQCqVolgsAiwpJ79maYRCoTl2TSaTC9ZL0Fw81113HVu2bAHgzW9+M0eOHCGZ\nTGo7XwK//OUv+cY3vsE3v/lNwuGwvpZXgHNtvFzX8aoU9euvv55du3YBzMs3r7k0fvzjH/PAAw8A\nMDo6yujoKLfffjuPPfYYgM7Jv4xM1zqAGbteeeWVHDhwgHQ6TSaTYe/evezcufMVbumrm7vvvpuX\nX34Z8PwYuru7tZ0vgXQ6zZe//GX+6Z/+iUjEKy6ir+XlpZaNl+s6XrVpYmvljtdcOplMhnvuuYfJ\nyUmUUnz4wx9my5YtOif/JbJv3z7+5m/+hrGxMQzDIBaL8eCDD3LvvffOs+tPf/pTvvnNbyKl5M47\n7+R3f/d3X+nmv2qoZee7776bf/zHfyQUChEKhfjCF75AIpHQdr5Ivv/97/PAAw/Q2dmJUgohBF/6\n0pf41Kc+pa/lZaKWjW+//XYeeuihS76OV62oazQajUajuTBW5fC7RqPRaDSaC0eLukaj0Wg0awQt\n6hqNRqPRrBG0qGs0Go1Gs0bQoq7RaDQazRpBi7pGo9FoNGsELeoajUaj0awRtKhrNBqNRrNG+P85\nNOeLUNYKXgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fabbf994a10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"ax.hist(sunspot_df['sunspot.year'].values, bins=40, normed=True, lw=0, alpha=0.75);\n",
"\n",
"ax.fill_between(x_plot, post_pmf_low, post_pmf_high,\n",
" color='gray', alpha=0.45)\n",
"ax.plot(x_plot, post_pmfs[0],\n",
" c='gray', label='Posterior sample densities');\n",
"ax.plot(x_plot, post_pmfs[::200].T, c='gray');\n",
"ax.plot(x_plot, post_pmfs.mean(axis=0),\n",
" c='k', label='Posterior expected density');\n",
"\n",
"ax.legend(loc=1);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Again, we can decompose the posterior expected density into weighted mixture densities."
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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7XzUCALO5uC66KYQQQjQIHw3qoQCo1Wqys7Ox2+0Vzi27Q5vOr3xQ79BjCIqi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\nSDWM1QAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fabbf7e51d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"ax.hist(sunspot_df['sunspot.year'].values, bins=40, normed=True, lw=0, alpha=0.75);\n",
"ax.plot(x_plot, post_pmfs.mean(axis=0),\n",
" c='k', label='Posterior expected density');\n",
"ax.plot(x_plot, (trace['beta'][:, np.newaxis, :] * post_pmf_contribs).mean(axis=0)[:, 0],\n",
" '--', c='k', label='Posterior expected\\nmixture components\\n(weighted)');\n",
"ax.plot(x_plot, (trace['beta'][:, np.newaxis, :] * post_pmf_contribs).mean(axis=0),\n",
" '--', c='k');\n",
"\n",
"ax.legend(loc=1);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We have only scratched the surface in terms of applications of the Dirichlet process and Bayesian nonparametric statistics in general. This post is the first in a series I have planned on Bayesian nonparametrics, so stay tuned.\n",
"\n",
"This post is available as an [IPython](http://ipython.org/) notebook [here](https://nbviewer.jupyter.org/gist/AustinRochford/62c283a3f0fae90b5e39)."
]
}
],
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"display_name": "Python 2",
"language": "python",
"name": "python2"
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"name": "ipython",
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"mimetype": "text/x-python",
"name": "python",
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}
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wuciawe commented Jul 14, 2017

Hi, thanks to this great post. I find that ElemwiseCategoricalStep doesn't exist in pymc3 any more, so I replace it with ElemwiseCategorical, and keep everything else the same as in the post, but I failed to obatin the expected result in estimate the density of waiting times between eruptions. The result of the estimated density looks like a single modal gaussian.

EDIT:

I find the reason, there are some typos in the post:

  1. In [24]: 1. / np.sqrt(trace['lambda'] * trace['tau'])[:, np.newaxis, :]) should be (trace['lambda'] * trace['tau'])[:, np.newaxis, :], there should be no inverse and square root.
  2. In the example of estimate the density of sunspots per year, multiple occurance of trace['beta'] should be trace['w'] and In [30]: w = pm.Deterministic('beta', beta * T.concatenate([[1], T.extra_ops.cumprod(1 - beta[:-1])])) should be w = pm.Deterministic('w', beta * T.concatenate([[1], T.extra_ops.cumprod(1 - beta[:-1])]))

I don't understand why in the second case, reassign beta variable does not raise an error in pymc3.

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