{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Bayesian Parametric Survival Analysis with PyMC3" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Running on PyMC3 v3.4.1\n" ] } ], "source": [ "%matplotlib inline\n", "\n", "from matplotlib import pyplot as plt\n", "from matplotlib.ticker import StrMethodFormatter\n", "import numpy as np\n", "import pymc3 as pm\n", "import scipy as sp\n", "import seaborn as sns\n", "from statsmodels import datasets\n", "from theano import shared, tensor as tt\n", "\n", "plt.style.use('seaborn-darkgrid')\n", "print('Running on PyMC3 v{}'.format(pm.__version__))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Survival analysis](https://en.wikipedia.org/wiki/Survival_analysis) studies the distribution of the time between when a subject comes under observation and when that subject experiences an event of interest. One of the fundamental challenges of survival analysis (which also makes is mathematically interesting) is that, in general, not every subject will experience the event of interest before we conduct our analysis. In more concrete terms, if we are studying the time between cancer treatment and death (as we will in this post), we will often want to analyze our data before every subject has died. This phenomenon is called censoring and is fundamental to survival analysis.\n", "\n", "I have previously [written](http://austinrochford.com/posts/2015-10-05-bayes-survival.html) about Bayesian survival analysis using the [semiparametric](https://en.wikipedia.org/wiki/Semiparametric_model) [Cox proportional hazards model](https://en.wikipedia.org/wiki/Proportional_hazards_model#The_Cox_model). Implementing that semiparametric model in PyMC3 involved some fairly complex `numpy` code and nonobvious probability theory equivalences. This post illustrates a parametric approach to Bayesian survival analysis in PyMC3. Parametric models of survival are simpler to both implement and understand than semiparametric models; statistically, they are also more [powerful](https://en.wikipedia.org/wiki/Statistical_power) than non- or semiparametric methods _when they are correctly specified_. This post will not further cover the differences between parametric and nonparametric models or the various methods for chosing between them.\n", "\n", "As in the previous post, we will analyze [mastectomy data](https://vincentarelbundock.github.io/Rdatasets/doc/HSAUR/mastectomy.html) from `R`'s [`HSAUR`](https://cran.r-project.org/web/packages/HSAUR/index.html) package. First, we load the data." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "sns.set()\n", "blue, green, red, purple, gold, teal = sns.color_palette()\n", "\n", "pct_formatter = StrMethodFormatter('{x:.1%}')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "df = (datasets.get_rdataset('mastectomy', 'HSAUR', cache=True)\n", " .data\n", " .assign(metastized=lambda df: 1. * (df.metastized == \"yes\"),\n", " event=lambda df: 1. * df.event))" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " time event metastized\n", "0 23 1.0 0.0\n", "1 47 1.0 0.0\n", "2 69 1.0 0.0\n", "3 70 0.0 0.0\n", "4 100 0.0 0.0" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The column `time` represents the survival time for a breast cancer patient after a mastectomy, measured in months. The column `event` indicates whether or not the observation is censored. If `event` is one, the patient's death was observed during the study; if `event` is zero, the patient lived past the end of the study and their survival time is censored. The column `metastized` indicates whether the cancer had [metastized](https://en.wikipedia.org/wiki/Metastasis) prior to the mastectomy. In this post, we will use Bayesian parametric survival regression to quantify the difference in survival times for patients whose cancer had and had not metastized." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Accelerated failure time models\n", "\n", "[Accenterated failure time models](https://en.wikipedia.org/wiki/Accelerated_failure_time_model) are the most common type of parametric survival regression models. The fundamental quantity of survival analysis is the [survival function](https://en.wikipedia.org/wiki/Survival_function); if $T$ is the random variable representing the time to the event in question, the survival function is $S(t) = P(T > t)$. Accelerated failure time models incorporate covariates $\\mathbf{x}$ into the survival function as\n", "\n", "$$S(t\\ |\\ \\beta, \\mathbf{x}) = S_0\\left(\\exp\\left(\\beta^{\\top} \\mathbf{x}\\right) \\cdot t\\right),$$\n", "\n", "where $S_0(t)$ is a fixed baseline survival function. These models are called \"accelerated failure time\" because, when $\\beta^{\\top} \\mathbf{x} > 0$, $\\exp\\left(\\beta^{\\top} \\mathbf{x}\\right) \\cdot t > t$, so the effect of the covariates is to accelerate the _effective_ passage of time for the individual in question. The following plot illustrates this phenomenon using an exponential survival function." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "S0 = sp.stats.expon.sf" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "t = np.linspace(0, 10, 100)\n", "\n", "ax.plot(t, S0(5 * t),\n", " label=r\"$\\beta^{\\top} \\mathbf{x} = \\log\\ 5$\");\n", "ax.plot(t, S0(2 * t),\n", " label=r\"$\\beta^{\\top} \\mathbf{x} = \\log\\ 2$\");\n", "ax.plot(t, S0(t),\n", " label=r\"$\\beta^{\\top} \\mathbf{x} = 0$ ($S_0$)\");\n", "ax.plot(t, S0(0.5 * t),\n", " label=r\"$\\beta^{\\top} \\mathbf{x} = -\\log\\ 2$\");\n", "ax.plot(t, S0(0.2 * t),\n", " label=r\"$\\beta^{\\top} \\mathbf{x} = -\\log\\ 5$\");\n", "\n", "ax.set_xlim(0, 10);\n", "ax.set_xlabel(r\"$t$\");\n", "\n", "ax.yaxis.set_major_formatter(pct_formatter);\n", "ax.set_ylim(-0.025, 1);\n", "ax.set_ylabel(r\"Survival probability, $S(t\\ |\\ \\beta, \\mathbf{x})$\");\n", "\n", "ax.legend(loc=1);\n", "ax.set_title(\"Accelerated failure times\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Accelerated failure time models are equivalent to log-linear models for $T$,\n", "\n", "$$Y = \\log T = \\beta^{\\top} \\mathbf{x} + \\varepsilon.$$\n", "\n", "A choice of distribution for the error term $\\varepsilon$ determines baseline survival function, $S_0$, of the accelerated failure time model. The following table shows the correspondence between the distribution of $\\varepsilon$ and $S_0$ for several common accelerated failure time models.\n", "\n", "
\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Log-linear error distribution ($\\varepsilon$)Baseline survival function ($S_0$)
[Normal](https://en.wikipedia.org/wiki/Normal_distribution)[Log-normal](https://en.wikipedia.org/wiki/Log-normal_distribution)
Extreme value ([Gumbel](https://en.wikipedia.org/wiki/Gumbel_distribution))[Weibull](https://en.wikipedia.org/wiki/Weibull_distribution)
[Logistic](https://en.wikipedia.org/wiki/Logistic_distribution)[Log-logistic](https://en.wikipedia.org/wiki/Log-logistic_distribution)
\n", "
\n", "\n", "Accelerated failure time models are conventionally named after their baseline survival function, $S_0$. The rest of this post will show how to implement Weibull and log-logistic survival regression models in PyMC3 using the mastectomy data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Weibull survival regression\n", "\n", "In this example, the covariates are $\\mathbf{x}_i = \\left(1\\ x^{\\textrm{met}}_i\\right)^{\\top}$, where\n", "\n", "$$\n", "\\begin{align*}\n", "x^{\\textrm{met}}_i\n", " & = \\begin{cases}\n", " 0 & \\textrm{if the } i\\textrm{-th patient's cancer had not metastized} \\\\\n", " 1 & \\textrm{if the } i\\textrm{-th patient's cancer had metastized}\n", " \\end{cases}.\n", "\\end{align*}\n", "$$\n", "\n", "We construct the matrix of covariates $\\mathbf{X}$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "n_patient, _ = df.shape\n", "\n", "X = np.empty((n_patient, 2))\n", "X[:, 0] = 1.\n", "X[:, 1] = df.metastized" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We place independent, vague normal prior distributions on the regression coefficients,\n", "\n", "$$\\beta \\sim N(0, 5^2 I_2).$$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "VAGUE_PRIOR_SD = 5." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "with pm.Model() as weibull_model:\n", " β = pm.Normal('β', 0., VAGUE_PRIOR_SD, shape=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The covariates, $\\mathbf{x}$, affect value of $Y = \\log T$ through $\\eta = \\beta^{\\top} \\mathbf{x}$." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "X_ = shared(X)\n", "\n", "with weibull_model:\n", " η = β.dot(X_.T)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For Weibull regression, we use\n", "\n", "$$\n", "\\begin{align*}\n", " \\varepsilon\n", " & \\sim \\textrm{Gumbel}(0, s) \\\\\n", " s\n", " & \\sim \\textrm{HalfNormal(5)}.\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "with weibull_model:\n", " s = pm.HalfNormal('s', 5.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are nearly ready to specify the likelihood of the observations given these priors. Before doing so, we transform the observed times to the log scale and standardize them." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "y = np.log(df.time.values)\n", "y_std = (y - y.mean()) / y.std()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The likelihood of the data is specified in two parts, one for uncensored samples, and one for censored samples. Since $Y = \\eta + \\varepsilon$, and $\\varepsilon \\sim \\textrm{Gumbel}(0, s)$, $Y \\sim \\textrm{Gumbel}(\\eta, s)$. For the uncensored survival times, the likelihood is implemented as" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "cens = df.event.values == 0." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "cens_ = shared(cens)\n", "\n", "with weibull_model:\n", " y_obs = pm.Gumbel(\n", " 'y_obs', η[~cens_], s,\n", " observed=y_std[~cens]\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For censored observations, we only know that their true survival time exceeded the total time that they were under observation. This probability is given by the survival function of the Gumbel distribution,\n", "\n", "$$P(Y \\geq y) = 1 - \\exp\\left(-\\exp\\left(-\\frac{y - \\mu}{s}\\right)\\right).$$\n", "\n", "This survival function is implemented below." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "def gumbel_sf(y, μ, σ):\n", " return 1. - tt.exp(-tt.exp(-(y - μ) / σ))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now specify the likelihood for the censored observations." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "with weibull_model:\n", " y_cens = pm.Potential(\n", " 'y_cens', gumbel_sf(y_std[cens], η[cens_], s)\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now sample from the model." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "SEED = 845199 # from random.org, for reproducibility\n", "\n", "SAMPLE_KWARGS = {\n", " 'njobs': 3,\n", " 'tune': 1000,\n", " 'random_seed': [\n", " SEED,\n", " SEED + 1,\n", " SEED + 2\n", " ]\n", "}" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (3 chains in 3 jobs)\n", "NUTS: [s, β]\n", "Sampling 3 chains: 100%|██████████| 4500/4500 [00:03<00:00, 1133.00draws/s]\n", "The acceptance probability does not match the target. It is 0.9186031973056857, but should be close to 0.8. Try to increase the number of tuning steps.\n" ] } ], "source": [ "with weibull_model:\n", " weibull_trace = pm.sample(**SAMPLE_KWARGS)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The energy plot and Bayesian fraction of missing information give no cause for concern about poor mixing in NUTS." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.energyplot(weibull_trace);" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.0895766652410845" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pm.bfmi(weibull_trace)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Gelman-Rubin statistics also indicate convergence." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.0033842131318067" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "max(np.max(gr_stats) for gr_stats in pm.gelman_rubin(weibull_trace).values())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below we plot posterior distributions of the parameters." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.plot_posterior(weibull_trace, lw=0, alpha=0.5);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These are somewhat interesting (espescially the fact that the posterior of $\\beta_1$ is fairly well-separated from zero), but the posterior predictive survival curves will be much more interpretable.\n", "\n", "The advantage of using [`theano.shared`](http://deeplearning.net/software/theano_versions/dev/library/compile/shared.html) variables is that we can now change their values to perform posterior predictive sampling. For posterior prediction, we set $X$ to have two rows, one for a subject whose cancer had not metastized and one for a subject whose cancer had metastized. Since we want to predict actual survival times, none of the posterior predictive rows are censored." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "X_pp = np.empty((2, 2))\n", "X_pp[:, 0] = 1.\n", "X_pp[:, 1] = [0, 1]\n", "X_.set_value(X_pp)\n", "\n", "cens_pp = np.repeat(False, 2)\n", "cens_.set_value(cens_pp)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "scrolled": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 1500/1500 [00:00<00:00, 1787.17it/s]\n" ] } ], "source": [ "with weibull_model:\n", " pp_weibull_trace = pm.sample_ppc(\n", " weibull_trace, samples=1500, vars=[y_obs]\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The posterior predictive survival times show that, on average, patients whose cancer had not metastized survived longer than those whose cancer had metastized." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "t_plot = np.linspace(0, 230, 100)\n", "\n", "weibull_pp_surv = (np.greater_equal\n", " .outer(np.exp(y.mean() + y.std() * pp_weibull_trace['y_obs']),\n", " t_plot))\n", "weibull_pp_surv_mean = weibull_pp_surv.mean(axis=0)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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ducmhMzepX9OJwJYetGnqjs5KW8yVhBBCCPNh0esMPKhbKH7tapJ2bMd96HCqdA687/cYTSbOXktk9/Fowq4kYDKB3k7H3zrUp3MLDzQaGdD4IJbSNWfOpA3UJ22gPktpA7O4TVDRuHR7DkWnI3H7Fkx/7CD2ZxpFwae+G6/38+Ozf7TnuXZ1MRhNrPjtIp8sP86NWyVfp10IIYRQixQDRbBydsb56Y7k375N2tHgYr+/ahU7+j/TkE9Gt6VNU3euxqTy0fchrPv9Mjl5D7ebmxBCCFGepBh4AJduPUCrJXHrL5j+mH5YHGe9Da/+zYcJ/f1xcbRh25HrTP33EfaHxWAo4TmEEEKI8iTFwAPo3NxwavckuTdjST95/KGO9fNyY8aotjzXri6pGXl8t+087//nKEfPxWG03GEaQgghzJAUA8Vwfa4HKAqJW3554J7w92NjraX/Mw359B/teKZ5LRKSs1j8UzgffRdCdEJG8ScQQghRpBMnjtGtWyfi4m4WPLZo0Xy2bt1c5DGpqSns2LG91DLs3buHhIT4hzomJyeHzZs3AbB162YOHNj7yNfftGk933yz5JGPv0uKgWJY16iJPqA1OdcjyQw/80jncHWyZXj3J5g5ui3tm1Xn+q10vlh9koSUrFJOK4QQlkWns+aTTz4q8Ye1y5cvcfDgo//x/bN161YVWhyvJBITbxcUAz169KZDh06lludRlds6AxWZa4+epB87SuKWzTj4+D7yedxd7Bnduxl13B1Zu+cyX64J473/a4mjvXUpphVCiPK3dvdlQs7fKtVztn7CnQGBDR/4PQEBrTAaTWzYsJa+fQcWem7VquXs2rUDrVaLv38LXnvtdZYt+5bLly/x008b+NvfXiz43uHDB+Lv35IrVy5Rr54nLi6uhIWdRKfTMWfOPLKzs/n0049ISUkBYMKEd4iLu8nlyxf5+OMPWbjwG775Zgnnz58lNTWFhg0bM2XKNE6dCmXBgrlYWVlha2vLxx9/xrJl33LtWgTfffdvjEYjbm5uuLi4sW7dKgDi42/h7l6d+fOXsHjxAsLCTmI0Ghk4cCiBgc8SFhbKV1/NwdHRCa1WS7NmPo/9WkvPQAnY1q2Hg58/WZcuknXp0mOfr3vbunRvW5ebiZnMXRdGdu79py4KIYQo3ttvT2bNmpVERd0oeOzKlcvs3v0bixd/y+LF3xIVdYODB/czfPhLBAS0KlQIAGRmZhIU1I2FC/9DWNhJfH39+Prrf5Ofn09ExBWWLfuWgIA2zJ+/hHffncqcObN48skONGzYmPff/4jc3BwcHR2ZO3ch//nPD4SHnyY+/hb79+8lMPBZFixYyvPP9yM1NY3hw1/C07M+f//76ILrd+rUmQULljJlyjQcHZ2YOnU6hw8fJDY2mkWLvmHevMUsW/YtaWlpfPHFLKZPn8lXXy2kVq1apfIaSs9ACbkEdSPjVBipR49g16jRY5+v/zNepGXkcvDMTb7eeIY3+vlhpZXaTAhRMQ0IbFjsp/iy4uxchddff4uZM6fh6+sPQGTkNZo188XK6s6fOX//5kREXMHbu+hP0U2aPAGAXu+Ip2cDABwdHcnJyeXq1cucOHGMXbt2AJCWVngZehsbW5KSkpg2bQr29vZkZWWRn5/PsGF/Z9myb3njjTFUq+aOt7cPeXn3XzL/9u0EPvhgMlOmTKNGjZrs2rWDCxfOM27cKwDk5+dz82YMiYmJ1K1bDwBfX/9CRdCjkr8+JWTXqDEae3sywk4+9EDC+1EUhRHPPYGflxvhEYl8s+WczDIQQohH1KFDR+rUqcfWrb8AUK+eJ2fPniE/Px+TyURo6Enq1KmHRqPBaCzq39qiV42tV8+TAQOGsGDBUmbM+JSuXZ8D+ON8Ro4cOcitW3H885+f8MorY8nJycZkMrFjx1Z69OjF/PlLqF+/AT//vAFF0WAyFZ5qnpaWxnvvvc348RPx8mpYcM0WLVqxYMFS5s1bTGDgs3h41KZatWpcuxYBwLlzZx/zlbtDegZKSLGywsHXj7TgI+TcuI7tH1XZ47DSahjzvA9frA4l+GwcjvY6BndpVLDVsxBCiJJ74423OH48BAAvr4YEBj7LmDF39rbx8/OnY8dnSEiI5+rVy6xdu5IBA4aU+NzDh7/Ep5/O4OefN5CZmcFLL935tO7j48fHH0/js8++5Pvvv2Hs2NEoikKtWh4kJMTTtKkPn376MXZ2diiKwrvvTsXFxYW8vHwWLpyHjY0NAEuXLiQhIZ7vvvs3BoMBnU7Hl18u4OTJ47z22stkZWXSsWNn7O0deOedKXz88TQcHBywt7cvtNvvo5K9CR5C2tFgYpcuwu1vL+DW+2+lliM9K4/PVpwgOiGDvp0a0LO9Z6md25xZynrg5kzaQH3SBuqzlDaQvQlKib2PL2i1pIeFlup59XY6Jg7wx9XJhh/3XmVfWEypnl8IIYR4ECkGHoLW3h77xk3IuRZBfnJSqZ7b1cmWtwY2R2+n47/bz3Py4sMtYiGEEEI8KikGHpKDfwsA0sPCSv3cNd0ceKO/HzorDYt/DufctcRSv4YQQgjxZ1IMPCS9f3MAMsJOlsn5vWo5M+4FX0wmE/9ad4rQSwllch0hhBDiLikGHpKuWjWsPWqTeTYcY05OmVzDp4Ebb/TzR6OBrzee5sjZm8UfJIQQQjwiKQYegd6/Oab8fDLPhpfZNZrVd+Wtgc2x1mn5989n+T00usyuJYQQwrJJMfAIHP64VZBeRrcK7mpUuwrvDm6B3l7Hsu0X2B58vUyvJ4QQFc2JE8fo0KEVO3f+WujxESMGMXPm9Pse86g7F4aGnuDy5TtL0k+Z8s5DH3+vPn26PdbxpU2KgUdgW78BWkcnMsLCMBmNxR/wGOrVcGTy0Ja4ONqwds9luWUghBB/Uq+eZ8EywXBnX4KsrKJ3hX3UnQu3bPm5YLviTz6Z/fBBzZisQPgIFI0GB//mpB7YR3bEVey8ynY97ppuDrw1sDkzfzjGt1vO417Fnga1nMr0mkII8TDi160m7VhIqZ7TsVVrqvUfVOz3NWzYiOvXI0lPT0ev1/Prr1vp2vU54uJusnv3TtasWYFGo8HPrzljxowvtHOhr68fkybNJzs7l+TkZN5+ezK+vv588sk/iYq6QU5ODv37D8LTswHBwYe5ePE8np4NeOWVEfz8869Mnvwm6enpAJw+HcbcuQtxcnJm7tzZmEwmnJ2dee+9adjZ2fH55zOJiLiKh0dtcnPvvz+BWqRn4BH9b1ZB6S5AVJRaVR34Rx8fDEYj8zecIimtbAYvCiFERdSpUyB79+7GZDJx7lw4Pj5+pKam8O23S/jqq0UsWvQNCQm3CAk5UmjnwoiIq0yaNImvvlrE0KEj2Lp1M5mZGYSGnmDmzNl88cV8NBotTzzRlLZt2zNmzOvUqFGj4LqffvolCxYsxcfHjyFDhtOiRQCfffYxb745iQULltK+/VOsWPFf9u3bQ25uLkuXfs8//jGOnJxsFV+tv5KegUdk790MRacjPfQkVV/sVy7X9PNyY2DnhqzefZl5P55i8tCW2Oi05XJtIYR4kGr9B5XoU3xZCQrqzhdffEqtWh74/7EejMFgIDk5ibfffh24s01xdHQUdet6FhxXtao7CxcuBLRkZmb+sd6/A6+//haffz6TzMyMgk2JirJy5Q8kJycxefIHAERGRvDFF5/+kSGf2rXrYmdnR9OmzQCoUaMG7u7VS/kVeDxSDDwijY0N9k29yTgVRl5CPLqq1crlukGt6xCdkMH+U7F8s+Ucr/6tGRrZ2EgIYeE8PGqTlZXF+vWr+cc/xhETE42iKLi7V2fu3IVYWVmxdetmGjVqTEZGRsHOhV99NZu5c/+Fk5M733yzhNjYGBISErhw4RyzZs0hJyeHvn170q1bDxRF+ctug7/8sonTp0P5+OPPCx6rW7ce77//ETVq1ODUqVBu305Aq7Vi165fgcEkJMQTH29eq8xKMfAYHHz9yTgVRsapMKoEPlsu11QUhWHdmhCXmMmx87fY5GrPix0blMu1hRDCnHXpEsSvv26lbt16xMREU6WKC88+241x417BYDBQs2YtAgODSEtLLdi5sGvX53jjjTews3OgWjV3UlKScXNzIzHxNq+++hIajYZBg/4PKysrvL19WLx4ATVregBw+3YCs2fPwtfXnwkTXsNkMtGnz4u89dZ7fPzxhxgMBhRFYfLkD6hTpy4hIcGMHj2CGjVqUqVKFZVfrcJk18LHkHf7NhGT3sLex4/aE94spVQlk5qZy8xlx4hPzubvzz3B0/61yvX6pcFSdgozZ9IG6pM2UJ+ltIHsWlhGdG5uWHvUJuv82TJbjbAoTvbWTBzQHAdbK5b9eoHwCNnHQAghxKORYuAxOfj531mN8NzZcr92DVd7xvf1Q1Fg4abTRN1KL/cMQgghKj4pBh6T3s8fgIzTpb+LYUk0rlOFUT29ycoxMHd9mEw5FEII8dCkGHhMtg280Ng7kHHqFGoNv2jrXZ2+nRqQmJrDvPWnyDeU7aqIQgghKhcpBh6TotXi4OtLflIiuVE3VMvRo109nvKpQWRcGr8cuqZaDiGEEBWPFAOlwOGPWwXpp9S5VQB3phwOfrYxLo42bDkcyfW4yj8yVgghROmQYqAUODTzBUUhQ8ViAMDe1oqRzz2BwWji263n5HaBEEKIEpFioBRo9XpsvRqSffUKhjR1P5H7NnDjKd8aXI9Lly2PhRBClIgUA6VE7+cPJhMZZ06rHYVBXRrhrLfm54MRRMfLdEMhhBAPJsVAKXFQeYrhvRxsdYzo9gT5BhPfbj2PwSi3C4QQQhRNioFSYu1RGytXVzLOnMZkMKgdh+aNqtKuWXUiYlPZdkRuFwghhCiaFAOlRFEUHPyaY8zMJOvKZbXjADDkj9kFm/ZHcDk6Re04QgghzJQUA6XIwdcPgEwzGDcAoLfT8Upvb0yYWPLTGTKy89SOJIQQwgxJMVCK7Js0Aa1WlX0KitKkrgt9nqrP7dQcvt96XrVVEoUQQpgvKQZKkcbWDrsGXmRfi8CQkaF2nAK9n/SkSZ0qHL8Yz+8no9WOI4QQwsxIMVDK7Jt6g8lE5oXzakcpoNEojO7tjd5Ox6pdl2V1QiGEEIVIMVDK7Js2AyDzXLjKSQpzdbLlpZ5NyTcYWbjxDLG3zafnQgghhLqkGChltvXro9jYknnWfMYN3NW8YVX6POXJreQsZvz3GCcuxqsdSQghhBmQYqCUKVZW2DdpQl7cTfJu31Y7zl88/3QDRvf2xmg0sWDDaX7cewWjUQYVCiGEJZNioAzYe9+9VWB+vQMA7ZvVYOrwVrhXsWPL4Uj+tTaU9CyZdiiEEJZKioEyYK7jBu5Vx13PByNb4eflRvi1JD7+7zFiEmQcgRBCWCIpBsqAda1aaJ2dyTx31qzn9TvY6ni9nx+9nqzHreQsZv5wjDNXze/WhhBCiLIlxUAZUBQF+6beGFJTyY0x73n9GkXhxY5ejO7tTV6+iX+tC2PX8Si1YwkhhChHUgyUkYJbBWfN91bBvdo3q8G7Q1rgaKdjxW8XWfHbRbPu1RBCCFF6pBgoI/ZNvQHzHUR4Pw09nHl/RCtqV3Ng1/Eo9p+KVTuSEEKIciDFQBnRubpiXaMmmRfOY8rPVztOiVV1tuONfv7Y2Vixaucl4hIz1Y4khBCijEkxUIbsvb0x5eSQHXFV7SgPxc3ZluHdmpCTZ2Dp5nDyDUa1IwkhhChDUgyUobvjBjIqyLiBe7X1rk77ZtWJiE3j54PX1I4jhBCiDEkxUIbsmjwBilJhBhH+2dCgJrg52bLl8DUu3khWO44QQogyIsVAGdLa22PXsBHZV6+Y5dLExbG3tWJ07zsDIf+9+SyZ2RVn7IMQQoiSk2KgjDk99TSYTKQc2Kd2lEfSuE4Verb35HZqNvN/PEVWjhQEQghR2UgxUMYcW7dBY2dH6oF9mAwGteM8kj5PeRLQuBoXbiQzZ/VJ2cdACCEqGSkGypjGxgbHdu3JT0oi4/QpteM8Eiuthlefb8ZTPjWIiE3js5UnSE7PUTuWEEKIUiLFQDmo0vEZAFL2/a5qjseh1Wj4e8+mdAmoTXR8Bp8uP0FCcpbasYRM3+ujAAAgAElEQVQQQpQCKQbKgU2dutjWb0DG6VPkJVa8gYR3aRSFIc82oteTntxKzuLTlSdIzcxVO5YQQojHJMVAOXHu2AlMJlIP7Fc7ymNRFIUXOzagz1OeJKbm8M0v5zDKHgZCCFGhlWsxkJeXx1tvvcWgQYMYMmQIV65cITIyksGDBzNkyBCmTZuG0Vh4tbvs7GzGjx/PkCFDGD16NImJiQAsWLCAgQMHsnjxYgDy8/N5/fXXMZjpID3H1m3R2NqSsn8fJmPFX9GvT4f6NKvvyumrt/kt5IbacYQQQjyGci0G9u7dS35+PqtXr2bs2LHMnTuXWbNmMWHCBFauXInJZGLXrl2Fjlm1ahWNGzdm5cqVPP/88yxcuBCAQ4cOsWbNGvbvv/NJe82aNfTt2xetVlueP1KJaWxtcWzbnvykRDLOVMyBhPfSKAov9/LGycGa9b9fISI2Ve1IQgghHlG5FgP169fHYDBgNBpJT0/HysqK8PBw2rRpA0DHjh05dOhQoWOOHz/O008/XfD84cOHAbCyssJgMKDRaEhLS+PEiRN06tSpPH+ch+bc6RkAUvbtVTdIKXF2sGZ0b2+MRhOLfzojaxAIIUQFZVWeF7O3tyc6OprnnnuOpKQkFi9eTEhICIqiAODg4EBaWlqhY9LT03F0dPzL88OGDWPixImMHDmSpUuXMmrUKGbPnk1mZiZjx46latWqxeapVs2xlH/C4i7oQ2JDL9JPheGkycXGza18r18GnqnmyPX4DNbtusSaPVd4+/8CCtqzJMq9DcRfSBuoT9pAfZbeBuVaDHz//fd06NCBt956i9jYWEaMGEFe3v8WsMnIyMDJyanQMXq9noyMjL88HxQURFBQEDdu3ODAgQPcvn0bV1dXunfvzg8//MDEiROLzRMfn1bs95Q2+/ZPk375CpHbd+PStXu5X78sBLX04MT5OPaFRlOnmgNdAmqX6Lhq1RxVaQPxP9IG6pM2UJ+ltMGDCp5yvU3g5ORU8Cnf2dmZ/Px8vL29CQ4OBmDfvn20atWq0DEtW7Zk7969Bc8HBAQUen7RokWMGTOG7OxstFotiqIUFA/myMHHF4DMSxdVTlJ6rLQa/tGnGY72OlbuvMjxC7fUjiSEEOIhlGsxMHLkSMLDwxkyZAgjRoxg4sSJfPjhh8yfP5+BAweSl5dHt27dAHjppZfIzc1l8ODBXLp0icGDB7NmzRrGjRtXcL6TJ09Sq1Yt3N3defLJJ9m9ezczZsygX79+5fljPRSdmxtWLq5kX76EqRJNyavqbMeE/v5Y67Qs+Tmc85FJakcSQghRQoqpMv1FekhqdQvFLllIWshRPGd+inX1GqpkKCvh1xKZuzYMa52GSUNaUrd60d1SltI1Z86kDdQnbaA+S2kDs7lNIO6wbdgIgKzLl1ROUvqaeboyurc32TkGvlwbxi1ZslgIIcyeFAMqsKvExQBAm6bVGRLUmNSMXL5cHSq7HAohhJmTYkAFNrXroNjYkH3lstpRykyXgNr0bF+PW8lZLP05HKPRYu9GCSGE2ZNiQAWKVotdAy9yY2IwpKerHafMvNCxAX5ebpyJSGTj/qtqxxFCCFEEKQZUUjBu4Grl7R3QKAqv9PbG3cWOLYcjOXZephwKIYQ5kmJAJXfHDWRfrrzFAIC9rY7xL/pio9PyzZZzRMdX3p4QIYSoqKQYUIltAy9QlEo7iPBeHtX0jOrZlJw8A/M3nCYzWwYUCiGEOZFiQCVaOztsatcmO+IqpvzKv8FPqyfc7wwoTMri+23nK9WCS0IIUdFJMaAi24aNMOXlkX09Uu0o5eKFpxvQqLYzxy7EE3wuTu04Qggh/iDFgIr+N26g8t8qANBoFEb1bIqNTsuKHRe5nSILEgkhhDmQYkBFlX3xoftxd7FnQGBDMrLzmbc2VG4XCCGEGZBiQEVWrm5YubiQVck2LSrOM81r0ay+KyfO32JvWIzacYQQwuJJMaAiRVGw9WqEITWVvPh4teOUG0VR+PtzT+Bga8WaXZdl/wIhhFCZFAMqs7RxA3e5Otnyjxf9yMkz8M0vZ8k3GNWOJIQQFkuKAZVZ4riBu55pWZtWTapxKSqFhRvPkJcvBYEQQqhBigGV2dS5s2lR1uWLakcpd4qi8HIvb5p5uhB6OYGFG09LQSCEECqQYkBlilaLXcNG5MbEWNS4gbusdVrG9/WjWX1Xwq7c5mspCIQQotxJMWAGHANaA5B2PETlJOqw1ml5va8vPvVdOVVQEBjUjiWEEBZDigEzoG8ZABoNaccssxgA0FlpGd/XF98Gbpy6cpv5G6QgEEKI8iLFgBnQ6vXYN/Um51oEufGWu82vzkrLuBd98PNy48zVROb/KAWBEEKUBykGzIRj6zYApFtw7wDcKQjGvuB7pyCISGTej6fJzZOCQAghypIUA2ZC37wlaLWkhRxVO4rqdFYaxr7gi7+XG+ERicz/8ZQUBEIIUYakGDATd24VNCPneiS5tyz3VsFdOisNr73gS/OGVQm/lsS8H0/JLAMhhCgjUgyYEcfWd2YVpB+T3gG4WxD40LxhVc5eS+LbrecwWtAeDkIIUV6kGDAjBbcKLHzcwL2stBpe/VszvDycCD4bx6b9V9WOJIQQlY4UA2ZE6+CAg/cftwribqodx2zcWYfAD3cXO345FMk+2elQCCFKlRQDZkbf6s6sAukdKMzR3pqJ/f3R2+lYtv0CZyJuqx1JCCEqDSkGzIy+RQvQamXcwH1Ud7VnfF9fNBqFhRvPcD0uTe1IQghRKUgxYGa09g44NPMh58YNcm/KrYI/a1S7CqN7e5Oda2D2qpNcjUlVO5IQQlR4UgyYobsLEKWFBKucxDy1fsKdUT2bkpmTz+zVJzkfmaR2JCGEqNCkGDBDDs1bolhZkXY0GJNMpbuvp3xr8trzPuTnG/lybRihlxPUjiSEEBWWFANmSGtnh4OfP7mxMeRGRakdx2wFNHHnjf5+aBT4esNpgs/GqR1JCCEqJCkGzJRjm3YApB49onIS8+ZT3403BzbHWqdh6c/h7Dx2Q+1IQghR4UgxYKYc/PzR2NqSFiK3CorTuE4V3h3cEicHa1buvMTaPZdlpUIhhHgIUgyYKY21NQ4tWpKfkED21StqxzF79Wo4MnVYADVc7dkefJ3/bD5LvkH2MhBCiJKQYsCMOf1xqyAtWG4VlETVKnZMGRaAl4cTR87G8a+1YWRm56sdSwghzJ4UA2bMvqk3Gr2etGNHMRlkC9+S0NvpeGdQC1o0qsq5yCRm/nCMmIQMtWMJIYRZk2LAjClWVjgGtMaQmkrmhfNqx6kwrHVaxr7gS7c2dYi9ncmMZcc4dl62hRZCiKJIMWDmHNv+catAZhU8FI1GYWBgI179WzMwwcJNZ1i75zIGo4wjEEKIP5NiwMzZNWyElYsr6cePYczLUztOhdOmaXXeHx5A9T8GFn6xOpTUjFy1YwkhhFmRYsDMKRoNjq3bYMzKIvPMabXjVEge1fR8MLwVLRpV5fz1ZP75fYjsaSCEEPeQYqACuLsAkdwqeHT2tlaMfdGXvp0akJyew6crjvN7aLSs4SCEEEgxUCHY1KuHrnoN0kNPYkhPVztOhaVRFHq29+TNAc2xtbZi2fYLfLftPHn5MlNDCGHZii0GevXqxX/+8x/i4+PLI4+4D0VRqPJMZ0x5eSTv3aN2nAqvWX1XPhzZino1HDlwKpbZq0NlPQIhhEUrthhYsmQJOTk5DB8+nFdeeYXt27eTJwPZyp1Th45o7OxI3r1TBhKWgqrOdkz5v5a0aerO5agUZq86SWqmDCwUQlimYosBDw8Pxo4dy7Zt2+jfvz+zZs2iQ4cOzJw5k6Qk2Ue+vGjt7HB+uhOGlBTSQ46qHadS0FlpeaV3Mzr61yQyLo3PVpwgKS1H7VhCCFHuii0GMjIy2LBhAyNGjOCLL75g8ODBrF+/Hk9PT0aNGlUeGcUfqnR5FjQakn7bLgPfSolGozCi+xMFCxTNWn6cW0mZascSQohyVWwx0KVLF0JCQhg3bhzbt2/n1VdfpU6dOgwZMoSaNWuWR0bxB51bVfQtW5Fz4wZZ58+pHafSUBSFAZ0b8vzT9UlIyWbW8hNcjk5RO5YQQpSbYouBmTNnMmvWLFq3bl3w2I4dO1AUha+//rpMw4m/cunaDYCk335VOUnloigKfZ6qz9CgxqRm5vLZihPsPhElPTBCCItgVdQTW7duJTc3l3nz5pGWllbweF5eHkuXLqVr167lElAUZtfAC1uvhmScCiP3ZizWNaR3pjR1CahNLTd7Fv0UzvIdF7kak8qwbk2w0WnVjiaEEGWmyJ6B9PR0goODycjIIDg4uOC/sLAwJk6cWJ4ZxZ/8r3dgh8pJKqemnq5M/3tr6td04tCZm3zyg4wjEEJUboqpmH7Qw4cP0759+/LKU67i49OK/yYzZDIauTZlEvmpKTT47Au0jo5qR3ok1ao5mnUb5OUbWbXzIr+HxmCj0zIwsCGdmtdCURS1o5Uac28DSyBtoD5LaYNq1Yr+W1FkMfDBBx8wY8YMhg0bdt9//JYtW1Z6CVVSkRs/aecO4levpOqL/XDt0UvtOI+korwBj4TfZPmOi2Tm5NOsvit/f+4JXJ1s1Y5VKipKG1Rm0gbqs5Q2eFAxUOSYgYEDBwIwfvz40k8kHpvTkx1I+HEdKQf34/Jcz0r1adXctGtWgyZ1Xfhu2znOXE3kg2+OMjSoEe2b1ZDXXQhRKRQ5ZiArK4uQkBAURbnvf0JdWnt79C1bkRcXR/blS2rHqfRcHG2Y2N+fEd2bYDSZ+M8v51iw4bRshyyEqBSK7BmYN29ekQcpilIpbhNUdM4dniYt+DApB/Zj16ix2nEqPUVR6NTcA29PV77dco6TlxK4FBXMiO5NCGjirnY8IYR4ZMUOIKzMKvo9IpPRSMSUdzGkpeH1xVw0tnZqR3ooFfk+ndFkYuexKH7ce4W8fCPtmlVnUGAjnBys1Y72UCpyG1QW0gbqs5Q2eKQxA5YwgLCiUzQanJ96mts/bSTtWAjOHTqqHcliaBSFrq3r4NvAlf/8co4j4XGEnLuFn5cb7ZvVwL9hVXRWskO4EKJikAGEFZzTk09x++dNpB48IMWACmq6OTBlWEt+PxnD/rAYTl5K4OSlBBxsrWjTtDpBretQw9Ve7ZhCCPFARRYDPj4+ALRp04bz588TEhKClZUVbdu2pUGDBuUWUDyYzq0q9k29yTwbTu7Nm1jXqKF2JIuj1WjoElCbLgG1ibqVzqHwmxwOv8mek9H8fjKagCbV6NG+Hp41nNSOKoQQ96WdPn369Ad9w7Jly/j8889xc3MjOTmZr7/+Gr1eT9OmTcspYtnJrCz712u1pB8/hmJjg4N3M7XTlJiDg03laYM/ODlY06y+K11b1aF2NT23krI4F5nE3tAYLkcl41FVTxW9jdoxC1TGNqhopA3UZylt4OBQ9L89xQ4g7N27N6tWrUKv1wOQkpLC//3f/7F58+bSTamCyjJgxJiXy9W3JqDorGnw+Rco2oqxjr4lDNoxmUycvZbE1iORnItMwtpKw6vP+9C8YVW1owGW0QbmTtpAfZbSBg8aQFjsCCc7Ozt0Ol2hr62tK9aI6cpOo7PGsW07DCnJZISfVjuOuIeiKDSr78o7g1sw/kVfAOb/eIq9odEqJxNCiP8pcszAggULAKhSpQqDBw+mR48eWFlZsX37djw9PR/5gkuWLGH37t3k5eUxePBg2rRpw+TJk1EUhUaNGjFt2jQ0mv/VKNnZ2bzzzjvcvn0bBwcHPvvsM1xdXVmwYAH79++nc+fOvPrqq+Tn5/Pmm2/yr3/9C20F+WRcmpyf6kjKnt2kHtiP3q+52nHEfbRoXI13hrTgq3Wn+O/2CySl5fC3DvVlES8hhOqK7Rnw8/MjMDCQ7Oxs0tPT6dChA/Xr13+kiwUHB3Py5ElWrVrFDz/8wM2bN5k1axYTJkxg5cqVmEwmdu3aVeiYVatW0bhxY1auXMnzzz/PwoULATh06BBr1qxh//79AKxZs4a+fftaZCEAYFOvHta165AeFkp+cpLacUQRvGo5M2VYAFWdbfn54DW+23aefINR7VhCCAtXZM/AuHHj7vu4yWQiKirqkS524MABGjduzNixY0lPT+fdd99l7dq1tGnTBoCOHTty8OBBgoKCCo45fvw4L7/8csHzd4sBKysrDAYDGo2GtLQ0Tpw4wdChQx8pV2WgKApVOnfh1g/fk/z7bqo+31ftSKIINVztmTq8FXPXhXHgVCw3b2cy5nkfXBzNZ2ChEMKyFFkM3LV8+XK+/PJLsrKyCh6rXbs2v/3220NfLCkpiZiYGBYvXkxUVBRjxozBZDIVdJM6ODiQllZ4EEd6ejqOf2zRe+/zw4YNY+LEiYwcOZKlS5cyatQoZs+eTWZmJmPHjqVq1eIHaD1oMEVF5Nq7K4mb1pO6by9NRgxBUwHGdlS2NiipatVgzusdmb82lH2h0cxYdoxJw1rh41X+AwsttQ3MibSB+iy9DYotBr799lt++ukn5s6dy8SJEzl69CgHDx58pItVqVKFBg0aYG1tTYMGDbCxseHmzZsFz2dkZODkVHgutl6vJyMj4y/PBwUFERQUxI0bNzhw4AC3b9/G1dWV7t2788MPPzBx4sRi81TG0aOOHTqRtG0LV7f8ZvaLEFnKCN4HGdGtMbXc7Fm7+zJTFx1iQGBDglrVLrdxBNIG6pM2UJ+ltMFjzSZwc3OjTp06NGnShIsXL/Liiy8SERHxSEECAgLYv38/JpOJuLg4srKyaN++PcHBwQDs27ePVq1aFTqmZcuW7N27t+D5gICAQs8vWrSIMWPGkJ2djVarRVGUguLBElXpHAgaDUk7f8OCt52oMJQ/ljV+Z3Bz9PY6Vu+6xOxVJzlxMR6DUcYSCCHKR4mmFh45coQmTZqwZ88e4uPjSU1NfaSLde7cmaZNm9KvXz/GjBnDhx9+yKRJk5g/fz4DBw4kLy+Pbt26AfDSSy+Rm5vL4MGDuXTpEoMHD2bNmjWFxjKcPHmSWrVq4e7uzpNPPsnu3buZMWMG/fr1e6R8lYHO1Q19y1bkRt0g68J5teOIEmpS14VpI1vTrL4r568ns2DDaSYtPswvh67JNslCiDJX7KJDly5dYt26dUyePJk33niDw4cPM27cOEaOHFlOEctOZe0Wyrp8iRufzsShRUs8xr6udpwiWUrX3MOKik9nz4loDp25SU6eASuthsCWHvRoXw8n+9IdByJtoD5pA/VZShs86DZBibcwTk9PR6fTYWNTeUY8V9bGN5lMXJ/5ETmR1/D85DOsq7mrHem+LOUN+Kgys/M5dCaWX4/e4HZqNjbWWrq2qkO3NnWxty12uE+JSBuoT9pAfZbSBo81ZuDChQu88MILdOnShY4dOzJ48GCuX79eqgFF6VIUBZdng8BkInn3ruIPEGbJ3taKZ1vV4ZNX2jE0qDE2Oi2bD11j0uJDrNtzmSsxKRhlXIgQohQU2zMwaNAgxowZQ6dOnQD47bff+O9//8vy5cvLJWBZqsyVoCk/n6uT3saUm0OD2V+isbVTO9JfWEo1Xlpycg3sOhHFtiORZGTnA+Cst6ZFo2oENKmGdz2Xh56FIG2gPmkD9VlKGzxWz0BOTk5BIQB3pvSlp6eXTjJRZhQrK6o80xljVhYp+/epHUeUAhtrLT3a1eOLsU8xvq8vHXxrYjCY+P1kNF+sDuXjZccIj0iUWSRCiIdW5BbGMTExpKWlcfXqVa5evUr9+vXJzc1l/fr12Nvb07Gjec9hL4nKvmWlTS0Pkn/fQ3bEVao8E4hiVTr3mUuLpWwbWtq0Wg013Rxo0bgaXdvUwbueC7l5RsKvJXE4/CYXbyRT3cUeVyfbYs8lbaA+aQP1WUobPNIWxoGBgSiKct9PGYqi/GUPgYrIErqFEjb9SOIvm6nabwCu3XuoHacQS+maKy+RN9PYuP8qp67cBqB9sxqM6N4Ea13R+3VIG6hP2kB9ltIGpTKboDKyhMY3ZGYQMfkdUBTqfzoHrZ35jB2wlDdgebt4I5k1uy8REZtG/ZpOjO/rSxX9/T8RSBuoT9pAfZbSBo81ZiAxMZEJEybQtm1bWrVqxbhx40hISCjVgKLsaO0dcOnaHWNGBsk7d6gdR5SDxnWqMHloAE/61CAiNpUZ/z1G5M3K/w+dEOLRFVsMfPjhh/j6+rJr1y52796Nv78/U6dOLY9sopS4PNsVrd6RpB3bMcjgT4ugs9IwqmdT+j3jRXJaDrNWHOf4hXi1YwkhzFSxxcCNGzcYNWoUer0eJycnRo8eTUxMTHlkE6VEY2uLa4+eGLOySNqxXe04opwoikKPdvUY+6IvAF9vPM2/1oZx8UayzDgQQhRSbDGgKAqxsbEFX8fExGBlZqPSRfGcnwlEW6UKSTt3kJ+SonYcUY5aNq7GlP8LoHFtZ05fvc2nK04wa/kJQi8nYDRKUSCEeMDUwruqV6/O2LFjOXHiBFu3bmXBggW89957eHp6lk/CMmQJU0nuUrRaNDprMkJPYDIacfDxVTuSxUznMQfOehs6+NXC29OFtIxczkUmEXw2jsOnY7DRaalV1R5NOW2bLAqT94H6LKUNHmlq4V3nz5/H3d2dU6dOYTQa8ff3x83NrdRDqsESRo/ey5SfT8T7kzEkJ1Nv+gysa9RUNY+ljOA1R1G30tkaHMnRc7cwGk1Udbale9u6dPCt+cCpiKL0yftAfZbSBo81tfC5555j27ZtpR7KHFhC4/9Z2vFjxC5agF3jJtR+exKKptg7RWXGUt6A5syg0bBy+zkOnIolL9+Ik4M1o3o2xbdB5Sj4KwJ5H6jPUtrgQcVAsbcJgoODuXr1Kjk5Ody6dYuYmBhiYmLw8PAo7ZzlzhK6hf7MplYtsm9cJzP8DFYuLtjW81Qti6V0zZmz6lX1NKzpSEf/WlhpFc5HJnP4zE00CjSqU+Wh9zoQD0/eB+qzlDZ40G2CYkcCJicnExwcTHBwcMFjiqKwbNmy0kknyp37kGFEnj9Hwro16P2aY1WlitqRhMqcHazp28mLlo2rsXDjaTbujyAiNo2XezXF3landjwhRBkr8QqEycnJaLVaHB2L7maoaCyhW6goyXt2c2vFMvQBrag1ZpwqGSyla86c3a8N0jJzWfJzOGevJeHuYsfYF3yp465XKWHlJ+8D9VlKGzzWCoTnz5+nT58+dOvWjS5dujBo0CCuX79eqgFF+XPu9Ay2DRuRfvwY6SdPqB1HmBFHe2veHNCcnu3rcSspixn/DWHbkUiZhihEJVZsMTBlyhQmTpxIcHAwR48eZdSoUUyePLk8sokypGg0VB8+ErRabq38AUNWltqRhBnRaBT6dvLi9X5+2NvqWPf7FT5dcYK4pEy1owkhykCxxYDJZKJz584FXwcFBZGZKf8gVAY2tTxw7dGL/KQk4teuUjuOMEPNG1bl45fb0voJdy5HpzDt26PsOh6FUVYwFKJSKXY2wZUrVzhz5gz169cnJyeHDRs2kJOTg6+vL2lpaRV6DIEljB4tjq1XQzJOhZF5+hTWtetgU7NWuV3bUkbwmrOStIG1TkvrJ9yp6WbPmauJHL8YT9iV29Ryc8DN2backlZe8j5Qn6W0wWMtOhQYGFj0wYrCrl27Hj2ZyixhwEhJ5MREc33GdBQbGzynz8Cqiku5XNdSBu2Ys4dtg+T0HNbuucyR8DgA2jR1p/8zDaUoeAzyPlCfpbTBYy06VJlZQuOXVPLundxauRx772Z4THirXBYjspQ3oDl71Da4HJ3Cqp0XiYhNQ2el4SnfmjTzdKFJXRf0djIV8WHI+0B9ltIGDyoGZMchAYBz5y5knD5FxulTJO/6DZegbmpHEmasoYczU4e34vCZm/y49wq/n4zm95PRKEDdGo5413OhqacLjWpXwUaWNxbC7EnPgCiQn5JC5PT3MWZlUff9adjUrlOm17OUatyclUYb5BuMRMSmcu5aEmcjk7gSnYLhj2mIVloFr1rONPV0+WPcgUNpxK5U5H2gPktpA7lNUARLaPyHlR4WSsz8uVh71Kbu+9PQ6Mquy9dS3oDmrCzaICfXwKWoZM5GJnHuWhLX49IwAYoCnVt48PzTDeRWwj3kfaA+S2mDR7pN8N577z3wpLNmzXr0RMJs6f2b49zpGVL2/k7S9q249f6b2pFEBWNjrcWngRs+f2x2lJ6Vx5mI2/x84Bq7T0QTfDaOPh3q07mFB1Za9TbKEkL8T5HFQJs2bcozhzAjVfsOID0slMQtm9EHtMamVvlNNxSVj95ORzvvGrRq4s7u41H8dPAaq3Ze4veT0Qzu0qigaBBCqKdEtwmSk5PJysrCZDJhMBiIioqiffv25ZGvTFlCt9CjSj95nJiv52PbsBF13n2vTGYXWErXnDlTow1SM3PZtD+CvaHRmEzg5+XGoC6NqOFqX645zIW8D9RnKW3wWLMJvvzyS1asWEF+fj4uLi7ExcXh4+PDunXrSjWkMC/6FgHoA1qRfvwYKft+p8ozRa83IcTDcLK3Zni3JnRu4cGqnRc5deU24RGJdAmoTe+nPHGQXRKFKHfFftz75Zdf2Lt3Lz169GDZsmV89913uLq6lkc2oTL3wf+Hxs6OhB/XkZeUpHYcUcnUcdfzzuAWjH3BBxdHG3aE3GDi/AP8a20Yv4dGk5Keo3ZEISxGscWAu7s7er2eRo0acf78edq1a0dCQkJ5ZBMqs6pShar9BmLMyiJ+5XK144hKSFEUApq4M3N0WwZ0bkgtNwdOX73Nsu0XeHPBQT5ZfpxzkVKIClHWir1NoNfr2bRpE82aNWP58uW4u7uTmppaHtmEGXB+uiNpRw6RfvI4acdDcAxorXYkUQnprLR0b1uX7m3rEp+cxclLCZy8GM/FG8nMXnWSp3xrMDCwkUxJFKKMFNszMHPmTBITExP1agAAACAASURBVGnbti0eHh58+OGHTJgwoTyyCTOgaDRUH/F3FCsrbq34AUN6utqRRCVXrYodXVvXYdLQlrw/ohV13fUcPH2TKUuPcPB0LBa8NIoQZabY2QTff/89vXr1omrVquWVqdxYwujR0pK4bQsJP67Dsf2T1Bz1Sqmc01JG8JqzitAGBqOR30Ki2HTgKrl5RhrWdqZXe098G7iiKIra8R5bRWiDys5S2uBBswmK7RmIi4tjwIABjBo1ip9++omsrKxSDScqBpeu3bHxrE/a4UOknwpVO46wIFqNhu5t6/Lxy21p0agql6NSmLsujOnfhRB8Ng6jUXoKhHhcJV6O+NixY2zdupWDBw/i5+fH7NmzyzpbmbOESrA05URHEfnRNLSOjnh+NBOt/eOtM28p1bg5q4htcD0uja1HIgk5fwuTCdyr2NG9bV2e8q2BzqribYpUEdugsrGUNnisngEAk8lEXl4eeXl5KIqCtbV1qYUTFYeNR23cevXBkJxM/No1ascRFqpudUde/ZsPn7zSjmea1yIxLZtlv17g3UWH2RYcSVZOvtoRhahwiu0ZmDFjBjt3/n97dx4fVX3vf/w1a5ZZkkwSshEgQMIq+74KFkUUXKrVioiit2pBxYWLoiJWbKVorYpovbX409Lb3irW68JVC0JkRwh72ISEbASyz0wyk8zM+f0RHA0Q1iRnkvN5Ph48DLPlE95+Zz75nu/5nn/To0cPpkyZwlVXXUVYWFhL1destNAJNjXF5+PYi7/Bm3eMlEefwNKr9yW/lla68VDWFjKocHn5emse32QV4Kn1ExFmZHSfJAZkxNM1JQq9PrTXFbSFDFo7rWRwWVct/OCDD7juuuva5EZDWgi/OXiO5XLsxd9gjIqiw9PzMUZFX9LraGUAhrK2lEG1p47V2wv4+rs8nNV1ANgjTfRLj6Nfejzp7aNCcnfDtpRBa6WVDC6pGfjHP/7BbbfdxpIlS876xFmzZjVNdSrSQvjNpfTzTyn9+CPCUlNpP+cpDJEXv6+8VgZgKGuLGdT5/GTnlrP94El2HCqh6lRjAJDgiCQtyUZakp2uKVF0TLCpPnPQFjNobbSSwSVdm0DO5RXn4ph0Pb6yUirXrqFwyWukPPo4epOsJRHqMxkN9OkSR58ucQSuUfi+sJJd35dytKiKo0VONu0tZtPeYgAiw4x06xBNz04OenaKIdER2SZOVxTiYjXaDNx+++1A/Q6EbXWfAXHpdDod7abehd/lwrXtO47/159IemBms1zdUIhLpdfrSG8fTXr7+kNZAUXhRHkNRworOZhXwb6c8vrdDg/Vb7HeLjqCARnx9M+Io0ty6K83EKKpnHc74h/2GUhLS2PKlClcffXVREREtERtIsTp9HoS77ufArcb1/ZtnPjr+7SbNl1+sxIhS6/TkeiIJNERyYjeSQCcrKghO7ecPUfL2H2klP/bcoz/23IMe6SJPl3i6NEphh4dY4i2to2F00KcjewzIC6bv6aG/MUv4T2WS+wNNxE7+YYLep5WjtOFMsmgoZ+uN8g6VBJciAiQHGehZ8cYrhnSgdio8Cb7npKB+rSSwSWtGfgp2WdAnIshIoKURx7j2O9eoPSTjzEnJWEbNETtsoS4aD9db3DXNQp5J1zsyy0jO6ecg/kV/Hubm3W7i/jlz9IZdUWSzIKJNuOC9hlYtWoV3bt3l30GxDl58/M49rsXQQmQ+p/zCO/U6ZyP10o3Hsokgwvn8wfYuOc4f199iBqvn75dYpl+bffLPnwgGahPKxlc1g6EsbGxrFixgrfffptJkya1mUZANL2w9qkk/cf9KHV1FL75Gr6KCrVLEqLJGA16RvdN5jczhtKjYww7vy/l2T9v5ttdhfj8AbXLE+KynLcZ+PTTT9vkhkOieVj79Sfu5lvxlZdTsOQ1ArW1apckRJOKjQrn8dv7MXVCBnX+AMu+2M8TSzewIvMIZVUetcsT4pIYFixYsOBcD9i8eTNHjhzB6/Vy4sQJCgsLKSwsJCUlpYVKbD7V1fJB1RzCu3bFV1JC9Z5d1J08gbX/wLMeW7VYwiQDlUkGl0an09E52c6wngnodDpyipzszSnj39/lk3fChS3CRFxU+AWtKZAM1KeVDCyWxmf2z7tmYNq0aWc+Safj/fffv/zKVKaFY0RqCdTVkf/yIjzfH8Y+ajQJd91zxh4EWjlOF8okg6bhrfOzeV8xq7flc+yEC4Ck2EjGD2jPiN6JRIQ1vlZbMlCfVjK4rGsTtGVaCF9Nfreb/FdfxptzFPuIUSTcPaNBQ6CVARjKJIOmpSgK3xdUsXp7Plv3n8AfUAgzGxjcrR0902Lo0dFBlKXh2ViSgfq0ksFlNQPTpk0761SXzAyIC+GvdpP/hx8agpEk3H1vsCHQygAMZZJB86l015K5s5A1WQWUO73B21PiLfTs6ODK/skkxVokgxCglQwuqxnYsmVL8Gufz8eqVauw2+088sgjTVehSrQQfijwV7spePUVPEePYB8+koR76hsCrQzAUCYZNL9AQCG32El2bjnZOWUcyq+k1hdAp4ORVyRxz+Te6Px+tcvUNK2MgyY/THDrrbfyz3/+87KKCgVaCD9U+KurKfjjy3iOHME2bDiJM/6DdglRkoHKtPImGErqfAF2Hi7hk3VHKShxYzToGdsvmUnDOhJjk1O31aCVcXBZOxAWFhYGv1YUhcOHD1Mh54+Li2SIjCRl9hMU/PEVnJs2ggLxcx9VuywhWpzJqGdQ93YMyIhn875iPt2Yw6pt+azalk9qOys9OsbQs1MMGanRhJsvaJNYIS7beWcGxo8fj06nQ1EUdDodDoeDWbNmMXbs2JaqsdlooRMMNf6aGgr++Aqe7w8TN2Y0MVPvRmcwqF2WZmnlN6JQFuOw8PHqg2zNPsGh/MrgBkYGvY6M1Oj6qyimx+GwN931EERDWhkHcjZBI7QQfij6aUNgGzKMxHv/QxoClWjlTTCU/TSD2jo/hwsqg1dRzD3+YzZpSTb6p8fTPyOe5NhIuS5CE9LKOLjkZuCbb76ha9eupKam8u9//5sPP/yQnj178utf/xqjsfVPX2kh/FAV8NRQ/OZrOLP3YxsylMT77j9jHwLR/LTyJhjKzpVBWZWHrEMlbD94kgPHKgicertOcEQyID2O/hnxpCXZMMjYuSxaGQeX1Ay8++67fPHFFyxatAifz8ftt9/O008/zeHDhwkEAjz99NPNVnBL0UL4oSzGYmTX/N9Qc+ggUWOvpN2d0+W3nRamlTfBUHahGbhq6tj9fSnbD55k99FSauvqDyeYjXo6JNpIS7STlmyjc5Kd+OgIGUsXQSvj4JIWEH7yySf84x//ICIigpdffpnx48dz6623oigKkyZNapZChbYYIyNIfvhR8n//OyrXrsFgjyLuhpvULkuIkGSNMDG8dyLDeydSW+dnX045O78v4fuCKr4vqORwfmXwsZZwI2lJdjol2emcZKdHpxjCTHIoTjSu0WZAp9MREREB1F+f4I477gjeLkRTMUREkDL7MfJeepGyTz/BaLMRPf5napclREgzmwz0S4+jX3ocAN5aP7nFTnKKqjh63MnRwir2HC1jz9EyoL45GNUniXH9U2gXE6lm6SJENdoMGAwGqqqqqK6uJjs7m5EjRwJQUFDQJtYLiNBhjIom5dE55L20kBP/vRyDzY5t8BC1yxKi1QgzG8hIjSYjNTp4m6umjpyiKrKPlbN+VxFfbsnjqy159O4cy5X9kund2YHJKLMFol6jn+q/+tWvuPHGG/H5fNxyyy20a9eOL774gldffZWZM2de1jctLS3l5ptv5i9/+QtGo5Enn3wSnU5Heno6zz33HPqfLIbxeDzMmTOH0tJSLBYLixYtwuFwsGTJEr799lvGjRvHAw88gM/n47HHHuPVV1/FICvTWx1zu3akzH6c/N//jqI//wmD1Upkj55qlyVEq2WNMNG7cyy9O8dy46jObDtwgtXbC9h9pJTdR0oJMxm4orOD/hnx9O0SS2S4Se2ShYrOeTZBcXEx5eXldO/eHYC1a9cSHh7O0KFDL/kb1tXVMXv2bA4fPszSpUtZvHgx99xzD0OHDmX+/PmMHj2aCRMmBB+/bNkyXC4XDz30EJ9//jlZWVk888wz3HHHHfztb39j6tSpLF++nOXLl9O+ffuL2v9ACwtGQtnZFu1U78+m4I+voDOb6TBvPubERJWq0watLJwKZS2dQe5xJ1uyi9l+8CTF5TVA/Z4GCY5IkmJP/XFYaOeIIMYaRpTV3ObPVtDKOLjkHQgTEhJISEgI/r0pNhpatGgRt99+O++88w4Ae/fuZciQ+inhMWPGsH79+gbNwLZt27jvvvuC9y9durS+cKMRv9+PXq/H6XSyfft2pk6detn1CXVFdu9Bu2l3U7zszxS88Uc6zHsWg8WidllCtBkdE210TLRxy5VdKCytJuvgSXZ9X0pBiYvCEvcZj9cBdouZGFsYKfEWOp9amJjazorR0LabBC1p0YP/K1aswOFwMHr06GAz8MPOhgAWiwWns2F35nK5sNlsZ9w/bdo0Hn30Ue6++27eeecd7r33XhYvXkx1dTUzZ84kLi7uvPWcq0sSLeNsGcTfeC3GipMUfPwJJX/5E72ee0Y2JWpGMg7Up1YG7drZ6dejfvZNURTKnV7yTzjJK3ZxvNRNWaWH0ioPZZUeCkrc5Bx3sn73cQCMBj0dEmzERocTGxVBbFQ4cVHh9EyLJTneqsrPczm0Pg5atBn46KOP0Ol0bNy4kezsbObOnUtZWVnwfrfbjd1ub/Acq9WK2+0+4/4JEyYwYcIE8vLyWLduHaWlpTgcDiZOnMgHH3zAo4+ef997LUwLhbJzTc1FXnsDlu9zqNy5k31L/kS7O6a1cHXaoJXp0VAWahkkRYWTFBUONPyFKhBQKCp1c6SoipwiJ0eKqsg/4eRIYeUZr5EcZ2FARhz90+PplGgL+bPQQi2D5nJZFypqSsuXLw9+PW3aNBYsWMDixYvZvHkzQ4cOJTMzk2HDhjV4zoABA1i7di19+vQhMzOTgQMHNrj/rbfeYvbs2ezcuRODwYBOpws2D6L10un1JP3qAY797kUqVq/CnJxC9JXj1S5LCM3S63WkxFtJibcyuk/9bYqiUO31UeH0Uu7ycrLCw+7vS9mbU8ZnG3L5bEMusfYwhvVKZETvRJJi5ZBfqFLt2gQ/NAN6vZ5nn32Wuro6OnfuzMKFCzEYDMyYMYO3334bv9/P3LlzOXnyJCaTiVdeeYX4+HgAsrKyWL9+PbNmzcLtdvPggw/i9Xp5/vnng4sez0ULnWAou5BuvK7kJMcW/ga/20XCtLuJGtP6L5AVSrTyG1Eoa4sZeGv97DlaxvaDJ8k6dBJPrR+ov77CiN5JDOoWT5Q1dC7X3BYzOBu5UFEjtBB+KLvQAVhz5AgFr/+BgMuFY/INxE65MeSnHVsLrbwJhrK2nkFtnZ+sQyVs3HucPUfKCCgKOqBLShT9M+IYkB5PgkPdjZDaegY/kGagEVoIP5RdzACsPX6cgj++Ql3JSeyjxpAwbbosKmwCWnkTDGVayqDS5WVL9gm2HzzJwfwKfvj0aRcdQUq8hcTYSJJj6/+b5LAQGd4yR7K1koE0A43QQvih7GIHoK+ygoLX/4g3NwdLn74k3f9r9GGhM9XYGmnlTTCUaTWDqupadh4uIetgCYfyK3B7fGc8JspiPrX3gYWOiTaG9kxolmssaCUDaQYaoYXwQ9mlDMCAx0Ph229SvWc3pvh42t05HUuv3s1UYdunlTfBUCYZ1C9EdFbXUVTqpqismqKSao6XVVNU6qa00sMPH1LWCBMTBrVn/MD2WJpwx0StZCDNQCO0EH4ou9QBqPh8lHz8EeVffwmBALahw4m/7ZcYTzstVZyfVt4EQ5lkcG7eOj/FZdVsO3CSVdvyqfb6CDMbuLJfMkN7JtA+/vI3P9JKBtIMNEIL4Yeyyx2AnmO5FL//Ht6co+gjLcT/4jbsI0fL4sKLoJU3wVAmGVy4Gq+PtTsK+WrrMSpctcAPmx9ZSUu006W9nSs6x170rIFWMpBmoBFaCD+UNcUAVAIBKlavouTjj1C8HiJ7X0HC9BmYYmKaqMq2TStvgqFMMrh4db4A2w6c4GB+JUeLqsg/4cIfqP8oM+h1dOsQzYCMePqnxxNjO/+6Iq1kIM1AI7QQfihrygFYV1ZK8f9bRvXePegjI2l3x53Yhg6XWYLz0MqbYCiTDC5fnc/PsRMusnPKyTp0kqNFP/57JjoiSUuyk5ZkIy3JTocE6xmXbtZKBtIMNEIL4Yeyph6AiqJQmbmGk//zdxSvF+uAgbSbNh2jTdYSNEYrb4KhTDJoemVVHnYcLiHrUAlHCiup8fqD95mMenp1ctA/I45+XeOwRZo1k4E0A43QQvihrLkGYO3JExQve5eagwcwOmJJeXg2Ye1Tm/z7tAVaeRMMZZJB8wooCsVl1RwtquJokZPs3PLg1Rl1OshoH82wPsl0iIukY4INvb7tziZKM9AIGYDqas43QSUQoOzzTyn95GN0YeEk/eoBrH37Ncv3as3kg0h9kkHLKy6rZvuhk2w/eJIjBVXBUxct4Ua6dYihV5qDQd3isUWaVa2zqUkz0AgZgOpqiTdB53dbOf6X/0KpqyPull8Qc/VEWUfwE/JBpD7JQF2V7loKymrYvLuQ7NxySio9QP1CxD5dYhneK5G+XeMwGS/v9MVQEDJXLRSipdkGDcYUF0fBktco+ec/qC0qJOHO6eiM8r++EKJ+l8OunWLpmRoFwImKGrIOnmTjnuNkHapfd2AJN5LePpqk2MjglslJsZFENuHGR2qTmQGhmpb8jaiuvJzCJa/hzc0hsldvkh+ciT48okW+dyiT30rVJxmor7EM8k+42LD3OJv3FVPu9J5xv91iJskReapJsJB8qllw2MPRh+AMpBwmaIQMQHW19JtgwOul6E9Lce/aSViHjqQ88ijGqOgW+/6hSD6I1CcZqO9CMnBW11JUWr9Fcv1/qzle5qak4sftkn9gNupJdNQ3BkmnZhESHfV/zM1wbYULJc1AI2QAqkuNN0HF7+fE8vepzFyLMS6O9rOfwJyY2KI1hBL5IFKfZKC+y8mgzuenuKyGwlI3x0urT11bwc3xsmpqfYEGj9UBKfFWenaKoUfHGDJSo4kIa7lDltIMNEIGoLrUehNUFIWyz/6X0k8+Rm+1kvLwo0R07tLidYQC+SBSn2SgvubIIKAolFV6Tl1wqb5JKDzp4uhxJ3WnmgSDXkdakp0eHWPo2SmGzslRzbpQUZqBRsgAVJfab4KV366l+IP/h95sJmX240R0TVetFrWonYGQDEJBi65f8vk5nF/Jvtxy9ueWc7TISeDUx7DZqCc9NZpERyQRYQbCzUbCzQbCTAZOX4IQYwunU6LtomYWpBlohAxAdYXCm6Dzu60UvfMWOpOZ9rMfJyJdWw1BKGSgdZKB+tTMoNrj42BeBftyy8jOLafgpPuCn6sDEmMj6Zxkp0OijVh7ODG2MKKtYURZzGdsoCTNQCNkAKorVN4Endu2UvTO2+iMRlIeeYzIjG5ql9RiQiUDLZMM1BdKGVRV11Lh9OKp9eOp9VHj9eOt8zd4jKIonCiv4WhRFTnHnXhq/We8jl6nIzYqjKRYC4mnzni4ZUL3Rr+vNANCNaE0AJ3bt1H0p6WaawhCKQOtkgzU15ozCAQUisqqyT/hotzppcLlpdzppdzl5UR5DVXu2uBjP33lhkZfR3ZeEQKwDRiI7oFfU/j2UgpefZnoqybgmDgJg9WqdmlCCNEovV5HSpyFlDjLWe93e+o4XlpNYem5Dz+0/v0VhWgi1v4DSZ75MAarlfL/+4KjT82h9NNPCHhq1C5NCCEuiSXcRJeUKEb3ST7n4+QwgVBNqE7NBepqqfzmG8q++Ay/y4nBaiNq3Hjsw0dibtdO7fKaVKhmoCWSgfq0koEsIGyEFsIPZaE+AAOeGsq//oryr/6PQE397EB4l67YR4zENmgIBsvZp+Vak1DPQAskA/VpJQNpBhqhhfBDWWsZgAGPB9f2bVRt3ED1/n2gKOhMJqJGjyHm6omY4uLVLvGStZYM2jLJQH1ayUCuWijEZdCHh2MfMRL7iJHUlZXh3LyRijWrqVi9ioo132AbOgzHxOsIS0lRu1QhhLgk0gwIcRFMDgeOa68jZsI1OLduoWzl5zg3bsC5cQORPXphHzECa/+B6MPD1S5VCCEumDQDQlwCndGIffgIbEOH4d61k/IvV1KdvZfq7L3owt7HOmAgUSNGEdGtOzq9nLQjhAht0gwIcRl0ej3Wfv2x9utPbXExVZs24Ny0IThbYEpIIPrK8dhHjsIQ2foXHAoh2iZZQChU01YX7SiKgufwISq/XYtzy2YUnw+d2Yx92HCixowjrGNHdKdfdUQlbTWD1kQyUJ9WMpCzCRqhhfBDmRYGoN/ppHLdt1SsXY2vpAQAc3Iy9mEjsA0bjskRq2p9Wsgg1EkG6tNKBtIMNEIL4YcyrQxAACUQwL1nF1Ub1uPekYXi84FOR0S37tgGDMTSfyCmmJgWr0tLGYQqyUB9WslATi0UQmU6vR5rn35Y+/TDX+3G+d1WnBs3ULM/m5r92fC3vxLWKQ3bgIHYhg7HFKvujIEQQlukGRCihRkiLUSPuZLoMVdSV1aKe0cWrqwsqg/ux5tzlNL//RdRY8fhmHQ9xqgotcsVQmiAHCYQqtHK1NyF8rvduLZ/R9nnn1FXchKd2UzMz64m5pprm23rY8lAfZKB+rSSgRwmEKIVMFgsRI0ei334SCrXZVL66f9S9sVnVKz+N5Y+/bAOGICl9xXowyPULlUI0cZIMyBEiNEZjfV7EwwfScU3q6j4ZhXOLZtwbtmEzmgkskdP7KNGY+0/UDY0EkI0CWkGhAhR+rAwHBMnEXPNtXjzjuHK2o57x3bcu3fh3r2LsA4dibv550T2uiJk9i0QQrROsmZAqEYrx+maWm1RIaWf/S/OLZtBUYhIzyD2pp8TkZ5x0U2BZKA+yUB9WslA9hlohBbCD2VaGYDNxZuXR8m/PsK9cwcAYZ3SiB43HtvgoejN5gt6DclAfZKB+rSSgTQDjdBC+KFMKwOwudV8f5iylZ/XNwWKgt5iIWrUGKKvHI8pPv6cz5UM1CcZqE8rGUgz0AgthB/KtDIAW0pdaQmVa9dQmbkWv8sJOh2WK/oQPf4qInv2PutiQ8lAfZKB+rSSgZxaKIQGmGLjiLv5FhyTp+D6bisV36zCvWsn7l07MbWrv3pi1Ngr0YeFqV2qECLEyMyAUI1WunE1eXJygqcmKnV1GOx2HNdPIWr0WPQmk2QQAiQD9WklAzlM0AgthB/KtDIAQ4Hf5aJ81deUf/UliteD0RFL7JQb6TLlGkrKqtUuT9NkHKhPKxlIM9AILYQfyrQyAEOJz1lF+RefU/HNKhSfD3NsLJbBQ7GPGElYcora5WmSjAP1aSUDaQYaoYXwQ5lWBmAoqisro2zlZ7g2b8JfXT8zENaxE7YhQzEnJGKMjsEYE43BZpddDpuZjAP1aSUDaQYaoYXwQ5lWBmAoc9jN5K5aR9XG9bj37IZAoOEDDAYiuqbjuHaS7HTYTGQcqE8rGcjZBEKIszKEhWEbPATb4CH4qqqozt6Lr6wcX0X9n7qSEmoO7KfgwH7CUjvguPY6rIMGy2yBEG2MNANCCACMdjv2ocPPuN1zLJfylZ/j/G4rRe+8hXHFP4ns3oPwtM6Ep3UmLDkFnVHeSoRozeQwgVCNVqbmQtnFZFBbXEz5Vyup2rgBpbY2eLvOZCIioxv24SOw9h8o+xhcJBkH6tNKBrJmoBFaCD+UaWUAhrJLyUDx+6ktLMSTcwTP0aPUHPme2vw8AHRh4dgGDsQ+fGT9hZNkxuC8ZByoTysZyJoBIUST0RkMhKWmEpaaStTosQDUHj9O1ab1VG3cQNWG9VRtWI8uLIyI9Awie/QkskdPwtqnyloDIUKUNANCiMtmTkwk7safEzvlJmoOHcS1bSvV2dlU79lN9Z7dABhjHNiGDcc+fITsaSBEiJFmQAjRZHR6PZHduhPZrTsAvory+qZg315cO7ZTvvJzyld+TljHTtiHj8Q2ZChGu13lqoUQsmZAqEYrx+lCWUtmEKirxb1zB1UbfrKngcGApVdv7CNGYunbD73J3CK1hBIZB+rTSgayZkAIoTq9yYxt0BBsg+r3NHBu2UTVxg3BKyvqIyKw9OuPpUcvInr0xBQTo3bJQmiGzAwI1WilGw9loZCBt6CAqo3rcW7eiK+8PHi7KTGRyB69iBoxkvC0zipW2LxCIQOt00oGcmphI7QQfijTygAMZaGUgRIIUFtQQHX2Pqr376P6wAEUrweAsE5pxIz/GdbBg9vcoYRQykCrtJKBNAON0EL4oUwrAzCUhXIGis9H9f59VHyzGveunaAoGKw2osaMJfpnV7eZhYehnIFWaCUDWTMghGh1dEYjlt59sPTuQ13JSSrWfEPlukzKvviM8q+/xD5qDI5rJmKKi1e7VCFaPZkZEKrRSjceylpbBoHaWqrWf0vZlyvxlZSAXo9t8FDsw0cQ2b1Hq9zxsLVl0BZpJQOZGRBCtAl6s5nocVcRNeZKnFs3U7byC5ybN+LcvLH+bIQr+mLtP4DIXr0wRFrULleIVqNFm4G6ujrmzZtHQUEBtbW1PPjgg3Tt2pUnn3wSnU5Heno6zz33HPqfbFnq8XiYM2cOpaWlWCwWFi1ahMPhYMmSJXz77beMGzeOBx54AJ/Px2OPPcarr76KwWBoyR9LCNHCdAYD9mEjsA0ZVr/jYdZ2XFnbcG7ZhHPLJqD+bITwTmmnrq7YhfBOnWQ7ZCEa0aKHCT766CP279/P008/TUVFBTfeeCPdu3fnnnvuYejQocyfP5/Ro0czYcKE4HOWAIfECAAAFqlJREFULVuGy+XioYce4vPPPycrK4tnnnmGO+64g7/97W9MnTqV5cuXs3z5ctq3b8/YsWMvuB4tTAuFMq1MzYWytpSBoih4847hytqO5/AhPDlHCdTUBO83Ohz1DcSwEYQlJ6tYaUNtKYPWSisZhMxhgokTJ3LNNdcA9QPXYDCwd+9ehgwZAsCYMWNYv359g2Zg27Zt3HfffcH7ly5dWl+40Yjf70ev1+N0Otm+fTtTp05tyR9HCBFCdDod4R06Et6hI1B/qmJd8XE8R49SfWA/rm1bKfviM8q++IywTmlE9uiJISICfXg4+ogI9JEWIrqmY7DI4QWhPS3aDFhODTKXy8XDDz/M7NmzWbRoETqdLni/09mwO3O5XNhstjPunzZtGo8++ih3330377zzDvfeey+LFy+murqamTNnEhcXd956ztUliZYhGaivTWeQEAV9ugET8Xu9lG3eysk1ayjP2ok35+gZD9cZDNh79yJ22FAcQwcTFhvbImW26QxaCa1n0OILCIuKipg5cyZ33HEHkydPZvHixcH73G439tPOHbZarbjd7jPunzBhAhMmTCAvL49169ZRWlqKw+Fg4sSJfPDBBzz66KPnrUUL00KhTCtTc6FMcxn06Et8j77EVFZSd6KYgMdDoKaGgMeDr6Ic166dVO7cReXOXRz5038R1qFj8BLMEekZ6MPCmrwkzWUQgrSSQcgcJigpKWHGjBnMnz+f4cOHA9CzZ082b97M0KFDyczMZNiwYQ2eM2DAANauXUufPn3IzMxk4MCBDe5/6623mD17Njt37sRgMKDT6YLNgxBCnI0xKgpjVNQZt8dOuZG6slLcO7JwZWVRc+gA3mO5lH+5EgwGIjp3wdQuAWN0NMboGIwxMYSlpmKKPf9MpBChrEUXEC5cuJCVK1fSufOP+4w//fTTLFy4kLq6Ojp37szChQsxGAzMmDGDt99+G7/fz9y5czl58iQmk4lXXnmF+Pj6TUaysrJYv349s2bNwu128+CDD+L1enn++efp3r37eevRQicYyrTSjYcyyeDcAl4vNYcP1W+RnL0P77FcOP0tU6cjstcVRI8fj6V3n4s+Y0EyUJ9WMpDtiBuhhfBDmVYGYCiTDC5OwOvFV1GOr7wcX2UFvrJyXDu24/n+MACm+HiirhyPtd8ATO3aBddDnYtkoD6tZCDNQCO0EH4o08oADGWSQdPwHMulYvUqnFs2odTWAmB0xJ5ab9CD8LQuGB0xZ73IkmSgPq1kIM1AI7QQfijTygAMZZJB0/K73Ti3bj515cVsAqetX9JbLKfWGjgIa9+e8LTOpAzqQ2XAdEGzCKJ5aGUcSDPQCC2EH8q0MgBDmWTQfJRAAG/eMaqz91FbWICvvKL+EENFeYPNkAAMUVFEdE3H2m8Alj59Za+DFqaVcRAyZxMIIYRW6PR6wjt2IrxjpzPu81e78ebm4jl6hEBhHlUHDuLa9h2ubd+BwUBkRncs/fsTmdENc3KKbKMsmp00A0II0cIMkZbg/gXx8TZOnKiitqjw1DUWtlOdvZfq7L0A6Mzm+qaiUxphHTtiTkrGnJjULHseCO2SZkAIIVSm0+kIS04hLDmF2Osm1+91sHs3nqPf4zl6lJrDh6g5dLDBc4yOWMxJSUR274l1wADMCYkqVS/aAlkzIFSjleN0oUwyUN+FZBDwePAcy8Wbn0dtURG1RYXUHi/CX1ERfIw5ORlr/4FE9uiJMcaBMSYGvfnMsxfEmbQyDmTNgBBCtGL68HAiM7oRmdGtwe0+ZxXunTtx7dhO9d49lH3+KWWff/rj8yIt9bslxsScOovh1M6Jp2YVTLFxsh5BANIMCCFEq2W02YkaNZqoUaMJeL249+zGm5uDr+LHMxd85WXUFhac9fk6kwlTQiLmxERMsbEYo2KCjYPBbg9e0VFnklMf2zppBoQQog3Qh4VhGzgI28BBZ9zXYOfEinLqSkrqDzccP/UnP+88L65HHx6BKS4Oc1IS5sQkzEnJGGNiQPfjzIJOB6Z2CXJqZCskzYAQQrRx+rAwzAmJZ11kqChK/UxCWemPMwrl5fidTgKe+is6BjweAtXV1BYV1l+f4TxMCQmEd+pMeFoa4Z27EN6xEzqDoTl+NNFEpBkQQggN0+l0mGJiMMXEnPexSiCAr7S0fjahqAhfZUXD+/1+agsL8OQcxbl5I87NGwHQR0QQkdEteDqlOSERnVE+fkKJpCGEEOKC6PR6TPHxmOLjsVzRp9HHKYEAdSdP4DlyhJrDB6nOzsa9cwfunTtOvZAOg81Wv5gxOhpDVBSG8Ah04eH16xTCI86YSdDp9Q3uN0SEY7DZ0Vsssp6hCUgzIIQQoknp9PrgYQn78BEA1JWWUr1/HzUHDlBXchJfRQW1x4su6LDDOb+XyVR/xsQPZ0kkJgbXNZgSEs56cShxJmkGhBBCNDtTbCxRI0cTNXJ08DZFUQhUV+N3Vv24NqGmfp2CEgg0fIGA/8fHnHqcr6qyfp1DeTk1hw+B0nBjJnQ6THHxPy56TEzCFB+PPjLy1AxD/SwDNH7+vVZIMyCEEEIVOp0Og8XSJGcfKH4/vrIyaouLfjxToqj+j3vXTty7djb63BybDWNC4qmzJE79SUzGFKedfRikGRBCCNHq6QyGH9cz9G64nsHvclFbfJzaoiLqSkuCsw8BT0391+WleL4/jOfwoYavaTTW78NwaoOm+j0Y6g9JGGx20Ddcq2CIiGy1axikGRBCCNGmGaxWIqxdiejS9az3x8fbKC4so+7kifqtnoN7MNQ3ELUF+Rf8vX66hsFgt9dvvnCux+t0pxZGRjQ4dFG/4dOpxZIWK+bExGY9PVOaASGEEJqnN5mCF4v6qYb7MJTjK6/fi8HvcoLS4IH4q93BjZ3q1zA03aV/dGYzYR06Et4pjfC0zkR0TccUG9tkry/NgBBCCNGIi9mH4acUvx9/tbthw3A2AT8Bj/fHwxbBwxee4Ne+ygo8OTlnHMowtUsgskeP+v0buvXAYLv0hZDSDAghhBBNTGcwYLTZm/Q1A14v3mO51Bz5npoD+6k5eIDKtWuoXLsGAIPdHtwq+sdto5MwxjjOuxBSmgEhhBCiFdCHhRGRnkFEegZccy2K348n5yjV2fuoOXyYuuNF1Bw6SM3BAw2epzObMSckEr/k1UZfW5oBIYQQohXSGQxEdGm4MDJQW0tdcfGPF6EqKqpfFFl8/JyvJc2AEEII0UbozWbCUlMJS01tcPsZmzid/rzmLEoIIYQQ6jvfmgFpBoQQQgiNk2ZACCGE0DhpBoQQQgiNk2ZACCGE0DhpBoQQQgiNk2ZACCGE0DhpBoQQQgiNk2ZACCGE0DhpBoQQQgiNk2ZACCGE0DhpBoQQQgiNk2ZACCGE0DhpBoQQQgiN0ymKoqhdhBBCCCHUIzMDQgghhMZJMyCEEEJonDQDQgghhMZJMyCEEEJonDQDQgghhMZJMyCEEEJonFHtAlpaIBBgwYIFHDhwALPZzMKFC+nYsaPaZWnCTTfdhNVqBaB9+/bcdtttvPjiixgMBkaNGsWsWbNUrrDt2rlzJy+//DIffPABubm5PPnkk+h0OtLT03nuuefQ6/UsWbKENWvWYDQamTdvHn369FG77Dblpxns27eP+++/n06dOgHwy1/+kkmTJkkGzaSuro558+ZRUFBAbW0tDz74IF27dpVx8FOKxnz55ZfK3LlzFUVRlKysLOWBBx5QuSJt8Hg8yg033NDgtilTpii5ublKIBBQ7rvvPmXv3r0qVde2vfPOO8r111+v3HrrrYqiKMr999+vbNq0SVEURXn22WeVr776StmzZ48ybdo0JRAIKAUFBcrNN9+sZsltzukZ/M///I/y7rvvNniMZNB8PvzwQ2XhwoWKoihKeXm5MnbsWBkHp9HcYYJt27YxevRoAPr168eePXtUrkgb9u/fT01NDTNmzOCuu+5i69at1NbW0qFDB3Q6HaNGjWLDhg1ql9kmdejQgTfeeCP497179zJkyBAAxowZw4YNG9i2bRujRo1Cp9ORnJyM3++nrKxMrZLbnNMz2LNnD2vWrGHq1KnMmzcPl8slGTSjiRMn8sgjjwCgKAoGg0HGwWk01wy4XK7gVDWAwWDA5/OpWJE2hIeHc++99/Luu+/y/PPP89RTTxERERG832Kx4HQ6Vayw7brmmmswGn88IqgoCjqdDvjx3/30cSF5NK3TM+jTpw//+Z//yfLly0lNTeXNN9+UDJqRxWLBarXicrl4+OGHmT17toyD02iuGbBarbjd7uDfA4FAg0EqmkdaWhpTpkxBp9ORlpaGzWajoqIieL/b7cZut6tYoXbo9T8O+x/+3U8fF263G5vNpkZ5mjBhwgR69+4d/Hrfvn2SQTMrKirirrvu4oYbbmDy5MkyDk6juWZgwIABZGZmArBjxw4yMjJUrkgbPvzwQ1566SUAiouLqampITIykmPHjqEoCuvWrWPQoEEqV6kNPXv2ZPPmzQBkZmYyaNAgBgwYwLp16wgEAhQWFhIIBHA4HCpX2nbde++97Nq1C4CNGzfSq1cvyaAZlZSUMGPGDObMmcMtt9wCyDg4neZ+JZ4wYQLr16/n9ttvR1EUfvvb36pdkibccsstPPXUU/zyl79Ep9Px29/+Fr1ezxNPPIHf72fUqFH07dtX7TI1Ye7cuTz77LP84Q9/oHPnzlxzzTUYDAYGDRrEbbfdRiAQYP78+WqX2aYtWLCAF154AZPJRFxcHC+88AJWq1UyaCZvv/02VVVVLF26lKVLlwLw9NNPs3DhQhkHp8hVC4UQQgiN09xhAiGEEEI0JM2AEEIIoXHSDAghhBAaJ82AEEIIoXHSDAghhBAaJ82AECq55557+Prrr4N/X7RoEf3796e2tjZ426hRo8jLy7vo137yySdZsWJFk9S5atUqXnvttSZ5rZaQl5fHvHnzLum5q1evZtmyZU1ckRChT5oBIVQyfPhwtm/fHvz7hg0b6Nu3L9u2bQMgNzeXyMhIUlNT1SoRgKuuuiq4r3trUFhYeEkNFNRft8HlcjVxRUKEPs1tOiREqBg2bFhw06vi4mLMZjMTJ05k3bp1DB8+nO+++44RI0YAsGvXLn73u9/h8XiIiYnh+eefJzU1ldzcXBYsWEBFRQXh4eE8++yz9OzZM/g9frg41PXXX88NN9zAY489RklJCQAzZ87kqquualDTsmXL+Pjjj9Hr9fTp04ff/OY3rFixgi1btvDSSy8xfvx4pkyZwrp166ipqWHRokX07t2b7Oxs5s+fj8fjISoqipdffpnExETeeecdVq5cGdxYas6cOcH94AHy8/OZOXMmqampHDx4kN69ezNkyBA+/vhjKisrefPNN+nSpQsrV65k2bJleDwevF4vCxcuZPDgwWetd+HCheTn5/P888/z3HPPNVrDe++9x3//939jMBgYN24cN910E3//+98BSE5OZtKkSTzzzDMcOHAAnU7Hvffey4033siKFStYs2YNJ06c4Pjx40yfPp3CwkI2bdpEdHQ0f/7zn3nrrbcIBAI89thjADz11FOMHj2aSZMmNd//UEJcDhWvmCiEpvl8PmX48OGKx+NRPvzwQ+XVV19Vjh07pkyZMkVRFEV58sknla+//lrxer3K5MmTlYKCAkVRFCUzM1OZPn26oiiKcttttwUv/Xzo0CHl6quvVhRFUebOnav8/e9/V2bMmKEsW7ZMURRFWbFihbJgwQJFURTl8OHDyksvvdSgnrq6OmXo0KFKbW2t4vf7lfnz5yvHjx9XPvroo+Blv8eNGxd8vffff1+ZNWuWoiiKMmnSJGX16tWKoijK8uXLlZdeeklZu3at8tBDDyk+n0/x+/3KY489pvzrX/9q8D3z8vKUbt26KXv37lX8fr/ys5/9THn55ZcVRVGUN954Q3nxxRcVv9+v3HXXXUppaamiKIryz3/+U7n//vsbrXfTpk3KnXfeqSiK0mgNO3fuVCZMmKBUVVUpdXV1yvTp05Xdu3crr7/+uvL6668riqIoixYtUl544QVFURSltLRUGT9+vJKdna189NFHypVXXqk4nU4lPz9fycjIUDIzMxVFUZQ777xT+frrr5Vjx44p48aNUwKBgOJ2u5WxY8cqXq/30v5HEaIFyMyAECoxGAz07duX3bt3s27dOqZOnUpqaioej4fKykqysrKYN28eOTk55OXl8eCDDwaf63K5cLvd7Nmzh6eeeip4e3V1NeXl5QC89tpr6PV6lixZAkD//v35wx/+QHFxMVdeeSUzZ85sUI/RaKR///7ccsstXHXVVUydOpWEhIQz6v7hEuDp6el89dVXlJWVcfLkScaNGwfAHXfcAdSvgdi1axc333wzAB6Ph+Tk5DNeLy4uLjibkZiYyPDhw4H6387z8/PR6/W8+eabrF69mqNHj7Jlyxb0en2j9ebk5ARfe+PGjWetoaSkhHHjxgUvQvPee+8B8M033wSfu2nTpuDMjcPh4KqrrmLLli1YrVYGDBiA1WoNXuHuh5pTUlKoqqoiNTWVlJQUtm7dSmFhIWPHjsVsNp/xswsRKqQZEEJFP6wb2LVrF4sXLw7etmrVKqKjo7HZbBQUFNC+fXs++eQTAPx+PyUlJQQCAcxmc/B2gOPHjxMdHQ3AddddR3V1Na+//jpz586lU6dOrFy5km+//ZZvvvmGv/zlL6xcubLBtP3SpUvZsWMHmZmZ3Hfffbz88stn1BwWFgYQfJ7JZGpwv9fr5cSJE/j9fqZPn84999wDQFVVFQaD4YzXO/1D8vTHuN1ufv7zn3PDDTcwePBgunXrxvLlyy+o3sZq+PDDDxs8rri4uMEltaH+Us+n/93v95/1Zz7blU9//vOf89lnn1FYWMhDDz10xv1ChBJZQCiEioYNG8Ynn3xCRkZG8ANl5MiRLFu2jJEjRwLQuXNnKisr+e677wD46KOPeOKJJ7DZbHTq1CnYDKxfv56pU6cGX7tHjx7MmTOHTz/9lOzsbP7617/yxhtvcO211/Lcc89RVlbW4FrtZWVlXHvttWRkZPDII48wcuRIDhw4cN6fwWazkZiYyPr16wH45JNPeO2114I/m9vtxufzMXPmTL788suL/jfKyclBr9fzwAMPMGzYMDIzM/H7/Y3WazAY8Pl8Df59T69h0KBBZGZmBm9//PHH2bNnzxnP/aFpKCsrY9WqVQwZMuSC6544cSIbN26kpKRELsIlQp7MDAihooyMDCoqKoJT61D/ITR79uxgM2A2m3nttdd48cUX8Xq9WK1WFi1aBMDixYtZsGABf/7znzGZTLz66qsNftOPjo7m8ccf55lnnuG9997j8ccfZ/LkyRiNRmbNmoXdbg8+1uFwcPvtt3PLLbcQERFBUlISN910E1999dV5f44f6vj9739PTEwMv//972nXrh379+/nF7/4BX6/n9GjR3PTTTdd9L9R9+7d6dGjB9deey3h4eEMHjyYwsLCRuutq6vD6XQyZ84cFi9efNYadDodd955J7fffjuBQIAJEyYwYsQITCYTc+fOJS4ujpkzZ7JgwQImT56M3+/ngQceoFevXhfUIAGEh4fTr18/uUy6aBXkqoVCCNHEFEXB7XZz22238d577xEfH692SUKckxwmEEKIJrZ7927Gjx/PL37xC2kERKsgMwNCCCGExsnMgBBCCKFx0gwIIYQQGifNgBBCCKFx0gwIIYQQGifNgBBCCKFx0gwIIYQQGvf/AUKqtu54vYPiAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "\n", "ax.plot(t_plot, weibull_pp_surv_mean[0],\n", " c=blue, label=\"Not metastized\");\n", "ax.plot(t_plot, weibull_pp_surv_mean[1],\n", " c=red, label=\"Metastized\");\n", "\n", "ax.set_xlim(0, 230);\n", "ax.set_xlabel(\"Weeks since mastectomy\");\n", "\n", "ax.set_ylim(top=1);\n", "ax.yaxis.set_major_formatter(pct_formatter);\n", "ax.set_ylabel(\"Survival probability\");\n", "\n", "ax.legend(loc=1);\n", "ax.set_title(\"Weibull survival regression model\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Log-logistic survival regression\n", "\n", "Other accelerated failure time models can be specificed in a modular way by changing the prior distribution on $\\varepsilon$. A log-logistic model corresponds to a [logistic](https://en.wikipedia.org/wiki/Logistic_distribution) prior on $\\varepsilon$. Most of the model specification is the same as for the Weibull model above." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "X_.set_value(X)\n", "cens_.set_value(cens)\n", "\n", "with pm.Model() as log_logistic_model:\n", " β = pm.Normal('β', 0., VAGUE_PRIOR_SD, shape=2)\n", " η = β.dot(X_.T)\n", " \n", " s = pm.HalfNormal('s', 5.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use the prior $\\varepsilon \\sim \\textrm{Logistic}(0, s)$. The survival function of the logistic distribution is\n", "\n", "$$P(Y \\geq y) = 1 - \\frac{1}{1 + \\exp\\left(-\\left(\\frac{y - \\mu}{s}\\right)\\right)},$$\n", "\n", "so we get the likelihood " ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "def logistic_sf(y, μ, s):\n", " return 1. - pm.math.sigmoid((y - μ) / s)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "with log_logistic_model:\n", " y_obs = pm.Logistic(\n", " 'y_obs', η[~cens_], s,\n", " observed=y_std[~cens]\n", " )\n", " y_cens = pm.Potential(\n", " 'y_cens', logistic_sf(y_std[cens], η[cens_], s)\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now sample from the log-logistic model." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (3 chains in 3 jobs)\n", "NUTS: [s, β]\n", "Sampling 3 chains: 100%|██████████| 4500/4500 [00:03<00:00, 1192.46draws/s]\n" ] } ], "source": [ "with log_logistic_model:\n", " log_logistic_trace = pm.sample(**SAMPLE_KWARGS)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "All of the sampling diagnostics look good for this model." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.energyplot(log_logistic_trace);" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.1175174682253362" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pm.bfmi(log_logistic_trace)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.0005486775766363" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "max(np.max(gr_stats) for gr_stats in pm.gelman_rubin(log_logistic_trace).values())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, we calculate the posterior expected survival functions for this model." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 1500/1500 [00:00<00:00, 1685.72it/s]\n" ] } ], "source": [ "X_.set_value(X_pp)\n", "cens_.set_value(cens_pp)\n", "\n", "with log_logistic_model:\n", " pp_log_logistic_trace = pm.sample_ppc(\n", " log_logistic_trace, samples=1500, vars=[y_obs]\n", " )" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "log_logistic_pp_surv = (np.greater_equal\n", " .outer(np.exp(y.mean() + y.std() * pp_log_logistic_trace['y_obs']),\n", " t_plot))\n", "log_logistic_pp_surv_mean = log_logistic_pp_surv.mean(axis=0)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "ax.plot(t_plot, weibull_pp_surv_mean[0],\n", " c=blue, label=\"Weibull, not metastized\");\n", "ax.plot(t_plot, weibull_pp_surv_mean[1],\n", " c=red, label=\"Weibull, metastized\");\n", "\n", "ax.plot(t_plot, log_logistic_pp_surv_mean[0],\n", " '--', c=blue, \n", " label=\"Log-logistic, not metastized\");\n", "ax.plot(t_plot, log_logistic_pp_surv_mean[1],\n", " '--', c=red,\n", " label=\"Log-logistic, metastized\");\n", "\n", "ax.set_xlim(0, 230);\n", "ax.set_xlabel(\"Weeks since mastectomy\");\n", "\n", "ax.set_ylim(top=1);\n", "ax.yaxis.set_major_formatter(pct_formatter);\n", "ax.set_ylabel(\"Survival probability\");\n", "\n", "ax.legend(loc=1);\n", "ax.set_title(\"Weibull and log-logistic\\nsurvival regression models\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This post has been a short introduction to implementing parametric survival regression models in PyMC3 with a fairly simple data set. The modular nature of probabilistic programming with PyMC3 should make it straightforward to generalize these techniques to more complex and interesting data set." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Authors\n", "\n", "- Originally authored as a blog post by [Austin Rochford](https://austinrochford.com/posts/2017-10-02-bayes-param-survival.html) on October 2, 2017.\n", "- Updated by [George Ho](https://eigenfoo.xyz/) on July 18, 2018." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }