{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Piecewise exponential models and creating custom models\n", "\n", "This section will be easier if we recall our three mathematical \"creatures\" and the relationships between them. First is the survival function, $S(t)$, that represents the probability of living past some time, $t$. Next is the _always non-negative and non-decreasing_ cumulative hazard function, $H(t)$. Its relation to $S(t)$ is:\n", "\n", "$$ S(t) = \\exp\\left(-H(t)\\right)$$\n", "\n", "Finally, the hazard function, $h(t)$, is the derivative of the cumulative hazard: \n", "\n", "$$h(t) = \\frac{dH(t)}{dt}$$\n", "\n", "which has the immediate relation to the survival function:\n", "\n", "$$S(t) = \\exp\\left(-\\int_{0}^t h(s) ds\\right)$$\n", "\n", "Notice that any of the three absolutely defines the other two. Some situations make it easier to define one vs the others. For example, in the Cox model, it's easist to work with the hazard, $h(t)$. In this section on parametric univariate models, it'll be easiest to work with the cumulative hazard. This is because of an asymmetry in math: derivatives are much easier to compute than integrals. So, if we define the cumulative hazard, both the hazard and survival function are much easier to reason about versus if we define the hazard and ask questions about the other two.\n", "\n", "First, let's revisit some simpler parametric models. \n", "\n", "#### The Exponential model\n", "\n", "Recall that the Exponential model has a constant hazard, that is:\n", "\n", "$$ h(t) = \\frac{1}{\\lambda} $$\n", "\n", "which implies that the cumulative hazard, $H(t)$, has a pretty simple form: $H(t) = \\frac{t}{\\lambda}$. Below we fit this model to some survival data. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "%config InlineBackend.figure_format = 'retina'\n", "\n", "from matplotlib import pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "\n", "from lifelines.datasets import load_waltons\n", "waltons = load_waltons()\n", "T, E = waltons['T'], waltons['E']" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "number of subjects = 163\n", " number of events = 156\n", " log-likelihood = 418612.094\n", " hypothesis = lambda_ != 1\n", "\n", "---\n", " coef se(coef) lower 0.95 upper 0.95 p -log2(p)\n", "lambda_ 51.840 12.490 27.360 76.320 <0.0005 14.379\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 263, "width": 614 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from lifelines import ExponentialFitter\n", "\n", "fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(10, 4))\n", "\n", "epf = ExponentialFitter().fit(T, E)\n", "epf.plot_hazard(ax=ax[0])\n", "epf.plot_cumulative_hazard(ax=ax[1])\n", "\n", "ax[0].set_title(\"hazard\"); ax[1].set_title(\"cumulative_hazard\")\n", "\n", "epf.print_summary(3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This model does a poor job of fitting to our data. If I fit a _non-parametric_ model, like the Nelson-Aalen model, to this data, the Exponential's lack of fit is very obvious. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 316, "width": 474 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from lifelines import NelsonAalenFitter\n", "\n", "ax = epf.plot(figsize=(8,5))\n", "\n", "naf = NelsonAalenFitter().fit(T, E)\n", "ax = naf.plot(ax=ax)\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It should be clear that the single parameter model is just averaging the hazards over the entire time period. In reality though, the true hazard rate exhibits some complex non-linear behaviour.\n", "\n", "#### Piecewise Exponential models\n", "\n", "What if we could break out model into different time periods, and fit an exponential model to each of those? For example, we define the hazard as:\n", "\n", "$$ \n", "h(t) = \\begin{cases}\n", " \\lambda_0, & \\text{if $t \\le \\tau_0$} \\\\\n", " \\lambda_1 & \\text{if $\\tau_0 < t \\le \\tau_1$} \\\\\n", " \\lambda_2 & \\text{if $\\tau_1 < t \\le \\tau_2$} \\\\\n", " ... \n", " \\end{cases}\n", "$$\n", "\n", "This model should be flexible enough to fit better to our dataset. \n", "\n", "The cumulative hazard is only slightly more complicated, but not too much and can still be defined in Python. In _lifelines_, univariate models are constructed such that one _only_ needs to define the cumulative hazard model with the parameters of interest, and all the hard work of fitting, creating confidence intervals, plotting, etc. is taken care. \n", "\n", "For example, _lifelines_ has implemented the `PiecewiseExponentialFitter` model. Internally, the code is a single function that defines the cumulative hazard. The user specifies where they believe the \"breaks\" are, and _lifelines_ estimates the best $\\lambda_i$. \n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "number of subjects = 163\n", " number of events = 156\n", " log-likelihood = -647.118\n", " hypothesis = lambda_0_ != 1, lambda_1_ != 1, lambda_2_ != 1\n", "\n", "---\n", " coef se(coef) lower 0.95 upper 0.95 p -log2(p)\n", "lambda_0_ 162.989 27.144 109.787 216.191 <0.0005 28.630\n", "lambda_1_ 31.366 4.043 23.442 39.290 <0.0005 43.957\n", "lambda_2_ 4.686 0.624 3.462 5.910 <0.0005 28.055\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 277, "width": 601 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from lifelines import PiecewiseExponentialFitter\n", "\n", "# looking at the above plot, I think there may be breaks at t=40 and t=60. \n", "pf = PiecewiseExponentialFitter(breakpoints=[40, 60]).fit(T, E)\n", "\n", "fig, axs = plt.subplots(nrows=1, ncols=2, figsize=(10, 4))\n", "\n", "ax = pf.plot(ax=axs[1])\n", "pf.plot_hazard(ax=axs[0])\n", "\n", "ax = naf.plot(ax=ax, ci_show=False)\n", "axs[0].set_title(\"hazard\"); axs[1].set_title(\"cumulative_hazard\")\n", "\n", "pf.print_summary(3)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see a much better fit in this model. A quantitative measure of fit is to compare the log-likelihood between exponential model and the piecewise exponential model (higher is better). The log-likelihood went from -772 to -647, respectively. We could keep going and add more and more breakpoints, but that would end up overfitting to the data. \n", "\n", "#### Univarite models in _lifelines_\n", "\n", "I mentioned that the `PiecewiseExponentialFitter` was implemented using only its cumulative hazard function. This is not a lie. _lifelines_ has very general semantics for univariate fitters. For example, this is how the entire `ExponentialFitter` is implemented:\n", "\n", "```python\n", "class ExponentialFitter(ParametericUnivariateFitter):\n", "\n", " _fitted_parameter_names = [\"lambda_\"]\n", "\n", " def _cumulative_hazard(self, params, times):\n", " lambda_ = params[0]\n", " return times / lambda_\n", "```\n", "\n", "We only need to specify the cumulative hazard function because of the 1:1:1 relationship between the cumulative hazard function and the survival function and the hazard rate. From there, _lifelines_ handles the rest. \n", "\n", "\n", "#### Defining our own survival models\n", "\n", "\n", "To show off the flexability of _lifelines_ univariate models, we'll create a brand new, never before seen, survival model. Looking at the Nelson-Aalen fit, the cumulative hazard looks looks like their might be an asymptote at $t=80$. This may correspond to an absolute upper limit of subjects' lives. Let's start with that functional form.\n", "\n", "$$ H_1(t; \\alpha) = \\frac{\\alpha}{(80 - t)} $$\n", "\n", "We subscript $1$ because we'll investigate other models. In a _lifelines_ univariate model, this is defined in the following code. \n", "\n", "**Important**: in order to compute derivatives, you must use the numpy imported from the `autograd` library. This is a thin wrapper around the original numpy. Note the `import autograd.numpy as np` below. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "from lifelines.fitters import ParametericUnivariateFitter\n", "\n", "import autograd.numpy as np\n", "\n", "class InverseTimeHazardFitter(ParametericUnivariateFitter):\n", " \n", " # we tell the model what we want the names of the unknown parameters to be\n", " _fitted_parameter_names = ['alpha_']\n", "\n", " \n", " # this is the only function we need to define. It always takes two arguments:\n", " # params: an iterable that unpacks the parameters you'll need in the order of _fitted_parameter_names\n", " # times: a vector of times that will be passed in.\n", " def _cumulative_hazard(self, params, times):\n", " alpha = params[0]\n", " return alpha /(80 - times)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "number of subjects = 163\n", " number of events = 156\n", " log-likelihood = -697.840\n", " hypothesis = alpha_ != 1\n", "\n", "---\n", " coef se(coef) lower 0.95 upper 0.95 p -log2(p)\n", "alpha_ 21.51 1.72 18.13 24.88 <0.005 106.22\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 316, "width": 474 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "itf = InverseTimeHazardFitter()\n", "itf.fit(T, E)\n", "itf.print_summary()\n", "\n", "ax = itf.plot(figsize=(8,5))\n", "ax = naf.plot(ax=ax, ci_show=False)\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The best fit of the model to the data is:\n", "\n", "$$H_1(t) = \\frac{21.51}{80-t}$$\n", "\n", "Our choice of 80 as an asymptote was maybe mistaken, so let's allow the asymptote to be another parameter:\n", "\n", "$$ H_2(t; \\alpha, \\beta) = \\frac{\\alpha}{\\beta-t} $$\n", "\n", "If we define the model this way, we need to add a bound to the values that $\\beta$ can take. Obviously it can't be smaller than or equal to the maximum observed duration. Generally, the cumulative hazard _must be positive and non-decreasing_. Otherwise the model fit will hit convergence problems. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "class TwoParamInverseTimeHazardFitter(ParametericUnivariateFitter):\n", " \n", " _fitted_parameter_names = ['alpha_', 'beta_']\n", " \n", " # Sequence of (min, max) pairs for each element in x. None is used to specify no bound\n", " _bounds = [(0, None), (75.0001, None)]\n", " \n", " def _cumulative_hazard(self, params, times):\n", " alpha, beta = params\n", " return alpha / (beta - times)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "number of subjects = 163\n", " number of events = 156\n", " log-likelihood = -685.572\n", " hypothesis = alpha_ != 1, beta_ != 76\n", "\n", "---\n", " coef se(coef) lower 0.95 upper 0.95 p -log2(p)\n", "alpha_ 16.50 1.51 13.55 19.46 <0.005 79.98\n", "beta_ 76.55 0.38 75.80 77.30 0.15 2.73\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 316, "width": 480 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "two_f = TwoParamInverseTimeHazardFitter()\n", "two_f.fit(T, E)\n", "two_f.print_summary()\n", "\n", "ax = itf.plot(ci_show=False, figsize=(8,5))\n", "ax = naf.plot(ax=ax, ci_show=False)\n", "two_f.plot(ax=ax)\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the output, we see that the value of 76.55 is the suggested asymptote, that is:\n", "\n", "$$H_2(t) = \\frac{16.50} {76.55 - t}$$\n", "\n", "The curve also appears to track against the Nelson-Aalen model better too. Let's try one additional parameter, $\\gamma$, some sort of measure of decay. \n", "\n", "$$H_3(t; \\alpha, \\beta, \\gamma) = \\frac{\\alpha}{(\\beta-t)^\\gamma} $$\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "from lifelines.fitters import ParametericUnivariateFitter\n", "\n", "class ThreeParamInverseTimeHazardFitter(ParametericUnivariateFitter):\n", " \n", " _fitted_parameter_names = ['alpha_', 'beta_', 'gamma_']\n", " _bounds = [(0, None), (75.0001, None), (0, None)]\n", " \n", " # this is the only function we need to define. It always takes two arguments:\n", " # params: an iterable that unpacks the parameters you'll need in the order of _fitted_parameter_names\n", " # times: a numpy vector of times that will be passed in by the optimizer\n", " def _cumulative_hazard(self, params, times):\n", " a, b, c = params\n", " return a / (b - times) ** c" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "number of subjects = 163\n", " number of events = 156\n", " log-likelihood = -649.378\n", " hypothesis = alpha_ != 1, beta_ != 76, gamma_ != 1\n", "\n", "---\n", " coef se(coef) lower 0.95 upper 0.95 p -log2(p)\n", "alpha_ 1588776.28 3775137.44 -5810357.13 8987909.70 0.67 0.57\n", "beta_ 100.88 5.88 89.35 112.41 <0.005 15.38\n", "gamma_ 3.83 0.50 2.85 4.81 <0.005 25.82\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 316, "width": 480 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "three_f = ThreeParamInverseTimeHazardFitter()\n", "three_f.fit(T, E)\n", "three_f.print_summary()\n", "\n", "ax = itf.plot(ci_show=False, figsize=(8,5))\n", "ax = naf.plot(ax=ax, ci_show=False)\n", "ax = two_f.plot(ax=ax, ci_show=False)\n", "ax = three_f.plot(ax=ax)\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our new asymptote is at $t\\approx 100, \\text{c.i.}=(87, 112)$. The model appears to fit the early times better than the previous models as well, however our $\\alpha$ parameter has more uncertainty now. Continuing to add parameters isn't advisable, as we will overfit to the data. \n", "\n", "Why fit parametric models anyways? Taking a step back, we are fitting parameteric models and comparing them to the non-parametric Nelson-Aalen. Why not just always use the Nelson-Aalen model? \n", "\n", "1) Sometimes we have scientific motivations to use a parametric model. That is, using domain knowledge, we may know the system has a parametric model and we wish to fit to that model. \n", "\n", "2) In a parametric model, we are borrowing information from _all_ observations to determine the best parameters. To make this more clear, imagine take a single observation and changing it's value wildly. The fitted parameters would change as well. On the other hand, imagine doing the same for a non-parametric model. In this case, only the local survival function or hazard function would change. Because parametric models can borrow information from all observations, and there are much _fewer_ unknowns than a non-parametric model, parametric models are said to be more _statistical efficient._ \n", "\n", "3) Extrapolation: non-parametric models are not easily extended to values outside the observed data. On the other hand, parametric models have no problem with this. However, extrapolation outside observed values is a very dangerous activity. " ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 465, "width": 427 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(3, figsize=(7, 8), sharex=True)\n", "\n", "\n", "new_timeline = np.arange(0, 85)\n", "\n", "three_f = ThreeParamInverseTimeHazardFitter().fit(T, E, timeline=new_timeline)\n", "\n", "\n", "three_f.plot_hazard(label='hazard', ax=axs[0]).legend()\n", "three_f.plot_cumulative_hazard(label='cumulative hazard', ax=axs[1]).legend()\n", "three_f.plot_survival_function(label='survival function', ax=axs[2]).legend()\n", "\n", "fig.subplots_adjust(hspace=0)\n", "# Hide x labels and tick labels for all but bottom plot.\n", "for ax in axs:\n", " ax.label_outer()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3-parameter Weibull distribution\n", "\n", "We can easily extend the built-in Weibull model (`lifelines.WeibullFitter`) to include a new _location_ parameter:\n", "\n", "$$ H(t) = \\left(\\frac{t - \\theta}{\\lambda}\\right)^\\rho $$\n", "\n", "(When $\\theta = 0$, this is just the 2-parameter case again). In *lifelines* custom models, this looks like:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", "from autograd.scipy.stats import norm\n", "\n", "# I'm shifting this to exaggerate the effect \n", "T = T + 10\n", "\n", "class ThreeParameterWeibullFitter(ParametericUnivariateFitter):\n", "\n", " _fitted_parameter_names = [\"lambda_\", \"rho_\", \"theta_\"]\n", " _bounds = [(0, None), (0, None), (0, T.min()-0.001)]\n", "\n", " def _cumulative_hazard(self, params, times):\n", " lambda_, rho_, theta_ = params\n", " return ((times - theta_) / lambda_) ** rho_\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "number of subjects = 163\n", " number of events = 156\n", " log-likelihood = -666.715\n", " hypothesis = lambda_ != 1, rho_ != 1, theta_ != 7\n", "\n", "---\n", " coef se(coef) lower 0.95 upper 0.95 p -log2(p)\n", "lambda_ 63.92 5.38 53.38 74.47 <0.005 102.58\n", "rho_ 4.20 0.56 3.11 5.29 <0.005 26.67\n", "theta_ 2.55 5.05 -7.35 12.45 0.28 1.83\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 316, "width": 474 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "tpw = ThreeParameterWeibullFitter()\n", "tpw.fit(T, E)\n", "tpw.print_summary()\n", "ax = tpw.plot_cumulative_hazard(figsize=(8,5))\n", "ax = NelsonAalenFitter().fit(T, E).plot(ax=ax, ci_show=False)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Inverse Gaussian distribution\n", "\n", "The inverse Gaussian distribution is another popular model for survival analysis. Unlike other model, it's hazard does not asympotically converge to 0, allowing for a long tail of survival. Let's model this, using the same parameterization from [Wikipedia](https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "from autograd.scipy.stats import norm\n", "\n", "\n", "class InverseGaussianFitter(ParametericUnivariateFitter):\n", " _fitted_parameter_names = ['lambda_', 'mu_']\n", " \n", " def _cumulative_density(self, params, times):\n", " mu_, lambda_ = params\n", " v = norm.cdf(np.sqrt(lambda_ / times) * (times / mu_ - 1), loc=0, scale=1) + \\\n", " np.exp(2 * lambda_ / mu_) * norm.cdf(-np.sqrt(lambda_ / times) * (times / mu_ + 1), loc=0, scale=1)\n", " return v\n", "\n", " def _cumulative_hazard(self, params, times):\n", " return -np.log(1-self._cumulative_density(params, times))" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "number of subjects = 432\n", " number of events = 114\n", " log-likelihood = -729.797\n", " hypothesis = lambda_ != 1, mu_ != 1\n", "\n", "---\n", " coef se(coef) lower 0.95 upper 0.95 p -log2(p)\n", "lambda_ 7441.43 9296.67 -10779.69 25662.56 0.42 1.24\n", "mu_ 47.86 3.31 41.38 54.35 <0.005 148.83\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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++OOccsopfPzjH+fMM89kwYIFVFVV9bu+nTt38sMf/pDnn3+enTt3Eg53nxe4Z8+erNf1nCMCqd8lgIaGfo/U7tTxO7hjx46s8yk2bdoEwMaNGzn//PM59thjmTt3Lg899BA7duzgkksu4QMf+AAnnXQSHo/nkOvvS7b3OmnSJADmz5+fcawjMNi9e3e3QGCgn3U2h/p55VsuHiOfmd4+a63tNgPDWttijHmFVKBwKqnhPr05FfCny2npUU7SGPMMqaDiTGBrlutzIZbexvs8axhwORx43an/ASQSCgVEREaqrk80u3K5XBkTG/1+Px/72Me49957efbZZznvvPOIRqM89NBDjBs3jvPOO6/z3I6Ju5s2bcp6E92htbU1Y19lZWXWc6dNm8batWtZvnw5q1ev5vHHHwdSN5rXXXcdy5YtA1I3nNZaampq+qw7W53V1dUZx6ZPn95tXlxVVVXGzdntt9/Ol770JUpLS/nIRz7C1KlTCQQCGGN44okneOuttzImKB+qRx55hB/+8If8z//8T2ePic/n44orruC///u/mTBhAgCXX345q1at4sc//jG/+tWvuOeee4DUzekPfvCDg86B2Lp1KyeffDINDQ188IMf5JxzzqG4uBin08n27du57777en0v2X6fOuZTJBKJQ37PHb9Hv/nNb/o8r+P3yOl08sc//pGbbrqJRx99tHM8fmFhIUuWLOEHP/gBBQUFh9yObIqLizP2dbzXvo7FYrHOfYfzWWdzqJ9XvuUiEDg6vX2vl+ObSAUCR9F3INCfckiXk3PGmGnA2UAIeKmf16zr5dCQrXWVSCb5W3UTR1cWUqGlREVkBBnM4Taj2ZIlS7j33nu57777OO+883jqqaeoq6vj2muv7TbspeNG6LLLLuu8Ye+vvnrYZ8+ezSOPPEI8Huett97iueee46c//SnXXnstwWCQz3zmM511n3jiiaxfv75fdS5YsIAVK1bw/PPPc9NNNx1Se+PxOMuXL6eyspL169dnPPXv2bMCdA7v6dlr0KGxsTHjptrv97N8+XKWL1/Orl27eOmll1i5ciUPPPAA27dv5+WXX+4894ILLuCCCy6gra2NN954g1WrVvHzn/+cCy+8kL/85S8ce+yxvb6fW2+9lbq6OlasWJGRbOuhhx7q7AEaCh3f5ZNPPsnFF1/cr2tKS0u57bbbuO2229i8eTMvvvgi99xzD3feeSeNjY1ZJ6jnS64/64F8XvmUi+VDO0Kupl6Od+zP/sgj9+UcMmOMF3gQ8ALL7SGscpRPJX43O+tC1LREaGsf9p0YIiKSAwsWLGDWrFk8+eSTNDU1dd6oLFmypNt5xxxzTOcqPV2fgOaKy+Vi/vz5fP3rX+ehhx4C4IknngCgoKCA973vffz973+nvr6+X+VdccUVlJSU8Oqrr/L88309N8xUW1tLY2Mjp59+ekYQ0NramjUY6RirvmvXroxjmzdvpqmpt9uRlClTprBo0SKeeeYZjjzySP70pz9lXT41GAxy1llnceutt3L99dcTjUb53//93z7L3rx5MwALFy7MONaxdOVQOfXUUwG6BTmH4sgjj+Qzn/kML774IgUFBTz55JOdxzqGtg2kpyJXBvJZ99Xuw/28htqYzyNgjHEC9wMLgEeA/+7vtdba+dl+SK2UdFiaQjHaY5lr3XZVXuBlQpHvcKsSEZERZsmSJUQiEe666y6efvpp5syZw4knntjtHJfLxRe/+EX27t3LsmXLMsY9A+zduzfrGvu9WbduXdYb5P379wN0Gyv/la98hWg0yqc//WkaGxszrmloaOh2g15cXNw5n+BjH/tYRh6FDqFQKCOwGT9+PIFAgHXr1nUbchGLxbj22mupra3NKOeYY46hqKiIJ598kgMHDnTuD4fDnUOcuqqpqeHtt9/O2N/W1kZraysul6tzDPxLL72Utach2+eUTcdSlB25Gzo888wz/PKXv+zz2ly75JJLmDlzJj/72c94+umns57z2muvEQqFANi2bRtbt2aO4G5oaKC9vb3bJOLS0lKMMXlNDjeQz7pjYni2dh/q55VvuRga1PEXIXMwVvf9mX8FBqecfksHAQ8A/wr8/8C/2a6DEPMkEkvw9p5GWiJxkklLP+ZAi4jIGLJ48WK+853vcMMNNxCLxTJ6Azp8+9vf5q233uLuu+/m97//PWeddRaTJ0/mwIEDbNq0iVdeeYXvfe97fQ5T6er+++/nnnvu4QMf+AAzZ86ktLSULVu28Pvf/x6v19uZEAxSOQTWrVvHXXfdxcyZMztXQqqvr2fbtm289NJLLF26lLvvvrvzmiVLltDe3s6yZcu46KKLmD17NgsWLGD8+PG0traye/dunn32WVpbW/nQhz7UeZ3D4WDZsmXccsstHH/88VxyySVEo1HWrFlDfX09Z555JmvWdF9U0O12c+2113LzzTdz4oknctlllxGPx/nDH/7ApEmTOieddtizZw8nnngixx9/PHPmzGHKlCk0NzezatUq9u3bx7JlyygsLARg2bJl7NmzhwULFjB9+nQ8Hg/r1q3jj3/8I9OmTePKK6/s83P+whe+wIoVK/jXf/1XrrjiCiZNmsTf/vY3Vq9ezcc+9jEeeeSRfn1fueB2u3n88cc599xzueCCCzj99NOZO3cugUCAXbt28ec//5mtW7eyd+9eAoEAb731Fpdffjnvf//7mT17NpMmTaKmpoYnn3ySWCzWbQ3/goICTjnlFF5++WUWLVrEUUcdhdPp5OKLL2bOnDlD8v4G8lmfffbZ/OY3v+Hyyy/n/PPPx+/3M23aNBYvXnzIn1e+5SIQeDe97W3s/qz0trex/7kup1+MMW5Sw4H+Ffgf4FPW2vz1TXURSySJxpNUN4apLPbjdh6846a6MYLX5aSyWD0EIiKj3dSpUznzzDN5/vnncblcLFq0KOt5brebJ554ggceeICVK1eyatUqWltbGTduHEcccQQ333xzr9dm84lPfIL29nZeffVV1q1bRzgcZvLkyVx55ZV89atf5bjjjut2/s9+9jPOO+887r77bp577jkaGxspKytj6tSpfO1rX+Pf/i0z9+fnPvc5zj//fH7+85/z3HPP8dhjj9HS0tKZxXfRokV84hOfyFia8eabb2bcuHH88pe/5J577qG4uJiPfOQjfPe73+11KdQbb7yRQCDAvffeyy9+8QsqKyu58sorWb58eUZwNH36dG688UZeeOEF1qxZQ21tLWVlZRx99NHccsst3W7ur7/+en7729/y5ptv8txzz+FwOJg6dSrXX39954TmvsyZM4c1a9bwrW99i6eeeop4PM4JJ5zA448/TklJyZAGAh3teeutt7j11ltZtWoVK1aswOFwMHHiRE488URuvPHGzmVRTzrpJL7xjW/w4osvsnr1ahoaGhg3bhzz589n2bJl3Sa0Qyq4/PKXv8zq1at56KGHsNZSVVU1ZIHAQD7rz372s+zYsYOHH36YH/3oR8TjcT784Q+zePHizjL7+3nlmzncB+Dp5UM3k1o+dGbXlYOMMYWkMgwbYHw/lg89ACSBiV1XDjLGOIAtwPR0HVlXDTLGnEEqj0CvmYXT53lI9QBcAvwaWNpzxaPDYYxZN2/evHkdabQPVUskxp+31bOvuZ0jKoJ9ntscjrGvOYzP7WTWhELmTc3d+rwiIoejY2nI2bNn57klIiIjT3//hs6fP5/169evTw9PPySHPUfAWrsFeJbUTfrVPQ7fCASB+7sGAcaYY4wx3VbWsda2khqrHyQzj8A16fKf6S0I6K/0xODfkgoC/i85DgKGWpHfzaSSAJFYkvwPahIRERGRkSJX6Wi/ALwK3GGMORvYCJxCas3/94Bv9ji/I4NIz9Hv1wNnAF8xxswF1gKzSd20HyAz0MAYcylwafplx8LHpxljVqb/XWutva7LJXcD5wO1wB7gO1mWSXvBWvtCr+92mPG6xvycbxERERE5RDkJBKy1W4wxJwE3AR8ldaO9F7gduLG/y3Faa+uMMaeRykh8KfBBoA5YAXzHWrs7y2VzgZ6zpGakfwB2AF0DgSPS2wrgO30054X+tHk4sdZire1XhmUREREZm7JlvM3m0ksvZe7cuYPbGMmrXPUIYK3dBSzt57m93qlaa+uBa9M//SlrOZlDifo6/4z+njvSRONJ1u9sYE5VSb8mGIuIiMjY099sz9OnT1cgMMrlLBCQ/HE5DG6ng417m5leESQcSygQEBERkayGwUrpMkzobnEUMMZwREUQv0dxnYiIiIj0jwIBEREREZExSI+Qh5nGUJSNe1sOfqKIiIiIjEpDNXxLPQLDTGMoxoHmCDvqQwQ8zgGV8fc9zTS0RXPcMhGRQ9OxglkyOWJTtYiI5EVHIDDYK0EqEBiGktZSHvQyoch3SNcFPE521LWxvzlMYzg2SK0TEekfr9cLQFtbr0nlRUQki46/mx1/RweLhgYNU44BBIATinw4HYZ4Qk/fRCT/CgsLiUQi7Nu3D4BgMIgxRrlORESy6MgH1dbW1vl3s7CwcFDrVCAwyjj0P1gRGSbKyspoa2sjFAqxe3e2fJAiItKbQCBAWVnZoNahQEBERAaFw+FgypQp1NfX09LSQnt7u9YvFxHpgzEGr9dLYWEhZWVlOByDO4pfgcAota8pQqHPRUXB4I4tExHpi8PhoKKigoqKinw3RUREelAgMMo4HYbW9jjVTWE8LocCARERERHJSoHAKFPkc2Gtl/3NEXXBi4iIiEivtHzoKGOMocCn+E5ERERE+qZAQERERERkDFIgMIrFEpb2eCLfzRARERGRYUiBwCgWjsb587Z6IjEFAyIiIiLSnQKBUcjlcFDkd7Otto1ILEl7TJmGRURERKQ7zSodpSYW+4nGFQCIiIiISHbqERhGalvb2dsUyXczRERERGQMUCAwjOyoC1HdFKa1PY7TYfLdHBEREREZxRQIDCuW1kiMigIvxX53zkrddKCFtvZ4zsoTERERkZFPgcAwVOB1Yczh9wi4HA4OtETY39zO/mYNORIRERGRf1IgMIpNLPbhcjiIxBPYfDdGRERERIYVBQKjmMNhKPBpYSgRERERyaRAQERERERkDFIgMEa0x5JYqwFCIiIiIpKiQGAMsElLbWuEv1c357spIiIiIjJMKBAY5YIeF+FYgi01bYSiiXw3R0RERESGCQUCo5zH5WBGRUG+myEiIiIiw4wCARERERGRMUhrS44wqzZU89j63URiSQB8bgcL51Vx4ZxJeW6ZiIiIiIwk6hEYQVZtqObBN3Z2BgEAkViSx9bv7tf1iaSlujGs1YNERERERIHASNLbDX8klmTVhureLzSpzb6mMO/tb6E5HB+E1omIiIjISKJAYATp2hOw6JSp+Nz//PoefGNnr8GAwximlgWob4sSiydJqkdAREREZMxTIDACrNpQzdKVa7vtu3DOJBbOq+q2r68hQgGPiwKfe1DaJyIiIiIjjwKBEaDr5GCgsyfgwjmTWHTK1M79Xc8REREREemLAoERoGcQ0LUnoOdqQUtXru17vgCggUEiIiIiokBghFlx1ckZN/9d5wocbBUhC7y7r5kDzZHBaqKIiIiIjAAKBEaBhfOqMoKBbAq8LnbVh9jTGKY5Ehuq5omIiIjIMKRAYJhoicSIxjMH7RxsmA+khgetuOrkg15XFvQwqcQ/8EaKiIiIyKihQGAYCEcTvLWrkeZwFGvpXPcfuq8E1PWpfzZdj/c3yZiIiIiIjE0KBIaBaCJJJJ5kd0OY8gIvLkf2YT49lwvtqetxrSAkIiIiIn1RIDCMBLwuKgq8vR7vOUn4YMf7GlZU0xKloS16aA0UERERkVFDgcAoc7DhQU6HIRxLcqA5wqYDrUPZNBEREREZRhQIjDIHGx5U4HVRHvRQ29ZO0iqjgIiIiMhYpUBglDnY8CFjDCV+9xC1RkRERESGKwUCw1h/lg49mP5kGhYRERGRsUeBwDB2KEuHdtXfTMPWQjyh1YVERERExiIFAsPYoSwd2lV/Mw1HEwnWbqsnFI0PvJEiIiIiMiLlLBAwxlQZY35ljKk2xrQbY7YbY35ijCk9xHLK0tdtT5dTnS43652wMeYKY8xPjTEvG2OajTHWGLamxRQAACAASURBVPNAP+o53RjztDGm3hgTNsZsMMZ8yRjjPJT2DpWDjf3veW7PTMNdGWMo9XvYvL+VlkiMcDSRiyaKiIiIyAiSk0DAGDMTWAcsBdYCtwFbgWuB14wx5f0spxx4LX3dlnQ5a9PlrjPGzMhy2beAa4C5wJ5+1nMJ8BLwIeC3wJ2AJ13fw/0pY6TpOU9gYomfQp8mDYuIiIiMVbnqEbgLGA8ss9Zeaq39hrX2LFI31kcD3+tnOd8HjgJutdaenS7nUlKBwfh0PT19OX1NEfAfB6vAGFME3AskgDOstZ+x1n6NVCDxGnCFMebKfrZ3WDtYTgERERERGbsOOxBI9wacA2wHftbj8A1AG7DYGBM8SDkFwOL0+ct7HL4T2AGc27NXwFq7xlq7ydp+L4p/BTAOeNha+2aXciKkehegHwHFSHCwnAIiIiIiMnblokfgzPT2WWttt7tNa20L8AoQAE49SDmnAn7glfR1XctJAs/0qG+gzkpvV2c59hIQAk43xngPs5686++8gvf2t9IYig5ya0RERERkOMlFIHB0evteL8c3pbdHDVE5B9NrPdbaOLANcAHZ5iN0Y4xZl+0HOOYw2zgoes4T8Lgc7G9pZ39zmAMt7XlqlYiIiIjkQy4CgeL0tqmX4x37S4aonIMZqnoGbNWGapauXJuTsvqaJzChyEeJ300s0d9RVSIiIiIyWrjy3YCRzFo7P9v+dK/AvIGW+9j63d3G9B9KMrGeFs6r4sE3dgLZ5wl4XU7a45o/ICIiIjLW5KJHoOMJenEvxzv2Nw5ROQczVPUMWM8g4FCSifV0KPkHRERERGTsyEUg8G5629vY/VnpbW9j/3NdzsH0Wo8xxgUcAcRJ5UHIuxVXnZzTm/mlK9dmzBUAqGuNUteqeQIiIiIiY0UuAoE16e05xphu5RljCoEFpFbief0g5bwOhIEF6eu6luMgtURp1/oG6o/p7UezHPsQqRWOXrXWjpq74q5DiyKxZLe5Ag6HIRJLsK8pzKYDrfR/FVYRERERGckOOxCw1m4BngWmA1f3OHwjEATut9a2dew0xhxjjOm2so61thW4P33+8h7lXJMu/xlr7eE+qX8UqAWuNMac1KVNPuC76Zc/P8w6hpWF86oygoEOQY+TcYU+6tuiCgJERERExpBcTRb+AvAqcIcx5mxgI3AKqTX/3wO+2eP8jemt6bH/euAM4CvGmLnAWmA2cAlwgMxAA2PMpcCl6ZeV6e1pxpiV6X/XWmuv6zjfWttsjPn/SAUELxhjHgbqgYtJLS36KPBIf9/4SHDhnElcOGcSn7g3s1PGGEOx382exp5fhYiIiIiMZrkYGtTRK3ASsJJUAPBVYCZwO3Cqtbaun+XUAacBdwBHpss5BVgBzE/X09NcYEn659z0vhld9l2RpZ4ngA+TSiC2EPgiEAO+Alx5CFmKR6xs8wREREREZOzI2fKh1tpdwNJ+ntvr42drbT1wbfqnP2UtJ3MoUX+uewU4/1CvG8l8bkfnsKDH1u/OOgm5prWdcQVejFEPgYiIiMholpMeARkZui5D2jOngMOkVg7aWN1MQyg21E0TERERkSGmQGAM6WsZ0sklfvY3RwjFEsSTSjAmIiIiMtopEBAACn1uiv2efDdDRERERIaIAoExTBOGRURERMYuBQJ51h5PsKs+NGT1dc0n0DWxWFcHmtuJxjU8SERERGQ0UyCQZ3sbI+xpCNHQFsVpzKA/pe9rwrAx0NaeYG9jmJ31bT0vFREREZFRRIFAniWtpS2aIBJLMqHI1+0pfden97nS14ThigIv4WiC+lCUWGLUp1IQERERGdMUCAwTZUEPHpej21P6rk/vB8vSlWs7eyE8LgcTiryDXqeIiIiI5J8CgWGsr6f3h6NrT0Mklux1roCIiIiIjF4KBEY4ay1t7XGaIzGi8STWHnxIz8J5VRnBQE+NoRiNoWhO2yoiIiIiw4cCgRGsMRRl495m9jaFaQxF2VLTwj/2tdAeT/R53YVzJrHiqpOzHnMYQzSepKYlwj/2tpBMaq6AiIiIyGikQGCEisQSVDeGmVzqZ1p5gKllQWZPLKbA62J7bRsNh/g0v2OeQMDjpCzopaalnXgySbIfPQwiIiIiMvIoEBiB4skkO+raKPK78XucvG9SMafNLGfGuCBTygKMK/SxtzFMUzjWZznZcgoYYygLenAYM6jvQURERETyS4HACJRIWpwOQ1VpgCPKCygvSK30M6HIx6wJBRT4nEwq8bO/OdJnOX3lFBARERGR0U2BwAgTjSfZ0xAGUk/0p5YHuh0vD3o4dmIxhT4X8USSXfWhXsf592dVoi01bcQSChJERERERhsFAiNMUziG1+VgYokfjyvz6zPGUB704HU5OKIiSDyRJBTre/Jwh645BVxOB3vSGYYPdb6BiIiIiAx/CgRGHIvH5WB8oZejJhRmPcPhMMydWkqBz43DYTjQHCEaz/5Uv7ecAtPLA0RiSWIJi+YLi4iIiIw+CgRGqNKAB7ez96/P7XRQEnBTGnDjdTmoa2vPel5vOQVcTgcFXlduGy0iIiIiw4YCgRGkNRKnpiX7DX0208oDTCzxE/S6iCd6nyfQW04BERERERm9FAiMIPtbIkwo8lHkd/fZG9DB63JSWeTDGAhF4+yoaxtQvVtr2tjTGB7QtSIiIiIyPCkQGEGshQKfi1kTChlf6O3XNYU+N+MKvcyaUEg42r9Jwx0ThoNeF3sbw2yva6VRE4ZFRERERhUFAiNQaSA1Cbg//B4nc6eUApC0lrb2eNbzsiUXK/a7mVoePMzWioiIiMhwpEBgDDDpn2K/mz2NYULRzGBAycVERERExhYFAsNIx5CcXHM4DDPGFTC5NIDP7SCRJcHYwZKLNYfjNEdig9I+ERERERl6CgSGkY4hOdB9qE7SWrbXtRGN92+MfzaVxT5Kg24A6tuixA+SLbgjKHEYiCdT17yzpzlrECEiIiIiI48CgWGk65CcrkN1ovEk8aRl1oQCgh4nXpdzQOU7jKHI58YYqGnNXIY02zwBv9tJid/NvqYwsURSgYCIiIjIKKFAYJjqOVTHAAGPi/nTynD2c6JwT1NKA4wv8lHsd5PM0iGQbZ6AMYaKAi+ufixXKiIiIiIjh+7uRhC309Hv1YKy8XucTC0LANAUjhKJdR9qdLB5AiIiIiIyeigQGGMcBjwuJ6VBDzvqQn2eu3Tl2owJzOt3NvS6BKmIiIiIjBwKBMaYkoCHWeMLmFjsI2Ezx/t3nScQiSU75woEPE4217RS1xrV6kEiIiIio4ACgTHG6TBUlfpTL6zNyDa8cF5VRjAAUFUaoMjnBjRZWERERGQ0UCAwAgzWSj0FPhe7Gtq6JRi7cM4kVlx1ctbzHWbg8xNEREREZHhRIDDMNYdj7GoIkctFe4wxTCsPMrUsSMDjIp7oO9DoOU9ge22IFg0PEhERERnRFAgMc+FYgooCL9PLC6go9Oas3EklfsoLPADEs/Q4ZMsp4HRAUzhGbWs7O+v7nmgsIiIiIsObAoERYmp5gMkl/pyX63AYaloi1PZIMJYtp0B50IvP5aQlEiPLPGMRERERGUEUCIxhZUEPk4r9TCz2ZUwazpZTwOEwFAfcQ9U8ERERERlECgTGsIoCL0dNKOjXuT3nCbRE4rQqn4CIiIjIiKVAQABoicTY1xTpti/bPAGDIZG0NIWjbNjVSDyRHNJ2ioiIiEhuKBAY43xuJwU+FzPHF1Afasd2GfyfbZ6Az+2gyOdmT0OYWDKZdaKxiIiIiAx/CgTGuKDXxfunl+N1OTOOZZsnYIxhfJEPdy7XMxURERGRIae7OcHjctCRK6y2NUqylyWBlq5cmzFXIBJLZD1XRERERIY3BQICgMthmFDoozUSozXyz0nAXecJRGLJzrkCAO2xJG/vbspYelREREREhj8FAnm0+UAL+5t7v4mua22nbohuso+uLKS8wIvH7ejWI7BwXlVGMABQXuBlV32IxnCM9rgmDIuIiIiMNAoE8qghFOPdfc00hGIEPJlj9OvbokwrD1IacON3Zx7PpUKfm3GFqUzD4Wiic9LwhXMmseKqkzPOLwt6KC/IXaZjERERERlaCgSGgaMnFOLr5Ubf7TIcX1VCWdAzBC0xeFwOQrFExlKiXfWcJxCOxrutNiQiIiIiw58CgRHA6xqar2l8kZdxBT4mFHqJ9sgPkC2nAEA8kWRPY5hNB1qHpI0iIiIikhsKBIaBp9/ey9KVa/PdDIp8bo6pLMx6LFtOgSKfm4ZQjN31Ya0eJCIiIjLCKBAYBh7/y+7Om2vo/vQ9X9ra4+yqD3W+7plTYNWGavweJ0dUBIe6aSIiIiKSA/m/45SMIKDr0/eh5vc4KQ64ObqykLZonESXzMG9DQ8CaGtPqFdAREREZARRIDDMrLjq5KwZfYeKz+3kpGllOB2ZvxrZhgcBJK2lLRrnLzsbiSW0lKiIiIjISJCzQMAYU2WM+ZUxptoY026M2W6M+YkxpvQQyylLX7c9XU51utxeH5Mfat3GGKcxZpEx5mVjzD5jTMgY854xZoUx5n2H+t5HG4fD4HSkUg3va4509gpkC1C8LgcBj4sdtW1E4wniCa0eJCIiIjIS5CQQMMbMBNYBS4G1wG3AVuBa4DVjTHk/yykHXktftyVdztp0ueuMMTNyVPf/AA8A04HHgZ8Cm4ElwHpjzFn9ae9o5nYaJhb7iCUStERiWc9ZunItT729l0klfjyuwc1zICIiIiK5lasegbuA8cAya+2l1tpvWGvPInVTfjTwvX6W833gKOBWa+3Z6XIuJXVTPz5dz2HVbYx5P/Ax4O/A0dbaL1hrv26tPR/4DOABvnVI734Umj2xiNKAB4/LSZdpAhlZhnvOFahpae82r0BEREREhqfDDgTST+TPAbYDP+tx+AagDVhsjOlzeRljTAGwOH3+8h6H7wR2AOd27RUYYN0d1z9vrQ31uObJ9HZcX20dC3xuJxWFqczBzZEY8WRq7P/CeVUZwQCAMdAUjrG5ppUDLb0nIxMRERGR4SEXPQJnprfPWmu7zRS11rYArwAB4NSDlHMq4AdeSV/XtZwk8EyP+gZa99/T27OMMf4ebbgwvX3uIG0FwBizLtsPcEx/rh/uHMYQcDsx0Jlp+MI5k1hx1ckZ51YW+ahpaac1EtM8AREREZERIBeBwNHp7Xu9HN+U3h41COUc8jXW2r+RGjZ0HPAPY8zPjDG3GGN+D/xf4GHyPDTIWsv+5kjeV+CpLPIxodhHRYGXeB/DfVZtqCbodTEu3YMgIiIiIsOfKwdlFKe3Tb0c79hfMgjlDKhua+1XjDHvkgoIvtDl0DrgPmtt20Ha2lHO/Gz7070C8/pTRjaRWJKWSIyqUj9uhwNXegWfoeb3OJlZUUB9az3xhCVpLQ6TaovP7egcFvTY+t3dVhTa3RAm6HVRFvTkpd0iIiIicnBjLo+ASbmD1JyCm4ApQCHwQcAC/2uMuTqPTcRicToMRX4Pc6eW4HLm92syBpI2ydaaVqxN9QxkyyngdDhoisTZ1xTulpVYRERERIafXNxhdjx1L+7leMf+xkEoZyDXLAG+CNxhrb3FWrvbWttqrf0TcBEQBm5JT17Oq0Kfi4AnF502Axf0OplQ5OOoCUUkre01p8CqDdWUBtyUBTy0RhNoloCIiIjI8JaLQODd9La3OQCz0tvexvEfTjkDuaZjQvCanidba/cB/wAK+Of8gzHN5XRw3ORiPK7M4UldVw96bP1ujDEEval8Aomk7ew9EBEREZHhJxeBQMcN9TnGmG7lGWMKgQVACHj9IOW8Tupp/IL0dV3LcZBaJrRrfQOtu2NGa29LhHbsjx6kvWPS1to22uMJIPvwoH++TrB+RwPxPE94FhEREZHsDjsQsNZuAZ4llaW359j6G4EgcH/XCbjGmGOMMd2W2LTWtgL3p89f3qOca9LlP2Ot3Xo4dQMvp7dfMcZ0G1JkjPk8UAXsA97p5S2PSX63iyMqggS9LlojcSBzeBCA2+nAAfxjbzPNkTjtcQUCIiIiIsNRrgagfwF4FbjDGHM2sBE4hdQ6/+8B3+xx/sb0tud4k+uBM0jdpM8F1gKzgUuAA2Te7A+k7ruARcAc4D1jzO9IzSGYB5wFJICrrbWJfr73MWH2xELe22+oa+29o2TpyrUsnFfFhXMmsaWmdQhbJyIiIiKHKifL0aSfzJ8ErCR1E/5VYCZwO3Cqtbaun+XUAacBdwBHpss5BVgBzE/Xc1h1p3seFpDKPLwX+CTwJVIBx2+A0621j/f7zY8Rxhi8rtSvy/7mSGevQM8sw4+t393tuurGcN7zIYiIiIhIppwtSWOt3QUs7ee5vS6Mb62tB65N/+S87vT5raSWDr2pv9cIuF0OSoMeXE4HNa3tFPhcLJxXxWPrd3fOEejYOoyhIRQlkbT4PU6qSgP5bLqIiIiI9DDm8gjIwE0s8jFzXAFBj7Nz34VzJrHiqpO7nbdqQzUTi300hWK0tcdJqkNAREREZNhRICD95nAYSgJuAMLROI2hf84X6LmUqM/tpKIwtUBTQsuIioiIiAw7CgTkkDgdBpfTML7Ix/7mSOfyoL0tJZq0lurGMJsPtAx5W0VERESkdwoE5JAEPC6OnVRMRYEXh8OQTjScNdNwwOOkvi3KlppWmtOTi0VERERkeFAgIIesosCLNz0UqCkcJZke+tNzeFDA4+LI8YVZyxARERGR/FIgIAPiMIYSv5vWSJzGUAzoO9NweyzJjro2rOYLiIiIiAwLCgSGoZGwys4RFUHGFfoIel2dPQLZMg07HYZE0rKrPsT22jbaosrTJiIiIjIcKBAYZhpDUXY3hnA6ek21MCwU+91MLvED0BSOdU4a7mrpyrX879/2Mr08SEskRiJp1SMgIiIiMkwoEBhmIrEk4wu9TC0LUl7gyXdz+mQMeN0O3E7DnsYwkD3TsM/txO9J5a6rbU0lGRMRERGR/FIgMExNrwgwsdif72b0aVyhl6rSAOMLfcTTN/cL51VlBAOQChpaInG21bRSnQ4aRERERCR/FAjk2atb6vLdhAHzuZ0cUREEoD2WIBxN9JppeHyhl9rWdprCMfUIiIiIiAwDCgTy7IV3azr/3fVJ+khhDDgcqTkDO+vbOucKZFtKdEKRD4DW9jhJBQMiIiIieTXy7jxHmWiXSbZdl98cKQIeFzMqCphcGsDpdJCw/xwi1KHrUqKJpKW2tZ139jYPeVtFRERE5J8UCAwj2ZbfHAmmlAXwe5wANIfjJK3Nmmm40OcmEk+yvbaNSEzLiIqIiIjkkwIByQmHgSKvi5ZIrDPBWM/hQR6Xg2llAQDiSavhQSIiIiJ5pEBAcmJaWZDxRT4KfS4S6YxofWUajieSvLmjnva4egZERERE8kGBgOREccBNVWlqudO61iiRWCJjeNDSlWtZ/bd9+NxO3t3XQnM4TiQ6AtIoi4iIiIxCCgQkZ5wOQ8DjoijgZm9TBMiSYOwvu5lWHiTgTSUYs2h4kIiIiEg+KBCQnBlX6GV6RYCKoKczV0BvCcYgFQRs3NtMTUv7kLdVREREZKxTICA543Y6mFySmgwcjSeoa23vNcFYodfFzroQ1U0RmiOxfDRXREREZExTICA55XQYnA7DxBI/dW3RzsnAPVcQKi/wUlmcmlOg1YNEREREhp4CAckpj8vB8VUllAY8uByGdH6xXlcQshYOtLTzj31KMCYiIiIylBQISM4V+90EvakEYzvqQllXEFq1oZqAx0lLJMZ7+1MrCImIiIjI0FEgIIPC63IyqcRPsd9FUzh7gjGf28ms8YUAJJKWWEJLiYqIiIgMFQUCeZBIWt7d10I8MXrHxs8aX8CkEj8u5z9/xbINDzLp19F4gj9vqyccVYIxERERkaGgQCAPWiIx9jSE2FbTmu+mDBqHw1Dgc2GAurZ2qhvDWROMPf23vRT53Gw+0Epbe5xITIGAiIiIyFBQIJAnCWuJjuIeAYBCn4vyAi9Hji+grT01ByAjwdj63Uwq8RNMJxhrCEU7cxCIiIiIyOBRIJBHXW+KIdVTUN82epJrFfncnDi1BIBYIkkklug1wZjDGMKxBNvrQuxuCOWlvSIiIiJjiQKBYWRfU4TKYh9BrwuXY3R8NcaA06SGCe2oa+OcYyuzJhgrL/BQ09JOfVu7Jg2LiIiIDIHRcbc5SlhST9GPqSyiosCT7+bkhNflZFp5kKllQTwuB/Fk6ia/5wpCAY+LSSWpBGM1LVEa2qJ5aa+IiIjIWKFAYBgqC3owxhz8xBFiSlmAQl9qDsDepgjReDJjBaFVG6pxOgzhWJL9zWE2j+KJ1CIiIiLDgQIBGRIup2FcoRef20FDKMqFcyZl9AoUeF1UBD3UtWnCsIiIiMhgUyAgQ2JGRQGVRX78bidJm7rJ79krYIyh2O8GwFr4254monHNFxAREREZDAoEZEh4XA4qCj2AoSEUZU9D9rwCT729F4/TyaYDLextCtMSieWnwSIiIiKjnAIBGTKFPjdlQQ9HjS+ktY+8AjPGBXEYQzJpaW2PY62GCYmIiIjkmgIBGTIFXhfzp5UCkEgmaQ7HsuYVcBiDx+mgPZFke20bO+uVV0BEREQk1xQIyJByGHA4DGVBD/uaI5x9zISseQVKgx5qmts50NJOu+YJiIiIiOScAgEZUi6ng6MmFFJZ7MfjMiTSw36yrSBUVRoAoK41yv7mSF7aKyIiIjJaKRCQITeu0EuRP5VXYGddGy2RWK95BULRBLsbQmytadVcAREREZEcUiAgeVHkczO1LEhlsY+WSDxrXoGg18XkEj/N4dTKQdGEhgiJiIiI5IoCAcmLKWUBjqgIYoyhMRQlHE1k9AoABL0uMIb2eJI/b6vvXG1IRERERA6PAgHJG7fTgc/loCzoYVdDKGtegVUbqikPethyoJXW9jjhaCJPrRUREREZXRQISN6UBT3MmlDIuEIv8aTFWps1r8CEIh/Ffg8Amw+00qwkYyIiIiKHTYGA5I3TYZhY7MMYg8Gy6UArl86dnBEMrNpQjctpqGuNUtMaYW+jVhASEREROVwKBCSvXM7U0KDZE4vxuR2cdcx4Vlx1csbE4XGFXvweJ+Fogvq2KJGYhgiJiIiIHA4FAnn00qaafDdhWJg9sYiSgBuAPY1hIrHMicOfue/PvLaljkTC0hqJsWF3o5YTFRERETkMCgTy6LmNBzr/3fUJ+FjkdjqoKPBS4ndT3xbNWE40Ekvy+w3V+NxOdtaHiCUsScUBIiIiIgM2tu8+8ywa/+e6+F2fgI9F08sDVJUG8HucNIVjRONJFs6ryggGJpb4cRgDwPqdDVpFSERERGSAFAgMEz2XzhxrXE4H5QUe3E4HhT4X2+vauHDOJFZcdXK381ZtqCbgdfHe/hZqW9tp0QpCIiIiIgOSs0DAGFNljPmVMabaGNNujNlujPmJMab0EMspS1+3PV1OdbrcXh+ZD7RuY8wVxphnjDG1xpiIMWanMeZJY8yph9JmyY0Sv5vpFUGqSv3EE0mS6TkAPScOTy0LUOB1gYUtNW1aTlRERERkAHISCBhjZgLrgKXAWuA2YCtwLfCaMaa8n+WUA6+lr9uSLmdtutx1xpgZuajbGOMyxjwI/AY4AngEuBV4DjgKmN/f9y6543I6mFERBMDhMGw60NI5RKhDx3KiHqeDhrbUcqJ7GsL5arKIiIjIiOXKUTl3AeOBZdban3bsNMbcCnwZ+B7w+X6U831SN+K3Wmu/2qWcZcDt6Xo+moO6bwQ+mT72HWttsutBY4y7H22VQWCMoSzo5ZhKw+6GEJFYggvnTOKx9buJxFJf02Prd3P+8RNJWgi1J2gMxWiOxCjy6WsTERER6a/D7hFIP5E/B9gO/KzH4RuANmCxMSZ4kHIKgMXp85f3OHwnsAM4t2uvwEDqNsZUAtcBr1trv9UzCACw1g75WJOd9SHiiYymjElHVxZSXpDKJLy7IURrJJ59OdGttcSSlvq2KO/saSahZYRERERE+i0XQ4POTG+f7XlTba1tAV4BAsDBxt2fCviBV9LXdS0nCTzTo76B1n0F4AEeNsb40/MEvmGMudoYc8JB2jhoEokkM8YV4HM7cDlMvpoxbPhcTsYXeZlQ5KMhlH050d+9VU2J382+pjDxZJLW9ngeWywiIiIysuQiEDg6vX2vl+Ob0tujBqGcgVzz/vQ2APyD1DyBH5DqdfirMeZRY0zgIG0FwBizLtsPcEx/ru9WlgMKfC5OnFqKQ4EAU8sDzKgowO00tERiNIaiWZcTfX1rHS6ng3A0wYZdjdS3RfPYahEREZGRIxeBQHF629TL8Y79JYNQzkCuGZ/e3kxqSNE8oIBUr8GbwEJS8w6GXMDjxOXUiq4divxufB4nk0r87G2KcMHxE1lx1ckZqwhVFHjZWR+iORKnTb0CIiIiIv0yFu86O95zPXCRtfYv1to2a+0bwMVAK6l5BZMPVpC1dn62H1I9DXKYinwu5kwuoSTgwWJpDMew1mbMFygLeigNekjYJDvq2the25bHVouIiIiMDLkIBDqeuhf3crxjf+MglDOQazr+/by1trnrydbavcAbpD6Xkw7SXhlkxhhKgx5cTkNF0Et9W5TW9nhG8rVVG6op9LmpaW5nZ31IcwVERERE+iEXgcC76W1vcwBmpbe9jeM/nHIO55reApOG9Nbfy3EZYrPGFzC+yIfP7aAhFCORtBnDgwq8LqancxC0ROK8vbsJa7WKkIiIiEhvchEIrElvzzHGdCvPGFMILABCwOsHKed1IAwsSF/XtRwHqWVCu9Y30LqfS2+P66Ud70tvtx2kvTJESgIexhV68btdJG2Sfc2RjOFBS1eu5fmNB4glLO9UN9EQaieq5VhFREREenXYgYC1dgvwLDAduLrH4RuBIHC/tbZz4LYx5hhjTLeVday1rcD96fOX9yjnSPI6SwAAIABJREFU/7F331F2ned977/vbqfPmY4ZYDCoBAGwAiwgRVmWRZmiKMsqjG9iK4qlmzgr13as2E5uinNtKytxbrKuu+MUO3ZiLUpuEsVY3ZZkWZEogJ2UWEASvQymz5ze9r5/7H3OdGAADGaAmd9nLayDOWXvfSAtzvmd532e96ej4385CIJjV3Nu4JvA88BbjTEfmP0CY8xPAPuANwgbh+U6sbk9zqa2GN2pGFOlGu+6pW/BBKHPPHeGPZsyrYbrZ09OapmQiIiIyBJWamfhnwS+DfyWMeZB4BXgEOGc/6PAL8x7/ivR7fw5mf8KeDvwc8aYO4EjhB/M3wcMs/DD/mWfOwiCwBjz48A3gE8bY/4iet4twLsJNyH78SAIGpfx/uUaS3oOu3vTPHtygnTM5vhogUcPDPDp52Z2HC7XfD734jnu3NrOmyMFejNhaEjHVur/5iIiIiLrx4pMDYq+mb8b+B+EH8J/HtgF/CZwXxAEY8s8zhhwP/BbwO7oOIeAPwTuis5z1ecOguBFwrGhf0S4r8A/AQ4Aj0Xn+fby3rmspkzcZbArxWBnCj8IeMe+3kXHiQ50JMnGXfwATo0VOTtZWsOrFhEREbk+rdhXpUEQnAY+usznLrljVhAE48DHoj8rfu5ZrzkOfORyXiNry7YMu3vTTBSrJD2bMxNFNmeTPHpwgMcOnwJmqgJvu6mHs5NF8pUaqZjNlnb1fouIiIjMthH3EZAb3EBHgsHOFOm4y1SpxiO39S+oCrQlXLZ1pfB9KFQavHRmCt/XFCERERGRJgUBueH0ZxNsaosRsy0q9Qbnp5aeIlT3A145P8V4sUK5rrYPERERkSYFAbkh9WRidGdibGqLM1Ws8tD+xacI3dSbxrYsfB9eOD3JZLG6hlctIiIicv1QEJAbUibusq+/DdsypOMOx0fzfPDAwIIw8PmXzpNNuBwbyTOSqzCar2ijMREREREUBOQGlok5bOtKMtgZ7ij8wO5u/uDH71nQL7CpLU5PJkbDDzg7WeL14fxaXbKIiIjIdUNBQG5YlmXY2ZPGcyyyCZfxYpXpcn1Bv8DnXjxHOuYyWaxxarzEWL5KsaqNxkRERGRjUxCQG96O7hR92QRpz2ZoqswP7t80pyrw2OFT/OQnn+G1Czl8PyBXrvHcqQmqdX8Nr1pERERkbSkIyA2vM+WxpT1BOu6QSTgMzZsiBGFl4LPPnyWbcDk9XqRaDzg1XqDWUBgQERGRjUlBQNaFvmycrZ1J2hMuhUqd+3Z28aFDgwuah586MU7Cc5goVjkxWuTCdHkNr1pERERk7SgIyLrgORbbu1LEHIstHQnG8hUevqWPP/zIvQuah/uzcSaLNQqVOqfHS4zkKmt45SIiIiJrQ0FA1o24a3P71nayCQ9jDMdGC1TqjQXNw3/1ygX6s3GmyjXOTpY4M1Fcw6sWERERWRsKArKutMVdsgmX7d1J0nGHqWKNH7p984KqQDbh0pOOUazWKdd8njs1QV39AiIiIrKBKAjIurOvP8OmtjiuZRgvVjk/VVpQFfg//+dTfPP1USxjePn8FBOFKsM5bTYmIiIiG4eCgKw7xhj62xL0ZOJs60oxUajyzn2bFjQOf/LIKV45P03CdSjVGrx+Icf5KTUPi4iIyMagICDrUjbpcsfWLLYFmbjLybECHziwZU4YgHCZUHfaY2iqzHihysmxIhOF6hpdtYiIiMjqURCQdSvh2mzvSrG1M4ltGe7c2sHvffhuPnRosPWccs3nG0dH2NyeoFBtcGG6xPGxwhpetYiIiMjqUBBYZeVagxNjmlKzGowxbOtKkYk79GRiQMBkafHm4baES0fSY6pUoxI1D2uzMREREVnPFARW2bnJEuenSoxr+cmq2d2bpicTI+HaDE+XGcmVFzQP//3/+RTffmMU27J45fwUY4UqZyZKNHw1D4uIiMj6pCCwyvwACpUG879s7kh62JZZm4ta5+KuzY7uNF3pGDu6U4zkKjy0v29B8/BjzeZhz6FYqXN8JM+5ydIaXrmIiIjItaMgsEY6ku6cn3vb4mzvSq3R1ax/nSmPO7a249iGVMzh+GieD9y5ePNwbybGSK7CZKnGmYmSwoCIiIisSwoC14kt7Qnirr3Wl7GupWMOg50ptnWlcG2LW7dk+a9/d2Hz8NdeHWawM8V0qcbJsQInx4qUa401vHIRERGRlacgIBvK9u4U2YRLb1uMmGMxXqgu2jycjoehoVRrUKjWefrEOMVqfQ2vXERERGRlKQjIhrO7N82mtjgJz2ayVOXsxMKdhz/6P47w1Vcv0JH0ODlaoFRr8OKZKfIVhQERERFZHxQE1sBfvzbMP/mT59f6MjYsz7HY0Z2iMxVjZ0+KqVKVt+7uXtg8fPgUT50Ypz3pMTJdYTRX4Y3hPHWNFRUREZF1QEFgDfzlyxeo1Gc+TMYc/c+w2jJxl7u2dWAbQ08mxnCuwvvuWLx5uC8bx3NtCtU6Y/kKL52dWqOrFhEREVk5+gS6BuaHgPfc3r+GV7NxeY7Fvv42ejJxXNuwZ1Oa3/o7BxY0D3/hpfNsysQIAjg5VqBc83ltKKfKgIiIiNzQnLW+gI3u33/gNuKepgWtla50jC2VBkEQMF6ocnq8yDv3beLTz56hXAs/6D92+BSffvYMjx4YYE9fhuOjeQrVOLZl2NGd0v4PIiIickNSRUA2vMGuJDt6UiQ8m46Ux5l5zcMws+HYq0PT1BoB+XKNU2MFTo0X1+iqRURERK6OgoAI0JOOsbMnTU86RrXeYG9fhh+9d+uCnoHHnzvL1o4kY4Ua44UqQ1Nl3hjOrdFVi4iIiFw5BQERwLEttnclySZd9vW34diGOwba+b0PL9xw7KuvXmBnd4p8pc5rQ9OM5KqcnSzh+8EavgMRERGRy6MgIBIxxnD7QDvtSY+OpIdlDBemK7zntv45lYHHDp/i/3rsGY5eyNPwAy5Mlzg6lOP8dJkgUBgQERGRG4OCgMg8O3tS9LbFySQc8pUap8aLi/YMfOa5M2zvTjGWr5Kv1HljOKeeAREREblhaGqQyDxx12ZfXxtBEJCJObw2lOOubR0EAXzmuZlpQuWaz9deHebtN/dyaqxAserg2TYNP2BnT3qN34WIiIjIxakiILKIhGdzYGsHrm0x0JGgVG1w745O/vuP37NgmdA//tSzHB3OU6o2eGMkz9BUmdPjRRrqGRAREZHrmIKAyBIsy3DH1nbaEh6ZuEOhUmckV1l0mdCfPHWa1y7kqNYaDOfKvD6c59R4UQ3EIiIict1SEBC5iLhrs39zuPtwZ9pjLF/hwGAHHzo0uOho0WbPQK5U48RogeNjhTW6chEREZGLUxAQuYRswuX2gSztCZc9mzJMFavcuz1cJjR/tOjXXh1me3eK0XyFC9NlhqcrfPfslKYJiYiIyHVHQUBkGVIxh3t3dOHYhs3tCfKVOsPTFR5ZZLToT33yWd4YzlOp+7x8forJYpWXz09TqTfW8B2IiIiIzKUgILJMtjWzz0Am4VCshmFgsZ6BTz11mqNDOTzb5vREkbMTJb57dopSVWFARERErg8KAiKXIRVzuGVLGz3pOF1pj/FChdu2ZBftGXjsyClePj+F78NEscrwdIXnT08qDIiIiMh1QUFA5DK1xV0ODLbTk4mxf3OWQqXOnVvb+f2/N7dnAMIG4sHOJAbDWKFKrlzjuVMTlGsKAyIiIrK2FARErkDctblrWyeeY7GtK0Xd9zk5VuCh/X0LGoh/4hNP88LpSZKezenxIuVag6dPjDNZrK7hOxAREZGNTkFA5CrctiVLZ9qjI+nhORYnxgo8fEvfnGVC5ZrPY0dO8czJCXoyMY6PFpgs1njlfI4zE8U1vHoRERHZyBQERK6C51js729jS3uSzpSH5xjeGMnzwQMDC3sGDp/i8PFxBjqSDOfKHB/Nc3q8xBvDOY0XFRERkVWnICBylZqbjg12JtnelcYAu3vT/OcP3bWgZ+Cxw6f42J88x9ELecq1BsdG8pybLPG9c9PqGxAREZFVpSAgsgJsy3DTpgw9mRg397WRTbocG8nz1t3dC8JAuebzx0+d5vXhPNW6z7nJMmcnijx3apLpcm2N3oGIiIhsNAoCIitod2+a7d1JetMxNnckODdZ4r6dXYuOF/3UkdMcHc7hBzBWqDKSL/O9s9OM5StrdPUiIiKykSgIiKyw/myC2wayZGIOWzuTjOYr3LO9k/++xHjRbZ1J0jGHiSgMvHJ+mjMTRRq++gZERETk2lEQELkG2pMedw52kIm79GbiFKt1To4XedctC8eL/v0/eorDx8fpzcQZma4wXqhydCjHy+emqdTVNyAiIiLXxooFAWPMgDHmD4wx54wxFWPMCWPMbxhjOi7zOJ3R605ExzkXHXfgWp3bGPOvjTFB9Oedl3O9IktJxxxuG8jSmfLoTHk4luH14TwP7V9kvOjhU/zvN0bZ3p1iJFdhNF/l/FSJZ09OUqjU1/BdiIiIyHq1IkHAGLMLeAb4KHAE+HXgGPAx4EljTNcyj9MFPBm97s3oOEei4z5jjNm50uc2xhwEfhHIL+caV5pWf6xv6ZjDgcF2BjqS9LbFSMds3hzJ8b47tiw6XvRrrw5z06YMAXB+qtTaiXg4V9aIUREREVlRK1UR+F2gF/iZIAjeHwTBvwiC4B2EH8pvBv7dMo/zK8Ae4NeCIHgwOs77CT/U90bnWbFzG2PiwCeAp4DHl3mNK2q6XMWsxYll1cRdm1ui8aKDnSlSMYf9mzP86o/cueh40X/4iad58cwk7QmP0+NFpko1Xjk3zSvnc9Qa/hq9CxEREVlvrjoIRN/IPwScAP7TvId/CSgAHzbGpC5xnDTw4ej5vzzv4d8BTgLvml0VWIFz/3tgB/ARYE0+Ye3ZlKErHSMTd9bi9LJKjDHs7AknCg12puhIeYzmy9y5tZ0P3btwvOhjh09x5MQ4WzuTDE2VuTBd4dxUiadPTFCsaqmQiIiIXL2VqAj8QHT7lSAI5nyYDoIgB3wLSAL3XeI49wEJ4FvR62Yfxwe+PO98V3VuY8w7CCsN/zIIgtcvcW3X1MHBdpKegsBG0J9NcMuWNnrScQY7U+QrdW7uy/Bj9y4cL/rY4VN84+gIN23K0AgCzowXyZdrPHtygqGpMr7WlYmIiMhVWIkgcHN0e3SJx5sfsvdcg+Nc0bmNMVngfwDfBH7rEte1JGPMM4v9AfZe6TFl/WuLu9y7o5OutMfevjaMgV09KX7nRw8uuVTou2en6Eh6nBovMl6s8sr5aV48O6XdiEVEROSKrcTX0NnodmqJx5v3t1+D41zpuX8b6ATeHqgDU9aAbRluH2jn+GgBgJFcmZNjBe7Z3gmEAaCpuVQI4O0393JqrEAx1qBab1CqNtjbl6Ej5a3+mxAREZEb2oZbj2KMeZSwF+GngiA4djXHCoLgriXO8Qxw8GqOLRvDju4UHUkXCMjEXY6N5NnX38aP3TvIZ547Q7k2s+KtGQYevrUv6hko0wjgpbOTbG5PMNiZwnO0NYiIiIgsz0p8amh+655d4vHm/ZPX4DiX9RpjTCfwX4CvAv/5Etcjsirakx73bO+kLeGwt78NuPhSoZ/4o6d57tQEm9rinJ8sMZKvcny0wDMnJ5gsVtfiLYiIiMgNaCUqAq9Ft0v1ANwU3S61jv9qjnO5rxkEuoEHAd+YRQd3/mV0/88GQfAbl7hmkRXh2BYHBzt4c6SAAUbzlWUtFfrB/Zs4PV6iVG1QjIX9Apvb42ztSGJZGkwrIiIiS1uJIPD16PYhY4w1e3qPMSYDPAAUge9c4jjfAUrAA8aYzOzJQcYYi3BM6OzzXcm5x4D/vsT530YYHL4InAO+e4nrFVlRxhh296bpSnm8OjRNNuHyxnCePZsy/Oi9W3n8ubOLLhV65LZ+pko1zk+VqPk+pVqDc5NlbtnSRlvcXau3IyIiIte5q14aFATBm8BXgO3AT817+ONACvhEEASF5p3GmL3GmDmTdYIgyBNu7pVi4T4CPx0d/8uz1/Vf7rmDIDgdBME/WOwP8O3odb8W3fdXy/9XEFk5HSmPe3d0kU167N+cxXMMN/Wm+f/+1h0L9hx47PApPvT7h/m5P32eo0N5cuU65yZLjOTLfO/sdKsZWURERGS+lWoW/knCD9K/ZYx5EHgFOEQ45/8o8Avznv9KdDt/7cK/At4O/Jwx5k7gCLAPeB8wzMIP+1dybpHrnm0Z7tzazpmJIgATxSojuTI394XVgU8dOT3n+eWaz588fZofu3eQt+zqYiRfYapYA+DCdJl9/W1kE6oOiIiIyIwVGTESfTN/N+Fs/kPAzwO7gN8E7guCYGyZxxkD7iec7b87Os4h4A+Bu6LzXJNzi1yPBjqS3LE1S08mxq6eNJZl2LMpw6MHBxZsQAbwySOn+Kd//gJHL+QAw8vnphjLV3jx9CQvnpnUvgMiIiLSsmLjQ4MgOA18dJnPXbKLMQiCccIdfz92Lc59kWN8BPjI1RxD5FpIeg73bO/kjeE8tmUxNFXizsF2Dgy2s7UjyVdeHlrQTPypI6f50CHD2/b0cGa8yFSpRrkWo1Cps6snTXc6pmZiERGRDW7D7SMgcqNqNhIDFCp1JopV3hjO8dbd3QB8+tnF9x145NZ+hqbLnBov0tsWp1KfJhVz2NuXIaNmYhERkQ1LQUDkBtKR8rh7ewenxoskp2w822IkX+GWzVke2t+3oDrw2OFTfPrZMzx6cIC37+nl1HiBXNmmLe5SbwTRkqMUS4zSFRERkXVMQUDkBuPaFrt60rQnXIwxJD2bqXKNN4ZzvGVXWB1YbN+Bxw6fIu5aPHxLH3dsbWeyVKPh+4zkymzvTrEpE9dyIRERkQ1kRZqFRWT1daVj3LWtg23dKXozMQY7kwxNldjf38aP3rN10Wbics3ns8+f4+hQDssYXhvKcWG6zKvncxw+Pq6diUVERDYQBQGRG5jnWOzZlOHgtk7ScZfdm9I4tmH3pjT/9v238WP3Di4aCD711Gm+d26KHd1pJot1Tk8UGc1X+N65aV4dmqZS13QhERGR9U5Lg0TWgXTM4dCOTs5MlPBsm0KlzvB0mV09KX7z7xwgE3P4/Evnl+wfeMuuboamShQq9bARuVCjO+2xvTuFa+v7AhERkfVIQWCV/dnTpy/9JJErYFmGwa4k/e1x3hzJk4o5nJsqMTxdZhjDO/dtAhbvH/j0s2f4wIEt3DXYyZmJInHXplRLMJKrhP0DbXFs9Q+IiIisKwoCq+yPnjzZ+runb1rlGnBti719bYzkKkA4anS6XOPYSJ57tncCC0eNNvceePy5s3zwwAC3D2Q5PpKnOx2jXGtwcqzI7t40PZnYmrwnERERWXkKAqusNGtn1++/uWcNr0TWu55MjPaky5mJEmcnirQnXE6MFdjZneLX/o87+dbro3z6uYWB4JNHTmHMIO/Y28up8SLT5RrJmAMEvDGcZ29fhvakq5GjIiIiNzgFgTX0ll1da30Jss65tsWO7hT92Tgvn59mn+cwmq8wXqiysyfFb//oQf76teFFNyNrjht97+2b2duXYbJQpS+b4MUzk3iOzf7+NrJJbUgmIiJyo9LaFJENIO7aHBzs4JYtbfRmYmztTNCdjnF6vMAdA+383ofv5kOHBhe8rlzz+bNnznBstMBANJ70zESJkVyZl89P89SJcabLtTV4RyIiInK1VBEQ2UDa4i737ujkwnSF46MFUjGHsUKFoxdy3D7Qju8HPP782TnVAZhbIXjPbf3s39zGeKHKpmyc4qk6McdmX38b2YQqBCIiIjcKBQGRDcYYQ182Tlfa4+RYkVTMplTzGZoqcdOmNP/x0dvpSsX4wnfnjhuFsELw6WfPEnNsHtjdzbmJEgnXJh13CAJwbMOe3gxtCUc9BCIiItc5BYFVVKpqkya5fri2xe7eNDu6UxwbyZNwbcYLFaZKNUZyFe7f2UUQwGfmNRQDUUMxPHJbP5PFGkPTJSaKVXoycYrVOp5ts7cvQ0fKW6N3JyIiIpeiILCKXj4/vdaXILKAbRlu2pShv73Oa0M5MnGHYrXBhekyu3rDCUPZhMsXFtmQrLlc6IMHBnhgdzfnJ0vEXJt0zG49b1dviu5UDEv7EIiIiFxXFARWUb3hX/pJImskHXO4a1sHhUqdV4emySY8RnJlJgpVzk+WeOvubgjgsSMLlwt98sgpPnmk2UOwmf39GSaKNbpSHqVag4Rrs7UzweZsQoFARETkOqGpQSIyRyrmcNe2Tvb3t9GTiTPQmaC/PcH5qRI7e1I8enALcXfx/3SEPQRnODZSYKA9yVi+yunxImcmipwYLfCdY2McG8lTrSsUi4iIrDVVBERkUdmky307O5ku1Xn5/DQdSY/h6TIHBzvY399Gf3ti0U3JIKwaPBZVCH74js3csjnLa0M5skmXfKXOhekKSc9md2+aVEz/GRIREVkL+g0sIksyxpBNuty/q4upYrhfQHujQbHSYGi6zM7eFL/6I3fSnnCXnDL0p0+f4UOHLB7a38fQdJmzkyUcq0xfNs50qUbCs9nRnaIz5WnSkIiIyCpSEBCRZZldIXhlaJr2pMdovsJUqcrQVIl7tncuOWVofmPx3ds7ODVWbI0eLVbruLbNtq4kfW1x9RGIiIisAgUBEVm2ZoXgvp1d5Mq1cLlPwqFS8xmaLrO7N8WvvP82ejIxvvS9oUUrBJ88corPPHeGDx4Y4K03dTM0VWYkV6ErHTYWN/c22NmTJq1lQyIiIteMfsuKyBXJxF3u3t5JsVrn6IU86bjLZKnKdKnG0Qs59vW38bfv3soTLyzcqXh2IHj04ADv2NvLuckSY4UqCcemPeWRL9dxHYutHUl6MjFsVQlERERWlIKAiFyVpOdw59Z2yrUGJ8YKjOWr1H2foaky+/oz3LJ5H33ZON94bWRBY3G55i9YNnRoRyfnJ0uM5StkEy65Uo2E55BNuOzoTpHw7ItcjYiIiCyXgsAa8v1grS9BZMXEXZu9fW00/IDT40U826ZUrZMr11ujR3/1R+7k228sPmloTpXgwABv29PDcK7MeKGK51j0ZuKM5Ss4tsW2riS9mRiOrQnIIiIiV0pBYA1t7UziORaWJqXIOmJbhu3dKbZ2JhnJVTgxVqC3LcZIvsJ4scrOnhS//N5beO70JE88v/iyodnjR99/5xbu2tbBybECMdcm5dlU6g1OjhXoSHlsbk+QiTmaOCQiInKZFATWUCbucvtAuyakyLpkW4a+bJy+bJypYo3Xh3N0pXxK1QaTpRp7etP8wiP76G2L8zeLLBuCMBT88VOn+eOnThN3LX7o9s3ctiXLeKFKJu4yWaoxPF3GtW36s3E2tyfwHFUJRERElkNBYA21J13irtY7y/qXTYaNxdW6z9nJEkNTZbpSHpPFKiO5Cjt7UvzKB27jqePjPL5IlQDCUPDnz5zhcy+e4wN3buHeHV2cmyhhW4Z03KVUa3BmoohrW2zrStGd9rR0SERE5CIUBERk1XiOxY7uFIOdSYZzZU6MFqk3fEq1BsO5Cjf3ZfiFR/bT1xbnr18bXrJK8KmnTvOpqErww3ds5o6Bdo6P5Im7NknPplxvcGzEIpt06c8maE+4qryJiIjMoyAgIqvOtgz92QT92QS5co3jowUycZdCtU6+XOPsZJGdPSn+wwdvpzPt8aXvDvHpZxcPBX/69Bn+9Okz4dKh2zZzy5Y2xgtV0nGHiaLDaK6C59i0J122dia1N4GIiEhEvxFFZE01e2XqDZ+RfIUTo0U2tSUYL1SZKlUZvVBhZ0+a3/zbB/ib10cWDQQQLR169gyfe8niAwe2cP/OLoZzFS5Ml0nFHKZKLsO5Mp5t05FyGehQKBARkY1NvwVF5Lrg2FarSpCv1DkxWiBX9qg2GkyVapybKrGzO8XHf/hWNrXF+MuXLyxZJfjUkdN86sjp1tShu7d3cnaihGMbYo5NruwxmqtgWxbdaY8tHQmSnv5zKCIiG4t+84nIdScdc7h1SxaA4VyZN4cL9KTj5Cs1pst13hzOs7M7xX989A46Uu5Flw7Nnjr0vjvCUaSnx4s4tkXSs5ksVRnNVwHY1BZjU1ucpGdrHKmIiKx7CgIicl3rzcTpzcSpNcLdis9MlNicDZcOTZerjOTL7OwONyv71hujfGaRBmMIQ8GfPH2aJ144y6MHB3hw7ybGi1XOTYRTjDJxh6lSlXOTJWzLoivt0ZeNa48CERFZtxQEROSG4NoWWzuTbO1Mzlk61PB9Joo1xgsVdvem+Jfv3kdvJsY3X188FJRrPo8dPsVjh8MNyx49MMA7929irFDl7EQJCMedTpWqnJ8q4dk2qZjNYGeSbMJVKBARkXVDQUBEbjizlw6NF6ocG8nTnY5RqjXIV2qM5MNQ8Is/dAtdKY9vHB1ZOhREuxgD4fKhO7dwz7awp8C2DJ5j0ZHymChW8WwbzzFsbk/QnY7hap8CERG5gSkIiMgNrTPl0ZnqxPcDRgsVjo3M9BMUKnVG8hV29aT41+/ZzwunJ/mLF88tunQIouVDT53mT56aaTQ+FG1cZgx4jk0m5pAv1zlmF3AsQ08mRn82QcLT5oAiInJjURAQkXXBssycfoIL02UuTJep1HyKtQbTpRp3bG1nb18G17Z48ewUn7tEKGg2GkNYLXj3rf3cMdDOaL5CzLWJuzaTxSpDU2WMMbQnXXozMdqTHrY2MBMRkeucgoCIrDuubTHQkWSgI0ml3uDCVIXzUyVqDZ+6HzBRqHLbliz7olDQlY5dtNEYwmDw+HNnefy5s8Rdi/fevpm7tnVwZqKKbZVJeDZjeYfh6TKeYxFzbXrSMXrbYsQcVQtEROT6oyAgIutazLEZ7Eoy2JWkWg8rBWecEn3ZgHLNJ1+pMzar0bgj6fLkm2M8/vzZi4aCP3vmDH/2zBkA4o7Fw7f2cdtAOxemyySZIZQ3AAAgAElEQVRcm4RnM5qrcGbCBaAj5dKVitGZUrVARESuDwoCIrJheM7M5KFmT8GJ0WKr0bhUrZOv1Nndm+afPXQznakY7UmXv3r5Ap++WLWg7vPZ58/xpe8N8cEDA7xtTw9TpRrj40Ug3D15LG9zziuRiDYu68vG6Ux5tMU1nlRERNaGgoCIbEizewp8P2A8WuufK9epNhoUKw0KlTonxwrs7Enxy++9hY6UxzdeW3wCEYSVgk8eOcUnZ00h+sCdW7hvZxcTxRoXcmUcy2rtWZDwbDzbxrENfW1xutIeCVebmYmIyOpQEBCRDc+yDN3pGN3pGL4fkKvUGcmVGcmFOw5Pl6oUqw1Gc+EEon/2rr30ZmK0xV2+8vLiuxpDGAw+9dRpPjWr4fi9t2/m0I4uzk+W8QmIO+E+BROFKgnXxrEtYq5FfzZOR9Ij7qq/QERErg0FARGRWSzLkE24ZBMuu3uhXGtwYbrMaL5CpeZT832mSuFo0rF8hZ3d4X4Fz52auOhoUpjbWxB3LT54YIDvu6mbqVKNsXwRDCRcm3TMYSxfIeHa2JZFwrPZ1BajI+kRcyxVDEREZEUoCIiIXETctdnWlWJbV4p6I9zFeGiqTL5Sp+H7lGoNpkp1bh/IsrcvA0BH0uPw8XGeeOHiDceLLSN6YHc30+U6I7kKGEh5DknPZiRXnhMMutMenSktJRIRkSunICAiskyObdGTidGTiQFQrNYZmiozkqvgBwG1hk++0iBXrrF/cxt7NqVxbIvOlMe33xi95CSi+cuIFgQDIBmzSXnhmNLZS4m6Uh7tSY9MzMHSVCIREVkGBQERkSuU9Bx29qTZ2ZMmCAImizXOTpbIlcNqQbURkK/UyJVq3NyX4Z89dDMx1+bZUxN84aXzl1xGtFgweOtNPeTKtVYwSHg2CdcOg8Gs5uP2hEt70qM96eLa1qr8e4iIyI1FQUBEZAUYY+hIeXSkPACqdZ+xQoXzU2UqaZ96w6fS8MmXaxwc7OD2LVkafkDCc3jm5Difv4Jg0OwxyFfqnJ0oAUQ7HlsMu3ZrPwMwZOIO2YRLdzoW3SciIhudgoCIyDXgORb92QT92QQApWqDkVyFC7ky9UZArdGgUvfJl+vcOdjBrVuy+JcZDGb3GDTFHIuHb+njwGAHDd/HsQ0xZyYUpGIOljE4dhgOulIxsgkXz1HVQERko1EQEBFZBQlvZodjgEKlznCuwkiuQsOfGwwOzAoGMdfmmZMTfPGl85TrSweDpkrd54kXzvHEC+eAcNfjd9/Wz93bOhjNh8uJPNcm4VgkPIehWBnHMtiWhecYOpIe3ZkYmZg2OhMRWe8UBERE1kAq5rAj5rCjOwXMBIPRfIV6I2gtJcqVatyzvYM7BsKlRI5t8dypCb703aFlBYNy3efx587y+HNngVl7GezsYni6jB8E2JbBs8NpRKO5Cqcninh2uHyoOaGoLeGS9tSILCKynqxYEDDGDAD/BngY6ALOA58FPh4EwcRlHKcT+EXg/UA/MAZ8CfjFIAjOXO25jTFbgA8CjwD7onPkgWeB/xwEwWeWe60iIitlfjAoVuuM5qqMFsL9C1rNx+Ua9+/q4uC2DmpREMgmPbJxl6+/NrzkrsdNs/cyaGpWDQ7t6GSyWMMPAizLkIwakS9MlYi7Np4ThoNswg17DpIuKc/BVjgQEbkhrUgQMMbsAr4N9AJPAK8C9wIfAx42xjwQBMHYMo7TFR1nD/A14I+BvcBHgfcYY+4PguDYVZ77HwP/HDgOfB0YArYRhoN3GmN+PQiCn7uifwgRkRWS9BwGu5zWUqJyrcF4ocp4oUquXMcPAup+uJSoVPMZzpXDXY8fuplkzCETc/jmG6M8cZGRpU3zqwYQhoOHb+3jvp1djOWr+AQ4liHhOoy4Fp5jtUKAMWFoaEu4dCY90nGFAxGRG8FKVQR+l/CD+M8EQfDbzTuNMb8G/Czw74B/tIzj/AphCPi1IAh+ftZxfgb4zeg8D1/luY8Abw+C4BuzD2KM2Qd8B/hZY8xjQRA8s4zrvSx/8eK5lT6kiGwQcddmc3uCze1h83G9Ee5wPF6oMl2uU603CALIlWtU6j6Fap19fRn2PHQzjh1+aH/y2Oglm5CbynWfzz5/js8+H/UauBbvu2NLa0pRc3yp61h4tkXMsUjFHGKuhWuFux+7tqE96dGRdMnEXVzbqO9AROQ6YoIguLoDhN/IvwGcAHYFQeDPeixDuEzHAL1BEBQucpw0MAz4QH8QBLlZj1nAMcJv7nc1qwIrde5Zr/lvwE8A/zQIgl9dzvtf4jjPHDx48OAzz8zNEnv/ny+2fgF7jsUTP/UA+/rbrvQ0IiItQRBQroUjS6dLdaZKNSCsJJTrDcrVBqVag3ItDAxe1Cz8nWNjfO7Fc8sKB4uJOxbvvrWPe3Z0UarWAVo9B8mYTcyxiTkWMdfGisJBJu6SitlkEy5JLS0SEbkqd911F88+++yzQRDcdbmvXYmKwA9Et1+Z/UEcIAiCnDHmW8BDwH3AVy9ynPuARHSc3OwHgiDwjTFfBv5hdL7m8qCVOndTLbqtL+O5GGOWqhrsXezO2b9of3Bf73JOISKyLMYYEp7NgJeEjvC+hh8wXaoxVaoxmq9QawRhr0Hdp1z3KVYb3DGQ5ZbNbfhRI3Im5vDksTH+YpnhoFz3efz5czz+/EzFs9lz8JZdXeTKVar1Rni/G4YCz7GIR/scNJcWeY5FW9wJd0eOO8Rd7XUgInKtrUQQuDm6PbrE468Tfhjfw8U/jC/nOETHWelzY4xpAx4FAuArF3vuSnjbnp5rfQoR2eBsa2aTs+1RE3K17jNdDoPBRCH87qPe8Kk1wmBQqjW4fWs7e/szEIBjWzx7coIvfW+IyjKmFMHiPQcQ7nHw7lv7uGd7Z2tpkWMbXHsmGHjRUiMn2g25LeGQjjmkYg5tce13ICKyklYiCGSj26klHm/e334NjrMi5zbhotXfBzYBvxsEwSsXv9TQUiWYqFJwcDnHEBFZTZ5j0Z2O0Z2Ote4r1xpMFKtMFGrkK3UafkAQBBRr4ZKi79vTw6EdnZRq4Tf7Mdcm7th8+9goX3hxefsbQLjHwey+AwirB4/c3s99O7oYrVSo1n0w4FhWFAzCDdHCc4a9B8ZAwrXJRBWEVLQESURELo/2EQj9KvAjwDcBTQwSkQ0l7tpzdkEGqNQbTBRq5Mo1cpU6lZof9SGEG5+Vaw3uHuzg9i3h/gYYQ8K1OXJ8jC9+9/KqB5959iyfefbsgsdijsUP7t/EXYMd+EEABtyoMTnu2MTcsHrgORa2FVYKMnGHhGeTjjlkEy6xKDyIiMhCKxEEmt+6Z5d4vHn/5DU4zlWf2xjzHwmnC/0N8J4gCCqXuE4RkXUv5tj0ZW36snEgbEauRz0Hk6UaE4UqtUZYOaj5PtVaOKno/l1d3LWtI/xmH/Acm5Rn8603R/n8ZVQPIKwgfO7F83zuxfOzritcXnTfzi6mSjVqDX9OQGgGg2Y/QtiIbHBsE+59EDUop2NqUhYRWYkg8Fp0u2eJx2+Kbpdax381x7mqcxtjfh34J4T7CfxQEATFS1yjiMiG1BwH2pWO0ZWOQdTm1PAD8pU6E9H+BqVag4bvEwRQrIbVg2q9wd3bO7hlcxtBQKs5+MixMb788oVlVw9g8eVFTc0Kwj3bO6k3wmM2JxjFPJtYFBKaPQkQ9ih4tkUqZtMWd0nHHRKurSqCiGwIKxEEvh7dPmSMsRYZ4fkAUCSc0X8x3wFKwAPGmMwi40Mfmne+Kz531BPwO8BPAn8JvC8IgtJy3uxKSXg2+j0jIjc62zJkEy7ZhNu6LwgCKnWf6VLYczBZqlGJJhBVGw2qdZ9Kzedte3o4tLOLWsMPlxcR7rCccG2++foon3vp8saaLlZBgDAgvOuWTbxlVzelfAPfD5cZeY6NFwWBuGvjOhaubfDsMCR4jkXSCysL6ZhDJu4Sd7XUSETWj6sOAkEQvGmM+QrhB/WfAn571sMfB1LAf509x98Yszd67auzjpM3xnyCcEToLwM/P+s4Pw1sB748e2fhKzy3Af4b8A+ALwIfDIKgfKXv/0r1pOOtjYFERNYTYwxx1ybu2swflFyIgsFUsUaxWp+zvKhcbVBp+FTrAQcH29m/OUMQAMYQcywOHxvjK5dZQYAwIPyvF87zv144v+CxmGPxzn2buG9nF/WG3+pFSDizgoETNiq7toVjh0uNANqTLgnXbvUkxKNxqCIiN4qr3lAMWht7fZtwh98ngFeAQ4Rz/o8CbwmCYGzW8wOAIAjMvON0RcfZA3yNcBfgfcD7CDcbe0sQBG9e5bl/iTBolIDfAKqLvKXngyD47OX/S7TOseiGYtv/xedbfz/yCw/Sm4lf6SlERNaNesOnUG2Qr9QpVupMFGtRhSCg2vBbFYRyPawm1Bo+9Ub4uyvhOXi2xf9+Y+SympSXoxkS7tneScMPj2uiSsJMMIh6ExyDbVlYUbUg7lpkEy4JLxyLmoo5uLZGn4rIylvrDcWa38zfDfwb4GHgEcJdfX8T+HgQBBPLPM6YMeZ+4JeA9wPfB4wBfwj8YhAEZ1bg3Dui2wTwL5e4lP8JXHEQEBGR5XNsi2zCmrO8CMD3wxGmk8Ww/6Bca0RLhQLqjXD5UbXhU6v73L+ri4PbOmj4Qbj0hzAkHD42dll7IMxWqft8/qXzfP6lxSsJ8/sRLMtgW6bVtOzaYUUh5tq49kxIsC1D0gt7EuKu1QoLjoKCiKyyFRsfGgTBaeCjy3zukrXTIAjGgY9Ff67FuT8CfGS5xxYRkbVhWYZ0LJzwM5vvhyEgV6lRqIRBodlL0PB9GkFAqdqg2vB528093Lerk0otvJ8AbCtsGr7akLBYP0JTzLF4cF8vdw12tO5rNi577symaa5l8FwL15rpPXBtQyp63zHXIuk5xB1LQUFEVpz2ERARkRuKZZnwW3TPhgyE7WChWsOnUKmTK9ep1BvkKw1K1XAjtHrDp+YH1OphZeH7burm0M7OOUuNvOgD95NvjvLl711+P0JTpe7zhZeG+MJLQ3PujzkWD9/Sx/ft6WG6XKUSbdJmTBhQWhUEy7R6EjzHwpm17Mixw4AUNjLbrT4F7bosIpdLQUBERNYN17ZoT3q0J70Fj5VrjVZIKEYVgzkhoREuNao2fN52Uw/37eyi1ghaS3+caPzot94Y5S+voGkZwoDwxAvneOKFheNPYVZQuKmHqVKVan12UAjDgeeEFQTHtsKpR9F+Cc1N1SDcWC3u2nh2uPQo6dlqZhaRBRQERERkQ2hOMupKx+bc3xx3Wqo2mC6HI0/LtTAYBEFAEIQ7IDfDwoN7e3nr7u6wkjCrJyEe9QL87zdG+fJVLDm6WFBoijkWP3BzL/dsj5YeGbBMFBSi3gQ7Go3arCzMriokPBvHCkNEwg2DQsKziTs2lsKCyIahICAiIhva7HGnHam5lYTmjsrFSoNirc50qU6xWqda9wk//wdhJaEejkCtNXzetqeb+3Z2htUE34doON/TJyf46qvDrV2Xr0al7vOl7w3xpe8NLfp4zLF4x95eDu3oak08woATVRVc25r1d4PTXIZkW4CZU4EIpx6Fy5BibvizJiCJrA8KAiIiIkto7qicTVpkcenPzn284QdU6g2K1UarolCqNqg1mqO5A6rRdKPN7QnefWtf6+cFQeHEBF99beWCwhe/O8QXv7t4UICZsPCWXV3UG0G4hwK0mpibFQWnVVFY2K8AzJp6FD6/WV2IOTaWQRuwiVzHFARWQa3h89pQ7tJPFBGRG0o4CtQh6S3+67ThBxSrdUq1MCg0m5jDjdTC51QbDWr1gC0dCR65vZ9KcxmSH/YnNJceubaFZRmefHOMv3rlyhuZm5YTFiBsoH7H7GVIhA3bzWBgR393omlMtmUWLEVybNOampSKOcTdsCoRd8Odm1VhEFkbCgKrIFeuMzS16psXi4jIGrMtQybukom7iz7u+0EYEmoNipVwU7VKvUHDD1pVhVqjQd1vNjQHvHNfLz9wcw/VqEeh1pipKliW4fCxcb7+2vCKba5WvcQyJJjpWbh/Vxd+MNM3EQaAcBlSs2JgR/stOM1eBjO30TkVs6NwEW7W1pyOFIvCgxqeRVaOgsAq8VdgB2cREVlfLCvcMyAVcyC98PFmI3O51qBQbVCq1qOKQUAxmngU9jGE99UaPj90ez/vumUTDT9oLUGa/eHcGMPTJ8f56isrFxYu1bMwm+dYvH1PD4d2dIZ3GDAwp6nZsWb6FhxjWv0KtmXmLDWKuRYpz4kej3o9otDgRRUUEVmagoCIiMh1anYjc3ty8ec0N1grVsOxqM0xqLlyvbU/QhCEYaDaCPdR2NS2mYdv6YuCgk/dh0bDpxGFBduysAw8eWyMr726coEBwgrDV16+wFdevnDJ53qOxQ/s6eHeWaHBNgY76mNwmhWFOdUGC9sCz7bnHMuxDQl3Zoyq51jEHYtYNGbVtY36GWTDURAQERG5gc3eYK1riec0oiVEpWqjVWEIlyGFH/6bAaDhhz83+xMeua2fh/Zviu4LqwuNWSNTAZ46McHXVqjJeb5q3efLL1/gy5cIDc0+hvt3dbX2fYBwaZZtW9iGOcuSmpu3tZYpRbdhbaJ5zLBa41jWguDg2gbXUsVBbnwKAiIiIutc+IE3/DZ8Kc1Rqc09Fcq1BpV6g7ofRD/PfMD2o+VIzSbn997R31qaVPfD49RnVRgg3Ofg8PGV7V9oWk4fw3yebfH2m2eWKDVHps7uabDNTD+DY5lWk/RiwcG1w+BgRa+JORYx1yJm27iOaY1sVdVBricKAiIiItIaleraFunY0h8PmoEhDAo+1WhZUnMTNj8IqNbDANAMDI2o2fm9bZt55La+VjN03Z+pSDRDg2UZLBNOR7pWlQaAamP5S5Rg8eBgtYJCNCXJCnsamlOSmkHCbk1RgmZ4aDZPt4KDG05Rau7v4Dlh1cKzLYUHuWYUBERERGTZZgeGzCWe2/DDfRRKtbDCUG+EDcyFSp1qVDFoztJohYZo+dEP3zkTGpqNz/NDA8CR4+N8/bURqo1rExiaLjc4QBge3ranm/t3hou2zKwdoC2LVnhwo/BjR1UIxzKzljHNVB5M1Fjt2BapmN0KF649U31w7Jnqg5YuyaUoCIiIiMg1Yc/qX7iYIJj5sF+uhT0M1Xq4zKha9ylUZxqfm5pjVbd1pfjAwS3hdCQ/oB4ENBrh0qR6NC2pFRyiD9nffmOUrx8duWbVhqZqw+evXhnmr14ZvqzXzQ8QrVDQDAuzqw2z/8wKE5aZuwwp7lqtYzV3jG6+znPCCoQXBYj505lk/VIQEBERkTVlouU0jm2R9C79fD8KDZW6T6W5RCnafK25eZs/Jzc0Kwrhaz9wcAvvvWNzWF2IQkit4dMIwI9Gsc6+tiePjfGNVag6NF1JgJgfHoiqD04UEKxZgaHZq9D8u9V6DguWMEHYOO3aFoaZZUwxJ1zW1Fzi1Bz/qibqG4uCgIiIiNxQLMsQbzY/JxbfrK0pHJ0KtXnBoe4HNHyfQqWxYJkShD0NfhQSBjoSfPDAFurRxKRa9NqGHx673vBpBEFrYzeAw8fH+etVqDo0XWn1AZZewtRsjrajpUvNZUzNEGGZmeVNdjN42HObqAESno1lwGBaY1xta+Z4njOzWZxrh0FEFYnVoSAgIiIi65Yx4YdUe5nBoakaVRkqtZmgEDZGh5OUmpu01VrVg6BVYag3AgY7k3zw4JZWo3SjuUwperwxf9kSYcB58s0x/noVqw9wdSECFgYJKwoJlmVF//YzVQlnXpCY/VhzuZNZUJEIlzVZJvx73LUxzCxz8pyZJU3N/gjHthZeqCygICAiIiIyT3Pd/MUmKM3mR2NTa9EmbWGI8Ft7NfjBzGjWucLXBEHYXD3QnuADB7e0QkLrTzD3Zz+YqWA8eWyMvzk6uqrhYbaVDhKzJzLZxmCs5s8zwcKYZqigVbFo/tx87nyWgaTn0HzIsSziroVjW1ETdri0yZ0VLJohZb1SEBARERG5SpZl8KJlLpcjCIJoh+ew4lCt+1HVIJy2VKtHH/phXoiIliX5Pjt60vydewZbS5nqftBqwJ4TIoJoB+lZy5jWOkTA1QeJ2WaHCnuJ6oOxDBbMaawOKximFUBMtIv1/KbrcOlTWK9wbau1N4dlwmlOzd4JywLXslpTnJpB5XoLFQoCIiIiImvEGEPMsYk5QGz5r5u9zKjm+60QUW+EwaEWBYl61PvgR89tagaFXb1pfvTewdbxmsHBj/ofZlcgmkHieqpGzLcSoWJOhSIa2Rr2NFjYgLHANuEI2NkhYiY4hNWGmV6LxUNF83VBALYF8ah3AsLnN3sngNb+Es6sHbGbS6muhoKAiIiIyA3GsgwWBteGBBcfz7qY5qSk5i7Qzc3h/Ki5ujnC1Y8+8c/eWRpmgsTu3jQ/du9gFBqak5eCVnUiDBXM+3lmadP1FiRgZSsUTa1wsaurtdyoFSLMzMhW28w0ajcfm738KaxwgMXMcwqVOsZLpq/kuhQERERERDaY8Fvlyw8QMDOJqR6NWm32RDSrEfVGQLneaFUg/CCgUJnfGxHev2dThg/fv6012rXh+/iA74fBohlM/FlLnYJgbrC4npY5LeVahotyzce4XuJKjqEgICIiIiLLNnsS0zJ7qReYHybqjWhnaT9sqq415lYjqg2fIPq5Wg8WOVZUnTi0Law2NKsPCyoUQDCzDKoZMppLo5588/oNE/M1w8X5qRL4fv1KjqEgICIiIiKraiXCBMwNFL5PVJnwWyNe640g2jfCj54PxWpjztjW2X/f19fGR96yfc6SpiA6fliJmAkOzb6JIJg7ycmf9/OqVCqaKekyKQiIiIiIyA1pdqCAK+uXmK05BjacvuS3mrGbS5KqrWpF+Pxwo7oGQRCOPZ1frYCAm/sy/L37t4UjYqOg0KxYtIJDEBA0eymCmSqHPyuQ+M3QsUjlwtjOMvbkXkhBQERERESEmTGwoasLFTCzLKkVLqIlUM2JTNVZ1Ypmk/bsCkVxwb4ToWblwg8C/sFfpHhz8kL5Sq5PQWAVfOLJE/zuX7+51pchIiIiIquoOd3JufpMMcfssa6pmI1fLRau5DgKAqvgv/7NMSr1mXVhcXdmAwoRERERkcvR3EsAwhGjBP7ipYNLuLzt7+SKzC7rxF2Ln3nwJtri7hpekYiIiIhsdKoIrLI/+PF7uG9n11pfhoiIiIhscKoIiIiIiIhsQAoCIiIiIiIbkIKAiIiIiMgGpCAgIiIiIrIBKQiIiIiIiGxACgIiIiIiIhuQgoCIiIiIyAakICAiIiIisgEpCIiIiIiIbEAKAiIiIiIiG5CCgIiIiIjIBqQgICIiIiKyASkIXGOFSn2tL0FEREREZAEFgWvs/FRprS9BRERERGQBBYFrLAjW+gpERERERBZSEBARERER2YAUBERERERENiAFARERERGRDUhB4Br7s2fOzPm5OxPDsswaXY2IiIiISGjFgoAxZsAY8wfGmHPGmIox5oQx5jeMMR2XeZzO6HUnouOci447sJLnNsbsN8b8qTFm2BhTNsa8Zoz5uDEmcTnXeymfePJk6+8J12bPpsxKHl5ERERE5Io4K3EQY8wu4NtAL/AE8CpwL/Ax4GFjzANBEIwt4zhd0XH2AF8D/hjYC3wUeI8x5v4gCI5d7bmNMYei47vAnwOngXcAvwg8aIx5MAiCypX8W8xXqjVaf/+7921biUOKiIiIiFy1laoI/C7hB/GfCYLg/UEQ/IsgCN4B/DpwM/DvlnmcXyEMAb8WBMGD0XHeT/ihvjc6z1Wd2xhjA38IJIG/FQTBjwVB8M+BQ8CngQeAn72cN79cf+uuJYsaIiIiIiKr6qqDQPSN/EPACeA/zXv4l4AC8GFjTOoSx0kDH46e/8vzHv4d4CTwLmPMzqs89/cD+4C/CYLgfzXvDILAB/7v6Md/ZIzRQn4RERERWbdWoiLwA9HtV6IP0y1BEOSAbxF++37fJY5zH5AAvhW9bvZxfODL8853ped+R3T7pfkXEC07OgpsA3bOf/xyVeqNSz9JRERERGQNrEQQuDm6PbrE469Ht3uuwXFW6zWLMsY8s9gfYO93z05x879ekDVERERERK4LKxEEstHt1BKPN+9vvwbHWa3XXLWYY+E5mtYqIiIiIteHFZkatFEFQXDXYvdHVYGDzZ+Tns0/+v6dbOtMrtq1iYiIiIhczEoEgeY36NklHm/eP3kNjrNar7lst27J8sz/+56rOYSIiIiIyDWzEmtVXotul1pTf1N0u9Sa/Ks5zmq9RkRERERkXVmJIPD16PYhY8yc4xljMoRz+YvAdy5xnO8AJeCB6HWzj2MRjgmdfb4rPffXotuH519ANJp0D+Go0mPzHxcRERERWS+uOggEQfAm8BVgO/BT8x7+OJACPhEEQaF5pzFmrzFm77zj5IFPRM//5XnH+eno+F+evbPwlZwb+AbwCvA2Y8wPz7omC/gP0Y//JQiC4CJvW0RERETkhrZSzcI/CXwb+C1jzIOEH7QPEc75Pwr8wrznvxLdzt+0618Bbwd+zhhzJ3CEcPOv9wHDLPywf9nnDoKgYYz5KGFl4M+NMX8OnPr/27v7UMuqMo7j35+K7zg5U2RlMFamQ0GUE74UpUZRoSWm5B/WaCkYpGkaQVSKYRll5ksvUJGYgcWERGAG5XuGZSkaamk5paWpMzamjmPW0x973zwc73HOvXPHc+9d3w8s9uy11zp371kP99xnvy3gbcBKurkHzp3BsUuSJEkLzpy8z7I/M78SuIjuj/BTgVcC5wH7VdXaMT9nLbA/cD7wqv5z9gW+C+zT/5zN/tlVdSPwRuDHdLccnUL3kPCZwNurauN4Ry5JkiQtTHP2+tCquhc4dsy2w1cCBretAz7Wlzn/2QN9bgeOnCzt6jwAAAciSURBVEkfSZIkabFwhitJkiSpQSYCkiRJUoNMBCRJkqQGmQhIkiRJDTIRkCRJkhpkIiBJkiQ1yERAkiRJapCJgCRJktQgEwFJkiSpQSYCkiRJUoNSVZPeh0Unydoddthh6YoVKya9K5IkSVrE7rjjDjZs2LCuqpbNtK+JwBaQ5B5gF2DNhHdF88fe/fLOie6F5iNjQ9MxLjSKsaFhy4FHq2qPmXY0EZCeB0l+C1BV+0x6XzS/GBuajnGhUYwNzSWfEZAkSZIaZCIgSZIkNchEQJIkSWqQiYAkSZLUIBMBSZIkqUG+NUiSJElqkFcEJEmSpAaZCEiSJEkNMhGQJEmSGmQiIEmSJDXIRECSJElqkImAJEmS1CATAUmSJKlBJgLSGJIckeSCJNcleTRJJblkE30OSHJ5knVJNiS5NcnJSbZ+jj6HJLk6yfokjyW5McmquT8izYUky5Icl+SyJHf347w+yfVJPpxk2t+xxsbil+SLSX6R5N5+jNcluTnJ6UmWjehjXDQoydH9d0olOW5EmxmPc5JVSX7dt1/f9z9kyxyFFionFJPGkOQW4HXAY8B9wN7A96vq6BHt3wv8CHgS+AGwDjgU2AtYXVVHTtPno8AFwNq+z1PAEcDuwDlVddocH5Y2U5ITgG8A9wNXAX8FXgwcDiyhi4Eja+AXrbHRhiRPAb8DbgceBHYC9gNWAn8H9quqewfaGxcNSvJy4DZga2Bn4Piq+vZQmxmPc5IvA6fSfV+tBrYFjgKWAidW1YVb6pi0wFSVxWLZRAEOAvYEAhwIFHDJiLa70H3xbwRWDtRvD9zQ9z1qqM9yuj8A1gLLB+p3Be7u++w/6f8Hy7PG+mC6P9a2GqrfjS4pKOB9xkZ7Bdh+RP1Z/Zh93bhou/TfJz8H/gR8qR+z4zZ3nIED+vq7gV2HPmtt/3nLt9RxWRZW8dYgaQxVdVVV3VVV41xCOwJ4EXBpVd008BlPAp/uVz8y1OdDwHbAhVW1ZqDPI8Dn+9UTZrn72kKq6sqq+klV/Xeo/gHgm/3qgQObjI1G9GM6nR/2yz0H6oyLNp1EdzLhWODxEW1mM85T62f17ab6rAG+1n/esZu571okTASkuXdwv7ximm3XAk8AByTZbsw+Px1qo4Xh3/3y6YE6Y0OH9stbB+qMi8YkWQGcDZxXVdc+R9PZjLOxobGZCEhzb69++cfhDVX1NHAPsA3wijH73E93tmj3JDvO7a5qS0iyDfDBfnXwy9jYaEyS05KckeTcJNcBn6NLAs4eaGZcNKT//fA9utsHP7WJ5jMa5yQ7AS8DHuu3D7urX756FruuRWibSe+AtAgt6ZfrR2yfqn/BDPvs1Ld7YrP2Ts+Hs4HXApdX1c8G6o2N9pxG9wD5lCuAY6rqoYE646ItnwVeD7y5qjZsou1Mx3k2saSGeUVAkuZQkpPo3tZxJ/CBCe+OJqyqdquq0D1AfjjdWf2bk7xhsnumSUiyL91VgHOq6leT3h/JRECae1NnXJaM2D5V/89Z9Bl1lkfzQP+av/PoXhl5UFWtG2pibDSqqv5RVZcB7wCWARcPbDYuGtDfEnQx3W0+nxmz20zHeTaxpIaZCEhz7w/98ln3YPZfBHvQPUD65zH7vITu0u99VeUl/nkqycl07/r+PV0S8MA0zYyNxlXVX+gSxdckeWFfbVy0YWe68VoBPDkwiVgBp/dtvtXXfbVfn9E4V9XjwN+Anfvtw6beVvWsZw7UJhMBae5d2S/fOc22twA7AjdU1cYx+7xrqI3mmSSfBM4FbqFLAh4c0dTYEMBL++V/+qVx0YaNwHdGlJv7Ntf361O3Dc1mnI0NjW/SExlYLAutMN6EYg8xs8mB9sDJgRZkobvEX8BNwNJNtDU2Gih0Z2+XTFO/Fc9MKPZL48IyMG5nMP2EYjMeZ5xQzDKD4luDpDEkOQw4rF/drV/un+Si/t8PVz/Ne1U9muR4umndr05yKbAOeA/dq+BW000T/39VdU+STwDnAzclmW4aeR8sm2eSrALOpDuzex1wUpLhZmuq6iIwNhrybuALSa6ne/XnWro3B72V7mHhB4DjpxobFxplNuNcVTck+QrwceDWJKuBbYH3A0uBE2tgcjI1btKZiMWyEArPnK0ZVdZM0+dNwOXAI8AG4DbgFGDr5/g5hwLXAP+iez/0b4BVkz5+y6zjooCrjY22Ct2rYy+ku1XsYbr7+9f3Y3YGI64cGRftFkZcEdiccQaO6ds93ve7Bjhk0sdqmV8lVbWJVEGSJEnSYuPDwpIkSVKDTAQkSZKkBpkISJIkSQ0yEZAkSZIaZCIgSZIkNchEQJIkSWqQiYAkSZLUIBMBSZIkqUEmApIkSVKDTAQkSZKkBpkISJIkSQ0yEZAkSZIaZCIgSZIkNchEQJIkSWqQiYAkSZLUIBMBSZIkqUEmApIkSVKD/geU7Rj6pdk6pgAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 248, "width": 385 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from lifelines.datasets import load_rossi\n", "rossi = load_rossi()\n", "\n", "igf = InverseGaussianFitter()\n", "igf.fit(rossi['week'], rossi['arrest'], timeline=np.arange(1, 500))\n", "igf.print_summary()\n", "igf.plot_hazard()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bounded lifetimes using the beta distribution\n", "\n", "Maybe your data is bounded between 0 and some (unknown) upperbound M? That is, lifetimes can't be more than M. Maybe you know M, maybe you don't." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "n = 100\n", "T = 5 * np.random.random(n)**2\n", "T_censor = 10 * np.random.random(n)**2\n", "E = T < T_censor\n", "T_obs = np.minimum(T, T_censor)\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "from autograd_gamma import betainc\n", "\n", "class BetaFitter(ParametericUnivariateFitter):\n", " _fitted_parameter_names = ['alpha_', 'beta_', \"m_\"]\n", " _bounds = [(0, None), (0, None), (T.max(), None)]\n", " \n", " def _cumulative_density(self, params, times):\n", " alpha_, beta_, m_ = params\n", " return betainc(alpha_, beta_, times / m_)\n", "\n", " def _cumulative_hazard(self, params, times):\n", " return -np.log(1-self._cumulative_density(params, times))" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "number of subjects = 100\n", " number of events = 68\n", " log-likelihood = -93.912\n", " hypothesis = alpha_ != 1, beta_ != 1, m_ != 5\n", "\n", "---\n", " coef se(coef) lower 0.95 upper 0.95 p -log2(p)\n", "alpha_ 0.52 0.07 0.39 0.65 <0.005 42.21\n", "beta_ 0.92 0.08 0.76 1.09 0.36 1.48\n", "m_ 4.86 nan nan nan nan nan\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/camerondavidson-pilon/venvs/data/lib/python3.7/site-packages/lifelines/fitters/__init__.py:454: RuntimeWarning: invalid value encountered in sqrt\n", " [np.sqrt(self.variance_matrix_.diagonal())], index=[\"se\"], columns=self._fitted_parameter_names\n", "/Users/camerondavidson-pilon/venvs/data/lib/python3.7/site-packages/scipy/stats/_distn_infrastructure.py:877: RuntimeWarning: invalid value encountered in greater\n", " return (self.a < x) & (x < self.b)\n", "/Users/camerondavidson-pilon/venvs/data/lib/python3.7/site-packages/scipy/stats/_distn_infrastructure.py:877: RuntimeWarning: invalid value encountered in less\n", " return (self.a < x) & (x < self.b)\n", "/Users/camerondavidson-pilon/venvs/data/lib/python3.7/site-packages/scipy/stats/_distn_infrastructure.py:1831: RuntimeWarning: invalid value encountered in less_equal\n", " cond2 = cond0 & (x <= self.a)\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 248, "width": 372 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "beta_fitter = BetaFitter().fit(T_obs, E)\n", "beta_fitter.plot()\n", "beta_fitter.print_summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Gompertz " ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "class GompertzFitter(ParametericUnivariateFitter):\n", " # this parameterization is slightly different than wikipedia. \n", " _fitted_parameter_names = ['nu_', 'b_']\n", "\n", " def _cumulative_hazard(self, params, times):\n", " nu_, b_ = params\n", " return nu_ * (np.expm1(times / b_))" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "number of subjects = 432\n", " number of events = 114\n", " log-likelihood = -697.815\n", " hypothesis = nu_ != 1, b_ != 1\n", "\n", "---\n", " coef se(coef) lower 0.95 upper 0.95 p -log2(p)\n", "nu_ 0.20 0.11 -0.01 0.40 <0.005 45.19\n", "b_ 55.19 19.26 17.45 92.93 <0.005 7.68\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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fK6+8UvRjvfa1ry36mj322INnn311ztjzz+d+ll5xxRVFz1Pw8ssv99g2cuTIIkeWbtmyZZxyyikMHTqUW265pcuIcTkKn8Ptt9/O7bffnnhc58/hJz/5Cd/4xje45pprttfE77jjjpx22ml885vfLPr1q0Qa93Xt2rW87W1vY8WKFUyYMIEzzjiDESNGsMMOO7B27VrmzZvHpk2bSr6mSr5e9ZalSaINobdAXGxk/d7lz/Pbx59j85aewb2UchiAnXccWHRk3XIYSaqu/pSNNJKJEyeyePFi7rjjDj760Y+W/LpC4CqUyHT3zDPPdDmumv7+97/zute9rsu2LVu28Nxzz7HLLq/+TCxcy1/+8hcOOeSQsj5G54mm5Xr22Wc57rjjWL9+PbfddluXUo9yFT6HefPmcc4555T0miFDhjB79mxmz57N008/zW9/+1sWLFjAwoULaW9v56677qr4etL2gx/8gBUrVhRd+Onee+9l3rx5ZZ2vkq9XvWWpzWJDK4ysd3987MjX82/vOpBrzzpi+2PHgclf9sLIemevG7FTj/MWQnuxh+0eJUnlmDFjBjvssAM//elPy/oz/1vf+lYA7r77brZs2dJj/+LFuQZtxTqipO3OO+/sse3uu+9m69at268T4IgjjgBINZAOGDAAgK1btxbdv2HDBk488UTa29u54oorSu6IkqS/n8M+++zDhz/8YW677Tbe8IY3cPfdd28fZYZcrXfS51ILf/3rXwE49dRTe+wrdp+h93tQjXtebQb0lBw0chfePmb3Ho+CzgH6yDfswaAdeg/pp19xX5fHzAX3c/ODr/7psVhoryS4G9olSWPGjOFLX/oSmzdv5t3vfjf33HNP0eO6l6qMGjWKf/7nf6a9vZ25c+d22ff73/+ea665ht122433vve9Vbv2gosuuogXXnh1qtrGjRv54he/CMDMma9Wzs6cOXP7xMD777+/x3m2bdtW9hL3hUmWTz31VI9927Zt4yMf+Qj3338/s2bN6lGLX4nDDjuMSZMmceONN3LllVcWPeahhx7aXtrzj3/8g4ceeqjHMR0dHbz88svssMMODBo0qMvn8/TTT/f7OitV6F/e/T488MADXHLJJUVf09s9KPfrlQWWuFRZsZr1N+61K29//e49tif1XYfSJ5om1bEnTUC1TEaSBPCVr3yFGCMXXXQREydOZPz48UyYMIERI0awdu1a2tvbty9oc9RRR21/3fe+9z0mTpzI5z//eRYtWsRhhx22vQ96W1sbV111FcOGDav69Y8dO5Y3velNXfqgP/HEExx//PHbO7hALsj99Kc/5b3vfS9HHHEEU6dO5U1vehMhBJ5++mnuvfdenn/+eTZu3Fjyxz7wwAPZe++9ue666xg4cCD77rsvIQSmT5/O73//e2688cbtAbLYJMWTTz6ZQw89tKzP95prruGYY47hYx/7GJdddhmHH344w4cPZ+XKlTz44IP8z//8D/feey977rknf/vb33jrW9/Km9/8Zg455BD22WcfXnrpJW6++WZWr17NOeec0+UeTZ06leuuu44TTzyRcePGMXDgQI466qgu972azjjjDC699FLOO+88Fi9ezP7778/jjz/OzTffzCmnnMJPfvKTHq+ZOnUql156KWeddRannnoqw4YNY/jw4Xz6058u++uVBQb0KisWcguBuHtgPvINeyTWqxdTbKJpkmLB3a4xkqSCwmqRp59+Ot/73vdYvHgx11xzDR0dHQwbNowxY8bwyU9+kunTp3cpWXn961/PH//4Ry6++GJuvfVWlixZwi677MK0adO44IILti/kU23/9V//xUUXXcSPf/xjVq1axd57783s2bM5//zze9SOT506lQcffJBvfvOb3Hbbbdx1110MGjSIvfbai2OOOaZoaUVvBgwYwM9+9jPOP/98rr/+etatW0eMkSOPPJL169cDuYmK3bvhFIwePbrsgD5q1CiWLl3K/PnzueGGG/jxj3/M1q1bGTlyJG984xv513/9V9785jdvP/+cOXNYsmQJixcv5rnnnmPEiBEceOCBfP3rX+/RenDevHmEELjjjju49dZb2bZtG7NmzapZQN9rr7246667OP/887n77ru57bbbOOigg/jud7/LO9/5zqIB/V3vehff+ta3uOKKK5g7dy6bN29m33333R7Qy/l6ZUEozMxuBSGEpePGjRtXbOnhWnpk9Uu80FF8FvrDq17sEY5vfnAVN/xpZeLoenfFRtbLUewaChxZl9RMCvXW/Zmwp/qaPHkyd955J62UZ1Rfpb5vjB8/nj/96U9/ijH27C/ZB0fQ6yAp4CaNrL9+j6HMOengLqPg5ZbDQOnBPalrDFgSI0mSVG0G9AxJ6rEOPUP7qeNGlTWqDqWXxJRbxw7Fg7uhXZIkqXwG9AwpZ2S92Kg69F0O0733ejnlMJVMQJUkSX2bO3du0QWdups8eXK/2zQq+wzoDSBpZL1YKD7hkL2Khu2kkphyJpomKRbck1Y/BUfWJUnpKbclYlbNnTuXJ598sqRjDejNz4DeAMrpBAO5GvLuobm3kphSVzQth3XskiSVrr29vd6XoAwxoDeocurVofjIel8TTfszsl5pHbskSVKrM6A3qHI7wUDPkfW+JppWY2Q9KbgnlcQ4qi5JklqNAb3JlDOyXm69OvS/hWOSpJIYy2EkSVJW1KrfvgG9yZQ7sl5uvXqSapTEWA4jqdpCCMQY2bZtG21tbfW+HEkZVwjo3VenTZsBvUWk0Qmmmi0ciym3HAYcWZdUnsGDB7Nx48bty9lLUm86OjqA3HtHNRnQW0QanWDq0cKxmHI7xBjaJSUZNmwYGzduZPXq1QAMHTqUEELVR8ckNY4YIzFGOjo6tr9XVPsXegN6Cyu3E0ySWrdwdMEkSWkZMWIEHR0drF+/npUrV9b7ciQ1gJ122okRI0ZU9WMY0FtYGp1goPYtHJO4YJKkcrW1tbHPPvuwZs0a1q1bx6ZNm2o2CUxS4wghMHjwYIYNG8aIESOqPmfFgK4e0hhZr0cLx2L6KoeRpLa2NvbYYw/22GOPel+KJAEGdBXR18h6KdJq4ehEU0mS1GoM6CpbqaUvxZTbwtGJppIkqdUY0FWyNEpfKmnh6ERTSZLUSgzoKlkaiyAlcaKpJElSjgFd/VbOIkjlcKKpJElqRQZ09VsaiyAVU+lE07RH1p1oKkmSasmArqpIaxGkYsodWa/GqDo4si5JkqrDgK6qSGsRpGLKHVmvZb06JI+sO6ouSZJKYUBXTdVrZL1W9eqQPLLuqLokSSqFAV01ZScY69UlSVLvDOjKhFbvBGNwlyRJBQZ0ZUKrdoJJWhgJLImRJKlVGdCVWa3QCcaJppIkqTsDujKrr3r1/shKJ5gkTjSVJKl1GdDVsPpT+pIkK51gnGgqSVLrMqCr4VSz9CUrnWCKcWEkSZJagwFdDaearRqLyUonmHLr1cGRdUmSGpEBXU2jWq0as9IJJokj65IkNRcDuppGtVo1JrETjCRJqgYDupparevVwU4wkiSpfwzoamrl1quDnWAkSVJ9GdDVkuwE05Mj65IkZYMBXS3JTjBdObIuSVJ2GNClTuwE05Mj65Ik1ZYBXeqkt04w1dAonWAkSVLtGNClElVjQmnWO8EU2KpRkqTaMaBLfajmhNIkWekEY6tGSZJqz4Au9aEerRqz0gnGVo2SJNWeAV2qUK1H1kupV68FJ5RKklRdBnSpQrVu1ZhUr9653MVWjZIkNT4DupSyarVqTLLjwDZbNUqS1EQM6FLKbNXYVdLIuqPqkiQVZ0CXaqgVWzXaCUaSpPIY0KUaaOVWjXaCkSSpPAZ0qQZauVVjMdarS5KUzIAu1VEWWzVmoROMJEmtzIAu1VFWWjVmZWS9wNIXSVIrM6BLGVTrVo0ugiRJUnYY0KUM6q1VYy07wSQtgmSrRkmSqseALjWIenSCSVoEyVaNkiRVjwFdahB91atXg60aJUmqPQO61CRs1fgqR9YlSY3MgC41OFs1duXIuiSp0RnQpQZnq8auHFmXJDW61AJ6CGEUcCEwDdgdeAa4CZgTY3yhjPMcCXweeAswEngW+B/gshjjr9K6XqnZtWqrRhdBkiQ1ulQCeghhDHAPsCfwc+ARYAJwLjAthDAxxtjnTLYQwieB7wIdwM+AlcAo4BTg3SGEL8UYv5rGNUvNrrdWjdWQlVaNfbFVoyQp69IaQf8uuXB+ToxxfmFjCOHbwGeArwKf6O0EIYSBwCXARmB8jPHRTvu+BjwAXBBC+GaMcVNK1y21pGpMKE1iq0ZJksrT74CeHz0/FmgHvtNt9yzgX4DpIYTPxhg7ejnVCGBX4MHO4RwgxrgshPAY8GZgZ8CALlWgHr3UbdUoSVJ50hhBn5J/XhRj7PITOMa4LoTwO3IB/gjgjl7O8yzwD+CAEML+McbHCztCCAcA+wN/LqVURlJx5U4oBVs1SpJUa2kE9APzz48l7H+cXEA/gF4CeowxhhDOBhYCS0MIPwNWAXsD7wX+F/hgKRcUQliasOugUl4vtRpbNXblyLokqZ7SCOiFn+pJP8UL24f3daIY4/UhhFXAtcAZnXb9HbgKWF7pRUpKZqvGrhxZlyTVU6b6oIcQPgJcAdwIXAQ8CewLfBm4HDgaeH9f54kxjk84/1JgXFrXKzU7WzV2lTSy7qi6JClNaQT0wk/qpGGlwva1vZ0kX2d+JfAgML1TPfsjIYTp5Epp3hdCmBxjXNK/S5ZUCls1dmUnGElSLaQR0AsdVw5I2L9//jmpRr3gWGAgcGeRyabbQgi/BcbnH0squ1RJaWnFVo29dYKRJCktaQT0xfnnY0MIbZ3DdQhhGDARWA/cV+zFnQzOP78mYX9h++ZKL1RS/7Vyq8beOKFUkpSWfgf0GOMTIYRF5EbAzwbmd9o9BxgKfL9zD/QQwkH51z7S6di78s+n5RcjerDT8YcCpwER+E1/r1lS5WzV2JUTSiVJaUtrkuingHuAy0IIU4FlwOHkeqQ/BlzQ7fhl+edQ2BBjvD+EcBUwE/hDvs3ik8Bo4GRgEDA3xvi/KV2zpBRlsVVjLdiqUZKUtlQCen4U/TDgQmAacBzwDDAPmBNjfKHEU30M+C0wA3gXMAx4CbgbuCLGeF0a1yspfX2NrKet3AmlUNvSF0fWJUmVSq3NYozxaXKj36UcGxK2R2BB/iGpiaTdSz1J0oRSqG3pi60aJUmVylQfdEnNJ4u91G3VKEnKMgO6pKrKSi/1pEmlWWrVaL26JAkM6JLqqJa91Ptq1VhP1qtLkjozoEuquXr0Ui82sp6VCaV91atLklqLAV1SzdWjl3oxWZlQ2hdLXySptRjQJWVGFnup26pRklRrBnRJmZGVXupZWaXURZAkqTUZ0CU1jFr1Us/KKqVJHFmXpOZmQJeUebXupV7uKqW17qXuIkiS1NwM6JIyr7de6rVs1Zg0qTQrE0pdBEmSmoMBXVJDqkerxr56qddzQim4CJIkNQsDuqSGVOsJpVC89CUrE0qTWK8uSY3HgC6pKdWq9CXrE0pdBEmSGo8BXVJTqXXpS7kTSqH2pS+9sfRFkrLHgC6pqdSj9KWYrK9SaumLJGWXAV1SS7GXeo6tGiUpuwzoklqCvdRLY6tGSao/A7qkltBbL/VaynovdVs1SlL9GdAltbxaLnaU9V7qxVivLkm1ZUCX1LLqsdhRI/ZSL7deHRxZl6T+MKBLall9dXyxl3rvHFmXpOowoEtSN/ZSL42dYCSpOgzoktSNvdT7x04wktQ/BnRJKpO91HtnJxhJ6h8DuiSVKOu91CEbpS/FWK8uSaUzoEtSibLeSx2yW/piJxhJKp0BXZJSkJVe6pDd0pdiHFmXpJ4M6JLUD1nppQ7JpS9ZLXsBO8FIUjEGdEnqh6x0fIHk0peslr30xk4wklqZAV2SqigrpS8bX9nWMBNKwU4wklqbAV2SqiArpS8zF9zfcBNKk1ivLqlVGNAlqQqyUvrSTBNK7QQjqVUY0CWpDmq12FEz9VJP4si6pGZjQJekGqr1YkdJGrGXehI7wUhqNgZ0SaqhrCx21EylL0nsBCOpURnQJSkjatnxpZl6qSexE4ykRmVAl6Q6q0fHl0gyoI0AACAASURBVCTN1Eu9GOvVJTUCA7ok1VlWOr5A373UG52dYCQ1AgO6JGm7YqUvzdTxJYkj65KyxIAuSRlXy9r0Ypqp40sSO8FIyhIDuiRlVFZq01uh40sSO8FIqgcDuiRlVFZq01thsaMkdoKRVA8GdElqUJa+1If16pKqzYAuSQ3G0pf6shOMpGozoEtSg2nU0pdmKXtJ4si6pLQY0CWpyXQPibUse4HmX+woiZ1gJKXFgC5JTSKp9KXWq5H2tdhRs04oTWInGEnlMqBLUpMoNhpbj9VIi5W+zFxwf0tOKAU7wUgqnwFdklpAvTu+tOqE0iTWq0vqjQFdkppYVjq+tHIv9WLsBCOpNwZ0SWpiWen4kqRVe6kncWRdEhjQJUl1ZOlLV3aCkQQGdElqafWuTbeXemnsBCO1FgO6JLWgrNSmJ2nVXupJ7AQjtRYDuiS1oKzXpvfVS11916sb3KXGZUCXJPVQ79VIi5W+tGrHlyRJ9+OpNeudaCo1OAO6JGm7rKxGWowdX0rjRFOp8RnQJUnbZWU10mLs+NI/TjSVGocBXZLUEFzsqH+caCo1DgO6JKkk9W7JmMTSl8q5MJKUTQZ0SVKvst6S0dKXypVbrw6OrEu1YECXJPUq6y0ZXewofY6sS/VlQJck9Uujlb5Y9tI3O8FI9WVAlyRVpJFLXyx7qYydYKTaMKBLkirSiKUvdnzpHzvBSLWRWkAPIYwCLgSmAbsDzwA3AXNijC+Uea5xwOeAo4DXAGuBR4D/jDFendY1S5Jaix1f0tdXvbrBXSpfKgE9hDAGuAfYE/g5uTA9ATgXmBZCmBhjLGlIJYTwaWAe8AJwC/A3YARwMHAcYECXpAbQPbRloS7dji/pS7qnT61Z70RTqUJpjaB/l1w4PyfGOL+wMYTwbeAzwFeBT/R1khDCscBlwO3AaTHGdd32D0zpeiVJVZJUm56FunQXO6odJ5pKlet3QM+Pnh8LtAPf6bZ7FvAvwPQQwmdjjB19nO5SYAPwoe7hHCDG+Ep/r1eSVF3FQlZW6tKTWPpSO040lfqWxgj6lPzzohhjl3e3GOO6EMLvyAX4I4A7kk4SQjgYOIRc3fqaEMIUYDwQgT8Di7ufX5KkNFj6UjtONJX6lkZAPzD//FjC/sfJBfQD6CWgA2/LPz8LLCE3QbSzh0IIp8QY/9rXBYUQlibsOqiv10qSqierPdNd7Ki+XBhJ6iqNgF74zkkqLixsH97HefbMP3+M3MTQ44G7gdcCXwE+AtwSQnhzjHFz5ZcrSaq1rPdMT+JiR7VRbr06OLKu5palPuht+ecBwAdjjPfm//1SCOEMcqPfhwGnAtf2dqIY4/hi2/Mj6+PSuVxJUqmy3jM9iYsd1Zcj62pVaQT0wndO0ndKYfvaPs5T2L+6UzgHIMYYQwg/JxfQJ9BHQJckKQ0udlRfdoJRq0ojoD+afz4gYf/++eekGvXu50kK8oXFjoaUeF2SpAaR1dr0Yuz4Un+9dYKxHEbNII2Avjj/fGwIoa1zp5UQwjBgIrAeuK/Yizu5D+gARocQhhZpyXhw/nlFCtcsScqARqxNt+NL/RX7xc2FkdRM+h3QY4xPhBAWkevUcjYwv9PuOcBQ4PudA3cI4aD8ax/pdJ71IYT/BM4BLg4h/J8YY8wf/2ZgBrAF+Gl/r1mSlA2NWJteSscX1Z4TTdVM0pok+ingHuCyEMJUYBlwOLke6Y8BF3Q7fln+OXTb/mVy7RXPA96e76H+WuAUYEfgvBjjEyldsyQp47qPiGa17KU7a9Ozw4mmakSpBPT8KPphwIXANOA44BlgHjAnxvhCb6/vdJ6XQgiTgC8C7wM+TW5l0buBb8YYF6VxvZKkbEsqfclq2QtYm55VTjRVI0qtzWKM8WlgZonHdh8577zvZXIj7t1H3SVJLaJYQMpy2QtYm95oeptoKtVblvqgS5LUsFyNtLEUG1m3Xl1ZYUCXJDWURmrJCK5G2kisV1dWGNAlSQ2hEVsygquRNhI7wSgrDOiSpIbQiC0ZwdVIm0FfI+tONFXaDOiSJNWYHV8aS9LIetLiSJbDqL8M6JKkptBItel2fGkOTjRVtRjQJUkNrRFr08vt+AKWvjQKJ5oqDQZ0SVJDa9Ta9GIsfWl8TjRVGgzokiRlhKUvzcuRdZXDgC5JamrdQ1FW69LBxY6amSPrKocBXZLUlJJq07Nal94bFztqXo6sqxgDuiSpKRUbeWzEunRwsaNmVu7IuqPqrcGALklSxrnYUetJGll3VL01GNAlSS2nkXqmJ7HjS3Ozx3prM6BLklpGI/ZMT2LHl9ZjvXrrMKBLklpGM/VMd7Gj1mMnmNZhQJckqYlY+tJ6HFlvPgZ0SZLymqE23dKX1mMnmOZjQJcktbxmqk0vpfRFraG3TjCWw2SbAV2S1PKaqTa9FK5G2hqKjaw/tWa95TANwIAuSVILcDVSgRNNG4UBXZKkPnQfcWy0unRwNVL1zomm2WJAlyQpQVJteqPVpYOrkap3TjTNFgO6JEkJigWQZqpLtyWj+tLbRFNVjwFdkqQWZUtG9aXYyLr16tVnQJckqUW5GqkqYb169RnQJUmqQDMsapTE0hf1xk4w1WdAlySpDM20qFESS19UCUfW02NAlySpDK2wqFG5pS+WvQjsBJMmA7okSSqJix2pEnaCKZ8BXZKkFDVzbbqLHakSdoIpnwFdkqQUtEJtuosdKS3Wq/fOgC5JUgpaoTa9GDu+qBJ2gumdAV2SJFXMji9KkyPrOQZ0SZJqoHvoaJa69FI6vkil6mtkvVUY0CVJqqKk2vRWChzWpistrdKq0YAuSVIVFQsPzV6XDtamK12t1qrRgC5JklJnbbrS1GqtGg3okiQpda5Gqmpr5gmlBnRJkuqkmRc1SuJqpEpLM7dqNKBLklRjrbCoURJXI1W1NcPIugFdkqQaa9VFjcDVSFV95Y6sZ3FU3YAuSZLqyo4vqoVG6gRjQJckKWNarTbdji+qhUbqBGNAlyQpI1q1Nr3cji9g6YvSkdV6dQO6JEkZ0cq16cVY+qJqy2onGAO6JEnKJEtfVC/1Hlk3oEuS1CC6B4ZmrksHFztS/fQ1sl5tBnRJkjIuqTa9mevSe+NiR6q3ardqNKBLkpRxxX7wt2pdOrjYkeqnVq0aDeiSJKmh9LXYkVQt5bRq7Ni0hbDD4B0r+TgGdEmS1FRsyahaShpV3/DKVmgbUFHWNqBLktTAWm1RoyS2ZFS9VON7zYAuSVIDatVFjZLYklFZM6At0DZwcEXp3YAuSVIDclGjrlyNVFkzaEAb217ZtL6S17alfTGSJElZsePA5KhTKH2RssYRdEmSmpC16TmWvqgRGdAlSWoi1qZ35WqkakQGdEmSmoi16aVxNVJlmTXokiSp5Zw6blRifbplL6o3R9AlSVLL6Ws1Uju+qJ4M6JIktZDudeitOHE0iYsdKSsM6JIktYCkyaOtOHE0iR1flBUGdEmSWkCxyaNOHO2qlI4vUi0Y0CVJkkpkbbpqIbUuLiGEUSGEK0MIq0IIm0II7SGEuSGE3fpxzqNCCFtDCDGEcHFa1ypJkl718KoXezyeWlPRCuVNydVIVWupjKCHEMYA9wB7Aj8HHgEmAOcC00IIE2OMZf0dLYQwDPghsB7YOY3rlCRJr3JRo9JYm65aS6vE5bvkwvk5Mcb5hY0hhG8DnwG+CnyizHPOA3YFLsm/XpIkpchFjUrjaqSqtX6XuORHz48F2oHvdNs9C+gApocQhpZxzvcAM4FzgFX9vUZJkqS09bbQkWUv6o80atCn5J8XxRi7/I0nxrgO+B2wE3BEKScLIewJXAHcFGNcWMkFhRCWFnsAB1VyPkmSpO5cjVTVkkaJy4H558cS9j9OboT9AOCOEs53BblfHMotiZEkSSkqVofuwkavcjVSVUsaAb0wuyRpNklh+/C+ThRC+ChwEvCBGOPfK72gGOP4hPMvBcZVel5JklqBk0cr52qkSkNm+qCHEEYDc4HrY4z/Vd+rkSSpdTl5tHJ2fFEa0gjohV+li/+q/er2tX2c50pgA/CpFK5JkiSp5srt+AKWvqinNCaJPpp/PiBh//7556Qa9YJx5Fo1/iO/MFEMIUTgqvz+C/Lbburf5UqSpP5wUaPyudiRypHGCPri/POxIYS2zp1c8osNTSS32NB9xV7cydXkur10tz9wFPBnYCnwQL+vWJIklS2pNt269L5Z+qJy9DugxxifCCEsItep5Wxgfqfdc4ChwPdjjB2FjSGEg/KvfaTTec4pdv4QwgxyAf2WGOOX+nu9kiSpMsVq061LL42lLypHGiUukKsbfxa4LIRwUwjhkhDCb8itIvoYcEG345flH5IkSS3L0hcVk0pAjzE+ARwGLAAOBz4LjAHmAUfEGP31WpIkqZveFjsCS19aVWptFmOMTwMzSzw2lHHeBeSCvyRJyigXNapMKaUvaj2Z6YMuSZIaj4saVV/nsG5demswoEuSpIq5qFF1JK1I6mqkrSGtSaKSJElKSW+16dalNz9H0CVJkjKmWG26LRlbhwFdkiRVjZNH05NU9gKWvjQbA7okSUqdk0fT52qkrcOALkmSUufk0fS5GmnrcJKoJElSA3M10ubjCLokSaq57mUu1qVXztKX5mNAlyRJNZNUm25deuXKLX2x7CX7DOiSJKlmitWmW5deHS521LisQZckSWpCLnbUuBxBlyRJakIudtS4DOiSJCkTXNSo+lzsqDEY0CVJUl25qFHt2PGlMRjQJUlSXbmoUe242FFjcJKoJElSi3Oxo2wxoEuSJLW43jq+gKUvtWaJiyRJyjQnj1afix1liwFdkiRlkpNH68/FjurDgC5JkjLJyaP111vXF8teqseALkmSpKL6WuxI1WFAlyRJDal7mYt16bVnS8bqMKBLkqSGklSbbl16bbgaafUZ0CVJUkMpVptuXXrtuBpp9RnQJUmSVDJXI60+FyqSJElSv7kaaXocQZckSU3DRY3qx9KX9BjQJUlSw3NRo/pzNdL0GNAlSVLDc1Gj7HI10vJZgy5JkqSqOXXcqMT6dMteinMEXZIkSVXT12qkdnzpyYAuSZKanpNHs8XFjnpnQJckSU3LyaPZZMeX3hnQJUlS03LyaDa52FHvnCQqSZKkTHCxoxxH0CVJUsvqXuZiXXp9WfqSY0CXJEktJ6k23br0+nKxoxwDuiRJajnFatOtS8+uVlvsyBp0SZIkZVqrLXbkCLokSZIyrdUWOzKgS5IkdeKiRo2hmRc7MqBLkiThokaNppk7vhjQJUmScFGjRtPMix05SVSSJElNoxkWO3IEXZIkqQTWpjeGUkpfst5L3YAuSZLUC2vTG0tS6cvMBfc3TC91A7okSVIvrE1vDr2NrGdtQqkBXZIkSU2vkXqpO0lUkiRJLSmrE0odQZckSeqH7nXoThxtHFntpW5AlyRJqkDS5FEnjjaOrPZSN6BLkiRVoNjkUSeONocdB7b1Oqpe7a4v1qBLkiRJnZw6blSf9enV5Ai6JEmS1Em5pS9pl70Y0CVJklLmqqPNKan0Je2yFwO6JElSSlx1tLnVarEjA7okSVJKXHW0uZWz2NEzz3VU/HGcJCpJkiRVqLfJpJVyBF2SJKlGrE1vPn0tdlQJA7okSVKVWZvevJI6vkxeUPk5DeiSJElVZm26ymENuiRJkpQhBnRJkiQpZfvtMbTi16ZW4hJCGAVcCEwDdgeeAW4C5sQYXyjh9UOBk4HjgXHAPsA24FHgWmB+jHFzWtcrSZKUFU4eVWepBPQQwhjgHmBP4OfAI8AE4FxgWghhYoyxryKrScBCYA2wmFy43w04CfgmcEoIYWqMcWMa1yxJklRvTh5VMWmNoH+XXDg/J8Y4v7AxhPBt4DPAV4FP9HGO1cBHgOs7j5SHED4HLAHeAZwNfCula5YkSaorJ4+qmH7XoOdHz48F2oHvdNs9C+gApudLWBLFGP8cY/xx9zKWGOM6Xg3lk/t7vZIkSVKWpTGCPiX/vCjG2KVDe4xxXQjhd+QC/BHAHRV+jFfyz1sqfL0kSVLD6V7mYl16a0gjoB+Yf34sYf/j5AL6AVQe0D+af/5VKQeHEJYm7Dqowo8vSZJUM0m16dalt4Y0Anrh/56k/2MK24dXcvIQwqfJdYb5M3BlJeeQJElqJMVq061Lbx2ZXkk0hHAKMJfcBNJTY4yv9PESAGKM4xPOt5RcC0dJkiQpk9JYqKgwQl68R9Cr29eWc9IQwsnAdcCzwOQY4/LKLk+SJElqHGmMoD+afz4gYf/++eekGvUeQgjvA64hN3J+TIzx8covT5IkqXm4qFHzSyOgL84/HxtCaOvcySWEMAyYCKwH7ivlZCGEDwM/BP4GTHHkXJIkyUWNWkm/A3qM8YkQwiJynVrOBuZ32j0HGAp8P8bYUdgYQjgo/9pHOp8rhHAmuYmgT5IL50/29/okSZKagYsatY60Jol+CrgHuCyEMBVYBhxOrkf6Y8AF3Y5fln8OhQ0hhCnkwnkbuVH5mSGEbi9jbYxxbkrXLEmSJGVOKgE9P4p+GHAhuZaIxwHPAPOAOTHGF0o4zb68Omn1ownHPEmuq4skSZI6sTa9eaTWZjHG+DQws8RjewyNxxgXAAvSuh5JkqRWYG1688l0H3RJkiT1ztr05pNGH3RJkiRJKTGgS5IkSRliiYskSVIT616H7sTR7DOgS5IkNaGkyaNOHM0+A7okSVITKjZ51ImjjcEadEmSJClDHEGXJElqMS5qlG0GdEmSpBbhokaNwYAuSZLUIlzUqDFYgy5JkiRliCPokiRJAqxNzwoDuiRJUouzNj1bDOiSJEktztr0bLEGXZIkScoQA7okSZKUIZa4SJIkqVfd69CdOFpdBnRJkiQVlTR51Imj1WVAlyRJUlHFJo86cbT6rEGXJEmSMsQRdEmSJJXNRY2qx4AuSZKkkrmoUfUZ0CVJklQyFzWqPmvQJUmSpAxxBF2SJEmpsTa9/wzokiRJ6jdr09NjQJckSVK/WZueHmvQJUmSpAxxBF2SJElV173Mxbr0ZAZ0SZIkVU1Sbbp16ckM6JIkSaqaYrXp1qX3zhp0SZIkKUMcQZckSVJd2DO9OAO6JEmSasqe6b0zoEuSJKmm7JneO2vQJUmSpAxxBF2SJEmZ0uq16QZ0SZIkZYK16TkGdEmSJGWCtek51qBLkiRJGeIIuiRJkhpC9zKXZq1LN6BLkiQp05Jq05u1Lt2ALkmSpEwrVpvezHXp1qBLkiRJGeIIuiRJkhpWM/ZMN6BLkiSp4TRzz3QDuiRJkhpOM/dMN6BLkiSp6TRy6YsBXZIkSU2jGUpfDOiSJElqGs1Q+mKbRUmSJClDHEGXJElSy+he5pLFunQDuiRJkppeUm16FuvSDeiSJElqesVq07Nal24NuiRJkpQhjqBLkiSppWWtZ7oBXZIkSS0pqz3TDeiSJElqSVntmW5AlyRJkoqoV+mLAV2SJEnqpN6lLwZ0SZIkqZN6l74Y0CVJkqQyVHs1UgO6JEmSVIJarUZqQJckSZJKUKvVSF1JVJIkScqQ1AJ6CGFUCOHKEMKqEMKmEEJ7CGFuCGG3Ms8zIv+69vx5VuXPOyqta5UkSZLS9PCqF7s8NryylbDDwMGVnCuVEpcQwhjgHmBP4OfAI8AE4FxgWghhYoyxz/H/EMLu+fMcAPwGuA44CJgJHB9CeHuMcXka1yxJkiT1V1Jd+pCBAwihbUAl50yrBv275ML5OTHG+YWNIYRvA58Bvgp8ooTzfI1cOP92jPGznc5zDjAv/3GmpXTNkiRJUr8ktWTsj36XuORHz48F2oHvdNs9C+gApocQhvZxnp2B6fnjZ3fbfTnwJPCuEMLr+3vNkiRJUlalUYM+Jf+8KMa4rfOOGOM64HfATsARfZznCGAI8Lv86zqfZxtwW7ePJ0mSJGXSgLbAtlc2ra/ktWmUuByYf34sYf/j5EbYDwDu6Od5yJ+nVyGEpQm7DurrtZIkSVJ/7ThwAHHz+pcreW0aI+iFqvikDu2F7cNrdB5JkiSpYTXlQkUxxvHFtudH1sfV+HIkSZKkkqUxgl4Y2e7ZX6br9rU1Oo8kSZLUsNII6I/mn5Nqw/fPPyfVlqd9HkmSJKlhpRHQF+efjw0hdDlfCGEYMBFYD9zXx3nuAzYAE/Ov63yeNnITTTt/PEmSJKnp9DugxxifABYBo4Gzu+2eAwwFfhRj7ChsDCEcFELo0lElxvgy8KP88bO7nefT+fPf5kqikiRJamZpTRL9FHAPcFkIYSqwDDicXM/yx4ALuh2/LP8cum3/d2Ay8H9CCIcC9wNjgfcAz9LzFwBJkiSpqaRR4lIYRT8MWEAumH8WGAPMA46IMT5f4nmeB94OXAa8IX+ew4GrgPH5jyNJkiQ1rdTaLMYYnwZmlnhs95HzzvvWAOfmH5IkSVJLSWUEXZIkSVI6DOiSJElShhjQJUmSpAwxoEuSJEkZYkCXJEmSMsSALkmSJGWIAV2SJEnKEAO6JEmSlCEhxljva6iZEMLzQ4YMGTF27Nh6X4okSZKa2LJly9iwYcOaGOPu5b621QL6CmAXoL3Ol6LSHJR/fqSuV6H+8j42Pu9hc/A+Nj7vYWMZDbwUY9yv3Be2VEBXYwkhLAWIMY6v97Woct7Hxuc9bA7ex8bnPWwd1qBLkiRJGWJAlyRJkjLEgC5JkiRliAFdkiRJyhADuiRJkpQhdnGRJEmSMsQRdEmSJClDDOiSJElShhjQJUmSpAwxoEuSJEkZYkCXJEmSMsSALkmSJGWIAV2SJEnKEAO6ai6EsHsI4eMhhJ+FEP4aQtgQQngxhHB3COFjIYSi/1+GEN4RQrg1hLAm/5oHQwjnhRAG1PpzUHEhhI+EEGL+8fGEY04IISzJ3/OXQwi/DyGcWetrVVchhKn578nVIYRNIYRVIYTbQgjHFTnW78WMCSEcH0JYFEJYmb8ny0MI14cQ3p5wvPewDkIIp4UQ5ocQ7gohvJR/r1zYx2vKvle+zzY+FypSzYUQPgH8B/AMsBh4CngtcAqwK3AD8L7Y6X/OEMJ78ts3Aj8B1gAnAgcCP40xvq+Wn4N6CiHsAzwEDAB2Bs6KMf6g2zGfBuYDz5O7j5uB04BRwLdijJ+r6UULgBDC/wt8HlgJ/DfwHPAaYDzw6xjjFzod6/dixoQQvgF8gdz31U3k7t8bgJOAHYAzYowLOx3vPayTEMKfgbcAL5P7fjsI+HGM8SMJx5d9r3yfbRIxRh8+avoAjiH3BtPWbftIcmE9Aqd22r4L8CywCTis0/YdgXvyx3+w3p9XKz+AAPwaeAK4NH9PPt7tmNHkfsg8D4zutH034K/517y93p9Lqz2As/Jf+wXAoCL7B3b6b78XM/bIv29uBVYDe3bbNyV/T5Z7D7PxyN+T/fPvmZPzX++FCceWfa98n22ehyUuqrkY429ijL+MMW7rtn018L38Pyd32nUaudG862KMf+x0/EbgS/l/frJ6V6wSnEPuF6+ZQEfCMR8FBgOXxxjbCxtjjC8AX8v/8xNVvEZ1E0IYDHyV3C/G/xJj3Nz9mBjjK53+6fdi9uxLrlz19zHGZzvviDEuBtaRu2cF3sM6ijEujjE+HvOpuQ+V3CvfZ5uEAV1ZUwgDWzptOyb//Ksix/8WWA+8Ix82VGMhhLHA14F5Mcbf9nJob/fxv7sdo9r4Z3IB4EZgW76O+d9CCOcm1C77vZg9j5MrYZgQQtij844QwlHAMHJ/3SrwHjaOSu6V77NNwoCuzAgh7ACckf9n5zeXA/PPj3V/TYxxC7CCXJ3l66t6geohf89+RG4E9t/7OLy3+/gMuZH3USGEnVK9SPXmbfnnjcADwM3kftmaC9wTQrgzhNB59NXvxYyJMa4B/o3cPJ6HQwj/XwjhkhDCfwGLgNuB/6fTS7yHjaOSe+X7bJMwoCtLvg4cDNwaY7yt0/Zd888vJryusH14tS5Mib4CvBWYEWPc0Mexpd7HXRP2K3175p8/T642dRK5EddDyIW7o4DrOx3v92IGxRjnkptkvwO5OQXnA+8DngYWdCt98R42jkrule+zTcKArkwIIZwDfBZ4BJhe58tRCUIIh5MbNf9WjPHeel+PKlL4GbAFOCnGeHeM8eUY40PAe8l1mTg6qVWfsiGE8AXgp+Qm+o4BhpLrwLMc+HG+S4+kBmJAV93lW0LNAx4GpuT/ZNtZX7/xF7avrcLlqYh8acvV5P6M+uUSX1bqfUwa+VH6Ct8zD3SeUAYQY1wPFP6SNSH/7PdixoQQJgPfAH4RY/w/McblMcb1McY/kfsl62/AZ0MIhTII72HjqORe+T7bJAzoqqsQwnnk+rX+D7lwvrrIYY/mnw8o8vodgP3IjQAur9Z1qoedyd2PscDGTosTRWBW/pgr8tvm5v/d2338J3KjfivzwVC1UbgnSWHshfzzkG7H+72YHSfknxd335H/Xrqf3M/6t+Y3ew8bRyX3yvfZJmFAV92EEP4N+L/An8mF82cTDv1N/nlakX1HATsB98QYN6V/lUqwCfjPhMcD+WPuzv+7UP7S2318d7djVBt3kKs9f2PCCr4H559X5J/9XsyeQgeP1yTsL2wvtND0HjaOSu6V77PNot6N2H205oNcWUQE/giM6OPYXYB/4MIaDfEAZlN8oaL9cAGNzD2An+e/9p/ptv1YYBu5UfRd89v8XszYA3h//uu+Gti727535+/hBmB372G2HpS2UFFZ98r32eZ5hPyNk2omhHAmuclMW8mVtxSrhWuPMS7o9JqTyU2C2ghcR26545PIL3cMvD/6P3MmhBBmkytzOSvG+INu+/4VuAyXoM6MEMIocj/s9yE3ov4AuR/yJ/NqALih0/F+L2ZI/i8ftwHvJLco0c/IhfWx5MpfAnBejHFep9d4D+sk/7U/Of/PkcC7yJWo3JXf9lzn98FK7pXvs02iny4m/AAAAPZJREFU3r8h+Gi9B6+OsPb2WFLkdROBW8mN6G0AHgI+Awyo9+fko+j9/XjC/hOBO8mFiQ7gD8CZ9b7uVn6QK4OYDzxJ7of5c+SC3oSE4/1ezNADGAicB9wHvESuLvlZcn3tj/UeZudRws+/9jTule+zjf9wBF2SJEnKECeJSpIkSRliQJckSZIyxIAuSZIkZYgBXZIkScoQA7okSZKUIQZ0SZIkKUMM6JIkSVKGGNAlSZKkDDGgS5IkSRliQJckSZIyxIAuSZIkZYgBXZIkScoQA7okSZKUIQZ0SZIkKUMM6JIkSVKGGNAlSZKkDDGgS5IkSRny/wOSUlmrdUbLGQAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "image/png": { "height": 248, "width": 372 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ggf = GompertzFitter()\n", "ggf.fit(rossi['week'], rossi['arrest'], timeline=np.arange(1, 120))\n", "ggf.print_summary()\n", "ggf.plot_survival_function()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Discrete survival models\n", "\n", "So far we have only been investigating continous time survival models, where times can take on any positive value. If we want to consider discrete survival times (for example, over the positive integers), we need to make a small adjustment. With discrete survival models, there is a slightly more complicated relationship between the hazard and cumulative hazard. This is because there are two ways to define the cumulative hazard. \n", "\n", "$$H_1(t) = \\sum_i^t h(t_i) $$ \n", "\n", "$$H_2(t) = -\\log(S(t))$$\n", "\n", "We also no longer have the relationship that $h(t) = \\frac{d H(t)}{dt}$, since $t$ is no longer continous. Instead, depending on which verion of the cumulative hazard you choose to use (inference will be the same), we have to redefine the hazard function in *lifelines*. \n", "\n", "$$ h(t) = H_1(t) - H_1(t-1) $$\n", "$$ h(t) = 1 - \\exp(H_2(t) - H_2(t+1)) $$\n", "\n", "[Here is an example](https://stats.stackexchange.com/questions/417303/what-is-the-likelihood-for-this-process) of a discrete survival model, that may not look like a survival model at first, where we use a redefined `_hazard` function. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looking for more examples of what you can build? See other unique survival models in the docs on [time-lagged survival](Modelling time-lagged conversion rates.ipynb)" ] } ], "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }