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@ljwolf
Created September 29, 2016 04:11
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While poking around some traces, I was surprised by discrepancies between PyMC3 and the R CODA package for convergence diagnostics. So, I documented the differences I saw in one of the estimators in the following notebook.
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Divergent Convergence Diagnostics\n",
"\n",
"28 September 2016\n",
"\n",
"[GH: ljwolf](https://github.com/ljwolf)\n",
"\n",
"[@levijohnwolf](https://twitter.com/levijohnwolf)\n",
"\n",
"[ljwolf.org](http://ljwolf.org)\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"sns.set_context('talk')\n",
"import pymc3 as mc\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"df = pd.read_csv('http://www.public.asu.edu/~lwolf2/data/example_trace.csv').drop('Unnamed: 0', axis=1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I've been working on a grant about spatially-correlated variance components models. Having built some custom Gibbs samplers for various specifications, I started conducting posterior convergence diagnostic tests. \n",
"\n",
"In doing these, I noticed that the PyMC3 concergence diagnostics were giving me quite different results from what `CODA`, the well-used `R` package, was providing. I'll focus on the Geweke statistic here, but I'm pretty suspect of the Brooks-Gelman-Rubin statistic implementation as well. I don't particularly trust the Raftery-Lewis statistics in general, so I haven't looked into them too deeply. \n",
"\n",
"\n",
"But, I hope I can document my surprise about the PyMC3 implementation of the Geweke statistic. Digging into it a little bit, here are three parameters from a model I've been working with. \n",
"\n",
"- $\\sigma^2$ is a variance paramter, and is well mixed away from the domain restriction on its boundary. \n",
"- $\\tau^2$ is also a variance parameter, and appears to be well mixed, but close to its domain boundary. \n",
"- $\\beta$ is one of a few effects parameters. Relative to the other two, its trace looks like it has higher serial autocorrelation. \n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/ljw/anaconda3/envs/py3/lib/python3.5/site-packages/statsmodels/nonparametric/kdetools.py:20: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
" y = X[:m/2+1] + np.r_[0,X[m/2+1:],0]*1j\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7ff02fce8c88>"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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bi3lvb8Vvn16Lmx/9Ave8+BWe+3AHPlzTiPX1h7C/zQW3L1SUSR4JgiCI4UGm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w9ZJsmj6zVGWkc8qLGlMay7GzpQdL5tbjPV2EfLPb+uaHrcpnhincRYRCoVAolI87QwlaJwiC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\nhBBCCCGE8Jgk30IIIYQQQgghhMf+PyEVtnNNCgxPAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff0322daac8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f,ax = plt.subplots(3,2, sharey='row', figsize=(2.1*8,8))\n",
"ax[0,0].plot(df.Sigma2, linewidth=.5)\n",
"sns.kdeplot(df.Sigma2, vertical=True, shade=True, ax=ax[0,1])\n",
"ax[0,0].set_title('Sigma2')\n",
"\n",
"ax[1,0].plot(df.Tau2, linewidth=.5)\n",
"sns.kdeplot(df.Tau2, vertical=True, shade=True, ax=ax[1,1])\n",
"ax[1,0].set_title('Tau2')\n",
"\n",
"ax[2,0].plot(df.Betas_0, linewidth=.5)\n",
"sns.kdeplot(df.Betas_0, vertical=True, shade=True, ax=ax[2,1])\n",
"ax[2,0].set_title('Beta')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A commonly-used convergence diagnostic is the Geweke diagnostic. PyMC3 provides a way to compute it using `mc.geweke`. They recommend that if this statistic is outside of $[-1,1]$, then convergence may be suspect. So, plotting these statistics:"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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RtEeStMuYYEmSdpJDwJWdIITwNOAlwGtH1iJJ0q7iTS4kSTtKCOE24ElAE/he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\nAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff02c0af7f0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f, ax = plt.subplots(3,1, figsize=(12,6))\n",
"tau2_pymc = mc.geweke(tau2, first=.1, last=.5, intervals=20).T[1]\n",
"sigma2_pymc = mc.geweke(sigma2, first=.1, last=.5, intervals=20).T[1]\n",
"beta_pymc = mc.geweke(beta, first=.1, last=.5, intervals=20).T[1]\n",
"ax[0].plot(tau2_pymc)\n",
"ax[0].hlines([-1,1], 0,20,color='k', linestyle=':')\n",
"ax[0].axis([0,20,-1.1,1.1])\n",
"ax[0].set_title('$\\\\tau^2$', fontsize=16)\n",
"\n",
"ax[1].plot(sigma2_pymc)\n",
"ax[1].hlines([-1,1], 0,20,color='k', linestyle=':')\n",
"ax[1].axis([0,20,-1.1,1.1])\n",
"ax[1].set_title('$\\sigma^2$', fontsize=16)\n",
"\n",
"ax[2].plot(beta_pymc)\n",
"ax[2].hlines([-1,1], 0,20,color='k', linestyle=':')\n",
"ax[2].axis([0,20,-1.1,1.1])\n",
"ax[2].set_title('$\\\\beta$', fontsize=16)\n",
"\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Those are pretty flat lines, and provide no evidence of lack of convergence. \n",
"\n",
"But, their suggestion that the deviate varies between -1 and 1 caught me off guard. The implementation I'm used to using with Stan, i.e. the one in `R`'s `CODA` package, is different from this. Indeed, the original Geweke (1992) paper suggests the statistic is asymptotically standard normal. So, while judging [-1,1] as indicating lack of convergence is a pretty strict $\\alpha$ level, it seemed strange to me that the implementation was different from what it was sourcing. \n",
"\n",
"### Looking into Geweke\n",
"\n",
"For this, I'll be interfacting with `R` using `rpy`2's line magic, popping results back and forth between `R`. It can be finnicky getting both working, since I think a readline bug in conda made it difficult for me to get this working initially."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%load_ext rpy2.ipython"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, let's just pop our series over to R and compute the same diagnostics. "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"tau2 = df.Tau2.values\n",
"sigma2 = df.Sigma2.values\n",
"beta = df.Betas_0.values"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%Rpush tau2 sigma2 beta"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`CODA` by itself only implements the single diagnostic and the plot version. It doesn't let you pull out the array of z-scores generated by the plotting logic. \n",
"\n",
"So, I'll show the code that does it, and then pull out the relevant bits. That feature, showing the source of a function at the interpreter, is something I sorely miss about `R` (and literally nothing else :)"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"function (x, frac1 = 0.1, frac2 = 0.5, nbins = 20, pvalue = 0.05, \n",
" auto.layout = TRUE, ask, ...) \n",
"{\n",
" if (missing(ask)) {\n",
" ask <- if (is.R()) {\n",
" dev.interactive()\n",
" }\n",
" else {\n",
" interactive()\n",
" }\n",
" }\n",
" x <- as.mcmc.list(x)\n",
" oldpar <- NULL\n",
" on.exit(par(oldpar))\n",
" if (auto.layout) \n",
" oldpar <- par(mfrow = set.mfrow(Nchains = nchain(x), \n",
" Nparms = nvar(x)))\n",
" ystart <- seq(from = start(x), to = (start(x) + end(x))/2, \n",
" length = nbins)\n",
" if (is.R()) \n",
" gcd <- array(dim = c(length(ystart), nvar(x), nchain(x)), \n",
" dimnames = c(ystart, varnames(x), chanames(x)))\n",
" else gcd <- array(dim = c(length(ystart), nvar(x), nchain(x)), \n",
" dimnames = list(ystart, varnames(x), chanames(x)))\n",
" for (n in 1:length(ystart)) {\n",
" geweke.out <- geweke.diag(window(x, start = ystart[n]), \n",
" frac1 = frac1, frac2 = frac2)\n",
" for (k in 1:nchain(x)) gcd[n, , k] <- geweke.out[[k]]$z\n",
" }\n",
" climit <- qnorm(1 - pvalue/2)\n",
" for (k in 1:nchain(x)) for (j in 1:nvar(x)) {\n",
" ylimit <- max(c(climit, abs(gcd[, j, k])))\n",
" plot(ystart, gcd[, j, k], type = \"p\", xlab = \"First iteration in segment\", \n",
" ylab = \"Z-score\", pch = 4, ylim = c(-ylimit, ylimit), \n",
" ...)\n",
" abline(h = c(climit, -climit), lty = 2)\n",
" if (nchain(x) > 1) {\n",
" title(main = paste(varnames(x, allow.null = FALSE)[j], \n",
" \" (\", chanames(x, allow.null = FALSE)[k], \")\", \n",
" sep = \"\"))\n",
" }\n",
" else {\n",
" title(main = paste(varnames(x, allow.null = FALSE)[j], \n",
" sep = \"\"))\n",
" }\n",
" if (k == 1 && j == 1) \n",
" oldpar <- c(oldpar, par(ask = ask))\n",
" }\n",
" invisible(list(start.iter = ystart, z = gcd))\n",
"}\n",
"<environment: namespace:coda>\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%%R\n",
"library(coda)\n",
"coda::geweke.plot"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you see, we need to extract the `ystart` lines, and the loop that constructs `geweke.out`. So, I'll write a function that wraps this up and puts it together below:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%%R\n",
"library(coda)\n",
"\n",
"tau2 <- as.mcmc(as.matrix(tau2))\n",
"sigma2 <- as.mcmc(as.matrix(sigma2))\n",
"beta <- as.mcmc(as.matrix(beta))\n",
"\n",
"geweke.diag.list <- function(data, drop, hold, n.bins){\n",
" start <- seq(from=start(data), to=(start(data) + end(data))/2, length=n.bins)\n",
" results <- c()\n",
" for(n in 1:length(start)){\n",
" this_result <- geweke.diag(window(data, start=start[n]), frac1=drop, frac2=hold)\n",
" results <- cbind(results, this_result$z)\n",
" }\n",
" results\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To be clear, the \"general\" theory of the Geweke diagnostic is that, for some sequence of random variates ${\\theta_1, \\theta_2, \\dots, \\theta_n}$ from a Markov process, a test statistic on whether two subsets, $A$, $B$, of this sequence have the same mean can be constructed:\n",
"\n",
"$$ g(\\theta) = \\frac{\\bar{\\theta_A} - \\bar{\\theta_B}}{\\sqrt{\\frac{1}{N_A}s(\\theta_A)^2 + \\frac{1}{N_B}s(\\theta_B)^2}}$$\n",
"\n",
"where $\\bar{\\theta}_.$ is the mean of the subsequence $A$, and $s(\\theta_A)^2$ is the sample variance of the subsequence $A$. This provides *a single statistic*, relating sets $A$ and $B$, and is asymptotically standard normal. \n",
"\n",
"So, for the plotted version of this statistic, you construct *multiple* sets $A,B$, and compute the geweke diagnostic for each pair of subsets. Typically, these sets are characterized as the \"first $p$%\" of a subset being compared to the \"last $q$%\" of the subset, in order to determine if the first $p$% can be discarded as burn-in. In `CODA`, these sets are constructed as shown above, by dividing the first half of the distribution into `n.bins` segments. Then, $g(\\theta)$ is computed for the sequence composed of *all* segments past the current segment, plus the latter half of the distribution. So, you can think of it as recursively testing the $i$th partition against the last $q$% of the chain containing segments $i<j<$`n.bins` plus the second half of the chain. \n",
"\n",
"Since we've pulled out the part of `geweke.plot` we need to get the z-scores, we can run the following to recover the segment-wise statistics we need to plot and compare to pymc3. "
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%%R\n",
"\n",
"tau2_coda <- geweke.diag.list(tau2, .1, .5, 20)\n",
"sigma2_coda <- geweke.diag.list(sigma2, .1, .5, 20)\n",
"beta_coda <- geweke.diag.list(beta, .1, .5, 20)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%Rpull tau2_coda sigma2_coda beta_coda"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Below, I show the same plot as before, but now the green line are the coda statistics. Indeed, the `CODA` diagnostics indicate that, in some cases, we get pretty close to, or go over, the confidence bounds for the diagnostics! But, the PyMC3 statistics aren't ever close to their stated bounds of -1,1."
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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IjwUnPsSjx0Q+0CeOCYWtK7/hdYrVs6l1ZuKza8r+GT/DXPi8nsj36DaP203YmuhUO53u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\n/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jrZACzPaUtKOXSio/P68U5CYSOtsyDXxgdvWcruDTXTLj3/QssrvHjpVQC+sOEzKCVT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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff01a0cb3c8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f, ax = plt.subplots(3,1, figsize=(12,6))\n",
"ax[0].plot(tau2_pymc)\n",
"ax[0].plot(tau2_coda.flatten())\n",
"ax[0].hlines([1.96, -1.96], 0,20,color='k', linestyle=':')\n",
"ax[0].axis([0,20,-2.1,2.1])\n",
"ax[0].set_title('$\\\\tau^2$', fontsize=16)\n",
"\n",
"ax[1].plot(sigma2_pymc)\n",
"ax[1].plot(sigma2_coda.flatten())\n",
"\n",
"ax[1].hlines([1.96, -1.96], 0,20,color='k', linestyle=':')\n",
"ax[1].axis([0,20,-2.1,2.1])\n",
"ax[1].set_title('$\\sigma^2$', fontsize=16)\n",
"\n",
"ax[2].plot(beta_pymc)\n",
"ax[2].plot(beta_coda.flatten())\n",
"ax[2].hlines([1.96, -1.96], 0,20,color='k', linestyle=':')\n",
"ax[2].axis([0,20,-2.1,2.1])\n",
"ax[2].set_title('$\\\\beta$', fontsize=16)\n",
"\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So...\n",
"\n",
"## Why are they so different?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, the [PyMC3 implementation](https://github.com/pymc-devs/pymc3/blob/a29f7f1602e239b042128fe0d05a55c482d66162/pymc3/diagnostics.py#L10) is quite different from the coda implementation. In short, the pymc3 implementation computes: \n",
"\n",
"```python\n",
"A.mean() - B.mean() / np.sqrt(A.var() + B.var())\n",
"```\n",
"\n",
"The original statistic, though, divides both $A$ and $B$ by their respective sample sizes. Since they are different (at least in the logic of the `CODA` implementation and the original suggestion in Geweke (1992)), this is necessary to rescale the variances correctly.\n",
"\n",
"In addition, if you read the coda implementation of the diagnostic, you'll see it's using this `spectrum0.ar` method to compute the variance term:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"function (x, frac1 = 0.1, frac2 = 0.5) \n",
"{\n",
" if (frac1 < 0 || frac1 > 1) {\n",
" stop(\"frac1 invalid\")\n",
" }\n",
" if (frac2 < 0 || frac2 > 1) {\n",
" stop(\"frac2 invalid\")\n",
" }\n",
" if (frac1 + frac2 > 1) {\n",
" stop(\"start and end sequences are overlapping\")\n",
" }\n",
" if (is.mcmc.list(x)) {\n",
" return(lapply(x, geweke.diag, frac1, frac2))\n",
" }\n",
" x <- as.mcmc(x)\n",
" xstart <- c(start(x), floor(end(x) - frac2 * (end(x) - start(x))))\n",
" xend <- c(ceiling(start(x) + frac1 * (end(x) - start(x))), \n",
" end(x))\n",
" y.variance <- y.mean <- vector(\"list\", 2)\n",
" for (i in 1:2) {\n",
" y <- window(x, start = xstart[i], end = xend[i])\n",
" y.mean[[i]] <- apply(as.matrix(y), 2, mean)\n",
" y.variance[[i]] <- spectrum0.ar(y)$spec/niter(y)\n",
" }\n",
" z <- (y.mean[[1]] - y.mean[[2]])/sqrt(y.variance[[1]] + y.variance[[2]])\n",
" out <- list(z = z, frac = c(frac1, frac2))\n",
" class(out) <- \"geweke.diag\"\n",
" return(out)\n",
"}\n",
"<environment: namespace:coda>\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%%R\n",
"coda::geweke.diag"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### What's that about?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Well, since the chain is likely serially correlated, using the simple MLE estimator of sample variance is an incorrect estimate of the \"true\" process variance. This is a well known concern with the Geweke statistic (and, indeed, any subset testing of correlated traces). This estimate of the variance, then, is the 0th-order spectral density. For a $k$-th order Markov process, this estimate is:\n",
"\n",
"$$S(0) = \\frac{1}{(1 - \\sum_i^k \\alpha_i)^2} $$\n",
"\n",
"In `R`, the `spectrum0.ar` function provides this estimate using the `ar` estimator function. In this way, it fits an `AR` to the chain (optimizing on the AIC), then then returns the estimator above. "
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"function (x) \n",
"{\n",
" x <- as.matrix(x)\n",
" v0 <- order <- numeric(ncol(x))\n",
" names(v0) <- names(order) <- colnames(x)\n",
" z <- 1:nrow(x)\n",
" for (i in 1:ncol(x)) {\n",
" lm.out <- lm(x[, i] ~ z)\n",
" if (identical(all.equal(sd(residuals(lm.out)), 0), TRUE)) {\n",
" v0[i] <- 0\n",
" order[i] <- 0\n",
" }\n",
" else {\n",
" ar.out <- ar(x[, i], aic = TRUE)\n",
" v0[i] <- ar.out$var.pred/(1 - sum(ar.out$ar))^2\n",
" order[i] <- ar.out$order\n",
" }\n",
" }\n",
" return(list(spec = v0, order = order))\n",
"}\n",
"<environment: namespace:coda>\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%%R\n",
"coda::spectrum0.ar"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can do a similar thing using `statsmodels.tsa`. I'm not sure if there's a better estimator in `scipy` for estimating spectral density, though. I know they do have the periodogram and some other fft-related spectral analysis functions, but I'm most comfortable using the AR tools."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from statsmodels.api import tsa\n",
"def spectrum0_ar(data):\n",
" AR = tsa.AR(data).fit(ic='aic')\n",
" alphas = AR.params[1:]\n",
" return AR.sigma2/(1 - alphas.sum())**2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Sometimes, these estimates of the variance are similar, and sometimes they're **very different** "
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7ff01a3888d0>"
]
},
"execution_count": 50,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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GyrR/78AW4JIOx+YAy2LaJyqlUrXWreFjc8PHATTQ2uF8WzKt7q7Xpq6umVAo4e5nJU6n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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff02c0aed68>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot([spectrum0_ar(x) for x in np.array_split(sigma2, 50)])\n",
"plt.plot([x.var(ddof=1) for x in np.array_split(sigma2, 50)])\n",
"plt.title('$s(\\\\sigma^2)^2$', fontsize=20)"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7ff018d0a7f0>"
]
},
"execution_count": 51,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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GmguM7wBuA/4QW0vYDGxTSl3SWn/d7cQ8HsPt0LLjmIgA6oJe/H4PXo9B0rRImCZeb3nm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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff02c081668>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot([spectrum0_ar(x) for x in np.array_split(tau2, 50)])\n",
"plt.plot([x.var(ddof=1) for x in np.array_split(tau2, 50)])\n",
"plt.title('$s(\\\\tau^2)^2$', fontsize=20)"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7ff02c0b78d0>"
]
},
"execution_count": 52,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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QKK7bODevn4pz2SIUtfnPwlb3Eki2DwCs8aBvqGimjz+Lmeu/MeeNp+cvy7IG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\nU7zcZJognr+f6mki+/TGRbV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x6e7RhucHM3Ha5tjLkKuqRoP0e7bq57nf7++5VxegQXcm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\nAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff02c0cdd68>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot([spectrum0_ar(x) for x in np.array_split(beta, 50)])\n",
"plt.plot([x.var(ddof=1) for x in np.array_split(beta, 50)])\n",
"plt.title('$s(\\\\beta)^2$', fontsize=20)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So, if these variances are quite different, does it really matter for the statistic? Since the naive variance is often smaller than the `spectrum0.ar` estimate, we might expect it to make the statistic more extreme. This isn't where my intuition is going with the PyMC3 version of the statistic, so I'm not really sure *what* is going on with their implementation. \n",
"\n",
"Regardless, it'd be good to have a `geweke` function that at least gets close to the `CODA` diagnostics. So, the following can compute the single diagnostic, as well as the chain of diagnostics like done inside of `CODA`'s `geweke.plot` function."
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def geweke(data, drop, hold, varfunc=spectrum0_ar):\n",
" hold_start = np.floor((len(data)-1) * hold)\n",
" bin_width = np.ceil((len(data)-1) * drop)\n",
" \n",
" drop_data = data[:bin_width]\n",
" hold_data = data[hold_start:]\n",
" \n",
" drop_mean = drop_data.mean()\n",
" drop_var = varfunc(drop_data)\n",
" n_drop = len(drop_data)\n",
" \n",
" hold_mean = hold_data.mean()\n",
" hold_var = varfunc(hold_data)\n",
" n_hold = len(hold_data)\n",
" \n",
" return (drop_mean - hold_mean)/np.sqrt((drop_var / n_drop) + (hold_var / n_hold))\n",
"\n",
"def geweke_list(data, drop, hold, n_bins, **kw):\n",
" in_play = len(data-1)//2\n",
" to_drop = np.linspace(0,in_play, num=n_bins).astype(int)\n",
" return np.squeeze([geweke(data[drop_idx:], drop, hold, **kw) for drop_idx in to_drop])"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/ljw/anaconda3/envs/py3/lib/python3.5/site-packages/ipykernel/__main__.py:5: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
"/home/ljw/anaconda3/envs/py3/lib/python3.5/site-packages/ipykernel/__main__.py:6: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n"
]
}
],
"source": [
"sigma2_geweke_ar = geweke_list(sigma2, .1, .5, 20)\n",
"sigma2_geweke_var = geweke_list(sigma2, .1, .5, 20, varfunc=lambda x: np.var(x, ddof=1))\n",
"tau2_geweke_ar = geweke_list(tau2, .1, .5, 20)\n",
"tau2_geweke_var = geweke_list(tau2, .1, .5, 20, varfunc=lambda x: np.var(x, ddof=1))\n",
"beta_geweke_ar = geweke_list(beta, .1, .5, 20)\n",
"beta_geweke_var = geweke_list(beta, .1, .5, 20, varfunc=lambda x: np.var(x, ddof=1))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Below are the plots of the Geweke diagnostics. \n",
"\n",
"1. The dashed black line is the pymc3 estimate. \n",
"2. The dashed red line is the estimate we wrote above using the spectral density variance estimate. \n",
"3. The green line is the estimate we wrote above using the naive variance estimate\n",
"4. The solid blue line is the CODA estimate. "
]
},
{
"cell_type": "code",
"execution_count": 76,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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+Gx515nC55hky7jmYp5LUdKjckV7V+/CMezNcy1eluJ8GFwmWINgxWZZZeGoe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mWoWNGKr6/Gjh1mLJGxfMoYXmMRhbn61DHvHzyJVuifM005A03T2Hl9O1OOTmDH9W0J23O456R/\n+UH0KN37P7u9vKjEXBTPBZ+l2ZIGRFkiqZyrKivarsXNlIjmxIfi9x/D0LU3geFZqcNfePuamTw5\nhoYNU2Y2ryM7IrnT7xu6PZiCCRuxuLLsh7M07J4jyV0e1l5eTe8N3bFpNl7OX5+FLf5I8kQiz2K1\nWVl1aQUTj4zndNDJhO2ls5dlWKW3aV20ne7d7g7e3s+wrQO5FGLvRlUqexkmN5xGWd+MNSmA3Dg6\nv1knZ/DBrhEANCzYmHn+ixJVT2Nj4aefXJk6XsM9NoT4bDlZsiSaMmWcdwZUZyX1xMGsVkwXzmM6\neoSoXccwHDrK91UXsln148wZIxbL44vZTupSijMcNlQhIEclYspUInO98pRonIciRVO31+uTa9Z5\nu/mwrM3qDHfN+DdOlWC9sFu3tIhlf2LesgnX7VsxPrCPY3mwcTtXfSuzZo2ZVavMHDxoQtMef2YP\nD42GDS20amWhUSN9F5D9LzFhcZwduYjSK78nnzUAsCcis/N/TJbv36dBA2ua7k7u8tdOPH4ch3nv\nboyW+ITtS2lPR5b+7d0aAW7FKBB7CQBLseLEtu9ETLuO2IroO636s1hsFlZfWsmUYxM5ce9YwvYi\n3kUZXPEtOhXvQiZzyjc3JvaiuPrSn/Te0B2AbiXfYPwrk5PW0hIRwfrFkQz6qigREfb9BgyI4+OP\nYx3WNSEsDFb320j7rcMpwHUAbnkVw/bTBFyb1H3O3v+0/9Y+Ov3ZmhhrDGV8y7Gy7VqHL4ioaRpb\nAjYy8ch49t/am7Ddz6swQyoO59USXZOUzDpCjCWG7w5+zU/HJmHTbJgMJoZVept3q4xySHKZ1siN\nY9ow+egEvthrnxurZZE2zGgyB7MxcU8WT5400rGjBw8eGMiWzSZJVjJIPXGM4GAwDxhKgb/+wNXy\ndKtUO5axgnYJ5fz5bVSqZKVWqSBK18pCufI2XdegvBZ2lTbL/bkZeYPMLllY0nollXJV0S8gJ5O+\nEqwn18GyWjEfPYzrrh1EvfXuU7Np3b5tYM0aM43GtuBoaBHW4c8WGhKGN5kyadSvb2/ZatrUgpcT\nLDgdEQFz57oQ8uOvTAzvA9gTq+25X8X46XuU6fiSzhE6liEiHJedO3DdvAHXzRu5PfAj1ufrzZ49\nJu7eNVC3rhV/fwuF/5yK8dYtYtp3wlqmrFMOVo62RLPo3AJ+PjY5YTwLQKWclRlS8W38C7dI1ZaL\npFwUxx74kvGHvrP//PIP9C7TN8nnu3LFQP/+7hw7Zv+M5ctbmT49miJFkv93Q9Ng9WozH37oxrQ7\n7WnLSuIMrlzt8i5Zv3uHRA3e+xs1+BytljchJDaEglkKsabD5ucu2vyi9t3ay+Qj49l0bUPCtlwe\nuRlQfgg9Svd67tgSRzh29whDtwxAfXAOsC8BMLnBNCrmqpzi53ZWcuOYdnx74Ct+OPQtAJ2Kd2Fy\nw2mJ7s77ZJKVNavG0qVRkmQlgdST5AsIMDB7tivr1pm5csXIdPrRj18ACCczh6nMcXNljpbpivfL\nZahUyUblytYU72qfFDcjbtB6hT8BYVfxMHvwW6vlTj+2OLWl3wTrOYxXr5C9WvmEssVgZo9Wi7X4\n8x0j0TDi6qpRr56VVq3iadrUQtZUXoD6/n0DM2e6MGuWK6GhBlyIQ0UhoEBN3L8cQWH/DDCAUNPs\n00E560Cqf/EgJpjZp35h1snp3I++n7C9UcEmDKk4nJp5a+sy9iYpF0WbZqPHutfYcHUdZqOZpa1X\nUTNv7SSfMy4OvvnGjalTXclKMPNNvQj9+EuaDPZL8rFu3DAwalQmNmywP6ku6hrA6oIDyDrzC4yl\nkrpsnt2tiJs0X9aIGxHXyZYpG2vab0rVwbmn759i8tHxrLi4LGEsno+bD73L9qNv2YFkd8/u8HPG\nWeMYf+hbJh4Zj1WzYsDAoArDeL/aR6nSkurM5MYx7dA0jc/2fMS041MA6FH6Tb57eXyi/7Y+lWT5\n2Dja7D2y1nyJ2Ne6p2TY6YLUk6QxXLvGyR2hjNtajfXrzdhsj39Ha7Gb2nkvo1UqT95XXqJSFQ1F\nsTntckN3ou7QdoU/l0Iu4mZy49cWf/By/lf0DsvpZNgEy3DnDu4L5+O6ZRPmQwcw2Ow3NvfzlKZL\nqWPs3GkiPv7x92I2a9SpY5/63d/fgq9vyn3uG1fimTbdjfmLPIiOtsfg5qbRpUs8Q98MoWAJHduE\nxX+6Hh7ItONTWHBmPlEW+4JgZqOZdi91ZHDFtyiVvbSu8SX1ohgeF0azJQ24EHIeX3dfNnXcSb4s\n+ZN17q1bTXi+0Y2WcSuIwJN51SbR/LdOieqSa7XCzJkufPONG1FR9jpRt66F77+PeaHWsLDYUFqv\n8OdM0Cncze4sbb2KKrmrJft4L+JK6GWmHp3Eb+cWEGeLA8Dd7E73kj0YVGFYsr/3vzt1/yRDtwxI\nGAtWxLsokxpMo1qeRM4Ymc7JjWPaomka7+14m/lnZgMwoPwQPq/1VZKTrO4PJjOJt9AMBsKnTCe2\nU5eUDDvNk3qSOPGnL/Bg5ASKH1zECcpRhUOAAV9fG927x1O3rn3WZF1mek6GoOgg2q1szrngs7gY\nXZjvv4iGhZroHZZTyrAJ1pMMIQ9w2bUD1y2bsBYpSvSwdwgNhQ0bzKxebWbbNjPFY0/SlhWspxlH\nDJWpVUejZUsLzZtbHNZse+G0hVPvLabJobF8wSfM5k0yZ9bo2TOO/v3jnap5WDztbtRdxh38hgVn\n52GxWQDwMHvyeqke9C8/mPxZnGOhveRcFC8+uEDTpfUJjwujfI6K/NlufaJm7XqWyOVb8RrSj2zx\ndwFYkbkbWReNo1T1f18l/vSBaK72/o6v7/bjAsXJls3G55/H0rmz5YV6hcZaY+myqj27b+7CaDAy\nz38RTf38k39AB7kTeZtpx6cy9/QsIuMjAHuS3rH4qwyt+DbFsiavpS7eGs/koz/yw6FvibfZxzj2\nLTuAj2qMxsMlDc3yk8LkxjHtsWk2hmzpz5LziwEYUWUUI6t9mOj9T5400rt9HEtDG1GZI2hGI+HT\nZxPbpn1KhZzmST35b0HbThP18XgqXFiC8eG8bXfISc+Se2k5OA9t2liS05tdVyExD2j/ZytO3T+B\nyWBiVtP/0bxIy+fvmEFJgpUI4eHwYOjXVF47FoB7+LKRJqzDn400oWiNbLRqZaFFCwt58yb93Ef3\nWzj3wWJanxqLH9cAuGIsyqz3T9KztwVvb4d+HOFAkfGRTDs+hSlHJybcDPu6+9Kn7AB6lelD1kwp\nPD9qEiX3orjp6nq6r30VDY2OxV9lasMZye/ieOcuIW0GUuzyJgAu8hLLPtlLzyFuTyVMkZGwZvBW\nWqx9Cz+usZX6zOi8ntGfx5E9+4vVcZtmo//G3qy8tAyA8a9MpnupHi90TEcLiXnA7FO/8MuJnwmK\nCQLAgIHmRVrxVqV3qJCzUqKPdS74LEO3DOD4vaMAFPTyY1L9n6iVr06KxJ6WyY1j2mSxWei7sSdr\nLv8JwKc1v2BIxbcSvf+pU0bebBfD8tAGlOcENqOJ8FnziWvRKqVCTtOknvyTpsH+/SZm/2Lkx1Ul\nEu7nAsnP+rLvkn90dyrXcXPG4eLPFR4XRqc/23Dk7mGMBiPTGs2ibbEOeofl1F40wTKNHj3ageG8\nsNHR0XE4Oudzc4PcN45iunwRY1gonkRRjpO0Zzm3yMOS67XZutXMtGmubNtmJjQUcuXS/jMx0jTY\nudPEd4Pv8Nq4WjS9+ys+hGLDwJnynfFc8CO122ZLtXWsLoVcoN/G3iw6u4Ac7jko7F3EqdbncTZW\nm5VFZxfQa0N3NlxdS7wtDi9Xb0ZW+4hpjWbxcoFXkt3Kk5KMRgPu7q4ktZ4U9XkJs8HMXzd2cibo\nNN5u3snvSpfZk0y9OxEQ4oX3kZ0soDvv7WzPiRMm6tWzr3f21x93CWozlO5nP8WHUOIxY+nQkQ4T\nq+GR+cVWLtY0jc92f8iv5+YD8F7VDxhYYcgLHTMlZDK7UzNvbXqV6UtOj5yowecIiwvjwgOV/52Z\ny/5b+8jjmZeCWQr9a1212qxMPTaJ/ht7cTPyBmAfpzLX/1eK+qSvyXEcJbl1ROjLaDDSvHBLjt87\nypXQy+y4vo3s7r5UzJm4CVty5tSo2cCFN1a+SoOYteTS7mI5cQ5Lr56k6mrpaYTUk8diYmDJEjPD\nh2di4kQ3zp03E48LJY0qGxp+RZbFU6g6rAp5C5nTZHIVGR/Ja2s6cujOAQAmNviJjsqrOkfl/B7W\nkc+Tu3+GaMF6fHQN08ULuG7dhOvWzbjs+Ys/P9vDgiNl2bDBTHj404MWPUsXpHq7nLRsGZ8wTsRm\ng7VrzUya5MqxYyYM2DhKRcpykouVO+Hzw3sYSikpE/8zP5LG/87M5dPdHxD1xBShFXNW4r2qHzjd\nQqh60zSNrQGbGLP3U84GnwHAxehCrzJ9eLvyyBSZkMCRXuSpo6ZpvLnhDVZfXonJYGJxq+UvPLA1\nZv9J3plRjiWr7AOxcue2Ub18JD9tUMjLLQCu5KlBpvkTMZd3zMKFPx2bzOg9HwHweqmejKs3MU38\njsdZ41h24Q8mH/mRCyHnE7ZXylmZYZXepVnh5k/NoHYp5AJDtwxMuCjmy5yfH+tP4ZUCDVI99rRE\nnsynbdGWaLqu7sjum7sAmNTgZ7qU6Jbo/U+dMjKofShfhwzmA6+p/LTcm7JlZXbBv5N6ArdvwbKp\n95myrBD37z/+21u6tJUBb0bSuo0V9yxpZFHSfxFtiab72lfZdX07AN/Xm0CP0r31DSqNkC6CLyIq\nCtzdwWAgNtbeIrV6tQvr1po4EVqIAlznOOVYTzPO+TXBq1l11m1x58KFx1PDVK5sZUyLv6jWyBOt\nROolVgD3o+/zzrYhrL+6FoCcHrnw8yrMgdv7Et5TIUdF3qv6AY0KNU0TN6Ep6eS944ze+0nCHxqA\n1kXb8VGNzyjsXUS/wJLgRS+KEfERtFjaiLPBZ8iWKRsbOm6nkJffC8WkabBwoQsffuiWMKnLe3zH\nx6ZvuPP2GHxGvOGwJ8hLz//OwM32pQ6a+vkzp9mviV47x1nYNBtrL69m0pEfOPawyx+AkrUEQyoO\np22xDsw7NYuv9n9OtCUagK4lXmdM7a/xcpP+xs8jN45pX0RcOJ1WteHwnUMYDUZmNJ5D65faPX/H\nh06dMtKxozvBwUZ8fDSWLImiXDlJsp6UUeuJpsHhg3D8iw003j+WbARRnPPYjGaaN7fQt288NWqk\n7TVJH4mzxtFzXVc2B2wE4MvaY+lXfpDOUaUdkmClAOvV6/jWrYI59ulF46YwmKFMBgzUq2fhrbfi\nqF1bn4q45dpGhm0dxL1o+2QDzQq3YPwrk8meKTu7b+7i+4PfsPfm7oT3V8hRkXerjqJJoWYZLtG6\nHh7IN/u/YMn5xWgPB6tWy12D0bW+1G3GueRyxEXxSuhlmix5hdDYEEplL8Oa9pvwdPn3SSoSS1WN\nDBmSicBAAx+NjOT1FnchV84XPu4jO69v57XVHYi3xVM5V1WWtl6Vpid30DSNnde3M+noj08l/R5m\nz4QZLHN55Gb8K5No7NdMpyjTnox645jehMQ8oN3KlpwOOonZaGZes4VJqgeSZP23jFZP4uLgz+UG\nAsatpNu1byjD6YTXprdYQtUxTSlQIP18D9GWaAZu6sPaK6sA+LjGaIZVekfnqNIWSbBSSkwMLvv3\nYt68CdvaLXgFnuWBKTsDm56nz9tulC+vzx/qaEs0Y/Z+wqyTMwDwMHvwRZ2xdC/Z4x+J0+4b9kRr\nz82/EraVy1GBEVVG0dTPP90nWmGxoUw8Mp4ZJ34i1hoL2McifVJjDP6FW6TJz++oi+K2gC28tqYD\nNs1Gm6LtmdFkjkO+D02zd6N19PofJ++foM1yfyLiwynq8xKr221y+u6cSXHkziEmHfkx4WII0KFY\nZ76u+53TTbTi7DLajWN6di/qHm1X+HMh5DxuJjcWtlhC3fz1Er3/6dNGOnR4ItwusBYAACAASURB\nVMn6I5IKPlewFfJLuaDTiIxST+7cMTB/vgvz5rnw091OdGBZwmvXijXAbcy7mBrUIT00WVlsFnZd\n38HSC7+z9vJqIuLDAXi3yvu8X+0jnaNLeyTBSiXG64GYjxwivmYdtBw5dInh5P0TDNrUB/XBOcA+\nzurnRjMp8pzB7rtv7GLcwbEJfdoByvqWZ0TVUTTza54mE43/EmeNY+6pmYw//B3BMcGAfWbAEVU/\n4PWSPXExpa1Fj5/kyIvi1KOT+HzvxwB8XONzhlV62xEhOty1sKu0WNaYu1F3yOmRi7XtN1PQq5De\nYaWI88Eqi9WFVM9TgyZOMOV8WpRRbhwzilsRN2m9ohnXwq7iYfbk91YrkrTm2+nTD1uygmC661B6\nmRcQvuJPLBUSP4tnepTe68mxY0ZmzHBl5Upzwpqonfid33mVW1Wa4zbmXaxVquoc5YvTNI3Ddw6y\n7MIfrLi4jPvR9xJeMxqMDK88gverfpTu7vNSg9MkWIqiuAKTgAZAbiAY+B34RFXV2EQexmkTLD3Z\nNBs/H5vC1/s/J94Wn1Bp3q38fpKShT03/mLcobH8dWNnwrayvuV5t8r7abZF50maprHq0gq+3Dea\nq2FXAPtCrwPKD2ZIxeFkcfXSOcIX58iLoqZpDNz8JssuLMGAgUUtl9CgYGMHReoYQdFBtFzemEsh\nF8nskoWV7dZR1rec3mEJJ5bebxwzooCwa7Re3oybkTfwcvVmWZtVlMtRIdH7nz5tZEj7B2x5UJlc\n3CU+sw/hK1djLZtx/5akx3oSHw+rV5uZOcPMwcOP7428vDS6do2nd49oisadw1qylI5ROoYafI5l\nF35n6YUlBIRdfeq1Sjkr075YJ9q81J5cnrn1CTAdeNEEy5Fzl5qBe0ALwBuoiz3Z+jaxB7h06dJT\n5StXLmf48o3w63T8szWf7/2YeFs8BbMUYmXb9Yyq9jHXAwKTdLw8cXlZ1mY1K9uuo24+ezeLk/eP\n03N9Vxr+UZc5e2di02yJPp4zlfff2kfDRXXps7EHV8OuYMBAy3xt2Nv1CB9U/5Qsrl5OFa8zlK9e\nvcL4V6ZQxrccGhp91/fkcshFp4nv7MXTdF/bmUshF3ExujC2wrinkiu945OylKWcOuWCXoWYUGkq\nvu45CIsLpfOqtmw5sTHR+5cubePDKZF08N7EfbLjEhGCR5uWmM6ecYrPJ+UXK9+/b+DTTyNoUDGO\n6/2/Z8Hh0mQmnGLFrHz7bQzHjkXQq9dZ/IoaE5IrZ4o/seXr4YFMPjqB+otrU/e3avx4eFxCclXI\n04/3q33Evm5HWd9xG429mj2VXDlD/Gm5nBwp2kVQUZT+wEBVVRP1qMlgMGhBQeEJT1Ny5vTi7t2w\nhNczXLm+F97dfQiNDbFvOAaXplxPaIl54eNX8aLup688NcC+dPayvFvlfZoXaUnuXD7O9X08o7z3\n/GG+2Dv6qbEr9Qs05NOaX1C/VC3d43N0OSgoPOGpY/bsWRxy/MDwAJr8UY+gmCCUrCVY12ELmV2z\n6Pp5LTYLed/OBg8n5vy50UwG1umj+/cvZecvP3oybzAYnCIeKTuuvO3MHtqtbE5IbAiEw8kh5xNu\nIhOz//btEXzWRmVZaCOy8YBYnxxErlmHtVhxp/h8qV3WNC2hBcsZ4klqecuWCGbOdGXn0gcMipvA\nEKbghX3c0XsUY8TtwwkT2DpDvMkpB0UHserSCkb+7234W8/4PJ55aVesIx2KdaJh6bpOEW96Kj+8\n30p2C1ZKz2/cEDie6HfXgIsh53nJp3jCJpPp6c+WEcphcWG8v30EdILQ2BB83LLyQ/0JvDm6Bz6z\nvJ+7f6LLAbCi3Sr23dzDdwfGsiNwG6eDTtJ7Q3dKZy8DJcFg1J5am8cZvh/A3s+4OdT9rToWm8X+\n4m1Y0n8l9Qs2eO7+abVsNBqe+q8jju/nU4hZ/vNpu7QF6oNzDNnan3nNf02Vz/OssqZpjNrxTkJy\n9XntL+lc8lUG0kf371/Kzl9+VDecJR4pO65cLldZ/mizgrbLWxKZJYJxh75hfINJid6/bFmNL1eX\noFPLjSwNbcSNsFwE38xG6RKO+3ualspAmqsvFgusXWsCdtCwoSd9+IXzvIUH9iUtrG7uxPfuzcKf\np/KBi/7xJqccERcBZaH72k5sDdhiv8d5mFz5uGWl9UttmP/eXE4cOuuU92fppfxk3UgWTdOe+694\n8eJzihcvbitevLj14X+f/GctXrz4mGfsM7x48eK3ixcvnj8x59A0DUajGUYbtA6LO2iHbhzSLl68\nqD0pI5T/uvaX5jfBT2M0GqPRGsxroAWGBqbK+RfvWaw1nt844dyMRiv7U1ntj9N/aFab1Sm+n8i4\nSO2rnV9pWb7OkhBj/vH5tblH52rqeVX3+NJy+ZPVnyR8p2O2j9EtntHbRifEMXzdcM1ms6Xq+aUs\nZSk7d3nc7nEao9FMn5u0s/fOJnn/kyc17ZUs+7Xs3NN8fDTt4EHn+nxS/mf54MHL2tixmlaggKbZ\n56u1/+uSb6emgWbxzKxpH36oaXfvOkW8SS2fUc9oq9RV2mtLXtM8vvJ46j7M/Ut3rcWcFtrKcyu1\nmPgYp4g3A5UTlb8861+iuggqiuIBZPqPt0SpqhrzxPvfBt4DGqqqejaxyV7BHwtqgWGPxxXVL9iQ\n4ZXfpXa+Oml+AobnibfG8/3Bsfx4aBw2zYar0ZWPa37GwIpDnnpCkRoO3trPdwfGsjVgc8K2ktlL\n8V7VUbR6qU2qxwNgtVlZrC7i671fcCvyJgCZXbIwvMo7DKgwGHeze6rHpAej0YCPjychIZHYbI7t\n3qtpGkM2D+C3cwsBWNDiN/yLtHDoOZ7nf6fnMnzrUADavtSeX5rN0eX3TaRdKVlHhHOIscRQfUEl\nrocH0qJIK+a3WJjkY5w9a6Rt20zcv2/Ey0tj6dJoKlWypUC0zimt1JMzZ4zMmOHCH3+YiYl5fB9Y\nv76F/v3jadjQSqZF84lv0QrNJ6uOkSadTbOx7+Yelp7/g5UXl/Mg5kHCayaDifoFG9KheCf8i7Qg\ni2sWHSPNmB7WkWQnHw4fg6UoyidAX6CBqqoXn/d+IYQQQgghhEgvHDoGS1GU74FOQD1VVa848thC\nCCGEEEII4ewcuQ5WQeAqEAvEPzo+cFVV1bIOOYkQQgghhBBCOLEUnaZdCCGEEEIIITISGT0uhBBC\nCCGEEA4iCZYQQgghhBBCOIgkWEIIIYQQQgjhIJJgCSGEEEIIIYSDSIIlhBBCCCGEEA4iCZYQQggh\nhBBCOIgkWEIIIYQQQgjhIGa9AwBQFMUIfAv0ANyAjcAAVVWDdA1MCCehKMocoBsQg30Bbw0Yqarq\nNF0DE0IniqK8CgwGygPuqqq6/u31N4BPgdzASWCwqqpHUj1QIXT0X/VEUZQewGwgksfXlVWqqnbT\nI1Yh9KAoyligJVAACAfWAu+rqvrgifck+XriFAkW8AHQCqgKBANzgP8BzfUMSggnM1dV1X56ByGE\nkwgGpgIewPQnX1AUpQ7wE9AG2AkMB9YqivKSqqoRqR2oEDr613ry0CVVVYunbkhCOBUL9gfYpwAf\n7PnHXOzXj2RfT5wlweoLjFZV9RqAoigjgYuKohRQVTVQ39CEEEI4G1VVNwEoilLvGS/3AZaqqrrl\nYfl7RVEGA+2wXzyFyBCeU0+EyPBUVf34iWKQoigTgcVPbEvW9UT3MViKongDBYGEpjZVVS8DYdib\ntIUQdh0URbmvKMo5RVG+UxTFU++AhHBS5YHDf9t2DLmmCPF3BRRFuakoyjVFURYpiuKnd0BC6KwR\ncPyJcrKuJ7onWEAW7P1+Q/+2PQTwSv1whHBKk4ASqqr6Yn9qUg+YoW9IQjitLMg1RYjn2QGUVVU1\nL/YhGjHAJkVR3PUNSwh9KIrSAegHDHtic7KuJ86QYIVjH1zp/bftPthbsYTI8FRVPaqq6r2HP5/F\n3ge4o6IoLvpGJoRTCkeuKUL8J1VVr6qqevHhz3exD9fIA9TQNTAhdKAoSifs4xRbqar6ZAtWsq4n\nuidYqqqGAgFApUfbFEUpij1jPKFXXEKkEQa9AxDCCR3niWvKQxV5utuHEOLZ5LoiMhRFUXoBPwMt\nVVXd+beXk3U9cZZJLmYA7yuKsh14gH3K9vWqqgboGpUQTuLhVLvrVVUNVRSlGDAOWKmqapzOoQmh\ni4fLe7hgX9oDRVHcAFRVjQV+AdYpijIP2I29xdcVWK5PtELo47/qiaIozYHjqqreUBQlGzAWuAfs\n0yteIVKboijDsE/B3lRV1b+PtYJkXk90b8F6aCywCjiIvTVLA17XNSIhnMsA4JKiKOHAemAP0Fvf\nkITQ1etANLAOMD38OUpRlIKqqu4GBgEzsT+0aw/4yxTtIgP613oCvAIceHhdOYm921NjVVWjdIpV\nCD1MwN5rbpuiKGGKooQripLQ/S+51xODpmkpGLMQQgghhBBCZBzO0oIlhBBCCCGEEGmeJFhCCCGE\nEEII4SCSYAkhhBBCCCGEg0iCJYQQQgghhBAOIgmWEEIIIYQQQjiIJFhCCCGEEEII4SCSYAkhhBBC\nCCGEg0iCJYQQQgghhBAOIgmWEEIIIYQQQjiIJFhCCCGEEEII4SCSYAkhhBBCCCGEg0iCJYQQQggh\nhBAOIgmWEEIIIYQQQjiIJFhCCCGEEEII4SCSYAkhhBBCCCGEg0iCJYQQQgghhBAOYtY7ACGEEMKR\nFEUxAf0AExAP+AEfqqqq6RmXEEKIjEESLCGEEOnNSGCGqqpBAIqiLAb8gbW6RiWEECJDkC6CQggh\n0g1FUXoBsx8lVw8VA4J1CkkIIUQGIwmWEEKIdEFRFBfAVVXVO09sawLcVFV1n36RCSGEyEiki6AQ\nQoj0oimwRVEUT2AWEA28BHTRNSohhBAZiiRYQggh0otiqqqufvhzFwBFUYYCXwC9dYtKCCFEhiJd\nBIUQQqQXtmds8wAqp3YgQgghMi5JsIQQQqR5iqJk49kTWVQEAlI5HCGEEBmYdBEUQgiRHtQD7j+5\nQVEUL6AV8JouEQkhhMiQpAVLCCFEepAHKPu3bWOB/6mq+qcO8QghhMigpAVLCCFEeqABqxRFGQHE\nAgWAE6qqTtM3LCGEEBmNJFhCCCHSNEVRfIH7qqqeBc7qHY8QQoiMTboICiGESOteAf7SOwghhBAC\nHNyCpSjKWKAl9q4Z4cBa4H1VVR848jxCCCHEE/KoqnpL7yCEEEIIcHwLlgXoBmQDygP5gbkOPocQ\nQgiRQFXVyXrHIIQQQjxi0DQtxQ6uKEpTYLGqqj4pdhIhhBBCCCGEcBIpPclFI+B4Yt+saZoWFBRJ\nSiR996Lu8crimtyLvkv5HBVZ034TriZXh5/nv3y46z1mnpwOwNSGM+ikdEnV84u0z2AwkD27JylV\nT/7NkvOLGbS5L+5mdy68GZhqdWffzT20XtEMgJlN5tH6pXapcl6RdulVR9K6GEsMNX6tyM3IG3Qo\n1pmfG8986vUroZfZfG0DG6+uZ8/Nv4i3xT/1eiEvP5oUakZjv2bUzFsbN5NbaoYvkkjqiUhJJWb7\nERwTzKQGP9OlRDe9w0kWg8GAr29mQ3L3T7FJLhRF6QD0A4Yldp/Lly9jNhswmez/AgKuJPz8ImWj\nEYZvG8i96Lt4ungyo+ks3F3dHHb8xJb7FOhLnXx1AXh3+zA2nFiTqueXctovm80GDAYDZnPqnv/A\n7X0AVM5VBXdXt1T7vLUL1KZhwcYAfLlnNJrB6lT/P6TsfOVHdSQw0DniSSvlSbvHcTPyBiaDifdr\nfPCP102hBgZUHMSydn9yoe81vqv8A11LdieHew4AroVd5ZeT0+i8qi0lZhfm1WXt+E1dQFDsPaf4\nfFJ+uhwYeCXhWuIM8Ug5/ZSjrBEExwQD4Ofjp3s8yS2bzcnOrYAU6iKoKEon4GegvaqqOxMdjMGg\nPRmPwWDAEeXJ+yczbL09z5vdeja9KvZy6PGTUr4bcZeqv1TlWug1CIXbY26TK3Mu3eKRspQTUy77\nc1lO3T3FR3U/4ssGX6bq+Q/fPEyVX6oAMKfNHHpW6Kn79yFlKaenclR8FJ4fekJm6FWhF7PbzE70\n/jbNxqGbh6j+enUqvlqRo7eP8nfV8lXjwP8OcOS3I1TIXQGDweBUn1/KUpay48on7pyg/LTyAFwb\nfo2C3gWdKr4klpOdZTm8i6CiKL2A74GWqqruS+r+ISGR2GyPP2RwcMRTrye1vOv8Pt7b9J69cApa\nD+n41Hte9PhJLZti3ZnnvxD/JY2I9o6m7cJ2LG+3OqHLVWrHI+W0VQ4JicTHx5OQkMhUO39IzANO\n3z0NQPmslVO9/hTOpNCqaBtWXVrJp1s/o2m+Vgndj/T+/yFl5ysbjQZ8fDydJp60UJ5yZCJkBrPR\nzNBy7yRsT+z+L7mXgm2weclObkTcYPPVDbwz7S3cS7sTbYnmwI0D0AAqzahEbs88NPVrBsXh+p27\neLh46P75M2oZnr7n0jseKaeP8onAMwC4GF1wj/dO8t8TZyk/ut9KLkdP0z4M+BRoqqrq4aTuf/Hi\nRWw2DavVXtn37z+W8HNyyjv27KPv+p7EWmPJn7kAc4b/is0G4JjjJ7dcKltZJtb/iX6berHv1l5G\n7RjJ9/V+1C0eKaed8qMLoc2mpdr599/cj4aGAQOVclR1WP1MSnlk1Y9YfelPAsMDmHdyLm+W7ecU\n/z+k7LzlQ4eOO1U8zlqOiAtn0uEfAehWsgf5Mxey1/tkHi+3e166l+xF7eH1yF0gD7tv7GTj1fWs\nu7SGOzG3uR15i3mn50BXKPZLIerke5nGfs1YuX2dU3wfGaV86JB9ePyjey6945Fy+ilfDbkKQL7M\n+UEzptnfrycbe5LDoV0EFUWxAfFA7KPjA5qqql6JPIQWHBzx1Id8Ee/vfIc5p2ZiNBhZ0XYdNfLU\ndMhxHeWLvZ8x+aj9wjau3kTeKN1L54iEszOZDGTLlhlH1pPn+Wrf50w88gOlspdh+6t7UuWczzJk\nS39+VxeR0yMXB7odf+rJtxCP6FFH0rIfD33PNwe+wM3kxv5ux8ibOV+KnEfTNM4EnWbTtfVsvLqe\nw3cOovH0/59S2cs8nCijKZVyVsFkNKVILELqiUg5H+0ayS8np/Fy/vosab1S73CS7WEdcY4ugqqq\nptikGUm17soa5pyyz4L0TuWRTpdcAXxY/VNOB51ka8BmPtg1AiVbSarnqaF3WEI85dEEF3r/bo6o\nMoplF/7gbtQdZp2awdCKw3WNR4i0LjQ2hJ+O25cQe6NUrxRLrsA+pqG0bxlK+5ZheOUR3I++z5Zr\nG9l0bQNbAzYTER/OmaBTnAk6xYQj48ieKTsNCzWhSaFmvFKgAV5u3ikWmxDCcQLCrwFQyKuQzpHo\ny2kSIke6FXGT4VsHAVA1d3XeqTJS54iezWQ0Ma3RLAp7FyHeFk/v9d25GXFD77CESBBnjePoHXtv\n32q59U2w/LwL071kDwCmHPmRsNhQXeMRIq2bdnwqobEhuJvdGVb53VQ9t6+7L6+W6MrMpvM41/sK\nS1uvon/5wRT2LgJAUEwQv6uL6LOxByXmFKbDylZMOz6FyyEXUzVOIUTSBIQFAFAwiyRY6YpNszFk\nS38exD4gi6sXPzeaidmY0st9JZ9PpqzM9/8NT5fM3Iu+S6/13YixxOgdlhAAnLh3jBir/fexuhO0\nAr9TZSSZTJl4EPuAn49P0TscIdKs4Jggph//CYDeZfqRyyOXbrG4mlypm78eX9T+hv3djrG362E+\nr/U1dfK9jMlgwmKzsOvGDj7d/SE1Flai5sJKTDz8AzbNplvMQoh/0jQtoQWrgFdBnaPRV7pLsKYe\nm8SuGzsAGFdvAgXTQBOlkq0EPzX6BYCjd48wYsdbOHJsnBDJtf+WvXtgvsz5yZ+lgM7RQG7PPPQu\n2w+wP30Pig7SOSIh0qapRycRER+Op0tmhjhZd9uiPsUYWGEIy9qs5lzvK8xoPIeOxV8lq1tWAC6F\nXOSr/Z/z27lfdY5UCPGk4JhgIuPts/FJC1Y6cuzuEb7ZPwaAV5WutCvWUeeIEs+/cAtGVv0QgN/V\nRcw48ZPOEQkB+2/vBaBa7uo6R/LY0Ipvk9klC5HxEUw6Ml7vcIRIc+5G3WXWyekA9Cs3gOzu2XWO\n6N95u/nQtlgHfmr0C2d6XWZVu43UzFsbgGnHp8jDSCGcSEDY1YSfC3r56RaHM0g3CVZEfAT9N/XG\nYrNQ2LsI39T9Xu+QkuydKiNpXrgVAKP3fMzO69v1DUhkaJqmcfBhC1Y1J+ge+Eh29+wMKD8YgDmn\nfuFWxE2dIxIibZl89EeiLFF4uXozsPxQvcNJNJPRRPU8Nfi4xmgAzgWfZcf1bfoGJYRI8Kh7oIfZ\ngxzuOXSORl/pJsH6aNdIroRexmw0M63RLDK7ZtE7pCQzGoxMaTiNEtlKYtWs9N3Qg6uhV/QOS2RQ\nl0IuEhRj74JXzclmtxxYYQhZ3bISY41h/OG09zBFCL3cirjJvFOzAHs98smUVeeIkq5q7upUzlUV\nsLdiCSGcw7Wwh+OvshTEYEj2DOfpQrpIsFZcWMqicwsAGFXtEyrmqqxzRMmX2TUL8/wX4e3mw4PY\nB/RY15WI+H+uvi5ESns0PXtmlyyUylZa52ielsXVi6GV3gHg17Pz5EGEEIk04cg4YqwxZHXLSr9y\nA/UOJ9ketWJvDdiMGnxO52iEEAABDxOstDD/QUpL8wlWQNg1RuywD9Ctm68eQyq+pXNEL66wdxFm\nNJ6D0WDkbPBp3to6SPqZi1S3/5Z9/FXV3NWccsHP3mX6ktMjFxabhe8PfqN3OEI4vcDwABacmQfA\n4IrDyeLqpXNEydeiSGvyZ7ZPvCNjloVwDgHhVwFJsCCNJ1gWm4VBm/sSFhdKVresTGk4HaMhTX+k\nBPULNuSTGvYJO1ZdWsHEIz/oHJHIaB4lWM7WPfARDxePhDXulpxfzLngszpHJIRz+/HQ98Tb4vF1\nz8GbD2fjTKvMRjN9yg0A4A/1N+5H39c5IiFEYPijNbD89A3ECaTpbOTHw98ndGP6sf5U8mTOq3NE\njjWowlA6FOsMwDf7v2DT1fU6RyQyintR97gceglwjvWv/k33kj0omKUQGhrfHvhK73CEcFqXQy8l\ndKV/q9I7eLp46hzRi+te8g08XTITY41h3ulZeocjRIZm02wEPlxkuECWjL0GFqThBGv/rX38cOhb\nAHqUfpPmRVrqHJHjGQwGxtefTLkcFdDQGLC5DxcenNc7LJEBPHpwYTaaqZjTecc0uppcGVF1FABr\nLv/JsbtHdI5ICOf0w8FvsWpWcnvmoUfpN/UOxyG83LzpVvJ1AGaf/IVYa6zOEQmRcd2JvE2cLQ6A\nQtJF0PEJlqIoryqKslNRlFBFUeIcfXyA0NgQBm3ug02zoWQtwee10u+Ta3ezO3Ob/Yqvuy/hcWH0\nWPcaYbGheocl0rlH3QPL+pZz+ifdnYp3oZhPccDe0iuEeNqFB+dZeuF3AIZXHkEmcyadI3KcPmUH\nYDQYuRd9l+UXlugdjhAZ1rWHU7SDjMGClGnBCgamAimyNLymaby3YziB4QG4mdyY1ng2Hi4eKXEq\np5E/SwFmN12A2WjmYsgFBm7ug9Vm1TsskY4dvO1861/9G5PRxKjqHwOwLXALe2/u1jkiIZzL9we/\nxqbZyJ+5AN1KvqF3OA7l510Y/8L2HizTjk+VCaGE0MmjRYa93XzwdvPRNxgn4PAES1XVTaqqLgYu\nO/rYAIvVhay4uAyAT2uOobRvmZQ4jdOpkbcWX9X5DoBN1zbIeBORYqLiozh+7xgA1XI75wQXf9ei\nSGvK5agAwNf7x8hNlhAPnb5/KuGa+W6V93EzuekckeMNKD8EgDNBp9h1Y4fO0QiRMSVM0Z5FWq8g\njY3BuhxykVE7RwDQsGBj+pQdoHNEqatn6TfpXrIHYF/L5M+Ly3WOSKRHx+4ewWKzAM47g+DfGQ1G\nPqhmb8Xaf2sv2wI36xyREM7hu4NfA+DnVZjOyms6R5MyquWuTsWclQCYfnyqztEIkTEFhMsaWE8y\n6x3A3xmNz175Oc4ax4DNfYiyRJLTIydTG0/HbE5T+aEDGPiu/g+oD85y8PYBhm0dSPHsxTNMK554\nXD/+rZ44woE79u6BRbyLkjdL7hQ7j6M1LtyEGnlqsu/WXr7Z/wWN/Bpn+JXkM6LUqCNpxbG7R1l3\nZTUAI6t/QCZXV50jSikGBlUcSt8Nvdh0bQOXQs9TPJuid1BOTeqJcLTAhwmWn3chTKa0/3v1onXD\n6RIsH59nD6gftXlUwgxh89vNR8lfODXDciKZWdl1BVV+qcLN8Jv0WNeVg30Pkt0ju96BiVT0b/XE\nEY7cPwBAXb86ZMuWOcXOkxK+bTqWenPrcfzeMbbf2UiHUh30DknoJCXrSFrxw/qxAJTwLUG/Gr2d\ncsFwR+lRtRuf7/2E62HXmXduJj+3/FnvkNIEqSfCUa5HBAJQMreS5u4dUoLTJVghIZHYbE+Pn9gR\nuJ3vdtvHHw2qMISq2WoTHByhR3hOwY0szG32K62WNeNKyBXaLerAkjYrMBud7n+ncDCj0YCPj+cz\n64kjWG1W9gTYZxCsmL1KmqtnZbJUokHBRmwN2MwHmz/k5ZyN0vVNpfinlK4jacXBW/tZe2EtAO9V\n+YDQkGidI0p5fcr2Z/TuT5h3fB7vVhxFNnd58PhvpJ4IR4q3xhMYZk+wsptypbl7h2d5VEeSy+F3\n5IqiGAEXwO1h2Q1AVdVELVBhs2lYrY8re1B0EIM29UNDo4xvOT6o/tlTr2dUFXJU5vt6Exi2dSC7\nru/g010f8UWdsXqHJVLJ3+uJo5y+f4awOPsyAFVy1kiTdW1UtY/ZGrCZCw/O89vZRXQp0U3vkIQO\nUqqOpBVf7fsSgFLZy9CicJsM8V10K9GD7/aPJcoSyZyTsxleeYTeITm9FmiaOwAAIABJREFUjF5P\nhGMEhAZi02wA5M9cSH6nSJlJLl4HooF1gOnhz1GKoiR5WWdN03h7+xBuR97C3ezO9Maz0+UMSMnV\npUQ3+pUbCMD0Ez+x+NxCnSMSad2jBYazZcpGsazFdY4meSrkrESLIq0BGHdwLHHWFFmOTwintefG\nX+y6vh2AkVU/xGjIGOOVvd186FqyOwCzTs6Qui9EKgl4Yg2sAlmSfLufLqXENO3zVFU1qqpqevjv\n0c8BST3W3NOzWH9lDQBf1vk2zd7wpaTRtb6ibr56AIzY8RZH7hzSOSKRlj1aYLha7hpJniDCeu0G\nwTU6ovmV487rn2A7cgJ0mi79/WofYcBAQPg1Fpydp0sMQuhB0zTGHrC3XpXPURH/wi10jih19S03\nEAMG7kTdZsXFpXqHI0SG8GiK9hzuORO9Nm1ICMSl42cgTvtY61zwWT7b/SFgX+Pm0fTk4mlmo5kZ\nTeZSMEshYq2xdF/7Kqsv/SnrAIlkOXDL3oJVNYnTsz/433oy1aiDcnkjOaOuUmbDRHI1q8NX/W7z\n118mbLaUiPbflchWko7FXwXgx0PfExUflboBCKGTHde3se/WHgBGVfsow82kWdi7CM0eJpWy8LAQ\nqSNhDaxETtF+9KiRSpUy4++fuGQsLXLKBCvGEkP/jb2JscaQ1zMf41+ZlOEuEkmR3T07c/0X4mH2\n5H70PXpv6E73tZ259nBVbSES40b49f+zd95hTV3vA/9khz0VGYIbF27cA2fVuvceVav9uWpr+61d\n2qld1i73nrhXraPuLU7cqKgIqMgMBMi+vz+iUXqxLhC0+TxPnpCT9557csnJPe95ly0LUJ1i9Z76\nuDWrZVz7cAnu5mTScGO510huUILD1OOXjeXo0sWR6tWdmDhRxblz0pdm1PogdAJyqZyErLvMPz/n\n5ZzUjp0CRBAEphz7CoBaPrVpFtiygEdUMIyoOhKA80lnOXz7YAGPxo6d159bGTcBCHoKBSs7G0aN\nUqPVSpAWSi0kbyiUH+2rI59zKeUCEiRMbzEHD7VnwQ7IbMZy7CRJE2eREBFbsGN5DJW9Q9jVYz+N\nAsIA+DtmO43D6/Drqal2P3Q7T8WD+CuVTEXVotWeKK/VwsiRav5vpCP9zQv4U9mZ/dMO0/LSZNJP\nn+XQ+HAqVzYDcOeOlBkzlDRv7sSI0EskNBpI2sI/Qf9UuW+eixJuJel73/L926mpZBjS8+1cduwU\nBv6O2capeycB+KjOp//Zjcm6vvWpWqQ6ADMjfy/g0dix8/oT88CC5VLiibKTJ6u4elWGVCowZYou\nn0dWcBQ6BWvHjW3MOTcTgHdrvk99/4YvfxCCABcvk/j5LBIb9kNdvCQ+7ZtSYcYHtGvnSLVqTgwf\nrmbePAXnzkkxm1/+EHOjtHtZ1rTfyIwWc/F2KEK2KZuvj06i+aqGHLl9qKCHZ6eQ8yD+qlrRGk9M\nJnPmjJTmzZ1YvVoBQEgTN0qcXEy9PsUB8POHQR96sHt3FgcOZDJunJ7AQKufYNitpVSOWk/ZD/ug\nLFGO2Pbvk7njaL7Ea71X8wPUMjWp+lRmnLEvtOy8vgiCwHcR3wJQ36+hLTb3v4hEImF41f8DYMfN\nbUSnXS3gEdmx83oTm2FNs/AkF8GjR2XMmmVdN4webaBmzZccP/ASKVQK1l3tXUbvsmbFq+lTi/G1\nJry0c1sscPGilFmzFPTv74ChaWcqzvyAilc24WJKA+AywcQQxO3bUtavVzBhgprmzZ0ILuNAVona\n3Gk0iNv/m4nx2BkKSuuSSCR0LdeDw71PMKjSECRIiEq9TMcNbRi7+/9Izk4ukHHZKfxE3D0G/Lt7\noCUjk4WTk2jb1pEbN6TI5QITJ+pYuTIbH5/cFaTgYAsTJhg4fjyTP//MRNGkDgflYQC4mVOpcWwO\nJfq1YkXjRaxZI0ebh+UzfJ39GFx5GGCNx7B//+28rmy5vplzSZGAtVTBC1mvtFokKcm89ODJPKRD\n6c74OvkhIDD7rL3osB07+UW2KZt7WQnAv2cQ1Gph9Gg1giChQgUz48e/3t5VksIUANp6aWthe/R2\nnBUu7O5xkBJuJfPvZPcSSVt/gD3ZdfnrQikOHZKRlPRQ31zIQN5kC0cdwkio1BR120ZU6FCSuwlS\nIiJkHDsm4/hxGcnJUqoQSSQ5Xaq0UheuFQ/j5Kfh1K5joVixgrnOJxOO88G+cZxPOguAh8qDz+t9\nRe8K/f4zqXtfJ2QyCZ6ezqSkaPO0zkSGIZ2y8wKxCBaWtl1JqxJtRDJp+y+gHDCY21nuNGY/ASVk\nzJqVTfXqz74IMxrh+NrbZMxaQ42LyykvXCKAOO7gh6OjQOvWJrp2NRIWZkaheLHPlpydTK2lIWQa\ntfxftTFMqv/1i3Vop1CTX3OkMGO2mGm6qj6XUy4RVrwZq9pvePZOjEaUO3egWL4M9c5tSM0mtN6B\n7F1wCTc3ATc3AVdXAUdHkGZoUK9YisXLG4unF4KXFxZPLyxe3uBYeILWfz01la+PTsJR7sjpARcL\nPtygEPFfnCd28ocrKVE0DA8F4FjfM5R0K5Wr3P/Gy7m9eB+75G+wfXsWISGFewPn/hx57p2qQqVg\nSb6QCAB/NJ9N9+Beedt3RjraLYfQrD+Ax6m9BGrOAzCWafzKWJuct7eFhg3NNKuZQp0WDpQoJeFx\nG4GCANHREs7vSkK1fi1Fow5TPfMgPtwDYC9NaMpeAAIDLdSpY6Z2bTP1qmZQtngWEq+X82NvspiY\nd24WUyK+IdNoNQ/ULlaXH5pMo4JXxZcyBjt5Q37dFPfc2kXPPzsDEPXWzZwLEUHg5oSFhMz/EDV6\nTMj4Nmwr/efXxdn5xc+tzRA4svQWCw6UZ88eGWbzwwnn7Wlik/sA1J1b4D+yLRLn56uq/l3EN/x0\n4jvUMjUR/SIp5uT74gO3Uyj5Ly4c111dzYi/hwCwretuavjUeqbjJdev4/JGC1SapBztp6hOTU7l\naJPJBOo5RXIgvbqonzvuwfw8LNKmjLm6gpubgJc5gVI7F6Dw9UTh542kyH2FzLsIgrf3M37apydV\nl0L1xRXJMmXxad1JjKnxXr6d61WjsM8Ti2CxbwK/IuyM2U6fLd2RSqTEvp2IQibeFd27V8axHtP5\nkQ+ILN8dv10zeeHd03zmRRUseV4OJi/oHtwrz5Sr1FQ4eFDOwYMyamycwaiUb3K8r0dJgDKBN5qa\naNTIRMOGZsqXt9zPavLkXTiJBMqUEShTxguGvw28TeI9OPTnTbK2HyHylheKWwJGo4Rbt6TcuiVl\n9WoFXdjCWrpx06kSCcH1UTSth0/XOijLFM+Tz/1P5FI5w6uOpH3pTnx2aAKbozcQcfcozVc3ZETV\nUbxf6384KZ5v4Wrn9eDYXWv8VXnPCjmUK8O9NBLajyX0xnoAbkkCOfHeQt7537Mt4P4NZxcJLd8J\nouU72SQlSdi4Uc66dQqOH5dROeUA9VJWwE8ryJzqxMXyHXEY2hOf3o1A/vQ/X+9UHcW8c7NI06cx\n9cT3fN/k5zwbvx07BYnJYuKH45MBaBXU+pmUq8uXpaxZI2fdmkoc1DgSBOwhjEUMJNapPFlZwD/W\n3mazhKx0M1GUw5skvEixvXctrQg//CCO36zLXY7wlaj9groGQ6oew82N+wqZ1VIWINyiYeQsBG8v\nJEU8kfl4o/L3RBlUDMfyAaj+PUTUhofak57l+7Dg/FzmnpvFiKqjUMqUT3197BQM6XoN7da3wmwx\ns737XpwVebCTZyffeJDgws/JP1flKj0dZo28whY+AaBsiILMQq5c5QWFyoK1I3qHUM2tNhJB9uwH\nm0wYj54m6kQWa9JaceCAjPPnpQiCVflswl520ZzTkppEBYRhaNgE/x61CamjfpZ12jOTnQ2RkVaX\nwogI62Oi5j3GMU0ku8RnHEe7TqF2bauly9s7f/43O2O289GBD7h1P417gHNxvm30A61Lts2X89nJ\nO/Jr17HLxnYcjN9P/4qD+SnsFwCuXZOws+siPrszCoDdbh1xW/0rgdU88uy8/0ZMjITjv52iwtop\nNMzcgZyHcY17XNqz771VdO5sws/v6a7Db6en8dWRz5FL5fzdbT+VvCvn19DtFCCFfWc+rwm/vIwx\nu62xy7u6HyCkSNXcBY1GlLv+5nbxUFbt82PNGgXnzz+814axB1W54tTrE0DnziZ8fQUEATIzQaOR\noNFISE+XkJ7OI39LyEg1Y0lKQZKcjDYDzlkq35eH9HQJBoOEOhzld0ZRhES8ScIJa1267bSiNdtF\nQ23GLnbRQtS+n0Y0YT9qtUBgoIUBA4z06WP8V0t6dNpV6i+vhYDA9BZzbPXx/usU5nky+diX/Hzy\nRwDmtFpIxzJdCnhEdv6NiYc+YUbkb9T3a8iGTn+J3n9/lITxq+pThXPoigWiPXgIwdWtAEb6bLxW\nLoKA8NSTXRAwR14kMXw/0r37CYo5gLM5nTNUpTpnbGIymUCNGhaa1M8mrJaGKk1cUavz8RM8AYsF\nok9rub32BJJDh/G/foSq+mM4oGMgC1nMw4LKpUtbqFPHRPuiR6hc0UTRNtWQqPJm9y3LmMW0kz/y\nx5lfMFqMALQu+SbfNvyeAJf8saTZeXHy46ZoNBspO684WaYsfm8+i+7lerNihZyPP1aTnSWwhm6Y\nmzSh/tLBKFUvP+2zIEDUgSTuTNtAmWPh1DBGMJyZzGY4EolA/fpmunY10a6dEXf3x/eTZcyi9rKq\ntmDcpsWbM7DSEFqVaI1cWuiM+Xaek8K8cMxrjGYj9VbU5Fb6TdqV6sj81ktEMrLz55AtWYZi9Woc\ntYl8KPmOH4QPbe/7+Vno2tVIt24mKlTI+5gInc6qkGVkPFTUspKyMd5JJjND4Ja0RA6FTaOBMgmH\nGXnnc9yNSXgJiXiRjBwz6+hMV9bl6N/FRWBEl3gGdEzCp2HpXMfQ/6+ebL+5lSpFqvF3t33/2fT1\nj1JY50lC5l3qLKtGlsmqhHcr15PpLex1DAszg7f1Y8v1TfQq35dfm+VMKLNjh4z4fpP4kB8QkKDZ\n+BfGeg0KaKTPxn9KwTKbITJSysGDcq7+HUv4sbIimRuUoHvFc4Q2VtK4sYm6dc15EieSn9yLNXBj\nzVl2xwez56zP/dTvD/+nm2lHO7aQhQNXPWuTVqkeDq3qEdCzNgr3F3Pti0q5zIf7x9nSuDvKHfkg\n9GPervJOrqZeOwVLftwUTyec5I21TQHY1SGS376swIYN1v990aIW/vg9myZhhSMY1WyGc2uvs3q/\nH6u2e6PRPJwnSqXAL6WnUTlUSYnx7VEVE1va9tzaxahdw0nMvmdr83Xyo2+FAfSvOAhfZ7+X8jns\n5B+FdeGYHyy+sIDx+8YiQcK+Xkcp71nB9p5k3wFk4yfgEXM2xzFzGMr7LrPp0MGqVNWrZy7UxT5N\nJsjQWNDGacjUmEmS+pCWJmHnThlr1yrQ6yV8ywT+x3ecLNoGy5h3KDWsMY8GTx+KP0DnjW8CsLHT\nVur5vRoLvPyksM6TD/eNY+GFebbXHioPLgyOtm+CFWKar2rEuaRIPgz9mPGhH9naU1KgZSMZfyXW\npjIX0I58l+yJXxbgSJ+NQqdgBQcHS4HvgIGACtgBjIiKinqa/Mg5FCzJ3bskrj7IBmUP9h9Scviw\nnPT0h581mlK4kEGEU1MSq4Th1KEJIR0D8cq/mNmXglYLp0/LbNkKf91fkxDLWZFcU+VBdDXq2JJn\nhIaa/3UH/3EIgsDKqOV8cfhTknXWf1MFz0r80GQatX3rvOjHsZOH5MdNcVbkH3x2aAKe8qI4zrpN\nXKzVbahlSxO//KLLN1fVF0Wvh5075axbJ2fHDjkWvZHb+OFNMnqURAa0xdSrJ6VGtUDm+DBow2A2\nsO3GFhZdmM+B+H22dplERqsSbRhY6S3CijezB1i/ohTWhWNeozfrqbusOvHaOLqU7cbMlvMRBDh9\nWsqaNQpurD7DTo319/sGJVgiHcj1hn1oPLA4LVuaCtSTI69ITJSwcIGcAT/XobL54T0yWl2J+K4j\nKPtFd+SujgiCQPPVjTifdJY2JduxqM3yAhx14aAwzpPraddosCIUs2Cmf8VBLLm4EIBNnbZR169+\nwQ7OzmMpNy+QNH0avzefRY/g3rb24cPVrF+vwEOdROTg31F/PIqnDqAsBBRGBesToD/wBpACLAAc\no6KinhjgI6SmCdfnbyN9w368IvcSmHEJgBqc5DQ1bHJ+fhYaNTLzRsgtarQtgl9A/pv7zWYzer0e\nmUyGUql8qS4GZjNc3xNH0oajqI4foUTsIYqbbuBBKgZyflkDi5vZmNoEnZMn2V5+mIv6gr8vypK+\nSFuGUcwPXF3JNTNiii6Zb45+YftRA+hfcRCf1p1kT29bSMiPm+Lgv/qy5eZmOl5Qcnr1Fe4qA5k4\nUc/QocbHZtD8J4IgMG3aj8TFxZGVlYmTkzNOTk44OzszbNgI3N3F1qRbt2JQKpU4Ozvj6OiE9AW2\n0dPTYXd4CqWnjad+0mbU6G3vJUu8mTT4Kh16Kaha1ZLjM11LvcriiwsIv7yUNH2arT3QtQQDKg6m\nd/l+FHEs8tzjsvPyKYwLx/xg3rlZTDjwAVKkrGx8ghPbK7JmjYLo6AfzSOAbPiEmuAWlB9WlY2cz\nnq/pz7guw8j5SZvxWz2dqroIW3vjohdpOqIk/fsb2X53BaN2DUeChCN9T1HKLXd3wv8KhXGeDNs+\niI3R6/B18uNo75O0WNOEq2lXGFltLBPri5Ok2Cl40vUaysyzhpU8UIQNBgO//nqK77/fD/yNUnmB\na9euo37FdnUKo4J1E5gUFRW18P7rUsA1ICgqKir234497NBMqK/bk6NNh4oxzvNIaNaDRo3MNGpk\nomRJAYkEkpOTSUtLITtbh16vQ6ezPpcrV56AAHEc0ebNGzlxIsIma5XXM2jQEJo0aSqS/+STDwkP\nX45Ol43RaLS1T578A0OGDBfJ//LLT/z112aUShUqlRq1WoVSqaJ//0E0bdpcJL9v3x4uX76ISqVG\npVKhUlnlq1SpSmCguBq2RpOG0WhCpVKSEmPiRFQRjh+Xc+yYjIsXrQk93EgjDfFiVocKB7IBCWq1\ngI+PQLFiFvx8TAy/+QmWYr5IA4qhKu1LdMAdfkiZTJTmIgBeai8m1f+GHsG97b7rBUxe3xTvHb9F\nk73VSXYyMm0rFLs0lCLrpxESYuHGjevEx8cRHx/HnTu3iY+P5/btOGbNmo+zs4uor4oVS5OUlChq\nj4y8jK+v2PWuatXy3Llz2/ba0dGqkO3cuZ9ixcRp1KdO/R6j0YizswvOzs44Ozvj5ORMkyZNcXBw\nePiZrqYT/cOfFNsZTi3tPrbzBm3ZCkCZMmY6dDBRooQFP1MsvtnXUfl6IPVzYB8HWH5zCcfvF1wG\nUEgVtCvVgUGVh1LXt779+/8KUBgXjnlN9t1YQtfW5Z4kg0Gn4eDGK1zjoct86dIWunUz0rFjNl5e\nGjIyMkhPT0cQLISEiJNg3L4dz9dfTyIjI52MjAwyMjIwmUz4+/uzfPkakXxCwl1GjBiCVCq1PWQy\nGT4+xfj5599F8omJiUya9EkOWYlEire3FxMmfC6ST01NYcaM35FKJUgkVnmpVIq7uwdvvTVMJG80\nGomKuoyLiyu3N97EafYStPd0dGIjAI6OAj16Z/JnmbIk6e8yNGQ43zb64Rmu+OtHYZsnZ+6dotWa\nMACmx9Xk7WWX+bCFwNSaWZR1L8ehPicKdoB2cuVc0lmar2oIwJkBl/jqg4ls3foXWVnaHHJr1myi\nceOwAhjh81Oo0rQHBwe7AYHwsHBGVFTU9eDg4HSgKvCvCtYknQodkIIT6QpHDA4KBJWEzz7PpGdP\nnUj+m28msXTpIlH7Dz9MY+DAt0Tt+/btYfHi+aL2xo3DclWwDAYjGRnponaVKnct/ObNG5w+fUrU\nnptyBbBp03qWLFkoan/c+L/8ciJLliywvZZIJKhUKqZM+Yn27ftz4oSM+As6tm3/BGXiHcLvHOCI\nLg6VYESCBGgGyNHp3iMmpg0xMVJ8ucc6psJZWAgcBGRAPZRc9W+AJeAYySHJjNaN4Nuty+km/YHW\nqXGoS/tyKfsaiYY7ODjKkcutD5lMRmhoHUqVEu8OXr16haSkRORyOUqlEoVCiVKpxMfHBxcX11yv\nkZ28R6/Xc+fObQ5NXoN2xw8kj7FuHsgk3akTMRknT2u8VbduHYiNvSU6Pj4+nuDg8qL2xo3DyMzU\n4uzsQmZm5v1HBi4uYmUMQKvN+QOclZVJVlYmqse4EMya9Qepqami9gsXonMoWEXLulJ0dh9q1ZqC\nVu6FxHwepb46BoML1645M3XqcsCdd9nCzzysi7MYqIYck0tFLvrL0Ltfxig1sr7pWtZfW4uPoQQd\nk+rQUt4aD5/ibLq4FamLCgcvJ5xcFMjlMmQyGb1790OpFCej2bbtLywWCzKZDJlMilRqXTQ2aNAI\nRS4pa+/du4ejoyNOTk52xe4/TlZWFhERR9EcPELKhm0ckJ7lXgkBqRQ+PwWzWcNc7//RubOJbt2M\nuLldpVmzBnz3XVaOfkqUKElERKSof71ez5o1K3M5b2au48nMzOTQoQOi9qCgErnKZ2Sks3p1eK7y\nuStYqUyb9mOu8rkpWHfv3qFZs4dxVRKJBCdnV7zVdcjMPEpWloSF85yh0Sho/ilLjy+gyElvfIr6\n4erqhpub9eHu7pHr5qadvCU29hb79+9Fo9GQnp5GWloamy9sBFcoXw6GzT+JzAKdImFqTbgafYVx\nE0ZRsVQlfH398ff3x88vgCJFiryQ54OdF+fW/RTtSqmSYk6+ZGVl2ZQriaQc3buH0a5dM2rUyLvS\nLq8KeR016IK1aobmH+1pwBNX0EIjfw4cAMgEYybcNxplZGiQycQLjEcXVY9iMhlzlS9fvjxNmjRF\nrVahVjvYrEzBwcG5yvfr15/GjRujVqvvW5mUmM0WypQpm6t8+/YdCAwMQq/X3X8Y0Ot1lC+fe/9F\nihShbNly6PV628Ng0OPo6JCrvMGQU8kUBAGdTodMJsXdXUKLFhZo4QxjrUGGc0eN4PyKqw+uCtwv\nejx4cFfKldNz964E8zUtpw81wSPzNruN11liS4VtgPhDEA8I1SDgDHdU+/nN3BCXy0Y+mQNLjVb/\nz3/StOksmjatQLFiAr5FDPh6ZFOkpBN//DGN5cuXiuSnTfuN/v0Hidrfe28Mq1aF31fEFDaFbOLE\nL+nYsbNIfvbsmRw8uP8R5c16TM+evQgNFceSHTiwn+vXr6FQKFGpVLZjQkKq4O8fIJLXaNIwmUw2\ni6NcLn/pC1+pVJLj+Z8YDAakUinyXGoPvPXWAA4fPkhi4j+sTMmg9lXRY/PsHIHE/v7+xMbewsPD\nA3//APz8/PDzC8DJKffv55w54s2Lf2PfvkNotVq02gy0Wi2ZmZlkZGTg7u6Wa/+hobVJSUm5f4zW\ndqybm0uu8omJCWRnZ99/FWdrL1sWNBoLXkmp8EjujjlAJibIuAiXH+koOASCzpGgvMlsv5ssMa6k\n1ylYuQmyctn4XbRoIJ6eDjQ27aZm5gEs7h4Inp68/ec76IzijaIbN+JRq8UKWaNGoaSmpiKTyXB1\ndcXNzR1XV1fWr9+cq8vl6tUrUalUuLi44ubmhqurK66ubnh7e/+nFiFPmiP5hSAIto0FrTaDzMxM\njEYjNWuKFxapqSl8/fWX9y1G6aSnWy1Hzs7O/PXX3zlkLRbYuVPD0KGdcnZyE+RqGQtrb6P6O/U4\n3zTLVrfz7l1nsrJyKlcAWm1GrnOlaFFvunXrgYuLKy4uLri4uKBQKHBxcc1V3tPTnTFjxmGxmLFY\nLFgsAmazGU9Pz1zlXV1d6Natp03ebLY+FylSNFd5R0c19es3sMlZj7Hg6+ubq7xWm3MjVBAEtFoN\nAQEZHDmSyaJFCubMUZBwYgTKxhPRZRiY/Mc3on5Kly5NRMQZUXt8fDzjx4/F1dXdpoy5ubnh7x9A\n585dRfKvAk87Tx58rzUaDSDkem88f/4cM2f+cV9h0pCWloZGo6FOnXrMmjVXJH/p0nnGjRslPllZ\n+CTWgaOWGqykJw3j9uCZtZ6UBFi2arFIvEWLVqxcuVbUnpycRGxsLP7+AXh7e9s3qPIAnU7HsWNH\n2bt3N/v27WH48P+jZ8/exGmtClZx1+Io5DJKl36bZjhxhM+ZMq0U/fqZCnjkz8+L3kPy1EXwvgUr\nFagWFRV19pH2NKBfVFTUn/92/KZNm4SjR4+iVqtxcHBArVajVqupX78+lSpVEsnfu3ePzMxMm6yD\ng8NLj496mcTGxpKYmGhzbXzwXL16dYKCxLtumzdvJjIyEpPJhMlkwmw2YzKZ6NGjB6GhoSL56X/8\nwa7tO8lK1pKVaSBD6kRWlokqVd4n0VPHEY/R6NVWI2TJVKi5GM6mWlW3LJTcpQjWV78A1lojIZzl\nLFVJx4UBSNiI2CK4YMEiBg0aIGofMGAAS5aI0w4vWrSIAQPE8gMHDmTxYvGP8IIFCxg0aJCofdCg\nQSxaJLaAzp8/n8GDB4vaBw8ezMKFC22vJRIJarWaWbNm0b9/f5H8lClT2Llz530F3eoCqlarGTJk\nCA0aiLNY7dmzh+jo6ByyKpWKkJAQ/PzELnbLli0jIiKCuLg4YmNjiY2NJSEhgX379tGoUSORfKtW\nrfj775yLN4VCgrG3QPPmzdk5YGeO9+7evYuLiwtOToW7CLUgCLnO+bVr19rcnbRare3vX375BalU\niiBAVnI2mhspaGOSGfPtu2SmZ5AldUArccRgMGMwmKlXfwux5rNI1COJLHUS3QNj0xxQZ4E0y5ks\nvQ9Wbc0CXAQc+YaP+ZjJtvEUBTIAAzIsCDzQ7mQyLV5eTvSVhdPCtBW9szfmWrXpta4vZrOZf5Kd\nnZ2rL7uDgwM6nViBS09Pz9WK2L9/f5RK5f2de3fbc58+fXK1qL0EfeANAAAgAElEQVRuGAwGsrKy\ncM8lM1B2djYLFiywfW8eKPQymYyZM2eK5BMSEvD19eWf91Nvb2/xhgZWl7miRYuK2t3d3a1WWpOJ\n85flLF0Ky5ZBXFwa4IEERxyUerJczaCS0KxyS3ZtE9eRMhgMbNq0yaZoP/pc2Ofz82AymUhMTLQt\n7NPSrFYRtVpNp05WxdRggFUrBcI3lGWLTzTylVAkxbr7+2AbJjQ0lIiICFH/J0+epFYtsaJctWpV\nzpwRK2Tnzp0jNDQUhUJh8+6Qy+XUqFGDLVu2iOQvXrzIW2+9lUNWJpNRoUIFpk0T18y8efMm3377\nrUg+KCiIUaPEiktCQgKrV68WyXt5edG2rTg8/tChQwwaNMh2HU0m6yK5ZcuW7NixQyS/a9cuWrQQ\n1y1r0qQJe/futb4QBDh7Flas4NCKFXTOMmK2eKBJd8fsdx7c0sEhCP+Lp2nb24MBA+DMGfhqf1vu\nqbbC3+4oUjwRhDhMJgMAQ4YMYe5csQK3bNky+vXrB4BKpSIgIIDixYvTqVMnxo4dK5K383h2797N\n999/z/79+x/ZsIS+ffuydOlSRv81mt+P/06r0q2YF7adaWX/4EfdKO44lqLYzWNIirziWeegcLgI\nRkVFaYKDg28BNYCzAMHBwaWxWrbEafD+QYcOHWjcuDkWi1jpS0nRitrkckfc3BwB6y5fZqaRzEyj\nSO51wcnJAyen3Iu85nZ9GjRoSoMGYtfHx8n36j2QXr0H5iJtRWuI4MfjU5h++ndueJi5MRaaW+ow\n6mZbJNmB7CrWhzt3JNy9K+HuXQsJCRL8MqwxNq5ksBYwYDVM7qMOHVgHGBgxwpNp08yUL2+hVlAC\ndWQnKNK4HIMHDaNlyzYYjUYMBgNGowGDwUhwcOVcxx8aWg+pVI7BYJWzyhvw8Ciaq7yDgzMBAcVt\ncgaDEYNBj8mU+/XJyMjpLiMIAtnZ2WRlGXKVP3nyNLt27RK1165dnwoVxHEQ06fPytVNZ/r02fTs\nac3MI5VKcHd3Ii0tk2XLVrB1q/hmfenSVSpVqv6PsUJAwNvI5T0xmQKRSPwZO7oof5VqyJW0KGoW\nqS36DEqlM3q9gF4v/myvAk2bvpFre1raIzv7UlCXdkNd2o3lzTY9piczUAnYS5oulZWXl7Mgci5X\nh13Dqs5ocZBKqOPQhxqWoag1MjQaA/5Hi3I5ujZOuhRcDcnctaQhRWAU0/iDUXBfyTKbpdy7B0Ec\noS2LIRGEG3AIFYecGnCrfiuKNfNFKk1Dq80gK8sk8m83Go24u3uQkZFOZubD76lUKsVgEH+fzWYz\nS5eKrckAbdp0FFlABUGgVKniODg44Obmdt97QIJCIWf79t2iPkwmE126tEciscbQWJ8lKBSKXHec\nTSYTgwf3Ryq1yj54lsvlzJo1TyRvNpsZN250DlmJRIJMJufHH6fa5siDe0l6ejqtWze/b13Skpmp\nxWg04urqxo0bcaL+09M1jBw5UtTu5OTMt9+KXdcMBkTKFVjdYHP7bTCbZbRu3RYXF9f7lkZXXByd\nUF+L53KFjlhuxhKiO8nDe7sbISF6OnRP4zdZeTCmMqzKcKY0+SHX/gGaNWstanuV5/OTUKlc8PFx\nwccnZ/z1o9en7ZtQpt4qtiyriWkMfL1GzVvndaSjoKLyFEFBThw5kklwcM7/pUSiZMiQt9FoNGRk\naNBorI8SJUrlev1v3bpt80p5lISEe7nKx8be5dixY6L25OSUXOWjoq4zZ464NlTNmrXo02eQqD0y\n8iKjR48WtTdo0ID69ZuI1lxarY5r166J5JOSch+Pi4snnTp1ua/IP9iwcScwMJC042dQrluDau1q\nZFevWM8LtGYRSxgAlVZC914AvOc5h3GdFTg6Ws9RsSKYy/fi3UNboaQW4w83QOdGWNgdhva7SLki\nxlzHc+VKtO1vvV5PdHQ00dHRlCkTnKt8ePhypk79Hj+/gPvuh/74+wdQs2YtQkKqiOT/S9y5k8j2\n7Q83cYKDy9O0aXNat25LSoqWK4lWLylfdQCfdD3PDN0HADg2qkaqVAWP+X16FXiw3npe8iPJxcdY\nswi2wWrNmgc4REVFvfkUhz99oWE7BcbF5At8sO9dWzIAJ4UzH9X+hCEhw0W1KrJup5F55AJZ1xIw\nxtyBG7dwuhXFMUstRqZPwWjMuTnQhbWspRsAmTgS51iOFJ/yJIW2Qujbk/LlzXjkrmPmO3FxsSQn\nJ6HTWV05DQY9Op2eatWq5+o2sW7das6ejUSv12EwGGw33KFDR1CnTl2R/IQJ49m6dYvNvdR6DgNz\n5iykY0drJftHA5N/+ukHDh8+iJ+ff45HSEhVihR5mPku5a6Bcf9zZetWq1XCz8/CjBk6gqvfo/z8\nkgCsar+BsOLN8uOyvZYIgsCR24dYeGEuW65vthXrBqhdrC4DK71F+9KdUMsfsTSZzUg0aehRkWp0\nIS1Ncv8BaWkSAvcso/iFHTimxFM68Rjy++66PQlnFT2pW9dE584m2rc3/WvqfKPRaHM702q1VK4c\nIpLR6/V89NH791160snIsD6bTCaOHxfvhWVmZlKypDjxiEKhID5eXIHDYDAQECDeuXwZ8nfvpoiC\n9x8nL5PJuH07RWQBNZvN1KlT/X4iFSdbQhUXFxemTftDJC8IArt3/42Tk8sjx1itv46OjqLzPoo+\n4hyJP66gxKGVeBgfWrtqcoJ7AdXp2tVI164mype38H3Et/x4YgpqmZrj/c7i41TsX/u2kzt9t3Tn\n75jtVHCuyqdr+nPrRCoTTF/b3m/e3MTw4QaaNDE/dSbVR0lOTubYsSOYzaYcHiQeHp688UYbkXx8\nfBwrVizN4WliMpkICAhg+HCxon/16hUmT/7qvvyDc5gpW7YsU6b8JJI/e/YMb789GJPJbJM3m03U\nqFGDFSvWitZcSUlJbNiwxqYsubq64+7ujoeHJz4+Ps90LZyGD8Vx/Srb6xgCCacX83kLfakgNP0q\nkSa9TovAVixvJ06okq7XUH5BSUwWE6VPLyV6Y18Apkgn8K7sN7TjJ2AZ9Q48YnW3WCwkJiZy+3Yc\nt2/f5vbtOOLj46lXr0Gu1/+7777hp5++E7WPGvUun38urtu0b98ejhw5hK+vn02ZdHNzo3jxILy9\nXx2LTVZWFkePHmbv3t1otRlMnfqbSCYjI50PPhhHWFgzmjRpKkpY1WhFbaJSL/Om/AsmfrqZUE6Q\n6VaM7IijCB6vdtrSwphFUApMAQYDSqx1sIZHRUWlPMXhdgXrFcEiWFhxaSlfHvmMVL018UBl7yr8\n2GQaNXyeLpjRaITr16VcuiTl8mXrc51j0/ksZRxScn4HZjKcd7C65vj4WKhQwUL58hYaukVSRTiL\nV6NyKCqXhdfM/cVisbqRPYihedbMTxeWnKX4h4MZZ/6RzXSgbVsjP/+sw8MDtt/cSv+/eiKVSLk2\nJBZnZe7JKOz8O/ey7hF+eSmLLyzgVkaMrd1D5UGv8v0YWGkwpdzLPFOfloQkYn/7C9mff/Jmxiru\nZDz838hkAo0bmxkZsofqgyvi4p//CWIMBgPbt28lIyMdjUaDXq9DEASkUiljx74vkjeZTEyZ8jWC\nIGCxWGzPUqmUSZO+FskbjUY++mg8IOQ4RiaT5XrTNxqNvPPOUFH/crmcRYuW5jpHZs78HUdHpxzK\nj7OzM1WrVn/pbuVGI+zdK2PNajlfb6xOReGi7b39sjAu1+mH/5j21ApzsBUBTtWlUGtpFTIM6bxT\ndTRfNBDHENl5OvbH7aXbpg4AbOq8nQqO9Vi6VMG8eUri4h7GKw4M3Mm7gWvw+fpt5BXLPq67V5I8\nzyJosfBoxerz56WEhytIX7GdaRlDWUUPVtCbc4516NDJTK9eJi46zeSjA+8jQcLuHoeo5F051667\nburAgbi9dC7TjVYZi/l+kpkDCcH4Y/WQSfarjGT2z5hrP1/dztOnT3Ls2JH7mXIfPsaOfT/XpCqT\nJn3K9Om/ito//XQSY8a8J2pfunQRO3ZsfURhtT7Xr98o1w2w/ESn0zF79gz27dvDsWOHMRis7pYK\nhYKoqBicnZ2fui9BECg5x5csUxa91nZhxbl1AKSFr8PYTOwy+qpR6BSsF8SuYL1iJGUn8eWRzwi/\nvAwACRIGVnqLT+pOxE31HFWPscbF3N57Hc3RK5jPX8HpVhSrDB2Zoeknkv2ML/mSibbXCQ5BpPgE\nE/fGINR9O1C6tIXXKZzkaW+KJqPA0b5zabt3AioM3KEYK7+9SJ8hctuO7JdHPuf309OoUqQaO7vv\nf0mf4PXFIljYG7uLhRfms+PmVizCwwwajQLCGFTpLVqXeBOF7Nm+kHo97N4tZ8MGOdu3y8nKkuCE\nlkSKIEHgTNGW6Np3ptS7b+DgY8/GWdjSTz/K7dsSFixQsGyZgqQk62J0PD/wf0zncJl+KIb2oV6f\ngFyLAH9z9At+OfUTjnInTvQ/h7fDq7NTXtgQBIGmqxpwMfk8b5bqwILWVndZkwm2bJEzc6aSkydl\nbKYd7bC6YV8q+QYOH72DU6emuReSfMXIi3ki0aSh3LoF9brVCGoHbvwcztq1csLDFZw/by1YL8WM\nBIF6DaFXLyNvvmnCyQm0Ri11llYjMfse3cr1ZHoLscvjA2ZHTufTQx/hpnLn4qBo9NkK5kzJoPTc\niQyxPIzBim8zEOXcqeT3TX/mzN/ZsGEtCQkJaDQatNoMAL7//mcGDRoikv/ww3EsXCh2df7mm+8Y\nNuwdUfukSZ8SHr7UZhmzPrvTt++AXLNSx8fHodNl25Kw5JbF9gEWi4XKlcuQlJRka6tcuQpNmjRl\n1Kh38fLyeqprAJCYlUilhdaM0RPmdODb+E2k9BmOedrrUQLBrmDZKRQcjj/Ih/vHcSU1CoAiDkX5\nssG3dCnbPc92h1NT4fJlWQ6LV7cznzNc/xsu5PTzHcMv/MYYFAqBMmWsFq8KFSw0122hNNG41C6H\nJTgYi6/fK3WzfJqbYvzZFNK7jaJxmjWnTKyiJEm/LSCgS40ccm+ua8nxu8fsNWHygfiMOJZeWsTS\ni4tIyLpray/q6EO/CgPoV3EQAS7iWn1PIjMTduyQc23uIb453gYFDzM06VESUbwLtybPIyzMzL/c\nY19rCpuCJUlJJvHHcPaccGPMuRGYzQ9/b+rUMdGzUyZvdgIPr8dnekzMSiR0aQhZpizerTGej+uK\nU5vbeTbCLy9jzO53kCDhWN8zlHArmeP94xES7n3wG80vTaf4I1lI41zLc+fXJZRoG/yyh5ynPPc8\nMRhQbf0T1bo1KHftQHLfAmKSyAmQ3SHB9FDxDwy00KuXkR49jAQG5jzHTye+47uIb1BIFRzuc5Ig\n1xKPPeVNzQ1qL7PGLa/vuIUG/tYkTtevSwgfc4rBEaOowjnW0JVN/ZczYYLhX92o8xqTyUR6ugal\nUpWrBWj9+jUcPnwIjSb1fvyeNRnLhAmf0aGDOCPy6NEjWLlyuah96tTf6NdPHCf//vtjc5TwcXR0\nxM3NnYkTv6JLl+4i+U8//R8ajYawsGY0ahSWa8Kdp+FkwnHarL2v8H1/jx3DDlBtXAN4glv0q4Jd\nwbJTaDCYDcw48xs/nfgOndka/t8oIIzvG/9Eaff8ca8QBLh7B24eukvakSsIF6JwjIlimnYohw3i\nTInh9KQnD/3Bs+UupPqUI3rIJDx7hFG0aOH+7j3pprhxg4yK77xBffNBACJKdsN308+ofdxyyOlM\nOsrMDcBgMTCn1UI6lunyUsb/X8NoNrIjZhuLLsxjb+zDZBBSiZQWga0YWOktmgW2RCaVPXPf6TdT\nuP7zNpy3b6Rmyk6UGFlBL/qwAnd3gXbtjHTubKJ+fTOyZ+/+laVQKFiCAIePkTp5AUHH16ES9Nyi\nOCW5gbunhP79jfTrZyQo6OnG9/mhj5kZ+TsuSldO9DuLh/rVjm0oDOjNemosrkRi9j3ervIOXzcU\nx+AAxF43cfqzv6i86w/qWI6QijsBxFGzkYoRIww0b27mVayC8CIKllelMkg1aYB1Y2crbVhBbzbS\nEZmjig4dTPTqZaRu3dyvTVJ2ErWXVkVrzPjXa/8oD2J9RlQdxZcNvs3x3q5tFqLfncuMlJ7EE4Cb\nm8D//qdn0CAjuVQsKfScPn2Sq1ev5Eh5n56uoV+/gbmWnBk6dCCbNq0Xtc+YMZeuXXvk2zhnHFjL\nxHODweBEl6gUZs7QP/mgVwi7gmWn0HFTc4OPD3zAzlvWdK5KqZIxNd5jTI33cgb95yNmM8TESLh0\n6aHF6/JlKWOvjqat8BcliMkh35yd7KY5Xl4WSpYUCAqyEBRkoVvUZIpKE1FVLoNTtVJYypTB4h9A\nQd1RH3dTzMyETz9VsWyZknocZjutOTd4CmWn9MvVQnf0zhE6rLdm2YsccBlfZ3EaeDt5y3VNNEsu\nLGTF5SWk6B6GpBZ3CaR/xUH0rtAfH8dnCyB/QNLVNKJ/3s6GC+WYd6lxjveKFrXwYehOWpa7ge+I\nNhRYlpiXREErWKkxGbi2bUWxxAu2tkwc+cutN4kffk27fk48poRjrtzNvEPtpVXRmXV8EDqBD0In\n5MOo/5s8sKI4KZyJHHAJV5XbY2W1Wtj7QyQnV93ij+Q+tvYyZcwMG2akRzc9Ts6SV8Yj4onzxGy2\nPh4xhaekwPr1Ckr/OBbX5JuE04v1dEaDO/XrW5Wqdu1MPCmM57ODHzHr7HScFS5E9It8KnfXr45M\n5LfTP1PKrTRH+54WvW8wwOzZCn76SUVmpvV/UKGCmW++0dOwvrHA7tkvg/R0DSkpKTbL2AMrWcOG\njSlRouSTO3gOTCaoNe5Xblf4FHlyZS6OPkwuFS9eaewKlp1CiSAIbLm+mU8OfsidTGsgakm3Ukxp\n9BNNA8U+xC8LnQ6uXZNy7UwWaceuYblwBceYKL7MGEcSRUTyZwkhhPM52vRSNT+024VQqwZBQVZl\nLDDQ8sSbSl6Q203x3Dkpw4eruXbNaqZo0MDErCl3KBr8+F+7X0/9zNdHJxLoEsSJ/ufyf+B2bOjN\nev6M3siiC/M5euewrV0uldO2ZHsGVnqLhv6Nn9u1NjZWwsaNctavV3DunPU7sYGOdGQTRuRcDWqG\npEcnvIe0Bc/XzxJSUArWxYtS5sxRsHatgp26hjTgMGcJYX+FYRT/qBv1Wjs/19p7woHxzDs3Gw+V\nB8f7nf1XJcDOs5GUnUSNxRXRmXVMqv8N/1dNnMr8n5jNsG2bnFmzFBw9+tA88rbjEj5xngZjRuAw\nsDOoVPk59Bcm13kiCMhPRKBavwb1xvVkTvgMba+B7NkjIzxcwfbtcgwGCdYSExKKF7fQo4fVBbBk\nyaeba7fSY6i/vCYGi4EPQz9mfOhHT3XcsTtHab++FQCHe5+kjEfuXjEJCRK++krFqlXWOKxgLrPT\nuSO6r7/BrU/upTvsPDu//qrk68jRUHMONZzasm1geEEPKc+xK1h2CjVaQwbfHf+WOWdn2IL+/1f7\nE96r+WGhKgidkQGXL0uJipIREyMhJkZKTIyUoRfHU05/jnJcIZBYm7wvt7lLzrTV3t4WdmfXw0Fh\nJr1YGQwlyiCvUBqXmqVxb1IZqerFA28fvSmaTAKzZ8n56ms1BoMEmUzgf/8zMHq04YkuYf229GBH\nzLYnBhfbyV8up1xi8YX5rIxaQYbhYRHuPuX7M63ZHy/c/7VrEtavkxM2sz/NtZtQYbC9Z0TO7L47\nqTW6JqVKvT6/uS9NwdJqEbL17DhVlNmzlRw48HCx3UJ9gOatLDSdUINSpZ//FHEZsdRdVh2DxcCn\ndScxpoY4Q5mdF+P9vWNYcnEhAc7FiegXKSo18m9ERkqZOVPJxg0yjphrU4uTAKSqfEjpPAC3akFY\nenZD4iSOSZFdu4ogk4FajaBSIajUoFbzsvx5H50nwvUbOCxegGrDWmSxt2wyUf5hNDbu4t69h9Yf\nBweBdu2s1qoGDZ7dPXLkzrdZfSUcb4ciRPSLxFnxdDuTZouZygvLkKxLZmK9rxlZfcy/yh8/LuXj\nj9V8F9mWN7B605wr1wnPxZNRlvJ/tkHbycHFCxJONP+CSX0PoC19jGEhI/im0fcFPaw8x65g2Xkl\nOJcYyfh9Yzl97xQAw0JG8FXDKUglhd9sn54OMTFS4q7oyIy8jvlSNGvpSswtGbGxEkwm6/yTYSIL\nR5SIi137Ke7hFORps3hZHwLlpVH4hPrj5PV0rpMPbopR51I52+4rYm5J+YAfCQy0MGNGNqGhlif2\nYREslJ9fgjR9Gt83/plBlcVZj+y8XDKNmWy8to4F5+cSmWh1f9nT4/Bj0xY/K4IAl45mcPP3HRQ7\nsJ4muu3oUVGUexhQUaWKmc6djXTqZMLf/9X+/c1vBUt24TyyefNRr17JcuUg3sp4mK45MNDCsGEG\nevc24poHCR0fLP69HbyJ6Hf2qRejdp6eqJTLNAqvDfDc8ah3bsP+r45QYtMM2ho35igzEqBMwOTh\njaengIeH9eHpKTB9tT/OuiRRX5f3Xce1jLcoEZ5bz86QnQ0qFYJabVXIVCq0U35EcBF/2VQrliIR\nhEeUN+uzsU49UCpzzBPprl249+hkO/amKpgF+t6E04srWJN51KljolcvEx06GHF5zooeF5LO02xV\nAwQEJjf6kSEhbz/T8aN3jWBl1HLq+TVgY6etT5S3WGDH1CuUnfoudU3WuGStxJkLPT+j5E/DkChe\nwQCtAsZohBm1V/FV/FBKj4HrnvBVg8kMryqu1/aqY1ew7Lwy6M16Rvw9hC3XNwHQtWwPfm0245nT\nVhcmzGZr6uWYGCmx0SY8d65FefMabveu4Zt+lVLmKxhQ4kUykHOeKjCQjQMSBGKlQdx2Lkuadxl0\ngWW41WE4QSUlBAVZ8PUVbJuaMpmEi5sTcB7ai2qmEwB81mAHgxbVfeoF3aMLin09j1LBq2JeXQ47\nL4jZYqbu8urEpN+ke7le/NFidp6fw2KBM/u1nFp8halHG9nShT+gRc1EZmX0Rd27Hcqe7RFeocKZ\nkE8Klk6HauM6JLPn43IuwtZ8jyL4cZt6DWHYMCOtWpnyzABxU3OD+itqYrKY+KL+t7xTbVTedGxH\nRK8/u7D71k5q+tRia9fdTz7gMWRmwvaZ8chnzqaB5i+cyKQiF9Ei1kjScRFlvwVwRUMGrri4PFTI\nPDwEthz0xNGUIZLfvTYOl+JueHgIuLo+DAHzKlMcabpGJJ90JQbB3cM2TxITtez520K1US3YmN6U\nZebeRFIVkODnZ6FnTyM9exrzxMr9oMBzkGsJDvU+gVL2bKlON0dvZMj2/sgkMi4Ojn7qZC+aVAuH\n317Jm/sm4EUKmTgysPZ5xv5YlPLln7wpaechcz6OZ/TcUBwlWhw+k2CUCixqs4I2Jd8s6KHlOXYF\ny84rhdli5sP941hycSEALQJbMfeNxTgqXo+0nv8kI13g9rlUrqUVzeF6GBMjxSEminMmsXJzjyL4\ncM/2WqEQKF5coExAFiPjPiHs+gJcsd5oTzZ7l+KLPkWievob1eILCxi/byxuKnei3rr5SlgR/0vM\nPz+Hj/a/j1wq53jfs/i7BOTbuUwmOHRIxoYNcv78U4FGI2EgC1nIYADMyIgv1xh1v45Iu7ZHKCKO\nUyxs5LWCJQhwcsMdWg2vgAzrYuwGJZgne5vkDv3oMdqTypXzfpH2YLfex7EYEf0icZA/Q2YMO8/E\n3tjd9NhsteBs6fI3ocWer2DtAywWiI6WkpwsISVFQmrqg2dIS7P+Lbt7G12aHr3G+pCZ9KjRsZcw\nLIi19I+YjBOZqNHleAxhHgas8V4y2UOFbFtcFVwsGtSCDoVFh9KcjVSwsGhGMq4+ahwdYe9eRxYu\ntHD37sN7gFot0Latid69jTRsmHcZSI/cPkTHDW0AmNVyPp3LdnvmPrSGDMrPL4nBYmB6izl0K9fz\nmY6PPpZC8tBJ7EmoxE+MRyYTGDLEyAcf6HGzhzY+kchTAurWb9KQg1wq4kHFkakA7O5xiMreL7dg\n8svArmDZeeUQBIFvj33JL6d+AqB2sbosbbsSd/Xrnd3sn5gNZpJPxaI5Ho3hfDTy69dwvnONRKM7\nfWQrRZaFSpznPNYfsRSZNwnfz8K7f8tnPu+oXcNZFbWCFoGtWN5uTZ58Fjt5R5Yxi5pLKpGsS841\nJXF+odfDnj0yrsw9So1D03nD/BeOZNve3+E/kJiJM2jVylSoy5zklYKVnQ3r1imYPVvBpUsy1tAV\nKRZWur9NqeFh9B9ozrdaO1dTr9AovDYWwfJcrlR2ng1BEAhbWY9LKRdpX7oT895Y/JLPb7V+paZK\ncjweKGePa9doQBCefv0nw4QZGf/0pgCoVctM795GOnbMG/fWRxEEgbbrWnAy4Tgh3lX5u/u+597Y\n67G5E3tjd9OpTBdmt1r4HGOBLX/KmPSFmlu3rGPw8rLwySdW197/UkmLZ0Gng5U1fmd80scAbPj1\nczqnfAlA9NA4XJSvX5F7u4Jl55Vl+pnfmHT4EwAqeFZiVfv1+DgVK+BRFR60Wh6xeElQHT3IW7sH\nkVwqFI9l3yMNeL5rFbq0CjHpN/mkzkTG1nw/j0dtJy/48fgUvj/+LU4KZ84MuIib6uXmv83MhD1/\n6rkzdwfBZ9fTRthCV9ayjTY4Ogo0bmwiJMRCpUoWGkcvoIglEXO5YMzlymEOKklBFp95XgVLevMG\nDksWcrt2O6afasDixQqSkx8uAmtUNTB0uJkOHUz5XsR5+I7BrL+2Fn/nAI72PY1KVrgz0r0OLL+0\nhHf3jEQqkRLRN5JA16CCHtITMZtBo+GxylhKisRmMXu0PSvLumb094fu3Q306GGgTJn8W3f9df1P\nBm2zprZf2W79C2USnnduFhMOfICr0o1Lg68/d4hBdjZMn67k11+VZGdbMyPOLTqBMl/2oGKX/Knb\n+Srz5ZdKUn9fzXT+j7RWXdj4aV3G7H4HD5UHUUNintzBK5H/5gwAACAASURBVIhdwbLzShN+eRnj\n9ozCLJgJdC3B6vYbKOlWqqCHVWh50d35hMy7hCwqB8DGTlup59cgr4doJw9Izk6mxpKKZJuyCzx7\nnEYDO9brWfunM3sPqrBYct5vDtKABjxMN2+SKckOKI32lz+Q16/1sof7bHPEZEK5YxsOi+ah3LML\ngBWSPvQRlt3vy5oxbdgwA6GhlpdS4uhS8kXCVtZDQOCnsF/pX3FQ/p/UDjqTjhpLKpGUncjwqiP5\nqsHkgh5SvqHTQWamlLJlndBo8nfNZbKYCFtZjyupUTTyb8KaDpteKINwbMYtai6xJv9Z22EzjQKa\nvND44uIkfPGFCvXGtYTTGwMKNlcYT/nF4yga9HLqdhZ2IiKktG/viCBI+Kz/FcZ84cx3F3/jxxNT\nqFqkOn9331fQQ8wXXlTBytPgi+Dg4NH/396dx0VZ7XEc/8wMi4Agi7soeFWOiktqbm3azdRKveae\n3bJyyfS6dCvTsrLS1LI0S7Nc06ys3MrUXEpbTDHNBYTHDcRdBJGdAea5fwyQejUWB54Bf+/Xi1ec\nYXier8TDM2fOOb+jlNqplEpVSh125LFF+TSg4aMs7rocd4s7sUkxdFvVmfCLsi9TSQk7txMAV7Mr\nt1VtaXAacSMBHgEMbPQYAJ8c+IiM7AzDslSqBH2fcOfLb7I4eDCV6dMz6NMni0aNcnBx0YmiIYdo\nRBb2USuXHCveJyL558M1uOMOT4YOrcCsWW5s3mzh9GkTnq+/gtcbr+L+5XJc9uzGlJxUQIKS4bJn\nN/4tQ6n0xMD8ztU5qhGlh+DrqzNqVCZ//JHK/PkZtGlTOp0rgLd3v4WOTpBPMAPUo6VzUkEFlwo8\n2WQIAMsPLb1q24TypkIFqFpVL5XpcCuiPufwJQ2Aie0m3fT2LLW969DIPxSATTEFVxIsSGCgzvz5\nGYye6M5Zl0DcyKJ35FQ82rRjw9htWK0FH6M8S02FUaM80HUTSuUwdEoN9IrexCbbR63KwkivURy9\nuv00MB2Y4uDjinKsa90HWdFtNd5uPsSlX6DnmgfZeWZHwd8oimzX2d8BaF6lhSyad3LDm/8Hs8nM\nhbTzfHN4hdFxAKhSRefJJ7OYOzeD7dvTiI5Ooe7W2WydvYcxQxJ5rNUBBlX8mpeZzBG9PkePWli7\n1pW33nLn0Uc9adHCi+y5S/D8cBY+o5/B74H7qFwvEL9mDTGfO1tq/46EBJi7NRTr+UQAtnAfffmK\nTg2i8X7nRf78M4VXXrGWesn6A3H78qusPn/7+DJdYbUseiJ0CO4Wd1KyklkeWbrrsMqj9Ox03t5t\nX0Pao97DtKjWyiHH7RJsL5bxQ8wGHDULq8HoTpgiw9h19xiysfAP/TiPf96DKa1+YOvWW3dh1pQp\n7kRHm7FYdD78MIMKuYN6sUm5HSxv6WDdiEMnymuatgpAKVX+VruJEnVHrbtY86/v6b+uFxfT4+j3\nXU8WdPmUzrl/SIVj7DprH8FqU6OdwUlEQYJ8gulRrydrjq5i7r7ZDGz0mNNVfHR3h6ZNbTRtaoMB\nAMHoejDnznWlSYSViIgcIiLMRESYOXbMjKstk2/03jQikkZE4oe9g5Nz7iId+wWhQs00bmwjNDSH\n0FAb1araqDSgFzmBtckJUWQ3UOSEKGy1AinskJL5/Dls/gHg6kpUlJn581355htX0tO92c8S/qQF\nwZ3qMmyYlQ4dskttpOp6pofZ35us79ugyBXSxM2r4lmFPiH9WR65lAUHPmZI0+FF2nhYXG3hwU84\nm3oGi8nChLYTHXbczsFdmbV3BjFJ0Ry5dJgQf+WQ41oqVeQfK9/k5I4BZA99FmtcEgvO9+CjR9zo\n3DmbN97IKFebshfkl18sLFhgX3A6dqyV5s3/qpaa38GSEawbkr8cwmk0rdKcdQ//QN/venIyOZZB\nGwYy69459G840Oho5UJKVgrhFw8A0LZGe4PTiMIYedsY1hxdxdHEI/wQs6FM7DViMkGNGjo1auTQ\nqVNO/uPp6aBpZiIi5rA4wkxEuIm48IsEpkRRg7OER7kTHgUrV/51rFC/U4Rf2vp/57AFBBAfcQzM\nN+hw2my4bPsJr8ULcdv4Pb/8Zxmv/tmH7dv/uuV5eup4D+jJ0iFW6tdPv/5xStEf58LYfOIHAF5o\nPQGL+dZ919xIw5qNYHnkUmKTT7Aheh3d6/Us+JvE/0nMuMTs3ErB/278BPV8HVc4omW126nsUYWL\n6XH8cGKDwzpYeSreEQoHN6Jtj6PFu2bCwmDTJhe2bfNi+HArY8daqVjO9/xOToaMx8cwnJb81mQo\nzz7711xJa46Vs6lnAAiSDtYNFaqDpZRaDAwCdP6/vqcOTNE07VVHBDKbDXz7UBiuQUAD1vfZTN+1\nPYlKiGTUj8NJykpk+G3lb5fw4si7Popznew7s4cc3f6Ct12ttlgscq05u5Y1WnJ3YAd+ObWdOftm\n0a1+N6MjFVvFitCqlU6rVtn5j+m6N6dOtSE83ExwRCbh4RYiIsxER5vQdRPxlyzM4Ln8Ea9gYjCj\ncyS1FpPGetKkib2SYZMmOfj7g+nMGXz69gRrJj7Hj+efJ37WCrbbh9ioXdvG0KFZ/PvfWVfsfWP8\ntZA3lapRQGN6qd6YjRxKu4U1qRrKvXXu46fYrXx8YA49Qx42OlKJuJl7SWF8uG8WiZmJeLp4Mq7t\neIfebyxY6Bzchc8jP2NzzAbG3v6sw47910ksNO5UnfX3ZbBypQuvvebGuXNmZs92R1u+n/4v16HH\n4xUNHfEuSRsGrWFk6gIGApEDfPHw6J7/tbPJp9Cxj+QFVQoqt68lbvbaKOwI1kjg7+o5p91Uiiv4\n+no56lCijPL3D+G3Ib/y0OcPsfPUTl7+ZTxpJPPmvW/e9ALZ8qI418nBg3sBUAGKkFp1HR1JlJCX\nO0yg6/LthJ3dRWTKfu6sU74qPwYEQPPmVz+WkgIHD8L+/TXYv38Gq/bDgQNgS01DoeGZkcaOL69e\nn1SrFgyqeYIpUZH5j+2iDfMYzgr6c889MGYM9OhhxsXFHXCe0uc/n/iZbSd/BGDKfZOpHCCz7I00\n7u7n+Wn5VsLO7uJIWgRtA29u42FnVhKvuU4nneaTAx8BMLbdWBrXru/wc/Rp2ovPIz8j7Nwu9AqZ\nBHgGOPwceYYNg4ED4a234JMZSSyMfxjLf3P4cN57dP30Edq2K1+vS35cdpqBv44CILp+JxpN6H/V\nbIE9ly7kf35bcCgVXKTa4vUUqoOlaVoaDuxE/Z3ExFRstltnjqu4ETe+6raGJ9c/xtbYzUz5ZQqn\nL53l7Q7v3dJTZ8xmE76+XsW6Tn46Zi+l2rpaWxISUkoinigBt/vdQWhAEyLiw5mybSqfdfvS6Eil\nQin7R79+9rbNBjExJsLDGxIRYcEnPJuICDMnT9pv/KdPw4rTdYHJeJHKN/Qhwq0FvXpls/7pLJo1\ns//OJzlZcThd15mwyb55Z/Mqt3FP1U5yfRqstd+dKP+GaAlRTP/5HRZ0XWJ0JIe7mXtJQV76cSIZ\n2Rn4VfBjaOMRJfL73MqvPW5mN6w2K1/tW0X/ho84/BzXev55eKLWdiqPTsDdlsFrhx9lV/v3eaX9\nm/R4/07q1Sv7r10TE2xYhjyBH4kkWXzx/vpDEhKvfvkfftr+JlY1r+qkJWWTRvn8e5V3jRSXQ9dg\nKaUsucd0A0xKKXcATdMyC3sMm02XfbAEABXMnnz6wBeM2vo0q4+uZEn4IuLTE5jbaf4tv/FmUa+T\nbFs2u8+FAdC6Wju5xsqYEbeNZuTWYWyI/p6oixoN/EKMjmSIoCCdoCAbDz301zTDpCQ4dMiSW0yj\nDhsixpOWZqFnz0yWPZZK1ar23/WcnBsd1VjbT/7EjjO/ATCu9UvYbAByfRptWLMRPLdtNN8eXcOJ\nxFgCvWsbHalEOPo115FLh/nskL0C49iWL+Dl4lMi9xsPixd3Bd7Dj7Fb2Hh8A30aDHD4Oa7Hr19H\nUtrsIn7YOGru+4G2hNH29y7MbPss856cxnPPWalSpexevz/1XcRg6xYAzr06E79aNf/v/19M4l8V\nBOW1xI05uiTVRCAdmAf8I/fzUhn5EuWTm8WNj+5fyFNNhgLw3bE1PPp9P1Kyyuc7JiUlMj6C1Nyf\nWVupIFjm9Kzfm1oVAwH4aN8HBqdxLj4+0K5dDoMHZ/Hee5ls2ZJOVBSMG5eV37lyVrquMy1sMgCt\nqrWmU1AXgxOJPH1C+hNQIYAcPYcFBz82Ok6Z8dauN7DpNmpVDMzfV6yk5FUZ/jF2C9ac0tuwyhZc\nF9dNX5Pw9Xecq2PfTH2t3oNFi9xo08aLd991IzW11OI4zLp1Lryzryu7uZ3wZv3we6b3dZ8XmxwD\nSIn2gji0g6Vp2uuappk1TbPkfpg1Tbt153MJhzCbzEy9ewbP3z4egJ9P/USftd2JT483OFnZkbf/\nVWWPytStVM/gNKKoXC2uDG9uL/TylfYF51PPGZxIOMKWEz+w5/xuAMa3mShrTJ2Ih4sHg5oMBmDZ\noSWkWJMNTuT89pzfnb+P24ttXi7xtTmdg7oCkJKVzI4zv5boua4np0MHLLu3cu6rjdz1cnu8vXVS\nU01Mn+5O27ZeLF3qSnZ2wcdxBhcvmhg3zh2NhjzX7meqrpp5w+fmlWiXCoJ/z7k2VRHiBkwmE+Pa\nvMTUu98BYO+FPfRY3YXTyacMTlY2hJ3L3f+qent5EVdGPdp4EJXcfbHarMw/MM/oOOIm6brO9NzK\nge1r3sk9gR2NDST+z5NNhuJmdiPZmsQXUZ8ZHcep6brOm7+/BkBD/0b0DSn5KXuB3rVpUrkZAJti\nNpT4+a7LZMLS8Q7GjLESFpbKsGFWXF11LlwwM/X5FNY3fo0fv0zAQfshlwhdhxdecOfiRTOenjrv\nfZCDycf7hs+PTc7bAyu4lBKWTdLBEmXK4KZP81GnBbiYXTiSeJhuqztz5NJho2M5NV3X2Zk7giX7\nX5VdFV0r8mSofcrNkoiF8o56Gbc+eh0H4vYBMnrlrKp5VqNXSF8APj7wETk2J13I5wR+jN2cP4r0\ncrtJpVaMqnOwfRRrU8xGdIN7MQEBOpMnZ/Lbb6n06pXFBKYyOHEmD45uwnctpvPnNuf8m71qlQvf\nf2+vyvr665kEBd3455ialcrF9IuAbDJcEOlgiTKnd0g/lj3wJR4uHpxOOUWP1V3Yd2Gv0bGc1snk\nWM6lngWgTY3yW274VjC42dO4W9xJsl5m2aFPjY4jismm23g7bAoAHQLvpX3N8lV6vzx5upl9am5s\nUgwbY9YbnMY52XQbk3e+DkCb6u3yp+6Vhi5B9nVYsckniEqILODZpSM4WGfevAy6DwsgxeKDNykM\nPjOFVv2a8u09czkekWF0xHznTmYzYby9aFjHjtk8/njW3z7/ZHJs/ue1veuUaLayTjpYoky6L6gz\nX3f/lkruvsRnxPPw2m78cmq70bGcUt70QA8XD5pWbl7As4Uzq+ZZjX7KXo744/1zyMr5+5uhcE7f\nHl1NZMIhAMa3nWhwGvF3Qis34e7c6Zvz9n9obBgnterI10TEHwTglfZvlOpobPOqLajqWQ0wcJrg\nDfhNHkV6+H4iu48lw1SBABIYHDWeEfed4oUX3Dl/3thRa12Hk92f5+PLAwjyjmfWrIwCN06OTYoB\nwGKy5BdeEtcnHSxRZrWp0Za1PTdQzbM6qVkpPLKuN+uOfWt0LKez66y9g9Wy6u24WdwMTiNu1jPN\nR2HCxJnU06w++o3RcUQRZduyeTt37dX9QV1oVa21wYlEQZ7JLTCz6+zv/Hl+j8FpnEtmTibTdtkr\nYXYNfrDUq9SaTeb8EbMfnKyDBUBAAJUXvkHSnn0cvHMwKz0eZa+tBZ9+6kbbtl68/bYbKQYVRd75\n0g88eGYR/fiaZZ0WUrNmwVMs8wpc1KoYiIvZoTs9lTvSwRJlWuOAUNb12kSwT12sNitDNj3OZzJ1\n6iphueuvZHpg+VDfrwEP1O0GwJw/3zd83YEompWHv+Jo4hHAXmlNOL9/1rmf+r4NAPj4wByD0ziX\npRGLiE0+gdlk5qV2rxmSIa9c+57zu4lLizMkQ0FMgTWpvnomrSPn8sormfj46KSlmZgxI7fi4Cc5\nZFlL72/52X1xtF80AoAI3ztQc4YV6vtO5Be4kPVXBZEOlijzgnyCWddrM6EBTbHpNv67bRSz986U\nF55AYsal/HnpUuCi/BjZYjQAkQmH+DF2s8FpRGFl5mTyzu6pADxYtzvNqtxmcCJRGGaTmadzR7G+\nPbZGqtfmSrEmM3OPvbJvP/UIDf0bGZLjnsCOVLBUQEdna+wmQzIUloeniVGjrOzencIzz1hxc9OJ\nizPjP/FZTtXvRtjM3SVecdCWo5M8YAxV9DhSqIjrlx9jcilcUZK8ESzZA6tg0sES5UJVz6qs7bk+\nf7H45J2vMWnHxFu+k/XH+TB0dEyYuL1aG6PjCAdpXb1tfod5zr7ZBqcRhXXlu/0T2r5idBxRBH1D\nBuDn7ke2LZuF4Z8YHccpzN33ARfTL+JucWdc65cMy+Hp6sndgR0AJ50meB1+fvaKfTt2pDKyaxSP\ns5Q2Gb/w0NT70EIeIeKLQyV27p1jV3NnwjoA9j4xA7+Whe8s5XewZASrQNLBEuWGj3slvuy2ii65\n0wU+2v8BY34aQbatjOz0VwLCzu4CoFFAKD7ulQxOIxzpPy3GAvDr6Z9lXUgZcOW7/f3VQJR/Q4MT\niaLwdPXkiSs3Hs4yaOGMk7iQdoG5+z4A4Kkmwwj0rm1onrxpgttO/khmTqahWYqiTh2d1z6tSfiU\nrzjq1RSAuy9/zz1j2vNni/9wWHNsIYzjx0089W1fZjGGnTX+RaPpjxT6e3Vdv2IPLOlgFUQ6WKJc\n8XDxYHHX5fRXAwH4Mmo5T238N+nZ6QYnM8auc3n7X5XuwmNR8u4P6kID3xBARrHKgnn75+S/2/9C\n6wlGxxHF8FSTYbiaXbmcmciKqOVGxzHUzD1vk5adirebD2Na/dfoOPmFLlKzUvjt9C8Gpykik4ma\nQztT6dgv/D56MbFu9TCjc+R0Re7p4MVzz7lz7tzNd7RycmDUKA8S0j15q8p7+G1ZQoFlA69wOTOR\nZGsSAHW8g286T3knHSxR7riYXXj/n3MZ3vw/AGyMWc8j63qTlHnZ4GSly5pjzR/ZaFNdOljljdlk\nZmSLMQCsO76W6MvHDU4kbuRi+sX8TvCTTYYa/m6/KJ5qXtV5uEEfAD65hTcejr58nKURiwEY1WIs\n/hUCDE4ENSrWzF/T6Gzl2gvNbKb+xN64Hwtj24DZLK75EjabiWXL3GjXzotp09xIvom9iufNc2X3\nbvtaq/fey8C/StE2g84bvQKo4yN7YBXEYR0spZSbUmqeUuqwUipJKRWjlHpbKeXuqHMIUVhmk5nX\n75jCxHaTANhx5ld6rn2IC2kXjA1Wig7E7SMjx76hoRS4KJ96h/Sjmmd1bLpN9uhxYu/vmUFqVgoV\nXb0Z0/I5o+OIm5BX7CL68nE2ndhocBpjTA+bTJYti2qe1Rna7Bmj4+TLG8XaFLOxTK+/Nru7Ejr7\nCVbv9GHSpAx8fe0VB997z15x8Nex35KVmFqkY2qamWnT7C/HBwzIokuXor85cCJ3/ZW7xT1/7zFx\nY44cwXIB4oCHgErA3cA/gekOPIcQhWYymRjd8r+823E2ZpOZ8IsH6L66c/4izfIub/+rml615B3z\ncsrd4p7/AueLyM+4mH7R4ETiWieTY1kcvgCwV38M8DD+3X5RfE0rN+OuWvcA9s2+bzUH4/az6oh9\n/73nW4/Hy9XL4ER/yVt/fSrlJIfiIwxOc/MqVIARI7IIC0th5Egr7u469S6G8fDn/8a14W0cGbsA\nPdNa4HGyktJ5cUQWmZkmatWyMXlyRrHy5L12qu1dB7NJJsAVxGE/IU3T0jRNe0XTtCOapumapp0E\n5gMdC3uMY8eOXdWOjj4ubWnfdPuxxk8wv/OnuJpcib58nG6rOxMZf8hp8pVUe9vxrcBf66+MziPt\nkmkPCn2Siq7eZORksOjgJ0X+fmmXbPud3VOx2qz4ufnnj344Uz5pF72d9/9xx5lfORC3z/A8pdme\nvHMSALU96zCw4WOG57my3azKbVT3qgHAij+XF/j8stL29YXHH4/k999TGdpyN1ZcqWI7zx2f/xdr\nvdbETllB9NEjN/z+6P5vsPRgK+7gN2bOzMDHp3h5YpNjAHuBC2f6+ZRGuzhMJTmMqpT6CkjXNG1Q\nocKYTHp8fDI5OfZMVav6cOFCUv7XpS3tm2q39cFrSEVSs1LwdfclcU4iF/Y6Ub5CtOPjk/H3r0hC\nQgoBAd43fL6u61SbUQm8YOrdMxjcdJhT5Jd2ybQn7ZjI3H2z8a/gz57HIvBy9XKqfKXZtlhM+PtX\nxGQyGZ7n56hddFzRHptug/VwYZ3xPx9p33zbptuoPtkXAqBPSH/mdprvVPkK29Z1nYSEFHJy9EI9\nf+Xe7+j9bXf7A1/BhW3O9e+5cCGJ57aNYdmhxXAKLrxlfJ6SaB/bEos2cAyP8SNm7K+Xn2UwvX5+\nn4YNbVc9/9TibbR4sQcA3zabQPstE4p9/vsW3c/W2M08ETqYJX0XOs3Po6Taua+3il1dxKUwT1JK\nLQYGATpw7cl0YIqmaa9e8z1jgXuA24sSyGy++vAWi7Sl7aB2NKx5eB39v+1FQkYCPA7bTm3hvqD7\nnSNfIdp510fef2/0/COXjkDuzI32tdrnP250fmmXTHt4ixHM3TObhIwEVmjLGdr8aafKV5rtK+8h\nRueZuusNbLqNOj5BxO45YXgeaTumbcECO4GHYM3Rlbx25xtOla+wbaBI10ve6FWLqq3489Aew/Nf\nr/3APx6wd7BqQXxmHFU9qzpVPke0Q7oE0Z6t1Jr1B+ZX36R50i8s4l1md/TkkUeyGT/ePm0wJ+4S\nNV8eDsAfNOG2VS9cdcyinj+vyEWwb3Cp/nuNal/bHykyXdcL/AgJCfEMCQnx/5uPCtc8/9mQkJAz\nISEhjQpz/LyPo0eP6leStrRLoh0ZF6kHvheoMwnd5Q0X/fMDnztVPke0F+5dqDMJ3fstbz07J9vw\nPNIu+Xavpb10JqHXnVVXz8rJMjzPrd7+6vevdCahMwl92f5lhueRtmPbB6IO6H7T/HQmoU/YMsHw\nPCXd/mDrB/m/z1uPbzU8z43aadY03WOyh84k9IV7Fxqep6TbOTm6vnLeBT0w0KqDroOue3jo+vCn\n4/W9DfrpOuhpVNC/e2fbTZ3vyJEjeoXJFXQmoX8d8bXT/PtLoV3oPsy1Hw6fIqiUegUYCvxT07Sj\nRe3vJSamYrOV3eovomw4nXyK3mv/xZFLhzFhYlqHGQxpNszoWAUym034+npR0HUyasszfB75GffW\nuY9v/rWmFBMKo0TGH+Kuz9sCsKDLEh4O6W1wImMU9hopSbqu02PVA+w48xuNA0LZNuA3LOailUQW\nzu/NHZOYteddfN39OPBkpFMVfChIUa6TbFs2dyxvzbHEo2XinvLouv5sjF7Pg//oxrKHvjA6TqnI\nzITFi1159103EhJM+BPPa7zOaD5gxV0zuX/tkJs6/vnU8zReVB+Arf1/5raqLRwR26nlXiPFHsZy\naAdLKfUO0Be4V9O0aIcdWAghhBBCCCHKAId1sJRSdYAYIBPIyjs+EKNpWlOHnEQIIYQQQgghnFiJ\nVhEUQgghhBBCiFuJ7BQmhBBCCCGEEA4iHSwhhBBCCCGEcBDpYAkhhBBCCCGEg0gHSwghhBBCCCEc\nRDpYQgghhBBCCOEg0sESQgghhBBCCAeRDpYQQgghhBBCOIh0sIQQQgghhBDCQVyMDgCglDID04FB\ngDuwCRiuaVq8ocGEcBJKqcXAo0AGYAJ0YJymafMMDSaEQZRS/YGRQHPAQ9M0t2u+/jjwKlAdOAiM\n1DRtb6kHFcJAf3edKKUGAYuAVP66r3ynadqjRmQVwghKqWlAN6A2kAysB17UNO3SFc8p8v3EKTpY\nwASgO9AaSAAWA8uAB40MJYSTWaJp2jCjQwjhJBKAOYAn8PGVX1BK3QXMBf4F/AyMBdYrpeprmpZS\n2kGFMNANr5NcxzRNCyndSEI4lWzsb2CHA77Y+x9LsN8/in0/cZYO1lBgkqZpJwCUUuOAo0qp2pqm\nnTQ2mhBCCGejadpmAKVUh+t8eQiwUtO0rbntd5RSI4GHsd88hbglFHCdCHHL0zRt4hXNeKXU+8CK\nKx4r1v3E8DVYSqlKQB0gf6hN07TjQBL2IW0hhF1vpdRFpVSUUuptpZSX0YGEcFLNgT3XPLYPuacI\nca3aSqkzSqkTSqkvlFLBRgcSwmCdgP1XtIt1PzG8gwV4Y5/3e/maxxMBn9KPI4RTmg001DStMvZ3\nTToAnxgbSQin5Y3cU4QoyHagqaZpNbEv0cgANiulPIyNJYQxlFK9gWHA6CseLtb9xBk6WMnYF1dW\nuuZxX+yjWELc8jRN+1PTtLjczyOxzwHuo5RyNTaZEE4pGbmnCPG3NE2L0TTtaO7nF7Av16gBtDM0\nmBAGUEr1xb5OsbumaVeOYBXrfmJ4B0vTtMtALNAy7zGlVD3sPcYDRuUSoowwGR1ACCe0nyvuKbla\ncPW0DyHE9cl9RdxSlFJPAh8B3TRN+/maLxfrfuIsRS4+AV5USm0DLmEv2b5R07RYQ1MJ4SRyS+1u\n1DTtslKqATADWKtpmtXgaEIYInd7D1fsW3uglHIH0DQtE5gPbFBKfQr8hn3E1w1YbUxaIYzxd9eJ\nUupBYL+maaeVUv7ANCAO2GlUXiFKm1JqNPYS7F00Tbt2rRUU835i+AhWrmnAd8Bu7KNZOvCYoYmE\ncC7DgWNKqWRgI7ADeMrYSEIY6jEgHdgAWHI/T1NK1dE07TdgBLAA+5t2vYAHpES7uAXd8DoBOgJh\nufeVg9inPd2vaVqaQVmFMMIs7LPmflJKJSmlkpVSIHoggwAAAHhJREFU+dP/ins/Mem6XoKZhRBC\nCCGEEOLW4SwjWEIIIYQQQghR5kkHSwghhBBCCCEcRDpYQgghhBBCCOEg0sESQgghhBBCCAeRDpYQ\nQgghhBBCOIh0sIQQQgghhBDCQaSDJYQQQgghhBAOIh0sIYQQQgghhHCQ/wFN4CmELDEZUgAAAABJ\nRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff018b97eb8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f, ax = plt.subplots(3,1, figsize=(12,6))\n",
"ax[0].plot(sigma2_coda.flatten(), 'b')\n",
"ax[0].plot(sigma2_geweke_ar, '--r')\n",
"ax[0].plot(sigma2_geweke_var, 'g')\n",
"ax[0].plot(sigma2_pymc, '--k')\n",
"ax[0].hlines([1.96, -1.96], 0,20,color='k', linestyle=':')\n",
"ax[0].axis([0,20,-2.1,2.1])\n",
"ax[0].set_title('$\\\\sigma^2$', fontsize=16)\n",
"\n",
"ax[1].plot(tau2_coda.flatten(), 'b')\n",
"ax[1].plot(tau2_geweke_ar, '--r')\n",
"ax[1].plot(tau2_geweke_var, 'g')\n",
"ax[1].plot(tau2_pymc, '--k')\n",
"ax[1].hlines([1.96, -1.96], 0,20,color='k', linestyle=':')\n",
"ax[1].axis([0,20,-2.1,2.1])\n",
"ax[1].set_title('$\\\\tau^2$', fontsize=16)\n",
"\n",
"ax[2].plot(beta_coda.flatten(), 'b')\n",
"ax[2].plot(beta_geweke_ar, '--r')\n",
"ax[2].plot(beta_geweke_var, 'g')\n",
"ax[2].plot(beta_pymc, '--k')\n",
"ax[2].hlines([1.96, -1.96], 0,20,color='k', linestyle=':')\n",
"ax[2].axis([0,20,-2.1,2.1])\n",
"ax[2].set_title('$\\\\beta$', fontsize=16)\n",
"\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, it's pretty clear that the estimates we wrote based on the spectral density recover the `CODA` estimates almost exactly. In addition, it looks like the naive variance estimate is all over the place, and is always at least as extreme as the spectral variance estimate. This is what we would expect if the naive variance is, at best, an underestimate of the typical variance of the signal. \n",
"\n",
"Finally, the PyMC3 statistic doesn't really move much at all. Even when I've rescaled it, it's just not varying like the rest of the estimates. So, I'm not really sure what to do, other than (eventually) submit a PR using that provides the `CODA`-style estimates like the implementation above. \n",
"\n",
"I'm not sure what it'd require to clean up my two `geweke` and `geweke_list` implementations (and,the `spectral0_ar` function is kinda slow), but I know that I'll be relying on this implementation going forward. "
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python [py3]",
"language": "python",
"name": "Python [py3]"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.2"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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